Finite Group Databasebeta

← #29685874

Subgroups — #29685874

Order 15616.

1320 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455037C211yesmaximal, characteristic
2C2×#16839882C211yesmaximal, characteristic, complemented
3C2×#16839877C211yesmaximal, characteristic, complemented
4#21454522C211yesmaximal, characteristic, complemented
5#21446146C211yesmaximal, characteristic, complemented
6#21446146C211yesmaximal, characteristic, complemented
7#21446121C211yesmaximal, characteristic, complemented
8#21446094C211yesmaximal, characteristic, complemented
9#21446094C211yesmaximal, characteristic, complemented
10#21446024C211yesmaximal, characteristic, complemented
11#21445763C211yesmaximal, characteristic, complemented
12#21445661C211yesmaximal, characteristic, complemented
13#21445654C211yesmaximal, characteristic, complemented
14#21445600C211yesmaximal, characteristic, complemented
15C2×C61×#568C211yesmaximal, characteristic, complemented
16C2×#14519797C2211yescharacteristic
17C2×#14519797C2211yescharacteristic
18C2×#14519783C2211yescharacteristic, complemented
19#16840273C2211yescharacteristic
20#16839924C411yescharacteristic, complemented
21#16839924C411yescharacteristic, complemented
22#16839918C411yescharacteristic, complemented
23#16839913C411yescharacteristic, complemented
24#16839907C411yescharacteristic, complemented
25#16839907C411yescharacteristic, complemented
26#16839901C411yescharacteristic, complemented
27#16839896C411yescharacteristic, complemented
28#16839882—24no—
29#16839877—24no—
30#16839838—21no—
31#16839838—21no—
32#16839831—21no—
33#16839831—21no—
34C2×#14519712C2211yescharacteristic, complemented
35C2×#14519712C2211yescharacteristic, complemented
36#16839788C2211yescharacteristic, complemented
37C2×#14519704C2211yescharacteristic
38C2×#14519704C2211yescharacteristic
39C2×#14519704C2211yescharacteristic
40C2×#14519704C2211yescharacteristic
41C2×#14519703C2211yescharacteristic, complemented
42C2×#14519703C2211yescharacteristic, complemented
43#16839758C2211yescharacteristic
44#16839758C2211yescharacteristic
45#16839728C2211yescharacteristic, complemented
46#16839726C2211yescharacteristic
47C2×C22⋊#92418C2211yescharacteristic
48#16839717C2211yescharacteristic, complemented
49C2×#14519687C2211yescharacteristic, complemented
50C2×C8×Dic61C2211yescharacteristic, complemented
51C4×C22⋊Dic61C2211yescharacteristic
52#16839526C2211yescharacteristic, complemented
53#16839526C2211yescharacteristic, complemented
54#16839523C2211yescharacteristic, complemented
55#16839523C2211yescharacteristic, complemented
56#16839516C2211yescharacteristic, complemented
57#16839516C2211yescharacteristic, complemented
