Finite Group Databasebeta

← #28402446

Subgroups — #28402446

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#20299303C211yesmaximal, characteristic
2Q8×C22⋊D113C211yesmaximal, characteristic
3#20298947C211yesmaximal, characteristic, complemented
4#20298933C211yesmaximal, characteristic, complemented
5#20298932C211yesmaximal, characteristic, complemented
6#20298891C211yesmaximal, characteristic, complemented
7#20298839C211yesmaximal, characteristic, complemented
8#20298838C211yesmaximal, characteristic, complemented
9#20298807C211yesmaximal, characteristic, complemented
10#20298755C211yesmaximal, characteristic, complemented
11#20298754C211yesmaximal, characteristic, complemented
12#20298690C211yesmaximal, characteristic, complemented
13C8×C22⋊D113C211yesmaximal, characteristic
14#103×D113C211yesmaximal, characteristic, complemented
15C2×#103×C113C211yesmaximal, characteristic, complemented
16C2×Q8×D113C2211yescharacteristic
17C2×Dic452C2211yescharacteristic
18C2×#14268637C2211yescharacteristic
19C2×#14268637C2211yescharacteristic
20C2×C8×D113C2211yescharacteristic
21#16813621C2211yescharacteristic
22#16813620—21no—
23#16813620C2211yescharacteristic
24#16813612—21no—
25#16813602C2211yescharacteristic
26#16813601—21no—
27#16813601—21no—
28#16813601C2211yescharacteristic
29#16813601C2211yescharacteristic
30#16813600—21no—
31#16813598—21no—
32#16813598C2211yescharacteristic
33Q8×Dic113C2211yescharacteristic
34#16813587C2211yescharacteristic
35C4×C22⋊D113—21no—
36C4×C22⋊D113—21no—
37C4×C22⋊D113C2211yescharacteristic
38C4⋊C4×D113C2211yescharacteristic
39#16813556C2211yescharacteristic
40#16813555C2211yescharacteristic
41#16813555C2211yescharacteristic
42#16813551C2211yescharacteristic
43#16813547C2211yescharacteristic
44#16813547C2211yescharacteristic
45#16813546C2211yescharacteristic
46#16813546C2211yescharacteristic
47#16813545C2211yescharacteristic
48#16813545C2211yescharacteristic
49C22⋊#11744751C2211yescharacteristic
50#16813534C2211yescharacteristic
51C8×Dic113C2211yescharacteristic
52C22×Q8×C113C2211yescharacteristic
53C22×C8×C113C2211yescharacteristic
54C2×C4⋊C4×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×D113—21no—
68C2×C4×D113C2311yescharacteristic
69Dic452—41no—
70#14268637—22no—
71#14268637—41no—
72C2×#11744751C2311yescharacteristic
73C2×#11744751C2311yescharacteristic
74C8×D113—41no—
75C4⋊Dic113—21no—
76C4⋊Dic113—21no—
77C4⋊Dic113C2311yescharacteristic
78C4⋊Dic113C2311yescharacteristic
79#14268626—21no—
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⋊Dic113—21no—
90C22⋊Dic113D411yescharacteristic
91#14268624—21no—
92#14268624—21no—
93#14268624D411yescharacteristic
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×C113—21no—
104C22×C4×C113C2311yescharacteristic
105C2×C8×C113—41no—
106C2×C8×C113C2311yescharacteristic
107C2×C8×C113C2311yescharacteristic
108C4⋊C4×C113—21no—
109C4⋊C4×C113C2311yescharacteristic
110C4⋊C4×C113C2311yescharacteristic
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×C113—81no—
126C2×C4×C113C2×D411yescharacteristic
127C2×C4×C113C2411yescharacteristic
128C22⋊D113Q1614yescomplemented
129C2×Dic113—21no—
130C2×Dic113—21no—
131C2×Dic113—21no—
132C2×Dic113—21no—
133C2×Dic113C2×D411yescharacteristic
134C2×Dic113C2×D411yescharacteristic
