Finite Group Databasebeta

← #28402115

Subgroups — #28402115

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×#16813647C211yesmaximal, characteristic, complemented
2C2×#16813642C211yesmaximal, characteristic, complemented
3#20299244C211yesmaximal, characteristic, complemented
4#20298985C211yesmaximal, characteristic, complemented
5#20298842C211yesmaximal, characteristic, complemented
6#20298832C211yesmaximal, characteristic, complemented
7#20298820C211yesmaximal, characteristic, complemented
8#20298790C211yesmaximal, characteristic, complemented
9#20298760C211yesmaximal, characteristic, complemented
10#20298743C211yesmaximal, characteristic, complemented
11#20298741C211yesmaximal, characteristic, complemented
12#20298731C211yesmaximal, characteristic, complemented
13#20298696C211yesmaximal, characteristic, complemented
14#20298670C211yesmaximal, characteristic, complemented
15#550×C113C211yesmaximal, characteristic, complemented
16C2×#14268647C2211yescharacteristic
17C22×D452C2211yescharacteristic
18#16813647—24no—
19#16813642—24no—
20C2×#14268637C2211yescharacteristic, complemented
21C2×#14268635C2211yescharacteristic, complemented
22C2×#14268635C2211yescharacteristic, complemented
23C2×#14268634C2211yescharacteristic
24C2×#14268634C2211yescharacteristic
25C2×#14268632C2211yescharacteristic
26C2×#14268632C2211yescharacteristic
27C2×#14268632C2211yescharacteristic
28C2×#14268632C2211yescharacteristic
29C2×#14268631C2211yescharacteristic
30C22×#11744751C2211yescharacteristic, complemented
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#16813545C2211yescharacteristic, complemented
43#16813543C2211yescharacteristic, complemented
44#16813543C2211yescharacteristic, complemented
45#16813542C2211yescharacteristic
46#16813542C2211yescharacteristic
47C22⋊#11744751C2211yescharacteristic
48C22⋊#11744751C2211yescharacteristic, complemented
49#16813533C2211yescharacteristic, complemented
50C2×#41×C113C2211yescharacteristic
51C2×#41×C113C2211yescharacteristic, complemented
52#127×C113—21no—
53#127×C113C2211yescharacteristic, complemented
54#121×C113—21no—
55#121×C113—21no—
56#121×C113C2211yescharacteristic
57#121×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#14268635—22no—
76#14268635—41no—
77#14268634—22no—
78#14268634D414yescomplemented
79#14268632—22no—
80#14268632—22no—
81#14268632—22no—
82#14268632—41no—
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—
96#41×C113—22no—
97#41×C113—22no—
98#41×C113—41no—
99#41×C113—41no—
100C2×Q8×C113C2311yescharacteristic
101C2×D4×C113—21no—
102C2×D4×C113—21no—
103C2×D4×C113—21no—
104C2×D4×C113—21no—
105C2×D4×C113—21no—
106C2×D4×C113—21no—
107C2×D4×C113D411yescharacteristic
108C2×D4×C113C2311yescharacteristic
109C2×D4×C113C2311yescharacteristic
110C22×C4×C113—21no—
111C22×C4×C113—21no—
112C22×C4×C113C2311yescharacteristic
113C22×C4×C113C2311yescharacteristic
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×C113—21no—
124C23×C113—21no—
125C23×C113C2×D411yescharacteristic
126C23×C113C2×D411yescharacteristic
127C22×D113—21no—
128C22×D113—21no—
129C22×D113—42no—
130C22×D113—42no—
131C22×D113—81no—
132Q8×C113—21no—
133Q8×C113C2×D412yes—
134D4×C113—21no—
135D4×C113—21no—
136D4×C113—21no—
137D4×C113—21no—
138D4×C113—41no—
139D4×C113—42no—
140D4×C113—42no—
141D4×C113—42no—
142D4×C113—81no—
143D4×C113—81no—
144D4×C113—81no—
145C2×C4×C113—21no—
146C2×C4×C113—21no—
147C2×C4×C113—21no—
148C2×C4×C113—21no—
149C2×C4×C113—21no—
150C2×C4×C113—21no—
151C2×C4×C113—42no—
152C2×C4×C113—42no—
153C2×C4×C113C2×D411yescharacteristic
154C2×C4×C113C2×D411yescharacteristic
155C2×C4×C113C2×D411yescharacteristic
156C2×C4×C113C2×D411yescharacteristic
157C2×C4×C113C2411yescharacteristic
158C22⋊D113—42no—
159C22⋊D113—81no—
160C2×Dic113—21no—
161C2×Dic113—21no—
162D452—21no—
163D452—21no—
164D452—21no—
165D452—42no—
166D452C2×D412yes—
167C4×D113—42no—
168C4×D113—81no—
169Dic226—21no—
170Dic226—21no—
171#11744751—21no—
172#11744751—21no—
173#11744751—21no—
174#11744751C2×D412yes—
175C22×C113—21no—
176C22×C113—21no—
177C22×C113—21no—
178C22×C113—21no—
179C22×C113—21no—
180C22×C113—21no—
181C22×C113—41no—
