Finite Group Databasebeta

← #33097176

Subgroups — #33097176

Order 18688.

1096 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988732C211yesmaximal, characteristic
2C4×#14556565C211yesmaximal, characteristic, complemented
3#22610796C211yesmaximal, characteristic, complemented
4#22610788C211yesmaximal, characteristic, complemented
5#22610617C211yesmaximal, characteristic, complemented
6#22610610C211yesmaximal, characteristic, complemented
7#22610569C211yesmaximal, characteristic, complemented
8#22610555C211yesmaximal, characteristic, complemented
9#22610282C211yesmaximal, characteristic, complemented
10#22610268C211yesmaximal, characteristic, complemented
11#22610253C211yesmaximal, characteristic, complemented
12#22610130C211yesmaximal, characteristic, complemented
13#22609871C211yesmaximal, characteristic, complemented
14C4×C22⋊#10596831C211yesmaximal, characteristic, complemented
15C73×#2297C211yesmaximal, characteristic, complemented
16C22×#11924015C2211yescharacteristic
17C22×#11924013C2211yescharacteristic
18C2×#14556565C2211yescharacteristic
19C2×C4×D292C2211yescharacteristic
20C2×C4×C22⋊D73—21no—
21#17988732C418yescomplemented
22C2×#14556524C2211yescharacteristic
23C2×#14556522C2211yescharacteristic
24C2×#14556515C2211yescharacteristic
25C2×#14556515C2211yescharacteristic
26C2×#14556515C2211yescharacteristic
27C2×#14556512C2211yescharacteristic
28C2×#14556512C2211yescharacteristic
29C2×#14556512C2211yescharacteristic
30C2×#14556511C2211yescharacteristic
31C2×#14556511C2211yescharacteristic
32C2×C22⋊#10596831C2211yescharacteristic
33C2×C22⋊#10596831C2211yescharacteristic
34C2×C4×#10596831C2211yescharacteristic
35C2×C4×#10596831C2211yescharacteristic
36#17988489C2211yescharacteristic
37#17988485C2211yescharacteristic
38#17988478—21no—
39#17988466—21no—
40#17988447C2211yescharacteristic
41C4×C4⋊Dic73C2211yescharacteristic
42C4×#11924005—21no—
43#17988349C2211yescharacteristic
44#17988349C2211yescharacteristic
45#17988349C2211yescharacteristic
46#17988349C2211yescharacteristic
47#17988342C2211yescharacteristic
48#17988342C2211yescharacteristic
49C22×#41×C73C2211yescharacteristic
50C2×#117×C73C2211yescharacteristic
51C22×C42×C73C2211yescharacteristic
52#391×C73C2211yescharacteristic
53#391×C73C2211yescharacteristic
54#390×C73C2211yescharacteristic
55#390×C73C2211yescharacteristic
56#386×C73—21no—
57#386×C73—21no—
58C4×C22⋊C4×C73—21no—
59C4×C22⋊C4×C73—21no—
60C22×D292C2311yescharacteristic
61C22×C22⋊D73—21no—
62C22×C4×D73—21no—
63C2×#11924015—41no—
64C2×#11924015—41no—
65C2×#11924015C2×C414yescomplemented
66C2×#11924013—41no—
67C2×#11924013—41no—
68C2×#11924013C2×C414yescomplemented
69C22×#10596831C2311yescharacteristic
70C22×#10596831C2311yescharacteristic
71C22×#10596831C2311yescharacteristic
72C22×#10596831C2311yescharacteristic
73#14556565—22no—
74#14556565C2×C414yes—
75C4×D292—41no—
76C4×D292—41no—
77C4×C22⋊D73—44no—
