Finite Group Databasebeta

← C4×C7×#557 #13211385

Subgroups — C4×C7×#557 #13211385

Order 1792.

2220 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#557C211yesmaximal, characteristic
2C7×#2370C216yesmaximal
3C7×#2365C213yesmaximal
4C7×#2355C213yesmaximal
5C7×#2351C212yesmaximal
6C7×Q8×C4⋊C4C211yesmaximal, characteristic
7C4×C7×C4⋊Q8C213yesmaximal
8C4×C7×#125C216yesmaximal
9C42×C7×Q8C212yesmaximal
10C42×C7×Q8C213yesmaximal
11C42×C7×Q8C211yesmaximal, characteristic
12C7×#557C4116yesdirect product factor
13C2×C7×C4⋊Q8C2213yes—
14C2×C7×#125C2216yes—
15C2×C4×C7×Q8C2213yes—
16C2×C4×C7×Q8C2212yes—
17C2×C4×C7×Q8C2211yescharacteristic
18C2×C4×C7×Q8C2213yes—
19C2×C4×C7×Q8C2211yescharacteristic
20C2×C4×C7×Q8C2212yes—
21C2×C4×C7×Q8C2213yes—
22C2×C4×C7×Q8C2211yescharacteristic
23C7×#391C2216yes—
24C7×#389C2216yes—
25C7×#389C2216yes—
26C7×#389C2216yes—
27C7×#389C2216yes—
28C7×#387C22112yes—
29C7×#387C22112yes—
30C7×#384C2213yes—
31C7×#382C2216yes—
32C4×C7×C4⋊C4C2211yescharacteristic
33C4×C7×C4⋊C4C2216yes—
34C4×C7×C4⋊C4C2213yes—
35C4×C7×C4⋊C4C2216yes—
36C4×C7×C4⋊C4C2213yes—
37C4×C7×C4⋊C4C2216yes—
38C4×C7×C4⋊C4C2213yes—
39C4×C7×C4⋊C4C2213yes—
40C4×C7×C4⋊C4C2216yes—
41C4×C7×C4⋊C4C2216yes—
42C4×C7×C4⋊C4C2216yes—
43C4×C7×C4⋊C4C2213yes—
44C4×C7×C4⋊C4C2216yes—
45C43×C7C2216yes—
46C43×C7C2213yes—
47C4×#557C711yesmaximal, characteristic, direct product factor, Sylow
48C22×C7×Q8C2313yes—
49C22×C7×Q8C2311yescharacteristic
50C7×C4⋊Q8C2×C4124yes—
51C7×#125C2×C4148yes—
52C4×C7×Q8—28no—
53C4×C7×Q8—24no—
54C4×C7×Q8—212no—
55C4×C7×Q8—212no—
56C4×C7×Q8C2×C4116yes—
57C4×C7×Q8C2×C4124yes—
58C4×C7×Q8C2×C418yes—
59C4×C7×Q8Q818yescomplemented
60C2×C7×C4⋊C4C2313yes—
61C2×C7×C4⋊C4C2316yes—
62C2×C7×C4⋊C4C2313yes—
63C2×C7×C4⋊C4C2316yes—
64C2×C7×C4⋊C4C2316yes—
65C2×C7×C4⋊C4C2316yes—
66C2×C7×C4⋊C4C2311yescharacteristic
67C2×C7×C4⋊C4C2316yes—
68C2×C7×C4⋊C4C2313yes—
69C2×C7×C4⋊C4C2316yes—
70C2×C7×C4⋊C4C2316yes—
71C2×C7×C4⋊C4C2313yes—
72C2×C7×C4⋊C4C2311yescharacteristic
73C2×C42×C7C2316yes—
74C2×C42×C7C2313yes—
75C2×C42×C7C2316yes—
76C2×C42×C7C2313yes—
77C2×C42×C7C2312yes—
78C2×C42×C7C2313yes—
79C2×C42×C7C2316yes—
80C2×C42×C7C2316yes—
81C2×C42×C7C2313yes—
82C2×C42×C7C2316yes—
83C2×C42×C7C2313yes—
84C2×C42×C7C2313yes—
85C2×C42×C7C2311yescharacteristic
86C7×#95C2312yes—
87C7×#95C2316yes—
88C7×#95C2316yes—
89C7×#95C2316yes—
90C7×#95C23112yes—
91C7×#95C23112yes—
92C2×#557C2×C711yescharacteristic
93#2370C2×C716yes—
94#2365C2×C713yes—
95#2355C2×C713yes—
96#2351C2×C712yes—
