Finite Group Databasebeta

← C7×#4665 #13055704

Subgroups — C7×#4665 #13055704

Order 1344.

572 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×D12C211yesmaximal, characteristic
2C22×C4×D3×C7C211yesmaximal, characteristic, complemented
3C2×C7×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
4C2×C7×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
5C2×C7×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
6C3×C7×#95C211yesmaximal, characteristic, complemented
7C7×C3⋊#95C211yesmaximal, characteristic, complemented
8C7×#386—31nomaximal, Hall
9C23×D3×C7C2211yescharacteristic
10C23×D3×C7C2211yescharacteristic
11C22×C3×C4×C7C2211yescharacteristic
12C22×C3×C4×C7C2211yescharacteristic
13C22×C3×C4×C7C2211yescharacteristic
14C22×C7×Dic3C2211yescharacteristic
15C22×C7×Dic3C2211yescharacteristic
16C2×C7×D12—22no—
17C2×C7×D12—22no—
18C2×C7×D12C414yescomplemented
19C2×C4×D3×C7—22no—
20C2×C4×D3×C7—22no—
21C2×C4×D3×C7—22no—
22C7×(C2×D3)⋊C4—22no—
23C7×(C2×D3)⋊C4—22no—
24C7×(C2×D3)⋊C4—22no—
25C22×C7×D4—31no—
26C23×C4×C7—31no—
27C2×C7×C22⋊C4—31no—
28C2×C7×C22⋊C4—31no—
29C2×C7×C22⋊C4—31no—
30C7×#95—31no—
31C7×#95D311yescharacteristic, complemented
32#4665C711yesmaximal, characteristic, direct product factor, Hall
33C23×C3×C7C2311yescharacteristic
34C22×D3×C7—21no—
35C22×D3×C7—21no—
36C22×D3×C7—21no—
37C22×D3×C7—21no—
38C22×D3×C7—21no—
39C22×D3×C7—21no—
40C22×D3×C7—21no—
41C22×D3×C7—21no—
42C22×D3×C7—21no—
43C22×D3×C7—21no—
44C22×D3×C7C2×C412yes—
45C22×D3×C7C2×C412yescomplemented
46C22×D3×C7D412yes—
47C22×D3×C7D412yes—
48C2×C3×C4×C7—21no—
49C2×C3×C4×C7—21no—
50C2×C3×C4×C7—21no—
51C2×C3×C4×C7—21no—
52C2×C3×C4×C7—21no—
53C2×C3×C4×C7—21no—
54C2×C3×C4×C7—21no—
55C2×C3×C4×C7C2×C412yescomplemented
56C2×C3×C4×C7D412yescomplemented
57C2×C7×Dic3—21no—
58C2×C7×Dic3—21no—
59C2×C7×Dic3—21no—
60C2×C7×Dic3—21no—
61C2×C7×Dic3—21no—
62C2×C7×Dic3D412yescomplemented
63C7×D12—28no—
64C4×D3×C7—28no—
65C24×C7—31no—
66C24×C7—31no—
67C2×C7×D4—34no—
68C2×C7×D4—62no—
69C2×C7×D4—62no—
70C22×C4×C7—31no—
71C22×C4×C7—31no—
72C22×C4×C7—62no—
73C22×C4×C7—62no—
74C22×C4×C7—62no—
75C22×C4×C7C2×D311yescharacteristic
76C22×C4×C7C2×D311yescharacteristic
77C22×C4×C7C2×D311yescharacteristic
78C7×C22⋊C4—62no—
79C7×C22⋊C4—62no—
80C7×C22⋊C4—62no—
81C22×D12C2×C711yescharacteristic
82C22×C4×D3C2×C711yescharacteristic, complemented
83C2×(C2×D3)⋊C4C2×C711yescharacteristic, complemented
84C2×(C2×D3)⋊C4C2×C711yescharacteristic, complemented
85C2×(C2×D3)⋊C4C2×C711yescharacteristic, complemented
86C3×#95C2×C711yescharacteristic, complemented
87C3⋊#95C2×C711yescharacteristic, complemented
88C22×C3×C7C22×C411yescharacteristic
89C22×C3×C7C2×D411yescharacteristic
90C22×C3×C7C2×D411yescharacteristic
91C22×C3×C7C2×D411yescharacteristic
92C22×C3×C7C2×D411yescharacteristic
93C22×C3×C7#4111yescharacteristic
94C22×C3×C7#4111yescharacteristic
95C2×D3×C7—22no—
96C2×D3×C7—22no—
97C2×D3×C7—22no—
98C2×D3×C7—22no—
99C2×D3×C7—22no—
100C2×D3×C7—22no—
101C2×D3×C7—22no—
