Finite Group Databasebeta

← #30599290

Subgroups — #30599290

Order 15616.

514 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 114 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#21461675C211yesmaximal, characteristic
2#21461675C211yesmaximal, characteristic
3#21460697C212yesmaximal, complemented
4#21460697C212yesmaximal, complemented
5#21448221C211yesmaximal, characteristic
6C2×#14519844C2212yes—
7C2×#14519844C2212yes—
8C2×C22⋊#92420—21no—
9C2×C22⋊#92420—21no—
10#16840628—21no—
11#16840628—21no—
12C2×#14519733—21no—
13C22×C4×Dic61C2211yescharacteristic
14#16839631C2211yescharacteristic
15#16839631C2211yescharacteristic
16#16839626—21no—
17#16839622C411yescharacteristic
18#16839620—21no—
19C4⋊C4×Dic61C411yescharacteristic
20C4⋊C4×Dic61C411yescharacteristic
21#16839613—21no—
22C61×#380C411yescharacteristic
23C22×#92420—22no—
24C22×#92420—22no—
25#14519844—24no—
26#14519844—24no—
27C22⋊#92420—42no—
28C22⋊#92420—42no—
29C23×Dic61D411yescharacteristic
30C23×Dic61D411yescharacteristic
31#14519733—44no—
32C2×C4⋊Dic61C2×C411yescharacteristic
33C2×C4⋊Dic61C2×C411yescharacteristic
34C2×#11758196—21no—
35C2×#11758196—21no—
36C2×#11758196—21no—
37C2×#11758196—21no—
38C2×C22⋊Dic61—21no—
39C2×C4×Dic61—24no—
40C2×C4×Dic61—21no—
41C2×C4×Dic61—21no—
42C2×C4×Dic61C2×C411yescharacteristic
43C2×C4×Dic61D411yescharacteristic
44C2×C4×Dic61D411yescharacteristic
45C2×C4×Dic61C2311yescharacteristic
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49C23×C4×C61C2×C411yescharacteristic
50C2×C4⋊C4×C61C2×C411yescharacteristic
51C2×C4⋊C4×C61C2×C411yescharacteristic
52C2×C22⋊C4×C61—21no—
53#95×C61—21no—
54C24×C61C22⋊C411yescharacteristic
55C22×C4×C61—22no—
56C22×C4×C61—21no—
57C22×C4×C61—21no—
58C22×C4×C61—41no—
59C22×C4×C61—41no—
60C22×C4×C61C22⋊C411yescharacteristic
61C22×C4×C61C22×C411yescharacteristic
62C22×Dic61—22no—
63C22×Dic61—22no—
64C22×Dic61—22no—
65C22×Dic61—22no—
66C22×Dic61—21no—
67C22×Dic61—21no—
68C22×Dic61—21no—
69C22×Dic61—21no—
70C22×Dic61C22⋊C411yescharacteristic
71C22×Dic61C22⋊C411yescharacteristic
72C22×Dic61SD1612yes—
73C22×Dic61Q1612yes—
74C22×Dic61C2×D411yescharacteristic
75C22×Dic61C2×D411yescharacteristic
76C2×#92420—42no—
77C2×#92420—42no—
78C2×#92420—42no—
79C2×#92420—42no—
80C2×#92420—42no—
81C2×#92420—42no—
82C4⋊C4×C61—41no—
83C4⋊C4×C61—41no—
84C22⋊C4×C61—42no—
85C22⋊Dic61—42no—
86C4⋊Dic61—41no—
87C4⋊Dic61—41no—
88#11758196—42no—
89#11758196—41no—
90#11758196—42no—
91#11758196—42no—
92#11758196—41no—
93C4×Dic61—22no—
94C4×Dic61—22no—
95C4×Dic61—22no—
96C4×Dic61—42no—
97C4×Dic61—42no—
98C4×Dic61#4114yes—
99C23×C61—21no—
100C23×C61—21no—
101C23×C61—21no—
102C23×C61—21no—
103C23×C61—21no—
104C23×C61—21no—
105C23×C61#10312yes—
106C23×C61C2×C22⋊C411yescharacteristic
107C2×C4×C61—21no—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61—44no—
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#11712yes—
120C2×Dic61—21no—
121C2×Dic61—21no—
122C2×Dic61—24no—
123C2×Dic61—24no—
124C2×Dic61—21no—
125C2×Dic61—21no—
126C2×Dic61—21no—
127C2×Dic61—42no—
128C2×Dic61—42no—
129C2×Dic61—41no—
130C2×Dic61—41no—
131C2×Dic61—41no—
132C2×Dic61—41no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61#10312yes—
136C2×Dic61#12312yes—
137C2×Dic61#12312yes—
138C2×Dic61C2×SD1611yescharacteristic
139C2×Dic61C2×Q1611yescharacteristic
140C2×Dic61#13512yes—
141C2×Dic61AGL(1,ℤ/8)12yes—
142C2×Dic61AGL(1,ℤ/8)11yescharacteristic
143C2×Dic61#13711yescharacteristic
144#92420—82no—
145#92420—82no—
146#8727—611nomaximal, Sylow
147C22×C61—22no—
148C22×C61—22no—
149C22×C61—22no—
150C22×C61—41no—
151C22×C61—41no—
152C22×C61—41no—
153C22×C61—41no—
154C22×C61#38111yescharacteristic
155C22×C61#41311yescharacteristic
156C22×C61#41311yescharacteristic
157C22×C61C2×#10311yescharacteristic
158C22×C61#41611yescharacteristic
159C22×C61#41711yescharacteristic
160C22×C61#41811yescharacteristic
161C4×C61—22no—
162C4×C61—41no—
163C4×C61—81no—
164C4×C61—81no—
165Dic61—22no—
166Dic61—41no—
167Dic61—81no—
168Dic61—81no—
169Dic61#48112yes—
170Dic61#48212yes—
171Dic61#48412yes—
