Finite Group Databasebeta

← #30610802

Subgroups — #30610802

Order 15616.

1004 conjugacy classes of subgroups.

The subgroup lattice has 914 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462629C211yesmaximal, characteristic, complemented
2#21462464C211yesmaximal, characteristic, complemented
3#21461177C211yesmaximal, characteristic, complemented
4#21461176C211yesmaximal, characteristic, complemented
5#21461167C211yesmaximal, characteristic, complemented
6#21461157C211yesmaximal, characteristic, complemented
7#21461156C211yesmaximal, characteristic, complemented
8#21461146C211yesmaximal, characteristic, complemented
9#21461137C211yesmaximal, characteristic, complemented
10#21461136C211yesmaximal, characteristic, complemented
11#21461127C211yesmaximal, characteristic, complemented
12#21461117C211yesmaximal, characteristic, complemented
13#21461116C211yesmaximal, characteristic, complemented
14C2×#16840610C211yesmaximal, characteristic, complemented
15#21459384C211yesmaximal, characteristic
16C2×#14519864—21no—
17#16840814—21no—
18#16840795—21no—
19#16840793—21no—
20#16840791—21no—
21#16840780C2211yescharacteristic, complemented
22#16840779C2211yescharacteristic
23#16840778C2211yescharacteristic, complemented
24#16840769—21no—
25#16840768—21no—
26#16840768—21no—
27#16840766C2211yescharacteristic, complemented
28#16840765C2211yescharacteristic
29#16840765C2211yescharacteristic, complemented
30D61⋊(C4⋊C8)C2211yescharacteristic, complemented
31C2×C4⋊#92420C2211yescharacteristic
32C2×C4⋊#92420C2211yescharacteristic, complemented
33C4×#11758213C2211yescharacteristic, complemented
34C4×#11758217C2211yescharacteristic, complemented
35C2×C4×#92420C2211yescharacteristic
36#16840612C2211yescharacteristic, complemented
37#16840612C2211yescharacteristic, complemented
38#16840612C2211yescharacteristic, complemented
39#16840612C2211yescharacteristic, complemented
40Q8⋊#92420C2211yescharacteristic, complemented
41Q8⋊#92420C2211yescharacteristic, complemented
42Q8⋊#92420C2211yescharacteristic, complemented
43Q8⋊#92420C2211yescharacteristic, complemented
44#16840610C2211yescharacteristic
45#16840610C2211yescharacteristic
46#16840610C2211yescharacteristic
47#16840610C2211yescharacteristic
48#16840610C2211yescharacteristic
49#16840610C2211yescharacteristic
50#16840610C2211yescharacteristic
51#16840610C2211yescharacteristic
52#16840484C411yescharacteristic
53#16840475C411yescharacteristic
54#16840468C411yescharacteristic
55#16840463—21no—
56#16840447C411yescharacteristic
57#16840444—21no—
58#16840436—21no—
59#16840435—21no—
60#16840414C411yescharacteristic
61#16840408C411yescharacteristic
62#16840403C411yescharacteristic
