Finite Group Databasebeta

← #22621968

Subgroups — #22621968

Order 9344.

402 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989305C211yesmaximal, characteristic, complemented
2#17989231C211yesmaximal, characteristic
3#17988945C211yesmaximal, characteristic, complemented
4#17988928C211yesmaximal, characteristic, complemented
5#17988910C211yesmaximal, characteristic, complemented
6#17988875C211yesmaximal, characteristic, complemented
7#17988845C211yesmaximal, characteristic, complemented
8#17988815C211yesmaximal, characteristic, complemented
9#17988808C211yesmaximal, characteristic, complemented
10#17988750C211yesmaximal, characteristic, complemented
11#17988738C211yesmaximal, characteristic, complemented
12#17988684C211yesmaximal, characteristic, complemented
13#17988656C211yesmaximal, characteristic, complemented
14#17988580C211yesmaximal, characteristic, complemented
15#418×C73C211yesmaximal, characteristic, complemented
16C2×#11924027C2211yescharacteristic
17C2×Dic292C2211yescharacteristic, complemented
18C2×#11924016C2211yescharacteristic
19C2×#11924016C2211yescharacteristic
20C2×C8×D73C2211yescharacteristic, complemented
21#14556590C2211yescharacteristic, complemented
22#14556585—21no—
23#14556584—21no—
24#14556578C2211yescharacteristic
25#14556577—21no—
26#14556572—21no—
27#14556571C2211yescharacteristic, complemented
28#14556570C2211yescharacteristic
29#14556570C2211yescharacteristic
30#14556563—21no—
31#14556562C2211yescharacteristic
32#14556560—21no—
33C4×Dic146—21no—
34#14556556C2211yescharacteristic, complemented
35D4×Dic73C2211yescharacteristic
36C4×C22⋊D73C2211yescharacteristic
37#14556549C2211yescharacteristic, complemented
38C2×C22⋊Dic73—21no—
39#14556524C2211yescharacteristic, complemented
40#14556523C2211yescharacteristic, complemented
41#14556522C2211yescharacteristic, complemented
42#14556520C2211yescharacteristic, complemented
43#14556516C2211yescharacteristic, complemented
44#14556516C2211yescharacteristic, complemented
45#14556514C2211yescharacteristic, complemented
46#14556514C2211yescharacteristic, complemented
47#14556512C2211yescharacteristic
48#14556512C2211yescharacteristic
49C22⋊#10596831C2211yescharacteristic
50#14556503C2211yescharacteristic, complemented
51#14556501C2211yescharacteristic, complemented
52C22×D4×C73C2211yescharacteristic
53C2×M16×C73C2211yescharacteristic
54#117×C73C2211yescharacteristic
55#102×C73C2211yescharacteristic
56#102×C73C2211yescharacteristic
57#102×C73C2211yescharacteristic
58#102×C73C2211yescharacteristic
59#11924027—22no—
60#11924027—41no—
61C2×Dic146—21no—
62C2×Dic146C2311yescharacteristic
63C2×Dic146C2311yescharacteristic
64C2×C22⋊D73—21no—
65C2×C22⋊D73—21no—
66C2×C22⋊D73D411yescharacteristic
67C22×Dic73—21no—
68C22×Dic73—21no—
69C2×C4×D73C2311yescharacteristic
70Dic292—41no—
71#11924016—22no—
72#11924016—41no—
73C2×#10596831C2311yescharacteristic
74C2×#10596831C2311yescharacteristic
75C8×D73—41no—
76C4⋊Dic73—21no—
77C4⋊Dic73C2311yescharacteristic
78C4⋊Dic73C2311yescharacteristic
79#11924007—21no—
80#11924007—21no—
81#11924007—21no—
82#11924007—21no—
83#11924007D411yescharacteristic
84C22⋊Dic73—21no—
85C22⋊Dic73—21no—
86C22⋊Dic73—21no—
87C22⋊Dic73—21no—
