Finite Group Databasebeta

← C7×#11809 #13189025

Subgroups — C7×#11809 #13189025

Order 1792.

616 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 616 conjugacy classes of subgroups — too many to draw. Only its 106 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
1C2×C7×#399C211yesmaximal, characteristic
2C7×#1819C211yesmaximal, characteristic
3C7×#1462C211yesmaximal, characteristic
4C7×#1352C214yesmaximal, complemented
5C22×C7×C4⋊C4—21no—
6C22×C7×C4⋊C4C411yescharacteristic, complemented
7C22×C7×C22⋊C4—21no—
8C22×C7×C22⋊C4C2211yescharacteristic
9C7×#407—21no—
10C7×#399—21no—
11C7×#399—21no—
12C7×#399C412yescomplemented
13C7×#399C2212yes—
14C7×#379—21no—
15C2×C7×#95C411yescharacteristic, complemented
16C7×#342—21no—
17C7×#342C2212yes—
18C7×#323—21no—
19C7×#323C2212yes—
20#11809C711yesmaximal, characteristic, direct product factor, Sylow
21C25×C7D411yescharacteristic
22C23×C4×C7—21no—
23C23×C4×C7—21no—
24C23×C4×C7C2×C411yescharacteristic
25C23×C4×C7D411yescharacteristic
26C2×C7×M16—41no—
27C2×C7×C4⋊C4—22no—
28C2×C7×C4⋊C4—21no—
29C2×C7×C4⋊C4—22no—
30C2×C7×C4⋊C4—41no—
31C2×C7×C4⋊C4—41no—
32C2×C7×C4⋊C4—44no—
33C2×C7×C4⋊C4C2×C412yes—
34C2×C7×C22⋊C4—22no—
35C2×C7×C22⋊C4—22no—
36C2×C7×C22⋊C4—22no—
37C2×C7×C22⋊C4—41no—
38C2×C7×C22⋊C4—41no—
39C2×C7×C22⋊C4—44no—
40C2×C7×C22⋊C4—41no—
41C2×C7×C22⋊C4—41no—
42C2×C7×C22⋊C4C2×C411yescharacteristic
43C2×C7×C22⋊C4D411yescharacteristic
44C2×C7×C22⋊C4D411yescharacteristic
45C2×C7×C22⋊C4C2311yescharacteristic
46C7×C22⋊C8—22no—
47C7×C22⋊C8—41no—
48C7×#95—21no—
49C7×#95C2×C412yes—
50C2×#399C2×C711yescharacteristic
51#1819C2×C711yescharacteristic
52#1462C2×C711yescharacteristic
53#1352C2×C714yescomplemented
54C24×C7—22no—
55C24×C7—21no—
56C24×C7—21no—
57C24×C7—41no—
58C24×C7—42no—
59C24×C7—42no—
60C24×C7C22⋊C411yescharacteristic
61C24×C7C22⋊C411yescharacteristic
62C24×C7C2×D411yescharacteristic
63C22×C4×C7—24no—
64C22×C4×C7—21no—
65C22×C4×C7—21no—
66C22×C4×C7—21no—
67C22×C4×C7—22no—
68C22×C4×C7—21no—
69C22×C4×C7—22no—
70C22×C4×C7—42no—
71C22×C4×C7—42no—
72C22×C4×C7—42no—
73C22×C4×C7—42no—
74C22×C4×C7—42no—
75C22×C4×C7—42no—
76C22×C4×C7—41no—
77C22×C4×C7—41no—
78C22×C4×C7—42no—
79C22×C4×C7C22⋊C411yescharacteristic
80C22×C4×C7C22⋊C411yescharacteristic
81C22×C4×C7C22×C411yescharacteristic
82C22×C4×C7C2×D411yescharacteristic
83C7×M16—82no—
84C2×C7×C8—42no—
85C7×C4⋊C4—42no—
86C7×C4⋊C4—44no—
87C7×C4⋊C4—44no—
88C7×C4⋊C4—42no—
89C7×C22⋊C4—41no—
90C7×C22⋊C4—41no—
91C7×C22⋊C4—41no—
92C7×C22⋊C4—41no—
93C7×C22⋊C4—44no—
94C7×C22⋊C4—44no—
95C7×C22⋊C4—42no—
96C7×C22⋊C4—42no—
97C7×C22⋊C4—82no—
98C7×C22⋊C4—82no—
99C22×C4⋊C4—21no—
100C22×C4⋊C4C4×C711yescharacteristic, complemented
