Finite Group Databasebeta

← #33097180

Subgroups — #33097180

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
1#121×Dic73C211yesmaximal, characteristic, complemented
2#22612422C211yesmaximal, characteristic, complemented
3#22610798C211yesmaximal, characteristic, complemented
4#22610787C211yesmaximal, characteristic, complemented
5#22610616C211yesmaximal, characteristic, complemented
6#22610609C211yesmaximal, characteristic, complemented
7#22610574C211yesmaximal, characteristic, complemented
8#22610560C211yesmaximal, characteristic, complemented
9#22610281C211yesmaximal, characteristic, complemented
10#22610267C211yesmaximal, characteristic, complemented
11#22610254C211yesmaximal, characteristic, complemented
12#22610132C211yesmaximal, characteristic, complemented
13#22609871C211yesmaximal, characteristic, complemented
14C22⋊C8×Dic73C211yesmaximal, characteristic, complemented
15C2×#449×C73C211yesmaximal, characteristic
16C2×D4×Dic73—21no—
17C2×D4×Dic73C2211yescharacteristic
18C2×#14556550C2211yescharacteristic
19C22×C4×Dic73C2211yescharacteristic
20C2×#14556525C2211yescharacteristic
21C2×#14556523C2211yescharacteristic
22C2×#14556515C2211yescharacteristic
23C2×#14556515C2211yescharacteristic
24C2×#14556512C2211yescharacteristic
25C2×#14556512C2211yescharacteristic
26C2×#14556512C2211yescharacteristic
27C2×#14556512C2211yescharacteristic
28C2×C22⋊#10596831C2211yescharacteristic
29C2×C8×Dic73C2211yescharacteristic
30C2×C8×Dic73C2211yescharacteristic
31#17988494C2211yescharacteristic
32#17988494C2211yescharacteristic
33#17988490C2211yescharacteristic
34#17988490C2211yescharacteristic
35#17988490C2211yescharacteristic
36#17988486C2211yescharacteristic
37#17988480—21no—
38#17988467—21no—
39#17988467—21no—
40#17988467—21no—
41#17988447C2211yescharacteristic
42C4⋊C4×Dic73C2211yescharacteristic
43C22⋊C4×Dic73—21no—
44C4×C22⋊Dic73—21no—
45C4×C22⋊Dic73—21no—
46#17988350C2211yescharacteristic
47#17988350C2211yescharacteristic
48#17988349C2211yescharacteristic
49#17988349C2211yescharacteristic
50#17988341C2211yescharacteristic
51#17988341C2211yescharacteristic
52C22×#41×C73C2211yescharacteristic
53C22×SD16×C73C2211yescharacteristic
54C22×D8×C73C2211yescharacteristic
55C2×#121×C73C2211yescharacteristic
56#449×C73C418yescomplemented
57C2×#103×C73C2211yescharacteristic
58C2×#102×C73C2211yescharacteristic
59C2×C22⋊C8×C73C2211yescharacteristic
60C23×Dic73—21no—
61C23×Dic73D411yescharacteristic
62C23×Dic73D411yescharacteristic
63C22×#10596831C2311yescharacteristic
64C22×#10596831C2311yescharacteristic
65D4×Dic73—41no—
66D4×Dic73—41no—
67D4×Dic73—44no—
68#14556550—41no—
69#14556550—41no—
70C2×C4⋊Dic73—21no—
71C2×C4⋊Dic73C2311yescharacteristic
72C2×C4⋊Dic73C2311yescharacteristic
73C2×C4⋊Dic73C2311yescharacteristic
74C2×C4⋊Dic73C2311yescharacteristic
