Finite Group Databasebeta

← #29583024

Subgroups — #29583024

Order 15616.

588 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21450845C211yesmaximal, characteristic, complemented
2#21446746C211yesmaximal, characteristic
3#21446745C211yesmaximal, characteristic
4#21446625C211yesmaximal, characteristic
5#21443703C211yesmaximal, characteristic, complemented
6#21443659C211yesmaximal, characteristic, complemented
7C61×#1279C211yesmaximal, characteristic, complemented
8C2×#14519777—21no—
9C2×#14519776—21no—
10C2×#14519774C2211yescharacteristic
11C2×C4⋊#92418C2211yescharacteristic
12C2×#14519699—21no—
13C2×#14519699—21no—
14C2×#14519699—22no—
15C2×#14519697—21no—
16C2×#14519697—21no—
17#16839683—22no—
18#16839661—21no—
19#16839660—21no—
20#16839632C2211yescharacteristic
21C4×C4⋊Dic61C2211yescharacteristic
22C2×C4⋊C8×C61C2211yescharacteristic
23C2×C4×C8×C61C2211yescharacteristic
24C4×C4⋊C4×C61C2211yescharacteristic
25C22×Dic122—22no—
26C22×D244—21no—
27C22×D244—21no—
28C22×D244—21no—
29C22×#92418—21no—
30#14519777—42no—
31#14519777—42no—
32#14519776—42no—
33#14519776—42no—
34#14519774—21no—
35#14519774—21no—
36#14519774—21no—
37#14519774Q812yescomplemented
38C2×C4⋊Dic61—22no—
39C2×C4⋊Dic61—21no—
40C2×C4⋊Dic61—21no—
41C2×C4⋊Dic61D411yescharacteristic
42C2×C4⋊Dic61D411yescharacteristic
43C2×C4⋊Dic61D412yes—
44C2×#11758196—22no—
45C2×C4×Dic61—21no—
46C4⋊#92418—21no—
47C4⋊#92418—21no—
48#14519699—44no—
49#14519699—42no—
50#14519699—42no—
51#14519697—42no—
52#14519697—42no—
53#14519684—22no—
54#14519684—21no—
55C22×C8×C61—21no—
56C22×C8×C61—21no—
57C2×C4⋊C4×C61D411yescharacteristic
58C2×C4⋊C4×C61D411yescharacteristic
59C2×C42×C61—21no—
60C2×C42×C61C2311yescharacteristic
61C4⋊C8×C61—21no—
62C4⋊C8×C61—21no—
63C4×C8×C61—21no—
64C4×C8×C61—21no—
65#95×C61—21no—
66C23×D61—41no—
67C22×C4×C61—21no—
68C22×C4×C61—21no—
69C22×C4×C61C2×D411yescharacteristic
70C22×C4×C61C2×D411yescharacteristic
71C22×C4×C61C2×D411yescharacteristic
72C22×Dic61—21no—
73C22×Dic61—21no—
74C22×Dic61—22no—
75C2×D244—22no—
76C2×D244—22no—
77C2×D244—22no—
78C2×D244—42no—
79C2×D244—42no—
80C2×D244—41no—
81C2×D244—41no—
82C2×D244—41no—
83C2×D244—41no—
84C2×D244—41no—
85C2×D244—41no—
86C2×D244—41no—
87C2×D244—41no—
88C2×D244—41no—
89C2×D244—41no—
90C2×D244—41no—
91C2×Dic122—44no—
92C2×Dic122—44no—
93C2×Dic122—82no—
94C2×C8×C61—22no—
95C2×C8×C61—41no—
96C2×C8×C61—41no—
97C2×C8×C61—41no—
98C2×C8×C61—41no—
99C2×C8×C61—41no—
100C4⋊C4×C61—21no—
101C4⋊C4×C61—21no—
102C4⋊C4×C61D812yes—
103C4⋊C4×C61SD1612yes—
104C42×C61—41no—
105C42×C61—41no—
106C42×C61C2×Q811yescharacteristic
107C42×C61#4111yescharacteristic
108C42×C61#4111yescharacteristic
109C42×C61#4111yescharacteristic
110C4⋊Dic61—21no—
111C4⋊Dic61—21no—
112C4⋊Dic61—44no—
113C4⋊Dic61—41no—
114C4⋊Dic61—41no—
115C4⋊Dic61—41no—
116C4⋊Dic61—41no—
117C4⋊Dic61—42no—
118C4⋊Dic61D812yes—
119C4⋊Dic61SD1612yes—
120#11758196—44no—
121C4×Dic61—41no—
122C4×Dic61—41no—
123C2×#92418—41no—
124C2×#92418—41no—
125C2×#92418—41no—
126C23×C61#12011yescharacteristic
127C22×D61—42no—
128C22×D61—81no—
129C22×D61—81no—
130C22×D61—81no—
131C22×D61—81no—
132C22×D61—81no—
133C22×D61—81no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61—22no—
137C2×C4×C61—22no—
138C2×C4×C61—41no—
139C2×C4×C61—41no—
140C2×C4×C61—41no—
141C2×C4×C61—41no—
142C2×C4×C61C22⋊Q811yescharacteristic
143C2×C4×C61C22⋊Q811yescharacteristic
144C2×C4×C61C22⋊Q811yescharacteristic
145C2×C4×C61#12411yescharacteristic
