Finite Group Databasebeta

← #29575939

Subgroups — #29575939

Order 15616.

446 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 111 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#21455624C211yesmaximal, characteristic
2#21448784C211yesmaximal, characteristic
3#21444384C211yesmaximal, characteristic
4#21444319C211yesmaximal, characteristic
5#21443721C211yesmaximal, characteristic
6#21443678C211yesmaximal, characteristic
7C61×#1479C211yesmaximal, characteristic
8#16840319C2211yescharacteristic
9#16840069—22no—
10#16840057C412yescomplemented
11#16840047C412yescomplemented
12#16839802—21no—
13#16839786C2211yescharacteristic
14#16839771—21no—
15#16839669—21no—
16#16839648—22no—
17#16839630—21no—
18#16839628C2211yescharacteristic
19C4⋊C4×Dic61—21no—
20C4×C4⋊Dic61C2211yescharacteristic
21#16839608—21no—
22#16839500—22no—
23#16839500—21no—
24#16839500—21no—
25C2×C4×Q8×C61C2211yescharacteristic
26C61×#431C2211yescharacteristic
27C61×#431C2211yescharacteristic
28C61×Q8⋊C8—22no—
29C2×#11758194—21no—
30#14519777C2×C411yescharacteristic
31#14519777C2×C411yescharacteristic
32#14519769—21no—
33#14519756—21no—
34#14519756—21no—
35C4×Dic122—21no—
36C4×Dic122—21no—
37#14519736—21no—
38C2×C4⋊Dic61—21no—
39C2×C4⋊Dic61—21no—
40C2×C4×Dic61—22no—
41C2×C4×Dic61—21no—
42#14519710—22no—
43#14519708—22no—
44C4⋊#92418—21no—
45C4⋊#92418C2×C412yes—
46#14519701—22no—
47#14519701—22no—
48#14519684—22no—
49#14519684—22no—
50#14519684—22no—
51#14519684—21no—
52#14519684D411yescharacteristic
53#14519684D411yescharacteristic
54#14519684D412yes—
55C22×Q8×C61D411yescharacteristic
56C4×Q8×C61—21no—
57C4×Q8×C61—21no—
58C4×Q8×C61C2×C412yes—
59C4×Q8×C61D412yes—
60C2×C4⋊C4×C61—21no—
61C2×C4⋊C4×C61D411yescharacteristic
62C2×C42×C61—21no—
63C2×C42×C61C2311yescharacteristic
64C4⋊C8×C61—21no—
65C4⋊C8×C61—21no—
66C22⋊C8×C61—21no—
67C22⋊C8×C61—21no—
68C4×C8×C61—21no—
69C4×C8×C61—21no—
70C2×Q8×C61—21no—
71C2×Q8×C61—21no—
72C2×Q8×C61—21no—
73C2×Q8×C61—21no—
74C2×Q8×C61—21no—
75C2×Q8×C61C22⋊C412yes—
76C22×C4×C61—21no—
77C22×C4×C61—21no—
78C22×C4×C61C2×D411yescharacteristic
79C22×C4×C61C2×D411yescharacteristic
80C22×C4×C61C2×D411yescharacteristic
81C22×Dic61—21no—
82C22×Dic61—22no—
83C22×Dic61—21no—
84C2×Dic122—21no—
85C2×Dic122—21no—
86C2×C8×C61—41no—
87C2×C8×C61—41no—
88C4⋊C4×C61—22no—
89C4⋊C4×C61—22no—
90C4⋊C4×C61—21no—
91C4⋊C4×C61C22⋊C412yes—
92C42×C61—22no—
93C42×C61—22no—
94C42×C61C22×C411yescharacteristic
95C42×C61C2×D411yescharacteristic
96C42×C61#4111yescharacteristic
97C42×C61#4111yescharacteristic
98C22⋊Dic61—41no—
99C4⋊Dic61—21no—
100C4⋊Dic61—21no—
101C4⋊Dic61—21no—
102C4⋊Dic61—21no—
103C4⋊Dic61—42no—
104C4⋊Dic61—41no—
105C4⋊Dic61—41no—
106#11758196—41no—
107#11758196—41no—
108C4×Dic61—44no—
109C4×Dic61—41no—
110C4×Dic61—41no—
111C4×Dic61—41no—
112#11758194—41no—
113#11758194—41no—
114C2×#92418—22no—
