Finite Group Databasebeta

← #30604759

Subgroups — #30604759

Order 15616.

514 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 80 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#21461522C211yesmaximal, characteristic, complemented
2D61⋊#324C211yesmaximal, characteristic, complemented
3#21460803C212yesmaximal, complemented
4#21460802C212yesmaximal, complemented
5#21451562C211yesmaximal, characteristic
6C2×D61⋊M16—21no—
7D61⋊(C22⋊C8)—21no—
8#16840642—21no—
9#16840642C2212yes—
10#16840608C2212yes—
11#16840607—21no—
12C2×#14519762—21no—
13C2×#14519752C411yescharacteristic
14C2×C4⋊C4×D61C2211yescharacteristic
15#16839693C2211yescharacteristic
16#16839686—21no—
17#16839684—21no—
18#16839680C2211yescharacteristic
19#16839679C411yescharacteristic
20#16839640—21no—
21#16839621C411yescharacteristic
22C61×#398C411yescharacteristic
23C2×#11758213—41no—
24D61⋊M16—24no—
25D61⋊M16—42no—
26C2×#11758217—22no—
27C2×D61⋊C8—41no—
28C2×D61⋊C8—41no—
29#14519834—41no—
30C22⋊#92420—22no—
31C22×D244—21no—
32C22×D244C2×C411yescharacteristic
33C22×C4×D61C2×C411yescharacteristic
34C22×C4×D61D411yescharacteristic
35C22×C4×D61D411yescharacteristic
36#14519762—42no—
37#14519762—42no—
38#14519752—41no—
39#14519752—41no—
40C2×C4⋊Dic61D411yescharacteristic
41C2×#11758196—21no—
42C2×#11758196—21no—
43C2×#11758196D411yescharacteristic
44C2×#11758196C2311yescharacteristic
45C4⋊C4×D61—41no—
46C4⋊C4×D61—41no—
47C2×#11758198—21no—
48C2×#11758198—21no—
49C2×#11758198—21no—
50C2×#11758198—21no—
51C2×#11758198—21no—
52C2×#11758198—21no—
53#14519684—21no—
54#14519684C2×C411yescharacteristic
55C2×C4⋊C4×C61—21no—
56C2×C4⋊C4×C61C2×C411yescharacteristic
57C2×C4⋊C4×C61C2×C411yescharacteristic
58#95×C61—21no—
59#95×C61C2×C411yescharacteristic
60C23×D61—21no—
61C23×D61C22⋊C411yescharacteristic
62C22×C4×C61—21no—
63C22×C4×C61—21no—
64C22×C4×C61C22⋊C411yescharacteristic
65C22×C4×C61C22⋊C411yescharacteristic
66C22×C4×C61C22×C411yescharacteristic
67C22×Dic61—21no—
68C22×Dic61C22⋊C411yescharacteristic
69C22×Dic61C2×D411yescharacteristic
70C22×Dic61C2×D411yescharacteristic
71C2×D244—41no—
72C2×D244—41no—
73C2×D244—41no—
74C2×D244—42no—
75C2×D244—42no—
76C2×D244—81no—
77C2×C4×D61—21no—
78C2×C4×D61—21no—
79C2×C4×D61—22no—
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×D61D812yes—
87C2×C4×D61SD1612yes—
88#11758217—24no—
89#11758217—42no—
90C2×#92420—42no—
91C2×#92420—42no—
92#11758213—44no—
93D61⋊C8—44no—
94D61⋊C8—82no—
95C4⋊C4×C61—41no—
96C4⋊C4×C61—41no—
97C4⋊C4×C61—42no—
98#11758198—42no—
99#11758198—42no—
100#11758198—42no—
101#11758198—41no—
102#11758198—41no—
103#11758198—81no—
104#11758198—81no—
105C4⋊Dic61—41no—
106#11758196—41no—
107#11758196—41no—
108#11758196—41no—
109#11758196—41no—
110#11758196—81no—
111C23×C61C2×C22⋊C411yescharacteristic
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—41no—
121C22×D61#9911yescharacteristic
122C22×D61#9911yescharacteristic
123C22×D61#10212yes—
124C22×D61#10412yes—
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×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61#10212yes—
138C2×Dic61—21no—
139C2×Dic61—21no—
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61C2×D811yescharacteristic
148C2×Dic61C2×SD1611yescharacteristic
149D244—82no—
150D244—82no—
151D244—82no—
152C4×D61—22no—
153C4×D61—22no—
154C4×D61—22no—
155C4×D61—22no—
156C4×D61—42no—
157C4×D61—81no—
158C4×D61—81no—
159C4×D61—81no—
160#92420—44no—
161#92420—82no—
162#11698—611nomaximal, Sylow
163C22×C61—21no—
164C22×C61—21no—
165C22×C61C2×#9911yescharacteristic
166C22×C61C2×#10211yescharacteristic
167C22×C61C2×#10411yescharacteristic
168C2×D61—21no—
169C2×D61—21no—
170C2×D61—21no—
171C2×D61—21no—
172C2×D61—42no—
173C2×D61—42no—
174C2×D61—81no—
175C2×D61—81no—
176C2×D61—81no—
177C2×D61—81no—
178C2×D61—81no—
179C2×D61—81no—
180C2×D61—81no—
181C2×D61#32712yes—
182C2×D61#32712yes—
183C4×C61—22no—
184C4×C61—41no—
185C4×C61—41no—
186C4×C61—81no—
187C4×C61—81no—
188Dic61—21no—
189Dic61—21no—
190Dic61—41no—
191Dic61—41no—
192Dic61—81no—
193#2618—611no—
194C2×#343—611no—
