Finite Group Databasebeta

← #13263270

Subgroups — #13263270

Order 1792.

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

normal subgroups only

This group has 460 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
1C4×#6499C211yesmaximal, characteristic
2C7×#1465C211yesmaximal, characteristic
3#11729356C211yesmaximal, characteristic
4#11725261C212yesmaximal, complemented
5#11725258C212yesmaximal, complemented
6C2×C4×C7×D4C2211yescharacteristic
7C2×#6499C411yescharacteristic
8C2×C4×Dic14C411yescharacteristic
9C7×#407—21no—
10#89993C411yescharacteristic
11C4×C22⋊Dic7—21no—
12C4×C22⋊Dic7—21no—
13#89979—21no—
14#89749C2211yescharacteristic
15#89746C2211yescharacteristic
16#89717—21no—
17#89717—21no—
18C42×Dic7C411yescharacteristic
19C7×#324C2212yes—
20C7×#323—21no—
21#89323C2212yes—
22#89320—21no—
23#11531—71nomaximal, Sylow
24C22×C7×D4C2×C411yescharacteristic
25C23×C4×C7D411yescharacteristic
26C23×C4×C7D411yescharacteristic
27C22×Dic14C2×C411yescharacteristic
28C2×C7×M16—41no—
29C4×C7×D4—41no—
30C4×C7×D4—41no—
31C2×C7×C4⋊C4C2311yescharacteristic
32C2×C7×C22⋊C4D411yescharacteristic
33C2×C7×C22⋊C4D411yescharacteristic
34C2×C42×C7C2×C411yescharacteristic
35C2×C22⋊Dic7—21no—
36C2×C22⋊Dic7—21no—
37C2×C22⋊Dic7—21no—
38C2×C22⋊Dic7—21no—
39#6499—22no—
40#6499—22no—
41C2×C4⋊Dic7C2×C411yescharacteristic
42C2×Dic7⋊C4—21no—
43C2×C4×Dic7—21no—
44C2×C4×Dic7—21no—
45C2×C4×Dic7—21no—
46C2×C4×Dic7C2×C411yescharacteristic
47C2×C4×Dic7C2×C411yescharacteristic
48C2×#1136—41no—
49C4×Dic14—41no—
50C4×Dic14—41no—
51C7×C22⋊C8—22no—
52C7×C22⋊C8—41no—
53C7⋊#95—21no—
54C7⋊#95—21no—
55C7⋊#95—21no—
56C7⋊#95—21no—
57C22⋊(C7⋊C8)—22no—
58C22⋊(C7⋊C8)—41no—
59C4×#124—71no—
60#1465—71no—
61#1465D711yescharacteristic
62#1324—72no—
63#1319—72no—
64C24×C7C22⋊C411yescharacteristic
65C24×C7C22⋊C411yescharacteristic
66C2×C7×D4—21no—
67C2×C7×D4—21no—
68C2×C7×D4—41no—
69C2×C7×D4—41no—
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×C7C2×D411yescharacteristic
80C22×C4×C7C2×D411yescharacteristic
81C22×Dic7—21no—
82C22×Dic7—21no—
83C22×Dic7—21no—
84C22×Dic7—21no—
85C2×Dic14—21no—
86C2×Dic14—41no—
87C2×Dic14—41no—
88C2×Dic14M1612yescomplemented
89C7×M16—82no—
90C2×C7×C8—42no—
91C7×C4⋊C4—41no—
92C7×C22⋊C4—41no—
93C7×C22⋊C4—41no—
94C42×C7—21no—
95C42×C7—21no—
96C22⋊Dic7—24no—
97C22⋊Dic7—24no—
98C22⋊Dic7—42no—
99C22⋊Dic7—42no—
100C4⋊Dic7—41no—
101Dic7⋊C4—42no—
102C4×Dic7—21no—
103C4×Dic7—42no—
104C4×Dic7—42no—
105C4×Dic7—41no—
106C4×Dic7—41no—
107C4×Dic7—41no—
108C4×Dic7M1612yescomplemented
109#1136—82no—
110C2×C7⋊C8—42no—
111C2×#124—71no—
112C2×C4×Q8—71no—
