Finite Group Databasebeta

← #22620181

Subgroups — #22620181

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#17989198C211yesmaximal, characteristic, complemented
2#17989059C211yesmaximal, characteristic
3#17988927C211yesmaximal, characteristic, complemented
4#17988926C211yesmaximal, characteristic, complemented
5#17988888C211yesmaximal, characteristic, complemented
6#17988887C211yesmaximal, characteristic, complemented
7#17988789C211yesmaximal, characteristic, complemented
8#17988736C211yesmaximal, characteristic
9#17988736C211yesmaximal, characteristic
10#17988690C211yesmaximal, characteristic, complemented
11#17988688C211yesmaximal, characteristic, complemented
12SD16×Dic73C211yesmaximal, characteristic, complemented
13#17988672C211yesmaximal, characteristic, complemented
14#17988647C211yesmaximal, characteristic, complemented
15#461×C73C211yesmaximal, characteristic, complemented
16C2×D4×D73C2211yescharacteristic
17C2×#11924015C2211yescharacteristic
18C2×#11924015C2211yescharacteristic
19#14556586—21no—
20#14556586—21no—
21#14556583C2211yescharacteristic, complemented
22#14556581—21no—
23#14556581—21no—
24#14556567C2211yescharacteristic
25#14556567C2211yescharacteristic
26Q8×Dic73C2211yescharacteristic, complemented
27Q8×Dic73C2211yescharacteristic, complemented
28C4×D292C2211yescharacteristic
29D4×Dic73C2211yescharacteristic
30#14556553C2211yescharacteristic
31C4×C22⋊D73—21no—
32#14556551—21no—
33#14556549C2211yescharacteristic
34#14556548C2211yescharacteristic
35C2×#11924005—21no—
36C22⋊C4×D73—21no—
37#14556525C2211yescharacteristic, complemented
38#14556524C2211yescharacteristic, complemented
39#14556523C2211yescharacteristic, complemented
40#14556522C2211yescharacteristic, complemented
41C4⋊#10596831C2211yescharacteristic, complemented
42#14556515C2211yescharacteristic, complemented
43#14556515C2211yescharacteristic, complemented
44#14556513C2211yescharacteristic
45#14556513C2211yescharacteristic
46#14556512C2211yescharacteristic
47#14556512C2211yescharacteristic
48#14556503C2211yescharacteristic
49#14556503C2211yescharacteristic
50#14556501C2211yescharacteristic, complemented
51C8×Dic73C2211yescharacteristic, complemented
52C2×SD16×C73C2211yescharacteristic
53C2×SD16×C73C2211yescharacteristic
54C4⋊Q8×C73C2211yescharacteristic, complemented
55C4×D4×C73C2211yescharacteristic
56C4⋊C8×C73C2211yescharacteristic, complemented
57#103×C73C2211yescharacteristic, complemented
58#103×C73C2211yescharacteristic, complemented
59C23×D73—21no—
60C2×D292C2311yescharacteristic
61C2×C22⋊D73—21no—
62D4×D73—22no—
63D4×D73—22no—
64C22×Dic73—21no—
65C2×C4×D73—21no—
66C2×C4×D73—21no—
67C2×C4×D73C2311yescharacteristic
68#11924015—22no—
69#11924015—22no—
70C2×#10596831C2311yescharacteristic
71C2×#10596831C2311yescharacteristic
72C4⋊Dic73—21no—
73C4⋊Dic73—21no—
74C4⋊Dic73C2311yescharacteristic
75C4⋊Dic73C2311yescharacteristic
76C4⋊Dic73C2311yescharacteristic
