Finite Group Databasebeta

← C7×#25919 #13203135

Subgroups — C7×#25919 #13203135

Order 1792.

954 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#3502C211yesmaximal, characteristic
2C7×#3139C212yesmaximal
3C7×#2546C211yesmaximal, characteristic
4C7×#2028C214yesmaximal
5C7×#1986C212yesmaximal
6C7×#1886C214yesmaximal
7C4×C7×#101C211yesmaximal, characteristic
8C7×Q82—22no—
9C7×#557—22no—
10C7×#557—24no—
11C7×#544—22no—
12C7×#544C2212yes—
13C7×#533—22no—
14C7×#533C2212yes—
15C2×C7×C4⋊Q8C2212yes—
16C2×C7×C4⋊Q8C2211yescharacteristic
17C7×#519C2212yes—
18C2×C4×C7×Q8C2211yescharacteristic
19C7×#491—24no—
20C7×#487—22no—
21C7×#487—22no—
22C7×#419C2218yes—
23C2×C7×#101C2212yes—
24C4×C7×M16C2212yes—
25C7×#398—22no—
26C7×#391C2212yes—
27C7×#389—22no—
28C4×C7×C4⋊C4C2211yescharacteristic
29C7×#343C2212yes—
30C7×#339C2218yes—
31#25919C711yesmaximal, characteristic, direct product factor, Sylow
32C22×C7×Q8C2312yes—
33C22×C7×Q8C2311yescharacteristic
34C2×C7×M16C2314yes—
35C7×C4⋊Q8—22no—
36C7×C4⋊Q8—22no—
37C7×C4⋊Q8—28no—
38C7×C4⋊Q8—24no—
39C7×C4⋊Q8—28no—
40C7×C4⋊Q8—22no—
41C7×C4⋊Q8—22no—
42C7×C4⋊Q8D412yes—
43C7×C4⋊Q8D412yes—
44C7×#125—24no—
45C7×#125—28no—
46C7×#125—24no—
47C7×#125D414yes—
48C7×C22⋊Q8—22no—
49C7×C22⋊Q8—24no—
50C7×C22⋊Q8—22no—
51C4×C7×Q8—24no—
52C4×C7×Q8—24no—
53C4×C7×Q8—24no—
54C4×C7×Q8—24no—
55C4×C7×Q8—22no—
56C4×C7×Q8—22no—
57C4×C7×Q8—22no—
58C4×C7×Q8—22no—
59C7×#117—24no—
60C7×#117C2314yes—
61C2×C7×C4⋊C4—21no—
62C2×C7×C4⋊C4—21no—
63C2×C7×C4⋊C4—24no—
64C2×C7×C4⋊C4—21no—
65C2×C7×C4⋊C4D412yes—
66C2×C7×C4⋊C4C2311yescharacteristic
67C2×C42×C7D412yes—
68C2×C42×C7C2312yes—
69C2×C42×C7C2311yescharacteristic
70C7×#103—28no—
71C7×#103—28no—
72C7×#101—24no—
73C7×#97—22no—
74C4×C7×C8—22no—
75C7×#95—21no—
76C7×#95—24no—
77#3502C2×C711yescharacteristic
78#3139C2×C712yes—
79#2546C2×C711yescharacteristic
80#2028C2×C714yes—
81#1986C2×C712yes—
82#1886C2×C714yes—
83C4×#101C2×C711yescharacteristic
84C2×C7×Q8—24no—
85C2×C7×Q8—22no—
86C2×C7×Q8—22no—
87C2×C7×Q8—22no—
88C2×C7×Q8—22no—
89C2×C7×Q8—24no—
90C2×C7×Q8—24no—
91C2×C7×Q8—24no—
92C2×C7×Q8#4114yes—
93C22×C4×C7—22no—
94C22×C4×C7—22no—
95C22×C4×C7C2×D411yescharacteristic
96C22×C4×C7C2×D412yes—
97C22×C4×C7C2×D412yes—
98C22×C4×C7C2×D411yescharacteristic
99C22×C4×C7C2411yescharacteristic
100C7×M16—24no—
101C7×M16—24no—
102C2×C7×C8—24no—
103C7×C4⋊C4—24no—
104C7×C4⋊C4—24no—
105C7×C4⋊C4—24no—
106C7×C4⋊C4—24no—
107C7×C4⋊C4—28no—
