Finite Group Databasebeta

← #46838837

Subgroups — #46838837

Order 34688.

500 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22576125C211yesmaximal, characteristic
2#31773801C211yesmaximal, characteristic
3#31773801C211yesmaximal, characteristic
4#31773794C211yesmaximal, characteristic
5#31773792C211yesmaximal, characteristic
6#31773783C211yesmaximal, characteristic
7#31773781C211yesmaximal, characteristic
8#31773779C211yesmaximal, characteristic
9C4⋊C4×Dic271C211yesmaximal, characteristic
10#31773748C211yesmaximal, characteristic
11#31773748C211yesmaximal, characteristic
12#31773742C211yesmaximal, characteristic
13#31773742C211yesmaximal, characteristic
14C42×Dic271C211yesmaximal, characteristic
15#387×C271C211yesmaximal, characteristic
16C22×Dic542C2211yescharacteristic
17#22576125C418yescomplemented
18C2×C4⋊Dic271C2211yescharacteristic
19C2×Dic271⋊C4C2211yescharacteristic
20C2×Dic271⋊C4C2211yescharacteristic
21C2×Dic271⋊C4C2211yescharacteristic
22C2×Dic271⋊C4C2211yescharacteristic
23C2×Dic271⋊C4C2211yescharacteristic
24C2×Dic271⋊C4C2211yescharacteristic
25C2×C4×Dic271C2211yescharacteristic
26C2×C4×Dic271C2211yescharacteristic
27C2×C4×Dic271C2211yescharacteristic
28C2×C4×Dic271C2211yescharacteristic
29C2×C4×Dic271C2211yescharacteristic
30C2×C4×Dic271C2211yescharacteristic
31C2×C4×Dic271C2211yescharacteristic
32C2×C4×Dic271C2211yescharacteristic
33C2×C4×Dic271C2211yescharacteristic
34C2×C4×Dic271C2211yescharacteristic
35C271⋊#95C2211yescharacteristic
36C271⋊#95C2211yescharacteristic
37C271⋊#95C2211yescharacteristic
38C271⋊#95C2211yescharacteristic
39C271⋊#95C2211yescharacteristic
40C271⋊#95C2211yescharacteristic
41C271⋊#95C2211yescharacteristic
42C271⋊#95C2211yescharacteristic
43C271⋊#95C2211yescharacteristic
44C271⋊#95C2211yescharacteristic
45C2×C4⋊C4×C271C2211yescharacteristic
46C2×C4⋊C4×C271C2211yescharacteristic
47C2×C42×C271C2211yescharacteristic
48#95×C271C2211yescharacteristic
49#95×C271C2211yescharacteristic
50#95×C271C2211yescharacteristic
51#95×C271C2211yescharacteristic
52C2×Dic542—22no—
53C2×Dic542—22no—
54C2×Dic542C2×C414yes—
55C22×Dic271C2311yescharacteristic
56C22×Dic271C2311yescharacteristic
57C22×Dic271C2311yescharacteristic
58C22×Dic271C2311yescharacteristic
59C22×Dic271C2311yescharacteristic
60C22×Dic271C2311yescharacteristic
61C22×Dic271C2311yescharacteristic
62C22×Dic271C2311yescharacteristic
63C4⋊Dic271—22no—
64Dic271⋊C4—22no—
65Dic271⋊C4—22no—
66Dic271⋊C4—22no—
67Dic271⋊C4—22no—
68Dic271⋊C4C2×C414yes—
69Dic271⋊C4C2×C414yes—
70C4×Dic271—22no—
71C4×Dic271—22no—
72C4×Dic271—22no—
73C4×Dic271—22no—
74C4×Dic271—22no—
75C4×Dic271—22no—
76C4×Dic271C2×C414yes—
77C4×Dic271C2×C414yes—
78C4×Dic271C2×C414yes—
79C4×Dic271Q814yescomplemented
80C22×C4×C271C2311yescharacteristic
81C22×C4×C271C2311yescharacteristic
82C22×C4×C271C2311yescharacteristic
83C22×C4×C271C2311yescharacteristic
