Finite Group Databasebeta

← #30602577

Subgroups — #30602577

Order 15616.

1186 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840840C211yesmaximal, characteristic
2C2×#16840760C211yesmaximal, characteristic
3C2×#16840644C211yesmaximal, characteristic, complemented
4#21461522C211yesmaximal, characteristic, complemented
5#21461506C211yesmaximal, characteristic, complemented
6C2×#16840631C211yesmaximal, characteristic, complemented
7C2×#16839760C211yesmaximal, characteristic
8#16840840—22no—
9#16840840—22no—
10#16840840—22no—
11#16840840C414yescomplemented
12C2×#14519864—22no—
13C2×#14519864—22no—
14C2×D61⋊M16C2211yescharacteristic
15C2×D61⋊M16C2211yescharacteristic
16C2×D61⋊M16C2211yescharacteristic
17C22×#11758217—22no—
18C2×#14519856C2211yescharacteristic
19#16840760—22no—
20#16840760C414yescomplemented
21C2×#14519841—22no—
22#16840644—22no—
23#16840642—22no—
24#16840635—22no—
25#16840631—22no—
26C22×#11758224C2211yescharacteristic
27C22×#11758189C2211yescharacteristic
28C2×C4⋊C4×D61C2211yescharacteristic
29#16839760—22no—
30#16839760—22no—
31C2×#14519702C411yescharacteristic, complemented
32C2×#14519700C411yescharacteristic, complemented
33C2×#14519698C411yescharacteristic, complemented
34C2×#102×C61C411yescharacteristic, complemented
35#14519864—28no—
36#14519864—28no—
37#14519864—28no—
38#14519864—28no—
39C2×#11758213—21no—
40C2×#11758213—21no—
41C2×#11758213—21no—
42D61⋊M16—21no—
43D61⋊M16—21no—
44D61⋊M16—21no—
45D61⋊M16—21no—
46D61⋊M16—21no—
47D61⋊M16—21no—
48D61⋊M16—21no—
49D61⋊M16C2×C412yes—
50D61⋊M16C2×C412yes—
51D61⋊M16C2×C412yes—
52D61⋊M16D412yes—
53D61⋊M16D412yes—
54C2×#11758217—24no—
55C2×#11758217—28no—
56C2×#11758217—21no—
57C2×#11758217—28no—
58C2×#11758217—21no—
59C2×#11758217D412yes—
60C2×D61⋊C8—21no—
61C2×D61⋊C8—21no—
62C2×D61⋊C8D412yes—
63C22×#92420—24no—
64#14519856—21no—
65#14519856—21no—
66#14519856—21no—
67#14519856C2×C412yes—
68C2×C4⋊#6923—21no—
69C2×C22⋊#6923—21no—
70C2×C4×#6923—21no—
71#14519841—28no—
72C2×#11758224—21no—
73C2×#11758224—21no—
74C2×#11758224—21no—
75C2×#11758224—21no—
76C2×#11758224—21no—
77C2×#11758224—21no—
78C2×#11758224C2×C412yes—
79C2×#11758224C2×C412yes—
80C2×#11758224D412yes—
81C2×#11758224D412yes—
82C2×#11758224D412yes—
83C2×#11758224Q812yes—
84C22×Dic122C2×C411yescharacteristic
85C22×C22⋊D61—21no—
86C23×Dic61—21no—
87C22×C4×D61—21no—
88C22×C4×D61C2311yescharacteristic
89C2×#11758189—21no—
90C2×#11758189—21no—
91C2×#11758189—21no—
92C2×#11758189—21no—
93C2×#11758189—21no—
94C2×#11758189—21no—
95C22×#92418C2×C411yescharacteristic
96C2×C4⋊Dic61C2×C411yescharacteristic
97C2×#11758196—21no—
98C4⋊C4×D61—21no—
99C4⋊C4×D61—21no—
100C4⋊C4×D61—21no—
101C4⋊C4×D61—21no—
102#14519702—22no—
103#14519700—22no—
104#14519698—22no—
105C22×D4×C61C2×C411yescharacteristic
106C22×C8×C61C2×C411yescharacteristic
107C2×C4⋊C4×C61C2×C411yescharacteristic
108#102×C61—22no—
109C24×C61—21no—
110C23×D61#4111yescharacteristic
111C22×#6923—41no—
