Finite Group Databasebeta

← #29578026

Subgroups — #29578026

Order 15616.

518 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 518 conjugacy classes of subgroups — too many to draw. Only its 91 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#21454858C211yesmaximal, characteristic
2#21451168C211yesmaximal, characteristic
3#21444155C211yesmaximal, characteristic
4#21444148C211yesmaximal, characteristic, complemented
5#21444148C211yesmaximal, characteristic, complemented
6#21443725C211yesmaximal, characteristic, complemented
7C61×#1305C211yesmaximal, characteristic, complemented
8C2×C4×C22⋊D61C2211yescharacteristic
9C22×#11758196C2211yescharacteristic
10#16839838—22no—
11#16839837—22no—
12#16839812—21no—
13#16839726C2211yescharacteristic
14#16839726C2211yescharacteristic
15#16839724—21no—
16#16839692—21no—
17#16839684—21no—
18#16839647—21no—
19#16839639C411yescharacteristic
20#16839639C411yescharacteristic
21#16839637C411yescharacteristic
22#16839637C411yescharacteristic
23#16839636—21no—
24#16839487—21no—
25#16839487—22no—
26#16839487—22no—
27#16839485—21no—
28C61×#407C2211yescharacteristic
29C61×#407C2211yescharacteristic
30C61×#380C2211yescharacteristic
31C22×C22⋊D61C2×C411yescharacteristic
32C23×Dic61C2×C411yescharacteristic
33C23×Dic61C2×C411yescharacteristic
34C22×C4×D61D411yescharacteristic
35C2×#11758194—21no—
36C2×#11758194—21no—
37C2×#11758189—22no—
38C4×C22⋊D61—21no—
39C4×C22⋊D61—21no—
40C4×C22⋊D61—21no—
41C4×C22⋊D61—21no—
42C2×C4⋊Dic61—21no—
43C2×C4⋊Dic61—21no—
44C2×#11758196—21no—
45C2×#11758196—21no—
46C2×#11758196—21no—
47C2×#11758196—21no—
48C2×#11758196—21no—
49C2×#11758196—21no—
50C2×#11758196D411yescharacteristic
51C2×C22⋊Dic61C2×C411yescharacteristic
52C2×#11758198—21no—
53C2×#11758198—21no—
54C2×#11758198D411yescharacteristic
55C2×C4×Dic61D411yescharacteristic
56#14519706—22no—
57C22⋊#92418—21no—
58C22⋊#92418—21no—
59C22⋊#92418—21no—
60C22⋊#92418D412yes—
61#14519689—22no—
62C8×Dic61—22no—
63#14519684—21no—
64#14519684—21no—
65#14519684—21no—
66#14519684—21no—
67C23×C4×C61C2311yescharacteristic
68C2×M16×C61—21no—
69C2×M16×C61—21no—
70C2×C4⋊C4×C61—21no—
71C2×C22⋊C4×C61C2×C411yescharacteristic
72C2×C22⋊C4×C61C2×C411yescharacteristic
73C22⋊C8×C61—21no—
74C22⋊C8×C61—21no—
75C22⋊C8×C61—21no—
76C22⋊C8×C61D412yes—
77#95×C61—21no—
78C24×C61C22×C411yescharacteristic
79C23×D61C22⋊C411yescharacteristic
80C22×C4×C61—21no—
81C22×C4×C61—21no—
82C22×C4×C61—81no—
83C22×C4×C61C2×D411yescharacteristic
84C22×C4×C61C2×D411yescharacteristic
85C22×C4×C61C2×D411yescharacteristic
86C22×C4×C61C2×D411yescharacteristic
87C22×C4×C61#4111yescharacteristic
88C22×C4×C61#4111yescharacteristic
89C2×C22⋊D61—21no—
90C2×C22⋊D61—21no—
91C2×C22⋊D61—22no—
92C2×C22⋊D61—41no—
93C22×Dic61—21no—
94C22×Dic61—21no—
95C22×Dic61—21no—
96C22×Dic61—21no—
97C22×Dic61—21no—
98C22×Dic61—21no—
99C22×Dic61—42no—
100C22×Dic61—81no—
101C22×Dic61C22⋊C411yescharacteristic
102C22×Dic61C22⋊C411yescharacteristic
103C22×Dic61C22⋊C411yescharacteristic
104C2×C4×D61—21no—
105C2×C4×D61—21no—
106C2×C4×D61—81no—
107M16×C61—81no—
108M16×C61—81no—
109C2×C8×C61—22no—
110C2×C8×C61—41no—
111C4⋊C4×C61—81no—
112C22⋊C4×C61—41no—
113C22⋊C4×C61—41no—
114C22⋊Dic61—21no—
115C22⋊Dic61—21no—
116#11758198—21no—
117#11758198—21no—
118#11758198—42no—
119#11758198—81no—
120C4⋊Dic61—42no—
121C4⋊Dic61—81no—
122#11758196—21no—
123#11758196—21no—
124#11758196—41no—
