Finite Group Databasebeta

← #19149106

Subgroups — #19149106

Order 5504.

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#14583645C211yesmaximal, characteristic, complemented
2#14583644C211yesmaximal, characteristic, complemented
3#14583642C211yesmaximal, characteristic, complemented
4#14583641C211yesmaximal, characteristic, complemented
5#14583633C211yesmaximal, characteristic, complemented
6#14583632C211yesmaximal, characteristic, complemented
7#14583559C211yesmaximal, characteristic, complemented
8#14583557C211yesmaximal, characteristic, complemented
9#14583546C211yesmaximal, characteristic, complemented
10#14583545C211yesmaximal, characteristic, complemented
11#14583541C211yesmaximal, characteristic, complemented
12#14583539C211yesmaximal, characteristic, complemented
13#14583539C211yesmaximal, characteristic, complemented
14#14583538C211yesmaximal, characteristic, complemented
15#14583533C211yesmaximal, characteristic, complemented
16#14583531C211yesmaximal, characteristic, complemented
17#14583517C211yesmaximal, characteristic, complemented
18#14583515C211yesmaximal, characteristic, complemented
19#14583488C211yesmaximal, characteristic, complemented
20#14583488C211yesmaximal, characteristic, complemented
21#14583483C211yesmaximal, characteristic, complemented
22#14583482C211yesmaximal, characteristic, complemented
23#14583481C211yesmaximal, characteristic, complemented
24#14583465C211yesmaximal, characteristic, complemented
25#14583464C211yesmaximal, characteristic, complemented
26#14583460C211yesmaximal, characteristic, complemented
27#14583459C211yesmaximal, characteristic, complemented
28#14583446C211yesmaximal, characteristic, complemented
29#14583432C211yesmaximal, characteristic, complemented
30#124×D43C211yesmaximal, characteristic, complemented
31C43×#538C211yesmaximal, characteristic, complemented
32C2×#10621898C2211yescharacteristic, complemented
33C2×#10621898C2211yescharacteristic, complemented
34C2×#10621898C2211yescharacteristic, complemented
35C2×#10621900C2211yescharacteristic, complemented
36C2×Q8×D43C2211yescharacteristic, complemented
37C22×D172C2211yescharacteristic, complemented
38C22×C22⋊D43C2211yescharacteristic, complemented
39C22×C22⋊D43C2211yescharacteristic, complemented
40C2×D4×D43C2211yescharacteristic
41C2×D4×D43C2211yescharacteristic, complemented
42C2×D4×D43C2211yescharacteristic, complemented
43C2×D4×D43C2211yescharacteristic, complemented
44#13063324C2211yescharacteristic, complemented
45#13063321C2211yescharacteristic
46#13063321C2211yescharacteristic
47#13063321C2211yescharacteristic, complemented
48#13063320C2211yescharacteristic, complemented
49#13063320C2211yescharacteristic, complemented
50#13063319C2211yescharacteristic, complemented
51#13063318C2211yescharacteristic, complemented
52#13063315C2211yescharacteristic, complemented
53#13063314C2211yescharacteristic, complemented
54#13063314C2211yescharacteristic, complemented
55#13063313C2211yescharacteristic, complemented
56#13063313C2211yescharacteristic, complemented
57#13063313C2211yescharacteristic, complemented
58#13063312C2211yescharacteristic, complemented
59#13063312C2211yescharacteristic, complemented
60#13063312C2211yescharacteristic, complemented
61#13063311C2211yescharacteristic, complemented
62#13063311C2211yescharacteristic, complemented
63#13063311C2211yescharacteristic, complemented
64#13063311C2211yescharacteristic, complemented
65#13063311C2211yescharacteristic, complemented
66#13063311C2211yescharacteristic, complemented
67#13063311C2211yescharacteristic, complemented
68#13063311C2211yescharacteristic, complemented
69#13063311C2211yescharacteristic, complemented
70#13063311C2211yescharacteristic, complemented
71#13063311C2211yescharacteristic, complemented
72#13063311C2211yescharacteristic, complemented
73#13063311C2211yescharacteristic, complemented
74#13063311C2211yescharacteristic, complemented
75#13063311C2211yescharacteristic, complemented
76#13063310C2211yescharacteristic, complemented
77#13063310C2211yescharacteristic, complemented
78#13063310C2211yescharacteristic, complemented
79#13063310C2211yescharacteristic, complemented
80#13063310C2211yescharacteristic, complemented
81#13063309C2211yescharacteristic, complemented
82#13063308C2211yescharacteristic, complemented
