Finite Group Databasebeta

← #30597235

Subgroups — #30597235

Order 15616.

994 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462263C211yesmaximal, characteristic
2#21462263C211yesmaximal, characteristic
3#21460718C214yesmaximal
4#21448201C211yesmaximal, characteristic
5C2×#14519856—21no—
6C2×#14519856C412yescomplemented
7#16840705—21no—
8#16840705C412yescomplemented
9#16840704—21no—
10#16840704—21no—
11#16840704—21no—
12#16840704C412yescomplemented
13#16840703C2212yes—
14#16840703C2212yes—
15C4×C22⋊#6923—21no—
16C4×C22⋊#6923—21no—
17C4×C22⋊#6923—21no—
18C4×C22⋊#6923C412yescomplemented
19C23×C4×D61C2211yescharacteristic
20C2×#14519735—21no—
21#16839624—21no—
22#16839622C411yescharacteristic, complemented
23#16839619—21no—
24#16839617C2212yes—
25C22⋊C4×Dic61C412yescomplemented
26#16839609—21no—
27C61×#380C411yescharacteristic, complemented
28#14519856—44no—
29#14519856—44no—
30C2×C4⋊#6923—22no—
31C2×C4⋊#6923—22no—
32C2×C22⋊#6923—22no—
33C2×C22⋊#6923—22no—
34C2×C22⋊#6923—22no—
35C2×C22⋊#6923—22no—
36C2×C22⋊#6923C2×C414yes—
37C2×C22⋊#6923C2×C414yes—
38C2×C4×#6923—22no—
39C2×C4×#6923—22no—
40(C2×#6923)⋊C4—22no—
41(C2×#6923)⋊C4—22no—
42(C2×#6923)⋊C4—22no—
43(C2×#6923)⋊C4—22no—
44C24×D61C2311yescharacteristic
45C23×Dic61C2×C411yescharacteristic
46C22×C4×D61—44no—
47C22×C4×D61C2×C411yescharacteristic
48C22×C4×D61C2×C411yescharacteristic
49C22×C4×D61C2×C411yescharacteristic
50C22×C4×D61C2×C411yescharacteristic
51C22×C4×D61D411yescharacteristic
52C22×C4×D61D411yescharacteristic
53C22×C4×D61D411yescharacteristic
54C22×C4×D61D411yescharacteristic
55C22×C4×D61D411yescharacteristic
56C22×C4×D61D411yescharacteristic
57C22×C4×D61Q811yescharacteristic
58C22×C4×D61Q811yescharacteristic
59#14519735—44no—
60C2×C4⋊Dic61—21no—
61C2×C22⋊Dic61C2×C412yes—
62C2×#11758198—22no—
63C2×#11758198—22no—
64C2×C4×Dic61—22no—
65#14519684—21no—
66#14519684—22no—
67C23×C4×C61C2×C411yescharacteristic
68C2×C4⋊C4×C61—21no—
69C2×C22⋊C4×C61C2×C412yes—
70#95×C61—21no—
71C24×C61C22×C411yescharacteristic
72C23×D61—42no—
73C23×D61—42no—
74C23×D61—41no—
75C23×D61—41no—
76C23×D61C22×C411yescharacteristic
77C23×D61C22×C411yescharacteristic
78C23×D61C2×D411yescharacteristic
79C23×D61C2×D411yescharacteristic
80C23×D61C2×D411yescharacteristic
81C23×D61C2×Q811yescharacteristic
82C22×#6923—24no—
83C22×#6923—24no—
84C22×C4×C61—22no—
85C22×C4×C61—42no—
86C22×C4×C61C4211yescharacteristic
87C22×C4×C61C4211yescharacteristic
88C22×C4×C61C22⋊C411yescharacteristic
89C22×C4×C61C22⋊C411yescharacteristic
