Finite Group Databasebeta

← #30610039

Subgroups — #30610039

Order 15616.

1174 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462718C212yesmaximal, complemented
2#21461079C212yesmaximal, complemented
3#21461078C212yesmaximal, complemented
4#21461072C212yesmaximal, complemented
5#21461071C212yesmaximal, complemented
6#21461058C212yesmaximal, complemented
7#21461051C212yesmaximal, complemented
8C2×#16840241C211yesmaximal, characteristic
9#16840814—28no—
10#16840783C2214yes—
11#16840782C2214yes—
12#16840779C2214yes—
13#16840608C2214yes—
14#16840606C2214yes—
15#16840605C2214yes—
16#16840605C2214yes—
17C22×#11758224C411yescharacteristic
18#16840241—28no—
19C2×C4×Dic122C411yescharacteristic
20C2×#14519742C2211yescharacteristic
21C2×D4×Dic61C2211yescharacteristic
22C2×C4×C22⋊D61C2211yescharacteristic
23C2×C4×C22⋊D61C2211yescharacteristic
24C2×#14519737C411yescharacteristic
25C2×#14519737C411yescharacteristic
26C2×#14519734C2211yescharacteristic
27C2×#14519733C2211yescharacteristic
28C2×#14519733C2211yescharacteristic
29C22×#11758196C411yescharacteristic
30C22×#11758196C411yescharacteristic
31C2×C4⋊C4×D61C411yescharacteristic
32C2×C4×D4×C61C411yescharacteristic
33#14519844—24no—
34#14519844—24no—
35C4⋊#92420—24no—
36C22⋊#92420C2318yes—
37#14519832—24no—
38#14519832—24no—
39C4×#92420—24no—
40C2×#11758224—24no—
41C2×#11758224—24no—
42C2×#11758224—24no—
43C22×Dic122C2×C411yescharacteristic
44C22×C22⋊D61C2×C411yescharacteristic
45C22×C22⋊D61C2×C411yescharacteristic
46C23×Dic61C2×C411yescharacteristic
47C23×Dic61C2×C411yescharacteristic
48C23×Dic61C2×C411yescharacteristic
49C23×Dic61C2×C411yescharacteristic
50C22×C4×D61C2×C411yescharacteristic
51C22×C4×D61C2×C411yescharacteristic
52C22×C4×D61C2×C411yescharacteristic
53C4×Dic122—24no—
54#14519742D418yes—
55D4×Dic61—24no—
56C4×C22⋊D61—24no—
57C4×C22⋊D61—24no—
58#14519737—24no—
59#14519737—24no—
60#14519734—24no—
61#14519733—24no—
62#14519733—24no—
63C2×C4⋊Dic61C2×C411yescharacteristic
64C2×#11758196—24no—
65C2×#11758196—24no—
66C2×#11758196C2×C411yescharacteristic
67C2×#11758196C2×C411yescharacteristic
68C2×#11758196C2×C411yescharacteristic
69C2×#11758196C2×C411yescharacteristic
70C2×#11758196C2×C411yescharacteristic
71C2×#11758196C2×C411yescharacteristic
72C2×#11758196C2×C411yescharacteristic
73C2×#11758196C2311yescharacteristic
74C4⋊C4×D61—24no—
75C2×C22⋊Dic61C2311yescharacteristic
76C2×C22⋊Dic61C2311yescharacteristic
77C2×#11758198C2×C411yescharacteristic
78C2×#11758198C2311yescharacteristic
79C2×C4×Dic61C2×C411yescharacteristic
80C2×C4×Dic61C2×C411yescharacteristic
81C2×C4×Dic61C2311yescharacteristic
82C2×C4×Dic61C2311yescharacteristic
83C2×C4×Dic61C2311yescharacteristic
84C22×D4×C61C2×C411yescharacteristic
85C23×C4×C61C2×C411yescharacteristic
86C23×C4×C61C2×C411yescharacteristic
87C4×D4×C61—24no—
88C2×C4⋊C4×C61C2×C411yescharacteristic
89C2×C22⋊C4×C61C2×C411yescharacteristic
90C2×C22⋊C4×C61C2×C411yescharacteristic
91C2×C42×C61C2×C411yescharacteristic
92C24×C61C22×C411yescharacteristic
