Finite Group Databasebeta

← #29718264

Subgroups — #29718264

Order 15616.

1360 conjugacy classes of subgroups.

The subgroup lattice has 1028 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455451C211yesmaximal, characteristic, complemented
2C2×#16839945C211yesmaximal, characteristic, complemented
3#21455079C211yesmaximal, characteristic, complemented
4C2×#16839779C211yesmaximal, characteristic, complemented
5#21451589C211yesmaximal, characteristic, complemented
6#21447045C211yesmaximal, characteristic, complemented
7#21447033C211yesmaximal, characteristic, complemented
8#21446866C211yesmaximal, characteristic, complemented
9#21446853C211yesmaximal, characteristic, complemented
10#21446288C211yesmaximal, characteristic, complemented
11#21446268C211yesmaximal, characteristic, complemented
12#21446188C211yesmaximal, characteristic, complemented
13#21446052C211yesmaximal, characteristic, complemented
14#21445778C211yesmaximal, characteristic, complemented
15C61×#3489C211yesmaximal, characteristic
16C2×#14519807C2211yescharacteristic
17C2×#14519807C2211yescharacteristic
18C2×#14519807C2211yescharacteristic, complemented
19C22×#11758194C2211yescharacteristic
20C2×#14519775C2211yescharacteristic, complemented
21C2×#14519756C2211yescharacteristic
22C2×#14519736C2211yescharacteristic
23#16840018—21no—
24#16840006—21no—
25#16840001—21no—
26#16839989—21no—
27#16839945—24no—
28#16839924—21no—
29#16839924—21no—
30#16839918—21no—
31#16839913—21no—
32#16839805C2211yescharacteristic, complemented
33#16839779—24no—
34C2×#14519704C2211yescharacteristic
35C2×#14519704C2211yescharacteristic
36C2×#14519704C2211yescharacteristic
37C2×#14519704C2211yescharacteristic
38C2×#14519704C2211yescharacteristic, complemented
39C2×#14519704C2211yescharacteristic, complemented
40#16839770C2211yescharacteristic, complemented
41#16839763C2211yescharacteristic
42#16839763C2211yescharacteristic
43#16839763C2211yescharacteristic, complemented
44C2×#14519696C2211yescharacteristic, complemented
45C2×#14519696C2211yescharacteristic, complemented
46#16839726C2211yescharacteristic
47#16839695—22no—
48#16839690—22no—
49#16839669C2211yescharacteristic, complemented
50#16839667C2211yescharacteristic, complemented
51#16839627C2211yescharacteristic, complemented
52#16839531C2211yescharacteristic, complemented
53#16839531C2211yescharacteristic, complemented
54#16839521C2211yescharacteristic, complemented
55#16839521C2211yescharacteristic, complemented
56C2×2−1+4×C61C2211yescharacteristic
57C22×#41×C61C2211yescharacteristic
58D4×Q8×C61—21no—
59C61×#548—21no—
60C61×#547—21no—
61C61×#547—22no—
62C61×#546—21no—
63C61×#546—22no—
64C61×#537—21no—
65C61×#537C2211yescharacteristic
66C61×#536—21no—
67C61×#536C2211yescharacteristic
68C61×#525—21no—
69C61×#525C2211yescharacteristic
70C2×C22⋊Q8×C61—21no—
71C2×C22⋊Q8×C61C2211yescharacteristic
