Finite Group Databasebeta

← #22614101

Subgroups — #22614101

Order 9344.

476 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556582C211yesmaximal, characteristic, complemented
2C2×#14556550C211yesmaximal, characteristic
3#17988527C211yesmaximal, characteristic, complemented
4#17988517C211yesmaximal, characteristic, complemented
5#17988515C211yesmaximal, characteristic
6#17988510C211yesmaximal, characteristic
7#17988482C211yesmaximal, characteristic, complemented
8#17988481C211yesmaximal, characteristic
9#17988480C211yesmaximal, characteristic
10#17988474C211yesmaximal, characteristic, complemented
11#17988473C211yesmaximal, characteristic, complemented
12#17988470C211yesmaximal, characteristic, complemented
13#17988460C211yesmaximal, characteristic
14#17988438C211yesmaximal, characteristic, complemented
15#385×C73C211yesmaximal, characteristic
16#14556582—24no—
17#14556550—24no—
18C2×C4⋊Dic73C2211yescharacteristic
19C2×C4⋊Dic73C2211yescharacteristic
20C2×C4⋊Dic73C2211yescharacteristic
21C2×C4⋊Dic73C2211yescharacteristic
22C2×#11924007C2211yescharacteristic
23C2×#11924007C2211yescharacteristic
24C2×#11924007C2211yescharacteristic
25C2×#11924007C2211yescharacteristic
26C2×#11924007C2211yescharacteristic
27C2×#11924007C2211yescharacteristic
28C2×C22⋊Dic73C2211yescharacteristic
29C2×C22⋊Dic73C2211yescharacteristic
30C2×C22⋊Dic73C2211yescharacteristic
31C2×C22⋊Dic73C2211yescharacteristic
32C2×C4×Dic73C2211yescharacteristic
33C2×C4×Dic73C2211yescharacteristic
34C2×C4×Dic73C2211yescharacteristic
35C2×C4×Dic73C2211yescharacteristic
36#14556498C2211yescharacteristic
37#14556498C2211yescharacteristic
38#14556498C2211yescharacteristic
39#14556498C2211yescharacteristic
40#14556498C2211yescharacteristic
41#14556498C2211yescharacteristic
42#14556498C2211yescharacteristic
43#14556498C2211yescharacteristic
44#14556498C2211yescharacteristic
45#14556498C2211yescharacteristic
46C23×C4×C73C2211yescharacteristic
47C2×C4⋊C4×C73C2211yescharacteristic
48C2×C4⋊C4×C73C2211yescharacteristic
49C2×C22⋊C4×C73C2211yescharacteristic
50C2×C22⋊C4×C73C2211yescharacteristic
51#95×C73C2211yescharacteristic
52#95×C73C2211yescharacteristic
53C22×Dic73C2311yescharacteristic
54C22×Dic73C2311yescharacteristic
55C22×Dic73C2311yescharacteristic
56C22×Dic73C2311yescharacteristic
57C22×Dic73C2311yescharacteristic
58C22×Dic73C2311yescharacteristic
59C22×Dic73C2311yescharacteristic
60C22×Dic73C2311yescharacteristic
61C4⋊Dic73—22no—
62C4⋊Dic73—22no—
63C4⋊Dic73—22no—
64C4⋊Dic73D414yes—
65#11924007—22no—
66#11924007—22no—
67#11924007—22no—
68#11924007—22no—
69#11924007—22no—
70#11924007—22no—
71C22⋊Dic73—22no—
72C22⋊Dic73—22no—
73C22⋊Dic73—22no—
74C22⋊Dic73—22no—
75C4×Dic73—22no—
76C4×Dic73—22no—
77C4×Dic73—22no—
78C4×Dic73—22no—
79C24×C73C2311yescharacteristic
80C22×C4×C73—22no—
81C22×C4×C73—22no—
82C22×C4×C73—22no—
83C22×C4×C73C2311yescharacteristic
84C22×C4×C73C2311yescharacteristic
85C22×C4×C73C2311yescharacteristic
86C22×C4×C73C2311yescharacteristic
87C22×C4×C73C2311yescharacteristic
88C22×C4×C73C2311yescharacteristic
89C4⋊C4×C73—22no—
90C4⋊C4×C73—22no—
91C22⋊C4×C73—22no—
92C22⋊C4×C73—22no—
93C23×C73—21no—
94C23×C73—21no—
95C23×C73—21no—
96C23×C73—21no—
97C23×C73—21no—
98C23×C73—21no—
99C23×C73#4112yes—
100C23×C73C2411yescharacteristic
101C2×C4×C73—28no—
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—21no—
115C2×C4×C73—21no—
116C2×C4×C73—21no—
117C2×C4×C73C2×D412yes—
118C2×C4×C73#4112yes—
119C2×C4×C73#4112yes—
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×Dic73—21no—
140C2×Dic73—21no—
141C2×Dic73C2×D412yes—
142C2×Dic73C2×D412yes—
143C2×Dic73#4112yes—
144C22×C73—22no—
145C22×C73—22no—
146C22×C73—22no—
147C22×C73—41no—
148C22×C73—41no—
149C22×C73—41no—
150C22×C73—41no—
151C22×C73C22×D411yescharacteristic
152C22×C73C2×#4111yescharacteristic
153C22×C73C2×#4111yescharacteristic
154C22×C73C2×#4111yescharacteristic