78C2×C4⋊Dic73C2311yescharacteristic
79C2×C4⋊Dic73C2311yescharacteristic
80C2×C4⋊Dic73C2311yescharacteristic
81C2×#11924007—21no—
82C2×C22⋊Dic73—21no—
83C2×#11924005—21no—
84C2×#11924005—21no—
85C2×#11924005—21no—
86C2×#11924005—21no—
87C2×C4×Dic73—21no—
88#14556524—41no—
89#14556522—41no—
90#14556515—41no—
91#14556515—41no—
92#14556515C2×C414yescomplemented
93#14556512—41no—
94#14556512—41no—
95#14556512C2×C414yescomplemented
96#14556511—41no—
97#14556511—41no—
98C22⋊#10596831—22no—
99C22⋊#10596831C2×C414yescomplemented
100C4×#10596831—41no—
101C4×#10596831—41no—
102#14556498—21no—
103#14556498—21no—
104#14556498—21no—
105C2×#41×C73—22no—
106C2×#41×C73—41no—
107C2×#41×C73—41no—
108C2×#41×C73—41no—
109C2×#41×C73—41no—
110C2×#41×C73C2×C414yescomplemented
111C22×Q8×C73C2311yescharacteristic
112C22×D4×C73—21no—
113C22×D4×C73C2311yescharacteristic
114C23×C4×C73—21no—
115C23×C4×C73D411yescharacteristic
116C23×C4×C73D411yescharacteristic
117C23×C4×C73C2311yescharacteristic
118#117×C73—41no—
119#117×C73—41no—
120C2×C4⋊C4×C73C2311yescharacteristic
121C2×C4⋊C4×C73C2311yescharacteristic
122C2×C22⋊C4×C73—21no—
123C2×C22⋊C4×C73—21no—
124C2×C22⋊C4×C73—21no—
125C2×C22⋊C4×C73—21no—
126C2×C22⋊C4×C73—21no—
127C2×C42×C73—21no—
128C2×C42×C73—41no—
129C2×C42×C73—41no—
130C2×C42×C73D411yescharacteristic
131C2×C42×C73D411yescharacteristic
132C2×C42×C73C2311yescharacteristic
133C2×C42×C73C2311yescharacteristic
134#95×C73—21no—
135#95×C73—21no—
136#95×C73—21no—
137#95×C73—21no—
138C23×D73—21no—
139C2×D292—21no—
140C2×D292—21no—
141C2×D292—21no—
142C2×D292—21no—
143C2×D292—21no—
144C2×D292C22×C412yes—
145C2×C22⋊D73—24no—
146C2×C22⋊D73—42no—
147C2×C22⋊D73—42no—
148C22×Dic73—21no—
149C22×Dic73—21no—
150C22×Dic73—21no—
151C2×C4×D73—42no—
152C2×C4×D73—42no—
153C2×C4×D73—42no—
154#11924015—44no—
155#11924013—44no—
156C2×#10596831—21no—
157C2×#10596831—21no—
158C2×#10596831—21no—
159C2×#10596831—21no—
160C2×#10596831—21no—
161C2×#10596831—21no—
162C2×#10596831—21no—
163C2×#10596831—21no—
164C2×#10596831—21no—
165C2×#10596831—21no—
166C2×#10596831C22×C412yes—
167C2×#10596831C22×C412yes—
168C4⋊Dic73—21no—
169C4⋊Dic73—21no—
170C4⋊Dic73—21no—
171C4⋊Dic73—21no—
172C4⋊Dic73—21no—
173C4⋊Dic73C22×C412yes—
174#11924007—42no—
175C22⋊Dic73—42no—
176#11924005—24no—
177#11924005—42no—
178#11924005—42no—
179#11924005—42no—
180C4×Dic73—42no—
181C24×C73—21no—
182C24×C73C2×D411yescharacteristic
183#41×C73—44no—
184#41×C73—44no—
185#41×C73—44no—
186#41×C73—44no—
187C2×Q8×C73—21no—
188C2×Q8×C73—21no—
189C2×Q8×C73—21no—
190C2×Q8×C73—21no—
191C2×Q8×C73—21no—
192C2×Q8×C73C22×C412yes—
193C2×D4×C73—24no—
194C2×D4×C73—21no—
195C2×D4×C73—21no—
196C2×D4×C73—21no—
197C2×D4×C73—21no—
198C2×D4×C73—21no—
199C2×D4×C73—42no—
200C2×D4×C73—42no—
201C2×D4×C73C22×C412yes—
202C22×C4×C73—21no—
203C22×C4×C73—21no—
204C22×C4×C73—21no—
205C22×C4×C73—21no—
206C22×C4×C73—21no—
207C22×C4×C73—24no—
208C22×C4×C73—22no—
