Finite Group Databasebeta

← #13263382

Subgroups — #13263382

Order 1792.

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

normal subgroups only

This group has 414 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×#2502C211yesmaximal, characteristic
2#11729306C211yesmaximal, characteristic
3C2×#89323C211yesmaximal, characteristic
4#11725449C212yesmaximal, complemented
5#11725441C212yesmaximal, complemented
6C2×C7×C22⋊Q8C411yescharacteristic
7C22×C7×C4⋊C4C2211yescharacteristic
8C7×#398—21no—
9C7×#398—21no—
10C7×#391C411yescharacteristic
11C7×#391C2211yescharacteristic
12C7×#385—21no—
13C7×#385—21no—
14C7×#384C411yescharacteristic
15C7×#384C2211yescharacteristic
16C4×C7×C22⋊C4C411yescharacteristic
17#89979—21no—
18C2×C22⋊(C7⋊C8)—21no—
19#89323—21no—
20#89323—21no—
21#89323C2212yes—
22#89323C2212yes—
23#11555—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—21no—
32C2×C7×C4⋊C4—21no—
33C2×C7×C4⋊C4—21no—
34C2×C7×C4⋊C4—21no—
35C2×C7×C4⋊C4—41no—
36C2×C7×C4⋊C4—41no—
37C2×C7×C4⋊C4C2×C411yescharacteristic
38C2×C7×C4⋊C4C2×C411yescharacteristic
39C2×C7×C4⋊C4D411yescharacteristic
40C2×C7×C4⋊C4D411yescharacteristic
41C2×C7×C4⋊C4C2311yescharacteristic
42C2×C7×C22⋊C4—21no—
43C2×C7×C22⋊C4—21no—
44C2×C42×C7C2×C411yescharacteristic
45C2×C42×C7C2×C411yescharacteristic
46C2×#1136—41no—
47C22×C7⋊C8—41no—
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#2502D711yescharacteristic
58#1463—71no—
59C2×#324—71no—
60#1325—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—21no—
73C22×C4×C7—21no—
74C22×C4×C7—22no—
75C22×C4×C7—21no—
76C22×C4×C7—21no—
77C22×C4×C7—41no—
78C22×C4×C7—81no—
79C22×C4×C7—81no—
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×C4⋊C4—81no—
93C7×C4⋊C4—81no—
94C7×C4⋊C4—81no—
95C7×C4⋊C4—81no—
96C7×C22⋊C4—24no—
97C7×C22⋊C4—41no—
98C7×C22⋊C4—41no—
99C42×C7—22no—
100C42×C7—41no—
101#1136—82no—
102C2×C7⋊C8—42no—
103C2×C7⋊C8—42no—
104C2×C7⋊C8—82no—
105C2×C22⋊Q8Dic711yescharacteristic
106C22×C4⋊C4C2×D711yescharacteristic
107#407—141no—
108C2×C22⋊C8—141no—
109#398—21no—
110#398—21no—
111#391Dic711yescharacteristic
112#391C2×D711yescharacteristic
113#385—21no—
114#385—21no—
115#384Dic711yescharacteristic
116#384C2×D711yescharacteristic
117C4×C22⋊C4Dic711yescharacteristic
118#324—72no—
119#324—72no—
120#324—141no—
121#324—141no—
122C23×C7—22no—
123C23×C7—21no—
124C23×C7—21no—
125C23×C7—41no—
126C23×C7#9911yescharacteristic
127C23×C7#9911yescharacteristic
128C23×C7C2×C22⋊C411yescharacteristic
129C7×Q8—82no—
130C2×C4×C7—21no—
131C2×C4×C7—21no—
132C2×C4×C7—22no—
133C2×C4×C7—22no—
134C2×C4×C7—21no—
135C2×C4×C7—21no—
136C2×C4×C7—21no—
137C2×C4×C7—21no—
138C2×C4×C7—21no—
139C2×C4×C7—21no—
140C2×C4×C7—21no—
141C2×C4×C7—42no—
142C2×C4×C7—42no—
143C2×C4×C7—42no—
144C2×C4×C7—42no—
145C2×C4×C7—41no—
146C2×C4×C7—41no—
147C2×C4×C7—41no—
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—41no—
155C2×C4×C7—41no—
156C2×C4×C7—41no—
157C2×C4×C7—41no—
158C2×C4×C7—41no—
159C2×C4×C7—81no—
160C2×C4×C7—81no—
161C2×C4×C7#13112yes—
162C7⋊C8—82no—
163C7⋊C8—82no—
164C22×Q8C2×Dic711yescharacteristic
165C23×C4C2×Dic711yescharacteristic
166C23×C4C22⋊D711yescharacteristic
167C23×C4C22⋊D711yescharacteristic
168C2×M16—281no—
169C22×C8—281no—
170C22⋊Q8—41no—
171C22⋊Q8—41no—
172C2×C4⋊C4—21no—
