Finite Group Databasebeta

← #22620554

Subgroups — #22620554

Order 9344.

362 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#17989197C211yesmaximal, characteristic, complemented
2#17989190C211yesmaximal, characteristic
3#17988988C211yesmaximal, characteristic, complemented
4#17988958C211yesmaximal, characteristic, complemented
5#17988954C211yesmaximal, characteristic, complemented
6#17988950C211yesmaximal, characteristic, complemented
7#17988833C211yesmaximal, characteristic, complemented
8#17988818C211yesmaximal, characteristic, complemented
9#17988814C211yesmaximal, characteristic, complemented
10#17988688C211yesmaximal, characteristic, complemented
11#17988686C211yesmaximal, characteristic, complemented
12#17988678C211yesmaximal, characteristic, complemented
13#17988672C211yesmaximal, characteristic, complemented
14#17988545C211yesmaximal, characteristic, complemented
15#468×C73C211yesmaximal, characteristic, complemented
16C2×#11924017C2211yescharacteristic
17C2×#11924016C2211yescharacteristic
18C2×#11924015C2211yescharacteristic
19C22×#10596831C2211yescharacteristic
20#14556589C2211yescharacteristic
21#14556587C2211yescharacteristic
22#14556584—21no—
23#14556584—21no—
24#14556582—21no—
25#14556582C2211yescharacteristic
26#14556582C2211yescharacteristic
27#14556581—21no—
28#14556575—21no—
29#14556573—21no—
30#14556570C2211yescharacteristic
31#14556565C2211yescharacteristic
32#14556563—21no—
33#14556562—21no—
34Q8×Dic73C2211yescharacteristic
35#14556556C2211yescharacteristic
36D4×Dic73C2211yescharacteristic
37#14556553C2211yescharacteristic
38#14556550C2211yescharacteristic
39#14556525C2211yescharacteristic
40#14556522C2211yescharacteristic
41#14556522C2211yescharacteristic
42#14556516C2211yescharacteristic
43#14556515C2211yescharacteristic
44#14556514C2211yescharacteristic
45#14556513C2211yescharacteristic
46#14556512C2211yescharacteristic
47#14556511C2211yescharacteristic
48#14556501C2211yescharacteristic
49#14556501C2211yescharacteristic
50C8×Dic73C2211yescharacteristic
51C8×Dic73C2211yescharacteristic
52C2×SD16×C73C2211yescharacteristic
53C2×M16×C73C2211yescharacteristic
54C22⋊Q8×C73C2211yescharacteristic
55#121×C73C2211yescharacteristic
56#107×C73C2211yescharacteristic
57#103×C73C2211yescharacteristic
58#102×C73C2211yescharacteristic
59C2×Dic146C2311yescharacteristic
60C2×D292C2311yescharacteristic
61C2×C22⋊D73—21no—
62C2×C22⋊D73—21no—
63C2×C22⋊D73—21no—
64C22×Dic73—21no—
65C2×C4×D73—21no—
66#11924017—22no—
67#11924016—22no—
68#11924015—22no—
69C2×#10596831—22no—
70C2×#10596831C2311yescharacteristic
71C2×#10596831C2311yescharacteristic
72C4⋊Dic73—21no—
73C4⋊Dic73—21no—
74C4⋊Dic73—21no—
75C4⋊Dic73D411yescharacteristic
76C4⋊Dic73D411yescharacteristic
77C4⋊Dic73C2311yescharacteristic
78C4⋊Dic73C2311yescharacteristic