75C2×C22⋊Dic73—21no—
76C2×C22⋊Dic73—21no—
77C2×C22⋊Dic73—21no—
78C2×C22⋊Dic73—21no—
79C2×C22⋊Dic73—21no—
80C2×C22⋊Dic73—21no—
81C2×C22⋊Dic73—21no—
82C2×C22⋊Dic73—21no—
83C2×C22⋊Dic73—21no—
84C2×C4×Dic73—21no—
85C2×C4×Dic73—21no—
86C2×C4×Dic73—41no—
87C2×C4×Dic73—41no—
88C2×C4×Dic73D411yescharacteristic
89C2×C4×Dic73D411yescharacteristic
90C2×C4×Dic73C2311yescharacteristic
91C2×C4×Dic73C2311yescharacteristic
92#14556525—41no—
93#14556523—41no—
94#14556515—41no—
95#14556515—41no—
96#14556512—41no—
97#14556512—41no—
98#14556512—41no—
99#14556512—41no—
100C22⋊#10596831—22no—
101C8×Dic73—41no—
102C8×Dic73—41no—
103#14556498—21no—
104#14556498—21no—
105#14556498—21no—
106#14556498—21no—
107#14556498—21no—
108#14556498—21no—
109#14556498—21no—
110C2×#41×C73—22no—
111C2×#41×C73—41no—
112C2×#41×C73—41no—
113C2×#41×C73—41no—
114C2×#41×C73—41no—
115C2×#41×C73C2×C414yescomplemented
116C22×Q8×C73C2311yescharacteristic
117C22×D4×C73—21no—
118C22×D4×C73—21no—
119C22×D4×C73C2311yescharacteristic
120C22×D4×C73C2311yescharacteristic
121C23×C4×C73—21no—
122C23×C4×C73C2311yescharacteristic
123C2×SD16×C73—41no—
124C2×SD16×C73—41no—
125C2×SD16×C73C2×C414yescomplemented
126C2×D8×C73—41no—
127C2×D8×C73—41no—
128C2×D8×C73C2×C414yescomplemented
129C22×C8×C73C2311yescharacteristic
130C22×C8×C73C2311yescharacteristic
131#121×C73—22no—
132#121×C73C2×C414yes—
133C2×C4⋊C4×C73C2311yescharacteristic
134C2×C22⋊C4×C73—21no—
135#103×C73C2×C414yescomplemented
136#102×C73C2×C414yescomplemented
137C22⋊C8×C73C2×C414yescomplemented
138C22×Dic73—22no—
139C22×Dic73—22no—
140C22×Dic73—22no—
141C22×Dic73—21no—
142C22×Dic73—21no—
143C22×Dic73—21no—
144C22×Dic73—21no—
145C22×Dic73—41no—
146C22×Dic73—41no—
147C22×Dic73—41no—
148C22×Dic73—42no—
149C22×Dic73—42no—
150C22×Dic73—42no—
151C22×Dic73C2×D411yescharacteristic
152C22×Dic73C2×D411yescharacteristic
153C22×Dic73C2×D411yescharacteristic
154C22×Dic73C2×D411yescharacteristic
155C2×#10596831—21no—
156C2×#10596831—21no—
157C2×#10596831—21no—
158C2×#10596831—21no—
159C2×#10596831—21no—
160C2×#10596831—21no—
161C4⋊Dic73—21no—
162C4⋊Dic73—21no—
163C4⋊Dic73—21no—
164C4⋊Dic73—21no—
165C4⋊Dic73—21no—
166C4⋊Dic73—21no—
167C4⋊Dic73—21no—
168C4⋊Dic73—21no—
169C4⋊Dic73—42no—
170C22⋊Dic73—42no—
171C22⋊Dic73—42no—
172C22⋊Dic73—42no—
173C22⋊Dic73—42no—
174C22⋊Dic73—42no—
175C22⋊Dic73—42no—
176C22⋊Dic73—42no—
177C22⋊Dic73—42no—
178C22⋊Dic73—42no—
179C4×Dic73—21no—
180C4×Dic73—21no—
181C4×Dic73—21no—
182C4×Dic73—21no—
183C4×Dic73—41no—
184C4×Dic73—41no—
185C4×Dic73—42no—
186C4×Dic73—42no—
187C24×C73—21no—
188C24×C73—21no—
189C24×C73C2×D411yescharacteristic
190#41×C73—44no—
191#41×C73—44no—
192#41×C73—44no—
193#41×C73—44no—
194C2×Q8×C73—21no—
195C2×Q8×C73—21no—
196C2×Q8×C73—21no—
197C2×Q8×C73—21no—
198C2×Q8×C73—21no—
199C2×Q8×C73C22×C412yes—
200C2×D4×C73—24no—
