Finite Group Databasebeta

← #29648708

Subgroups — #29648708

Order 15616.

1240 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459595C211yesmaximal, characteristic
2#21454938C211yesmaximal, characteristic, complemented
3#21454486C211yesmaximal, characteristic, complemented
4#21444542C211yesmaximal, characteristic, complemented
5#21444538C211yesmaximal, characteristic, complemented
6#21444531C211yesmaximal, characteristic, complemented
7#21444525C211yesmaximal, characteristic, complemented
8#21444521C211yesmaximal, characteristic, complemented
9#21444493C211yesmaximal, characteristic, complemented
10#21444487C211yesmaximal, characteristic, complemented
11#21444485C211yesmaximal, characteristic, complemented
12#21444485C211yesmaximal, characteristic, complemented
13#21444465C211yesmaximal, characteristic, complemented
14#331×D61C211yesmaximal, characteristic, complemented
15C61×#1555C211yesmaximal, characteristic, complemented
16C2×#14519822—21no—
17#16840432—21no—
18#16840432C412yes—
19#16840397—21no—
20#16840397C412yes—
21D4×C22⋊D61—21no—
22D4×C22⋊D61—21no—
23D4×C22⋊D61C412yes—
24D4×C22⋊D61C412yes—
25#16840329—21no—
26#16840325—21no—
27#16840325—21no—
28#16840312C2211yescharacteristic
29#16840310C2211yescharacteristic
30#16840310C2211yescharacteristic
31#127×D61C2211yescharacteristic
32#127×D61C2211yescharacteristic
33C4×#11758222C2211yescharacteristic
34#16839890—21no—
35#16839837—21no—
36#16839836—21no—
37#16839835—21no—
38#16839824—21no—
39#16839820—21no—
40#16839818C2211yescharacteristic, complemented
41#16839818C2211yescharacteristic, complemented
42#16839815C2211yescharacteristic, complemented
43#16839814C2211yescharacteristic, complemented
44#16839814C2211yescharacteristic, complemented
45#16839786C2211yescharacteristic, complemented
46#16839784C2211yescharacteristic, complemented
47#16839784C2211yescharacteristic, complemented
48C4⋊C8×D61C2211yescharacteristic, complemented
49C4⋊C8×D61C2211yescharacteristic, complemented
50#16839727—21no—
51#16839719—21no—
52#16839509C2211yescharacteristic, complemented
53#16839509C2211yescharacteristic, complemented
54#16839507C2211yescharacteristic, complemented
55#16839507C2211yescharacteristic, complemented
56#16839506C2211yescharacteristic, complemented
57#16839506C2211yescharacteristic, complemented
58#16839506C2211yescharacteristic, complemented
59#16839506C2211yescharacteristic, complemented
60#16839505C2211yescharacteristic, complemented
61#16839505C2211yescharacteristic, complemented
62#16839505C2211yescharacteristic, complemented
63#16839505C2211yescharacteristic, complemented
64C2×#127×C61C2211yescharacteristic
65C61×#432C2211yescharacteristic, complemented
66C61×#432C2211yescharacteristic, complemented
67C61×#331C2211yescharacteristic, complemented
68C61×#331C2211yescharacteristic, complemented
69C61×#331C2211yescharacteristic, complemented
