Finite Group Databasebeta

← #31807451

Subgroups — #31807451

Order 17792.

370 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 75 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×#17984872C212yesmaximal, complemented
2C2×#17984769C212yesmaximal, complemented
3#22580858C211yesmaximal, characteristic, complemented
4#22580722C211yesmaximal, characteristic, complemented
5#537×C139C211yesmaximal, characteristic
6C22×Dic278C2211yescharacteristic
7#17984872—24no—
8#17984872—24no—
9C2×#14555775—22no—
10C2×#14555773—22no—
11C2×#14555769C2212yes—
12C2×C4×Dic139C2211yescharacteristic
13#17984769—24no—
14C139⋊#95—22no—
15C2×#41×C139C2212yes—
16C22⋊Q8×C139—22no—
17#121×C139—22no—
18#121×C139—22no—
19C2×C4⋊C4×C139C2211yescharacteristic
20C2×Dic278—22no—
21C2×Dic278—22no—
22C2×Dic278—21no—
23C2×Dic278D412yescomplemented
24C22×Dic139—21no—
25C22×Dic139—21no—
26#14555775—28no—
27#14555773—28no—
28#14555769—22no—
29#14555769D414yescomplemented
30C2×C139⋊C8—22no—
31C4×Dic139—22no—
32#41×C139—22no—
33#41×C139—22no—
34#41×C139—22no—
35#41×C139—22no—
36C2×Q8×C139D412yes—
37C2×D4×C139—22no—
38C2×D4×C139—22no—
39C2×D4×C139D412yes—
40C22×C4×C139—22no—
41C22×C4×C139D412yes—
42C22×C4×C139C2311yescharacteristic
43C4⋊C4×C139—22no—
44C4⋊C4×C139—22no—
45C22⋊C4×C139—24no—
46Dic278—24no—
47Dic278—42no—
48C2×Dic139—22no—
49C2×Dic139—22no—
50C2×Dic139—41no—
51C2×Dic139—41no—
52C2×Dic139—41no—
53C2×Dic139—41no—
54C139⋊C8—24no—
55C23×C139—22no—
56C23×C139C2×D411yescharacteristic
57Q8×C139—22no—
58Q8×C139—22no—
59D4×C139—22no—
60D4×C139—22no—
61D4×C139—42no—
62D4×C139—42no—
63D4×C139—82no—
64C2×C4×C139—22no—
65C2×C4×C139—22no—
66C2×C4×C139—42no—
67C2×C4×C139—42no—
68C2×C4×C139—42no—
69C2×C4×C139C2×D411yescharacteristic
70C2×C4×C139C2×D412yes—
71C2×C4×C139C2×D412yes—
72C2×C4×C139#4111yescharacteristic
73C22×C139—21no—
74C22×C139—21no—
75C22×C139—42no—
76C22×C139—42no—
77C22×C139—42no—
78C22×C139#12011yescharacteristic
79C22×C139#12111yescharacteristic
80C22×C139#12711yescharacteristic
81C4×C139—42no—
82C4×C139—42no—
83C4×C139#12012yes—
84C4×C139#12112yes—
85Dic139—42no—
86Dic139—42no—
87C2×C139—21no—
88C2×C139—21no—
89C2×C139—82no—
90C2×C139#39211yescharacteristic
91C2×C139#45511yescharacteristic
92C2×C139#45611yescharacteristic
93C139#200711yescharacteristic, complemented, Sylow
94#2007—1391nomaximal, Sylow
95C2×#137—1392no—
96#537D13911yescharacteristic
97C2×#104—1392no—
98#391—1391no—
99#343—1391no—
100C2×#41C2×D13912yes—
101C22×Q8—1391no—
102#137—2784no—
103#137—2784no—
104C2×Q16—2782no—
105C2×SD16—2782no—
106C2×M16—1392no—
107C22⋊Q8—22no—
108#121—22no—
109#121—22no—
110C2×C4⋊C4C2×D13911yescharacteristic
111C2×C42—1391no—
112#104—2784no—
113#95—2782no—
114#41—22no—
115#41—22no—
116#41—22no—
117#41—22no—
118C2×Q8—2781no—
119C2×Q8—2782no—
120C2×Q8—2782no—
121C2×Q8—1392no—
122C2×Q8C22⋊D13912yes—
123C2×D4—22no—
124C2×D4—22no—
125C2×D4C22⋊D13912yes—
126C22×C4—22no—
127C22×C4—2781no—
128C22×C4—2781no—
129C22×C4C22⋊D13912yes—
130C22×C4C22×D13911yescharacteristic
131Q16—2788no—
132SD16—2788no—
133M16—2782no—
134M16—1394no—
135C2×C8—2782no—
136C4⋊C4—22no—
137C4⋊C4—22no—
138C22⋊C4—24no—
139C42—2782no—
140C23—22no—
141C23C2×C22⋊D13911yescharacteristic
142Q8—22no—
143Q8—22no—
144Q8—2784no—
145Q8—5562no—
146D4—22no—
147D4—22no—
148D4—42no—
149D4—42no—
150D4—82no—
151C2×C4—22no—
152C2×C4—22no—
153C2×C4—42no—
154C2×C4—42no—
155C2×C4—42no—
156C2×C4—2782no—
157C2×C4—2782no—
158C2×C4—5561no—
159C2×C4—5561no—
160C2×C4—5561no—
161C2×C4—5561no—
162C2×C4D4×D13911yescharacteristic
163C2×C4D4×D13912yes—
164C2×C4C2×C22⋊D13912yes—
165C2×C4#1455578411yescharacteristic
166C8—2784no—
167C22—21no—
168C22—21no—
169C22—42no—
170C22—42no—
171C22—42no—
172C22#1798481111yescharacteristic
173C22#1798481311yescharacteristic
174C22#1798483811yescharacteristic
175C4—42no—
176C4—42no—
177C4—5562no—
178C4—5562no—
179C4#1798481012yes—
180C4#1798481412yes—
181C2—21no—
182C2—21no—
183C2—82no—
184C2#2258086111yescharacteristic
185C2#2258113111yescharacteristic
186C2#2258113611yescharacteristic
subgroupG/H
centerC22#17984811
commutator, cosocleC22×C4×C139C23
FrattiniC22×C4C22×D139
Fitting, prime radical#537×C139C2
socleC22×C139#120
hypercenter#537D139
hypocenterC139#2007
LCSG ▷ C22×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C22×C4 ◁ #537

Complements

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

NH ≅ G/Ntype
1. C2×#17984872C2semidirect
2. C2×#17984769C2semidirect
3. #22580858C2semidirect
4. #22580722C2semidirect
23. C2×Dic278D4semidirect
29. #14555769D4semidirect
93. C139#2007semidirect

Maximal subgroups

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

subgroupindex
C2×#179848722
C2×#179847692
#225808582
#225807222
#537×C1392
#2007139