Finite Group Databasebeta

← #13263483

Subgroups — #13263483

Order 1792.

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

normal subgroups only

This group has 426 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×#2579C211yesmaximal, characteristic
2#11729357C211yesmaximal, characteristic
3#11729354C211yesmaximal, characteristic
4#11725442C212yesmaximal, complemented
5#11725442C212yesmaximal, complemented
6C2×C4×C7×D4C2211yescharacteristic
7C22×C7×C4⋊C4C411yescharacteristic
8C7×#398—21no—
9C7×#396—21no—
10C7×#387—21no—
11C7×#386C411yescharacteristic
12C7×#386C411yescharacteristic
13C7×#385—21no—
14C7×#385C2211yescharacteristic
15C7×#385C2211yescharacteristic
16C7×#380C411yescharacteristic
17C2×C22⋊(C7⋊C8)—21no—
18#89698—21no—
19#89323—21no—
20#89320—21no—
21#89320C2212yes—
22#89320C2212yes—
23#11578—71nomaximal, Sylow
24C22×C7×D4C2×C411yescharacteristic
25C23×C4×C7C2×C411yescharacteristic
26C23×C4×C7C2×C411yescharacteristic
27C23×C4×C7C2×C411yescharacteristic
28C23×C4×C7D411yescharacteristic
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⋊C4—41no—
37C2×C7×C4⋊C4—41no—
38C2×C7×C4⋊C4D411yescharacteristic
39C2×C7×C22⋊C4—21no—
40C2×C7×C22⋊C4—21no—
41C2×C7×C22⋊C4C2×C411yescharacteristic
42C2×C7×C22⋊C4C2×C411yescharacteristic
43C2×C7×C22⋊C4D411yescharacteristic
44C2×C7×C22⋊C4C2311yescharacteristic
45C2×C42×C7D411yescharacteristic
46C22×C7⋊C8—41no—
47C7×#95—21no—
48C7×#95—21no—
49C7×#95—21no—
50C7×#95—21no—
51C7×#95—21no—
52C22⋊(C7⋊C8)—22no—
53C22⋊(C7⋊C8)—22no—
54C22⋊(C7⋊C8)—41no—
55C4⋊(C7⋊C8)—41no—
56#6377—41no—
57#2579D711yescharacteristic
58#1466—71no—
59#1459—71no—
60#1326—72no—
61#1326—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—42no—
76C22×C4×C7—41no—
77C22×C4×C7—41no—
78C22×C4×C7—81no—
79C22×C4×C7—81no—
80C22×C4×C7—81no—
81C22×C4×C7C22⋊C411yescharacteristic
82C22×C4×C7C22⋊C411yescharacteristic
83C22×C4×C7C22⋊C411yescharacteristic
84C22×C4×C7C2×D411yescharacteristic
85C22×C4×C7C2×D411yescharacteristic
86C7×C4⋊C4—41no—
87C7×C4⋊C4—42no—
88C7×C4⋊C4—42no—
89C7×C4⋊C4—41no—
90C7×C4⋊C4—41no—
91C7×C4⋊C4—81no—
92C7×C4⋊C4—81no—
93C7×C22⋊C4—22no—
94C7×C22⋊C4—22no—
95C7×C22⋊C4—41no—
96C7×C22⋊C4—41no—
97C7×C22⋊C4—42no—
98C7×C22⋊C4—81no—
99C42×C7—21no—
100C42×C7—21no—
101C2×C7⋊C8—42no—
102C2×C7⋊C8—42no—
103C2×C7⋊C8—82no—
104C2×C4×D4C2×D711yescharacteristic
105C22×C4⋊C4Dic711yescharacteristic
106#432—141no—
107C2×C22⋊C8—141no—
108#398—21no—
109#396—21no—
110#387—21no—
111#386Dic711yescharacteristic
112#386Dic711yescharacteristic
113#385—21no—
114#385C2×D711yescharacteristic
115#385C2×D711yescharacteristic
116#380Dic711yescharacteristic
117#324—141no—
118#323—72no—
119#323—72no—
120#323—141no—
121C23×C7—21no—
122C23×C7—21no—
123C23×C7—21no—
124C23×C7—21no—
125C23×C7—41no—
126C23×C7—41no—
127C23×C7—41no—
128C23×C7—41no—
129C23×C7#10112yes—
130C23×C7C2×C22⋊C411yescharacteristic
131C23×C7#13112yes—
132C7×D4—44no—
133C2×C4×C7—22no—
134C2×C4×C7—21no—
135C2×C4×C7—21no—
136C2×C4×C7—21no—
137C2×C4×C7—21no—
138C2×C4×C7—21no—
139C2×C4×C7—21no—
140C2×C4×C7—41no—
141C2×C4×C7—42no—
142C2×C4×C7—41no—
143C2×C4×C7—42no—
144C2×C4×C7—41no—
145C2×C4×C7—41no—
146C2×C4×C7—41no—
147C2×C4×C7—41no—
148C2×C4×C7—42no—
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—41no—
158C2×C4×C7—81no—
159C2×C4×C7—81no—
160C2×C4×C7—81no—
161C2×C4×C7—82no—
162C2×C4×C7#9911yescharacteristic
163C2×C4×C7#9911yescharacteristic
164C7⋊C8—82no—
165C7⋊C8—82no—
166C22×D4C2×Dic711yescharacteristic
167C23×C4C2×Dic711yescharacteristic
168C23×C4C2×Dic711yescharacteristic
169C23×C4C2×Dic711yescharacteristic
170C23×C4C22⋊D711yescharacteristic
171C22×C8—281no—
172C4×D4—41no—
