Finite Group Databasebeta

← #29835206

Subgroups — #29835206

Order 15616.

546 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456461C211yesmaximal, characteristic, complemented
2#21454694C211yesmaximal, characteristic, complemented
3#21448023C211yesmaximal, characteristic, complemented
4#21448001C211yesmaximal, characteristic, complemented
5#21447953C211yesmaximal, characteristic, complemented
6#21447881C211yesmaximal, characteristic, complemented
7#21447875C211yesmaximal, characteristic, complemented
8#21447762C211yesmaximal, characteristic, complemented
9#21447745C211yesmaximal, characteristic
10#21447686C211yesmaximal, characteristic, complemented
11#21447682C211yesmaximal, characteristic, complemented
12#21447675C211yesmaximal, characteristic, complemented
13#21447665C211yesmaximal, characteristic, complemented
14#21447625C211yesmaximal, characteristic, complemented
15C61×#2227C211yesmaximal, characteristic, complemented
16C2×#14519800C2211yescharacteristic
17#16840386—21no—
18#16840244—21no—
19C2×#14519723C2211yescharacteristic
20C2×#14519722C2211yescharacteristic
21C2×#14519720C2211yescharacteristic
22C2×D976C2211yescharacteristic
23#16840146C2211yescharacteristic
24#16840124—21no—
25#16840009—21no—
26#16840004C2211yescharacteristic
27#16839999C2211yescharacteristic
28#16839865—21no—
29#16839861—21no—
30#16839860—21no—
31Q16×Dic61C2211yescharacteristic
32#16839856C2211yescharacteristic
33C4×D488C2211yescharacteristic
34#16839844C2211yescharacteristic
35#16839844C2211yescharacteristic
36#107×D61C2211yescharacteristic
37#16839762—21no—
38#16839716C2211yescharacteristic
39#16839587C2211yescharacteristic
40#16839587C2211yescharacteristic
41C4⋊#11758185C2211yescharacteristic
42#16839567C2211yescharacteristic
43#16839565C2211yescharacteristic
44#16839564C2211yescharacteristic
45#16839562C2211yescharacteristic
46#16839562C2211yescharacteristic
47#16839562C2211yescharacteristic
48#16839541C2211yescharacteristic
49#16839541C2211yescharacteristic
50#16839537C2211yescharacteristic
51C16×Dic61C2211yescharacteristic
52C61×#500C2211yescharacteristic
53C4×Q16×C61C2211yescharacteristic
54C61×#366C2211yescharacteristic
55C61×#366C2211yescharacteristic
56C61×C4⋊C16C2211yescharacteristic
57C61×#358C2211yescharacteristic
58C61×#358C2211yescharacteristic
59C2×#11758226—21no—
60#14519800—22no—
61#14519800—22no—
62C2×Dic244C2311yescharacteristic
63C2×#11758190—21no—
64C2×#11758201—21no—
65C2×D488C2311yescharacteristic
66C2×D488C2311yescharacteristic
67C2×#11758189D411yescharacteristic
68C2×C8×D61C2311yescharacteristic
69#14519772—41no—
70#14519766—41no—
71#14519765—21no—
72#14519762—41no—
73#14519757—21no—
74#14519753—41no—
75#14519752—21no—
76Q8×Dic61—21no—
77#14519742—21no—
78C4×D244—21no—
79C4×D244—41no—
80#14519739—21no—
81#14519739—21no—
82#14519739—41no—
83#14519734—41no—
84#14519734D411yescharacteristic
85C4⋊C4×D61—21no—
86C4⋊C4×D61—41no—
87#14519723—22no—
88#14519722—22no—
