Finite Group Databasebeta

← #30598723

Subgroups — #30598723

Order 15616.

910 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 910 conjugacy classes of subgroups — too many to draw. Only its 100 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#21461352C212yesmaximal, complemented
2#21461298C212yesmaximal, complemented
3#21461070C212yesmaximal, complemented
4C2×#16840333C211yesmaximal, characteristic
5#16840782C2214yes—
6#16840622—24no—
7#16840617—24no—
8#16840607—22no—
9#16840605—22no—
10C23×Dic122C411yescharacteristic
11#16840333—24no—
12#16840333—24no—
13C2×#14519775C411yescharacteristic
14C2×#14519775C2211yescharacteristic
15C2×#14519764C411yescharacteristic
16C2×#14519764C2211yescharacteristic
17C2×#14519758—22no—
18C2×#14519756—22no—
19C2×#14519736C2211yescharacteristic
20C22×#41×C61C411yescharacteristic
21#14519844—24no—
22C22⋊#92420—24no—
23#14519832—24no—
24C22×Dic122—21no—
25C22×Dic122—22no—
26C22×Dic122—22no—
27C22×Dic122—42no—
28C22×Dic122—42no—
29C22×Dic122C2×C411yescharacteristic
30C22×Dic122C2×C411yescharacteristic
31C23×Dic61—21no—
32#14519775—22no—
33#14519775—22no—
34#14519775—22no—
35#14519775D414yes—
36#14519764—22no—
37#14519764—22no—
38#14519764—22no—
39#14519764D414yes—
40#14519758—216no—
41#14519756—216no—
42#14519736—22no—
43#14519736—22no—
44C2×C4⋊Dic61D412yes—
45C2×#11758196—22no—
46C2×#11758196—22no—
47C2×C22⋊Dic61—22no—
48C2×C22⋊Dic61—22no—
49C2×C22⋊Dic61D412yes—
50C2×C4×Dic61C2×C411yescharacteristic
51C2×C4×Dic61C2311yescharacteristic
52C2×#41×C61—22no—
53C2×#41×C61—22no—
54C2×#41×C61—42no—
55C2×#41×C61—42no—
56C22×Q8×C61C2×C411yescharacteristic
57C22×D4×C61—21no—
58C22×D4×C61C2×C411yescharacteristic
59C23×C4×C61—21no—
60C23×C4×C61C2×C411yescharacteristic
61C24×C61—21no—
62C24×C61C22⋊C411yescharacteristic
63#41×C61—48no—
64#41×C61—48no—
65C2×Q8×C61—21no—
66C2×Q8×C61—41no—
67C2×Q8×C61—41no—
68C2×Q8×C61C22⋊C412yes—
69C2×D4×C61—24no—
70C2×D4×C61—21no—
71C2×D4×C61—41no—
72C2×D4×C61—41no—
73C2×D4×C61—42no—
74C2×D4×C61—42no—
75C2×D4×C61C22⋊C412yes—
76C22×C4×C61—22no—
77C22×C4×C61—22no—
78C22×C4×C61—21no—
79C22×C4×C61—21no—
80C22×C4×C61—24no—
81C22×C4×C61—21no—
82C22×C4×C61—42no—
83C22×C4×C61—42no—
84C22×C4×C61C22⋊C411yescharacteristic
85C22×C4×C61C22×C411yescharacteristic
86C22×Dic61—24no—
87C22×Dic61—21no—
88C22×Dic61—21no—
89C22×Dic61—42no—
90C22×Dic61—42no—
91C22×Dic61C22⋊C412yes—
92C22×Dic61C2×D412yes—
93C2×Dic122—24no—
94C2×Dic122—21no—
95C2×Dic122—21no—
96C2×Dic122—42no—
97C2×Dic122—48no—
98C2×Dic122—48no—
99C2×Dic122—42no—
100C2×Dic122—41no—
101C2×Dic122—41no—
102C2×Dic122—41no—
103C2×Dic122—41no—
104C2×Dic122C22⋊C412yes—
105C2×Dic122C22⋊C412yes—
106C2×#92420—44no—
107C22⋊Dic61—28no—
