Finite Group Databasebeta

← #23777583

Subgroups — #23777583

Order 10112.

1166 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#19099310C211yesmaximal, characteristic, complemented
2#19099308C211yesmaximal, characteristic, complemented
3#19099301C211yesmaximal, characteristic, complemented
4#19099300C211yesmaximal, characteristic, complemented
5#19099258C211yesmaximal, characteristic, complemented
6#19099257C211yesmaximal, characteristic, complemented
7#19099242C211yesmaximal, characteristic, complemented
8#19099237C211yesmaximal, characteristic, complemented
9#19099210C211yesmaximal, characteristic, complemented
10#19099209C211yesmaximal, characteristic, complemented
11#19099205C211yesmaximal, characteristic, complemented
12#19099205C211yesmaximal, characteristic, complemented
13#19099202C211yesmaximal, characteristic, complemented
14#19099202C211yesmaximal, characteristic, complemented
15#19099198C211yesmaximal, characteristic, complemented
16#19099197C211yesmaximal, characteristic, complemented
17#19099163C211yesmaximal, characteristic, complemented
18#19099161C211yesmaximal, characteristic, complemented
19#19099161C211yesmaximal, characteristic, complemented
20#19099156C211yesmaximal, characteristic, complemented
21#19099149C211yesmaximal, characteristic, complemented
22#19099146C211yesmaximal, characteristic, complemented
23#19099145C211yesmaximal, characteristic, complemented
24#19099142C211yesmaximal, characteristic, complemented
25#19099124C211yesmaximal, characteristic, complemented
26#19099121C211yesmaximal, characteristic, complemented
27#19099121C211yesmaximal, characteristic, complemented
28#19099072C211yesmaximal, characteristic, complemented
29#123×D79C211yesmaximal, characteristic, complemented
30#121×D79C211yesmaximal, characteristic, complemented
31#540×C79C211yesmaximal, characteristic, complemented
32C2×#11929624C2211yescharacteristic, complemented
33C2×#11929624C2211yescharacteristic, complemented
34C2×#11929623C2211yescharacteristic, complemented
35C22×D316C2211yescharacteristic, complemented
36C2×D4×D79C2211yescharacteristic
37C2×D4×D79C2211yescharacteristic, complemented
38C2×D4×D79C2211yescharacteristic, complemented
39C2×D4×D79C2211yescharacteristic, complemented
40C2×D4×D79C2211yescharacteristic, complemented
41C2×D4×D79C2211yescharacteristic, complemented
42C2×D4×D79C2211yescharacteristic, complemented
43C22×C4×D79C2211yescharacteristic, complemented
44#14579157C2211yescharacteristic, complemented
45#14579156C2211yescharacteristic, complemented
46#14579156C2211yescharacteristic, complemented
47#14579156C2211yescharacteristic, complemented
48#14579155C2211yescharacteristic, complemented
49#14579155C2211yescharacteristic, complemented
50#14579155C2211yescharacteristic, complemented
51#14579154C2211yescharacteristic, complemented
52#14579154C2211yescharacteristic, complemented
53#14579152C2211yescharacteristic, complemented
54#14579151C2211yescharacteristic, complemented
55#14579151C2211yescharacteristic, complemented
56#14579149C2211yescharacteristic, complemented
57#14579148C2211yescharacteristic, complemented
58#14579147C2211yescharacteristic, complemented
59#14579147C2211yescharacteristic, complemented
60#14579147C2211yescharacteristic, complemented
61#14579147C2211yescharacteristic, complemented
62#14579146C2211yescharacteristic, complemented
63#14579146C2211yescharacteristic, complemented
64#14579146C2211yescharacteristic, complemented
65#14579146C2211yescharacteristic, complemented
66#14579146C2211yescharacteristic, complemented
