Finite Group Databasebeta

← C7×#9295 #13186511

Subgroups — C7×#9295 #13186511

Order 1792.

594 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#3208C211yesmaximal, characteristic
2C7×#2328C211yesmaximal, characteristic
3C7×#1995C211yesmaximal, characteristic, complemented
4C7×#1545C211yesmaximal, characteristic
5C7×#1518C211yesmaximal, characteristic, complemented
6C7×#1286C211yesmaximal, characteristic, complemented
7C7×#1274C211yesmaximal, characteristic, complemented
8C7×#533C2211yescharacteristic
9C2×C7×#127C2211yescharacteristic
10C2×C4×C7×D4—21no—
11C7×#492C412yescomplemented
12C7×#486C412yescomplemented
13C7×#460—22no—
14C7×#450—22no—
15C7×#431C2211yescharacteristic
16C7×#431C2211yescharacteristic
17C7×#423C2211yescharacteristic
18C7×#390—21no—
19C7×#386—22no—
20C7×#386—22no—
21C7×#382C2211yescharacteristic
22C7×#376C2211yescharacteristic
23C7×#339—21no—
24C7×#339—21no—
25C7×#331—22no—
26C7×#328—22no—
27#9295C711yesmaximal, characteristic, direct product factor, Sylow
28C22×C7×D4—21no—
29C22×C7×D4—21no—
30C22×C7×D4D412yes—
31C23×C4×C7—22no—
32C2×C7×SD16—24no—
33C2×C7×M16—21no—
34C7×C4⋊Q8C2×C411yescharacteristic, complemented
35C7×C4⋊Q8C2×C411yescharacteristic, complemented
36C7×#127—21no—
37C7×#127—21no—
38C7×#127C2×C412yes—
39C7×#127D412yes—
40C7×#125—21no—
41C7×C22⋊Q8—21no—
42C7×C22⋊Q8—21no—
43C4×C7×Q8—21no—
44C4×C7×Q8—21no—
45C4×C7×D4—42no—
46C4×C7×D4—42no—
47C7×#117—21no—
48C2×C7×C4⋊C4—21no—
49C2×C7×C22⋊C4—22no—
50C2×C7×C22⋊C4—22no—
51C2×C7×C22⋊C4—22no—
52C2×C42×C7D411yescharacteristic
53C2×C42×C7D411yescharacteristic
54C2×C42×C7C2311yescharacteristic
55C7×C4⋊C8—21no—
56C7×C4⋊C8—21no—
57C7×C4⋊C8—21no—
58C7×C4⋊C8—21no—
59C7×#102—24no—
60C7×C22⋊C8—21no—
61C7×C22⋊C8—21no—
62C4×C7×C8—21no—
63C4×C7×C8C2×C412yescomplemented
64C7×#95—21no—
65C7×#95—21no—
66C7×#95—21no—
67C7×#95D412yes—
68#3208C2×C711yescharacteristic
69#2328C2×C711yescharacteristic
70#1995C2×C711yescharacteristic, complemented
71#1545C2×C711yescharacteristic
72#1518C2×C711yescharacteristic, complemented
73#1286C2×C711yescharacteristic, complemented
74#1274C2×C711yescharacteristic, complemented
75C24×C7—22no—
76C2×C7×Q8—21no—
77C2×C7×Q8—21no—
78C2×C7×D4—22no—
79C2×C7×D4—22no—
80C2×C7×D4—22no—
81C2×C7×D4—22no—
82C2×C7×D4—22no—
83C2×C7×D4—41no—
84C2×C7×D4—41no—
85C2×C7×D4—41no—
86C2×C7×D4—41no—
87C2×C7×D4—82no—
88C2×C7×D4—82no—
89C2×C7×D4C22⋊C414yes—
90C22×C4×C7—21no—
91C22×C4×C7—21no—
92C22×C4×C7—22no—
93C22×C4×C7—44no—
94C22×C4×C7—82no—
95C22×C4×C7—82no—
96C22×C4×C7C2×D411yescharacteristic
97C22×C4×C7C2×D411yescharacteristic
98C22×C4×C7C2×D411yescharacteristic
99C7×SD16—84no—
100C7×M16—41no—
101C7×M16—41no—
102C2×C7×C8—22no—
103C2×C7×C8—41no—
104C2×C7×C8—41no—
105C7×C4⋊C4—21no—
106C7×C4⋊C4—21no—
107C7×C4⋊C4—21no—
108C7×C4⋊C4—21no—
109C7×C4⋊C4—41no—
110C7×C4⋊C4—41no—
111C7×C4⋊C4—41no—
112C7×C4⋊C4—41no—
113C7×C22⋊C4—44no—
114C7×C22⋊C4—41no—
115C7×C22⋊C4—82no—
116C7×C22⋊C4—82no—
117C42×C7—21no—
118C42×C7—21no—
119C42×C7—21no—
120C42×C7—41no—
121C42×C7SD1612yescomplemented
122C42×C7C22×C411yescharacteristic
123C42×C7C2×D411yescharacteristic
124C42×C7#4111yescharacteristic
