Finite Group Databasebeta

← #30617816

Subgroups — #30617816

Order 15616.

1386 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462495C212yesmaximal, complemented
2#21461963C218yesmaximal, complemented
3#21461653C212yesmaximal, complemented
4#21461651C212yesmaximal
5C22×#14519763C211yesmaximal, characteristic
6#16840783—22no—
7#16840782—22no—
8#16840779—22no—
9#16840778—22no—
10#16840765C2214yescomplemented
11C2×#14519838C2218yescomplemented
12C2×#14519837C2218yes—
13#16840732C2214yes—
14C4×#11758217C2214yescomplemented
15C23×Dic122C2211yescharacteristic
16C23×C22⋊D61C2211yescharacteristic
17C2×#14519763—22no—
18C2×#14519763—22no—
19C2×#14519763—22no—
20C2×#14519763—22no—
21C2×#14519763C414yes—
22C2×#14519763C2214yes—
23C22×C22⋊Dic61C411yescharacteristic
24C22×#11758198C411yescharacteristic
25C22×#11758198C411yescharacteristic
26C22×C4×Dic61C2211yescharacteristic
27C22×C22⋊C4×C61C411yescharacteristic
28C2×#11758217C2318yes—
29#14519844—24no—
30C4⋊#92420—24no—
31#14519838—48no—
32#14519837—48no—
33C22⋊#92420—24no—
34C22⋊#92420—24no—
35#14519832—24no—
36C4×#92420—24no—
37C24×D61C2×C411yescharacteristic
38C22×Dic122—22no—
39C22×Dic122—22no—
40C22×Dic122—44no—
41C22×Dic122C2×C412yes—
42C22×Dic122C2312yes—
43C22×C22⋊D61—22no—
44C22×C22⋊D61—22no—
45C22×C22⋊D61—44no—
46C22×C22⋊D61C2×C412yes—
47C22×C22⋊D61C2312yes—
48C23×Dic61C2×C411yescharacteristic
49C23×Dic61C2×C411yescharacteristic
50C23×Dic61C2311yescharacteristic
51#14519763—24no—
52#14519763—24no—
53#14519763—24no—
54#14519763—24no—
55#14519763—24no—
56#14519763—24no—
57#14519763—24no—
58#14519763—24no—
59C2×C22⋊Dic61—22no—
60C2×C22⋊Dic61—21no—
61C2×C22⋊Dic61—21no—
62C2×C22⋊Dic61C2×C414yes—
63C2×#11758198—22no—
64C2×#11758198—21no—
65C2×#11758198—21no—
66C2×#11758198—22no—
67C2×#11758198—21no—
68C2×#11758198—21no—
69C2×#11758198C2×C414yes—
70C2×#11758198C2×C414yes—
71C2×C4×Dic61C2×C412yes—
72C2×C4×Dic61D412yes—
73C2×C4×Dic61D412yes—
74C2×C4×Dic61D412yes—
75C2×C4×Dic61D412yes—
76C2×C4×Dic61C2312yes—
77C25×C61C2×C411yescharacteristic
78C23×C4×C61C2×C411yescharacteristic
79C23×C4×C61C2×C411yescharacteristic
80C2×C22⋊C4×C61—22no—
81C2×C22⋊C4×C61—21no—
82C2×C22⋊C4×C61—21no—
83C2×C22⋊C4×C61C2×C414yes—
84C24×C61—21no—
85C24×C61—21no—
86C24×C61—42no—
87C24×C61—42no—
88C24×C61—42no—
89C24×C61C22×C411yescharacteristic
90C24×C61C22×C412yes—
91C23×D61—21no—
92C23×D61—21no—
93C23×D61—42no—
94C23×D61—42no—
95C23×D61—42no—
96C23×D61C22×C412yes—
97C22×C4×C61—21no—
98C22×C4×C61—21no—
99C22×C4×C61—42no—
100C22×C4×C61—42no—
101C22×C4×C61C22⋊C412yes—
102C22×C4×C61C22⋊C411yescharacteristic
103C22×C4×C61C22⋊C411yescharacteristic