67#14579146C2211yescharacteristic, complemented
68#14579146C2211yescharacteristic, complemented
69#14579146C2211yescharacteristic, complemented
70#14579146C2211yescharacteristic, complemented
71#14579146C2211yescharacteristic, complemented
72#14579145C2211yescharacteristic, complemented
73#14579144C2211yescharacteristic, complemented
74#14579144C2211yescharacteristic, complemented
75#14579144C2211yescharacteristic, complemented
76#14579143C2211yescharacteristic, complemented
77#14579143C2211yescharacteristic, complemented
78#14579143C2211yescharacteristic, complemented
79#14579143C2211yescharacteristic, complemented
80#14579143C2211yescharacteristic, complemented
81#14579143C2211yescharacteristic, complemented
82#14579142C2211yescharacteristic, complemented
83#14579142C2211yescharacteristic, complemented
84#14579142C2211yescharacteristic, complemented
85#14579142C2211yescharacteristic, complemented
86#14579141C2211yescharacteristic, complemented
87#14579141C2211yescharacteristic, complemented
88#14579140C2211yescharacteristic, complemented
89#14579140C2211yescharacteristic, complemented
90#14579139C2211yescharacteristic, complemented
91#14579139C2211yescharacteristic, complemented
92#14579139C2211yescharacteristic, complemented
93#14579139C2211yescharacteristic, complemented
94#14579139C2211yescharacteristic, complemented
95#14579138C2211yescharacteristic, complemented
96#14579138C2211yescharacteristic, complemented
97#14579138C2211yescharacteristic, complemented
98#14579136C2211yescharacteristic
99#14579136C2211yescharacteristic
100#14579136C2211yescharacteristic, complemented
101#14579135C2211yescharacteristic, complemented
102#14579135C2211yescharacteristic, complemented
103#14579135C2211yescharacteristic, complemented
104#14579134C2211yescharacteristic, complemented
105#14579134C2211yescharacteristic, complemented
106#14579134C2211yescharacteristic, complemented
107#14579134C2211yescharacteristic, complemented
108#14579134C2211yescharacteristic, complemented
109#14579134C2211yescharacteristic, complemented
110#14579134C2211yescharacteristic, complemented
111#14579134C2211yescharacteristic, complemented
112#14579133C2211yescharacteristic, complemented
113#14579133C2211yescharacteristic, complemented
114#14579133C2211yescharacteristic, complemented
115#14579133C2211yescharacteristic, complemented
116#14579133C2211yescharacteristic, complemented
117#14579133C2211yescharacteristic, complemented
118#14579133C2211yescharacteristic, complemented
119#14579133C2211yescharacteristic, complemented
120#14579133C2211yescharacteristic, complemented
121#14579133C2211yescharacteristic, complemented
122#14579132C2211yescharacteristic
123#14579132C2211yescharacteristic, complemented
124#14579132C2211yescharacteristic, complemented
125#14579132C2211yescharacteristic, complemented
126#14579132C2211yescharacteristic, complemented
127#14579132C2211yescharacteristic, complemented
128#14579131C2211yescharacteristic
129#14579131C2211yescharacteristic, complemented
130#14579131C2211yescharacteristic, complemented
131#14579131C2211yescharacteristic, complemented
132#14579131C2211yescharacteristic, complemented
133#14579131C2211yescharacteristic, complemented
134#14579129C2211yescharacteristic
135#14579129C2211yescharacteristic, complemented
136#14579129C2211yescharacteristic, complemented
137#14579129C2211yescharacteristic, complemented
138#14579129C2211yescharacteristic, complemented
139#14579129C2211yescharacteristic, complemented
140#14579129C2211yescharacteristic, complemented
