Finite Group Databasebeta

← #22620532

Subgroups — #22620532

Order 9344.

364 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989139C211yesmaximal, characteristic, complemented
2#17989123C211yesmaximal, characteristic
3#17988994C211yesmaximal, characteristic, complemented
4#17988980C211yesmaximal, characteristic, complemented
5#17988954C211yesmaximal, characteristic, complemented
6#17988948C211yesmaximal, characteristic, complemented
7#17988843C211yesmaximal, characteristic, complemented
8#17988835C211yesmaximal, characteristic
9#17988833C211yesmaximal, characteristic
10Q16×Dic73C211yesmaximal, characteristic, complemented
11#17988679C211yesmaximal, characteristic, complemented
12#17988674C211yesmaximal, characteristic, complemented
13#17988672C211yesmaximal, characteristic, complemented
14M16×Dic73C211yesmaximal, characteristic, complemented
15#470×C73C211yesmaximal, characteristic, complemented
16C2×#11924018C2211yescharacteristic
17C2×#11924017C2211yescharacteristic
18C2×#11924015C2211yescharacteristic
19C2×#11924012C2211yescharacteristic
20#14556590C2211yescharacteristic
21#14556589C2211yescharacteristic
22#14556586—21no—
23#14556582C2211yescharacteristic
24#14556581—21no—
25#14556580C2211yescharacteristic
26#14556575—21no—
27#14556570C2211yescharacteristic
28#14556568—21no—
29#14556565C2211yescharacteristic
30Q8×Dic73C2211yescharacteristic
31Q8×Dic73C2211yescharacteristic
32#14556556—21no—
33#14556556C2211yescharacteristic
34#14556553C2211yescharacteristic
35#14556551—21no—
36#14556549—21no—
37#14556547—21no—
38C2×C4×Dic73C2211yescharacteristic
39#14556525C2211yescharacteristic
40#14556524C2211yescharacteristic
41#14556522C2211yescharacteristic
42#14556516C2211yescharacteristic
43#14556515C2211yescharacteristic
44#14556515C2211yescharacteristic
45#14556514C2211yescharacteristic
46#14556513C2211yescharacteristic
47#14556511C2211yescharacteristic
48#14556501C2211yescharacteristic
49#14556501C2211yescharacteristic
50C8×Dic73C2211yescharacteristic
51C8×Dic73C2211yescharacteristic
52C2×Q16×C73C2211yescharacteristic
53C2×M16×C73C2211yescharacteristic
54C22⋊Q8×C73C2211yescharacteristic
55C22⋊Q8×C73C2211yescharacteristic
56#106×C73C2211yescharacteristic
57#103×C73C2211yescharacteristic
58#103×C73C2211yescharacteristic
59C2×Dic146—21no—
60C2×Dic146C2311yescharacteristic
61C2×D292C2311yescharacteristic
62C2×C22⋊D73—21no—
63C22×Dic73D411yescharacteristic
64C22×Dic73D411yescharacteristic
65C2×C4×D73—21no—
66#11924018—22no—
67#11924017—22no—
68#11924015—22no—
69#11924012—22no—
70C2×#10596831C2311yescharacteristic
71C2×#10596831C2311yescharacteristic
72C4⋊Dic73—21no—
73C4⋊Dic73—21no—
74C4⋊Dic73—21no—
75C4⋊Dic73C2311yescharacteristic
76C4⋊Dic73C2311yescharacteristic
77#11924007—21no—
78#11924007—21no—
79#11924007—21no—
80#11924007—21no—
81#11924007—21no—
82#11924007—21no—
83C22⋊Dic73—21no—
84#11924005—21no—
85#11924005—21no—
86#11924005—21no—
87#11924005—21no—
88C4×Dic73—21no—
89C4×Dic73—21no—
90C4×Dic73—21no—
91C4×Dic73D411yescharacteristic
92C4×Dic73D411yescharacteristic
93C4×Dic73C2311yescharacteristic
94C4×Dic73C2311yescharacteristic
95C2×Q8×C73C2311yescharacteristic
96C2×Q8×C73C2311yescharacteristic
97C22×C4×C73C2311yescharacteristic
98Q16×C73—22no—
99M16×C73—22no—
100C2×C8×C73C2311yescharacteristic
101C2×C8×C73C2311yescharacteristic
102C4⋊C4×C73—21no—
103C4⋊C4×C73—21no—
104C4⋊C4×C73C2311yescharacteristic
105C4⋊C4×C73C2311yescharacteristic
106C22⋊C4×C73—21no—
107C22⋊C4×C73—21no—
108C23×C73C2×D411yescharacteristic
109C22×D73—21no—
110Q8×C73—21no—
111Q8×C73—21no—
112Q8×C73—21no—
113Q8×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×D411yescharacteristic
121C2×C4×C73C2411yescharacteristic
122C22⋊D73—42no—
123C2×Dic73—22no—
124C2×Dic73—21no—
125C2×Dic73—21no—
126C2×Dic73—21no—
127C2×Dic73—41no—
128C2×Dic73C2×D411yescharacteristic
129C2×Dic73C2×D411yescharacteristic
130C2×Dic73C2×D411yescharacteristic
131C2×Dic73C2×D411yescharacteristic
132D292—21no—
133D292—21no—
134C4×D73—42no—
135Dic146—21no—
136Dic146—21no—
137Dic146—42no—
138C8×C73—21no—
139C8×C73#4112yes—
140#10596831—21no—
141#10596831#4112yes—
142C22×C73—21no—
143C22×C73—21no—