125C42×C7#4111yescharacteristic
126#533C22×C711yescharacteristic
127C2×#127C22×C711yescharacteristic
128C2×C4×D4—21no—
129#492C4×C712yescomplemented
130#486C4×C712yescomplemented
131#460—22no—
132#450—22no—
133#431C22×C711yescharacteristic
134#431C22×C711yescharacteristic
135#423C22×C711yescharacteristic
136#390—21no—
137#386—22no—
138#386—22no—
139#382C22×C711yescharacteristic
140#376C22×C711yescharacteristic
141#339—21no—
142#339—21no—
143#331—22no—
144#328—22no—
145C23×C7—24no—
146C23×C7—42no—
147C23×C7—42no—
148C23×C7—42no—
149C23×C7—42no—
150C23×C7—42no—
151C23×C7—42no—
152C23×C7#12011yescharacteristic
153C7×Q8—42no—
154C7×Q8—81no—
155C7×D4—44no—
156C7×D4—42no—
157C7×D4—42no—
158C7×D4—42no—
159C7×D4—42no—
160C7×D4—82no—
161C7×D4—82no—
162C7×D4—82no—
163C2×C4×C7—22no—
164C2×C4×C7—41no—
165C2×C4×C7—41no—
166C2×C4×C7—41no—
167C2×C4×C7—41no—
168C2×C4×C7—41no—
169C2×C4×C7—41no—
170C2×C4×C7—42no—
171C2×C4×C7—42no—
172C2×C4×C7—41no—
173C2×C4×C7—41no—
174C2×C4×C7—42no—
175C2×C4×C7—41no—
176C2×C4×C7—88no—
177C2×C4×C7C2×C22⋊C411yescharacteristic
178C2×C4×C7C4×D411yescharacteristic
179C2×C4×C7C4×D411yescharacteristic
180C2×C4×C7#12111yescharacteristic
181C2×C4×C7#12111yescharacteristic
182C2×C4×C7#12311yescharacteristic
183C2×C4×C7C2×SD1611yescharacteristic
184C2×C4×C7#13511yescharacteristic
185C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
186C2×C4×C7#13711yescharacteristic
187C7×C8—42no—
188C7×C8—81no—
189C7×C8—81no—
190C22×D4—21no—
191C22×D4—21no—
192C22×D4C7×D412yes—
193C23×C4—22no—
194C2×SD16—24no—
195C2×M16—21no—
196C4⋊Q8C2×C4×C711yescharacteristic, complemented
197C4⋊Q8C2×C4×C711yescharacteristic, complemented
198#127—21no—
199#127—21no—
200#127C2×C4×C712yes—
201#127C7×D412yes—
202#125—21no—
203C22⋊Q8—21no—
204C22⋊Q8—21no—
205C4×Q8—21no—
206C4×Q8—21no—
207C4×D4—42no—
208C4×D4—42no—
209#117—21no—
210C2×C4⋊C4—21no—
211C2×C22⋊C4—22no—
212C2×C22⋊C4—22no—
213C2×C22⋊C4—22no—
214C2×C42C7×D411yescharacteristic
215C2×C42C7×D411yescharacteristic
216C2×C42C23×C711yescharacteristic
217C4⋊C8—21no—
218C4⋊C8—21no—
219C4⋊C8—21no—
220C4⋊C8—21no—
221#102—24no—
222C22⋊C8—21no—
223C22⋊C8—21no—
224C4×C8—21no—
225C4×C8C2×C4×C712yescomplemented
226#95—21no—
227#95—21no—
228#95—21no—
229#95C7×D412yes—
230C22×C7—21no—
231C22×C7—21no—
232C22×C7—44no—
233C22×C7—44no—
234C22×C7—44no—
235C22×C7—82no—
236C22×C7—82no—
237C22×C7—82no—
238C22×C7—82no—
239C22×C7#38611yescharacteristic
240C22×C7#45011yescharacteristic
241C22×C7#45211yescharacteristic
242C4×C7—21no—
243C4×C7—21no—
244C4×C7—21no—
245C4×C7—21no—
246C4×C7—42no—
247C4×C7—81no—
248C4×C7—82no—
249C4×C7—81no—
250C4×C7—81no—
251C4×C7C4×SD1611yescharacteristic
252C4×C7#44011yescharacteristic
253C4×C7#46111yescharacteristic
254C4×C7#46311yescharacteristic
255C24—22no—
256C2×Q8—21no—
257C2×Q8—21no—
258C2×D4—22no—
259C2×D4—22no—
260C2×D4—22no—
261C2×D4—22no—
262C2×D4—22no—
263C2×D4—41no—
264C2×D4—41no—
265C2×D4—41no—
266C2×D4—41no—
267C2×D4—82no—
268C2×D4—82no—
269C2×D4C7×C22⋊C414yes—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—22no—
273C22×C4—44no—
274C22×C4—82no—
275C22×C4—82no—
