Finite Group Databasebeta

← #29682574

Subgroups — #29682574

Order 15616.

990 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454406C211yesmaximal, characteristic
2C2×#16839769C211yesmaximal, characteristic
3#419×D61C211yesmaximal, characteristic
4C2×#101×D61C211yesmaximal, characteristic
5#21454235C211yesmaximal, characteristic
6#21446477C211yesmaximal, characteristic, complemented
7#21446476C211yesmaximal, characteristic, complemented
8#21446475C211yesmaximal, characteristic, complemented
9#21446474C211yesmaximal, characteristic, complemented
10#21446473C211yesmaximal, characteristic, complemented
11#21446472C211yesmaximal, characteristic, complemented
12#21446471C211yesmaximal, characteristic, complemented
13#21445556C211yesmaximal, characteristic
14#21445544C211yesmaximal, characteristic
15C61×#1930C211yesmaximal, characteristic, complemented
16C22×Q8×D61C2211yescharacteristic
17C22×#11758189C2211yescharacteristic
18C2×M16×D61C2211yescharacteristic
19C2×M16×D61C2211yescharacteristic
20C2×M16×D61C2211yescharacteristic
21C2×#14519735C2211yescharacteristic
22#117×D61C2211yescharacteristic
23#16839805C2211yescharacteristic
24#16839804C2211yescharacteristic
25#16839803—21no—
26#16839802C2211yescharacteristic
27#16839801—21no—
28#16839799—21no—
29#16839797—21no—
30#16839772C2211yescharacteristic
31#16839771C2211yescharacteristic
32#16839770C2211yescharacteristic
33#16839769—21no—
34#16839769—21no—
35#16839769—21no—
36#16839769—21no—
37#16839769—21no—
38#16839769—21no—
39C2×#14519702C2211yescharacteristic
40C2×#14519701C2211yescharacteristic
41C2×#14519700C2211yescharacteristic
42#103×D61—21no—
43#103×D61—21no—
44C2×#14519696C2211yescharacteristic
45C2×#14519695C2211yescharacteristic
46C2×#14519695C2211yescharacteristic
47#101×D61C418yescomplemented
48#16839720C2211yescharacteristic
49#16839719—21no—
50#16839718C2211yescharacteristic
51#16839717C2211yescharacteristic
52#16839716—21no—
53#16839714—21no—
54C4×#11758189—21no—
55#16839531C2211yescharacteristic
56#16839530C2211yescharacteristic
57#16839530C2211yescharacteristic
58#16839527C2211yescharacteristic
59#16839526C2211yescharacteristic
60#16839526C2211yescharacteristic
61C61×#428C2211yescharacteristic
62C61×#419C2211yescharacteristic
63C2×#103×C61C2211yescharacteristic
64C2×#101×C61C2211yescharacteristic
65C61×#405C2211yescharacteristic
66C61×#343C2211yescharacteristic
67C61×#341C2211yescharacteristic
68C22×Dic122—21no—
69C22×Dic122C2311yescharacteristic
70C2×Q8×D61—22no—
71C2×Q8×D61—21no—
72C2×Q8×D61—21no—
73C2×Q8×D61—21no—
74C2×Q8×D61—21no—
75C2×Q8×D61—22no—
76C2×Q8×D61—22no—
77C2×Q8×D61C2×C414yes—
78C22×C4×D61—21no—
79C22×C4×D61C2311yescharacteristic
80C2×#11758194C2311yescharacteristic
81C2×#11758194C2311yescharacteristic
