Finite Group Databasebeta

← #23777910

Subgroups — #23777910

Order 10112.

1160 conjugacy classes of subgroups.

The subgroup lattice has 1082 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099309C211yesmaximal, characteristic, complemented
2#19099308C211yesmaximal, characteristic, complemented
3#19099306C211yesmaximal, characteristic, complemented
4#19099305C211yesmaximal, characteristic, complemented
5#19099297C211yesmaximal, characteristic, complemented
6#19099296C211yesmaximal, characteristic, complemented
7#19099222C211yesmaximal, characteristic, complemented
8#19099219C211yesmaximal, characteristic, complemented
9#19099205C211yesmaximal, characteristic, complemented
10#19099203C211yesmaximal, characteristic, complemented
11#19099203C211yesmaximal, characteristic, complemented
12#19099202C211yesmaximal, characteristic, complemented
13#19099201C211yesmaximal, characteristic, complemented
14D4×C22⋊D79C211yesmaximal, characteristic, complemented
15#19099195C211yesmaximal, characteristic, complemented
16#19099183C211yesmaximal, characteristic, complemented
17#19099177C211yesmaximal, characteristic, complemented
18#19099151C211yesmaximal, characteristic, complemented
19#19099149C211yesmaximal, characteristic, complemented
20#19099148C211yesmaximal, characteristic, complemented
21#19099146C211yesmaximal, characteristic, complemented
22#19099146C211yesmaximal, characteristic, complemented
23#19099145C211yesmaximal, characteristic, complemented
24#19099129C211yesmaximal, characteristic, complemented
25#19099128C211yesmaximal, characteristic, complemented
26#19099122C211yesmaximal, characteristic, complemented
27#19099121C211yesmaximal, characteristic, complemented
28#19099109C211yesmaximal, characteristic, complemented
29#19099090C211yesmaximal, characteristic, complemented
30C2×#14579147C211yesmaximal, characteristic, complemented
31#546×C79C211yesmaximal, characteristic, complemented
32C2×#11929624C2211yescharacteristic, complemented
33C2×#11929624C2211yescharacteristic, complemented
34C2×#11929623C2211yescharacteristic, complemented
35C22×Dic158C2211yescharacteristic, complemented
36C22×C22⋊D79C2211yescharacteristic
37C22×C22⋊D79C2211yescharacteristic, complemented
38C22×C22⋊D79C2211yescharacteristic, complemented
39C2×D4×D79C2211yescharacteristic, complemented
40C2×D4×D79C2211yescharacteristic, complemented
41C2×D4×D79C2211yescharacteristic, complemented
42#14579159C2211yescharacteristic, complemented
43#14579157C2211yescharacteristic
44#14579157C2211yescharacteristic
45#14579157C2211yescharacteristic, complemented
46#14579156C2211yescharacteristic, complemented
47#14579156C2211yescharacteristic, complemented
48#14579155C2211yescharacteristic, complemented
49#14579154C2211yescharacteristic, complemented
50#14579154C2211yescharacteristic, complemented
51#14579154C2211yescharacteristic, complemented
52#14579151C2211yescharacteristic, complemented
53#14579150C2211yescharacteristic, complemented
54#14579150C2211yescharacteristic, complemented
55#14579149C2211yescharacteristic, complemented
56#14579149C2211yescharacteristic, complemented
57#14579148C2211yescharacteristic, complemented
58#14579148C2211yescharacteristic, complemented
59#14579148C2211yescharacteristic, complemented
60#14579147C2211yescharacteristic, complemented
61#14579147C2211yescharacteristic, complemented
62#14579147C2211yescharacteristic, complemented
63#14579147C2211yescharacteristic, complemented
64#14579147C2211yescharacteristic, complemented
65#14579147C2211yescharacteristic, complemented
66#14579147C2211yescharacteristic, complemented
67#14579147C2211yescharacteristic, complemented
68#14579147C2211yescharacteristic, complemented
69#14579147C2211yescharacteristic, complemented
70#14579147C2211yescharacteristic, complemented
71#14579147C2211yescharacteristic, complemented
72#14579147C2211yescharacteristic, complemented
73#14579147C2211yescharacteristic, complemented
74#14579147C2211yescharacteristic, complemented
75#14579147C2211yescharacteristic, complemented
76#14579147C2211yescharacteristic, complemented
77#14579146C2211yescharacteristic, complemented
78#14579146C2211yescharacteristic, complemented
79#14579146C2211yescharacteristic, complemented
80#14579146C2211yescharacteristic, complemented
81#14579144C2211yescharacteristic, complemented
