Finite Group Databasebeta

← #30543835

Subgroups — #30543835

Order 15616.

2038 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459018C211yesmaximal, characteristic
2#21454487C213yesmaximal, complemented
3#21454484C213yesmaximal, complemented
4#21454476C213yesmaximal, complemented
5#21454476C213yesmaximal, complemented
6#21454469C213yesmaximal, complemented
7#21454462C213yesmaximal, complemented
8#21454456C213yesmaximal, complemented
9C2×#16839822C213yesmaximal, complemented
10#21454387C211yesmaximal, characteristic, complemented
11#21454266C211yesmaximal, characteristic
12#21454266C211yesmaximal, characteristic
13#21454245C211yesmaximal, characteristic, complemented
14#131×Dic61C211yesmaximal, characteristic, complemented
15C61×#2906C211yesmaximal, characteristic, complemented
16C2×#41×D61C2211yescharacteristic
17C2×#14519784C2211yescharacteristic
18C2×#14519784C2211yescharacteristic
19#16840244C411yescharacteristic
20#16840244C411yescharacteristic
21#16840241C413yes—
22#16840241C413yes—
23#16840238C411yescharacteristic
24#16840238C411yescharacteristic
25#16840234C413yes—
26#16840234C413yes—
27#41×Dic61C2211yescharacteristic
28C4×#11758222C2213yes—
29#16840230C2213yes—
30C2×#14519734C2213yes—
31#117×D61C2213yes—
32#16839822C2211yescharacteristic
33#16839822C2213yes—
34#16839822C2213yes—
35#16839822C2213yes—
36#16839822C2216yes—
37#16839822C2213yescomplemented
38#16839822C2213yescomplemented
39#16839822C2213yescomplemented
40#16839822C2213yescomplemented
41#16839822C2216yescomplemented
42#16839822C2216yescomplemented
43#16839818C2216yescomplemented
44#16839818C2216yescomplemented
45#16839814C2216yescomplemented
46#16839814C2216yescomplemented
47#16839789C2213yescomplemented
48#16839789C2213yescomplemented
49#16839786C2213yescomplemented
50C2×C4⋊#92418C2213yescomplemented
51#16839730C2213yes—
52#16839730C2213yes—
53#16839728C2213yes—
54#16839728C2213yes—
55#16839725C2213yes—
56#16839725C2213yes—
57C2×#14519689C2213yes—
58C2×#14519689C2213yes—
59#16839720C2213yescomplemented
60#16839720C2213yescomplemented
61#16839717C2213yescomplemented
62#16839717C2213yescomplemented
63M16×Dic61C2213yescomplemented
64M16×Dic61C2213yescomplemented
65C2×#14519687C2213yescomplemented
66C2×C8×Dic61C2213yescomplemented
67C2×#131×C61C2211yescharacteristic
68C2×#131×C61C2211yescharacteristic
69C4×#41×C61C2211yescharacteristic
70C61×#424C2213yescomplemented
71C61×#424C2213yescomplemented
72C61×#423C2213yescomplemented
73C2×C4⋊C8×C61C2213yescomplemented
74C2×#11758226C2×C411yescharacteristic
75C2×#11758222C2313yes—
76C2×#11758224C2×C413yes—
77#41×D61—24no—
78#41×D61—24no—
79C2×Q8×D61C2×C411yescharacteristic
