Finite Group Databasebeta

← #29695537

Subgroups — #29695537

Order 15616.

1530 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840432C211yesmaximal, characteristic
2C2×#16839835C211yesmaximal, characteristic, complemented
3C2×#16839760C211yesmaximal, characteristic, complemented
4C2×#16839755C211yesmaximal, characteristic, complemented
5#21448745C211yesmaximal, characteristic, complemented
6#21446747C211yesmaximal, characteristic, complemented
7#21446254C211yesmaximal, characteristic, complemented
8#21446244C211yesmaximal, characteristic, complemented
9#21446138C211yesmaximal, characteristic, complemented
10#21446133C211yesmaximal, characteristic, complemented
11#21445831C211yesmaximal, characteristic, complemented
12#21445756C211yesmaximal, characteristic, complemented
13#21445756C211yesmaximal, characteristic, complemented
14#21445650C211yesmaximal, characteristic, complemented
15C61×#1961C211yesmaximal, characteristic, complemented
16C22×#11758224C2211yescharacteristic
17C22×#11758224C2211yescharacteristic
18C22×#11758189C2211yescharacteristic
19C22×C8×D61C2211yescharacteristic
20#16840432—24no—
21#16840432C418yescomplemented
22C2×#14519773—21no—
23C2×#14519749—21no—
24C2×#14519749—21no—
25C2×#14519748C2211yescharacteristic
26C2×#14519748C2211yescharacteristic
27C2×C4×Dic122C2211yescharacteristic
28C2×C4×D244C2211yescharacteristic
29C2×D4×Dic61—21no—
30C2×#14519735C2211yescharacteristic
31C2×C4⋊C4×D61C2211yescharacteristic
32#16839835—24no—
33C2×C4⋊#92418C2211yescharacteristic
34#16839760—24no—
35#16839755—24no—
36C2×#14519702C2211yescharacteristic
37C2×#14519702C2211yescharacteristic
38C2×#14519700C2211yescharacteristic
39C2×#14519700C2211yescharacteristic
40C2×#14519698C2211yescharacteristic
41C2×#14519698C2211yescharacteristic
42C2×#14519698C2211yescharacteristic
43C2×#14519698C2211yescharacteristic
44C2×#14519689C2211yescharacteristic
45C2×#14519689C2211yescharacteristic
46#16839651—21no—
47#16839645—21no—
48#16839640—21no—
49#16839619C2211yescharacteristic
50#16839619C2211yescharacteristic
51C4×C4⋊Dic61C2211yescharacteristic
52#16839609—21no—
53#16839525C2211yescharacteristic
54#16839525C2211yescharacteristic
55#16839524C2211yescharacteristic
56#16839524C2211yescharacteristic
57C2×#127×C61C2211yescharacteristic
58C2×#102×C61C2211yescharacteristic
59C2×#102×C61C2211yescharacteristic
60C2×#102×C61C2211yescharacteristic
61C2×#102×C61C2211yescharacteristic
62C2×#97×C61C2211yescharacteristic
63C61×#382C2211yescharacteristic
64C2×#11758224—22no—
65C2×#11758224—22no—
66C2×#11758224—22no—
67C2×#11758224—22no—
68C2×#11758224—22no—
69C2×#11758224—22no—
70C2×#11758224—41no—
71C2×#11758224—41no—
72C2×#11758224—41no—
73C2×#11758224—41no—
74C2×#11758224C2×C414yes—
75C2×#11758224C2×C414yescomplemented
