Finite Group Databasebeta

← #33088503

Subgroups — #33088503

Order 18688.

1018 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#108×D73C211yesmaximal, characteristic, complemented
2C2×#17988602C211yesmaximal, characteristic
3#416×D73C211yesmaximal, characteristic
4#22618373C211yesmaximal, characteristic
5#22618347C211yesmaximal, characteristic, complemented
6#22610582C211yesmaximal, characteristic, complemented
7#22610581C211yesmaximal, characteristic, complemented
8#22610580C211yesmaximal, characteristic, complemented
9#22610579C211yesmaximal, characteristic, complemented
10#22610578C211yesmaximal, characteristic, complemented
11#22610577C211yesmaximal, characteristic, complemented
12#22610576C211yesmaximal, characteristic, complemented
13#22609639C211yesmaximal, characteristic, complemented
14#22609626C211yesmaximal, characteristic, complemented
15C73×#1929C211yesmaximal, characteristic, complemented
16C2×#41×D73C2211yescharacteristic
17C22×#11924011C2211yescharacteristic
18C2×M16×D73C2211yescharacteristic
19C2×M16×D73C2211yescharacteristic
20C22×C8×D73C2211yescharacteristic
21C2×#14556548C2211yescharacteristic
22#117×D73C2211yescharacteristic
23C2×#14556527C2211yescharacteristic, complemented
24C2×#14556526C2211yescharacteristic, complemented
25C2×#14556526C2211yescharacteristic, complemented
26#108×D73—24no—
27#17988602—24no—
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#17988555C2211yescharacteristic
43#17988554C2211yescharacteristic
44#17988553C2211yescharacteristic
45#17988552—21no—
46#17988552—21no—
47#17988549—21no—
48#17988549—21no—
49#17988545C2211yescharacteristic, complemented
50#17988544—21no—
51#17988543C2211yescharacteristic, complemented
52#17988542C2211yescharacteristic, complemented
53#17988541—21no—
54#17988539—21no—
55C4×#11924011—21no—
56#17988348C2211yescharacteristic, complemented
57#17988347C2211yescharacteristic, complemented
58#17988346C2211yescharacteristic, complemented
59#17988342C2211yescharacteristic, complemented
60#17988341C2211yescharacteristic, complemented
61#17988341C2211yescharacteristic, complemented
62C2×#108×C73C2211yescharacteristic, complemented
63C2×#104×C73C2211yescharacteristic
64#416×C73C2211yescharacteristic
65#408×C73C2211yescharacteristic
66#405×C73C2211yescharacteristic, complemented
67#339×C73C2211yescharacteristic, complemented
68#336×C73C2211yescharacteristic, complemented
69C2×#11924029C2×C411yescharacteristic
70C2×#11924028—21no—
71C2×#11924028C2311yescharacteristic
72C2×#11924027—21no—
73C2×#11924027C2×C411yescharacteristic
74#41×D73—22no—
75#41×D73—22no—
76#41×D73—22no—
77#41×D73—22no—
78C2×Q8×D73C2×C411yescharacteristic
79C2×D4×D73—21no—
80C2×D4×D73C2×C411yescharacteristic
81C22×C4×D73—21no—
82C22×C4×D73C2311yescharacteristic
