Finite Group Databasebeta

← #28402199

Subgroups — #28402199

Order 14464.

498 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×#16813649C211yesmaximal, characteristic, complemented
2#20299259C211yesmaximal, characteristic, complemented
3#20299236C211yesmaximal, characteristic, complemented
4#20298983C211yesmaximal, characteristic, complemented
5#20298853C211yesmaximal, characteristic, complemented
6#20298851C211yesmaximal, characteristic, complemented
7#20298822C211yesmaximal, characteristic, complemented
8#20298815C211yesmaximal, characteristic, complemented
9#20298759C211yesmaximal, characteristic, complemented
10#20298747C211yesmaximal, characteristic, complemented
11#20298743C211yesmaximal, characteristic, complemented
12#20298737C211yesmaximal, characteristic, complemented
13SD16×Dic113C211yesmaximal, characteristic, complemented
14#20298674C211yesmaximal, characteristic, complemented
15C2×#137×C113C211yesmaximal, characteristic, complemented
16C2×#14268648C2211yescharacteristic
17C2×D4×D113C2211yescharacteristic
18#16813649—24no—
19C2×#14268634C2211yescharacteristic
20C2×#14268634C2211yescharacteristic
21C2×#14268634C2211yescharacteristic, complemented
22C2×D904C2211yescharacteristic
23C2×#14268632C2211yescharacteristic
24C2×#14268630C2211yescharacteristic
25#16813611—21no—
26#16813611C2211yescharacteristic
27#16813611C2211yescharacteristic, complemented
28#16813605—21no—
29#16813598—21no—
30#16813598C2211yescharacteristic
31#16813598C2211yescharacteristic
32#16813596—21no—
33#16813596C2211yescharacteristic
34#16813596C2211yescharacteristic, complemented
35#16813594—21no—
36#16813590—21no—
37Q8×Dic113C2211yescharacteristic, complemented
38D4×Dic113C2211yescharacteristic
39C4×C22⋊D113—21no—
40C4×C22⋊D113C2211yescharacteristic
41C2×#14268624—21no—
42#16813554C2211yescharacteristic, complemented
43#16813551C2211yescharacteristic, complemented
44#16813546C2211yescharacteristic, complemented
45#16813546C2211yescharacteristic, complemented
46#16813546C2211yescharacteristic, complemented
47#16813544C2211yescharacteristic
48#16813544C2211yescharacteristic, complemented
49#16813543C2211yescharacteristic
50C22⋊#11744751C2211yescharacteristic, complemented
51#16813534C2211yescharacteristic
52C8×Dic113C2211yescharacteristic, complemented
53C2×#41×C113C2211yescharacteristic
54C22×Q8×C113C2211yescharacteristic, complemented
55#137×C113—24no—
56C2×Q16×C113C2211yescharacteristic, complemented
57C2×Q16×C113C2211yescharacteristic, complemented
58C2×SD16×C113C2211yescharacteristic
59C2×SD16×C113C2211yescharacteristic
60C2×M16×C113C2211yescharacteristic, complemented
61C23×D113—21no—
62#14268648—22no—
63#14268648—41no—
64C2×D452—21no—
65C2×D452C2311yescharacteristic
66C2×D452C2311yescharacteristic
67C2×C22⋊D113—21no—
68C2×C22⋊D113—21no—
69C2×C22⋊D113—21no—
70C2×C22⋊D113D411yescharacteristic
71D4×D113—22no—
72D4×D113—41no—
73C22×Dic113—21no—
74C2×C4×D113—21no—
75C2×C4×D113C2311yescharacteristic
76#14268634—22no—
77#14268634—41no—
78#14268634—41no—
79D904—22no—
80#14268632—22no—
81#14268630—22no—
82C2×#11744751C2311yescharacteristic
83C2×#11744751C2311yescharacteristic
84C4⋊Dic113—21no—
85C4⋊Dic113C2311yescharacteristic
86C4⋊Dic113C2311yescharacteristic
87#14268626—21no—
88#14268626—21no—
89#14268626D411yescharacteristic
90C22⋊Dic113—21no—
91C22⋊Dic113D411yescharacteristic
92#14268624—21no—
93#14268624—21no—
94#14268624—21no—
95#14268624—21no—
96#14268624—21no—
97#14268624—21no—
98#14268624—21no—
99#14268624—21no—
100#14268624D411yescharacteristic
101C4×Dic113—21no—
102C4×Dic113C2311yescharacteristic
103#41×C113—22no—
104#41×C113—41no—
105C2×Q8×C113—21no—
106C2×Q8×C113—22no—
107C2×Q8×C113—41no—