76C22×Dic122C2311yescharacteristic
77C22×D244D411yescharacteristic
78C22×C22⋊D61—21no—
79C22×C22⋊D61—21no—
80C22×C22⋊D61—21no—
81C22×C22⋊D61—21no—
82C23×Dic61—21no—
83C23×Dic61—21no—
84C22×C4×D61—21no—
85C22×C4×D61C2311yescharacteristic
86C22×C4×D61C2311yescharacteristic
87C2×#11758189—22no—
88C2×#11758189—22no—
89C2×#11758189—41no—
90C22×#92418C2311yescharacteristic
91C22×#92418C2311yescharacteristic
92C2×C8×D61—22no—
93C2×C8×D61—22no—
94C2×C8×D61—41no—
95#14519773—28no—
96#14519749—28no—
97#14519749—28no—
98#14519748—22no—
99#14519748—22no—
100#14519748C2×C414yes—
101#14519748C2×C414yescomplemented
102C4×Dic122—22no—
103C4×Dic122C2×C414yescomplemented
104C4×D244C2×C414yes—
105C4×D244D414yes—
106D4×Dic61—28no—
107#14519735—22no—
108#14519735—41no—
109C2×C4⋊Dic61D411yescharacteristic
110C2×C4⋊Dic61C2311yescharacteristic
111C2×C4⋊Dic61C2311yescharacteristic
112C2×C4⋊Dic61C2311yescharacteristic
113C2×#11758196—21no—
114C2×#11758196—21no—
115C4⋊C4×D61—22no—
116C4⋊C4×D61—41no—
117C2×C22⋊Dic61—21no—
118C2×C22⋊Dic61—21no—
119C2×#11758198—21no—
120C2×#11758198—21no—
121C2×#11758198—21no—
122C2×#11758198D411yescharacteristic
123C2×#11758198D411yescharacteristic
124C2×C4×Dic61—21no—
125C2×C4×Dic61—21no—
126C2×C4×Dic61—21no—
127C4⋊#92418—22no—
128#14519702—22no—
129#14519702D414yescomplemented
130#14519700—22no—
131#14519700—22no—
132#14519698—22no—
133#14519698—22no—
134#14519698—41no—
135#14519698—41no—
136#14519689—22no—
137#14519689—22no—
138#14519684—21no—
139#14519684—21no—
140#14519684—21no—
141C22×D4×C61—21no—
142C22×D4×C61—21no—
143C22×D4×C61C2311yescharacteristic
144C22×D4×C61C2311yescharacteristic
145C22×C8×C61C2311yescharacteristic
146C22×C8×C61C2311yescharacteristic
147#127×C61—22no—
148#127×C61C2×C414yescomplemented
149C2×C4⋊C4×C61C2311yescharacteristic
150C2×C4⋊C4×C61C2311yescharacteristic
151C2×C42×C61C2311yescharacteristic
152#102×C61—22no—
153#102×C61—22no—
154#102×C61—41no—
155#102×C61—41no—
156#97×C61—22no—
157#95×C61—21no—
158#95×C61—21no—
159C24×C61—21no—
160C24×C61—21no—
161C23×D61C2×D411yescharacteristic
162C23×D61C2×D411yescharacteristic
163C2×D4×C61—24no—
164C2×D4×C61—24no—
165C2×D4×C61—21no—
166C2×D4×C61—21no—
167C2×D4×C61—21no—
168C2×D4×C61—21no—
169C2×D4×C61—21no—
170C2×D4×C61—21no—
171C2×D4×C61—21no—
172C2×D4×C61—21no—
173C2×D4×C61—21no—
174C2×D4×C61—21no—
175C2×D4×C61—42no—
176C2×D4×C61—42no—
177C2×D4×C61—81no—
178C2×D4×C61—81no—
179C2×D4×C61C22×C412yes—
180C2×D4×C61C22×C412yes—
181C22×C4×C61—21no—
182C22×C4×C61—21no—
183C22×C4×C61C2×D411yescharacteristic
184C22×C4×C61C2×D411yescharacteristic
185C22×C4×C61C2411yescharacteristic
186C2×C22⋊D61—24no—
187C2×C22⋊D61—24no—
188C2×C22⋊D61—24no—
189C2×C22⋊D61—24no—
190C2×C22⋊D61—42no—
191C2×C22⋊D61—42no—
192C2×C22⋊D61—42no—
193C2×C22⋊D61—42no—
