Finite Group Databasebeta

← #29718174

Subgroups — #29718174

Order 15616.

1600 conjugacy classes of subgroups.

The subgroup lattice has 1100 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455440C211yesmaximal, characteristic, complemented
2C2×#16839930C211yesmaximal, characteristic, complemented
3#21455071C211yesmaximal, characteristic, complemented
4C22×#14519704C211yesmaximal, characteristic, complemented
5#21454162C211yesmaximal, characteristic, complemented
6#21447040C211yesmaximal, characteristic, complemented
7#21447026C211yesmaximal, characteristic, complemented
8#21446861C211yesmaximal, characteristic, complemented
9#21446832C211yesmaximal, characteristic, complemented
10#21446283C211yesmaximal, characteristic, complemented
11#21446263C211yesmaximal, characteristic, complemented
12#21446195C211yesmaximal, characteristic, complemented
13#21446045C211yesmaximal, characteristic, complemented
14#21445773C211yesmaximal, characteristic, complemented
15C61×#3488C211yesmaximal, characteristic, complemented
16C2×#14519802C2211yescharacteristic
17C2×#14519802C2211yescharacteristic, complemented
18C2×#14519802C2211yescharacteristic, complemented
19C22×#11758194C2211yescharacteristic, complemented
20C2×#14519773C2211yescharacteristic, complemented
21C2×#14519751C2211yescharacteristic, complemented
22C2×#14519749—22no—
23C22×C4×Dic61C2211yescharacteristic, complemented
24#16840013—21no—
25#16840010—21no—
26#16839996—21no—
27#16839993—21no—
28#16839930—24no—
29#16839907—21no—
30#16839907—21no—
31#16839901—21no—
32#16839896—21no—
33#16839805C2211yescharacteristic, complemented
34C2×#14519704—24no—
35C2×#14519704C2211yescharacteristic
36C2×#14519704C2211yescharacteristic
37C2×#14519704C2211yescharacteristic, complemented
38C2×#14519704C2211yescharacteristic, complemented
39C2×#14519704C2211yescharacteristic, complemented
40C2×#14519704C2211yescharacteristic, complemented
41#16839766C2211yescharacteristic, complemented
42#16839763C2211yescharacteristic
43#16839763C2211yescharacteristic, complemented
44#16839763C2211yescharacteristic, complemented
45C2×#14519694C2211yescharacteristic, complemented
46C2×#14519694C2211yescharacteristic, complemented
47#16839726C2211yescharacteristic, complemented
48#16839665C2211yescharacteristic, complemented
49#16839663C2211yescharacteristic, complemented
50#16839662—22no—
51#16839631C2211yescharacteristic, complemented
52#16839531C2211yescharacteristic, complemented
53#16839531C2211yescharacteristic, complemented
54#16839521C2211yescharacteristic, complemented
55#16839521C2211yescharacteristic, complemented
56C2×H(5,𝔽2)×C61C2211yescharacteristic
57C22×#41×C61C2211yescharacteristic
58C61×#550—21no—
59C61×#548—21no—
60C61×#546—21no—
61C61×#546—22no—
62D42×C61—22no—
63D42×C61—21no—
64C61×#537—21no—
65C61×#537C2211yescharacteristic
66C61×#535—21no—
67C61×#535C2211yescharacteristic
68C61×#525—21no—
69C61×#525C2211yescharacteristic
70C2×#121×C61—21no—
71C2×#121×C61C2211yescharacteristic
72C61×#520C2211yescharacteristic
73C22×D244C2311yescharacteristic
74C22×C22⋊D61—21no—
75C22×C22⋊D61—22no—
76C23×Dic61—21no—
77#14519802—22no—
78#14519802—22no—
79#14519802—22no—
