Finite Group Databasebeta

← #30604318

Subgroups — #30604318

Order 15616.

494 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 70 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#21461076C211yesmaximal, characteristic, complemented
2#21461056C211yesmaximal, characteristic, complemented
3#21460749C212yesmaximal, complemented
4#21460747C212yesmaximal, complemented
5#21450791C211yesmaximal, characteristic
6#16840733—21no—
7D61⋊(C22⋊C8)—21no—
8#16840607C2212yes—
9#16840607C2212yes—
10#16840606—21no—
11#16840606—21no—
12C2×#14519773C411yescharacteristic
13C2×#14519766C411yescharacteristic
14C2×C4×D244C2211yescharacteristic
15#16839678—21no—
16#16839678—21no—
17#16839669C2211yescharacteristic
18#16839665C2211yescharacteristic
19#16839638—21no—
20#16839638—21no—
21C4×C4⋊Dic61C411yescharacteristic
22C2×#124×C61C411yescharacteristic
23C2×#11758213—41no—
24C2×D61⋊C8—41no—
25#14519834—41no—
26#14519834—41no—
27C22⋊#92420—22no—
28C22⋊#92420—22no—
29C22×D244C2×C411yescharacteristic
30C22×C22⋊D61—21no—
31C22×C22⋊D61—21no—
32C22×C4×D61D411yescharacteristic
33C22×C4×D61D411yescharacteristic
34#14519773—42no—
35#14519766—42no—
36C4×D244—41no—
37C4×D244—41no—
38C2×C4⋊Dic61—21no—
39C2×C4⋊Dic61C2311yescharacteristic
40C2×C22⋊Dic61—21no—
41C2×C22⋊Dic61—21no—
42C2×#11758198—21no—
43C2×#11758198—21no—
44C2×#11758198D411yescharacteristic
45C2×#11758198D411yescharacteristic
46C2×C4×Dic61C2×C411yescharacteristic
47C2×C4×Dic61C2×C411yescharacteristic
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51C22×Q8×C61C2×C411yescharacteristic
52C22×D4×C61C2×C411yescharacteristic
53#124×C61—41no—
54#124×C61—41no—
55C2×C22⋊C4×C61—21no—
56C2×C22⋊C4×C61—21no—
57C2×C42×C61C2×C411yescharacteristic
58C24×C61—21no—
59C23×D61C22⋊C411yescharacteristic
60C23×D61C22⋊C411yescharacteristic
61C2×Q8×C61—22no—
62C2×Q8×C61—41no—
63C2×Q8×C61—41no—
64C2×D4×C61—22no—
65C2×D4×C61—41no—
66C2×D4×C61—41no—
67C22×C4×C61—21no—
68C22×C4×C61C22⋊C411yescharacteristic
69C22×C4×C61C22⋊C411yescharacteristic
70C22×C4×C61C22×C411yescharacteristic
71C2×C22⋊D61—42no—
72C2×C22⋊D61—42no—
73C2×C22⋊D61—42no—
74C2×C22⋊D61—42no—
75C2×C22⋊D61—81no—
76C2×C22⋊D61—81no—
77C22×Dic61—21no—
78C22×Dic61—21no—
79C22×Dic61C2×D411yescharacteristic
80C22×Dic61C2×D411yescharacteristic
81C2×D244—22no—
82C2×D244—22no—
83C2×D244—41no—
84C2×C4×D61—21no—
85C2×C4×D61—21no—
86C2×C4×D61—21no—
87C2×C4×D61—21no—
88C2×C4×D61—81no—
89C2×C4×D61—81no—
90C2×#92420—42no—
91C2×#92420—42no—
92#11758213—82no—
93D61⋊C8—82no—
94C22⋊C4×C61—42no—
95C22⋊C4×C61—41no—
96C22⋊C4×C61—41no—
97C42×C61—21no—
98C42×C61—21no—
99C22⋊Dic61—81no—
100C22⋊Dic61—81no—
101#11758198—41no—
102#11758198—41no—
103#11758198—42no—
104#11758198—42no—
