Finite Group Databasebeta

← #29717739

Subgroups — #29717739

Order 15616.

1550 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839996C211yesmaximal, characteristic, complemented
2C2×#16839907C211yesmaximal, characteristic, complemented
3C2×#16839907C211yesmaximal, characteristic, complemented
4C2×#16839758C211yesmaximal, characteristic, complemented
5#21449237C211yesmaximal, characteristic, complemented
6#21447050C211yesmaximal, characteristic, complemented
7#21446998C211yesmaximal, characteristic, complemented
8#21446890C211yesmaximal, characteristic, complemented
9#21446815C211yesmaximal, characteristic, complemented
10#21446174C211yesmaximal, characteristic, complemented
11#21446142C211yesmaximal, characteristic, complemented
12#21446112C211yesmaximal, characteristic, complemented
13#21446073C211yesmaximal, characteristic, complemented
14#21445759C211yesmaximal, characteristic, complemented
15C2×C61×#550C211yesmaximal, characteristic, complemented
16C22×#11758201C2211yescharacteristic
17C22×#11758199C2211yescharacteristic
18C22×#11758199C2211yescharacteristic
19C23×#92418C2211yescharacteristic
20C2×#14519751C2211yescharacteristic
21C2×#14519751C2211yescharacteristic
22C2×#14519736C2211yescharacteristic
23#16839996—24no—
24#16839907—24no—
25#16839907—24no—
26C2×#14519710C2211yescharacteristic
27#16839758—24no—
28C2×#14519701C2211yescharacteristic
29C2×#14519701C2211yescharacteristic
30C2×#14519701C2211yescharacteristic
31C2×#14519698C2211yescharacteristic
32C2×#14519698C2211yescharacteristic
33C2×#14519698C2211yescharacteristic
34C2×#14519698C2211yescharacteristic
35C2×#14519698C2211yescharacteristic
36C2×#14519698C2211yescharacteristic
37C2×#14519697C2211yescharacteristic
38C2×C22⋊#92418C2211yescharacteristic
39C2×C22⋊#92418C2211yescharacteristic
40C2×C22⋊#92418C2211yescharacteristic
41#16839677—21no—
42#16839670—21no—
43#16839664C2211yescharacteristic
44#16839662—21no—
45#16839660C2211yescharacteristic
46#16839652—21no—
47#16839622C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839517C2211yescharacteristic
51#16839517C2211yescharacteristic
52C22×#41×C61C2211yescharacteristic
53C22×#41×C61C2211yescharacteristic
54C61×#550—24no—
55C61×#550—24no—
56C2×#127×C61—21no—
57C2×#127×C61C2211yescharacteristic
58C2×#121×C61—21no—
59C2×#121×C61—21no—
60C2×#121×C61C2211yescharacteristic
61C2×#121×C61C2211yescharacteristic
62C2×C4×Q8×C61C2211yescharacteristic
63C2×C4×D4×C61—21no—
64C2×C4×D4×C61C2211yescharacteristic
65C22×D244C2311yescharacteristic
66C22×C22⋊D61—21no—
67C22×C22⋊D61—21no—
68C2×#11758201—22no—
69C2×#11758201—22no—
70C2×#11758201—22no—
71C2×#11758199—22no—
72C2×#11758199—22no—
73C2×#11758199—22no—
74C2×#11758199—41no—
75C2×#11758199—41no—
76C2×#11758199—41no—
77C22×#92418—22no—
78C22×#92418—22no—
79C22×#92418—41no—
80C22×#92418C2311yescharacteristic
81C22×#92418C2311yescharacteristic