82C2×#11758194C2311yescharacteristic
83C2×#11758189—21no—
84C2×#11758189—21no—
85C2×#11758189—22no—
86C2×#11758189—22no—
87C2×#11758189—21no—
88C2×#11758189D411yescharacteristic
89C2×#11758189D411yescharacteristic
90C2×#11758189D411yescharacteristic
91C2×#11758189D411yescharacteristic
92M16×D61—22no—
93M16×D61—22no—
94M16×D61—22no—
95M16×D61—22no—
96M16×D61C2×C414yes—
97M16×D61C2×C414yes—
98C22×#92418C2311yescharacteristic
99C2×C8×D61—21no—
100C2×C8×D61—21no—
101C2×C8×D61—21no—
102#14519736C2311yescharacteristic
103#14519735—21no—
104#14519735—21no—
105#14519735—21no—
106#14519735—21no—
107#14519735D411yescharacteristic
108#14519735D411yescharacteristic
109#14519734—21no—
110#14519733—21no—
111C2×C4⋊Dic61C2311yescharacteristic
112C4⋊C4×D61D411yescharacteristic
113C4⋊C4×D61D411yescharacteristic
114C2×#11758198—21no—
115C22⋊C4×D61—21no—
116C2×C4×Dic61—21no—
117C42×D61—21no—
118#14519711—21no—
119#14519710—21no—
120#14519710—21no—
121#14519709—21no—
122#14519708—21no—
123#14519708—21no—
124#14519702—21no—
125#14519702—21no—
126#14519702—21no—
127#14519702—21no—
128#14519701—21no—
129#14519701—21no—
130#14519701—21no—
131#14519701—21no—
132#14519700—21no—
133#14519700—21no—
134#14519700—21no—
135#14519700—21no—
136#14519696C2×C414yescomplemented
137#14519695C2×C414yescomplemented
138#14519695C2×C414yescomplemented
139#14519688—21no—
140#14519687—21no—
141#14519687—21no—
142C4×#92418—21no—
143C8×Dic61—21no—
144C8×Dic61—21no—
145C22×Q8×C61C2311yescharacteristic
146C2×M16×C61C2311yescharacteristic
147C2×M16×C61C2311yescharacteristic
148C2×M16×C61C2311yescharacteristic
149C22×C8×C61C2311yescharacteristic
150#117×C61C2311yescharacteristic
151C2×C4⋊C4×C61C2311yescharacteristic
152#107×C61—21no—
153#106×C61—21no—
154#103×C61—21no—
155#103×C61—21no—
156#103×C61—21no—
157#103×C61—21no—
158#101×C61C2×C414yescomplemented
159#97×C61—21no—
160C4×C8×C61—21no—
161C23×D61#4111yescharacteristic
162C2×Q8×C61—21no—
163C2×Q8×C61—21no—
164C2×Q8×C61—21no—
165C2×Q8×C61—21no—
166C2×Q8×C61—21no—
167C2×Q8×C61C22×C412yes—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61C2411yescharacteristic
171C22×Dic61—21no—
172C22×Dic61—21no—
173C22×Dic61#4111yescharacteristic
174Q8×D61—24no—
175Q8×D61—24no—
176Q8×D61—24no—
177Q8×D61—24no—
178Q8×D61—42no—
179Q8×D61—42no—
180Q8×D61—42no—
181Q8×D61—42no—
182C2×C4×D61—24no—
183C2×C4×D61—21no—
184C2×C4×D61—21no—
185C2×C4×D61—41no—
186C2×C4×D61—41no—
187C2×C4×D61—42no—
188C2×C4×D61C22×C412yes—
189C2×C4×D61C2×D411yescharacteristic
190C2×C4×D61C2×D411yescharacteristic
191C2×C4×D61C2×D411yescharacteristic
192C2×C4×D61C2×D411yescharacteristic
193C2×C4×D61#4112yes—
194C2×C4×D61#4112yes—
195C2×C4×D61#4112yes—
196C2×Dic122—21no—
197C2×Dic122—21no—
198C2×Dic122—21no—
199C2×Dic122—21no—
