Finite Group Databasebeta

← #28402850

Subgroups — #28402850

Order 14464.

374 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299319C211yesmaximal, characteristic
2Q8×C22⋊D113C211yesmaximal, characteristic
3#20298947C211yesmaximal, characteristic, complemented
4#20298940C211yesmaximal, characteristic, complemented
5#20298938C211yesmaximal, characteristic, complemented
6#20298881C211yesmaximal, characteristic, complemented
7#20298854C211yesmaximal, characteristic, complemented
8#20298853C211yesmaximal, characteristic, complemented
9#20298806C211yesmaximal, characteristic, complemented
10#20298752C211yesmaximal, characteristic, complemented
11Q16×Dic113C211yesmaximal, characteristic, complemented
12#20298673C211yesmaximal, characteristic
13#20298607C211yesmaximal, characteristic, complemented
14#20298605C211yesmaximal, characteristic, complemented
15#451×C113C211yesmaximal, characteristic, complemented
16C2×Q8×D113C2211yescharacteristic
17C2×#14268637C2211yescharacteristic
18C2×#14268631C2211yescharacteristic
19C2×#14268630C2211yescharacteristic
20#16813621C2211yescharacteristic
21#16813620—21no—
22#16813620C2211yescharacteristic
23#16813617—21no—
24#16813615—21no—
25#16813608—21no—
26#16813601—21no—
27#16813601C2211yescharacteristic
28#16813598—21no—
29#16813598C2211yescharacteristic
30#16813598C2211yescharacteristic
31Q8×Dic113C2211yescharacteristic
32Q8×Dic113C2211yescharacteristic
33#16813587—21no—
34C4×C22⋊D113—21no—
35C4×C22⋊D113C2211yescharacteristic
36#16813581C2211yescharacteristic
37#16813580C2211yescharacteristic
38#16813556C2211yescharacteristic
39#16813554C2211yescharacteristic
40#16813553C2211yescharacteristic
41#16813551C2211yescharacteristic
42#16813547C2211yescharacteristic
43#16813547C2211yescharacteristic
44#16813546C2211yescharacteristic
45#16813546C2211yescharacteristic
46#16813546C2211yescharacteristic
47#16813546C2211yescharacteristic
48#16813546C2211yescharacteristic
49#16813545C2211yescharacteristic
50#16813534C2211yescharacteristic
51C8×Dic113C2211yescharacteristic
52C22×Q8×C113C2211yescharacteristic
53C2×Q16×C113C2211yescharacteristic
54C2×Q16×C113C2211yescharacteristic
55C22⋊Q8×C113C2211yescharacteristic
56#103×C113C2211yescharacteristic
57#103×C113C2211yescharacteristic
58C22⋊C8×C113C2211yescharacteristic
59C2×Dic226—21no—
60C2×Dic226—21no—
61C2×Dic226C2311yescharacteristic
62Q8×D113—22no—
63Q8×D113—41no—
64C2×C22⋊D113D411yescharacteristic
65C2×C4×D113—21no—
66C2×C4×D113C2311yescharacteristic
67#14268637—41no—
68#14268631—41no—
69#14268630—41no—
70C2×#11744751C2311yescharacteristic
71C2×#11744751C2311yescharacteristic
72C4⋊Dic113—21no—
73C4⋊Dic113—21no—
74C4⋊Dic113C2311yescharacteristic
75C4⋊Dic113C2311yescharacteristic
76C4⋊Dic113C2311yescharacteristic
77#14268626—21no—
78#14268626—21no—
79#14268626—21no—
80#14268626—21no—
81#14268626—21no—
82#14268626—21no—
83#14268626D411yescharacteristic
84C22⋊Dic113—21no—
85C22⋊Dic113—21no—
86C22⋊Dic113D411yescharacteristic
87#14268624—21no—
88#14268624—21no—
