Finite Group Databasebeta

← #47985808

Subgroups — #47985808

Order 35456.

540 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22579840C211yesmaximal, characteristic
2#31799902C211yesmaximal, characteristic
3#31799902C211yesmaximal, characteristic
4#31799899C211yesmaximal, characteristic, complemented
5#31799897C211yesmaximal, characteristic, complemented
6#31799895C211yesmaximal, characteristic, complemented
7#31799893C211yesmaximal, characteristic, complemented
8#31799891C211yesmaximal, characteristic, complemented
9#31799864C211yesmaximal, characteristic, complemented
10#31799863C211yesmaximal, characteristic, complemented
11#31799860C211yesmaximal, characteristic, complemented
12#31799859C211yesmaximal, characteristic, complemented
13C4×#17984542C211yesmaximal, characteristic, complemented
14#31799847C211yesmaximal, characteristic, complemented
15#388×C277C211yesmaximal, characteristic, complemented
16C22×C22⋊D277C2211yescharacteristic
17C23×Dic277C2211yescharacteristic
18C22×C4×D277C2211yescharacteristic
19#22579840C418yescomplemented
20C2×C4⋊Dic277C2211yescharacteristic
21C2×#17984542C2211yescharacteristic
22C2×#17984542C2211yescharacteristic
23C2×#17984542C2211yescharacteristic
24C2×#17984542C2211yescharacteristic
25C2×#17984542C2211yescharacteristic
26C2×C22⋊Dic277C2211yescharacteristic
27C2×C22⋊Dic277C2211yescharacteristic
28C2×#17984540C2211yescharacteristic
29C2×#17984540C2211yescharacteristic
30C2×#17984540C2211yescharacteristic
31C2×#17984540C2211yescharacteristic
32C2×#17984540C2211yescharacteristic
33C2×C4×Dic277C2211yescharacteristic
34C2×C4×Dic277C2211yescharacteristic
35C2×C4×Dic277C2211yescharacteristic
36C2×C4×Dic277C2211yescharacteristic
37#22579787C2211yescharacteristic
38#22579787C2211yescharacteristic
39#22579787C2211yescharacteristic
40#22579787C2211yescharacteristic
41#22579787C2211yescharacteristic
42#22579787C2211yescharacteristic
43#22579787C2211yescharacteristic
44#22579787C2211yescharacteristic
45C2×C4⋊C4×C277C2211yescharacteristic
46C2×C22⋊C4×C277C2211yescharacteristic
47C2×C22⋊C4×C277C2211yescharacteristic
48C2×C22⋊C4×C277C2211yescharacteristic
49C2×C42×C277C2211yescharacteristic
50#95×C277C2211yescharacteristic
51#95×C277C2211yescharacteristic
52C23×D277C2311yescharacteristic
53C2×C22⋊D277—22no—
54C2×C22⋊D277—22no—
55C2×C22⋊D277C2×C414yes—
56C22×Dic277—41no—
57C22×Dic277—41no—
58C22×Dic277C2×C414yes—
59C22×Dic277C2311yescharacteristic
60C22×Dic277C2311yescharacteristic
61C22×Dic277C2311yescharacteristic
62C22×Dic277C2311yescharacteristic
63C22×Dic277C2311yescharacteristic
64C22×Dic277C2311yescharacteristic
65C22×Dic277C2311yescharacteristic
66C2×C4×D277—41no—
67C2×C4×D277—41no—
68C2×C4×D277C2×C414yes—
69C4⋊Dic277—41no—
70#17984542—22no—
71#17984542—22no—
72#17984542—41no—
73#17984542—41no—
74#17984542C2×C414yes—
75C22⋊Dic277—41no—
76C22⋊Dic277—41no—
77#17984540—41no—
78#17984540—41no—
79#17984540—41no—
80#17984540—41no—
81#17984540C2×C414yes—
82C4×Dic277—22no—
83C4×Dic277—22no—
84C4×Dic277—41no—
85C4×Dic277C2×C414yes—
86C24×C277C2311yescharacteristic
87C22×C4×C277C2311yescharacteristic
