Finite Group Databasebeta

← #13247428

Subgroups — #13247428

Order 1792.

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

normal subgroups only

This group has 480 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#11739781C211yesmaximal, characteristic
2C4×C7×#99C211yesmaximal, characteristic
3#11729356C211yesmaximal, characteristic
4#11725424C212yesmaximal, complemented
5#11725422C212yesmaximal, complemented
6C2×C4×C7×D4C2211yescharacteristic
7C2×C7×#99—21no—
8C4×C7×C22⋊C4C2212yes—
9#89992—21no—
10#89984C411yescharacteristic, complemented
11#89983C2211yescharacteristic
12C4×C22⋊Dic7C2211yescharacteristic
13C2×C7⋊#95C411yescharacteristic, complemented
14#89979C2212yes—
15#89753—21no—
16#89723—21no—
17C22⋊C4×Dic7—21no—
18#89709C411yescharacteristic, complemented
19#89704C411yescharacteristic, complemented
20C7×#342—21no—
21#89323—21no—
22#89320—21no—
23#8777—71nomaximal, Sylow
24C22×C7×D4D411yescharacteristic
25C23×C4×C7C2×C411yescharacteristic
26C23×C4×C7C2311yescharacteristic
27C23×Dic7—21no—
28C4×C7×D4—22no—
29C4×C7×D4—22no—
30C2×C7×C4⋊C4D411yescharacteristic
31C2×C7×C22⋊C4—22no—
32C2×C7×C22⋊C4D411yescharacteristic
33C2×C7×C22⋊C4D411yescharacteristic
34C2×C42×C7—22no—
35C2×C42×C7C2×C411yescharacteristic
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×#1136—22no—
43C7×#99—24no—
44C7×#95—22no—
45C7⋊#95—21no—
46C7⋊#95—21no—
47C7⋊#95—21no—
48C7⋊#95—21no—
49C7⋊#95—21no—
50C7⋊#95C2×C411yescharacteristic
51C7⋊#95C2×C411yescharacteristic
52C7⋊#95C2×C411yescharacteristic
53C7⋊#95C2×C411yescharacteristic
54C22⋊(C7⋊C8)—22no—
55C22⋊(C7⋊C8)—22no—
56#2353—71no—
57C4×#99D711yescharacteristic
58#1465—71no—
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—42no—
69C22×C4×C7—81no—
70C22×C4×C7—81no—
71C22×C4×C7C22⋊C411yescharacteristic
72C22×C4×C7C22⋊C411yescharacteristic
73C22×C4×C7C22⋊C411yescharacteristic
74C22×C4×C7C22×C411yescharacteristic
75C22×C4×C7C2×D411yescharacteristic
76C22×C4×C7#4112yes—
77C22×C4×C7#4112yes—
78C22×Dic7—21no—
79C22×Dic7—21no—
80C22×Dic7—21no—
81C22×Dic7—21no—
82C22×Dic7—42no—
83C22×Dic7—42no—
84C22×Dic7—81no—
85C7×C4⋊C4—22no—
86C7×C22⋊C4—22no—
87C7×C22⋊C4—22no—
88C7×C22⋊C4—24no—
89C7×C22⋊C4—42no—
90C42×C7—21no—
91C42×C7—21no—
92C42×C7—82no—
93C22⋊Dic7—42no—
94C22⋊Dic7—42no—
95C22⋊Dic7—81no—
96C4⋊Dic7—81no—
97C4×Dic7—42no—
98C4×Dic7—81no—
99#1136—82no—
100C2×C7⋊C8—42no—
101C2×C4×D4C2×D711yescharacteristic
102C2×#99—21no—
103#407—72no—
104#388—141no—
105#387—141no—
106#386—141no—
107#383—71no—
108#381—71no—
109#380—71no—
110C4×C22⋊C4—71no—
111C4×C22⋊C4—141no—
112C4×C22⋊C4C2×D712yes—
113#376—71no—
114C2×#95—71no—
115#342—21no—
116#324—141no—
117#323—141no—
118C23×C7—21no—
119C23×C7—21no—
120C23×C7—21no—
121C23×C7—21no—
122C23×C7—41no—
123C23×C7—41no—
124C23×C7—41no—
125C23×C7—41no—
126C23×C7#10412yes—
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—21no—
135C2×C4×C7—42no—
136C2×C4×C7—41no—
137C2×C4×C7—42no—
138C2×C4×C7—41no—
139C2×C4×C7—41no—
140C2×C4×C7—41no—
141C2×C4×C7—44no—
142C2×C4×C7—81no—
143C2×C4×C7—81no—
144C2×C4×C7—82no—
145C2×C4×C7—82no—
146C2×C4×C7#11711yescharacteristic
147C2×C4×C7#11711yescharacteristic
148C2×C4×C7#12312yes—
149C2×Dic7—22no—
150C2×Dic7—41no—
151C2×Dic7—41no—
152C2×Dic7—41no—
153C2×Dic7—41no—
154C2×Dic7—41no—
155C2×Dic7—41no—
156C2×Dic7—41no—
157C2×Dic7—41no—
158C2×Dic7—41no—
159C2×Dic7—41no—
160C2×Dic7—41no—
161C2×Dic7—84no—
162C7⋊C8—82no—
163C22×D4C22⋊D711yescharacteristic
164C23×C4—141no—
165C23×C4C4×D711yescharacteristic
166C23×C4C22×D711yescharacteristic
167C2×M16—142no—
168C4×D4—22no—
169C4×D4—22no—
170C2×C4⋊C4—141no—
171C2×C4⋊C4D2811yescharacteristic
172C2×C22⋊C4—22no—
173C2×C22⋊C4—141no—
174C2×C22⋊C4—141no—
175C2×C22⋊C4—141no—
