Finite Group Databasebeta

← #29837778

Subgroups — #29837778

Order 15616.

494 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#21458832C211yesmaximal, characteristic, complemented
2#21458687C211yesmaximal, characteristic, complemented
3#21448061C211yesmaximal, characteristic, complemented
4#21448056C211yesmaximal, characteristic, complemented
5#21448051C211yesmaximal, characteristic, complemented
6#21447984C211yesmaximal, characteristic, complemented
7#21447977C211yesmaximal, characteristic, complemented
8#21447957C211yesmaximal, characteristic, complemented
9#21447875C211yesmaximal, characteristic, complemented
10#21447875C211yesmaximal, characteristic, complemented
11#21447855C211yesmaximal, characteristic
12#21447696C211yesmaximal, characteristic, complemented
13#21447685C211yesmaximal, characteristic, complemented
14C4×D976C211yesmaximal, characteristic, complemented
15C61×#2183C211yesmaximal, characteristic, complemented
16#16840497—21no—
17#16840472—21no—
18C2×#14519722C2211yescharacteristic
19C2×D976C2211yescharacteristic
20C2×D976C2211yescharacteristic
21#16840167C2211yescharacteristic
22#16840164C2211yescharacteristic
23#16840164C2211yescharacteristic
24#16840146C2211yescharacteristic
25#16840146C2211yescharacteristic
26#16840139C2211yescharacteristic
27#16840063—21no—
28#16840063—21no—
29#16840053—21no—
30#16839978—21no—
31#16839978—21no—
32#16839963—21no—
33C4×Dic244C2211yescharacteristic
34C4×D488C2211yescharacteristic
35C4×D488C2211yescharacteristic
36C4×D488C2211yescharacteristic
37C4×D488C2211yescharacteristic
38C4×D488C2211yescharacteristic
39#16839590C2211yescharacteristic
40#16839588C2211yescharacteristic
41#16839588C2211yescharacteristic
42#16839567C2211yescharacteristic
43#16839567C2211yescharacteristic
44#16839567C2211yescharacteristic
45#16839564C2211yescharacteristic
46#16839564C2211yescharacteristic
47#16839564C2211yescharacteristic
48#16839564C2211yescharacteristic
49#16839564C2211yescharacteristic
50#16839564C2211yescharacteristic
51#16839564C2211yescharacteristic
52C8×Q8×C61C2211yescharacteristic
53C61×C4⋊C16C2211yescharacteristic
54C61×C4⋊C16C2211yescharacteristic
55C61×C4⋊C16C2211yescharacteristic
56C61×#346C2211yescharacteristic
57C61×#346C2211yescharacteristic
58C4×C16×C61C2211yescharacteristic
59C2×Dic244C2311yescharacteristic
60C2×#11758190—21no—
61C2×#11758190—21no—
62C2×D488—21no—
63C2×D488C2311yescharacteristic
64C2×D488C2311yescharacteristic
65C2×D488C2311yescharacteristic
66#14519777—21no—
67#14519774—21no—
68#14519769—21no—
69#14519769—21no—
70#14519766—41no—
71#14519765—21no—
72#14519765—21no—
73#14519762—41no—
74#14519762—41no—
75#14519755—41no—
76#14519755—41no—
77#14519753—41no—
78C4×Dic122—21no—
79C4×D244—21no—
80C4×D244—21no—
81C4×D244—21no—
82C4×D244—21no—
83C4×D244—21no—
84#14519739—41no—
85C4⋊C4×D61—41no—
86#14519722—22no—
87D976—22no—
88D976—22no—
89#14519711—21no—
90#14519711C2311yescharacteristic
91#14519711C2311yescharacteristic
