Finite Group Databasebeta

← #28393550

Subgroups — #28393550

Order 14464.

928 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16813592C211yesmaximal, characteristic
2C2×#16813584C211yesmaximal, characteristic, complemented
3C2×C4×C22⋊D113C211yesmaximal, characteristic, complemented
4C22×#14268624C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×D113C211yesmaximal, characteristic, complemented
6#20298499C211yesmaximal, characteristic, complemented
7#20298488C211yesmaximal, characteristic, complemented
8#20298487C211yesmaximal, characteristic, complemented
9#20298476C211yesmaximal, characteristic, complemented
10#20298476C211yesmaximal, characteristic, complemented
11#20298475C211yesmaximal, characteristic, complemented
12#20298469C211yesmaximal, characteristic, complemented
13C22⋊C4×Dic113C211yesmaximal, characteristic, complemented
14#20298445C211yesmaximal, characteristic, complemented
15#385×C113C211yesmaximal, characteristic, complemented
16C24×D113C2211yescharacteristic
17C22×D452C2211yescharacteristic
18C22×D452C2211yescharacteristic
19C22×C22⋊D113C2211yescharacteristic
20C23×Dic113C2211yescharacteristic
21C22×C4×D113C2211yescharacteristic
22C22×C4×D113C2211yescharacteristic
23C22×C4×D113C2211yescharacteristic, complemented
24#16813592C418yescomplemented
25#16813584—24no—
26C4×C22⋊D113—24no—
27C2×#14268626C2211yescharacteristic, complemented
28C2×C22⋊Dic113C2211yescharacteristic
29C2×#14268624—24no—
30C2×#14268624C2211yescharacteristic
31C2×#14268624C2211yescharacteristic
32C2×#14268624C2211yescharacteristic
33C2×#14268624C2211yescharacteristic
34C2×#14268624C2211yescharacteristic
35C2×#14268624C2211yescharacteristic
36C2×#14268624C2211yescharacteristic
37C2×#14268624C2211yescharacteristic
38C2×#14268624C2211yescharacteristic, complemented
39C2×#14268624C2211yescharacteristic, complemented
40C2×#14268624C2211yescharacteristic, complemented
41C22⋊C4×D113—24no—
42C2×C4×Dic113C2211yescharacteristic, complemented
43C2×C4×Dic113C2211yescharacteristic, complemented
44C2×C4×Dic113C2211yescharacteristic, complemented
45#16813529C2211yescharacteristic, complemented
46#16813529C2211yescharacteristic, complemented
47#16813529C2211yescharacteristic, complemented
48#16813529C2211yescharacteristic, complemented
49C23×C4×C113C2211yescharacteristic
50C2×C4⋊C4×C113C2211yescharacteristic, complemented
51C2×C4⋊C4×C113C2211yescharacteristic, complemented
52C2×C22⋊C4×C113C2211yescharacteristic
53C2×C22⋊C4×C113C2211yescharacteristic
54#95×C113C2211yescharacteristic, complemented
55#95×C113C2211yescharacteristic, complemented
56C23×D113—22no—
57C23×D113—22no—
58C23×D113—22no—
59C23×D113—22no—
60C23×D113—41no—
61C23×D113—41no—
62C23×D113C2×C414yescomplemented
63C23×D113C2311yescharacteristic