176C2×C22⋊C4D2811yescharacteristic
177C2×C22⋊C4C22⋊D711yescharacteristic
178C2×C42—22no—
179C2×C42—141no—
180C2×C42—141no—
181C2×C42C4×D711yescharacteristic
182#99—24no—
183C22⋊C8—142no—
184C22⋊C8—142no—
185#95—22no—
186#95—71no—
187#95—71no—
188#95—71no—
189#95—71no—
190#95—141no—
191#95—141no—
192#95—141no—
193#95—141no—
194#95—141no—
195C22×C7—21no—
196C22×C7—21no—
197C22×C7—22no—
198C22×C7—22no—
199C22×C7—22no—
200C22×C7—22no—
201C22×C7—42no—
202C22×C7—42no—
203C22×C7—41no—
204C22×C7—41no—
205C22×C7—81no—
206C22×C7—81no—
207C22×C7#38111yescharacteristic
208C22×C7C2×#10411yescharacteristic
209C22×C7#42111yescharacteristic
210C4×C7—22no—
211C4×C7—21no—
212C4×C7—21no—
213C4×C7—41no—
214C4×C7—41no—
215C4×C7—41no—
216C4×C7—84no—
217Dic7—42no—
218Dic7—81no—
219Dic7—81no—
220Dic7—81no—
221C24(C2×D7)⋊C411yescharacteristic
222C24C2×C22⋊D711yescharacteristic
223C2×D4—22no—
224C2×D4—22no—
225C2×D4—41no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—42no—
229C22×C4—81no—
230C22×C4—81no—
231C22×C4—141no—
232C22×C4—141no—
233C22×C4—141no—
234C22×C4—141no—
235C22×C4—282no—
236C22×C4—282no—
237C22×C4—561no—
238C22×C4(C2×D7)⋊C411yescharacteristic
239C22×C4(C2×D7)⋊C411yescharacteristic
240C22×C4(C2×D7)⋊C411yescharacteristic
241C22×C4C2×C4×D711yescharacteristic
242C22×C4C2×D2811yescharacteristic
243C22×C4#115912yes—
244C22×C4#115912yes—
245M16—562no—
246C2×C8—282no—
247C4⋊C4—22no—
248C4⋊C4—561no—
249C22⋊C4—22no—
250C22⋊C4—22no—
251C22⋊C4—24no—
252C22⋊C4—42no—
253C22⋊C4—282no—
254C22⋊C4—282no—
255C22⋊C4—561no—
256C42—21no—
257C42—21no—
258C42—82no—
259C42—282no—
260C42—561no—
261C2×C7—21no—
262C2×C7—21no—
263C2×C7—42no—
264C2×C7—42no—
265C2×C7#182611yescharacteristic
266C2×C7#182711yescharacteristic
267C2×C7#182811yescharacteristic
268C23—21no—
269C23—21no—
270C23—21no—
271C23—21no—
272C23—41no—
273C23—41no—
274C23—41no—
275C23—41no—
276C23#637912yes—
277C23C2×(C2×D7)⋊C411yescharacteristic
278C23#649812yes—
279D4—44no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—42no—
286C2×C4—41no—
287C2×C4—42no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—44no—
292C2×C4—81no—
293C2×C4—81no—
294C2×C4—82no—
295C2×C4—82no—
296C2×C4—142no—
297C2×C4—281no—
298C2×C4—281no—
299C2×C4—281no—
300C2×C4—281no—
301C2×C4—281no—
302C2×C4—281no—
303C2×C4—281no—
304C2×C4—281no—
305C2×C4—281no—
306C2×C4—281no—
307C2×C4—281no—
308C2×C4—564no—
309C2×C4#644011yescharacteristic
310C2×C4#644011yescharacteristic
311C2×C4#644912yes—
312C8—562no—
313C7#877711yescharacteristic, complemented, Sylow
314C22—21no—
315C22—21no—
316C22—22no—
317C22—22no—
318C22—22no—
319C22—22no—
320C22—42no—
321C22—42no—
322C22—41no—
323C22—41no—
324C22—81no—
325C22—81no—
326C22C2×#637911yescharacteristic
327C22#8971511yescharacteristic
328C22#8977711yescharacteristic
329C4—22no—
330C4—21no—
331C4—21no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—84no—
336C4—282no—
337C4—561no—
338C4—561no—
339C4—561no—
340C2—21no—
341C2—21no—
342C2—42no—
343C2—42no—
344C2#1172719611yescharacteristic
345C2#1172777411yescharacteristic
346C2#1172779311yescharacteristic
subgroupG/H
centerC22#89715
commutatorC22×C4×C7C22×C4
FrattiniC23×C4C22×D7
FittingC4×C7×#99C2
socleC22×C7#381
prime radicalC22×C7×D4D4
cosocleC23×C4×C7C23
hypercenterC4×#99D7
hypocenterC7#8777
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C22 ◁ C23×C4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
4. #11725424C2semidirect
5. #11725422C2semidirect
10. #89984C4semidirect
13. C2×C7⋊#95C4semidirect
18. #89709C4semidirect
19. #89704C4semidirect
313. C7#8777semidirect

Maximal subgroups

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

subgroupindex
#117397812
C4×C7×#992
#117293562
#117254242
#117254222
#87777