112C2×D4×C61—21no—
113C2×D4×C61—21no—
114C2×D4×C61—21no—
115C2×D4×C61C4212yes—
116C2×D4×C61C22⋊C412yes—
117C2×D4×C61C4⋊C412yes—
118C22×C4×C61—21no—
119C22×C4×C61C22×C411yescharacteristic
120C2×C22⋊D61—22no—
121C2×C22⋊D61—22no—
122C2×C22⋊D61—22no—
123C2×C22⋊D61—22no—
124C2×C22⋊D61—22no—
125C2×C22⋊D61—22no—
126C22×Dic61—21no—
127C22×Dic61—22no—
128C22×Dic61—22no—
129C22×Dic61—22no—
130C22×Dic61—22no—
131C22×Dic61—22no—
132C22×Dic61—22no—
133C22×Dic61—21no—
134C22×Dic61C2×D411yescharacteristic
135#11758224—22no—
136#11758224—22no—
137#11758224—22no—
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—22no—
147#11758224C22⋊C414yes—
148#11758224C22⋊C414yes—
149#11758224C4⋊C414yes—
150#11758224C4⋊C414yes—
151C2×C4×D61—41no—
152C2×C4×D61—41no—
153C2×C4×D61—82no—
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×D61C2×D411yescharacteristic
162C2×C4×D61C2×Q811yescharacteristic
163C2×C4×D61#4111yescharacteristic
164C2×C4×D61#4111yescharacteristic
165C2×C4×D61#4111yescharacteristic
166C2×Dic122—21no—
167C2×Dic122—21no—
168C2×Dic122—21no—
169C2×Dic122C4212yes—
170C2×Dic122C22⋊C412yes—
171C2×Dic122C4⋊C412yes—
172C22⋊#6923—22no—
173C22⋊#6923—41no—
174#11758217—216no—
175#11758217—22no—
176#11758217—22no—
177#11758217—22no—
178#11758217—22no—
179#11758217—41no—
180#11758217C22⋊C414yes—
181C2×#92420—216no—
182C2×#92420—22no—
183C2×#92420—22no—
184C2×#92420—41no—
185C4⋊#6923—22no—
186C4⋊#6923—41no—
187C4×#6923—22no—
188C4×#6923—41no—
189#11758213—22no—
190#11758213—22no—
191#11758213—22no—
192#11758213—22no—
193#11758213—22no—
194#11758213—41no—
195D61⋊C8—22no—
196D61⋊C8—22no—
197D61⋊C8—22no—
198D61⋊C8—22no—
199D61⋊C8—41no—
200D61⋊C8C22⋊C414yes—
201C2×C8×C61—21no—
202C2×C8×C61—21no—
203C2×C8×C61—21no—
204C4⋊C4×C61—21no—
205C4⋊C4×C61—21no—
206C4⋊Dic61—21no—
207C4⋊Dic61—21no—
208#11758196—41no—
209#11758196—41no—
210C2×#92418—21no—
211C2×#92418—21no—
212C2×#92418—21no—
213#11758189—41no—
214#11758189—41no—
215#11758189—41no—
216#11758189—41no—
217C23×C61—22no—
218C23×C61—22no—
219C23×C61—22no—
220C23×C61—81no—
221C23×C61—81no—
222C23×C61C4×D411yescharacteristic
223C22×D61—41no—
224C22×D61—41no—
225C22×D61#11711yescharacteristic
226C22×D61C4×D411yescharacteristic
227C22×D61#12111yescharacteristic
228C22×D61C22⋊Q811yescharacteristic
229C22×D61#12311yescharacteristic
230C22×D61#12311yescharacteristic
231C2×#6923—42no—
232C2×#6923—81no—
233C2×#6923—81no—
234D4×C61—22no—
235D4×C61—22no—
236D4×C61—22no—
237D4×C61#9514yes—
238C2×C4×C61—41no—
239C2×C4×C61—81no—
240C2×C4×C61C2×C4211yescharacteristic
241C2×C4×C61C2×C22⋊C411yescharacteristic
242C2×C4×C61C2×C4⋊C411yescharacteristic
243C2×C4×C61C4×D411yescharacteristic
244C2×C4×C61C4×D411yescharacteristic
245C2×C4×C61C4×D411yescharacteristic
246C22⋊D61—24no—
247C22⋊D61—24no—
248C22⋊D61—24no—
249C22⋊D61—24no—
250C2×Dic61—22no—
251C2×Dic61—22no—
252C2×Dic61—22no—
253C2×Dic61—24no—
254C2×Dic61—24no—
255C2×Dic61—24no—
256C2×Dic61—24no—
257C2×Dic61—41no—