113C2×C4×D4C2×D711yescharacteristic
114#407—21no—
115#407—141no—
116#391—71no—
117#390—71no—
118#388—141no—
119#388—141no—
120#382—71no—
121C4×C22⋊C4—141no—
122C4×C22⋊C4—141no—
123C43—71no—
124#324—72no—
125#324C2×D712yes—
126#323—21no—
127#323—141no—
128C23×C7—21no—
129C23×C7—21no—
130C23×C7—21no—
131C23×C7—21no—
132C23×C7—21no—
133C23×C7—21no—
134C23×C7—41no—
135C23×C7—41no—
136C23×C7—41no—
137C23×C7—41no—
138C23×C7C2×C22⋊C411yescharacteristic
139C7×D4—42no—
140C7×D4—42no—
141C2×C4×C7—21no—
142C2×C4×C7—21no—
143C2×C4×C7—22no—
144C2×C4×C7—21no—
145C2×C4×C7—21no—
146C2×C4×C7—21no—
147C2×C4×C7—42no—
148C2×C4×C7—42no—
149C2×C4×C7—41no—
150C2×C4×C7—41no—
151C2×C4×C7—41no—
152C2×C4×C7—81no—
153C2×C4×C7—81no—
154C2×C4×C7#9911yescharacteristic
155C2×C4×C7#9911yescharacteristic
156C2×C4×C7C2×M1611yescharacteristic
157C2×C4×C7C2×M1611yescharacteristic
158C2×Dic7—22no—
159C2×Dic7—22no—
160C2×Dic7—22no—
161C2×Dic7—41no—
162C2×Dic7—41no—
163C2×Dic7—41no—
164C2×Dic7—41no—
165C2×Dic7—41no—
166C2×Dic7—41no—
167C2×Dic7—41no—
168C2×Dic7—41no—
169C2×Dic7—41no—
170Dic14—42no—
171Dic14—42no—
172C7×C8—82no—
173C7⋊C8—82no—
174C22×Q8—71no—
175C22×D4C4×D711yescharacteristic
176C23×C4D2811yescharacteristic
177C23×C4C22⋊D711yescharacteristic
178C2×M16—41no—
179C2×M16—281no—
180#124—142no—
181#124—142no—
182C4×Q8—281no—
183C4×Q8—281no—
184C4×D4—41no—
185C4×D4—41no—
186C2×C4⋊C4—71no—
187C2×C4⋊C4—141no—
188C2×C4⋊C4C22×D711yescharacteristic
189C2×C22⋊C4—141no—
190C2×C22⋊C4—141no—
191C2×C22⋊C4—141no—
192C2×C22⋊C4—141no—
193C2×C22⋊C4D2811yescharacteristic
194C2×C22⋊C4C22⋊D711yescharacteristic
195C2×C42—71no—
196C2×C42—71no—
197C2×C42—141no—
198C2×C42—141no—
199C2×C42—141no—
200C2×C42C4×D711yescharacteristic
201C22⋊C8—22no—
202C22⋊C8—41no—
203C22⋊C8—142no—
204C22⋊C8—281no—
205#95—141no—
206#95—141no—
207#95—141no—
208#95—141no—
209C22×C7—21no—
210C22×C7—21no—
211C22×C7—42no—
212C22×C7—42no—
213C22×C7—41no—
214C22×C7—41no—
215C22×C7—41no—
216C22×C7—41no—
217C22×C7—41no—
218C22×C7—41no—
219C22×C7—81no—
220C22×C7—81no—
221C22×C7#40711yescharacteristic
222C22×C7C2×#9911yescharacteristic
223C22×C7#41311yescharacteristic
224C4×C7—21no—
225C4×C7—21no—
226C4×C7—21no—
227C4×C7—41no—
228C4×C7—41no—
229C4×C7—41no—
230C4×C7#35412yes—
231Dic7—42no—
232Dic7—42no—
233Dic7—42no—
234Dic7—81no—
235C24(C2×D7)⋊C411yescharacteristic
236C24(C2×D7)⋊C411yescharacteristic
237C2×Q8—72no—
238C2×Q8—141no—
239C2×Q8—281no—
240C2×Q8—281no—
241C2×D4—21no—
242C2×D4—21no—
243C2×D4—41no—
244C2×D4—41no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—42no—
250C22×C4—42no—
