Finite Group Databasebeta

← #22619420

Subgroups — #22619420

Order 9344.

500 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556620C211yesmaximal, characteristic, complemented
2C2×#14556615C211yesmaximal, characteristic
3#124×D73C211yesmaximal, characteristic, complemented
4C4×#11924027C211yesmaximal, characteristic, complemented
5#17988812C211yesmaximal, characteristic, complemented
6#17988810C211yesmaximal, characteristic, complemented
7#17988808C211yesmaximal, characteristic, complemented
8#17988806C211yesmaximal, characteristic, complemented
9#17988804C211yesmaximal, characteristic, complemented
10#17988802C211yesmaximal, characteristic, complemented
11#17988800C211yesmaximal, characteristic, complemented
12#17988609C211yesmaximal, characteristic, complemented
13#17988594C211yesmaximal, characteristic, complemented
14#17988590C211yesmaximal, characteristic, complemented
15#463×C73C211yesmaximal, characteristic, complemented
16C2×#11924027C2211yescharacteristic
17C2×Q8×D73C2211yescharacteristic
18C2×D4×D73C2211yescharacteristic
19#14556620—24no—
20#14556615—24no—
21C2×Dic292C2211yescharacteristic, complemented
22C2×#11924018C2211yescharacteristic, complemented
23C2×#11924017C2211yescharacteristic
24C2×#11924016C2211yescharacteristic
25C2×#11924016C2211yescharacteristic, complemented
26C2×#11924013C2211yescharacteristic
27C2×#11924011C2211yescharacteristic
28C2×#11924011C2211yescharacteristic
29#14556580C2211yescharacteristic
30#14556579C2211yescharacteristic
31#14556578C2211yescharacteristic
32#14556577—21no—
33#14556577—21no—
34C4×Dic146C2211yescharacteristic, complemented
35#14556556C2211yescharacteristic, complemented
36D4×Dic73C2211yescharacteristic, complemented
37C4×C22⋊D73—21no—
38#14556551—21no—
39#14556549C2211yescharacteristic
40#14556547—21no—
41C22⋊C4×D73—21no—
42C22⋊C4×D73—21no—
43C2×C4×Dic73—21no—
44C42×D73C2211yescharacteristic
45C4⋊#10596831C2211yescharacteristic, complemented
46#14556520C2211yescharacteristic, complemented
47#14556520C2211yescharacteristic, complemented
48#14556516C2211yescharacteristic, complemented
49#14556515C2211yescharacteristic, complemented
50#14556514C2211yescharacteristic, complemented
51#14556513C2211yescharacteristic
52#14556512C2211yescharacteristic
53#14556511C2211yescharacteristic
54C2×SD16×C73C2211yescharacteristic, complemented
55C2×D8×C73C2211yescharacteristic
56#124×C73C2211yescharacteristic
57C4×D4×C73C2211yescharacteristic, complemented
58C4⋊C8×C73C2211yescharacteristic, complemented
59#103×C73C2211yescharacteristic, complemented
60#102×C73C2211yescharacteristic
61C23×D73—21no—
62#11924027—22no—
63#11924027D414yes—
64C2×Dic146—21no—
65C2×Dic146C2311yescharacteristic
66C2×Dic146C2311yescharacteristic
67Q8×D73—22no—
68Q8×D73—22no—
69C2×D292C2311yescharacteristic
70C2×C22⋊D73—21no—
71C2×C22⋊D73—21no—
72D4×D73—22no—
73D4×D73—22no—
74C22×Dic73—21no—
75C22×Dic73—21no—
76C2×C4×D73—21no—
77C2×C4×D73D411yescharacteristic
78C2×C4×D73D411yescharacteristic
79C2×C4×D73C2311yescharacteristic
80Dic292—22no—
81#11924018—22no—
82#11924017—22no—
83#11924016—22no—
84#11924016—22no—
85#11924013—22no—
86#11924011—22no—
87#11924011—22no—
88C2×#10596831C2311yescharacteristic
89C2×#10596831C2311yescharacteristic
90C4⋊Dic73C2311yescharacteristic
91#11924007—21no—
92#11924007—21no—
93C22⋊Dic73—21no—
94C22⋊Dic73—21no—
95C22⋊Dic73—21no—
96#11924005—21no—
97#11924005—21no—
98#11924005—21no—
99#11924005—21no—
