Finite Group Databasebeta

← #13249795

Subgroups — #13249795

Order 1792.

436 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 107 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×#2634C211yesmaximal, characteristic
2#11739881C211yesmaximal, characteristic
3#11729489C212yesmaximal
4C4×#6410C211yesmaximal, characteristic
5#11725439C212yesmaximal
6C2×C7×#125C2211yescharacteristic
7C2×C4×C7×Q8C2211yescharacteristic
8C7×#400—21no—
9C7×#400C411yescharacteristic
10C7×#400C411yescharacteristic
11C7×#398C411yescharacteristic
12C7×#398C411yescharacteristic
13C7×#395—21no—
14C7×#387—21no—
15C7×#387—21no—
16C7×#383C2211yescharacteristic
17C2×#6410—21no—
18#89796—24no—
19#89698—21no—
20#89698C2212yes—
21#89697—21no—
22C4×#1136C2212yes—
23#89338—24no—
24#89325—21no—
25#9190—71nomaximal, Sylow
26C22×C7×Q8D411yescharacteristic
27C7×#125—22no—
28C7×#125—22no—
29C4×C7×Q8—22no—
30C4×C7×Q8—22no—
31C2×C7×C4⋊C4—21no—
32C2×C7×C4⋊C4—21no—
33C2×C7×C4⋊C4—21no—
34C2×C7×C4⋊C4—21no—
35C2×C7×C4⋊C4C2×C411yescharacteristic
36C2×C7×C4⋊C4C2×C411yescharacteristic
37C2×C7×C4⋊C4C2×C411yescharacteristic
38C2×C7×C4⋊C4C2×C411yescharacteristic
39C2×C7×C4⋊C4D411yescharacteristic
40C2×C42×C7D411yescharacteristic
41C2×C42×C7D411yescharacteristic
42C2×C42×C7C2311yescharacteristic
43C2×#1136—22no—
44C7×#95—21no—
45C7×#95—21no—
46C7×#95—21no—
47C7×#95—21no—
48C7×#95—21no—
49C7×#95—21no—
50C7×#95—21no—
51C7×#95—21no—
52C7×#95C2×C411yescharacteristic
53C7×#95C2×C411yescharacteristic
54#6410—24no—
55C22⋊(C7⋊C8)—22no—
56C4⋊(C7⋊C8)—22no—
57C4⋊(C7⋊C8)—22no—
58C4⋊(C7⋊C8)—22no—
59#6377—22no—
60#6377—22no—
61#6377D414yes—
62C4×C7⋊C8—22no—
63C4×C7⋊C8—22no—
64#2983—71no—
65#2634D711yescharacteristic
66C4×#101—71no—
67#1528—72no—
68#1288—72no—
69C2×C7×Q8—22no—
70C2×C7×Q8—22no—
71C2×C7×Q8—41no—
72C22×C4×C7—21no—
73C22×C4×C7—21no—
74C22×C4×C7—21no—
75C22×C4×C7—21no—
76C22×C4×C7C22⋊C411yescharacteristic
77C22×C4×C7C22⋊C411yescharacteristic
78C22×C4×C7C22⋊C411yescharacteristic
79C22×C4×C7C22⋊C411yescharacteristic
80C22×C4×C7C22×C411yescharacteristic
81C22×C4×C7C2×D411yescharacteristic
82C22×C4×C7C2×D411yescharacteristic
83C7×C4⋊C4—22no—
84C7×C4⋊C4—22no—
85C7×C4⋊C4—22no—
86C7×C4⋊C4—22no—
87C7×C4⋊C4—22no—
88C7×C4⋊C4—42no—
89C7×C4⋊C4—42no—
90C7×C4⋊C4—41no—
91C7×C4⋊C4—42no—
92C7×C4⋊C4—41no—
93C42×C7—21no—
94C42×C7—21no—
95C42×C7—21no—
96C42×C7—21no—
97C42×C7C2×D412yes—
98C42×C7#4112yes—
99#1136—24no—
100#1136—42no—
101C2×C7⋊C8—24no—
102C2×C7⋊C8—42no—
103C2×#125C2×D711yescharacteristic
104C2×C4×Q8C2×D711yescharacteristic
105#446—144no—
106#432—72no—
107#432—141no—
108#431—141no—
109C2×#101—141no—
110C4×M16—72no—
111#400—21no—
112#400Dic711yescharacteristic
113#400Dic711yescharacteristic
114#398Dic711yescharacteristic
115#398Dic711yescharacteristic
116#395—21no—
117#387—21no—
118#387—21no—
119#383C2×D711yescharacteristic
120#343—141no—
121#330—144no—
122C23×C7C2×C22⋊C411yescharacteristic
123C7×Q8—44no—
124C2×C4×C7—21no—
125C2×C4×C7—21no—
126C2×C4×C7—21no—
127C2×C4×C7—21no—
128C2×C4×C7—21no—
129C2×C4×C7—21no—
130C2×C4×C7—21no—
131C2×C4×C7—21no—
132C2×C4×C7—21no—
133C2×C4×C7—41no—
134C2×C4×C7—41no—
135C2×C4×C7—41no—
136C2×C4×C7—41no—
137C2×C4×C7—41no—
138C2×C4×C7—41no—
139C2×C4×C7—41no—
140C2×C4×C7—41no—
141C2×C4×C7—42no—
142C2×C4×C7—41no—
143C2×C4×C7—41no—
144C2×C4×C7—41no—
145C2×C4×C7—41no—
146C2×C4×C7—41no—