276C22×C4C2×C7×D411yescharacteristic
277C22×C4C2×C7×D411yescharacteristic
278C22×C4C2×C7×D411yescharacteristic
279SD16—84no—
280M16—41no—
281M16—41no—
282C2×C8—22no—
283C2×C8—41no—
284C2×C8—41no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4—21no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C22⋊C4—44no—
294C22⋊C4—41no—
295C22⋊C4—82no—
296C22⋊C4—82no—
297C42—21no—
298C42—21no—
299C42—21no—
300C42—41no—
301C42C7×SD1612yescomplemented
302C42C22×C4×C711yescharacteristic
303C42C2×C7×D411yescharacteristic
304C42C7×#4111yescharacteristic
305C42C7×#4111yescharacteristic
306C2×C7—21no—
307C2×C7—21no—
308C2×C7—84no—
309C2×C7#187711yescharacteristic
310C2×C7#190411yescharacteristic
311C2×C7#191111yescharacteristic
312C23—24no—
313C23—42no—
314C23—42no—
315C23—42no—
316C23—42no—
317C23—42no—
318C23—42no—
319C23C7×#12011yescharacteristic
320Q8—42no—
321Q8—81no—
322D4—44no—
323D4—42no—
324D4—42no—
325D4—42no—
326D4—42no—
327D4—82no—
328D4—82no—
329D4—82no—
330C2×C4—22no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—42no—
342C2×C4—41no—
343C2×C4—88no—
344C2×C4C2×C7×C22⋊C411yescharacteristic
345C2×C4C4×C7×D411yescharacteristic
346C2×C4C4×C7×D411yescharacteristic
347C2×C4C7×#12111yescharacteristic
348C2×C4C7×#12111yescharacteristic
349C2×C4C7×#12311yescharacteristic
350C2×C4C2×C7×SD1611yescharacteristic
351C2×C4C7×#13511yescharacteristic
352C2×C4C7×AGL(1,ℤ/8)11yescharacteristic
353C2×C4C7×#13711yescharacteristic
354C8—42no—
355C8—81no—
356C8—81no—
357C7#929511yescharacteristic, direct product factor, Sylow
358C22—21no—
359C22—21no—
360C22—44no—
361C22—44no—
362C22—44no—
363C22—82no—
364C22—82no—
365C22—82no—
366C22—82no—
367C22C7×#38611yescharacteristic
368C22C7×#45011yescharacteristic
369C22C7×#45211yescharacteristic
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—42no—
375C4—82no—
376C4—81no—
377C4—81no—
378C4—81no—
379C4C4×C7×SD1611yescharacteristic
380C4C7×#44011yescharacteristic
381C4C7×#46111yescharacteristic
382C4C7×#46311yescharacteristic
383C2—21no—
384C2—21no—
385C2—84no—
386C2C7×#187711yescharacteristic
387C2C7×#190411yescharacteristic
388C2C7×#191111yescharacteristic
subgroupG/H
center, socleC22×C7#386
commutatorC42C22×C4×C7
Frattini, cosocleC2×C42C23×C7
prime radicalC2×C7×#127C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G

Complements

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

NH ≅ G/Ntype
3. C7×#1995C2semidirect
5. C7×#1518C2semidirect
6. C7×#1286C2semidirect
7. C7×#1274C2semidirect
11. C7×#492C4semidirect
12. C7×#486C4semidirect
27. #9295C7direct (N × H)
34. C7×C4⋊Q8C2×C4semidirect
35. C7×C4⋊Q8C2×C4semidirect
63. C4×C7×C8C2×C4semidirect
70. #1995C2×C7semidirect
72. #1518C2×C7semidirect
73. #1286C2×C7semidirect
74. #1274C2×C7semidirect
121. C42×C7SD16semidirect
129. #492C4×C7semidirect
130. #486C4×C7semidirect
196. C4⋊Q8C2×C4×C7semidirect
197. C4⋊Q8C2×C4×C7semidirect
225. C4×C8C2×C4×C7semidirect
301. C42C7×SD16semidirect
357. C7#9295direct (N × H)

Maximal subgroups

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

subgroupindex
C7×#32082
C7×#23282
C7×#19952
C7×#15452
C7×#15182
C7×#12862
C7×#12742
#92957