Finite Group Databasebeta

← #47985799

Subgroups — #47985799

Order 35456.

568 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22579842C211yesmaximal, characteristic
2#31799893C211yesmaximal, characteristic, complemented
3#31799891C211yesmaximal, characteristic, complemented
4#31799888C211yesmaximal, characteristic, complemented
5#31799880C211yesmaximal, characteristic
6#31799880C211yesmaximal, characteristic
7#31799876C211yesmaximal, characteristic, complemented
8#31799873C211yesmaximal, characteristic, complemented
9#31799869C211yesmaximal, characteristic, complemented
10#31799866C211yesmaximal, characteristic, complemented
11#31799864C211yesmaximal, characteristic, complemented
12#31799859C211yesmaximal, characteristic, complemented
13C4×#17984540C211yesmaximal, characteristic, complemented
14#95×D277C211yesmaximal, characteristic, complemented
15#387×C277C211yesmaximal, characteristic, complemented
16C22×D1108C2211yescharacteristic
17C22×C4×D277C2211yescharacteristic
18C22×C4×D277C2211yescharacteristic
19C22×C4×D277C2211yescharacteristic
20C22×C4×D277C2211yescharacteristic
21#22579842C418yescomplemented
22C2×C4⋊Dic277C2211yescharacteristic
23C2×#17984542C2211yescharacteristic
24C2×#17984542C2211yescharacteristic
25C2×#17984540C2211yescharacteristic
26C2×#17984540C2211yescharacteristic
27C2×#17984540C2211yescharacteristic
28C2×#17984540C2211yescharacteristic
29C2×#17984540C2211yescharacteristic
30C2×#17984540C2211yescharacteristic
31C2×#17984540C2211yescharacteristic
32C2×#17984540C2211yescharacteristic
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
53C23×D277C2311yescharacteristic
54C2×D1108—22no—
55C2×D1108—22no—
56C2×D1108C2×C414yes—
57C22×Dic277C2311yescharacteristic
58C22×Dic277C2311yescharacteristic
59C22×Dic277C2311yescharacteristic
60C22×Dic277C2311yescharacteristic
61C22×Dic277C2311yescharacteristic
62C22×Dic277C2311yescharacteristic
63C2×C4×D277—22no—
64C2×C4×D277—22no—
65C2×C4×D277—41no—
66C2×C4×D277—41no—
67C2×C4×D277—41no—
68C2×C4×D277—41no—
69C2×C4×D277—41no—
70C2×C4×D277—41no—
71C2×C4×D277—41no—
72C2×C4×D277—41no—
73C2×C4×D277C2×C414yes—
74C2×C4×D277C2×C414yescomplemented
75C4⋊Dic277—41no—
76#17984542—41no—
77#17984542—41no—
78#17984540—22no—
79#17984540—22no—
80#17984540—41no—
81#17984540—41no—
82#17984540—41no—
83#17984540—41no—
84#17984540C2×C414yes—
85#17984540C2×C414yescomplemented
86C4×Dic277—41no—
87C4×Dic277C2×C414yescomplemented
88C22×C4×C277C2311yescharacteristic
89C22×C4×C277C2311yescharacteristic
90C22×C4×C277C2311yescharacteristic
91C22×C4×C277C2311yescharacteristic
92C22×C4×C277C2311yescharacteristic
93C22×C4×C277C2311yescharacteristic
94C22×C4×C277C2311yescharacteristic
95C4⋊C4×C277—41no—
96C4⋊C4×C277C2×C414yescomplemented
97C42×C277—41no—
98C22×D277—21no—
99C22×D277—21no—
100C22×D277—21no—
101C22×D277—21no—
102C22×D277—21no—
103C22×D277—21no—
104C22×D277—21no—
105C22×D277—21no—
106C22×D277—21no—
107C22×D277—21no—
108C22×D277C22×C412yes—
109C22×D277C22×C412yes—
110C22×D277#4112yes—
111C22×D277#4112yes—
112D1108—28no—
113C2×Dic277—21no—
114C2×Dic277—21no—
115C2×Dic277—21no—
116C2×Dic277—21no—
117C2×Dic277—21no—
118C2×Dic277—21no—
119C2×Dic277—21no—
120C2×Dic277—21no—
121C2×Dic277—21no—
122C2×Dic277—21no—
