Finite Group Databasebeta

← #30601036

Subgroups — #30601036

Order 15616.

644 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 644 conjugacy classes of subgroups — too many to draw. Only its 84 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#21462257C211yesmaximal, characteristic, complemented
2#21461215C212yesmaximal
3#21461068C211yesmaximal, characteristic, complemented
4#21460700C212yesmaximal, complemented
5#21451293C211yesmaximal, characteristic
6C2×#14519856—21no—
7#16840733C2212yes—
8C4⋊C4×#6923—24no—
9C4×C22⋊#6923—21no—
10C4×C22⋊#6923C2212yes—
11#16840613—24no—
12#16840608—21no—
13#16840607—21no—
14C2×#14519748C2211yescharacteristic
15C2×C4⋊C4×D61C2211yescharacteristic
16#16839702C411yescharacteristic, complemented
17#16839701C411yescharacteristic, complemented
18#16839676C411yescharacteristic, complemented
19#16839655—21no—
20#16839650—21no—
21#16839638—21no—
22#16839638—21no—
23#16839609C2211yescharacteristic
24C61×#394C411yescharacteristic, complemented
25C2×#11758213—22no—
26#14519856—24no—
27#14519856—24no—
28C2×C4⋊#6923—22no—
29C2×C22⋊#6923—22no—
30C2×C4×#6923—22no—
31C2×C4×#6923—22no—
32C2×C4×#6923—22no—
33#14519834—22no—
34C22⋊#92420—22no—
35(C2×#6923)⋊C4—22no—
36(C2×#6923)⋊C4D414yes—
37C22×C22⋊D61—21no—
38C22×C4×D61D411yescharacteristic
39C22×C4×D61D411yescharacteristic
40C22×C4×D61C2311yescharacteristic
41#14519748—22no—
42#14519748—22no—
43C2×C4⋊Dic61C2×C411yescharacteristic
44C2×C4⋊Dic61D411yescharacteristic
45C2×#11758196C2×C411yescharacteristic
46C2×#11758196D411yescharacteristic
47C4⋊C4×D61—22no—
48C4⋊C4×D61—22no—
49C2×C22⋊Dic61—21no—
50C2×C22⋊Dic61—21no—
51C2×C22⋊Dic61—21no—
52C2×#11758198—21no—
53C2×C4×Dic61—21no—
54#14519684—21no—
55#14519684—21no—
56#14519684—21no—
57#14519684—21no—
58#14519684C2×C411yescharacteristic
59C22×D4×C61C2×C411yescharacteristic
60C2×C4⋊C4×C61C2×C411yescharacteristic
61C2×C22⋊C4×C61—21no—
62C2×C22⋊C4×C61—21no—
63#95×C61C2×C411yescharacteristic
64C24×C61—21no—
65C23×D61C2×D411yescharacteristic
66C22×#6923—24no—
67C2×D4×C61—22no—
68C2×D4×C61—81no—
69C22×C4×C61—21no—
70C22×C4×C61C22⋊C411yescharacteristic
71C22×C4×C61C22⋊C411yescharacteristic
72C22×C4×C61C22×C411yescharacteristic
73C2×C22⋊D61—42no—
74C2×C22⋊D61—42no—
75C2×C22⋊D61—41no—
76C2×C22⋊D61—41no—
77C22×Dic61—21no—
78C22×Dic61—21no—
79C22×Dic61C22⋊C411yescharacteristic
80C22×Dic61C22⋊C411yescharacteristic
81C22×Dic61C2×D411yescharacteristic
82C2×C4×D61—21no—
83C2×C4×D61—21no—
84C2×C4×D61—22no—
85C2×C4×D61—22no—
86C2×C4×D61—21no—
87C2×C4×D61—21no—
88C2×C4×D61—81no—
89C2×C4×D61—81no—
90C2×C4×D61C2×D412yes—
91C2×C4×D61#4112yes—
92C22⋊#6923—24no—
93C22⋊#6923—24no—
94C2×#92420—42no—
95C4⋊#6923—28no—
96C4×#6923—28no—
97C4×#6923—82no—
98C4×#6923—82no—
99#11758213—82no—
100C4⋊C4×C61—22no—
101C22⋊C4×C61—42no—
102C22⋊C4×C61—81no—
103C22⋊Dic61—42no—
104C22⋊Dic61—42no—
105C22⋊Dic61—81no—
106#11758198—42no—
