Finite Group Databasebeta

← #29646205

Subgroups — #29646205

Order 15616.

1046 conjugacy classes of subgroups.

The subgroup lattice has 958 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840442C211yesmaximal, characteristic
2#21454478C211yesmaximal, characteristic, complemented
3#21454472C211yesmaximal, characteristic, complemented
4#21444185C211yesmaximal, characteristic, complemented
5#21444185C211yesmaximal, characteristic, complemented
6#21444171C211yesmaximal, characteristic, complemented
7#21444164C211yesmaximal, characteristic, complemented
8#21444164C211yesmaximal, characteristic, complemented
9#21444158C211yesmaximal, characteristic, complemented
10#21444151C211yesmaximal, characteristic, complemented
11#21444144C211yesmaximal, characteristic, complemented
12#21444138C211yesmaximal, characteristic, complemented
13#21444131C211yesmaximal, characteristic, complemented
14#323×D61C211yesmaximal, characteristic, complemented
15C61×#1469C211yesmaximal, characteristic, complemented
16#16840442—21no—
17#16840442—21no—
18#16840442—21no—
19#16840442—21no—
20#16840442—21no—
21#16840442—21no—
22#16840442—21no—
23#16840442—21no—
24C2×#14519770C411yescharacteristic
25C2×#14519770C2211yescharacteristic
26C2×#14519759C411yescharacteristic
27C2×#14519759C2211yescharacteristic
28C2×#14519758C411yescharacteristic
29C2×#14519753C411yescharacteristic
30C2×#14519753C411yescharacteristic
31C2×#14519745C411yescharacteristic
32C2×#14519737C411yescharacteristic
33C2×#14519737C2211yescharacteristic
34C2×#14519734C2211yescharacteristic
35C2×#14519734C2211yescharacteristic
36C2×C22⋊C4×D61C411yescharacteristic
37C2×C22⋊C4×D61C2211yescharacteristic
38#16839824—21no—
39#16839822—21no—
40#16839822—21no—
41#16839821—21no—
42#16839819C2211yescharacteristic, complemented
43#16839816C2211yescharacteristic, complemented
44#16839816C2211yescharacteristic, complemented
45#16839815C2211yescharacteristic, complemented
46#16839812C2211yescharacteristic, complemented
47#16839812C2211yescharacteristic, complemented
48#16839787—21no—
49#16839787—21no—
50#16839724C2211yescharacteristic
51#16839724C2211yescharacteristic
52C22⋊C8×D61C2211yescharacteristic
53C22⋊C8×D61C2211yescharacteristic
54#16839719—21no—
55#16839716—21no—
56#16839487C2211yescharacteristic, complemented
57#16839487C2211yescharacteristic, complemented
58#16839487C2211yescharacteristic, complemented
59#16839487C2211yescharacteristic, complemented
60#16839486C2211yescharacteristic
61#16839486C2211yescharacteristic
62#16839486C2211yescharacteristic, complemented
63#16839486C2211yescharacteristic, complemented
64#16839485C2211yescharacteristic
65#16839485C2211yescharacteristic
66#16839485C2211yescharacteristic
67#16839485C2211yescharacteristic
68C2×#124×C61C2211yescharacteristic