82C22×#92418C2311yescharacteristic
83C22×#92418C2311yescharacteristic
84#14519751—22no—
85#14519751—22no—
86#14519751—22no—
87#14519751—41no—
88#14519736—22no—
89#14519736—41no—
90C2×C4⋊Dic61C2311yescharacteristic
91C2×C4⋊Dic61C2311yescharacteristic
92C2×C4⋊Dic61C2311yescharacteristic
93C2×#11758196—21no—
94C2×C22⋊Dic61—21no—
95C2×C22⋊Dic61—21no—
96C2×#11758198—21no—
97C2×#11758198—21no—
98C2×#11758198—21no—
99C2×#11758198—21no—
100C2×C4×Dic61—21no—
101#14519710—22no—
102#14519701—22no—
103#14519701—22no—
104#14519701D414yescomplemented
105#14519698—22no—
106#14519698—22no—
107#14519698—22no—
108#14519698—22no—
109#14519698—22no—
110#14519698—41no—
111#14519697—22no—
112C22⋊#92418—22no—
113C22⋊#92418—22no—
114C22⋊#92418—41no—
115#14519684—21no—
116#14519684—21no—
117C2×#41×C61—22no—
118C2×#41×C61—22no—
119C2×#41×C61—22no—
120C2×#41×C61—22no—
121C2×#41×C61—22no—
122C2×#41×C61—22no—
123C2×#41×C61—22no—
124C2×#41×C61—41no—
125C2×#41×C61—41no—
126C2×#41×C61—41no—
127C2×#41×C61—41no—
128C2×#41×C61D414yescomplemented
129C22×Q8×C61C2311yescharacteristic
130C22×D4×C61—21no—
131C22×D4×C61—21no—
132C22×D4×C61—21no—
133C22×D4×C61—21no—
134C22×D4×C61—21no—
135C22×D4×C61—21no—
136C22×D4×C61D411yescharacteristic
137C22×D4×C61C2311yescharacteristic
138C22×D4×C61C2311yescharacteristic
139C23×C4×C61—21no—
140C23×C4×C61—21no—
141C23×C4×C61C2311yescharacteristic
142C23×C4×C61C2311yescharacteristic
143#127×C61—28no—
144#127×C61—22no—
145#127×C61—22no—
146#121×C61—28no—
147#121×C61—28no—
148#121×C61—22no—
149#121×C61—22no—
150#121×C61—22no—
151#121×C61D414yescomplemented
152C4×Q8×C61—22no—
153C4×Q8×C61—22no—
154C4×D4×C61—28no—
155C4×D4×C61—22no—
156C4×D4×C61—22no—
157C2×C4⋊C4×C61—21no—
158C2×C4⋊C4×C61D411yescharacteristic
159C2×C4⋊C4×C61C2311yescharacteristic
160C2×C22⋊C4×C61—21no—
161C2×C22⋊C4×C61—21no—
162C2×C22⋊C4×C61D411yescharacteristic
163C2×C22⋊C4×C61D411yescharacteristic
164C2×C42×C61—21no—
165C2×C42×C61C2311yescharacteristic
166C24×C61—21no—
167C24×C61—21no—
168C24×C61C2×D411yescharacteristic
169C24×C61C2×D411yescharacteristic
170C23×D61—21no—
171#41×C61—28no—
172#41×C61—44no—
173#41×C61—44no—
174#41×C61—44no—
175#41×C61—44no—
176#41×C61—44no—
177#41×C61—44no—
178#41×C61—44no—
179C2×Q8×C61—21no—
180C2×Q8×C61—21no—
181C2×Q8×C61—21no—
182C2×Q8×C61C2×D412yes—
183C2×Q8×C61C2×D412yes—
184C2×Q8×C61#4112yes—
185C2×D4×C61—24no—
186C2×D4×C61—24no—
187C2×D4×C61—22no—
188C2×D4×C61—24no—
189C2×D4×C61—24no—
190C2×D4×C61—24no—
191C2×D4×C61—24no—
192C2×D4×C61—22no—
193C2×D4×C61—21no—
194C2×D4×C61—21no—
195C2×D4×C61—21no—
196C2×D4×C61—21no—
197C2×D4×C61—21no—
198C2×D4×C61—21no—
199C2×D4×C61—21no—
200C2×D4×C61—21no—
201C2×D4×C61—21no—
202C2×D4×C61—21no—
203C2×D4×C61—41no—
204C2×D4×C61—42no—
205C2×D4×C61—42no—
206C2×D4×C61—42no—
207C2×D4×C61—42no—
208C2×D4×C61—42no—
209C2×D4×C61—42no—
210C2×D4×C61—81no—
211C2×D4×C61—81no—
212C2×D4×C61—81no—
213C2×D4×C61—81no—
