Finite Group Databasebeta

← #47982145

Subgroups — #47982145

Order 35456.

260 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 49 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#31800590C211yesmaximal, characteristic
2#31800158C211yesmaximal, characteristic, complemented
3#31800141C211yesmaximal, characteristic, complemented
4#31799738C211yesmaximal, characteristic, complemented
5#31799735C211yesmaximal, characteristic, complemented
6#31799726C211yesmaximal, characteristic, complemented
7#393×C277C211yesmaximal, characteristic, complemented
8C2×#17984553—21no—
9C2×#17984550—21no—
10#22579873—21no—
11#22579866—21no—
12#22579862—21no—
13#22579859C2211yescharacteristic
14#22579854C2211yescharacteristic
15#22579853—21no—
16#22579849—21no—
17C4×C22⋊D277—21no—
18#22579804—21no—
19#22579804—21no—
20C22⋊#14555660C2211yescharacteristic
21C22⋊#14555660C2211yescharacteristic
22C22×Q8×C277C2211yescharacteristic
23C2×C22⋊C4×C277—21no—
24C2×C22⋊C4×C277C2211yescharacteristic
25#95×C277—21no—
26#95×C277C2211yescharacteristic
27C2×Dic554D411yescharacteristic
28C2×D1108D411yescharacteristic
29C2×C22⋊D277—21no—
30C2×C22⋊D277—21no—
31C2×C22⋊D277—21no—
32C2×C4×D277—21no—
33#17984553—42no—
34#17984550—42no—
35C2×#14555660—21no—
36C2×#14555660—21no—
37C4⋊Dic277D411yescharacteristic
38C4⋊Dic277D411yescharacteristic
39#17984542—21no—
40#17984542—21no—
41C22⋊Dic277—21no—
42C22⋊Dic277—21no—
43C22⋊Dic277—21no—
44#17984540—21no—
45#17984540—21no—
46C4×Dic277—21no—
47C24×C277D411yescharacteristic
48C2×Q8×C277—21no—
49C2×Q8×C277—21no—
50C2×Q8×C277—42no—
51C22×C4×C277—21no—
52C22×C4×C277—21no—
53C22×C4×C277D411yescharacteristic
54C22×C4×C277C2311yescharacteristic
55C22⋊C4×C277—21no—
56C22⋊C4×C277—21no—
57C22⋊C4×C277—42no—
58C22×D277—21no—
59Dic554—41no—
60D1108—41no—
61C22⋊D277—41no—
62C22⋊D277—41no—
63C22⋊D277—81no—
64C22⋊D277—81no—
65C2×Dic277—21no—
66C2×Dic277—21no—
67C2×Dic277—21no—
68C4×D277—81no—
69#14555660—41no—
70#14555660—41no—
71C23×C277—21no—
72C23×C277—21no—
73C23×C277—21no—
74C23×C277—41no—
75C23×C277—41no—
76C23×C277C2×D411yescharacteristic
77Q8×C277—22no—
78Q8×C277—22no—
79Q8×C277—41no—
80Q8×C277—41no—
81C2×C4×C277—22no—
82C2×C4×C277—21no—
83C2×C4×C277—41no—
84C2×C4×C277—41no—
85C2×C4×C277—41no—
86C2×C4×C277—41no—
87C2×C4×C277—41no—
88C2×C4×C277—41no—
89C2×C4×C277—41no—
90C2×C4×C277C2×D411yescharacteristic
91C2×C4×C277C2×D411yescharacteristic
92C22×C277—21no—
93C22×C277—21no—
94C22×C277—42no—
95C22×C277—41no—
96C22×C277—41no—
97C22×C277—41no—
98C22×C277—81no—
99C22×C277#12011yescharacteristic
100C22×C277#13511yescharacteristic
101C22×C277#13711yescharacteristic
102C2×D277—41no—
103C2×D277—41no—
104C2×D277—41no—
105C4×C277—21no—
106C4×C277—21no—
107C4×C277—41no—
108C4×C277—42no—
109C4×C277—81no—
110Dic277—41no—
111Dic277—41no—
112Dic277—41no—
113C2×C277—21no—
114C2×C277—21no—
115C2×C277—81no—
116C2×C277#45211yescharacteristic
117C2×C277#45511yescharacteristic
118C2×C277B(4,𝔽2)11yescharacteristic