72C61×#520C2211yescharacteristic
73C22×Dic122C2311yescharacteristic
74#14519807—22no—
75#14519807—22no—
76#14519807—22no—
77#14519807—41no—
78#14519807—41no—
79#14519807—41no—
80C2×#11758202—21no—
81C2×#11758202—21no—
82C2×#11758202—21no—
83C2×#11758200—21no—
84C2×#11758200—21no—
85C2×#11758200—21no—
86C2×#11758194—21no—
87C2×#11758194—22no—
88C2×#11758194—41no—
89C2×#11758194C2311yescharacteristic
90C2×#11758194C2311yescharacteristic
91C2×#11758194C2311yescharacteristic
92C2×#11758194C2311yescharacteristic
93C22×#92418—21no—
94#14519775—22no—
95#14519775—41no—
96#14519756—21no—
97#14519756—21no—
98#14519756—21no—
99#14519756—21no—
100#14519736—22no—
101#14519736—41no—
102C2×C4⋊Dic61—21no—
103C2×C4⋊Dic61C2311yescharacteristic
104C2×#11758196—22no—
105C2×#11758196—21no—
106C2×C22⋊Dic61—21no—
107C2×C22⋊Dic61—21no—
108C2×C4×Dic61C2311yescharacteristic
109C2×C4×Dic61C2311yescharacteristic
110#14519710—21no—
111#14519708—21no—
112#14519704—22no—
113#14519704—22no—
114#14519704—22no—
115#14519704—22no—
116#14519704—41no—
117#14519704D414yescomplemented
118#14519701—21no—
119#14519701—21no—
120#14519701—21no—
121#14519700—21no—
122#14519700—21no—
123#14519698—21no—
124#14519698—21no—
125#14519698—21no—
126#14519696—22no—
127#14519696—41no—
128C22⋊#92418—21no—
129C22⋊#92418—21no—
130#14519684—22no—
131#14519684—22no—
132#14519684—22no—
1332−1+4×C61—22no—
1342−1+4×C61—22no—
1352−1+4×C61—41no—
1362−1+4×C61—41no—
137C2×#41×C61—21no—
138C2×#41×C61—21no—
139C2×#41×C61—21no—
140C2×#41×C61—22no—
141C2×#41×C61—21no—
142C2×#41×C61—22no—
143C2×#41×C61—22no—
144C2×#41×C61—41no—
145C2×#41×C61—41no—
146C2×#41×C61D411yescharacteristic
147C2×#41×C61D411yescharacteristic
148C2×#41×C61C2311yescharacteristic
149C2×#41×C61C2311yescharacteristic
150C2×#41×C61C2311yescharacteristic
151C22×Q8×C61—21no—
152C22×Q8×C61—21no—
153C22×Q8×C61D411yescharacteristic
154C22×Q8×C61C2311yescharacteristic
155C22×D4×C61—21no—
156C22×D4×C61D411yescharacteristic
157C23×C4×C61—21no—
158C23×C4×C61C2311yescharacteristic
159C4⋊Q8×C61—22no—
160C4⋊Q8×C61—21no—
161#124×C61—22no—
162#124×C61—21no—
163#123×C61—22no—
164#123×C61—22no—
165#123×C61—22no—
166#123×C61—22no—
167#123×C61—21no—
168C22⋊Q8×C61—22no—
169C22⋊Q8×C61—22no—
170C22⋊Q8×C61—22no—
171C22⋊Q8×C61—21no—
172C22⋊Q8×C61—21no—
173C22⋊Q8×C61—21no—
174C22⋊Q8×C61—21no—
175C22⋊Q8×C61—21no—
176C22⋊Q8×C61—21no—
177C22⋊Q8×C61—21no—
178C22⋊Q8×C61—21no—
179C22⋊Q8×C61D411yescharacteristic
180C22⋊Q8×C61D411yescharacteristic
181#121×C61—22no—
182#121×C61—22no—
183#121×C61—22no—
184#121×C61—21no—
185#121×C61—21no—
186#121×C61—22no—
187#121×C61D411yescharacteristic
188#121×C61D411yescharacteristic
189#120×C61—22no—
190#120×C61—21no—
191C4×Q8×C61—21no—
192C4×D4×C61—22no—
193C4×D4×C61—22no—
194C4×D4×C61—21no—
195C4×D4×C61—22no—
196C4×D4×C61—21no—
197C4×D4×C61—21no—
198#117×C61—21no—
