Finite Group Databasebeta

← #29646207

Subgroups — #29646207

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×#16840437C211yesmaximal, characteristic
2#21454478C211yesmaximal, characteristic, complemented
3#21454472C211yesmaximal, characteristic, complemented
4#21444188C211yesmaximal, characteristic, complemented
5#21444169C211yesmaximal, characteristic, complemented
6#21444169C211yesmaximal, characteristic, complemented
7#21444166C211yesmaximal, characteristic, complemented
8#21444166C211yesmaximal, characteristic, complemented
9#21444159C211yesmaximal, characteristic, complemented
10#21444152C211yesmaximal, characteristic, complemented
11#21444144C211yesmaximal, characteristic, complemented
12#21444139C211yesmaximal, characteristic, complemented
13#21444132C211yesmaximal, characteristic, complemented
14#323×D61C211yesmaximal, characteristic, complemented
15C61×#1473C211yesmaximal, characteristic, complemented
16#16840437—21no—
17#16840437—21no—
18#16840437—21no—
19#16840437—21no—
20#16840437—21no—
21#16840437—21no—
22#16840437—21no—
23#16840437—21no—
24C2×#14519770C411yescharacteristic
25C2×#14519763C2211yescharacteristic
26C2×#14519762C411yescharacteristic
27C2×#14519762C2211yescharacteristic
28C2×#14519759C411yescharacteristic
29C2×#14519757C411yescharacteristic
30C2×#14519755C411yescharacteristic
31C2×#14519747C411yescharacteristic
32C2×C4×D244C2211yescharacteristic
33C2×#14519739C411yescharacteristic
34C2×#14519735C2211yescharacteristic
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#16839488C2211yescharacteristic, complemented
57#16839488C2211yescharacteristic, complemented
58#16839486C2211yescharacteristic
59#16839486C2211yescharacteristic
60#16839485C2211yescharacteristic
61#16839485C2211yescharacteristic
62#16839485C2211yescharacteristic
63#16839485C2211yescharacteristic
64#16839485C2211yescharacteristic, complemented
65#16839485C2211yescharacteristic, complemented
66#16839485C2211yescharacteristic, complemented
67#16839485C2211yescharacteristic, complemented
68C2×#126×C61C2211yescharacteristic
69C61×#432C2211yescharacteristic, complemented
70C61×#431C2211yescharacteristic, complemented
71C61×#324C2211yescharacteristic, complemented
72C61×#324C2211yescharacteristic, complemented
73C61×#323C2211yescharacteristic
74C61×#323C2211yescharacteristic
75C24×D61C2×C411yescharacteristic
76C22×Dic122C2×C411yescharacteristic
77C22×D244C2×C411yescharacteristic
78C22×D244C2×C411yescharacteristic
79C22×C22⋊D61C2×C411yescharacteristic
80C22×C4×D61C2×C411yescharacteristic
81C22×C4×D61C2×C411yescharacteristic
82C22×C4×D61C2×C411yescharacteristic
83C22×C4×D61C2×C411yescharacteristic
84C22×C4×D61C2311yescharacteristic
85C2×#11758189—21no—
86C2×#11758189—21no—
87C2×C8×D61—21no—
88C2×C8×D61—21no—
89#14519770—21no—
90#14519770—21no—
91#14519770—21no—
92#14519770—21no—
93#14519763—21no—
94#14519763—21no—
95#14519763—21no—
96#14519763—21no—
97#14519762—21no—
98#14519762—21no—
99#14519762—21no—
100#14519762—21no—
101#14519762—21no—
