Finite Group Databasebeta

← #30595760

Subgroups — #30595760

Order 15616.

568 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 106 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#21461483C211yesmaximal, characteristic
2#21461480C211yesmaximal, characteristic
3#21460639C212yesmaximal, complemented
4#21460637C212yesmaximal, complemented
5#21454160C211yesmaximal, characteristic
6C22×#11758213—21no—
7C22×D61⋊C8—21no—
8#16840628—21no—
9#16840628—21no—
10#16840628C2212yes—
11#16840628C2212yes—
12C2×#14519753C411yescharacteristic
13C2×C42×D61C2211yescharacteristic
14#16839669C2211yescharacteristic
15#16839661C2211yescharacteristic
16#16839660C411yescharacteristic
17#16839645—21no—
18#16839644—21no—
19#16839636—21no—
20#16839624—21no—
21#16839619C411yescharacteristic
22C61×#391C411yescharacteristic
23C2×#11758213—24no—
24C2×#11758213—42no—
25C2×#11758213—42no—
26C2×D61⋊C8—24no—
27C2×D61⋊C8—42no—
28C2×D61⋊C8—42no—
29C22×#92420—22no—
30C22×#92420—22no—
31C22×C4×D61C2×C411yescharacteristic
32C22×C4×D61D411yescharacteristic
33C22×C4×D61D411yescharacteristic
34#14519753—42no—
35C2×C4⋊Dic61—21no—
36C2×C4⋊Dic61C2×C411yescharacteristic
37C2×C4⋊Dic61C2×C411yescharacteristic
38C2×#11758196—21no—
39C2×#11758196—21no—
40C2×#11758198—21no—
41C2×#11758198—21no—
42C2×C4×Dic61D411yescharacteristic
43C2×C4×Dic61D411yescharacteristic
44C2×C4×Dic61C2311yescharacteristic
45C42×D61—42no—
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51C22×Q8×C61C2×C411yescharacteristic
52C2×C4⋊C4×C61C2×C411yescharacteristic
53C2×C42×C61C2×C411yescharacteristic
54#95×C61—21no—
55#95×C61—21no—
56C23×D61C22⋊C411yescharacteristic
57C2×Q8×C61—22no—
58C2×Q8×C61—41no—
59C2×Q8×C61—41no—
60C22×C4×C61—21no—
61C22×C4×C61—21no—
62C22×C4×C61C22⋊C411yescharacteristic
63C22×C4×C61C22⋊C411yescharacteristic
64C22×C4×C61C22×C411yescharacteristic
65C22×Dic61—21no—
66C22×Dic61—21no—
67C22×Dic61C22⋊C411yescharacteristic
68C22×Dic61C2×D411yescharacteristic
69C22×Dic61C2×D411yescharacteristic
70C2×C4×D61—22no—
71C2×C4×D61—22no—
72C2×C4×D61—22no—
73C2×C4×D61—22no—
74C2×C4×D61—21no—
75C2×C4×D61—21no—
76C2×C4×D61—22no—
77C2×C4×D61—22no—
78C2×C4×D61—41no—
79C2×C4×D61SD1612yes—
80C2×C4×D61Q1612yes—
81C2×#92420—24no—
82C2×#92420—24no—
83C2×#92420—42no—
84C2×#92420—42no—
85C2×#92420—42no—
86C2×#92420—42no—
87#11758213—48no—
88D61⋊C8—48no—
89C4⋊C4×C61—22no—
90C42×C61—41no—
91#11758198—42no—
92#11758198—42no—
93C4⋊Dic61—41no—
94C4⋊Dic61—41no—
95C4⋊Dic61—41no—
96C4⋊Dic61—41no—
97#11758196—42no—
98#11758196—42no—
99C4×Dic61—41no—
100C4×Dic61—41no—
101C4×Dic61—41no—
102C23×C61C2×C22⋊C411yescharacteristic
103C22×D61—21no—
104C22×D61—21no—
105C22×D61—21no—
106C22×D61—21no—
107C22×D61#9912yes—
108C22×D61#10312yes—
109C22×D61#10412yes—
110Q8×C61—82no—
111C2×C4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
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—41no—
123C2×C4×C61#10312yes—
124C2×C4×C61#10412yes—
125C2×C4×C61#13112yes—
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×Dic61C2×SD1611yescharacteristic
140C2×Dic61C2×Q1611yescharacteristic
141C2×Dic61AGL(1,ℤ/8)11yescharacteristic
142C2×Dic61#13711yescharacteristic
143C4×D61—24no—
144C4×D61—24no—
145C4×D61—24no—
146C4×D61—24no—
147C4×D61—44no—
148#92420—44no—
149#92420—44no—
150#7681—611nomaximal, Sylow
151C22×C61#40811yescharacteristic
152C22×C61C2×#9911yescharacteristic
153C22×C61#41311yescharacteristic
154C22×C61C2×#10311yescharacteristic
155C22×C61#41711yescharacteristic
156C22×C61C2×#10411yescharacteristic
157C22×C61C2×#10411yescharacteristic
158C2×D61—22no—
159C2×D61—22no—
160C2×D61—22no—
161C2×D61—22no—
162C2×D61—22no—
163C2×D61—22no—
164C2×D61#32814yes—
165C4×C61—22no—
166C4×C61—22no—
167C4×C61—22no—
168C4×C61—81no—
169C4×C61—81no—
170Dic61—21no—
171Dic61—21no—
172Dic61—21no—
173Dic61—21no—
174Dic61—41no—
175Dic61—81no—
176Dic61—81no—
177#2855—611no—
178#1728—611no—
179C2×#336—611no—
180#1272—612no—
181#1271—612no—
182C2×C61#146811yescharacteristic
183C2×C61#148311yescharacteristic