146C2×C4×C61#12411yescharacteristic
147C2×C4×C61#12411yescharacteristic
148C2×C4×C61C2×D811yescharacteristic
149C2×C4×C61C2×D811yescharacteristic
150C2×C4×C61C2×SD1611yescharacteristic
151C2×C4×C61C2×SD1611yescharacteristic
152C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
153C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
154C2×C4×C61#13711yescharacteristic
155C2×C4×C61#13711yescharacteristic
156C2×Dic61—22no—
157C2×Dic61—22no—
158C2×Dic61—41no—
159C2×Dic61—41no—
160C2×Dic61—41no—
161C2×Dic61—41no—
162C2×Dic61—42no—
163C2×Dic61—42no—
164C2×Dic61—42no—
165D244—44no—
166D244—42no—
167D244—42no—
168D244—42no—
169D244—42no—
170D244—82no—
171D244—81no—
172D244—81no—
173D244—81no—
174D244—81no—
175Dic122—88no—
176C8×C61—42no—
177C8×C61—81no—
178#92418—81no—
179#10348—611nomaximal, Sylow
180C22×C61#39311yescharacteristic
181C22×C61#44711yescharacteristic
182C22×C61#44711yescharacteristic
183C22×C61#44811yescharacteristic
184C22×C61#44811yescharacteristic
185C22×C61#45311yescharacteristic
186C22×C61#45411yescharacteristic
187C2×D61—82no—
188C2×D61—82no—
189C2×D61—82no—
190C2×D61—161no—
191C2×D61—161no—
192C2×D61—161no—
193C2×D61—161no—
194C4×C61—21no—
195C4×C61—21no—
196C4×C61—42no—
197C4×C61—42no—
198C4×C61#47411yescharacteristic
199C4×C61#47411yescharacteristic
200C4×C61#47611yescharacteristic
201C4×C61#47611yescharacteristic
202C4×C61#48611yescharacteristic
203C4×C61#48611yescharacteristic
204C4×C61#48911yescharacteristic
205C4×C61#48911yescharacteristic
206Dic61—42no—
207Dic61—42no—
208Dic61—82no—
209#2551—611no—
210#1982—611no—
211#1982—611no—
212#1957—611no—
213#1296—611no—
214#1279—611no—
215#1279D6111yescharacteristic, complemented
216C2×C61#161911yescharacteristic
217C2×C61#162311yescharacteristic
218C2×C61#162711yescharacteristic
219C2×C61#162711yescharacteristic
220C2×C61#202311yescharacteristic
221C2×C61#202311yescharacteristic
222C2×C61#202711yescharacteristic
223D61—162no—
224C2×C4⋊Q8—1221no—
225C2×C4⋊Q8—1221no—
226C2×#127—611no—
227C2×C4⋊C8—611no—
228C2×C4⋊C8C2×D6111yescharacteristic
229C2×#102—1222no—
230C2×#102—1221no—
231C2×#102—1221no—
232C2×#102—1221no—
233C2×#102—1221no—
234C2×C4×C8C2×D6111yescharacteristic
235#395—1222no—
236#389—1221no—
237#389—1221no—
238#384—611no—
239C4×C4⋊C4—611no—
240C4×C4⋊C4C2×D6111yescharacteristic
241C61#1034811yescharacteristic, complemented, Sylow
242C22×Q8—1222no—
243C22×D4—1221no—
244C22×D4—1221no—
245C22×D4—1221no—
246C22×C8—21no—
247C22×C8—21no—
248C22×C8—1221no—
249C4⋊Q8—2442no—
250C4⋊Q8—2442no—
251C4⋊Q8—2442no—
252C4⋊Q8—2442no—
253#127—612no—
254#127—1221no—
255#127—1221no—
256#127—1221no—
257C2×C4⋊C4—611no—
258C2×C4⋊C4—611no—
259C2×C4⋊C4—612no—
260C2×C4⋊C4—1222no—
261C2×C4⋊C4—1222no—
262C2×C4⋊C4—1221no—
263C2×C4⋊C4—1221no—
264C2×C4⋊C4D24411yescharacteristic
265C2×C4⋊C4D24411yescharacteristic
266C2×C42—21no—
267C2×C42—1221no—
268C2×C42C22×D6111yescharacteristic
269C4⋊C8—21no—
270C4⋊C8—21no—
271C4⋊C8—1221no—
272C4⋊C8—1221no—
273#102—2442no—
274#102—2442no—
275#102—2444no—
276#102—2442no—
277#102—2442no—
278C4×C8—21no—
279C4×C8—21no—
280#95—21no—
281#95—1222no—
282#95—1221no—
283C24—2441no—
284C2×Q8—4882no—
285C2×Q8—2444no—
286C2×Q8—2444no—
287C2×D4—1222no—
288C2×D4—1222no—
289C2×D4—1222no—
290C2×D4—2442no—
291C2×D4—2442no—
292C2×D4—2441no—
293C2×D4—2441no—
294C2×D4—2441no—
295C2×D4—2441no—
296C2×D4—2441no—
297C2×D4—2441no—
298C2×D4—2441no—
299C2×D4—2441no—
300C2×D4—2441no—
301C2×D4—2441no—
