Finite Group Databasebeta

← #28399788

Subgroups — #28399788

Order 14464.

764 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×D113C211yesmaximal, characteristic, complemented
2C2×#16813642C211yesmaximal, characteristic, complemented
3#20299105C211yesmaximal, characteristic, complemented
4#20298759C211yesmaximal, characteristic, complemented
5#20298757C211yesmaximal, characteristic, complemented
6#20298752C211yesmaximal, characteristic, complemented
7#20298747C211yesmaximal, characteristic, complemented
8#20298742C211yesmaximal, characteristic, complemented
9#20298740C211yesmaximal, characteristic, complemented
10#20298735C211yesmaximal, characteristic, complemented
11#20298730C211yesmaximal, characteristic, complemented
12#20298595C211yesmaximal, characteristic, complemented
13#20298594C211yesmaximal, characteristic, complemented
14C2×#16813534C211yesmaximal, characteristic, complemented
15C2×#135×C113C211yesmaximal, characteristic, complemented
16C2×#14268648C2211yescharacteristic
17C2×#14268647—21no—
18C2×#14268647C2211yescharacteristic
19C2×#14268646—21no—
20C2×#14268646C2211yescharacteristic
21#41×D113—24no—
22#41×D113—24no—
23C2×Q8×D113C2211yescharacteristic
24C2×D4×D113—21no—
25C2×D4×D113C2211yescharacteristic
26C22×C4×D113—21no—
27C22×C4×D113C2211yescharacteristic
28#16813642—24no—
29C2×#14268637C2211yescharacteristic, complemented
30C2×#14268635C2211yescharacteristic, complemented
31C2×#14268634C2211yescharacteristic, complemented
32C2×#14268632C2211yescharacteristic, complemented
33C22×#11744751C2211yescharacteristic, complemented
34#16813603—21no—
35#16813598C2211yescharacteristic
36#16813598C2211yescharacteristic, complemented
37#16813593C2211yescharacteristic
38#16813593C2211yescharacteristic, complemented
39#16813590—21no—
40C4×C22⋊D113—21no—
41C4×C22⋊D113—21no—
42#16813581C2211yescharacteristic, complemented
43#16813547C2211yescharacteristic, complemented
44#16813547C2211yescharacteristic, complemented
45#16813546C2211yescharacteristic, complemented
46#16813546C2211yescharacteristic, complemented
47#16813544C2211yescharacteristic, complemented
48#16813544C2211yescharacteristic, complemented
49#16813543C2211yescharacteristic, complemented
50#16813543C2211yescharacteristic, complemented
51#16813534C2211yescharacteristic
52#16813534C2211yescharacteristic
53#16813534C2211yescharacteristic, complemented
54#16813534C2211yescharacteristic, complemented
55C2×#41×C113C2211yescharacteristic
56C2×#41×C113C2211yescharacteristic, complemented
57#135×C113—24no—
58C2×Q16×C113C2211yescharacteristic, complemented
59C2×SD16×C113C2211yescharacteristic, complemented
60C2×SD16×C113C2211yescharacteristic, complemented
61C2×D8×C113C2211yescharacteristic, complemented
62C22×C8×C113C2211yescharacteristic, complemented
63C23×D113—21no—
64C23×D113D411yescharacteristic
65#14268648—22no—
66#14268648—22no—
67#14268647—28no—
68#14268647—22no—
69#14268647D414yescomplemented
70#14268646—28no—
71#14268646—22no—
72#14268646—22no—
73C2×Dic226—21no—
74C2×Dic226C2311yescharacteristic
75Q8×D113—22no—
76Q8×D113—22no—
77C2×D452—21no—
78C2×D452C2311yescharacteristic
79C2×C22⋊D113—21no—
80C2×C22⋊D113—21no—
81C2×C22⋊D113—21no—
82C2×C22⋊D113—21no—
83C2×C22⋊D113—21no—
