Finite Group Databasebeta

← C7×#11908 #13189124

Subgroups — C7×#11908 #13189124

Order 1792.

388 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 118 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
1C7×#2567C211yesmaximal, characteristic
2C7×#1801C211yesmaximal, characteristic
3C7×#1461C211yesmaximal, characteristic
4C7×#1354C214yesmaximal
5C2×C7×C4⋊Q8C411yescharacteristic
6C2×C4×C7×Q8C2211yescharacteristic
7C7×#431—21no—
8C7×#423—21no—
9C2×C7×#101—21no—
10C7×#395C412yes—
11C7×#395C2212yes—
12C7×#391—21no—
13C7×#389—21no—
14C7×#389—21no—
15C7×#384—21no—
16C4×C7×C4⋊C4C411yescharacteristic
17C7×#343C2212yes—
18C7×#324—21no—
19C7×#324C2212yes—
20#11908C711yesmaximal, characteristic, direct product factor, Sylow
21C22×C7×Q8C2×C412yes—
22C22×C7×Q8D411yescharacteristic
23C2×C7×M16—22no—
24C7×C4⋊Q8—41no—
25C7×C4⋊Q8—41no—
26C4×C7×Q8—41no—
27C4×C7×Q8—41no—
28C2×C7×C4⋊C4—21no—
29C2×C7×C4⋊C4—21no—
30C2×C7×C4⋊C4—21no—
31C2×C7×C4⋊C4—22no—
32C2×C7×C4⋊C4—22no—
33C2×C7×C4⋊C4C2×C411yescharacteristic
34C2×C7×C4⋊C4D411yescharacteristic
35C2×C7×C4⋊C4C2311yescharacteristic
36C2×C42×C7—21no—
37C2×C42×C7C2×C411yescharacteristic
38C2×C42×C7D411yescharacteristic
39C2×C42×C7D411yescharacteristic
40C7×C4⋊C8—41no—
41C7×C4⋊C8—41no—
42C7×C4⋊C8—41no—
43C7×#101—42no—
44C7×C22⋊C8—22no—
45C4×C7×C8—41no—
46C7×#95—22no—
47C7×#95—22no—
48C7×#95C2×C412yes—
49#2567C2×C711yescharacteristic
50#1801C2×C711yescharacteristic
51#1461C2×C711yescharacteristic
52#1354C2×C714yes—
53C2×C7×Q8—41no—
54C2×C7×Q8—41no—
55C2×C7×Q8—42no—
56C2×C7×Q8—82no—
57C2×C7×Q8SD1612yes—
58C2×C7×Q8Q1612yes—
59C22×C4×C7—22no—
60C22×C4×C7—22no—
61C22×C4×C7C22⋊C411yescharacteristic
62C22×C4×C7C22⋊C411yescharacteristic
63C22×C4×C7C22⋊C411yescharacteristic
64C22×C4×C7C22⋊C411yescharacteristic
65C22×C4×C7C22×C411yescharacteristic
66C22×C4×C7C2×D411yescharacteristic
67C22×C4×C7C2×D411yescharacteristic
68C7×M16—42no—
69C7×M16—42no—
70C2×C7×C8—42no—
71C2×C7×C8—42no—
72C7×C4⋊C4—24no—
73C7×C4⋊C4—41no—
74C7×C4⋊C4—41no—
75C7×C4⋊C4—41no—
76C7×C4⋊C4—42no—
77C7×C4⋊C4—41no—
78C7×C4⋊C4—41no—
79C7×C4⋊C4—82no—
80C7×C4⋊C4—82no—
81C42×C7—21no—
82C42×C7—21no—
83C42×C7—21no—
84C42×C7—21no—
85C42×C7—21no—
86C42×C7—21no—
87C42×C7—42no—
88C2×C4⋊Q8C4×C711yescharacteristic
89C2×C4×Q8C22×C711yescharacteristic
90#431—21no—
91#423—21no—
92C2×#101—21no—
93#395C4×C712yes—
94#395C22×C712yes—
95#391—21no—
96#389—21no—
97#389—21no—
98#384—21no—
99C4×C4⋊C4C4×C711yescharacteristic
100#343C22×C712yes—
101#324—21no—
102#324C22×C712yes—
103C23×C7C2×C22⋊C411yescharacteristic
104C7×Q8—42no—
105C7×Q8—42no—
106C7×Q8—84no—
107C2×C4×C7—21no—
108C2×C4×C7—21no—
109C2×C4×C7—21no—
110C2×C4×C7—21no—
111C2×C4×C7—21no—
112C2×C4×C7—21no—
113C2×C4×C7—22no—
114C2×C4×C7—24no—
115C2×C4×C7—21no—
116C2×C4×C7—21no—
117C2×C4×C7—21no—
118C2×C4×C7—42no—
119C2×C4×C7—42no—
120C2×C4×C7—41no—
121C2×C4×C7—41no—
122C2×C4×C7—41no—
123C2×C4×C7—42no—
124C2×C4×C7—42no—
125C2×C4×C7—42no—
126C2×C4×C7#9911yescharacteristic
127C2×C4×C7#9911yescharacteristic
128C2×C4×C7#10312yes—
129C2×C4×C7#10312yes—
130C2×C4×C7C2×SD1611yescharacteristic
131C2×C4×C7C2×Q1611yescharacteristic
132C7×C8—82no—
133C7×C8—82no—
