Finite Group Databasebeta

← #13264690

Subgroups — #13264690

Order 1792.

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

normal subgroups only

This group has 382 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#11739706C211yesmaximal, characteristic
2C7×#1458C211yesmaximal, characteristic
3#11729348C211yesmaximal, characteristic
4#11725257C212yesmaximal
5#11725256C212yesmaximal
6C2×C7×#117C2211yescharacteristic
7C2×#6433C411yescharacteristic, complemented
8C7×#431—21no—
9#89983—21no—
10#89982—21no—
11#89758C411yescharacteristic, complemented
12#89755C411yescharacteristic, complemented
13#89744—21no—
14#89725C2211yescharacteristic
15#89721C2211yescharacteristic
16#89717—21no—
17#89705—21no—
18#89704C411yescharacteristic, complemented
19C7×#324—21no—
20C7×#323C2212yes—
21#89321—21no—
22#89321C2212yes—
23#11846—71nomaximal, Sylow
24C23×C4×C7D411yescharacteristic
25C7×#117—41no—
26C7×#117—41no—
27C2×C7×C4⋊C4C2×C411yescharacteristic
28C2×C7×C4⋊C4D411yescharacteristic
29C2×C7×C22⋊C4D411yescharacteristic
30C2×C7×C22⋊C4C2311yescharacteristic
31C2×C42×C7C2×C411yescharacteristic
32C2×C42×C7D411yescharacteristic
33C2×C22⋊Dic7—21no—
34C2×C22⋊Dic7—21no—
35C2×C22⋊Dic7—22no—
36C2×C4⋊Dic7C2×C411yescharacteristic
37C2×C4⋊Dic7C2×C411yescharacteristic
38C2×Dic7⋊C4—21no—
39C2×Dic7⋊C4—21no—
40C2×Dic7⋊C4—21no—
41C2×Dic7⋊C4—21no—
42C2×C4×Dic7—21no—
43#6433—41no—
44#6433—41no—
45C7×C4⋊C8—41no—
46C7×C22⋊C8—22no—
47C4×C7×C8—41no—
48C7⋊#95—21no—
49C7⋊#95—21no—
50C7⋊#95—21no—
51C7⋊#95—21no—
52C7⋊#95—21no—
53C7⋊#95—41no—
54C7⋊#95—41no—
55C7⋊#95C2×C411yescharacteristic
56C7⋊#95C2×C411yescharacteristic
57#2611—71no—
58#1820—71no—
59#1458D711yescharacteristic
60#1352—72no—
61#1344—72no—
62C24×C7C2×D411yescharacteristic
63C22×C4×C7—22no—
64C22×C4×C7—21no—
65C22×C4×C7—21no—
66C22×C4×C7—41no—
67C22×C4×C7C22⋊C411yescharacteristic
68C22×C4×C7C22⋊C411yescharacteristic
69C22×C4×C7C22⋊C411yescharacteristic
70C22×C4×C7C22⋊C411yescharacteristic
71C22×C4×C7C22×C411yescharacteristic
72C22×C4×C7C2×D411yescharacteristic
73C22×Dic7—21no—
74C22×Dic7—21no—
75C22×Dic7—21no—
76C22×Dic7—21no—
77C22×Dic7—42no—
78C2×C7×C8—42no—
79C7×C4⋊C4—41no—
80C7×C4⋊C4—41no—
81C7×C22⋊C4—41no—
82C7×C22⋊C4—41no—
83C42×C7—21no—
84C42×C7—21no—
85C42×C7—21no—
86C42×C7—21no—
87C22⋊Dic7—42no—
88C22⋊Dic7—42no—
89C22⋊Dic7—42no—
90C22⋊Dic7—42no—
91C4⋊Dic7—41no—
92C4⋊Dic7—41no—
93Dic7⋊C4—42no—
94Dic7⋊C4—42no—
95Dic7⋊C4—42no—
96Dic7⋊C4—41no—
97Dic7⋊C4—41no—
98C4×Dic7—42no—
99C2×#125—71no—
100C2×#117C2×D711yescharacteristic
101#431—21no—
102#400—71no—
103#399—71no—
104#398—71no—
105#397—71no—
106#389—141no—
107#388—141no—
108#387—141no—
109#385—141no—
110#381—141no—
111#376—71no—
112#342—72no—
113#342—141no—
114#324—21no—
115#323C2×D712yes—
116C23×C7—21no—
117C23×C7—21no—
118C23×C7—41no—
119C23×C7—41no—
120C23×C7C2×C22⋊C411yescharacteristic
121C23×C7#13512yes—
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—21no—
131C2×C4×C7—42no—
132C2×C4×C7—42no—
133C2×C4×C7—41no—
134C2×C4×C7—41no—
135C2×C4×C7—41no—
136C2×C4×C7—41no—
137C2×C4×C7#9911yescharacteristic
138C2×C4×C7#9911yescharacteristic
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—
151C2×Dic7—82no—
152C2×Dic7—82no—
153C2×Dic7—82no—
154C7×C8—82no—
155C23×C4D2811yescharacteristic
156#125—281no—
157#125—281no—
158#117—41no—
159#117—41no—
160C2×C4⋊C4—71no—
161C2×C4⋊C4—71no—