80#14519802—41no—
81#14519802—41no—
82#14519802—41no—
83C2×#11758201—21no—
84C2×#11758201—21no—
85C2×#11758201—21no—
86C2×#11758199—21no—
87C2×#11758199—21no—
88C2×#11758199—21no—
89C2×#11758194—21no—
90C2×#11758194—22no—
91C2×#11758194—41no—
92C2×#11758194C2311yescharacteristic
93C2×#11758194C2311yescharacteristic
94C2×#11758194C2311yescharacteristic
95C2×#11758194C2311yescharacteristic
96C22×#92418—21no—
97#14519773—22no—
98#14519773—41no—
99#14519751—21no—
100#14519751—21no—
101#14519751—21no—
102#14519751—21no—
103#14519749—48no—
104C2×C4⋊Dic61C2311yescharacteristic
105C2×#11758196—22no—
106C2×C22⋊Dic61—22no—
107C2×#11758198—22no—
108C2×#11758198—21no—
109C2×C4×Dic61—22no—
110C2×C4×Dic61—21no—
111C2×C4×Dic61—41no—
112C2×C4×Dic61C2311yescharacteristic
113C2×C4×Dic61C2311yescharacteristic
114#14519710—21no—
115#14519708—21no—
116#14519704—22no—
117#14519704—22no—
118#14519704—22no—
119#14519704—22no—
120#14519704—41no—
121#14519704D414yescomplemented
122#14519701—21no—
123#14519701—21no—
124#14519701—21no—
125#14519698—21no—
126#14519698—21no—
127#14519698—21no—
128#14519697—21no—
129#14519697—21no—
130#14519694—22no—
131#14519694—41no—
132C22⋊#92418—21no—
133C22⋊#92418—21no—
134H(5,𝔽2)×C61—22no—
135H(5,𝔽2)×C61—22no—
136H(5,𝔽2)×C61—41no—
137H(5,𝔽2)×C61—41no—
138C2×#41×C61—21no—
139C2×#41×C61—21no—
140C2×#41×C61—21no—
141C2×#41×C61—21no—
142C2×#41×C61—22no—
143C2×#41×C61—22no—
144C2×#41×C61—41no—
145C2×#41×C61—41no—
146C2×#41×C61D411yescharacteristic, complemented
147C2×#41×C61D411yescharacteristic, complemented
148C2×#41×C61C2311yescharacteristic
149C2×#41×C61C2311yescharacteristic
150C2×#41×C61C2311yescharacteristic
151C22×Q8×C61D411yescharacteristic, complemented
152C22×D4×C61—21no—
153C22×D4×C61—22no—
154C22×D4×C61—22no—
155C22×D4×C61—21no—
156C22×D4×C61—21no—
157C22×D4×C61D412yes—
158C22×D4×C61D411yescharacteristic, complemented
159C22×D4×C61C2311yescharacteristic
160C23×C4×C61—21no—
161C23×C4×C61C2311yescharacteristic
162#127×C61—22no—
163#127×C61—21no—
164#124×C61—22no—
165#124×C61—21no—
166#123×C61—22no—
167#123×C61—21no—
168C22⋊Q8×C61—22no—
169C22⋊Q8×C61—21no—
170C22⋊Q8×C61—21no—
171C22⋊Q8×C61D411yescharacteristic, complemented
172C22⋊Q8×C61D411yescharacteristic, complemented
173#121×C61—22no—
174#121×C61—22no—
175#121×C61—22no—
176#121×C61—22no—
177#121×C61—22no—
178#121×C61—21no—
179#121×C61—21no—
180#121×C61—21no—
181#121×C61—22no—
182#121×C61—21no—
183#121×C61—21no—
184#121×C61—21no—
185#121×C61—21no—
186#121×C61—21no—
187#121×C61D411yescharacteristic, complemented
188#121×C61D411yescharacteristic, complemented
189#120×C61—22no—
190#120×C61—22no—
191#120×C61—22no—
192#120×C61—22no—
193#120×C61—21no—
194C4×Q8×C61—21no—
195C4×D4×C61—22no—
196C4×D4×C61—22no—
197C4×D4×C61—21no—
198C4×D4×C61—22no—
199C4×D4×C61—21no—
200C4×D4×C61—21no—
201#117×C61—21no—
202#117×C61C2311yescharacteristic
203C2×C4⋊C4×C61—21no—
204C2×C4⋊C4×C61C2311yescharacteristic
205C2×C22⋊C4×C61—22no—
206C2×C22⋊C4×C61D412yes—
207C24×C61—22no—
208C24×C61—21no—
209C24×C61C2×D411yescharacteristic
210C24×C61C2×D412yes—
211C23×D61—21no—
212#41×C61—21no—
213#41×C61—21no—
214#41×C61—22no—
215#41×C61—22no—
216#41×C61—21no—
217#41×C61—21no—
