Finite Group Databasebeta

← #354×D281 #49096962

Subgroups — #354×D281 #49096962

Order 35968.

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

normal subgroups only

This group has 284 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#124×D281C211yesmaximal, characteristic
2#99×D281C212yesmaximal
3#31823258C211yesmaximal, characteristic, complemented
4#31823257C212yesmaximal, complemented
5#354×C281C211yesmaximal, characteristic, complemented
6C2×Q8×D281C411yescharacteristic, complemented
7C2×D4×D281C2211yescharacteristic
8#22582868C411yescharacteristic, complemented
9#22582867C411yescharacteristic, complemented
10#22582866C2211yescharacteristic
11#22582865—22no—
12C22⋊C4×D281—22no—
13C22⋊C4×D281—22no—
14C42×D281C411yescharacteristic, complemented
15#22582794C2212yes—
16#22582793—22no—
17#124×C281C2211yescharacteristic
18#99×C281C2212yes—
19C23×D281D412yes—
20C2×Dic562—21no—
21C2×Dic562C2×C411yescharacteristic, complemented
22Q8×D281—41no—
23Q8×D281—41no—
24C2×D1124C2×C411yescharacteristic
25C2×C22⋊D281D412yes—
26D4×D281—41no—
27D4×D281—41no—
28C2×C4×D281—21no—
29C2×C4×D281—21no—
30C2×C4×D281—42no—
31C2×C4×D281C2×C411yescharacteristic
32C22⋊Dic281—22no—
33C22⋊Dic281—22no—
34#17985115—22no—
35#17985115—22no—
36#17985115—42no—
37C4×Dic281—21no—
38C4×Dic281C2×C411yescharacteristic, complemented
39C2×Q8×C281C2×C411yescharacteristic, complemented
40C2×D4×C281C2311yescharacteristic
41C22⋊C4×C281—22no—
42C22⋊C4×C281—22no—
43C42×C281C2×C411yescharacteristic, complemented
44C22×D281—22no—
45C22×D281—22no—
46C22×D281—44no—
47C22×D281C22⋊C411yescharacteristic
48C22×D281C22⋊C412yes—
49Dic562—42no—
50Dic562—41no—
51D1124—41no—
52C22⋊D281—42no—
53C2×Dic281—21no—
54C2×Dic281—21no—
55C2×Dic281—42no—
56C2×Dic281C22⋊C411yescharacteristic
57C4×D281—21no—
58C4×D281—21no—
59C4×D281—42no—
60C4×D281—41no—
61C4×D281—41no—
62C4×D281—84no—
63C23×C281C2×D412yes—
64Q8×C281—41no—
65D4×C281—41no—
66C2×C4×C281—21no—
67C2×C4×C281—21no—
68C2×C4×C281—42no—
69C2×C4×C281C22×C411yescharacteristic
70C22×C281—22no—
71C22×C281—42no—
72C22×C281C2×C22⋊C411yescharacteristic
73C2×D281—22no—
74C2×D281—22no—
75C2×D281—44no—
76C2×D281—42no—
77C2×D281—82no—
78C2×D281#9911yescharacteristic
79C2×D281#9911yescharacteristic
80C4×C281—21no—
81C4×C281—41no—
82C4×C281—41no—
83C4×C281—82no—
84Dic281—21no—
85Dic281—41no—
86Dic281—41no—
87Dic281—82no—
88C2×C281—21no—
89C2×C281—42no—
90C2×C281C2×#9911yescharacteristic
91D281—21no—
92D281—42no—
93D281#35412yesdirect product factor
94C281C2×#35411yescharacteristic, complemented, Sylow
95C2×#354—2811nomaximal, Sylow
96C2×#124—2811no—
97C2×#99—2812no—
98#354—2811no—
99#354—2812no—
100#354D28111yescharacteristic, direct product factor
101C22×Q8—2811no—
102C22×D4—2811no—
103#124—2811no—
104#124—2811no—
105#124—2811no—
106#124—5622no—
107#124C2×D28111yescharacteristic
108C2×C22⋊C4—5622no—
109C2×C22⋊C4—5622no—
110C2×C42—2811no—
111#99—2812no—
112#99—5622no—
113#99C2×D28112yes—
114C24—2812no—
115C2×Q8—2811no—
116C2×Q8—5621no—
117C2×Q8—11241no—
118C2×Q8—11241no—
119C2×Q8C4×D28111yescharacteristic, complemented
120C2×D4—2812no—
121C2×D4—2811no—
122C2×D4—11241no—
123C2×D4—11241no—
124C2×D4C22×D28111yescharacteristic
125C22×C4—2811no—
126C22×C4—5621no—
127C22×C4—5621no—
128C22×C4—11242no—
129C22⋊C4—22no—
130C22⋊C4—22no—
131C22⋊C4—5622no—
132C22⋊C4—5622no—
133C22⋊C4—5622no—
134C22⋊C4—5622no—
135C22⋊C4—11242no—
136C42—2811no—
137C42—5621no—
138C42C4×D28111yescharacteristic, complemented
139C23—2811no—
140C23—2812no—
141C23—5622no—
142C23—5622no—
143C23—11244no—
144C23D4×D28112yes—
145Q8—41no—
146Q8—11241no—
147Q8—11242no—
148D4—41no—
149D4—11241no—
150D4—11242no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—42no—
154C2×C4—2811no—
155C2×C4—5621no—
156C2×C4—5621no—
157C2×C4—5621no—
158C2×C4—5621no—
159C2×C4—11241no—
160C2×C4—11241no—
161C2×C4—11242no—
162C2×C4—11242no—
163C2×C4—22484no—
164C2×C4C2×C4×D28111yescharacteristic
165C22—22no—
166C22—42no—
167C22—2811no—
168C22—2811no—
169C22—5622no—
170C22—5622no—
171C22—11242no—
172C22—11244no—
173C22—22482no—
174C22C22⋊C4×D28111yescharacteristic
175C4—21no—
176C4—41no—
177C4—41no—
178C4—82no—
179C4—5621no—
180C4—11241no—
181C4—11241no—
182C4—22482no—
183C2—21no—
184C2—42no—
185C2—2812no—
186C2—5621no—
187C2—11242no—
188C2#99×D28111yescharacteristic
subgroupG/H
centerC2#99×D281
commutatorC2×C4×C281C22×C4
FrattiniC2×D4C22×D281
Fitting#354×C281C2
socleC2×C281C2×#99
prime radicalC2×D4×D281C22
cosocleC2×D4×C281C23
hypercenter#354D281
hypocenterC281C2×#354
LCSG ▷ C2×C4×C281 ▷ C22×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #354

Complements

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

NH ≅ G/Ntype
3. #31823258C2semidirect
4. #31823257C2semidirect
5. #354×C281C2semidirect
6. C2×Q8×D281C4semidirect
8. #22582868C4semidirect
9. #22582867C4semidirect
14. C42×D281C4semidirect
21. C2×Dic562C2×C4semidirect
38. C4×Dic281C2×C4semidirect
39. C2×Q8×C281C2×C4semidirect
43. C42×C281C2×C4semidirect
93. D281#354direct (N × H)
94. C281C2×#354semidirect
100. #354D281direct (N × H)
119. C2×Q8C4×D281semidirect
138. C42C4×D281semidirect

Maximal subgroups

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

subgroupindex
#124×D2812
#99×D2812
#318232582
#318232572
#354×C2812
C2×#354281