Finite Group Databasebeta

← #28400119

Subgroups — #28400119

Order 14464.

472 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16813651C211yesmaximal, characteristic, complemented
2C2×#16813643C211yesmaximal, characteristic
3#20299173C211yesmaximal, characteristic, complemented
4#20299077C211yesmaximal, characteristic, complemented
5#20298823C211yesmaximal, characteristic, complemented
6#20298821C211yesmaximal, characteristic, complemented
7#20298815C211yesmaximal, characteristic, complemented
8#20298813C211yesmaximal, characteristic, complemented
9#20298807C211yesmaximal, characteristic, complemented
10#20298805C211yesmaximal, characteristic, complemented
11#20298801C211yesmaximal, characteristic, complemented
12#20298623C211yesmaximal, characteristic, complemented
13#20298598C211yesmaximal, characteristic, complemented
14#103×D113C211yesmaximal, characteristic, complemented
15#461×C113C211yesmaximal, characteristic, complemented
16C2×#14268648C2211yescharacteristic
17C2×#14268646C2211yescharacteristic
18C2×Q8×D113C2211yescharacteristic
19#16813651—24no—
20#16813643—24no—
21C2×Dic452C2211yescharacteristic
22C2×#14268637C2211yescharacteristic
23C2×#14268637C2211yescharacteristic
24C2×#14268636C2211yescharacteristic
25C2×#14268635C2211yescharacteristic
26C2×#14268632C2211yescharacteristic
27C2×#14268630C2211yescharacteristic
28C2×C8×D113C2211yescharacteristic
29#16813620C2211yescharacteristic
30#16813611C2211yescharacteristic
31#16813610C2211yescharacteristic
32#16813607—21no—
33#16813607—21no—
34#16813600—21no—
35#16813600—21no—
36C4×Dic226C2211yescharacteristic
37#16813587C2211yescharacteristic
38D4×Dic113C2211yescharacteristic
39C4×C22⋊D113—21no—
40#16813582—21no—
41#16813579C2211yescharacteristic
42#16813578—21no—
43C2×#14268626—21no—
44C4⋊C4×D113C2211yescharacteristic
45C4⋊#11744751C2211yescharacteristic
46#16813551C2211yescharacteristic
47#16813551C2211yescharacteristic
48#16813547C2211yescharacteristic
49#16813546C2211yescharacteristic
50#16813546C2211yescharacteristic
51#16813545C2211yescharacteristic
52#16813544C2211yescharacteristic
53#16813542C2211yescharacteristic
54C2×SD16×C113C2211yescharacteristic
55C2×SD16×C113C2211yescharacteristic
56C4⋊Q8×C113C2211yescharacteristic
57C4×D4×C113C2211yescharacteristic
58C4⋊C8×C113C2211yescharacteristic
59#103×C113C2211yescharacteristic
60#103×C113C2211yescharacteristic
61#14268648—22no—
62#14268648—22no—
63#14268646—22no—
64#14268646D414yes—
65C2×Dic226—21no—
66C2×Dic226C2311yescharacteristic
67C2×Dic226C2311yescharacteristic
68Q8×D113—22no—
69Q8×D113—22no—
70C2×D452—21no—
71C2×D452C2311yescharacteristic
72C2×C22⋊D113—21no—
73C22×Dic113—21no—
74C22×Dic113—21no—
75C2×C4×D113—21no—
76C2×C4×D113—21no—
77C2×C4×D113—21no—
78C2×C4×D113C2311yescharacteristic
79Dic452—22no—
80#14268637—22no—
81#14268637—22no—
82#14268636—22no—
83#14268635—22no—
84#14268632—22no—
85#14268630—22no—
86C2×#11744751C2311yescharacteristic
87C2×#11744751C2311yescharacteristic
88C8×D113—22no—
89C4⋊Dic113C2311yescharacteristic
90#14268626—21no—
91#14268626—21no—
92#14268626—21no—
93#14268626—21no—
94#14268626—21no—
95#14268626D411yescharacteristic
96#14268626D411yescharacteristic
97C22⋊Dic113—21no—
98#14268624—21no—
99#14268624—21no—