83C2×#11924012C2311yescharacteristic
84C2×#11924012C2311yescharacteristic
85C2×#11924011—21no—
86C2×#11924011—22no—
87C2×#11924011—22no—
88C2×#11924011—21no—
89C2×#11924011D411yescharacteristic
90C2×#11924011D411yescharacteristic
91C2×#11924011D411yescharacteristic
92C2×#11924011D411yescharacteristic
93M16×D73—22no—
94M16×D73—22no—
95M16×D73—22no—
96M16×D73D414yes—
97C22×#10596831C2311yescharacteristic
98C22×#10596831C2311yescharacteristic
99C2×C8×D73—22no—
100C2×C8×D73—21no—
101C2×C8×D73—22no—
102C2×C8×D73—21no—
103C2×C8×D73C2×C411yescharacteristic
104C2×C8×D73C2×C411yescharacteristic
105C2×C8×D73C2×C411yescharacteristic
106C2×C8×D73C2×C411yescharacteristic
107#14556550C2311yescharacteristic
108#14556549C2×C411yescharacteristic
109#14556549C2×C411yescharacteristic
110#14556548—21no—
111#14556548—22no—
112#14556548—22no—
113#14556547—21no—
114C2×#11924007—21no—
115C4⋊C4×D73C2×C411yescharacteristic
116C4⋊C4×D73C2×C411yescharacteristic
117C2×#11924005—21no—
118C22⋊C4×D73—21no—
119C2×C4×Dic73C2311yescharacteristic
120C42×D73—21no—
121#14556527—22no—
122#14556526—22no—
123#14556526—22no—
124#14556519—22no—
125#14556518—22no—
126#14556517—22no—
127#14556516C2×C411yescharacteristic
128#14556516C2×C411yescharacteristic
129#14556515C2×C411yescharacteristic
130#14556515C2×C411yescharacteristic
131#14556514C2×C411yescharacteristic
132#14556514C2×C411yescharacteristic
133#14556513C2×C411yescharacteristic
134#14556513C2×C411yescharacteristic
135#14556512C2×C411yescharacteristic
136#14556512C2×C411yescharacteristic
137#14556511C2×C411yescharacteristic
138#14556511C2×C411yescharacteristic
139C22⋊#10596831—21no—
140C22⋊#10596831—21no—
141#14556503—21no—
142#14556503—21no—
143#14556503—21no—
144#14556503—21no—
145#14556502—21no—
146#14556501—21no—
147#14556501—21no—
148C4×#10596831—21no—
149C8×Dic73—21no—
150C8×Dic73—21no—
151C2×#41×C73C2311yescharacteristic
152C2×M16×C73C2311yescharacteristic
153C2×M16×C73C2311yescharacteristic
154C22×C8×C73C2311yescharacteristic
155C22×C8×C73C2311yescharacteristic
156#117×C73C2311yescharacteristic
157C2×C42×C73C2311yescharacteristic
158#108×C73—22no—
159#104×C73—22no—
160#103×C73C2×C411yescharacteristic
161#103×C73C2×C411yescharacteristic
162#102×C73C2×C411yescharacteristic
163#102×C73C2×C411yescharacteristic
164C22⋊C8×C73—21no—
165C22⋊C8×C73—21no—
166#97×C73—21no—
167C4×C8×C73—21no—
168C23×D73—21no—
169C23×D73#4111yescharacteristic
170#11924029—22no—
171#11924029—22no—
172#11924028—21no—
173#11924028—21no—
174#11924028—21no—
175#11924028—21no—
176#11924028—42no—
177#11924028—42no—
178#11924027—22no—
179#11924027—22no—
180#11924027—42no—
181#11924027—42no—
182C2×Dic146—21no—
183C2×Dic146C22×C411yescharacteristic
184Q8×D73—22no—
185Q8×D73—22no—
