Finite Group Databasebeta

← #33103343

Subgroups — #33103343

Order 18688.

906 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22618588C211yesmaximal, characteristic, complemented
2#416×D73C211yesmaximal, characteristic
3#22618379C211yesmaximal, characteristic
4#22610637C211yesmaximal, characteristic, complemented
5#22610582C211yesmaximal, characteristic, complemented
6#22610576C211yesmaximal, characteristic, complemented
7#22610207C211yesmaximal, characteristic, complemented
8#22610205C211yesmaximal, characteristic, complemented
9#22610029C211yesmaximal, characteristic, complemented
10#22609968C211yesmaximal, characteristic, complemented
11#22609873C211yesmaximal, characteristic
12#22609768C211yesmaximal, characteristic, complemented
13#22609767C211yesmaximal, characteristic, complemented
14C8×#11924005C211yesmaximal, characteristic, complemented
15C73×#1937C211yesmaximal, characteristic, complemented
16C2×#41×D73C2211yescharacteristic
17C2×#14556599C2211yescharacteristic
18C2×#14556597C2211yescharacteristic
19C22×C8×D73C2211yescharacteristic
20#117×D73C2211yescharacteristic
21#17988647—21no—
22#17988647—21no—
23#17988643—21no—
24#17988639—21no—
25C2×#14556526C2211yescharacteristic, complemented
26C2×#14556526C2211yescharacteristic, complemented
27#17988614C2211yescharacteristic, complemented
28C2×#14556519C2211yescharacteristic
29C2×#14556518C2211yescharacteristic
30C2×#14556517C2211yescharacteristic
31#17988584C2211yescharacteristic
32#17988583C2211yescharacteristic
33#17988582C411yescharacteristic, complemented
34#17988582C411yescharacteristic, complemented
35#17988581C2211yescharacteristic
36#17988580C411yescharacteristic, complemented
37#17988580C411yescharacteristic, complemented
38#103×D73C411yescharacteristic, complemented
39#103×D73C411yescharacteristic, complemented
40#102×D73C411yescharacteristic, complemented
41#102×D73C411yescharacteristic, complemented
42#17988554C2211yescharacteristic
43#17988552—21no—
44#17988552—21no—
45#17988550C2211yescharacteristic
46#17988550C2211yescharacteristic
47#17988549—21no—
48C2×#14556503C2211yescharacteristic
49C22⋊C8×D73—21no—
50#17988545C2211yescharacteristic, complemented
51#17988542C2211yescharacteristic, complemented
52C2×C8×Dic73C2211yescharacteristic, complemented
53C4×#11924005C2211yescharacteristic
54#17988352C2211yescharacteristic, complemented
55#17988348C2211yescharacteristic, complemented
56#17988347C2211yescharacteristic, complemented
57#17988346C2211yescharacteristic, complemented
58#17988342C2211yescharacteristic, complemented
59#17988341C2211yescharacteristic, complemented
60#424×C73C2211yescharacteristic, complemented
61C2×#104×C73C2211yescharacteristic
62#416×C73C2211yescharacteristic
63#408×C73C2211yescharacteristic