63#16840314C2211yescharacteristic
64#16840298C2211yescharacteristic
65#16840297—21no—
66#16840297C2211yescharacteristic
67#16840295—21no—
68#16840270—21no—
69C4×#11758226C2211yescharacteristic
70#16840230C2211yescharacteristic
71C4×#11758224C2211yescharacteristic
72C2×#14519739C2211yescharacteristic
73#117×D61—21no—
74C61×#552C411yescharacteristic
75#14519864—44no—
76C2×#11758213—21no—
77C2×#11758213—21no—
78C2×#11758217—21no—
79C2×#11758217—21no—
80C2×#11758217—21no—
81C2×D61⋊C8—21no—
82C22×#92420—21no—
83C22×#92420—21no—
84C22×#92420—21no—
85#14519844—21no—
86#14519844—21no—
87#14519844—21no—
88#14519844—21no—
89#14519844—21no—
90C4⋊#92420—21no—
91C4⋊#92420—21no—
92C4⋊#92420—21no—
93C4⋊#92420—21no—
94C4⋊#92420C2311yescharacteristic
95C4⋊#92420C2311yescharacteristic
96C4⋊#92420C2311yescharacteristic
97C4⋊#92420C2311yescharacteristic
98#14519834—21no—
99C22⋊#92420—21no—
100C22⋊#92420—21no—
101#14519832—21no—
102#14519832—21no—
103C4×#92420—21no—
104C4×#92420C2311yescharacteristic
105C4×#92420C2311yescharacteristic
106C4×#92420C2311yescharacteristic
107C4×#92420C2311yescharacteristic
108C2×#11758226C2×C411yescharacteristic
109C2×#11758222C2×C411yescharacteristic
110C2×#11758224D411yescharacteristic
111C22×D244C2×C411yescharacteristic
112C22×C4×D61—21no—
113#14519776C2×C411yescharacteristic
114#14519775C2×C411yescharacteristic
115#14519772—21no—
116#14519772—21no—
117#14519772—21no—
118#14519772—21no—
119#14519771—21no—
120#14519768C2×C411yescharacteristic
121#14519767—21no—
122#14519767—21no—
123#14519766C2×C411yescharacteristic
124#14519765—21no—
125#14519765C2×C411yescharacteristic
126#14519763—21no—
127#14519762—21no—
128#14519762—21no—
129#14519762—21no—
130#14519762—21no—
131#14519761—21no—
132#14519760—21no—
133#14519759—21no—
134#14519757—21no—
135#14519757C2×C411yescharacteristic
136#14519756C2×C411yescharacteristic
137#14519755—21no—
138#14519755—21no—
139#14519755—21no—
140#14519754—21no—
141#14519752—21no—
142#14519752C2×C411yescharacteristic
143#14519751C2×C411yescharacteristic
144#14519750—21no—
145#14519750—21no—
146#14519750—21no—
147#14519747—21no—
148#14519745—21no—
149Q8×Dic61C2311yescharacteristic
150C4×Dic122C2×C411yescharacteristic
151#14519742—21no—
152#14519742C2×C411yescharacteristic
153#14519742D411yescharacteristic
154#14519742C2311yescharacteristic
155C4×D244—21no—
156C4×D244C2×C411yescharacteristic
157D4×Dic61D411yescharacteristic
158#14519739—21no—
159#14519739—21no—
160#14519739—21no—
161#14519739—21no—
162#14519739C2×C411yescharacteristic
163#14519739C2×C411yescharacteristic
164#14519739C2×C411yescharacteristic
165#14519739C2311yescharacteristic
166#14519739C2311yescharacteristic
167C4×C22⋊D61C2×C411yescharacteristic
