Finite Group Databasebeta

← #13263362

Subgroups — #13263362

Order 1792.

398 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 91 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×#2503C211yesmaximal, characteristic
2#11729306C211yesmaximal, characteristic
3C2×#89323C211yesmaximal, characteristic
4#11725449C212yesmaximal, complemented
5#11725438C212yesmaximal, complemented
6C2×C7×C22⋊Q8C411yescharacteristic
7C22×C7×C4⋊C4C2211yescharacteristic
8C7×#400—21no—
9C7×#400—21no—
10C7×#391C411yescharacteristic
11C7×#391C2211yescharacteristic
12C7×#382C411yescharacteristic
13C7×#382C2211yescharacteristic
14C7×#381—21no—
15C7×#381—21no—
16C4×C7×C22⋊C4C411yescharacteristic
17#89979—21no—
18C2×C22⋊(C7⋊C8)—21no—
19#89323—21no—
20#89323—21no—
21#89323C2212yes—
22#89323C2212yes—
23#11551—71nomaximal, Sylow
24C22×C7×Q8C2×C411yescharacteristic
25C23×C4×C7C2×C411yescharacteristic
26C23×C4×C7D411yescharacteristic
27C23×C4×C7D411yescharacteristic
28C7×C22⋊Q8—41no—
29C7×C22⋊Q8—41no—
30C2×C7×C4⋊C4—21no—
31C2×C7×C4⋊C4—41no—
32C2×C7×C4⋊C4—41no—
33C2×C7×C4⋊C4C2×C411yescharacteristic
34C2×C7×C4⋊C4C2×C411yescharacteristic
35C2×C7×C4⋊C4D411yescharacteristic
36C2×C7×C4⋊C4D411yescharacteristic
37C2×C7×C4⋊C4C2311yescharacteristic
38C2×C7×C22⋊C4—21no—
39C2×C7×C22⋊C4—21no—
40C2×C42×C7C2×C411yescharacteristic
41C2×C42×C7C2×C411yescharacteristic
42C2×#1136—41no—
43C22×C7⋊C8—41no—
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×#95—21no—
53C22⋊(C7⋊C8)—22no—
54C22⋊(C7⋊C8)—22no—
55C22⋊(C7⋊C8)—41no—
56C22⋊(C7⋊C8)—41no—
57#2503D711yescharacteristic
58#1463—71no—
59C2×#324—71no—
60#1324—72no—
61#1319—72no—
62C24×C7C22⋊C411yescharacteristic
63C2×C7×Q8—22no—
64C2×C7×Q8—41no—
65C2×C7×Q8—41no—
66C22×C4×C7—21no—
67C22×C4×C7—21no—
68C22×C4×C7—21no—
69C22×C4×C7—21no—
70C22×C4×C7—21no—
71C22×C4×C7—21no—
72C22×C4×C7—22no—
73C22×C4×C7—21no—
74C22×C4×C7—21no—
75C22×C4×C7—21no—
76C22×C4×C7—21no—
77C22×C4×C7—41no—
78C22×C4×C7—42no—
79C22×C4×C7—42no—
80C22×C4×C7C22⋊C411yescharacteristic
81C22×C4×C7C22⋊C411yescharacteristic
82C22×C4×C7C22⋊C411yescharacteristic
83C22×C4×C7C22×C411yescharacteristic
84C22×C4×C7C2×D411yescharacteristic
85C22×C4×C7C2×D411yescharacteristic
86C7×C4⋊C4—41no—
87C7×C4⋊C4—41no—
88C7×C4⋊C4—41no—
89C7×C4⋊C4—41no—
90C7×C4⋊C4—41no—
91C7×C4⋊C4—42no—
92C7×C22⋊C4—42no—
93C7×C22⋊C4—41no—
94C7×C22⋊C4—41no—
95C42×C7—22no—
96C42×C7—41no—
97#1136—82no—
98C2×C7⋊C8—42no—
99C2×C7⋊C8—42no—
100C2×C7⋊C8—82no—
101C2×C22⋊Q8Dic711yescharacteristic
102C22×C4⋊C4C2×D711yescharacteristic
103#407—141no—
104C2×C22⋊C8—141no—
105#400—21no—
106#400—21no—
107#391Dic711yescharacteristic
108#391C2×D711yescharacteristic
109#382Dic711yescharacteristic
110#382C2×D711yescharacteristic
111#381—21no—
112#381—21no—
113C4×C22⋊C4Dic711yescharacteristic
114#324—72no—
115#324—72no—
116#324—141no—
117#324—141no—
118C23×C7—22no—
119C23×C7—21no—
120C23×C7—21no—
121C23×C7—41no—
122C23×C7#9911yescharacteristic
123C23×C7#9911yescharacteristic
124C23×C7C2×C22⋊C411yescharacteristic
125C7×Q8—82no—
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—21no—
134C2×C4×C7—21no—
135C2×C4×C7—42no—
136C2×C4×C7—42no—
137C2×C4×C7—42no—
138C2×C4×C7—42no—
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—41no—
146C2×C4×C7—41no—
147C2×C4×C7—42no—
148C2×C4×C7—41no—
149C2×C4×C7—41no—
150C2×C4×C7—41no—
151C2×C4×C7—41no—
152C2×C4×C7—41no—
153C2×C4×C7—41no—
154C2×C4×C7—81no—
155C2×C4×C7—81no—
156C2×C4×C7#13112yes—
157C7⋊C8—82no—