92#14519711C2311yescharacteristic
93#14519711C2311yescharacteristic
94#14519709—21no—
95#14519709—21no—
96#14519702—21no—
97#14519699—21no—
98#14519699—21no—
99#14519699—21no—
100#14519699—21no—
101#14519699—21no—
102C4×Q8×C61D411yescharacteristic
103C2×C16×C61C2311yescharacteristic
104C2×C16×C61C2311yescharacteristic
105C2×C16×C61C2311yescharacteristic
106C2×C16×C61C2311yescharacteristic
107C4⋊C8×C61D411yescharacteristic
108C4⋊C8×C61D411yescharacteristic
109C4⋊C8×C61D411yescharacteristic
110C4×C8×C61C2311yescharacteristic
111C4×C8×C61C2311yescharacteristic
112C4×C8×C61C2311yescharacteristic
113C2×Q8×C61D811yescharacteristic
114C2×D244—21no—
115C2×D244—21no—
116C2×D244—21no—
117C2×D244—41no—
118C2×D244—41no—
119C2×C4×D61—41no—
120C2×C4×D61—41no—
121C2×C4×D61—41no—
122C2×C4×D61—41no—
123C2×C4×D61—41no—
124C2×Dic122—21no—
125C2×Dic122—41no—
126C2×C8×C61C2×D411yescharacteristic
127C2×C8×C61C2×D411yescharacteristic
128C2×C8×C61C2×D411yescharacteristic
129C2×C8×C61C2411yescharacteristic
130C4⋊C4×C61D811yescharacteristic
131C4⋊C4×C61D811yescharacteristic
132C4⋊C4×C61D811yescharacteristic
133C42×C61C2×D411yescharacteristic
134C42×C61C2×D411yescharacteristic
135C42×C61C2×D411yescharacteristic
136#11758198—41no—
137#11758198—41no—
138#11758198—41no—
139#11758198—41no—
140#11758198—41no—
141#11758198—41no—
142#11758198—41no—
143#11758198—41no—
144#11758198—41no—
145C4⋊Dic61—21no—
146C4⋊Dic61—21no—
147C4⋊Dic61—21no—
148C4⋊Dic61—21no—
149C4⋊Dic61—41no—
150#11758196—41no—
151#11758196—41no—
152#11758196—41no—
153#11758196—41no—
154#11758196—41no—
155C4×Dic61—41no—
156Dic244—21no—
157Dic244—21no—
158D488—21no—
159D488—21no—
160D488—21no—
161D488—21no—
162D488—21no—
163D488—81no—
164D488#4112yes—
165#11758190—81no—
166#11758190—81no—
167C16×C61—21no—
168C16×C61—21no—
169C16×C61—21no—
170C16×C61—21no—
171C22×D61—41no—
172C22×D61—41no—
173C22×D61—41no—
174Q8×C61—41no—
175C2×C4×C61C2×D811yescharacteristic
176C2×C4×C61C2×D811yescharacteristic
177C2×C4×C61C2×D811yescharacteristic
178C2×C4×C61C2×D811yescharacteristic
179C2×C4×C61C2×D811yescharacteristic
180C2×C4×C61C2×D811yescharacteristic
181C2×C4×C61C22×D411yescharacteristic
182C2×Dic61—41no—
183C2×Dic61—41no—
184C2×Dic61—41no—
185C2×Dic61—41no—
186C2×Dic61—41no—
187D244—22no—
188D244—41no—
189D244—41no—
190D244—41no—
191D244—41no—
192D244—41no—
193D244—82no—
194D244—161no—
195C4×D61—82no—
196C4×D61—161no—
197C4×D61—161no—
198C4×D61—161no—
199C4×D61—161no—
200Dic122—41no—
201Dic122—41no—
202Dic122—161no—
203C8×C61—21no—
204C8×C61—21no—
205C8×C61—21no—
206C8×C61C2×#4111yescharacteristic
207C8×C612−1+411yescharacteristic
208#33937—611nomaximal, Sylow
209C22×C61C22×D811yescharacteristic
210C2×D61—42no—
211C2×D61—81no—
212C2×D61—81no—
213C2×D61—81no—
214C2×D61—81no—
215C2×D61—81no—
216C2×D61—81no—
217C2×D61—81no—
218C2×D61—81no—
219C4×C61—21no—
220C4×C61—21no—
221C4×C61—21no—
222C4×C61—21no—
223C4×C61—21no—
224C4×C61—21no—