201C2×D4×C73—24no—
202C2×D4×C73—21no—
203C2×D4×C73—21no—
204C2×D4×C73—21no—
205C2×D4×C73—21no—
206C2×D4×C73—21no—
207C2×D4×C73—21no—
208C2×D4×C73—21no—
209C2×D4×C73—21no—
210C2×D4×C73—21no—
211C2×D4×C73—21no—
212C2×D4×C73—42no—
213C2×D4×C73—42no—
214C2×D4×C73—42no—
215C2×D4×C73—42no—
216C2×D4×C73C22×C412yes—
217C2×D4×C73C22×C412yes—
218C22×C4×C73—21no—
219C22×C4×C73—21no—
220C22×C4×C73—21no—
221C22×C4×C73—21no—
222C22×C4×C73—21no—
223C22×C4×C73—21no—
224C22×C4×C73—24no—
225C22×C4×C73—42no—
226C22×C4×C73—42no—
227C22×C4×C73C22×C412yes—
228C22×C4×C73C2×D411yescharacteristic
229C22×C4×C73#4112yes—
230C22×C4×C73C2411yescharacteristic
231SD16×C73—44no—
232D8×C73—44no—
233C2×C8×C73—21no—
234C2×C8×C73—21no—
235C2×C8×C73—21no—
236C2×C8×C73—21no—
237C2×C8×C73C22×C412yes—
238C2×C8×C73C22×C412yes—
239C4⋊C4×C73—21no—
240C4⋊C4×C73C22×C412yes—
241C22⋊C4×C73—24no—
242C23×C73—21no—
243C23×C73—21no—
244C23×C73—21no—
245C23×C73—21no—
246C23×C73—21no—
247C23×C73—21no—
248C23×C73—22no—
249C23×C73—22no—
250C23×C73—41no—
251C23×C73—41no—
252C23×C73—41no—
253C23×C73—41no—
254C23×C73—41no—
255C23×C73—41no—
256C23×C73—41no—
257C23×C73—41no—
258C23×C73—41no—
259C23×C73—41no—
260C23×C73—41no—
261C23×C73—41no—
262C23×C73C4×D412yes—
263C23×C73C22×D411yescharacteristic
264Q8×C73—22no—
265Q8×C73—22no—
266Q8×C73—41no—
267Q8×C73—41no—
268D4×C73—22no—
269D4×C73—22no—
270D4×C73—22no—
271D4×C73—22no—
272D4×C73—48no—
273D4×C73—48no—
274D4×C73—41no—
275D4×C73—41no—
276D4×C73—41no—
277D4×C73—41no—
278C2×C4×C73—21no—
279C2×C4×C73—21no—
280C2×C4×C73—22no—
281C2×C4×C73—22no—
282C2×C4×C73—22no—
283C2×C4×C73—22no—
284C2×C4×C73—22no—
285C2×C4×C73—22no—
286C2×C4×C73—48no—
287C2×C4×C73—41no—
288C2×C4×C73—41no—
289C2×C4×C73—41no—
290C2×C4×C73—41no—
291C2×C4×C73C4×D412yes—
292C2×C4×C73C23×C411yescharacteristic
293C2×C4×C73C2×#4111yescharacteristic
294C2×C4×C73H(5,𝔽2)11yescharacteristic
295C2×C4×C73H(5,𝔽2)11yescharacteristic
296C2×C4×C73H(5,𝔽2)11yescharacteristic
297C2×C4×C73H(5,𝔽2)11yescharacteristic
298C2×Dic73—21no—
299C2×Dic73—21no—
300C2×Dic73—21no—
301C2×Dic73—21no—
302C2×Dic73—21no—
303C2×Dic73—21no—
304C2×Dic73—21no—
305C2×Dic73—21no—
306C2×Dic73—21no—
307C2×Dic73—44no—
308C2×Dic73—44no—
309C2×Dic73—41no—
310C2×Dic73—41no—
311C2×Dic73—41no—
312C2×Dic73—41no—
313C2×Dic73—41no—
314C2×Dic73—41no—
315C2×Dic73—41no—
316C2×Dic73—41no—
317C2×Dic73—41no—
318C2×Dic73—41no—
319C2×Dic73—41no—
320C2×Dic73—41no—
321C2×Dic73—84no—
322C2×Dic73#13512yes—
323C2×Dic73#13512yes—
324C2×Dic73AGL(1,ℤ/8)12yes—
325C8×C73—22no—
326C8×C73—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—42no—
340C22×C73—42no—
341C22×C73—42no—
342C22×C73—81no—
343C22×C73—81no—
344C22×C73—81no—
345C22×C73—81no—
346C22×C73—81no—
347C22×C73—81no—
348C22×C73—81no—
349C22×C73—81no—
350C22×C73C2×C4×D411yescharacteristic
