Finite Group Databasebeta

← #47986033

Subgroups — #47986033

Order 35456.

604 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22579838C211yesmaximal, characteristic
2C2×#22579837C211yesmaximal, characteristic
3C2×C4⋊C4×D277C211yesmaximal, characteristic
4#31799899C211yesmaximal, characteristic, complemented
5#31799897C211yesmaximal, characteristic, complemented
6#31799888C211yesmaximal, characteristic, complemented
7#31799887C211yesmaximal, characteristic, complemented
8#31799885C211yesmaximal, characteristic, complemented
9#31799864C211yesmaximal, characteristic
10#31799864C211yesmaximal, characteristic
11#31799861C211yesmaximal, characteristic
12C4×#17984542C211yesmaximal, characteristic, complemented
13#31799853C211yesmaximal, characteristic, complemented
14#31799849C211yesmaximal, characteristic
15#387×C277C211yesmaximal, characteristic, complemented
16C22×C4×D277C2211yescharacteristic
17C22×C4×D277C2211yescharacteristic
18C22×C4×D277C2211yescharacteristic
19#22579838—24no—
20#22579837—24no—
21C2×C4⋊Dic277C2211yescharacteristic
22C2×C4⋊Dic277C2211yescharacteristic
23C2×#17984542C2211yescharacteristic
24C2×#17984542C2211yescharacteristic
25C2×#17984542C2211yescharacteristic
26C2×#17984542C2211yescharacteristic
27C2×#17984542C2211yescharacteristic
28C2×#17984542C2211yescharacteristic
29C4⋊C4×D277C418yescomplemented
30C2×#17984540C2211yescharacteristic
31C2×#17984540C2211yescharacteristic
32C2×#17984540C2211yescharacteristic
33C2×#17984540C2211yescharacteristic
34C2×C4×Dic277C2211yescharacteristic
35C2×C4×Dic277C2211yescharacteristic
36C2×C4×Dic277C2211yescharacteristic
37C2×C4×Dic277C2211yescharacteristic
38C2×C4×Dic277C2211yescharacteristic
39#22579787C2211yescharacteristic
40#22579787C2211yescharacteristic
41#22579787C2211yescharacteristic
42#22579787C2211yescharacteristic
43#22579787C2211yescharacteristic
44#22579787C2211yescharacteristic
45#22579787C2211yescharacteristic
46#22579787C2211yescharacteristic
47C2×C4⋊C4×C277C2211yescharacteristic
48C2×C4⋊C4×C277C2211yescharacteristic
49C2×C42×C277C2211yescharacteristic
50#95×C277C2211yescharacteristic
51#95×C277C2211yescharacteristic
52#95×C277C2211yescharacteristic
53#95×C277C2211yescharacteristic
54C23×D277C2311yescharacteristic
55C22×Dic277C2311yescharacteristic
56C22×Dic277C2311yescharacteristic
57C22×Dic277C2311yescharacteristic
58C22×Dic277C2311yescharacteristic
59C22×Dic277C2311yescharacteristic
60C22×Dic277C2311yescharacteristic
61C22×Dic277C2311yescharacteristic
62C2×C4×D277—22no—
63C2×C4×D277—22no—
64C2×C4×D277—22no—
65C2×C4×D277—22no—
66C2×C4×D277—22no—
67C2×C4×D277—22no—
68C2×C4×D277C2×C414yes—
69C2×C4×D277C2×C414yes—
70C2×C4×D277C2×C414yes—
71C4⋊Dic277—22no—
72C4⋊Dic277C2×C414yes—
73#17984542—22no—
74#17984542—22no—
75#17984542—22no—
76#17984542—22no—
77#17984542C2×C414yes—
78#17984542C2×C414yes—
79#17984540—22no—
80#17984540—22no—
81#17984540—22no—
82#17984540D414yes—
83C4×Dic277—22no—
84C4×Dic277—22no—
85C4×Dic277—22no—
86C4×Dic277—22no—
87C4×Dic277—22no—
88C22×C4×C277C2311yescharacteristic
89C22×C4×C277C2311yescharacteristic
90C22×C4×C277C2311yescharacteristic
