Finite Group Databasebeta

← #22620533

Subgroups — #22620533

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#17989141C211yesmaximal, characteristic, complemented
2#17989119C211yesmaximal, characteristic
3#17988994C211yesmaximal, characteristic, complemented
4#17988978C211yesmaximal, characteristic, complemented
5#17988954C211yesmaximal, characteristic, complemented
6#17988945C211yesmaximal, characteristic, complemented
7#17988846C211yesmaximal, characteristic, complemented
8#17988844C211yesmaximal, characteristic, complemented
9#17988832C211yesmaximal, characteristic
10#17988830C211yesmaximal, characteristic
11C4×Dic292C211yesmaximal, characteristic, complemented
12C4×#11924018C211yesmaximal, characteristic, complemented
13C4×#11924016C211yesmaximal, characteristic, complemented
14C4×#11924011C211yesmaximal, characteristic, complemented
15C4×SD16×C73C211yesmaximal, characteristic, complemented
16C2×Dic292C2211yescharacteristic
17C2×#11924018C2211yescharacteristic
18C2×#11924016C2211yescharacteristic
19C2×#11924011C2211yescharacteristic
20C2×#11924011C2211yescharacteristic
21#14556590C2211yescharacteristic
22#14556589C2211yescharacteristic
23#14556584—21no—
24#14556582C2211yescharacteristic
25#14556581—21no—
26#14556578C2211yescharacteristic
27#14556573—21no—
28#14556571C2211yescharacteristic
29#14556571C2211yescharacteristic
30#14556569—21no—
31#14556567C2211yescharacteristic
32#14556562C2211yescharacteristic
33C4×Dic146—21no—
34C4×Dic146C2211yescharacteristic
35C4×Dic146C2211yescharacteristic
36C4×C22⋊D73—21no—
37#14556550—21no—
38#14556548—21no—
39C42×D73C2211yescharacteristic
40#14556525C2211yescharacteristic
41#14556524C2211yescharacteristic
42#14556522C2211yescharacteristic
43#14556516C2211yescharacteristic
44#14556516C2211yescharacteristic
45#14556515C2211yescharacteristic
46#14556514C2211yescharacteristic
47#14556514C2211yescharacteristic
48#14556512C2211yescharacteristic
49#14556501C2211yescharacteristic
50#14556501C2211yescharacteristic
51C4×#10596831C2211yescharacteristic
52C2×SD16×C73C2211yescharacteristic
53C4×Q8×C73C2211yescharacteristic
54C4×D4×C73C2211yescharacteristic
55#106×C73C2211yescharacteristic
56#103×C73C2211yescharacteristic
57#102×C73C2211yescharacteristic
58C4×C8×C73C2211yescharacteristic
59C2×Dic146—21no—
60C2×Dic146C2311yescharacteristic
61C2×Dic146C2311yescharacteristic
62C2×C22⋊D73—21no—
63C2×C4×D73D411yescharacteristic
64C2×C4×D73D411yescharacteristic
65C2×C4×D73C2311yescharacteristic
66Dic292—22no—
67#11924018—22no—
68#11924016—22no—
69#11924011—22no—
70#11924011—22no—
71C2×#10596831C2311yescharacteristic
72C2×#10596831C2311yescharacteristic
73C4⋊Dic73—21no—
74C4⋊Dic73—21no—
75C4⋊Dic73—21no—
76C4⋊Dic73C2311yescharacteristic
77C4⋊Dic73C2311yescharacteristic
78#11924007—21no—
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⋊Dic73—21no—
88#11924005—21no—
89#11924005—21no—
90#11924005—21no—
91C4×Dic73—21no—
92C4×Dic73—21no—
93C4×Dic73D411yescharacteristic
94C4×Dic73D411yescharacteristic
95C4×Dic73C2311yescharacteristic
96C2×Q8×C73C2311yescharacteristic
97C2×D4×C73C2311yescharacteristic
98C22×C4×C73—21no—
99SD16×C73—22no—
100C2×C8×C73C2311yescharacteristic
101C2×C8×C73C2311yescharacteristic
102C4⋊C4×C73—21no—
103C4⋊C4×C73C2311yescharacteristic
104C4⋊C4×C73C2311yescharacteristic
105C22⋊C4×C73—21no—
106C42×C73—21no—
107C42×C73C2311yescharacteristic
108C23×C73—21no—
109C22×D73C2×D411yescharacteristic
110Q8×C73—21no—
111Q8×C73—21no—
112D4×C73—21no—
113D4×C73—21no—
114C2×C4×C73—21no—
115C2×C4×C73—21no—
116C2×C4×C73—21no—
117C2×C4×C73—42no—
118C2×C4×C73C2×D411yescharacteristic
119C2×C4×C73C2×D411yescharacteristic
120C2×C4×C73C2411yescharacteristic
121C22⋊D73—42no—
122C2×Dic73—21no—
123C2×Dic73—21no—
124C2×Dic73—21no—
125C2×Dic73—21no—
126C2×Dic73C2×D411yescharacteristic
127C2×Dic73C2×D411yescharacteristic
128C2×Dic73C2×D411yescharacteristic
129C4×D73—22no—
130C4×D73—21no—