194C2×C22⋊D61—81no—
195C2×C22⋊D61—81no—
196C2×C22⋊D61—81no—
197C2×C22⋊D61—81no—
198C22×Dic61—21no—
199C22×Dic61—21no—
200C22×Dic61—21no—
201C22×Dic61—24no—
202C22×Dic61—24no—
203C22×Dic61—21no—
204C22×Dic61—42no—
205C22×Dic61—42no—
206C22×Dic61—42no—
207C22×Dic61—42no—
208C22×Dic61C2×D411yescharacteristic
209C22×Dic61C2×D411yescharacteristic
210#11758224—28no—
211#11758224—28no—
212#11758224—44no—
213#11758224—44no—
214#11758224—44no—
215#11758224—44no—
216#11758224—44no—
217#11758224—44no—
218C2×D244—41no—
219C2×D244—41no—
220C2×D244C22⋊C414yes—
221C2×C4×D61—21no—
222C2×C4×D61—21no—
223C2×C4×D61—21no—
224C2×C4×D61—21no—
225C2×C4×D61—21no—
226C2×C4×D61—21no—
227C2×C4×D61—21no—
228C2×C4×D61—21no—
229C2×C4×D61—42no—
230C2×C4×D61—42no—
231C2×C4×D61—81no—
232C2×C4×D61C22×C412yes—
233C2×C4×D61C22×C412yes—
234C2×C4×D61C2×D412yes—
235C2×C4×D61C2×D412yes—
236C2×Dic122—21no—
237C2×Dic122—21no—
238C2×Dic122—21no—
239C2×Dic122C22×C412yes—
240C2×Dic122C2×D412yes—
241C2×Dic122#4112yes—
242C2×C8×C61—21no—
243C2×C8×C61—21no—
244C2×C8×C61—21no—
245C2×C8×C61—21no—
246C2×C8×C61—21no—
247C2×C8×C61C2×D412yes—
248C4⋊C4×C61—21no—
249C4⋊C4×C61—21no—
250C4⋊C4×C61—21no—
251C4⋊C4×C61—21no—
252C42×C61C22×C412yes—
253C42×C61C2×D412yes—
254C22⋊Dic61—24no—
255C22⋊Dic61—24no—
256#11758198—42no—
257#11758198—42no—
258#11758198—81no—
259#11758198C22⋊C414yes—
260#11758198C22⋊C414yes—
261C4⋊Dic61—21no—
262C4⋊Dic61—21no—
263C4⋊Dic61—21no—
264C4⋊Dic61—21no—
265C4⋊Dic61C22⋊C414yes—
266C4⋊Dic61C22×C412yes—
267C4⋊Dic61C2×D412yes—
268#11758196—24no—
269#11758196—42no—
270C4×Dic61—24no—
271C4×Dic61—42no—
272C4×Dic61—81no—
273C2×#92418—21no—
274C2×#92418—21no—
275C2×#92418—21no—
276C2×#92418—21no—
277C2×#92418—21no—
278C2×#92418—21no—
279#11758189—44no—
280C8×D61—44no—
281C23×C61—22no—
282C23×C61—22no—
283C23×C61—41no—
284C23×C61—41no—
285C23×C61—41no—
286C23×C61—41no—
287C23×C61—41no—
288C23×C61—41no—
289C23×C61—41no—
290C23×C61—41no—
291C23×C61—41no—
292C23×C61—41no—
293C23×C61—41no—
294C23×C61—41no—
295C23×C61C22×D411yescharacteristic
296C22×D61—21no—
297C22×D61—21no—
298C22×D61—21no—
299C22×D61—21no—
300C22×D61—21no—
301C22×D61—21no—
302C22×D61—21no—
303C22×D61—21no—
304C22×D61—21no—
305C22×D61—21no—
306C22×D61—21no—
307C22×D61—21no—
308C22×D61C2×C22⋊C412yes—
309C22×D61C2×C22⋊C412yes—
310D4×C61—22no—
311D4×C61—22no—
312D4×C61—22no—
313D4×C61—22no—
314D4×C61—48no—
315D4×C61—41no—
316D4×C61—41no—
317D4×C61—41no—
318D4×C61—41no—
319D4×C61—84no—
320C2×C4×C61—21no—
321C2×C4×C61—21no—
322C2×C4×C61—21no—
323C2×C4×C61—21no—
324C2×C4×C61—41no—
325C2×C4×C61—41no—
326C2×C4×C61—41no—
327C2×C4×C61—41no—
328C2×C4×C61—41no—
329C2×C4×C61—41no—
330C2×C4×C61C2×C22⋊C412yes—
331C2×C4×C61C2×C22⋊C412yes—
332C2×C4×C61C23×C411yescharacteristic