64C2×C4×C8×C73C2211yescharacteristic, complemented
65#341×C73C2211yescharacteristic, complemented
66#339×C73C2211yescharacteristic, complemented
67C2×#11924029C2×C411yescharacteristic
68C2×#11924028—21no—
69C2×#11924028C2311yescharacteristic
70C2×#11924027—21no—
71C2×#11924027C2×C411yescharacteristic
72#41×D73—22no—
73#41×D73—22no—
74#41×D73—41no—
75#41×D73—41no—
76C2×Q8×D73C2×C411yescharacteristic
77C2×D4×D73—21no—
78C2×D4×D73C2×C411yescharacteristic
79C22×C4×D73—21no—
80C22×C4×D73C2311yescharacteristic
81#14556599—22no—
82#14556599—41no—
83#14556597—22no—
84#14556597—41no—
85C2×#11924012C2311yescharacteristic
86C2×#11924012C2311yescharacteristic
87C2×#11924011—21no—
88C2×#11924011—21no—
89C22×#10596831C2311yescharacteristic
90C22×#10596831C2311yescharacteristic
91C2×C8×D73—21no—
92C2×C8×D73—21no—
93C2×C8×D73—41no—
94C2×C8×D73—41no—
95C2×C8×D73C2×C411yescharacteristic
96C2×C8×D73C2×C411yescharacteristic
97C2×C8×D73C2×C411yescharacteristic
98C2×C8×D73C2×C411yescharacteristic
99#14556550C2311yescharacteristic
100#14556549C2×C411yescharacteristic
101#14556549C2×C411yescharacteristic
102#14556548—21no—
103#14556547—21no—
104C4⋊C4×D73C2×C411yescharacteristic
105C4⋊C4×D73C2×C411yescharacteristic
106C2×#11924005—21no—
107C22⋊C4×D73—21no—
108C2×C4×Dic73C2311yescharacteristic
109C42×D73—21no—
110#14556526—41no—
111#14556526—41no—
112C4⋊#10596831—21no—
113C4⋊#10596831—21no—
114#14556519—22no—
115#14556518—41no—
116#14556517—22no—
117#14556516C2×C411yescharacteristic
118#14556516C2×C411yescharacteristic
119#14556515C2×C411yescharacteristic
120#14556515C2×C411yescharacteristic
121#14556514C2×C411yescharacteristic
122#14556514C2×C411yescharacteristic
123#14556513C2×C411yescharacteristic
124#14556513C2×C411yescharacteristic
125#14556512C2×C411yescharacteristic
126#14556512C2×C411yescharacteristic
127#14556511C2×C411yescharacteristic
128#14556511C2×C411yescharacteristic
129C22⋊#10596831—21no—
130C22⋊#10596831—21no—
131#14556503—21no—
132#14556503—21no—
133#14556503—21no—
134#14556503—21no—
135#14556503D411yescharacteristic
136#14556503D411yescharacteristic
137#14556503D411yescharacteristic
138#14556503D411yescharacteristic
139#14556501—21no—
140#14556501—21no—
141C8×Dic73—21no—
142C8×Dic73—21no—
143C8×Dic73—41no—
144#14556498—21no—
145C2×#41×C73C2311yescharacteristic
146C2×M16×C73C2311yescharacteristic
147C2×M16×C73C2311yescharacteristic
148C22×C8×C73C2311yescharacteristic
149C22×C8×C73C2311yescharacteristic
150#117×C73C2311yescharacteristic
151C2×C42×C73C2311yescharacteristic
152C4⋊C8×C73—21no—
153C4⋊C8×C73—21no—
154#104×C73—41no—
155#103×C73C2×C411yescharacteristic
156#103×C73C2×C411yescharacteristic
157#102×C73C2×C411yescharacteristic
158#102×C73C2×C411yescharacteristic
159C22⋊C8×C73—21no—
160C22⋊C8×C73—21no—
