Finite Group Databasebeta

← #33130438

Subgroups — #33130438

Order 18688.

796 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22614239C211yesmaximal, characteristic
2#22611498C211yesmaximal, characteristic, complemented
3#22611413C211yesmaximal, characteristic, complemented
4#22611367C211yesmaximal, characteristic, complemented
5#22611362C211yesmaximal, characteristic, complemented
6#22610523C211yesmaximal, characteristic, complemented
7#22610516C211yesmaximal, characteristic, complemented
8#22610224C211yesmaximal, characteristic
9#22610130C211yesmaximal, characteristic, complemented
10#22610124C211yesmaximal, characteristic, complemented
11#22610026C211yesmaximal, characteristic, complemented
12#22610015C211yesmaximal, characteristic, complemented
13#22609958C211yesmaximal, characteristic, complemented
14C2×#17988349C211yesmaximal, characteristic, complemented
15C73×#2352C211yesmaximal, characteristic
16C23×#10596831C2211yescharacteristic
17C2×#14556572—21no—
18C22×C4⋊Dic73C2211yescharacteristic
19C2×#14556524C2211yescharacteristic
20C2×#14556524C2211yescharacteristic
21C2×#14556522C2211yescharacteristic
22C2×#14556522C2211yescharacteristic
23C2×C22⋊#10596831C2211yescharacteristic
24C2×C22⋊#10596831C2211yescharacteristic
25C2×C22⋊#10596831C2211yescharacteristic
26#17988517—21no—
27#17988512—21no—
28#17988485C2211yescharacteristic
29#17988485C2211yescharacteristic
30#17988448—21no—
31#17988447C2211yescharacteristic
32#17988447C2211yescharacteristic
33#17988447C2211yescharacteristic
34#17988349C2211yescharacteristic
35#17988349C2211yescharacteristic
36#17988349C2211yescharacteristic
37#17988349C2211yescharacteristic
38#17988349C2211yescharacteristic
39#17988349C2211yescharacteristic
40#17988349C2211yescharacteristic
41#17988349C2211yescharacteristic
42#17988349C2211yescharacteristic
43#17988349C2211yescharacteristic
44#17988349C2211yescharacteristic
45#17988349C2211yescharacteristic
46#17988342C2211yescharacteristic
47#17988342C2211yescharacteristic
48C2×C4×D4×C73C2211yescharacteristic
49C2×#117×C73C2211yescharacteristic
50C22×C4⋊C4×C73C2211yescharacteristic
51#388×C73—21no—
52#387×C73—21no—
53#386×C73—21no—
54#382×C73C2211yescharacteristic
55#380×C73C2211yescharacteristic
56#380×C73C2211yescharacteristic
57C4×C4⋊C4×C73C2211yescharacteristic
58C4×C22⋊C4×C73—21no—
59C23×Dic73—21no—
60C22×#10596831—22no—
61C22×#10596831—22no—
62C22×#10596831—41no—
63C22×#10596831C2311yescharacteristic
64C22×#10596831C2311yescharacteristic
65C22×#10596831C2311yescharacteristic
66C22×#10596831C2311yescharacteristic
67#14556572—44no—
68C2×C4⋊Dic73—21no—
69C2×C4⋊Dic73—22no—
70C2×C4⋊Dic73—22no—
71C2×C4⋊Dic73C2311yescharacteristic
72C2×C4⋊Dic73C2311yescharacteristic
73C2×C4⋊Dic73C2311yescharacteristic
74C2×C4⋊Dic73C2311yescharacteristic
75C2×#11924007—21no—
76C2×#11924007—21no—
77C2×C22⋊Dic73—21no—
78C2×C22⋊Dic73—21no—
79C2×C22⋊Dic73—21no—
80#14556524—22no—
81#14556524—41no—
82#14556522—22no—
83#14556522—41no—
