Finite Group Databasebeta

← #47986381

Subgroups — #47986381

Order 35456.

944 conjugacy classes of subgroups; only the 163 normal subgroups are shown.

normal subgroups only

This group has 944 conjugacy classes of subgroups — too many to draw. Only its 163 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#17984562C211yesmaximal, characteristic, complemented
2C2×#22579842C211yesmaximal, characteristic, complemented
3C2×#22579840C212yesmaximal, complemented
4#31799922C211yesmaximal, characteristic, complemented
5#31799917C212yesmaximal, complemented
6#31799915C211yesmaximal, characteristic, complemented
7#31799911C212yesmaximal, complemented
8#31799910C211yesmaximal, characteristic, complemented
9C22⋊C4×Dic277C212yesmaximal, complemented
10#31799849C211yesmaximal, characteristic, complemented
11#394×C277C211yesmaximal, characteristic, complemented
12C2×#17984562—28no—
13C2×#17984562—24no—
14C22×Dic554C2211yescharacteristic
15C22×D1108C2211yescharacteristic
16C22×C22⋊D277C2212yes—
17C22×C22⋊D277C2212yes—
18C23×Dic277C2212yes—
19C22×C4×D277C2211yescharacteristic
20C22×C4×D277C2211yescharacteristic
21#22579842—24no—
22#22579840—28no—
23C2×#17984542C2212yes—
24C2×C22⋊Dic277C2212yes—
25C2×#17984540C2212yes—
26C2×#17984540C2211yescharacteristic
27C2×#17984540C2212yes—
28C2×#17984540C2211yescharacteristic
29C2×C4×Dic277C2212yes—
30C2×C4×Dic277C2211yescharacteristic
31#22579787C2211yescharacteristic
32#22579787C2212yes—
33#22579787C2212yes—
34C22×D4×C277C2211yescharacteristic
35C2×C4⋊C4×C277C2211yescharacteristic
36C2×C22⋊C4×C277C2212yes—
37C2×C22⋊C4×C277C2212yes—
38#95×C277C2211yescharacteristic
39C23×D277C2311yescharacteristic
40C23×D277C2311yescharacteristic
41#17984562—232no—
42C2×Dic554—24no—
43C2×Dic554—22no—
44C2×D1108—22no—
45C2×D1108—22no—
46C2×D1108—22no—
47C2×C22⋊D277—24no—
48C2×C22⋊D277—24no—
49C2×C22⋊D277—24no—
50C2×C22⋊D277—24no—
51C2×C22⋊D277—24no—
52C2×C22⋊D277—24no—
53C22×Dic277—24no—
54C22×Dic277—24no—
55C22×Dic277D418yescomplemented
56C22×Dic277C2311yescharacteristic
57C22×Dic277C2312yes—
58C22×Dic277C2312yes—
59C22×Dic277C2311yescharacteristic
60C2×C4×D277—24no—
61C2×C4×D277—24no—
62C2×C4×D277—22no—
63C2×C4×D277D414yescomplemented
64#17984542—24no—
65C22⋊Dic277—24no—
66#17984540—22no—
67#17984540—24no—
68#17984540—24no—
69#17984540—22no—
70C4×Dic277—24no—
71C4×Dic277—22no—
72C24×C277C2312yes—
73C2×D4×C277—24no—
74C2×D4×C277—22no—
75C22×C4×C277C2312yes—
76C22×C4×C277C2311yescharacteristic
77C22×C4×C277C2311yescharacteristic
78C22×C4×C277C2311yescharacteristic
79C4⋊C4×C277—22no—
80C22⋊C4×C277—24no—
81C22⋊C4×C277—24no—
82C22×D277—22no—
83C22×D277—21no—
84C22×D277—22no—
85C22×D277—22no—
86C22×D277—22no—
87C22×D277—21no—
88C22×D277—21no—
89C22×D277—21no—
90C22×D277C2×D412yes—
91C22×D277#4112yescomplemented
92Dic554—28no—
93D1108—28no—
