Finite Group Databasebeta

← #14217248

Subgroups — #14217248

Order 1792.

5134 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C7×#41C211yesmaximal, characteristic
2C2×#90510C212yesmaximal, complemented
3#11741520C2116yesmaximal, complemented
4#11741519C216yesmaximal, complemented
5C2×#89979C216yesmaximal, complemented
6C22×C7×#41—216no—
7C22×C7×#41C418yes—
8C22×C7×#41C411yescharacteristic
9C22×C7×#41C413yes—
10C22×C7×#41C2213yes—
11C22×C7×#41C2218yes—
12C22×C7×#41C2211yescharacteristic
13C23×C7×Q8C411yescharacteristic
14C23×C7×D4C413yes—
15C24×C4×C7C2213yes—
16#90510—216no—
17C2×#6511C22116yescomplemented
18C22×#1136C22112yescomplemented
19#90006C22148yescomplemented
20#89979C2214yes—
21#89979C22124yescomplemented
22#89979C22112yescomplemented
23C2×C22⋊(C7⋊C8)C22124yescomplemented
24#60064—71nomaximal, Sylow
25C25×C7C2×C413yes—
26C2×C7×#41—264no—
27C2×C7×#41—264no—
28C2×C7×#41—28no—
29C2×C7×#41—224no—
30C2×C7×#41—224no—
31C2×C7×#41C2×C418yes—
32C2×C7×#41C2×C4124yes—
33C2×C7×#41C2×C4112yes—
34C2×C7×#41C2×C414yes—
35C2×C7×#41D4116yes—
36C2×C7×#41C23112yes—
37C2×C7×#41C2314yes—
38C22×C7×Q8—28no—
39C22×C7×Q8C2×C418yes—
40C22×C7×Q8C2×C413yes—
41C22×C7×Q8C2×C411yescharacteristic
42C22×C7×D4—224no—
43C22×C7×D4C2×C416yes—
44C22×C7×D4C2×C4124yes—
45C22×C7×D4C2×C413yes—
46C22×C7×D4C2×C413yes—
47C23×C4×C7—224no—
48C23×C4×C7C2×C413yes—
49C23×C4×C7C2×C413yes—
50C23×C4×C7C2×C4112yes—
51C23×C4×C7C2×C413yes—
52C23×C4×C7C23112yes—
53C23×C4×C7C2313yes—
54C23×C4×C7C2311yescharacteristic
55C23×C4×C7C2313yes—
56#6511—264no—
57C2×#1136—248no—
58C2×#1136C2318yes—
59C2×#1136C23124yescomplemented
60C22×C7⋊C8C23124yescomplemented
61C22⋊(C7⋊C8)C23116yes—
62C22⋊(C7⋊C8)C23148yescomplemented
63C23×#41D711yescharacteristic
64C2×#568—72no—
65#2880—716no—
66#2879—76no—
67C2×#407—76no—
68C24×C7—212no—
69C24×C7—412no—
70C24×C7C22×C411yescharacteristic
71C24×C7C22×C4112yes—
72C24×C7C22×C413yes—
73C24×C7C22×C413yes—
74C7×#41—232no—
75C7×#41—296no—
76C7×#41—248no—
77C7×#41—248no—
78C7×#41C22⋊C4132yes—
79C7×#41C2×D4132yes—
80C2×C7×Q8—232no—
81C2×C7×Q8—212no—
82C2×C7×Q8C22⋊C418yes—
83C2×C7×Q8C22×C4112yes—
84C2×C7×Q8C22×C414yes—
85C2×C7×D4—224no—
86C2×C7×D4—296no—
87C2×C7×D4—212no—
88C2×C7×D4C22⋊C4124yes—
89C2×C7×D4C22×C4124yes—
90C2×C7×D4C22×C4112yes—
91C2×C7×D4C22×C4112yes—
92C22×C4×C7—212no—
93C22×C4×C7—212no—
94C22×C4×C7—212no—
95C22×C4×C7—248no—
96C22×C4×C7—24no—
97C22×C4×C7—212no—
98C22×C4×C7—248no—
99C22×C4×C7C22×C411yescharacteristic
100C22×C4×C7C22×C412yes—
101C22×C4×C7C22×C413yes—
102C22×C4×C7C22×C4112yes—
103C22×C4×C7C22×C4112yes—
104C22×C4×C7C22×C4112yes—
105C22×C4×C7C22×C416yes—
106C22×C4×C7C22×C413yes—
107C22×C4×C7C22×C416yes—
108C22×C4×C7C2×D4124yes—
109C22×C4×C7C2412yes—
110C22×C4×C7C2416yes—
111C22×C4×C7C2416yes—
112C22×C4×C7C2411yescharacteristic
113#1136—216no—
114#1136—248no—
