Finite Group Databasebeta

← #29647627

Subgroups — #29647627

Order 15616.

1004 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459554C211yesmaximal, characteristic
2#21448679C211yesmaximal, characteristic, complemented
3#21444397C211yesmaximal, characteristic, complemented
4#21444380C211yesmaximal, characteristic, complemented
5#21444376C211yesmaximal, characteristic, complemented
6#21444367C211yesmaximal, characteristic, complemented
7#21444358C211yesmaximal, characteristic, complemented
8#21444349C211yesmaximal, characteristic, complemented
9#21444345C211yesmaximal, characteristic, complemented
10#21444328C211yesmaximal, characteristic, complemented
11#21444324C211yesmaximal, characteristic, complemented
12#21444315C211yesmaximal, characteristic, complemented
13#21444306C211yesmaximal, characteristic, complemented
14C2×#16839497C211yesmaximal, characteristic, complemented
15C61×#2924C211yesmaximal, characteristic, complemented
16#16840475—21no—
17#16840460—21no—
18#16840456—21no—
19#16840436—21no—
20#16840436—21no—
21#16840413—21no—
22#16840402—21no—
23#16840402—21no—
24#16840390C411yescharacteristic, complemented
25#16840383C411yescharacteristic, complemented
26#16840383C411yescharacteristic, complemented
27#16840367C411yescharacteristic, complemented
28#16840367C411yescharacteristic, complemented
29#16840331C411yescharacteristic, complemented
30#16840312C2211yescharacteristic
31#16840312C2211yescharacteristic
32#16840296C2211yescharacteristic
33#16840296C2211yescharacteristic
34#16840273C2211yescharacteristic
35C2×#14519751C2211yescharacteristic
36#16840242C411yescharacteristic, complemented
37#16840236C411yescharacteristic, complemented
38#16839648—21no—
39#16839648—21no—
40#16839637—21no—
41#16839630C2211yescharacteristic, complemented
42#16839628C2211yescharacteristic, complemented
43#16839625C2211yescharacteristic
44C4×C4⋊Dic61C2211yescharacteristic, complemented
45C22⋊C4×Dic61—21no—
46#16839608C2211yescharacteristic, complemented
47C2×#14519684C2211yescharacteristic
48#16839500C2211yescharacteristic, complemented
49#16839500C2211yescharacteristic, complemented
50#16839500C2211yescharacteristic, complemented
51#16839500C2211yescharacteristic, complemented
52#16839497C2211yescharacteristic
53#16839497C2211yescharacteristic
54#16839497C2211yescharacteristic
55#16839497C2211yescharacteristic
56#16839497C2211yescharacteristic
57#16839497C2211yescharacteristic
58#16839497C2211yescharacteristic
59#16839497C2211yescharacteristic
60#16839497C2211yescharacteristic, complemented
61#16839497C2211yescharacteristic, complemented
62#16839497C2211yescharacteristic, complemented
63#16839497C2211yescharacteristic, complemented
64C2×#117×C61C2211yescharacteristic