70C61×#331C2211yescharacteristic, complemented
71#14519822—44no—
72#14519822—44no—
73C2×#11758222—21no—
74C2×#11758222D411yescharacteristic
75C2×#11758224—21no—
76C2×#11758224—21no—
77C2×#11758224—22no—
78C22×C22⋊D61—22no—
79C22×C22⋊D61—22no—
80C2×D4×D61—22no—
81C2×D4×D61—21no—
82C2×D4×D61—21no—
83C2×D4×D61—21no—
84C2×D4×D61—21no—
85C2×D4×D61C2×C412yes—
86C2×D4×D61C2×C412yes—
87C2×#11758194—21no—
88C2×#11758189—21no—
89C2×#11758189—21no—
90C2×C8×D61—21no—
91C2×C8×D61—21no—
92#14519777C2311yescharacteristic
93#14519774C2311yescharacteristic
94#14519773—21no—
95#14519773—21no—
96#14519773—21no—
97#14519773—21no—
98#14519773C2×C412yes—
99#14519773C2×C412yes—
100#14519765—21no—
101#14519764—21no—
102#14519764—21no—
103#14519751—21no—
104#14519751C2×C412yes—
105#14519749—22no—
106#14519749—22no—
107#14519749—22no—
108#14519749—22no—
109#14519748—21no—
110#14519748—21no—
111#14519748—22no—
112#14519748—22no—
113#14519748C2×C412yes—
114#14519748C2×C412yes—
115#14519746—22no—
116#14519746—22no—
117#14519745—22no—
118#14519745—22no—
119#14519745—22no—
120#14519745—22no—
121C4×Dic122C2×C411yescharacteristic
122C4×Dic122D411yescharacteristic
123C4×D244—21no—
124C4×D244C2×C411yescharacteristic
125C4×D244C2×C412yes—
126C4×D244D411yescharacteristic
127D4×Dic61—21no—
128D4×Dic61—21no—
129D4×Dic61C2×C412yes—
130D4×Dic61C2×C412yes—
131C4×C22⋊D61C2×C411yescharacteristic
132C4×C22⋊D61C2×C411yescharacteristic
133C4×C22⋊D61D411yescharacteristic
134C4×C22⋊D61D411yescharacteristic
135#14519736D411yescharacteristic
136#14519734D411yescharacteristic
137#14519734D411yescharacteristic
138C42×D61C2311yescharacteristic
139C42×D61C2311yescharacteristic
140C4⋊#92418—21no—
141C4⋊#92418C2311yescharacteristic
142C4⋊#92418C2311yescharacteristic
143C4⋊#92418C2311yescharacteristic
144C4⋊#92418C2311yescharacteristic
145#14519706—21no—
146#14519706—21no—
147#14519706—21no—
148#14519706—21no—
149C22⋊#92418—21no—
150#14519689—21no—
151#14519689—21no—
152#14519689—21no—
153#14519689—21no—
154#14519687—21no—
155#14519687—21no—
156C4×#92418—21no—
157C8×Dic61—21no—
158C8×Dic61—21no—
159C22×D4×C61—21no—
160C22×D4×C61—21no—
161C22×D4×C61C2×C412yes—
162#127×C61—21no—
163#127×C61—21no—
164#127×C61C2×C412yes—
165#127×C61C2311yescharacteristic
166#127×C61C2311yescharacteristic
167C2×C42×C61C2311yescharacteristic
168C4⋊C8×C61C2311yescharacteristic
169C4⋊C8×C61C2311yescharacteristic
170C4⋊C8×C61C2311yescharacteristic
171C4⋊C8×C61C2311yescharacteristic
172C22⋊C8×C61—21no—
173C22⋊C8×C61—21no—
174#97×C61—21no—
175#97×C61—21no—
176C24×C61—22no—
177C23×D61—22no—
178C23×D61—22no—
179C2×D4×C61—22no—
180C2×D4×C61—22no—
181C2×D4×C61—22no—
182C2×D4×C61—21no—
183C2×D4×C61—21no—
184C2×D4×C61—21no—
185C2×D4×C61—21no—
186C2×D4×C61—42no—
187C2×D4×C61—42no—
188C2×D4×C61—81no—
189C2×D4×C61—81no—
190C2×D4×C61—82no—
191C2×D4×C61C22×C412yes—
192C2×D4×C61C22×C412yes—
193C22×C4×C61C22×C411yescharacteristic
