Finite Group Databasebeta

← #28402853

Subgroups — #28402853

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#20299316C211yesmaximal, characteristic
2Q8×C22⋊D113C211yesmaximal, characteristic
3#20298947C211yesmaximal, characteristic, complemented
4#20298939C211yesmaximal, characteristic, complemented
5#20298937C211yesmaximal, characteristic, complemented
6#20298881C211yesmaximal, characteristic, complemented
7#20298856C211yesmaximal, characteristic, complemented
8#20298855C211yesmaximal, characteristic, complemented
9#20298807C211yesmaximal, characteristic, complemented
10#20298755C211yesmaximal, characteristic, complemented
11#20298754C211yesmaximal, characteristic, complemented
12#20298690C211yesmaximal, characteristic, complemented
13#20298674C211yesmaximal, characteristic
14#20298605C211yesmaximal, characteristic, complemented
15#419×C113C211yesmaximal, characteristic, complemented
16C2×Q8×D113C2211yescharacteristic
17C2×Dic452C2211yescharacteristic
18C2×#14268637C2211yescharacteristic
19C2×#14268637C2211yescharacteristic
20C2×#14268630C2211yescharacteristic
21#16813621C2211yescharacteristic
22#16813620—21no—
23#16813620C2211yescharacteristic
24#16813616—21no—
25#16813615—21no—
26#16813608—21no—
27#16813602C2211yescharacteristic
28#16813601—21no—
29#16813601C2211yescharacteristic
30#16813601C2211yescharacteristic
31#16813598—21no—
32#16813598C2211yescharacteristic
33Q8×Dic113C2211yescharacteristic
34C4×Dic226—21no—
35#16813587C2211yescharacteristic
36C4×C22⋊D113—21no—
37C4×C22⋊D113C2211yescharacteristic
38#16813580C2211yescharacteristic
39#16813555C2211yescharacteristic
40#16813554C2211yescharacteristic
41#16813553C2211yescharacteristic
42#16813551C2211yescharacteristic
43#16813547C2211yescharacteristic
44#16813547C2211yescharacteristic
45#16813546C2211yescharacteristic
46#16813546C2211yescharacteristic
47#16813545C2211yescharacteristic
48#16813545C2211yescharacteristic
49C22⋊#11744751C2211yescharacteristic
50#16813534C2211yescharacteristic
51C8×Dic113C2211yescharacteristic
52C22×Q8×C113C2211yescharacteristic
53C2×M16×C113C2211yescharacteristic
54#117×C113C2211yescharacteristic
55#103×C113C2211yescharacteristic
56#103×C113C2211yescharacteristic
57#103×C113C2211yescharacteristic
58#103×C113C2211yescharacteristic
59C2×Dic226—21no—
60C2×Dic226—21no—
61C2×Dic226C2311yescharacteristic
62C2×Dic226C2311yescharacteristic
63Q8×D113—22no—
64Q8×D113—41no—
65C2×C22⋊D113D411yescharacteristic
66C2×C4×D113—21no—
67C2×C4×D113C2311yescharacteristic
68Dic452—41no—
69#14268637—22no—
70#14268637—41no—
71#14268630—41no—
72C2×#11744751C2311yescharacteristic
73C2×#11744751C2311yescharacteristic
74C4⋊Dic113—21no—
75C4⋊Dic113—21no—
76C4⋊Dic113C2311yescharacteristic
77C4⋊Dic113C2311yescharacteristic
78#14268626—21no—
79#14268626—21no—
80#14268626—21no—
81#14268626—21no—
82#14268626—21no—
83#14268626—21no—
84#14268626—21no—
85#14268626D411yescharacteristic
86C22⋊Dic113—21no—
87C22⋊Dic113—21no—
88C22⋊Dic113D411yescharacteristic
89#14268624—21no—
90#14268624—21no—
91#14268624—21no—
92#14268624D411yescharacteristic
93C4×Dic113—21no—
94C4×Dic113—21no—
95C4×Dic113—21no—
96C4×Dic113C2311yescharacteristic
97C2×Q8×C113—21no—
98C2×Q8×C113—22no—
99C2×Q8×C113—41no—
100C2×Q8×C113C2311yescharacteristic
101C2×Q8×C113C2311yescharacteristic
102C22×C4×C113—21no—
103C22×C4×C113C2311yescharacteristic
104M16×C113—41no—
105C2×C8×C113C2311yescharacteristic
106C2×C8×C113C2311yescharacteristic
107C4⋊C4×C113C2311yescharacteristic
108C4⋊C4×C113C2311yescharacteristic
109C22⋊C4×C113—21no—
110C42×C113—21no—
111C23×C113C2×D411yescharacteristic