168C4×C22⋊D61C2×C411yescharacteristic
169#14519737—21no—
170#14519737—21no—
171#14519737—21no—
172#14519737D411yescharacteristic
173#14519737D411yescharacteristic
174#14519736—21no—
175#14519735—21no—
176#14519735—21no—
177#14519735—21no—
178#14519735C2×C411yescharacteristic
179#14519735D411yescharacteristic
180#14519734—21no—
181#14519734—21no—
182#14519734—21no—
183#14519733—21no—
184#14519733D411yescharacteristic
185#14519733D411yescharacteristic
186C4⋊C4×D61—21no—
187C4⋊C4×D61—21no—
188C2×#11758198—21no—
189C22⋊C4×D61—21no—
190C22⋊C4×D61—21no—
191C2×C4×Dic61C2311yescharacteristic
192C2×C4×Dic61C2311yescharacteristic
193C42×D61—21no—
194C42×D61—21no—
195C42×D61C2311yescharacteristic
196#126×C61—21no—
197#125×C61—21no—
198#125×C61C2×C411yescharacteristic
199#123×C61—21no—
200C22⋊Q8×C61C2×C411yescharacteristic
201C22⋊Q8×C61C2×C411yescharacteristic
202C4×Q8×C61C2×C411yescharacteristic
203C4×D4×C61C2×C411yescharacteristic
204#117×C61—21no—
205#117×C61C2×C411yescharacteristic
206C2×C4⋊C4×C61C2×C411yescharacteristic
207C23×D61—21no—
208C2×Q8×C61C22×C411yescharacteristic
209C2×D4×C61C22⋊C411yescharacteristic
210C22×C4×C61—21no—
211C22×C4×C61C22×C411yescharacteristic
212C22×C4×C61C22×C411yescharacteristic
213C2×C22⋊D61—21no—
214C2×C22⋊D61—21no—
215C2×C22⋊D61C22⋊C411yescharacteristic
216C2×C22⋊D61C22⋊C411yescharacteristic
217C22×Dic61C2×D411yescharacteristic
218C22×Dic61C2×D411yescharacteristic
219C22×Dic61C2×D411yescharacteristic
220C22×Dic61C2×D411yescharacteristic
221#11758226—22no—
222#11758226—41no—
223#11758224—22no—
224#11758224—22no—
225#11758222—22no—
226#11758222—41no—
227C2×D244—22no—
228C2×D244—21no—
229C2×D244—21no—
230C2×D244—21no—
231C2×D244—41no—
232C2×D244C22×C411yescharacteristic
233C2×D244C22×C411yescharacteristic
234C2×C4×D61—21no—
235C2×C4×D61—21no—
236C2×C4×D61—21no—
237C2×C4×D61—21no—
238C2×C4×D61—21no—
239C2×C4×D61—21no—
240C2×C4×D61—21no—
241C2×C4×D61—21no—
242C2×C4×D61—42no—
243C2×C4×D61—42no—
244C2×C4×D61C22×C411yescharacteristic
245C2×C4×D61C2×D411yescharacteristic
246C2×C4×D61C2×D411yescharacteristic
247C2×Dic122—21no—
248C2×Dic122C22⋊C411yescharacteristic
249C2×Dic122C22×C411yescharacteristic
250#11758217—42no—
251#11758217—42no—
252#11758217—42no—
253C2×#92420—21no—
254C2×#92420—21no—
255C2×#92420—21no—
256C2×#92420—21no—
257C2×#92420—21no—
258C2×#92420—21no—
259C2×#92420—21no—
260C2×#92420—21no—
261C2×#92420—42no—
262C2×#92420—42no—
263C2×#92420—42no—
264#11758213—42no—
265#11758213—42no—
266D61⋊C8—42no—
267C4⋊C4×C61—21no—
268C4⋊C4×C61—21no—
269C4⋊C4×C61—21no—
270C4⋊C4×C61—21no—
271C4⋊C4×C61—21no—
272C4⋊C4×C61—21no—
273C4⋊C4×C61C22⋊C411yescharacteristic
274C4⋊C4×C61C22×C411yescharacteristic