93C24×C61C22×C411yescharacteristic
94C23×D61C22×C411yescharacteristic
95C2×D4×C61—22no—
96C2×D4×C61—22no—
97C2×D4×C61—22no—
98C22×C4×C61—22no—
99C22×C4×C61—22no—
100C22×C4×C61—81no—
101C22×C4×C61—81no—
102C22×C4×C61C22×C411yescharacteristic
103C22×C4×C61C22×C411yescharacteristic
104C22×C4×C61C22×C411yescharacteristic
105C22×C4×C61C22×C411yescharacteristic
106C22×C4×C61C22×C411yescharacteristic
107C2×C22⋊D61—22no—
108C2×C22⋊D61—22no—
109C2×C22⋊D61—22no—
110C2×C22⋊D61—22no—
111C2×C22⋊D61—22no—
112C2×C22⋊D61M1614yes—
113C22×Dic61—22no—
114C22×Dic61—22no—
115C22×Dic61—22no—
116C22×Dic61—22no—
117C22×Dic61—22no—
118C22×Dic61—22no—
119C22×Dic61—22no—
120C22×Dic61—81no—
121C22×Dic61—81no—
122C22×Dic61M1614yes—
123C22×Dic61C22×C411yescharacteristic
124C22×Dic61C22×C411yescharacteristic
125C22×Dic61C22×C411yescharacteristic
126C22×Dic61C22×C411yescharacteristic
127C22×Dic61C22×C411yescharacteristic
128C22×Dic61C22×C411yescharacteristic
129C22×Dic61C2411yescharacteristic
130#11758224—232no—
131C2×C4×D61—22no—
132C2×C4×D61—22no—
133C2×C4×D61—22no—
134C2×C4×D61—22no—
135C2×C4×D61—22no—
136C2×C4×D61—81no—
137C2×C4×D61—81no—
138C2×Dic122—22no—
139C2×Dic122—22no—
140C2×Dic122C22⋊C414yes—
141C2×#92420—28no—
142C4⋊C4×C61C22⋊C414yes—
143C22⋊C4×C61—22no—
144C22⋊C4×C61—22no—
145C42×C61—22no—
146C22⋊Dic61—22no—
147C22⋊Dic61—22no—
148#11758198—22no—
149#11758198—22no—
150C4⋊Dic61—22no—
151#11758196—22no—
152#11758196—22no—
153#11758196—22no—
154#11758196—22no—
155#11758196—22no—
156#11758196—22no—
157#11758196C22⋊C414yes—
158#11758196C22⋊C414yes—
159C4×Dic61—22no—
160C4×Dic61—22no—
161C4×Dic61C2×D414yes—
162C4×Dic61C2×D414yes—
163C4×Dic61C2×D414yes—
164C23×C61—21no—
165C23×C61—21no—
166C23×C61—21no—
167C23×C61—21no—
168C23×C61—41no—
169C23×C61—41no—
170C23×C61—41no—
171C23×C61—41no—
172C23×C61C2×M1612yes—
173C23×C61C2×M1612yes—
174C23×C61C23×C411yescharacteristic
175C22×D61—21no—
176C22×D61—21no—
177C22×D61—41no—
178C22×D61—41no—
179C22×D61C2×M1612yes—
180D4×C61—28no—
181C2×C4×C61—21no—
182C2×C4×C61—21no—
183C2×C4×C61—21no—
184C2×C4×C61—21no—
185C2×C4×C61—41no—
186C2×C4×C61—41no—
187C2×C4×C61—41no—
188C2×C4×C61—41no—
189C2×C4×C61—82no—
190C2×C4×C61—82no—
191C2×C4×C61C2×C22⋊C412yes—
192C2×C4×C61C2×C22⋊C412yes—
193C2×C4×C61C2×C22⋊C412yes—
194C22⋊D61—28no—
195C22⋊D61—28no—
196C2×Dic61—28no—
197C2×Dic61—21no—
198C2×Dic61—21no—
199C2×Dic61—21no—
200C2×Dic61—21no—
201C2×Dic61—28no—
202C2×Dic61—21no—
203C2×Dic61—21no—
204C2×Dic61—41no—
205C2×Dic61—41no—
206C2×Dic61—41no—
207C2×Dic61—41no—
208C2×Dic61—82no—
209C2×Dic61—82no—
210C2×Dic61C2×C22⋊C412yes—
211C2×Dic61C2×C22⋊C412yes—
212C2×Dic61C2×C22⋊C412yes—
213C2×Dic61C2×M1612yes—
214C2×Dic61C2×M1612yes—
215C2×Dic61C2×M1612yes—
216C2×Dic61C22×D412yes—
217C4×D61—28no—
218C4×D61—82no—
219C4×D61—82no—
220Dic122—28no—
221#92420—48no—
222#17372—611nomaximal, Sylow
223C22×C61—21no—
224C22×C61—21no—
225C22×C61—22no—
226C22×C61—22no—
227C22×C61—42no—
228C22×C61—42no—
229C22×C61—42no—
230C22×C61—42no—
231C22×C61—41no—
232C22×C61—41no—