218#41×C61—21no—
219#41×C61—21no—
220#41×C61—21no—
221#41×C61—21no—
222#41×C61—21no—
223#41×C61—21no—
224#41×C61—42no—
225#41×C61—42no—
226#41×C61—41no—
227#41×C61—41no—
228#41×C61—42no—
229#41×C61—42no—
230#41×C61—42no—
231#41×C61—42no—
232#41×C61—42no—
233#41×C61—42no—
234#41×C61C2×D412yes—
235#41×C61#4112yes—
236C2×Q8×C61—21no—
237C2×Q8×C61—22no—
238C2×Q8×C61—41no—
239C2×Q8×C61C2×D411yescharacteristic
240C2×Q8×C61C2×D411yescharacteristic
241C2×Q8×C61C2×D411yescharacteristic
242C2×D4×C61—21no—
243C2×D4×C61—22no—
244C2×D4×C61—22no—
245C2×D4×C61—22no—
246C2×D4×C61—22no—
247C2×D4×C61—21no—
248C2×D4×C61—21no—
249C2×D4×C61—21no—
250C2×D4×C61—21no—
251C2×D4×C61—21no—
252C2×D4×C61—22no—
253C2×D4×C61—22no—
254C2×D4×C61—22no—
255C2×D4×C61—21no—
256C2×D4×C61—22no—
257C2×D4×C61—21no—
258C2×D4×C61—21no—
259C2×D4×C61—21no—
260C2×D4×C61—21no—
261C2×D4×C61—21no—
262C2×D4×C61—21no—
263C2×D4×C61—21no—
264C2×D4×C61—41no—
265C2×D4×C61—42no—
266C2×D4×C61—42no—
267C2×D4×C61—42no—
268C2×D4×C61—42no—
269C2×D4×C61—44no—
270C2×D4×C61—44no—
271C2×D4×C61—42no—
272C2×D4×C61—42no—
273C2×D4×C61—44no—
274C2×D4×C61—84no—
275C2×D4×C61C2×D411yescharacteristic
276C2×D4×C61C2×D411yescharacteristic
277C2×D4×C61C2×D411yescharacteristic
278C22×C4×C61—21no—
279C22×C4×C61—21no—
280C22×C4×C61—21no—
281C22×C4×C61—21no—
282C22×C4×C61—21no—
283C22×C4×C61—22no—
284C22×C4×C61—21no—
285C22×C4×C61—22no—
286C22×C4×C61—21no—
287C22×C4×C61—21no—
288C22×C4×C61—21no—
289C22×C4×C61—21no—
290C22×C4×C61—42no—
291C22×C4×C61—42no—
292C22×C4×C61C2×D411yescharacteristic
293C22×C4×C61C2×D411yescharacteristic
294C22×C4×C61C2×D411yescharacteristic
295C22×C4×C61C2×D411yescharacteristic
296C22×C4×C61C2×D411yescharacteristic
297C22×C4×C61C2×D412yes—
298C22×C4×C61C2411yescharacteristic
299C2×C22⋊D61—44no—
300C2×C22⋊D61—44no—
301C2×C22⋊D61—44no—
302C2×C22⋊D61—44no—
303C2×C22⋊D61—41no—
304C2×C22⋊D61—41no—
305C22×Dic61—21no—
306C22×Dic61—24no—
307C22×Dic61—21no—
308C22×Dic61—21no—
309C22×Dic61—42no—
310C22×Dic61—42no—
311C2×D244—21no—
312C2×D244—21no—
313C2×D244—21no—
314C2×D244—21no—
315C2×D244—21no—
316C2×D244—21no—
317C4⋊C4×C61—22no—
318C4⋊C4×C61—22no—
319C4⋊C4×C61—21no—
320C4⋊C4×C61—21no—
321C4⋊C4×C61—21no—
322C4⋊C4×C61—21no—
323C4⋊C4×C61C2×D411yescharacteristic
324C4⋊C4×C61C2×D411yescharacteristic
325C22⋊C4×C61—22no—
326C22⋊C4×C61—22no—
327C22⋊C4×C61—22no—
328C22⋊C4×C61—22no—
329C22⋊C4×C61—22no—
330C22⋊C4×C61—21no—
331C22⋊C4×C61—21no—
332C22⋊C4×C61—21no—
333C22⋊C4×C61—21no—
334C22⋊C4×C61—22no—
335C22⋊C4×C61—22no—
336C22⋊C4×C61—21no—
337C42×C61—22no—
338C42×C61—21no—
339C22⋊Dic61—44no—
340#11758201—42no—
341#11758201—42no—
342#11758201—42no—
343#11758199—42no—
344#11758199—42no—
345#11758199—42no—
346#11758198—44no—
347#11758198—41no—
348#11758198—41no—
349C4⋊Dic61—21no—
350C4⋊Dic61—21no—
351#11758196—44no—
352C4×Dic61—21no—
353C4×Dic61—21no—
354C4×Dic61—21no—
355C4×Dic61—42no—
356C4×Dic61C2×D412yescomplemented
357#11758194—21no—
358#11758194—21no—
359#11758194—21no—
360#11758194—21no—
361#11758194—21no—
362#11758194—21no—
363#11758194—21no—
364#11758194—42no—
365#11758194C2×D412yescomplemented
366C2×#92418—21no—
367C2×#92418—21no—
368C2×#92418—21no—
