Finite Group Databasebeta

← #30615877

Subgroups — #30615877

Order 15616.

1178 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840768C211yesmaximal, characteristic, complemented
2C2×#16840735C211yesmaximal, characteristic
3C2×#16840735C211yesmaximal, characteristic
4C22×C4×#92420C211yesmaximal, characteristic, complemented
5#21461891C212yesmaximal, complemented
6#21461890C212yesmaximal, complemented
7#21461889C212yesmaximal, complemented
8#21461888C212yesmaximal, complemented
9#21461485C211yesmaximal, characteristic, complemented
10#21461482C211yesmaximal, characteristic, complemented
11#21448304C211yesmaximal, characteristic
12C22×#11758217C2211yescharacteristic
13C22×#11758217C2211yescharacteristic
14C23×#92420C2211yescharacteristic
15C23×#92420C2211yescharacteristic
16#16840768—24no—
17C2×#14519844C2212yes—
18C2×C4⋊#92420C2212yes—
19#16840735—24no—
20#16840735—24no—
21C2×#14519834C2211yescharacteristic
22C2×#14519834C2212yes—
23C2×#14519834C2211yescharacteristic
24C2×C22⋊#92420C2211yescharacteristic
25C2×C22⋊#92420C2212yes—
26C2×C22⋊#92420C2211yescharacteristic
27C2×C4×#92420—24no—
28C2×C4×#92420C2212yes—
29C2×C4×#92420C2212yes—
30#16840628C2212yes—
31#16840628C2212yes—
32#16840628C2212yes—
33#16840628C2212yes—
34C22×#11758224C2211yescharacteristic
35C2×#14519733C2211yescharacteristic
36C22×C4×Dic61C2211yescharacteristic
37#16839666C412yes—
38#16839662C412yes—
39#16839642C411yescharacteristic
40#16839641C411yescharacteristic
41#16839639C411yescharacteristic
42C22⋊C4×Dic61C2212yes—
43#16839609C2212yes—
44C61×#386C411yescharacteristic
45C2×#11758217—22no—
46C2×#11758217—22no—
47C2×#11758217—22no—
48C2×#11758217—22no—
49C2×#11758217—22no—
50C2×#11758217—22no—
51C22×#92420—22no—
52C22×#92420—22no—
53C22×#92420—22no—
54C22×#92420—22no—
55C22×#92420D414yes—
56C22×#92420D414yes—
57C22×#92420C2311yescharacteristic
58C22×#92420C2311yescharacteristic
59C22×#92420C2312yes—
60C22×#92420C2312yes—
61C22×#92420C2311yescharacteristic
62C22×#92420C2311yescharacteristic
63#14519844—24no—
64C4⋊#92420—24no—
65#14519834—22no—
66#14519834—22no—
67#14519834—24no—
68C22⋊#92420—22no—
69C22⋊#92420—22no—
70C22⋊#92420—24no—
71C4×#92420—24no—
72C4×#92420—24no—
73C2×#11758224—22no—
74C2×#11758224—22no—
75C2×#11758224—22no—
76C2×#11758224—22no—
77C2×#11758224—22no—
78C2×#11758224—22no—
79C22×Dic122C2×C411yescharacteristic
80C22×C22⋊D61C2×C411yescharacteristic
81C22×C22⋊D61C2×C411yescharacteristic
82C23×Dic61C2×C411yescharacteristic
83C23×Dic61C2311yescharacteristic
84C23×Dic61C2311yescharacteristic
85C22×C4×D61C2311yescharacteristic
86#14519733—22no—
87#14519733—22no—
