Finite Group Databasebeta

← #33112438

Subgroups — #33112438

Order 18688.

622 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22613205C211yesmaximal, characteristic
2#22610869C211yesmaximal, characteristic, complemented
3#22610866C211yesmaximal, characteristic, complemented
4#22610654C211yesmaximal, characteristic, complemented
5#22610651C211yesmaximal, characteristic, complemented
6#22610541C211yesmaximal, characteristic
7#22610541C211yesmaximal, characteristic
8#22610539C211yesmaximal, characteristic
9#22610498C211yesmaximal, characteristic, complemented
10#22610495C211yesmaximal, characteristic, complemented
11#22610494C211yesmaximal, characteristic, complemented
12#22610486C211yesmaximal, characteristic, complemented
13#22610000C211yesmaximal, characteristic
14#22609913C211yesmaximal, characteristic
15C73×#1924C211yesmaximal, characteristic
16C2×C4×Dic146C2211yescharacteristic
17C2×#14556550C2211yescharacteristic
18C2×C4⋊#10596831C2211yescharacteristic
19C2×#14556520C2211yescharacteristic
20C2×#14556520C2211yescharacteristic
21C2×#14556520C2211yescharacteristic
22C2×#14556520C2211yescharacteristic
23C2×C22⋊#10596831C2211yescharacteristic
24C2×C22⋊#10596831C2211yescharacteristic
25C2×#14556501C2211yescharacteristic
26C2×#14556501C2211yescharacteristic
27C2×C4×#10596831C2211yescharacteristic
28#17988529C411yescharacteristic
29#17988523C411yescharacteristic
30#17988521C411yescharacteristic
31#17988519C411yescharacteristic
32#17988510C411yescharacteristic
33#17988510C411yescharacteristic
34#17988508C411yescharacteristic
35#17988499C411yescharacteristic
36C4×#11924007C2211yescharacteristic
37C4×#11924007C2211yescharacteristic
38C4×C4⋊Dic73C2211yescharacteristic
39C4×C22⋊Dic73C2211yescharacteristic
40#17988342C2211yescharacteristic
41#17988342C2211yescharacteristic
42#17988341C2211yescharacteristic
43#17988341C2211yescharacteristic
44#17988341C2211yescharacteristic
45#17988341C2211yescharacteristic
46#17988341C2211yescharacteristic
47#17988341C2211yescharacteristic
48#17988341C2211yescharacteristic
49#17988341C2211yescharacteristic
50#17988341C2211yescharacteristic
51#17988341C2211yescharacteristic
52C2×C4⋊C8×C73C2211yescharacteristic
53C2×C22⋊C8×C73C2211yescharacteristic
54C2×C22⋊C8×C73C2211yescharacteristic
55C2×#97×C73C2211yescharacteristic
56C4×C22⋊C4×C73C2211yescharacteristic
57#336×C73C2211yescharacteristic
58#336×C73C2211yescharacteristic
59C22×Dic146C2×C411yescharacteristic
60C22×#10596831C2311yescharacteristic
61C22×#10596831C2311yescharacteristic
62C22×#10596831C2311yescharacteristic
63C22×#10596831C2311yescharacteristic
64C4×Dic146—41no—
65C4×Dic146—41no—
66#14556550—41no—
67#14556550—41no—
68C2×C4⋊Dic73C2×C411yescharacteristic
69C2×C4⋊Dic73C2×C411yescharacteristic
70C2×C4⋊Dic73C2×C411yescharacteristic
71C2×C4⋊Dic73C2×C411yescharacteristic
72C2×C4⋊Dic73C2×C411yescharacteristic
73C2×#11924007C2×C411yescharacteristic
