Finite Group Databasebeta

← #13263358

Subgroups — #13263358

Order 1792.

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

normal subgroups only

This group has 408 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#11739702C211yesmaximal, characteristic
2C7×#1464C211yesmaximal, characteristic, complemented
3#11729325C211yesmaximal, characteristic, complemented
4#11725260C212yesmaximal, complemented
5#11725258C212yesmaximal, complemented
6C2×C7×#117C2211yescharacteristic
7C2×#6493C411yescharacteristic
8C7×#432—21no—
9C4×C22⋊Dic7C411yescharacteristic
10#89760C411yescharacteristic
11#89760C2211yescharacteristic
12#89749C2211yescharacteristic
13#89748C411yescharacteristic
14#89731—21no—
15#89731—21no—
16#89712—21no—
17#89712—21no—
18#89697—21no—
19C7×#324C2212yes—
20C7×#323—21no—
21#89323C2212yes—
22#89320—21no—
23#11550—71nomaximal, Sylow
24C23×C4×C7C2×C411yescharacteristic
25C22×C22⋊D7—21no—
26C22×D28C2×C411yescharacteristic
27C7×#117—41no—
28C7×#117—41no—
29C2×C7×C4⋊C4C2×C411yescharacteristic
30C2×C7×C4⋊C4C2311yescharacteristic
31C2×C7×C22⋊C4D411yescharacteristic
32C2×C7×C22⋊C4D411yescharacteristic
33C2×C42×C7D411yescharacteristic
34C2×C42×C7D411yescharacteristic
35C2×C22⋊Dic7—21no—
36#6493—41no—
37#6493—41no—
38C2×(C2×D7)⋊C4—21no—
39C2×(C2×D7)⋊C4—21no—
40C2×(C2×D7)⋊C4—21no—
41C2×(C2×D7)⋊C4—21no—
42C2×(C2×D7)⋊C4—21no—
43C2×C4⋊Dic7C2×C411yescharacteristic
44C2×Dic7⋊C4—21no—
45C2×Dic7⋊C4—21no—
46C2×C4×Dic7C2×C411yescharacteristic
47C2×C4×Dic7C2×C411yescharacteristic
48C7×C4⋊C8—41no—
49C7×C22⋊C8—22no—
50C7×#97—41no—
51C7⋊#95—21no—
52C7⋊#95—21no—
53C7⋊#95—21no—
54C22⋊(C7⋊C8)—22no—
55C4⋊(C7⋊C8)—41no—
56C4×C7⋊C8—41no—
57#2500—71no—
58#1464D711yescharacteristic, complemented
59#1458—71no—
60#1324—72no—
61#1318—72no—
62C24×C7C22⋊C411yescharacteristic
63C23×D7—21no—
64C22×C4×C7—21no—
65C22×C4×C7—21no—
66C22×C4×C7—22no—
67C22×C4×C7—41no—
68C22×C4×C7C22⋊C411yescharacteristic
69C22×C4×C7C22⋊C411yescharacteristic
70C22×C4×C7C22⋊C411yescharacteristic
71C22×C4×C7C22×C411yescharacteristic
72C22×C4×C7C2×D411yescharacteristic
73C22×C4×C7C2×D411yescharacteristic
74C2×C22⋊D7—42no—
75C2×C22⋊D7—81no—
76C2×C22⋊D7—81no—
77C22×Dic7—21no—
78C22×Dic7—21no—
79C22×Dic7—21no—
80C2×D28—22no—
81C2×D28—41no—
82C2×D28—41no—
83C2×C7×C8—42no—
84C7×C4⋊C4—41no—
85C7×C4⋊C4—41no—
86C7×C22⋊C4—41no—
87C7×C22⋊C4—41no—
88C42×C7—21no—
89C42×C7—21no—
90C42×C7—21no—
91C42×C7—21no—
92C22⋊Dic7—42no—
93(C2×D7)⋊C4—42no—
94(C2×D7)⋊C4—42no—
95(C2×D7)⋊C4—41no—
96(C2×D7)⋊C4—41no—
97(C2×D7)⋊C4—81no—
98(C2×D7)⋊C4—81no—
