Finite Group Databasebeta

← #31806933

Subgroups — #31806933

Order 17792.

362 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 79 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#22581517C211yesmaximal, characteristic
2#22581427C211yesmaximal, characteristic, complemented
3#22580970C211yesmaximal, characteristic, complemented
4C2×#17984758C211yesmaximal, characteristic, complemented
5#22580710C211yesmaximal, characteristic, complemented
6#22580709C211yesmaximal, characteristic, complemented
7#421×C139C211yesmaximal, characteristic, complemented
8C22×D556C2211yescharacteristic
9C2×#14555769C2211yescharacteristic
10#17984838C412yescomplemented
11#17984831C412yescomplemented
12#17984816—22no—
13#17984810—22no—
14C4×D556—22no—
15#17984804—22no—
16#17984801C2211yescharacteristic
17#17984801C2211yescharacteristic
18C22⋊C4×D139—22no—
19#17984769—22no—
20#17984758—22no—
21C2×#41×C139C2211yescharacteristic
22C2×M16×C139C2211yescharacteristic
23#117×C139C2211yescharacteristic
24#104×C139—22no—
25C23×D139D412yes—
26C2×D556—21no—
27C2×D556—21no—
28C2×D556—21no—
29C2×D556—21no—
30C2×D556C2×C412yes—
31C2×D556D412yes—
32C2×C22⋊D139—24no—
33C2×C4×D139—24no—
34#14555769—21no—
35#14555769—21no—
36C2×C139⋊C8—21no—
37C4⋊Dic139—21no—
38C4⋊Dic139—21no—
39C22⋊Dic139—21no—
40C22⋊Dic139—21no—
41(C2×D139)⋊C4—24no—
42(C2×D139)⋊C4—24no—
43C4×Dic139C2×C412yescomplemented
44C4×Dic139D412yescomplemented
45#41×C139—21no—
46#41×C139—21no—
47#41×C139—21no—
48#41×C139—21no—
49C2×Q8×C139C2×C411yescharacteristic, complemented
50C2×D4×C139—21no—
51C2×D4×C139C2×C411yescharacteristic, complemented
52C22×C4×C139—21no—
53C22×C4×C139C2311yescharacteristic
54M16×C139—21no—
55M16×C139—21no—
56C2×C8×C139—21no—
57C4⋊C4×C139—21no—
58C22⋊C4×C139—21no—
59C42×C139D412yescomplemented
60C22×D139—22no—
61C22×D139—22no—
62C22×D139—82no—
63C22×D139C22⋊C414yes—
64D556—22no—
65D556—22no—
66D556—22no—
67D556—22no—
68C22⋊D139—84no—
69C2×Dic139—22no—
70C2×Dic139—22no—
71C4×D139—84no—
72C139⋊C8—41no—
73C23×C139—21no—
74C23×C139C2×D411yescharacteristic
75Q8×C139—21no—
76Q8×C139—21no—
77D4×C139—21no—
78D4×C139—21no—
79D4×C139—41no—
80D4×C139—41no—
81C2×C4×C139—21no—
82C2×C4×C139—22no—
83C2×C4×C139—41no—
84C2×C4×C139—41no—
85C2×C4×C139C22×C411yescharacteristic
86C2×C4×C139C2×D411yescharacteristic
87C2×C4×C139C2×D411yescharacteristic
88C2×C4×C139C2×D411yescharacteristic
89C2×C4×C139#4111yescharacteristic
90C2×C4×C139#4111yescharacteristic
91C8×C139—41no—
92C22×C139—41no—
93C22×C139—42no—
94C22×C139—41no—
95C22×C139C2×C22⋊C411yescharacteristic
96C22×C139#12011yescharacteristic
97C22×C139#12311yescharacteristic
98C2×D139—24no—
99C2×D139—44no—
100C2×D139—44no—
101C2×D139—82no—
102C4×C139—42no—
103C4×C139—41no—
104C4×C139C4×D411yescharacteristic
105C4×C139C4×D411yescharacteristic
106C4×C139#12111yescharacteristic
107C4×C139#12111yescharacteristic
108Dic139—42no—
109Dic139—42no—
110C2×C139—21no—
111C2×C139—21no—
112C2×C139—21no—
113C2×C139—81no—
114C2×C139#38611yescharacteristic
115D139—44no—
116C139#191111yescharacteristic, complemented, Sylow
117#1911—1391nomaximal, Sylow
118#535—1391no—
119#518—1391no—
120#421—1391no—
121#421D13911yescharacteristic, complemented