58C22×#41×C61C2211yescharacteristic
59C61×#568—24no—
60C61×#568—24no—
61C2×#131×C61—21no—
62C2×#131×C61—21no—
63C2×#131×C61C2211yescharacteristic
64C2×#131×C61C2211yescharacteristic
65C2×#131×C61C2211yescharacteristic
66C2×#131×C61C2211yescharacteristic
67C22×M16×C61—21no—
68C22×M16×C61—21no—
69C22×M16×C61C2211yescharacteristic
70C22×M16×C61C2211yescharacteristic
71C2×#11758222C2311yescharacteristic
72#14519797—22no—
73#14519797—22no—
74#14519797—22no—
75#14519797—22no—
76C2×#11758202C2×C411yescharacteristic
77C2×#11758202C2×C411yescharacteristic
78C2×#11758200C2×C411yescharacteristic
79C2×#11758200C2×C411yescharacteristic
80C2×#11758201C2×C411yescharacteristic
81C2×#11758201C2×C411yescharacteristic
82C2×#11758199C2×C411yescharacteristic
83C2×#11758199C2×C411yescharacteristic
84#14519783—22no—
85#14519783—22no—
86C2×#11758194C2311yescharacteristic
87C2×#11758194C2311yescharacteristic
88C2×#11758189—21no—
89C22×#92418C2311yescharacteristic
90C22×#92418C2311yescharacteristic
91C2×C8×D61—21no—
92#14519760—21no—
93#14519756C2×C411yescharacteristic
94#14519756C2×C411yescharacteristic
95#14519751C2×C411yescharacteristic
96#14519751C2×C411yescharacteristic
97#14519746—21no—
98C4×C22⋊D61—21no—
99C4×C22⋊D61—21no—
100#14519736C2311yescharacteristic
101C2×C22⋊Dic61—21no—
102C2×C4×Dic61C2311yescharacteristic
103C2×C4×Dic61C2311yescharacteristic
104#14519712—22no—
105#14519712—22no—
106#14519706—21no—
107#14519706—21no—
108#14519704—22no—
109#14519704—22no—
110#14519704—22no—
111#14519704—22no—
112#14519703—22no—
113#14519703—22no—
114#14519701C2×C411yescharacteristic
115#14519701C2×C411yescharacteristic
116#14519701C2×C411yescharacteristic
117#14519701C2×C411yescharacteristic
118#14519698C2×C411yescharacteristic
119#14519698C2×C411yescharacteristic
120#14519698C2×C411yescharacteristic
121#14519698C2×C411yescharacteristic
122C22⋊#92418—21no—
123C22⋊#92418—21no—
124C22⋊#92418C2×C411yescharacteristic
125C22⋊#92418C2×C411yescharacteristic
126C22⋊#92418C2×C411yescharacteristic
127C22⋊#92418C2×C411yescharacteristic
128#14519689—21no—
129#14519689—21no—
130#14519687—22no—
131#14519687—21no—
132C8×Dic61—22no—
133C8×Dic61—21no—
134#14519684—21no—
135C2×#41×C61—22no—
136C2×#41×C61—22no—
137C2×#41×C61—22no—
138C2×#41×C61—22no—
139C2×#41×C61—21no—
140C2×#41×C61—21no—
141C2×#41×C61C2×C411yescharacteristic
142C2×#41×C61C2×C411yescharacteristic
143C2×#41×C61C2311yescharacteristic
144C2×#41×C61C2311yescharacteristic
145C22×Q8×C61C2×C411yescharacteristic
146C22×D4×C61—21no—
147C22×D4×C61C2×C411yescharacteristic
148C23×C4×C61—21no—
149C23×C4×C61C2311yescharacteristic
150#131×C61—28no—
151#131×C61—28no—
152#131×C61—22no—
153#131×C61—22no—