88C22⋊Dic73—21no—
89C22⋊Dic73—21no—
90C22⋊Dic73D411yescharacteristic
91#11924005—21no—
92#11924005—21no—
93#11924005D411yescharacteristic
94C4×Dic73—21no—
95C4×Dic73—21no—
96C4×Dic73C2311yescharacteristic
97C24×C73—21no—
98C2×D4×C73—22no—
99C2×D4×C73—21no—
100C2×D4×C73—41no—
101C2×D4×C73C2311yescharacteristic
102C2×D4×C73C2311yescharacteristic
103C22×C4×C73C2311yescharacteristic
104M16×C73—41no—
105C2×C8×C73C2311yescharacteristic
106C2×C8×C73C2311yescharacteristic
107C4⋊C4×C73C2311yescharacteristic
108C4⋊C4×C73C2311yescharacteristic
109C22⋊C4×C73—21no—
110C42×C73—21no—
111C23×C73—21no—
112C23×C73—21no—
113C23×C73—42no—
114C23×C73—42no—
115C23×C73—81no—
116C23×C73C2×D411yescharacteristic
117C22×D73C2×D411yescharacteristic
118D4×C73—21no—
119D4×C73—21no—
120D4×C73—21no—
121D4×C73—42no—
122D4×C73#4112yes—
123C2×C4×C73—21no—
124C2×C4×C73—21no—
125C2×C4×C73—21no—
126C2×C4×C73—21no—
127C2×C4×C73C2×D411yescharacteristic
128C2×C4×C73C2411yescharacteristic
129C22⋊D73—41no—
130C22⋊D73—42no—
131C22⋊D73—81no—
132C2×Dic73—21no—
133C2×Dic73—21no—
134C2×Dic73—21no—
135C2×Dic73—21no—
136C2×Dic73—42no—
137C2×Dic73—81no—
138C2×Dic73C2×D411yescharacteristic
139C2×Dic73C2×D411yescharacteristic
140C2×Dic73C2×D411yescharacteristic
141C4×D73—21no—
142C4×D73—21no—
143Dic146—21no—
144Dic146—21no—
145Dic146—21no—
146Dic146—21no—
147Dic146—42no—
148C8×C73—21no—
149C8×C73—21no—
150#10596831—21no—
151#10596831—21no—
152C22×C73—22no—
153C22×C73—21no—
154C22×C73—21no—
155C22×C73—21no—
156C22×C73—41no—
157C22×C73—41no—
158C22×C73—41no—
159C22×C73—41no—
160C22×C73—41no—
161C22×C73—84no—
162C22×C73C22×D411yescharacteristic
163C2×D73—21no—
164C2×D73—21no—
165C2×D73—21no—
166C4×C73—21no—
167C4×C73—41no—
168C4×C73—41no—
169C4×C73C2×#4111yescharacteristic
170C4×C73H(5,𝔽2)11yescharacteristic
171Dic73—21no—
172Dic73—21no—
173Dic73—21no—
174Dic73—41no—
175Dic73—41no—
176Dic73—41no—
177Dic73—41no—
178C2×C73—41no—
179C2×C73—42no—
180C2×C73—81no—
181C2×C73#54611yescharacteristic
182C2×C73#57511yescharacteristic
183C2×C73#57711yescharacteristic
184D73—41no—
185#3311—731nomaximal, Sylow
186C73#331111yescharacteristic, complemented, Sylow
187#556—731no—
188#546—731no—
189#489—731no—
190#485—731no—
191#482—731no—
192#476—731no—
193#470—731no—
194#465—731no—
195#464—731no—
196#452—731no—
197#450—731no—
198#440—731no—
199#435—731no—
200#418D7311yescharacteristic, complemented
201#416—731no—
202C2×#41—731no—
203C22×D4C2×D7311yescharacteristic
204C2×Q16—731no—
205C2×SD16—731no—
206C2×SD16—731no—
207C2×M16C2×D7311yescharacteristic
208C22×C8—731no—
209C4⋊Q8—731no—
210#126—1461no—
211#126—1461no—
212#124—731no—
213#124—1461no—
214#123—1461no—
215C22⋊Q8—731no—
216C22⋊Q8—731no—
217C22⋊Q8—731no—
218#121—731no—
219#121—1461no—
220#120—1461no—
221C4×Q8—731no—
222C4×Q8—1461no—
223C4×D4—731no—
224C4×D4—731no—
225#117—731no—
226#117C2×D7311yescharacteristic
227C2×C22⋊C4—1461no—
228#107—731no—
229#106—731no—
230#106—731no—
231C4⋊C8—731no—
232#103—731no—
233#103—731no—
234#103—731no—
235#103—731no—
236#102—731no—
237#102—731no—
238#102C2×D7311yescharacteristic
239#102C2×D7311yescharacteristic
240#102C2×D7311yescharacteristic
241#102C2×D7311yescharacteristic
242C22⋊C8—731no—
243C22⋊C8—731no—