351C22×C73#53411yescharacteristic
352C22×C73#53511yescharacteristic
353C22×C73C2×#13511yescharacteristic
354C22×C73C2×#13511yescharacteristic
355C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
356C22×C73#57511yescharacteristic
357C4×C73—22no—
358C4×C73—42no—
359C4×C73—42no—
360C4×C73#51811yescharacteristic
361C4×C73#51811yescharacteristic
362C4×C73#53811yescharacteristic
363C4×C73#53811yescharacteristic
364Dic73—22no—
365Dic73—22no—
366Dic73—22no—
367Dic73—41no—
368Dic73—81no—
369Dic73—81no—
370Dic73—81no—
371Dic73—81no—
372#22045—731nomaximal, Sylow
373C2×C73—42no—
374C2×C73—82no—
375C2×C73—82no—
376C2×C73#232111yescharacteristic
377C2×C73C4×#13511yescharacteristic
378C2×C73C4×AGL(1,ℤ/8)11yescharacteristic
379C2×C73#318811yescharacteristic
380C2×C73#319111yescharacteristic
381C2×C73#320711yescharacteristic
382C2×C73#321211yescharacteristic
383C2×#449D7311yescharacteristic
384C4×#121—731no—
385#2297—731no—
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×SD16C2×D7311yescharacteristic
401C22×D8C2×D7311yescharacteristic
402C2×#121C2×D7311yescharacteristic
403C2×C4×D4—731no—
404C2×C4×D4—1461no—
405C2×#117—731no—
406C22×C42—731no—
407#449Dic7318yescomplemented
408C2×#107—731no—
409C2×#106—731no—
410C2×#103—731no—
411C2×#103—731no—
412C2×#103C2×D7311yescharacteristic
413C2×#102—731no—
414C2×#102—731no—
415C2×#102—731no—
416C2×#102—731no—
417C2×#102C2×D7311yescharacteristic
418C2×C22⋊C8—731no—
419C2×C22⋊C8C2×D7311yescharacteristic
420C2×C4×C8—731no—
421C2×C4×C8—731no—
422#391—731no—
423#391—731no—
424#390—731no—
425#390—731no—
426#390—731no—
427#389—731no—
428#388—1461no—
429#386—1461no—
430#386—1461no—
431#386—1461no—
432#380—731no—
433C4×C4⋊C4—731no—
434C4×C22⋊C4—1461no—
435C4×C22⋊C4—1461no—
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×#41C2×Dic7314yescomplemented
449C22×Q8C22×D7311yescharacteristic
450C22×D4—21no—
451C22×D4—21no—
452C22×D4C22×D7311yescharacteristic
453C22×D4C22×D7311yescharacteristic
454C23×C4—21no—
455C23×C4—731no—
456C23×C4—731no—
457C23×C4—1461no—
458C23×C4C22×D7311yescharacteristic
459C2×SD16—41no—
460C2×SD16—41no—
461C2×SD16C2×Dic7314yescomplemented
462C2×D8—41no—
463C2×D8—41no—
464C2×D8C2×Dic7314yescomplemented
465C22×C8—731no—
466C22×C8—731no—
467C22×C8C22×D7311yescharacteristic
468C22×C8C22×D7311yescharacteristic
469#121—22no—
470#121C2×Dic7314yes—
471C4×D4—2924no—
472C4×D4—2921no—
473C4×D4—2921no—
474#117—2921no—
475#117—2921no—
476C2×C4⋊C4—731no—
477C2×C4⋊C4—731no—
478C2×C4⋊C4—731no—
479C2×C4⋊C4—731no—
480C2×C4⋊C4—1461no—
481C2×C4⋊C4C22×D7311yescharacteristic
482C2×C22⋊C4—21no—
483C2×C22⋊C4—1461no—
484C2×C22⋊C4—1461no—
485C2×C22⋊C4—1461no—
486C2×C22⋊C4—1461no—
487C2×C22⋊C4—1461no—
488C2×C22⋊C4—1461no—
489C2×C22⋊C4—1461no—
490C2×C22⋊C4—1461no—
491C2×C22⋊C4—1461no—
492C2×C42—2921no—
493C2×C42—2921no—
494C2×C42—731no—