233C22×C61—41no—
234C22×C61—41no—
235C22×C61C22×C22⋊C411yescharacteristic
236C22×C61C22×M1611yescharacteristic
237C22×C61C22×M1611yescharacteristic
238C2×D61—22no—
239C2×D61—42no—
240C2×D61—41no—
241C2×D61—41no—
242C2×D61—42no—
243C4×C61—22no—
244C4×C61—22no—
245C4×C61—22no—
246C4×C61—41no—
247C4×C61—41no—
248Dic61—22no—
249Dic61—22no—
250Dic61—22no—
251Dic61—22no—
252Dic61—41no—
253Dic61—41no—
254Dic61#40714yes—
255C2×#520—611no—
256#2983—612no—
257#1466—612no—
258#1466—612no—
259#1464—612no—
260#1464—612no—
261#1460—612no—
262#1458—612no—
263C2×C61—21no—
264C2×C61—21no—
265C2×C61—42no—
266C2×C61—42no—
267C2×C61C2×#40711yescharacteristic
268C2×C61#288411yescharacteristic
269C2×C61#288811yescharacteristic
270D61—42no—
271C22×#41—611no—
272#520—1228no—
273C2×C4×Q8—611no—
274C2×C4×Q8—611no—
275C2×C4×D4—611no—
276C2×C4×D4—611no—
277C2×C4×D4—611no—
278C2×C4×D4—611no—
279C2×C4×D4—611no—
280C2×C4×D4#692311yescharacteristic
281C2×#117—611no—
282C2×#117—611no—
283C2×#117—611no—
284C22×C4⋊C4—611no—
285C22×C4⋊C4—611no—
286C22×C4⋊C4—611no—
287#446—1228no—
288#432—614no—
289#432—614no—
290#431—614no—
291#324—614no—
292#323—614no—
293#323—614no—
294#323—614no—
295C61#1737211yescharacteristic, complemented, Sylow
296C2×#41—1224no—
297C2×#41—1224no—
298C2×#41—1224no—
299C22×Q8—611no—
300C22×D4—611no—
301C22×D4—611no—
302C22×D4C2×#692311yescharacteristic
303C23×C4—611no—
304C23×C4—611no—
305C23×C4—611no—
306C23×C4—611no—
307C23×C4—611no—
308C23×C4—611no—
309C23×C4—611no—
310C23×C4C2×#692311yescharacteristic
311C23×C4C2×#692311yescharacteristic
312C4×Q8—618no—
313C4×Q8—1224no—
314C4×D4—24no—
315C4×D4—1224no—
316C4×D4—1224no—
317C4×D4—1224no—
318C4×D4—1224no—
319C4×D4—1224no—
320#117—1224no—
321#117—1224no—
322#117—1224no—
323C2×C4⋊C4—611no—
324C2×C4⋊C4—611no—
325C2×C4⋊C4—611no—
326C2×C4⋊C4—611no—
327C2×C4⋊C4—611no—
328C2×C4⋊C4—611no—
329C2×C4⋊C4—611no—
330C2×C4⋊C4—611no—
331C2×C4⋊C4—611no—
332C2×C4⋊C4—1224no—
333C2×C4⋊C4—1224no—
334C2×C4⋊C4—1224no—
335C2×C4⋊C4C2×#692311yescharacteristic
336C2×C22⋊C4—611no—
337C2×C22⋊C4—611no—
338C2×C22⋊C4—611no—
339C2×C22⋊C4—611no—
340C2×C22⋊C4C2×#692311yescharacteristic
341C2×C22⋊C4C2×#692311yescharacteristic
342C2×C42—611no—
343C2×C42—611no—
344C2×C42—611no—
345C2×C42—611no—
346C2×C42—611no—
347C2×C42C2×#692311yescharacteristic
348C4⋊C8—1224no—
349C4⋊C8—1224no—
350C4⋊C8—1224no—
351C22⋊C8—618no—
352#97—1224no—
353#97—1224no—
354C4×C8—1224no—
355C24—611no—
356C24C22×#692311yescharacteristic
357C24C22×#692311yescharacteristic
358#41—12232no—
359C2×Q8—614no—
360C2×Q8—1222no—
361C2×Q8—1222no—
362C2×D4—22no—
363C2×D4—22no—
364C2×D4—22no—
365C2×D4—614no—
366C2×D4—1222no—
367C2×D4—1222no—
368C2×D4—1222no—
369C2×D4—1222no—
370C2×D4—1222no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—81no—
374C22×C4—81no—
375C22×C4—611no—
376C22×C4—614no—
377C22×C4—611no—
378C22×C4—611no—
379C22×C4—611no—
380C22×C4—611no—
381C22×C4—611no—
382C22×C4—611no—
383C22×C4—1222no—
384C22×C4—1222no—
385C22×C4—1222no—
386C22×C4—1222no—
387C22×C4—1222no—
