Finite Group Databasebeta

← #33106737

Subgroups — #33106737

Order 18688.

1020 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22619147C211yesmaximal, characteristic
2C2×#17988707C211yesmaximal, characteristic, complemented
3C2×#17988603C211yesmaximal, characteristic, complemented
4#22618377C211yesmaximal, characteristic, complemented
5#22610818C211yesmaximal, characteristic, complemented
6#22610641C211yesmaximal, characteristic, complemented
7#22610579C211yesmaximal, characteristic, complemented
8#22610380C211yesmaximal, characteristic, complemented
9#22610261C211yesmaximal, characteristic, complemented
10#22610258C211yesmaximal, characteristic, complemented
11#22610205C211yesmaximal, characteristic, complemented
12#22610136C211yesmaximal, characteristic, complemented
13#22609770C211yesmaximal, characteristic, complemented
14#22609699C211yesmaximal, characteristic, complemented
15C73×#2933C211yesmaximal, characteristic, complemented
16C22×#11924028C2211yescharacteristic
17C2×#14556611C2211yescharacteristic
18C2×#14556611C2211yescharacteristic
19C2×#14556597C2211yescharacteristic
20C2×#14556597C2211yescharacteristic
21C2×#14556550C2211yescharacteristic
22#17988747C411yescharacteristic, complemented
23#17988747C411yescharacteristic, complemented
24#17988742C411yescharacteristic, complemented
25#17988737C411yescharacteristic, complemented
26#17988730C411yescharacteristic, complemented
27#17988730C411yescharacteristic, complemented
28#17988725C411yescharacteristic, complemented
29#17988720C411yescharacteristic, complemented
30#17988707—24no—
31C2×#14556526C2211yescharacteristic, complemented
32C2×#14556526C2211yescharacteristic, complemented
33#17988603—24no—
34C2×#14556518C2211yescharacteristic, complemented
35C2×#14556518C2211yescharacteristic, complemented
36C2×#14556517C2211yescharacteristic
37C2×#14556517C2211yescharacteristic
38C2×#14556517C2211yescharacteristic
39C2×#14556517C2211yescharacteristic
40#17988581C2211yescharacteristic
41#17988581C2211yescharacteristic
42#17988553C2211yescharacteristic
43#17988553C2211yescharacteristic
44#17988552—21no—
45#17988552—21no—
46#17988551C2211yescharacteristic
47#17988549—21no—
48C2×C22⋊#10596831C2211yescharacteristic
49C22⋊C8×D73—21no—
50C2×#14556501C2211yescharacteristic, complemented
51C2×C8×Dic73C2211yescharacteristic, complemented
52#17988351C2211yescharacteristic, complemented
53#17988351C2211yescharacteristic, complemented
54#17988346C2211yescharacteristic, complemented
55#17988346C2211yescharacteristic, complemented
56#17988341C2211yescharacteristic, complemented
57#17988341C2211yescharacteristic, complemented
58C2×#131×C73C2211yescharacteristic, complemented
59C22×M16×C73C2211yescharacteristic
60#525×C73C2211yescharacteristic
61#436×C73—21no—
62#435×C73—21no—
63#435×C73—21no—
64C8×D4×C73—21no—
65#424×C73C2211yescharacteristic, complemented
66#408×C73C2211yescharacteristic, complemented
67C2×C22⋊C8×C73C2211yescharacteristic
68#405×C73C2211yescharacteristic, complemented
