Finite Group Databasebeta

← #29717324

Subgroups — #29717324

Order 15616.

1358 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840030C211yesmaximal, characteristic, complemented
2C2×#16840027C211yesmaximal, characteristic, complemented
3#21455071C211yesmaximal, characteristic, complemented
4C2×#16839907C211yesmaximal, characteristic, complemented
5#21454268C211yesmaximal, characteristic, complemented
6#21447115C211yesmaximal, characteristic, complemented
7#21447108C211yesmaximal, characteristic, complemented
8#21446930C211yesmaximal, characteristic, complemented
9#21446925C211yesmaximal, characteristic, complemented
10#21446336C211yesmaximal, characteristic, complemented
11#21446329C211yesmaximal, characteristic, complemented
12#21446282C211yesmaximal, characteristic, complemented
13#21446024C211yesmaximal, characteristic, complemented
14#21445747C211yesmaximal, characteristic, complemented
15C2×C61×#575C211yesmaximal, characteristic, complemented
16C2×#14519802C2211yescharacteristic
17C2×#14519802C2211yescharacteristic
18C22×#11758201C2211yescharacteristic, complemented
19C22×#11758199C2211yescharacteristic, complemented
20C2×#14519784C2211yescharacteristic
21C2×#14519784C2211yescharacteristic
22C2×#14519751C2211yescharacteristic
23#16840030—24no—
24#16840027—24no—
25#16839907—21no—
26#16839907—21no—
27#16839907—21no—
28#16839907—21no—
29#16839907—21no—
30#16839907—21no—
31#16839901—21no—
32#16839896—21no—
33C2×#14519712C2211yescharacteristic, complemented
34C2×#14519712C2211yescharacteristic, complemented
35#16839763C2211yescharacteristic
36#16839763C2211yescharacteristic
37C2×#14519701C2211yescharacteristic, complemented
38C2×#14519698C2211yescharacteristic, complemented
39C2×#14519696C2211yescharacteristic, complemented
40C2×#14519696C2211yescharacteristic, complemented
41C2×#14519694C2211yescharacteristic, complemented
42C2×#14519694C2211yescharacteristic, complemented
43C2×#14519693C2211yescharacteristic, complemented
44C2×#14519693C2211yescharacteristic, complemented
45#16839729—21no—
46#16839729—21no—
47#16839729C2211yescharacteristic
48#16839729C2211yescharacteristic
49#16839726—21no—
50#16839726C2211yescharacteristic
51#16839726C2211yescharacteristic
52C2×C22⋊#92418—21no—
53C2×C22⋊#92418C2211yescharacteristic
54#16839530C2211yescharacteristic, complemented
55#16839530C2211yescharacteristic, complemented
56#16839526C2211yescharacteristic, complemented
57#16839526C2211yescharacteristic, complemented
58C22×#41×C61C2211yescharacteristic
59C22×#41×C61C2211yescharacteristic
60C61×#575—24no—
61C61×#575—24no—
62C2×#137×C61—21no—
63C2×#137×C61C2211yescharacteristic
64C2×#137×C61C2211yescharacteristic
65C2×AGL(1,ℤ/8)×C61—21no—
