Finite Group Databasebeta

← #22612708

Subgroups — #22612708

Order 9344.

476 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556584C211yesmaximal, characteristic
2#17988485C211yesmaximal, characteristic, complemented
3#17988484C211yesmaximal, characteristic, complemented
4#17988481C211yesmaximal, characteristic
5#17988480C211yesmaximal, characteristic
6#17988475C211yesmaximal, characteristic
7#17988472C211yesmaximal, characteristic, complemented
8#17988471C211yesmaximal, characteristic, complemented
9#17988469C211yesmaximal, characteristic, complemented
10#17988460C211yesmaximal, characteristic
11#17988460C211yesmaximal, characteristic
12#17988451C211yesmaximal, characteristic, complemented
13C4×#11924007C211yesmaximal, characteristic, complemented
14C4×#11924007C211yesmaximal, characteristic, complemented
15C4×C22⋊C4×C73C211yesmaximal, characteristic
16#14556584C418yescomplemented
17C2×C4⋊Dic73C2211yescharacteristic
18C2×C4⋊Dic73C2211yescharacteristic
19C2×#11924007C2211yescharacteristic
20C2×#11924007C2211yescharacteristic
21C2×#11924007C2211yescharacteristic
22C2×#11924007C2211yescharacteristic
23C2×#11924007C2211yescharacteristic
24C2×#11924007C2211yescharacteristic
25C2×#11924007C2211yescharacteristic
26C2×#11924007C2211yescharacteristic
27C2×C22⋊Dic73C2211yescharacteristic
28C2×C22⋊Dic73C2211yescharacteristic
29C2×C22⋊Dic73C2211yescharacteristic
30C2×C22⋊Dic73C2211yescharacteristic
31C2×C4×Dic73C2211yescharacteristic
32C2×C4×Dic73C2211yescharacteristic
33C2×C4×Dic73C2211yescharacteristic
34C2×C4×Dic73C2211yescharacteristic
35#14556498C2211yescharacteristic
36#14556498C2211yescharacteristic
37#14556498C2211yescharacteristic
38#14556498C2211yescharacteristic
39#14556498C2211yescharacteristic
40#14556498C2211yescharacteristic
41#14556498C2211yescharacteristic
42#14556498C2211yescharacteristic
43#14556498C2211yescharacteristic
44#14556498C2211yescharacteristic
45C23×C4×C73C2211yescharacteristic
46C2×C22⋊C4×C73C2211yescharacteristic
47C2×C22⋊C4×C73C2211yescharacteristic
48C2×C42×C73C2211yescharacteristic
49C2×C42×C73C2211yescharacteristic
50#95×C73C2211yescharacteristic
51#95×C73C2211yescharacteristic
52C22×Dic73C2311yescharacteristic
53C22×Dic73C2311yescharacteristic
54C22×Dic73C2311yescharacteristic
55C22×Dic73C2311yescharacteristic
56C22×Dic73C2311yescharacteristic
57C22×Dic73C2311yescharacteristic
58C22×Dic73C2311yescharacteristic
59C22×Dic73C2311yescharacteristic
60C4⋊Dic73—41no—
61C4⋊Dic73C2×C414yescomplemented
62#11924007—22no—
63#11924007—22no—
64#11924007—22no—
65#11924007—41no—
66#11924007—41no—
67#11924007—41no—
68#11924007C2×C414yescomplemented
69#11924007C2×C414yescomplemented
70C22⋊Dic73—41no—
71C22⋊Dic73—41no—
72C22⋊Dic73C2×C414yes—
73C22⋊Dic73C2×C414yes—
74C4×Dic73—22no—
75C4×Dic73—41no—
76C4×Dic73—41no—
77C4×Dic73C2×C414yescomplemented
78C24×C73C2311yescharacteristic
79C22×C4×C73—22no—
80C22×C4×C73—41no—
81C22×C4×C73—41no—
82C22×C4×C73C2311yescharacteristic
83C22×C4×C73C2311yescharacteristic
