Finite Group Databasebeta

← C7×#13121 #13190337

Subgroups — C7×#13121 #13190337

Order 1792.

382 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×C4⋊C16C211yesmaximal, characteristic, complemented
2C2×C7×C22⋊C16C211yesmaximal, characteristic
3C2×C7×C22⋊C16C211yesmaximal, characteristic
4C2×C7×#346C211yesmaximal, characteristic, complemented
5C7×C8×C22⋊C4C211yesmaximal, characteristic
6C7×#1374C211yesmaximal, characteristic, complemented
7C7×#1374C211yesmaximal, characteristic, complemented
8C23×C7×C8C2211yescharacteristic
9C22×C7×C16C2211yescharacteristic
10C22×C7×C16C2211yescharacteristic
11C22×C7×C16C2211yescharacteristic
12C22×C7×C16C2211yescharacteristic
13C2×C7×C22⋊C8C411yescharacteristic
14C2×C4×C7×C8C2211yescharacteristic
15C2×C4×C7×C8C2211yescharacteristic
16C4×C7×C22⋊C4C411yescharacteristic
17C7×C4⋊C16—22no—
18C7×C22⋊C16—22no—
19C7×C22⋊C16—22no—
20C7×#346—22no—
21C7×#336C411yescharacteristic
22C7×#336C411yescharacteristic
23#13121C711yesmaximal, characteristic, direct product factor, Sylow
24C23×C4×C7C2×C411yescharacteristic
25C22×C7×C8—21no—
26C22×C7×C8—21no—
27C22×C7×C8—21no—
28C22×C7×C8—21no—
29C22×C7×C8—21no—
30C22×C7×C8—21no—
31C22×C7×C8C2×C411yescharacteristic
32C22×C7×C8C2×C411yescharacteristic
33C22×C7×C8C2×C411yescharacteristic
34C22×C7×C8C2311yescharacteristic
35C2×C7×C22⋊C4C811yescharacteristic
36C2×C7×C22⋊C4C811yescharacteristic
37C2×C42×C7C2×C411yescharacteristic
38C2×C42×C7C2×C411yescharacteristic
39C2×C7×C16—21no—
40C2×C7×C16—21no—
41C2×C7×C16—21no—
42C2×C7×C16—21no—
43C2×C7×C16—21no—
44C2×C7×C16—21no—
45C2×C7×C16—21no—
46C2×C7×C16—21no—
47C2×C7×C16—21no—
48C2×C7×C16—21no—
49C2×C7×C16D412yes—
50C2×C7×C16D412yes—
51C7×C22⋊C8—22no—
52C4×C7×C8—21no—
53C4×C7×C8—21no—
54C4×C7×C8—21no—
55C4×C7×C8—21no—
56C7×#95C811yescharacteristic
57C7×#95C811yescharacteristic
58C2×C4⋊C16C2×C711yescharacteristic, complemented
59C2×C22⋊C16C2×C711yescharacteristic
60C2×C22⋊C16C2×C711yescharacteristic
61C2×#346C2×C711yescharacteristic, complemented
62C8×C22⋊C4C2×C711yescharacteristic
63#1374C2×C711yescharacteristic, complemented
64#1374C2×C711yescharacteristic, complemented
65C24×C7C2×C811yescharacteristic
66C22×C4×C7—21no—
67C22×C4×C7—21no—
68C22×C4×C7—21no—
69C22×C4×C7—21no—
70C22×C4×C7—21no—
71C22×C4×C7—21no—
72C22×C4×C7C2×C811yescharacteristic
73C22×C4×C7C2×C811yescharacteristic
74C22×C4×C7C2×C811yescharacteristic
75C22×C4×C7C2×C811yescharacteristic
76C22×C4×C7C2×C811yescharacteristic
77C22×C4×C7C22×C411yescharacteristic
78C2×C7×C8—21no—
79C2×C7×C8—21no—
80C2×C7×C8—21no—
81C2×C7×C8—21no—
82C2×C7×C8—21no—
83C2×C7×C8—21no—
84C2×C7×C8—21no—
85C2×C7×C8—21no—
86C2×C7×C8—41no—
87C2×C7×C8—41no—
88C2×C7×C8—41no—
89C2×C7×C8—41no—
90C2×C7×C8M1612yes—
91C2×C7×C8C2×D411yescharacteristic
92C2×C7×C8C2×D411yescharacteristic
93C2×C7×C8#4111yescharacteristic
94C2×C7×C8#4111yescharacteristic
95C2×C7×C8#4111yescharacteristic