99C4⋊Dic7—41no—
100Dic7⋊C4—81no—
101Dic7⋊C4—81no—
102C4×Dic7—22no—
103C4×Dic7—41no—
104C2×C7⋊C8—42no—
105C2×#121—71no—
106C2×#117C2×D711yescharacteristic
107#432—21no—
108#431—141no—
109#394—141no—
110#394—141no—
111#390—71no—
112#390—71no—
113#388—141no—
114#388—141no—
115#384—71no—
116#382—71no—
117C4×C22⋊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—41no—
126C23×C7—41no—
127C23×C7C2×C22⋊C411yescharacteristic
128C22×D7—41no—
129C22×D7—41no—
130C22×D7—41no—
131C22×D7—41no—
132C22×D7—41no—
133C22×D7—41no—
134C22×D7—41no—
135C2×C4×C7—21no—
136C2×C4×C7—21no—
137C2×C4×C7—21no—
138C2×C4×C7—21no—
139C2×C4×C7—21no—
140C2×C4×C7—21no—
141C2×C4×C7—21no—
142C2×C4×C7—21no—
143C2×C4×C7—42no—
144C2×C4×C7—42no—
145C2×C4×C7—41no—
146C2×C4×C7—41no—
147C2×C4×C7—41no—
148C2×C4×C7—41no—
149C2×C4×C7#9911yescharacteristic
150C2×C4×C7#9911yescharacteristic
151C2×C4×C7#13112yes—
152C22⋊D7—84no—
153C2×Dic7—22no—
154C2×Dic7—41no—
155C2×Dic7—41no—
156C2×Dic7—41no—
157C2×Dic7—41no—
158C2×Dic7—41no—
159C2×Dic7—41no—
160C2×Dic7—41no—
161C2×Dic7—41no—
162D28—82no—
163C7×C8—82no—
164C7⋊C8—82no—
165C22×D4—71no—
166C22×D4—141no—
167C23×C4C4×D711yescharacteristic
168#121—281no—
169#121—281no—
170#117—41no—
171#117—41no—
172C2×C4⋊C4—71no—
173C2×C4⋊C4—141no—
174C2×C4⋊C4—141no—
175C2×C4⋊C4C4×D711yescharacteristic
176C2×C4⋊C4C22×D711yescharacteristic
177C2×C22⋊C4—141no—
178C2×C22⋊C4—141no—
179C2×C22⋊C4—141no—
180C2×C22⋊C4—141no—
181C2×C22⋊C4—141no—
182C2×C22⋊C4—141no—
183C2×C22⋊C4D2811yescharacteristic
184C2×C22⋊C4C22⋊D711yescharacteristic
185C2×C42—71no—
186C2×C42—71no—
187C2×C42D2811yescharacteristic
188C2×C42C22⋊D711yescharacteristic
189C4⋊C8—41no—
190C4⋊C8—281no—
191C22⋊C8—22no—
192C22⋊C8—142no—
193#97—41no—
194C4×C8—281no—
195#95—141no—
196#95—141no—
197#95—141no—
198C22×C7—21no—
199C22×C7—21no—
200C22×C7—41no—
201C22×C7—41no—
202C22×C7—41no—
203C22×C7—81no—
204C22×C7—81no—
205C22×C7#40811yescharacteristic
206C22×C7C2×#9911yescharacteristic
207C22×C7#41311yescharacteristic
208C2×D7—81no—
209C2×D7—81no—
210C2×D7—81no—
211C2×D7—81no—
212C2×D7—81no—
213C2×D7—81no—
214C2×D7—81no—
215C4×C7—22no—
216C4×C7—21no—
217C4×C7—21no—
218C4×C7—41no—
219C4×C7—41no—
220C4×C7—41no—
221C4×C7—41no—
222Dic7—42no—
223Dic7—81no—
224Dic7—81no—
225C24—141no—
226C24(C2×D7)⋊C411yescharacteristic
227C2×D4—142no—
228C2×D4—281no—
229C2×D4—281no—
230C2×D4—282no—
231C2×D4—561no—
232C2×D4—561no—
233C22×C4—22no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—41no—
237C22×C4—141no—
238C22×C4—141no—
239C22×C4—141no—
