Finite Group Databasebeta

← #22621568

Subgroups — #22621568

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×#14556620C211yesmaximal, characteristic, complemented
2C2×#14556615C211yesmaximal, characteristic, complemented
3#17989245C211yesmaximal, characteristic, complemented
4#17989232C211yesmaximal, characteristic, complemented
5#17988969C211yesmaximal, characteristic, complemented
6#17988844C211yesmaximal, characteristic, complemented
7#17988839C211yesmaximal, characteristic, complemented
8#17988810C211yesmaximal, characteristic, complemented
9#17988750C211yesmaximal, characteristic, complemented
10#17988736C211yesmaximal, characteristic, complemented
11#17988729C211yesmaximal, characteristic, complemented
12#17988727C211yesmaximal, characteristic, complemented
13C4×#11924016C211yesmaximal, characteristic, complemented
14#17988664C211yesmaximal, characteristic, complemented
15#463×C73C211yesmaximal, characteristic, complemented
16C2×#11924027C2211yescharacteristic
17C2×#11924027C2211yescharacteristic
18C2×Q8×D73C2211yescharacteristic, complemented
19C2×D4×D73C2211yescharacteristic
20#14556620—24no—
21#14556615—24no—
22C2×Dic292C2211yescharacteristic, complemented
23C2×#11924018C2211yescharacteristic, complemented
24C2×#11924017C2211yescharacteristic
25C2×#11924016C2211yescharacteristic
26C2×#11924016C2211yescharacteristic, complemented
27C2×#11924015C2211yescharacteristic
28C2×#11924013C2211yescharacteristic
29C2×#11924011C2211yescharacteristic
30C2×#11924011C2211yescharacteristic, complemented
31#14556579C2211yescharacteristic
32#14556577—21no—
33#14556575—21no—
34#14556571C2211yescharacteristic
35#14556568—21no—
36#14556567C2211yescharacteristic
37#14556566C2211yescharacteristic
38#14556565—21no—
39#14556564—21no—
40#14556562C2211yescharacteristic, complemented
41#14556561—21no—
42C4×Dic146C2211yescharacteristic, complemented
43C4×D292C2211yescharacteristic
44#14556551—21no—
45C2×#11924005—21no—
46#14556522C2211yescharacteristic, complemented
47#14556516C2211yescharacteristic, complemented
48#14556514C2211yescharacteristic, complemented
49#14556513C2211yescharacteristic
50#14556512C2211yescharacteristic
51#14556503C2211yescharacteristic
52#14556503C2211yescharacteristic, complemented
53C4×#10596831C2211yescharacteristic, complemented
54C2×SD16×C73C2211yescharacteristic
55C2×D8×C73C2211yescharacteristic
56#124×C73C2211yescharacteristic, complemented
57C4×D4×C73C2211yescharacteristic
58C4⋊C8×C73C2211yescharacteristic, complemented
59#103×C73C2211yescharacteristic, complemented
60#102×C73C2211yescharacteristic, complemented
61C23×D73—21no—
62#11924027—22no—
63#11924027—22no—
64#11924027—41no—
65#11924027—41no—
66C2×Dic146—21no—
67C2×Dic146C2311yescharacteristic
68C2×Dic146C2311yescharacteristic
69Q8×D73—22no—
70Q8×D73—41no—
71C2×D292—21no—
72C2×D292D411yescharacteristic
73C2×D292C2311yescharacteristic
74C2×C22⋊D73—21no—
75C2×C22⋊D73—21no—
76C2×C22⋊D73—21no—
77C2×C22⋊D73—21no—
78D4×D73—22no—
79D4×D73—41no—
80C22×Dic73—21no—
81C22×Dic73—21no—
82C2×C4×D73—21no—
83C2×C4×D73C2311yescharacteristic
84C2×C4×D73C2311yescharacteristic
85Dic292—22no—
86#11924018—22no—
87#11924017—22no—
88#11924016—41no—
89#11924016D414yescomplemented
90#11924015—41no—
91#11924013—22no—
92#11924011—22no—
93#11924011—22no—
94C2×#10596831C2311yescharacteristic
