Finite Group Databasebeta

← #46846328

Subgroups — #46846328

Order 34688.

386 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31774470C211yesmaximal, characteristic
2#31774377C211yesmaximal, characteristic
3#31774240C211yesmaximal, characteristic, complemented
4#31774238C211yesmaximal, characteristic, complemented
5#31774237C211yesmaximal, characteristic, complemented
6#31774233C211yesmaximal, characteristic, complemented
7#31774231C211yesmaximal, characteristic, complemented
8#31774229C211yesmaximal, characteristic, complemented
9#31774225C211yesmaximal, characteristic, complemented
10#31773936C211yesmaximal, characteristic, complemented
11#31773934C211yesmaximal, characteristic, complemented
12#31773904C211yesmaximal, characteristic, complemented
13#103×D271C211yesmaximal, characteristic, complemented
14#31773862C211yesmaximal, characteristic
15#485×C271C211yesmaximal, characteristic, complemented
16C2×#16864654C2211yescharacteristic
17C2×Q8×D271C2211yescharacteristic
18C2×#16864637C2211yescharacteristic
19C2×C8×D271C2211yescharacteristic
20#22576159—21no—
21#22576146—21no—
22#22576145—21no—
23#22576142—21no—
24#22576140C2211yescharacteristic
25#22576139C2211yescharacteristic
26#22576136C2211yescharacteristic
27C4×Dic542—21no—
28C4×D1084—21no—
29(C22⋊D271)⋊C4—21no—
30(C22⋊D271)⋊C4—21no—
31#22576118C2211yescharacteristic
32#22576118C2211yescharacteristic
33#22576118C2211yescharacteristic
34C2×C4⋊Dic271C2211yescharacteristic
35C4⋊C4×D271C2211yescharacteristic
36C4⋊C4×D271C2211yescharacteristic
37#22576094C2211yescharacteristic
38#22576094C2211yescharacteristic
39#22576093C2211yescharacteristic
40#22576091C2211yescharacteristic
41#22576091C2211yescharacteristic
42#22576091C2211yescharacteristic
43#22576085C2211yescharacteristic
44#22576085C2211yescharacteristic
45#22576084C2211yescharacteristic
46#22576084C2211yescharacteristic
47#22576083C2211yescharacteristic
48#22576083C2211yescharacteristic
49C22⋊(C271⋊C8)C2211yescharacteristic
50(C2×D271)⋊C8C2211yescharacteristic
51(C2×D271)⋊C8C2211yescharacteristic
52C22⋊Q8×C271C2211yescharacteristic
53#117×C271C2211yescharacteristic
54#107×C271C2211yescharacteristic
55#106×C271C2211yescharacteristic
56#103×C271C2211yescharacteristic
57#103×C271C2211yescharacteristic
58C22⋊C8×C271C2211yescharacteristic
59#16864654—22no—
60#16864654—22no—
61C2×Dic542—21no—
62C2×Dic542D411yescharacteristic
63C2×Dic542C2311yescharacteristic
64Q8×D271—22no—
65Q8×D271—22no—
66C2×D1084D411yescharacteristic
67C2×C22⋊D271D411yescharacteristic
68C2×C22⋊D271D411yescharacteristic
69C22×Dic271—21no—
70C2×C4×D271—21no—
71C2×C4×D271—21no—
72C2×C4×D271—21no—
73C2×C4×D271C2311yescharacteristic
74C2×C4×D271C2311yescharacteristic
75#16864637—22no—
76C2×C271⋊C8C2311yescharacteristic
77C2×C271⋊C8C2311yescharacteristic
78C8×D271—22no—
79C4⋊Dic271—21no—
80C4⋊Dic271—21no—
81C4⋊Dic271C2311yescharacteristic
82C4⋊Dic271C2311yescharacteristic
83C4⋊Dic271C2311yescharacteristic
84Dic271⋊C4—21no—
85Dic271⋊C4—21no—
86Dic271⋊C4—21no—
87Dic271⋊C4—21no—
88C22⋊Dic271—21no—
89(C2×D271)⋊C4—21no—
