Finite Group Databasebeta

← #28402443

Subgroups — #28402443

Order 14464.

388 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299306C211yesmaximal, characteristic
2Q8×C22⋊D113C211yesmaximal, characteristic
3#20298947C211yesmaximal, characteristic, complemented
4#20298934C211yesmaximal, characteristic, complemented
5#20298932C211yesmaximal, characteristic, complemented
6#20298891C211yesmaximal, characteristic, complemented
7#20298837C211yesmaximal, characteristic, complemented
8#20298836C211yesmaximal, characteristic, complemented
9#20298806C211yesmaximal, characteristic, complemented
10#20298752C211yesmaximal, characteristic, complemented
11Q16×Dic113C211yesmaximal, characteristic, complemented
12#20298661C211yesmaximal, characteristic
13C2×#16813546C211yesmaximal, characteristic, complemented
14#103×D113C211yesmaximal, characteristic, complemented
15#451×C113C211yesmaximal, characteristic, complemented
16C2×Q8×D113C2211yescharacteristic
17C2×#14268637C2211yescharacteristic
18C22×#11744751C2211yescharacteristic
19C2×C8×D113C2211yescharacteristic
20#16813621C2211yescharacteristic
21#16813620—21no—
22#16813620C2211yescharacteristic
23#16813612—21no—
24#16813602—21no—
25#16813601—21no—
26#16813601C2211yescharacteristic
27#16813599—21no—
28#16813598—21no—
29#16813598C2211yescharacteristic
30#16813598C2211yescharacteristic
31Q8×Dic113C2211yescharacteristic
32Q8×Dic113C2211yescharacteristic
33C4×C22⋊D113—21no—
34C4×C22⋊D113C2211yescharacteristic
35#16813582—21no—
36C2×C4⋊Dic113C2211yescharacteristic
37C4⋊C4×D113C2211yescharacteristic
38#16813556C2211yescharacteristic
39#16813556C2211yescharacteristic
40#16813555C2211yescharacteristic
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
65C22×Dic113—21no—
66C2×C4×D113—21no—
67C2×C4×D113—21no—
68C2×C4×D113C2311yescharacteristic
69#14268637—41no—
70C2×#11744751—41no—
71C2×#11744751C2311yescharacteristic
72C2×#11744751C2311yescharacteristic
73C8×D113—41no—
74C4⋊Dic113—21no—
75C4⋊Dic113—21no—
76C4⋊Dic113—21no—
77C4⋊Dic113C2311yescharacteristic
78C4⋊Dic113C2311yescharacteristic
79C4⋊Dic113C2311yescharacteristic
80#14268626—21no—
81#14268626—21no—
82#14268626—21no—
83#14268626—21no—
84#14268626—21no—
85#14268626—21no—
86#14268626—21no—
87#14268626D411yescharacteristic
88C22⋊Dic113—21no—
89C22⋊Dic113D411yescharacteristic
90#14268624—21no—
91#14268624—21no—
92#14268624D411yescharacteristic
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⋊D113Q1614yescomplemented
130C2×Dic113—21no—
131C2×Dic113—21no—
132C2×Dic113—21no—
133C2×Dic113—21no—
134C2×Dic113—81no—
135C2×Dic113C2×D411yescharacteristic
136C2×Dic113C2×D411yescharacteristic
137C2×Dic113C2×D411yescharacteristic
138C4×D113—21no—
139C4×D113—21no—
140C4×D113—42no—
141C4×D113—81no—
142Dic226—21no—
143Dic226—21no—
144Dic226—42no—
145Dic226—81no—
146C8×C113—21no—
147C8×C113—21no—
148#11744751—21no—
149#11744751—21no—
150C22×C113—21no—
151C22×C113—21no—
152C22×C113C2×Q1612yes—
153C22×C113C22×D411yescharacteristic
154C2×D113—21no—
155C2×D113—21no—
156C2×D113C2×Q1612yes—
157C4×C113—22no—
158C4×C113—21no—
159C4×C113—41no—
160C4×C113—41no—
161C4×C113—41no—
162C4×C113C2×#4111yescharacteristic
163C4×C113H(5,𝔽2)11yescharacteristic
164Dic113—21no—
165Dic113—21no—
166Dic113—41no—
167Dic113—41no—
168Dic113—41no—
169Dic113—41no—
170Dic113C2×Q1612yes—
171C2×C113—22no—
172C2×C113#54611yescharacteristic
173C2×C113C22×Q1611yescharacteristic
174C2×C113#57711yescharacteristic
175D113—22no—
176#3299—1131nomaximal, Sylow
177C113#329911yescharacteristic, complemented, Sylow
178#554—1131no—
179D4×Q8—1131no—
180#487—1131no—
181#484—1131no—
182#484—1131no—
183#477—1131no—
184#467—1131no—
185#467—1131no—
186#462—1131no—
187#451—1131no—
188#451D11311yescharacteristic, complemented
189C4×Q16—1131no—