97Q8×C4⋊C4C2×C711yescharacteristic
98C4×C4⋊Q8C2×C713yes—
99C4×#125C2×C716yes—
100C42×Q8C2×C713yes—
101C42×Q8C2×C712yes—
102C42×Q8C2×C711yescharacteristic
103C2×C7×Q8—26no—
104C2×C7×Q8—26no—
105C2×C7×Q8C22×C4112yes—
106C2×C7×Q8C22×C414yes—
107C2×C7×Q8C2×Q814yes—
108C2×C7×Q8#4114yes—
109C22×C4×C7C2413yes—
110C22×C4×C7C2416yes—
111C22×C4×C7C2412yes—
112C22×C4×C7C2413yes—
113C22×C4×C7C2416yes—
114C22×C4×C7C2413yes—
115C22×C4×C7C2412yes—
116C22×C4×C7C2411yescharacteristic
117C22×C4×C7C2413yes—
118C22×C4×C7C2411yescharacteristic
119C22×C4×C7C2411yescharacteristic
120C7×C4⋊C4—212no—
121C7×C4⋊C4—212no—
122C7×C4⋊C4—26no—
123C7×C4⋊C4—212no—
124C7×C4⋊C4—26no—
125C7×C4⋊C4—46no—
126C7×C4⋊C4C22×C414yes—
127C7×C4⋊C4C22×C4124yes—
128C7×C4⋊C4C22×C4112yes—
129C7×C4⋊C4C22×C4124yes—
130C7×C4⋊C4C22×C4124yes—
131C7×C4⋊C4C2×Q8112yes—
132C7×C4⋊C4#4114yes—
133C42×C7—212no—
134C42×C7—26no—
135C42×C7—212no—
136C42×C7—26no—
137C42×C7—212no—
138C42×C7—24no—
139C42×C7—26no—
140C42×C7—43no—
141C42×C7—46no—
142C42×C7C22×C4124yes—
143C42×C7C22×C4112yes—
144C42×C7C2×Q8112yes—
145C42×C7#4114yes—
146#557C4×C7116yesdirect product factor
147C2×C4⋊Q8C22×C713yes—
148C2×#125C22×C716yes—
149C2×C4×Q8C22×C713yes—
150C2×C4×Q8C22×C712yes—
151C2×C4×Q8C22×C711yescharacteristic
152C2×C4×Q8C22×C713yes—
153C2×C4×Q8C22×C711yescharacteristic
154C2×C4×Q8C22×C712yes—
155C2×C4×Q8C22×C713yes—
156C2×C4×Q8C22×C711yescharacteristic
157#391C22×C716yes—
158#389C22×C716yes—
159#389C22×C716yes—
160#389C22×C716yes—
161#389C22×C716yes—
162#387C22×C7112yes—
163#387C22×C7112yes—
164#384C22×C713yes—
165#382C22×C716yes—
166C4×C4⋊C4C22×C716yes—
167C4×C4⋊C4C22×C716yes—
168C4×C4⋊C4C22×C713yes—
169C4×C4⋊C4C22×C716yes—
170C4×C4⋊C4C22×C713yes—
171C4×C4⋊C4C22×C716yes—
172C4×C4⋊C4C22×C713yes—
173C4×C4⋊C4C22×C713yes—
174C4×C4⋊C4C22×C716yes—
175C4×C4⋊C4C22×C716yes—
176C4×C4⋊C4C22×C716yes—
177C4×C4⋊C4C22×C713yes—
178C4×C4⋊C4C22×C711yescharacteristic
179C43C22×C716yes—
180C43C22×C713yes—
181C23×C7C2511yescharacteristic
182C7×Q8—224no—
183C7×Q8C4×Q8116yescomplemented
184C2×C4×C7—23no—
185C2×C4×C7—21no—
186C2×C4×C7—22no—
187C2×C4×C7—26no—
188C2×C4×C7—26no—
189C2×C4×C7—22no—
190C2×C4×C7—23no—
191C2×C4×C7—22no—
192C2×C4×C7—22no—
193C2×C4×C7—23no—
194C2×C4×C7—21no—
195C2×C4×C7—23no—
196C2×C4×C7—26no—
197C2×C4×C7—26no—
198C2×C4×C7—23no—
199C2×C4×C7—23no—
200C2×C4×C7—23no—
201C2×C4×C7—26no—
202C2×C4×C7C23×C414yes—
203C2×C4×C7C23×C416yes—
204C2×C4×C7C23×C4112yes—
205C2×C4×C7C23×C416yes—
206C2×C4×C7C23×C412yes—