199#117×C61C2311yescharacteristic
200C2×C4⋊C4×C61—22no—
201C2×C4⋊C4×C61—21no—
202C2×C4⋊C4×C61D412yes—
203C2×C4⋊C4×C61C2311yescharacteristic
204C2×C22⋊C4×C61—22no—
205C2×C22⋊C4×C61D412yes—
206C24×C61—21no—
207C24×C61C2×D411yescharacteristic
208#41×C61—21no—
209#41×C61—21no—
210#41×C61—22no—
211#41×C61—22no—
212#41×C61—21no—
213#41×C61—21no—
214#41×C61—21no—
215#41×C61—21no—
216#41×C61—21no—
217#41×C61—21no—
218#41×C61—21no—
219#41×C61—21no—
220#41×C61—42no—
221#41×C61—42no—
222#41×C61—41no—
223#41×C61—41no—
224#41×C61—42no—
225#41×C61—42no—
226#41×C61—42no—
227#41×C61—42no—
228#41×C61—44no—
229#41×C61—44no—
230#41×C61—42no—
231#41×C61—42no—
232#41×C61C2×D412yes—
233#41×C61#4112yes—
234C2×Q8×C61—22no—
235C2×Q8×C61—21no—
236C2×Q8×C61—21no—
237C2×Q8×C61—21no—
238C2×Q8×C61—21no—
239C2×Q8×C61—21no—
240C2×Q8×C61—21no—
241C2×Q8×C61—21no—
242C2×Q8×C61—22no—
243C2×Q8×C61—41no—
244C2×Q8×C61—42no—
245C2×Q8×C61—42no—
246C2×Q8×C61—42no—
247C2×Q8×C61—42no—
248C2×Q8×C61C2×D411yescharacteristic
249C2×Q8×C61C2×D411yescharacteristic
250C2×Q8×C61C2×D411yescharacteristic
251C2×D4×C61—21no—
252C2×D4×C61—22no—
253C2×D4×C61—22no—
254C2×D4×C61—21no—
255C2×D4×C61—21no—
256C2×D4×C61—21no—
257C2×D4×C61—21no—
258C2×D4×C61—21no—
259C2×D4×C61—22no—
260C2×D4×C61—21no—
261C2×D4×C61—21no—
262C2×D4×C61—41no—
263C2×D4×C61—42no—
264C2×D4×C61—42no—
265C2×D4×C61C2×D411yescharacteristic
266C2×D4×C61C2×D411yescharacteristic
267C2×D4×C61C2×D411yescharacteristic
268C22×C4×C61—21no—
269C22×C4×C61—21no—
270C22×C4×C61—21no—
271C22×C4×C61—21no—
272C22×C4×C61—21no—
273C22×C4×C61—22no—
274C22×C4×C61—22no—
275C22×C4×C61—21no—
276C22×C4×C61—22no—
277C22×C4×C61—21no—
278C22×C4×C61—21no—
279C22×C4×C61—21no—
280C22×C4×C61—21no—
281C22×C4×C61—42no—
282C22×C4×C61—42no—
283C22×C4×C61C2×D412yes—
284C22×C4×C61C2×D411yescharacteristic
285C22×C4×C61C2×D411yescharacteristic
286C22×C4×C61C2×D411yescharacteristic
287C22×C4×C61C2×D411yescharacteristic
288C22×C4×C61C2×D411yescharacteristic
289C22×C4×C61C2×D412yes—
290C22×C4×C61C2411yescharacteristic
291C22×Dic61—21no—
292C22×Dic61—21no—
293C22×Dic61—21no—
294C22×Dic61—21no—
295C2×Dic122—21no—
296C2×Dic122—21no—
297C2×Dic122—21no—
298C2×Dic122—21no—
299C2×Dic122—21no—
300C2×Dic122—21no—
301C4⋊C4×C61—22no—
302C4⋊C4×C61—22no—
303C4⋊C4×C61—22no—
304C4⋊C4×C61—22no—
305C4⋊C4×C61—21no—
306C4⋊C4×C61—22no—
307C4⋊C4×C61—22no—
308C4⋊C4×C61—21no—
309C4⋊C4×C61—21no—
310C4⋊C4×C61—21no—
311C4⋊C4×C61C2×D411yescharacteristic
312C4⋊C4×C61C2×D411yescharacteristic
313C22⋊C4×C61—22no—
314C22⋊C4×C61—22no—
315C22⋊C4×C61—22no—
316C22⋊C4×C61—22no—
317C22⋊C4×C61—22no—
318C22⋊C4×C61—21no—
319C22⋊C4×C61—22no—
320C22⋊C4×C61—22no—
321C22⋊C4×C61—21no—
322C22⋊C4×C61—21no—
323C22⋊C4×C61—21no—
324C22⋊C4×C61—21no—
325C42×C61—22no—
326C42×C61—21no—
327C22⋊Dic61—42no—
328C22⋊Dic61—41no—
329C22⋊Dic61—41no—
330#11758202—42no—
331#11758202—42no—
