Finite Group Databasebeta

← #30603020

Subgroups — #30603020

Order 15616.

982 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519841C211yesmaximal, characteristic
2C2×#16840736C211yesmaximal, characteristic
3C2×#16840727C211yesmaximal, characteristic, complemented
4C2×#16840638C211yesmaximal, characteristic, complemented
5C2×#16840632C211yesmaximal, characteristic, complemented
6C2×(C2×#6923)⋊C8C211yesmaximal, characteristic, complemented
7C2×#16839755C211yesmaximal, characteristic
8C22×#11758213C2211yescharacteristic
9C22×#11758213C2211yescharacteristic
10C22×D61⋊C8C2211yescharacteristic
11C22×C4×#6923C2211yescharacteristic
12C2×#14519841—22no—
13C2×#14519841—22no—
14C2×#14519841C414yescomplemented
15#16840736—22no—
16#16840736C414yescomplemented
17C2×C22⋊#92420—21no—
18C2×C22⋊#92420—21no—
19#16840727—22no—
20#16840727—22no—
21C2×#14519832—21no—
22C2×C4×#92420—21no—
23#16840638—22no—
24#16840632—22no—
25(C2×#6923)⋊C8—22no—
26C22×#11758224C2211yescharacteristic
27C22×C8×D61C2211yescharacteristic
28C2×#14519735C2211yescharacteristic
29#16839755—22no—
30#16839755—22no—
31C2×#14519702C411yescharacteristic, complemented
32C2×#14519700C411yescharacteristic, complemented
33C2×#14519698C411yescharacteristic, complemented
34C2×#102×C61C411yescharacteristic, complemented
35C23×#6923—21no—
36C2×#11758213—21no—
37C2×#11758213—21no—
38C2×#11758213—21no—
39C2×#11758213—21no—
40C2×#11758213—21no—
41C2×#11758213—21no—
42C2×#11758213—21no—
43C2×#11758213—21no—
44C2×#11758213C2×C412yes—
45C2×#11758213C2×C412yes—
46C2×#11758213D412yes—
47C2×#11758213D412yes—
48C2×D61⋊C8—21no—
49C2×D61⋊C8—21no—
50C2×D61⋊C8—21no—
51C2×D61⋊C8—21no—
52C2×D61⋊C8C2×C412yes—
53C2×D61⋊C8D412yes—
54C22×#92420—21no—
55C22×#92420—21no—
56C22×#92420D411yescharacteristic
57C22×#92420D411yescharacteristic
58C2×C4×#6923—21no—
59C2×C4×#6923—21no—
60C2×C4×#6923—21no—
61C2×C4×#6923—21no—
62C2×C4×#6923—21no—
63C2×C4×#6923C2×C412yes—
64#14519841—28no—
65C22⋊#92420—24no—
66C22⋊#92420—24no—
67#14519832—24no—
68C4×#92420—24no—
69C2×#11758224—21no—
70C2×#11758224—21no—
71C2×#11758224—21no—
72C2×#11758224—21no—
73C2×#11758224—21no—
74C2×#11758224—21no—
75C2×#11758224—21no—
76C2×#11758224—21no—
77C2×#11758224—21no—
78C2×#11758224—21no—
79C2×#11758224C2×C412yes—
80C2×#11758224C2×C412yes—
81C22×Dic122C2×C411yescharacteristic
82C22×C22⋊D61—21no—
83C23×Dic61—21no—
84C22×C4×D61C2311yescharacteristic
85C22×#92418C2×C411yescharacteristic
86C2×C8×D61—21no—
87C2×C8×D61—21no—
88C2×C8×D61—21no—
89C2×C8×D61—21no—
90C2×C8×D61—21no—
91C2×C8×D61—21no—
92#14519735—21no—
93#14519735—21no—
94#14519735D412yes—
95#14519735D412yes—
96C2×C4⋊Dic61C2×C411yescharacteristic
