Finite Group Databasebeta

← #33096183

Subgroups — #33096183

Order 18688.

670 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22612329C211yesmaximal, characteristic
2#22610547C211yesmaximal, characteristic
3#22610541C211yesmaximal, characteristic
4#22610540C211yesmaximal, characteristic
5#22610534C211yesmaximal, characteristic
6#22610496C211yesmaximal, characteristic, complemented
7#22610494C211yesmaximal, characteristic, complemented
8#22610489C211yesmaximal, characteristic, complemented
9#22610487C211yesmaximal, characteristic, complemented
10#22610084C211yesmaximal, characteristic, complemented
11#22610050C211yesmaximal, characteristic, complemented
12#22609911C211yesmaximal, characteristic
13#22609790C211yesmaximal, characteristic, complemented
14#22609790C211yesmaximal, characteristic, complemented
15C73×#1797C211yesmaximal, characteristic
16C2×C4⋊#10596831C2211yescharacteristic
17C2×C4⋊#10596831C2211yescharacteristic
18C2×#14556520C2211yescharacteristic
19C2×#14556520C2211yescharacteristic
20C2×#14556520C2211yescharacteristic
21C2×#14556520C2211yescharacteristic
22C2×C22⋊#10596831C2211yescharacteristic
23C2×C22⋊#10596831C2211yescharacteristic
24C2×#14556501C2211yescharacteristic
25C2×#14556501C2211yescharacteristic
26C2×C8×Dic73C2211yescharacteristic
27C2×C8×Dic73C2211yescharacteristic
28#17988455C411yescharacteristic
29#17988455C411yescharacteristic
30#17988453C411yescharacteristic
31#17988453C411yescharacteristic
32#17988450C411yescharacteristic
33#17988450C411yescharacteristic
34#17988447C411yescharacteristic
35#17988447C411yescharacteristic
36C4×C4⋊Dic73C2211yescharacteristic
37C4×C4⋊Dic73C2211yescharacteristic
38C4×C22⋊Dic73C2211yescharacteristic
39C4×C22⋊Dic73C2211yescharacteristic
40#17988433C2211yescharacteristic
41#17988433C2211yescharacteristic
42#17988342C2211yescharacteristic
43#17988342C2211yescharacteristic
44#17988341C2211yescharacteristic
45#17988341C2211yescharacteristic
46#17988341C2211yescharacteristic
47#17988341C2211yescharacteristic
48#17988341C2211yescharacteristic
49#17988341C2211yescharacteristic
50#17988341C2211yescharacteristic
51#17988341C2211yescharacteristic
52C22×C42×C73C2211yescharacteristic
53C2×C4⋊C8×C73C2211yescharacteristic
54C2×C4⋊C8×C73C2211yescharacteristic
55C2×C22⋊C8×C73C2211yescharacteristic
56C2×C22⋊C8×C73C2211yescharacteristic
57#336×C73C2211yescharacteristic
58#336×C73C2211yescharacteristic
59C22×#10596831C2311yescharacteristic
60C22×#10596831C2311yescharacteristic
61C22×#10596831C2311yescharacteristic
62C22×#10596831C2311yescharacteristic
63C2×C4⋊Dic73C2×C411yescharacteristic
64C2×C4⋊Dic73C2×C411yescharacteristic
65C2×C4⋊Dic73C2×C411yescharacteristic
66C2×C4⋊Dic73C2×C411yescharacteristic
67C2×C22⋊Dic73C2×C411yescharacteristic
68C2×C22⋊Dic73C2×C411yescharacteristic
69C2×C22⋊Dic73C2×C411yescharacteristic
70C2×C22⋊Dic73C2×C411yescharacteristic
71C2×C4×Dic73C2311yescharacteristic
72C2×C4×Dic73C2311yescharacteristic
73C2×C4×Dic73C2311yescharacteristic
74C2×C4×Dic73C2311yescharacteristic
75C4⋊#10596831—22no—
76C4⋊#10596831—22no—
77#14556520—41no—
78#14556520—41no—
79#14556520—41no—
80#14556520—41no—
81C22⋊#10596831—41no—
82C22⋊#10596831—41no—
83#14556501—41no—
84#14556501—41no—
85C8×Dic73—41no—
