Finite Group Databasebeta

← #31805455

Subgroups — #31805455

Order 17792.

240 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 49 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#22581543C211yesmaximal, characteristic
2#22581286C211yesmaximal, characteristic, complemented
3#22581272C211yesmaximal, characteristic, complemented
4#22580890C211yesmaximal, characteristic, complemented
5#22580686C211yesmaximal, characteristic, complemented
6#22580676C211yesmaximal, characteristic, complemented
7#328×C139C211yesmaximal, characteristic, complemented
8#17984837—21no—
9#17984831—21no—
10#17984827—21no—
11#17984817—21no—
12#17984816C2211yescharacteristic
13#17984812—21no—
14(C22⋊D139)⋊C4—21no—
15C2×C4⋊Dic139—21no—
16C2×C4⋊Dic139C2211yescharacteristic
17C2×(C2×D139)⋊C4—21no—
18C2×(C2×D139)⋊C4C2211yescharacteristic
19#17984775—21no—
20#17984774—21no—
21#17984766—21no—
22#17984764—21no—
23C22⋊(C139⋊C8)C2211yescharacteristic
24C22⋊Q8×C139C2211yescharacteristic
25C22⋊C8×C139C2211yescharacteristic
26#95×C139C2211yescharacteristic
27C23×D139D411yescharacteristic
28C2×D556—21no—
29C2×D556—21no—
30C2×D556D411yescharacteristic
31C2×C22⋊D139—21no—
32C22×Dic139—21no—
33C22×Dic139D411yescharacteristic
34C2×C4×D139—21no—
35C2×C139⋊C8—21no—
36C4⋊Dic139—21no—
37C4⋊Dic139—21no—
38C4⋊Dic139—42no—
39C4⋊Dic139D411yescharacteristic
40Dic139⋊C4—21no—
41(C2×D139)⋊C4—21no—
42(C2×D139)⋊C4—21no—
43(C2×D139)⋊C4—21no—
44(C2×D139)⋊C4—21no—
45(C2×D139)⋊C4—21no—
46(C2×D139)⋊C4—21no—
47(C2×D139)⋊C4—42no—
48C4×Dic139—21no—
49C2×Q8×C139D411yescharacteristic
50C22×C4×C139—21no—
51C22×C4×C139C2311yescharacteristic
52C2×C8×C139—21no—
53C4⋊C4×C139—21no—
54C4⋊C4×C139D411yescharacteristic
55C22⋊C4×C139—21no—
56C22×D139—21no—
57C22×D139—21no—
58C22×D139—21no—
59C22×D139—21no—
60C22×D139—41no—
61C22×D139—41no—
62D556—41no—
63D556—81no—
64D556—81no—
65C22⋊D139—41no—
66C22⋊D139—41no—
67C2×Dic139—21no—
68C2×Dic139—21no—
69C2×Dic139—41no—
70C2×Dic139—41no—
71C2×Dic139—41no—
72C2×Dic139—41no—
73C4×D139—81no—
74C139⋊C8—41no—
75C23×C139C2×D411yescharacteristic
76Q8×C139—41no—
77C2×C4×C139—22no—
78C2×C4×C139—21no—
79C2×C4×C139—21no—
80C2×C4×C139—41no—
81C2×C4×C139—41no—
82C2×C4×C139—41no—
83C2×C4×C139C2×D411yescharacteristic
84C2×C4×C139C2×D411yescharacteristic
85C8×C139—41no—
86C22×C139—21no—
87C22×C139—21no—
88C22×C139#12011yescharacteristic
89C22×C139#13511yescharacteristic
90C22×C139#13711yescharacteristic
91C2×D139—42no—
92C2×D139—41no—
93C2×D139—41no—
94C2×D139—41no—
95C2×D139—41no—
96C2×D139—41no—
97C2×D139—41no—
98C2×D139—81no—
99C4×C139—21no—
100C4×C139—21no—
101C4×C139—42no—
102C4×C139—41no—
103C4×C139—41no—
104Dic139—41no—
105Dic139—41no—
106Dic139—81no—
107C2×C139—21no—
108C2×C139—21no—
109C2×C139#45211yescharacteristic
110C2×C139#45311yescharacteristic
111C2×C139#45811yescharacteristic