65C61×#433—21no—
66C61×#433—21no—
67C61×#432C2211yescharacteristic, complemented
68C61×#432C2211yescharacteristic, complemented
69C61×#431C2211yescharacteristic, complemented
70C61×#431C2211yescharacteristic, complemented
71C61×#424—21no—
72C61×#407C2211yescharacteristic
73C2×C22⋊C8×C61C2211yescharacteristic
74C61×#405—21no—
75C2×#11758222—21no—
76C2×#11758222—21no—
77C2×#11758222C2×C411yescharacteristic
78C22×D244C2×C411yescharacteristic
79C22×C22⋊D61—21no—
80C23×Dic61—21no—
81#14519777C2×C411yescharacteristic, complemented
82#14519777C2×C411yescharacteristic, complemented
83#14519776—21no—
84#14519774C2×C411yescharacteristic, complemented
85#14519774C2×C411yescharacteristic, complemented
86#14519772—21no—
87#14519772—21no—
88#14519771—21no—
89#14519771—21no—
90#14519769C2×C411yescharacteristic, complemented
91#14519769C2×C411yescharacteristic, complemented
92#14519768—21no—
93#14519765—21no—
94#14519765—21no—
95#14519765C2×C411yescharacteristic, complemented
96#14519765C2×C411yescharacteristic, complemented
97#14519763—21no—
98#14519763—21no—
99#14519762—21no—
100#14519762—21no—
101#14519762—21no—
102#14519762—21no—
103#14519760—21no—
104#14519760—21no—
105#14519760—21no—
106#14519759—21no—
107#14519759—21no—
108#14519756C2×C411yescharacteristic
109#14519756C2311yescharacteristic
110#14519755—21no—
111#14519755—21no—
112#14519754—21no—
113#14519754—21no—
114#14519752—21no—
115#14519752—21no—
116#14519751—21no—
117#14519751—21no—
118#14519751—21no—
119#14519751—21no—
120#14519751C2×C411yescharacteristic
121#14519751C2×C411yescharacteristic
122#14519751C2×C411yescharacteristic
123#14519751C2311yescharacteristic
124#14519751C2311yescharacteristic
125#14519751C2311yescharacteristic
126#14519750—21no—
127#14519750—21no—
128#14519750—21no—
129#14519750—21no—
130#14519747—21no—
131#14519747—21no—
132#14519746—21no—
133C4×Dic122C2×C411yescharacteristic, complemented
134C4×Dic122C2×C411yescharacteristic, complemented
135C4×D244—21no—
136C4×D244—21no—
137C4×D244C2×C411yescharacteristic, complemented
138C4×D244C2×C411yescharacteristic, complemented
139C4×D244C2×C411yescharacteristic, complemented
140C4×D244C2×C411yescharacteristic, complemented
141C4×D244C2×C411yescharacteristic, complemented
142C4×D244C2×C411yescharacteristic, complemented
143#14519739—21no—
144#14519739—21no—
145C4×C22⋊D61—21no—
146C4×C22⋊D61—21no—
147C4×C22⋊D61—21no—
148C4×C22⋊D61—21no—
149#14519737—21no—
150#14519737—21no—
151#14519736C2×C411yescharacteristic
152#14519735—21no—
153#14519734—21no—
154#14519734—21no—
155C2×C4⋊Dic61—21no—
156C2×C4⋊Dic61—21no—
157C2×C4⋊Dic61C2×C411yescharacteristic
158C4⋊C4×D61—21no—
159C2×C22⋊Dic61—21no—
160C2×#11758198—21no—
161C22⋊C4×D61—21no—
162C22⋊C4×D61—21no—
163C2×C4×Dic61—21no—
