Finite Group Databasebeta

← #30600563

Subgroups — #30600563

Order 15616.

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

normal subgroups only

This group has 578 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#21462296C211yesmaximal, characteristic, complemented
2#21461256C212yesmaximal
3D61⋊#324C211yesmaximal, characteristic, complemented
4#21460681C212yesmaximal, complemented
5#21451562C211yesmaximal, characteristic
6D61⋊(C22⋊C8)C2212yes—
7#16840711—24no—
8#16840705—21no—
9#16840704C2212yes—
10C4×C22⋊#6923—21no—
11#16840614—24no—
12#16840608—21no—
13#16840607—21no—
14C2×#14519762—21no—
15C2×#14519752C2211yescharacteristic
16C2×C4⋊C4×D61C2211yescharacteristic
17#16839693C411yescharacteristic, complemented
18#16839686—21no—
19#16839684—21no—
20#16839680C411yescharacteristic, complemented
21#16839679C411yescharacteristic, complemented
22#16839640—21no—
23#16839621C2211yescharacteristic
24C61×#398C411yescharacteristic, complemented
25C2×D61⋊C8—22no—
26C2×C4⋊#6923—22no—
27C2×C22⋊#6923—22no—
28C2×C4×#6923—22no—
29#14519834—22no—
30C22⋊#92420—22no—
31(C2×#6923)⋊C4—24no—
32(C2×#6923)⋊C4—22no—
33(C2×#6923)⋊C4D414yes—
34C22×D244—21no—
35C22×D244C2×C411yescharacteristic
36C22×C4×D61D411yescharacteristic
37C22×C4×D61D411yescharacteristic
38C22×C4×D61C2311yescharacteristic
39#14519762—44no—
40#14519752—22no—
41#14519752—22no—
42C2×C4⋊Dic61D411yescharacteristic
43C2×#11758196—21no—
44C2×#11758196—21no—
45C2×#11758196C2×C411yescharacteristic
46C2×#11758196D411yescharacteristic
47C4⋊C4×D61—22no—
48C4⋊C4×D61—22no—
49C2×#11758198—21no—
50C2×#11758198—21no—
51C2×#11758198—21no—
52C2×#11758198—21no—
53C2×#11758198—21no—
54C2×#11758198—21no—
55#14519684—21no—
56#14519684C2×C411yescharacteristic
57C2×C4⋊C4×C61—21no—
58C2×C4⋊C4×C61C2×C411yescharacteristic
59C2×C4⋊C4×C61C2×C411yescharacteristic
60#95×C61—21no—
61#95×C61C2×C411yescharacteristic
62C23×D61—21no—
63C23×D61C2×D411yescharacteristic
64C22×#6923—24no—
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61C22⋊C411yescharacteristic
68C22×C4×C61C22⋊C411yescharacteristic
69C22×C4×C61C22×C411yescharacteristic
70C22×Dic61—21no—
71C22×Dic61C22⋊C411yescharacteristic
72C22×Dic61C22⋊C411yescharacteristic
73C22×Dic61C2×D411yescharacteristic
74C2×D244—22no—
75C2×D244—41no—
76C2×D244—41no—
77C2×D244—42no—
78C2×D244—42no—
79C2×D244—81no—
80C2×C4×D61—21no—
81C2×C4×D61—21no—
82C2×C4×D61—21no—
83C2×C4×D61—22no—
84C2×C4×D61—22no—
85C2×C4×D61—21no—
86C2×C4×D61—81no—
87C2×C4×D61—81no—
88C2×C4×D61C2×D412yes—
89C2×C4×D61#4112yes—
90C22⋊#6923—42no—
91C22⋊#6923—42no—
92C2×#92420—42no—
93C4⋊#6923—82no—
94C4×#6923—82no—
95D61⋊C8—82no—
96C4⋊C4×C61—22no—
97C4⋊C4×C61—22no—
98C4⋊C4×C61—42no—
99#11758198—42no—
100#11758198—42no—
101#11758198—42no—
102#11758198—42no—
103#11758198—81no—
104#11758198—81no—
105C4⋊Dic61—22no—
106#11758196—22no—
107#11758196—22no—