74C2×#11924007C2×C411yescharacteristic
75C2×#11924007C2×C411yescharacteristic
76C2×#11924007C2×C411yescharacteristic
77C2×#11924007C2×C411yescharacteristic
78C2×#11924007C2×C411yescharacteristic
79C2×C22⋊Dic73C2×C411yescharacteristic
80C2×C22⋊Dic73C2×C411yescharacteristic
81C2×C22⋊Dic73C2×C411yescharacteristic
82C2×C22⋊Dic73C2×C411yescharacteristic
83C2×C4×Dic73C2311yescharacteristic
84C2×C4×Dic73C2311yescharacteristic
85C2×C4×Dic73C2311yescharacteristic
86C2×C4×Dic73C2311yescharacteristic
87C4⋊#10596831—41no—
88#14556520—41no—
89#14556520—41no—
90#14556520—41no—
91#14556520—41no—
92C22⋊#10596831—41no—
93C22⋊#10596831—41no—
94#14556501—41no—
95#14556501—41no—
96C4×#10596831—41no—
97#14556498C2×C411yescharacteristic
98#14556498C2×C411yescharacteristic
99#14556498C2×C411yescharacteristic
100#14556498C2×C411yescharacteristic
101#14556498C2×C411yescharacteristic
102#14556498C2×C411yescharacteristic
103#14556498C2×C411yescharacteristic
104#14556498C2×C411yescharacteristic
105C23×C4×C73C2311yescharacteristic
106C22×C8×C73C2311yescharacteristic
107C22×C8×C73C2311yescharacteristic
108C22×C8×C73C2311yescharacteristic
109C22×C8×C73C2311yescharacteristic
110C2×C22⋊C4×C73C2×C411yescharacteristic
111C2×C22⋊C4×C73C2×C411yescharacteristic
112C2×C42×C73C2311yescharacteristic
113C2×C42×C73C2311yescharacteristic
114C4⋊C8×C73—41no—
115C22⋊C8×C73—41no—
116C22⋊C8×C73—41no—
117#97×C73—41no—
118#95×C73C2×C411yescharacteristic
119#95×C73C2×C411yescharacteristic
120C2×Dic146—22no—
121C2×Dic146—41no—
122C2×Dic146—41no—
123C22×Dic73C22×C411yescharacteristic
124C22×Dic73C22×C411yescharacteristic
125C22×Dic73C22×C411yescharacteristic
126C22×Dic73C22×C411yescharacteristic
127C22×Dic73C22×C411yescharacteristic
128C22×Dic73C22×C411yescharacteristic
129C22×Dic73C22×C411yescharacteristic
130C22×Dic73C22×C411yescharacteristic
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—21no—
140C2×#10596831—21no—
141C2×#10596831—21no—
142C2×#10596831—21no—
143C4⋊Dic73—41no—
144C4⋊Dic73—41no—
145C4⋊Dic73—41no—
146C4⋊Dic73—41no—
147C4⋊Dic73—41no—
148#11924007—22no—
149#11924007—41no—
150#11924007—41no—
151#11924007—41no—
152#11924007—41no—
153#11924007—41no—
154C22⋊Dic73—41no—
155C22⋊Dic73—41no—
156C22⋊Dic73—41no—
157C22⋊Dic73—41no—
158C4×Dic73—21no—
159C4×Dic73—21no—
160C4×Dic73—21no—
161C4×Dic73—21no—
162C4×Dic73—21no—
163C4×Dic73—21no—
164C4×Dic73—21no—
165C4×Dic73—21no—
166C24×C73C22×C411yescharacteristic
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×C73C22×C411yescharacteristic
174C22×C4×C73C22×C411yescharacteristic
175C22×C4×C73C22×C411yescharacteristic
176C22×C4×C73C22×C411yescharacteristic
177C22×C4×C73C22×C411yescharacteristic
178C22×C4×C73C2411yescharacteristic
179C2×C8×C73—21no—
180C2×C8×C73—21no—
181C2×C8×C73—21no—
182C2×C8×C73—21no—
183C2×C8×C73—21no—
184C2×C8×C73—21no—
185C2×C8×C73—21no—
186C2×C8×C73—21no—
187C2×C8×C73—21no—
188C2×C8×C73—21no—
189C2×C8×C73—21no—
