Finite Group Databasebeta

← #31807450

Subgroups — #31807450

Order 17792.

370 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 73 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×#17984873C212yesmaximal, complemented
2#22581534C211yesmaximal, characteristic
3C2×#17984770C212yesmaximal, complemented
4#22580722C211yesmaximal, characteristic, complemented
5#391×C139C211yesmaximal, characteristic, complemented
6C2×#14555785C2212yes—
7#17984873—24no—
8#17984873—24no—
9C2×#14555775—22no—
10C2×#14555772—22no—
11C2×#14555769C2212yes—
12#17984822—22no—
13#17984817—22no—
14#17984816—22no—
15#17984770—24no—
16C22×Q8×C139C2211yescharacteristic
17C2×C4⋊C4×C139C2211yescharacteristic
18C2×C42×C139C2211yescharacteristic
19#95×C139—22no—
20#14555785—22no—
21#14555785—22no—
22#14555785—22no—
23#14555785—22no—
24C2×Dic278D412yes—
25C2×D556—22no—
26C2×D556D412yes—
27C2×C22⋊D139—22no—
28C2×C4×D139—22no—
29#14555775—28no—
30#14555772—28no—
31#14555769—22no—
32#14555769D414yescomplemented
33C2×C139⋊C8—22no—
34C4⋊Dic139—22no—
35(C2×D139)⋊C4—24no—
36C2×Q8×C139—21no—
37C2×Q8×C139—22no—
38C2×Q8×C139—22no—
39C2×Q8×C139D412yescomplemented
40C22×C4×C139—21no—
41C22×C4×C139—21no—
42C22×C4×C139D412yes—
43C22×C4×C139C2311yescharacteristic
44C4⋊C4×C139—22no—
45C42×C139—22no—
46C22×D139—22no—
47Dic278—22no—
48Dic278—22no—
49D556—22no—
50D556—22no—
51D556—82no—
52C22⋊D139—42no—
53C22⋊D139—42no—
54C2×Dic139—22no—
55C4×D139—42no—
56C4×D139—42no—
57C139⋊C8—24no—
58C23×C139C2×D411yescharacteristic
59Q8×C139—24no—
60Q8×C139—42no—
61C2×C4×C139—22no—
62C2×C4×C139—22no—
63C2×C4×C139—22no—
64C2×C4×C139—41no—
65C2×C4×C139—41no—
66C2×C4×C139—41no—
67C2×C4×C139—41no—
68C2×C4×C139—42no—
69C2×C4×C139C2×D412yes—
70C2×C4×C139C2×D412yes—
71C2×C4×C139C2×D411yescharacteristic
72C2×C4×C139#4111yescharacteristic
73C22×C139—21no—
74C22×C139—21no—
75C22×C139#12011yescharacteristic
76C22×C139#12111yescharacteristic
77C22×C139#12711yescharacteristic
78C2×D139—42no—
79C2×D139—42no—
80C2×D139—42no—
81C4×C139—42no—
82C4×C139—42no—
83C4×C139—42no—
84C4×C139#12012yes—
85C4×C139#12112yes—
86Dic139—42no—
87C2×C139—21no—
88C2×C139—21no—
89C2×C139#39211yescharacteristic
90C2×C139#45511yescharacteristic
91C2×C139#45611yescharacteristic
92D139—82no—
93C139#200711yescharacteristic, complemented, Sylow
94#2007—1391nomaximal, Sylow
95C2×#137—1392no—
96#537—1391no—
97C2×#104—1392no—
98#391D13911yescharacteristic, complemented
99#343—1391no—
100C2×#41—1392no—
101C22×Q8C2×D13911yescharacteristic
102#137—2784no—
103#137—2784no—
104C2×Q16—2782no—
105C2×SD16—2782no—
106C2×M16—1392no—
107C22⋊Q8—2782no—
108#121—2782no—
109#121—2782no—
110C2×C4⋊C4C2×D13911yescharacteristic
111C2×C42C2×D13911yescharacteristic
112#104—2784no—
113#95—22no—
114#41—2782no—
115#41—2782no—
116#41—2782no—
117#41—2782no—
118C2×Q8—21no—
119C2×Q8—22no—
120C2×Q8—22no—
121C2×Q8—1392no—
122C2×Q8D55612yescomplemented
123C2×D4—2782no—
124C2×D4—2782no—
125C2×D4—1392no—
126C22×C4—21no—
127C22×C4—21no—
128C22×C4—2782no—
129C22×C4C22⋊D13912yes—
130C22×C4C22×D13911yescharacteristic
131Q16—2788no—
132SD16—2788no—
133M16—2782no—
134M16—1394no—
135C2×C8—2782no—
136C4⋊C4—22no—
137C4⋊C4—2782no—
138C22⋊C4—2784no—
139C42—22no—
140C23—2782no—
141C23C2×C22⋊D13911yescharacteristic
142Q8—24no—
143Q8—42no—
144Q8—2782no—
145Q8—2782no—
146D4—2782no—
147D4—2782no—
148D4—5562no—
149D4—5562no—
150D4—11122no—
151C2×C4—22no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—42no—
159C2×C4—2782no—
160C2×C4—5562no—
161C2×C4—5562no—
162C2×C4D4×D13912yes—
163C2×C4D4×D13912yes—
164C2×C4C2×D55611yescharacteristic
165C2×C4#1455578511yescharacteristic
166C8—2784no—
167C22—21no—
168C22—21no—
169C22—5562no—
170C22—5562no—
171C22—5562no—
172C22#1798481011yescharacteristic
173C22#1798481611yescharacteristic
174C22#1798483811yescharacteristic
175C4—42no—
176C4—42no—
177C4—42no—
178C4—5562no—
179C4#1798481212yes—
180C4#1798481512yes—
181C2—21no—
182C2—21no—
183C2—11122no—
184C2#2258086211yescharacteristic
185C2#2258113011yescharacteristic
186C2#2258113511yescharacteristic
subgroupG/H
centerC22#17984810
commutator, cosocleC22×C4×C139C23
FrattiniC22×C4C22×D139
Fitting#391×C139C2
socleC22×C139#120
prime radical#22581534C2
hypercenter#391D139
hypocenterC139#2007
LCSG ▷ C22×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C22×C4 ◁ #391

Complements

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

NH ≅ G/Ntype
1. C2×#17984873C2semidirect
3. C2×#17984770C2semidirect
4. #22580722C2semidirect
5. #391×C139C2semidirect
32. #14555769D4semidirect
39. C2×Q8×C139D4semidirect
93. C139#2007semidirect
98. #391D139semidirect
122. C2×Q8D556semidirect

Maximal subgroups

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

subgroupindex
C2×#179848732
#225815342
C2×#179847702
#225807222
#391×C1392
#2007139