Finite Group Databasebeta

← #13263385

Subgroups — #13263385

Order 1792.

366 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 79 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
1#11739701C211yesmaximal, characteristic
2C7×#1458C211yesmaximal, characteristic
3#11729326C211yesmaximal, characteristic
4#11725261C212yesmaximal, complemented
5#11725258C212yesmaximal, complemented
6C2×C7×#117C2211yescharacteristic
7C2×#6487C411yescharacteristic
8C7×#431—21no—
9C4×C22⋊Dic7C411yescharacteristic
10#89749C2211yescharacteristic
11#89748C411yescharacteristic
12#89746C411yescharacteristic
13#89746C2211yescharacteristic
14#89724—21no—
15#89724—21no—
16#89705—21no—
17#89705—21no—
18#89698—21no—
19C7×#324C2212yes—
20C7×#323—21no—
21#89323C2212yes—
22#89320—21no—
23#11556—71nomaximal, Sylow
24C23×C4×C7C2×C411yescharacteristic
25C22×Dic14C2×C411yescharacteristic
26C7×#117—41no—
27C7×#117—41no—
28C2×C7×C4⋊C4C2×C411yescharacteristic
29C2×C7×C4⋊C4C2311yescharacteristic
30C2×C7×C22⋊C4D411yescharacteristic
31C2×C7×C22⋊C4D411yescharacteristic
32C2×C42×C7D411yescharacteristic
33C2×C42×C7D411yescharacteristic
34C2×C22⋊Dic7—21no—
35C2×C22⋊Dic7—21no—
36C2×C4⋊Dic7C2×C411yescharacteristic
37#6487—41no—
38#6487—41no—
39C2×Dic7⋊C4—21no—
40C2×Dic7⋊C4—21no—
41C2×Dic7⋊C4—21no—
42C2×C4×Dic7C2×C411yescharacteristic
43C2×C4×Dic7C2×C411yescharacteristic
44C7×C4⋊C8—41no—
45C7×C22⋊C8—22no—
46C4×C7×C8—41no—
47C7⋊#95—21no—
48C7⋊#95—21no—
49C7⋊#95—21no—
50C7⋊#95—21no—
51C7⋊#95—21no—
52C7⋊#95—21no—
53C7⋊#95—21no—
54C22⋊(C7⋊C8)—22no—
55C4⋊(C7⋊C8)—41no—
56#6377—41no—
57#2499—71no—
58#1464—71no—
59#1458D711yescharacteristic
60#1324—72no—
61#1319—72no—
62C24×C7C22⋊C411yescharacteristic
63C22×C4×C7—21no—
64C22×C4×C7—21no—
65C22×C4×C7—22no—
66C22×C4×C7—41no—
67C22×C4×C7C22⋊C411yescharacteristic
68C22×C4×C7C22⋊C411yescharacteristic
69C22×C4×C7C22⋊C411yescharacteristic
70C22×C4×C7C22×C411yescharacteristic
71C22×C4×C7C2×D411yescharacteristic
72C22×C4×C7C2×D411yescharacteristic
73C22×Dic7—21no—
74C22×Dic7—21no—
75C22×Dic7—21no—
76C22×Dic7—21no—
77C2×Dic14—22no—
78C2×Dic14—41no—
79C2×Dic14—41no—
80C2×C7×C8—42no—
81C7×C4⋊C4—41no—
82C7×C4⋊C4—41no—
83C7×C22⋊C4—41no—
84C7×C22⋊C4—41no—
85C42×C7—21no—
86C42×C7—21no—
87C42×C7—21no—
88C42×C7—21no—
89C22⋊Dic7—42no—
90C22⋊Dic7—42no—
91C4⋊Dic7—41no—
92Dic7⋊C4—42no—
93Dic7⋊C4—42no—
94Dic7⋊C4—41no—
95Dic7⋊C4—41no—
96C4×Dic7—22no—
97C4×Dic7—41no—
98C2×C7⋊C8—42no—
99C2×C22⋊Q8—71no—
100C2×#117C2×D711yescharacteristic
101#432—141no—
102#431—21no—
103#397—141no—
104#397—141no—
105#391—71no—
106#391—71no—
107#387—141no—
108#387—141no—
109#384—71no—
110#382—71no—
111C4×C22⋊C4—71no—
112#324—72no—
113#324C2×D712yes—
114#323—21no—
115#323—141no—
116C23×C7—21no—
117C23×C7—21no—
118C23×C7—21no—
119C23×C7—41no—
120C23×C7—41no—
121C23×C7C2×C22⋊C411yescharacteristic
122C2×C4×C7—21no—
123C2×C4×C7—21no—
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—42no—
131C2×C4×C7—42no—
132C2×C4×C7—41no—
133C2×C4×C7—41no—
134C2×C4×C7—41no—
135C2×C4×C7—41no—
136C2×C4×C7#9911yescharacteristic
137C2×C4×C7#9911yescharacteristic
138C2×C4×C7#13112yes—
139C2×Dic7—22no—
140C2×Dic7—41no—
141C2×Dic7—41no—
142C2×Dic7—41no—
143C2×Dic7—41no—
144C2×Dic7—41no—
145C2×Dic7—41no—
146C2×Dic7—41no—
147C2×Dic7—41no—
148C2×Dic7—41no—
149C2×Dic7—41no—
150C2×Dic7—41no—
151Dic14—82no—
152C7×C8—82no—
153C7⋊C8—82no—
154C22×Q8—71no—
155C23×C4C4×D711yescharacteristic
156C22⋊Q8—281no—
157C22⋊Q8—281no—
158#117—41no—
159#117—41no—