84C22×C4×C271C2311yescharacteristic
85C22×C4×C271C2311yescharacteristic
86C22×C4×C271C2311yescharacteristic
87C4⋊C4×C271—22no—
88C4⋊C4×C271C2×C414yes—
89C42×C271—22no—
90Dic542—28no—
91C2×Dic271—21no—
92C2×Dic271—21no—
93C2×Dic271—21no—
94C2×Dic271—21no—
95C2×Dic271—21no—
96C2×Dic271—21no—
97C2×Dic271—21no—
98C2×Dic271—21no—
99C2×Dic271—21no—
100C2×Dic271—21no—
101C2×Dic271—21no—
102C2×Dic271—21no—
103C2×Dic271—21no—
104C2×Dic271—21no—
105C2×Dic271C22×C412yes—
106C2×Dic271C22×C412yes—
107C2×Dic271C22×C412yes—
108C2×Dic271C22×C412yes—
109C2×Dic271C2×Q812yes—
110C2×Dic271C2×Q812yes—
111C2×Dic271#4112yes—
112C2×Dic271#4112yes—
113C2×Dic271#4112yes—
114C2×Dic271#4112yes—
115C23×C271C2411yescharacteristic
116C2×C4×C271—21no—
117C2×C4×C271—21no—
118C2×C4×C271—21no—
119C2×C4×C271—21no—
120C2×C4×C271—21no—
121C2×C4×C271—21no—
122C2×C4×C271—21no—
123C2×C4×C271—21no—
124C2×C4×C271—21no—
125C2×C4×C271—21no—
126C2×C4×C271—21no—
127C2×C4×C271—21no—
128C2×C4×C271—21no—
129C2×C4×C271—21no—
130C2×C4×C271—21no—
131C2×C4×C271—21no—
132C2×C4×C271C22×C412yes—
133C2×C4×C271C22×C412yes—
134C2×C4×C271C22×C412yes—
135C2×C4×C271C2×Q812yes—
136C2×C4×C271#4112yes—
137C22×C271C23×C411yescharacteristic
138C22×C271C22×Q811yescharacteristic
139C22×C271C2×#4111yescharacteristic
140C22×C271C2×#4111yescharacteristic
141C22×C271C2×#4111yescharacteristic
142C22×C271C2×#4111yescharacteristic
143C22×C271C2×#4111yescharacteristic
144C4×C271—22no—
145C4×C271—22no—
146C4×C271—22no—
147C4×C271—22no—
148C4×C271—22no—
149C4×C271—41no—
150C4×C271—41no—
151Dic271—22no—
152Dic271—22no—
153Dic271—22no—
154Dic271—22no—
155Dic271—41no—
156Dic271—41no—
157Dic271#11714yes—
158Dic271C4×Q814yes—
159C2×C271C2×#11711yescharacteristic
160C2×C271C2×C4×Q811yescharacteristic
161C2×C271C4×#4111yescharacteristic
162C2×C271#52911yescharacteristic
163C2×C271#52911yescharacteristic
164C2×C271#53311yescharacteristic
165C2×C271#53311yescharacteristic
166C271#229511yescharacteristic, complemented, Sylow
167#2295—2711nomaximal, Sylow
168C2×C4×Q8—2711no—
169#391—2711no—
170#391—2711no—
171#389—2711no—
172#389—2711no—
173#387—2711no—
174#387—2711no—
175#387—2711no—
176#387D27111yescharacteristic
177C4×C4⋊C4—2711no—
178C4×C4⋊C4—2711no—
179C4×C4⋊C4—2711no—
180#376—2711no—
181#376—2711no—
182C43—2711no—
183C22×Q8—2711no—
184C4×Q8—2718no—
185C2×C4⋊C4—2711no—
186C2×C4⋊C4—2711no—
187C2×C4⋊C4—2711no—
188C2×C4⋊C4—2711no—
189C2×C4⋊C4—2711no—
190C2×C4⋊C4—2711no—
191C2×C4⋊C4—2711no—
192C2×C4⋊C4C2×D27111yescharacteristic
193C2×C4⋊C4C2×D27111yescharacteristic
194C2×C42—2711no—
195C2×C42—2711no—
196C2×C42—2711no—
197C2×C42—2711no—
198C2×C42—2711no—
199C2×C42—2711no—
200C2×C42—2711no—
201C2×C42—2711no—
202C2×C42—2711no—
203C2×C42—2711no—
204C2×C42C2×D27111yescharacteristic
205#95—2711no—
206#95—2711no—
207#95—2711no—
208#95—2711no—
209#95—2711no—