107C4⋊Dic61—22no—
108C4⋊Dic61—22no—
109#11758196—22no—
110#11758196—22no—
111C4×Dic61—81no—
112C23×C61—41no—
113C23×C61—41no—
114C23×C61—41no—
115C23×C61—41no—
116C23×C61—41no—
117C23×C61—41no—
118C23×C61—41no—
119C23×C61C2×C22⋊C411yescharacteristic
120C22×D61—21no—
121C22×D61—21no—
122C22×D61—22no—
123C22×D61—41no—
124C22×D61#12011yescharacteristic
125C22×D61#12311yescharacteristic
126C2×#6923—28no—
127C2×#6923—44no—
128C2×#6923—44no—
129D4×C61—82no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61#10412yes—
139C2×C4×C61C4×D412yes—
140C22⋊D61—82no—
141C22⋊D61—82no—
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61#10412yes—
154C2×Dic61#12112yes—
155C4×D61—22no—
156C4×D61—22no—
157C4×D61—24no—
158C4×D61—42no—
159C4×D61—42no—
160C4×D61—42no—
161C4×D61—81no—
162#92420—82no—
163#9410—611nomaximal, Sylow
164C22×C61—21no—
165C22×C61—21no—
166C22×C61—81no—
167C22×C61—81no—
168C22×C61—81no—
169C22×C61—81no—
170C22×C61—81no—
171C22×C61—81no—
172C22×C61—81no—
173C22×C61#38611yescharacteristic
174C22×C61C2×#10411yescharacteristic
175C22×C61C2×#10411yescharacteristic
176C2×D61—21no—
177C2×D61—21no—
178C2×D61—21no—
179C2×D61—21no—
180C2×D61—21no—
181C2×D61—42no—
182C2×D61—42no—
183C2×D61#45412yes—
184#6923—48no—
185C4×C61—22no—
186C4×C61—22no—
187C4×C61—41no—
188C4×C61—81no—
189Dic61—22no—
190Dic61—22no—
191Dic61—41no—
192Dic61—81no—
193Dic61—81no—
194#2591—611no—
195#2274—611no—
196#1507—612no—
197#1463—611no—
198#1297—612no—
199C2×C61—21no—
200C2×C61—21no—
201C2×C61—161no—
202C2×C61#188811yescharacteristic
203C2×C61#189611yescharacteristic
204C2×C61#191311yescharacteristic
205D61—22no—
206D61—41no—
207C2×#121—611no—
208C2×#117—1221no—
209C22×C4⋊C4—611no—
210#407—612no—
211#400—611no—
212#400—611no—
213#394—611no—
214#394#692311yescharacteristic, complemented
215#388—1221no—
216#388—1221no—
217#386—1221no—
218#386—1221no—
219C4×C4⋊C4—1224no—
220C4×C22⋊C4—612no—
221C4×C22⋊C4—611no—
222C4×C22⋊C4—1221no—
223#327—1224no—
224#324—1221no—
225#324—1221no—
226C61#941011yescharacteristic, complemented, Sylow
227C22×D4—1221no—
228C22×D4C2×#692311yescharacteristic
229C23×C4—611no—
230C23×C4—611no—
231C23×C4—611no—
232C2×M16—1222no—
233#121—1222no—
234#121—1222no—
235#117—1224no—
236#117—1224no—
237C2×C4⋊C4—611no—
238C2×C4⋊C4—611no—
239C2×C4⋊C4—611no—
240C2×C4⋊C4—611no—
241C2×C4⋊C4—1222no—
242C2×C4⋊C4—1222no—
243C2×C4⋊C4—1222no—
244C2×C4⋊C4C2×#692311yescharacteristic
245C2×C22⋊C4—21no—
246C2×C22⋊C4—21no—
247C2×C22⋊C4—1222no—
248C2×C22⋊C4—1221no—
249C2×C22⋊C4—1221no—
250C2×C22⋊C4—1221no—
251C2×C22⋊C4—1221no—
252C2×C42—1222no—
253C2×C42—1221no—
254C2×C42—1222no—
255C2×C42—1222no—
256C22⋊C8—1222no—
257C22⋊C8—1222no—
258#95—614no—
259#95—611no—
260#95—1221no—
261#95—1221no—
262#95—1222no—
263#95—1221no—
264#95—1221no—
265#95C2×#692311yescharacteristic
266C24—21no—
267C24—611no—
268C2×D4—22no—
269C2×D4—81no—
270C2×D4—2441no—