194C22×C4×C61C2×D411yescharacteristic
195C22×C4×C61C2×D411yescharacteristic
196C2×C22⋊D61—22no—
197C2×C22⋊D61—22no—
198C2×C22⋊D61—22no—
199C2×C22⋊D61—22no—
200C2×C22⋊D61—22no—
201C2×C22⋊D61—22no—
202C2×C22⋊D61—22no—
203C2×C22⋊D61—22no—
204C2×C22⋊D61—22no—
205C2×C22⋊D61—48no—
206C2×C22⋊D61—48no—
207C2×C22⋊D61C22⋊C411yescharacteristic
208C2×C22⋊D61C22⋊C411yescharacteristic
209C22×Dic61—22no—
210C22×Dic61—22no—
211#11758224—48no—
212#11758224—42no—
213#11758224—42no—
214#11758224—42no—
215#11758224—42no—
216D4×D61—42no—
217D4×D61—42no—
218D4×D61—48no—
219D4×D61—42no—
220D4×D61—42no—
221D4×D61—81no—
222D4×D61—81no—
223D4×D61—81no—
224D4×D61—81no—
225D4×D61—82no—
226D4×D61—82no—
227#11758222—22no—
228#11758222—22no—
229#11758222—42no—
230#11758222—42no—
231C2×D244—21no—
232C2×D244—21no—
233C2×D244C22⋊C411yescharacteristic
234C2×D244C22×C412yes—
235C2×C4×D61—22no—
236C2×C4×D61C22×C411yescharacteristic
237C2×C4×D61C22×C411yescharacteristic
238C2×C4×D61C2×D411yescharacteristic
239C2×C4×D61C2×D411yescharacteristic
240C2×C4×D61C2×D411yescharacteristic
241C2×C4×D61C2×D411yescharacteristic
242C2×Dic122—21no—
243C2×Dic122C22⋊C411yescharacteristic
244C2×C8×C61—21no—
245C2×C8×C61—21no—
246C2×C8×C61—21no—
247C2×C8×C61—21no—
248C42×C61C22×C411yescharacteristic
249C42×C61C2×D411yescharacteristic
250C42×C61C2×D411yescharacteristic
251C42×C61C2411yescharacteristic
252C22⋊Dic61—22no—
253C22⋊Dic61—22no—
254C22⋊Dic61—22no—
255C22⋊Dic61—22no—
256C22⋊Dic61C22⋊C411yescharacteristic
257C22⋊Dic61C22⋊C411yescharacteristic
258#11758198—22no—
259#11758198—22no—
260#11758198C22⋊C411yescharacteristic
261#11758198C22⋊C411yescharacteristic
262#11758198C22⋊C411yescharacteristic
263#11758198C22⋊C411yescharacteristic
264C4⋊Dic61—21no—
265C4⋊Dic61C22⋊C411yescharacteristic
266C4⋊Dic61C22⋊C411yescharacteristic
267C4⋊Dic61C22×C412yes—
268#11758196C22⋊C411yescharacteristic
269#11758196C22⋊C411yescharacteristic
270#11758196C22⋊C411yescharacteristic
271#11758196C22⋊C411yescharacteristic
272C4×Dic61C22×C411yescharacteristic
273C4×Dic61C22×C411yescharacteristic
274C4×Dic61C2×D411yescharacteristic
275C4×Dic61C2×D411yescharacteristic
276C4×Dic61C2×D411yescharacteristic
277C4×Dic61C2×D411yescharacteristic
278#11758194—81no—
279C2×#92418—21no—
280C2×#92418—21no—
281C2×#92418—21no—
282C2×#92418—21no—
283#11758189—42no—
284#11758189—81no—
285C8×D61—42no—
286C8×D61—81no—
287C23×C61—22no—
288C23×C61—22no—
289C23×C61—44no—
290C23×C61—82no—
291C23×C61—82no—
292C23×C61C2×C22⋊C411yescharacteristic
293C22×D61—22no—
294C22×D61—44no—
295C22×D61—44no—
296C22×D61—82no—
297C22×D61—82no—
298C22×D61—82no—
299C22×D61—82no—
300C22×D61C2×C22⋊C411yescharacteristic
301C22×D61C2×C22⋊C411yescharacteristic
302D4×C61—42no—
303D4×C61—42no—
304D4×C61—44no—
305D4×C61—41no—
306D4×C61—41no—
307D4×C61—41no—
308D4×C61—41no—
309D4×C61—41no—
310D4×C61—41no—
311D4×C61—41no—
312D4×C61—41no—
313D4×C61—82no—