186C2×D292—21no—
187C2×D292C22×C411yescharacteristic
188C2×C22⋊D73—21no—
189C2×C22⋊D73—21no—
190C2×C22⋊D73—21no—
191D4×D73—22no—
192D4×D73—22no—
193D4×D73—42no—
194D4×D73—42no—
195C22×Dic73—21no—
196C22×Dic73—21no—
197C22×Dic73#4111yescharacteristic
198C2×C4×D73—21no—
199C2×C4×D73—21no—
200C2×C4×D73—21no—
201C2×C4×D73—21no—
202C2×C4×D73—21no—
203C2×C4×D73—42no—
204C2×C4×D73—42no—
205C2×C4×D73C22×C411yescharacteristic
206C2×C4×D73C22×C411yescharacteristic
207C2×C4×D73C2×D412yes—
208C2×C4×D73C2×D411yescharacteristic
209C2×C4×D73C2×D411yescharacteristic
210C2×C4×D73#4112yes—
211C2×C4×D73#4112yes—
212C2×C4×D73#4112yes—
213#11924012—21no—
214#11924012—21no—
215#11924012—21no—
216#11924012C2×D412yes—
217#11924011—24no—
218#11924011—22no—
219#11924011—22no—
220#11924011—22no—
221#11924011—22no—
222#11924011—42no—
223C2×#10596831—21no—
224C2×#10596831—21no—
225C2×#10596831—21no—
226C2×#10596831—21no—
227C2×#10596831—21no—
228C2×#10596831—21no—
229C2×#10596831C22×C411yescharacteristic
230C2×#10596831C22×C411yescharacteristic
231C2×#10596831C2×D411yescharacteristic
232C2×#10596831C2×D411yescharacteristic
233C8×D73—22no—
234C8×D73—22no—
235C8×D73—22no—
236C8×D73—22no—
237C8×D73—24no—
238C8×D73—42no—
239C4⋊Dic73C22×C411yescharacteristic
240C4⋊Dic73C22×C411yescharacteristic
241#11924007—21no—
242#11924007—21no—
243#11924007—42no—
244C22⋊Dic73—21no—
245#11924005—21no—
246#11924005—21no—
247#11924005—42no—
248C4×Dic73—21no—
249C4×Dic73—21no—
250C4×Dic73—21no—
251C4×Dic73—21no—
252C4×Dic73—21no—
253#41×C73—21no—
254#41×C73—21no—
255#41×C73—21no—
256#41×C73—21no—
257C2×Q8×C73C22×C411yescharacteristic
258C2×D4×C73—21no—
259C2×D4×C73C22×C411yescharacteristic
260C22×C4×C73—21no—
261C22×C4×C73—21no—
262C22×C4×C73C2411yescharacteristic
263M16×C73—21no—
264M16×C73—21no—
265M16×C73—21no—
266M16×C73C2×D412yes—
267C2×C8×C73—21no—
268C2×C8×C73—21no—
269C2×C8×C73—21no—
270C2×C8×C73—21no—
271C2×C8×C73—21no—
272C2×C8×C73—21no—
273C2×C8×C73C22×C411yescharacteristic
274C2×C8×C73C22×C411yescharacteristic
275C2×C8×C73C2×D411yescharacteristic
276C2×C8×C73C2×D411yescharacteristic
277C4⋊C4×C73C22×C411yescharacteristic
278C4⋊C4×C73C22×C411yescharacteristic
279C22⋊C4×C73—21no—
280C42×C73—21no—
281C42×C73—21no—
282C42×C73—21no—
283C23×C73—21no—
284C23×C73C2×#4111yescharacteristic
285C22×D73—21no—
286C22×D73—41no—
287C22×D73—41no—
288C22×D73—42no—
289C22×D73—81no—
290C22×D73—81no—
291C22×D73C4×D411yescharacteristic
292C22×D73C4×D411yescharacteristic
293C22×D73#12412yes—
294C22×D73#12612yes—
295Q8×C73—21no—
296Q8×C73—21no—
297D4×C73—21no—
298D4×C73—21no—
299D4×C73—41no—
300D4×C73—41no—
301C2×C4×C73—21no—
302C2×C4×C73—21no—
303C2×C4×C73—21no—
304C2×C4×C73—41no—
305C2×C4×C73—41no—
306C2×C4×C73—41no—
307C2×C4×C73—41no—
308C2×C4×C73—41no—