134C22×Q8C2×C4×C712yes—
135C22×Q8C7×D411yescharacteristic
136C2×M16—22no—
137C4⋊Q8—41no—
138C4⋊Q8—41no—
139C4×Q8—41no—
140C4×Q8—41no—
141C2×C4⋊C4—21no—
142C2×C4⋊C4—21no—
143C2×C4⋊C4—21no—
144C2×C4⋊C4—22no—
145C2×C4⋊C4—22no—
146C2×C4⋊C4C2×C4×C711yescharacteristic
147C2×C4⋊C4C7×D411yescharacteristic
148C2×C4⋊C4C23×C711yescharacteristic
149C2×C42—21no—
150C2×C42C2×C4×C711yescharacteristic
151C2×C42C7×D411yescharacteristic
152C2×C42C7×D411yescharacteristic
153C4⋊C8—41no—
154C4⋊C8—41no—
155C4⋊C8—41no—
156#101—42no—
157C22⋊C8—22no—
158C4×C8—41no—
159#95—22no—
160#95—22no—
161#95C2×C4×C712yes—
162C22×C7—21no—
163C22×C7—21no—
164C22×C7C2×#9911yescharacteristic
165C22×C7C2×#10311yescharacteristic
166C22×C7#42111yescharacteristic
167C4×C7—21no—
168C4×C7—21no—
169C4×C7—22no—
170C4×C7—22no—
171C4×C7—21no—
172C4×C7—44no—
173C4×C7—41no—
174C4×C7—41no—
175C4×C7—41no—
176C4×C7—82no—
177C4×C7#35612yes—
178C2×Q8—41no—
179C2×Q8—41no—
180C2×Q8—42no—
181C2×Q8—82no—
182C2×Q8C7×SD1612yes—
183C2×Q8C7×Q1612yes—
184C22×C4—22no—
185C22×C4—22no—
186C22×C4C7×C22⋊C411yescharacteristic
187C22×C4C7×C22⋊C411yescharacteristic
188C22×C4C7×C22⋊C411yescharacteristic
189C22×C4C7×C22⋊C411yescharacteristic
190C22×C4C22×C4×C711yescharacteristic
191C22×C4C2×C7×D411yescharacteristic
192C22×C4C2×C7×D411yescharacteristic
193M16—42no—
194M16—42no—
195C2×C8—42no—
196C2×C8—42no—
197C4⋊C4—24no—
198C4⋊C4—41no—
199C4⋊C4—41no—
200C4⋊C4—41no—
201C4⋊C4—42no—
202C4⋊C4—41no—
203C4⋊C4—41no—
204C4⋊C4—82no—
205C4⋊C4—82no—
206C42—21no—
207C42—21no—
208C42—21no—
209C42—21no—
210C42—21no—
211C42—21no—
212C42—42no—
213C2×C7—21no—
214C2×C7—21no—
215C2×C7#152011yescharacteristic
216C2×C7#212211yescharacteristic
217C2×C7C2×#35611yescharacteristic
218C23C2×C7×C22⋊C411yescharacteristic
219Q8—42no—
220Q8—42no—
221Q8—84no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—22no—
229C2×C4—24no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—42no—
234C2×C4—42no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4C7×#9911yescharacteristic
242C2×C4C7×#9911yescharacteristic
243C2×C4C7×#10312yes—
244C2×C4C7×#10312yes—
245C2×C4C2×C7×SD1611yescharacteristic
246C2×C4C2×C7×Q1611yescharacteristic
247C8—82no—
248C8—82no—
249C7#1190811yescharacteristic, direct product factor, Sylow
250C22—21no—
251C22—21no—
252C22C2×C7×#9911yescharacteristic
253C22C2×C7×#10311yescharacteristic
254C22C7×#42111yescharacteristic
255C4—21no—
256C4—22no—
257C4—22no—
258C4—21no—
259C4—21no—
260C4—44no—
261C4—41no—
262C4—41no—
263C4—41no—
264C4—82no—
265C4C7×#35612yes—
266C2—21no—
267C2—21no—
268C2C7×#152011yescharacteristic
269C2C7×#212211yescharacteristic
270C2C2×C7×#35611yescharacteristic
subgroupG/H
center, socleC22×C7C2×#99
commutatorC22×C4C22×C4×C7
Frattini, cosocleC2×C4⋊C4C23×C7
prime radicalC23×C7C2×C22⋊C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C7 ◁ C22×C4×C7 ◁ C2×C4×C7×Q8 ◁ G

Complements

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

NH ≅ G/Ntype
20. #11908C7direct (N × H)
249. C7#11908direct (N × H)

Maximal subgroups

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

subgroupindex
C7×#25672
C7×#18012
C7×#14612
C7×#13542
#119087