Finite Group Databasebeta

← #22614861

Subgroups — #22614861

Order 9344.

900 conjugacy classes of subgroups; only the 169 normal subgroups are shown.

normal subgroups only

This group has 900 conjugacy classes of subgroups — too many to draw. Only its 169 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
1C2×#14556574C211yesmaximal, characteristic, complemented
2C2×#14556563C211yesmaximal, characteristic, complemented
3C2×#14556561C211yesmaximal, characteristic, complemented
4C2×#14556559C211yesmaximal, characteristic, complemented
5C22×#11924005C211yesmaximal, characteristic, complemented
6#17988522C212yesmaximal, complemented
7#17988496C212yesmaximal, complemented
8#17988488C212yesmaximal, complemented
9#17988487C212yesmaximal, complemented
10C22⋊C4×Dic73C211yesmaximal, characteristic, complemented
11C2×#123×C73C211yesmaximal, characteristic, complemented
12C24×D73C2211yescharacteristic
13C22×D292C2212yes—
14C22×C22⋊D73C2211yescharacteristic
15C22×C22⋊D73C2212yes—
16C22×C22⋊D73C2211yescharacteristic, complemented
17C23×Dic73C2211yescharacteristic
18#14556574—24no—
19#14556563—24no—
20#14556561—24no—
21#14556559—24no—
22C2×#11924007C2212yescomplemented
23C2×#11924007C2211yescharacteristic, complemented
24C2×C22⋊Dic73C2211yescharacteristic
25C2×C22⋊Dic73C2211yescharacteristic, complemented
26C2×#11924005—24no—
27C2×#11924005C2212yes—
28C2×#11924005C2212yes—
29C2×#11924005C2212yes—
30C2×#11924005C2212yes—
31C2×#11924005C2211yescharacteristic, complemented
32C2×#11924005C2212yescomplemented
33C2×C4×Dic73C2212yescomplemented
34#14556498C2212yescomplemented
35C22×D4×C73C2211yescharacteristic
36C23×C4×C73C2211yescharacteristic
37#123×C73—24no—
38C2×C4⋊C4×C73C2212yescomplemented
39C2×C22⋊C4×C73C2211yescharacteristic
40C2×C22⋊C4×C73C2212yescomplemented
41C23×D73—22no—
42C23×D73—24no—
43C23×D73—22no—
44C23×D73—22no—
45C23×D73—42no—
46C23×D73C2311yescharacteristic
47C23×D73C2312yes—
48C2×D292—24no—
49C2×D292—24no—
50C2×D292—42no—
51C2×C22⋊D73—22no—
52C2×C22⋊D73—22no—
53C2×C22⋊D73—22no—
54C2×C22⋊D73—24no—
55C2×C22⋊D73—24no—
56C2×C22⋊D73—22no—
57C2×C22⋊D73—42no—
58C2×C22⋊D73—42no—
59C22×Dic73—42no—
60C22×Dic73D414yescomplemented
61C22×Dic73C2311yescharacteristic
62C22×Dic73C2311yescharacteristic
63C22×Dic73C2312yes—
64C22×Dic73C2311yescharacteristic
65#11924007—22no—
66#11924007—24no—
67C22⋊Dic73—22no—
68C22⋊Dic73D414yescomplemented
69#11924005—24no—
70#11924005—24no—
71#11924005—24no—
72#11924005—24no—
73#11924005—22no—
74#11924005—24no—
75C4×Dic73—42no—
76C24×C73C2311yescharacteristic
77C24×C73C2311yescharacteristic
78C2×D4×C73—22no—
79C2×D4×C73—22no—
80C2×D4×C73—22no—
81C22×C4×C73—22no—
82C22×C4×C73—22no—
83C22×C4×C73—22no—
84C22×C4×C73C2312yes—
85C22×C4×C73C2311yescharacteristic
86C22×C4×C73C2312yes—
87C4⋊C4×C73—24no—
88C22⋊C4×C73—24no—
89C22⋊C4×C73D414yescomplemented
90C23×C73—22no—
91C23×C73—22no—
92C23×C73—21no—
93C23×C73—21no—
94C23×C73—21no—
95C23×C73—22no—
96C23×C73—22no—
97C23×C73C2×D412yes—
98C23×C73C2×D412yes—
99C23×C73C2×D412yes—
100C23×C73C2411yescharacteristic
