Finite Group Databasebeta

← #47984185

Subgroups — #47984185

Order 35456.

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

normal subgroups only

This group has 478 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×#22579908C211yesmaximal, characteristic, complemented
2#31800571C211yesmaximal, characteristic, complemented
3C2×#22579877C211yesmaximal, characteristic, complemented
4C2×#22579808C211yesmaximal, characteristic, complemented
5#31800006C211yesmaximal, characteristic, complemented
6C2×#22579796C211yesmaximal, characteristic, complemented
7#339×C277C211yesmaximal, characteristic, complemented
8C2×#17984563C2211yescharacteristic
9C22×D1108—22no—
10C22×D1108C2211yescharacteristic
11C22×D1108C2211yescharacteristic
12#22579908—22no—
13#22579908—22no—
14C2×#17984552—21no—
15C2×D2216—21no—
16C2×#17984547C2211yescharacteristic
17#22579877—22no—
18#22579877—21no—
19#22579877—22no—
20#22579868—21no—
21#22579855—22no—
22#22579850—22no—
23#22579808—22no—
24#22579800—22no—
25#22579796—22no—
26C2×M16×C277C2211yescharacteristic
27#117×C277C2211yescharacteristic
28C2×C42×C277C2211yescharacteristic
29C23×D277—21no—
30C23×D277D412yes—
31#17984563—21no—
32#17984563—21no—
33#17984563—21no—
34#17984563—21no—
35C2×Dic554D411yescharacteristic, complemented
36C2×D1108—28no—
37C2×D1108—24no—
38C2×D1108—21no—
39C2×D1108—21no—
40C2×D1108—21no—
41C2×D1108—21no—
42C2×D1108—21no—
43C2×D1108—21no—
44C2×D1108—21no—
45C2×D1108—21no—
46C2×D1108—21no—
47C2×D1108—21no—
48C2×D1108—21no—
49C2×D1108—48no—
50C2×D1108D411yescharacteristic, complemented
51C2×D1108D412yescomplemented
52C2×C22⋊D277—21no—
53C2×C4×D277—21no—
54#17984552—24no—
55D2216—24no—
56#17984547—21no—
57#17984547—21no—
58C2×#14555660—21no—
59#17984540—24no—
60C22×C4×C277—21no—
61C22×C4×C277C2311yescharacteristic
62M16×C277—21no—
63M16×C277D412yescomplemented
64C2×C8×C277—21no—
65C4⋊C4×C277D412yescomplemented
66C22⋊C4×C277—21no—
67C42×C277—21no—
68C42×C277—21no—
69C42×C277D412yescomplemented
70C22×D277—22no—
71C22×D277—21no—
72C22×D277—22no—
73C22×D277—22no—
74C22×D277—22no—
75C22×D277—44no—
76C22×D277—44no—
77C22×D277—41no—
78C22×D277—41no—
79Dic554—21no—
80Dic554—21no—
81D1108—21no—
82D1108—22no—
83D1108—22no—
84D1108—21no—
85D1108—416no—
86D1108—41no—
87D1108—41no—
88D1108—41no—
89D1108—41no—
90D1108—41no—
91D1108—41no—
92D1108—84no—
93C22⋊D277—41no—
94C22⋊D277—41no—
95C2×Dic277—21no—
96C4×D277—41no—
97C4×D277—41no—
98#14555660—41no—
99C23×C277C2×D411yescharacteristic
100C2×C4×C277—24no—
101C2×C4×C277—22no—
102C2×C4×C277—22no—
103C2×C4×C277C2×D411yescharacteristic
104C2×C4×C277C2×D411yescharacteristic
105C2×C4×C277C2×D411yescharacteristic
106C2×C4×C277C2×D411yescharacteristic
107C2×C4×C277C2×D411yescharacteristic
108C2×C4×C277#4111yescharacteristic
109C8×C277—22no—
110C22×C277—22no—
111C22×C277#12011yescharacteristic
112C22×C277#12011yescharacteristic
113C22×C277#12111yescharacteristic
114C2×D277—44no—
115C2×D277—44no—
116C2×D277—41no—
117C2×D277—42no—
118C2×D277—42no—
119C2×D277—42no—
120C2×D277—44no—
121C2×D277—82no—
122C2×D277—82no—
123C2×D277—82no—
124C4×C277—24no—
125C4×C277—42no—
126C4×C277#12011yescharacteristic
127C4×C277#12111yescharacteristic
128C4×C277#12111yescharacteristic
129C4×C277#12711yescharacteristic
130Dic277—41no—
131C2×C277—21no—
132C2×C277—21no—
133C2×C277#39211yescharacteristic
134C2×C277#45312yes—
135D277—81no—
136D277—82no—
137D277—82no—
138C277#200211yescharacteristic, complemented, Sylow
139#2002—2771nomaximal, Sylow
140C2×AGL(1,ℤ/8)—2771no—
