Finite Group Databasebeta

← #30605204

Subgroups — #30605204

Order 15616.

476 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 66 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#21461680C211yesmaximal, characteristic, complemented
2#21461076C211yesmaximal, characteristic, complemented
3#21460814C212yesmaximal, complemented
4#21460797C212yesmaximal, complemented
5#21451672C211yesmaximal, characteristic
6C2×#14519836—21no—
7#16840733—21no—
8#16840704—21no—
9#16840640C2212yes—
10#16840607—21no—
11#16840606C2212yes—
12C2×C4×D244C2211yescharacteristic
13#16839687—21no—
14#16839673C411yescharacteristic, complemented
15#16839673C2211yescharacteristic
16#16839671—21no—
17#16839670C411yescharacteristic, complemented
18#16839670C2211yescharacteristic
19#16839638—21no—
20#16839638—21no—
21#16839630C411yescharacteristic, complemented
22C2×#124×C61C411yescharacteristic, complemented
23C2×#11758213—41no—
24C2×C4⋊#6923—41no—
25C2×C22⋊#6923—22no—
26#14519836—42no—
27#14519834—41no—
28C22⋊#92420—22no—
29(C2×#6923)⋊C4—41no—
30C22×D244D411yescharacteristic
31C22×C22⋊D61—21no—
32C22×C22⋊D61—21no—
33C22×C4×D61D411yescharacteristic
34C22×C4×D61D411yescharacteristic
35C4×D244—41no—
36C4×D244—41no—
37C2×C4⋊Dic61D411yescharacteristic
38C2×C22⋊Dic61—21no—
39C2×C22⋊Dic61—21no—
40C2×#11758198—21no—
41C2×#11758198—21no—
42C2×#11758198C2×C411yescharacteristic
43C2×#11758198C2311yescharacteristic
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48#14519684C2×C411yescharacteristic
49#14519684C2×C411yescharacteristic
50C22×Q8×C61C2×C411yescharacteristic
51C22×D4×C61C2×C411yescharacteristic
52#124×C61—41no—
53#124×C61—41no—
54C2×C22⋊C4×C61—21no—
55C2×C22⋊C4×C61—21no—
56C2×C42×C61C2×C411yescharacteristic
57C24×C61—21no—
58C23×D61C22⋊C411yescharacteristic
59C23×D61C2×D411yescharacteristic
60C22×#6923—42no—
61C2×Q8×C61—41no—
62C2×Q8×C61—81no—
63C2×D4×C61—41no—
64C2×D4×C61—81no—
65C22×C4×C61—21no—
66C22×C4×C61C22⋊C411yescharacteristic
67C22×C4×C61C22⋊C411yescharacteristic
68C22×C4×C61C22×C411yescharacteristic
69C2×C22⋊D61—42no—
70C2×C22⋊D61—41no—
71C2×C22⋊D61—41no—
72C2×C22⋊D61—81no—
73C2×C22⋊D61—81no—
74C2×C22⋊D61—81no—
75C2×C22⋊D61—81no—
76C22×Dic61—21no—
77C22×Dic61—21no—
78C22×Dic61C22⋊C411yescharacteristic
79C22×Dic61C2×D411yescharacteristic
80C2×D244—21no—
81C2×D244—21no—
82C2×D244—41no—
83C2×D244—41no—
84C2×C4×D61—21no—
85C2×C4×D61—21no—
86C2×C4×D61—21no—
87C2×C4×D61—21no—
88C2×C4×D61—81no—
89C2×C4×D61—81no—
90C22⋊#6923—42no—
91C22⋊#6923—42no—
92C2×#92420—42no—
93C4⋊#6923—82no—
94#11758213—82no—
95C22⋊C4×C61—42no—
96C22⋊C4×C61—41no—
97C22⋊C4×C61—41no—
98C42×C61—21no—
99C42×C61—21no—
100C22⋊Dic61—81no—
101C22⋊Dic61—81no—
102#11758198—41no—
103#11758198—41no—
104#11758198—81no—
105#11758198—81no—
106C4⋊Dic61—41no—
107C23×C61—41no—
108C23×C61—41no—
109C23×C61—41no—
110C23×C61—41no—
111C23×C61—41no—
112C23×C61—41no—
113C23×C61—41no—