209C22×C4×C73—22no—
210C22×C4×C73—22no—
211C22×C4×C73—21no—
212C22×C4×C73—21no—
213C22×C4×C73—41no—
214C22×C4×C73—41no—
215C22×C4×C73—41no—
216C22×C4×C73—42no—
217C22×C4×C73—42no—
218C22×C4×C73C22×C412yes—
219C22×C4×C73C2×D411yescharacteristic
220C22×C4×C73C2×D411yescharacteristic
221C22×C4×C73C2×D411yescharacteristic
222C22×C4×C73C2×D411yescharacteristic
223C22×C4×C73C2×D411yescharacteristic
224C22×C4×C73#4112yes—
225C22×C4×C73C2411yescharacteristic
226C4⋊C4×C73—21no—
227C4⋊C4×C73—21no—
228C4⋊C4×C73—21no—
229C4⋊C4×C73—21no—
230C22⋊C4×C73—42no—
231C22⋊C4×C73—42no—
232C22⋊C4×C73—42no—
233C22⋊C4×C73—42no—
234C22⋊C4×C73—42no—
235C42×C73—21no—
236C42×C73—21no—
237C42×C73—21no—
238C42×C73—21no—
239C42×C73—41no—
240C42×C73—41no—
241C42×C73—42no—
242C23×C73—21no—
243C23×C73—21no—
244C23×C73—21no—
245C23×C73—21no—
246C23×C73—21no—
247C23×C73—21no—
248C23×C73—22no—
249C23×C73—41no—
250C23×C73—41no—
251C23×C73—41no—
252C23×C73—41no—
253C23×C73—41no—
254C23×C73—41no—
255C23×C73C4×D412yes—
256C23×C73C22×D411yescharacteristic
257C22×D73—22no—
258C22×D73—41no—
259C22×D73—41no—
260C22×D73—41no—
261C22×D73—41no—
262C22×D73—41no—
263C22×D73—41no—
264Q8×C73—22no—
265Q8×C73—22no—
266Q8×C73—41no—
267Q8×C73—41no—
268D4×C73—22no—
269D4×C73—22no—
270D4×C73—48no—
271D4×C73—41no—
272D4×C73—41no—
273C2×C4×C73—21no—
274C2×C4×C73—21no—
275C2×C4×C73—21no—
276C2×C4×C73—21no—
277C2×C4×C73—21no—
278C2×C4×C73—21no—
279C2×C4×C73—21no—
280C2×C4×C73—21no—
281C2×C4×C73—22no—
282C2×C4×C73—22no—
283C2×C4×C73—22no—
284C2×C4×C73—22no—
285C2×C4×C73—22no—
286C2×C4×C73—21no—
287C2×C4×C73—21no—
288C2×C4×C73—21no—
289C2×C4×C73—44no—
290C2×C4×C73—44no—
291C2×C4×C73—48no—
292C2×C4×C73—41no—
293C2×C4×C73—41no—
294C2×C4×C73—41no—
295C2×C4×C73—41no—
296C2×C4×C73—41no—
297C2×C4×C73—41no—
298C2×C4×C73—41no—
299C2×C4×C73—41no—
300C2×C4×C73C4×D412yes—
301C2×C4×C73#13512yes—
302C2×C4×C73#13512yes—
303C2×C4×C73AGL(1,ℤ/8)12yes—
304C2×C4×C73C23×C411yescharacteristic
305C2×C4×C73C2×#4111yescharacteristic
306C2×C4×C73H(5,𝔽2)11yescharacteristic
307C2×C4×C73H(5,𝔽2)11yescharacteristic
308C2×C4×C73H(5,𝔽2)11yescharacteristic
309C2×C4×C73H(5,𝔽2)11yescharacteristic
310C22⋊D73—48no—
311C2×Dic73—22no—
312C2×Dic73—41no—
313C2×Dic73—41no—
314C2×Dic73—41no—
315C2×Dic73—41no—
316C2×Dic73—41no—
317C2×Dic73—41no—
318C2×Dic73—41no—
319C2×Dic73—41no—
320D292—22no—
321D292—22no—
322D292—41no—
323D292—41no—
324C4×D73—84no—
325#10596831—22no—
326#10596831—22no—
327#10596831—41no—
328#10596831—41no—
329C22×C73—22no—
330C22×C73—22no—
331C22×C73—22no—
332C22×C73—41no—
333C22×C73—41no—
334C22×C73—41no—
335C22×C73—41no—
336C22×C73—42no—
337C22×C73—42no—
338C22×C73—42no—
339C22×C73—81no—
340C22×C73—81no—
341C22×C73—81no—
342C22×C73—81no—
343C22×C73C2×C4×D411yescharacteristic
344C22×C73#53411yescharacteristic
345C22×C73#53511yescharacteristic
346C22×C73C2×#13511yescharacteristic
347C22×C73C2×#13511yescharacteristic