314D4×C61—82no—
315C2×C4×C61—21no—
316C2×C4×C61—21no—
317C2×C4×C61—21no—
318C2×C4×C61—21no—
319C2×C4×C61—41no—
320C2×C4×C61C2×C22⋊C411yescharacteristic
321C2×C4×C61C2×C22⋊C411yescharacteristic
322C2×C4×C61C2×C22⋊C411yescharacteristic
323C2×C4×C61C23×C411yescharacteristic
324C2×C4×C61C22×D411yescharacteristic
325C2×C4×C61C22×D411yescharacteristic
326C22⋊D61—22no—
327C22⋊D61—22no—
328C22⋊D61—44no—
329C22⋊D61—44no—
330C22⋊D61—44no—
331C22⋊D61—44no—
332C22⋊D61—44no—
333C22⋊D61—82no—
334C22⋊D61—82no—
335C22⋊D61—82no—
336C22⋊D61—82no—
337C2×Dic61—22no—
338C2×Dic61—44no—
339C2×Dic61—44no—
340C2×Dic61C2×C22⋊C411yescharacteristic
341C2×Dic61C2×C22⋊C411yescharacteristic
342C2×Dic61C2×C22⋊C411yescharacteristic
343C2×Dic61C2×C22⋊C411yescharacteristic
344C2×Dic61C2×C22⋊C411yescharacteristic
345C2×Dic61C2×C22⋊C411yescharacteristic
346D244—22no—
347D244—42no—
348D244—41no—
349D244—41no—
350D244—41no—
351D244—41no—
352C4×D61—21no—
353C4×D61—21no—
354C4×D61—21no—
355C4×D61—21no—
356C4×D61—21no—
357C4×D61—21no—
358C4×D61—41no—
359C4×D61—41no—
360C4×D61—44no—
361C4×D61AGL(1,ℤ/8)12yes—
362C4×D61AGL(1,ℤ/8)12yes—
363Dic122—22no—
364Dic122—41no—
365Dic122—41no—
366C8×C61—41no—
367C8×C61—41no—
368C8×C61—41no—
369C8×C61—41no—
370#92418—41no—
371#92418—41no—
372#92418—41no—
373#92418—41no—
374#17758—611nomaximal, Sylow
375C22×C61—21no—
376C22×C61—21no—
377C22×C61—21no—
378C22×C61—42no—
379C22×C61—42no—
380C22×C61—42no—
381C22×C61—42no—
382C22×C61—42no—
383C22×C61—42no—
384C22×C61—164no—
385C22×C61C22×C22⋊C411yescharacteristic
386C2×D61—21no—
387C2×D61—21no—
388C2×D61—21no—
389C2×D61—21no—
390C2×D61—21no—
391C2×D61—42no—
392C2×D61—42no—
393C2×D61—42no—
394C2×D61—164no—
395C2×D61—164no—
396C2×D61#41812yes—
397C4×C61—21no—
398C4×C61—21no—
399C4×C61—21no—
400C4×C61—21no—
401C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
402C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
403C4×C61#57611yescharacteristic
404C4×C61#57711yescharacteristic
405Dic61—21no—
406Dic61—21no—
407Dic61—21no—
408Dic61—21no—
409Dic61—21no—
410Dic61—42no—
411Dic61#41812yes—
412#3498—611no—
413#2989—611no—
414#2925—611no—
415#1557—611no—
416#1557—611no—
417#1555—611no—
418#1555D6111yescharacteristic, complemented
419#1553—611no—
420#1553—611no—
421#1547—611no—
422#1545—611no—
423#1545—611no—
424#1545—611no—
425#1540—611no—
426C2×#331—611no—
427C2×C61—41no—
428C2×C61—82no—
429C2×C61—82no—
430C2×C61#288811yescharacteristic
431C2×C61C2×#41811yescharacteristic
432C2×C61#289711yescharacteristic
433D61—22no—
434D61—41no—
435D61—82no—
436C2×H(5,𝔽2)—1221no—
437#550—612no—
438#550—1221no—
439D42—612no—
440D42—612no—
441D42—612no—
442D42—1221no—
443D42—1221no—
444D42—1221no—
445#535—1221no—
446#535—1221no—
447#535—1221no—
448#532—611no—
449#532—611no—
450#532—611no—
451C2×#127—611no—
452C2×#127—611no—
453C2×#127C2×D6111yescharacteristic
454C4×#41—611no—
455#446—1221no—
456#436—1221no—
