Finite Group Databasebeta

← #47983688

Subgroups — #47983688

Order 35456.

312 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 79 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#31800768C211yesmaximal, characteristic
2#31800578C211yesmaximal, characteristic
3#31800012C211yesmaximal, characteristic, complemented
4#31800010C211yesmaximal, characteristic, complemented
5#31799975C211yesmaximal, characteristic
6#31799758C211yesmaximal, characteristic, complemented
7H(3,ℤ/4)×C277C211yesmaximal, characteristic, complemented
8C2×#17984563C2211yescharacteristic
9C22×Dic554C2211yescharacteristic
10#22579888—22no—
11#22579886—22no—
12C2×#17984547C2211yescharacteristic
13M16×D277—22no—
14#22579880C412yescomplemented
15#22579868C412yescomplemented
16#22579864—22no—
17#22579860—22no—
18#22579839C2211yescharacteristic
19#22579805—22no—
20#22579803—22no—
21#22579794—22no—
22C2×M16×C277C2211yescharacteristic
23#117×C277C2211yescharacteristic
24#117×C277C2211yescharacteristic
25#17984563—21no—
26#17984563—21no—
27#17984563—21no—
28#17984563—21no—
29C2×Dic554—21no—
30C2×Dic554—21no—
31C2×Dic554—21no—
32C2×Dic554—21no—
33C2×Dic554—21no—
34C2×Dic554C2×C412yes—
35C2×Dic554C2×C411yescharacteristic
36C2×D1108C2×C411yescharacteristic
37C2×C22⋊D277D412yes—
38C22×Dic277—21no—
39C2×C4×D277D412yes—
40#17984547—21no—
41#17984547—21no—
42#17984546—24no—
43C2×#14555660D412yes—
44C8×D277—24no—
45C4⋊Dic277—24no—
46C4⋊Dic277—21no—
47C22⋊Dic277—21no—
48#17984540—24no—
49C4×Dic277—21no—
50C22×C4×C277C2311yescharacteristic
51M16×C277—21no—
52M16×C277—21no—
53C2×C8×C277D412yes—
54C4⋊C4×C277—21no—
55C4⋊C4×C277—21no—
56C22⋊C4×C277—21no—
57C22⋊C4×C277—21no—
58C42×C277—21no—
59C42×C277C2×C412yes—
60C22×D277C22⋊C412yes—
61Dic554—21no—
62Dic554—21no—
63Dic554—22no—
64Dic554—22no—
65Dic554—41no—
66Dic554—41no—
67D1108—21no—
68D1108—21no—
69C22⋊D277—22no—
70C22⋊D277—22no—
71C2×Dic277—22no—
72C2×Dic277—41no—
73C2×Dic277—41no—
74C2×Dic277—41no—
75C2×Dic277C22⋊C412yes—
76C4×D277—22no—
77C4×D277—22no—
78#14555660—22no—
79C23×C277C2×D411yescharacteristic
80C2×C4×C277—22no—
81C2×C4×C277—41no—
82C2×C4×C277C22×C411yescharacteristic
83C2×C4×C277C2×D411yescharacteristic
84C2×C4×C277C2×D411yescharacteristic
85C2×C4×C277C2×D411yescharacteristic
86C2×C4×C277#4111yescharacteristic
87C2×C4×C277#4111yescharacteristic
88C8×C277—22no—
89C22×C277—41no—
90C22×C277C2×C22⋊C411yescharacteristic
91C22×C277#12111yescharacteristic
92C22×C277#12111yescharacteristic
93C2×D277—22no—
94C2×D277—42no—
95C4×C277—42no—
96C4×C277—81no—
97C4×C277C4×D411yescharacteristic
98C4×C277C4×D411yescharacteristic
99C4×C277#12011yescharacteristic
100C4×C277#12311yescharacteristic
101Dic277—22no—
102Dic277—42no—
103Dic277—81no—
104C2×C277—21no—
105C2×C277—21no—
106C2×C277—21no—
107C2×C277#38611yescharacteristic
108D277—42no—
109C277#190911yescharacteristic, complemented, Sylow
