Finite Group Databasebeta

← #30615164

Subgroups — #30615164

Order 15616.

1350 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840782C211yesmaximal, characteristic, complemented
2C2×#16840779C211yesmaximal, characteristic, complemented
3#21461712C212yesmaximal, complemented
4#21461676C212yesmaximal, complemented
5#21461675C212yesmaximal, complemented
6#21461643C212yesmaximal
7#21461549C212yesmaximal, complemented
8#21461548C212yesmaximal, complemented
9C2×C4×#11758224C211yesmaximal, characteristic
10#16840782—24no—
11#16840779—24no—
12C2×#14519844C2212yes—
13C2×#14519844C2212yes—
14C2×#14519834C2214yes—
15C2×C22⋊#92420C2214yes—
16C2×C22⋊#92420C2212yes—
17C2×C22⋊#92420C2212yes—
18C2×#14519832C2212yes—
19C2×C4×#92420C2212yes—
20#16840628C2214yes—
21#16840628C2214yes—
22C22×#11758224C2211yescharacteristic
23C4×#11758224—24no—
24C4×#11758224—24no—
25C2×C4×Dic122C411yescharacteristic
26C2×#14519742C411yescharacteristic
27C2×D4×Dic61C411yescharacteristic
28C2×C4×C22⋊D61C411yescharacteristic
29C2×C4×C22⋊D61C411yescharacteristic
30C2×#14519737C411yescharacteristic
31C2×#14519737C411yescharacteristic
32C2×#14519735C2211yescharacteristic
33C2×#14519733C2211yescharacteristic
34C2×#14519733C2211yescharacteristic
35C22×C4×Dic61C2211yescharacteristic
36C22×C4×Dic61C2211yescharacteristic
37C2×C42×D61C2211yescharacteristic
38C2×C4×D4×C61C411yescharacteristic
39C22×#92420C2314yes—
40C22×#92420C2314yes—
41#14519844—24no—
42#14519844—24no—
43#14519834—28no—
44C22⋊#92420—24no—
45C22⋊#92420—24no—
46C22⋊#92420—28no—
47#14519832—24no—
48C4×#92420—24no—
49C2×#11758224—22no—
50C2×#11758224—22no—
51C2×#11758224—24no—
52C2×#11758224—24no—
53C22×Dic122C2×C411yescharacteristic
54C22×C22⋊D61C2×C411yescharacteristic
55C22×C22⋊D61C2×C411yescharacteristic
56C23×Dic61C2×C411yescharacteristic
57C23×Dic61C2×C411yescharacteristic
58C23×Dic61C2311yescharacteristic
59C23×Dic61C2311yescharacteristic
60C22×C4×D61C2×C411yescharacteristic
61C22×C4×D61C2×C411yescharacteristic
62C22×C4×D61C2311yescharacteristic
63C4×Dic122—24no—
64#14519742—24no—
65D4×Dic61—24no—
66C4×C22⋊D61—24no—
67C4×C22⋊D61—24no—
68#14519737—24no—
69#14519737—24no—
70#14519735—22no—
71#14519735—22no—
72#14519733—22no—
73#14519733—22no—
74#14519733—22no—
75#14519733—22no—
76C2×C4⋊Dic61C2×C411yescharacteristic
77C2×#11758196C2×C411yescharacteristic
78C2×#11758196C2×C411yescharacteristic
79C2×#11758196C2×C411yescharacteristic
80C2×#11758196C2×C411yescharacteristic
81C2×C22⋊Dic61C2×C411yescharacteristic
82C2×C22⋊Dic61C2×C411yescharacteristic
83C2×#11758198C2×C411yescharacteristic
84C2×#11758198C2×C411yescharacteristic
85C2×C4×Dic61—22no—
86C2×C4×Dic61—22no—
87C2×C4×Dic61C2×C411yescharacteristic