88C2×#11758196C2×C412yes—
89C2×C22⋊Dic61C2×C411yescharacteristic
90C2×C22⋊Dic61C2×C412yes—
91C2×#11758198C2×C412yes—
92C2×#11758198C2×C412yes—
93C2×C4×Dic61—22no—
94C2×C4×Dic61—22no—
95C2×C4×Dic61C2×C412yes—
96C2×C4×Dic61C2312yes—
97C2×C4×Dic61C2312yes—
98#14519684C2×C412yes—
99#14519684C2×C412yes—
100#14519684C2×C412yes—
101C22×D4×C61C2×C411yescharacteristic
102C23×C4×C61C2×C411yescharacteristic
103C2×C22⋊C4×C61C2×C411yescharacteristic
104C2×C22⋊C4×C61C2×C412yes—
105#95×C61C2×C412yes—
106C24×C61C22×C411yescharacteristic
107C24×C61C22×C411yescharacteristic
108C23×D61C22×C411yescharacteristic
109C2×D4×C61—22no—
110C2×D4×C61—22no—
111C2×D4×C61—22no—
112C22×C4×C61—22no—
113C22×C4×C61—24no—
114C22×C4×C61C22×C411yescharacteristic
115C22×C4×C61C22×C412yes—
116C22×C4×C61C22×C412yes—
117C2×C22⋊D61—22no—
118C2×C22⋊D61—22no—
119C2×C22⋊D61—22no—
120C2×C22⋊D61—22no—
121C2×C22⋊D61—22no—
122C2×C22⋊D61—22no—
123C22×Dic61—22no—
124C22×Dic61—24no—
125C22×Dic61—21no—
126C22×Dic61—21no—
127C22×Dic61—21no—
128C22×Dic61—21no—
129C22×Dic61—21no—
130C22×Dic61—21no—
131C22×Dic61C22×C411yescharacteristic
132C22×Dic61C22×C412yes—
133C22×Dic61C22×C412yes—
134C22×Dic61C22×C411yescharacteristic
135C22×Dic61C2×D412yes—
136C22×Dic61C2×D412yes—
137C22×Dic61#4112yes—
138C22×Dic61#4112yes—
139C22×Dic61#4112yes—
140C22×Dic61#4112yes—
141C22×Dic61C2411yescharacteristic
142#11758224—44no—
143#11758224—44no—
144#11758224—44no—
145#11758224—44no—
146C2×C4×D61—21no—
147C2×C4×D61—21no—
148C2×C4×D61—21no—
149C2×C4×D61—21no—
150C2×C4×D61—21no—
151C2×C4×D61—21no—
152C2×Dic122—22no—
153C2×Dic122—22no—
154C2×Dic122—22no—
155#11758217—44no—
156#11758217—44no—
157C2×#92420—28no—
158C2×#92420—28no—
159C2×#92420—22no—
160C2×#92420—22no—
161C2×#92420—21no—
162C2×#92420—21no—
163C2×#92420—21no—
164C2×#92420—21no—
165C2×#92420—21no—
166C2×#92420—21no—
167C2×#92420—22no—
168C2×#92420—21no—
169C2×#92420—21no—
170C2×#92420—21no—
171C2×#92420—21no—
172C2×#92420—22no—
173C2×#92420—22no—
174C2×#92420C2×D412yes—
175C2×#92420C2×D412yes—
176C2×#92420C2×D414yes—
177C22⋊C4×C61—22no—
178C22⋊C4×C61—24no—
179C22⋊Dic61—22no—
180C22⋊Dic61—24no—
181#11758198—24no—
182#11758198—24no—
183#11758196—24no—
184C4×Dic61—24no—
185C4×Dic61—22no—
186C4×Dic61—22no—
187C4×Dic61—22no—
188C4×Dic61—22no—
189C23×C61—22no—
190C23×C61—22no—
191C23×C61—21no—
192C23×C61—21no—
193C23×C61—21no—
194C23×C61—22no—
195C23×C61—22no—
196C23×C61#11712yes—
197C23×C61C4×D412yes—
198C23×C61C4×D412yes—
199C23×C61C23×C411yescharacteristic
200C22×D61—21no—
201C22×D61—21no—
202C22×D61—21no—
203C22×D61—22no—
204C22×D61—22no—
205D4×C61—44no—
206C2×C4×C61—28no—