90C22×C4×C61C4⋊C411yescharacteristic
91C22×C4×C61C4⋊C411yescharacteristic
92C22×Dic61—22no—
93C22×Dic61—42no—
94C22×Dic61C4211yescharacteristic
95C22×Dic61C4211yescharacteristic
96C22×Dic61C22⋊C411yescharacteristic
97C22×Dic61C22⋊C411yescharacteristic
98C22×Dic61C4⋊C411yescharacteristic
99C22×Dic61C4⋊C411yescharacteristic
100C2×C4×D61—24no—
101C2×C4×D61—24no—
102C2×C4×D61—24no—
103C2×C4×D61—42no—
104C2×C4×D61—42no—
105C2×C4×D61—42no—
106C2×C4×D61—42no—
107C2×C4×D61—42no—
108C2×C4×D61—42no—
109C2×C4×D61—42no—
110C2×C4×D61—42no—
111C2×C4×D61—42no—
112C2×C4×D61C22⋊C411yescharacteristic
113C2×C4×D61C22⋊C411yescharacteristic
114C2×C4×D61C22⋊C411yescharacteristic
115C2×C4×D61C22⋊C411yescharacteristic
116C2×C4×D61C22⋊C411yescharacteristic
117C2×C4×D61C22⋊C411yescharacteristic
118C2×C4×D61C22⋊C411yescharacteristic
119C2×C4×D61C22⋊C411yescharacteristic
120C2×C4×D61C4⋊C411yescharacteristic
121C2×C4×D61C4⋊C411yescharacteristic
122C2×C4×D61C4⋊C411yescharacteristic
123C2×C4×D61C4⋊C411yescharacteristic
124C2×C4×D61C4⋊C411yescharacteristic
125C2×C4×D61C4⋊C411yescharacteristic
126C2×C4×D61C4⋊C411yescharacteristic
127C2×C4×D61C4⋊C411yescharacteristic
128C22⋊#6923—42no—
129C22⋊#6923—42no—
130C22⋊#6923—42no—
131C22⋊#6923—42no—
132C22⋊#6923—44no—
133C22⋊#6923—44no—
134C22⋊#6923—44no—
135C22⋊#6923—44no—
136C4⋊#6923—44no—
137C4⋊#6923—44no—
138C4×#6923—44no—
139C4×#6923—44no—
140C4⋊C4×C61—42no—
141C22⋊C4×C61—42no—
142C22⋊Dic61—42no—
143#11758198—44no—
144#11758198—44no—
145C4⋊Dic61—42no—
146C4×Dic61—44no—
147C23×C61—21no—
148C23×C61—21no—
149C23×C61—41no—
150C23×C61—41no—
151C23×C61C2×C4211yescharacteristic
152C23×C61C2×C22⋊C411yescharacteristic
153C23×C61C2×C4⋊C411yescharacteristic
154C22×D61—21no—
155C22×D61—21no—
156C22×D61—21no—
157C22×D61—21no—
158C22×D61—22no—
159C22×D61—22no—
160C22×D61—22no—
161C22×D61—22no—
162C22×D61—22no—
163C22×D61—22no—
164C22×D61—41no—
165C22×D61—41no—
166C22×D61—41no—
167C22×D61—41no—
168C22×D61—41no—
169C22×D61—41no—
170C22×D61—41no—
171C22×D61—41no—
172C22×D61—41no—
173C22×D61—41no—
174C22×D61—48no—
175C22×D61—48no—
176C22×D61C2×C22⋊C411yescharacteristic
177C22×D61C2×C22⋊C411yescharacteristic
178C22×D61C2×C4⋊C411yescharacteristic
179C22×D61C2×C4⋊C411yescharacteristic
180C2×#6923—44no—
181C2×#6923—44no—
182C2×#6923—44no—
183C2×#6923—44no—
184C2×#6923—44no—
185C2×#6923—44no—
186C2×C4×C61—22no—
187C2×C4×C61—22no—
188C2×C4×C61—22no—
189C2×C4×C61—41no—
190C2×C4×C61—41no—
191C2×C4×C61—41no—
192C2×C4×C61—42no—
