Finite Group Databasebeta

← #13247429

Subgroups — #13247429

Order 1792.

466 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 95 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#11739783C211yesmaximal, characteristic
2C7×#1465C211yesmaximal, characteristic
3C4×#6408C211yesmaximal, characteristic
4#11725489C212yesmaximal, complemented
5#11725488C212yesmaximal, complemented
6C2×C4×C7×D4C2211yescharacteristic
7C7×#407C2212yes—
8#89993—21no—
9C2×#6408—21no—
10#89983C411yescharacteristic, complemented
11#89983C2211yescharacteristic
12C4×C22⋊Dic7C411yescharacteristic, complemented
13C4×C22⋊Dic7C2212yes—
14C4×C22⋊Dic7C2211yescharacteristic
15C4⋊C4×Dic7—21no—
16#89723—21no—
17#89723—21no—
18#89708C411yescharacteristic, complemented
19C4×C4⋊Dic7C411yescharacteristic, complemented
20C7×#324—21no—
21C7×#323—21no—
22#89321—21no—
23#8778—71nomaximal, Sylow
24C22×C7×D4D411yescharacteristic
25C23×C4×C7C2×C411yescharacteristic
26C23×C4×C7C2311yescharacteristic
27C2×C7×M16—22no—
28C4×C7×D4—22no—
29C4×C7×D4—22no—
30C2×C7×C4⋊C4D411yescharacteristic
31C2×C7×C22⋊C4D411yescharacteristic
32C2×C7×C22⋊C4D411yescharacteristic
33C2×C42×C7C2×C411yescharacteristic
34C2×C22⋊Dic7—22no—
35C2×C22⋊Dic7—21no—
36C2×C22⋊Dic7—21no—
37C2×C22⋊Dic7—21no—
38C2×C22⋊Dic7—21no—
39C2×C4⋊Dic7—21no—
40C2×C4⋊Dic7—21no—
41C2×C4×Dic7—21no—
42C2×C4×Dic7—21no—
43C2×C4×Dic7—21no—
44C2×C4×Dic7—22no—
45C7×C22⋊C8—22no—
46C7×C22⋊C8—22no—
47#6408—24no—
48C7⋊#95—21no—
49C7⋊#95—21no—
50C7⋊#95—21no—
51C7⋊#95—22no—
52C7⋊#95C2×C411yescharacteristic
53C7⋊#95C2×C411yescharacteristic
54C7⋊#95C2×C411yescharacteristic
55C7⋊#95C2×C411yescharacteristic
56#2357—71no—
57C4×#99—71no—
58#1465D711yescharacteristic
59#1297—72no—
60#1284—72no—
61C24×C7C22⋊C411yescharacteristic
62C24×C7C2×D411yescharacteristic
63C2×C7×D4—22no—
64C2×C7×D4—22no—
65C2×C7×D4—41no—
66C22×C4×C7—21no—
67C22×C4×C7—21no—
68C22×C4×C7—81no—
69C22×C4×C7—81no—
70C22×C4×C7C22⋊C411yescharacteristic
71C22×C4×C7C22⋊C411yescharacteristic
72C22×C4×C7C22⋊C411yescharacteristic
73C22×C4×C7C22×C411yescharacteristic
74C22×C4×C7C2×D411yescharacteristic
75C22×C4×C7#4112yes—
76C22×C4×C7#4112yes—
77C22×Dic7—21no—
78C22×Dic7—21no—
79C22×Dic7—21no—
80C22×Dic7—21no—
81C22×Dic7—42no—
82C7×M16—82no—
83C2×C7×C8—42no—
84C7×C4⋊C4—22no—
85C7×C22⋊C4—22no—
86C7×C22⋊C4—22no—
87C42×C7—21no—
88C42×C7—21no—
89C22⋊Dic7—24no—
90C22⋊Dic7—42no—
91C22⋊Dic7—42no—
92C22⋊Dic7—42no—
93C22⋊Dic7—81no—
94C22⋊Dic7—81no—
95C4⋊Dic7—42no—
96C4⋊Dic7—42no—
97C4×Dic7—42no—
98C4×Dic7—81no—
99C4×Dic7—81no—
100C4×Dic7—82no—
101C2×C4×D4C2×D711yescharacteristic
