Finite Group Databasebeta

← #34023174

Subgroups — #34023174

Order 18688.

900 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22626419C211yesmaximal, characteristic
2#22626368C211yesmaximal, characteristic, complemented
3#22626009C211yesmaximal, characteristic, complemented
4#22626009C211yesmaximal, characteristic, complemented
5#22625994C211yesmaximal, characteristic, complemented
6#22625992C211yesmaximal, characteristic, complemented
7#22625918C211yesmaximal, characteristic
8#22625881C211yesmaximal, characteristic, complemented
9#22625836C211yesmaximal, characteristic, complemented
10#22625746C211yesmaximal, characteristic, complemented
11#106×#64408C211yesmaximal, characteristic, complemented
12#22625702C211yesmaximal, characteristic, complemented
13#102×#64408C211yesmaximal, characteristic, complemented
14#22625662C211yesmaximal, characteristic, complemented
15#482×D73C211yesmaximal, characteristic
16C2×D4×#64408C2211yescharacteristic
17C2×#14556670C2211yescharacteristic
18C22×C4⋊#64408C2211yescharacteristic
19C2×#14556659C2211yescharacteristic
20C2×#14556659C2211yescharacteristic
21C2×#14556653C2211yescharacteristic
22C2×#14556653C2211yescharacteristic
23#17989555C2211yescharacteristic
24C2×#14556645C2211yescharacteristic
25C2×C8×#64408C2211yescharacteristic
26#17989539—21no—
27#17989539C2211yescharacteristic
28#17989538C2211yescharacteristic
29#17989537—21no—
30#17989535—21no—
31#17989534—21no—
32#17989529C2211yescharacteristic
33C4⋊C4×#64408C2211yescharacteristic
34C4⋊C4×#64408C2211yescharacteristic
35C4⋊C4×#64408C2211yescharacteristic
36C4⋊C4×#64408C2211yescharacteristic
37C4⋊C4×#64408C2211yescharacteristic
38C4×C4⋊#64408—21no—
39C4×C4⋊#64408—21no—
40C22⋊C4×#64408—21no—
41C22⋊C4×#64408—21no—
42#17989461C2211yescharacteristic
43#17989461C2211yescharacteristic
44#17989460C2211yescharacteristic
45#17989460C2211yescharacteristic
46#17989460C2211yescharacteristic
47#17989460C2211yescharacteristic
48#17989460C2211yescharacteristic
49#17989460C2211yescharacteristic
50#17989452C2211yescharacteristic
51#17989452C2211yescharacteristic
52#121×D73C2211yescharacteristic
53#117×D73C2211yescharacteristic
54#17988914C411yescharacteristic, complemented
55#17988913C411yescharacteristic, complemented
56#17988912C411yescharacteristic, complemented
57#17988911C411yescharacteristic, complemented
58#17988910C411yescharacteristic, complemented
59#17988909C411yescharacteristic, complemented
60#17988908C411yescharacteristic, complemented
61#107×D73C2211yescharacteristic
62#106×D73C2211yescharacteristic
63#102×D73C2211yescharacteristic
64#102×D73C2211yescharacteristic
65C22⋊C8×D73C2211yescharacteristic
66#482×C73C411yescharacteristic, complemented
67C23×#64408—21no—
68C23×#64408—21no—
69C2×#11924036C2311yescharacteristic
70C2×#11924036C2311yescharacteristic
71D4×#64408—22no—
72D4×#64408—22no—
73#14556670—22no—
74#14556670—22no—
75C2×C4⋊#64408—22no—
