Finite Group Databasebeta

← #30600551

Subgroups — #30600551

Order 15616.

560 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 94 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#21462299C211yesmaximal, characteristic
2#21461259C212yesmaximal
3D61⋊#324C211yesmaximal, characteristic
4#21460681C212yesmaximal
5#21451631C211yesmaximal, characteristic
6C2×#14519856—21no—
7D61⋊(C22⋊C8)C2212yes—
8#16840713—24no—
9#16840704—21no—
10#16840704C2212yes—
11#16840616—24no—
12#16840608—21no—
13#16840607—21no—
14C2×#14519753C2211yescharacteristic
15C2×C4⋊C4×D61C2211yescharacteristic
16#16839702C411yescharacteristic, complemented
17#16839701C411yescharacteristic, complemented
18#16839696—21no—
19#16839693—21no—
20#16839681C411yescharacteristic, complemented
21#16839633—21no—
22#16839624—21no—
23#16839621C2211yescharacteristic
24C61×#395C411yescharacteristic, complemented
25C2×D61⋊C8—22no—
26#14519856—42no—
27#14519856—42no—
28C2×C4⋊#6923—22no—
29C2×C4⋊#6923—22no—
30C2×C4⋊#6923—22no—
31C2×C22⋊#6923—22no—
32C2×C4×#6923—22no—
33#14519834—22no—
34C22⋊#92420—22no—
35(C2×#6923)⋊C4—22no—
36(C2×#6923)⋊C4D414yes—
37C22×C4×D61D411yescharacteristic
38C22×C4×D61D411yescharacteristic
39C22×C4×D61C2311yescharacteristic
40#14519753—22no—
41#14519753—22no—
42C2×C4⋊Dic61C2×C411yescharacteristic
43C2×C4⋊Dic61D411yescharacteristic
44C2×#11758196—21no—
45C2×#11758196—21no—
46C2×#11758196—21no—
47C2×#11758196C2×C411yescharacteristic
48C2×#11758196D411yescharacteristic
49C4⋊C4×D61—22no—
50C4⋊C4×D61—22no—
51C2×#11758198—21no—
52C2×#11758198—21no—
53#14519684—21no—
54#14519684—21no—
55#14519684—21no—
56#14519684—21no—
57#14519684—21no—
58#14519684C2×C411yescharacteristic
59C22×Q8×C61C2×C411yescharacteristic
60C2×C4⋊C4×C61—21no—
61C2×C4⋊C4×C61C2×C411yescharacteristic
62#95×C61—21no—
63#95×C61C2×C411yescharacteristic
64C23×D61C2×D411yescharacteristic
65C22×#6923—24no—
66C2×Q8×C61—22no—
67C2×Q8×C61—81no—
68C22×C4×C61—21no—
69C22×C4×C61—21no—
70C22×C4×C61C22⋊C411yescharacteristic
71C22×C4×C61C22⋊C411yescharacteristic
72C22×C4×C61C22×C411yescharacteristic
73C22×Dic61—21no—
74C22×Dic61—21no—
75C22×Dic61C22⋊C411yescharacteristic
76C22×Dic61C22⋊C411yescharacteristic
77C22×Dic61C2×D411yescharacteristic
78C2×C4×D61—21no—
79C2×C4×D61—21no—
80C2×C4×D61—21no—
81C2×C4×D61—21no—
82C2×C4×D61—21no—
83C2×C4×D61—21no—
84C2×C4×D61—81no—
85C2×C4×D61—81no—
86C2×C4×D61SD1612yes—
87C2×C4×D61Q1612yes—
88C2×C4×D61C2×D412yes—
89C2×C4×D61#4112yes—
90C22⋊#6923—42no—
91C22⋊#6923—42no—
92C2×#92420—42no—
93C4⋊#6923—44no—
94C4⋊#6923—82no—
95C4⋊#6923—82no—
96C4×#6923—44no—
97D61⋊C8—82no—
98C4⋊C4×C61—22no—
99C4⋊C4×C61—81no—
100#11758198—41no—
101#11758198—41no—
102#11758198—41no—
103#11758198—41no—
104C4⋊Dic61—22no—
105C4⋊Dic61—22no—
106#11758196—22no—
107#11758196—22no—
108#11758196—42no—
109#11758196—81no—
110#11758196—81no—