164C2×C4×Dic61—21no—
165#14519684—21no—
166#14519684—21no—
167#14519684—21no—
168#14519684—21no—
169#14519684—21no—
170#14519684—21no—
171#14519684C2311yescharacteristic
172#14519684C2311yescharacteristic
173#14519684C2311yescharacteristic
174#14519684C2311yescharacteristic
175C23×C4×C61C2311yescharacteristic
176C2×M16×C61—21no—
177C22×C8×C61—21no—
178#117×C61C2×C411yescharacteristic
179#117×C61C2×C411yescharacteristic
180#117×C61C2×C411yescharacteristic
181#117×C61C2×C411yescharacteristic
182#117×C61D411yescharacteristic
183#117×C61D411yescharacteristic
184#117×C61D411yescharacteristic
185#117×C61D411yescharacteristic
186C2×C4⋊C4×C61D411yescharacteristic
187C2×C4⋊C4×C61D411yescharacteristic
188C2×C22⋊C4×C61D411yescharacteristic
189C2×C22⋊C4×C61D411yescharacteristic
190C2×C42×C61C2311yescharacteristic
191C2×C42×C61C2311yescharacteristic
192C4⋊C8×C61—21no—
193C4⋊C8×C61—21no—
194C4⋊C8×C61—21no—
195C4⋊C8×C61—21no—
196C22⋊C8×C61—21no—
197C22⋊C8×C61—21no—
198C22⋊C8×C61C2311yescharacteristic
199C22⋊C8×C61C2311yescharacteristic
200C22⋊C8×C61C2311yescharacteristic
201C22⋊C8×C61C2311yescharacteristic
202#97×C61—21no—
203#97×C61—21no—
204C4×C8×C61—21no—
205C4×C8×C61—21no—
206C24×C61C2×D411yescharacteristic
207C23×D61—21no—
208C22×C4×C61—42no—
209C22×C4×C61C22×C411yescharacteristic
210C22×C4×C61C22×C411yescharacteristic
211C22×C4×C61C2×D411yescharacteristic
212C22×C4×C61C2×D411yescharacteristic
213C22×C4×C61C2×D411yescharacteristic
214C22×C4×C61C2×D411yescharacteristic
215C22×C4×C61C2×D411yescharacteristic
216C22×C4×C61C2×D411yescharacteristic
217C22×C4×C61C2×D411yescharacteristic
218C22×C4×C61C2411yescharacteristic
219C2×C22⋊D61—21no—
220C2×C22⋊D61—21no—
221C2×C22⋊D61—21no—
222C2×C22⋊D61—21no—
223C2×C22⋊D61—21no—
224C2×C22⋊D61—21no—
225C2×C22⋊D61—21no—
226C2×C22⋊D61—81no—
227C2×C22⋊D61—81no—
228C22×Dic61—21no—
229C22×Dic61—21no—
230C22×Dic61—21no—
231C22×Dic61—21no—
232C22×Dic61—21no—
233C22×Dic61—42no—
234C22×Dic61—42no—
235C22×Dic61—81no—
236#11758222—42no—
237#11758222—81no—
238#11758222—81no—
239#11758222—81no—
240#11758222—81no—
241C2×D244—21no—
242C2×D244—21no—
243C2×D244—21no—
244C2×D244—21no—
245C2×D244—21no—
246C2×D244—42no—
247C2×D244C22×C411yescharacteristic
248C2×D244C22×C411yescharacteristic
249C2×D244C22×C411yescharacteristic
250C2×C4×D61—21no—
251C2×C4×D61—21no—
252C2×C4×D61—21no—
253C2×C4×D61—21no—
254C2×C4×D61—21no—
255C2×C4×D61—21no—
256C2×C4×D61—21no—
257C2×Dic122—21no—
258C2×Dic122—21no—
259C2×Dic122C22×C411yescharacteristic
260M16×C61—42no—
261C2×C8×C61—21no—
262C2×C8×C61—21no—
263C2×C8×C61—21no—
264C2×C8×C61—21no—
265C2×C8×C61—42no—
266C4⋊C4×C61C22⋊C411yescharacteristic
267C4⋊C4×C61C22⋊C411yescharacteristic
268C4⋊C4×C61C22⋊C411yescharacteristic
