Finite Group Databasebeta

← #22620600

Subgroups — #22620600

Order 9344.

350 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989210C211yesmaximal, characteristic
2#17989197C211yesmaximal, characteristic, complemented
3#17988994C211yesmaximal, characteristic, complemented
4#17988980C211yesmaximal, characteristic, complemented
5#17988943C211yesmaximal, characteristic, complemented
6#17988936C211yesmaximal, characteristic, complemented
7#17988833C211yesmaximal, characteristic
8#17988826C211yesmaximal, characteristic, complemented
9#17988818C211yesmaximal, characteristic
10#17988691C211yesmaximal, characteristic, complemented
11#17988690C211yesmaximal, characteristic, complemented
12Q16×Dic73C211yesmaximal, characteristic, complemented
13#17988674C211yesmaximal, characteristic, complemented
14#17988545C211yesmaximal, characteristic, complemented
15#470×C73C211yesmaximal, characteristic, complemented
16C2×#11924018C2211yescharacteristic
17C2×#11924017C2211yescharacteristic
18C2×#11924015C2211yescharacteristic
19C22×#10596831C2211yescharacteristic
20#14556590C2211yescharacteristic
21#14556589C2211yescharacteristic
22#14556586—21no—
23#14556584—21no—
24#14556584—21no—
25#14556582—21no—
26#14556582C2211yescharacteristic
27#14556581—21no—
28#14556580C2211yescharacteristic
29#14556577—21no—
30#14556573—21no—
31#14556571—21no—
32#14556570C2211yescharacteristic
33#14556565C2211yescharacteristic
34Q8×Dic73C2211yescharacteristic
35Q8×Dic73C2211yescharacteristic
36#14556556C2211yescharacteristic
37#14556553C2211yescharacteristic
38#14556550C2211yescharacteristic
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—
63C2×C4×D73—21no—
64#11924018—22no—
65#11924017—22no—
66#11924015—22no—
67C2×#10596831—22no—
68C2×#10596831C2311yescharacteristic
69C2×#10596831C2311yescharacteristic
70C4⋊Dic73—21no—
71C4⋊Dic73—21no—
72C4⋊Dic73—21no—
73C4⋊Dic73D411yescharacteristic
74C4⋊Dic73D411yescharacteristic
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—
84C22⋊Dic73D411yescharacteristic
85C22⋊Dic73D411yescharacteristic
86#11924005—21no—
87#11924005—21no—
88#11924005—21no—
89#11924005—21no—
90C4×Dic73—21no—
91C4×Dic73—21no—
92C4×Dic73—21no—
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—81no—
123C2×Dic73—21no—
124C2×Dic73—21no—
125C2×Dic73—21no—
126C2×Dic73C2×D411yescharacteristic
127C2×Dic73C2×D411yescharacteristic
128C2×Dic73C2×D411yescharacteristic
129C2×Dic73C2×D411yescharacteristic
130D292—21no—
131D292—21no—
132C4×D73—81no—
133Dic146—21no—
134Dic146—21no—
135Dic146—81no—
136C8×C73—21no—
137C8×C73#4112yes—
138#10596831—21no—
139#10596831#4112yes—
140C22×C73—21no—
141C22×C73—21no—
142C22×C73—21no—
143C22×C73C22×D411yescharacteristic
144C2×D73—41no—
145C2×D73—41no—
146C2×D73—41no—
147C4×C73—21no—
148C4×C73—41no—
149C4×C73—41no—
150C4×C73—41no—
151C4×C73—41no—
152C4×C73C2×#4111yescharacteristic
153C4×C73C2×#4111yescharacteristic
154Dic73—21no—
155Dic73—21no—
156Dic73—21no—
157Dic73—21no—
158Dic73—41no—
159Dic73—41no—
160Dic73—41no—
161C2×C73—41no—
162C2×C73#53211yescharacteristic
163C2×C73#57711yescharacteristic
164C2×C73#57811yescharacteristic
165D73—81no—
166#3178—731nomaximal, Sylow
167C73#317811yescharacteristic, complemented, Sylow
168#542—731no—
169#541—731no—
170#501—731no—
171#497—731no—
172#488—731no—
173#487—731no—
