Finite Group Databasebeta

← #28402255

Subgroups — #28402255

Order 14464.

526 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16813642C211yesmaximal, characteristic, complemented
2C22×#14268632C211yesmaximal, characteristic, complemented
3#20299244C211yesmaximal, characteristic, complemented
4#20298980C211yesmaximal, characteristic, complemented
5#20298837C211yesmaximal, characteristic, complemented
6#20298832C211yesmaximal, characteristic, complemented
7#20298813C211yesmaximal, characteristic, complemented
8#20298810C211yesmaximal, characteristic, complemented
9#20298749C211yesmaximal, characteristic, complemented
10#20298748C211yesmaximal, characteristic, complemented
11#20298743C211yesmaximal, characteristic, complemented
12#20298741C211yesmaximal, characteristic, complemented
13C4×#14268632C211yesmaximal, characteristic, complemented
14D4×#11744751C211yesmaximal, characteristic, complemented
15#546×C113C211yesmaximal, characteristic, complemented
16C2×#14268647C2211yescharacteristic, complemented
17C22×D452C2211yescharacteristic
18#16813642—24no—
19C2×#14268637C2211yescharacteristic, complemented
20C2×#14268635C2211yescharacteristic, complemented
21C2×#14268635C2211yescharacteristic, complemented
22C2×#14268634C2211yescharacteristic, complemented
23C2×#14268634C2211yescharacteristic, complemented
24C2×#14268632—24no—
25C2×#14268632C2211yescharacteristic
26C2×#14268632C2211yescharacteristic
27C2×#14268632C2211yescharacteristic
28C2×#14268632C2211yescharacteristic
29C22×#11744751C2211yescharacteristic
30C22×#11744751C2211yescharacteristic, complemented
31#16813610C2211yescharacteristic, complemented
32#16813607—21no—
33#16813601C2211yescharacteristic
34#16813596C2211yescharacteristic, complemented
35#16813595—21no—
36#16813590—21no—
37C4×D452C2211yescharacteristic, complemented
38C22⋊C4×D113—21no—
39#16813555C2211yescharacteristic, complemented
40C4⋊#11744751C2211yescharacteristic, complemented
41#16813546C2211yescharacteristic, complemented
42#16813545C2211yescharacteristic, complemented
43#16813543C2211yescharacteristic, complemented
44#16813543C2211yescharacteristic, complemented
45#16813542C2211yescharacteristic, complemented
46#16813542C2211yescharacteristic, complemented
47C22⋊#11744751C2211yescharacteristic
48C22⋊#11744751C2211yescharacteristic, complemented
49C4×#11744751C2211yescharacteristic, complemented
50C2×#41×C113C2211yescharacteristic, complemented
51C22×D4×C113C2211yescharacteristic
52#124×C113C2211yescharacteristic, complemented
53#123×C113—21no—
54C22⋊Q8×C113C2211yescharacteristic
55#121×C113—21no—
56#121×C113C2211yescharacteristic, complemented
57#120×C113—21no—
58C4×D4×C113C2211yescharacteristic
59C4×D4×C113C2211yescharacteristic, complemented
60C2×C22⋊C4×C113—21no—
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#14268634—41no—
79#14268632—22no—
80#14268632—22no—
81#14268632—22no—
82#14268632D414yescomplemented
83C2×#11744751—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—
96C24×C113—21no—
97#41×C113—22no—
98#41×C113—41no—
99C2×Q8×C113C2311yescharacteristic
100C2×D4×C113—22no—
101C2×D4×C113—21no—
102C2×D4×C113—21no—
103C2×D4×C113—21no—
104C2×D4×C113—41no—
105C2×D4×C113D411yescharacteristic
106C2×D4×C113C2311yescharacteristic
107C2×D4×C113C2311yescharacteristic
108C22×C4×C113—21no—
109C22×C4×C113—21no—
110C22×C4×C113C2311yescharacteristic
111C22×C4×C113C2311yescharacteristic
112C4⋊C4×C113—21no—
113C4⋊C4×C113D411yescharacteristic
114C4⋊C4×C113C2311yescharacteristic
115C22⋊C4×C113—21no—
116C22⋊C4×C113—21no—
117C22⋊C4×C113—21no—
118C22⋊C4×C113—21no—