97C2×#11758198—21no—
98C2×C4×Dic61—21no—
99#14519702—22no—
100#14519700—22no—
101#14519698—22no—
102C22×D4×C61C2×C411yescharacteristic
103C22×C8×C61C2×C411yescharacteristic
104C2×C4⋊C4×C61C2×C411yescharacteristic
105#102×C61—22no—
106C24×C61—21no—
107C23×D61#4111yescharacteristic
108C22×#6923—22no—
109C22×#6923—22no—
110C22×#6923—22no—
111C22×#6923—41no—
112C22×#6923—41no—
113C22×#6923—41no—
114C22×#6923—41no—
115C2×D4×C61—21no—
116C2×D4×C61—21no—
117C2×D4×C61—21no—
118C2×D4×C61—21no—
119C2×D4×C61—21no—
120C2×D4×C61C4212yes—
121C22×C4×C61—21no—
122C22×C4×C61C22×C411yescharacteristic
123C2×C22⋊D61—22no—
124C2×C22⋊D61—22no—
125C2×C22⋊D61—41no—
126C2×C22⋊D61—41no—
127C2×C22⋊D61—41no—
128C2×C22⋊D61—41no—
129C22×Dic61—21no—
130C22×Dic61—21no—
131C22×Dic61—22no—
132C22×Dic61—22no—
133C22×Dic61—41no—
134C22×Dic61—41no—
135C22×Dic61—41no—
136C22×Dic61—41no—
137C22×Dic61C2×D411yescharacteristic
138#11758224—22no—
139#11758224—22no—
140#11758224—22no—
141#11758224—22no—
142#11758224—22no—
143#11758224—22no—
144#11758224—22no—
145#11758224—22no—
146#11758224—41no—
147#11758224—41no—
148#11758224—41no—
149#11758224—41no—
150#11758224—41no—
151#11758224—41no—
152#11758224—41no—
153#11758224—41no—
154C2×C4×D61C22×C411yescharacteristic
155C2×C4×D61C22×C411yescharacteristic
156C2×C4×D61C2×D411yescharacteristic
157C2×C4×D61C2×D411yescharacteristic
158C2×C4×D61C2×D411yescharacteristic
159C2×C4×D61C2×D411yescharacteristic
160C2×C4×D61C2×D411yescharacteristic
161C2×C4×D61#4111yescharacteristic
162C2×C4×D61#4111yescharacteristic
163C2×C4×D61#4111yescharacteristic
164C2×C4×D61#4111yescharacteristic
165C2×C4×D61#4111yescharacteristic
166C2×Dic122—21no—
167C2×Dic122—21no—
168C2×Dic122—21no—
169C2×Dic122—21no—
170C2×Dic122—21no—
171C2×Dic122C4212yes—
172C2×#92420—22no—
173C2×#92420—21no—
174C2×#92420—22no—
175C2×#92420—21no—
176C2×#92420—22no—
177C2×#92420—21no—
178C2×#92420—21no—
179C2×#92420—22no—
180C2×#92420—41no—
181C2×#92420—41no—
182C2×#92420C22⋊C412yes—
183C2×#92420C22⋊C412yes—
184C4×#6923—22no—
185C4×#6923—22no—
186C4×#6923—41no—
187C4×#6923—41no—
188#11758213—22no—
189#11758213—22no—
190#11758213—22no—
191#11758213—22no—
192#11758213—22no—
193#11758213—41no—
194#11758213—41no—
195#11758213C22⋊C414yes—
196D61⋊C8—22no—
197D61⋊C8—22no—
198D61⋊C8—22no—
199D61⋊C8—22no—
200C2×C8×C61—21no—
201C2×C8×C61—21no—
202C2×C8×C61—21no—
203C4⋊C4×C61—21no—
204C4⋊C4×C61C22⋊C412yes—
205#11758198—22no—
206#11758198—22no—
207C4⋊Dic61—21no—
208C4⋊Dic61C22⋊C412yes—
209C4×Dic61—22no—
210C4×Dic61—22no—
211C2×#92418—21no—
212C2×#92418—21no—
213C2×#92418—21no—
214C8×D61—41no—
215C8×D61—41no—
216C8×D61—41no—
217C8×D61—41no—
218C23×C61—22no—
