Finite Group Databasebeta

← #31806362

Subgroups — #31806362

Order 17792.

552 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 101 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×#17984890C211yesmaximal, characteristic
2C2×#17984770C212yesmaximal, complemented
3#22580952C212yesmaximal, complemented
4C2×#17984761C211yesmaximal, characteristic, complemented
5#391×C139C211yesmaximal, characteristic, complemented
6#17984890—24no—
7#17984890—22no—
8#17984890C414yescomplemented
9C2×#14555786—22no—
10C2×#14555785—22no—
11C2×#14555785C2212yes—
12C2×Q8×D139—22no—
13C2×#14555769C2212yes—
14#17984770—24no—
15#17984765—22no—
16#17984762—22no—
17#17984761—22no—
18C22×Q8×C139C2211yescharacteristic
19C2×C4⋊C4×C139C2211yescharacteristic
20C2×C42×C139C2211yescharacteristic
21#95×C139—22no—
22#14555786—28no—
23#14555786—28no—
24#14555785—28no—
25#14555785—28no—
26#14555785—22no—
27#14555785—22no—
28#14555785C2×C414yes—
29#14555785D414yes—
30C2×Dic278—22no—
31C2×Dic278D412yes—
32Q8×D139—28no—
33Q8×D139—28no—
34C2×D556—22no—
35C2×D556D412yes—
36C2×C22⋊D139—22no—
37C2×C4×D139—24no—
38C2×C4×D139—22no—
39#14555769—22no—
40#14555769—22no—
41C2×C139⋊C8—22no—
42C2×Q8×C139—22no—
43C2×Q8×C139—22no—
44C2×Q8×C139C2×C412yes—
45C2×Q8×C139D412yes—
46C22×C4×C139—21no—
47C22×C4×C139—21no—
48C22×C4×C139D412yes—
49C22×C4×C139C2311yescharacteristic
50C4⋊C4×C139—22no—
51C42×C139—22no—
52C22×D139—22no—
53Dic278—28no—
54Dic278—22no—
55Dic278C22⋊C414yes—
56D556—28no—
57D556—22no—
58D556C22⋊C414yes—
59C22⋊D139—24no—
60C22⋊D139—24no—
61C2×Dic139—22no—
62C4×D139—216no—
63C4×D139—24no—
64C4×D139—24no—
65C139⋊C8—42no—
66C23×C139C2×D411yescharacteristic
67Q8×C139—24no—
68Q8×C139—24no—
69C2×C4×C139—22no—
70C2×C4×C139—22no—
71C2×C4×C139—22no—
72C2×C4×C139—41no—
73C2×C4×C139—41no—
74C2×C4×C139—42no—
75C2×C4×C139—41no—
76C2×C4×C139C22⋊C414yes—
77C2×C4×C139C22×C411yescharacteristic
78C2×C4×C139C2×D412yes—
79C2×C4×C139C2×D412yes—
80C2×C4×C139C2×D411yescharacteristic
81C22×C139—21no—
82C22×C139—21no—
83C22×C139C2×C22⋊C411yescharacteristic
84C22×C139#12011yescharacteristic
85C22×C139#12011yescharacteristic
86C2×D139—24no—
87C2×D139—42no—
88C2×D139—42no—
89C4×C139—24no—
90C4×C139—42no—
91C4×C139—81no—
92C4×C139C2×C22⋊C412yes—
93C4×C139#12012yes—
94Dic139—24no—
95C2×C139—21no—
96C2×C139—21no—
97C2×C139#37911yescharacteristic
98C2×C139#45411yescharacteristic
99C2×C139#45611yescharacteristic
100D139—44no—
101C139#179311yescharacteristic, complemented, Sylow
102#1793—1391nomaximal, Sylow
103C2×2−1+4—1391no—
104C2×#104—1392no—
105#417—1392no—
106C2×#101—1391no—
107#391D13911yescharacteristic, complemented
1082−1+4—2784no—
1092−1+4—2782no—
1102−1+4—1394no—
111C2×#41—2782no—
112C2×#41—2782no—
113C2×#41—1392no—
114C22×Q8—2782no—
115C22×Q8C2×D13911yescharacteristic
116C2×M16—1392no—
117C2×C4⋊C4C2×D13911yescharacteristic
118C2×C42C2×D13911yescharacteristic
119#104—2784no—
120#103—2782no—
121#102—2782no—
122#101—2782no—
123#95—22no—
124#41—2788no—
125#41—2788no—
126#41—2788no—
127#41—2788no—
128#41—2782no—
129#41—2782no—
130#41—1394no—
131#41—1394no—
132C2×Q8—22no—
133C2×Q8—22no—
134C2×Q8—2782no—
135C2×Q8—2788no—
136C2×Q8—2788no—
137C2×Q8—1392no—
138C2×Q8C4×D13912yes—
139C2×Q8D55612yes—
140C2×D4—2782no—
141C2×D4—2782no—
142C2×D4—1392no—
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—2784no—
146C22×C4—2782no—
147C22×C4C22⋊D13912yes—
148C22×C4C22×D13911yescharacteristic
149M16—2782no—
150M16—2782no—
151C2×C8—2782no—
152C4⋊C4—22no—
153C42—22no—
154C23—2782no—
155C23C2×C22⋊D13911yescharacteristic
156Q8—24no—
157Q8—24no—
158Q8—2788no—
159Q8—2782no—
160Q8—1394no—
161D4—2788no—
162D4—2784no—
163D4—2784no—
164D4—2782no—
165D4—1394no—
166C2×C4—22no—
167C2×C4—22no—
168C2×C4—22no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—42no—
172C2×C4—41no—
173C2×C4—27816no—
174C2×C4—2782no—
175C2×C4—2784no—
176C2×C4—2784no—
177C2×C4(C2×D139)⋊C414yes—
178C2×C4C2×C4×D13911yescharacteristic
179C2×C4D4×D13912yes—
180C2×C4D4×D13912yes—
181C2×C4C2×D55611yescharacteristic
182C8—5562no—
183C22—21no—
184C22—21no—
185C22—2784no—
186C22—5562no—
187C22—5562no—
188C22C2×(C2×D139)⋊C411yescharacteristic
189C22#1798481011yescharacteristic
190C22#1798481011yescharacteristic
191C4—24no—
192C4—42no—
193C4—81no—
194C4—2784no—
195C4C22⋊C4×D13912yes—
196C4#1798481212yes—
197C2—21no—
198C2—21no—
199C2—5564no—
200C2#2258080811yescharacteristic
201C2#2258112511yescharacteristic
202C2#2258113511yescharacteristic
subgroupG/H
centerC22#17984810
commutatorC2×C4×C139C22×C4
FrattiniC22×C4C22×D139
Fitting#391×C139C2
socleC22×C139#120
prime radicalC2×#17984890C2
cosocleC22×C4×C139C23
hypercenter#391D139
hypocenterC139#1793
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C22×C4 ◁ #391

Complements

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

NH ≅ G/Ntype
2. C2×#17984770C2semidirect
3. #22580952C2semidirect
4. C2×#17984761C2semidirect
5. #391×C139C2semidirect
8. #17984890C4semidirect
101. C139#1793semidirect
107. #391D139semidirect

Maximal subgroups

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

subgroupindex
C2×#179848902
C2×#179847702
#225809522
C2×#179847612
#391×C1392
#1793139