Finite Group Databasebeta

← #30616352

Subgroups — #30616352

Order 15616.

818 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840787C211yesmaximal, characteristic, complemented
2C2×#16840786C211yesmaximal, characteristic, complemented
3#21461944C211yesmaximal, characteristic
4#21461944C211yesmaximal, characteristic
5#21461920C211yesmaximal, characteristic, complemented
6#21461919C211yesmaximal, characteristic, complemented
7#21461895C211yesmaximal, characteristic, complemented
8#21461894C211yesmaximal, characteristic, complemented
9#21461893C211yesmaximal, characteristic, complemented
10#21461892C211yesmaximal, characteristic, complemented
11#21461605C211yesmaximal, characteristic, complemented
12#21461549C211yesmaximal, characteristic, complemented
13#21461548C211yesmaximal, characteristic, complemented
14C4×#14519832C211yesmaximal, characteristic, complemented
15#21448279C211yesmaximal, characteristic
16#16840787—24no—
17#16840786—24no—
18C2×#14519844C2211yescharacteristic
19C2×#14519844C2211yescharacteristic
20C2×C4⋊#92420C2211yescharacteristic
21C2×C4⋊#92420C2211yescharacteristic
22C2×C4⋊#92420C2211yescharacteristic
23C2×C4⋊#92420C2211yescharacteristic
24C2×#14519834C2211yescharacteristic
25C2×#14519834C2211yescharacteristic
26C2×#14519834C2211yescharacteristic
27C2×#14519834C2211yescharacteristic
28C2×C22⋊#92420C2211yescharacteristic
29C2×C22⋊#92420C2211yescharacteristic
30C2×C22⋊#92420C2211yescharacteristic
31C2×C22⋊#92420C2211yescharacteristic
32C2×#14519832C2211yescharacteristic
33C2×#14519832C2211yescharacteristic
34C2×#14519832C2211yescharacteristic
35C2×#14519832C2211yescharacteristic
36C2×#14519832C2211yescharacteristic
37C2×#14519832C2211yescharacteristic
38C2×C4×#92420C2211yescharacteristic
39C2×C4×#92420C2211yescharacteristic
40#16840628C2211yescharacteristic
41#16840628C2211yescharacteristic
42#16840628C2211yescharacteristic
43#16840628C2211yescharacteristic
44#16840628C2211yescharacteristic
45#16840628C2211yescharacteristic
46C2×#14519737C2211yescharacteristic
47C2×#14519735C2211yescharacteristic
48C2×#14519733C2211yescharacteristic
49#16839662C411yescharacteristic
50#16839662C411yescharacteristic
51#16839659C411yescharacteristic
52#16839657C411yescharacteristic
53#16839655C411yescharacteristic
54#16839653C411yescharacteristic
55#16839651C411yescharacteristic
56#16839613C2211yescharacteristic
57C22⋊C4×Dic61C2211yescharacteristic
58#16839609C2211yescharacteristic
59C42×Dic61C2211yescharacteristic
60C61×#388C411yescharacteristic
61C22×#92420C2311yescharacteristic
62C22×#92420C2311yescharacteristic
63C22×#92420C2311yescharacteristic
64C22×#92420C2311yescharacteristic