94C22⋊D277—216no—
95C22⋊D277—216no—
96C2×Dic277—22no—
97C2×Dic277—22no—
98C2×Dic277—22no—
99C2×Dic277—22no—
100C2×Dic277—216no—
101C2×Dic277—21no—
102C2×Dic277—22no—
103C2×Dic277C2×D414yes—
104C2×Dic277C2×D414yes—
105C2×Dic277C2×D412yes—
106C2×Dic277#4114yescomplemented
107C4×D277—28no—
108C4×D277—44no—
109C23×C277—22no—
110C23×C277—22no—
111C23×C277—22no—
112C23×C277—22no—
113C23×C277—22no—
114C23×C277—22no—
115C23×C277C2×D414yes—
116C23×C277C2411yescharacteristic
117D4×C277—28no—
118C2×C4×C277—21no—
119C2×C4×C277—22no—
120C2×C4×C277—21no—
121C2×C4×C277—22no—
122C2×C4×C277—22no—
123C2×C4×C277—21no—
124C2×C4×C277—22no—
125C2×C4×C277—22no—
126C2×C4×C277C2×D412yes—
127C2×C4×C277#4112yescomplemented
128C22×C277—24no—
129C22×C277—24no—
130C22×C277—24no—
131C22×C277—42no—
132C22×C277—42no—
133C22×C277—42no—
134C22×C277—42no—
135C22×C277C22×D412yes—
136C22×C277C22×D411yescharacteristic
137C22×C277C2×#4111yescharacteristic
138C22×C277C2×#4112yes—
139C22×C277C2×#4111yescharacteristic
140C2×D277—22no—
141C2×D277—24no—
142C2×D277—22no—
143C2×D277—22no—
144C2×D277—22no—
145C2×D277—41no—
146C2×D277—42no—
147C2×D277—42no—
148C2×D277—42no—
149C2×D277—41no—
150C4×C277—22no—
151C4×C277—22no—
152C4×C277—41no—
153C4×C277—42no—
154Dic277—24no—
155Dic277—24no—
156Dic277—41no—
157Dic277#12014yes—
158C2×C277—44no—
159C2×C277C2×#12011yescharacteristic
160C2×C277#52512yes—
161C2×C277#52511yescharacteristic
162C2×C277#53212yes—
163C2×C277#53211yescharacteristic
164D277—42no—
165D277—42no—
166C277#238811yescharacteristic, complemented, Sylow
167#2388—2771nomaximal, Sylow
168C22×#41—2771no—
169C2×C4×D4—2771no—
170C2×C4×D4—2772no—
171#395—2771no—
172#394—2772no—
173#394D27711yescharacteristic, complemented
174#393—2771no—
175#392—2771no—
176#392—2772no—
177C4×C22⋊C4—2772no—
178C4×C22⋊C4—2771no—
179C2×#41—5548no—
180C2×#41—5544no—
181C22×Q8—2771no—
182C22×D4—2772no—
183C22×D4—2772no—
184C22×D4—2771no—
185C22×D4C2×D27711yescharacteristic
186C23×C4—2772no—
187C23×C4—2771no—
188C23×C4—2771no—
189C4×D4—5548no—
190C4×D4—5544no—
191C2×C4⋊C4—2772no—
192C2×C4⋊C4C2×D27711yescharacteristic
193C2×C22⋊C4—2772no—
194C2×C22⋊C4—2772no—
195C2×C22⋊C4—2771no—
196C2×C22⋊C4—2771no—
197C2×C22⋊C4—2772no—
198C2×C22⋊C4C2×D27712yes—
199C2×C22⋊C4C2×D27712yes—
200C2×C42—2772no—
201C2×C42—2771no—
202#95—2771no—
203#95—2772no—
204#95—2772no—
205#95C2×D27711yescharacteristic
206C24—2771no—
207C24—2771no—
208C24C22×D27712yes—
209#41—55432no—
210C2×Q8—5544no—
211C2×Q8—5542no—
212C2×D4—24no—
213C2×D4—22no—
214C2×D4—5542no—
215C2×D4—5542no—
216C2×D4—5544no—
217C2×D4—5544no—
218C2×D4—5544no—
219C2×D4—5544no—
220C2×D4—5544no—
221C2×D4—5544no—
222C2×D4—5542no—
223C22×C4—2771no—
224C22×C4—2778no—
225C22×C4—2772no—
226C22×C4—2772no—
227C22×C4—2774no—
228C22×C4—2771no—
229C22×C4—5544no—
230C22×C4—5544no—