69C2×#11924028—22no—
70C2×#11924028—22no—
71C2×#11924028—21no—
72C2×#11924028—21no—
73C2×#11924028—41no—
74C2×#11924028—41no—
75C2×#11924028C2×C411yescharacteristic
76C2×#11924028C2×C411yescharacteristic
77C2×#11924028C2311yescharacteristic
78C2×#11924028C2311yescharacteristic
79C22×Dic146C2×C411yescharacteristic
80C22×D292C2×C411yescharacteristic
81C22×C22⋊D73—21no—
82C22×C4×D73—21no—
83#14556611—22no—
84#14556611—22no—
85#14556611—41no—
86#14556611—41no—
87C2×#11924018C2×C411yescharacteristic
88C2×#11924018C2×C411yescharacteristic
89C2×#11924016C2×C411yescharacteristic
90C2×#11924016C2×C411yescharacteristic
91C2×#11924015C2×C411yescharacteristic
92C2×#11924015C2×C411yescharacteristic
93C2×#11924013C2×C411yescharacteristic
94C2×#11924013C2×C411yescharacteristic
95#14556597—22no—
96#14556597—22no—
97#14556597—41no—
98#14556597—41no—
99C2×#11924012C2311yescharacteristic
100C2×#11924012C2311yescharacteristic
101C2×#11924011—21no—
102C2×#11924011—21no—
103C22×#10596831C2311yescharacteristic
104C22×#10596831C2311yescharacteristic
105C2×C8×D73—21no—
106C2×C8×D73—21no—
107#14556550—22no—
108#14556550—41no—
109C2×C4⋊Dic73—21no—
110C2×C22⋊Dic73—21no—
111C2×C4×Dic73C2311yescharacteristic
112C2×C4×Dic73C2311yescharacteristic
113#14556526—22no—
114#14556526—41no—
115#14556518—22no—
116#14556518—41no—
117#14556517—22no—
118#14556517—22no—
119#14556517—22no—
120#14556517D414yescomplemented
121#14556514C2×C411yescharacteristic
122#14556514C2×C411yescharacteristic
123#14556514C2×C411yescharacteristic
124#14556514C2×C411yescharacteristic
125#14556511C2×C411yescharacteristic
126#14556511C2×C411yescharacteristic
127#14556511C2×C411yescharacteristic
128#14556511C2×C411yescharacteristic
129C22⋊#10596831—21no—
130C22⋊#10596831—21no—
131C22⋊#10596831C2×C411yescharacteristic
132C22⋊#10596831C2×C411yescharacteristic
133C22⋊#10596831C2×C411yescharacteristic
134C22⋊#10596831C2×C411yescharacteristic
135#14556503—21no—
136#14556503—21no—
137#14556503—21no—
138#14556503—21no—
139#14556501—22no—
140C8×Dic73—41no—
141C2×#41×C73C2311yescharacteristic
142C23×C4×C73C2311yescharacteristic
143#131×C73—22no—
144#131×C73—41no—
145C2×M16×C73—21no—
146C2×M16×C73—21no—
147C2×M16×C73—22no—
148C2×M16×C73—41no—
149C2×M16×C73C2311yescharacteristic
150C2×M16×C73C2311yescharacteristic
151C22×C8×C73—21no—
152C22×C8×C73—21no—
153C22×C8×C73C2311yescharacteristic
154C22×C8×C73C2311yescharacteristic
155#123×C73—21no—
156C22⋊Q8×C73C2×C411yescharacteristic
157C22⋊Q8×C73C2×C411yescharacteristic
158#121×C73C2×C411yescharacteristic
159#121×C73C2×C411yescharacteristic
160#120×C73—21no—
161C4×D4×C73—21no—
162C4×D4×C73—21no—
163#117×C73C2311yescharacteristic
164C4⋊C8×C73—21no—
165C4⋊C8×C73—21no—
166C22⋊C8×C73—21no—
167C22⋊C8×C73—21no—
168C22⋊C8×C73D411yescharacteristic
169C22⋊C8×C73D411yescharacteristic
170C22⋊C8×C73D411yescharacteristic
171C22⋊C8×C73D411yescharacteristic
172#97×C73—21no—
173C4×C8×C73—21no—
174C23×D73—21no—
175#11924028—21no—