89#14519720—22no—
90D976—22no—
91C2×#11758185C2311yescharacteristic
92C2×#11758185C2311yescharacteristic
93#14519711C2311yescharacteristic
94#14519710—21no—
95#14519701—21no—
96#14519700—21no—
97#14519700—21no—
98#14519699—21no—
99#14519697—21no—
100#14519697—21no—
101#14519697—21no—
102#14519688D411yescharacteristic
103#14519687D411yescharacteristic
104C8×Dic61C2311yescharacteristic
105C2×Q16×C61C2311yescharacteristic
106C4⋊Q8×C61—21no—
107C4×Q8×C61—21no—
108C2×C16×C61C2311yescharacteristic
109C2×C16×C61C2311yescharacteristic
110#107×C61—21no—
111#107×C61C2311yescharacteristic
112#107×C61C2311yescharacteristic
113#107×C61C2311yescharacteristic
114#103×C61—21no—
115C4×C8×C61C2311yescharacteristic
116C2×Q8×C61—21no—
117C2×Q8×C61—41no—
118#11758226—24no—
119#11758226—42no—
120C2×D244—21no—
121C2×D244—21no—
122C2×D244—41no—
123C2×D244—41no—
124C2×C4×D61—41no—
125C2×C4×D61—41no—
126C2×C4×D61—41no—
127C2×C4×D61—41no—
128C2×C4×D61—41no—
129C2×C4×D61C2×D411yescharacteristic
130C2×Dic122—21no—
131Q16×C61—21no—
132Q16×C61#4112yes—
133C2×C8×C61C2×D411yescharacteristic
134C2×C8×C61C2411yescharacteristic
135C4⋊C4×C61—21no—
136C4⋊C4×C61—21no—
137C4⋊C4×C61—21no—
138C4⋊C4×C61—41no—
139C4⋊C4×C61—41no—
140C42×C61—41no—
141C42×C61C2×D411yescharacteristic
142#11758201—24no—
143#11758198—41no—
144#11758198—41no—
145#11758198—41no—
146#11758198—41no—
147#11758198—41no—
148#11758198—41no—
149#11758198—41no—
150#11758198D811yescharacteristic
151#11758198D811yescharacteristic
152C4⋊Dic61—21no—
153C4⋊Dic61—41no—
154C4⋊Dic61—41no—
155#11758196—41no—
156#11758196—41no—
157#11758196D811yescharacteristic
158#11758196D811yescharacteristic
159C4×Dic61—41no—
160C4×Dic61—41no—
161C4×Dic61C2×D411yescharacteristic
162C2×#92418C2×D411yescharacteristic
163C2×#92418C2×D411yescharacteristic
164Dic244—21no—
165Dic244—21no—
166D488—21no—
167D488—21no—
168D488—21no—
169D488#4112yes—
170#11758190—42no—
171#11758189—41no—
172C8×D61—21no—
173C8×D61—21no—
174C16×C61—21no—
175C16×C61—21no—
176#11758185—21no—
177#11758185—21no—
178C22×D61—41no—
179C22×D61—41no—
180C22×D61C2×D811yescharacteristic
181Q8×C61—22no—
182Q8×C61—41no—
183Q8×C61—161no—
184C2×C4×C61—41no—
185C2×C4×C61—41no—
186C2×C4×C61—41no—
187C2×C4×C61—41no—
188C2×C4×C61C2×D811yescharacteristic
189C2×C4×C61C2×D811yescharacteristic
190C2×C4×C61C22×D411yescharacteristic
191C2×Dic61—41no—
192C2×Dic61—41no—
193C2×Dic61C2×D811yescharacteristic
194C2×Dic61C2×D811yescharacteristic
195C2×Dic61C2×D811yescharacteristic
196D244—22no—
197D244—44no—
198D244—41no—
199D244—41no—
200D244—41no—
201D244—161no—
202C4×D61—21no—
203C4×D61—21no—
204C4×D61—44no—
205C4×D61—161no—
206C4×D61—161no—
207C4×D61—161no—
208C4×D61—161no—
209Dic122—41no—
210Dic122—41no—
211C8×C61—21no—
212C8×C61C2×#4111yescharacteristic
213C8×C61C2×#4111yescharacteristic
214#92418—21no—
215#92418—21no—
216#33684—611nomaximal, Sylow
217C22×C61C22×D811yescharacteristic
218C2×D61—21no—
219C2×D61—21no—
