Finite Group Databasebeta

← #30601044

Subgroups — #30601044

Order 15616.

552 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 78 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#21462296C211yesmaximal, characteristic, complemented
2#21461215C212yesmaximal
3#21461068C211yesmaximal, characteristic, complemented
4#21460700C212yesmaximal, complemented
5#21451293C211yesmaximal, characteristic
6#16840733C2212yes—
7#16840711—24no—
8#16840705—21no—
9#16840704—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—
26C2×C4⋊#6923—22no—
27C2×C22⋊#6923—22no—
28C2×C4×#6923—22no—
29#14519834—22no—
30C22⋊#92420—22no—
31(C2×#6923)⋊C4—22no—
32(C2×#6923)⋊C4—24no—
33(C2×#6923)⋊C4D414yes—
34C22×C22⋊D61—21no—
35C22×C4×D61D411yescharacteristic
36C22×C4×D61D411yescharacteristic
37C22×C4×D61C2311yescharacteristic
38#14519748—22no—
39#14519748—22no—
40C2×C4⋊Dic61C2×C411yescharacteristic
41C2×C4⋊Dic61D411yescharacteristic
42C2×#11758196C2×C411yescharacteristic
43C2×#11758196D411yescharacteristic
44C4⋊C4×D61—22no—
45C4⋊C4×D61—22no—
46C2×C22⋊Dic61—21no—
47C2×C22⋊Dic61—21no—
48C2×C22⋊Dic61—21no—
49C2×#11758198—21no—
50C2×C4×Dic61—21no—
51#14519684—21no—
52#14519684—21no—
53#14519684—21no—
54#14519684—21no—
55#14519684C2×C411yescharacteristic
56C22×D4×C61C2×C411yescharacteristic
57C2×C4⋊C4×C61C2×C411yescharacteristic
58C2×C22⋊C4×C61—21no—
59C2×C22⋊C4×C61—21no—
60#95×C61C2×C411yescharacteristic
61C24×C61—21no—
62C23×D61C2×D411yescharacteristic
63C22×#6923—24no—
64C2×D4×C61—22no—
65C2×D4×C61—81no—
66C22×C4×C61—21no—
67C22×C4×C61C22⋊C411yescharacteristic
68C22×C4×C61C22⋊C411yescharacteristic
69C22×C4×C61C22×C411yescharacteristic
70C2×C22⋊D61—42no—
71C2×C22⋊D61—42no—
72C2×C22⋊D61—41no—
73C2×C22⋊D61—41no—
74C22×Dic61—21no—
75C22×Dic61—21no—
76C22×Dic61C22⋊C411yescharacteristic
77C22×Dic61C22⋊C411yescharacteristic
78C22×Dic61C2×D411yescharacteristic
79C2×C4×D61—21no—
80C2×C4×D61—21no—
81C2×C4×D61—21no—
82C2×C4×D61—21no—
83C2×C4×D61—41no—
84C2×C4×D61—41no—
85C2×C4×D61—81no—
86C2×C4×D61—81no—
87C2×C4×D61C2×D412yes—
88C2×C4×D61#4112yes—
89C22⋊#6923—42no—
90C22⋊#6923—42no—
91C2×#92420—42no—
92C4⋊#6923—82no—
93C4×#6923—82no—
94#11758213—82no—
95C4⋊C4×C61—22no—
96C22⋊C4×C61—42no—
97C22⋊C4×C61—81no—
98C22⋊Dic61—42no—
99C22⋊Dic61—42no—
100C22⋊Dic61—81no—
101#11758198—42no—
102C4⋊Dic61—22no—
103C4⋊Dic61—22no—
104#11758196—22no—
105#11758196—22no—
106C4×Dic61—81no—
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—22no—
118C22×D61—41no—
119C22×D61#12011yescharacteristic
120C22×D61#12311yescharacteristic
121C2×#6923—44no—
122C2×#6923—44no—
123C2×#6923—44no—
124D4×C61—82no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61C4×D412yes—
135C22⋊D61—82no—
136C22⋊D61—82no—
137C2×Dic61—21no—
138C2×Dic61—21no—
139C2×Dic61—21no—
140C2×Dic61—21no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61#12112yes—
150C4×D61—42no—
151C4×D61—42no—
152C4×D61—42no—
153C4×D61—42no—
154C4×D61—42no—
155C4×D61—81no—
156#92420—82no—
157#9414—611nomaximal, Sylow
158C22×C61—21no—
159C22×C61—21no—
160C22×C61—81no—
161C22×C61—81no—
162C22×C61—81no—
163C22×C61—81no—
164C22×C61—81no—
165C22×C61—81no—
166C22×C61—81no—
167C22×C61#38611yescharacteristic
168C22×C61#42111yescharacteristic
169C22×C61#42111yescharacteristic
170C2×D61—21no—
171C2×D61—21no—
172C2×D61—21no—
173C2×D61—21no—
174C2×D61—21no—
175C2×D61—42no—
176C2×D61—42no—
177C2×D61#45412yes—
178#6923—84no—
179C4×C61—22no—
180C4×C61—41no—
181C4×C61—41no—
182C4×C61—81no—
183Dic61—22no—
184Dic61—41no—
185Dic61—41no—
186Dic61—81no—
187Dic61—81no—
188#2591—611no—
189#2313—611no—
190#1507—612no—
191#1463—611no—
192#1297—612no—
193C2×C61—21no—
194C2×C61—21no—
195C2×C61—161no—
196C2×C61#188811yescharacteristic
197C2×C61#189711yescharacteristic
198C2×C61#191311yescharacteristic
199D61—22no—
