Finite Group Databasebeta

← #28402119

Subgroups — #28402119

Order 14464.

510 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16813650C211yesmaximal, characteristic, complemented
2C2×#16813644C211yesmaximal, characteristic, complemented
3#20299269C211yesmaximal, characteristic, complemented
4#20299244C211yesmaximal, characteristic, complemented
5#20298987C211yesmaximal, characteristic, complemented
6#20298844C211yesmaximal, characteristic, complemented
7#20298834C211yesmaximal, characteristic, complemented
8#20298821C211yesmaximal, characteristic, complemented
9#20298794C211yesmaximal, characteristic, complemented
10#20298762C211yesmaximal, characteristic, complemented
11#20298745C211yesmaximal, characteristic, complemented
12#20298745C211yesmaximal, characteristic, complemented
13#20298734C211yesmaximal, characteristic, complemented
14#20298700C211yesmaximal, characteristic, complemented
15#435×C113C211yesmaximal, characteristic, complemented
16C2×#14268647C2211yescharacteristic
17C2×#14268647C2211yescharacteristic
18C2×#14268647C2211yescharacteristic, complemented
19C22×D452C2211yescharacteristic
20#16813650—24no—
21#16813644—24no—
22C2×Dic452C2211yescharacteristic, complemented
23C2×#14268636C2211yescharacteristic
24C2×#14268636C2211yescharacteristic
25C2×#14268636C2211yescharacteristic, complemented
26C2×#14268636C2211yescharacteristic, complemented
27C2×D904C2211yescharacteristic
28C2×D904C2211yescharacteristic
29C2×D904C2211yescharacteristic
30C2×D904C2211yescharacteristic
31#16813619C2211yescharacteristic, complemented
32#16813618—21no—
33#16813610C2211yescharacteristic
34#16813607—21no—
35#16813601C2211yescharacteristic
36#16813596C2211yescharacteristic
37#16813596C2211yescharacteristic
38#16813596C2211yescharacteristic, complemented
39#16813595—21no—
40#16813595—21no—
41#16813595—21no—
42#16813590—21no—
43C4×Dic226C2211yescharacteristic, complemented
44C4×D452C2211yescharacteristic
45#16813584—21no—
46C22⋊C4×D113—21no—
47#16813556C2211yescharacteristic, complemented
48#16813547C2211yescharacteristic, complemented
49#16813547C2211yescharacteristic, complemented
50#16813544C2211yescharacteristic
51#16813544C2211yescharacteristic
52#16813544C2211yescharacteristic, complemented
53#16813544C2211yescharacteristic, complemented
54C2×M16×C113C2211yescharacteristic
55C22×C8×C113C2211yescharacteristic, complemented
56C4×D4×C113C2211yescharacteristic
57C4⋊C8×C113C2211yescharacteristic, complemented
58C22⋊C8×C113C2211yescharacteristic
59C22⋊C8×C113C2211yescharacteristic, complemented
60#97×C113C2211yescharacteristic, complemented
61C23×D113—21no—
62#14268647—22no—
63#14268647—22no—
64#14268647—22no—
65#14268647—41no—
66#14268647—41no—
67#14268647—41no—
68C2×Dic226C2311yescharacteristic
69C2×Dic226C2311yescharacteristic
70C2×D452—22no—
71C2×D452—21no—
72C2×D452—21no—
