Finite Group Databasebeta

← #22614400

Subgroups — #22614400

Order 9344.

708 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556575C211yesmaximal, characteristic, complemented
2C2×#14556574C211yesmaximal, characteristic, complemented
3C2×#14556572C211yesmaximal, characteristic, complemented
4C2×#14556563C211yesmaximal, characteristic
5C22×#11924007C211yesmaximal, characteristic, complemented
6#17988523C212yesmaximal, complemented
7#17988522C212yesmaximal, complemented
8#17988487C212yesmaximal, complemented
9#17988456C212yesmaximal, complemented
10C22⋊C4×Dic73C211yesmaximal, characteristic, complemented
11C2×#123×C73C211yesmaximal, characteristic, complemented
12C22×C22⋊D73C2211yescharacteristic
13C22×C22⋊D73C2211yescharacteristic
14C23×Dic73C2211yescharacteristic
15C23×Dic73C2211yescharacteristic
16#14556575—24no—
17#14556574—24no—
18#14556572—24no—
19#14556563—24no—
20C2×C4⋊Dic73C2212yes—
21C2×#11924007—24no—
22C2×#11924007C2211yescharacteristic
23C2×#11924007C2212yes—
24C2×#11924007C2212yes—
25C2×#11924007C2212yes—
26C2×#11924007C2212yes—
27C2×C22⋊Dic73C2212yes—
28C2×C22⋊Dic73C2211yescharacteristic
29C2×C22⋊Dic73C2211yescharacteristic
30C2×#11924005C2212yes—
31C2×#11924005C2212yes—
32C2×#11924005C2211yescharacteristic
33C2×C4×Dic73C2212yes—
34#14556498C2212yes—
35C22×D4×C73C2211yescharacteristic
36C23×C4×C73C2211yescharacteristic
37#123×C73—24no—
38C2×C4⋊C4×C73C2212yes—
39C2×C22⋊C4×C73C2212yes—
40C2×C22⋊C4×C73C2211yescharacteristic
41C23×D73C2311yescharacteristic
42C2×C22⋊D73—22no—
43C2×C22⋊D73—22no—
44C2×C22⋊D73—22no—
45C2×C22⋊D73—22no—
46C2×C22⋊D73—24no—
47C22×Dic73—24no—
48C22×Dic73—22no—
49C22×Dic73—22no—
50C22×Dic73—22no—
51C22×Dic73D414yes—
52C22×Dic73C2312yes—
53C22×Dic73C2311yescharacteristic
54C22×Dic73C2311yescharacteristic
55C22×Dic73C2312yes—
56C22×Dic73C2311yescharacteristic
57C4⋊Dic73—24no—
58#11924007—24no—
59#11924007—24no—
60#11924007—22no—
61#11924007—24no—
62#11924007—24no—
63C22⋊Dic73—22no—
64C22⋊Dic73—24no—
65C22⋊Dic73D414yescomplemented
66#11924005—24no—
67#11924005—22no—
68#11924005—24no—
69C4×Dic73—24no—
70C24×C73C2311yescharacteristic
71C24×C73C2311yescharacteristic
72C2×D4×C73—22no—
73C2×D4×C73—22no—
74C2×D4×C73—22no—
75C22×C4×C73—22no—
76C22×C4×C73—22no—
77C22×C4×C73—22no—
78C22×C4×C73C2312yes—
79C22×C4×C73C2311yescharacteristic
80C22×C4×C73C2312yes—
81C4⋊C4×C73—24no—
82C22⋊C4×C73—24no—
83C22⋊C4×C73D414yescomplemented
84C23×C73—22no—
85C23×C73—22no—
86C23×C73—21no—
87C23×C73—21no—
88C23×C73—21no—
89C23×C73—22no—
90C23×C73—22no—
91C23×C73C2×D412yes—
