Finite Group Databasebeta

← #47984307

Subgroups — #47984307

Order 35456.

290 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 87 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×#22579879C211yesmaximal, characteristic
2C2×#22579805C211yesmaximal, characteristic
3C2×#22579803C211yesmaximal, characteristic
4#31799907C211yesmaximal, characteristic
5#31799764C211yesmaximal, characteristic
6#31799756C211yesmaximal, characteristic
7#340×C277C211yesmaximal, characteristic
8C22×Dic554—21no—
9C22×Dic554C2211yescharacteristic
10C22×#14555660C2211yescharacteristic
11#22579879—22no—
12#22579879—22no—
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—24no—
24C2×Dic554—21no—
25C2×Dic554—21no—
26C2×Dic554—21no—
27C2×Dic554—21no—
28C2×Dic554—21no—
29C2×Dic554—42no—
30C2×Dic554—42no—
31C2×Dic554Q812yescomplemented
32C22×Dic277—21no—
33C22×Dic277—21no—
34C22×Dic277D411yescharacteristic
35C22×Dic277D411yescharacteristic
36C2×#14555660—21no—
37C2×#14555660—21no—
38C2×#14555660—21no—
39C4⋊Dic277—21no—
40C4⋊Dic277D412yes—
41#17984542—24no—
42C4×Dic277—21no—
43C4×Dic277—21no—
44C22×C4×C277—21no—
45C22×C4×C277—21no—
46C22×C4×C277C2311yescharacteristic
47C2×C8×C277—21no—
48C2×C8×C277—21no—
49C2×C8×C277—21no—
50C4⋊C4×C277—21no—
51C4⋊C4×C277—21no—
52C4⋊C4×C277—21no—
53C4⋊C4×C277D412yes—
54Dic554—22no—
55Dic554—22no—
56Dic554—48no—
57Dic554—41no—
58Dic554—41no—
59C2×Dic277—21no—
60C2×Dic277—21no—
61C2×Dic277—21no—
62C2×Dic277—21no—
63C2×Dic277—22no—
64C2×Dic277—22no—
65C2×Dic277—41no—
66C2×Dic277—41no—
67C2×Dic277—41no—
68C2×Dic277—41no—
69C2×Dic277SD1612yes—
70C2×Dic277Q1612yes—
71#14555660—41no—
72C23×C277C2×D411yescharacteristic
73C2×C4×C277—22no—
74C2×C4×C277—41no—
75C2×C4×C277—41no—
76C2×C4×C277—41no—
77C2×C4×C277—41no—
78C2×C4×C277—41no—
79C2×C4×C277C2×D411yescharacteristic
80C2×C4×C277C2×D411yescharacteristic
81C2×C4×C277C2×Q811yescharacteristic
82C2×C4×C277#4111yescharacteristic
83C2×C4×C277#4111yescharacteristic
84C2×C4×C277#4111yescharacteristic
85C8×C277—41no—
86C22×C277#12011yescharacteristic
87C22×C277C22⋊Q811yescharacteristic
88C22×C277#12411yescharacteristic
89C22×C277C2×SD1611yescharacteristic
90C22×C277C2×Q1611yescharacteristic
91C22×C277AGL(1,ℤ/8)11yescharacteristic
92C22×C277#13711yescharacteristic
93C4×C277—42no—
94C4×C277—81no—
95C4×C277C22⋊Q811yescharacteristic
96C4×C277C22⋊Q811yescharacteristic
97C4×C277#12411yescharacteristic
98C4×C277#12411yescharacteristic
99Dic277—22no—
100Dic277—22no—
101Dic277—42no—
102Dic277—42no—
103C2×C277#39311yescharacteristic
104C2×C277#45011yescharacteristic
105C2×C277#45111yescharacteristic
106C2×C277#47511yescharacteristic
107C2×C277#47711yescharacteristic
108C2×C277#48711yescharacteristic
109C2×C277#48911yescharacteristic
110C277#202411yescharacteristic, complemented, Sylow
111#2024—2771nomaximal, Sylow