495C2×C42—731no—
496C2×C42—731no—
497C2×C42—731no—
498C2×C42—1461no—
499C2×C42—1461no—
500#107—2921no—
501#106—2921no—
502#103—2921no—
503#103—2921no—
504#103C2×Dic7314yescomplemented
505#102—2921no—
506#102—2921no—
507#102—2921no—
508#102—2921no—
509#102C2×Dic7314yescomplemented
510C22⋊C8—1462no—
511C22⋊C8C2×Dic7314yescomplemented
512C4×C8—2921no—
513C4×C8—2921no—
514#95—1461no—
515#95—1461no—
516#95—1461no—
517#95—1461no—
518#95—1461no—
519#95—1461no—
520#95—1461no—
521C24—21no—
522C24—21no—
523C24D4×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×Q8C22×Dic7312yes—
534C2×D4—24no—
535C2×D4—24no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—42no—
547C2×D4—42no—
548C2×D4—42no—
549C2×D4—42no—
550C2×D4C22×Dic7312yes—
551C2×D4C22×Dic7312yes—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—24no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—2921no—
562C22×C4—2921no—
563C22×C4—2921no—
564C22×C4—2922no—
565C22×C4—2922no—
566C22×C4—2922no—
567C22×C4—731no—
568C22×C4—731no—
569C22×C4—731no—
570C22×C4—731no—
571C22×C4—1461no—
572C22×C4—1461no—
573C22×C4—1461no—
574C22×C4—1461no—
575C22×C4—1462no—
576C22×C4—1462no—
577C22×C4—1462no—
578C22×C4C22×Dic7312yes—
579C22×C4D4×D7311yescharacteristic
580C22×C4#1192402712yes—
581C22×C4C23×D7311yescharacteristic
582SD16—44no—
583D8—44no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—1461no—
589C2×C8—1461no—
590C2×C8—1461no—
591C2×C8—1461no—
592C2×C8—1461no—
593C2×C8—1461no—
594C2×C8C22×Dic7312yes—
595C2×C8C22×Dic7312yes—
596C4⋊C4—21no—
597C4⋊C4—2922no—
598C4⋊C4—1461no—
599C4⋊C4—1461no—
600C4⋊C4—1461no—
601C4⋊C4—1461no—
602C4⋊C4—1461no—
603C4⋊C4—1461no—
604C4⋊C4—1461no—
605C4⋊C4—1461no—
606C4⋊C4C22×Dic7312yes—
607C22⋊C4—24no—
608C22⋊C4—2922no—
609C22⋊C4—2922no—
610C22⋊C4—2922no—
611C22⋊C4—2922no—
612C22⋊C4—2922no—
613C22⋊C4—2922no—
614C22⋊C4—2922no—
615C22⋊C4—2922no—
616C22⋊C4—2922no—
617C42—2922no—
618C42—2921no—
619C42—2921no—
620C42—2922no—
621C42—1461no—
622C42—1461no—
623C42—1461no—
624C42—1461no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—22no—
632C23—22no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23D4×Dic7312yes—
646C23C2×D4×D7311yescharacteristic
647Q8—22no—
648Q8—22no—
649Q8—41no—
650Q8—41no—
651D4—22no—
652D4—22no—
653D4—22no—
654D4—22no—
655D4—48no—
656D4—48no—
657D4—41no—
658D4—41no—
659D4—41no—
660D4—41no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—48no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—2924no—
675C2×C4—2921no—
676C2×C4—2921no—
677C2×C4—2921no—
678C2×C4—2921no—
679C2×C4—2921no—
680C2×C4—2921no—
681C2×C4—2921no—
682C2×C4—2921no—
683C2×C4—2921no—
684C2×C4—2921no—
685C2×C4—2921no—
686C2×C4—2921no—
687C2×C4—2924no—
688C2×C4—5844no—
689C2×C4—732no—
690C2×C4—732no—
691C2×C4—732no—
692C2×C4—1461no—
693C2×C4—1461no—
694C2×C4—1461no—
