Finite Group Databasebeta

← #28402100

Subgroups — #28402100

Order 14464.

500 conjugacy classes of subgroups.

The subgroup lattice has 418 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#20298990C211yesmaximal, characteristic, complemented
5#20298854C211yesmaximal, characteristic, complemented
6#20298829C211yesmaximal, characteristic, complemented
7#20298813C211yesmaximal, characteristic, complemented
8#20298800C211yesmaximal, characteristic, complemented
9#20298760C211yesmaximal, characteristic, complemented
10#20298758C211yesmaximal, characteristic, complemented
11#20298748C211yesmaximal, characteristic, complemented
12#20298743C211yesmaximal, characteristic, complemented
13#20298708C211yesmaximal, characteristic, complemented
14#20298670C211yesmaximal, characteristic, complemented
15#547×C113C211yesmaximal, characteristic, complemented
16C2×#14268647C2211yescharacteristic
17C22×D452C2211yescharacteristic
18#16813647—24no—
19#16813642—24no—
20C2×#14268637C2211yescharacteristic, complemented
21C2×#14268637C2211yescharacteristic, complemented
22C2×#14268635C2211yescharacteristic, complemented
23C2×#14268634C2211yescharacteristic
24C2×#14268634C2211yescharacteristic
25C2×#14268634C2211yescharacteristic
26C2×#14268634C2211yescharacteristic
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#16813553C2211yescharacteristic, complemented
40C4⋊#11744751C2211yescharacteristic, complemented
41#16813546C2211yescharacteristic, complemented
42#16813546C2211yescharacteristic, complemented
43#16813545C2211yescharacteristic, complemented
44#16813543C2211yescharacteristic, complemented
45#16813542C2211yescharacteristic
46#16813542C2211yescharacteristic
47C22⋊#11744751C2211yescharacteristic
48C22⋊#11744751C2211yescharacteristic, complemented
49#16813533C2211yescharacteristic, complemented
50C2×#41×C113C2211yescharacteristic
51C2×#41×C113C2211yescharacteristic, complemented
52C4⋊Q8×C113C2211yescharacteristic, complemented
53#123×C113—21no—
54#123×C113—21no—
55C22⋊Q8×C113C2211yescharacteristic
56C22⋊Q8×C113C2211yescharacteristic, complemented
57#121×C113—21no—
58C4×D4×C113C2211yescharacteristic
59C4×D4×C113C2211yescharacteristic, complemented
60C2×C4⋊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#14268637—41no—
76#14268635—22no—
77#14268634—22no—
78#14268634—22no—
79#14268634—22no—
80#14268634—41no—
81#14268632—22no—
82#14268632D414yescomplemented
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×Q8×C113C2311yescharacteristic
102C2×D4×C113—21no—
103C2×D4×C113—21no—
104C2×D4×C113D411yescharacteristic
105C2×D4×C113C2311yescharacteristic
106C22×C4×C113—21no—
107C22×C4×C113—21no—
108C22×C4×C113—21no—
109C22×C4×C113C2311yescharacteristic
110C22×C4×C113C2311yescharacteristic
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×C113—21no—
120C22⋊C4×C113D411yescharacteristic
121C22⋊C4×C113D411yescharacteristic
122C42×C113C2311yescharacteristic
123C23×C113—21no—
124C23×C113C2×D411yescharacteristic
125C23×C113C2×D411yescharacteristic
126C22×D113—21no—
127C22×D113—21no—
128C22×D113—42no—
129C22×D113—42no—
130C22×D113—81no—
131Q8×C113—21no—
132Q8×C113—21no—
133Q8×C113—21no—
134Q8×C113—21no—
135D4×C113—21no—
136D4×C113—41no—
137D4×C113—42no—
138D4×C113—42no—
139D4×C113C2×D412yes—
