Finite Group Databasebeta

← #34026809

Subgroups — #34026809

Order 18688.

744 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22626033C211yesmaximal, characteristic, complemented
2#22626029C211yesmaximal, characteristic, complemented
3#22625991C211yesmaximal, characteristic, complemented
4#22625987C211yesmaximal, characteristic, complemented
5#22625986C211yesmaximal, characteristic, complemented
6#22625985C211yesmaximal, characteristic, complemented
7#22625790C211yesmaximal, characteristic
8#22625790C211yesmaximal, characteristic
9#22625788C211yesmaximal, characteristic
10#22625730C211yesmaximal, characteristic, complemented
11#22625723C211yesmaximal, characteristic, complemented
12#22625660C211yesmaximal, characteristic
13#22625660C211yesmaximal, characteristic
14C4×#14556648C211yesmaximal, characteristic
15#22612412C211yesmaximal, characteristic
16C2×#14556658C2211yescharacteristic
17C2×#14556658C2211yescharacteristic
18C2×#14556658C2211yescharacteristic
19C2×#14556658C2211yescharacteristic
20C2×C4⋊#10596833C2211yescharacteristic
21C2×C4⋊#10596833C2211yescharacteristic
22C2×#14556648C2211yescharacteristic
23C2×#14556648C2211yescharacteristic
24C2×#14556648C2211yescharacteristic
25C2×#14556648C2211yescharacteristic
26C2×#14556646C2211yescharacteristic
27C2×#14556646C2211yescharacteristic
28C2×C4×#10596833C2211yescharacteristic
29C2×C4×#10596833C2211yescharacteristic
30C2×C4×#10596833C2211yescharacteristic
31C2×C4×#10596833C2211yescharacteristic
32#17989453C2211yescharacteristic
33#17989453C2211yescharacteristic
34#17989453C2211yescharacteristic
35#17989453C2211yescharacteristic
36#17989453C2211yescharacteristic
37#17989453C2211yescharacteristic
38#17989453C2211yescharacteristic
39#17989453C2211yescharacteristic
40#17989453C2211yescharacteristic
41#17989453C2211yescharacteristic
42#17989453C2211yescharacteristic
43#17989453C2211yescharacteristic
44C2×#14556549C2211yescharacteristic
45C2×#14556549C2211yescharacteristic
46C2×C42×D73C2211yescharacteristic
47#17988486C411yescharacteristic
48#17988485C411yescharacteristic
49#17988483C411yescharacteristic
50#17988461C411yescharacteristic
51#17988461C411yescharacteristic
52#17988458C411yescharacteristic
53#17988458C411yescharacteristic
54C4⋊C4×Dic73C2211yescharacteristic
55C4⋊C4×Dic73C2211yescharacteristic
56#17988438C2211yescharacteristic
57#17988438C2211yescharacteristic
58#389×C73C411yescharacteristic
59C22×#10596833C2311yescharacteristic
60C22×#10596833C2311yescharacteristic
61C22×#10596833C2311yescharacteristic
62C22×#10596833C2311yescharacteristic
63C22×#10596833C2311yescharacteristic
64C22×#10596833C2311yescharacteristic
65C22×#10596833C2311yescharacteristic
66C22×#10596833C2311yescharacteristic
67#14556658—22no—
68#14556658—41no—
69#14556658—41no—
70#14556658—41no—
71C4⋊#10596833—22no—
72C4⋊#10596833—41no—
73#14556648—22no—
74#14556648—22no—
75#14556648—22no—
76#14556648Q814yes—
77#14556646—22no—
78#14556646—41no—