162C2×C4⋊C4—141no—
163C2×C4⋊C4—141no—
164C2×C4⋊C4—141no—
165C2×C4⋊C4—141no—
166C2×C4⋊C4C4×D711yescharacteristic
167C2×C4⋊C4C22⋊D711yescharacteristic
168C2×C22⋊C4—141no—
169C2×C22⋊C4—141no—
170C2×C22⋊C4—142no—
171C2×C22⋊C4D2811yescharacteristic
172C2×C22⋊C4C22×D711yescharacteristic
173C2×C42—141no—
174C2×C42C4×D711yescharacteristic
175C2×C42C22⋊D711yescharacteristic
176C4⋊C8—41no—
177C22⋊C8—22no—
178C4×C8—41no—
179#95—71no—
180#95—71no—
181#95—141no—
182#95—141no—
183#95—141no—
184#95—141no—
185#95—141no—
186#95—281no—
187#95—281no—
188C22×C7—21no—
189C22×C7—21no—
190C22×C7—22no—
191C22×C7—42no—
192C22×C7—41no—
193C22×C7—41no—
194C22×C7—81no—
195C22×C7C2×#9911yescharacteristic
196C22×C7#41611yescharacteristic
197C22×C7#42111yescharacteristic
198C4×C7—21no—
199C4×C7—21no—
200C4×C7—41no—
201C4×C7—41no—
202C4×C7—41no—
203C4×C7—41no—
204C4×C7—41no—
205Dic7—42no—
206Dic7—81no—
207Dic7—81no—
208Dic7—81no—
209Dic7—162no—
210C24C2×D2811yescharacteristic
211C22×C4—22no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—41no—
215C22×C4—141no—
216C22×C4—141no—
217C22×C4—141no—
218C22×C4—141no—
219C22×C4—282no—
220C22×C4(C2×D7)⋊C411yescharacteristic
221C22×C4(C2×D7)⋊C411yescharacteristic
222C22×C4(C2×D7)⋊C411yescharacteristic
223C22×C4(C2×D7)⋊C411yescharacteristic
224C22×C4C2×C4×D711yescharacteristic
225C22×C4C2×C22⋊D711yescharacteristic
226C2×C8—42no—
227C4⋊C4—41no—
228C4⋊C4—41no—
229C4⋊C4—281no—
230C4⋊C4—281no—
231C4⋊C4—282no—
232C4⋊C4—282no—
233C4⋊C4—282no—
234C4⋊C4—281no—
235C4⋊C4—281no—
236C22⋊C4—41no—
237C22⋊C4—41no—
238C22⋊C4—282no—
239C22⋊C4—282no—
240C22⋊C4—282no—
241C22⋊C4—282no—
242C42—21no—
243C42—21no—
244C42—21no—
245C42—21no—
246C42—282no—
247C2×C7—21no—
248C2×C7—21no—
249C2×C7—42no—
250C2×C7#151611yescharacteristic
251C2×C7#212311yescharacteristic
252C2×C7#212611yescharacteristic
253C23—21no—
254C23—21no—
255C23—41no—
256C23—41no—
257C23#646712yes—
258C23C2×(C2×D7)⋊C411yescharacteristic
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—42no—
269C2×C4—42no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—142no—
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—281no—
285C2×C4—281no—
286C2×C4—562no—
287C2×C4—562no—
288C2×C4—562no—
289C2×C4#638011yescharacteristic
290C2×C4#638011yescharacteristic
291C8—82no—
292C7#1184611yescharacteristic, complemented, Sylow
293C22—21no—
294C22—21no—
295C22—22no—
296C22—42no—
297C22—41no—
298C22—41no—
299C22—81no—
300C22C2×#638011yescharacteristic
301C22#8988511yescharacteristic
302C22#8991111yescharacteristic
303C4—21no—
304C4—21no—
305C4—41no—
306C4—41no—
307C4—41no—
308C4—41no—
309C4—41no—
310C4—282no—
311C4—561no—
312C4—561no—
313C4—561no—
314C4—1122no—
315C2—21no—
316C2—21no—
317C2—42no—
318C2#1172769711yescharacteristic
319C2#1172781411yescharacteristic
320C2#1172790111yescharacteristic
subgroupG/H
centerC22C2×#6380
commutatorC22×C4×C7C22×C4
FrattiniC2×C22⋊C4C22×D7
FittingC7×#1458C2
socleC22×C7C2×#99
prime radicalC24×C7C2×D4
cosocleC2×C7×C22⋊C4C23
hypercenter#1458D7
hypocenterC7#11846
LCSG ▷ C22×C4×C7 ▷ C23×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
7. C2×#6433C4semidirect
11. #89758C4semidirect
12. #89755C4semidirect
18. #89704C4semidirect
292. C7#11846semidirect

Maximal subgroups

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

subgroupindex
#117397062
C7×#14582
#117293482
#117252572
#117252562
#118467