161C4×C8×C73—41no—
162C23×D73—21no—
163C23×D73#4111yescharacteristic
164#11924029—22no—
165#11924029—41no—
166#11924028—21no—
167#11924028—21no—
168#11924028—42no—
169#11924028—42no—
170#11924028#4112yes—
171#11924028#4112yes—
172#11924027—22no—
173#11924027—41no—
174#11924027—42no—
175#11924027—42no—
176C2×Dic146—21no—
177C2×Dic146C22×C411yescharacteristic
178Q8×D73—22no—
179Q8×D73—41no—
180C2×D292—21no—
181C2×D292C22×C411yescharacteristic
182C2×C22⋊D73—21no—
183C2×C22⋊D73—21no—
184C2×C22⋊D73—21no—
185D4×D73—22no—
186D4×D73—41no—
187D4×D73—42no—
188D4×D73—42no—
189C22×Dic73—21no—
190C22×Dic73—21no—
191C22×Dic73#4111yescharacteristic
192C2×C4×D73—21no—
193C2×C4×D73—21no—
194C2×C4×D73—21no—
195C2×C4×D73—21no—
196C2×C4×D73—21no—
197C2×C4×D73—21no—
198C2×C4×D73—21no—
199C2×C4×D73—21no—
200C2×C4×D73—21no—
201C2×C4×D73—42no—
202C2×C4×D73—42no—
203C2×C4×D73C22×C411yescharacteristic
204C2×C4×D73C22×C411yescharacteristic
205C2×C4×D73C2×D411yescharacteristic
206C2×C4×D73C2×D411yescharacteristic
207#11924012—21no—
208#11924012—21no—
209#11924012—21no—
210#11924012—21no—
211#11924011—42no—
212#11924011—42no—
213C2×#10596831—21no—
214C2×#10596831—21no—
215C2×#10596831—21no—
216C2×#10596831—21no—
217C2×#10596831—21no—
218C2×#10596831—21no—
219C2×#10596831C22×C411yescharacteristic
220C2×#10596831C22×C411yescharacteristic
221C2×#10596831C2×D411yescharacteristic
222C2×#10596831C2×D411yescharacteristic
223C8×D73—41no—
224C8×D73—41no—
225C8×D73—41no—
226C8×D73—41no—
227C8×D73—42no—
228C8×D73—42no—
229C4⋊Dic73C22×C411yescharacteristic
230C4⋊Dic73C22×C411yescharacteristic
231#11924007—21no—
232#11924007—21no—
233C22⋊Dic73—21no—
234#11924005—24no—
235#11924005—21no—
236#11924005—21no—
237C4×Dic73—21no—
238C4×Dic73—21no—
239C4×Dic73—21no—
240C4×Dic73—21no—
241C4×Dic73—21no—
242#41×C73—21no—
243#41×C73—21no—
244#41×C73—21no—
245#41×C73—21no—
246C2×Q8×C73C22×C411yescharacteristic
247C2×D4×C73—21no—
248C2×D4×C73C22×C411yescharacteristic
249C22×C4×C73—21no—
250C22×C4×C73—21no—
251C22×C4×C73C2411yescharacteristic
252M16×C73—21no—
253M16×C73—21no—
254M16×C73—21no—
255M16×C73—21no—
256C2×C8×C73—21no—
257C2×C8×C73—21no—
258C2×C8×C73—21no—
259C2×C8×C73—21no—
260C2×C8×C73—21no—
261C2×C8×C73—21no—
262C2×C8×C73C22×C411yescharacteristic
263C2×C8×C73C22×C411yescharacteristic
264C2×C8×C73C2×D411yescharacteristic
265C2×C8×C73C2×D411yescharacteristic
266C4⋊C4×C73C22×C411yescharacteristic
267C4⋊C4×C73C22×C411yescharacteristic
268C22⋊C4×C73—21no—
269C42×C73—21no—
270C42×C73—21no—
271C42×C73—21no—
272C23×C73—21no—
273C23×C73C2×#4111yescharacteristic
274C22×D73—21no—
275C22×D73—21no—
276C22×D73—21no—
277C22×D73—22no—
278C22×D73—41no—
279C22×D73—42no—
280C22×D73—42no—
281C22×D73—81no—
282C22×D73C4×D411yescharacteristic
283C22×D73C4×D411yescharacteristic
