Finite Group Databasebeta

← #47984182

Subgroups — #47984182

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×#22579906C211yesmaximal, characteristic, complemented
2#31800569C211yesmaximal, characteristic, complemented
3C2×#22579808C211yesmaximal, characteristic, complemented
4#31800007C211yesmaximal, characteristic, complemented
5C2×#22579797C211yesmaximal, characteristic, complemented
6#31799762C211yesmaximal, characteristic, complemented
7C2×#127×C277C211yesmaximal, characteristic, complemented
8C2×#17984563C2211yescharacteristic
9#22579906—22no—
10#22579906—22no—
11C2×#17984551—21no—
12C2×#17984548—21no—
13C2×#17984547C2211yescharacteristic
14C2×#17984547C2211yescharacteristic
15#22579876—21no—
16#22579867—21no—
17#22579851—22no—
18#22579849—22no—
19#22579839C2211yescharacteristic
20#22579808—22no—
21#22579801—22no—
22#22579797—22no—
23C22×D4×C277—22no—
24C22×D4×C277C2211yescharacteristic
25C22×D4×C277C2211yescharacteristic
26#127×C277—22no—
27#127×C277—22no—
28C2×C42×C277C2211yescharacteristic
29#17984563—21no—
30#17984563—21no—
31#17984563—21no—
32#17984563—21no—
33C2×Dic554D411yescharacteristic, complemented
34C2×D1108D411yescharacteristic, complemented
35C2×C22⋊D277—24no—
36C2×C22⋊D277—21no—
37C2×C4×D277—21no—
38#17984551—24no—
39#17984548—24no—
40#17984547—21no—
41#17984547—21no—
42#17984547—21no—
43#17984547D412yescomplemented
44C2×#14555660—21no—
45C2×#14555660—21no—
46C4⋊Dic277D412yescomplemented
47C22⋊Dic277—24no—
48C22⋊Dic277—21no—
49C4×Dic277—21no—
50C24×C277—21no—
51C24×C277D412yes—
52C2×D4×C277—28no—
53C2×D4×C277—21no—
54C2×D4×C277—21no—
55C2×D4×C277—21no—
56C2×D4×C277—21no—
57C2×D4×C277—21no—
58C2×D4×C277—21no—
59C2×D4×C277—21no—
60C2×D4×C277—21no—
61C2×D4×C277—21no—
62C2×D4×C277—21no—
63C2×D4×C277—21no—
64C2×D4×C277—48no—
65C2×D4×C277D412yescomplemented
66C22×C4×C277—21no—
67C22×C4×C277C2311yescharacteristic
68C42×C277—21no—
69C42×C277D412yescomplemented
70C22×D277—21no—
71Dic554—21no—
72Dic554—21no—
73D1108—21no—
74D1108—21no—
75C22⋊D277—41no—
76C22⋊D277—41no—
77C22⋊D277—84no—
78C2×Dic277—22no—
79C2×Dic277—21no—
80C4×D277—41no—
81C4×D277—41no—
82#14555660—22no—
83#14555660—41no—
84C23×C277—22no—
85C23×C277—22no—
86C23×C277—22no—
87C23×C277—22no—
88C23×C277—44no—
89C23×C277—44no—
90C23×C277—41no—
91C23×C277—41no—
92C23×C277C2×D411yescharacteristic
93D4×C277—22no—
94D4×C277—22no—
95D4×C277—416no—
96D4×C277—41no—
97D4×C277—41no—
98D4×C277—41no—
99D4×C277—41no—
100D4×C277—41no—
101D4×C277—41no—
102C2×C4×C277—24no—
103C2×C4×C277—22no—
104C2×C4×C277C2×D411yescharacteristic
105C2×C4×C277C2×D411yescharacteristic
106C2×C4×C277C2×D411yescharacteristic
107C2×C4×C277C2×D411yescharacteristic
108C2×C4×C277C2×D411yescharacteristic
109C2×C4×C277#4111yescharacteristic
110C22×C277—22no—
111C22×C277—44no—
112C22×C277—44no—
113C22×C277—42no—
114C22×C277—42no—
115C22×C277—44no—
116C22×C277—82no—
117C22×C277—82no—
118C22×C277—82no—
119C22×C277#12011yescharacteristic
120C22×C277#12011yescharacteristic
121C22×C277#12111yescharacteristic
122C2×D277—41no—
123C2×D277—42no—
124C4×C277—24no—
125C4×C277#12011yescharacteristic
126C4×C277#12111yescharacteristic
127C4×C277#12111yescharacteristic
128C4×C277#12711yescharacteristic
129Dic277—41no—
130Dic277—42no—
131C2×C277—21no—
132C2×C277—21no—
133C2×C277—82no—
134C2×C277—82no—
135C2×C277#39211yescharacteristic
136C2×C277#45312yes—
137D277—81no—
138C277#200211yescharacteristic, complemented, Sylow
139#2002—2771nomaximal, Sylow