190C2×C8×C73—21no—
191C22⋊C4×C73—22no—
192C22⋊C4×C73—41no—
193C42×C73—21no—
194C42×C73—21no—
195C42×C73—21no—
196C42×C73—21no—
197C23×C73—21no—
198C23×C73—21no—
199C23×C73—21no—
200C23×C73—21no—
201C23×C73—21no—
202C23×C73—21no—
203C23×C73—21no—
204C23×C73C23×C411yescharacteristic
205C2×C4×C73—21no—
206C2×C4×C73—21no—
207C2×C4×C73—21no—
208C2×C4×C73—21no—
209C2×C4×C73—21no—
210C2×C4×C73—21no—
211C2×C4×C73—21no—
212C2×C4×C73—21no—
213C2×C4×C73—21no—
214C2×C4×C73—21no—
215C2×C4×C73—21no—
216C2×C4×C73—21no—
217C2×C4×C73—21no—
218C2×C4×C73—21no—
219C2×C4×C73—41no—
220C2×C4×C73—41no—
221C2×C4×C73—41no—
222C2×C4×C73—41no—
223C2×C4×C73#13112yes—
224C2×C4×C73H(5,𝔽2)11yescharacteristic
225C2×C4×C73H(5,𝔽2)11yescharacteristic
226C2×C4×C73H(5,𝔽2)11yescharacteristic
227C2×C4×C732−1+411yescharacteristic
228C2×C4×C732−1+411yescharacteristic
229C2×C4×C732−1+411yescharacteristic
230C2×Dic73—21no—
231C2×Dic73—21no—
232C2×Dic73—21no—
233C2×Dic73—21no—
234C2×Dic73—21no—
235C2×Dic73—21no—
236C2×Dic73—21no—
237C2×Dic73—21no—
238C2×Dic73—21no—
239C2×Dic73—21no—
240C2×Dic73—21no—
241C2×Dic73—21no—
242C2×Dic73—21no—
243C2×Dic73—21no—
244C2×Dic73—21no—
245C2×Dic73—21no—
246C2×Dic73—21no—
247C2×Dic73—21no—
248C2×Dic73—21no—
249C2×Dic73—21no—
250C2×Dic73—21no—
251C2×Dic73—21no—
252C2×Dic73—21no—
253C2×Dic73—21no—
254Dic146—44no—
255C8×C73—41no—
256C8×C73—41no—
257C8×C73—41no—
258C8×C73—41no—
259#10596831—41no—
260#10596831—41no—
261#10596831—41no—
262#10596831—41no—
263C22×C73—41no—
264C22×C73—41no—
265C22×C73—41no—
266C22×C73—41no—
267C22×C73—41no—
268C22×C73—41no—
269C22×C73—41no—
270C22×C73#51811yescharacteristic
271C22×C73#51911yescharacteristic
272C22×C73#52011yescharacteristic
273C22×C73C2×#13111yescharacteristic
274C22×C73#56811yescharacteristic
275C22×C73#56811yescharacteristic
276C22×C73#56811yescharacteristic
277C4×C73—22no—
278C4×C73—41no—
279C4×C73—41no—
280C4×C73—41no—
281C4×C73—41no—
282C4×C73#56211yescharacteristic
283C4×C73#56211yescharacteristic
284C4×C73#56311yescharacteristic
285C4×C73#56311yescharacteristic
286Dic73—41no—
287Dic73—41no—
288Dic73—41no—
289Dic73—41no—
290Dic73—41no—
291Dic73—41no—
292Dic73—41no—
293Dic73—41no—
294#23345—731nomaximal, Sylow
295C2×C73—81no—
296C2×C73#237811yescharacteristic
297C2×C73#297611yescharacteristic
298C2×C73#298011yescharacteristic
299C2×C73#298511yescharacteristic
300C2×C73#298711yescharacteristic
301C2×C73#299311yescharacteristic
302C2×C73#299511yescharacteristic
303#2396—731no—
304#1985—731no—
305#1984—731no—
306#1940—731no—
307#1940—731no—
308#1924—731no—
309#1924—731no—
310#1924D7311yescharacteristic
311#1923—731no—
312#1917—731no—
313#1917—731no—
314#1917—731no—
315#1916—731no—
316#1818—731no—
317#1798—731no—
318C73#2334511yescharacteristic, complemented, Sylow
319C2×C4×Q8—731no—
320C2×#117—731no—
321C2×C4⋊C8—731no—
322C2×C4⋊C8—731no—
323C2×C4⋊C8—731no—
324C2×C4⋊C8—731no—
325C2×C4⋊C8—731no—