69C61×#432C2211yescharacteristic, complemented
70C61×#431C2211yescharacteristic, complemented
71C61×#323C2211yescharacteristic
72C61×#323C2211yescharacteristic
73C61×#323C2211yescharacteristic, complemented
74C61×#323C2211yescharacteristic, complemented
75C24×D61C2×C411yescharacteristic
76C22×C22⋊D61C2×C411yescharacteristic
77C22×C22⋊D61C2×C411yescharacteristic
78C23×Dic61C2×C411yescharacteristic
79C22×C4×D61C2×C411yescharacteristic
80C22×C4×D61C2×C411yescharacteristic
81C22×C4×D61C2×C411yescharacteristic
82C22×C4×D61C2311yescharacteristic
83C2×#11758189—21no—
84C2×#11758189—21no—
85C2×C8×D61—21no—
86C2×C8×D61—21no—
87#14519770—21no—
88#14519770—21no—
89#14519770—21no—
90#14519770—21no—
91#14519770—21no—
92#14519770—21no—
93#14519770—21no—
94#14519770—21no—
95#14519759—21no—
96#14519759—21no—
97#14519759—21no—
98#14519759—21no—
99#14519759—21no—
100#14519759—21no—
101#14519759—21no—
102#14519759—21no—
103#14519758—21no—
104#14519758—21no—
105#14519758—21no—
106#14519758—21no—
107#14519753—21no—
108#14519753—21no—
109#14519753—21no—
110#14519753—21no—
111#14519753—21no—
112#14519753—21no—
113#14519753—21no—
114#14519753—21no—
115#14519745—21no—
116#14519745—21no—
117#14519745—21no—
118#14519745—21no—
119#14519737—21no—
120#14519737—21no—
121#14519737—21no—
122#14519737—21no—
123#14519737—21no—
124#14519737—21no—
125#14519737—21no—
126#14519737—21no—
127#14519734—21no—
128#14519734—21no—
129#14519734—21no—
130#14519734—21no—
131#14519734D411yescharacteristic
132#14519734D411yescharacteristic
133#14519734D411yescharacteristic
134#14519734D411yescharacteristic
135#14519734D411yescharacteristic
136#14519734D411yescharacteristic
137#14519734D411yescharacteristic
138#14519734D411yescharacteristic
139C2×C4⋊Dic61C2×C411yescharacteristic
140C2×C4⋊Dic61C2×C411yescharacteristic
141C2×#11758196C2×C411yescharacteristic
142C2×#11758196C2×C411yescharacteristic
143C2×#11758196C2×C411yescharacteristic
144C2×#11758196C2×C411yescharacteristic
145C2×#11758196C2×C411yescharacteristic
146C2×#11758196C2311yescharacteristic
147C2×C22⋊Dic61C2×C411yescharacteristic
148C2×C22⋊Dic61C2×C411yescharacteristic
149C2×C22⋊Dic61C2×C411yescharacteristic
150C2×C22⋊Dic61C2×C411yescharacteristic
151C2×#11758198C2×C411yescharacteristic
152C2×#11758198C2×C411yescharacteristic
153C2×#11758198C2×C411yescharacteristic
154C2×#11758198C2×C411yescharacteristic
155C2×#11758198C2×C411yescharacteristic
156C2×#11758198C2311yescharacteristic
157C22⋊C4×D61—21no—
158C22⋊C4×D61—21no—
159C22⋊C4×D61—21no—
160C22⋊C4×D61—21no—
161C22⋊C4×D61—21no—
162C22⋊C4×D61—21no—
163C22⋊C4×D61—21no—
164C22⋊C4×D61—21no—
165C2×C4×Dic61C2×C411yescharacteristic
166C2×C4×Dic61C2311yescharacteristic
167C4⋊#92418—21no—
168C4⋊#92418—21no—
169#14519706—21no—
170#14519706—21no—
171#14519706—21no—
172#14519706—21no—
173C22⋊#92418C2311yescharacteristic
