Finite Group Databasebeta

← #29583041

Subgroups — #29583041

Order 15616.

500 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21451058C211yesmaximal, characteristic, complemented
2#21446746C211yesmaximal, characteristic
3#21446745C211yesmaximal, characteristic
4#21446625C211yesmaximal, characteristic
5#21443703C211yesmaximal, characteristic, complemented
6#21443659C211yesmaximal, characteristic, complemented
7C61×#1279C211yesmaximal, characteristic, complemented
8C2×#14519774C2211yescharacteristic
9C2×C4⋊#92418C2211yescharacteristic
10C2×#14519699—21no—
11C2×#14519699—21no—
12C2×#14519699—22no—
13C2×#14519697—21no—
14C2×#14519697—21no—
15#16839704—22no—
16#16839660—21no—
17#16839658—21no—
18#16839632C2211yescharacteristic
19#16839628—21no—
20#16839627—21no—
21C4×C4⋊Dic61C2211yescharacteristic
22C2×C4⋊C8×C61C2211yescharacteristic
23C2×C4×C8×C61C2211yescharacteristic
24C4×C4⋊C4×C61C2211yescharacteristic
25C22×D244—21no—
26C22×D244—21no—
27C22×D244—21no—
28C22×#92418—21no—
29#14519774—21no—
30#14519774—21no—
31#14519774—21no—
32#14519774Q812yes—
33C2×C4⋊Dic61—21no—
34C2×C4⋊Dic61—21no—
35C2×C4⋊Dic61D411yescharacteristic
36C2×C4⋊Dic61D411yescharacteristic
37C2×C4⋊Dic61D412yes—
38C2×#11758196—22no—
39C2×C4×Dic61—21no—
40C4⋊#92418—21no—
41C4⋊#92418—21no—
42#14519699—42no—
43#14519699—42no—
44#14519699—44no—
45#14519697—42no—
46#14519697—42no—
47#14519684—22no—
48#14519684—22no—
49#14519684—22no—
50#14519684—21no—
51C22×C8×C61—21no—
52C22×C8×C61—21no—
53C2×C4⋊C4×C61D411yescharacteristic
54C2×C4⋊C4×C61D411yescharacteristic
55C2×C42×C61—21no—
56C2×C42×C61C2311yescharacteristic
57C4⋊C8×C61—21no—
58C4⋊C8×C61—21no—
59C4×C8×C61—21no—
60C4×C8×C61—21no—
61#95×C61—21no—
62C23×D61—41no—
63C22×C4×C61—21no—
64C22×C4×C61—21no—
65C22×C4×C61C2×D411yescharacteristic
66C22×C4×C61C2×D411yescharacteristic
67C22×C4×C61C2×D411yescharacteristic
68C22×Dic61—21no—
69C22×Dic61—21no—
70C22×Dic61—22no—
71C2×D244—22no—
72C2×D244—22no—
73C2×D244—22no—
74C2×D244—42no—
75C2×D244—42no—
76C2×D244—41no—
77C2×D244—41no—
78C2×D244—41no—
79C2×D244—41no—
80C2×D244—41no—
81C2×D244—41no—
82C2×D244—41no—
83C2×D244—41no—
84C2×D244—41no—
85C2×D244—41no—
86C2×D244—41no—
87C2×C8×C61—22no—
88C2×C8×C61—41no—
89C2×C8×C61—41no—
90C2×C8×C61—41no—
91C2×C8×C61—41no—
92C2×C8×C61—41no—
93C4⋊C4×C61—21no—
94C4⋊C4×C61—21no—
95C4⋊C4×C61—21no—
96C4⋊C4×C61—21no—
97C42×C61—41no—
98C42×C61—41no—
99C42×C61C2×Q811yescharacteristic
100C42×C61#4111yescharacteristic
101C42×C61#4111yescharacteristic
102C42×C61#4111yescharacteristic
103C4⋊Dic61—21no—
104C4⋊Dic61—21no—
105C4⋊Dic61—21no—
106C4⋊Dic61—21no—
107C4⋊Dic61—41no—
108C4⋊Dic61—41no—
109C4⋊Dic61—41no—
110C4⋊Dic61—41no—
111C4⋊Dic61—42no—
112#11758196—82no—
113C4×Dic61—41no—
114C4×Dic61—41no—
115C2×#92418—41no—
116C2×#92418—41no—
117C2×#92418—41no—
118C23×C61#12011yescharacteristic
119C22×D61—42no—
120C22×D61—81no—
121C22×D61—81no—
122C22×D61—81no—
123C22×D61—81no—
124C22×D61—81no—
125C22×D61—81no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61C22⋊Q811yescharacteristic
135C2×C4×C61C22⋊Q811yescharacteristic
136C2×C4×C61C22⋊Q811yescharacteristic
137C2×C4×C61#12411yescharacteristic
138C2×C4×C61#12411yescharacteristic
139C2×C4×C61#12411yescharacteristic