102C2×D3×C7—22no—
103C2×D3×C7—22no—
104C2×D3×C7—41no—
105C2×D3×C7—41no—
106C2×D3×C7—41no—
107C2×D3×C7—41no—
108C2×D3×C7C22⋊C414yescomplemented
109C3×C4×C7—22no—
110C3×C4×C7—22no—
111C3×C4×C7—41no—
112C7×Dic3—22no—
113C7×Dic3—41no—
114#386—31noSylow
115C23×C7—32no—
116C23×C7—32no—
117C23×C7—32no—
118C23×C7—32no—
119C23×C7—61no—
120C23×C7—61no—
121C23×C7—61no—
122C23×C7—61no—
123C23×C7—61no—
124C23×C7—61no—
125C23×C7—61no—
126C23×C7—61no—
127C23×C7—61no—
128C23×C7—61no—
129C23×C7C22×D311yescharacteristic
130C7×D4—68no—
131C2×C4×C7—21no—
132C2×C4×C7—21no—
133C2×C4×C7—21no—
134C2×C4×C7—21no—
135C2×C4×C7—21no—
136C2×C4×C7—21no—
137C2×C4×C7—21no—
138C2×C4×C7—32no—
139C2×C4×C7—68no—
140C2×C4×C7—61no—
141C2×C4×C7—61no—
142C2×C4×C7—61no—
143C2×C4×C7—61no—
144C2×C4×C7—61no—
145C2×C4×C7C4×D312yescomplemented
146C2×C4×C7D1212yescomplemented
147C23×D3C22×C711yescharacteristic
148C23×D3C22×C711yescharacteristic
149C22×C3×C4C22×C711yescharacteristic
150C22×C3×C4C22×C711yescharacteristic
151C22×C3×C4C22×C711yescharacteristic
152C22×Dic3C22×C711yescharacteristic
153C22×Dic3C22×C711yescharacteristic
154C2×D12—22no—
155C2×D12—22no—
156C2×D12C4×C714yescomplemented
157C2×C4×D3—22no—
158C2×C4×D3—22no—
159C2×C4×D3—22no—
160(C2×D3)⋊C4—22no—
161(C2×D3)⋊C4—22no—
162(C2×D3)⋊C4—22no—
163C2×C3×C7C2×C22⋊C411yescharacteristic
164C2×C3×C7C4×D411yescharacteristic
165C2×C3×C7C4×D411yescharacteristic
166C2×C3×C7#12011yescharacteristic
167C2×C3×C7#12111yescharacteristic
168C2×C3×C7#12111yescharacteristic
169C2×C3×C7#12311yescharacteristic
170D3×C7—24no—
171D3×C7—42no—
172C22×D4—31no—
173C23×C4—31no—
174C2×C22⋊C4—31no—
175C2×C22⋊C4—31no—
176C2×C22⋊C4—31no—
177#95—31no—
178#95D3×C711yescharacteristic, complemented
179C22×C7—34no—
180C22×C7—62no—
181C22×C7—62no—
182C22×C7—62no—
183C22×C7—62no—
184C22×C7—62no—
185C22×C7—62no—
186C22×C7—62no—
187C22×C7—62no—
188C22×C7—62no—
189C22×C7—121no—
190C22×C7—121no—
191C22×C7—121no—
192C22×C7—121no—
193C22×C7C2×C4×D311yescharacteristic
194C22×C7C2×D1211yescharacteristic
195C22×C7#23511yescharacteristic
196C22×C7D3×D411yescharacteristic
197C22×C7D3×D411yescharacteristic
198C22×C7D3×D411yescharacteristic
199C22×C7#23911yescharacteristic
200C4×C7—22no—
201C4×C7—22no—
202C4×C7—41no—
203C4×C7—62no—
204C4×C7—121no—
205C23×C3C23×C711yescharacteristic
206C22×D3—21no—
207C22×D3—21no—
208C22×D3—21no—
209C22×D3—21no—
210C22×D3—21no—
211C22×D3—21no—
212C22×D3—21no—
213C22×D3—21no—
214C22×D3—21no—
215C22×D3—21no—
216C22×D3C2×C4×C712yes—
217C22×D3C2×C4×C712yescomplemented
218C22×D3C7×D412yes—
219C22×D3C7×D412yes—
220C2×C3×C4—21no—
221C2×C3×C4—21no—
222C2×C3×C4—21no—
223C2×C3×C4—21no—
224C2×C3×C4—21no—
225C2×C3×C4—21no—
226C2×C3×C4—21no—
227C2×C3×C4C2×C4×C712yescomplemented
228C2×C3×C4C7×D412yescomplemented
229C2×Dic3—21no—
230C2×Dic3—21no—
231C2×Dic3—21no—
232C2×Dic3—21no—
233C2×Dic3—21no—
234C2×Dic3C7×D412yescomplemented
235D12—28no—
236C4×D3—28no—
237C3×C7#38611yescharacteristic, complemented, Hall
238C24—31no—