83#13063308C2211yescharacteristic, complemented
84#13063308C2211yescharacteristic, complemented
85#13063307C2211yescharacteristic, complemented
86#13063307C2211yescharacteristic, complemented
87#13063307C2211yescharacteristic, complemented
88#13063307C2211yescharacteristic, complemented
89#13063307C2211yescharacteristic, complemented
90#13063306C2211yescharacteristic, complemented
91#13063306C2211yescharacteristic, complemented
92#13063305C2211yescharacteristic, complemented
93#13063304C2211yescharacteristic, complemented
94#13063303C2211yescharacteristic, complemented
95#13063303C2211yescharacteristic, complemented
96#13063303C2211yescharacteristic, complemented
97#13063303C2211yescharacteristic, complemented
98#13063302C2211yescharacteristic, complemented
99#13063302C2211yescharacteristic, complemented
100#13063302C2211yescharacteristic, complemented
101#13063301C2211yescharacteristic, complemented
102#13063300C2211yescharacteristic, complemented
103#13063300C2211yescharacteristic, complemented
104#13063300C2211yescharacteristic, complemented
105#13063300C2211yescharacteristic, complemented
106#13063299C2211yescharacteristic, complemented
107#13063299C2211yescharacteristic, complemented
108#13063298C2211yescharacteristic
109#13063298C2211yescharacteristic
110#13063298C2211yescharacteristic, complemented
111#13063298C2211yescharacteristic, complemented
112#13063298C2211yescharacteristic, complemented
113#13063298C2211yescharacteristic, complemented
114#13063298C2211yescharacteristic, complemented
115#13063298C2211yescharacteristic, complemented
116#13063298C2211yescharacteristic, complemented
117#13063298C2211yescharacteristic, complemented
118#13063298C2211yescharacteristic, complemented
119#13063297C2211yescharacteristic
120#13063297C2211yescharacteristic, complemented
121#13063297C2211yescharacteristic, complemented
122#13063297C2211yescharacteristic, complemented
123#13063296C2211yescharacteristic, complemented
124#13063296C2211yescharacteristic, complemented
125#13063296C2211yescharacteristic, complemented
126#13063295C2211yescharacteristic, complemented
127#13063295C2211yescharacteristic, complemented
128#13063295C2211yescharacteristic, complemented
129#13063295C2211yescharacteristic, complemented
130#13063295C2211yescharacteristic, complemented
131#13063295C2211yescharacteristic, complemented
132#13063295C2211yescharacteristic, complemented
133#13063295C2211yescharacteristic, complemented
134#13063294C2211yescharacteristic, complemented
135#13063294C2211yescharacteristic, complemented
136#13063293C2211yescharacteristic, complemented
137#13063293C2211yescharacteristic, complemented
138#13063293C2211yescharacteristic, complemented
139#13063293C2211yescharacteristic, complemented
140#13063293C2211yescharacteristic, complemented
141#13063293C2211yescharacteristic, complemented
142#13063293C2211yescharacteristic, complemented
143#13063293C2211yescharacteristic, complemented
144C4×Dic86C2211yescharacteristic, complemented
145#13063290C2211yescharacteristic, complemented
146#13063290C2211yescharacteristic, complemented
147C4×D172C2211yescharacteristic, complemented
148C4×D172C2211yescharacteristic, complemented
149#13063287C2211yescharacteristic, complemented
150#13063287C2211yescharacteristic, complemented
151#13063287C2211yescharacteristic, complemented
152C4×C22⋊D43C2211yescharacteristic, complemented
153C4×C22⋊D43C2211yescharacteristic, complemented
154C4×C22⋊D43C2211yescharacteristic, complemented
155C4×C22⋊D43C2211yescharacteristic, complemented
156C4×C22⋊D43C2211yescharacteristic, complemented
157(C22⋊D43)⋊C4C2211yescharacteristic, complemented
158(C22⋊D43)⋊C4C2211yescharacteristic, complemented
159(C22⋊D43)⋊C4C2211yescharacteristic, complemented
160(C22⋊D43)⋊C4C2211yescharacteristic, complemented
161(C22⋊D43)⋊C4C2211yescharacteristic, complemented
162#13063283C2211yescharacteristic, complemented
163#13063281C2211yescharacteristic, complemented
164C2×(C2×D43)⋊C4C2211yescharacteristic, complemented
165C22⋊C4×D43C2211yescharacteristic, complemented
166C22⋊C4×D43C2211yescharacteristic, complemented
167C22⋊C4×D43C2211yescharacteristic, complemented
168C22⋊C4×D43C2211yescharacteristic, complemented
169C22⋊C4×D43C2211yescharacteristic, complemented