105C4⋊Dic61—41no—
106C4⋊Dic61—42no—
107C4×Dic61—41no—
108C4×Dic61—41no—
109C23×C61—41no—
110C23×C61—41no—
111C23×C61—41no—
112C23×C61—41no—
113C23×C61—41no—
114C23×C61—41no—
115C23×C61—41no—
116C23×C61C2×C22⋊C411yescharacteristic
117C22×D61—21no—
118C22×D61—21no—
119C22×D61—21no—
120C22×D61—21no—
121C22×D61—21no—
122C22×D61—41no—
123C22×D61—41no—
124C22×D61—41no—
125C22×D61—41no—
126C22×D61#10012yes—
127Q8×C61—82no—
128D4×C61—82no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61#9911yescharacteristic
138C2×C4×C61#9911yescharacteristic
139C2×C4×C61#13112yes—
140C22⋊D61—84no—
141C22⋊D61—84no—
142C2×Dic61—22no—
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152D244—44no—
153C4×D61—42no—
154C4×D61—42no—
155C4×D61—81no—
156C4×D61—81no—
157#92420—82no—
158#92420—82no—
159#11566—611nomaximal, Sylow
160C22×C61—21no—
161C22×C61—21no—
162C22×C61—81no—
163C22×C61—81no—
164C22×C61—81no—
165C22×C61—81no—
166C22×C61—81no—
167C22×C61—81no—
168C22×C61—81no—
169C22×C61#40811yescharacteristic
170C22×C61C2×#9911yescharacteristic
171C22×C61C2×#10011yescharacteristic
172C2×D61—22no—
173C2×D61—41no—
174C2×D61—41no—
175C2×D61—42no—
176C2×D61—42no—
177C2×D61—41no—
178C2×D61—41no—
179C2×D61—41no—
180C2×D61—81no—
181C2×D61—81no—
182C4×C61—21no—
183C4×C61—21no—
184C4×C61—22no—
185C4×C61—41no—
186C4×C61—81no—
187Dic61—42no—
188Dic61—41no—
189Dic61—41no—
190Dic61—81no—
191#2544—611no—
192#1465—611no—
193#1459—611no—
194#1319—612no—
195#1318—612no—
196C2×C61—21no—
197C2×C61—21no—
198C2×C61—161no—
199C2×C61#147111yescharacteristic
200C2×C61#212711yescharacteristic
201C2×C61#213211yescharacteristic
202D61—42no—
203D61—81no—
204C2×#127—611no—
205C2×#124—611no—
206C2×#124#692311yescharacteristic
207C2×C4×D4—611no—
208#407—1221no—
209C2×C22⋊C8—1221no—
210#394—1221no—
211#394—1221no—
212#391—611no—
213#390—611no—
214#386—1221no—
215#386—1221no—
216C4×C4⋊C4—611no—
217#324—612no—
218#324—612no—
219#323—1221no—
220#323—1221no—
221C61#1156611yescharacteristic, complemented, Sylow
222C22×Q8C2×#692311yescharacteristic
223C22×D4—611no—
224C22×D4—1221no—
225C22×D4—1221no—
226C22×D4C2×#692311yescharacteristic
227C23×C4—611no—
228C23×C4—611no—
229C2×M16—2441no—
230C22×C8—2441no—
231#127—2442no—
232#124—41no—
233#124—41no—
234#124—2442no—
235C4×D4—2441no—
236C4×D4—2441no—
237C2×C4⋊C4—611no—
238C2×C4⋊C4—1221no—
239C2×C22⋊C4—21no—
240C2×C22⋊C4—21no—
241C2×C22⋊C4—611no—
242C2×C22⋊C4—611no—
243C2×C22⋊C4—1221no—
244C2×C22⋊C4—1221no—
245C2×C22⋊C4—1221no—
246C2×C22⋊C4—1221no—
247C2×C42—611no—
248C2×C42—611no—
249C2×C42C2×#692311yescharacteristic
250C22⋊C8—1222no—
251C22⋊C8—1222no—
252C22⋊C8—2441no—
253C22⋊C8—2441no—
254#95—1221no—
255#95—1221no—
256#95—1221no—
