Finite Group Databasebeta

← #29573633

Subgroups — #29573633

Order 15616.

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

normal subgroups only

This group has 384 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#21448785C211yesmaximal, characteristic
2C4×#14519695C211yesmaximal, characteristic
3#21444162C211yesmaximal, characteristic
4#21443712C211yesmaximal, characteristic
5#21443685C211yesmaximal, characteristic
6#21443684C211yesmaximal, characteristic
7C61×#1300C211yesmaximal, characteristic
8C2×C4×Dic122C2211yescharacteristic
9#16839819C2211yescharacteristic
10C2×#14519695—21no—
11C4×#11758194C2211yescharacteristic
12#16839666—21no—
13#16839647—21no—
14#16839646—21no—
15#16839630C2211yescharacteristic
16#16839629C411yescharacteristic
17#16839626C411yescharacteristic
18C4×#11758196—21no—
19#16839613C411yescharacteristic
20#16839607C411yescharacteristic
21#16839530—21no—
22#16839487—21no—
23#16839487—21no—
24C61×#432C2211yescharacteristic
25C4×M16×C61C2211yescharacteristic
26C61×#376C2211yescharacteristic
27C22×Dic122D411yescharacteristic
28C2×#11758194—21no—
29C4×Dic122—21no—
30C4×Dic122—21no—
31C4×Dic122—21no—
32C4×Dic122—21no—
33C2×C4⋊Dic61D411yescharacteristic
34C2×#11758196—21no—
35C2×#11758196—21no—
36C2×#11758196D411yescharacteristic
37C2×#11758196D411yescharacteristic
38C2×C4×Dic61—21no—
39C2×C4×Dic61—21no—
40C2×C4×Dic61C2×C411yescharacteristic
41C2×C4×Dic61C2×C411yescharacteristic
42C4⋊#92418—21no—
43#14519695—24no—
44C22⋊#92418—21no—
45#14519688—21no—
46#14519688—21no—
47C4×#92418—21no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51#14519684—21no—
52#14519684—21no—
53#14519684—21no—
54#14519684C2×C411yescharacteristic
55#14519684C2×C411yescharacteristic
56C2×M16×C61—21no—
57C2×C42×C61—21no—
58C2×C42×C61C2311yescharacteristic
59C4⋊C8×C61—21no—
60C22⋊C8×C61—21no—
61#97×C61—21no—
62#97×C61—21no—
63C4×C8×C61—21no—
64#95×C61—21no—
65#95×C61C2×C411yescharacteristic
66#95×C61C2×C411yescharacteristic
67C22×C4×C61—21no—
68C22×C4×C61—21no—
69C22×C4×C61C22×C411yescharacteristic
70C22×C4×C61C2×D411yescharacteristic
71C22×C4×C61C2×D411yescharacteristic
72C22×Dic61—21no—
73C22×Dic61—21no—
74C22×Dic61C22⋊C411yescharacteristic
75C22×Dic61C22⋊C411yescharacteristic
76C22×Dic61C22⋊C411yescharacteristic
77C22×Dic61C22⋊C411yescharacteristic
78C2×Dic122—21no—
79C2×Dic122—21no—
80C2×Dic122—22no—
81C2×Dic122—41no—
82M16×C61—22no—
83M16×C61—41no—
84C2×C8×C61—41no—
85C2×C8×C61—41no—
86C42×C61—42no—
87C42×C61#4111yescharacteristic
88C42×C61#4111yescharacteristic
89C42×C61#4111yescharacteristic
90C42×C61#4111yescharacteristic
91C4⋊Dic61—21no—
92C4⋊Dic61—21no—
93#11758196—21no—
94#11758196—21no—
95#11758196—21no—
96#11758196—21no—
97#11758196—42no—
98#11758196—42no—
99C4×Dic61—21no—
100C4×Dic61—21no—
101C4×Dic61—21no—
102C4×Dic61—21no—
103C4×Dic61—42no—
104C4×Dic61—42no—
105#11758194—22no—
106#11758194—41no—
107C2×#92418—41no—
108C2×#92418—41no—
109C23×C61C2×C22⋊C411yescharacteristic
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61—22no—
113C2×C4×C61—41no—
114C2×C4×C61—41no—
115C2×C4×C61—41no—
116C2×C4×C61—41no—
117C2×C4×C61—41no—
118C2×C4×C61—41no—
119C2×C4×C61—41no—
120C2×C4×C61#11711yescharacteristic
121C2×C4×C61#11711yescharacteristic
122C2×C4×C61#12311yescharacteristic
123C2×C4×C61#12311yescharacteristic
124C2×C4×C61#12311yescharacteristic
125C2×C4×C61#12311yescharacteristic
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—21no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61#10412yes—
142Dic122—42no—
143Dic122—42no—
144C8×C61—42no—
145C8×C61—81no—
146#92418—42no—
147#92418—81no—
148#8775—611nomaximal, Sylow
149C22×C61—21no—
150C22×C61—21no—
151C22×C61#38111yescharacteristic
152C22×C61C2×#10411yescharacteristic
153C22×C61#42111yescharacteristic
154C4×C61—21no—
155C4×C61—21no—
156C4×C61—21no—
157C4×C61—21no—
158C4×C61—21no—
159C4×C61—21no—
160C4×C61—42no—
161C4×C61—81no—
162Dic61—22no—
163Dic61—41no—
164Dic61—41no—