102#14519762—21no—
103#14519762—21no—
104#14519762—21no—
105#14519759—21no—
106#14519759—21no—
107#14519759—21no—
108#14519759—21no—
109#14519757—21no—
110#14519757—21no—
111#14519757—21no—
112#14519757—21no—
113#14519755—21no—
114#14519755—21no—
115#14519755—21no—
116#14519755—21no—
117#14519747—21no—
118#14519747—21no—
119#14519747—21no—
120#14519747—21no—
121C4×D244—21no—
122C4×D244—21no—
123C4×D244—21no—
124C4×D244—21no—
125#14519739—21no—
126#14519739—21no—
127#14519739—21no—
128#14519739—21no—
129#14519735—21no—
130#14519735—21no—
131#14519735—21no—
132#14519735—21no—
133#14519734D411yescharacteristic
134#14519734D411yescharacteristic
135#14519734D411yescharacteristic
136#14519734D411yescharacteristic
137#14519734D411yescharacteristic
138#14519734D411yescharacteristic
139#14519734D411yescharacteristic
140#14519734D411yescharacteristic
141C2×C4⋊Dic61C2×C411yescharacteristic
142C2×C4⋊Dic61C2×C411yescharacteristic
143C2×#11758196C2×C411yescharacteristic
144C2×#11758196C2×C411yescharacteristic
145C2×#11758196C2×C411yescharacteristic
146C2×C22⋊Dic61C2×C411yescharacteristic
147C2×C22⋊Dic61C2×C411yescharacteristic
148C2×#11758198C2×C411yescharacteristic
149C2×#11758198C2×C411yescharacteristic
150C2×#11758198C2×C411yescharacteristic
151C2×#11758198C2×C411yescharacteristic
152C2×#11758198C2×C411yescharacteristic
153C2×#11758198C2×C411yescharacteristic
154C2×#11758198C2×C411yescharacteristic
155C2×#11758198C2311yescharacteristic
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—
187#126×C61—21no—
188#126×C61—21no—
189#126×C61—21no—
190#126×C61—21no—
191C2×C4⋊C4×C61C2×C411yescharacteristic
192C2×C4⋊C4×C61C2×C411yescharacteristic
193C2×C4⋊C4×C61C2311yescharacteristic
194C2×C22⋊C4×C61C2×C411yescharacteristic
195C2×C22⋊C4×C61C2×C411yescharacteristic
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
207C23×D61—21no—
208C23×D61—21no—
209C23×D61—22no—
210C23×D61—41no—
211C23×D61—42no—
212C23×D61—81no—
213C23×D61C22×C411yescharacteristic
214C23×D61C22×C411yescharacteristic
215C23×D61C22×C411yescharacteristic
216C22×C4×C61C22×C411yescharacteristic
217C22×C4×C61C22×C411yescharacteristic
218C22×C4×C61C22×C411yescharacteristic
219C22×C4×C61C22×C411yescharacteristic
220C22×C4×C61C22×C411yescharacteristic
221C22×C4×C61C2411yescharacteristic
222C2×C22⋊D61—21no—
223C2×C22⋊D61—21no—
224C2×C22⋊D61—81no—
225C22×Dic61C22×C411yescharacteristic
226C22×Dic61C22×C411yescharacteristic
227C22×Dic61C22×C411yescharacteristic
228C22×Dic61C22×C411yescharacteristic
229C22×Dic61C22×C411yescharacteristic
230C2×D244—21no—
231C2×D244—21no—
232C2×D244—22no—
233C2×D244—21no—
234C2×D244—21no—
235C2×D244—41no—
236C2×D244—42no—
237C2×C4×D61—22no—
238C2×C4×D61—21no—
239C2×C4×D61—21no—
240C2×C4×D61—21no—
241C2×C4×D61—21no—
242C2×C4×D61—21no—
243C2×C4×D61—21no—
244C2×C4×D61—21no—
245C2×C4×D61—21no—
246C2×C4×D61—42no—
247C2×C4×D61—41no—
248C2×C4×D61—81no—
249C2×C4×D61—81no—
250C2×C4×D61—81no—
251C2×C4×D61C2×D411yescharacteristic
252C2×C4×D61C2×D411yescharacteristic