82#14579144C2211yescharacteristic, complemented
83#14579144C2211yescharacteristic, complemented
84#14579144C2211yescharacteristic, complemented
85#14579144C2211yescharacteristic, complemented
86#14579143C2211yescharacteristic, complemented
87#14579143C2211yescharacteristic, complemented
88#14579143C2211yescharacteristic, complemented
89#14579143C2211yescharacteristic, complemented
90#14579142C2211yescharacteristic, complemented
91#14579142C2211yescharacteristic, complemented
92#14579142C2211yescharacteristic, complemented
93#14579141C2211yescharacteristic, complemented
94#14579140C2211yescharacteristic, complemented
95#14579139C2211yescharacteristic, complemented
96#14579139C2211yescharacteristic, complemented
97#14579139C2211yescharacteristic, complemented
98#14579138C2211yescharacteristic, complemented
99#14579138C2211yescharacteristic, complemented
100#14579138C2211yescharacteristic, complemented
101#14579138C2211yescharacteristic, complemented
102#14579137C2211yescharacteristic, complemented
103#14579136C2211yescharacteristic, complemented
104#14579135C2211yescharacteristic, complemented
105#14579135C2211yescharacteristic, complemented
106#14579135C2211yescharacteristic, complemented
107#14579135C2211yescharacteristic, complemented
108#14579134C2211yescharacteristic
109#14579134C2211yescharacteristic, complemented
110#14579134C2211yescharacteristic, complemented
111#14579134C2211yescharacteristic, complemented
112#14579134C2211yescharacteristic, complemented
113#14579134C2211yescharacteristic, complemented
114#14579133C2211yescharacteristic
115#14579133C2211yescharacteristic
116#14579133C2211yescharacteristic, complemented
117#14579133C2211yescharacteristic, complemented
118#14579133C2211yescharacteristic, complemented
119#14579133C2211yescharacteristic, complemented
120#14579133C2211yescharacteristic, complemented
121#14579133C2211yescharacteristic, complemented
122#14579133C2211yescharacteristic, complemented
123#14579133C2211yescharacteristic, complemented
124#14579133C2211yescharacteristic, complemented
125#14579132C2211yescharacteristic, complemented
126#14579132C2211yescharacteristic, complemented
127#14579131C2211yescharacteristic, complemented
128#14579131C2211yescharacteristic, complemented
129#14579131C2211yescharacteristic, complemented
130#14579131C2211yescharacteristic, complemented
131#14579131C2211yescharacteristic, complemented
132#14579131C2211yescharacteristic, complemented
133#14579130C2211yescharacteristic, complemented
134#14579130C2211yescharacteristic, complemented
135#14579130C2211yescharacteristic, complemented
136#14579130C2211yescharacteristic, complemented
137#14579129C2211yescharacteristic, complemented
138#14579129C2211yescharacteristic, complemented
139#14579129C2211yescharacteristic, complemented
140#14579129C2211yescharacteristic, complemented
141#14579129C2211yescharacteristic, complemented
142#14579129C2211yescharacteristic, complemented
143#14579129C2211yescharacteristic, complemented
144#14579129C2211yescharacteristic, complemented
145C4×Dic158C2211yescharacteristic, complemented
146#14579126C2211yescharacteristic, complemented
147#14579126C2211yescharacteristic, complemented
148D4×Dic79C2211yescharacteristic, complemented
149D4×Dic79C2211yescharacteristic, complemented
150#14579123C2211yescharacteristic, complemented
151C4×C22⋊D79C2211yescharacteristic, complemented
152C4×C22⋊D79C2211yescharacteristic, complemented
153C4×C22⋊D79C2211yescharacteristic, complemented
154C4×C22⋊D79C2211yescharacteristic, complemented
155C4×C22⋊D79C2211yescharacteristic, complemented
156C4×C22⋊D79C2211yescharacteristic, complemented
157C4×C22⋊D79C2211yescharacteristic, complemented
158(C22⋊D79)⋊C4C2211yescharacteristic, complemented
159(C22⋊D79)⋊C4C2211yescharacteristic, complemented
160(C22⋊D79)⋊C4C2211yescharacteristic, complemented
161(C22⋊D79)⋊C4C2211yescharacteristic, complemented
162(C22⋊D79)⋊C4C2211yescharacteristic, complemented
163#14579119C2211yescharacteristic, complemented
164#14579117C2211yescharacteristic, complemented
165C2×C22⋊Dic79C2211yescharacteristic, complemented
166C2×(C2×D79)⋊C4C2211yescharacteristic, complemented
167C2×(C2×D79)⋊C4C2211yescharacteristic, complemented
168C2×(C2×D79)⋊C4C2211yescharacteristic, complemented
169C22⋊C4×D79C2211yescharacteristic, complemented