91C22×C4×C277C2311yescharacteristic
92C22×C4×C277C2311yescharacteristic
93C22×C4×C277C2311yescharacteristic
94C22×C4×C277C2311yescharacteristic
95C4⋊C4×C277—22no—
96C4⋊C4×C277C2×C414yes—
97C42×C277—22no—
98C22×D277—21no—
99C22×D277—21no—
100C22×D277—21no—
101C22×D277—21no—
102C22×D277C22×C412yes—
103C22×D277C2×D412yes—
104C22×D277#4112yes—
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×Dic277—21no—
119C2×Dic277—21no—
120C2×Dic277C22×C412yes—
121C2×Dic277C22×C412yes—
122C2×Dic277C22×C412yes—
123C2×Dic277C2×D412yes—
124C2×Dic277#4112yes—
125C2×Dic277#4112yes—
126C4×D277—28no—
127C4×D277—28no—
128C4×D277—28no—
129C23×C277C2411yescharacteristic
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×C277—21no—
143C2×C4×C277—21no—
144C2×C4×C277—21no—
145C2×C4×C277—21no—
146C2×C4×C277—21no—
147C2×C4×C277C22×C412yes—
148C2×C4×C277C22×C412yes—
149C2×C4×C277C22×C412yes—
150C2×C4×C277C2×D412yes—
151C22×C277C23×C411yescharacteristic
152C22×C277C22×D411yescharacteristic
153C22×C277C2×#4111yescharacteristic
154C22×C277C2×#4111yescharacteristic
155C22×C277C2×#4111yescharacteristic
156C22×C2772−1+411yescharacteristic
157C22×C2772−1+411yescharacteristic
158C2×D277—22no—
159C2×D277—22no—
160C2×D277—22no—
161C2×D277—22no—
162C2×D277—22no—
163C2×D277—22no—
164C2×D277C4×D414yes—
165C4×C277—22no—
166C4×C277—22no—
167C4×C277—22no—
168C4×C277—22no—
169C4×C277—41no—
170C4×C277—41no—
171C4×C277—41no—
172Dic277—22no—
173Dic277—22no—
174Dic277—22no—
175Dic277—41no—
176Dic277—41no—
177Dic277—41no—
178Dic277#11714yescomplemented
179C2×C277C2×#11711yescharacteristic
180C2×C277C2×C4×D411yescharacteristic
181C2×C277#51911yescharacteristic
182C2×C277#54711yescharacteristic
183C2×C277#54711yescharacteristic
184C2×C277#55211yescharacteristic
185C2×C277#55211yescharacteristic
186D277—24no—
187C277#234411yescharacteristic, complemented, Sylow
188#2344—2771nomaximal, Sylow
189C2×#117—2771no—
190C2×#117—2771no—
191C22×C4⋊C4—2771no—
192#389—2771no—
193#389—2771no—
194#387—2771no—
195#387—2771no—
196#387—2771no—
197#387D27711yescharacteristic, complemented
198#381—2771no—
199#381—2771no—
200#380—2771no—
201C4×C4⋊C4—2771no—
202C4×C4⋊C4—2771no—
203C4×C22⋊C4—2771no—
204C23×C4—2771no—
205C23×C4—2771no—
206C23×C4—2771no—
207#117—5544no—
208#117—5544no—
209C2×C4⋊C4—2771no—
210C2×C4⋊C4—2771no—
211C2×C4⋊C4—2771no—
212C2×C4⋊C4—2778no—
213C2×C4⋊C4—2771no—
214C2×C4⋊C4—2771no—
215C2×C4⋊C4—2771no—
216C2×C4⋊C4—2771no—
217C2×C4⋊C4—2771no—
218C2×C4⋊C4C2×D27711yescharacteristic
219C2×C4⋊C4C2×D27711yescharacteristic
220C2×C22⋊C4—2771no—
221C2×C22⋊C4—2771no—
222C2×C22⋊C4—2771no—
223C2×C22⋊C4—2771no—
224C2×C42—2771no—
225C2×C42—2771no—
226C2×C42—2771no—
227C2×C42—2771no—
228C2×C42—2771no—
229C2×C42C2×D27711yescharacteristic
230#95—2771no—
231#95—2771no—
232#95—2771no—
233#95—2771no—
234#95—2771no—
235#95—2771no—
236#95—2771no—
237#95—2771no—
238#95C2×D27711yescharacteristic
239#95C2×D27711yescharacteristic
240#95C2×D27711yescharacteristic
241#95C2×D27711yescharacteristic
242C24—2771no—
243C22×C4—2771no—
244C22×C4—2771no—
245C22×C4—2771no—
246C22×C4—2771no—
247C22×C4—2774no—
248C22×C4—2774no—