135C2×Dic113C2×D411yescharacteristic
136C4×D113—21no—
137C4×D113—21no—
138C4×D113—42no—
139C4×D113—81no—
140Dic226—21no—
141Dic226—21no—
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#451—1131no—
189C4×Q16—1131no—
190C8×D4—1131no—
191C2×#103—1131no—
192C2×#103D11311yescharacteristic, complemented
193C22×Q8—1131no—
194C22×Q8C2×D11311yescharacteristic
195C2×Q16—1131no—
196C2×Q16—1131no—
197C2×Q16—1131no—
198C22×C8—1131no—
199C22×C8C2×D11311yescharacteristic
200C4⋊Q8—1131no—
201C4⋊Q8—1131no—
202C4⋊Q8—2261no—
203#125—2261no—
204C22⋊Q8—1131no—
205C22⋊Q8—1131no—
206C22⋊Q8—1131no—
207C22⋊Q8—1131no—
208C22⋊Q8—2261no—
209C22⋊Q8—2261no—
210C22⋊Q8—2261no—
211C22⋊Q8—2261no—
212C4×Q8—1131no—
213C4×Q8—1131no—
214C4×D4—1131no—
215C4×D4—2261no—
216C4×D4—2261no—
217C2×C4⋊C4—1131no—
218C2×C4⋊C4C2×D11311yescharacteristic
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#103C2×D11311yescharacteristic
230#103C2×D11311yescharacteristic
231#103C2×D11311yescharacteristic
232#103C2×D11311yescharacteristic
233C22⋊C8—1131no—
234C22⋊C8—1131no—
235C4×C8—1131no—
236C2×Q8—21no—
237C2×Q8—22no—
238C2×Q8—41no—
239C2×Q8—1131no—
240C2×Q8—1131no—
241C2×Q8—4521no—
242C2×Q8—2261no—
243C2×Q8—2261no—
244C2×Q8—2262no—
245C2×Q8C22×D11311yescharacteristic
246C2×Q8C22×D11311yescharacteristic
247C2×D4—1131no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—1131no—
251C22×C4—2261no—
252C22×C4—2261no—
253C22×C4C22×D11311yescharacteristic
254Q16—4521no—
255Q16—4521no—
256Q16—2262no—
257C2×C8—41no—
258C2×C8—1131no—
259C2×C8—1131no—
260C2×C8—4521no—
261C2×C8C22×D11311yescharacteristic
262C2×C8C22×D11311yescharacteristic
263C4⋊C4—21no—
264C4⋊C4—1131no—
265C4⋊C4—1131no—
266C4⋊C4—1131no—
267C4⋊C4—2261no—
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⋊C4C22×D11311yescharacteristic
278C4⋊C4C22×D11311yescharacteristic
279C22⋊C4—1131no—
280C22⋊C4—1131no—
281C22⋊C4—2261no—
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—42no—
294Q8—9041no—
295Q8—4522no—
296Q8—2261no—
297Q8—2261no—
298Q8—2261no—
299Q8—2261no—
300Q8#1426864712yes—
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—81no—
310C2×C4—1131no—
311C2×C4—1131no—
312C2×C4—1131no—
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×#1426864711yescharacteristic
347C4#1681366711yescharacteristic
348C2—22no—
349C2—2262no—
350C2#2029923811yescharacteristic
351C2C2×Q16×D11311yescharacteristic
352C2#2029940411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC2×#103×C113C2
socleC22×C113C22×D4
prime radicalC2×C22⋊D113D4
hypercenterC2×#103D113
hypocenterC113#3299
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
3. #20298947C2semidirect
4. #20298933C2semidirect
5. #20298932C2semidirect
6. #20298891C2semidirect
7. #20298839C2semidirect
8. #20298838C2semidirect
9. #20298807C2semidirect
10. #20298755C2semidirect
11. #20298754C2semidirect
12. #20298690C2semidirect
14. #103×D113C2semidirect
15. C2×#103×C113C2semidirect
128. C22⋊D113Q16semidirect
177. C113#3299semidirect
192. C2×#103D113semidirect

Maximal subgroups

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

subgroupindex
#202993032
Q8×C22⋊D1132
#202989472
#202989332
#202989322
#202988912
#202988392
#202988382
#202988072
#202987552
#202987542
#202986902
C8×C22⋊D1132
#103×D1132
C2×#103×C1132
#3299113