253C2×C4×D61C2×D411yescharacteristic
254C2×C4×D61C2×D411yescharacteristic
255C2×Dic122—21no—
256C2×Dic122—21no—
257C2×Dic122—81no—
258C2×C8×C61—21no—
259C2×C8×C61—21no—
260C2×C8×C61—21no—
261C2×C8×C61—21no—
262C4⋊C4×C61—21no—
263C4⋊C4×C61—21no—
264C4⋊C4×C61—21no—
265C4⋊C4×C61—21no—
266C4⋊C4×C61—21no—
267C4⋊C4×C61—21no—
268C22⋊C4×C61—21no—
269C22⋊C4×C61—21no—
270C22⋊C4×C61—21no—
271C22⋊C4×C61—21no—
272C22⋊C4×C61—21no—
273C22⋊C4×C61—21no—
274C42×C61C2×D411yescharacteristic
275C42×C61C2×D411yescharacteristic
276C42×C61C2×D411yescharacteristic
277C42×C61C2×D411yescharacteristic
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#11758198—21no—
291#11758198—21no—
292#11758198—21no—
293#11758198—21no—
294#11758198—21no—
295#11758198—21no—
296#11758198C22⋊C411yescharacteristic
297#11758198C22⋊C411yescharacteristic
298#11758198C22⋊C411yescharacteristic
299#11758198C22⋊C411yescharacteristic
300#11758198C22⋊C411yescharacteristic
301#11758198C22⋊C411yescharacteristic
302#11758198C22⋊C411yescharacteristic
303#11758198C22⋊C411yescharacteristic
304C4⋊Dic61—21no—
305C4⋊Dic61—21no—
306C4⋊Dic61—21no—
307C4⋊Dic61—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—41no—
336C23×C61—41no—
337C23×C61C23×C411yescharacteristic
338C22×D61—21no—
339C22×D61—21no—
340C22×D61—21no—
341C22×D61—21no—
342C22×D61—22no—
343C22×D61—21no—
344C22×D61—21no—
345C22×D61—21no—
346C22×D61—41no—
347C22×D61—42no—
348C22×D61—42no—
349C22×D61—42no—
350C22×D61—41no—
351C22×D61—41no—
352C22×D61—42no—
353C22×D61—41no—
354C22×D61—41no—
355C22×D61—81no—
356C22×D61—81no—
357C22×D61—84no—
358C22×D61—84no—
359C22×D61C2×C22⋊C411yescharacteristic
360C22×D61C2×C22⋊C411yescharacteristic
361C22×D61#13112yes—
362C2×C4×C61—21no—
363C2×C4×C61—21no—
364C2×C4×C61—21no—
365C2×C4×C61—21no—
366C2×C4×C61—21no—
367C2×C4×C61—21no—
368C2×C4×C61—21no—
369C2×C4×C61—41no—
370C2×C4×C61—41no—
371C2×C4×C61—41no—
372C2×C4×C61—41no—
373C2×C4×C61C2×C22⋊C411yescharacteristic
374C2×C4×C61C2×C22⋊C411yescharacteristic
375C2×C4×C61C2×C22⋊C411yescharacteristic
376C2×C4×C61C2×C22⋊C411yescharacteristic
377C2×C4×C61C22×D411yescharacteristic
378C2×C4×C61C22×D411yescharacteristic
379C22⋊D61—81no—
380C22⋊D61—81no—
381C2×Dic61—21no—
382C2×Dic61—21no—
383C2×Dic61—21no—
384C2×Dic61—21no—
385C2×Dic61—41no—
386C2×Dic61—41no—
387C2×Dic61—41no—
388C2×Dic61—41no—
389C2×Dic61C2×C22⋊C411yescharacteristic
390C2×Dic61C2×C22⋊C411yescharacteristic
391C2×Dic61C2×C22⋊C411yescharacteristic
392C2×Dic61C2×C22⋊C411yescharacteristic
393C2×Dic61C2×C22⋊C411yescharacteristic
394C2×Dic61C2×C22⋊C411yescharacteristic
395D244—42no—
396D244—42no—
397D244—42no—
398D244—42no—
399C4×D61—22no—
400C4×D61—22no—
401C4×D61—41no—
402C4×D61—41no—
403C4×D61—42no—
404C4×D61—42no—
405C4×D61—81no—
406C4×D61—81no—
407C4×D61—81no—
408C4×D61—81no—
409C4×D61—81no—
410C4×D61—81no—
411Dic122—81no—
412Dic122—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—81no—
428C22×C61—81no—
429C22×C61C22×C22⋊C411yescharacteristic
430C22×C61C2×#13111yescharacteristic
