Finite Group Databasebeta

← #47986331

Subgroups — #47986331

Order 35456.

464 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22579860C211yesmaximal, characteristic
2#31799906C211yesmaximal, characteristic, complemented
3#31799906C211yesmaximal, characteristic, complemented
4#31799900C211yesmaximal, characteristic, complemented
5#31799898C211yesmaximal, characteristic, complemented
6#31799894C211yesmaximal, characteristic
7#31799893C211yesmaximal, characteristic
8#31799892C211yesmaximal, characteristic
9#31799891C211yesmaximal, characteristic
10#31799888C211yesmaximal, characteristic, complemented
11#31799887C211yesmaximal, characteristic, complemented
12#31799885C211yesmaximal, characteristic, complemented
13#31799864C211yesmaximal, characteristic
14#31799861C211yesmaximal, characteristic
15#387×C277C211yesmaximal, characteristic, complemented
16C22×Dic554C2211yescharacteristic
17C22×C4×D277C2211yescharacteristic
18#22579860C418yescomplemented
19C2×C4⋊Dic277C2211yescharacteristic
20C2×C4⋊Dic277C2211yescharacteristic
21C2×C4⋊Dic277C2211yescharacteristic
22C2×#17984542C2211yescharacteristic
23C2×#17984542C2211yescharacteristic
24C2×#17984542C2211yescharacteristic
25C2×#17984542C2211yescharacteristic
26C2×#17984540C2211yescharacteristic
27C2×#17984540C2211yescharacteristic
28C2×#17984540C2211yescharacteristic
29C2×#17984540C2211yescharacteristic
30C2×#17984540C2211yescharacteristic
31C2×#17984540C2211yescharacteristic
32C2×C4×Dic277C2211yescharacteristic
33C2×C4×Dic277C2211yescharacteristic
34C2×C4×Dic277C2211yescharacteristic
35#22579787C2211yescharacteristic
36#22579787C2211yescharacteristic
37#22579787C2211yescharacteristic
38#22579787C2211yescharacteristic
39#22579787C2211yescharacteristic
40#22579787C2211yescharacteristic
41#22579787C2211yescharacteristic
42#22579787C2211yescharacteristic
43#22579787C2211yescharacteristic
44#22579787C2211yescharacteristic
45C2×C4⋊C4×C277C2211yescharacteristic
46C2×C4⋊C4×C277C2211yescharacteristic
47C2×C42×C277C2211yescharacteristic
48#95×C277C2211yescharacteristic
49#95×C277C2211yescharacteristic
50#95×C277C2211yescharacteristic
51#95×C277C2211yescharacteristic
52C23×D277C2311yescharacteristic
53C2×Dic554—41no—
54C2×Dic554—41no—
55C2×Dic554C2×C414yes—
56C22×Dic277C2311yescharacteristic
57C22×Dic277C2311yescharacteristic
58C22×Dic277C2311yescharacteristic
59C22×Dic277C2311yescharacteristic
60C22×Dic277C2311yescharacteristic
61C22×Dic277C2311yescharacteristic
62C22×Dic277C2311yescharacteristic
63C2×C4×D277—41no—
64C2×C4×D277—41no—
65C2×C4×D277C2×C414yes—
66C4⋊Dic277—41no—
67C4⋊Dic277C2×C414yes—
68C4⋊Dic277C2×C414yes—
69#17984542—41no—
70#17984542—41no—
71#17984542—41no—
72#17984542—41no—
73#17984540—41no—
74#17984540—41no—
75#17984540—41no—
76#17984540—41no—
77#17984540C2×C414yes—
78#17984540C2×C414yes—
79C4×Dic277—41no—
80C4×Dic277—41no—
81C4×Dic277—41no—
82C22×C4×C277C2311yescharacteristic
83C22×C4×C277C2311yescharacteristic
84C22×C4×C277C2311yescharacteristic
85C22×C4×C277C2311yescharacteristic
86C22×C4×C277C2311yescharacteristic
87C22×C4×C277C2311yescharacteristic
88C22×C4×C277C2311yescharacteristic