88C2×C4×Dic61C2×C411yescharacteristic
89C2×C4×Dic61C2×C411yescharacteristic
90C2×C4×Dic61C2×C411yescharacteristic
91C2×C4×Dic61C2×C411yescharacteristic
92C2×C4×Dic61D414yes—
93C2×C4×Dic61D414yes—
94C2×C4×Dic61C2311yescharacteristic
95C2×C4×Dic61C2311yescharacteristic
96C2×C4×Dic61C2311yescharacteristic
97C2×C4×Dic61C2311yescharacteristic
98C42×D61—22no—
99C42×D61—22no—
100C22×D4×C61C2×C411yescharacteristic
101C23×C4×C61C2×C411yescharacteristic
102C23×C4×C61C2×C411yescharacteristic
103C4×D4×C61—24no—
104C2×C4⋊C4×C61C2×C411yescharacteristic
105C2×C22⋊C4×C61C2×C411yescharacteristic
106C2×C22⋊C4×C61C2×C411yescharacteristic
107C2×C42×C61C2×C411yescharacteristic
108C24×C61C22×C411yescharacteristic
109C24×C61C22×C411yescharacteristic
110C23×D61C22×C411yescharacteristic
111C2×D4×C61—22no—
112C2×D4×C61—22no—
113C2×D4×C61—22no—
114C22×C4×C61—22no—
115C22×C4×C61—42no—
116C22×C4×C61—42no—
117C22×C4×C61C22⋊C414yes—
118C22×C4×C61C22×C411yescharacteristic
119C22×C4×C61C22×C411yescharacteristic
120C22×C4×C61C22×C411yescharacteristic
121C22×C4×C61C22×C411yescharacteristic
122C22×C4×C61C22×C411yescharacteristic
123C2×C22⋊D61—22no—
124C2×C22⋊D61—22no—
125C2×C22⋊D61—22no—
126C2×C22⋊D61—22no—
127C2×C22⋊D61—22no—
128C2×C22⋊D61—22no—
129C22×Dic61—24no—
130C22×Dic61—21no—
131C22×Dic61—21no—
132C22×Dic61—22no—
133C22×Dic61—22no—
134C22×Dic61—22no—
135C22×Dic61—22no—
136C22×Dic61—24no—
137C22×Dic61C22⋊C414yes—
138C22×Dic61C22×C411yescharacteristic
139C22×Dic61C22×C411yescharacteristic
140C22×Dic61C22×C411yescharacteristic
141C22×Dic61C22×C411yescharacteristic
142C22×Dic61C22×C411yescharacteristic
143C22×Dic61C22×C411yescharacteristic
144C22×Dic61C2×D412yes—
145C22×Dic61C2×D412yes—
146C22×Dic61#4114yes—
147C22×Dic61C2411yescharacteristic
148#11758224—216no—
149#11758224—216no—
150C2×C4×D61—21no—
151C2×C4×D61—21no—
152C2×C4×D61—22no—
153C2×C4×D61—22no—
154C2×C4×D61—22no—
155C2×C4×D61—24no—
156C2×C4×D61—42no—
157C2×C4×D61#4114yes—
158C2×Dic122—22no—
159C2×Dic122—22no—
160C2×Dic122—22no—
161C2×#92420—24no—
162C2×#92420—24no—
163C2×#92420—24no—
164C2×#92420—24no—
165C2×#92420—24no—
166C2×#92420—24no—
167C4⋊C4×C61—22no—
168C22⋊C4×C61—22no—
169C22⋊C4×C61—22no—
170C42×C61—22no—
171C22⋊Dic61—22no—
172C22⋊Dic61—22no—
173#11758198—22no—
174#11758198—22no—
175C4⋊Dic61—22no—
176#11758196—22no—
177#11758196—22no—
178#11758196—22no—
179#11758196—22no—
180C4×Dic61—22no—
181C4×Dic61—22no—
182C4×Dic61—22no—
183C4×Dic61—21no—
184C4×Dic61—21no—
185C4×Dic61—21no—
186C4×Dic61—21no—
187C4×Dic61C22⋊C414yes—
188C4×Dic61C22⋊C414yes—
189C4×Dic61C2×D412yes—
190C4×Dic61C2×D412yes—
191C4×Dic61C2×D412yes—
192C4×Dic61C2×D412yes—
193C23×C61—21no—
194C23×C61—21no—
195C23×C61—21no—
