Finite Group Databasebeta

← #30610272

Subgroups — #30610272

Order 15616.

944 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462510C212yesmaximal, complemented
2#21461097C212yesmaximal, complemented
3#21461092C214yesmaximal, complemented
4#21461076C211yesmaximal, characteristic
5#21461073C212yesmaximal, complemented
6#21461056C211yesmaximal, characteristic
7#21461053C212yesmaximal, complemented
8C2×#16840450C211yesmaximal, characteristic
9#16840787—24no—
10#16840783C2214yes—
11#16840779C2214yes—
12#16840769—22no—
13#16840733C2212yes—
14D61⋊(C22⋊C8)C2212yes—
15#16840727—22no—
16#16840607C2214yes—
17#16840607C2212yes—
18#16840607C2214yes—
19#16840607C2212yes—
20#16840606C2211yescharacteristic
21#16840606C2212yes—
22#16840606C2211yescharacteristic
23#16840450—22no—
24#16840450—22no—
25#16840450—24no—
26C2×#14519772C412yes—
27C2×#14519768C2212yes—
28C2×#14519762C412yes—
29C2×#14519757C411yescharacteristic
30C2×#14519757C2211yescharacteristic
31C2×C4×Dic122C411yescharacteristic
32C2×C4×D244C2211yescharacteristic
33C2×#14519735C2212yes—
34C2×#14519735C2211yescharacteristic
35C2×C4⋊C4×D61C411yescharacteristic
36C2×#125×C61C411yescharacteristic
37C2×#11758213—22no—
38C2×D61⋊C8—22no—
39#14519844—24no—
40C4⋊#92420—24no—
41#14519834—22no—
42#14519834—22no—
43C22⋊#92420C2312yes—
44C22⋊#92420C2312yes—
45C22⋊#92420C2314yes—
46#14519832—24no—
47C4×#92420—24no—
48C22×Dic122C2×C411yescharacteristic
49C22×D244C2×C411yescharacteristic
50C22×C4×D61C2×C412yes—
51C22×C4×D61C2×C411yescharacteristic
52C22×C4×D61C2311yescharacteristic
53#14519772—24no—
54#14519772—24no—
55#14519768—24no—
56#14519768—24no—
57#14519762—24no—
58#14519762—24no—
59#14519757—22no—
60#14519757—22no—
61#14519757—22no—
62#14519757—22no—
63C4×Dic122—22no—
64C4×Dic122—21no—
65C4×Dic122—21no—
66C4×D244—22no—
67C4×D244—22no—
68#14519735—24no—
69#14519735—24no—
70#14519735D412yes—
71#14519735D412yes—
72#14519735D414yes—
73C2×C4⋊Dic61C2×C412yes—
74C2×C4⋊Dic61C2×C411yescharacteristic
75C2×C4⋊Dic61C2312yes—
76C2×C4⋊Dic61C2311yescharacteristic
77C2×#11758196C2×C412yes—
78C2×#11758196C2×C412yes—
79C4⋊C4×D61—22no—
80C4⋊C4×D61—21no—
81C4⋊C4×D61—21no—
82C2×#11758198C2×C412yes—
83C2×#11758198C2×C411yescharacteristic
84C2×#11758198C2×C412yes—
85C2×#11758198C2×C412yes—
86C2×#11758198C2311yescharacteristic
87C2×C4×Dic61C2×C412yes—
88C2×C4×Dic61C2312yes—
89#125×C61—22no—
90#125×C61—22no—
91C2×C4⋊C4×C61C2×C411yescharacteristic
92C2×C4⋊C4×C61C2×C412yes—
93C2×C4⋊C4×C61C2×C412yes—
94C2×C4⋊C4×C61C2×C411yescharacteristic
95C2×C42×C61C2×C411yescharacteristic