275C4⋊C4×C61C22×C411yescharacteristic
276C4⋊C4×C61C22×C411yescharacteristic
277C22⋊C4×C61—21no—
278C22⋊C4×C61—21no—
279C22⋊C4×C61—21no—
280C22⋊C4×C61C22⋊C411yescharacteristic
281C22⋊C4×C61C22⋊C411yescharacteristic
282C42×C61—21no—
283C42×C61—21no—
284C42×C61C22×C411yescharacteristic
285C22⋊Dic61—21no—
286C22⋊Dic61C22⋊C411yescharacteristic
287C22⋊Dic61C22⋊C411yescharacteristic
288#11758198—21no—
289#11758198—21no—
290#11758198—21no—
291#11758198—21no—
292#11758198—21no—
293#11758198—21no—
294#11758198—21no—
295#11758198—21no—
296#11758198—21no—
297#11758198—21no—
298#11758198—21no—
299#11758198—21no—
300#11758198—21no—
301#11758198—21no—
302#11758198C22⋊C411yescharacteristic
303#11758198C22⋊C411yescharacteristic
304C4⋊Dic61—21no—
305C4⋊Dic61—21no—
306C4⋊Dic61—21no—
307C4⋊Dic61C22⋊C411yescharacteristic
308C4⋊Dic61C22×C411yescharacteristic
309#11758196—21no—
310#11758196—21no—
311#11758196—21no—
312#11758196—21no—
313#11758196—21no—
314#11758196—21no—
315#11758196—21no—
316#11758196C22⋊C411yescharacteristic
317#11758196C22⋊C411yescharacteristic
318#11758196C22⋊C411yescharacteristic
319#11758196C22⋊C411yescharacteristic
320C4×Dic61—21no—
321C4×Dic61—21no—
322C4×Dic61—21no—
323C4×Dic61—21no—
324C4×Dic61C22×C411yescharacteristic
325C4×Dic61C22×C411yescharacteristic
326C4×Dic61C2×D411yescharacteristic
327C4×Dic61C2×D411yescharacteristic
328C4×Dic61C2×D411yescharacteristic
329C4×Dic61C2×D411yescharacteristic
330C4×Dic61C2×D411yescharacteristic
331C4×Dic61C2×D411yescharacteristic
332C4×Dic61C2411yescharacteristic
333C23×C61C2×C22⋊C411yescharacteristic
334C23×C61C2×C22⋊C411yescharacteristic
335C22×D61—21no—
336C22×D61—21no—
337C22×D61—42no—
338C22×D61—42no—
339C22×D61—81no—
340C22×D61C2×C22⋊C411yescharacteristic
341Q8×C61—21no—
342Q8×C61—21no—
343D4×C61—22no—
344C2×C4×C61—21no—
345C2×C4×C61—21no—
346C2×C4×C61—21no—
347C2×C4×C61—21no—
348C2×C4×C61—21no—
349C2×C4×C61—21no—
350C2×C4×C61—21no—
351C2×C4×C61—21no—
352C2×C4×C61—42no—
353C2×C4×C61C2×C22⋊C411yescharacteristic
354C2×C4×C61C2×C22⋊C411yescharacteristic
355C2×C4×C61C2×C22⋊C411yescharacteristic
356C2×C4×C61C2×C22⋊C411yescharacteristic
357C2×C4×C61C23×C411yescharacteristic
358C22⋊D61—22no—
359C22⋊D61—22no—
360C22⋊D61—42no—
361C22⋊D61—81no—
362C2×Dic61—21no—
363C2×Dic61—21no—
364C2×Dic61—21no—
365C2×Dic61—21no—
366C2×Dic61—41no—
367C2×Dic61—41no—
368C2×Dic61C2×C22⋊C411yescharacteristic
369C2×Dic61C2×C22⋊C411yescharacteristic
370C2×Dic61C2×C22⋊C411yescharacteristic
371C2×Dic61C2×C22⋊C411yescharacteristic
372C2×Dic61C2×C22⋊C411yescharacteristic
373C2×Dic61AGL(1,ℤ/8)12yes—
374C2×Dic61#13712yes—
375C2×Dic61C22×D411yescharacteristic
376C2×Dic61C22×D411yescharacteristic
