Finite Group Databasebeta

← #22620177

Subgroups — #22620177

Order 9344.

394 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989197C211yesmaximal, characteristic, complemented
2#17989062C211yesmaximal, characteristic
3#17988929C211yesmaximal, characteristic, complemented
4#17988925C211yesmaximal, characteristic, complemented
5#17988889C211yesmaximal, characteristic, complemented
6#17988885C211yesmaximal, characteristic, complemented
7#17988790C211yesmaximal, characteristic, complemented
8#17988790C211yesmaximal, characteristic, complemented
9#17988738C211yesmaximal, characteristic
10#17988688C211yesmaximal, characteristic, complemented
11#17988684C211yesmaximal, characteristic, complemented
12#17988678C211yesmaximal, characteristic, complemented
13SD16×Dic73C211yesmaximal, characteristic, complemented
14#17988645C211yesmaximal, characteristic, complemented
15#450×C73C211yesmaximal, characteristic
16C2×#11924016C2211yescharacteristic
17C2×#11924016C2211yescharacteristic
18#14556589C2211yescharacteristic, complemented
19#14556584—21no—
20#14556584—21no—
21#14556582—21no—
22#14556582C2211yescharacteristic, complemented
23#14556581—21no—
24#14556570C2211yescharacteristic
25Q8×Dic73C2211yescharacteristic, complemented
26#14556556C2211yescharacteristic, complemented
27D4×Dic73—21no—
28D4×Dic73—21no—
29D4×Dic73C2211yescharacteristic
30D4×Dic73C2211yescharacteristic
31D4×Dic73C2211yescharacteristic
32D4×Dic73C2211yescharacteristic
33#14556550C2211yescharacteristic
34#14556550C2211yescharacteristic
35C2×C22⋊Dic73—21no—
36C2×C22⋊Dic73—21no—
37#14556525C2211yescharacteristic, complemented
38#14556524C2211yescharacteristic, complemented
39#14556523C2211yescharacteristic, complemented
40#14556522C2211yescharacteristic, complemented
41#14556520C2211yescharacteristic, complemented
42#14556520C2211yescharacteristic, complemented
43#14556516C2211yescharacteristic, complemented
44#14556516C2211yescharacteristic, complemented
45#14556515C2211yescharacteristic, complemented
46#14556515C2211yescharacteristic, complemented
47#14556512C2211yescharacteristic
48#14556512C2211yescharacteristic
49C22⋊#10596831C2211yescharacteristic
50#14556501C2211yescharacteristic, complemented
51C8×Dic73C2211yescharacteristic, complemented
52C22×D4×C73C2211yescharacteristic
53C2×SD16×C73C2211yescharacteristic
54C2×SD16×C73C2211yescharacteristic
55C22⋊Q8×C73C2211yescharacteristic
56#102×C73C2211yescharacteristic
57#102×C73C2211yescharacteristic
58C22⋊C8×C73C2211yescharacteristic
59C2×Dic146C2311yescharacteristic
60C22×Dic73—21no—
61C22×Dic73—21no—
62C22×Dic73—21no—
63C22×Dic73—21no—
64#11924016—22no—
65#11924016—22no—
66C2×#10596831C2311yescharacteristic
67C2×#10596831C2311yescharacteristic
68C4⋊Dic73—21no—
69C4⋊Dic73—21no—
70C4⋊Dic73D411yescharacteristic
71C4⋊Dic73D411yescharacteristic
72C4⋊Dic73C2311yescharacteristic
73C4⋊Dic73C2311yescharacteristic
74C4⋊Dic73C2311yescharacteristic
75#11924007—21no—
76#11924007—21no—
77#11924007—21no—
78#11924007—21no—
79#11924007—21no—
80C22⋊Dic73—21no—
81C22⋊Dic73—21no—
82C22⋊Dic73—21no—
