Finite Group Databasebeta

← #29837626

Subgroups — #29837626

Order 15616.

488 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458223C211yesmaximal, characteristic, complemented
2#21458220C211yesmaximal, characteristic, complemented
3#21448095C211yesmaximal, characteristic, complemented
4#21448012C211yesmaximal, characteristic, complemented
5#21448009C211yesmaximal, characteristic, complemented
6#21448001C211yesmaximal, characteristic, complemented
7#21447998C211yesmaximal, characteristic, complemented
8#21447977C211yesmaximal, characteristic, complemented
9#21447921C211yesmaximal, characteristic, complemented
10#21447921C211yesmaximal, characteristic, complemented
11C4×#14519718C211yesmaximal, characteristic, complemented
12#21447650C211yesmaximal, characteristic, complemented
13#21447606C211yesmaximal, characteristic, complemented
14#21447604C211yesmaximal, characteristic, complemented
15C61×#2228C211yesmaximal, characteristic, complemented
16#16840465—21no—
17#16840462—21no—
18C2×#14519718C2211yescharacteristic
19C2×#14519716C2211yescharacteristic
20C2×#14519716C2211yescharacteristic
21#16840164C2211yescharacteristic
22#16840088—21no—
23#16840085—21no—
24#16840082—21no—
25#16840079—21no—
26#16840062—21no—
27#16840059—21no—
28#16839999C2211yescharacteristic
29#16839999C2211yescharacteristic
30#16839995C2211yescharacteristic
31#16839995C2211yescharacteristic
32C4×D488C2211yescharacteristic
33C8×D244C2211yescharacteristic
34#16839799C2211yescharacteristic
35#16839799C2211yescharacteristic
36#107×D61C2211yescharacteristic
37#107×D61C2211yescharacteristic
38#16839590C2211yescharacteristic
39#16839589C2211yescharacteristic
40#16839589C2211yescharacteristic
41#16839588C2211yescharacteristic
42#16839587C2211yescharacteristic
43#16839587C2211yescharacteristic
44#16839587C2211yescharacteristic
45#16839564C2211yescharacteristic
46#16839564C2211yescharacteristic
47#16839563C2211yescharacteristic
48#16839562C2211yescharacteristic
49#16839541C2211yescharacteristic
50#16839541C2211yescharacteristic
51C4×#11758185C2211yescharacteristic
52C61×#499C2211yescharacteristic
53C4×D8×C61C2211yescharacteristic
54C61×#367C2211yescharacteristic
55C61×#366C2211yescharacteristic
56C61×C4⋊C16C2211yescharacteristic
57C61×#357C2211yescharacteristic
58C61×#357C2211yescharacteristic
59C2×D488C2311yescharacteristic
60C2×C8×D61C2311yescharacteristic
61C2×C8×D61C2311yescharacteristic
62#14519772—41no—
63#14519770—41no—
64#14519769—21no—
65#14519762—41no—
66#14519760—41no—
67#14519752—21no—
68#14519752—21no—
69#14519752—41no—
70#14519750—41no—
71#14519748—21no—
72#14519748—21no—
73C4×D244—21no—
74C4×D244D411yescharacteristic
75#14519739—41no—
76C4×C22⋊D61—41no—
77#14519735—21no—
78#14519735—21no—
79C4⋊C4×D61—21no—
80C4⋊C4×D61—21no—
81#14519718—22no—
82#14519716—22no—
83#14519716—22no—
84C2×#11758185C2311yescharacteristic