309C2×C4×C73C23×C411yescharacteristic
310C2×C4×C73C22×D411yescharacteristic
311C2×C4×C73C22×D411yescharacteristic
312C2×C4×C73C2×#4111yescharacteristic
313C2×C4×C73C2×#4111yescharacteristic
314C2×C4×C73C2×#4111yescharacteristic
315C22⋊D73—41no—
316C22⋊D73—41no—
317C22⋊D73—42no—
318C22⋊D73—42no—
319C2×Dic73—21no—
320C2×Dic73—21no—
321C2×Dic73—21no—
322C2×Dic73—42no—
323C2×Dic73—41no—
324C2×Dic73—41no—
325C2×Dic73—41no—
326C2×Dic73C4×D411yescharacteristic
327C2×Dic73C4×D411yescharacteristic
328C2×Dic73#12412yes—
329C2×Dic73#12612yes—
330D292—21no—
331D292—21no—
332D292—42no—
333C4×D73—42no—
334C4×D73—41no—
335C4×D73—41no—
336C4×D73—42no—
337C4×D73—81no—
338C4×D73—81no—
339C4×D73#11712yes—
340C4×D73#11712yes—
341C4×D73C4×D412yes—
342C4×D73C4×D412yes—
343C4×D73#12112yes—
344C4×D73#12112yes—
345C4×D73#12312yes—
346C4×D73#12312yes—
347Dic146—21no—
348Dic146—21no—
349Dic146—42no—
350C8×C73—21no—
351C8×C73—21no—
352C8×C73—22no—
353C8×C73—21no—
354C8×C73—21no—
355C8×C73—41no—
356#10596831—21no—
357#10596831—21no—
358#10596831—22no—
359#10596831—21no—
360#10596831—21no—
361#10596831—41no—
362C22×C73—21no—
363C22×C73—21no—
364C22×C73—41no—
365C22×C73—41no—
366C22×C73—41no—
367C22×C73C2×C4×D411yescharacteristic
368C22×C73C2×#12411yescharacteristic
369C22×C73C2×#12611yescharacteristic
370C2×D73—21no—
371C2×D73—21no—
372C2×D73—21no—
373C2×D73—21no—
374C2×D73—42no—
375C2×D73—42no—
376C2×D73—41no—
377C2×D73—41no—
378C2×D73—41no—
379C2×D73—84no—
380C2×D73#38812yes—
381C2×D73#38812yes—
382C4×C73—41no—
383C4×C73—41no—
384C4×C73—41no—
385C4×C73—81no—
386C4×C73C2×#11711yescharacteristic
387C4×C73C2×C4×D411yescharacteristic
388C4×C73C2×#12111yescharacteristic
389C4×C73C2×#12311yescharacteristic
390Dic73—41no—
391Dic73—41no—
392Dic73—41no—
393Dic73—81no—
394Dic73#38812yes—
395Dic73#38812yes—
396#21072—731nomaximal, Sylow
397C2×C73—21no—
398C2×C73—21no—
399C2×C73—81no—
400C2×C73C2×#38811yescharacteristic
401C2×C73#295711yescharacteristic
402C2×C73#295711yescharacteristic
403D73—22no—
404D73—22no—
405D73—81no—
406C22×#108—731no—
407C2×#421—731no—
408C2×#416—731no—
409#2879—731no—
410#2873—731no—
411#1929—731no—
412#1929—731no—
413#1929—731no—
414#1929—731no—
415#1929—731no—
416#1929—731no—
417#1929—731no—
418#1929D7311yescharacteristic, complemented
419#1733—731no—
420#1729—731no—
421C73#2107211yescharacteristic, complemented, Sylow
422C22×#41—731no—
423C22×M16—731no—
424C22×M16—731no—
425C22×M16—731no—
426C23×C8—731no—
427C2×#117—731no—
428C2×#117—731no—
429C2×#108—731no—
430C2×#108—731no—
431C2×#108—731no—
432C2×#108—1464no—
433C2×#108C2×D7311yescharacteristic, complemented
434#421—1464no—
435C2×#104—731no—
436C2×#104—731no—
437C2×#104—731no—
438C2×#104C2×D7311yescharacteristic
439#416—731no—
440#416—731no—