207C2×C4×C61—22no—
208C2×C4×C61—22no—
209C2×C4×C61—21no—
210C2×C4×C61—22no—
211C2×C4×C61—21no—
212C2×C4×C61—21no—
213C2×C4×C61—22no—
214C2×C4×C61—22no—
215C2×C4×C61#13114yes—
216C22⋊D61—44no—
217C22⋊D61—44no—
218C2×Dic61—28no—
219C2×Dic61—22no—
220C2×Dic61—22no—
221C2×Dic61—21no—
222C2×Dic61—22no—
223C2×Dic61—21no—
224C2×Dic61—21no—
225C2×Dic61—22no—
226C2×Dic61—22no—
227C2×Dic61—41no—
228C2×Dic61—41no—
229C2×Dic61—41no—
230C2×Dic61—41no—
231C2×Dic61#11712yes—
232C2×Dic61C4×D412yes—
233C2×Dic61C4×D412yes—
234C2×Dic61#12114yes—
235C2×Dic61#12314yes—
236C2×Dic61#12414yes—
237C2×Dic61#12614yes—
238C2×Dic61#13114yes—
239C2×Dic61C22×D411yescharacteristic
240C2×Dic61C22×D411yescharacteristic
241C2×Dic61C2×#4111yescharacteristic
242C2×Dic61C2×#4111yescharacteristic
243C2×Dic61C2×#4111yescharacteristic
244C2×Dic61C2×#4111yescharacteristic
245C4×D61—41no—
246C4×D61—41no—
247C4×D61—41no—
248C4×D61—41no—
249Dic122—44no—
250#92420—24no—
251#92420—22no—
252#92420—22no—
253#92420—41no—
254#92420—41no—
255#92420—42no—
256#21046—611nomaximal, Sylow
257C22×C61—24no—
258C22×C61—22no—
259C22×C61—22no—
260C22×C61—24no—
261C22×C61—42no—
262C22×C61—41no—
263C22×C61—41no—
264C22×C61—42no—
265C22×C61—41no—
266C22×C61#38814yes—
267C22×C61C2×#11711yescharacteristic
268C22×C61C2×C4×D411yescharacteristic
269C22×C61C2×C4×D411yescharacteristic
270C22×C61C2×#13112yes—
271C22×C61C2×#13112yes—
272C2×D61—42no—
273C2×D61—41no—
274C2×D61—41no—
275C2×D61—42no—
276C2×D61—41no—
277C4×C61—24no—
278C4×C61—42no—
279C4×C61—41no—
280Dic61—24no—
281Dic61—42no—
282Dic61—41no—
283Dic61#38814yes—
284Dic61C2×#12111yescharacteristic
285Dic61C2×#12311yescharacteristic
286Dic61C2×#12411yescharacteristic
287Dic61C2×#12611yescharacteristic
288C2×#424—611no—
289C2×#408—611no—
290C2×#408—611no—
291C22×C4×C8—611no—
292#2297—611no—
293#1923—612no—
294#1923—612no—
295#1923—612no—
296#1923—612no—
297#1729—611no—
298#1728—611no—
299C2×C61—24no—
300C2×C61—81no—
301C2×C61C2×#38811yescharacteristic
302C2×C61#292212yes—
303C2×C61#292911yescharacteristic
304C2×C61#292911yescharacteristic
305C2×C61#293112yes—
306D61—81no—
307C22×#41—611no—
308C22×M16—611no—
309C22×M16—611no—
310C23×C8—611no—
311C23×C8—611no—
312C2×#117—611no—
313C22×C42—611no—
314#424—1224no—
315C2×C4⋊C8—612no—
316C2×C4⋊C8—612no—
317#408—1224no—
318#408—1224no—
319C2×C22⋊C8—611no—
320C2×C22⋊C8—611no—
321C2×C22⋊C8—612no—
322C2×C22⋊C8—611no—
323C2×C22⋊C8—611no—
324C2×C22⋊C8—612no—
325C2×C4×C8—612no—
326C2×C4×C8—612no—
327C2×C4×C8—1224no—
328#391—612no—
329#390—612no—
330#386—611no—
331#386—611no—
332#386—611no—
333#386#692311yescharacteristic