369C2×#92418—21no—
370C2×#92418—42no—
371C23×C61—21no—
372C23×C61—21no—
373C23×C61—21no—
374C23×C61—22no—
375C23×C61—22no—
376C23×C61—21no—
377C23×C61—21no—
378C23×C61—22no—
379C23×C61—22no—
380C23×C61—41no—
381C23×C61—42no—
382C23×C61—44no—
383C23×C61—42no—
384C23×C61—42no—
385C23×C61—42no—
386C23×C61—81no—
387C23×C61—82no—
388C23×C61—82no—
389C23×C61#12011yescharacteristic
390C23×C61#12011yescharacteristic
391C23×C61C22×D411yescharacteristic
392C22×D61—42no—
393C22×D61—42no—
394C22×D61—41no—
395C22×D61—41no—
396C22×D61—41no—
397Q8×C61—21no—
398Q8×C61—21no—
399Q8×C61—21no—
400Q8×C61—21no—
401Q8×C61—21no—
402Q8×C61—42no—
403Q8×C61#12112yescomplemented
404D4×C61—22no—
405D4×C61—22no—
406D4×C61—21no—
407D4×C61—21no—
408D4×C61—21no—
409D4×C61—21no—
410D4×C61—21no—
411D4×C61—42no—
412D4×C61—42no—
413D4×C61—44no—
414D4×C61—42no—
415D4×C61—44no—
416D4×C61—41no—
417D4×C61—41no—
418D4×C61—41no—
419D4×C61—41no—
420D4×C61—44no—
421D4×C61—42no—
422D4×C61—41no—
423D4×C61—41no—
424D4×C61—41no—
425D4×C61—41no—
426D4×C61—81no—
427D4×C61—82no—
428D4×C61—82no—
429D4×C61—82no—
430D4×C61—82no—
431D4×C61#12112yescomplemented
432C2×C4×C61—21no—
433C2×C4×C61—21no—
434C2×C4×C61—21no—
435C2×C4×C61—21no—
436C2×C4×C61—21no—
437C2×C4×C61—21no—
438C2×C4×C61—21no—
439C2×C4×C61—21no—
440C2×C4×C61—21no—
441C2×C4×C61—22no—
442C2×C4×C61—21no—
443C2×C4×C61—21no—
444C2×C4×C61—22no—
445C2×C4×C61—21no—
446C2×C4×C61—22no—
447C2×C4×C61—21no—
448C2×C4×C61—21no—
449C2×C4×C61—21no—
450C2×C4×C61—42no—
451C2×C4×C61—42no—
452C2×C4×C61—42no—
453C2×C4×C61—44no—
454C2×C4×C61—41no—
455C2×C4×C61—41no—
456C2×C4×C61—41no—
457C2×C4×C61—41no—
458C2×C4×C61—42no—
459C2×C4×C61—82no—
460C2×C4×C61#12011yescharacteristic
461C2×C4×C61#12011yescharacteristic
462C2×C4×C61C22×D411yescharacteristic
463C2×C4×C61C22×D411yescharacteristic
464C2×C4×C61C22×D411yescharacteristic
465C2×C4×C61C2×#4111yescharacteristic
466C2×C4×C61H(5,𝔽2)11yescharacteristic
467C2×C4×C61H(5,𝔽2)11yescharacteristic
468C22⋊D61—88no—
469C22⋊D61—82no—
470C22⋊D61—82no—
471C2×Dic61—22no—
472C2×Dic61—22no—
473C2×Dic61—22no—
474C2×Dic61—22no—
475C2×Dic61—48no—
476C2×Dic61—41no—
477C2×Dic61—41no—
478C2×Dic61—42no—
479C2×Dic61—41no—
480D244—41no—
481D244—41no—
482D244—41no—
483D244—41no—
484#92418—22no—
485#92418—41no—
486#92418—41no—
487#92418—41no—
488#24464—611nomaximal, Sylow
489C22×C61—21no—
490C22×C61—21no—
491C22×C61—21no—
492C22×C61—21no—
493C22×C61—21no—
494C22×C61—22no—
495C22×C61—21no—
496C22×C61—21no—
497C22×C61—42no—
498C22×C61—42no—
499C22×C61—41no—
500C22×C61—41no—
501C22×C61—41no—
502C22×C61—41no—
503C22×C61—42no—
504C22×C61—42no—
505C22×C61—41no—
506C22×C61—41no—
507C22×C61—41no—
508C22×C61—42no—
509C22×C61—41no—
510C22×C61—84no—
511C22×C61—82no—
512C22×C61—82no—
513C22×C61—164no—
514C22×C61#45312yescomplemented
515C22×C61C2×#12011yescharacteristic
516C22×C61D4211yescharacteristic
517C22×C61#54611yescharacteristic
518C2×D61—82no—
519C2×D61—82no—
520C2×D61—81no—
521C2×D61—81no—
522C2×D61—81no—
523C4×C61—21no—
524C4×C61—21no—
525C4×C61—22no—
526C4×C61—41no—
527C4×C61—41no—
528C4×C61—42no—
529C4×C61—41no—
530C4×C61—41no—
531C4×C61C2×#12111yescharacteristic
532C4×C61#53411yescharacteristic