214C2×D4×C61—81no—
215C2×D4×C61—81no—
216C2×D4×C61C2×D412yes—
217C2×D4×C61C2×D412yes—
218C22×C4×C61—21no—
219C22×C4×C61—21no—
220C22×C4×C61—21no—
221C22×C4×C61—21no—
222C22×C4×C61—21no—
223C22×C4×C61—24no—
224C22×C4×C61—21no—
225C22×C4×C61—24no—
226C22×C4×C61—21no—
227C22×C4×C61—21no—
228C22×C4×C61—21no—
229C22×C4×C61—21no—
230C22×C4×C61—21no—
231C22×C4×C61—21no—
232C22×C4×C61—42no—
233C22×C4×C61—42no—
234C22×C4×C61—42no—
235C22×C4×C61—42no—
236C22×C4×C61C2×D411yescharacteristic
237C22×C4×C61C2×D411yescharacteristic
238C22×C4×C61C2×D411yescharacteristic
239C22×C4×C61C2×D412yes—
240C22×C4×C61C2×D412yes—
241C22×C4×C61C2×D411yescharacteristic
242C22×C4×C61C2411yescharacteristic
243C2×C22⋊D61—42no—
244C2×C22⋊D61—42no—
245C2×C22⋊D61—42no—
246C2×C22⋊D61—81no—
247C2×C22⋊D61—81no—
248C2×C22⋊D61—81no—
249C22×Dic61—21no—
250C22×Dic61—21no—
251C22×Dic61—21no—
252C2×D244—21no—
253C2×D244—21no—
254C2×D244—21no—
255C2×D244—21no—
256C2×D244—21no—
257C2×D244—21no—
258C4⋊C4×C61—24no—
259C4⋊C4×C61—22no—
260C4⋊C4×C61—21no—
261C4⋊C4×C61C2×D412yes—
262C22⋊C4×C61—24no—
263C22⋊C4×C61—22no—
264C22⋊C4×C61—24no—
265C22⋊C4×C61—22no—
266C42×C61—24no—
267C42×C61—21no—
268C42×C61—21no—
269C22⋊Dic61—42no—
270C22⋊Dic61—81no—
271#11758201—44no—
272#11758199—44no—
273#11758199—44no—
274#11758198—42no—
275#11758198—42no—
276#11758198—42no—
277#11758198—81no—
278C4⋊Dic61—21no—
279C4⋊Dic61—21no—
280C4⋊Dic61—21no—
281C4⋊Dic61—21no—
282C4⋊Dic61—21no—
283C4⋊Dic61C2×D412yes—
284#11758196—81no—
285C4×Dic61—42no—
286C2×#92418—21no—
287C2×#92418—21no—
288C2×#92418—21no—
289C2×#92418—21no—
290C2×#92418—21no—
291C2×#92418—21no—
292C2×#92418—21no—
293C2×#92418—21no—
294C2×#92418—21no—
295C2×#92418—21no—
296C2×#92418—21no—
297C2×#92418—44no—
298C2×#92418C2×D412yes—
299C23×C61—21no—
300C23×C61—21no—
301C23×C61—21no—
302C23×C61—21no—
303C23×C61—21no—
304C23×C61—21no—
305C23×C61—21no—
306C23×C61—22no—
307C23×C61—22no—
308C23×C61—21no—
309C23×C61—21no—
310C23×C61—21no—
311C23×C61—21no—
312C23×C61—21no—
313C23×C61—21no—
314C23×C61—41no—
315C23×C61—41no—
316C23×C61—41no—
317C23×C61—41no—
318C23×C61—41no—
319C23×C61—41no—
320C23×C61—41no—
321C23×C61—41no—
322C23×C61—41no—
323C23×C61—41no—
324C23×C61—41no—
325C23×C61—41no—
326C23×C61#12012yes—
327C23×C61C22×D411yescharacteristic
328C22×D61—41no—
329C22×D61—41no—
330C22×D61—41no—
331C22×D61—41no—
332C22×D61—41no—
333C22×D61—41no—
334C22×D61—41no—
335Q8×C61—22no—
336Q8×C61—22no—
337Q8×C61—22no—
338Q8×C61#12114yes—
339D4×C61—22no—
340D4×C61—22no—
341D4×C61—22no—
342D4×C61—22no—
343D4×C61—44no—
344D4×C61—48no—
345D4×C61—48no—
346D4×C61—48no—
347D4×C61—41no—
348D4×C61—41no—
349D4×C61—41no—
350D4×C61—41no—
351D4×C61—84no—
352D4×C61—84no—
353D4×C61—84no—
354C2×C4×C61—21no—
355C2×C4×C61—22no—
356C2×C4×C61—21no—
357C2×C4×C61—22no—
358C2×C4×C61—21no—
359C2×C4×C61—22no—
360C2×C4×C61—21no—
361C2×C4×C61—22no—
362C2×C4×C61—22no—