173C2×C4⋊C4—21no—
174C2×C4⋊C4—21no—
175C2×C4⋊C4—21no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4—41no—
178C2×C4⋊C4—41no—
179C2×C4⋊C4C2×Dic711yescharacteristic
180C2×C4⋊C4C2×Dic711yescharacteristic
181C2×C4⋊C4C22⋊D711yescharacteristic
182C2×C4⋊C4C22⋊D711yescharacteristic
183C2×C4⋊C4C22×D711yescharacteristic
184C2×C22⋊C4—21no—
185C2×C22⋊C4—21no—
186C2×C42C2×Dic711yescharacteristic
187C2×C42C2×Dic711yescharacteristic
188C22⋊C8—142no—
189C22⋊C8—142no—
190C22⋊C8—281no—
191C22⋊C8—281no—
192#95—21no—
193#95—21no—
194#95—21no—
195#95—21no—
196#95—21no—
197C22×C7—21no—
198C22×C7—21no—
199C22×C7—21no—
200C22×C7—21no—
201C22×C7—21no—
202C22×C7—21no—
203C22×C7—21no—
204C22×C7—42no—
205C22×C7—42no—
206C22×C7#35612yes—
207C22×C7#40811yescharacteristic
208C22×C7C2×#9911yescharacteristic
209C22×C7#41311yescharacteristic
210C4×C7—22no—
211C4×C7—42no—
212C4×C7—42no—
213C4×C7—41no—
214C4×C7—41no—
215C4×C7—41no—
216C4×C7—41no—
217C4×C7—41no—
218C4×C7—81no—
219C4×C7—81no—
220C24C22⋊Dic711yescharacteristic
221C2×Q8—22no—
222C2×Q8—41no—
223C2×Q8—41no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—22no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—41no—
236C22×C4—81no—
237C22×C4—81no—
238C22×C4C22⋊Dic711yescharacteristic
239C22×C4C22⋊Dic711yescharacteristic
240C22×C4C22⋊Dic711yescharacteristic
241C22×C4C22×Dic711yescharacteristic
242C22×C4C2×C22⋊D711yescharacteristic
243C22×C4C2×C22⋊D711yescharacteristic
244M16—562no—
245C2×C8—282no—
246C2×C8—282no—
247C2×C8—562no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—42no—
254C4⋊C4—81no—
255C4⋊C4—81no—
256C4⋊C4—81no—
257C4⋊C4—81no—
258C22⋊C4—24no—
259C22⋊C4—41no—
260C22⋊C4—41no—
261C42—22no—
262C42—41no—
263C2×C7—21no—
264C2×C7—21no—
265C2×C7—22no—
266C2×C7—41no—
267C2×C7#146811yescharacteristic
268C2×C7#212711yescharacteristic
269C2×C7C2×#35611yescharacteristic
270C23—21no—
271C23—21no—
272C23—22no—
273C23—41no—
274C23#640811yescharacteristic
275C23#640811yescharacteristic
276C23C2×C22⋊Dic711yescharacteristic
277Q8—82no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—81no—
308C2×C4—81no—
309C2×C4#651112yes—
310C8—562no—
311C8—562no—
312C7#1155511yescharacteristic, complemented, Sylow
313C22—21no—
314C22—21no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—42no—
321C22—42no—
322C22#8934312yes—
323C22C2×#640811yescharacteristic
324C22#9000611yescharacteristic
325C22#9000911yescharacteristic
326C4—22no—
327C4—42no—
328C4—42no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—41no—
334C4—81no—
335C4—81no—
336C2—21no—
337C2—21no—
338C2—22no—
339C2—41no—
340C2#1172945611yescharacteristic
341C2C2×#8934311yescharacteristic
342C2#1172961411yescharacteristic
subgroupG/H
centerC22C2×#6408
commutatorC22×C4×C7C22×C4
FrattiniC2×C4⋊C4C22×D7
FittingC7×#2502C2
socleC22×C7C2×#99
prime radicalC24×C7C22⋊C4
cosocleC2×C7×C4⋊C4C23
hypercenter#2502D7
hypocenterC7#11555
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ #2502

Complements

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

NH ≅ G/Ntype
4. #11725449C2semidirect
5. #11725441C2semidirect
312. C7#11555semidirect

Maximal subgroups

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

subgroupindex
C7×#25022
#117293062
C2×#893232
#117254492
#117254412
#115557