193C2×C4×C61—42no—
194C2×C4×C61—42no—
195C2×C4×C61#9511yescharacteristic
196C2×C4×C61#9511yescharacteristic
197C2×C4×C61#9511yescharacteristic
198C2×C4×C61#9511yescharacteristic
199C2×Dic61—22no—
200C2×Dic61—22no—
201C2×Dic61—22no—
202C2×Dic61—41no—
203C2×Dic61—41no—
204C2×Dic61—41no—
205C2×Dic61—42no—
206C2×Dic61—42no—
207C2×Dic61—42no—
208C2×Dic61#9511yescharacteristic
209C2×Dic61#9511yescharacteristic
210C2×Dic61#9511yescharacteristic
211C2×Dic61#9511yescharacteristic
212C4×D61—22no—
213C4×D61—22no—
214C4×D61—22no—
215C4×D61—22no—
216C4×D61—22no—
217C4×D61—22no—
218C4×D61—22no—
219C4×D61—22no—
220C4×D61—22no—
221C4×D61—41no—
222C4×D61—41no—
223C4×D61—41no—
224C4×D61—41no—
225C4×D61—41no—
226C4×D61—41no—
227C4×D61#9914yes—
228#8100—611nomaximal, Sylow
229C22×C61—21no—
230C22×C61—21no—
231C22×C61—21no—
232C22×C61—21no—
233C22×C61—21no—
234C22×C61—21no—
235C22×C61—21no—
236C22×C61—21no—
237C22×C61—42no—
238C22×C61—42no—
239C22×C61C2×#9511yescharacteristic
240C22×C61#41011yescharacteristic
241C22×C61#41011yescharacteristic
242C2×D61—21no—
243C2×D61—21no—
244C2×D61—21no—
245C2×D61—21no—
246C2×D61—21no—
247C2×D61—21no—
248C2×D61—21no—
249C2×D61—21no—
250C2×D61—21no—
251C2×D61—21no—
252C2×D61—44no—
253C2×D61—42no—
254C2×D61—42no—
255C2×D61—42no—
256C2×D61—42no—
257C2×D61—44no—
258C2×D61—44no—
259C2×D61—44no—
260C2×D61C2×#9912yes—
261C2×D61#41012yes—
262#6923—84no—
263#6923—84no—
264C4×C61—21no—
265C4×C61—21no—
266C4×C61—21no—
267C4×C61—82no—
268C4×C61#34212yes—
269Dic61—21no—
270Dic61—21no—
271Dic61—21no—
272Dic61—82no—
273Dic61#34212yes—
274#2280—611no—
275#2280—611no—
276#2280—611no—
277#1304—614no—
278C2×C61—21no—
279C2×C61—21no—
280C2×C61—41no—
281C2×C61—41no—
282C2×C61C2×#34211yescharacteristic
283C2×C61#174011yescharacteristic
284C2×C61#174011yescharacteristic
285D61—22no—
286D61—22no—
287D61—41no—
288D61—41no—
289C24×C4—611no—
290C2×#117—612no—
291C2×#117—1221no—
292C2×#117—1221no—
293#381—612no—
294#381—1221no—
295#381—1221no—
296#380—612no—
297#380—611no—
298#380—1221no—
299#380—1221no—
300#380—1221no—
301#380—1221no—
302#380#692311yescharacteristic, complemented
303#379—612no—
304#379—612no—
305#379—612no—
306C4×C22⋊C4—612no—
307C4×C22⋊C4—612no—
308C4×C22⋊C4—1221no—
309C4×C22⋊C4—1221no—
310C4×C22⋊C4—1221no—
311C4×C22⋊C4—1221no—
312C61#810011yescharacteristic, complemented, Sylow
313C25—611no—
314C23×C4—611no—
315C23×C4—611no—
316C23×C4—611no—
317C23×C4—611no—
318C23×C4—611no—
319C23×C4—611no—
320C23×C4—611no—
321C23×C4—611no—