79C4×#10596833—22no—
80C4×#10596833—41no—
81C4×#10596833—41no—
82C4×#10596833—41no—
83C22×C4×D73C2×C411yescharacteristic
84C22×C4×D73C2×C411yescharacteristic
85C22×C4×D73C2311yescharacteristic
86#14556549—22no—
87#14556549—22no—
88#14556549—41no—
89#14556549—41no—
90C2×C4⋊Dic73C2×C411yescharacteristic
91C2×C4⋊Dic73C2×C411yescharacteristic
92C2×C4⋊Dic73C2×C411yescharacteristic
93C2×C4⋊Dic73C2×C411yescharacteristic
94C2×#11924007C2×C411yescharacteristic
95C2×#11924007C2×C411yescharacteristic
96C2×#11924007C2×C411yescharacteristic
97C2×#11924007C2×C411yescharacteristic
98C2×#11924005C2×C411yescharacteristic
99C2×#11924005C2×C411yescharacteristic
100C2×#11924005C2×C411yescharacteristic
101C2×#11924005C2×C411yescharacteristic
102C2×C4×Dic73C2×C411yescharacteristic
103C2×C4×Dic73C2311yescharacteristic
104C2×C4×Dic73C2311yescharacteristic
105C2×C4×Dic73C2311yescharacteristic
106C2×C4×Dic73C2311yescharacteristic
107C2×C4×Dic73C2311yescharacteristic
108C2×C4×Dic73C2311yescharacteristic
109C42×D73—41no—
110C42×D73—41no—
111#14556498C2×C411yescharacteristic
112#14556498C2×C411yescharacteristic
113#14556498C2×C411yescharacteristic
114#14556498C2×C411yescharacteristic
115#14556498C2×C411yescharacteristic
116#14556498C2×C411yescharacteristic
117C2×C4⋊C4×C73C2×C411yescharacteristic
118C2×C4⋊C4×C73C2×C411yescharacteristic
119C2×C4⋊C4×C73C2×C411yescharacteristic
120C2×C4⋊C4×C73C2×C411yescharacteristic
121C2×C42×C73C2×C411yescharacteristic
122#95×C73C2×C411yescharacteristic
123#95×C73C2×C411yescharacteristic
124C2×#10596833—21no—
125C2×#10596833—21no—
126C2×#10596833—21no—
127C2×#10596833—21no—
128C2×#10596833—21no—
129C2×#10596833—21no—
130C2×#10596833—21no—
131C2×#10596833—21no—
132C2×#10596833—21no—
133C2×#10596833—21no—
134C2×#10596833—21no—
135C2×#10596833—21no—
136C2×#10596833—21no—
137C2×#10596833—21no—
138C2×#10596833—21no—
139C2×#10596833—21no—
140C2×#10596833—21no—
141C2×#10596833—21no—
142C2×#10596833—21no—
143C2×#10596833—21no—
144C2×#10596833—21no—
145C2×#10596833—21no—
146C2×#10596833C2×Q812yes—
147C2×#10596833C2×Q812yes—
148C23×D73C22×C411yescharacteristic
149C22×Dic73C22×C411yescharacteristic
150C22×Dic73C22×C411yescharacteristic
151C22×Dic73C22×C411yescharacteristic
152C22×Dic73C22×C411yescharacteristic
153C22×Dic73C22×C411yescharacteristic
154C22×Dic73C22×C411yescharacteristic
155C22×Dic73C2411yescharacteristic
156C2×C4×D73—21no—
157C2×C4×D73—21no—
158C2×C4×D73—21no—
159C2×C4×D73—21no—
160C2×C4×D73—22no—
161C2×C4×D73—22no—
162C2×C4×D73—22no—
163C2×C4×D73—41no—
164C2×C4×D73—41no—
165C2×C4×D73—41no—
166C2×C4×D73C2×Q812yes—
167C2×C4×D73#4112yes—
168C4⋊Dic73—22no—
169C4⋊Dic73—22no—
170C4⋊Dic73—22no—
171C4⋊Dic73—41no—
172#11924007—22no—
173#11924007—22no—
174#11924007—22no—
175#11924007—22no—
176#11924005—22no—
177#11924005—22no—
178#11924005—41no—
179#11924005—41no—
180C4×Dic73—21no—
181C4×Dic73—21no—
182C4×Dic73—21no—
183C4×Dic73—21no—
184C4×Dic73—21no—
185C4×Dic73—21no—
