Finite Group Databasebeta

← #28337496

Subgroups — #28337496

Order 13696.

362 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 73 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×#16812139C211yesmaximal, characteristic
2#20293198C211yesmaximal, characteristic
3C2×#16812109C211yesmaximal, characteristic, complemented
4#20292637C211yesmaximal, characteristic, complemented
5C2×#16812027C211yesmaximal, characteristic, complemented
6#20292387C211yesmaximal, characteristic, complemented
7C2×#104×C107C211yesmaximal, characteristic
8C22×Dic214C2211yescharacteristic
9C22×Dic214C2211yescharacteristic
10#16812139—22no—
11#16812139—22no—
12C2×#13133808—21no—
13C2×#13133806—21no—
14C2×#13133802C2211yescharacteristic
15#16812109—22no—
16#16812109—22no—
17#16812107—21no—
18#16812096—21no—
19#16812090—22no—
20#16812088—22no—
21#16812068C2211yescharacteristic
22C2×C4⋊Dic107—22no—
23#16812034—22no—
24#16812027—22no—
25C2×#41×C107C2211yescharacteristic
26C2×M16×C107C2211yescharacteristic
27C2×C42×C107C2211yescharacteristic
28#104×C107—22no—
29C2×Dic214—21no—
30C2×Dic214—21no—
31C2×Dic214—21no—
32C2×Dic214—21no—
33C2×Dic214—21no—
34C2×Dic214—21no—
35C2×Dic214—21no—
36C2×Dic214—21no—
37C2×Dic214—21no—
38C2×Dic214—21no—
39C2×Dic214—21no—
40C2×Dic214D412yes—
41C22×Dic107—21no—
42C22×Dic107D412yes—
43#13133808—24no—
44#13133806—24no—
45#13133802—21no—
46#13133802D412yes—
47C2×C107⋊C8—21no—
48C4⋊Dic107—28no—
49C4⋊Dic107D412yes—
50Dic107⋊C4—24no—
51C22⋊Dic107—24no—
52C22⋊Dic107—21no—
53C4×Dic107—21no—
54#41×C107—21no—
55#41×C107—21no—
56#41×C107—21no—
57#41×C107—21no—
58C2×Q8×C107D411yescharacteristic
59C2×D4×C107—21no—
60C2×D4×C107D411yescharacteristic
61C22×C4×C107—21no—
62C22×C4×C107—21no—
63C22×C4×C107C2311yescharacteristic
64M16×C107—21no—
65M16×C107—21no—
66C2×C8×C107—21no—
67C42×C107—21no—
68C42×C107D412yes—
69C23×C107—21no—
70C23×C107C2×D411yescharacteristic
71Q8×C107—21no—
72Q8×C107—21no—
73D4×C107—21no—
74D4×C107—21no—
75D4×C107—41no—
76D4×C107—41no—
77C2×C4×C107—24no—
78C2×C4×C107—22no—
79C2×C4×C107—21no—
80C2×C4×C107—41no—
81C2×C4×C107—41no—
82C2×C4×C107C2×D411yescharacteristic
83C2×C4×C107C2×D411yescharacteristic
84C2×C4×C107C2×D411yescharacteristic
85C2×C4×C107C2×D411yescharacteristic
86C2×C4×C107C2×D411yescharacteristic
87C2×C4×C107#4111yescharacteristic
88C2×Dic107—22no—
89C2×Dic107—22no—
90C2×Dic107—22no—
91C2×Dic107—22no—
92C2×Dic107—22no—
93C2×Dic107—41no—
94C2×Dic107—41no—
95Dic214—22no—
96Dic214—22no—
97Dic214—41no—
98Dic214—41no—
99Dic214—41no—
100Dic214—41no—
101Dic214—41no—
102Dic214—41no—
103C8×C107—41no—
104C107⋊C8—22no—
105C22×C107—22no—
106C22×C107—41no—
107C22×C107—42no—
108C22×C107#12011yescharacteristic
109C22×C107#12011yescharacteristic
110C22×C107#12111yescharacteristic
111C4×C107—24no—
112C4×C107—41no—
113C4×C107#12011yescharacteristic
114C4×C107#12111yescharacteristic
115C4×C107#12111yescharacteristic
116C4×C107#12711yescharacteristic
117Dic107—42no—
118Dic107—42no—
119Dic107—42no—
120C2×C107—21no—
121C2×C107—21no—
122C2×C107—81no—
123C2×C107#39211yescharacteristic