333C2×C4×C61C22×D411yescharacteristic
334C2×C4×C61C22×D411yescharacteristic
335C2×C4×C61C2×#4111yescharacteristic
336C2×C4×C61H(5,𝔽2)11yescharacteristic
337C2×C4×C61H(5,𝔽2)11yescharacteristic
338C22⋊D61—48no—
339C22⋊D61—48no—
340C22⋊D61—84no—
341C22⋊D61—84no—
342C2×Dic61—22no—
343C2×Dic61—21no—
344C2×Dic61—21no—
345C2×Dic61—22no—
346C2×Dic61—22no—
347C2×Dic61—21no—
348C2×Dic61—21no—
349C2×Dic61—22no—
350C2×Dic61—22no—
351C2×Dic61—48no—
352C2×Dic61—48no—
353C2×Dic61—41no—
354C2×Dic61—41no—
355C2×Dic61—41no—
356C2×Dic61—41no—
357C2×Dic61—41no—
358C2×Dic61—41no—
359C2×Dic61—41no—
360C2×Dic61C2×C22⋊C412yes—
361C2×Dic61C2×C22⋊C412yes—
362D244—44no—
363C4×D61—22no—
364C4×D61—22no—
365C4×D61—22no—
366C4×D61—22no—
367C4×D61—22no—
368C4×D61—22no—
369C4×D61—22no—
370C4×D61—22no—
371C4×D61—84no—
372Dic122—22no—
373Dic122—22no—
374Dic122—22no—
375Dic122C4×D414yes—
376C8×C61—22no—
377C8×C61—41no—
378#92418—41no—
379#92418—41no—
380#22422—611nomaximal, Sylow
381C22×C61—42no—
382C22×C61—42no—
383C22×C61—42no—
384C22×C61—42no—
385C22×C61—42no—
386C22×C61—42no—
387C22×C61—81no—
388C22×C61—81no—
389C22×C61—81no—
390C22×C61—81no—
391C22×C61—81no—
392C22×C61—81no—
393C22×C61—81no—
394C22×C61—81no—
395C22×C61C22×C22⋊C411yescharacteristic
396C22×C61D4211yescharacteristic
397C22×C61#54611yescharacteristic
398C22×C61#57511yescharacteristic
399C22×C61#57511yescharacteristic
400C22×C61#57611yescharacteristic
401C22×C61#57711yescharacteristic
402C2×D61—22no—
403C2×D61—22no—
404C2×D61—22no—
405C2×D61—22no—
406C2×D61—22no—
407C2×D61—22no—
408C2×D61—41no—
409C2×D61—41no—
410C2×D61—41no—
411C2×D61—41no—
412C2×D61—41no—
413C2×D61—41no—
414C2×D61—41no—
415C2×D61—41no—
416C4×C61—22no—
417C4×C61—22no—
418C4×C61—81no—
419C4×C61—81no—
420C4×C61C2×C4×D411yescharacteristic
421C4×C61#51811yescharacteristic
422C4×C61D4211yescharacteristic
423C4×C61#54611yescharacteristic
424Dic61—24no—
425Dic61—22no—
426Dic61—22no—
427Dic61—42no—
428Dic61—42no—
429Dic61—81no—
430C2×#550—611no—
431C2×#435—611no—
432C2×#417—611no—
433C2×#416—611no—
434#2352—611no—
435#1982—611no—
436#1961D6111yescharacteristic, complemented
437#1895—611no—
438#1893—611no—
439#1875—611no—
440#1874—611no—
441#1805—611no—
442#1788—611no—
443#1788—611no—
444#1763—611no—
445C2×C61—82no—
446C2×C61—82no—
447C2×C61D4×C22⋊C411yescharacteristic
448C2×C61#289611yescharacteristic
449C2×C61#289711yescharacteristic
450C2×C61#326811yescharacteristic
451C2×C61#327111yescharacteristic
452C2×C61#330911yescharacteristic
453C2×C61#331711yescharacteristic
454D61—42no—
455D61—42no—
456C22×#41—611no—
457C22×#41—611no—
458C22×M16—611no—
459C23×C8—611no—
460#550—618no—
461#550—1224no—
462C2×#127—1221no—
463C2×#127C2×D6111yescharacteristic
464C2×#121—611no—
465C2×#121—611no—
466C2×#121—1221no—
467C2×#121—1221no—
