Finite Group Databasebeta

← #47981795

Subgroups — #47981795

Order 35456.

200 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 57 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#31800531C211yesmaximal, characteristic
2#31800057C211yesmaximal, characteristic, complemented
3#31800057C211yesmaximal, characteristic, complemented
4#31799743C211yesmaximal, characteristic, complemented
5#31799743C211yesmaximal, characteristic, complemented
6#31799742C211yesmaximal, characteristic, complemented
7#329×C277C211yesmaximal, characteristic, complemented
8#22579873—21no—
9#22579872C2211yescharacteristic
10#22579862—21no—
11#22579856C411yescharacteristic
12#22579851C411yescharacteristic
13Q8×Dic277C411yescharacteristic
14D4×Dic277C411yescharacteristic
15#22579840—21no—
16#22579836—21no—
17C42×D277C2211yescharacteristic
18#22579809—21no—
19#22579809—21no—
20#22579792—21no—
21#22579792—21no—
22#22579791C2211yescharacteristic
23#22579791C2211yescharacteristic
24#124×C277C2211yescharacteristic
25#97×C277C2211yescharacteristic
26#97×C277C2211yescharacteristic
27C2×C22⋊D277—21no—
28C22×Dic277—21no—
29C2×C4×D277C2×C411yescharacteristic
30C2×C4×D277D411yescharacteristic
31C2×C4×D277D411yescharacteristic
32C2×#14555660—21no—
33C2×#14555660—21no—
34C4⋊Dic277—21no—
35C4⋊Dic277C2×C411yescharacteristic
36C4⋊Dic277C2×C411yescharacteristic
37#17984542—21no—
38#17984542—21no—
39#17984542—21no—
40C22⋊Dic277—21no—
41C22⋊Dic277—21no—
42#17984540—21no—
43C4×Dic277—21no—
44C4×Dic277C2×C411yescharacteristic
45C4×Dic277D411yescharacteristic
46C4×Dic277D411yescharacteristic
47C2×Q8×C277C2×C411yescharacteristic
48C2×D4×C277C2×C411yescharacteristic
49C2×C8×C277—21no—
50C2×C8×C277—21no—
51C22⋊C4×C277—21no—
52C22⋊C4×C277—21no—
53C42×C277C2311yescharacteristic
54C22×D277C22⋊C411yescharacteristic
55C22⋊D277—42no—
56C2×Dic277—21no—
57C2×Dic277—21no—
58C2×Dic277—42no—
59C2×Dic277C22⋊C411yescharacteristic
60C2×Dic277C22⋊C411yescharacteristic
61C2×Dic277C22⋊C411yescharacteristic
62C4×D277—41no—
63C4×D277—41no—
64C4×D277—41no—
65#14555660—41no—
66#14555660—41no—
67C23×C277—21no—
68Q8×C277—41no—
69D4×C277—41no—
70C2×C4×C277—21no—
71C2×C4×C277C22×C411yescharacteristic
72C2×C4×C277C2×D411yescharacteristic
73C2×C4×C277C2×D411yescharacteristic
74C8×C277—41no—
75C8×C277—41no—
76C22×C277—41no—
77C22×C277—41no—
78C22×C277—41no—
79C22×C277C2×C22⋊C411yescharacteristic
80C2×D277—21no—
81C2×D277—21no—
82C2×D277—21no—
83C4×C277—21no—
84C4×C277—21no—
85C4×C277—21no—
86C4×C277—41no—
87Dic277—21no—
88Dic277—21no—
89Dic277—21no—
90Dic277—41no—
91Dic277—41no—
92C2×C277—81no—
93C2×C277#41311yescharacteristic
94C2×C277#42111yescharacteristic
95C2×C277#42111yescharacteristic
96D277—41no—
97C277#153511yescharacteristic, complemented, Sylow
98#1535—2771nomaximal, Sylow
99#529—2771no—
100#432—2771no—
101#432—2771no—
102#330—2771no—
103#330—2771no—
104#329—2771no—
105#329D27711yescharacteristic, complemented
106#126—5541no—
107#125—2771no—
108#124C2×D27711yescharacteristic
109#123—5541no—
110C22⋊Q8—2771no—
111#121—2771no—
112C4×Q8—2771no—
113C4×D4—2771no—
114C4×D4—5541no—
115#117—5541no—
116C2×C42—2771no—
117C4⋊C8—5541no—
118C4⋊C8—5541no—
119C22⋊C8—5541no—
120C22⋊C8—5541no—
121#97—2771no—
122#97—2771no—
123#97C2×D27711yescharacteristic
124#97C2×D27711yescharacteristic
125C2×Q8C4×D27711yescharacteristic
126C2×D4—5541no—
127C2×D4C4×D27711yescharacteristic
128C22×C4—2771no—
129C22×C4—2771no—
130C22×C4—2771no—
131C22×C4—5541no—
132C2×C8—21no—
133C2×C8—21no—
134C2×C8—5541no—
135C2×C8—5541no—
136C4⋊C4—2771no—
137C4⋊C4—2771no—
138C4⋊C4—5541no—
139C4⋊C4—5541no—
140C4⋊C4—5541no—
141C4⋊C4—5541no—
142C22⋊C4—21no—
143C22⋊C4—21no—
144C22⋊C4—5541no—
145C22⋊C4—5541no—
146C22⋊C4—5541no—
147C42—2771no—
148C42—2771no—
149C42—2771no—
150C42—5541no—
151C42C22×D27711yescharacteristic
152C23—21no—
153C23—2771no—
154Q8—41no—
155D4—41no—
156D4—11082no—
157C2×C4—21no—
158C2×C4—2771no—
159C2×C4—2771no—
160C2×C4—2771no—
161C2×C4—5541no—
162C2×C4—5541no—
163C2×C4—11081no—
164C2×C4—11081no—
165C2×C4—11081no—
166C2×C4—11082no—
167C2×C4C2×C4×D27711yescharacteristic
168C2×C4D4×D27711yescharacteristic
169C2×C4D4×D27711yescharacteristic
170C8—41no—
171C8—41no—
172C8—11081no—
173C8—11081no—
174C22—41no—
175C22—41no—
176C22—41no—
177C22—5541no—
178C22—5541no—
179C22—5541no—
180C22C22⋊C4×D27711yescharacteristic
181C4—21no—
182C4—21no—
183C4—21no—
184C4—41no—
185C4—5541no—
186C4—5541no—
187C4—5541no—
188C4—11081no—
189C4—11081no—
190C2—81no—
191C2—11081no—
192C2#3179998311yescharacteristic
193C2#3180001711yescharacteristic
194C2#3180001711yescharacteristic
subgroupG/H
centerC22C22⋊C4×D277
commutatorC2×C4×C277C22×C4
FrattiniC42C22×D277
Fitting#329×C277C2
socleC22×C277C2×C22⋊C4
prime radical#22579851C4
cosocleC42×C277C23
hypercenter#329D277
hypocenterC277#1535
LCSG ▷ C2×C4×C277 ▷ C22×C277 ▷ C277
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #31800057C2semidirect
3. #31800057C2semidirect
4. #31799743C2semidirect
5. #31799743C2semidirect
6. #31799742C2semidirect
7. #329×C277C2semidirect
97. C277#1535semidirect
105. #329D277semidirect

Maximal subgroups

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

subgroupindex
#318005312
#318000572
#317997432
#317997422
#329×C2772
#1535277