64C23×D113C2311yescharacteristic
65C23×D113C2311yescharacteristic
66C2×D452—22no—
67C2×D452—22no—
68C2×D452—41no—
69C2×D452—41no—
70C2×D452C2×C414yescomplemented
71C2×D452C2×C414yescomplemented
72C2×C22⋊D113—22no—
73C2×C22⋊D113—22no—
74C2×C22⋊D113C2×C414yescomplemented
75C22×Dic113—22no—
76C22×Dic113—22no—
77C22×Dic113—41no—
78C22×Dic113C2311yescharacteristic
79C22×Dic113C2311yescharacteristic
80C22×Dic113C2311yescharacteristic
81C22×Dic113C2311yescharacteristic
82C22×Dic113C2311yescharacteristic
83C2×C4×D113—22no—
84C2×C4×D113—22no—
85C2×C4×D113—22no—
86C2×C4×D113—22no—
87C2×C4×D113—22no—
88C2×C4×D113—22no—
89C2×C4×D113—41no—
90C2×C4×D113—41no—
91C2×C4×D113—41no—
92#14268626—22no—
93C22⋊Dic113D414yescomplemented
94#14268624—22no—
95#14268624—22no—
96#14268624—22no—
97#14268624—22no—
98#14268624—22no—
99#14268624—22no—
100#14268624—22no—
101#14268624—41no—
102#14268624C2×C414yescomplemented
103#14268624C2×C414yescomplemented
104#14268624D414yescomplemented
105C4×Dic113—22no—
106C4×Dic113—22no—
107C4×Dic113—41no—
108C24×C113C2311yescharacteristic
109C22×C4×C113—22no—
110C22×C4×C113—22no—
111C22×C4×C113—41no—
112C22×C4×C113C2311yescharacteristic
113C22×C4×C113C2311yescharacteristic
114C22×C4×C113C2311yescharacteristic
115C22×C4×C113C2311yescharacteristic
116C22×C4×C113C2311yescharacteristic
117C22×C4×C113C2311yescharacteristic
118C4⋊C4×C113—22no—
119C4⋊C4×C113—41no—
120C22⋊C4×C113—22no—
121C22⋊C4×C113C2×C414yescomplemented
122C23×C113—21no—
123C23×C113—21no—
124C23×C113—21no—
125C23×C113—21no—
126C23×C113C22×C412yes—
127C23×C113C2×D412yes—
128C23×C113#4112yes—
129C23×C113C2411yescharacteristic
130C22×D113—21no—
131C22×D113—21no—
132C22×D113—21no—
133C22×D113—21no—
134C22×D113—28no—
135C22×D113—21no—
136C22×D113—21no—
137C22×D113—21no—
138C22×D113—21no—
139C22×D113—21no—
140C22×D113—21no—
141C22×D113—21no—
142C22×D113—21no—
143C22×D113—21no—
144C22×D113—21no—
145C22×D113—21no—
146C22×D113—21no—
147C22×D113—28no—
148C22×D113—44no—
149C22×D113—44no—
150C22×D113—44no—
151C22×D113—44no—
152C22×D113—44no—
153C22×D113C22×C412yes—
154C22×D113C22×C412yes—
155C22×D113C22×C412yes—
156C22×D113C2×D412yes—
157C22×D113#4112yes—
158C2×C4×C113—21no—
159C2×C4×C113—21no—
160C2×C4×C113—21no—
161C2×C4×C113—21no—
162C2×C4×C113—21no—
163C2×C4×C113—21no—
164C2×C4×C113—21no—
165C2×C4×C113—21no—
166C2×C4×C113—21no—
167C2×C4×C113—21no—
168C2×C4×C113—21no—
169C2×C4×C113—21no—
170C2×C4×C113—21no—
171C2×C4×C113—21no—
172C2×C4×C113—21no—
173C2×C4×C113—44no—
174C2×C4×C113C22×C412yes—
175C2×C4×C113C22×C412yes—
176C2×C4×C113C2×D412yes—
177C22⋊D113—28no—
178C2×Dic113—21no—
179C2×Dic113—21no—
180C2×Dic113—21no—
181C2×Dic113—21no—
182C2×Dic113—21no—
183C2×Dic113—21no—
184C2×Dic113—21no—
185C2×Dic113—21no—
186C2×Dic113—21no—
187C2×Dic113—21no—
