Finite Group Databasebeta

← #47984819

Subgroups — #47984819

Order 35456.

234 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 55 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#31800574C211yesmaximal, characteristic
2#31799983C211yesmaximal, characteristic
3#31799974C211yesmaximal, characteristic
4#31799793C211yesmaximal, characteristic, complemented
5#31799792C211yesmaximal, characteristic, complemented
6#31799791C211yesmaximal, characteristic, complemented
7#352×C277C211yesmaximal, characteristic, complemented
8C2×#17984562C2211yescharacteristic
9C22×Dic554C411yescharacteristic, complemented
10M16×D277—21no—
11#22579879—21no—
12#22579866—21no—
13#22579864C411yescharacteristic, complemented
14#22579863C411yescharacteristic, complemented
15#22579861C2211yescharacteristic
16#22579858—21no—
17#22579857—21no—
18#22579836—21no—
19#22579836C411yescharacteristic, complemented
20#22579798—21no—
21#22579797C2211yescharacteristic
22#22579795C2211yescharacteristic
23#22579794—21no—
24#123×C277C2211yescharacteristic
25#100×C277C2211yescharacteristic
26#99×C277C2211yescharacteristic
27#17984562—41no—
28#17984562—41no—
29C2×Dic554—21no—
30C2×Dic554—21no—
31C2×Dic554—41no—
32C2×Dic554—41no—
33C2×Dic554D411yescharacteristic
34C2×C22⋊D277C2×C411yescharacteristic
35C2×C22⋊D277D411yescharacteristic
36C22×Dic277C2×C411yescharacteristic
37C22×Dic277C2×C411yescharacteristic
38C22×Dic277D411yescharacteristic
39C2×C4×D277D411yescharacteristic
40#17984547—21no—
41#17984546—41no—
42C8×D277—41no—
43C4⋊Dic277—21no—
44#17984542—21no—
45#17984542—21no—
46#17984542—21no—
47#17984542—41no—
48C22⋊Dic277—21no—
49C22⋊Dic277—21no—
50C22⋊Dic277C2×C411yescharacteristic
51#17984540—21no—
52#17984540—21no—
53C4×Dic277—21no—
54C4×Dic277—41no—
55C2×D4×C277C2311yescharacteristic
56C22×C4×C277C2×C411yescharacteristic
57M16×C277—21no—
58C4⋊C4×C277—21no—
59C22⋊C4×C277—21no—
60C22⋊C4×C277—21no—
61C22⋊C4×C277C2×C411yescharacteristic
62C22×D277C22⋊C411yescharacteristic
63Dic554—41no—
64Dic554—42no—
65Dic554—41no—
66Dic554—41no—
67C22⋊D277—41no—
68C22⋊D277—41no—
69C2×Dic277—21no—
70C2×Dic277—21no—
71C2×Dic277—21no—
72C2×Dic277—21no—
73C2×Dic277—21no—
74C2×Dic277—21no—
75C2×Dic277—41no—
76C2×Dic277—41no—
77C2×Dic277C22⋊C411yescharacteristic
78C2×Dic277C22⋊C411yescharacteristic
79C2×Dic277C22⋊C411yescharacteristic
80C4×D277—21no—
81C4×D277—21no—
82#14555660—41no—
83C23×C277C22×C411yescharacteristic
84C23×C277C2×D411yescharacteristic
85D4×C277—41no—
86C2×C4×C277—21no—
87C2×C4×C277—21no—
88C2×C4×C277—41no—
89C2×C4×C277—41no—
90C2×C4×C277C2×D411yescharacteristic
91C8×C277—41no—
92C22×C277—21no—
93C22×C277—21no—
94C22×C277—41no—
95C22×C277—41no—
96C22×C277C2×C22⋊C411yescharacteristic
97C2×D277—21no—
98C2×D277—41no—
99C4×C277—21no—
100C4×C277—41no—
101C4×C277—41no—
102C4×C277—81no—
103Dic277—21no—
104Dic277—21no—
105Dic277—41no—
106Dic277—41no—
107Dic277—81no—
108Dic277#9911yescharacteristic
109Dic277#9911yescharacteristic
110C2×C277—21no—
111C2×C277—41no—
112C2×C277—41no—