115C23×C61#12011yescharacteristic
116Q8×C61—22no—
117Q8×C61—22no—
118Q8×C61—41no—
119Q8×C61—41no—
120C2×C4×C61—22no—
121C2×C4×C61—22no—
122C2×C4×C61—41no—
123C2×C4×C61—41no—
124C2×C4×C61—42no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61C2×C22⋊C411yescharacteristic
128C2×C4×C61C4×D411yescharacteristic
129C2×C4×C61C4×D411yescharacteristic
130C2×C4×C61#12111yescharacteristic
131C2×C4×C61#12111yescharacteristic
132C2×C4×C61#12311yescharacteristic
133C2×C4×C61#13511yescharacteristic
134C2×C4×C61#13511yescharacteristic
135C2×C4×C61#13711yescharacteristic
136C2×C4×C61#13711yescharacteristic
137C2×Dic61—22no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—42no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—42no—
144C2×Dic61—41no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61—42no—
148Dic122—81no—
149Dic122—81no—
150C8×C61—81no—
151C8×C61—81no—
152#92418—42no—
153#9178—611nomaximal, Sylow
154C22×C61—21no—
155C22×C61—21no—
156C22×C61#38611yescharacteristic
157C22×C61#45211yescharacteristic
158C22×C61#45211yescharacteristic
159C4×C61—21no—
160C4×C61—21no—
161C4×C61—21no—
162C4×C61—21no—
163C4×C61—42no—
164C4×C61—42no—
165C4×C61#41611yescharacteristic
166C4×C61#41911yescharacteristic
167C4×C61#48511yescharacteristic
168C4×C61#48511yescharacteristic
169Dic61—42no—
170Dic61—81no—
171Dic61—82no—
172Dic61—81no—
173Dic61—81no—
174#3078—611no—
175#2356—611no—
176#1518—611no—
177#1503—611no—
178#1479D6111yescharacteristic
179#1303—611no—
180#1286—611no—
181C2×C61—21no—
182C2×C61—21no—
183C2×C61#187311yescharacteristic
184C2×C61#190511yescharacteristic
185C2×C61#190611yescharacteristic
186#533—611no—
187C2×C4×Q8C2×D6111yescharacteristic
188#479—1222no—
189#477—612no—
190#475—612no—
191#431C2×D6111yescharacteristic
192#431C2×D6111yescharacteristic
193#428—1221no—
194#423—611no—
195#419—1221no—
196#391—1221no—
197#387—1222no—
198#383—1221no—
199#382—611no—
200C4×C4⋊C4—611no—
201C4×C4⋊C4—1221no—
202#376—1221no—
203#328—1221no—
204#328—1221no—
205#328—1222no—
206Q8⋊C8—22no—
207C61#917811yescharacteristic, complemented, Sylow
208C22×Q8D24411yescharacteristic
209C2×M16—1221no—
210C4⋊Q8—611no—
211C4⋊Q8—611no—
212#125—1221no—
213C22⋊Q8—1221no—
214C22⋊Q8—1221no—
215C4×Q8—21no—
216C4×Q8—21no—
217C4×Q8—1221no—
218C4×Q8—1221no—
219C4×Q8C4×D6112yes—
220C4×Q8C22⋊D6112yes—
221#117—1221no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—1221no—
224C2×C4⋊C4—1221no—
225C2×C4⋊C4D24411yescharacteristic
226C2×C42—21no—
227C2×C42—1222no—
228C2×C42—1221no—
229C2×C42C22×D6111yescharacteristic
230#107—1222no—
231#106—1222no—
232C4⋊C8—21no—
233C4⋊C8—21no—
234C4⋊C8—612no—
235C4⋊C8—1221no—
236#103—1222no—
237#103—1222no—
238C22⋊C8—21no—
239C22⋊C8—21no—
240C4×C8—21no—
241C4×C8—21no—
242#95—611no—
243#95—611no—
244#95—612no—
245#95—1222no—
246#95—1222no—
247#95—1222no—