188C2×Dic113—21no—
189C2×Dic113—44no—
190C2×Dic113C22×C412yes—
191C2×Dic113C2×D412yes—
192C2×Dic113C2×D412yes—
193C2×Dic113C2×D412yes—
194D452—28no—
195D452—44no—
196C4×D113—44no—
197C4×D113—44no—
198C4×D113—44no—
199C22×C113—22no—
200C22×C113—22no—
201C22×C113—22no—
202C22×C113—22no—
203C22×C113—22no—
204C22×C113—22no—
205C22×C113C4×D414yescomplemented
206C22×C113C23×C411yescharacteristic
207C22×C113C22×D411yescharacteristic
208C22×C113C22×D411yescharacteristic
209C22×C113C2×#4111yescharacteristic
210C22×C113C2×#4111yescharacteristic
211C22×C113H(5,𝔽2)11yescharacteristic
212C22×C113H(5,𝔽2)11yescharacteristic
213C2×D113—22no—
214C2×D113—22no—
215C2×D113—22no—
216C2×D113—22no—
217C2×D113—22no—
218C2×D113—22no—
219C2×D113—22no—
220C2×D113—22no—
221C2×D113—22no—
222C2×D113—22no—
223C2×D113—22no—
224C2×D113—22no—
225C2×D113—416no—
226C2×D113—41no—
227C2×D113—41no—
228C2×D113—41no—
229C2×D113—41no—
230C2×D113—41no—
231C2×D113—41no—
232C2×D113—41no—
233C2×D113—41no—
234C2×D113C4×D414yescomplemented
235C4×C113—22no—
236C4×C113—22no—
237C4×C113—22no—
238C4×C113—41no—
239C4×C113—41no—
240C4×C113—41no—
241Dic113—22no—
242Dic113—22no—
243Dic113—22no—
244Dic113—22no—
245Dic113—41no—
246C2×C113—24no—
247C2×C113C2×C4×D411yescharacteristic
248C2×C113C2×C4×D411yescharacteristic
249C2×C113#51811yescharacteristic
250C2×C113D4211yescharacteristic
251C2×C113#54611yescharacteristic
252C2×C113#54611yescharacteristic
253C2×C113#55111yescharacteristic
254D113—24no—
255D113—42no—
256D113—42no—
257#2358—1131nomaximal, Sylow
258C113#235811yescharacteristic, complemented, Sylow
259C2×#120—1131no—
260C2×C4×D4—1131no—
261C2×C4×D4—1131no—
262C22×C22⋊C4—1131no—
263C22×C22⋊C4—1131no—
264#390—1131no—
265#388—1131no—
266#388—1131no—
267#386—1131no—
268#386—1131no—
269#386—1131no—
270#385—1131no—
271#385D11311yescharacteristic, complemented
272C4×C22⋊C4—1131no—
273C4×C22⋊C4—1131no—
274C25—1131no—
275C22×D4—1131no—
276C22×D4—1131no—
277C22×D4—1131no—
278C23×C4—1131no—
279C23×C4—1131no—
280C23×C4—1131no—
281C23×C4—1131no—
282C23×C4C2×D11311yescharacteristic
283#120—1138no—
284C4×D4—2264no—
285C4×D4—2264no—
286C2×C4⋊C4—1131no—
287C2×C4⋊C4C2×D11311yescharacteristic, complemented
288C2×C4⋊C4C2×D11311yescharacteristic, complemented
289C2×C22⋊C4—1131no—
290C2×C22⋊C4—1131no—
291C2×C22⋊C4—1131no—
292C2×C22⋊C4—1131no—
293C2×C22⋊C4—1131no—
294C2×C22⋊C4—1131no—
295C2×C22⋊C4—1131no—
296C2×C22⋊C4—1131no—
297C2×C22⋊C4—1131no—
298C2×C22⋊C4—1131no—
299C2×C22⋊C4—1131no—
300C2×C22⋊C4—1131no—
301C2×C22⋊C4—2264no—
302C2×C22⋊C4—2264no—
303C2×C22⋊C4C2×D11311yescharacteristic
304C2×C22⋊C4C2×D11311yescharacteristic
305C2×C42—1131no—
306C2×C42—1131no—
307C2×C42—1131no—
308#95—1131no—
309#95—1131no—
310#95—1131no—
311#95—1131no—
