Finite Group Databasebeta

← #28400099

Subgroups — #28400099

Order 14464.

458 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16813654C211yesmaximal, characteristic
2C2×Q16×D113C211yesmaximal, characteristic, complemented
3#20299173C211yesmaximal, characteristic
4#20299074C211yesmaximal, characteristic, complemented
5#20298823C211yesmaximal, characteristic, complemented
6#20298822C211yesmaximal, characteristic, complemented
7#20298821C211yesmaximal, characteristic, complemented
8#20298820C211yesmaximal, characteristic, complemented
9#20298807C211yesmaximal, characteristic, complemented
10#20298806C211yesmaximal, characteristic, complemented
11#20298805C211yesmaximal, characteristic, complemented
12#20298623C211yesmaximal, characteristic, complemented
13#20298605C211yesmaximal, characteristic, complemented
14#20298593C211yesmaximal, characteristic
15#462×C113C211yesmaximal, characteristic, complemented
16C2×#14268648C2211yescharacteristic
17C2×Q8×D113C2211yescharacteristic
18C2×Q8×D113C2211yescharacteristic
19#16813654—24no—
20C2×Dic452C2211yescharacteristic
21C2×#14268637C2211yescharacteristic
22C2×#14268637C2211yescharacteristic
23C2×#14268637C2211yescharacteristic
24Q16×D113—24no—
25C2×#14268636C2211yescharacteristic
26C2×#14268634C2211yescharacteristic
27C2×#14268630C2211yescharacteristic
28C2×C8×D113C2211yescharacteristic
29#16813620C2211yescharacteristic
30#16813611C2211yescharacteristic
31#16813610C2211yescharacteristic
32#16813607—21no—
33#16813607—21no—
34#16813600—21no—
35#16813600—21no—
36Q8×Dic113C2211yescharacteristic
37C4×Dic226—21no—
38C4×Dic226C2211yescharacteristic
39#16813587—21no—
40#16813587C2211yescharacteristic
41#16813580—21no—
42#16813580C2211yescharacteristic
43#16813579—21no—
44#16813579C2211yescharacteristic
45C4⋊#11744751C2211yescharacteristic
46#16813551C2211yescharacteristic
47#16813551C2211yescharacteristic
48#16813547C2211yescharacteristic
49#16813546C2211yescharacteristic
50#16813546C2211yescharacteristic
51#16813545C2211yescharacteristic
52#16813544C2211yescharacteristic
53#16813542C2211yescharacteristic
54C2×Q16×C113C2211yescharacteristic
55C2×Q16×C113C2211yescharacteristic
56C4⋊Q8×C113C2211yescharacteristic
57C4×Q8×C113C2211yescharacteristic
58C4⋊C8×C113C2211yescharacteristic
59#103×C113C2211yescharacteristic
60#103×C113C2211yescharacteristic
61#14268648—22no—
62#14268648—22no—
63C2×Dic226—21no—
64C2×Dic226—21no—
65C2×Dic226C2311yescharacteristic
66C2×Dic226C2311yescharacteristic
67Q8×D113—22no—
68Q8×D113—22no—
69Q8×D113—22no—
70Q8×D113D414yes—
71C2×D452—21no—
72C2×D452C2311yescharacteristic
73C2×C4×D113—21no—
74C2×C4×D113—21no—
75C2×C4×D113—21no—
76C2×C4×D113C2311yescharacteristic
77Dic452—22no—
78#14268637—22no—
79#14268637—22no—
80#14268637—22no—
81#14268636—22no—
82#14268634—22no—
83#14268630—22no—
84C2×#11744751C2311yescharacteristic
85C2×#11744751C2311yescharacteristic
86C8×D113—22no—
87C4⋊Dic113—21no—
88C4⋊Dic113C2311yescharacteristic
89#14268626—21no—
90#14268626—21no—
91#14268626—21no—
92#14268626—21no—
93#14268626D411yescharacteristic
94#14268626D411yescharacteristic
95#14268624—21no—
96#14268624—21no—