154#131×C61—22no—
155#131×C61—22no—
156#131×C61—22no—
157#131×C61—22no—
158#131×C61D414yescomplemented
159#131×C61D414yescomplemented
160C2×M16×C61—28no—
161C2×M16×C61—28no—
162C2×M16×C61—21no—
163C2×M16×C61—22no—
164C2×M16×C61—22no—
165C2×M16×C61—21no—
166C2×M16×C61—21no—
167C2×M16×C61—21no—
168C2×M16×C61—21no—
169C2×M16×C61—22no—
170C2×M16×C61—22no—
171C2×M16×C61D411yescharacteristic
172C2×M16×C61D411yescharacteristic
173C2×M16×C61D411yescharacteristic
174C2×M16×C61D411yescharacteristic
175C2×M16×C61C2311yescharacteristic
176C2×M16×C61C2311yescharacteristic
177C22×C8×C61—21no—
178C22×C8×C61—21no—
179C22×C8×C61—21no—
180C22×C8×C61—21no—
181C22×C8×C61—21no—
182C22×C8×C61C2311yescharacteristic
183C22×C8×C61C2311yescharacteristic
184C24×C61—21no—
185C24×C61#4111yescharacteristic
186#41×C61—24no—
187#41×C61—24no—
188#41×C61—24no—
189#41×C61—24no—
190#41×C61—22no—
191#41×C61—22no—
192#41×C61—22no—
193#41×C61—22no—
194#41×C61—21no—
195#41×C61—21no—
196#41×C61—21no—
197#41×C61—21no—
198#41×C61C2×D412yes—
199#41×C61C2×D412yes—
200#41×C61#4112yes—
201#41×C61#4112yes—
202C2×Q8×C61—22no—
203C2×Q8×C61—22no—
204C2×Q8×C61—21no—
205C2×Q8×C61C22×C411yescharacteristic
206C2×Q8×C61C22×C411yescharacteristic
207C2×D4×C61—24no—
208C2×D4×C61—24no—
209C2×D4×C61—21no—
210C2×D4×C61—21no—
211C2×D4×C61—21no—
212C2×D4×C61—21no—
213C2×D4×C61—22no—
214C2×D4×C61—22no—
215C2×D4×C61—21no—
216C2×D4×C61C22×C411yescharacteristic
217C2×D4×C61C22×C411yescharacteristic
218C22×C4×C61—24no—
219C22×C4×C61—24no—
220C22×C4×C61—21no—
221C22×C4×C61—21no—
222C22×C4×C61—21no—
223C22×C4×C61—21no—
224C22×C4×C61—21no—
225C22×C4×C61—21no—
226C22×C4×C61—21no—
227C22×C4×C61—21no—
228C22×C4×C61—21no—
229C22×C4×C61C22×C411yescharacteristic
230C22×C4×C61C22×C411yescharacteristic
231C22×C4×C61C2×D411yescharacteristic
232C22×C4×C61C2×D411yescharacteristic
233C22×C4×C61#4111yescharacteristic
234C22×C4×C61C2411yescharacteristic
235C2×C22⋊D61—21no—
236C2×C22⋊D61—21no—
237C2×C22⋊D61—21no—
238C22×Dic61—21no—
239C22×Dic61—21no—
240#11758222—21no—
241#11758222—21no—
242#11758222—21no—
243#11758222—21no—
244C2×D244C22×C411yescharacteristic
245C2×C4×D61—21no—
246C2×Dic122C22×C411yescharacteristic
247M16×C61—24no—
248M16×C61—24no—
249M16×C61—24no—
250M16×C61—21no—
251M16×C61—21no—
252M16×C61—22no—
253M16×C61—22no—
254M16×C61—24no—
255M16×C61—24no—
256M16×C61—22no—
257M16×C61—22no—
258M16×C61C2×D412yes—
259M16×C61C2×D412yes—
260C2×C8×C61—24no—
261C2×C8×C61—24no—
262C2×C8×C61—24no—
263C2×C8×C61—21no—
264C2×C8×C61—21no—
265C2×C8×C61—21no—
266C2×C8×C61—21no—
267C2×C8×C61—24no—
268C2×C8×C61—24no—
269C2×C8×C61C2×D411yescharacteristic
270C2×C8×C61C2×D411yescharacteristic