457#435—1221no—
458#435—1221no—
459#433—1221no—
460#433—1221no—
461#432—611no—
462#432—611no—
463#432C2×D6111yescharacteristic, complemented
464#432C2×D6111yescharacteristic, complemented
465#431—611no—
466#431—611no—
467#431—611no—
468#423—611no—
469#423—611no—
470#423—611no—
471C2×C4⋊C8—611no—
472C2×C4⋊C8—611no—
473#408—1221no—
474#405—1221no—
475#332—611no—
476#332—611no—
477#332—611no—
478#332—611no—
479#331—611no—
480#331—611no—
481#331—611no—
482#331—611no—
483#331—611no—
484#331—611no—
485#331—611no—
486#331—611no—
487#331C2×D6111yescharacteristic, complemented
488#331C2×D6111yescharacteristic, complemented
489#331C2×D6111yescharacteristic, complemented
490#331C2×D6111yescharacteristic, complemented
491C61#1775811yescharacteristic, complemented, Sylow
492H(5,𝔽2)—2444no—
493H(5,𝔽2)—2444no—
494C2×#41—611no—
495C2×#41—1221no—
496C2×#41—1221no—
497C2×#41—1222no—
498C2×#41—1221no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—612no—
502C22×D4—612no—
503C22×D4—1221no—
504C22×D4—1221no—
505C22×D4—1221no—
506C22×D4—1221no—
507C22×D4—1222no—
508C22×D4—1222no—
509C22×D4—1222no—
510C22×D4C4×D6112yes—
511C2×M16—1221no—
512C2×M16—1221no—
513C2×M16—1221no—
514C22×C8—1221no—
515C22×C8—1221no—
516C4⋊Q8—611no—
517#127—21no—
518#127—21no—
519#127—612no—
520#127—612no—
521#127—611no—
522#127—1221no—
523#127—1221no—
524#127—1221no—
525#127—1221no—
526#127C4×D6112yes—
527#127C22×D6111yescharacteristic
528#127C22×D6111yescharacteristic
529#124—1221no—
530#124—1221no—
531#124—1221no—
532#121—612no—
533#121—612no—
534#121—612no—
535#121—1222no—
536#121—1222no—
537#121—1222no—
538#121—1222no—
539#121—1222no—
540#121—1222no—
541#121—1221no—
542#121—1221no—
543#121—1221no—
544#120—1222no—
545#120—1222no—
546#120—1222no—
547#120—1222no—
548#120—1222no—
549#120—1222no—
550C4×Q8—611no—
551C4×Q8—611no—
552C4×D4—611no—
553C4×D4—611no—
554C4×D4—611no—
555C4×D4—611no—
556C4×D4—612no—
557C4×D4—612no—
558C4×D4—611no—
559C4×D4—612no—
560C4×D4—611no—
561C4×D4—1221no—
562C4×D4—1221no—
563C4×D4—1221no—
564#117—611no—
565#117—611no—
566#117—611no—
567C2×C42—611no—
568C2×C42—611no—
569C2×C42C22×D6111yescharacteristic
570C4⋊C8—611no—
571C4⋊C8—611no—
572C4⋊C8—611no—
573C4⋊C8—611no—
574C4⋊C8—1221no—
575C4⋊C8—1221no—
576C4⋊C8—1221no—
577C4⋊C8—1221no—
578C4⋊C8—1221no—
579C4⋊C8C22×D6111yescharacteristic
580C4⋊C8C22×D6111yescharacteristic
581C4⋊C8C22×D6111yescharacteristic
582C4⋊C8C22×D6111yescharacteristic
583C22⋊C8—21no—
584C22⋊C8—21no—
585C22⋊C8—1221no—
586C22⋊C8—1221no—
587C22⋊C8—1221no—
588C22⋊C8—1221no—
589C22⋊C8—1221no—
590#97—21no—
591#97—21no—
592#97—1221no—
593#97—1221no—
594C4×C8—1221no—
595C4×C8—1221no—
596C4×C8—1221no—
597C24—22no—
598C24—1222no—
599C24—1222no—
600#41—1222no—
601#41—1222no—
602#41—2442no—
603#41—2442no—
604#41—2442no—
605#41—2442no—
606#41—2442no—
607#41—2442no—
608#41—2448no—
609C2×Q8—611no—
