Finite Group Databasebeta

← #22620116

Subgroups — #22620116

Order 9344.

406 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989210C211yesmaximal, characteristic, complemented
2#17989062C211yesmaximal, characteristic, complemented
3#17988925C211yesmaximal, characteristic, complemented
4#17988912C211yesmaximal, characteristic, complemented
5#17988875C211yesmaximal, characteristic, complemented
6#17988865C211yesmaximal, characteristic, complemented
7#17988804C211yesmaximal, characteristic, complemented
8#17988804C211yesmaximal, characteristic, complemented
9#17988721C211yesmaximal, characteristic
10#17988696C211yesmaximal, characteristic, complemented
11#17988688C211yesmaximal, characteristic, complemented
12SD16×Dic73C211yesmaximal, characteristic, complemented
13#17988667C211yesmaximal, characteristic, complemented
14#17988645C211yesmaximal, characteristic, complemented
15#450×C73C211yesmaximal, characteristic, complemented
16C2×#11924013C2211yescharacteristic
17C2×#11924013C2211yescharacteristic
18#14556590C2211yescharacteristic, complemented
19#14556586—21no—
20#14556580C2211yescharacteristic, complemented
21#14556577—21no—
22#14556573—21no—
23#14556571—21no—
24#14556565C2211yescharacteristic
25Q8×Dic73C2211yescharacteristic, complemented
26D4×Dic73—21no—
27D4×Dic73—21no—
28D4×Dic73C2211yescharacteristic
29D4×Dic73C2211yescharacteristic
30D4×Dic73C2211yescharacteristic
31D4×Dic73C2211yescharacteristic
32#14556553C2211yescharacteristic, complemented
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#14556515C2211yescharacteristic, complemented
44#14556515C2211yescharacteristic, complemented
45#14556513C2211yescharacteristic, complemented
46#14556513C2211yescharacteristic, 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×Dic146—21no—
60C2×D292C2311yescharacteristic
61C2×C22⋊D73—21no—
62C22×Dic73—21no—
63C22×Dic73—21no—
64C22×Dic73—21no—
65C22×Dic73—21no—
66C2×C4×D73—21no—
67#11924013—22no—
68#11924013—22no—
69C2×#10596831C2311yescharacteristic
70C2×#10596831C2311yescharacteristic
71C4⋊Dic73—21no—
72C4⋊Dic73D411yescharacteristic
73C4⋊Dic73D411yescharacteristic
74C4⋊Dic73C2311yescharacteristic
75C4⋊Dic73C2311yescharacteristic
76C4⋊Dic73C2311yescharacteristic
77#11924007—21no—
78C22⋊Dic73—21no—
79C22⋊Dic73—21no—
80C22⋊Dic73—21no—
81C22⋊Dic73—21no—
82C22⋊Dic73—21no—
83C22⋊Dic73D411yescharacteristic
84C22⋊Dic73D411yescharacteristic
85#11924005—21no—
86#11924005—21no—
87#11924005—21no—
88#11924005—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
114C22×D73—21no—
115Q8×C73—21no—
116Q8×C73—21no—
117D4×C73—24no—
118D4×C73—21no—
119D4×C73—21no—
120D4×C73#4112yes—
121D4×C73#4112yes—
122C2×C4×C73—21no—
123C2×C4×C73—21no—
124C2×C4×C73—21no—
125C2×C4×C73—21no—
126C2×C4×C73C2×D411yescharacteristic
127C2×C4×C73C2411yescharacteristic
128C22⋊D73—81no—
129C2×Dic73—21no—
130C2×Dic73—21no—
131C2×Dic73—21no—
132C2×Dic73—81no—
133C2×Dic73—81no—
134C2×Dic73—81no—
135C2×Dic73—81no—
136C2×Dic73C2×D411yescharacteristic
137C2×Dic73C2×D411yescharacteristic
138C2×Dic73C2×D411yescharacteristic
139C2×Dic73C2×D411yescharacteristic
140D292—21no—
141D292—21no—
142C4×D73—81no—
143Dic146—81no—
144C8×C73—21no—
145C8×C73—21no—
146#10596831—21no—
147#10596831—21no—
148C22×C73—21no—
149C22×C73—22no—
150C22×C73—22no—
151C22×C73—21no—
152C22×C73—21no—
153C22×C73—41no—
154C22×C73—41no—
155C22×C73—41no—
156C22×C73—41no—
157C22×C73—84no—
158C22×C73C22×D411yescharacteristic
159C2×D73—41no—
160C2×D73—41no—
161C2×D73—41no—
162C4×C73—21no—
163C4×C73—41no—
164C4×C73—41no—
165C4×C73C2×#4111yescharacteristic
166C4×C73C2×#4111yescharacteristic
167Dic73—21no—
168Dic73—21no—
169Dic73—21no—
170Dic73—21no—
171Dic73—41no—
172Dic73—41no—
173Dic73—41no—
174C2×C73—41no—
175C2×C73—42no—
176C2×C73—42no—
177C2×C73#52511yescharacteristic
178C2×C73#57611yescharacteristic
179C2×C73#57711yescharacteristic
180D73—81no—
181#3118—731nomaximal, Sylow
182C73#311811yescharacteristic, complemented, Sylow
183#542—731no—
184#518—731no—
185#485—731no—
186#482—731no—
187#476—731no—
188#474—731no—
189#463—731no—
190#463—731no—