271C2×C8×C61C2×D411yescharacteristic
272C2×C8×C61C2×D411yescharacteristic
273C2×C8×C61C2×D412yes—
274C2×C8×C61C2×D412yes—
275C22⋊Dic61—21no—
276C22⋊Dic61—21no—
277C22⋊Dic61—21no—
278C22⋊Dic61—42no—
279#11758202—22no—
280#11758202—22no—
281#11758201—22no—
282#11758201—22no—
283#11758200—22no—
284#11758200—22no—
285#11758199—22no—
286#11758199—22no—
287#11758198—21no—
288#11758198—21no—
289C4⋊Dic61C22×C411yescharacteristic
290C4⋊Dic61C22×C411yescharacteristic
291#11758196—21no—
292#11758196—21no—
293C4×Dic61—21no—
294C4×Dic61—21no—
295C4×Dic61—21no—
296C4×Dic61—21no—
297C4×Dic61—21no—
298#11758194—21no—
299#11758194—21no—
300#11758194—21no—
301#11758194—21no—
302C2×#92418—21no—
303C2×#92418—21no—
304C2×#92418—21no—
305C2×#92418—21no—
306C2×#92418—21no—
307C2×#92418—21no—
308C2×#92418C22×C411yescharacteristic
309C2×#92418C22×C411yescharacteristic
310C2×#92418C22×C411yescharacteristic
311C2×#92418C22×C411yescharacteristic
312#11758189—42no—
313C8×D61—42no—
314C23×C61—24no—
315C23×C61—21no—
316C23×C61—21no—
317C23×C61—21no—
318C23×C61—21no—
319C23×C61—41no—
320C23×C61—41no—
321C23×C61—81no—
322C23×C61—81no—
323C23×C61C4×D411yescharacteristic
324C23×C61C4×D411yescharacteristic
325C23×C61C2×#4111yescharacteristic
326C22×D61—21no—
327Q8×C61—24no—
328Q8×C61—21no—
329Q8×C61—21no—
330Q8×C61C4×D412yes—
331Q8×C61C4×D412yes—
332D4×C61—24no—
333D4×C61—24no—
334D4×C61—24no—
335D4×C61—22no—
336D4×C61—22no—
337D4×C61—22no—
338D4×C61—22no—
339D4×C61—21no—
340D4×C61—21no—
341D4×C61C4×D412yes—
342D4×C61C4×D412yes—
343C2×C4×C61—24no—
344C2×C4×C61—24no—
345C2×C4×C61—24no—
346C2×C4×C61—21no—
347C2×C4×C61—21no—
348C2×C4×C61—21no—
349C2×C4×C61—21no—
350C2×C4×C61—21no—
351C2×C4×C61—21no—
352C2×C4×C61—21no—
353C2×C4×C61—21no—
354C2×C4×C61—22no—
355C2×C4×C61—22no—
356C2×C4×C61—21no—
357C2×C4×C61—21no—
358C2×C4×C61—21no—
359C2×C4×C61—22no—
360C2×C4×C61—22no—
361C2×C4×C61—21no—
362C2×C4×C61C4×D411yescharacteristic
363C2×C4×C61C4×D411yescharacteristic
364C2×C4×C61C23×C411yescharacteristic
365C2×C4×C61C22×D411yescharacteristic
366C2×C4×C61C22×D411yescharacteristic
367C2×C4×C61C22×D411yescharacteristic
368C2×C4×C61C2×#4111yescharacteristic
369C2×C4×C61C2×#4111yescharacteristic
370C22⋊D61—41no—
371C22⋊D61—41no—
372C22⋊D61—81no—
373C22⋊D61—81no—
374C2×Dic61—22no—
375C2×Dic61—21no—
376C2×Dic61—21no—
377C2×Dic61—21no—
378C2×Dic61—41no—
379C2×Dic61—41no—
380C2×Dic61—41no—
381C2×Dic61—41no—
382C2×Dic61—41no—
383D244—21no—
384D244—21no—
385C4×D61—41no—
386C4×D61—41no—
387Dic122—21no—
388Dic122—21no—
389C8×C61—22no—
390C8×C61—22no—
391C8×C61—21no—
392C8×C61—21no—
393C8×C61#12012yes—
394C8×C61#12012yes—
395#92418—21no—
396#92418—21no—
397#92418—21no—
398#92418—21no—