363C2×C4×C61—22no—
364C2×C4×C61—22no—
365C2×C4×C61—21no—
366C2×C4×C61—22no—
367C2×C4×C61—21no—
368C2×C4×C61—21no—
369C2×C4×C61—21no—
370C2×C4×C61—21no—
371C2×C4×C61—21no—
372C2×C4×C61—48no—
373C2×C4×C61—48no—
374C2×C4×C61—41no—
375C2×C4×C61—41no—
376C2×C4×C61—41no—
377C2×C4×C61—41no—
378C2×C4×C61—41no—
379C2×C4×C61—41no—
380C2×C4×C61#12012yes—
381C2×C4×C61#13512yes—
382C2×C4×C61C22×D411yescharacteristic
383C2×C4×C61C22×D411yescharacteristic
384C2×C4×C61C22×D411yescharacteristic
385C2×C4×C61C2×#4111yescharacteristic
386C2×C4×C61H(5,𝔽2)11yescharacteristic
387C2×C4×C61H(5,𝔽2)11yescharacteristic
388C22⋊D61—84no—
389C22⋊D61—84no—
390C2×Dic61—22no—
391C2×Dic61—41no—
392C2×Dic61—41no—
393C2×Dic61—41no—
394C2×Dic61—41no—
395C2×Dic61—41no—
396C2×Dic61—41no—
397C2×Dic61—41no—
398C2×Dic61—41no—
399D244—41no—
400D244—41no—
401D244—41no—
402D244—41no—
403#92418—22no—
404#92418—41no—
405#92418—41no—
406#92418—41no—
407#24435—611nomaximal, Sylow
408C22×C61—22no—
409C22×C61—22no—
410C22×C61—22no—
411C22×C61—41no—
412C22×C61—41no—
413C22×C61—41no—
414C22×C61—41no—
415C22×C61—42no—
416C22×C61—42no—
417C22×C61—41no—
418C22×C61—41no—
419C22×C61—42no—
420C22×C61—42no—
421C22×C61—41no—
422C22×C61—42no—
423C22×C61—42no—
424C22×C61—41no—
425C22×C61—41no—
426C22×C61—41no—
427C22×C61—41no—
428C22×C61—81no—
429C22×C61—81no—
430C22×C61—81no—
431C22×C61—81no—
432C22×C61—81no—
433C22×C61—81no—
434C22×C61—81no—
435C22×C61—81no—
436C22×C61C2×#12011yescharacteristic
437C22×C61D4211yescharacteristic
438C22×C61#54611yescharacteristic
439C22×C61C2×#13511yescharacteristic
440C22×C61#57511yescharacteristic
441C22×C61#57611yescharacteristic
442C22×C61#57611yescharacteristic
443C2×D61—81no—
444C2×D61—81no—
445C2×D61—81no—
446C2×D61—81no—
447C2×D61—81no—
448C2×D61—81no—
449C2×D61—81no—
450C4×C61—22no—
451C4×C61—24no—
452C4×C61—22no—
453C4×C61—41no—
454C4×C61—41no—
455C4×C61—42no—
456C4×C61C2×#12111yescharacteristic
457C4×C61#53411yescharacteristic
458C4×C61D4211yescharacteristic
459C4×C61#54611yescharacteristic
460Dic61—42no—
461Dic61—81no—
462Dic61—81no—
463C2×#550D6111yescharacteristic, complemented
464C2×#466—611no—
465C2×#449—611no—
466C2×#449—611no—
467C2×#416—611no—
468#2414—611no—
469#2041—611no—
470#2033—611no—
471#2011—611no—
472#1999—611no—
473#1880—611no—
474#1875—611no—
475#1869—611no—
476#1863—611no—
477#1788—611no—
478C2×C61—42no—
479C2×C61—81no—
480C2×C61—82no—
481C2×C61—82no—
482C2×C61#241011yescharacteristic
483C2×C61#300211yescharacteristic
484C2×C61#300811yescharacteristic
485C2×C61#326811yescharacteristic
486C2×C61#328711yescharacteristic
487C2×C61#330511yescharacteristic
488C2×C61#330911yescharacteristic
489D61—161no—
490C22×#41C2×D6111yescharacteristic
491C22×#41C2×D6111yescharacteristic
492C22×SD16—611no—
493C22×D8—611no—
494C22×D8—611no—
495C23×C8—611no—
496#550—24no—
497#550—24no—
498C2×#127—21no—
499C2×#127C2×D6111yescharacteristic