89C4⋊C4×C277—41no—
90C4⋊C4×C277C2×C414yes—
91C42×C277—41no—
92C22×D277—21no—
93C22×D277—21no—
94C22×D277—21no—
95C22×D277—21no—
96C22×D277—21no—
97C22×D277—21no—
98C22×D277C22×C412yes—
99Dic554—44no—
100C2×Dic277—21no—
101C2×Dic277—21no—
102C2×Dic277—21no—
103C2×Dic277—21no—
104C2×Dic277—21no—
105C2×Dic277—21no—
106C2×Dic277—21no—
107C2×Dic277—21no—
108C2×Dic277—21no—
109C2×Dic277—21no—
110C2×Dic277—21no—
111C2×Dic277—21no—
112C2×Dic277—21no—
113C2×Dic277—21no—
114C2×Dic277—21no—
115C2×Dic277—21no—
116C2×Dic277—21no—
117C2×Dic277—21no—
118C2×Dic277C22×C412yes—
119C2×Dic277C22×C412yes—
120C2×Dic277C22×C412yes—
121C4×D277—44no—
122C23×C277C2411yescharacteristic
123C2×C4×C277—21no—
124C2×C4×C277—21no—
125C2×C4×C277—21no—
126C2×C4×C277—21no—
127C2×C4×C277—21no—
128C2×C4×C277—21no—
129C2×C4×C277—21no—
130C2×C4×C277—21no—
131C2×C4×C277—21no—
132C2×C4×C277—21no—
133C2×C4×C277—21no—
134C2×C4×C277—21no—
135C2×C4×C277—21no—
136C2×C4×C277—21no—
137C2×C4×C277—21no—
138C2×C4×C277—21no—
139C2×C4×C277—21no—
140C2×C4×C277—21no—
141C2×C4×C277C22×C412yes—
142C2×C4×C277C22×C412yes—
143C2×C4×C277C22×C412yes—
144C22×C277C23×C411yescharacteristic
145C22×C277H(5,𝔽2)11yescharacteristic
146C22×C277H(5,𝔽2)11yescharacteristic
147C22×C277H(5,𝔽2)11yescharacteristic
148C22×C2772−1+411yescharacteristic
149C22×C2772−1+411yescharacteristic
150C22×C2772−1+411yescharacteristic
151C2×D277—22no—
152C2×D277—22no—
153C2×D277—22no—
154C2×D277—41no—
155C2×D277—41no—
156C2×D277—41no—
157C2×D277—41no—
158C4×C277—22no—
159C4×C277—22no—
160C4×C277—22no—
161C4×C277—41no—
162C4×C277—41no—
163C4×C277—41no—
164C4×C277—41no—
165Dic277—22no—
166Dic277—22no—
167Dic277—22no—
168Dic277—41no—
169Dic277—41no—
170Dic277—41no—
171Dic277—41no—
172C2×C277#51811yescharacteristic
173C2×C277#51911yescharacteristic
174C2×C277#52011yescharacteristic
175C2×C277#56211yescharacteristic
176C2×C277#56211yescharacteristic
177C2×C277#56311yescharacteristic
178C2×C277#56311yescharacteristic
179D277—42no—
180C277#237811yescharacteristic, complemented, Sylow
181#2378—2771nomaximal, Sylow
182C2×C22⋊Q8—2771no—
183#391—2771no—
184#391—2771no—
185#389—2771no—
186#389—2771no—
187#388—2771no—
188#388—2771no—
189#388—2771no—
190#388—2771no—
191#387—2771no—
192#387—2771no—
193#387—2771no—
194#387D27711yescharacteristic, complemented
195#381—2771no—
196#380—2771no—
197C22×Q8—2771no—
198C23×C4—2771no—
199C22⋊Q8—2778no—
200C2×C4⋊C4—2771no—
201C2×C4⋊C4—2771no—
202C2×C4⋊C4—2771no—
203C2×C4⋊C4—2771no—
204C2×C4⋊C4—2771no—
205C2×C4⋊C4—2771no—
206C2×C4⋊C4—2771no—
207C2×C4⋊C4C2×D27711yescharacteristic
208C2×C4⋊C4C2×D27711yescharacteristic
209C2×C22⋊C4—2771no—
210C2×C22⋊C4—2771no—
211C2×C22⋊C4—2771no—
212C2×C22⋊C4—2771no—
213C2×C22⋊C4—2771no—
214C2×C22⋊C4—2771no—
215C2×C42—2771no—
216C2×C42—2771no—
217C2×C42—2771no—
218C2×C42C2×D27711yescharacteristic
219#95—2771no—
220#95—2771no—
221#95—2771no—
222#95—2771no—
223#95—2771no—
224#95—2771no—
225#95—2771no—
226#95—2771no—
227#95—2771no—
228#95—2771no—
229#95C2×D27711yescharacteristic
230#95C2×D27711yescharacteristic
231#95C2×D27711yescharacteristic
232#95C2×D27711yescharacteristic