182C22×C113—41no—
183C22×C113—41no—
184C22×C113—41no—
185C22×C113—41no—
186C22×C113—41no—
187C22×C113C22×D411yescharacteristic
188C2×D113—22no—
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—22no—
198C4×C113—21no—
199C4×C113—21no—
200C4×C113—41no—
201C4×C113C22×D411yescharacteristic
202C4×C113H(5,𝔽2)11yescharacteristic
203Dic113—41no—
204Dic113—41no—
205C2×C113—41no—
206C2×C113—41no—
207C2×C113—81no—
208C2×C113—81no—
209C2×C113D4211yescharacteristic
210C2×C113#57511yescharacteristic
211C2×C113#57611yescharacteristic
212D113—42no—
213D113—81no—
214#3268—1131nomaximal, Sylow
215C113#326811yescharacteristic, complemented, Sylow
216C2×AGL(1,ℤ/8)—1131no—
217C2×#135—1131no—
218#550D11311yescharacteristic, complemented
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#435—1131no—
231C2×#41—1131no—
232C2×#41C2×D11311yescharacteristic
233C2×#41C2×D11311yescharacteristic, complemented
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×M16—1131no—
247C22×C8—1131no—
248#127—21no—
249#127C2×D11311yescharacteristic, complemented
250#124—1131no—
251#123—2261no—
252C22⋊Q8—1131no—
253#121—21no—
254#121—21no—
255#121—1131no—
256#121—2261no—
257#121C2×D11311yescharacteristic
258#121C2×D11311yescharacteristic, complemented
259#120—2261no—
260C4×Q8C2×D11311yescharacteristic, complemented
261C4×D4—21no—
262C4×D4—1131no—
263C4×D4C2×D11311yescharacteristic
264C2×C22⋊C4—2261no—
265#107—1131no—
266C4⋊C8—1131no—
267#103—1131no—
268#103—1131no—
269#102—1131no—
270#102—1131no—
271#102—1131no—
272#102—1131no—
273C22⋊C8—1131no—
274C22⋊C8—1131no—
275#97—1131no—
276C24—2261no—
277#41—22no—
278#41—22no—
279#41—41no—
280#41—41no—
281#41—4521no—
282#41—2262no—
283C2×Q8—1131no—
284C2×Q8C22×D11311yescharacteristic
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—21no—
289C2×D4—21no—
290C2×D4—21no—
291C2×D4—1131no—
292C2×D4—1131no—
293C2×D4—4521no—
294C2×D4—2262no—
295C2×D4—2261no—
296C2×D4—2261no—
297C2×D4—2261no—
298C2×D4C22⋊D11311yescharacteristic
299C2×D4C22×D11311yescharacteristic
300C2×D4C22×D11311yescharacteristic
301C22×C4—21no—
302C22×C4—21no—
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—2262no—
317C2×C8—1131no—
318C2×C8—1131no—
319C2×C8—1131no—
320C2×C8—1131no—
321C2×C8—2262no—
322C4⋊C4—21no—
323C4⋊C4—1131no—
324C4⋊C4—2261no—
325C4⋊C4C22⋊D11311yescharacteristic
326C4⋊C4C22×D11311yescharacteristic
327C22⋊C4—21no—
328C22⋊C4—21no—
329C22⋊C4—2261no—
330C22⋊C4—2261no—
331C22⋊C4—2261no—
332C22⋊C4—2261no—
333C22⋊C4—2261no—
334C22⋊C4C22⋊D11311yescharacteristic
335C22⋊C4C22⋊D11311yescharacteristic
336C42—21no—
337C42C22×D11311yescharacteristic
338C23—21no—
339C23—21no—
340C23—9041no—
341C23—4522no—
342C23—4522no—
343C23—2261no—
344C23—2261no—
345C23C2×C22⋊D11311yescharacteristic
346C23C2×C22⋊D11311yescharacteristic
347Q8—21no—
348Q8—2261no—
349Q8—2261no—
350Q8D4×D11312yes—
351D4—21no—
352D4—21no—
353D4—21no—
354D4—21no—
355D4—41no—
356D4—42no—
357D4—42no—
358D4—42no—
359D4—81no—
360D4—81no—
361D4—81no—
362D4—1132no—
363D4—9041no—
364D4—4522no—
365D4—4522no—
366D4—2261no—
367D4—2261no—
368D4—2261no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—9041no—
378C2×C4—4522no—
379C2×C4—2261no—
380C2×C4—2261no—
381C2×C4C2×C22⋊D11311yescharacteristic
382C2×C4C2×C22⋊D11311yescharacteristic
383C2×C4C2×C22⋊D11311yescharacteristic
384C2×C4C2×C22⋊D11311yescharacteristic
385C2×C4C23×D11311yescharacteristic
386C8—1132no—
387C8—2261no—
388C8—2261no—
389C8—2261no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—9044no—
403C22—4521no—
404C22—4521no—
405C22—4521no—
406C22—4521no—
407C22—4521no—
408C22—2262no—
409C22C22×C22⋊D11311yescharacteristic
410C4—21no—
411C4—21no—
412C4—21no—
413C4—21no—
414C4—22no—
415C4—41no—
416C4—4521no—
417C4—4521no—
418C4C2×D4×D11311yescharacteristic
419C4#1681366711yescharacteristic
420C2—41no—
421C2—41no—
422C2—81no—
423C2—81no—
424C2—9041no—
425C2—4522no—
426C2D4×C22⋊D11311yescharacteristic
427C2#2029939611yescharacteristic
428C2#2029940111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#550×C113C2
socleC22×C113C22×D4
hypercenter#550D113
hypocenterC113#3268
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C4×D4 ◁ #550