108C2×Q8×C113C2311yescharacteristic
109C2×Q8×C113C2311yescharacteristic
110C2×Q8×C113C2311yescharacteristic
111C2×D4×C113—21no—
112C2×D4×C113C2311yescharacteristic
113C22×C4×C113—21no—
114C22×C4×C113—21no—
115C22×C4×C113C2311yescharacteristic
116Q16×C113—22no—
117Q16×C113—22no—
118SD16×C113—22no—
119SD16×C113D414yescomplemented
120M16×C113—22no—
121C2×C8×C113C2311yescharacteristic
122C2×C8×C113C2311yescharacteristic
123C23×C113—21no—
124C23×C113C2×D411yescharacteristic
125C22×D113—21no—
126C22×D113—21no—
127C22×D113—42no—
128C22×D113—42no—
129C22×D113—81no—
130C22×D113C2×D411yescharacteristic
131Q8×C113—21no—
132Q8×C113—21no—
133Q8×C113—21no—
134Q8×C113—21no—
135Q8×C113—21no—
136Q8×C113—42no—
137Q8×C113C2×D412yes—
138D4×C113—21no—
139D4×C113—42no—
140D4×C113C2×D412yes—
141C2×C4×C113—21no—
142C2×C4×C113—21no—
143C2×C4×C113—21no—
144C2×C4×C113—21no—
145C2×C4×C113—21no—
146C2×C4×C113—42no—
147C2×C4×C113—42no—
148C2×C4×C113C2×D411yescharacteristic
149C2×C4×C113C2411yescharacteristic
150C22⋊D113—41no—
151C22⋊D113—42no—
152C22⋊D113—42no—
153C22⋊D113—81no—
154C2×Dic113—21no—
155C2×Dic113—21no—
156C2×Dic113—81no—
157C2×Dic113C2×D411yescharacteristic
158C2×Dic113C2×D411yescharacteristic
159C2×Dic113C2×D411yescharacteristic
160D452—21no—
161D452—21no—
162D452—21no—
163D452—21no—
164D452—42no—
165C4×D113—21no—
166C4×D113—21no—
167C4×D113—42no—
168C8×C113—21no—
169C8×C113C2×D412yes—
170#11744751—21no—
171#11744751—21no—
172C22×C113—22no—
173C22×C113—21no—
174C22×C113—21no—
175C22×C113—21no—
176C22×C113—41no—
177C22×C113—41no—
178C22×C113C22×D411yescharacteristic
179C2×D113—21no—
180C2×D113—21no—
181C2×D113—21no—
182C2×D113—41no—
183C2×D113—41no—
184C2×D113—41no—
185C2×D113—41no—
186C2×D113—41no—
187C2×D113—41no—
188C2×D113—84no—
189C4×C113—22no—
190C4×C113—21no—
191C4×C113—41no—
192C4×C113—41no—
193C4×C113C22×D411yescharacteristic
194C4×C113H(5,𝔽2)11yescharacteristic
195Dic113—21no—
196Dic113—21no—
197Dic113—21no—
198Dic113—41no—
199Dic113—41no—
200C2×C113—42no—
201C2×C113—41no—
202C2×C113D4211yescharacteristic
203C2×C113#57511yescharacteristic
204C2×C113#57711yescharacteristic
205D113—41no—
206D113—81no—
207D113—81no—
208#3275—1131nomaximal, Sylow
209C113#327511yescharacteristic, complemented, Sylow
210C2×#137D11311yescharacteristic, complemented
211C2×AGL(1,ℤ/8)—1131no—
212#548—1131no—
213#546—1131no—
214#495—1131no—
215#470—1131no—
216#469—1131no—
217#464—1131no—
218#463—1131no—
219#452—1131no—
220#450—1131no—
221#449—1131no—
222#448—1131no—
223C4×SD16—1131no—
224#436—1131no—
225C2×#41—1131no—
226C2×#41C2×D11311yescharacteristic
227C22×Q8C2×D11311yescharacteristic, complemented
228C22×D4—1131no—
229#137—24no—
230AGL(1,ℤ/8)—2264no—
231C2×Q16C2×D11311yescharacteristic, complemented
232C2×Q16C2×D11311yescharacteristic, complemented
233C2×SD16—1131no—
234C2×SD16—1131no—
235C2×SD16—1131no—
236C2×SD16C2×D11311yescharacteristic
237C2×SD16C2×D11311yescharacteristic
238C2×D8—1131no—
239C2×D8—1131no—
240C2×M16—1131no—
241C2×M16C2×D11311yescharacteristic, complemented
242#124—1131no—
243#124—1131no—
244#124—2261no—
245#123—2261no—
246C22⋊Q8—1131no—
247C22⋊Q8—1131no—
248C22⋊Q8—2261no—
249#121—1131no—
250#121—1131no—
251#121—2261no—
252#121—2261no—
253#120—2261no—
254C4×Q8—1131no—
255C4×D4—1131no—
256C4×D4—1131no—
257C4×D4—2261no—
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—
269C4×C8—1131no—
270C24—2261no—
271#41—22no—
272#41—41no—
273#41—4521no—
274#41—2262no—
275C2×Q8—21no—
276C2×Q8—22no—
277C2×Q8—41no—
278C2×Q8C22×D11311yescharacteristic
279C2×Q8C22×D11311yescharacteristic
280C2×Q8C22×D11311yescharacteristic
281C2×D4—21no—
282C2×D4—1131no—
283C2×D4—1131no—
284C2×D4—1131no—
285C2×D4—4521no—
286C2×D4—2261no—