141#14579129C2211yescharacteristic, complemented
142#14579129C2211yescharacteristic, complemented
143#14579129C2211yescharacteristic, complemented
144C4×D316C2211yescharacteristic, complemented
145C4×D316C2211yescharacteristic, complemented
146C4×D316C2211yescharacteristic, complemented
147#14579123C2211yescharacteristic, complemented
148#14579123C2211yescharacteristic, complemented
149#14579123C2211yescharacteristic, complemented
150C4×C22⋊D79C2211yescharacteristic, complemented
151C4×C22⋊D79C2211yescharacteristic, complemented
152C4×C22⋊D79C2211yescharacteristic, complemented
153C4×C22⋊D79C2211yescharacteristic, complemented
154C4×C22⋊D79C2211yescharacteristic, complemented
155(C22⋊D79)⋊C4C2211yescharacteristic, complemented
156(C22⋊D79)⋊C4C2211yescharacteristic, complemented
157(C22⋊D79)⋊C4C2211yescharacteristic, complemented
158#14579118C2211yescharacteristic, complemented
159#14579117C2211yescharacteristic, complemented
160C4⋊C4×D79C2211yescharacteristic, complemented
161C4⋊C4×D79C2211yescharacteristic, complemented
162C4⋊C4×D79C2211yescharacteristic, complemented
163C2×(C2×D79)⋊C4C2211yescharacteristic, complemented
164C2×(C2×D79)⋊C4C2211yescharacteristic, complemented
165C2×(C2×D79)⋊C4C2211yescharacteristic, complemented
166C22⋊C4×D79C2211yescharacteristic, complemented
167C22⋊C4×D79C2211yescharacteristic, complemented
168C22⋊C4×D79C2211yescharacteristic, complemented
169C22⋊C4×D79C2211yescharacteristic, complemented
170C22⋊C4×D79C2211yescharacteristic, complemented
171C22⋊C4×D79C2211yescharacteristic, complemented
172#127×C79C2211yescharacteristic, complemented
173#125×C79C2211yescharacteristic, complemented
174#123×C79C2211yescharacteristic, complemented
175#123×C79C2211yescharacteristic, complemented
176#123×C79C2211yescharacteristic, complemented
177#123×C79C2211yescharacteristic, complemented
178#121×C79C2211yescharacteristic, complemented
179#121×C79C2211yescharacteristic, complemented
180#121×C79C2211yescharacteristic, complemented
181#121×C79C2211yescharacteristic, complemented
182#121×C79C2211yescharacteristic, complemented
183#121×C79C2211yescharacteristic, complemented
184C4×D4×C79C2211yescharacteristic, complemented
185C4×D4×C79C2211yescharacteristic, complemented
186#117×C79C2211yescharacteristic, complemented
187C23×D79C2311yescharacteristic
188C23×D79C2311yescharacteristic
189C23×D79C2311yescharacteristic
190C23×D79C2311yescharacteristic
191C23×D79C2311yescharacteristic
192C23×D79C2311yescharacteristic
193#11929624—42no—
194#11929624—42no—
195#11929623—42no—
196C2×Dic158C2311yescharacteristic
197C2×Dic158C2311yescharacteristic
198C2×Dic158C2311yescharacteristic
199C2×D316—42no—
200C2×D316C2311yescharacteristic
201C2×D316C2311yescharacteristic
202C2×D316C2311yescharacteristic
203C2×D316C2311yescharacteristic
204C2×D316C2311yescharacteristic
205C2×D316C2311yescharacteristic
206C2×D316C2311yescharacteristic
207C2×D316C2311yescharacteristic
208C2×D316C2311yescharacteristic
209C2×C22⋊D79C2311yescharacteristic
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
227D4×D79—42no—
228D4×D79—42no—
229D4×D79—42no—
230D4×D79—42no—
231D4×D79—42no—
232D4×D79—42no—
233D4×D79—42no—
234C22×Dic79C2311yescharacteristic
235C22×Dic79C2311yescharacteristic
236C22×Dic79C2311yescharacteristic
237C22×Dic79C2311yescharacteristic
238C2×C4×D79—42no—
239C2×C4×D79C2311yescharacteristic
240C2×C4×D79C2311yescharacteristic
241C2×C4×D79C2311yescharacteristic
242C2×C4×D79C2311yescharacteristic
243C2×C4×D79C2311yescharacteristic
244C2×C4×D79C2311yescharacteristic