95C2×#10596831C2311yescharacteristic
96C4⋊Dic73—21no—
97C4⋊Dic73D411yescharacteristic
98C4⋊Dic73C2311yescharacteristic
99#11924007—21no—
100#11924007—21no—
101C22⋊Dic73—21no—
102#11924005—21no—
103#11924005—21no—
104#11924005—21no—
105#11924005—21no—
106#11924005—21no—
107#11924005D411yescharacteristic
108#11924005D411yescharacteristic
109C4×Dic73—21no—
110C2×Q8×C73C2311yescharacteristic
111C2×D4×C73C2311yescharacteristic
112C2×D4×C73C2311yescharacteristic
113C22×C4×C73—21no—
114SD16×C73—22no—
115D8×C73—22no—
116C2×C8×C73C2311yescharacteristic
117C2×C8×C73C2311yescharacteristic
118C4⋊C4×C73C2311yescharacteristic
119C22⋊C4×C73—21no—
120C22⋊C4×C73—21no—
121C22⋊C4×C73—21no—
122C42×C73C2311yescharacteristic
123C23×C73—21no—
124C23×C73—21no—
125C22×D73—21no—
126C22×D73—42no—
127C22×D73—42no—
128C22×D73—81no—
129C22×D73C2×D411yescharacteristic
130C22×D73C2×D411yescharacteristic
131Q8×C73—21no—
132Q8×C73—21no—
133D4×C73—21no—
134D4×C73—21no—
135D4×C73—21no—
136D4×C73C2×D412yes—
137C2×C4×C73—21no—
138C2×C4×C73—21no—
139C2×C4×C73—81no—
140C2×C4×C73C2×D411yescharacteristic
141C2×C4×C73C2×D411yescharacteristic
142C2×C4×C73C2411yescharacteristic
143C22⋊D73—42no—
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
154D292—21no—
155D292—21no—
156D292—41no—
157D292—81no—
158C4×D73—21no—
159C4×D73—21no—
160C4×D73—21no—
161C4×D73—21no—
162C4×D73—42no—
163Dic146—21no—
164Dic146—21no—
165Dic146—21no—
166Dic146—42no—
167Dic146C2×D412yes—
168C8×C73—21no—
169C8×C73—21no—
170#10596831—21no—
171#10596831C2×D412yes—
172C22×C73—22no—
173C22×C73—41no—
174C22×C73—41no—
175C22×C73—41no—
176C22×C73—41no—
177C22×C73—41no—
178C22×C73C22×D411yescharacteristic
179C2×D73—21no—
180C2×D73—21no—
181C2×D73—21no—
182C2×D73—21no—
183C2×D73—21no—
184C2×D73—21no—
185C2×D73—41no—
186C2×D73—41no—
187C2×D73—41no—
188C2×D73—84no—
189C4×C73—21no—
190C4×C73—21no—
191C4×C73—41no—
192C4×C73—41no—
193C4×C73C22×D411yescharacteristic
194C4×C73H(5,𝔽2)11yescharacteristic
195Dic73—22no—
196Dic73—21no—
197Dic73—21no—
198Dic73—41no—
199Dic73—41no—
200C2×C73—42no—
201C2×C73—81no—
202C2×C73D4211yescharacteristic
203C2×C73#57511yescharacteristic
204C2×C73#57711yescharacteristic
205D73—41no—
206D73—41no—
207D73—81no—
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#469—731no—
217#464—731no—
218#463D7311yescharacteristic, complemented
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×SD16C2×D7311yescharacteristic
238C2×D8—731no—
239C2×D8C2×D7311yescharacteristic
240C2×M16—731no—
241C2×M16—731no—
242#124—731no—
243#124—1461no—
244#124C2×D7311yescharacteristic, complemented
245#123—1461no—
246C22⋊Q8—731no—
247C22⋊Q8—731no—
248C22⋊Q8—1461no—
249#121—731no—
250#121—731no—
251#121—1461no—
252#121—1461no—
253#120—1461no—
254C4×Q8—731no—
255C4×D4—731no—
256C4×D4—1461no—
257C4×D4C2×D7311yescharacteristic
258C2×C22⋊C4—1461no—
259#106—731no—
260C4⋊C8C2×D7311yescharacteristic, complemented
261#103—731no—
262#103—731no—
263#103C2×D7311yescharacteristic, complemented
264#102—731no—
265#102—731no—
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—1461no—
279C2×Q8—1462no—
280C2×Q8C22×D7311yescharacteristic
281C2×D4—2921no—
282C2×D4—731no—
283C2×D4—731no—
284C2×D4—1461no—
285C2×D4—1461no—
286C2×D4—1461no—
287C2×D4—1461no—
288C2×D4—1461no—
289C2×D4—1462no—
290C2×D4C22×D7311yescharacteristic
