Finite Group Databasebeta

← #13263457

Subgroups — #13263457

Order 1792.

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

normal subgroups only

This group has 416 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×#2566C211yesmaximal, characteristic
2#11729356C211yesmaximal, characteristic
3#11729354C211yesmaximal, characteristic
4#11725441C212yesmaximal, complemented
5#11725438C212yesmaximal, complemented
6C2×C7×#125C411yescharacteristic
7C2×C4×C7×D4C2211yescharacteristic
8C7×#396—21no—
9C7×#396—21no—
10C7×#390C411yescharacteristic
11C7×#390C411yescharacteristic
12C7×#385—21no—
13C7×#385—21no—
14C7×#384C2211yescharacteristic
15C7×#382C2211yescharacteristic
16C4×C7×C4⋊C4C411yescharacteristic
17#89979—21no—
18C2×C22⋊(C7⋊C8)—21no—
19#89323C2212yes—
20#89323C2212yes—
21#89320—21no—
22#89320—21no—
23#11572—71nomaximal, Sylow
24C22×C7×D4C2×C411yescharacteristic
25C23×C4×C7D411yescharacteristic
26C23×C4×C7D411yescharacteristic
27C7×#125—41no—
28C7×#125—41no—
29C4×C7×D4—41no—
30C4×C7×D4—41no—
31C2×C7×C4⋊C4—21no—
32C2×C7×C4⋊C4—21no—
33C2×C7×C4⋊C4—21no—
34C2×C7×C4⋊C4—21no—
35C2×C7×C4⋊C4—21no—
36C2×C7×C4⋊C4C2×C411yescharacteristic
37C2×C7×C4⋊C4C2×C411yescharacteristic
38C2×C7×C4⋊C4C2311yescharacteristic
39C2×C7×C22⋊C4—21no—
40C2×C7×C22⋊C4—21no—
41C2×C7×C22⋊C4—21no—
42C2×C7×C22⋊C4—21no—
43C2×C7×C22⋊C4D411yescharacteristic
44C2×C7×C22⋊C4D411yescharacteristic
45C2×C42×C7C2×C411yescharacteristic
46C2×C42×C7C2×C411yescharacteristic
47C2×C42×C7C2×C411yescharacteristic
48C2×#1136—41no—
49C22×C7⋊C8—41no—
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#2566D711yescharacteristic
58#1465—71no—
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—21no—
72C22×C4×C7—21no—
73C22×C4×C7—21no—
74C22×C4×C7—21no—
75C22×C4×C7—81no—
76C22×C4×C7—81no—
77C22×C4×C7C22⋊C411yescharacteristic
78C22×C4×C7C22⋊C411yescharacteristic
79C22×C4×C7C22×C411yescharacteristic
80C22×C4×C7C2×D411yescharacteristic
81C22×C4×C7C2×D411yescharacteristic
82C7×C4⋊C4—41no—
83C7×C4⋊C4—41no—
84C7×C4⋊C4—41no—
85C7×C4⋊C4—42no—
86C7×C4⋊C4—42no—
87C7×C4⋊C4—41no—
88C7×C4⋊C4—41no—
89C7×C4⋊C4—81no—
90C7×C4⋊C4—81no—
91C7×C22⋊C4—41no—
92C7×C22⋊C4—41no—
93C7×C22⋊C4—42no—
94C7×C22⋊C4—42no—
95C7×C22⋊C4—81no—
96C7×C22⋊C4—81no—
97C42×C7—21no—
98C42×C7—21no—
99C42×C7—22no—
100C42×C7—22no—
101#1136—82no—
102C2×C7⋊C8—42no—
103C2×C7⋊C8—42no—
104C2×C7⋊C8—82no—
105C2×#125Dic711yescharacteristic
106C2×C4×D4C2×D711yescharacteristic
107#407—141no—
108C2×C22⋊C8—141no—
109#396—21no—
110#396—21no—
111#390Dic711yescharacteristic
112#390Dic711yescharacteristic
113#385—21no—
114#385—21no—
115#384C2×D711yescharacteristic
116#382C2×D711yescharacteristic
117C4×C4⋊C4Dic711yescharacteristic
118#324—72no—
119#324—72no—
120#323—141no—
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—22no—
137C2×C4×C7—21no—
138C2×C4×C7—21no—
139C2×C4×C7—21no—
140C2×C4×C7—41no—
141C2×C4×C7—42no—
142C2×C4×C7—42no—
143C2×C4×C7—41no—
144C2×C4×C7—41no—
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—81no—
158C2×C4×C7—81no—
159C2×C4×C7#9911yescharacteristic
160C2×C4×C7#9911yescharacteristic
161C2×C4×C7#13112yes—
162C7⋊C8—82no—
163C7⋊C8—82no—