245C2×C4×D79C2311yescharacteristic
246C2×C4×D79C2311yescharacteristic
247C2×C4×D79C2311yescharacteristic
248C2×C4×D79C2311yescharacteristic
249C2×C4×D79C2311yescharacteristic
250C2×C4×D79C2311yescharacteristic
251C2×C4×D79C2311yescharacteristic
252C2×C4×D79C2311yescharacteristic
253C4⋊Dic79C2311yescharacteristic
254C4⋊Dic79C2311yescharacteristic
255C4⋊Dic79C2311yescharacteristic
256C4⋊Dic79C2311yescharacteristic
257C4⋊Dic79C2311yescharacteristic
258C4⋊Dic79C2311yescharacteristic
259Dic79⋊C4C2311yescharacteristic
260Dic79⋊C4C2311yescharacteristic
261Dic79⋊C4C2311yescharacteristic
262Dic79⋊C4C2311yescharacteristic
263Dic79⋊C4C2311yescharacteristic
264Dic79⋊C4C2311yescharacteristic
265Dic79⋊C4C2311yescharacteristic
266Dic79⋊C4C2311yescharacteristic
267Dic79⋊C4C2311yescharacteristic
268Dic79⋊C4C2311yescharacteristic
269Dic79⋊C4C2311yescharacteristic
270Dic79⋊C4C2311yescharacteristic
271Dic79⋊C4C2311yescharacteristic
272Dic79⋊C4C2311yescharacteristic
273Dic79⋊C4C2311yescharacteristic
274Dic79⋊C4C2311yescharacteristic
275C22⋊Dic79C2311yescharacteristic
276C22⋊Dic79C2311yescharacteristic
277C22⋊Dic79C2311yescharacteristic
278C22⋊Dic79C2311yescharacteristic
279C22⋊Dic79C2311yescharacteristic
280C22⋊Dic79C2311yescharacteristic
281C22⋊Dic79C2311yescharacteristic
282C22⋊Dic79C2311yescharacteristic
283C22⋊Dic79C2311yescharacteristic
284C22⋊Dic79C2311yescharacteristic
285C22⋊Dic79C2311yescharacteristic
286C22⋊Dic79C2311yescharacteristic
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
308(C2×D79)⋊C4C2311yescharacteristic
309(C2×D79)⋊C4C2311yescharacteristic
310(C2×D79)⋊C4C2311yescharacteristic
311(C2×D79)⋊C4C2311yescharacteristic
312(C2×D79)⋊C4C2311yescharacteristic
313(C2×D79)⋊C4C2311yescharacteristic
314(C2×D79)⋊C4C2311yescharacteristic
315C4×Dic79C2311yescharacteristic
316C4×Dic79C2311yescharacteristic
317C4×Dic79C2311yescharacteristic
318C4×Dic79C2311yescharacteristic
319C2×D4×C79C2311yescharacteristic
320C2×D4×C79C2311yescharacteristic
321C2×D4×C79C2311yescharacteristic
322C2×D4×C79C2311yescharacteristic
323C2×D4×C79C2311yescharacteristic
324C2×D4×C79C2311yescharacteristic
325C2×D4×C79C2311yescharacteristic
326C2×D4×C79C2311yescharacteristic
327C2×D4×C79C2311yescharacteristic
328C2×D4×C79C2311yescharacteristic
329C22×C4×C79C2311yescharacteristic
330C22×C4×C79C2311yescharacteristic
331C22×C4×C79C2311yescharacteristic
332C22×C4×C79C2311yescharacteristic
333C22×C4×C79C2311yescharacteristic
334C4⋊C4×C79C2311yescharacteristic
335C4⋊C4×C79C2311yescharacteristic
336C4⋊C4×C79C2311yescharacteristic
337C4⋊C4×C79C2311yescharacteristic
338C4⋊C4×C79C2311yescharacteristic
339C4⋊C4×C79C2311yescharacteristic
340C4⋊C4×C79C2311yescharacteristic
341C4⋊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
352C42×C79C2311yescharacteristic
353C42×C79C2311yescharacteristic
354C23×C79C2411yescharacteristic
355C23×C79C2411yescharacteristic
356C23×C79C2411yescharacteristic
357C23×C79C2411yescharacteristic
358C23×C79C2411yescharacteristic
359C22×D79—22no—
360C22×D79—22no—
361C22×D79—22no—
362C22×D79—22no—
363C22×D79—22no—
364C22×D79—41no—
365C22×D79—41no—
366C22×D79—41no—
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×D79C2411yescharacteristic
378C22×D79C2411yescharacteristic
379C22×D79C2411yescharacteristic
380C22×D79C2411yescharacteristic
381C22×D79C2411yescharacteristic
382C22×D79C2411yescharacteristic
383D4×C79—41no—
384D4×C79—41no—
385D4×C79—41no—
386D4×C79—41no—
387D4×C79—41no—
388D4×C79—41no—
389D4×C79—41no—
390D4×C79—41no—
391D4×C79—41no—
392D4×C79—41no—
393C2×C4×C79—41no—