85C2×#11758185C2311yescharacteristic
86#14519711C2311yescharacteristic
87#14519711C2311yescharacteristic
88#14519711C2311yescharacteristic
89#14519710—21no—
90#14519710—21no—
91#14519709—21no—
92#14519708—21no—
93#14519708—21no—
94C4⋊#92418D411yescharacteristic
95#14519699—21no—
96#14519698—21no—
97#14519698—21no—
98#14519697—21no—
99#14519697—21no—
100#14519689D411yescharacteristic
101#14519689D411yescharacteristic
102C2×D8×C61C2311yescharacteristic
103#125×C61—21no—
104C4×D4×C61—21no—
105C2×C16×C61C2311yescharacteristic
106C2×C16×C61C2311yescharacteristic
107#107×C61C2311yescharacteristic
108#107×C61C2311yescharacteristic
109#107×C61C2311yescharacteristic
110#106×C61—21no—
111#102×C61—21no—
112C4×C8×C61C2311yescharacteristic
113C2×D4×C61—21no—
114C22×C4×C61—41no—
115C2×C22⋊D61—41no—
116C2×C22⋊D61—41no—
117C2×D244—21no—
118C2×D244—41no—
119C2×D244—41no—
120C2×D244D811yescharacteristic
121C2×C4×D61—41no—
122C2×C4×D61—41no—
123C2×C4×D61—41no—
124C2×C4×D61C2×D411yescharacteristic
125C2×C4×D61C2×D411yescharacteristic
126D8×C61—21no—
127D8×C61—21no—
128C2×C8×C61C2×D411yescharacteristic
129C2×C8×C61C2411yescharacteristic
130C4⋊C4×C61—21no—
131C4⋊C4×C61—21no—
132C4⋊C4×C61—21no—
133C4⋊C4×C61—41no—
134C4⋊C4×C61—41no—
135C22⋊C4×C61—41no—
136C42×C61C2×D411yescharacteristic
137C22⋊Dic61—41no—
138C22⋊Dic61—41no—
139#11758198—41no—
140#11758198—41no—
141#11758198—41no—
142#11758198—41no—
143#11758198—41no—
144#11758198D811yescharacteristic
145#11758198D811yescharacteristic
146C4⋊Dic61—21no—
147C4⋊Dic61—21no—
148C4⋊Dic61—21no—
149C4⋊Dic61D811yescharacteristic
150#11758196—41no—
151#11758196—41no—
152#11758196—41no—
153#11758196—41no—
154C4×Dic61—41no—
155C4×Dic61—41no—
156C2×#92418C2×D411yescharacteristic
157C2×#92418C2×D411yescharacteristic
158D488—21no—
159D488—21no—
160C8×D61—21no—
161C8×D61—21no—
162C8×D61—21no—
163C8×D61—21no—
164C16×C61—21no—
165C16×C61—21no—
166#11758185—21no—
167#11758185#4112yes—
168C23×C61—41no—
169C22×D61—41no—
170C22×D61C2×D811yescharacteristic
171C22×D61C2×D811yescharacteristic
172D4×C61—41no—
173D4×C61—41no—
174C2×C4×C61—41no—
175C2×C4×C61—41no—
176C2×C4×C61—41no—
177C2×C4×C61—161no—
178C2×C4×C61C2×D811yescharacteristic
179C2×C4×C61C2×D811yescharacteristic
180C2×C4×C61C22×D411yescharacteristic
181C22⋊D61—82no—
182C22⋊D61—161no—
183C2×Dic61—41no—
184C2×Dic61—41no—
185C2×Dic61—41no—
186C2×Dic61C2×D811yescharacteristic
187C2×Dic61C2×D811yescharacteristic
188D244—41no—
189D244—41no—
190D244—41no—
191D244—82no—
192D244—161no—
193C4×D61—21no—
194C4×D61—21no—
195C4×D61—21no—
196C4×D61—21no—
197C4×D61—161no—
198C4×D61—161no—
199C4×D61—161no—
200C8×C61—21no—
201C8×C61C2×#4111yescharacteristic
202C8×C612−1+411yescharacteristic
203#92418—21no—
204#92418—21no—
205#33922—611nomaximal, Sylow
206C22×C61—81no—
207C22×C61—81no—
208C22×C61—81no—
209C22×C61C22×D811yescharacteristic
210C2×D61—21no—
