Finite Group Databasebeta

← #28393556

Subgroups — #28393556

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×C4×D452C211yesmaximal, characteristic, complemented
3C2×#16813582C211yesmaximal, characteristic, complemented
4C22×#14268624C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×D113C211yesmaximal, characteristic, complemented
6#20298500C211yesmaximal, characteristic, complemented
7#20298490C211yesmaximal, characteristic, complemented
8#20298489C211yesmaximal, characteristic, complemented
9#20298477C211yesmaximal, characteristic, complemented
10#20298476C211yesmaximal, characteristic, complemented
11#20298476C211yesmaximal, characteristic, complemented
12#20298473C211yesmaximal, characteristic, complemented
13#20298472C211yesmaximal, characteristic, complemented
14C4×#14268624C211yesmaximal, characteristic, complemented
15C4×C22⋊C4×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
25C4×D452—24no—
26#16813582—24no—
27C2×C4⋊Dic113C2211yescharacteristic, complemented
28C2×C4⋊Dic113C2211yescharacteristic, complemented
29C2×#14268626C2211yescharacteristic, complemented
30C2×C22⋊Dic113C2211yescharacteristic
31C2×#14268624—24no—
32C2×#14268624C2211yescharacteristic
33C2×#14268624C2211yescharacteristic
34C2×#14268624C2211yescharacteristic
35C2×#14268624C2211yescharacteristic
36C2×#14268624C2211yescharacteristic
37C2×#14268624C2211yescharacteristic
38C2×#14268624C2211yescharacteristic
39C2×#14268624C2211yescharacteristic
40C2×#14268624C2211yescharacteristic, complemented
41C2×#14268624C2211yescharacteristic, complemented
42C2×#14268624C2211yescharacteristic, complemented
43C22⋊C4×D113—24no—
44C2×C4×Dic113C2211yescharacteristic, complemented
45#16813529C2211yescharacteristic, complemented
46#16813529C2211yescharacteristic, complemented
47#16813529C2211yescharacteristic, complemented
48#16813529C2211yescharacteristic, complemented
49C23×C4×C113C2211yescharacteristic
50C2×C22⋊C4×C113C2211yescharacteristic
51C2×C22⋊C4×C113C2211yescharacteristic
52C2×C42×C113C2211yescharacteristic, complemented
53C2×C42×C113C2211yescharacteristic, complemented
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—
92C4⋊Dic113—22no—
93C4⋊Dic113—41no—
94#14268626—22no—
95C22⋊Dic113—22no—
96#14268624—22no—
97#14268624—22no—
98#14268624—22no—
99#14268624—22no—
100#14268624—22no—
101#14268624—22no—
102#14268624—22no—
103#14268624—41no—
104#14268624C2×C414yescomplemented
105#14268624C2×C414yescomplemented
106#14268624D414yescomplemented
107C4×Dic113—22no—
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
118C22⋊C4×C113C2×C414yescomplemented
119C22⋊C4×C113D414yescomplemented
120C42×C113—22no—
121C42×C113—41no—
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—44no—
172C2×C4×C113C22×C412yes—
173C2×C4×C113C22×C412yes—
174C2×C4×C113C2×D412yes—
175C2×C4×C113C2×D412yes—
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—21no—
190C2×Dic113—21no—
191C2×Dic113—44no—
192C2×Dic113C22×C412yes—
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—22no—
239C4×C113—22no—
240C4×C113—41no—
241Dic113—22no—
242Dic113—22no—
243Dic113—41no—
244Dic113—41no—
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#385—1131no—
272C4×C22⋊C4—1131no—
273C4×C22⋊C4D11311yescharacteristic, complemented
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⋊C4—1131no—
288C2×C4⋊C4—1131no—
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×C42C2×D11311yescharacteristic, complemented
307C2×C42C2×D11311yescharacteristic, complemented
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—4521no—
361C4⋊C4—2262no—