160C2×C4⋊C4—71no—
161C2×C4⋊C4—141no—
162C2×C4⋊C4—141no—
163C2×C4⋊C4—141no—
164C2×C4⋊C4C4×D711yescharacteristic
165C2×C4⋊C4C22×D711yescharacteristic
166C2×C22⋊C4—141no—
167C2×C22⋊C4—141no—
168C2×C22⋊C4D2811yescharacteristic
169C2×C22⋊C4C22⋊D711yescharacteristic
170C2×C42—71no—
171C2×C42—71no—
172C2×C42D2811yescharacteristic
173C2×C42C22⋊D711yescharacteristic
174C4⋊C8—41no—
175C4⋊C8—281no—
176C22⋊C8—22no—
177C22⋊C8—142no—
178#97—281no—
179C4×C8—41no—
180#95—141no—
181#95—141no—
182#95—141no—
183#95—141no—
184#95—141no—
185#95—141no—
186#95—141no—
187C22×C7—21no—
188C22×C7—21no—
189C22×C7—41no—
190C22×C7—41no—
191C22×C7—41no—
192C22×C7—81no—
193C22×C7—81no—
194C22×C7#40811yescharacteristic
195C22×C7C2×#9911yescharacteristic
196C22×C7#41311yescharacteristic
197C4×C7—22no—
198C4×C7—21no—
199C4×C7—21no—
200C4×C7—41no—
201C4×C7—41no—
202C4×C7—41no—
203C4×C7—41no—
204Dic7—42no—
205Dic7—81no—
206Dic7—81no—
207Dic7—81no—
208C24(C2×D7)⋊C411yescharacteristic
209C2×Q8—142no—
210C2×Q8—281no—
211C2×Q8—281no—
212C22×C4—22no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—41no—
216C22×C4—141no—
217C22×C4—141no—
218C22×C4—141no—
219C22×C4—141no—
220C22×C4(C2×D7)⋊C411yescharacteristic
221C22×C4(C2×D7)⋊C411yescharacteristic
222C22×C4(C2×D7)⋊C411yescharacteristic
223C22×C4C2×C4×D711yescharacteristic
224C22×C4C2×D2811yescharacteristic
225C22×C4C2×C22⋊D711yescharacteristic
226C2×C8—42no—
227C2×C8—282no—
228C4⋊C4—41no—
229C4⋊C4—41no—
230C4⋊C4—281no—
231C4⋊C4—282no—
232C4⋊C4—282no—
233C4⋊C4—281no—
234C4⋊C4—281no—
235C22⋊C4—41no—
236C22⋊C4—41no—
237C22⋊C4—282no—
238C22⋊C4—282no—
239C42—21no—
240C42—21no—
241C42—21no—
242C42—21no—
243C42—142no—
244C42—281no—
245C2×C7—21no—
246C2×C7—21no—
247C2×C7—81no—
248C2×C7#146811yescharacteristic
249C2×C7#212911yescharacteristic
250C2×C7#213211yescharacteristic
251C23—21no—
252C23—21no—
253C23—21no—
254C23—41no—
255C23—41no—
256C23C2×(C2×D7)⋊C411yescharacteristic
257Q8—562no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—42no—
267C2×C4—42no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—142no—
273C2×C4—281no—
274C2×C4—281no—
275C2×C4—281no—
276C2×C4—281no—
277C2×C4—281no—
278C2×C4—281no—
279C2×C4—281no—
280C2×C4—281no—
281C2×C4—281no—
282C2×C4—281no—
283C2×C4—281no—
284C2×C4#638011yescharacteristic
285C2×C4#638011yescharacteristic
286C2×C4#646412yes—
287C8—82no—
288C8—562no—
289C7#1155611yescharacteristic, complemented, Sylow
290C22—21no—
291C22—21no—
292C22—41no—
293C22—41no—
294C22—41no—
295C22—81no—
296C22—81no—
297C22C2×#638011yescharacteristic
298C22#8988211yescharacteristic
299C22#8990411yescharacteristic
300C4—22no—
301C4—21no—
302C4—21no—
303C4—41no—
304C4—41no—
305C4—41no—
306C4—41no—
307C4—282no—
308C4—561no—
309C4—561no—
310C4—561no—
311C2—21no—
312C2—21no—
313C2—81no—
314C2#1172767411yescharacteristic
315C2#1172781311yescharacteristic
316C2#1172790211yescharacteristic
subgroupG/H
centerC22C2×#6380
commutatorC22×C4×C7C22×C4
FrattiniC2×C4⋊C4C22×D7
FittingC7×#1458C2
socleC22×C7C2×#99
prime radicalC24×C7C22⋊C4
cosocleC2×C7×C4⋊C4C23
hypercenter#1458D7
hypocenterC7#11556
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1458

Complements

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

NH ≅ G/Ntype
4. #11725261C2semidirect
5. #11725258C2semidirect
289. C7#11556semidirect

Maximal subgroups

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

subgroupindex
#117397012
C7×#14582
#117293262
#117252612
#117252582
#115567