76C2×C4⋊#64408—22no—
77C2×C4⋊#64408—21no—
78C2×C4⋊#64408—21no—
79C2×C4⋊#64408D411yescharacteristic
80C2×C4⋊#64408D411yescharacteristic
81C2×C4⋊#64408C2311yescharacteristic
82C2×C4⋊#64408C2311yescharacteristic
83C2×C4⋊#64408C2311yescharacteristic
84C2×C4⋊#64408C2311yescharacteristic
85C2×C22⋊#64408—21no—
86C2×C22⋊#64408—21no—
87C2×C22⋊#64408—21no—
88C2×C22⋊#64408—21no—
89C2×C22⋊#64408D411yescharacteristic
90C2×C22⋊#64408D411yescharacteristic
91C2×C4×#64408—21no—
92C2×C4×#64408—21no—
93C2×C4×#64408—21no—
94C2×C4×#64408—21no—
95C2×C4×#64408—21no—
96C2×C4×#64408C2311yescharacteristic
97C2×C4×#64408C2311yescharacteristic
98#14556659—22no—
99#14556659—22no—
100#14556653—22no—
101#14556653—22no—
102#14556648—21no—
103C22⋊#10596833—21no—
104#14556645—22no—
105C8×#64408—22no—
106(C2×#64408)⋊C4—21no—
107(C2×#64408)⋊C4—21no—
108(C2×#64408)⋊C4—21no—
109(C2×#64408)⋊C4—21no—
110(C2×#64408)⋊C4—21no—
111(C2×#64408)⋊C4—21no—
112(C2×#64408)⋊C4—21no—
113C2×D4×D73—21no—
114C2×D4×D73C2311yescharacteristic
115C22×C4×D73C2311yescharacteristic
116C2×C8×D73C2311yescharacteristic
117C2×C8×D73C2311yescharacteristic
118#14556566C2×C411yescharacteristic
119#14556565C2×C411yescharacteristic
120#14556564—21no—
121#14556563—21no—
122#14556562C2×C411yescharacteristic
123#14556550C2×C411yescharacteristic, complemented
124#14556549C2×C411yescharacteristic, complemented
125#14556549C2×C411yescharacteristic, complemented
126#14556548—21no—
127#14556547—21no—
128C4⋊C4×D73C2311yescharacteristic
129C4⋊C4×D73C2311yescharacteristic
130C4⋊C4×D73C2311yescharacteristic
131C22⋊C4×D73—21no—
132C22⋊C4×D73—21no—
133C42×D73—21no—
134#14556525C2×C411yescharacteristic, complemented
135#14556524C2×C411yescharacteristic, complemented
136#14556524C2×C411yescharacteristic, complemented
137#14556523C2×C411yescharacteristic, complemented
138#14556522C2×C411yescharacteristic, complemented
139#14556522C2×C411yescharacteristic, complemented
140#14556513C2×C411yescharacteristic, complemented
141#14556513C2×C411yescharacteristic, complemented
142#14556512C2×C411yescharacteristic, complemented
143#14556512C2×C411yescharacteristic, complemented
144#14556511C2×C411yescharacteristic, complemented
145#14556511C2×C411yescharacteristic, complemented
146C22⋊#10596831C2×C411yescharacteristic, complemented
147#14556503C2×C411yescharacteristic, complemented
148#14556503C2×C411yescharacteristic, complemented
149#121×C73C2×C411yescharacteristic
150#117×C73C2×C411yescharacteristic, complemented
151#107×C73C2×C411yescharacteristic, complemented
152#106×C73C2×C411yescharacteristic, complemented
153#102×C73C2×C411yescharacteristic, complemented
154#102×C73C2×C411yescharacteristic, complemented
155C22⋊C8×C73C2×C411yescharacteristic, complemented
156C22×#64408—21no—
157C22×#64408—21no—
158C22×#64408—24no—
159C22×#64408—21no—
160C22×#64408—21no—
161C22×#64408—42no—
162C22×#64408—81no—
163C22×#64408—81no—
164C22×#64408—81no—