399#92418—41no—
400#92418—41no—
401#21468—611nomaximal, Sylow
402C22×C61—21no—
403C22×C61—21no—
404C22×C61—21no—
405C22×C61—21no—
406C22×C61—21no—
407C22×C61—21no—
408C22×C61—21no—
409C22×C61—21no—
410C22×C61—22no—
411C22×C61—22no—
412C22×C61—41no—
413C22×C61—41no—
414C22×C61—41no—
415C22×C61—41no—
416C22×C61—81no—
417C22×C61—81no—
418C22×C61—84no—
419C22×C61C2×C4×D411yescharacteristic
420C22×C61#52511yescharacteristic
421C22×C61#52511yescharacteristic
422C2×D61—41no—
423C2×D61—41no—
424C2×D61—41no—
425C4×C61—21no—
426C4×C61—22no—
427C4×C61—22no—
428C4×C61—21no—
429C4×C61C2×C4×D411yescharacteristic
430C4×C61C2×C4×D411yescharacteristic
431C4×C61C2×#12011yescharacteristic
432C4×C61#52511yescharacteristic
433Dic61—42no—
434Dic61—41no—
435Dic61—41no—
436Dic61—41no—
437Dic61—81no—
438C2×#568D6111yescharacteristic, complemented
439#3002—611no—
440C2×#444—611no—
441C2×#443—611no—
442#2930—611no—
443#1876—611no—
444#1876—611no—
445#1871—611no—
446#1866—611no—
447#1866—611no—
448#1855—611no—
449#1789—611no—
450#1765—611no—
451#1764—611no—
452#1753—611no—
453C2×C61—21no—
454C2×C61—21no—
455C2×C61—41no—
456C2×C61—41no—
457C2×C61—42no—
458C2×C61—42no—
459C2×C61C4×#12011yescharacteristic
460C2×C61#295611yescharacteristic
461C2×C61#295711yescharacteristic
462D61—81no—
463C22×#41C2×D6111yescharacteristic
464C2×#135—611no—
465C2×#135—611no—
466#568—24no—
467#568—24no—
468C2×#131—21no—
469C2×#131—21no—
470C2×#131—611no—
471C2×#131C2×D6111yescharacteristic
472C2×#131C2×D6111yescharacteristic
473C2×#131C2×D6111yescharacteristic
474C2×#131C2×D6111yescharacteristic
475C22×M16—21no—
476C22×M16—21no—
477C22×M16C2×D6111yescharacteristic
478C22×M16C2×D6111yescharacteristic
479#525—611no—
480#452—611no—
481#452—611no—
482#451—611no—
483#450—611no—
484#449—611no—
485#449—611no—
486#448—611no—
487#447—611no—
488#444—1224no—
489#443—1224no—
490#436—1221no—
491#436—1221no—
492#435—1221no—
493#435—1221no—
494C2×#108—611no—
495C2×#108—611no—
496#424—611no—
497C2×#104—611no—
498C2×#104—611no—
499C2×#104—611no—
500C2×#104—611no—
501C2×#104—611no—
502C2×#104—611no—
503#416—611no—
504#416—611no—
505#408—611no—
506#407—611no—
507C2×C22⋊C8—611no—
508#405—611no—
509C2×#97—611no—
510C2×C4×C8—611no—
511C4×C22⋊C4—611no—
512#341—611no—
513#341—611no—
514#339—611no—
515#339—611no—
516#336—611no—
517#336—611no—
518C61#2146811yescharacteristic, complemented, Sylow
519C2×#41—22no—
520C2×#41—22no—
521C2×#41—22no—
522C2×#41—22no—
523C2×#41—21no—
524C2×#41—21no—
525C2×#41—611no—
526C2×#41C4×D6111yescharacteristic
527C2×#41C4×D6111yescharacteristic
528C2×#41C22×D6111yescharacteristic
529C2×#41C22×D6111yescharacteristic
530C22×Q8C4×D6111yescharacteristic
531C22×D4—21no—
