Finite Group Databasebeta

← #22622018

Subgroups — #22622018

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#17989228C211yesmaximal, characteristic
3#17988948C211yesmaximal, characteristic, complemented
4#17988920C211yesmaximal, characteristic, complemented
5#17988902C211yesmaximal, characteristic, complemented
6#17988866C211yesmaximal, characteristic, complemented
7#17988836C211yesmaximal, characteristic, complemented
8#17988811C211yesmaximal, characteristic, complemented
9#17988748C211yesmaximal, characteristic, complemented
10#17988737C211yesmaximal, characteristic, complemented
11#17988690C211yesmaximal, characteristic, complemented
12#17988658C211yesmaximal, characteristic, complemented
13#17988587C211yesmaximal, characteristic, complemented
14C2×#14556513C211yesmaximal, characteristic, complemented
15#467×C73C211yesmaximal, characteristic, complemented
16C2×#11924029C2211yescharacteristic
17C22×D292C2211yescharacteristic
18C2×#11924015C2211yescharacteristic
19C2×#11924015C2211yescharacteristic
20C2×#11924011C2211yescharacteristic, complemented
21#14556590C2211yescharacteristic, complemented
22#14556581—21no—
23#14556580C2211yescharacteristic
24#14556576—21no—
25#14556571—21no—
26#14556568—21no—
27#14556567C2211yescharacteristic, complemented
28#14556566—21no—
29#14556566C2211yescharacteristic
30#14556561—21no—
31Q8×Dic73C2211yescharacteristic, complemented
32#14556553C2211yescharacteristic
33C4×C22⋊D73C2211yescharacteristic
34#14556551—21no—
35C2×C4⋊Dic73C2211yescharacteristic
36C4⋊C4×D73C2211yescharacteristic, complemented
37C22⋊C4×D73—21no—
38#14556524C2211yescharacteristic, complemented
39#14556524C2211yescharacteristic, complemented
40#14556520C2211yescharacteristic, complemented
41#14556515C2211yescharacteristic, complemented
42#14556515C2211yescharacteristic, complemented
43#14556513C2211yescharacteristic
44#14556513C2211yescharacteristic
45#14556513C2211yescharacteristic
46#14556513C2211yescharacteristic
47#14556511C2211yescharacteristic
48#14556511C2211yescharacteristic
49C22⋊#10596831C2211yescharacteristic
50#14556503C2211yescharacteristic, complemented
51#14556501C2211yescharacteristic, complemented
52C2×Q16×C73C2211yescharacteristic, complemented
53C22×C8×C73C2211yescharacteristic
54C22⋊Q8×C73C2211yescharacteristic
55C22⋊Q8×C73C2211yescharacteristic
56#107×C73C2211yescharacteristic, complemented
57#103×C73C2211yescharacteristic, complemented
58#103×C73C2211yescharacteristic, complemented
59C23×D73—21no—
60#11924029—22no—
61#11924029—41no—
62C2×Dic146—21no—
63C2×D292—22no—
64C2×D292—21no—
65C2×D292—21no—
66C2×D292—21no—
67C2×D292—41no—
68C2×D292C2311yescharacteristic
69C2×D292C2311yescharacteristic
70C2×C22⋊D73D411yescharacteristic
71C22×Dic73—21no—
72C2×C4×D73—21no—
73C2×C4×D73—21no—
74C2×C4×D73—21no—
75C2×C4×D73C2311yescharacteristic
76#11924015—22no—
77#11924015—41no—
78#11924011—41no—
79C2×#10596831C2311yescharacteristic
80C2×#10596831C2311yescharacteristic
81C4⋊Dic73—21no—
82C4⋊Dic73—21no—
83C4⋊Dic73C2311yescharacteristic
84C4⋊Dic73C2311yescharacteristic
85#11924007—21no—