112C22×D113C2×D411yescharacteristic
113Q8×C113—21no—
114Q8×C113—21no—
115Q8×C113—21no—
116Q8×C113—42no—
117Q8×C113#4112yes—
118C2×C4×C113—21no—
119C2×C4×C113—21no—
120C2×C4×C113—21no—
121C2×C4×C113—21no—
122C2×C4×C113—21no—
123C2×C4×C113—21no—
124C2×C4×C113—42no—
125C2×C4×C113C2×D411yescharacteristic
126C2×C4×C113C2411yescharacteristic
127C22⋊D113—22no—
128C2×Dic113—21no—
129C2×Dic113—21no—
130C2×Dic113—21no—
131C2×Dic113—21no—
132C2×Dic113C2×D411yescharacteristic
133C2×Dic113C2×D411yescharacteristic
134C2×Dic113C2×D411yescharacteristic
135C4×D113—21no—
136C4×D113—21no—
137C4×D113—42no—
138Dic226—21no—
139Dic226—21no—
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#451—1131no—
187C4×Q16—1131no—
188#436—1131no—
189#419—1131no—
190#419D11311yescharacteristic, complemented
191C22×Q8—1131no—
192C22×Q8C2×D11311yescharacteristic
193C2×Q16—1131no—
194C2×Q16—1131no—
195C2×Q16—1131no—
196C2×M16—1131no—
197C2×M16C2×D11311yescharacteristic
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—1131no—
208C22⋊Q8—2261no—
209C22⋊Q8—2261no—
210C4×Q8—1131no—
211C4×Q8—1131no—
212C4×Q8—2261no—
213C4×D4—1131no—
214C4×D4—2261no—
215#117—1131no—
216#117C2×D11311yescharacteristic
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#103C2×D11311yescharacteristic
228#103C2×D11311yescharacteristic
229#103C2×D11311yescharacteristic
230#103C2×D11311yescharacteristic
231C22⋊C8—1131no—
232C22⋊C8—1131no—
233C4×C8—1131no—
234C2×Q8—21no—
235C2×Q8—22no—
236C2×Q8—41no—
237C2×Q8—1131no—
238C2×Q8—1131no—
239C2×Q8—4521no—
240C2×Q8—2261no—
241C2×Q8—2261no—
242C2×Q8—2262no—
243C2×Q8C22×D11311yescharacteristic
244C2×Q8C22×D11311yescharacteristic
245C2×D4—1131no—
246C22×C4—21no—
247C22×C4—1131no—
248C22×C4—2261no—
249C22×C4C22×D11311yescharacteristic
250Q16—4521no—
251Q16—4521no—
252Q16—2262no—
253M16—41no—
254M16—4521no—
255C2×C8—1131no—
256C2×C8—1131no—
257C2×C8C22×D11311yescharacteristic
258C2×C8C22×D11311yescharacteristic
259C4⋊C4—1131no—
260C4⋊C4—1131no—
261C4⋊C4—1131no—
262C4⋊C4—2261no—
263C4⋊C4—2261no—
264C4⋊C4—2261no—
265C4⋊C4—2261no—
266C4⋊C4—2261no—
267C4⋊C4—2261no—
268C4⋊C4—2261no—
269C4⋊C4—2261no—
270C4⋊C4—2261no—
271C4⋊C4C22×D11311yescharacteristic
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—21no—
282C42—1131no—
283C42—2261no—
284C42—2261no—
285C42—2261no—
286C23—1131no—
287C23D4×D11311yescharacteristic
288Q8—21no—
289Q8—21no—
290Q8—21no—
291Q8—42no—
292Q8—4522no—
293Q8—4522no—
294Q8—2261no—
295Q8—2261no—
296Q8—2261no—
297Q8—2261no—
298Q8#1426864712yes—
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×#1426864711yescharacteristic
343C4#1681366711yescharacteristic
344C2—41no—
345C2—4521no—
346C2#2029923811yescharacteristic
347C2#137×D11311yescharacteristic
348C2#2029941411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#419×C113C2
socleC22×C113C22×D4
prime radicalC2×C22⋊D113D4
hypercenter#419D113
hypocenterC113#3328
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
3. #20298947C2semidirect
4. #20298939C2semidirect
5. #20298937C2semidirect
6. #20298881C2semidirect
7. #20298856C2semidirect
8. #20298855C2semidirect
9. #20298807C2semidirect
10. #20298755C2semidirect
11. #20298754C2semidirect
12. #20298690C2semidirect
14. #20298605C2semidirect
15. #419×C113C2semidirect
175. C113#3328semidirect
190. #419D113semidirect

Maximal subgroups

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

subgroupindex
#202993162
Q8×C22⋊D1132
#202989472
#202989392
#202989372
#202988812
#202988562
#202988552
#202988072
#202987552
#202987542
#202986902
#202986742
#202986052
#419×C1132
#3328113