Finite Group Databasebeta

← #47984199

Subgroups — #47984199

Order 35456.

394 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 75 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
1C2×#22579913C211yesmaximal, characteristic, complemented
2#31800571C211yesmaximal, characteristic
3C2×#22579868C211yesmaximal, characteristic, complemented
4C2×#22579808C211yesmaximal, characteristic, complemented
5#31800010C211yesmaximal, characteristic, complemented
6C2×#22579796C211yesmaximal, characteristic, complemented
7#339×C277C211yesmaximal, characteristic, complemented
8C2×#17984563C2211yescharacteristic
9C22×Dic554C2211yescharacteristic
10C22×D1108C2211yescharacteristic
11#22579913—22no—
12#22579913—22no—
13C2×Dic1108—21no—
14C2×#17984552—21no—
15C2×#17984547C2211yescharacteristic
16#22579877—21no—
17#22579868—21no—
18#22579868—22no—
19#22579868—22no—
20#22579855—22no—
21#22579850—22no—
22C2×#17984540—22no—
23#22579808—22no—
24#22579803—22no—
25#22579796—22no—
26C2×M16×C277C2211yescharacteristic
27#117×C277C2211yescharacteristic
28C2×C42×C277C2211yescharacteristic
29C23×D277D412yes—
30#17984563—21no—
31#17984563—21no—
32#17984563—21no—
33#17984563—21no—
34C2×Dic554—21no—
35C2×Dic554—21no—
36C2×Dic554—21no—
37C2×Dic554—21no—
38C2×Dic554—21no—
39C2×Dic554D411yescharacteristic
40C2×Dic554D412yescomplemented
41C2×D1108—24no—
42C2×D1108—21no—
43C2×D1108—21no—
44C2×D1108—21no—
45C2×D1108—21no—
46C2×D1108—21no—
47C2×D1108—21no—
48C2×D1108D411yescharacteristic
49C2×C22⋊D277—21no—
50C22×Dic277—21no—
51C2×C4×D277—21no—
52Dic1108—24no—
53#17984552—24no—
54#17984547—21no—
55#17984547—21no—
56C2×#14555660—21no—
57#17984540—28no—
58#17984540—24no—
59C22×C4×C277—21no—
60C22×C4×C277C2311yescharacteristic
61M16×C277—21no—
62M16×C277D412yescomplemented
63C2×C8×C277—21no—
64C4⋊C4×C277D412yes—
65C22⋊C4×C277—21no—
66C42×C277—21no—
67C42×C277—21no—
68C42×C277D412yescomplemented
69C22×D277—22no—
70C22×D277—22no—
71C22×D277—21no—
72C22×D277—22no—
73C22×D277—44no—
74Dic554—22no—
75Dic554—21no—
76Dic554—22no—
77Dic554—21no—
78Dic554—41no—
79Dic554—41no—
80D1108—21no—
81D1108—21no—
82D1108—41no—
83D1108—41no—
84D1108—41no—
85D1108—41no—
86D1108—84no—
87C22⋊D277—41no—
88C22⋊D277—41no—
89C2×Dic277—21no—
90C2×Dic277—22no—
91C2×Dic277—41no—
92C2×Dic277—41no—
93C4×D277—41no—
94C4×D277—41no—
95#14555660—41no—
96C23×C277C2×D411yescharacteristic
97C2×C4×C277—22no—
98C2×C4×C277—22no—
99C2×C4×C277—42no—
100C2×C4×C277C2×D411yescharacteristic
101C2×C4×C277C2×D411yescharacteristic
102C2×C4×C277C2×D411yescharacteristic
103C2×C4×C277C2×D411yescharacteristic
104C2×C4×C277C2×D411yescharacteristic
105C2×C4×C277#4111yescharacteristic
106C8×C277—22no—
107C22×C277—22no—
108C22×C277#12011yescharacteristic
109C22×C277#12011yescharacteristic
110C22×C277#12111yescharacteristic
111C2×D277—44no—
112C2×D277—41no—
113C2×D277—42no—
114C2×D277—42no—
115C2×D277—44no—
116C2×D277—82no—
117C4×C277—42no—
118C4×C277—42no—
119C4×C277#12011yescharacteristic
120C4×C277#12111yescharacteristic
121C4×C277#12111yescharacteristic
122C4×C277#12711yescharacteristic
123Dic277—41no—
124Dic277—42no—
125C2×C277—21no—
126C2×C277—21no—
127C2×C277#39211yescharacteristic
128C2×C277#45512yes—
129D277—81no—
130D277—82no—
131C277#200411yescharacteristic, complemented, Sylow
132#2004—2771nomaximal, Sylow
133C2×#137—2771no—