441#416—731no—
442#416—731no—
443#416—731no—
444#416—731no—
445#416—731no—
446#416C2×D7311yescharacteristic
447C2×#103—731no—
448C2×#103—731no—
449C2×#102—731no—
450C2×#102—731no—
451#408—731no—
452#408—731no—
453#408—731no—
454#408—1461no—
455#408—1461no—
456#408C2×D7311yescharacteristic
457#407—1461no—
458#407—1461no—
459#405—731no—
460#405—731no—
461#405—731no—
462#405—1461no—
463#405—1461no—
464#405C2×D7311yescharacteristic, complemented
465C4×M16—1461no—
466C4×M16—1461no—
467#339—731no—
468#339—731no—
469#339—731no—
470#339C2×D7311yescharacteristic, complemented
471#336—731no—
472#336—731no—
473#336—731no—
474#336C2×D7311yescharacteristic, complemented
475C2×#41—731no—
476C2×#41—731no—
477C2×#41—731no—
478C2×#41—1461no—
479C2×#41—1462no—
480C2×#41—1462no—
481C2×#41—1462no—
482C2×#41—1462no—
483C2×#41—1461no—
484C2×#41C22×D7311yescharacteristic
485C22×Q8—731no—
486C22×D4—731no—
487C22×D4—1461no—
488C23×C4—731no—
489C23×C4—1461no—
490C2×M16—731no—
491C2×M16—731no—
492C2×M16—731no—
493C2×M16—731no—
494C2×M16—731no—
495C2×M16—734no—
496C2×M16—731no—
497C2×M16—1461no—
498C2×M16—1461no—
499C2×M16—1462no—
500C2×M16—1462no—
501C2×M16—1462no—
502C2×M16—1462no—
503C2×M16—1462no—
504C2×M16C22×D7311yescharacteristic
505C2×M16C22×D7311yescharacteristic
506C22×C8—731no—
507C22×C8—731no—
508C22×C8—731no—
509C22×C8—731no—
510C22×C8—731no—
511C22×C8—731no—
512C22×C8—1461no—
513C22×C8—1462no—
514C22×C8—1462no—
515C22×C8—1461no—
516C22×C8C22×D7311yescharacteristic
517C22×C8C22×D7311yescharacteristic
518#117—731no—
519#117—731no—
520#117—731no—
521#117—1462no—
522#117—1462no—
523#117—1461no—
524#117—1461no—
525#117C22×D7311yescharacteristic
526C2×C4⋊C4—731no—
527C2×C4⋊C4—731no—
528C2×C4⋊C4—1461no—
529C2×C22⋊C4—1461no—
530C2×C22⋊C4—1461no—
531C2×C42—731no—
532C2×C42—1461no—
533C2×C42C22×D7311yescharacteristic
534#108—22no—
535#108—1462no—
536#108—1462no—
537#108—1462no—
538#104—22no—
539#104—1462no—
540#104—1462no—
541#104—1462no—
542#103—731no—
543#103—731no—
544#103—731no—
545#103—731no—
546#103—731no—
547#103—731no—
548#103C4×D7311yescharacteristic
549#103C4×D7311yescharacteristic
550#102—731no—
551#102—731no—
552#102—731no—
553#102—731no—
554#102—731no—
555#102—731no—
556#102C4×D7311yescharacteristic
557#102C4×D7311yescharacteristic
558C22⋊C8—21no—
559C22⋊C8—21no—
560C22⋊C8—1461no—
561C22⋊C8—1461no—
562C22⋊C8—1461no—
563C22⋊C8—1461no—
564C22⋊C8—1461no—
565C22⋊C8—1461no—
566#97—21no—
567#97—1461no—
568#97—1461no—
569#97—1461no—
570C4×C8—21no—
571C4×C8—1461no—
572C4×C8—1461no—
573C4×C8—1461no—
574C24—731no—
575C24—1461no—
576#41—21no—
577#41—21no—
578#41—21no—
579#41—21no—
580#41—2922no—
581#41—2922no—
582#41—2922no—
583#41—2922no—
584#41—1462no—
585#41—1462no—
586#41—1462no—
587#41—1462no—