322C23×C4—611no—
323C23×C4—611no—
324C23×C4—611no—
325C23×C4—611no—
326C23×C4—611no—
327C23×C4—2444no—
328C23×C4C2×#692311yescharacteristic
329#117—2444no—
330#117—2444no—
331#117—2444no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—1222no—
334C2×C4⋊C4—1222no—
335C2×C4⋊C4—1221no—
336C2×C22⋊C4—614no—
337C2×C22⋊C4—614no—
338C2×C22⋊C4—612no—
339C2×C22⋊C4—1222no—
340C2×C22⋊C4—1222no—
341C2×C22⋊C4—1222no—
342C2×C22⋊C4—1222no—
343C2×C22⋊C4—1222no—
344C2×C22⋊C4—1222no—
345C2×C22⋊C4C2×#692312yes—
346C2×C42—1222no—
347C2×C42—1222no—
348C2×C42—1222no—
349#95—21no—
350#95—1222no—
351#95—1222no—
352#95—1222no—
353#95—1222no—
354#95—1222no—
355#95—1221no—
356C24—611no—
357C24—611no—
358C24—611no—
359C24—611no—
360C24—611no—
361C24—611no—
362C24—2441no—
363C24—2441no—
364C24—2442no—
365C24—2442no—
366C24C22×#692311yescharacteristic
367C22×C4—22no—
368C22×C4—42no—
369C22×C4—611no—
370C22×C4—611no—
371C22×C4—611no—
372C22×C4—611no—
373C22×C4—611no—
374C22×C4—611no—
375C22×C4—611no—
376C22×C4—611no—
377C22×C4—611no—
378C22×C4—611no—
379C22×C4—611no—
380C22×C4—611no—
381C22×C4—611no—
382C22×C4—611no—
383C22×C4—611no—
384C22×C4—611no—
385C22×C4—611no—
386C22×C4—611no—
387C22×C4—611no—
388C22×C4—611no—
389C22×C4—611no—
390C22×C4—611no—
391C22×C4—1224no—
392C22×C4—1224no—
393C22×C4—1224no—
394C22×C4—1224no—
395C22×C4—1224no—
396C22×C4—1222no—
397C22×C4—2442no—
398C22×C4—2442no—
399C22×C4—2442no—
400C22×C4—2442no—
401C22×C4—2442no—
402C22×C4—2442no—
403C22×C4—2442no—
404C22×C4—2442no—
405C22×C4—2442no—
406C22×C4—2442no—
407C22×C4C4×#692311yescharacteristic
408C22×C4C4×#692311yescharacteristic
409C22×C4C4⋊#692311yescharacteristic
410C22×C4C4⋊#692311yescharacteristic
411C22×C4C22⋊#692311yescharacteristic
412C22×C4C22⋊#692311yescharacteristic
413C4⋊C4—42no—
414C4⋊C4—2442no—
415C4⋊C4—2444no—
416C4⋊C4—2444no—
417C22⋊C4—42no—
418C22⋊C4—2444no—
419C22⋊C4—2444no—
420C22⋊C4—2444no—
421C22⋊C4—2444no—
422C22⋊C4—2442no—
423C22⋊C4—2442no—
424C22⋊C4—2442no—
425C22⋊C4—2442no—
426C22⋊C4—2442no—
427C22⋊C4—2444no—
428C22⋊C4—2444no—
429C42—2444no—
430C42—2444no—
431C42—2444no—
432C23—21no—
433C23—21no—
434C23—41no—
435C23—41no—
436C23—611no—
437C23—611no—
438C23—611no—
439C23—611no—
440C23—1222no—
441C23—1222no—
442C23—1222no—
443C23—1222no—
444C23—1222no—
445C23—1222no—
446C23—1221no—
447C23—1221no—
448C23—1221no—
449C23—1221no—
450C23—2441no—
451C23—2441no—
452C23—2441no—
453C23—2441no—
454C23—2441no—
455C23—2441no—
456C23—2441no—
457C23—2441no—
458C23—2441no—