200C2×Dic122—21no—
201C2×Dic122—24no—
202C2×Dic122—41no—
203C2×Dic122—41no—
204C2×Dic122—42no—
205C2×Dic122C22×C412yes—
206M16×C61—21no—
207M16×C61—21no—
208M16×C61—21no—
209M16×C61—21no—
210M16×C61C22×C412yes—
211M16×C61C22×C412yes—
212C2×C8×C61—21no—
213C2×C8×C61—21no—
214C2×C8×C61—21no—
215C2×C8×C61—21no—
216C2×C8×C61—21no—
217C2×C8×C61C2×D411yescharacteristic
218C2×C8×C61C2×D411yescharacteristic
219C4⋊C4×C61—21no—
220C4⋊C4×C61—21no—
221C4⋊C4×C61C2×D411yescharacteristic
222C4⋊C4×C61C2×D411yescharacteristic
223C22⋊C4×C61—21no—
224C42×C61—21no—
225C22⋊Dic61—21no—
226#11758198—21no—
227#11758198—21no—
228#11758198—41no—
229#11758198—41no—
230C4⋊Dic61—21no—
231C4⋊Dic61—21no—
232C4⋊Dic61C2×D411yescharacteristic
233C4⋊Dic61C2×D411yescharacteristic
234#11758196—21no—
235#11758196—21no—
236C4×Dic61—21no—
237C4×Dic61—21no—
238C4×Dic61—21no—
239C4×Dic61—41no—
240C4×Dic61—41no—
241#11758194—21no—
242#11758194—21no—
243#11758194—21no—
244#11758194—21no—
245#11758194C22×C412yes—
246#11758194C22×C412yes—
247C2×#92418—21no—
248C2×#92418—21no—
249C2×#92418—21no—
250C2×#92418—21no—
251C2×#92418—21no—
252C2×#92418C2×D411yescharacteristic
253C2×#92418C2×D411yescharacteristic
254#11758189—24no—
255#11758189—24no—
256#11758189—22no—
257#11758189—22no—
258#11758189—22no—
259#11758189—22no—
260#11758189—42no—
261C8×D61—24no—
262C8×D61—24no—
263C8×D61—42no—
264C23×C61C2×#4111yescharacteristic
265C22×D61—41no—
266C22×D61—41no—
267C22×D61#11712yes—
268C22×D61#12111yescharacteristic
269C22×D61#12111yescharacteristic
270C22×D61#12612yes—
271Q8×C61—22no—
272Q8×C61—22no—
273Q8×C61—41no—
274Q8×C61—41no—
275C2×C4×C61—22no—
276C2×C4×C61—21no—
277C2×C4×C61—21no—
278C2×C4×C61—41no—
279C2×C4×C61—41no—
280C2×C4×C61—41no—
281C2×C4×C61—81no—
282C2×C4×C61C23×C411yescharacteristic
283C2×C4×C61C22×D411yescharacteristic
284C2×C4×C61C22×D411yescharacteristic
285C2×C4×C61C2×#4111yescharacteristic
286C2×C4×C61C2×#4111yescharacteristic
287C2×C4×C61C2×#4111yescharacteristic
288C2×Dic61—22no—
289C2×Dic61—21no—
290C2×Dic61—21no—
291C2×Dic61—41no—
292C2×Dic61—41no—
293C2×Dic61—41no—
294C2×Dic61—81no—
295C2×Dic61#11712yes—
296C2×Dic61#12111yescharacteristic
297C2×Dic61#12111yescharacteristic
298C2×Dic61#12612yes—
299C4×D61—44no—
300C4×D61—44no—
301C4×D61—81no—
302C4×D61—81no—
303C4×D61C4×D412yes—
304C4×D61C4×D412yes—
305C4×D61C4×D412yes—
306C4×D61C4×D412yes—
307C4×D61#12312yes—
308C4×D61#12312yes—
309C4×D61#12412yes—
310C4×D61#12412yes—
311Dic122—22no—
312Dic122—22no—
313Dic122—41no—
314Dic122—41no—
315Dic122—44no—
316Dic122—44no—
317C8×C61—22no—
318C8×C61—22no—
319C8×C61—21no—
320C8×C61—21no—
321C8×C61—41no—
322#92418—22no—
323#92418—22no—
324#92418—21no—
325#92418—21no—
326#92418—41no—
327#21077—611nomaximal, Sylow
328C22×C61—21no—
