Finite Group Databasebeta

← #13264514

Subgroups — #13264514

Order 1792.

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

normal subgroups only

This group has 402 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#11739690C211yesmaximal, characteristic
2C7×#1464C211yesmaximal, characteristic
3#11729348C211yesmaximal, characteristic
4#11725257C212yesmaximal
5#11725255C212yesmaximal
6C2×C7×#117C2211yescharacteristic
7C2×C4×Dic14C411yescharacteristic, complemented
8C7×#432—21no—
9#89983—21no—
10C4×C22⋊Dic7—21no—
11#89758C411yescharacteristic, complemented
12#89756—21no—
13#89751C411yescharacteristic, complemented
14#89721C2211yescharacteristic
15#89720—21no—
16#89719C2211yescharacteristic
17C4×C4⋊Dic7C411yescharacteristic, complemented
18C4×Dic7⋊C4—21no—
19C7×#324—21no—
20C7×#323C2212yes—
21#89321—21no—
22#89321C2212yes—
23#11810—71nomaximal, Sylow
24C23×C4×C7D411yescharacteristic
25C22×Dic14C2×C411yescharacteristic
26C7×#117—41no—
27C7×#117—41no—
28C2×C7×C4⋊C4C2×C411yescharacteristic
29C2×C7×C4⋊C4D411yescharacteristic
30C2×C7×C22⋊C4D411yescharacteristic
31C2×C7×C22⋊C4C2311yescharacteristic
32C2×C42×C7C2×C411yescharacteristic
33C2×C42×C7D411yescharacteristic
34C2×C22⋊Dic7—21no—
35C2×C22⋊Dic7—21no—
36C2×C22⋊Dic7—22no—
37C2×C4⋊Dic7—21no—
38C2×C4⋊Dic7C2×C411yescharacteristic
39C2×Dic7⋊C4—21no—
40C2×Dic7⋊C4—21no—
41C2×Dic7⋊C4—21no—
42C2×C4×Dic7—21no—
43C2×C4×Dic7—21no—
44C4×Dic14—41no—
45C4×Dic14—41no—
46C7×C4⋊C8—41no—
47C7×C22⋊C8—22no—
48C7×#97—41no—
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#2396—71no—
58#1820—71no—
59#1464D711yescharacteristic
60#1352—72no—
61#1351—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×Dic14—41no—
79C2×Dic14—42no—
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—
91C22⋊Dic7—42no—
92C22⋊Dic7—42no—
93C4⋊Dic7—42no—
94C4⋊Dic7—41no—
95Dic7⋊C4—42no—
96Dic7⋊C4—42no—
97Dic7⋊C4—42no—
98C4×Dic7—42no—
99C4×Dic7—41no—
100C4×Dic7—41no—
101C2×C4×Q8—71no—
102C2×#117C2×D711yescharacteristic
103#432—21no—
104#400—71no—
105#399—71no—
106#398—141no—
107#396—141no—
108#395—71no—
109#393—71no—
110#381—141no—
111C4×C4⋊C4—71no—
112C4×C4⋊C4—141no—
113C4×C22⋊C4—141no—
114#342—72no—
115#342—141no—
116#324—21no—
117#323C2×D712yes—
118C23×C7—21no—
119C23×C7—21no—
120C23×C7—41no—
121C23×C7—41no—
122C23×C7C2×C22⋊C411yescharacteristic
123C23×C7#13712yes—
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—21no—
132C2×C4×C7—21no—
133C2×C4×C7—42no—
134C2×C4×C7—42no—
135C2×C4×C7—41no—
136C2×C4×C7—41no—
137C2×C4×C7—41no—
138C2×C4×C7—41no—
139C2×C4×C7#9911yescharacteristic
140C2×C4×C7#9911yescharacteristic
141C2×Dic7—22no—
142C2×Dic7—22no—
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—41no—
152C2×Dic7—41no—
153C2×Dic7—82no—
154C2×Dic7—82no—
155C2×Dic7—82no—
156Dic14—42no—
157Dic14—42no—
158C7×C8—82no—
159C22×Q8—71no—
160C23×C4D2811yescharacteristic
161C4×Q8—281no—
162C4×Q8—281no—
163#117—41no—
164#117—41no—
165C2×C4⋊C4—71no—
166C2×C4⋊C4—141no—
167C2×C4⋊C4—141no—
168C2×C4⋊C4—141no—
169C2×C4⋊C4—141no—
170C2×C4⋊C4C4×D711yescharacteristic
171C2×C4⋊C4C22⋊D711yescharacteristic
172C2×C22⋊C4—141no—
173C2×C22⋊C4—141no—
174C2×C22⋊C4—142no—
175C2×C22⋊C4D2811yescharacteristic
176C2×C22⋊C4C22×D711yescharacteristic
177C2×C42—141no—