468C2×C4×Q8—611no—
469C2×C4×D4—611no—
470C2×C4×D4—1221no—
471C2×#117—611no—
472C22×C4⋊C4—611no—
473#435—1224no—
474C2×C4⋊C8—611no—
475#417—1224no—
476#416—1224no—
477C2×#103—611no—
478C2×#103—611no—
479C2×#103—611no—
480C2×#103—611no—
481C2×#102—611no—
482C2×#102—611no—
483C2×#102—611no—
484C2×#102—611no—
485C2×#102C2×D6111yescharacteristic
486C2×#102C2×D6111yescharacteristic
487C2×#102C2×D6111yescharacteristic
488C2×#102C2×D6111yescharacteristic
489C2×C22⋊C8—611no—
490C2×C22⋊C8—611no—
491C2×#97C2×D6111yescharacteristic
492#388—1221no—
493#387—1221no—
494#386—1221no—
495#382C2×D6111yescharacteristic
496#380—611no—
497#380—611no—
498C4×C4⋊C4—611no—
499C4×C22⋊C4—1221no—
500#340—611no—
501#340—611no—
502#340—611no—
503#340—611no—
504C61#2242211yescharacteristic, complemented, Sylow
505C2×#41—614no—
506C2×#41—614no—
507C2×#41—1222no—
508C2×#41—1222no—
509C2×#41—1222no—
510C2×#41—1222no—
511C2×#41—1222no—
512C2×#41—1222no—
513C2×#41—2441no—
514C2×#41—2441no—
515C2×#41—2441no—
516C2×#41—2441no—
517C22×Q8—611no—
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—611no—
521C22×D4—1221no—
522C22×D4—1221no—
523C22×D4—1221no—
524C22×D4—1221no—
525C22×D4C22×D6111yescharacteristic
526C22×D4C22×D6111yescharacteristic
527C23×C4—611no—
528C23×C4—611no—
529C23×C4—1221no—
530C23×C4—1221no—
531C23×C4—1221no—
532C2×M16—1222no—
533C2×M16—1222no—
534C2×M16—2441no—
535C22×C8—611no—
536C22×C8—611no—
537C22×C8—1222no—
538C22×C8—1222no—
539C22×C8—2441no—
540C22×C8C22×D6111yescharacteristic
541C22×C8C22×D6111yescharacteristic
542#127—22no—
543#127—1228no—
544#127C4×D6114yescomplemented
545#121—614no—
546#121—614no—
547#121—1228no—
548#121—1228no—
549#121—1222no—
550#121—1222no—
551C4×Q8—614no—
552C4×Q8—1222no—
553C4×D4—614no—
554C4×D4—614no—
555C4×D4—1228no—
556#117—1222no—
557#117—2441no—
558C2×C4⋊C4—611no—
559C2×C4⋊C4—611no—
560C2×C4⋊C4—611no—
561C2×C4⋊C4—611no—
562C2×C4⋊C4—1222no—
563C2×C4⋊C4—1221no—
564C2×C4⋊C4—1221no—
565C2×C4⋊C4—2441no—
566C2×C4⋊C4C22×D6111yescharacteristic
567C2×C4⋊C4C22×D6111yescharacteristic
568C2×C22⋊C4—611no—
569C2×C22⋊C4—611no—
570C2×C22⋊C4—1221no—
571C2×C22⋊C4—1221no—
572C2×C22⋊C4—1221no—
573C2×C22⋊C4—1221no—
574C2×C22⋊C4—1221no—
575C2×C42—1221no—
576C2×C42—1221no—
577C2×C42—1221no—
578C2×C42C22×D6111yescharacteristic
579C4⋊C8—1222no—
580#103—614no—
581#103—1222no—
582#103—1222no—
583#103—1222no—
584#102—22no—
585#102—22no—
586#102—41no—
587#102—41no—
588#102—1222no—
589#102—1222no—
590#102—2441no—
591#102—2441no—
592C22⋊C8—1222no—
593C22⋊C8—1222no—
594#97—22no—
595#95—21no—
596#95—21no—
597#95—1221no—
598#95—1221no—
599#95—1221no—
600C24—21no—
601C24—21no—
602C24—611no—
603C24—611no—
604#41—1228no—
605#41—1228no—
606#41—2444no—
607#41—2444no—
608#41—2444no—
609#41—2444no—
610#41—2444no—
611#41—2444no—