211C2×D61—21no—
212C2×D61—21no—
213C2×D61—21no—
214C2×D61—21no—
215C2×D61—21no—
216C2×D61—81no—
217C2×D61—81no—
218C2×D61—81no—
219C4×C61—21no—
220C4×C61—21no—
221C4×C61—81no—
222C4×C61—81no—
223C4×C61—81no—
224C4×C61#54711yescharacteristic
225C4×C61#57811yescharacteristic
226Dic61—21no—
227Dic61—21no—
228Dic61—81no—
229Dic61—81no—
230Dic61—81no—
231#3339—611no—
232#3339—611no—
233#2253—611no—
234#2234—611no—
235#2234—611no—
236#2232—611no—
237#2232—611no—
238#2228—611no—
239#2228D6111yescharacteristic, complemented
240#2218—611no—
241#2218—611no—
242C4×D16—611no—
243#2169—611no—
244#2159—611no—
245#2159—611no—
246C2×C61—161no—
247C2×C61#333411yescharacteristic
248C2×C61#341411yescharacteristic
249C2×C61#341511yescharacteristic
250D61—41no—
251D61—41no—
252D61—161no—
253#553—1221no—
254#553—1221no—
255C2×D16—611no—
256C2×M32—611no—
257C2×M32—611no—
258#499—611no—
259#499C2×D6111yescharacteristic
260#482—1221no—
261#482—1221no—
262#481—1221no—
263#481—1221no—
264#478—1221no—
265#478—1221no—
266#466—611no—
267#466—611no—
268#466—611no—
269#466—611no—
270C4×D8—611no—
271C4×D8C2×D6111yescharacteristic
272C8×D4—611no—
273#427—611no—
274#427—611no—
275C2×#107—611no—
276C2×#107—611no—
277#367—611no—
278#367—611no—
279#367—611no—
280#367C2×D6111yescharacteristic
281#366—611no—
282#366—611no—
283#366—611no—
284#366—611no—
285#366C2×D6111yescharacteristic
286C4⋊C16C2×D6111yescharacteristic
287#357—611no—
288#357—611no—
289#357—611no—
290#357—611no—
291#357C2×D6111yescharacteristic
292#357C2×D6111yescharacteristic
293C22⋊C16—611no—
294C22⋊C16—611no—
295C4×C16—611no—
296C61#3392211yescharacteristic, complemented, Sylow
297C2×D8—611no—
298C2×D8C22×D6111yescharacteristic
299C22×C8—611no—
300C22×C8—611no—
301#126—2441no—
302#126—2441no—
303#125—21no—
304#125—1221no—
305#123—2441no—
306#123—2441no—
307#121—1221no—
308#121—1221no—
309#121—1221no—
310#121—1221no—
311#121—2441no—
312#121—2441no—
313C4×D4—21no—
314C4×D4—611no—
315C4×D4—1221no—
316C4×D4—2441no—
317C4×D4—2441no—
318#117—1221no—
319#117—1221no—
320C2×C4⋊C4—1221no—
321C2×C4⋊C4—1221no—
322D16—1222no—
323M32—1222no—
324M32—1222no—
325C2×C16—611no—
326C2×C16—611no—
327C2×C16C22×D6111yescharacteristic
328C2×C16C22×D6111yescharacteristic
329#107—611no—
330#107—611no—
331#107—611no—
332#107—1221no—
333#107—1221no—
334#107C22×D6111yescharacteristic
335#107C22×D6111yescharacteristic
336#107C22×D6111yescharacteristic
337#106—21no—
338#106—1221no—
339#106—1221no—
340#106—1221no—
341C4⋊C8—611no—
342#102—21no—
343#102—1221no—
344#102—1221no—
345#102—1221no—
346#102—1221no—
347#102—1221no—
348C22⋊C8—611no—
349C22⋊C8—611no—
350C4×C8C22×D6111yescharacteristic
351C2×D4—21no—
352C2×D4—611no—
353C2×D4—1221no—
354C2×D4—2441no—
355C2×D4—2441no—
356C2×D4—2441no—
357C2×D4—2441no—
358C22×C4—41no—
359C22×C4—611no—
360C22×C4—611no—
361C22×C4—2441no—
362C22×C4—2441no—