271C2×D4—2441no—
272C2×D4—2442no—
273C2×D4—2442no—
274C22×C4—21no—
275C22×C4—611no—
276C22×C4—611no—
277C22×C4—612no—
278C22×C4—612no—
279C22×C4—611no—
280C22×C4—1222no—
281C22×C4—1221no—
282C22×C4—1221no—
283C22×C4—1221no—
284C22×C4—1221no—
285C22×C4—1222no—
286C22×C4—1224no—
287C22×C4—1221no—
288C22×C4—1221no—
289C22×C4—4881no—
290C22×C4—4881no—
291C22×C4C22⋊#692311yescharacteristic
292C22×C4C22⋊#692311yescharacteristic
293C22×C4C22×#692311yescharacteristic
294M16—4882no—
295C2×C8—2442no—
296C4⋊C4—22no—
297C4⋊C4—1222no—
298C4⋊C4—1222no—
299C4⋊C4—1228no—
300C4⋊C4—1222no—
301C4⋊C4—1222no—
302C22⋊C4—42no—
303C22⋊C4—81no—
304C22⋊C4—1224no—
305C22⋊C4—1224no—
306C22⋊C4—4881no—
307C22⋊C4—2442no—
308C22⋊C4—2442no—
309C22⋊C4—2442no—
310C42—1228no—
311C42—4881no—
312C42—4882no—
313C42—4882no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23—611no—
322C23—611no—
323C23—1222no—
324C23—1221no—
325C23—1221no—
326C23—2441no—
327C23C2×C22⋊#692311yescharacteristic
328D4—82no—
329D4—4882no—
330D4—4882no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—612no—
340C2×C4—612no—
341C2×C4—1222no—
342C2×C4—1222no—
343C2×C4—1224no—
344C2×C4—1221no—
345C2×C4—1221no—
346C2×C4—1228no—
347C2×C4—1221no—
348C2×C4—4881no—
349C2×C4—2442no—
350C2×C4—2442no—
351C2×C4—2442no—
352C2×C4—2441no—
353C2×C4—2441no—
354C2×C4—2441no—
355C2×C4—2441no—
356C2×C4—2441no—
357C2×C4—2441no—
358C2×C4—2441no—
359C2×C4—2444no—
360C2×C4—2444no—
361C2×C4—2441no—
362C2×C4#1451984112yes—
363C2×C4D4×#692312yes—
364C8—4882no—
365C22—21no—
366C22—21no—
367C22—81no—
368C22—81no—
369C22—81no—
370C22—81no—
371C22—81no—
372C22—81no—
373C22—81no—
374C22—612no—
375C22—1221no—
376C22—1221no—
377C22—1221no—
378C22—1221no—
379C22—1221no—
380C22—2442no—
381C22—2442no—
382C22#1684071011yescharacteristic
383C22C2×#1451984111yescharacteristic
384C22D61⋊#10411yescharacteristic
385C4—22no—
386C4—22no—
387C4—41no—
388C4—81no—
389C4—1222no—
390C4—1222no—
391C4—4881no—
392C4—4881no—
393C4—2448no—
394C4—2441no—
395C2—21no—
396C2—21no—
397C2—161no—
398C2—1222no—
399C2—2441no—
400C2#2146182711yescharacteristic
401C2#2146183711yescharacteristic
402C2#2146186811yescharacteristic
subgroupG/H
centerC22#16840710
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#394C4
socleC22×C61#386
prime radicalC2×#14519748C22
cosocleC22×C4×D61C23
hypercenter#394#6923
hypocenterC61#9410
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #394

Complements

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

NH ≅ G/Ntype
1. #21462257C2semidirect
3. #21461068C2semidirect
4. #21460700C2semidirect
16. #16839702C4semidirect
17. #16839701C4semidirect
18. #16839676C4semidirect
24. C61×#394C4semidirect
214. #394#6923semidirect
226. C61#9410semidirect

Maximal subgroups

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

subgroupindex
#214622572
#214612152
#214610682
#214607002
#214512932
#941061