533C4×C61D4211yescharacteristic
534C4×C61#54611yescharacteristic
535Dic61—24no—
536Dic61—42no—
537Dic61—81no—
538#3488D6111yescharacteristic, complemented
539#3055—611no—
540C2×#453—611no—
541#3006—611no—
542C22×#104—611no—
543#2856—611no—
544#2039—611no—
545#2037—611no—
546#2006—611no—
547#2002—611no—
548#1900—611no—
549#1896—611no—
550#1883—611no—
551#1859—611no—
552#1792—611no—
553C2×C61—21no—
554C2×C61—21no—
555C2×C61—22no—
556C2×C61—41no—
557C2×C61—42no—
558C2×C61—81no—
559C2×C61—82no—
560C2×C61—81no—
561C2×C61#241011yescharacteristic
562C2×C61C2×#45311yescharacteristic
563C2×C61#301811yescharacteristic
564D61—161no—
565C2×H(5,𝔽2)C2×D6111yescharacteristic
566C22×#41C2×D6111yescharacteristic
567C2×AGL(1,ℤ/8)—611no—
568C2×AGL(1,ℤ/8)—611no—
569C2×AGL(1,ℤ/8)—611no—
570C22×M16—611no—
571#550—21no—
572#548—21no—
573#546—21no—
574#546—22no—
575D42—22no—
576D42—21no—
577#537—21no—
578#537C2×D6111yescharacteristic
579#535—21no—
580#535C2×D6111yescharacteristic
581C2×#127—611no—
582#525—21no—
583#525C2×D6111yescharacteristic
584C2×#121—21no—
585C2×#121—611no—
586C2×#121—1222no—
587C2×#121C2×D6111yescharacteristic
588#520C2×D6111yescharacteristic
589C22×C42—611no—
590#469—1221no—
591#468—1221no—
592#466—1221no—
593#465—1221no—
594#453—1224no—
595#449—1221no—
596#449—1221no—
597#448—1221no—
598#447—1221no—
599#428—611no—
600C2×#104—611no—
601C2×#104—611no—
602C2×#104—611no—
603C2×#104—611no—
604C2×#104—611no—
605C2×#104—611no—
606C2×#104—1224no—
607#418—611no—
608#417—611no—
609#417—611no—
610#417—611no—
611C2×#100—611no—
612C2×#100—611no—
613#407—611no—
614#390—611no—
615#390—611no—
616#390—1222no—
617#384—611no—
618#343—611no—
619#343—611no—
620#339—611no—
621#339—611no—
622C61#2446411yescharacteristic, complemented, Sylow
623H(5,𝔽2)—22no—
624H(5,𝔽2)—22no—
625H(5,𝔽2)—41no—
626H(5,𝔽2)—41no—
627C2×#41—21no—
628C2×#41—21no—
629C2×#41—21no—
630C2×#41—21no—
631C2×#41—22no—
632C2×#41—22no—
633C2×#41—41no—
634C2×#41—41no—
635C2×#41C22⋊D6111yescharacteristic, complemented
636C2×#41C22⋊D6111yescharacteristic, complemented
637C2×#41C22×D6111yescharacteristic
638C2×#41C22×D6111yescharacteristic
639C2×#41C22×D6111yescharacteristic
640C22×Q8C22⋊D6111yescharacteristic, complemented
641C22×D4—21no—
642C22×D4—22no—
643C22×D4—22no—
644C22×D4—21no—
645C22×D4—21no—
646C22×D4—611no—
647C22×D4—1221no—
648C22×D4—1222no—
649C22×D4C22⋊D6112yes—
650C22×D4C22⋊D6111yescharacteristic, complemented
651C22×D4C22×D6111yescharacteristic
652C23×C4—21no—
653C23×C4—1221no—
654C23×C4C22×D6111yescharacteristic
655AGL(1,ℤ/8)—1222no—
656AGL(1,ℤ/8)—1222no—
657AGL(1,ℤ/8)—1222no—
658AGL(1,ℤ/8)—2441no—
659AGL(1,ℤ/8)—2441no—
660AGL(1,ℤ/8)—2441no—
661C2×SD16—1221no—
662C2×SD16—1221no—
663C2×SD16—1221no—
664C2×D8—1221no—
665C2×D8—1221no—
666C2×D8—1221no—
667C2×M16—611no—
668C2×M16—611no—
669C2×M16—611no—
670C2×M16—611no—
671C2×M16—1221no—
672C2×M16—1222no—
673C2×M16—2441no—
674C22×C8—1221no—
675#127—22no—
676#127—21no—
677#127—1222no—
678#127—2441no—
679#124—22no—
680#124—21no—
681#123—22no—
682#123—21no—
683C22⋊Q8—22no—
684C22⋊Q8—21no—
685C22⋊Q8—21no—
686C22⋊Q8C22⋊D6111yescharacteristic, complemented
687C22⋊Q8C22⋊D6111yescharacteristic, complemented