332#11758202—42no—
333#11758200—42no—
334#11758200—42no—
335#11758200—42no—
336C4⋊Dic61—21no—
337C4⋊Dic61—21no—
338C4⋊Dic61—42no—
339#11758196—44no—
340#11758196—41no—
341#11758196—41no—
342C4×Dic61—21no—
343C4×Dic61—21no—
344C4×Dic61—21no—
345C4×Dic61C2×D412yes—
346#11758194—21no—
347#11758194—21no—
348#11758194—21no—
349#11758194—21no—
350#11758194—21no—
351#11758194—21no—
352#11758194—21no—
353#11758194—42no—
354#11758194C2×D412yes—
355C2×#92418—21no—
356C2×#92418—21no—
357C2×#92418—21no—
358C2×#92418—21no—
359C2×#92418—42no—
360C23×C61—21no—
361C23×C61—21no—
362C23×C61—21no—
363C23×C61—21no—
364C23×C61—21no—
365C23×C61—41no—
366C23×C61—41no—
367C23×C61—42no—
368C23×C61—42no—
369C23×C61—81no—
370C23×C61#12011yescharacteristic
371C23×C61#12011yescharacteristic
372C23×C61C22×D411yescharacteristic
373Q8×C61—21no—
374Q8×C61—21no—
375Q8×C61—21no—
376Q8×C61—21no—
377Q8×C61—21no—
378Q8×C61—42no—
379Q8×C61—44no—
380Q8×C61—41no—
381Q8×C61—41no—
382Q8×C61—41no—
383Q8×C61—41no—
384Q8×C61#12112yes—
385D4×C61—22no—
386D4×C61—22no—
387D4×C61—21no—
388D4×C61—21no—
389D4×C61—21no—
390D4×C61—21no—
391D4×C61—21no—
392D4×C61—42no—
393D4×C61—42no—
394D4×C61—42no—
395D4×C61—42no—
396D4×C61—44no—
397D4×C61—41no—
398D4×C61—41no—
399D4×C61—41no—
400D4×C61—41no—
401D4×C61—81no—
402D4×C61—82no—
403D4×C61#12112yes—
404C2×C4×C61—21no—
405C2×C4×C61—21no—
406C2×C4×C61—21no—
407C2×C4×C61—21no—
408C2×C4×C61—21no—
409C2×C4×C61—21no—
410C2×C4×C61—21no—
411C2×C4×C61—21no—
412C2×C4×C61—21no—
413C2×C4×C61—22no—
414C2×C4×C61—21no—
415C2×C4×C61—21no—
416C2×C4×C61—22no—
417C2×C4×C61—21no—
418C2×C4×C61—22no—
419C2×C4×C61—21no—
420C2×C4×C61—21no—
421C2×C4×C61—22no—
422C2×C4×C61—21no—
423C2×C4×C61—22no—
424C2×C4×C61—22no—
425C2×C4×C61—42no—
426C2×C4×C61—42no—
427C2×C4×C61—42no—
428C2×C4×C61—44no—
429C2×C4×C61—44no—
430C2×C4×C61—41no—
431C2×C4×C61—41no—
432C2×C4×C61—41no—
433C2×C4×C61—41no—
434C2×C4×C61—42no—
435C2×C4×C61—82no—
436C2×C4×C61#12011yescharacteristic
437C2×C4×C61#12011yescharacteristic
438C2×C4×C61C22×D411yescharacteristic
439C2×C4×C61C22×D411yescharacteristic
440C2×C4×C61C22×D411yescharacteristic
441C2×C4×C61C2×#4111yescharacteristic
442C2×C4×C61H(5,𝔽2)11yescharacteristic
443C2×C4×C61H(5,𝔽2)11yescharacteristic
444C2×Dic61—22no—
445C2×Dic61—41no—
446C2×Dic61—41no—
447C2×Dic61—41no—
448C2×Dic61—41no—
449C2×Dic61—42no—
450C2×Dic61—41no—
451C2×Dic61—41no—
452C2×Dic61—41no—
453C2×Dic61—41no—
454C2×Dic61—41no—
455Dic122—41no—
456Dic122—41no—
457Dic122—41no—
458Dic122—41no—
459#92418—22no—
460#92418—41no—
461#92418—41no—
462#92418—41no—
463#24470—611nomaximal, Sylow
464C22×C61—21no—
465C22×C61—21no—
466C22×C61—21no—
467C22×C61—21no—
468C22×C61—22no—
469C22×C61—21no—
470C22×C61—21no—
471C22×C61—21no—
472C22×C61—21no—
473C22×C61—41no—
474C22×C61—41no—
475C22×C61—41no—
476C22×C61—41no—
477C22×C61—41no—
478C22×C61—41no—