225C4×C61#54811yescharacteristic
226C4×C61#57711yescharacteristic
227Dic61—81no—
228Dic61—81no—
229Dic61—81no—
230Dic61—81no—
231Dic61—81no—
232#3396—611no—
233#3380—611no—
234#2244—611no—
235#2243—611no—
236#2242—611no—
237#2229—611no—
238#2228—611no—
239#2224—611no—
240#2210—611no—
241#2210—611no—
242#2206—611no—
243#2183D6111yescharacteristic, complemented
244#2177—611no—
245#2175—611no—
246C4×D16—611no—
247C2×C61#335811yescharacteristic
248C2×C61#341411yescharacteristic
249C2×C61#341511yescharacteristic
250D61—82no—
251D61—161no—
252D61—161no—
253#559—1221no—
254#554—1221no—
255C2×SD32—611no—
256C2×D16—611no—
257C2×D16—611no—
258#500—611no—
259#499—611no—
260#499—611no—
261#495—611no—
262#495—611no—
263#493—611no—
264#478—1221no—
265#478—1221no—
266#476—1221no—
267#463—1221no—
268#463—1221no—
269#460—1221no—
270C8×Q8C2×D6111yescharacteristic
271C4×Q16—611no—
272C4×D8—611no—
273C4×D8—611no—
274C4×D8—611no—
275C4×D8—611no—
276C4×D8—611no—
277#367—611no—
278#366—611no—
279#366—611no—
280C4⋊C16C2×D6111yescharacteristic
281C4⋊C16C2×D6111yescharacteristic
282C4⋊C16C2×D6111yescharacteristic
283#358—611no—
284#358—611no—
285#358—611no—
286#357—611no—
287#357—611no—
288#357—611no—
289#357—611no—
290#357—611no—
291#357—611no—
292#357—611no—
293#346C2×D6111yescharacteristic
294#346C2×D6111yescharacteristic
295C4×C16C2×D6111yescharacteristic
296C61#3393711yescharacteristic, complemented, Sylow
297C2×Q16—611no—
298C2×SD16—1221no—
299C2×SD16—1221no—
300C2×D8—611no—
301C2×D8—611no—
302C2×D8—611no—
303C2×D8—1221no—
304C4⋊Q8—1221no—
305#127—1221no—
306#125—1221no—
307#125—1221no—
308#124—1221no—
309#124—1221no—
310#124—2441no—
311#123—2441no—
312#123—2441no—
313C22⋊Q8—2441no—
314C22⋊Q8—2441no—
315C22⋊Q8—2441no—
316C4×Q8—1221no—
317C4×Q8D24411yescharacteristic
318C4×D4—1221no—
319C4×D4—1221no—
320C4×D4—1221no—
321C4×D4—1221no—
322C4×D4—1221no—
323C4×D4—2441no—
324C2×C4⋊C4—2441no—
325SD32—1222no—
326D16—1222no—
327D16—1222no—
328C2×C16C22×D6111yescharacteristic
329C2×C16C22×D6111yescharacteristic
330C2×C16C22×D6111yescharacteristic
331C2×C16C22×D6111yescharacteristic
332#107—611no—
333#107—611no—
334#107—611no—
335#107—611no—
336#107—1221no—
337#106—1221no—
338#106—1221no—
339C4⋊C8D24411yescharacteristic
340C4⋊C8D24411yescharacteristic
341C4⋊C8D24411yescharacteristic
342#103—1221no—
343#102—1221no—
344#102—1221no—
345#102—1221no—
346#102—1221no—
347#102—1221no—
348C4×C8C22×D6111yescharacteristic
349C4×C8C22×D6111yescharacteristic
350C4×C8C22×D6111yescharacteristic
351C2×Q8—1221no—
352C2×Q8—2441no—
353C2×Q8D48811yescharacteristic
354C2×D4—1221no—
355C2×D4—1221no—
356C2×D4—1221no—
357C2×D4—2441no—
358C2×D4—2441no—
359C22×C4—2441no—
360C22×C4—2441no—
361C22×C4—2441no—
362C22×C4—2441no—
363C22×C4—2441no—
364Q16—1221no—
365Q16—1221no—
366SD16—4881no—
367SD16—4881no—
368D8—612no—
369D8—1221no—
370D8—1221no—
371D8—1221no—
372D8—1221no—
373D8—1221no—
374D8—4881no—
375C2×C8C2×D24411yescharacteristic