86C8×Dic73—41no—
87#14556498C2×C411yescharacteristic
88#14556498C2×C411yescharacteristic
89#14556498C2×C411yescharacteristic
90#14556498C2×C411yescharacteristic
91#14556498C2×C411yescharacteristic
92#14556498C2×C411yescharacteristic
93#14556498C2×C411yescharacteristic
94#14556498C2×C411yescharacteristic
95#14556498C2×C411yescharacteristic
96#14556498C2×C411yescharacteristic
97#14556498C2×C411yescharacteristic
98#14556498C2×C411yescharacteristic
99#14556498C2×C411yescharacteristic
100#14556498C2×C411yescharacteristic
101#14556498C2×C411yescharacteristic
102#14556498C2×C411yescharacteristic
103C23×C4×C73C2×C411yescharacteristic
104C23×C4×C73C2×C411yescharacteristic
105C23×C4×C73C2311yescharacteristic
106C22×C8×C73C2311yescharacteristic
107C22×C8×C73C2311yescharacteristic
108C22×C8×C73C2311yescharacteristic
109C22×C8×C73C2311yescharacteristic
110C2×C42×C73—22no—
111C2×C42×C73—22no—
112C2×C42×C73C2×C411yescharacteristic
113C2×C42×C73C2×C411yescharacteristic
114C2×C42×C73C2311yescharacteristic
115C2×C42×C73C2311yescharacteristic
116C4⋊C8×C73—22no—
117C4⋊C8×C73—22no—
118C22⋊C8×C73—41no—
119C22⋊C8×C73—41no—
120C22×Dic73C22×C411yescharacteristic
121C22×Dic73C22×C411yescharacteristic
122C22×Dic73C22×C411yescharacteristic
123C22×Dic73C22×C411yescharacteristic
124C22×Dic73C22×C411yescharacteristic
125C22×Dic73C22×C411yescharacteristic
126C22×Dic73C22×C411yescharacteristic
127C22×Dic73C22×C411yescharacteristic
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—21no—
140C4⋊Dic73—22no—
141C4⋊Dic73—22no—
142C4⋊Dic73—41no—
143C4⋊Dic73—41no—
144C22⋊Dic73—22no—
145C22⋊Dic73—22no—
146C22⋊Dic73—41no—
147C22⋊Dic73—41no—
148C4×Dic73—21no—
149C4×Dic73—21no—
150C4×Dic73—21no—
151C4×Dic73—21no—
152C4×Dic73—21no—
153C4×Dic73—21no—
154C4×Dic73—21no—
155C4×Dic73—21no—
156C24×C73C22×C411yescharacteristic
157C22×C4×C73—22no—
158C22×C4×C73—22no—
159C22×C4×C73—22no—
160C22×C4×C73—22no—
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—41no—
168C22×C4×C73—41no—
169C22×C4×C73C22×C411yescharacteristic
170C22×C4×C73C22×C411yescharacteristic
171C22×C4×C73C22×C411yescharacteristic
172C22×C4×C73C22×C411yescharacteristic
173C22×C4×C73C22×C411yescharacteristic
174C22×C4×C73C2411yescharacteristic
175C2×C8×C73—21no—
176C2×C8×C73—21no—
177C2×C8×C73—21no—
178C2×C8×C73—21no—
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—
187C42×C73—22no—
188C42×C73—22no—
189C42×C73—21no—
190C42×C73—21no—
191C42×C73#4112yes—
192C42×C73#4112yes—
193C23×C73—21no—
194C23×C73—21no—
195C23×C73—21no—
196C23×C73—21no—
197C23×C73—21no—
198C23×C73—21no—
199C23×C73#13112yes—
200C23×C73C23×C411yescharacteristic
201C2×C4×C73—21no—
202C2×C4×C73—21no—
203C2×C4×C73—21no—
204C2×C4×C73—21no—
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—44no—
214C2×C4×C73—44no—
215C2×C4×C73—41no—
216C2×C4×C73—41no—
217C2×C4×C73—41no—
218C2×C4×C73—41no—
219C2×C4×C73#11712yes—
220C2×C4×C73#11712yes—
221C2×C4×C73#13112yes—
222C2×C4×C73C2×#4111yescharacteristic
223C2×C4×C73C2×#4111yescharacteristic
224C2×C4×C73H(5,𝔽2)11yescharacteristic
225C2×C4×C73H(5,𝔽2)11yescharacteristic
226C2×C4×C732−1+411yescharacteristic
227C2×C4×C732−1+411yescharacteristic
228C2×Dic73—21no—
229C2×Dic73—21no—
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—