101C22×C22⋊C4—21no—
102C22×C22⋊C4C22×C711yescharacteristic
103#407—21no—
104#399—21no—
105#399—21no—
106#399C4×C712yescomplemented
107#399C22×C712yes—
108#379—21no—
109C2×#95C4×C711yescharacteristic, complemented
110#342—21no—
111#342C22×C712yes—
112#323—21no—
113#323C22×C712yes—
114C23×C7—22no—
115C23×C7—22no—
116C23×C7—21no—
117C23×C7—21no—
118C23×C7—21no—
119C23×C7—21no—
120C23×C7—21no—
121C23×C7—21no—
122C23×C7—21no—
123C23×C7—42no—
124C23×C7—42no—
125C23×C7—41no—
126C23×C7—41no—
127C23×C7—41no—
128C23×C7—41no—
129C23×C7—48no—
130C23×C7—42no—
131C23×C7—42no—
132C23×C7—81no—
133C23×C7—81no—
134C23×C7—84no—
135C23×C7#9911yescharacteristic
136C23×C7#9911yescharacteristic
137C23×C7C2×C22⋊C411yescharacteristic
138C23×C7#13712yes—
139C2×C4×C7—24no—
140C2×C4×C7—21no—
141C2×C4×C7—21no—
142C2×C4×C7—21no—
143C2×C4×C7—21no—
144C2×C4×C7—48no—
145C2×C4×C7—42no—
146C2×C4×C7—42no—
147C2×C4×C7—42no—
148C2×C4×C7—42no—
149C2×C4×C7—42no—
150C2×C4×C7—41no—
151C2×C4×C7—41no—
152C2×C4×C7—41no—
153C2×C4×C7—41no—
154C2×C4×C7—42no—
155C2×C4×C7—42no—
156C2×C4×C7—42no—
157C2×C4×C7—81no—
158C2×C4×C7—82no—
159C2×C4×C7—82no—
160C2×C4×C7—82no—
161C2×C4×C7—82no—
162C2×C4×C7—82no—
163C7×C8—82no—
164C25C7×D411yescharacteristic
165C23×C4—21no—
166C23×C4—21no—
167C23×C4C2×C4×C711yescharacteristic
168C23×C4C7×D411yescharacteristic
169C2×M16—41no—
170C2×C4⋊C4—22no—
171C2×C4⋊C4—21no—
172C2×C4⋊C4—22no—
173C2×C4⋊C4—41no—
174C2×C4⋊C4—41no—
175C2×C4⋊C4—44no—
176C2×C4⋊C4C2×C4×C712yes—
177C2×C22⋊C4—22no—
178C2×C22⋊C4—22no—
179C2×C22⋊C4—22no—
180C2×C22⋊C4—41no—
181C2×C22⋊C4—41no—
182C2×C22⋊C4—44no—
183C2×C22⋊C4—41no—
184C2×C22⋊C4—41no—
185C2×C22⋊C4C2×C4×C711yescharacteristic
186C2×C22⋊C4C7×D411yescharacteristic
187C2×C22⋊C4C7×D411yescharacteristic
188C2×C22⋊C4C23×C711yescharacteristic
189C22⋊C8—22no—
190C22⋊C8—41no—
191#95—21no—
192#95C2×C4×C712yes—
193C22×C7—24no—
194C22×C7—24no—
195C22×C7—21no—
196C22×C7—21no—
197C22×C7—21no—
198C22×C7—21no—
199C22×C7—21no—
200C22×C7—21no—
201C22×C7—22no—
202C22×C7—42no—
203C22×C7—42no—
204C22×C7—41no—
205C22×C7—41no—
206C22×C7—41no—
207C22×C7—41no—
208C22×C7—41no—
209C22×C7—81no—
210C22×C7—84no—
211C22×C7—84no—
212C22×C7—81no—
213C22×C7#35212yes—
214C22×C7#35312yes—
215C22×C7C2×#9911yescharacteristic
216C22×C7#41911yescharacteristic
217C22×C7#42111yescharacteristic
218C4×C7—44no—
219C4×C7—41no—
220C4×C7—41no—
221C4×C7—41no—
222C4×C7—41no—
223C4×C7—82no—
224C4×C7—162no—
225C24—22no—
226C24—21no—
227C24—21no—
228C24—41no—
229C24—42no—
230C24—42no—
231C24C7×C22⋊C411yescharacteristic
232C24C7×C22⋊C411yescharacteristic
233C24C2×C7×D411yescharacteristic
234C22×C4—24no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—22no—