284Q8×C73—21no—
285Q8×C73—21no—
286D4×C73—21no—
287D4×C73—21no—
288D4×C73—41no—
289D4×C73—41no—
290C2×C4×C73—22no—
291C2×C4×C73—21no—
292C2×C4×C73—21no—
293C2×C4×C73—21no—
294C2×C4×C73—41no—
295C2×C4×C73—41no—
296C2×C4×C73—41no—
297C2×C4×C73—41no—
298C2×C4×C73C23×C411yescharacteristic
299C2×C4×C73C22×D411yescharacteristic
300C2×C4×C73C2×#4111yescharacteristic
301C2×C4×C73C2×#4111yescharacteristic
302C2×C4×C73H(5,𝔽2)11yescharacteristic
303C2×C4×C73H(5,𝔽2)11yescharacteristic
304C22⋊D73—22no—
305C22⋊D73—22no—
306C22⋊D73—42no—
307C22⋊D73—42no—
308C2×Dic73—21no—
309C2×Dic73—21no—
310C2×Dic73—21no—
311C2×Dic73—22no—
312C2×Dic73—21no—
313C2×Dic73—21no—
314C2×Dic73—42no—
315C2×Dic73—41no—
316C2×Dic73—41no—
317C2×Dic73C4×D411yescharacteristic
318C2×Dic73C4×D411yescharacteristic
319D292—21no—
320D292—42no—
321D292#11712yes—
322C4×D73—21no—
323C4×D73—21no—
324C4×D73—21no—
325C4×D73—21no—
326C4×D73—22no—
327C4×D73—22no—
328C4×D73—21no—
329C4×D73—21no—
330C4×D73—21no—
331C4×D73—21no—
332C4×D73—42no—
333C4×D73—42no—
334C4×D73—42no—
335C4×D73—81no—
336Dic146—21no—
337Dic146—42no—
338Dic146#11712yes—
339C8×C73—21no—
340C8×C73—21no—
341C8×C73—21no—
342C8×C73—21no—
343C8×C73—41no—
344C8×C73—41no—
345#10596831—21no—
346#10596831—21no—
347#10596831—21no—
348#10596831—21no—
349#10596831—41no—
350#10596831—41no—
351C22×C73—21no—
352C22×C73—21no—
353C22×C73—41no—
354C22×C73—41no—
355C22×C73—41no—
356C22×C73C2×C4×D411yescharacteristic
357C22×C73#55111yescharacteristic
358C22×C73#55111yescharacteristic
359C2×D73—21no—
360C2×D73—21no—
361C2×D73—21no—
362C2×D73—22no—
363C2×D73—21no—
364C2×D73—21no—
365C2×D73—42no—
366C2×D73—42no—
367C2×D73—41no—
368C2×D73—41no—
369C2×D73—84no—
370C2×D73#44312yes—
371C4×C73—42no—
372C4×C73—41no—
373C4×C73—41no—
374C4×C73—41no—
375C4×C73C2×#11711yescharacteristic
376C4×C73#51811yescharacteristic
377C4×C73#54611yescharacteristic
378C4×C73#54611yescharacteristic
379Dic73—22no—
380Dic73—21no—
381Dic73—21no—
382Dic73—42no—
383Dic73—41no—
384Dic73—41no—
385#22587—731nomaximal, Sylow
386C2×C73—21no—
387C2×C73—21no—
388C2×C73—81no—
389C2×C73#234211yescharacteristic
390C2×C73C2×#44311yescharacteristic
391C2×C73#295711yescharacteristic
392D73—22no—
393D73—41no—
394D73—42no—
395#2924—731no—
396C2×#416—731no—
397#2880—731no—
398#1937—731no—
399#1937D7311yescharacteristic, complemented
400#1929—731no—
401#1929—731no—
402#1866—731no—
403#1866—731no—
404#1826—731no—
405#1810—731no—
406#1789—731no—
407#1764—731no—
408#1764—731no—
409C8×C22⋊C4—731no—
410C73#2258711yescharacteristic, complemented, Sylow
411C22×#41—731no—
412C2×#131—731no—
413C2×#131—731no—
414C23×C8—731no—
415C2×#117—731no—
416#433—1461no—
417#433—1461no—
418#432—1461no—
419#431—1461no—
420C2×#108—731no—
421C2×#108—731no—
422#424—731no—