165C22×#64408—81no—
166C22×#64408C2×D411yescharacteristic
167C22×#64408C2×D411yescharacteristic
168C22×#64408C2×D411yescharacteristic
169C22×#64408C2×D411yescharacteristic
170#11924036—21no—
171#11924036—21no—
172#11924036—21no—
173#11924036—21no—
174C2×#10596833—21no—
175C2×#10596833—21no—
176C4⋊#64408—24no—
177C4⋊#64408—22no—
178C4⋊#64408—22no—
179C4⋊#64408—21no—
180C4⋊#64408—21no—
181C4⋊#64408—21no—
182C4⋊#64408—21no—
183C4⋊#64408—21no—
184C4⋊#64408—21no—
185C4⋊#64408—81no—
186C4⋊#64408#4112yes—
187C4⋊#64408#4112yes—
188C22⋊#64408—22no—
189C22⋊#64408—22no—
190C22⋊#64408—42no—
191C22⋊#64408—81no—
192C22⋊#64408—81no—
193C22⋊#64408—81no—
194C4×#64408—21no—
195C4×#64408—21no—
196C4×#64408—81no—
197C4×#64408—81no—
198C4×#64408—81no—
199C4×#64408—81no—
200C4×#64408—81no—
201C4×#64408#4112yes—
202C4×#64408#4112yes—
203C23×D73—21no—
204C23×D73C2×D411yescharacteristic
205C2×D292—21no—
206C2×D292C22×C411yescharacteristic
207C2×C22⋊D73—21no—
208C2×C22⋊D73—21no—
209C2×C22⋊D73—21no—
210D4×D73—21no—
211D4×D73—21no—
212D4×D73—21no—
213D4×D73—21no—
214D4×D73—81no—
215D4×D73—81no—
216C22×Dic73#4111yescharacteristic
217C2×C4×D73—21no—
218C2×C4×D73—21no—
219C2×C4×D73—21no—
220C2×C4×D73—21no—
221C2×C4×D73—21no—
222C2×C4×D73—21no—
223C2×C4×D73—21no—
224C2×C4×D73C22×C411yescharacteristic
225C2×C4×D73C2×D411yescharacteristic
226C2×C4×D73#4111yescharacteristic
227C2×C4×D73C2411yescharacteristic
228C2×#10596831C22×C411yescharacteristic
229C2×#10596831C22×C411yescharacteristic
230C8×D73—21no—
231C8×D73—21no—
232C8×D73—21no—
233C8×D73—21no—
234C4⋊Dic73C22×C411yescharacteristic
235C4⋊Dic73C22×C411yescharacteristic
236C4⋊Dic73C22×C411yescharacteristic
237#11924007—21no—
238#11924007—21no—
239#11924007—21no—
240C22⋊Dic73—21no—
241C22⋊Dic73—21no—
242#11924005—21no—
243#11924005—21no—
244#11924005—21no—
245#11924005—21no—
246C4×Dic73—21no—
247C4×Dic73—21no—
248C4×Dic73—21no—
249C2×D4×C73—21no—
250C2×D4×C73C22×C411yescharacteristic
251C22×C4×C73C22×C411yescharacteristic
252C2×C8×C73C22×C411yescharacteristic
253C2×C8×C73C22×C411yescharacteristic
254C4⋊C4×C73C22×C411yescharacteristic
255C4⋊C4×C73C22×C411yescharacteristic
256C4⋊C4×C73C22×C411yescharacteristic
257C22⋊C4×C73—21no—
258C22⋊C4×C73—21no—
259C42×C73—21no—
260C23×C73—21no—
261C23×C73C4×D411yescharacteristic
262C22×D73—21no—
263C22×D73—21no—
264C22×D73—21no—
265C22×D73—21no—
266C22×D73—21no—
267C22×D73—21no—
268C22×D73—21no—
269C22×D73—41no—
270C22×D73—41no—
271C22×D73—41no—
272C22×D73—41no—
273C22×D73—41no—
274C22×D73—41no—
275C22×D73C4×D411yescharacteristic
276C22×D73C22×D411yescharacteristic
277C2×#64408—21no—
278C2×#64408—21no—
279C2×#64408—21no—
280C2×#64408—21no—
281C2×#64408—21no—
282C2×#64408—21no—
283C2×#64408—22no—
284C2×#64408—22no—
285C2×#64408—21no—
286C2×#64408—21no—
287C2×#64408—21no—
288C2×#64408—21no—
289C2×#64408—41no—
290C2×#64408—41no—
291C2×#64408—41no—
292C2×#64408—41no—
293C2×#64408—41no—
