Finite Group Databasebeta

← #47981605

Subgroups — #47981605

Order 35456.

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

normal subgroups only

This group has 266 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
1C4×#17984564C211yesmaximal, characteristic
2#31800024C211yesmaximal, characteristic, complemented
3C4×#17984546C211yesmaximal, characteristic, complemented
4Q8⋊#14555660C211yesmaximal, characteristic, complemented
5#31799731C211yesmaximal, characteristic, complemented
6#31799729C211yesmaximal, characteristic, complemented
7Q8⋊C8×C277C211yesmaximal, characteristic, complemented
8C2×#17984564C411yescharacteristic
9C2×#17984546—21no—
10C2×#17984546—21no—
11Q8×Dic277C411yescharacteristic
12C4×D1108—21no—
13C4×D1108C2211yescharacteristic
14#22579842—21no—
15#22579842C411yescharacteristic
16#22579838—21no—
17#22579838C411yescharacteristic
18C42×D277—21no—
19C42×D277C2211yescharacteristic
20C4⋊#14555660C2211yescharacteristic
21#22579809—21no—
22#22579790—21no—
23C4×#14555660C2211yescharacteristic
24C4×Q8×C277C2211yescharacteristic
25C4⋊C8×C277C2211yescharacteristic
26C4×C8×C277C2211yescharacteristic
27#17984564—22no—
28#17984564—22no—
29C2×D1108—21no—
30C2×D1108C2×C411yescharacteristic
31C2×C4×D277—21no—
32C2×C4×D277—21no—
33C2×C4×D277—21no—
34C2×C4×D277C2×C411yescharacteristic
35C2×C4×D277D411yescharacteristic
36C2×C4×D277D411yescharacteristic
37#17984546—24no—
38#17984546—42no—
39C2×#14555660—21no—
40C2×#14555660—21no—
41C4⋊Dic277—21no—
42C4⋊Dic277C2×C411yescharacteristic
43#17984540—21no—
44#17984540—21no—
45#17984540—21no—
46C4×Dic277—21no—
47C4×Dic277—21no—
48C4×Dic277C2×C411yescharacteristic
49C4×Dic277D411yescharacteristic
50C4×Dic277D411yescharacteristic
51C2×Q8×C277C2×C411yescharacteristic
52C2×C8×C277—21no—
53C2×C8×C277—21no—
54C4⋊C4×C277—21no—
55C4⋊C4×C277C2×C411yescharacteristic
56C42×C277—21no—
57C42×C277C2311yescharacteristic
58C22×D277—21no—
59C22×D277C22⋊C411yescharacteristic
60D1108—24no—
61D1108—21no—
62D1108M1612yescomplemented
63C2×Dic277—21no—
64C2×Dic277C22⋊C411yescharacteristic
65C2×Dic277C22⋊C411yescharacteristic
66C2×Dic277C22⋊C411yescharacteristic
67C4×D277—24no—
68C4×D277—21no—
69C4×D277—21no—
70C4×D277—21no—
71C4×D277—21no—
72C4×D277—22no—
73C4×D277—41no—
74C4×D277—41no—
75C4×D277—42no—
76#14555660—22no—
77#14555660—41no—
78Q8×C277—21no—
79Q8×C277M1612yescomplemented
80C2×C4×C277—21no—
81C2×C4×C277—21no—
82C2×C4×C277C22×C411yescharacteristic
83C2×C4×C277C2×D411yescharacteristic
84C2×C4×C277C2×D411yescharacteristic
85C8×C277—22no—
86C8×C277—41no—
87C22×C277C2×C22⋊C411yescharacteristic
88C2×D277—21no—
89C2×D277—22no—
90C2×D277—21no—
91C2×D277—21no—
92C2×D277—41no—
93C2×D277—41no—
94C4×C277—22no—
95C4×C277—21no—
96C4×C277—41no—
97C4×C277C2×M1611yescharacteristic
98C4×C277C2×M1611yescharacteristic
99C4×C277AGL(1,ℤ/8)11yescharacteristic
100C4×C277#13711yescharacteristic
101Dic277—21no—
102Dic277—21no—
103Dic277—41no—
104Dic277#10412yes—
105C2×C277#40711yescharacteristic
106C2×C277#41711yescharacteristic
107C2×C277C2×#10411yescharacteristic