101C22×D73—28no—
102C22×D73—22no—
103C22×D73—22no—
104C22×D73—22no—
105C22×D73—22no—
106C22×D73—22no—
107C22×D73—22no—
108C22×D73—21no—
109C22×D73—21no—
110C22×D73—21no—
111C22×D73—22no—
112C22×D73—22no—
113C22×D73—48no—
114C22×D73—48no—
115C22×D73—44no—
116C22×D73—44no—
117C22×D73#4114yes—
118D4×C73—44no—
119C2×C4×C73—22no—
120C2×C4×C73—22no—
121C2×C4×C73—22no—
122C2×C4×C73—21no—
123C2×C4×C73—22no—
124C2×C4×C73—22no—
125C2×C4×C73—21no—
126C2×C4×C73—21no—
127C2×C4×C73—44no—
128C2×C4×C73C2×D414yes—
129C22⋊D73—48no—
130C22⋊D73—44no—
131C22⋊D73—44no—
132C2×Dic73—22no—
133C2×Dic73—22no—
134C2×Dic73—22no—
135C2×Dic73—22no—
136C2×Dic73—21no—
137C2×Dic73—21no—
138C2×Dic73—21no—
139C2×Dic73—44no—
140C2×Dic73C2×D412yes—
141C2×Dic73C2×D414yes—
142C2×Dic73C2×D412yes—
143D292—48no—
144C22×C73—22no—
145C22×C73—22no—
146C22×C73—24no—
147C22×C73—24no—
148C22×C73—41no—
149C22×C73—41no—
150C22×C73—41no—
151C22×C73—42no—
152C22×C73—42no—
153C22×C73#12714yes—
154C22×C73C22×D411yescharacteristic
155C22×C73C22×D411yescharacteristic
156C22×C73C22×D411yescharacteristic
157C22×C73C2×#4112yes—
158C22×C73H(5,𝔽2)12yes—
159C2×D73—24no—
160C2×D73—24no—
161C2×D73—24no—
162C2×D73—416no—
163C2×D73—42no—
164C2×D73—42no—
165C2×D73—42no—
166C2×D73—42no—
167C2×D73—41no—
168C2×D73—41no—
169C2×D73—41no—
170C2×D73—42no—
171C2×D73—42no—
172C4×C73—24no—
173C4×C73—42no—
174C4×C73—41no—
175Dic73—22no—
176Dic73—22no—
177Dic73—24no—
178Dic73—41no—
179C2×C73—24no—
180C2×C73—81no—
181C2×C73#52511yescharacteristic
182C2×C73C2×#12711yescharacteristic
183C2×C73#53411yescharacteristic
184C2×C73#54612yes—
185C2×C73#54612yes—
186D73—44no—
187D73—81no—
188#2539—731nomaximal, Sylow
189C73#253911yescharacteristic, complemented, Sylow
190C2×#123—731no—
191C2×#123D7311yescharacteristic, complemented
192C2×#121—731no—
193C2×#120—731no—
194C2×#120—731no—
195C22×C22⋊C4—731no—
196#399—732no—
197#392—732no—
198#390—732no—
199#390—732no—
200C4×C22⋊C4—731no—
201C25—731no—
202C22×D4—731no—
203C22×D4—732no—
204C22×D4—731no—
205C22×D4—732no—
206C22×D4C2×D7311yescharacteristic
207C23×C4—731no—
208C23×C4C2×D7311yescharacteristic
209#123—24no—
210#123—1464no—
211#121—1464no—
212#120—1464no—
213#120—1464no—
214C2×C4⋊C4—731no—
215C2×C4⋊C4—732no—
216C2×C4⋊C4C2×D7312yescomplemented
217C2×C22⋊C4—731no—
218C2×C22⋊C4—731no—
219C2×C22⋊C4—732no—
220C2×C22⋊C4—732no—
221C2×C22⋊C4—732no—
222C2×C22⋊C4—732no—
223C2×C22⋊C4—731no—
224C2×C22⋊C4—732no—
225C2×C22⋊C4—1464no—
226C2×C22⋊C4C2×D7311yescharacteristic
227C2×C22⋊C4C2×D7312yescomplemented
228C2×C42—732no—
229#95—732no—
230C24—2922no—
231C24—732no—
232C24—731no—
233C24—1464no—
234C24—1462no—
235C24—1462no—
236C24—1462no—
237C24C22×D7311yescharacteristic
238C24C22×D7311yescharacteristic
239C2×D4—22no—
240C2×D4—22no—
241C2×D4—22no—
242C2×D4—2922no—
243C2×D4—2922no—
244C2×D4—2922no—
245C2×D4—1464no—
246C2×D4—1464no—
247C2×D4—1462no—
248C2×D4—1464no—
249C2×D4—1462no—
250C2×D4—1462no—
251C2×D4—1462no—
252C2×D4—1464no—
253C22×C4—22no—
254C22×C4—22no—
255C22×C4—22no—
256C22×C4—2922no—