113C2×C277C2×#9911yescharacteristic
114D277—41no—
115C277#212311yescharacteristic, complemented, Sylow
116#2123—2771nomaximal, Sylow
117#536—2771no—
118#413—2771no—
119#410—2771no—
120#352—2771no—
121#352—2771no—
122#352—2771no—
123#352D27711yescharacteristic, complemented
124C2×#41—2771no—
125C22×Q8—2771no—
126C2×M16—5541no—
127C4⋊Q8—5541no—
128#124—5541no—
129#123—2771no—
130#123—2771no—
131#123—2771no—
132#123C2×D27711yescharacteristic
133C22⋊Q8—5541no—
134C22⋊Q8—5541no—
135#117—2771no—
136#117—5541no—
137#101—5541no—
138#100—2771no—
139#100C2×D27711yescharacteristic
140#99—2771no—
141#99—5541no—
142#99C2×D27711yescharacteristic
143#41—11081no—
144#41—11081no—
145C2×Q8—2771no—
146C2×Q8—5541no—
147C2×Q8—5541no—
148C2×Q8—11081no—
149C2×Q8—11081no—
150C2×D4—2771no—
151C2×D4—2771no—
152C2×D4C22×D27711yescharacteristic
153C22×C4—2771no—
154C22×C4—2771no—
155C22×C4—2771no—
156C22×C4—2771no—
157C22×C4C4×D27711yescharacteristic
158M16—21no—
159M16—5541no—
160M16—11081no—
161C2×C8—11081no—
162C4⋊C4—21no—
163C4⋊C4—5541no—
164C4⋊C4—5541no—
165C4⋊C4—5541no—
166C4⋊C4—5541no—
167C4⋊C4—11081no—
168C22⋊C4—21no—
169C22⋊C4—21no—
170C22⋊C4—2771no—
171C22⋊C4—5541no—
172C22⋊C4—5541no—
173C22⋊C4—5541no—
174C22⋊C4—5541no—
175C22⋊C4C4×D27711yescharacteristic
176C42—5541no—
177C42—11081no—
178C23—2771no—
179C23C2×C4×D27711yescharacteristic
180C23D4×D27711yescharacteristic
181Q8—11081no—
182Q8—11081no—
183Q8—11081no—
184Q8—11082no—
185D4—41no—
186D4—11081no—
187D4—11081no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—2771no—
193C2×C4—2771no—
194C2×C4—2771no—
195C2×C4—5541no—
196C2×C4—5541no—
197C2×C4—5541no—
198C2×C4—5541no—
199C2×C4—5541no—
200C2×C4—5541no—
201C2×C4—5541no—
202C2×C4—5541no—
203C2×C4—11081no—
204C2×C4—11081no—
205C2×C4D4×D27711yescharacteristic
206C8—41no—
207C8—11081no—
208C22—21no—
209C22—21no—
210C22—41no—
211C22—41no—
212C22—5541no—
213C22—11081no—
214C22C22⋊C4×D27711yescharacteristic
215C4—21no—
216C4—41no—
217C4—41no—
218C4—81no—
219C4—2771no—
220C4—2771no—
221C4—5541no—
222C4—5541no—
223C4—11081no—
224C4—11081no—
225C4—22161no—
226C2—21no—
227C2—41no—
228C2—41no—
229C2—11081no—
230C2#99×D27711yescharacteristic
subgroupG/H
centerC2#99×D277
commutatorC23×C277C22×C4
FrattiniC2×D4C22×D277
Fitting#352×C277C2
socleC2×C277C2×#99
prime radicalC2×#17984562C22
cosocleC2×D4×C277C23
hypercenter#352D277
hypocenterC277#2123
LCSG ▷ C23×C277 ▷ C22×C277 ▷ C2×C277 ▷ C277
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #352

Complements

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

NH ≅ G/Ntype
4. #31799793C2semidirect
5. #31799792C2semidirect
6. #31799791C2semidirect
7. #352×C277C2semidirect
9. C22×Dic554C4semidirect
13. #22579864C4semidirect
14. #22579863C4semidirect
19. #22579836C4semidirect
115. C277#2123semidirect
123. #352D277semidirect

Maximal subgroups

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

subgroupindex
#318005742
#317999832
#317999742
#317997932
#317997922
#317997912
#352×C2772
#2123277