Finite Group Databasebeta

← #30605294

Subgroups — #30605294

Order 15616.

572 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 572 conjugacy classes of subgroups — too many to draw. Only its 66 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#21461719C211yesmaximal, characteristic, complemented
2D61⋊#324C211yesmaximal, characteristic, complemented
3#21460819C212yesmaximal, complemented
4#21460801C212yesmaximal, complemented
5#21449149C211yesmaximal, characteristic
6#16840734—21no—
7D61⋊(C22⋊C8)—21no—
8#16840642—21no—
9#16840642C2212yes—
10#16840608C2212yes—
11#16840607—21no—
12C22×#11758224C411yescharacteristic
13C2×#14519759—21no—
14C2×C4⋊C4×D61C2211yescharacteristic
15#16839683C2211yescharacteristic
16#16839682C411yescharacteristic
17#16839676C2211yescharacteristic
18#16839638—21no—
19#16839637—21no—
20#16839634—21no—
21#16839624C411yescharacteristic
22C61×#394C411yescharacteristic
23C2×#11758217—22no—
24C2×D61⋊C8—41no—
25#14519834—41no—
26#14519834—41no—
27#14519834—41no—
28C22⋊#92420—22no—
29C2×#11758224—41no—
30C2×#11758224—41no—
31C2×#11758224—44no—
32C22×Dic122C2×C411yescharacteristic
33C22×C22⋊D61—21no—
34C23×Dic61—21no—
35C22×C4×D61C2×C411yescharacteristic
36C22×C4×D61D411yescharacteristic
37C22×C4×D61D411yescharacteristic
38#14519759—44no—
39C2×C4⋊Dic61—21no—
40C2×C4⋊Dic61D411yescharacteristic
41C2×#11758196—21no—
42C2×#11758196D411yescharacteristic
43C2×#11758196C2311yescharacteristic
44C4⋊C4×D61—41no—
45C4⋊C4×D61—41no—
46C2×C22⋊Dic61—21no—
47C2×C22⋊Dic61—21no—
48C2×#11758198—21no—
49#14519684—21no—
50#14519684—21no—
51#14519684—21no—
52#14519684C2×C411yescharacteristic
53C22×D4×C61C2×C411yescharacteristic
54C2×C4⋊C4×C61C2×C411yescharacteristic
55C2×C22⋊C4×C61—21no—
56C2×C22⋊C4×C61—21no—
57#95×C61C2×C411yescharacteristic
58C24×C61—21no—
59C23×D61C22⋊C411yescharacteristic
60C2×D4×C61—41no—
61C2×D4×C61—42no—
62C22×C4×C61—21no—
63C22×C4×C61C22⋊C411yescharacteristic
64C22×C4×C61C22⋊C411yescharacteristic
65C22×C4×C61C22×C411yescharacteristic
66C2×C22⋊D61—24no—
67C2×C22⋊D61—42no—
68C2×C22⋊D61—41no—
69C2×C22⋊D61—41no—
70C22×Dic61—21no—
71C22×Dic61—21no—
72C22×Dic61—42no—
73C22×Dic61—42no—
74C22×Dic61—42no—
75C22×Dic61C22⋊C411yescharacteristic
76C22×Dic61C2×D411yescharacteristic
77C22×Dic61C2×D411yescharacteristic
78#11758224—44no—
79#11758224—44no—
80#11758224—44no—
81#11758224—44no—
82C2×C4×D61—21no—
83C2×C4×D61—21no—
84C2×C4×D61—21no—
85C2×C4×D61—21no—
86C2×C4×D61—21no—
87C2×C4×D61—22no—
88C2×C4×D61—21no—
89C2×C4×D61—41no—
90C2×C4×D61—42no—
91C2×C4×D61—42no—
92C2×Dic122—41no—
93C2×Dic122—42no—
94#11758217—42no—
95#11758217—42no—
96C2×#92420—42no—
97C2×#92420—42no—
98D61⋊C8—82no—
99C4⋊C4×C61—41no—
100C22⋊C4×C61—42no—
101C22⋊C4×C61—42no—
102C22⋊Dic61—42no—
103C22⋊Dic61—42no—
104#11758198—42no—
105C4⋊Dic61—41no—
