Finite Group Databasebeta

← #33097284

Subgroups — #33097284

Order 18688.

1024 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22612626C211yesmaximal, characteristic, complemented
2#22612523C211yesmaximal, characteristic, complemented
3#22610808C211yesmaximal, characteristic, complemented
4#22610787C211yesmaximal, characteristic, complemented
5#22610623C211yesmaximal, characteristic, complemented
6#22610616C211yesmaximal, characteristic, complemented
7#22610567C211yesmaximal, characteristic, complemented
8#22610560C211yesmaximal, characteristic, complemented
9#22610281C211yesmaximal, characteristic, complemented
10#22610267C211yesmaximal, characteristic, complemented
11#22610249C211yesmaximal, characteristic, complemented
12#22610126C211yesmaximal, characteristic, complemented
13#22609871C211yesmaximal, characteristic, complemented
14#22609699C211yesmaximal, characteristic, complemented
15C2×#449×C73C211yesmaximal, characteristic
16C2×D4×Dic73C2211yescharacteristic
17C2×#14556550C2211yescharacteristic
18C22×C4⋊Dic73C2211yescharacteristic
19C2×#14556523C2211yescharacteristic
20C2×#14556523C2211yescharacteristic
21C2×#14556515C2211yescharacteristic
22C2×#14556515C2211yescharacteristic
23C2×#14556512C2211yescharacteristic
24C2×#14556512C2211yescharacteristic
25C2×#14556512C2211yescharacteristic
26C2×#14556512C2211yescharacteristic
27C2×C22⋊#10596831C2211yescharacteristic
28C2×#14556501C2211yescharacteristic
29C2×C8×Dic73C2211yescharacteristic
30#17988494C2211yescharacteristic
31#17988494C2211yescharacteristic
32#17988490—21no—
33#17988490C2211yescharacteristic
34#17988490C2211yescharacteristic
35#17988490C2211yescharacteristic
36#17988486C2211yescharacteristic
37#17988480—21no—
38#17988467—21no—
39#17988467—21no—
40#17988467—21no—
41#17988462—21no—
42#17988447—21no—
43#17988447—21no—
44#17988447C2211yescharacteristic
45C4⋊C4×Dic73C2211yescharacteristic
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×Dic73—21no—
62C22×#10596831C2311yescharacteristic
63C22×#10596831C2311yescharacteristic
64D4×Dic73—41no—
65D4×Dic73—41no—
66#14556550—41no—
67#14556550—41no—
68C2×C4⋊Dic73—21no—
69C2×C4⋊Dic73—21no—
70C2×C4⋊Dic73—41no—
71C2×C4⋊Dic73—41no—
72C2×C4⋊Dic73D411yescharacteristic
73C2×C4⋊Dic73D411yescharacteristic
74C2×C4⋊Dic73C2311yescharacteristic
75C2×C4⋊Dic73C2311yescharacteristic
76C2×C4⋊Dic73C2311yescharacteristic
77C2×C4⋊Dic73C2311yescharacteristic
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×C22⋊Dic73—21no—
85C2×C22⋊Dic73—21no—
86C2×C22⋊Dic73D411yescharacteristic
87C2×C22⋊Dic73D411yescharacteristic
88C2×C4×Dic73—21no—
89C2×C4×Dic73C2311yescharacteristic
90C2×C4×Dic73C2311yescharacteristic
91#14556523—41no—
92#14556523—41no—
93#14556515—41no—
94#14556515—41no—
95#14556512—41no—
96#14556512—41no—
97#14556512—41no—
98#14556512—41no—
99C22⋊#10596831—22no—
100#14556501—41no—
101C8×Dic73—41no—
102#14556498—21no—
103#14556498—21no—
104#14556498—21no—
105#14556498—21no—
106#14556498—21no—
107#14556498—21no—
108#14556498—21no—
109C2×#41×C73—22no—
110C2×#41×C73—41no—
111C2×#41×C73—41no—
112C2×#41×C73—41no—
113C2×#41×C73—41no—
114C2×#41×C73C2×C414yescomplemented
115C22×Q8×C73C2311yescharacteristic
116C22×D4×C73—21no—