239C22×C4—21no—
240C22×C4—22no—
241C22×C4—42no—
242C22×C4—42no—
243C22×C4—42no—
244C22×C4—42no—
245C22×C4—42no—
246C22×C4—42no—
247C22×C4—41no—
248C22×C4—41no—
249C22×C4—42no—
250C22×C4C7×C22⋊C411yescharacteristic
251C22×C4C7×C22⋊C411yescharacteristic
252C22×C4C22×C4×C711yescharacteristic
253C22×C4C2×C7×D411yescharacteristic
254M16—82no—
255C2×C8—42no—
256C4⋊C4—42no—
257C4⋊C4—44no—
258C4⋊C4—44no—
259C4⋊C4—42no—
260C22⋊C4—41no—
261C22⋊C4—41no—
262C22⋊C4—41no—
263C22⋊C4—41no—
264C22⋊C4—44no—
265C22⋊C4—44no—
266C22⋊C4—42no—
267C22⋊C4—42no—
268C22⋊C4—82no—
269C22⋊C4—82no—
270C2×C7—21no—
271C2×C7—21no—
272C2×C7—22no—
273C2×C7—22no—
274C2×C7—42no—
275C2×C7—81no—
276C2×C7#151111yescharacteristic
277C2×C7C2×#35211yescharacteristic
278C2×C7C2×#35311yescharacteristic
279C23—22no—
280C23—22no—
281C23—21no—
282C23—21no—
283C23—21no—
284C23—21no—
285C23—21no—
286C23—21no—
287C23—21no—
288C23—42no—
289C23—42no—
290C23—41no—
291C23—41no—
292C23—41no—
293C23—41no—
294C23—48no—
295C23—42no—
296C23—42no—
297C23—81no—
298C23—81no—
299C23—84no—
300C23C7×#9911yescharacteristic
301C23C7×#9911yescharacteristic
302C23C2×C7×C22⋊C411yescharacteristic
303C23C7×#13712yes—
304C2×C4—24no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—48no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—81no—
323C2×C4—82no—
324C2×C4—82no—
325C2×C4—82no—
326C2×C4—82no—
327C2×C4—82no—
328C8—82no—
329C7#1180911yescharacteristic, direct product factor, Sylow
330C22—24no—
331C22—24no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—22no—
339C22—42no—
340C22—42no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—81no—
347C22—84no—
348C22—84no—
349C22—81no—
350C22C7×#35212yes—
351C22C7×#35312yes—
352C22C2×C7×#9911yescharacteristic
353C22C7×#41911yescharacteristic
354C22C7×#42111yescharacteristic
355C4—44no—
356C4—41no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—82no—
361C4—162no—
362C2—21no—
363C2—21no—
364C2—22no—
365C2—22no—
366C2—42no—
367C2—81no—
368C2C7×#151111yescharacteristic
369C2C2×C7×#35211yescharacteristic
370C2C2×C7×#35311yescharacteristic
subgroupG/H
center, socleC22×C7C2×#99
commutatorC22×C4C22×C4×C7
Frattini, cosocleC2×C22⋊C4C23×C7
prime radicalC25×C7D4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C7 ◁ C24×C7 ◁ C22×C7×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
4. C7×#1352C2semidirect
6. C22×C7×C4⋊C4C4semidirect
12. C7×#399C4semidirect
15. C2×C7×#95C4semidirect
20. #11809C7direct (N × H)
53. #1352C2×C7semidirect
100. C22×C4⋊C4C4×C7semidirect
106. #399C4×C7semidirect
109. C2×#95C4×C7semidirect
329. C7#11809direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#3992
C7×#18192
C7×#14622
C7×#13522
#118097