377D244—21no—
378D244—21no—
379D244—21no—
380D244—42no—
381D244—42no—
382D244—81no—
383D244#13112yescomplemented
384C4×D61—21no—
385C4×D61—21no—
386C4×D61—21no—
387C4×D61—21no—
388C4×D61—41no—
389C4×D61—42no—
390C4×D61—42no—
391C4×D61—41no—
392C4×D61—41no—
393C4×D61—41no—
394C4×D61—41no—
395C4×D61—42no—
396C4×D61—42no—
397C4×D61—81no—
398C4×D61—81no—
399Dic122—22no—
400Dic122—21no—
401Dic122—21no—
402Dic122—81no—
403#92420—22no—
404#92420—41no—
405#92420—41no—
406#92420—41no—
407#92420—41no—
408#92420—41no—
409#92420—41no—
410#92420—41no—
411#17512—611nomaximal, Sylow
412C22×C61—21no—
413C22×C61—21no—
414C22×C61—21no—
415C22×C61—21no—
416C22×C61—21no—
417C22×C61#41712yes—
418C22×C61C22×C22⋊C411yescharacteristic
419C2×D61—21no—
420C2×D61—22no—
421C2×D61—21no—
422C2×D61—21no—
423C2×D61—41no—
424C2×D61—41no—
425C2×D61—41no—
426C2×D61—41no—
427C2×D61—41no—
428C2×D61—84no—
429C4×C61—21no—
430C4×C61—21no—
431C4×C61—21no—
432C4×C61—21no—
433C4×C61—41no—
434C4×C61—41no—
435C4×C61—41no—
436C4×C61—41no—
437C4×C61C2×#13111yescharacteristic
438C4×C61#56811yescharacteristic
439Dic61—21no—
440Dic61—21no—
441Dic61—21no—
442Dic61—21no—
443Dic61—21no—
444Dic61—41no—
445Dic61—41no—
446Dic61#41712yes—
447Dic61C2×AGL(1,ℤ/8)11yescharacteristic
448Dic61C2×#13711yescharacteristic
449#3475—611no—
450#2965—611no—
451#2906—611no—
452#1495—611no—
453#1495—611no—
454#1493—611no—
455#1489—611no—
456#1489—611no—
457#1486—611no—
458#1483—611no—
459#1483—611no—
460#1481—611no—
461#1477—611no—
462#1477—611no—
463C2×D4⋊C8—611no—
464C2×C61—22no—
465C2×C61—41no—
466C2×C61#288011yescharacteristic
467C2×C61C2×#41711yescharacteristic
468C2×C61#290111yescharacteristic
469D61—41no—
470D61—42no—
471D61—81no—
472C2×#131—1221no—
473#556—611no—
474#555—611no—
475#554—611no—
476#553—1221no—
477#552—611no—
478#552—1221no—
479#552#692311yescharacteristic
480#551—1221no—
481#551—1221no—
482#547—611no—
483#546—611no—
484#546—611no—
485#533—611no—
486#529—611no—
487#529—611no—
488#529—1221no—
489#529—1221no—
490#525—1221no—
491C4×#41—611no—
492C4×#41—611no—
493C4×#41—611no—
494C2×C4×D4—611no—
495C2×#117—1221no—
496#446—1221no—
497#436—1221no—
498#435—1221no—
499#435—1221no—
500#431—611no—
501#431—611no—
502#431—611no—
503#424—1221no—
504#424—1221no—
505#424—1221no—
506#423—611no—
507#423—611no—
508#423—611no—
509C2×C4⋊C8—611no—
510C2×C4⋊C8—611no—
511C2×C4⋊C8—611no—
512C4×M16—611no—
513C4×M16—611no—
514C2×C4×C8—611no—
515Q8⋊C8—611no—
516Q8⋊C8—611no—
517Q8⋊C8—611no—
518Q8⋊C8—611no—
519Q8⋊C8—611no—
520Q8⋊C8—611no—
521Q8⋊C8—611no—
522Q8⋊C8—611no—
523D4⋊C8—611no—
524D4⋊C8—611no—
525D4⋊C8—611no—
526D4⋊C8—611no—
527D4⋊C8—611no—
528D4⋊C8—611no—
529D4⋊C8—611no—
530D4⋊C8—611no—