388C22×C4—1222no—
389C22×C4—1222no—
390C22×C4—1222no—
391C22×C4—1222no—
392C22×C4—1222no—
393C22×C4—1222no—
394C22×C4—1222no—
395C22×C4—4881no—
396C22×C4—4881no—
397C22×C4—4881no—
398C22×C4—4881no—
399C22×C4C22×#692311yescharacteristic
400C22×C4C22×#692311yescharacteristic
401C22×C4C22×#692311yescharacteristic
402C22×C4C22×#692311yescharacteristic
403C22×C4C22×#692311yescharacteristic
404C2×C8—1228no—
405C4⋊C4—614no—
406C4⋊C4—614no—
407C4⋊C4—1222no—
408C4⋊C4—1222no—
409C4⋊C4—1222no—
410C4⋊C4—1222no—
411C4⋊C4—1222no—
412C4⋊C4—1222no—
413C4⋊C4—1222no—
414C4⋊C4C22⋊#692314yes—
415C22⋊C4—22no—
416C22⋊C4—22no—
417C22⋊C4—1222no—
418C22⋊C4—1222no—
419C22⋊C4—1222no—
420C22⋊C4—1222no—
421C42—22no—
422C42—614no—
423C42—614no—
424C42—614no—
425C42—1222no—
426C42—1222no—
427C23—21no—
428C23—21no—
429C23—21no—
430C23—21no—
431C23—41no—
432C23—41no—
433C23—41no—
434C23—41no—
435C23—612no—
436C23—1221no—
437C23—1221no—
438C23—2441no—
439C23—2441no—
440C23D61⋊M1612yes—
441C23D61⋊M1612yes—
442C23C23×#692311yescharacteristic
443Q8—1228no—
444D4—28no—
445D4—1228no—
446D4—1228no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—82no—
456C2×C4—82no—
457C2×C4—612no—
458C2×C4—612no—
459C2×C4—612no—
460C2×C4—612no—
461C2×C4—612no—
462C2×C4—612no—
463C2×C4—612no—
464C2×C4—1228no—
465C2×C4—1228no—
466C2×C4—1228no—
467C2×C4—1221no—
468C2×C4—1221no—
469C2×C4—1221no—
470C2×C4—1221no—
471C2×C4—1221no—
472C2×C4—1221no—
473C2×C4—4882no—
474C2×C4—4882no—
475C2×C4—4882no—
476C2×C4—4882no—
477C2×C4—2441no—
478C2×C4—2441no—
479C2×C4—2441no—
480C2×C4—2441no—
481C2×C4C2×C22⋊#692312yes—
482C2×C4C2×C22⋊#692312yes—
483C2×C4C2×C22⋊#692312yes—
484C8—2448no—
485C22—21no—
486C22—21no—
487C22—22no—
488C22—22no—
489C22—42no—
490C22—42no—
491C22—42no—
492C22—42no—
493C22—41no—
494C22—41no—
495C22—41no—
496C22—41no—
497C22—1222no—
498C22—2442no—
499C22—2442no—
500C22—2441no—
501C22—2441no—
502C22C22×C22⋊#692311yescharacteristic
503C22C2×D61⋊M1611yescharacteristic
504C22C2×D61⋊M1611yescharacteristic
505C4—22no—
506C4—22no—
507C4—22no—
508C4—41no—
509C4—41no—
510C4—614no—
511C4—1222no—
512C4—1222no—
513C4—1222no—
514C4—1222no—
515C4—2441no—
516C4—2441no—
517C2—21no—
518C2—21no—
519C2—42no—
520C2—42no—
521C2—2442no—
522C2D61⋊#40711yescharacteristic
523C2#2146242111yescharacteristic
524C2#2146242911yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC2×C4×D4×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC22×#11758224C4
cosocleC22×Dic61C24
hypercenterC2×C4×D4#6923
hypocenterC61#17372
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4⋊C4 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. #21462718C2semidirect
2. #21461079C2semidirect
3. #21461078C2semidirect
4. #21461072C2semidirect
5. #21461071C2semidirect
6. #21461058C2semidirect
7. #21461051C2semidirect
295. C61#17372semidirect

Maximal subgroups

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

subgroupindex
#214627182
#214610792
#214610782
#214610722
#214610712
#214610582
#214610512
C2×#168402412
#1737261