170C22⋊C4×D43C2211yescharacteristic, complemented
171C42×D43C2211yescharacteristic, complemented
172#126×C43C2211yescharacteristic, complemented
173#126×C43C2211yescharacteristic, complemented
174#124×C43C2211yescharacteristic, complemented
175#124×C43C2211yescharacteristic, complemented
176#123×C43C2211yescharacteristic, complemented
177#123×C43C2211yescharacteristic, complemented
178C22⋊Q8×C43C2211yescharacteristic, complemented
179#121×C43C2211yescharacteristic, complemented
180#121×C43C2211yescharacteristic, complemented
181#121×C43C2211yescharacteristic, complemented
182#120×C43C2211yescharacteristic, complemented
183#120×C43C2211yescharacteristic, complemented
184C4×D4×C43C2211yescharacteristic, complemented
185C4×D4×C43C2211yescharacteristic, complemented
186C2×C22⋊C4×C43C2211yescharacteristic, complemented
187C24×C43C2311yescharacteristic
188C23×D43C2311yescharacteristic
189C23×D43C2311yescharacteristic
190C23×D43C2311yescharacteristic
191C23×D43C2311yescharacteristic
192C23×D43C2311yescharacteristic
193C2×Q8×C43C2311yescharacteristic
194C2×D4×C43C2311yescharacteristic
195C2×D4×C43C2311yescharacteristic
196C2×D4×C43C2311yescharacteristic
197C2×D4×C43C2311yescharacteristic
198C2×D4×C43C2311yescharacteristic
199C2×D4×C43C2311yescharacteristic
200C2×D4×C43C2311yescharacteristic
201C22×C4×C43C2311yescharacteristic
202C22×C4×C43C2311yescharacteristic
203C22×C4×C43C2311yescharacteristic
204C22×C4×C43C2311yescharacteristic
205C2×C22⋊D43—42no—
206C2×C22⋊D43—42no—
207C2×C22⋊D43C2311yescharacteristic
208C2×C22⋊D43C2311yescharacteristic
209C2×C22⋊D43C2311yescharacteristic
210C2×C22⋊D43C2311yescharacteristic
211C2×C22⋊D43C2311yescharacteristic
212C2×C22⋊D43C2311yescharacteristic
213C2×C22⋊D43C2311yescharacteristic
214C2×C22⋊D43C2311yescharacteristic
215C2×C22⋊D43C2311yescharacteristic
216C2×C22⋊D43C2311yescharacteristic
217C2×C22⋊D43C2311yescharacteristic
218C2×C22⋊D43C2311yescharacteristic
219C2×C22⋊D43C2311yescharacteristic
220C2×C22⋊D43C2311yescharacteristic
221C2×C22⋊D43C2311yescharacteristic
222C2×C22⋊D43C2311yescharacteristic
223C2×C22⋊D43C2311yescharacteristic
224C2×C22⋊D43C2311yescharacteristic
225C2×C22⋊D43C2311yescharacteristic
226C2×C22⋊D43C2311yescharacteristic
227C22×Dic43C2311yescharacteristic
228C22×Dic43C2311yescharacteristic
229C22×Dic43C2311yescharacteristic
230Q8×D43—42no—
231#10621900—42no—
232D4×D43—42no—
233D4×D43—42no—
234D4×D43—42no—
235D4×D43—42no—
236#10621898—42no—
237#10621898—42no—
238#10621898—42no—
239C2×D172—42no—
240C2×D172C2311yescharacteristic
241C2×D172C2311yescharacteristic
242C2×D172C2311yescharacteristic
243C2×D172C2311yescharacteristic
244C2×D172C2311yescharacteristic
245C2×D172C2311yescharacteristic
246C2×D172C2311yescharacteristic
247C2×D172C2311yescharacteristic
248C2×D172C2311yescharacteristic
249C2×D172C2311yescharacteristic
250C2×C4×D43C2311yescharacteristic
251C2×C4×D43C2311yescharacteristic
252C2×C4×D43C2311yescharacteristic
253C2×C4×D43C2311yescharacteristic
254C2×C4×D43C2311yescharacteristic
255C2×C4×D43C2311yescharacteristic
256C2×C4×D43C2311yescharacteristic
257C2×C4×D43C2311yescharacteristic
258C2×C4×D43C2311yescharacteristic
259C2×C4×D43C2311yescharacteristic
260C2×C4×D43C2311yescharacteristic
261C2×C4×D43C2311yescharacteristic
262C2×Dic86C2311yescharacteristic
263C2×Dic86C2311yescharacteristic
264C2×Dic86C2311yescharacteristic
265C2×Dic86C2311yescharacteristic
266C2×Dic86C2311yescharacteristic
267C2×Dic86C2311yescharacteristic
268C4⋊C4×C43C2311yescharacteristic
269C4⋊C4×C43C2311yescharacteristic
270C4⋊C4×C43C2311yescharacteristic
271C4⋊C4×C43C2311yescharacteristic
272C4⋊C4×C43C2311yescharacteristic
273C4⋊C4×C43C2311yescharacteristic
274C22⋊C4×C43C2311yescharacteristic
275C22⋊C4×C43C2311yescharacteristic
276C22⋊C4×C43C2311yescharacteristic
277C22⋊C4×C43C2311yescharacteristic
278C22⋊C4×C43C2311yescharacteristic
279C22⋊C4×C43C2311yescharacteristic
280C22⋊C4×C43C2311yescharacteristic
281C22⋊C4×C43C2311yescharacteristic
282C22⋊C4×C43C2311yescharacteristic
283C22⋊C4×C43C2311yescharacteristic
284C22⋊C4×C43C2311yescharacteristic
285C22⋊C4×C43C2311yescharacteristic
286C22⋊C4×C43C2311yescharacteristic
287C22⋊C4×C43C2311yescharacteristic
288C42×C43C2311yescharacteristic
289C42×C43C2311yescharacteristic
290C22⋊Dic43C2311yescharacteristic