119D277—81no—
120C277#160611yescharacteristic, complemented, Sylow
121#1606—2771nomaximal, Sylow
122#538—2771no—
123#451—2771no—
124#448—2771no—
125#393D27711yescharacteristic, complemented
126#328—2771no—
127#327—2771no—
128#323—2771no—
129C22×Q8C2×D27711yescharacteristic
130C2×Q16—5541no—
131C2×SD16—5541no—
132#126—5541no—
133#124—5541no—
134#123—5541no—
135C22⋊Q8—2771no—
136#121—2771no—
137#121—5541no—
138#120—5541no—
139C4×D4—5541no—
140C2×C22⋊C4—21no—
141C2×C22⋊C4C2×D27711yescharacteristic
142#103—5541no—
143#103—5541no—
144C22⋊C8—2771no—
145C22⋊C8—2771no—
146#95—21no—
147#95C2×D27711yescharacteristic
148C24C22⋊D27711yescharacteristic
149C2×Q8—21no—
150C2×Q8—21no—
151C2×Q8—42no—
152C2×Q8—2771no—
153C2×D4—2771no—
154C2×D4—5541no—
155C2×D4—5541no—
156C2×D4—5541no—
157C22×C4—21no—
158C22×C4—21no—
159C22×C4—5541no—
160C22×C4C22⋊D27711yescharacteristic
161C22×C4C22×D27711yescharacteristic
162Q16—11082no—
163SD16—11082no—
164C2×C8—5541no—
165C2×C8—5541no—
166C4⋊C4—2771no—
167C4⋊C4—2771no—
168C4⋊C4—5541no—
169C4⋊C4—5541no—
170C22⋊C4—21no—
171C22⋊C4—21no—
172C22⋊C4—42no—
173C22⋊C4—5541no—
174C22⋊C4—5541no—
175C22⋊C4—5541no—
176C22⋊C4—5541no—
177C22⋊C4—5541no—
178C42—5541no—
179C23—21no—
180C23—21no—
181C23—21no—
182C23—41no—
183C23—41no—
184C23—5541no—
185C23C2×C22⋊D27711yescharacteristic
186Q8—22no—
187Q8—22no—
188Q8—41no—
189Q8—41no—
190Q8—11081no—
191D4—11081no—
192D4—11081no—
193D4—11081no—
194D4—22161no—
195D4—22161no—
196C2×C4—22no—
197C2×C4—21no—
198C2×C4—41no—
199C2×C4—41no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—5541no—
206C2×C4—5541no—
207C2×C4—5541no—
208C2×C4—22161no—
209C2×C4D4×D27711yescharacteristic
210C2×C4D4×D27711yescharacteristic
211C8—11081no—
212C8—11081no—
213C22—21no—
214C22—21no—
215C22—42no—
216C22—41no—
217C22—41no—
218C22—41no—
219C22—81no—
220C22—11081no—
221C22—11081no—
222C22—11081no—
223C22#2257984811yescharacteristic
224C22#2257990011yescharacteristic
225C22#2257991111yescharacteristic
226C4—21no—
227C4—21no—
228C4—41no—
229C4—42no—
230C4—81no—
231C4—11081no—
232C4—11081no—
233C4—11081no—
234C2—21no—
235C2—21no—
236C2—81no—
237C2—22161no—
238C2#3180016211yescharacteristic
239C2#3180017911yescharacteristic
240C2#3180018811yescharacteristic
subgroupG/H
centerC22#22579848
commutator, cosocleC22×C4×C277C23
FrattiniC22×C4C22×D277
Fitting#393×C277C2
socleC22×C277#120
prime radical#31800590C2
hypercenter#393D277
hypocenterC277#1606
LCSG ▷ C22×C4×C277 ▷ C22×C277 ▷ C277
UCSC1 ◁ C22 ◁ C22×C4 ◁ #393

Complements

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

NH ≅ G/Ntype
2. #31800158C2semidirect
3. #31800141C2semidirect
4. #31799738C2semidirect
5. #31799735C2semidirect
6. #31799726C2semidirect
7. #393×C277C2semidirect
120. C277#1606semidirect
125. #393D277semidirect

Maximal subgroups

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

subgroupindex
#318005902
#318001582
#318001412
#317997382
#317997352
#317997262
#393×C2772
#1606277