66C2×AGL(1,ℤ/8)×C61C2211yescharacteristic
67C2×AGL(1,ℤ/8)×C61C2211yescharacteristic
68C2×#135×C61—21no—
69C2×#135×C61—21no—
70C22×M16×C61C2211yescharacteristic
71C22×D244C2311yescharacteristic
72C22×C22⋊D61—21no—
73#14519802—22no—
74#14519802—22no—
75#14519802—41no—
76#14519802—41no—
77C2×#11758201—22no—
78C2×#11758201—21no—
79C2×#11758201—21no—
80C2×#11758201—21no—
81C2×#11758201—21no—
82C2×#11758201—41no—
83C2×#11758199—22no—
84C2×#11758199—21no—
85C2×#11758199—21no—
86C2×#11758199—21no—
87C2×#11758199—21no—
88C2×#11758199—41no—
89#14519784—22no—
90#14519784—22no—
91#14519784—41no—
92#14519784—41no—
93C2×#11758194—21no—
94C2×#11758194—21no—
95C2×#11758194C2311yescharacteristic
96C2×#11758194C2311yescharacteristic
97C2×#11758194C2311yescharacteristic
98C2×#11758194C2311yescharacteristic
99C22×#92418—21no—
100C22×#92418—21no—
101C22×#92418C2311yescharacteristic
102C22×#92418C2311yescharacteristic
103#14519751—21no—
104#14519751—21no—
105#14519751—21no—
106#14519751—21no—
107C2×C4⋊Dic61C2311yescharacteristic
108C2×#11758198—21no—
109#14519712—22no—
110#14519712—22no—
111#14519701—21no—
112#14519701—21no—
113#14519701—21no—
114#14519701—21no—
115#14519698—21no—
116#14519698—21no—
117#14519698—21no—
118#14519698—21no—
119#14519696—22no—
120#14519696—41no—
121#14519694—22no—
122#14519694—41no—
123#14519693—22no—
124#14519693—22no—
125C22⋊#92418—21no—
126C22⋊#92418—21no—
127C22⋊#92418—21no—
128C22⋊#92418—21no—
129C22⋊#92418—21no—
130C22⋊#92418—21no—
131C22⋊#92418—21no—
132C22⋊#92418—21no—
133C22⋊#92418D411yescharacteristic
134C22⋊#92418D411yescharacteristic
135C22⋊#92418D411yescharacteristic
136C22⋊#92418D411yescharacteristic
137C2×#41×C61—21no—
138C2×#41×C61—21no—
139C2×#41×C61—22no—
140C2×#41×C61—22no—
141C2×#41×C61—22no—
142C2×#41×C61—22no—
143C2×#41×C61—21no—
144C2×#41×C61—21no—
145C2×#41×C61—21no—
146C2×#41×C61—21no—
147C2×#41×C61—41no—
148C2×#41×C61—41no—
149C2×#41×C61—41no—
150C2×#41×C61—41no—
151C2×#41×C61D411yescharacteristic
152C2×#41×C61D411yescharacteristic
153C2×#41×C61C2311yescharacteristic
154C2×#41×C61C2311yescharacteristic
155C22×Q8×C61D411yescharacteristic
156C22×Q8×C61C2311yescharacteristic
157C22×D4×C61—21no—
158C22×D4×C61—21no—
159C22×D4×C61D411yescharacteristic
160C22×D4×C61C2311yescharacteristic
161C23×C4×C61—21no—
162C23×C4×C61—21no—
163C23×C4×C61C2311yescharacteristic
164#137×C61—28no—
165#137×C61—22no—
166#137×C61—22no—
167#137×C61—22no—
168#137×C61D414yescomplemented
169AGL(1,ℤ/8)×C61—28no—
170AGL(1,ℤ/8)×C61—22no—
171AGL(1,ℤ/8)×C61—22no—
172AGL(1,ℤ/8)×C61—22no—
173AGL(1,ℤ/8)×C61D414yescomplemented
174#135×C61—28no—
175#135×C61—28no—
176C2×Q16×C61—21no—
177C2×Q16×C61—21no—
178C2×SD16×C61—21no—
179C2×SD16×C61—21no—