170C22⋊C4×D79C2211yescharacteristic, complemented
171C2×C4×Dic79C2211yescharacteristic, complemented
172C2×#41×C79C2211yescharacteristic, complemented
173C22×D4×C79C2211yescharacteristic, complemented
174#124×C79C2211yescharacteristic, complemented
175#123×C79C2211yescharacteristic, complemented
176#123×C79C2211yescharacteristic, complemented
177C22⋊Q8×C79C2211yescharacteristic, complemented
178#121×C79C2211yescharacteristic, complemented
179#121×C79C2211yescharacteristic, complemented
180#121×C79C2211yescharacteristic, complemented
181#120×C79C2211yescharacteristic, complemented
182#120×C79C2211yescharacteristic, complemented
183C4×D4×C79C2211yescharacteristic, complemented
184C4×D4×C79C2211yescharacteristic, complemented
185C2×C22⋊C4×C79C2211yescharacteristic, complemented
186C2×C22⋊C4×C79C2211yescharacteristic, complemented
187C23×D79C2311yescharacteristic
188C23×D79C2311yescharacteristic
189C23×D79C2311yescharacteristic
190C23×D79C2311yescharacteristic
191#11929624—42no—
192#11929624—42no—
193#11929623—42no—
194C2×Dic158—42no—
195C2×Dic158C2311yescharacteristic
196C2×Dic158C2311yescharacteristic
197C2×Dic158C2311yescharacteristic
198C2×Dic158C2311yescharacteristic
199C2×Dic158C2311yescharacteristic
200C2×Dic158C2311yescharacteristic
201C2×D316C2311yescharacteristic
202C2×D316C2311yescharacteristic
203C2×D316C2311yescharacteristic
204C2×D316C2311yescharacteristic
205C2×D316C2311yescharacteristic
206C2×D316C2311yescharacteristic
207C2×C22⋊D79—42no—
208C2×C22⋊D79—42no—
209C2×C22⋊D79—42no—
210C2×C22⋊D79C2311yescharacteristic
211C2×C22⋊D79C2311yescharacteristic
212C2×C22⋊D79C2311yescharacteristic
213C2×C22⋊D79C2311yescharacteristic
214C2×C22⋊D79C2311yescharacteristic
215C2×C22⋊D79C2311yescharacteristic
216C2×C22⋊D79C2311yescharacteristic
217C2×C22⋊D79C2311yescharacteristic
218C2×C22⋊D79C2311yescharacteristic
219C2×C22⋊D79C2311yescharacteristic
220C2×C22⋊D79C2311yescharacteristic
221C2×C22⋊D79C2311yescharacteristic
222C2×C22⋊D79C2311yescharacteristic
223C2×C22⋊D79C2311yescharacteristic
224C2×C22⋊D79C2311yescharacteristic
225C2×C22⋊D79C2311yescharacteristic
226C2×C22⋊D79C2311yescharacteristic
227C2×C22⋊D79C2311yescharacteristic
228C2×C22⋊D79C2311yescharacteristic
229C2×C22⋊D79C2311yescharacteristic
230C2×C22⋊D79C2311yescharacteristic
231C2×C22⋊D79C2311yescharacteristic
232D4×D79—42no—
233D4×D79—42no—
234D4×D79—42no—
235C22×Dic79C2311yescharacteristic
236C22×Dic79C2311yescharacteristic
237C22×Dic79C2311yescharacteristic
238C22×Dic79C2311yescharacteristic
239C22×Dic79C2311yescharacteristic
240C22×Dic79C2311yescharacteristic
241C2×C4×D79C2311yescharacteristic
242C2×C4×D79C2311yescharacteristic
243C2×C4×D79C2311yescharacteristic
244C2×C4×D79C2311yescharacteristic
245C2×C4×D79C2311yescharacteristic
246C2×C4×D79C2311yescharacteristic
247C2×C4×D79C2311yescharacteristic
248C4⋊Dic79C2311yescharacteristic
249C4⋊Dic79C2311yescharacteristic
250C4⋊Dic79C2311yescharacteristic
251C4⋊Dic79C2311yescharacteristic
252Dic79⋊C4C2311yescharacteristic
253Dic79⋊C4C2311yescharacteristic
254Dic79⋊C4C2311yescharacteristic
255Dic79⋊C4C2311yescharacteristic
256Dic79⋊C4C2311yescharacteristic
257Dic79⋊C4C2311yescharacteristic
258Dic79⋊C4C2311yescharacteristic
259Dic79⋊C4C2311yescharacteristic
260Dic79⋊C4C2311yescharacteristic
261Dic79⋊C4C2311yescharacteristic
262Dic79⋊C4C2311yescharacteristic
263Dic79⋊C4C2311yescharacteristic
264Dic79⋊C4C2311yescharacteristic
265Dic79⋊C4C2311yescharacteristic
266C22⋊Dic79C2311yescharacteristic
267C22⋊Dic79C2311yescharacteristic
268C22⋊Dic79C2311yescharacteristic
269C22⋊Dic79C2311yescharacteristic
270C22⋊Dic79C2311yescharacteristic
271C22⋊Dic79C2311yescharacteristic
272C22⋊Dic79C2311yescharacteristic
273C22⋊Dic79C2311yescharacteristic
274C22⋊Dic79C2311yescharacteristic
275C22⋊Dic79C2311yescharacteristic
276C22⋊Dic79C2311yescharacteristic
277C22⋊Dic79C2311yescharacteristic
278C22⋊Dic79C2311yescharacteristic
279C22⋊Dic79C2311yescharacteristic
280C22⋊Dic79C2311yescharacteristic
281C22⋊Dic79C2311yescharacteristic
282(C2×D79)⋊C4C2311yescharacteristic
283(C2×D79)⋊C4C2311yescharacteristic
284(C2×D79)⋊C4C2311yescharacteristic
285(C2×D79)⋊C4C2311yescharacteristic
286(C2×D79)⋊C4C2311yescharacteristic
287(C2×D79)⋊C4C2311yescharacteristic
288(C2×D79)⋊C4C2311yescharacteristic
289(C2×D79)⋊C4C2311yescharacteristic
290(C2×D79)⋊C4C2311yescharacteristic