117C22×D4×C73—21no—
118C22×D4×C73C2311yescharacteristic
119C22×D4×C73C2311yescharacteristic
120C23×C4×C73—21no—
121C23×C4×C73C2311yescharacteristic
122C2×SD16×C73—41no—
123C2×SD16×C73—41no—
124C2×SD16×C73C2×C414yescomplemented
125C2×D8×C73—41no—
126C2×D8×C73—41no—
127C2×D8×C73C2×C414yescomplemented
128C22×C8×C73C2311yescharacteristic
129C22×C8×C73C2311yescharacteristic
130#121×C73—22no—
131#121×C73C2×C414yes—
132C2×C4⋊C4×C73C2311yescharacteristic
133C2×C22⋊C4×C73—21no—
134#103×C73C2×C414yescomplemented
135#102×C73C2×C414yescomplemented
136C22⋊C8×C73C2×C414yescomplemented
137C22×Dic73—21no—
138C22×Dic73—21no—
139C22×Dic73—21no—
140C22×Dic73—21no—
141C22×Dic73—42no—
142C22×Dic73—42no—
143C22×Dic73—81no—
144C22×Dic73—81no—
145C22×Dic73—81no—
146C22×Dic73—81no—
147C22×Dic73C2×D411yescharacteristic
148C22×Dic73C2×D411yescharacteristic
149C22×Dic73C2×D411yescharacteristic
150C22×Dic73C2×D411yescharacteristic
151C2×#10596831—21no—
152C2×#10596831—21no—
153C2×#10596831—21no—
154C2×#10596831—21no—
155C2×#10596831—21no—
156C2×#10596831—21no—
157C4⋊Dic73—21no—
158C4⋊Dic73—21no—
159C4⋊Dic73—21no—
160C4⋊Dic73—21no—
161C4⋊Dic73—21no—
162C4⋊Dic73—21no—
163C4⋊Dic73—21no—
164C4⋊Dic73—21no—
165C4⋊Dic73—41no—
166C4⋊Dic73—41no—
167C4⋊Dic73—42no—
168C4⋊Dic73—81no—
169C22⋊Dic73—41no—
170C22⋊Dic73—41no—
171C22⋊Dic73—42no—
172C22⋊Dic73—81no—
173C22⋊Dic73—81no—
174C22⋊Dic73—81no—
175C22⋊Dic73—81no—
176C22⋊Dic73—81no—
177C22⋊Dic73—81no—
178C22⋊Dic73—81no—
179C4×Dic73—21no—
180C4×Dic73—21no—
181C4×Dic73—21no—
182C4×Dic73—21no—
183C4×Dic73—81no—
184C24×C73—21no—
185C24×C73—21no—
186C24×C73C2×D411yescharacteristic
187#41×C73—44no—
188#41×C73—44no—
189#41×C73—44no—
190#41×C73—44no—
191C2×Q8×C73—21no—
192C2×Q8×C73—21no—
193C2×Q8×C73—21no—
194C2×Q8×C73—21no—
195C2×Q8×C73—21no—
196C2×Q8×C73C22×C412yes—
197C2×D4×C73—24no—
198C2×D4×C73—24no—
199C2×D4×C73—21no—
200C2×D4×C73—21no—
201C2×D4×C73—21no—
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—42no—
210C2×D4×C73—42no—
211C2×D4×C73—81no—
212C2×D4×C73—81no—
213C2×D4×C73C22×C412yes—
214C2×D4×C73C22×C412yes—
215C22×C4×C73—21no—
216C22×C4×C73—21no—
217C22×C4×C73—21no—
218C22×C4×C73—21no—
219C22×C4×C73—21no—
220C22×C4×C73—21no—
221C22×C4×C73—24no—
222C22×C4×C73—42no—
223C22×C4×C73—42no—
224C22×C4×C73C22×C412yes—
225C22×C4×C73C2×D411yescharacteristic
226C22×C4×C73#4112yes—
227C22×C4×C73C2411yescharacteristic
228SD16×C73—44no—
229D8×C73—44no—
230C2×C8×C73—21no—
231C2×C8×C73—21no—
232C2×C8×C73—21no—
233C2×C8×C73—21no—
234C2×C8×C73C22×C412yes—
235C2×C8×C73C22×C412yes—
236C4⋊C4×C73—21no—
237C4⋊C4×C73C22×C412yes—
238C22⋊C4×C73—24no—
239C23×C73—21no—
240C23×C73—21no—
241C23×C73—21no—
242C23×C73—21no—
243C23×C73—21no—
244C23×C73—21no—
245C23×C73—22no—
246C23×C73—22no—
247C23×C73—41no—
248C23×C73—41no—
249C23×C73—41no—
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×C73C4×D412yes—
260C23×C73C22×D411yescharacteristic
261Q8×C73—22no—
262Q8×C73—22no—
263Q8×C73—41no—
264Q8×C73—41no—
265D4×C73—22no—
266D4×C73—22no—
267D4×C73—22no—
268D4×C73—22no—
269D4×C73—48no—
270D4×C73—41no—
271D4×C73—41no—
272D4×C73—41no—
273D4×C73—41no—
274D4×C73—84no—
275C2×C4×C73—21no—
276C2×C4×C73—21no—
277C2×C4×C73—22no—
278C2×C4×C73—22no—