122C2×#100—1391no—
123H(3,ℤ/4)—1391no—
124H(3,ℤ/4)—1391no—
125C2×#41C2×D13911yescharacteristic
126C22×D4—1391no—
127C2×M16—1391no—
128C2×M16C2×D13911yescharacteristic
129#127—1392no—
130#124—1392no—
131#121—2782no—
132#120—2782no—
133C4×D4—2782no—
134C4×D4—2782no—
135#117—1391no—
136#117—1391no—
137#117C2×D13911yescharacteristic
138C2×C22⋊C4—2782no—
139#104—22no—
140#104—2782no—
141#100—2782no—
142C24—1392no—
143#41—21no—
144#41—21no—
145#41—21no—
146#41—21no—
147C2×Q8C4×D13911yescharacteristic, complemented
148C2×D4—21no—
149C2×D4—2784no—
150C2×D4—2781no—
151C2×D4—2781no—
152C2×D4—2781no—
153C2×D4—2781no—
154C2×D4—1392no—
155C2×D4—1392no—
156C2×D4C4×D13911yescharacteristic, complemented
157C22×C4—21no—
158C22×C4—2784no—
159C22×C4C22×D13911yescharacteristic
160M16—21no—
161M16—21no—
162M16—2781no—
163M16—2781no—
164C2×C8—21no—
165C2×C8—2781no—
166C4⋊C4—21no—
167C4⋊C4—2781no—
168C4⋊C4—2781no—
169C22⋊C4—21no—
170C22⋊C4—2784no—
171C22⋊C4—2784no—
172C22⋊C4—2781no—
173C22⋊C4—2781no—
174C42—1392no—
175C42—1392no—
176C42C22⋊D13912yescomplemented
177C23—21no—
178C23—2782no—
179C23—2782no—
180C23—11122no—
181C23—1394no—
182C23D4×D13911yescharacteristic
183Q8—21no—
184Q8—21no—
185D4—21no—
186D4—21no—
187D4—41no—
188D4—41no—
189D4—2782no—
190D4—2782no—
191D4—2782no—
192D4—2782no—
193D4—11124no—
194C2×C4—21no—
195C2×C4—22no—
196C2×C4—41no—
197C2×C4—41no—
198C2×C4—2782no—
199C2×C4—2782no—
200C2×C4—11124no—
201C2×C4C2×C4×D13911yescharacteristic
202C2×C4D4×D13911yescharacteristic
203C2×C4D4×D13911yescharacteristic
204C2×C4C2×C22⋊D13911yescharacteristic
205C2×C4#1455578411yescharacteristic
206C2×C4#1455578511yescharacteristic
207C8—41no—
208C8—5561no—
209C22—41no—
210C22—42no—
211C22—41no—
212C22—2784no—
213C22—5564no—
214C22—5564no—
215C22—11122no—
216C22C22⋊C4×D13911yescharacteristic
217C22#1798481011yescharacteristic
218C22#1798482411yescharacteristic
219C4—42no—
220C4—41no—
221C4—5562no—
222C4—5562no—
223C4(C22⋊D139)⋊C411yescharacteristic
224C4C4×C22⋊D13911yescharacteristic
225C4#1798481311yescharacteristic
226C4#1798481511yescharacteristic
227C2—21no—
228C2—21no—
229C2—21no—
230C2—81no—
231C2—5564no—
232C2#2258082911yescharacteristic
subgroupG/H
centerC2#22580829
commutatorC2×C4×C139C22×C4
FrattiniC22×C4C22×D139
Fitting#421×C139C2
socleC2×C139#386
prime radical#22581517C2
cosocleC22×C4×C139C23
hypercenter#421D139
hypocenterC139#1911
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C2 ◁ C22×C4 ◁ #421

Complements

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

NH ≅ G/Ntype
2. #22581427C2semidirect
3. #22580970C2semidirect
4. C2×#17984758C2semidirect
5. #22580710C2semidirect
6. #22580709C2semidirect
7. #421×C139C2semidirect
10. #17984838C4semidirect
11. #17984831C4semidirect
43. C4×Dic139C2×C4semidirect
44. C4×Dic139D4semidirect
49. C2×Q8×C139C2×C4semidirect
51. C2×D4×C139C2×C4semidirect
59. C42×C139D4semidirect
116. C139#1911semidirect
121. #421D139semidirect
147. C2×Q8C4×D139semidirect
156. C2×D4C4×D139semidirect
176. C42C22⋊D139semidirect

Maximal subgroups

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

subgroupindex
#225815172
#225814272
#225809702
C2×#179847582
#225807102
#225807092
#421×C1392
#1911139