100#11924005—21no—
101C4×Dic73—21no—
102C4×Dic73—21no—
103C4×Dic73—21no—
104C4×Dic73D411yescharacteristic
105C4×Dic73D411yescharacteristic
106C4×Dic73C2311yescharacteristic
107C2×Q8×C73C2311yescharacteristic
108C2×D4×C73C2311yescharacteristic
109C2×D4×C73C2311yescharacteristic
110C22×C4×C73—21no—
111SD16×C73—22no—
112D8×C73—22no—
113C2×C8×C73C2311yescharacteristic
114C2×C8×C73C2311yescharacteristic
115C4⋊C4×C73C2311yescharacteristic
116C22⋊C4×C73—21no—
117C22⋊C4×C73—21no—
118C22⋊C4×C73—21no—
119C42×C73C2311yescharacteristic
120C23×C73—21no—
121C23×C73—21no—
122C22×D73—21no—
123C22×D73—42no—
124C22×D73—42no—
125C22×D73—42no—
126C22×D73C2×D411yescharacteristic
127Q8×C73—21no—
128Q8×C73—21no—
129D4×C73—21no—
130D4×C73—21no—
131D4×C73—21no—
132D4×C73C2×D412yes—
133C2×C4×C73—21no—
134C2×C4×C73—21no—
135C2×C4×C73—42no—
136C2×C4×C73C2×D411yescharacteristic
137C2×C4×C73C2×D411yescharacteristic
138C2×C4×C73C2411yescharacteristic
139C22⋊D73—24no—
140C22⋊D73—42no—
141C2×Dic73—21no—
142C2×Dic73—24no—
143C2×Dic73—21no—
144C2×Dic73—21no—
145C2×Dic73—42no—
146C2×Dic73C2×D411yescharacteristic
147C2×Dic73C2×D411yescharacteristic
148C2×Dic73C2×D411yescharacteristic
149D292—21no—
150D292—21no—
151C4×D73—41no—
152C4×D73—41no—
153C4×D73—42no—
154C4×D73C2×D412yes—
155C4×D73#4112yes—
156Dic146—21no—
157Dic146—21no—
158Dic146—21no—
159Dic146—42no—
160Dic146C2×D412yes—
161C8×C73—21no—
162C8×C73—21no—
163#10596831—21no—
164#10596831—21no—
165C22×C73—22no—
166C22×C73—41no—
167C22×C73—41no—
168C22×C73—41no—
169C22×C73—41no—
170C22×C73—41no—
171C22×C73C22×D411yescharacteristic
172C2×D73—21no—
173C2×D73—21no—
174C2×D73—41no—
175C2×D73—41no—
176C2×D73—41no—
177C2×D73—84no—
178C2×D73#12112yes—
179C4×C73—21no—
180C4×C73—21no—
181C4×C73—41no—
182C4×C73—41no—
183C4×C73C22×D411yescharacteristic
184C4×C73C2×#4111yescharacteristic
185Dic73—22no—
186Dic73—21no—
187Dic73—21no—
188Dic73—41no—
189Dic73—41no—
190Dic73#12112yes—
191C2×C73—42no—
192C2×C73—81no—
193C2×C73C2×#12111yescharacteristic
194C2×C73#57511yescharacteristic
195C2×C73#57511yescharacteristic
196D73—22no—
197D73—81no—
198#3040—731nomaximal, Sylow
199C73#304011yescharacteristic, complemented, Sylow
200C2×#137—731no—
201C2×AGL(1,ℤ/8)—731no—
202C2×#124—731no—
203C4×#41—731no—
204#464—731no—
205#464—731no—
206#464—731no—
207#464—731no—
208#463—731no—
209#463—731no—
210#463—731no—
211#463D7311yescharacteristic, complemented
212#423—731no—
213#419—731no—
214#418—731no—
215C2×#41—731no—
216C22×Q8—731no—
217C22×D4—731no—
218#137—1464no—
219AGL(1,ℤ/8)—1464no—
220C2×Q16—731no—
221C2×Q16—731no—
222C2×SD16—731no—
223C2×SD16—731no—
224C2×SD16—731no—
225C2×SD16C2×D7311yescharacteristic, complemented
226C2×D8—731no—
227C2×D8C2×D7311yescharacteristic
228C2×M16—731no—
229C2×M16—731no—
230#124—731no—
231#124—731no—
232#124—731no—
233#124—1461no—
234#124—1461no—
235#124C2×D7311yescharacteristic
236C4×Q8—731no—
237C4×Q8—731no—
238C4×D4—731no—
239C4×D4—1461no—
240C4×D4—1461no—
241C4×D4C2×D7311yescharacteristic, complemented
242#117—731no—
243#117—1461no—
244C2×C22⋊C4—1461no—
245C2×C22⋊C4—1461no—
246C2×C42—731no—
247C2×C42—1461no—
248C4⋊C8—731no—
249C4⋊C8—731no—
250C4⋊C8—731no—
251C4⋊C8C2×D7311yescharacteristic, complemented
252#103—731no—
253#103—731no—
254#103—731no—
255#103C2×D7311yescharacteristic, complemented
256#102—731no—
257#102—731no—
258#102—731no—
259#102C2×D7311yescharacteristic
260C24—1461no—
261#41—734no—
262#41—1462no—
263C2×Q8—731no—