196C23×C61—21no—
197C23×C61—22no—
198C23×C61—22no—
199C23×C61—22no—
200C23×C61—22no—
201C23×C61C2×C22⋊C412yes—
202C23×C61#11712yes—
203C23×C61C23×C411yescharacteristic
204C22×D61—21no—
205C22×D61—21no—
206C22×D61—22no—
207C22×D61—22no—
208C22×D61#11712yes—
209D4×C61—28no—
210C2×C4×C61—21no—
211C2×C4×C61—21no—
212C2×C4×C61—22no—
213C2×C4×C61—22no—
214C2×C4×C61—21no—
215C2×C4×C61—21no—
216C2×C4×C61—22no—
217C2×C4×C61—22no—
218C2×C4×C61—44no—
219C2×C4×C61—44no—
220C2×C4×C61C2×C22⋊C412yes—
221C2×C4×C61C2×C22⋊C412yes—
222C2×C4×C61#11712yes—
223C22⋊D61—28no—
224C22⋊D61—28no—
225C2×Dic61—21no—
226C2×Dic61—21no—
227C2×Dic61—21no—
228C2×Dic61—21no—
229C2×Dic61—22no—
230C2×Dic61—24no—
231C2×Dic61—24no—
232C2×Dic61—24no—
233C2×Dic61—24no—
234C2×Dic61—28no—
235C2×Dic61—21no—
236C2×Dic61—21no—
237C2×Dic61—22no—
238C2×Dic61—22no—
239C2×Dic61—44no—
240C2×Dic61C2×C22⋊C412yes—
241C2×Dic61C2×C22⋊C412yes—
242C2×Dic61C2×C22⋊C412yes—
243C2×Dic61#11712yes—
244C2×Dic61#13114yes—
245C2×Dic61C22×D411yescharacteristic
246C2×Dic61C22×D411yescharacteristic
247C2×Dic61C2×#4112yes—
248C2×Dic61C2×#4112yes—
249C4×D61—24no—
250C4×D61—24no—
251C4×D61—44no—
252C4×D61—44no—
253Dic122—28no—
254#92420—44no—
255#92420—44no—
256#20721—611nomaximal, Sylow
257C22×C61—22no—
258C22×C61—22no—
259C22×C61—24no—
260C22×C61—22no—
261C22×C61—22no—
262C22×C61—41no—
263C22×C61—41no—
264C22×C61—42no—
265C22×C61—42no—
266C22×C61—42no—
267C22×C61C22×C22⋊C411yescharacteristic
268C22×C61C2×#11711yescharacteristic
269C22×C61C2×#11711yescharacteristic
270C22×C61C2×#13112yes—
271C22×C61#56812yes—
272C2×D61—24no—
273C2×D61—22no—
274C2×D61—41no—
275C2×D61—41no—
276C2×D61—42no—
277C4×C61—22no—
278C4×C61—22no—
279C4×C61—22no—
280C4×C61—41no—
281C4×C61—41no—
282Dic61—22no—
283Dic61—22no—
284Dic61—22no—
285Dic61—41no—
286Dic61—41no—
287Dic61#40814yes—
288Dic61#52512yes—
289Dic61#52512yes—
290C2×C4×#41—611no—
291C2×#432—611no—
292C2×#431—611no—
293#1818—612no—
294#1797—612no—
295#1797—612no—
296#1780—612no—
297#1750—612no—
298#1750—612no—
299C2×C61—42no—
300C2×C61—42no—
301C2×C61#228011yescharacteristic
302C2×C61C2×#40811yescharacteristic
303C2×C61#287911yescharacteristic
304C2×C61#292512yes—
305C2×C61#292512yes—
306D61—42no—
307C22×#41—611no—
308C4×#41—1224no—
309C4×#41—1224no—
310C2×C4×Q8—611no—
311C2×C4×Q8—611no—
312C2×C4×D4—611no—
313C2×C4×D4—611no—
314C2×C4×D4—611no—
315C2×C4×D4—611no—
316C2×C4×D4—611no—
317C2×C4×D4#692311yescharacteristic
318C2×#117—611no—
319C2×#117—611no—
320C2×#117—611no—
321C22×C42—611no—
322C22×C42—611no—
323C22×C42—611no—
324#432—1224no—
325#431—1224no—
326C2×C4⋊C8—612no—
327C2×C4⋊C8—612no—
328C2×C22⋊C8—614no—
329C2×C22⋊C8—614no—
330C2×C22⋊C8—612no—
331C2×C22⋊C8—612no—