329C22×C61—21no—
330C22×C61C2×#11711yescharacteristic
331C22×C61C2×#12111yescharacteristic
332C22×C61C2×#12611yescharacteristic
333C2×D61—21no—
334C2×D61—21no—
335C2×D61—21no—
336C2×D61—21no—
337C2×D61—42no—
338C2×D61—42no—
339C2×D61#38812yes—
340C2×D61#38812yes—
341C4×C61—42no—
342C4×C61—41no—
343C4×C61—41no—
344C4×C61—81no—
345C4×C61C2×C4×D411yescharacteristic
346C4×C61C2×C4×D411yescharacteristic
347C4×C61C2×#12311yescharacteristic
348C4×C61C2×#12411yescharacteristic
349Dic61—42no—
350Dic61—41no—
351Dic61—41no—
352Dic61—81no—
353Dic61#38812yes—
354Dic61#38812yes—
355#2911—611no—
356C2×#419—611no—
357C2×#419—611no—
358C22×#101—611no—
359#2873—611no—
360#1930—611no—
361#1930—611no—
362#1930—611no—
363#1930—611no—
364#1930—611no—
365#1930—611no—
366#1930—611no—
367#1930D6111yescharacteristic, complemented
368#1742—611no—
369#1738—611no—
370C2×C61—21no—
371C2×C61—21no—
372C2×C61C2×#38811yescharacteristic
373C2×C61#306911yescharacteristic
374C2×C61#306911yescharacteristic
375D61—22no—
376D61—22no—
377C23×Q8—611no—
378C22×M16—611no—
379C22×M16—611no—
380C22×M16—611no—
381C22×M16—611no—
382C2×#117—611no—
383C2×#117—611no—
384#428—611no—
385#428—611no—
386#428—611no—
387#428—1221no—
388#428—1221no—
389#428C2×D6111yescharacteristic
390#427—1221no—
391#427—1221no—
392#419—611no—
393#419—611no—
394#419—611no—
395#419—1221no—
396#419—1221no—
397#419—1221no—
398#419—1221no—
399#419—1221no—
400#419—1221no—
401#419C2×D6111yescharacteristic
402C2×#103—611no—
403C2×#103—611no—
404C2×#103—611no—
405C2×#103—1221no—
406C2×#103—1221no—
407C2×#103C2×D6111yescharacteristic
408C2×#101—611no—
409C2×#101—611no—
410C2×#101—611no—
411C2×#101—618no—
412C2×#101C2×D6111yescharacteristic
413#405—611no—
414#405—611no—
415#405—611no—
416#405—1221no—
417#405—1221no—
418#405C2×D6111yescharacteristic
419C4×M16—1221no—
420C4×M16—1221no—
421#343—611no—
422#343—611no—
423#343—611no—
424#343C2×D6111yescharacteristic
425#341—611no—
426#341—611no—
427#341—611no—
428#341C2×D6111yescharacteristic
429C61#2107711yescharacteristic, complemented, Sylow
430C22×Q8—614no—
431C22×Q8—611no—
432C22×Q8—1221no—
433C22×Q8—1222no—
434C22×Q8—1222no—
435C22×Q8—1222no—
436C22×Q8—1221no—
437C22×Q8—1221no—
438C22×Q8—1221no—
439C22×Q8—1221no—
440C22×Q8C22×D6111yescharacteristic
441C23×C4—611no—
442C23×C4—1221no—
443C2×M16—611no—
444C2×M16—611no—
445C2×M16—611no—
446C2×M16—611no—
447C2×M16—611no—
448C2×M16—611no—
449C2×M16—614no—
450C2×M16—614no—
451C2×M16—611no—
452C2×M16—1221no—
453C2×M16—1221no—
454C2×M16—1222no—
455C2×M16—1222no—
456C2×M16—1221no—
457C2×M16—1222no—
458C2×M16—1222no—
459C2×M16—1222no—
460C2×M16—1222no—
461C2×M16C22×D6111yescharacteristic
462C2×M16C22×D6111yescharacteristic
463C2×M16C22×D6111yescharacteristic
464C22×C8—611no—
465C22×C8—1221no—