176#11924028—21no—
177#11924028—21no—
178#11924028—21no—
179#11924028—21no—
180#11924028—21no—
181#11924028—22no—
182#11924028—22no—
183#11924028—41no—
184#11924028—41no—
185#11924028—42no—
186#11924028—42no—
187#11924028—42no—
188#11924028—42no—
189#11924028C2×D412yes—
190#11924028#4112yes—
191C2×Dic146—22no—
192C2×Dic146—21no—
193C2×Dic146—41no—
194C2×Dic146C22×C411yescharacteristic
195C2×Dic146C22×C411yescharacteristic
196C2×D292—22no—
197C2×D292—21no—
198C2×D292—41no—
199C2×D292C22×C411yescharacteristic
200C2×D292C22×C411yescharacteristic
201C2×C22⋊D73—21no—
202C2×C22⋊D73—21no—
203C2×C22⋊D73—21no—
204C2×C22⋊D73—21no—
205C2×C22⋊D73—42no—
206C2×C22⋊D73—42no—
207C22×Dic73—21no—
208C22×Dic73—21no—
209C22×Dic73—21no—
210C2×C4×D73—21no—
211C2×C4×D73—21no—
212C2×C4×D73—21no—
213C2×C4×D73—21no—
214C2×C4×D73—42no—
215C2×C4×D73—42no—
216#11924018—22no—
217#11924018—41no—
218#11924016—22no—
219#11924016—41no—
220#11924015—22no—
221#11924015—41no—
222#11924013—22no—
223#11924013—41no—
224#11924012—21no—
225#11924012—21no—
226#11924012—21no—
227#11924012—21no—
228#11924011—42no—
229#11924011—42no—
230C2×#10596831—21no—
231C2×#10596831—21no—
232C2×#10596831—21no—
233C2×#10596831—21no—
234C2×#10596831—21no—
235C2×#10596831—21no—
236C2×#10596831C22×C411yescharacteristic
237C2×#10596831C22×C411yescharacteristic
238C2×#10596831C22×C411yescharacteristic
239C2×#10596831C22×C411yescharacteristic
240C8×D73—42no—
241C8×D73—42no—
242C4⋊Dic73—42no—
243C22⋊Dic73—42no—
244C4×Dic73—21no—
245C4×Dic73—21no—
246C4×Dic73—21no—
247C4×Dic73C2×D412yes—
248C24×C73#4111yescharacteristic
249#41×C73—21no—
250#41×C73—21no—
251#41×C73—21no—
252#41×C73—21no—
253C2×Q8×C73C22×C411yescharacteristic
254C2×D4×C73—21no—
255C2×D4×C73—21no—
256C2×D4×C73—21no—
257C2×D4×C73C22×C411yescharacteristic
258C22×C4×C73—21no—
259C22×C4×C73—21no—
260C22×C4×C73—21no—
261C22×C4×C73—21no—
262C22×C4×C73—21no—
263C22×C4×C73C22×C411yescharacteristic
264C22×C4×C73C22×C411yescharacteristic
265C22×C4×C73C2×D411yescharacteristic
266C22×C4×C73C2×D411yescharacteristic
267C22×C4×C73#4111yescharacteristic
268C22×C4×C73C2411yescharacteristic
269M16×C73—21no—
270M16×C73—21no—
271M16×C73—21no—
272M16×C73—42no—
273M16×C73—42no—
274M16×C73C2×D412yes—
275C2×C8×C73—21no—
276C2×C8×C73—21no—
277C2×C8×C73—21no—
278C2×C8×C73—21no—
279C2×C8×C73—21no—
280C2×C8×C73—21no—
281C2×C8×C73—42no—
282C2×C8×C73—42no—
283C2×C8×C73C2×D411yescharacteristic
284C2×C8×C73C2×D411yescharacteristic
285C2×C8×C73C2×D411yescharacteristic
286C2×C8×C73C2×D411yescharacteristic
287C4⋊C4×C73—21no—
288C4⋊C4×C73—21no—
289C4⋊C4×C73C22×C411yescharacteristic
290C4⋊C4×C73C22×C411yescharacteristic
291C22⋊C4×C73—21no—
292C22⋊C4×C73—21no—
293C22⋊C4×C73—21no—
294C22⋊C4×C73—21no—
295C22⋊C4×C73—21no—
296C42×C73—21no—
297C23×C73—21no—
298C23×C73—21no—
299C23×C73—21no—
300C23×C73—41no—
301C23×C73—41no—
302C23×C73C4×D411yescharacteristic
303C23×C73C4×D411yescharacteristic
304C23×C73C2×#4111yescharacteristic
305C22×D73—21no—
306C22×D73—21no—
