Finite Group Databasebeta

← #28402085

Subgroups — #28402085

Order 14464.

494 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16813653C211yesmaximal, characteristic, complemented
2C22×#14268634C211yesmaximal, characteristic, complemented
3#20299244C211yesmaximal, characteristic
4#20298990C211yesmaximal, characteristic, complemented
5#20298846C211yesmaximal, characteristic, complemented
6#20298837C211yesmaximal, characteristic, complemented
7#20298820C211yesmaximal, characteristic, complemented
8#20298800C211yesmaximal, characteristic, complemented
9#20298758C211yesmaximal, characteristic, complemented
10#20298754C211yesmaximal, characteristic, complemented
11#20298748C211yesmaximal, characteristic, complemented
12#20298737C211yesmaximal, characteristic, complemented
13#20298696C211yesmaximal, characteristic, complemented
14#20298670C211yesmaximal, characteristic, complemented
15D4×Q8×C113C211yesmaximal, characteristic, complemented
16C2×#14268647C2211yescharacteristic
17C22×D452C2211yescharacteristic
18#16813653—24no—
19C2×#14268637C2211yescharacteristic, complemented
20C2×#14268637C2211yescharacteristic, complemented
21C2×#14268637C2211yescharacteristic, complemented
22C2×#14268634—24no—
23C2×#14268634C2211yescharacteristic
24C2×#14268634C2211yescharacteristic
25C2×#14268634C2211yescharacteristic
26C2×#14268634C2211yescharacteristic
27C2×#14268634C2211yescharacteristic
28C2×#14268634C2211yescharacteristic
29C2×#14268631C2211yescharacteristic, complemented
30C22×#11744751C2211yescharacteristic
31#16813610C2211yescharacteristic
32#16813607—21no—
33#16813601C2211yescharacteristic
34#16813596C2211yescharacteristic
35#16813595—21no—
36#16813590—21no—
37C4×D452C2211yescharacteristic
38C22⋊C4×D113—21no—
39#16813555C2211yescharacteristic, complemented
40C4⋊#11744751C2211yescharacteristic, complemented
41#16813546C2211yescharacteristic, complemented
42#16813546C2211yescharacteristic, complemented
43#16813546C2211yescharacteristic, complemented
44#16813545C2211yescharacteristic, complemented
45#16813542C2211yescharacteristic
46#16813542C2211yescharacteristic
47C22⋊#11744751C2211yescharacteristic
48C22⋊#11744751C2211yescharacteristic, complemented
49#16813533C2211yescharacteristic, complemented
50C22×Q8×C113C2211yescharacteristic
51C22×Q8×C113C2211yescharacteristic, complemented
52C4⋊Q8×C113—21no—
53C4⋊Q8×C113C2211yescharacteristic, complemented
54C22⋊Q8×C113—21no—
55C22⋊Q8×C113—21no—
56C22⋊Q8×C113C2211yescharacteristic
57C22⋊Q8×C113C2211yescharacteristic, complemented
58C4×Q8×C113C2211yescharacteristic, complemented
59C4×D4×C113—21no—
60C4×D4×C113C2211yescharacteristic
61C23×D113—21no—
62#14268647—22no—
63#14268647—41no—
64C2×Dic226C2311yescharacteristic
65C2×D452—22no—
66C2×D452—21no—
67C2×D452—41no—
68C2×D452C2311yescharacteristic
69C2×D452C2311yescharacteristic