178C2×C42—141no—
179C2×C42C4×D711yescharacteristic
180C2×C42C22⋊D711yescharacteristic
181C4⋊C8—41no—
182C22⋊C8—22no—
183#97—41no—
184#95—71no—
185#95—71no—
186#95—141no—
187#95—141no—
188#95—141no—
189#95—141no—
190#95—281no—
191#95—281no—
192C22×C7—21no—
193C22×C7—21no—
194C22×C7—22no—
195C22×C7—42no—
196C22×C7—41no—
197C22×C7—41no—
198C22×C7—81no—
199C22×C7C2×#9911yescharacteristic
200C22×C7#41911yescharacteristic
201C22×C7#42111yescharacteristic
202C4×C7—21no—
203C4×C7—21no—
204C4×C7—41no—
205C4×C7—41no—
206C4×C7—41no—
207C4×C7—41no—
208C4×C7—41no—
209Dic7—42no—
210Dic7—42no—
211Dic7—81no—
212Dic7—81no—
213Dic7—162no—
214C24C2×D2811yescharacteristic
215C2×Q8—281no—
216C2×Q8—282no—
217C22×C4—22no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—41no—
221C22×C4—141no—
222C22×C4—141no—
223C22×C4—141no—
224C22×C4—141no—
225C22×C4—282no—
226C22×C4(C2×D7)⋊C411yescharacteristic
227C22×C4(C2×D7)⋊C411yescharacteristic
228C22×C4(C2×D7)⋊C411yescharacteristic
229C22×C4(C2×D7)⋊C411yescharacteristic
230C22×C4C2×C4×D711yescharacteristic
231C22×C4C2×C22⋊D711yescharacteristic
232C2×C8—42no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—281no—
236C4⋊C4—282no—
237C4⋊C4—282no—
238C4⋊C4—282no—
239C4⋊C4—282no—
240C22⋊C4—41no—
241C22⋊C4—41no—
242C22⋊C4—282no—
243C22⋊C4—282no—
244C22⋊C4—282no—
245C22⋊C4—282no—
246C42—21no—
247C42—21no—
248C42—21no—
249C42—21no—
250C42—282no—
251C42—281no—
252C42—281no—
253C2×C7—21no—
254C2×C7—21no—
255C2×C7—42no—
256C2×C7#151111yescharacteristic
257C2×C7#212011yescharacteristic
258C2×C7#212611yescharacteristic
259C23—21no—
260C23—21no—
261C23—41no—
262C23—41no—
263C23#647212yes—
264C23C2×(C2×D7)⋊C411yescharacteristic
265Q8—282no—
266Q8—282no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—142no—
283C2×C4—142no—
284C2×C4—281no—
285C2×C4—281no—
286C2×C4—281no—
287C2×C4—281no—
288C2×C4—281no—
289C2×C4—281no—
290C2×C4—281no—
291C2×C4—281no—
292C2×C4—281no—
293C2×C4—281no—
294C2×C4—562no—
295C2×C4—562no—
296C2×C4—562no—
297C2×C4#638011yescharacteristic
298C2×C4#638011yescharacteristic
299C8—82no—
300C7#1181011yescharacteristic, complemented, Sylow
301C22—21no—
302C22—21no—
303C22—22no—
304C22—42no—
305C22—41no—
306C22—41no—
307C22—81no—
308C22C2×#638011yescharacteristic
309C22#8989211yescharacteristic
310C22#8991111yescharacteristic
311C4—21no—
312C4—21no—
313C4—41no—
314C4—41no—
315C4—41no—
316C4—41no—
317C4—41no—
318C4—282no—
319C4—282no—
320C4—561no—
321C4—561no—
322C4—1122no—
323C2—21no—
324C2—21no—
325C2—42no—
326C2#1172773511yescharacteristic
327C2#1172781411yescharacteristic
328C2#1172789911yescharacteristic
subgroupG/H
centerC22C2×#6380
commutatorC22×C4×C7C22×C4
FrattiniC2×C22⋊C4C22×D7
FittingC7×#1464C2
socleC22×C7C2×#99
prime radicalC24×C7C2×D4
cosocleC2×C7×C22⋊C4C23
hypercenter#1464D7
hypocenterC7#11810
LCSG ▷ C22×C4×C7 ▷ C23×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1464

Complements

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

NH ≅ G/Ntype
7. C2×C4×Dic14C4semidirect
11. #89758C4semidirect
13. #89751C4semidirect
17. C4×C4⋊Dic7C4semidirect
300. C7#11810semidirect

Maximal subgroups

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

subgroupindex
#117396902
C7×#14642
#117293482
#117252572
#117252552
#118107