688#121—22no—
689#121—22no—
690#121—22no—
691#121—22no—
692#121—22no—
693#121—21no—
694#121—21no—
695#121—21no—
696#121—21no—
697#121—21no—
698#121—21no—
699#121—22no—
700#121—21no—
701#121—21no—
702#121—1221no—
703#121—1221no—
704#121—1221no—
705#121—1221no—
706#121—2448no—
707#121C22⋊D6111yescharacteristic, complemented
708#121C22⋊D6111yescharacteristic, complemented
709#120—22no—
710#120—22no—
711#120—22no—
712#120—21no—
713#120—22no—
714C4×Q8—21no—
715C4×D4—22no—
716C4×D4—22no—
717C4×D4—21no—
718C4×D4—22no—
719C4×D4—21no—
720C4×D4—21no—
721#117—21no—
722#117C22×D6111yescharacteristic
723C2×C4⋊C4—21no—
724C2×C4⋊C4—611no—
725C2×C4⋊C4—1222no—
726C2×C4⋊C4C22×D6111yescharacteristic
727C2×C22⋊C4—22no—
728C2×C22⋊C4—1222no—
729C2×C22⋊C4—1221no—
730C2×C22⋊C4—1222no—
731C2×C22⋊C4C22⋊D6112yes—
732C2×C42—611no—
733C2×C42—611no—
734C2×C42—1222no—
735C2×C42—1221no—
736C2×C42—2441no—
737#107—1221no—
738#106—1221no—
739#104—614no—
740#104—1222no—
741#104—1222no—
742#104—1222no—
743#104—1222no—
744#104—2441no—
745#103—1221no—
746#103—1221no—
747#103—1221no—
748#102—1221no—
749#102—1221no—
750#102—1221no—
751#102—1221no—
752#102—1221no—
753#100—1222no—
754#100—2441no—
755C22⋊C8—1221no—
756C22⋊C8—1221no—
757C24—22no—
758C24—21no—
759C24—1221no—
760C24C2×C22⋊D6111yescharacteristic
761C24C2×C22⋊D6112yes—
762#41—21no—
763#41—21no—
764#41—22no—
765#41—22no—
766#41—21no—
767#41—21no—
768#41—21no—
769#41—21no—
770#41—21no—
771#41—21no—
772#41—21no—
773#41—21no—
774#41—42no—
775#41—42no—
776#41—41no—
777#41—41no—
778#41—42no—
779#41—42no—
780#41—42no—
781#41—42no—
782#41—42no—
783#41—42no—
784#41D4×D6112yes—
785#41#1175822412yes—
786C2×Q8—21no—
787C2×Q8—22no—
788C2×Q8—41no—
789C2×Q8C2×C22⋊D6111yescharacteristic
790C2×Q8C2×C22⋊D6111yescharacteristic
791C2×Q8C2×C22⋊D6111yescharacteristic
792C2×D4—21no—
793C2×D4—22no—
794C2×D4—22no—
795C2×D4—22no—
796C2×D4—21no—
797C2×D4—21no—
798C2×D4—22no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4—21no—
802C2×D4—22no—
803C2×D4—22no—
804C2×D4—22no—
805C2×D4—21no—
806C2×D4—22no—
807C2×D4—21no—
808C2×D4—21no—
809C2×D4—21no—
810C2×D4—21no—
811C2×D4—21no—
812C2×D4—21no—
813C2×D4—21no—
814C2×D4—41no—
815C2×D4—42no—
816C2×D4—42no—
817C2×D4—42no—
818C2×D4—42no—
819C2×D4—44no—
820C2×D4—44no—
821C2×D4—42no—
822C2×D4—42no—
823C2×D4—44no—
824C2×D4—84no—
825C2×D4—1221no—
826C2×D4—1221no—
827C2×D4—1221no—
828C2×D4—1221no—
829C2×D4—1221no—
830C2×D4—1221no—
831C2×D4—2444no—
832C2×D4—2444no—
833C2×D4—2444no—
834C2×D4—2444no—
835C2×D4—2441no—
836C2×D4—2441no—
837C2×D4C2×C22⋊D6111yescharacteristic
838C2×D4C2×C22⋊D6111yescharacteristic
839C2×D4C2×C22⋊D6111yescharacteristic
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—22no—
846C22×C4—21no—
847C22×C4—22no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—42no—
853C22×C4—42no—
854C22×C4—1221no—
855C22×C4—1224no—
856C22×C4—1221no—
857C22×C4—1221no—
858C22×C4—2442no—
859C22×C4—2442no—
860C22×C4C2×C22⋊D6111yescharacteristic
861C22×C4C2×C22⋊D6111yescharacteristic
862C22×C4C2×C22⋊D6111yescharacteristic
863C22×C4C2×C22⋊D6111yescharacteristic
864C22×C4C2×C22⋊D6111yescharacteristic
865C22×C4C2×C22⋊D6112yes—
866C22×C4C23×D6111yescharacteristic