165Dic61—41no—
166Dic61—81no—
167Dic61—81no—
168#2356—611no—
169C4×#101—611no—
170#1467—611no—
171#1300—611no—
172#1300D6111yescharacteristic
173#1288—611no—
174#1288—611no—
175C2×C61—21no—
176C2×C61—21no—
177C2×C61#182611yescharacteristic
178C2×C61#182711yescharacteristic
179C2×C61#183011yescharacteristic
180C2×C4×Q8—611no—
181#432—611no—
182#432C2×D6111yescharacteristic
183C2×#101—1221no—
184C4×M16—611no—
185C4×M16C2×D6111yescharacteristic
186#391—1221no—
187#387—1221no—
188#387—1221no—
189#383—611no—
190#383—611no—
191#382—611no—
192C4×C4⋊C4—611no—
193C4×C4⋊C4—1221no—
194#376—611no—
195#376C2×D6111yescharacteristic
196#343—1221no—
197#324—1221no—
198#324—1221no—
199C61#877511yescharacteristic, complemented, Sylow
200C22×Q8—611no—
201C2×M16—21no—
202C2×M16—1221no—
203C4×Q8—1221no—
204C4×Q8—1221no—
205C4×Q8—1221no—
206C4×Q8—1221no—
207C2×C4⋊C4—611no—
208C2×C4⋊C4—611no—
209C2×C4⋊C4—611no—
210C2×C4⋊C4—1221no—
211C2×C4⋊C4—1221no—
212C2×C42—21no—
213C2×C42—611no—
214C2×C42—611no—
215C2×C42—1221no—
216C2×C42—1221no—
217C2×C42C22×D6111yescharacteristic
218C4⋊C8—21no—
219C4⋊C8—1221no—
220#101—1224no—
221C22⋊C8—21no—
222C22⋊C8—1221no—
223#97—21no—
224#97—21no—
225#97—1221no—
226#97—1221no—
227C4×C8—21no—
228C4×C8—1221no—
229#95—21no—
230#95—611no—
231#95—611no—
232#95—1221no—
233#95—1221no—
234#95—1221no—
235#95—1221no—
236#95—1221no—
237#95—1221no—
238#95C4×D6111yescharacteristic
239#95C4×D6111yescharacteristic
240C2×Q8—1222no—
241C2×Q8—1221no—
242C2×Q8—1221no—
243C2×Q8—2441no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—611no—
247C22×C4—611no—
248C22×C4—611no—
249C22×C4—611no—
250C22×C4—1221no—
251C22×C4—1221no—
252C22×C4C2×C4×D6111yescharacteristic
253C22×C4D4×D6111yescharacteristic
254C22×C4D4×D6111yescharacteristic
255M16—22no—
256M16—41no—
257M16—1222no—
258M16—2441no—
259C2×C8—41no—
260C2×C8—41no—
261C2×C8—2441no—
262C2×C8—2441no—
263C4⋊C4—1221no—
264C4⋊C4—1221no—
265C4⋊C4—1221no—
266C4⋊C4—1221no—
267C4⋊C4—1221no—
268C4⋊C4—1221no—
269C4⋊C4—2442no—
270C4⋊C4—2442no—
271C42—42no—
272C42—1221no—
273C42—1221no—
274C42—1221no—
275C42—1221no—
276C42—2442no—
277C42—2442no—
278C42#1175822211yescharacteristic
279C42#1175822211yescharacteristic
280C42#1175822411yescharacteristic
281C42#1175822611yescharacteristic
282C23C22⋊C4×D6111yescharacteristic
283Q8—2442no—
284Q8—2442no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—22no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—612no—
296C2×C4—1221no—
297C2×C4—1221no—
298C2×C4—1221no—
299C2×C4—1221no—
300C2×C4—1221no—
301C2×C4—1221no—
302C2×C4—1221no—
303C2×C4—2441no—
304C2×C4—2441no—
305C2×C4—2441no—
306C2×C4—2441no—
307C2×C4—2441no—
308C2×C4—2441no—
309C2×C4—2441no—
310C2×C4—2441no—
311C2×C4#1451973411yescharacteristic
312C2×C4#1451973511yescharacteristic
313C2×C4#1451975911yescharacteristic
314C2×C4#1451975911yescharacteristic
315C2×C4#1451976211yescharacteristic
316C2×C4#1451976211yescharacteristic
317C8—42no—
318C8—81no—
319C8—4881no—
320C8—2442no—
321C22—21no—
322C22—21no—
323C22#1683962411yescharacteristic
324C22#104×D6111yescharacteristic
325C22#1683977711yescharacteristic
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—21no—
332C4—42no—
333C4—81no—
334C4—1222no—
335C4—4881no—
336C4—4881no—
337C4—2441no—
338C4—2441no—
339C4—2441no—
340C2—21no—
341C2—21no—
342C2#2144591711yescharacteristic
343C2#2144592211yescharacteristic
344C2#2144593211yescharacteristic
subgroupG/H
centerC22#16839624
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1300C2
socleC22×C61#381
prime radicalC23×C61C2×C22⋊C4
cosocleC2×C42×C61C23
hypercenter#1300D61
hypocenterC61#8775
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1300

Complements

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

NH ≅ G/Ntype
199. C61#8775semidirect

Maximal subgroups

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

subgroupindex
#214487852
C4×#145196952
#214441622
#214437122
#214436852
#214436842
C61×#13002
#877561