302C2×D4—2441no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—1221no—
306C22×C4—1221no—
307C22×C4—1222no—
308C22×C4C2×D24411yescharacteristic
309C22×C4D4×D6111yescharacteristic
310C22×C4D4×D6111yescharacteristic
311C2×C8—22no—
312C2×C8—41no—
313C2×C8—41no—
314C2×C8—41no—
315C2×C8—41no—
316C2×C8—41no—
317C2×C8—2441no—
318C2×C8—2441no—
319C2×C8—2441no—
320C4⋊C4—21no—
321C4⋊C4—21no—
322C4⋊C4—612no—
323C4⋊C4—612no—
324C4⋊C4—1221no—
325C4⋊C4—1221no—
326C4⋊C4—2442no—
327C4⋊C4—2444no—
328C4⋊C4—2444no—
329C4⋊C4—2441no—
330C4⋊C4—2441no—
331C4⋊C4—2441no—
332C4⋊C4—2441no—
333C4⋊C4#1175819012yes—
334C4⋊C4D48812yes—
335C42—41no—
336C42—41no—
337C42—2441no—
338C42—2441no—
339C42#1175822211yescharacteristic
340C42#1175822211yescharacteristic
341C42#1175822411yescharacteristic
342C42Q8×D6111yescharacteristic
343C23—4881no—
344C23—4881no—
345C23—4881no—
346C23—4881no—
347C23—4881no—
348C23—4881no—
349C23—2442no—
350C23#1451974711yescharacteristic
351Q8—4888no—
352D4—4882no—
353D4—4881no—
354D4—4881no—
355D4—4881no—
356D4—4881no—
357D4—2444no—
358D4—2442no—
359D4—2442no—
360D4—2442no—
361D4—2442no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—22no—
365C2×C4—22no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—1222no—
371C2×C4—1222no—
372C2×C4—2442no—
373C2×C4—2442no—
374C2×C4—2442no—
375C2×C4—2441no—
376C2×C4—2441no—
377C2×C4—2441no—
378C2×C4—2441no—
379C2×C4#1451975511yescharacteristic
380C2×C4#1451975511yescharacteristic
381C2×C4#1451975711yescharacteristic
382C2×C4#1451976311yescharacteristic
383C2×C4#1451976311yescharacteristic
384C2×C4#1451976511yescharacteristic
385C2×C4D8×D6111yescharacteristic
386C2×C4C2×D48811yescharacteristic
387C2×C4SD16×D6111yescharacteristic
388C2×C4C2×#1175819011yescharacteristic
389C2×C4#1451980411yescharacteristic
390C2×C4#1451980511yescharacteristic
391C2×C4#1451980911yescharacteristic
392C2×C4#1451981011yescharacteristic
393C8—42no—
394C8—81no—
395C8—4881no—
396C22—9761no—
397C22—9761no—
398C22—9761no—
399C22—9761no—
400C22—4882no—
401C22—4882no—
402C22—4882no—
403C22#1683967511yescharacteristic
404C22#1683989711yescharacteristic
405C22#1683989811yescharacteristic
406C22#1683990211yescharacteristic
407C22#1683990311yescharacteristic
408C22#1683993111yescharacteristic
409C22#1683993611yescharacteristic
410C4—21no—
411C4—21no—
412C4—42no—
413C4—42no—
414C4—4882no—
415C4—2442no—
416C4—2442no—
417C4#1684004111yescharacteristic
418C4#1684004311yescharacteristic
419C4#1684005111yescharacteristic
420C4#1684005311yescharacteristic
421C4#1684010711yescharacteristic
422C4#1684010911yescharacteristic
423C4#1684012211yescharacteristic
424C4#1684012311yescharacteristic
425C2—9762no—
426C2#2144487511yescharacteristic
427C2#2144489911yescharacteristic
428C2#2144492411yescharacteristic
429C2#2144492511yescharacteristic
430C2#2144695411yescharacteristic
431C2#2144695611yescharacteristic
432C2#2144697411yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1279C2
socleC23×C61#120
prime radicalC2×#14519774C22
hypercenter#1279D61
hypocenterC61#10348
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. #21450845C2semidirect
5. #21443703C2semidirect
6. #21443659C2semidirect
7. C61×#1279C2semidirect
37. #14519774Q8semidirect
215. #1279D61semidirect
241. C61#10348semidirect

Maximal subgroups

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

subgroupindex
#214508452
#214467462
#214467452
#214466252
#214437032
#214436592
C61×#12792
#1034861