Finite Group Databasebeta

← #13264128

Subgroups — #13264128

Order 1792.

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

normal subgroups only

This group has 456 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#11739791C211yesmaximal, characteristic
2C4×C7×#99C211yesmaximal, characteristic
3#11729355C211yesmaximal, characteristic
4#11725298C212yesmaximal, complemented
5#11725297C212yesmaximal, complemented
6C2×C4×C7×D4C2211yescharacteristic
7C2×#6489C411yescharacteristic, complemented
8C2×C7×#99—21no—
9C4×C7×C22⋊C4—21no—
10#89994—21no—
11C4×C22⋊Dic7—21no—
12C4×C22⋊Dic7C411yescharacteristic, complemented
13#89758C411yescharacteristic, complemented
14#89755C411yescharacteristic, complemented
15#89725C2211yescharacteristic
16#89724—21no—
17#89721C2211yescharacteristic
18C4×Dic7⋊C4—21no—
19#89697—21no—
20C7×#342C2212yes—
21#89320—21no—
22#89320C2212yes—
23#11727—71nomaximal, Sylow
24C22×C7×D4D411yescharacteristic
25C23×C4×C7C2×C411yescharacteristic
26C23×C4×C7D411yescharacteristic
27C4×C7×D4—41no—
28C4×C7×D4—41no—
29C2×C7×C4⋊C4C2×C411yescharacteristic
30C2×C7×C22⋊C4—22no—
31C2×C7×C22⋊C4D411yescharacteristic
32C2×C7×C22⋊C4C2311yescharacteristic
33C2×C42×C7—41no—
34C2×C42×C7D411yescharacteristic
35C2×C22⋊Dic7—21no—
36C2×C22⋊Dic7—21no—
37C2×C22⋊Dic7—21no—
38C2×C22⋊Dic7—21no—
39#6489—41no—
40#6489—41no—
41C2×C4⋊Dic7C2×C411yescharacteristic
42C2×C4⋊Dic7C2×C411yescharacteristic
43C2×Dic7⋊C4—21no—
44C2×Dic7⋊C4—21no—
45C2×C4×Dic7—21no—
46C2×C4×Dic7—21no—
47C7×#99—24no—
48C7×#95—41no—
49C7⋊#95—21no—
50C7⋊#95—21no—
51C7⋊#95—21no—
52C7⋊#95—21no—
53C7⋊#95C2×C411yescharacteristic
54C7⋊#95C2×C411yescharacteristic
55C22⋊(C7⋊C8)—22no—
56C4⋊(C7⋊C8)—41no—
57C4×C7⋊C8—41no—
58#2395—71no—
59C4×#99D711yescharacteristic
60#1460—71no—
61#1352—72no—
62#1344—72no—
63C24×C7C22⋊C411yescharacteristic
64C24×C7C2×D411yescharacteristic
65C2×C7×D4—22no—
66C2×C7×D4—22no—
67C2×C7×D4—41no—
68C22×C4×C7—21no—
69C22×C4×C7—21no—
70C22×C4×C7—21no—
71C22×C4×C7—21no—
72C22×C4×C7—42no—
73C22×C4×C7—42no—
74C22×C4×C7—42no—
75C22×C4×C7C22⋊C411yescharacteristic
76C22×C4×C7C22⋊C411yescharacteristic
77C22×C4×C7C22⋊C411yescharacteristic
78C22×C4×C7C22×C411yescharacteristic
79C22×C4×C7C2×D411yescharacteristic
80C22×Dic7—21no—
81C22×Dic7—21no—
82C22×Dic7—21no—
83C22×Dic7—21no—
84C7×C4⋊C4—41no—
85C7×C22⋊C4—24no—
86C7×C22⋊C4—41no—
87C7×C22⋊C4—41no—
88C7×C22⋊C4—42no—
89C42×C7—21no—
90C42×C7—21no—
91C42×C7—82no—
92C22⋊Dic7—42no—
93C22⋊Dic7—42no—
94C22⋊Dic7—42no—
95C22⋊Dic7—42no—
96C4⋊Dic7—41no—
97C4⋊Dic7—41no—
98Dic7⋊C4—42no—
99Dic7⋊C4—42no—
100C4×Dic7—42no—
101C4×Dic7—41no—
102C4×Dic7—41no—
103C2×C7⋊C8—42no—
104C2×C4×D4C2×D711yescharacteristic
105C2×#117—71no—
106#431—141no—
107C2×#99—21no—
108#400—71no—
109#399—71no—
110#398—71no—
111#397—71no—
112#397—141no—
113#394—141no—
114C4×C4⋊C4—141no—
115C4×C22⋊C4—21no—
116C4×C22⋊C4—71no—
117C4×C22⋊C4—141no—
118#342C2×D712yes—
119#323—72no—
120#323—141no—
121C23×C7—21no—
122C23×C7—21no—
123C23×C7—21no—
124C23×C7—21no—
125C23×C7—21no—
126C23×C7—41no—
127C23×C7—41no—
128C23×C7—41no—
129C23×C7—41no—
130C23×C7C2×C22⋊C411yescharacteristic
131C23×C7#13512yes—
132C7×D4—44no—
133C2×C4×C7—21no—
134C2×C4×C7—21no—
135C2×C4×C7—22no—
136C2×C4×C7—21no—
137C2×C4×C7—21no—
138C2×C4×C7—21no—
139C2×C4×C7—42no—
140C2×C4×C7—42no—
141C2×C4×C7—42no—
142C2×C4×C7—41no—
143C2×C4×C7—41no—
144C2×C4×C7—41no—
145C2×C4×C7—44no—
146C2×C4×C7—81no—
147C2×C4×C7—82no—
148C2×C4×C7—82no—
149C2×C4×C7#9911yescharacteristic
150C2×C4×C7#9911yescharacteristic
151C2×C4×C7#10412yes—
152C2×Dic7—22no—
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—41no—
162C2×Dic7—41no—
163C2×Dic7—41no—
164C7⋊C8—82no—