326C2×C4⋊C8C2×D7311yescharacteristic
327C2×C22⋊C8—731no—
328C2×C22⋊C8—731no—
329C2×C22⋊C8C2×D7311yescharacteristic
330C2×C22⋊C8C2×D7311yescharacteristic
331C2×#97—731no—
332C2×#97—731no—
333C2×#97C2×D7311yescharacteristic
334C2×C4×C8—731no—
335#400—731no—
336#399—731no—
337#398—731no—
338#398—731no—
339#396—731no—
340#396—731no—
341#395—731no—
342#393—731no—
343C4×C4⋊C4—731no—
344C4×C4⋊C4—731no—
345C4×C4⋊C4—731no—
346C4×C22⋊C4—731no—
347C4×C22⋊C4C2×D7311yescharacteristic
348#336—731no—
349#336—731no—
350#336—731no—
351#336—731no—
352#336—731no—
353#336—731no—
354#336—731no—
355#336—731no—
356#336—731no—
357#336—731no—
358#336—731no—
359#336—731no—
360#336C2×D7311yescharacteristic
361#336C2×D7311yescharacteristic
362C22×Q8—731no—
363C23×C4C22×D7311yescharacteristic
364C22×C8—731no—
365C22×C8—731no—
366C22×C8—731no—
367C22×C8—731no—
368C22×C8C22×D7311yescharacteristic
369C22×C8C22×D7311yescharacteristic
370C22×C8C22×D7311yescharacteristic
371C22×C8C22×D7311yescharacteristic
372C4×Q8—2921no—
373C4×Q8—2921no—
374#117—2921no—
375#117—2921no—
376C2×C4⋊C4—731no—
377C2×C4⋊C4—731no—
378C2×C4⋊C4—731no—
379C2×C4⋊C4—731no—
380C2×C4⋊C4—731no—
381C2×C4⋊C4—731no—
382C2×C4⋊C4—731no—
383C2×C4⋊C4—731no—
384C2×C4⋊C4—731no—
385C2×C4⋊C4—731no—
386C2×C4⋊C4—731no—
387C2×C22⋊C4—731no—
388C2×C22⋊C4—731no—
389C2×C22⋊C4—731no—
390C2×C22⋊C4—731no—
391C2×C22⋊C4C4×D7311yescharacteristic
392C2×C22⋊C4C4×D7311yescharacteristic
393C2×C42—731no—
394C2×C42—731no—
395C2×C42—731no—
396C2×C42—731no—
397C2×C42C22×D7311yescharacteristic
398C2×C42C22×D7311yescharacteristic
399C4⋊C8—41no—
400C4⋊C8—2921no—
401C4⋊C8—2921no—
402C4⋊C8—2921no—
403C4⋊C8—2921no—
404C4⋊C8—2921no—
405C22⋊C8—41no—
406C22⋊C8—41no—
407C22⋊C8—2921no—
408C22⋊C8—2921no—
409#97—41no—
410#97—2921no—
411#97—2921no—
412C4×C8—2921no—
413#95—731no—
414#95—731no—
415#95—731no—
416#95—731no—
417#95—731no—
418#95—731no—
419#95—731no—
420#95—731no—
421#95C4×D7311yescharacteristic
422#95C4×D7311yescharacteristic
423C24C2×C4×D7311yescharacteristic
424C2×Q8—2921no—
425C2×Q8—2921no—
426C2×Q8—1462no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—731no—
434C22×C4—731no—
435C22×C4—731no—
436C22×C4—731no—
437C22×C4—731no—
438C22×C4—731no—
439C22×C4—731no—
440C22×C4—731no—
441C22×C4C2×C4×D7311yescharacteristic
442C22×C4C2×C4×D7311yescharacteristic
443C22×C4C2×C4×D7311yescharacteristic
444C22×C4C2×C4×D7311yescharacteristic
445C22×C4C2×C4×D7311yescharacteristic
446C22×C4C23×D7311yescharacteristic
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—1461no—
460C2×C8—1461no—
461C2×C8—1461no—
462C2×C8—1461no—
463C2×C8—1461no—
464C2×C8—1461no—
465C2×C8—1461no—
466C2×C8—1461no—
467C2×C8—1461no—
468C2×C8—1461no—
469C2×C8—1461no—
470C2×C8—1461no—
471C4⋊C4—2921no—
472C4⋊C4—2921no—
473C4⋊C4—2921no—
474C4⋊C4—2921no—
475C4⋊C4—2921no—
476C4⋊C4—2921no—
477C4⋊C4—2921no—
478C4⋊C4—2921no—
479C4⋊C4—2921no—
480C4⋊C4—2921no—
481C4⋊C4—1462no—
