Finite Group Databasebeta

← #22620115

Subgroups — #22620115

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#17989208C211yesmaximal, characteristic, complemented
2#17988928C211yesmaximal, characteristic, complemented
3#17988911C211yesmaximal, characteristic, complemented
4#17988877C211yesmaximal, characteristic, complemented
5#17988867C211yesmaximal, characteristic, complemented
6#17988802C211yesmaximal, characteristic, complemented
7#17988802C211yesmaximal, characteristic, complemented
8#17988738C211yesmaximal, characteristic, complemented
9#17988721C211yesmaximal, characteristic
10#17988697C211yesmaximal, characteristic, complemented
11#17988687C211yesmaximal, characteristic, complemented
12C4×#11924016C211yesmaximal, characteristic, complemented
13C4×#11924013C211yesmaximal, characteristic, complemented
14#17988648C211yesmaximal, characteristic, complemented
15#518×C73C211yesmaximal, characteristic, complemented
16C2×#11924016C2211yescharacteristic
17C2×#11924016C2211yescharacteristic
18C2×#11924013C2211yescharacteristic
19C2×#11924013C2211yescharacteristic
20#14556591C2211yescharacteristic, complemented
21#14556586—21no—
22#14556579C2211yescharacteristic, complemented
23#14556577—21no—
24#14556573—21no—
25#14556570C2211yescharacteristic
26#14556569—21no—
27#14556565C2211yescharacteristic
28C4×Dic146C2211yescharacteristic, complemented
29C4×D292C2211yescharacteristic, complemented
30#14556524C2211yescharacteristic, complemented
31#14556524C2211yescharacteristic, complemented
32#14556522C2211yescharacteristic, complemented
33#14556522C2211yescharacteristic, complemented
34C4⋊#10596831C2211yescharacteristic, complemented
35C4⋊#10596831C2211yescharacteristic, complemented
36#14556514C2211yescharacteristic, complemented
37#14556514C2211yescharacteristic, complemented
38#14556512C2211yescharacteristic
39#14556512C2211yescharacteristic
40#14556512C2211yescharacteristic
41#14556512C2211yescharacteristic
42#14556511C2211yescharacteristic, complemented
43#14556511C2211yescharacteristic, complemented
44C22⋊#10596831C2211yescharacteristic
45C22⋊#10596831C2211yescharacteristic
46#14556502C2211yescharacteristic, complemented
47C4×#10596831C2211yescharacteristic, complemented
48C22×D4×C73C2211yescharacteristic
49C4×D4×C73—21no—
50C4×D4×C73—21no—
51C4×D4×C73C2211yescharacteristic
52C4×D4×C73C2211yescharacteristic
53C4×D4×C73C2211yescharacteristic
54C4×D4×C73C2211yescharacteristic
55#117×C73C2211yescharacteristic
56#117×C73C2211yescharacteristic
57C2×C22⋊C4×C73—21no—
58C2×C22⋊C4×C73—21no—
59C2×Dic146—21no—
60C2×Dic146C2311yescharacteristic
61C2×D292C2311yescharacteristic
62C2×C22⋊D73—21no—
63C2×C4×D73—21no—
64#11924016—22no—
65#11924016—22no—
66#11924013—22no—
67#11924013—22no—
68C2×#10596831C2311yescharacteristic
69C2×#10596831C2311yescharacteristic
70C2×#10596831C2311yescharacteristic
71C2×#10596831C2311yescharacteristic
72C4⋊Dic73—21no—
73C4⋊Dic73C2311yescharacteristic
74C4⋊Dic73C2311yescharacteristic
75#11924007—21no—
76#11924007—21no—
77C22⋊Dic73—21no—
78#11924005—21no—
79#11924005—21no—
80#11924005—21no—
81#11924005—21no—
82C4×Dic73—21no—
83C24×C73—21no—
84C2×D4×C73—22no—
85C2×D4×C73—22no—
86C2×D4×C73—21no—
87C2×D4×C73C2311yescharacteristic
88C2×D4×C73C2311yescharacteristic
89C22×C4×C73—21no—
90C22×C4×C73—21no—
91C22×C4×C73—21no—
92C22×C4×C73—21no—
93C22×C4×C73C2311yescharacteristic
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—24no—
109C23×C73—21no—
110C23×C73—21no—
111C23×C73—81no—
112C23×C73—81no—
113C23×C73C2×D411yescharacteristic
114C22×D73—21no—
115D4×C73—24no—
116D4×C73—21no—
117D4×C73—21no—
118D4×C73#4112yes—
119D4×C73#4112yes—
120C2×C4×C73—21no—
121C2×C4×C73—21no—
122C2×C4×C73—21no—
123C2×C4×C73—21no—
124C2×C4×C73—81no—
125C2×C4×C73—81no—
126C2×C4×C73—81no—
127C2×C4×C73—81no—
128C2×C4×C73C2×D411yescharacteristic
129C2×C4×C73C2×D411yescharacteristic
130C2×C4×C73C2×D411yescharacteristic
131C2×C4×C73C2×D411yescharacteristic
132C2×C4×C73C2×D411yescharacteristic
133C2×C4×C73C2411yescharacteristic
134C22⋊D73—81no—
135C2×Dic73—21no—
136C2×Dic73—21no—
137C2×Dic73—21no—
138D292—21no—
139D292—21no—
140C4×D73—81no—
141Dic146—21no—
142Dic146—21no—
143Dic146—81no—
144#10596831—21no—
145#10596831—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—21no—
