Finite Group Databasebeta

← #47983367

Subgroups — #47983367

Order 35456.

316 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 99 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×#22579838C211yesmaximal, characteristic
2C2×#22579813C211yesmaximal, characteristic, complemented
3C2×#22579812C211yesmaximal, characteristic, complemented
4C2×#22579792C211yesmaximal, characteristic
5#31799859C211yesmaximal, characteristic
6#31799764C211yesmaximal, characteristic, complemented
7#340×C277C211yesmaximal, characteristic, complemented
8C22×C4×D277C2211yescharacteristic
9C22×#14555660C2211yescharacteristic
10#22579838—22no—
11#22579838—22no—
12C2×C4⋊Dic277C2211yescharacteristic
13C2×C4⋊Dic277C2211yescharacteristic
14C2×#17984540—21no—
15C2×#17984540—21no—
16C2×C4×Dic277—21no—
17#22579813—22no—
18#22579812—22no—
19#22579792C414yescomplemented
20#22579787—21no—
21C22×C8×C277C2211yescharacteristic
22C2×C4⋊C4×C277C2211yescharacteristic
23C2×C4⋊C4×C277C2211yescharacteristic
24C23×D277D411yescharacteristic
25C22×Dic277—21no—
26C22×Dic277—21no—
27C22×Dic277D411yescharacteristic
28C2×C4×D277—21no—
29C2×C4×D277—21no—
30C2×C4×D277—21no—
31C2×C4×D277—21no—
32C2×C4×D277C2×C412yes—
33C2×C4×D277Q812yes—
34C2×#14555660—21no—
35C2×#14555660—21no—
36C2×#14555660C2×C412yes—
37C4⋊Dic277—21no—
38C4⋊Dic277—21no—
39C4⋊Dic277—21no—
40C4⋊Dic277D412yes—
41#17984540—24no—
42#17984540—42no—
43C4×Dic277—24no—
44C22×C4×C277—21no—
45C22×C4×C277—21no—
46C22×C4×C277C2311yescharacteristic
47C2×C8×C277—21no—
48C2×C8×C277—21no—
49C2×C8×C277C2×C412yes—
50C4⋊C4×C277—21no—
51C4⋊C4×C277—21no—
52C4⋊C4×C277—21no—
53C4⋊C4×C277D412yes—
54C22×D277—21no—
55C22×D277—21no—
56C22×D277—21no—
57C22×D277—21no—
58C22×D277—21no—
59C22×D277—21no—
60C22×D277C4⋊C412yes—
61C2×Dic277—21no—
62C2×Dic277—21no—
63C2×Dic277—22no—
64C2×Dic277—41no—
65C2×Dic277—41no—
66C2×Dic277—41no—
67C2×Dic277—41no—
68C2×Dic277—41no—
69C2×Dic277C4⋊C412yes—
70C4×D277—22no—
71C4×D277—22no—
72C4×D277—22no—
73C4×D277—22no—
74#14555660—22no—
75C23×C277C2×D411yescharacteristic
76C2×C4×C277—22no—
77C2×C4×C277—41no—
78C2×C4×C277—41no—
79C2×C4×C277—41no—
80C2×C4×C277—41no—
81C2×C4×C277—41no—
82C2×C4×C277C22×C411yescharacteristic
83C2×C4×C277C2×D411yescharacteristic
84C2×C4×C277C2×D411yescharacteristic
85C2×C4×C277C2×Q811yescharacteristic
86C2×C4×C277#4111yescharacteristic
87C2×C4×C277#4111yescharacteristic
88C8×C277—22no—
89C22×C277C2×C4⋊C411yescharacteristic
90C22×C277#12011yescharacteristic
91C22×C277#12311yescharacteristic
92C22×C277#13511yescharacteristic
93C22×C277#13511yescharacteristic
94C22×C277AGL(1,ℤ/8)11yescharacteristic
95C22×C277#13711yescharacteristic
96C2×D277—22no—
97C2×D277—22no—
98C2×D277—22no—
99C2×D277—41no—
100C2×D277—41no—
101C2×D277—41no—
102C2×D277—41no—
103C4×C277—42no—
104C4×C277—81no—
105C4×C277C4×D411yescharacteristic
106C4×C277C4×D411yescharacteristic
107C4×C277C22⋊Q811yescharacteristic
108C4×C277C22⋊Q811yescharacteristic
109Dic277—22no—
110Dic277—42no—
111Dic277—81no—
112C2×C277#38511yescharacteristic
113C2×C277#42711yescharacteristic
114C2×C277#42811yescharacteristic
115C2×C277#44911yescharacteristic
116C2×C277#45211yescharacteristic
117C2×C277#48211yescharacteristic
118C2×C277#48511yescharacteristic
119D277—42no—