96C2×C7×C8#4111yescharacteristic
97C7×C22⋊C4—22no—
98C7×C22⋊C4—22no—
99C42×C7—21no—
100C42×C7—21no—
101C42×C7—21no—
102C42×C7—21no—
103C7×C16—22no—
104C7×C16—22no—
105C7×C16—41no—
106C7×C16—41no—
107C23×C8C22×C711yescharacteristic
108C22×C16C22×C711yescharacteristic
109C22×C16C22×C711yescharacteristic
110C22×C16C22×C711yescharacteristic
111C22×C16C22×C711yescharacteristic
112C2×C22⋊C8C4×C711yescharacteristic
113C2×C4×C8C22×C711yescharacteristic
114C2×C4×C8C22×C711yescharacteristic
115C4×C22⋊C4C4×C711yescharacteristic
116C4⋊C16—22no—
117C22⋊C16—22no—
118C22⋊C16—22no—
119#346—22no—
120#336C4×C711yescharacteristic
121#336C4×C711yescharacteristic
122C23×C7—21no—
123C23×C7—21no—
124C23×C7—21no—
125C23×C7—21no—
126C23×C7—21no—
127C23×C7—21no—
128C23×C7M3212yes—
129C23×C7C22×C811yescharacteristic
130C2×C4×C7—21no—
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—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—41no—
146C2×C4×C7—41no—
147C2×C4×C7—41no—
148C2×C4×C7M3212yes—
149C2×C4×C7#11711yescharacteristic
150C2×C4×C7C4×D411yescharacteristic
151C2×C4×C7C4×D411yescharacteristic
152C2×C4×C7C2×M1611yescharacteristic
153C2×C4×C7#13111yescharacteristic
154C2×C4×C7#13111yescharacteristic
155C7×C8—22no—
156C7×C8—41no—
157C7×C8—41no—
158C7×C8#12111yescharacteristic
159C7×C8#12311yescharacteristic
160C7×C8#12411yescharacteristic
161C7×C8#12611yescharacteristic
162C23×C4C2×C4×C711yescharacteristic
163C22×C8—21no—
164C22×C8—21no—
165C22×C8—21no—
166C22×C8—21no—
167C22×C8—21no—
168C22×C8—21no—
169C22×C8C2×C4×C711yescharacteristic
170C22×C8C2×C4×C711yescharacteristic
171C22×C8C2×C4×C711yescharacteristic
172C22×C8C23×C711yescharacteristic
173C2×C22⋊C4C7×C811yescharacteristic
174C2×C22⋊C4C7×C811yescharacteristic
175C2×C42C2×C4×C711yescharacteristic
176C2×C42C2×C4×C711yescharacteristic
177C2×C16—21no—
178C2×C16—21no—
179C2×C16—21no—
180C2×C16—21no—
181C2×C16—21no—
182C2×C16—21no—
183C2×C16—21no—
184C2×C16—21no—
185C2×C16—21no—
186C2×C16—21no—
187C2×C16C7×D412yes—
188C2×C16C7×D412yes—
189C22⋊C8—22no—
190C4×C8—21no—
191C4×C8—21no—
192C4×C8—21no—
193C4×C8—21no—
194#95C7×C811yescharacteristic
195#95C7×C811yescharacteristic
196C22×C7—22no—
197C22×C7—22no—
198C22×C7—22no—
199C22×C7—41no—
200C22×C7—41no—
201C22×C7—41no—
202C22×C7—41no—
203C22×C7#43111yescharacteristic
204C22×C7C8×D411yescharacteristic
205C22×C7C8×D411yescharacteristic
206C22×C7C2×M3211yescharacteristic
207C22×C7C2×M3211yescharacteristic
208C22×C7#50411yescharacteristic
209C22×C7#50411yescharacteristic
210C4×C7—22no—
211C4×C7—41no—
212C4×C7—41no—
213C4×C7—41no—
214C4×C7—41no—
215C4×C7#38811yescharacteristic
216C4×C7#43311yescharacteristic
217C4×C7#43511yescharacteristic
218C4×C7#43611yescharacteristic
219C24C2×C7×C811yescharacteristic
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4C2×C7×C811yescharacteristic
227C22×C4C2×C7×C811yescharacteristic
228C22×C4C2×C7×C811yescharacteristic