65C22×#92420C2311yescharacteristic
66C22×#92420C2311yescharacteristic
67C22×#92420C2311yescharacteristic
68C22×#92420C2311yescharacteristic
69#14519844—22no—
70#14519844—22no—
71C4⋊#92420—22no—
72C4⋊#92420—22no—
73C4⋊#92420—22no—
74C4⋊#92420—22no—
75#14519834—22no—
76#14519834—22no—
77#14519834—22no—
78#14519834—22no—
79C22⋊#92420—22no—
80C22⋊#92420—22no—
81C22⋊#92420—22no—
82C22⋊#92420—22no—
83#14519832—22no—
84#14519832—22no—
85#14519832—22no—
86#14519832—22no—
87#14519832—22no—
88#14519832—22no—
89C4×#92420—22no—
90C4×#92420D414yescomplemented
91C22×C22⋊D61C2×C411yescharacteristic
92C23×Dic61C2311yescharacteristic
93C22×C4×D61C2311yescharacteristic
94#14519737—22no—
95#14519737—22no—
96#14519735—22no—
97#14519735—22no—
98#14519733—22no—
99#14519733—22no—
100C2×C4⋊Dic61C2×C411yescharacteristic
101C2×#11758196C2×C411yescharacteristic
102C2×#11758196C2×C411yescharacteristic
103C2×#11758196C2×C411yescharacteristic
104C2×#11758196C2×C411yescharacteristic
105C2×#11758196C2×C411yescharacteristic
106C2×C22⋊Dic61C2×C411yescharacteristic
107C2×C22⋊Dic61C2×C411yescharacteristic
108C2×#11758198C2×C411yescharacteristic
109C2×#11758198C2×C411yescharacteristic
110C2×#11758198C2×C411yescharacteristic
111C2×#11758198C2×C411yescharacteristic
112C2×#11758198C2×C411yescharacteristic
113C2×C4×Dic61C2×C411yescharacteristic
114C2×C4×Dic61C2×C411yescharacteristic
115C2×C4×Dic61C2×C411yescharacteristic
116C2×C4×Dic61C2311yescharacteristic
117C2×C4×Dic61C2311yescharacteristic
118C2×C4×Dic61C2311yescharacteristic
119C2×C4×Dic61C2311yescharacteristic
120C2×C4×Dic61C2311yescharacteristic
121#14519684C2×C411yescharacteristic
122#14519684C2×C411yescharacteristic
123#14519684C2×C411yescharacteristic
124#14519684C2×C411yescharacteristic
125C2×C4⋊C4×C61C2×C411yescharacteristic
126C2×C22⋊C4×C61C2×C411yescharacteristic
127C2×C22⋊C4×C61C2×C411yescharacteristic
128C2×C22⋊C4×C61C2×C411yescharacteristic
129C2×C42×C61C2×C411yescharacteristic
130#95×C61C2×C411yescharacteristic
131#95×C61C2×C411yescharacteristic
132C24×C61C22×C411yescharacteristic
133C23×D61C22×C411yescharacteristic
134C22×C4×C61C22×C411yescharacteristic
135C22×C4×C61C22×C411yescharacteristic
136C22×C4×C61C22×C411yescharacteristic
137C22×C4×C61C22×C411yescharacteristic
138C22×C4×C61C22×C411yescharacteristic
139C22×C4×C61C22×C411yescharacteristic
140C2×C22⋊D61—22no—
141C2×C22⋊D61—41no—
142C2×C22⋊D61—41no—
143C22×Dic61—21no—
144C22×Dic61—21no—
145C22×Dic61—21no—
146C22×Dic61—21no—
147C22×Dic61—21no—
148C22×Dic61—21no—
149C22×Dic61C22×C411yescharacteristic
150C22×Dic61C22×C411yescharacteristic
151C22×Dic61C22×C411yescharacteristic
152C22×Dic61C22×C411yescharacteristic