348C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
349C22×C73#57511yescharacteristic
350C2×D73—42no—
351C2×D73—42no—
352C2×D73—42no—
353C2×D73—81no—
354C2×D73—81no—
355C2×D73—81no—
356C2×D73—81no—
357C4×C73—22no—
358C4×C73—22no—
359C4×C73—22no—
360C4×C73—22no—
361C4×C73—42no—
362C4×C73—41no—
363C4×C73—81no—
364C4×C73—81no—
365C4×C73#51811yescharacteristic
366C4×C73#51811yescharacteristic
367C4×C73#53811yescharacteristic
368C4×C73#53811yescharacteristic
369Dic73—42no—
370Dic73—81no—
371Dic73—81no—
372#22045—731nomaximal, Sylow
373C2×C73—42no—
374C2×C73—82no—
375C2×C73#232111yescharacteristic
376C2×C73C4×#13511yescharacteristic
377C2×C73C4×AGL(1,ℤ/8)11yescharacteristic
378C2×C73#318811yescharacteristic
379C2×C73#319111yescharacteristic
380C2×C73#320711yescharacteristic
381C2×C73#321211yescharacteristic
382D73—82no—
383C2×#449—731no—
384C4×#121—731no—
385#2297D7311yescharacteristic, complemented
386#1970—731no—
387#1968—731no—
388#1934—731no—
389#1933—731no—
390#1928—731no—
391#1926—731no—
392#1879—731no—
393#1877—731no—
394#1875—731no—
395#1854—731no—
396#1788—731no—
397C4×C22⋊C8—731no—
398C73#2204511yescharacteristic, complemented, Sylow
399C22×#41C2×D7311yescharacteristic
400C22×SD16—731no—
401C22×D8—731no—
402C2×#121—731no—
403C2×C4×D4—731no—
404C2×C4×D4—1461no—
405C2×#117C2×D7311yescharacteristic
406C22×C42C2×D7311yescharacteristic
407#449—738no—
408C2×#107—731no—
409C2×#106—731no—
410C2×#103—731no—
411C2×#103—731no—
412C2×#103—731no—
413C2×#102—731no—
414C2×#102—731no—
415C2×#102—731no—
416C2×#102—731no—
417C2×#102—731no—
418C2×C22⋊C8—731no—
419C2×C22⋊C8—731no—
420C2×C4×C8—731no—
421C2×C4×C8—731no—
422#391C2×D7311yescharacteristic
423#391C2×D7311yescharacteristic
424#390—731no—
425#390C2×D7311yescharacteristic
426#390C2×D7311yescharacteristic
427#389—731no—
428#388—1461no—
429#386—21no—
430#386—21no—
431#386—1461no—
432#380—731no—
433C4×C4⋊C4—731no—
434C4×C22⋊C4—21no—
435C4×C22⋊C4—21no—
436C4×C22⋊C4—1461no—
437#340—731no—
438#340—731no—
439#340—731no—
440#340—731no—
441#336—731no—
442#336—731no—
443C2×#41—22no—
444C2×#41—41no—
445C2×#41—41no—
446C2×#41—41no—
447C2×#41—41no—
448C2×#41C4×D7314yescomplemented
449C22×Q8C22×D7311yescharacteristic
450C22×D4—21no—
451C22×D4—731no—
452C22×D4—1461no—
453C22×D4C22×D7311yescharacteristic
454C23×C4—21no—
455C23×C4—1461no—
456C23×C4C22⋊D7311yescharacteristic
457C23×C4C22⋊D7311yescharacteristic
458C23×C4C22×D7311yescharacteristic
459C2×SD16—2921no—
460C2×SD16—2921no—
461C2×SD16—734no—
462C2×D8—2921no—
463C2×D8—2921no—
464C2×D8—734no—
465C22×C8—731no—
466C22×C8—731no—
467C22×C8—731no—
468C22×C8—731no—
469#121—734no—
470#121—1462no—
471C4×D4—2921no—
472C4×D4—2921no—
473C4×D4—2924no—
474#117—41no—
475#117—41no—
476C2×C4⋊C4—731no—
477C2×C4⋊C4—731no—
478C2×C4⋊C4—731no—
479C2×C4⋊C4—1461no—
480C2×C4⋊C4C22×D7311yescharacteristic
481C2×C4⋊C4C22×D7311yescharacteristic
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—21no—