291C22⋊Dic43C2311yescharacteristic
292C22⋊Dic43C2311yescharacteristic
293C22⋊Dic43C2311yescharacteristic
294C22⋊Dic43C2311yescharacteristic
295C22⋊Dic43C2311yescharacteristic
296C22⋊Dic43C2311yescharacteristic
297C22⋊Dic43C2311yescharacteristic
298C22⋊Dic43C2311yescharacteristic
299C22⋊Dic43C2311yescharacteristic
300C22⋊Dic43C2311yescharacteristic
301C22⋊Dic43C2311yescharacteristic
302(C2×D43)⋊C4C2311yescharacteristic
303(C2×D43)⋊C4C2311yescharacteristic
304(C2×D43)⋊C4C2311yescharacteristic
305(C2×D43)⋊C4C2311yescharacteristic
306(C2×D43)⋊C4C2311yescharacteristic
307(C2×D43)⋊C4C2311yescharacteristic
308(C2×D43)⋊C4C2311yescharacteristic
309(C2×D43)⋊C4C2311yescharacteristic
310(C2×D43)⋊C4C2311yescharacteristic
311(C2×D43)⋊C4C2311yescharacteristic
312(C2×D43)⋊C4C2311yescharacteristic
313(C2×D43)⋊C4C2311yescharacteristic
314(C2×D43)⋊C4C2311yescharacteristic
315(C2×D43)⋊C4C2311yescharacteristic
316(C2×D43)⋊C4C2311yescharacteristic
317(C2×D43)⋊C4C2311yescharacteristic
318(C2×D43)⋊C4C2311yescharacteristic
319(C2×D43)⋊C4C2311yescharacteristic
320(C2×D43)⋊C4C2311yescharacteristic
321(C2×D43)⋊C4C2311yescharacteristic
322(C2×D43)⋊C4C2311yescharacteristic
323(C2×D43)⋊C4C2311yescharacteristic
324(C2×D43)⋊C4C2311yescharacteristic
325(C2×D43)⋊C4C2311yescharacteristic
326(C2×D43)⋊C4C2311yescharacteristic
327(C2×D43)⋊C4C2311yescharacteristic
328(C2×D43)⋊C4C2311yescharacteristic
329(C2×D43)⋊C4C2311yescharacteristic
330C4⋊Dic43C2311yescharacteristic
331C4⋊Dic43C2311yescharacteristic
332C4⋊Dic43C2311yescharacteristic
333C4⋊Dic43C2311yescharacteristic
334Dic43⋊C4C2311yescharacteristic
335Dic43⋊C4C2311yescharacteristic
336Dic43⋊C4C2311yescharacteristic
337Dic43⋊C4C2311yescharacteristic
338Dic43⋊C4C2311yescharacteristic
339Dic43⋊C4C2311yescharacteristic
340Dic43⋊C4C2311yescharacteristic
341Dic43⋊C4C2311yescharacteristic
342Dic43⋊C4C2311yescharacteristic
343Dic43⋊C4C2311yescharacteristic
344Dic43⋊C4C2311yescharacteristic
345Dic43⋊C4C2311yescharacteristic
346C4×Dic43C2311yescharacteristic
347C4×Dic43C2311yescharacteristic
348C4×Dic43C2311yescharacteristic
349C4×Dic43C2311yescharacteristic
350C4×Dic43C2311yescharacteristic
351C4×Dic43C2311yescharacteristic
352C4×Dic43C2311yescharacteristic
353C4×Dic43C2311yescharacteristic
354C23×C43—41no—
355C23×C43—41no—
356C23×C43—41no—
357C23×C43C2411yescharacteristic
358C23×C43C2411yescharacteristic
359C23×C43C2411yescharacteristic
360C23×C43C2411yescharacteristic
361C23×C43C2411yescharacteristic
362C22×D43—22no—
363C22×D43—22no—
364C22×D43—41no—
365C22×D43—41no—
366C22×D43—41no—
367C22×D43—41no—
368C22×D43—41no—
369C22×D43—41no—
370C22×D43—41no—
371C22×D43—41no—
372C22×D43—41no—
373C22×D43—41no—
374C22×D43—41no—
375C22×D43—41no—
376C22×D43—41no—
377C22×D43C2411yescharacteristic
378C22×D43C2411yescharacteristic
379C22×D43C2411yescharacteristic
380C22×D43C2411yescharacteristic
381C22×D43C2411yescharacteristic
382C22×D43C2411yescharacteristic
383Q8×C43—41no—
384D4×C43—41no—
385D4×C43—41no—
386D4×C43—41no—
387D4×C43—41no—
388D4×C43—41no—
389D4×C43—41no—
390D4×C43—41no—
391C2×C4×C43—41no—
392C2×C4×C43—41no—
393C2×C4×C43—41no—
394C2×C4×C43—41no—
395C2×C4×C43C2411yescharacteristic
396C2×C4×C43C2411yescharacteristic
397C2×C4×C43C2411yescharacteristic
398C2×C4×C43C2411yescharacteristic
399C2×C4×C43C2411yescharacteristic
400C2×C4×C43C2411yescharacteristic
401C2×C4×C43C2411yescharacteristic
402C2×C4×C43C2411yescharacteristic
403C2×C4×C43C2411yescharacteristic
404C2×C4×C43C2411yescharacteristic
405C22⋊D43—22no—
406C22⋊D43—22no—
407C22⋊D43—22no—
408C22⋊D43—22no—
409C22⋊D43—22no—
410C22⋊D43—22no—
411C22⋊D43—22no—
412C22⋊D43—41no—
413C22⋊D43—41no—
414C22⋊D43—41no—
415C22⋊D43—41no—
416C22⋊D43—41no—
417C22⋊D43—41no—
418C22⋊D43—41no—
419C22⋊D43—41no—
420C22⋊D43—41no—
421C22⋊D43—41no—
422C22⋊D43—41no—
423C22⋊D43—41no—
424C22⋊D43—41no—
425C2×Dic43—22no—
426C2×Dic43—41no—
427C2×Dic43—41no—
428C2×Dic43C2411yescharacteristic
429C2×Dic43C2411yescharacteristic
430C2×Dic43C2411yescharacteristic
431C2×Dic43C2411yescharacteristic
432C2×Dic43C2411yescharacteristic
433C2×Dic43C2411yescharacteristic
434C2×Dic43C2411yescharacteristic
435C2×Dic43C2411yescharacteristic
436C2×Dic43C2411yescharacteristic
437C2×Dic43C2411yescharacteristic
438D172—22no—
439D172—22no—
440D172—22no—
441D172—41no—
442D172—41no—
