Finite Group Databasebeta

← #13263458

Subgroups — #13263458

Order 1792.

416 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 83 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#11739831C211yesmaximal, characteristic
2C7×#1465C211yesmaximal, characteristic
3#11729354C211yesmaximal, characteristic
4#11725259C212yesmaximal, complemented
5#11725258C212yesmaximal, complemented
6C2×C4×C7×D4C2211yescharacteristic
7C2×#6433C411yescharacteristic
8C7×#407—21no—
9#89993C411yescharacteristic
10#89993C411yescharacteristic
11#89982—21no—
12#89982—21no—
13C2×C22⋊(C7⋊C8)—21no—
14#89749C2211yescharacteristic
15#89748C2211yescharacteristic
16#89720—21no—
17#89720—21no—
18C4×C4⋊Dic7C411yescharacteristic
19C7×#324C2212yes—
20C7×#323—21no—
21#89323C2212yes—
22#89320—21no—
23#11572—71nomaximal, Sylow
24C22×C7×D4C2×C411yescharacteristic
25C23×C4×C7D411yescharacteristic
26C23×C4×C7D411yescharacteristic
27C2×C7×M16—41no—
28C4×C7×D4—41no—
29C4×C7×D4—41no—
30C2×C7×C4⋊C4C2311yescharacteristic
31C2×C7×C22⋊C4D411yescharacteristic
32C2×C7×C22⋊C4D411yescharacteristic
33C2×C42×C7C2×C411yescharacteristic
34C2×C22⋊Dic7—21no—
35C2×C22⋊Dic7—21no—
36C2×C22⋊Dic7—21no—
37C2×C22⋊Dic7—21no—
38C2×C4⋊Dic7—21no—
39C2×C4⋊Dic7C2×C411yescharacteristic
40C2×C4⋊Dic7C2×C411yescharacteristic
41C2×Dic7⋊C4—21no—
42C2×Dic7⋊C4—21no—
43C2×Dic7⋊C4—21no—
44C2×Dic7⋊C4—21no—
45C2×C4×Dic7C2×C411yescharacteristic
46C2×C4×Dic7C2×C411yescharacteristic
47C22×C7⋊C8—41no—
48#6433—41no—
49#6433—41no—
50C7×C22⋊C8—22no—
51C7×C22⋊C8—41no—
52C7⋊#95—21no—
53C7⋊#95—21no—
54C7⋊#95—21no—
55C22⋊(C7⋊C8)—22no—
56C22⋊(C7⋊C8)—41no—
57#2566—71no—
58#1465D711yescharacteristic
59#1459—71no—
60#1325—72no—
61#1324—72no—
62C24×C7C22⋊C411yescharacteristic
63C24×C7C22⋊C411yescharacteristic
64C2×C7×D4—22no—
65C2×C7×D4—22no—
66C2×C7×D4—41no—
67C22×C4×C7—21no—
68C22×C4×C7—21no—
69C22×C4×C7—21no—
70C22×C4×C7—21no—
71C22×C4×C7—81no—
72C22×C4×C7—81no—
73C22×C4×C7C22⋊C411yescharacteristic
74C22×C4×C7C22⋊C411yescharacteristic
75C22×C4×C7C22×C411yescharacteristic
76C22×C4×C7C2×D411yescharacteristic
77C22×C4×C7C2×D411yescharacteristic
78C22×Dic7—21no—
79C22×Dic7—21no—
80C22×Dic7—21no—
81C22×Dic7—21no—
82C7×M16—82no—
83C2×C7×C8—42no—
84C7×C4⋊C4—41no—
85C7×C22⋊C4—41no—
86C7×C22⋊C4—41no—
87C42×C7—21no—
88C42×C7—21no—
89C22⋊Dic7—42no—
90C22⋊Dic7—42no—
91C22⋊Dic7—81no—
92C22⋊Dic7—81no—
93C4⋊Dic7—42no—
94C4⋊Dic7—41no—
95C4⋊Dic7—41no—
96Dic7⋊C4—42no—
97Dic7⋊C4—41no—
98Dic7⋊C4—41no—
99Dic7⋊C4—81no—
100Dic7⋊C4—81no—
101C4×Dic7—22no—