164C4×C73—21no—
165C4×C73—21no—
166C4×C73—21no—
167C4×C73—41no—
168C4×C73—41no—
169C4×C73C2×#4111yescharacteristic
170C4×C73C2×#4111yescharacteristic
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#518D7311yescharacteristic, complemented
185#485—731no—
186#482—731no—
187#476—731no—
188#474—731no—
189#463—731no—
190#463—731no—
191#450—731no—
192#447—731no—
193#442—731no—
194#440—731no—
195C4×SD16—731no—
196C4×D8—731no—
197#433—731no—
198C22×D4C2×D7311yescharacteristic
199C2×SD16—731no—
200C2×SD16—731no—
201C2×D8—731no—
202C2×D8—731no—
203C4⋊Q8—731no—
204#126—1461no—
205#124—731no—
206#124—1461no—
207#123—1461no—
208C22⋊Q8—731no—
209C22⋊Q8—1461no—
210#121—731no—
211C4×Q8—731no—
212C4×D4—21no—
213C4×D4—21no—
214C4×D4—731no—
215C4×D4C2×D7311yescharacteristic
216C4×D4C2×D7311yescharacteristic
217C4×D4C2×D7311yescharacteristic
218C4×D4C2×D7311yescharacteristic
219#117C2×D7311yescharacteristic
220#117C2×D7311yescharacteristic
221C2×C22⋊C4—21no—
222C2×C22⋊C4—21no—
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#102—731no—
236#102—731no—
237C22⋊C8—731no—
238C22⋊C8—731no—
239#97—731no—
240C4×C8—731no—
241C24—21no—
242C2×Q8—731no—
243C2×Q8—1461no—
244C2×D4—22no—
245C2×D4—22no—
246C2×D4—21no—
247C2×D4—731no—
248C2×D4—1461no—
249C2×D4C22×D7311yescharacteristic
250C2×D4C22×D7311yescharacteristic
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—1461no—
256C22×C4C22×D7311yescharacteristic
257SD16—1462no—
258SD16—1462no—
259D8—1462no—
260D8—1462no—
261C2×C8—731no—
262C2×C8—731no—
263C2×C8—731no—
264C2×C8—731no—
265C4⋊C4—731no—
266C4⋊C4—731no—
267C4⋊C4—1461no—
268C4⋊C4—1461no—
269C4⋊C4—1461no—
270C4⋊C4C22⋊D7311yescharacteristic
271C4⋊C4C22⋊D7311yescharacteristic
272C4⋊C4C22×D7311yescharacteristic
273C4⋊C4C22×D7311yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—1461no—
280C22⋊C4—1461no—
281C22⋊C4—1461no—
282C22⋊C4—1461no—
283C22⋊C4—1461no—
284C22⋊C4C22⋊D7311yescharacteristic
285C22⋊C4C22⋊D7311yescharacteristic
286C42—21no—
287C42—1461no—
288C42C22×D7311yescharacteristic
289C42C22×D7311yescharacteristic
290C23—24no—
291C23—21no—
292C23—21no—
293C23—81no—
294C23—81no—
295C23—1461no—
296C23C2×C22⋊D7311yescharacteristic
297Q8—5841no—
298Q8—1461no—
299Q8—1461no—
300D4—24no—
301D4—21no—
302D4—21no—
303D4—5841no—
304D4—1461no—
305D4—1461no—
306D4#1192402812yes—
307D4#1192402812yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4—81no—
316C2×C4—5841no—
317C2×C4—1461no—
318C2×C4—1461no—
319C2×C4—1461no—
320C2×C4C2×C22⋊D7311yescharacteristic
321C2×C4C2×C22⋊D7311yescharacteristic
322C2×C4C2×C22⋊D7311yescharacteristic
323C2×C4C2×C22⋊D7311yescharacteristic
324C2×C4C2×C22⋊D7311yescharacteristic
325C2×C4C23×D7311yescharacteristic
326C8—1461no—
327C8—1461no—
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—
343C22C22×C22⋊D7311yescharacteristic
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—41no—
350C4—41no—
351C4—2921no—
352C4—2921no—
353C4—2921no—
354C4C2×#1192402811yescharacteristic
355C4C2×#1192402811yescharacteristic
356C2—41no—
357C2—42no—
358C2—42no—
359C2—5841no—
360C2#1798909811yescharacteristic
361C2#1798939011yescharacteristic
362C2#1798939811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#518×C73C2
socleC22×C73C22×D4
hypercenter#518D73
hypocenterC73#3118
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ #117 ◁ #518

Complements

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

NH ≅ G/Ntype
1. #17989208C2semidirect
2. #17988928C2semidirect
3. #17988911C2semidirect
4. #17988877C2semidirect
5. #17988867C2semidirect
6. #17988802C2semidirect
7. #17988802C2semidirect
8. #17988738C2semidirect
10. #17988697C2semidirect
11. #17988687C2semidirect
12. C4×#11924016C2semidirect
13. C4×#11924013C2semidirect
14. #17988648C2semidirect
15. #518×C73C2semidirect
20. #14556591C22semidirect
22. #14556579C22semidirect
28. C4×Dic146C22semidirect
29. C4×D292C22semidirect
30. #14556524C22semidirect
31. #14556524C22semidirect
32. #14556522C22semidirect
33. #14556522C22semidirect
34. C4⋊#10596831C22semidirect
35. C4⋊#10596831C22semidirect
36. #14556514C22semidirect
37. #14556514C22semidirect
42. #14556511C22semidirect
43. #14556511C22semidirect
46. #14556502C22semidirect
47. C4×#10596831C22semidirect
182. C73#3118semidirect
184. #518D73semidirect