Finite Group Databasebeta

← #29580417

Subgroups — #29580417

Order 15616.

654 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 654 conjugacy classes of subgroups — too many to draw. Only its 85 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455763C211yesmaximal, characteristic, complemented
2#21450093C211yesmaximal, characteristic
3#21445919C211yesmaximal, characteristic, complemented
4#21444352C211yesmaximal, characteristic, complemented
5#21444146C211yesmaximal, characteristic
6#21443672C211yesmaximal, characteristic, complemented
7C61×#2561C211yesmaximal, characteristic
8C2×#14519736C2211yescharacteristic
9#16840100—22no—
10#16840095—21no—
11#16840090—21no—
12#16839802—21no—
13#16839771—21no—
14#16839726C2211yescharacteristic
15#16839726C2211yescharacteristic
16#16839698—21no—
17#16839687—21no—
18#16839650—22no—
19#16839635—21no—
20#16839625C2211yescharacteristic
21#16839618—21no—
22#16839522—22no—
23#16839499—22no—
24#16839486—22no—
25C2×C22⋊Q8×C61C2211yescharacteristic
26C22×C22⋊C4×C61C2211yescharacteristic
27C61×#397—21no—
28C61×#393—21no—
29C61×#388—22no—
30C61×#381—21no—
31C61×#379—21no—
32C4×C22⋊C4×C61C2211yescharacteristic
33C2×#11758194—21no—
34C2×#11758194—21no—
35#14519736—21no—
36#14519736—21no—
37#14519736—21no—
38#14519736—21no—
39C2×C4⋊Dic61D411yescharacteristic
40C2×C4⋊Dic61D411yescharacteristic
41C2×#11758196—22no—
42C2×C22⋊Dic61—22no—
43C2×C22⋊Dic61—21no—
44C2×C22⋊Dic61—21no—
45C2×C22⋊Dic61—22no—
46C2×C4×Dic61—21no—
47#14519710—22no—
48#14519708—22no—
49#14519701—22no—
50#14519701—22no—
51C22⋊#92418—21no—
52C22⋊#92418—21no—
53C22⋊#92418—21no—
54C22⋊#92418D412yes—
55#14519684—22no—
56#14519684—21no—
57#14519684D412yes—
58C25×C61D411yescharacteristic
59C22×Q8×C61D411yescharacteristic
60C23×C4×C61D411yescharacteristic
61C23×C4×C61C2311yescharacteristic
62C22⋊Q8×C61—21no—
63C22⋊Q8×C61—21no—
64C22⋊Q8×C61—21no—
65C22⋊Q8×C61—21no—
66C2×C4⋊C4×C61—21no—
67C2×C4⋊C4×C61D411yescharacteristic
68C2×C22⋊C4×C61—22no—
69C2×C22⋊C4×C61—21no—
70C2×C22⋊C4×C61—21no—
71C2×C22⋊C4×C61—21no—
72C2×C22⋊C4×C61—21no—
73C2×C22⋊C4×C61—21no—
74C2×C22⋊C4×C61—21no—
75C2×C22⋊C4×C61—21no—
76C2×C22⋊C4×C61—21no—
77C2×C22⋊C4×C61—22no—
78C2×C42×C61D412yes—
79#95×C61—22no—
80#95×C61—22no—
81#95×C61—21no—
82C24×C61—21no—
83C24×C61—21no—
84C24×C61—21no—
85C24×C61—42no—
86C24×C61—42no—
87C24×C61—42no—
88C24×C61C2×D411yescharacteristic
89C2×Q8×C61—21no—
90C2×Q8×C61—21no—
91C2×Q8×C61—42no—
92C22×C4×C61—21no—
93C22×C4×C61—22no—
94C22×C4×C61—21no—
95C22×C4×C61—21no—
96C22×C4×C61—21no—
97C22×C4×C61—21no—
98C22×C4×C61—42no—
99C22×C4×C61—42no—
100C22×C4×C61C2×D411yescharacteristic
101C22×C4×C61C2×D411yescharacteristic
102C22×C4×C61C2×D411yescharacteristic
103C22×C4×C61C2×D411yescharacteristic
104C22×C4×C61C2×D411yescharacteristic
105C22×C4×C61#4111yescharacteristic
106C22×Dic61—22no—
107C22×Dic61—21no—
108C22×Dic61—21no—
109C4⋊C4×C61—21no—
110C4⋊C4×C61—21no—
111C4⋊C4×C61—41no—
112C4⋊C4×C61—41no—
113C22⋊C4×C61—42no—
114C22⋊C4×C61—44no—
115C22⋊C4×C61—41no—
116C22⋊C4×C61—41no—
117C22⋊C4×C61—41no—
118C22⋊C4×C61—41no—
119C22⋊C4×C61—41no—
120C22⋊C4×C61—41no—
121C22⋊C4×C61—82no—
122C42×C61—42no—
123C22⋊Dic61—42no—
124C22⋊Dic61—44no—
125C22⋊Dic61—41no—
126C22⋊Dic61—41no—
127C22⋊Dic61—82no—
128C4⋊Dic61—21no—
129C4⋊Dic61—21no—