131C4×D73—21no—
132C4×D73—41no—
133Dic146—21no—
134Dic146—21no—
135Dic146—21no—
136Dic146—21no—
137Dic146—42no—
138C8×C73—21no—
139C8×C73#4112yes—
140#10596831—21no—
141#10596831#4112yes—
142C22×C73—41no—
143C22×C73—41no—
144C22×C73—41no—
145C22×C73C22×D411yescharacteristic
146C2×D73—21no—
147C2×D73—21no—
148C2×D73—21no—
149C4×C73—21no—
150C4×C73—41no—
151C4×C73—41no—
152C4×C73—41no—
153C4×C73#13712yes—
154C4×C73C2×#4111yescharacteristic
155C4×C73C2×#4111yescharacteristic
156Dic73—21no—
157Dic73—21no—
158Dic73—21no—
159Dic73—41no—
160Dic73—41no—
161Dic73—41no—
162Dic73—41no—
163C2×C73—81no—
164C2×C73#53211yescharacteristic
165C2×C73C2×#13711yescharacteristic
166C2×C73#57511yescharacteristic
167D73—41no—
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#470—731no—
178#468—731no—
179#468—731no—
180C4×Q16—731no—
181C4×Q16—731no—
182C4×SD16—731no—
183C4×SD16D7311yescharacteristic, complemented
184C4×M16—731no—
185C2×Q16—731no—
186C2×Q16—731no—
187C2×SD16—731no—
188C2×SD16C2×D7311yescharacteristic
189C2×M16—731no—
190C2×M16—731no—
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—731no—
200C22⋊Q8—731no—
201C22⋊Q8—1461no—
202#121—731no—
203C4×Q8—731no—
204C4×Q8—731no—
205C4×Q8—1461no—
206C4×Q8C2×D7311yescharacteristic
207C4×D4—1461no—
208C4×D4C2×D7311yescharacteristic
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#103—731no—
221#103C2×D7311yescharacteristic
222#102—731no—
223#102C2×D7311yescharacteristic
224#97—731no—
225#97—731no—
226C4×C8—731no—
227C4×C8C2×D7311yescharacteristic
228C2×Q8—731no—
229C2×Q8—731no—
230C2×Q8—1461no—
231C2×Q8C22×D7311yescharacteristic
232C2×D4—1461no—
233C2×D4C22×D7311yescharacteristic
234C22×C4—21no—
235C22×C4—731no—
236C22×C4—731no—
237C22×C4—731no—
238Q16—1462no—
239Q16—1462no—
240SD16—22no—
241SD16—1462no—
242M16—1462no—
243M16—1462no—
244C2×C8—731no—
245C2×C8—731no—
246C2×C8C22×D7311yescharacteristic
247C2×C8C22×D7311yescharacteristic
248C4⋊C4—21no—
249C4⋊C4—731no—
250C4⋊C4—731no—
251C4⋊C4—1461no—
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—1461no—
265C22⋊C4—1461no—
266C22⋊C4—1461no—
267C22⋊C4—1461no—
268C22⋊C4—1461no—
269C22⋊C4—1461no—
270C42—21no—
271C42—731no—
272C42—731no—
273C42—731no—
274C42—1461no—
275C42—1461no—
276C42C22×D7311yescharacteristic
277C23—21no—
278C23—731no—
279Q8—21no—
280Q8—21no—
281Q8—2922no—
282Q8—1461no—
283Q8—1461no—
284Q8—1461no—
285Q8—1461no—
286D4—21no—
287D4—21no—
288D4—2922no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—42no—
293C2×C4—2921no—
294C2×C4—731no—
295C2×C4—731no—
296C2×C4—731no—
297C2×C4—1461no—
298C2×C4—1461no—
299C2×C4—1461no—
300C2×C4—1461no—
301C2×C4—1462no—
302C2×C4—1461no—
303C2×C4—1461no—
304C2×C4D4×D7311yescharacteristic
305C2×C4D4×D7311yescharacteristic
306C2×C4C23×D7311yescharacteristic
307C8—21no—
308C8—732no—
309C8—1461no—
310C8#1192402812yes—
311C22—41no—
312C22—41no—
313C22—41no—
314C22—1461no—
315C22—1461no—
316C22—1461no—
317C22C2×D4×D7311yescharacteristic
318C4—21no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4—2921no—
323C4—2921no—
324C4—2921no—
325C4—2921no—
326C4—1461no—
327C4—1461no—
328C4—1461no—
329C4#1455662012yes—
330C4#41×D7311yescharacteristic
331C4C2×#1192402811yescharacteristic
332C2—81no—
333C2—2921no—
334C2#1798913411yescharacteristic
335C2C2×#1455662011yescharacteristic
336C2#1798938411yescharacteristic
subgroupG/H
centerC2×C4D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
FittingC4×SD16×C73C2
socleC22×C73C22×D4
hypercenterC4×SD16D73
hypocenterC73#3172
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. #17989141C2semidirect
3. #17988994C2semidirect
4. #17988978C2semidirect
5. #17988954C2semidirect
6. #17988945C2semidirect
7. #17988846C2semidirect
8. #17988844C2semidirect
11. C4×Dic292C2semidirect
12. C4×#11924018C2semidirect
13. C4×#11924016C2semidirect
14. C4×#11924011C2semidirect
15. C4×SD16×C73C2semidirect
169. C73#3172semidirect
183. C4×SD16D73semidirect