88C22×C4×C277C2311yescharacteristic
89C22×C4×C277C2311yescharacteristic
90C22×C4×C277C2311yescharacteristic
91C22×C4×C277C2311yescharacteristic
92C22×C4×C277C2311yescharacteristic
93C4⋊C4×C277—41no—
94C22⋊C4×C277—41no—
95C22⋊C4×C277—41no—
96C22⋊C4×C277C2×C414yes—
97C42×C277—41no—
98C22×D277—21no—
99C22×D277—21no—
100C22×D277—21no—
101C22×D277—21no—
102C22×D277—21no—
103C22×D277—21no—
104C22×D277C22×C412yes—
105C22⋊D277—28no—
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×Dic277—21no—
121C2×Dic277—21no—
122C2×Dic277—44no—
123C2×Dic277C22×C412yes—
124C2×Dic277C22×C412yes—
125C2×Dic277C22×C412yes—
126C2×Dic277#4112yes—
127C2×Dic277#4112yes—
128C4×D277—44no—
129C23×C277—21no—
130C23×C277—21no—
131C23×C277—21no—
132C23×C277—21no—
133C23×C277—21no—
134C23×C277—21no—
135C23×C277C22×C412yes—
136C23×C277C2411yescharacteristic
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×C277C22×C412yes—
154C2×C4×C277C22×C412yes—
155C22×C277—22no—
156C22×C277—22no—
157C22×C277—22no—
158C22×C277—41no—
159C22×C277—41no—
160C22×C277—41no—
161C22×C277—41no—
162C22×C277C23×C411yescharacteristic
163C22×C277C2×#4111yescharacteristic
164C22×C277C2×#4111yescharacteristic
165C22×C277H(5,𝔽2)11yescharacteristic
166C22×C277H(5,𝔽2)11yescharacteristic
167C22×C277H(5,𝔽2)11yescharacteristic
168C22×C2772−1+411yescharacteristic
169C2×D277—22no—
170C2×D277—22no—
171C2×D277—22no—
172C2×D277—41no—
173C2×D277—41no—
174C2×D277—41no—
175C2×D277—41no—
176C4×C277—22no—
177C4×C277—22no—
178C4×C277—41no—
179C4×C277—41no—
180C4×C277—41no—
181C4×C277—41no—
182Dic277—22no—
183Dic277—22no—
184Dic277—41no—
185Dic277—41no—
186Dic277—41no—
187Dic277—41no—
188Dic277#11714yes—
189C2×C277—42no—
190C2×C277C2×#11711yescharacteristic
191C2×C277#51811yescharacteristic
192C2×C277#52011yescharacteristic
193C2×C277#54011yescharacteristic
194C2×C277#54011yescharacteristic
195C2×C277#54211yescharacteristic
196C2×C277#54211yescharacteristic
197D277—42no—
198C277#231911yescharacteristic, complemented, Sylow
199#2319—2771nomaximal, Sylow
200C2×C4×D4—2771no—
201#390—2771no—
202#390—2771no—
203#389—2771no—
204#389—2771no—
205#388—2771no—
206#388—2771no—
207#388—2771no—
208#388D27711yescharacteristic, complemented
209#381—2771no—
210#381—2771no—
211#380—2771no—
212#380—2771no—
213C4×C4⋊C4—2771no—
214#376—2771no—
215C22×D4—2771no—
216C23×C4—2771no—
217C23×C4—2771no—
218C4×D4—2778no—
219C2×C4⋊C4—2771no—
220C2×C4⋊C4—2771no—
221C2×C4⋊C4—2771no—
222C2×C4⋊C4—2771no—
223C2×C4⋊C4—2771no—
224C2×C4⋊C4—2771no—
225C2×C4⋊C4C2×D27711yescharacteristic
226C2×C22⋊C4—2771no—
227C2×C22⋊C4—2771no—
228C2×C22⋊C4—2771no—
229C2×C22⋊C4—2771no—
230C2×C22⋊C4—2771no—
231C2×C22⋊C4—2771no—
232C2×C22⋊C4—2771no—
233C2×C22⋊C4C2×D27711yescharacteristic
234C2×C22⋊C4C2×D27711yescharacteristic
235C2×C22⋊C4C2×D27711yescharacteristic
236C2×C42—2771no—
237C2×C42—2771no—
238C2×C42—2771no—
239C2×C42—2771no—
240C2×C42C2×D27711yescharacteristic
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
251C24—2771no—
252C24C22×D27711yescharacteristic
253C2×D4—2774no—
254C2×D4—5542no—
255C2×D4—5542no—
256C22×C4—2771no—
257C22×C4—2771no—
258C22×C4—2771no—