130C4⋊Dic61—21no—
131C4⋊Dic61—21no—
132#11758196—82no—
133C4×Dic61—41no—
134C4×Dic61—41no—
135#11758194—42no—
136#11758194—42no—
137C2×#92418—22no—
138C2×#92418—41no—
139C23×C61—22no—
140C23×C61—22no—
141C23×C61—22no—
142C23×C61—22no—
143C23×C61—22no—
144C23×C61—41no—
145C23×C61—42no—
146C23×C61—41no—
147C23×C61—41no—
148C23×C61—42no—
149C23×C61—41no—
150C23×C61—41no—
151C23×C61—42no—
152C23×C61—42no—
153C23×C61—81no—
154C23×C61—81no—
155C23×C61—88no—
156C23×C61#12011yescharacteristic
157C23×C61#12011yescharacteristic
158C23×C61#12111yescharacteristic
159Q8×C61—42no—
160Q8×C61—81no—
161C2×C4×C61—22no—
162C2×C4×C61—22no—
163C2×C4×C61—41no—
164C2×C4×C61—41no—
165C2×C4×C61—41no—
166C2×C4×C61—41no—
167C2×C4×C61—42no—
168C2×C4×C61—42no—
169C2×C4×C61—42no—
170C2×C4×C61—42no—
171C2×C4×C61—41no—
172C2×C4×C61—41no—
173C2×C4×C61—41no—
174C2×C4×C61—42no—
175C2×C4×C61—42no—
176C2×C4×C61—42no—
177C2×C4×C61—81no—
178C2×C4×C61#12011yescharacteristic
179C2×C4×C61#12111yescharacteristic
180C2×C4×C61#12111yescharacteristic
181C2×C4×C61#12711yescharacteristic
182C2×Dic61—42no—
183C2×Dic61—42no—
184C2×Dic61—42no—
185C2×Dic61—41no—
186C2×Dic61—41no—
187C2×Dic61—42no—
188C2×Dic61—42no—
189#92418—42no—
190#92418—81no—
191#9944—611nomaximal, Sylow
192C22×C61—21no—
193C22×C61—21no—
194C22×C61—21no—
195C22×C61—21no—
196C22×C61—21no—
197C22×C61—21no—
198C22×C61—21no—
199C22×C61—44no—
200C22×C61—44no—
201C22×C61—44no—
202C22×C61—42no—
203C22×C61—82no—
204C22×C61—82no—
205C22×C61—82no—
206C22×C61—82no—
207C22×C61—81no—
208C22×C61—81no—
209C22×C61#39211yescharacteristic
210C22×C61#45512yes—
211C22×C61#45812yes—
212C4×C61—21no—
213C4×C61—21no—
214C4×C61—21no—
215C4×C61—21no—
216C4×C61—82no—
217C4×C61—81no—
218C4×C61—81no—
219C4×C61—81no—
220Dic61—82no—
221Dic61—81no—
222Dic61—81no—
223#3095—611no—
224#2561D6111yescharacteristic
225#2482—611no—
226#1826—611no—
227#1511—611no—
228#1462—611no—
229#1284—611no—
230C2×C61—22no—
231C2×C61—22no—
232C2×C61—41no—
233C2×C61—82no—
234C2×C61#200411yescharacteristic
235C2×C61#201011yescharacteristic
236C2×C61#202211yescharacteristic
237C2×C22⋊Q8C2×D6111yescharacteristic
238C2×#117—611no—
239C22×C22⋊C4C2×D6111yescharacteristic
240#485—1222no—
241#484—1221no—
242#483—1221no—
243#428—1221no—
244#419—1221no—
245#407—611no—
246#407—611no—
247#399—1221no—
248#397—21no—
249#397—1221no—
250#393—21no—
251#388—22no—
252#388—1222no—
253#385—1221no—
254#381—21no—
255#381—611no—
256#379—21no—
257#379—1221no—
258C4×C22⋊C4C2×D6111yescharacteristic
259#339—1222no—
260#328—1222no—
261#323—1222no—
262C61#994411yescharacteristic, complemented, Sylow
263C25C22⋊D6111yescharacteristic
264C22×Q8C22⋊D6111yescharacteristic
265C23×C4C22⋊D6111yescharacteristic
266C23×C4C22×D6111yescharacteristic
267C2×M16—1221no—
268C2×M16—1221no—
269C22⋊Q8—21no—
270C22⋊Q8—21no—
271C22⋊Q8—21no—
272C22⋊Q8—21no—
273#117—1221no—
274#117—1221no—
275#117—1221no—
276#117—1221no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—611no—
279C2×C4⋊C4—611no—
280C2×C4⋊C4—1222no—
281C2×C4⋊C4C22⋊D6111yescharacteristic
282C2×C22⋊C4—22no—
283C2×C22⋊C4—21no—
284C2×C22⋊C4—21no—
285C2×C22⋊C4—21no—
286C2×C22⋊C4—21no—
287C2×C22⋊C4—21no—
288C2×C22⋊C4—21no—
289C2×C22⋊C4—21no—
290C2×C22⋊C4—21no—
291C2×C22⋊C4—22no—
292C2×C22⋊C4—1222no—
293C2×C22⋊C4—1222no—
