Finite Group Databasebeta

← #34029772

Subgroups — #34029772

Order 18688.

606 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22626033C211yesmaximal, characteristic, complemented
2#22626031C211yesmaximal, characteristic, complemented
3#22626029C211yesmaximal, characteristic, complemented
4#22626007C211yesmaximal, characteristic
5#22626006C211yesmaximal, characteristic
6#22626002C211yesmaximal, characteristic
7#22625988C211yesmaximal, characteristic, complemented
8#22625988C211yesmaximal, characteristic, complemented
9#22625986C211yesmaximal, characteristic, complemented
10#22625879C211yesmaximal, characteristic
11#22625877C211yesmaximal, characteristic
12#22625877C211yesmaximal, characteristic
13#22625865C211yesmaximal, characteristic, complemented
14#22625860C211yesmaximal, characteristic, complemented
15#22613230C211yesmaximal, characteristic
16C22×#11924038C2211yescharacteristic
17C2×#14556658C2211yescharacteristic
18C2×#14556658C2211yescharacteristic
19C2×#14556658C2211yescharacteristic
20C2×#14556658C2211yescharacteristic
21C2×C4⋊#10596833C2211yescharacteristic
22C2×C4⋊#10596833C2211yescharacteristic
23C2×C4⋊#10596833C2211yescharacteristic
24C2×C4⋊#10596833C2211yescharacteristic
25C2×C4⋊#10596833C2211yescharacteristic
26C2×#14556648C2211yescharacteristic
27C2×#14556648C2211yescharacteristic
28C2×#14556648C2211yescharacteristic
29C2×#14556646C2211yescharacteristic
30C2×#14556646C2211yescharacteristic
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
44C73⋊#401C411yescharacteristic
45#17988529C411yescharacteristic
46#17988527C411yescharacteristic
47#17988516C411yescharacteristic
48#17988514C411yescharacteristic
49#17988513C411yescharacteristic
50#17988509C411yescharacteristic
51C4⋊C4×Dic73C2211yescharacteristic
52C4⋊C4×Dic73C2211yescharacteristic
53#17988438C2211yescharacteristic
54#17988434C2211yescharacteristic
55#17988434C2211yescharacteristic
56#17988434C2211yescharacteristic
57#17988432C2211yescharacteristic
58#400×C73C411yescharacteristic
59C2×#11924038—41no—
60C2×#11924038—41no—
61C2×#11924038—41no—
62C22×#10596833C2311yescharacteristic
63C22×#10596833C2311yescharacteristic
64C22×#10596833C2311yescharacteristic
65C22×#10596833C2311yescharacteristic
66C22×#10596833C2311yescharacteristic
67C22×#10596833C2311yescharacteristic
68C22×#10596833C2311yescharacteristic
69C22×#10596833C2311yescharacteristic
70#14556658—41no—
71#14556658—41no—
72#14556658—41no—
73#14556658—41no—
74C4⋊#10596833—41no—
75C4⋊#10596833—41no—
76C4⋊#10596833—41no—
77C4⋊#10596833—41no—
78C4⋊#10596833—41no—
79#14556648—41no—
80#14556648—41no—
81#14556648—41no—
82#14556646—41no—
83#14556646—41no—
84C4×#10596833—41no—
85C22×C4×D73C2311yescharacteristic
86C2×C4⋊Dic73C2×C411yescharacteristic
87C2×C4⋊Dic73C2×C411yescharacteristic
88C2×#11924007C2×C411yescharacteristic
89C2×#11924007C2×C411yescharacteristic
90C2×#11924005C2×C411yescharacteristic
91C2×#11924005C2×C411yescharacteristic
92C2×#11924005C2×C411yescharacteristic
93C2×#11924005C2×C411yescharacteristic
94C2×#11924005C2×C411yescharacteristic
95C2×#11924005C2×C411yescharacteristic
96C2×C4×Dic73C2311yescharacteristic
97C2×C4×Dic73C2311yescharacteristic
98C2×C4×Dic73C2311yescharacteristic
99C2×C4×Dic73C2311yescharacteristic