312#95C2×D11311yescharacteristic, complemented
313#95C2×D11311yescharacteristic, complemented
314C24—1131no—
315C24—1134no—
316C24—1131no—
317C24—1131no—
318C24—4521no—
319C24—4521no—
320C24—2262no—
321C24—2262no—
322C24—2262no—
323C24—2262no—
324C24C22×D11311yescharacteristic
325C2×D4—1134no—
326C2×D4—1134no—
327C2×D4—1134no—
328C2×D4—4521no—
329C2×D4—4521no—
330C2×D4—2262no—
331C2×D4—2262no—
332C2×D4—2262no—
333C2×D4—2262no—
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—41no—
337C22×C4—1131no—
338C22×C4—1131no—
339C22×C4—1131no—
340C22×C4—1131no—
341C22×C4—1131no—
342C22×C4—4521no—
343C22×C4—4521no—
344C22×C4—4521no—
345C22×C4—4521no—
346C22×C4—2262no—
347C22×C4—2262no—
348C22×C4—2262no—
349C22×C4—2262no—
350C22×C4—2262no—
351C22×C4—2262no—
352C22×C4—2262no—
353C22×C4—2262no—
354C22×C4C22×D11311yescharacteristic
355C22×C4C22×D11311yescharacteristic
356C22×C4C22×D11311yescharacteristic
357C22×C4C22×D11311yescharacteristic
358C22×C4C22×D11311yescharacteristic
359C22×C4C22×D11311yescharacteristic
360C4⋊C4—22no—
361C4⋊C4—41no—
362C4⋊C4—2262no—
363C22⋊C4—22no—
364C22⋊C4—1134no—
365C22⋊C4—1134no—
366C22⋊C4—1134no—
367C22⋊C4—1134no—
368C22⋊C4—4521no—
369C22⋊C4—2262no—
370C22⋊C4—2262no—
371C22⋊C4—2262no—
372C22⋊C4—2262no—
373C22⋊C4—2262no—
374C22⋊C4—2262no—
375C22⋊C4—2262no—
376C22⋊C4C4×D11314yescomplemented
377C42—4521no—
378C42—2262no—
379C42—2262no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—1132no—
385C23—1132no—
386C23—1132no—
387C23—1132no—
388C23—1132no—
389C23—4524no—
390C23—4524no—
391C23—4524no—
392C23—4524no—
393C23—4524no—
394C23—2268no—
395C23—2268no—
396C23—2261no—
397C23—2261no—
398C23—2261no—
399C23—2261no—
400C23—2261no—
401C23—2261no—
402C23—2261no—
403C23—2261no—
404C23—2261no—
405C23—2261no—
406C23—2261no—
407C23—2261no—
408C23—2261no—
409C23—2261no—
410C23—2261no—
411C23—2261no—
412C23C2×C4×D11312yes—
413C23D4×D11312yes—
414C23#1426864812yes—
415C23C23×D11311yescharacteristic
416D4—4524no—
417D4—2268no—
418D4—2268no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—44no—
435C2×C4—1132no—
436C2×C4—1132no—
437C2×C4—1132no—
438C2×C4—1132no—
439C2×C4—4524no—
440C2×C4—4524no—
441C2×C4—4524no—
442C2×C4—4524no—
443C2×C4—2261no—
444C2×C4—2261no—
445C2×C4—2261no—
446C2×C4—2261no—
447C2×C4—2261no—
448C2×C4—2261no—
449C2×C4—2261no—
450C2×C4—2261no—
451C2×C4—2261no—
452C2×C4—2261no—
453C2×C4—2261no—
454C2×C4C2×C4×D11312yes—
455C2×C4C2×C4×D11312yes—
456C2×C4D4×D11312yes—
457C22—22no—
458C22—22no—
459C22—22no—
460C22—22no—
461C22—22no—
462C22—22no—
463C22—1134no—
464C22—45216no—
465C22—4521no—
466C22—4521no—
467C22—4521no—
468C22—4521no—
469C22—4521no—
470C22—4521no—
471C22—4521no—
472C22—4521no—
473C22—2262no—
474C22—2262no—
475C22—2262no—
476C22—2262no—
477C22—2262no—
478C22—2262no—
