Finite Group Databasebeta

← C7×#13590 #13190806

Subgroups — C7×#13590 #13190806

Order 1792.

398 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 90 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×#3152C211yesmaximal, characteristic
2C2×C7×#356C212yesmaximal, complemented
3C7×#1411C212yesmaximal, complemented
4C7×#1410C212yesmaximal, complemented
5C2×C7×#137—22no—
6C7×#532C411yescharacteristic
7C2×C7×C4⋊Q8C2211yescharacteristic
8C7×#497—22no—
9C7×#494C411yescharacteristic
10C7×#494C2211yescharacteristic
11C7×#492C411yescharacteristic
12C7×#492C2211yescharacteristic
13C2×C7×#101—22no—
14C4×C7×M16C411yescharacteristic
15C7×#356—22no—
16C7×#356C2214yes—
17#13590C711yesmaximal, characteristic, direct product factor, Sylow
18C2×C7×#41—21no—
19C22×C7×Q8D412yes—
20C7×#137—44no—
21C7×#137—44no—
22C2×C7×Q16—22no—
23C2×C7×Q16—22no—
24C2×C7×SD16—22no—
25C2×C7×SD16—22no—
26C2×C7×M16—21no—
27C2×C7×M16—42no—
28C7×C4⋊Q8—41no—
29C7×C4⋊Q8C2×C411yescharacteristic
30C7×C4⋊Q8C2×C411yescharacteristic
31C7×C4⋊Q8D412yes—
32C7×C4⋊Q8C2311yescharacteristic
33C7×#127C2×C411yescharacteristic
34C7×#124—21no—
35C7×#121—41no—
36C4×C7×D4—41no—
37C2×C7×C4⋊C4—41no—
38C2×C42×C7C2×C411yescharacteristic
39C7×#101—24no—
40C7×#101—42no—
41C7×#97—21no—
42C4×C7×C8C2×C411yescharacteristic
43C4×C7×C8C2×C411yescharacteristic
44#3152C2×C711yescharacteristic
45C2×#356C2×C712yescomplemented
46#1411C2×C712yescomplemented
47#1410C2×C712yescomplemented
48C7×#41—42no—
49C7×#41—42no—
50C2×C7×Q8—22no—
51C2×C7×Q8—21no—
52C2×C7×Q8—42no—
53C2×C7×Q8—42no—
54C2×C7×Q8C22⋊C412yes—
55C2×C7×Q8C2×D412yes—
56C2×C7×D4—21no—
57C2×C7×D4—41no—
58C2×C7×D4—41no—
59C22×C4×C7—21no—
60C22×C4×C7—22no—
61C22×C4×C7—41no—
62C22×C4×C7C22⋊C411yescharacteristic
63C7×Q16—44no—
64C7×Q16—44no—
65C7×SD16—44no—
66C7×SD16—44no—
67C7×M16—24no—
68C7×M16—44no—
69C7×M16—82no—
70C2×C7×C8—21no—
71C2×C7×C8—21no—
72C2×C7×C8—82no—
73C7×C4⋊C4—41no—
74C7×C4⋊C4—42no—
75C7×C4⋊C4—41no—
76C7×C4⋊C4—41no—
77C7×C22⋊C4—42no—
78C42×C7—21no—
79C42×C7C22⋊C411yescharacteristic
80C42×C7C22×C411yescharacteristic
81C2×#137—22no—
82#532C4×C711yescharacteristic
83C2×C4⋊Q8C22×C711yescharacteristic
84#497—22no—
85#494C4×C711yescharacteristic
86#494C22×C711yescharacteristic
87#492C4×C711yescharacteristic
88#492C22×C711yescharacteristic
89C2×#101—22no—
90C4×M16C4×C711yescharacteristic
91#356—22no—
92#356C22×C714yes—
93C23×C7—41no—
94C23×C7#9911yescharacteristic
95C7×Q8—42no—
96C7×Q8—42no—
97C7×Q8—42no—
98C7×Q8—82no—
99C7×D4—42no—
100C7×D4—82no—
101C7×D4—82no—
102C2×C4×C7—22no—
103C2×C4×C7—21no—
104C2×C4×C7—21no—
105C2×C4×C7—22no—
106C2×C4×C7—22no—
107C2×C4×C7—42no—
108C2×C4×C7—42no—
109C2×C4×C7—42no—
110C2×C4×C7—41no—
111C2×C4×C7—81no—
112C2×C4×C7—81no—
113C2×C4×C7#9911yescharacteristic