220C2×D61—21no—
221C2×D61—42no—
222C2×D61—81no—
223C2×D61—81no—
224C2×D61—81no—
225C2×D61—81no—
226C2×D61—81no—
227C4×C61—21no—
228C4×C61—21no—
229C4×C61—42no—
230C4×C61—81no—
231C4×C61—81no—
232C4×C61—81no—
233C4×C61#52511yescharacteristic
234C4×C61#57511yescharacteristic
235Dic61—21no—
236Dic61—21no—
237Dic61—21no—
238Dic61—81no—
239Dic61—81no—
240#3175—611no—
241#2951—611no—
242#2236—611no—
243#2232—611no—
244#2227D6111yescharacteristic, complemented
245#2224—611no—
246#2211—611no—
247#2210—611no—
248#2189—611no—
249#2186—611no—
250#2175—611no—
251#2175—611no—
252C4×Q32—611no—
253C4×D16—611no—
254#2164—611no—
255C2×C61#310011yescharacteristic
256C2×C61#341511yescharacteristic
257C2×C61#341711yescharacteristic
258D61—41no—
259D61—82no—
260D61—161no—
261C2×#135—611no—
262#542—1221no—
263#520—1221no—
264C2×Q32—611no—
265C2×SD32—611no—
266C2×SD32—611no—
267C2×D16—611no—
268#500C2×D6111yescharacteristic
269#495—611no—
270#489—1221no—
271#468—1221no—
272#467—611no—
273#466—611no—
274#440—1221no—
275#440—1221no—
276#440—1221no—
277C4×Q16—611no—
278C4×Q16—611no—
279C4×Q16C2×D6111yescharacteristic
280C4×D8—611no—
281C4×D8—611no—
282C4×D8—611no—
283C2×#107—611no—
284#417—1221no—
285#405—611no—
286#366—611no—
287#366—611no—
288#366C2×D6111yescharacteristic
289#366C2×D6111yescharacteristic
290C4⋊C16—611no—
291C4⋊C16C2×D6111yescharacteristic
292#358—611no—
293#358—611no—
294#358C2×D6111yescharacteristic
295#358C2×D6111yescharacteristic
296#357—611no—
297#357—611no—
298#357—611no—
299#357—611no—
300C22⋊C16—611no—
301C22⋊C16—611no—
302#346—611no—
303C4×C16—611no—
304C61#3368411yescharacteristic, complemented, Sylow
305C2×#41—1221no—
306#135—1222no—
307#135—1222no—
308C2×Q16—611no—
309C2×Q16C22×D6111yescharacteristic
310C2×SD16—1221no—
311C2×SD16—1221no—
312C2×D8—611no—
313C2×D8—611no—
314C2×M16—611no—
315C22×C8—611no—
316C4⋊Q8—21no—
317#126—2441no—
318#124—1221no—
319#124—2441no—
320#123—2441no—
321C22⋊Q8—1221no—
322C22⋊Q8—2441no—
323#121—1221no—
324C4×Q8—21no—
325C4×Q8—1221no—
326C4×Q8—1221no—
327C4×D4—1221no—
328C4×D4—1221no—
329C4×D4—1221no—
330C4×D4—2441no—
331C4×D4—2441no—
332#117—611no—
333#117—2441no—
334C2×C4⋊C4—1221no—
335C2×C4⋊C4—2441no—
336Q32—1222no—
337SD32—1222no—
338SD32—1222no—
339D16—1222no—
340C2×C16—611no—
341C2×C16—611no—
342C2×C16C22×D6111yescharacteristic
343C2×C16C22×D6111yescharacteristic
344#107—21no—
345#107—611no—
346#107—1221no—
347#107C22×D6111yescharacteristic
348#107C22×D6111yescharacteristic
349#107C22×D6111yescharacteristic
350#103—21no—
351#103—1221no—
352#103—1221no—
353#103—1221no—
354#102—1221no—
355#102—1221no—
356#102—1221no—
357#102—1221no—
358#97—611no—
359#97—611no—
360C4×C8—611no—
361C4×C8C22×D6111yescharacteristic
362#41—1224no—
363#41—2442no—
364C2×Q8—21no—
365C2×Q8—41no—
366C2×Q8—1221no—
367C2×D4—1221no—
368C2×D4—1221no—
369C2×D4—2441no—
370C2×D4—2441no—
371C22×C4—611no—
372C22×C4—2441no—
373C22×C4—2441no—
374C22×C4—2441no—
375C22×C4—2441no—
