Finite Group Databasebeta

← C7×#11827 #13189043

Subgroups — C7×#11827 #13189043

Order 1792.

418 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 98 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×#2633C211yesmaximal, characteristic
2C7×#1799C211yesmaximal, characteristic
3C7×#1465C211yesmaximal, characteristic
4C7×#1352C212yesmaximal, complemented
5C7×#1344C212yesmaximal, complemented
6C2×C7×#125C411yescharacteristic, complemented
7C2×C4×C7×D4C2211yescharacteristic
8C2×C7×#99—21no—
9C7×#407—21no—
10C7×#399C411yescharacteristic, complemented
11C7×#399C2211yescharacteristic
12C7×#398—21no—
13C7×#397C411yescharacteristic, complemented
14C7×#397C2211yescharacteristic
15C7×#394—21no—
16C7×#385—21no—
17C7×#385—21no—
18C7×#383C411yescharacteristic, complemented
19C7×#380—21no—
20C7×#342C2212yes—
21C7×#324—21no—
22C7×#323C2212yes—
23#11827C711yesmaximal, characteristic, direct product factor, Sylow
24C22×C7×D4D411yescharacteristic
25C23×C4×C7D411yescharacteristic
26C23×C4×C7D411yescharacteristic
27C2×C7×M16—41no—
28C7×#125—41no—
29C7×#125—41no—
30C4×C7×D4—41no—
31C4×C7×D4—41no—
32C2×C7×C4⋊C4—21no—
33C2×C7×C4⋊C4—21no—
34C2×C7×C4⋊C4—21no—
35C2×C7×C4⋊C4—21no—
36C2×C7×C4⋊C4—41no—
37C2×C7×C4⋊C4C2×C411yescharacteristic
38C2×C7×C4⋊C4C2×C411yescharacteristic
39C2×C7×C4⋊C4D411yescharacteristic
40C2×C7×C22⋊C4—21no—
41C2×C7×C22⋊C4—21no—
42C2×C7×C22⋊C4—22no—
43C2×C7×C22⋊C4—21no—
44C2×C7×C22⋊C4—21no—
45C2×C7×C22⋊C4C2×C411yescharacteristic
46C2×C7×C22⋊C4C2311yescharacteristic
47C2×C42×C7C2×C411yescharacteristic
48C7×#99—42no—
49C7×C22⋊C8—22no—
50C7×C22⋊C8—41no—
51C7×#95—21no—
52C7×#95—21no—
53C7×#95—21no—
54C7×#95—21no—
55C7×#95—41no—
56C7×#95C2×C411yescharacteristic
57C7×#95C2×C411yescharacteristic
58#2633C2×C711yescharacteristic
59#1799C2×C711yescharacteristic
60#1465C2×C711yescharacteristic
61#1352C2×C712yescomplemented
62#1344C2×C712yescomplemented
63C24×C7C22⋊C411yescharacteristic
64C24×C7C2×D411yescharacteristic
65C2×C7×D4—21no—
66C2×C7×D4—21no—
67C2×C7×D4—41no—
68C2×C7×D4—41no—
69C22×C4×C7—21no—
70C22×C4×C7—21no—
71C22×C4×C7—21no—
72C22×C4×C7—21no—
73C22×C4×C7—21no—
74C22×C4×C7—21no—
75C22×C4×C7—21no—
76C22×C4×C7—21no—
77C22×C4×C7—42no—
78C22×C4×C7—81no—
79C22×C4×C7—81no—
80C22×C4×C7C22⋊C411yescharacteristic
81C22×C4×C7C22⋊C411yescharacteristic
82C22×C4×C7C22⋊C411yescharacteristic
83C22×C4×C7C22×C411yescharacteristic
84C22×C4×C7C2×D411yescharacteristic
85C7×M16—82no—
86C2×C7×C8—42no—
87C7×C4⋊C4—41no—
88C7×C4⋊C4—41no—
89C7×C4⋊C4—41no—
90C7×C4⋊C4—42no—
91C7×C4⋊C4—41no—
92C7×C4⋊C4—41no—
93C7×C4⋊C4—81no—
94C7×C4⋊C4—81no—
95C7×C4⋊C4—82no—
96C7×C22⋊C4—41no—
97C7×C22⋊C4—41no—
98C7×C22⋊C4—42no—
99C7×C22⋊C4—41no—
100C7×C22⋊C4—41no—
101C7×C22⋊C4—42no—
102C7×C22⋊C4—42no—
