Finite Group Databasebeta

← #28400102

Subgroups — #28400102

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×#16813651C211yesmaximal, characteristic
2C2×Q16×D113C211yesmaximal, characteristic, complemented
3#20299168C211yesmaximal, characteristic
4#20299074C211yesmaximal, characteristic, complemented
5#20298819C211yesmaximal, characteristic, complemented
6#20298818C211yesmaximal, characteristic, complemented
7#20298817C211yesmaximal, characteristic, complemented
8#20298809C211yesmaximal, characteristic, complemented
9#20298808C211yesmaximal, characteristic, complemented
10#20298807C211yesmaximal, characteristic, complemented
11#20298806C211yesmaximal, characteristic, complemented
12#20298623C211yesmaximal, characteristic, complemented
13#20298605C211yesmaximal, characteristic, complemented
14#20298591C211yesmaximal, characteristic
15#464×C113C211yesmaximal, characteristic, complemented
16C2×#14268646C2211yescharacteristic
17C2×Q8×D113C2211yescharacteristic
18C2×Q8×D113C2211yescharacteristic
19#16813651—24no—
20C2×Dic452C2211yescharacteristic
21C2×Dic452C2211yescharacteristic
22C2×#14268637C2211yescharacteristic
23C2×#14268637C2211yescharacteristic
24C2×#14268637C2211yescharacteristic
25Q16×D113—24no—
26C2×#14268635C2211yescharacteristic
27C2×#14268630C2211yescharacteristic
28C2×C8×D113C2211yescharacteristic
29#16813622C2211yescharacteristic
30#16813620C2211yescharacteristic
31#16813609C2211yescharacteristic
32#16813604—21no—
33#16813604—21no—
34#16813599—21no—
35#16813599—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#16813547C2211yescharacteristic
50#16813546C2211yescharacteristic
51#16813545C2211yescharacteristic
52#16813545C2211yescharacteristic
53#16813543C2211yescharacteristic
54C2×Q16×C113C2211yescharacteristic
55C2×SD16×C113C2211yescharacteristic
56#124×C113C2211yescharacteristic
57C4×Q8×C113C2211yescharacteristic
58C4⋊C8×C113C2211yescharacteristic
59#103×C113C2211yescharacteristic
60#102×C113C2211yescharacteristic
61#14268646—22no—
62#14268646—22no—
63C2×Dic226—21no—
64C2×Dic226—21no—
65C2×Dic226C2311yescharacteristic
66C2×Dic226C2311yescharacteristic
67C2×Dic226C2311yescharacteristic
68Q8×D113—22no—
69Q8×D113—22no—
70Q8×D113—22no—
71Q8×D113D414yes—
72C2×C22⋊D113—21no—
73C22×Dic113—21no—
74C2×C4×D113—21no—
75C2×C4×D113—21no—
76C2×C4×D113C2311yescharacteristic
77Dic452—22no—
78Dic452—22no—
79#14268637—22no—
80#14268637—22no—
81#14268637—22no—
82#14268635—22no—
83#14268630—22no—
84C2×#11744751C2311yescharacteristic
85C2×#11744751C2311yescharacteristic
86C8×D113—22no—
87C4⋊Dic113—21no—
88C4⋊Dic113—21no—
89C4⋊Dic113—21no—
90C4⋊Dic113C2311yescharacteristic
91#14268626—21no—
92#14268626—21no—
93#14268626—21no—
94#14268626—21no—
95#14268626D411yescharacteristic
96#14268626D411yescharacteristic
97C22⋊Dic113—21no—
98C22⋊Dic113—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×D4×C113C2311yescharacteristic
110Q16×C113—22no—
111SD16×C113—22no—
112C2×C8×C113C2311yescharacteristic
113C2×C8×C113C2311yescharacteristic
114C4⋊C4×C113—21no—
115C4⋊C4×C113C2311yescharacteristic
116C22⋊C4×C113—21no—
117C22⋊C4×C113—21no—
118C42×C113—21no—
119C42×C113C2311yescharacteristic
120C23×C113—21no—
121C22×D113C2×D411yescharacteristic
122Q8×C113—21no—
123Q8×C113—21no—
124Q8×C113—21no—
125Q8×C113C2×D412yes—
126D4×C113—21no—
127D4×C113—21no—
128C2×C4×C113—21no—
129C2×C4×C113—21no—
130C2×C4×C113—21no—
131C2×C4×C113C2×D411yescharacteristic
132C2×C4×C113C2×D411yescharacteristic
133C2×C4×C113C2411yescharacteristic
134C22⋊D113—42no—
135C2×Dic113—21no—
136C2×Dic113—21no—
137C2×Dic113—21no—
138C2×Dic113—21no—
139C2×Dic113—42no—
140C2×Dic113C2×D411yescharacteristic
141C2×Dic113C2×D411yescharacteristic
142C2×Dic113C2×D411yescharacteristic
143C4×D113—24no—
144C4×D113—42no—
145C4×D113C2×D412yes—
146C4×D113#4112yes—
147Dic226—21no—
148Dic226—24no—
149Dic226—21no—
150Dic226—21no—
151Dic226—21no—
152Dic226—21no—
153Dic226—42no—
154Dic226C2×D412yes—
155C8×C113—21no—
156C8×C113—21no—
157#11744751—21no—
158#11744751—21no—