362C4⋊C4—2262no—
363C22⋊C4—1134no—
364C22⋊C4—1134no—
365C22⋊C4—1134no—
366C22⋊C4—4521no—
367C22⋊C4—2262no—
368C22⋊C4—2262no—
369C22⋊C4—2262no—
370C22⋊C4—2262no—
371C22⋊C4—2262no—
372C22⋊C4—2262no—
373C22⋊C4—2262no—
374C22⋊C4—2262no—
375C22⋊C4C4×D11314yescomplemented
376C22⋊C4D45214yescomplemented
377C42—22no—
378C42—41no—
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—
413C23C2×D45212yes—
414C23#1426864712yes—
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—44no—
433C2×C4—1132no—
434C2×C4—1132no—
435C2×C4—4524no—
436C2×C4—4524no—
437C2×C4—4524no—
438C2×C4—4524no—
439C2×C4—2261no—
440C2×C4—2261no—
441C2×C4—2261no—
442C2×C4—2261no—
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×C4C2×C4×D11312yes—
453C2×C4C2×C4×D11312yes—
454C2×C4D4×D11312yes—
455C2×C4C2×D45212yes—
456C2×C4C2×D45212yes—
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—
485C22C4×D45214yescomplemented
486C22C22×C4×D11311yescharacteristic
487C22C2×D4×D11311yescharacteristic
488C22C22×D45211yescharacteristic
489C22#41×D11311yescharacteristic
490C22C2×#1426864711yescharacteristic
491C22#1681366711yescharacteristic
492C22#1681366811yescharacteristic
493C4—22no—
494C4—22no—
495C4—22no—
496C4—22no—
497C4—22no—
498C4—41no—
499C4—4521no—
500C4—4521no—
501C4—4521no—
502C4—2262no—
503C4—2262no—
504C2—24no—
505C2—4522no—
506C2—4522no—
507C2—2264no—
508C2C4×D4×D11311yescharacteristic
509C2C2×C4×D45211yescharacteristic
510C2#2029907011yescharacteristic
511C2D4×D45211yescharacteristic
512C2#2029923811yescharacteristic
513C2#2029924311yescharacteristic
514C2#2029927211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D113
commutatorC22×C113C23×C4
FittingC4×C22⋊C4×C113C2
socle, cosocleC23×C113C24
prime radicalC2×#16813592C2
hypercenterC4×C22⋊C4D113
hypocenterC113#2358
LCSG ▷ C22×C113 ▷ C113
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×D452C2semidirect
3. C2×#16813582C2semidirect
4. C22×#14268624C2semidirect
5. C2×C22⋊C4×D113C2semidirect
6. #20298500C2semidirect
7. #20298490C2semidirect
8. #20298489C2semidirect
9. #20298477C2semidirect
10. #20298476C2semidirect
11. #20298476C2semidirect
12. #20298473C2semidirect
13. #20298472C2semidirect
14. C4×#14268624C2semidirect
15. C4×C22⋊C4×C113C2semidirect
23. C22×C4×D113C22semidirect
24. #16813592C4semidirect
27. C2×C4⋊Dic113C22semidirect
28. C2×C4⋊Dic113C22semidirect
29. C2×#14268626C22semidirect
40. C2×#14268624C22semidirect
41. C2×#14268624C22semidirect
42. C2×#14268624C22semidirect
44. C2×C4×Dic113C22semidirect
45. #16813529C22semidirect
46. #16813529C22semidirect
47. #16813529C22semidirect
48. #16813529C22semidirect
52. C2×C42×C113C22semidirect
53. C2×C42×C113C22semidirect
54. #95×C113C22semidirect
55. #95×C113C22semidirect
62. C23×D113C2×C4semidirect
70. C2×D452C2×C4semidirect
71. C2×D452C2×C4semidirect
74. C2×C22⋊D113C2×C4semidirect
104. #14268624C2×C4semidirect
105. #14268624C2×C4semidirect
106. #14268624D4semidirect
118. C22⋊C4×C113C2×C4semidirect
119. C22⋊C4×C113D4semidirect
205. C22×C113C4×D4semidirect
234. C2×D113C4×D4semidirect
258. C113#2358semidirect
273. C4×C22⋊C4D113semidirect
306. C2×C42C2×D113semidirect
307. C2×C42C2×D113semidirect
312. #95C2×D113semidirect
313. #95C2×D113semidirect
375. C22⋊C4C4×D113semidirect
376. C22⋊C4D452semidirect
485. C22C4×D452semidirect

Maximal subgroups

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

subgroupindex
C2×#168135922
C2×C4×D4522
C2×#168135822
C22×#142686242
C2×C22⋊C4×D1132
#202985002
#202984902
#202984892
#202984772
#202984762
#202984732
#202984722
C4×#142686242
C4×C22⋊C4×C1132
#2358113