207C2×C4×C7C22×Q816yes—
208C2×C4×C7C22×Q816yes—
209C2×C4×C7C22×Q812yes—
210C2×C4×C7C2×#4114yes—
211C2×C4×C7C2×#4112yes—
212C2×C4×C7C2×#4116yes—
213C2×C4×C7C2×#4112yes—
214C2×C4×C7C2×#4112yes—
215C2×C4×C7C2×#4112yes—
216C2×C4×C72−1+412yes—
217C22×Q8C23×C713yes—
218C22×Q8C23×C711yescharacteristic
219C4⋊Q8C2×C4×C7124yes—
220#125C2×C4×C7148yes—
221C4×Q8—28no—
222C4×Q8—24no—
223C4×Q8—212no—
224C4×Q8—212no—
225C4×Q8C2×C4×C7116yes—
226C4×Q8C2×C4×C7124yes—
227C4×Q8C2×C4×C718yes—
228C4×Q8C7×Q818yescomplemented
229C2×C4⋊C4C23×C713yes—
230C2×C4⋊C4C23×C716yes—
231C2×C4⋊C4C23×C713yes—
232C2×C4⋊C4C23×C716yes—
233C2×C4⋊C4C23×C716yes—
234C2×C4⋊C4C23×C716yes—
235C2×C4⋊C4C23×C711yescharacteristic
236C2×C4⋊C4C23×C716yes—
237C2×C4⋊C4C23×C713yes—
238C2×C4⋊C4C23×C716yes—
239C2×C4⋊C4C23×C716yes—
240C2×C4⋊C4C23×C713yes—
241C2×C4⋊C4C23×C711yescharacteristic
242C2×C42C23×C716yes—
243C2×C42C23×C716yes—
244C2×C42C23×C713yes—
245C2×C42C23×C716yes—
246C2×C42C23×C713yes—
247C2×C42C23×C712yes—
248C2×C42C23×C713yes—
249C2×C42C23×C716yes—
250C2×C42C23×C713yes—
251C2×C42C23×C716yes—
252C2×C42C23×C713yes—
253C2×C42C23×C713yes—
254C2×C42C23×C711yescharacteristic
255#95C23×C712yes—
256#95C23×C716yes—
257#95C23×C716yes—
258#95C23×C716yes—
259#95C23×C7112yes—
260#95C23×C7112yes—
261C22×C7C24×C411yescharacteristic
262C22×C7C23×Q811yescharacteristic
263C22×C7C22×#4111yescharacteristic
264C22×C7C22×#4111yescharacteristic
265C22×C7C22×#4111yescharacteristic
266C22×C7C2×2−1+411yescharacteristic
267C22×C7#58511yescharacteristic
268C4×C7—212no—
269C4×C7—24no—
270C4×C7—26no—
271C4×C7—26no—
272C4×C7—22no—
273C4×C7—24no—
274C4×C7—46no—
275C4×C7—43no—
276C4×C7C2×C4×Q8112yes—
277C4×C7C4×#4114yes—
278C4×C7#55714yesdirect product factor
279C2×Q8—26no—
280C2×Q8—26no—
281C2×Q8C22×C4×C7112yes—
282C2×Q8C22×C4×C714yes—
283C2×Q8C2×C7×Q814yes—
284C2×Q8C7×#4114yes—
285C22×C4C24×C713yes—
286C22×C4C24×C716yes—
287C22×C4C24×C712yes—
288C22×C4C24×C713yes—
289C22×C4C24×C716yes—
290C22×C4C24×C713yes—
291C22×C4C24×C712yes—
292C22×C4C24×C711yescharacteristic
293C22×C4C24×C713yes—
294C22×C4C24×C711yescharacteristic
295C22×C4C24×C711yescharacteristic
296C4⋊C4—212no—
297C4⋊C4—212no—
298C4⋊C4—26no—
299C4⋊C4—212no—
300C4⋊C4—26no—
301C4⋊C4—46no—
302C4⋊C4C22×C4×C714yes—
303C4⋊C4C22×C4×C7124yes—
304C4⋊C4C22×C4×C7112yes—
305C4⋊C4C22×C4×C7124yes—
306C4⋊C4C22×C4×C7124yes—
307C4⋊C4C2×C7×Q8112yes—
308C4⋊C4C7×#4114yes—
309C42—212no—
310C42—26no—
311C42—212no—
312C42—26no—
313C42—212no—
314C42—24no—
315C42—26no—