174C22⋊#92418C2311yescharacteristic
175C22⋊#92418C2311yescharacteristic
176C22⋊#92418C2311yescharacteristic
177#14519689—21no—
178#14519689—21no—
179#14519689—21no—
180#14519689—21no—
181#14519688—21no—
182#14519687—21no—
183#14519687—21no—
184C4×#92418—21no—
185C8×Dic61—21no—
186C8×Dic61—21no—
187C22×Q8×C61C2×C411yescharacteristic
188C22×D4×C61C2×C411yescharacteristic
189#124×C61—21no—
190#124×C61—21no—
191#124×C61—21no—
192#124×C61—21no—
193C2×C22⋊C4×C61C2×C411yescharacteristic
194C2×C22⋊C4×C61C2×C411yescharacteristic
195C2×C22⋊C4×C61C2311yescharacteristic
196C2×C22⋊C4×C61C2311yescharacteristic
197C2×C42×C61C2311yescharacteristic
198C4⋊C8×C61—21no—
199C4⋊C8×C61—21no—
200C22⋊C8×C61C2311yescharacteristic
201C22⋊C8×C61C2311yescharacteristic
202C22⋊C8×C61C2311yescharacteristic
203C22⋊C8×C61C2311yescharacteristic
204#97×C61—21no—
205C4×C8×C61—21no—
206C24×C61C22×C411yescharacteristic
207C24×C61C22×C411yescharacteristic
208C23×D61—21no—
209C23×D61—21no—
210C23×D61—22no—
211C23×D61—41no—
212C23×D61—42no—
213C23×D61—81no—
214C23×D61C22×C411yescharacteristic
215C23×D61C22×C411yescharacteristic
216C2×Q8×C61—21no—
217C2×Q8×C61—21no—
218C2×Q8×C61—81no—
219C2×D4×C61—21no—
220C2×D4×C61—21no—
221C2×D4×C61—81no—
222C22×C4×C61C22×C411yescharacteristic
223C22×C4×C61C22×C411yescharacteristic
224C22×C4×C61C22×C411yescharacteristic
225C22×C4×C61C22×C411yescharacteristic
226C22×C4×C61C2411yescharacteristic
227C2×C22⋊D61—21no—
228C2×C22⋊D61—21no—
229C2×C22⋊D61—22no—
230C2×C22⋊D61—21no—
231C2×C22⋊D61—21no—
232C2×C22⋊D61—41no—
233C2×C22⋊D61—42no—
234C22×Dic61—21no—
235C22×Dic61—21no—
236C22×Dic61—81no—
237C22×Dic61C22×C411yescharacteristic
238C22×Dic61C22×C411yescharacteristic
239C22×Dic61C22×C411yescharacteristic
240C22×Dic61C22×C411yescharacteristic
241C22×Dic61C22×C411yescharacteristic
242C22×Dic61C22×C411yescharacteristic
243C2×C4×D61—22no—
244C2×C4×D61—21no—
245C2×C4×D61—21no—
246C2×C4×D61—21no—
247C2×C4×D61—21no—
248C2×C4×D61—21no—
249C2×C4×D61—21no—
250C2×C4×D61—42no—
251C2×C4×D61—41no—
252C2×C4×D61—81no—
253C2×C4×D61—81no—
254C2×C4×D61C2×D411yescharacteristic
255C2×C4×D61C2×D411yescharacteristic
256C2×C4×D61C2×D411yescharacteristic
257C2×C4×D61C2×D411yescharacteristic
258C2×C8×C61—21no—
259C2×C8×C61—21no—
260C2×C8×C61—21no—
261C2×C8×C61—21no—
262C22⋊C4×C61—21no—
263C22⋊C4×C61—21no—
264C22⋊C4×C61—21no—
265C22⋊C4×C61—21no—
266C22⋊C4×C61—21no—
267C22⋊C4×C61—21no—
268C22⋊C4×C61—21no—
269C22⋊C4×C61—21no—
270C42×C61C2×D411yescharacteristic
271C42×C61C2×D411yescharacteristic
272C42×C61C2×D411yescharacteristic
273C42×C61C2×D411yescharacteristic
274C22⋊Dic61—21no—
275C22⋊Dic61—21no—
276C22⋊Dic61—21no—
277C22⋊Dic61—21no—
278C22⋊Dic61—21no—
279C22⋊Dic61—21no—
280C22⋊Dic61—21no—
281C22⋊Dic61—21no—
282#11758198—21no—
283#11758198—21no—
284#11758198—21no—