307C22×D73—42no—
308C22×D73—42no—
309C22×D73—81no—
310Q8×C73—21no—
311Q8×C73—21no—
312D4×C73—21no—
313D4×C73—21no—
314D4×C73—42no—
315D4×C73—41no—
316D4×C73—41no—
317D4×C73—81no—
318C2×C4×C73—21no—
319C2×C4×C73—21no—
320C2×C4×C73—21no—
321C2×C4×C73—21no—
322C2×C4×C73—21no—
323C2×C4×C73—21no—
324C2×C4×C73—21no—
325C2×C4×C73—21no—
326C2×C4×C73—21no—
327C2×C4×C73—21no—
328C2×C4×C73—21no—
329C2×C4×C73—21no—
330C2×C4×C73—21no—
331C2×C4×C73—41no—
332C2×C4×C73—41no—
333C2×C4×C73C4×D411yescharacteristic
334C2×C4×C73C4×D411yescharacteristic
335C2×C4×C73C23×C411yescharacteristic
336C2×C4×C73C22×D411yescharacteristic
337C2×C4×C73C22×D411yescharacteristic
338C2×C4×C73C2×#4111yescharacteristic
339C2×C4×C73H(5,𝔽2)11yescharacteristic
340C2×C4×C73H(5,𝔽2)11yescharacteristic
341C22⋊D73—22no—
342C22⋊D73—22no—
343C22⋊D73—42no—
344C22⋊D73—42no—
345C22⋊D73—41no—
346C22⋊D73—41no—
347C2×Dic73—21no—
348C2×Dic73—21no—
349C2×Dic73—22no—
350C2×Dic73—42no—
351C2×Dic73—41no—
352C2×Dic73—41no—
353C2×Dic73—41no—
354C2×Dic73—41no—
355C2×Dic73—41no—
356D292—21no—
357D292—21no—
358D292—21no—
359D292—42no—
360D292C4×D412yes—
361C4×D73—22no—
362C4×D73—22no—
363C4×D73—42no—
364C4×D73—42no—
365C4×D73—41no—
366C4×D73—41no—
367Dic146—21no—
368Dic146—21no—
369Dic146—21no—
370Dic146—42no—
371Dic146C4×D412yes—
372C8×C73—21no—
373C8×C73—21no—
374C8×C73—22no—
375C8×C73—21no—
376C8×C73—21no—
377C8×C73—41no—
378#10596831—21no—
379#10596831—21no—
380#10596831—21no—
381#10596831—21no—
382#10596831—41no—
383#10596831—41no—
384C22×C73—21no—
385C22×C73—21no—
386C22×C73—21no—
387C22×C73—21no—
388C22×C73—21no—
389C22×C73—21no—
390C22×C73—21no—
391C22×C73—21no—
392C22×C73—41no—
393C22×C73—41no—
394C22×C73—41no—
395C22×C73—81no—
396C22×C73—81no—
397C22×C73C2×C4×D411yescharacteristic
398C22×C73#54611yescharacteristic
399C22×C73#55111yescharacteristic
400C2×D73—22no—
401C2×D73—41no—
402C2×D73—41no—
403C2×D73—41no—
404C2×D73—41no—
405C2×D73—41no—
406C2×D73—84no—
407C4×C73—21no—
408C4×C73—21no—
409C4×C73—41no—
410C4×C73—41no—
411C4×C73—41no—
412C4×C73C2×C4×D411yescharacteristic
413C4×C73#51811yescharacteristic
414C4×C73D4211yescharacteristic
415C4×C73#54611yescharacteristic
416Dic73—22no—
417Dic73—42no—
418Dic73—41no—
419Dic73—81no—
420#22887—731nomaximal, Sylow
421C2×C73—21no—
422C2×C73—21no—
423C2×C73—41no—
424C2×C73—41no—
425C2×C73—81no—
426C2×C73#235811yescharacteristic
427C2×C73#295511yescharacteristic
428C2×C73#295711yescharacteristic
429D73—42no—
430D73—81no—
431#3002—731no—
432C2×#444—731no—
433#2933D7311yescharacteristic, complemented
434C2×#421—731no—
435#2880—731no—
436#1974—731no—
437#1938—731no—
438#1929—731no—
439#1897—731no—
440#1876—731no—
441#1876—731no—
442#1866—731no—
443#1855—731no—
444#1764—731no—
445#1750—731no—
446C73#2288711yescharacteristic, complemented, Sylow
447C22×#41—731no—
448C2×#135—731no—
449C2×#135—731no—
450C2×#131—731no—
451C2×#131—731no—
452C2×#131C2×D7311yescharacteristic, complemented
453C22×M16C2×D7311yescharacteristic