423#424C2×D7311yescharacteristic, complemented
424C2×#104—731no—
425C2×#104—731no—
426C2×#104—731no—
427C2×#104C2×D7311yescharacteristic
428#416—731no—
429#416—731no—
430#416—731no—
431#416—731no—
432#416—731no—
433#416—731no—
434#416—731no—
435#416C2×D7311yescharacteristic
436C2×#103—731no—
437C2×#103—731no—
438C2×#102—731no—
439C2×#102—731no—
440#408—731no—
441#408—1461no—
442#408—1461no—
443#408C2×D7311yescharacteristic
444#407—731no—
445#407—731no—
446#407—1461no—
447C2×C22⋊C8—731no—
448C2×C22⋊C8—1461no—
449#405—731no—
450#405—731no—
451C2×C4×C8—731no—
452C2×C4×C8C2×D7311yescharacteristic, complemented
453C4×C22⋊C4—731no—
454#341—731no—
455#341C2×D7311yescharacteristic, complemented
456#339—731no—
457#339—731no—
458#339—731no—
459#339C2×D7311yescharacteristic, complemented
460#336—731no—
461#336—731no—
462C2×#41—2921no—
463C2×#41—2921no—
464C2×#41—731no—
465C2×#41—731no—
466C2×#41—731no—
467C2×#41—1461no—
468C2×#41—1462no—
469C2×#41—1462no—
470C2×#41—1461no—
471C2×#41C22×D7311yescharacteristic
472C22×Q8—731no—
473C22×D4—731no—
474C22×D4—1461no—
475C23×C4—731no—
476C23×C4—1461no—
477#131—2921no—
478#131—2921no—
479#131—1462no—
480#131—1462no—
481C2×M16—731no—
482C2×M16—731no—
483C2×M16—1461no—
484C2×M16—1461no—
485C2×M16C22×D7311yescharacteristic
486C2×M16C22×D7311yescharacteristic
487C22×C8—2921no—
488C22×C8—2921no—
489C22×C8—731no—
490C22×C8—731no—
491C22×C8—731no—
492C22×C8—731no—
493C22×C8—731no—
494C22×C8—731no—
495C22×C8—1461no—
496C22×C8—1461no—
497C22×C8C22×D7311yescharacteristic
498C22×C8C22×D7311yescharacteristic
499#117—731no—
500#117—731no—
501#117—731no—
502#117—1461no—
503#117—1461no—
504#117C22×D7311yescharacteristic
505C2×C4⋊C4—731no—
506C2×C4⋊C4—731no—
507C2×C22⋊C4—1461no—
508C2×C22⋊C4—1461no—
509C2×C42—731no—
510C2×C42—1461no—
511C2×C42C22×D7311yescharacteristic
512#108—2921no—
513#108—2921no—
514C4⋊C8—21no—
515C4⋊C8—21no—
516C4⋊C8—1461no—
517C4⋊C8—1461no—
518#104—41no—
519#104—2921no—
520#104—1462no—
521#104—1462no—
522#103—731no—
523#103—731no—
524#103—731no—
525#103—731no—
526#103—731no—
527#103—731no—
528#103C4×D7311yescharacteristic
529#103C4×D7311yescharacteristic
530#102—731no—
531#102—731no—
532#102—731no—
533#102—731no—
534#102—731no—
535#102—731no—
536#102C4×D7311yescharacteristic
537#102C4×D7311yescharacteristic
538C22⋊C8—21no—
539C22⋊C8—21no—
540C22⋊C8—731no—
541C22⋊C8—731no—
542C22⋊C8—731no—
543C22⋊C8—731no—
544C22⋊C8—1461no—
545C22⋊C8—1461no—
546C22⋊C8—1461no—
547C22⋊C8—1461no—
548C22⋊C8—1461no—
549C22⋊C8—1461no—
550#97—1461no—
551#97—1461no—
552C4×C8—41no—
553C4×C8—2921no—
554C4×C8—1461no—
555C4×C8—1461no—
556#95—1461no—
557C24—731no—
558C24—1461no—
559#41—21no—
560#41—21no—
561#41—21no—
562#41—21no—
563#41—2922no—
564#41—2922no—
565#41—2921no—
566#41—2922no—