531C61#1751211yescharacteristic, complemented, Sylow
532C2×#41—611no—
533C2×#41—611no—
534C2×#41—611no—
535C22×D4—611no—
536C23×C4—1221no—
537#131—2444no—
538C2×M16—1221no—
539C2×M16—1221no—
540C2×M16—1221no—
541C2×M16—1221no—
542C2×M16—1221no—
543C22×C8—1221no—
544C22×C8—1221no—
545C22×C8—1221no—
546C22×C8—1221no—
547C4⋊Q8—611no—
548C4⋊Q8—611no—
549#126—21no—
550#126—1221no—
551#126—1221no—
552#126—1221no—
553#126—1221no—
554#126—1221no—
555#125—21no—
556#125—611no—
557#125—1221no—
558#125—1221no—
559#125C2×#692311yescharacteristic
560#124—611no—
561#124—611no—
562#124—1221no—
563#124—1221no—
564#123—21no—
565#123—1221no—
566#123—1221no—
567#123—1221no—
568#123—1221no—
569#123—1221no—
570#123—1221no—
571#123—1221no—
572C22⋊Q8—611no—
573C22⋊Q8—611no—
574C22⋊Q8—1221no—
575C22⋊Q8—1221no—
576C22⋊Q8—1221no—
577C22⋊Q8—1221no—
578C22⋊Q8—1221no—
579C22⋊Q8C2×#692311yescharacteristic
580C22⋊Q8C2×#692311yescharacteristic
581#121—611no—
582#121—611no—
583#121—1221no—
584#121—1221no—
585#121—1221no—
586#121—1221no—
587#120—1221no—
588#120—1221no—
589C4×Q8—611no—
590C4×Q8—611no—
591C4×Q8—611no—
592C4×Q8—611no—
593C4×Q8—611no—
594C4×Q8—1221no—
595C4×Q8C2×#692311yescharacteristic
596C4×D4—611no—
597C4×D4—611no—
598C4×D4—611no—
599C4×D4—611no—
600C4×D4—611no—
601C4×D4—611no—
602C4×D4—611no—
603C4×D4—611no—
604C4×D4—611no—
605C4×D4—611no—
606C4×D4—611no—
607C4×D4—1221no—
608C4×D4—1221no—
609C4×D4—1221no—
610C4×D4—1221no—
611C4×D4—1221no—
612C4×D4—1221no—
613C4×D4—1221no—
614C4×D4—1221no—
615C4×D4C2×#692311yescharacteristic
616#117—21no—
617#117—611no—
618#117—611no—
619#117—611no—
620#117—611no—
621#117—1221no—
622#117—1221no—
623#117—1221no—
624#117—1221no—
625#117—1221no—
626#117—1221no—
627#117—1221no—
628#117—1221no—
629#117C2×#692311yescharacteristic
630C2×C4⋊C4—1221no—
631C2×C4⋊C4—1221no—
632C2×C4⋊C4C2×#692311yescharacteristic
633C2×C22⋊C4—1221no—
634C2×C22⋊C4—1221no—
635C2×C22⋊C4—1221no—
636C2×C42—611no—
637C2×C42—611no—
638C2×C42—611no—
639C2×C42—1221no—
640C2×C42—1221no—
641C4⋊C8—611no—
642C4⋊C8—611no—
643C4⋊C8—611no—
644C4⋊C8—611no—
645C4⋊C8—1221no—
646C4⋊C8—1221no—
647C4⋊C8—1221no—
648C4⋊C8—1221no—
649C4⋊C8—1221no—
650C4⋊C8—1221no—
651C4⋊C8—1221no—
652C4⋊C8—1221no—
653C4⋊C8—1221no—
654C22⋊C8—1221no—
655C22⋊C8—1221no—
656C22⋊C8—1221no—
657#97—1221no—
658#97—1221no—
659C4×C8—611no—
660C4×C8—611no—
661C4×C8—611no—
662C4×C8—611no—
663C4×C8—1221no—
664C24—1221no—
665#41—1222no—
666#41—1222no—
667#41—1222no—
668#41—1222no—
669#41—2441no—
670#41—2441no—
671C2×Q8—611no—
672C2×Q8—611no—
673C2×Q8—1221no—
674C2×Q8C22×#692311yescharacteristic
675C2×D4—611no—
676C2×D4—611no—
677C2×D4—611no—
678C2×D4—611no—
679C2×D4—1222no—
680C2×D4—1221no—
681C2×D4—1221no—