454#525C2×D7311yescharacteristic
455C2×#117—731no—
456#452—731no—
457#452—731no—
458#451—731no—
459#450—731no—
460#449—731no—
461#449—731no—
462#448—731no—
463#447—731no—
464#444—1464no—
465#436—21no—
466#435—21no—
467#435—21no—
468C8×D4—21no—
469C2×#108—731no—
470C2×#108—731no—
471#424C2×D7311yescharacteristic, complemented
472#421—1464no—
473C2×#104—731no—
474C2×#104—731no—
475C2×#104—731no—
476C2×#104—731no—
477C2×#104—731no—
478C2×#104—731no—
479#416—731no—
480#416—731no—
481#408—731no—
482#408—731no—
483#408—1461no—
484#408—1461no—
485#408C2×D7311yescharacteristic, complemented
486#407—731no—
487#407—1461no—
488C2×C22⋊C8—731no—
489C2×C22⋊C8—1461no—
490C2×C22⋊C8C2×D7311yescharacteristic
491#405C2×D7311yescharacteristic, complemented
492C2×#97—731no—
493C2×C4×C8—731no—
494#341—731no—
495#341—731no—
496#339—731no—
497#339—731no—
498#336—731no—
499#336—731no—
500C2×#41—2921no—
501C2×#41—2921no—
502C2×#41—731no—
503C2×#41—731no—
504C2×#41—731no—
505C2×#41—731no—
506C2×#41—1462no—
507C2×#41—1462no—
508C2×#41—1461no—
509C2×#41—1461no—
510C2×#41C22×D7311yescharacteristic
511C22×Q8—731no—
512C22×D4—731no—
513C22×D4—1461no—
514C23×C4—1461no—
515C23×C4C22×D7311yescharacteristic
516#135—2921no—
517#135—2921no—
518#135—1462no—
519#135—1462no—
520C2×Q16—731no—
521C2×Q16—731no—
522C2×SD16—731no—
523C2×SD16—731no—
524C2×SD16—731no—
525C2×SD16—731no—
526C2×D8—731no—
527C2×D8—731no—
528#131—22no—
529#131—41no—
530#131—2921no—
531#131—2921no—
532#131—1462no—
533#131—1462no—
534C2×M16—21no—
535C2×M16—21no—
536C2×M16—22no—
537C2×M16—41no—
538C2×M16—731no—
539C2×M16—731no—
540C2×M16—1461no—
541C2×M16—1461no—
542C2×M16C22×D7311yescharacteristic
543C2×M16C22×D7311yescharacteristic
544C22×C8—21no—
545C22×C8—21no—
546C22×C8—731no—
547C22×C8—731no—
548C22×C8—1461no—
549C22×C8—1461no—
550C22×C8C22×D7311yescharacteristic
551C22×C8C22×D7311yescharacteristic
552#123—21no—
553C22⋊Q8C4×D7311yescharacteristic
554C22⋊Q8C4×D7311yescharacteristic
555#121C4×D7311yescharacteristic
556#121C4×D7311yescharacteristic
557#120—21no—
558C4×D4—21no—
559C4×D4—21no—
560#117—2921no—
561#117—1462no—
562#117C22×D7311yescharacteristic
563C2×C4⋊C4—1461no—
564C2×C22⋊C4—1461no—
565C2×C42—731no—
566C2×C42—731no—
567#108—2921no—
568#108—1462no—
569C4⋊C8—21no—
570C4⋊C8—21no—
571#104—2921no—
572#104—734no—
573#104—1462no—
574#104—1462no—
575#104—1462no—
576#104—1462no—
577#103—731no—
578#103—731no—
579#103—731no—
580#103—731no—
581#102—731no—
582#102—731no—
583#102—731no—
584#102—731no—
585C22⋊C8—21no—
586C22⋊C8—21no—
587C22⋊C8—731no—
588C22⋊C8—731no—
589C22⋊C8—731no—
590C22⋊C8—731no—
591C22⋊C8—1461no—
592C22⋊C8—1461no—
593C22⋊C8—1461no—
594C22⋊C8—1461no—
595C22⋊C8—1461no—
596C22⋊C8—1461no—
597C22⋊C8C22⋊D7311yescharacteristic
598C22⋊C8C22⋊D7311yescharacteristic
599C22⋊C8C22⋊D7311yescharacteristic
600C22⋊C8C22⋊D7311yescharacteristic
601#97—21no—
602#97—1462no—
603C4×C8—21no—
604C4×C8—2921no—
605C24—1461no—
606C24#1192402811yescharacteristic
607#41—21no—
608#41—21no—
609#41—21no—