285#11758198—21no—
286#11758198—21no—
287#11758198—21no—
288#11758198—21no—
289#11758198—21no—
290#11758198C22⋊C411yescharacteristic
291#11758198C22⋊C411yescharacteristic
292#11758198C22⋊C411yescharacteristic
293#11758198C22⋊C411yescharacteristic
294#11758198C22⋊C411yescharacteristic
295#11758198C22⋊C411yescharacteristic
296#11758198C22⋊C411yescharacteristic
297#11758198C22⋊C411yescharacteristic
298C4⋊Dic61—21no—
299C4⋊Dic61—21no—
300C4⋊Dic61—21no—
301C4⋊Dic61—21no—
302#11758196—21no—
303#11758196—21no—
304#11758196—21no—
305#11758196—21no—
306#11758196—21no—
307#11758196—21no—
308#11758196—21no—
309#11758196—21no—
310#11758196C22⋊C411yescharacteristic
311#11758196C22⋊C411yescharacteristic
312#11758196C22⋊C411yescharacteristic
313#11758196C22⋊C411yescharacteristic
314#11758196C22⋊C411yescharacteristic
315#11758196C22⋊C411yescharacteristic
316#11758196C22⋊C411yescharacteristic
317#11758196C22⋊C411yescharacteristic
318C4×Dic61—21no—
319C4×Dic61—21no—
320C4×Dic61C2×D411yescharacteristic
321C4×Dic61C2×D411yescharacteristic
322C4×Dic61C2×D411yescharacteristic
323C4×Dic61C2×D411yescharacteristic
324C2×#92418—21no—
325C2×#92418—21no—
326C2×#92418—21no—
327C2×#92418—21no—
328#11758189—42no—
329#11758189—42no—
330C8×D61—42no—
331C8×D61—42no—
332C23×C61—21no—
333C23×C61—21no—
334C23×C61—21no—
335C23×C61—21no—
336C23×C61—21no—
337C23×C61—21no—
338C23×C61—41no—
339C23×C61—41no—
340C23×C61—41no—
341C23×C61—41no—
342C23×C61C23×C411yescharacteristic
343C22×D61—21no—
344C22×D61—21no—
345C22×D61—21no—
346C22×D61—21no—
347C22×D61—22no—
348C22×D61—41no—
349C22×D61—42no—
350C22×D61—42no—
351C22×D61—42no—
352C22×D61—41no—
353C22×D61—41no—
354C22×D61—42no—
355C22×D61—81no—
356C22×D61—81no—
357C22×D61—84no—
358C22×D61—84no—
359C22×D61C2×C22⋊C411yescharacteristic
360C22×D61C2×C22⋊C411yescharacteristic
361C22×D61#13112yes—
362Q8×C61—81no—
363Q8×C61—81no—
364D4×C61—81no—
365D4×C61—81no—
366C2×C4×C61—21no—
367C2×C4×C61—21no—
368C2×C4×C61—21no—
369C2×C4×C61—21no—
370C2×C4×C61—41no—
371C2×C4×C61—41no—
372C2×C4×C61—41no—
373C2×C4×C61—41no—
374C2×C4×C61C2×C22⋊C411yescharacteristic
375C2×C4×C61C2×C22⋊C411yescharacteristic
376C2×C4×C61C2×C22⋊C411yescharacteristic
377C2×C4×C61C2×C22⋊C411yescharacteristic
378C2×C4×C61C22×D411yescharacteristic
379C2×C4×C61C22×D411yescharacteristic
380C22⋊D61—42no—
381C22⋊D61—42no—
382C22⋊D61—42no—
383C22⋊D61—42no—
384C2×Dic61—21no—
385C2×Dic61—21no—
386C2×Dic61—21no—
387C2×Dic61—21no—
388C2×Dic61—21no—
389C2×Dic61—21no—
390C2×Dic61—21no—
391C2×Dic61—41no—
392C2×Dic61—41no—
393C2×Dic61—41no—
394C2×Dic61—41no—
395C2×Dic61—81no—
396C2×Dic61—81no—
397C2×Dic61C2×C22⋊C411yescharacteristic
398C2×Dic61C2×C22⋊C411yescharacteristic
399C2×Dic61C2×C22⋊C411yescharacteristic
400C2×Dic61C2×C22⋊C411yescharacteristic
401C2×Dic61C2×C22⋊C411yescharacteristic