84C22⋊#10596831—22no—
85C22⋊#10596831—22no—
86C22⋊#10596831—41no—
87#14556498—21no—
88#14556498—21no—
89#14556498—21no—
90#14556498—21no—
91#14556498—21no—
92C22×D4×C73D411yescharacteristic
93C23×C4×C73—21no—
94C23×C4×C73C2311yescharacteristic
95C23×C4×C73C2311yescharacteristic
96C4×D4×C73—22no—
97C4×D4×C73—22no—
98#117×C73—22no—
99#117×C73—41no—
100C2×C4⋊C4×C73—22no—
101C2×C4⋊C4×C73—21no—
102C2×C4⋊C4×C73—41no—
103C2×C4⋊C4×C73D411yescharacteristic
104C2×C4⋊C4×C73C2311yescharacteristic
105C2×C4⋊C4×C73C2311yescharacteristic
106C2×C4⋊C4×C73C2311yescharacteristic
107C2×C4⋊C4×C73C2311yescharacteristic
108C2×C22⋊C4×C73—21no—
109C2×C22⋊C4×C73—21no—
110C2×C22⋊C4×C73—21no—
111C2×C22⋊C4×C73D411yescharacteristic
112C2×C22⋊C4×C73D411yescharacteristic
113C2×C42×C73—21no—
114C2×C42×C73—21no—
115C2×C42×C73C2311yescharacteristic
116#95×C73—21no—
117#95×C73—21no—
118#95×C73—21no—
119#95×C73—21no—
120#95×C73—21no—
121C22×Dic73—21no—
122C22×Dic73—21no—
123C22×Dic73—21no—
124C22×Dic73—21no—
125C22×Dic73—42no—
126C22×Dic73—42no—
127C22×Dic73—42no—
128C2×#10596831—21no—
129C2×#10596831—21no—
130C2×#10596831—21no—
131C2×#10596831—21no—
132C2×#10596831—21no—
133C2×#10596831—21no—
134C2×#10596831—21no—
135C2×#10596831—21no—
136C2×#10596831—21no—
137C2×#10596831—21no—
138C2×#10596831—21no—
139C2×#10596831—44no—
140C2×#10596831#4112yes—
141C4⋊Dic73—21no—
142C4⋊Dic73—21no—
143C4⋊Dic73—21no—
144C4⋊Dic73—21no—
145C4⋊Dic73—21no—
146C4⋊Dic73—21no—
147C4⋊Dic73—21no—
148C4⋊Dic73—21no—
149C4⋊Dic73—42no—
150#11924007—42no—
151#11924007—42no—
152C22⋊Dic73—42no—
153C22⋊Dic73—42no—
154C22⋊Dic73—42no—
155C24×C73C2×D411yescharacteristic
156C24×C73C2×D411yescharacteristic
157C2×D4×C73—22no—
158C2×D4×C73—22no—
159C2×D4×C73—22no—
160C22×C4×C73—21no—
161C22×C4×C73—21no—
162C22×C4×C73—21no—
163C22×C4×C73—21no—
164C22×C4×C73—21no—
165C22×C4×C73—21no—
166C22×C4×C73—21no—
167C22×C4×C73—21no—
168C22×C4×C73—21no—
169C22×C4×C73—21no—
170C22×C4×C73—21no—
171C22×C4×C73—21no—
172C22×C4×C73—21no—
173C22×C4×C73—21no—
174C22×C4×C73—42no—
175C22×C4×C73—42no—
176C22×C4×C73—81no—
177C22×C4×C73C2×D411yescharacteristic
178C22×C4×C73C2×D411yescharacteristic
179C22×C4×C73C2×D411yescharacteristic
180C22×C4×C73C2×D411yescharacteristic
181C22×C4×C73#4112yes—
182C22×C4×C73#4112yes—
183C22×C4×C73C2411yescharacteristic
184C4⋊C4×C73—22no—
185C4⋊C4×C73—21no—
186C4⋊C4×C73—21no—
187C4⋊C4×C73—21no—
188C4⋊C4×C73—21no—
189C4⋊C4×C73—21no—
190C4⋊C4×C73—21no—
191C4⋊C4×C73—21no—
192C4⋊C4×C73—42no—
193C4⋊C4×C73#4112yes—
194C22⋊C4×C73—22no—
195C22⋊C4×C73—22no—
196C22⋊C4×C73—42no—
197C22⋊C4×C73—42no—
198C22⋊C4×C73—81no—
199C42×C73—21no—
200C42×C73—21no—
201C42×C73—42no—
202C42×C73—81no—
203C23×C73—21no—
204C23×C73—21no—
205C23×C73—21no—
206C23×C73—21no—
207C23×C73—21no—
208C23×C73—21no—
209C23×C73—21no—
210C23×C73—21no—
211C23×C73—21no—
212C23×C73—21no—
213C23×C73—21no—
214C23×C73#12312yes—
215C23×C73#13512yes—
216C23×C73AGL(1,ℤ/8)12yes—
217C23×C73C22×D411yescharacteristic