210#95—2711no—
211#95—2711no—
212#95—2711no—
213#95—2711no—
214#95—2711no—
215#95C2×D27111yescharacteristic
216#95C2×D27111yescharacteristic
217#95C2×D27111yescharacteristic
218#95C2×D27111yescharacteristic
219C2×Q8—2714no—
220C2×Q8—5422no—
221C2×Q8—5422no—
222C22×C4—2711no—
223C22×C4—2711no—
224C22×C4—2711no—
225C22×C4—2711no—
226C22×C4—2711no—
227C22×C4—2711no—
228C22×C4—2711no—
229C22×C4—2711no—
230C22×C4C22×D27111yescharacteristic
231C22×C4C22×D27111yescharacteristic
232C22×C4C22×D27111yescharacteristic
233C22×C4C22×D27111yescharacteristic
234C22×C4C22×D27111yescharacteristic
235C22×C4C22×D27111yescharacteristic
236C22×C4C22×D27111yescharacteristic
237C4⋊C4—22no—
238C4⋊C4—2714no—
239C4⋊C4—2714no—
240C4⋊C4—5422no—
241C4⋊C4—5422no—
242C4⋊C4—5422no—
243C4⋊C4—5422no—
244C4⋊C4—5422no—
245C4⋊C4C4×D27114yes—
246C42—22no—
247C42—2714no—
248C42—2714no—
249C42—2714no—
250C42—2714no—
251C42—5422no—
252C42—5422no—
253C42—5422no—
254C42—5422no—
255C42—5422no—
256C42—5422no—
257C23C23×D27111yescharacteristic
258Q8—5428no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—2712no—
276C2×C4—2712no—
277C2×C4—2712no—
278C2×C4—2712no—
279C2×C4—2712no—
280C2×C4—2712no—
281C2×C4—2712no—
282C2×C4—2712no—
283C2×C4—2712no—
284C2×C4—2712no—
285C2×C4—5421no—
286C2×C4—5421no—
287C2×C4—5421no—
288C2×C4—5421no—
289C2×C4—5421no—
290C2×C4—5421no—
291C2×C4—5421no—
292C2×C4—5421no—
293C2×C4—5421no—
294C2×C4—5421no—
295C2×C4—5421no—
296C2×C4—5421no—
297C2×C4—5421no—
298C2×C4—5421no—
299C2×C4C2×C4×D27112yes—
300C2×C4C2×C4×D27112yes—
301C2×C4C2×C4×D27112yes—
302C2×C4Q8×D27112yes—
303C2×C4#1686465312yes—
304C22C22×C4×D27111yescharacteristic
305C22C2×Q8×D27111yescharacteristic
306C22#41×D27111yescharacteristic
307C22#41×D27111yescharacteristic
308C22#41×D27111yescharacteristic
309C22#41×D27111yescharacteristic
310C22C2×#1686465311yescharacteristic
311C4—22no—
312C4—22no—
313C4—22no—
314C4—22no—
315C4—22no—
316C4—41no—
317C4—41no—
318C4—2714no—
319C4—2714no—
320C4—5422no—
321C4—5422no—
322C4—5422no—
323C4—5422no—
324C4—10841no—
325C4—10841no—
326C2#117×D27111yescharacteristic
327C2C4×Q8×D27111yescharacteristic
328C2C4×#1686465311yescharacteristic
329C2#3177442411yescharacteristic
330C2#3177443011yescharacteristic
331C2#3177444911yescharacteristic
332C2#3177445311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D271
commutatorC22×C271C23×C4
Fitting#387×C271C2
socle, prime radical, cosocleC23×C271C24
hypercenter#387D271
hypocenterC271#2295
LCSG ▷ C22×C271 ▷ C271
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
17. #22576125C4semidirect
79. C4×Dic271Q8semidirect
166. C271#2295semidirect

Maximal subgroups

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

subgroupindex
C2×#225761252
#317738012
#317737942
#317737922
#317737832
#317737812
#317737792
C4⋊C4×Dic2712
#317737482
#317737422
C42×Dic2712
#387×C2712
#2295271