Finite Group Databasebeta

← #47984317

Subgroups — #47984317

Order 35456.

258 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 83 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×#22579871C211yesmaximal, characteristic
2C2×#22579805C211yesmaximal, characteristic
3C2×#22579803C211yesmaximal, characteristic
4#31799907C211yesmaximal, characteristic
5#31799764C211yesmaximal, characteristic
6#31799756C211yesmaximal, characteristic
7#340×C277C211yesmaximal, characteristic
8C22×Dic554C2211yescharacteristic
9C22×#14555660C2211yescharacteristic
10#22579871—22no—
11#22579871—22no—
12C2×C4⋊Dic277—21no—
13C2×C4⋊Dic277C2211yescharacteristic
14C2×#17984542—21no—
15C2×C4×Dic277C2211yescharacteristic
16#22579805—22no—
17#22579803—22no—
18#22579787—21no—
19#22579787—21no—
20C22×C8×C277C2211yescharacteristic
21C2×C4⋊C4×C277C2211yescharacteristic
22C2×C4⋊C4×C277C2211yescharacteristic
23C2×Dic554—21no—
24C2×Dic554—21no—
25C2×Dic554—21no—
26C2×Dic554—21no—
27C2×Dic554—21no—
28C2×Dic554Q812yes—
29C22×Dic277—21no—
30C22×Dic277—21no—
31C22×Dic277D411yescharacteristic
32C22×Dic277D411yescharacteristic
33C2×#14555660—21no—
34C2×#14555660—21no—
35C2×#14555660—21no—
36C4⋊Dic277—24no—
37C4⋊Dic277—21no—
38C4⋊Dic277D412yes—
39#17984542—24no—
40C4×Dic277—21no—
41C4×Dic277—21no—
42C22×C4×C277—21no—
43C22×C4×C277—21no—
44C22×C4×C277C2311yescharacteristic
45C2×C8×C277—21no—
46C2×C8×C277—21no—
47C2×C8×C277—21no—
48C4⋊C4×C277—21no—
49C4⋊C4×C277—21no—
50C4⋊C4×C277—21no—
51C4⋊C4×C277D412yes—
52Dic554—22no—
53Dic554—22no—
54Dic554—41no—
55Dic554—41no—
56C2×Dic277—21no—
57C2×Dic277—21no—
58C2×Dic277—22no—
59C2×Dic277—22no—
60C2×Dic277—21no—
61C2×Dic277—21no—
62C2×Dic277—21no—
63C2×Dic277—21no—
64C2×Dic277—41no—
65C2×Dic277—41no—
66C2×Dic277—41no—
67C2×Dic277—41no—
68#14555660—41no—
69C23×C277C2×D411yescharacteristic
70C2×C4×C277—22no—
71C2×C4×C277—41no—
72C2×C4×C277—41no—
73C2×C4×C277—41no—
74C2×C4×C277—41no—
75C2×C4×C277—41no—
76C2×C4×C277C2×D411yescharacteristic
77C2×C4×C277C2×D411yescharacteristic
78C2×C4×C277C2×Q811yescharacteristic
79C2×C4×C277#4111yescharacteristic
80C2×C4×C277#4111yescharacteristic
81C2×C4×C277#4111yescharacteristic
82C8×C277—41no—
83C22×C277#12011yescharacteristic
84C22×C277C22⋊Q811yescharacteristic
85C22×C277#12411yescharacteristic
86C22×C277#13511yescharacteristic
87C22×C277#13511yescharacteristic
88C22×C277#13711yescharacteristic
89C22×C277#13711yescharacteristic
90C4×C277—42no—
91C4×C277—81no—
92C4×C277C22⋊Q811yescharacteristic
93C4×C277C22⋊Q811yescharacteristic
94C4×C277#12411yescharacteristic
95C4×C277#12411yescharacteristic
96Dic277—42no—
97Dic277—41no—
98Dic277—41no—
99Dic277—42no—
100C2×C277#39311yescharacteristic
101C2×C277#45211yescharacteristic
102C2×C277#45211yescharacteristic
103C2×C277#47911yescharacteristic
104C2×C277#47911yescharacteristic
105C2×C277#48811yescharacteristic