233C24—2771no—
234C2×Q8—2774no—
235C2×Q8—11081no—
236C2×Q8—11081no—
237C22×C4—2771no—
238C22×C4—2771no—
239C22×C4—2771no—
240C22×C4—2774no—
241C22×C4—2771no—
242C22×C4—2771no—
243C22×C4—2771no—
244C22×C4—2771no—
245C22×C4—11081no—
246C22×C4—11081no—
247C22×C4C22×D27711yescharacteristic
248C22×C4C22×D27711yescharacteristic
249C22×C4C22×D27711yescharacteristic
250C22×C4C22×D27711yescharacteristic
251C22×C4C22×D27711yescharacteristic
252C22×C4C22×D27711yescharacteristic
253C22×C4C22×D27711yescharacteristic
254C4⋊C4—41no—
255C4⋊C4—2774no—
256C4⋊C4—2774no—
257C4⋊C4—11081no—
258C4⋊C4—11081no—
259C4⋊C4—11081no—
260C4⋊C4—11081no—
261C4⋊C4—11081no—
262C4⋊C4C4×D27714yes—
263C22⋊C4—2774no—
264C22⋊C4—2774no—
265C22⋊C4—11081no—
266C22⋊C4—11081no—
267C22⋊C4—11081no—
268C22⋊C4—11081no—
269C42—41no—
270C42—11081no—
271C42—11081no—
272C42—11081no—
273C23—2772no—
274C23—5541no—
275C23—5541no—
276C23—5541no—
277C23—5541no—
278C23—5541no—
279C23—5541no—
280C23C23×D27711yescharacteristic
281Q8—11084no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—2772no—
301C2×C4—2772no—
302C2×C4—2772no—
303C2×C4—5541no—
304C2×C4—5541no—
305C2×C4—5541no—
306C2×C4—5541no—
307C2×C4—5541no—
308C2×C4—5541no—
309C2×C4—5541no—
310C2×C4—5541no—
311C2×C4—5541no—
312C2×C4—5541no—
313C2×C4—5541no—
314C2×C4—5541no—
315C2×C4—5541no—
316C2×C4—5541no—
317C2×C4—5541no—
318C2×C4—5541no—
319C2×C4—5541no—
320C2×C4—5541no—
321C2×C4—11084no—
322C2×C4C2×C4×D27712yes—
323C2×C4C2×C4×D27712yes—
324C2×C4C2×C4×D27712yes—
325C22—5542no—
326C22—5542no—
327C22—5542no—
328C22—11081no—
329C22—11081no—
330C22—11081no—
331C22—11081no—
332C22C22×C4×D27711yescharacteristic
333C22#2257992511yescharacteristic
334C22#2257992611yescharacteristic
335C22#2257992611yescharacteristic
336C22#2257992711yescharacteristic
337C22#2257992711yescharacteristic
338C22#2257992811yescharacteristic
339C4—22no—
340C4—22no—
341C4—22no—
342C4—41no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—5542no—
347C4—5542no—
348C4—5542no—
349C4—11081no—
350C4—11081no—
351C4—11081no—
352C4—11081no—
353C2—11082no—
354C2#3180047611yescharacteristic
355C2#3180047811yescharacteristic
356C2#3180048111yescharacteristic
357C2#3180074811yescharacteristic
358C2#3180074911yescharacteristic
359C2#3180075411yescharacteristic
360C2#3180075611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D277
commutatorC22×C277C23×C4
Fitting#387×C277C2
socle, cosocleC23×C277C24
prime radicalC23×D277C23
hypercenter#387D277
hypocenterC277#2378
LCSG ▷ C22×C277 ▷ C277
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
2. #31799906C2semidirect
3. #31799906C2semidirect
4. #31799900C2semidirect
5. #31799898C2semidirect
10. #31799888C2semidirect
11. #31799887C2semidirect
12. #31799885C2semidirect
15. #387×C277C2semidirect
18. #22579860C4semidirect
180. C277#2378semidirect
194. #387D277semidirect

Maximal subgroups

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

subgroupindex
C2×#225798602
#317999062
#317999002
#317998982
#317998942
#317998932
#317998922
#317998912
#317998882
#317998872
#317998852
#317998642
#317998612
#387×C2772
#2378277