610#41—21no—
611#41—2922no—
612#41—2922no—
613#41—2921no—
614#41—2921no—
615#41—2922no—
616#41—2922no—
617#41—732no—
618#41—732no—
619#41—1462no—
620#41—1462no—
621#41—1461no—
622#41—1461no—
623#41—1461no—
624#41—1461no—
625#41—1461no—
626#41—1461no—
627C2×Q8—2921no—
628C2×Q8—731no—
629C2×Q8—731no—
630C2×Q8—1462no—
631C2×Q8—1461no—
632C2×Q8C2×C4×D7311yescharacteristic
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—2921no—
637C2×D4—2922no—
638C2×D4—2922no—
639C2×D4—731no—
640C2×D4—731no—
641C2×D4—1462no—
642C2×D4—1461no—
643C2×D4—1461no—
644C2×D4—1461no—
645C2×D4—1461no—
646C2×D4—1461no—
647C2×D4C2×C4×D7311yescharacteristic
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—2922no—
654C22×C4—2922no—
655C22×C4—1461no—
656C22×C4—1461no—
657C22×C4—1461no—
658C22×C4—1461no—
659C22×C4—1461no—
660C22×C4—1461no—
661C22×C4—1461no—
662C22×C4C2×C4×D7311yescharacteristic
663C22×C4C2×C4×D7311yescharacteristic
664C22×C4C2×C22⋊D7311yescharacteristic
665C22×C4C2×C22⋊D7311yescharacteristic
666C22×C4#1192402811yescharacteristic
667C22×C4C23×D7311yescharacteristic
668Q16—2921no—
669Q16—1462no—
670SD16—2921no—
671SD16—2921no—
672SD16—1462no—
673SD16—1462no—
674D8—2921no—
675D8—1462no—
676M16—21no—
677M16—21no—
678M16—21no—
679M16—42no—
680M16—42no—
681M16—2922no—
682M16—2922no—
683M16—1461no—
684M16—1461no—
685M16—1461no—
686M16—1461no—
687M16D4×D7312yes—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—42no—
695C2×C8—42no—
696C2×C8—2922no—
697C2×C8—2922no—
698C2×C8—731no—
699C2×C8—731no—
700C2×C8—731no—
701C2×C8—731no—
702C2×C8—1461no—
703C2×C8—1461no—
704C2×C8—1461no—
705C2×C8—1461no—
706C2×C8—1461no—
707C2×C8—1461no—
708C2×C8C2×C22⋊D7311yescharacteristic
709C2×C8C2×C22⋊D7311yescharacteristic
710C2×C8C2×C22⋊D7311yescharacteristic
711C2×C8C2×C22⋊D7311yescharacteristic
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—2922no—
715C4⋊C4C2×C4×D7311yescharacteristic
716C4⋊C4C2×C4×D7311yescharacteristic
717C22⋊C4—21no—
718C22⋊C4—21no—
719C22⋊C4—21no—
720C22⋊C4—21no—
721C22⋊C4—21no—
722C22⋊C4—2922no—
723C42—21no—
724C42—732no—
725C42—1461no—
726C42—1461no—
727C42—1461no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—41no—
732C23—41no—
733C23—2922no—
734C23—2922no—
735C23—5841no—
736C23—1461no—
737C23—1461no—
738C23C4×C22⋊D7311yescharacteristic
739C23C4×C22⋊D7311yescharacteristic
740C23C2×#1192402811yescharacteristic
741Q8—21no—
742Q8—21no—
743Q8—2922no—
744Q8—732no—
745Q8—1461no—
746Q8—1461no—
747Q8—1461no—
748D4—21no—
749D4—21no—
750D4—42no—
751D4—41no—
752D4—41no—
753D4—81no—
754D4—2922no—
755D4—2922no—
756D4—2921no—
757D4—2921no—
758D4—2922no—
759D4—732no—
760D4—1462no—
761D4—1462no—
762D4—1461no—
763D4—1461no—
764D4—1461no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—2922no—
781C2×C4—2922no—
782C2×C4—2921no—
783C2×C4—2921no—
784C2×C4—2922no—
785C2×C4—2921no—
786C2×C4—2921no—
787C2×C4—2921no—
788C2×C4—2921no—
789C2×C4—2921no—
790C2×C4—1462no—
791C2×C4—1461no—
792C2×C4—1461no—
793C2×C4—1462no—
