Finite Group Databasebeta

← #31806851

Subgroups — #31806851

Order 17792.

358 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 83 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#22581465C211yesmaximal, characteristic
2C2×#17984799C211yesmaximal, characteristic, complemented
3C2×#17984770C211yesmaximal, characteristic, complemented
4C2×#17984768C211yesmaximal, characteristic, complemented
5#22580916C211yesmaximal, characteristic, complemented
6#22580712C211yesmaximal, characteristic, complemented
7#339×C139C211yesmaximal, characteristic, complemented
8C2×#14555785C2211yescharacteristic
9C22×C4×D139C2211yescharacteristic
10C2×#14555769C2211yescharacteristic
11#17984826—21no—
12#17984822C412yescomplemented
13#17984817C412yescomplemented
14#17984812—21no—
15C4×D556—22no—
16#17984799—22no—
17#17984799—22no—
18C2×Dic139⋊C4—21no—
19C2×(C2×D139)⋊C4—21no—
20C2×C4×Dic139C2211yescharacteristic
21#17984770—22no—
22#17984768—22no—
23(C2×D139)⋊C8—22no—
24C2×M16×C139C2211yescharacteristic
25#117×C139C2211yescharacteristic
26C2×C42×C139C2211yescharacteristic
27C23×D139D411yescharacteristic
28#14555785—21no—
29#14555785—21no—
30#14555785—21no—
31#14555785—21no—
32C2×Dic278C2×C411yescharacteristic
33C2×D556—22no—
34C2×D556C2×C411yescharacteristic
35C2×C22⋊D139—21no—
36C22×Dic139—21no—
37C22×Dic139D411yescharacteristic
38C2×C4×D139—21no—
39C2×C4×D139—21no—
40C2×C4×D139—21no—
41C2×C4×D139—21no—
42C2×C4×D139—21no—
43C2×C4×D139C2×C412yes—
44C2×C4×D139D412yes—
45#14555769—21no—
46#14555769—21no—
47C2×C139⋊C8—21no—
48C4⋊Dic139—22no—
49Dic139⋊C4—24no—
50(C2×D139)⋊C4—24no—
51(C2×D139)⋊C4—22no—
52(C2×D139)⋊C4—22no—
53C4×Dic139—21no—
54C4×Dic139D412yescomplemented
55C22×C4×C139—21no—
56C22×C4×C139C2311yescharacteristic
57M16×C139—21no—
58M16×C139—21no—
59C2×C8×C139—21no—
60C4⋊C4×C139C2×C412yes—
61C22⋊C4×C139—21no—
62C42×C139—21no—
63C42×C139—21no—
64C42×C139D412yescomplemented
65C22×D139—21no—
66C22×D139—21no—
67C22×D139—21no—
68C22×D139—42no—
69C22×D139C22⋊C412yes—
70Dic278—21no—
71Dic278—21no—
72D556—21no—
73D556—21no—
74D556—44no—
75C22⋊D139—41no—
76C22⋊D139—41no—
77C2×Dic139—21no—
78C2×Dic139—21no—
79C2×Dic139—21no—
80C2×Dic139—22no—
81C2×Dic139—42no—
82C2×Dic139C22⋊C412yes—
83C4×D139—22no—
84C4×D139—22no—
85C4×D139—22no—
86C4×D139—22no—
87C4×D139—41no—
88C4×D139—41no—
89C139⋊C8—41no—
90C23×C139C2×D411yescharacteristic
91C2×C4×C139—22no—
92C2×C4×C139—22no—
93C2×C4×C139—42no—
94C2×C4×C139C22×C411yescharacteristic
95C2×C4×C139C2×D411yescharacteristic
96C2×C4×C139C2×D411yescharacteristic
97C2×C4×C139C2×D411yescharacteristic
98C2×C4×C139#4111yescharacteristic
99C2×C4×C139#4111yescharacteristic
100C8×C139—41no—
101C22×C139—22no—
102C22×C139C2×C22⋊C411yescharacteristic
103C22×C139#12011yescharacteristic
104C22×C139#12311yescharacteristic
105C2×D139—22no—
106C2×D139—22no—
107C2×D139—22no—
108C2×D139—42no—
109C2×D139—42no—
110C2×D139—41no—
111C2×D139—42no—
112C4×C139—42no—
113C4×C139—42no—
114C4×C139C4×D411yescharacteristic
115C4×C139C4×D411yescharacteristic
116C4×C139#12111yescharacteristic
117C4×C139#12111yescharacteristic
118Dic139—22no—
119Dic139—42no—
120Dic139—41no—
121C2×C139—21no—
122C2×C139—21no—
123C2×C139#38611yescharacteristic
124C2×C139#42112yes—
125D139—42no—
126D139—81no—
127C139#189711yescharacteristic, complemented, Sylow