588#41—1461no—
589#41—1461no—
590#41—1461no—
591#41—1461no—
592C2×Q8—731no—
593C2×Q8—1461no—
594C2×Q8—1462no—
595C2×Q8—1462no—
596C2×Q8C2×C4×D7311yescharacteristic
597C2×D4—21no—
598C2×D4—2922no—
599C2×D4—2922no—
600C2×D4—731no—
601C2×D4—1461no—
602C2×D4—1462no—
603C2×D4—1462no—
604C2×D4—1461no—
605C2×D4—1461no—
606C2×D4—1461no—
607C2×D4C2×C4×D7311yescharacteristic
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—2922no—
611C22×C4—2922no—
612C22×C4—731no—
613C22×C4—731no—
614C22×C4—731no—
615C22×C4—732no—
616C22×C4—731no—
617C22×C4—731no—
618C22×C4—732no—
619C22×C4—732no—
620C22×C4—732no—
621C22×C4—1461no—
622C22×C4—1461no—
623C22×C4—1461no—
624C22×C4—1461no—
625C22×C4—1461no—
626C22×C4—1461no—
627C22×C4—1461no—
628C22×C4C23×D7311yescharacteristic
629M16—21no—
630M16—21no—
631M16—21no—
632M16—2922no—
633M16—732no—
634M16—1464no—
635M16—1462no—
636M16—1462no—
637M16—1462no—
638M16—1462no—
639M16—1461no—
640M16—1461no—
641M16—1461no—
642M16D4×D7312yes—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—2922no—
650C2×C8—731no—
651C2×C8—731no—
652C2×C8—731no—
653C2×C8—731no—
654C2×C8—1462no—
655C2×C8—1462no—
656C2×C8—1462no—
657C2×C8—1462no—
658C2×C8—1464no—
659C2×C8—1461no—
660C2×C8—1461no—
661C2×C8—1461no—
662C2×C8—1461no—
663C2×C8—1461no—
664C2×C8—1461no—
665C2×C8C2×C4×D7311yescharacteristic
666C2×C8C2×C4×D7311yescharacteristic
667C2×C8D4×D7311yescharacteristic
668C2×C8D4×D7311yescharacteristic
669C4⋊C4—2922no—
670C4⋊C4—731no—
671C4⋊C4—731no—
672C4⋊C4—1461no—
673C4⋊C4—1461no—
674C4⋊C4C2×C4×D7311yescharacteristic
675C4⋊C4C2×C4×D7311yescharacteristic
676C22⋊C4—21no—
677C22⋊C4—2922no—
678C22⋊C4—1461no—
679C22⋊C4—1461no—
680C22⋊C4—1461no—
681C42—21no—
682C42—21no—
683C42—21no—
684C42—1461no—
685C42—1461no—
686C42—1461no—
687C42—1461no—
688C42—1461no—
689C23—21no—
690C23—2921no—
691C23—2921no—
692C23—2922no—
693C23—5841no—
694C23—5841no—
695C23—732no—
696C23—732no—
697C23—731no—
698C23—731no—
699C23—1461no—
700C23#41×D7311yescharacteristic
701Q8—21no—
702Q8—21no—
703Q8—2922no—
704Q8—1461no—
705Q8—1461no—
706D4—21no—
707D4—21no—
708D4—41no—
709D4—41no—
710D4—2922no—
711D4—2922no—
712D4—2921no—
713D4—2921no—
714D4—2922no—
715D4—1461no—
716D4—1461no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—2922no—
726C2×C4—2922no—
727C2×C4—2922no—
728C2×C4—2921no—
729C2×C4—2921no—
730C2×C4—2921no—
731C2×C4—2921no—
732C2×C4—2921no—
733C2×C4—5841no—
734C2×C4—5841no—
735C2×C4—731no—
736C2×C4—731no—
737C2×C4—732no—
738C2×C4—732no—
739C2×C4—732no—
740C2×C4—732no—
741C2×C4—732no—
742C2×C4—732no—
743C2×C4—732no—
744C2×C4—732no—
745C2×C4—732no—
746C2×C4—732no—
747C2×C4—1461no—
748C2×C4—1461no—
749C2×C4—1461no—
750C2×C4C22×C4×D7311yescharacteristic
751C2×C4C2×D4×D7311yescharacteristic
752C2×C4C2×D4×D7311yescharacteristic
