Finite Group Databasebeta

← #22614721

Subgroups — #22614721

Order 9344.

420 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17988528C211yesmaximal, characteristic, complemented
2#17988516C211yesmaximal, characteristic
3#17988500C211yesmaximal, characteristic
4#17988491C211yesmaximal, characteristic, complemented
5#17988491C211yesmaximal, characteristic, complemented
6#17988476C211yesmaximal, characteristic
7#17988476C211yesmaximal, characteristic
8#17988474C211yesmaximal, characteristic, complemented
9#17988472C211yesmaximal, characteristic, complemented
10#17988469C211yesmaximal, characteristic, complemented
11#17988461C211yesmaximal, characteristic
12#17988449C211yesmaximal, characteristic
13#17988434C211yesmaximal, characteristic
14#17988432C211yesmaximal, characteristic, complemented
15#401×C73C211yesmaximal, characteristic, complemented
16C22×Dic146C2211yescharacteristic
17C22×C4×D73C2211yescharacteristic
18C2×C4⋊Dic73C2211yescharacteristic
19C2×#11924007C2211yescharacteristic
20C2×#11924007C2211yescharacteristic
21C2×#11924007C2211yescharacteristic
22C2×#11924007C2211yescharacteristic
23C2×#11924005C2211yescharacteristic
24C2×#11924005C2211yescharacteristic
25C2×#11924005C2211yescharacteristic
26C2×#11924005C2211yescharacteristic
27C2×#11924005C2211yescharacteristic
28C2×#11924005C2211yescharacteristic
29C2×C4×Dic73C2211yescharacteristic
30C2×C4×Dic73C2211yescharacteristic
31C2×C4×Dic73C2211yescharacteristic
32C2×C4×Dic73C2211yescharacteristic
33#14556498C2211yescharacteristic
34#14556498C2211yescharacteristic
35#14556498C2211yescharacteristic
36#14556498C2211yescharacteristic
37#14556498C2211yescharacteristic
38#14556498C2211yescharacteristic
39#14556498C2211yescharacteristic
40#14556498C2211yescharacteristic
41#14556498C2211yescharacteristic
42#14556498C2211yescharacteristic
43#14556498C2211yescharacteristic
44#95×C73C2211yescharacteristic
45#95×C73C2211yescharacteristic
46#95×C73C2211yescharacteristic
47#95×C73C2211yescharacteristic
48#95×C73C2211yescharacteristic
49#95×C73C2211yescharacteristic
50#95×C73C2211yescharacteristic
51C23×D73C2311yescharacteristic
52C2×Dic146—22no—
53C2×Dic146—22no—
54C2×Dic146—41no—
55C22×Dic73C2311yescharacteristic
56C22×Dic73C2311yescharacteristic
57C22×Dic73C2311yescharacteristic
58C22×Dic73C2311yescharacteristic
59C22×Dic73C2311yescharacteristic
60C22×Dic73C2311yescharacteristic
61C22×Dic73C2311yescharacteristic
62C2×C4×D73—22no—
63C2×C4×D73—22no—
64C2×C4×D73—41no—
65C4⋊Dic73—22no—
66#11924007—22no—
67#11924007—22no—
68#11924007—41no—
69#11924007—41no—
70#11924005—22no—
71#11924005—22no—
72#11924005—22no—
73#11924005—22no—
74#11924005—22no—
75#11924005—41no—
76C4×Dic73—22no—
77C4×Dic73—22no—
78C4×Dic73—22no—
79C4×Dic73—41no—
80C22×C4×C73C2311yescharacteristic
81C22×C4×C73C2311yescharacteristic
82C22×C4×C73C2311yescharacteristic
83C22×C4×C73C2311yescharacteristic
84C22×C4×C73C2311yescharacteristic
85C22×C4×C73C2311yescharacteristic
86C22×C4×C73C2311yescharacteristic
87C23×C73C2411yescharacteristic
88C22×D73—21no—
89C22×D73—21no—
90C22×D73—21no—
91C22×D73—21no—
92C22×D73—21no—
93C22×D73—21no—
94C22×D73#4112yes—
95C2×C4×C73—21no—
96C2×C4×C73—21no—
97C2×C4×C73—21no—
98C2×C4×C73—21no—
99C2×C4×C73—21no—
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—21no—
115C2×C4×C73—21no—
116C2×Dic73—21no—
117C2×Dic73—21no—
118C2×Dic73—21no—
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#4112yes—
134C2×Dic73#4112yes—
135C2×Dic73#4112yes—
136C2×Dic73#4112yes—
137C4×D73—44no—
138Dic146—44no—
139C22×C73C2×#4111yescharacteristic
140C22×C73C2×#4111yescharacteristic
141C22×C73C2×#4111yescharacteristic
142C22×C73C2×#4111yescharacteristic
143C22×C73C2×#4111yescharacteristic
144C22×C73H(5,𝔽2)11yescharacteristic
145C22×C732−1+411yescharacteristic
146C2×D73—22no—
147C2×D73—22no—
148C2×D73—22no—
149C2×D73—41no—
150C2×D73—41no—
151C2×D73—41no—
152C2×D73—41no—