96C23×D61C22×C411yescharacteristic
97C23×D61C22×C411yescharacteristic
98C22×C4×C61C22×C412yes—
99C22×C4×C61C22×C411yescharacteristic
100C22×C4×C61C22×C411yescharacteristic
101C22×C4×C61C22×C411yescharacteristic
102C22×C4×C61C22×C412yes—
103C22×Dic61C22×C412yes—
104C22×Dic61C22×C411yescharacteristic
105C22×Dic61C22×C412yes—
106C22×Dic61C2411yescharacteristic
107C2×D244—22no—
108C2×D244—22no—
109C2×D244—41no—
110C2×C4×D61—24no—
111C2×C4×D61—21no—
112C2×C4×D61—21no—
113C2×C4×D61—22no—
114C2×C4×D61—22no—
115C2×C4×D61—42no—
116C2×C4×D61—42no—
117C2×C4×D61—42no—
118C2×C4×D61C2×D412yes—
119C2×C4×D61C2×D412yes—
120C2×Dic122—21no—
121C2×Dic122—21no—
122C2×Dic122—42no—
123C2×#92420—22no—
124C2×#92420—24no—
125C2×#92420—22no—
126#11758213—44no—
127D61⋊C8—44no—
128C4⋊C4×C61—21no—
129C4⋊C4×C61—21no—
130C4⋊C4×C61—24no—
131C4⋊C4×C61—24no—
132C4⋊C4×C61C22⋊C412yes—
133C4⋊C4×C61C22⋊C412yes—
134C42×C61—21no—
135C42×C61—21no—
136#11758198—22no—
137#11758198—24no—
138#11758198—24no—
139#11758198—22no—
140#11758198C22⋊C414yes—
141#11758198C22⋊C414yes—
142C4⋊Dic61—24no—
143C4⋊Dic61—24no—
144C4⋊Dic61—22no—
145C4⋊Dic61C22⋊C412yes—
146C4⋊Dic61C22⋊C411yescharacteristic
147C4⋊Dic61C22⋊C411yescharacteristic
148#11758196—22no—
149#11758196—22no—
150#11758196—22no—
151#11758196—22no—
152C4×Dic61—22no—
153C4×Dic61—22no—
154C4×Dic61C2×D414yes—
155C4×Dic61C2×D414yes—
156C23×C61C23×C411yescharacteristic
157C22×D61—21no—
158C22×D61—21no—
159C22×D61—21no—
160C22×D61—21no—
161C22×D61—41no—
162C22×D61—41no—
163C22×D61—41no—
164C22×D61—41no—
165C22×D61C2×C22⋊C412yes—
166C22×D61#13112yes—
167C2×C4×C61—22no—
168C2×C4×C61—21no—
169C2×C4×C61—21no—
170C2×C4×C61—22no—
171C2×C4×C61—22no—
172C2×C4×C61—21no—
173C2×C4×C61—22no—
174C2×C4×C61—21no—
175C2×C4×C61—42no—
176C2×C4×C61—41no—
177C2×C4×C61C2×C22⋊C414yes—
178C2×C4×C61C2×C22⋊C411yescharacteristic
179C2×C4×C61C2×C22⋊C411yescharacteristic
180C2×Dic61—22no—
181C2×Dic61—22no—
182C2×Dic61—22no—
183C2×Dic61—21no—
184C2×Dic61—41no—
185C2×Dic61—42no—
186C2×Dic61—41no—
187C2×Dic61C2×C22⋊C412yes—
188C2×Dic61C2×C22⋊C412yes—
189C2×Dic61C22×D412yes—
190D244—44no—
191C4×D61—24no—
192C4×D61—42no—
193C4×D61—44no—
194C4×D61—44no—
195C4×D61—42no—
196C4×D61—42no—
197Dic122—42no—
198Dic122—42no—
199#92420—42no—
200#92420—42no—
201#92420—44no—
202#17413—611nomaximal, Sylow
203C22×C61—21no—
204C22×C61—21no—
205C22×C61C22×C22⋊C411yescharacteristic
206C22×C61C2×#13111yescharacteristic
207C22×C61#56811yescharacteristic
208C2×D61—22no—
209C2×D61—22no—
210C2×D61—22no—
211C2×D61—22no—
212C2×D61—42no—
213C2×D61—41no—