164C22×D4C2×Dic711yescharacteristic
165C23×C4C22⋊D711yescharacteristic
166C23×C4C22⋊D711yescharacteristic
167C2×M16—281no—
168C22×C8—281no—
169#125—41no—
170#125—41no—
171C4×D4—41no—
172C4×D4—41no—
173C2×C4⋊C4—21no—
174C2×C4⋊C4—21no—
175C2×C4⋊C4—21no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4—21no—
178C2×C4⋊C4C2×Dic711yescharacteristic
179C2×C4⋊C4C2×Dic711yescharacteristic
180C2×C4⋊C4C22×D711yescharacteristic
181C2×C22⋊C4—21no—
182C2×C22⋊C4—21no—
183C2×C22⋊C4—21no—
184C2×C22⋊C4—21no—
185C2×C22⋊C4C22⋊D711yescharacteristic
186C2×C22⋊C4C22⋊D711yescharacteristic
187C2×C42C2×Dic711yescharacteristic
188C2×C42C2×Dic711yescharacteristic
189C2×C42C2×Dic711yescharacteristic
190C22⋊C8—142no—
191C22⋊C8—142no—
192C22⋊C8—281no—
193C22⋊C8—281no—
194#95—21no—
195#95—21no—
196#95—21no—
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—42no—
216C4×C7—41no—
217C4×C7—41no—
218C4×C7—41no—
219C4×C7—81no—
220C4×C7—81no—
221C4×C7—81no—
222C24C22⋊Dic711yescharacteristic
223C24C22⋊Dic711yescharacteristic
224C2×D4—22no—
225C2×D4—22no—
226C2×D4—41no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—81no—
236C22×C4—81no—
237C22×C4C22⋊Dic711yescharacteristic
238C22×C4C22⋊Dic711yescharacteristic
239C22×C4C22×Dic711yescharacteristic
240C22×C4C2×C22⋊D711yescharacteristic
241C22×C4C2×C22⋊D711yescharacteristic
242M16—562no—
243C2×C8—282no—
244C2×C8—282no—
245C2×C8—562no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—42no—
250C4⋊C4—42no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—81no—
254C4⋊C4—81no—
255C22⋊C4—41no—
256C22⋊C4—41no—
257C22⋊C4—42no—
258C22⋊C4—42no—
259C22⋊C4—81no—
260C22⋊C4—81no—
261C42—21no—
262C42—21no—
263C42—22no—
264C42—22no—
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#641012yes—
282C23C2×C22⋊Dic711yescharacteristic
283D4—44no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—22no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—41no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—41no—
294C2×C4—41no—
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#640811yescharacteristic
310C2×C4#640811yescharacteristic
311C2×C4#651112yes—
312C8—562no—
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×#640811yescharacteristic
328C22C2×#641011yescharacteristic
329C22#9000611yescharacteristic
330C4—22no—
331C4—21no—
332C4—21no—
333C4—42no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—81no—
338C4—81no—
339C4—81no—
340C2—21no—
341C2—21no—
342C2—42no—
343C2—81no—
344C2#1172944511yescharacteristic
345C2#1172957411yescharacteristic
346C2#1172961411yescharacteristic
subgroupG/H
centerC22C2×#6408
commutatorC22×C4×C7C22×C4
FrattiniC2×C4⋊C4C22×D7
FittingC7×#2566C2
socleC22×C7C2×#99
prime radicalC22×C7×D4C2×C4
cosocleC2×C7×C4⋊C4C23
hypercenter#2566D7
hypocenterC7#11572
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2566

Complements

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

NH ≅ G/Ntype
4. #11725441C2semidirect
5. #11725438C2semidirect
314. C7#11572semidirect

Maximal subgroups

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

subgroupindex
C7×#25662
#117293562
#117293542
#117254412
#117254382
#115727