219C23×C61—41no—
220C23×C61—41no—
221C23×C61—41no—
222C23×C61—41no—
223C23×C61—41no—
224C23×C61—41no—
225C23×C61C4×D411yescharacteristic
226C22×D61—21no—
227C22×D61—21no—
228C22×D61—21no—
229C22×D61—21no—
230C22×D61#11711yescharacteristic
231C22×D61C4×D411yescharacteristic
232C22×D61#12111yescharacteristic
233C22×D61#12311yescharacteristic
234C22×D61#12411yescharacteristic
235C22×D61#12611yescharacteristic
236C2×#6923—24no—
237C2×#6923—42no—
238C2×#6923—42no—
239C2×#6923—42no—
240C2×#6923—42no—
241C2×#6923—42no—
242C2×#6923—42no—
243D4×C61—22no—
244D4×C61—22no—
245D4×C61—41no—
246D4×C61—41no—
247C2×C4×C61—22no—
248C2×C4×C61—41no—
249C2×C4×C61—41no—
250C2×C4×C61C2×C4211yescharacteristic
251C2×C4×C61C2×C22⋊C411yescharacteristic
252C2×C4×C61#11711yescharacteristic
253C2×C4×C61C4×D411yescharacteristic
254C2×C4×C61C4×D411yescharacteristic
255C2×C4×C61C4×D411yescharacteristic
256C22⋊D61—42no—
257C22⋊D61—42no—
258C22⋊D61—42no—
259C22⋊D61—42no—
260C2×Dic61—22no—
261C2×Dic61—22no—
262C2×Dic61—41no—
263C2×Dic61—41no—
264C2×Dic61—41no—
265C2×Dic61—41no—
266C2×Dic61—42no—
267C2×Dic61—42no—
268C2×Dic61—42no—
269C2×Dic61—42no—
270C2×Dic61C2×C22⋊C411yescharacteristic
271C2×Dic61C4×D411yescharacteristic
272C2×Dic61#12011yescharacteristic
273C2×Dic61#12111yescharacteristic
274C2×Dic61#12111yescharacteristic
275C2×Dic61#12311yescharacteristic
276C4×D61C2×C22⋊C411yescharacteristic
277C4×D61#11711yescharacteristic
278C4×D61C4×D411yescharacteristic
279C4×D61C4×D411yescharacteristic
280C4×D61C4×D411yescharacteristic
281C4×D61C4×D411yescharacteristic
282C4×D61C4×D411yescharacteristic
283C4×D61C4×D411yescharacteristic
284C4×D61#12111yescharacteristic
285C4×D61#12111yescharacteristic
286C4×D61#12111yescharacteristic
287C4×D61#12311yescharacteristic
288C4×D61#12411yescharacteristic
289C4×D61#12411yescharacteristic
290C4×D61#12611yescharacteristic
291C4×D61#12711yescharacteristic
292Dic122—22no—
293Dic122—22no—
294Dic122—41no—
295Dic122—41no—
296#92420—22no—
297#92420—22no—
298#92420—24no—
299#92420—42no—
300C8×C61—41no—
301#92418—41no—
302#10934—611nomaximal, Sylow
303C22×C61—42no—
304C22×C61—42no—
305C22×C61—42no—
306C22×C61—81no—
307C22×C61—81no—
308C22×C61—81no—
309C22×C61—81no—
310C22×C61C4×C22⋊C411yescharacteristic
311C22×C61#38611yescharacteristic
312C22×C61#38811yescharacteristic
313C22×C61#44311yescharacteristic
314C22×C61#44311yescharacteristic
315C22×C61#44411yescharacteristic
316C22×C61#44411yescharacteristic
317C2×D61—21no—
318C2×D61—21no—
319C2×D61—21no—
320C2×D61—21no—
321C2×D61—21no—
322C2×D61—21no—
323C2×D61—21no—
324C2×D61—21no—
325C2×D61—21no—
326C2×D61—21no—
327C2×D61—21no—
328C2×D61—21no—