70C2×C22⋊D113—21no—
71C2×C22⋊D113—21no—
72C2×C4×D113—21no—
73C2×C4×D113—21no—
74#14268637—22no—
75#14268637—22no—
76#14268637—41no—
77#14268634—22no—
78#14268634—22no—
79#14268634—22no—
80#14268634—22no—
81#14268634—41no—
82#14268634D414yescomplemented
83#14268631—22no—
84C2×#11744751—22no—
85C2×#11744751C2311yescharacteristic
86C2×#11744751C2311yescharacteristic
87C2×#11744751C2311yescharacteristic
88C2×#11744751C2311yescharacteristic
89C4⋊Dic113C2311yescharacteristic
90#14268626—21no—
91C22⋊Dic113—21no—
92#14268624—21no—
93#14268624—21no—
94#14268624—21no—
95#14268624—21no—
96C2×Q8×C113—21no—
97C2×Q8×C113—21no—
98C2×Q8×C113—22no—
99C2×Q8×C113—22no—
100C2×Q8×C113—41no—
101C2×Q8×C113—41no—
102C2×Q8×C113C2311yescharacteristic
103C2×Q8×C113C2311yescharacteristic
104C2×Q8×C113C2311yescharacteristic
105C2×D4×C113D411yescharacteristic
106C22×C4×C113—21no—
107C22×C4×C113—21no—
108C22×C4×C113C2311yescharacteristic
109C22×C4×C113C2311yescharacteristic
110C4⋊C4×C113—21no—
111C4⋊C4×C113—21no—
112C4⋊C4×C113—21no—
113C4⋊C4×C113—21no—
114C4⋊C4×C113—21no—
115C4⋊C4×C113D411yescharacteristic
116C4⋊C4×C113C2311yescharacteristic
117C22⋊C4×C113—21no—
118C22⋊C4×C113—21no—
119C22⋊C4×C113D411yescharacteristic
120C22⋊C4×C113D411yescharacteristic
121C42×C113—21no—
122C42×C113C2311yescharacteristic
123C23×C113C2×D411yescharacteristic
124C23×C113C2×D411yescharacteristic
125C22×D113—21no—
126C22×D113—21no—
127C22×D113—42no—
128C22×D113—42no—
129C22×D113—81no—
130Q8×C113—21no—
131Q8×C113—21no—
132Q8×C113—21no—
133Q8×C113—21no—
134Q8×C113—21no—
135Q8×C113—42no—
136Q8×C113—42no—
137Q8×C113C2×D412yes—
138D4×C113—22no—
139C2×C4×C113—21no—
140C2×C4×C113—21no—
141C2×C4×C113—21no—
142C2×C4×C113—21no—
143C2×C4×C113—21no—
144C2×C4×C113—21no—
145C2×C4×C113—21no—
146C2×C4×C113—21no—
147C2×C4×C113—42no—
148C2×C4×C113—42no—
149C2×C4×C113C2×D411yescharacteristic
150C2×C4×C113C2×D411yescharacteristic
151C2×C4×C113C2×D411yescharacteristic
152C2×C4×C113C2×D411yescharacteristic
153C2×C4×C113C2411yescharacteristic
154C22⋊D113—42no—
155C22⋊D113—81no—
156C2×Dic113—21no—
157C2×Dic113—21no—
158D452—21no—
159D452—21no—
160D452—21no—
161D452—42no—
162D452C2×D412yes—
163C4×D113—42no—
164C4×D113—81no—
165Dic226—21no—
166Dic226—21no—
167#11744751—21no—
168#11744751—21no—
169#11744751—21no—
170#11744751C2×D412yes—
171C22×C113—21no—
172C22×C113—21no—
173C22×C113—21no—
174C22×C113—21no—
175C22×C113—21no—
176C22×C113#13712yescomplemented
177C22×C113C22×D411yescharacteristic
178C2×D113—22no—
179C2×D113—41no—
180C2×D113—41no—
181C2×D113—41no—
182C2×D113—41no—
183C2×D113—41no—
184C2×D113—84no—
185C4×C113—21no—
186C4×C113—21no—
187C4×C113—22no—
188C4×C113—21no—
189C4×C113—21no—
190C4×C113—41no—
191C4×C113—41no—
192C4×C113—41no—
193C4×C113C22×D411yescharacteristic
194C4×C113H(5,𝔽2)11yescharacteristic
195Dic113—41no—