140C2×AGL(1,ℤ/8)—2771no—
141#535—2771no—
142C2×#127D27711yescharacteristic, complemented
143C2×#104—2771no—
144#418—2771no—
145C2×#100—2771no—
146#339—2771no—
147C2×#41—2771no—
148C22×D4—22no—
149C22×D4C2×D27711yescharacteristic
150C22×D4C2×D27711yescharacteristic
151AGL(1,ℤ/8)—5542no—
152AGL(1,ℤ/8)—5542no—
153C2×SD16—5541no—
154C2×D8—5541no—
155C2×M16—2771no—
156C2×M16—2771no—
157#127—22no—
158#127—22no—
159#127—5541no—
160#124—5541no—
161#121—5542no—
162#120—5542no—
163#117—2771no—
164C2×C42C2×D27711yescharacteristic
165#104—5542no—
166#102—5542no—
167#100—5542no—
168C24—21no—
169C24C22⋊D27712yes—
170#41—5541no—
171#41—5541no—
172#41—5541no—
173#41—5541no—
174C2×Q8—2771no—
175C2×D4—28no—
176C2×D4—21no—
177C2×D4—21no—
178C2×D4—21no—
179C2×D4—21no—
180C2×D4—21no—
181C2×D4—21no—
182C2×D4—21no—
183C2×D4—21no—
184C2×D4—21no—
185C2×D4—21no—
186C2×D4—21no—
187C2×D4—48no—
188C2×D4—2771no—
189C2×D4—5541no—
190C2×D4—5544no—
191C2×D4C22⋊D27712yescomplemented
192C22×C4—21no—
193C22×C4—5541no—
194C22×C4C22×D27711yescharacteristic
195SD16—5544no—
196D8—5544no—
197M16—2772no—
198M16—5541no—
199M16—5541no—
200M16—5541no—
201C2×C8—5541no—
202C2×C8—5541no—
203C4⋊C4—2772no—
204C22⋊C4—5544no—
205C22⋊C4—5541no—
206C42—21no—
207C42—5541no—
208C42C22⋊D27712yescomplemented
209C23—22no—
210C23—22no—
211C23—22no—
212C23—22no—
213C23—44no—
214C23—44no—
215C23—41no—
216C23—41no—
217C23—5541no—
218C23C2×C22⋊D27711yescharacteristic
219Q8—5541no—
220Q8—5541no—
221D4—22no—
222D4—22no—
223D4—416no—
224D4—41no—
225D4—41no—
226D4—41no—
227D4—41no—
228D4—41no—
229D4—41no—
230D4—5541no—
231D4—5541no—
232D4—11081no—
233D4—11081no—
234D4—22164no—
235C2×C4—24no—
236C2×C4—22no—
237C2×C4—5542no—
238C2×C4—5541no—
239C2×C4—11081no—
240C2×C4—11081no—
241C2×C4D4×D27711yescharacteristic
242C2×C4D4×D27711yescharacteristic
243C2×C4D4×D27711yescharacteristic
244C2×C4C2×C22⋊D27711yescharacteristic
245C2×C4C2×C22⋊D27711yescharacteristic
246C2×C4#1798456211yescharacteristic
247C8—5542no—
248C8—11081no—
249C22—22no—
250C22—44no—
251C22—44no—
252C22—42no—
253C22—42no—
254C22—44no—
255C22—82no—
256C22—82no—
257C22—82no—
258C22—11081no—
259C22—11082no—
260C22#2257984811yescharacteristic
261C22#2257984911yescharacteristic
262C22#2257985211yescharacteristic
263C4—24no—
264C4—11081no—
265C4—11082no—
266C4#2257984811yescharacteristic
267C4#2257985111yescharacteristic
268C4#2257985211yescharacteristic
269C4#2257987611yescharacteristic
270C2—21no—
271C2—21no—
272C2—82no—
273C2—82no—
274C2—22161no—
275C2#3179991011yescharacteristic
276C2#3180016912yes—
subgroupG/H
centerC22#22579848
commutator, cosocleC22×C4×C277C23
FrattiniC22×C4C22×D277
FittingC2×#127×C277C2
socleC22×C277#120
hypercenterC2×#127D277
hypocenterC277#2002
LCSG ▷ C22×C4×C277 ▷ C2×C277 ▷ C277
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. C2×#22579906C2semidirect
2. #31800569C2semidirect
3. C2×#22579808C2semidirect
4. #31800007C2semidirect
5. C2×#22579797C2semidirect
6. #31799762C2semidirect
7. C2×#127×C277C2semidirect
33. C2×Dic554D4semidirect
34. C2×D1108D4semidirect
43. #17984547D4semidirect
46. C4⋊Dic277D4semidirect
65. C2×D4×C277D4semidirect
69. C42×C277D4semidirect
138. C277#2002semidirect
142. C2×#127D277semidirect
191. C2×D4C22⋊D277semidirect
208. C42C22⋊D277semidirect

Maximal subgroups

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

subgroupindex
C2×#225799062
#318005692
C2×#225798082
#318000072
C2×#225797972
#317997622
C2×#127×C2772
#2002277