753C2×C4#41×D7311yescharacteristic
754C2×C4#41×D7311yescharacteristic
755C2×C4#41×D7311yescharacteristic
756C8—21no—
757C8—21no—
758C8—22no—
759C8—21no—
760C8—21no—
761C8—41no—
762C8—2921no—
763C8—1461no—
764C8—1461no—
765C8—1462no—
766C8—1461no—
767C8—1461no—
768C22—21no—
769C22—21no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—2922no—
774C22—2922no—
775C22—2921no—
776C22—2921no—
777C22—2921no—
778C22—5844no—
779C22—732no—
780C22—732no—
781C22—1461no—
782C22—1461no—
783C22—1461no—
784C22—1461no—
785C22C4×D4×D7311yescharacteristic
786C22#124×D7311yescharacteristic
787C22#126×D7311yescharacteristic
788C4—41no—
789C4—41no—
790C4—41no—
791C4—81no—
792C4—2921no—
793C4—2921no—
794C4—2921no—
795C4—5841no—
796C4—732no—
797C4—732no—
798C4#117×D7311yescharacteristic
799C4C4×D4×D7311yescharacteristic
800C4#121×D7311yescharacteristic
801C4#123×D7311yescharacteristic
802C2—21no—
803C2—21no—
804C2—81no—
805C2—5841no—
806C2—1462no—
807C2—1462no—
808C2#388×D7311yescharacteristic
809C2#2261884311yescharacteristic
810C2#2261884511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#1929C2
socleC22×C73C2×C4×D4
prime radicalC2×#41×D73C22
cosocleC22×C4×C73C24
hypercenter#1929D73
hypocenterC73#21072
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1929

Complements

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

NH ≅ G/Ntype
1. C2×#108×D73C2semidirect
5. #22618347C2semidirect
6. #22610582C2semidirect
7. #22610581C2semidirect
8. #22610580C2semidirect
9. #22610579C2semidirect
10. #22610578C2semidirect
11. #22610577C2semidirect
12. #22610576C2semidirect
13. #22609639C2semidirect
14. #22609626C2semidirect
15. C73×#1929C2semidirect
23. C2×#14556527C22semidirect
24. C2×#14556526C22semidirect
25. C2×#14556526C22semidirect
33. #17988582C4semidirect
34. #17988582C4semidirect
36. #17988580C4semidirect
37. #17988580C4semidirect
38. #103×D73C4semidirect
39. #103×D73C4semidirect
40. #102×D73C4semidirect
41. #102×D73C4semidirect
49. #17988545C22semidirect
51. #17988543C22semidirect
52. #17988542C22semidirect
56. #17988348C22semidirect
57. #17988347C22semidirect
58. #17988346C22semidirect
59. #17988342C22semidirect
60. #17988341C22semidirect
61. #17988341C22semidirect
62. C2×#108×C73C22semidirect
66. #405×C73C22semidirect
67. #339×C73C22semidirect
68. #336×C73C22semidirect
418. #1929D73semidirect
421. C73#21072semidirect
433. C2×#108C2×D73semidirect
464. #405C2×D73semidirect
470. #339C2×D73semidirect
474. #336C2×D73semidirect

Maximal subgroups

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

subgroupindex
C2×#108×D732
C2×#179886022
#416×D732
#226183732
#226183472
#226105822
#226105812
#226105802
#226105792
#226105782
#226105772
#226105762
#226096392
#226096262
C73×#19292
#2107273