291(C2×D79)⋊C4C2311yescharacteristic
292(C2×D79)⋊C4C2311yescharacteristic
293(C2×D79)⋊C4C2311yescharacteristic
294(C2×D79)⋊C4C2311yescharacteristic
295(C2×D79)⋊C4C2311yescharacteristic
296(C2×D79)⋊C4C2311yescharacteristic
297(C2×D79)⋊C4C2311yescharacteristic
298(C2×D79)⋊C4C2311yescharacteristic
299(C2×D79)⋊C4C2311yescharacteristic
300(C2×D79)⋊C4C2311yescharacteristic
301(C2×D79)⋊C4C2311yescharacteristic
302(C2×D79)⋊C4C2311yescharacteristic
303(C2×D79)⋊C4C2311yescharacteristic
304(C2×D79)⋊C4C2311yescharacteristic
305(C2×D79)⋊C4C2311yescharacteristic
306(C2×D79)⋊C4C2311yescharacteristic
307(C2×D79)⋊C4C2311yescharacteristic
308C4×Dic79C2311yescharacteristic
309C4×Dic79C2311yescharacteristic
310C4×Dic79C2311yescharacteristic
311C4×Dic79C2311yescharacteristic
312C4×Dic79C2311yescharacteristic
313C4×Dic79C2311yescharacteristic
314C4×Dic79C2311yescharacteristic
315C4×Dic79C2311yescharacteristic
316C4×Dic79C2311yescharacteristic
317C24×C79C2311yescharacteristic
318C24×C79C2311yescharacteristic
319#41×C79—42no—
320C2×Q8×C79C2311yescharacteristic
321C2×D4×C79—42no—
322C2×D4×C79C2311yescharacteristic
323C2×D4×C79C2311yescharacteristic
324C2×D4×C79C2311yescharacteristic
325C2×D4×C79C2311yescharacteristic
326C2×D4×C79C2311yescharacteristic
327C2×D4×C79C2311yescharacteristic
328C2×D4×C79C2311yescharacteristic
329C2×D4×C79C2311yescharacteristic
330C2×D4×C79C2311yescharacteristic
331C22×C4×C79C2311yescharacteristic
332C22×C4×C79C2311yescharacteristic
333C22×C4×C79C2311yescharacteristic
334C22×C4×C79C2311yescharacteristic
335C22×C4×C79C2311yescharacteristic
336C22×C4×C79C2311yescharacteristic
337C4⋊C4×C79C2311yescharacteristic
338C4⋊C4×C79C2311yescharacteristic
339C4⋊C4×C79C2311yescharacteristic
340C4⋊C4×C79C2311yescharacteristic
341C22⋊C4×C79C2311yescharacteristic
342C22⋊C4×C79C2311yescharacteristic
343C22⋊C4×C79C2311yescharacteristic
344C22⋊C4×C79C2311yescharacteristic
345C22⋊C4×C79C2311yescharacteristic
346C22⋊C4×C79C2311yescharacteristic
347C22⋊C4×C79C2311yescharacteristic
348C22⋊C4×C79C2311yescharacteristic
349C22⋊C4×C79C2311yescharacteristic
350C22⋊C4×C79C2311yescharacteristic
351C22⋊C4×C79C2311yescharacteristic
352C22⋊C4×C79C2311yescharacteristic
353C42×C79C2311yescharacteristic
354C23×C79—22no—
355C23×C79—41no—
356C23×C79—41no—
357C23×C79—41no—
358C23×C79—41no—
359C23×C79—41no—
360C23×C79C2411yescharacteristic
361C23×C79C2411yescharacteristic
362C23×C79C2411yescharacteristic
363C23×C79C2411yescharacteristic
364C23×C79C2411yescharacteristic
365C23×C79C2411yescharacteristic
366C22×D79—22no—
367C22×D79—41no—
368C22×D79—41no—
369C22×D79—41no—
370C22×D79—41no—
371C22×D79—41no—
372C22×D79—41no—
373C22×D79—41no—
374C22×D79—41no—
375C22×D79—41no—
376C22×D79—41no—
377C22×D79—41no—
378C22×D79C2411yescharacteristic
379C22×D79C2411yescharacteristic
380C22×D79C2411yescharacteristic
381C22×D79C2411yescharacteristic
382C22×D79C2411yescharacteristic
383Q8×C79—41no—
384D4×C79—22no—
385D4×C79—22no—
386D4×C79—22no—
387D4×C79—41no—
388D4×C79—41no—
389D4×C79—41no—
390D4×C79—41no—
391D4×C79—41no—
392D4×C79—41no—
393C2×C4×C79—22no—
394C2×C4×C79—41no—
395C2×C4×C79—41no—
396C2×C4×C79—41no—
397C2×C4×C79—41no—
398C2×C4×C79—41no—
399C2×C4×C79C2411yescharacteristic
400C2×C4×C79C2411yescharacteristic
401C2×C4×C79C2411yescharacteristic
402C2×C4×C79C2411yescharacteristic
403C2×C4×C79C2411yescharacteristic
404C2×C4×C79C2411yescharacteristic
405C2×C4×C79C2411yescharacteristic
406C2×C4×C79C2411yescharacteristic
407C2×C4×C79C2411yescharacteristic
408C22⋊D79—22no—
409C22⋊D79—22no—
410C22⋊D79—22no—
411C22⋊D79—22no—
412C22⋊D79—22no—
413C22⋊D79—22no—
414C22⋊D79—22no—
415C22⋊D79—41no—
416C22⋊D79—41no—
417C22⋊D79—41no—
418C22⋊D79—41no—
419C22⋊D79—41no—
420C22⋊D79—41no—
421C22⋊D79—41no—
422C22⋊D79—41no—
423C22⋊D79—41no—
424C22⋊D79—41no—
425C22⋊D79—41no—
426C22⋊D79—41no—
427C22⋊D79—41no—
428C22⋊D79—41no—
429C22⋊D79—41no—
430C2×Dic79—22no—
431C2×Dic79—22no—
432C2×Dic79—41no—
433C2×Dic79—41no—
434C2×Dic79—41no—
435C2×Dic79—41no—
436C2×Dic79C2411yescharacteristic
437C2×Dic79C2411yescharacteristic
438C2×Dic79C2411yescharacteristic
439C2×Dic79C2411yescharacteristic
440C2×Dic79C2411yescharacteristic
441C2×Dic79C2411yescharacteristic
442C2×Dic79C2411yescharacteristic
443C2×Dic79C2411yescharacteristic
444C2×Dic79C2411yescharacteristic
445C2×Dic79C2411yescharacteristic
