Finite Group Databasebeta

← #22620564

Subgroups — #22620564

Order 9344.

362 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989208C211yesmaximal, characteristic, complemented
2#17988990C211yesmaximal, characteristic, complemented
3#17988969C211yesmaximal, characteristic, complemented
4#17988949C211yesmaximal, characteristic, complemented
5#17988946C211yesmaximal, characteristic, complemented
6#17988835C211yesmaximal, characteristic, complemented
7#17988831C211yesmaximal, characteristic, complemented
8#17988826C211yesmaximal, characteristic, complemented
9#17988821C211yesmaximal, characteristic
10#17988687C211yesmaximal, characteristic, complemented
11#17988685C211yesmaximal, characteristic, complemented
12C4×#11924018C211yesmaximal, characteristic, complemented
13C4×#11924013C211yesmaximal, characteristic, complemented
14#17988543C211yesmaximal, characteristic, complemented
15#542×C73C211yesmaximal, characteristic, complemented
16C2×#11924018C2211yescharacteristic
17C2×#11924016C2211yescharacteristic
18C2×#11924015C2211yescharacteristic
19C2×#11924013C2211yescharacteristic
20C2×#11924012C2211yescharacteristic
21C22×#10596831C2211yescharacteristic
22#14556591C2211yescharacteristic
23#14556586—21no—
24#14556579C2211yescharacteristic
25#14556577—21no—
26#14556573—21no—
27#14556570C2211yescharacteristic
28#14556569—21no—
29#14556565C2211yescharacteristic
30C4×Dic146C2211yescharacteristic
31C4×D292C2211yescharacteristic
32#14556524C2211yescharacteristic
33#14556524C2211yescharacteristic
34#14556524C2211yescharacteristic
35#14556524C2211yescharacteristic
36#14556515C2211yescharacteristic
37#14556515C2211yescharacteristic
38#14556514C2211yescharacteristic
39#14556514C2211yescharacteristic
40#14556512C2211yescharacteristic
41#14556512C2211yescharacteristic
42#14556511C2211yescharacteristic
43#14556511C2211yescharacteristic
44#14556502C2211yescharacteristic
45#14556502C2211yescharacteristic
46C4×#10596831C2211yescharacteristic
47C4×#10596831C2211yescharacteristic
48C4⋊Q8×C73C2211yescharacteristic
49#126×C73—21no—
50#124×C73—21no—
51#124×C73C2211yescharacteristic
52#123×C73—21no—
53C22⋊Q8×C73—21no—
54C22⋊Q8×C73C2211yescharacteristic
55#121×C73C2211yescharacteristic
56C4×Q8×C73C2211yescharacteristic
57C4×D4×C73C2211yescharacteristic
58#117×C73C2211yescharacteristic
59C2×Dic146—21no—
60C2×Dic146C2311yescharacteristic
61C2×D292C2311yescharacteristic
62C2×C22⋊D73—21no—
63C2×C4×D73—21no—
64#11924018—22no—
65#11924016—22no—
66#11924015—22no—
67#11924013—22no—
68#11924012—22no—
69C2×#10596831—22no—
70C2×#10596831C2311yescharacteristic
71C2×#10596831C2311yescharacteristic
72C2×#10596831C2311yescharacteristic
73C2×#10596831C2311yescharacteristic
74C4⋊Dic73—21no—
75C4⋊Dic73C2311yescharacteristic
76C4⋊Dic73C2311yescharacteristic
77#11924007—21no—
78#11924007—21no—
79C22⋊Dic73—21no—
80#11924005—21no—
81#11924005—21no—
82#11924005—21no—
83#11924005—21no—