258C2×Dic61—81no—
259C2×Dic61C2×C22⋊C411yescharacteristic
260C2×Dic61C4×D411yescharacteristic
261C2×Dic61#12011yescharacteristic
262C2×Dic61#12011yescharacteristic
263C2×Dic61#12111yescharacteristic
264C2×Dic61C22⋊Q811yescharacteristic
265C4×D61—82no—
266C4×D61—82no—
267C4×D61C2×C22⋊C411yescharacteristic
268C4×D61C2×C22⋊C411yescharacteristic
269C4×D61C2×C22⋊C411yescharacteristic
270C4×D61C2×C4⋊C411yescharacteristic
271C4×D61C2×C4⋊C411yescharacteristic
272C4×D61#11711yescharacteristic
273C4×D61C4×D411yescharacteristic
274C4×D61C4×D411yescharacteristic
275C4×D61#12011yescharacteristic
276C4×D61#12011yescharacteristic
277C4×D61#12111yescharacteristic
278C4×D61#12111yescharacteristic
279C4×D61C22⋊Q811yescharacteristic
280C4×D61C22⋊Q811yescharacteristic
281C4×D61#12311yescharacteristic
282C4×D61#12311yescharacteristic
283Dic122—22no—
284Dic122—22no—
285Dic122—22no—
286Dic122#9514yes—
287#92420—24no—
288#92420—24no—
289#92420—42no—
290C8×C61—41no—
291#92418—41no—
292#10784—611nomaximal, Sylow
293C22×C61—21no—
294C22×C61—21no—
295C22×C61—24no—
296C22×C61—42no—
297C22×C61—42no—
298C22×C61—82no—
299C22×C61—82no—
300C22×C61C4×C22⋊C411yescharacteristic
301C22×C61#38511yescharacteristic
302C22×C61#38611yescharacteristic
303C2×D61—21no—
304C2×D61—21no—
305C2×D61—21no—
306C2×D61—21no—
307C2×D61—41no—
308C2×D61—41no—
309C2×D61—41no—
310C2×D61—41no—
311C2×D61#38011yescharacteristic
312C2×D61#38111yescharacteristic
313C2×D61#38511yescharacteristic
314C2×D61#38611yescharacteristic
315#6923—82no—
316C4×C61—81no—
317C4×C61C2×#9511yescharacteristic
318C4×C61C4×C22⋊C411yescharacteristic
319C4×C61#38511yescharacteristic
320C4×C61#38611yescharacteristic
321Dic61—24no—
322Dic61—81no—
323Dic61#37911yescharacteristic
324Dic61#38011yescharacteristic
325Dic61#38511yescharacteristic
326Dic61#38611yescharacteristic
327C2×#568—611no—
328C2×#421—611no—
329C2×#417—611no—
330C2×#344—611no—
331C2×#343—611no—
332#1736—611no—
333C2×#338—611no—
334C2×C61—21no—
335C2×C61—21no—
336C2×C61—44no—
337C2×C61C22⋊#9511yescharacteristic
338C2×C61#190211yescharacteristic
339C2×C61#190311yescharacteristic
340D61—21no—
341D61—21no—
342D61—21no—
343D61—21no—
344C22×#41—611no—
345#568—614no—
346#568—1222no—
347#568—1222no—
348#568—1222no—
349C2×#131—1222no—
350C2×#131—1222no—
351C22×M16—611no—
352C22×M16—611no—
353C22×M16—611no—
354C22×M16—611no—
355C22×M16—1222no—
356C2×#117—611no—
357C22×C4⋊C4—611no—
358#421—614no—
359#421—1222no—
360C2×#104—1222no—
361#417—1222no—
362#417—1222no—
363C2×#103—611no—
364C2×#103—611no—
365C2×#102—611no—
366C2×#102#692311yescharacteristic, complemented
367#344—1222no—
368#343—1222no—
369#340—1222no—
370#338—1222no—
371C61#1078411yescharacteristic, complemented, Sylow
372C2×#41—612no—
373C2×#41—612no—
374C2×#41—612no—
375C2×#41—612no—
376C2×#41—612no—
377C2×#41—612no—
378C2×#41—1221no—
379C2×#41—1221no—
380C2×#41—1221no—
381C2×#41—1221no—
382C2×#41—1221no—
383C2×#41—1221no—
384C22×Q8—611no—