240C22×C4(C2×D7)⋊C411yescharacteristic
241C22×C4(C2×D7)⋊C411yescharacteristic
242C22×C4(C2×D7)⋊C411yescharacteristic
243C22×C4C2×C4×D711yescharacteristic
244C22×C4C2×D2811yescharacteristic
245C22×C4C2×C22⋊D711yescharacteristic
246C2×C8—42no—
247C2×C8—282no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—281no—
251C4⋊C4—561no—
252C4⋊C4—561no—
253C22⋊C4—41no—
254C22⋊C4—41no—
255C22⋊C4—282no—
256C22⋊C4—282no—
257C22⋊C4—282no—
258C22⋊C4—281no—
259C22⋊C4—281no—
260C22⋊C4—561no—
261C22⋊C4—561no—
262C42—21no—
263C42—21no—
264C42—21no—
265C42—21no—
266C42—142no—
267C42—281no—
268C2×C7—21no—
269C2×C7—21no—
270C2×C7—81no—
271C2×C7#146811yescharacteristic
272C2×C7#212611yescharacteristic
273C2×C7#213411yescharacteristic
274D7—161no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23—41no—
279C23—41no—
280C23—281no—
281C23—281no—
282C23—281no—
283C23—281no—
284C23—281no—
285C23—281no—
286C23—281no—
287C23C2×(C2×D7)⋊C411yescharacteristic
288D4—562no—
289D4—564no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—42no—
299C2×C4—42no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—142no—
305C2×C4—281no—
306C2×C4—281no—
307C2×C4—281no—
308C2×C4—281no—
309C2×C4—281no—
310C2×C4—281no—
311C2×C4—281no—
312C2×C4—281no—
313C2×C4#638011yescharacteristic
314C2×C4#638011yescharacteristic
315C2×C4#647012yes—
316C8—82no—
317C8—562no—
318C7#1155011yescharacteristic, complemented, Sylow
319C22—21no—
320C22—21no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—81no—
325C22—81no—
326C22—561no—
327C22—561no—
328C22—561no—
329C22—561no—
330C22—561no—
331C22—561no—
332C22—561no—
333C22C2×#638011yescharacteristic
334C22#8990111yescharacteristic
335C22#8990411yescharacteristic
336C4—22no—
337C4—21no—
338C4—21no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—282no—
344C4—561no—
345C4—561no—
346C2—21no—
347C2—21no—
348C2—81no—
349C2—1121no—
350C2#1172772311yescharacteristic
351C2#1172781411yescharacteristic
352C2#1172790311yescharacteristic
subgroupG/H
centerC22C2×#6380
commutatorC22×C4×C7C22×C4
FrattiniC2×C4⋊C4C22×D7
FittingC7×#1464C2
socleC22×C7C2×#99
prime radicalC2×#6493C4
cosocleC2×C7×C4⋊C4C23
hypercenter#1464D7
hypocenterC7#11550
LCSG ▷ C22×C4×C7 ▷ C22×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
2. C7×#1464C2semidirect
3. #11729325C2semidirect
4. #11725260C2semidirect
5. #11725258C2semidirect
58. #1464D7semidirect
318. C7#11550semidirect

Maximal subgroups

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

subgroupindex
#117397022
C7×#14642
#117293252
#117252602
#117252582
#115507