114C2×C4×C7C2×C22⋊C411yescharacteristic
115C7×C8—22no—
116C7×C8—22no—
117C7×C8—84no—
118C2×#41—21no—
119C22×Q8C7×D412yes—
120#137—44no—
121#137—44no—
122C2×Q16—22no—
123C2×Q16—22no—
124C2×SD16—22no—
125C2×SD16—22no—
126C2×M16—21no—
127C2×M16—42no—
128C4⋊Q8—41no—
129C4⋊Q8C2×C4×C711yescharacteristic
130C4⋊Q8C2×C4×C711yescharacteristic
131C4⋊Q8C7×D412yes—
132C4⋊Q8C23×C711yescharacteristic
133#127C2×C4×C711yescharacteristic
134#124—21no—
135#121—41no—
136C4×D4—41no—
137C2×C4⋊C4—41no—
138C2×C42C2×C4×C711yescharacteristic
139#101—24no—
140#101—42no—
141#97—21no—
142C4×C8C2×C4×C711yescharacteristic
143C4×C8C2×C4×C711yescharacteristic
144C22×C7—41no—
145C22×C7—82no—
146C22×C7—81no—
147C22×C7#35312yes—
148C22×C7C2×#9911yescharacteristic
149C4×C7—22no—
150C4×C7—21no—
151C4×C7—21no—
152C4×C7—41no—
153C4×C7—42no—
154C4×C7—42no—
155C4×C7—81no—
156#41—42no—
157#41—42no—
158C2×Q8—22no—
159C2×Q8—21no—
160C2×Q8—42no—
161C2×Q8—42no—
162C2×Q8C7×C22⋊C412yes—
163C2×Q8C2×C7×D412yes—
164C2×D4—21no—
165C2×D4—41no—
166C2×D4—41no—
167C22×C4—21no—
168C22×C4—22no—
169C22×C4—41no—
170C22×C4C7×C22⋊C411yescharacteristic
171Q16—44no—
172Q16—44no—
173SD16—44no—
174SD16—44no—
175M16—24no—
176M16—44no—
177M16—82no—
178C2×C8—21no—
179C2×C8—21no—
180C2×C8—82no—
181C4⋊C4—41no—
182C4⋊C4—42no—
183C4⋊C4—41no—
184C4⋊C4—41no—
185C22⋊C4—42no—
186C42—21no—
187C42C7×C22⋊C411yescharacteristic
188C42C22×C4×C711yescharacteristic
189C2×C7—21no—
190C2×C7—22no—
191C2×C7—161no—
192C2×C7C2×#35311yescharacteristic
193C23—41no—
194C23C7×#9911yescharacteristic
195Q8—42no—
196Q8—42no—
197Q8—42no—
198Q8—82no—
199D4—42no—
200D4—82no—
201D4—82no—
202C2×C4—22no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—42no—
210C2×C4—41no—
211C2×C4—81no—
212C2×C4—81no—
213C2×C4C7×#9911yescharacteristic
214C2×C4C2×C7×C22⋊C411yescharacteristic
215C8—22no—
216C8—22no—
217C8—84no—
218C7#1359011yescharacteristic, direct product factor, Sylow
219C22—41no—
220C22—82no—
221C22—81no—
222C22C7×#35312yes—
223C22C2×C7×#9911yescharacteristic
224C4—22no—
225C4—21no—
226C4—21no—
227C4—41no—
228C4—42no—
229C4—42no—
230C4—81no—
231C2—21no—
232C2—22no—
233C2—161no—
234C2C2×C7×#35311yescharacteristic
subgroupG/H
center, socleC2×C7C2×#353
commutatorC42C22×C4×C7
Frattini, cosocleC4⋊Q8C23×C7
prime radicalC7×#532C4
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C7 ◁ C23×C7 ◁ C22×C4×C7 ◁ C2×C7×C4⋊Q8 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C7×#356C2semidirect
3. C7×#1411C2semidirect
4. C7×#1410C2semidirect
17. #13590C7direct (N × H)
45. C2×#356C2×C7semidirect
46. #1411C2×C7semidirect
47. #1410C2×C7semidirect
218. C7#13590direct (N × H)

Maximal subgroups

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

subgroupindex
C7×#31522
C2×C7×#3562
C7×#14112
C7×#14102
#135907