Finite Group Databasebeta

← #29593046

Subgroups — #29593046

Order 15616.

398 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 59 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#21453233C211yesmaximal, characteristic
2#21444776C211yesmaximal, characteristic
3#21444776C211yesmaximal, characteristic
4#21443839C211yesmaximal, characteristic
5#21443839C211yesmaximal, characteristic
6#21443767C211yesmaximal, characteristic
7C61×#2062C211yesmaximal, characteristic
8#16839917—21no—
9#16839917—21no—
10#16839704—21no—
11#16839682—21no—
12#16839674C2211yescharacteristic
13#16839674C2211yescharacteristic
14#16839666—21no—
15#16839655—21no—
16#16839635—21no—
17#16839627—21no—
18#16839499—21no—
19#16839499—21no—
20#16839486C2211yescharacteristic
21#16839486C2211yescharacteristic
22C61×#543C2211yescharacteristic
23C61×#385—21no—
24C61×#385C2211yescharacteristic
25C61×#342—21no—
26C61×#342C2211yescharacteristic
27C22×Dic122D411yescharacteristic
28C22×Dic122D411yescharacteristic
29C2×#11758202—41no—
30C2×#11758202—41no—
31C2×C4⋊Dic61—21no—
32C2×#11758196—21no—
33C2×#11758196—21no—
34C2×C22⋊Dic61—21no—
35C2×C22⋊Dic61—21no—
36C2×C4×Dic61—21no—
37#14519700—41no—
38#14519700—41no—
39C22⋊#92418—21no—
40C22⋊#92418—21no—
41#14519684—21no—
42#14519684—21no—
43#14519684—21no—
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47#14519684D411yescharacteristic
48#14519684D411yescharacteristic
49C23×C4×C61D411yescharacteristic
50C22⋊Q8×C61—21no—
51C22⋊Q8×C61—21no—
52C22⋊Q8×C61—41no—
53C22⋊Q8×C61—41no—
54C2×C4⋊C4×C61—21no—
55C2×C4⋊C4×C61—41no—
56C2×C22⋊C4×C61—21no—
57C2×C22⋊C4×C61—21no—
58C2×C22⋊C4×C61D411yescharacteristic
59C2×C22⋊C4×C61C2311yescharacteristic
60#95×C61—21no—
61#95×C61—41no—
62C24×C61C2×D411yescharacteristic
63C2×Q8×C61—21no—
64C2×Q8×C61—21no—
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61—21no—
68C22×C4×C61—21no—
69C22×C4×C61—41no—
70C22×C4×C61—41no—
71C22×C4×C61—81no—
72C22×C4×C61C2×D411yescharacteristic
73C22×C4×C61C2×D411yescharacteristic
74C22×Dic61—21no—
75C22×Dic61—21no—
76C22×Dic61—21no—
77C22×Dic61—21no—
78C2×Dic122—41no—
79C2×Dic122—41no—
80C2×Dic122—42no—
81C2×Dic122—81no—
82C4⋊C4×C61—21no—
83C4⋊C4×C61—21no—
84C4⋊C4×C61—41no—
85C4⋊C4×C61—41no—
86C4⋊C4×C61—81no—
87C4⋊C4×C61—82no—
88C22⋊C4×C61—21no—
89C22⋊C4×C61—22no—
90C22⋊C4×C61—41no—
91C22⋊C4×C61—41no—
92C22⋊C4×C61—41no—
93C22⋊C4×C61—41no—
94C22⋊C4×C61Q1612yescomplemented
95C22⋊Dic61—42no—
96C22⋊Dic61—81no—
97#11758202—82no—
98#11758202—82no—
99C4⋊Dic61—81no—
100#11758196—81no—
101#11758196—81no—
102C4×Dic61—42no—
103C2×#92418—41no—
104C2×#92418—41no—
105C23×C61—21no—
106C23×C61—21no—
107C23×C61—41no—
108C23×C61—41no—
109C23×C61#12011yescharacteristic
110C23×C61C2×Q1611yescharacteristic
111C23×C61#13711yescharacteristic
112Q8×C61—81no—
113Q8×C61—81no—
114C2×C4×C61—22no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—41no—
118C2×C4×C61—41no—
119C2×C4×C61—41no—
120C2×C4×C61—41no—
121C2×C4×C61—41no—
122C2×C4×C61—42no—
123C2×C4×C61—41no—
124C2×C4×C61—42no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61—81no—
129C2×C4×C61—81no—
130C2×C4×C61—81no—
131C2×C4×C61—81no—
132C2×C4×C61—81no—
133C2×Dic61—22no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145Dic122—42no—
146Dic122—42no—
147Dic122—81no—
148Dic122—81no—
149#92418—81no—
150#92418—81no—
151#12253—611nomaximal, Sylow
152C22×C61—21no—
153C22×C61—21no—
154C22×C61—21no—
155C22×C61—21no—
156C22×C61—41no—
157C22×C61—41no—
158C22×C61—41no—
159C22×C61—41no—
160C22×C61—81no—
161C22×C61#45111yescharacteristic
162C22×C61#45611yescharacteristic
163C22×C61B(4,𝔽2)11yescharacteristic
164C4×C61—42no—
165C4×C61—41no—
166C4×C61—41no—
167C4×C61—82no—
168C4×C61—81no—
169C4×C61—81no—
170C4×C61—81no—
171Dic61—42no—
172Dic61—81no—
173Dic61—81no—
174Dic61—81no—
175#2763—611no—
176#2062D6111yescharacteristic