90(C2×D271)⋊C4—21no—
91(C2×D271)⋊C4—21no—
92(C2×D271)⋊C4—21no—
93(C2×D271)⋊C4—21no—
94C4×Dic271—21no—
95C4×Dic271—21no—
96C4×Dic271—21no—
97C2×Q8×C271C2311yescharacteristic
98C22×C4×C271C2311yescharacteristic
99C2×C8×C271C2311yescharacteristic
100C2×C8×C271C2311yescharacteristic
101C4⋊C4×C271—21no—
102C4⋊C4×C271C2311yescharacteristic
103C4⋊C4×C271C2311yescharacteristic
104C4⋊C4×C271C2311yescharacteristic
105C22⋊C4×C271—21no—
106C22⋊C4×C271—21no—
107C42×C271—21no—
108C22×D271C2×D411yescharacteristic
109C22×D271C2×D411yescharacteristic
110Dic542—22no—
111Dic542—21no—
112Dic542—21no—
113Dic542—42no—
114D1084—22no—
115C22⋊D271—22no—
116C22⋊D271—22no—
117C2×Dic271—21no—
118C2×Dic271—21no—
119C2×Dic271—21no—
120C2×Dic271—21no—
121C2×Dic271—81no—
122C2×Dic271C2×D411yescharacteristic
123C2×Dic271C2×D411yescharacteristic
124C4×D271—21no—
125C4×D271—21no—
126C4×D271—42no—
127C4×D271—81no—
128C4×D271—81no—
129C4×D271#4112yes—
130C4×D271#4112yes—
131C271⋊C8—21no—
132C271⋊C8—21no—
133C23×C271C2×D411yescharacteristic
134Q8×C271—21no—
135Q8×C271—21no—
136C2×C4×C271—21no—
137C2×C4×C271—21no—
138C2×C4×C271—21no—
139C2×C4×C271—21no—
140C2×C4×C271—21no—
141C2×C4×C271—21no—
142C2×C4×C271C2×D411yescharacteristic
143C2×C4×C271C2411yescharacteristic
144C8×C271—21no—
145C8×C271—21no—
146C22×C271—21no—
147C22×C271—21no—
148C22×C271—21no—
149C22×C271C22×D411yescharacteristic
150C2×D271—21no—
151C2×D271—21no—
152C2×D271—21no—
153C2×D271—21no—
154C2×D271—21no—
155C2×D271#12312yes—
156C4×C271—21no—
157C4×C271—41no—
158C4×C271—41no—
159C4×C271—41no—
160C4×C271—41no—
161C4×C271C2×#4111yescharacteristic
162C4×C271C2×#4111yescharacteristic
163Dic271—21no—
164Dic271—41no—
165Dic271—41no—
166Dic271—41no—
167Dic271—41no—
168Dic271#12312yes—
169C2×C271—41no—
170C2×C271C2×#12311yescharacteristic
171C2×C271#57711yescharacteristic
172C2×C271#57811yescharacteristic
173D271—22no—
174D271—41no—
175C271#309711yescharacteristic, complemented, Sylow
176#3097—2711nomaximal, Sylow
177#536—2711no—
178#520—2711no—
179#485—2711no—
180#485—2711no—
181#485—2711no—
182#485D27111yescharacteristic, complemented
183#484—2711no—
184#484—2711no—
185#483—2711no—
186#483—2711no—
187#428—2711no—
188#427—2711no—
189#419—2711no—
190C2×#103—2711no—
191#408—2711no—
192C2×#41—2711no—
193C22×Q8—2711no—
194C2×M16—2711no—
195C22×C8—2711no—
196C4⋊Q8—5421no—
197#124—5421no—
198#123—5421no—
199#123—5421no—
200C22⋊Q8—2711no—
201C22⋊Q8—2711no—
202C22⋊Q8—2711no—
203C22⋊Q8C2×D27111yescharacteristic
204C4×Q8—5421no—
205C4×D4—5421no—
206C4×D4—5421no—
207C4×D4—5421no—
208#117—2711no—
209#117—2711no—
210#117—2711no—
211#117C2×D27111yescharacteristic
212C2×C4⋊C4—2711no—
213C2×C4⋊C4—2711no—
214C2×C4⋊C4—2711no—
215#107—2711no—
216#107—2711no—
217#107—2711no—
218#107C2×D27111yescharacteristic
219#106—2711no—
220#106—2711no—
221#106—2711no—
222#106C2×D27111yescharacteristic
223#103—2711no—
224#103—2711no—
225#103—2711no—
226#103—2711no—
227#103—2711no—
228#103—2711no—
229#103C2×D27111yescharacteristic
230#103C2×D27111yescharacteristic
231C22⋊C8—2711no—
232C22⋊C8—2711no—