108C22⋊Dic61—28no—
109C22⋊Dic61—24no—
110C4⋊Dic61—24no—
111#11758196—28no—
112#11758196—28no—
113C4×Dic61—21no—
114C4×Dic61—21no—
115C4×Dic61C2×D412yes—
116C4×Dic61C2×D412yes—
117C23×C61—21no—
118C23×C61—21no—
119C23×C61—22no—
120C23×C61—42no—
121C23×C61—44no—
122C23×C61—41no—
123C23×C61—41no—
124C23×C61#10012yes—
125C23×C61C2×C22⋊C411yescharacteristic
126Q8×C61—42no—
127Q8×C61—42no—
128D4×C61—42no—
129D4×C61—42no—
130D4×C61—48no—
131C2×C4×C61—24no—
132C2×C4×C61—24no—
133C2×C4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61—21no—
137C2×C4×C61—22no—
138C2×C4×C61—48no—
139C2×C4×C61—41no—
140C2×C4×C61—41no—
141C2×C4×C61#10012yes—
142C2×C4×C61C2×C22⋊C411yescharacteristic
143C2×C4×C61C2×C22⋊C411yescharacteristic
144C2×Dic61—22no—
145C2×Dic61—22no—
146C2×Dic61—22no—
147C2×Dic61—42no—
148C2×Dic61—48no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61—42no—
154C2×Dic61#12014yes—
155Dic122—48no—
156Dic122—42no—
157Dic122—42no—
158Dic122—42no—
159Dic122—42no—
160#92420—84no—
161#8524—611nomaximal, Sylow
162C22×C61—22no—
163C22×C61—22no—
164C22×C61—42no—
165C22×C61—42no—
166C22×C61—42no—
167C22×C61—44no—
168C22×C61—42no—
169C22×C61—82no—
170C22×C61—82no—
171C22×C61#37911yescharacteristic
172C22×C61C2×#10011yescharacteristic
173C22×C61C2×#10011yescharacteristic
174C4×C61—22no—
175C4×C61—21no—
176C4×C61—21no—
177C4×C61—42no—
178Dic61—24no—
179Dic61—42no—
180Dic61—42no—
181Dic61—42no—
182C2×#536—611no—
183#1558—612no—
184#1533—612no—
185#1464—612no—
186C2×C61—21no—
187C2×C61—21no—
188C2×C61—42no—
189C2×C61—82no—
190C2×C61#178311yescharacteristic
191C2×C61#179612yes—
192C22×#41#692311yescharacteristic
193C23×Q8—611no—
194#536—1224no—
195#536—1224no—
196C2×C4⋊Q8—611no—
197C2×C4⋊Q8—611no—
198C2×#124—611no—
199C2×#124—611no—
200C2×#123—1222no—
201C2×C22⋊Q8—1222no—
202C2×#117—611no—
203#432—614no—
204#333—1224no—
205#329—1224no—
206#324—1222no—
207#323—1222no—
208C61#852411yescharacteristic, complemented, Sylow
209C2×#41—22no—
210C2×#41—22no—
211C2×#41—42no—
212C2×#41—42no—
213C22×Q8—611no—
214C22×Q8—611no—
215C22×Q8—1222no—
216C22×Q8—1222no—
217C22×Q8—1221no—
218C22×Q8—2442no—
219C22×Q8—2442no—
220C22×Q8C2×#692311yescharacteristic
221C22×D4—21no—
222C22×D4C2×#692311yescharacteristic
223C23×C4—21no—
224C23×C4—1221no—
225C23×C4C2×#692311yescharacteristic
226C4⋊Q8—614no—
227C4⋊Q8—1222no—
228C4⋊Q8—1222no—
229C4⋊Q8—1222no—
230#124—614no—
231#124—1222no—
232#124—1222no—
233#124—1222no—
234#123—12216no—
235C22⋊Q8—12216no—
236#117—1222no—
237#117—1222no—
238C2×C4⋊C4—612no—
239C2×C4⋊C4—1222no—
240C2×C4⋊C4—1222no—
241C2×C22⋊C4—612no—
242C2×C22⋊C4—1222no—
243C2×C22⋊C4—1222no—
244C2×C42—611no—
245C2×C42—611no—
246C4⋊C8—1224no—
247C22⋊C8—1224no—
