Finite Group Databasebeta

← #22622016

Subgroups — #22622016

Order 9344.

410 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989295C211yesmaximal, characteristic, complemented
2#17989231C211yesmaximal, characteristic
3#17988945C211yesmaximal, characteristic, complemented
4#17988923C211yesmaximal, characteristic, complemented
5#17988899C211yesmaximal, characteristic, complemented
6#17988865C211yesmaximal, characteristic, complemented
7#17988830C211yesmaximal, characteristic, complemented
8#17988826C211yesmaximal, characteristic, complemented
9#17988807C211yesmaximal, characteristic, complemented
10#17988746C211yesmaximal, characteristic, complemented
11#17988688C211yesmaximal, characteristic, complemented
12#17988655C211yesmaximal, characteristic, complemented
13#17988585C211yesmaximal, characteristic, complemented
14C2×#14556512C211yesmaximal, characteristic, complemented
15#450×C73C211yesmaximal, characteristic, complemented
16C2×#11924027C2211yescharacteristic
17C2×#11924018C2211yescharacteristic, complemented
18C2×#11924011C2211yescharacteristic, complemented
19C22×#10596831C2211yescharacteristic
20#14556590C2211yescharacteristic, complemented
21#14556581—21no—
22#14556578C2211yescharacteristic
23#14556572—21no—
24#14556571—21no—
25#14556570C2211yescharacteristic
26#14556568—21no—
27#14556567C2211yescharacteristic, complemented
28#14556563—21no—
29#14556562C2211yescharacteristic
30#14556560—21no—
31Q8×Dic73C2211yescharacteristic, complemented
32D4×Dic73C2211yescharacteristic
33C4×C22⋊D73C2211yescharacteristic
34#14556551—21no—
35C2×C4⋊Dic73C2211yescharacteristic
36C4⋊C4×D73C2211yescharacteristic, complemented
37C2×C22⋊Dic73—21no—
38#14556525C2211yescharacteristic, complemented
39#14556525C2211yescharacteristic, complemented
40#14556524C2211yescharacteristic, complemented
41#14556520C2211yescharacteristic, complemented
42#14556516C2211yescharacteristic, complemented
43#14556516C2211yescharacteristic, complemented
44#14556515C2211yescharacteristic, complemented
45#14556514C2211yescharacteristic, complemented
46#14556512C2211yescharacteristic
47#14556512C2211yescharacteristic
48#14556512C2211yescharacteristic
49#14556512C2211yescharacteristic
50#14556503C2211yescharacteristic, complemented
51#14556501C2211yescharacteristic, complemented
52C22×D4×C73C2211yescharacteristic
53C2×SD16×C73C2211yescharacteristic
54C2×SD16×C73C2211yescharacteristic
55C22⋊Q8×C73C2211yescharacteristic
56#102×C73C2211yescharacteristic
57#102×C73C2211yescharacteristic
58C22⋊C8×C73C2211yescharacteristic
59#11924027—22no—
60#11924027—41no—
61C2×Dic146—21no—
62C2×Dic146C2311yescharacteristic
63C2×C22⋊D73—21no—
64C2×C22⋊D73—21no—
65C2×C22⋊D73D411yescharacteristic
66C22×Dic73—21no—
67C22×Dic73—21no—
68C22×Dic73—21no—
69C2×C4×D73—21no—
70C2×C4×D73C2311yescharacteristic
71#11924018—41no—
72#11924011—41no—
73C2×#10596831—41no—
74C2×#10596831C2311yescharacteristic
75C2×#10596831C2311yescharacteristic
76C4⋊Dic73—21no—
77C4⋊Dic73—21no—
78C4⋊Dic73C2311yescharacteristic
79C4⋊Dic73C2311yescharacteristic
80C4⋊Dic73C2311yescharacteristic
81#11924007—21no—
82#11924007—21no—
83#11924007—21no—
84#11924007—21no—
85#11924007D411yescharacteristic
86C22⋊Dic73—21no—
87C22⋊Dic73—21no—
88C22⋊Dic73—21no—
