Finite Group Databasebeta

← #22620161

Subgroups — #22620161

Order 9344.

370 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#17989210C211yesmaximal, characteristic
2#17989065C211yesmaximal, characteristic, complemented
3#17988925C211yesmaximal, characteristic, complemented
4#17988912C211yesmaximal, characteristic
5#17988880C211yesmaximal, characteristic, complemented
6#17988870C211yesmaximal, characteristic, complemented
7#17988811C211yesmaximal, characteristic, complemented
8#17988811C211yesmaximal, characteristic, complemented
9#17988726C211yesmaximal, characteristic
10#17988694C211yesmaximal, characteristic, complemented
11#17988690C211yesmaximal, characteristic, complemented
12Q16×Dic73C211yesmaximal, characteristic, complemented
13#17988672C211yesmaximal, characteristic, complemented
14#17988645C211yesmaximal, characteristic, complemented
15#451×C73C211yesmaximal, characteristic, complemented
16C2×#11924015C2211yescharacteristic
17C2×#11924015C2211yescharacteristic
18#14556590C2211yescharacteristic
19#14556586—21no—
20#14556580C2211yescharacteristic
21#14556577—21no—
22#14556573—21no—
23#14556571—21no—
24#14556565C2211yescharacteristic
25Q8×Dic73—21no—
26Q8×Dic73—21no—
27Q8×Dic73C2211yescharacteristic
28Q8×Dic73C2211yescharacteristic
29Q8×Dic73C2211yescharacteristic
30Q8×Dic73C2211yescharacteristic
31Q8×Dic73C2211yescharacteristic
32#14556553C2211yescharacteristic
33#14556550—21no—
34#14556550—21no—
35#14556550C2211yescharacteristic
36#14556550C2211yescharacteristic
37#14556525C2211yescharacteristic
38#14556524C2211yescharacteristic
39#14556523C2211yescharacteristic
40#14556522C2211yescharacteristic
41#14556520C2211yescharacteristic
42#14556520C2211yescharacteristic
43#14556515C2211yescharacteristic
44#14556515C2211yescharacteristic
45#14556515C2211yescharacteristic
46#14556515C2211yescharacteristic
47#14556513C2211yescharacteristic
48#14556513C2211yescharacteristic
49C22⋊#10596831C2211yescharacteristic
50#14556501C2211yescharacteristic
51C8×Dic73C2211yescharacteristic
52C22×Q8×C73C2211yescharacteristic
53C2×Q16×C73C2211yescharacteristic
54C2×Q16×C73C2211yescharacteristic
55C22⋊Q8×C73C2211yescharacteristic
56#103×C73C2211yescharacteristic
57#103×C73C2211yescharacteristic
58C22⋊C8×C73C2211yescharacteristic
59C2×Dic146—21no—
60C2×D292C2311yescharacteristic
61C2×C22⋊D73—21no—
62C2×C4×D73—21no—
63#11924015—22no—
64#11924015—22no—
65C2×#10596831C2311yescharacteristic
66C2×#10596831C2311yescharacteristic
67C4⋊Dic73—21no—
68C4⋊Dic73—21no—
69C4⋊Dic73—21no—
70C4⋊Dic73—21no—
71C4⋊Dic73—21no—
72C4⋊Dic73D411yescharacteristic
73C4⋊Dic73D411yescharacteristic
74C4⋊Dic73C2311yescharacteristic
75C4⋊Dic73C2311yescharacteristic
76C4⋊Dic73C2311yescharacteristic
77#11924007—21no—
78C22⋊Dic73—21no—
79C22⋊Dic73D411yescharacteristic
80C22⋊Dic73D411yescharacteristic
81#11924005—21no—
82#11924005—21no—
83#11924005—21no—
84#11924005—21no—
85C4×Dic73—21no—
86C4×Dic73—21no—
87C4×Dic73—21no—
88C4×Dic73—21no—
89C4×Dic73—21no—
90C4×Dic73—21no—
91C4×Dic73C2311yescharacteristic
92C4×Dic73C2311yescharacteristic
93C2×Q8×C73—22no—
94C2×Q8×C73—22no—
95C2×Q8×C73—21no—
96C2×Q8×C73C2311yescharacteristic
97C2×Q8×C73C2311yescharacteristic
98C2×Q8×C73C2311yescharacteristic
99C22×C4×C73—21no—
100C22×C4×C73C2311yescharacteristic
101Q16×C73—22no—
102Q16×C73—22no—
103C2×C8×C73C2311yescharacteristic
104C2×C8×C73C2311yescharacteristic
105C4⋊C4×C73—21no—
106C4⋊C4×C73C2311yescharacteristic
107C22⋊C4×C73—21no—
108C23×C73C2×D411yescharacteristic
109C22×D73—21no—
110Q8×C73—24no—
111Q8×C73—21no—
112Q8×C73—21no—
113Q8×C73—21no—
114Q8×C73—21no—
115Q8×C73#4112yes—
116Q8×C73#4112yes—
117C2×C4×C73—24no—
118C2×C4×C73—21no—
119C2×C4×C73—21no—
120C2×C4×C73—21no—
121C2×C4×C73—21no—
122C2×C4×C73—21no—
123C2×C4×C73—21no—
124C2×C4×C73C2×D411yescharacteristic
125C2×C4×C73C2411yescharacteristic
126C22⋊D73—81no—
127C2×Dic73—21no—