79#11924007—21no—
80#11924007—21no—
81#11924007—21no—
82#11924007—21no—
83#11924007—21no—
84#11924007—21no—
85C22⋊Dic73—21no—
86C22⋊Dic73—21no—
87C22⋊Dic73D411yescharacteristic
88C22⋊Dic73D411yescharacteristic
89#11924005—21no—
90#11924005—21no—
91C4×Dic73—21no—
92C4×Dic73—21no—
93C4×Dic73C2311yescharacteristic
94C4×Dic73C2311yescharacteristic
95C2×Q8×C73C2311yescharacteristic
96C2×D4×C73—21no—
97C2×D4×C73C2311yescharacteristic
98C22×C4×C73C2311yescharacteristic
99SD16×C73—22no—
100M16×C73—22no—
101C2×C8×C73C2311yescharacteristic
102C2×C8×C73C2311yescharacteristic
103C4⋊C4×C73—21no—
104C4⋊C4×C73C2311yescharacteristic
105C4⋊C4×C73C2311yescharacteristic
106C22⋊C4×C73—21no—
107C22⋊C4×C73—21no—
108C23×C73—21no—
109C23×C73C2×D411yescharacteristic
110C22×D73—21no—
111Q8×C73—21no—
112Q8×C73—21no—
113D4×C73—21no—
114D4×C73—21no—
115D4×C73—81no—
116C2×C4×C73—21no—
117C2×C4×C73—21no—
118C2×C4×C73—21no—
119C2×C4×C73—21no—
120C2×C4×C73—21no—
121C2×C4×C73C2×D411yescharacteristic
122C2×C4×C73C2411yescharacteristic
123C22⋊D73—81no—
124C22⋊D73—81no—
125C22⋊D73—81no—
126C2×Dic73—21no—
127C2×Dic73—21no—
128C2×Dic73—21no—
129C2×Dic73—81no—
130C2×Dic73C2×D411yescharacteristic
131C2×Dic73C2×D411yescharacteristic
132C2×Dic73C2×D411yescharacteristic
133C2×Dic73C2×D411yescharacteristic
134D292—21no—
135D292—21no—
136C4×D73—81no—
137Dic146—21no—
138Dic146—21no—
139C8×C73—21no—
140C8×C73#4112yes—
141#10596831—21no—
142#10596831#4112yes—
143C22×C73—21no—
144C22×C73—21no—
145C22×C73—21no—
146C22×C73—41no—
147C22×C73—41no—
148C22×C73—41no—
149C22×C73C22×D411yescharacteristic
150C2×D73—41no—
151C2×D73—41no—
152C2×D73—41no—
153C4×C73—21no—
154C4×C73—41no—
155C4×C73—41no—
156C4×C73—41no—
157C4×C73C2×#4111yescharacteristic
158C4×C73C2×#4111yescharacteristic
159Dic73—21no—
160Dic73—21no—
161Dic73—21no—
162Dic73—21no—
163Dic73—41no—
164Dic73—41no—
165Dic73—41no—
166C2×C73—41no—
167C2×C73—81no—
168C2×C73#53211yescharacteristic
169C2×C73#57711yescharacteristic
170C2×C73#57711yescharacteristic
171D73—81no—
172#3174—731nomaximal, Sylow
173C73#317411yescharacteristic, complemented, Sylow
174#541—731no—
175#540—731no—
176#499—731no—
177#492—731no—
178#491—731no—
179#490—731no—
180#468—731no—
181#468D7311yescharacteristic, complemented
182#465—731no—
183#465—731no—
184#440—731no—
185#440—731no—
186C4×SD16—731no—
187C4×SD16—731no—
188#405—731no—
189C2×SD16—731no—
190C2×SD16—731no—
191C2×SD16—731no—
192C2×SD16C2×D7311yescharacteristic
193C2×M16C2×D7311yescharacteristic
194C22×C8—731no—
195C4⋊Q8—731no—
196#127—731no—
197#126—1461no—
198#126—1461no—
199#125—731no—
200#125—731no—
201#125—1461no—
202#125—1461no—
203#123—1461no—
204#123—1461no—
205C22⋊Q8—731no—
206C22⋊Q8C2×D7311yescharacteristic
207#121—731no—
208#121—1461no—
209#121—1461no—
210#121C2×D7311yescharacteristic
211C4×Q8—731no—