532C22×D4C4×D6111yescharacteristic
533C23×C4—21no—
534C23×C4C22×D6111yescharacteristic
535#135—1222no—
536#135—1222no—
537#135—1222no—
538#135—1222no—
539C2×Q16—611no—
540C2×Q16—611no—
541C2×SD16—611no—
542C2×SD16—611no—
543C2×SD16—611no—
544C2×SD16—611no—
545C2×D8—611no—
546C2×D8—611no—
547#131—28no—
548#131—28no—
549#131—22no—
550#131—22no—
551#131—22no—
552#131—22no—
553#131—22no—
554#131—22no—
555#131—1222no—
556#131—1222no—
557#131C22⋊D6114yescomplemented
558#131C22⋊D6114yescomplemented
559C2×M16—28no—
560C2×M16—28no—
561C2×M16—21no—
562C2×M16—22no—
563C2×M16—22no—
564C2×M16—21no—
565C2×M16—21no—
566C2×M16—21no—
567C2×M16—21no—
568C2×M16—22no—
569C2×M16—22no—
570C2×M16—611no—
571C2×M16—611no—
572C2×M16—1221no—
573C2×M16C22⋊D6111yescharacteristic
574C2×M16C22⋊D6111yescharacteristic
575C2×M16C22⋊D6111yescharacteristic
576C2×M16C22⋊D6111yescharacteristic
577C2×M16C22×D6111yescharacteristic
578C2×M16C22×D6111yescharacteristic
579C22×C8—21no—
580C22×C8—21no—
581C22×C8—21no—
582C22×C8—21no—
583C22×C8—21no—
584C22×C8—611no—
585C22×C8—611no—
586C22×C8—1221no—
587C22×C8C22×D6111yescharacteristic
588C22×C8C22×D6111yescharacteristic
589#123—1221no—
590C22⋊Q8—611no—
591C22⋊Q8—611no—
592#121—611no—
593#121—611no—
594#120—1221no—
595C4×D4—1221no—
596C4×D4—1221no—
597#117—611no—
598C2×C22⋊C4—1221no—
599C2×C42—611no—
600C2×C42—611no—
601#108—1222no—
602#108—1222no—
603C4⋊C8—1221no—
604C4⋊C8—1221no—
605#104—1222no—
606#104—1222no—
607#104—1222no—
608#104—1222no—
609#104—1222no—
610#104—1222no—
611#103—611no—
612#103—611no—
613#103—611no—
614#103—611no—
615#102—611no—
616#102—611no—
617#102—611no—
618#102—611no—
619C22⋊C8—611no—
620C22⋊C8—611no—
621C22⋊C8—611no—
622C22⋊C8—611no—
623C22⋊C8—1221no—
624C22⋊C8—1221no—
625C22⋊C8—1221no—
626C22⋊C8—1221no—
627#97—1222no—
628#97—1221no—
629C4×C8—1222no—
630C4×C8—1221no—
631#95—1221no—
632C24—21no—
633C24#1175822211yescharacteristic
634#41—24no—
635#41—24no—
636#41—24no—
637#41—24no—
638#41—22no—
639#41—22no—
640#41—22no—
641#41—22no—
642#41—21no—
643#41—21no—
644#41—21no—
645#41—21no—
646#41—1221no—
647#41—1221no—
648#41—1221no—
649#41—1221no—
650#41#1175822212yes—
651#41#1175822212yes—
652#41C2×C22⋊D6112yes—
653#41C2×C22⋊D6112yes—
654C2×Q8—22no—
655C2×Q8—22no—
656C2×Q8—21no—
657C2×Q8—611no—
658C2×Q8C2×C4×D6111yescharacteristic
659C2×Q8C2×C4×D6111yescharacteristic
660C2×D4—24no—
661C2×D4—24no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—22no—
667C2×D4—22no—
668C2×D4—21no—
669C2×D4—611no—
670C2×D4—1221no—
671C2×D4—1221no—
672C2×D4—1221no—
673C2×D4C2×C4×D6111yescharacteristic
674C2×D4C2×C4×D6111yescharacteristic
675C22×C4—24no—
676C22×C4—24no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—1221no—
