Finite Group Databasebeta

← #13263337

Subgroups — #13263337

Order 1792.

460 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 87 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×#2482C211yesmaximal, characteristic
2#11729326C211yesmaximal, characteristic, complemented
3#11729325C211yesmaximal, characteristic, complemented
4#11725442C212yesmaximal, complemented
5#11725428C212yesmaximal
6C2×C7×#117C2211yescharacteristic
7C22×C7×C22⋊C4C411yescharacteristic
8C7×#399—21no—
9C7×#397—21no—
10C7×#388—21no—
11C7×#388—21no—
12C7×#385C411yescharacteristic
13C7×#385C2211yescharacteristic
14C7×#381C411yescharacteristic
15C7×#379C411yescharacteristic
16C7×#379C2211yescharacteristic
17#89698—21no—
18#89697—21no—
19#89323—21no—
20#89323—21no—
21#89320C2212yes—
22#89320C2212yes—
23#11546—71nomaximal, Sylow
24C25×C7C2×C411yescharacteristic
25C23×C4×C7C2×C411yescharacteristic
26C23×C4×C7C2×C411yescharacteristic
27C7×#117—41no—
28C7×#117—41no—
29C2×C7×C4⋊C4—21no—
30C2×C7×C4⋊C4—21no—
31C2×C7×C4⋊C4D411yescharacteristic
32C2×C7×C4⋊C4D411yescharacteristic
33C2×C7×C22⋊C4—21no—
34C2×C7×C22⋊C4—21no—
35C2×C7×C22⋊C4—21no—
36C2×C7×C22⋊C4—21no—
37C2×C7×C22⋊C4—21no—
38C2×C7×C22⋊C4—21no—
39C2×C7×C22⋊C4—41no—
40C2×C7×C22⋊C4—41no—
41C2×C7×C22⋊C4C2×C411yescharacteristic
42C2×C7×C22⋊C4C2×C411yescharacteristic
43C2×C7×C22⋊C4C2×C411yescharacteristic
44C2×C7×C22⋊C4C2311yescharacteristic
45C2×C42×C7D411yescharacteristic
46C2×C42×C7D411yescharacteristic
47C7×#95—21no—
48C7×#95—21no—
49C7×#95—21no—
50C7×#95—21no—
51C22⋊(C7⋊C8)—22no—
52C22⋊(C7⋊C8)—22no—
53C4⋊(C7⋊C8)—41no—
54C4⋊(C7⋊C8)—41no—
55#6377—41no—
56C4×C7⋊C8—41no—
57#2482D711yescharacteristic
58#1464—71no—
59#1458—71no—
60#1326—72no—
61#1316—72no—
62C24×C7—21no—
63C24×C7—22no—
64C24×C7—41no—
65C24×C7—42no—
66C24×C7—41no—
67C24×C7—81no—
68C24×C7C22×C411yescharacteristic
69C22×C4×C7—22no—
70C22×C4×C7—21no—
71C22×C4×C7—21no—
72C22×C4×C7—21no—
73C22×C4×C7—21no—
74C22×C4×C7—21no—
75C22×C4×C7—41no—
76C22×C4×C7—41no—
77C22×C4×C7—81no—
78C22×C4×C7C22⋊C411yescharacteristic
79C22×C4×C7C22⋊C411yescharacteristic
80C22×C4×C7C22⋊C411yescharacteristic
81C22×C4×C7C22⋊C411yescharacteristic
82C22×C4×C7C2×D411yescharacteristic
83C22×C4×C7C2×D411yescharacteristic
84C7×C4⋊C4—41no—
85C7×C4⋊C4—41no—
86C7×C4⋊C4—81no—
87C7×C4⋊C4—81no—
88C7×C22⋊C4—22no—
89C7×C22⋊C4—41no—
90C7×C22⋊C4—41no—
91C7×C22⋊C4—42no—
92C7×C22⋊C4—42no—
93C7×C22⋊C4—42no—
94C7×C22⋊C4—41no—
95C7×C22⋊C4—41no—
96C7×C22⋊C4—41no—
97C7×C22⋊C4—81no—
98C7×C22⋊C4—81no—
99C42×C7—21no—
100C42×C7—21no—
101C42×C7—21no—
102C42×C7—21no—
103C2×C7⋊C8—42no—