73C2×D452—21no—
74C2×D452—41no—
75C2×D452C2311yescharacteristic
76C2×D452C2311yescharacteristic
77C2×D452C2311yescharacteristic
78C2×D452C2311yescharacteristic
79C2×C22⋊D113—21no—
80C2×C22⋊D113—21no—
81C2×C22⋊D113—21no—
82C2×C22⋊D113—21no—
83C2×C22⋊D113—21no—
84C2×C22⋊D113—21no—
85C2×C4×D113—21no—
86C2×C4×D113—21no—
87C2×C4×D113—21no—
88C2×C4×D113—21no—
89Dic452—22no—
90#14268636—22no—
91#14268636—22no—
92#14268636—41no—
93#14268636D414yescomplemented
94D904—22no—
95D904—22no—
96D904—22no—
97D904—41no—
98C4⋊Dic113C2311yescharacteristic
99C4⋊Dic113C2311yescharacteristic
100#14268626—21no—
101#14268626—21no—
102C22⋊Dic113—21no—
103#14268624—21no—
104#14268624—21no—
105#14268624—21no—
106#14268624—21no—
107#14268624—21no—
108#14268624—21no—
109C4×Dic113—21no—
110C2×D4×C113D411yescharacteristic
111C22×C4×C113C2311yescharacteristic
112C22×C4×C113C2311yescharacteristic
113M16×C113—22no—
114C2×C8×C113—22no—
115C2×C8×C113C2311yescharacteristic
116C2×C8×C113C2311yescharacteristic
117C2×C8×C113C2311yescharacteristic
118C2×C8×C113C2311yescharacteristic
119C4⋊C4×C113D411yescharacteristic
120C22⋊C4×C113D411yescharacteristic
121C22⋊C4×C113D411yescharacteristic
122C42×C113C2311yescharacteristic
123C23×C113C2×D411yescharacteristic
124C23×C113C2×D411yescharacteristic
125C22×D113—21no—
126C22×D113—21no—
127C22×D113—21no—
128C22×D113—21no—
129C22×D113—42no—
130C22×D113—42no—
131C22×D113—81no—
132D4×C113—41no—
133C2×C4×C113—21no—
134C2×C4×C113—21no—
135C2×C4×C113—21no—
136C2×C4×C113—21no—
137C2×C4×C113C2×D411yescharacteristic
138C2×C4×C113C2×D411yescharacteristic
139C2×C4×C113C2×D411yescharacteristic
140C2×C4×C113C2×D411yescharacteristic
141C2×C4×C113C2411yescharacteristic
142C22⋊D113—42no—
143C22⋊D113—42no—
144C22⋊D113—42no—
145C22⋊D113—81no—
146C22⋊D113—81no—
147C22⋊D113—81no—
148C2×Dic113—21no—
149C2×Dic113—21no—
150C2×Dic113—21no—
151C2×Dic113—21no—
152D452—21no—
153D452—21no—
154D452—21no—
155D452—21no—
156D452—21no—
157D452—21no—
158D452—21no—
159D452—42no—
160D452—42no—
161D452—81no—
162D452C2×D412yes—
163C4×D113—42no—
164C4×D113—42no—
165C4×D113—42no—
166C4×D113—81no—
167Dic226—21no—
168Dic226—21no—
169Dic226—21no—
170Dic226C2×D412yes—
171C8×C113—21no—
172C8×C113—21no—
173C8×C113—21no—
174C8×C113C2×D412yes—
175C22×C113—21no—
176C22×C113—21no—
177C22×C113—21no—
178C22×C113—21no—
179C22×C113—21no—
180C22×C113—21no—
181C22×C113C22×D411yescharacteristic
182C2×D113—22no—
183C2×D113—41no—
184C2×D113—41no—
185C2×D113—41no—
186C2×D113—41no—
187C2×D113—41no—
188C2×D113—41no—
189C2×D113—41no—
190C2×D113—41no—
191C2×D113—41no—
192C2×D113—41no—
193C2×D113—41no—
194C2×D113—84no—
195C4×C113—21no—
196C4×C113—21no—
197C4×C113—21no—
198C4×C113—21no—
199C4×C113C22×D411yescharacteristic
200C4×C113H(5,𝔽2)11yescharacteristic
201Dic113—22no—
202Dic113—41no—
203Dic113—41no—
204Dic113—41no—
205C2×C113—41no—