100#14268624—21no—
101#14268624—21no—
102#14268624D411yescharacteristic
103#14268624D411yescharacteristic
104C4×Dic113—21no—
105C4×Dic113—21no—
106C4×Dic113C2311yescharacteristic
107C2×Q8×C113C2311yescharacteristic
108C2×Q8×C113C2311yescharacteristic
109C2×D4×C113C2311yescharacteristic
110C22×C4×C113—21no—
111SD16×C113—22no—
112SD16×C113—22no—
113C2×C8×C113C2311yescharacteristic
114C2×C8×C113C2311yescharacteristic
115C4⋊C4×C113—21no—
116C4⋊C4×C113—21no—
117C4⋊C4×C113C2311yescharacteristic
118C22⋊C4×C113—21no—
119C42×C113C2311yescharacteristic
120C23×C113—21no—
121C22×D113—21no—
122C22×D113C2×D411yescharacteristic
123Q8×C113—21no—
124Q8×C113—21no—
125Q8×C113—21no—
126Q8×C113—21no—
127D4×C113—21no—
128D4×C113C2×D412yes—
129C2×C4×C113—21no—
130C2×C4×C113—21no—
131C2×C4×C113—21no—
132C2×C4×C113—81no—
133C2×C4×C113C2×D411yescharacteristic
134C2×C4×C113C2×D411yescharacteristic
135C2×C4×C113C2411yescharacteristic
136C22⋊D113—24no—
137C2×Dic113—21no—
138C2×Dic113—24no—
139C2×Dic113—21no—
140C2×Dic113—21no—
141C2×Dic113—81no—
142C2×Dic113C2×D411yescharacteristic
143C2×Dic113C2×D411yescharacteristic
144C2×Dic113C2×D411yescharacteristic
145D452—21no—
146D452—21no—
147D452—42no—
148C4×D113—42no—
149C4×D113—42no—
150C4×D113—81no—
151C4×D113C2×D412yes—
152C4×D113#4112yes—
153Dic226—21no—
154Dic226—21no—
155Dic226—21no—
156Dic226—42no—
157Dic226C2×D412yes—
158C8×C113—21no—
159C8×C113—21no—
160#11744751—21no—
161#11744751—21no—
162C22×C113—22no—
163C22×C113—41no—
164C22×C113—41no—
165C22×C113C22×D411yescharacteristic
166C2×D113—21no—
167C2×D113—21no—
168C2×D113—41no—
169C2×D113—41no—
170C2×D113—41no—
171C2×D113#12112yes—
172C4×C113—21no—
173C4×C113—21no—
174C4×C113—41no—
175C4×C113—41no—
176C4×C113—41no—
177C4×C113C22×D411yescharacteristic
178C4×C113C2×#4111yescharacteristic
179Dic113—22no—
180Dic113—21no—
181Dic113—21no—
182Dic113—41no—
183Dic113—41no—
184Dic113#12112yes—
185C2×C113—42no—
186C2×C113C2×#12111yescharacteristic
187C2×C113#57711yescharacteristic
188C2×C113#57811yescharacteristic
189D113—22no—
190D113—81no—
191#3046—1131nomaximal, Sylow
192C113#304611yescharacteristic, complemented, Sylow
193C2×#137—1131no—
194C2×#135—1131no—
195#536—1131no—
196#520—1131no—
197#464—1131no—
198#464—1131no—
199#463—1131no—
200#463—1131no—
201#462—1131no—
202#462—1131no—
203#461—1131no—
204#461D11311yescharacteristic, complemented
205#424—1131no—
206#417—1131no—
207C2×#103—1131no—
208C2×#41—1131no—
209C2×#41—1131no—
210C22×Q8—1131no—
211#137—2264no—
212#135—2264no—
213C2×Q16—1131no—
214C2×Q16—1131no—
215C2×Q16—1131no—
216C2×SD16—1131no—
217C2×SD16—1131no—
218C2×SD16C2×D11311yescharacteristic
219C2×SD16C2×D11311yescharacteristic
220C2×D8—1131no—
221C2×M16—1131no—
222C22×C8—1131no—
223C4⋊Q8—1131no—
224C4⋊Q8C2×D11311yescharacteristic
225#124—1131no—
226#124—1131no—
227#123—2261no—
228#123—2261no—
229C22⋊Q8—2261no—
230C22⋊Q8—2261no—
231C4×Q8—1131no—
232C4×Q8—1131no—
233C4×D4—1131no—
234C4×D4—2261no—
235C4×D4—2261no—
236C4×D4C2×D11311yescharacteristic
237#117—1131no—
238#117—2261no—
239C2×C4⋊C4—1131no—
240C2×C4⋊C4—2261no—
241C4⋊C8—1131no—
242C4⋊C8—1131no—
243C4⋊C8—1131no—
244C4⋊C8C2×D11311yescharacteristic
245#103—1131no—
246#103—1131no—
247#103—1131no—
248#103—1131no—