257C24—21no—
258C24—611no—
259C24—611no—
260C2×Q8—22no—
261C2×Q8—41no—
262C2×Q8—41no—
263C2×D4—22no—
264C2×D4—41no—
265C2×D4—41no—
266C2×D4—1222no—
267C2×D4—1222no—
268C2×D4—4881no—
269C2×D4—4881no—
270C2×D4—2441no—
271C2×D4—2442no—
272C2×D4—2442no—
273C2×D4—2442no—
274C2×D4—2442no—
275C22×C4—21no—
276C22×C4—611no—
277C22×C4—611no—
278C22×C4—1221no—
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—4882no—
290C2×C8—4882no—
291C2×C8—2442no—
292C2×C8—2442no—
293C4⋊C4—2441no—
294C4⋊C4—2442no—
295C22⋊C4—42no—
296C22⋊C4—41no—
297C22⋊C4—41no—
298C22⋊C4—4881no—
299C22⋊C4—4881no—
300C22⋊C4—2441no—
301C22⋊C4—2441no—
302C22⋊C4—2442no—
303C22⋊C4—2442no—
304C42—21no—
305C42—21no—
306C42—2441no—
307C42—2441no—
308C23—41no—
309C23—41no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23—41no—
314C23—41no—
315C23—612no—
316C23—1221no—
317C23—1221no—
318C23—1221no—
319C23—1221no—
320C23—1221no—
321C23—2441no—
322C23—2441no—
323C23—2441no—
324C23—2441no—
325C23C2×C22⋊#692311yescharacteristic
326Q8—82no—
327D4—82no—
328D4—4884no—
329D4—4884no—
330D4—2444no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—1222no—
340C2×C4—1221no—
341C2×C4—1221no—
342C2×C4—4881no—
343C2×C4—4881no—
344C2×C4—2442no—
345C2×C4—2442no—
346C2×C4—2441no—
347C2×C4—2441no—
348C2×C4—2441no—
349C2×C4—2441no—
350C2×C4—2441no—
351C2×C4—2441no—
352C2×C4—2441no—
353C2×C4#1451983511yescharacteristic
354C2×C4#1451983511yescharacteristic
355C2×C4#1451986412yes—
356C8—4882no—
357C8—4882no—
358C22—21no—
359C22—21no—
360C22—81no—
361C22—81no—
362C22—81no—
363C22—81no—
364C22—81no—
365C22—81no—
366C22—81no—
367C22—1222no—
368C22—4881no—
369C22—4881no—
370C22—2442no—
371C22—2442no—
372C22—2441no—
373C22—2441no—
374C22—2441no—
375C22—2441no—
376C22—2441no—
377C22#1684073611yescharacteristic
378C22C2×#1451983511yescharacteristic
379C22D61⋊#10011yescharacteristic
380C4—21no—
381C4—21no—
382C4—22no—
383C4—41no—
384C4—81no—
385C4—4881no—
386C4—2442no—
387C4—2441no—
388C4—2441no—
389C2—21no—
390C2—21no—
391C2—161no—
392C2—4881no—
393C2—2442no—
394C2#2146109411yescharacteristic
395C2#2146209411yescharacteristic
396C2#2146211011yescharacteristic
subgroupG/H
centerC22C2×#14519835
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×#124×C61C4
socleC22×C61C2×#99
prime radicalC2×#14519773C4
cosocleC2×C4⋊Dic61C23
hypercenterC2×#124#6923
hypocenterC61#11566
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. #21461076C2semidirect
2. #21461056C2semidirect
3. #21460749C2semidirect
4. #21460747C2semidirect
221. C61#11566semidirect

Maximal subgroups

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

subgroupindex
#214610762
#214610562
#214607492
#214607472
#214507912
#1156661