134#535—2771no—
135C2×#124—2771no—
136C2×#104—2771no—
137#419—2771no—
138C2×#100—2771no—
139#339D27711yescharacteristic, complemented
140C2×#41—2771no—
141C22×Q8—2771no—
142C22×D4—2771no—
143#137—5542no—
144#137—5542no—
145C2×Q16—5541no—
146C2×SD16—5541no—
147C2×M16—2771no—
148C2×M16C2×D27711yescharacteristic
149#127—5541no—
150#124—5542no—
151#124—5541no—
152#124—5542no—
153#121—5542no—
154#120—5542no—
155#117C2×D27711yescharacteristic
156C2×C22⋊C4—5542no—
157C2×C42C2×D27711yescharacteristic
158#104—5542no—
159#103—5542no—
160#100—5542no—
161C24—2772no—
162#41—5541no—
163#41—5541no—
164#41—5541no—
165#41—5541no—
166C2×Q8—2771no—
167C2×Q8—2772no—
168C2×Q8—5541no—
169C2×Q8—5541no—
170C2×Q8—5541no—
171C2×Q8—5541no—
172C2×Q8—5541no—
173C2×D4—2771no—
174C2×D4—5544no—
175C2×D4—5541no—
176C2×D4—5541no—
177C2×D4—5541no—
178C2×D4—5541no—
179C2×D4—5541no—
180C2×D4—5541no—
181C2×D4—5541no—
182C22×C4—21no—
183C22×C4—5541no—
184C22×C4—5541no—
185C22×C4C22×D27711yescharacteristic
186Q16—5544no—
187SD16—5544no—
188M16—21no—
189M16—5541no—
190M16—5541no—
191M16D110812yescomplemented
192C2×C8—21no—
193C2×C8—5541no—
194C4⋊C4D110812yes—
195C22⋊C4—21no—
196C22⋊C4—5548no—
197C22⋊C4—5544no—
198C42—21no—
199C42—21no—
200C42D110812yescomplemented
201C23—5542no—
202C23—5542no—
203C23—5541no—
204C23—5542no—
205C23—11084no—
206C23D4×D27711yescharacteristic
207Q8—5542no—
208Q8—5541no—
209Q8—5542no—
210Q8—5541no—
211Q8—11081no—
212Q8—11081no—
213D4—5541no—
214D4—5541no—
215D4—11081no—
216D4—11081no—
217D4—11081no—
218D4—11081no—
219D4—11081no—
220D4—11081no—
221D4—22164no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—42no—
225C2×C4—5542no—
226C2×C4—5541no—
227C2×C4—11081no—
228C2×C4—11081no—
229C2×C4—11081no—
230C2×C4—11081no—
231C2×C4D4×D27711yescharacteristic
232C2×C4D4×D27711yescharacteristic
233C2×C4C2×D110811yescharacteristic
234C2×C4C2×D110811yescharacteristic
235C2×C4C2×D110811yescharacteristic
236C2×C4#1798456411yescharacteristic
237C8—22no—
238C8—11081no—
239C22—22no—
240C22—11084no—
241C22—11081no—
242C22—11082no—
243C22—11082no—
244C22—11084no—
245C22—22162no—
246C22#2257985011yescharacteristic
247C22#2257985011yescharacteristic
248C22#2257985511yescharacteristic
249C4—42no—
250C4—42no—
251C4—11081no—
252C4—11082no—
253C4#2257985011yescharacteristic
254C4#2257985511yescharacteristic
255C4#2257985511yescharacteristic
256C4#2257987711yescharacteristic
257C2—21no—
258C2—21no—
259C2—22162no—
260C2—22161no—
261C2#3179991211yescharacteristic
262C2#3180018112yes—
subgroupG/H
centerC22#22579850
commutator, cosocleC22×C4×C277C23
FrattiniC22×C4C22×D277
Fitting#339×C277C2
socleC22×C277#120
prime radical#31800571C2
hypercenter#339D277
hypocenterC277#2004
LCSG ▷ C22×C4×C277 ▷ C2×C277 ▷ C277
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
1. C2×#22579913C2semidirect
3. C2×#22579868C2semidirect
4. C2×#22579808C2semidirect
5. #31800010C2semidirect
6. C2×#22579796C2semidirect
7. #339×C277C2semidirect
40. C2×Dic554D4semidirect
62. M16×C277D4semidirect
68. C42×C277D4semidirect
131. C277#2004semidirect
139. #339D277semidirect
191. M16D1108semidirect
200. C42D1108semidirect

Maximal subgroups

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

subgroupindex
C2×#225799132
#318005712
C2×#225798682
C2×#225798082
#318000102
C2×#225797962
#339×C2772
#2004277