Finite Group Databasebeta

← #22621569

Subgroups — #22621569

Order 9344.

498 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556624C211yesmaximal, characteristic, complemented
2C2×#14556615C211yesmaximal, characteristic, complemented
3#17989243C211yesmaximal, characteristic, complemented
4#17989234C211yesmaximal, characteristic, complemented
5#17988970C211yesmaximal, characteristic, complemented
6#17988846C211yesmaximal, characteristic, complemented
7#17988808C211yesmaximal, characteristic, complemented
8#17988801C211yesmaximal, characteristic, complemented
9#17988750C211yesmaximal, characteristic, complemented
10#17988739C211yesmaximal, characteristic, complemented
11#17988730C211yesmaximal, characteristic, complemented
12#17988725C211yesmaximal, characteristic, complemented
13#17988674C211yesmaximal, characteristic, complemented
14#17988663C211yesmaximal, characteristic, complemented
15#469×C73C211yesmaximal, characteristic, complemented
16C2×#11924028C2211yescharacteristic
17C2×#11924027C2211yescharacteristic
18C22×Dic146C2211yescharacteristic, complemented
19C2×D4×D73C2211yescharacteristic
20#14556624—24no—
21#14556615—24no—
22C2×Dic292C2211yescharacteristic, complemented
23C2×Dic292C2211yescharacteristic, complemented
24C2×#11924017C2211yescharacteristic
25C2×#11924017C2211yescharacteristic
26C2×#11924016C2211yescharacteristic
27C2×#11924016C2211yescharacteristic
28C2×#11924016C2211yescharacteristic, complemented
29C2×#11924013C2211yescharacteristic
30C2×#11924011C2211yescharacteristic
31#14556578C2211yescharacteristic
32#14556578C2211yescharacteristic, complemented
33#14556577—21no—
34#14556573—21no—
35#14556571C2211yescharacteristic
36#14556571C2211yescharacteristic
37#14556568—21no—
38#14556563—21no—
39#14556562—21no—
40#14556559—21no—
41#14556556C2211yescharacteristic, complemented
42D4×Dic73—21no—
43#14556553C2211yescharacteristic
44C4×C22⋊D73C2211yescharacteristic
45C22⋊C4×D73—21no—
46#14556520C2211yescharacteristic, complemented
47#14556514C2211yescharacteristic, complemented
48#14556514C2211yescharacteristic, complemented
49#14556514C2211yescharacteristic, complemented
50#14556511C2211yescharacteristic
51C22⋊#10596831C2211yescharacteristic, complemented
52#14556503C2211yescharacteristic
53C8×Dic73C2211yescharacteristic, complemented
54C2×D8×C73C2211yescharacteristic
55C2×M16×C73C2211yescharacteristic, complemented
56#121×C73C2211yescharacteristic
57#121×C73C2211yescharacteristic, complemented
58#106×C73C2211yescharacteristic, complemented
59#102×C73C2211yescharacteristic
60#102×C73C2211yescharacteristic, complemented
61C23×D73—21no—
62#11924028—22no—
63#11924028—41no—
64#11924027—22no—
65#11924027—41no—
66C2×Dic146—22no—
67C2×Dic146—21no—
68C2×Dic146—41no—
69C2×Dic146C2311yescharacteristic
70C2×Dic146C2311yescharacteristic
71C2×Dic146C2311yescharacteristic
72C2×D292C2311yescharacteristic
73C2×C22⋊D73—21no—
74C2×C22⋊D73—21no—
75C2×C22⋊D73—21no—
76C2×C22⋊D73D411yescharacteristic
77D4×D73—22no—
78D4×D73—41no—
79C22×Dic73—21no—
80C22×Dic73—21no—
81C2×C4×D73—21no—
82C2×C4×D73—21no—
83C2×C4×D73C2311yescharacteristic
84Dic292—22no—
85Dic292—22no—
86#11924017—22no—
87#11924017D414yescomplemented
88#11924016—22no—
89#11924016—41no—
90#11924016—41no—
91#11924013—22no—
92#11924011—22no—
93C2×#10596831C2311yescharacteristic
94C2×#10596831C2311yescharacteristic
95C4⋊Dic73—21no—
96C4⋊Dic73—21no—
97#11924007—21no—
98#11924007D411yescharacteristic
99C22⋊Dic73—21no—
100C22⋊Dic73—21no—
101C22⋊Dic73—21no—
102C22⋊Dic73—21no—
103C22⋊Dic73D411yescharacteristic