84D4×D113—28no—
85D4×D113—22no—
86D4×D113—22no—
87C22×Dic113—21no—
88C22×Dic113D411yescharacteristic
89C2×C4×D113—28no—
90C2×C4×D113—21no—
91C2×C4×D113—21no—
92C2×C4×D113—22no—
93C2×C4×D113—22no—
94C2×C4×D113—21no—
95C2×C4×D113D411yescharacteristic
96C2×C4×D113D411yescharacteristic
97C2×C4×D113C2311yescharacteristic
98C2×C4×D113C2311yescharacteristic
99#14268637—22no—
100#14268635—22no—
101#14268634—22no—
102#14268632—22no—
103C2×#11744751—22no—
104C2×#11744751C2311yescharacteristic
105C2×#11744751C2311yescharacteristic
106C4⋊Dic113C2311yescharacteristic
107C4⋊Dic113C2311yescharacteristic
108#14268626—21no—
109#14268626—21no—
110C22⋊Dic113—21no—
111C22⋊Dic113—21no—
112C22⋊Dic113—21no—
113#14268624—21no—
114#14268624—21no—
115C4×Dic113—21no—
116#41×C113—22no—
117#41×C113—22no—
118#41×C113—22no—
119#41×C113D414yescomplemented
120C2×Q8×C113C2311yescharacteristic
121C2×Q8×C113C2311yescharacteristic
122C2×D4×C113—21no—
123C2×D4×C113—21no—
124C2×D4×C113C2311yescharacteristic
125C2×D4×C113C2311yescharacteristic
126C22×C4×C113—21no—
127C22×C4×C113—21no—
128C22×C4×C113C2311yescharacteristic
129Q16×C113—22no—
130SD16×C113—22no—
131SD16×C113—22no—
132D8×C113—22no—
133C2×C8×C113—22no—
134C2×C8×C113C2311yescharacteristic
135C2×C8×C113C2311yescharacteristic
136C23×C113—21no—
137C23×C113—21no—
138C23×C113C2×D411yescharacteristic
139C22×D113—24no—
140C22×D113—22no—
141C22×D113—21no—
142C22×D113—22no—
143C22×D113—41no—
144C22×D113—42no—
145C22×D113—42no—
146C22×D113C2×D411yescharacteristic
147C22×D113C2×D411yescharacteristic
148Q8×C113—21no—
149Q8×C113—21no—
150Q8×C113—21no—
151Q8×C113C2×D412yes—
152D4×C113—24no—
153D4×C113—21no—
154D4×C113—21no—
155D4×C113—21no—
156D4×C113—42no—
157D4×C113C2×D412yes—
158C2×C4×C113—21no—
159C2×C4×C113—24no—
160C2×C4×C113—21no—
161C2×C4×C113—42no—
162C2×C4×C113C2×D412yes—
163C2×C4×C113C2×D411yescharacteristic
164C2×C4×C113C2×D412yes—
165C2×C4×C113C2411yescharacteristic
166C22⋊D113—24no—
167C22⋊D113—24no—
168C22⋊D113—24no—
169C22⋊D113—42no—
170C22⋊D113—42no—
171C2×Dic113—24no—
172C2×Dic113—22no—
173C2×Dic113—21no—
174C2×Dic113—21no—
175C2×Dic113—21no—
176C2×Dic113C2×D411yescharacteristic
177C2×Dic113C2×D411yescharacteristic
178D452—24no—
179D452—21no—
180D452C2×D412yes—
181C4×D113—24no—
182C4×D113—24no—
183C4×D113—22no—
184C4×D113—24no—
185C4×D113—22no—
186C4×D113—21no—
187C4×D113—21no—
188C4×D113—21no—
189C4×D113—21no—
190Dic226—24no—
191Dic226—21no—
192Dic226C2×D412yes—
193C8×C113—21no—
194C8×C113—21no—
195#11744751—21no—
196#11744751—21no—
197C22×C113—21no—
198C22×C113—21no—
199C22×C113—22no—
200C22×C113—41no—
201C22×C113—41no—
202C22×C113—41no—
203C22×C113—41no—
204C22×C113—41no—
205C22×C113#12012yes—
206C22×C113C22×D411yescharacteristic
207C2×D113—21no—
208C2×D113—21no—
209C2×D113—21no—
210C2×D113—22no—
211C2×D113—21no—
212C2×D113—21no—
213C2×D113—44no—
214C2×D113—48no—
215C2×D113—41no—
216C2×D113—41no—
217C2×D113#13512yescomplemented
218C4×C113—22no—
219C4×C113—41no—
220C4×C113#12012yes—
221C4×C113C22×D411yescharacteristic
222C4×C113C22×D411yescharacteristic
223Dic113—21no—
224Dic113—22no—
225Dic113—21no—
226Dic113—41no—
227Dic113—41no—
228C2×C113—22no—
229C2×C113—42no—
230C2×C113—81no—
231C2×C113C2×#12011yescharacteristic