431C22×C61#56811yescharacteristic
432C2×D61—21no—
433C2×D61—21no—
434C2×D61—22no—
435C2×D61—21no—
436C2×D61—21no—
437C2×D61—21no—
438C2×D61—42no—
439C2×D61—42no—
440C2×D61—42no—
441C2×D61—41no—
442C2×D61—41no—
443C2×D61—42no—
444C2×D61—41no—
445C2×D61—41no—
446C2×D61—41no—
447C2×D61—84no—
448C2×D61—84no—
449C2×D61—81no—
450C2×D61—81no—
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—
460C4×C61—41no—
461Dic61—21no—
462Dic61—21no—
463Dic61—21no—
464Dic61—21no—
465Dic61—21no—
466Dic61—21no—
467Dic61—41no—
468Dic61—41no—
469C2×#551—611no—
470#2924—611no—
471#2924—611no—
472#1473—611no—
473#1473D6111yescharacteristic, complemented
474#1469—611no—
475#1469—611no—
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#288011yescharacteristic
488C2×C61C2×#41011yescharacteristic
489C2×C61#288811yescharacteristic
490D61—22no—
491D61—41no—
492D61—42no—
493D61—81no—
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×#126C2×D6111yescharacteristic
504C2×#124—611no—
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#324C2×D6111yescharacteristic, complemented
540#324C2×D6111yescharacteristic, complemented
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#323—611no—
550#323—611no—
551#323C2×D6111yescharacteristic
552#323C2×D6111yescharacteristic
553C61#1741211yescharacteristic, complemented, Sylow
554C25—611no—
555C22×Q8—611no—
556C22×D4—611no—
557C22×D4—611no—
558C22×D4—611no—
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—21no—
569#126—21no—
570#126—21no—
571#126—21no—
572#126—1221no—
573#126—1221no—
574#126—1221no—
575#126—1221no—
576#124—1221no—
577#124—1221no—
578#124—1221no—
579#124—1221no—
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⋊C4C4×D6111yescharacteristic
630C2×C4⋊C4C4×D6111yescharacteristic
631C2×C4⋊C4C22×D6111yescharacteristic
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—611no—
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⋊C4—1221no—
651C2×C22⋊C4C4×D6111yescharacteristic
652C2×C22⋊C4C4×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—611no—
688C24—1222no—
689C24—1221no—
690C24—1221no—
691C24—4881no—
692C24—2441no—
693C24—2442no—
694C24C2×C4×D6111yescharacteristic
695C2×Q8—1221no—
696C2×Q8—1221no—
697C2×Q8—4881no—
698C2×D4—1221no—
699C2×D4—1221no—
700C2×D4—1222no—
701C2×D4—1221no—
702C2×D4—1221no—
703C2×D4—1221no—
704C2×D4—1221no—
705C2×D4—4881no—
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—1221no—
718C22×C4—1221no—
719C22×C4—1221no—
720C22×C4—1221no—
721C22×C4—1222no—
722C22×C4—1221no—
723C22×C4—1221no—
724C22×C4—1221no—
725C22×C4—1221no—
726C22×C4—4881no—
727C22×C4—4881no—
728C22×C4—4881no—
729C22×C4—2441no—
730C22×C4—2442no—
731C22×C4C2×C4×D6111yescharacteristic
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—21no—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—611no—
756C4⋊C4—611no—
757C4⋊C4—611no—
758C4⋊C4—611no—
759C4⋊C4—611no—
760C4⋊C4—611no—
761C4⋊C4—611no—
762C4⋊C4—611no—
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—611no—
776C22⋊C4—611no—
777C22⋊C4—611no—
