Finite Group Databasebeta

← #22622281

Subgroups — #22622281

Order 9344.

388 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989295C211yesmaximal, characteristic, complemented
2#17989238C211yesmaximal, characteristic
3#17988984C211yesmaximal, characteristic, complemented
4#17988916C211yesmaximal, characteristic, complemented
5#17988907C211yesmaximal, characteristic, complemented
6#17988906C211yesmaximal, characteristic, complemented
7#17988876C211yesmaximal, characteristic, complemented
8#17988870C211yesmaximal, characteristic, complemented
9#17988819C211yesmaximal, characteristic, complemented
10#17988818C211yesmaximal, characteristic, complemented
11#17988672C211yesmaximal, characteristic, complemented
12#17988650C211yesmaximal, characteristic, complemented
13C2×#14556522C211yesmaximal, characteristic, complemented
14#106×D73C211yesmaximal, characteristic, complemented
15#483×C73C211yesmaximal, characteristic, complemented
16C2×#11924028—21no—
17C2×#11924015C2211yescharacteristic
18C22×#10596831C2211yescharacteristic
19C2×C8×D73C2211yescharacteristic
20#14556590C2211yescharacteristic
21#14556590C2211yescharacteristic
22#14556581—21no—
23#14556576—21no—
24#14556574—21no—
25#14556571—21no—
26#14556569—21no—
27#14556568—21no—
28#14556567C2211yescharacteristic
29#14556566C2211yescharacteristic
30#14556565C2211yescharacteristic
31Q8×Dic73C2211yescharacteristic
32#14556553C2211yescharacteristic
33C4×C22⋊D73C2211yescharacteristic
34#14556551—21no—
35C2×C4⋊Dic73C2211yescharacteristic
36C4⋊C4×D73C2211yescharacteristic
37C4⋊C4×D73C2211yescharacteristic
38#14556523C2211yescharacteristic
39#14556523C2211yescharacteristic
40#14556522C2211yescharacteristic
41#14556522C2211yescharacteristic
42#14556522C2211yescharacteristic
43#14556522C2211yescharacteristic
44#14556522C2211yescharacteristic
45#14556520C2211yescharacteristic
46#14556515C2211yescharacteristic
47#14556513C2211yescharacteristic
48#14556513C2211yescharacteristic
49#14556511C2211yescharacteristic
50#14556503C2211yescharacteristic
51C8×Dic73C2211yescharacteristic
52C22⋊Q8×C73C2211yescharacteristic
53C2×C4⋊C4×C73C2211yescharacteristic
54#106×C73C2211yescharacteristic
55#106×C73C2211yescharacteristic
56#103×C73C2211yescharacteristic
57#103×C73C2211yescharacteristic
58C22⋊C8×C73C2211yescharacteristic
59#11924028—44no—
60C2×Dic146—21no—
61C2×Dic146—21no—
62C2×D292—21no—
63C2×D292C2311yescharacteristic
64C2×C22⋊D73—21no—
65C2×C22⋊D73D411yescharacteristic
66C22×Dic73—21no—
67C2×C4×D73—21no—
68C2×C4×D73—21no—
69C2×C4×D73—21no—
70C2×C4×D73C2311yescharacteristic
71#11924015—22no—
72C2×#10596831—22no—
73C2×#10596831C2311yescharacteristic
74C2×#10596831C2311yescharacteristic
75C8×D73—22no—
76C4⋊Dic73—21no—
77C4⋊Dic73—21no—
78C4⋊Dic73C2311yescharacteristic
79C4⋊Dic73C2311yescharacteristic
80C4⋊Dic73C2311yescharacteristic
81#11924007—21no—
82#11924007—21no—