294C2×#64408—41no—
295C2×#64408—41no—
296C2×#64408—41no—
297C2×#64408—41no—
298C2×#64408—41no—
299C2×#64408—84no—
300C2×#64408—84no—
301C2×#64408#12312yes—
302C2×#64408#12312yes—
303D4×C73—21no—
304D4×C73—21no—
305D4×C73—81no—
306C2×C4×C73—21no—
307C2×C4×C73—21no—
308C2×C4×C73—21no—
309C2×C4×C73—21no—
310C2×C4×C73—21no—
311C2×C4×C73C4×D411yescharacteristic
312C2×C4×C73C23×C411yescharacteristic
313C22⋊D73—41no—
314C22⋊D73—41no—
315C22⋊D73—81no—
316C22⋊D73—81no—
317C2×Dic73—21no—
318C2×Dic73—21no—
319C2×Dic73—21no—
320C2×Dic73—21no—
321C2×Dic73—21no—
322C2×Dic73C4×D411yescharacteristic
323C2×Dic73C2×#4111yescharacteristic
324D292—21no—
325D292—21no—
326D292—81no—
327C4×D73—21no—
328C4×D73—21no—
329C4×D73—21no—
330C4×D73—21no—
331C4×D73—21no—
332C4×D73—21no—
333C4×D73—41no—
334C4×D73—41no—
335C4×D73—41no—
336C4×D73—41no—
337C4×D73—41no—
338C4×D73—41no—
339C4×D73C2×#4111yescharacteristic
340C4×D73C2×#4111yescharacteristic
341C4×D73C2×#4111yescharacteristic
342C4×D73C2×#4111yescharacteristic
343#10596833—41no—
344#10596833—41no—
345C8×C73—21no—
346C8×C73—21no—
347#10596831—21no—
348#10596831—21no—
349C22×C73—21no—
350C22×C73—21no—
351C22×C73—21no—
352C22×C73—41no—
353C22×C73—41no—
354C22×C73—41no—
355C22×C73C2×C4×D411yescharacteristic
356C2×D73—21no—
357C2×D73—21no—
358C2×D73—21no—
359C2×D73—41no—
360C2×D73—41no—
361C2×D73—41no—
362C2×D73—41no—
363C2×D73—41no—
364C2×D73—41no—
365C2×D73—41no—
366C2×D73—81no—
367C2×D73—81no—
368C2×D73—81no—
369C2×D73—81no—
370C2×D73C2×#12311yescharacteristic
371C2×D73#52511yescharacteristic
372C2×D73#57611yescharacteristic
373C2×D73#57711yescharacteristic
374C2×D73#57711yescharacteristic
375C2×D73#57711yescharacteristic
376#64408—22no—
377#64408—22no—
378#64408—41no—
379#64408—41no—
380#64408—42no—
381#64408—42no—
382#64408—81no—
383#64408—81no—
384C4×C73—21no—
385C4×C73—41no—
386C4×C73—41no—
387C4×C73—41no—
388C4×C73C4×#4111yescharacteristic
389C4×C73C4×#4111yescharacteristic
390Dic73—21no—
391Dic73—41no—
392Dic73—41no—
393Dic73—41no—
394Dic73#52911yescharacteristic
395Dic73#52911yescharacteristic
396#21588—731nomaximal, Sylow
397C2×C73—41no—
398C2×C73—81no—
399C2×C73C4×#12311yescharacteristic
400C2×C73#294611yescharacteristic
401C2×C73#295211yescharacteristic
402D73—41no—
403D73—81no—
404D73#309611yescharacteristic
405D73#309911yescharacteristic
406D73#311811yescharacteristic
407D73#312611yescharacteristic
408C2×#482—731no—
409#2324—731no—
410#2274—731no—
411#1926—731no—
412#1926—731no—
413#1920—731no—
414#1918—731no—
415#1874—731no—
416#1853—731no—
417#1825—731no—
418#1776—731no—
419C4×#106—731no—
420#1762—731no—
421C4×#102—731no—
422#1750—731no—
423C73#2158811yescharacteristic, complemented, Sylow
424C2×#121—731no—
425C2×C4×D4—731no—
426C2×#117—731no—
427C2×#117—731no—
428C22×C4⋊C4—731no—
429#482—731no—
430#482—731no—
431#482—731no—
432#482—731no—
433#482—731no—
434#482—731no—
435#482—731no—
