Finite Group Databasebeta

← #47983698

Subgroups — #47983698

Order 35456.

362 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 79 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
1#31800571C211yesmaximal, characteristic
2#31800476C211yesmaximal, characteristic, complemented
3#31800020C211yesmaximal, characteristic, complemented
4#31800018C211yesmaximal, characteristic, complemented
5C2×#22579796C211yesmaximal, characteristic, complemented
6#31799758C211yesmaximal, characteristic, complemented
7H(3,ℤ/4)×C277C211yesmaximal, characteristic, complemented
8C2×#17984563C2211yescharacteristic
9C22×D1108C2211yescharacteristic
10C2×#17984547C2211yescharacteristic
11#22579877C412yescomplemented
12#22579868C412yescomplemented
13#22579855—22no—
14#22579850—22no—
15C4×D1108—22no—
16#22579842—22no—
17#22579839C2211yescharacteristic
18C22⋊C4×D277—22no—
19#22579808—22no—
20#22579806—22no—
21#22579796—22no—
22C2×M16×C277C2211yescharacteristic
23#117×C277C2211yescharacteristic
24#117×C277C2211yescharacteristic
25C23×D277D412yes—
26#17984563—21no—
27#17984563—21no—
28#17984563—21no—
29#17984563—21no—
30C2×Dic554C2×C411yescharacteristic, complemented
31C2×D1108—24no—
32C2×D1108—21no—
33C2×D1108—21no—
34C2×D1108—21no—
35C2×D1108—21no—
36C2×D1108C2×C412yes—
37C2×D1108C2×C411yescharacteristic, complemented
38C2×D1108D412yes—
39C2×C22⋊D277—21no—
40C2×C4×D277—24no—
41C2×C4×D277—21no—
42#17984547—21no—
43#17984547—21no—
44C2×#14555660—21no—
45C4⋊Dic277—21no—
46C22⋊Dic277—21no—
47#17984540—24no—
48#17984540—24no—
49C4×Dic277D412yescomplemented
50C22×C4×C277C2311yescharacteristic
51M16×C277—21no—
52M16×C277—21no—
53C2×C8×C277—21no—
54C4⋊C4×C277—21no—
55C4⋊C4×C277—21no—
56C22⋊C4×C277—21no—
57C22⋊C4×C277—21no—
58C42×C277C2×C412yescomplemented
59C42×C277D412yescomplemented
60C22×D277—22no—
61C22×D277—22no—
62C22×D277—21no—
63C22×D277—82no—
64C22×D277C22⋊C414yes—
65Dic554—21no—
66Dic554—21no—
67D1108—22no—
68D1108—22no—
69D1108—21no—
70D1108—21no—
71D1108—22no—
72D1108—22no—
73D1108—84no—
74C22⋊D277—41no—
75C22⋊D277—41no—
76C2×Dic277—21no—
77C2×Dic277—22no—
78C4×D277—41no—
79C4×D277—41no—
80C4×D277—84no—
81#14555660—41no—
82C23×C277C2×D411yescharacteristic
83C2×C4×C277—22no—
84C2×C4×C277—22no—
85C2×C4×C277C22×C411yescharacteristic
86C2×C4×C277C2×D411yescharacteristic
87C2×C4×C277C2×D411yescharacteristic
88C2×C4×C277C2×D411yescharacteristic
89C2×C4×C277#4111yescharacteristic
90C2×C4×C277#4111yescharacteristic
91C8×C277—41no—
92C22×C277—41no—
93C22×C277C2×C22⋊C411yescharacteristic
94C22×C277#12011yescharacteristic
95C22×C277#12311yescharacteristic
96C2×D277—24no—
97C2×D277—44no—
98C2×D277—44no—
99C2×D277—42no—
100C2×D277—41no—
101C2×D277—82no—
102C4×C277—42no—
103C4×C277—42no—
104C4×C277C4×D411yescharacteristic
105C4×C277C4×D411yescharacteristic
106C4×C277#12111yescharacteristic
107C4×C277#12111yescharacteristic
108Dic277—42no—
109Dic277—41no—
110C2×C277—21no—
111C2×C277—21no—
112C2×C277—21no—
113C2×C277#38611yescharacteristic
114D277—44no—
115D277—81no—
116C277#191111yescharacteristic, complemented, Sylow
117#1911—2771nomaximal, Sylow
118#535—2771no—
119#518—2771no—
120#421—2771no—
121#421—2771no—
