Finite Group Databasebeta

← #21459374

Subgroups — #21459374

Order 7808.

1132 conjugacy classes of subgroups.

The subgroup lattice has 982 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840479C211yesmaximal, characteristic, complemented
2#16840474C211yesmaximal, characteristic, complemented
3#16840466C211yesmaximal, characteristic, complemented
4#16840461C211yesmaximal, characteristic, complemented
5#16840457C211yesmaximal, characteristic, complemented
6#16840449C211yesmaximal, characteristic, complemented
7#16840448C211yesmaximal, characteristic, complemented
8#16840445C211yesmaximal, characteristic, complemented
9#16840445C211yesmaximal, characteristic, complemented
10#16840441C211yesmaximal, characteristic, complemented
11#16840439C211yesmaximal, characteristic, complemented
12#16840438C211yesmaximal, characteristic, complemented
13#16840410C211yesmaximal, characteristic, complemented
14#16840402C211yesmaximal, characteristic, complemented
15#16840399C211yesmaximal, characteristic, complemented
16#16840314C211yesmaximal, characteristic, complemented
17#16840298C211yesmaximal, characteristic, complemented
18#16840295C211yesmaximal, characteristic, complemented
19#16840295C211yesmaximal, characteristic, complemented
20#16840291C211yesmaximal, characteristic, complemented
21#16840289C211yesmaximal, characteristic, complemented
22#16840289C211yesmaximal, characteristic, complemented
23#16840270C211yesmaximal, characteristic, complemented
24#16840268C211yesmaximal, characteristic, complemented
25#16840230C211yesmaximal, characteristic, complemented
26C4×#11758224C211yesmaximal, characteristic, complemented
27C4×#11758224C211yesmaximal, characteristic, complemented
28C2×#14519737C211yesmaximal, characteristic, complemented
29C2×#14519733C211yesmaximal, characteristic, complemented
30#117×D61C211yesmaximal, characteristic, complemented
31C61×#551C211yesmaximal, characteristic, complemented
32C2×#11758222C2211yescharacteristic
33C2×#11758224C2211yescharacteristic
34C2×#11758224C2211yescharacteristic
35C22×C22⋊D61C2211yescharacteristic
36C23×Dic61C2211yescharacteristic
37C22×C4×D61C2211yescharacteristic
38#14519776C2211yescharacteristic, complemented
39#14519775C2211yescharacteristic, complemented
40#14519772C2211yescharacteristic, complemented
41#14519772C2211yescharacteristic, complemented
42#14519772C2211yescharacteristic, complemented
43#14519772C2211yescharacteristic, complemented
44#14519771C2211yescharacteristic, complemented
45#14519771C2211yescharacteristic, complemented
46#14519770C2211yescharacteristic, complemented
47#14519770C2211yescharacteristic, complemented
48#14519770C2211yescharacteristic, complemented
49#14519770C2211yescharacteristic, complemented
50#14519769C2211yescharacteristic, complemented
51#14519768C2211yescharacteristic, complemented
52#14519767C2211yescharacteristic, complemented
53#14519767C2211yescharacteristic, complemented
54#14519767C2211yescharacteristic, complemented
55#14519767C2211yescharacteristic, complemented
56#14519767C2211yescharacteristic, complemented
57#14519767C2211yescharacteristic, complemented
58#14519766C2211yescharacteristic, complemented
59#14519763C2211yescharacteristic
60#14519763C2211yescharacteristic
61#14519763C2211yescharacteristic, complemented
62#14519763C2211yescharacteristic, complemented
63#14519762C2211yescharacteristic, complemented
64#14519762C2211yescharacteristic, complemented
65#14519761C2211yescharacteristic
66#14519761C2211yescharacteristic
67#14519761C2211yescharacteristic, complemented
68#14519760C2211yescharacteristic
69#14519760C2211yescharacteristic
70#14519760C2211yescharacteristic, complemented
71#14519759C2211yescharacteristic
72#14519759C2211yescharacteristic
73#14519759C2211yescharacteristic, complemented
74#14519759C2211yescharacteristic, complemented