487C2×C22⋊C4—1461no—
488C2×C22⋊C4—1461no—
489C2×C22⋊C4—1461no—
490C2×C22⋊C4—1461no—
491C2×C22⋊C4—1461no—
492C2×C42—21no—
493C2×C42—41no—
494C2×C42—41no—
495C2×C42—1461no—
496C2×C42C22⋊D7311yescharacteristic
497C2×C42C22⋊D7311yescharacteristic
498C2×C42C22×D7311yescharacteristic
499C2×C42C22×D7311yescharacteristic
500#107—2921no—
501#106—2921no—
502#103—2921no—
503#103—2921no—
504#103—734no—
505#102—2921no—
506#102—2921no—
507#102—2921no—
508#102—2921no—
509#102—734no—
510C22⋊C8—734no—
511C22⋊C8—1462no—
512C4×C8—2921no—
513C4×C8—2921no—
514#95—21no—
515#95—21no—
516#95—21no—
517#95—21no—
518#95—1461no—
519#95—1461no—
520#95—1461no—
521C24—21no—
522C24—1461no—
523C24C2×C22⋊D7311yescharacteristic
524#41—44no—
525#41—44no—
526#41—44no—
527#41—44no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8C2×C4×D7312yes—
534C2×D4—24no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—42no—
541C2×D4—42no—
542C2×D4—2922no—
543C2×D4—2922no—
544C2×D4—732no—
545C2×D4—1464no—
546C2×D4—1461no—
547C2×D4—1461no—
548C2×D4—1461no—
549C2×D4—1461no—
550C2×D4—1461no—
551C2×D4C2×C4×D7312yes—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—24no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—41no—
564C22×C4—41no—
565C22×C4—41no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—2922no—
569C22×C4—2922no—
570C22×C4—2922no—
571C22×C4—1461no—
572C22×C4—1461no—
573C22×C4—1461no—
574C22×C4C2×C4×D7312yes—
575C22×C4C2×C22⋊D7311yescharacteristic
576C22×C4C2×C22⋊D7311yescharacteristic
577C22×C4C2×C22⋊D7311yescharacteristic
578C22×C4C2×C22⋊D7311yescharacteristic
579C22×C4C2×C22⋊D7311yescharacteristic
580C22×C4#1192402812yes—
581C22×C4C23×D7311yescharacteristic
582SD16—2924no—
583D8—2924no—
584C2×C8—732no—
585C2×C8—732no—
586C2×C8—1461no—
587C2×C8—1461no—
588C2×C8—1461no—
589C2×C8—1461no—
590C2×C8—1461no—
591C2×C8—1461no—
592C2×C8—1461no—
593C2×C8—1461no—
594C2×C8—1461no—
595C2×C8—1461no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—2922no—
601C4⋊C4—732no—
602C4⋊C4—1461no—
603C4⋊C4—1461no—
604C4⋊C4—1461no—
605C4⋊C4—1461no—
606C4⋊C4—1461no—
607C22⋊C4—42no—
608C22⋊C4—42no—
609C22⋊C4—42no—
610C22⋊C4—42no—
611C22⋊C4—42no—
612C22⋊C4—2922no—
613C22⋊C4—2922no—
614C22⋊C4—2922no—
615C22⋊C4—2922no—
616C22⋊C4—1464no—
617C42—21no—
618C42—21no—
619C42—21no—
620C42—21no—
621C42—41no—
622C42—41no—
623C42—42no—
624C42—2922no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—22no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—2921no—
639C23—2921no—
640C23—2921no—
641C23—2921no—
642C23—2921no—
643C23—2921no—
644C23—1462no—
645C23C4×C22⋊D7312yes—
646C23C22×C22⋊D7311yescharacteristic
647Q8—22no—
648Q8—22no—
649Q8—41no—
650Q8—41no—
651D4—22no—
652D4—22no—
653D4—48no—
654D4—41no—
655D4—41no—
656D4—2928no—
657D4—2921no—
658D4—2921no—
659D4—1462no—
660D4—1462no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—22no—
676C2×C4—21no—
677C2×C4—44no—
678C2×C4—48no—
