Finite Group Databasebeta

← #22622661

Subgroups — #22622661

Order 9344.

382 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989313C211yesmaximal, characteristic, complemented
2#17989258C211yesmaximal, characteristic
3#17988952C211yesmaximal, characteristic, complemented
4#17988950C211yesmaximal, characteristic, complemented
5#17988932C211yesmaximal, characteristic, complemented
6#17988890C211yesmaximal, characteristic, complemented
7#17988887C211yesmaximal, characteristic, complemented
8#17988866C211yesmaximal, characteristic, complemented
9#17988787C211yesmaximal, characteristic, complemented
10#17988785C211yesmaximal, characteristic, complemented
11#17988785C211yesmaximal, characteristic, complemented
12#17988715C211yesmaximal, characteristic, complemented
13#17988690C211yesmaximal, characteristic, complemented
14#17988672C211yesmaximal, characteristic, complemented
15#440×C73C211yesmaximal, characteristic, complemented
16C2×#11924028—21no—
17C2×#11924015C2211yescharacteristic
18C2×#11924015C2211yescharacteristic
19#14556590—21no—
20#14556590C2211yescharacteristic
21#14556588C2211yescharacteristic
22#14556587C2211yescharacteristic
23#14556587C2211yescharacteristic
24#14556583—21no—
25#14556583C2211yescharacteristic
26#14556582—21no—
27#14556582C2211yescharacteristic
28#14556565—21no—
29#14556564—21no—
30#14556564—21no—
31Q8×Dic73C2211yescharacteristic
32Q8×Dic73C2211yescharacteristic
33C4×Dic146—21no—
34C4×Dic146C2211yescharacteristic
35#14556553C2211yescharacteristic
36#14556553C2211yescharacteristic
37#14556524C2211yescharacteristic
38#14556522C2211yescharacteristic
39C4⋊#10596831C2211yescharacteristic
40#14556520C2211yescharacteristic
41#14556520C2211yescharacteristic
42#14556513C2211yescharacteristic
43#14556513C2211yescharacteristic
44#14556513C2211yescharacteristic
45#14556513C2211yescharacteristic
46#14556512C2211yescharacteristic
47#14556512C2211yescharacteristic
48#14556511C2211yescharacteristic
49#14556511C2211yescharacteristic
50#14556501C2211yescharacteristic
51C8×Dic73C2211yescharacteristic
52C2×SD16×C73C2211yescharacteristic
53C4×Q8×C73C2211yescharacteristic
54C4×D4×C73C2211yescharacteristic
55#107×C73C2211yescharacteristic
56#103×C73C2211yescharacteristic
57#102×C73C2211yescharacteristic
58#97×C73C2211yescharacteristic
59#11924028—44no—
60C2×Dic146—21no—
61C2×Dic146D411yescharacteristic
62C2×D292—21no—
63C2×D292—21no—
64C2×D292C2311yescharacteristic
65C2×D292C2311yescharacteristic
66C2×C22⋊D73—21no—
67C2×C22⋊D73—21no—
68C2×C22⋊D73—21no—
69C2×C22⋊D73—21no—
70C2×C4×D73—21no—
71C2×C4×D73—21no—
72#11924015—22no—
73#11924015—22no—
74C2×#10596831C2311yescharacteristic
75C2×#10596831C2311yescharacteristic
76C4⋊Dic73—21no—
77C4⋊Dic73—21no—
78C4⋊Dic73—21no—
79C4⋊Dic73D411yescharacteristic
80C4⋊Dic73C2311yescharacteristic
81C4⋊Dic73C2311yescharacteristic
82#11924007—21no—
83#11924007—21no—