80C2×D4×D61C2×C413yes—
81C22×C4×D61C2313yes—
82#14519784—24no—
83#14519784—24no—
84C2×#11758194C2313yes—
85C2×#11758194C2313yes—
86C22×#92418C2313yes—
87C22×#92418C2313yes—
88Q8×Dic61C2×C411yescharacteristic
89Q8×Dic61C2×C411yescharacteristic
90C4×Dic122C2×C413yes—
91C4×Dic122C2×C413yes—
92#14519742C2×C413yes—
93#14519742C2×C413yes—
94C4×D244C2×C413yes—
95C4×D244C2×C413yes—
96D4×Dic61C2×C413yes—
97D4×Dic61C2×C413yes—
98#14519739C2×C413yes—
99#14519739C2×C413yes—
100C4×C22⋊D61C2×C416yes—
101C4×C22⋊D61C2×C416yes—
102#14519737C2×C416yes—
103#14519737C2×C416yes—
104#14519736C2313yes—
105#14519735C2×C413yes—
106#14519735C2×C413yes—
107#14519734C2×C413yes—
108#14519734C2×C413yes—
109#14519734C2×C413yes—
110#14519734C2×C413yes—
111#14519734C2313yes—
112#14519734C2311yescharacteristic
113#14519734C2313yes—
114#14519734C2313yes—
115#14519733C2×C416yes—
116C2×#11758196C2×C413yes—
117C2×#11758196C2×C413yes—
118C4⋊C4×D61C2×C413yes—
119C4⋊C4×D61C2×C413yes—
120C2×#11758198C2×C413yes—
121C2×#11758198C2×C413yes—
122C22⋊C4×D61C2×C416yes—
123C2×C4×Dic61C2313yes—
124C42×D61C2316yes—
125C4⋊#92418C2311yescharacteristic
126C4⋊#92418C2313yes—
127C4⋊#92418C2313yes—
128C4⋊#92418C2313yes—
129C4⋊#92418C2316yes—
130#14519689C2311yescharacteristic
131#14519689C2311yescharacteristic
132#14519689C2313yes—
133#14519689C2313yes—
134#14519689C2313yes—
135#14519689C2313yes—
136#14519689C2313yes—
137#14519689C2313yes—
138#14519689C2316yes—
139#14519689C2316yes—
140#14519687C2311yescharacteristic
141#14519687C2313yes—
142#14519687C2313yes—
143#14519687C2313yes—
144#14519687C2316yes—
145C8×Dic61C2311yescharacteristic
146C8×Dic61C2313yes—
147C8×Dic61C2313yes—
148C8×Dic61C2313yes—
149C8×Dic61C2316yes—
150C2×#41×C61C2311yescharacteristic
151#131×C61—24no—
152#131×C61—24no—
153C2×M16×C61C2313yes—
154C2×M16×C61C2313yes—
155C22×C8×C61C2313yes—
156C22×C8×C61C2313yes—
157C4×Q8×C61C2×C411yescharacteristic
158C4×Q8×C61C2×C411yescharacteristic
159C4×D4×C61C2×C413yes—
160C4×D4×C61C2×C413yes—
161#117×C61C2313yes—
162C2×C42×C61C2313yes—
163C4⋊C8×C61C2313yes—
164C4⋊C8×C61C2316yes—
165C4⋊C8×C61C2313yes—
166C4⋊C8×C61C2311yescharacteristic
167C4⋊C8×C61C2313yes—
168C23×D61C22×C413yes—
169#41×C61#4114yes—
170#41×C61#4114yes—
171C2×Q8×C61C22×C411yescharacteristic
172C2×D4×C61C22×C413yes—
173C22×C4×C61C22×C413yes—
174C22×C4×C61C22×C413yes—
175C22×C4×C61C2413yes—
176C2×C22⋊D61C22×C416yes—
177C22×Dic61C22×C413yes—
178C22×Dic61C22×C413yes—
179C22×Dic61C22×C413yes—
180#11758226—24no—
181Q8×D61—24no—
182#11758224—212no—
183D4×D61—212no—
184#11758222—26no—
185#11758222—26no—
186C2×D244C22×C413yes—
187C2×C4×D61—26no—
188C2×C4×D61—26no—
189C2×C4×D61C22×C413yes—