466C22×C8—1221no—
467C22×C8—1221no—
468C22×C8C22×D6111yescharacteristic
469#117—611no—
470#117—611no—
471#117—611no—
472#117—1221no—
473#117—1221no—
474#117—1221no—
475#117—1221no—
476#117—1221no—
477#117—1221no—
478#117C22×D6111yescharacteristic
479C2×C4⋊C4—611no—
480C2×C4⋊C4—611no—
481C2×C4⋊C4—611no—
482C2×C4⋊C4C22×D6111yescharacteristic
483C2×C22⋊C4—1221no—
484C2×C22⋊C4—1221no—
485C2×C42—1221no—
486C2×C42—1221no—
487#107—21no—
488#107—1221no—
489#107—1221no—
490#107—1221no—
491#106—21no—
492#106—1221no—
493#106—1221no—
494#106—1221no—
495#103—21no—
496#103—21no—
497#103—21no—
498#103—21no—
499#103—1221no—
500#103—1221no—
501#103—1221no—
502#103—1221no—
503#103—1221no—
504#103—1221no—
505#103—1221no—
506#103—1221no—
507#103—1221no—
508#103—1221no—
509#103—1221no—
510#103—1221no—
511#101—614no—
512#101—614no—
513#101—614no—
514#101C4×D6114yescomplemented
515#97—21no—
516#97—1221no—
517#97—1221no—
518#97—1221no—
519C4×C8—21no—
520C4×C8—1221no—
521C4×C8—1221no—
522C4×C8—1221no—
523C24—611no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—612no—
530C2×Q8—1224no—
531C2×Q8—1224no—
532C2×Q8—1224no—
533C2×Q8—1224no—
534C2×Q8—1224no—
535C2×Q8—1221no—
536C2×Q8—1221no—
537C2×Q8—1221no—
538C2×Q8—1221no—
539C2×Q8—1221no—
540C2×Q8—2441no—
541C2×Q8—2441no—
542C2×Q8—2442no—
543C2×Q8—2442no—
544C2×Q8—2442no—
545C2×Q8—2442no—
546C2×Q8—2442no—
547C2×Q8C2×C4×D6112yes—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—611no—
551C22×C4—612no—
552C22×C4—611no—
553C22×C4—611no—
554C22×C4—611no—
555C22×C4—611no—
556C22×C4—612no—
557C22×C4—612no—
558C22×C4—612no—
559C22×C4—1221no—
560C22×C4—1221no—
561C22×C4—1224no—
562C22×C4—1221no—
563C22×C4—1221no—
564C22×C4—2441no—
565C22×C4—2441no—
566C22×C4—2442no—
567C22×C4C23×D6111yescharacteristic
568M16—21no—
569M16—21no—
570M16—21no—
571M16—21no—
572M16—612no—
573M16—612no—
574M16—1224no—
575M16—1224no—
576M16—1222no—
577M16—1222no—
578M16—1222no—
579M16—1222no—
580M16—1221no—
581M16—1221no—
582M16—1221no—
583M16—1221no—
584M16—2442no—
585M16C2×C4×D6112yes—
586M16C2×C4×D6112yes—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—611no—
593C2×C8—611no—
594C2×C8—1224no—
595C2×C8—1224no—
596C2×C8—1221no—
597C2×C8—1221no—
598C2×C8—1221no—
599C2×C8—1221no—
600C2×C8—1221no—
601C2×C8—2442no—
602C2×C8D4×D6111yescharacteristic
603C2×C8D4×D6111yescharacteristic
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—611no—
607C4⋊C4—611no—
608C4⋊C4—1221no—
609C4⋊C4—1221no—
610C4⋊C4—1221no—
611C4⋊C4—1221no—
612C4⋊C4D4×D6111yescharacteristic
613C4⋊C4D4×D6111yescharacteristic
614C22⋊C4—21no—
615C22⋊C4—1221no—
616C22⋊C4—1221no—
617C22⋊C4—1221no—
618C22⋊C4—2441no—
619C22⋊C4—2441no—
620C42—21no—
621C42—1221no—
622C42—1221no—
623C42—1221no—
624C42—2441no—
625C42—2441no—