84#11924007—21no—
85#11924007—21no—
86#11924007D411yescharacteristic
87#11924007D411yescharacteristic
88#11924005—21no—
89#11924005—21no—
90C4×Dic73—21no—
91C4×Dic73—21no—
92C4×Dic73C2311yescharacteristic
93C4×Dic73C2311yescharacteristic
94C2×Q8×C73C2311yescharacteristic
95C2×D4×C73C2311yescharacteristic
96C22×C4×C73—21no—
97SD16×C73—22no—
98C2×C8×C73C2311yescharacteristic
99C2×C8×C73C2311yescharacteristic
100C4⋊C4×C73—21no—
101C4⋊C4×C73C2311yescharacteristic
102C4⋊C4×C73C2311yescharacteristic
103C22⋊C4×C73—21no—
104C42×C73—21no—
105C42×C73C2311yescharacteristic
106C23×C73—21no—
107C22×D73—21no—
108C22×D73—21no—
109Q8×C73—21no—
110Q8×C73#4112yescomplemented
111D4×C73—21no—
112D4×C73—21no—
113C2×C4×C73—21no—
114C2×C4×C73—21no—
115C2×C4×C73—21no—
116C2×C4×C73—42no—
117C2×C4×C73C2×D411yescharacteristic
118C2×C4×C73C2×D411yescharacteristic
119C2×C4×C73C2411yescharacteristic
120C22⋊D73—42no—
121C22⋊D73—42no—
122C22⋊D73—81no—
123C22⋊D73—81no—
124C2×Dic73—21no—
125C2×Dic73—21no—
126C2×Dic73C2×D411yescharacteristic
127C2×Dic73C2×D411yescharacteristic
128C2×Dic73C2×D411yescharacteristic
129C2×Dic73C2×D411yescharacteristic
130D292—21no—
131D292—21no—
132D292—21no—
133D292—21no—
134D292—42no—
135D292—81no—
136C4×D73—42no—
137C4×D73—42no—
138Dic146—22no—
139Dic146—42no—
140C8×C73—21no—
141C8×C73—21no—
142#10596831—21no—
143#10596831—21no—
144C22×C73—41no—
145C22×C73—41no—
146C22×C73—41no—
147C22×C73C22×D411yescharacteristic
148C2×D73—41no—
149C2×D73—41no—
150C2×D73—41no—
151C2×D73—41no—
152C2×D73—41no—
153C2×D73—41no—
154C4×C73—22no—
155C4×C73—21no—
156C4×C73—21no—
157C4×C73—41no—
158C4×C73—41no—
159C4×C73C2×#4111yescharacteristic
160C4×C732−1+411yescharacteristic
161Dic73—21no—
162Dic73—21no—
163Dic73—21no—
164Dic73—41no—
165Dic73—41no—
166Dic73AGL(1,ℤ/8)12yes—
167C2×C73—81no—
168C2×C73#54811yescharacteristic
169C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
170C2×C73#57711yescharacteristic
171D73—81no—
172D73—81no—
173#3368—731nomaximal, Sylow
174C73#336811yescharacteristic, complemented, Sylow
175#557—731no—
176#550—731no—
177#490—731no—
178#490—731no—
179#486—731no—
180#478—731no—
181#478—731no—
182#474—731no—
183#460—731no—
184#460—731no—
185#460—731no—
186#446—731no—
187#440—731no—
188#440D7311yescharacteristic, complemented
189C4×SD16—731no—
190C2×#41—1461no—
191C2×SD16—731no—
192C2×SD16—731no—
193C2×SD16C2×D7311yescharacteristic
194C4⋊Q8—731no—
195C4⋊Q8—1461no—
196#127—731no—
197#127—731no—
198#127—731no—
199#125—731no—
200#125—731no—
201#125—1461no—
202#125—1461no—
203#121—1461no—
204#121—1461no—
205#121—1461no—
206C4×Q8—731no—
207C4×Q8—731no—
208C4×Q8—731no—
209C4×Q8—1461no—
210C4×Q8C2×D7311yescharacteristic
211C4×D4—731no—
212C4×D4—731no—
213C4×D4C2×D7311yescharacteristic
214#107—731no—
215#107C2×D7311yescharacteristic
216#106—731no—
217C4⋊C8—731no—
218C4⋊C8—731no—
219C4⋊C8—731no—
220#103C2×D7311yescharacteristic