500C2×#121—21no—
501C2×#121—21no—
502C2×#121—611no—
503C2×#121—611no—
504C2×#121C2×D6111yescharacteristic
505C2×#121C2×D6111yescharacteristic
506C2×C4×Q8C2×D6111yescharacteristic
507C2×C4×D4—21no—
508C2×C4×D4C2×D6111yescharacteristic
509C2×#117—611no—
510#466—1224no—
511#449—1224no—
512#449—1224no—
513C2×#107—611no—
514#416—1224no—
515C2×#103—611no—
516C2×#103—611no—
517C2×#103—611no—
518C2×#102—611no—
519C2×#102—611no—
520C2×#102—611no—
521C2×#102—611no—
522C2×#102—611no—
523C2×#102—611no—
524C2×#102—611no—
525C2×C22⋊C8—611no—
526C2×C22⋊C8—611no—
527C2×C22⋊C8—611no—
528#394—1221no—
529#392—1221no—
530#390—611no—
531#390—1221no—
532#389—611no—
533#388—1221no—
534#380—611no—
535#340—611no—
536#340—611no—
537#336—611no—
538#336—611no—
539C61#2443511yescharacteristic, complemented, Sylow
540C2×#41—22no—
541C2×#41—22no—
542C2×#41—22no—
543C2×#41—22no—
544C2×#41—22no—
545C2×#41—22no—
546C2×#41—22no—
547C2×#41—41no—
548C2×#41—41no—
549C2×#41—41no—
550C2×#41—41no—
551C2×#41C22⋊D6114yescomplemented
552C22×Q8C22×D6111yescharacteristic
553C22×D4—21no—
554C22×D4—21no—
555C22×D4—21no—
556C22×D4—21no—
557C22×D4—21no—
558C22×D4—21no—
559C22×D4—611no—
560C22×D4—1221no—
561C22×D4—1221no—
562C22×D4C22⋊D6111yescharacteristic
563C22×D4C22×D6111yescharacteristic
564C22×D4C22×D6111yescharacteristic
565C23×C4—21no—
566C23×C4—21no—
567C23×C4C22×D6111yescharacteristic
568C23×C4C22×D6111yescharacteristic
569C2×SD16—1222no—
570C2×SD16—1222no—
571C2×SD16—1222no—
572C2×D8—1222no—
573C2×D8—1222no—
574C2×D8—1222no—
575C2×D8—2441no—
576C2×D8—2441no—
577C2×D8—2441no—
578C22×C8—611no—
579C22×C8—611no—
580C22×C8—611no—
581C22×C8—611no—
582C22×C8—1222no—
583C22×C8—1222no—
584C22×C8—2441no—
585#127—28no—
586#127—22no—
587#127—22no—
588#121—28no—
589#121—28no—
590#121—22no—
591#121—22no—
592#121—22no—
593#121—1222no—
594#121—1222no—
595#121—1222no—
596#121—2441no—
597#121C22⋊D6114yescomplemented
598C4×Q8—22no—
599C4×Q8—22no—
600C4×D4—28no—
601C4×D4—22no—
602C4×D4—22no—
603#117—1222no—
604#117—2441no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—611no—
607C2×C4⋊C4—611no—
608C2×C4⋊C4—611no—
609C2×C4⋊C4—1221no—
610C2×C4⋊C4C22⋊D6111yescharacteristic
611C2×C4⋊C4C22×D6111yescharacteristic
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4—1221no—
615C2×C22⋊C4—1221no—
616C2×C22⋊C4—1221no—
617C2×C22⋊C4—1221no—
618C2×C22⋊C4—1221no—
619C2×C22⋊C4—1221no—
620C2×C22⋊C4C22⋊D6111yescharacteristic
621C2×C22⋊C4C22⋊D6111yescharacteristic
622C2×C42—21no—
623C2×C42—1221no—
624C2×C42C22×D6111yescharacteristic
625#107—1222no—
626#103—614no—
627#103—1222no—
628#103—1222no—
629#102—1222no—
630#102—1222no—
631#102—1222no—
632#102—1222no—
633#102—1222no—
634#102—1222no—
635#102—2441no—
636C22⋊C8—1222no—
637C22⋊C8—1222no—
638C22⋊C8—2441no—
639#95—1221no—
640#95—1221no—
641C24—21no—
642C24—21no—
643C24—1221no—
644C24C2×C22⋊D6111yescharacteristic