128#1897—1391nomaximal, Sylow
129#525—1391no—
130C2×#117—1391no—
131C2×#104—1391no—
132C2×#104—1391no—
133#407—1391no—
134#339—1391no—
135#339D13911yescharacteristic, complemented
136C2×#41—1391no—
137C23×C4—1391no—
138C2×M16—1391no—
139C2×M16C2×D13911yescharacteristic
140#123—2781no—
141C22⋊Q8—1392no—
142#121—1392no—
143#120—2781no—
144C4×D4—2782no—
145#117—2782no—
146#117—2782no—
147#117C2×D13911yescharacteristic
148C2×C4⋊C4—2781no—
149C2×C22⋊C4—2781no—
150C2×C42—1391no—
151C2×C42C2×D13911yescharacteristic
152#104—2782no—
153#104—2782no—
154C22⋊C8—2782no—
155C24—1391no—
156#41—2781no—
157#41—2781no—
158#41—2781no—
159#41—2781no—
160C2×Q8—1391no—
161C2×D4—2782no—
162C2×D4—2781no—
163C2×D4—1391no—
164C22×C4—21no—
165C22×C4—2781no—
166C22×C4—2781no—
167C22×C4—2781no—
168C22×C4—2781no—
169C22×C4—2781no—
170C22×C4—2781no—
171C22×C4—1391no—
172C22×C4—1392no—
173C22×C4—1392no—
174C22×C4C22×D13911yescharacteristic
175M16—21no—
176M16—21no—
177M16—2781no—
178M16—2781no—
179C2×C8—21no—
180C2×C8—2781no—
181C4⋊C4—2784no—
182C4⋊C4—2782no—
183C4⋊C4C4×D13912yes—
184C22⋊C4—21no—
185C22⋊C4—2784no—
186C22⋊C4—2782no—
187C22⋊C4—2782no—
188C42—21no—
189C42—21no—
190C42—2781no—
191C42—1392no—
192C42D55612yescomplemented
193C23—2781no—
194C23—2781no—
195C23—2781no—
196C23—5562no—
197C23—1392no—
198C23D4×D13911yescharacteristic
199Q8—2781no—
200Q8—2781no—
201D4—2781no—
202D4—2781no—
203D4—5564no—
204D4—5561no—
205D4—5561no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—42no—
209C2×C4—2781no—
210C2×C4—2781no—
211C2×C4—2782no—
212C2×C4—2782no—
213C2×C4—2782no—
214C2×C4—2782no—
215C2×C4—2781no—
216C2×C4—2782no—
217C2×C4—5562no—
218C2×C4—5561no—
219C2×C4—5561no—
220C2×C4—1392no—
221C2×C4C2×C4×D13911yescharacteristic
222C2×C4D4×D13911yescharacteristic
223C2×C4D4×D13911yescharacteristic
224C2×C4C2×D55611yescharacteristic
225C2×C4#1455578511yescharacteristic
226C2×C4#1455578611yescharacteristic
227C8—41no—
228C8—5561no—
229C22—22no—
230C22—2782no—
231C22—2782no—
232C22—2782no—
233C22—5562no—
234C22—5562no—
235C22—5561no—
236C22—5562no—
237C22C22⋊C4×D13911yescharacteristic
238C22#1798481211yescharacteristic
239C22#1798482711yescharacteristic
240C4—42no—
241C4—42no—
242C4—2782no—
243C4—5562no—
244C4—5561no—
245C4#1798480411yescharacteristic
246C4C4×D55611yescharacteristic
247C4#1798481511yescharacteristic
248C4#1798481711yescharacteristic
249C2—21no—
250C2—21no—
251C2—5562no—
252C2—11121no—
253C2#2258083111yescharacteristic
254C2#2258096812yes—
subgroupG/H
centerC2×C4D4×D139
commutatorC2×C4×C139C22×C4
FrattiniC22×C4C22×D139
Fitting#339×C139C2
socleC22×C139C2×C22⋊C4
prime radical#22581465C2
cosocleC22×C4×C139C23
hypercenter#339D139
hypocenterC139#1897
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
2. C2×#17984799C2semidirect
3. C2×#17984770C2semidirect
4. C2×#17984768C2semidirect
5. #22580916C2semidirect
6. #22580712C2semidirect
7. #339×C139C2semidirect
12. #17984822C4semidirect
13. #17984817C4semidirect
54. C4×Dic139D4semidirect
64. C42×C139D4semidirect
127. C139#1897semidirect
135. #339D139semidirect
192. C42D556semidirect

Maximal subgroups

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

subgroupindex
#225814652
C2×#179847992
C2×#179847702
C2×#179847682
#225809162
#225807122
#339×C1392
#1897139