Finite Group Databasebeta

← #22616404

Subgroups — #22616404

Order 9344.

456 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556582C211yesmaximal, characteristic, complemented
2C2×#14556571C211yesmaximal, characteristic
3#17988529C211yesmaximal, characteristic, complemented
4#17988519C211yesmaximal, characteristic, complemented
5#17988516C211yesmaximal, characteristic
6#17988513C211yesmaximal, characteristic
7#17988508C211yesmaximal, characteristic, complemented
8#17988491C211yesmaximal, characteristic, complemented
9#17988479C211yesmaximal, characteristic
10#17988479C211yesmaximal, characteristic
11#17988470C211yesmaximal, characteristic, complemented
12#17988468C211yesmaximal, characteristic, complemented
13#17988461C211yesmaximal, characteristic
14#17988446C211yesmaximal, characteristic
15#400×C73C211yesmaximal, characteristic, complemented
16C22×Dic146C2211yescharacteristic
17C22×C4×D73C2211yescharacteristic
18#14556582—24no—
19#14556571—24no—
20C2×C4⋊Dic73C2211yescharacteristic
21C2×C4⋊Dic73C2211yescharacteristic
22C2×C4⋊Dic73C2211yescharacteristic
23C2×C4⋊Dic73C2211yescharacteristic
24C2×C4⋊Dic73C2211yescharacteristic
25C2×#11924007C2211yescharacteristic
26C2×#11924007C2211yescharacteristic
27C2×#11924007C2211yescharacteristic
28C2×#11924007C2211yescharacteristic
29C2×#11924005C2211yescharacteristic
30C2×#11924005C2211yescharacteristic
31C2×#11924005C2211yescharacteristic
32C2×#11924005C2211yescharacteristic
33C2×#11924005C2211yescharacteristic
34C2×#11924005C2211yescharacteristic
35C2×C4×Dic73C2211yescharacteristic
36C2×C4×Dic73C2211yescharacteristic
37#14556498C2211yescharacteristic
38#14556498C2211yescharacteristic
39#14556498C2211yescharacteristic
40#14556498C2211yescharacteristic
41#14556498C2211yescharacteristic
42#14556498C2211yescharacteristic
43#14556498C2211yescharacteristic
44#14556498C2211yescharacteristic
45#14556498C2211yescharacteristic
46C2×C4⋊C4×C73C2211yescharacteristic
47C2×C4⋊C4×C73C2211yescharacteristic
48#95×C73C2211yescharacteristic
49#95×C73C2211yescharacteristic
50#95×C73C2211yescharacteristic
51#95×C73C2211yescharacteristic
52#95×C73C2211yescharacteristic
53C23×D73C2311yescharacteristic
54C2×Dic146—22no—
55C2×Dic146—22no—
56C2×Dic146—41no—
57C22×Dic73C2311yescharacteristic
58C22×Dic73C2311yescharacteristic
59C22×Dic73C2311yescharacteristic
60C22×Dic73C2311yescharacteristic
61C22×Dic73C2311yescharacteristic
62C22×Dic73C2311yescharacteristic
63C22×Dic73C2311yescharacteristic
64C2×C4×D73—22no—
65C2×C4×D73—22no—
66C2×C4×D73—41no—
67C4⋊Dic73—22no—
68C4⋊Dic73—22no—
69C4⋊Dic73—22no—
70C4⋊Dic73—41no—
71C4⋊Dic73D414yes—
72#11924007—22no—
73#11924007—22no—
74#11924007—22no—
75#11924007—41no—
76#11924005—22no—
77#11924005—22no—
78#11924005—22no—
79#11924005—22no—
80#11924005—22no—
81#11924005—41no—
82C4×Dic73—22no—
83C4×Dic73—41no—
84C22×C4×C73C2311yescharacteristic
85C22×C4×C73C2311yescharacteristic
86C22×C4×C73C2311yescharacteristic
87C22×C4×C73C2311yescharacteristic
88C22×C4×C73C2311yescharacteristic
89C22×C4×C73C2311yescharacteristic
90C22×C4×C73C2311yescharacteristic
91C4⋊C4×C73—22no—
92C4⋊C4×C73—22no—
93C23×C73C2411yescharacteristic
94C22×D73—21no—
95C22×D73—21no—
96C22×D73—21no—
97C22×D73—21no—
98C22×D73—21no—
99C22×D73—21no—
100C22×D73#4112yes—
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—21no—
115C2×C4×C73—21no—
116C2×C4×C73—21no—
117C2×C4×C73—21no—
118C2×C4×C73—21no—
119C2×C4×C73—21no—
120C2×C4×C73C2×D412yes—
121C2×C4×C73#4112yes—
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—
143C4×D73—44no—
144Dic146—44no—
145C22×C73C22×D411yescharacteristic
146C22×C73C2×#4111yescharacteristic
147C22×C73C2×#4111yescharacteristic
148C22×C73H(5,𝔽2)11yescharacteristic
149C22×C732−1+411yescharacteristic
150C22×C732−1+411yescharacteristic
151C22×C732−1+411yescharacteristic
152C2×D73—22no—
153C2×D73—22no—