75#14519758C2211yescharacteristic
76#14519756C2211yescharacteristic
77#14519755C2211yescharacteristic, complemented
78#14519755C2211yescharacteristic, complemented
79#14519755C2211yescharacteristic, complemented
80#14519755C2211yescharacteristic, complemented
81#14519754C2211yescharacteristic
82#14519754C2211yescharacteristic
83#14519754C2211yescharacteristic, complemented
84#14519754C2211yescharacteristic, complemented
85#14519754C2211yescharacteristic, complemented
86#14519754C2211yescharacteristic, complemented
87#14519753C2211yescharacteristic, complemented
88#14519751C2211yescharacteristic
89#14519750C2211yescharacteristic
90#14519750C2211yescharacteristic
91#14519750C2211yescharacteristic, complemented
92#14519750C2211yescharacteristic, complemented
93#14519749C2211yescharacteristic
94#14519749C2211yescharacteristic
95#14519749C2211yescharacteristic, complemented
96#14519749C2211yescharacteristic, complemented
97#14519748C2211yescharacteristic
98#14519747C2211yescharacteristic
99#14519746C2211yescharacteristic
100#14519745C2211yescharacteristic
101Q8×Dic61C2211yescharacteristic, complemented
102C4×Dic122C2211yescharacteristic, complemented
103C4×Dic122C2211yescharacteristic, complemented
104#14519742C2211yescharacteristic, complemented
105#14519742C2211yescharacteristic, complemented
106#14519742C2211yescharacteristic, complemented
107#14519742C2211yescharacteristic, complemented
108#14519742C2211yescharacteristic, complemented
109D4×Dic61C2211yescharacteristic
110D4×Dic61C2211yescharacteristic, complemented
111D4×Dic61C2211yescharacteristic, complemented
112#14519739C2211yescharacteristic, complemented
113#14519739C2211yescharacteristic, complemented
114#14519739C2211yescharacteristic, complemented
115C4×C22⋊D61C2211yescharacteristic
116C4×C22⋊D61C2211yescharacteristic
117C4×C22⋊D61C2211yescharacteristic, complemented
118C4×C22⋊D61C2211yescharacteristic, complemented
119#14519737C2211yescharacteristic
120#14519737C2211yescharacteristic
121#14519737C2211yescharacteristic
122#14519737C2211yescharacteristic
123#14519737C2211yescharacteristic
124#14519737C2211yescharacteristic
125#14519737C2211yescharacteristic
126#14519737C2211yescharacteristic
127#14519737C2211yescharacteristic
128#14519737C2211yescharacteristic
129#14519737C2211yescharacteristic, complemented
130#14519737C2211yescharacteristic, complemented
131#14519737C2211yescharacteristic, complemented
132#14519737C2211yescharacteristic, complemented
133#14519737C2211yescharacteristic, complemented
134#14519737C2211yescharacteristic, complemented
135#14519736C2211yescharacteristic
136#14519735C2211yescharacteristic, complemented
137#14519735C2211yescharacteristic, complemented
138#14519735C2211yescharacteristic, complemented
139#14519735C2211yescharacteristic, complemented
140#14519734C2211yescharacteristic, complemented
141#14519734C2211yescharacteristic, complemented
142#14519734C2211yescharacteristic, complemented
143#14519734C2211yescharacteristic, complemented
144#14519733C2211yescharacteristic
145#14519733C2211yescharacteristic
146#14519733C2211yescharacteristic
147#14519733C2211yescharacteristic
148#14519733C2211yescharacteristic
149#14519733C2211yescharacteristic, complemented
150#14519733C2211yescharacteristic, complemented
151#14519733C2211yescharacteristic, complemented
152#14519733C2211yescharacteristic, complemented
153#14519733C2211yescharacteristic, complemented
154#14519733C2211yescharacteristic, complemented
155#14519733C2211yescharacteristic, complemented
156C2×#11758196C2211yescharacteristic
157C2×#11758196C2211yescharacteristic, complemented
158C2×#11758196C2211yescharacteristic, complemented
159C4⋊C4×D61C2211yescharacteristic, complemented
160C4⋊C4×D61C2211yescharacteristic, complemented
161C2×C22⋊Dic61C2211yescharacteristic
