Finite Group Databasebeta

← #30610348

Subgroups — #30610348

Order 15616.

996 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462680C212yesmaximal
2#21461097C214yesmaximal, complemented
3#21461092C212yesmaximal, complemented
4#21461081C211yesmaximal, characteristic, complemented
5#21461068C212yesmaximal, complemented
6#21461061C211yesmaximal, characteristic, complemented
7D61⋊#324C212yesmaximal, complemented
8C2×#16840468C211yesmaximal, characteristic
9#16840796—22no—
10#16840792—24no—
11#16840790—22no—
12#16840783C2212yes—
13#16840779C2212yes—
14#16840733C2214yes—
15D61⋊(C22⋊C8)C2214yes—
16#16840608C2211yescharacteristic
17#16840608C2212yes—
18#16840608C2211yescharacteristic
19#16840607C2214yes—
20#16840607C2212yes—
21#16840607C2214yes—
22#16840607C2212yes—
23#16840468—22no—
24#16840468—24no—
25#16840468—22no—
26C2×#14519776C411yescharacteristic
27C2×#14519768C2211yescharacteristic
28C2×#14519757C2212yes—
29C2×#14519755C412yes—
30C2×#14519755C412yes—
31C2×C4×Dic122C2211yescharacteristic
32C2×C4×D244C411yescharacteristic
33C2×#14519739C411yescharacteristic
34C2×#14519739C2211yescharacteristic
35C2×C4⋊C4×D61C2212yes—
36C2×#125×C61C411yescharacteristic
37C2×#11758213—24no—
38C2×D61⋊C8—24no—
39#14519844—22no—
40C4⋊#92420—22no—
41#14519834—24no—
42#14519834—24no—
43C22⋊#92420C2312yes—
44C22⋊#92420C2314yes—
45C22⋊#92420C2312yes—
46#14519832—22no—
47C4×#92420—22no—
48C22×Dic122C2×C411yescharacteristic
49C22×Dic122C2×C412yes—
50C22×D244C2×C411yescharacteristic
51C22×C4×D61C2×C412yes—
52C22×C4×D61C2×C412yes—
53C22×C4×D61C2312yes—
54#14519776—22no—
55#14519776—22no—
56#14519768—22no—
57#14519768—22no—
58#14519757—24no—
59#14519757—24no—
60#14519755—24no—
61#14519755—24no—
62#14519755—24no—
63#14519755—24no—
64C4×Dic122—22no—
65C4×Dic122—22no—
66C4×D244—22no—
67C4×D244—21no—
68C4×D244—21no—
69#14519739—22no—
70#14519739—21no—
71#14519739—21no—
72#14519739D412yes—
73#14519739D414yes—
74#14519739D412yes—
75C2×C4⋊Dic61C2×C411yescharacteristic
76C2×C4⋊Dic61C2312yes—
77C2×C4⋊Dic61C2311yescharacteristic
78C2×#11758196C2×C412yes—
79C2×#11758196C2×C411yescharacteristic
80C2×#11758196C2×C412yes—
81C2×#11758196C2311yescharacteristic
82C4⋊C4×D61—24no—
83C4⋊C4×D61—24no—
84C2×#11758198C2×C412yes—
85C2×#11758198C2×C412yes—
86C2×#11758198C2×C412yes—
87C2×C4×Dic61C2×C411yescharacteristic
88C2×C4×Dic61C2311yescharacteristic
89#125×C61—22no—
90#125×C61—22no—
91C2×C4⋊C4×C61C2×C412yes—
92C2×C4⋊C4×C61C2×C411yescharacteristic
93C2×C4⋊C4×C61C2×C412yes—
94C2×C4⋊C4×C61C2×C411yescharacteristic
95C2×C42×C61C2×C411yescharacteristic
96C23×D61C22×C412yes—
97C22×C4×C61C22×C412yes—