394C2×C4×C79—41no—
395C2×C4×C79—41no—
396C2×C4×C79—41no—
397C2×C4×C79—41no—
398C2×C4×C79C2411yescharacteristic
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—41no—
414C22⋊D79—41no—
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—
426C2×Dic79—41no—
427C2×Dic79—41no—
428C2×Dic79—41no—
429C2×Dic79—41no—
430C2×Dic79C2411yescharacteristic
431C2×Dic79C2411yescharacteristic
432C2×Dic79C2411yescharacteristic
433C2×Dic79C2411yescharacteristic
434C2×Dic79C2411yescharacteristic
435C2×Dic79C2411yescharacteristic
436C2×Dic79C2411yescharacteristic
437C2×Dic79C2411yescharacteristic
438C2×Dic79C2411yescharacteristic
439C2×Dic79C2411yescharacteristic
440D316—22no—
441D316—22no—
442D316—22no—
443D316—22no—
444D316—22no—
445D316—41no—
446D316—41no—
447D316—41no—
448D316—41no—
449C4×D79—22no—
450C4×D79—22no—
451C4×D79—22no—
452C4×D79—41no—
453C4×D79—41no—
454C4×D79—41no—
455C4×D79—41no—
456C4×D79—41no—
457C4×D79—41no—
458C4×D79—41no—
459C4×D79—41no—
460C4×D79—41no—
461C4×D79—41no—
462C4×D79—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×C79C2511yescharacteristic
482C2×D79—21no—
483C2×D79—21no—
484C2×D79—21no—
485C2×D79—21no—
486C2×D79—21no—
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—44no—
499C2×D79—82no—
500C2×D79—82no—
501C2×D79—82no—
502C2×D79—82no—
503C2×D79—82no—
504C2×D79H(5,𝔽2)12yes—
505C2×D79H(5,𝔽2)12yes—
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—
515C4×C79—21no—
516Dic79—21no—
517Dic79—21no—
518Dic79—21no—
519Dic79—21no—
520Dic79—21no—
521Dic79—21no—
522Dic79—21no—
523Dic79—21no—
524Dic79—21no—
525Dic79—21no—
526C2×C79—41no—
527C2×C79—41no—
528C2×C79—41no—
529C2×C79—41no—
530C2×C79—41no—
531C2×C79C2×H(5,𝔽2)11yescharacteristic
532C2×C79C2×H(5,𝔽2)11yescharacteristic
533C2×C79#58511yescharacteristic
534D79—22no—
535D79—22no—
536D79—41no—
537D79—41no—
538D79—41no—
539D79—41no—
540#3534—791nomaximal, Sylow
541C79#353411yescharacteristic, complemented, Sylow
542#562—791no—
543#562—791no—
544#560—791no—
545#560—791no—
546#553—791no—
547#553—791no—
548#551—791no—
549#551—791no—
550#546—791no—
551#546—791no—
552#546—791no—
553#546—791no—
554#546—791no—
555#546—791no—
556D42—791no—
557D42—791no—
558#540—791no—
559#540D7911yescharacteristic, complemented
560#539—791no—
561#539—791no—
562#539—791no—
563#538—791no—
564#538—791no—
565#538—791no—
566#537—791no—
567#534—791no—
568#534—791no—
569#534—791no—
570#525—791no—
571C2×#123—791no—
572C2×#121—791no—
573C2×#41—791no—
574C2×#41—791no—
575C2×#41—791no—
576C22×D4—791no—
577C22×D4—791no—
578C22×D4—791no—
579C22×D4—791no—
580C22×D4—791no—
581C22×D4—791no—
582C22×D4—791no—
583C22×D4—791no—
584C23×C4—791no—
585#127—791no—
586#127C2×D7911yescharacteristic, complemented
587#126—791no—
588#126—791no—
589#126—791no—
590#126—791no—
591#126—791no—
592#126—791no—
593#126—791no—
594#126—791no—
595#125—791no—
596#125—791no—
597#125—791no—
598#125C2×D7911yescharacteristic, complemented
599#124—791no—
600#124—791no—
601#124—791no—
602#124—791no—
603#124—791no—
604#124—791no—
605#123—791no—
606#123—791no—
607#123—791no—
608#123—791no—
609#123—791no—
610#123—791no—
611#123—791no—
612#123—791no—
613#123—791no—
614#123—791no—
615#123—791no—
616#123—791no—
617#123—791no—
618#123—791no—
619#123—791no—
620#123—791no—
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#123C2×D7911yescharacteristic, complemented
630#123C2×D7911yescharacteristic, complemented
631#123C2×D7911yescharacteristic, complemented
632#123C2×D7911yescharacteristic, complemented
633C22⋊Q8—791no—
634C22⋊Q8—791no—
635C22⋊Q8—791no—
636C22⋊Q8—791no—