402C2×Dic61C2×C22⋊C411yescharacteristic
403C4×D61—22no—
404C4×D61—22no—
405C4×D61—41no—
406C4×D61—41no—
407C4×D61—42no—
408C4×D61—42no—
409C4×D61—81no—
410C4×D61—81no—
411C4×D61—81no—
412C4×D61—81no—
413C8×C61—41no—
414C8×C61—41no—
415C8×C61—41no—
416C8×C61—41no—
417#92418—41no—
418#92418—41no—
419#92418—41no—
420#92418—41no—
421#17412—611nomaximal, Sylow
422C22×C61—21no—
423C22×C61—21no—
424C22×C61—41no—
425C22×C61—41no—
426C22×C61—41no—
427C22×C61—41no—
428C22×C61—41no—
429C22×C61—41no—
430C22×C61—81no—
431C22×C61—81no—
432C22×C61—81no—
433C22×C61—81no—
434C22×C61C22×C22⋊C411yescharacteristic
435C22×C61C2×#13111yescharacteristic
436C22×C61#56811yescharacteristic
437C2×D61—21no—
438C2×D61—21no—
439C2×D61—22no—
440C2×D61—21no—
441C2×D61—21no—
442C2×D61—21no—
443C2×D61—42no—
444C2×D61—42no—
445C2×D61—42no—
446C2×D61—41no—
447C2×D61—41no—
448C2×D61—42no—
449C2×D61—84no—
450C2×D61—84no—
451C2×D61#41012yes—
452C4×C61—21no—
453C4×C61—21no—
454C4×C61—21no—
455C4×C61—21no—
456C4×C61—21no—
457C4×C61—21no—
458C4×C61—41no—
459C4×C61—41no—
460Dic61—21no—
461Dic61—21no—
462Dic61—21no—
463Dic61—21no—
464Dic61—21no—
465Dic61—21no—
466Dic61—41no—
467Dic61—41no—
468Dic61—41no—
469C2×#551—611no—
470#2924—611no—
471#2924—611no—
472#1473—611no—
473#1473—611no—
474#1469—611no—
475#1469D6111yescharacteristic, complemented
476#1468—611no—
477#1468—611no—
478#1466—611no—
479#1464—611no—
480#1462—611no—
481#1460—611no—
482#1458—611no—
483C2×#323—611no—
484C2×C61—21no—
485C2×C61—21no—
486C2×C61—81no—
487C2×C61—81no—
488C2×C61#288011yescharacteristic
489C2×C61C2×#41011yescharacteristic
490C2×C61#288811yescharacteristic
491D61—22no—
492D61—41no—
493D61—42no—
494#551—1221no—
495#551—1221no—
496#551—1221no—
497#551—1221no—
498#551—1221no—
499#551—1221no—
500#551—1221no—
501#551—1221no—
502C2×#126—611no—
503C2×#126—611no—
504C2×#124C2×D6111yescharacteristic
505C2×#123—611no—
506C2×#123—611no—
507C2×#123—611no—
508C2×C22⋊Q8—611no—
509C2×C22⋊Q8—611no—
510C2×#120—611no—
511C2×C4×D4—611no—
512C2×C4×D4—611no—
513C2×#117—611no—
514C2×#117—611no—
515C22×C22⋊C4—611no—
516C22×C22⋊C4—611no—
517#433—1221no—
518#433—1221no—
519#433—1221no—
520#433—1221no—
521#432—611no—
522#432—611no—
523#432—611no—
524#432C2×D6111yescharacteristic, complemented
525#431—611no—
526#431—611no—
527#431—611no—
528#431C2×D6111yescharacteristic, complemented
529#424—1221no—
530#424—1221no—
531#407—611no—
532#407—611no—
533C2×C22⋊C8—611no—
534C2×C22⋊C8—611no—
535#405—1221no—
536#405—1221no—
537#324—611no—
538#324—611no—
539#324—611no—
540#324—611no—
541#323—611no—
542#323—611no—
543#323—611no—
544#323—611no—
545#323—611no—
546#323—611no—
547#323—611no—
548#323—611no—
549#323C2×D6111yescharacteristic
550#323C2×D6111yescharacteristic
551#323C2×D6111yescharacteristic, complemented