443D172—41no—
444D172—41no—
445D172—41no—
446D172—41no—
447D172—41no—
448C4×D43—22no—
449C4×D43—22no—
450C4×D43—22no—
451C4×D43—41no—
452C4×D43—41no—
453C4×D43—41no—
454C4×D43—41no—
455C4×D43—41no—
456C4×D43—41no—
457C4×D43—41no—
458C4×D43—41no—
459C4×D43—41no—
460Dic86—22no—
461Dic86—22no—
462Dic86—41no—
463Dic86—41no—
464Dic86—41no—
465Dic86—41no—
466C22×C43—21no—
467C22×C43—21no—
468C22×C43—21no—
469C22×C43—21no—
470C22×C43—21no—
471C22×C43—21no—
472C22×C43—21no—
473C22×C43—21no—
474C22×C43—21no—
475C22×C43—21no—
476C22×C43—21no—
477C22×C43—21no—
478C22×C43—21no—
479C22×C43—21no—
480C22×C43—21no—
481C22×C43—82no—
482C22×C43C2511yescharacteristic
483C2×D43—21no—
484C2×D43—21no—
485C2×D43—21no—
486C2×D43—21no—
487C2×D43—21no—
488C2×D43—21no—
489C2×D43—21no—
490C2×D43—21no—
491C2×D43—21no—
492C2×D43—21no—
493C2×D43—21no—
494C2×D43—21no—
495C2×D43—21no—
496C2×D43—21no—
497C2×D43—21no—
498C2×D43—21no—
499C2×D43—21no—
500C2×D43—82no—
501C2×D43—82no—
502C2×D43—82no—
503C2×D43—82no—
504C2×D43—82no—
505C2×D43H(5,𝔽2)12yes—
506C4×C43—21no—
507C4×C43—21no—
508C4×C43—21no—
509C4×C43—21no—
510C4×C43—21no—
511C4×C43—21no—
512C4×C43—21no—
513C4×C43—21no—
514C4×C43—21no—
515C4×C43—21no—
516Dic43—21no—
517Dic43—21no—
518Dic43—21no—
519Dic43—21no—
520Dic43—21no—
521Dic43—21no—
522Dic43—21no—
523Dic43—21no—
524Dic43—21no—
525Dic43H(5,𝔽2)12yes—
526#3558—431nomaximal, Sylow
527C2×C43—41no—
528C2×C43—41no—
529C2×C43—41no—
530C2×C43—41no—
531C2×C43—41no—
532C2×C43C2×H(5,𝔽2)11yescharacteristic
533C2×C43C2×H(5,𝔽2)11yescharacteristic
534C2×C43#58511yescharacteristic
535D43—22no—
536D43—41no—
537D43—41no—
538D43—41no—
539D43—41no—
540D43—41no—
541#562—431no—
542#562—431no—
543H(3,𝔽4)—431no—
544H(3,𝔽4)—431no—
545#559—431no—
546#559—431no—
547#548—431no—
548#548—431no—
549#546—431no—
550#546—431no—
551#546—431no—
552#546—431no—
553#546—431no—
554#546—431no—
555D42—431no—
556D42—431no—
557#542—431no—
558#542—431no—
559#538—431no—
560#538—431no—
561#538—431no—
562#538—431no—
563#538—431no—
564#538D4311yescharacteristic, complemented
565#535—431no—
566#535—431no—
567#534—431no—
568#534—431no—
569#532—431no—
570#529—431no—
571C2×#124—431no—
572C43#355811yescharacteristic, complemented, Sylow
573C2×#41—431no—
574C2×#41—431no—
575C2×#41—431no—
576C2×#41—431no—
577C22×Q8—431no—
578C22×D4—431no—
579C22×D4—431no—
580C22×D4—431no—
581C22×D4—431no—
582C22×D4—431no—
583C22×D4—431no—
584C22×D4—431no—
585C4⋊Q8—431no—
586#127—431no—
587#127—431no—
588#127—431no—
589#126—431no—
590#126—431no—
591#126—431no—
592#126—431no—
593#126C2×D4311yescharacteristic, complemented
594#126C2×D4311yescharacteristic, complemented
595#125—431no—
596#124—431no—
597#124—431no—
598#124—431no—
599#124—431no—
600#124—431no—
601#124—431no—
602#124—431no—
603#124—431no—
604#124—431no—
605#124—431no—
606#124—431no—
607#124—431no—
608#124—431no—
609#124—431no—
610#124—431no—
611#124—431no—
612#124—431no—
613#124—431no—
614#124—431no—
615#124—431no—
616#124—431no—
617#124—431no—
618#124—431no—
619#124C2×D4311yescharacteristic, complemented
620#124C2×D4311yescharacteristic, complemented
621#123—431no—
622#123—431no—
623#123—431no—
624#123—431no—
625#123—431no—
626#123—431no—
627#123—431no—
628#123—431no—
629#123—431no—
630#123—431no—
631#123—431no—
632#123—431no—
633#123—431no—
634#123—431no—
635#123—431no—
636#123—431no—
637#123C2×D4311yescharacteristic, complemented
638#123C2×D4311yescharacteristic, complemented
639C22⋊Q8—431no—
640C22⋊Q8—431no—
641C22⋊Q8—431no—
642C22⋊Q8—431no—
643C22⋊Q8—431no—
644C22⋊Q8—431no—
645C22⋊Q8—431no—
646C22⋊Q8—431no—
647C22⋊Q8—431no—
648C22⋊Q8—431no—
649C22⋊Q8C2×D4311yescharacteristic, complemented
650#121—431no—
651#121—431no—
652#121—431no—
653#121—431no—
654#121—431no—
655#121—431no—
656#121—431no—
657#121—431no—
658#121—431no—
659#121—431no—
660#121—431no—
661#121—431no—
662#121—431no—
663#121—431no—
664#121—431no—
665#121—431no—
666#121—431no—
667#121—431no—
668#121—431no—
669#121—431no—
670#121—431no—
671#121—431no—
672#121—431no—
673#121—431no—
674#121C2×D4311yescharacteristic, complemented
675#121C2×D4311yescharacteristic, complemented
676#121C2×D4311yescharacteristic, complemented
677#120—431no—
678#120—431no—
679#120—431no—
680#120—431no—
681#120—431no—
682#120—431no—
683#120—431no—
684#120—431no—
685#120—431no—