214C2×D61—41no—
215C2×D61—42no—
216C2×D61—81no—
217C2×D61—81no—
218C4×C61—21no—
219C4×C61—24no—
220C4×C61—42no—
221C4×C61—41no—
222C4×C61—41no—
223C4×C61#41012yes—
224Dic61—22no—
225Dic61—22no—
226Dic61—22no—
227Dic61—42no—
228Dic61—41no—
229C2×#552—611no—
230#2924—612no—
231#1472—612no—
232#1470—614no—
233#1465—611no—
234#1464—612no—
235#1459—611no—
236#1458—612no—
237C2×C61—21no—
238C2×C61—21no—
239C2×C61#288011yescharacteristic
240C2×C61C2×#41011yescharacteristic
241C2×C61#288911yescharacteristic
242D61—42no—
243D61—42no—
244#552—1222no—
245#552—1222no—
246#552—1224no—
247C2×#126—612no—
248C2×#125—612no—
249C2×#125#692311yescharacteristic
250C2×#123—612no—
251C2×C22⋊Q8—611no—
252C2×C22⋊Q8—611no—
253C2×C4×Q8—611no—
254C2×C4×D4—611no—
255C2×#117—612no—
256C2×#117—611no—
257C22×C4⋊C4—611no—
258#433—1224no—
259#432—614no—
260#431—614no—
261#424—1222no—
262#407—612no—
263C2×C22⋊C8—612no—
264#405—1222no—
265#324—614no—
266#324—612no—
267#324—614no—
268#324—612no—
269#323—611no—
270#323—612no—
271#323—611no—
272C61#1741311yescharacteristic, complemented, Sylow
273C22×Q8—611no—
274C22×D4—611no—
275C23×C4—611no—
276C23×C4—612no—
277C23×C4—611no—
278C2×M16—1222no—
279C22×C8—1222no—
280#126—1224no—
281#126—1224no—
282#125—22no—
283#125—22no—
284#125—1224no—
285#125—1224no—
286#123—1224no—
287#123—1224no—
288C22⋊Q8—1222no—
289C22⋊Q8—1222no—
290C22⋊Q8—1222no—
291C22⋊Q8—1222no—
292C4×Q8—1222no—
293C4×Q8—1221no—
294C4×Q8—1221no—
295C4×D4—1222no—
296C4×D4—1222no—
297#117—612no—
298#117—612no—
299#117—614no—
300#117—1224no—
301#117—1224no—
302C2×C4⋊C4—611no—
303C2×C4⋊C4—612no—
304C2×C4⋊C4—612no—
305C2×C4⋊C4—611no—
306C2×C4⋊C4—612no—
307C2×C4⋊C4—612no—
308C2×C4⋊C4—1222no—
309C2×C4⋊C4—1221no—
310C2×C4⋊C4—1221no—
311C2×C4⋊C4C2×#692311yescharacteristic
312C2×C4⋊C4C2×#692312yes—
313C2×C4⋊C4C2×#692312yes—
314C2×C4⋊C4C2×#692311yescharacteristic
315C2×C22⋊C4—612no—
316C2×C22⋊C4—611no—
317C2×C22⋊C4—612no—
318C2×C22⋊C4—611no—
319C2×C22⋊C4—612no—
320C2×C42—612no—
321C2×C42—612no—
322C2×C42C2×#692311yescharacteristic
323C4⋊C8—1224no—
324C4⋊C8—1224no—
325C22⋊C8—612no—
326C22⋊C8—612no—
327C22⋊C8—614no—
328C22⋊C8—1222no—
329C22⋊C8—1222no—
330#97—1224no—
331C4×C8—1224no—
332C24—611no—
333C24—611no—
334C2×Q8—1221no—
335C2×Q8—1221no—
336C2×Q8—2442no—
337C2×D4—1222no—
338C2×D4—1222no—
339C2×D4—2441no—
340C22×C4—612no—
341C22×C4—611no—
342C22×C4—612no—
343C22×C4—612no—
344C22×C4—612no—
345C22×C4—611no—
346C22×C4—1222no—
347C22×C4—1222no—
348C22×C4—1224no—
349C22×C4—1221no—
350C22×C4—1221no—
351C22×C4—2442no—
352C22×C4—2442no—
