Finite Group Databasebeta

← #13264308

Subgroups — #13264308

Order 1792.

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

normal subgroups only

This group has 446 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
1#11739621C211yesmaximal, characteristic
2C7×#1463C211yesmaximal, characteristic
3C2×#89325C211yesmaximal, characteristic
4#11725265C212yesmaximal, complemented
5#11725264C212yesmaximal, complemented
6C22×C7×C4⋊C4C2211yescharacteristic
7C2×#6489C411yescharacteristic
8C22×#1136—21no—
9C7×#407—21no—
10#89983—21no—
11#89983C411yescharacteristic
12#89982—21no—
13#89758C411yescharacteristic
14#89758C2211yescharacteristic
15#89755C411yescharacteristic
16#89755C2211yescharacteristic
17#89750—21no—
18#89750—21no—
19C7×#324—21no—
20C7×#324C2212yes—
21#89325—21no—
22#89325C2212yes—
23#11764—71nomaximal, Sylow
24C23×C4×C7C2×C411yescharacteristic
25C23×C4×C7D411yescharacteristic
26C23×C4×C7D411yescharacteristic
27C2×C7×M16—41no—
28C2×C7×C4⋊C4—41no—
29C2×C7×C4⋊C4—41no—
30C2×C7×C4⋊C4C2×C411yescharacteristic
31C2×C7×C4⋊C4D411yescharacteristic
32C2×C7×C4⋊C4D411yescharacteristic
33C2×C7×C4⋊C4C2311yescharacteristic
34C2×C22⋊Dic7—21no—
35C2×C22⋊Dic7—21no—
36#6489—41no—
37#6489—41no—
38C2×C4⋊Dic7C2×C411yescharacteristic
39C2×C4⋊Dic7C2×C411yescharacteristic
40C2×Dic7⋊C4—21no—
41C2×Dic7⋊C4—21no—
42C2×C4×Dic7—21no—
43C2×#1136—24no—
44C2×#1136—22no—
45C2×#1136—41no—
46C2×#1136—42no—
47C22×C7⋊C8—41no—
48C7×C22⋊C8—22no—
49C7×C22⋊C8—41no—
50C7⋊#95—21no—
51C7⋊#95—21no—
52C7⋊#95—21no—
53C7⋊#95—21no—
54C7⋊#95—21no—
55C7⋊#95—21no—
56C7⋊#95—21no—
57C7⋊#95C2×C411yescharacteristic
58C7⋊#95C2×C411yescharacteristic
59#2484—71no—
60C2×#343—71no—
61#1463D711yescharacteristic
62#1353—72no—
63#1346—72no—
64C24×C7C22⋊C411yescharacteristic
65C22×C4×C7—21no—
66C22×C4×C7—21no—
67C22×C4×C7—22no—
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—42no—
75C22×C4×C7—42no—
76C22×C4×C7C22⋊C411yescharacteristic
77C22×C4×C7C22⋊C411yescharacteristic
78C22×C4×C7C22⋊C411yescharacteristic
79C22×C4×C7C22×C411yescharacteristic
80C22×C4×C7C2×D411yescharacteristic
81C22×C4×C7C2×D411yescharacteristic
82C22×Dic7—21no—
83C22×Dic7—21no—
84C22×Dic7—21no—
85C22×Dic7—21no—
86C7×M16—82no—
87C2×C7×C8—42no—
88C7×C4⋊C4—41no—
89C7×C4⋊C4—41no—
90C7×C4⋊C4—41no—
91C7×C4⋊C4—41no—
92C22⋊Dic7—42no—
93C22⋊Dic7—41no—
94C22⋊Dic7—41no—
95C4⋊Dic7—41no—
96C4⋊Dic7—41no—
97Dic7⋊C4—42no—
98Dic7⋊C4—41no—
99Dic7⋊C4—41no—
100C4×Dic7—42no—
101#1136—24no—
102#1136—44no—
103#1136—42no—
104C2×C7⋊C8—44no—
105C2×C7⋊C8—42no—
106C22×M16—141no—
107C2×#117—71no—
108C22×C4⋊C4C2×D711yescharacteristic
109#407—21no—
110#400—71no—
111#400—71no—
112#398—71no—
113#398—71no—
114#387—141no—
115#387—141no—
116#385—141no—
117#381—71no—
118#381—141no—
119#343—72no—
120#343—141no—
121#324—21no—
122#324C2×D712yes—
123C23×C7—22no—
124C23×C7—21no—
125C23×C7—21no—
126C23×C7—41no—
127C23×C7#9911yescharacteristic
128C23×C7#9911yescharacteristic
129C23×C7C2×C22⋊C411yescharacteristic
130C2×C4×C7—22no—
131C2×C4×C7—22no—
132C2×C4×C7—22no—
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—21no—
141C2×C4×C7—21no—
142C2×C4×C7—42no—
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—81no—
150C2×C4×C7#10412yes—
151C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
152C2×C4×C7#13711yescharacteristic
153C2×Dic7—41no—
154C2×Dic7—41no—
155C2×Dic7—41no—
156C2×Dic7—41no—
157C2×Dic7—42no—
158C2×Dic7—41no—
159C2×Dic7—41no—
160C2×Dic7—41no—
161C2×Dic7—41no—
162C2×Dic7—41no—
163C2×Dic7—41no—
164C7×C8—82no—
165C7⋊C8—44no—
166C23×C4C4×D711yescharacteristic
167C23×C4D2811yescharacteristic
168C23×C4C22⋊D711yescharacteristic