612C2×Q8—612no—
613C2×Q8—612no—
614C2×Q8—612no—
615C2×Q8—1221no—
616C2×Q8—1221no—
617C2×Q8—1221no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—24no—
629C2×D4—24no—
630C2×D4—42no—
631C2×D4—42no—
632C2×D4—81no—
633C2×D4—81no—
634C2×D4—614no—
635C2×D4—1224no—
636C2×D4—1224no—
637C2×D4—1224no—
638C2×D4—1224no—
639C2×D4—4881no—
640C2×D4—4881no—
641C2×D4—4881no—
642C2×D4—4881no—
643C2×D4—2441no—
644C2×D4—2441no—
645C2×D4—2442no—
646C2×D4—2442no—
647C2×D4—2442no—
648C2×D4—2442no—
649C2×D4C2×C4×D6112yes—
650C2×D4C2×C4×D6112yes—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—611no—
654C22×C4—611no—
655C22×C4—612no—
656C22×C4—612no—
657C22×C4—612no—
658C22×C4—612no—
659C22×C4—1224no—
660C22×C4—1224no—
661C22×C4—1221no—
662C22×C4—1221no—
663C22×C4—1221no—
664C22×C4—1221no—
665C22×C4—1221no—
666C22×C4—1221no—
667C22×C4—1221no—
668C22×C4—1221no—
669C22×C4—1221no—
670C22×C4—1221no—
671C22×C4—1221no—
672C22×C4—1221no—
673C22×C4—4881no—
674C22×C4—2442no—
675C22×C4—2442no—
676C22×C4—2442no—
677C22×C4—2442no—
678C22×C4—2442no—
679C22×C4—2442no—
680C22×C4D4×D6111yescharacteristic
681C22×C4D4×D6111yescharacteristic
682C22×C4C23×D6111yescharacteristic
683M16—2444no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—1221no—
690C2×C8—1221no—
691C2×C8—1221no—
692C2×C8—1221no—
693C2×C8—1221no—
694C2×C8—1221no—
695C2×C8—2444no—
696C2×C8D4×D6112yes—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—614no—
702C4⋊C4—612no—
703C4⋊C4—612no—
704C4⋊C4—1221no—
705C4⋊C4—1221no—
706C4⋊C4—1224no—
707C4⋊C4—1221no—
708C4⋊C4—1221no—
709C4⋊C4—2442no—
710C22⋊C4—614no—
711C22⋊C4—614no—
712C22⋊C4—1224no—
713C22⋊C4—1224no—
714C22⋊C4—4881no—
715C22⋊C4—2442no—
716C22⋊C4—2442no—
717C42—1224no—
718C42—4881no—
719C42—2442no—
720C42C2×C4×D6112yes—
721C42D4×D6112yes—
722C23—22no—
723C23—22no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—612no—
737C23—612no—
738C23—1221no—
739C23—1221no—
740C23—1221no—
741C23—1221no—
742C23—1221no—
743C23—1221no—
744C23—1221no—
745C23—1221no—
746C23—1221no—
747C23—1221no—
748C23—1221no—
749C23—1221no—
750C23C2×D4×D6111yescharacteristic
751Q8—614no—
752Q8—1222no—
753Q8—1222no—
754Q8—1222no—
755D4—22no—
756D4—22no—
757D4—22no—
758D4—22no—
759D4—48no—
760D4—41no—
761D4—41no—
762D4—41no—
763D4—41no—
764D4—84no—
765D4—4884no—
766D4—4884no—
767D4—2444no—
768D4—2448no—
769D4—2448no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—612no—
781C2×C4—612no—
782C2×C4—1222no—
783C2×C4—1221no—
784C2×C4—1221no—
785C2×C4—1222no—
786C2×C4—1221no—
787C2×C4—1221no—
788C2×C4—1222no—
789C2×C4—1222no—
790C2×C4—1222no—
791C2×C4—1222no—
792C2×C4—1222no—
793C2×C4—1222no—
794C2×C4—1222no—
795C2×C4—1222no—
796C2×C4—1222no—
797C2×C4—1222no—
798C2×C4—1222no—
799C2×C4—4884no—
800C2×C4—2448no—
801C2×C4—2448no—