84C22×C4×C73C2311yescharacteristic
85C22×C4×C73C2311yescharacteristic
86C22×C4×C73C2311yescharacteristic
87C22×C4×C73C2311yescharacteristic
88C22⋊C4×C73—22no—
89C22⋊C4×C73C2×C414yes—
90C42×C73—41no—
91C42×C73—41no—
92C23×C73—21no—
93C23×C73—21no—
94C23×C73—21no—
95C23×C73—21no—
96C23×C73—21no—
97C23×C73—21no—
98C23×C73C22×C412yes—
99C23×C73C2411yescharacteristic
100C2×C4×C73—21no—
101C2×C4×C73—21no—
102C2×C4×C73—21no—
103C2×C4×C73—21no—
104C2×C4×C73—21no—
105C2×C4×C73—21no—
106C2×C4×C73—21no—
107C2×C4×C73—21no—
108C2×C4×C73—21no—
109C2×C4×C73—21no—
110C2×C4×C73—21no—
111C2×C4×C73—21no—
112C2×C4×C73—21no—
113C2×C4×C73—21no—
114C2×C4×C73—44no—
115C2×C4×C73C22×C412yes—
116C2×C4×C73C22×C412yes—
117C2×C4×C73#4112yes—
118C2×C4×C73#4112yes—
119C2×Dic73—21no—
120C2×Dic73—21no—
121C2×Dic73—21no—
122C2×Dic73—21no—
123C2×Dic73—21no—
124C2×Dic73—21no—
125C2×Dic73—21no—
126C2×Dic73—21no—
127C2×Dic73—21no—
128C2×Dic73—21no—
129C2×Dic73—21no—
130C2×Dic73—21no—
131C2×Dic73—21no—
132C2×Dic73—21no—
133C2×Dic73—21no—
134C2×Dic73—21no—
135C2×Dic73—21no—
136C2×Dic73—21no—
137C2×Dic73—21no—
138C2×Dic73—21no—
139C2×Dic73C22×C412yes—
140C2×Dic73C22×C412yes—
141C2×Dic73C22×C412yes—
142C2×Dic73C22×C412yes—
143C22×C73—22no—
144C22×C73—22no—
145C22×C73—22no—
146C22×C73—41no—
147C22×C73—41no—
148C22×C73—41no—
149C22×C73—41no—
150C22×C73C23×C411yescharacteristic
151C22×C73C2×#4111yescharacteristic
152C22×C73C2×#4111yescharacteristic
153C22×C73H(5,𝔽2)11yescharacteristic
154C22×C73H(5,𝔽2)11yescharacteristic
155C22×C732−1+411yescharacteristic
156C22×C732−1+411yescharacteristic
157C4×C73—22no—
158C4×C73—22no—
159C4×C73—22no—
160C4×C73—22no—
161C4×C73—41no—
162C4×C73—41no—
163Dic73—22no—
164Dic73—22no—
165Dic73—22no—
166Dic73—22no—
167Dic73—41no—
168Dic73—41no—
169Dic73—41no—
170Dic73—41no—
171C2×C73—42no—
172C2×C73C4×#4111yescharacteristic
173C2×C73#52011yescharacteristic
174C2×C73#52011yescharacteristic
175C2×C73#53811yescharacteristic
176C2×C73#53911yescharacteristic
177C2×C73#54111yescharacteristic
178C2×C73#54211yescharacteristic
179#2334—731nomaximal, Sylow
180C73#233411yescharacteristic, complemented, Sylow
181C2×#126—731no—
182#389—731no—
183#389—731no—
184#388—731no—
185#388—731no—
186#388—731no—
187#387—731no—
188#387—731no—
189#387—731no—
190#385—731no—
191#385—731no—
192#382—731no—
193C4×C4⋊C4—731no—
194C4×C4⋊C4—731no—
195C4×C22⋊C4D7311yescharacteristic
196C23×C4C2×D7311yescharacteristic
197#126—738no—
198C2×C4⋊C4—731no—
199C2×C4⋊C4—731no—
200C2×C4⋊C4—731no—
201C2×C4⋊C4—731no—
202C2×C4⋊C4—731no—
203C2×C4⋊C4—731no—
204C2×C4⋊C4—731no—
205C2×C4⋊C4—731no—
206C2×C4⋊C4—731no—
207C2×C4⋊C4—731no—
208C2×C22⋊C4—731no—
209C2×C22⋊C4—731no—
210C2×C22⋊C4—731no—
211C2×C22⋊C4—731no—
212C2×C22⋊C4C2×D7311yescharacteristic
213C2×C22⋊C4C2×D7311yescharacteristic
214C2×C42—731no—
215C2×C42—731no—
216C2×C42—731no—
217C2×C42—731no—
218C2×C42C2×D7311yescharacteristic
219C2×C42C2×D7311yescharacteristic
220#95—731no—
221#95—731no—
222#95—731no—