294C2×C22⋊C4—1221no—
295C2×C22⋊C4—1221no—
296C2×C42—1221no—
297C2×C42C22⋊D6112yes—
298#107—1222no—
299#106—1222no—
300#103—1222no—
301#103—1222no—
302C22⋊C8—612no—
303C22⋊C8—1221no—
304C22⋊C8—1221no—
305C22⋊C8—1221no—
306#95—22no—
307#95—22no—
308#95—21no—
309#95—612no—
310#95—1222no—
311#95—1221no—
312C24—21no—
313C24—21no—
314C24—21no—
315C24—42no—
316C24—42no—
317C24—42no—
318C24C2×C22⋊D6111yescharacteristic
319C2×Q8—21no—
320C2×Q8—21no—
321C2×Q8—42no—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—22no—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—42no—
329C22×C4—42no—
330C22×C4—1222no—
331C22×C4—1221no—
332C22×C4—1221no—
333C22×C4D4×D6111yescharacteristic
334C22×C4D4×D6111yescharacteristic
335C22×C4D4×D6111yescharacteristic
336C22×C4#1175822411yescharacteristic
337C22×C4C2×C22⋊D6111yescharacteristic
338C22×C4C2×C22⋊D6111yescharacteristic
339M16—2442no—
340M16—2442no—
341C2×C8—1222no—
342C2×C8—2441no—
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—41no—
346C4⋊C4—41no—
347C4⋊C4—1221no—
348C4⋊C4—1221no—
349C4⋊C4—1221no—
350C4⋊C4—1221no—
351C4⋊C4—4882no—
352C22⋊C4—42no—
353C22⋊C4—44no—
354C22⋊C4—41no—
355C22⋊C4—41no—
356C22⋊C4—41no—
357C22⋊C4—41no—
358C22⋊C4—41no—
359C22⋊C4—41no—
360C22⋊C4—82no—
361C22⋊C4—4882no—
362C22⋊C4—2442no—
363C22⋊C4—2444no—
364C22⋊C4—2441no—
365C22⋊C4—2441no—
366C42—42no—
367C42—2441no—
368C42—2441no—
369C23—22no—
370C23—22no—
371C23—22no—
372C23—22no—
373C23—22no—
374C23—41no—
375C23—42no—
376C23—42no—
377C23—41no—
378C23—41no—
379C23—41no—
380C23—42no—
381C23—42no—
382C23—41no—
383C23—81no—
384C23—81no—
385C23—88no—
386C23#1451974511yescharacteristic
387C23#1451974611yescharacteristic
388C23#1451974911yescharacteristic
389Q8—42no—
390Q8—81no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—81no—
408C2×C4—2442no—
409C2×C4—2442no—
410C2×C4—2442no—
411C2×C4—2442no—
412C2×C4—2442no—
413C2×C4—2441no—
414C2×C4—2441no—
415C2×C4#1451974511yescharacteristic
416C2×C4#1451974811yescharacteristic
417C2×C4#1451974911yescharacteristic
418C2×C4#1451977311yescharacteristic
419C8—4881no—
420C8—2442no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—21no—
428C22—44no—
429C22—44no—
430C22—44no—
431C22—42no—
432C22—82no—
433C22—82no—
434C22—82no—
435C22—82no—
436C22—81no—
437C22—81no—
438C22#1683967011yescharacteristic
439C22#1683993912yes—
440C22#1683995212yes—
441C4—21no—
442C4—21no—
443C4—21no—
444C4—21no—
445C4—82no—
446C4—81no—
447C4—81no—
448C4—81no—
449C4—4882no—
450C4—4881no—
451C4—4881no—
452C2—22no—
453C2—22no—
454C2—41no—
455C2—82no—
456C2#2144684811yescharacteristic
457C2#2144688411yescharacteristic
458C2#2144694811yescharacteristic
subgroupG/H
centerC22#16839670
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
FittingC61×#2561C2
socleC22×C61#392
prime radicalC25×C61D4
hypercenter#2561D61
hypocenterC61#9944
LCSG ▷ C23×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2561

Complements

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

NH ≅ G/Ntype
1. #21455763C2semidirect
3. #21445919C2semidirect
4. #21444352C2semidirect
6. #21443672C2semidirect
262. C61#9944semidirect

Maximal subgroups

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

subgroupindex
#214557632
#214500932
#214459192
#214443522
#214441462
#214436722
C61×#25612
#994461