103C7×C22⋊C4—81no—
104C7×C22⋊C4—81no—
105C42×C7—21no—
106C42×C7—21no—
107C2×#125C4×C711yescharacteristic, complemented
108C2×C4×D4C22×C711yescharacteristic
109C2×#99—21no—
110#407—21no—
111#399C4×C711yescharacteristic, complemented
112#399C22×C711yescharacteristic
113#398—21no—
114#397C4×C711yescharacteristic, complemented
115#397C22×C711yescharacteristic
116#394—21no—
117#385—21no—
118#385—21no—
119#383C4×C711yescharacteristic, complemented
120#380—21no—
121#342C22×C712yes—
122#324—21no—
123#323C22×C712yes—
124C23×C7—21no—
125C23×C7—21no—
126C23×C7—21no—
127C23×C7—21no—
128C23×C7—21no—
129C23×C7—41no—
130C23×C7—41no—
131C23×C7—41no—
132C23×C7—41no—
133C23×C7C2×C22⋊C411yescharacteristic
134C23×C7AGL(1,ℤ/8)11yescharacteristic
135C23×C7#13711yescharacteristic
136C7×D4—42no—
137C7×D4—42no—
138C2×C4×C7—21no—
139C2×C4×C7—21no—
140C2×C4×C7—21no—
141C2×C4×C7—21no—
142C2×C4×C7—21no—
143C2×C4×C7—21no—
144C2×C4×C7—41no—
145C2×C4×C7—42no—
146C2×C4×C7—42no—
147C2×C4×C7—41no—
148C2×C4×C7—41no—
149C2×C4×C7—41no—
150C2×C4×C7—41no—
151C2×C4×C7—41no—
152C2×C4×C7—41no—
153C2×C4×C7—41no—
154C2×C4×C7—41no—
155C2×C4×C7—41no—
156C2×C4×C7—41no—
157C2×C4×C7—41no—
158C2×C4×C7—41no—
159C2×C4×C7—41no—
160C2×C4×C7—41no—
161C2×C4×C7—41no—
162C2×C4×C7—81no—
163C2×C4×C7—81no—
164C2×C4×C7—82no—
165C2×C4×C7—82no—
166C2×C4×C7—82no—
167C2×C4×C7#9911yescharacteristic
168C2×C4×C7#9911yescharacteristic
169C7×C8—82no—
170C22×D4C7×D411yescharacteristic
171C23×C4C7×D411yescharacteristic
172C23×C4C7×D411yescharacteristic
173C2×M16—41no—
174#125—41no—
175#125—41no—
176C4×D4—41no—
177C4×D4—41no—
178C2×C4⋊C4—21no—
179C2×C4⋊C4—21no—
180C2×C4⋊C4—21no—
181C2×C4⋊C4—21no—
182C2×C4⋊C4—41no—
183C2×C4⋊C4C2×C4×C711yescharacteristic
184C2×C4⋊C4C2×C4×C711yescharacteristic
185C2×C4⋊C4C7×D411yescharacteristic
186C2×C22⋊C4—21no—
187C2×C22⋊C4—21no—
188C2×C22⋊C4—22no—
189C2×C22⋊C4—21no—
190C2×C22⋊C4—21no—
191C2×C22⋊C4C2×C4×C711yescharacteristic
192C2×C22⋊C4C23×C711yescharacteristic
193C2×C42C2×C4×C711yescharacteristic
194#99—42no—
195C22⋊C8—22no—
196C22⋊C8—41no—
197#95—21no—
198#95—21no—
199#95—21no—
200#95—21no—
201#95—41no—
202#95C2×C4×C711yescharacteristic
203#95C2×C4×C711yescharacteristic
204C22×C7—21no—
205C22×C7—21no—
206C22×C7—21no—
207C22×C7—21no—
208C22×C7—41no—
209C22×C7—41no—
210C22×C7—42no—
211C22×C7—41no—
212C22×C7—41no—
213C22×C7—41no—
214C22×C7—41no—
215C22×C7—41no—
216C22×C7—81no—
217C22×C7—81no—
218C22×C7C2×#9911yescharacteristic
219C22×C7#41711yescharacteristic
220C22×C7#42111yescharacteristic
221C4×C7—21no—
222C4×C7—21no—
223C4×C7—41no—
224C4×C7—41no—
225C4×C7—41no—
226C4×C7—41no—
227C4×C7—81no—
228C4×C7—81no—
229C4×C7—81no—
230C4×C7—81no—
231C4×C7—162no—
232C24C7×C22⋊C411yescharacteristic