446C2×Dic79C2411yescharacteristic
447D316—41no—
448D316—41no—
449D316—41no—
450D316—41no—
451D316—41no—
452D316—41no—
453C4×D79—22no—
454C4×D79—41no—
455C4×D79—41no—
456C4×D79—41no—
457C4×D79—41no—
458C4×D79—41no—
459C4×D79—41no—
460Dic158—22no—
461Dic158—22no—
462Dic158—41no—
463Dic158—41no—
464Dic158—41no—
465Dic158—41no—
466C22×C79—21no—
467C22×C79—21no—
468C22×C79—21no—
469C22×C79—21no—
470C22×C79—21no—
471C22×C79—21no—
472C22×C79—21no—
473C22×C79—21no—
474C22×C79—21no—
475C22×C79—21no—
476C22×C79—21no—
477C22×C79—21no—
478C22×C79—21no—
479C22×C79—21no—
480C22×C79—21no—
481C22×C79—21no—
482C22×C79—21no—
483C22×C79—82no—
484C22×C79—82no—
485C22×C79H(5,𝔽2)12yes—
486C22×C79C2511yescharacteristic
487C2×D79—21no—
488C2×D79—21no—
489C2×D79—21no—
490C2×D79—21no—
491C2×D79—21no—
492C2×D79—21no—
493C2×D79—21no—
494C2×D79—21no—
495C2×D79—21no—
496C2×D79—21no—
497C2×D79—21no—
498C2×D79—21no—
499C2×D79—21no—
500C2×D79—21no—
501C2×D79—21no—
502C2×D79—82no—
503C2×D79—82no—
504C2×D79—82no—
505C2×D79—82no—
506C4×C79—21no—
507C4×C79—21no—
508C4×C79—21no—
509C4×C79—21no—
510C4×C79—21no—
511C4×C79—21no—
512C4×C79—21no—
513C4×C79—21no—
514C4×C79—21no—
515Dic79—21no—
516Dic79—21no—
517Dic79—21no—
518Dic79—21no—
519Dic79—21no—
520Dic79—21no—
521Dic79—21no—
522Dic79—21no—
523Dic79—21no—
524Dic79—21no—
525Dic79H(5,𝔽2)12yes—
526C2×C79—22no—
527C2×C79—41no—
528C2×C79—41no—
529C2×C79—41no—
530C2×C79—41no—
531C2×C79—41no—
532C2×C79C2×H(5,𝔽2)11yescharacteristic
533C2×C79C2×H(5,𝔽2)11yescharacteristic
534C2×C79#58511yescharacteristic
535D79—41no—
536D79—41no—
537D79—41no—
538D79—41no—
539D79—41no—
540#3558—791nomaximal, Sylow
541C79#355811yescharacteristic, complemented, Sylow
542#562—791no—
543#562—791no—
544H(3,𝔽4)—791no—
545H(3,𝔽4)—791no—
546#559—791no—
547#559—791no—
548#548—791no—
549#548—791no—
550#546—791no—
551#546—791no—
552#546—791no—
553#546—791no—
554#546—791no—
555#546D7911yescharacteristic, complemented
556D42—791no—
557D42—791no—
558#542—791no—
559#542—791no—
560#538—791no—
561#538—791no—
562#538—791no—
563#538—791no—
564#538—791no—
565#538—791no—
566#535—791no—
567#535—791no—
568#534—791no—
569#534—791no—
570#532—791no—
571#529—791no—
572C2×#124—791no—
573C2×#41—791no—
574C2×#41—791no—
575C2×#41—791no—
576C2×#41C2×D7911yescharacteristic, complemented
577C22×Q8—791no—
578C22×D4—791no—
579C22×D4—791no—
580C22×D4—791no—
581C22×D4—791no—
582C22×D4—791no—
583C22×D4—791no—
584C22×D4C2×D7911yescharacteristic, complemented
585C4⋊Q8—791no—
586#127—791no—
587#127—791no—
588#127—791no—
589#126—791no—
590#126—791no—
591#126—791no—
592#126—791no—
593#126—791no—
594#126—791no—
595#125—791no—
596#124—791no—
597#124—791no—
598#124—791no—
599#124—791no—
600#124—791no—
601#124—791no—
602#124—791no—
603#124—791no—
604#124—791no—
605#124—791no—
606#124—791no—
607#124—791no—
608#124—791no—
609#124—791no—
610#124—791no—
611#124—791no—
612#124—791no—
613#124—791no—
614#124—791no—
615#124—791no—
616#124—791no—
617#124—791no—
618#124—791no—
619#124—791no—
620#124C2×D7911yescharacteristic, complemented
621#123—791no—
622#123—791no—
623#123—791no—
624#123—791no—
625#123—791no—
626#123—791no—
627#123—791no—
628#123—791no—
629#123—791no—
630#123—791no—
631#123—791no—
632#123—791no—
633#123—791no—
634#123—791no—
635#123—791no—
636#123—791no—
637#123C2×D7911yescharacteristic, complemented
638#123C2×D7911yescharacteristic, complemented
639C22⋊Q8—791no—
640C22⋊Q8—791no—
641C22⋊Q8—791no—
642C22⋊Q8—791no—
643C22⋊Q8—791no—
644C22⋊Q8—791no—
645C22⋊Q8—791no—
646C22⋊Q8—791no—
647C22⋊Q8—791no—
648C22⋊Q8—791no—
649C22⋊Q8C2×D7911yescharacteristic, complemented
650#121—791no—
651#121—791no—
652#121—791no—
653#121—791no—
654#121—791no—
655#121—791no—
656#121—791no—
657#121—791no—
658#121—791no—
659#121—791no—
660#121—791no—
661#121—791no—
662#121—791no—
663#121—791no—
664#121—791no—
665#121—791no—
666#121—791no—
667#121—791no—
668#121—791no—
669#121—791no—
670#121—791no—
671#121—791no—
672#121—791no—
673#121—791no—
674#121C2×D7911yescharacteristic, complemented
675#121C2×D7911yescharacteristic, complemented
676#121C2×D7911yescharacteristic, complemented
677#120—791no—
678#120—791no—
679#120—791no—
680#120—791no—
681#120—791no—
682#120—791no—
683#120—791no—
684#120—791no—
685#120—791no—
686#120—791no—
687#120—791no—
688#120—791no—
689#120—791no—
690#120—791no—
691#120—791no—
692#120—791no—
