Finite Group Databasebeta

← #29577309

Subgroups — #29577309

Order 15616.

424 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 103 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#21448625C211yesmaximal, characteristic
2#21446764C211yesmaximal, characteristic
3#21444421C211yesmaximal, characteristic
4#21444370C211yesmaximal, characteristic
5#21443685C211yesmaximal, characteristic
6#21443674C211yesmaximal, characteristic
7C61×#3236C211yesmaximal, characteristic
8#16839819C2211yescharacteristic
9C4×#11758194C2211yescharacteristic
10#16839661—21no—
11#16839648—21no—
12#16839648—21no—
13#16839648—21no—
14#16839648—21no—
15#16839630C2211yescharacteristic
16C4⋊C4×Dic61—21no—
17C4×C4⋊Dic61C2211yescharacteristic
18#16839521—21no—
19#16839521—21no—
20#16839504—22no—
21#16839499—21no—
22#16839499—21no—
23C61×#533C2211yescharacteristic
24C2×#125×C61C2211yescharacteristic
25C61×#501C412yescomplemented
26C61×#491C412yescomplemented
27C61×#484—21no—
28C61×#483—21no—
29C61×#479—22no—
30C61×#432C2211yescharacteristic
31C2×#11758194—21no—
32C2×C4⋊Dic61—21no—
33C2×C4⋊Dic61—21no—
34C2×C4⋊Dic61—21no—
35C2×C4×Dic61—21no—
36C2×C4×Dic61—21no—
37C2×C4×Dic61D411yescharacteristic
38C2×C4×Dic61D411yescharacteristic
39C4⋊#92418—21no—
40C22⋊#92418—21no—
41#14519688—21no—
42#14519688—21no—
43C4×#92418—21no—
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51#14519684D411yescharacteristic
52#14519684D411yescharacteristic
53C4⋊Q8×C61C2×C411yescharacteristic
54C4⋊Q8×C61C2×C411yescharacteristic
55#125×C61—21no—
56#125×C61—21no—
57#125×C61—21no—
58#125×C61C2×C412yes—
59#125×C61D412yes—
60C22⋊Q8×C61—21no—
61C22⋊Q8×C61—21no—
62C4×Q8×C61—21no—
63C4×Q8×C61—21no—
64#117×C61—21no—
65C2×C4⋊C4×C61—21no—
66C2×C4⋊C4×C61—21no—
67C2×C4⋊C4×C61D411yescharacteristic
68C2×C4⋊C4×C61D411yescharacteristic
69C2×C42×C61C2311yescharacteristic
70#107×C61—22no—
71#106×C61—22no—
72C4⋊C8×C61—21no—
73#103×C61—22no—
74#103×C61—22no—
75C22⋊C8×C61—21no—
76#97×C61C2×C412yes—
77C2×Q8×C61—21no—
78C2×Q8×C61—21no—
79C22×C4×C61—21no—
80C22×C4×C61—21no—
81C22×C4×C61C2×D411yescharacteristic
82C22×C4×C61C2×D411yescharacteristic
83C22×C4×C61C2×D411yescharacteristic
84C22×Dic61—21no—
85C22×Dic61—21no—
86C22×Dic61—21no—
87C22×Dic61—21no—
88C2×C8×C61—22no—
89C4⋊C4×C61—22no—
90C4⋊C4×C61—22no—
91C4⋊C4×C61—22no—
92C4⋊C4×C61—22no—
93C4⋊C4×C61—21no—
94C4⋊C4×C61—21no—
95C4⋊C4×C61—21no—
96C4⋊C4×C61—21no—
97C4⋊C4×C61—21no—
98C4⋊C4×C61—21no—
99C4⋊C4×C61—41no—
100C4⋊C4×C61—41no—
101C4⋊C4×C61C22⋊C412yes—
102C4⋊C4×C61C22⋊C412yes—
103C22⋊C4×C61—41no—
104C42×C61—41no—
105C42×C61C22×C411yescharacteristic
106C42×C61C2×D411yescharacteristic
107C42×C61#4111yescharacteristic
108C42×C61#4111yescharacteristic
109C4⋊Dic61—42no—
110C4⋊Dic61—42no—
111C4⋊Dic61—81no—
112C4×Dic61—42no—
113C4×Dic61—41no—
114C4×Dic61—41no—
115C4×Dic61—81no—
116#11758194—22no—
117#11758194—41no—
118C2×#92418—41no—
119C2×#92418—41no—
120C23×C61#12011yescharacteristic
121Q8×C61—42no—
122Q8×C61—81no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—22no—
126C2×C4×C61—22no—
127C2×C4×C61—41no—
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×C61—41no—
135C2×C4×C61C2×C22⋊C411yescharacteristic
136C2×C4×C61C4×D411yescharacteristic
137C2×C4×C61C4×D411yescharacteristic
138C2×C4×C61#12111yescharacteristic
139C2×C4×C61#12111yescharacteristic
140C2×C4×C61#12311yescharacteristic
141C2×Dic61—22no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C8×C61—42no—
154#92418—42no—
155#92418—81no—
156#9380—611nomaximal, Sylow
157C22×C61—21no—
158C22×C61—21no—
159C22×C61#38611yescharacteristic
160C22×C61#45511yescharacteristic
161C22×C61#45611yescharacteristic
162C4×C61—21no—
163C4×C61—21no—
164C4×C61—21no—
165C4×C61—21no—
166C4×C61—21no—
167C4×C61—21no—
168C4×C61—42no—
169C4×C61—42no—
170C4×C61—81no—
171C4×C61—81no—
172Dic61—42no—
173Dic61—81no—
174Dic61—81no—
175Dic61—81no—
176#3236D6111yescharacteristic
177#2336—611no—
178#1986—611no—
179#1528—611no—
180#1515—611no—
181#1288—611no—