248#95—1221no—
249C2×Q8—21no—
250C2×Q8—21no—
251C2×Q8—21no—
252C2×Q8—21no—
253C2×Q8—21no—
254C2×Q8—1221no—
255C2×Q8—1221no—
256C2×Q8#1175819812yes—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—1221no—
260C22×C4—1222no—
261C22×C4—1221no—
262C22×C4C2×D24411yescharacteristic
263C22×C4D4×D6111yescharacteristic
264C22×C4D4×D6111yescharacteristic
265M16—2441no—
266M16—2441no—
267C2×C8—41no—
268C2×C8—41no—
269C2×C8—1222no—
270C4⋊C4—22no—
271C4⋊C4—22no—
272C4⋊C4—21no—
273C4⋊C4—1221no—
274C4⋊C4—1221no—
275C4⋊C4—1221no—
276C4⋊C4—1221no—
277C4⋊C4—2442no—
278C4⋊C4—2441no—
279C4⋊C4—2441no—
280C4⋊C4—2441no—
281C4⋊C4—2441no—
282C4⋊C4#1175819812yes—
283C22⋊C4—2441no—
284C42—22no—
285C42—22no—
286C42—2444no—
287C42—2441no—
288C42—2441no—
289C42—2441no—
290C42C2×C4×D6111yescharacteristic
291C42#1175822411yescharacteristic
292C42#1175822411yescharacteristic
293C42C2×C22⋊D6111yescharacteristic
294C23#1451974711yescharacteristic
295Q8—22no—
296Q8—22no—
297Q8—41no—
298Q8—41no—
299Q8—4881no—
300Q8—4881no—
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—42no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—1222no—
309C2×C4—2442no—
310C2×C4—2441no—
311C2×C4—2442no—
312C2×C4—2441no—
313C2×C4—2441no—
314C2×C4—2441no—
315C2×C4—2441no—
316C2×C4—2442no—
317C2×C4—2441no—
318C2×C4—2441no—
319C2×C4C2×#1175819811yescharacteristic
320C2×C4#1451973711yescharacteristic
321C2×C4#1451973711yescharacteristic
322C2×C4#1451974911yescharacteristic
323C2×C4#1451974911yescharacteristic
324C2×C4#1451976111yescharacteristic
325C2×C4#1451979911yescharacteristic
326C2×C4#1451979911yescharacteristic
327C2×C4#1451981011yescharacteristic
328C2×C4#1451981011yescharacteristic
329C8—81no—
330C8—81no—
331C8—2442no—
332C22—21no—
333C22—21no—
334C22#1683963911yescharacteristic
335C22#1683992611yescharacteristic
336C22#1683992611yescharacteristic
337C4—21no—
338C4—21no—
339C4—21no—
340C4—21no—
341C4—42no—
342C4—42no—
343C4—4882no—
344C4—4881no—
345C4—4881no—
346C4—4881no—
347C4—2442no—
348C4#1683975911yescharacteristic
349C4#1683977211yescharacteristic
350C4#1684010411yescharacteristic
351C4#1684010411yescharacteristic
352C2—21no—
353C2—21no—
354C2#2144612911yescharacteristic
355C2#2144631111yescharacteristic
356C2#2144631811yescharacteristic
subgroupG/H
centerC22#16839639
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1479C2
socleC22×C61#386
prime radicalC23×C61#120
cosocleC2×C42×C61C23
hypercenter#1479D61
hypocenterC61#9178
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1479

Complements

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

NH ≅ G/Ntype
10. #16840057C4semidirect
11. #16840047C4semidirect
207. C61#9178semidirect

Maximal subgroups

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

subgroupindex
#214556242
#214487842
#214443842
#214443192
#214437212
#214436782
C61×#14792
#917861