89#14268624—21no—
90#14268624D411yescharacteristic
91C4×Dic113—21no—
92C4×Dic113—21no—
93C4×Dic113—21no—
94C4×Dic113—21no—
95C4×Dic113C2311yescharacteristic
96C2×Q8×C113—21no—
97C2×Q8×C113—22no—
98C2×Q8×C113—41no—
99C2×Q8×C113C2311yescharacteristic
100C2×Q8×C113C2311yescharacteristic
101C2×Q8×C113C2311yescharacteristic
102C22×C4×C113—21no—
103C22×C4×C113C2311yescharacteristic
104Q16×C113—22no—
105Q16×C113—41no—
106C2×C8×C113C2311yescharacteristic
107C2×C8×C113C2311yescharacteristic
108C4⋊C4×C113—21no—
109C4⋊C4×C113C2311yescharacteristic
110C22⋊C4×C113—21no—
111C23×C113C2×D411yescharacteristic
112C22×D113C2×D411yescharacteristic
113Q8×C113—21no—
114Q8×C113—21no—
115Q8×C113—21no—
116Q8×C113—21no—
117Q8×C113—21no—
118Q8×C113—42no—
119Q8×C113#4112yes—
120C2×C4×C113—21no—
121C2×C4×C113—21no—
122C2×C4×C113—21no—
123C2×C4×C113—21no—
124C2×C4×C113—21no—
125C2×C4×C113—21no—
126C2×C4×C113—42no—
127C2×C4×C113C2×D411yescharacteristic
128C2×C4×C113C2411yescharacteristic
129C22⋊D113—22no—
130C2×Dic113—21no—
131C2×Dic113—21no—
132C2×Dic113—21no—
133C2×Dic113—21no—
134C2×Dic113C2×D411yescharacteristic
135C2×Dic113C2×D411yescharacteristic
136C2×Dic113C2×D411yescharacteristic
137C4×D113—21no—
138C4×D113—21no—
139C4×D113—42no—
140Dic226—21no—
141Dic226—21no—
142Dic226—42no—
143Dic226—42no—
144C8×C113—21no—
145C8×C113—21no—
146#11744751—21no—
147#11744751—21no—
148C22×C113—21no—
149C22×C113—21no—
150C22×C113—21no—
151C22×C113C22×D411yescharacteristic
152C2×D113—21no—
153C2×D113—21no—
154C2×D113—21no—
155C4×C113—22no—
156C4×C113—21no—
157C4×C113—41no—
158C4×C113—41no—
159C4×C113—41no—
160C4×C113C2×#4111yescharacteristic
161C4×C113H(5,𝔽2)11yescharacteristic
162Dic113—21no—
163Dic113—21no—
164Dic113—41no—
165Dic113—41no—
166Dic113—41no—
167Dic113—41no—
168Dic113#13712yes—
169C2×C113—41no—
170C2×C113#54611yescharacteristic
171C2×C113C2×#13711yescharacteristic
172C2×C113#57811yescharacteristic
173D113—41no—
174#3328—1131nomaximal, Sylow
175C113#332811yescharacteristic, complemented, Sylow
176#556—1131no—
177D4×Q8—1131no—
178#487—1131no—
179#485—1131no—
180#485—1131no—
181#475—1131no—
182#470—1131no—
183#470—1131no—
184#462—1131no—
185#451—1131no—
186#451D11311yescharacteristic, complemented
187C4×Q16—1131no—
188#436—1131no—
189#419—1131no—
190#419—1131no—
191C22×Q8—1131no—
192C22×Q8C2×D11311yescharacteristic
193C2×Q16—1131no—
194C2×Q16C2×D11311yescharacteristic
195C2×Q16C2×D11311yescharacteristic
196C2×M16—1131no—
197C2×M16—1131no—
198C4⋊Q8—1131no—
199C4⋊Q8—1131no—
200C4⋊Q8—2261no—
201#126—2261no—
202#126—2261no—
203#124—2261no—
204C22⋊Q8—1131no—
205C22⋊Q8—1131no—
206C22⋊Q8—1131no—
207C22⋊Q8—2261no—
208C22⋊Q8—2261no—
209C22⋊Q8C2×D11311yescharacteristic
210C4×Q8—1131no—
211C4×Q8—1131no—
212C4×Q8—2261no—
213C4×D4—1131no—
214C4×D4—2261no—
215#117—1131no—
216#117—1131no—
217#107—1131no—
218#106—1131no—
219#106—1131no—
220C4⋊C8—1131no—
221#103—1131no—
222#103—1131no—
223#103—1131no—
224#103—1131no—
225#103—1131no—
226#103—1131no—
227#103—1131no—
228#103—1131no—