153C22×Dic61C22×C411yescharacteristic
154C22×Dic61C22×C411yescharacteristic
155C22×Dic61C2411yescharacteristic
156C2×C4×D61—21no—
157C2×C4×D61—21no—
158C2×C4×D61—21no—
159C2×C4×D61—21no—
160C2×C4×D61—21no—
161C2×C4×D61—21no—
162C2×#92420—21no—
163C2×#92420—21no—
164C2×#92420—21no—
165C2×#92420—21no—
166C2×#92420—21no—
167C2×#92420—21no—
168C2×#92420—21no—
169C2×#92420—21no—
170C2×#92420—21no—
171C2×#92420—21no—
172C2×#92420—21no—
173C2×#92420—21no—
174C2×#92420—21no—
175C2×#92420—21no—
176C2×#92420—21no—
177C2×#92420—21no—
178C2×#92420—21no—
179C2×#92420—21no—
180C2×#92420—21no—
181C2×#92420—21no—
182C2×#92420C2×D412yes—
183C2×#92420C2×D412yes—
184C2×#92420#4112yes—
185C2×#92420#4112yes—
186C4⋊C4×C61—22no—
187C22⋊C4×C61—22no—
188C22⋊C4×C61—22no—
189C22⋊C4×C61—41no—
190C42×C61—41no—
191C22⋊Dic61—22no—
192C22⋊Dic61—41no—
193#11758198—22no—
194#11758198—22no—
195#11758198—22no—
196#11758198—41no—
197#11758198—41no—
198C4⋊Dic61—22no—
199#11758196—22no—
200#11758196—22no—
201#11758196—22no—
202#11758196—41no—
203#11758196—41no—
204C4×Dic61—21no—
205C4×Dic61—21no—
206C4×Dic61—21no—
207C4×Dic61—21no—
208C4×Dic61—21no—
209C4×Dic61—21no—
210C4×Dic61—41no—
211C4×Dic61—41no—
212C4×Dic61—41no—
213C4×Dic61C2×D412yes—
214C4×Dic61#4112yes—
215C4×Dic61#4112yes—
216C4×Dic61#4112yes—
217C23×C61—21no—
218C23×C61—21no—
219C23×C61—21no—
220C23×C61—21no—
221C23×C61—21no—
222C23×C61—21no—
223C23×C61—21no—
224C23×C61C23×C411yescharacteristic
225C22×D61—21no—
226C22×D61—21no—
227C22×D61—21no—
228C22×D61—21no—
229C22×D61—21no—
230C22×D61—21no—
231C22×D61—21no—
232C2×C4×C61—21no—
233C2×C4×C61—21no—
234C2×C4×C61—21no—
235C2×C4×C61—21no—
236C2×C4×C61—21no—
237C2×C4×C61—21no—
238C2×C4×C61—21no—
239C2×C4×C61—21no—
240C2×C4×C61—21no—
241C2×C4×C61—21no—
242C2×C4×C61—21no—
243C2×C4×C61—21no—
244C2×C4×C61—21no—
245C2×C4×C61—21no—
246C2×C4×C61—21no—
247C2×C4×C61—21no—
248C2×C4×C61#11712yes—
249C2×C4×C61C4×D412yes—
250C22⋊D61—44no—
251C2×Dic61—21no—
252C2×Dic61—21no—
253C2×Dic61—21no—
254C2×Dic61—21no—
255C2×Dic61—21no—
256C2×Dic61—21no—
257C2×Dic61—21no—
258C2×Dic61—21no—
259C2×Dic61—21no—
260C2×Dic61—21no—
261C2×Dic61—21no—
262C2×Dic61—21no—
263C2×Dic61—21no—
264C2×Dic61—21no—
265C2×Dic61—21no—
266C2×Dic61—21no—
267C2×Dic61—41no—
268C2×Dic61—41no—
269C2×Dic61—41no—
270C2×Dic61—41no—
271C2×Dic61#11712yes—
272C2×Dic61C4×D412yes—
273C2×Dic61C22×D411yescharacteristic
274C2×Dic61C2×#4111yescharacteristic
275C2×Dic61C2×#4111yescharacteristic
276C2×Dic61C2×#4111yescharacteristic
277C2×Dic61C2×#4111yescharacteristic
278C2×Dic61C2×#4111yescharacteristic
279C4×D61—41no—
280C4×D61—41no—
281C4×D61—41no—
282C4×D61—41no—
283#92420—22no—