169C2×M16—41no—
170C2×M16—144no—
171C2×M16—142no—
172C2×M16—281no—
173C2×M16—282no—
174C22×C8—281no—
175#117—281no—
176#117—281no—
177C2×C4⋊C4—41no—
178C2×C4⋊C4—41no—
179C2×C4⋊C4—71no—
180C2×C4⋊C4—71no—
181C2×C4⋊C4—141no—
182C2×C4⋊C4—141no—
183C2×C4⋊C4C4×D711yescharacteristic
184C2×C4⋊C4D2811yescharacteristic
185C2×C4⋊C4C22⋊D711yescharacteristic
186C2×C4⋊C4C22×D711yescharacteristic
187C2×C22⋊C4—141no—
188C2×C22⋊C4—141no—
189C2×C42—141no—
190C22⋊C8—22no—
191C22⋊C8—41no—
192#95—71no—
193#95—71no—
194#95—141no—
195#95—141no—
196#95—141no—
197#95—141no—
198#95—141no—
199#95—141no—
200#95—141no—
201C22×C7—21no—
202C22×C7—21no—
203C22×C7—21no—
204C22×C7—21no—
205C22×C7—21no—
206C22×C7—21no—
207C22×C7—21no—
208C22×C7—42no—
209C22×C7—42no—
210C22×C7#35212yes—
211C22×C7C2×#9911yescharacteristic
212C22×C7#41711yescharacteristic
213C22×C7C2×#10411yescharacteristic
214C4×C7—21no—
215C4×C7—22no—
216C4×C7—21no—
217C4×C7—41no—
218C4×C7—41no—
219C4×C7—41no—
220C4×C7—41no—
221Dic7—81no—
222Dic7—81no—
223Dic7—81no—
224Dic7—81no—
225C24(C2×D7)⋊C411yescharacteristic
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—22no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—42no—
236C22×C4—42no—
237C22×C4—141no—
238C22×C4—141no—
239C22×C4—141no—
240C22×C4—141no—
241C22×C4(C2×D7)⋊C411yescharacteristic
242C22×C4(C2×D7)⋊C411yescharacteristic
243C22×C4(C2×D7)⋊C411yescharacteristic
244C22×C4C2×C4×D711yescharacteristic
245C22×C4C2×D2811yescharacteristic
246C22×C4C2×C22⋊D711yescharacteristic
247M16—82no—
248M16—144no—
249M16—284no—
250M16—282no—
251C2×C8—42no—
252C2×C8—284no—
253C2×C8—282no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—281no—
259C4⋊C4—281no—
260C4⋊C4—281no—
261C4⋊C4—281no—
262C4⋊C4—282no—
263C22⋊C4—282no—
264C22⋊C4—281no—
265C22⋊C4—281no—
266C42—282no—
267C2×C7—21no—
268C2×C7—21no—
269C2×C7—22no—
270C2×C7—41no—
271C2×C7#150411yescharacteristic
272C2×C7C2×#35211yescharacteristic
273C2×C7#213311yescharacteristic
274C23—21no—
275C23—21no—
276C23—22no—
277C23—41no—
278C23#638011yescharacteristic
279C23#638011yescharacteristic
280C23C2×(C2×D7)⋊C411yescharacteristic
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—81no—
301C2×C4—281no—
302C2×C4—281no—
303C2×C4—281no—
304C2×C4—281no—
305C2×C4—282no—
306C2×C4—281no—
307C2×C4—281no—
308C2×C4—281no—
309C2×C4—281no—
310C2×C4—281no—
311C2×C4—281no—
312C2×C4#639912yes—
313C2×C4#647111yescharacteristic
314C2×C4#647211yescharacteristic
315C8—82no—
316C8—284no—
317C7#1176411yescharacteristic, complemented, Sylow
318C22—21no—
319C22—21no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—42no—
326C22—42no—
327C22#8926712yes—
328C22C2×#638011yescharacteristic
329C22#8990511yescharacteristic
330C22C2×#639911yescharacteristic
331C4—21no—
332C4—21no—
333C4—22no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—561no—
339C4—561no—
340C4—561no—
341C4—561no—
342C2—21no—
343C2—21no—
344C2—22no—
345C2—41no—
346C2#1172773011yescharacteristic
347C2C2×#8926711yescharacteristic
348C2#1172788211yescharacteristic
subgroupG/H
centerC22C2×#6380
commutatorC22×C4×C7C22×C4
FrattiniC2×C4⋊C4C22×D7
FittingC7×#1463C2
socleC22×C7C2×#99
prime radicalC24×C7C22⋊C4
cosocleC2×C7×C4⋊C4C23
hypercenter#1463D7
hypocenterC7#11764
LCSG ▷ C22×C4×C7 ▷ C23×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ #1463

Complements

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

NH ≅ G/Ntype
4. #11725265C2semidirect
5. #11725264C2semidirect
317. C7#11764semidirect

Maximal subgroups

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

subgroupindex
#117396212
C7×#14632
C2×#893252
#117252652
#117252642
#117647