162C2×#11758198C2211yescharacteristic
163C22⋊C4×D61C2211yescharacteristic
164C22⋊C4×D61C2211yescharacteristic
165C2×C4×Dic61C2211yescharacteristic
166C2×C4×Dic61C2211yescharacteristic, complemented
167C2×C4×Dic61C2211yescharacteristic, complemented
168C2×C4×Dic61C2211yescharacteristic, complemented
169C42×D61C2211yescharacteristic, complemented
170C42×D61C2211yescharacteristic, complemented
171C42×D61C2211yescharacteristic, complemented
172#126×C61C2211yescharacteristic, complemented
173#126×C61C2211yescharacteristic, complemented
174#124×C61C2211yescharacteristic, complemented
175#123×C61C2211yescharacteristic
176#123×C61C2211yescharacteristic, complemented
177#123×C61C2211yescharacteristic, complemented
178C22⋊Q8×C61C2211yescharacteristic
179C22⋊Q8×C61C2211yescharacteristic, complemented
180#120×C61C2211yescharacteristic
181C4×D4×C61C2211yescharacteristic
182C4×D4×C61C2211yescharacteristic, complemented
183#117×C61C2211yescharacteristic
184#117×C61C2211yescharacteristic, complemented
185C2×C22⋊C4×C61C2211yescharacteristic
186C2×C22⋊C4×C61C2211yescharacteristic
187C24×C61C2311yescharacteristic
188C23×D61C2311yescharacteristic
189C2×Q8×C61C2311yescharacteristic
190C2×D4×C61C2311yescharacteristic
191C2×D4×C61C2311yescharacteristic
192C2×D4×C61C2311yescharacteristic
193C22×C4×C61C2311yescharacteristic
194C22×C4×C61C2311yescharacteristic
195C22×C4×C61C2311yescharacteristic
196C22×C4×C61C2311yescharacteristic
197C22×C4×C61C2311yescharacteristic
198C2×C22⋊D61—24no—
199C2×C22⋊D61C2311yescharacteristic
200C2×C22⋊D61C2311yescharacteristic
201C2×C22⋊D61C2311yescharacteristic
202C2×C22⋊D61C2311yescharacteristic
203C2×C22⋊D61C2311yescharacteristic
204C2×C22⋊D61C2311yescharacteristic
205C2×C22⋊D61C2311yescharacteristic
206C2×C22⋊D61C2311yescharacteristic
207C2×C22⋊D61C2311yescharacteristic
208C2×C22⋊D61C2311yescharacteristic
209C22×Dic61—24no—
210C22×Dic61C2311yescharacteristic
211C22×Dic61C2311yescharacteristic
212C22×Dic61C2311yescharacteristic
213C22×Dic61C2311yescharacteristic
214C22×Dic61C2311yescharacteristic
215C22×Dic61C2311yescharacteristic
216C22×Dic61C2311yescharacteristic
217C22×Dic61C2311yescharacteristic
218C22×Dic61C2311yescharacteristic
219C22×Dic61C2311yescharacteristic
220C22×Dic61C2311yescharacteristic
221#11758224—24no—
222#11758224—24no—
223#11758222—24no—
224C2×D244C2311yescharacteristic
225C2×D244C2311yescharacteristic
226C2×C4×D61—24no—
227C2×C4×D61C2311yescharacteristic
228C2×C4×D61C2311yescharacteristic
229C2×C4×D61C2311yescharacteristic
230C2×C4×D61C2311yescharacteristic
231C2×C4×D61C2311yescharacteristic
232C2×C4×D61C2311yescharacteristic
233C2×C4×D61C2311yescharacteristic
234C2×C4×D61C2311yescharacteristic
235C2×C4×D61C2311yescharacteristic
236C2×C4×D61C2311yescharacteristic
237C2×C4×D61C2311yescharacteristic
238C2×Dic122C2311yescharacteristic
239C2×Dic122C2311yescharacteristic
240C2×Dic122C2311yescharacteristic
241C2×Dic122C2311yescharacteristic
242C4⋊C4×C61C2311yescharacteristic
243C4⋊C4×C61C2311yescharacteristic
244C4⋊C4×C61C2311yescharacteristic
245C4⋊C4×C61C2311yescharacteristic
246C4⋊C4×C61C2311yescharacteristic
247C4⋊C4×C61C2311yescharacteristic
248C4⋊C4×C61C2311yescharacteristic
249C4⋊C4×C61C2311yescharacteristic
250C22⋊C4×C61C2311yescharacteristic
251C22⋊C4×C61C2311yescharacteristic
252C22⋊C4×C61C2311yescharacteristic
253C22⋊C4×C61C2311yescharacteristic
254C22⋊C4×C61C2311yescharacteristic
255C22⋊C4×C61C2311yescharacteristic
256C22⋊C4×C61C2311yescharacteristic
257C22⋊C4×C61C2311yescharacteristic
258C22⋊C4×C61C2311yescharacteristic
259C22⋊C4×C61C2311yescharacteristic
260C22⋊C4×C61C2311yescharacteristic
261C22⋊C4×C61C2311yescharacteristic
262C22⋊C4×C61C2311yescharacteristic
263C22⋊C4×C61C2311yescharacteristic
264C42×C61C2311yescharacteristic
265C42×C61C2311yescharacteristic
266C42×C61C2311yescharacteristic