316C42—43no—
317C42—46no—
318C42C22×C4×C7124yes—
319C42C22×C4×C7112yes—
320C42C2×C7×Q8112yes—
321C42C7×#4114yes—
322C2×C7C22×C4×Q811yescharacteristic
323C2×C7C2×C4×#4111yescharacteristic
324C2×C7C4×2−1+411yescharacteristic
325C2×C7C2×#55711yescharacteristic
326C2×C7Q8×#4111yescharacteristic
327C2×C7#348011yescharacteristic
328C2×C7#348211yescharacteristic
329C23C25×C711yescharacteristic
330Q8—224no—
331Q8C4×C7×Q8116yescomplemented
332C2×C4—23no—
333C2×C4—21no—
334C2×C4—22no—
335C2×C4—26no—
336C2×C4—26no—
337C2×C4—22no—
338C2×C4—23no—
339C2×C4—22no—
340C2×C4—22no—
341C2×C4—23no—
342C2×C4—21no—
343C2×C4—23no—
344C2×C4—26no—
345C2×C4—26no—
346C2×C4—23no—
347C2×C4—23no—
348C2×C4—23no—
349C2×C4—26no—
350C2×C4C23×C4×C714yes—
351C2×C4C23×C4×C716yes—
352C2×C4C23×C4×C7112yes—
353C2×C4C23×C4×C716yes—
354C2×C4C23×C4×C712yes—
355C2×C4C22×C7×Q816yes—
356C2×C4C22×C7×Q816yes—
357C2×C4C22×C7×Q812yes—
358C2×C4C2×C7×#4114yes—
359C2×C4C2×C7×#4112yes—
360C2×C4C2×C7×#4116yes—
361C2×C4C2×C7×#4112yes—
362C2×C4C2×C7×#4112yes—
363C2×C4C2×C7×#4112yes—
364C2×C4C7×2−1+412yes—
365C7C4×#55711yescharacteristic, direct product factor, Sylow
366C22C24×C4×C711yescharacteristic
367C22C23×C7×Q811yescharacteristic
368C22C22×C7×#4111yescharacteristic
369C22C22×C7×#4111yescharacteristic
370C22C22×C7×#4111yescharacteristic
371C22C2×C7×2−1+411yescharacteristic
372C22C7×#58511yescharacteristic
373C4—212no—
374C4—24no—
375C4—26no—
376C4—26no—
377C4—22no—
378C4—24no—
379C4—46no—
380C4—43no—
381C4C2×C4×C7×Q8112yes—
382C4C4×C7×#4114yes—
383C4C7×#55714yesdirect product factor
384C2C22×C4×C7×Q811yescharacteristic
385C2C2×C4×C7×#4111yescharacteristic
386C2C4×C7×2−1+411yescharacteristic
387C2C2×C7×#55711yescharacteristic
388C2C7×Q8×#4111yescharacteristic
389C2C7×#348011yescharacteristic
390C2C7×#348211yescharacteristic
subgroupG/H
centerC22×C4×C7C24
commutatorC22C24×C4×C7
Frattini, cosocleC23C25×C7
socle, prime radicalC23×C7C25
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C4×C7 ◁ G

Complements

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

NH ≅ G/Ntype
12. C7×#557C4direct (N × H)
47. C4×#557C7direct (N × H)
59. C4×C7×Q8Q8semidirect
146. #557C4×C7direct (N × H)
183. C7×Q8C4×Q8semidirect
228. C4×Q8C7×Q8semidirect
278. C4×C7#557direct (N × H)
331. Q8C4×C7×Q8semidirect
365. C7C4×#557direct (N × H)
383. C4C7×#557direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5572
C7×#23702
C7×#23652
C7×#23552
C7×#23512
C7×Q8×C4⋊C42
C4×C7×C4⋊Q82
C4×C7×#1252
C42×C7×Q82
C4×#5577