123C2×Dic277—21no—
124C2×Dic277—21no—
125C2×Dic277—21no—
126C2×Dic277—21no—
127C2×Dic277—21no—
128C2×Dic277—21no—
129C2×Dic277C22×C412yes—
130C2×Dic277C22×C412yes—
131C4×D277—44no—
132C4×D277—44no—
133C4×D277—44no—
134C4×D277—44no—
135C23×C277C2411yescharacteristic
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×C277—21no—
143C2×C4×C277—21no—
144C2×C4×C277—21no—
145C2×C4×C277—21no—
146C2×C4×C277—21no—
147C2×C4×C277—21no—
148C2×C4×C277—21no—
149C2×C4×C277—21no—
150C2×C4×C277—21no—
151C2×C4×C277—21no—
152C2×C4×C277—21no—
153C2×C4×C277—21no—
154C2×C4×C277C22×C412yes—
155C2×C4×C277C22×C412yes—
156C2×C4×C277C22×C412yes—
157C22×C277C23×C411yescharacteristic
158C22×C277C2×#4111yescharacteristic
159C22×C277C2×#4111yescharacteristic
160C22×C277H(5,𝔽2)11yescharacteristic
161C22×C277H(5,𝔽2)11yescharacteristic
162C22×C277H(5,𝔽2)11yescharacteristic
163C22×C2772−1+411yescharacteristic
164C2×D277—22no—
165C2×D277—22no—
166C2×D277—22no—
167C2×D277—22no—
168C2×D277—22no—
169C2×D277—22no—
170C2×D277—22no—
171C2×D277—22no—
172C2×D277—22no—
173C2×D277—41no—
174C2×D277—41no—
175C2×D277—41no—
176C2×D277—41no—
177C2×D277#11714yes—
178C4×C277—22no—
179C4×C277—22no—
180C4×C277—22no—
181C4×C277—41no—
182C4×C277—41no—
183C4×C277—41no—
184C4×C277—41no—
185Dic277—22no—
186Dic277—22no—
187Dic277—41no—
188Dic277—41no—
189Dic277—41no—
190Dic277—41no—
191C2×C277C2×#11711yescharacteristic
192C2×C277#51811yescharacteristic
193C2×C277#52011yescharacteristic
194C2×C277#53811yescharacteristic
195C2×C277#53811yescharacteristic
196C2×C277#53911yescharacteristic
197C2×C277#53911yescharacteristic
198D277—24no—
199D277—42no—
200C277#231811yescharacteristic, complemented, Sylow
201#2318—2771nomaximal, Sylow
202C2×C4×D4—2771no—
203#388—2771no—
204#388—2771no—
205#387—2771no—
206#387D27711yescharacteristic, complemented
207#386—2771no—
208#386—2771no—
209#385—2771no—
210#385—2771no—
211#383—2771no—
212#382—2771no—
213#381—2771no—
214#380—2771no—
215C4×C22⋊C4—2771no—
216C2×#95—2771no—
217C22×D4—2771no—
218C23×C4—2771no—
219C23×C4—2771no—
220C23×C4—2771no—
221C23×C4—2771no—
222C4×D4—2778no—
223C2×C4⋊C4—2771no—
224C2×C4⋊C4—2771no—
225C2×C4⋊C4—2771no—
226C2×C4⋊C4C2×D27711yescharacteristic
227C2×C4⋊C4C2×D27711yescharacteristic
228C2×C22⋊C4—2771no—
229C2×C22⋊C4—2771no—
230C2×C22⋊C4—2771no—
231C2×C22⋊C4—2771no—
232C2×C22⋊C4—2771no—
233C2×C22⋊C4—2771no—
234C2×C22⋊C4—2771no—
235C2×C22⋊C4—2771no—
236C2×C42—2771no—
237C2×C42—2771no—
238C2×C42C2×D27711yescharacteristic
239#95—2771no—
240#95—2771no—
241#95—2771no—
242#95—2771no—
243#95—2771no—
244#95—2771no—
245#95—2771no—
246#95—2771no—
247#95—2771no—
248#95—2771no—
249#95C2×D27711yescharacteristic
250#95C2×D27711yescharacteristic
251#95C2×D27711yescharacteristic
252#95C2×D27711yescharacteristic
253C24—2771no—
254C24—2771no—
255C2×D4—2774no—
256C2×D4—5542no—
257C2×D4—5542no—
258C22×C4—2771no—
259C22×C4—2771no—
260C22×C4—2774no—
261C22×C4—2774no—
262C22×C4—2771no—
263C22×C4—2771no—
264C22×C4—2771no—
265C22×C4—2771no—
266C22×C4—5542no—
267C22×C4—5542no—
268C22×C4—11081no—
269C22×C4—11081no—
270C22×C4—11081no—
271C22×C4—11081no—
272C22×C4—11081no—
273C22×C4—11081no—
274C22×C4—11081no—
275C22×C4—11081no—
276C22×C4C22×D27711yescharacteristic