83#11924007—21no—
84#11924007—21no—
85#11924007—21no—
86#11924007D411yescharacteristic
87C22⋊Dic73D411yescharacteristic
88#11924005—21no—
89#11924005—21no—
90#11924005—21no—
91#11924005—21no—
92#11924005D411yescharacteristic
93C4×Dic73—21no—
94C4×Dic73C2311yescharacteristic
95C2×Q8×C73C2311yescharacteristic
96C22×C4×C73—21no—
97C22×C4×C73C2311yescharacteristic
98C2×C8×C73C2311yescharacteristic
99C2×C8×C73C2311yescharacteristic
100C4⋊C4×C73—21no—
101C4⋊C4×C73—21no—
102C4⋊C4×C73C2311yescharacteristic
103C4⋊C4×C73C2311yescharacteristic
104C4⋊C4×C73C2311yescharacteristic
105C22⋊C4×C73—21no—
106C23×C73C2×D411yescharacteristic
107C22×D73—21no—
108C22×D73C2×D411yescharacteristic
109Q8×C73—21no—
110Q8×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—42no—
118C2×C4×C73C2×D411yescharacteristic
119C2×C4×C73C2411yescharacteristic
120C22⋊D73—42no—
121C22⋊D73SD1614yescomplemented
122C2×Dic73—21no—
123C2×Dic73—21no—
124C2×Dic73—21no—
125C2×Dic73—81no—
126C2×Dic73C2×D411yescharacteristic
127C2×Dic73C2×D411yescharacteristic
128C2×Dic73C2×D411yescharacteristic
129D292—21no—
130D292—21no—
131D292—42no—
132C4×D73—21no—
133C4×D73—21no—
134C4×D73—42no—
135C4×D73—42no—
136C4×D73—81no—
137Dic146—42no—
138Dic146—81no—
139C8×C73—21no—
140C8×C73—21no—
141#10596831—21no—
142#10596831#4112yescomplemented
143C22×C73—21no—
144C22×C73—21no—
145C22×C73C2×SD1612yes—
146C22×C73C22×D411yescharacteristic
147C2×D73—21no—
148C2×D73—21no—
149C2×D73—41no—
150C2×D73—41no—
151C2×D73—41no—
152C2×D73C2×SD1612yes—
153C4×C73—21no—
154C4×C73—41no—
155C4×C73—41no—
156C4×C73—41no—
157C4×C73—41no—
158C4×C73C2×#4111yescharacteristic
159C4×C732−1+411yescharacteristic
160Dic73—21no—
161Dic73—21no—
162Dic73—41no—
163Dic73—41no—
164Dic73—41no—
165Dic73C2×SD1612yes—
166C2×C73—22no—
167C2×C73#54711yescharacteristic
168C2×C73C22×SD1611yescharacteristic
169C2×C73#57711yescharacteristic
170D73—22no—
171D73—81no—
172#3335—731nomaximal, Sylow
173C73#333511yescharacteristic, complemented, Sylow
174#554—731no—
175#547—731no—
176#498—731no—
177#483—731no—
178#483D7311yescharacteristic, complemented
179#481—731no—
180#481—731no—
181#476—731no—
182#475—731no—
183#465—731no—
184#465—731no—
185C4×SD16—731no—
186C8×D4—731no—
187C2×#106—731no—
188C2×#106—731no—
189C2×#41—1461no—
190C2×SD16—731no—
191C22×C8—731no—
192C22×C8—731no—
193C4⋊Q8—731no—
194C4⋊Q8—731no—
195#125—1461no—
196#123—1461no—
197#123—1461no—
198C22⋊Q8—731no—
199C22⋊Q8—1461no—
200C22⋊Q8—1461no—
201C22⋊Q8—1461no—
202C22⋊Q8C2×D7311yescharacteristic
203#121—731no—
204#121—731no—
205C4×Q8—731no—
206C4×D4—731no—
207C4×D4—731no—
208C4×D4—1461no—
209C2×C4⋊C4—731no—
210C2×C4⋊C4—731no—
211C2×C4⋊C4—731no—
212C2×C4⋊C4C2×D7311yescharacteristic
213#106—731no—
214#106—731no—
215#106—731no—
216#106—731no—
217#106—731no—
218#106—731no—
219#106—731no—
220#106C2×D7311yescharacteristic
221#106C2×D7311yescharacteristic