102C2×#99—141no—
103#407C2×D712yes—
104#390—141no—
105#388—141no—
106#388—141no—
107#382—71no—
108#381—71no—
109#381—71no—
110C4×C4⋊C4—71no—
111C4×C4⋊C4—141no—
112C4×C22⋊C4—71no—
113C4×C22⋊C4—71no—
114C4×C22⋊C4—72no—
115#342—141no—
116#324—21no—
117#323—21no—
118C23×C7—21no—
119C23×C7—21no—
120C23×C7—21no—
121C23×C7—21no—
122C23×C7—21no—
123C23×C7—41no—
124C23×C7—41no—
125C23×C7—41no—
126C23×C7—41no—
127C23×C7C2×C22⋊C411yescharacteristic
128C23×C7#12312yes—
129C7×D4—44no—
130C2×C4×C7—21no—
131C2×C4×C7—21no—
132C2×C4×C7—21no—
133C2×C4×C7—21no—
134C2×C4×C7—41no—
135C2×C4×C7—42no—
136C2×C4×C7—42no—
137C2×C4×C7—41no—
138C2×C4×C7—41no—
139C2×C4×C7—41no—
140C2×C4×C7—81no—
141C2×C4×C7—81no—
142C2×C4×C7#10412yes—
143C2×C4×C7#11711yescharacteristic
144C2×C4×C7#11711yescharacteristic
145C2×C4×C7#12312yes—
146C2×Dic7—22no—
147C2×Dic7—41no—
148C2×Dic7—41no—
149C2×Dic7—41no—
150C2×Dic7—41no—
151C2×Dic7—41no—
152C2×Dic7—44no—
153C2×Dic7—41no—
154C2×Dic7—41no—
155C2×Dic7—41no—
156C2×Dic7—41no—
157C2×Dic7—41no—
158C2×Dic7—41no—
159C2×Dic7—82no—
160C2×Dic7—82no—
161C7×C8—82no—
162C22×D4D2811yescharacteristic
163C23×C4C4×D711yescharacteristic
164C23×C4C22×D711yescharacteristic
165C2×M16—22no—
166C4×D4—22no—
167C4×D4—22no—
168C2×C4⋊C4—141no—
169C2×C4⋊C4—141no—
170C2×C4⋊C4C22⋊D711yescharacteristic
171C2×C22⋊C4—142no—
172C2×C22⋊C4—141no—
173C2×C22⋊C4—141no—
174C2×C22⋊C4—141no—
175C2×C22⋊C4—141no—
176C2×C22⋊C4D2811yescharacteristic
177C2×C22⋊C4C22⋊D711yescharacteristic
178C2×C42—141no—
179C2×C42—141no—
180C2×C42—141no—
181C2×C42—142no—
182C2×C42C4×D711yescharacteristic
183#99—144no—
184C22⋊C8—22no—
185C22⋊C8—22no—
186#95—71no—
187#95—71no—
188#95—71no—
189#95—71no—
190#95—141no—
191#95—141no—
192#95—141no—
193#95—142no—
194C22×C7—21no—
195C22×C7—21no—
196C22×C7—22no—
197C22×C7—22no—
198C22×C7—22no—
199C22×C7—41no—
200C22×C7—41no—
201C22×C7—41no—
202C22×C7—81no—
203C22×C7—81no—
204C22×C7—81no—
205C22×C7—81no—
206C22×C7#38111yescharacteristic
207C22×C7C2×#10411yescharacteristic
208C22×C7#42111yescharacteristic
209C4×C7—22no—
210C4×C7—22no—
211C4×C7—21no—
212C4×C7—21no—
213C4×C7—41no—
214C4×C7—41no—
215Dic7—42no—
216Dic7—81no—
217Dic7—81no—
218Dic7—81no—
219Dic7—84no—
220C24(C2×D7)⋊C411yescharacteristic
221C24C2×D2811yescharacteristic
222C2×D4—22no—
223C2×D4—22no—
224C2×D4—41no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—81no—
228C22×C4—81no—
229C22×C4—141no—
230C22×C4—141no—
231C22×C4—141no—
232C22×C4—141no—
233C22×C4—282no—
234C22×C4(C2×D7)⋊C411yescharacteristic
235C22×C4(C2×D7)⋊C411yescharacteristic