233C24C2×C7×D411yescharacteristic
234C2×D4—21no—
235C2×D4—21no—
236C2×D4—41no—
237C2×D4—41no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—42no—
247C22×C4—81no—
248C22×C4—81no—
249C22×C4C7×C22⋊C411yescharacteristic
250C22×C4C7×C22⋊C411yescharacteristic
251C22×C4C7×C22⋊C411yescharacteristic
252C22×C4C22×C4×C711yescharacteristic
253C22×C4C2×C7×D411yescharacteristic
254M16—82no—
255C2×C8—42no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—42no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—81no—
263C4⋊C4—81no—
264C4⋊C4—82no—
265C22⋊C4—41no—
266C22⋊C4—41no—
267C22⋊C4—42no—
268C22⋊C4—41no—
269C22⋊C4—41no—
270C22⋊C4—42no—
271C22⋊C4—42no—
272C22⋊C4—81no—
273C22⋊C4—81no—
274C42—21no—
275C42—21no—
276C2×C7—21no—
277C2×C7—21no—
278C2×C7—41no—
279C2×C7—41no—
280C2×C7—81no—
281C2×C7#151311yescharacteristic
282C2×C7#212311yescharacteristic
283C2×C7#212711yescharacteristic
284C23—21no—
285C23—21no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23—41no—
290C23—41no—
291C23—41no—
292C23—41no—
293C23C2×C7×C22⋊C411yescharacteristic
294C23C7×AGL(1,ℤ/8)11yescharacteristic
295C23C7×#13711yescharacteristic
296D4—42no—
297D4—42no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—41no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—81no—
323C2×C4—81no—
324C2×C4—82no—
325C2×C4—82no—
326C2×C4—82no—
327C2×C4C7×#9911yescharacteristic
328C2×C4C7×#9911yescharacteristic
329C8—82no—
330C7#1182711yescharacteristic, direct product factor, Sylow
331C22—21no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—41no—
336C22—41no—
337C22—42no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—81no—
344C22—81no—
345C22C2×C7×#9911yescharacteristic
346C22C7×#41711yescharacteristic
347C22C7×#42111yescharacteristic
348C4—21no—
349C4—21no—
350C4—41no—
351C4—41no—
352C4—41no—
353C4—41no—
354C4—81no—
355C4—81no—
356C4—81no—
357C4—81no—
358C4—162no—
359C2—21no—
360C2—21no—
361C2—41no—
362C2—41no—
363C2—81no—
364C2C7×#151311yescharacteristic
365C2C7×#212311yescharacteristic
366C2C7×#212711yescharacteristic
subgroupG/H
center, socleC22×C7C2×#99
commutatorC22×C4C22×C4×C7
Frattini, cosocleC2×C22⋊C4C23×C7
prime radicalC22×C7×D4D4
LCSG ▷ C22×C4 ▷ C23 ▷ 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×#1352C2semidirect
5. C7×#1344C2semidirect
6. C2×C7×#125C4semidirect
10. C7×#399C4semidirect
13. C7×#397C4semidirect
18. C7×#383C4semidirect
23. #11827C7direct (N × H)
61. #1352C2×C7semidirect
62. #1344C2×C7semidirect
107. C2×#125C4×C7semidirect
111. #399C4×C7semidirect
114. #397C4×C7semidirect
119. #383C4×C7semidirect
330. C7#11827direct (N × H)

Maximal subgroups

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

subgroupindex
C7×#26332
C7×#17992
C7×#14652
C7×#13522
C7×#13442
#118277