97#14268624—21no—
98#14268624—21no—
99#14268624—21no—
100#14268624D411yescharacteristic
101#14268624D411yescharacteristic
102C4×Dic113—21no—
103C4×Dic113—21no—
104C4×Dic113—21no—
105C4×Dic113—21no—
106C4×Dic113C2311yescharacteristic
107C2×Q8×C113C2311yescharacteristic
108C2×Q8×C113C2311yescharacteristic
109C2×Q8×C113C2311yescharacteristic
110Q16×C113—22no—
111Q16×C113—22no—
112C2×C8×C113C2311yescharacteristic
113C2×C8×C113C2311yescharacteristic
114C4⋊C4×C113—21no—
115C4⋊C4×C113—21no—
116C4⋊C4×C113—21no—
117C4⋊C4×C113C2311yescharacteristic
118C42×C113—21no—
119C42×C113C2311yescharacteristic
120C22×D113—21no—
121C22×D113C2×D411yescharacteristic
122Q8×C113—21no—
123Q8×C113—21no—
124Q8×C113—21no—
125Q8×C113—21no—
126Q8×C113—21no—
127Q8×C113C2×D412yes—
128C2×C4×C113—21no—
129C2×C4×C113—21no—
130C2×C4×C113—21no—
131C2×C4×C113—21no—
132C2×C4×C113C2×D411yescharacteristic
133C2×C4×C113C2×D411yescharacteristic
134C2×C4×C113C2411yescharacteristic
135C2×Dic113—21no—
136C2×Dic113—21no—
137C2×Dic113—21no—
138C2×Dic113C2×D411yescharacteristic
139C2×Dic113C2×D411yescharacteristic
140C2×Dic113C2×D411yescharacteristic
141D452—21no—
142D452—21no—
143D452—42no—
144C4×D113—24no—
145C4×D113—42no—
146C4×D113—42no—
147C4×D113C2×D412yes—
148C4×D113#4112yes—
149Dic226—21no—
150Dic226—24no—
151Dic226—21no—
152Dic226—21no—
153Dic226—42no—
154Dic226C2×D412yes—
155C8×C113—21no—
156C8×C113—21no—
157#11744751—21no—
158#11744751—21no—
159C22×C113C22×D411yescharacteristic
160C2×D113—21no—
161C2×D113—21no—
162C2×D113—41no—
163C2×D113—41no—
164C2×D113—41no—
165C2×D113#12112yes—
166C4×C113—22no—
167C4×C113—21no—
168C4×C113—21no—
169C4×C113—41no—
170C4×C113—41no—
171C4×C113—41no—
172C4×C113C22×D411yescharacteristic
173C4×C113C2×#4111yescharacteristic
174Dic113—22no—
175Dic113—21no—
176Dic113—21no—
177Dic113—41no—
178Dic113—41no—
179Dic113#12112yes—
180C2×C113C2×#12111yescharacteristic
181C2×C113#57811yescharacteristic
182C2×C113#57811yescharacteristic
183D113—22no—
184D113—81no—
185#3044—1131nomaximal, Sylow
186C113#304411yescharacteristic, complemented, Sylow
187C2×#137—1131no—
188C22×Q16—1131no—
189#536—1131no—
190#519—1131no—
191#464—1131no—
192#464—1131no—
193#464—1131no—
194#464—1131no—
195#462—1131no—
196#462—1131no—
197#462—1131no—
198#462D11311yescharacteristic, complemented
199#424—1131no—
200#419—1131no—
201#416—1131no—
202C2×#41—1131no—
203C22×Q8—1131no—
204C22×Q8—1131no—
205#137—2264no—
206C2×Q16—1131no—
207C2×Q16—1131no—
208C2×Q16—1131no—
209C2×Q16—1131no—
210C2×Q16—2264no—
211C2×Q16C2×D11311yescharacteristic
212C2×Q16C2×D11311yescharacteristic
213C2×SD16—1131no—
214C2×SD16—1131no—
215C2×M16—1131no—
216C22×C8—1131no—
217C4⋊Q8—1131no—
218C4⋊Q8C2×D11311yescharacteristic
219#124—1131no—
220#124—1131no—
221#123—2261no—
222#123—2261no—
223C22⋊Q8—2261no—
224C22⋊Q8—2261no—
225C4×Q8—1131no—
226C4×Q8—1131no—
227C4×Q8—1131no—
228C4×Q8—2261no—
229C4×Q8—2261no—
230C4×Q8C2×D11311yescharacteristic
231#117—1131no—
232#117—1131no—
233#117—2261no—
234#117—2261no—
235C4⋊C8—1131no—
236C4⋊C8—1131no—
237C4⋊C8—1131no—
238C4⋊C8C2×D11311yescharacteristic
239#103—1131no—
240#103—1131no—