186C4×Dic73—21no—
187C4×Dic73—21no—
188C4×Dic73—21no—
189C4×Dic73—21no—
190C4×Dic73—41no—
191C4×Dic73#4112yes—
192C4×Dic73#4112yes—
193C22×C4×C73C22×C411yescharacteristic
194C22×C4×C73C22×C411yescharacteristic
195C22×C4×C73C22×C411yescharacteristic
196C22×C4×C73C22×C411yescharacteristic
197C22×C4×C73C22×C411yescharacteristic
198C22×C4×C73C22×C411yescharacteristic
199C22×C4×C73C22×C411yescharacteristic
200C4⋊C4×C73—22no—
201C4⋊C4×C73—41no—
202C4⋊C4×C73—41no—
203C4⋊C4×C73—41no—
204C42×C73—41no—
205C23×C73C23×C411yescharacteristic
206C22×D73—21no—
207C22×D73—21no—
208C22×D73—21no—
209C22×D73—21no—
210C22×D73—21no—
211C22×D73—21no—
212C22×D73C4×Q812yes—
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—21no—
220C2×C4×C73—21no—
221C2×C4×C73—21no—
222C2×C4×C73—21no—
223C2×C4×C73—21no—
224C2×C4×C73—21no—
225C2×C4×C73—21no—
226C2×C4×C73—21no—
227C2×C4×C73—21no—
228C2×C4×C73—21no—
229C2×C4×C73—21no—
230C2×C4×C73—21no—
231C2×C4×C73#11712yes—
232C2×C4×C73C4×Q812yes—
233C2×C4×C73#13112yes—
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#11712yes—
250C2×Dic73#13112yes—
251C2×Dic73#13112yes—
252C2×Dic73C22×Q811yescharacteristic
253C2×Dic73C2×#4111yescharacteristic
254C2×Dic73C2×#4111yescharacteristic
255C2×Dic73C2×#4111yescharacteristic
256C2×Dic73H(5,𝔽2)11yescharacteristic
257C2×Dic73H(5,𝔽2)11yescharacteristic
258C4×D73—22no—
259C4×D73—22no—
260C4×D73—22no—
261C4×D73—22no—
262C4×D73—44no—
263C4×D73—44no—
264#10596833—22no—
265#10596833—22no—
266#10596833—41no—
267#10596833—41no—
268#10596833—41no—
269#10596833—41no—
270#10596833—41no—
271#10596833—41no—
272C22×C73C2×#11711yescharacteristic
273C22×C73C2×C4×Q811yescharacteristic
274C22×C73#51811yescharacteristic
275C22×C73C2×#13111yescharacteristic
276C22×C73C2×#13111yescharacteristic
277C22×C73C2×#13111yescharacteristic
278C22×C73#56811yescharacteristic
279C2×D73—22no—
280C2×D73—22no—
281C2×D73—22no—
282C2×D73—41no—
283C2×D73—41no—
284C2×D73—41no—
285C2×D73—41no—
286C4×C73—22no—
287C4×C73—22no—
288C4×C73—22no—
289C4×C73—41no—
290C4×C73—41no—
291C4×C73—41no—
292C4×C73—41no—
293Dic73—22no—
294Dic73—22no—
295Dic73—22no—
296Dic73—41no—
297Dic73—41no—
298Dic73—41no—
299Dic73#55311yescharacteristic
300Dic73#55311yescharacteristic
301Dic73#55411yescharacteristic
302Dic73#55411yescharacteristic
303#22630—731nomaximal, Sylow
304C2×C73#234511yescharacteristic
305C2×C73#292211yescharacteristic
306C2×C73#292511yescharacteristic
307C2×C73#296011yescharacteristic
308C2×C73#296211yescharacteristic
309C2×C73#297611yescharacteristic
310C2×C73#297711yescharacteristic
311D73—42no—
312#2296—731no—
313#1940—731no—
314#1939—731no—
315#1917—731no—
316#1916—731no—
317#1916—731no—
318#1916—731no—
319#1798—731no—
320#1798—731no—
321#1797—731no—
322#1771—731no—
323C8×C4⋊C4—731no—
324#1750—731no—
325#1750—731no—
326C4×C22⋊C8—731no—
327C73#2263011yescharacteristic, complemented, Sylow
328C2×#117—731no—
329C2×#117—731no—
330C22×C42—731no—
331C2×C4⋊C8—731no—