174#470D7311yescharacteristic, complemented
175#468—731no—
176#467—731no—
177#465—731no—
178#441—731no—
179#440—731no—
180C4×Q16—731no—
181C4×SD16—731no—
182#405—731no—
183C2×Q16—731no—
184C2×Q16C2×D7311yescharacteristic
185C2×SD16—731no—
186C2×SD16—731no—
187C2×M16C2×D7311yescharacteristic
188C22×C8—731no—
189C4⋊Q8—731no—
190C4⋊Q8—731no—
191#126—1461no—
192#126—1461no—
193#126—1461no—
194#125—731no—
195#125—1461no—
196#125—1461no—
197#124—731no—
198#124—1461no—
199#123—1461no—
200C22⋊Q8—731no—
201C22⋊Q8—1461no—
202C22⋊Q8C2×D7311yescharacteristic
203C22⋊Q8C2×D7311yescharacteristic
204#121—731no—
205C4×Q8—731no—
206C4×Q8—731no—
207C4×Q8—731no—
208C4×D4—731no—
209#117—731no—
210#107—731no—
211#107—731no—
212#106—731no—
213#106C2×D7311yescharacteristic
214#103—731no—
215#103—731no—
216#103—731no—
217#103—731no—
218#103C2×D7311yescharacteristic
219#103C2×D7311yescharacteristic
220#102—731no—
221#102—731no—
222#97—731no—
223#97—731no—
224C4×C8—731no—
225C4×C8—731no—
226C2×Q8—731no—
227C2×Q8—1461no—
228C2×Q8C22×D7311yescharacteristic
229C2×Q8C22×D7311yescharacteristic
230C2×D4—731no—
231C2×D4—1461no—
232C22×C4—1461no—
233C22×C4C22×D7311yescharacteristic
234Q16—22no—
235Q16—1462no—
236SD16—1462no—
237SD16—1462no—
238M16—22no—
239C2×C8—731no—
240C2×C8—731no—
241C2×C8—1462no—
242C2×C8C22×D7311yescharacteristic
243C2×C8C22×D7311yescharacteristic
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—731no—
247C4⋊C4—731no—
248C4⋊C4—731no—
249C4⋊C4—731no—
250C4⋊C4—1461no—
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⋊C4C22×D7311yescharacteristic
260C4⋊C4C22×D7311yescharacteristic
261C22⋊C4—21no—
262C22⋊C4—21no—
263C22⋊C4—731no—
264C22⋊C4—731no—
265C22⋊C4—1461no—
266C22⋊C4—1461no—
267C22⋊C4—1461no—
268C22⋊C4—1461no—
269C22⋊C4—1461no—
270C42—731no—
271C42—731no—
272C42—1461no—
273C42—1461no—
274C42—1461no—
275C23—1461no—
276C23D4×D7311yescharacteristic
277Q8—21no—
278Q8—21no—
279Q8—21no—
280Q8—21no—
281Q8—5841no—
282Q8—1461no—
283Q8—1461no—
284D4—5841no—
285D4—1461no—
286D4—1461no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—5841no—
294C2×C4—731no—
295C2×C4—731no—
296C2×C4—731no—
297C2×C4—731no—
298C2×C4—1461no—
299C2×C4—1461no—
300C2×C4—1461no—
301C2×C4D4×D7311yescharacteristic
302C2×C4C23×D7311yescharacteristic
303C8—21no—
304C8—732no—
305C8—1461no—
306C8#1192402712yes—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—2921no—
311C22—2921no—
312C22—2921no—
313C22C2×D4×D7311yescharacteristic
314C4—21no—
315C4—41no—
316C4—41no—
317C4—41no—
318C4—41no—
319C4—2921no—
320C4—2921no—
321C4—2921no—
322C4—1461no—
323C4—1461no—
324C4—1461no—
325C4—1461no—
326C4#41×D7311yescharacteristic
327C4C2×#1192402711yescharacteristic
328C2—41no—
329C2—5841no—
330C2#1798913211yescharacteristic
331C2#1798939611yescharacteristic
332C2#1798940311yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#470×C73C2
socleC22×C73C22×D4
hypercenter#470D73
hypocenterC73#3178
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
2. #17989197C2semidirect
3. #17988994C2semidirect
4. #17988980C2semidirect
5. #17988943C2semidirect
6. #17988936C2semidirect
8. #17988826C2semidirect
10. #17988691C2semidirect
11. #17988690C2semidirect
12. Q16×Dic73C2semidirect
13. #17988674C2semidirect
14. #17988545C2semidirect
15. #470×C73C2semidirect
167. C73#3178semidirect
174. #470D73semidirect