100C2×C4×Dic73C2311yescharacteristic
101C2×C4×Dic73C2311yescharacteristic
102#14556498C2×C411yescharacteristic
103#14556498C2×C411yescharacteristic
104#14556498C2×C411yescharacteristic
105#14556498C2×C411yescharacteristic
106#14556498C2×C411yescharacteristic
107#14556498C2×C411yescharacteristic
108#14556498C2×C411yescharacteristic
109#14556498C2×C411yescharacteristic
110#14556498C2×C411yescharacteristic
111#14556498C2×C411yescharacteristic
112#14556498C2×C411yescharacteristic
113C2×C4⋊C4×C73C2×C411yescharacteristic
114C2×C4⋊C4×C73C2×C411yescharacteristic
115#95×C73C2×C411yescharacteristic
116#95×C73C2×C411yescharacteristic
117#95×C73C2×C411yescharacteristic
118#95×C73C2×C411yescharacteristic
119#95×C73C2×C411yescharacteristic
120#11924038—44no—
121C2×#10596833—21no—
122C2×#10596833—21no—
123C2×#10596833—21no—
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—
145C23×D73C22×C411yescharacteristic
146C22×Dic73C22×C411yescharacteristic
147C22×Dic73C22×C411yescharacteristic
148C22×Dic73C22×C411yescharacteristic
149C22×Dic73C22×C411yescharacteristic
150C22×Dic73C22×C411yescharacteristic
151C22×Dic73C22×C411yescharacteristic
152C22×Dic73C2411yescharacteristic
153C2×C4×D73—21no—
154C2×C4×D73—21no—
155C2×C4×D73—21no—
156C2×C4×D73—21no—
157C2×C4×D73—21no—
158C2×C4×D73—21no—
159C4⋊Dic73—22no—
160C4⋊Dic73—41no—
161#11924007—22no—
162#11924007—41no—
163#11924005—22no—
164#11924005—41no—
165#11924005—41no—
166#11924005—41no—
167#11924005—41no—
168#11924005—41no—
169C4×Dic73—21no—
170C4×Dic73—21no—
171C4×Dic73—21no—
172C4×Dic73—21no—
173C4×Dic73—21no—
174C4×Dic73—21no—
175C4×Dic73—21no—
176C4×Dic73—21no—
177C4×Dic73—21no—
178C4×Dic73—21no—
179C4×Dic73—21no—
180C4×Dic73—21no—
181C22×C4×C73C22×C411yescharacteristic
182C22×C4×C73C22×C411yescharacteristic
183C22×C4×C73C22×C411yescharacteristic
184C22×C4×C73C22×C411yescharacteristic
185C22×C4×C73C22×C411yescharacteristic
186C22×C4×C73C22×C411yescharacteristic
187C22×C4×C73C22×C411yescharacteristic
188C4⋊C4×C73—41no—
189C4⋊C4×C73—41no—
190C23×C73C23×C411yescharacteristic
191C22×D73—21no—
192C22×D73—21no—
193C22×D73—21no—
194C22×D73—21no—
195C22×D73—21no—
196C22×D73—21no—
197C22×D73—21no—
198C2×C4×C73—21no—
199C2×C4×C73—21no—
200C2×C4×C73—21no—
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—21no—
214C2×C4×C73—21no—
215C2×C4×C73—21no—
216C2×C4×C73—21no—
217C2×C4×C73—21no—
218C2×C4×C73#13112yes—
219C2×Dic73—21no—
220C2×Dic73—21no—
221C2×Dic73—21no—
222C2×Dic73—21no—
223C2×Dic73—21no—
224C2×Dic73—21no—
225C2×Dic73—21no—
226C2×Dic73—21no—
227C2×Dic73—21no—
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×Dic73H(5,𝔽2)11yescharacteristic
238C2×Dic73H(5,𝔽2)11yescharacteristic
239C2×Dic73H(5,𝔽2)11yescharacteristic
240C2×Dic732−1+411yescharacteristic
241C2×Dic732−1+411yescharacteristic
242C2×Dic732−1+411yescharacteristic
243C4×D73—41no—
244C4×D73—41no—
245C4×D73—41no—
246C4×D73—41no—
247#10596833—41no—
248#10596833—41no—
249#10596833—41no—
250#10596833—41no—
251#10596833—41no—
252#10596833—41no—
253#10596833—41no—
254#10596833—41no—
255C22×C73#52011yescharacteristic
256C22×C73#52011yescharacteristic
257C22×C73#52011yescharacteristic
258C22×C73C2×#13111yescharacteristic
259C22×C73#56811yescharacteristic
260C22×C73#56811yescharacteristic