104#11924005—21no—
105#11924005—21no—
106#11924005—21no—
107#11924005D411yescharacteristic
108C4×Dic73—21no—
109C4×Dic73C2311yescharacteristic
110C2×D4×C73—21no—
111C2×D4×C73—21no—
112C2×D4×C73C2311yescharacteristic
113C2×D4×C73C2311yescharacteristic
114C22×C4×C73C2311yescharacteristic
115D8×C73—22no—
116M16×C73—22no—
117C2×C8×C73C2311yescharacteristic
118C2×C8×C73C2311yescharacteristic
119C4⋊C4×C73C2311yescharacteristic
120C4⋊C4×C73C2311yescharacteristic
121C22⋊C4×C73—21no—
122C22⋊C4×C73—21no—
123C23×C73—21no—
124C23×C73—21no—
125C23×C73C2×D411yescharacteristic
126C22×D73—21no—
127C22×D73—42no—
128C22×D73—42no—
129C22×D73—81no—
130C22×D73C2×D411yescharacteristic
131D4×C73—21no—
132D4×C73—21no—
133D4×C73—21no—
134D4×C73—21no—
135D4×C73—42no—
136D4×C73—81no—
137C2×C4×C73—21no—
138C2×C4×C73—21no—
139C2×C4×C73—21no—
140C2×C4×C73—21no—
141C2×C4×C73C2×D411yescharacteristic
142C2×C4×C73C2411yescharacteristic
143C22⋊D73—41no—
144C22⋊D73—42no—
145C22⋊D73—42no—
146C22⋊D73—42no—
147C2×Dic73—21no—
148C2×Dic73—21no—
149C2×Dic73—21no—
150C2×Dic73—42no—
151C2×Dic73—42no—
152C2×Dic73C2×D411yescharacteristic
153C2×Dic73C2×D411yescharacteristic
154C2×Dic73C2×D411yescharacteristic
155D292—21no—
156D292C2×D412yes—
157C4×D73—21no—
158C4×D73—21no—
159C4×D73—42no—
160C4×D73—81no—
161Dic146—21no—
162Dic146—21no—
163Dic146—21no—
164Dic146—21no—
165Dic146—21no—
166Dic146—42no—
167Dic146C2×D412yes—
168C8×C73—21no—
169C8×C73C2×D412yes—
170#10596831—21no—
171#10596831—21no—
172C22×C73—21no—
173C22×C73—21no—
174C22×C73—21no—
175C22×C73—41no—
176C22×C73—41no—
177C22×C73—41no—
178C22×C73—41no—
179C22×C73—41no—
180C22×C73—41no—
181C22×C73C22×D411yescharacteristic
182C2×D73—21no—
183C2×D73—22no—
184C2×D73—21no—
185C2×D73—21no—
186C2×D73—41no—
187C2×D73—41no—
188C2×D73—84no—
189C4×C73—21no—
190C4×C73—41no—
191C4×C73—41no—
192C4×C73C22×D411yescharacteristic
193C4×C73H(5,𝔽2)11yescharacteristic
194Dic73—22no—
195Dic73—21no—
196Dic73—21no—
197Dic73—21no—
198Dic73—41no—
199Dic73—41no—
200C2×C73—41no—
201C2×C73—81no—
202C2×C73—81no—
203C2×C73D4211yescharacteristic
204C2×C73#57511yescharacteristic
205C2×C73#57711yescharacteristic
206D73—41no—
207D73—42no—
208#3275—731nomaximal, Sylow
209C73#327511yescharacteristic, complemented, Sylow
210C2×#137—731no—
211C2×AGL(1,ℤ/8)—731no—
212#548—731no—
213#546—731no—
214#495—731no—
215#470—731no—
216#469D7311yescharacteristic, complemented
217#464—731no—
218#463—731no—
219#452—731no—
220#450—731no—
221#449—731no—
222#448—731no—
223C4×SD16—731no—
224#436—731no—
225C2×#41—731no—
226C2×#41—731no—
227C22×Q8—731no—
228C22×D4—731no—
229#137—1464no—
230AGL(1,ℤ/8)—1464no—
231C2×Q16—731no—
232C2×Q16—731no—
233C2×SD16—731no—
234C2×SD16—731no—
235C2×SD16—731no—
236C2×SD16—731no—
237C2×SD16—731no—
238C2×D8—731no—
239C2×D8C2×D7311yescharacteristic
240C2×M16—731no—
241C2×M16C2×D7311yescharacteristic, complemented
242#124—731no—
243#124—731no—
244#124—1461no—
245#123—1461no—
246C22⋊Q8—731no—
247C22⋊Q8—731no—
248C22⋊Q8—1461no—
249#121—1461no—
250#121—1461no—
251#121C2×D7311yescharacteristic
252#121C2×D7311yescharacteristic, complemented
253#120—1461no—
254C4×Q8—731no—
255C4×D4—731no—
256C4×D4—731no—
257C4×D4—1461no—
258C2×C22⋊C4—1461no—
259#106C2×D7311yescharacteristic, complemented
260C4⋊C8—731no—
261#103—731no—
262#103—731no—
263#103—731no—
264#102—731no—
265#102C2×D7311yescharacteristic
266#102C2×D7311yescharacteristic, complemented
267C22⋊C8—731no—
268C22⋊C8—731no—
269C4×C8—731no—
270C24—1461no—
271#41—2921no—
272#41—2921no—
273#41—1462no—
274#41—1462no—