153C4×C73—41no—
154C4×C73—41no—
155C4×C73—41no—
156C4×C73—41no—
157C4×C73—41no—
158C4×C73—41no—
159C4×C73—41no—
160Dic73—22no—
161Dic73—22no—
162Dic73—22no—
163Dic73—22no—
164Dic73—41no—
165Dic73—41no—
166Dic73—41no—
167C2×C73#52911yescharacteristic
168C2×C73#52911yescharacteristic
169C2×C73#54211yescharacteristic
170C2×C73#55111yescharacteristic
171C2×C73#55111yescharacteristic
172C2×C73#55211yescharacteristic
173C2×C73#55611yescharacteristic
174D73—42no—
175#2527—731nomaximal, Sylow
176C73#252711yescharacteristic, complemented, Sylow
177#401D7311yescharacteristic, complemented
178#400—731no—
179#397—731no—
180#393—731no—
181#391—731no—
182#391—731no—
183#388—731no—
184#388—731no—
185#387—731no—
186#387—731no—
187#387—731no—
188#385—731no—
189#381—731no—
190C4×C22⋊C4—731no—
191#376—731no—
192C22×Q8—731no—
193C23×C4—731no—
194C2×C4⋊C4—731no—
195C2×C4⋊C4—731no—
196C2×C4⋊C4—731no—
197C2×C4⋊C4—731no—
198C2×C4⋊C4—731no—
199C2×C22⋊C4—731no—
200C2×C22⋊C4—731no—
201C2×C22⋊C4—731no—
202C2×C22⋊C4—731no—
203C2×C22⋊C4—731no—
204C2×C22⋊C4—731no—
205C2×C42—731no—
206C2×C42—731no—
207C2×C42—731no—
208C2×C42—731no—
209#95—731no—
210#95—731no—
211#95—731no—
212#95—731no—
213#95—731no—
214#95—731no—
215#95—731no—
216#95—731no—
217#95—731no—
218#95—731no—
219#95—731no—
220#95C2×D7311yescharacteristic
221#95C2×D7311yescharacteristic
222#95C2×D7311yescharacteristic
223#95C2×D7311yescharacteristic
224#95C2×D7311yescharacteristic
225#95C2×D7311yescharacteristic
226#95C2×D7311yescharacteristic
227C24—731no—
228C2×Q8—2921no—
229C2×Q8—1462no—
230C2×Q8—1462no—
231C22×C4—2921no—
232C22×C4—731no—
233C22×C4—731no—
234C22×C4—731no—
235C22×C4—731no—
236C22×C4—731no—
237C22×C4—731no—
238C22×C4—731no—
239C22×C4—1462no—
240C22×C4—1462no—
241C22×C4C22×D7311yescharacteristic
242C22×C4C22×D7311yescharacteristic
243C22×C4C22×D7311yescharacteristic
244C22×C4C22×D7311yescharacteristic
245C22×C4C22×D7311yescharacteristic
246C22×C4C22×D7311yescharacteristic
247C22×C4C22×D7311yescharacteristic
248C4⋊C4—2921no—
249C4⋊C4—2921no—
250C4⋊C4—1462no—
251C4⋊C4—1462no—
252C4⋊C4—1462no—
253C22⋊C4—2921no—
254C22⋊C4—1462no—
255C22⋊C4—1462no—
256C22⋊C4—1462no—
257C22⋊C4—1462no—
258C22⋊C4—1462no—
259C42—2921no—
260C42—1462no—
261C42—1462no—
262C42—1462no—
263C23—732no—
264C23—1461no—
265C23—1461no—
266C23—1461no—
267C23—1461no—
268C23—1461no—
269C23—1461no—
270C23C23×D7311yescharacteristic
271Q8—2924no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
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—2924no—
294C2×C4—732no—
295C2×C4—732no—
296C2×C4—732no—
297C2×C4—732no—
298C2×C4—1461no—
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—
315C22—2921no—
316C22—2921no—
317C22—2921no—
318C22—2921no—
319C22—1462no—
320C22—1462no—
321C22—1462no—
322C22#41×D7311yescharacteristic
323C22#41×D7311yescharacteristic
324C22#41×D7311yescharacteristic
325C22#41×D7311yescharacteristic
326C22#41×D7311yescharacteristic
327C22#1455663711yescharacteristic
328C22#1455663811yescharacteristic
329C4—41no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—2921no—
337C4—2921no—
338C4—2921no—
339C4—1462no—
340C4—1462no—
341C4—1462no—
342C4—1462no—
343C2—2922no—
344C2#1798912011yescharacteristic
345C2#1798912011yescharacteristic
346C2#1798920311yescharacteristic
347C2#1798926211yescharacteristic
348C2#1798926211yescharacteristic
349C2#1798927311yescharacteristic
350C2#1798930411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#401×C73C2
hypercenter#401D73
hypocenterC73#2527
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #401

Complements

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

NH ≅ G/Ntype
1. #17988528C2semidirect
4. #17988491C2semidirect
5. #17988491C2semidirect
8. #17988474C2semidirect
9. #17988472C2semidirect
10. #17988469C2semidirect
14. #17988432C2semidirect
15. #401×C73C2semidirect
176. C73#2527semidirect
177. #401D73semidirect