610C2×Q8—1221no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—22no—
616C2×D4—22no—
617C2×D4—22no—
618C2×D4—42no—
619C2×D4—42no—
620C2×D4—81no—
621C2×D4—81no—
622C2×D4—82no—
623C2×D4—611no—
624C2×D4—611no—
625C2×D4—612no—
626C2×D4—611no—
627C2×D4—1222no—
628C2×D4—1222no—
629C2×D4—1222no—
630C2×D4—1222no—
631C2×D4—1222no—
632C2×D4—1222no—
633C2×D4—1222no—
634C2×D4—1222no—
635C2×D4—1222no—
636C2×D4—1221no—
637C2×D4—1221no—
638C2×D4—4881no—
639C2×D4—4881no—
640C2×D4—4881no—
641C2×D4—4881no—
642C2×D4—4882no—
643C2×D4—4882no—
644C2×D4—2442no—
645C2×D4—2442no—
646C2×D4—2442no—
647C2×D4—2442no—
648C2×D4—2448no—
649C2×D4—2448no—
650C2×D4—2448no—
651C2×D4C2×C4×D6112yes—
652C2×D4C2×C4×D6112yes—
653C22×C4—611no—
654C22×C4—611no—
655C22×C4—611no—
656C22×C4—611no—
657C22×C4—611no—
658C22×C4—611no—
659C22×C4—1222no—
660C22×C4—1222no—
661C22×C4—1222no—
662C22×C4C2×C4×D6111yescharacteristic
663C22×C4D4×D6111yescharacteristic
664C22×C4D4×D6111yescharacteristic
665M16—4881no—
666M16—4881no—
667M16—2442no—
668C2×C8—21no—
669C2×C8—21no—
670C2×C8—21no—
671C2×C8—21no—
672C2×C8—1221no—
673C2×C8—1221no—
674C2×C8—1221no—
675C2×C8—1221no—
676C2×C8—4881no—
677C2×C8—2442no—
678C4⋊C4—611no—
679C4⋊C4—611no—
680C4⋊C4—611no—
681C4⋊C4—611no—
682C4⋊C4—611no—
683C4⋊C4—611no—
684C4⋊C4—612no—
685C4⋊C4—1221no—
686C22⋊C4—611no—
687C22⋊C4—611no—
688C22⋊C4—611no—
689C22⋊C4—611no—
690C22⋊C4—611no—
691C22⋊C4—611no—
692C22⋊C4—1222no—
693C22⋊C4—1222no—
694C22⋊C4—1222no—
695C22⋊C4—1222no—
696C22⋊C4—1222no—
697C22⋊C4—1222no—
698C42—611no—
699C42—611no—
700C42—611no—
701C42—611no—
702C42—611no—
703C42—611no—
704C42C2×C4×D6111yescharacteristic
705C42D4×D6111yescharacteristic
706C42D4×D6111yescharacteristic
707C42C23×D6111yescharacteristic
708C23—22no—
709C23—22no—
710C23—44no—
711C23—82no—
712C23—82no—
713C23—611no—
714C23—611no—
715C23—1222no—
716C23—4882no—
717C23—4882no—
718C23—4882no—
719C23—4882no—
720C23—2444no—
721C23—2444no—
722C23C22⋊C4×D6111yescharacteristic
723Q8—1222no—
724Q8—2441no—
725Q8—2441no—
726D4—42no—
727D4—42no—
728D4—44no—
729D4—41no—
730D4—41no—
731D4—41no—
732D4—41no—
733D4—41no—
734D4—41no—
735D4—41no—
736D4—41no—
737D4—82no—
738D4—82no—
739D4—1222no—
740D4—1222no—
741D4—1222no—
742D4—4882no—
743D4—4882no—
744D4—4882no—
745D4—4882no—
746D4—2442no—
747D4—2444no—
748D4—2444no—
749D4—2444no—
750D4—2444no—
751D4—2444no—
752D4—2441no—
753D4—2441no—
754D4—2441no—
755D4—2441no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—41no—
761C2×C4—611no—
762C2×C4—612no—
763C2×C4—612no—
764C2×C4—611no—
765C2×C4—611no—
766C2×C4—611no—
767C2×C4—611no—
768C2×C4—611no—
769C2×C4—1221no—
770C2×C4—1221no—
771C2×C4—1221no—
772C2×C4—1221no—
773C2×C4—1221no—
774C2×C4—1221no—
775C2×C4—1222no—
776C2×C4—2441no—
777C2×C4—2441no—
778C2×C4—2444no—
779C2×C4—2444no—
780C2×C4—2444no—
781C2×C4C22⋊C4×D6111yescharacteristic
782C2×C4C22⋊C4×D6111yescharacteristic
783C2×C4C22⋊C4×D6111yescharacteristic