687C22×C4—1221no—
688C22×C4—1221no—
689C22×C4C2×C4×D6111yescharacteristic
690C22×C4C2×C4×D6111yescharacteristic
691C22×C4#1175822211yescharacteristic
692C22×C4C2×C22⋊D6111yescharacteristic
693C22×C4C2×C22⋊D6111yescharacteristic
694C22×C4C23×D6111yescharacteristic
695Q16—1222no—
696Q16—1222no—
697SD16—1222no—
698SD16—1222no—
699SD16—1222no—
700SD16—1222no—
701D8—1222no—
702D8—1222no—
703M16—24no—
704M16—24no—
705M16—24no—
706M16—21no—
707M16—21no—
708M16—22no—
709M16—22no—
710M16—24no—
711M16—24no—
712M16—22no—
713M16—22no—
714M16—1221no—
715M16—1221no—
716M16—1221no—
717M16—1221no—
718M16—2442no—
719M16C2×C22⋊D6112yes—
720M16C2×C22⋊D6112yes—
721C2×C8—24no—
722C2×C8—24no—
723C2×C8—24no—
724C2×C8—21no—
725C2×C8—21no—
726C2×C8—21no—
727C2×C8—21no—
728C2×C8—24no—
729C2×C8—24no—
730C2×C8—611no—
731C2×C8—611no—
732C2×C8—611no—
733C2×C8—611no—
734C2×C8—1221no—
735C2×C8—1221no—
736C2×C8—1221no—
737C2×C8—1221no—
738C2×C8—1221no—
739C2×C8—1221no—
740C2×C8—2442no—
741C2×C8C2×C22⋊D6111yescharacteristic
742C2×C8C2×C22⋊D6111yescharacteristic
743C2×C8C2×C22⋊D6112yes—
744C2×C8C2×C22⋊D6112yes—
745C2×C8C2×C22⋊D6111yescharacteristic
746C2×C8C2×C22⋊D6111yescharacteristic
747C4⋊C4—611no—
748C4⋊C4—611no—
749C4⋊C4—1221no—
750C4⋊C4—1221no—
751C22⋊C4—1221no—
752C22⋊C4—1221no—
753C22⋊C4—1221no—
754C22⋊C4—1221no—
755C22⋊C4—1221no—
756C22⋊C4—2442no—
757C42—1221no—
758C42—1221no—
759C42—1221no—
760C42—1221no—
761C42—1221no—
762C23—24no—
763C23—21no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—41no—
768C23—41no—
769C23—81no—
770C23—81no—
771C23—1221no—
772C23C4×C22⋊D6111yescharacteristic
773C23C4×C22⋊D6111yescharacteristic
774C23C2×#1175822211yescharacteristic
775Q8—24no—
776Q8—21no—
777Q8—21no—
778Q8—1221no—
779Q8—1221no—
780Q8C4×C22⋊D6112yes—
781Q8C4×C22⋊D6112yes—
782D4—24no—
783D4—24no—
784D4—24no—
785D4—22no—
786D4—22no—
787D4—22no—
788D4—22no—
789D4—21no—
790D4—21no—
791D4—1221no—
792D4—1221no—
793D4—4881no—
794D4—4881no—
795D4—2441no—
796D4—2441no—
797D4C4×C22⋊D6112yes—
798D4C4×C22⋊D6112yes—
799C2×C4—24no—
800C2×C4—24no—
801C2×C4—24no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—21no—
818C2×C4—1222no—
819C2×C4—1221no—
820C2×C4—1221no—
821C2×C4—1221no—
822C2×C4—2441no—
823C2×C4—2441no—
824C2×C4—2441no—
825C2×C4—2441no—
826C2×C4—2441no—
827C2×C4—2441no—
828C2×C4—2441no—
829C2×C4C4×C22⋊D6111yescharacteristic
830C2×C4C4×C22⋊D6111yescharacteristic
831C2×C4C22×C4×D6111yescharacteristic
832C2×C4C22×C22⋊D6111yescharacteristic
833C2×C4C22×C22⋊D6111yescharacteristic
834C2×C4C22×C22⋊D6111yescharacteristic
835C2×C4C2×#1175822211yescharacteristic
836C2×C4C2×#1175822211yescharacteristic
837C8—22no—
