Finite Group Databasebeta

← #29593048

Subgroups — #29593048

Order 15616.

398 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 63 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#21447172C211yesmaximal, characteristic
2#21444775C211yesmaximal, characteristic
3#21444775C211yesmaximal, characteristic
4#21443840C211yesmaximal, characteristic
5#21443840C211yesmaximal, characteristic
6#21443767C211yesmaximal, characteristic
7C61×#2763C211yesmaximal, characteristic
8#16840388C2211yescharacteristic
9#16839918—21no—
10#16839918—21no—
11#16839635—21no—
12#16839529C2211yescharacteristic
13#16839528—21no—
14#16839498—21no—
15#16839498—21no—
16#16839486C2211yescharacteristic
17#16839486C2211yescharacteristic
18C61×#400—21no—
19C61×#395—21no—
20C61×#393C2211yescharacteristic
21C61×#393C2211yescharacteristic
22C61×#391—21no—
23C61×#388—21no—
24C61×#385—21no—
25C61×#385C2211yescharacteristic
26C61×#382—21no—
27C2×#11758202—41no—
28C2×#11758202—41no—
29#14519756—21no—
30#14519756—21no—
31#14519754—41no—
32#14519754—41no—
33C2×#11758196—41no—
34C2×C22⋊Dic61—21no—
35C2×C22⋊Dic61—21no—
36#14519701—41no—
37#14519701—41no—
38C22⋊#92418—21no—
39C22⋊#92418—21no—
40#14519684—41no—
41C22×Q8×C61D411yescharacteristic
42C22×Q8×C61D411yescharacteristic
43C23×C4×C61D411yescharacteristic
44C2×C4⋊C4×C61—21no—
45C2×C4⋊C4×C61—21no—
46C2×C4⋊C4×C61—21no—
47C2×C4⋊C4×C61—21no—
48C2×C22⋊C4×C61—21no—
49C2×C22⋊C4×C61—21no—
50C2×C22⋊C4×C61D411yescharacteristic
51C2×C22⋊C4×C61C2311yescharacteristic
52C2×C42×C61—21no—
53#95×C61—21no—
54#95×C61—21no—
55#95×C61—21no—
56#95×C61—21no—
57#95×C61—21no—
58#95×C61—21no—
59#95×C61—21no—
60#95×C61D411yescharacteristic
61#95×C61D411yescharacteristic
62C24×C61C2×D411yescharacteristic
63C2×Q8×C61—42no—
64C2×Q8×C61—41no—
65C2×Q8×C61—41no—
66C2×Q8×C61—81no—
67C22×C4×C61—21no—
68C22×C4×C61—21no—
69C22×C4×C61—21no—
70C22×C4×C61—21no—
71C22×C4×C61—21no—
72C22×C4×C61—21no—
73C22×C4×C61—41no—
74C22×C4×C61—81no—
75C22×C4×C61C2×D411yescharacteristic
76C22×C4×C61C2×D411yescharacteristic
77C22×Dic61—21no—
78C22×Dic61—21no—
79C22×Dic61—41no—
80C2×Dic122—21no—
81C2×Dic122—21no—
82C4⋊C4×C61—81no—
83C4⋊C4×C61—81no—
84C4⋊C4×C61—81no—
85C4⋊C4×C61—81no—
86C22⋊C4×C61—21no—
87C22⋊C4×C61—41no—
88C22⋊C4×C61—42no—
89C22⋊C4×C61—81no—
90C22⋊C4×C61Q1612yescomplemented
91C42×C61—42no—
92C22⋊Dic61—22no—
93C22⋊Dic61—41no—
94C22⋊Dic61—41no—
95C22⋊Dic61—41no—
96#11758202—82no—
97#11758202—82no—
98C4⋊Dic61—21no—
99C4⋊Dic61—21no—
100#11758196—41no—
101#11758196—41no—
102#11758196—82no—
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—42no—
113Q8×C61—42no—
114Q8×C61—81no—
115Q8×C61—81no—
116C2×C4×C61—22no—
117C2×C4×C61—22no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—41no—
121C2×C4×C61—41no—
122C2×C4×C61—41no—
123C2×C4×C61—41no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
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—42no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61—41no—
139C2×C4×C61—81no—
140C2×Dic61—42no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—81no—
144C2×Dic61—81no—
145C2×Dic61—81no—
146C2×Dic61—81no—
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—42no—
167C4×C61—41no—
168C4×C61—81no—
169C4×C61—81no—
170C4×C61—81no—
171C4×C61—81no—
172Dic61—82no—
173Dic61—81no—
174Dic61—81no—