114C23×C61C2×C22⋊C411yescharacteristic
115C22×D61—21no—
116C22×D61—21no—
117C22×D61—21no—
118C22×D61—21no—
119C22×D61—21no—
120C22×D61—41no—
121C22×D61—41no—
122C22×D61—41no—
123C22×D61—41no—
124C22×D61AGL(1,ℤ/8)11yescharacteristic
125C22×D61#13711yescharacteristic
126C2×#6923—82no—
127C2×#6923—82no—
128C2×#6923—82no—
129Q8×C61—82no—
130D4×C61—82no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61—41no—
139C2×C4×C61—41no—
140C2×C4×C61#9911yescharacteristic
141C2×C4×C61#9911yescharacteristic
142C22⋊D61—82no—
143C22⋊D61—82no—
144C22⋊D61—84no—
145C2×Dic61—21no—
146C2×Dic61—21no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61—41no—
154C2×Dic61—41no—
155D244—42no—
156D244—42no—
157C4×D61—42no—
158C4×D61—42no—
159C4×D61—81no—
160C4×D61—81no—
161#92420—82no—
162#11825—611nomaximal, Sylow
163C22×C61—21no—
164C22×C61—21no—
165C22×C61—81no—
166C22×C61—81no—
167C22×C61—81no—
168C22×C61—81no—
169C22×C61—81no—
170C22×C61—81no—
171C22×C61—81no—
172C22×C61C2×#9911yescharacteristic
173C22×C61#41711yescharacteristic
174C22×C61#42111yescharacteristic
175C2×D61—21no—
176C2×D61—21no—
177C2×D61—41no—
178C2×D61—41no—
179C2×D61—41no—
180C2×D61—41no—
181C2×D61—42no—
182C2×D61—41no—
183C2×D61—41no—
184C2×D61—41no—
185C2×D61—81no—
186C2×D61—81no—
187#6923—162no—
188C4×C61—21no—
189C4×C61—21no—
190C4×C61—41no—
191C4×C61—41no—
192C4×C61—81no—
193Dic61—41no—
194Dic61—41no—
195Dic61—81no—
196Dic61—81no—
197#2631—611no—
198#1799—611no—
199#1465—611no—
200#1351—612no—
201#1343—612no—
202C2×C61—21no—
203C2×C61—21no—
204C2×C61—161no—
205C2×C61#151311yescharacteristic
206C2×C61#212211yescharacteristic
207C2×C61#212711yescharacteristic
208D61—41no—
209D61—41no—
210D61—81no—
211C2×#124#692311yescharacteristic, complemented
212C2×C4×D4—611no—
213C2×#99—1221no—
214#407—1221no—
215#397—1221no—
216#393—611no—
217#393—611no—
218#392—611no—
219#392—611no—
220#392—1221no—
221#386—1221no—
222#386—1221no—
223#383—611no—
224#380—1221no—
225#342—612no—
226#324—1221no—
227#323—612no—
228C61#1182511yescharacteristic, complemented, Sylow
229C22×Q8C2×#692311yescharacteristic
230C22×D4—611no—
231C22×D4—1221no—
232C22×D4—1221no—
233C22×D4C2×#692311yescharacteristic
234C23×C4—611no—
235C23×C4—611no—
236C2×M16—2441no—
237#124—41no—
238#124—41no—
239C4×D4—2441no—
240C4×D4—2441no—
241C2×C4⋊C4—611no—
242C2×C4⋊C4—2441no—
243C2×C22⋊C4—21no—
244C2×C22⋊C4—21no—
245C2×C22⋊C4—611no—
246C2×C22⋊C4—611no—
247C2×C22⋊C4—1221no—
248C2×C22⋊C4—1221no—
249C2×C22⋊C4—1221no—
250C2×C22⋊C4—1221no—
251C2×C22⋊C4—1222no—
252C2×C42C2×#692311yescharacteristic
253#99—2442no—
254C22⋊C8—1222no—
255C22⋊C8—2441no—
256#95—611no—
257#95—611no—
258#95—1221no—
259#95—1221no—
260#95—1221no—
261#95—1221no—
262#95—2441no—
263C24—21no—
264C24—611no—
265C24—611no—
266C2×Q8—41no—
267C2×Q8—81no—
268C2×D4—41no—
269C2×D4—81no—
270C2×D4—1221no—
271C2×D4—1221no—
272C2×D4—4881no—
273C2×D4—4881no—
274C2×D4—4881no—