108C7×C4⋊C4—24no—
109C7×C4⋊C4—24no—
110C7×C4⋊C4—22no—
111C7×C4⋊C4—22no—
112C7×C4⋊C4—24no—
113C7×C4⋊C4—22no—
114C7×C4⋊C4—41no—
115C7×C4⋊C4—42no—
116C7×C4⋊C4—41no—
117C7×C4⋊C4—48no—
118C7×C4⋊C4C2×D414yes—
119C7×C4⋊C4C2×D414yes—
120C7×C22⋊C4—24no—
121C42×C7—28no—
122C42×C7—22no—
123C42×C7—22no—
124C42×C7—24no—
125C42×C7—24no—
126C42×C7C2×D412yes—
127C42×C7C2×D412yes—
128Q82—22no—
129#557—22no—
130#557—24no—
131#544—22no—
132#544C22×C712yes—
133#533—22no—
134#533C22×C712yes—
135C2×C4⋊Q8C22×C711yescharacteristic
136C2×C4⋊Q8C22×C712yes—
137#519C22×C712yes—
138C2×C4×Q8C22×C711yescharacteristic
139#491—24no—
140#487—22no—
141#487—22no—
142#419C22×C718yes—
143C2×#101C22×C712yes—
144C4×M16C22×C712yes—
145#398—22no—
146#391C22×C712yes—
147#389—22no—
148C4×C4⋊C4C22×C711yescharacteristic
149#343C22×C712yes—
150#339C22×C718yes—
151C23×C7C22×D411yescharacteristic
152C7×Q8—28no—
153C7×Q8—44no—
154C7×Q8—48no—
155C7×Q8—82no—
156C7×Q8—84no—
157C2×C4×C7—22no—
158C2×C4×C7—22no—
159C2×C4×C7—22no—
160C2×C4×C7—24no—
161C2×C4×C7—24no—
162C2×C4×C7—24no—
163C2×C4×C7—22no—
164C2×C4×C7—41no—
165C2×C4×C7—42no—
166C2×C4×C7—42no—
167C2×C4×C7—42no—
168C2×C4×C7—42no—
169C2×C4×C7—42no—
170C2×C4×C7—42no—
171C2×C4×C7#12011yescharacteristic
172C2×C4×C7#12012yes—
173C2×C4×C7#12011yescharacteristic
174C2×C4×C7#12414yes—
175C2×C4×C7C22×D412yes—
176C2×C4×C7C2×#4112yes—
177C2×C4×C72−1+412yes—
178C7×C8—44no—
179C22×Q8C23×C712yes—
180C22×Q8C23×C711yescharacteristic
181C2×M16C23×C714yes—
182C4⋊Q8—22no—
183C4⋊Q8—22no—
184C4⋊Q8—28no—
185C4⋊Q8—24no—
186C4⋊Q8—28no—
187C4⋊Q8—22no—
188C4⋊Q8—22no—
189C4⋊Q8C7×D412yes—
190C4⋊Q8C7×D412yes—
191#125—24no—
192#125—28no—
193#125—24no—
194#125C7×D414yes—
195C22⋊Q8—22no—
196C22⋊Q8—24no—
197C22⋊Q8—22no—
198C4×Q8—24no—
199C4×Q8—24no—
200C4×Q8—24no—
201C4×Q8—24no—
202C4×Q8—22no—
203C4×Q8—22no—
204C4×Q8—22no—
205C4×Q8—22no—
206#117—24no—
207#117C23×C714yes—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—24no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4C7×D412yes—
213C2×C4⋊C4C23×C711yescharacteristic
214C2×C42C7×D412yes—
215C2×C42C23×C712yes—
216C2×C42C23×C711yescharacteristic
217#103—28no—
218#103—28no—
219#101—24no—
220#97—22no—
221C4×C8—22no—
222#95—21no—
223#95—24no—
224C22×C7—21no—
225C22×C7—21no—
226C22×C7C2×#12011yescharacteristic
227C22×C7C2×#12411yescharacteristic
228C22×C7#53611yescharacteristic
229C4×C7—24no—
230C4×C7—21no—
231C4×C7—22no—
232C4×C7—44no—