778C22⋊C4—611no—
779C22⋊C4—611no—
780C22⋊C4—611no—
781C22⋊C4—611no—
782C22⋊C4—611no—
783C22⋊C4—1221no—
784C22⋊C4—1221no—
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—41no—
815C23—41no—
816C23—611no—
817C23—611no—
818C23—612no—
819C23—1222no—
820C23—1221no—
821C23—1221no—
822C23—1221no—
823C23—1221no—
824C23—1221no—
825C23—1221no—
826C23—1221no—
827C23—4881no—
828C23—4881no—
829C23—4884no—
830C23—4884no—
831C23—2441no—
832C23—2441no—
833C23—2441no—
834C23—2441no—
835C23—2441no—
836C23—2442no—
837C23—2442no—
838C23—2442no—
839C23—2442no—
840C23C22×C4×D6111yescharacteristic
841Q8—4881no—
842Q8—4881no—
843D4—4881no—
844D4—4881no—
845D4—2442no—
846D4—2442no—
847D4—2442no—
848D4—2442no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—611no—
861C2×C4—611no—
862C2×C4—611no—
863C2×C4—611no—
864C2×C4—611no—
865C2×C4—611no—
866C2×C4—1222no—
867C2×C4—1222no—
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—81no—
906C22—81no—
907C22—612no—
908C22—1221no—
909C22—1221no—
910C22—1222no—
911C22—1221no—
912C22—1221no—
913C22—1221no—
914C22—4881no—
915C22—4881no—
916C22—4884no—
917C22—4884no—
918C22—2442no—
919C22—2442no—
920C22—2442no—
921C22—2442no—
922C22—2441no—
923C22—2441no—
924C22—2441no—
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—41no—
939C4—1221no—
940C4—1221no—
941C4—1221no—
942C4—1221no—
943C4—1221no—
944C4—1221no—
945C4—2441no—
946C4—2441no—
947C2—21no—
948C2—21no—
949C2—81no—
950C2—1222no—
951C2—4881no—
952C2—2441no—
953C2—2442no—
954C2#2145426711yescharacteristic
955C2#410×D6111yescharacteristic
956C2#2145429611yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1473C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#14519747C4
cosocleC22×C4×C61C24
hypercenter#1473D61
hypocenterC61#17412
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1473

Complements

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

NH ≅ G/Ntype
2. #21454478C2semidirect
3. #21454472C2semidirect
4. #21444188C2semidirect
5. #21444169C2semidirect
6. #21444169C2semidirect
7. #21444166C2semidirect
8. #21444166C2semidirect
9. #21444159C2semidirect
10. #21444152C2semidirect
11. #21444144C2semidirect
12. #21444139C2semidirect
13. #21444132C2semidirect
14. #323×D61C2semidirect
15. C61×#1473C2semidirect
42. #16839819C22semidirect
43. #16839816C22semidirect
44. #16839816C22semidirect
45. #16839815C22semidirect
46. #16839812C22semidirect
47. #16839812C22semidirect
56. #16839488C22semidirect
57. #16839488C22semidirect
64. #16839485C22semidirect
65. #16839485C22semidirect
66. #16839485C22semidirect
67. #16839485C22semidirect
69. C61×#432C22semidirect
70. C61×#431C22semidirect
71. C61×#324C22semidirect
72. C61×#324C22semidirect
473. #1473D61semidirect
524. #432C2×D61semidirect
528. #431C2×D61semidirect
539. #324C2×D61semidirect
540. #324C2×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×#168404372
#214544782
#214544722
#214441882
#214441692
#214441662
#214441592
#214441522
#214441442
#214441392
#214441322
#323×D612
C61×#14732
#1741261