140C2×C4×C61#13511yescharacteristic
141C2×C4×C61#13511yescharacteristic
142C2×C4×C61#13511yescharacteristic
143C2×C4×C61#13511yescharacteristic
144C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
145C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
146C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
147C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61—42no—
153C2×Dic61—42no—
154C2×Dic61—41no—
155C2×Dic61—42no—
156C2×Dic61—41no—
157D244—44no—
158D244—42no—
159D244—42no—
160D244—42no—
161D244—42no—
162D244—82no—
163D244—81no—
164D244—81no—
165D244—81no—
166D244—81no—
167C8×C61—42no—
168C8×C61—81no—
169#92418—81no—
170#10351—611nomaximal, Sylow
171C22×C61#39311yescharacteristic
172C22×C61#44911yescharacteristic
173C22×C61#44911yescharacteristic
174C22×C61#44911yescharacteristic
175C22×C61#44911yescharacteristic
176C22×C61#45311yescharacteristic
177C22×C61#45411yescharacteristic
178C2×D61—82no—
179C2×D61—82no—
180C2×D61—82no—
181C2×D61—161no—
182C2×D61—161no—
183C2×D61—161no—
184C2×D61—161no—
185C4×C61—21no—
186C4×C61—21no—
187C4×C61—81no—
188C4×C61—81no—
189C4×C61#47811yescharacteristic
190C4×C61#47811yescharacteristic
191C4×C61#47811yescharacteristic
192C4×C61#47811yescharacteristic
193C4×C61#48811yescharacteristic
194C4×C61#48811yescharacteristic
195C4×C61#49011yescharacteristic
196C4×C61#49011yescharacteristic
197Dic61—82no—
198Dic61—81no—
199Dic61—81no—
200#2571—611no—
201#1982—611no—
202#1982—611no—
203#1957—611no—
204#1296—611no—
205#1279—611no—
206#1279D6111yescharacteristic, complemented
207C2×C61#162011yescharacteristic
208C2×C61#162411yescharacteristic
209C2×C61#162811yescharacteristic
210C2×C61#162811yescharacteristic
211C2×C61#202511yescharacteristic
212C2×C61#202511yescharacteristic
213C2×C61#202711yescharacteristic
214D61—162no—
215C2×#127—611no—
216C2×C4⋊C8—611no—
217C2×C4⋊C8C2×D6111yescharacteristic
218C2×#102—1222no—
219C2×#102—1221no—
220C2×#102—1221no—
221C2×#102—1221no—
222C2×#102—1221no—
223C2×C4×C8C2×D6111yescharacteristic
224#400—1222no—
225#389—1221no—
226#389—1221no—
227#384—611no—
228#382—1221no—
229#382—1221no—
230C4×C4⋊C4—611no—
231C4×C4⋊C4C2×D6111yescharacteristic
232C61#1035111yescharacteristic, complemented, Sylow
233C22×D4—1221no—
234C22×D4—1221no—
235C22×D4—1221no—
236C22×C8—21no—
237C22×C8—21no—
238C22×C8—1221no—
239#127—612no—
240#127—1221no—
241#127—1221no—
242#127—1221no—
243C2×C4⋊C4—611no—
244C2×C4⋊C4—611no—
245C2×C4⋊C4—612no—
246C2×C4⋊C4—1222no—
247C2×C4⋊C4—1221no—
248C2×C4⋊C4—1221no—
249C2×C4⋊C4D24411yescharacteristic
250C2×C4⋊C4D24411yescharacteristic
251C2×C42—21no—
252C2×C42—1221no—
253C2×C42C22×D6111yescharacteristic
254C4⋊C8—21no—
255C4⋊C8—21no—
256C4⋊C8—1221no—
257C4⋊C8—1221no—
258#102—2442no—
259#102—2442no—
260#102—2442no—
261#102—2442no—
262#102—2444no—
263C4×C8—21no—
264C4×C8—21no—
265#95—21no—
266#95—1222no—
267#95—1222no—
268#95—1222no—
269#95—1221no—
270C24—2441no—
271C2×D4—1222no—
272C2×D4—1222no—
273C2×D4—1222no—
274C2×D4—2442no—
275C2×D4—2442no—
276C2×D4—2441no—
277C2×D4—2441no—
278C2×D4—2441no—
279C2×D4—2441no—
280C2×D4—2441no—
281C2×D4—2441no—
282C2×D4—2441no—
283C2×D4—2441no—
284C2×D4—2441no—
285C2×D4—2441no—
286C2×D4—2441no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—1221no—