104C22×C4×C61C22×C412yes—
105C22×C4×C61C22×C412yes—
106C2×C22⋊D61—24no—
107C2×C22⋊D61—24no—
108C2×C22⋊D61—28no—
109C2×C22⋊D61—44no—
110C2×C22⋊D61—48no—
111C2×C22⋊D61—48no—
112C22×Dic61—24no—
113C22×Dic61—21no—
114C22×Dic61—21no—
115C22×Dic61—42no—
116C22×Dic61—42no—
117C22×Dic61C22⋊C412yes—
118C22×Dic61C22⋊C411yescharacteristic
119C22×Dic61C22⋊C411yescharacteristic
120C22×Dic61C22×C412yes—
121C22×Dic61C22×C411yescharacteristic
122C22×Dic61C22×C412yes—
123C22×Dic61C2×D412yes—
124C22×Dic61C2×D412yes—
125C22×Dic61C2411yescharacteristic
126C2×Dic122—24no—
127C2×Dic122—24no—
128C2×Dic122—28no—
129C2×Dic122—44no—
130C2×Dic122—48no—
131C2×Dic122—48no—
132#11758217—216no—
133C2×#92420—28no—
134C22⋊C4×C61—24no—
135C22⋊C4×C61—24no—
136C22⋊Dic61—24no—
137C22⋊Dic61—24no—
138#11758198—24no—
139#11758198—24no—
140#11758198—24no—
141#11758198—24no—
142C4×Dic61C22⋊C412yes—
143C4×Dic61C22⋊C412yes—
144C4×Dic61C22⋊C412yes—
145C4×Dic61C22⋊C412yes—
146C4×Dic61C2×D412yes—
147C4×Dic61C2×D412yes—
148C4×Dic61C2×D412yes—
149C4×Dic61C2×D412yes—
150C23×C61—22no—
151C23×C61—22no—
152C23×C61—22no—
153C23×C61—22no—
154C23×C61—24no—
155C23×C61—42no—
156C23×C61—42no—
157C23×C61—42no—
158C23×C61—42no—
159C23×C61—42no—
160C23×C61—42no—
161C23×C61—42no—
162C23×C61—42no—
163C23×C61—88no—
164C23×C61C2×C22⋊C411yescharacteristic
165C23×C61C2×C22⋊C411yescharacteristic
166C23×C61C23×C411yescharacteristic
167C22×D61—22no—
168C22×D61—24no—
169C22×D61—42no—
170C22×D61—42no—
171C22×D61—42no—
172C22×D61—42no—
173C22×D61—42no—
174C22×D61—42no—
175C22×D61—42no—
176C22×D61—42no—
177C22×D61—88no—
178C2×C4×C61—24no—
179C2×C4×C61—22no—
180C2×C4×C61—24no—
181C2×C4×C61—41no—
182C2×C4×C61—41no—
183C2×C4×C61—42no—
184C2×C4×C61—42no—
185C2×C4×C61—42no—
186C2×C4×C61C2×C22⋊C412yes—
187C2×C4×C61C2×C22⋊C412yes—
188C22⋊D61—48no—
189C22⋊D61—48no—
190C2×Dic61—22no—
191C2×Dic61—24no—
192C2×Dic61—24no—
193C2×Dic61—24no—
194C2×Dic61—22no—
195C2×Dic61—24no—
196C2×Dic61—41no—
197C2×Dic61—41no—
198C2×Dic61—42no—
199C2×Dic61—42no—
200C2×Dic61—42no—
201C2×Dic61C2×C22⋊C412yes—
202C2×Dic61C2×C22⋊C412yes—
203C2×Dic61C2×C22⋊C412yes—
204C2×Dic61C22×D412yes—
205C2×Dic61H(5,𝔽2)14yes—
206Dic122—48no—
207Dic122—48no—
208#92420—48no—
209#21798—611nomaximal, Sylow
210C22×C61—28no—
211C22×C61—21no—
212C22×C61—21no—
213C22×C61—21no—
214C22×C61—21no—
215C22×C61—21no—
216C22×C61—21no—
217C22×C61—42no—
218C22×C61—42no—
219C22×C61—42no—
220C22×C61—84no—
221C22×C61—84no—
222C22×C61—84no—
223C22×C61#41312yes—
224C22×C61#41312yes—
225C22×C61C22×C22⋊C411yescharacteristic
226C22×C61#51812yes—
227C2×D61—42no—
228C2×D61—42no—
229C2×D61—42no—
230C2×D61—84no—
231C2×D61—84no—