275C2×D4—4881no—
276C2×D4—2441no—
277C2×D4—2441no—
278C2×D4—2441no—
279C2×D4—2441no—
280C2×D4—2442no—
281C22×C4—21no—
282C22×C4—611no—
283C22×C4—611no—
284C22×C4—1221no—
285C22×C4—1221no—
286C22×C4—1221no—
287C22×C4—1221no—
288C22×C4—1221no—
289C22×C4—1221no—
290C22×C4—4881no—
291C22×C4—4881no—
292C22×C4—2442no—
293C22×C4C22⋊#692311yescharacteristic
294C22×C4C22⋊#692311yescharacteristic
295C22×C4C22×#692311yescharacteristic
296M16—4882no—
297C2×C8—2442no—
298C4⋊C4—4882no—
299C4⋊C4—2441no—
300C22⋊C4—42no—
301C22⋊C4—41no—
302C22⋊C4—41no—
303C22⋊C4—4881no—
304C22⋊C4—4881no—
305C22⋊C4—4881no—
306C22⋊C4—4881no—
307C22⋊C4—2441no—
308C22⋊C4—2441no—
309C22⋊C4—2442no—
310C22⋊C4—2442no—
311C42—21no—
312C42—21no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—611no—
321C23—611no—
322C23—1221no—
323C23—1221no—
324C23—1221no—
325C23—1221no—
326C23—1221no—
327C23—2441no—
328C23—2441no—
329C23—2441no—
330C23—2441no—
331C23C2×C22⋊#692311yescharacteristic
332Q8—82no—
333D4—82no—
334D4—4884no—
335D4—4882no—
336D4—4882no—
337D4—2442no—
338D4—2442no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—1221no—
349C2×C4—1221no—
350C2×C4—4881no—
351C2×C4—4881no—
352C2×C4—4882no—
353C2×C4—4882no—
354C2×C4—4882no—
355C2×C4—2442no—
356C2×C4—2442no—
357C2×C4—2441no—
358C2×C4—2441no—
359C2×C4—2441no—
360C2×C4—2441no—
361C2×C4—2441no—
362C2×C4—2441no—
363C2×C4—2441no—
364C2×C4—2441no—
365C2×C4#1451983511yescharacteristic
366C2×C4#1451983511yescharacteristic
367C8—4882no—
368C22—21no—
369C22—21no—
370C22—81no—
371C22—81no—
372C22—81no—
373C22—81no—
374C22—81no—
375C22—81no—
376C22—81no—
377C22—1221no—
378C22—1221no—
379C22—4881no—
380C22—4881no—
381C22—2442no—
382C22—2441no—
383C22—2441no—
384C22—2441no—
385C22—2441no—
386C22—2441no—
387C22—2441no—
388C22—2441no—
389C22C2×#1451983511yescharacteristic
390C22#1684075311yescharacteristic
391C22#1684075911yescharacteristic
392C4—21no—
393C4—21no—
394C4—41no—
395C4—41no—
396C4—81no—
397C4—9762no—
398C4—4881no—
399C4—4881no—
400C4—2441no—
401C4—2441no—
402C2—21no—
403C2—21no—
404C2—161no—
405C2—4881no—
406C2—2441no—
407C2—2441no—
408C2#2146123411yescharacteristic
409C2#2146207811yescharacteristic
410C2#2146209411yescharacteristic
subgroupG/H
centerC22C2×#14519835
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×#124×C61C4
socleC22×C61C2×#99
prime radical#21451672C2
cosocleC2×#11758198C23
hypercenterC2×#124#6923
hypocenterC61#11825
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. #21461680C2semidirect
2. #21461076C2semidirect
3. #21460814C2semidirect
4. #21460797C2semidirect
14. #16839673C4semidirect
17. #16839670C4semidirect
21. #16839630C4semidirect
22. C2×#124×C61C4semidirect
211. C2×#124#6923semidirect
228. C61#11825semidirect

Maximal subgroups

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

subgroupindex
#214616802
#214610762
#214608142
#214607972
#214516722
#1182561