Finite Group Databasebeta

← #29717339

Subgroups — #29717339

Order 15616.

1332 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840035C211yesmaximal, characteristic, complemented
2C2×#16840023C211yesmaximal, characteristic, complemented
3#21455079C211yesmaximal, characteristic, complemented
4C2×#16839924C211yesmaximal, characteristic, complemented
5#21454268C211yesmaximal, characteristic, complemented
6#21447115C211yesmaximal, characteristic, complemented
7#21447108C211yesmaximal, characteristic, complemented
8#21446937C211yesmaximal, characteristic, complemented
9#21446933C211yesmaximal, characteristic, complemented
10#21446336C211yesmaximal, characteristic, complemented
11#21446329C211yesmaximal, characteristic, complemented
12#21446287C211yesmaximal, characteristic, complemented
13#21446024C211yesmaximal, characteristic, complemented
14#21445747C211yesmaximal, characteristic, complemented
15C2×C61×#575C211yesmaximal, characteristic
16C2×#14519807C2211yescharacteristic
17C2×#14519807C2211yescharacteristic
18C22×#11758202C2211yescharacteristic, complemented
19C22×#11758200C2211yescharacteristic, complemented
20C2×#14519784C2211yescharacteristic
21C2×#14519784C2211yescharacteristic
22C2×#14519756C2211yescharacteristic
23#16840035—24no—
24#16840023—24no—
25#16839924—21no—
26#16839924—21no—
27#16839924—21no—
28#16839924—21no—
29#16839924—21no—
30#16839924—21no—
31#16839918—21no—
32#16839913—21no—
33C2×#14519712C2211yescharacteristic, complemented
34C2×#14519712C2211yescharacteristic, complemented
35#16839763C2211yescharacteristic
36#16839763C2211yescharacteristic
37C2×#14519701C2211yescharacteristic, complemented
38C2×#14519698C2211yescharacteristic, complemented
39C2×#14519696C2211yescharacteristic, complemented
40C2×#14519696C2211yescharacteristic, complemented
41C2×#14519695C2211yescharacteristic, complemented
42C2×#14519695C2211yescharacteristic, complemented
43C2×#14519694C2211yescharacteristic, complemented
44C2×#14519694C2211yescharacteristic, 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×Dic122C2311yescharacteristic
72#14519807—22no—
73#14519807—22no—
74#14519807—41no—
75#14519807—41no—
76C2×#11758202—22no—
77C2×#11758202—21no—
78C2×#11758202—21no—
79C2×#11758202—21no—
80C2×#11758202—21no—
81C2×#11758202—41no—
82C2×#11758200—22no—
83C2×#11758200—21no—
84C2×#11758200—21no—
85C2×#11758200—21no—
86C2×#11758200—21no—
87C2×#11758200—41no—
88#14519784—22no—
89#14519784—22no—
90#14519784—41no—
91#14519784—41no—
92C2×#11758194—21no—
93C2×#11758194—21no—
94C2×#11758194C2311yescharacteristic
95C2×#11758194C2311yescharacteristic
96C2×#11758194C2311yescharacteristic
97C2×#11758194C2311yescharacteristic
98C22×#92418—21no—
99C22×#92418—21no—
100C22×#92418C2311yescharacteristic
101C22×#92418C2311yescharacteristic
102#14519756—21no—
103#14519756—21no—
104#14519756—21no—
105#14519756—21no—
106C2×C4⋊Dic61C2311yescharacteristic
107C2×#11758196—21no—
108C2×C22⋊Dic61—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#14519695—22no—
122#14519695—22no—