190C2×C4×D61C22×C413yes—
191C2×C4×D61C22×C416yes—
192C2×C4×D61C22×C416yes—
193C2×C4×D61C2411yescharacteristic
194C2×C4×D61C2413yes—
195C2×Dic122C22×C413yes—
196M16×C61—26no—
197M16×C61—26no—
198C2×C8×C61—26no—
199C2×C8×C61—26no—
200C2×C8×C61C2411yescharacteristic
201C2×C8×C61C2411yescharacteristic
202C2×C8×C61C2413yes—
203C2×C8×C61C2413yes—
204C4⋊C4×C61C22×C413yes—
205C4⋊C4×C61C22×C413yes—
206C22⋊C4×C61C22×C416yes—
207C42×C61C22×C413yes—
208C42×C61C22×C413yes—
209C42×C61C2411yescharacteristic
210C42×C61C2413yes—
211C22⋊Dic61C22×C416yes—
212#11758198C22×C413yes—
213#11758198C22×C413yes—
214#11758198C22×C411yescharacteristic
215#11758198C22×C411yescharacteristic
216#11758198C22×C413yes—
217#11758198C22×C413yes—
218#11758198C22×C413yes—
219#11758198C22×C413yes—
220C4⋊Dic61C22×C413yes—
221C4⋊Dic61C22×C413yes—
222#11758196C22×C413yes—
223#11758196C22×C413yes—
224#11758196C22×C411yescharacteristic
225#11758196C22×C411yescharacteristic
226#11758196C22×C413yes—
227#11758196C22×C413yes—
228#11758196C22×C413yes—
229#11758196C22×C413yes—
230C4×Dic61C22×C416yes—
231C4×Dic61C22×C416yes—
232C4×Dic61C22×C413yes—
233C4×Dic61C22×C413yes—
234C4×Dic61C2413yes—
235C4×Dic61C2411yescharacteristic
236#11758194—26no—
237#11758194—26no—
238C2×#92418—26no—
239C2×#92418—26no—
240C2×#92418C2411yescharacteristic
241C2×#92418C2413yes—
242C2×#92418C2413yes—
243C2×#92418C2411yescharacteristic
244C23×C61C23×C413yes—
245C22×D61—26no—
246C22×D61—43no—
247C22×D61—43no—
248C22×D61C23×C411yescharacteristic
249C22×D61C23×C413yes—
250Q8×C61#11714yes—
251D4×C61#117112yes—
252C2×C4×C61—43no—
253C2×C4×C61—43no—
254C2×C4×C61C23×C413yes—
255C2×C4×C61C23×C413yes—
256C2×C4×C61C23×C411yescharacteristic
257C2×C4×C61C23×C411yescharacteristic
258C2×C4×C61C23×C413yes—
259C2×C4×C61C2×#4116yes—
260C2×C4×C61C2×#4116yes—
261C2×C4×C61C2511yescharacteristic
262C22⋊D61—212no—
263C2×Dic61—26no—
264C2×Dic61—43no—
265C2×Dic61—43no—
266C2×Dic61C23×C413yes—
267C2×Dic61C23×C411yescharacteristic
268C2×Dic61C23×C411yescharacteristic
269C2×Dic61C23×C413yes—
270C2×Dic61C23×C413yes—
271C2×Dic61C23×C411yescharacteristic
272D244—26no—
273C4×D61—26no—
274C4×D61—26no—
275C4×D61—21no—
276C4×D61—21no—
277C4×D61—23no—
278C4×D61—23no—
279C4×D61—46no—
280C4×D61—46no—
281Dic122—26no—
282C8×C61—21no—
283C8×C61—21no—
284C8×C61—23no—
285C8×C61—23no—
286#92418—21no—
287#92418—21no—
288#92418—23no—
289#92418—23no—
290#60129—611nomaximal, Sylow
291C22×C61—23no—
292C22×C61—23no—
293C22×C61C2×#11716yes—
294C22×C61C24×C411yescharacteristic
295C2×D61—21no—
296C2×D61—23no—
297C2×D61—23no—
298C2×D61—23no—
299C2×D61—21no—
300C2×D61—21no—
301C2×D61—86no—
302C4×C61—23no—
303C4×C61—23no—
304C4×C61—21no—