479C22—2262no—
480C22—2262no—
481C22—2262no—
482C22—2262no—
483C22—2262no—
484C22—2262no—
485C22#1681358414yescomplemented
486C22C22×C4×D11311yescharacteristic
487C22C2×D4×D11311yescharacteristic
488C22C2×D4×D11311yescharacteristic
489C22#41×D11311yescharacteristic
490C22C2×#1426864811yescharacteristic
491C22#1681366711yescharacteristic
492C22#1681366811yescharacteristic
493C4—22no—
494C4—22no—
495C4—22no—
496C4—41no—
497C4—41no—
498C4—41no—
499C4—4521no—
500C4—2262no—
501C4—2262no—
502C4—2262no—
503C4—2262no—
504C2—24no—
505C2—4522no—
506C2—4522no—
507C2—2264no—
508C2C4×D4×D11311yescharacteristic
509C2C2×#1681358411yescharacteristic
510C2#2029907011yescharacteristic
511C2#2029923011yescharacteristic
512C2#2029923911yescharacteristic
513C2#2029924011yescharacteristic
514C2#2029927511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D113
commutatorC22×C113C23×C4
Fitting#385×C113C2
socle, cosocleC23×C113C24
prime radicalC2×#16813592C2
hypercenter#385D113
hypocenterC113#2358
LCSG ▷ C22×C113 ▷ C113
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
2. C2×#16813584C2semidirect
3. C2×C4×C22⋊D113C2semidirect
4. C22×#14268624C2semidirect
5. C2×C22⋊C4×D113C2semidirect
6. #20298499C2semidirect
7. #20298488C2semidirect
8. #20298487C2semidirect
9. #20298476C2semidirect
10. #20298476C2semidirect
11. #20298475C2semidirect
12. #20298469C2semidirect
13. C22⋊C4×Dic113C2semidirect
14. #20298445C2semidirect
15. #385×C113C2semidirect
23. C22×C4×D113C22semidirect
24. #16813592C4semidirect
27. C2×#14268626C22semidirect
38. C2×#14268624C22semidirect
39. C2×#14268624C22semidirect
40. C2×#14268624C22semidirect
42. C2×C4×Dic113C22semidirect
43. C2×C4×Dic113C22semidirect
44. C2×C4×Dic113C22semidirect
45. #16813529C22semidirect
46. #16813529C22semidirect
47. #16813529C22semidirect
48. #16813529C22semidirect
50. C2×C4⋊C4×C113C22semidirect
51. C2×C4⋊C4×C113C22semidirect
54. #95×C113C22semidirect
55. #95×C113C22semidirect
62. C23×D113C2×C4semidirect
70. C2×D452C2×C4semidirect
71. C2×D452C2×C4semidirect
74. C2×C22⋊D113C2×C4semidirect
93. C22⋊Dic113D4semidirect
102. #14268624C2×C4semidirect
103. #14268624C2×C4semidirect
104. #14268624D4semidirect
121. C22⋊C4×C113C2×C4semidirect
205. C22×C113C4×D4semidirect
234. C2×D113C4×D4semidirect
258. C113#2358semidirect
271. #385D113semidirect
287. C2×C4⋊C4C2×D113semidirect
288. C2×C4⋊C4C2×D113semidirect
312. #95C2×D113semidirect
313. #95C2×D113semidirect
376. C22⋊C4C4×D113semidirect
485. C22#16813584semidirect

Maximal subgroups

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

subgroupindex
C2×#168135922
C2×#168135842
C2×C4×C22⋊D1132
C22×#142686242
C2×C22⋊C4×D1132
#202984992
#202984882
#202984872
#202984762
#202984752
#202984692
C22⋊C4×Dic1132
#202984452
#385×C1132
#2358113