257C22×C4—734no—
258C22×C4—731no—
259C22×C4—732no—
260C22×C4—731no—
261C22×C4—731no—
262C22×C4C22×D7312yes—
263C22×C4C22×D7311yescharacteristic
264C22×C4C22×D7312yes—
265C4⋊C4—24no—
266C4⋊C4—1462no—
267C4⋊C4—1464no—
268C22⋊C4—24no—
269C22⋊C4—734no—
270C22⋊C4—1464no—
271C22⋊C4—1464no—
272C22⋊C4—1464no—
273C22⋊C4—1462no—
274C22⋊C4—1464no—
275C22⋊C4—1462no—
276C22⋊C4—1464no—
277C22⋊C4C22⋊D7314yescomplemented
278C42—2922no—
279C23—22no—
280C23—22no—
281C23—21no—
282C23—21no—
283C23—21no—
284C23—22no—
285C23—22no—
286C23—2924no—
287C23—2928no—
288C23—2928no—
289C23—2924no—
290C23—734no—
291C23—1468no—
292C23—1461no—
293C23—1461no—
294C23—1461no—
295C23—1462no—
296C23—1462no—
297C23—1462no—
298C23—1462no—
299C23—1462no—
300C23—1462no—
301C23—1462no—
302C23—1462no—
303C23D4×D7312yes—
304C23D4×D7312yes—
305C23C2×C22⋊D7312yes—
306C23C23×D7311yescharacteristic
307D4—44no—
308D4—2928no—
309D4—2924no—
310D4—2924no—
311D4—2928no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—21no—
316C2×C4—22no—
317C2×C4—21no—
318C2×C4—22no—
319C2×C4—21no—
320C2×C4—44no—
321C2×C4—2924no—
322C2×C4—734no—
323C2×C4—732no—
324C2×C4—732no—
325C2×C4—1461no—
326C2×C4—1461no—
327C2×C4—1461no—
328C2×C4—1462no—
329C2×C4—1462no—
330C2×C4—1462no—
331C2×C4—1462no—
332C2×C4C2×C22⋊D7314yes—
333C22—22no—
334C22—24no—
335C22—24no—
336C22—22no—
337C22—41no—
338C22—41no—
339C22—42no—
340C22—42no—
341C22—41no—
342C22—29216no—
343C22—2922no—
344C22—2922no—
345C22—2922no—
346C22—2922no—
347C22—2921no—
348C22—2921no—
349C22—2922no—
350C22—2922no—
351C22—2921no—
352C22—1464no—
353C22—1464no—
354C22—1464no—
355C22#1455658714yes—
356C22C2×D4×D7311yescharacteristic
357C22C2×D4×D7311yescharacteristic
358C22C22×C22⋊D7311yescharacteristic
359C22#41×D7312yes—
360C22#1455663712yes—
361C4—24no—
362C4—42no—
363C4—41no—
364C4—2921no—
365C4—1462no—
366C4—1462no—
367C4—1464no—
368C2—24no—
369C2—81no—
370C2—2924no—
371C2—5841no—
372C2#1798909511yescharacteristic
373C2C2×#1455658711yescharacteristic
374C2#1798914811yescharacteristic
375C2#1798922512yes—
376C2#1798922912yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
FittingC2×#123×C73C2
hypercenterC2×#123D73
hypocenterC73#2539
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. C2×#14556574C2semidirect
2. C2×#14556563C2semidirect
3. C2×#14556561C2semidirect
4. C2×#14556559C2semidirect
5. C22×#11924005C2semidirect
6. #17988522C2semidirect
7. #17988496C2semidirect
8. #17988488C2semidirect
9. #17988487C2semidirect
10. C22⋊C4×Dic73C2semidirect
11. C2×#123×C73C2semidirect
16. C22×C22⋊D73C22semidirect
22. C2×#11924007C22semidirect
23. C2×#11924007C22semidirect
25. C2×C22⋊Dic73C22semidirect
31. C2×#11924005C22semidirect
32. C2×#11924005C22semidirect
33. C2×C4×Dic73C22semidirect
34. #14556498C22semidirect
38. C2×C4⋊C4×C73C22semidirect
40. C2×C22⋊C4×C73C22semidirect
60. C22×Dic73D4semidirect
68. C22⋊Dic73D4semidirect
89. C22⋊C4×C73D4semidirect
189. C73#2539semidirect
191. C2×#123D73semidirect
216. C2×C4⋊C4C2×D73semidirect
227. C2×C22⋊C4C2×D73semidirect
277. C22⋊C4C22⋊D73semidirect