196Dic113—41no—
197C2×C113—22no—
198C2×C113—41no—
199C2×C113D4211yescharacteristic
200C2×C113C2×#13711yescharacteristic
201C2×C113#57711yescharacteristic
202D113—42no—
203D113—81no—
204#3266—1131nomaximal, Sylow
205C113#326611yescharacteristic, complemented, Sylow
206C2×#137—1131no—
207C22×SD16—1131no—
208D4×Q8D11311yescharacteristic, complemented
209#546—1131no—
210#497—1131no—
211#468—1131no—
212#467—1131no—
213#464—1131no—
214#461—1131no—
215#452—1131no—
216#451—1131no—
217#450—1131no—
218#448—1131no—
219#440—1131no—
220#435—1131no—
221C2×#41—1131no—
222C22×Q8C2×D11311yescharacteristic
223C22×Q8C2×D11311yescharacteristic, complemented
224C22×D4—1131no—
225#137—2264no—
226C2×Q16—1131no—
227C2×Q16—1131no—
228C2×Q16—1131no—
229C2×SD16—1131no—
230C2×SD16—1131no—
231C2×SD16—1131no—
232C2×SD16—1131no—
233C2×SD16—1131no—
234C2×SD16—1131no—
235C2×SD16—2264no—
236C2×M16—1131no—
237C22×C8—1131no—
238C4⋊Q8—21no—
239C4⋊Q8C2×D11311yescharacteristic, complemented
240#124—1131no—
241#123—2261no—
242C22⋊Q8—21no—
243C22⋊Q8—21no—
244C22⋊Q8—1131no—
245C22⋊Q8C2×D11311yescharacteristic
246C22⋊Q8C2×D11311yescharacteristic, complemented
247#121—1131no—
248#121—2261no—
249#120—2261no—
250C4×Q8C2×D11311yescharacteristic, complemented
251C4×D4—21no—
252C4×D4—1131no—
253C4×D4C2×D11311yescharacteristic
254C2×C22⋊C4—2261no—
255#107—1131no—
256C4⋊C8—1131no—
257#103—1131no—
258#103—1131no—
259#103—1131no—
260#103—1131no—
261#102—1131no—
262#102—1131no—
263C22⋊C8—1131no—
264C22⋊C8—1131no—
265#97—1131no—
266C24—2261no—
267#41—4521no—
268#41—2262no—
269C2×Q8—21no—
270C2×Q8—21no—
271C2×Q8—22no—
272C2×Q8—22no—
273C2×Q8—41no—
274C2×Q8—41no—
275C2×Q8—1131no—
276C2×Q8C22×D11311yescharacteristic
277C2×Q8C22×D11311yescharacteristic
278C2×Q8C22×D11311yescharacteristic
279C2×D4—1131no—
280C2×D4—1131no—
281C2×D4—4521no—
282C2×D4—2262no—
283C2×D4—2261no—
284C2×D4—2261no—
285C2×D4—2261no—
286C2×D4C22⋊D11311yescharacteristic
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—2261no—
290C22×C4—2261no—
291C22×C4C22×D11311yescharacteristic
292C22×C4C22×D11311yescharacteristic
293Q16—4521no—
294Q16—2262no—
295Q16—2262no—
296SD16—1134no—
297SD16—4521no—
298SD16—2262no—
299SD16—2262no—
300SD16—2262no—
301SD16—2262no—
302M16—2262no—
303C2×C8—1131no—
304C2×C8—1131no—
305C2×C8—1131no—
306C2×C8—1131no—
307C2×C8—2262no—
308C4⋊C4—21no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—1131no—
314C4⋊C4—2261no—
315C4⋊C4C22⋊D11311yescharacteristic
316C4⋊C4C22×D11311yescharacteristic
317C22⋊C4—21no—
318C22⋊C4—21no—
319C22⋊C4—2261no—
320C22⋊C4—2261no—
321C22⋊C4—2261no—
322C22⋊C4—2261no—
323C22⋊C4—2261no—
324C22⋊C4C22⋊D11311yescharacteristic
325C22⋊C4C22⋊D11311yescharacteristic
326C42—21no—
327C42C22×D11311yescharacteristic
328C23—9041no—
329C23—4522no—
330C23—4522no—
331C23—2261no—
332C23—2261no—
333C23C2×C22⋊D11311yescharacteristic