645C24C2×C22⋊D6111yescharacteristic
646#41—28no—
647#41—44no—
648#41—44no—
649#41—44no—
650#41—44no—
651#41—44no—
652#41—44no—
653#41—44no—
654C2×Q8—21no—
655C2×Q8—21no—
656C2×Q8—21no—
657C2×Q8D4×D6112yes—
658C2×Q8#1175822412yes—
659C2×Q8C2×C22⋊D6112yes—
660C2×D4—24no—
661C2×D4—24no—
662C2×D4—22no—
663C2×D4—24no—
664C2×D4—24no—
665C2×D4—24no—
666C2×D4—24no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—22no—
678C2×D4—41no—
679C2×D4—42no—
680C2×D4—42no—
681C2×D4—42no—
682C2×D4—42no—
683C2×D4—42no—
684C2×D4—42no—
685C2×D4—81no—
686C2×D4—81no—
687C2×D4—81no—
688C2×D4—81no—
689C2×D4—81no—
690C2×D4—81no—
691C2×D4—1221no—
692C2×D4—1221no—
693C2×D4—1221no—
694C2×D4—1221no—
695C2×D4—1221no—
696C2×D4—1221no—
697C2×D4—4881no—
698C2×D4—4881no—
699C2×D4—4881no—
700C2×D4—2442no—
701C2×D4—2442no—
702C2×D4—2442no—
703C2×D4C2×C22⋊D6112yes—
704C2×D4C2×C22⋊D6112yes—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—24no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—24no—
719C22×C4—42no—
720C22×C4—42no—
721C22×C4—42no—
722C22×C4—42no—
723C22×C4—1221no—
724C22×C4—1221no—
725C22×C4—1221no—
726C22×C4C2×C22⋊D6111yescharacteristic
727C22×C4C2×C22⋊D6111yescharacteristic
728C22×C4C2×C22⋊D6112yes—
729C22×C4C2×C22⋊D6112yes—
730C22×C4C2×C22⋊D6111yescharacteristic
731C22×C4C2×C22⋊D6111yescharacteristic
732C22×C4C23×D6111yescharacteristic
733SD16—2444no—
734D8—2444no—
735D8—2444no—
736C2×C8—612no—
737C2×C8—1221no—
738C2×C8—1221no—
739C2×C8—1221no—
740C2×C8—1221no—
741C2×C8—1221no—
742C2×C8—1221no—
743C2×C8—1221no—
744C2×C8—1221no—
745C2×C8—1221no—
746C2×C8—1221no—
747C2×C8—1221no—
748C2×C8—2444no—
749C4⋊C4—24no—
750C4⋊C4—21no—
751C4⋊C4—22no—
752C4⋊C4—612no—
753C4⋊C4—1221no—
754C4⋊C4—1221no—
755C4⋊C4—1221no—
756C4⋊C4—1221no—
757C4⋊C4—1221no—
758C4⋊C4—4881no—
759C4⋊C4C2×C22⋊D6112yes—
760C22⋊C4—24no—
761C22⋊C4—22no—
762C22⋊C4—24no—
763C22⋊C4—22no—
764C22⋊C4—4881no—
765C22⋊C4—4881no—
766C22⋊C4—2442no—
767C22⋊C4—2442no—
768C22⋊C4—2442no—
769C22⋊C4—2442no—
770C42—24no—
771C42—21no—
772C42—21no—
773C42—2442no—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—21no—
779C23—21no—
780C23—21no—
781C23—22no—
782C23—22no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—21no—
788C23—21no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—2441no—
802C23—2441no—
803C23—2441no—
804C23—2441no—
805C23—2441no—
806C23—2441no—
807C23—2441no—
808C23#1451974612yes—
809C23C22×C22⋊D6111yescharacteristic
810Q8—22no—
811Q8—22no—
812Q8—22no—
813Q8#1451974914yes—
814D4—22no—
815D4—22no—
816D4—22no—
817D4—22no—
818D4—44no—
819D4—48no—
820D4—48no—
821D4—48no—
822D4—41no—
823D4—41no—
824D4—41no—
825D4—41no—
826D4—84no—
827D4—84no—
828D4—84no—
829D4—4884no—
830D4—4884no—
831D4—2441no—
832D4—2441no—
833D4—2441no—
834D4—2441no—
835C2×C4—21no—
836C2×C4—22no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—22no—
840C2×C4—21no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—21no—