249C22×C4—2774no—
250C22×C4—2771no—
251C22×C4—2771no—
252C22×C4—2771no—
253C22×C4—5542no—
254C22×C4—5542no—
255C22×C4—5542no—
256C22×C4—5542no—
257C22×C4—5542no—
258C22×C4—5542no—
259C22×C4C22×D27711yescharacteristic
260C22×C4C22×D27711yescharacteristic
261C22×C4C22×D27711yescharacteristic
262C22×C4C22×D27711yescharacteristic
263C22×C4C22×D27711yescharacteristic
264C22×C4C22×D27711yescharacteristic
265C22×C4C22×D27711yescharacteristic
266C4⋊C4—22no—
267C4⋊C4—2774no—
268C4⋊C4—2774no—
269C4⋊C4—2774no—
270C4⋊C4—5542no—
271C4⋊C4—5542no—
272C4⋊C4—5542no—
273C4⋊C4—5542no—
274C4⋊C4—5542no—
275C4⋊C4C4×D27714yes—
276C22⋊C4—2774no—
277C22⋊C4—5542no—
278C22⋊C4—5542no—
279C22⋊C4—5542no—
280C42—22no—
281C42—5542no—
282C42—5542no—
283C42—5542no—
284C42—5542no—
285C42—5542no—
286C23—2772no—
287C23—2772no—
288C23—2772no—
289C23—5541no—
290C23—5541no—
291C23—5541no—
292C23—5541no—
293C23C23×D27711yescharacteristic
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—2772no—
312C2×C4—2772no—
313C2×C4—2772no—
314C2×C4—2772no—
315C2×C4—2772no—
316C2×C4—2772no—
317C2×C4—5548no—
318C2×C4—5548no—
319C2×C4—5548no—
320C2×C4—5541no—
321C2×C4—5541no—
322C2×C4—5541no—
323C2×C4—5541no—
324C2×C4—5541no—
325C2×C4—5541no—
326C2×C4—5541no—
327C2×C4—5541no—
328C2×C4—5541no—
329C2×C4—5541no—
330C2×C4—5541no—
331C2×C4—5541no—
332C2×C4—5541no—
333C2×C4—5541no—
334C2×C4—5541no—
335C2×C4C2×C4×D27712yes—
336C2×C4C2×C4×D27712yes—
337C2×C4C2×C4×D27712yes—
338C2×C4D4×D27712yes—
339C22—2774no—
340C22—5542no—
341C22—5542no—
342C22—5542no—
343C22—5542no—
344C22—5542no—
345C22—5542no—
346C22C22×C4×D27711yescharacteristic
347C22C2×D4×D27711yescharacteristic
348C22#41×D27711yescharacteristic
349C22#41×D27711yescharacteristic
350C22#41×D27711yescharacteristic
351C22#2257992711yescharacteristic
352C22#2257992811yescharacteristic
353C4—22no—
354C4—22no—
355C4—22no—
356C4—22no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—2774no—
361C4—5542no—
362C4—5542no—
363C4—5542no—
364C4—11081no—
365C4—11081no—
366C4—11081no—
367C2—5544no—
368C2#117×D27711yescharacteristic
369C2C4×D4×D27711yescharacteristic
370C2#3180047811yescharacteristic
371C2#3180065011yescharacteristic
372C2#3180065411yescharacteristic
373C2#3180068411yescharacteristic
374C2#3180068811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D277
commutatorC22×C277C23×C4
Fitting#387×C277C2
socle, cosocleC23×C277C24
prime radicalC23×D277C23
hypercenter#387D277
hypocenterC277#2344
LCSG ▷ C22×C277 ▷ C277
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
4. #31799899C2semidirect
5. #31799897C2semidirect
6. #31799888C2semidirect
7. #31799887C2semidirect
8. #31799885C2semidirect
12. C4×#17984542C2semidirect
13. #31799853C2semidirect
15. #387×C277C2semidirect
29. C4⋊C4×D277C4semidirect
178. Dic277#117semidirect
187. C277#2344semidirect
197. #387D277semidirect

Maximal subgroups

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

subgroupindex
C2×#225798382
C2×#225798372
C2×C4⋊C4×D2772
#317998992
#317998972
#317998882
#317998872
#317998852
#317998642
#317998612
C4×#179845422
#317998532
#317998492
#387×C2772
#2344277