119C22⋊C4×C113—21no—
120C22⋊C4×C113D411yescharacteristic
121C22⋊C4×C113D411yescharacteristic
122C42×C113C2311yescharacteristic
123C23×C113—21no—
124C23×C113—21no—
125C23×C113—42no—
126C23×C113—42no—
127C23×C113—81no—
128C23×C113C2×D411yescharacteristic
129C23×C113C2×D411yescharacteristic
130C22×D113—21no—
131C22×D113—21no—
132C22×D113—42no—
133C22×D113—42no—
134C22×D113—81no—
135Q8×C113—21no—
136Q8×C113—21no—
137D4×C113—22no—
138D4×C113—21no—
139D4×C113—21no—
140D4×C113—21no—
141D4×C113—42no—
142D4×C113—42no—
143D4×C113—81no—
144D4×C113C2×D412yes—
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—81no—
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—22no—
179C22×C113—21no—
180C22×C113—21no—
181C22×C113—41no—
182C22×C113—41no—
183C22×C113—41no—
184C22×C113—41no—
185C22×C113—41no—
186C22×C113—84no—
187C22×C113#13512yescomplemented
188C22×C113C22×D411yescharacteristic
189C2×D113—22no—
190C2×D113—41no—
191C2×D113—41no—
192C2×D113—41no—
193C2×D113—41no—
194C2×D113—41no—
195C2×D113—84no—
196C4×C113—21no—
197C4×C113—21no—
198C4×C113—21no—
199C4×C113—21no—
200C4×C113—41no—
201C4×C113—41no—
202C4×C113C22×D411yescharacteristic
203C4×C113H(5,𝔽2)11yescharacteristic
204Dic113—41no—
205Dic113—41no—
206C2×C113—22no—
207C2×C113—41no—
208C2×C113—42no—
209C2×C113—81no—
210C2×C113D4211yescharacteristic
211C2×C113C2×#13511yescharacteristic
212C2×C113#57611yescharacteristic
213D113—42no—
214D113—81no—
215#3280—1131nomaximal, Sylow
216C113#328011yescharacteristic, complemented, Sylow
217C2×#135—1131no—
218C22×D8—1131no—
219#546—1131no—
220#546D11311yescharacteristic, complemented
221#495—1131no—
222#467—1131no—
223#466—1131no—
224#463—1131no—
225#463—1131no—
226#450—1131no—
227#450—1131no—
228#449—1131no—
229#449—1131no—
230C4×D8—1131no—
231C8×D4—1131no—
232C2×#41—1131no—
233C2×#41C2×D11311yescharacteristic, complemented
234C22×D4—1131no—
235C22×D4C2×D11311yescharacteristic
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×D8—2264no—
247C22×C8—1131no—
248C22×C8—1131no—
249#124—1131no—
250#124C2×D11311yescharacteristic, complemented
251#123—21no—
252#123—2261no—
253C22⋊Q8—1131no—
254C22⋊Q8C2×D11311yescharacteristic
255#121—21no—
256#121—1131no—
257#121—2261no—
258#121C2×D11311yescharacteristic, complemented
259#120—21no—
260#120—2261no—
261C4×D4—1131no—
262C4×D4C2×D11311yescharacteristic
263C4×D4C2×D11311yescharacteristic, complemented
264C2×C22⋊C4—21no—
265C2×C22⋊C4—2261no—
266#107—1131no—
267C4⋊C8—1131no—
268#103—1131no—
269#103—1131no—
270#102—1131no—
271#102—1131no—
272#102—1131no—
273#102—1131no—
274C22⋊C8—1131no—
275C22⋊C8—1131no—
276C4×C8—1131no—
277C24—21no—
278C24—2261no—
279#41—22no—
280#41—41no—
281#41—4521no—
282#41—2262no—
283C2×Q8—1131no—
284C2×Q8C22×D11311yescharacteristic
285C2×D4—22no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—21no—
289C2×D4—41no—
290C2×D4—1131no—
291C2×D4—1131no—
292C2×D4—4521no—
293C2×D4—2262no—
294C2×D4—2261no—
295C2×D4—2261no—
296C2×D4—2261no—
297C2×D4C22⋊D11311yescharacteristic
298C2×D4C22×D11311yescharacteristic
299C2×D4C22×D11311yescharacteristic
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—2261no—
303C22×C4—2261no—
304C22×C4C22×D11311yescharacteristic
305C22×C4C22×D11311yescharacteristic
306Q16—2262no—
307SD16—4521no—
308SD16—4521no—
309SD16—2262no—
310SD16—2262no—
311D8—1134no—
312D8—2262no—
313D8—2262no—
314D8—2262no—
315C2×C8—1131no—
316C2×C8—1131no—
317C2×C8—1131no—
318C2×C8—1131no—
319C2×C8—2262no—
320C2×C8—2262no—
321C4⋊C4—21no—
322C4⋊C4—1131no—
323C4⋊C4—2261no—
324C4⋊C4C22⋊D11311yescharacteristic
325C4⋊C4C22×D11311yescharacteristic