279C2×C4×C73—22no—
280C2×C4×C73—22no—
281C2×C4×C73—22no—
282C2×C4×C73—22no—
283C2×C4×C73—48no—
284C2×C4×C73—41no—
285C2×C4×C73—41no—
286C2×C4×C73—41no—
287C2×C4×C73—41no—
288C2×C4×C73C4×D412yes—
289C2×C4×C73C23×C411yescharacteristic
290C2×C4×C73C2×#4111yescharacteristic
291C2×C4×C73H(5,𝔽2)11yescharacteristic
292C2×C4×C73H(5,𝔽2)11yescharacteristic
293C2×C4×C73H(5,𝔽2)11yescharacteristic
294C2×C4×C73H(5,𝔽2)11yescharacteristic
295C2×Dic73—21no—
296C2×Dic73—21no—
297C2×Dic73—21no—
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—41no—
308C2×Dic73—41no—
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—84no—
320C2×Dic73—84no—
321C8×C73—22no—
322C8×C73—22no—
323#10596831—41no—
324#10596831—41no—
325C22×C73—22no—
326C22×C73—22no—
327C22×C73—22no—
328C22×C73—41no—
329C22×C73—41no—
330C22×C73—41no—
331C22×C73—41no—
332C22×C73—42no—
333C22×C73—42no—
334C22×C73—42no—
335C22×C73—42no—
336C22×C73—42no—
337C22×C73—42no—
338C22×C73—81no—
339C22×C73—81no—
340C22×C73—81no—
341C22×C73—81no—
342C22×C73—81no—
343C22×C73—81no—
344C22×C73—81no—
345C22×C73—81no—
346C22×C73C2×C4×D411yescharacteristic
347C22×C73#53411yescharacteristic
348C22×C73#53511yescharacteristic
349C22×C73#57611yescharacteristic
350C22×C73#57711yescharacteristic
351C22×C73#57711yescharacteristic
352C22×C73#57711yescharacteristic
353C4×C73—22no—
354C4×C73—42no—
355C4×C73—42no—
356C4×C73#51811yescharacteristic
357C4×C73#51811yescharacteristic
358C4×C73#53811yescharacteristic
359C4×C73#53811yescharacteristic
360Dic73—41no—
361Dic73—41no—
362Dic73—41no—
363Dic73—41no—
364Dic73—81no—
365Dic73—81no—
366Dic73—81no—
367Dic73—81no—
368#22053—731nomaximal, Sylow
369C2×C73—42no—
370C2×C73—82no—
371C2×C73—82no—
372C2×C73#232111yescharacteristic
373C2×C73#294611yescharacteristic
374C2×C73#295211yescharacteristic
375C2×C73#319811yescharacteristic
376C2×C73#320411yescharacteristic
377C2×C73#322111yescharacteristic
378C2×C73#322411yescharacteristic
379C2×#449D7311yescharacteristic
380#2324—731no—
381#2311—731no—
382#1972—731no—
383#1968—731no—
384#1935—731no—
385#1934—731no—
386#1927—731no—
387#1926—731no—
388#1879—731no—
389#1877—731no—
390#1874—731no—
391#1853—731no—
392#1788—731no—
393#1750—731no—
394C73#2205311yescharacteristic, complemented, Sylow
395C22×#41C2×D7311yescharacteristic
396C22×SD16C2×D7311yescharacteristic
397C22×D8C2×D7311yescharacteristic
398C2×#121C2×D7311yescharacteristic
399C2×C4×D4—731no—
400C2×#117—731no—
401C22×C4⋊C4—731no—
402#449Dic7318yescomplemented
403C2×#106—731no—
404C2×#106—731no—
405C2×#103—731no—
406C2×#103—731no—
407C2×#103C2×D7311yescharacteristic
408C2×#102—731no—
409C2×#102—731no—
410C2×#102—731no—
411C2×#102—731no—
412C2×#102C2×D7311yescharacteristic
413C2×C22⋊C8—731no—
414C2×C22⋊C8C2×D7311yescharacteristic
415C2×#97—731no—
416C2×C4×C8—731no—
417#391—731no—
418#391—731no—
419#390—731no—
420#390—731no—
421#390—731no—
422#390—1461no—
423#389—731no—
424#388—1461no—
425#386—1461no—
426#386—1461no—
427#386—1461no—
428#385—1461no—
429#380—731no—
430#380—1461no—
431#380—1461no—
432C4×C4⋊C4—731no—
433#340—731no—
434#340—731no—
435#340—731no—
436#340—731no—
437#336—731no—
438#336—731no—
439C2×#41—22no—
440C2×#41—41no—
441C2×#41—41no—