867SD16—2442no—
868SD16—2442no—
869SD16—2442no—
870D8—2442no—
871D8—2442no—
872D8—2442no—
873M16—612no—
874M16—1221no—
875M16—1221no—
876M16—1221no—
877M16—1221no—
878M16—1221no—
879M16—1221no—
880M16—1221no—
881M16—2442no—
882C2×C8—1221no—
883C2×C8—1221no—
884C2×C8—1221no—
885C2×C8—1221no—
886C2×C8—2442no—
887C4⋊C4—22no—
888C4⋊C4—22no—
889C4⋊C4—21no—
890C4⋊C4—21no—
891C4⋊C4—21no—
892C4⋊C4—21no—
893C4⋊C4—1221no—
894C4⋊C4—1221no—
895C4⋊C4—2444no—
896C4⋊C4C2×C22⋊D6111yescharacteristic
897C4⋊C4C2×C22⋊D6111yescharacteristic
898C22⋊C4—22no—
899C22⋊C4—22no—
900C22⋊C4—22no—
901C22⋊C4—22no—
902C22⋊C4—22no—
903C22⋊C4—21no—
904C22⋊C4—21no—
905C22⋊C4—21no—
906C22⋊C4—21no—
907C22⋊C4—22no—
908C22⋊C4—22no—
909C22⋊C4—21no—
910C22⋊C4—2444no—
911C22⋊C4—2444no—
912C22⋊C4—2441no—
913C22⋊C4—2441no—
914C42—22no—
915C42—21no—
916C42—612no—
917C42—1221no—
918C42—1221no—
919C42—1221no—
920C42—2442no—
921C23—21no—
922C23—21no—
923C23—21no—
924C23—22no—
925C23—22no—
926C23—21no—
927C23—21no—
928C23—22no—
929C23—22no—
930C23—41no—
931C23—42no—
932C23—44no—
933C23—42no—
934C23—42no—
935C23—42no—
936C23—81no—
937C23—82no—
938C23—82no—
939C23—2442no—
940C23—2442no—
941C23—2441no—
942C23—2441no—
943C23—2441no—
944C23#1451974611yescharacteristic
945C23#1451974611yescharacteristic
946C23C22×C22⋊D6111yescharacteristic
947Q8—21no—
948Q8—21no—
949Q8—21no—
950Q8—21no—
951Q8—21no—
952Q8—42no—
953Q8#1451974912yescomplemented
954D4—22no—
955D4—22no—
956D4—21no—
957D4—21no—
958D4—21no—
959D4—21no—
960D4—21no—
961D4—42no—
962D4—42no—
963D4—44no—
964D4—42no—
965D4—44no—
966D4—41no—
967D4—41no—
968D4—41no—
969D4—41no—
970D4—44no—
971D4—42no—
972D4—41no—
973D4—41no—
974D4—41no—
975D4—41no—
976D4—81no—
977D4—82no—
978D4—82no—
979D4—82no—
980D4—82no—
981D4—4888no—
982D4—4882no—
983D4—4882no—
984D4—2441no—
985D4—2441no—
986D4—2441no—
987D4—2441no—
988D4#1451974912yescomplemented
989C2×C4—21no—
990C2×C4—21no—
991C2×C4—21no—
992C2×C4—21no—
993C2×C4—21no—
994C2×C4—21no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—22no—
999C2×C4—21no—
1000C2×C4—21no—
1001C2×C4—22no—
1002C2×C4—21no—
1003C2×C4—22no—
1004C2×C4—21no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—42no—
1008C2×C4—42no—
1009C2×C4—42no—
1010C2×C4—44no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—42no—
1016C2×C4—82no—
1017C2×C4—1222no—
1018C2×C4—1222no—
1019C2×C4—1222no—
1020C2×C4—1222no—
1021C2×C4—2448no—
1022C2×C4—2442no—
1023C2×C4—2441no—
1024C2×C4—2441no—
1025C2×C4—2441no—
1026C2×C4#1451974611yescharacteristic
1027C2×C4#1451974611yescharacteristic
1028C2×C4C2×D4×D6111yescharacteristic
1029C2×C4C22×C22⋊D6111yescharacteristic
1030C2×C4C22×C22⋊D6111yescharacteristic
1031C2×C4C2×#1175822411yescharacteristic
1032C2×C4#1451982211yescharacteristic
1033C2×C4#1451982211yescharacteristic
1034C8—1222no—
1035C8—2441no—
1036C8—2441no—
1037C8—2441no—
1038C22—21no—
1039C22—21no—
1040C22—21no—
1041C22—21no—
1042C22—21no—
1043C22—21no—
1044C22—21no—
1045C22—22no—
1046C22—42no—
1047C22—42no—
1048C22—41no—
1049C22—41no—
1050C22—42no—
1051C22—41no—
1052C22—41no—
1053C22—41no—
1054C22—42no—
1055C22—41no—
1056C22—41no—
1057C22—41no—
1058C22—42no—
1059C22—84no—
1060C22—82no—