229#103C2×D11311yescharacteristic
230#103C2×D11311yescharacteristic
231C22⋊C8—1131no—
232C22⋊C8C2×D11311yescharacteristic
233C4×C8—1131no—
234C2×Q8—21no—
235C2×Q8—22no—
236C2×Q8—41no—
237C2×Q8—1131no—
238C2×Q8—4521no—
239C2×Q8—2261no—
240C2×Q8—2261no—
241C2×Q8—2262no—
242C2×Q8C22×D11311yescharacteristic
243C2×Q8C22×D11311yescharacteristic
244C2×Q8C22×D11311yescharacteristic
245C2×D4—1131no—
246C22×C4—21no—
247C22×C4—1131no—
248C22×C4—2261no—
249C22×C4C22×D11311yescharacteristic
250Q16—22no—
251Q16—41no—
252Q16—4521no—
253M16—4521no—
254M16—4521no—
255C2×C8—1131no—
256C2×C8—1131no—
257C2×C8C22×D11311yescharacteristic
258C2×C8C22×D11311yescharacteristic
259C4⋊C4—21no—
260C4⋊C4—1131no—
261C4⋊C4—1131no—
262C4⋊C4—1131no—
263C4⋊C4—1131no—
264C4⋊C4—2261no—
265C4⋊C4—2261no—
266C4⋊C4—2261no—
267C4⋊C4—2261no—
268C4⋊C4—2261no—
269C4⋊C4—2261no—
270C4⋊C4—2261no—
271C4⋊C4—2261no—
272C4⋊C4C22×D11311yescharacteristic
273C22⋊C4—21no—
274C22⋊C4—1131no—
275C22⋊C4—1131no—
276C22⋊C4—2261no—
277C22⋊C4—2261no—
278C22⋊C4—2261no—
279C22⋊C4—2261no—
280C22⋊C4—2261no—
281C42—1131no—
282C42—2261no—
283C42—2261no—
284C42—2261no—
285C42—2261no—
286C23—1131no—
287C23D4×D11311yescharacteristic
288Q8—21no—
289Q8—21no—
290Q8—21no—
291Q8—21no—
292Q8—21no—
293Q8—42no—
294Q8—4522no—
295Q8—4522no—
296Q8—2261no—
297Q8—2261no—
298Q8#1426864612yes—
299D4—2262no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—42no—
307C2×C4—1131no—
308C2×C4—1131no—
309C2×C4—1131no—
310C2×C4—4522no—
311C2×C4—2261no—
312C2×C4—2261no—
313C2×C4—2261no—
314C2×C4—2261no—
315C2×C4—2261no—
316C2×C4—2261no—
317C2×C4D4×D11311yescharacteristic
318C2×C4C23×D11311yescharacteristic
319C8—21no—
320C8—21no—
321C8—2261no—
322C8—2261no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—2261no—
327C22—2261no—
328C22—2261no—
329C22C2×D4×D11311yescharacteristic
330C4—21no—
331C4—22no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—1132no—
336C4—4521no—
337C4—4521no—
338C4—4521no—
339C4—4521no—
340C4—2261no—
341C4—2261no—
342C4C2×#1426864611yescharacteristic
343C4#1681366711yescharacteristic
344C2—41no—
345C2—4521no—
346C2#2029923511yescharacteristic
347C2#137×D11311yescharacteristic
348C2#2029941111yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#451×C113C2
socleC22×C113C22×D4
prime radicalC2×C22⋊D113D4
hypercenter#451D113
hypocenterC113#3328
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
3. #20298947C2semidirect
4. #20298940C2semidirect
5. #20298938C2semidirect
6. #20298881C2semidirect
7. #20298854C2semidirect
8. #20298853C2semidirect
9. #20298806C2semidirect
10. #20298752C2semidirect
11. Q16×Dic113C2semidirect
13. #20298607C2semidirect
14. #20298605C2semidirect
15. #451×C113C2semidirect
175. C113#3328semidirect
186. #451D113semidirect

Maximal subgroups

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

subgroupindex
#202993192
Q8×C22⋊D1132
#202989472
#202989402
#202989382
#202988812
#202988542
#202988532
#202988062
#202987522
Q16×Dic1132
#202986732
#202986072
#202986052
#451×C1132
#3328113