479C22×C61—41no—
480C22×C61—41no—
481C22×C61—81no—
482C22×C61—81no—
483C22×C61—84no—
484C22×C61C2×#12011yescharacteristic
485C22×C61D4211yescharacteristic
486C22×C61#54611yescharacteristic
487C4×C61—21no—
488C4×C61—21no—
489C4×C61—22no—
490C4×C61—42no—
491C4×C61—41no—
492C4×C61—41no—
493C4×C61—41no—
494C4×C61—42no—
495C4×C61—41no—
496C4×C61C2×#12111yescharacteristic
497C4×C61#53411yescharacteristic
498C4×C61D4211yescharacteristic
499C4×C61#54611yescharacteristic
500Dic61—42no—
501Dic61—81no—
502Dic61—81no—
503Dic61—81no—
504#3489D6111yescharacteristic
505#3056—611no—
506C2×#456—611no—
507#3007—611no—
508C2×#421—611no—
509#2621—611no—
510#2040—611no—
511#2038—611no—
512#2007—611no—
513#2005—611no—
514#1901—611no—
515#1897—611no—
516#1882—611no—
517#1860—611no—
518#1793—611no—
519C2×C61—21no—
520C2×C61—21no—
521C2×C61—41no—
522C2×C61—41no—
523C2×C61—42no—
524C2×C61—81no—
525C2×C61—81no—
526C2×C61#241011yescharacteristic
527C2×C61#302011yescharacteristic
528C2×C61#302211yescharacteristic
529C2×2−1+4C2×D6111yescharacteristic
530C22×#41C2×D6111yescharacteristic
531C2×#137—611no—
532C2×#137—611no—
533C2×#137—611no—
534C22×M16—611no—
535D4×Q8—21no—
536#548—21no—
537#547—21no—
538#547—22no—
539#546—21no—
540#546—22no—
541#537—21no—
542#537C2×D6111yescharacteristic
543#536—21no—
544#536C2×D6111yescharacteristic
545C2×C4⋊Q8—611no—
546#525—21no—
547#525C2×D6111yescharacteristic
548C2×C22⋊Q8—21no—
549C2×C22⋊Q8—611no—
550C2×C22⋊Q8C2×D6111yescharacteristic
551#520C2×D6111yescharacteristic
552C2×#117—611no—
553#470—1221no—
554#468—1221no—
555#467—1221no—
556#465—1221no—
557#456—1224no—
558#452—1221no—
559#452—1221no—
560#451—1221no—
561#450—1221no—
562#428—611no—
563#421—1224no—
564C2×#104—611no—
565C2×#104—611no—
566C2×#104—611no—
567C2×#104—611no—
568C2×#104—611no—
569C2×#104—611no—
570#419—611no—
571#417—611no—
572#417—611no—
573#417—611no—
574C2×#101—611no—
575C2×#101—611no—
576#407—611no—
577#398—1222no—
578#397—1222no—
579#391—611no—
580#391—611no—
581#382—611no—
582#343—611no—
583#343—611no—
584#339—611no—
585#339—611no—
586C61#2447011yescharacteristic, complemented, Sylow
5872−1+4—22no—
5882−1+4—22no—
5892−1+4—41no—
5902−1+4—41no—
591C2×#41—21no—
592C2×#41—21no—
593C2×#41—21no—
594C2×#41—22no—
595C2×#41—21no—
596C2×#41—22no—
597C2×#41—22no—
598C2×#41—41no—
599C2×#41—41no—
600C2×#41C22⋊D6111yescharacteristic
601C2×#41C22⋊D6111yescharacteristic
602C2×#41C22×D6111yescharacteristic
603C2×#41C22×D6111yescharacteristic
604C2×#41C22×D6111yescharacteristic
605C22×Q8—21no—
606C22×Q8—21no—
607C22×Q8—611no—
608C22×Q8C22⋊D6111yescharacteristic
609C22×Q8C22×D6111yescharacteristic
610C22×D4—21no—
611C22×D4C22⋊D6111yescharacteristic
612C23×C4—21no—
613C23×C4C22×D6111yescharacteristic
614#137—1222no—
615#137—1222no—
616#137—1222no—
617#137—2441no—
618#137—2441no—
619#137—2441no—
620C2×Q16—1221no—