269C4⋊C4×C61C22⋊C411yescharacteristic
270C4⋊C4×C61C22⋊C411yescharacteristic
271C4⋊C4×C61C22⋊C411yescharacteristic
272C4⋊C4×C61C22⋊C411yescharacteristic
273C4⋊C4×C61C22⋊C411yescharacteristic
274C22⋊C4×C61C22⋊C411yescharacteristic
275C22⋊C4×C61C22⋊C411yescharacteristic
276C22⋊C4×C61C22⋊C411yescharacteristic
277C22⋊C4×C61C22⋊C411yescharacteristic
278C22⋊C4×C61C22⋊C411yescharacteristic
279C22⋊C4×C61C22⋊C411yescharacteristic
280C22⋊C4×C61C22⋊C411yescharacteristic
281C22⋊C4×C61C22⋊C411yescharacteristic
282C42×C61C22×C411yescharacteristic
283C42×C61C22×C411yescharacteristic
284C42×C61C22×C411yescharacteristic
285C42×C61C22×C411yescharacteristic
286C42×C61C2×D411yescharacteristic
287C42×C61C2×D411yescharacteristic
288C42×C61C2×D411yescharacteristic
289C42×C61C2×D411yescharacteristic
290C22⋊Dic61—21no—
291C22⋊Dic61—21no—
292C22⋊Dic61—21no—
293C22⋊Dic61—42no—
294#11758198—21no—
295#11758198—21no—
296#11758198—21no—
297#11758198—21no—
298#11758198—21no—
299#11758198—21no—
300#11758198—21no—
301#11758198—21no—
302#11758198—21no—
303#11758198—21no—
304#11758198—21no—
305#11758198—21no—
306#11758198—21no—
307#11758198—21no—
308#11758198—21no—
309#11758198—21no—
310C4⋊Dic61—21no—
311C4⋊Dic61—21no—
312C4⋊Dic61—21no—
313C4⋊Dic61—42no—
314C4⋊Dic61—81no—
315C4⋊Dic61C22×C411yescharacteristic
316C4⋊Dic61C22×C411yescharacteristic
317C4⋊Dic61C22×C411yescharacteristic
318C4⋊Dic61C22×C411yescharacteristic
319#11758196—21no—
320#11758196—21no—
321#11758196—21no—
322#11758196—21no—
323#11758196—21no—
324#11758196—21no—
325#11758196—21no—
326#11758196—21no—
327C4×Dic61—21no—
328C4×Dic61—21no—
329C4×Dic61—21no—
330C4×Dic61—42no—
331C4×Dic61—81no—
332C23×C61—21no—
333C23×C61—21no—
334C23×C61—22no—
335C23×C61—41no—
336C23×C61C2×C22⋊C411yescharacteristic
337C23×C61C2×C22⋊C411yescharacteristic
338C23×C61C22×D411yescharacteristic
339C22×D61—21no—
340C22×D61—21no—
341C22×D61—21no—
342C22×D61—42no—
343C22×D61—81no—
344C22×D61—81no—
345C2×C4×C61—21no—
346C2×C4×C61—21no—
347C2×C4×C61—21no—
348C2×C4×C61—21no—
349C2×C4×C61—22no—
350C2×C4×C61—22no—
351C2×C4×C61—41no—
352C2×C4×C61—41no—
353C2×C4×C61—41no—
354C2×C4×C61—41no—
355C2×C4×C61—41no—
356C2×C4×C61—41no—
357C2×C4×C61C2×C22⋊C411yescharacteristic
358C2×C4×C61C2×C22⋊C411yescharacteristic
359C2×C4×C61C2×C22⋊C411yescharacteristic
360C2×C4×C61C2×C22⋊C411yescharacteristic
361C2×C4×C61C2×C22⋊C411yescharacteristic
362C2×C4×C61C2×C22⋊C411yescharacteristic
363C2×C4×C61C2×C22⋊C411yescharacteristic
364C2×C4×C61C2×C22⋊C411yescharacteristic
365C2×C4×C61C2×C22⋊C411yescharacteristic
366C2×C4×C61C2×C22⋊C411yescharacteristic
367C2×C4×C61C23×C411yescharacteristic
368C2×C4×C61C22×D411yescharacteristic
369C22⋊D61—41no—
370C22⋊D61—41no—
371C22⋊D61—41no—
372C22⋊D61—41no—
373C22⋊D61—41no—