847C2×C4—22no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—48no—
854C2×C4—48no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—1222no—
862C2×C4—2441no—
863C2×C4—2441no—
864C2×C4—2441no—
865C2×C4—2441no—
866C2×C4—2441no—
867C2×C4—2441no—
868C2×C4—2441no—
869C2×C4—2441no—
870C2×C4#1451974612yes—
871C2×C4#1451979712yes—
872C2×C4C2×D4×D6111yescharacteristic
873C2×C4C22×C22⋊D6111yescharacteristic
874C2×C4C22×C22⋊D6111yescharacteristic
875C2×C4C2×#1175822411yescharacteristic
876C2×C4#1451982211yescharacteristic
877C2×C4#1451982211yescharacteristic
878C8—1222no—
879C8—2441no—
880C8—2441no—
881C8—2441no—
882C22—22no—
883C22—22no—
884C22—22no—
885C22—41no—
886C22—41no—
887C22—41no—
888C22—41no—
889C22—41no—
890C22—41no—
891C22—41no—
892C22—41no—
893C22—42no—
894C22—42no—
895C22—41no—
896C22—42no—
897C22—42no—
898C22—41no—
899C22—41no—
900C22—42no—
901C22—42no—
902C22—81no—
903C22—81no—
904C22—81no—
905C22—81no—
906C22—81no—
907C22—81no—
908C22—81no—
909C22—81no—
910C22—4881no—
911C22—4881no—
912C22—4881no—
913C22—4881no—
914C22—4881no—
915C22—4881no—
916C22—4881no—
917C22C2×#1451974611yescharacteristic
918C22D4×C22⋊D6111yescharacteristic
919C22#1684040611yescharacteristic
920C22C2×#1451979711yescharacteristic
921C22#1684056011yescharacteristic
922C22#1684056511yescharacteristic
923C22#1684056511yescharacteristic
924C4—22no—
925C4—22no—
926C4—24no—
927C4—41no—
928C4—41no—
929C4—42no—
930C4—4881no—
931C4—4881no—
932C4—2442no—
933C4C2×#1451974911yescharacteristic
934C4#1684032111yescharacteristic
935C4D4×C22⋊D6111yescharacteristic
936C4#1684040611yescharacteristic
937C2—42no—
938C2—81no—
939C2—82no—
940C2—82no—
941C2—9761no—
942C2#2144919311yescharacteristic
943C2#2145503711yescharacteristic
944C2#2145508711yescharacteristic
945C2#2145736011yescharacteristic
946C2#2145757511yescharacteristic
947C2#2145776911yescharacteristic
948C2#2145782511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#550C2
socleC23×C61C22×D4
hypercenterC2×#550D61
hypocenterC61#24435
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
1. C2×#16839996C2semidirect
2. C2×#16839907C2semidirect
3. C2×#16839907C2semidirect
4. C2×#16839758C2semidirect
5. #21449237C2semidirect
6. #21447050C2semidirect
7. #21446998C2semidirect
8. #21446890C2semidirect
9. #21446815C2semidirect
10. #21446174C2semidirect
11. #21446142C2semidirect
12. #21446112C2semidirect
13. #21446073C2semidirect
14. #21445759C2semidirect
15. C2×C61×#550C2semidirect
104. #14519701D4semidirect
128. C2×#41×C61D4semidirect
151. #121×C61D4semidirect
463. C2×#550D61semidirect
539. C61#24435semidirect
551. C2×#41C22⋊D61semidirect
597. #121C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168399962
C2×#168399072
C2×#168397582
#214492372
#214470502
#214469982
#214468902
#214468152
#214461742
#214461422
#214461122
#214460732
#214457592
C2×C61×#5502
#2443561