329C2×D61#38811yescharacteristic
330C2×D61#38811yescharacteristic
331C2×D61#38811yescharacteristic
332C2×D61#39011yescharacteristic
333#6923—44no—
334C4×C61—42no—
335C4×C61C4×C22⋊C411yescharacteristic
336C4×C61C4×C22⋊C411yescharacteristic
337C4×C61#38811yescharacteristic
338C4×C61#39011yescharacteristic
339Dic61—42no—
340Dic61—42no—
341Dic61#38611yescharacteristic
342Dic61#38611yescharacteristic
343Dic61#38811yescharacteristic
344Dic61#39011yescharacteristic
345C22×#104—611no—
346C2×#416—611no—
347C2×#408—611no—
348C2×#405—611no—
349C2×#341—611no—
350C2×#339—611no—
351C2×#336—611no—
352C2×C61—82no—
353C2×C61#143711yescharacteristic
354C2×C61#176411yescharacteristic
355C2×C61#176511yescharacteristic
356C2×C61#187611yescharacteristic
357C2×C61#187611yescharacteristic
358C2×C61#192911yescharacteristic
359C2×C61#192911yescharacteristic
360D61—21no—
361D61—21no—
362D61—21no—
363D61—21no—
364C22×#41—611no—
365C22×M16—611no—
366C22×M16—611no—
367C23×C8—611no—
368C23×C8—611no—
369C2×#117—611no—
370C22×C42—611no—
371C2×#104—614no—
372C2×#104—1222no—
373C2×#104—1222no—
374#416—1222no—
375#416—1222no—
376C2×#103—611no—
377C2×#103—611no—
378C2×#102—611no—
379C2×#102#692311yescharacteristic, complemented
380#408—614no—
381#408—1222no—
382C2×C22⋊C8—1221no—
383C2×C22⋊C8—1221no—
384#405—1222no—
385#405—1222no—
386C2×#97—1221no—
387C2×C4×C8—1221no—
388#341—1222no—
389#339—1222no—
390#336—1222no—
391C61#1093411yescharacteristic, complemented, Sylow
392C2×#41—612no—
393C2×#41—612no—
394C2×#41—1221no—
395C2×#41—1221no—
396C2×#41—1221no—
397C2×#41—1221no—
398C2×#41—1221no—
399C2×#41—1221no—
400C2×#41—1221no—
401C2×#41—1221no—
402C2×#41—1221no—
403C2×#41—1221no—
404C22×Q8—611no—
405C22×D4—1221no—
406C22×D4C2×#692311yescharacteristic
407C23×C4—611no—
408C23×C4—1221no—
409C23×C4—1221no—
410C2×M16—612no—
411C2×M16—612no—
412C2×M16—612no—
413C2×M16—612no—
414C2×M16—1221no—
415C2×M16—1221no—
416C2×M16—1221no—
417C2×M16—1221no—
418C2×M16—1221no—
419C2×M16—1221no—
420C2×M16—1221no—
421C2×M16—1221no—
422C22×C8—611no—
423C22×C8—611no—
424C22×C8—612no—
425C22×C8—612no—
426C22×C8—611no—
427C22×C8—1221no—
428C22×C8—1221no—
429C22×C8—1221no—
430C22×C8—1221no—
431C22×C8—1221no—
432C22×C8—1221no—
433C22×C8—1221no—
434C22×C8—1221no—
435C22×C8—1221no—
436C22×C8—1221no—
437C22×C8—1221no—
438C22×C8—1221no—
439C22×C8C2×#692311yescharacteristic
440#117—612no—
441#117—612no—
442#117—1221no—
443#117—1221no—
444C2×C4⋊C4—611no—
445C2×C4⋊C4C2×#692311yescharacteristic
446C2×C22⋊C4—1221no—
447C2×C42—612no—
448C2×C42—1221no—
449C2×C42—1221no—
450C2×C42—1221no—
451C2×C42—1221no—
452C2×C42—1221no—
453C2×C42—1221no—
454#104—1228no—
455#103—1222no—
456#103—1222no—