102C4×Dic7—22no—
103C2×C7⋊C8—42no—
104C2×C7⋊C8—82no—
105C2×#125—71no—
106C2×C4×D4C2×D711yescharacteristic
107#407—21no—
108C2×C22⋊C8—141no—
109#396—141no—
110#396—141no—
111#390—71no—
112#390—71no—
113#385—141no—
114#385—141no—
115#384—71no—
116#382—71no—
117C4×C4⋊C4—71no—
118#324—72no—
119#324C2×D712yes—
120#323—21no—
121#323—141no—
122C23×C7—21no—
123C23×C7—21no—
124C23×C7—21no—
125C23×C7—21no—
126C23×C7—21no—
127C23×C7—41no—
128C23×C7—41no—
129C23×C7—41no—
130C23×C7—41no—
131C23×C7#10112yes—
132C23×C7C2×C22⋊C411yescharacteristic
133C7×D4—44no—
134C2×C4×C7—21no—
135C2×C4×C7—21no—
136C2×C4×C7—21no—
137C2×C4×C7—21no—
138C2×C4×C7—21no—
139C2×C4×C7—41no—
140C2×C4×C7—42no—
141C2×C4×C7—42no—
142C2×C4×C7—41no—
143C2×C4×C7—41no—
144C2×C4×C7—41no—
145C2×C4×C7—81no—
146C2×C4×C7—81no—
147C2×C4×C7#9911yescharacteristic
148C2×C4×C7#9911yescharacteristic
149C2×C4×C7#13112yes—
150C2×Dic7—22no—
151C2×Dic7—41no—
152C2×Dic7—41no—
153C2×Dic7—41no—
154C2×Dic7—41no—
155C2×Dic7—41no—
156C2×Dic7—41no—
157C2×Dic7—41no—
158C2×Dic7—41no—
159C2×Dic7—41no—
160C2×Dic7—41no—
161C2×Dic7—41no—
162C7×C8—82no—
163C7⋊C8—82no—
164C22×D4C4×D711yescharacteristic
165C23×C4D2811yescharacteristic
166C23×C4C22⋊D711yescharacteristic
167C2×M16—41no—
168C22×C8—281no—
169#125—281no—
170#125—281no—
171C4×D4—41no—
172C4×D4—41no—
173C2×C4⋊C4—71no—
174C2×C4⋊C4—71no—
175C2×C4⋊C4—141no—
176C2×C4⋊C4—141no—
177C2×C4⋊C4—141no—
178C2×C4⋊C4—141no—
179C2×C4⋊C4—141no—
180C2×C4⋊C4C22×D711yescharacteristic
181C2×C22⋊C4—141no—
182C2×C22⋊C4—141no—
183C2×C22⋊C4—141no—
184C2×C22⋊C4—141no—
185C2×C22⋊C4D2811yescharacteristic
186C2×C22⋊C4C22⋊D711yescharacteristic
187C2×C42—71no—
188C2×C42—71no—
189C2×C42C4×D711yescharacteristic
190C22⋊C8—22no—
191C22⋊C8—41no—
192C22⋊C8—142no—
193C22⋊C8—281no—
194#95—141no—
195#95—141no—
196#95—141no—
197C22×C7—21no—
198C22×C7—21no—
199C22×C7—22no—
200C22×C7—42no—
201C22×C7—42no—
202C22×C7—41no—
203C22×C7—41no—
204C22×C7—41no—
205C22×C7—41no—
206C22×C7—41no—
207C22×C7—81no—
208C22×C7—81no—
209C22×C7#40811yescharacteristic
210C22×C7C2×#9911yescharacteristic
211C22×C7C2×#10111yescharacteristic
212C4×C7—21no—
213C4×C7—21no—
214C4×C7—22no—
215C4×C7—41no—
216C4×C7—41no—
217C4×C7—41no—
218Dic7—42no—
219Dic7—81no—
220Dic7—81no—
221Dic7—81no—
222C24(C2×D7)⋊C411yescharacteristic
223C24(C2×D7)⋊C411yescharacteristic
224C2×D4—22no—
225C2×D4—22no—
226C2×D4—41no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—81no—
232C22×C4—81no—
233C22×C4—141no—
234C22×C4—141no—
235C22×C4—141no—