177#1602—611no—
178#1602—611no—
179#1351—611no—
180#1351—611no—
181#1326—611no—
182C2×C61—21no—
183C2×C61—21no—
184C2×C61—41no—
185C2×C61—41no—
186C2×C61#160511yescharacteristic
187C2×C61#219711yescharacteristic
188C2×C61#219911yescharacteristic
189#543C2×D6111yescharacteristic
190#451—1221no—
191#451—1221no—
192#400—1221no—
193#395—1221no—
194#393—611no—
195#393—611no—
196#391—1221no—
197#388—1221no—
198#385—21no—
199#385—1221no—
200#385C2×D6111yescharacteristic
201#382—1221no—
202#342—21no—
203#342C2×D6111yescharacteristic
204#328—1221no—
205#328—1221no—
206#323—611no—
207#323—611no—
208C61#1225311yescharacteristic, complemented, Sylow
209C22×Q8—611no—
210C22×Q8—611no—
211C23×C4C22⋊D6111yescharacteristic
212C2×Q16—2441no—
213C2×Q16—2441no—
214C22⋊Q8—21no—
215C22⋊Q8—21no—
216C22⋊Q8—41no—
217C22⋊Q8—41no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—41no—
220C2×C4⋊C4—1221no—
221C2×C4⋊C4—1221no—
222C2×C4⋊C4—1221no—
223C2×C22⋊C4—21no—
224C2×C22⋊C4—21no—
225C2×C22⋊C4—1221no—
226C2×C22⋊C4—1221no—
227C2×C22⋊C4C22⋊D6111yescharacteristic
228C2×C22⋊C4C22×D6111yescharacteristic
229C2×C42—1221no—
230#103—2441no—
231#103—2441no—
232C22⋊C8—1221no—
233C22⋊C8—1221no—
234#95—21no—
235#95—41no—
236#95—611no—
237#95—611no—
238#95—1221no—
239#95—1221no—
240#95—1221no—
241#95—1221no—
242#95—1221no—
243#95—1221no—
244C24C2×C22⋊D6111yescharacteristic
245C2×Q8—21no—
246C2×Q8—21no—
247C2×Q8—4881no—
248C2×Q8—2441no—
249C2×Q8—2441no—
250C2×Q8—2442no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—41no—
256C22×C4—41no—
257C22×C4—81no—
258C22×C4—1221no—
259C22×C4—1221no—
260C22×C4—1221no—
261C22×C4—1221no—
262C22×C4D4×D6111yescharacteristic
263C22×C4D4×D6111yescharacteristic
264Q16—4882no—
265Q16—4882no—
266C2×C8—2441no—
267C2×C8—2441no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—81no—
273C4⋊C4—82no—
274C4⋊C4—4881no—
275C4⋊C4—4881no—
276C4⋊C4—4881no—
277C22⋊C4—21no—
278C22⋊C4—22no—
279C22⋊C4—41no—
280C22⋊C4—41no—
281C22⋊C4—41no—
282C22⋊C4—41no—
283C22⋊C4—4881no—
284C22⋊C4—2442no—
285C22⋊C4#1175820212yescomplemented
286C42—2442no—
287C23—21no—
288C23—21no—
289C23—41no—
290C23—41no—
291C23#1451974511yescharacteristic
292C23C2×#1175820211yescharacteristic
293C23#1451980711yescharacteristic
294Q8—81no—
295Q8—81no—
296Q8—4881no—
297Q8—4881no—
298Q8—2442no—
299Q8—2442no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—22no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—42no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—42no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—81no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—81no—
319C2×C4—1222no—
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×C4—2441no—
329C2×C4—2441no—
330C2×C4—2441no—
331C8—4881no—
332C8—4881no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—81no—
342C22#1683991711yescharacteristic
343C22#1683994411yescharacteristic
344C22#1683994811yescharacteristic
345C4—42no—
346C4—41no—
347C4—41no—
348C4—82no—
349C4—81no—
350C4—81no—
351C4—81no—
352C4—4881no—
353C4—4881no—
354C4—4881no—
355C4—2442no—
356C2—21no—
357C2—21no—
358C2—41no—
359C2—41no—
360C2#2144479211yescharacteristic
361C2#2144780611yescharacteristic
362C2#2144781811yescharacteristic
subgroupG/H
centerC22#16839948
commutator, cosocleC2×C22⋊C4×C61C23
FrattiniC2×C22⋊C4C22×D61
FittingC61×#2062C2
socleC22×C61B(4,𝔽2)
prime radicalC24×C61C2×D4
hypercenter#2062D61
hypocenterC61#12253
LCSG ▷ C2×C22⋊C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #2062

Complements

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

NH ≅ G/Ntype
94. C22⋊C4×C61Q16semidirect
208. C61#12253semidirect
285. C22⋊C4#11758202semidirect

Maximal subgroups

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

subgroupindex
#214532332
#214447762
#214438392
#214437672
C61×#20622
#1225361