86#11924007—21no—
87#11924007—21no—
88#11924007D411yescharacteristic
89C22⋊Dic73D411yescharacteristic
90#11924005—21no—
91#11924005—21no—
92#11924005—21no—
93#11924005—21no—
94#11924005—21no—
95#11924005D411yescharacteristic
96C4×Dic73—21no—
97C4×Dic73C2311yescharacteristic
98C2×Q8×C73C2311yescharacteristic
99C2×Q8×C73C2311yescharacteristic
100C22×C4×C73C2311yescharacteristic
101Q16×C73—41no—
102C2×C8×C73—41no—
103C2×C8×C73C2311yescharacteristic
104C2×C8×C73C2311yescharacteristic
105C4⋊C4×C73—21no—
106C4⋊C4×C73—21no—
107C4⋊C4×C73C2311yescharacteristic
108C4⋊C4×C73C2311yescharacteristic
109C22⋊C4×C73—21no—
110C22⋊C4×C73—21no—
111C23×C73C2×D411yescharacteristic
112C22×D73—21no—
113C22×D73—21no—
114C22×D73—42no—
115C22×D73—42no—
116C22×D73—81no—
117C22×D73C2×D411yescharacteristic
118Q8×C73—21no—
119Q8×C73—21no—
120Q8×C73—21no—
121Q8×C73—21no—
122C2×C4×C73—21no—
123C2×C4×C73—21no—
124C2×C4×C73—21no—
125C2×C4×C73—21no—
126C2×C4×C73—21no—
127C2×C4×C73—21no—
128C2×C4×C73C2×D411yescharacteristic
129C2×C4×C73C2411yescharacteristic
130C22⋊D73—22no—
131C2×Dic73—21no—
132C2×Dic73—21no—
133C2×Dic73—81no—
134C2×Dic73C2×D411yescharacteristic
135C2×Dic73C2×D411yescharacteristic
136C2×Dic73C2×D411yescharacteristic
137D292—21no—
138D292—21no—
139D292—21no—
140D292—42no—
141D292—42no—
142D292—81no—
143D292#4112yes—
144C4×D73—21no—
145C4×D73—21no—
146C4×D73—42no—
147C4×D73—81no—
148C4×D73—81no—
149Dic146—81no—
150C8×C73—21no—
151C8×C73—21no—
152#10596831—21no—
153#10596831—21no—
154C22×C73—21no—
155C22×C73—21no—
156C22×C73#13712yes—
157C22×C73C22×D411yescharacteristic
158C2×D73—21no—
159C2×D73—22no—
160C2×D73—21no—
161C2×D73—21no—
162C2×D73—41no—
163C2×D73—41no—
164C2×D73—41no—
165C2×D73—41no—
166C2×D73—41no—
167C2×D73—84no—
168C4×C73—21no—
169C4×C73—41no—
170C4×C73—41no—
171C4×C73—41no—
172C4×C73—41no—
173C4×C73C2×#4111yescharacteristic
174C4×C73H(5,𝔽2)11yescharacteristic
175Dic73—21no—
176Dic73—21no—
177Dic73—21no—
178Dic73—41no—
179Dic73—41no—
180C2×C73—22no—
181C2×C73#54611yescharacteristic
182C2×C73C2×#13711yescharacteristic
183C2×C73#57611yescharacteristic
184D73—41no—
185D73—42no—
186D73—81no—
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#467D7311yescharacteristic, complemented
197#464—731no—
198#452—731no—
199#450—731no—
200#440—731no—
201#435—731no—
202#417—731no—
203C2×#102—731no—
204C2×#41—731no—
205C22×D4—731no—
206C2×Q16C2×D7311yescharacteristic, complemented
207C2×SD16—731no—
208C2×SD16—731no—
209C2×M16—731no—
210C22×C8C2×D7311yescharacteristic
211C4⋊Q8—731no—
212#125—1461no—
213#124—731no—
214#123—1461no—
215C22⋊Q8—731no—
216C22⋊Q8—1461no—
217C22⋊Q8—1461no—
218C22⋊Q8C2×D7311yescharacteristic
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#107C2×D7311yescharacteristic, complemented
233C4⋊C8—731no—
234#103—731no—
235#103—731no—
236#103C2×D7311yescharacteristic, complemented
237#103C2×D7311yescharacteristic, complemented
238#102—731no—
239#102—731no—
240#102—731no—
241#102—731no—
242#102—731no—
243#102—731no—
244C22⋊C8—731no—
245C22⋊C8—731no—
246#97—731no—
247C24—1461no—
248#41—2921no—