267C22⋊Dic61C2311yescharacteristic
268C22⋊Dic61C2311yescharacteristic
269C22⋊Dic61C2311yescharacteristic
270C22⋊Dic61C2311yescharacteristic
271C22⋊Dic61C2311yescharacteristic
272C22⋊Dic61C2311yescharacteristic
273C22⋊Dic61C2311yescharacteristic
274C22⋊Dic61C2311yescharacteristic
275C22⋊Dic61C2311yescharacteristic
276C22⋊Dic61C2311yescharacteristic
277#11758198C2311yescharacteristic
278#11758198C2311yescharacteristic
279#11758198C2311yescharacteristic
280#11758198C2311yescharacteristic
281#11758198C2311yescharacteristic
282#11758198C2311yescharacteristic
283#11758198C2311yescharacteristic
284#11758198C2311yescharacteristic
285#11758198C2311yescharacteristic
286#11758198C2311yescharacteristic
287#11758198C2311yescharacteristic
288#11758198C2311yescharacteristic
289#11758198C2311yescharacteristic
290#11758198C2311yescharacteristic
291#11758198C2311yescharacteristic
292#11758198C2311yescharacteristic
293#11758198C2311yescharacteristic
294#11758198C2311yescharacteristic
295C4⋊Dic61C2311yescharacteristic
296C4⋊Dic61C2311yescharacteristic
297C4⋊Dic61C2311yescharacteristic
298C4⋊Dic61C2311yescharacteristic
299C4⋊Dic61C2311yescharacteristic
300C4⋊Dic61C2311yescharacteristic
301C4⋊Dic61C2311yescharacteristic
302C4⋊Dic61C2311yescharacteristic
303#11758196C2311yescharacteristic
304#11758196C2311yescharacteristic
305#11758196C2311yescharacteristic
306#11758196C2311yescharacteristic
307#11758196C2311yescharacteristic
308#11758196C2311yescharacteristic
309#11758196C2311yescharacteristic
310#11758196C2311yescharacteristic
311#11758196C2311yescharacteristic
312#11758196C2311yescharacteristic
313#11758196C2311yescharacteristic
314#11758196C2311yescharacteristic
315#11758196C2311yescharacteristic
316#11758196C2311yescharacteristic
317#11758196C2311yescharacteristic
318#11758196C2311yescharacteristic
319#11758196C2311yescharacteristic
320#11758196C2311yescharacteristic
321#11758196C2311yescharacteristic
322#11758196C2311yescharacteristic
323#11758196C2311yescharacteristic
324#11758196C2311yescharacteristic
325#11758196C2311yescharacteristic
326#11758196C2311yescharacteristic
327#11758196C2311yescharacteristic
328#11758196C2311yescharacteristic
329C4×Dic61C2311yescharacteristic
330C4×Dic61C2311yescharacteristic
331C4×Dic61C2311yescharacteristic
332C4×Dic61C2311yescharacteristic
333C4×Dic61C2311yescharacteristic
334C4×Dic61C2311yescharacteristic
335C4×Dic61C2311yescharacteristic
336C4×Dic61C2311yescharacteristic
337C4×Dic61C2311yescharacteristic
338C4×Dic61C2311yescharacteristic
339C4×Dic61C2311yescharacteristic
340C4×Dic61C2311yescharacteristic
341C4×Dic61C2311yescharacteristic
342C4×Dic61C2311yescharacteristic
343C4×Dic61C2311yescharacteristic
344C4×Dic61C2311yescharacteristic
345C4×Dic61C2311yescharacteristic
346C4×Dic61C2311yescharacteristic
347C4×Dic61C2311yescharacteristic
348C23×C61—22no—
349C23×C61—22no—
350C23×C61—41no—
351C23×C61C2411yescharacteristic
352C23×C61C2411yescharacteristic
353C23×C61C2411yescharacteristic
354C23×C61C2411yescharacteristic
355C22×D61—22no—
356C22×D61—22no—
357C22×D61—41no—
358C22×D61C2411yescharacteristic
359C22×D61C2411yescharacteristic
360C22×D61C2411yescharacteristic
361Q8×C61—41no—
362D4×C61—22no—
363D4×C61—22no—
364D4×C61—41no—
365C2×C4×C61—22no—
366C2×C4×C61—22no—
367C2×C4×C61—41no—
368C2×C4×C61—41no—
369C2×C4×C61—41no—
370C2×C4×C61C2411yescharacteristic
371C2×C4×C61C2411yescharacteristic
372C2×C4×C61C2411yescharacteristic
373C2×C4×C61C2411yescharacteristic
374C2×C4×C61C2411yescharacteristic
375C2×C4×C61C2411yescharacteristic
376C2×C4×C61C2411yescharacteristic
377C2×C4×C61C2411yescharacteristic
378C2×C4×C61C2411yescharacteristic
379C2×C4×C61C2411yescharacteristic
380C2×C4×C61C2411yescharacteristic
381C22⋊D61—22no—
382C22⋊D61—22no—
383C22⋊D61—22no—
384C22⋊D61—22no—
385C22⋊D61—22no—
386C22⋊D61—22no—