180C2×SD16×C61—21no—
181C2×SD16×C61—21no—
182C2×D8×C61—21no—
183C2×D8×C61—21no—
184C2×M16×C61—21no—
185C2×M16×C61—22no—
186C2×M16×C61—22no—
187C2×M16×C61C2311yescharacteristic
188C2×M16×C61C2311yescharacteristic
189C22×C8×C61—21no—
190C24×C61—21no—
191C24×C61—21no—
192C24×C61#4111yescharacteristic
193C23×D61—21no—
194#41×C61—21no—
195#41×C61—21no—
196#41×C61—24no—
197#41×C61—24no—
198#41×C61—22no—
199#41×C61—22no—
200#41×C61—21no—
201#41×C61—21no—
202#41×C61—21no—
203#41×C61—21no—
204#41×C61—42no—
205#41×C61—42no—
206#41×C61—41no—
207#41×C61—41no—
208#41×C61—42no—
209#41×C61—42no—
210#41×C61—42no—
211#41×C61—42no—
212#41×C61—42no—
213#41×C61—42no—
214#41×C61—42no—
215#41×C61—42no—
216#41×C61C2×D412yes—
217#41×C61C2×D412yes—
218C2×Q8×C61—21no—
219C2×Q8×C61—21no—
220C2×Q8×C61—22no—
221C2×Q8×C61—21no—
222C2×Q8×C61—21no—
223C2×Q8×C61—21no—
224C2×Q8×C61—21no—
225C2×Q8×C61—41no—
226C2×Q8×C61C2×D411yescharacteristic
227C2×Q8×C61C2×D412yes—
228C2×Q8×C61C2×D411yescharacteristic
229C2×D4×C61—21no—
230C2×D4×C61—22no—
231C2×D4×C61—21no—
232C2×D4×C61—21no—
233C2×D4×C61—21no—
234C2×D4×C61—21no—
235C2×D4×C61—21no—
236C2×D4×C61—21no—
237C2×D4×C61—21no—
238C2×D4×C61—21no—
239C2×D4×C61—21no—
240C2×D4×C61—41no—
241C2×D4×C61—42no—
242C2×D4×C61—42no—
243C2×D4×C61—42no—
244C2×D4×C61—42no—
245C2×D4×C61—41no—
246C2×D4×C61—41no—
247C2×D4×C61C2×D411yescharacteristic
248C2×D4×C61C2×D412yes—
249C2×D4×C61C2×D411yescharacteristic
250C22×C4×C61—21no—
251C22×C4×C61—21no—
252C22×C4×C61—21no—
253C22×C4×C61—21no—
254C22×C4×C61—21no—
255C22×C4×C61—21no—
256C22×C4×C61—21no—
257C22×C4×C61—21no—
258C22×C4×C61—21no—
259C22×C4×C61—21no—
260C22×C4×C61—42no—
261C22×C4×C61—42no—
262C22×C4×C61—42no—
263C22×C4×C61—42no—
264C22×C4×C61—41no—
265C22×C4×C61—41no—
266C22×C4×C61C2×D411yescharacteristic
267C22×C4×C61C2×D411yescharacteristic
268C22×C4×C61C2×D411yescharacteristic
269C22×C4×C61C2×D411yescharacteristic
270C22×C4×C61#4111yescharacteristic
271C22×C4×C61C2411yescharacteristic
272C2×C22⋊D61—41no—
273C2×C22⋊D61—41no—
274C2×C22⋊D61—82no—
275C22×Dic61—21no—
276C2×D244—21no—
277C2×D244—21no—
278C2×D244—21no—
279C2×D244—21no—
280C2×D244—21no—
281C2×D244—21no—
282Q16×C61—24no—
283Q16×C61—24no—
284SD16×C61—24no—
285SD16×C61—24no—
286SD16×C61—24no—
287SD16×C61—24no—
288D8×C61—24no—
289D8×C61—24no—
290M16×C61—24no—
291M16×C61—21no—
292M16×C61—21no—
293M16×C61C2×D412yes—
294M16×C61C2×D412yes—
295C2×C8×C61—24no—
296C2×C8×C61—21no—
297C2×C8×C61—21no—
298#11758201—42no—
299#11758201—42no—
300#11758201—42no—
301#11758201—42no—
302#11758199—42no—
303#11758199—42no—
304#11758199—42no—
305#11758199—42no—
306#11758198—41no—
307#11758198—41no—
308C4⋊Dic61—21no—
309C4⋊Dic61—21no—
310#11758194—21no—