252C8×C73—41no—
253C8×C73—41no—
254C8×C73—41no—
255C8×C73—41no—
256#10596831—41no—
257#10596831—41no—
258#10596831—41no—
259#10596831—41no—
260C22×C73—22no—
261C22×C73—22no—
262C22×C73—22no—
263C22×C73—41no—
264C22×C73—41no—
265C22×C73—41no—
266C22×C73—41no—
267C22×C73C2×#11711yescharacteristic
268C22×C73#52011yescharacteristic
269C22×C73#52011yescharacteristic
270C22×C73C2×#13111yescharacteristic
271C22×C73C2×#13111yescharacteristic
272C22×C73#56811yescharacteristic
273C22×C73#56811yescharacteristic
274C4×C73—22no—
275C4×C73—22no—
276C4×C73—22no—
277C4×C73—41no—
278C4×C73—41no—
279C4×C73#54011yescharacteristic
280C4×C73#54111yescharacteristic
281C4×C73#54211yescharacteristic
282C4×C73#54211yescharacteristic
283Dic73—41no—
284Dic73—41no—
285Dic73—41no—
286Dic73—41no—
287Dic73—41no—
288Dic73—41no—
289Dic73—41no—
290Dic73—41no—
291#21928—731nomaximal, Sylow
292C2×C73—42no—
293C2×C73#231411yescharacteristic
294C2×C73#292411yescharacteristic
295C2×C73#292411yescharacteristic
296C2×C73#299211yescharacteristic
297C2×C73#299311yescharacteristic
298C2×C73#299411yescharacteristic
299C2×C73#299511yescharacteristic
300#2283—731no—
301#1924—731no—
302#1924—731no—
303#1923—731no—
304#1923—731no—
305#1917—731no—
306#1917—731no—
307#1916—731no—
308#1916—731no—
309#1843—731no—
310#1832—731no—
311#1797—731no—
312#1797D7311yescharacteristic
313#1768—731no—
314#1768—731no—
315C73#2192811yescharacteristic, complemented, Sylow
316C22×C42C2×D7311yescharacteristic
317C2×C4⋊C8—731no—
318C2×C4⋊C8—731no—
319C2×C4⋊C8—731no—
320C2×C4⋊C8—731no—
321C2×C4⋊C8—731no—
322C2×C4⋊C8—731no—
323C2×C4⋊C8C2×D7311yescharacteristic
324C2×C4⋊C8C2×D7311yescharacteristic
325C2×C22⋊C8—731no—
326C2×C22⋊C8—731no—
327C2×C22⋊C8C2×D7311yescharacteristic
328C2×C22⋊C8C2×D7311yescharacteristic
329C2×#97—731no—
330C2×#97—731no—
331C2×C4×C8—731no—
332C2×C4×C8—731no—
333#383—731no—
334#383—731no—
335#382—731no—
336#382—731no—
337#381—731no—
338#381—731no—
339#380—731no—
340#380—731no—
341C4×C4⋊C4—731no—
342C4×C4⋊C4—731no—
343C4×C22⋊C4—731no—
344C4×C22⋊C4—731no—
345#376—731no—
346#376—731no—
347#336—731no—
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#336C2×D7311yescharacteristic
358#336C2×D7311yescharacteristic
359C23×C4C4×D7311yescharacteristic
360C23×C4C4×D7311yescharacteristic
361C23×C4C22×D7311yescharacteristic
362C22×C8—731no—
363C22×C8—731no—
364C22×C8—731no—
365C22×C8—731no—
366C22×C8C22×D7311yescharacteristic
367C22×C8C22×D7311yescharacteristic
368C22×C8C22×D7311yescharacteristic
369C22×C8C22×D7311yescharacteristic
370C2×C4⋊C4—731no—
371C2×C4⋊C4—731no—
372C2×C4⋊C4—731no—
373C2×C4⋊C4—731no—
374C2×C22⋊C4—731no—
375C2×C22⋊C4—731no—
376C2×C22⋊C4—731no—
377C2×C22⋊C4—731no—
378C2×C42—22no—
379C2×C42—22no—
380C2×C42—731no—
381C2×C42—731no—
382C2×C42—731no—
383C2×C42—731no—
384C2×C42C4×D7311yescharacteristic
385C2×C42C4×D7311yescharacteristic
386C2×C42C22×D7311yescharacteristic
387C2×C42C22×D7311yescharacteristic
388C4⋊C8—22no—
389C4⋊C8—22no—
390C4⋊C8—2921no—
391C4⋊C8—2921no—
392C4⋊C8—2921no—
393C4⋊C8—2921no—
394C4⋊C8—1462no—
395C4⋊C8—1462no—
396C22⋊C8—41no—
397C22⋊C8—41no—
398C22⋊C8—2921no—
399C22⋊C8—2921no—
400#97—2921no—
401#97—2921no—
402C4×C8—2921no—
403C4×C8—2921no—
404#95—731no—
405#95—731no—