115C2×C7⋊C8—248no—
116C2×C7⋊C8C24116yes—
117C22×#41—216no—
118C22×#41Dic718yes—
119C22×#41Dic711yescharacteristic
120C22×#41Dic713yes—
121C22×#41C2×D713yes—
122C22×#41C2×D718yes—
123C22×#41C2×D711yescharacteristic
124C23×Q8Dic711yescharacteristic
125C23×D4Dic713yes—
126C24×C4C2×D713yes—
127#568—1416no—
128C2×#131—716no—
129C22×M16—712no—
130#408—748no—
131#407—74no—
132#407—712no—
133#407—724no—
134C2×C22⋊C8—724no—
135C23×C7—22no—
136C23×C7—24no—
137C23×C7—224no—
138C23×C7—26no—
139C23×C7—224no—
140C23×C7—46no—
141C23×C7—412no—
142C23×C7—46no—
143C23×C7—448no—
144C23×C7C2×C22⋊C4112yes—
145C23×C7C23×C416yes—
146C23×C7C23×C411yescharacteristic
147C23×C7C23×C416yes—
148C23×C7C23×C412yes—
149C7×Q8—224no—
150C7×Q8C2×C22⋊C4116yes—
151C7×D4—248no—
152C7×D4—224no—
153C7×D4C2×C22⋊C4148yes—
154C2×C4×C7—22no—
155C2×C4×C7—26no—
156C2×C4×C7—224no—
157C2×C4×C7—24no—
158C2×C4×C7—224no—
159C2×C4×C7—224no—
160C2×C4×C7—212no—
161C2×C4×C7—24no—
162C2×C4×C7—212no—
163C2×C4×C7C2×C22⋊C4112yes—
164C2×C4×C7C2×C22⋊C4124yes—
165C2×C4×C7C23×C412yes—
166C2×C4×C7C23×C416yes—
167C2×C4×C7C23×C411yescharacteristic
168C2×C4×C7C23×C416yes—
169C2×C4×C7C22×D4124yes—
170C2×C4×C7C22×D414yes—
171C2×C4×C7C2511yescharacteristic
172C7⋊C8—216no—
173C25C2×Dic713yes—
174C2×#41—264no—
175C2×#41—264no—
176C2×#41—28no—
177C2×#41—224no—
178C2×#41—224no—
179C2×#41C2×Dic718yes—
180C2×#41C2×Dic7124yes—
181C2×#41C2×Dic7112yes—
182C2×#41C2×Dic714yes—
183C2×#41C22⋊D7116yes—
184C2×#41C22×D7112yes—
185C2×#41C22×D714yes—
186C22×Q8—28no—
187C22×Q8C2×Dic718yes—
188C22×Q8C2×Dic713yes—
189C22×Q8C2×Dic711yescharacteristic
190C22×D4—224no—
191C22×D4C2×Dic716yes—
192C22×D4C2×Dic7124yes—
193C22×D4C2×Dic713yes—
194C22×D4C2×Dic713yes—
195C23×C4—224no—
196C23×C4C2×Dic713yes—
197C23×C4C2×Dic713yes—
198C23×C4C2×Dic7112yes—
199C23×C4C2×Dic713yes—
200C23×C4C22×D711yescharacteristic
201C23×C4C22×D7112yes—
202C23×C4C22×D713yes—
203C23×C4C22×D713yes—
204#131—1464no—
205C2×M16—78no—
206C2×M16—724no—
207C2×M16—1448no—
208C22×C8—724no—
209C22⋊C8—716no—
210C22⋊C8—748no—
211C22×C7—28no—
212C22×C7—22no—
213C22×C7—22no—
214C22×C7—22no—
215C22×C7—212no—
216C22×C7—26no—
217C22×C7—212no—
218C22×C7—412no—
219C22×C7—448no—
220C22×C7—412no—
221C22×C7C22×C22⋊C412yes—
222C22×C7C22×C22⋊C4112yes—
223C22×C7#56814yescomplemented
224C22×C7C24×C411yescharacteristic
225C4×C7—22no—
226C4×C7—26no—
227C4×C7C22×C22⋊C412yes—
228C4×C7C22×C22⋊C4112yes—
229C4×C7C23×D412yes—
230C24—212no—
231C24—412no—
232C24C22×Dic711yescharacteristic
233C24C22×Dic7112yes—
234C24C22×Dic713yes—
235C24C22×Dic713yes—
236#41—232no—
237#41—296no—
238#41—248no—
239#41—248no—
240#41C22⋊Dic7132yes—
241#41C2×C22⋊D7132yes—
242C2×Q8—232no—
243C2×Q8—212no—
244C2×Q8C22⋊Dic718yes—
245C2×Q8C22×Dic7112yes—
246C2×Q8C22×Dic714yes—
247C2×D4—224no—
248C2×D4—296no—
249C2×D4—212no—
250C2×D4C22⋊Dic7124yes—
251C2×D4C22×Dic7124yes—