436#482#6440811yescharacteristic, complemented
437C2×#107—731no—
438C2×#106—731no—
439C2×#106—731no—
440C2×#106—731no—
441C2×#102—731no—
442C2×#102—731no—
443C2×#102—731no—
444C2×#102—731no—
445C2×C22⋊C8—731no—
446C2×C22⋊C8—731no—
447C2×#97—731no—
448C2×C4×C8—731no—
449#390—731no—
450#390—1461no—
451#389—731no—
452#388—1461no—
453#386—1461no—
454#385—1461no—
455#380—731no—
456C4×C4⋊C4—731no—
457C4×C4⋊C4—731no—
458C4×C4⋊C4—731no—
459C4×C4⋊C4—731no—
460C4×C4⋊C4—731no—
461C4×C4⋊C4—1461no—
462C4×C4⋊C4—1461no—
463C4×C22⋊C4—1461no—
464C4×C22⋊C4—1461no—
465#340—731no—
466#340—731no—
467#340—731no—
468#340—731no—
469#340—731no—
470#340—731no—
471#340—731no—
472#340—731no—
473#336—731no—
474#336—731no—
475C22×D4—731no—
476C22×D4—1461no—
477C23×C4—731no—
478C23×C4—1461no—
479C23×C4—1461no—
480C22×C8—731no—
481C22×C8—731no—
482C22×C8—731no—
483C22×C8—731no—
484#121—731no—
485#121—731no—
486#121—731no—
487#121—1461no—
488#121—1461no—
489#121C2×#6440811yescharacteristic
490C4×D4—1462no—
491C4×D4—1462no—
492#117—731no—
493#117—731no—
494#117—731no—
495#117—1461no—
496#117—1462no—
497#117—1462no—
498#117—1461no—
499#117C2×#6440811yescharacteristic, complemented
500C2×C4⋊C4—731no—
501C2×C4⋊C4—731no—
502C2×C4⋊C4—731no—
503C2×C4⋊C4—731no—
504C2×C4⋊C4—731no—
505C2×C4⋊C4—731no—
506C2×C4⋊C4—731no—
507C2×C4⋊C4—731no—
508C2×C4⋊C4—731no—
509C2×C4⋊C4—1461no—
510C2×C4⋊C4—1462no—
511C2×C4⋊C4—1462no—
512C2×C4⋊C4—1461no—
513C2×C22⋊C4—731no—
514C2×C22⋊C4—731no—
515C2×C22⋊C4—1461no—
516C2×C22⋊C4—1461no—
517C2×C22⋊C4—1461no—
518C2×C22⋊C4—1461no—
519C2×C22⋊C4—1461no—
520C2×C22⋊C4—1461no—
521C2×C42—731no—
522C2×C42—731no—
523C2×C42—1461no—
524C2×C42—1461no—
525C2×C42—1461no—
526C2×C42—1461no—
527C2×C42—1461no—
528C2×C42—1461no—
529#107—731no—
530#107—731no—
531#107—731no—
532#107C2×#6440811yescharacteristic, complemented
533#106—731no—
534#106—731no—
535#106—731no—
536#106—1462no—
537#106—1462no—
538#106C2×#6440811yescharacteristic, complemented
539#102—731no—
540#102—731no—
541#102—731no—
542#102—731no—
543#102—731no—
544#102—731no—
545#102—1462no—
546#102—1462no—
547#102C2×#6440811yescharacteristic, complemented
548#102C2×#6440811yescharacteristic, complemented
549C22⋊C8—731no—
550C22⋊C8—731no—
551C22⋊C8—731no—
552C22⋊C8—1461no—
553C22⋊C8—1461no—
554C22⋊C8C2×#6440811yescharacteristic, complemented
555#97—1462no—
556C4×C8—1462no—
557#95—1461no—
558#95—1461no—
559#95—1461no—
560#95—1461no—
561#95—1461no—
562#95—1461no—
563#95—1461no—
564C24—731no—
565C24—1461no—
566C2×D4—21no—
567C2×D4—5841no—
568C2×D4—5841no—
569C2×D4—731no—
570C2×D4—1461no—
571C2×D4—1461no—
572C2×D4—1461no—
573C2×D4—1461no—
574C2×D4—1461no—
575C2×D4—1461no—
576C2×D4—1461no—
577C2×D4—1461no—
578C2×D4C22×#6440811yescharacteristic
579C22×C4—2922no—
580C22×C4—5841no—
581C22×C4—5841no—
582C22×C4—5841no—
583C22×C4—5841no—
584C22×C4—731no—
585C22×C4—731no—
586C22×C4—731no—
587C22×C4—731no—
588C22×C4—731no—
589C22×C4—731no—
