Finite Group Databasebeta

← C7×#13463 #13190679

Subgroups — C7×#13463 #13190679

Order 1792.

484 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 98 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
1C7×#2804C211yesmaximal, characteristic
2C7×#1867C212yesmaximal
3C7×#1856C211yesmaximal, characteristic
4C7×#1393C211yesmaximal, characteristic
5C7×#1390C212yesmaximal
6C7×#518C2211yescharacteristic
7C7×#428—21no—
8C2×C7×#100C2211yescharacteristic
9C2×C7×#99C2212yes—
10C7×#400—21no—
11C7×#393—22no—
12C7×#391—21no—
13C7×#390C2211yescharacteristic
14C7×#386C2212yes—
15C7×#385—22no—
16C7×#385—22no—
17C7×#342—22no—
18C7×#339—21no—
19#13463C711yesmaximal, characteristic, direct product factor, Sylow
20C22×C7×Q8—21no—
21C22×C7×D4C2311yescharacteristic
22C23×C4×C7D412yes—
23C2×C7×M16—21no—
24C4×C7×D4—41no—
25C4×C7×D4—41no—
26C7×#117—21no—
27C2×C7×C4⋊C4—21no—
28C2×C7×C4⋊C4—21no—
29C2×C7×C4⋊C4—42no—
30C2×C7×C4⋊C4D411yescharacteristic
31C2×C7×C22⋊C4—22no—
32C2×C7×C22⋊C4—22no—
33C2×C7×C22⋊C4—22no—
34C2×C7×C22⋊C4—22no—
35C2×C7×C22⋊C4D412yes—
36C2×C42×C7D411yescharacteristic
37C7×#107—41no—
38C7×#106—41no—
39C7×#100—21no—
40C7×#100Q812yescomplemented
41C7×#99—22no—
42C7×#99Q814yescomplemented
43C7×#95—22no—
44C7×#95—22no—
45C7×#95—21no—
46C7×#95—22no—
47C7×#95—42no—
48#2804C2×C711yescharacteristic
49#1867C2×C712yes—
50#1856C2×C711yescharacteristic
51#1393C2×C711yescharacteristic
52#1390C2×C712yes—
53C24×C7C2×D412yes—
54C2×C7×Q8—42no—
55C2×C7×Q8—81no—
56C2×C7×Q8—81no—
57C2×C7×D4—41no—
58C2×C7×D4—41no—
59C2×C7×D4C2×Q811yescharacteristic
60C2×C7×D4C2×Q812yes—
61C2×C7×D4#4111yescharacteristic
62C22×C4×C7—21no—
63C22×C4×C7—22no—
64C22×C4×C7—21no—
65C22×C4×C7—22no—
66C22×C4×C7—22no—
67C22×C4×C7—22no—
68C22×C4×C7—42no—
69C22×C4×C7—42no—
70C22×C4×C7—82no—
71C22×C4×C7C2×D411yescharacteristic
72C7×M16—22no—
73C7×M16—41no—
74C2×C7×C8—41no—
75C7×C4⋊C4—21no—
76C7×C4⋊C4—21no—
77C7×C4⋊C4—41no—
78C7×C4⋊C4—81no—
79C7×C4⋊C4—81no—
80C7×C4⋊C4—84no—
81C7×C22⋊C4—24no—
82C7×C22⋊C4—44no—
83C7×C22⋊C4—42no—
84C7×C22⋊C4—42no—
85C7×C22⋊C4—41no—
86C7×C22⋊C4—42no—
87C7×C22⋊C4—82no—
88C42×C7—41no—
89C42×C7—41no—
90#518C22×C711yescharacteristic
91#428—21no—
92C2×#100C22×C711yescharacteristic
93C2×#99C22×C712yes—
94#400—21no—
95#393—22no—
96#391—21no—
97#390C22×C711yescharacteristic
98#386C22×C712yes—
99#385—22no—
100#385—22no—
101#342—22no—
102#339—21no—
103C23×C7—22no—
104C23×C7—22no—
105C23×C7—42no—
106C23×C7—42no—
107C23×C7#12011yescharacteristic
108C23×C7C22⋊Q812yes—
109C23×C7C4⋊Q812yes—
110C7×Q8—84no—
111C7×D4—41no—
112C7×D4—42no—
113C7×D4—41no—
114C2×C4×C7—21no—
115C2×C4×C7—21no—
116C2×C4×C7—22no—
117C2×C4×C7—41no—
118C2×C4×C7—41no—
119C2×C4×C7—44no—
120C2×C4×C7—42no—
121C2×C4×C7—42no—
122C2×C4×C7—42no—
123C2×C4×C7—42no—
124C2×C4×C7—42no—
125C2×C4×C7—44no—
126C2×C4×C7—41no—
127C2×C4×C7—41no—
128C2×C4×C7—41no—
129C2×C4×C7—42no—
130C2×C4×C7—42no—
131C2×C4×C7—82no—
132C2×C4×C7—82no—
133C2×C4×C7—82no—
134C2×C4×C7—82no—
135C2×C4×C7—82no—
136C2×C4×C7C22⋊Q811yescharacteristic
137C2×C4×C7C4⋊Q811yescharacteristic
138C7×C8—42no—
139C22×Q8—21no—
140C22×D4C23×C711yescharacteristic
141C23×C4C7×D412yes—
142C2×M16—21no—
143C4×D4—41no—
144C4×D4—41no—
145#117—21no—
146C2×C4⋊C4—21no—
147C2×C4⋊C4—21no—