784C2×C4C22×C4×D6111yescharacteristic
785C2×C4C2×D4×D6111yescharacteristic
786C2×C4C2×D4×D6111yescharacteristic
787C8—41no—
788C8—41no—
789C8—41no—
790C8—41no—
791C8—2441no—
792C8—2441no—
793C8—2441no—
794C8—2441no—
795C22—21no—
796C22—21no—
797C22—21no—
798C22—42no—
799C22—42no—
800C22—42no—
801C22—42no—
802C22—42no—
803C22—42no—
804C22—164no—
805C22—612no—
806C22—1221no—
807C22—1221no—
808C22—1221no—
809C22—1221no—
810C22—1221no—
811C22—9764no—
812C22—9764no—
813C22—2442no—
814C22—2442no—
815C22—2442no—
816C22C2×C22⋊C4×D6111yescharacteristic
817C4—21no—
818C4—21no—
819C4—21no—
820C4—21no—
821C4—612no—
822C4—1221no—
823C4—1221no—
824C4—1221no—
825C4—1221no—
826C4—1221no—
827C4—2442no—
828C4AGL(1,ℤ/8)×D6111yescharacteristic
829C4AGL(1,ℤ/8)×D6111yescharacteristic
830C4#1684056611yescharacteristic
831C4#1684057211yescharacteristic
832C2—41no—
833C2—82no—
834C2—82no—
835C2—1222no—
836C2—4882no—
837C2—2441no—
838C2#2145429511yescharacteristic
839C2#418×D6111yescharacteristic
840C2#2145434411yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1555C2
socleC22×C61C22×C22⋊C4
prime radical#21459595C2
cosocleC42×C61C24
hypercenter#1555D61
hypocenterC61#17758
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1555

Complements

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

NH ≅ G/Ntype
2. #21454938C2semidirect
3. #21454486C2semidirect
4. #21444542C2semidirect
5. #21444538C2semidirect
6. #21444531C2semidirect
7. #21444525C2semidirect
8. #21444521C2semidirect
9. #21444493C2semidirect
10. #21444487C2semidirect
11. #21444485C2semidirect
12. #21444485C2semidirect
13. #21444465C2semidirect
14. #331×D61C2semidirect
15. C61×#1555C2semidirect
40. #16839818C22semidirect
41. #16839818C22semidirect
42. #16839815C22semidirect
43. #16839814C22semidirect
44. #16839814C22semidirect
45. #16839786C22semidirect
46. #16839784C22semidirect
47. #16839784C22semidirect
48. C4⋊C8×D61C22semidirect
49. C4⋊C8×D61C22semidirect
52. #16839509C22semidirect
53. #16839509C22semidirect
54. #16839507C22semidirect
55. #16839507C22semidirect
56. #16839506C22semidirect
57. #16839506C22semidirect
58. #16839506C22semidirect
59. #16839506C22semidirect
60. #16839505C22semidirect
61. #16839505C22semidirect
62. #16839505C22semidirect
63. #16839505C22semidirect
65. C61×#432C22semidirect
66. C61×#432C22semidirect
67. C61×#331C22semidirect
68. C61×#331C22semidirect
69. C61×#331C22semidirect
70. C61×#331C22semidirect
418. #1555D61semidirect
463. #432C2×D61semidirect
464. #432C2×D61semidirect
487. #331C2×D61semidirect
488. #331C2×D61semidirect
489. #331C2×D61semidirect
490. #331C2×D61semidirect
491. C61#17758semidirect

Maximal subgroups

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

subgroupindex
#214595952
#214549382
#214544862
#214445422
#214445382
#214445312
#214445252
#214445212
#214444932
#214444872
#214444852
#214444652
#331×D612
C61×#15552
#1775861