191#450D7311yescharacteristic, complemented
192#447—731no—
193#442—731no—
194#440—731no—
195C4×SD16—731no—
196C4×D8—731no—
197#433—731no—
198C22×D4C2×D7311yescharacteristic
199C2×SD16C2×D7311yescharacteristic
200C2×SD16C2×D7311yescharacteristic
201C2×D8—731no—
202C2×D8—731no—
203C4⋊Q8—731no—
204#126—1461no—
205#124—731no—
206#124—1461no—
207#123—1461no—
208C22⋊Q8—1461no—
209C22⋊Q8C2×D7311yescharacteristic
210#121—731no—
211C4×Q8—731no—
212C4×D4—731no—
213C4×D4—731no—
214C4×D4—731no—
215C4×D4—731no—
216C4×D4—731no—
217C4×D4—1461no—
218C4×D4—1461no—
219#117—731no—
220#117—731no—
221C2×C22⋊C4—1461no—
222C2×C22⋊C4—1461no—
223#107—731no—
224#107—731no—
225#106—731no—
226#106—731no—
227C4⋊C8—731no—
228C4⋊C8—731no—
229#103—731no—
230#103—731no—
231#102—731no—
232#102—731no—
233#102—731no—
234#102—731no—
235#102C2×D7311yescharacteristic
236#102C2×D7311yescharacteristic
237C22⋊C8—731no—
238C22⋊C8C2×D7311yescharacteristic
239#97—731no—
240C4×C8—731no—
241C24—21no—
242C2×Q8—1461no—
243C2×Q8C22×D7311yescharacteristic
244C2×D4—22no—
245C2×D4—22no—
246C2×D4—21no—
247C2×D4—731no—
248C2×D4—1461no—
249C2×D4C22×D7311yescharacteristic
250C2×D4C22×D7311yescharacteristic
251C22×C4—1461no—
252C22×C4—1461no—
253C22×C4—1461no—
254C22×C4—1461no—
255C22×C4—1461no—
256C22×C4C22×D7311yescharacteristic
257SD16—22no—
258SD16—22no—
259D8—1462no—
260D8—1462no—
261C2×C8—731no—
262C2×C8—731no—
263C2×C8C22×D7311yescharacteristic
264C2×C8C22×D7311yescharacteristic
265C4⋊C4—21no—
266C4⋊C4—731no—
267C4⋊C4—731no—
268C4⋊C4—731no—
269C4⋊C4—731no—
270C4⋊C4—731no—
271C4⋊C4—1461no—
272C4⋊C4—1461no—
273C4⋊C4C22×D7311yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—731no—
276C22⋊C4—731no—
277C22⋊C4—1461no—
278C22⋊C4—1461no—
279C22⋊C4—1461no—
280C22⋊C4—1461no—
281C22⋊C4—1461no—
282C22⋊C4—1461no—
283C22⋊C4—1461no—
284C22⋊C4—1461no—
285C22⋊C4—1461no—
286C42—731no—
287C42—731no—
288C42—1461no—
289C42—1461no—
290C23—24no—
291C23—21no—
292C23—21no—
293C23—81no—
294C23—81no—
295C23—1461no—
296C23D4×D7311yescharacteristic
297Q8—21no—
298Q8—21no—
299Q8—5841no—
300D4—24no—
301D4—21no—
302D4—21no—
303D4—5841no—
304D4—1461no—
305D4—1461no—
306D4#1192402712yes—
307D4#1192402712yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—5841no—
313C2×C4—5841no—
314C2×C4—5841no—
315C2×C4—5841no—
316C2×C4—5841no—
317C2×C4—731no—
318C2×C4—731no—
319C2×C4—731no—
320C2×C4—731no—
321C2×C4—1461no—
322C2×C4—1461no—
323C2×C4—1461no—
324C2×C4D4×D7311yescharacteristic
325C2×C4C23×D7311yescharacteristic
326C8—21no—
327C8—21no—
328C8—1461no—
329C8—1461no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—22no—
334C22—22no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—84no—
340C22—2921no—
341C22—2921no—
342C22—2921no—
343C22C2×D4×D7311yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—2921no—
348C4—2921no—
349C4—2921no—
350C4—1461no—
351C4—1461no—
352C4—1461no—
353C4—1461no—
354C4C2×#1192402711yescharacteristic
355C4C2×#1192402711yescharacteristic
356C2—41no—
357C2—42no—
358C2—42no—
359C2—5841no—
360C2#1798909311yescharacteristic
361C2#1798939111yescharacteristic
362C2#1798939311yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#450×C73C2
socleC22×C73C22×D4
hypercenter#450D73
hypocenterC73#3118
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. #17989210C2semidirect
2. #17989062C2semidirect
3. #17988925C2semidirect
4. #17988912C2semidirect
5. #17988875C2semidirect
6. #17988865C2semidirect
7. #17988804C2semidirect
8. #17988804C2semidirect
10. #17988696C2semidirect
11. #17988688C2semidirect
12. SD16×Dic73C2semidirect
13. #17988667C2semidirect
14. #17988645C2semidirect
15. #450×C73C2semidirect
18. #14556590C22semidirect
20. #14556580C22semidirect
25. Q8×Dic73C22semidirect
32. #14556553C22semidirect
37. #14556525C22semidirect
38. #14556524C22semidirect
39. #14556523C22semidirect
40. #14556522C22semidirect
41. #14556520C22semidirect
42. #14556520C22semidirect
43. #14556515C22semidirect
44. #14556515C22semidirect
45. #14556513C22semidirect
46. #14556513C22semidirect
50. #14556501C22semidirect
51. C8×Dic73C22semidirect
182. C73#3118semidirect
191. #450D73semidirect