155C22×C73C2×#4111yescharacteristic
156C22×C732−1+411yescharacteristic
157C22×C732−1+411yescharacteristic
158C4×C73—22no—
159C4×C73—22no—
160C4×C73—22no—
161C4×C73—41no—
162C4×C73—41no—
163C4×C73—41no—
164Dic73—22no—
165Dic73—22no—
166Dic73—22no—
167Dic73—41no—
168Dic73—41no—
169Dic73—41no—
170Dic73—41no—
171Dic73—41no—
172C2×C73—42no—
173C2×C73#52511yescharacteristic
174C2×C73#52911yescharacteristic
175C2×C73#54111yescharacteristic
176C2×C73#54711yescharacteristic
177C2×C73#54811yescharacteristic
178C2×C73#55211yescharacteristic
179C2×C73#55211yescharacteristic
180#2475—731nomaximal, Sylow
181C73#247511yescharacteristic, complemented, Sylow
182C2×#125—731no—
183C2×#117—731no—
184#400—731no—
185#398—731no—
186#397—731no—
187#396—731no—
188#389—731no—
189#388—731no—
190#388—731no—
191#387—731no—
192#387—731no—
193#387—731no—
194#385—731no—
195#385D7311yescharacteristic
196C4×C4⋊C4—731no—
197C23×C4C2×D7311yescharacteristic
198#125—1464no—
199#117—1464no—
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×C4⋊C4—731no—
209C2×C4⋊C4—731no—
210C2×C4⋊C4C2×D7311yescharacteristic
211C2×C4⋊C4C2×D7311yescharacteristic
212C2×C22⋊C4—731no—
213C2×C22⋊C4—731no—
214C2×C22⋊C4—731no—
215C2×C22⋊C4—731no—
216C2×C22⋊C4C2×D7311yescharacteristic
217C2×C22⋊C4C2×D7311yescharacteristic
218C2×C42—731no—
219C2×C42—731no—
220C2×C42—731no—
221C2×C42—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#95—731no—
231#95—731no—
232#95C2×D7311yescharacteristic
233#95C2×D7311yescharacteristic
234C24C22×D7311yescharacteristic
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—731no—
239C22×C4—731no—
240C22×C4—731no—
241C22×C4—731no—
242C22×C4—731no—
243C22×C4—731no—
244C22×C4—731no—
245C22×C4—731no—
246C22×C4C22×D7311yescharacteristic
247C22×C4C22×D7311yescharacteristic
248C22×C4C22×D7311yescharacteristic
249C22×C4C22×D7311yescharacteristic
250C22×C4C22×D7311yescharacteristic
251C22×C4C22×D7311yescharacteristic
252C4⋊C4—22no—
253C4⋊C4—22no—
254C4⋊C4—734no—
255C4⋊C4—1462no—
256C4⋊C4—1462no—
257C4⋊C4—1462no—
258C4⋊C4—1462no—
259C4⋊C4—1462no—
260C4⋊C4—1462no—
261C4⋊C4—1462no—
262C4⋊C4—1462no—
263C4⋊C4—1462no—
264C22⋊C4—22no—
265C22⋊C4—22no—
266C22⋊C4—1462no—
267C22⋊C4—1462no—
268C22⋊C4—1462no—
269C22⋊C4—1462no—
270C42—1462no—
271C42—1462no—
272C42—1462no—
273C42—1462no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23—21no—
279C23—21no—
280C23#1192402712yes—
281C23C23×D7311yescharacteristic
282C2×C4—28no—
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—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—732no—
299C2×C4—732no—
300C2×C4—732no—
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×C4—1461no—
320C2×C4—1461no—
321C2×C4—1461no—
322C2×C4D4×D7312yes—
323C2×C4#1192402712yes—
324C2×C4#1192402812yes—
325C22—22no—
326C22—22no—
327C22—22no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22C2×D4×D7311yescharacteristic
333C22#41×D7311yescharacteristic
334C22C2×#1192402711yescharacteristic
335C22C2×#1192402711yescharacteristic
336C22C2×#1192402811yescharacteristic
337C22#1455663811yescharacteristic
338C22#1455663911yescharacteristic
339C4—22no—
340C4—22no—
341C4—22no—
342C4—41no—
343C4—41no—
344C4—41no—
345C4—2921no—
346C4—2921no—
347C4—2921no—
348C4—2921no—
349C4—2921no—
350C4—1462no—
351C4—1462no—
352C4—1462no—
353C2—42no—
354C2#1798909311yescharacteristic
355C2#1798911911yescharacteristic
356C2#1798919711yescharacteristic
357C2#1798923911yescharacteristic
358C2#1798924611yescharacteristic
359C2#1798927211yescharacteristic
360C2#1798927411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#385×C73C2
hypercenter#385D73
hypocenterC73#2475
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
1. C2×#14556582C2semidirect
3. #17988527C2semidirect
4. #17988517C2semidirect
7. #17988482C2semidirect
10. #17988474C2semidirect
11. #17988473C2semidirect
12. #17988470C2semidirect
14. #17988438C2semidirect
181. C73#2475semidirect