232C2×D61—84no—
233C4×C61—22no—
234C4×C61—22no—
235C4×C61—42no—
236Dic61—22no—
237Dic61—22no—
238Dic61—22no—
239Dic61—42no—
240Dic61#53514yes—
241C22×#124—611no—
242#2920—612no—
243#1967—618no—
244#1784—612no—
245#1783—612no—
246C2×C61—22no—
247C2×C61—22no—
248C2×C61—22no—
249C2×C61—82no—
250C2×C61#230911yescharacteristic
251C2×C61C2×#41311yescharacteristic
252C2×C61C2×#41311yescharacteristic
253D61—82no—
254C23×Q8—611no—
255C23×D4—611no—
256C2×#124—614no—
257C2×#124—614no—
258C2×#124—1222no—
259C2×#124—1222no—
260C2×#124—1222no—
261C2×#124—1222no—
262C22×C22⋊C4—611no—
263C22×C22⋊C4—611no—
264C22×C22⋊C4—611no—
265C22×C22⋊C4#692311yescharacteristic
266C22×C42—611no—
267#432—1222no—
268#432—1222no—
269#431—1222no—
270#431—1222no—
271#423—614no—
272C2×#101—618no—
273C2×#100—618no—
274#407—614no—
275C4×M16—614no—
276C61#2179811yescharacteristic, complemented, Sylow
277C25—611no—
278C25C2×#692311yescharacteristic
279C22×Q8—612no—
280C22×Q8—612no—
281C22×Q8—1222no—
282C22×Q8—1222no—
283C22×Q8—2444no—
284C22×D4—612no—
285C22×D4—612no—
286C22×D4—1222no—
287C22×D4—1222no—
288C22×D4—2444no—
289C23×C4—611no—
290C23×C4—611no—
291C23×C4—611no—
292C23×C4C2×#692311yescharacteristic
293C23×C4C2×#692311yescharacteristic
294C2×M16—618no—
295#124—1224no—
296#124—1224no—
297#124—1224no—
298#124—1224no—
299#124—1224no—
300#124—1224no—
301#124—1224no—
302#124—1224no—
303C2×C22⋊C4—22no—
304C2×C22⋊C4—21no—
305C2×C22⋊C4—21no—
306C2×C22⋊C4—614no—
307C2×C22⋊C4—614no—
308C2×C22⋊C4—614no—
309C2×C22⋊C4—1222no—
310C2×C22⋊C4—1221no—
311C2×C22⋊C4—1221no—
312C2×C22⋊C4—1222no—
313C2×C22⋊C4—1221no—
314C2×C22⋊C4—1221no—
315C2×C22⋊C4—1222no—
316C2×C22⋊C4—1221no—
317C2×C22⋊C4—1221no—
318C2×C22⋊C4C2×#692314yes—
319C2×C42—612no—
320C2×C42—612no—
321C2×C42—612no—
322C2×C42—612no—
323C2×C42—612no—
324C2×C42—612no—
325C4⋊C8—1224no—
326C4⋊C8—1224no—
327#101—2448no—
328#100—2448no—
329C22⋊C8—1224no—
330C22⋊C8—1224no—
331#97—1224no—
332C4×C8—1224no—
333C24—21no—
334C24—21no—
335C24—42no—
336C24—42no—
337C24—42no—
338C24—612no—
339C24—1221no—
340C24—1221no—
341C24—2442no—
342C24—2442no—
343C24—2442no—
344C24C22×#692311yescharacteristic
345C24C22×#692312yes—
346C2×Q8—1228no—
347C2×Q8—1224no—
348C2×Q8—1224no—
349C2×Q8—2444no—
350C2×Q8—2448no—
351C2×Q8—2448no—
352C2×D4—1228no—
353C2×D4—1224no—
354C2×D4—1224no—
355C2×D4—2444no—
356C2×D4—2448no—
357C2×D4—2448no—
358C22×C4—21no—
359C22×C4—21no—
360C22×C4—42no—
361C22×C4—42no—
362C22×C4—611no—
363C22×C4—612no—
364C22×C4—612no—
365C22×C4—612no—
366C22×C4—611no—
367C22×C4—611no—
368C22×C4—611no—
369C22×C4—612no—
370C22×C4—612no—
371C22×C4—1224no—
372C22×C4—1221no—
373C22×C4—1221no—