305C4×C61—21no—
306C4×C61C2×#11716yes—
307C4×C61C22×#4111yescharacteristic
308C4×C61C22×#4111yescharacteristic
309Dic61—23no—
310Dic61—21no—
311Dic61—23no—
312Dic61—23no—
313Dic61—21no—
314Dic61—21no—
315#3428—611no—
316#2925—613no—
317#2925—613no—
318#2924—613no—
319#2924—613no—
320#2923—613no—
321#2922—613no—
322#2921—613no—
323C2×#433—613no—
324#2906—611no—
325#2906D6111yescharacteristic, complemented
326#2880—611no—
327#2880—611no—
328#2875—611no—
329C4×#131—611no—
330C2×C61—26no—
331C2×C61C22×#11711yescharacteristic
332C2×C61#357311yescharacteristic
333C2×C61#357311yescharacteristic
334D61—43no—
335D61—41no—
336C22×#41—611no—
337C2×#131—611no—
338C2×#131—611no—
339C2×#131C2×D6111yescharacteristic
340C2×#131C2×D6111yescharacteristic
341#520—611no—
342#520—611no—
343#520—613no—
344#520—613no—
345#519—611no—
346#519—611no—
347#518—613no—
348#518—613no—
349C4×#41—611no—
350C4×#41—613no—
351C4×#41—613no—
352C4×#41C2×D6111yescharacteristic
353C2×#117—613no—
354C2×#117—613no—
355#433—611no—
356#433—613no—
357#433—613no—
358#433—613no—
359#433—613no—
360#433—613no—
361#433—613no—
362#433—613no—
363#433—616no—
364#433—616no—
365#433—616no—
366#432—616no—
367#432—616no—
368#431—616no—
369#431—616no—
370#424—613no—
371#424—613no—
372#424C2×D6113yescomplemented
373#424C2×D6113yescomplemented
374#423—613no—
375#423C2×D6113yescomplemented
376C2×C4⋊C8—613no—
377C2×C4⋊C8C2×D6113yescomplemented
378#408—613no—
379#408—613no—
380#408—613no—
381#408—613no—
382#407—613no—
383#407—613no—
384C2×C22⋊C8—613no—
385C2×C22⋊C8—613no—
386#405—613no—
387#405—613no—
388#405—613no—
389#405—613no—
390C4×M16—613no—
391C4×M16—613no—
392C2×#97—613no—
393C2×C4×C8—613no—
394C61#6012911yescharacteristic, complemented, Sylow
395C2×#41—611no—
396C2×#41—613no—
397C2×#41—613no—
398C2×#41—1224no—
399C2×#41—1224no—
400C2×#41C22×D6111yescharacteristic
401C22×Q8—611no—
402C22×D4—613no—
403C23×C4—613no—
404#131—24no—
405#131—24no—
406#131—1224no—
407#131—1224no—
408C2×M16—613no—
409C2×M16—613no—
410C2×M16C22×D6113yes—
411C2×M16C22×D6113yes—
412C22×C8—613no—
413C22×C8—613no—
414C22×C8C22×D6113yes—
415C22×C8C22×D6113yes—
416C4×Q8—611no—
417C4×Q8—611no—
418C4×Q8—613no—
419C4×Q8—613no—
420C4×Q8—613no—
421C4×Q8—613no—
422C4×Q8C4×D6111yescharacteristic
423C4×Q8C4×D6111yescharacteristic
424C4×D4—613no—
425C4×D4—613no—
426C4×D4—616no—
427C4×D4—616no—
428C4×D4—613no—
429C4×D4—613no—
430C4×D4—616no—
431C4×D4—616no—
432C4×D4—613no—
433C4×D4—613no—
434C4×D4C4×D6113yes—
435C4×D4C4×D6113yes—
436#117—613no—
437#117—613no—
438#117—613no—
439#117—616no—
440#117—613no—
441#117—613no—
442#117—613no—
443#117—613no—
444#117—613no—
445#117—611no—
446#117—613no—