128C2×Dic73—21no—
129C2×Dic73—21no—
130C2×Dic73C2×D411yescharacteristic
131C2×Dic73C2×D411yescharacteristic
132C2×Dic73C2×D411yescharacteristic
133C2×Dic73C2×D411yescharacteristic
134D292—21no—
135D292—21no—
136C4×D73—81no—
137Dic146—81no—
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—41no—
147C2×D73—41no—
148C2×D73—41no—
149C4×C73—22no—
150C4×C73—22no—
151C4×C73—21no—
152C4×C73—41no—
153C4×C73—41no—
154C4×C73C2×#4111yescharacteristic
155C4×C73C2×#4111yescharacteristic
156Dic73—21no—
157Dic73—21no—
158Dic73—21no—
159Dic73—21no—
160Dic73—41no—
161Dic73—41no—
162Dic73—41no—
163C2×C73—41no—
164C2×C73#52511yescharacteristic
165C2×C73#57711yescharacteristic
166C2×C73#57811yescharacteristic
167D73—81no—
168#3121—731nomaximal, Sylow
169C73#312111yescharacteristic, complemented, Sylow
170#542—731no—
171#519—731no—
172#485—731no—
173#482—731no—
174#477—731no—
175#475—731no—
176#464—731no—
177#464—731no—
178#451D7311yescharacteristic, complemented
179#448—731no—
180#441—731no—
181#440—731no—
182C4×Q16—731no—
183C4×SD16—731no—
184#433—731no—
185C22×Q8C2×D7311yescharacteristic
186C2×Q16C2×D7311yescharacteristic
187C2×Q16C2×D7311yescharacteristic
188C2×SD16—731no—
189C2×SD16—731no—
190C4⋊Q8—731no—
191#126—1461no—
192#124—731no—
193#124—1461no—
194#123—1461no—
195C22⋊Q8—1461no—
196C22⋊Q8C2×D7311yescharacteristic
197#121—731no—
198C4×Q8—731no—
199C4×Q8—731no—
200C4×Q8—731no—
201C4×Q8—731no—
202C4×Q8—731no—
203C4×Q8—1461no—
204C4×Q8—1461no—
205C4×D4—731no—
206#117—731no—
207#117—731no—
208#117—1461no—
209#117—1461no—
210#107—731no—
211#107—731no—
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—
228C2×Q8—22no—
229C2×Q8—22no—
230C2×Q8—21no—
231C2×Q8—1461no—
232C2×Q8C22×D7311yescharacteristic
233C2×Q8C22×D7311yescharacteristic
234C2×Q8C22×D7311yescharacteristic
235C2×D4—731no—
236C2×D4—1461no—
237C22×C4—21no—
238C22×C4—1461no—
239C22×C4C22×D7311yescharacteristic
240Q16—22no—
241Q16—22no—
242SD16—1462no—
243SD16—1462no—
244C2×C8—731no—
245C2×C8—731no—
246C2×C8C22×D7311yescharacteristic
247C2×C8C22×D7311yescharacteristic
248C4⋊C4—21no—
249C4⋊C4—731no—
250C4⋊C4—731no—
251C4⋊C4—731no—
252C4⋊C4—731no—
253C4⋊C4—731no—
254C4⋊C4—1461no—
255C4⋊C4—1461no—
256C4⋊C4—1461no—
257C4⋊C4—1461no—
258C4⋊C4—1461no—
259C4⋊C4—1461no—
260C4⋊C4C22×D7311yescharacteristic
261C22⋊C4—21no—
262C22⋊C4—731no—
263C22⋊C4—731no—
264C22⋊C4—1461no—
265C22⋊C4—1461no—
266C22⋊C4—1461no—
267C22⋊C4—1461no—
268C22⋊C4—1461no—
269C42—731no—
270C42—731no—
271C42—1461no—
272C42—1461no—
273C42—1461no—
274C42—1461no—
275C42—1461no—
276C42—1461no—
277C23—1461no—
278C23D4×D7311yescharacteristic
279Q8—24no—
280Q8—21no—
281Q8—21no—
282Q8—21no—
283Q8—21no—
284Q8—5841no—
285Q8#1192402712yes—
286Q8#1192402712yes—
287D4—5841no—
288D4—1461no—
289D4—1461no—
290C2×C4—24no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—5841no—
298C2×C4—731no—
299C2×C4—731no—
300C2×C4—731no—
301C2×C4—731no—
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—2921no—
317C22C2×D4×D7311yescharacteristic
318C4—22no—
319C4—22no—
320C4—21no—
321C4—41no—
322C4—41no—
323C4—2921no—
324C4—2921no—
325C4—2921no—
326C4—1461no—
327C4—1461no—
328C4—1461no—
329C4—1461no—
330C4C2×#1192402711yescharacteristic
331C4C2×#1192402711yescharacteristic
332C2—41no—
333C2—5841no—
334C2#1798909311yescharacteristic
335C2#1798939611yescharacteristic
336C2#1798940011yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#451×C73C2
socleC22×C73C22×D4
hypercenter#451D73
hypocenterC73#3121
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
2. #17989065C2semidirect
3. #17988925C2semidirect
5. #17988880C2semidirect
6. #17988870C2semidirect
7. #17988811C2semidirect
8. #17988811C2semidirect
10. #17988694C2semidirect
11. #17988690C2semidirect
12. Q16×Dic73C2semidirect
13. #17988672C2semidirect
14. #17988645C2semidirect
15. #451×C73C2semidirect
169. C73#3121semidirect
178. #451D73semidirect