123#14519694—22no—
124#14519694—41no—
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×C61D414yes—
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)×C61D414yes—
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
193#41×C61—21no—
194#41×C61—21no—
195#41×C61—24no—
196#41×C61—24no—
197#41×C61—22no—
198#41×C61—22no—
199#41×C61—21no—
200#41×C61—21no—
201#41×C61—21no—
202#41×C61—21no—
203#41×C61—42no—
204#41×C61—42no—
205#41×C61—41no—
206#41×C61—41no—
207#41×C61—42no—
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×C61C2×D412yes—
216#41×C61C2×D412yes—
217C2×Q8×C61—21no—
218C2×Q8×C61—21no—
219C2×Q8×C61—22no—
220C2×Q8×C61—21no—
221C2×Q8×C61—21no—
222C2×Q8×C61—21no—
223C2×Q8×C61—21no—
224C2×Q8×C61—41no—
225C2×Q8×C61C2×D411yescharacteristic
226C2×Q8×C61C2×D412yes—
227C2×Q8×C61C2×D411yescharacteristic
228C2×D4×C61—21no—
229C2×D4×C61—22no—
230C2×D4×C61—21no—
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—41no—
240C2×D4×C61—42no—
241C2×D4×C61—42no—
242C2×D4×C61—42no—
243C2×D4×C61—42no—
244C2×D4×C61—41no—
245C2×D4×C61—41no—
246C2×D4×C61C2×D411yescharacteristic
247C2×D4×C61C2×D412yes—
248C2×D4×C61C2×D411yescharacteristic
249C22×C4×C61—21no—
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—42no—
260C22×C4×C61—42no—
261C22×C4×C61—42no—
262C22×C4×C61—42no—
263C22×C4×C61—41no—
264C22×C4×C61—41no—
265C22×C4×C61C2×D411yescharacteristic
266C22×C4×C61C2×D411yescharacteristic
267C22×C4×C61C2×D411yescharacteristic
268C22×C4×C61C2×D411yescharacteristic
269C22×C4×C61#4111yescharacteristic
270C22×C4×C61C2411yescharacteristic
271C22×Dic61—21no—
272C22×Dic61—21no—
273C2×Dic122—21no—
274C2×Dic122—21no—
275C2×Dic122—21no—
276C2×Dic122—21no—
277C2×Dic122—21no—
278C2×Dic122—21no—
279Q16×C61—24no—
280Q16×C61—24no—
281SD16×C61—24no—
282SD16×C61—24no—
283SD16×C61—24no—
284SD16×C61—24no—
285D8×C61—24no—
286D8×C61—24no—
287M16×C61—24no—
288M16×C61—21no—
289M16×C61—21no—
290M16×C61C2×D412yes—
291M16×C61C2×D412yes—
292C2×C8×C61—24no—
293C2×C8×C61—21no—
294C2×C8×C61—21no—
295C22⋊Dic61—41no—
296C22⋊Dic61—41no—
297#11758202—42no—
298#11758202—42no—
299#11758202—42no—
300#11758202—42no—
301#11758200—42no—
302#11758200—42no—
303#11758200—42no—
304#11758200—42no—
305C4⋊Dic61—21no—
306C4⋊Dic61—21no—
307#11758196—41no—
308#11758196—41no—
309#11758194—21no—
310#11758194—21no—
311#11758194—21no—
312#11758194—21no—
313#11758194—21no—
314#11758194—21no—
315#11758194—21no—
316#11758194—21no—
317#11758194—42no—
318#11758194—42no—
319C2×#92418—21no—
320C2×#92418—21no—
321C2×#92418—21no—
322C2×#92418—21no—
323C2×#92418—21no—
324C2×#92418—21no—
325C2×#92418—21no—
326C2×#92418—21no—
327C2×#92418—42no—
328C2×#92418—42no—
329C2×#92418C2×D411yescharacteristic
330C2×#92418C2×D411yescharacteristic
331C2×#92418C2×D411yescharacteristic
332C2×#92418C2×D411yescharacteristic
333C23×C61—21no—
334C23×C61—21no—
335C23×C61—21no—
336C23×C61—21no—
337C23×C61—22no—
338C23×C61—41no—
339C23×C61—41no—
340C23×C61—42no—
341C23×C61—42no—
342C23×C61—41no—
343C23×C61—41no—
344C23×C61—81no—
345C23×C61—81no—
346C23×C61—81no—