232C2×C113C2×#13511yescharacteristic
233C2×C113#57511yescharacteristic
234D113—22no—
235D113—41no—
236D113—42no—
237#3002—1131nomaximal, Sylow
238C113#300211yescharacteristic, complemented, Sylow
239C22×#41—1131no—
240C2×#135—1131no—
241C2×#135D11311yescharacteristic, complemented
242#525—1131no—
243#452—1131no—
244#452—1131no—
245#451—1131no—
246#450—1131no—
247#449—1131no—
248#449—1131no—
249#448—1131no—
250#447—1131no—
251#416—1131no—
252#416—1131no—
253C2×C22⋊C8—1131no—
254C2×#41—1131no—
255C2×#41—1131no—
256C2×#41—1131no—
257C2×#41—2261no—
258C2×#41—2261no—
259C2×#41—2264no—
260C2×#41—2264no—
261C2×#41C2×D11311yescharacteristic
262C2×#41C2×D11311yescharacteristic, complemented
263C22×Q8—1131no—
264C22×D4—1131no—
265C22×D4—2261no—
266C23×C4—1131no—
267C23×C4—2261no—
268#135—24no—
269#135—2264no—
270C2×Q16—1131no—
271C2×Q16C2×D11311yescharacteristic, complemented
272C2×SD16—1131no—
273C2×SD16—1131no—
274C2×SD16C2×D11311yescharacteristic, complemented
275C2×SD16C2×D11311yescharacteristic, complemented
276C2×D8—1131no—
277C2×D8C2×D11311yescharacteristic, complemented
278C22×C8—1131no—
279C22×C8C2×D11311yescharacteristic, complemented
280#123—2261no—
281C22⋊Q8—1131no—
282C22⋊Q8—1131no—
283#121—1131no—
284#121—1131no—
285#120—2261no—
286C4×D4—2261no—
287C4×D4—2261no—
288#117—1131no—
289#103—1131no—
290#103—1131no—
291#103—1131no—
292#103—1131no—
293#102—1131no—
294#102—1131no—
295#102—1131no—
296#102—1131no—
297C22⋊C8—1131no—
298C22⋊C8—1131no—
299C22⋊C8—1131no—
300C22⋊C8—1131no—
301C24—1131no—
302C24—2261no—
303#41—22no—
304#41—22no—
305#41—22no—
306#41—1134no—
307#41—2268no—
308#41—2262no—
309#41—2268no—
310#41—2262no—
311#41—2262no—
312#41—2262no—
313#41—2262no—
314#41C22⋊D11314yescomplemented
315C2×Q8—1131no—
316C2×Q8—2261no—
317C2×Q8—2262no—
318C2×Q8—2262no—
319C2×Q8C22×D11311yescharacteristic
320C2×Q8C22×D11311yescharacteristic
321C2×D4—21no—
322C2×D4—21no—
323C2×D4—1131no—
324C2×D4—2261no—
325C2×D4—2261no—
326C2×D4—2262no—
327C2×D4—2268no—
328C2×D4—2261no—
329C2×D4—2261no—
330C2×D4—2261no—
331C2×D4—2261no—
332C2×D4—2262no—
333C2×D4C22×D11311yescharacteristic
334C2×D4C22×D11311yescharacteristic
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—1131no—
338C22×C4—1131no—
339C22×C4—1131no—
340C22×C4—1131no—
341C22×C4—1131no—
342C22×C4—2261no—
343C22×C4—2261no—
344C22×C4—2268no—
345C22×C4—2261no—
346C22×C4—2262no—
347C22×C4—2261no—
348C22×C4—2262no—
349C22×C4C22×D11311yescharacteristic
350Q16—22no—
351Q16—2262no—
352SD16—22no—
353SD16—22no—
354SD16—2262no—
355SD16—2262no—
356D8—22no—
357D8—2262no—
358C2×C8—22no—
359C2×C8—1131no—
360C2×C8—1131no—
361C2×C8—2262no—
362C2×C8C22×D11311yescharacteristic
363C2×C8C22×D11311yescharacteristic
364C4⋊C4—1131no—
365C4⋊C4—1131no—
366C4⋊C4—2261no—
367C4⋊C4—2261no—
368C22⋊C4—2261no—
369C22⋊C4—2261no—
370C22⋊C4—2261no—
371C22⋊C4—2261no—
372C22⋊C4—2261no—
373C42—2261no—
374C23—21no—
375C23—21no—
376C23—1131no—
377C23—1131no—
378C23—4521no—
379C23—4522no—
380C23—4522no—
381C23—2262no—
382C23—2264no—
383C23—2262no—
384C23—2261no—
385C23D4×D11311yescharacteristic
386Q8—21no—
387Q8—21no—
388Q8—21no—
389Q8—1132no—
390Q8—2264no—
391Q8—2261no—
392Q8C2×C22⋊D11312yes—
393D4—24no—
394D4—21no—
395D4—21no—
396D4—21no—
397D4—42no—