110#1909—2771nomaximal, Sylow
111#568—2771no—
112#536—2771no—
113#419—2771no—
114#419—2771no—
115#410—2771no—
116H(3,ℤ/4)—2771no—
117H(3,ℤ/4)D27711yescharacteristic, complemented
118C2×#41—2771no—
119C22×Q8—2771no—
120#131—5542no—
121#131—5542no—
122C2×M16—2771no—
123C2×M16—5542no—
124C2×M16C2×D27711yescharacteristic
125C4⋊Q8—2772no—
126#124—2772no—
127#123—5542no—
128C22⋊Q8—5542no—
129#117—2771no—
130#117C2×D27711yescharacteristic
131#117C2×D27711yescharacteristic
132#103—5542no—
133#103—5542no—
134#99—5542no—
135#41—5541no—
136#41—5541no—
137#41—5541no—
138#41—5541no—
139C2×Q8—2771no—
140C2×Q8—2772no—
141C2×Q8—5541no—
142C2×Q8—5541no—
143C2×Q8—5541no—
144C2×Q8—5541no—
145C2×Q8—5541no—
146C2×D4—2772no—
147C2×D4—2771no—
148C22×C4—2772no—
149C22×C4—5541no—
150C22×C4C22×D27711yescharacteristic
151M16—21no—
152M16—21no—
153M16—5544no—
154M16—5541no—
155M16—5541no—
156C2×C8—2772no—
157C2×C8—5544no—
158C2×C8D110812yes—
159C4⋊C4—21no—
160C4⋊C4—21no—
161C4⋊C4—5544no—
162C4⋊C4—5541no—
163C22⋊C4—21no—
164C22⋊C4—21no—
165C22⋊C4—5544no—
166C22⋊C4—5541no—
167C42—21no—
168C42—5541no—
169C42C4×D27712yes—
170C23—2772no—
171C23D4×D27711yescharacteristic
172Q8—5541no—
173Q8—5541no—
174Q8—5542no—
175Q8—5542no—
176Q8—11081no—
177Q8—11081no—
178D4—5542no—
179D4—5542no—
180D4—5541no—
181D4—5541no—
182C2×C4—22no—
183C2×C4—41no—
184C2×C4—2772no—
185C2×C4—5542no—
186C2×C4—5542no—
187C2×C4—5542no—
188C2×C4—11081no—
189C2×C4—11081no—
190C2×C4—11081no—
191C2×C4C2×C4×D27711yescharacteristic
192C2×C4D4×D27711yescharacteristic
193C2×C4D4×D27711yescharacteristic
194C2×C4C2×D110811yescharacteristic
195C2×C4#1798456311yescharacteristic
196C2×C4#1798456411yescharacteristic
197C8—22no—
198C8—5542no—
199C22—41no—
200C22—5542no—
201C22—11082no—
202C22C22⋊C4×D27711yescharacteristic
203C22#2257985311yescharacteristic
204C22#2257985511yescharacteristic
205C4—42no—
206C4—81no—
207C4—5542no—
208C4—11082no—
209C4—22161no—
210C4#2257984211yescharacteristic
211C4C4×D110811yescharacteristic
212C4#2257985011yescharacteristic
213C4#2257986511yescharacteristic
214C2—21no—
215C2—21no—
216C2—21no—
217C2—11082no—
218C2#3179988011yescharacteristic
subgroupG/H
centerC2#31799880
commutatorC2×C4×C277C22×C4
FrattiniC22×C4C22×D277
FittingH(3,ℤ/4)×C277C2
socleC2×C277#386
prime radicalC2×#17984563C22
cosocleC22×C4×C277C23
hypercenterH(3,ℤ/4)D277
hypocenterC277#1909
LCSG ▷ C2×C4×C277 ▷ C2×C277 ▷ C277
UCSC1 ◁ C2 ◁ C22×C4 ◁ H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
3. #31800012C2semidirect
4. #31800010C2semidirect
6. #31799758C2semidirect
7. H(3,ℤ/4)×C277C2semidirect
14. #22579880C4semidirect
15. #22579868C4semidirect
109. C277#1909semidirect
117. H(3,ℤ/4)D277semidirect

Maximal subgroups

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

subgroupindex
#318007682
#318005782
#318000122
#318000102
#317999752
#317997582
H(3,ℤ/4)×C2772
#1909277