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×C113—42no—
150C2×C4×C113C2×D411yescharacteristic
151C2×C4×C113C2×D411yescharacteristic
152C2×C4×C113C2×D411yescharacteristic
153C2×C4×C113C2×D411yescharacteristic
154C2×C4×C113C2411yescharacteristic
155C22⋊D113—42no—
156C22⋊D113—81no—
157C2×Dic113—21no—
158C2×Dic113—21no—
159D452—21no—
160D452—21no—
161D452—21no—
162D452—42no—
163D452C2×D412yes—
164C4×D113—42no—
165C4×D113—81no—
166Dic226—21no—
167Dic226—21no—
168#11744751—21no—
169#11744751—21no—
170#11744751—21no—
171#11744751C2×D412yes—
172C22×C113—21no—
173C22×C113—21no—
174C22×C113—22no—
175C22×C113—21no—
176C22×C113—21no—
177C22×C113—21no—
178C22×C113—21no—
179C22×C113—41no—
180C22×C113—41no—
181C22×C113C22×D411yescharacteristic
182C2×D113—22no—
183C2×D113—41no—
184C2×D113—41no—
185C2×D113—41no—
186C2×D113—41no—
187C2×D113—41no—
188C2×D113—84no—
189C4×C113—21no—
190C4×C113—21no—
191C4×C113—21no—
192C4×C113—21no—
193C4×C113—41no—
194C4×C113—41no—
195C4×C113—41no—
196C4×C113C22×D411yescharacteristic
197C4×C113H(5,𝔽2)11yescharacteristic
198Dic113—41no—
199Dic113—41no—
200C2×C113—41no—
201C2×C113—41no—
202C2×C113—42no—
203C2×C113D4211yescharacteristic
204C2×C113#57511yescharacteristic
205C2×C113#57711yescharacteristic
206D113—42no—
207D113—81no—
208#3267—1131nomaximal, Sylow
209C113#326711yescharacteristic, complemented, Sylow
210C2×AGL(1,ℤ/8)—1131no—
211C2×#135—1131no—
212#547D11311yescharacteristic, complemented
213#546—1131no—
214#497—1131no—
215#470—1131no—
216#465—1131no—
217#463—1131no—
218#461—1131no—
219#452—1131no—
220#452—1131no—
221#450—1131no—
222#449—1131no—
223#442—1131no—
224#435—1131no—
225C2×#41—1131no—
226C2×#41C2×D11311yescharacteristic
227C2×#41C2×D11311yescharacteristic, complemented
228C22×D4—1131no—
229AGL(1,ℤ/8)—2264no—
230#135—2264no—
231C2×Q16—1131no—
232C2×Q16—1131no—
233C2×SD16—1131no—
234C2×SD16—1131no—
235C2×SD16—1131no—
236C2×SD16—1131no—
237C2×SD16—1131no—
238C2×D8—1131no—
239C2×D8—1131no—
240C2×M16—1131no—
241C22×C8—1131no—
242C4⋊Q8C2×D11311yescharacteristic, complemented
243#124—1131no—
244#123—21no—
245#123—21no—
246#123—2261no—
247C22⋊Q8—1131no—
248C22⋊Q8C2×D11311yescharacteristic
249C22⋊Q8C2×D11311yescharacteristic, complemented
250#121—21no—
251#121—1131no—
252#121—2261no—
253#120—2261no—
254C4×D4—1131no—
255C4×D4C2×D11311yescharacteristic
256C4×D4C2×D11311yescharacteristic, complemented
257C2×C4⋊C4—21no—
258C2×C22⋊C4—2261no—
259#106—1131no—
260C4⋊C8—1131no—
261#103—1131no—
262#103—1131no—
263#103—1131no—
264#102—1131no—
265#102—1131no—
266#102—1131no—
267C22⋊C8—1131no—
268C22⋊C8—1131no—
269#97—1131no—
270C24—2261no—
271#41—22no—
272#41—22no—
273#41—41no—
274#41—41no—
275#41—4521no—
276#41—2262no—
277C2×Q8—1131no—
278C2×Q8C22×D11311yescharacteristic
279C2×Q8C22×D11311yescharacteristic
280C2×D4—21no—
281C2×D4—21no—
282C2×D4—1131no—
283C2×D4—1131no—
284C2×D4—4521no—
285C2×D4—2262no—
286C2×D4—2261no—
287C2×D4—2261no—
288C2×D4—2261no—
289C2×D4C22⋊D11311yescharacteristic
290C2×D4C22×D11311yescharacteristic
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—2261no—
295C22×C4—2261no—
296C22×C4C22×D11311yescharacteristic
297C22×C4C22×D11311yescharacteristic
298Q16—4521no—
299Q16—2262no—
300SD16—4521no—
301SD16—2262no—
302SD16—2262no—
303SD16—2262no—
304SD16—2262no—