98C22×C4×C61C22×C411yescharacteristic
99C22×C4×C61C22×C411yescharacteristic
100C22×C4×C61C22×C411yescharacteristic
101C22×C4×C61C22×C412yes—
102C22×Dic61C22×C411yescharacteristic
103C22×Dic61C22×C411yescharacteristic
104C22×Dic61C22×C412yes—
105C22×Dic61C22×C411yescharacteristic
106C22×Dic61C2411yescharacteristic
107C2×D244—24no—
108C2×D244C22⋊C412yes—
109C2×D244C22⋊C411yescharacteristic
110C2×D244C22⋊C411yescharacteristic
111C2×C4×D61—22no—
112C2×C4×D61—22no—
113C2×C4×D61—24no—
114C2×C4×D61—22no—
115C2×C4×D61—22no—
116C2×C4×D61—42no—
117C2×C4×D61—82no—
118C2×C4×D61—82no—
119C2×C4×D61C2×D414yes—
120C2×C4×D61C2×D414yes—
121C2×Dic122—22no—
122C2×Dic122—22no—
123C2×Dic122—24no—
124C2×Dic122—41no—
125C2×Dic122—82no—
126C2×#92420—22no—
127C2×#92420—22no—
128C2×#92420—24no—
129#11758213—84no—
130D61⋊C8—84no—
131C4⋊C4×C61—24no—
132C4⋊C4×C61—21no—
133C4⋊C4×C61—21no—
134C4⋊C4×C61—24no—
135C4⋊C4×C61C22⋊C412yes—
136C4⋊C4×C61C22⋊C412yes—
137C42×C61—21no—
138C42×C61—21no—
139#11758198—22no—
140#11758198—22no—
141#11758198—22no—
142#11758198—22no—
143#11758198C22⋊C414yes—
144#11758198C22⋊C414yes—
145C4⋊Dic61—21no—
146C4⋊Dic61—21no—
147C4⋊Dic61—24no—
148C4⋊Dic61—22no—
149#11758196—24no—
150#11758196—22no—
151#11758196—24no—
152#11758196—22no—
153C4×Dic61—21no—
154C4×Dic61—21no—
155C4×Dic61C2×D412yes—
156C4×Dic61C2×D412yes—
157C23×C61C23×C411yescharacteristic
158C22×D61—22no—
159C22×D61—22no—
160C22×D61—24no—
161C22×D61—42no—
162C22×D61C2×C22⋊C412yes—
163C22×D61C2×C22⋊C412yes—
164C2×C4×C61—22no—
165C2×C4×C61—21no—
166C2×C4×C61—22no—
167C2×C4×C61—21no—
168C2×C4×C61—21no—
169C2×C4×C61—22no—
170C2×C4×C61—21no—
171C2×C4×C61—22no—
172C2×C4×C61—42no—
173C2×C4×C61—41no—
174C2×C4×C61C2×C22⋊C411yescharacteristic
175C2×C4×C61C2×C22⋊C414yes—
176C2×C4×C61C2×C22⋊C411yescharacteristic
177C2×Dic61—21no—
178C2×Dic61—21no—
179C2×Dic61—21no—
180C2×Dic61—21no—
181C2×Dic61—21no—
182C2×Dic61—22no—
183C2×Dic61—41no—
184C2×Dic61—41no—
185C2×Dic61—42no—
186C2×Dic61C2×C22⋊C412yes—
187C2×Dic61#13112yes—
188C2×Dic61C22×D412yes—
189D244—24no—
190D244—22no—
191D244#10114yes—
192C4×D61—44no—
193C4×D61—44no—
194C4×D61—44no—
195C4×D61—44no—
196C4×D61—82no—
197C4×D61—82no—
198Dic122—44no—
199Dic122—84no—
200#92420—42no—
201#92420—44no—
202#92420—42no—
203#17426—611nomaximal, Sylow
204C22×C61—21no—
205C22×C61—21no—
206C22×C61C22×C22⋊C411yescharacteristic
207C22×C61C2×#13111yescharacteristic
208C22×C61#56811yescharacteristic
209C2×D61—22no—
210C2×D61—22no—
211C2×D61—22no—
212C2×D61—22no—
213C2×D61—22no—
214C2×D61—44no—
215C2×D61—44no—
216C2×D61C2×#10114yes—
217C4×C61—24no—
218C4×C61—21no—
219C4×C61—41no—