686#120—431no—
687#120—431no—
688#120—431no—
689#120—431no—
690#120—431no—
691#120—431no—
692#120—431no—
693#120—431no—
694#120—431no—
695#120C2×D4311yescharacteristic, complemented
696#120C2×D4311yescharacteristic, complemented
697C4×Q8—431no—
698C4×Q8—431no—
699C4×Q8—431no—
700C4×D4—431no—
701C4×D4—431no—
702C4×D4—431no—
703C4×D4—431no—
704C4×D4—431no—
705C4×D4—431no—
706C4×D4—431no—
707C4×D4—431no—
708C4×D4—431no—
709C4×D4—431no—
710C4×D4—431no—
711C4×D4—431no—
712C4×D4—431no—
713C4×D4—431no—
714C4×D4—431no—
715C4×D4C2×D4311yescharacteristic, complemented
716C4×D4C2×D4311yescharacteristic, complemented
717#117—431no—
718#117—431no—
719C2×C22⋊C4—431no—
720C2×C22⋊C4—431no—
721C2×C22⋊C4—431no—
722C2×C22⋊C4—431no—
723C2×C22⋊C4—431no—
724C2×C22⋊C4—431no—
725C2×C22⋊C4—431no—
726C2×C22⋊C4C2×D4311yescharacteristic, complemented
727C2×C42—431no—
728C24—431no—
729C24—431no—
730C24—431no—
731C24—431no—
732C24—431no—
733C24C22×D4311yescharacteristic
734#41—1722no—
735#41—1722no—
736#41—1722no—
737#41—1722no—
738C2×Q8—431no—
739C2×Q8—431no—
740C2×Q8—431no—
741C2×Q8—431no—
742C2×Q8—431no—
743C2×Q8—431no—
744C2×Q8—1722no—
745C2×Q8C22×D4311yescharacteristic
746C2×D4—431no—
747C2×D4—431no—
748C2×D4—431no—
749C2×D4—431no—
750C2×D4—431no—
751C2×D4—431no—
752C2×D4—431no—
753C2×D4—431no—
754C2×D4—431no—
755C2×D4—431no—
756C2×D4—431no—
757C2×D4—431no—
758C2×D4—431no—
759C2×D4—431no—
760C2×D4—431no—
761C2×D4—431no—
762C2×D4—431no—
763C2×D4—431no—
764C2×D4—431no—
765C2×D4—431no—
766C2×D4—431no—
767C2×D4—431no—
768C2×D4—431no—
769C2×D4—431no—
770C2×D4—431no—
771C2×D4—431no—
772C2×D4—431no—
773C2×D4—431no—
774C2×D4—431no—
775C2×D4—431no—
776C2×D4—1722no—
777C2×D4—1722no—
778C2×D4—1722no—
779C2×D4—1722no—
780C2×D4—1722no—
781C2×D4—1722no—
782C2×D4—1722no—
783C2×D4C22×D4311yescharacteristic
784C2×D4C22×D4311yescharacteristic
785C2×D4C22×D4311yescharacteristic
786C2×D4C22×D4311yescharacteristic
787C2×D4C22×D4311yescharacteristic
788C2×D4C22×D4311yescharacteristic
789C2×D4C22×D4311yescharacteristic
790C22×C4—431no—
791C22×C4—431no—
792C22×C4—431no—
793C22×C4—431no—
794C22×C4—431no—
795C22×C4—431no—
796C22×C4—431no—
797C22×C4—431no—
798C22×C4—431no—
799C22×C4—431no—
800C22×C4—431no—
801C22×C4—431no—
802C22×C4—431no—
803C22×C4—431no—
804C22×C4—431no—
805C22×C4C22×D4311yescharacteristic
806C22×C4C22×D4311yescharacteristic
807C22×C4C22×D4311yescharacteristic
808C22×C4C22×D4311yescharacteristic
809C4⋊C4—431no—
810C4⋊C4—431no—
811C4⋊C4—431no—
812C4⋊C4—431no—
813C4⋊C4—431no—
814C4⋊C4—431no—
815C4⋊C4—431no—
816C4⋊C4—431no—
817C4⋊C4—431no—
818C4⋊C4—431no—
819C4⋊C4—431no—
820C4⋊C4—431no—
821C4⋊C4—431no—
822C4⋊C4—431no—
823C4⋊C4—431no—
824C4⋊C4—431no—
825C4⋊C4C22×D4311yescharacteristic
826C4⋊C4C22×D4311yescharacteristic
827C4⋊C4C22×D4311yescharacteristic
828C4⋊C4C22×D4311yescharacteristic
829C4⋊C4C22×D4311yescharacteristic
830C4⋊C4C22×D4311yescharacteristic
831C22⋊C4—431no—
832C22⋊C4—431no—
833C22⋊C4—431no—
834C22⋊C4—431no—
835C22⋊C4—431no—
836C22⋊C4—431no—
837C22⋊C4—431no—
838C22⋊C4—431no—
839C22⋊C4—431no—
840C22⋊C4—431no—
841C22⋊C4—431no—
842C22⋊C4—431no—
843C22⋊C4—431no—
844C22⋊C4—431no—
845C22⋊C4—431no—
846C22⋊C4—431no—
847C22⋊C4—431no—
848C22⋊C4—431no—
849C22⋊C4—431no—
850C22⋊C4—431no—
851C22⋊C4—431no—
852C22⋊C4—431no—
853C22⋊C4—431no—
854C22⋊C4—431no—
855C22⋊C4—431no—
856C22⋊C4—431no—
857C22⋊C4—431no—
858C22⋊C4—431no—
859C22⋊C4—431no—
860C22⋊C4—431no—
861C22⋊C4—431no—
862C22⋊C4—431no—
863C22⋊C4—431no—
864C22⋊C4—431no—
865C22⋊C4—431no—
866C22⋊C4—431no—
867C22⋊C4—431no—
868C22⋊C4—431no—
869C22⋊C4—431no—
870C22⋊C4—431no—
871C22⋊C4C22×D4311yescharacteristic
872C22⋊C4C22×D4311yescharacteristic
873C22⋊C4C22×D4311yescharacteristic
874C22⋊C4C22×D4311yescharacteristic
875C22⋊C4C22×D4311yescharacteristic
876C22⋊C4C22×D4311yescharacteristic
877C22⋊C4C22×D4311yescharacteristic
878C22⋊C4C22×D4311yescharacteristic
879C22⋊C4C22×D4311yescharacteristic
880C22⋊C4C22×D4311yescharacteristic
881C22⋊C4C22×D4311yescharacteristic
882C22⋊C4C22×D4311yescharacteristic
883C22⋊C4C22×D4311yescharacteristic
884C22⋊C4C22×D4311yescharacteristic
885C42—431no—
886C42—431no—
887C42—431no—
888C42—431no—
889C42—431no—
890C42—431no—
891C42—431no—
892C42—431no—
893C42C22×D4311yescharacteristic
894C42C22×D4311yescharacteristic
895C23—41no—