290C22×C4—1221no—
291C22×C4—1222no—
292C22×C4C2×D24411yescharacteristic
293C22×C4D4×D6111yescharacteristic
294C22×C4D4×D6111yescharacteristic
295C2×C8—22no—
296C2×C8—41no—
297C2×C8—41no—
298C2×C8—41no—
299C2×C8—41no—
300C2×C8—41no—
301C2×C8—2441no—
302C2×C8—2441no—
303C2×C8—2441no—
304C4⋊C4—21no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—21no—
308C4⋊C4—1221no—
309C4⋊C4—1221no—
310C4⋊C4—1221no—
311C4⋊C4—1221no—
312C4⋊C4—4882no—
313C4⋊C4—2442no—
314C4⋊C4—2441no—
315C4⋊C4—2441no—
316C4⋊C4—2441no—
317C4⋊C4—2441no—
318C42—41no—
319C42—41no—
320C42—2441no—
321C42—2441no—
322C42#1175822211yescharacteristic
323C42#1175822211yescharacteristic
324C42#1175822411yescharacteristic
325C42Q8×D6111yescharacteristic
326C23—4881no—
327C23—4881no—
328C23—4881no—
329C23—4881no—
330C23—4881no—
331C23—4881no—
332C23—2442no—
333C23#1451974711yescharacteristic
334D4—4882no—
335D4—4881no—
336D4—4881no—
337D4—4881no—
338D4—4881no—
339D4—2444no—
340D4—2442no—
341D4—2442no—
342D4—2442no—
343D4—2442no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—2441no—
353C2×C4—2441no—
354C2×C4—2441no—
355C2×C4—2441no—
356C2×C4—2442no—
357C2×C4—2441no—
358C2×C4—2442no—
359C2×C4—2441no—
360C2×C4—2442no—
361C2×C4#1451975511yescharacteristic
362C2×C4#1451975511yescharacteristic
363C2×C4#1451975711yescharacteristic
364C2×C4#1451976311yescharacteristic
365C2×C4#1451976311yescharacteristic
366C2×C4#1451976511yescharacteristic
367C2×C4#1451979811yescharacteristic
368C2×C4#1451979911yescharacteristic
369C2×C4#1451979911yescharacteristic
370C2×C4#1451980011yescharacteristic
371C2×C4#1451980111yescharacteristic
372C2×C4#1451980411yescharacteristic
373C2×C4#1451980511yescharacteristic
374C2×C4#1451980511yescharacteristic
375C8—42no—
376C8—81no—
377C8—4881no—
378C22—9761no—
379C22—9761no—
380C22—9761no—
381C22—9761no—
382C22—4882no—
383C22—4882no—
384C22—4882no—
385C22#1683967511yescharacteristic
386C22#1683990811yescharacteristic
387C22#1683990911yescharacteristic
388C22#1683990911yescharacteristic
389C22#1683991011yescharacteristic
390C22#1683993111yescharacteristic
391C22#1683993611yescharacteristic
392C4—21no—
393C4—21no—
394C4—81no—
395C4—81no—
396C4—4882no—
397C4—4881no—
398C4—4881no—
399C4#1684006111yescharacteristic
400C4#1684006311yescharacteristic
401C4#1684006311yescharacteristic
402C4#1684006511yescharacteristic
403C4#1684011711yescharacteristic
404C4#1684011811yescharacteristic
405C4#1684012511yescharacteristic
406C4#1684012711yescharacteristic
407C2—9762no—
408C2#2144488011yescharacteristic
409C2#2144490411yescharacteristic
410C2#2144493111yescharacteristic
411C2#2144493211yescharacteristic
412C2#2144696411yescharacteristic
413C2#2144696611yescharacteristic
414C2#2144697411yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1279C2
socleC23×C61#120
prime radicalC2×#14519774C22
hypercenter#1279D61
hypocenterC61#10351
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
1. #21451058C2semidirect
5. #21443703C2semidirect
6. #21443659C2semidirect
7. C61×#1279C2semidirect
206. #1279D61semidirect
232. C61#10351semidirect

Maximal subgroups

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

subgroupindex
#214510582
#214467462
#214467452
#214466252
#214437032
#214436592
C61×#12792
#1035161