92C23×C73C2×D412yes—
93C23×C73C2×D412yes—
94C23×C73C2411yescharacteristic
95C22×D73—21no—
96C22×D73—21no—
97C22×D73—21no—
98C22×D73—22no—
99C22×D73—22no—
100D4×C73—44no—
101C2×C4×C73—22no—
102C2×C4×C73—22no—
103C2×C4×C73—22no—
104C2×C4×C73—21no—
105C2×C4×C73—22no—
106C2×C4×C73—22no—
107C2×C4×C73—21no—
108C2×C4×C73—21no—
109C2×C4×C73—44no—
110C2×C4×C73C2×D414yes—
111C22⋊D73—44no—
112C22⋊D73—44no—
113C2×Dic73—22no—
114C2×Dic73—22no—
115C2×Dic73—22no—
116C2×Dic73—28no—
117C2×Dic73—22no—
118C2×Dic73—22no—
119C2×Dic73—21no—
120C2×Dic73—22no—
121C2×Dic73—21no—
122C2×Dic73—21no—
123C2×Dic73—44no—
124C2×Dic73C2×D414yes—
125C2×Dic73C2×D412yes—
126C2×Dic73C2×D412yes—
127C2×Dic73#4114yes—
128C22×C73—22no—
129C22×C73—22no—
130C22×C73—24no—
131C22×C73—24no—
132C22×C73—41no—
133C22×C73—41no—
134C22×C73—41no—
135C22×C73—42no—
136C22×C73—42no—
137C22×C73#12714yes—
138C22×C73C22×D411yescharacteristic
139C22×C73C22×D411yescharacteristic
140C22×C73C22×D411yescharacteristic
141C22×C73C2×#4112yes—
142C22×C732−1+412yes—
143C2×D73—41no—
144C2×D73—41no—
145C2×D73—41no—
146C2×D73—42no—
147C2×D73—42no—
148C4×C73—24no—
149C4×C73—42no—
150C4×C73—41no—
151Dic73—22no—
152Dic73—24no—
153Dic73—42no—
154Dic73—41no—
155Dic73#12314yescomplemented
156C2×C73—24no—
157C2×C73—81no—
158C2×C73C2×#12311yescharacteristic
159C2×C73C2×#12711yescharacteristic
160C2×C73#53611yescharacteristic
161C2×C73#54712yes—
162C2×C73#54712yes—
163D73—81no—
164#2501—731nomaximal, Sylow
165C73#250111yescharacteristic, complemented, Sylow
166C2×#123—731no—
167C2×#123—731no—
168C2×#123—731no—
169C2×#123D7311yescharacteristic, complemented
170C2×#121—731no—
171C22×C4⋊C4—731no—
172#399—732no—
173#399—732no—
174#390—732no—
175#384—732no—
176C4×C22⋊C4—731no—
177C22×D4—731no—
178C22×D4—731no—
179C22×D4C2×D7311yescharacteristic
180C23×C4—731no—
181C23×C4—731no—
182C23×C4C2×D7311yescharacteristic
183#123—24no—
184#123—1464no—
185#123—1464no—
186#123—1464no—
187#121—1464no—
188C2×C4⋊C4—732no—
189C2×C4⋊C4—732no—
190C2×C4⋊C4—731no—
191C2×C4⋊C4—732no—
192C2×C4⋊C4—732no—
193C2×C4⋊C4—732no—
194C2×C4⋊C4—1464no—
195C2×C4⋊C4C2×D7312yes—
196C2×C22⋊C4—731no—
197C2×C22⋊C4—731no—
198C2×C22⋊C4—732no—
199C2×C22⋊C4—731no—
200C2×C22⋊C4—732no—
201C2×C22⋊C4—732no—
202C2×C22⋊C4C2×D7312yes—
203C2×C22⋊C4C2×D7311yescharacteristic
204C2×C42—732no—
205#95—732no—
206C24—731no—
207C24C22×D7311yescharacteristic
208C24C22×D7311yescharacteristic
209C2×D4—22no—
210C2×D4—22no—
211C2×D4—22no—
212C2×D4—1462no—
213C2×D4—1464no—
214C2×D4—1462no—
215C2×D4—1462no—
216C2×D4—1462no—
217C22×C4—22no—