111C23×C61C2×C22⋊C411yescharacteristic
112C22×D61—41no—
113C22×D61—41no—
114C22×D61#12011yescharacteristic
115C22×D61#12311yescharacteristic
116C22×D61C2×SD1611yescharacteristic
117C22×D61C2×Q1611yescharacteristic
118C22×D61AGL(1,ℤ/8)11yescharacteristic
119C22×D61#13711yescharacteristic
120C2×#6923—44no—
121C2×#6923—44no—
122C2×#6923—44no—
123Q8×C61—82no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61#10312yes—
136C2×C4×C61C4×D412yes—
137C2×Dic61—21no—
138C2×Dic61—21no—
139C2×Dic61—21no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61—42no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61#10312yes—
148C2×Dic61#12112yes—
149C4×D61—22no—
150C4×D61—22no—
151C4×D61—22no—
152C4×D61—22no—
153C4×D61—42no—
154C4×D61—42no—
155C4×D61—42no—
156C4×D61—81no—
157#92420—82no—
158#9200—611nomaximal, Sylow
159C22×C61—21no—
160C22×C61—21no—
161C22×C61#38611yescharacteristic
162C22×C61C2×#10311yescharacteristic
163C22×C61#41711yescharacteristic
164C2×D61—21no—
165C2×D61—21no—
166C2×D61—21no—
167C2×D61—21no—
168C2×D61—41no—
169C2×D61—41no—
170C2×D61—41no—
171C2×D61—41no—
172C2×D61#45011yescharacteristic
173C2×D61#45111yescharacteristic
174C2×D61#48311yescharacteristic
175C2×D61#48411yescharacteristic
176#6923—84no—
177C4×C61—22no—
178C4×C61—22no—
179C4×C61—41no—
180C4×C61—81no—
181C4×C61—81no—
182Dic61—22no—
183Dic61—22no—
184Dic61—41no—
185Dic61—81no—
186Dic61—81no—
187#2627—611no—
188#2316—611no—
189#1520—612no—
190C2×#324—611no—
191#1289—612no—
192C2×C61—21no—
193C2×C61—21no—
194C2×C61#187211yescharacteristic
195C2×C61#191211yescharacteristic
196C2×C61#191311yescharacteristic
197D61—21no—
198D61—21no—
199D61—21no—
200D61—21no—
201C2×C22⋊Q8—611no—
202C2×#117—1221no—
203C22×C4⋊C4—611no—
204C2×C22⋊C8—612no—
205#400—611no—
206#400—611no—
207#398—1221no—
208#398—1221no—
209#395—611no—
210#395#692311yescharacteristic, complemented
211#389—1224no—
212#385—1221no—
213#381—1221no—
214#380—612no—
215#380—611no—
216#380—1221no—
217#328—1224no—
218#324—1221no—
219#324—1221no—
220C61#920011yescharacteristic, complemented, Sylow
221C22×Q8C2×#692311yescharacteristic
222C23×C4—611no—
223C23×C4—611no—
224C23×C4—611no—
225C22×C8—1222no—
226C22⋊Q8—1222no—
227C22⋊Q8—1222no—
228#117—2442no—
229#117—2442no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—611no—
232C2×C4⋊C4—611no—
233C2×C4⋊C4—611no—
234C2×C4⋊C4—611no—
235C2×C4⋊C4—1222no—
236C2×C4⋊C4—1222no—
237C2×C4⋊C4—1221no—
238C2×C4⋊C4—1221no—
239C2×C4⋊C4—1222no—
240C2×C4⋊C4—1222no—
241C2×C4⋊C4—1221no—
242C2×C4⋊C4—1222no—
243C2×C4⋊C4C2×#692311yescharacteristic
244C2×C22⋊C4—1221no—
245C2×C22⋊C4—1221no—
246C2×C22⋊C4—1222no—
247C2×C42—1222no—
248C22⋊C8—1222no—
249C22⋊C8—1222no—
250#95—21no—
251#95—614no—
252#95—611no—
253#95—1221no—
254#95—1221no—
255#95—1221no—
256#95—1222no—
257#95—1221no—
258#95—1221no—
259#95C2×#692311yescharacteristic