552#323C2×D6111yescharacteristic, complemented
553C61#1741211yescharacteristic, complemented, Sylow
554C25—611no—
555C22×Q8C4×D6111yescharacteristic
556C22×D4—611no—
557C22×D4—611no—
558C22×D4C4×D6111yescharacteristic
559C23×C4—611no—
560C23×C4—611no—
561C23×C4—611no—
562C23×C4—611no—
563C23×C4—611no—
564C2×M16—1221no—
565C2×M16—1221no—
566C22×C8—1221no—
567C22×C8—1221no—
568#126—1221no—
569#126—1221no—
570#126—1221no—
571#126—1221no—
572#126—1221no—
573#126—1221no—
574#126—1221no—
575#126—1221no—
576#124—21no—
577#124—21no—
578#124—21no—
579#124—21no—
580#123—1221no—
581#123—1221no—
582#123—1221no—
583#123—1221no—
584#123—1221no—
585#123—1221no—
586#123—1221no—
587#123—1221no—
588#123—1221no—
589#123—1221no—
590#123—1221no—
591#123—1221no—
592C22⋊Q8—1221no—
593C22⋊Q8—1221no—
594C22⋊Q8—1221no—
595C22⋊Q8—1221no—
596C22⋊Q8—1221no—
597C22⋊Q8—1221no—
598C22⋊Q8—1221no—
599C22⋊Q8—1221no—
600#120—1221no—
601#120—1221no—
602#120—1221no—
603#120—1221no—
604C4×D4—1221no—
605C4×D4—1221no—
606C4×D4—1221no—
607C4×D4—1221no—
608C4×D4—1221no—
609C4×D4—1221no—
610C4×D4—1221no—
611C4×D4—1221no—
612#117—611no—
613#117—611no—
614#117—611no—
615#117—611no—
616#117—611no—
617#117—611no—
618#117—611no—
619#117—611no—
620#117—1221no—
621#117—1221no—
622#117—1221no—
623#117—1221no—
624C2×C4⋊C4—611no—
625C2×C4⋊C4—611no—
626C2×C4⋊C4—611no—
627C2×C4⋊C4—611no—
628C2×C4⋊C4—611no—
629C2×C4⋊C4—611no—
630C2×C4⋊C4—611no—
631C2×C4⋊C4—611no—
632C2×C22⋊C4—611no—
633C2×C22⋊C4—611no—
634C2×C22⋊C4—611no—
635C2×C22⋊C4—611no—
636C2×C22⋊C4—611no—
637C2×C22⋊C4—611no—
638C2×C22⋊C4—611no—
639C2×C22⋊C4—611no—
640C2×C22⋊C4—611no—
641C2×C22⋊C4—611no—
642C2×C22⋊C4—1221no—
643C2×C22⋊C4—1221no—
644C2×C22⋊C4—1221no—
645C2×C22⋊C4—1221no—
646C2×C22⋊C4—1221no—
647C2×C22⋊C4—1221no—
648C2×C22⋊C4—1221no—
649C2×C22⋊C4—1221no—
650C2×C22⋊C4C4×D6111yescharacteristic
651C2×C22⋊C4C4×D6111yescharacteristic
652C2×C22⋊C4C22×D6111yescharacteristic
653C2×C22⋊C4C22×D6111yescharacteristic
654C2×C42—611no—
655C2×C42—611no—
656C2×C42C22×D6111yescharacteristic
657C4⋊C8—21no—
658C4⋊C8—21no—
659C4⋊C8—1221no—
660C4⋊C8—1221no—
661C4⋊C8—1221no—
662C4⋊C8—1221no—
663C4⋊C8—1221no—
664C4⋊C8—1221no—
665C22⋊C8—611no—
666C22⋊C8—611no—
667C22⋊C8—611no—
668C22⋊C8—611no—
669C22⋊C8—1221no—
670C22⋊C8—1221no—
671C22⋊C8—1221no—
672C22⋊C8—1221no—
673C22⋊C8C22×D6111yescharacteristic
674C22⋊C8C22×D6111yescharacteristic
675C22⋊C8C22×D6111yescharacteristic
676C22⋊C8C22×D6111yescharacteristic
677#97—21no—
678#97—1221no—
679#97—1221no—
680#97—1221no—
681C4×C8—21no—
682C4×C8—1221no—
683C4×C8—1221no—
684C4×C8—1221no—
685C24—611no—
686C24—611no—
687C24—1222no—
688C24—1221no—
689C24—1221no—
690C24—4881no—
691C24—2441no—
692C24—2442no—
693C24C2×C4×D6111yescharacteristic
694C24C2×C4×D6111yescharacteristic
695C2×Q8—21no—
696C2×Q8—21no—