442C2×#41—41no—
443C2×#41—41no—
444C2×#41C2×Dic7314yescomplemented
445C22×Q8C22×D7311yescharacteristic
446C22×D4—21no—
447C22×D4—21no—
448C22×D4C22×D7311yescharacteristic
449C22×D4C22×D7311yescharacteristic
450C23×C4—21no—
451C23×C4—1461no—
452C23×C4—1461no—
453C23×C4C22×D7311yescharacteristic
454C2×SD16—41no—
455C2×SD16—41no—
456C2×SD16C2×Dic7314yescomplemented
457C2×D8—41no—
458C2×D8—41no—
459C2×D8C2×Dic7314yescomplemented
460C22×C8—731no—
461C22×C8—731no—
462C22×C8C22×D7311yescharacteristic
463C22×C8C22×D7311yescharacteristic
464#121—22no—
465#121C2×Dic7314yes—
466C4×D4—2921no—
467C4×D4—2921no—
468#117—2921no—
469#117—2921no—
470C2×C4⋊C4—2921no—
471C2×C4⋊C4—2921no—
472C2×C4⋊C4—731no—
473C2×C4⋊C4—731no—
474C2×C4⋊C4—731no—
475C2×C4⋊C4—731no—
476C2×C4⋊C4—731no—
477C2×C4⋊C4—731no—
478C2×C4⋊C4—1461no—
479C2×C4⋊C4—1461no—
480C2×C4⋊C4C22×D7311yescharacteristic
481C2×C22⋊C4—21no—
482C2×C22⋊C4—731no—
483C2×C22⋊C4—731no—
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—731no—
493C2×C42—731no—
494C2×C42—1461no—
495#106—2921no—
496#106—2921no—
497#103—2921no—
498#103—2921no—
499#103C2×Dic7314yescomplemented
500#102—2921no—
501#102—2921no—
502#102—2921no—
503#102—2921no—
504#102C2×Dic7314yescomplemented
505C22⋊C8—1462no—
506C22⋊C8C2×Dic7314yescomplemented
507#97—2921no—
508C4×C8—2921no—
509#95—1461no—
510#95—1461no—
511#95—1461no—
512#95—1461no—
513#95—1461no—
514#95—1461no—
515#95—1461no—
516C24—21no—
517C24—21no—
518C24D4×D7311yescharacteristic
519#41—44no—
520#41—44no—
521#41—44no—
522#41—44no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8C22×Dic7312yes—
529C2×D4—24no—
530C2×D4—24no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—42no—
542C2×D4—42no—
543C2×D4—81no—
544C2×D4—81no—
545C2×D4C22×Dic7312yes—
546C2×D4C22×Dic7312yes—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—24no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—2922no—
557C22×C4—2922no—
558C22×C4—5841no—
559C22×C4—5841no—
560C22×C4—5841no—
561C22×C4—5841no—
562C22×C4—731no—
563C22×C4—731no—
564C22×C4—731no—
565C22×C4—731no—
566C22×C4—1461no—
567C22×C4—1461no—
568C22×C4—1461no—
569C22×C4—1461no—
570C22×C4C22×Dic7312yes—
571C22×C4D4×D7311yescharacteristic
572C22×C4#1192402712yes—
573C22×C4C23×D7311yescharacteristic
574SD16—44no—
575D8—44no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—1461no—
581C2×C8—1461no—
582C2×C8—1461no—
583C2×C8—1461no—
584C2×C8—1461no—
585C2×C8—1461no—
586C2×C8C22×Dic7312yes—
587C2×C8C22×Dic7312yes—
588C4⋊C4—21no—
589C4⋊C4—2922no—
590C4⋊C4—2921no—
591C4⋊C4—2921no—
592C4⋊C4—5841no—
593C4⋊C4—1461no—
594C4⋊C4—1461no—
595C4⋊C4—1461no—
596C4⋊C4—1461no—
597C4⋊C4—1461no—
598C4⋊C4—1461no—
599C4⋊C4—1461no—
600C4⋊C4—1461no—
601C4⋊C4C22×Dic7312yes—
602C22⋊C4—24no—
603C22⋊C4—2922no—
604C22⋊C4—2921no—
605C22⋊C4—2921no—
606C22⋊C4—5841no—
607C22⋊C4—5841no—
608C22⋊C4—5841no—
609C22⋊C4—5841no—
610C22⋊C4—5841no—
611C22⋊C4—5841no—
612C22⋊C4—5841no—
613C42—5841no—
614C42—1461no—
615C42—1461no—
616C42—1461no—
617C42—1461no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—22no—
625C23—22no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23D4×Dic7312yes—
639C23C2×D4×D7311yescharacteristic
640Q8—22no—
641Q8—22no—
642Q8—41no—