112C2×C4⋊Q8—2771no—
113C2×#103—2771no—
114C2×#103—2771no—
115#391—2771no—
116#340—2771no—
117#340D27711yescharacteristic
118#336—2771no—
119C22×Q8—2771no—
120C22×Q8—5541no—
121C22×C8—2771no—
122C22×C8C2×D27711yescharacteristic
123C4⋊Q8—5542no—
124C4⋊Q8—5542no—
125C2×C4⋊C4—2771no—
126C2×C4⋊C4—5541no—
127C2×C4⋊C4C2×D27711yescharacteristic
128C2×C4⋊C4C2×D27711yescharacteristic
129C2×C42—2771no—
130#103—5542no—
131#103—5542no—
132#95—5541no—
133#95—5541no—
134C2×Q8—2772no—
135C2×Q8—5544no—
136C2×Q8—5541no—
137C2×Q8—5541no—
138C2×Q8—5541no—
139C2×Q8—5541no—
140C2×Q8—5541no—
141C2×Q8—11082no—
142C2×Q8—11082no—
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—2771no—
146C22×C4—2771no—
147C22×C4—5541no—
148C22×C4—5541no—
149C22×C4C22×D27711yescharacteristic
150C2×C8—21no—
151C2×C8—21no—
152C2×C8—21no—
153C2×C8—5541no—
154C2×C8—5541no—
155C2×C8—5541no—
156C4⋊C4—21no—
157C4⋊C4—21no—
158C4⋊C4—21no—
159C4⋊C4—2772no—
160C4⋊C4—5544no—
161C4⋊C4—5541no—
162C4⋊C4D110812yes—
163C42—5541no—
164C42—5541no—
165C23D4×D27711yescharacteristic
166Q8—5542no—
167Q8—5542no—
168Q8—11088no—
169Q8—11081no—
170Q8—11081no—
171C2×C4—22no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—2772no—
178C2×C4—2772no—
179C2×C4—5541no—
180C2×C4—5541no—
181C2×C4—5541no—
182C2×C4—5541no—
183C2×C4—5542no—
184C2×C4—5542no—
185C2×C4—11081no—
186C2×C4—11081no—
187C2×C4—11081no—
188C2×C4—11081no—
189C2×C4D4×D27711yescharacteristic
190C2×C4C2×D110811yescharacteristic
191C2×C4Q8×D27711yescharacteristic
192C2×C4#1798456211yescharacteristic
193C2×C4#1798456311yescharacteristic
194C2×C4#1798456311yescharacteristic
195C8—41no—
196C8—11081no—
197C22#2257985011yescharacteristic
198C22#2257985811yescharacteristic
199C22#2257986611yescharacteristic
200C22SD16×D27711yescharacteristic
201C22Q16×D27711yescharacteristic
202C22#2257990411yescharacteristic
203C22#2257990911yescharacteristic
204C4—42no—
205C4—81no—
206C4—5542no—
207C4—5542no—
208C4—11082no—
209C4—11082no—
210C4#2257985811yescharacteristic
211C4#2257986011yescharacteristic
212C4#2257986611yescharacteristic
213C4#2257986811yescharacteristic
214C2#3179991511yescharacteristic
215C2#3180015411yescharacteristic
216C2#3180015911yescharacteristic
217C2#3180028611yescharacteristic
218C2#3180029611yescharacteristic
219C2#3180035111yescharacteristic
220C2#3180036011yescharacteristic
subgroupG/H
centerC23D4×D277
commutator, cosocleC22×C4×C277C23
FrattiniC22×C4C22×D277
Fitting#340×C277C2
socle, prime radicalC23×C277C2×D4
hypercenter#340D277
hypocenterC277#2024
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
31. C2×Dic554Q8semidirect
110. C277#2024semidirect

Maximal subgroups

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

subgroupindex
C2×#225798792
C2×#225798052
C2×#225798032
#317999072
#317997642
#317997562
#340×C2772
#2024277