347C23×C61#12111yescharacteristic
348C23×C61#12111yescharacteristic
349C23×C61C2×#4111yescharacteristic
350Q8×C61—21no—
351Q8×C61—21no—
352Q8×C61—22no—
353Q8×C61—21no—
354Q8×C61—22no—
355Q8×C61—42no—
356Q8×C61—41no—
357Q8×C61—41no—
358Q8×C61#12012yes—
359D4×C61—22no—
360D4×C61—22no—
361D4×C61—21no—
362D4×C61—22no—
363D4×C61—21no—
364D4×C61—21no—
365D4×C61—22no—
366D4×C61—42no—
367D4×C61—42no—
368D4×C61—42no—
369D4×C61—44no—
370D4×C61—44no—
371D4×C61—41no—
372D4×C61—41no—
373D4×C61—41no—
374D4×C61—41no—
375D4×C61#12012yes—
376C2×C4×C61—21no—
377C2×C4×C61—21no—
378C2×C4×C61—21no—
379C2×C4×C61—21no—
380C2×C4×C61—21no—
381C2×C4×C61—21no—
382C2×C4×C61—21no—
383C2×C4×C61—22no—
384C2×C4×C61—22no—
385C2×C4×C61—21no—
386C2×C4×C61—21no—
387C2×C4×C61—21no—
388C2×C4×C61—21no—
389C2×C4×C61—21no—
390C2×C4×C61—22no—
391C2×C4×C61—42no—
392C2×C4×C61—42no—
393C2×C4×C61—42no—
394C2×C4×C61—44no—
395C2×C4×C61—44no—
396C2×C4×C61—41no—
397C2×C4×C61—41no—
398C2×C4×C61—41no—
399C2×C4×C61—41no—
400C2×C4×C61#12111yescharacteristic
401C2×C4×C61#12111yescharacteristic
402C2×C4×C61C22×D411yescharacteristic
403C2×C4×C61C22×D411yescharacteristic
404C2×C4×C61C22×D411yescharacteristic
405C2×C4×C61C22×D411yescharacteristic
406C2×C4×C61H(5,𝔽2)11yescharacteristic
407C2×C4×C61H(5,𝔽2)11yescharacteristic
408C2×Dic61—41no—
409C2×Dic61—41no—
410C2×Dic61—41no—
411C2×Dic61—41no—
412C2×Dic61—81no—
413Dic122—41no—
414Dic122—41no—
415Dic122—41no—
416Dic122—41no—
417C8×C61—22no—
418C8×C61—22no—
419#92418—21no—
420#92418—21no—
421#92418—21no—
422#92418—21no—
423#92418—41no—
424#92418—41no—
425#92418—41no—
426#92418—41no—
427#24403—611nomaximal, Sylow
428C22×C61—21no—
429C22×C61—21no—
430C22×C61—21no—
431C22×C61—21no—
432C22×C61—22no—
433C22×C61—21no—
434C22×C61—21no—
435C22×C61—21no—
436C22×C61—21no—
437C22×C61—41no—
438C22×C61—41no—
439C22×C61—41no—
440C22×C61—42no—
441C22×C61—41no—
442C22×C61—41no—
443C22×C61—81no—
444C22×C61—81no—
445C22×C61—82no—
446C22×C61—82no—
447C22×C61—84no—
448C22×C61—81no—
449C22×C61—81no—
450C22×C61C2×#12111yescharacteristic
451C22×C61#54611yescharacteristic
452C22×C61#54611yescharacteristic
453C4×C61—21no—
454C4×C61—21no—
455C4×C61—22no—
456C4×C61—41no—
457C4×C61—42no—
458C4×C61C2×#12011yescharacteristic
459C4×C61#53411yescharacteristic
460C4×C61D4211yescharacteristic
461C4×C61D4211yescharacteristic
462Dic61—81no—
463Dic61—81no—
464C2×#575D6111yescharacteristic
465C2×#473—611no—
466C2×#471—611no—
467#3007—611no—
468C2×#452—611no—
469#2880—611no—
470#2052—611no—
471#2051—611no—
472#2020—611no—
473#2019—611no—
474#1908—611no—
475#1907—611no—
476#1901—611no—
477#1855—611no—
478#1785—611no—
479C2×C61—21no—
480C2×C61—21no—
481C2×C61—41no—
482C2×C61—41no—
483C2×C61—42no—
484C2×C61—81no—
485C2×C61—82no—
486C2×C61#241011yescharacteristic
487C2×C61#306711yescharacteristic
488C2×C61#306911yescharacteristic
489C22×#41C2×D6111yescharacteristic
490C22×#41C2×D6111yescharacteristic
491#575—24no—
492#575—24no—
493C2×#137—21no—
494C2×#137—611no—
495C2×#137—611no—
496C2×#137C2×D6111yescharacteristic