682C2×D4—1221no—
683C2×D4—1221no—
684C2×D4—1221no—
685C2×D4—2441no—
686C2×D4C22⋊#692311yescharacteristic
687C22×C4—21no—
688C22×C4—611no—
689C22×C4—611no—
690C22×C4—611no—
691C22×C4—611no—
692C22×C4—611no—
693C22×C4—611no—
694C22×C4—611no—
695C22×C4—1221no—
696C22×C4—1221no—
697C22×C4—1221no—
698C22×C4—1221no—
699C22×C4—1221no—
700C22×C4—1221no—
701C22×C4—1221no—
702C22×C4—1221no—
703C22×C4—2442no—
704C22×C4—2442no—
705C22×C4C22×#692311yescharacteristic
706C22×C4C22×#692311yescharacteristic
707M16—2442no—
708M16—2442no—
709M16—2442no—
710M16—2442no—
711M16—2442no—
712C2×C8—1221no—
713C2×C8—1221no—
714C2×C8—1221no—
715C2×C8—1221no—
716C2×C8—1221no—
717C2×C8—1221no—
718C2×C8—1221no—
719C2×C8—1221no—
720C2×C8—2442no—
721C2×C8—2442no—
722C2×C8—2442no—
723C2×C8—2442no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4—611no—
731C4⋊C4—611no—
732C4⋊C4—611no—
733C4⋊C4—611no—
734C4⋊C4—611no—
735C4⋊C4—611no—
736C4⋊C4—1221no—
737C4⋊C4—1221no—
738C4⋊C4—1221no—
739C4⋊C4—1221no—
740C4⋊C4—1221no—
741C4⋊C4—1221no—
742C4⋊C4—1221no—
743C4⋊C4—1221no—
744C4⋊C4—1221no—
745C4⋊C4—1221no—
746C4⋊C4C22⋊#692311yescharacteristic
747C4⋊C4C22×#692311yescharacteristic
748C4⋊C4C22×#692311yescharacteristic
749C4⋊C4C22×#692311yescharacteristic
750C22⋊C4—21no—
751C22⋊C4—21no—
752C22⋊C4—21no—
753C22⋊C4—611no—
754C22⋊C4—611no—
755C22⋊C4—611no—
756C22⋊C4—611no—
757C22⋊C4—1221no—
758C22⋊C4—1221no—
759C22⋊C4—1221no—
760C22⋊C4—1221no—
761C22⋊C4—1221no—
762C22⋊C4—1221no—
763C22⋊C4—1221no—
764C22⋊C4—1221no—
765C22⋊C4—1221no—
766C22⋊C4—1221no—
767C22⋊C4—1221no—
768C22⋊C4—1221no—
769C22⋊C4—1221no—
770C22⋊C4—1221no—
771C22⋊C4—1221no—
772C22⋊C4C22⋊#692311yescharacteristic
773C22⋊C4C22⋊#692311yescharacteristic
774C42—21no—
775C42—21no—
776C42—611no—
777C42—611no—
778C42—611no—
779C42—611no—
780C42—611no—
781C42—611no—
782C42—611no—
783C42—611no—
784C42—611no—
785C42—1221no—
786C42—1221no—
787C42—1221no—
788C42—1221no—
789C42C22×#692311yescharacteristic
790C23—611no—
791C23—1221no—
792C23—1221no—
793C23—4881no—
794C23—2442no—
795C23—2442no—
796C23C2×C22⋊#692311yescharacteristic
797C23C2×C22⋊#692311yescharacteristic
798Q8—21no—
799Q8—21no—
800Q8—1222no—
801Q8—1221no—
802Q8—1221no—
803Q8—4881no—
804D4—22no—
805D4—612no—
806D4—1222no—
807D4—1222no—
808D4—1221no—
809D4—1221no—
810D4—1221no—
811D4—4881no—
812D4—4881no—
813D4—2442no—
814D4—2442no—
815D4—2442no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—42no—
825C2×C4—612no—
826C2×C4—612no—
827C2×C4—611no—
828C2×C4—611no—
829C2×C4—611no—
830C2×C4—611no—
831C2×C4—611no—
832C2×C4—611no—
833C2×C4—611no—
834C2×C4—1221no—
835C2×C4—1221no—
836C2×C4—1221no—
837C2×C4—1221no—
838C2×C4—1221no—
839C2×C4—1221no—