334C23C2×C22⋊D11311yescharacteristic
335Q8—21no—
336Q8—21no—
337Q8—21no—
338Q8—21no—
339Q8—21no—
340Q8—42no—
341Q8—42no—
342Q8—2261no—
343Q8—2261no—
344Q8D4×D11312yes—
345D4—22no—
346D4—1132no—
347D4—9041no—
348D4—4522no—
349D4—4522no—
350D4—2261no—
351D4—2261no—
352D4—2261no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—9041no—
364C2×C4—4522no—
365C2×C4—2261no—
366C2×C4—2261no—
367C2×C4C2×C22⋊D11311yescharacteristic
368C2×C4C2×C22⋊D11311yescharacteristic
369C2×C4C2×C22⋊D11311yescharacteristic
370C2×C4C2×C22⋊D11311yescharacteristic
371C2×C4C23×D11311yescharacteristic
372C8—1132no—
373C8—2261no—
374C8—2261no—
375C8—2261no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—9044no—
382C22—4521no—
383C22—4521no—
384C22—4521no—
385C22—4521no—
386C22—4521no—
387C22—2262no—
388C22#1681365312yescomplemented
389C22C22×C22⋊D11311yescharacteristic
390C4—21no—
391C4—21no—
392C4—21no—
393C4—21no—
394C4—22no—
395C4—41no—
396C4—41no—
397C4—41no—
398C4—4521no—
399C4—4521no—
400C4C2×D4×D11311yescharacteristic
401C4#1681366711yescharacteristic
402C2—22no—
403C2—41no—
404C2—9041no—
405C2—4522no—
406C2D4×C22⋊D11311yescharacteristic
407C2C2×#1681365311yescharacteristic
408C2#2029940611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingD4×Q8×C113C2
socleC22×C113C22×D4
prime radical#20299244C2
hypercenterD4×Q8D113
hypocenterC113#3266
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C4×D4 ◁ D4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#16813653C2semidirect
2. C22×#14268634C2semidirect
4. #20298990C2semidirect
5. #20298846C2semidirect
6. #20298837C2semidirect
7. #20298820C2semidirect
8. #20298800C2semidirect
9. #20298758C2semidirect
10. #20298754C2semidirect
11. #20298748C2semidirect
12. #20298737C2semidirect
13. #20298696C2semidirect
14. #20298670C2semidirect
15. D4×Q8×C113C2semidirect
19. C2×#14268637C22semidirect
20. C2×#14268637C22semidirect
21. C2×#14268637C22semidirect
29. C2×#14268631C22semidirect
39. #16813555C22semidirect
40. C4⋊#11744751C22semidirect
41. #16813546C22semidirect
42. #16813546C22semidirect
43. #16813546C22semidirect
44. #16813545C22semidirect
48. C22⋊#11744751C22semidirect
49. #16813533C22semidirect
51. C22×Q8×C113C22semidirect
53. C4⋊Q8×C113C22semidirect
57. C22⋊Q8×C113C22semidirect
58. C4×Q8×C113C22semidirect
82. #14268634D4semidirect
176. C22×C113#137semidirect
205. C113#3266semidirect
208. D4×Q8D113semidirect
223. C22×Q8C2×D113semidirect
239. C4⋊Q8C2×D113semidirect
246. C22⋊Q8C2×D113semidirect
250. C4×Q8C2×D113semidirect
388. C22#16813653semidirect

Maximal subgroups

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

subgroupindex
C2×#168136532
C22×#142686342
#202992442
#202989902
#202988462
#202988372
#202988202
#202988002
#202987582
#202987542
#202987482
#202987372
#202986962
#202986702
D4×Q8×C1132
#3266113