497C2×#137C2×D6111yescharacteristic
498C2×AGL(1,ℤ/8)—21no—
499C2×AGL(1,ℤ/8)C2×D6111yescharacteristic
500C2×AGL(1,ℤ/8)C2×D6111yescharacteristic
501C2×#135—21no—
502C2×#135—21no—
503C22×Q16—611no—
504C22×SD16—611no—
505C2×#131—611no—
506C2×#131—611no—
507C22×M16C2×D6111yescharacteristic
508C2×C22⋊Q8—611no—
509#473—1224no—
510#471—1224no—
511#452—1221no—
512#452—1221no—
513#452—1221no—
514#452—1221no—
515#452—1221no—
516#452—1221no—
517#451—1221no—
518#450—1221no—
519C2×#108—611no—
520C2×#108—611no—
521#417—611no—
522#417—611no—
523C2×#103—611no—
524C2×#102—611no—
525C2×#101—611no—
526C2×#101—611no—
527C2×#101—611no—
528C2×#101—611no—
529C2×#100—611no—
530C2×#100—611no—
531#408—611no—
532#408—611no—
533#408—1221no—
534#408—1221no—
535#407—611no—
536#407—611no—
537#407—1221no—
538C2×C22⋊C8—611no—
539C2×C22⋊C8—1221no—
540#343—611no—
541#343—611no—
542#341—611no—
543#341—611no—
544C61#2440311yescharacteristic, complemented, Sylow
545C2×#41—21no—
546C2×#41—21no—
547C2×#41—22no—
548C2×#41—22no—
549C2×#41—22no—
550C2×#41—22no—
551C2×#41—21no—
552C2×#41—21no—
553C2×#41—21no—
554C2×#41—21no—
555C2×#41—41no—
556C2×#41—41no—
557C2×#41—41no—
558C2×#41—41no—
559C2×#41C22⋊D6111yescharacteristic
560C2×#41C22⋊D6111yescharacteristic
561C2×#41C22×D6111yescharacteristic
562C2×#41C22×D6111yescharacteristic
563C22×Q8—611no—
564C22×Q8C22⋊D6111yescharacteristic
565C22×Q8C22×D6111yescharacteristic
566C22×D4—21no—
567C22×D4—21no—
568C22×D4C22⋊D6111yescharacteristic
569C22×D4C22×D6111yescharacteristic
570C23×C4—21no—
571C23×C4—21no—
572C23×C4C22×D6111yescharacteristic
573#137—28no—
574#137—22no—
575#137—22no—
576#137—22no—
577#137—1222no—
578#137—1222no—
579#137—2441no—
580#137—2441no—
581#137C22⋊D6114yes—
582AGL(1,ℤ/8)—28no—
583AGL(1,ℤ/8)—22no—
584AGL(1,ℤ/8)—22no—
585AGL(1,ℤ/8)—22no—
586AGL(1,ℤ/8)C22⋊D6114yes—
587#135—28no—
588#135—28no—
589C2×Q16—21no—
590C2×Q16—21no—
591C2×Q16—1221no—
592C2×Q16—1221no—
593C2×Q16—1222no—
594C2×Q16—1221no—
595C2×Q16—1221no—
596C2×Q16—2441no—
597C2×SD16—21no—
598C2×SD16—21no—
599C2×SD16—21no—
600C2×SD16—21no—
601C2×SD16—1221no—
602C2×SD16—1221no—
603C2×SD16—1222no—
604C2×SD16—1221no—
605C2×SD16—1221no—
606C2×SD16—2441no—
607C2×D8—21no—
608C2×D8—21no—
609#131—1222no—
610#131—1222no—
611#131—2441no—
612#131—2441no—
613C2×M16—21no—
614C2×M16—22no—
615C2×M16—22no—
616C2×M16—611no—
617C2×M16—611no—
618C2×M16—611no—
619C2×M16—611no—
620C2×M16—1221no—
621C2×M16—1221no—
622C2×M16C22×D6111yescharacteristic
623C2×M16C22×D6111yescharacteristic
624C22×C8—21no—
625C22×C8—611no—
626C22×C8—611no—
627C22×C8—1221no—
628C22×C8—1221no—
629C22⋊Q8—1221no—
630C22⋊Q8—1221no—
631C22⋊Q8—1221no—
632C22⋊Q8—1221no—
633C2×C4⋊C4—611no—
634C2×C4⋊C4—1221no—
635C2×C22⋊C4—1221no—
636#108—1222no—
637#108—1222no—
638#103—1221no—
639#103—1221no—
640#103—1221no—
641#103—1221no—
642#102—1221no—
643#102—1221no—
644#102—1221no—
645#102—1221no—
646#101—1222no—
647#101—1222no—
648#101—1222no—
649#101—2441no—
650#100—1222no—
651#100—2441no—
652C22⋊C8—611no—
653C22⋊C8—611no—
654C22⋊C8—611no—