260C24—611no—
261C2×Q8—22no—
262C2×Q8—81no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—611no—
266C22×C4—611no—
267C22×C4—612no—
268C22×C4—612no—
269C22×C4—612no—
270C22×C4—612no—
271C22×C4—611no—
272C22×C4—1221no—
273C22×C4—1221no—
274C22×C4—1221no—
275C22×C4—1221no—
276C22×C4—1221no—
277C22×C4—1221no—
278C22×C4—1224no—
279C22×C4—1221no—
280C22×C4—1221no—
281C22×C4—4881no—
282C22×C4—4881no—
283C22×C4C22⋊#692311yescharacteristic
284C22×C4C22⋊#692311yescharacteristic
285C22×C4C22×#692311yescharacteristic
286C2×C8—4882no—
287C2×C8—2442no—
288C4⋊C4—22no—
289C4⋊C4—81no—
290C4⋊C4—1222no—
291C4⋊C4—1222no—
292C4⋊C4—1222no—
293C4⋊C4—1222no—
294C4⋊C4—4881no—
295C4⋊C4—4881no—
296C4⋊C4—4882no—
297C4⋊C4—4882no—
298C4⋊C4—2442no—
299C4⋊C4—2444no—
300C22⋊C4—2441no—
301C22⋊C4—2441no—
302C22⋊C4—2441no—
303C22⋊C4—2441no—
304C22⋊C4—2442no—
305C22⋊C4—2442no—
306C42—2444no—
307C23—611no—
308C23—611no—
309C23—611no—
310C23—611no—
311C23—611no—
312C23—611no—
313C23—2441no—
314C23—2441no—
315C23C2×C22⋊#692311yescharacteristic
316Q8—82no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—612no—
329C2×C4—612no—
330C2×C4—1222no—
331C2×C4—1222no—
332C2×C4—1222no—
333C2×C4—1222no—
334C2×C4—1221no—
335C2×C4—1221no—
336C2×C4—1221no—
337C2×C4—4881no—
338C2×C4—2442no—
339C2×C4—2442no—
340C2×C4—2442no—
341C2×C4—2441no—
342C2×C4—2441no—
343C2×C4—2441no—
344C2×C4—2442no—
345C2×C4—2444no—
346C2×C4—2444no—
347C2×C4—2444no—
348C2×C4—2441no—
349C2×C4—2441no—
350C2×C4—2441no—
351C2×C4#1451984012yes—
352C2×C4D4×#692312yes—
353C8—4882no—
354C22—21no—
355C22—21no—
356C22—611no—
357C22—611no—
358C22—611no—
359C22—611no—
360C22—1221no—
361C22—1221no—
362C22—1221no—
363C22—1221no—
364C22—2441no—
365C22—2441no—
366C22—2441no—
367C22—2441no—
368C22#1684071011yescharacteristic
369C22C2×#1451984011yescharacteristic
370C22#1684075311yescharacteristic
371C4—22no—
372C4—22no—
373C4—41no—
374C4—81no—
375C4—81no—
376C4—1222no—
377C4—1222no—
378C4—4881no—
379C4—4884no—
380C4—4881no—
381C4—2441no—
382C2—21no—
383C2—21no—
384C2—1221no—
385C2—1221no—
386C2—1221no—
387C2—1221no—
388C2#2146180411yescharacteristic
389C2#2146186611yescharacteristic
390C2#2146186811yescharacteristic
subgroupG/H
centerC22#16840710
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#395C4
socleC22×C61#386
prime radicalC23×D61C2×D4
cosocleC22×C4×D61C23
hypercenter#395#6923
hypocenterC61#9200
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #395

Complements

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

NH ≅ G/Ntype
16. #16839702C4semidirect
17. #16839701C4semidirect
20. #16839681C4semidirect
24. C61×#395C4semidirect
210. #395#6923semidirect
220. C61#9200semidirect

Maximal subgroups

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

subgroupindex
#214622992
#214612592
D61⋊#3242
#214606812
#214516312
#920061