261C22×C73#56811yescharacteristic
262C2×D73—41no—
263C2×D73—41no—
264C2×D73—41no—
265C2×D73—41no—
266C2×D73—41no—
267C2×D73—41no—
268C2×D73—41no—
269C4×C73—22no—
270C4×C73—41no—
271C4×C73—41no—
272C4×C73—41no—
273C4×C73—41no—
274C4×C73—41no—
275C4×C73—41no—
276Dic73—41no—
277Dic73—41no—
278Dic73—41no—
279Dic73—41no—
280Dic73—41no—
281Dic73—41no—
282Dic73#56011yescharacteristic
283Dic73#56311yescharacteristic
284Dic73#56311yescharacteristic
285Dic73#56311yescharacteristic
286#23382—731nomaximal, Sylow
287C2×C73#238311yescharacteristic
288C2×C73#299211yescharacteristic
289C2×C73#299311yescharacteristic
290C2×C73#299311yescharacteristic
291C2×C73#299511yescharacteristic
292C2×C73#299511yescharacteristic
293C2×C73#299511yescharacteristic
294D73—81no—
295#2401—731no—
296#1940—731no—
297#1940—731no—
298#1939—731no—
299#1924—731no—
300#1924—731no—
301#1923—731no—
302#1917—731no—
303#1917—731no—
304#1916—731no—
305#1851—731no—
306#1851—731no—
307#1851—731no—
308#1843—731no—
309#1840—731no—
310C73#2338211yescharacteristic, complemented, Sylow
311C22×M16—731no—
312C2×C4⋊C8—731no—
313C2×C4⋊C8—731no—
314C2×C4⋊C8—731no—
315C2×C4⋊C8—731no—
316C2×C4⋊C8—731no—
317C2×C4⋊C8—731no—
318C2×C4⋊C8—731no—
319C2×C4⋊C8—731no—
320C2×C4⋊C8—731no—
321C2×C22⋊C8—731no—
322C2×C22⋊C8—731no—
323C2×C22⋊C8—731no—
324C2×#97—731no—
325C2×#97—731no—
326C2×C4×C8—731no—
327#401—731no—
328#400—731no—
329#400—731no—
330#400#6440811yescharacteristic
331#397—731no—
332#397—731no—
333#397—731no—
334#396—731no—
335C4×C4⋊C4—731no—
336C4×C4⋊C4—731no—
337C4×C4⋊C4—731no—
338C4×C22⋊C4—731no—
339C4×C22⋊C4—731no—
340C4×C22⋊C4—731no—
341#376—731no—
342#336—731no—
343#336—731no—
344#336—731no—
345#336—731no—
346#336—731no—
347#336—731no—
348#336—731no—
349#336—731no—
350#336—731no—
351#336—731no—
352#336—731no—
353#336—731no—
354C23×C4—731no—
355C2×M16—2921no—
356C2×M16—2921no—
357C2×M16—2921no—
358C22×C8—731no—
359C22×C8—731no—
360C22×C8—731no—
361C22×C8—731no—
362C22×C8—731no—
363C22×C8—731no—
364C22×C8—731no—
365C22×C8—731no—
366C2×C4⋊C4—731no—
367C2×C4⋊C4—731no—
368C2×C4⋊C4—731no—
369C2×C4⋊C4—731no—
370C2×C4⋊C4C2×#6440811yescharacteristic
371C2×C4⋊C4C2×#6440811yescharacteristic
372C2×C22⋊C4—731no—
373C2×C22⋊C4—731no—
374C2×C22⋊C4—731no—
375C2×C22⋊C4—731no—
376C2×C22⋊C4—731no—
377C2×C22⋊C4—731no—
378C2×C42—731no—
379C2×C42—731no—
380C2×C42—731no—
381C2×C42—731no—
382C2×C42—731no—
383C2×C42—731no—
384C4⋊C8—2921no—
385C4⋊C8—2921no—
386C4⋊C8—2921no—
387C4⋊C8—2921no—
388C4⋊C8—2921no—
389C4⋊C8—2921no—
390C4⋊C8—2921no—
391C4⋊C8—2921no—
392C4⋊C8—2921no—
393C22⋊C8—2921no—
394C22⋊C8—2921no—
395C22⋊C8—2921no—
396#97—2921no—
397#97—2921no—
398C4×C8—2921no—
399#95—731no—
400#95—731no—
401#95—731no—
402#95—731no—
403#95—731no—
404#95—731no—
405#95—731no—
406#95—731no—
407#95—731no—
408#95—731no—
409#95—731no—
410#95C2×#6440811yescharacteristic
411#95C2×#6440811yescharacteristic
412#95C2×#6440811yescharacteristic
413#95C2×#6440811yescharacteristic
414#95C2×#6440811yescharacteristic
415C24—731no—
416C22×C4—731no—
417C22×C4—731no—
418C22×C4—731no—
419C22×C4—731no—
420C22×C4—731no—
421C22×C4—731no—
422C22×C4—731no—
423C22×C4—1461no—
424C22×C4—1461no—
425C22×C4—1461no—
426C22×C4—1461no—
427C22×C4—1461no—