655C22⋊C8—611no—
656C22⋊C8—1221no—
657C22⋊C8—1221no—
658C22⋊C8—1221no—
659C22⋊C8—1221no—
660C22⋊C8—1221no—
661C22⋊C8—1221no—
662C22⋊C8—1221no—
663C22⋊C8—1221no—
664C24—21no—
665C24—21no—
666C24#1175822411yescharacteristic
667#41—21no—
668#41—21no—
669#41—24no—
670#41—24no—
671#41—22no—
672#41—22no—
673#41—21no—
674#41—21no—
675#41—21no—
676#41—21no—
677#41—42no—
678#41—42no—
679#41—41no—
680#41—41no—
681#41—42no—
682#41—42no—
683#41—42no—
684#41—42no—
685#41—42no—
686#41—42no—
687#41—42no—
688#41—42no—
689#41C2×C22⋊D6112yes—
690#41C2×C22⋊D6112yes—
691C2×Q8—21no—
692C2×Q8—21no—
693C2×Q8—22no—
694C2×Q8—21no—
695C2×Q8—21no—
696C2×Q8—21no—
697C2×Q8—21no—
698C2×Q8—41no—
699C2×Q8—1221no—
700C2×Q8—1221no—
701C2×Q8—1221no—
702C2×Q8—1221no—
703C2×Q8—1221no—
704C2×Q8—1221no—
705C2×Q8C2×C22⋊D6112yes—
706C2×Q8C2×C22⋊D6111yescharacteristic
707C2×Q8C2×C22⋊D6111yescharacteristic
708C2×D4—21no—
709C2×D4—22no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—21no—
716C2×D4—21no—
717C2×D4—21no—
718C2×D4—21no—
719C2×D4—41no—
720C2×D4—42no—
721C2×D4—42no—
722C2×D4—42no—
723C2×D4—42no—
724C2×D4—41no—
725C2×D4—41no—
726C2×D4C2×C22⋊D6112yes—
727C2×D4C2×C22⋊D6111yescharacteristic
728C2×D4C2×C22⋊D6111yescharacteristic
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—42no—
740C22×C4—42no—
741C22×C4—42no—
742C22×C4—42no—
743C22×C4—41no—
744C22×C4—41no—
745C22×C4—1221no—
746C22×C4—1221no—
747C22×C4D4×D6111yescharacteristic
748C22×C4D4×D6111yescharacteristic
749C22×C4#1175822411yescharacteristic
750C22×C4C2×C22⋊D6111yescharacteristic
751C22×C4C2×C22⋊D6111yescharacteristic
752C22×C4C23×D6111yescharacteristic
753Q16—24no—
754Q16—24no—
755Q16—2442no—
756Q16—2442no—
757Q16—2442no—
758Q16—2442no—
759SD16—24no—
760SD16—24no—
761SD16—24no—
762SD16—24no—
763SD16—2442no—
764SD16—2442no—
765SD16—2442no—
766SD16—2442no—
767D8—24no—
768D8—24no—
769M16—24no—
770M16—21no—
771M16—21no—
772M16—1221no—
773M16—1221no—
774M16—1221no—
775M16—1221no—
776M16—1221no—
777M16—1221no—
778M16—1221no—
779M16—1221no—
780M16—2442no—
781M16—2442no—
782M16C2×C22⋊D6112yes—
783M16C2×C22⋊D6112yes—
784C2×C8—24no—
785C2×C8—21no—
786C2×C8—21no—
787C2×C8—611no—
788C2×C8—611no—
789C2×C8—611no—
790C2×C8—611no—
791C2×C8—1221no—
792C2×C8—1221no—
793C2×C8—1221no—
794C2×C8—1221no—
795C2×C8—1221no—
796C2×C8—1221no—
797C2×C8—1221no—
798C2×C8—1221no—
799C2×C8—2442no—
800C2×C8—2442no—
801C4⋊C4—1221no—
802C4⋊C4—1221no—
803C4⋊C4—2441no—
804C4⋊C4—2441no—
805C22⋊C4—2441no—
806C22⋊C4—2441no—
807C23—21no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—22no—
812C23—41no—
813C23—41no—
814C23—42no—
815C23—42no—
816C23—41no—
817C23—41no—
818C23—81no—
819C23—81no—
820C23—81no—
821C23#1451974911yescharacteristic
822C23#1451974911yescharacteristic
823C23C2×#1175822411yescharacteristic
824Q8—21no—
825Q8—21no—
826Q8—22no—
827Q8—21no—
828Q8—22no—
829Q8—42no—
830Q8—41no—
831Q8—41no—
832Q8—2441no—
833Q8—2441no—
834Q8—2441no—
835Q8—2441no—
836Q8#1451974612yes—
837D4—22no—
838D4—22no—
839D4—21no—
840D4—22no—
841D4—21no—
842D4—21no—
843D4—22no—
844D4—42no—