637C22⋊Q8—791no—
638C22⋊Q8—791no—
639C22⋊Q8—791no—
640C22⋊Q8—791no—
641C22⋊Q8—791no—
642C22⋊Q8—791no—
643C22⋊Q8—791no—
644C22⋊Q8—791no—
645#121—791no—
646#121—791no—
647#121—791no—
648#121—791no—
649#121—791no—
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#121—791no—
675#121C2×D7911yescharacteristic, complemented
676#121C2×D7911yescharacteristic, complemented
677#121C2×D7911yescharacteristic, complemented
678#121C2×D7911yescharacteristic, complemented
679#121C2×D7911yescharacteristic, complemented
680#121C2×D7911yescharacteristic, complemented
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#120—791no—
696#120—791no—
697C4×D4—791no—
698C4×D4—791no—
699C4×D4—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×D4C2×D7911yescharacteristic, complemented
712C4×D4C2×D7911yescharacteristic, complemented
713#117—791no—
714#117—791no—
715#117C2×D7911yescharacteristic, complemented
716C2×C4⋊C4—791no—
717C2×C4⋊C4—791no—
718C2×C4⋊C4—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⋊C4—791no—
726C2×C22⋊C4—791no—
727C2×C22⋊C4—791no—
728C24—791no—
729C24—791no—
730C24—791no—
731C24—791no—
732C24—791no—
733C24—791no—
734#41—3162no—
735#41—3162no—
736#41—3162no—
737C2×Q8—791no—
738C2×Q8—791no—
739C2×Q8—791no—
740C2×D4—3162no—
741C2×D4—3162no—
742C2×D4—3162no—
743C2×D4—3162no—
744C2×D4—3162no—
745C2×D4—3162no—
746C2×D4—3162no—
747C2×D4—3162no—
748C2×D4—791no—
749C2×D4—791no—
750C2×D4—791no—
751C2×D4—791no—
752C2×D4—791no—
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×D4C22×D7911yescharacteristic
776C2×D4C22×D7911yescharacteristic
777C2×D4C22×D7911yescharacteristic
778C2×D4C22×D7911yescharacteristic
779C2×D4C22×D7911yescharacteristic
780C2×D4C22×D7911yescharacteristic
781C2×D4C22×D7911yescharacteristic
782C2×D4C22×D7911yescharacteristic
783C2×D4C22×D7911yescharacteristic
784C2×D4C22×D7911yescharacteristic
785C22×C4—3162no—
786C22×C4—791no—
787C22×C4—791no—
788C22×C4—791no—
789C22×C4—791no—
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×C4—791no—
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⋊C4—791no—
828C4⋊C4—791no—
829C4⋊C4—791no—
830C4⋊C4—791no—
831C4⋊C4C22×D7911yescharacteristic
832C4⋊C4C22×D7911yescharacteristic
833C4⋊C4C22×D7911yescharacteristic
834C4⋊C4C22×D7911yescharacteristic
835C4⋊C4C22×D7911yescharacteristic
836C4⋊C4C22×D7911yescharacteristic
837C4⋊C4C22×D7911yescharacteristic
838C4⋊C4C22×D7911yescharacteristic
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⋊C4—791no—
874C22⋊C4—791no—
875C22⋊C4—791no—
876C22⋊C4—791no—
877C22⋊C4—791no—
878C22⋊C4—791no—
879C22⋊C4C22×D7911yescharacteristic
880C22⋊C4C22×D7911yescharacteristic
881C22⋊C4C22×D7911yescharacteristic
882C22⋊C4C22×D7911yescharacteristic
883C22⋊C4C22×D7911yescharacteristic
884C22⋊C4C22×D7911yescharacteristic
885C22⋊C4C22×D7911yescharacteristic
886C22⋊C4C22×D7911yescharacteristic
887C22⋊C4C22×D7911yescharacteristic
888C22⋊C4C22×D7911yescharacteristic
889C42—791no—
890C42—791no—
891C42—791no—
892C42—791no—
893C42C22×D7911yescharacteristic
894C42C22×D7911yescharacteristic
895C23—3161no—
896C23—3161no—
897C23—3161no—
898C23—3161no—
899C23—3161no—
900C23—3161no—
901C23—3161no—
902C23—3161no—
903C23—3161no—
904C23—3161no—
905C23—3161no—
906C23—3161no—
907C23—3161no—
908C23—791no—
909C23—791no—
910C23—791no—
911C23—791no—
912C23—791no—
913C23—791no—
914C23—1582no—
915C23—1582no—
916C23—1582no—
917C23—1582no—
918C23—1582no—
919C23C23×D7911yescharacteristic
920C23C23×D7911yescharacteristic
921C23C23×D7911yescharacteristic
922C23C23×D7911yescharacteristic
923C23C23×D7911yescharacteristic