106C2×C277#49111yescharacteristic
107C277#202611yescharacteristic, complemented, Sylow
108#2026—2771nomaximal, Sylow
109C2×#125—2771no—
110C2×#103—2771no—
111C2×#103—2771no—
112#391—2771no—
113#340—2771no—
114#340D27711yescharacteristic
115#336—2771no—
116C22×Q8—2771no—
117C22×C8—2771no—
118C22×C8C2×D27711yescharacteristic
119#125—5542no—
120#125—5542no—
121C2×C4⋊C4—2771no—
122C2×C4⋊C4—5541no—
123C2×C4⋊C4—5541no—
124C2×C4⋊C4C2×D27711yescharacteristic
125C2×C4⋊C4C2×D27711yescharacteristic
126C2×C42—2771no—
127#103—5542no—
128#103—5542no—
129#95—5541no—
130#95—5541no—
131C2×Q8—2772no—
132C2×Q8—5541no—
133C2×Q8—5541no—
134C2×Q8—5541no—
135C2×Q8—5541no—
136C2×Q8—5541no—
137C22×C4—21no—
138C22×C4—21no—
139C22×C4—2771no—
140C22×C4—2771no—
141C22×C4—5541no—
142C22×C4—5541no—
143C22×C4C22×D27711yescharacteristic
144C2×C8—21no—
145C2×C8—21no—
146C2×C8—21no—
147C2×C8—5541no—
148C2×C8—5541no—
149C2×C8—5541no—
150C4⋊C4—21no—
151C4⋊C4—21no—
152C4⋊C4—21no—
153C4⋊C4—2772no—
154C4⋊C4—5544no—
155C4⋊C4—5544no—
156C4⋊C4—5541no—
157C4⋊C4D110812yes—
158C42—5541no—
159C42—5541no—
160C23D4×D27711yescharacteristic
161Q8—5542no—
162Q8—5542no—
163Q8—11081no—
164Q8—11081no—
165C2×C4—22no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—5541no—
172C2×C4—5541no—
173C2×C4—5542no—
174C2×C4—5542no—
175C2×C4—5541no—
176C2×C4—5541no—
177C2×C4—5541no—
178C2×C4—5541no—
179C2×C4—11081no—
180C2×C4—11081no—
181C2×C4—11081no—
182C2×C4—11081no—
183C2×C4D4×D27711yescharacteristic
184C2×C4C2×D110811yescharacteristic
185C2×C4Q8×D27711yescharacteristic
186C2×C4#1798456211yescharacteristic
187C2×C4#1798456311yescharacteristic
188C2×C4#1798456311yescharacteristic
189C8—41no—
190C8—11081no—
191C22#2257985011yescharacteristic
192C22#2257985811yescharacteristic
193C22#2257986611yescharacteristic
194C22#2257989911yescharacteristic
195C22#2257990111yescharacteristic
196C22#2257990911yescharacteristic
197C22#2257991211yescharacteristic
198C4—42no—
199C4—81no—
200C4—11081no—
201C4—11081no—
202C4—11082no—
203C4—11082no—
204C4#2257985811yescharacteristic
205C4#2257986011yescharacteristic
206C4#2257986611yescharacteristic
207C4#2257986811yescharacteristic
208C2#3179991511yescharacteristic
209C2#3180016511yescharacteristic
210C2#3180016711yescharacteristic
211C2#3180030811yescharacteristic
212C2#3180031211yescharacteristic
213C2#3180035511yescharacteristic
214C2#3180036911yescharacteristic
subgroupG/H
centerC23D4×D277
commutator, cosocleC22×C4×C277C23
FrattiniC22×C4C22×D277
Fitting#340×C277C2
socle, prime radicalC23×C277C2×D4
hypercenter#340D277
hypocenterC277#2026
LCSG ▷ C22×C4×C277 ▷ C2×C277 ▷ C277
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
107. C277#2026semidirect

Maximal subgroups

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

subgroupindex
C2×#225798712
C2×#225798052
C2×#225798032
#317999072
#317997642
#317997562
#340×C2772
#2026277