845D4—42no—
846D4—42no—
847D4—44no—
848D4—44no—
849D4—41no—
850D4—41no—
851D4—41no—
852D4—41no—
853D4#1451974612yes—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—22no—
869C2×C4—42no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—44no—
873C2×C4—44no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—4881no—
879C2×C4—2441no—
880C2×C4—2441no—
881C2×C4—2441no—
882C2×C4—2441no—
883C2×C4#1451974911yescharacteristic
884C2×C4#1451974911yescharacteristic
885C2×C4C2×D4×D6111yescharacteristic
886C2×C4C22×C22⋊D6111yescharacteristic
887C2×C4C22×C22⋊D6111yescharacteristic
888C2×C4C22×C22⋊D6111yescharacteristic
889C2×C4#1451982211yescharacteristic
890C2×C4#1451982211yescharacteristic
891C8—22no—
892C8—22no—
893C8—1221no—
894C8—1221no—
895C8—1221no—
896C8—1221no—
897C8—2441no—
898C8—2441no—
899C8—2441no—
900C8—2441no—
901C22—21no—
902C22—21no—
903C22—21no—
904C22—21no—
905C22—21no—
906C22—21no—
907C22—21no—
908C22—21no—
909C22—22no—
910C22—41no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—41no—
915C22—42no—
916C22—81no—
917C22—81no—
918C22—82no—
919C22—82no—
920C22—84no—
921C22—81no—
922C22—81no—
923C22C2×#1451974911yescharacteristic
924C22#1684040611yescharacteristic
925C22#1684040611yescharacteristic
926C4—21no—
927C4—21no—
928C4—22no—
929C4—41no—
930C4—42no—
931C4—4881no—
932C4—4881no—
933C4C2×#1451974611yescharacteristic
934C4#1684032111yescharacteristic
935C4D4×C22⋊D6111yescharacteristic
936C4D4×C22⋊D6111yescharacteristic
937C2—21no—
938C2—21no—
939C2—41no—
940C2—41no—
941C2—42no—
942C2—81no—
943C2—82no—
944C2#2144919311yescharacteristic
945C2#2145553611yescharacteristic
946C2#2145555811yescharacteristic
subgroupG/H
centerC22C2×#14519749
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
Fitting, prime radicalC2×C61×#575C2
socleC22×C61C2×#121
hypercenterC2×#575D61
hypocenterC61#24403
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×#16840035C2semidirect
2. C2×#16840023C2semidirect
3. #21455079C2semidirect
4. C2×#16839924C2semidirect
5. #21454268C2semidirect
6. #21447115C2semidirect
7. #21447108C2semidirect
8. #21446937C2semidirect
9. #21446933C2semidirect
10. #21446336C2semidirect
11. #21446329C2semidirect
12. #21446287C2semidirect
13. #21446024C2semidirect
14. #21445747C2semidirect
18. C22×#11758202C22semidirect
19. C22×#11758200C22semidirect
33. C2×#14519712C22semidirect
34. C2×#14519712C22semidirect
37. C2×#14519701C22semidirect
38. C2×#14519698C22semidirect
39. C2×#14519696C22semidirect
40. C2×#14519696C22semidirect
41. C2×#14519695C22semidirect
42. C2×#14519695C22semidirect
43. C2×#14519694C22semidirect
44. C2×#14519694C22semidirect
54. #16839530C22semidirect
55. #16839530C22semidirect
56. #16839526C22semidirect
57. #16839526C22semidirect
544. C61#24403semidirect

Maximal subgroups

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

subgroupindex
C2×#168400352
C2×#168400232
#214550792
C2×#168399242
#214542682
#214471152
#214471082
#214469372
#214469332
#214463362
#214463292
#214462872
#214460242
#214457472
C2×C61×#5752
#2440361