376C22×C4—2441no—
377Q16—21no—
378Q16—1221no—
379Q16—1221no—
380Q16#1175822612yes—
381SD16—1224no—
382SD16—2442no—
383D8—612no—
384D8—1221no—
385D8—1221no—
386D8—1221no—
387M16—2441no—
388C2×C8—611no—
389C2×C8—611no—
390C2×C8—1221no—
391C2×C8—1221no—
392C2×C8D4×D6111yescharacteristic
393C2×C8C23×D6111yescharacteristic
394C4⋊C4—21no—
395C4⋊C4—21no—
396C4⋊C4—21no—
397C4⋊C4—41no—
398C4⋊C4—41no—
399C4⋊C4—611no—
400C4⋊C4—611no—
401C4⋊C4—1221no—
402C4⋊C4—2441no—
403C4⋊C4—2441no—
404C4⋊C4—2441no—
405C4⋊C4—2441no—
406C22⋊C4—611no—
407C22⋊C4—611no—
408C22⋊C4—2441no—
409C22⋊C4—2441no—
410C22⋊C4—2441no—
411C22⋊C4—2441no—
412C22⋊C4—2441no—
413C22⋊C4—2441no—
414C22⋊C4—2441no—
415C42—41no—
416C42—611no—
417C42—2441no—
418C42—2441no—
419C42D4×D6111yescharacteristic
420C16—21no—
421C16—21no—
422C16—1221no—
423C16—1221no—
424C23—611no—
425C23—2441no—
426C23—2441no—
427Q8—22no—
428Q8—41no—
429Q8—161no—
430Q8—2441no—
431Q8—2441no—
432D4—1222no—
433D4—9761no—
434D4—2444no—
435D4—2441no—
436D4—2441no—
437D4—2441no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—611no—
443C2×C4—611no—
444C2×C4—611no—
445C2×C4—1221no—
446C2×C4—1221no—
447C2×C4—9761no—
448C2×C4—9761no—
449C2×C4—9761no—
450C2×C4—9761no—
451C2×C4—2444no—
452C2×C4—2441no—
453C2×C4—2441no—
454C2×C4D8×D6111yescharacteristic
455C2×C4D8×D6111yescharacteristic
456C2×C4C2×D4×D6111yescharacteristic
457C8—21no—
458C8—1221no—
459C8—1221no—
460C8#41×D6111yescharacteristic
461C8C2×#1175822611yescharacteristic
462C22—1221no—
463C22—1221no—
464C22—1221no—
465C22—4881no—
466C22—4881no—
467C22—4881no—
468C22—4881no—
469C22—4881no—
470C22—2442no—
471C22C2×D8×D6111yescharacteristic
472C4—21no—
473C4—21no—
474C4—42no—
475C4—81no—
476C4—81no—
477C4—81no—
478C4—1221no—
479C4—1221no—
480C4—1221no—
481C4—4881no—
482C4—4881no—
483C4#1684027511yescharacteristic
484C4#1684056111yescharacteristic
485C2—9761no—
486C2—4882no—
487C2—2441no—
488C2#2145582111yescharacteristic
489C2#2145895911yescharacteristic
490C2#2145896811yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2227C2
socleC22×C61C22×D8
prime radical#21447745C2
hypercenter#2227D61
hypocenterC61#33684
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2227

Complements

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

NH ≅ G/Ntype
1. #21456461C2semidirect
2. #21454694C2semidirect
3. #21448023C2semidirect
4. #21448001C2semidirect
5. #21447953C2semidirect
6. #21447881C2semidirect
7. #21447875C2semidirect
8. #21447762C2semidirect
10. #21447686C2semidirect
11. #21447682C2semidirect
12. #21447675C2semidirect
13. #21447665C2semidirect
14. #21447625C2semidirect
15. C61×#2227C2semidirect
244. #2227D61semidirect
304. C61#33684semidirect

Maximal subgroups

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

subgroupindex
#214564612
#214546942
#214480232
#214480012
#214479532
#214478812
#214478752
#214477622
#214477452
#214476862
#214476822
#214476752
#214476652
#214476252
C61×#22272
#3368461