206C2×C113—41no—
207C2×C113D4211yescharacteristic
208C2×C113#57511yescharacteristic
209C2×C113#57611yescharacteristic
210D113—42no—
211D113—81no—
212D113—81no—
213D113—81no—
214#3268—1131nomaximal, Sylow
215C113#326811yescharacteristic, complemented, Sylow
216C2×AGL(1,ℤ/8)—1131no—
217C2×#135—1131no—
218#550—1131no—
219#546—1131no—
220#496—1131no—
221#468—1131no—
222#466—1131no—
223#464—1131no—
224#459—1131no—
225#452—1131no—
226#449—1131no—
227#449—1131no—
228#447—1131no—
229#440—1131no—
230#435D11311yescharacteristic, complemented
231C2×#41—1131no—
232C2×#41—1131no—
233C2×#41—1131no—
234C22×D4—1131no—
235AGL(1,ℤ/8)—2264no—
236#135—2264no—
237C2×Q16—1131no—
238C2×SD16—1131no—
239C2×SD16—1131no—
240C2×SD16—1131no—
241C2×SD16—1131no—
242C2×D8—1131no—
243C2×D8—1131no—
244C2×D8—1131no—
245C2×D8—1131no—
246C2×M16C2×D11311yescharacteristic
247C22×C8C2×D11311yescharacteristic, complemented
248#127—1131no—
249#127—2261no—
250#124—1131no—
251#123—2261no—
252C22⋊Q8—1131no—
253#121—1131no—
254#121—1131no—
255#121—1131no—
256#121—2261no—
257#121—2261no—
258#121—2261no—
259#120—2261no—
260C4×Q8—1131no—
261C4×D4—1131no—
262C4×D4—2261no—
263C4×D4C2×D11311yescharacteristic
264C2×C22⋊C4—2261no—
265#107—1131no—
266C4⋊C8C2×D11311yescharacteristic, complemented
267#103—1131no—
268#103—1131no—
269#102—1131no—
270#102—1131no—
271#102—1131no—
272#102—1131no—
273C22⋊C8C2×D11311yescharacteristic
274C22⋊C8C2×D11311yescharacteristic, complemented
275#97C2×D11311yescharacteristic, complemented
276C24—2261no—
277#41—4521no—
278#41—4521no—
279#41—4521no—
280#41—2262no—
281#41—2262no—
282#41—2262no—
283C2×Q8—1131no—
284C2×Q8—1131no—
285C2×D4—1131no—
286C2×D4—1131no—
287C2×D4—1131no—
288C2×D4—1131no—
289C2×D4—4521no—
290C2×D4—2262no—
291C2×D4—2261no—
292C2×D4—2261no—
293C2×D4—2261no—
294C2×D4—2261no—
295C2×D4—2261no—
296C2×D4—2261no—
297C2×D4—2261no—
298C2×D4—2261no—
299C2×D4—2261no—
300C2×D4D45211yescharacteristic
301C22×C4—2261no—
302C22×C4—2261no—
303C22×C4—2261no—
304C22×C4—2261no—
305C22×C4C22×D11311yescharacteristic
306C22×C4C22×D11311yescharacteristic
307Q16—2262no—
308SD16—1134no—
309SD16—4521no—
310SD16—2262no—
311SD16—2262no—
312D8—4521no—
313D8—2262no—
314D8—2262no—
315D8—2262no—
316M16—22no—
317C2×C8—22no—
318C2×C8C22×D11311yescharacteristic
319C2×C8C22×D11311yescharacteristic
320C2×C8C22×D11311yescharacteristic
321C2×C8C22×D11311yescharacteristic
322C4⋊C4—1131no—
323C4⋊C4—1131no—
324C4⋊C4—2261no—
325C4⋊C4—2261no—
326C4⋊C4D45211yescharacteristic
327C22⋊C4—2261no—
328C22⋊C4—2261no—
329C22⋊C4—2261no—
330C22⋊C4—2261no—
331C22⋊C4—2261no—
332C22⋊C4—2261no—
333C22⋊C4—2261no—
334C22⋊C4D45211yescharacteristic
335C22⋊C4D45211yescharacteristic
336C42—2261no—
337C42C22×D11311yescharacteristic
338C23—9041no—
339C23—4522no—
340C23—4522no—
341C23—2261no—
342C23—2261no—
343C23—2261no—
344C23—2261no—