447#117—613no—
448#117C22×D6113yes—
449C2×C4⋊C4—613no—
450C2×C4⋊C4—613no—
451C2×C4⋊C4—613no—
452C2×C4⋊C4—613no—
453C2×C22⋊C4—613no—
454C2×C22⋊C4—613no—
455C2×C22⋊C4—616no—
456C2×C42—613no—
457C2×C42—616no—
458C2×C42C22×D6113yes—
459C4⋊C8—611no—
460C4⋊C8—613no—
461C4⋊C8—613no—
462C4⋊C8—613no—
463C4⋊C8—616no—
464C4⋊C8C22×D6111yescharacteristic
465C4⋊C8C22×D6113yes—
466C4⋊C8C22×D6113yes—
467C4⋊C8C22×D6113yes—
468C4⋊C8C22×D6116yes—
469C22⋊C8—611no—
470C22⋊C8—611no—
471C22⋊C8—613no—
472C22⋊C8—613no—
473C22⋊C8—613no—
474C22⋊C8—613no—
475C22⋊C8—613no—
476C22⋊C8—613no—
477C22⋊C8—616no—
478C22⋊C8—616no—
479#97—611no—
480#97—613no—
481#97—613no—
482#97—613no—
483#97—616no—
484C4×C8—611no—
485C4×C8—613no—
486C4×C8—613no—
487C4×C8—613no—
488C4×C8—616no—
489C24—613no—
490#41—1224no—
491#41—12212no—
492#41—1226no—
493#41—1226no—
494#41#1175822414yes—
495#41#1175822614yes—
496C2×Q8—613no—
497C2×Q8—1224no—
498C2×Q8C2×C4×D6111yescharacteristic
499C2×D4—616no—
500C2×D4—613no—
501C2×D4—12212no—
502C2×D4C2×C4×D6113yes—
503C22×C4—613no—
504C22×C4—613no—
505C22×C4—613no—
506C22×C4—613no—
507C22×C4—613no—
508C22×C4—613no—
509C22×C4—611no—
510C22×C4—616no—
511C22×C4—616no—
512C22×C4—1226no—
513C22×C4—1226no—
514C22×C4C2×C4×D6113yes—
515C22×C4C2×C4×D6113yes—
516C22×C4C23×D6113yes—
517M16—26no—
518M16—26no—
519M16—1226no—
520M16—1226no—
521C2×C8—26no—
522C2×C8—26no—
523C2×C8—611no—
524C2×C8—613no—
525C2×C8—613no—
526C2×C8—611no—
527C2×C8—1226no—
528C2×C8—1226no—
529C2×C8C23×D6111yescharacteristic
530C2×C8C23×D6113yes—
531C2×C8C23×D6113yes—
532C2×C8C23×D6111yescharacteristic
533C4⋊C4—613no—
534C4⋊C4—613no—
535C4⋊C4—611no—
536C4⋊C4—611no—
537C4⋊C4—613no—
538C4⋊C4—613no—
539C4⋊C4—613no—
540C4⋊C4—613no—
541C4⋊C4—613no—
542C4⋊C4—613no—
543C4⋊C4C2×C4×D6113yes—
544C4⋊C4C2×C4×D6113yes—
545C22⋊C4—616no—
546C22⋊C4—613no—
547C22⋊C4—613no—
548C22⋊C4—611no—
549C22⋊C4—611no—
550C22⋊C4—613no—
551C22⋊C4—613no—
552C22⋊C4—613no—
553C22⋊C4—613no—
554C22⋊C4C2×C4×D6116yes—
555C42—613no—
556C42—613no—
557C42—616no—
558C42—616no—
559C42—611no—
560C42—613no—
561C42C2×C4×D6113yes—
562C42C2×C4×D6113yes—
563C42C23×D6113yes—
564C42C23×D6111yescharacteristic
565C23—611no—
566C23—613no—
567C23—1226no—
568C23—2443no—
569C23—2443no—
570C23C22×C4×D6113yes—
571Q8—1226no—
572Q8#1451973514yes—
573D4—12212no—
574D4—1226no—
575D4#14519735112yes—
576C2×C4—43no—
577C2×C4—43no—
578C2×C4—611no—
579C2×C4—613no—
580C2×C4—611no—
581C2×C4—613no—
582C2×C4—613no—
583C2×C4—611no—
584C2×C4—1226no—
585C2×C4—1226no—
586C2×C4—1226no—
587C2×C4—1221no—
588C2×C4—1223no—
589C2×C4—1221no—
590C2×C4—1223no—
591C2×C4—2446no—
592C2×C4—2446no—
593C2×C4—2443no—
594C2×C4—2443no—