125#11758196—41no—
126#11758196—41no—
127#11758196—41no—
128C4×Dic61—21no—
129C4×Dic61—21no—
130#11758194—81no—
131#11758194—81no—
132C2×#92418—22no—
133C2×#92418—41no—
134#11758189—82no—
135C23×C61—21no—
136C23×C61—21no—
137C23×C61—41no—
138C23×C61—41no—
139C23×C61C2×C22⋊C411yescharacteristic
140C23×C61C4×D411yescharacteristic
141C23×C61C4×D411yescharacteristic
142C22×D61—21no—
143C22×D61—21no—
144C22×D61—21no—
145C22×D61—41no—
146C22×D61—41no—
147C2×C4×C61—41no—
148C2×C4×C61—41no—
149C2×C4×C61—41no—
150C2×C4×C61—41no—
151C2×C4×C61—41no—
152C2×C4×C61—41no—
153C2×C4×C61—41no—
154C2×C4×C61—41no—
155C2×C4×C61—41no—
156C2×C4×C61—41no—
157C2×C4×C61—41no—
158C2×C4×C61—41no—
159C2×C4×C61#12011yescharacteristic
160C2×C4×C61#12111yescharacteristic
161C2×C4×C61#12111yescharacteristic
162C2×C4×C61#12311yescharacteristic
163C22⋊D61—42no—
164C22⋊D61—42no—
165C2×Dic61—21no—
166C2×Dic61—21no—
167C2×Dic61—22no—
168C2×Dic61—22no—
169C2×Dic61—22no—
170C2×Dic61—21no—
171C2×Dic61—21no—
172C2×Dic61—41no—
173C2×Dic61—41no—
174C2×Dic61—41no—
175C2×Dic61—41no—
176C2×Dic61—41no—
177C2×Dic61—41no—
178C2×Dic61—41no—
179C2×Dic61—41no—
180C2×Dic61—41no—
181C2×Dic61—81no—
182C2×Dic61—81no—
183C2×Dic61#10112yes—
184C4×D61—42no—
185C4×D61—81no—
186C8×C61—42no—
187C8×C61—81no—
188#92418—42no—
189#92418—81no—
190#9518—611nomaximal, Sylow
191C22×C61—21no—
192C22×C61—21no—
193C22×C61—21no—
194C22×C61—21no—
195C22×C61—21no—
196C22×C61—21no—
197C22×C61—21no—
198C22×C61—21no—
199C22×C61—42no—
200C22×C61—42no—
201C22×C61#38611yescharacteristic
202C22×C61C2×#10111yescharacteristic
203C22×C61#41311yescharacteristic
204C2×D61—42no—
205C2×D61—41no—
206C2×D61—41no—
207C2×D61—41no—
208C2×D61—81no—
209C4×C61—21no—
210C4×C61—21no—
211C4×C61—21no—
212C4×C61—21no—
213C4×C61—81no—
214C4×C61—81no—
215Dic61—22no—
216Dic61—42no—
217Dic61—41no—
218Dic61—41no—
219Dic61—81no—
220#2975—611no—
221#2579—611no—
222#1465—611no—
223#1463—611no—
224#1463—611no—
225#1305—611no—
226#1305D6111yescharacteristic, complemented
227C2×C61—21no—
228C2×C61—21no—
229C2×C61—41no—
230C2×C61—41no—
231C2×C61#189111yescharacteristic
232C2×C61#190111yescharacteristic
233C2×C61#191311yescharacteristic
234D61—81no—
235C2×C4×D4—611no—
236C22×C4⋊C4—611no—
237#436—1222no—
238#436—1222no—
239#431—1221no—
240#407—611no—
241#407—611no—
242#407—1221no—
243#407C2×D6111yescharacteristic
244#407C2×D6111yescharacteristic
245#398—1221no—
246#396—1221no—
247#387—1221no—
248#386—611no—
249#386—611no—
250#385—611no—
251#385—611no—
252#385—1221no—
253#380C2×D6111yescharacteristic
254#324—1222no—
255#324—1221no—
256#324—1222no—
257#323—1221no—
258C61#951811yescharacteristic, complemented, Sylow
259C22×D4—611no—
260C23×C4—611no—
261C23×C4—611no—
262C23×C4—611no—
263C23×C4C22×D6111yescharacteristic
264C2×M16—21no—
265C2×M16—21no—
266C2×M16—1222no—
267C2×M16—1221no—
268C2×M16—1221no—
269C4×D4—1221no—
270C4×D4—1221no—
271C4×D4—1221no—
272C4×D4—1221no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—611no—
275C2×C4⋊C4—1221no—
276C2×C4⋊C4—1221no—
277C2×C4⋊C4—1221no—
278C2×C4⋊C4—1221no—
279C2×C4⋊C4—1221no—
280C2×C4⋊C4—1221no—
281C2×C4⋊C4—1221no—
282C2×C4⋊C4—1221no—
283C2×C22⋊C4—611no—
284C2×C22⋊C4—611no—
285C2×C22⋊C4—1221no—
286C2×C22⋊C4—1221no—
287C2×C22⋊C4C4×D6111yescharacteristic
288C2×C22⋊C4C4×D6111yescharacteristic
289C2×C42—611no—
290C4⋊C8—1222no—
291C22⋊C8—21no—
292C22⋊C8—21no—
293C22⋊C8—21no—
294C22⋊C8—612no—