220C4×C61—42no—
221C4×C61—41no—
222C4×C61C2×#10112yes—
223Dic61—22no—
224Dic61—22no—
225Dic61—22no—
226Dic61—41no—
227Dic61—42no—
228C2×#554—611no—
229#2974—612no—
230#1472—614no—
231#1470—612no—
232#1467—611no—
233#1463—612no—
234#1461—611no—
235C2×#324—612no—
236C2×C61—21no—
237C2×C61—21no—
238C2×C61#288011yescharacteristic
239C2×C61#288311yescharacteristic
240C2×C61C22×#10111yescharacteristic
241D61—24no—
242D61—42no—
243#554—1222no—
244#554—1224no—
245#554—1222no—
246C2×C4⋊Q8—611no—
247C2×#125—611no—
248C2×#125#692311yescharacteristic
249C2×C22⋊Q8—612no—
250C2×C22⋊Q8—612no—
251C2×C22⋊Q8—612no—
252C2×C4×Q8—611no—
253C2×C4×D4—611no—
254C2×C4×D4—611no—
255C2×C4×D4—611no—
256C22×C4⋊C4—612no—
257#436—1222no—
258#435—1224no—
259C8×D4—1222no—
260#432—612no—
261#431—612no—
262#407—614no—
263C2×C22⋊C8—614no—
264#324—614no—
265#324—612no—
266#324—614no—
267#324—612no—
268#324—611no—
269#324—612no—
270#324—611no—
271C61#1742611yescharacteristic, complemented, Sylow
272C22×Q8—611no—
273C22×Q8—612no—
274C22×D4—611no—
275C23×C4—612no—
276C23×C4—612no—
277C23×C4—612no—
278C2×M16—1224no—
279C22×C8—1224no—
280C4⋊Q8—1222no—
281C4⋊Q8—1222no—
282#125—22no—
283#125—22no—
284#125—1222no—
285#125—1222no—
286C22⋊Q8—1224no—
287C22⋊Q8—1224no—
288C22⋊Q8—1224no—
289C22⋊Q8—1224no—
290C22⋊Q8—1224no—
291C22⋊Q8—1224no—
292C4×Q8—1222no—
293C4×Q8—1222no—
294C4×D4—612no—
295C4×D4—614no—
296C4×D4—612no—
297C4×D4—1221no—
298C4×D4—1222no—
299C4×D4—1221no—
300C4×D4—1221no—
301C4×D4—1222no—
302C4×D4—1221no—
303C2×C4⋊C4—611no—
304C2×C4⋊C4—612no—
305C2×C4⋊C4—612no—
306C2×C4⋊C4—611no—
307C2×C4⋊C4—611no—
308C2×C4⋊C4—611no—
309C2×C4⋊C4—612no—
310C2×C4⋊C4—1224no—
311C2×C4⋊C4—1224no—
312C2×C4⋊C4C2×#692312yes—
313C2×C4⋊C4C2×#692311yescharacteristic
314C2×C4⋊C4C2×#692312yes—
315C2×C4⋊C4C2×#692311yescharacteristic
316C2×C22⋊C4—612no—
317C2×C22⋊C4—612no—
318C2×C22⋊C4—612no—
319C2×C42—611no—
320C2×C42—611no—
321C2×C42C2×#692311yescharacteristic
322C4⋊C8—1222no—
323C4⋊C8—1222no—
324C22⋊C8—612no—
325C22⋊C8—614no—
326C22⋊C8—612no—
327C22⋊C8—1224no—
328C22⋊C8—1224no—
329#97—1222no—
330C4×C8—1222no—
331C24—612no—
332C2×Q8—1222no—
333C2×Q8—1222no—
334C2×Q8—1224no—
335C2×Q8—4882no—
336C2×Q8—2441no—
337C2×D4—611no—
338C2×D4—612no—
339C2×D4—611no—
340C2×D4—1224no—
341C22×C4—611no—
342C22×C4—611no—
343C22×C4—611no—
344C22×C4—614no—
345C22×C4—614no—
346C22×C4—611no—
347C22×C4—612no—
348C22×C4—1224no—
349C22×C4—1222no—
350C22×C4—1222no—
351C22×C4—1222no—
352C22×C4—1222no—
353C22×C4—4882no—
354C22×C4—4882no—
355C22×C4—2442no—
356C22×C4C22×#692311yescharacteristic
357C22×C4C22×#692312yes—
358C22×C4C22×#692311yescharacteristic