239C24—31no—
240C2×D4—34no—
241C2×D4—62no—
242C2×D4—62no—
243C22×C4—31no—
244C22×C4—31no—
245C22×C4—62no—
246C22×C4—62no—
247C22×C4—62no—
248C22×C4C2×D3×C711yescharacteristic
249C22×C4C2×D3×C711yescharacteristic
250C22×C4C2×D3×C711yescharacteristic
251C22⋊C4—62no—
252C22⋊C4—62no—
253C22⋊C4—62no—
254C2×C7—64no—
255C2×C7—122no—
256C2×C7C4×D1211yescharacteristic
257C2×C7D3×C22⋊C411yescharacteristic
258C2×C7#88211yescharacteristic
259C2×C7#88411yescharacteristic
260C2×C7#89311yescharacteristic
261C2×C7#89411yescharacteristic
262C2×C7#89511yescharacteristic
263C22×C3C22×C4×C711yescharacteristic
264C22×C3C2×C7×D411yescharacteristic
265C22×C3C2×C7×D411yescharacteristic
266C22×C3C2×C7×D411yescharacteristic
267C22×C3C2×C7×D411yescharacteristic
268C22×C3C7×#4111yescharacteristic
269C22×C3C7×#4111yescharacteristic
270C2×D3—22no—
271C2×D3—22no—
272C2×D3—22no—
273C2×D3—22no—
274C2×D3—22no—
275C2×D3—22no—
276C2×D3—22no—
277C2×D3—22no—
278C2×D3—22no—
279C2×D3—41no—
280C2×D3—41no—
281C2×D3—41no—
282C2×D3—41no—
283C2×D3C7×C22⋊C414yescomplemented
284C3×C4—22no—
285C3×C4—22no—
286C3×C4—41no—
287Dic3—22no—
288Dic3—41no—
289C23—32no—
290C23—32no—
291C23—32no—
292C23—32no—
293C23—61no—
294C23—61no—
295C23—61no—
296C23—61no—
297C23—61no—
298C23—61no—
299C23—61no—
300C23—61no—
301C23—61no—
302C23—61no—
303C23C22×D3×C711yescharacteristic
304D4—68no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—32no—
313C2×C4—68no—
314C2×C4—61no—
315C2×C4—61no—
316C2×C4—61no—
317C2×C4—61no—
318C2×C4—61no—
319C2×C4C4×D3×C712yescomplemented
320C2×C4C7×D1212yescomplemented
321C7#466511yescharacteristic, direct product factor, Sylow
322C2×C3C2×C7×C22⋊C411yescharacteristic
323C2×C3C4×C7×D411yescharacteristic
324C2×C3C4×C7×D411yescharacteristic
325C2×C3C7×#12011yescharacteristic
326C2×C3C7×#12111yescharacteristic
327C2×C3C7×#12111yescharacteristic
328C2×C3C7×#12311yescharacteristic
329D3—24no—
330D3—42no—
331C22—34no—
332C22—62no—
333C22—62no—
334C22—62no—
335C22—62no—
336C22—62no—
337C22—62no—
338C22—62no—
339C22—62no—
340C22—62no—
341C22—121no—
342C22—121no—
343C22—121no—
344C22—121no—
345C22C2×C4×D3×C711yescharacteristic
346C22C2×C7×D1211yescharacteristic
347C22C7×#23511yescharacteristic
348C22D3×C7×D411yescharacteristic
349C22D3×C7×D411yescharacteristic
350C22D3×C7×D411yescharacteristic
351C22C7×#23911yescharacteristic
352C4—22no—
353C4—22no—
354C4—41no—
355C4—62no—
356C4—121no—
357C3C7×#38611yescharacteristic, complemented, Sylow
358C2—64no—
359C2—122no—
360C2C4×C7×D1211yescharacteristic
361C2D3×C7×C22⋊C411yescharacteristic
362C2C7×#88211yescharacteristic
363C2C7×#88411yescharacteristic
364C2C7×#89311yescharacteristic
365C2C7×#89411yescharacteristic
366C2C7×#89511yescharacteristic
subgroupG/H
centerC23×C7C22×D3
commutatorC22×C3C22×C4×C7
FrattiniC23C22×D3×C7
FittingC3×C7×#95C2
socleC23×C3×C7C23
prime radicalC22×C7×D12C2
cosocleC23×C3C23×C7
hypercenterC7×#95D3
hypocenterC3C7×#386
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C7 ◁ C7×#95