89C22⋊Dic73—21no—
90C22⋊Dic73—21no—
91C22⋊Dic73D411yescharacteristic
92#11924005—21no—
93#11924005D411yescharacteristic
94C4×Dic73—21no—
95C4×Dic73C2311yescharacteristic
96C24×C73—21no—
97C2×Q8×C73C2311yescharacteristic
98C2×D4×C73—22no—
99C2×D4×C73—21no—
100C2×D4×C73—41no—
101C2×D4×C73C2311yescharacteristic
102C2×D4×C73C2311yescharacteristic
103C22×C4×C73C2311yescharacteristic
104SD16×C73—22no—
105SD16×C73—41no—
106C2×C8×C73C2311yescharacteristic
107C2×C8×C73C2311yescharacteristic
108C4⋊C4×C73—21no—
109C4⋊C4×C73C2311yescharacteristic
110C22⋊C4×C73—21no—
111C23×C73—21no—
112C23×C73—21no—
113C23×C73—42no—
114C23×C73—42no—
115C23×C73—81no—
116C23×C73C2×D411yescharacteristic
117C22×D73C2×D411yescharacteristic
118Q8×C73—21no—
119Q8×C73—21no—
120D4×C73—21no—
121D4×C73—21no—
122D4×C73—21no—
123D4×C73—42no—
124D4×C73#4112yes—
125C2×C4×C73—21no—
126C2×C4×C73—21no—
127C2×C4×C73—21no—
128C2×C4×C73—21no—
129C2×C4×C73C2×D411yescharacteristic
130C2×C4×C73C2411yescharacteristic
131C22⋊D73—22no—
132C22⋊D73—42no—
133C22⋊D73—81no—
134C2×Dic73—21no—
135C2×Dic73—21no—
136C2×Dic73—21no—
137C2×Dic73—21no—
138C2×Dic73—42no—
139C2×Dic73—81no—
140C2×Dic73—81no—
141C2×Dic73C2×D411yescharacteristic
142C2×Dic73C2×D411yescharacteristic
143C2×Dic73C2×D411yescharacteristic
144C4×D73—21no—
145C4×D73—21no—
146C4×D73—81no—
147Dic146—21no—
148Dic146—21no—
149Dic146—81no—
150C8×C73—21no—
151C8×C73—21no—
152#10596831—21no—
153#10596831—21no—
154C22×C73—21no—
155C22×C73—21no—
156C22×C73—22no—
157C22×C73—41no—
158C22×C73—41no—
159C22×C73—41no—
160C22×C73—41no—
161C22×C73—41no—
162C22×C73—84no—
163C22×C73#13712yes—
164C22×C73C22×D411yescharacteristic
165C2×D73—21no—
166C2×D73—21no—
167C2×D73—21no—
168C4×C73—21no—
169C4×C73—41no—
170C4×C73—41no—
171C4×C73C2×#4111yescharacteristic
172C4×C73H(5,𝔽2)11yescharacteristic
173Dic73—21no—
174Dic73—21no—
175Dic73—21no—
176Dic73—41no—
177Dic73—41no—
178Dic73—41no—
179Dic73—41no—
180C2×C73—22no—
181C2×C73—42no—
182C2×C73—81no—
183C2×C73#54611yescharacteristic
184C2×C73C2×#13711yescharacteristic
185C2×C73#57611yescharacteristic
186D73—41no—
187#3314—731nomaximal, Sylow
188C73#331411yescharacteristic, complemented, Sylow
189#554—731no—
190#546—731no—
191#489—731no—
192#484—731no—
193#480—731no—
194#474—731no—
195#468—731no—
196#467—731no—
197#464—731no—
198#452—731no—
199#450D7311yescharacteristic, complemented
200#440—731no—
201#435—731no—
202#417—731no—
203C2×#102—731no—
204C2×#41—731no—
205C22×D4C2×D7311yescharacteristic
206C2×Q16—731no—
207C2×SD16C2×D7311yescharacteristic
208C2×SD16C2×D7311yescharacteristic
209C2×M16—731no—
210C22×C8—731no—
211C4⋊Q8—731no—
212#125—1461no—
213#124—731no—
214#123—1461no—
215C22⋊Q8—731no—
216C22⋊Q8—731no—
217C22⋊Q8—1461no—
218C22⋊Q8—1461no—
219C22⋊Q8C2×D7311yescharacteristic
220#121—731no—
221#121—1461no—
222#120—1461no—
223C4×Q8—731no—
224C4×D4—731no—
225C4×D4—731no—
226C4×D4—1461no—
227C2×C4⋊C4—731no—
228C2×C4⋊C4—731no—
229C2×C22⋊C4—1461no—
230#107—731no—
231#107—731no—
232#107—731no—
233C4⋊C8—731no—
234#103—731no—
235#103—731no—
236#103—731no—
237#103—731no—
238#102—731no—
239#102—731no—
240#102—731no—
241#102—731no—
242#102C2×D7311yescharacteristic
243#102C2×D7311yescharacteristic
244C22⋊C8—731no—
245C22⋊C8C2×D7311yescharacteristic
246#97—731no—