218D4×C73—44no—
219C2×C4×C73—21no—
220C2×C4×C73—21no—
221C2×C4×C73—22no—
222C2×C4×C73—22no—
223C2×C4×C73—22no—
224C2×C4×C73—22no—
225C2×C4×C73—21no—
226C2×C4×C73—21no—
227C2×C4×C73—21no—
228C2×C4×C73—21no—
229C2×C4×C73—22no—
230C2×C4×C73—21no—
231C2×C4×C73—21no—
232C2×C4×C73—21no—
233C2×C4×C73—21no—
234C2×C4×C73—21no—
235C2×C4×C73—41no—
236C2×C4×C73—41no—
237C2×C4×C73—41no—
238C2×C4×C73—41no—
239C2×C4×C73—41no—
240C2×C4×C73—41no—
241C2×C4×C73—41no—
242C2×C4×C73—41no—
243C2×C4×C73—41no—
244C2×C4×C73—41no—
245C2×C4×C73—41no—
246C2×C4×C73—41no—
247C2×C4×C73—41no—
248C2×C4×C73—41no—
249C2×C4×C73—41no—
250C2×C4×C73—84no—
251C2×C4×C73#12312yes—
252C2×C4×C73C2×#4111yescharacteristic
253C2×C4×C73C2×#4111yescharacteristic
254C2×C4×C73C2×#4111yescharacteristic
255C2×C4×C73C2×#4111yescharacteristic
256C2×C4×C73H(5,𝔽2)11yescharacteristic
257C2×C4×C732−1+411yescharacteristic
258C2×Dic73—41no—
259C2×Dic73—41no—
260C2×Dic73—41no—
261C2×Dic73—41no—
262C2×Dic73—41no—
263C2×Dic73—41no—
264C2×Dic73—41no—
265C2×Dic73—41no—
266C2×Dic73—41no—
267C2×Dic73—41no—
268C2×Dic73—41no—
269C2×Dic73—41no—
270C2×Dic73—84no—
271#10596831—22no—
272#10596831—41no—
273#10596831—41no—
274#10596831—41no—
275C22×C73—22no—
276C22×C73—22no—
277C22×C73—22no—
278C22×C73—22no—
279C22×C73—22no—
280C22×C73—22no—
281C22×C73—41no—
282C22×C73—41no—
283C22×C73—41no—
284C22×C73—41no—
285C22×C73—41no—
286C22×C73—41no—
287C22×C73—41no—
288C22×C73#48214yes—
289C22×C73C2×#12311yescharacteristic
290C22×C73#54611yescharacteristic
291C22×C73#54711yescharacteristic
292C22×C73C2×#13511yescharacteristic
293C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
294C22×C73#57711yescharacteristic
295C22×C73#57811yescharacteristic
296C4×C73—22no—
297C4×C73—41no—
298C4×C73—41no—
299C4×C73—41no—
300C4×C73—42no—
301C4×C73—81no—
302C4×C73—81no—
303C4×C73—81no—
304C4×C73#52911yescharacteristic
305C4×C73#53911yescharacteristic
306C4×C73#55111yescharacteristic
307C4×C73#55211yescharacteristic
308Dic73—81no—
309Dic73—81no—
310Dic73—81no—
311Dic73—81no—
312#24941—731nomaximal, Sylow
313C2×C73—24no—
314C2×C73—81no—
315C2×C73#241911yescharacteristic
316C2×C73C2×#48211yescharacteristic
317C2×C73#309711yescharacteristic
318C2×C73#329611yescharacteristic
319C2×C73#330811yescharacteristic
320C2×C73#333611yescharacteristic
321C2×C73#334511yescharacteristic
322#2486—731no—
323#2352D7311yescharacteristic
324#2101—731no—
325#2085—731no—
326#2077—731no—
327#2076—731no—
328#1921—731no—
329#1920—731no—
330#1869—731no—
331#1854—731no—
332#1853—731no—
333#1825—731no—
334#1823—731no—
335#1808—731no—
336C2×#340—731no—
337C73#2494111yescharacteristic, complemented, Sylow
338C23×C8—731no—
339C2×#123—1461no—
340C2×C4×D4C2×D7311yescharacteristic
341C2×#117C2×D7311yescharacteristic
342C22×C4⋊C4—731no—
343C22×C4⋊C4C2×D7311yescharacteristic
344C2×#107—731no—
345C2×#107—731no—
346C2×#106—731no—
347C2×#106—731no—
348C2×C22⋊C8—731no—
349C2×C22⋊C8—731no—
350C2×C22⋊C8—731no—
351#398—1461no—
