Finite Group Databasebeta

← #47984195

Subgroups — #47984195

Order 35456.

394 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 73 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×#22579910C211yesmaximal, characteristic, complemented
2#31800566C211yesmaximal, characteristic
3C2×#22579868C211yesmaximal, characteristic, complemented
4#31800012C211yesmaximal, characteristic, complemented
5C2×#22579796C211yesmaximal, characteristic, complemented
6#31799762C211yesmaximal, characteristic, complemented
7C2×#104×C277C211yesmaximal, characteristic, complemented
8C22×Dic554C2211yescharacteristic
9C22×D1108C2211yescharacteristic
10#22579910—22no—
11#22579910—22no—
12C2×#17984553—21no—
13C2×#17984551—21no—
14C2×#17984547C2211yescharacteristic
15#22579876—21no—
16#22579869—21no—
17#22579868—22no—
18#22579868—22no—
19#22579854—22no—
20#22579848—22no—
21#22579839C2211yescharacteristic
22C2×#17984540—22no—
23#22579805—22no—
24#22579796—22no—
25C2×#41×C277C2211yescharacteristic
26C2×M16×C277C2211yescharacteristic
27C2×C42×C277C2211yescharacteristic
28#104×C277—22no—
29C23×D277D412yes—
30C2×Dic554—21no—
31C2×Dic554—21no—
32C2×Dic554—21no—
33C2×Dic554—21no—
34C2×Dic554—21no—
35C2×Dic554D412yescomplemented
36C2×D1108—21no—
37C2×D1108—21no—
38C2×D1108—21no—
39C2×D1108—21no—
40C2×D1108—21no—
41C2×D1108—21no—
42C2×C22⋊D277—24no—
43C22×Dic277—21no—
44#17984553—24no—
45#17984551—24no—
46#17984547—21no—
47#17984547D412yescomplemented
48C2×#14555660—21no—
49C4⋊Dic277D412yes—
50C22⋊Dic277—21no—
51#17984540—28no—
52#17984540—24no—
53C4×Dic277—21no—
54#41×C277—21no—
55#41×C277—21no—
56#41×C277—21no—
57#41×C277—21no—
58C2×Q8×C277D411yescharacteristic
59C2×D4×C277—21no—
60C2×D4×C277D411yescharacteristic
61C22×C4×C277—21no—
62C22×C4×C277—21no—
63C22×C4×C277C2311yescharacteristic
64M16×C277—21no—
65M16×C277—21no—
66C2×C8×C277—21no—
67C42×C277—21no—
68C42×C277D412yescomplemented
69C22×D277—22no—
70C22×D277—22no—
71C22×D277—22no—
72C22×D277—44no—
73Dic554—22no—
74Dic554—22no—
75Dic554—41no—
76Dic554—41no—
77D1108—41no—
78D1108—41no—
79D1108—41no—
80D1108—41no—
81C22⋊D277—84no—
82C2×Dic277—22no—
83C2×Dic277—22no—
84C2×Dic277—41no—
85C2×Dic277—41no—
86#14555660—22no—
87C23×C277—21no—
88C23×C277C2×D411yescharacteristic
89Q8×C277—21no—
90Q8×C277—21no—
91D4×C277—21no—
92D4×C277—21no—
93D4×C277—41no—
94D4×C277—41no—
95C2×C4×C277—22no—
96C2×C4×C277—21no—
97C2×C4×C277—42no—
98C2×C4×C277—41no—
99C2×C4×C277—41no—
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—41no—
107C22×C277—22no—
108C22×C277—41no—
109C22×C277—42no—
110C22×C277#12011yescharacteristic
111C22×C277#12011yescharacteristic
112C22×C277#12111yescharacteristic
113C2×D277—44no—
114C2×D277—42no—
115C2×D277—44no—
116C2×D277—82no—
117C4×C277—42no—
118C4×C277—41no—
119C4×C277#12011yescharacteristic
120C4×C277#12111yescharacteristic
121C4×C277#12111yescharacteristic
122C4×C277#12711yescharacteristic
123Dic277—42no—
124Dic277—42no—
125C2×C277—21no—
126C2×C277—21no—
127C2×C277—81no—
128C2×C277#39211yescharacteristic
129C2×C277#45512yes—
130D277—82no—
131C277#200411yescharacteristic, complemented, Sylow
