Finite Group Databasebeta

← C7×#11570 #13188786

Subgroups — C7×#11570 #13188786

Order 1792.

480 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 106 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×#2542C211yesmaximal, characteristic
2C7×#1465C211yesmaximal, characteristic
3C7×#1459C211yesmaximal, characteristic
4C7×#1325C214yesmaximal, complemented
5C2×C7×C4⋊Q8C411yescharacteristic
6C2×C7×C22⋊Q8—21no—
7C2×C7×C22⋊Q8—21no—
8C2×C4×C7×D4C2211yescharacteristic
9C7×#407—21no—
10C2×C7×C22⋊C8—21no—
11C7×#399—21no—
12C7×#399—21no—
13C7×#390C412yes—
14C7×#384C2212yes—
15C4×C7×C4⋊C4C411yescharacteristic
16C7×#324C2212yes—
17C7×#324C2212yes—
18C7×#323—21no—
19C7×#323—21no—
20#11570C711yesmaximal, characteristic, direct product factor, Sylow
21C22×C7×Q8—21no—
22C22×C7×D4C2×C411yescharacteristic
23C23×C4×C7D411yescharacteristic
24C23×C4×C7D411yescharacteristic
25C2×C7×M16—41no—
26C22×C7×C8—41no—
27C7×C4⋊Q8—41no—
28C7×C4⋊Q8—41no—
29C7×C22⋊Q8—44no—
30C7×C22⋊Q8—44no—
31C4×C7×D4—41no—
32C4×C7×D4—41no—
33C2×C7×C4⋊C4—21no—
34C2×C7×C4⋊C4—21no—
35C2×C7×C4⋊C4—22no—
36C2×C7×C4⋊C4—22no—
37C2×C7×C4⋊C4C2×C412yes—
38C2×C7×C4⋊C4C2311yescharacteristic
39C2×C7×C22⋊C4—22no—
40C2×C7×C22⋊C4—22no—
41C2×C7×C22⋊C4D411yescharacteristic
42C2×C7×C22⋊C4D411yescharacteristic
43C2×C42×C7C2×C412yes—
44C2×C42×C7C2×C411yescharacteristic
45C7×C22⋊C8—22no—
46C7×C22⋊C8—22no—
47C7×C22⋊C8—41no—
48C7×C22⋊C8—41no—
49C7×#95—21no—
50#2542C2×C711yescharacteristic
51#1465C2×C711yescharacteristic
52#1459C2×C711yescharacteristic
53#1325C2×C714yescomplemented
54C24×C7C22⋊C411yescharacteristic
55C24×C7C22⋊C411yescharacteristic
56C2×C7×Q8—42no—
57C2×C7×Q8—42no—
58C2×C7×Q8—41no—
59C2×C7×Q8—41no—
60C2×C7×D4—22no—
61C2×C7×D4—22no—
62C2×C7×D4—41no—
63C22×C4×C7—22no—
64C22×C4×C7—21no—
65C22×C4×C7—21no—
66C22×C4×C7—21no—
67C22×C4×C7—21no—
68C22×C4×C7—22no—
69C22×C4×C7—42no—
70C22×C4×C7—42no—
71C22×C4×C7C22⋊C411yescharacteristic
72C22×C4×C7C22⋊C411yescharacteristic
73C22×C4×C7C22×C411yescharacteristic
74C22×C4×C7C2×D411yescharacteristic
75C22×C4×C7C2×D411yescharacteristic
76C7×M16—82no—
77C2×C7×C8—42no—
78C2×C7×C8—42no—
79C2×C7×C8—82no—
80C7×C4⋊C4—24no—
81C7×C4⋊C4—41no—
82C7×C4⋊C4—42no—
83C7×C4⋊C4—44no—
84C7×C4⋊C4—44no—
85C7×C4⋊C4—42no—
86C7×C22⋊C4—41no—
87C7×C22⋊C4—41no—
88C7×C22⋊C4—44no—
89C7×C22⋊C4—44no—
90C42×C7—21no—
91C42×C7—21no—
92C42×C7—24no—
93C2×C4⋊Q8C4×C711yescharacteristic
94C2×C22⋊Q8—21no—
95C2×C22⋊Q8—21no—
96C2×C4×D4C22×C711yescharacteristic
97#407—21no—
98C2×C22⋊C8—21no—
99#399—21no—
100#399—21no—
101#390C4×C712yes—
102#384C22×C712yes—
103C4×C4⋊C4C4×C711yescharacteristic
104#324C22×C712yes—
105#324C22×C712yes—
106#323—21no—
107#323—21no—
108C23×C7—21no—
109C23×C7—21no—
110C23×C7—21no—
111C23×C7—21no—
112C23×C7—21no—
113C23×C7—41no—
114C23×C7—41no—
115C23×C7—41no—
116C23×C7—41no—
117C23×C7#10112yes—
118C23×C7C2×C22⋊C411yescharacteristic
119C7×Q8—82no—
120C7×Q8—82no—
121C7×D4—44no—
122C2×C4×C7—21no—
123C2×C4×C7—21no—
124C2×C4×C7—22no—
125C2×C4×C7—24no—
126C2×C4×C7—21no—
127C2×C4×C7—21no—
128C2×C4×C7—21no—
129C2×C4×C7—42no—
130C2×C4×C7—42no—
131C2×C4×C7—42no—
132C2×C4×C7—42no—
133C2×C4×C7—41no—
134C2×C4×C7—41no—
135C2×C4×C7—41no—
136C2×C4×C7—42no—
137C2×C4×C7—42no—
138C2×C4×C7—42no—
139C2×C4×C7—81no—
140C2×C4×C7—81no—
141C2×C4×C7#9911yescharacteristic
142C2×C4×C7#9911yescharacteristic
143C2×C4×C7#13112yes—
144C7×C8—82no—
145C7×C8—82no—
146C22×Q8—21no—
147C22×D4C2×C4×C711yescharacteristic
148C23×C4C7×D411yescharacteristic
149C23×C4C7×D411yescharacteristic
150C2×M16—41no—
151C22×C8—41no—
