Finite Group Databasebeta

← #22622425

Subgroups — #22622425

Order 9344.

360 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989302C211yesmaximal, characteristic, complemented
2#17988997C211yesmaximal, characteristic, complemented
3#17988911C211yesmaximal, characteristic, complemented
4#17988908C211yesmaximal, characteristic, complemented
5#17988908C211yesmaximal, characteristic, complemented
6#17988900C211yesmaximal, characteristic, complemented
7#17988884C211yesmaximal, characteristic, complemented
8#17988867C211yesmaximal, characteristic, complemented
9#17988838C211yesmaximal, characteristic, complemented
10#17988821C211yesmaximal, characteristic, complemented
11#17988697C211yesmaximal, characteristic, complemented
12#17988659C211yesmaximal, characteristic, complemented
13#17988627C211yesmaximal, characteristic, complemented
14#17988623C211yesmaximal, characteristic, complemented
15#553×C73C211yesmaximal, characteristic, complemented
16C2×#11924013C2211yescharacteristic
17C2×#11924012C2211yescharacteristic
18C22×#10596831C2211yescharacteristic
19#14556591C2211yescharacteristic
20#14556577—21no—
21#14556577—21no—
22#14556565C2211yescharacteristic
23#14556565C2211yescharacteristic
24#14556562—21no—
25C4×D292C2211yescharacteristic
26#14556550C2211yescharacteristic
27#14556550C2211yescharacteristic
28#14556549—21no—
29#14556524C2211yescharacteristic
30#14556524C2211yescharacteristic
31#14556524C2211yescharacteristic
32#14556524C2211yescharacteristic
33#14556524C2211yescharacteristic
34#14556522C2211yescharacteristic
35#14556522C2211yescharacteristic
36#14556522C2211yescharacteristic
37#14556522C2211yescharacteristic
38C4⋊#10596831C2211yescharacteristic
39#14556512C2211yescharacteristic
40#14556512C2211yescharacteristic
41#14556512C2211yescharacteristic
42#14556511C2211yescharacteristic
43#14556511C2211yescharacteristic
44#14556511C2211yescharacteristic
45C22⋊#10596831C2211yescharacteristic
46C22⋊#10596831C2211yescharacteristic
47#14556502C2211yescharacteristic
48#126×C73—21no—
49#125×C73C2211yescharacteristic
50#123×C73—21no—
51#121×C73—21no—
52#121×C73C2211yescharacteristic
53#121×C73C2211yescharacteristic
54C4×D4×C73—21no—
55C4×D4×C73C2211yescharacteristic
56C4×D4×C73C2211yescharacteristic
57#117×C73C2211yescharacteristic
58C2×C4⋊C4×C73C2211yescharacteristic
59C2×Dic146—21no—
60C2×D292C2311yescharacteristic
61C2×C22⋊D73—21no—
62C2×C22⋊D73—21no—
63C2×C4×D73—21no—
64#11924013—22no—
65#11924012—22no—
66C2×#10596831—22no—
67C2×#10596831C2311yescharacteristic
68C2×#10596831C2311yescharacteristic
69C2×#10596831C2311yescharacteristic
70C2×#10596831C2311yescharacteristic
71C4⋊Dic73—21no—
72C4⋊Dic73C2311yescharacteristic
73C4⋊Dic73C2311yescharacteristic
74C4⋊Dic73C2311yescharacteristic
75C22⋊Dic73—21no—
76C22⋊Dic73—21no—
77#11924005—21no—
78#11924005—21no—
79#11924005—21no—
80C4×Dic73—21no—
81C4×Dic73—21no—
82C2×D4×C73—21no—
83C2×D4×C73—21no—
84C2×D4×C73D411yescharacteristic
85C2×D4×C73C2311yescharacteristic
86C22×C4×C73—21no—
87C22×C4×C73—21no—
88C22×C4×C73C2311yescharacteristic
89C22×C4×C73C2311yescharacteristic
90C4⋊C4×C73—21no—
91C4⋊C4×C73—21no—
92C4⋊C4×C73—21no—
93C4⋊C4×C73D411yescharacteristic
94C4⋊C4×C73C2311yescharacteristic
95C4⋊C4×C73C2311yescharacteristic
96C4⋊C4×C73C2311yescharacteristic
97C22⋊C4×C73—21no—
98C22⋊C4×C73—21no—
99C22⋊C4×C73—21no—
100C22⋊C4×C73—21no—
101C22⋊C4×C73D411yescharacteristic
102C22⋊C4×C73D411yescharacteristic
103C42×C73—21no—
104C42×C73C2311yescharacteristic
105C23×C73—21no—
106C23×C73C2×D411yescharacteristic
107C23×C73C2×D411yescharacteristic
108C22×D73—21no—
109D4×C73—21no—
110D4×C73—21no—
111D4×C73—41no—
112D4×C73—42no—
113D4×C73—81no—
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×C73—21no—
121C2×C4×C73—81no—
122C2×C4×C73—81no—
123C2×C4×C73C2×D411yescharacteristic
124C2×C4×C73C2×D411yescharacteristic
125C2×C4×C73C2×D411yescharacteristic
126C2×C4×C73C2×D411yescharacteristic
127C2×C4×C73C2411yescharacteristic
128C22⋊D73—81no—
129C22⋊D73—81no—
130C2×Dic73—21no—
131C2×Dic73—21no—
132C2×Dic73—21no—
133D292—21no—
134D292—21no—
135C4×D73—42no—
136Dic146—81no—
137#10596831—21no—
138#10596831—21no—
139#10596831—21no—
140#10596831#4112yes—