459C23—2441no—
460C23—2448no—
461C23—2448no—
462C23C2×C4×#692311yescharacteristic
463C23C2×C22⋊#692311yescharacteristic
464C23C2×C4⋊#692311yescharacteristic
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—611no—
475C2×C4—614no—
476C2×C4—611no—
477C2×C4—611no—
478C2×C4—611no—
479C2×C4—1222no—
480C2×C4—1222no—
481C2×C4—1222no—
482C2×C4—1222no—
483C2×C4—1222no—
484C2×C4—1222no—
485C2×C4—1222no—
486C2×C4—1222no—
487C2×C4—1222no—
488C2×C4—1222no—
489C2×C4—1222no—
490C2×C4—1222no—
491C2×C4—2441no—
492C2×C4—2441no—
493C2×C4—2441no—
494C2×C4—2441no—
495C2×C4—2441no—
496C2×C4—2441no—
497C2×C4—2441no—
498C2×C4—2441no—
499C2×C4—2441no—
500C2×C4—2442no—
501C2×C4—2442no—
502C2×C4—2444no—
503C2×C4—2444no—
504C2×C4—2444no—
505C2×C4—2444no—
506C2×C4—2444no—
507C2×C4—2444no—
508C2×C4—2442no—
509C2×C4(C2×#6923)⋊C411yescharacteristic
510C2×C4(C2×#6923)⋊C411yescharacteristic
511C2×C4(C2×#6923)⋊C411yescharacteristic
512C2×C4(C2×#6923)⋊C411yescharacteristic
513C22—21no—
514C22—21no—
515C22—21no—
516C22—21no—
517C22—21no—
518C22—21no—
519C22—21no—
520C22—21no—
521C22—42no—
522C22—42no—
523C22—612no—
524C22—612no—
525C22—1221no—
526C22—1221no—
527C22—1221no—
528C22—1221no—
529C22—1221no—
530C22—1221no—
531C22—1221no—
532C22—1221no—
533C22—1221no—
534C22—1221no—
535C22—2442no—
536C22—2442no—
537C22—2442no—
538C22—2442no—
539C22—2444no—
540C22—2444no—
541C22—2444no—
542C22—2444no—
543C22C2×(C2×#6923)⋊C411yescharacteristic
544C22#1684074211yescharacteristic
545C22#1684074311yescharacteristic
546C4—21no—
547C4—21no—
548C4—21no—
549C4—82no—
550C4—612no—
551C4—1221no—
552C4—1221no—
553C4—1221no—
554C4—4882no—
555C4—4884no—
556C4—4884no—
557C4#1684063912yes—
558C2—21no—
559C2—21no—
560C2—41no—
561C2—41no—
562C2—1222no—
563C2—1222no—
564C2—2441no—
565C2—2441no—
566C2C2×#1684063911yescharacteristic
567C2#2146151711yescharacteristic
568C2#2146151911yescharacteristic
subgroupG/H
centerC22C2×(C2×#6923)⋊C4
commutatorC23×C61C2×C42
FrattiniC24C22×#6923
FittingC61×#380C4
socleC22×C61C2×#95
prime radical, cosocleC24×D61C23
hypercenter#380#6923
hypocenterC61#8100
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
6. C2×#14519856C4semidirect
8. #16840705C4semidirect
12. #16840704C4semidirect
18. C4×C22⋊#6923C4semidirect
22. #16839622C4semidirect
25. C22⋊C4×Dic61C4semidirect
27. C61×#380C4semidirect
302. #380#6923semidirect
312. C61#8100semidirect

Maximal subgroups

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

subgroupindex
#214622632
#214607182
#214482012
#810061