152C4⋊Q8—41no—
153C4⋊Q8—41no—
154C22⋊Q8—44no—
155C22⋊Q8—44no—
156C4×D4—41no—
157C4×D4—41no—
158C2×C4⋊C4—21no—
159C2×C4⋊C4—21no—
160C2×C4⋊C4—22no—
161C2×C4⋊C4—22no—
162C2×C4⋊C4C2×C4×C712yes—
163C2×C4⋊C4C23×C711yescharacteristic
164C2×C22⋊C4—22no—
165C2×C22⋊C4—22no—
166C2×C22⋊C4C7×D411yescharacteristic
167C2×C22⋊C4C7×D411yescharacteristic
168C2×C42C2×C4×C712yes—
169C2×C42C2×C4×C711yescharacteristic
170C22⋊C8—22no—
171C22⋊C8—22no—
172C22⋊C8—41no—
173C22⋊C8—41no—
174#95—21no—
175C22×C7—21no—
176C22×C7—21no—
177C22×C7—22no—
178C22×C7—42no—
179C22×C7—42no—
180C22×C7—41no—
181C22×C7—41no—
182C22×C7—41no—
183C22×C7—41no—
184C22×C7—41no—
185C22×C7—81no—
186C22×C7—81no—
187C22×C7#40811yescharacteristic
188C22×C7C2×#9911yescharacteristic
189C22×C7C2×#10111yescharacteristic
190C4×C7—21no—
191C4×C7—22no—
192C4×C7—44no—
193C4×C7—41no—
194C4×C7—41no—
195C4×C7—41no—
196C4×C7—82no—
197C4×C7#35312yes—
198C24C7×C22⋊C411yescharacteristic
199C24C7×C22⋊C411yescharacteristic
200C2×Q8—42no—
201C2×Q8—42no—
202C2×Q8—41no—
203C2×Q8—41no—
204C2×D4—22no—
205C2×D4—22no—
206C2×D4—41no—
207C22×C4—22no—
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—22no—
213C22×C4—42no—
214C22×C4—42no—
215C22×C4C7×C22⋊C411yescharacteristic
216C22×C4C7×C22⋊C411yescharacteristic
217C22×C4C22×C4×C711yescharacteristic
218C22×C4C2×C7×D411yescharacteristic
219C22×C4C2×C7×D411yescharacteristic
220M16—82no—
221C2×C8—42no—
222C2×C8—42no—
223C2×C8—82no—
224C4⋊C4—24no—
225C4⋊C4—41no—
226C4⋊C4—42no—
227C4⋊C4—44no—
228C4⋊C4—44no—
229C4⋊C4—42no—
230C22⋊C4—41no—
231C22⋊C4—41no—
232C22⋊C4—44no—
233C22⋊C4—44no—
234C42—21no—
235C42—21no—
236C42—24no—
237C2×C7—21no—
238C2×C7—21no—
239C2×C7—42no—
240C2×C7—81no—
241C2×C7#147211yescharacteristic
242C2×C7C2×#35311yescharacteristic
243C2×C7#213511yescharacteristic
244C23—21no—
245C23—21no—
246C23—21no—
247C23—21no—
248C23—21no—
249C23—41no—
250C23—41no—
251C23—41no—
252C23—41no—
253C23C7×#10112yes—
254C23C2×C7×C22⋊C411yescharacteristic
255Q8—82no—
256Q8—82no—
257D4—44no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—22no—
261C2×C4—24no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—42no—
266C2×C4—42no—
267C2×C4—42no—
268C2×C4—42no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—42no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—81no—
276C2×C4—81no—
277C2×C4C7×#9911yescharacteristic
278C2×C4C7×#9911yescharacteristic
279C2×C4C7×#13112yes—
280C8—82no—
281C8—82no—
282C7#1157011yescharacteristic, direct product factor, Sylow
283C22—21no—
284C22—21no—
285C22—22no—
286C22—42no—
287C22—42no—
288C22—41no—
289C22—41no—
290C22—41no—
291C22—41no—
292C22—41no—
293C22—81no—
294C22—81no—
295C22C7×#40811yescharacteristic
296C22C2×C7×#9911yescharacteristic
297C22C2×C7×#10111yescharacteristic
298C4—22no—
299C4—21no—
300C4—44no—
301C4—41no—
302C4—41no—
303C4—41no—
304C4—82no—
305C4C7×#35312yes—
306C2—21no—
307C2—21no—
308C2—42no—
309C2—81no—
310C2C7×#147211yescharacteristic
311C2C2×C7×#35311yescharacteristic
312C2C7×#213511yescharacteristic
subgroupG/H
center, socleC22×C7C2×#99
commutatorC22×C4C22×C4×C7
Frattini, cosocleC2×C4⋊C4C23×C7
prime radicalC22×C7×D4C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C7 ◁ C22×C4×C7 ◁ C2×C4×C7×D4 ◁ G

Complements

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

NH ≅ G/Ntype
4. C7×#1325C2semidirect
20. #11570C7direct (N × H)
53. #1325C2×C7semidirect
282. C7#11570direct (N × H)

Maximal subgroups

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

subgroupindex
C7×#25422
C7×#14652
C7×#14592
C7×#13252
#115707