154C2×D73—22no—
155C2×D73—41no—
156C2×D73—41no—
157C2×D73—41no—
158C2×D73—41no—
159C4×C73—22no—
160C4×C73—22no—
161C4×C73—41no—
162C4×C73—41no—
163C4×C73—41no—
164C4×C73—41no—
165C4×C73—41no—
166Dic73—22no—
167Dic73—22no—
168Dic73—41no—
169Dic73—41no—
170Dic73—41no—
171Dic73—41no—
172Dic73—41no—
173C2×C73#53611yescharacteristic
174C2×C73#53911yescharacteristic
175C2×C73#54111yescharacteristic
176C2×C73#54611yescharacteristic
177C2×C73#54811yescharacteristic
178C2×C73#55211yescharacteristic
179C2×C73#56311yescharacteristic
180D73—42no—
181#2690—731nomaximal, Sylow
182C73#269011yescharacteristic, complemented, Sylow
183C2×#125—731no—
184C2×C22⋊Q8—731no—
185#400—731no—
186#400D7311yescharacteristic, complemented
187#398—731no—
188#397—731no—
189#397—731no—
190#395—731no—
191#391—731no—
192#388—731no—
193#388—731no—
194#387—731no—
195#387—731no—
196#385—731no—
197#380—731no—
198C22×Q8—731no—
199C23×C4—731no—
200#125—1464no—
201C22⋊Q8—1464no—
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⋊C4—731no—
211C2×C4⋊C4C2×D7311yescharacteristic
212C2×C4⋊C4C2×D7311yescharacteristic
213C2×C22⋊C4—731no—
214C2×C22⋊C4—731no—
215C2×C22⋊C4—731no—
216C2×C22⋊C4—731no—
217C2×C22⋊C4—731no—
218C2×C22⋊C4—731no—
219C2×C42—731no—
220C2×C42—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
232#95C2×D7311yescharacteristic
233#95C2×D7311yescharacteristic
234#95C2×D7311yescharacteristic
235C24—731no—
236C2×Q8—2921no—
237C2×Q8—1462no—
238C2×Q8—1462no—
239C22×C4—2921no—
240C22×C4—731no—
241C22×C4—731no—
242C22×C4—731no—
243C22×C4—731no—
244C22×C4—731no—
245C22×C4—731no—
246C22×C4—731no—
247C22×C4—1462no—
248C22×C4—1462no—
249C22×C4C22×D7311yescharacteristic
250C22×C4C22×D7311yescharacteristic
251C22×C4C22×D7311yescharacteristic
252C22×C4C22×D7311yescharacteristic
253C22×C4C22×D7311yescharacteristic
254C22×C4C22×D7311yescharacteristic
255C22×C4C22×D7311yescharacteristic
256C4⋊C4—22no—
257C4⋊C4—22no—
258C4⋊C4—2921no—
259C4⋊C4—2921no—
260C4⋊C4—734no—
261C4⋊C4—1462no—
262C4⋊C4—1462no—
263C4⋊C4—1462no—
264C4⋊C4—1462no—
265C4⋊C4—1462no—
266C4⋊C4—1462no—
267C22⋊C4—2921no—
268C22⋊C4—1462no—
269C22⋊C4—1462no—
270C22⋊C4—1462no—
271C22⋊C4—1462no—
272C22⋊C4—1462no—
273C42—2921no—
274C42—1462no—
275C23—732no—
276C23—1461no—
277C23—1461no—
278C23—1461no—
279C23—1461no—
280C23—1461no—
281C23—1461no—
282C23C23×D7311yescharacteristic
283Q8—2924no—
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—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—2924no—
304C2×C4—732no—
305C2×C4—732no—
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×C4—1461no—
323C2×C4—1461no—
324C2×C4—1461no—
325C2×C4D4×D7312yes—
326C2×C4#1192402912yes—
327C22—2921no—
328C22—2921no—
329C22—2921no—
330C22—2921no—
331C22—1462no—
332C22—1462no—
333C22—1462no—
334C22C2×D4×D7311yescharacteristic
335C22#41×D7311yescharacteristic
336C22C2×#1192402911yescharacteristic
337C22#1455663711yescharacteristic
338C22#1455663811yescharacteristic
339C22#1455663811yescharacteristic
340C22#1455663811yescharacteristic
341C4—22no—
342C4—22no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—2921no—
349C4—2921no—
350C4—2921no—
351C4—2921no—
352C4—2921no—
353C4—1462no—
354C4—1462no—
355C2—2922no—
356C2#1798915911yescharacteristic
357C2#1798917811yescharacteristic
358C2#1798920011yescharacteristic
359C2#1798922811yescharacteristic
360C2#1798924511yescharacteristic
361C2#1798927511yescharacteristic
362C2#1798933911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#400×C73C2
hypercenter#400D73
hypocenterC73#2690
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
1. C2×#14556582C2semidirect
3. #17988529C2semidirect
4. #17988519C2semidirect
7. #17988508C2semidirect
8. #17988491C2semidirect
11. #17988470C2semidirect
12. #17988468C2semidirect
15. #400×C73C2semidirect
182. C73#2690semidirect
186. #400D73semidirect