106C4⋊Dic61—42no—
107#11758196—41no—
108#11758196—41no—
109#11758196—42no—
110C23×C61—22no—
111C23×C61—41no—
112C23×C61—41no—
113C23×C61—41no—
114C23×C61—41no—
115C23×C61—41no—
116C23×C61—41no—
117C23×C61C2×C22⋊C411yescharacteristic
118C22×D61—21no—
119C22×D61—21no—
120C22×D61—22no—
121C22×D61—41no—
122C22×D61#9911yescharacteristic
123C22×D61#9911yescharacteristic
124D4×C61—42no—
125D4×C61—42no—
126C2×C4×C61—21no—
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—
136C22⋊D61—44no—
137C22⋊D61—44no—
138C2×Dic61—21no—
139C2×Dic61—21no—
140C2×Dic61—22no—
141C2×Dic61—21no—
142C2×Dic61—21no—
143C2×Dic61—41no—
144C2×Dic61—48no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61#13512yes—
152C4×D61—42no—
153C4×D61—42no—
154C4×D61—42no—
155C4×D61—42no—
156C4×D61—42no—
157C4×D61—81no—
158Dic122—42no—
159Dic122—42no—
160#92420—82no—
161#92420—82no—
162#11848—611nomaximal, Sylow
163C22×C61—21no—
164C22×C61—21no—
165C22×C61—42no—
166C22×C61—42no—
167C22×C61—42no—
168C22×C61—81no—
169C22×C61—81no—
170C22×C61—81no—
171C22×C61—81no—
172C22×C61C2×#9911yescharacteristic
173C22×C61#41611yescharacteristic
174C22×C61#42111yescharacteristic
175C2×D61—21no—
176C2×D61—21no—
177C2×D61—21no—
178C2×D61—21no—
179C2×D61—21no—
180C2×D61—42no—
181C2×D61—42no—
182C2×D61AΣL(1,𝔽16)12yes—
183C4×C61—41no—
184C4×C61—41no—
185C4×C61—41no—
186C4×C61—81no—
187Dic61—22no—
188Dic61—41no—
189Dic61—42no—
190Dic61—41no—
191Dic61—81no—
192#2406—611no—
193#1821—611no—
194C2×#324—611no—
195#1354—612no—
196#1345—612no—
197C2×C61—21no—
198C2×C61—21no—
199C2×C61—82no—
200C2×C61#151611yescharacteristic
201C2×C61C2×AΣL(1,𝔽16)11yescharacteristic
202C2×C61#213311yescharacteristic
203D61—22no—
204D61—41no—
205C22×#41—611no—
206C2×#123—1221no—
207C22×C4⋊C4—611no—
208#407—1221no—
209C2×C22⋊C8—1221no—
210#395—611no—
211#395—611no—
212#394—611no—
213#394#692311yescharacteristic
214#386—1221no—
215#385—1221no—
216#385—1221no—
217#381—611no—
218#343—612no—
219#343—1221no—
220#324—612no—
221#324—1221no—
222C61#1184811yescharacteristic, complemented, Sylow
223C2×#41—2441no—
224C2×#41—2441no—
225C2×#41—2444no—
226C22×Q8—611no—
227C22×D4—1221no—
228C22×D4C2×#692311yescharacteristic
229C23×C4—611no—
230C23×C4—611no—
231C23×C4—611no—
232C23×C4—1221no—
233C2×M16—1222no—
234C22×C8—2441no—
235#123—2444no—
236C2×C4⋊C4—611no—
237C2×C4⋊C4—611no—
238C2×C4⋊C4—611no—
239C2×C4⋊C4—1221no—
240C2×C4⋊C4—1221no—
241C2×C4⋊C4—2441no—
242C2×C4⋊C4—2441no—
243C2×C4⋊C4C2×#692311yescharacteristic
244C2×C22⋊C4—21no—
245C2×C22⋊C4—21no—
246C2×C22⋊C4—1221no—
247C2×C22⋊C4—1221no—
248C2×C22⋊C4—1221no—
249C22⋊C8—1222no—
250C22⋊C8—2441no—
251C22⋊C8—2441no—
252C22⋊C8—2441no—
253#95—611no—
254#95—1221no—
255#95—1221no—
256#95—1221no—
257#95C2×#692311yescharacteristic
258C24—21no—
259C24—611no—
260#41—2444no—
261#41—2444no—