385C22×D4—1221no—
386C22×D4C2×#692311yescharacteristic
387C23×C4—611no—
388C23×C4—1221no—
389C23×C4—1221no—
390#131—1228no—
391#131—1228no—
392#131—1228no—
393#131—1228no—
394C2×M16—612no—
395C2×M16—612no—
396C2×M16—612no—
397C2×M16—612no—
398C2×M16—612no—
399C2×M16—612no—
400C2×M16—1221no—
401C2×M16—1221no—
402C2×M16—1221no—
403C2×M16—1221no—
404C2×M16—1221no—
405C2×M16—1221no—
406C2×M16—1228no—
407C2×M16—1221no—
408C2×M16—1221no—
409C2×M16—1221no—
410C2×M16—1221no—
411C2×M16—1221no—
412C2×M16—1221no—
413C2×M16—1221no—
414C2×M16—1224no—
415C2×M16—1228no—
416C2×M16—1221no—
417C2×M16—1221no—
418C2×M16—1221no—
419C2×M16—1221no—
420C2×M16—1221no—
421C22×C8—612no—
422C22×C8—611no—
423C22×C8—1221no—
424C22×C8—1224no—
425C22×C8—1221no—
426C22×C8C2×#692311yescharacteristic
427#117—612no—
428#117—1221no—
429#117—1221no—
430#117—1221no—
431C2×C4⋊C4—611no—
432C2×C4⋊C4—1221no—
433C2×C4⋊C4—1221no—
434C2×C4⋊C4—1221no—
435C2×C4⋊C4—1221no—
436C2×C4⋊C4—1221no—
437C2×C4⋊C4—1221no—
438C2×C4⋊C4C2×#692311yescharacteristic
439C2×C22⋊C4—1221no—
440C2×C42—1221no—
441#104—1228no—
442#103—1222no—
443#103—1222no—
444#102—22no—
445#102—1222no—
446C24—21no—
447C24—611no—
448#41—614no—
449#41—614no—
450#41—614no—
451#41—614no—
452#41—1222no—
453#41—1222no—
454#41—1222no—
455#41—1222no—
456#41—1222no—
457#41—1222no—
458#41—1222no—
459#41—1222no—
460#41—1222no—
461#41—1222no—
462#41—1222no—
463#41—1222no—
464C2×Q8—612no—
465C2×Q8—612no—
466C2×Q8—612no—
467C2×Q8—1221no—
468C2×Q8—1221no—
469C2×Q8—1221no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—1222no—
474C2×D4—1222no—
475C2×D4—1222no—
476C2×D4—1222no—
477C2×D4—1222no—
478C2×D4—1222no—
479C2×D4C4×#692312yes—
480C2×D4C4⋊#692312yes—
481C2×D4C22⋊#692312yes—
482C22×C4—21no—
483C22×C4—611no—
484C22×C4—611no—
485C22×C4—611no—
486C22×C4—611no—
487C22×C4—611no—
488C22×C4—611no—
489C22×C4—611no—
490C22×C4—611no—
491C22×C4—611no—
492C22×C4—611no—
493C22×C4—611no—
494C22×C4—611no—
495C22×C4—611no—
496C22×C4—1222no—
497C22×C4—1222no—
498C22×C4—1222no—
499C22×C4—1222no—
500C22×C4—1222no—
501C22×C4—1222no—
502C22×C4—1221no—
503C22×C4—1221no—
504C22×C4—4882no—
505C22×C4—2441no—
506C22×C4—2441no—
507C22×C4—2441no—
508C22×C4C22×#692311yescharacteristic
509M16—614no—
510M16—1222no—
511M16—1222no—
512M16—1222no—
513M16—1222no—
514M16—1222no—
515M16—1222no—
516M16—1222no—
517M16—12216no—
518M16—1222no—
519M16—1222no—
520M16—2441no—
521M16—2441no—
522M16—2441no—
523M16—2441no—
524M16—2441no—
525M16—2441no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—614no—
530C2×C8—1222no—
531C2×C8—1222no—
532C2×C8—1222no—
533C2×C8—1222no—
534C2×C8—1222no—
535C2×C8—12216no—
536C2×C8—1222no—
537C2×C8—1221no—
538C2×C8—1221no—
539C2×C8—1221no—
540C2×C8—2441no—
541C2×C8—2441no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—1222no—
545C4⋊C4—1221no—
546C4⋊C4—1221no—
547C4⋊C4—2441no—
548C4⋊C4—2441no—
549C4⋊C4—2441no—
550C22⋊C4—1222no—
551C22⋊C4—2441no—
552C42—1222no—