387C22⋊D61—22no—
388C22⋊D61—41no—
389C22⋊D61—41no—
390C22⋊D61#4114yescomplemented
391C2×Dic61—22no—
392C2×Dic61—22no—
393C2×Dic61—22no—
394C2×Dic61—22no—
395C2×Dic61—22no—
396C2×Dic61—22no—
397C2×Dic61—22no—
398C2×Dic61—22no—
399C2×Dic61—22no—
400C2×Dic61—41no—
401C2×Dic61#4114yescomplemented
402C2×Dic61C2411yescharacteristic
403C2×Dic61C2411yescharacteristic
404C2×Dic61C2411yescharacteristic
405C2×Dic61C2411yescharacteristic
406C2×Dic61C2411yescharacteristic
407C2×Dic61C2411yescharacteristic
408C2×Dic61C2411yescharacteristic
409C2×Dic61C2411yescharacteristic
410C2×Dic61C2411yescharacteristic
411C2×Dic61C2411yescharacteristic
412C2×Dic61C2411yescharacteristic
413C2×Dic61C2411yescharacteristic
414C2×Dic61C2411yescharacteristic
415D244—22no—
416D244—41no—
417C4×D61—22no—
418C4×D61—22no—
419C4×D61—22no—
420C4×D61—22no—
421C4×D61—22no—
422C4×D61—22no—
423C4×D61—22no—
424C4×D61—22no—
425C4×D61—41no—
426C4×D61—41no—
427C4×D61—41no—
428Dic122—22no—
429Dic122—22no—
430Dic122—22no—
431Dic122—41no—
432C22×C61—21no—
433C22×C61—21no—
434C22×C61—21no—
435C22×C61—21no—
436C22×C61—21no—
437C22×C61—21no—
438C22×C61—21no—
439C22×C61—21no—
440C22×C61—21no—
441C22×C61—21no—
442C22×C61—44no—
443C22×C61C2×#4112yes—
444C22×C61C2×#4112yes—
445C22×C61C2511yescharacteristic
446C2×D61—21no—
447C2×D61—21no—
448C2×D61—21no—
449C2×D61—21no—
450C2×D61—21no—
451C2×D61—21no—
452C2×D61—21no—
453C2×D61—21no—
454C2×D61—44no—
455C2×D61C2×#4112yes—
456C4×C61—21no—
457C4×C61—21no—
458C4×C61—21no—
459C4×C61—21no—
460C4×C61—21no—
461C4×C61—21no—
462C4×C61—21no—
463C4×C61—21no—
464C4×C61—21no—
465C4×C61—21no—
466C4×C61—21no—
467Dic61—21no—
468Dic61—21no—
469Dic61—21no—
470Dic61—21no—
471Dic61—21no—
472Dic61—21no—
473Dic61—21no—
474Dic61—21no—
475Dic61—21no—
476Dic61—21no—
477Dic61C2×#4112yes—
478Dic61C2×#4112yes—
479Dic61C2×#4112yes—
480#3475—611nomaximal, Sylow
481C2×C61—22no—
482C2×C61—22no—
483C2×C61—41no—
484C2×C61—41no—
485C2×C61C22×#4111yescharacteristic
486C2×C61C22×#4111yescharacteristic
487C2×C61#58511yescharacteristic
488D61—22no—
489D61—41no—
490D61—41no—
491#556—611no—
492#555—611no—
493#554—611no—
494#553—611no—
495#553—611no—
496#552—611no—
497#552—611no—
498#552—611no—
499#552—611no—
500#551—611no—
501#551—611no—
502#551—611no—
503#551D6111yescharacteristic, complemented
504#547—611no—
505#546—611no—
506#546—611no—
507#533—611no—
508#529—611no—
509#529—611no—
510#529—611no—
511#529—611no—
512#529—611no—
513#529—611no—
514#525—611no—
515#525—611no—
516C4×#41—611no—
517C4×#41—611no—
518C4×#41—611no—
519C2×C4×D4—611no—
520C2×#117—611no—
521C2×#117—611no—
522C61#347511yescharacteristic, complemented, Sylow
523C2×#41—611no—
524C2×#41—611no—
525C2×#41—611no—
526C22×D4—611no—
527C23×C4—611no—
528C23×C4—611no—
529C4⋊Q8—611no—
530C4⋊Q8—611no—
531#126—611no—
532#126—611no—
533#126—611no—
534#126—611no—
535#126—611no—
536#126—611no—
537#126—611no—
538#126—611no—
539#126—611no—
540#126—611no—
541#126C2×D6111yescharacteristic, complemented
542#126C2×D6111yescharacteristic, complemented
543#125—611no—
544#125—611no—
545#125—611no—
546#125—611no—
547#125—611no—
548#125—611no—
549#125—611no—
550#125—611no—
551#124—611no—
552#124—611no—
553#124—611no—
554#124—611no—
555#124—611no—
556#124C2×D6111yescharacteristic, complemented
557#123—611no—
558#123—611no—
559#123—611no—
560#123—611no—
561#123—611no—
562#123—611no—
563#123—611no—
564#123—611no—
565#123—611no—
566#123—611no—
567#123—611no—
568#123—611no—
569#123—611no—
570#123C2×D6111yescharacteristic
571#123C2×D6111yescharacteristic, complemented
572#123C2×D6111yescharacteristic, complemented
573C22⋊Q8—611no—
574C22⋊Q8—611no—
575C22⋊Q8—611no—
576C22⋊Q8—611no—
577C22⋊Q8—611no—
578C22⋊Q8—611no—
579C22⋊Q8—611no—
580C22⋊Q8—611no—
581C22⋊Q8—611no—
582C22⋊Q8—611no—
583C22⋊Q8—611no—
584C22⋊Q8—611no—
585C22⋊Q8C2×D6111yescharacteristic