590C22×C4—731no—
591C22×C4—731no—
592C22×C4—731no—
593C22×C4—1461no—
594C22×C4—1461no—
595C22×C4—1461no—
596C22×C4—1461no—
597C22×C4—1461no—
598C22×C4—1461no—
599C22×C4—1461no—
600C22×C4—1461no—
601C22×C4—1461no—
602C22×C4—1461no—
603C22×C4—1461no—
604C22×C4—1464no—
605C22×C4C22×#6440811yescharacteristic
606C2×C8—731no—
607C2×C8—731no—
608C2×C8—1461no—
609C2×C8—1461no—
610C2×C8—1461no—
611C2×C8—1461no—
612C2×C8—1461no—
613C2×C8—1461no—
614C2×C8—1461no—
615C2×C8—1461no—
616C2×C8—1461no—
617C2×C8—1461no—
618C2×C8C22×#6440811yescharacteristic
619C2×C8C22×#6440811yescharacteristic
620C4⋊C4—5841no—
621C4⋊C4—732no—
622C4⋊C4—732no—
623C4⋊C4—731no—
624C4⋊C4—731no—
625C4⋊C4—731no—
626C4⋊C4—1461no—
627C4⋊C4—1461no—
628C4⋊C4—1461no—
629C4⋊C4—1461no—
630C4⋊C4—1461no—
631C4⋊C4—1461no—
632C4⋊C4—1461no—
633C4⋊C4—1461no—
634C4⋊C4—1461no—
635C4⋊C4—1462no—
636C4⋊C4—1462no—
637C4⋊C4—1464no—
638C4⋊C4C22×#6440811yescharacteristic
639C4⋊C4C22×#6440811yescharacteristic
640C4⋊C4C22×#6440811yescharacteristic
641C22⋊C4—21no—
642C22⋊C4—21no—
643C22⋊C4—2922no—
644C22⋊C4—5841no—
645C22⋊C4—5841no—
646C22⋊C4—5841no—
647C22⋊C4—1461no—
648C22⋊C4—1461no—
649C22⋊C4—1461no—
650C22⋊C4—1461no—
651C22⋊C4—1462no—
652C22⋊C4—1462no—
653C22⋊C4—1461no—
654C22⋊C4—1461no—
655C42—21no—
656C42—5841no—
657C42—5841no—
658C42—5841no—
659C42—5841no—
660C42—5841no—
661C42—732no—
662C42—732no—
663C42—1461no—
664C42—1461no—
665C42—1461no—
666C42—1461no—
667C42—1461no—
668C23—21no—
669C23—2921no—
670C23—2921no—
671C23—2921no—
672C23—2921no—
673C23—2921no—
674C23—2921no—
675C23—731no—
676C23—731no—
677C23—1461no—
678C23—1461no—
679C23—1461no—
680C23—1461no—
681C23—1461no—
682C23—1461no—
683C23—1461no—
684C23D4×#6440811yescharacteristic
685D4—21no—
686D4—21no—
687D4—81no—
688D4—2921no—
689D4—2921no—
690D4—5841no—
691D4—5841no—
692D4—5841no—
693D4—1461no—
694D4—1461no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—2921no—
701C2×C4—2921no—
702C2×C4—2921no—
703C2×C4—2921no—
704C2×C4—2921no—
705C2×C4—2921no—
706C2×C4—2921no—
707C2×C4—2921no—
708C2×C4—2921no—
709C2×C4—2921no—
710C2×C4—2921no—
711C2×C4—2921no—
712C2×C4—2921no—
713C2×C4—2921no—
714C2×C4—2921no—
715C2×C4—2921no—
716C2×C4—5844no—
717C2×C4—5844no—
718C2×C4—731no—
719C2×C4—731no—
720C2×C4—731no—
721C2×C4—731no—
722C2×C4—731no—
723C2×C4—732no—
724C2×C4—732no—
725C2×C4—731no—
726C2×C4—1461no—
727C2×C4—1461no—
728C2×C4—1461no—
729C2×C4—1461no—
730C2×C4—1461no—
731C2×C4—1461no—
732C2×C4—1461no—
733C2×C4—1461no—
734C2×C4—1461no—
735C2×C4—1461no—
736C2×C4—1462no—
737C2×C4—1462no—
738C2×C4—1461no—
739C2×C4—1461no—
740C2×C4—1461no—
741C2×C4—1461no—
742C2×C4—1461no—
743C2×C4—1461no—
744C2×C4—1461no—
745C2×C4—1461no—
746C2×C4—1461no—
747C2×C4—1461no—
748C2×C4—1461no—
749C2×C4D4×#6440811yescharacteristic
750C2×C4C23×#6440811yescharacteristic
751C8—21no—
752C8—21no—
753C8—2921no—
754C8—2921no—
755C8—1461no—
756C8—1461no—
757C22—21no—
758C22—21no—