679C2×C4—44no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—2921no—
689C2×C4—2921no—
690C2×C4—2921no—
691C2×C4—2921no—
692C2×C4—2921no—
693C2×C4—2921no—
694C2×C4—2921no—
695C2×C4—2921no—
696C2×C4—5844no—
697C2×C4—1462no—
698C2×C4C4×C22⋊D7312yes—
699C2×C4#1455661112yes—
700C2×C4#1455661112yes—
701C2×C4#1455661612yes—
702C2×C4C22×C4×D7311yescharacteristic
703C2×C4C2×#1192402811yescharacteristic
704C2×C4#1455663611yescharacteristic
705C2×C4#1455663611yescharacteristic
706C2×C4#1455663611yescharacteristic
707C2×C4#1455663611yescharacteristic
708C8—2921no—
709C8—2921no—
710C8—1462no—
711C8—1462no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—42no—
720C22—42no—
721C22—42no—
722C22—81no—
723C22—81no—
724C22—81no—
725C22—81no—
726C22—2922no—
727C22—2922no—
728C22—2922no—
729C22—5841no—
730C22—5841no—
731C22—5841no—
732C22—5841no—
733C22C2×C4×C22⋊D7311yescharacteristic
734C22#1798914611yescharacteristic
735C22#1798915411yescharacteristic
736C22C2×#1455661111yescharacteristic
737C22C2×#1455661111yescharacteristic
738C22C2×#1455661611yescharacteristic
739C22#1798938511yescharacteristic
740C4—22no—
741C4—22no—
742C4—22no—
743C4—22no—
744C4—41no—
745C4—42no—
746C4—81no—
747C4—81no—
748C4—2922no—
749C4—5841no—
750C4—5841no—
751C4#1798906011yescharacteristic
752C4#1798906011yescharacteristic
753C4#1798917511yescharacteristic
754C4#1798917511yescharacteristic
755C2—42no—
756C2—82no—
757C2—5842no—
758C2#2261258911yescharacteristic
759C2C4×#1455661111yescharacteristic
760C2C4×#1455661611yescharacteristic
761C2#2262069211yescharacteristic
762C2#2262071911yescharacteristic
763C2#2262086411yescharacteristic
764C2#2262090711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#2297C2
socleC23×C73C22×D4
prime radicalC2×#17988732C2
cosocleC22×C4×C73C24
hypercenter#2297D73
hypocenterC73#22045
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2297

Complements

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

NH ≅ G/Ntype
2. C4×#14556565C2semidirect
3. #22610796C2semidirect
4. #22610788C2semidirect
5. #22610617C2semidirect
6. #22610610C2semidirect
7. #22610569C2semidirect
8. #22610555C2semidirect
9. #22610282C2semidirect
10. #22610268C2semidirect
11. #22610253C2semidirect
12. #22610130C2semidirect
13. #22609871C2semidirect
14. C4×C22⋊#10596831C2semidirect
15. C73×#2297C2semidirect
21. #17988732C4semidirect
65. C2×#11924015C2×C4semidirect
68. C2×#11924013C2×C4semidirect
92. #14556515C2×C4semidirect
95. #14556512C2×C4semidirect
99. C22⋊#10596831C2×C4semidirect
110. C2×#41×C73C2×C4semidirect
385. #2297D73semidirect
398. C73#22045semidirect
448. C2×#41C4×D73semidirect

Maximal subgroups

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

subgroupindex
C2×#179887322
C4×#145565652
#226107962
#226107882
#226106172
#226106102
#226105692
#226105552
#226102822
#226102682
#226102532
#226101302
#226098712
C4×C22⋊#105968312
C73×#22972
#2204573