172Dic61#48512yes—
173#2285—611no—
174#1797—611no—
175#1797—611no—
176#1296—612no—
177#1296—612no—
178C2×C61—42no—
179C2×C61#154211yescharacteristic
180C2×C61#155011yescharacteristic
181C2×C61#155311yescharacteristic
182C2×C61#155711yescharacteristic
183C2×C61#182211yescharacteristic
184C2×C61#182411yescharacteristic
185C2×C61#182511yescharacteristic
186C2×#117—1221no—
187C22×C42—611no—
188C2×C4⋊C8—612no—
189C2×C4⋊C8—612no—
190C2×C22⋊C8—1221no—
191C2×C22⋊C8—1221no—
192#384—611no—
193#384—611no—
194#382—1221no—
195#380—611no—
196#380—1221no—
197#380#692311yescharacteristic
198C4×C4⋊C4—611no—
199C4×C4⋊C4—611no—
200C4×C4⋊C4—1221no—
201#336—1221no—
202#336—1221no—
203C61#872711yescharacteristic, complemented, Sylow
204C23×C4—611no—
205C23×C4—611no—
206C23×C4C2×#692311yescharacteristic
207C22×C8—1222no—
208C22×C8—1222no—
209#117—2444no—
210C2×C4⋊C4—611no—
211C2×C4⋊C4—611no—
212C2×C4⋊C4—1221no—
213C2×C4⋊C4—1221no—
214C2×C4⋊C4—1221no—
215C2×C4⋊C4—1221no—
216C2×C4⋊C4C2×#692311yescharacteristic
217C2×C4⋊C4C2×#692311yescharacteristic
218C2×C22⋊C4—21no—
219C2×C22⋊C4—1221no—
220C2×C42—611no—
221C2×C42—611no—
222C2×C42—611no—
223C2×C42—611no—
224C2×C42—1224no—
225C2×C42—1221no—
226C2×C42—1221no—
227C4⋊C8—1224no—
228C4⋊C8—1224no—
229C22⋊C8—2442no—
230C22⋊C8—2442no—
231#95—21no—
232#95—1221no—
233#95—1221no—
234#95—1221no—
235C24C22⋊#692311yescharacteristic
236C22×C4—22no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—41no—
240C22×C4—41no—
241C22×C4—611no—
242C22×C4—611no—
243C22×C4—612no—
244C22×C4—612no—
245C22×C4—611no—
246C22×C4—611no—
247C22×C4—1222no—
248C22×C4—1222no—
249C22×C4—1221no—
250C22×C4—1222no—
251C22×C4—1222no—
252C22×C4—1221no—
253C22×C4—1221no—
254C22×C4—1221no—
255C22×C4C22⋊#692311yescharacteristic
256C22×C4C22×#692311yescharacteristic
257C2×C8—2442no—
258C2×C8—2442no—
259C2×C8—2442no—
260C2×C8—2442no—
261C2×C8—2442no—
262C2×C8—2442no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—2441no—
266C4⋊C4—2441no—
267C4⋊C4—2442no—
268C4⋊C4—2441no—
269C4⋊C4—2441no—
270C4⋊C4—2442no—
271C4⋊C4—2442no—
272C22⋊C4—42no—
273C22⋊C4—2442no—
274C42—614no—
275C42—1222no—
276C42—1222no—
277C42—1222no—
278C42—2442no—
279C42—2442no—
280C23—21no—
281C23—21no—
282C23—21no—
283C23—21no—
284C23—21no—
285C23—21no—
286C23#1451984012yes—
287C23C2×C22⋊#692311yescharacteristic
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—44no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—612no—
301C2×C4—612no—
302C2×C4—611no—
303C2×C4—611no—
304C2×C4—612no—
305C2×C4—611no—
306C2×C4—611no—
307C2×C4—612no—
308C2×C4—612no—
309C2×C4—1224no—
310C2×C4—1224no—
311C2×C4—1221no—
312C2×C4—1221no—
313C2×C4—1221no—
314C2×C4—1221no—
315C2×C4—1221no—
316C2×C4—2442no—
317C2×C4—2442no—
318C2×C4—2441no—
319C2×C4—2441no—
320C2×C4—2441no—
321C2×C4—2441no—
322C2×C4—2441no—
323C2×C4—2441no—
324C2×C4#1451985612yes—
325C8—4882no—
326C8—4882no—
327C22—22no—
328C22—22no—
329C22—22no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22#1684070511yescharacteristic
335C22#1684074911yescharacteristic
336C22#1684074911yescharacteristic
337C22C2×#1451984011yescharacteristic
338C22#1684075211yescharacteristic
339C22#1684075311yescharacteristic
340C22#1684075411yescharacteristic
341C4—22no—
342C4—41no—
343C4—81no—
344C4—81no—
345C4—612no—
346C4—612no—
347C4—612no—
348C4—612no—
349C4—1222no—
350C4—4881no—
351C4—4881no—
352C4—2441no—
353C2—42no—
354C2#2146132111yescharacteristic
355C2#2146133711yescharacteristic
356C2#2146134311yescharacteristic
357C2#2146135111yescharacteristic
358C2#2146172111yescharacteristic
359C2#2146172311yescharacteristic
360C2#2146172411yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#380C4
socleC23×C61C2×C22⋊C4
prime radicalC24×C61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenter#380#6923
hypocenterC61#8727
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
3. #21460697C2semidirect
4. #21460697C2semidirect
203. C61#8727semidirect

Maximal subgroups

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

subgroupindex
#214616752
#214606972
#214482212
#872761