120C277#185411yescharacteristic, complemented, Sylow
121#1854—2771nomaximal, Sylow
122C2×#117—2771no—
123C2×#107—2771no—
124C2×#106—2771no—
125C2×C22⋊C8—2771no—
126#380—2771no—
127#340—2771no—
128#340D27711yescharacteristic, complemented
129C23×C4—2771no—
130C22×C8—2771no—
131C22×C8C2×D27711yescharacteristic
132#117—5542no—
133#117—5542no—
134C2×C4⋊C4—2771no—
135C2×C4⋊C4—2771no—
136C2×C4⋊C4C2×D27711yescharacteristic
137C2×C4⋊C4C2×D27711yescharacteristic
138C2×C22⋊C4—5541no—
139C2×C22⋊C4—5541no—
140C2×C42—5541no—
141#107—5542no—
142#106—5542no—
143C22⋊C8—2774no—
144#95—5541no—
145C24—2771no—
146C22×C4—21no—
147C22×C4—21no—
148C22×C4—2771no—
149C22×C4—2772no—
150C22×C4—2772no—
151C22×C4—5541no—
152C22×C4—5541no—
153C22×C4—5541no—
154C22×C4—5541no—
155C22×C4—5541no—
156C22×C4—5541no—
157C22×C4C22×D27711yescharacteristic
158C2×C8—21no—
159C2×C8—21no—
160C2×C8—2772no—
161C2×C8—5541no—
162C2×C8—5541no—
163C2×C8C4×D27712yes—
164C4⋊C4—21no—
165C4⋊C4—21no—
166C4⋊C4—21no—
167C4⋊C4—2772no—
168C4⋊C4—5541no—
169C4⋊C4—5541no—
170C4⋊C4—5541no—
171C4⋊C4D110812yes—
172C22⋊C4—5544no—
173C22⋊C4—11082no—
174C42—5544no—
175C23—2772no—
176C23—5541no—
177C23—5541no—
178C23—5541no—
179C23—5541no—
180C23—5541no—
181C23—5541no—
182C23D4×D27711yescharacteristic
183C2×C4—22no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—2772no—
190C2×C4—5541no—
191C2×C4—5541no—
192C2×C4—5542no—
193C2×C4—5542no—
194C2×C4—5542no—
195C2×C4—5542no—
196C2×C4—5542no—
197C2×C4—11081no—
198C2×C4—11081no—
199C2×C4—11081no—
200C2×C4—11081no—
201C2×C4—11081no—
202C2×C4C2×C4×D27711yescharacteristic
203C2×C4D4×D27711yescharacteristic
204C2×C4C2×D110811yescharacteristic
205C2×C4Q8×D27711yescharacteristic
206C2×C4#1798456211yescharacteristic
207C2×C4#1798456311yescharacteristic
208C8—22no—
209C8—5542no—
210C22—5542no—
211C22—5542no—
212C22—5542no—
213C22—11081no—
214C22—11081no—
215C22—11081no—
216C22—11081no—
217C22C4⋊C4×D27711yescharacteristic
218C22#2257985011yescharacteristic
219C22#2257986211yescharacteristic
220C22#2257990111yescharacteristic
221C22#2257990111yescharacteristic
222C22#2257990411yescharacteristic
223C22#2257991211yescharacteristic
224C4—42no—
225C4—81no—
226C4—5542no—
227C4—11082no—
228C4—22161no—
229C4#2257984011yescharacteristic
230C4C4×D110811yescharacteristic
231C4#2257985811yescharacteristic
232C4#2257986011yescharacteristic
233C2—11082no—
234C2#3179987611yescharacteristic
235C2#3180003711yescharacteristic
236C2#3180004311yescharacteristic
237C2#3180014811yescharacteristic
238C2#3180016711yescharacteristic
239C2#3180032511yescharacteristic
240C2#3180034111yescharacteristic
subgroupG/H
centerC23D4×D277
commutatorC2×C4×C277C22×C4
FrattiniC22×C4C22×D277
Fitting#340×C277C2
socleC23×C277C2×D4
prime radicalC23×D277D4
cosocleC22×C4×C277C23
hypercenter#340D277
hypocenterC277#1854
LCSG ▷ C2×C4×C277 ▷ C2×C277 ▷ C277
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
2. C2×#22579813C2semidirect
3. C2×#22579812C2semidirect
6. #31799764C2semidirect
7. #340×C277C2semidirect
19. #22579792C4semidirect
120. C277#1854semidirect
128. #340D277semidirect

Maximal subgroups

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

subgroupindex
C2×#225798382
C2×#225798132
C2×#225798122
C2×#225797922
#317998592
#317997642
#340×C2772
#1854277