284#92420—22no—
285#92420—22no—
286#92420—22no—
287#92420—41no—
288#92420—41no—
289#92420—41no—
290#92420—41no—
291#21267—611nomaximal, Sylow
292C22×C61—41no—
293C22×C61—41no—
294C22×C61—41no—
295C22×C61—41no—
296C22×C61—41no—
297C22×C61—41no—
298C22×C61—41no—
299C22×C61C2×#11711yescharacteristic
300C22×C61C2×C4×D411yescharacteristic
301C22×C61C4×#4111yescharacteristic
302C22×C61#56811yescharacteristic
303C22×C61#56811yescharacteristic
304C22×C61#56811yescharacteristic
305C22×C61#56811yescharacteristic
306C2×D61—41no—
307C2×D61—41no—
308C2×D61—41no—
309C2×D61—41no—
310C2×D61—41no—
311C2×D61—41no—
312C2×D61—41no—
313C4×C61—22no—
314C4×C61—22no—
315C4×C61—41no—
316C4×C61—41no—
317C4×C61—41no—
318C4×C61—41no—
319Dic61—22no—
320Dic61—22no—
321Dic61—41no—
322Dic61—41no—
323Dic61—41no—
324Dic61—41no—
325Dic61#52911yescharacteristic
326Dic61#52911yescharacteristic
327Dic61#53211yescharacteristic
328Dic61#53211yescharacteristic
329C2×#433—611no—
330C2×#433—611no—
331#2293—611no—
332#1955—611no—
333#1955—611no—
334#1940—611no—
335#1940—611no—
336#1924—611no—
337#1924—611no—
338#1924—611no—
339#1924—611no—
340#1767—611no—
341#1750—611no—
342#1750—611no—
343C4×#97—611no—
344C2×C61—81no—
345C2×C61#229311yescharacteristic
346C2×C61#292111yescharacteristic
347C2×C61#292311yescharacteristic
348C2×C61#293211yescharacteristic
349C2×C61#293211yescharacteristic
350C2×C61#296711yescharacteristic
351C2×C61#296711yescharacteristic
352D61—81no—
353C2×C4×D4—611no—
354C2×#117—611no—
355C2×#117—611no—
356#433—1224no—
357#433—1224no—
358C2×C4⋊C8—611no—
359C2×C4⋊C8—611no—
360C2×C4⋊C8—611no—
361C2×C4⋊C8—611no—
362C2×C4⋊C8—611no—
363C2×C4⋊C8—611no—
364C2×C22⋊C8—611no—
365C2×C22⋊C8—611no—
366C2×C22⋊C8—611no—
367C2×C22⋊C8—611no—
368C2×C22⋊C8—611no—
369C2×C22⋊C8—611no—
370C2×C22⋊C8—611no—
371C2×C22⋊C8—611no—
372C2×#97—611no—
373C2×#97—611no—
374C2×#97—611no—
375C2×#97—611no—
376C2×#97—611no—
377C2×#97—611no—
378C2×C4×C8—611no—
379C2×C4×C8—611no—
380#390—611no—
381#390—611no—
382#389—611no—
383#389—611no—
384#388—611no—
385#388—611no—
386#388—611no—
387#388#692311yescharacteristic
388C4×C4⋊C4—611no—
389C4×C22⋊C4—611no—
390C4×C22⋊C4—611no—
391C43—611no—
392#336—611no—
393#336—611no—
394#336—611no—
395#336—611no—
396#336—611no—
397#336—611no—
398C61#2126711yescharacteristic, complemented, Sylow
399C22×D4—611no—
400C23×C4—611no—
401C23×C4—611no—
402C22×C8—611no—
403C22×C8—611no—
404C22×C8—611no—
405C22×C8—611no—
406C22×C8—611no—
407C22×C8—611no—
408C22×C8—611no—
409C22×C8—611no—
410C4×D4—1222no—
411C4×D4—1222no—
412#117—1222no—
413#117—1222no—
414#117—1222no—
415#117—1222no—
416C2×C4⋊C4—611no—
417C2×C4⋊C4—611no—