141#535—2771no—
142C2×#127—2771no—
143C2×#104—2771no—
144#418—2771no—
145C2×#100—2771no—
146#339D27711yescharacteristic, complemented
147C2×#41—2771no—
148C22×D4—2771no—
149C22×D4—2771no—
150C22×D4—5542no—
151AGL(1,ℤ/8)—5542no—
152AGL(1,ℤ/8)—5542no—
153C2×SD16—5541no—
154C2×D8—5541no—
155C2×M16—2771no—
156C2×M16C2×D27711yescharacteristic
157#127—5542no—
158#127—5541no—
159#127—5542no—
160#124—5541no—
161#121—5542no—
162#120—5542no—
163#117C2×D27711yescharacteristic
164C2×C42C2×D27711yescharacteristic
165#104—5542no—
166#102—5542no—
167#100—5542no—
168C24—2772no—
169C24—5541no—
170#41—5541no—
171#41—5541no—
172#41—5541no—
173#41—5541no—
174C2×Q8—2771no—
175C2×D4—2771no—
176C2×D4—2772no—
177C2×D4—5548no—
178C2×D4—5544no—
179C2×D4—5541no—
180C2×D4—5541no—
181C2×D4—5541no—
182C2×D4—5541no—
183C2×D4—5541no—
184C2×D4—5541no—
185C2×D4—5541no—
186C2×D4—5541no—
187C2×D4—5541no—
188C2×D4—5541no—
189C2×D4—5541no—
190C2×D4—5541no—
191C2×D4—11088no—
192C22×C4—21no—
193C22×C4—5541no—
194C22×C4C22×D27711yescharacteristic
195SD16—5544no—
196D8—5544no—
197M16—21no—
198M16—5541no—
199M16—5541no—
200M16D110812yescomplemented
201C2×C8—21no—
202C2×C8—5541no—
203C4⋊C4D110812yescomplemented
204C22⋊C4—21no—
205C22⋊C4—5544no—
206C42—21no—
207C42—21no—
208C42D110812yescomplemented
209C23—5542no—
210C23—5542no—
211C23—5542no—
212C23—5541no—
213C23—5542no—
214C23—11084no—
215C23—11084no—
216C23—11081no—
217C23—11081no—
218C23D4×D27711yescharacteristic
219Q8—5541no—
220Q8—5541no—
221D4—5541no—
222D4—5542no—
223D4—5542no—
224D4—5541no—
225D4—110816no—
226D4—11081no—
227D4—11081no—
228D4—11081no—
229D4—11081no—
230D4—11081no—
231D4—11081no—
232D4—11081no—
233D4—11081no—
234D4—22164no—
235C2×C4—24no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—5541no—
239C2×C4—11081no—
240C2×C4—11081no—
241C2×C4D4×D27711yescharacteristic
242C2×C4D4×D27711yescharacteristic
243C2×C4C2×D110811yescharacteristic
244C2×C4C2×D110811yescharacteristic
245C2×C4C2×D110811yescharacteristic
246C2×C4#1798456411yescharacteristic
247C8—22no—
248C8—11081no—
249C22—22no—
250C22—11084no—
251C22—11084no—
252C22—11081no—
253C22—11082no—
254C22—11082no—
255C22—11082no—
256C22—11084no—
257C22—22162no—
258C22—22162no—
259C22—22162no—
260C22#2257985011yescharacteristic
261C22#2257985011yescharacteristic
262C22#2257985511yescharacteristic
263C4—24no—
264C4—42no—
265C4—11081no—
266C4#2257985011yescharacteristic
267C4#2257985511yescharacteristic
268C4#2257985511yescharacteristic
269C4#2257987711yescharacteristic
270C2—21no—
271C2—21no—
272C2—22162no—
273C2—22162no—
274C2—22161no—
275C2#3179991211yescharacteristic
276C2#3180017112yes—
subgroupG/H
centerC22#22579850
commutator, cosocleC22×C4×C277C23
FrattiniC22×C4C22×D277
Fitting#339×C277C2
socleC22×C277#120
hypercenter#339D277
hypocenterC277#2002
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×#22579908C2semidirect
2. #31800571C2semidirect
3. C2×#22579877C2semidirect
4. C2×#22579808C2semidirect
5. #31800006C2semidirect
6. C2×#22579796C2semidirect
7. #339×C277C2semidirect
35. C2×Dic554D4semidirect
50. C2×D1108D4semidirect
51. C2×D1108D4semidirect
63. M16×C277D4semidirect
65. C4⋊C4×C277D4semidirect
69. C42×C277D4semidirect
138. C277#2002semidirect
146. #339D277semidirect
200. M16D1108semidirect
203. C4⋊C4D1108semidirect
208. C42D1108semidirect

Maximal subgroups

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

subgroupindex
C2×#225799082
#318005712
C2×#225798772
C2×#225798082
#318000062
C2×#225797962
#339×C2772
#2002277