141C22×C73—21no—
142C22×C73—21no—
143C22×C73—21no—
144C22×C73—21no—
145C22×C73—21no—
146C22×C73—21no—
147C22×C73—41no—
148C22×C73—41no—
149C22×C73—41no—
150C22×C73C22×D411yescharacteristic
151C2×D73—41no—
152C2×D73—41no—
153C2×D73—41no—
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×C732−1+411yescharacteristic
163Dic73—41no—
164Dic73—41no—
165Dic73—41no—
166C2×C73—41no—
167C2×C73—41no—
168C2×C73—81no—
169C2×C73#54711yescharacteristic
170C2×C73#57511yescharacteristic
171C2×C73#57611yescharacteristic
172D73—81no—
173#3347—731nomaximal, Sylow
174C73#334711yescharacteristic, complemented, Sylow
175#555—731no—
176#553D7311yescharacteristic, complemented
177#501—731no—
178#482—731no—
179#482—731no—
180#482—731no—
181#480—731no—
182#478—731no—
183#474—731no—
184#469—731no—
185#466—731no—
186#442—731no—
187#435—731no—
188#428—731no—
189#427—731no—
190C2×D8—731no—
191C2×M16—731no—
192C22×C8—731no—
193C4⋊Q8—731no—
194#126—21no—
195#125C2×D7311yescharacteristic
196#124—1461no—
197#124—1461no—
198#123—21no—
199#121—21no—
200#121—731no—
201#121—731no—
202#121—1461no—
203#121C2×D7311yescharacteristic
204#121C2×D7311yescharacteristic
205C4×D4—21no—
206C4×D4—731no—
207C4×D4C2×D7311yescharacteristic
208C4×D4C2×D7311yescharacteristic
209#117—731no—
210#117—731no—
211#117—1461no—
212#117C2×D7311yescharacteristic
213C2×C4⋊C4C2×D7311yescharacteristic
214#107—731no—
215#107—731no—
216#107—731no—
217#107—731no—
218#107—731no—
219#106—731no—
220#106—731no—
221#106—731no—
222#106—731no—
223C4⋊C8—731no—
224#102—731no—
225#102—731no—
226#102—731no—
227#102—731no—
228#102—731no—
229#102—731no—
230C22⋊C8—731no—
231C22⋊C8—731no—
232#97—731no—
233C2×Q8—1461no—
234C2×D4—21no—
235C2×D4—21no—
236C2×D4—731no—
237C2×D4—1461no—
238C2×D4—1461no—
239C2×D4C22⋊D7311yescharacteristic
240C2×D4C22×D7311yescharacteristic
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—1461no—
244C22×C4C22×D7311yescharacteristic
245C22×C4C22×D7311yescharacteristic
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—731no—
259C4⋊C4—1461no—
260C4⋊C4C22⋊D7311yescharacteristic
261C4⋊C4C22×D7311yescharacteristic
262C4⋊C4C22×D7311yescharacteristic
263C4⋊C4C22×D7311yescharacteristic
264C22⋊C4—21no—
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—1461no—
269C22⋊C4—1461no—
270C22⋊C4—1461no—
271C22⋊C4—1461no—
272C22⋊C4—1461no—
273C22⋊C4C22⋊D7311yescharacteristic
274C22⋊C4C22⋊D7311yescharacteristic
275C42—21no—
276C42—1461no—
277C42—1461no—
278C42C22×D7311yescharacteristic
279C23—21no—
280C23—1461no—
281C23C2×C22⋊D7311yescharacteristic
282C23C2×C22⋊D7311yescharacteristic
283Q8—5841no—
284D4—21no—
285D4—21no—
286D4—41no—
287D4—42no—
288D4—81no—
289D4—5841no—
290D4—5841no—
291D4—1461no—
292D4—1461no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—81no—
301C2×C4—81no—
302C2×C4—2922no—
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×C4C23×D7311yescharacteristic
311C8—732no—
312C8—1461no—
313C8—1461no—
314C8—1461no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—21no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—2921no—
325C22—2921no—
326C22—2921no—
327C22C22×C22⋊D7311yescharacteristic
328C4—21no—
329C4—21no—
330C4—21no—
331C4—21no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—2921no—
336C4—2921no—
337C4—2921no—
338C4#41×D7311yescharacteristic
339C4#1455663811yescharacteristic
340C2—41no—
341C2—41no—
342C2—81no—
343C2—5841no—
344C2#1798923611yescharacteristic
345C2#1798938511yescharacteristic
346C2#1798939011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#553×C73C2
socleC22×C73C22×D4
hypercenter#553D73
hypocenterC73#3347
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C4×D4 ◁ #553

Complements

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

NH ≅ G/Ntype
1. #17989302C2semidirect
2. #17988997C2semidirect
3. #17988911C2semidirect
4. #17988908C2semidirect
5. #17988908C2semidirect
6. #17988900C2semidirect
7. #17988884C2semidirect
8. #17988867C2semidirect
9. #17988838C2semidirect
10. #17988821C2semidirect
11. #17988697C2semidirect
12. #17988659C2semidirect
13. #17988627C2semidirect
14. #17988623C2semidirect
15. #553×C73C2semidirect
174. C73#3347semidirect
176. #553D73semidirect