83C22⋊Dic73—21no—
84C22⋊Dic73—21no—
85C22⋊Dic73—21no—
86C22⋊Dic73D411yescharacteristic
87C22⋊Dic73D411yescharacteristic
88C4×Dic73—21no—
89C4×Dic73—21no—
90C4×Dic73—21no—
91C4×Dic73C2311yescharacteristic
92C4×Dic73C2311yescharacteristic
93C24×C73—21no—
94C2×Q8×C73C2311yescharacteristic
95C2×D4×C73—22no—
96C2×D4×C73—22no—
97C2×D4×C73—21no—
98C2×D4×C73C2311yescharacteristic
99C2×D4×C73C2311yescharacteristic
100C22×C4×C73C2311yescharacteristic
101SD16×C73—22no—
102SD16×C73—22no—
103C2×C8×C73C2311yescharacteristic
104C2×C8×C73C2311yescharacteristic
105C4⋊C4×C73—21no—
106C4⋊C4×C73C2311yescharacteristic
107C22⋊C4×C73—21no—
108C23×C73—24no—
109C23×C73—21no—
110C23×C73—21no—
111C23×C73—81no—
112C23×C73—81no—
113C23×C73C2×D411yescharacteristic
114Q8×C73—21no—
115Q8×C73—21no—
116D4×C73—24no—
117D4×C73—21no—
118D4×C73—21no—
119D4×C73#4112yes—
120D4×C73#4112yes—
121C2×C4×C73—21no—
122C2×C4×C73—21no—
123C2×C4×C73—21no—
124C2×C4×C73—21no—
125C2×C4×C73C2×D411yescharacteristic
126C2×C4×C73C2411yescharacteristic
127C2×Dic73—21no—
128C2×Dic73—21no—
129C2×Dic73—21no—
130C2×Dic73—21no—
131C2×Dic73—81no—
132C2×Dic73—81no—
133C2×Dic73—81no—
134C2×Dic73—81no—
135C2×Dic73C2×D411yescharacteristic
136C2×Dic73C2×D411yescharacteristic
137C2×Dic73C2×D411yescharacteristic
138C2×Dic73C2×D411yescharacteristic
139Dic146—21no—
140Dic146—21no—
141C8×C73—21no—
142C8×C73—21no—
143#10596831—21no—
144#10596831—21no—
145C22×C73—21no—
146C22×C73—22no—
147C22×C73—22no—
148C22×C73—21no—
149C22×C73—21no—
150C22×C73—41no—
151C22×C73—41no—
152C22×C73—41no—
153C22×C73—41no—
154C22×C73—84no—
155C22×C73C22×D411yescharacteristic
156C4×C73—21no—
157C4×C73—41no—
158C4×C73—41no—
159C4×C73C2×#4111yescharacteristic
160C4×C73C2×#4111yescharacteristic
161Dic73—21no—
162Dic73—21no—
163Dic73—21no—
164Dic73—21no—
165Dic73—41no—
166Dic73—41no—
167Dic73—41no—
168Dic73—41no—
169C2×C73—41no—
170C2×C73—42no—
171C2×C73—42no—
172C2×C73#52511yescharacteristic
173C2×C73#57711yescharacteristic
174C2×C73#57711yescharacteristic
175#3123—731nomaximal, Sylow
176C73#312311yescharacteristic, complemented, Sylow
177#541—731no—
178#518—731no—
179#485—731no—
180#485—731no—
181#478—731no—
182#478—731no—
183#461—731no—
184#461—731no—
185#450—731no—
186#450D7311yescharacteristic
187#440—731no—
188#440—731no—
189C4×SD16—731no—
190C4×SD16—731no—
191#433—731no—
192C22×D4C2×D7311yescharacteristic
193C2×SD16—731no—
194C2×SD16—731no—
195C2×SD16C2×D7311yescharacteristic
196C2×SD16C2×D7311yescharacteristic
197C4⋊Q8—731no—
198#126—1461no—
199#126—1461no—
200#125—731no—
201#125—1461no—
202#125—1461no—
203C22⋊Q8—731no—
204C22⋊Q8C2×D7311yescharacteristic
205C4×Q8—731no—
206C4×Q8—731no—
207C4×D4—731no—
208C4×D4—731no—
209C4×D4—731no—
210C4×D4—731no—
211C4×D4—1461no—
212C4×D4—1461no—
213#117—731no—
214#117—731no—
215C2×C22⋊C4—1461no—
216C2×C22⋊C4—1461no—
217#107—731no—
218#107—731no—
219#106—731no—
220#106—731no—
221C4⋊C8—731no—
222C4⋊C8—731no—
223#103—731no—
224#103—731no—
225#103—731no—
226#103—731no—
227#102—731no—
228#102—731no—
229#102C2×D7311yescharacteristic
230#102C2×D7311yescharacteristic