212C4×Q8—731no—
213C4×D4—731no—
214C4×D4—731no—
215#117—731no—
216#107—731no—
217#107C2×D7311yescharacteristic
218#106—731no—
219#106—731no—
220#103—731no—
221#103—731no—
222#103—731no—
223#103C2×D7311yescharacteristic
224#102—731no—
225#102—731no—
226#102—731no—
227#102C2×D7311yescharacteristic
228#97—731no—
229#97—731no—
230C4×C8—731no—
231C4×C8—731no—
232C2×Q8—731no—
233C2×Q8C22×D7311yescharacteristic
234C2×D4—21no—
235C2×D4—731no—
236C2×D4—1461no—
237C2×D4—1461no—
238C2×D4—1461no—
239C2×D4C22×D7311yescharacteristic
240C22×C4—1461no—
241C22×C4—1461no—
242C22×C4C22×D7311yescharacteristic
243SD16—22no—
244SD16—1462no—
245SD16—1462no—
246SD16—1462no—
247M16—22no—
248C2×C8—731no—
249C2×C8—731no—
250C2×C8—1462no—
251C2×C8C22×D7311yescharacteristic
252C2×C8C22×D7311yescharacteristic
253C4⋊C4—21no—
254C4⋊C4—731no—
255C4⋊C4—731no—
256C4⋊C4—731no—
257C4⋊C4—731no—
258C4⋊C4—1461no—
259C4⋊C4—1461no—
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
269C22⋊C4—21no—
270C22⋊C4—21no—
271C22⋊C4—731no—
272C22⋊C4—731no—
273C22⋊C4—1461no—
274C22⋊C4—1461no—
275C22⋊C4—1461no—
276C22⋊C4—1461no—
277C42—731no—
278C42—731no—
279C42—1461no—
280C42—1461no—
281C23—21no—
282C23—1461no—
283C23D4×D7311yescharacteristic
284Q8—21no—
285Q8—21no—
286Q8—1461no—
287Q8—1461no—
288D4—21no—
289D4—21no—
290D4—81no—
291D4—5841no—
292D4—5841no—
293D4—5841no—
294D4—1461no—
295D4—1461no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—5841no—
302C2×C4—5841no—
303C2×C4—731no—
304C2×C4—731no—
305C2×C4—731no—
306C2×C4—731no—
307C2×C4—1461no—
308C2×C4—1461no—
309C2×C4—1461no—
310C2×C4D4×D7311yescharacteristic
311C2×C4C23×D7311yescharacteristic
312C8—21no—
313C8—732no—
314C8—1461no—
315C8#1192402712yes—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—41no—
320C22—41no—
321C22—41no—
322C22—2921no—
323C22—2921no—
324C22—2921no—
325C22C2×D4×D7311yescharacteristic
326C4—21no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—2921no—
331C4—2921no—
332C4—2921no—
333C4—1461no—
334C4—1461no—
335C4—1461no—
336C4—1461no—
337C4#41×D7311yescharacteristic
338C4C2×#1192402711yescharacteristic
339C2—41no—
340C2—81no—
341C2—5841no—
342C2#1798913211yescharacteristic
343C2#1798939611yescharacteristic
344C2#1798939711yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#468×C73C2
socleC22×C73C22×D4
hypercenter#468D73
hypocenterC73#3174
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. #17989197C2semidirect
3. #17988988C2semidirect
4. #17988958C2semidirect
5. #17988954C2semidirect
6. #17988950C2semidirect
7. #17988833C2semidirect
8. #17988818C2semidirect
9. #17988814C2semidirect
10. #17988688C2semidirect
11. #17988686C2semidirect
12. #17988678C2semidirect
13. #17988672C2semidirect
14. #17988545C2semidirect
15. #468×C73C2semidirect
173. C73#3174semidirect
181. #468D73semidirect