924Q8—3161no—
925Q8—3161no—
926Q8—3161no—
927D4—41no—
928D4—41no—
929D4—41no—
930D4—41no—
931D4—41no—
932D4—41no—
933D4—41no—
934D4—41no—
935D4—41no—
936D4—41no—
937D4—3161no—
938D4—3161no—
939D4—3161no—
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—1582no—
955D4—1582no—
956D4—1582no—
957D4—1582no—
958D4—1582no—
959D4—1582no—
960D4—1582no—
961D4—1582no—
962D4—1582no—
963D4—1582no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—3161no—
970C2×C4—3161no—
971C2×C4—3161no—
972C2×C4—3161no—
973C2×C4—3161no—
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—1582no—
995C2×C4—1582no—
996C2×C4—1582no—
997C2×C4C23×D7911yescharacteristic
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—3164no—
1023C22—792no—
1024C22—792no—
1025C22—6322no—
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—1581no—
1046C22C24×D7911yescharacteristic
1047C4—21no—
1048C4—21no—
1049C4—21no—
1050C4—21no—
1051C4—21no—
1052C4—21no—
1053C4—21no—
1054C4—21no—
1055C4—21no—
1056C4—21no—
1057C4—1581no—
1058C4—1581no—
1059C4—1581no—
1060C4—1581no—
1061C4—1581no—
1062C4—1581no—
1063C4—1581no—
1064C4—1581no—
1065C4—1581no—
1066C4—1581no—
1067C2—41no—
1068C2—41no—
1069C2—41no—
1070C2—41no—
1071C2—41no—
1072C2—3161no—
1073C2—3161no—
1074C2—3161no—
1075C2—3161no—
1076C2—1582no—
1077C2—1582no—
1078C2H(5,𝔽2)×D7911yescharacteristic
1079C2H(5,𝔽2)×D7911yescharacteristic
1080C2#1909939911yescharacteristic
subgroupG/H
center, FrattiniC22C24×D79
commutator, socle, cosocleC22×C79C25
Fitting#540×C79C2
hypercenter#540D79
hypocenterC79#3534
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #540

Complements

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

NH ≅ G/Ntype
1. #19099310C2semidirect
2. #19099308C2semidirect
3. #19099301C2semidirect
4. #19099300C2semidirect
5. #19099258C2semidirect
6. #19099257C2semidirect
7. #19099242C2semidirect
8. #19099237C2semidirect
9. #19099210C2semidirect
10. #19099209C2semidirect
11. #19099205C2semidirect
12. #19099205C2semidirect
13. #19099202C2semidirect
14. #19099202C2semidirect
15. #19099198C2semidirect
16. #19099197C2semidirect
17. #19099163C2semidirect
18. #19099161C2semidirect
19. #19099161C2semidirect
20. #19099156C2semidirect
21. #19099149C2semidirect
22. #19099146C2semidirect
23. #19099145C2semidirect
24. #19099142C2semidirect
25. #19099124C2semidirect
26. #19099121C2semidirect
27. #19099121C2semidirect
28. #19099072C2semidirect
29. #123×D79C2semidirect
30. #121×D79C2semidirect
31. #540×C79C2semidirect
32. C2×#11929624C22semidirect
33. C2×#11929624C22semidirect
34. C2×#11929623C22semidirect
35. C22×D316C22semidirect
37. C2×D4×D79C22semidirect
38. C2×D4×D79C22semidirect
39. C2×D4×D79C22semidirect
40. C2×D4×D79C22semidirect
41. C2×D4×D79C22semidirect
42. C2×D4×D79C22semidirect
43. C22×C4×D79C22semidirect
44. #14579157C22semidirect
45. #14579156C22semidirect
46. #14579156C22semidirect
47. #14579156C22semidirect
48. #14579155C22semidirect
49. #14579155C22semidirect
50. #14579155C22semidirect
51. #14579154C22semidirect
52. #14579154C22semidirect
53. #14579152C22semidirect
54. #14579151C22semidirect
55. #14579151C22semidirect
56. #14579149C22semidirect
57. #14579148C22semidirect
58. #14579147C22semidirect
59. #14579147C22semidirect
60. #14579147C22semidirect
61. #14579147C22semidirect
62. #14579146C22semidirect
63. #14579146C22semidirect
64. #14579146C22semidirect
65. #14579146C22semidirect
66. #14579146C22semidirect
67. #14579146C22semidirect
68. #14579146C22semidirect
69. #14579146C22semidirect
70. #14579146C22semidirect