108#11758196—42no—
109#11758196—81no—
110C23×C61C2×C22⋊C411yescharacteristic
111C22×D61—41no—
112C22×D61—41no—
113C22×D61—41no—
114C22×D61—41no—
115C22×D61—41no—
116C22×D61—41no—
117C22×D61—41no—
118C22×D61—41no—
119C22×D61—41no—
120C22×D61#12011yescharacteristic
121C22×D61#12311yescharacteristic
122C22×D61#13512yes—
123C22×D61AGL(1,ℤ/8)12yes—
124C2×#6923—44no—
125C2×#6923—44no—
126C2×#6923—44no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61—41no—
139C2×C4×C61C4×D412yes—
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61—41no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61#12112yes—
150D244—82no—
151D244—82no—
152D244—82no—
153C4×D61—42no—
154C4×D61—42no—
155C4×D61—42no—
156C4×D61—42no—
157C4×D61—42no—
158C4×D61—81no—
159#92420—82no—
160#9206—611nomaximal, Sylow
161C22×C61—21no—
162C22×C61—21no—
163C22×C61#38611yescharacteristic
164C22×C61#41611yescharacteristic
165C22×C61#41811yescharacteristic
166C2×D61—21no—
167C2×D61—21no—
168C2×D61—21no—
169C2×D61—21no—
170C2×D61—42no—
171C2×D61—42no—
172C2×D61—81no—
173C2×D61—81no—
174C2×D61—81no—
175C2×D61—81no—
176C2×D61—81no—
177C2×D61—81no—
178C2×D61—81no—
179C2×D61#44912yes—
180C2×D61#48212yes—
181#6923—84no—
182C4×C61—22no—
183C4×C61—41no—
184C4×C61—41no—
185C4×C61—81no—
186C4×C61—81no—
187Dic61—22no—
188Dic61—41no—
189Dic61—41no—
190Dic61—81no—
191#2618—611no—
192#2313—611no—
193#1519—612no—
194C2×#324—611no—
195#1289—612no—
196C2×C61—21no—
197C2×C61—21no—
198C2×C61#187511yescharacteristic
199C2×C61#191211yescharacteristic
200C2×C61#191311yescharacteristic
201D61—22no—
202D61—22no—
203D61—161no—
204C2×#123—1221no—
205C2×#121—611no—
206C22×C4⋊C4—611no—
207C2×C22⋊C8—612no—
208#398—611no—
209#398#692311yescharacteristic, complemented
210#396—1221no—
211#396—1221no—
212#394—611no—
213#394—611no—
214#387—1224no—
215#386—1221no—
216#381—1221no—
217#380—612no—
218#380—611no—
219C4×C22⋊C4—1221no—
220#327—1224no—
221#324—1221no—
222#324—1221no—
223C61#920611yescharacteristic, complemented, Sylow
224C22×D4—611no—
225C22×D4—1221no—
226C23×C4—611no—
227C23×C4—611no—
228C23×C4—611no—
229C22×C8—1222no—
230#123—2444no—
231#121—1222no—
232#121—1222no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—611no—
235C2×C4⋊C4—611no—
236C2×C4⋊C4—611no—
237C2×C4⋊C4—1222no—
238C2×C4⋊C4—1222no—
239C2×C4⋊C4—1221no—
240C2×C4⋊C4—1222no—
241C2×C4⋊C4—1221no—
242C2×C4⋊C4C2×#692311yescharacteristic
243C2×C4⋊C4C2×#692311yescharacteristic
244C2×C22⋊C4—1221no—
245C2×C22⋊C4—1221no—
246C2×C22⋊C4—1221no—
247C2×C22⋊C4—1221no—
248C2×C22⋊C4—1221no—
249C2×C22⋊C4—1222no—
250C2×C22⋊C4—1221no—
251C2×C42—1222no—
252C22⋊C8—1222no—
253C22⋊C8—1222no—
254#95—21no—
255#95—614no—
256#95—611no—
257#95—1221no—
258#95—1222no—
259#95—1224no—
260#95C2×#692311yescharacteristic
261C24—611no—
262C24—1221no—
263C2×D4—1222no—
264C2×D4—4881no—
265C2×D4—2441no—
266C2×D4—2441no—