165C22×D4C22⋊D711yescharacteristic
166C23×C4C4×D711yescharacteristic
167C23×C4C22⋊D711yescharacteristic
168C4×D4—41no—
169C4×D4—41no—
170#117—281no—
171#117—281no—
172C2×C4⋊C4—71no—
173C2×C4⋊C4—71no—
174C2×C4⋊C4—141no—
175C2×C4⋊C4—141no—
176C2×C4⋊C4C4×D711yescharacteristic
177C2×C22⋊C4—22no—
178C2×C22⋊C4—141no—
179C2×C22⋊C4—141no—
180C2×C22⋊C4—141no—
181C2×C22⋊C4—141no—
182C2×C22⋊C4D2811yescharacteristic
183C2×C22⋊C4C22×D711yescharacteristic
184C2×C42—41no—
185C2×C42—141no—
186C2×C42—141no—
187C2×C42D2811yescharacteristic
188C4⋊C8—281no—
189#99—24no—
190C22⋊C8—142no—
191C4×C8—281no—
192#95—41no—
193#95—71no—
194#95—71no—
195#95—141no—
196#95—141no—
197#95—141no—
198#95—141no—
199C22×C7—21no—
200C22×C7—21no—
201C22×C7—22no—
202C22×C7—42no—
203C22×C7—41no—
204C22×C7—41no—
205C22×C7—41no—
206C22×C7—41no—
207C22×C7—41no—
208C22×C7—81no—
209C22×C7—81no—
210C22×C7—81no—
211C22×C7C2×#9911yescharacteristic
212C22×C7#41611yescharacteristic
213C22×C7C2×#10411yescharacteristic
214C4×C7—21no—
215C4×C7—22no—
216C4×C7—41no—
217C4×C7—41no—
218C4×C7—41no—
219C4×C7—84no—
220C4×C7#35212yes—
221Dic7—42no—
222Dic7—81no—
223Dic7—81no—
224Dic7—81no—
225C24(C2×D7)⋊C411yescharacteristic
226C24C2×C22⋊D711yescharacteristic
227C2×D4—22no—
228C2×D4—22no—
229C2×D4—41no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—42no—
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
246C2×C8—282no—
247C4⋊C4—41no—
248C4⋊C4—281no—
249C4⋊C4—281no—
250C4⋊C4—282no—
251C4⋊C4—282no—
252C22⋊C4—24no—
253C22⋊C4—41no—
254C22⋊C4—41no—
255C22⋊C4—42no—
256C22⋊C4—282no—
257C22⋊C4—282no—
258C22⋊C4—282no—
259C22⋊C4—282no—
260C42—21no—
261C42—21no—
262C42—82no—
263C42—282no—
264C42—281no—
265C42—281no—
266C2×C7—21no—
267C2×C7—21no—
268C2×C7—42no—
269C2×C7—81no—
270C2×C7#150111yescharacteristic
271C2×C7C2×#35211yescharacteristic
272C2×C7#212611yescharacteristic
273C23—21no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23—41no—
279C23—41no—
280C23—41no—
281C23—41no—
282C23C2×(C2×D7)⋊C411yescharacteristic
283C23#651312yes—
284D4—44no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—22no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—44no—
298C2×C4—81no—
299C2×C4—82no—
300C2×C4—82no—
301C2×C4—142no—
302C2×C4—281no—
303C2×C4—281no—
304C2×C4—281no—
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#637912yes—
314C2×C4#638011yescharacteristic
315C2×C4#638011yescharacteristic
316C8—562no—
317C7#1172711yescharacteristic, complemented, Sylow
318C22—21no—
319C22—21no—
320C22—22no—
321C22—42no—
322C22—41no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22—81no—
328C22—81no—
329C22—81no—
330C22C2×#637911yescharacteristic
331C22C2×#638011yescharacteristic
332C22#8977411yescharacteristic
333C4—22no—
334C4—21no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—84no—
339C4—282no—
340C4—561no—
341C4—561no—
342C4—561no—
343C4#8926712yes—
344C2—21no—
345C2—21no—
346C2—42no—
347C2—81no—
348C2#1172719711yescharacteristic
349C2C2×#8926711yescharacteristic
350C2#1172781411yescharacteristic
subgroupG/H
centerC2×C4#6380
commutatorC22×C4×C7C22×C4
FrattiniC2×C22⋊C4C22×D7
FittingC4×C7×#99C2
socleC22×C7C2×#99
prime radicalC22×C7×D4D4
cosocleC2×C7×C22⋊C4C23
hypercenterC4×#99D7
hypocenterC7#11727
LCSG ▷ C22×C4×C7 ▷ C23×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C4×D4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
4. #11725298C2semidirect
5. #11725297C2semidirect
7. C2×#6489C4semidirect
12. C4×C22⋊Dic7C4semidirect
13. #89758C4semidirect
14. #89755C4semidirect
317. C7#11727semidirect

Maximal subgroups

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

subgroupindex
#117397912
C4×C7×#992
#117293552
#117252982
#117252972
#117277