108D277—41no—
109D277—42no—
110C277#148911yescharacteristic, complemented, Sylow
111#1489—2771nomaximal, Sylow
112C4×#41—2771no—
113#423—2771no—
114C4×M16—2771no—
115Q8⋊C8—2771no—
116Q8⋊C8D27711yescharacteristic, complemented
117D4⋊C8—2771no—
118D4⋊C8—2771no—
119C2×#41—2771no—
120C2×M16—5541no—
121C2×M16—5541no—
122C4×Q8—2771no—
123C4×Q8C2×D27711yescharacteristic
124C4×D4—2771no—
125C4×D4—2771no—
126C4×D4—5541no—
127C4×D4—5541no—
128#117—2771no—
129#117—5541no—
130C2×C42—2771no—
131C2×C42—5541no—
132C4⋊C8—2771no—
133C4⋊C8—5541no—
134C4⋊C8C2×D27711yescharacteristic
135#97—5541no—
136C4×C8—2771no—
137C4×C8C2×D27711yescharacteristic
138#41—5542no—
139#41—5542no—
140C2×Q8C4×D27711yescharacteristic
141C2×D4—2771no—
142C2×D4—5541no—
143C22×C4—2771no—
144C22×C4—2771no—
145C22×C4—2771no—
146C22×C4—5541no—
147C22×C4—5541no—
148C22×C4—5541no—
149M16—5544no—
150M16—11082no—
151C2×C8—21no—
152C2×C8—21no—
153C2×C8—5541no—
154C2×C8—5541no—
155C4⋊C4—21no—
156C4⋊C4—2771no—
157C4⋊C4—5541no—
158C4⋊C4C4×D27711yescharacteristic
159C22⋊C4—5541no—
160C22⋊C4—5541no—
161C22⋊C4—5541no—
162C42—21no—
163C42—2771no—
164C42—2771no—
165C42—2771no—
166C42—5541no—
167C42—5541no—
168C42C22×D27711yescharacteristic
169C23—2771no—
170C23—5541no—
171Q8—21no—
172Q8#1798454612yescomplemented
173D4—2772no—
174D4—5544no—
175D4—5541no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—2771no—
179C2×C4—2771no—
180C2×C4—2771no—
181C2×C4—5542no—
182C2×C4—5544no—
183C2×C4—5541no—
184C2×C4—5541no—
185C2×C4—5541no—
186C2×C4—5541no—
187C2×C4—5541no—
188C2×C4—11082no—
189C2×C4—11081no—
190C2×C4—11081no—
191C2×C4C2×C4×D27711yescharacteristic
192C2×C4D4×D27711yescharacteristic
193C2×C4D4×D27711yescharacteristic
194C8—22no—
195C8—41no—
196C8—5542no—
197C8—11081no—
198C22—5542no—
199C22—5541no—
200C22—5541no—
201C22—5541no—
202C22—11081no—
203C22—11081no—
204C22C22⋊C4×D27711yescharacteristic
205C4—22no—
206C4—21no—
207C4—41no—
208C4—2772no—
209C4—5541no—
210C4—5541no—
211C4—11081no—
212C4M16×D27711yescharacteristic
213C4C2×#1798454611yescharacteristic
214C4#2257990711yescharacteristic
215C4#2257991211yescharacteristic
216C2—11081no—
217C2—11082no—
218C2#3179996411yescharacteristic
219C2#3180000211yescharacteristic
220C2#104×D27711yescharacteristic
subgroupG/H
centerC2×C4D4×D277
commutatorC2×C4×C277C22×C4
FrattiniC42C22×D277
FittingQ8⋊C8×C277C2
socleC22×C277C2×C22⋊C4
prime radicalC2×#17984564C4
cosocleC42×C277C23
hypercenterQ8⋊C8D277
hypocenterC277#1489
LCSG ▷ C2×C4×C277 ▷ C2×C277 ▷ C277
UCSC1 ◁ C2×C4 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
2. #31800024C2semidirect
3. C4×#17984546C2semidirect
4. Q8⋊#14555660C2semidirect
5. #31799731C2semidirect
6. #31799729C2semidirect
7. Q8⋊C8×C277C2semidirect
62. D1108M16semidirect
79. Q8×C277M16semidirect
110. C277#1489semidirect
116. Q8⋊C8D277semidirect
172. Q8#17984546semidirect

Maximal subgroups

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

subgroupindex
C4×#179845642
#318000242
C4×#179845462
Q8⋊#145556602
#317997312
#317997292
Q8⋊C8×C2772
#1489277