249#103C2×D11311yescharacteristic
250#103C2×D11311yescharacteristic
251#102—1131no—
252#102—1131no—
253#41—1134no—
254#41—2262no—
255#41—2262no—
256#41—2262no—
257C2×Q8—1131no—
258C2×Q8—1131no—
259C2×Q8—2261no—
260C2×Q8—2262no—
261C2×Q8—2262no—
262C2×Q8C22×D11311yescharacteristic
263C2×Q8C22×D11311yescharacteristic
264C2×D4—1131no—
265C2×D4—2261no—
266C2×D4—2261no—
267C2×D4C22×D11311yescharacteristic
268C22×C4—21no—
269C22×C4—1131no—
270C22×C4—2261no—
271C22×C4—2261no—
272C22×C4—2261no—
273C22×C4—2261no—
274C22×C4—2261no—
275Q16—2262no—
276Q16—2262no—
277Q16—2262no—
278SD16—22no—
279SD16—22no—
280SD16—2262no—
281SD16—2262no—
282D8—2262no—
283M16—2262no—
284C2×C8—1131no—
285C2×C8—1131no—
286C2×C8—2262no—
287C2×C8C22×D11311yescharacteristic
288C2×C8C22×D11311yescharacteristic
289C4⋊C4—21no—
290C4⋊C4—21no—
291C4⋊C4—1131no—
292C4⋊C4—1131no—
293C4⋊C4—1131no—
294C4⋊C4—2261no—
295C4⋊C4—2261no—
296C4⋊C4—2261no—
297C4⋊C4—2261no—
298C4⋊C4—2261no—
299C4⋊C4C22×D11311yescharacteristic
300C22⋊C4—21no—
301C22⋊C4—1131no—
302C22⋊C4—1131no—
303C22⋊C4—2261no—
304C22⋊C4—2261no—
305C22⋊C4—2261no—
306C22⋊C4—2261no—
307C22⋊C4—2261no—
308C42—1131no—
309C42—2261no—
310C42—2261no—
311C42C22×D11311yescharacteristic
312C23—21no—
313C23—1131no—
314C23—2261no—
315Q8—21no—
316Q8—21no—
317Q8—21no—
318Q8—21no—
319Q8—1132no—
320Q8—4522no—
321Q8—2261no—
322Q8—2261no—
323Q8—2261no—
324D4—21no—
325D4—4522no—
326D4—2264no—
327D4—2261no—
328D4—2261no—
329D4D4×D11312yes—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—81no—
334C2×C4—1131no—
335C2×C4—1132no—
336C2×C4—1132no—
337C2×C4—1131no—
338C2×C4—1131no—
339C2×C4—9041no—
340C2×C4—9041no—
341C2×C4—4522no—
342C2×C4—4522no—
343C2×C4—2264no—
344C2×C4—2261no—
345C2×C4—2261no—
346C2×C4—2261no—
347C2×C4D4×D11311yescharacteristic
348C2×C4D4×D11311yescharacteristic
349C2×C4C23×D11311yescharacteristic
350C8—21no—
351C8—21no—
352C8—2261no—
353C8—2261no—
354C22—22no—
355C22—41no—
356C22—41no—
357C22—1132no—
358C22—4521no—
359C22—4521no—
360C22—4521no—
361C22—2261no—
362C22—2261no—
363C22C2×D4×D11311yescharacteristic
364C4—21no—
365C4—21no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—1132no—
370C4—4521no—
371C4—4521no—
372C4—2262no—
373C4—2261no—
374C4—2261no—
375C4C2×D4×D11311yescharacteristic
376C4#41×D11311yescharacteristic
377C2—42no—
378C2—9041no—
379C2—2262no—
380C2#121×D11311yescharacteristic
381C2#2029940411yescharacteristic
382C2#2029941411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#461×C113C2
socleC22×C113C22×D4
prime radicalC2×#16813643C2
hypercenter#461D113
hypocenterC113#3046
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. C2×#16813651C2semidirect
3. #20299173C2semidirect
4. #20299077C2semidirect
5. #20298823C2semidirect
6. #20298821C2semidirect
7. #20298815C2semidirect
8. #20298813C2semidirect
9. #20298807C2semidirect
10. #20298805C2semidirect
11. #20298801C2semidirect
12. #20298623C2semidirect
13. #20298598C2semidirect
14. #103×D113C2semidirect
15. #461×C113C2semidirect
192. C113#3046semidirect
204. #461D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136512
C2×#168136432
#202991732
#202990772
#202988232
#202988212
#202988152
#202988132
#202988072
#202988052
#202988012
#202986232
#202985982
#103×D1132
#461×C1132
#3046113