626C23—611no—
627C23—611no—
628C23—612no—
629C23—612no—
630C23—2441no—
631C23—2441no—
632C23#41×D6111yescharacteristic
633Q8—22no—
634Q8—22no—
635Q8—41no—
636Q8—41no—
637Q8—1222no—
638Q8—1222no—
639Q8—2444no—
640Q8—2444no—
641Q8—2441no—
642Q8—2441no—
643C2×C4—22no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—81no—
650C2×C4—612no—
651C2×C4—611no—
652C2×C4—611no—
653C2×C4—612no—
654C2×C4—612no—
655C2×C4—612no—
656C2×C4—612no—
657C2×C4—612no—
658C2×C4—612no—
659C2×C4—612no—
660C2×C4—612no—
661C2×C4—612no—
662C2×C4—1222no—
663C2×C4—1221no—
664C2×C4—1221no—
665C2×C4—4881no—
666C2×C4—4881no—
667C2×C4—4881no—
668C2×C4—2444no—
669C2×C4—2444no—
670C2×C4—2441no—
671C2×C4—2441no—
672C2×C4—2441no—
673C2×C4C22×C4×D6111yescharacteristic
674C2×C4C2×D4×D6111yescharacteristic
675C2×C4C2×D4×D6111yescharacteristic
676C2×C4#41×D6111yescharacteristic
677C2×C4#41×D6111yescharacteristic
678C2×C4#41×D6111yescharacteristic
679C8—22no—
680C8—22no—
681C8—21no—
682C8—21no—
683C8—41no—
684C8—1222no—
685C8—1222no—
686C8—1221no—
687C8—1221no—
688C8—2441no—
689C22—21no—
690C22—21no—
691C22—612no—
692C22—612no—
693C22—1221no—
694C22—1221no—
695C22—1221no—
696C22—1221no—
697C22—2442no—
698C22—2442no—
699C22#117×D6111yescharacteristic
700C22#121×D6111yescharacteristic
701C22#126×D6111yescharacteristic
702C4—42no—
703C4—41no—
704C4—41no—
705C4—81no—
706C4—612no—
707C4—612no—
708C4—4881no—
709C4—2442no—
710C4—2441no—
711C4—2441no—
712C4C4×D4×D6111yescharacteristic
713C4C4×D4×D6111yescharacteristic
714C4#123×D6111yescharacteristic
715C4#124×D6111yescharacteristic
716C2—21no—
717C2—21no—
718C2—1222no—
719C2—1222no—
720C2#388×D6111yescharacteristic
721C2#2145555111yescharacteristic
722C2#2145555411yescharacteristic
subgroupG/H
centerC22#121×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1930C2
socleC22×C61C2×#121
prime radicalC23×D61#41
cosocleC22×C4×C61C24
hypercenter#1930D61
hypocenterC61#21077
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #1930

Complements

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

NH ≅ G/Ntype
6. #21446477C2semidirect
7. #21446476C2semidirect
8. #21446475C2semidirect
9. #21446474C2semidirect
10. #21446473C2semidirect
11. #21446472C2semidirect
12. #21446471C2semidirect
15. C61×#1930C2semidirect
47. #101×D61C4semidirect
136. #14519696C2×C4semidirect
137. #14519695C2×C4semidirect
138. #14519695C2×C4semidirect
158. #101×C61C2×C4semidirect
367. #1930D61semidirect
429. C61#21077semidirect
514. #101C4×D61semidirect

Maximal subgroups

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

subgroupindex
#214544062
C2×#168397692
#419×D612
C2×#101×D612
#214542352
#214464772
#214464762
#214464752
#214464742
#214464732
#214464722
#214464712
#214455562
#214455442
C61×#19302
#2107761