71. #14579146C22semidirect
72. #14579145C22semidirect
73. #14579144C22semidirect
74. #14579144C22semidirect
75. #14579144C22semidirect
76. #14579143C22semidirect
77. #14579143C22semidirect
78. #14579143C22semidirect
79. #14579143C22semidirect
80. #14579143C22semidirect
81. #14579143C22semidirect
82. #14579142C22semidirect
83. #14579142C22semidirect
84. #14579142C22semidirect
85. #14579142C22semidirect
86. #14579141C22semidirect
87. #14579141C22semidirect
88. #14579140C22semidirect
89. #14579140C22semidirect
90. #14579139C22semidirect
91. #14579139C22semidirect
92. #14579139C22semidirect
93. #14579139C22semidirect
94. #14579139C22semidirect
95. #14579138C22semidirect
96. #14579138C22semidirect
97. #14579138C22semidirect
100. #14579136C22semidirect
101. #14579135C22semidirect
102. #14579135C22semidirect
103. #14579135C22semidirect
104. #14579134C22semidirect
105. #14579134C22semidirect
106. #14579134C22semidirect
107. #14579134C22semidirect
108. #14579134C22semidirect
109. #14579134C22semidirect
110. #14579134C22semidirect
111. #14579134C22semidirect
112. #14579133C22semidirect
113. #14579133C22semidirect
114. #14579133C22semidirect
115. #14579133C22semidirect
116. #14579133C22semidirect
117. #14579133C22semidirect
118. #14579133C22semidirect
119. #14579133C22semidirect
120. #14579133C22semidirect
121. #14579133C22semidirect
123. #14579132C22semidirect
124. #14579132C22semidirect
125. #14579132C22semidirect
126. #14579132C22semidirect
127. #14579132C22semidirect
129. #14579131C22semidirect
130. #14579131C22semidirect
131. #14579131C22semidirect
132. #14579131C22semidirect
133. #14579131C22semidirect
135. #14579129C22semidirect
136. #14579129C22semidirect
137. #14579129C22semidirect
138. #14579129C22semidirect
139. #14579129C22semidirect
140. #14579129C22semidirect
141. #14579129C22semidirect
142. #14579129C22semidirect
143. #14579129C22semidirect
144. C4×D316C22semidirect
145. C4×D316C22semidirect
146. C4×D316C22semidirect
147. #14579123C22semidirect
148. #14579123C22semidirect
149. #14579123C22semidirect
150. C4×C22⋊D79C22semidirect
151. C4×C22⋊D79C22semidirect
152. C4×C22⋊D79C22semidirect
153. C4×C22⋊D79C22semidirect
154. C4×C22⋊D79C22semidirect
155. (C22⋊D79)⋊C4C22semidirect
156. (C22⋊D79)⋊C4C22semidirect
157. (C22⋊D79)⋊C4C22semidirect
158. #14579118C22semidirect
159. #14579117C22semidirect
160. C4⋊C4×D79C22semidirect
161. C4⋊C4×D79C22semidirect
162. C4⋊C4×D79C22semidirect
163. C2×(C2×D79)⋊C4C22semidirect
164. C2×(C2×D79)⋊C4C22semidirect
165. C2×(C2×D79)⋊C4C22semidirect
166. C22⋊C4×D79C22semidirect
167. C22⋊C4×D79C22semidirect
168. C22⋊C4×D79C22semidirect
169. C22⋊C4×D79C22semidirect
170. C22⋊C4×D79C22semidirect
171. C22⋊C4×D79C22semidirect
172. #127×C79C22semidirect
173. #125×C79C22semidirect
174. #123×C79C22semidirect
175. #123×C79C22semidirect
176. #123×C79C22semidirect
177. #123×C79C22semidirect
178. #121×C79C22semidirect
179. #121×C79C22semidirect
180. #121×C79C22semidirect
181. #121×C79C22semidirect
182. #121×C79C22semidirect
183. #121×C79C22semidirect
184. C4×D4×C79C22semidirect
185. C4×D4×C79C22semidirect
186. #117×C79C22semidirect
541. C79#3534semidirect
559. #540D79semidirect
586. #127C2×D79semidirect
598. #125C2×D79semidirect
629. #123C2×D79semidirect
630. #123C2×D79semidirect
631. #123C2×D79semidirect
632. #123C2×D79semidirect
675. #121C2×D79semidirect
676. #121C2×D79semidirect
677. #121C2×D79semidirect
678. #121C2×D79semidirect
679. #121C2×D79semidirect
680. #121C2×D79semidirect
711. C4×D4C2×D79semidirect
712. C4×D4C2×D79semidirect
715. #117C2×D79semidirect