144C22×C73—21no—
145C22×C73C22×D411yescharacteristic
146C2×D73—41no—
147C2×D73—41no—
148C2×D73—41no—
149C4×C73—21no—
150C4×C73—41no—
151C4×C73—41no—
152C4×C73—41no—
153C4×C73—41no—
154C4×C73C2×#4111yescharacteristic
155C4×C73C2×#4111yescharacteristic
156Dic73—21no—
157Dic73—21no—
158Dic73—21no—
159Dic73—41no—
160Dic73—41no—
161Dic73—41no—
162Dic73#13712yes—
163C2×C73—41no—
164C2×C73#53211yescharacteristic
165C2×C73C2×#13711yescharacteristic
166C2×C73#57511yescharacteristic
167D73—81no—
168#3172—731nomaximal, Sylow
169C73#317211yescharacteristic, complemented, Sylow
170#533—731no—
171#529—731no—
172#501—731no—
173#497—731no—
174#491—731no—
175#489—731no—
176#470—731no—
177#470D7311yescharacteristic, complemented
178#468—731no—
179#468—731no—
180C4×Q16—731no—
181C4×Q16—731no—
182C4×SD16—731no—
183C4×SD16—731no—
184C4×M16—731no—
185C2×Q16—731no—
186C2×Q16C2×D7311yescharacteristic
187C2×SD16—731no—
188C2×SD16—731no—
189C2×M16—731no—
190C2×M16C2×D7311yescharacteristic
191C4⋊Q8—731no—
192C4⋊Q8—731no—
193#126—1461no—
194#125—731no—
195#125—1461no—
196#124—731no—
197#123—1461no—
198C22⋊Q8—731no—
199C22⋊Q8—1461no—
200C22⋊Q8C2×D7311yescharacteristic
201C22⋊Q8C2×D7311yescharacteristic
202#121—731no—
203C4×Q8—731no—
204C4×Q8—731no—
205C4×Q8—731no—
206C4×Q8—1461no—
207C4×D4—731no—
208C4×D4—1461no—
209#117—1461no—
210#117—1461no—
211C2×C42—731no—
212#107—731no—
213#107—731no—
214#106—731no—
215#106C2×D7311yescharacteristic
216#103—731no—
217#103—731no—
218#103—731no—
219#103—731no—
220#103C2×D7311yescharacteristic
221#103C2×D7311yescharacteristic
222#102—731no—
223#102—731no—
224#97—731no—
225#97—731no—
226C4×C8—731no—
227C4×C8—731no—
228C2×Q8—731no—
229C2×Q8—1461no—
230C2×Q8C22×D7311yescharacteristic
231C2×Q8C22×D7311yescharacteristic
232C2×D4—731no—
233C2×D4—1461no—
234C22×C4—731no—
235C22×C4—731no—
236C22×C4—1461no—
237C22×C4C22×D7311yescharacteristic
238Q16—22no—
239Q16—1462no—
240SD16—1462no—
241SD16—1462no—
242M16—22no—
243M16—1462no—
244C2×C8—731no—
245C2×C8—731no—
246C2×C8C22×D7311yescharacteristic
247C2×C8C22×D7311yescharacteristic
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—731no—
251C4⋊C4—731no—
252C4⋊C4—1461no—
253C4⋊C4—1461no—
254C4⋊C4—1461no—
255C4⋊C4—1461no—
256C4⋊C4—1461no—
257C4⋊C4—1461no—
258C4⋊C4—1461no—
259C4⋊C4—1461no—
260C4⋊C4—1461no—
261C4⋊C4C22×D7311yescharacteristic
262C4⋊C4C22×D7311yescharacteristic
263C22⋊C4—21no—
264C22⋊C4—21no—
265C22⋊C4—1461no—
266C22⋊C4—1461no—
267C22⋊C4—1461no—
268C22⋊C4—1461no—
269C22⋊C4—1461no—
270C42—731no—
271C42—731no—
272C42—731no—
273C42—731no—
274C42—1461no—
275C42—1461no—
276C42—1461no—
277C23—1461no—
278C23D4×D7311yescharacteristic
279Q8—21no—
280Q8—21no—
281Q8—21no—
282Q8—21no—
283Q8—2922no—
284Q8—1461no—
285Q8—1461no—
286D4—2922no—
287D4—1461no—
288D4—1461no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—2922no—
296C2×C4—2921no—
297C2×C4—731no—
298C2×C4—731no—
299C2×C4—731no—
300C2×C4—731no—
301C2×C4—1461no—
302C2×C4—1461no—
303C2×C4—1461no—
304C2×C4—1462no—
305C2×C4D4×D7311yescharacteristic
306C2×C4C23×D7311yescharacteristic
307C8—21no—
308C8—732no—
309C8—1461no—
310C8#1192402712yes—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—2921no—
315C22—2921no—
316C22—2921no—
317C22C2×D4×D7311yescharacteristic
318C4—21no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4—41no—
323C4—2921no—
324C4—2921no—
325C4—2921no—
326C4—732no—
327C4—1461no—
328C4—1461no—
329C4—1461no—
330C4#41×D7311yescharacteristic
331C4C2×#1192402711yescharacteristic
332C2—41no—
333C2—5841no—
334C2#1798913211yescharacteristic
335C2#137×D7311yescharacteristic
336C2#1798938611yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#470×C73C2
socleC22×C73C22×D4
hypercenter#470D73
hypocenterC73#3172
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
1. #17989139C2semidirect
3. #17988994C2semidirect
4. #17988980C2semidirect
5. #17988954C2semidirect
6. #17988948C2semidirect
7. #17988843C2semidirect
10. Q16×Dic73C2semidirect
11. #17988679C2semidirect
12. #17988674C2semidirect
13. #17988672C2semidirect
14. M16×Dic73C2semidirect
15. #470×C73C2semidirect
169. C73#3172semidirect
177. #470D73semidirect