267C2×D4—2442no—
268C2×D4—2442no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—611no—
272C22×C4—612no—
273C22×C4—612no—
274C22×C4—611no—
275C22×C4—611no—
276C22×C4—1221no—
277C22×C4—1221no—
278C22×C4—1221no—
279C22×C4—1221no—
280C22×C4—1222no—
281C22×C4—1222no—
282C22×C4—1224no—
283C22×C4—1221no—
284C22×C4—4881no—
285C22×C4—4881no—
286C22×C4C22⋊#692311yescharacteristic
287C22×C4C22⋊#692311yescharacteristic
288C22×C4C22×#692311yescharacteristic
289C2×C8—4882no—
290C2×C8—2442no—
291C4⋊C4—22no—
292C4⋊C4—22no—
293C4⋊C4—42no—
294C4⋊C4—1222no—
295C4⋊C4—1222no—
296C4⋊C4—1222no—
297C4⋊C4—4881no—
298C4⋊C4—4882no—
299C4⋊C4—2442no—
300C22⋊C4—4881no—
301C22⋊C4—4881no—
302C22⋊C4—2442no—
303C22⋊C4—2442no—
304C22⋊C4—2442no—
305C22⋊C4—2442no—
306C22⋊C4—2442no—
307C22⋊C4—2442no—
308C42—4882no—
309C23—611no—
310C23—611no—
311C23—612no—
312C23—612no—
313C23—2441no—
314C23—2441no—
315C23—2441no—
316C23—2441no—
317C23—2441no—
318C23—2441no—
319C23—2441no—
320C23—2441no—
321C23—2441no—
322C23C2×C22⋊#692311yescharacteristic
323D4—4882no—
324D4—4882no—
325D4—4882no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—612no—
339C2×C4—1221no—
340C2×C4—1221no—
341C2×C4—1221no—
342C2×C4—1221no—
343C2×C4—4881no—
344C2×C4—2442no—
345C2×C4—2442no—
346C2×C4—2442no—
347C2×C4—2442no—
348C2×C4—2442no—
349C2×C4—2441no—
350C2×C4—2441no—
351C2×C4—2441no—
352C2×C4—2444no—
353C2×C4—2444no—
354C2×C4—2444no—
355C2×C4—2441no—
356C2×C4—2441no—
357C2×C4D4×#692312yes—
358C8—4882no—
359C22—21no—
360C22—21no—
361C22—612no—
362C22—612no—
363C22—1221no—
364C22—1221no—
365C22—1221no—
366C22—1221no—
367C22—4881no—
368C22—4881no—
369C22—4881no—
370C22—4881no—
371C22—4881no—
372C22—4881no—
373C22—4881no—
374C22—2442no—
375C22—2442no—
376C22#1684071011yescharacteristic
377C22#1684075211yescharacteristic
378C22#1684075411yescharacteristic
379C4—22no—
380C4—41no—
381C4—41no—
382C4—81no—
383C4—81no—
384C4—1222no—
385C4—4881no—
386C4—4884no—
387C4—2441no—
388C4—2441no—
389C2—21no—
390C2—21no—
391C2—1222no—
392C2—1222no—
393C2—9761no—
394C2#2146180711yescharacteristic
395C2#2146186611yescharacteristic
396C2#2146186911yescharacteristic
subgroupG/H
centerC22#16840710
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#398C4
socleC22×C61#386
prime radicalC2×#14519752C22
cosocleC22×C4×D61C23
hypercenter#398#6923
hypocenterC61#9206
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #398

Complements

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

NH ≅ G/Ntype
1. #21462296C2semidirect
3. D61⋊#324C2semidirect
4. #21460681C2semidirect
17. #16839693C4semidirect
20. #16839680C4semidirect
21. #16839679C4semidirect
24. C61×#398C4semidirect
209. #398#6923semidirect
223. C61#9206semidirect

Maximal subgroups

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

subgroupindex
#214622962
#214612562
D61⋊#3242
#214606812
#214515622
#920661