428C22×C4—1461no—
429C22×C4C22×#6440811yescharacteristic
430C22×C4C22×#6440811yescharacteristic
431C22×C4C22×#6440811yescharacteristic
432C22×C4C22×#6440811yescharacteristic
433C22×C4C22×#6440811yescharacteristic
434C22×C4C22×#6440811yescharacteristic
435C22×C4C22×#6440811yescharacteristic
436M16—2924no—
437C2×C8—1461no—
438C2×C8—1461no—
439C2×C8—1461no—
440C2×C8—1461no—
441C2×C8—1461no—
442C2×C8—1461no—
443C2×C8—1461no—
444C2×C8—1461no—
445C2×C8—1461no—
446C2×C8—1461no—
447C2×C8—1461no—
448C2×C8—1461no—
449C2×C8—1461no—
450C2×C8—1461no—
451C2×C8—1461no—
452C2×C8—1461no—
453C2×C8—1461no—
454C2×C8—1461no—
455C2×C8—1461no—
456C2×C8—1461no—
457C2×C8—1461no—
458C2×C8—1461no—
459C2×C8—1461no—
460C2×C8—1461no—
461C4⋊C4—41no—
462C4⋊C4—41no—
463C4⋊C4—2921no—
464C4⋊C4—2921no—
465C4⋊C4—1462no—
466C4⋊C4—1462no—
467C22⋊C4—2921no—
468C22⋊C4—2921no—
469C22⋊C4—2921no—
470C22⋊C4—2921no—
471C22⋊C4—2921no—
472C22⋊C4—1462no—
473C42—1461no—
474C42—1461no—
475C42—1461no—
476C42—1461no—
477C42—1461no—
478C42—1461no—
479C42—1461no—
480C42—1461no—
481C42—1461no—
482C42—1461no—
483C42—1461no—
484C42—1461no—
485C23—1461no—
486C23—1461no—
487C23—1461no—
488C23—1461no—
489C23—1461no—
490C23—1461no—
491C23—1461no—
492C23C23×#6440811yescharacteristic
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
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—2921no—
514C2×C4—2921no—
515C2×C4—2921no—
516C2×C4—2921no—
517C2×C4—731no—
518C2×C4—731no—
519C2×C4—731no—
520C2×C4—731no—
521C2×C4—731no—
522C2×C4—731no—
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#1455667912yes—
542C8—2921no—
543C8—2921no—
544C8—2921no—
545C8—2921no—
546C8—2921no—
547C8—2921no—
548C8—2921no—
549C8—2921no—
550C22—2921no—
551C22—2921no—
552C22—2921no—
553C22—2921no—
554C22—2921no—
555C22—2921no—
556C22—2921no—
557C22#1798965611yescharacteristic
558C22#1798965611yescharacteristic
559C22#1798965611yescharacteristic
560C22C2×#1455667911yescharacteristic
561C22#1798966511yescharacteristic
562C22#1798966611yescharacteristic
563C22#1798966611yescharacteristic
564C4—22no—
565C4—41no—
566C4—41no—
567C4—41no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4—2921no—
572C4—2921no—
573C4—2921no—
574C4—2921no—
575C4—2921no—
576C4—2921no—
577C4—731no—
578C4—731no—
579C4—731no—
580C4—731no—
581C2—5841no—
582C2#2262647811yescharacteristic
583C2#2262687011yescharacteristic
584C2#2262687711yescharacteristic
585C2#2262687711yescharacteristic
586C2#2262688511yescharacteristic
587C2#2262688611yescharacteristic
588C2#2262688711yescharacteristic
subgroupG/H
center, FrattiniC23C23×#64408
commutator, socleC23×C73C23×C4
Fitting#400×C73C4
prime radicalC23×D73C22×C4
cosocleC22×Dic73C24
hypercenter#400#64408
hypocenterC73#23382
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
1. #22626033C2semidirect
2. #22626031C2semidirect
3. #22626029C2semidirect
7. #22625988C2semidirect
8. #22625988C2semidirect
9. #22625986C2semidirect
13. #22625865C2semidirect
14. #22625860C2semidirect
310. C73#23382semidirect

Maximal subgroups

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

subgroupindex
#226260332
#226260312
#226260292
#226260072
#226260062
#226260022
#226259882
#226259862
#226258792
#226258772
#226258652
#226258602
#226132302
#2338273