332C2×#97—612no—
333C2×C4×C8—612no—
334#336—614no—
335#336—614no—
336C61#2072111yescharacteristic, complemented, Sylow
337C2×#41—1222no—
338C2×#41—1222no—
339C2×#41—1224no—
340C2×#41—1224no—
341C22×Q8—611no—
342C22×D4—611no—
343C22×D4—611no—
344C22×D4C2×#692311yescharacteristic
345C23×C4—611no—
346C23×C4—611no—
347C23×C4—611no—
348C23×C4—611no—
349C23×C4—611no—
350C23×C4—611no—
351C23×C4—611no—
352C23×C4C2×#692311yescharacteristic
353C23×C4C2×#692311yescharacteristic
354C22×C8—614no—
355C22×C8—614no—
356C4×Q8—1224no—
357C4×Q8—1224no—
358C4×D4—24no—
359C4×D4—1224no—
360C4×D4—1224no—
361C4×D4—1224no—
362C4×D4—1224no—
363C4×D4—1224no—
364#117—1222no—
365#117—1222no—
366#117—1222no—
367#117—1222no—
368#117—1222no—
369#117—1222no—
370C2×C4⋊C4—611no—
371C2×C4⋊C4—611no—
372C2×C4⋊C4—611no—
373C2×C4⋊C4—611no—
374C2×C4⋊C4—611no—
375C2×C4⋊C4C2×#692311yescharacteristic
376C2×C22⋊C4—611no—
377C2×C22⋊C4—611no—
378C2×C22⋊C4—611no—
379C2×C22⋊C4—611no—
380C2×C22⋊C4C2×#692311yescharacteristic
381C2×C22⋊C4C2×#692311yescharacteristic
382C2×C42—614no—
383C2×C42—614no—
384C2×C42—611no—
385C2×C42—611no—
386C2×C42—611no—
387C2×C42—611no—
388C2×C42—611no—
389C2×C42—611no—
390C2×C42—611no—
391C2×C42—611no—
392C2×C42—611no—
393C2×C42—1222no—
394C2×C42—1222no—
395C2×C42—1222no—
396C2×C42—1222no—
397C2×C42C2×#692311yescharacteristic
398C4⋊C8—1224no—
399C4⋊C8—1224no—
400C22⋊C8—1228no—
401C22⋊C8—1224no—
402C22⋊C8—1224no—
403C22⋊C8—1228no—
404#97—1224no—
405C4×C8—1224no—
406C24—611no—
407C24C22×#692311yescharacteristic
408C24C22×#692311yescharacteristic
409#41—12216no—
410#41—12216no—
411C2×Q8—1222no—
412C2×Q8—1222no—
413C2×Q8—1222no—
414C2×D4—22no—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—1222no—
418C2×D4—1222no—
419C2×D4—1222no—
420C2×D4—1222no—
421C2×D4—1222no—
422C2×D4—1222no—
423C22×C4—22no—
424C22×C4—42no—
425C22×C4—42no—
426C22×C4—611no—
427C22×C4—611no—
428C22×C4—612no—
429C22×C4—612no—
430C22×C4—614no—
431C22×C4—614no—
432C22×C4—611no—
433C22×C4—611no—
434C22×C4—611no—
435C22×C4—614no—
436C22×C4—611no—
437C22×C4—611no—
438C22×C4—1221no—
439C22×C4—1221no—
440C22×C4—1222no—
441C22×C4—1222no—
442C22×C4—1224no—
443C22×C4—1221no—
444C22×C4—1221no—
445C22×C4—1222no—
446C22×C4—1222no—
447C22×C4—1222no—
448C22×C4—1224no—
449C22×C4—1222no—
450C22×C4—1224no—
451C22×C4—1222no—
452C22×C4—2442no—
453C22×C4C22⋊#692314yes—
454C22×C4C22×#692311yescharacteristic
455C22×C4C22×#692311yescharacteristic
456C22×C4C22×#692311yescharacteristic
457C22×C4C22×#692311yescharacteristic
458C22×C4C22×#692311yescharacteristic
459C2×C8—1224no—
460C2×C8—1224no—
461C2×C8—1224no—
462C2×C8—1224no—
463C2×C8—1224no—
464C2×C8—1224no—
465C4⋊C4—22no—
466C4⋊C4—1222no—