838C8—22no—
839C8—21no—
840C8—21no—
841C8—1221no—
842C8—1221no—
843C8—1221no—
844C8—1221no—
845C8—2441no—
846C8—2441no—
847C8#1451974612yes—
848C8#1451974612yes—
849C22—21no—
850C22—21no—
851C22—21no—
852C22—21no—
853C22—22no—
854C22—22no—
855C22—21no—
856C22—21no—
857C22—21no—
858C22—21no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—81no—
864C22—81no—
865C22—84no—
866C22—2441no—
867C22—2441no—
868C22—2441no—
869C22C2×C4×C22⋊D6111yescharacteristic
870C22#1684027311yescharacteristic
871C22#1684027311yescharacteristic
872C4—21no—
873C4—22no—
874C4—22no—
875C4—21no—
876C4—4881no—
877C4—2442no—
878C4—2441no—
879C4—2441no—
880C4—2441no—
881C4C2×C4×C22⋊D6111yescharacteristic
882C4C2×C4×C22⋊D6111yescharacteristic
883C4C2×#1451974611yescharacteristic
884C4#1684027311yescharacteristic
885C2—21no—
886C2—21no—
887C2—41no—
888C2—41no—
889C2—42no—
890C2—42no—
891C2—4881no—
892C2C4×#1451974611yescharacteristic
893C2#2145472611yescharacteristic
894C2#2145473411yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#568C2
socleC22×C61C2×C4×D4
prime radical#21455037C2
cosocleC22×C4×C61C24
hypercenterC2×#568D61
hypocenterC61#21468
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×M16 ◁ C2×#568

Complements

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

NH ≅ G/Ntype
2. C2×#16839882C2semidirect
3. C2×#16839877C2semidirect
4. #21454522C2semidirect
5. #21446146C2semidirect
6. #21446146C2semidirect
7. #21446121C2semidirect
8. #21446094C2semidirect
9. #21446094C2semidirect
10. #21446024C2semidirect
11. #21445763C2semidirect
12. #21445661C2semidirect
13. #21445654C2semidirect
14. #21445600C2semidirect
15. C2×C61×#568C2semidirect
18. C2×#14519783C22semidirect
20. #16839924C4semidirect
21. #16839924C4semidirect
22. #16839918C4semidirect
23. #16839913C4semidirect
24. #16839907C4semidirect
25. #16839907C4semidirect
26. #16839901C4semidirect
27. #16839896C4semidirect
34. C2×#14519712C22semidirect
35. C2×#14519712C22semidirect
36. #16839788C22semidirect
41. C2×#14519703C22semidirect
42. C2×#14519703C22semidirect
45. #16839728C22semidirect
48. #16839717C22semidirect
49. C2×#14519687C22semidirect
50. C2×C8×Dic61C22semidirect
52. #16839526C22semidirect
53. #16839526C22semidirect
54. #16839523C22semidirect
55. #16839523C22semidirect
56. #16839516C22semidirect
57. #16839516C22semidirect
158. #131×C61D4semidirect
159. #131×C61D4semidirect
438. C2×#568D61semidirect
518. C61#21468semidirect
557. #131C22⋊D61semidirect
558. #131C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
#214550372
C2×#168398822
C2×#168398772
#214545222
#214461462
#214461212
#214460942
#214460242
#214457632
#214456612
#214456542
#214456002
C2×C61×#5682
#2146861