697C2×Q8—81no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—81no—
701C2×D4—1221no—
702C2×D4—1221no—
703C2×D4—1221no—
704C2×D4—1221no—
705C2×D4—1222no—
706C2×D4—2441no—
707C2×D4—2442no—
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—1221no—
719C22×C4—1221no—
720C22×C4—1221no—
721C22×C4—1221no—
722C22×C4—1222no—
723C22×C4—1221no—
724C22×C4—1221no—
725C22×C4—1221no—
726C22×C4—1221no—
727C22×C4—4881no—
728C22×C4—4881no—
729C22×C4—4881no—
730C22×C4—2441no—
731C22×C4—2442no—
732C22×C4C2×C4×D6111yescharacteristic
733C22×C4C2×C4×D6111yescharacteristic
734C22×C4C2×C4×D6111yescharacteristic
735C22×C4C2×C4×D6111yescharacteristic
736C22×C4C23×D6111yescharacteristic
737M16—2442no—
738M16—2442no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—21no—
742C2×C8—21no—
743C2×C8—1221no—
744C2×C8—1221no—
745C2×C8—1221no—
746C2×C8—1221no—
747C2×C8—2442no—
748C2×C8—2442no—
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—1221no—
758C4⋊C4—1221no—
759C4⋊C4—1221no—
760C4⋊C4—1221no—
761C4⋊C4—1221no—
762C4⋊C4—1221no—
763C4⋊C4—1221no—
764C4⋊C4—1221no—
765C4⋊C4—1221no—
766C4⋊C4—1221no—
767C4⋊C4—1221no—
768C4⋊C4—1221no—
769C22⋊C4—21no—
770C22⋊C4—21no—
771C22⋊C4—21no—
772C22⋊C4—21no—
773C22⋊C4—21no—
774C22⋊C4—21no—
775C22⋊C4—21no—
776C22⋊C4—21no—
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—1221no—
786C22⋊C4—1221no—
787C22⋊C4—1221no—
788C22⋊C4—1221no—
789C22⋊C4—1221no—
790C22⋊C4—1221no—
791C22⋊C4—1221no—
792C22⋊C4—1221no—
793C22⋊C4—1221no—
794C22⋊C4—1221no—
795C22⋊C4—1221no—
796C22⋊C4—1221no—
797C22⋊C4—1221no—
798C22⋊C4—1221no—
799C22⋊C4—1221no—
800C22⋊C4—1221no—
801C42—611no—
802C42—611no—
803C42—611no—
804C42—611no—
805C42—1221no—
806C42—1221no—
807C42D4×D6111yescharacteristic
808C42D4×D6111yescharacteristic
809C42D4×D6111yescharacteristic
810C42D4×D6111yescharacteristic
811C23—21no—
812C23—21no—
813C23—21no—
814C23—21no—
815C23—21no—
816C23—21no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—611no—
822C23—611no—
823C23—612no—
824C23—1222no—
825C23—1221no—
826C23—1221no—
827C23—1221no—
828C23—1221no—
829C23—4881no—
830C23—4881no—
831C23—4884no—
832C23—4884no—
833C23—2441no—
834C23—2441no—
835C23—2441no—
836C23—2442no—
837C23—2442no—
838C23—2442no—
839C23—2442no—
840C23C22×C4×D6111yescharacteristic
841Q8—81no—
842Q8—81no—
843D4—81no—
844D4—81no—
845D4—2442no—
846D4—2442no—
847D4—2442no—
848D4—2442no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—611no—
858C2×C4—611no—
859C2×C4—611no—
860C2×C4—611no—
861C2×C4—611no—
862C2×C4—611no—
863C2×C4—1222no—
864C2×C4—1222no—
865C2×C4—1221no—
866C2×C4—1221no—
867C2×C4—1221no—
868C2×C4—1221no—
869C2×C4—1221no—
870C2×C4—1221no—
871C2×C4—1221no—
872C2×C4—4881no—
873C2×C4—4881no—
874C2×C4—4881no—
875C2×C4—4881no—
876C2×C4—4881no—
877C2×C4—4881no—
878C2×C4—2441no—
879C2×C4—2441no—
880C2×C4—2442no—
881C2×C4—2442no—