104C2×C7⋊C8—42no—
105C2×#117C2×D711yescharacteristic
106C22×C22⋊C4Dic711yescharacteristic
107#432—141no—
108#431—141no—
109#399—21no—
110#397—21no—
111#388—21no—
112#388—21no—
113#385Dic711yescharacteristic
114#385C2×D711yescharacteristic
115#381Dic711yescharacteristic
116#379Dic711yescharacteristic
117#379C2×D711yescharacteristic
118#324—141no—
119#324—141no—
120#323—72no—
121#323—72no—
122C23×C7—21no—
123C23×C7—21no—
124C23×C7—22no—
125C23×C7—41no—
126C23×C7—41no—
127C23×C7—41no—
128C23×C7—41no—
129C23×C7—41no—
130C23×C7—42no—
131C23×C7—42no—
132C23×C7—41no—
133C23×C7—41no—
134C23×C7—41no—
135C23×C7—82no—
136C23×C7—84no—
137C23×C7—84no—
138C23×C7—82no—
139C23×C7C2×C22⋊C411yescharacteristic
140C23×C7#13112yes—
141C2×C4×C7—21no—
142C2×C4×C7—21no—
143C2×C4×C7—21no—
144C2×C4×C7—21no—
145C2×C4×C7—21no—
146C2×C4×C7—21no—
147C2×C4×C7—21no—
148C2×C4×C7—21no—
149C2×C4×C7—21no—
150C2×C4×C7—42no—
151C2×C4×C7—42no—
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—41no—
159C2×C4×C7—41no—
160C2×C4×C7—41no—
161C2×C4×C7—41no—
162C2×C4×C7—41no—
163C2×C4×C7—41no—
164C2×C4×C7—41no—
165C2×C4×C7—82no—
166C2×C4×C7#9911yescharacteristic
167C2×C4×C7#9911yescharacteristic
168C7⋊C8—82no—
169C7⋊C8—82no—
170C25C2×Dic711yescharacteristic
171C23×C4C2×Dic711yescharacteristic
172C23×C4C2×Dic711yescharacteristic
173#117—41no—
174#117—41no—
175C2×C4⋊C4—21no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4C22⋊D711yescharacteristic
178C2×C4⋊C4C22⋊D711yescharacteristic
179C2×C22⋊C4—21no—
180C2×C22⋊C4—21no—
181C2×C22⋊C4—21no—
182C2×C22⋊C4—21no—
183C2×C22⋊C4—21no—
184C2×C22⋊C4—21no—
185C2×C22⋊C4—41no—
186C2×C22⋊C4—41no—
187C2×C22⋊C4C2×Dic711yescharacteristic
188C2×C22⋊C4C2×Dic711yescharacteristic
189C2×C22⋊C4C2×Dic711yescharacteristic
190C2×C22⋊C4C22×D711yescharacteristic
191C2×C42C22⋊D711yescharacteristic
192C2×C42C22⋊D711yescharacteristic
193C4⋊C8—281no—
194C4⋊C8—281no—
195C22⋊C8—142no—
196C22⋊C8—142no—
197#97—281no—
198C4×C8—281no—
199#95—21no—
200#95—21no—
201#95—21no—
202#95—21no—
203C22×C7—21no—
204C22×C7—21no—
205C22×C7—22no—
206C22×C7—42no—
207C22×C7—42no—
208C22×C7—42no—
209C22×C7—42no—
210C22×C7—41no—
211C22×C7—41no—
212C22×C7—42no—
213C22×C7—81no—
214C22×C7—81no—
215C22×C7—84no—
216C22×C7—84no—
217C22×C7—81no—
218C22×C7—81no—
219C22×C7#40811yescharacteristic
220C22×C7C2×#9911yescharacteristic
221C22×C7#41311yescharacteristic
222C4×C7—21no—
223C4×C7—21no—
224C4×C7—41no—
225C4×C7—41no—
226C4×C7—41no—
227C4×C7—41no—
228C4×C7—41no—
229C4×C7—81no—
230C4×C7—81no—
231C4×C7—81no—
232C24—21no—
233C24—22no—
234C24—41no—
235C24—42no—