248#97—1224no—
249C24—21no—
250C24C22⋊#692311yescharacteristic
251#41—48no—
252#41—48no—
253C2×Q8—21no—
254C2×Q8—41no—
255C2×Q8—41no—
256C2×Q8—612no—
257C2×Q8—612no—
258C2×Q8—1224no—
259C2×Q8—1221no—
260C2×Q8—1221no—
261C2×Q8—2448no—
262C2×Q8—2448no—
263C2×Q8—2442no—
264C2×Q8—2441no—
265C2×Q8—2441no—
266C2×Q8—2441no—
267C2×Q8—2441no—
268C2×Q8—2442no—
269C2×Q8C22⋊#692312yes—
270C2×D4—24no—
271C2×D4—21no—
272C2×D4—41no—
273C2×D4—41no—
274C2×D4—42no—
275C2×D4—42no—
276C2×D4C22⋊#692312yes—
277C22×C4—22no—
278C22×C4—22no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—24no—
282C22×C4—21no—
283C22×C4—42no—
284C22×C4—42no—
285C22×C4—612no—
286C22×C4—612no—
287C22×C4—1224no—
288C22×C4—1221no—
289C22×C4—1221no—
290C22×C4—2442no—
291C22×C4—2442no—
292C22×C4C22⋊#692311yescharacteristic
293C22×C4C22×#692311yescharacteristic
294C2×C8—2444no—
295C4⋊C4—1224no—
296C4⋊C4—1228no—
297C4⋊C4—1228no—
298C22⋊C4—1224no—
299C22⋊C4—1228no—
300C22⋊C4—1228no—
301C42—612no—
302C42—612no—
303C42—1221no—
304C42—1221no—
305C23—21no—
306C23—21no—
307C23—22no—
308C23—42no—
309C23—44no—
310C23—41no—
311C23—41no—
312C23#1451983712yes—
313C23C2×C22⋊#692311yescharacteristic
314Q8—42no—
315Q8—42no—
316Q8—2442no—
317Q8—2442no—
318Q8—2448no—
319Q8—2442no—
320Q8—2442no—
321D4—42no—
322D4—42no—
323D4—48no—
324C2×C4—24no—
325C2×C4—24no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—22no—
331C2×C4—48no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—614no—
335C2×C4—1222no—
336C2×C4—1222no—
337C2×C4—1222no—
338C2×C4—2442no—
339C2×C4—2448no—
340C2×C4—2441no—
341C2×C4—2441no—
342C2×C4—2441no—
343C2×C4—2441no—
344C2×C4—2442no—
345C2×C4#1451983712yes—
346C2×C4C2×C22⋊#692311yescharacteristic
347C2×C4C2×C22⋊#692311yescharacteristic
348C8—4884no—
349C22—22no—
350C22—22no—
351C22—42no—
352C22—42no—
353C22—42no—
354C22—42no—
355C22—44no—
356C22—82no—
357C22—82no—
358C22#1684070311yescharacteristic
359C22C2×#1451983711yescharacteristic
360C22C2×#1451983711yescharacteristic
361C4—22no—
362C4—21no—
363C4—21no—
364C4—42no—
365C4—1224no—
366C4—2442no—
367C4—2442no—
368C4—2442no—
369C2—21no—
370C2—21no—
371C2—42no—
372C2—82no—
373C2#2146165111yescharacteristic
374C2#2146167212yes—
subgroupG/H
centerC22#16840703
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
Fitting, prime radicalC22×#41×C61C4
socleC22×C61#379
cosocleC2×C4×Dic61C23
hypercenterC22×#41#6923
hypocenterC61#8524
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. #21461352C2semidirect
2. #21461298C2semidirect
3. #21461070C2semidirect
208. C61#8524semidirect

Maximal subgroups

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

subgroupindex
#214613522
#214612982
#214610702
C2×#168403332
#852461