345C23C2×D45211yescharacteristic
346C23C2×D45211yescharacteristic
347Q8—1132no—
348Q8—2261no—
349Q8—2261no—
350Q8—2261no—
351D4—41no—
352D4—1132no—
353D4—9041no—
354D4—9041no—
355D4—9041no—
356D4—9041no—
357D4—4522no—
358D4—4522no—
359D4—4522no—
360D4—4522no—
361D4—4522no—
362D4—2261no—
363D4—2261no—
364D4—2261no—
365D4—2261no—
366D4—2261no—
367D4—2261no—
368D4—2261no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—9041no—
374C2×C4—4522no—
375C2×C4—4522no—
376C2×C4—4522no—
377C2×C4—2261no—
378C2×C4—2261no—
379C2×C4—2261no—
380C2×C4—2261no—
381C2×C4C2×D45211yescharacteristic
382C2×C4C2×D45211yescharacteristic
383C2×C4C2×D45211yescharacteristic
384C2×C4C2×D45211yescharacteristic
385C2×C4C23×D11311yescharacteristic
386C8—21no—
387C8—21no—
388C8—21no—
389C8D4×D11312yes—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—9044no—
397C22—4521no—
398C22—4521no—
399C22—4521no—
400C22—4521no—
401C22—4521no—
402C22—4521no—
403C22—4521no—
404C22—4521no—
405C22—4521no—
406C22—4521no—
407C22—4521no—
408C22—2262no—
409C22C22×D45211yescharacteristic
410C4—21no—
411C4—21no—
412C4—21no—
413C4—21no—
414C4—4521no—
415C4—4521no—
416C4—4521no—
417C4—2262no—
418C4C2×D4×D11311yescharacteristic
419C4#1681366811yescharacteristic
420C2—41no—
421C2—41no—
422C2—9041no—
423C2—9041no—
424C2—9041no—
425C2—4522no—
426C2D4×D45211yescharacteristic
427C2#2029939811yescharacteristic
428C2#2029940311yescharacteristic
subgroupG/H
centerC22C22×D452
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#435×C113C2
socleC22×C113C22×D4
hypercenter#435D113
hypocenterC113#3268
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. C2×#16813650C2semidirect
2. C2×#16813644C2semidirect
3. #20299269C2semidirect
4. #20299244C2semidirect
5. #20298987C2semidirect
6. #20298844C2semidirect
7. #20298834C2semidirect
8. #20298821C2semidirect
9. #20298794C2semidirect
10. #20298762C2semidirect
11. #20298745C2semidirect
12. #20298745C2semidirect
13. #20298734C2semidirect
14. #20298700C2semidirect
15. #435×C113C2semidirect
18. C2×#14268647C22semidirect
22. C2×Dic452C22semidirect
25. C2×#14268636C22semidirect
26. C2×#14268636C22semidirect
31. #16813619C22semidirect
38. #16813596C22semidirect
43. C4×Dic226C22semidirect
47. #16813556C22semidirect
48. #16813547C22semidirect
49. #16813547C22semidirect
52. #16813544C22semidirect
53. #16813544C22semidirect
55. C22×C8×C113C22semidirect
57. C4⋊C8×C113C22semidirect
59. C22⋊C8×C113C22semidirect
60. #97×C113C22semidirect
93. #14268636D4semidirect
215. C113#3268semidirect
230. #435D113semidirect
247. C22×C8C2×D113semidirect
266. C4⋊C8C2×D113semidirect
274. C22⋊C8C2×D113semidirect
275. #97C2×D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136502
C2×#168136442
#202992692
#202992442
#202989872
#202988442
#202988342
#202988212
#202987942
#202987622
#202987452
#202987342
#202987002
#435×C1132
#3268113