295C22⋊C8—1222no—
296C22⋊C8—1221no—
297C22⋊C8—1221no—
298C22⋊C8—1221no—
299C22⋊C8D24412yes—
300C4×C8—1222no—
301#95—21no—
302#95—1221no—
303#95—1221no—
304#95—1221no—
305#95—1221no—
306C24—611no—
307C24C2×C4×D6111yescharacteristic
308C2×D4—1222no—
309C2×D4—1221no—
310C2×D4—1221no—
311C2×D4—2441no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—81no—
315C22×C4—611no—
316C22×C4—611no—
317C22×C4—611no—
318C22×C4—1221no—
319C22×C4—1221no—
320C22×C4—1221no—
321C22×C4—1221no—
322C22×C4—1221no—
323C22×C4—1221no—
324C22×C4—1221no—
325C22×C4—1221no—
326C22×C4—4881no—
327C22×C4—4881no—
328C22×C4—2442no—
329C22×C4C2×D24411yescharacteristic
330C22×C4#1175822211yescharacteristic
331C22×C4D4×D6111yescharacteristic
332C22×C4D4×D6111yescharacteristic
333C22×C4D4×D6111yescharacteristic
334C22×C4#1175822611yescharacteristic
335M16—81no—
336M16—81no—
337M16—4882no—
338M16—4881no—
339M16—4881no—
340C2×C8—22no—
341C2×C8—41no—
342C2×C8—1222no—
343C2×C8—2441no—
344C4⋊C4—81no—
345C4⋊C4—1221no—
346C4⋊C4—1221no—
347C4⋊C4—4881no—
348C4⋊C4—2442no—
349C4⋊C4—2441no—
350C4⋊C4—2441no—
351C4⋊C4—2441no—
352C4⋊C4—2441no—
353C22⋊C4—41no—
354C22⋊C4—41no—
355C22⋊C4—1221no—
356C22⋊C4—1221no—
357C22⋊C4—1221no—
358C22⋊C4—1221no—
359C22⋊C4—4881no—
360C22⋊C4—2442no—
361C42—1221no—
362C42—1221no—
363C23—21no—
364C23—21no—
365C23—41no—
366C23—41no—
367C23—1221no—
368C23—1221no—
369C23—1221no—
370C23—2441no—
371C23—2441no—
372C23C22⋊C4×D6111yescharacteristic
373C23#1451973911yescharacteristic
374C23C4×D24411yescharacteristic
375D4—2442no—
376D4—2442no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—612no—
390C2×C4—1221no—
391C2×C4—1221no—
392C2×C4—1222no—
393C2×C4—1222no—
394C2×C4—1222no—
395C2×C4—1221no—
396C2×C4—1221no—
397C2×C4—4881no—
398C2×C4—4881no—
399C2×C4—4881no—
400C2×C4—2442no—
401C2×C4—2441no—
402C2×C4—2441no—
403C2×C4—2441no—
404C2×C4—2441no—
405C2×C4—2441no—
406C2×C4—2441no—
407C2×C4—2441no—
408C2×C4—2441no—
409C2×C4—2441no—
410C2×C4#1451974711yescharacteristic
411C2×C4#1451975011yescharacteristic
412C2×C4#1451975211yescharacteristic
413C2×C4#1451976211yescharacteristic
414C8—42no—
415C8—81no—
416C8—4881no—
417C8—2442no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—42no—
427C22—42no—
428C22—4881no—
429C22—2442no—
430C22—2441no—
431C22—2441no—
432C22—2441no—
433C22#1683964011yescharacteristic
434C22#101×D6111yescharacteristic
435C22#1683974311yescharacteristic
436C4—21no—
437C4—21no—
438C4—21no—
439C4—21no—
440C4—81no—
441C4—81no—
442C4—1222no—
443C4—4881no—
444C4—2442no—
445C4—2441no—
446C4—2441no—
447C2—21no—
448C2—21no—
449C2—41no—
450C2—41no—
451C2—4881no—
452C2#2144623611yescharacteristic
453C2#2144628611yescharacteristic
454C2#2144636011yescharacteristic
subgroupG/H
centerC22#16839640
commutatorC24×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1305C2
socleC22×C61#386
prime radicalC22×C22⋊D61C2×C4
cosocleC23×C4×C61C23
hypercenter#1305D61
hypocenterC61#9518
LCSG ▷ C24×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1305

Complements

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

NH ≅ G/Ntype
4. #21444148C2semidirect
5. #21444148C2semidirect
6. #21443725C2semidirect
7. C61×#1305C2semidirect
226. #1305D61semidirect
258. C61#9518semidirect

Maximal subgroups

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

subgroupindex
#214548582
#214511682
#214441552
#214441482
#214437252
C61×#13052
#951861