221#102—731no—
222#102—731no—
223#102—731no—
224#102—731no—
225#102—731no—
226#102—731no—
227#102—731no—
228#102—731no—
229#102C2×D7311yescharacteristic
230#97—731no—
231#97C2×D7311yescharacteristic
232C4×C8—731no—
233#41—2924no—
234C2×Q8—731no—
235C2×Q8—1461no—
236C2×Q8C22×D7311yescharacteristic
237C2×D4—731no—
238C2×D4—731no—
239C2×D4—1461no—
240C2×D4—1461no—
241C2×D4—1461no—
242C2×D4—1461no—
243C2×D4—1461no—
244C2×D4—1461no—
245C2×D4C22×D7311yescharacteristic
246C22×C4—21no—
247C22×C4—1461no—
248C22×C4—1461no—
249SD16—22no—
250SD16—1462no—
251SD16—1462no—
252C2×C8—731no—
253C2×C8—731no—
254C2×C8C22×D7311yescharacteristic
255C2×C8C22×D7311yescharacteristic
256C4⋊C4—21no—
257C4⋊C4—731no—
258C4⋊C4—731no—
259C4⋊C4—731no—
260C4⋊C4—731no—
261C4⋊C4—731no—
262C4⋊C4—1461no—
263C4⋊C4—1461no—
264C4⋊C4—1461no—
265C4⋊C4—1461no—
266C4⋊C4—1461no—
267C4⋊C4—1461no—
268C4⋊C4—1461no—
269C4⋊C4C22×D7311yescharacteristic
270C4⋊C4C22×D7311yescharacteristic
271C22⋊C4—21no—
272C22⋊C4—1461no—
273C22⋊C4—1461no—
274C42—21no—
275C42—731no—
276C42—731no—
277C42—1461no—
278C42—1461no—
279C42C22×D7311yescharacteristic
280C23—21no—
281C23—1461no—
282C23—1461no—
283Q8—21no—
284Q8—2922no—
285Q8—1462no—
286Q8#1192402812yescomplemented
287D4—21no—
288D4—21no—
289D4—2922no—
290D4—2922no—
291D4—2922no—
292D4—5841no—
293D4—5841no—
294D4—5841no—
295D4—1461no—
296D4—1461no—
297D4—1461no—
298D4—1461no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—42no—
303C2×C4—2922no—
304C2×C4—2922no—
305C2×C4—731no—
306C2×C4—731no—
307C2×C4—731no—
308C2×C4—731no—
309C2×C4—1461no—
310C2×C4—1461no—
311C2×C4D4×D7311yescharacteristic
312C2×C4D4×D7311yescharacteristic
313C2×C4C23×D7311yescharacteristic
314C8—21no—
315C8—21no—
316C8—1461no—
317C8—1461no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—2921no—
322C22—2921no—
323C22—2921no—
324C22—2921no—
325C22—2921no—
326C22—2921no—
327C22C2×D4×D7311yescharacteristic
328C4—21no—
329C4—22no—
330C4—21no—
331C4—41no—
332C4—41no—
333C4—2921no—
334C4—2921no—
335C4—732no—
336C4—1461no—
337C4—1461no—
338C4—1461no—
339C4C2×#1192402811yescharacteristic
340C4#1455663811yescharacteristic
341C2—81no—
342C2—5841no—
343C2—5841no—
344C2#1798924611yescharacteristic
345C2AGL(1,ℤ/8)×D7311yescharacteristic
346C2#1798939611yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#440×C73C2
socleC22×C73C22×D4
hypercenter#440D73
hypocenterC73#3368
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #17989313C2semidirect
3. #17988952C2semidirect
4. #17988950C2semidirect
5. #17988932C2semidirect
6. #17988890C2semidirect
7. #17988887C2semidirect
8. #17988866C2semidirect
9. #17988787C2semidirect
10. #17988785C2semidirect
11. #17988785C2semidirect
12. #17988715C2semidirect
13. #17988690C2semidirect
14. #17988672C2semidirect
15. #440×C73C2semidirect
110. Q8×C73#41semidirect
174. C73#3368semidirect
188. #440D73semidirect
286. Q8#11924028semidirect