264C2×Q8—731no—
265C2×Q8—1461no—
266C2×Q8—1462no—
267C2×Q8—1462no—
268C2×Q8C22×D7311yescharacteristic
269C2×D4—731no—
270C2×D4—1462no—
271C2×D4—1462no—
272C2×D4—1461no—
273C2×D4—1461no—
274C2×D4C22×D7311yescharacteristic
275C2×D4C22×D7311yescharacteristic
276C22×C4—21no—
277C22×C4—731no—
278C22×C4—731no—
279C22×C4—731no—
280C22×C4—1461no—
281C22×C4—1461no—
282C22×C4—1461no—
283Q16—1462no—
284Q16—1462no—
285SD16—22no—
286SD16—1462no—
287SD16—1462no—
288SD16—1462no—
289D8—22no—
290D8—1462no—
291M16—1462no—
292M16—1462no—
293C2×C8—731no—
294C2×C8—731no—
295C2×C8C22×D7311yescharacteristic
296C2×C8C22×D7311yescharacteristic
297C4⋊C4—731no—
298C4⋊C4—1461no—
299C4⋊C4—1461no—
300C4⋊C4C22×D7311yescharacteristic
301C22⋊C4—21no—
302C22⋊C4—21no—
303C22⋊C4—21no—
304C22⋊C4—1461no—
305C22⋊C4—1461no—
306C22⋊C4—1461no—
307C22⋊C4—1461no—
308C22⋊C4—1461no—
309C22⋊C4—1461no—
310C22⋊C4—1461no—
311C22⋊C4—1461no—
312C42—731no—
313C42—731no—
314C42—731no—
315C42—1461no—
316C42—1461no—
317C42—1461no—
318C42C22×D7311yescharacteristic
319C23—21no—
320C23—21no—
321C23—2922no—
322C23—2922no—
323C23—2922no—
324C23—731no—
325C23—1461no—
326Q8—21no—
327Q8—21no—
328Q8—2922no—
329Q8—732no—
330Q8—1461no—
331Q8—1461no—
332Q8—1461no—
333D4—21no—
334D4—21no—
335D4—21no—
336D4—2922no—
337D4—1464no—
338D4—1461no—
339D4—1461no—
340D4D4×D7312yes—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—42no—
344C2×C4—2921no—
345C2×C4—2921no—
346C2×C4—2922no—
347C2×C4—2922no—
348C2×C4—731no—
349C2×C4—732no—
350C2×C4—732no—
351C2×C4—731no—
352C2×C4—731no—
353C2×C4—1461no—
354C2×C4—1461no—
355C2×C4—1464no—
356C2×C4—1461no—
357C2×C4D4×D7311yescharacteristic
358C2×C4D4×D7311yescharacteristic
359C2×C4C23×D7311yescharacteristic
360C8—21no—
361C8—21no—
362C8—1461no—
363C8—1461no—
364C22—22no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—2921no—
371C22—2921no—
372C22—2921no—
373C22—5844no—
374C22—732no—
375C22—1461no—
376C22—1461no—
377C22C2×D4×D7311yescharacteristic
378C4—21no—
379C4—21no—
380C4—41no—
381C4—41no—
382C4—2921no—
383C4—2921no—
384C4—732no—
385C4—1461no—
386C4—1461no—
387C4—1462no—
388C4C2×D4×D7311yescharacteristic
389C4#41×D7311yescharacteristic
390C2—42no—
391C2—81no—
392C2—5841no—
393C2—1462no—
394C2#121×D7311yescharacteristic
395C2#1798938311yescharacteristic
396C2#1798938411yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#463×C73C2
socleC22×C73C22×D4
hypercenter#463D73
hypocenterC73#3040
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. C2×#14556620C2semidirect
3. #124×D73C2semidirect
4. C4×#11924027C2semidirect
5. #17988812C2semidirect
6. #17988810C2semidirect
7. #17988808C2semidirect
8. #17988806C2semidirect
9. #17988804C2semidirect
10. #17988802C2semidirect
11. #17988800C2semidirect
12. #17988609C2semidirect
13. #17988594C2semidirect
14. #17988590C2semidirect
15. #463×C73C2semidirect
21. C2×Dic292C22semidirect
22. C2×#11924018C22semidirect
25. C2×#11924016C22semidirect
34. C4×Dic146C22semidirect
35. #14556556C22semidirect
36. D4×Dic73C22semidirect
45. C4⋊#10596831C22semidirect
46. #14556520C22semidirect
47. #14556520C22semidirect
48. #14556516C22semidirect
49. #14556515C22semidirect
50. #14556514C22semidirect
54. C2×SD16×C73C22semidirect
57. C4×D4×C73C22semidirect
58. C4⋊C8×C73C22semidirect
59. #103×C73C22semidirect
199. C73#3040semidirect
211. #463D73semidirect
225. C2×SD16C2×D73semidirect
241. C4×D4C2×D73semidirect
251. C4⋊C8C2×D73semidirect
255. #103C2×D73semidirect