Complements

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

NH ≅ G/Ntype
2. C22×C4×D3×C7C2semidirect
3. C2×C7×(C2×D3)⋊C4C2semidirect
4. C2×C7×(C2×D3)⋊C4C2semidirect
5. C2×C7×(C2×D3)⋊C4C2semidirect
6. C3×C7×#95C2semidirect
7. C7×C3⋊#95C2semidirect
18. C2×C7×D12C4semidirect
31. C7×#95D3semidirect
32. #4665C7direct (N × H)
45. C22×D3×C7C2×C4semidirect
55. C2×C3×C4×C7C2×C4semidirect
56. C2×C3×C4×C7D4semidirect
62. C2×C7×Dic3D4semidirect
82. C22×C4×D3C2×C7semidirect
83. C2×(C2×D3)⋊C4C2×C7semidirect
84. C2×(C2×D3)⋊C4C2×C7semidirect
85. C2×(C2×D3)⋊C4C2×C7semidirect
86. C3×#95C2×C7semidirect
87. C3⋊#95C2×C7semidirect
108. C2×D3×C7C22⋊C4semidirect
145. C2×C4×C7C4×D3semidirect
146. C2×C4×C7D12semidirect
156. C2×D12C4×C7semidirect
178. #95D3×C7semidirect
217. C22×D3C2×C4×C7semidirect
227. C2×C3×C4C2×C4×C7semidirect
228. C2×C3×C4C7×D4semidirect
234. C2×Dic3C7×D4semidirect
237. C3×C7#386semidirect
283. C2×D3C7×C22⋊C4semidirect
319. C2×C4C4×D3×C7semidirect
320. C2×C4C7×D12semidirect
321. C7#4665direct (N × H)
357. C3C7×#386semidirect

Maximal subgroups

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

subgroupindex
C22×C7×D122
C22×C4×D3×C72
C2×C7×(C2×D3)⋊C42
C3×C7×#952
C7×C3⋊#952
C7×#3863
#46657