252C2×D4C22×Dic7112yes—
253C2×D4C22×Dic7112yes—
254C22×C4—212no—
255C22×C4—212no—
256C22×C4—212no—
257C22×C4—248no—
258C22×C4—24no—
259C22×C4—212no—
260C22×C4—248no—
261C22×C4C22×Dic711yescharacteristic
262C22×C4C22×Dic712yes—
263C22×C4C22×Dic713yes—
264C22×C4C22×Dic7112yes—
265C22×C4C22×Dic7112yes—
266C22×C4C22×Dic7112yes—
267C22×C4C22×Dic716yes—
268C22×C4C22×Dic713yes—
269C22×C4C22×Dic716yes—
270C22×C4C2×C22⋊D7124yes—
271C22×C4C23×D712yes—
272C22×C4C23×D716yes—
273C22×C4C23×D716yes—
274C22×C4C23×D711yescharacteristic
275M16—1416no—
276M16—1448no—
277C2×C8—716no—
278C2×C8—1448no—
279C2×C7—22no—
280C2×C7—24no—
281C2×C7—212no—
282C2×C7—46no—
283C2×C7C23×C22⋊C411yescharacteristic
284C2×C7C2×#56812yes—
285C23—24no—
286C23—22no—
287C23—224no—
288C23—224no—
289C23—26no—
290C23—46no—
291C23—412no—
292C23—46no—
293C23—448no—
294C23C2×C22⋊Dic7112yes—
295C23C23×Dic716yes—
296C23C23×Dic712yes—
297C23C23×Dic711yescharacteristic
298C23C23×Dic716yes—
299Q8—224no—
300Q8C2×C22⋊Dic7116yes—
301D4—248no—
302D4—224no—
303D4C2×C22⋊Dic7148yes—
304C2×C4—22no—
305C2×C4—26no—
306C2×C4—224no—
307C2×C4—24no—
308C2×C4—224no—
309C2×C4—224no—
310C2×C4—212no—
311C2×C4—24no—
312C2×C4—212no—
313C2×C4C2×C22⋊Dic7112yes—
314C2×C4C2×C22⋊Dic7124yes—
315C2×C4C23×Dic712yes—
316C2×C4C23×Dic716yes—
317C2×C4C23×Dic711yescharacteristic
318C2×C4C23×Dic716yes—
319C2×C4C22×C22⋊D7124yes—
320C2×C4C22×C22⋊D714yes—
321C2×C4C24×D711yescharacteristic
322C8—1416no—
323C7#6006411yescharacteristic, complemented, Sylow
324C22—28no—
325C22—22no—
326C22—22no—
327C22—212no—
328C22—22no—
329C22—212no—
330C22—26no—
331C22—412no—
332C22—448no—
333C22—412no—
334C22#9051014yescomplemented
335C22C22×C22⋊Dic712yes—
336C22C22×C22⋊Dic7112yes—
337C22C24×Dic711yescharacteristic
338C4—22no—
339C4—26no—
340C4C22×C22⋊Dic712yes—
341C4C22×C22⋊Dic7112yes—
342C4C23×C22⋊D712yes—
343C2—24no—
344C2—22no—
345C2—212no—
346C2—46no—
347C2C2×#9051012yes—
348C2C23×C22⋊Dic711yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D7
commutator, socleC22×C7C24×C4
Fitting, prime radicalC23×C7×#41C2
cosocleC2×C4×C7C25
hypercenterC23×#41D7
hypocenterC7#60064
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C23×#41

Complements

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

NH ≅ G/Ntype
2. C2×#90510C2semidirect
3. #11741520C2semidirect
4. #11741519C2semidirect
5. C2×#89979C2semidirect
17. C2×#6511C22semidirect
18. C22×#1136C22semidirect
19. #90006C22semidirect
21. #89979C22semidirect
22. #89979C22semidirect
23. C2×C22⋊(C7⋊C8)C22semidirect
59. C2×#1136C23semidirect
60. C22×C7⋊C8C23semidirect
62. C22⋊(C7⋊C8)C23semidirect
223. C22×C7#568semidirect
323. C7#60064semidirect
334. C22#90510semidirect

Maximal subgroups

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

subgroupindex
C23×C7×#412
C2×#905102
#117415202
#117415192
C2×#899792
#600647