482C22⋊C4—22no—
483C22⋊C4—41no—
484C22⋊C4—2921no—
485C22⋊C4—2921no—
486C22⋊C4—2921no—
487C22⋊C4—2921no—
488C42—21no—
489C42—21no—
490C42—21no—
491C42—21no—
492C42—1461no—
493C42—1461no—
494C42—1461no—
495C42—1461no—
496C42—1461no—
497C42—1461no—
498C42—1461no—
499C42—1461no—
500C23—21no—
501C23—21no—
502C23—21no—
503C23—21no—
504C23—21no—
505C23—21no—
506C23—21no—
507C23C22×C4×D7311yescharacteristic
508Q8—2924no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—1461no—
528C2×C4—1461no—
529C2×C4—1461no—
530C2×C4—1461no—
531C2×C4—1461no—
532C2×C4—1461no—
533C2×C4—1461no—
534C2×C4—1461no—
535C2×C4—1461no—
536C2×C4—1461no—
537C2×C4—1461no—
538C2×C4—1461no—
539C2×C4—1461no—
540C2×C4—1461no—
541C2×C4—1461no—
542C2×C4—1461no—
543C2×C4—1461no—
544C2×C4—1461no—
545C2×C4—1461no—
546C2×C4—1461no—
547C2×C4—1461no—
548C2×C4—1461no—
549C2×C4—1461no—
550C2×C4—1461no—
551C2×C4#1455659912yes—
552C2×C4#1455663611yescharacteristic
553C2×C4#1455663611yescharacteristic
554C2×C4#1455663711yescharacteristic
555C2×C4#1455663811yescharacteristic
556C2×C4#1455663811yescharacteristic
557C2×C4#1455663811yescharacteristic
558C8—41no—
559C8—41no—
560C8—41no—
561C8—41no—
562C8—2921no—
563C8—2921no—
564C8—2921no—
565C8—2921no—
566C22—41no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22#1798905911yescharacteristic
574C22#1798906411yescharacteristic
575C22#1798906611yescharacteristic
576C22C2×#1455659911yescharacteristic
577C22#1798935211yescharacteristic
578C22#1798935211yescharacteristic
579C22#1798935311yescharacteristic
580C4—22no—
581C4—41no—
582C4—41no—
583C4—41no—
584C4—41no—
585C4—2921no—
586C4—2921no—
587C4—2921no—
588C4—2921no—
589C4—2921no—
590C4—2921no—
591C4—2921no—
592C4—2921no—
593C4#1798933211yescharacteristic
594C4#1798933411yescharacteristic
595C4#1798933711yescharacteristic
596C4#1798933911yescharacteristic
597C2—81no—
598C2#2261309111yescharacteristic
599C2#2261898011yescharacteristic
600C2#2261899911yescharacteristic
601C2#2261902811yescharacteristic
602C2#2261903511yescharacteristic
603C2#2261907511yescharacteristic
604C2#2261910211yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D73
commutator, socleC23×C73C23×C4
FittingC73×#1924C2
prime radicalC24×C73C22×C4
cosocleC22×C4×C73C24
hypercenter#1924D73
hypocenterC73#23345
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ #1924

Complements

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

NH ≅ G/Ntype
2. #22610869C2semidirect
3. #22610866C2semidirect
4. #22610654C2semidirect
5. #22610651C2semidirect
9. #22610498C2semidirect
10. #22610495C2semidirect
11. #22610494C2semidirect
12. #22610486C2semidirect
318. C73#23345semidirect

Maximal subgroups

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

subgroupindex
#226132052
#226108692
#226108662
#226106542
#226106512
#226105412
#226105392
#226104982
#226104952
#226104942
#226104862
#226100002
#226099132
C73×#19242
#2334573