112D139—81no—
113D139—81no—
114C139#161811yescharacteristic, complemented, Sylow
115#1618—1391nomaximal, Sylow
116#538—1391no—
117#484—1391no—
118#481—1391no—
119#399—1391no—
120#328D13911yescharacteristic, complemented
121#327—1391no—
122#323—1391no—
123#126—2781no—
124#124—2781no—
125#123—2781no—
126C22⋊Q8C2×D13911yescharacteristic
127#121—2781no—
128#121—1391no—
129#120—2781no—
130C4×D4—2781no—
131C2×C4⋊C4—2781no—
132C2×C4⋊C4—1391no—
133C2×C22⋊C4—2781no—
134C2×C22⋊C4—1391no—
135#107—2781no—
136#106—2781no—
137#103—2781no—
138#102—2781no—
139C22⋊C8—1391no—
140C22⋊C8C2×D13911yescharacteristic
141#95C2×D13911yescharacteristic
142C24—1391no—
143C2×Q8D55611yescharacteristic
144C2×D4—2781no—
145C2×D4—2781no—
146C2×D4—2781no—
147C2×D4—1391no—
148C22×C4—21no—
149C22×C4—2781no—
150C22×C4—2781no—
151C22×C4—1391no—
152C22×C4C22×D13911yescharacteristic
153C2×C8—21no—
154C2×C8—2781no—
155C4⋊C4—21no—
156C4⋊C4—2781no—
157C4⋊C4—2781no—
158C4⋊C4—2781no—
159C4⋊C4—5562no—
160C4⋊C4—1391no—
161C4⋊C4D55611yescharacteristic
162C22⋊C4—21no—
163C22⋊C4—2781no—
164C22⋊C4—2781no—
165C22⋊C4—2781no—
166C22⋊C4—2781no—
167C22⋊C4—2781no—
168C22⋊C4—2781no—
169C22⋊C4—5562no—
170C42—2781no—
171C23—2781no—
172C23—2781no—
173C23—2781no—
174C23—2781no—
175C23—5561no—
176C23—5561no—
177C23D4×D13911yescharacteristic
178Q8—41no—
179D4—5561no—
180D4—5561no—
181D4—5561no—
182D4—11121no—
183D4—11121no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—2781no—
191C2×C4—2781no—
192C2×C4—5561no—
193C2×C4—5561no—
194C2×C4—5561no—
195C2×C4—5561no—
196C2×C4—11121no—
197C2×C4D4×D13911yescharacteristic
198C2×C4C2×D55611yescharacteristic
199C8—41no—
200C8—5561no—
201C22—21no—
202C22—21no—
203C22—5562no—
204C22—5561no—
205C22—5561no—
206C22—5561no—
207C22—5561no—
208C22—5561no—
209C22—5561no—
210C22—11121no—
211C22#1798481211yescharacteristic
212C22#1798486311yescharacteristic
213C22#1798487411yescharacteristic
214C4—21no—
215C4—21no—
216C4—42no—
217C4—41no—
218C4—41no—
219C4—5561no—
220C4—5561no—
221C4—11121no—
222C2—21no—
223C2—21no—
224C2—11121no—
225C2—11121no—
226C2#2258111811yescharacteristic
227C2#2258112211yescharacteristic
228C2#2258114411yescharacteristic
subgroupG/H
centerC22#17984812
commutator, cosocleC22×C4×C139C23
FrattiniC22×C4C22×D139
Fitting#328×C139C2
socleC22×C139#120
prime radical#22581543C2
hypercenter#328D139
hypocenterC139#1618
LCSG ▷ C22×C4×C139 ▷ C22×C139 ▷ C139
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. #22581286C2semidirect
3. #22581272C2semidirect
4. #22580890C2semidirect
5. #22580686C2semidirect
6. #22580676C2semidirect
7. #328×C139C2semidirect
114. C139#1618semidirect
120. #328D139semidirect

Maximal subgroups

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

subgroupindex
#225815432
#225812862
#225812722
#225808902
#225806862
#225806762
#328×C1392
#1618139