840C2×C4—1221no—
841C2×C4—1221no—
842C2×C4—4881no—
843C2×C4—4881no—
844C2×C4—2441no—
845C2×C4—2442no—
846C2×C4—2441no—
847C2×C4—2441no—
848C2×C4—2441no—
849C2×C4—2441no—
850C2×C4—2442no—
851C2×C4—2442no—
852C2×C4—2442no—
853C2×C4—2441no—
854C2×C4—2441no—
855C2×C4C2×C22⋊#692311yescharacteristic
856C2×C4C2×C22⋊#692311yescharacteristic
857C2×C4C2×C22⋊#692311yescharacteristic
858C2×C4C2×C22⋊#692311yescharacteristic
859C2×C4C23×#692311yescharacteristic
860C8—1222no—
861C8—2441no—
862C8—2441no—
863C8—2441no—
864C8—2441no—
865C8—2441no—
866C8—2441no—
867C8—2441no—
868C22—21no—
869C22—21no—
870C22—21no—
871C22—21no—
872C22—21no—
873C22—1221no—
874C22—1222no—
875C22—1221no—
876C22—1221no—
877C22—4884no—
878C22—2441no—
879C22—2441no—
880C22—2441no—
881C22—2441no—
882C22—2441no—
883C22#1684075312yes—
884C22C22×C22⋊#692311yescharacteristic
885C4—21no—
886C4—21no—
887C4—21no—
888C4—21no—
889C4—41no—
890C4—41no—
891C4—41no—
892C4—41no—
893C4—611no—
894C4—611no—
895C4—612no—
896C4—1221no—
897C4—1221no—
898C4—1221no—
899C4—1221no—
900C4—1221no—
901C4—2441no—
902C4—2441no—
903C4D61⋊#13111yescharacteristic
904C4#1684084111yescharacteristic
905C2—22no—
906C2—41no—
907C2—4881no—
908C2—2441no—
909C2—2442no—
910C2#2146240911yescharacteristic
911C2C2×#1684075311yescharacteristic
912C2#2146245011yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#552C4
socleC22×C61C22×C22⋊C4
prime radical#21459384C2
cosocleC4×Dic61C24
hypercenter#552#6923
hypocenterC61#17512
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #552

Complements

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

NH ≅ G/Ntype
1. #21462629C2semidirect
2. #21462464C2semidirect
3. #21461177C2semidirect
4. #21461176C2semidirect
5. #21461167C2semidirect
6. #21461157C2semidirect
7. #21461156C2semidirect
8. #21461146C2semidirect
9. #21461137C2semidirect
10. #21461136C2semidirect
11. #21461127C2semidirect
12. #21461117C2semidirect
13. #21461116C2semidirect
14. C2×#16840610C2semidirect
21. #16840780C22semidirect
23. #16840778C22semidirect
27. #16840766C22semidirect
29. #16840765C22semidirect
30. D61⋊(C4⋊C8)C22semidirect
32. C2×C4⋊#92420C22semidirect
33. C4×#11758213C22semidirect
34. C4×#11758217C22semidirect
36. #16840612C22semidirect
37. #16840612C22semidirect
38. #16840612C22semidirect
39. #16840612C22semidirect
40. Q8⋊#92420C22semidirect
41. Q8⋊#92420C22semidirect
42. Q8⋊#92420C22semidirect
43. Q8⋊#92420C22semidirect
383. D244#131semidirect
531. C61#17512semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#214626292
#214624642
#214611772
#214611762
#214611672
#214611572
#214611562
#214611462
#214611372
#214611362
#214611272
#214611172
#214611162
C2×#168406102
#214593842
#1751261