311#11758194—21no—
312#11758194—21no—
313#11758194—21no—
314#11758194—21no—
315#11758194—21no—
316#11758194—21no—
317#11758194—21no—
318#11758194—42no—
319#11758194—42no—
320C2×#92418—21no—
321C2×#92418—21no—
322C2×#92418—21no—
323C2×#92418—21no—
324C2×#92418—21no—
325C2×#92418—21no—
326C2×#92418—21no—
327C2×#92418—21no—
328C2×#92418—42no—
329C2×#92418—42no—
330C2×#92418C2×D411yescharacteristic
331C2×#92418C2×D411yescharacteristic
332C2×#92418C2×D411yescharacteristic
333C2×#92418C2×D411yescharacteristic
334C23×C61—21no—
335C23×C61—21no—
336C23×C61—21no—
337C23×C61—21no—
338C23×C61—22no—
339C23×C61—41no—
340C23×C61—41no—
341C23×C61—42no—
342C23×C61—42no—
343C23×C61—41no—
344C23×C61—41no—
345C23×C61—81no—
346C23×C61—81no—
347C23×C61—81no—
348C23×C61#12111yescharacteristic
349C23×C61#12111yescharacteristic
350C23×C61C2×#4111yescharacteristic
351C22×D61—41no—
352C22×D61—41no—
353C22×D61—41no—
354C22×D61—81no—
355C22×D61—81no—
356Q8×C61—21no—
357Q8×C61—21no—
358Q8×C61—22no—
359Q8×C61—21no—
360Q8×C61—22no—
361Q8×C61—42no—
362Q8×C61—41no—
363Q8×C61—41no—
364Q8×C61#12012yes—
365D4×C61—22no—
366D4×C61—22no—
367D4×C61—21no—
368D4×C61—22no—
369D4×C61—21no—
370D4×C61—21no—
371D4×C61—22no—
372D4×C61—42no—
373D4×C61—42no—
374D4×C61—42no—
375D4×C61—44no—
376D4×C61—44no—
377D4×C61—41no—
378D4×C61—41no—
379D4×C61—41no—
380D4×C61—41no—
381D4×C61#12012yes—
382C2×C4×C61—21no—
383C2×C4×C61—21no—
384C2×C4×C61—21no—
385C2×C4×C61—21no—
386C2×C4×C61—21no—
387C2×C4×C61—21no—
388C2×C4×C61—21no—
389C2×C4×C61—22no—
390C2×C4×C61—22no—
391C2×C4×C61—21no—
392C2×C4×C61—21no—
393C2×C4×C61—21no—
394C2×C4×C61—21no—
395C2×C4×C61—21no—
396C2×C4×C61—22no—
397C2×C4×C61—42no—
398C2×C4×C61—42no—
399C2×C4×C61—42no—
400C2×C4×C61—44no—
401C2×C4×C61—44no—
402C2×C4×C61—41no—
403C2×C4×C61—41no—
404C2×C4×C61—41no—
405C2×C4×C61—41no—
406C2×C4×C61#12111yescharacteristic
407C2×C4×C61#12111yescharacteristic
408C2×C4×C61C22×D411yescharacteristic
409C2×C4×C61C22×D411yescharacteristic
410C2×C4×C61C22×D411yescharacteristic
411C2×C4×C61C22×D411yescharacteristic
412C2×C4×C61H(5,𝔽2)11yescharacteristic
413C2×C4×C61H(5,𝔽2)11yescharacteristic
414C22⋊D61—82no—
415C22⋊D61—82no—
416C2×Dic61—41no—
417C2×Dic61—81no—
418D244—41no—
419D244—41no—
420D244—41no—
421D244—41no—
422C8×C61—22no—
423C8×C61—22no—
424#92418—21no—
425#92418—21no—
426#92418—21no—
427#92418—21no—
428#92418—41no—
429#92418—41no—
430#92418—41no—
431#92418—41no—
432#24402—611nomaximal, Sylow
433C22×C61—21no—
434C22×C61—21no—
435C22×C61—21no—
436C22×C61—21no—
437C22×C61—22no—
438C22×C61—21no—
439C22×C61—21no—
440C22×C61—21no—
441C22×C61—21no—
442C22×C61—41no—
443C22×C61—41no—
444C22×C61—41no—
445C22×C61—42no—
446C22×C61—41no—
447C22×C61—41no—