184C2×C61#149311yescharacteristic
185C2×C61C2×#32811yescharacteristic
186C2×C61#150411yescharacteristic
187C2×C61#152411yescharacteristic
188C2×C61#155011yescharacteristic
189D61—24no—
190C22×M16—1221no—
191C23×C8—1221no—
192C2×C22⋊Q8—611no—
193C22×C42—611no—
194#391—611no—
195#391#692311yescharacteristic
196#389—611no—
197#389—611no—
198#387—1221no—
199#387—1221no—
200#385—1221no—
201#381—1221no—
202#380—611no—
203#336—612no—
204#336—612no—
205#336—1221no—
206#336—1221no—
207C61#768111yescharacteristic, complemented, Sylow
208C22×Q8C2×#692311yescharacteristic
209C23×C4—611no—
210C23×C4—611no—
211C23×C4—611no—
212C2×M16—1224no—
213C2×M16—2442no—
214C2×M16—2442no—
215C22×C8—1222no—
216C22×C8—1222no—
217C22×C8—1224no—
218C22×C8—2442no—
219C22×C8—2442no—
220C22⋊Q8—2442no—
221C2×C4⋊C4—611no—
222C2×C4⋊C4—611no—
223C2×C4⋊C4—1221no—
224C2×C4⋊C4—1221no—
225C2×C4⋊C4—1221no—
226C2×C4⋊C4C2×#692311yescharacteristic
227C2×C22⋊C4—1221no—
228C2×C22⋊C4—1221no—
229C2×C42—611no—
230C2×C42—611no—
231C2×C42—611no—
232C2×C42—2442no—
233C2×C42C2×#692311yescharacteristic
234#95—21no—
235#95—21no—
236#95—1221no—
237#95—1221no—
238#95—1221no—
239#95—1221no—
240#95—1221no—
241C24—611no—
242C2×Q8—22no—
243C2×Q8—41no—
244C2×Q8—41no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—611no—
248C22×C4—611no—
249C22×C4—612no—
250C22×C4—612no—
251C22×C4—611no—
252C22×C4—1221no—
253C22×C4—1221no—
254C22×C4—1222no—
255C22×C4—1222no—
256C22×C4—1222no—
257C22×C4—1222no—
258C22×C4—1222no—
259C22×C4—1222no—
260C22×C4—1221no—
261C22×C4—1221no—
262C22×C4—2441no—
263C22×C4C22⋊#692311yescharacteristic
264C22×C4C22⋊#692311yescharacteristic
265C22×C4C22×#692311yescharacteristic
266M16—2448no—
267C2×C8—1224no—
268C2×C8—1224no—
269C2×C8—2442no—
270C2×C8—2442no—
271C2×C8—2448no—
272C2×C8—2442no—
273C2×C8—2442no—
274C4⋊C4—22no—
275C4⋊C4—2441no—
276C4⋊C4—2441no—
277C4⋊C4—2441no—
278C4⋊C4—2441no—
279C4⋊C4—2442no—
280C4⋊C4—2442no—
281C22⋊C4—2442no—
282C22⋊C4—2442no—
283C42—41no—
284C42—2441no—
285C42—2441no—
286C42—2441no—
287C23—612no—
288C23—612no—
289C23—612no—
290C23—1221no—
291C23—1221no—
292C23—1221no—
293C23—1221no—
294C23C2×C22⋊#692311yescharacteristic
295Q8—82no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—611no—
309C2×C4—611no—
310C2×C4—611no—
311C2×C4—611no—
312C2×C4—1224no—
313C2×C4—1224no—
314C2×C4—1224no—
315C2×C4—1224no—
316C2×C4—1221no—
317C2×C4—1221no—
318C2×C4—1221no—
319C2×C4—1221no—
320C2×C4—1221no—
321C2×C4—1221no—
322C2×C4—1221no—
323C2×C4—2444no—
324C2×C4—2441no—
325C2×C4—2441no—
326C2×C4—2441no—
327C2×C4—2441no—
328C2×C4—2441no—
329C2×C4—2441no—
330C2×C4#1451984012yes—
331C2×C4#1451984212yes—
332C2×C4#1451986412yes—
333C8—2444no—
334C8—2444no—
335C22—614no—
336C22—1222no—
337C22—1222no—
338C22—1222no—
339C22—1222no—
340C22—1222no—
341C22—1222no—
342C22#1684073611yescharacteristic
343C22D61⋊#9911yescharacteristic
344C22#1684074811yescharacteristic
345C22C2×#1451984011yescharacteristic
346C22#1684075311yescharacteristic
347C22D61⋊#10411yescharacteristic
348C22C2×#1451984211yescharacteristic
349C4—22no—
350C4—22no—
351C4—22no—
352C4—81no—
353C4—81no—
354C4—1221no—
355C4—1221no—
356C4—1221no—
357C4—1221no—
358C4—4881no—
359C4—4881no—
360C4—2441no—
361C2—1224no—
362C2#2146108511yescharacteristic
363C2#2146113511yescharacteristic
364C2#2146116811yescharacteristic
365C2D61⋊#32811yescharacteristic
366C2#2146120611yescharacteristic
367C2#2146127111yescharacteristic
368C2#2146133611yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#391C4
socleC23×C61C2×C22⋊C4
prime radicalC23×D61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenter#391#6923
hypocenterC61#7681
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #391

Complements

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

NH ≅ G/Ntype
3. #21460639C2semidirect
4. #21460637C2semidirect
207. C61#7681semidirect

Maximal subgroups

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

subgroupindex
#214614832
#214614802
#214606392
#214606372
#214541602
#768161