621C2×Q16—1221no—
622C2×Q16—1221no—
623C2×SD16—1221no—
624C2×SD16—1221no—
625C2×SD16—1221no—
626C2×M16—611no—
627C2×M16—611no—
628C2×M16—611no—
629C2×M16—611no—
630C2×M16—1221no—
631C2×M16—1222no—
632C2×M16—2441no—
633C22×C8—1221no—
634C4⋊Q8—22no—
635C4⋊Q8—21no—
636C4⋊Q8—1222no—
637C4⋊Q8—2441no—
638#124—22no—
639#124—21no—
640#123—22no—
641#123—22no—
642#123—22no—
643#123—21no—
644#123—22no—
645C22⋊Q8—22no—
646C22⋊Q8—22no—
647C22⋊Q8—22no—
648C22⋊Q8—21no—
649C22⋊Q8—21no—
650C22⋊Q8—21no—
651C22⋊Q8—21no—
652C22⋊Q8—21no—
653C22⋊Q8—21no—
654C22⋊Q8—21no—
655C22⋊Q8—21no—
656C22⋊Q8—1221no—
657C22⋊Q8—1221no—
658C22⋊Q8—1221no—
659C22⋊Q8—1221no—
660C22⋊Q8C22⋊D6111yescharacteristic
661C22⋊Q8C22⋊D6111yescharacteristic
662#121—22no—
663#121—22no—
664#121—22no—
665#121—21no—
666#121—21no—
667#121—22no—
668#121C22⋊D6111yescharacteristic
669#121C22⋊D6111yescharacteristic
670#120—22no—
671#120—21no—
672C4×Q8—21no—
673C4×D4—22no—
674C4×D4—22no—
675C4×D4—21no—
676C4×D4—22no—
677C4×D4—21no—
678C4×D4—21no—
679#117—21no—
680#117—1222no—
681#117—2441no—
682#117C22×D6111yescharacteristic
683C2×C4⋊C4—22no—
684C2×C4⋊C4—21no—
685C2×C4⋊C4—611no—
686C2×C4⋊C4—1221no—
687C2×C4⋊C4—1221no—
688C2×C4⋊C4—1222no—
689C2×C4⋊C4C22⋊D6112yes—
690C2×C4⋊C4C22×D6111yescharacteristic
691C2×C22⋊C4—22no—
692C2×C22⋊C4—1221no—
693C2×C22⋊C4—1221no—
694C2×C22⋊C4C22⋊D6112yes—
695C2×C42—611no—
696C2×C42—611no—
697#107—1221no—
698#106—1221no—
699#104—614no—
700#104—1222no—
701#104—1222no—
702#104—1222no—
703#104—1222no—
704#104—2441no—
705#103—1221no—
706#103—1221no—
707#103—1221no—
708#103—1221no—
709#103—1221no—
710#102—1221no—
711#102—1221no—
712#102—1221no—
713#101—1222no—
714#101—2441no—
715C22⋊C8—1221no—
716C22⋊C8—1221no—
717#95—1222no—
718#95—1222no—
719#95—1222no—
720C24—21no—
721C24C2×C22⋊D6111yescharacteristic
722#41—21no—
723#41—21no—
724#41—22no—
725#41—22no—
726#41—21no—
727#41—21no—
728#41—21no—
729#41—21no—
730#41—21no—
731#41—21no—
732#41—21no—
733#41—21no—
734#41—42no—
735#41—42no—
736#41—41no—
737#41—41no—
738#41—42no—
739#41—42no—
740#41—42no—
741#41—42no—
742#41—44no—
743#41—44no—
744#41—42no—
745#41—42no—
746#41D4×D6112yes—
747#41#1175822412yes—
748C2×Q8—22no—
749C2×Q8—21no—
750C2×Q8—21no—
751C2×Q8—21no—
752C2×Q8—21no—
753C2×Q8—21no—
754C2×Q8—21no—
755C2×Q8—21no—
756C2×Q8—22no—
757C2×Q8—41no—
758C2×Q8—42no—
759C2×Q8—42no—
760C2×Q8—42no—
761C2×Q8—42no—
762C2×Q8—1221no—
763C2×Q8—1221no—
764C2×Q8—1221no—
765C2×Q8—1221no—
766C2×Q8—1221no—
767C2×Q8—1221no—
768C2×Q8C2×C22⋊D6111yescharacteristic
769C2×Q8C2×C22⋊D6111yescharacteristic
770C2×Q8C2×C22⋊D6111yescharacteristic
771C2×D4—21no—
772C2×D4—22no—
773C2×D4—22no—
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—21no—
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—22no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—41no—
783C2×D4—42no—
784C2×D4—42no—