190C8×D4—1131no—
191C2×#103—1131no—
192C2×#103—1131no—
193C22×Q8—1131no—
194C22×Q8C2×D11311yescharacteristic
195C2×Q16—1131no—
196C2×Q16C2×D11311yescharacteristic
197C2×Q16C2×D11311yescharacteristic
198C22×C8—1131no—
199C22×C8—1131no—
200C4⋊Q8—1131no—
201C4⋊Q8—1131no—
202C4⋊Q8—2261no—
203#125—2261no—
204C22⋊Q8—1131no—
205C22⋊Q8—1131no—
206C22⋊Q8—1131no—
207C22⋊Q8—2261no—
208C22⋊Q8—2261no—
209C22⋊Q8—2261no—
210C22⋊Q8—2261no—
211C22⋊Q8C2×D11311yescharacteristic
212C4×Q8—1131no—
213C4×Q8—1131no—
214C4×D4—1131no—
215C4×D4—2261no—
216C4×D4—2261no—
217C2×C4⋊C4—1131no—
218C2×C4⋊C4—1131no—
219#107—1131no—
220#107—1131no—
221#107—1131no—
222C4⋊C8—1131no—
223#103—1131no—
224#103—1131no—
225#103—1131no—
226#103—1131no—
227#103—1131no—
228#103—1131no—
229#103—1131no—
230#103—1131no—
231#103C2×D11311yescharacteristic
232#103C2×D11311yescharacteristic
233C22⋊C8—1131no—
234C22⋊C8C2×D11311yescharacteristic
235C4×C8—1131no—
236C2×Q8—21no—
237C2×Q8—22no—
238C2×Q8—41no—
239C2×Q8—1131no—
240C2×Q8—4521no—
241C2×Q8—2261no—
242C2×Q8—2261no—
243C2×Q8—2262no—
244C2×Q8C22×D11311yescharacteristic
245C2×Q8C22×D11311yescharacteristic
246C2×Q8C22×D11311yescharacteristic
247C2×D4—1131no—
248C22×C4—21no—
249C22×C4—1131no—
250C22×C4—2261no—
251C22×C4—2261no—
252C22×C4—2261no—
253C22×C4C22×D11311yescharacteristic
254Q16—22no—
255Q16—41no—
256Q16—4521no—
257C2×C8—1131no—
258C2×C8—1131no—
259C2×C8—4521no—
260C2×C8—4521no—
261C2×C8C22×D11311yescharacteristic
262C2×C8C22×D11311yescharacteristic
263C4⋊C4—21no—
264C4⋊C4—1131no—
265C4⋊C4—1131no—
266C4⋊C4—1131no—
267C4⋊C4—1131no—
268C4⋊C4—2261no—
269C4⋊C4—2261no—
270C4⋊C4—2261no—
271C4⋊C4—2261no—
272C4⋊C4—2261no—
273C4⋊C4—2261no—
274C4⋊C4—2261no—
275C4⋊C4—2261no—
276C4⋊C4—2261no—
277C4⋊C4—2261no—
278C4⋊C4C22×D11311yescharacteristic
279C22⋊C4—21no—
280C22⋊C4—1131no—
281C22⋊C4—1131no—
282C22⋊C4—2261no—
283C22⋊C4—2261no—
284C22⋊C4—2261no—
285C42—1131no—
286C42—2261no—
287C42—2261no—
288C23—1131no—
289C23D4×D11311yescharacteristic
290Q8—21no—
291Q8—21no—
292Q8—21no—
293Q8—21no—
294Q8—21no—
295Q8—42no—
296Q8—9041no—
297Q8—4522no—
298Q8—2261no—
299Q8—2261no—
300Q8#1426864612yes—
301D4—1134no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—42no—
309C2×C4—1131no—
310C2×C4—1131no—
311C2×C4—1131no—
312C2×C4—9041no—
313C2×C4—9041no—
314C2×C4—4522no—
315C2×C4—2261no—
316C2×C4—2261no—
317C2×C4—2261no—
318C2×C4—2261no—
319C2×C4—2261no—
320C2×C4—2261no—
321C2×C4D4×D11311yescharacteristic
322C2×C4C23×D11311yescharacteristic
323C8—21no—
324C8—21no—
325C8—2261no—
326C8—2261no—
327C22—21no—
328C22—21no—
329C22—1132no—
330C22—2261no—
331C22—2261no—
332C22Q16×D11312yes—
333C22C2×D4×D11311yescharacteristic
334C4—21no—
335C4—22no—
336C4—41no—
337C4—41no—
338C4—41no—
339C4—1132no—
340C4—4521no—
341C4—4521no—
342C4—4521no—
343C4—4521no—
344C4—2261no—
345C4—2261no—
346C4C2×#1426864611yescharacteristic
347C4#1681366711yescharacteristic
348C2—22no—
349C2—2262no—
350C2#2029923511yescharacteristic
351C2C2×Q16×D11311yescharacteristic
352C2#2029940711yescharacteristic
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#3299
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. #20298934C2semidirect
5. #20298932C2semidirect
6. #20298891C2semidirect
7. #20298837C2semidirect
8. #20298836C2semidirect
9. #20298806C2semidirect
10. #20298752C2semidirect
11. Q16×Dic113C2semidirect
13. C2×#16813546C2semidirect
14. #103×D113C2semidirect
15. #451×C113C2semidirect
129. C22⋊D113Q16semidirect
177. C113#3299semidirect
188. #451D113semidirect

Maximal subgroups

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

subgroupindex
#202993062
Q8×C22⋊D1132
#202989472
#202989342
#202989322
#202988912
#202988372
#202988362
#202988062
#202987522
Q16×Dic1132
#202986612
C2×#168135462
#103×D1132
#451×C1132
#3299113