448C22×C61—81no—
449C22×C61—81no—
450C22×C61—82no—
451C22×C61—82no—
452C22×C61—84no—
453C22×C61—81no—
454C22×C61—81no—
455C22×C61C2×#12111yescharacteristic
456C22×C61#54611yescharacteristic
457C22×C61#54611yescharacteristic
458C2×D61—81no—
459C2×D61—81no—
460C2×D61—81no—
461C2×D61—161no—
462C2×D61—161no—
463C4×C61—21no—
464C4×C61—21no—
465C4×C61—22no—
466C4×C61—41no—
467C4×C61—42no—
468C4×C61C2×#12011yescharacteristic
469C4×C61#53411yescharacteristic
470C4×C61D4211yescharacteristic
471C4×C61D4211yescharacteristic
472Dic61—81no—
473C2×#575D6111yescharacteristic, complemented
474C2×#472—611no—
475C2×#471—611no—
476#3006—611no—
477C2×#449—611no—
478#2880—611no—
479#2052—611no—
480#2051—611no—
481#2019—611no—
482#2018—611no—
483#1908—611no—
484#1907—611no—
485#1900—611no—
486#1855—611no—
487#1785—611no—
488C2×C61—21no—
489C2×C61—21no—
490C2×C61—41no—
491C2×C61—41no—
492C2×C61—42no—
493C2×C61—81no—
494C2×C61—82no—
495C2×C61#241011yescharacteristic
496C2×C61#306711yescharacteristic
497C2×C61#306811yescharacteristic
498D61—161no—
499C22×#41C2×D6111yescharacteristic
500C22×#41C2×D6111yescharacteristic
501#575—24no—
502#575—24no—
503C2×#137—21no—
504C2×#137C2×D6111yescharacteristic
505C2×#137C2×D6111yescharacteristic
506C2×AGL(1,ℤ/8)—21no—
507C2×AGL(1,ℤ/8)—611no—
508C2×AGL(1,ℤ/8)—611no—
509C2×AGL(1,ℤ/8)C2×D6111yescharacteristic
510C2×AGL(1,ℤ/8)C2×D6111yescharacteristic
511C2×#135—21no—
512C2×#135—21no—
513C22×SD16—611no—
514C22×D8—611no—
515C2×#131—611no—
516C2×#131—611no—
517C22×M16C2×D6111yescharacteristic
518C2×#121—611no—
519#472—1224no—
520#471—1224no—
521#449—1221no—
522#449—1221no—
523#449—1221no—
524#449—1221no—
525#449—1221no—
526#449—1221no—
527#448—1221no—
528#447—1221no—
529C2×#108—611no—
530C2×#108—611no—
531#417—611no—
532#417—611no—
533C2×#103—611no—
534C2×#102—611no—
535C2×#101—611no—
536C2×#101—611no—
537C2×#100—611no—
538C2×#100—611no—
539C2×#100—611no—
540C2×#100—611no—
541#408—611no—
542#408—611no—
543#408—1221no—
544#408—1221no—
545#407—611no—
546#407—611no—
547#407—1221no—
548C2×C22⋊C8—611no—
549C2×C22⋊C8—1221no—
550#343—611no—
551#343—611no—
552#341—611no—
553#341—611no—
554C61#2440211yescharacteristic, complemented, Sylow
555C2×#41—21no—
556C2×#41—21no—
557C2×#41—22no—
558C2×#41—22no—
559C2×#41—22no—
560C2×#41—22no—
561C2×#41—21no—
562C2×#41—21no—
563C2×#41—21no—
564C2×#41—21no—
565C2×#41—41no—
566C2×#41—41no—
567C2×#41—41no—
568C2×#41—41no—
569C2×#41C22⋊D6111yescharacteristic
570C2×#41C22⋊D6111yescharacteristic
571C2×#41C22×D6111yescharacteristic
572C2×#41C22×D6111yescharacteristic
573C22×Q8C22⋊D6111yescharacteristic
574C22×Q8C22×D6111yescharacteristic
575C22×D4—21no—
576C22×D4—21no—
577C22×D4—611no—
578C22×D4—1221no—