Complements

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

NH ≅ G/Ntype
1. C2×#16813647C2semidirect
2. C2×#16813642C2semidirect
3. #20299244C2semidirect
4. #20298985C2semidirect
5. #20298842C2semidirect
6. #20298832C2semidirect
7. #20298820C2semidirect
8. #20298790C2semidirect
9. #20298760C2semidirect
10. #20298743C2semidirect
11. #20298741C2semidirect
12. #20298731C2semidirect
13. #20298696C2semidirect
14. #20298670C2semidirect
15. #550×C113C2semidirect
20. C2×#14268637C22semidirect
21. C2×#14268635C22semidirect
22. C2×#14268635C22semidirect
30. C22×#11744751C22semidirect
39. #16813555C22semidirect
40. C4⋊#11744751C22semidirect
41. #16813546C22semidirect
42. #16813545C22semidirect
43. #16813543C22semidirect
44. #16813543C22semidirect
48. C22⋊#11744751C22semidirect
49. #16813533C22semidirect
51. C2×#41×C113C22semidirect
53. #127×C113C22semidirect
57. #121×C113C22semidirect
58. C4×Q8×C113C22semidirect
78. #14268634D4semidirect
215. C113#3268semidirect
218. #550D113semidirect
233. C2×#41C2×D113semidirect
249. #127C2×D113semidirect
258. #121C2×D113semidirect
260. C4×Q8C2×D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136472
C2×#168136422
#202992442
#202989852
#202988422
#202988322
#202988202
#202987902
#202987602
#202987432
#202987412
#202987312
#202986962
#202986702
#550×C1132
#3268113