353C22×C4—2442no—
354C22×C4C22×#692311yescharacteristic
355C22×C4C22×#692312yes—
356C22×C4C22×#692311yescharacteristic
357C22×C4C22×#692311yescharacteristic
358C22×C4C22×#692312yes—
359M16—2444no—
360C2×C8—1222no—
361C2×C8—1224no—
362C2×C8—1222no—
363C2×C8—2444no—
364C4⋊C4—21no—
365C4⋊C4—21no—
366C4⋊C4—24no—
367C4⋊C4—24no—
368C4⋊C4—612no—
369C4⋊C4—611no—
370C4⋊C4—611no—
371C4⋊C4—1222no—
372C4⋊C4—1222no—
373C4⋊C4—1222no—
374C4⋊C4—1222no—
375C4⋊C4—1224no—
376C4⋊C4—1222no—
377C4⋊C4—1224no—
378C4⋊C4C22⋊#692312yes—
379C4⋊C4C22⋊#692312yes—
380C22⋊C4—614no—
381C22⋊C4—614no—
382C22⋊C4—1222no—
383C22⋊C4—1222no—
384C22⋊C4—1224no—
385C22⋊C4—1224no—
386C42—21no—
387C42—21no—
388C42—614no—
389C42—614no—
390C42—1222no—
391C42—1222no—
392C23—612no—
393C23—612no—
394C23—1221no—
395C23—1221no—
396C23—1221no—
397C23—1221no—
398C23—2441no—
399C23—2441no—
400C23—2441no—
401C23—2441no—
402C23C23×#692311yescharacteristic
403Q8—2442no—
404Q8—2442no—
405D4—2444no—
406C2×C4—22no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—21no—
412C2×C4—22no—
413C2×C4—21no—
414C2×C4—42no—
415C2×C4—41no—
416C2×C4—612no—
417C2×C4—612no—
418C2×C4—612no—
419C2×C4—1222no—
420C2×C4—1222no—
421C2×C4—1224no—
422C2×C4—1222no—
423C2×C4—1221no—
424C2×C4—2442no—
425C2×C4—2442no—
426C2×C4—2444no—
427C2×C4—2444no—
428C2×C4—2441no—
429C2×C4—2442no—
430C2×C4—2441no—
431C2×C4—2442no—
432C2×C4C2×C22⋊#692311yescharacteristic
433C2×C4C2×C22⋊#692314yes—
434C2×C4C2×C22⋊#692311yescharacteristic
435C8—2442no—
436C8—2442no—
437C8—2444no—
438C22—21no—
439C22—21no—
440C22—1222no—
441C22—1222no—
442C22—1222no—
443C22—1222no—
444C22—4881no—
445C22—4881no—
446C22—2442no—
447C22—2442no—
448C22—2441no—
449C22—2441no—
450C22C22×C22⋊#692311yescharacteristic
451C22D61⋊#13111yescharacteristic
452C22#1684084111yescharacteristic
453C4—21no—
454C4—24no—
455C4—42no—
456C4—41no—
457C4—41no—
458C4—1222no—
459C4—1222no—
460C4—1222no—
461C4—2441no—
462C4—2442no—
463C4#1684074312yes—
464C2—21no—
465C2—21no—
466C2—2442no—
467C2—2442no—
468C2#2146241011yescharacteristic
469C2C2×#1684074311yescharacteristic
470C2#2146243111yescharacteristic
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#17413
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
1. #21462510C2semidirect
2. #21461097C2semidirect
3. #21461092C2semidirect
5. #21461073C2semidirect
7. #21461053C2semidirect
272. C61#17413semidirect

Maximal subgroups

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

subgroupindex
#214625102
#214610972
#214610922
#214610762
#214610732
#214610562
#214610532
C2×#168404502
#1741361