334C4×C22⋊C4—612no—
335C4×C22⋊C4—612no—
336#336—612no—
337#336—612no—
338#336—612no—
339#336—612no—
340C61#2104611yescharacteristic, complemented, Sylow
341C2×#41—1222no—
342C2×#41—1222no—
343C2×#41—1222no—
344C2×#41—1222no—
345C2×#41—1222no—
346C2×#41—1222no—
347C22×Q8—611no—
348C22×D4—611no—
349C22×D4—611no—
350C22×D4C2×#692311yescharacteristic
351C23×C4—611no—
352C23×C4—611no—
353C23×C4—611no—
354C23×C4—611no—
355C23×C4C2×#692311yescharacteristic
356C2×M16—1222no—
357C2×M16—1222no—
358C2×M16—1222no—
359C2×M16—1222no—
360C2×M16—1222no—
361C2×M16—1222no—
362C22×C8—614no—
363C22×C8—614no—
364C22×C8—611no—
365C22×C8—611no—
366C22×C8—612no—
367C22×C8—612no—
368C22×C8—611no—
369C22×C8—611no—
370C22×C8—1222no—
371C22×C8—1222no—
372C22×C8—1222no—
373C22×C8—1222no—
374#117—1222no—
375#117—1222no—
376C2×C4⋊C4—612no—
377C2×C22⋊C4—611no—
378C2×C22⋊C4—612no—
379C2×C22⋊C4—612no—
380C2×C22⋊C4—612no—
381C2×C22⋊C4C2×#692311yescharacteristic
382C2×C22⋊C4C2×#692312yes—
383C2×C42—612no—
384C2×C42—612no—
385C2×C42—612no—
386C2×C42—1222no—
387C2×C42—1222no—
388C4⋊C8—1224no—
389C4⋊C8—1224no—
390C22⋊C8—1222no—
391C22⋊C8—1222no—
392C22⋊C8—1224no—
393C22⋊C8—1222no—
394C22⋊C8—1222no—
395C22⋊C8—1224no—
396C4×C8—1224no—
397C4×C8—1224no—
398#95—612no—
399#95—612no—
400#95—612no—
401#95C2×#692312yes—
402C24—611no—
403C24C22×#692311yescharacteristic
404C24C22×#692311yescharacteristic
405#41—2444no—
406#41—2444no—
407#41—2444no—
408#41—2444no—
409C2×Q8—1222no—
410C2×Q8—1222no—
411C2×Q8—1222no—
412C2×D4—22no—
413C2×D4—22no—
414C2×D4—22no—
415C2×D4—1222no—
416C2×D4—1222no—
417C2×D4—1222no—
418C2×D4—1222no—
419C2×D4—1222no—
420C2×D4—1222no—
421C22×C4—22no—
422C22×C4—24no—
423C22×C4—612no—
424C22×C4—612no—
425C22×C4—612no—
426C22×C4—612no—
427C22×C4—612no—
428C22×C4—612no—
429C22×C4—611no—
430C22×C4—611no—
431C22×C4—612no—
432C22×C4—611no—
433C22×C4—612no—
434C22×C4—1221no—
435C22×C4—1221no—
436C22×C4—1221no—
437C22×C4—1221no—
438C22×C4—1221no—
439C22×C4—1221no—
440C22×C4—1224no—
441C22×C4—1221no—
442C22×C4—1221no—
443C22×C4—1221no—
444C22×C4—1221no—
445C22×C4—1221no—
446C22×C4—1221no—
447C22×C4—1222no—
448C22×C4C22×#692311yescharacteristic
449C22×C4C22×#692312yes—
450C22×C4C22×#692312yes—
451M16—2444no—
452M16—2444no—
453C2×C8—612no—
454C2×C8—612no—
455C2×C8—614no—
456C2×C8—1222no—
457C2×C8—1228no—
458C2×C8—1228no—
459C2×C8—1221no—
460C2×C8—1221no—
461C2×C8—1222no—
462C2×C8—1221no—
463C2×C8—1221no—
464C2×C8—1222no—
465C2×C8—1221no—
466C2×C8—1221no—
467C2×C8—1221no—
468C2×C8—1221no—
469C2×C8—1222no—
470C2×C8—1221no—
471C2×C8—1221no—
472C2×C8—1222no—
473C4⋊C4—1224no—
474C22⋊C4—22no—