233C22⋊C8—2711no—
234C22⋊C8C2×D27111yescharacteristic
235#41—5422no—
236#41—5422no—
237C2×Q8—2711no—
238C2×Q8—2711no—
239C2×Q8—5421no—
240C2×Q8—5422no—
241C2×Q8—5422no—
242C2×Q8C22×D27111yescharacteristic
243C2×D4—2711no—
244C2×D4—2711no—
245C2×D4—2711no—
246C22×C4—2711no—
247C22×C4—2711no—
248C22×C4—5421no—
249C22×C4—5421no—
250C22×C4—5421no—
251C22×C4—5421no—
252C22×C4C22×D27111yescharacteristic
253M16—5422no—
254C2×C8—2711no—
255C2×C8—2711no—
256C2×C8—5422no—
257C2×C8C22×D27111yescharacteristic
258C2×C8C22×D27111yescharacteristic
259C4⋊C4—21no—
260C4⋊C4—2711no—
261C4⋊C4—2711no—
262C4⋊C4—2711no—
263C4⋊C4—5421no—
264C4⋊C4—5421no—
265C4⋊C4—5421no—
266C4⋊C4—5421no—
267C4⋊C4—5421no—
268C4⋊C4—5421no—
269C4⋊C4C22×D27111yescharacteristic
270C4⋊C4C22×D27111yescharacteristic
271C4⋊C4C22×D27111yescharacteristic
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—5421no—
275C22⋊C4—5421no—
276C22⋊C4—5421no—
277C22⋊C4—5421no—
278C22⋊C4—5421no—
279C22⋊C4—5421no—
280C42—21no—
281C42—5421no—
282C42—5421no—
283C42—5421no—
284C23—2711no—
285C23—2711no—
286C23D4×D27111yescharacteristic
287Q8—21no—
288Q8—21no—
289Q8—5422no—
290Q8—5421no—
291Q8—5421no—
292Q8—10842no—
293D4—5422no—
294D4—5422no—
295D4—5422no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—2711no—
303C2×C4—2712no—
304C2×C4—2712no—
305C2×C4—2711no—
306C2×C4—5421no—
307C2×C4—5421no—
308C2×C4—5421no—
309C2×C4—5421no—
310C2×C4—5421no—
311C2×C4—5421no—
312C2×C4—10842no—
313C2×C4—21681no—
314C2×C4—21681no—
315C2×C4—21681no—
316C2×C4D4×D27111yescharacteristic
317C2×C4C23×D27111yescharacteristic
318C8—21no—
319C8—21no—
320C8—5421no—
321C8—5421no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—2712no—
326C22—5421no—
327C22—5421no—
328C22—5421no—
329C22—5421no—
330C22—5421no—
331C22C2×D4×D27111yescharacteristic
332C4—21no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—2712no—
338C4—5421no—
339C4—10841no—
340C4—10841no—
341C4—10841no—
342C4—10841no—
343C4#41×D27111yescharacteristic
344C4#41×D27111yescharacteristic
345C2—41no—
346C2—5422no—
347C2—10841no—
348C2#123×D27111yescharacteristic
349C2#3177470611yescharacteristic
350C2#3177471111yescharacteristic
subgroupG/H
centerC22C2×D4×D271
commutator, cosocleC2×C4×C271C24
FrattiniC2×C4C23×D271
Fitting#485×C271C2
socleC22×C271C22×D4
prime radicalC2×#16864654C22
hypercenter#485D271
hypocenterC271#3097
LCSG ▷ C2×C4×C271 ▷ C2×C271 ▷ C271
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
3. #31774240C2semidirect
4. #31774238C2semidirect
5. #31774237C2semidirect
6. #31774233C2semidirect
7. #31774231C2semidirect
8. #31774229C2semidirect
9. #31774225C2semidirect
10. #31773936C2semidirect
11. #31773934C2semidirect
12. #31773904C2semidirect
13. #103×D271C2semidirect
15. #485×C271C2semidirect
175. C271#3097semidirect
182. #485D271semidirect

Maximal subgroups

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

subgroupindex
#317744702
#317743772
#317742402
#317742382
#317742372
#317742332
#317742312
#317742292
#317742252
#317739362
#317739342
#317739042
#103×D2712
#317738622
#485×C2712
#3097271