241#103—1131no—
242#103—1131no—
243#103C2×D11311yescharacteristic
244#103C2×D11311yescharacteristic
245#102—1131no—
246#102—1131no—
247#41—2262no—
248#41—2262no—
249C2×Q8—1134no—
250C2×Q8—1131no—
251C2×Q8—1131no—
252C2×Q8—2261no—
253C2×Q8—2261no—
254C2×Q8—2262no—
255C2×Q8—2262no—
256C2×Q8—2262no—
257C2×Q8C22×D11311yescharacteristic
258C2×Q8C22×D11311yescharacteristic
259C2×Q8C22×D11311yescharacteristic
260C2×D4—1131no—
261C2×D4—2261no—
262C22×C4—1131no—
263C22×C4—2261no—
264C22×C4—2261no—
265C22×C4—2261no—
266Q16—22no—
267Q16—22no—
268Q16—2262no—
269Q16—2262no—
270Q16—2262no—
271Q16—2262no—
272SD16—2262no—
273SD16—2262no—
274M16—2262no—
275C2×C8—1131no—
276C2×C8—1131no—
277C2×C8—2262no—
278C2×C8C22×D11311yescharacteristic
279C2×C8C22×D11311yescharacteristic
280C4⋊C4—21no—
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—1131no—
284C4⋊C4—1131no—
285C4⋊C4—1131no—
286C4⋊C4—2261no—
287C4⋊C4—2261no—
288C4⋊C4—2261no—
289C4⋊C4—2261no—
290C4⋊C4—2261no—
291C4⋊C4C22×D11311yescharacteristic
292C22⋊C4—1131no—
293C22⋊C4—1131no—
294C22⋊C4—2261no—
295C22⋊C4—2261no—
296C22⋊C4—2261no—
297C22⋊C4—2261no—
298C22⋊C4—2261no—
299C42—21no—
300C42—1131no—
301C42—2261no—
302C42—2261no—
303C42—2261no—
304C42—2261no—
305C42C22×D11311yescharacteristic
306C23—1131no—
307C23—2261no—
308Q8—21no—
309Q8—21no—
310Q8—21no—
311Q8—21no—
312Q8—21no—
313Q8—1132no—
314Q8—4522no—
315Q8—2264no—
316Q8—2261no—
317Q8—2261no—
318Q8—2261no—
319Q8D4×D11312yes—
320D4—4522no—
321D4—2261no—
322D4—2261no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—1131no—
328C2×C4—1132no—
329C2×C4—1132no—
330C2×C4—1131no—
331C2×C4—1131no—
332C2×C4—4522no—
333C2×C4—4522no—
334C2×C4—2264no—
335C2×C4—2261no—
336C2×C4—2261no—
337C2×C4—2261no—
338C2×C4D4×D11311yescharacteristic
339C2×C4D4×D11311yescharacteristic
340C2×C4C23×D11311yescharacteristic
341C8—21no—
342C8—21no—
343C8—2261no—
344C8—2261no—
345C22—1132no—
346C22—4521no—
347C22—4521no—
348C22—4521no—
349C22—2261no—
350C22—2261no—
351C22C2×D4×D11311yescharacteristic
352C4—22no—
353C4—21no—
354C4—21no—
355C4—41no—
356C4—41no—
357C4—41no—
358C4—1132no—
359C4—4521no—
360C4—4521no—
361C4—2262no—
362C4—2261no—
363C4—2261no—
364C4C2×D4×D11311yescharacteristic
365C4#41×D11311yescharacteristic
366C2—9041no—
367C2—2262no—
368C2#121×D11311yescharacteristic
369C2#2029941111yescharacteristic
370C2#2029941411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#462×C113C2
socleC22×C113C22×D4
prime radicalC2×#14268648C22
hypercenter#462D113
hypocenterC113#3044
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
2. C2×Q16×D113C2semidirect
4. #20299074C2semidirect
5. #20298823C2semidirect
6. #20298822C2semidirect
7. #20298821C2semidirect
8. #20298820C2semidirect
9. #20298807C2semidirect
10. #20298806C2semidirect
11. #20298805C2semidirect
12. #20298623C2semidirect
13. #20298605C2semidirect
15. #462×C113C2semidirect
186. C113#3044semidirect
198. #462D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136542
C2×Q16×D1132
#202991732
#202990742
#202988232
#202988222
#202988212
#202988202
#202988072
#202988062
#202988052
#202986232
#202986052
#202985932
#462×C1132
#3044113