175#2763D6111yescharacteristic
176#2062—611no—
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#543—611no—
190#451—1221no—
191#451—1221no—
192#400—21no—
193#395—21no—
194#393C2×D6111yescharacteristic
195#393C2×D6111yescharacteristic
196#391—21no—
197#388—21no—
198#385—21no—
199#385—1221no—
200#385C2×D6111yescharacteristic
201#382—21no—
202#342—611no—
203#342—1221no—
204#328—1221no—
205#328—1221no—
206#323—611no—
207#323—611no—
208C61#1225311yescharacteristic, complemented, Sylow
209C22×Q8C22⋊D6111yescharacteristic
210C22×Q8C22⋊D6111yescharacteristic
211C23×C4C22⋊D6111yescharacteristic
212C2×Q16—2441no—
213C2×Q16—2441no—
214C22⋊Q8—1221no—
215C22⋊Q8—1221no—
216C22⋊Q8—2441no—
217C22⋊Q8—2441no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—2441no—
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—21no—
230#103—2441no—
231#103—2441no—
232C22⋊C8—1221no—
233C22⋊C8—1221no—
234#95—21no—
235#95—21no—
236#95—21no—
237#95—21no—
238#95—21no—
239#95—21no—
240#95—21no—
241#95—2441no—
242#95C22⋊D6111yescharacteristic
243#95C22⋊D6111yescharacteristic
244C24C2×C22⋊D6111yescharacteristic
245C2×Q8—42no—
246C2×Q8—41no—
247C2×Q8—41no—
248C2×Q8—81no—
249C2×Q8—1221no—
250C2×Q8—1221no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—41no—
258C22×C4—81no—
259C22×C4—1221no—
260C22×C4—1221no—
261C22×C4—2441no—
262C22×C4C2×C22⋊D6111yescharacteristic
263C22×C4C2×C22⋊D6111yescharacteristic
264Q16—4882no—
265Q16—4882no—
266C2×C8—2441no—
267C2×C8—2441no—
268C4⋊C4—81no—
269C4⋊C4—81no—
270C4⋊C4—81no—
271C4⋊C4—81no—
272C4⋊C4—1221no—
273C4⋊C4—1221no—
274C4⋊C4—4882no—
275C4⋊C4—2441no—
276C4⋊C4—2441no—
277C22⋊C4—21no—
278C22⋊C4—41no—
279C22⋊C4—42no—
280C22⋊C4—81no—
281C22⋊C4—1222no—
282C22⋊C4—2441no—
283C22⋊C4—2441no—
284C22⋊C4—2441no—
285C22⋊C4#1175820212yescomplemented
286C42—42no—
287C23—21no—
288C23—21no—
289C23—41no—
290C23—41no—
291C23#1451974611yescharacteristic
292C23C2×#1175820211yescharacteristic
293C23#1451980811yescharacteristic
294Q8—42no—
295Q8—42no—
296Q8—81no—
297Q8—81no—
298Q8—4881no—
299Q8—4881no—
300C2×C4—22no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—22no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
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—41no—
317C2×C4—41no—
318C2×C4—42no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—81no—
324C2×C4—4881no—
325C2×C4—4881no—
326C2×C4—4881no—
327C2×C4—4881no—
328C2×C4—2442no—
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#1683991811yescharacteristic
343C22#1683994511yescharacteristic
344C22#1683994911yescharacteristic
345C4—42no—
346C4—41no—
347C4—42no—
348C4—41no—
349C4—81no—
350C4—81no—
351C4—81no—
352C4—81no—
353C4—4882no—
354C4—4881no—
355C4—4881no—
356C2—21no—
357C2—21no—
358C2—41no—
359C2—41no—
360C2#2144479311yescharacteristic
361C2#2144780911yescharacteristic
362C2#2144782011yescharacteristic
subgroupG/H
centerC22#16839949
commutator, cosocleC2×C22⋊C4×C61C23
FrattiniC2×C22⋊C4C22×D61
FittingC61×#2763C2
socleC22×C61B(4,𝔽2)
prime radicalC24×C61C2×D4
hypercenter#2763D61
hypocenterC61#12253
LCSG ▷ C2×C22⋊C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #2763

Complements

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

NH ≅ G/Ntype
90. 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
#214471722
#214447752
#214438402
#214437672
C61×#27632
#1225361