259C22×C4—2774no—
260C22×C4—2774no—
261C22×C4—2771no—
262C22×C4—2771no—
263C22×C4—2771no—
264C22×C4—2771no—
265C22×C4—11081no—
266C22×C4—11081no—
267C22×C4—11081no—
268C22×C4—11081no—
269C22×C4C22×D27711yescharacteristic
270C22×C4C22×D27711yescharacteristic
271C22×C4C22×D27711yescharacteristic
272C22×C4C22×D27711yescharacteristic
273C22×C4C22×D27711yescharacteristic
274C22×C4C22×D27711yescharacteristic
275C4⋊C4—41no—
276C4⋊C4—2774no—
277C4⋊C4—5542no—
278C4⋊C4—5542no—
279C4⋊C4—11081no—
280C4⋊C4—11081no—
281C4⋊C4—11081no—
282C22⋊C4—41no—
283C22⋊C4—41no—
284C22⋊C4—2774no—
285C22⋊C4—11081no—
286C22⋊C4—11081no—
287C22⋊C4—11081no—
288C22⋊C4—11081no—
289C22⋊C4—11081no—
290C22⋊C4—11081no—
291C22⋊C4C4×D27714yes—
292C42—41no—
293C42—2774no—
294C42—5542no—
295C42—5542no—
296C42—11081no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—2772no—
304C23—5541no—
305C23—5541no—
306C23—5541no—
307C23—5541no—
308C23—5541no—
309C23—5541no—
310C23C2×C4×D27712yes—
311C23C23×D27711yescharacteristic
312D4—5548no—
313C2×C4—21no—
314C2×C4—21no—
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—2772no—
330C2×C4—2772no—
331C2×C4—2772no—
332C2×C4—2772no—
333C2×C4—2772no—
334C2×C4—5541no—
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—11084no—
351C2×C4—11084no—
352C2×C4C2×C4×D27712yes—
353C2×C4C2×C4×D27712yes—
354C22—22no—
355C22—22no—
356C22—22no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—5542no—
362C22—5542no—
363C22—5542no—
364C22—11081no—
365C22—11081no—
366C22—11081no—
367C22—11081no—
368C22C22×C4×D27711yescharacteristic
369C22#41×D27711yescharacteristic
370C22#41×D27711yescharacteristic
371C22#2257992511yescharacteristic
372C22#2257992511yescharacteristic
373C22#2257992611yescharacteristic
374C22#2257992711yescharacteristic
375C4—22no—
376C4—22no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—41no—
381C4—2774no—
382C4—5542no—
383C4—5542no—
384C4—11081no—
385C4—11081no—
386C4—11081no—
387C4—11081no—
388C2—42no—
389C2—11082no—
390C2#117×D27711yescharacteristic
391C2#3180047411yescharacteristic
392C2#3180048111yescharacteristic
393C2#3180060211yescharacteristic
394C2#3180060411yescharacteristic
395C2#3180061611yescharacteristic
396C2#3180061811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D277
commutatorC22×C277C23×C4
Fitting#388×C277C2
socle, cosocleC23×C277C24
prime radicalC22×C22⋊D277C22
hypercenter#388D277
hypocenterC277#2319
LCSG ▷ C22×C277 ▷ C277
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
4. #31799899C2semidirect
5. #31799897C2semidirect
6. #31799895C2semidirect
7. #31799893C2semidirect
8. #31799891C2semidirect
9. #31799864C2semidirect
10. #31799863C2semidirect
11. #31799860C2semidirect
12. #31799859C2semidirect
13. C4×#17984542C2semidirect
14. #31799847C2semidirect
15. #388×C277C2semidirect
19. #22579840C4semidirect
198. C277#2319semidirect
208. #388D277semidirect

Maximal subgroups

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

subgroupindex
C2×#225798402
#317999022
#317998992
#317998972
#317998952
#317998932
#317998912
#317998642
#317998632
#317998602
#317998592
C4×#179845422
#317998472
#388×C2772
#2319277