148C2×C4⋊C4—42no—
149C2×C4⋊C4C7×D411yescharacteristic
150C2×C22⋊C4—22no—
151C2×C22⋊C4—22no—
152C2×C22⋊C4—22no—
153C2×C22⋊C4—22no—
154C2×C22⋊C4C7×D412yes—
155C2×C42C7×D411yescharacteristic
156#107—41no—
157#106—41no—
158#100—21no—
159#100C7×Q812yescomplemented
160#99—22no—
161#99C7×Q814yescomplemented
162#95—22no—
163#95—22no—
164#95—21no—
165#95—22no—
166#95—42no—
167C22×C7—21no—
168C22×C7—21no—
169C22×C7—22no—
170C22×C7—22no—
171C22×C7—42no—
172C22×C7—42no—
173C22×C7—42no—
174C22×C7—42no—
175C22×C7—82no—
176C22×C7#39511yescharacteristic
177C22×C7B(4,𝔽2)11yescharacteristic
178C22×C7#45811yescharacteristic
179C4×C7—21no—
180C4×C7—21no—
181C4×C7—42no—
182C4×C7—82no—
183C4×C7—84no—
184C4×C7—81no—
185C4×C7—81no—
186C4×C7—82no—
187C4×C7—81no—
188C24C2×C7×D412yes—
189C2×Q8—42no—
190C2×Q8—81no—
191C2×Q8—81no—
192C2×D4—41no—
193C2×D4—41no—
194C2×D4C2×C7×Q811yescharacteristic
195C2×D4C2×C7×Q812yes—
196C2×D4C7×#4111yescharacteristic
197C22×C4—21no—
198C22×C4—22no—
199C22×C4—21no—
200C22×C4—22no—
201C22×C4—22no—
202C22×C4—22no—
203C22×C4—42no—
204C22×C4—42no—
205C22×C4—82no—
206C22×C4C2×C7×D411yescharacteristic
207M16—22no—
208M16—41no—
209C2×C8—41no—
210C4⋊C4—21no—
211C4⋊C4—21no—
212C4⋊C4—41no—
213C4⋊C4—81no—
214C4⋊C4—81no—
215C4⋊C4—84no—
216C22⋊C4—24no—
217C22⋊C4—44no—
218C22⋊C4—42no—
219C22⋊C4—42no—
220C22⋊C4—41no—
221C22⋊C4—42no—
222C22⋊C4—82no—
223C42—41no—
224C42—41no—
225C2×C7—21no—
226C2×C7—21no—
227C2×C7—42no—
228C2×C7—42no—
229C2×C7#206211yescharacteristic
230C2×C7#219811yescharacteristic
231C2×C7#219911yescharacteristic
232C23—22no—
233C23—22no—
234C23—42no—
235C23—42no—
236C23C7×#12011yescharacteristic
237C23C7×C22⋊Q812yes—
238C23C7×C4⋊Q812yes—
239Q8—84no—
240D4—41no—
241D4—42no—
242D4—41no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—22no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—44no—
249C2×C4—42no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4—44no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—82no—
261C2×C4—82no—
262C2×C4—82no—
263C2×C4—82no—
264C2×C4—82no—
265C2×C4C7×C22⋊Q811yescharacteristic
266C2×C4C7×C4⋊Q811yescharacteristic
267C8—42no—
268C7#1346311yescharacteristic, direct product factor, Sylow
269C22—21no—
270C22—21no—
271C22—22no—
272C22—22no—
273C22—42no—
274C22—42no—
275C22—42no—
276C22—42no—
277C22—82no—
278C22C7×#39511yescharacteristic
279C22C7×B(4,𝔽2)11yescharacteristic
280C22C7×#45811yescharacteristic
281C4—21no—
282C4—21no—
283C4—42no—
284C4—82no—
285C4—84no—
286C4—81no—
287C4—81no—
288C4—82no—
289C4—81no—
290C2—21no—
291C2—21no—
292C2—42no—
293C2—42no—
294C2C7×#206211yescharacteristic
295C2C7×#219811yescharacteristic
296C2C7×#219911yescharacteristic
subgroupG/H
center, socleC22×C7B(4,𝔽2)
commutator, Frattini, cosocleC22×D4C23×C7
prime radicalC22×C7×D4C23
LCSG ▷ C22×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C7 ◁ C23×C7 ◁ C22×C7×D4 ◁ G

Complements

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

NH ≅ G/Ntype
19. #13463C7direct (N × H)
40. C7×#100Q8semidirect
42. C7×#99Q8semidirect
159. #100C7×Q8semidirect
161. #99C7×Q8semidirect
268. C7#13463direct (N × H)

Maximal subgroups

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

subgroupindex
C7×#28042
C7×#18672
C7×#18562
C7×#13932
C7×#13902
#134637