785C2×D4C2×C22⋊D6111yescharacteristic
786C2×D4C2×C22⋊D6111yescharacteristic
787C2×D4C2×C22⋊D6111yescharacteristic
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—21no—
796C22×C4—22no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—42no—
802C22×C4—42no—
803C22×C4—1221no—
804C22×C4—1221no—
805C22×C4—1221no—
806C22×C4—1221no—
807C22×C4C2×C22⋊D6112yes—
808C22×C4C2×C22⋊D6111yescharacteristic
809C22×C4C2×C22⋊D6111yescharacteristic
810C22×C4C2×C22⋊D6111yescharacteristic
811C22×C4C2×C22⋊D6111yescharacteristic
812C22×C4C2×C22⋊D6111yescharacteristic
813C22×C4C2×C22⋊D6112yes—
814C22×C4C23×D6111yescharacteristic
815Q16—2442no—
816Q16—2442no—
817Q16—2442no—
818SD16—2442no—
819SD16—2442no—
820SD16—2442no—
821M16—612no—
822M16—1221no—
823M16—1221no—
824M16—1221no—
825M16—1221no—
826M16—1221no—
827M16—1221no—
828M16—1221no—
829M16—2442no—
830C2×C8—1221no—
831C2×C8—1221no—
832C2×C8—1221no—
833C2×C8—1221no—
834C2×C8—2442no—
835C4⋊C4—22no—
836C4⋊C4—22no—
837C4⋊C4—22no—
838C4⋊C4—22no—
839C4⋊C4—21no—
840C4⋊C4—21no—
841C4⋊C4—21no—
842C4⋊C4—22no—
843C4⋊C4—22no—
844C4⋊C4—21no—
845C4⋊C4—1221no—
846C4⋊C4—1221no—
847C4⋊C4—2444no—
848C4⋊C4—2442no—
849C4⋊C4—2441no—
850C4⋊C4—2441no—
851C4⋊C4C2×C22⋊D6111yescharacteristic
852C4⋊C4C2×C22⋊D6111yescharacteristic
853C22⋊C4—22no—
854C22⋊C4—22no—
855C22⋊C4—22no—
856C22⋊C4—22no—
857C22⋊C4—22no—
858C22⋊C4—21no—
859C22⋊C4—21no—
860C22⋊C4—22no—
861C22⋊C4—22no—
862C22⋊C4—21no—
863C22⋊C4—21no—
864C22⋊C4—21no—
865C22⋊C4—2442no—
866C22⋊C4—2441no—
867C22⋊C4—2441no—
868C42—22no—
869C42—21no—
870C42—612no—
871C42—1221no—
872C42—1221no—
873C42—1221no—
874C23—21no—
875C23—21no—
876C23—21no—
877C23—21no—
878C23—21no—
879C23—41no—
880C23—41no—
881C23—42no—
882C23—42no—
883C23—81no—
884C23#1451974611yescharacteristic
885C23#1451974611yescharacteristic
886C23C22×C22⋊D6111yescharacteristic
887Q8—21no—
888Q8—21no—
889Q8—21no—
890Q8—21no—
891Q8—21no—
892Q8—42no—
893Q8—44no—
894Q8—41no—
895Q8—41no—
896Q8—41no—
897Q8—41no—
898Q8—2441no—
899Q8—2441no—
900Q8—2441no—
901Q8—2441no—
902Q8#1451974912yes—
903D4—22no—
904D4—22no—
905D4—21no—
906D4—21no—
907D4—21no—
908D4—21no—
909D4—21no—
910D4—42no—
911D4—42no—
912D4—42no—
913D4—42no—
914D4—44no—
915D4—41no—
916D4—41no—
917D4—41no—
918D4—41no—
919D4—81no—
920D4—82no—
921D4#1451974912yes—
922C2×C4—21no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—21no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—21no—
929C2×C4—21no—
930C2×C4—21no—
931C2×C4—22no—
932C2×C4—21no—
933C2×C4—21no—
934C2×C4—22no—
935C2×C4—21no—
936C2×C4—22no—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—22no—
940C2×C4—21no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—42no—
944C2×C4—42no—
945C2×C4—42no—
946C2×C4—44no—
947C2×C4—44no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—42no—
953C2×C4—82no—
954C2×C4—1222no—
955C2×C4—2441no—
956C2×C4—2441no—