553C42—2441no—
554C23—22no—
555C23—22no—
556C23—22no—
557C23—81no—
558C23—81no—
559C23—611no—
560C23—611no—
561C23—611no—
562C23—611no—
563C23—611no—
564C23—611no—
565C23—2441no—
566C23—2441no—
567C23D4×#692311yescharacteristic
568Q8—614no—
569Q8—1222no—
570Q8—1222no—
571Q8—1222no—
572D4—22no—
573D4—22no—
574D4—22no—
575D4—1224no—
576D4—1224no—
577D4—1224no—
578D4—1224no—
579D4(C2×#6923)⋊C414yes—
580C2×C4—41no—
581C2×C4—81no—
582C2×C4—611no—
583C2×C4—611no—
584C2×C4—611no—
585C2×C4—611no—
586C2×C4—611no—
587C2×C4—611no—
588C2×C4—611no—
589C2×C4—611no—
590C2×C4—611no—
591C2×C4—611no—
592C2×C4—611no—
593C2×C4—611no—
594C2×C4—611no—
595C2×C4—611no—
596C2×C4—611no—
597C2×C4—611no—
598C2×C4—611no—
599C2×C4—611no—
600C2×C4—611no—
601C2×C4—611no—
602C2×C4—611no—
603C2×C4—611no—
604C2×C4—1224no—
605C2×C4—1224no—
606C2×C4—1224no—
607C2×C4—1224no—
608C2×C4—1222no—
609C2×C4—1222no—
610C2×C4—1222no—
611C2×C4—4882no—
612C2×C4—4882no—
613C2×C4—4881no—
614C2×C4—4881no—
615C2×C4—4881no—
616C2×C4—2442no—
617C2×C4—2441no—
618C2×C4C2×C4×#692311yescharacteristic
619C2×C4C2×C22⋊#692311yescharacteristic
620C2×C4C2×C4⋊#692311yescharacteristic
621C2×C4D4×#692311yescharacteristic
622C2×C4D4×#692311yescharacteristic
623C2×C4D4×#692311yescharacteristic
624C8—41no—
625C8—1224no—
626C8—1224no—
627C8—2442no—
628C8—2441no—
629C22—21no—
630C22—21no—
631C22—24no—
632C22—42no—
633C22—42no—
634C22—82no—
635C22—82no—
636C22—611no—
637C22—611no—
638C22—611no—
639C22—611no—
640C22—1221no—
641C22—1221no—
642C22—1221no—
643C22—1221no—
644C22—2441no—
645C22—2441no—
646C22—2441no—
647C22—2441no—
648C22C22⋊C4×#692311yescharacteristic
649C22#1684070911yescharacteristic
650C22#1684071011yescharacteristic
651C4—81no—
652C4—611no—
653C4—611no—
654C4—611no—
655C4—611no—
656C4—1224no—
657C4—4882no—
658C4—4881no—
659C4C2×(C2×#6923)⋊C411yescharacteristic
660C4C22⋊C4×#692311yescharacteristic
661C4#1684070911yescharacteristic
662C4#1684071011yescharacteristic
663C2—21no—
664C2—21no—
665C2—44no—
666C2—1221no—
667C2—1221no—
668C2—1221no—
669C2—1221no—
670C2#2146099211yescharacteristic
671C2#2146184811yescharacteristic
672C2#2146185011yescharacteristic
subgroupG/H
centerC22#16840710
commutatorC2×C4×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC2×#102×C61C4
socleC22×C61#386
prime radicalC22×#11758224C22
cosocleC22×C4×D61C23
hypercenterC2×#102#6923
hypocenterC61#10784
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
3. C2×#16840644C2semidirect
4. #21461522C2semidirect
5. #21461506C2semidirect
6. C2×#16840631C2semidirect
11. #16840840C4semidirect
20. #16840760C4semidirect
31. C2×#14519702C4semidirect
32. C2×#14519700C4semidirect
33. C2×#14519698C4semidirect
34. C2×#102×C61C4semidirect
366. C2×#102#6923semidirect
371. C61#10784semidirect

Maximal subgroups

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

subgroupindex
C2×#168408402
C2×#168407602
C2×#168406442
#214615222
#214615062
C2×#168406312
C2×#168397602
#1078461