595C2×C4C22×C4×D6113yes—
596C2×C4C22×C4×D6113yes—
597C2×C4C22×C4×D6111yescharacteristic
598C2×C4C22×C4×D6111yescharacteristic
599C2×C4C22×C4×D6113yes—
600C2×C4C2×#1175822416yes—
601C2×C4C2×#1175822616yes—
602C2×C4C24×D6111yescharacteristic
603C8—21no—
604C8—21no—
605C8—23no—
606C8—23no—
607C8—1221no—
608C8—1221no—
609C8—1223no—
610C8—1223no—
611C22—23no—
612C22—23no—
613C22—1221no—
614C22—1223no—
615C22—1223no—
616C22—1221no—
617C22—1223no—
618C22—1221no—
619C22—4886no—
620C22C2×#1451973516yes—
621C22C23×C4×D6111yescharacteristic
622C4—21no—
623C4—23no—
624C4—21no—
625C4—23no—
626C4—1221no—
627C4—1223no—
628C4—1223no—
629C4—1221no—
630C4—1223no—
631C4—1221no—
632C4C2×#1451973516yes—
633C4C22×#1175822411yescharacteristic
634C4C22×#1175822611yescharacteristic
635C2—26no—
636C2—2441no—
637C2—2443no—
638C2C22×#1451973511yescharacteristic
639C2#2146053011yescharacteristic
640C2#2146053211yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D61
commutator, socleC22×C61C24×C4
FittingC61×#2906C2
prime radicalC2×#41×D61C22
cosocleC2×C4×C61C25
hypercenter#2906D61
hypocenterC61#60129
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ #2906

Complements

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

NH ≅ G/Ntype
2. #21454487C2semidirect
3. #21454484C2semidirect
4. #21454476C2semidirect
5. #21454476C2semidirect
6. #21454469C2semidirect
7. #21454462C2semidirect
8. #21454456C2semidirect
9. C2×#16839822C2semidirect
10. #21454387C2semidirect
13. #21454245C2semidirect
14. #131×Dic61C2semidirect
15. C61×#2906C2semidirect
37. #16839822C22semidirect
38. #16839822C22semidirect
39. #16839822C22semidirect
40. #16839822C22semidirect
41. #16839822C22semidirect
42. #16839822C22semidirect
43. #16839818C22semidirect
44. #16839818C22semidirect
45. #16839814C22semidirect
46. #16839814C22semidirect
47. #16839789C22semidirect
48. #16839789C22semidirect
49. #16839786C22semidirect
50. C2×C4⋊#92418C22semidirect
59. #16839720C22semidirect
60. #16839720C22semidirect
61. #16839717C22semidirect
62. #16839717C22semidirect
63. M16×Dic61C22semidirect
64. M16×Dic61C22semidirect
65. C2×#14519687C22semidirect
66. C2×C8×Dic61C22semidirect
70. C61×#424C22semidirect
71. C61×#424C22semidirect
72. C61×#423C22semidirect
73. C2×C4⋊C8×C61C22semidirect
325. #2906D61semidirect
372. #424C2×D61semidirect
373. #424C2×D61semidirect
375. #423C2×D61semidirect
377. C2×C4⋊C8C2×D61semidirect
394. C61#60129semidirect

Maximal subgroups

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

subgroupindex
#214590182
#214544872
#214544842
#214544762
#214544692
#214544622
#214544562
C2×#168398222
#214543872
#214542662
#214542452
#131×Dic612
C61×#29062
#6012961