802C2×C4—2441no—
803C2×C4—2441no—
804C2×C4—2441no—
805C2×C4—2441no—
806C2×C4—2441no—
807C2×C4—2441no—
808C2×C4—2441no—
809C2×C4C22⋊C4×D6112yes—
810C2×C4C22⋊C4×D6112yes—
811C2×C4C22×C4×D6111yescharacteristic
812C2×C4C2×D4×D6111yescharacteristic
813C2×C4C2×D4×D6111yescharacteristic
814C2×C4#41×D6111yescharacteristic
815C2×C4#1451982211yescharacteristic
816C2×C4#1451982311yescharacteristic
817C8—22no—
818C8—41no—
819C8—2441no—
820C8—2441no—
821C22—42no—
822C22—42no—
823C22—42no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—81no—
828C22—81no—
829C22—81no—
830C22—81no—
831C22—81no—
832C22—81no—
833C22—81no—
834C22—81no—
835C22—1222no—
836C22—1222no—
837C22—1222no—
838C22—1222no—
839C22—1222no—
840C22—1222no—
841C22—2441no—
842C22—2441no—
843C22—2441no—
844C22—2441no—
845C22—2441no—
846C22—2441no—
847C22—2441no—
848C22—2441no—
849C22C2×C22⋊C4×D6111yescharacteristic
850C22#1684039711yescharacteristic
851C22#1684040511yescharacteristic
852C22#1684055811yescharacteristic
853C22#1684055811yescharacteristic
854C22#1684056611yescharacteristic
855C22#1684057211yescharacteristic
856C4—22no—
857C4—22no—
858C4—81no—
859C4—81no—
860C4—1222no—
861C4—1222no—
862C4—1224no—
863C4—4881no—
864C4—2442no—
865C4—2442no—
866C4C4×D4×D6111yescharacteristic
867C4#1684023411yescharacteristic
868C4#1684039611yescharacteristic
869C4#1684040911yescharacteristic
870C2—82no—
871C2—82no—
872C2—2442no—
873C2—2442no—
874C2#2144864011yescharacteristic
875C2#2145433311yescharacteristic
876C2#2145434411yescharacteristic
877C2#2145735811yescharacteristic
878C2#2145740311yescharacteristic
879C2#2145782411yescharacteristic
880C2#2145794411yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1961C2
socleC23×C61C22×D4
prime radicalC2×#16840432C2
cosocleC22×C4×C61C24
hypercenter#1961D61
hypocenterC61#22422
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1961

Complements

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

NH ≅ G/Ntype
2. C2×#16839835C2semidirect
3. C2×#16839760C2semidirect
4. C2×#16839755C2semidirect
5. #21448745C2semidirect
6. #21446747C2semidirect
7. #21446254C2semidirect
8. #21446244C2semidirect
9. #21446138C2semidirect
10. #21446133C2semidirect
11. #21445831C2semidirect
12. #21445756C2semidirect
13. #21445756C2semidirect
14. #21445650C2semidirect
15. C61×#1961C2semidirect
21. #16840432C4semidirect
75. C2×#11758224C2×C4semidirect
101. #14519748C2×C4semidirect
103. C4×Dic122C2×C4semidirect
129. #14519702D4semidirect
148. #127×C61C2×C4semidirect
436. #1961D61semidirect
504. C61#22422semidirect
544. #127C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168404322
C2×#168398352
C2×#168397602
C2×#168397552
#214487452
#214467472
#214462542
#214462442
#214461382
#214461332
#214458312
#214457562
#214456502
C61×#19612
#2242261