896C23—41no—
897C23—41no—
898C23—431no—
899C23—431no—
900C23—431no—
901C23—431no—
902C23—431no—
903C23—431no—
904C23—862no—
905C23—862no—
906C23—1721no—
907C23—1721no—
908C23—1721no—
909C23—1721no—
910C23—1721no—
911C23—1721no—
912C23—1721no—
913C23—1721no—
914C23—1721no—
915C23—1721no—
916C23—1721no—
917C23—1721no—
918C23—1721no—
919C23C23×D4311yescharacteristic
920C23C23×D4311yescharacteristic
921C23C23×D4311yescharacteristic
922C23C23×D4311yescharacteristic
923C23C23×D4311yescharacteristic
924Q8—41no—
925Q8—862no—
926Q8—862no—
927Q8—1721no—
928Q8—1721no—
929Q8—1721no—
930Q8—1721no—
931D4—41no—
932D4—41no—
933D4—41no—
934D4—41no—
935D4—41no—
936D4—41no—
937D4—41no—
938D4—862no—
939D4—862no—
940D4—862no—
941D4—862no—
942D4—862no—
943D4—862no—
944D4—862no—
945D4—862no—
946D4—862no—
947D4—862no—
948D4—1721no—
949D4—1721no—
950D4—1721no—
951D4—1721no—
952D4—1721no—
953D4—1721no—
954D4—1721no—
955D4—1721no—
956D4—1721no—
957D4—1721no—
958D4—1721no—
959D4—1721no—
960D4—1721no—
961D4—1721no—
962D4—1721no—
963D4—1721no—
964D4—1721no—
965D4—1721no—
966D4—1721no—
967D4—1721no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—431no—
973C2×C4—431no—
974C2×C4—431no—
975C2×C4—431no—
976C2×C4—431no—
977C2×C4—431no—
978C2×C4—431no—
979C2×C4—431no—
980C2×C4—431no—
981C2×C4—431no—
982C2×C4—862no—
983C2×C4—862no—
984C2×C4—862no—
985C2×C4—862no—
986C2×C4—1721no—
987C2×C4—1721no—
988C2×C4—1721no—
989C2×C4—1721no—
990C2×C4—1721no—
991C2×C4—1721no—
992C2×C4—1721no—
993C2×C4—1721no—
994C2×C4—1721no—
995C2×C4—1721no—
996C2×C4—1721no—
997C2×C4C23×D4311yescharacteristic
998C2×C4C23×D4311yescharacteristic
999C2×C4C23×D4311yescharacteristic
1000C2×C4C23×D4311yescharacteristic
1001C2×C4C23×D4311yescharacteristic
1002C2×C4C23×D4311yescharacteristic
1003C2×C4C23×D4311yescharacteristic
1004C2×C4C23×D4311yescharacteristic
1005C2×C4C23×D4311yescharacteristic
1006C2×C4C23×D4311yescharacteristic
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—82no—
1023C22—432no—
1024C22—861no—
1025C22—861no—
1026C22—861no—
1027C22—861no—
1028C22—861no—
1029C22—861no—
1030C22—861no—
1031C22—861no—
1032C22—861no—
1033C22—861no—
1034C22—861no—
1035C22—861no—
1036C22—861no—
1037C22—861no—
1038C22—861no—
1039C22—861no—
1040C22—861no—
1041C22—3442no—
1042C22—3442no—
1043C22—3442no—
1044C22—3442no—
1045C22—3442no—
1046C22C24×D4311yescharacteristic
1047C4—21no—
1048C4—21no—
1049C4—21no—
1050C4—21no—
1051C4—21no—
1052C4—21no—
1053C4—21no—
1054C4—21no—
1055C4—21no—
1056C4—21no—
1057C4—432no—
1058C4—861no—
1059C4—861no—
1060C4—861no—
1061C4—861no—
1062C4—861no—
1063C4—861no—
1064C4—861no—
1065C4—861no—
1066C4—861no—
1067C2—41no—
1068C2—41no—
1069C2—41no—
1070C2—41no—
1071C2—41no—
1072C2—862no—
1073C2—1721no—
1074C2—1721no—
1075C2—1721no—
1076C2—1721no—
1077C2—1721no—
1078C2H(5,𝔽2)×D4311yescharacteristic
1079C2H(5,𝔽2)×D4311yescharacteristic
1080C2#1458373511yescharacteristic
subgroupG/H
center, FrattiniC22C24×D43
commutator, socleC22×C43C25
FittingC43×#538C2
hypercenter#538D43
hypocenterC43#3558
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ #538

Complements

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

NH ≅ G/Ntype
1. #14583645C2semidirect
2. #14583644C2semidirect
3. #14583642C2semidirect
4. #14583641C2semidirect
5. #14583633C2semidirect
6. #14583632C2semidirect
7. #14583559C2semidirect
8. #14583557C2semidirect
9. #14583546C2semidirect
10. #14583545C2semidirect
11. #14583541C2semidirect
12. #14583539C2semidirect
13. #14583539C2semidirect
14. #14583538C2semidirect
15. #14583533C2semidirect
16. #14583531C2semidirect
17. #14583517C2semidirect
18. #14583515C2semidirect
19. #14583488C2semidirect
20. #14583488C2semidirect
21. #14583483C2semidirect
22. #14583482C2semidirect
23. #14583481C2semidirect
24. #14583465C2semidirect
25. #14583464C2semidirect
26. #14583460C2semidirect
27. #14583459C2semidirect
28. #14583446C2semidirect
29. #14583432C2semidirect
30. #124×D43C2semidirect
31. C43×#538C2semidirect
32. C2×#10621898C22semidirect
33. C2×#10621898C22semidirect
34. C2×#10621898C22semidirect
35. C2×#10621900C22semidirect
36. C2×Q8×D43C22semidirect
37. C22×D172C22semidirect
38. C22×C22⋊D43C22semidirect
39. C22×C22⋊D43C22semidirect
41. C2×D4×D43C22semidirect
42. C2×D4×D43C22semidirect
43. C2×D4×D43C22semidirect
44. #13063324C22semidirect