236C22×C4—141no—
237C22×C4(C2×D7)⋊C411yescharacteristic
238C22×C4(C2×D7)⋊C411yescharacteristic
239C22×C4C2×C4×D711yescharacteristic
240C22×C4C2×D2811yescharacteristic
241C22×C4C2×C22⋊D711yescharacteristic
242M16—82no—
243C2×C8—42no—
244C2×C8—282no—
245C2×C8—562no—
246C4⋊C4—41no—
247C4⋊C4—281no—
248C4⋊C4—281no—
249C4⋊C4—282no—
250C4⋊C4—282no—
251C4⋊C4—281no—
252C4⋊C4—281no—
253C4⋊C4—561no—
254C4⋊C4—561no—
255C22⋊C4—41no—
256C22⋊C4—41no—
257C22⋊C4—282no—
258C22⋊C4—282no—
259C22⋊C4—561no—
260C22⋊C4—561no—
261C42—21no—
262C42—21no—
263C42—142no—
264C42—142no—
265C2×C7—21no—
266C2×C7—21no—
267C2×C7—42no—
268C2×C7—81no—
269C2×C7#147211yescharacteristic
270C2×C7#212711yescharacteristic
271C2×C7#213211yescharacteristic
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23—41no—
278C23—41no—
279C23—41no—
280C23—41no—
281C23#639812yes—
282C23C2×(C2×D7)⋊C411yescharacteristic
283D4—44no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—41no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—81no—
296C2×C4—81no—
297C2×C4—142no—
298C2×C4—281no—
299C2×C4—281no—
300C2×C4—281no—
301C2×C4—281no—
302C2×C4—281no—
303C2×C4—281no—
304C2×C4—281no—
305C2×C4—281no—
306C2×C4—281no—
307C2×C4—281no—
308C2×C4—281no—
309C2×C4#638011yescharacteristic
310C2×C4#638011yescharacteristic
311C2×C4#647012yes—
312C8—82no—
313C8—562no—
314C7#1157211yescharacteristic, complemented, Sylow
315C22—21no—
316C22—21no—
317C22—22no—
318C22—42no—
319C22—42no—
320C22—41no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—41no—
325C22—81no—
326C22—81no—
327C22C2×#638011yescharacteristic
328C22#8990111yescharacteristic
329C22C2×#639811yescharacteristic
330C4—22no—
331C4—21no—
332C4—21no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—282no—
337C4—561no—
338C4—561no—
339C4—561no—
340C2—21no—
341C2—21no—
342C2—42no—
343C2—81no—
344C2#1172772611yescharacteristic
345C2#1172777311yescharacteristic
346C2#1172790211yescharacteristic
subgroupG/H
centerC22C2×#6380
commutatorC22×C4×C7C22×C4
FrattiniC2×C4⋊C4C22×D7
FittingC7×#1465C2
socleC22×C7C2×#99
prime radicalC22×C7×D4C2×C4
cosocleC2×C7×C4⋊C4C23
hypercenter#1465D7
hypocenterC7#11572
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1465

Complements

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

NH ≅ G/Ntype
4. #11725259C2semidirect
5. #11725258C2semidirect
314. C7#11572semidirect

Maximal subgroups

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

subgroupindex
#117398312
C7×#14652
#117293542
#117252592
#117252582
#115727