882C2×C4—2441no—
883C2×C4—2441no—
884C2×C4—2441no—
885C2×C4—2441no—
886C2×C4C22⋊C4×D6111yescharacteristic
887C2×C4C22⋊C4×D6111yescharacteristic
888C2×C4C22⋊C4×D6111yescharacteristic
889C2×C4C22⋊C4×D6111yescharacteristic
890C2×C4C2×D4×D6111yescharacteristic
891C2×C4C2×D4×D6111yescharacteristic
892C8—41no—
893C8—41no—
894C8—41no—
895C8—41no—
896C8—2441no—
897C8—2441no—
898C8—2441no—
899C8—2441no—
900C22—21no—
901C22—21no—
902C22—41no—
903C22—41no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—81no—
909C22—81no—
910C22—81no—
911C22—81no—
912C22—612no—
913C22—1221no—
914C22—1221no—
915C22—1222no—
916C22—1221no—
917C22—1221no—
918C22—1221no—
919C22—4884no—
920C22—4884no—
921C22—2442no—
922C22—2442no—
923C22—2442no—
924C22—2442no—
925C22—2441no—
926C22—2441no—
927C22C2×C22⋊C4×D6111yescharacteristic
928C22#131×D6111yescharacteristic
929C22#1684052711yescharacteristic
930C4—21no—
931C4—21no—
932C4—21no—
933C4—21no—
934C4—21no—
935C4—21no—
936C4—41no—
937C4—41no—
938C4—1221no—
939C4—1221no—
940C4—1221no—
941C4—1221no—
942C4—1221no—
943C4—1221no—
944C4—2441no—
945C4—2441no—
946C4—2441no—
947C2—21no—
948C2—21no—
949C2—81no—
950C2—81no—
951C2—1222no—
952C2—2441no—
953C2—2442no—
954C2#2145426711yescharacteristic
955C2#410×D6111yescharacteristic
956C2#2145429511yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1469C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#14519745C4
cosocleC22×C4×C61C24
hypercenter#1469D61
hypocenterC61#17412
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1469

Complements

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

NH ≅ G/Ntype
2. #21454478C2semidirect
3. #21454472C2semidirect
4. #21444185C2semidirect
5. #21444185C2semidirect
6. #21444171C2semidirect
7. #21444164C2semidirect
8. #21444164C2semidirect
9. #21444158C2semidirect
10. #21444151C2semidirect
11. #21444144C2semidirect
12. #21444138C2semidirect
13. #21444131C2semidirect
14. #323×D61C2semidirect
15. C61×#1469C2semidirect
42. #16839819C22semidirect
43. #16839816C22semidirect
44. #16839816C22semidirect
45. #16839815C22semidirect
46. #16839812C22semidirect
47. #16839812C22semidirect
56. #16839487C22semidirect
57. #16839487C22semidirect
58. #16839487C22semidirect
59. #16839487C22semidirect
62. #16839486C22semidirect
63. #16839486C22semidirect
69. C61×#432C22semidirect
70. C61×#431C22semidirect
73. C61×#323C22semidirect
74. C61×#323C22semidirect
475. #1469D61semidirect
524. #432C2×D61semidirect
528. #431C2×D61semidirect
551. #323C2×D61semidirect
552. #323C2×D61semidirect
553. C61#17412semidirect

Maximal subgroups

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

subgroupindex
C2×#168404422
#214544782
#214544722
#214441852
#214441712
#214441642
#214441582
#214441512
#214441442
#214441382
#214441312
#323×D612
C61×#14692
#1741261