233C4×C7—44no—
234C4×C7—42no—
235C4×C7—44no—
236C4×C7—82no—
237C4×C7#45612yes—
238C4×C7#54814yes—
239C2×Q8—24no—
240C2×Q8—22no—
241C2×Q8—22no—
242C2×Q8—22no—
243C2×Q8—22no—
244C2×Q8—24no—
245C2×Q8—24no—
246C2×Q8—24no—
247C2×Q8C7×#4114yes—
248C22×C4—22no—
249C22×C4—22no—
250C22×C4C2×C7×D411yescharacteristic
251C22×C4C2×C7×D412yes—
252C22×C4C2×C7×D412yes—
253C22×C4C2×C7×D411yescharacteristic
254C22×C4C24×C711yescharacteristic
255M16—24no—
256M16—24no—
257C2×C8—24no—
258C4⋊C4—24no—
259C4⋊C4—24no—
260C4⋊C4—24no—
261C4⋊C4—24no—
262C4⋊C4—28no—
263C4⋊C4—24no—
264C4⋊C4—24no—
265C4⋊C4—22no—
266C4⋊C4—22no—
267C4⋊C4—24no—
268C4⋊C4—22no—
269C4⋊C4—41no—
270C4⋊C4—42no—
271C4⋊C4—41no—
272C4⋊C4—48no—
273C4⋊C4C2×C7×D414yes—
274C4⋊C4C2×C7×D414yes—
275C22⋊C4—24no—
276C42—28no—
277C42—22no—
278C42—22no—
279C42—24no—
280C42—24no—
281C42C2×C7×D412yes—
282C42C2×C7×D412yes—
283C2×C7—21no—
284C2×C7—21no—
285C2×C7#243611yescharacteristic
286C2×C7C2×#45611yescharacteristic
287C2×C7#302211yescharacteristic
288C23C22×C7×D411yescharacteristic
289Q8—28no—
290Q8—44no—
291Q8—48no—
292Q8—82no—
293Q8—84no—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—22no—
297C2×C4—24no—
298C2×C4—24no—
299C2×C4—24no—
300C2×C4—22no—
301C2×C4—41no—
302C2×C4—42no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—42no—
308C2×C4C7×#12011yescharacteristic
309C2×C4C7×#12012yes—
310C2×C4C7×#12011yescharacteristic
311C2×C4C7×#12414yes—
312C2×C4C22×C7×D412yes—
313C2×C4C2×C7×#4112yes—
314C2×C4C7×2−1+412yes—
315C8—44no—
316C7#2591911yescharacteristic, direct product factor, Sylow
317C22—21no—
318C22—21no—
319C22C2×C7×#12011yescharacteristic
320C22C2×C7×#12411yescharacteristic
321C22C7×#53611yescharacteristic
322C4—24no—
323C4—21no—
324C4—22no—
325C4—44no—
326C4—44no—
327C4—42no—
328C4—44no—
329C4—82no—
330C4C7×#45612yes—
331C4C7×#54814yes—
332C2—21no—
333C2—21no—
334C2C7×#243611yescharacteristic
335C2C2×C7×#45611yescharacteristic
336C2C7×#302211yescharacteristic
subgroupG/H
center, socleC22×C7C2×#120
commutator, Frattini, cosocleC22×C4C24×C7
prime radicalC23×C7C22×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G

Complements

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

NH ≅ G/Ntype
31. #25919C7direct (N × H)
316. C7#25919direct (N × H)

Maximal subgroups

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

subgroupindex
C7×#35022
C7×#31392
C7×#25462
C7×#20282
C7×#19862
C7×#18862
C4×C7×#1012
#259197