158C7⋊C8—82no—
159C22×Q8C2×Dic711yescharacteristic
160C23×C4C2×Dic711yescharacteristic
161C23×C4C22⋊D711yescharacteristic
162C23×C4C22⋊D711yescharacteristic
163C2×M16—281no—
164C22×C8—281no—
165C22⋊Q8—41no—
166C22⋊Q8—41no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4—41no—
169C2×C4⋊C4—41no—
170C2×C4⋊C4C2×Dic711yescharacteristic
171C2×C4⋊C4C2×Dic711yescharacteristic
172C2×C4⋊C4C22⋊D711yescharacteristic
173C2×C4⋊C4C22⋊D711yescharacteristic
174C2×C4⋊C4C22×D711yescharacteristic
175C2×C22⋊C4—21no—
176C2×C22⋊C4—21no—
177C2×C42C2×Dic711yescharacteristic
178C2×C42C2×Dic711yescharacteristic
179C22⋊C8—142no—
180C22⋊C8—142no—
181C22⋊C8—281no—
182C22⋊C8—281no—
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#95—21no—
192C22×C7—21no—
193C22×C7—21no—
194C22×C7—21no—
195C22×C7—21no—
196C22×C7—21no—
197C22×C7—21no—
198C22×C7—21no—
199C22×C7—42no—
200C22×C7—42no—
201C22×C7#35412yes—
202C22×C7#40811yescharacteristic
203C22×C7C2×#9911yescharacteristic
204C22×C7#41311yescharacteristic
205C4×C7—22no—
206C4×C7—41no—
207C4×C7—41no—
208C4×C7—41no—
209C4×C7—41no—
210C4×C7—41no—
211C4×C7—81no—
212C4×C7—81no—
213C4×C7—81no—
214C4×C7—81no—
215C24C22⋊Dic711yescharacteristic
216C2×Q8—22no—
217C2×Q8—41no—
218C2×Q8—41no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—22no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—41no—
231C22×C4—42no—
232C22×C4—42no—
233C22×C4C22⋊Dic711yescharacteristic
234C22×C4C22⋊Dic711yescharacteristic
235C22×C4C22⋊Dic711yescharacteristic
236C22×C4C22×Dic711yescharacteristic
237C22×C4C2×C22⋊D711yescharacteristic
238C22×C4C2×C22⋊D711yescharacteristic
239M16—562no—
240C2×C8—282no—
241C2×C8—282no—
242C2×C8—562no—
243C4⋊C4—41no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—42no—
249C22⋊C4—42no—
250C22⋊C4—41no—
251C22⋊C4—41no—
252C42—22no—
253C42—41no—
254C2×C7—21no—
255C2×C7—21no—
256C2×C7—22no—
257C2×C7—41no—
258C2×C7#146811yescharacteristic
259C2×C7C2×#35411yescharacteristic
260C2×C7#213311yescharacteristic
261C23—21no—
262C23—21no—
263C23—22no—
264C23—41no—
265C23#640811yescharacteristic
266C23#640811yescharacteristic
267C23C2×C22⋊Dic711yescharacteristic
268Q8—82no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—42no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—81no—
298C2×C4—81no—
299C2×C4#651112yes—
300C8—562no—
301C8—562no—
302C7#1155111yescharacteristic, complemented, Sylow
303C22—21no—
304C22—21no—
305C22—21no—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—42no—
311C22—42no—
312C22#8933612yes—
313C22C2×#640811yescharacteristic
314C22#9000611yescharacteristic
315C22#9000911yescharacteristic
316C4—22no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4—81no—
323C4—81no—
324C4—81no—
325C4—81no—
326C2—21no—
327C2—21no—
328C2—22no—
329C2—41no—
330C2#1172945611yescharacteristic
331C2C2×#8933611yescharacteristic
332C2#1172962611yescharacteristic
subgroupG/H
centerC22C2×#6408
commutatorC22×C4×C7C22×C4
FrattiniC2×C4⋊C4C22×D7
FittingC7×#2503C2
socleC22×C7C2×#99
prime radicalC24×C7C22⋊C4
cosocleC2×C7×C4⋊C4C23
hypercenter#2503D7
hypocenterC7#11551
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ #2503

Complements

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

NH ≅ G/Ntype
4. #11725449C2semidirect
5. #11725438C2semidirect
302. C7#11551semidirect

Maximal subgroups

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

subgroupindex
C7×#25032
#117293062
C2×#893232
#117254492
#117254382
#115517