84C4×Dic73—21no—
85C2×Q8×C73—21no—
86C2×Q8×C73C2311yescharacteristic
87C2×D4×C73—21no—
88C2×D4×C73C2311yescharacteristic
89C22×C4×C73—21no—
90C22×C4×C73C2311yescharacteristic
91C4⋊C4×C73—21no—
92C4⋊C4×C73—21no—
93C4⋊C4×C73—21no—
94C4⋊C4×C73D411yescharacteristic
95C4⋊C4×C73D411yescharacteristic
96C4⋊C4×C73C2311yescharacteristic
97C4⋊C4×C73C2311yescharacteristic
98C22⋊C4×C73—21no—
99C22⋊C4×C73—21no—
100C22⋊C4×C73—21no—
101C22⋊C4×C73—21no—
102C22⋊C4×C73—21no—
103C22⋊C4×C73D411yescharacteristic
104C22⋊C4×C73D411yescharacteristic
105C42×C73—21no—
106C42×C73C2311yescharacteristic
107C42×C73C2311yescharacteristic
108C23×C73—21no—
109C23×C73C2×D411yescharacteristic
110C22×D73—21no—
111Q8×C73—21no—
112Q8×C73—21no—
113Q8×C73—81no—
114D4×C73—21no—
115D4×C73—21no—
116D4×C73—81no—
117C2×C4×C73—21no—
118C2×C4×C73—21no—
119C2×C4×C73—21no—
120C2×C4×C73—21no—
121C2×C4×C73—21no—
122C2×C4×C73—81no—
123C2×C4×C73C2×D411yescharacteristic
124C2×C4×C73C2×D411yescharacteristic
125C2×C4×C73C2×D411yescharacteristic
126C2×C4×C73C2×D411yescharacteristic
127C2×C4×C73C2×D411yescharacteristic
128C2×C4×C73C2411yescharacteristic
129C22⋊D73—81no—
130C2×Dic73—21no—
131C2×Dic73—21no—
132C2×Dic73—21no—
133D292—21no—
134D292—21no—
135C4×D73—81no—
136Dic146—21no—
137Dic146—21no—
138Dic146—81no—
139#10596831—21no—
140#10596831—21no—
141#10596831#4112yes—
142#10596831#4112yes—
143C22×C73—21no—
144C22×C73—21no—
145C22×C73—21no—
146C22×C73—41no—
147C22×C73—41no—
148C22×C73—41no—
149C22×C73C22×D411yescharacteristic
150C2×D73—41no—
151C2×D73—41no—
152C2×D73—41no—
153C4×C73—21no—
154C4×C73—21no—
155C4×C73—21no—
156C4×C73—21no—
157C4×C73—21no—
158C4×C73—41no—
159C4×C73—41no—
160C4×C73—41no—
161C4×C73C2×#4111yescharacteristic
162C4×C73C2×#4111yescharacteristic
163Dic73—41no—
164Dic73—41no—
165Dic73—41no—
166C2×C73—41no—
167C2×C73—81no—
168C2×C73#53211yescharacteristic
169C2×C73#57611yescharacteristic
170C2×C73#57811yescharacteristic
171D73—81no—
172#3175—731nomaximal, Sylow
173C73#317511yescharacteristic, complemented, Sylow
174#542—731no—
175#542D7311yescharacteristic, complemented
176#500—731no—
177#495—731no—
178#489—731no—
179#489—731no—
180#468—731no—
181#468—731no—
182#467—731no—
183#466—731no—
184#440—731no—
185#440—731no—
186C4×Q16—731no—
187C4×D8—731no—
188#405—731no—
189C2×Q16—731no—
190C2×SD16—731no—
191C2×SD16—731no—
192C2×D8—731no—
193C2×M16—731no—
194C22×C8—731no—
195C4⋊Q8—731no—
196C4⋊Q8C2×D7311yescharacteristic
197#126—21no—
198#126—1461no—
199#124—21no—
200#124—731no—
201#124—1461no—
202#124C2×D7311yescharacteristic
203#123—21no—
204#123—1461no—
205C22⋊Q8—21no—
206C22⋊Q8—731no—
207C22⋊Q8—1461no—
208C22⋊Q8C2×D7311yescharacteristic
209#121—731no—
210#121C2×D7311yescharacteristic
211C4×Q8—731no—
212C4×Q8C2×D7311yescharacteristic
213C4×D4—731no—
214C4×D4C2×D7311yescharacteristic
215#117C2×D7311yescharacteristic
216#107—731no—
217#107—731no—
218#107—731no—
219#107—731no—