262#41—2444no—
263#41—2444no—
264C2×Q8—2441no—
265C2×Q8—2442no—
266C2×D4—41no—
267C2×D4—42no—
268C2×D4—1224no—
269C2×D4—2441no—
270C2×D4—2441no—
271C2×D4—2442no—
272C22×C4—21no—
273C22×C4—611no—
274C22×C4—611no—
275C22×C4—611no—
276C22×C4—1222no—
277C22×C4—1221no—
278C22×C4—1221no—
279C22×C4—1221no—
280C22×C4—1221no—
281C22×C4—1221no—
282C22×C4—1221no—
283C22×C4—1221no—
284C22×C4—1221no—
285C22×C4—2441no—
286C22×C4—2442no—
287C22×C4—2442no—
288C22×C4—2442no—
289C22×C4—2442no—
290C22×C4—2442no—
291C22×C4C22⋊#692311yescharacteristic
292C22×C4C22⋊#692311yescharacteristic
293C22×C4C22×#692311yescharacteristic
294M16—2442no—
295M16—2442no—
296C2×C8—4882no—
297C2×C8—2442no—
298C2×C8—2442no—
299C4⋊C4—41no—
300C4⋊C4—2441no—
301C4⋊C4—2441no—
302C4⋊C4—2441no—
303C4⋊C4—2442no—
304C4⋊C4—2442no—
305C22⋊C4—42no—
306C22⋊C4—42no—
307C22⋊C4—2442no—
308C22⋊C4—2442no—
309C22⋊C4—2442no—
310C23—22no—
311C23—41no—
312C23—41no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23—611no—
318C23—611no—
319C23—1222no—
320C23—1221no—
321C23—1221no—
322C23—2441no—
323C23C2×C22⋊#692311yescharacteristic
324Q8—2442no—
325Q8—2442no—
326D4—42no—
327D4—42no—
328D4—2444no—
329D4—2444no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—612no—
341C2×C4—1221no—
342C2×C4—1221no—
343C2×C4—1222no—
344C2×C4—1221no—
345C2×C4—1221no—
346C2×C4—4881no—
347C2×C4—2442no—
348C2×C4—2442no—
349C2×C4—2442no—
350C2×C4—2442no—
351C2×C4—2442no—
352C2×C4—2441no—
353C2×C4—2441no—
354C2×C4—2441no—
355C2×C4—2441no—
356C2×C4—2448no—
357C2×C4—2441no—
358C2×C4—2441no—
359C2×C4—2441no—
360C8—4882no—
361C8—4882no—
362C22—21no—
363C22—21no—
364C22—42no—
365C22—42no—
366C22—42no—
367C22—81no—
368C22—81no—
369C22—81no—
370C22—81no—
371C22—612no—
372C22—1221no—
373C22—1221no—
374C22—1221no—
375C22—1221no—
376C22—1221no—
377C22—2442no—
378C22—2442no—
379C22D61⋊#9911yescharacteristic
380C22#1684075211yescharacteristic
381C22#1684076011yescharacteristic
382C4—41no—
383C4—41no—
384C4—41no—
385C4—81no—
386C4—1222no—
387C4—4881no—
388C4—2441no—
389C4—2441no—
390C4—2442no—
391C2—21no—
392C2—21no—
393C2—82no—
394C2—1222no—
395C2—2441no—
396C2#2146124411yescharacteristic
397C2D61⋊AΣL(1,𝔽16)11yescharacteristic
398C2#2146211511yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#394C4
socleC22×C61C2×#99
prime radicalC22×#11758224C4
cosocleC2×#11758196C23
hypercenter#394#6923
hypocenterC61#11848
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #394

Complements

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

NH ≅ G/Ntype
1. #21461719C2semidirect
2. D61⋊#324C2semidirect
3. #21460819C2semidirect
4. #21460801C2semidirect
222. C61#11848semidirect

Maximal subgroups

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

subgroupindex
#214617192
D61⋊#3242
#214608192
#214608012
#214491492
#1184861