376C2×C8C2×D24411yescharacteristic
377C2×C8C2×D24411yescharacteristic
378C2×C8C23×D6111yescharacteristic
379C4⋊C4—1221no—
380C4⋊C4—1221no—
381C4⋊C4—1221no—
382C4⋊C4—1221no—
383C4⋊C4—2441no—
384C4⋊C4—2441no—
385C4⋊C4—2441no—
386C4⋊C4—2441no—
387C4⋊C4—2441no—
388C4⋊C4—2441no—
389C4⋊C4D48811yescharacteristic
390C4⋊C4D48811yescharacteristic
391C4⋊C4D48811yescharacteristic
392C22⋊C4—2441no—
393C22⋊C4—2441no—
394C22⋊C4—2441no—
395C22⋊C4—2441no—
396C22⋊C4—2441no—
397C22⋊C4—2441no—
398C22⋊C4—2441no—
399C22⋊C4—2441no—
400C22⋊C4—2441no—
401C42—2441no—
402C42C2×D24411yescharacteristic
403C42C2×D24411yescharacteristic
404C42C2×D24411yescharacteristic
405C16—21no—
406C16—21no—
407C16—21no—
408C16—21no—
409C23—2441no—
410C23—2441no—
411C23—2441no—
412Q8—41no—
413Q8—9761no—
414Q8—2441no—
415Q8—2441no—
416D4—1222no—
417D4—9761no—
418D4—4882no—
419D4—2441no—
420D4—2441no—
421D4—2441no—
422D4—2441no—
423D4—2441no—
424C2×C4—9761no—
425C2×C4—9761no—
426C2×C4—9761no—
427C2×C4—9761no—
428C2×C4—4882no—
429C2×C4—2441no—
430C2×C4—2441no—
431C2×C4—2441no—
432C2×C4—2441no—
433C2×C4—2441no—
434C2×C4C2×D48811yescharacteristic
435C2×C4C2×D48811yescharacteristic
436C2×C4C2×D48811yescharacteristic
437C2×C4C2×D48811yescharacteristic
438C2×C4C2×D48811yescharacteristic
439C2×C4C2×D48811yescharacteristic
440C2×C4C22×D24411yescharacteristic
441C8—21no—
442C8—21no—
443C8—21no—
444C8#41×D6111yescharacteristic
445C8#1451982511yescharacteristic
446C22—4881no—
447C22—4881no—
448C22—4881no—
449C22—4881no—
450C22—4881no—
451C22—4881no—
452C22—4881no—
453C22—4881no—
454C22—2442no—
455C22C22×D48811yescharacteristic
456C4—21no—
457C4—21no—
458C4—21no—
459C4—21no—
460C4—21no—
461C4—21no—
462C4—4881no—
463C4—4881no—
464C4—4881no—
465C4—4881no—
466C4—4881no—
467C4#1684042411yescharacteristic
468C4#1684057411yescharacteristic
469C2—9761no—
470C2—9761no—
471C2—4882no—
472C2#2145845511yescharacteristic
473C2#2145895511yescharacteristic
474C2#2145896011yescharacteristic
subgroupG/H
centerC22C22×D488
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2183C2
socleC22×C61C22×D8
prime radical#21447855C2
hypercenter#2183D61
hypocenterC61#33937
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×Q8 ◁ C8×Q8 ◁ #2183

Complements

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

NH ≅ G/Ntype
1. #21458832C2semidirect
2. #21458687C2semidirect
3. #21448061C2semidirect
4. #21448056C2semidirect
5. #21448051C2semidirect
6. #21447984C2semidirect
7. #21447977C2semidirect
8. #21447957C2semidirect
9. #21447875C2semidirect
10. #21447875C2semidirect
12. #21447696C2semidirect
13. #21447685C2semidirect
14. C4×D976C2semidirect
15. C61×#2183C2semidirect
243. #2183D61semidirect
296. C61#33937semidirect

Maximal subgroups

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

subgroupindex
#214588322
#214586872
#214480612
#214480562
#214480512
#214479842
#214479772
#214479572
#214478752
#214478552
#214476962
#214476852
C4×D9762
C61×#21832
#3393761