457#102—22no—
458#102—1222no—
459C22⋊C8—1224no—
460C22⋊C8—1224no—
461#97—1224no—
462C4×C8—1224no—
463C24—21no—
464C24—611no—
465#41—1222no—
466#41—1222no—
467#41—1222no—
468#41—1222no—
469#41—1222no—
470#41—1222no—
471#41—1222no—
472#41—1222no—
473#41—2441no—
474#41—2441no—
475#41—2441no—
476#41—2441no—
477#41—2441no—
478#41—2441no—
479#41—2441no—
480#41—2441no—
481C2×Q8—612no—
482C2×Q8—1221no—
483C2×Q8—1221no—
484C2×Q8—1221no—
485C2×Q8—1221no—
486C2×Q8—1221no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—1222no—
493C2×D4—1222no—
494C2×D4—2441no—
495C2×D4—2441no—
496C2×D4—2441no—
497C2×D4—2441no—
498C2×D4C4×#692312yes—
499C22×C4—21no—
500C22×C4—611no—
501C22×C4—611no—
502C22×C4—611no—
503C22×C4—611no—
504C22×C4—611no—
505C22×C4—611no—
506C22×C4—611no—
507C22×C4—611no—
508C22×C4—611no—
509C22×C4—611no—
510C22×C4—611no—
511C22×C4—611no—
512C22×C4—611no—
513C22×C4—1222no—
514C22×C4—1222no—
515C22×C4—1222no—
516C22×C4—1222no—
517C22×C4—1222no—
518C22×C4—1221no—
519C22×C4—1221no—
520C22×C4—2441no—
521C22×C4—2441no—
522C22×C4—2441no—
523C22×C4—2441no—
524C22×C4—2441no—
525C22×C4—2441no—
526C22×C4—2441no—
527C22×C4—2441no—
528C22×C4C22×#692311yescharacteristic
529M16—614no—
530M16—1222no—
531M16—1222no—
532M16—1222no—
533M16—1222no—
534M16—1222no—
535M16—2441no—
536M16—2441no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—612no—
541C2×C8—612no—
542C2×C8—1221no—
543C2×C8—1222no—
544C2×C8—1221no—
545C2×C8—1222no—
546C2×C8—1222no—
547C2×C8—1222no—
548C2×C8—1222no—
549C2×C8—1221no—
550C2×C8—1221no—
551C2×C8—1222no—
552C2×C8—1222no—
553C2×C8—1222no—
554C2×C8—1221no—
555C2×C8—1221no—
556C2×C8—1221no—
557C2×C8—2441no—
558C2×C8—2441no—
559C2×C8—2441no—
560C2×C8—2441no—
561C2×C8—2441no—
562C2×C8—2441no—
563C4⋊C4—21no—
564C4⋊C4—612no—
565C4⋊C4—1221no—
566C4⋊C4C22⋊#692312yes—
567C22⋊C4—1222no—
568C22⋊C4—1222no—
569C42—1222no—
570C42—1222no—
571C42—1222no—
572C42—1222no—
573C42—2441no—
574C42—2441no—
575C23—22no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23—611no—
583C23—611no—
584C23—611no—
585C23—611no—
586C23—611no—
587C23—611no—
588C23—1221no—
589C23—1221no—
590C23—1221no—
591C23—1221no—
592C23D4×#692311yescharacteristic
593Q8—1222no—
594Q8—1222no—
595Q8—2441no—
596Q8—2441no—
597D4—22no—
598D4—22no—
599D4—41no—
600D4—41no—
601D4—2442no—
602D4—2442no—
603D4—2442no—
604D4—2442no—
605C2×C4—22no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—611no—
609C2×C4—611no—
610C2×C4—611no—
611C2×C4—611no—
612C2×C4—611no—
613C2×C4—611no—
614C2×C4—611no—
615C2×C4—611no—
616C2×C4—611no—
617C2×C4—611no—
618C2×C4—611no—
619C2×C4—611no—
620C2×C4—611no—
621C2×C4—611no—
622C2×C4—611no—
623C2×C4—611no—