182#1285—611no—
183C2×C61—21no—
184C2×C61—21no—
185C2×C61#188211yescharacteristic
186C2×C61#190611yescharacteristic
187C2×C61#191211yescharacteristic
188#533C2×D6111yescharacteristic
189C2×#125C2×D6111yescharacteristic
190#501Dic6112yescomplemented
191#491Dic6112yescomplemented
192#484—21no—
193#483—21no—
194#479—22no—
195#432—611no—
196#432C2×D6111yescharacteristic
197C4×M16—611no—
198#389—1221no—
199#387—1221no—
200#387—1221no—
201#387—1221no—
202#387—1221no—
203#383—611no—
204C4×C4⋊C4—611no—
205C4×C4⋊C4—1221no—
206#339—1221no—
207#339—1221no—
208#330—1222no—
209#328—1221no—
210#328—1221no—
211C61#938011yescharacteristic, complemented, Sylow
212C2×M16—1221no—
213C4⋊Q8C2×Dic6111yescharacteristic
214C4⋊Q8C2×Dic6111yescharacteristic
215#125—21no—
216#125—21no—
217#125—21no—
218#125C2×Dic6112yes—
219#125C22⋊D6112yes—
220C22⋊Q8—21no—
221C22⋊Q8—21no—
222C4×Q8—21no—
223C4×Q8—21no—
224#117—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—1221no—
228C2×C4⋊C4—1221no—
229C2×C4⋊C4—1221no—
230C2×C4⋊C4C22⋊D6111yescharacteristic
231C2×C4⋊C4C22⋊D6111yescharacteristic
232C2×C42—611no—
233C2×C42—611no—
234C2×C42—1221no—
235C2×C42—1221no—
236C2×C42C22×D6111yescharacteristic
237#107—22no—
238#106—22no—
239C4⋊C8—21no—
240C4⋊C8—1221no—
241#103—22no—
242#103—22no—
243C22⋊C8—21no—
244C22⋊C8—1221no—
245#97—1221no—
246#97—1221no—
247#97C2×Dic6112yes—
248C4×C8—1221no—
249#95—611no—
250#95—611no—
251#95—1221no—
252#95—1221no—
253#95—1221no—
254#95—1221no—
255#95—1221no—
256#95—1221no—
257#95—1221no—
258C2×Q8—21no—
259C2×Q8—21no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—1221no—
263C22×C4—1221no—
264C22×C4—1221no—
265C22×C4—1221no—
266C22×C4D4×D6111yescharacteristic
267C22×C4D4×D6111yescharacteristic
268C22×C4C2×C22⋊D6111yescharacteristic
269M16—1222no—
270M16—2441no—
271C2×C8—22no—
272C2×C8—2441no—
273C2×C8—2441no—
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4—22no—
277C4⋊C4—22no—
278C4⋊C4—21no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—21no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—4881no—
287C4⋊C4—2442no—
288C4⋊C4—2442no—
289C4⋊C4C22⋊Dic6112yes—
290C4⋊C4C22⋊Dic6112yes—
291C22⋊C4—41no—
292C42—41no—
293C42—4881no—
294C42—2441no—
295C42—2441no—
296C42—2442no—
297C42#1175822411yescharacteristic
298C42#1175822411yescharacteristic
299C42C22×Dic6111yescharacteristic
300C42C2×C22⋊D6111yescharacteristic
301C23#1451974511yescharacteristic
302Q8—42no—
303Q8—81no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—1222no—
317C2×C4—2441no—
318C2×C4—2441no—
319C2×C4—2441no—
320C2×C4—2441no—
321C2×C4—2441no—
322C2×C4—2441no—
323C2×C4—2441no—
324C2×C4—2441no—
325C2×C4—2441no—
326C2×C4—2441no—
327C2×C4—2441no—
328C2×C4C2×C22⋊Dic6111yescharacteristic
329C2×C4D4×Dic6111yescharacteristic
330C2×C4D4×Dic6111yescharacteristic
331C2×C4#1451974911yescharacteristic
332C2×C4#1451974911yescharacteristic
333C2×C4#1451975811yescharacteristic
334C8—42no—
335C8—4881no—
336C8—2442no—
337C22—21no—
338C22—21no—
339C22#1683964211yescharacteristic
340C22#1683993811yescharacteristic
341C22#1683994311yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—42no—
349C4—42no—
350C4—81no—
351C4—81no—
352C4—4881no—
353C4—4881no—
354C4—4881no—
355C4—2442no—
356C2—21no—
357C2—21no—
358C2#2144619011yescharacteristic
359C2#2144632211yescharacteristic
360C2#2144635711yescharacteristic
subgroupG/H
centerC22#16839642
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#3236C2
socleC22×C61#386
prime radicalC23×C61#120
cosocleC2×C42×C61C23
hypercenter#3236D61
hypocenterC61#9380
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3236

Complements

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

NH ≅ G/Ntype
25. C61×#501C4semidirect
26. C61×#491C4semidirect
190. #501Dic61semidirect
191. #491Dic61semidirect
211. C61#9380semidirect

Maximal subgroups

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

subgroupindex
#214486252
#214467642
#214444212
#214443702
#214436852
#214436742
C61×#32362
#938061