352#397—1461no—
353#389—731no—
354#389—731no—
355#388—21no—
356#387—21no—
357#386—21no—
358#382C2×D7311yescharacteristic
359#381—1461no—
360#380—731no—
361#380—731no—
362#380—731no—
363#380C2×D7311yescharacteristic
364#380C2×D7311yescharacteristic
365C4×C4⋊C4C2×D7311yescharacteristic
366C4×C22⋊C4—21no—
367#340—731no—
368#340—731no—
369#340—731no—
370#340—731no—
371#340—731no—
372#340—731no—
373#340—731no—
374#340—731no—
375#340—731no—
376#340—731no—
377#340—731no—
378#340—731no—
379#336—731no—
380#336—731no—
381C22×D4C22⋊D7311yescharacteristic
382C23×C4—21no—
383C23×C4—1461no—
384C23×C4C22×D7311yescharacteristic
385C23×C4C22×D7311yescharacteristic
386C22×C8—2921no—
387C22×C8—731no—
388C22×C8—731no—
389C22×C8—731no—
390C22×C8—731no—
391C22×C8—1462no—
392C22×C8—1462no—
393#123—2924no—
394C4×D4—22no—
395C4×D4—22no—
396#117—22no—
397#117—41no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—41no—
401C2×C4⋊C4—731no—
402C2×C4⋊C4—731no—
403C2×C4⋊C4—731no—
404C2×C4⋊C4—731no—
405C2×C4⋊C4—1461no—
406C2×C4⋊C4—1461no—
407C2×C4⋊C4—1461no—
408C2×C4⋊C4—1462no—
409C2×C4⋊C4—1462no—
410C2×C4⋊C4C22⋊D7311yescharacteristic
411C2×C4⋊C4C22×D7311yescharacteristic
412C2×C4⋊C4C22×D7311yescharacteristic
413C2×C4⋊C4C22×D7311yescharacteristic
414C2×C4⋊C4C22×D7311yescharacteristic
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—1461no—
419C2×C22⋊C4—1461no—
420C2×C22⋊C4—1461no—
421C2×C22⋊C4C22⋊D7311yescharacteristic
422C2×C22⋊C4C22⋊D7311yescharacteristic
423C2×C42—21no—
424C2×C42—21no—
425C2×C42C22×D7311yescharacteristic
426#107—2921no—
427#107—1462no—
428#106—2921no—
429#106—1462no—
430C22⋊C8—2921no—
431C22⋊C8—1462no—
432C22⋊C8—1462no—
433#95—21no—
434#95—21no—
435#95—21no—
436#95—21no—
437#95—21no—
438#95—1461no—
439#95—1461no—
440#95—1461no—
441#95—1461no—
442#95—1461no—
443C24C2×C22⋊D7311yescharacteristic
444C24C2×C22⋊D7311yescharacteristic
445C2×D4—22no—
446C2×D4—22no—
447C2×D4—22no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—42no—
463C22×C4—42no—
464C22×C4—81no—
465C22×C4—2922no—
466C22×C4—2922no—
467C22×C4—2922no—
468C22×C4—1461no—
469C22×C4—1461no—
470C22×C4—1461no—
471C22×C4—1461no—
472C22×C4C2×C22⋊D7311yescharacteristic
473C22×C4C2×C22⋊D7311yescharacteristic
474C22×C4C2×C22⋊D7311yescharacteristic
475C22×C4C2×C22⋊D7311yescharacteristic
476C22×C4#1192402812yes—
477C22×C4#1192402812yes—
478C22×C4C23×D7311yescharacteristic
479C2×C8—2924no—
480C2×C8—732no—
481C2×C8—1461no—
482C2×C8—1461no—
483C2×C8—1461no—
484C2×C8—1461no—
485C2×C8—1461no—
486C2×C8—1461no—
487C2×C8—1461no—
488C2×C8—1461no—
489C2×C8—1461no—
490C2×C8—1461no—
491C2×C8—1461no—
492C4⋊C4—22no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—42no—
501C4⋊C4—2922no—
502C4⋊C4—2922no—
503C4⋊C4—2922no—
504C4⋊C4—1461no—
505C4⋊C4—1461no—
506C4⋊C4—1461no—
507C4⋊C4—1461no—
508C4⋊C4—1461no—
509C4⋊C4—1461no—
510C4⋊C4—1461no—
511C4⋊C4—1461no—
512C4⋊C4#1192402712yes—
513C22⋊C4—22no—
514C22⋊C4—22no—
515C22⋊C4—42no—
516C22⋊C4—42no—
517C22⋊C4—81no—