624C2×C4—611no—
625C2×C4—611no—
626C2×C4—611no—
627C2×C4—611no—
628C2×C4—611no—
629C2×C4—611no—
630C2×C4—1224no—
631C2×C4—1222no—
632C2×C4—1222no—
633C2×C4—2442no—
634C2×C4—2442no—
635C2×C4—2442no—
636C2×C4—2442no—
637C2×C4—2442no—
638C2×C4—2442no—
639C2×C4—2442no—
640C2×C4—2442no—
641C2×C4—2442no—
642C2×C4—2442no—
643C2×C4—2441no—
644C2×C4—2441no—
645C2×C4—2441no—
646C2×C4—2441no—
647C2×C4C2×C4×#692311yescharacteristic
648C2×C4C2×C22⋊#692311yescharacteristic
649C2×C4#1451985611yescharacteristic
650C2×C4D4×#692311yescharacteristic
651C2×C4D4×#692311yescharacteristic
652C2×C4D4×#692311yescharacteristic
653C8—41no—
654C8—1222no—
655C8—1222no—
656C8—1224no—
657C8—2442no—
658C8—2441no—
659C22—42no—
660C22—42no—
661C22—42no—
662C22—81no—
663C22—81no—
664C22—81no—
665C22—81no—
666C22—611no—
667C22—611no—
668C22—611no—
669C22—611no—
670C22—1221no—
671C22—1221no—
672C22—1221no—
673C22—1221no—
674C22—1221no—
675C22—1221no—
676C22—1221no—
677C22—1221no—
678C22—1221no—
679C22—1221no—
680C22—1221no—
681C22—1221no—
682C22C22⋊C4×#692311yescharacteristic
683C22#1684071011yescharacteristic
684C22#1684071211yescharacteristic
685C22#1684080411yescharacteristic
686C22#1684080511yescharacteristic
687C22#1684080711yescharacteristic
688C22#1684080911yescharacteristic
689C4—42no—
690C4—611no—
691C4—611no—
692C4—611no—
693C4—611no—
694C4—2444no—
695C4—2442no—
696C4—2442no—
697C4C4×C22⋊#692311yescharacteristic
698C4C22⋊C4×#692311yescharacteristic
699C4#1684071211yescharacteristic
700C4#1684071411yescharacteristic
701C2—82no—
702C2—1221no—
703C2—1221no—
704C2—1221no—
705C2—1221no—
706C2#2146100011yescharacteristic
707C2#2146159411yescharacteristic
708C2#2146159811yescharacteristic
709C2#2146181011yescharacteristic
710C2#2146181111yescharacteristic
711C2#2146190011yescharacteristic
712C2#2146190111yescharacteristic
subgroupG/H
centerC23D4×#6923
commutatorC2×C4×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC2×#102×C61C4
socleC23×C61C4×D4
prime radicalC22×#11758224C22
cosocleC22×C4×D61C23
hypercenterC2×#102#6923
hypocenterC61#10934
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
3. C2×#16840727C2semidirect
4. C2×#16840638C2semidirect
5. C2×#16840632C2semidirect
6. C2×(C2×#6923)⋊C8C2semidirect
14. C2×#14519841C4semidirect
16. #16840736C4semidirect
31. C2×#14519702C4semidirect
32. C2×#14519700C4semidirect
33. C2×#14519698C4semidirect
34. C2×#102×C61C4semidirect
379. C2×#102#6923semidirect
391. C61#10934semidirect

Maximal subgroups

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

subgroupindex
C22×#145198412
C2×#168407362
C2×#168407272
C2×#168406382
C2×#168406322
C2×(C2×#6923)⋊C82
C2×#168397552
#1093461