236C22×C4(C2×D7)⋊C411yescharacteristic
237C22×C4C2×C4×D711yescharacteristic
238C22×C4#115912yes—
239C22×C4#115912yes—
240C22×C4C2×C22⋊D711yescharacteristic
241M16—82no—
242C2×C8—42no—
243C4⋊C4—22no—
244C4⋊C4—282no—
245C4⋊C4—282no—
246C22⋊C4—22no—
247C22⋊C4—22no—
248C22⋊C4—144no—
249C22⋊C4—282no—
250C22⋊C4—282no—
251C22⋊C4—282no—
252C22⋊C4—561no—
253C22⋊C4—561no—
254C42—21no—
255C42—21no—
256C42—282no—
257C42—561no—
258C42—561no—
259C42—562no—
260C2×C7—21no—
261C2×C7—21no—
262C2×C7—42no—
263C2×C7—81no—
264C2×C7#182611yescharacteristic
265C2×C7#182711yescharacteristic
266C2×C7#182811yescharacteristic
267C23—21no—
268C23—21no—
269C23—21no—
270C23—21no—
271C23—21no—
272C23—41no—
273C23—41no—
274C23—41no—
275C23—41no—
276C23#644912yes—
277C23C2×(C2×D7)⋊C411yescharacteristic
278D4—44no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—42no—
284C2×C4—41no—
285C2×C4—42no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—81no—
290C2×C4—81no—
291C2×C4—142no—
292C2×C4—281no—
293C2×C4—281no—
294C2×C4—281no—
295C2×C4—281no—
296C2×C4—284no—
297C2×C4—281no—
298C2×C4—281no—
299C2×C4—281no—
300C2×C4—281no—
301C2×C4—281no—
302C2×C4—281no—
303C2×C4—281no—
304C2×C4—562no—
305C2×C4—562no—
306C2×C4#639912yes—
307C2×C4#644011yescharacteristic
308C2×C4#644011yescharacteristic
309C2×C4#649812yes—
310C8—82no—
311C7#877811yescharacteristic, complemented, Sylow
312C22—21no—
313C22—21no—
314C22—22no—
315C22—22no—
316C22—22no—
317C22—41no—
318C22—41no—
319C22—41no—
320C22—81no—
321C22—81no—
322C22—81no—
323C22—81no—
324C22#8971511yescharacteristic
325C22C2×#639911yescharacteristic
326C22#8991111yescharacteristic
327C4—22no—
328C4—22no—
329C4—21no—
330C4—21no—
331C4—41no—
332C4—41no—
333C4—282no—
334C4—561no—
335C4—561no—
336C4—561no—
337C4—564no—
338C2—21no—
339C2—21no—
340C2—42no—
341C2—81no—
342C2#1172772911yescharacteristic
343C2#1172777411yescharacteristic
344C2#1172788511yescharacteristic
subgroupG/H
centerC22#89715
commutatorC22×C4×C7C22×C4
FrattiniC23×C4C22×D7
FittingC7×#1465C2
socleC22×C7#381
prime radicalC22×C7×D4D4
cosocleC23×C4×C7C23
hypercenter#1465D7
hypocenterC7#8778
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1465

Complements

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

NH ≅ G/Ntype
4. #11725489C2semidirect
5. #11725488C2semidirect
10. #89983C4semidirect
12. C4×C22⋊Dic7C4semidirect
18. #89708C4semidirect
19. C4×C4⋊Dic7C4semidirect
311. C7#8778semidirect

Maximal subgroups

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

subgroupindex
#117397832
C7×#14652
C4×#64082
#117254892
#117254882
#87787