251C22×C4—141no—
252C22×C4—141no—
253C22×C4—141no—
254C22×C4—141no—
255C22×C4(C2×D7)⋊C411yescharacteristic
256C22×C4(C2×D7)⋊C411yescharacteristic
257C22×C4C2×C4×D711yescharacteristic
258C22×C4C2×D2811yescharacteristic
259C22×C4C2×C22⋊D711yescharacteristic
260M16—82no—
261M16—562no—
262C2×C8—42no—
263C2×C8—282no—
264C4⋊C4—41no—
265C4⋊C4—281no—
266C4⋊C4—282no—
267C22⋊C4—41no—
268C22⋊C4—41no—
269C22⋊C4—144no—
270C22⋊C4—144no—
271C22⋊C4—282no—
272C22⋊C4—282no—
273C42—21no—
274C42—21no—
275C42—72no—
276C42—141no—
277C42—281no—
278C42—282no—
279C42—282no—
280C42—281no—
281C42—281no—
282C2×C7—21no—
283C2×C7—21no—
284C2×C7—81no—
285C2×C7—81no—
286C2×C7#146511yescharacteristic
287C2×C7C2×#35411yescharacteristic
288C2×C7#213211yescharacteristic
289C23—21no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23—41no—
296C23—41no—
297C23—41no—
298C23—41no—
299C23C2×(C2×D7)⋊C411yescharacteristic
300Q8—282no—
301Q8—282no—
302D4—42no—
303D4—42no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—22no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4—142no—
318C2×C4—142no—
319C2×C4—142no—
320C2×C4—281no—
321C2×C4—281no—
322C2×C4—281no—
323C2×C4—281no—
324C2×C4—281no—
325C2×C4—281no—
326C2×C4—281no—
327C2×C4—281no—
328C2×C4—281no—
329C2×C4#638011yescharacteristic
330C2×C4#638011yescharacteristic
331C2×C4D7×M1611yescharacteristic
332C2×C4D7×M1611yescharacteristic
333C8—82no—
334C8—562no—
335C7#1153111yescharacteristic, complemented, Sylow
336C22—21no—
337C22—21no—
338C22—42no—
339C22—42no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—81no—
347C22—81no—
348C22C2×#638011yescharacteristic
349C22#8989811yescharacteristic
350C22#8990411yescharacteristic
351C4—21no—
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—282no—
358C4—282no—
359C4—282no—
360C4—561no—
361C4#8926812yes—
362C2—21no—
363C2—21no—
364C2—81no—
365C2—81no—
366C2#1172772211yescharacteristic
367C2C2×#8926811yescharacteristic
368C2#1172790211yescharacteristic
subgroupG/H
centerC22C2×#6380
commutatorC22×C4×C7C22×C4
FrattiniC2×C4⋊C4C22×D7
FittingC7×#1465C2
socleC22×C7C2×#99
prime radicalC22×C7×D4C2×C4
cosocleC2×C7×C4⋊C4C23
hypercenter#1465D7
hypocenterC7#11531
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1465

Complements

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

NH ≅ G/Ntype
4. #11725261C2semidirect
5. #11725258C2semidirect
88. C2×Dic14M16semidirect
108. C4×Dic7M16semidirect
335. C7#11531semidirect

Maximal subgroups

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

subgroupindex
C4×#64992
C7×#14652
#117293562
#117252612
#117252582
#115317