229C22×C4C2×C7×C811yescharacteristic
230C22×C4C2×C7×C811yescharacteristic
231C22×C4C22×C4×C711yescharacteristic
232C2×C8—21no—
233C2×C8—21no—
234C2×C8—21no—
235C2×C8—21no—
236C2×C8—21no—
237C2×C8—21no—
238C2×C8—21no—
239C2×C8—21no—
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8C7×M1612yes—
245C2×C8C2×C7×D411yescharacteristic
246C2×C8C2×C7×D411yescharacteristic
247C2×C8C7×#4111yescharacteristic
248C2×C8C7×#4111yescharacteristic
249C2×C8C7×#4111yescharacteristic
250C2×C8C7×#4111yescharacteristic
251C22⋊C4—22no—
252C22⋊C4—22no—
253C42—21no—
254C42—21no—
255C42—21no—
256C42—21no—
257C16—22no—
258C16—22no—
259C16—41no—
260C16—41no—
261C2×C7—42no—
262C2×C7#192311yescharacteristic
263C2×C7#216311yescharacteristic
264C2×C7#216411yescharacteristic
265C2×C7#216811yescharacteristic
266C2×C7#216811yescharacteristic
267C2×C7#216811yescharacteristic
268C2×C7#216911yescharacteristic
269C23—21no—
270C23—21no—
271C23—21no—
272C23—21no—
273C23—21no—
274C23—21no—
275C23C7×M3212yes—
276C23C22×C7×C811yescharacteristic
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4C7×M3212yes—
296C2×C4C7×#11711yescharacteristic
297C2×C4C4×C7×D411yescharacteristic
298C2×C4C4×C7×D411yescharacteristic
299C2×C4C2×C7×M1611yescharacteristic
300C2×C4C7×#13111yescharacteristic
301C2×C4C7×#13111yescharacteristic
302C8—22no—
303C8—41no—
304C8—41no—
305C8C7×#12111yescharacteristic
306C8C7×#12311yescharacteristic
307C8C7×#12411yescharacteristic
308C8C7×#12611yescharacteristic
309C7#1312111yescharacteristic, direct product factor, Sylow
310C22—22no—
311C22—22no—
312C22—22no—
313C22—41no—
314C22—41no—
315C22—41no—
316C22—41no—
317C22C7×#43111yescharacteristic
318C22C7×C8×D411yescharacteristic
319C22C7×C8×D411yescharacteristic
320C22C2×C7×M3211yescharacteristic
321C22C2×C7×M3211yescharacteristic
322C22C7×#50411yescharacteristic
323C22C7×#50411yescharacteristic
324C4—22no—
325C4—41no—
326C4—41no—
327C4—41no—
328C4—41no—
329C4C7×#38811yescharacteristic
330C4C7×#43311yescharacteristic
331C4C7×#43511yescharacteristic
332C4C7×#43611yescharacteristic
333C2—42no—
334C2C7×#192311yescharacteristic
335C2C7×#216311yescharacteristic
336C2C7×#216411yescharacteristic
337C2C7×#216811yescharacteristic
338C2C7×#216811yescharacteristic
339C2C7×#216811yescharacteristic
340C2C7×#216911yescharacteristic
subgroupG/H
centerC22×C7×C8C23
commutatorC23C22×C7×C8
Frattini, cosocleC22×C8C23×C7
socleC23×C7C22×C8
prime radicalC24×C7C2×C8
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C7×C8 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C7×C4⋊C16C2semidirect
4. C2×C7×#346C2semidirect
6. C7×#1374C2semidirect
7. C7×#1374C2semidirect
23. #13121C7direct (N × H)
58. C2×C4⋊C16C2×C7semidirect
61. C2×#346C2×C7semidirect
63. #1374C2×C7semidirect
64. #1374C2×C7semidirect
309. C7#13121direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×C4⋊C162
C2×C7×C22⋊C162
C2×C7×#3462
C7×C8×C22⋊C42
C7×#13742
#131217