695C2×C4—1461no—
696C2×C4—1461no—
697C2×C4—1461no—
698C2×C4—1461no—
699C2×C4—1461no—
700C2×C4—1461no—
701C2×C4D4×Dic7312yes—
702C2×C4C23×Dic7311yescharacteristic
703C2×C4C2×#1192402711yescharacteristic
704C2×C4#1455663611yescharacteristic
705C2×C4#1455663611yescharacteristic
706C2×C4#1455663611yescharacteristic
707C2×C4#1455663611yescharacteristic
708C8—22no—
709C8—22no—
710C8—2921no—
711C8—2921no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—42no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—81no—
726C22—81no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22—81no—
731C22—81no—
732C22—81no—
733C22C2×D4×Dic7311yescharacteristic
734C22#1798914711yescharacteristic
735C22#1798915211yescharacteristic
736C22#135×D7311yescharacteristic
737C22#135×D7311yescharacteristic
738C22AGL(1,ℤ/8)×D7311yescharacteristic
739C22#1798938311yescharacteristic
740C4—22no—
741C4—42no—
742C4—42no—
743C4—2921no—
744C4—5841no—
745C4—5841no—
746C4—5841no—
747C4—5841no—
748C4—1462no—
749C4—1462no—
750C4—1462no—
751C4#1798906211yescharacteristic
752C4#1798906211yescharacteristic
753C4#1798917211yescharacteristic
754C4#1798917211yescharacteristic
755C2—42no—
756C2—82no—
757C2—82no—
758C2#2261259211yescharacteristic
759C2#135×Dic7311yescharacteristic
760C2AGL(1,ℤ/8)×Dic7311yescharacteristic
761C2#2262069411yescharacteristic
762C2#2262072111yescharacteristic
763C2#2262086211yescharacteristic
764C2#2262090411yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
Fitting, prime radicalC2×#449×C73C2
socleC23×C73C22×D4
cosocleC22×C4×C73C24
hypercenterC2×#449D73
hypocenterC73#22045
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#449

Complements

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

NH ≅ G/Ntype
1. #121×Dic73C2semidirect
2. #22612422C2semidirect
3. #22610798C2semidirect
4. #22610787C2semidirect
5. #22610616C2semidirect
6. #22610609C2semidirect
7. #22610574C2semidirect
8. #22610560C2semidirect
9. #22610281C2semidirect
10. #22610267C2semidirect
11. #22610254C2semidirect
12. #22610132C2semidirect
13. #22609871C2semidirect
14. C22⋊C8×Dic73C2semidirect
56. #449×C73C4semidirect
115. C2×#41×C73C2×C4semidirect
125. C2×SD16×C73C2×C4semidirect
128. C2×D8×C73C2×C4semidirect
135. #103×C73C2×C4semidirect
136. #102×C73C2×C4semidirect
137. C22⋊C8×C73C2×C4semidirect
398. C73#22045semidirect
407. #449Dic73semidirect
448. C2×#41C2×Dic73semidirect
461. C2×SD16C2×Dic73semidirect
464. C2×D8C2×Dic73semidirect
504. #103C2×Dic73semidirect
509. #102C2×Dic73semidirect
511. C22⋊C8C2×Dic73semidirect

Maximal subgroups

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

subgroupindex
#121×Dic732
#226124222
#226107982
#226107872
#226106162
#226106092
#226105742
#226105602
#226102812
#226102672
#226102542
#226101322
#226098712
C22⋊C8×Dic732
C2×#449×C732
#2204573