759C22—21no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—2921no—
764C22—2921no—
765C22—2921no—
766C22—2921no—
767C22—2921no—
768C22—2921no—
769C22—2921no—
770C22—5841no—
771C22—5841no—
772C22—5841no—
773C22—5841no—
774C22—731no—
775C22—731no—
776C22—731no—
777C22—731no—
778C22—731no—
779C22—731no—
780C22—1461no—
781C22—1461no—
782C22—1461no—
783C22C2×D4×#6440811yescharacteristic
784C4—21no—
785C4—41no—
786C4—41no—
787C4—41no—
788C4—2922no—
789C4—2922no—
790C4—2921no—
791C4—2921no—
792C4—2921no—
793C4—2921no—
794C4—2921no—
795C4—5841no—
796C4—5841no—
797C4—731no—
798C4—731no—
799C4—1462no—
800C4—1462no—
801C4—1461no—
802C4#41×#6440811yescharacteristic
803C4#41×#6440811yescharacteristic
804C2—41no—
805C2—81no—
806C2—2921no—
807C2—5841no—
808C2—731no—
809C2—731no—
810C2—731no—
811C2—731no—
812C2#123×#6440811yescharacteristic
813C2#2262668811yescharacteristic
814C2#2262669411yescharacteristic
subgroupG/H
centerC22C2×D4×#64408
commutatorC2×C4×C73C23×C4
FrattiniC2×C4C23×#64408
Fitting#482×C73C4
socleC22×C73C2×C4×D4
prime radical#121×D73C22
cosocleC2×C4×D73C24
hypercenter#482#64408
hypocenterC73#21588
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
2. #22626368C2semidirect
3. #22626009C2semidirect
4. #22626009C2semidirect
5. #22625994C2semidirect
6. #22625992C2semidirect
8. #22625881C2semidirect
9. #22625836C2semidirect
10. #22625746C2semidirect
11. #106×#64408C2semidirect
12. #22625702C2semidirect
13. #102×#64408C2semidirect
14. #22625662C2semidirect
54. #17988914C4semidirect
55. #17988913C4semidirect
56. #17988912C4semidirect
57. #17988911C4semidirect
58. #17988910C4semidirect
59. #17988909C4semidirect
60. #17988908C4semidirect
66. #482×C73C4semidirect
123. #14556550C2×C4semidirect
124. #14556549C2×C4semidirect
125. #14556549C2×C4semidirect
134. #14556525C2×C4semidirect
135. #14556524C2×C4semidirect
136. #14556524C2×C4semidirect
137. #14556523C2×C4semidirect
138. #14556522C2×C4semidirect
139. #14556522C2×C4semidirect
140. #14556513C2×C4semidirect
141. #14556513C2×C4semidirect
142. #14556512C2×C4semidirect
143. #14556512C2×C4semidirect
144. #14556511C2×C4semidirect
145. #14556511C2×C4semidirect
146. C22⋊#10596831C2×C4semidirect
147. #14556503C2×C4semidirect
148. #14556503C2×C4semidirect
150. #117×C73C2×C4semidirect
151. #107×C73C2×C4semidirect
152. #106×C73C2×C4semidirect
153. #102×C73C2×C4semidirect
154. #102×C73C2×C4semidirect
155. C22⋊C8×C73C2×C4semidirect
423. C73#21588semidirect
436. #482#64408semidirect
499. #117C2×#64408semidirect
532. #107C2×#64408semidirect
538. #106C2×#64408semidirect
547. #102C2×#64408semidirect
548. #102C2×#64408semidirect
554. C22⋊C8C2×#64408semidirect

Maximal subgroups

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

subgroupindex
#226264192
#226263682
#226260092
#226259942
#226259922
#226259182
#226258812
#226258362
#226257462
#106×#644082
#226257022
#102×#644082
#226256622
#482×D732
#2158873