122C2×#100—2771no—
123H(3,ℤ/4)—2771no—
124H(3,ℤ/4)D27711yescharacteristic, complemented
125C2×#41—2771no—
126C22×D4—2771no—
127C2×M16—2771no—
128C2×M16C2×D27711yescharacteristic
129#127—2772no—
130#124—2772no—
131#121—5542no—
132#120—5542no—
133C4×D4—5542no—
134C4×D4—5542no—
135#117—2771no—
136#117C2×D27711yescharacteristic
137#117C2×D27711yescharacteristic
138C2×C22⋊C4—5542no—
139#104—5542no—
140#104—5542no—
141#100—5542no—
142C24—2772no—
143#41—5541no—
144#41—5541no—
145#41—5541no—
146#41—5541no—
147C2×Q8—2771no—
148C2×D4—2772no—
149C2×D4—2771no—
150C2×D4—2772no—
151C2×D4—5544no—
152C2×D4—5541no—
153C2×D4—5541no—
154C2×D4—5541no—
155C2×D4—5541no—
156C2×D4—5541no—
157C22×C4—5544no—
158C22×C4—5541no—
159C22×C4C22×D27711yescharacteristic
160M16—21no—
161M16—21no—
162M16—5541no—
163M16—5541no—
164C2×C8—21no—
165C2×C8—5541no—
166C4⋊C4—21no—
167C4⋊C4—21no—
168C4⋊C4—5541no—
169C22⋊C4—21no—
170C22⋊C4—21no—
171C22⋊C4—5544no—
172C22⋊C4—5544no—
173C22⋊C4—5541no—
174C42—2772no—
175C42C4×D27712yescomplemented
176C42D110812yescomplemented
177C23—2774no—
178C23—5542no—
179C23—5542no—
180C23—5541no—
181C23—22162no—
182C23D4×D27711yescharacteristic
183Q8—5541no—
184Q8—5541no—
185D4—5542no—
186D4—5541no—
187D4—5542no—
188D4—5541no—
189D4—5542no—
190D4—5542no—
191D4—11081no—
192D4—11081no—
193D4—22164no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—5541no—
197C2×C4—5542no—
198C2×C4—11081no—
199C2×C4—11081no—
200C2×C4—22164no—
201C2×C4C2×C4×D27711yescharacteristic
202C2×C4D4×D27711yescharacteristic
203C2×C4D4×D27711yescharacteristic
204C2×C4C2×D110811yescharacteristic
205C2×C4#1798456311yescharacteristic
206C2×C4#1798456411yescharacteristic
207C8—41no—
208C8—11081no—
209C22—41no—
210C22—5544no—
211C22—11084no—
212C22—11084no—
213C22—11082no—
214C22—11081no—
215C22—22162no—
216C22C22⋊C4×D27711yescharacteristic
217C22#2257985011yescharacteristic
218C22#2257986511yescharacteristic
219C4—42no—
220C4—42no—
221C4—11082no—
222C4—11081no—
223C4#2257984211yescharacteristic
224C4C4×D110811yescharacteristic
225C4#2257985311yescharacteristic
226C4#2257985511yescharacteristic
227C2—21no—
228C2—21no—
229C2—21no—
230C2—11084no—
231C2—22161no—
232C2#3179988011yescharacteristic
subgroupG/H
centerC2#31799880
commutatorC2×C4×C277C22×C4
FrattiniC22×C4C22×D277
FittingH(3,ℤ/4)×C277C2
socleC2×C277#386
prime radical#31800571C2
cosocleC22×C4×C277C23
hypercenterH(3,ℤ/4)D277
hypocenterC277#1911
LCSG ▷ C2×C4×C277 ▷ C2×C277 ▷ C277
UCSC1 ◁ C2 ◁ C22×C4 ◁ H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
2. #31800476C2semidirect
3. #31800020C2semidirect
4. #31800018C2semidirect
5. C2×#22579796C2semidirect
6. #31799758C2semidirect
7. H(3,ℤ/4)×C277C2semidirect
11. #22579877C4semidirect
12. #22579868C4semidirect
30. C2×Dic554C2×C4semidirect
37. C2×D1108C2×C4semidirect
49. C4×Dic277D4semidirect
58. C42×C277C2×C4semidirect
59. C42×C277D4semidirect
116. C277#1911semidirect
124. H(3,ℤ/4)D277semidirect
175. C42C4×D277semidirect
176. C42D1108semidirect

Maximal subgroups

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

subgroupindex
#318005712
#318004762
#318000202
#318000182
C2×#225797962
#317997582
H(3,ℤ/4)×C2772
#1911277