332C2×C4⋊C8—731no—
333C2×C4⋊C8—731no—
334C2×C4⋊C8—731no—
335C2×C4⋊C8—731no—
336C2×C4⋊C8—731no—
337C2×C22⋊C8—731no—
338C2×C22⋊C8—731no—
339C2×C22⋊C8—731no—
340C2×C22⋊C8—731no—
341C2×#97—731no—
342C2×#97—731no—
343C2×C4×C8—731no—
344C2×C4×C8—731no—
345C2×C4×C8—731no—
346C2×C4×C8—731no—
347#389—731no—
348#389—731no—
349#389—731no—
350#389#6440811yescharacteristic
351#385—731no—
352#385—731no—
353#385—731no—
354#385—731no—
355C4×C4⋊C4—731no—
356C4×C4⋊C4—731no—
357C4×C4⋊C4—731no—
358C4×C4⋊C4—731no—
359#336—731no—
360#336—731no—
361#336—731no—
362#336—731no—
363#336—731no—
364#336—731no—
365#336—731no—
366#336—731no—
367#336—731no—
368#336—731no—
369#336—731no—
370#336—731no—
371C23×C4—731no—
372C23×C4—731no—
373C23×C4—731no—
374C22×C8—731no—
375C22×C8—731no—
376C22×C8—731no—
377C22×C8—731no—
378C22×C8—731no—
379C22×C8—731no—
380C22×C8—731no—
381C22×C8—731no—
382#117—2921no—
383#117—2921no—
384#117—1462no—
385#117—1462no—
386C2×C4⋊C4—731no—
387C2×C4⋊C4—731no—
388C2×C4⋊C4—731no—
389C2×C4⋊C4—731no—
390C2×C4⋊C4—731no—
391C2×C4⋊C4—731no—
392C2×C4⋊C4—731no—
393C2×C4⋊C4—731no—
394C2×C4⋊C4C2×#6440811yescharacteristic
395C2×C4⋊C4C2×#6440811yescharacteristic
396C2×C4⋊C4C2×#6440811yescharacteristic
397C2×C4⋊C4C2×#6440811yescharacteristic
398C2×C22⋊C4—731no—
399C2×C22⋊C4—731no—
400C2×C22⋊C4—731no—
401C2×C22⋊C4—731no—
402C2×C42—2921no—
403C2×C42—2921no—
404C2×C42—731no—
405C2×C42—731no—
406C2×C42—731no—
407C2×C42—731no—
408C2×C42—731no—
409C2×C42—731no—
410C2×C42—731no—
411C2×C42C2×#6440811yescharacteristic
412C4⋊C8—2921no—
413C4⋊C8—2921no—
414C4⋊C8—2921no—
415C4⋊C8—2921no—
416C4⋊C8—1462no—
417C4⋊C8—1462no—
418C22⋊C8—734no—
419C22⋊C8—1462no—
420C22⋊C8—1462no—
421C22⋊C8—1462no—
422#97—2921no—
423#97—1462no—
424C4×C8—2921no—
425C4×C8—2921no—
426C4×C8—2921no—
427C4×C8—1462no—
428#95—731no—
429#95—731no—
430#95—731no—
431#95—731no—
432#95—731no—
433#95—731no—
434#95C2×#6440811yescharacteristic
435#95C2×#6440811yescharacteristic
436C24—731no—
437C22×C4—2921no—
438C22×C4—2921no—
439C22×C4—2921no—
440C22×C4—731no—
441C22×C4—731no—
442C22×C4—731no—
443C22×C4—731no—
444C22×C4—732no—
445C22×C4—732no—
446C22×C4—731no—
447C22×C4—731no—
448C22×C4—731no—
449C22×C4—1462no—
450C22×C4—1462no—
451C22×C4—1461no—
452C22×C4—1461no—
453C22×C4—1461no—
454C22×C4—1461no—
455C22×C4—1462no—
456C22×C4C22×#6440811yescharacteristic
457C22×C4C22×#6440811yescharacteristic
458C22×C4C22×#6440811yescharacteristic
459C22×C4C22×#6440811yescharacteristic
460C22×C4C22×#6440811yescharacteristic
461C22×C4C22×#6440811yescharacteristic
462C22×C4C22×#6440811yescharacteristic
463C2×C8—732no—
464C2×C8—732no—
465C2×C8—1461no—
466C2×C8—1461no—
467C2×C8—1461no—
468C2×C8—1461no—
469C2×C8—1461no—
470C2×C8—1461no—
471C2×C8—1461no—
472C2×C8—1461no—
473C2×C8—1461no—
474C2×C8—1461no—
475C2×C8—1461no—
476C2×C8—1461no—
477C2×C8—1461no—
478C2×C8—1461no—
479C2×C8—1461no—
480C2×C8—1461no—
481C2×C8—1461no—
482C2×C8—1461no—
483C2×C8—1461no—