77#11924007—21no—
78#11924007—21no—
79#11924007—21no—
80#11924007—21no—
81#11924007D411yescharacteristic
82#11924007D411yescharacteristic
83C22⋊Dic73—21no—
84#11924005—21no—
85#11924005—21no—
86#11924005—21no—
87#11924005—21no—
88#11924005—21no—
89#11924005D411yescharacteristic
90#11924005D411yescharacteristic
91C4×Dic73—21no—
92C4×Dic73—21no—
93C4×Dic73—21no—
94C4×Dic73C2311yescharacteristic
95C2×Q8×C73C2311yescharacteristic
96C2×Q8×C73C2311yescharacteristic
97C2×D4×C73C2311yescharacteristic
98C22×C4×C73—21no—
99SD16×C73—22no—
100SD16×C73—22no—
101C2×C8×C73C2311yescharacteristic
102C2×C8×C73C2311yescharacteristic
103C4⋊C4×C73—21no—
104C4⋊C4×C73—21no—
105C4⋊C4×C73C2311yescharacteristic
106C22⋊C4×C73—21no—
107C42×C73C2311yescharacteristic
108C23×C73—21no—
109C22×D73—21no—
110C22×D73—24no—
111C22×D73—81no—
112C22×D73—81no—
113C22×D73C2×D411yescharacteristic
114Q8×C73—21no—
115Q8×C73—21no—
116Q8×C73—21no—
117Q8×C73—21no—
118D4×C73—21no—
119D4×C73#4112yes—
120C2×C4×C73—21no—
121C2×C4×C73—21no—
122C2×C4×C73—21no—
123C2×C4×C73—81no—
124C2×C4×C73C2×D411yescharacteristic
125C2×C4×C73C2×D411yescharacteristic
126C2×C4×C73C2411yescharacteristic
127C22⋊D73—24no—
128C2×Dic73—21no—
129C2×Dic73—21no—
130C2×Dic73—21no—
131C2×Dic73—81no—
132C2×Dic73C2×D411yescharacteristic
133C2×Dic73C2×D411yescharacteristic
134C2×Dic73C2×D411yescharacteristic
135D292—21no—
136D292#4112yes—
137C4×D73—21no—
138C4×D73—21no—
139C4×D73—81no—
140C4×D73—81no—
141C8×C73—21no—
142C8×C73—21no—
143#10596831—21no—
144#10596831—21no—
145C22×C73—22no—
146C22×C73—41no—
147C22×C73—41no—
148C22×C73C22×D411yescharacteristic
149C2×D73—21no—
150C2×D73—22no—
151C2×D73—21no—
152C2×D73—21no—
153C2×D73—41no—
154C2×D73—41no—
155C2×D73—84no—
156C4×C73—21no—
157C4×C73—21no—
158C4×C73—41no—
159C4×C73—41no—
160C4×C73—41no—
161C4×C73C2×#4111yescharacteristic
162C4×C73C2×#4111yescharacteristic
163Dic73—21no—
164Dic73—21no—
165Dic73—21no—
166Dic73—41no—
167Dic73—41no—
168Dic73—41no—
169C2×C73—42no—
170C2×C73#52511yescharacteristic
171C2×C73#57711yescharacteristic
172C2×C73#57711yescharacteristic
173D73—41no—
174D73—42no—
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#461D7311yescharacteristic, complemented
185#450—731no—
186#450—731no—
187#440—731no—
188#440—731no—
189C4×SD16—731no—
190C4×SD16—731no—
191#433—731no—
192C22×D4—731no—
193C2×SD16—731no—
194C2×SD16—731no—
195C2×SD16C2×D7311yescharacteristic
196C2×SD16C2×D7311yescharacteristic
197C4⋊Q8C2×D7311yescharacteristic, complemented
198#126—1461no—
199#126—1461no—
200#125—731no—
201#125—1461no—
202#125—1461no—
203C22⋊Q8—731no—
204C22⋊Q8—731no—
205C4×Q8—731no—
206C4×Q8—731no—
207C4×D4—731no—
208C4×D4—731no—
209C4×D4—731no—
210C4×D4—1461no—
211C4×D4—1461no—
212C4×D4C2×D7311yescharacteristic
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⋊C8C2×D7311yescharacteristic, complemented
223#103—731no—
224#103—731no—
225#103C2×D7311yescharacteristic, complemented