406#95—731no—
407#95—731no—
408#95—731no—
409#95—731no—
410#95—731no—
411#95—731no—
412#95—731no—
413#95—731no—
414#95—731no—
415#95—731no—
416#95—731no—
417#95—731no—
418#95—731no—
419#95—731no—
420C24C2×C4×D7311yescharacteristic
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—41no—
432C22×C4—41no—
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—1462no—
474C4⋊C4—1462no—
475C22⋊C4—2921no—
476C22⋊C4—2921no—
477C22⋊C4—1462no—
478C22⋊C4—1462no—
479C42—22no—
480C42—22no—
481C42—21no—
482C42—21no—
483C42—1461no—
484C42—1461no—
485C42—1461no—
486C42—1461no—
487C42—1461no—
488C42—1461no—
489C42—1461no—
490C42—1461no—
491C42#1192402712yes—
492C42#1192402712yes—
493C23—21no—
494C23—21no—
495C23—21no—
496C23—21no—
497C23—21no—
498C23—21no—
499C23#1455659912yes—
500C23C22×C4×D7311yescharacteristic
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—44no—
514C2×C4—44no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—1461no—
520C2×C4—1461no—
521C2×C4—1461no—
522C2×C4—1461no—
523C2×C4—1461no—
524C2×C4—1461no—
525C2×C4—1461no—
526C2×C4—1461no—
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#1455654712yes—
544C2×C4#1455654712yes—
545C2×C4#1455659712yes—
546C2×C4C2×#1192402711yescharacteristic
547C2×C4C2×#1192402711yescharacteristic
548C2×C4#1455663611yescharacteristic
549C2×C4#1455663711yescharacteristic
550C2×C4#1455663811yescharacteristic
551C2×C4#1455663911yescharacteristic
552C8—41no—
553C8—41no—
554C8—41no—
555C8—41no—
556C8—2921no—
557C8—2921no—
558C8—2921no—
559C8—2921no—
560C22—22no—
561C22—22no—
562C22—22no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22C2×#1455654711yescharacteristic
568C22#1798906711yescharacteristic
569C22#1798906811yescharacteristic
570C22C2×#1455659711yescharacteristic
571C22C2×#1455659911yescharacteristic
572C22#1798935311yescharacteristic
573C22#1798935311yescharacteristic
574C4—22no—
575C4—22no—
576C4—22no—
577C4—41no—
578C4—41no—
579C4—2921no—
580C4—2921no—
581C4—2921no—
582C4—2921no—
583C4—2921no—
584C4—2921no—
585C4—2921no—
586C4—2921no—
587C4#1798919011yescharacteristic
588C4#1798919711yescharacteristic
589C4#1798920411yescharacteristic
590C4#1798921011yescharacteristic
591C2—42no—
592C2#2261253811yescharacteristic
593C2#2261858511yescharacteristic
594C2#2261859111yescharacteristic
595C2#2261907211yescharacteristic
596C2#2261908211yescharacteristic
597C2#2261908711yescharacteristic
598C2#2261909811yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D73
commutator, socleC23×C73C23×C4
FittingC73×#1797C2
prime radicalC24×C73C22×C4
cosocleC22×C4×C73C24
hypercenter#1797D73
hypocenterC73#21928
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ #1797

Complements

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

NH ≅ G/Ntype
6. #22610496C2semidirect
7. #22610494C2semidirect
8. #22610489C2semidirect
9. #22610487C2semidirect
10. #22610084C2semidirect
11. #22610050C2semidirect
13. #22609790C2semidirect
14. #22609790C2semidirect
315. C73#21928semidirect

Maximal subgroups

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

subgroupindex
#226123292
#226105472
#226105412
#226105402
#226105342
#226104962
#226104942
#226104892
#226104872
#226100842
#226100502
#226099112
#226097902
C73×#17972
#2192873