231C22⋊C8—731no—
232C22⋊C8C2×D7311yescharacteristic
233#97—731no—
234C4×C8—731no—
235C24—21no—
236C2×Q8—731no—
237C2×Q8C22×D7311yescharacteristic
238C2×D4—22no—
239C2×D4—22no—
240C2×D4—21no—
241C2×D4C22×D7311yescharacteristic
242C2×D4C22×D7311yescharacteristic
243C22×C4—1461no—
244C22×C4—1461no—
245C22×C4—1461no—
246C22×C4—1461no—
247C22×C4C22×D7311yescharacteristic
248SD16—22no—
249SD16—22no—
250SD16—1462no—
251SD16—1462no—
252C2×C8—731no—
253C2×C8—731no—
254C2×C8C22×D7311yescharacteristic
255C2×C8C22×D7311yescharacteristic
256C4⋊C4—21no—
257C4⋊C4—731no—
258C4⋊C4—731no—
259C4⋊C4—731no—
260C4⋊C4—731no—
261C4⋊C4—731no—
262C4⋊C4—1461no—
263C4⋊C4—1461no—
264C4⋊C4—1461no—
265C4⋊C4—1461no—
266C4⋊C4—1461no—
267C4⋊C4—1461no—
268C4⋊C4—1461no—
269C4⋊C4C22×D7311yescharacteristic
270C22⋊C4—21no—
271C22⋊C4—731no—
272C22⋊C4—731no—
273C22⋊C4—1461no—
274C22⋊C4—1461no—
275C22⋊C4—1461no—
276C22⋊C4—1461no—
277C22⋊C4—1461no—
278C22⋊C4—1461no—
279C42—731no—
280C42—731no—
281C42—1461no—
282C42—1461no—
283C42—1461no—
284C23—24no—
285C23—21no—
286C23—21no—
287C23—81no—
288C23—81no—
289C23D4×D7311yescharacteristic
290Q8—21no—
291Q8—21no—
292Q8—1461no—
293Q8—1461no—
294D4—24no—
295D4—21no—
296D4—21no—
297D4#1192402712yes—
298D4#1192402712yes—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—5841no—
304C2×C4—5841no—
305C2×C4—5841no—
306C2×C4—5841no—
307C2×C4—731no—
308C2×C4—731no—
309C2×C4—731no—
310C2×C4—731no—
311C2×C4—1461no—
312C2×C4—1461no—
313C2×C4—1461no—
314C2×C4—1461no—
315C2×C4D4×D7311yescharacteristic
316C2×C4C23×D7311yescharacteristic
317C8—21no—
318C8—21no—
319C8—1461no—
320C8—1461no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—22no—
325C22—22no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—84no—
331C22C2×D4×D7311yescharacteristic
332C4—21no—
333C4—41no—
334C4—41no—
335C4—2921no—
336C4—2921no—
337C4—2921no—
338C4—2921no—
339C4—1461no—
340C4—1461no—
341C4—1461no—
342C4—1461no—
343C4C2×#1192402711yescharacteristic
344C4C2×#1192402711yescharacteristic
345C2—41no—
346C2—42no—
347C2—42no—
348C2#1798909311yescharacteristic
349C2#1798939311yescharacteristic
350C2#1798939711yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#450×C73C2
socleC22×C73C22×D4
hypercenter#450D73
hypocenterC73#3123
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #17989197C2semidirect
3. #17988929C2semidirect
4. #17988925C2semidirect
5. #17988889C2semidirect
6. #17988885C2semidirect
7. #17988790C2semidirect
8. #17988790C2semidirect
10. #17988688C2semidirect
11. #17988684C2semidirect
12. #17988678C2semidirect
13. SD16×Dic73C2semidirect
14. #17988645C2semidirect
18. #14556589C22semidirect
22. #14556582C22semidirect
25. Q8×Dic73C22semidirect
26. #14556556C22semidirect
37. #14556525C22semidirect
38. #14556524C22semidirect
39. #14556523C22semidirect
40. #14556522C22semidirect
41. #14556520C22semidirect
42. #14556520C22semidirect
43. #14556516C22semidirect
44. #14556516C22semidirect
45. #14556515C22semidirect
46. #14556515C22semidirect
50. #14556501C22semidirect
51. C8×Dic73C22semidirect
176. C73#3123semidirect