Finite Group Databasebeta

← #47985766

Subgroups — #47985766

Order 35456.

512 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊C4×D277C211yesmaximal, characteristic
2#31799889C211yesmaximal, characteristic, complemented
3#31799888C211yesmaximal, characteristic, complemented
4#31799887C211yesmaximal, characteristic, complemented
5#31799886C211yesmaximal, characteristic, complemented
6#31799885C211yesmaximal, characteristic, complemented
7#31799884C211yesmaximal, characteristic, complemented
8#31799883C211yesmaximal, characteristic, complemented
9#31799864C211yesmaximal, characteristic
10#31799864C211yesmaximal, characteristic
11#31799861C211yesmaximal, characteristic
12#31799859C211yesmaximal, characteristic
13C4×#17984540C211yesmaximal, characteristic
14#31799849C211yesmaximal, characteristic
15#387×C277C211yesmaximal, characteristic, complemented
16C22×C4×D277C2211yescharacteristic
17C22×C4×D277C2211yescharacteristic
18C22×C4×D277C2211yescharacteristic
19C2×C4⋊Dic277C2211yescharacteristic
20C2×C4⋊Dic277C2211yescharacteristic
21C2×#17984542C2211yescharacteristic
22C2×#17984542C2211yescharacteristic
23C2×#17984542C2211yescharacteristic
24C2×#17984542C2211yescharacteristic
25C4⋊C4×D277C418yescomplemented
26C2×#17984540C2211yescharacteristic
27C2×#17984540C2211yescharacteristic
28C2×#17984540C2211yescharacteristic
29C2×#17984540C2211yescharacteristic
30C2×C4×Dic277C2211yescharacteristic
31C2×C4×Dic277C2211yescharacteristic
32C2×C4×Dic277C2211yescharacteristic
33#22579787C2211yescharacteristic
34#22579787C2211yescharacteristic
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
53C22×Dic277C2311yescharacteristic
54C22×Dic277C2311yescharacteristic
55C22×Dic277C2311yescharacteristic
56C22×Dic277C2311yescharacteristic
57C22×Dic277C2311yescharacteristic
58C22×Dic277C2311yescharacteristic
59C22×Dic277C2311yescharacteristic
60C2×C4×D277—22no—
61C2×C4×D277—22no—
62C2×C4×D277—41no—
63C2×C4×D277—41no—
64C2×C4×D277—41no—
65C2×C4×D277—41no—
66C2×C4×D277C2×C414yes—
67C2×C4×D277C2×C414yes—
68C2×C4×D277C2×C414yes—
69C4⋊Dic277—41no—
70C4⋊Dic277C2×C414yes—
71#17984542—41no—
72#17984542—41no—
73#17984542C2×C414yes—
74#17984542C2×C414yes—
75#17984540—22no—
76#17984540—22no—
77#17984540—22no—
78#17984540—22no—
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×D277C22×C412yes—
97C22×D277#4112yes—
98C22×D277#4112yes—
99C2×Dic277—21no—
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×Dic277C22×C412yes—
118C2×Dic277C22×C412yes—
119C2×Dic277C22×C412yes—
120C4×D277—28no—
121C4×D277—44no—
122C4×D277—44no—
123C23×C277C2411yescharacteristic
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×C277—21no—
142C2×C4×C277C22×C412yes—
143C2×C4×C277C22×C412yes—
144C2×C4×C277C22×C412yes—
145C22×C277C23×C411yescharacteristic
146C22×C277C2×#4111yescharacteristic
147C22×C277C2×#4111yescharacteristic
148C22×C277H(5,𝔽2)11yescharacteristic
149C22×C277H(5,𝔽2)11yescharacteristic
150C22×C2772−1+411yescharacteristic
151C22×C2772−1+411yescharacteristic
152C2×D277—22no—
153C2×D277—22no—
154C2×D277—22no—
155C2×D277—22no—
156C2×D277—22no—
157C2×D277—22no—
158C2×D277#11714yes—
159C4×C277—22no—
160C4×C277—22no—
161C4×C277—22no—
162C4×C277—41no—
163C4×C277—41no—
164C4×C277—41no—
165C4×C277—41no—
166Dic277—22no—
167Dic277—22no—
168Dic277—22no—
169Dic277—41no—
170Dic277—41no—
171Dic277—41no—
172Dic277—41no—
173C2×C277C2×#11711yescharacteristic
174C2×C277#51811yescharacteristic
175C2×C277#51911yescharacteristic
176C2×C277#53911yescharacteristic
177C2×C277#53911yescharacteristic
178C2×C277#53911yescharacteristic
179C2×C277#53911yescharacteristic
180D277—24no—
181C277#231311yescharacteristic, complemented, Sylow
182#2313—2771nomaximal, Sylow