398D4—1132no—
399D4—4522no—
400D4—4522no—
401D4—2264no—
402D4—2264no—
403D4—2264no—
404D4—2264no—
405D4—2261no—
406D4C2×C22⋊D11312yes—
407C2×C4—21no—
408C2×C4—24no—
409C2×C4—21no—
410C2×C4—42no—
411C2×C4—1131no—
412C2×C4—1131no—
413C2×C4—2264no—
414C2×C4—2264no—
415C2×C4—2261no—
416C2×C4—2261no—
417C2×C4—2264no—
418C2×C4—2262no—
419C2×C4—2261no—
420C2×C4—2262no—
421C2×C4—2262no—
422C2×C4—2264no—
423C2×C4—2261no—
424C2×C4—2261no—
425C2×C4—2261no—
426C2×C4—2261no—
427C2×C4D4×D11312yes—
428C2×C4D4×D11311yescharacteristic
429C2×C4C2×C22⋊D11312yes—
430C2×C4C23×D11311yescharacteristic
431C8—21no—
432C8—21no—
433C8—2261no—
434C8—2261no—
435C22—21no—
436C22—21no—
437C22—22no—
438C22—41no—
439C22—41no—
440C22—41no—
441C22—41no—
442C22—41no—
443C22—1132no—
444C22—4524no—
445C22—4528no—
446C22—4521no—
447C22—4521no—
448C22—2262no—
449C22—2261no—
450C22—2261no—
451C22—2261no—
452C22—2261no—
453C22—2261no—
454C22#1681359012yes—
455C22C2×D4×D11311yescharacteristic
456C4—22no—
457C4—41no—
458C4—4521no—
459C4—4521no—
460C4—2261no—
461C4—2261no—
462C4—2262no—
463C4#1681359012yes—
464C4C2×D4×D11311yescharacteristic
465C4C22×C22⋊D11311yescharacteristic
466C2—22no—
467C2—42no—
468C2—81no—
469C2—4522no—
470C2—4521no—
471C2—2262no—
472C2C2×#1681359011yescharacteristic
473C2#135×D11311yescharacteristic
474C2#2029939511yescharacteristic
subgroupG/H
centerC2×C4D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC2×#135×C113C2
socleC22×C113C22×D4
hypercenterC2×#135D113
hypocenterC113#3002
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×#41×D113C2semidirect
2. C2×#16813642C2semidirect
3. #20299105C2semidirect
4. #20298759C2semidirect
5. #20298757C2semidirect
6. #20298752C2semidirect
7. #20298747C2semidirect
8. #20298742C2semidirect
9. #20298740C2semidirect
10. #20298735C2semidirect
11. #20298730C2semidirect
12. #20298595C2semidirect
13. #20298594C2semidirect
14. C2×#16813534C2semidirect
15. C2×#135×C113C2semidirect
29. C2×#14268637C22semidirect
30. C2×#14268635C22semidirect
31. C2×#14268634C22semidirect
32. C2×#14268632C22semidirect
33. C22×#11744751C22semidirect
36. #16813598C22semidirect
38. #16813593C22semidirect
42. #16813581C22semidirect
43. #16813547C22semidirect
44. #16813547C22semidirect
45. #16813546C22semidirect
46. #16813546C22semidirect
47. #16813544C22semidirect
48. #16813544C22semidirect
49. #16813543C22semidirect
50. #16813543C22semidirect
53. #16813534C22semidirect
54. #16813534C22semidirect
56. C2×#41×C113C22semidirect
58. C2×Q16×C113C22semidirect
59. C2×SD16×C113C22semidirect
60. C2×SD16×C113C22semidirect
61. C2×D8×C113C22semidirect
62. C22×C8×C113C22semidirect
69. #14268647D4semidirect
119. #41×C113D4semidirect
217. C2×D113#135semidirect
238. C113#3002semidirect
241. C2×#135D113semidirect
262. C2×#41C2×D113semidirect
271. C2×Q16C2×D113semidirect
274. C2×SD16C2×D113semidirect
275. C2×SD16C2×D113semidirect
277. C2×D8C2×D113semidirect
279. C22×C8C2×D113semidirect
314. #41C22⋊D113semidirect

Maximal subgroups

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

subgroupindex
C2×#41×D1132
C2×#168136422
#202991052
#202987592
#202987572
#202987522
#202987472
#202987422
#202987402
#202987352
#202987302
#202985952
#202985942
C2×#168135342
C2×#135×C1132
#3002113