467C4⋊C4—1222no—
468C4⋊C4—1222no—
469C4⋊C4—1222no—
470C4⋊C4—1222no—
471C22⋊C4—22no—
472C22⋊C4—22no—
473C22⋊C4—1222no—
474C22⋊C4—1222no—
475C22⋊C4—1222no—
476C22⋊C4—1222no—
477C42—22no—
478C42—612no—
479C42—612no—
480C42—612no—
481C42—612no—
482C42—614no—
483C42—614no—
484C42—1221no—
485C42—1221no—
486C42—1221no—
487C42—1221no—
488C42—1222no—
489C42—1222no—
490C42—1222no—
491C23—21no—
492C23—21no—
493C23—21no—
494C23—21no—
495C23—22no—
496C23—22no—
497C23—22no—
498C23—22no—
499C23—612no—
500C23—1221no—
501C23—1221no—
502C23—1222no—
503C23—1222no—
504C23C2×C22⋊#692312yes—
505C23#1451985612yes—
506C23C23×#692311yescharacteristic
507Q8—1228no—
508D4—28no—
509D4—1228no—
510D4—1228no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—44no—
520C2×C4—44no—
521C2×C4—612no—
522C2×C4—611no—
523C2×C4—611no—
524C2×C4—612no—
525C2×C4—612no—
526C2×C4—614no—
527C2×C4—612no—
528C2×C4—612no—
529C2×C4—612no—
530C2×C4—1224no—
531C2×C4—1224no—
532C2×C4—1228no—
533C2×C4—1224no—
534C2×C4—1224no—
535C2×C4—1224no—
536C2×C4—1224no—
537C2×C4—1221no—
538C2×C4—1221no—
539C2×C4—1221no—
540C2×C4—1221no—
541C2×C4—1222no—
542C2×C4—1221no—
543C2×C4—1221no—
544C2×C4—1222no—
545C2×C4—1222no—
546C2×C4—2444no—
547C2×C4—2444no—
548C2×C4—2444no—
549C2×C4C2×C22⋊#692312yes—
550C2×C4C2×C22⋊#692312yes—
551C2×C4#1451985612yes—
552C8—2444no—
553C8—2444no—
554C22—22no—
555C22—22no—
556C22—24no—
557C22—22no—
558C22—22no—
559C22—41no—
560C22—41no—
561C22—42no—
562C22—42no—
563C22—42no—
564C22—1224no—
565C22—1222no—
566C22—2441no—
567C22—2441no—
568C22—2442no—
569C22C22×C22⋊#692311yescharacteristic
570C22C2×#1451985611yescharacteristic
571C22C2×#1451985611yescharacteristic
572C22D61⋊#13112yes—
573C22#1684084012yes—
574C4—22no—
575C4—22no—
576C4—22no—
577C4—41no—
578C4—41no—
579C4—614no—
580C4—612no—
581C4—612no—
582C4—1222no—
583C4—1222no—
584C4—1222no—
585C4—2441no—
586C4—2441no—
587C2—42no—
588C2—42no—
589C2—2442no—
590C2#2146226311yescharacteristic
591C2D61⋊#40811yescharacteristic
592C2#2146240311yescharacteristic
593C2#2146251612yes—
594C2#2146251712yes—
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC2×C4×D4×C61C4
prime radicalC22×#11758224C22
cosocleC22×Dic61C24
hypercenterC2×C4×D4#6923
hypocenterC61#20721
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×#16840782C2semidirect
2. C2×#16840779C2semidirect
3. #21461712C2semidirect
4. #21461676C2semidirect
5. #21461675C2semidirect
7. #21461549C2semidirect
8. #21461548C2semidirect
336. C61#20721semidirect

Maximal subgroups

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

subgroupindex
C2×#168407822
C2×#168407792
#214617122
#214616762
#214616752
#214616432
#214615492
#214615482
C2×C4×#117582242
#2072161