693#120—791no—
694#120—791no—
695#120C2×D7911yescharacteristic, complemented
696#120C2×D7911yescharacteristic, complemented
697C4×Q8—791no—
698C4×Q8—791no—
699C4×Q8—791no—
700C4×D4—791no—
701C4×D4—791no—
702C4×D4—791no—
703C4×D4—791no—
704C4×D4—791no—
705C4×D4—791no—
706C4×D4—791no—
707C4×D4—791no—
708C4×D4—791no—
709C4×D4—791no—
710C4×D4—791no—
711C4×D4—791no—
712C4×D4—791no—
713C4×D4—791no—
714C4×D4—791no—
715C4×D4C2×D7911yescharacteristic, complemented
716C4×D4C2×D7911yescharacteristic, complemented
717#117—791no—
718#117—791no—
719C2×C22⋊C4—791no—
720C2×C22⋊C4—791no—
721C2×C22⋊C4—791no—
722C2×C22⋊C4—791no—
723C2×C22⋊C4—791no—
724C2×C22⋊C4—791no—
725C2×C22⋊C4C2×D7911yescharacteristic, complemented
726C2×C22⋊C4C2×D7911yescharacteristic, complemented
727C2×C42—791no—
728C24—791no—
729C24—791no—
730C24—791no—
731C24—791no—
732C24C22×D7911yescharacteristic
733C24C22×D7911yescharacteristic
734#41—42no—
735#41—3162no—
736#41—3162no—
737#41—3162no—
738C2×Q8—3162no—
739C2×Q8—791no—
740C2×Q8—791no—
741C2×Q8—791no—
742C2×Q8—791no—
743C2×Q8—791no—
744C2×Q8—791no—
745C2×Q8C22×D7911yescharacteristic
746C2×D4—42no—
747C2×D4—3162no—
748C2×D4—3162no—
749C2×D4—3162no—
750C2×D4—3162no—
751C2×D4—3162no—
752C2×D4—3162no—
753C2×D4—791no—
754C2×D4—791no—
755C2×D4—791no—
756C2×D4—791no—
757C2×D4—791no—
758C2×D4—791no—
759C2×D4—791no—
760C2×D4—791no—
761C2×D4—791no—
762C2×D4—791no—
763C2×D4—791no—
764C2×D4—791no—
765C2×D4—791no—
766C2×D4—791no—
767C2×D4—791no—
768C2×D4—791no—
769C2×D4—791no—
770C2×D4—791no—
771C2×D4—791no—
772C2×D4—791no—
773C2×D4—791no—
774C2×D4—791no—
775C2×D4—791no—
776C2×D4—791no—
777C2×D4—791no—
778C2×D4—791no—
779C2×D4—791no—
780C2×D4—791no—
781C2×D4C22×D7911yescharacteristic
782C2×D4C22×D7911yescharacteristic
783C2×D4C22×D7911yescharacteristic
784C2×D4C22×D7911yescharacteristic
785C2×D4C22×D7911yescharacteristic
786C2×D4C22×D7911yescharacteristic
787C2×D4C22×D7911yescharacteristic
788C2×D4C22×D7911yescharacteristic
789C2×D4C22×D7911yescharacteristic
790C22×C4—791no—
791C22×C4—791no—
792C22×C4—791no—
793C22×C4—791no—
794C22×C4—791no—
795C22×C4—791no—
796C22×C4—791no—
797C22×C4—791no—
798C22×C4—791no—
799C22×C4—791no—
800C22×C4—791no—
801C22×C4—791no—
802C22×C4—791no—
803C22×C4C22×D7911yescharacteristic
804C22×C4C22×D7911yescharacteristic
805C22×C4C22×D7911yescharacteristic
806C22×C4C22×D7911yescharacteristic
807C22×C4C22×D7911yescharacteristic
808C22×C4C22×D7911yescharacteristic
809C4⋊C4—791no—
810C4⋊C4—791no—
811C4⋊C4—791no—
812C4⋊C4—791no—
813C4⋊C4—791no—
814C4⋊C4—791no—
815C4⋊C4—791no—
816C4⋊C4—791no—
817C4⋊C4—791no—
818C4⋊C4—791no—
819C4⋊C4—791no—
820C4⋊C4—791no—
821C4⋊C4—791no—
822C4⋊C4—791no—
823C4⋊C4—791no—
824C4⋊C4—791no—
825C4⋊C4—791no—
826C4⋊C4—791no—
827C4⋊C4C22×D7911yescharacteristic
828C4⋊C4C22×D7911yescharacteristic
829C4⋊C4C22×D7911yescharacteristic
830C4⋊C4C22×D7911yescharacteristic
831C22⋊C4—791no—
832C22⋊C4—791no—
833C22⋊C4—791no—
834C22⋊C4—791no—
835C22⋊C4—791no—
836C22⋊C4—791no—
837C22⋊C4—791no—
838C22⋊C4—791no—
839C22⋊C4—791no—
840C22⋊C4—791no—
841C22⋊C4—791no—
842C22⋊C4—791no—
843C22⋊C4—791no—
844C22⋊C4—791no—
845C22⋊C4—791no—
846C22⋊C4—791no—
847C22⋊C4—791no—
848C22⋊C4—791no—
849C22⋊C4—791no—
850C22⋊C4—791no—
851C22⋊C4—791no—
852C22⋊C4—791no—
853C22⋊C4—791no—
854C22⋊C4—791no—
855C22⋊C4—791no—
856C22⋊C4—791no—
857C22⋊C4—791no—
858C22⋊C4—791no—
859C22⋊C4—791no—
860C22⋊C4—791no—
861C22⋊C4—791no—
862C22⋊C4—791no—
863C22⋊C4—791no—
864C22⋊C4—791no—
865C22⋊C4—791no—
866C22⋊C4—791no—
867C22⋊C4—791no—
868C22⋊C4—791no—
869C22⋊C4—791no—
870C22⋊C4—791no—
871C22⋊C4—791no—
872C22⋊C4—791no—
873C22⋊C4C22×D7911yescharacteristic
874C22⋊C4C22×D7911yescharacteristic
875C22⋊C4C22×D7911yescharacteristic
876C22⋊C4C22×D7911yescharacteristic
877C22⋊C4C22×D7911yescharacteristic
878C22⋊C4C22×D7911yescharacteristic
879C22⋊C4C22×D7911yescharacteristic
880C22⋊C4C22×D7911yescharacteristic
881C22⋊C4C22×D7911yescharacteristic
882C22⋊C4C22×D7911yescharacteristic
883C22⋊C4C22×D7911yescharacteristic
884C22⋊C4C22×D7911yescharacteristic
885C42—791no—
886C42—791no—
887C42—791no—
888C42—791no—
889C42—791no—
890C42—791no—
891C42—791no—
892C42—791no—
893C42—791no—
894C42C22×D7911yescharacteristic
895C23—22no—
896C23—41no—
897C23—41no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—3161no—
902C23—3161no—
903C23—3161no—
904C23—3161no—