418C2×C4⋊C4—611no—
419C2×C4⋊C4—611no—
420C2×C4⋊C4—611no—
421C2×C4⋊C4—611no—
422C2×C4⋊C4C2×#692311yescharacteristic
423C2×C22⋊C4—611no—
424C2×C22⋊C4—611no—
425C2×C22⋊C4—611no—
426C2×C22⋊C4—611no—
427C2×C22⋊C4—611no—
428C2×C22⋊C4—611no—
429C2×C22⋊C4—611no—
430C2×C22⋊C4C2×#692311yescharacteristic
431C2×C22⋊C4C2×#692311yescharacteristic
432C2×C22⋊C4C2×#692311yescharacteristic
433C2×C42—611no—
434C2×C42—611no—
435C2×C42—611no—
436C2×C42—611no—
437C2×C42—611no—
438C2×C42—611no—
439C2×C42—611no—
440C2×C42—611no—
441C2×C42C2×#692311yescharacteristic
442C4⋊C8—1222no—
443C4⋊C8—1222no—
444C4⋊C8—1222no—
445C4⋊C8—1222no—
446C4⋊C8—1222no—
447C4⋊C8—1222no—
448C22⋊C8—1222no—
449C22⋊C8—1222no—
450C22⋊C8—1222no—
451C22⋊C8—1222no—
452C22⋊C8—1222no—
453C22⋊C8—1222no—
454C22⋊C8—1222no—
455C22⋊C8—1222no—
456#97—1222no—
457#97—1222no—
458#97—1222no—
459#97—1222no—
460#97—1222no—
461#97—1222no—
462C4×C8—614no—
463C4×C8—1222no—
464#95—611no—
465#95—611no—
466#95—611no—
467#95—611no—
468#95C2×#692311yescharacteristic
469#95C2×#692311yescharacteristic
470C24—611no—
471C24C22×#692311yescharacteristic
472C2×D4—1222no—
473C2×D4—2441no—
474C2×D4—2441no—
475C22×C4—611no—
476C22×C4—611no—
477C22×C4—611no—
478C22×C4—611no—
479C22×C4—611no—
480C22×C4—611no—
481C22×C4—611no—
482C22×C4—1221no—
483C22×C4—1221no—
484C22×C4—1221no—
485C22×C4—1221no—
486C22×C4—1221no—
487C22×C4—1221no—
488C22×C4—1221no—
489C22×C4—1221no—
490C22×C4—1221no—
491C22×C4—1221no—
492C22×C4—1221no—
493C22×C4—1221no—
494C22×C4C22×#692311yescharacteristic
495C22×C4C22×#692311yescharacteristic
496C22×C4C22×#692311yescharacteristic
497C22×C4C22×#692311yescharacteristic
498C22×C4C22×#692311yescharacteristic
499C22×C4C22×#692311yescharacteristic
500C2×C8—612no—
501C2×C8—612no—
502C2×C8—612no—
503C2×C8—612no—
504C2×C8—1221no—
505C2×C8—1221no—
506C2×C8—1221no—
507C2×C8—1221no—
508C2×C8—1221no—
509C2×C8—1221no—
510C2×C8—1221no—
511C2×C8—1221no—
512C2×C8—1221no—
513C2×C8—1221no—
514C2×C8—1221no—
515C2×C8—1221no—
516C2×C8—1221no—
517C2×C8—1221no—
518C2×C8—1221no—
519C2×C8—1221no—
520C2×C8—1221no—
521C2×C8—1221no—
522C2×C8—1221no—
523C2×C8—1221no—
524C4⋊C4—22no—
525C4⋊C4—1222no—
526C4⋊C4—1222no—
527C4⋊C4—1222no—
528C4⋊C4—1222no—
529C4⋊C4—2441no—
530C4⋊C4—2441no—
531C22⋊C4—22no—
532C22⋊C4—22no—
533C22⋊C4—41no—
534C22⋊C4—1222no—
535C22⋊C4—1222no—
536C22⋊C4—1222no—
537C22⋊C4—1222no—
538C22⋊C4—2441no—
539C22⋊C4—2441no—
540C22⋊C4—2441no—
541C42—41no—
542C42—612no—
543C42—612no—
544C42—612no—
545C42—612no—
546C42—1221no—
547C42—1221no—
548C42—1221no—
549C42—1221no—
550C42—1221no—
551C42—1221no—
552C42—2441no—
553C42—2441no—
554C42—2441no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—1221no—