475C22⋊C4—24no—
476C22⋊C4—1224no—
477C22⋊C4—1224no—
478C22⋊C4—1222no—
479C22⋊C4—1224no—
480C42—1222no—
481C42—1222no—
482C42—1224no—
483C42—1222no—
484C42—1222no—
485C23—22no—
486C23—22no—
487C23—21no—
488C23—21no—
489C23—21no—
490C23—22no—
491C23—22no—
492C23—1221no—
493C23—1221no—
494C23—1221no—
495C23—1222no—
496C23—1222no—
497C23#1451985612yes—
498C23D4×#692312yes—
499C23D4×#692312yes—
500C23C23×#692311yescharacteristic
501Q8—2444no—
502D4—44no—
503D4—2444no—
504D4—2444no—
505C2×C4—28no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—21no—
509C2×C4—22no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—614no—
515C2×C4—614no—
516C2×C4—614no—
517C2×C4—614no—
518C2×C4—612no—
519C2×C4—611no—
520C2×C4—611no—
521C2×C4—612no—
522C2×C4—612no—
523C2×C4—611no—
524C2×C4—611no—
525C2×C4—611no—
526C2×C4—611no—
527C2×C4—614no—
528C2×C4—1228no—
529C2×C4—1222no—
530C2×C4—1222no—
531C2×C4—1221no—
532C2×C4—1222no—
533C2×C4—1221no—
534C2×C4—1221no—
535C2×C4—1222no—
536C2×C4—1222no—
537C2×C4—2441no—
538C2×C4—2441no—
539C2×C4—2441no—
540C2×C4—2441no—
541C2×C4—2441no—
542C2×C4—2441no—
543C2×C4—2441no—
544C2×C4—2441no—
545C2×C4#1451986414yes—
546C8—1224no—
547C8—1222no—
548C8—1222no—
549C8—2441no—
550C8—2441no—
551C8—2442no—
552C22—22no—
553C22—22no—
554C22—24no—
555C22—24no—
556C22—41no—
557C22—41no—
558C22—41no—
559C22—42no—
560C22—42no—
561C22—2441no—
562C22—2441no—
563C22—2441no—
564C22—2442no—
565C22—2442no—
566C22#1684071214yes—
567C22C2×#1451985611yescharacteristic
568C22C2×D4×#692311yescharacteristic
569C22C2×D4×#692311yescharacteristic
570C22C2×#1451986412yes—
571C22D61⋊#13112yes—
572C4—24no—
573C4—41no—
574C4—42no—
575C4—611no—
576C4—611no—
577C4—611no—
578C4—611no—
579C4—614no—
580C4—1224no—
581C4—2441no—
582C4—2442no—
583C2—24no—
584C2—81no—
585C2—4881no—
586C2C2×#1684071211yescharacteristic
587C2#2146250212yes—
588C2#2146253411yescharacteristic
589C2#2146253611yescharacteristic
590C2#2146254212yes—
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC61×#386C4
prime radicalC22×#11758224C22
cosocleC22×Dic61C24
hypercenter#386#6923
hypocenterC61#21046
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
1. C2×#16840768C2semidirect
4. C22×C4×#92420C2semidirect
5. #21461891C2semidirect
6. #21461890C2semidirect
7. #21461889C2semidirect
8. #21461888C2semidirect
9. #21461485C2semidirect
10. #21461482C2semidirect
340. C61#21046semidirect

Maximal subgroups

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

subgroupindex
C2×#168407682
C2×#168407352
C22×C4×#924202
#214618912
#214618902
#214618892
#214618882
#214614852
#214614822
#214483042
#2104661