484C2×C8—1461no—
485C2×C8—1461no—
486C2×C8—1461no—
487C4⋊C4—22no—
488C4⋊C4—41no—
489C4⋊C4—41no—
490C4⋊C4—41no—
491C4⋊C4—2921no—
492C4⋊C4—1462no—
493C4⋊C4—1462no—
494C4⋊C4—1462no—
495C4⋊C4—1462no—
496C4⋊C4—1462no—
497C4⋊C4—1462no—
498C4⋊C4—1462no—
499C22⋊C4—2921no—
500C22⋊C4—2921no—
501C22⋊C4—1462no—
502C22⋊C4—1462no—
503C42—41no—
504C42—2921no—
505C42—732no—
506C42—732no—
507C42—1461no—
508C42—1461no—
509C42—1461no—
510C42—1461no—
511C42—1461no—
512C42—1461no—
513C42—1461no—
514C42—1461no—
515C42—1461no—
516C42—1461no—
517C23—732no—
518C23—1461no—
519C23—1461no—
520C23—1461no—
521C23—1461no—
522C23—1461no—
523C23—1461no—
524C23C23×#6440811yescharacteristic
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—2924no—
544C2×C4—2924no—
545C2×C4—731no—
546C2×C4—731no—
547C2×C4—731no—
548C2×C4—731no—
549C2×C4—731no—
550C2×C4—731no—
551C2×C4—732no—
552C2×C4—732no—
553C2×C4—732no—
554C2×C4—1462no—
555C2×C4—1462no—
556C2×C4—1462no—
557C2×C4—1462no—
558C2×C4—1461no—
559C2×C4—1461no—
560C2×C4—1461no—
561C2×C4—1461no—
562C2×C4—1461no—
563C2×C4—1461no—
564C2×C4—1461no—
565C2×C4—1461no—
566C2×C4—1461no—
567C2×C4—1461no—
568C2×C4—1461no—
569C2×C4—1461no—
570C2×C4—1461no—
571C2×C4—1461no—
572C2×C4—1461no—
573C2×C4#1455667012yes—
574C2×C4Q8×#6440812yes—
575C2×C4#1455667912yes—
576C8—2921no—
577C8—2921no—
578C8—2921no—
579C8—2921no—
580C8—2921no—
581C8—2921no—
582C8—1462no—
583C8—1462no—
584C22—2921no—
585C22—2921no—
586C22—2921no—
587C22—2921no—
588C22—1462no—
589C22—1462no—
590C22—1462no—
591C22C2×#1455667011yescharacteristic
592C22C2×Q8×#6440811yescharacteristic
593C22#1798965411yescharacteristic
594C22D73⋊#13111yescharacteristic
595C22D73⋊#13111yescharacteristic
596C22C2×#1455667911yescharacteristic
597C22#1798966511yescharacteristic
598C4—22no—
599C4—22no—
600C4—22no—
601C4—41no—
602C4—41no—
603C4—41no—
604C4—41no—
605C4—2921no—
606C4—2921no—
607C4—2921no—
608C4—731no—
609C4—731no—
610C4—731no—
611C4—731no—
612C4—1462no—
613C4—1462no—
614C4—1462no—
615C2—2922no—
616C2#2262644011yescharacteristic
617C2#2262661611yescharacteristic
618C2#2262662911yescharacteristic
619C2#2262672111yescharacteristic
620C2#2262672711yescharacteristic
621C2#2262680011yescharacteristic
622C2#2262680611yescharacteristic
subgroupG/H
center, FrattiniC23C23×#64408
commutator, socleC23×C73C23×C4
Fitting#389×C73C4
prime radicalC23×D73C22×C4
cosocleC22×Dic73C24
hypercenter#389#64408
hypocenterC73#22630
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
1. #22626033C2semidirect
2. #22626029C2semidirect
3. #22625991C2semidirect
4. #22625987C2semidirect
5. #22625986C2semidirect
6. #22625985C2semidirect
10. #22625730C2semidirect
11. #22625723C2semidirect
327. C73#22630semidirect

Maximal subgroups

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

subgroupindex
#226260332
#226260292
#226259912
#226259872
#226259862
#226259852
#226257902
#226257882
#226257302
#226257232
#226256602
C4×#145566482
#226124122
#2263073