905C23—3161no—
906C23—3161no—
907C23—3161no—
908C23—3161no—
909C23—3161no—
910C23—3161no—
911C23—3161no—
912C23—791no—
913C23—791no—
914C23—791no—
915C23—791no—
916C23—791no—
917C23—1582no—
918C23C23×D7911yescharacteristic
919C23C23×D7911yescharacteristic
920C23C23×D7911yescharacteristic
921C23C23×D7911yescharacteristic
922C23C23×D7911yescharacteristic
923C23C23×D7911yescharacteristic
924Q8—41no—
925Q8—3161no—
926Q8—3161no—
927Q8—3161no—
928Q8—3161no—
929Q8—1582no—
930Q8—1582no—
931D4—22no—
932D4—22no—
933D4—22no—
934D4—41no—
935D4—41no—
936D4—41no—
937D4—41no—
938D4—41no—
939D4—41no—
940D4—3161no—
941D4—3161no—
942D4—3161no—
943D4—3161no—
944D4—3161no—
945D4—3161no—
946D4—3161no—
947D4—3161no—
948D4—3161no—
949D4—3161no—
950D4—3161no—
951D4—3161no—
952D4—3161no—
953D4—3161no—
954D4—3161no—
955D4—3161no—
956D4—3161no—
957D4—3161no—
958D4—3161no—
959D4—3161no—
960D4—3161no—
961D4—1582no—
962D4—1582no—
963D4—1582no—
964D4—1582no—
965D4—1582no—
966D4—1582no—
967D4—1582no—
968C2×C4—22no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—3161no—
975C2×C4—3161no—
976C2×C4—3161no—
977C2×C4—3161no—
978C2×C4—3161no—
979C2×C4—3161no—
980C2×C4—3161no—
981C2×C4—3161no—
982C2×C4—3161no—
983C2×C4—3161no—
984C2×C4—791no—
985C2×C4—791no—
986C2×C4—791no—
987C2×C4—791no—
988C2×C4—791no—
989C2×C4—791no—
990C2×C4—791no—
991C2×C4—791no—
992C2×C4—791no—
993C2×C4—791no—
994C2×C4—791no—
995C2×C4—1582no—
996C2×C4—1582no—
997C2×C4—1582no—
998C2×C4C23×D7911yescharacteristic
999C2×C4C23×D7911yescharacteristic
1000C2×C4C23×D7911yescharacteristic
1001C2×C4C23×D7911yescharacteristic
1002C2×C4C23×D7911yescharacteristic
1003C2×C4C23×D7911yescharacteristic
1004C2×C4C23×D7911yescharacteristic
1005C2×C4C23×D7911yescharacteristic
1006C2×C4C23×D7911yescharacteristic
1007C22—21no—
1008C22—21no—
1009C22—21no—
1010C22—21no—
1011C22—21no—
1012C22—21no—
1013C22—21no—
1014C22—21no—
1015C22—21no—
1016C22—21no—
1017C22—21no—
1018C22—21no—
1019C22—21no—
1020C22—21no—
1021C22—21no—
1022C22—21no—
1023C22—21no—
1024C22—82no—
1025C22—82no—
1026C22—6322no—
1027C22—6322no—
1028C22—6322no—
1029C22—6322no—
1030C22—1581no—
1031C22—1581no—
1032C22—1581no—
1033C22—1581no—
1034C22—1581no—
1035C22—1581no—
1036C22—1581no—
1037C22—1581no—
1038C22—1581no—
1039C22—1581no—
1040C22—1581no—
1041C22—1581no—
1042C22—1581no—
1043C22—1581no—
1044C22—1581no—
1045C22#1457920612yes—
1046C22C24×D7911yescharacteristic
1047C4—21no—
1048C4—21no—
1049C4—21no—
1050C4—21no—
1051C4—21no—
1052C4—21no—
1053C4—21no—
1054C4—21no—
1055C4—21no—
1056C4—792no—
1057C4—1581no—
1058C4—1581no—
1059C4—1581no—
1060C4—1581no—
1061C4—1581no—
1062C4—1581no—
1063C4—1581no—
1064C4—1581no—
1065C4—1581no—
1066C4—1581no—
1067C2—22no—
1068C2—41no—
1069C2—41no—
1070C2—41no—
1071C2—41no—
1072C2—41no—
1073C2—3161no—
1074C2—3161no—
1075C2—3161no—
1076C2—3161no—
1077C2—3161no—
1078C2H(5,𝔽2)×D7911yescharacteristic
1079C2C2×#1457920611yescharacteristic
1080C2#1909939911yescharacteristic
subgroupG/H
center, FrattiniC22C24×D79
commutator, socle, cosocleC22×C79C25
Fitting#546×C79C2
hypercenter#546D79
hypocenterC79#3558
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #546

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #19099309C2semidirect
2. #19099308C2semidirect
3. #19099306C2semidirect
4. #19099305C2semidirect
5. #19099297C2semidirect
6. #19099296C2semidirect
7. #19099222C2semidirect
8. #19099219C2semidirect
9. #19099205C2semidirect
10. #19099203C2semidirect
11. #19099203C2semidirect
12. #19099202C2semidirect
13. #19099201C2semidirect
14. D4×C22⋊D79C2semidirect
15. #19099195C2semidirect
16. #19099183C2semidirect
17. #19099177C2semidirect
18. #19099151C2semidirect
19. #19099149C2semidirect
20. #19099148C2semidirect
21. #19099146C2semidirect
22. #19099146C2semidirect
23. #19099145C2semidirect
24. #19099129C2semidirect
25. #19099128C2semidirect
26. #19099122C2semidirect
27. #19099121C2semidirect
28. #19099109C2semidirect
29. #19099090C2semidirect
30. C2×#14579147C2semidirect
31. #546×C79C2semidirect
32. C2×#11929624C22semidirect
33. C2×#11929624C22semidirect
34. C2×#11929623C22semidirect
35. C22×Dic158C22semidirect
37. C22×C22⋊D79C22semidirect
38. C22×C22⋊D79C22semidirect
39. C2×D4×D79C22semidirect
40. C2×D4×D79C22semidirect
41. C2×D4×D79C22semidirect
42. #14579159C22semidirect
45. #14579157C22semidirect