586C22⋊Q8C2×D6111yescharacteristic, complemented
587#121—611no—
588#121—611no—
589#121—611no—
590#121—611no—
591#121—611no—
592#121—611no—
593#121—611no—
594#121—611no—
595#121—611no—
596#121—611no—
597#120—611no—
598#120—611no—
599#120—611no—
600#120C2×D6111yescharacteristic
601C4×Q8—611no—
602C4×Q8—611no—
603C4×Q8—611no—
604C4×Q8—611no—
605C4×Q8—611no—
606C4×Q8—611no—
607C4×Q8—611no—
608C4×Q8—611no—
609C4×D4—611no—
610C4×D4—611no—
611C4×D4—611no—
612C4×D4—611no—
613C4×D4—611no—
614C4×D4—611no—
615C4×D4—611no—
616C4×D4—611no—
617C4×D4—611no—
618C4×D4—611no—
619C4×D4—611no—
620C4×D4—611no—
621C4×D4—611no—
622C4×D4—611no—
623C4×D4—611no—
624C4×D4—611no—
625C4×D4—611no—
626C4×D4—611no—
627C4×D4—611no—
628C4×D4—611no—
629C4×D4—611no—
630C4×D4—611no—
631C4×D4—611no—
632C4×D4—611no—
633C4×D4—611no—
634C4×D4—611no—
635C4×D4C2×D6111yescharacteristic
636C4×D4C2×D6111yescharacteristic, complemented
637#117—611no—
638#117—611no—
639#117—611no—
640#117—611no—
641#117—611no—
642#117—611no—
643#117—611no—
644#117—611no—
645#117—611no—
646#117—611no—
647#117—611no—
648#117—611no—
649#117—611no—
650#117—611no—
651#117—611no—
652#117—611no—
653#117—611no—
654#117—611no—
655#117—611no—
656#117—611no—
657#117—611no—
658#117C2×D6111yescharacteristic
659#117C2×D6111yescharacteristic, complemented
660C2×C4⋊C4—611no—
661C2×C4⋊C4—611no—
662C2×C4⋊C4—611no—
663C2×C4⋊C4—611no—
664C2×C4⋊C4—611no—
665C2×C22⋊C4—611no—
666C2×C22⋊C4—611no—
667C2×C22⋊C4—611no—
668C2×C22⋊C4—611no—
669C2×C22⋊C4C2×D6111yescharacteristic
670C2×C22⋊C4C2×D6111yescharacteristic
671C2×C42—611no—
672C2×C42—611no—
673C2×C42—611no—
674C2×C42—611no—
675C2×C42—611no—
676C2×C42—611no—
677C2×C42—611no—
678C24—611no—
679C24C22×D6111yescharacteristic
680#41—1224no—
681#41—1224no—
682#41—1224no—
683C2×Q8—611no—
684C2×Q8—611no—
685C2×Q8—611no—
686C2×Q8—611no—
687C2×Q8C22×D6111yescharacteristic
688C2×D4—611no—
689C2×D4—611no—
690C2×D4—611no—
691C2×D4—611no—
692C2×D4—611no—
693C2×D4—611no—
694C2×D4—611no—
695C2×D4—611no—
696C2×D4—611no—
697C2×D4—611no—
698C2×D4—611no—
699C2×D4—611no—
700C2×D4—1224no—
701C2×D4C22×D6111yescharacteristic
702C2×D4C22×D6111yescharacteristic
703C2×D4C22×D6111yescharacteristic
704C22×C4—611no—
705C22×C4—611no—
706C22×C4—611no—
707C22×C4—611no—
708C22×C4—611no—
709C22×C4—611no—
710C22×C4—611no—
711C22×C4—611no—
712C22×C4—611no—
713C22×C4—611no—
714C22×C4—611no—
715C22×C4—611no—
716C22×C4—611no—
717C22×C4—611no—
718C22×C4—611no—
719C22×C4—611no—
720C22×C4—611no—
721C22×C4—611no—
722C22×C4—611no—
723C22×C4—611no—
724C22×C4—611no—
725C22×C4—611no—
726C22×C4—1224no—
727C22×C4—1224no—
728C22×C4C22×D6111yescharacteristic
729C22×C4C22×D6111yescharacteristic
730C22×C4C22×D6111yescharacteristic
731C22×C4C22×D6111yescharacteristic
732C22×C4C22×D6111yescharacteristic
733C4⋊C4—611no—
734C4⋊C4—611no—
735C4⋊C4—611no—
736C4⋊C4—611no—
737C4⋊C4—611no—
738C4⋊C4—611no—
739C4⋊C4—611no—
740C4⋊C4—611no—
741C4⋊C4—611no—
742C4⋊C4—611no—
743C4⋊C4—611no—
744C4⋊C4—611no—
745C4⋊C4—611no—
746C4⋊C4—611no—
747C4⋊C4—611no—
748C4⋊C4—611no—
749C4⋊C4—611no—
750C4⋊C4—611no—
751C4⋊C4—611no—
752C4⋊C4—611no—
753C4⋊C4—611no—
754C4⋊C4—611no—
755C4⋊C4—611no—
756C4⋊C4—611no—
757C4⋊C4—611no—
758C4⋊C4—611no—
759C4⋊C4—611no—
760C4⋊C4—611no—
761C4⋊C4—611no—
762C4⋊C4—611no—
763C4⋊C4—611no—
764C4⋊C4—611no—
765C4⋊C4—611no—
766C4⋊C4—611no—
767C4⋊C4C22×D6111yescharacteristic
768C4⋊C4C22×D6111yescharacteristic
769C4⋊C4C22×D6111yescharacteristic
770C4⋊C4C22×D6111yescharacteristic
771C4⋊C4C22×D6111yescharacteristic
772C4⋊C4C22×D6111yescharacteristic
773C4⋊C4C22×D6111yescharacteristic
774C4⋊C4C22×D6111yescharacteristic
775C22⋊C4—611no—
776C22⋊C4—611no—
777C22⋊C4—611no—
778C22⋊C4—611no—
779C22⋊C4—611no—
780C22⋊C4—611no—
781C22⋊C4—611no—
782C22⋊C4—611no—
783C22⋊C4—611no—
784C22⋊C4—611no—
785C22⋊C4—611no—