132#2004—2771nomaximal, Sylow
133C2×#137—2771no—
134#535—2771no—
135C2×#124—2771no—
136C2×#104D27711yescharacteristic, complemented
137#419—2771no—
138C2×#100—2771no—
139#339—2771no—
140C2×#41C2×D27711yescharacteristic
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#117—2771no—
156C2×C22⋊C4—5542no—
157C2×C42C2×D27711yescharacteristic
158#104—22no—
159#103—5542no—
160#100—5542no—
161C24—2772no—
162#41—21no—
163#41—21no—
164#41—21no—
165#41—21no—
166C2×Q8—2772no—
167C2×Q8—5541no—
168C2×Q8—5541no—
169C2×Q8—5541no—
170C2×Q8—5541no—
171C2×Q8—5541no—
172C2×Q8D110811yescharacteristic
173C2×D4—21no—
174C2×D4—5544no—
175C2×D4—5541no—
176C2×D4—5541no—
177C2×D4—5541no—
178C2×D4—5541no—
179C2×D4—5541no—
180C2×D4—5541no—
181C2×D4D110811yescharacteristic
182C22×C4—21no—
183C22×C4—21no—
184C22×C4—5541no—
185C22×C4C22×D27711yescharacteristic
186Q16—5544no—
187SD16—5544no—
188M16—21no—
189M16—21no—
190M16—2772no—
191M16—5541no—
192C2×C8—21no—
193C2×C8—5541no—
194C4⋊C4—2772no—
195C22⋊C4—5548no—
196C22⋊C4—5544no—
197C22⋊C4—5541no—
198C42—21no—
199C42—5541no—
200C42C22⋊D27712yescomplemented
201C23—21no—
202C23—5542no—
203C23—5542no—
204C23—5542no—
205C23—11084no—
206C23D4×D27711yescharacteristic
207Q8—21no—
208Q8—21no—
209Q8—5542no—
210Q8—5542no—
211Q8—11081no—
212Q8—11081no—
213D4—21no—
214D4—21no—
215D4—41no—
216D4—41no—
217D4—11081no—
218D4—11081no—
219D4—11081no—
220D4—11081no—
221D4—22164no—
222C2×C4—22no—
223C2×C4—21no—
224C2×C4—42no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—5542no—
228C2×C4—5542no—
229C2×C4—11081no—
230C2×C4—11081no—
231C2×C4D4×D27711yescharacteristic
232C2×C4D4×D27711yescharacteristic
233C2×C4D4×D27711yescharacteristic
234C2×C4C2×C22⋊D27711yescharacteristic
235C2×C4C2×D110811yescharacteristic
236C2×C4#1798456311yescharacteristic
237C8—41no—
238C8—5542no—
239C22—22no—
240C22—41no—
241C22—42no—
242C22—11084no—
243C22—11082no—
244C22—11084no—
245C22—22162no—
246C22#2257984811yescharacteristic
247C22#2257985011yescharacteristic
248C22#2257985311yescharacteristic
249C4—42no—
250C4—41no—
251C4—11082no—
252C4—11082no—
253C4#2257985011yescharacteristic
254C4#2257985311yescharacteristic
255C4#2257985411yescharacteristic
256C4#2257987611yescharacteristic
257C2—21no—
258C2—21no—
259C2—81no—
260C2—22162no—
261C2#3179991111yescharacteristic
262C2#3180018112yes—
subgroupG/H
centerC22#22579850
commutator, cosocleC22×C4×C277C23
FrattiniC22×C4C22×D277
FittingC2×#104×C277C2
socleC22×C277#120
prime radical#31800566C2
hypercenterC2×#104D277
hypocenterC277#2004
LCSG ▷ C22×C4×C277 ▷ C2×C277 ▷ C277
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
1. C2×#22579910C2semidirect
3. C2×#22579868C2semidirect
4. #31800012C2semidirect
5. C2×#22579796C2semidirect
6. #31799762C2semidirect
7. C2×#104×C277C2semidirect
35. C2×Dic554D4semidirect
47. #17984547D4semidirect
68. C42×C277D4semidirect
131. C277#2004semidirect
136. C2×#104D277semidirect
200. C42C22⋊D277semidirect

Maximal subgroups

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

subgroupindex
C2×#225799102
#318005662
C2×#225798682
#318000122
C2×#225797962
#317997622
C2×#104×C2772
#2004277