579C22×D4C22⋊D6111yescharacteristic
580C22×D4C22×D6111yescharacteristic
581C23×C4—21no—
582C23×C4—21no—
583C23×C4C22×D6111yescharacteristic
584#137—28no—
585#137—22no—
586#137—22no—
587#137—22no—
588#137C22⋊D6114yescomplemented
589AGL(1,ℤ/8)—28no—
590AGL(1,ℤ/8)—22no—
591AGL(1,ℤ/8)—22no—
592AGL(1,ℤ/8)—22no—
593AGL(1,ℤ/8)—1222no—
594AGL(1,ℤ/8)—1222no—
595AGL(1,ℤ/8)—2441no—
596AGL(1,ℤ/8)—2441no—
597AGL(1,ℤ/8)C22⋊D6114yescomplemented
598#135—28no—
599#135—28no—
600C2×Q16—21no—
601C2×Q16—21no—
602C2×SD16—21no—
603C2×SD16—21no—
604C2×SD16—21no—
605C2×SD16—21no—
606C2×SD16—1221no—
607C2×SD16—1221no—
608C2×SD16—1222no—
609C2×SD16—1221no—
610C2×SD16—1221no—
611C2×SD16—2441no—
612C2×D8—21no—
613C2×D8—21no—
614C2×D8—1221no—
615C2×D8—1221no—
616C2×D8—1222no—
617C2×D8—1221no—
618C2×D8—1221no—
619C2×D8—2441no—
620#131—1222no—
621#131—1222no—
622#131—2441no—
623#131—2441no—
624C2×M16—21no—
625C2×M16—22no—
626C2×M16—22no—
627C2×M16—611no—
628C2×M16—611no—
629C2×M16—611no—
630C2×M16—611no—
631C2×M16—1221no—
632C2×M16—1221no—
633C2×M16C22×D6111yescharacteristic
634C2×M16C22×D6111yescharacteristic
635C22×C8—21no—
636C22×C8—611no—
637C22×C8—611no—
638C22×C8—1221no—
639C22×C8—1221no—
640#121—1221no—
641#121—1221no—
642#121—1221no—
643#121—1221no—
644C2×C4⋊C4—611no—
645C2×C22⋊C4—1221no—
646#108—1222no—
647#108—1222no—
648#103—1221no—
649#103—1221no—
650#103—1221no—
651#103—1221no—
652#102—1221no—
653#102—1221no—
654#102—1221no—
655#102—1221no—
656#101—1222no—
657#101—2441no—
658#100—1222no—
659#100—1222no—
660#100—1222no—
661#100—2441no—
662C22⋊C8—611no—
663C22⋊C8—611no—
664C22⋊C8—611no—
665C22⋊C8—611no—
666C22⋊C8—1221no—
667C22⋊C8—1221no—
668C22⋊C8—1221no—
669C22⋊C8—1221no—
670C22⋊C8—1221no—
671C22⋊C8—1221no—
672C22⋊C8—1221no—
673C22⋊C8—1221no—
674C24—21no—
675C24—21no—
676C24—1221no—
677C24#1175822411yescharacteristic
678#41—21no—
679#41—21no—
680#41—24no—
681#41—24no—
682#41—22no—
683#41—22no—
684#41—21no—
685#41—21no—
686#41—21no—
687#41—21no—
688#41—42no—
689#41—42no—
690#41—41no—
691#41—41no—
692#41—42no—
693#41—42no—
694#41—42no—
695#41—42no—
696#41—42no—
697#41—42no—
698#41—42no—
699#41—42no—
700#41C2×C22⋊D6112yes—
701#41C2×C22⋊D6112yes—
702C2×Q8—21no—
703C2×Q8—21no—
704C2×Q8—22no—
705C2×Q8—21no—
706C2×Q8—21no—
707C2×Q8—21no—
708C2×Q8—21no—
709C2×Q8—41no—
710C2×Q8C2×C22⋊D6112yes—
711C2×Q8C2×C22⋊D6111yescharacteristic
712C2×Q8C2×C22⋊D6111yescharacteristic
713C2×D4—21no—
714C2×D4—22no—
715C2×D4—21no—
716C2×D4—21no—
717C2×D4—21no—
718C2×D4—21no—
719C2×D4—21no—
720C2×D4—21no—
721C2×D4—21no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—41no—
725C2×D4—42no—
726C2×D4—42no—
727C2×D4—42no—
728C2×D4—42no—
729C2×D4—41no—
730C2×D4—41no—
731C2×D4—1221no—