159C22×C113—41no—
160C22×C113—41no—
161C22×C113—41no—
162C22×C113C22×D411yescharacteristic
163C2×D113—21no—
164C2×D113—21no—
165C2×D113#12112yes—
166C4×C113—22no—
167C4×C113—21no—
168C4×C113—21no—
169C4×C113—41no—
170C4×C113—41no—
171C4×C113C22×D411yescharacteristic
172C4×C113C2×#4111yescharacteristic
173Dic113—22no—
174Dic113—21no—
175Dic113—21no—
176Dic113—41no—
177Dic113—41no—
178Dic113—41no—
179Dic113#12112yes—
180C2×C113—81no—
181C2×C113C2×#12111yescharacteristic
182C2×C113#57811yescharacteristic
183C2×C113#57811yescharacteristic
184D113—22no—
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#464D11311yescharacteristic, complemented
195#462—1131no—
196#462—1131no—
197#462—1131no—
198#462—1131no—
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—1131no—
211C2×Q16—2264no—
212C2×Q16C2×D11311yescharacteristic
213C2×SD16—1131no—
214C2×SD16C2×D11311yescharacteristic
215C2×M16—1131no—
216C22×C8—1131no—
217C4⋊Q8—1131no—
218C4⋊Q8—1131no—
219#124—1131no—
220#124C2×D11311yescharacteristic
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#103—1131no—
244#103C2×D11311yescharacteristic
245#102—1131no—
246#102C2×D11311yescharacteristic
247#41—2262no—
248#41—2262no—
249C2×Q8—1134no—
250C2×Q8—1131no—
251C2×Q8—1131no—
252C2×Q8—1131no—
253C2×Q8—2261no—
254C2×Q8—2261no—
255C2×Q8—2262no—
256C2×Q8—2262no—
257C2×Q8—2262no—
258C2×Q8C22×D11311yescharacteristic
259C2×Q8C22×D11311yescharacteristic
260C2×D4—2261no—
261C2×D4C22×D11311yescharacteristic
262C22×C4—1131no—
263C22×C4—2261no—
264C22×C4—2261no—
265C22×C4—2261no—
266Q16—22no—
267Q16—2262no—
268Q16—2262no—
269Q16—2262no—
270Q16—2262no—
271Q16—2262no—
272SD16—22no—
273SD16—2262no—
274M16—2262no—
275C2×C8—1131no—
276C2×C8—1131no—
277C2×C8—2262no—
278C2×C8C22×D11311yescharacteristic
279C2×C8C22×D11311yescharacteristic
280C4⋊C4—21no—
281C4⋊C4—1131no—
282C4⋊C4—1131no—
283C4⋊C4—1131no—
284C4⋊C4—2261no—
285C4⋊C4—2261no—
286C4⋊C4—2261no—
287C4⋊C4—2261no—
288C4⋊C4—2261no—
289C4⋊C4—2261no—
290C4⋊C4—2261no—
291C4⋊C4C22×D11311yescharacteristic
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—1131no—
295C22⋊C4—1131no—
296C22⋊C4—2261no—
297C22⋊C4—2261no—
298C22⋊C4—2261no—
299C42—21no—
300C42—1131no—
301C42—2261no—
302C42—2261no—
303C42—2261no—
304C42—2261no—
305C42C22×D11311yescharacteristic
306C23—21no—
307C23—1131no—
308Q8—21no—
309Q8—21no—
310Q8—21no—
311Q8—1132no—
312Q8—4522no—
313Q8—2264no—
314Q8—2261no—
315Q8—2261no—
316Q8—2261no—
317Q8—2261no—
318Q8—2261no—
319Q8D4×D11312yes—
320D4—21no—
321D4—21no—
322D4—4522no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—1131no—
327C2×C4—1132no—
328C2×C4—1132no—
329C2×C4—1131no—
330C2×C4—1131no—
331C2×C4—4522no—
332C2×C4—4522no—
333C2×C4—2264no—
334C2×C4—2261no—
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—41no—
346C22—41no—
347C22—41no—
348C22—1132no—
349C22—2261no—
350C22—2261no—
351C22C2×D4×D11311yescharacteristic
352C4—22no—
353C4—21no—
354C4—21no—
355C4—41no—
356C4—41no—
357C4—1132no—
358C4—4521no—
359C4—4521no—
360C4—4521no—
361C4—2262no—
362C4—2261no—
363C4—2261no—
364C4C2×D4×D11311yescharacteristic
365C4#41×D11311yescharacteristic
366C2—81no—
367C2—2262no—
368C2#121×D11311yescharacteristic
369C2#2029941211yescharacteristic
370C2#2029941411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#464×C113C2
socleC22×C113C22×D4
prime radicalC2×#14268646C22
hypercenter#464D113
hypocenterC113#3044
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
2. C2×Q16×D113C2semidirect
4. #20299074C2semidirect
5. #20298819C2semidirect
6. #20298818C2semidirect
7. #20298817C2semidirect
8. #20298809C2semidirect
9. #20298808C2semidirect
10. #20298807C2semidirect
11. #20298806C2semidirect
12. #20298623C2semidirect
13. #20298605C2semidirect
15. #464×C113C2semidirect
186. C113#3044semidirect
194. #464D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136512
C2×Q16×D1132
#202991682
#202990742
#202988192
#202988182
#202988172
#202988092
#202988082
#202988072
#202988062
#202986232
#202986052
#202985912
#464×C1132
#3044113