222C4⋊C8—731no—
223#103—731no—
224#103C2×D7311yescharacteristic
225#103C2×D7311yescharacteristic
226#102—731no—
227#102—731no—
228#102—731no—
229C22⋊C8—731no—
230C22⋊C8C2×D7311yescharacteristic
231C4×C8—731no—
232#41—2924no—
233C2×Q8—1461no—
234C2×Q8—1461no—
235C2×Q8C22×D7311yescharacteristic
236C2×D4—731no—
237C2×D4—731no—
238C2×D4—1461no—
239C2×D4—1461no—
240C22×C4—21no—
241C22×C4—731no—
242C22×C4—1461no—
243C22×C4—1461no—
244C22×C4—1461no—
245C22×C4—1461no—
246C22×C4C22×D7311yescharacteristic
247SD16—1462no—
248C2×C8—731no—
249C2×C8—731no—
250C2×C8—1462no—
251C2×C8—1462no—
252C2×C8C22×D7311yescharacteristic
253C2×C8C22×D7311yescharacteristic
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—731no—
257C4⋊C4—731no—
258C4⋊C4—731no—
259C4⋊C4—731no—
260C4⋊C4—1461no—
261C4⋊C4—1461no—
262C4⋊C4—1461no—
263C4⋊C4—1461no—
264C4⋊C4—1461no—
265C4⋊C4—1461no—
266C4⋊C4—1461no—
267C4⋊C4C22×D7311yescharacteristic
268C4⋊C4C22×D7311yescharacteristic
269C4⋊C4C22×D7311yescharacteristic
270C22⋊C4—21no—
271C22⋊C4—731no—
272C22⋊C4—731no—
273C22⋊C4—1461no—
274C22⋊C4—1461no—
275C22⋊C4—1461no—
276C22⋊C4—1461no—
277C42—731no—
278C42—1461no—
279C23—731no—
280C23—1461no—
281C23D4×D7311yescharacteristic
282Q8—21no—
283Q8—21no—
284Q8—2922no—
285Q8—5841no—
286D4—2922no—
287D4—2922no—
288D4—734no—
289D4—1461no—
290D4—1461no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—42no—
298C2×C4—2922no—
299C2×C4—2922no—
300C2×C4—5841no—
301C2×C4—5841no—
302C2×C4—731no—
303C2×C4—731no—
304C2×C4—731no—
305C2×C4—1461no—
306C2×C4—1461no—
307C2×C4—1461no—
308C2×C4—1461no—
309C2×C4—1461no—
310C2×C4D4×D7311yescharacteristic
311C2×C4C23×D7311yescharacteristic
312C8—21no—
313C8—21no—
314C8—732no—
315C8—1461no—
316C22—21no—
317C22—21no—
318C22—2921no—
319C22—2921no—
320C22—2921no—
321C22—732no—
322C22—1461no—
323C22—1461no—
324C22SD16×D7312yes—
325C22C2×D4×D7311yescharacteristic
326C4—21no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—2921no—
332C4—2921no—
333C4—2921no—
334C4—732no—
335C4—1461no—
336C4—1461no—
337C4#41×D7311yescharacteristic
338C4#1455663811yescharacteristic
339C2—22no—
340C2—5841no—
341C2—1462no—
342C2#1798923511yescharacteristic
343C2C2×SD16×D7311yescharacteristic
344C2#1798939611yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#483×C73C2
socleC22×C73C22×D4
hypercenter#483D73
hypocenterC73#3335
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
1. #17989295C2semidirect
3. #17988984C2semidirect
4. #17988916C2semidirect
5. #17988907C2semidirect
6. #17988906C2semidirect
7. #17988876C2semidirect
8. #17988870C2semidirect
9. #17988819C2semidirect
10. #17988818C2semidirect
11. #17988672C2semidirect
12. #17988650C2semidirect
13. C2×#14556522C2semidirect
14. #106×D73C2semidirect
15. #483×C73C2semidirect
121. C22⋊D73SD16semidirect
142. #10596831#41semidirect
173. C73#3335semidirect
178. #483D73semidirect