275C2×Q8—2921no—
276C2×Q8—731no—
277C2×Q8—731no—
278C2×Q8—731no—
279C2×Q8—1462no—
280C2×Q8—1461no—
281C2×D4—21no—
282C2×D4—21no—
283C2×D4—2921no—
284C2×D4—731no—
285C2×D4—731no—
286C2×D4—1461no—
287C2×D4—1462no—
288C2×D4—1461no—
289C2×D4—1461no—
290C2×D4C22×D7311yescharacteristic
291C2×D4C22×D7311yescharacteristic
292C22×C4—731no—
293C22×C4—1461no—
294C22×C4—1461no—
295C22×C4—1461no—
296C22×C4—1461no—
297C22×C4C22×D7311yescharacteristic
298Q16—1462no—
299Q16—1462no—
300SD16—2921no—
301SD16—2921no—
302SD16—734no—
303SD16—1462no—
304SD16—1462no—
305D8—22no—
306D8—1462no—
307M16—22no—
308M16—1462no—
309C2×C8—731no—
310C2×C8—731no—
311C2×C8C22×D7311yescharacteristic
312C2×C8C22×D7311yescharacteristic
313C4⋊C4—731no—
314C4⋊C4—1461no—
315C4⋊C4—1461no—
316C4⋊C4—1461no—
317C4⋊C4C22×D7311yescharacteristic
318C4⋊C4C22×D7311yescharacteristic
319C22⋊C4—21no—
320C22⋊C4—21no—
321C22⋊C4—731no—
322C22⋊C4—731no—
323C22⋊C4—1461no—
324C22⋊C4—1461no—
325C22⋊C4—1461no—
326C22⋊C4—1461no—
327C22⋊C4—1461no—
328C22⋊C4—1461no—
329C22⋊C4—1461no—
330C42—731no—
331C42—1461no—
332C23—21no—
333C23—21no—
334C23—2922no—
335C23—2922no—
336C23—5841no—
337C23—731no—
338C23—1461no—
339C23D4×D7311yescharacteristic
340Q8—2922no—
341Q8—732no—
342Q8—1461no—
343Q8—1461no—
344Q8—1461no—
345Q8—1461no—
346Q8—1461no—
347D4—21no—
348D4—21no—
349D4—21no—
350D4—21no—
351D4—42no—
352D4—81no—
353D4—2922no—
354D4—2921no—
355D4—2922no—
356D4—2922no—
357D4—732no—
358D4—1461no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—2922no—
364C2×C4—2922no—
365C2×C4—2922no—
366C2×C4—5841no—
367C2×C4—731no—
368C2×C4—731no—
369C2×C4—731no—
370C2×C4—1461no—
371C2×C4—1461no—
372C2×C4—1461no—
373C2×C4—1461no—
374C2×C4—1461no—
375C2×C4D4×D7311yescharacteristic
376C2×C4C23×D7311yescharacteristic
377C8—21no—
378C8—1461no—
379C8—1461no—
380C8D4×D7312yes—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—2921no—
391C22—2921no—
392C22—5844no—
393C22—1461no—
394C22—1461no—
395C22—1462no—
396C22—1461no—
397C22C2×D4×D7311yescharacteristic
398C4—21no—
399C4—41no—
400C4—41no—
401C4—2921no—
402C4—2921no—
403C4—1461no—
404C4—1461no—
405C4—1461no—
406C4—1462no—
407C4C2×D4×D7311yescharacteristic
408C4#1455663711yescharacteristic
409C2—41no—
410C2—81no—
411C2—81no—
412C2—2922no—
413C2—2921no—
414C2#1798922111yescharacteristic
415C2#1798938311yescharacteristic
416C2#1798939711yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#469×C73C2
socleC22×C73C22×D4
hypercenter#469D73
hypocenterC73#3275
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. C2×#14556624C2semidirect
2. C2×#14556615C2semidirect
3. #17989243C2semidirect
4. #17989234C2semidirect
5. #17988970C2semidirect
6. #17988846C2semidirect
7. #17988808C2semidirect
8. #17988801C2semidirect
9. #17988750C2semidirect
10. #17988739C2semidirect
11. #17988730C2semidirect
12. #17988725C2semidirect
13. #17988674C2semidirect
14. #17988663C2semidirect
15. #469×C73C2semidirect
18. C22×Dic146C22semidirect
22. C2×Dic292C22semidirect
23. C2×Dic292C22semidirect
28. C2×#11924016C22semidirect
32. #14556578C22semidirect
41. #14556556C22semidirect
46. #14556520C22semidirect
47. #14556514C22semidirect
48. #14556514C22semidirect
49. #14556514C22semidirect
51. C22⋊#10596831C22semidirect
53. C8×Dic73C22semidirect
55. C2×M16×C73C22semidirect
57. #121×C73C22semidirect
58. #106×C73C22semidirect
60. #102×C73C22semidirect
87. #11924017D4semidirect
209. C73#3275semidirect
216. #469D73semidirect
241. C2×M16C2×D73semidirect
252. #121C2×D73semidirect
259. #106C2×D73semidirect
266. #102C2×D73semidirect