374C22×C4—2442no—
375C22×C4—2442no—
376C22×C4C22⋊#692312yes—
377C22×C4C22⋊#692311yescharacteristic
378C22×C4C22⋊#692311yescharacteristic
379C22×C4C22×#692312yes—
380C22×C4C22×#692312yes—
381M16—12216no—
382C2×C8—1228no—
383C22⋊C4—24no—
384C22⋊C4—24no—
385C22⋊C4—1224no—
386C22⋊C4—1224no—
387C22⋊C4—1224no—
388C22⋊C4—1224no—
389C22⋊C4—1224no—
390C22⋊C4—1224no—
391C42—612no—
392C42—612no—
393C42—612no—
394C42—612no—
395C42—612no—
396C42—612no—
397C42—612no—
398C42—612no—
399C23—22no—
400C23—22no—
401C23—22no—
402C23—22no—
403C23—24no—
404C23—42no—
405C23—42no—
406C23—42no—
407C23—42no—
408C23—42no—
409C23—42no—
410C23—42no—
411C23—42no—
412C23—88no—
413C23—1224no—
414C23—1222no—
415C23—4888no—
416C23—2442no—
417C23—2442no—
418C23—2442no—
419C23—2442no—
420C23—2442no—
421C23—2442no—
422C23—2442no—
423C23—2442no—
424C23C2×C22⋊#692311yescharacteristic
425C23C2×C22⋊#692311yescharacteristic
426C23C23×#692311yescharacteristic
427Q8—2448no—
428Q8—2448no—
429D4—2448no—
430D4—2448no—
431C2×C4—24no—
432C2×C4—22no—
433C2×C4—24no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—612no—
440C2×C4—614no—
441C2×C4—612no—
442C2×C4—612no—
443C2×C4—612no—
444C2×C4—1224no—
445C2×C4—1224no—
446C2×C4—1224no—
447C2×C4—1222no—
448C2×C4—1222no—
449C2×C4—1224no—
450C2×C4—2441no—
451C2×C4—2441no—
452C2×C4—2442no—
453C2×C4—2442no—
454C2×C4—2442no—
455C2×C4C2×C22⋊#692312yes—
456C2×C4C2×C22⋊#692312yes—
457C8—2448no—
458C22—28no—
459C22—21no—
460C22—21no—
461C22—21no—
462C22—21no—
463C22—21no—
464C22—21no—
465C22—42no—
466C22—42no—
467C22—42no—
468C22—84no—
469C22—84no—
470C22—84no—
471C22—4884no—
472C22—4884no—
473C22—4884no—
474C22—2442no—
475C22—2442no—
476C22—2442no—
477C22#1684074812yes—
478C22#1684074912yes—
479C22C22×C22⋊#692311yescharacteristic
480C22#1684082912yes—
481C4—22no—
482C4—22no—
483C4—42no—
484C4—614no—
485C4—1222no—
486C4—1222no—
487C4—1222no—
488C4—2442no—
489C2—22no—
490C2—22no—
491C2—22no—
492C2—82no—
493C2—4882no—
494C2#2146229211yescharacteristic
495C2C2×#1684074811yescharacteristic
496C2C2×#1684074911yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC22×C22⋊C4×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC23×C22⋊D61C22
cosocleC22×Dic61C24
hypercenterC22×C22⋊C4#6923
hypocenterC61#21798
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #21462495C2semidirect
2. #21461963C2semidirect
3. #21461653C2semidirect
10. #16840765C22semidirect
11. C2×#14519838C22semidirect
14. C4×#11758217C22semidirect
276. C61#21798semidirect

Maximal subgroups

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

subgroupindex
#214624952
#214619632
#214616532
#214616512
C22×#145197632
#2179861