1061C22—82no—
1062C22—164no—
1063C22—4882no—
1064C22—4882no—
1065C22—4881no—
1066C22—4881no—
1067C22—4881no—
1068C22#1683993012yescomplemented
1069C22C2×#1451974611yescharacteristic
1070C22D4×C22⋊D6111yescharacteristic
1071C22#1684040611yescharacteristic
1072C4—21no—
1073C4—21no—
1074C4—22no—
1075C4—42no—
1076C4—41no—
1077C4—41no—
1078C4—41no—
1079C4—41no—
1080C4—1224no—
1081C4—4881no—
1082C4—2442no—
1083C4C2×#1451974911yescharacteristic
1084C4#1684032111yescharacteristic
1085C4D4×C22⋊D6111yescharacteristic
1086C4#1684040611yescharacteristic
1087C2—21no—
1088C2—21no—
1089C2—22no—
1090C2—41no—
1091C2—42no—
1092C2—81no—
1093C2—82no—
1094C2—81no—
1095C2—9761no—
1096C2#2144919311yescharacteristic
1097C2C2×#1683993011yescharacteristic
1098C2#2145516811yescharacteristic
subgroupG/H
centerC22C2×#14519746
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#3488C2
socleC22×C61C2×#120
hypercenter#3488D61
hypocenterC61#24464
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3488

Complements

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

NH ≅ G/Ntype
1. #21455440C2semidirect
2. C2×#16839930C2semidirect
3. #21455071C2semidirect
4. C22×#14519704C2semidirect
5. #21454162C2semidirect
6. #21447040C2semidirect
7. #21447026C2semidirect
8. #21446861C2semidirect
9. #21446832C2semidirect
10. #21446283C2semidirect
11. #21446263C2semidirect
12. #21446195C2semidirect
13. #21446045C2semidirect
14. #21445773C2semidirect
15. C61×#3488C2semidirect
17. C2×#14519802C22semidirect
18. C2×#14519802C22semidirect
19. C22×#11758194C22semidirect
20. C2×#14519773C22semidirect
21. C2×#14519751C22semidirect
23. C22×C4×Dic61C22semidirect
33. #16839805C22semidirect
37. C2×#14519704C22semidirect
38. C2×#14519704C22semidirect
39. C2×#14519704C22semidirect
40. C2×#14519704C22semidirect
41. #16839766C22semidirect
43. #16839763C22semidirect
44. #16839763C22semidirect
45. C2×#14519694C22semidirect
46. C2×#14519694C22semidirect
47. #16839726C22semidirect
48. #16839665C22semidirect
49. #16839663C22semidirect
51. #16839631C22semidirect
52. #16839531C22semidirect
53. #16839531C22semidirect
54. #16839521C22semidirect
55. #16839521C22semidirect
121. #14519704D4semidirect
146. C2×#41×C61D4semidirect
147. C2×#41×C61D4semidirect
151. C22×Q8×C61D4semidirect
158. C22×D4×C61D4semidirect
171. C22⋊Q8×C61D4semidirect
172. C22⋊Q8×C61D4semidirect
187. #121×C61D4semidirect
188. #121×C61D4semidirect
356. C4×Dic61C2×D4semidirect
365. #11758194C2×D4semidirect
403. Q8×C61#121semidirect
431. D4×C61#121semidirect
514. C22×C61#453semidirect
538. #3488D61semidirect
622. C61#24464semidirect
635. C2×#41C22⋊D61semidirect
636. C2×#41C22⋊D61semidirect
640. C22×Q8C22⋊D61semidirect
650. C22×D4C22⋊D61semidirect
686. C22⋊Q8C22⋊D61semidirect
687. C22⋊Q8C22⋊D61semidirect
707. #121C22⋊D61semidirect
708. #121C22⋊D61semidirect
953. Q8#14519749semidirect
988. D4#14519749semidirect
1068. C22#16839930semidirect

Maximal subgroups

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

subgroupindex
#214554402
C2×#168399302
#214550712
C22×#145197042
#214541622
#214470402
#214470262
#214468612
#214468322
#214462832
#214462632
#214461952
#214460452
#214457732
C61×#34882
#2446461