518C22⋊C4—2922no—
519C22⋊C4—2922no—
520C22⋊C4—2922no—
521C42—21no—
522C42—21no—
523C42—42no—
524C42—81no—
525C23—21no—
526C23—21no—
527C23—21no—
528C23—21no—
529C23—21no—
530C23—21no—
531C23—21no—
532C23—21no—
533C23—21no—
534C23—21no—
535C23—21no—
536C23#1455657412yes—
537C23#1455661112yes—
538C23#1455661612yes—
539C23C22×C22⋊D7311yescharacteristic
540D4—44no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—22no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—84no—
573C2×C4—2921no—
574C2×C4—2921no—
575C2×C4—2921no—
576C2×C4—2921no—
577C2×C4—2921no—
578C2×C4—2921no—
579C2×C4—2921no—
580C2×C4—2921no—
581C2×C4—2921no—
582C2×C4—2921no—
583C2×C4—2921no—
584C2×C4—2921no—
585C2×C4—5844no—
586C2×C4#1455657412yes—
587C2×C4#41×D7311yescharacteristic
588C2×C4C2×#1192402711yescharacteristic
589C2×C4C2×#1192402811yescharacteristic
590C2×C4C2×#1192402811yescharacteristic
591C2×C4#1455663611yescharacteristic
592C2×C4#1455663811yescharacteristic
593C8—2921no—
594C8—2921no—
595C8—2921no—
596C8—1462no—
597C22—22no—
598C22—22no—
599C22—22no—
600C22—22no—
601C22—22no—
602C22—22no—
603C22—41no—
604C22—41no—
605C22—41no—
606C22—41no—
607C22—41no—
608C22—41no—
609C22—41no—
610C22#1798891114yes—
611C22C2×#1455657411yescharacteristic
612C22#1798923111yescharacteristic
613C22#1798923611yescharacteristic
614C22C2×#1455661111yescharacteristic
615C22C2×#1455661611yescharacteristic
616C22#1798939811yescharacteristic
617C22#1798940211yescharacteristic
618C4—22no—
619C4—42no—
620C4—41no—
621C4—41no—
622C4—41no—
623C4—81no—
624C4—81no—
625C4—81no—
626C4—5841no—
627C4—5841no—
628C4—5841no—
629C4—5841no—
630C4#1798911711yescharacteristic
631C4#1798917911yescharacteristic
632C4#1798926611yescharacteristic
633C4#1798927711yescharacteristic
634C2—24no—
635C2—81no—
636C2#2261340211yescharacteristic
637C2C2×#1798891111yescharacteristic
638C2#2261990011yescharacteristic
639C2#2262176611yescharacteristic
640C2#2262192211yescharacteristic
641C2#2262229311yescharacteristic
642C2#2262239511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D73
commutator, cosocleC22×C4×C73C24
FrattiniC22×C4C23×D73
FittingC73×#2352C2
socleC23×C73C22×D4
prime radicalC22×D4×C73D4
hypercenter#2352D73
hypocenterC73#24941
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2352

Complements

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

NH ≅ G/Ntype
2. #22611498C2semidirect
3. #22611413C2semidirect
4. #22611367C2semidirect
5. #22611362C2semidirect
6. #22610523C2semidirect
7. #22610516C2semidirect
9. #22610130C2semidirect
10. #22610124C2semidirect
11. #22610026C2semidirect
12. #22610015C2semidirect
13. #22609958C2semidirect
14. C2×#17988349C2semidirect
337. C73#24941semidirect

Maximal subgroups

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

subgroupindex
#226142392
#226114982
#226114132
#226113672
#226113622
#226105232
#226105162
#226102242
#226101302
#226101242
#226100262
#226100152
#226099582
C2×#179883492
C73×#23522
#2494173