359C22×C4C22×#692311yescharacteristic
360C22×C4C22×#692312yes—
361M16—4884no—
362C2×C8—1222no—
363C2×C8—1222no—
364C2×C8—1224no—
365C2×C8—4884no—
366C4⋊C4—24no—
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—24no—
370C4⋊C4—1222no—
371C4⋊C4—1224no—
372C4⋊C4—1222no—
373C4⋊C4—1224no—
374C4⋊C4—1222no—
375C4⋊C4—1224no—
376C4⋊C4—1221no—
377C4⋊C4—1221no—
378C4⋊C4C22⋊#692312yes—
379C4⋊C4C22⋊#692312yes—
380C22⋊C4—614no—
381C22⋊C4—614no—
382C22⋊C4—1222no—
383C22⋊C4—1222no—
384C22⋊C4—1222no—
385C22⋊C4—1222no—
386C42—21no—
387C42—21no—
388C42—612no—
389C42—612no—
390C42—1221no—
391C42—1221no—
392C23—612no—
393C23—612no—
394C23—1224no—
395C23—1222no—
396C23—1222no—
397C23—2442no—
398C23C23×#692311yescharacteristic
399Q8—4884no—
400Q8—2444no—
401D4—614no—
402D4—1224no—
403D4—1222no—
404C2×C4—22no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—21no—
410C2×C4—22no—
411C2×C4—21no—
412C2×C4—42no—
413C2×C4—41no—
414C2×C4—612no—
415C2×C4—612no—
416C2×C4—612no—
417C2×C4—1221no—
418C2×C4—1221no—
419C2×C4—1221no—
420C2×C4—1221no—
421C2×C4—1221no—
422C2×C4—1222no—
423C2×C4—4882no—
424C2×C4—4882no—
425C2×C4—2444no—
426C2×C4—2444no—
427C2×C4—2444no—
428C2×C4—2444no—
429C2×C4—2441no—
430C2×C4—2442no—
431C2×C4—2441no—
432C2×C4C2×C22⋊#692311yescharacteristic
433C2×C4C2×C22⋊#692314yes—
434C2×C4C2×C22⋊#692311yescharacteristic
435C8—2442no—
436C8—2444no—
437C8—2442no—
438C22—21no—
439C22—21no—
440C22—614no—
441C22—1222no—
442C22—1222no—
443C22—1222no—
444C22—1222no—
445C22—1222no—
446C22—2444no—
447C22—2444no—
448C22C22×C22⋊#692311yescharacteristic
449C22D61⋊#13111yescharacteristic
450C22#1684084111yescharacteristic
451C4—24no—
452C4—21no—
453C4—42no—
454C4—41no—
455C4—41no—
456C4—1222no—
457C4—1222no—
458C4—1222no—
459C4—2442no—
460C4—2441no—
461C4D61⋊#10112yes—
462C2—21no—
463C2—21no—
464C2—1224no—
465C2—2442no—
466C2#2146241011yescharacteristic
467C2#2146241911yescharacteristic
468C2C2×D61⋊#10111yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC2×#125×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC22×D244C2×C4
cosocleC22×Dic61C24
hypercenterC2×#125#6923
hypocenterC61#17426
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4⋊C4 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
2. #21461097C2semidirect
3. #21461092C2semidirect
4. #21461081C2semidirect
5. #21461068C2semidirect
6. #21461061C2semidirect
7. D61⋊#324C2semidirect
271. C61#17426semidirect

Maximal subgroups

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

subgroupindex
#214626802
#214610972
#214610922
#214610812
#214610682
#214610612
D61⋊#3242
C2×#168404682
#1742661