183C22×C4⋊C4—2771no—
184#387—2771no—
185#387—2771no—
186#387—2771no—
187#387—2771no—
188#387—2771no—
189#387—2771no—
190#387—2771no—
191#387D27711yescharacteristic, complemented
192#381—2771no—
193#381—2771no—
194#380—2771no—
195#380—2771no—
196C4×C22⋊C4—2771no—
197C4×C22⋊C4—2771no—
198C23×C4—2771no—
199C23×C4—2771no—
200C23×C4—2771no—
201C2×C4⋊C4—2771no—
202C2×C4⋊C4—2771no—
203C2×C4⋊C4—2771no—
204C2×C4⋊C4—2778no—
205C2×C4⋊C4—2771no—
206C2×C4⋊C4—2771no—
207C2×C4⋊C4—2771no—
208C2×C4⋊C4C2×D27711yescharacteristic
209C2×C4⋊C4C2×D27711yescharacteristic
210C2×C22⋊C4—2771no—
211C2×C22⋊C4—2771no—
212C2×C22⋊C4—2771no—
213C2×C22⋊C4—2771no—
214C2×C42—2771no—
215C2×C42—2771no—
216C2×C42—2771no—
217C2×C42C2×D27711yescharacteristic
218#95—2771no—
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#95—2771no—
230#95C2×D27711yescharacteristic
231#95C2×D27711yescharacteristic
232#95C2×D27711yescharacteristic
233#95C2×D27711yescharacteristic
234C24—2771no—
235C22×C4—2771no—
236C22×C4—2771no—
237C22×C4—2771no—
238C22×C4—2774no—
239C22×C4—2774no—
240C22×C4—2774no—
241C22×C4—2771no—
242C22×C4—2771no—
243C22×C4—2771no—
244C22×C4—2771no—
245C22×C4—5542no—
246C22×C4—5542no—
247C22×C4—11081no—
248C22×C4—11081no—
249C22×C4—11081no—
250C22×C4—11081no—
251C22×C4C22×D27711yescharacteristic
252C22×C4C22×D27711yescharacteristic
253C22×C4C22×D27711yescharacteristic
254C22×C4C22×D27711yescharacteristic
255C22×C4C22×D27711yescharacteristic
256C22×C4C22×D27711yescharacteristic
257C22×C4C22×D27711yescharacteristic
258C4⋊C4—41no—
259C4⋊C4—2774no—
260C4⋊C4—2774no—
261C4⋊C4—2774no—
262C4⋊C4—11081no—
263C4⋊C4—11081no—
264C4⋊C4—11081no—
265C4⋊C4C4×D27714yes—
266C22⋊C4—5542no—
267C22⋊C4—5542no—
268C22⋊C4—5542no—
269C22⋊C4—5542no—
270C42—41no—
271C42—11081no—
272C42—11081no—
273C42—11081no—
274C23—2772no—
275C23—2772no—
276C23—2772no—
277C23—5541no—
278C23—5541no—
279C23—5541no—
280C23—5541no—
281C23C23×D27711yescharacteristic
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—5548no—
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—5541no—
322C2×C4—11084no—
323C2×C4—11084no—
324C2×C4C2×C4×D27712yes—
325C2×C4C2×C4×D27712yes—
326C2×C4C2×C4×D27712yes—
327C22—2774no—
328C22—5542no—
329C22—5542no—
330C22—5542no—
331C22—5542no—
332C22—5542no—
333C22—5542no—
334C22C22×C4×D27711yescharacteristic
335C22#41×D27711yescharacteristic
336C22#41×D27711yescharacteristic
337C22#2257992511yescharacteristic
338C22#2257992611yescharacteristic
339C22#2257992711yescharacteristic
340C22#2257992811yescharacteristic
341C4—22no—
342C4—22no—
343C4—22no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—5542no—
349C4—5542no—
350C4—5542no—
351C4—11081no—
352C4—11081no—
353C4—11081no—
354C4—11081no—
355C2—5544no—
356C2#117×D27711yescharacteristic
357C2#3180047411yescharacteristic
358C2#3180047811yescharacteristic
359C2#3180059311yescharacteristic
360C2#3180059511yescharacteristic
361C2#3180059811yescharacteristic
362C2#3180060011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D277
commutatorC22×C277C23×C4
Fitting#387×C277C2
socle, cosocleC23×C277C24
prime radicalC23×D277C23
hypercenter#387D277
hypocenterC277#2313
LCSG ▷ C22×C277 ▷ C277
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
2. #31799889C2semidirect
3. #31799888C2semidirect
4. #31799887C2semidirect
5. #31799886C2semidirect
6. #31799885C2semidirect
7. #31799884C2semidirect
8. #31799883C2semidirect
15. #387×C277C2semidirect
25. C4⋊C4×D277C4semidirect
181. C277#2313semidirect
191. #387D277semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×D2772
#317998892
#317998882
#317998872
#317998862
#317998852
#317998842
#317998832
#317998642
#317998612
#317998592
C4×#179845402
#317998492
#387×C2772
#2313277