247C24—21no—
248#41—2921no—
249#41—1462no—
250C2×Q8—731no—
251C2×Q8—1461no—
252C2×Q8C22×D7311yescharacteristic
253C2×D4—22no—
254C2×D4—21no—
255C2×D4—41no—
256C2×D4—731no—
257C2×D4—1461no—
258C2×D4—1461no—
259C2×D4C22×D7311yescharacteristic
260C2×D4C22×D7311yescharacteristic
261C22×C4—731no—
262C22×C4—1461no—
263C22×C4—1461no—
264C22×C4—1461no—
265C22×C4—1461no—
266C22×C4C22×D7311yescharacteristic
267Q16—2921no—
268SD16—22no—
269SD16—41no—
270M16—2921no—
271C2×C8—2921no—
272C2×C8—731no—
273C2×C8—731no—
274C2×C8C22×D7311yescharacteristic
275C2×C8C22×D7311yescharacteristic
276C4⋊C4—21no—
277C4⋊C4—731no—
278C4⋊C4—731no—
279C4⋊C4—731no—
280C4⋊C4—731no—
281C4⋊C4—1461no—
282C4⋊C4—1461no—
283C4⋊C4—1461no—
284C4⋊C4—1461no—
285C4⋊C4—1461no—
286C4⋊C4—1461no—
287C4⋊C4C22×D7311yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—731no—
290C22⋊C4—731no—
291C22⋊C4—1461no—
292C22⋊C4—1461no—
293C22⋊C4—1461no—
294C22⋊C4—1461no—
295C22⋊C4—1461no—
296C22⋊C4—1461no—
297C42—731no—
298C42—1461no—
299C23—21no—
300C23—21no—
301C23—42no—
302C23—42no—
303C23—81no—
304C23—731no—
305C23D4×D7311yescharacteristic
306Q8—21no—
307Q8—21no—
308Q8—5841no—
309Q8—1461no—
310Q8—1461no—
311D4—21no—
312D4—21no—
313D4—21no—
314D4—42no—
315D4—2922no—
316D4—5841no—
317D4—1462no—
318D4#1192402712yes—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—2922no—
324C2×C4—5841no—
325C2×C4—5841no—
326C2×C4—5841no—
327C2×C4—731no—
328C2×C4—731no—
329C2×C4—731no—
330C2×C4—1461no—
331C2×C4—1461no—
332C2×C4—1461no—
333C2×C4—1461no—
334C2×C4—1461no—
335C2×C4—1461no—
336C2×C4D4×D7311yescharacteristic
337C2×C4C23×D7311yescharacteristic
338C8—21no—
339C8—21no—
340C8—1461no—
341C8—1461no—
342C22—21no—
343C22—21no—
344C22—22no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—84no—
351C22—1461no—
352C22—1461no—
353C22—1461no—
354C22#1455662012yes—
355C22C2×D4×D7311yescharacteristic
356C4—21no—
357C4—41no—
358C4—41no—
359C4—2921no—
360C4—2921no—
361C4—2921no—
362C4—2921no—
363C4—1461no—
364C4—1461no—
365C4—1461no—
366C4C2×#1192402711yescharacteristic
367C4#1455663611yescharacteristic
368C2—22no—
369C2—42no—
370C2—81no—
371C2—2921no—
372C2#1798922411yescharacteristic
373C2C2×#1455662011yescharacteristic
374C2#1798939111yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#450×C73C2
socleC22×C73C22×D4
hypercenter#450D73
hypocenterC73#3314
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. #17989295C2semidirect
3. #17988945C2semidirect
4. #17988923C2semidirect
5. #17988899C2semidirect
6. #17988865C2semidirect
7. #17988830C2semidirect
8. #17988826C2semidirect
9. #17988807C2semidirect
10. #17988746C2semidirect
11. #17988688C2semidirect
12. #17988655C2semidirect
13. #17988585C2semidirect
14. C2×#14556512C2semidirect
15. #450×C73C2semidirect
17. C2×#11924018C22semidirect
18. C2×#11924011C22semidirect
20. #14556590C22semidirect
27. #14556567C22semidirect
31. Q8×Dic73C22semidirect
36. C4⋊C4×D73C22semidirect
38. #14556525C22semidirect
39. #14556525C22semidirect
40. #14556524C22semidirect
41. #14556520C22semidirect
42. #14556516C22semidirect
43. #14556516C22semidirect
44. #14556515C22semidirect
45. #14556514C22semidirect
50. #14556503C22semidirect
51. #14556501C22semidirect
188. C73#3314semidirect
199. #450D73semidirect