326C22⋊C4—21no—
327C22⋊C4—21no—
328C22⋊C4—21no—
329C22⋊C4—21no—
330C22⋊C4—21no—
331C22⋊C4—2261no—
332C22⋊C4—2261no—
333C22⋊C4—2261no—
334C22⋊C4—2261no—
335C22⋊C4—2261no—
336C22⋊C4C22⋊D11311yescharacteristic
337C22⋊C4C22⋊D11311yescharacteristic
338C42C22×D11311yescharacteristic
339C23—21no—
340C23—21no—
341C23—42no—
342C23—42no—
343C23—81no—
344C23—9041no—
345C23—4522no—
346C23—4522no—
347C23—2261no—
348C23—2261no—
349C23C2×C22⋊D11311yescharacteristic
350C23C2×C22⋊D11311yescharacteristic
351Q8—21no—
352Q8—21no—
353Q8—2261no—
354Q8—2261no—
355D4—22no—
356D4—21no—
357D4—21no—
358D4—21no—
359D4—42no—
360D4—42no—
361D4—81no—
362D4—1132no—
363D4—9041no—
364D4—4522no—
365D4—4522no—
366D4—2261no—
367D4—2261no—
368D4—2261no—
369D4D4×D11312yes—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—42no—
377C2×C4—81no—
378C2×C4—9041no—
379C2×C4—4522no—
380C2×C4—2261no—
381C2×C4—2261no—
382C2×C4C2×C22⋊D11311yescharacteristic
383C2×C4C2×C22⋊D11311yescharacteristic
384C2×C4C2×C22⋊D11311yescharacteristic
385C2×C4C2×C22⋊D11311yescharacteristic
386C2×C4C23×D11311yescharacteristic
387C8—1132no—
388C8—2261no—
389C8—2261no—
390C8—2261no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—22no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—84no—
403C22—9044no—
404C22—4521no—
405C22—4521no—
406C22—4521no—
407C22—4521no—
408C22—4521no—
409C22—2262no—
410C22#1681364212yescomplemented
411C22C22×C22⋊D11311yescharacteristic
412C4—21no—
413C4—21no—
414C4—21no—
415C4—21no—
416C4—41no—
417C4—41no—
418C4—4521no—
419C4—4521no—
420C4C2×D4×D11311yescharacteristic
421C4#1681366711yescharacteristic
422C2—22no—
423C2—41no—
424C2—42no—
425C2—81no—
426C2—9041no—
427C2—4522no—
428C2D4×C22⋊D11311yescharacteristic
429C2C2×#1681364211yescharacteristic
430C2#2029940111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#546×C113C2
socleC22×C113C22×D4
hypercenter#546D113
hypocenterC113#3280
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. C2×#16813642C2semidirect
2. C22×#14268632C2semidirect
3. #20299244C2semidirect
4. #20298980C2semidirect
5. #20298837C2semidirect
6. #20298832C2semidirect
7. #20298813C2semidirect
8. #20298810C2semidirect
9. #20298749C2semidirect
10. #20298748C2semidirect
11. #20298743C2semidirect
12. #20298741C2semidirect
13. C4×#14268632C2semidirect
14. D4×#11744751C2semidirect
15. #546×C113C2semidirect
16. C2×#14268647C22semidirect
19. C2×#14268637C22semidirect
20. C2×#14268635C22semidirect
21. C2×#14268635C22semidirect
22. C2×#14268634C22semidirect
23. C2×#14268634C22semidirect
30. C22×#11744751C22semidirect
31. #16813610C22semidirect
34. #16813596C22semidirect
37. C4×D452C22semidirect
39. #16813555C22semidirect
40. C4⋊#11744751C22semidirect
41. #16813546C22semidirect
42. #16813545C22semidirect
43. #16813543C22semidirect
44. #16813543C22semidirect
45. #16813542C22semidirect
46. #16813542C22semidirect
48. C22⋊#11744751C22semidirect
49. C4×#11744751C22semidirect
50. C2×#41×C113C22semidirect
52. #124×C113C22semidirect
56. #121×C113C22semidirect
59. C4×D4×C113C22semidirect
82. #14268632D4semidirect
187. C22×C113#135semidirect
216. C113#3280semidirect
220. #546D113semidirect
233. C2×#41C2×D113semidirect
250. #124C2×D113semidirect
258. #121C2×D113semidirect
263. C4×D4C2×D113semidirect
410. C22#16813642semidirect

Maximal subgroups

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

subgroupindex
C2×#168136422
C22×#142686322
#202992442
#202989802
#202988372
#202988322
#202988132
#202988102
#202987492
#202987482
#202987432
#202987412
C4×#142686322
D4×#117447512
#546×C1132
#3280113