732C2×D4—1221no—
733C2×D4—1221no—
734C2×D4—1221no—
735C2×D4—1221no—
736C2×D4—1221no—
737C2×D4—4882no—
738C2×D4—2441no—
739C2×D4—2441no—
740C2×D4C2×C22⋊D6112yes—
741C2×D4C2×C22⋊D6111yescharacteristic
742C2×D4C2×C22⋊D6111yescharacteristic
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—42no—
754C22×C4—42no—
755C22×C4—42no—
756C22×C4—42no—
757C22×C4—41no—
758C22×C4—41no—
759C22×C4—1221no—
760C22×C4D4×D6111yescharacteristic
761C22×C4D4×D6111yescharacteristic
762C22×C4#1175822411yescharacteristic
763C22×C4C2×C22⋊D6111yescharacteristic
764C22×C4C2×C22⋊D6111yescharacteristic
765C22×C4C23×D6111yescharacteristic
766Q16—24no—
767Q16—24no—
768SD16—24no—
769SD16—24no—
770SD16—24no—
771SD16—24no—
772SD16—2442no—
773SD16—2442no—
774SD16—2442no—
775SD16—2442no—
776D8—24no—
777D8—24no—
778D8—2442no—
779D8—2442no—
780D8—2442no—
781D8—2442no—
782M16—24no—
783M16—21no—
784M16—21no—
785M16—1221no—
786M16—1221no—
787M16—1221no—
788M16—1221no—
789M16—1221no—
790M16—1221no—
791M16—1221no—
792M16—1221no—
793M16—2442no—
794M16—2442no—
795M16C2×C22⋊D6112yes—
796M16C2×C22⋊D6112yes—
797C2×C8—24no—
798C2×C8—21no—
799C2×C8—21no—
800C2×C8—611no—
801C2×C8—611no—
802C2×C8—611no—
803C2×C8—611no—
804C2×C8—1221no—
805C2×C8—1221no—
806C2×C8—1221no—
807C2×C8—1221no—
808C2×C8—1221no—
809C2×C8—1221no—
810C2×C8—1221no—
811C2×C8—1221no—
812C2×C8—2442no—
813C2×C8—2442no—
814C4⋊C4—1221no—
815C4⋊C4—1221no—
816C22⋊C4—2441no—
817C22⋊C4—2441no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—21no—
822C23—22no—
823C23—41no—
824C23—41no—
825C23—42no—
826C23—42no—
827C23—41no—
828C23—41no—
829C23—81no—
830C23—81no—
831C23—81no—
832C23—4881no—
833C23—4881no—
834C23—2441no—
835C23—2441no—
836C23—2441no—
837C23#1451974911yescharacteristic
838C23#1451974911yescharacteristic
839C23C2×#1175822411yescharacteristic
840Q8—21no—
841Q8—21no—
842Q8—22no—
843Q8—21no—
844Q8—22no—
845Q8—42no—
846Q8—41no—
847Q8—41no—
848Q8#1451974612yes—
849D4—22no—
850D4—22no—
851D4—21no—
852D4—22no—
853D4—21no—
854D4—21no—
855D4—22no—
856D4—42no—
857D4—42no—
858D4—42no—
859D4—44no—
860D4—44no—
861D4—41no—
862D4—41no—
863D4—41no—
864D4—41no—
865D4—4882no—
866D4—4882no—
867D4—2441no—
868D4—2441no—
869D4—2441no—
870D4—2441no—
871D4#1451974612yes—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—21no—
882C2×C4—21no—
883C2×C4—21no—
884C2×C4—21no—
885C2×C4—21no—
886C2×C4—22no—
887C2×C4—42no—
888C2×C4—42no—
889C2×C4—42no—
890C2×C4—44no—
891C2×C4—44no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—4881no—
897C2×C4—2441no—
898C2×C4#1451974911yescharacteristic
899C2×C4#1451974911yescharacteristic
900C2×C4C2×D4×D6111yescharacteristic
901C2×C4C22×C22⋊D6111yescharacteristic
902C2×C4C22×C22⋊D6111yescharacteristic
