Finite Group Databasebeta

← #22620140

Subgroups — #22620140

Order 9344.

372 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#17989197C211yesmaximal, characteristic, complemented
2#17989068C211yesmaximal, characteristic
3#17988917C211yesmaximal, characteristic, complemented
4#17988893C211yesmaximal, characteristic, complemented
5#17988890C211yesmaximal, characteristic, complemented
6#17988796C211yesmaximal, characteristic, complemented
7#17988791C211yesmaximal, characteristic, complemented
8#17988751C211yesmaximal, characteristic
9#17988747C211yesmaximal, characteristic
10#17988691C211yesmaximal, characteristic, complemented
11#17988686C211yesmaximal, characteristic, complemented
12#17988681C211yesmaximal, characteristic, complemented
13#17988672C211yesmaximal, characteristic, complemented
14#17988645C211yesmaximal, characteristic, complemented
15#484×C73C211yesmaximal, characteristic, complemented
16C2×#11924028C2211yescharacteristic
17C2×Dic292C2211yescharacteristic
18C2×#11924018C2211yescharacteristic
19C2×#11924017C2211yescharacteristic
20C2×#11924015C2211yescharacteristic
21#14556589C2211yescharacteristic
22#14556584—21no—
23#14556584—21no—
24#14556582—21no—
25#14556582C2211yescharacteristic
26#14556581—21no—
27#14556570C2211yescharacteristic
28Q8×Dic73C2211yescharacteristic
29#14556556C2211yescharacteristic
30#14556556C2211yescharacteristic
31#14556556C2211yescharacteristic
32#14556553C2211yescharacteristic
33#14556553C2211yescharacteristic
34C4×C22⋊D73—21no—
35C4×C22⋊D73—21no—
36#14556550C2211yescharacteristic
37#14556549—21no—
38C4⋊C4×D73—21no—
39#14556522C2211yescharacteristic
40#14556522C2211yescharacteristic
41#14556520C2211yescharacteristic
42#14556520C2211yescharacteristic
43#14556516C2211yescharacteristic
44#14556514C2211yescharacteristic
45#14556514C2211yescharacteristic
46#14556514C2211yescharacteristic
47#14556513C2211yescharacteristic
48#14556511C2211yescharacteristic
49C22⋊#10596831C2211yescharacteristic
50#14556501C2211yescharacteristic
51C8×Dic73C2211yescharacteristic
52C22⋊Q8×C73C2211yescharacteristic
53C2×C4⋊C4×C73C2211yescharacteristic
54#107×C73C2211yescharacteristic
55#107×C73C2211yescharacteristic
56#103×C73C2211yescharacteristic
57#103×C73C2211yescharacteristic
58C22⋊C8×C73C2211yescharacteristic
59#11924028—22no—
60#11924028—22no—
61C2×Dic146C2311yescharacteristic
62C2×Dic146C2311yescharacteristic
63C2×D292C2311yescharacteristic
64C2×C22⋊D73—21no—
65C2×C4×D73—21no—
66C2×C4×D73—21no—
67C2×C4×D73—21no—
68Dic292—22no—
69#11924018—22no—
70#11924017—22no—
71#11924015—22no—
72C2×#10596831C2311yescharacteristic
73C2×#10596831C2311yescharacteristic
74C4⋊Dic73—21no—
75C4⋊Dic73—21no—
76C4⋊Dic73D411yescharacteristic
77C4⋊Dic73D411yescharacteristic
78C4⋊Dic73C2311yescharacteristic
79#11924007—21no—
80#11924007—21no—
81#11924007—21no—
82#11924007—21no—
83#11924007—21no—
84#11924007—21no—
85#11924007—21no—
86C22⋊Dic73—21no—
87C22⋊Dic73D411yescharacteristic
88C22⋊Dic73D411yescharacteristic
89#11924005—21no—
90#11924005—21no—
91C4×Dic73—21no—
92C4×Dic73—21no—
93C4×Dic73—21no—
94C4×Dic73—21no—
95C4×Dic73C2311yescharacteristic
96C4×Dic73C2311yescharacteristic
97C2×Q8×C73C2311yescharacteristic
98C22×C4×C73—21no—
99C22×C4×C73C2311yescharacteristic
100C2×C8×C73C2311yescharacteristic
101C2×C8×C73C2311yescharacteristic
102C4⋊C4×C73—21no—
103C4⋊C4×C73—21no—
104C4⋊C4×C73C2311yescharacteristic
105C4⋊C4×C73C2311yescharacteristic
106C4⋊C4×C73C2311yescharacteristic
107C22⋊C4×C73—21no—
108C23×C73C2×D411yescharacteristic
109C22×D73—21no—
110Q8×C73—21no—
111Q8×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—21no—
118C2×C4×C73—81no—
119C2×C4×C73C2×D411yescharacteristic
120C2×C4×C73C2411yescharacteristic
121C22⋊D73—24no—
122C2×Dic73—21no—
123C2×Dic73—21no—
124C2×Dic73—21no—
125C2×Dic73C2×D411yescharacteristic
126C2×Dic73C2×D411yescharacteristic
127C2×Dic73C2×D411yescharacteristic
128C2×Dic73C2×D411yescharacteristic
129D292—21no—
130D292#4112yes—
131C4×D73—24no—