786C22⋊C4—611no—
787C22⋊C4—611no—
788C22⋊C4—611no—
789C22⋊C4—611no—
790C22⋊C4—611no—
791C22⋊C4—611no—
792C22⋊C4—611no—
793C22⋊C4—611no—
794C22⋊C4—611no—
795C22⋊C4—611no—
796C22⋊C4—611no—
797C22⋊C4—611no—
798C22⋊C4—611no—
799C22⋊C4—611no—
800C22⋊C4—611no—
801C22⋊C4—611no—
802C22⋊C4—611no—
803C22⋊C4C22×D6111yescharacteristic
804C22⋊C4C22×D6111yescharacteristic
805C22⋊C4C22×D6111yescharacteristic
806C22⋊C4C22×D6111yescharacteristic
807C22⋊C4C22×D6111yescharacteristic
808C22⋊C4C22×D6111yescharacteristic
809C22⋊C4C22×D6111yescharacteristic
810C22⋊C4C22×D6111yescharacteristic
811C22⋊C4C22×D6111yescharacteristic
812C22⋊C4C22×D6111yescharacteristic
813C22⋊C4C22×D6111yescharacteristic
814C22⋊C4C22×D6111yescharacteristic
815C22⋊C4C22×D6111yescharacteristic
816C22⋊C4C22×D6111yescharacteristic
817C42—611no—
818C42—611no—
819C42—611no—
820C42—611no—
821C42—611no—
822C42—611no—
823C42—611no—
824C42—611no—
825C42—611no—
826C42—611no—
827C42—611no—
828C42—611no—
829C42—611no—
830C42—611no—
831C42—611no—
832C42—611no—
833C42—611no—
834C42—611no—
835C42—611no—
836C42C22×D6111yescharacteristic
837C42C22×D6111yescharacteristic
838C42C22×D6111yescharacteristic
839C23—22no—
840C23—22no—
841C23—41no—
842C23—611no—
843C23—611no—
844C23—611no—
845C23—1222no—
846C23—1222no—
847C23—2441no—
848C23C23×D6111yescharacteristic
849C23C23×D6111yescharacteristic
850C23C23×D6111yescharacteristic
851C23C23×D6111yescharacteristic
852Q8—41no—
853Q8—1222no—
854Q8—1222no—
855Q8—1222no—
856Q8—2441no—
857D4—22no—
858D4—22no—
859D4—41no—
860D4—614no—
861D4—1222no—
862D4—1222no—
863D4—1222no—
864D4—1222no—
865D4—1222no—
866D4—1222no—
867D4—1222no—
868D4—1222no—
869D4—2441no—
870D4—2441no—
871D4—2441no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—614no—
878C2×C4—611no—
879C2×C4—611no—
880C2×C4—611no—
881C2×C4—611no—
882C2×C4—611no—
883C2×C4—611no—
884C2×C4—611no—
885C2×C4—611no—
886C2×C4—611no—
887C2×C4—611no—
888C2×C4—611no—
889C2×C4—611no—
890C2×C4—611no—
891C2×C4—1222no—
892C2×C4—1222no—
893C2×C4—1222no—
894C2×C4—1222no—
895C2×C4—1222no—
896C2×C4—1222no—
897C2×C4—1222no—
898C2×C4—1222no—
899C2×C4—1222no—
900C2×C4—1222no—
901C2×C4—1222no—
902C2×C4—1222no—
903C2×C4—1222no—
904C2×C4—1222no—
905C2×C4—1222no—
906C2×C4—1222no—
907C2×C4—1222no—
908C2×C4—2441no—
909C2×C4—2441no—
910C2×C4—2441no—
911C2×C4—2441no—
912C2×C4C23×D6111yescharacteristic
913C2×C4C23×D6111yescharacteristic
914C2×C4C23×D6111yescharacteristic
915C2×C4C23×D6111yescharacteristic
916C2×C4C23×D6111yescharacteristic
917C2×C4C23×D6111yescharacteristic
918C2×C4C23×D6111yescharacteristic
919C2×C4C23×D6111yescharacteristic
920C2×C4C23×D6111yescharacteristic
921C2×C4C23×D6111yescharacteristic
922C2×C4C23×D6111yescharacteristic
923C22—21no—
924C22—21no—
925C22—21no—
926C22—21no—
927C22—21no—
928C22—21no—
929C22—21no—
930C22—21no—
931C22—21no—
932C22—21no—
933C22—44no—
934C22—612no—
935C22—1221no—
936C22—1221no—
937C22—1221no—
938C22—1221no—
939C22—1221no—
940C22—1221no—
941C22—1221no—
942C22—1221no—
943C22—2444no—
944C22#41×D6112yes—
945C22#41×D6112yes—
946C22C24×D6111yescharacteristic
947C4—21no—
948C4—21no—
949C4—21no—
950C4—21no—
951C4—21no—
952C4—21no—
953C4—21no—
954C4—21no—
955C4—21no—
956C4—21no—
957C4—21no—
958C4—612no—
959C4—612no—
960C4—612no—
961C4—1221no—
962C4—1221no—
963C4—1221no—
964C4—1221no—
965C4—1221no—
966C4—1221no—
967C4—1221no—
968C4—1221no—
969C4—1221no—
970C4—1221no—
971C2—22no—
972C2—22no—
973C2—41no—
974C2—41no—
975C2—1222no—
976C2—2441no—
977C2—2441no—
978C2C2×#41×D6111yescharacteristic
979C2C2×#41×D6111yescharacteristic
980C2#1684059711yescharacteristic
subgroupG/H
center, FrattiniC22C24×D61
commutator, socleC22×C61C25
FittingC61×#551C2
hypercenter#551D61
hypocenterC61#3475
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ #551

Complements

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

