Finite Group Databasebeta

← #13272489

Subgroups — #13272489

Order 1792.

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

normal subgroups only

This group has 396 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×#2565C211yesmaximal, characteristic
2#11729391C211yesmaximal, characteristic
3C4×#6410C211yesmaximal, characteristic
4#11725450C212yesmaximal
5#11725450C212yesmaximal
6C2×C7×#125C411yescharacteristic
7C2×C4×C7×Q8C2211yescharacteristic
8C7×#398—21no—
9C7×#398—21no—
10C7×#391C2211yescharacteristic
11C7×#391C2211yescharacteristic
12C7×#387—21no—
13C7×#387—21no—
14C7×#384C411yescharacteristic
15C7×#382C411yescharacteristic
16C4×C7×C4⋊C4C411yescharacteristic
17C2×#6410C2212yes—
18C2×#6410C2212yes—
19#89696—21no—
20C4×#1136—21no—
21#89325—21no—
22#89325—21no—
23#13303—71nomaximal, Sylow
24C22×C7×Q8C2311yescharacteristic
25C7×#125—41no—
26C7×#125—41no—
27C4×C7×Q8—41no—
28C4×C7×Q8—41no—
29C2×C7×C4⋊C4—21no—
30C2×C7×C4⋊C4—21no—
31C2×C7×C4⋊C4—21no—
32C2×C7×C4⋊C4—21no—
33C2×C7×C4⋊C4—21no—
34C2×C7×C4⋊C4C2×C411yescharacteristic
35C2×C7×C4⋊C4C2×C411yescharacteristic
36C2×C7×C4⋊C4C2×C411yescharacteristic
37C2×C7×C4⋊C4D411yescharacteristic
38C2×C7×C4⋊C4D411yescharacteristic
39C2×C42×C7C2×C411yescharacteristic
40C2×C42×C7C2×C411yescharacteristic
41C2×C42×C7C2×C411yescharacteristic
42C2×C42×C7D411yescharacteristic
43C2×C42×C7D411yescharacteristic
44C2×#1136—22no—
45C2×#1136—22no—
46C7×#95—21no—
47C7×#95—21no—
48C7×#95—21no—
49C7×#95—21no—
50C7×#95—21no—
51C7×#95—21no—
52C7×#95—21no—
53#6410—22no—
54#6410—24no—
55#6410Q814yes—
56C4⋊(C7⋊C8)—41no—
57C4⋊(C7⋊C8)—41no—
58#6377—41no—
59C4×C7⋊C8—41no—
60#2565D711yescharacteristic
61#1801—71no—
62C4×#101—71no—
63#1394—72no—
64#1394—72no—
65C2×C7×Q8—41no—
66C2×C7×Q8—41no—
67C2×C7×Q8C2×Q812yes—
68C2×C7×Q8#4112yes—
69C22×C4×C7—21no—
70C22×C4×C7—21no—
71C22×C4×C7—21no—
72C22×C4×C7—21no—
73C22×C4×C7C22⋊C411yescharacteristic
74C22×C4×C7C22⋊C411yescharacteristic
75C22×C4×C7C22⋊C411yescharacteristic
76C22×C4×C7C22⋊C411yescharacteristic
77C22×C4×C7C22×C411yescharacteristic
78C22×C4×C7C2×D411yescharacteristic
79C22×C4×C7C2×D411yescharacteristic
80C7×C4⋊C4—41no—
81C7×C4⋊C4—41no—
82C7×C4⋊C4—41no—
83C7×C4⋊C4—41no—
84C7×C4⋊C4—41no—
85C7×C4⋊C4—42no—
86C7×C4⋊C4—42no—
87C7×C4⋊C4—42no—
88C7×C4⋊C4—42no—
89C7×C4⋊C4—41no—
90C7×C4⋊C4—41no—
91C42×C7—21no—
92C42×C7—21no—
93C42×C7—21no—
94C42×C7—21no—
95C42×C7—21no—
96C42×C7—21no—
97C42×C7—41no—
98C42×C7—41no—
99#1136—24no—
100#1136—42no—
101#1136—42no—
102#1136—42no—
103C2×C7⋊C8—42no—
104C2×C7⋊C8—42no—
105C2×#125Dic711yescharacteristic
106C2×C4×Q8C2×D711yescharacteristic
107#423—141no—
108C2×#101—72no—
109C2×#101—72no—
110C4×M16—141no—
111#398—21no—
112#398—21no—
113#391C2×D711yescharacteristic
114#391C2×D711yescharacteristic
115#387—21no—
116#387—21no—
117#384Dic711yescharacteristic
118#382Dic711yescharacteristic
119C4×C4⋊C4Dic711yescharacteristic
120#343—141no—
121#343—141no—
122C23×C7C2×C22⋊C411yescharacteristic
123C7×Q8—42no—
124C7×Q8—42no—
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—22no—
132C2×C4×C7—21no—
133C2×C4×C7—21no—
134C2×C4×C7—21no—
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—41no—
142C2×C4×C7—41no—
143C2×C4×C7—41no—
144C2×C4×C7—41no—
145C2×C4×C7—42no—
146C2×C4×C7—41no—
147C2×C4×C7—41no—
148C2×C4×C7—41no—
149C2×C4×C7#9911yescharacteristic
150C2×C4×C7#9911yescharacteristic
151C2×C4×C7C4×Q812yes—
152C2×C4×C7C22⋊Q812yes—
153C2×C4×C7#12411yescharacteristic