563C23—1221no—
564C23—1221no—
565C23—1221no—
566C23—1221no—
567C23—1221no—
568C23—1221no—
569C23C23×#692311yescharacteristic
570D4—2444no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—611no—
588C2×C4—611no—
589C2×C4—611no—
590C2×C4—611no—
591C2×C4—611no—
592C2×C4—611no—
593C2×C4—612no—
594C2×C4—612no—
595C2×C4—1221no—
596C2×C4—1221no—
597C2×C4—1221no—
598C2×C4—1221no—
599C2×C4—1221no—
600C2×C4—1221no—
601C2×C4—1221no—
602C2×C4—1221no—
603C2×C4—1221no—
604C2×C4—1221no—
605C2×C4—1221no—
606C2×C4—1221no—
607C2×C4—1221no—
608C2×C4—1221no—
609C2×C4—1221no—
610C2×C4—1221no—
611C2×C4—2441no—
612C2×C4—2441no—
613C2×C4—2441no—
614C2×C4—2441no—
615C2×C4—2441no—
616C2×C4—2441no—
617C2×C4—2441no—
618C2×C4—2441no—
619C2×C4#1451985612yes—
620C2×C4D4×#692312yes—
621C8—1222no—
622C8—1222no—
623C8—1222no—
624C8—1222no—
625C8—2441no—
626C8—2441no—
627C8—2441no—
628C8—2441no—
629C22—41no—
630C22—41no—
631C22—41no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22—41no—
636C22—2441no—
637C22—2441no—
638C22—2441no—
639C22—2441no—
640C22—2441no—
641C22—2441no—
642C22—2441no—
643C22C2×#1451985611yescharacteristic
644C22C2×D4×#692311yescharacteristic
645C22#41×#692311yescharacteristic
646C22#1684084011yescharacteristic
647C22#1684084111yescharacteristic
648C22#1684084111yescharacteristic
649C22#1684084111yescharacteristic
650C4—22no—
651C4—22no—
652C4—41no—
653C4—41no—
654C4—41no—
655C4—41no—
656C4—611no—
657C4—611no—
658C4—611no—
659C4—611no—
660C4—1222no—
661C4—1222no—
662C4—2441no—
663C4—2441no—
664C4—2441no—
665C4—2441no—
666C2—81no—
667C2—4881no—
668C2#2146227611yescharacteristic
669C2#2146250011yescharacteristic
670C2#2146250511yescharacteristic
671C2#2146254511yescharacteristic
672C2#2146254711yescharacteristic
673C2#2146264111yescharacteristic
674C2#2146264211yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC61×#388C4
prime radicalC22×C22⋊D61C2×C4
cosocleC22×Dic61C24
hypercenter#388#6923
hypocenterC61#21267
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×#16840787C2semidirect
2. C2×#16840786C2semidirect
5. #21461920C2semidirect
6. #21461919C2semidirect
7. #21461895C2semidirect
8. #21461894C2semidirect
9. #21461893C2semidirect
10. #21461892C2semidirect
11. #21461605C2semidirect
12. #21461549C2semidirect
13. #21461548C2semidirect
14. C4×#14519832C2semidirect
90. C4×#92420D4semidirect
398. C61#21267semidirect

Maximal subgroups

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

subgroupindex
C2×#168407872
C2×#168407862
#214619442
#214619202
#214619192
#214618952
#214618942
#214618932
#214618922
#214616052
#214615492
#214615482
C4×#145198322
#214482792
#2126761