287C2×D4—2261no—
288C2×D4—2261no—
289C2×D4—2261no—
290C2×D4—2262no—
291C2×D4C22×D11311yescharacteristic
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—1131no—
295C22×C4—2261no—
296C22×C4—2261no—
297C22×C4C22×D11311yescharacteristic
298Q16—22no—
299Q16—22no—
300SD16—22no—
301SD16—4521no—
302SD16—4521no—
303SD16—2262no—
304SD16C22⋊D11314yescomplemented
305D8—2262no—
306D8—2262no—
307M16—22no—
308M16—2262no—
309C2×C8—1131no—
310C2×C8—1131no—
311C2×C8C22×D11311yescharacteristic
312C2×C8C22×D11311yescharacteristic
313C4⋊C4—1131no—
314C4⋊C4—1131no—
315C4⋊C4—1131no—
316C4⋊C4—2261no—
317C4⋊C4—2261no—
318C4⋊C4—2261no—
319C22⋊C4—1131no—
320C22⋊C4—1131no—
321C22⋊C4—2261no—
322C22⋊C4—2261no—
323C22⋊C4—2261no—
324C22⋊C4—2261no—
325C22⋊C4—2261no—
326C22⋊C4—2261no—
327C22⋊C4—2261no—
328C22⋊C4—2261no—
329C22⋊C4—2261no—
330C42—1131no—
331C42—2261no—
332C23—21no—
333C23—1131no—
334C23—9041no—
335C23—4522no—
336C23—4522no—
337C23—2261no—
338C23—2261no—
339C23D4×D11311yescharacteristic
340Q8—21no—
341Q8—21no—
342Q8—21no—
343Q8—21no—
344Q8—21no—
345Q8—42no—
346Q8C2×C22⋊D11312yes—
347D4—21no—
348D4—42no—
349D4—9041no—
350D4—4522no—
351D4—4522no—
352D4—4522no—
353D4—4521no—
354D4—2261no—
355D4—2261no—
356D4—2261no—
357D4—2261no—
358D4C2×C22⋊D11312yes—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—1131no—
367C2×C4—1131no—
368C2×C4—1131no—
369C2×C4—9041no—
370C2×C4—4522no—
371C2×C4—2261no—
372C2×C4—2261no—
373C2×C4—2261no—
374C2×C4—2261no—
375C2×C4D4×D11311yescharacteristic
376C2×C4C23×D11311yescharacteristic
377C8—21no—
378C8—2261no—
379C8—2261no—
380C8C2×C22⋊D11312yes—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—22no—
385C22—41no—
386C22—41no—
387C22—9044no—
388C22—4521no—
389C22—4521no—
390C22—4521no—
391C22—4521no—
392C22—4521no—
393C22—4521no—
394C22—2261no—
395C22—2261no—
396C22—2261no—
397C22C2×D4×D11311yescharacteristic
398C4—21no—
399C4—22no—
400C4—41no—
401C4—41no—
402C4—4521no—
403C4—4521no—
404C4—2261no—
405C4—2261no—
406C4—2261no—
407C4C22×C22⋊D11311yescharacteristic
408C4#1681366711yescharacteristic
409C2—41no—
410C2—42no—
411C2—9041no—
412C2—9041no—
413C2—4521no—
414C2D4×C22⋊D11311yescharacteristic
415C2#2029939711yescharacteristic
416C2#2029940711yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC2×#137×C113C2
socleC22×C113C22×D4
hypercenterC2×#137D113
hypocenterC113#3275
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C2×#16813649C2semidirect
2. #20299259C2semidirect
3. #20299236C2semidirect
4. #20298983C2semidirect
5. #20298853C2semidirect
6. #20298851C2semidirect
7. #20298822C2semidirect
8. #20298815C2semidirect
9. #20298759C2semidirect
10. #20298747C2semidirect
11. #20298743C2semidirect
12. #20298737C2semidirect
13. SD16×Dic113C2semidirect
14. #20298674C2semidirect
15. C2×#137×C113C2semidirect
21. C2×#14268634C22semidirect
27. #16813611C22semidirect
34. #16813596C22semidirect
37. Q8×Dic113C22semidirect
42. #16813554C22semidirect
43. #16813551C22semidirect
44. #16813546C22semidirect
45. #16813546C22semidirect
46. #16813546C22semidirect
48. #16813544C22semidirect
50. C22⋊#11744751C22semidirect
52. C8×Dic113C22semidirect
54. C22×Q8×C113C22semidirect
56. C2×Q16×C113C22semidirect
57. C2×Q16×C113C22semidirect
60. C2×M16×C113C22semidirect
119. SD16×C113D4semidirect
209. C113#3275semidirect
210. C2×#137D113semidirect
227. C22×Q8C2×D113semidirect
231. C2×Q16C2×D113semidirect
232. C2×Q16C2×D113semidirect
241. C2×M16C2×D113semidirect
304. SD16C22⋊D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136492
#202992592
#202992362
#202989832
#202988532
#202988512
#202988222
#202988152
#202987592
#202987472
#202987432
#202987372
SD16×Dic1132
#202986742
C2×#137×C1132
#3275113