957C2×C4—2442no—
958C2×C4—2441no—
959C2×C4—2441no—
960C2×C4—2441no—
961C2×C4—2441no—
962C2×C4—2441no—
963C2×C4—2441no—
964C2×C4—2441no—
965C2×C4#1451974611yescharacteristic
966C2×C4#1451974611yescharacteristic
967C2×C4C2×D4×D6111yescharacteristic
968C2×C4C22×C22⋊D6111yescharacteristic
969C2×C4C22×C22⋊D6111yescharacteristic
970C2×C4C2×#1175822411yescharacteristic
971C2×C4#1451982211yescharacteristic
972C2×C4#1451982211yescharacteristic
973C8—1222no—
974C8—2441no—
975C8—2441no—
976C8—2441no—
977C22—21no—
978C22—21no—
979C22—21no—
980C22—21no—
981C22—21no—
982C22—21no—
983C22—21no—
984C22—21no—
985C22—22no—
986C22—41no—
987C22—41no—
988C22—41no—
989C22—41no—
990C22—41no—
991C22—41no—
992C22—41no—
993C22—41no—
994C22—81no—
995C22—81no—
996C22—84no—
997C22C2×#1451974611yescharacteristic
998C22D4×C22⋊D6111yescharacteristic
999C22#1684040611yescharacteristic
1000C4—21no—
1001C4—21no—
1002C4—22no—
1003C4—41no—
1004C4—42no—
1005C4—41no—
1006C4—42no—
1007C4—41no—
1008C4—41no—
1009C4—4881no—
1010C4—4881no—
1011C4—4881no—
1012C4—2442no—
1013C4C2×#1451974911yescharacteristic
1014C4#1684032111yescharacteristic
1015C4D4×C22⋊D6111yescharacteristic
1016C4#1684040611yescharacteristic
1017C2—21no—
1018C2—21no—
1019C2—41no—
1020C2—41no—
1021C2—42no—
1022C2—81no—
1023C2—81no—
1024C2#2144919311yescharacteristic
1025C2#2145518311yescharacteristic
1026C2#2145519811yescharacteristic
subgroupG/H
centerC22C2×#14519746
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
Fitting, prime radicalC61×#3489C2
socleC22×C61C2×#120
hypercenter#3489D61
hypocenterC61#24470
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3489

Complements

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

NH ≅ G/Ntype
1. #21455451C2semidirect
2. C2×#16839945C2semidirect
3. #21455079C2semidirect
4. C2×#16839779C2semidirect
5. #21451589C2semidirect
6. #21447045C2semidirect
7. #21447033C2semidirect
8. #21446866C2semidirect
9. #21446853C2semidirect
10. #21446288C2semidirect
11. #21446268C2semidirect
12. #21446188C2semidirect
13. #21446052C2semidirect
14. #21445778C2semidirect
18. C2×#14519807C22semidirect
20. C2×#14519775C22semidirect
32. #16839805C22semidirect
38. C2×#14519704C22semidirect
39. C2×#14519704C22semidirect
40. #16839770C22semidirect
43. #16839763C22semidirect
44. C2×#14519696C22semidirect
45. C2×#14519696C22semidirect
49. #16839669C22semidirect
50. #16839667C22semidirect
51. #16839627C22semidirect
52. #16839531C22semidirect
53. #16839531C22semidirect
54. #16839521C22semidirect
55. #16839521C22semidirect
117. #14519704D4semidirect
586. C61#24470semidirect

Maximal subgroups

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

subgroupindex
#214554512
C2×#168399452
#214550792
C2×#168397792
#214515892
#214470452
#214470332
#214468662
#214468532
#214462882
#214462682
#214461882
#214460522
#214457782
C61×#34892
#2447061