244#97—731no—
245C24—21no—
246#41—2921no—
247#41—1462no—
248C2×Q8—731no—
249C2×Q8—731no—
250C2×Q8—1461no—
251C2×D4—22no—
252C2×D4—21no—
253C2×D4—41no—
254C2×D4—731no—
255C2×D4—1461no—
256C2×D4—1461no—
257C2×D4C22×D7311yescharacteristic
258C2×D4C22×D7311yescharacteristic
259C22×C4—731no—
260C22×C4—1461no—
261C22×C4—1461no—
262C22×C4C22×D7311yescharacteristic
263Q16—2921no—
264SD16—2921no—
265SD16—1462no—
266M16—41no—
267C2×C8—2921no—
268C2×C8—731no—
269C2×C8—731no—
270C2×C8C22×D7311yescharacteristic
271C2×C8C22×D7311yescharacteristic
272C4⋊C4—731no—
273C4⋊C4—731no—
274C4⋊C4—731no—
275C4⋊C4—1461no—
276C4⋊C4—1461no—
277C4⋊C4—1461no—
278C4⋊C4—1461no—
279C4⋊C4—1461no—
280C4⋊C4C22×D7311yescharacteristic
281C4⋊C4C22×D7311yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—731no—
284C22⋊C4—731no—
285C22⋊C4—1461no—
286C22⋊C4—1461no—
287C22⋊C4—1461no—
288C22⋊C4—1461no—
289C22⋊C4—1461no—
290C22⋊C4—1461no—
291C22⋊C4—1461no—
292C22⋊C4—1461no—
293C42—21no—
294C42—731no—
295C42—1461no—
296C42—1461no—
297C23—21no—
298C23—21no—
299C23—42no—
300C23—42no—
301C23—81no—
302C23—731no—
303C23D4×D7311yescharacteristic
304Q8—2922no—
305Q8—1461no—
306Q8—1461no—
307Q8—1461no—
308Q8—1461no—
309D4—21no—
310D4—21no—
311D4—21no—
312D4—42no—
313D4—2922no—
314D4—2921no—
315D4—5841no—
316D4#1192402812yes—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—2922no—
322C2×C4—5841no—
323C2×C4—731no—
324C2×C4—731no—
325C2×C4—731no—
326C2×C4—1461no—
327C2×C4—1461no—
328C2×C4—1461no—
329C2×C4—1461no—
330C2×C4—1461no—
331C2×C4—1461no—
332C2×C4D4×D7311yescharacteristic
333C2×C4C23×D7311yescharacteristic
334C8—21no—
335C8—21no—
336C8—1461no—
337C8—1461no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—22no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—84no—
348C22—1461no—
349C22—1461no—
350C22—1461no—
351C22C2×D4×D7311yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—2921no—
356C4—2921no—
357C4—2921no—
358C4—2921no—
359C4—1461no—
360C4—1461no—
361C4—1461no—
362C4C2×#1192402811yescharacteristic
363C4#1455663611yescharacteristic
364C2—41no—
365C2—42no—
366C2—81no—
367C2—2921no—
368C2#1798922711yescharacteristic
369C2#1798938311yescharacteristic
370C2#1798939711yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#418×C73C2
socleC22×C73C22×D4
hypercenter#418D73
hypocenterC73#3311
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. #17989305C2semidirect
3. #17988945C2semidirect
4. #17988928C2semidirect
5. #17988910C2semidirect
6. #17988875C2semidirect
7. #17988845C2semidirect
8. #17988815C2semidirect
9. #17988808C2semidirect
10. #17988750C2semidirect
11. #17988738C2semidirect
12. #17988684C2semidirect
13. #17988656C2semidirect
14. #17988580C2semidirect
15. #418×C73C2semidirect
17. C2×Dic292C22semidirect
20. C2×C8×D73C22semidirect
21. #14556590C22semidirect
27. #14556571C22semidirect
34. #14556556C22semidirect
37. #14556549C22semidirect
39. #14556524C22semidirect
40. #14556523C22semidirect
41. #14556522C22semidirect
42. #14556520C22semidirect
43. #14556516C22semidirect
44. #14556516C22semidirect
45. #14556514C22semidirect
46. #14556514C22semidirect
50. #14556503C22semidirect
51. #14556501C22semidirect
186. C73#3311semidirect
200. #418D73semidirect