226#103C2×D7311yescharacteristic, complemented
227#102—731no—
228#102—731no—
229#102—731no—
230#102—731no—
231C22⋊C8—731no—
232C22⋊C8—731no—
233#97—731no—
234C4×C8—731no—
235C24—1461no—
236C2×Q8C22×D7311yescharacteristic
237C2×Q8C22×D7311yescharacteristic
238C2×D4—731no—
239C2×D4—1461no—
240C2×D4—1462no—
241C2×D4—1462no—
242C2×D4C22×D7311yescharacteristic
243C22×C4—21no—
244C22×C4—731no—
245C22×C4—1461no—
246C22×C4—1461no—
247C22×C4—1461no—
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—21no—
258C4⋊C4—731no—
259C4⋊C4—731no—
260C4⋊C4—731no—
261C4⋊C4—731no—
262C4⋊C4—731no—
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—1461no—
281C42—1461no—
282C42—1461no—
283C42C22×D7311yescharacteristic
284C23—21no—
285C23—5841no—
286C23—5841no—
287C23—731no—
288C23—1464no—
289C23—1461no—
290Q8—21no—
291Q8—21no—
292Q8—21no—
293Q8—21no—
294D4—21no—
295D4—732no—
296D4—1464no—
297D4—1461no—
298D4#1192402712yes—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—81no—
303C2×C4—5841no—
304C2×C4—5841no—
305C2×C4—5841no—
306C2×C4—731no—
307C2×C4—731no—
308C2×C4—731no—
309C2×C4—1461no—
310C2×C4—1461no—
311C2×C4—1461no—
312C2×C4—1461no—
313C2×C4—1461no—
314C2×C4D4×D7311yescharacteristic
315C2×C4D4×D7311yescharacteristic
316C2×C4C23×D7311yescharacteristic
317C8—21no—
318C8—21no—
319C8—1461no—
320C8—1461no—
321C22—22no—
322C22—41no—
323C22—41no—
324C22—2921no—
325C22—2921no—
326C22—5844no—
327C22—1461no—
328C22—1461no—
329C22—1461no—
330C22—1462no—
331C22C2×D4×D7311yescharacteristic
332C4—21no—
333C4—21no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—2921no—
338C4—2921no—
339C4—2921no—
340C4—1461no—
341C4—1461no—
342C4—1461no—
343C4#41×D7311yescharacteristic
344C4C2×#1192402711yescharacteristic
345C2—42no—
346C2—2922no—
347C2—2921no—
348C2#1798909711yescharacteristic
349C2#1798939311yescharacteristic
350C2#1798939611yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#461×C73C2
socleC22×C73C22×D4
hypercenter#461D73
hypocenterC73#3123
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. #17989198C2semidirect
3. #17988927C2semidirect
4. #17988926C2semidirect
5. #17988888C2semidirect
6. #17988887C2semidirect
7. #17988789C2semidirect
10. #17988690C2semidirect
11. #17988688C2semidirect
12. SD16×Dic73C2semidirect
13. #17988672C2semidirect
14. #17988647C2semidirect
15. #461×C73C2semidirect
21. #14556583C22semidirect
26. Q8×Dic73C22semidirect
27. Q8×Dic73C22semidirect
37. #14556525C22semidirect
38. #14556524C22semidirect
39. #14556523C22semidirect
40. #14556522C22semidirect
41. C4⋊#10596831C22semidirect
42. #14556515C22semidirect
43. #14556515C22semidirect
50. #14556501C22semidirect
51. C8×Dic73C22semidirect
54. C4⋊Q8×C73C22semidirect
56. C4⋊C8×C73C22semidirect
57. #103×C73C22semidirect
58. #103×C73C22semidirect
176. C73#3123semidirect
184. #461D73semidirect
197. C4⋊Q8C2×D73semidirect
222. C4⋊C8C2×D73semidirect
225. #103C2×D73semidirect
226. #103C2×D73semidirect