291C2×D4C22×D7311yescharacteristic
292C22×C4—21no—
293C22×C4—731no—
294C22×C4—731no—
295C22×C4—1461no—
296C22×C4—1461no—
297C22×C4—1461no—
298Q16—1462no—
299Q16—1462no—
300SD16—22no—
301SD16—2921no—
302SD16—2921no—
303SD16—734no—
304SD16—1462no—
305D8—22no—
306D8—1462no—
307M16—1462no—
308M16—1462no—
309C2×C8—731no—
310C2×C8—731no—
311C2×C8C22×D7311yescharacteristic
312C2×C8C22×D7311yescharacteristic
313C4⋊C4—731no—
314C4⋊C4—731no—
315C4⋊C4—1461no—
316C4⋊C4—1461no—
317C4⋊C4—1461no—
318C4⋊C4C22×D7311yescharacteristic
319C22⋊C4—21no—
320C22⋊C4—21no—
321C22⋊C4—21no—
322C22⋊C4—731no—
323C22⋊C4—731no—
324C22⋊C4—1461no—
325C22⋊C4—1461no—
326C22⋊C4—1461no—
327C22⋊C4—1461no—
328C22⋊C4—1461no—
329C22⋊C4—1461no—
330C42—1461no—
331C42C22×D7311yescharacteristic
332C23—21no—
333C23—21no—
334C23—2922no—
335C23—2922no—
336C23—5841no—
337C23—731no—
338C23—731no—
339C23—1461no—
340Q8—21no—
341Q8—21no—
342Q8—2922no—
343Q8—732no—
344Q8—1461no—
345Q8—1461no—
346Q8—1461no—
347D4—21no—
348D4—21no—
349D4—21no—
350D4—2921no—
351D4—2922no—
352D4—2922no—
353D4—2922no—
354D4—2922no—
355D4—5841no—
356D4—1461no—
357D4—1461no—
358D4D4×D7312yes—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—81no—
362C2×C4—2922no—
363C2×C4—2922no—
364C2×C4—2922no—
365C2×C4—731no—
366C2×C4—731no—
367C2×C4—1461no—
368C2×C4—1461no—
369C2×C4—1461no—
370C2×C4—1461no—
371C2×C4—1461no—
372C2×C4—1461no—
373C2×C4—1461no—
374C2×C4D4×D7311yescharacteristic
375C2×C4D4×D7311yescharacteristic
376C2×C4C23×D7311yescharacteristic
377C8—21no—
378C8—21no—
379C8—732no—
380C8—1461no—
381C22—22no—
382C22—41no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—2921no—
388C22—2921no—
389C22—2921no—
390C22—5844no—
391C22—1461no—
392C22—1461no—
393C22—1461no—
394C22—1461no—
395C22—1461no—
396C22—1461no—
397C22C2×D4×D7311yescharacteristic
398C4—21no—
399C4—21no—
400C4—41no—
401C4—41no—
402C4—2921no—
403C4—2921no—
404C4—1461no—
405C4—1461no—
406C4—1462no—
407C4C2×D4×D7311yescharacteristic
408C4#1455663711yescharacteristic
409C2—42no—
410C2—81no—
411C2—2921no—
412C2—2921no—
413C2—5841no—
414C2#1798922111yescharacteristic
415C2#1798938411yescharacteristic
416C2#1798939711yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#463×C73C2
socleC22×C73C22×D4
hypercenter#463D73
hypocenterC73#3275
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
2. C2×#14556615C2semidirect
3. #17989245C2semidirect
4. #17989232C2semidirect
5. #17988969C2semidirect
6. #17988844C2semidirect
7. #17988839C2semidirect
8. #17988810C2semidirect
9. #17988750C2semidirect
10. #17988736C2semidirect
11. #17988729C2semidirect
12. #17988727C2semidirect
13. C4×#11924016C2semidirect
14. #17988664C2semidirect
15. #463×C73C2semidirect
18. C2×Q8×D73C22semidirect
22. C2×Dic292C22semidirect
23. C2×#11924018C22semidirect
26. C2×#11924016C22semidirect
30. C2×#11924011C22semidirect
40. #14556562C22semidirect
42. C4×Dic146C22semidirect
46. #14556522C22semidirect
47. #14556516C22semidirect
48. #14556514C22semidirect
52. #14556503C22semidirect
53. C4×#10596831C22semidirect
56. #124×C73C22semidirect
58. C4⋊C8×C73C22semidirect
59. #103×C73C22semidirect
60. #102×C73C22semidirect
89. #11924016D4semidirect
209. C73#3275semidirect
218. #463D73semidirect
244. #124C2×D73semidirect
260. C4⋊C8C2×D73semidirect
263. #103C2×D73semidirect
266. #102C2×D73semidirect