220#103—731no—
221#103—731no—
222#103—731no—
223#103—731no—
224#102—731no—
225#102—731no—
226#102—731no—
227#102—731no—
228#97—731no—
229#97—731no—
230C4×C8—731no—
231C4×C8—731no—
232C2×Q8—21no—
233C2×Q8—731no—
234C2×Q8—1461no—
235C2×Q8C22×D7311yescharacteristic
236C2×D4—21no—
237C2×D4—731no—
238C2×D4—1461no—
239C2×D4C22×D7311yescharacteristic
240C22×C4—21no—
241C22×C4—1461no—
242C22×C4C22×D7311yescharacteristic
243Q16—1462no—
244SD16—1462no—
245SD16—1462no—
246D8—1462no—
247M16—1462no—
248C2×C8—731no—
249C2×C8—731no—
250C2×C8—731no—
251C2×C8—731no—
252C2×C8—1462no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—731no—
257C4⋊C4—731no—
258C4⋊C4—1461no—
259C4⋊C4—1461no—
260C4⋊C4—1461no—
261C4⋊C4C22⋊D7311yescharacteristic
262C4⋊C4C22⋊D7311yescharacteristic
263C4⋊C4C22×D7311yescharacteristic
264C4⋊C4C22×D7311yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—1461no—
271C22⋊C4—1461no—
272C22⋊C4—1461no—
273C22⋊C4—1461no—
274C22⋊C4—1461no—
275C22⋊C4C22⋊D7311yescharacteristic
276C22⋊C4C22⋊D7311yescharacteristic
277C42—21no—
278C42—1461no—
279C42C22×D7311yescharacteristic
280C42C22×D7311yescharacteristic
281C23—21no—
282C23—1461no—
283C23C2×C22⋊D7311yescharacteristic
284Q8—21no—
285Q8—21no—
286Q8—81no—
287Q8—5841no—
288Q8—1461no—
289Q8—1461no—
290D4—21no—
291D4—21no—
292D4—81no—
293D4—5841no—
294D4—1461no—
295D4—1461no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—81no—
302C2×C4—5841no—
303C2×C4—1461no—
304C2×C4—1461no—
305C2×C4—1461no—
306C2×C4C2×C22⋊D7311yescharacteristic
307C2×C4C2×C22⋊D7311yescharacteristic
308C2×C4C2×C22⋊D7311yescharacteristic
309C2×C4C2×C22⋊D7311yescharacteristic
310C2×C4C2×C22⋊D7311yescharacteristic
311C2×C4C23×D7311yescharacteristic
312C8—732no—
313C8—732no—
314C8—1461no—
315C8—1461no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—41no—
320C22—41no—
321C22—41no—
322C22—2921no—
323C22—2921no—
324C22—2921no—
325C22C22×C22⋊D7311yescharacteristic
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—41no—
332C4—41no—
333C4—41no—
334C4—2921no—
335C4—2921no—
336C4—2921no—
337C4#41×D7311yescharacteristic
338C4#41×D7311yescharacteristic
339C2—41no—
340C2—81no—
341C2—5841no—
342C2#1798913311yescharacteristic
343C2#1798939011yescharacteristic
344C2#1798940211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#542×C73C2
socleC22×C73C22×D4
hypercenter#542D73
hypocenterC73#3175
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ #117 ◁ #542

Complements

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

NH ≅ G/Ntype
1. #17989208C2semidirect
2. #17988990C2semidirect
3. #17988969C2semidirect
4. #17988949C2semidirect
5. #17988946C2semidirect
6. #17988835C2semidirect
7. #17988831C2semidirect
8. #17988826C2semidirect
10. #17988687C2semidirect
11. #17988685C2semidirect
12. C4×#11924018C2semidirect
13. C4×#11924013C2semidirect
14. #17988543C2semidirect
15. #542×C73C2semidirect
173. C73#3175semidirect
175. #542D73semidirect