46. #14579156C22semidirect
47. #14579156C22semidirect
48. #14579155C22semidirect
49. #14579154C22semidirect
50. #14579154C22semidirect
51. #14579154C22semidirect
52. #14579151C22semidirect
53. #14579150C22semidirect
54. #14579150C22semidirect
55. #14579149C22semidirect
56. #14579149C22semidirect
57. #14579148C22semidirect
58. #14579148C22semidirect
59. #14579148C22semidirect
60. #14579147C22semidirect
61. #14579147C22semidirect
62. #14579147C22semidirect
63. #14579147C22semidirect
64. #14579147C22semidirect
65. #14579147C22semidirect
66. #14579147C22semidirect
67. #14579147C22semidirect
68. #14579147C22semidirect
69. #14579147C22semidirect
70. #14579147C22semidirect
71. #14579147C22semidirect
72. #14579147C22semidirect
73. #14579147C22semidirect
74. #14579147C22semidirect
75. #14579147C22semidirect
76. #14579147C22semidirect
77. #14579146C22semidirect
78. #14579146C22semidirect
79. #14579146C22semidirect
80. #14579146C22semidirect
81. #14579144C22semidirect
82. #14579144C22semidirect
83. #14579144C22semidirect
84. #14579144C22semidirect
85. #14579144C22semidirect
86. #14579143C22semidirect
87. #14579143C22semidirect
88. #14579143C22semidirect
89. #14579143C22semidirect
90. #14579142C22semidirect
91. #14579142C22semidirect
92. #14579142C22semidirect
93. #14579141C22semidirect
94. #14579140C22semidirect
95. #14579139C22semidirect
96. #14579139C22semidirect
97. #14579139C22semidirect
98. #14579138C22semidirect
99. #14579138C22semidirect
100. #14579138C22semidirect
101. #14579138C22semidirect
102. #14579137C22semidirect
103. #14579136C22semidirect
104. #14579135C22semidirect
105. #14579135C22semidirect
106. #14579135C22semidirect
107. #14579135C22semidirect
109. #14579134C22semidirect
110. #14579134C22semidirect
111. #14579134C22semidirect
112. #14579134C22semidirect
113. #14579134C22semidirect
116. #14579133C22semidirect
117. #14579133C22semidirect
118. #14579133C22semidirect
119. #14579133C22semidirect
120. #14579133C22semidirect
121. #14579133C22semidirect
122. #14579133C22semidirect
123. #14579133C22semidirect
124. #14579133C22semidirect
125. #14579132C22semidirect
126. #14579132C22semidirect
127. #14579131C22semidirect
128. #14579131C22semidirect
129. #14579131C22semidirect
130. #14579131C22semidirect
131. #14579131C22semidirect
132. #14579131C22semidirect
133. #14579130C22semidirect
134. #14579130C22semidirect
135. #14579130C22semidirect
136. #14579130C22semidirect
137. #14579129C22semidirect
138. #14579129C22semidirect
139. #14579129C22semidirect
140. #14579129C22semidirect
141. #14579129C22semidirect
142. #14579129C22semidirect
143. #14579129C22semidirect
144. #14579129C22semidirect
145. C4×Dic158C22semidirect
146. #14579126C22semidirect
147. #14579126C22semidirect
148. D4×Dic79C22semidirect
149. D4×Dic79C22semidirect
150. #14579123C22semidirect
151. C4×C22⋊D79C22semidirect
152. C4×C22⋊D79C22semidirect
153. C4×C22⋊D79C22semidirect
154. C4×C22⋊D79C22semidirect
155. C4×C22⋊D79C22semidirect
156. C4×C22⋊D79C22semidirect
157. C4×C22⋊D79C22semidirect
158. (C22⋊D79)⋊C4C22semidirect
159. (C22⋊D79)⋊C4C22semidirect
160. (C22⋊D79)⋊C4C22semidirect
161. (C22⋊D79)⋊C4C22semidirect
162. (C22⋊D79)⋊C4C22semidirect
163. #14579119C22semidirect
164. #14579117C22semidirect
165. C2×C22⋊Dic79C22semidirect
166. C2×(C2×D79)⋊C4C22semidirect
167. C2×(C2×D79)⋊C4C22semidirect
168. C2×(C2×D79)⋊C4C22semidirect
169. C22⋊C4×D79C22semidirect
170. C22⋊C4×D79C22semidirect
171. C2×C4×Dic79C22semidirect
172. C2×#41×C79C22semidirect
173. C22×D4×C79C22semidirect
174. #124×C79C22semidirect
175. #123×C79C22semidirect
176. #123×C79C22semidirect
177. C22⋊Q8×C79C22semidirect
178. #121×C79C22semidirect
179. #121×C79C22semidirect
180. #121×C79C22semidirect
181. #120×C79C22semidirect
182. #120×C79C22semidirect
183. C4×D4×C79C22semidirect
184. C4×D4×C79C22semidirect
185. C2×C22⋊C4×C79C22semidirect
186. C2×C22⋊C4×C79C22semidirect
541. C79#3558semidirect
555. #546D79semidirect
576. C2×#41C2×D79semidirect
584. C22×D4C2×D79semidirect
620. #124C2×D79semidirect
637. #123C2×D79semidirect
638. #123C2×D79semidirect
649. C22⋊Q8C2×D79semidirect
674. #121C2×D79semidirect
675. #121C2×D79semidirect
676. #121C2×D79semidirect
695. #120C2×D79semidirect
696. #120C2×D79semidirect
715. C4×D4C2×D79semidirect
716. C4×D4C2×D79semidirect
725. C2×C22⋊C4C2×D79semidirect
726. C2×C22⋊C4C2×D79semidirect