124C2×C107#45612yes—
125#2005—1071nomaximal, Sylow
126C107#200511yescharacteristic, complemented, Sylow
127C2×#137—1071no—
128#536—1071no—
129C2×C4⋊Q8—1071no—
130C2×#104D10711yescharacteristic
131#419—1071no—
132C2×#101—1071no—
133#339—1071no—
134C2×#41C2×D10711yescharacteristic
135C22×Q8—1071no—
136C22×Q8—1071no—
137#137—2142no—
138#137—2142no—
139C2×Q16—2141no—
140C2×SD16—2141no—
141C2×M16—1071no—
142C2×M16C2×D10711yescharacteristic
143C4⋊Q8—2142no—
144C4⋊Q8—2141no—
145C4⋊Q8—2142no—
146#124—2141no—
147#123—2142no—
148C22⋊Q8—2142no—
149#117—1071no—
150C2×C4⋊C4—2142no—
151C2×C42C2×D10711yescharacteristic
152#104—22no—
153#103—2142no—
154#101—2142no—
155#41—21no—
156#41—21no—
157#41—21no—
158#41—21no—
159C2×Q8—1072no—
160C2×Q8—2141no—
161C2×Q8—2141no—
162C2×Q8—2141no—
163C2×Q8—2141no—
164C2×Q8—2141no—
165C2×Q8—2141no—
166C2×Q8—2141no—
167C2×Q8—2141no—
168C2×Q8—2141no—
169C2×Q8—2141no—
170C2×Q8—2141no—
171C2×Q8D42811yescharacteristic
172C2×D4—21no—
173C2×D4D42811yescharacteristic
174C22×C4—21no—
175C22×C4—21no—
176C22×C4—1072no—
177C22×C4—2141no—
178C22×C4C22×D10711yescharacteristic
179Q16—2144no—
180SD16—2144no—
181M16—21no—
182M16—21no—
183M16—1072no—
184M16—2141no—
185C2×C8—21no—
186C2×C8—2141no—
187C4⋊C4—1072no—
188C4⋊C4—2148no—
189C4⋊C4—2144no—
190C22⋊C4—2144no—
191C22⋊C4—2141no—
192C42—21no—
193C42—2141no—
194C42C22⋊D10712yes—
195C23—21no—
196C23D4×D10711yescharacteristic
197Q8—21no—
198Q8—21no—
199Q8—4281no—
200Q8—4281no—
201Q8—4281no—
202Q8—4281no—
203Q8—4281no—
204Q8—4281no—
205Q8—2142no—
206Q8—2142no—
207D4—21no—
208D4—21no—
209D4—41no—
210D4—41no—
211C2×C4—24no—
212C2×C4—22no—
213C2×C4—21no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—4281no—
217C2×C4—4281no—
218C2×C4—2142no—
219C2×C4—2142no—
220C2×C4—2142no—
221C2×C4—2142no—
222C2×C4—2142no—
223C2×C4D4×D10711yescharacteristic
224C2×C4D4×D10711yescharacteristic
225C2×C4D4×D10711yescharacteristic
226C2×C4C2×C22⋊D10711yescharacteristic
227C2×C4C2×D42811yescharacteristic
228C2×C4#1313381811yescharacteristic
229C8—41no—
230C8—2142no—
231C22—22no—
232C22—41no—
233C22—42no—
234C22#1681207711yescharacteristic
235C22#1681207911yescharacteristic
236C22#1681208211yescharacteristic
237C4—24no—
238C4—41no—
239C4—4282no—
240C4—4282no—
241C4—4282no—
242C4#1681207911yescharacteristic
243C4#1681208211yescharacteristic
244C4#1681208311yescharacteristic
245C4#1681210511yescharacteristic
246C2—21no—
247C2—21no—
248C2—81no—
249C2#2029253611yescharacteristic
250C2#2029281112yes—
subgroupG/H
centerC22#16812079
commutator, cosocleC22×C4×C107C23
FrattiniC22×C4C22×D107
FittingC2×#104×C107C2
socleC22×C107#120
prime radicalC2×#41×C107C22
hypercenterC2×#104D107
hypocenterC107#2005
LCSG ▷ C22×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
3. C2×#16812109C2semidirect
4. #20292637C2semidirect
5. C2×#16812027C2semidirect
6. #20292387C2semidirect
126. C107#2005semidirect

Maximal subgroups

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

subgroupindex
C2×#168121392
#202931982
C2×#168121092
#202926372
C2×#168120272
#202923872
C2×#104×C1072
#2005107