NH ≅ G/Ntype
1. #16840479C2semidirect
2. #16840474C2semidirect
3. #16840466C2semidirect
4. #16840461C2semidirect
5. #16840457C2semidirect
6. #16840449C2semidirect
7. #16840448C2semidirect
8. #16840445C2semidirect
9. #16840445C2semidirect
10. #16840441C2semidirect
11. #16840439C2semidirect
12. #16840438C2semidirect
13. #16840410C2semidirect
14. #16840402C2semidirect
15. #16840399C2semidirect
16. #16840314C2semidirect
17. #16840298C2semidirect
18. #16840295C2semidirect
19. #16840295C2semidirect
20. #16840291C2semidirect
21. #16840289C2semidirect
22. #16840289C2semidirect
23. #16840270C2semidirect
24. #16840268C2semidirect
25. #16840230C2semidirect
26. C4×#11758224C2semidirect
27. C4×#11758224C2semidirect
28. C2×#14519737C2semidirect
29. C2×#14519733C2semidirect
30. #117×D61C2semidirect
31. C61×#551C2semidirect
38. #14519776C22semidirect
39. #14519775C22semidirect
40. #14519772C22semidirect
41. #14519772C22semidirect
42. #14519772C22semidirect
43. #14519772C22semidirect
44. #14519771C22semidirect
45. #14519771C22semidirect
46. #14519770C22semidirect
47. #14519770C22semidirect
48. #14519770C22semidirect
49. #14519770C22semidirect
50. #14519769C22semidirect
51. #14519768C22semidirect
52. #14519767C22semidirect
53. #14519767C22semidirect
54. #14519767C22semidirect
55. #14519767C22semidirect
56. #14519767C22semidirect
57. #14519767C22semidirect
58. #14519766C22semidirect
61. #14519763C22semidirect
62. #14519763C22semidirect
63. #14519762C22semidirect
64. #14519762C22semidirect
67. #14519761C22semidirect
70. #14519760C22semidirect
73. #14519759C22semidirect
74. #14519759C22semidirect
77. #14519755C22semidirect
78. #14519755C22semidirect
79. #14519755C22semidirect
80. #14519755C22semidirect
83. #14519754C22semidirect
84. #14519754C22semidirect
85. #14519754C22semidirect
86. #14519754C22semidirect
87. #14519753C22semidirect
91. #14519750C22semidirect
92. #14519750C22semidirect
95. #14519749C22semidirect
96. #14519749C22semidirect
101. Q8×Dic61C22semidirect
102. C4×Dic122C22semidirect
103. C4×Dic122C22semidirect
104. #14519742C22semidirect
105. #14519742C22semidirect
106. #14519742C22semidirect
107. #14519742C22semidirect
108. #14519742C22semidirect
110. D4×Dic61C22semidirect
111. D4×Dic61C22semidirect
112. #14519739C22semidirect
113. #14519739C22semidirect
114. #14519739C22semidirect
117. C4×C22⋊D61C22semidirect
118. C4×C22⋊D61C22semidirect
129. #14519737C22semidirect
130. #14519737C22semidirect
131. #14519737C22semidirect
132. #14519737C22semidirect
133. #14519737C22semidirect
134. #14519737C22semidirect
136. #14519735C22semidirect
137. #14519735C22semidirect
138. #14519735C22semidirect
139. #14519735C22semidirect
140. #14519734C22semidirect
141. #14519734C22semidirect
142. #14519734C22semidirect
143. #14519734C22semidirect
149. #14519733C22semidirect
150. #14519733C22semidirect
151. #14519733C22semidirect
152. #14519733C22semidirect
153. #14519733C22semidirect
154. #14519733C22semidirect
155. #14519733C22semidirect
157. C2×#11758196C22semidirect
158. C2×#11758196C22semidirect
159. C4⋊C4×D61C22semidirect
160. C4⋊C4×D61C22semidirect
166. C2×C4×Dic61C22semidirect
167. C2×C4×Dic61C22semidirect
168. C2×C4×Dic61C22semidirect
169. C42×D61C22semidirect
170. C42×D61C22semidirect
171. C42×D61C22semidirect
172. #126×C61C22semidirect
173. #126×C61C22semidirect
174. #124×C61C22semidirect
176. #123×C61C22semidirect
177. #123×C61C22semidirect
179. C22⋊Q8×C61C22semidirect
182. C4×D4×C61C22semidirect
184. #117×C61C22semidirect
390. C22⋊D61#41semidirect
401. C2×Dic61#41semidirect
503. #551D61semidirect
522. C61#3475semidirect
541. #126C2×D61semidirect
542. #126C2×D61semidirect
556. #124C2×D61semidirect
571. #123C2×D61semidirect
572. #123C2×D61semidirect
586. C22⋊Q8C2×D61semidirect
636. C4×D4C2×D61semidirect
659. #117C2×D61semidirect