277C22×C4C22×D27711yescharacteristic
278C22×C4C22×D27711yescharacteristic
279C22×C4C22×D27711yescharacteristic
280C22×C4C22×D27711yescharacteristic
281C22×C4C22×D27711yescharacteristic
282C22×C4C22×D27711yescharacteristic
283C4⋊C4—41no—
284C4⋊C4—11081no—
285C4⋊C4—11081no—
286C4⋊C4—11081no—
287C4⋊C4C4×D27714yescomplemented
288C22⋊C4—2774no—
289C22⋊C4—2774no—
290C22⋊C4—5542no—
291C22⋊C4—5542no—
292C22⋊C4—11081no—
293C22⋊C4—11081no—
294C22⋊C4—11081no—
295C22⋊C4—11081no—
296C42—41no—
297C42—2774no—
298C42—11081no—
299C23—2772no—
300C23—2772no—
301C23—2772no—
302C23—2772no—
303C23—5541no—
304C23—5541no—
305C23—5541no—
306C23—5541no—
307C23—5541no—
308C23—5541no—
309C23—5541no—
310C23—5541no—
311C23—5541no—
312C23—5541no—
313C23C23×D27711yescharacteristic
314D4—5548no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—2772no—
334C2×C4—2772no—
335C2×C4—5541no—
336C2×C4—5541no—
337C2×C4—5541no—
338C2×C4—5541no—
339C2×C4—5541no—
340C2×C4—5541no—
341C2×C4—5541no—
342C2×C4—5541no—
343C2×C4—5541no—
344C2×C4—5541no—
345C2×C4—5541no—
346C2×C4—5541no—
347C2×C4—5541no—
348C2×C4—5541no—
349C2×C4—5541no—
350C2×C4—5541no—
351C2×C4—11084no—
352C2×C4—11084no—
353C2×C4—11084no—
354C2×C4—11084no—
355C2×C4C2×C4×D27712yes—
356C2×C4C2×C4×D27712yes—
357C2×C4C2×C4×D27712yes—
358C22—2774no—
359C22—5542no—
360C22—5542no—
361C22—5542no—
362C22—5542no—
363C22—5542no—
364C22—5542no—
365C22—5542no—
366C22—5542no—
367C22—5542no—
368C22—11081no—
369C22—11081no—
370C22—11081no—
371C22—11081no—
372C22C22×C4×D27711yescharacteristic
373C22#41×D27711yescharacteristic
374C22#41×D27711yescharacteristic
375C22#2257992511yescharacteristic
376C22#2257992611yescharacteristic
377C22#2257992611yescharacteristic
378C22#2257992811yescharacteristic
379C4—22no—
380C4—22no—
381C4—22no—
382C4—41no—
383C4—41no—
384C4—41no—
385C4—41no—
386C4—5542no—
387C4—5542no—
388C4—11081no—
389C4—11081no—
390C4—11081no—
391C4—11081no—
392C2—5544no—
393C2—11082no—
394C2#117×D27711yescharacteristic
395C2#3180047411yescharacteristic
396C2#3180048411yescharacteristic
397C2#3180058811yescharacteristic
398C2#3180059111yescharacteristic
399C2#3180059811yescharacteristic
400C2#3180060011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D277
commutatorC22×C277C23×C4
Fitting#387×C277C2
socle, cosocleC23×C277C24
prime radicalC22×D1108C22
hypercenter#387D277
hypocenterC277#2318
LCSG ▷ C22×C277 ▷ C277
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
2. #31799893C2semidirect
3. #31799891C2semidirect
4. #31799888C2semidirect
7. #31799876C2semidirect
8. #31799873C2semidirect
9. #31799869C2semidirect
10. #31799866C2semidirect
11. #31799864C2semidirect
12. #31799859C2semidirect
13. C4×#17984540C2semidirect
14. #95×D277C2semidirect
15. #387×C277C2semidirect
21. #22579842C4semidirect
74. C2×C4×D277C2×C4semidirect
85. #17984540C2×C4semidirect
87. C4×Dic277C2×C4semidirect
96. C4⋊C4×C277C2×C4semidirect
200. C277#2318semidirect
206. #387D277semidirect
287. C4⋊C4C4×D277semidirect

Maximal subgroups

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

subgroupindex
C2×#225798422
#317998932
#317998912
#317998882
#317998802
#317998762
#317998732
#317998692
#317998662
#317998642
#317998592
C4×#179845402
#95×D2772
#387×C2772
#2318277