236C24—41no—
237C24—81no—
238C24C22×Dic711yescharacteristic
239C22×C4—22no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—41no—
246C22×C4—41no—
247C22×C4—81no—
248C22×C4C22⋊Dic711yescharacteristic
249C22×C4C22⋊Dic711yescharacteristic
250C22×C4C22⋊Dic711yescharacteristic
251C22×C4C22⋊Dic711yescharacteristic
252C22×C4C2×C22⋊D711yescharacteristic
253C22×C4C2×C22⋊D711yescharacteristic
254C2×C8—282no—
255C2×C8—282no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—81no—
259C4⋊C4—81no—
260C22⋊C4—22no—
261C22⋊C4—41no—
262C22⋊C4—41no—
263C22⋊C4—42no—
264C22⋊C4—42no—
265C22⋊C4—42no—
266C22⋊C4—41no—
267C22⋊C4—41no—
268C22⋊C4—41no—
269C22⋊C4—81no—
270C22⋊C4—81no—
271C42—21no—
272C42—21no—
273C42—21no—
274C42—21no—
275C2×C7—21no—
276C2×C7—21no—
277C2×C7—42no—
278C2×C7—82no—
279C2×C7#146811yescharacteristic
280C2×C7#212011yescharacteristic
281C2×C7#212211yescharacteristic
282C23—21no—
283C23—21no—
284C23—22no—
285C23—41no—
286C23—41no—
287C23—41no—
288C23—41no—
289C23—41no—
290C23—42no—
291C23—42no—
292C23—41no—
293C23—41no—
294C23—41no—
295C23—82no—
296C23—84no—
297C23—84no—
298C23—82no—
299C23#651112yes—
300C23C2×C22⋊Dic711yescharacteristic
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—82no—
326C2×C4#640811yescharacteristic
327C2×C4#640811yescharacteristic
328C8—562no—
329C8—562no—
330C7#1154611yescharacteristic, complemented, Sylow
331C22—21no—
332C22—21no—
333C22—22no—
334C22—42no—
335C22—42no—
336C22—42no—
337C22—42no—
338C22—41no—
339C22—41no—
340C22—42no—
341C22—81no—
342C22—81no—
343C22—84no—
344C22—84no—
345C22—81no—
346C22—81no—
347C22C2×#640811yescharacteristic
348C22#9000611yescharacteristic
349C22#9000911yescharacteristic
350C4—21no—
351C4—21no—
352C4—41no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—81no—
358C4—81no—
359C4—81no—
360C2—21no—
361C2—21no—
362C2—42no—
363C2—82no—
364C2#1172945611yescharacteristic
365C2#1172947011yescharacteristic
366C2#1172961311yescharacteristic
subgroupG/H
centerC22C2×#6408
commutatorC24×C7C22×C4
FrattiniC2×C22⋊C4C22×D7
FittingC7×#2482C2
socleC22×C7C2×#99
prime radicalC25×C7C2×C4
cosocleC2×C7×C22⋊C4C23
hypercenter#2482D7
hypocenterC7#11546
LCSG ▷ C24×C7 ▷ C22×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #2482

Complements

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

NH ≅ G/Ntype
2. #11729326C2semidirect
3. #11729325C2semidirect
4. #11725442C2semidirect
330. C7#11546semidirect

Maximal subgroups

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

subgroupindex
C7×#24822
#117293262
#117293252
#117254422
#117254282
#115467