231C22×C4—5542no—
232C22×C4—5544no—
233C22×C4—5544no—
234C22×C4C22×D27712yes—
235C22×C4C22×D27711yescharacteristic
236C22×C4C22×D27711yescharacteristic
237C22×C4C22×D27711yescharacteristic
238C4⋊C4—22no—
239C4⋊C4—5544no—
240C22⋊C4—24no—
241C22⋊C4—24no—
242C22⋊C4—5544no—
243C22⋊C4—5544no—
244C22⋊C4—5542no—
245C22⋊C4—5544no—
246C22⋊C4—5542no—
247C42—5542no—
248C42—5544no—
249C23—22no—
250C23—22no—
251C23—22no—
252C23—22no—
253C23—22no—
254C23—22no—
255C23—2772no—
256C23—2772no—
257C23—5542no—
258C23—5541no—
259C23—5542no—
260C23—5542no—
261C23—5542no—
262C23—5541no—
263C23—5541no—
264C23—5541no—
265C23D4×D27714yes—
266C23C23×D27711yescharacteristic
267Q8—5548no—
268D4—28no—
269D4—5548no—
270D4—55416no—
271D4—55416no—
272C2×C4—21no—
273C2×C4—22no—
274C2×C4—21no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—21no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—2774no—
281C2×C4—2772no—
282C2×C4—2774no—
283C2×C4—2774no—
284C2×C4—5548no—
285C2×C4—55416no—
286C2×C4—5542no—
287C2×C4—5542no—
288C2×C4—5542no—
289C2×C4—5542no—
290C2×C4—5541no—
291C2×C4—5542no—
292C2×C4—11084no—
293C2×C4D4×D27712yes—
294C2×C4#1798456212yescomplemented
295C22—24no—
296C22—24no—
297C22—24no—
298C22—42no—
299C22—42no—
300C22—42no—
301C22—42no—
302C22—5542no—
303C22—5544no—
304C22—5542no—
305C22—5542no—
306C22—5542no—
307C22—11081no—
308C22—11082no—
309C22—11082no—
310C22—11082no—
311C22—11081no—
312C22C2×D4×D27712yes—
313C22C2×D4×D27711yescharacteristic
314C22#41×D27711yescharacteristic
315C22#41×D27712yes—
316C22C2×#1798456211yescharacteristic
317C4—22no—
318C4—22no—
319C4—41no—
320C4—42no—
321C4—2774no—
322C4—5544no—
323C4—5544no—
324C4—11081no—
325C2—44no—
326C2—11082no—
327C2—11082no—
328C2#120×D27711yescharacteristic
329C2#3180051012yes—
330C2#3180051211yescharacteristic
331C2#3180054712yes—
332C2#3180055111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D277
commutator, socle, cosocleC23×C277C24
Fitting#394×C277C2
hypercenter#394D277
hypocenterC277#2388
LCSG ▷ C23×C277 ▷ C277
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C22×#17984562C2semidirect
2. C2×#22579842C2semidirect
3. C2×#22579840C2semidirect
4. #31799922C2semidirect
5. #31799917C2semidirect
6. #31799915C2semidirect
7. #31799911C2semidirect
8. #31799910C2semidirect
9. C22⋊C4×Dic277C2semidirect
10. #31799849C2semidirect
11. #394×C277C2semidirect
55. C22×Dic277D4semidirect
63. C2×C4×D277D4semidirect
91. C22×D277#41semidirect
106. C2×Dic277#41semidirect
127. C2×C4×C277#41semidirect
166. C277#2388semidirect
173. #394D277semidirect
294. C2×C4#17984562semidirect

Maximal subgroups

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

subgroupindex
C22×#179845622
C2×#225798422
C2×#225798402
#317999222
#317999172
#317999152
#317999112
#317999102
C22⋊C4×Dic2772
#317998492
#394×C2772
#2388277