195C2×#324—611no—
196#1346—612no—
197#1345—612no—
198C2×C61—21no—
199C2×C61—21no—
200C2×C61C2×#32711yescharacteristic
201C2×C61#212111yescharacteristic
202C2×C61#213311yescharacteristic
203D61—22no—
204D61—22no—
205D61—161no—
206C22×M16—1221no—
207C2×#123—1221no—
208C2×#121—611no—
209C22×C4⋊C4—611no—
210C2×C22⋊C8—1221no—
211#398—611no—
212#398#692311yescharacteristic
213#396—1221no—
214#396—1221no—
215#394—611no—
216#394—611no—
217#386—1221no—
218#380—611no—
219#343—612no—
220#343—1221no—
221#324—612no—
222#324—1221no—
223C61#1169811yescharacteristic, complemented, Sylow
224C22×D4—611no—
225C22×D4—1221no—
226C23×C4—611no—
227C23×C4—611no—
228C23×C4—611no—
229C2×M16—1222no—
230C2×M16—1224no—
231C2×M16—2442no—
232C2×M16—2441no—
233C22×C8—2441no—
234C22×C8—2441no—
235#123—2442no—
236#123—2442no—
237#121—2441no—
238#121—2441no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—611no—
241C2×C4⋊C4—611no—
242C2×C4⋊C4—611no—
243C2×C4⋊C4—1221no—
244C2×C4⋊C4—1221no—
245C2×C4⋊C4—2441no—
246C2×C4⋊C4—2441no—
247C2×C4⋊C4C2×#692311yescharacteristic
248C2×C4⋊C4C2×#692311yescharacteristic
249C2×C22⋊C4—1221no—
250C2×C22⋊C4—1221no—
251C2×C22⋊C4—1221no—
252C2×C22⋊C4—1221no—
253C2×C22⋊C4—1221no—
254C2×C22⋊C4—1221no—
255C22⋊C8—1222no—
256C22⋊C8—2441no—
257#95—21no—
258#95—611no—
259#95—1221no—
260#95C2×#692311yescharacteristic
261C24—611no—
262C24—1221no—
263C2×D4—4881no—
264C2×D4—2441no—
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—1222no—
279C22×C4—1221no—
280C22×C4—1221no—
281C22×C4—1221no—
282C22×C4—1221no—
283C22×C4—1221no—
284C22×C4—4881no—
285C22×C4—4881no—
286C22×C4C22⋊#692311yescharacteristic
287C22×C4C22⋊#692311yescharacteristic
288C22×C4C22×#692311yescharacteristic
289M16—1224no—
290M16—2442no—
291M16—2444no—
292C2×C8—4882no—
293C2×C8—2442no—
294C2×C8—2444no—
295C2×C8—2442no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—42no—
299C4⋊C4—4881no—
300C4⋊C4—2441no—
301C4⋊C4—2441no—
302C4⋊C4—2441no—
303C4⋊C4—2441no—
304C4⋊C4—2441no—
305C22⋊C4—4881no—
306C22⋊C4—4881no—
307C22⋊C4—2441no—
308C22⋊C4—2441no—
309C22⋊C4—2442no—
310C22⋊C4—2442no—
311C22⋊C4—2442no—
312C23—611no—
313C23—611no—
314C23—612no—
315C23—612no—
316C23—2441no—
317C23—2441no—
318C23—2441no—
319C23—2441no—
320C23—2441no—
321C23—2441no—
322C23—2441no—
323C23—2441no—
324C23—2441no—
325C23C2×C22⋊#692311yescharacteristic
326D4—4882no—
327D4—4882no—
328D4—4882no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—611no—
342C2×C4—611no—
343C2×C4—1222no—
344C2×C4—1222no—
345C2×C4—1222no—
346C2×C4—1222no—
347C2×C4—1221no—
348C2×C4—1221no—
349C2×C4—1221no—
350C2×C4—1221no—
351C2×C4—4881no—
352C2×C4—4881no—
353C2×C4—4881no—
354C2×C4—2442no—
355C2×C4—2441no—
356C2×C4—2441no—
357C2×C4—2441no—
358C2×C4—2441no—
359C2×C4—2441no—
360C2×C4#1451983912yes—
361C8—4882no—
362C8—2444no—
363C22—21no—
364C22—21no—
365C22—612no—
366C22—612no—
367C22—1221no—
368C22—1221no—
369C22—1221no—
370C22—1221no—
371C22—4881no—
372C22—4881no—
373C22—4881no—
374C22—4881no—
375C22—4881no—
376C22—4881no—
377C22—4881no—
378C22—2442no—
379C22—2442no—
380C22D61⋊#9911yescharacteristic
381C22C2×#1451983911yescharacteristic
382C22D61⋊#10411yescharacteristic
383C4—22no—
384C4—41no—
385C4—41no—
386C4—81no—
387C4—81no—
388C4—1221no—
389C4—1221no—
390C4—4881no—
391C4—2441no—
392C4—2441no—
393C2—21no—
394C2—21no—
395C2—1222no—
396C2—1222no—
397C2—9761no—
398C2D61⋊#32711yescharacteristic
399C2#2146207711yescharacteristic
400C2#2146211711yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#398C4
socleC22×C61C2×#99
prime radicalC2×#14519752C4
cosocleC2×#11758196C23
hypercenter#398#6923
hypocenterC61#11698
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #398

Complements

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

NH ≅ G/Ntype
1. #21461522C2semidirect
2. D61⋊#324C2semidirect
3. #21460803C2semidirect
4. #21460802C2semidirect
223. C61#11698semidirect

Maximal subgroups

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

subgroupindex
#214615222
D61⋊#3242
#214608032
#214608022
#214515622
#1169861