223#95—731no—
224#95—731no—
225#95—731no—
226#95—731no—
227#95—731no—
228#95—731no—
229#95—731no—
230#95C2×D7311yescharacteristic
231#95C2×D7311yescharacteristic
232C24C22×D7311yescharacteristic
233C22×C4—22no—
234C22×C4—41no—
235C22×C4—41no—
236C22×C4—731no—
237C22×C4—731no—
238C22×C4—731no—
239C22×C4—731no—
240C22×C4—731no—
241C22×C4—731no—
242C22×C4—731no—
243C22×C4—731no—
244C22×C4C22×D7311yescharacteristic
245C22×C4C22×D7311yescharacteristic
246C22×C4C22×D7311yescharacteristic
247C22×C4C22×D7311yescharacteristic
248C22×C4C22×D7311yescharacteristic
249C22×C4C22×D7311yescharacteristic
250C4⋊C4—2921no—
251C4⋊C4—2921no—
252C4⋊C4—2921no—
253C4⋊C4—2921no—
254C4⋊C4—734no—
255C4⋊C4—734no—
256C4⋊C4—734no—
257C4⋊C4—1462no—
258C4⋊C4—1462no—
259C4⋊C4—1462no—
260C22⋊C4—22no—
261C22⋊C4—2921no—
262C22⋊C4—2921no—
263C22⋊C4—734no—
264C22⋊C4—734no—
265C22⋊C4C4×D7314yes—
266C42—41no—
267C42—41no—
268C42—2921no—
269C42—2921no—
270C42—734no—
271C42—1462no—
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23C2×C4×D7312yes—
279C23C23×D7311yescharacteristic
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—44no—
295C2×C4—732no—
296C2×C4—732no—
297C2×C4—732no—
298C2×C4—732no—
299C2×C4—1461no—
300C2×C4—1461no—
301C2×C4—1461no—
302C2×C4—1461no—
303C2×C4—1461no—
304C2×C4—1461no—
305C2×C4—1461no—
306C2×C4—1461no—
307C2×C4—1461no—
308C2×C4—1461no—
309C2×C4—1461no—
310C2×C4—1461no—
311C2×C4—1461no—
312C2×C4—1461no—
313C2×C4—1461no—
314C2×C4—1461no—
315C2×C4—1461no—
316C2×C4—1461no—
317C2×C4—1461no—
318C2×C4—1461no—
319C2×C4C2×C4×D7312yes—
320C2×C4C2×C4×D7312yes—
321C2×C4#1192402812yes—
322C2×C4#1192402812yes—
323C22—22no—
324C22—22no—
325C22—22no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22C22×C4×D7311yescharacteristic
331C22C2×#1192402811yescharacteristic
332C22C2×#1192402811yescharacteristic
333C22#1455663611yescharacteristic
334C22#1455663611yescharacteristic
335C22#1455663811yescharacteristic
336C22#1455663811yescharacteristic
337C4—22no—
338C4—22no—
339C4—22no—
340C4—22no—
341C4—41no—
342C4—41no—
343C4—2921no—
344C4—2921no—
345C4—2921no—
346C4—2921no—
347C4—1462no—
348C4—1462no—
349C4—1462no—
350C4—1462no—
351C2—42no—
352C2C4×#1192402811yescharacteristic
353C2#1798906611yescharacteristic
354C2#1798906611yescharacteristic
355C2#1798917511yescharacteristic
356C2#1798917911yescharacteristic
357C2#1798919911yescharacteristic
358C2#1798920211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutatorC22×C73C23×C4
FittingC4×C22⋊C4×C73C2
socleC23×C73C24
hypercenterC4×C22⋊C4D73
hypocenterC73#2334
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #17988485C2semidirect
3. #17988484C2semidirect
7. #17988472C2semidirect
8. #17988471C2semidirect
9. #17988469C2semidirect
12. #17988451C2semidirect
13. C4×#11924007C2semidirect
14. C4×#11924007C2semidirect
16. #14556584C4semidirect
61. C4⋊Dic73C2×C4semidirect
68. #11924007C2×C4semidirect
69. #11924007C2×C4semidirect
77. C4×Dic73C2×C4semidirect
180. C73#2334semidirect