47. #13063321C22semidirect
48. #13063320C22semidirect
49. #13063320C22semidirect
50. #13063319C22semidirect
51. #13063318C22semidirect
52. #13063315C22semidirect
53. #13063314C22semidirect
54. #13063314C22semidirect
55. #13063313C22semidirect
56. #13063313C22semidirect
57. #13063313C22semidirect
58. #13063312C22semidirect
59. #13063312C22semidirect
60. #13063312C22semidirect
61. #13063311C22semidirect
62. #13063311C22semidirect
63. #13063311C22semidirect
64. #13063311C22semidirect
65. #13063311C22semidirect
66. #13063311C22semidirect
67. #13063311C22semidirect
68. #13063311C22semidirect
69. #13063311C22semidirect
70. #13063311C22semidirect
71. #13063311C22semidirect
72. #13063311C22semidirect
73. #13063311C22semidirect
74. #13063311C22semidirect
75. #13063311C22semidirect
76. #13063310C22semidirect
77. #13063310C22semidirect
78. #13063310C22semidirect
79. #13063310C22semidirect
80. #13063310C22semidirect
81. #13063309C22semidirect
82. #13063308C22semidirect
83. #13063308C22semidirect
84. #13063308C22semidirect
85. #13063307C22semidirect
86. #13063307C22semidirect
87. #13063307C22semidirect
88. #13063307C22semidirect
89. #13063307C22semidirect
90. #13063306C22semidirect
91. #13063306C22semidirect
92. #13063305C22semidirect
93. #13063304C22semidirect
94. #13063303C22semidirect
95. #13063303C22semidirect
96. #13063303C22semidirect
97. #13063303C22semidirect
98. #13063302C22semidirect
99. #13063302C22semidirect
100. #13063302C22semidirect
101. #13063301C22semidirect
102. #13063300C22semidirect
103. #13063300C22semidirect
104. #13063300C22semidirect
105. #13063300C22semidirect
106. #13063299C22semidirect
107. #13063299C22semidirect
110. #13063298C22semidirect
111. #13063298C22semidirect
112. #13063298C22semidirect
113. #13063298C22semidirect
114. #13063298C22semidirect
115. #13063298C22semidirect
116. #13063298C22semidirect
117. #13063298C22semidirect
118. #13063298C22semidirect
120. #13063297C22semidirect
121. #13063297C22semidirect
122. #13063297C22semidirect
123. #13063296C22semidirect
124. #13063296C22semidirect
125. #13063296C22semidirect
126. #13063295C22semidirect
127. #13063295C22semidirect
128. #13063295C22semidirect
129. #13063295C22semidirect
130. #13063295C22semidirect
131. #13063295C22semidirect
132. #13063295C22semidirect
133. #13063295C22semidirect
134. #13063294C22semidirect
135. #13063294C22semidirect
136. #13063293C22semidirect
137. #13063293C22semidirect
138. #13063293C22semidirect
139. #13063293C22semidirect
140. #13063293C22semidirect
141. #13063293C22semidirect
142. #13063293C22semidirect
143. #13063293C22semidirect
144. C4×Dic86C22semidirect
145. #13063290C22semidirect
146. #13063290C22semidirect
147. C4×D172C22semidirect
148. C4×D172C22semidirect
149. #13063287C22semidirect
150. #13063287C22semidirect
151. #13063287C22semidirect
152. C4×C22⋊D43C22semidirect
153. C4×C22⋊D43C22semidirect
154. C4×C22⋊D43C22semidirect
155. C4×C22⋊D43C22semidirect
156. C4×C22⋊D43C22semidirect
157. (C22⋊D43)⋊C4C22semidirect
158. (C22⋊D43)⋊C4C22semidirect
159. (C22⋊D43)⋊C4C22semidirect
160. (C22⋊D43)⋊C4C22semidirect
161. (C22⋊D43)⋊C4C22semidirect
162. #13063283C22semidirect
163. #13063281C22semidirect
164. C2×(C2×D43)⋊C4C22semidirect
165. C22⋊C4×D43C22semidirect
166. C22⋊C4×D43C22semidirect
167. C22⋊C4×D43C22semidirect
168. C22⋊C4×D43C22semidirect
169. C22⋊C4×D43C22semidirect
170. C22⋊C4×D43C22semidirect
171. C42×D43C22semidirect
172. #126×C43C22semidirect
173. #126×C43C22semidirect
174. #124×C43C22semidirect
175. #124×C43C22semidirect
176. #123×C43C22semidirect
177. #123×C43C22semidirect
178. C22⋊Q8×C43C22semidirect
179. #121×C43C22semidirect
180. #121×C43C22semidirect
181. #121×C43C22semidirect
182. #120×C43C22semidirect
183. #120×C43C22semidirect
184. C4×D4×C43C22semidirect
185. C4×D4×C43C22semidirect
186. C2×C22⋊C4×C43C22semidirect
564. #538D43semidirect
572. C43#3558semidirect
593. #126C2×D43semidirect
594. #126C2×D43semidirect
619. #124C2×D43semidirect
620. #124C2×D43semidirect
637. #123C2×D43semidirect
638. #123C2×D43semidirect
649. C22⋊Q8C2×D43semidirect
674. #121C2×D43semidirect
675. #121C2×D43semidirect
676. #121C2×D43semidirect
695. #120C2×D43semidirect
696. #120C2×D43semidirect
715. C4×D4C2×D43semidirect
716. C4×D4C2×D43semidirect
726. C2×C22⋊C4C2×D43semidirect