154C2×C4×C7C4⋊Q811yescharacteristic
155C7⋊C8—44no—
156C7⋊C8—82no—
157C22×Q8C22×D711yescharacteristic
158C2×M16—142no—
159C2×M16—142no—
160#125—41no—
161#125—41no—
162C4×Q8—41no—
163C4×Q8—41no—
164C2×C4⋊C4—21no—
165C2×C4⋊C4—21no—
166C2×C4⋊C4—21no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4—21no—
169C2×C4⋊C4C2×Dic711yescharacteristic
170C2×C4⋊C4C2×Dic711yescharacteristic
171C2×C4⋊C4C2×Dic711yescharacteristic
172C2×C4⋊C4C22⋊D711yescharacteristic
173C2×C4⋊C4C22⋊D711yescharacteristic
174C2×C42C2×Dic711yescharacteristic
175C2×C42C2×Dic711yescharacteristic
176C2×C42C2×Dic711yescharacteristic
177C2×C42C22⋊D711yescharacteristic
178C2×C42C22⋊D711yescharacteristic
179C4⋊C8—281no—
180C4⋊C8—281no—
181#101—74no—
182#101—142no—
183#101—144no—
184#97—281no—
185C4×C8—281no—
186#95—21no—
187#95—21no—
188#95—21no—
189#95—21no—
190#95—21no—
191#95—21no—
192#95—21no—
193C22×C7—21no—
194C22×C7—21no—
195C22×C7#39111yescharacteristic
196C22×C7C2×#9911yescharacteristic
197C22×C7#41011yescharacteristic
198C4×C7—21no—
199C4×C7—21no—
200C4×C7—22no—
201C4×C7—21no—
202C4×C7—22no—
203C4×C7—21no—
204C4×C7—42no—
205C4×C7—41no—
206C4×C7—41no—
207C4×C7—41no—
208C4×C7—81no—
209C4×C7—81no—
210C4×C7—81no—
211C2×Q8—41no—
212C2×Q8—41no—
213C2×Q8Q8×D712yes—
214C2×Q8#116112yes—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4C22⋊Dic711yescharacteristic
220C22×C4C22⋊Dic711yescharacteristic
221C22×C4C22⋊Dic711yescharacteristic
222C22×C4C22⋊Dic711yescharacteristic
223C22×C4C22×Dic711yescharacteristic
224C22×C4C2×C22⋊D711yescharacteristic
225C22×C4C2×C22⋊D711yescharacteristic
226M16—144no—
227M16—282no—
228M16—282no—
229M16—282no—
230C2×C8—282no—
231C2×C8—282no—
232C4⋊C4—41no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—41no—
237C4⋊C4—42no—
238C4⋊C4—42no—
239C4⋊C4—42no—
240C4⋊C4—42no—
241C4⋊C4—41no—
242C4⋊C4—41no—
243C42—21no—
244C42—21no—
245C42—21no—
246C42—21no—
247C42—21no—
248C42—21no—
249C42—41no—
250C42—41no—
251C2×C7—21no—
252C2×C7—21no—
253C2×C7#199611yescharacteristic
254C2×C7#213211yescharacteristic
255C2×C7#213311yescharacteristic
256C23C2×C22⋊Dic711yescharacteristic
257Q8—42no—
258Q8—42no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—22no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—42no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4#640811yescharacteristic
284C2×C4#640811yescharacteristic
285C2×C4#650711yescharacteristic
286C2×C4Q8×Dic712yes—
287C2×C4#650912yes—
288C2×C4#651011yescharacteristic
289C8—284no—
290C8—562no—
291C7#1330311yescharacteristic, complemented, Sylow
292C22—21no—
293C22—21no—
294C22C2×#640811yescharacteristic
295C22#9000211yescharacteristic
296C22#9001211yescharacteristic
297C4—22no—
298C4—21no—
299C4—21no—
300C4—22no—
301C4—21no—
302C4—21no—
303C4—42no—
304C4—41no—
305C4—41no—
306C4—41no—
307C4—81no—
308C4—81no—
309C4—81no—
310C2—21no—
311C2—21no—
312C2#1172945511yescharacteristic
313C2#1172957411yescharacteristic
314C2#1172962611yescharacteristic
subgroupG/H
centerC22C2×#6408
commutatorC22×C4×C7C22×C4
FrattiniC22×Q8C22×D7
FittingC7×#2565C2
socleC22×C7C2×#99
prime radicalC23×C7C2×C22⋊C4
cosocleC22×C7×Q8C23
hypercenter#2565D7
hypocenterC7#13303
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2565

Complements

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

NH ≅ G/Ntype
291. C7#13303semidirect

Maximal subgroups

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

subgroupindex
C7×#25652
#117293912
C4×#64102
#117254502
#133037