249#41—1462no—
250C2×Q8—1461no—
251C2×Q8C22×D7311yescharacteristic
252C2×Q8C22×D7311yescharacteristic
253C2×D4—2921no—
254C2×D4—731no—
255C2×D4—731no—
256C2×D4—731no—
257C2×D4—1461no—
258C2×D4—1462no—
259C2×D4—1461no—
260C2×D4—1461no—
261C22×C4—731no—
262C22×C4—1461no—
263C22×C4—1461no—
264C22×C4—1461no—
265C22×C4—1461no—
266C22×C4C22×D7311yescharacteristic
267Q16—41no—
268SD16—2921no—
269SD16—1462no—
270M16—2921no—
271C2×C8—41no—
272C2×C8—731no—
273C2×C8—731no—
274C2×C8C22×D7311yescharacteristic
275C2×C8C22×D7311yescharacteristic
276C4⋊C4—21no—
277C4⋊C4—21no—
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⋊C4C22×D7311yescharacteristic
287C4⋊C4C22×D7311yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—21no—
290C22⋊C4—731no—
291C22⋊C4—731no—
292C22⋊C4—1461no—
293C22⋊C4—1461no—
294C22⋊C4—1461no—
295C22⋊C4—1461no—
296C22⋊C4—1461no—
297C42—731no—
298C42—1461no—
299C23—2922no—
300C23—2922no—
301C23—5841no—
302C23—731no—
303C23—1461no—
304C23—1461no—
305C23D4×D7311yescharacteristic
306Q8—21no—
307Q8—21no—
308Q8—21no—
309Q8—21no—
310Q8—5841no—
311D4—2922no—
312D4—2922no—
313D4—5841no—
314D4—732no—
315D4—1462no—
316D4—1461no—
317D4—1461no—
318D4—1461no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—2922no—
326C2×C4—5841no—
327C2×C4—5841no—
328C2×C4—5841no—
329C2×C4—731no—
330C2×C4—731no—
331C2×C4—731no—
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—2921no—
345C22—2921no—
346C22—2921no—
347C22—2921no—
348C22—2921no—
349C22—5844no—
350C22—1461no—
351C22—1461no—
352C22—1462no—
353C22—1461no—
354C22#1455662312yes—
355C22C2×D4×D7311yescharacteristic
356C4—21no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—41no—
361C4—2921no—
362C4—2921no—
363C4—1461no—
364C4—1461no—
365C4—1461no—
366C4#41×D7311yescharacteristic
367C4#1455663611yescharacteristic
368C2—22no—
369C2—2922no—
370C2—2921no—
371C2—5841no—
372C2#1798922611yescharacteristic
373C2C2×#1455662311yescharacteristic
374C2#1798938911yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#467×C73C2
socleC22×C73C22×D4
hypercenter#467D73
hypocenterC73#3314
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
1. #17989295C2semidirect
3. #17988948C2semidirect
4. #17988920C2semidirect
5. #17988902C2semidirect
6. #17988866C2semidirect
7. #17988836C2semidirect
8. #17988811C2semidirect
9. #17988748C2semidirect
10. #17988737C2semidirect
11. #17988690C2semidirect
12. #17988658C2semidirect
13. #17988587C2semidirect
14. C2×#14556513C2semidirect
15. #467×C73C2semidirect
20. C2×#11924011C22semidirect
21. #14556590C22semidirect
27. #14556567C22semidirect
31. Q8×Dic73C22semidirect
36. C4⋊C4×D73C22semidirect
38. #14556524C22semidirect
39. #14556524C22semidirect
40. #14556520C22semidirect
41. #14556515C22semidirect
42. #14556515C22semidirect
50. #14556503C22semidirect
51. #14556501C22semidirect
52. C2×Q16×C73C22semidirect
56. #107×C73C22semidirect
57. #103×C73C22semidirect
58. #103×C73C22semidirect
188. C73#3314semidirect
196. #467D73semidirect
206. C2×Q16C2×D73semidirect
232. #107C2×D73semidirect
236. #103C2×D73semidirect
237. #103C2×D73semidirect