305D8—1134no—
306D8—2262no—
307M16—2262no—
308C2×C8—1131no—
309C2×C8—1131no—
310C2×C8—1131no—
311C2×C8—1131no—
312C2×C8—2262no—
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—1131no—
318C4⋊C4—2261no—
319C4⋊C4C22⋊D11311yescharacteristic
320C4⋊C4C22×D11311yescharacteristic
321C22⋊C4—21no—
322C22⋊C4—21no—
323C22⋊C4—21no—
324C22⋊C4—2261no—
325C22⋊C4—2261no—
326C22⋊C4—2261no—
327C22⋊C4—2261no—
328C22⋊C4—2261no—
329C22⋊C4C22⋊D11311yescharacteristic
330C22⋊C4C22⋊D11311yescharacteristic
331C42C22×D11311yescharacteristic
332C23—21no—
333C23—9041no—
334C23—4522no—
335C23—4522no—
336C23—2261no—
337C23—2261no—
338C23C2×C22⋊D11311yescharacteristic
339C23C2×C22⋊D11311yescharacteristic
340Q8—21no—
341Q8—21no—
342Q8—21no—
343Q8—21no—
344Q8—2261no—
345Q8—2261no—
346D4—21no—
347D4—41no—
348D4—42no—
349D4—42no—
350D4—1132no—
351D4—9041no—
352D4—4522no—
353D4—4522no—
354D4—2261no—
355D4—2261no—
356D4—2261no—
357D4D4×D11312yes—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—9041no—
369C2×C4—4522no—
370C2×C4—2261no—
371C2×C4—2261no—
372C2×C4C2×C22⋊D11311yescharacteristic
373C2×C4C2×C22⋊D11311yescharacteristic
374C2×C4C2×C22⋊D11311yescharacteristic
375C2×C4C2×C22⋊D11311yescharacteristic
376C2×C4C23×D11311yescharacteristic
377C8—1132no—
378C8—2261no—
379C8—2261no—
380C8—2261no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—22no—
388C22—41no—
389C22—41no—
390C22—9044no—
391C22—4521no—
392C22—4521no—
393C22—4521no—
394C22—4521no—
395C22—4521no—
396C22—2262no—
397C22C22×C22⋊D11311yescharacteristic
398C4—21no—
399C4—21no—
400C4—21no—
401C4—21no—
402C4—41no—
403C4—41no—
404C4—41no—
405C4—4521no—
406C4—4521no—
407C4C2×D4×D11311yescharacteristic
408C4#1681366711yescharacteristic
409C2—41no—
410C2—41no—
411C2—42no—
412C2—9041no—
413C2—4522no—
414C2D4×C22⋊D11311yescharacteristic
415C2#2029939611yescharacteristic
416C2#2029940611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#547×C113C2
socleC22×C113C22×D4
hypercenter#547D113
hypocenterC113#3267
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
1. C2×#16813647C2semidirect
2. C2×#16813642C2semidirect
3. #20299244C2semidirect
4. #20298990C2semidirect
5. #20298854C2semidirect
6. #20298829C2semidirect
7. #20298813C2semidirect
8. #20298800C2semidirect
9. #20298760C2semidirect
10. #20298758C2semidirect
11. #20298748C2semidirect
12. #20298743C2semidirect
13. #20298708C2semidirect
14. #20298670C2semidirect
15. #547×C113C2semidirect
20. C2×#14268637C22semidirect
21. C2×#14268637C22semidirect
22. C2×#14268635C22semidirect
30. C22×#11744751C22semidirect
39. #16813553C22semidirect
40. C4⋊#11744751C22semidirect
41. #16813546C22semidirect
42. #16813546C22semidirect
43. #16813545C22semidirect
44. #16813543C22semidirect
48. C22⋊#11744751C22semidirect
49. #16813533C22semidirect
51. C2×#41×C113C22semidirect
52. C4⋊Q8×C113C22semidirect
56. C22⋊Q8×C113C22semidirect
59. C4×D4×C113C22semidirect
82. #14268632D4semidirect
209. C113#3267semidirect
212. #547D113semidirect
227. C2×#41C2×D113semidirect
242. C4⋊Q8C2×D113semidirect
249. C22⋊Q8C2×D113semidirect
256. C4×D4C2×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
#202989902
#202988542
#202988292
#202988132
#202988002
#202987602
#202987582
#202987482
#202987432
#202987082
#202986702
#547×C1132
#3267113