363C22×C4—2441no—
364D8—21no—
365D8—21no—
366D8—1221no—
367D8—1221no—
368C2×C8—611no—
369C2×C8—611no—
370C2×C8—1221no—
371C2×C8—1221no—
372C2×C8—1221no—
373C2×C8—1221no—
374C2×C8D4×D6111yescharacteristic
375C2×C8C23×D6111yescharacteristic
376C4⋊C4—21no—
377C4⋊C4—21no—
378C4⋊C4—21no—
379C4⋊C4—41no—
380C4⋊C4—41no—
381C4⋊C4—611no—
382C4⋊C4—1221no—
383C4⋊C4—1221no—
384C4⋊C4—1221no—
385C4⋊C4—2441no—
386C4⋊C4—2441no—
387C4⋊C4—2441no—
388C4⋊C4—2441no—
389C22⋊C4—41no—
390C22⋊C4—611no—
391C22⋊C4—611no—
392C22⋊C4—2441no—
393C22⋊C4—2441no—
394C22⋊C4—2441no—
395C22⋊C4—2441no—
396C22⋊C4—2441no—
397C22⋊C4—2441no—
398C22⋊C4—2441no—
399C42—2441no—
400C42—2441no—
401C42D4×D6111yescharacteristic
402C16—21no—
403C16—21no—
404C16—612no—
405C16—1221no—
406C23—41no—
407C23—611no—
408C23—611no—
409C23—2441no—
410D4—41no—
411D4—41no—
412D4—9761no—
413D4—9761no—
414D4—4882no—
415D4—4882no—
416D4—2441no—
417D4—2441no—
418D4—2441no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—161no—
423C2×C4—611no—
424C2×C4—611no—
425C2×C4—1221no—
426C2×C4—1221no—
427C2×C4—1221no—
428C2×C4—1221no—
429C2×C4—9761no—
430C2×C4—9761no—
431C2×C4—9761no—
432C2×C4—2441no—
433C2×C4—2441no—
434C2×C4—2441no—
435C2×C4D8×D6111yescharacteristic
436C2×C4D8×D6111yescharacteristic
437C2×C4C2×D4×D6111yescharacteristic
438C8—21no—
439C8—1221no—
440C8—1221no—
441C8#41×D6111yescharacteristic
442C8#1451982511yescharacteristic
443C22—81no—
444C22—81no—
445C22—81no—
446C22—1221no—
447C22—1221no—
448C22—1221no—
449C22—1221no—
450C22—1221no—
451C22—1221no—
452C22—4881no—
453C22—4881no—
454C22—4881no—
455C22C2×D8×D6111yescharacteristic
456C4—21no—
457C4—21no—
458C4—81no—
459C4—81no—
460C4—81no—
461C4—1221no—
462C4—1221no—
463C4—4881no—
464C4—4881no—
465C4—4881no—
466C4#1684041411yescharacteristic
467C4#1684057811yescharacteristic
468C2—161no—
469C2—9761no—
470C2—2441no—
471C2—2441no—
472C2#2145816511yescharacteristic
473C2#2145895211yescharacteristic
474C2#2145895911yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2228C2
socleC22×C61C22×D8
hypercenter#2228D61
hypocenterC61#33922
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2228

Complements

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

NH ≅ G/Ntype
1. #21458223C2semidirect
2. #21458220C2semidirect
3. #21448095C2semidirect
4. #21448012C2semidirect
5. #21448009C2semidirect
6. #21448001C2semidirect
7. #21447998C2semidirect
8. #21447977C2semidirect
9. #21447921C2semidirect
10. #21447921C2semidirect
11. C4×#14519718C2semidirect
12. #21447650C2semidirect
13. #21447606C2semidirect
14. #21447604C2semidirect
15. C61×#2228C2semidirect
239. #2228D61semidirect
296. C61#33922semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#214582232
#214582202
#214480952
#214480122
#214480092
#214480012
#214479982
#214479772
#214479212
C4×#145197182
#214476502
#214476062
#214476042
C61×#22282
#3392261