200D61—41no—
201C2×#121—611no—
202C22×C4⋊C4—611no—
203#407—612no—
204#400—611no—
205#400—611no—
206#394—611no—
207#394#692311yescharacteristic, complemented
208#388—1221no—
209#388—1221no—
210#387—1224no—
211#386—1221no—
212#386—1221no—
213#381—1221no—
214#380—1221no—
215C4×C22⋊C4—612no—
216C4×C22⋊C4—611no—
217#327—1224no—
218#324—1221no—
219#324—1221no—
220C61#941411yescharacteristic, complemented, Sylow
221C22×D4—1221no—
222C22×D4C2×#692311yescharacteristic
223C23×C4—611no—
224C23×C4—611no—
225C23×C4—611no—
226C2×M16—1222no—
227#121—1222no—
228#121—1222no—
229C2×C4⋊C4—611no—
230C2×C4⋊C4—611no—
231C2×C4⋊C4—611no—
232C2×C4⋊C4—611no—
233C2×C4⋊C4—1222no—
234C2×C4⋊C4—1222no—
235C2×C4⋊C4—1222no—
236C2×C4⋊C4C2×#692311yescharacteristic
237C2×C22⋊C4—21no—
238C2×C22⋊C4—21no—
239C2×C22⋊C4—1221no—
240C2×C22⋊C4—1221no—
241C2×C22⋊C4—1221no—
242C2×C22⋊C4—1221no—
243C2×C22⋊C4—1222no—
244C2×C42—1221no—
245C2×C42—1222no—
246C22⋊C8—1222no—
247C22⋊C8—1222no—
248#95—614no—
249#95—611no—
250#95—1221no—
251#95—1221no—
252#95—1222no—
253#95—1224no—
254#95—1221no—
255#95—1221no—
256#95C2×#692311yescharacteristic
257C24—21no—
258C24—611no—
259C2×D4—22no—
260C2×D4—81no—
261C2×D4—2441no—
262C2×D4—2441no—
263C2×D4—2442no—
264C2×D4—2442no—
265C22×C4—21no—
266C22×C4—611no—
267C22×C4—612no—
268C22×C4—612no—
269C22×C4—611no—
270C22×C4—611no—
271C22×C4—1221no—
272C22×C4—1221no—
273C22×C4—1221no—
274C22×C4—1221no—
275C22×C4—1224no—
276C22×C4—1221no—
277C22×C4—1221no—
278C22×C4—4881no—
279C22×C4—4881no—
280C22×C4—2441no—
281C22×C4—2441no—
282C22×C4C22⋊#692311yescharacteristic
283C22×C4C22⋊#692311yescharacteristic
284C22×C4C22×#692311yescharacteristic
285M16—4882no—
286C2×C8—2442no—
287C4⋊C4—22no—
288C4⋊C4—1222no—
289C4⋊C4—1222no—
290C4⋊C4—1222no—
291C4⋊C4—1222no—
292C4⋊C4—4882no—
293C22⋊C4—42no—
294C22⋊C4—81no—
295C22⋊C4—4881no—
296C22⋊C4—2442no—
297C22⋊C4—2442no—
298C22⋊C4—2442no—
299C22⋊C4—2442no—
300C22⋊C4—2442no—
301C42—4881no—
302C42—4882no—
303C23—41no—
304C23—41no—
305C23—41no—
306C23—41no—
307C23—41no—
308C23—41no—
309C23—41no—
310C23—611no—
311C23—611no—
312C23—1222no—
313C23—1221no—
314C23—1221no—
315C23—2441no—
316C23C2×C22⋊#692311yescharacteristic
317D4—82no—
318D4—4882no—
319D4—4882no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—612no—
330C2×C4—1221no—
331C2×C4—1221no—
332C2×C4—1221no—
333C2×C4—1221no—
334C2×C4—4881no—
335C2×C4—2442no—
336C2×C4—2442no—
337C2×C4—2442no—
338C2×C4—2442no—
339C2×C4—2442no—
340C2×C4—2441no—
341C2×C4—2441no—
342C2×C4—2441no—
343C2×C4—2441no—
344C2×C4—2441no—
345C2×C4—2444no—
346C2×C4—2444no—
347C2×C4—2444no—
348C2×C4—2441no—
349C2×C4—2441no—
350C2×C4—2441no—
351C2×C4D4×#692312yes—
352C8—4882no—
353C22—21no—
354C22—21no—
355C22—81no—
356C22—81no—
357C22—81no—
358C22—81no—
359C22—81no—
360C22—81no—
361C22—81no—
362C22—612no—
363C22—1221no—
364C22—1221no—
365C22—1221no—
366C22—1221no—
367C22—1221no—
368C22—2442no—
369C22—2442no—
370C22#1684071011yescharacteristic
371C22#1684075911yescharacteristic
372C22#1684076011yescharacteristic
373C4—22no—
374C4—41no—
375C4—41no—
376C4—81no—
377C4—1222no—
378C4—4881no—
379C4—4884no—
380C4—4881no—
381C4—2441no—
382C4—2441no—
383C2—21no—
384C2—21no—
385C2—161no—
386C2—1222no—
387C2—2441no—
388C2#2146182711yescharacteristic
389C2#2146183911yescharacteristic
390C2#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#9414
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. #21462296C2semidirect
3. #21461068C2semidirect
4. #21460700C2semidirect
16. #16839702C4semidirect
17. #16839701C4semidirect
18. #16839676C4semidirect
24. C61×#394C4semidirect
207. #394#6923semidirect
220. C61#9414semidirect

Maximal subgroups

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

subgroupindex
#214622962
#214612152
#214610682
#214607002
#214512932
#941461