567#41—2922no—
568#41—2921no—
569#41—732no—
570#41—732no—
571#41—1462no—
572#41—1462no—
573#41—1461no—
574#41—1461no—
575C2×Q8—2921no—
576C2×Q8—731no—
577C2×Q8—1461no—
578C2×Q8—1462no—
579C2×Q8C2×C4×D7311yescharacteristic
580C2×D4—21no—
581C2×D4—2922no—
582C2×D4—2922no—
583C2×D4—2921no—
584C2×D4—731no—
585C2×D4—1461no—
586C2×D4—1461no—
587C2×D4—1462no—
588C2×D4—1461no—
589C2×D4—1461no—
590C2×D4C2×C4×D7311yescharacteristic
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—2922no—
594C22×C4—2922no—
595C22×C4—731no—
596C22×C4—731no—
597C22×C4—731no—
598C22×C4—731no—
599C22×C4—731no—
600C22×C4—1461no—
601C22×C4—1461no—
602C22×C4—1461no—
603C22×C4—1461no—
604C22×C4—1461no—
605C22×C4—1461no—
606C22×C4—1461no—
607C22×C4—1461no—
608C22×C4—1461no—
609C22×C4—1461no—
610C22×C4—1461no—
611C22×C4C23×D7311yescharacteristic
612M16—21no—
613M16—21no—
614M16—21no—
615M16—21no—
616M16—2922no—
617M16—2922no—
618M16—1461no—
619M16—1461no—
620M16—1461no—
621M16—1461no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—2922no—
629C2×C8—2921no—
630C2×C8—2921no—
631C2×C8—2921no—
632C2×C8—2921no—
633C2×C8—2922no—
634C2×C8—731no—
635C2×C8—731no—
636C2×C8—731no—
637C2×C8—731no—
638C2×C8—1461no—
639C2×C8—1461no—
640C2×C8—1461no—
641C2×C8—1461no—
642C2×C8—1461no—
643C2×C8—1461no—
644C2×C8C2×C4×D7311yescharacteristic
645C2×C8C2×C4×D7311yescharacteristic
646C2×C8D4×D7311yescharacteristic
647C2×C8D4×D7311yescharacteristic
648C4⋊C4—731no—
649C4⋊C4—731no—
650C4⋊C4—1461no—
651C4⋊C4—1461no—
652C4⋊C4C2×C4×D7311yescharacteristic
653C4⋊C4C2×C4×D7311yescharacteristic
654C22⋊C4—21no—
655C22⋊C4—1461no—
656C22⋊C4—1461no—
657C22⋊C4—1464no—
658C22⋊C4—1461no—
659C42—21no—
660C42—21no—
661C42—21no—
662C42—1461no—
663C42—1461no—
664C42—1461no—
665C42—1461no—
666C42—1461no—
667C23—21no—
668C23—2921no—
669C23—2922no—
670C23—2922no—
671C23—5841no—
672C23—731no—
673C23—731no—
674C23—1462no—
675C23—1461no—
676C23—1461no—
677C23—1461no—
678C23#41×D7311yescharacteristic
679Q8—21no—
680Q8—21no—
681Q8—2922no—
682Q8—732no—
683Q8—1461no—
684D4—21no—
685D4—21no—
686D4—41no—
687D4—41no—
688D4—2922no—
689D4—2922no—
690D4—2922no—
691D4—732no—
692D4—1462no—
693D4—1462no—
694D4—1461no—
695C2×C4—22no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—2922no—
704C2×C4—2922no—
705C2×C4—2922no—
706C2×C4—2921no—
707C2×C4—2921no—
708C2×C4—2922no—
709C2×C4—5841no—
710C2×C4—731no—
711C2×C4—731no—
712C2×C4—1462no—
713C2×C4—1461no—
714C2×C4—1461no—
715C2×C4—1461no—
716C2×C4—1461no—
717C2×C4—1461no—
718C2×C4—1462no—
719C2×C4—1461no—
720C2×C4—1461no—
721C2×C4—1462no—
722C2×C4—1461no—
723C2×C4—1461no—
724C2×C4—1461no—
725C2×C4—1461no—
726C2×C4—1461no—
727C2×C4—1461no—
728C2×C4C22×C4×D7311yescharacteristic
729C2×C4C2×D4×D7311yescharacteristic
730C2×C4#41×D7311yescharacteristic