132C4×D73—81no—
133C4×D73—81no—
134Dic146—21no—
135Dic146—21no—
136Dic146—21no—
137Dic146#4112yes—
138C8×C73—21no—
139C8×C73—21no—
140#10596831—21no—
141#10596831—21no—
142C22×C73—21no—
143C22×C73—21no—
144C22×C73—21no—
145C22×C73C22×D411yescharacteristic
146C2×D73—22no—
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—22no—
157Dic73—21no—
158Dic73—21no—
159Dic73—21no—
160Dic73—21no—
161Dic73—41no—
162Dic73—41no—
163C2×C73—41no—
164C2×C73#52511yescharacteristic
165C2×C73#57711yescharacteristic
166C2×C73#57811yescharacteristic
167D73—42no—
168#3120—731nomaximal, Sylow
169C73#312011yescharacteristic, complemented, Sylow
170#541—731no—
171#520—731no—
172#484D7311yescharacteristic, complemented
173#483—731no—
174#479—731no—
175#478—731no—
176#462—731no—
177#461—731no—
178#452—731no—
179#452—731no—
180#441—731no—
181#440—731no—
182C4×Q16—731no—
183C4×SD16—731no—
184#433—731no—
185C2×#41—731no—
186C2×Q16—731no—
187C2×Q16—731no—
188C2×SD16—731no—
189C2×SD16—731no—
190C4⋊Q8—731no—
191#126—1461no—
192#126—1461no—
193#125—731no—
194#125—1461no—
195#125—1461no—
196C22⋊Q8—731no—
197C22⋊Q8C2×D7311yescharacteristic
198C4×Q8—731no—
199C4×Q8—731no—
200C4×Q8—731no—
201C4×Q8—731no—
202C4×D4—731no—
203C4×D4—731no—
204C4×D4—1461no—
205C4×D4—1461no—
206#117—731no—
207#117—1461no—
208C2×C4⋊C4—1461no—
209C2×C4⋊C4C2×D7311yescharacteristic
210#107C2×D7311yescharacteristic
211#107C2×D7311yescharacteristic
212#106—731no—
213#106—731no—
214C4⋊C8—731no—
215C4⋊C8—731no—
216#103—731no—
217#103—731no—
218#103—731no—
219#103—731no—
220#103C2×D7311yescharacteristic
221#103C2×D7311yescharacteristic
222#102—731no—
223#102—731no—
224C22⋊C8—731no—
225C22⋊C8C2×D7311yescharacteristic
226#97—731no—
227C4×C8—731no—
228#41—1462no—
229#41—1462no—
230C2×Q8—731no—
231C2×Q8—731no—
232C2×Q8C22×D7311yescharacteristic
233C2×D4—731no—
234C2×D4—1461no—
235C22×C4—21no—
236C22×C4—1461no—
237C22×C4—1461no—
238C22×C4—1461no—
239C22×C4C22×D7311yescharacteristic
240Q16—1462no—
241Q16—1462no—
242SD16—1462no—
243SD16—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—731no—
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⋊C4—1461no—
262C4⋊C4C22×D7311yescharacteristic
263C4⋊C4C22×D7311yescharacteristic
264C4⋊C4C22×D7311yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—731no—
267C22⋊C4—731no—
268C22⋊C4—1461no—
269C22⋊C4—1461no—
270C22⋊C4—1461no—
271C42—731no—
272C42—731no—
273C42—1461no—
274C42—1461no—
275C42—1461no—
276C42—1461no—
277C23—1461no—
278C23D4×D7311yescharacteristic
279Q8—21no—
280Q8—21no—
281Q8—732no—
282Q8—1461no—
283Q8—1461no—
284Q8—1461no—
285D4—732no—
286D4—1464no—
287D4—1461no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—81no—
295C2×C4—5841no—
296C2×C4—5841no—
297C2×C4—731no—
298C2×C4—731no—
299C2×C4—731no—
300C2×C4—731no—
301C2×C4—1464no—
302C2×C4—1461no—
303C2×C4—1461no—
304C2×C4—1461no—
305C2×C4D4×D7311yescharacteristic
306C2×C4C23×D7311yescharacteristic
307C8—21no—
308C8—21no—
309C8—1461no—
310C8—1461no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—2921no—
315C22—2921no—
316C22—1462no—
317C22C2×D4×D7311yescharacteristic
318C4—21no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4—41no—
323C4—2921no—
324C4—2921no—
325C4—1461no—
326C4—1461no—
327C4—1461no—
328C4—1461no—
329C4—1462no—
330C4#41×D7311yescharacteristic
331C4#41×D7311yescharacteristic
332C2—41no—
333C2—2922no—
334C2#1798909511yescharacteristic
335C2#1798939711yescharacteristic
336C2#1798940011yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#484×C73C2
socleC22×C73C22×D4
hypercenter#484D73
hypocenterC73#3120
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
1. #17989197C2semidirect
3. #17988917C2semidirect
4. #17988893C2semidirect
5. #17988890C2semidirect
6. #17988796C2semidirect
7. #17988791C2semidirect
10. #17988691C2semidirect
11. #17988686C2semidirect
12. #17988681C2semidirect
13. #17988672C2semidirect
14. #17988645C2semidirect
15. #484×C73C2semidirect
169. C73#3120semidirect
172. #484D73semidirect