173C4×D4—41no—
174C2×C4⋊C4—21no—
175C2×C4⋊C4—21no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4—21no—
178C2×C4⋊C4—21no—
179C2×C4⋊C4—41no—
180C2×C4⋊C4—41no—
181C2×C4⋊C4C22⋊D711yescharacteristic
182C2×C22⋊C4—21no—
183C2×C22⋊C4—21no—
184C2×C22⋊C4C2×Dic711yescharacteristic
185C2×C22⋊C4C2×Dic711yescharacteristic
186C2×C22⋊C4C22⋊D711yescharacteristic
187C2×C22⋊C4C22×D711yescharacteristic
188C2×C42C22⋊D711yescharacteristic
189C4⋊C8—281no—
190C22⋊C8—142no—
191C22⋊C8—142no—
192C22⋊C8—281no—
193#97—281no—
194#95—21no—
195#95—21no—
196#95—21no—
197#95—21no—
198#95—21no—
199C22×C7—21no—
200C22×C7—21no—
201C22×C7—22no—
202C22×C7—22no—
203C22×C7—42no—
204C22×C7—42no—
205C22×C7—42no—
206C22×C7—41no—
207C22×C7—41no—
208C22×C7—41no—
209C22×C7—41no—
210C22×C7—81no—
211C22×C7#40811yescharacteristic
212C22×C7C2×#9911yescharacteristic
213C22×C7C2×#10111yescharacteristic
214C4×C7—21no—
215C4×C7—21no—
216C4×C7—41no—
217C4×C7—42no—
218C4×C7—41no—
219C4×C7—41no—
220C4×C7—41no—
221C4×C7—81no—
222C4×C7—81no—
223C4×C7—81no—
224C24C22⋊Dic711yescharacteristic
225C24C22×Dic711yescharacteristic
226C2×D4—22no—
227C2×D4—22no—
228C2×D4—41no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—42no—
238C22×C4—41no—
239C22×C4—41no—
240C22×C4—81no—
241C22×C4—81no—
242C22×C4—81no—
243C22×C4C22⋊Dic711yescharacteristic
244C22×C4C22⋊Dic711yescharacteristic
245C22×C4C22⋊Dic711yescharacteristic
246C22×C4C2×C22⋊D711yescharacteristic
247C22×C4C2×C22⋊D711yescharacteristic
248C2×C8—282no—
249C2×C8—282no—
250C2×C8—562no—
251C4⋊C4—41no—
252C4⋊C4—42no—
253C4⋊C4—42no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—81no—
257C4⋊C4—81no—
258C22⋊C4—22no—
259C22⋊C4—22no—
260C22⋊C4—41no—
261C22⋊C4—41no—
262C22⋊C4—42no—
263C22⋊C4—81no—
264C42—21no—
265C42—21no—
266C2×C7—21no—
267C2×C7—21no—
268C2×C7—42no—
269C2×C7—42no—
270C2×C7#147211yescharacteristic
271C2×C7#212011yescharacteristic
272C2×C7#212111yescharacteristic
273C23—21no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23—41no—
278C23—41no—
279C23—41no—
280C23—41no—
281C23#641012yes—
282C23#651112yes—
283C23C2×C22⋊Dic711yescharacteristic
284D4—44no—
285C2×C4—22no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—41no—
293C2×C4—42no—
294C2×C4—41no—
295C2×C4—42no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—42no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—81no—
313C2×C4—82no—
314C2×C4#640811yescharacteristic
315C2×C4#640811yescharacteristic
316C8—562no—
317C8—562no—
318C7#1157811yescharacteristic, complemented, Sylow
319C22—21no—
320C22—21no—
321C22—22no—
322C22—22no—
323C22—42no—
324C22—42no—
325C22—42no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—81no—
331C22C2×#640811yescharacteristic
332C22C2×#641011yescharacteristic
333C22#9000611yescharacteristic
334C4—21no—
335C4—21no—
336C4—41no—
337C4—41no—
338C4—42no—
339C4—41no—
340C4—41no—
341C4—81no—
342C4—81no—
343C4—81no—
344C2—21no—
345C2—21no—
346C2—42no—
347C2—42no—
348C2#1172944511yescharacteristic
349C2#1172947011yescharacteristic
350C2#1172960111yescharacteristic
subgroupG/H
centerC22C2×#6408
commutatorC24×C7C22×C4
FrattiniC2×C22⋊C4C22×D7
FittingC7×#2579C2
socleC22×C7C2×#99
prime radicalC22×C7×D4C2×C4
cosocleC2×C7×C22⋊C4C23
hypercenter#2579D7
hypocenterC7#11578
LCSG ▷ C24×C7 ▷ C22×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2579

Complements

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

NH ≅ G/Ntype
4. #11725442C2semidirect
5. #11725442C2semidirect
318. C7#11578semidirect

Maximal subgroups

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

subgroupindex
C7×#25792
#117293572
#117293542
#117254422
#115787