147C2×C4×C7—41no—
148C2×C4×C7#10412yes—
149C2×C4×C7C4×D412yes—
150C2×C4×C7#12011yescharacteristic
151C2×C4×C7#12112yes—
152C2×C4×C7#12311yescharacteristic
153C7⋊C8—44no—
154C7⋊C8—44no—
155C22×Q8C22⋊D711yescharacteristic
156C2×M16—142no—
157#125—22no—
158#125—22no—
159C4×Q8—22no—
160C4×Q8—22no—
161C2×C4⋊C4—21no—
162C2×C4⋊C4—21no—
163C2×C4⋊C4—21no—
164C2×C4⋊C4—21no—
165C2×C4⋊C4C2×Dic711yescharacteristic
166C2×C4⋊C4C2×Dic711yescharacteristic
167C2×C4⋊C4C2×Dic711yescharacteristic
168C2×C4⋊C4C2×Dic711yescharacteristic
169C2×C4⋊C4C22⋊D711yescharacteristic
170C2×C42C22⋊D711yescharacteristic
171C2×C42C22⋊D711yescharacteristic
172C2×C42C22×D711yescharacteristic
173C4⋊C8—142no—
174C4⋊C8—142no—
175C4⋊C8—142no—
176#101—144no—
177C22⋊C8—142no—
178#97—74no—
179#97—142no—
180#97—142no—
181C4×C8—142no—
182C4×C8—142no—
183#95—21no—
184#95—21no—
185#95—21no—
186#95—21no—
187#95—21no—
188#95—21no—
189#95—21no—
190#95—21no—
191#95C2×Dic711yescharacteristic
192#95C2×Dic711yescharacteristic
193C22×C7—21no—
194C22×C7—21no—
195C22×C7#38611yescharacteristic
196C22×C7C2×#10411yescharacteristic
197C22×C7#42111yescharacteristic
198C4×C7—22no—
199C4×C7—22no—
200C4×C7—21no—
201C4×C7—21no—
202C4×C7—22no—
203C4×C7—41no—
204C4×C7—41no—
205C4×C7—41no—
206C4×C7—81no—
207C4×C7—81no—
208C4×C7—81no—
209C4×C7—81no—
210C2×Q8—22no—
211C2×Q8—22no—
212C2×Q8—41no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4C22⋊Dic711yescharacteristic
218C22×C4C22⋊Dic711yescharacteristic
219C22×C4C22⋊Dic711yescharacteristic
220C22×C4C22⋊Dic711yescharacteristic
221C22×C4C22×Dic711yescharacteristic
222C22×C4C2×C22⋊D711yescharacteristic
223C22×C4C2×C22⋊D711yescharacteristic
224M16—144no—
225M16—282no—
226C2×C8—144no—
227C2×C8—282no—
228C4⋊C4—22no—
229C4⋊C4—22no—
230C4⋊C4—22no—
231C4⋊C4—22no—
232C4⋊C4—22no—
233C4⋊C4—42no—
234C4⋊C4—42no—
235C4⋊C4—41no—
236C4⋊C4—41no—
237C4⋊C4—42no—
238C42—21no—
239C42—21no—
240C42—21no—
241C42—21no—
242C42D4×D712yes—
243C42#115912yes—
244C2×C7—21no—
245C2×C7—21no—
246C2×C7#187111yescharacteristic
247C2×C7#191211yescharacteristic
248C2×C7#191511yescharacteristic
249C23C2×C22⋊Dic711yescharacteristic
250Q8—44no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—42no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4#641112yes—
276C2×C4D4×Dic712yes—
277C2×C4#649811yescharacteristic
278C2×C4#650011yescharacteristic
279C2×C4#650212yes—
280C8—284no—
281C8—284no—
282C7#919011yescharacteristic, complemented, Sylow
283C22—21no—
284C22—21no—
285C22#8999211yescharacteristic
286C22C2×#641111yescharacteristic
287C22#9000811yescharacteristic
288C4—22no—
289C4—22no—
290C4—21no—
291C4—21no—
292C4—22no—
293C4—41no—
294C4—41no—
295C4—41no—
296C4—81no—
297C4—81no—
298C4—81no—
299C4—81no—
300C2—21no—
301C2—21no—
302C2#1172946711yescharacteristic
303C2#1172961811yescharacteristic
304C2#1172962011yescharacteristic
subgroupG/H
centerC22#89992
commutatorC22×C4×C7C22×C4
FrattiniC2×C42C22×D7
FittingC7×#2634C2
socleC22×C7#386
prime radicalC23×C7C2×C22⋊C4
cosocleC2×C42×C7C23
hypercenter#2634D7
hypocenterC7#9190
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2634

Complements

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

NH ≅ G/Ntype
282. C7#9190semidirect

Maximal subgroups

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

subgroupindex
C7×#26342
#117398812
#117294892
C4×#64102
#117254392
#91907