643Q8—41no—
644D4—22no—
645D4—22no—
646D4—22no—
647D4—22no—
648D4—48no—
649D4—41no—
650D4—41no—
651D4—41no—
652D4—41no—
653D4—84no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—48no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—2921no—
668C2×C4—2921no—
669C2×C4—2921no—
670C2×C4—2921no—
671C2×C4—2921no—
672C2×C4—2921no—
673C2×C4—2921no—
674C2×C4—2921no—
675C2×C4—2921no—
676C2×C4—2921no—
677C2×C4—2921no—
678C2×C4—2921no—
679C2×C4—5844no—
680C2×C4—5844no—
681C2×C4—1461no—
682C2×C4—1461no—
683C2×C4—1461no—
684C2×C4—1461no—
685C2×C4—1461no—
686C2×C4—1461no—
687C2×C4—1461no—
688C2×C4—1461no—
689C2×C4—1461no—
690C2×C4—1461no—
691C2×C4—1461no—
692C2×C4—1461no—
693C2×C4D4×Dic7312yes—
694C2×C4C23×Dic7311yescharacteristic
695C2×C4C2×#1192402711yescharacteristic
696C2×C4#1455663611yescharacteristic
697C2×C4#1455663611yescharacteristic
698C2×C4#1455663611yescharacteristic
699C2×C4#1455663611yescharacteristic
700C8—22no—
701C8—22no—
702C8—2921no—
703C8—2921no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—42no—
712C22—42no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22—42no—
717C22—81no—
718C22—81no—
719C22—81no—
720C22—81no—
721C22—81no—
722C22—81no—
723C22—81no—
724C22—81no—
725C22C2×D4×Dic7311yescharacteristic
726C22#1798914711yescharacteristic
727C22#1798915211yescharacteristic
728C22#1798939111yescharacteristic
729C22#1798939411yescharacteristic
730C22#1798939411yescharacteristic
731C22#1798939711yescharacteristic
732C4—22no—
733C4—42no—
734C4—42no—
735C4—2921no—
736C4—2921no—
737C4—2921no—
738C4—2921no—
739C4—5841no—
740C4—5841no—
741C4—5841no—
742C4—5841no—
743C4#1798906211yescharacteristic
744C4#1798906211yescharacteristic
745C4#1798917211yescharacteristic
746C4#1798917211yescharacteristic
747C2—42no—
748C2—82no—
749C2—82no—
750C2#2261259211yescharacteristic
751C2#2261876411yescharacteristic
752C2#2261881511yescharacteristic
753C2#2262078211yescharacteristic
754C2#2262084011yescharacteristic
755C2#2262099011yescharacteristic
756C2#2262102311yescharacteristic
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#22053
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. #22612626C2semidirect
2. #22612523C2semidirect
3. #22610808C2semidirect
4. #22610787C2semidirect
5. #22610623C2semidirect
6. #22610616C2semidirect
7. #22610567C2semidirect
8. #22610560C2semidirect
9. #22610281C2semidirect
10. #22610267C2semidirect
11. #22610249C2semidirect
12. #22610126C2semidirect
13. #22609871C2semidirect
14. #22609699C2semidirect
56. #449×C73C4semidirect
114. C2×#41×C73C2×C4semidirect
124. C2×SD16×C73C2×C4semidirect
127. C2×D8×C73C2×C4semidirect
134. #103×C73C2×C4semidirect
135. #102×C73C2×C4semidirect
136. C22⋊C8×C73C2×C4semidirect
394. C73#22053semidirect
402. #449Dic73semidirect
444. C2×#41C2×Dic73semidirect
456. C2×SD16C2×Dic73semidirect
459. C2×D8C2×Dic73semidirect
499. #103C2×Dic73semidirect
504. #102C2×Dic73semidirect
506. C22⋊C8C2×Dic73semidirect

Maximal subgroups

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

subgroupindex
#226126262
#226125232
#226108082
#226107872
#226106232
#226106162
#226105672
#226105602
#226102812
#226102672
#226102492
#226101262
#226098712
#226096992
C2×#449×C732
#2205373