903C2×C4C22×C22⋊D6111yescharacteristic
904C2×C4#1451982211yescharacteristic
905C2×C4#1451982211yescharacteristic
906C8—22no—
907C8—22no—
908C8—1221no—
909C8—1221no—
910C8—1221no—
911C8—1221no—
912C8—2441no—
913C8—2441no—
914C8—2441no—
915C8—2441no—
916C22—21no—
917C22—21no—
918C22—21no—
919C22—21no—
920C22—21no—
921C22—21no—
922C22—21no—
923C22—21no—
924C22—22no—
925C22—41no—
926C22—41no—
927C22—41no—
928C22—41no—
929C22—41no—
930C22—42no—
931C22—81no—
932C22—81no—
933C22—82no—
934C22—82no—
935C22—84no—
936C22—81no—
937C22—81no—
938C22—9761no—
939C22—9761no—
940C22—4881no—
941C22—4881no—
942C22—4881no—
943C22C2×#1451974911yescharacteristic
944C22#1684040611yescharacteristic
945C22#1684040611yescharacteristic
946C4—21no—
947C4—21no—
948C4—22no—
949C4—41no—
950C4—42no—
951C4—4881no—
952C4C2×#1451974611yescharacteristic
953C4#1684032111yescharacteristic
954C4D4×C22⋊D6111yescharacteristic
955C4D4×C22⋊D6111yescharacteristic
956C2—21no—
957C2—21no—
958C2—41no—
959C2—41no—
960C2—42no—
961C2—81no—
962C2—82no—
963C2—9761no—
964C2#2144919311yescharacteristic
965C2#2145553611yescharacteristic
966C2#2145554911yescharacteristic
subgroupG/H
centerC22C2×#14519749
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#575C2
socleC22×C61C2×#121
hypercenterC2×#575D61
hypocenterC61#24402
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#575

Complements

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

NH ≅ G/Ntype
1. C2×#16840030C2semidirect
2. C2×#16840027C2semidirect
3. #21455071C2semidirect
4. C2×#16839907C2semidirect
5. #21454268C2semidirect
6. #21447115C2semidirect
7. #21447108C2semidirect
8. #21446930C2semidirect
9. #21446925C2semidirect
10. #21446336C2semidirect
11. #21446329C2semidirect
12. #21446282C2semidirect
13. #21446024C2semidirect
14. #21445747C2semidirect
15. C2×C61×#575C2semidirect
18. C22×#11758201C22semidirect
19. C22×#11758199C22semidirect
33. C2×#14519712C22semidirect
34. C2×#14519712C22semidirect
37. C2×#14519701C22semidirect
38. C2×#14519698C22semidirect
39. C2×#14519696C22semidirect
40. C2×#14519696C22semidirect
41. C2×#14519694C22semidirect
42. C2×#14519694C22semidirect
43. C2×#14519693C22semidirect
44. C2×#14519693C22semidirect
54. #16839530C22semidirect
55. #16839530C22semidirect
56. #16839526C22semidirect
57. #16839526C22semidirect
168. #137×C61D4semidirect
173. AGL(1,ℤ/8)×C61D4semidirect
473. C2×#575D61semidirect
554. C61#24402semidirect
588. #137C22⋊D61semidirect
597. AGL(1,ℤ/8)C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168400302
C2×#168400272
#214550712
C2×#168399072
#214542682
#214471152
#214471082
#214469302
#214469252
#214463362
#214463292
#214462822
#214460242
#214457472
C2×C61×#5752
#2440261