794C2×C4—1462no—
795C2×C4C4×C22⋊D7311yescharacteristic
796C2×C4C4×C22⋊D7311yescharacteristic
797C2×C4C22×C4×D7311yescharacteristic
798C2×C4C2×D4×D7311yescharacteristic
799C2×C4C22×C22⋊D7311yescharacteristic
800C2×C4#41×D7311yescharacteristic
801C2×C4#1455663611yescharacteristic
802C2×C4#1455663711yescharacteristic
803C8—21no—
804C8—21no—
805C8—22no—
806C8—21no—
807C8—21no—
808C8—41no—
809C8—2921no—
810C8—2921no—
811C8—1461no—
812C8—1461no—
813C8—1461no—
814C8—1461no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—81no—
827C22—81no—
828C22—2921no—
829C22—2921no—
830C22—2921no—
831C22—2921no—
832C22—2921no—
833C22—5844no—
834C22—1462no—
835C22C2×C4×C22⋊D7311yescharacteristic
836C22#1798923311yescharacteristic
837C22#1798926611yescharacteristic
838C4—21no—
839C4—21no—
840C4—41no—
841C4—41no—
842C4—41no—
843C4—2922no—
844C4—2921no—
845C4—5841no—
846C4—1462no—
847C4C4×D4×D7311yescharacteristic
848C4#1798905911yescharacteristic
849C4D4×C22⋊D7311yescharacteristic
850C4#1798922511yescharacteristic
851C2—21no—
852C2—21no—
853C2—41no—
854C2—41no—
855C2—81no—
856C2—2922no—
857C2—5841no—
858C2#2261290811yescharacteristic
859C2#2261883211yescharacteristic
860C2#2261884611yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#2933C2
socleC22×C73C2×C4×D4
prime radical#22619147C2
cosocleC22×C4×C73C24
hypercenter#2933D73
hypocenterC73#22887
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C22⋊C8 ◁ #2933

Complements

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

NH ≅ G/Ntype
2. C2×#17988707C2semidirect
3. C2×#17988603C2semidirect
4. #22618377C2semidirect
5. #22610818C2semidirect
6. #22610641C2semidirect
7. #22610579C2semidirect
8. #22610380C2semidirect
9. #22610261C2semidirect
10. #22610258C2semidirect
11. #22610205C2semidirect
12. #22610136C2semidirect
13. #22609770C2semidirect
14. #22609699C2semidirect
15. C73×#2933C2semidirect
22. #17988747C4semidirect
23. #17988747C4semidirect
24. #17988742C4semidirect
25. #17988737C4semidirect
26. #17988730C4semidirect
27. #17988730C4semidirect
28. #17988725C4semidirect
29. #17988720C4semidirect
31. C2×#14556526C22semidirect
32. C2×#14556526C22semidirect
34. C2×#14556518C22semidirect
35. C2×#14556518C22semidirect
50. C2×#14556501C22semidirect
51. C2×C8×Dic73C22semidirect
52. #17988351C22semidirect
53. #17988351C22semidirect
54. #17988346C22semidirect
55. #17988346C22semidirect
56. #17988341C22semidirect
57. #17988341C22semidirect
58. C2×#131×C73C22semidirect
65. #424×C73C22semidirect
66. #408×C73C22semidirect
68. #405×C73C22semidirect
120. #14556517D4semidirect
433. #2933D73semidirect
446. C73#22887semidirect
452. C2×#131C2×D73semidirect
471. #424C2×D73semidirect
485. #408C2×D73semidirect
491. #405C2×D73semidirect

Maximal subgroups

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

subgroupindex
#226191472
C2×#179887072
C2×#179886032
#226183772
#226108182
#226106412
#226105792
#226103802
#226102612
#226102582
#226102052
#226101362
#226097702
#226096992
C73×#29332
#2288773