218C22×C4—22no—
219C22×C4—22no—
220C22×C4—731no—
221C22×C4—734no—
222C22×C4—731no—
223C22×C4—732no—
224C22×C4—732no—
225C22×C4—731no—
226C22×C4—1462no—
227C22×C4—1462no—
228C22×C4—1462no—
229C22×C4—1464no—
230C22×C4C22×D7312yes—
231C22×C4C22×D7311yescharacteristic
232C22×C4C22×D7312yes—
233C4⋊C4—24no—
234C4⋊C4—1464no—
235C4⋊C4—1464no—
236C4⋊C4—1462no—
237C4⋊C4—1464no—
238C4⋊C4—1464no—
239C4⋊C4—1464no—
240C22⋊C4—24no—
241C22⋊C4—734no—
242C22⋊C4—1462no—
243C22⋊C4—1464no—
244C22⋊C4—1462no—
245C22⋊C4—1464no—
246C22⋊C4—1464no—
247C22⋊C4C22⋊D7314yescomplemented
248C42—1464no—
249C23—22no—
250C23—22no—
251C23—21no—
252C23—21no—
253C23—21no—
254C23—22no—
255C23—22no—
256C23—1461no—
257C23—1461no—
258C23—1461no—
259C23—1462no—
260C23—1462no—
261C23D4×D7312yes—
262C23D4×D7312yes—
263C23C2×C22⋊D7312yes—
264C23C23×D7311yescharacteristic
265D4—44no—
266D4—2924no—
267D4—2924no—
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—21no—
272C2×C4—22no—
273C2×C4—21no—
274C2×C4—22no—
275C2×C4—21no—
276C2×C4—44no—
277C2×C4—2924no—
278C2×C4—732no—
279C2×C4—734no—
280C2×C4—734no—
281C2×C4—732no—
282C2×C4—1462no—
283C2×C4—1461no—
284C2×C4—1462no—
285C2×C4—1461no—
286C2×C4—1462no—
287C2×C4—1461no—
288C2×C4—1468no—
289C2×C4—1462no—
290C2×C4—1462no—
291C2×C4—1462no—
292C2×C4C2×C22⋊D7314yes—
293C22—22no—
294C22—24no—
295C22—24no—
296C22—22no—
297C22—41no—
298C22—41no—
299C22—42no—
300C22—42no—
301C22—41no—
302C22—2921no—
303C22—2921no—
304C22—2922no—
305C22—2922no—
306C22—2921no—
307C22#1455658714yes—
308C22C2×D4×D7311yescharacteristic
309C22C2×D4×D7311yescharacteristic
310C22C22×C22⋊D7311yescharacteristic
311C22#41×D7312yes—
312C22#1455663812yes—
313C4—24no—
314C4—42no—
315C4—41no—
316C4—2922no—
317C4—2921no—
318C4—734no—
319C4—1464no—
320C4—1462no—
321C2—24no—
322C2—81no—
323C2—5841no—
324C2#123×D7311yescharacteristic
325C2C2×#1455658711yescharacteristic
326C2#1798915911yescharacteristic
327C2#1798923512yes—
328C2#1798923612yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
FittingC2×#123×C73C2
hypercenterC2×#123D73
hypocenterC73#2501
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. C2×#14556575C2semidirect
2. C2×#14556574C2semidirect
3. C2×#14556572C2semidirect
5. C22×#11924007C2semidirect
6. #17988523C2semidirect
7. #17988522C2semidirect
8. #17988487C2semidirect
9. #17988456C2semidirect
10. C22⋊C4×Dic73C2semidirect
11. C2×#123×C73C2semidirect
65. C22⋊Dic73D4semidirect
83. C22⋊C4×C73D4semidirect
155. Dic73#123semidirect
165. C73#2501semidirect
169. C2×#123D73semidirect
247. C22⋊C4C22⋊D73semidirect