731C2×C4#41×D7311yescharacteristic
732C2×C4#1455663611yescharacteristic
733C2×C4#1455663711yescharacteristic
734C8—21no—
735C8—21no—
736C8—21no—
737C8—21no—
738C8—41no—
739C8—41no—
740C8—2921no—
741C8—2921no—
742C8—1461no—
743C8—1461no—
744C8—1461no—
745C8—1461no—
746C22—21no—
747C22—21no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—2922no—
752C22—2922no—
753C22—2921no—
754C22—2921no—
755C22—5844no—
756C22—732no—
757C22—1462no—
758C22—1461no—
759C22—1461no—
760C22—1461no—
761C22—1461no—
762C22—1461no—
763C22C4×D4×D7311yescharacteristic
764C22#1798926211yescharacteristic
765C22#1798926511yescharacteristic
766C4—42no—
767C4—41no—
768C4—41no—
769C4—41no—
770C4—2922no—
771C4—2921no—
772C4—2921no—
773C4—1461no—
774C4—1462no—
775C4—1461no—
776C4#117×D7311yescharacteristic
777C4#1798905911yescharacteristic
778C4#1798922611yescharacteristic
779C4#1798923011yescharacteristic
780C2—21no—
781C2—21no—
782C2—81no—
783C2—2921no—
784C2—2922no—
785C2—1462no—
786C2#2261277911yescharacteristic
787C2#443×D7311yescharacteristic
788C2#2261884311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#1937C2
socleC22×C73C2×C4×D4
prime radicalC2×#41×D73C22
cosocleC22×C4×C73C24
hypercenter#1937D73
hypocenterC73#22587
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1937

Complements

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

NH ≅ G/Ntype
1. #22618588C2semidirect
4. #22610637C2semidirect
5. #22610582C2semidirect
6. #22610576C2semidirect
7. #22610207C2semidirect
8. #22610205C2semidirect
9. #22610029C2semidirect
10. #22609968C2semidirect
12. #22609768C2semidirect
13. #22609767C2semidirect
14. C8×#11924005C2semidirect
15. C73×#1937C2semidirect
25. C2×#14556526C22semidirect
26. C2×#14556526C22semidirect
27. #17988614C22semidirect
33. #17988582C4semidirect
34. #17988582C4semidirect
36. #17988580C4semidirect
37. #17988580C4semidirect
38. #103×D73C4semidirect
39. #103×D73C4semidirect
40. #102×D73C4semidirect
41. #102×D73C4semidirect
50. #17988545C22semidirect
51. #17988542C22semidirect
52. C2×C8×Dic73C22semidirect
54. #17988352C22semidirect
55. #17988348C22semidirect
56. #17988347C22semidirect
57. #17988346C22semidirect
58. #17988342C22semidirect
59. #17988341C22semidirect
60. #424×C73C22semidirect
64. C2×C4×C8×C73C22semidirect
65. #341×C73C22semidirect
66. #339×C73C22semidirect
399. #1937D73semidirect
410. C73#22587semidirect
423. #424C2×D73semidirect
452. C2×C4×C8C2×D73semidirect
455. #341C2×D73semidirect
459. #339C2×D73semidirect

Maximal subgroups

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

subgroupindex
#226185882
#416×D732
#226183792
#226106372
#226105822
#226105762
#226102072
#226102052
#226100292
#226099682
#226098732
#226097682
#226097672
C8×#119240052
C73×#19372
#2258773