374C22⋊D61—41no—
375C22⋊D61—42no—
376C22⋊D61—81no—
377C22⋊D61—81no—
378C22⋊D61—81no—
379C2×Dic61—22no—
380C2×Dic61—21no—
381C2×Dic61—21no—
382C2×Dic61—21no—
383C2×Dic61—21no—
384C2×Dic61—21no—
385C2×Dic61—41no—
386C2×Dic61—41no—
387C2×Dic61—41no—
388C2×Dic61—41no—
389C2×Dic61—41no—
390C2×Dic61—41no—
391C2×Dic61—41no—
392C2×Dic61—41no—
393C2×Dic61—41no—
394C2×Dic61—41no—
395C2×Dic61—41no—
396C2×Dic61—81no—
397C2×Dic61—84no—
398D244—41no—
399D244—41no—
400D244—41no—
401D244—42no—
402D244—81no—
403D244—81no—
404D244—81no—
405D244—81no—
406C4×D61—42no—
407C4×D61—81no—
408C4×D61—81no—
409C4×D61—81no—
410C4×D61—81no—
411C4×D61—81no—
412C4×D61—81no—
413Dic122—41no—
414Dic122—81no—
415Dic122—81no—
416C8×C61—41no—
417C8×C61—41no—
418C8×C61—41no—
419C8×C61—41no—
420#17604—611nomaximal, Sylow
421C22×C61—21no—
422C22×C61—21no—
423C22×C61—21no—
424C22×C61—21no—
425C22×C61—21no—
426C22×C61—21no—
427C22×C61—21no—
428C22×C61—42no—
429C22×C61—42no—
430C22×C61#41012yes—
431C22×C61C22×C22⋊C411yescharacteristic
432C22×C61#57611yescharacteristic
433C22×C61#57711yescharacteristic
434C2×D61—41no—
435C2×D61—41no—
436C2×D61—41no—
437C2×D61—41no—
438C2×D61—41no—
439C2×D61—41no—
440C2×D61—41no—
441C2×D61—41no—
442C2×D61—41no—
443C2×D61—162no—
444C4×C61—21no—
445C4×C61—21no—
446C4×C61—21no—
447C4×C61—21no—
448C4×C61—21no—
449C4×C61—21no—
450C4×C61—21no—
451C4×C61—21no—
452C4×C61—21no—
453C4×C61—21no—
454C4×C61—21no—
455C4×C61—21no—
456Dic61—42no—
457Dic61—41no—
458Dic61—41no—
459Dic61—41no—
460Dic61—41no—
461Dic61—41no—
462Dic61—81no—
463Dic61—81no—
464Dic61—81no—
465#3494—611no—
466#2924D6111yescharacteristic, complemented
467#2343—611no—
468#1521—611no—
469#1517—611no—
470#1516—611no—
471#1514—611no—
472#1512—611no—
473#1510—611no—
474#1509—611no—
475#1505—611no—
476#1504—611no—
477#1502—611no—
478#1500—611no—
479C2×#327—611no—
480C2×C61—21no—
481C2×C61—21no—
482C2×C61—22no—
483C2×C61—41no—
484C2×C61C2×#41011yescharacteristic
485C2×C61#289711yescharacteristic
486C2×C61#290111yescharacteristic
487D61—81no—
488D61—81no—
489D61—81no—
490#555—1221no—
491#553—1221no—
492#553—1221no—
493#551—1221no—
494#551—1221no—
495#547—1221no—
496#546—1221no—
497#546—1221no—
498#544—611no—
499#542—611no—
500#542—611no—
501#540—611no—
502#540—611no—
503#535—611no—
504#532—611no—
505#532—611no—
506#529—611no—
507#529—611no—
508#525—611no—
509C2×#121—611no—
510#520—611no—
511#518—611no—
512C2×#117C2×D6111yescharacteristic
513#433—21no—
514#433—21no—
515#432C2×D6111yescharacteristic, complemented
516#432C2×D6111yescharacteristic, complemented
517#431C2×D6111yescharacteristic, complemented
518#431C2×D6111yescharacteristic, complemented
519#424—21no—
520#407C2×D6111yescharacteristic
521C2×C22⋊C8C2×D6111yescharacteristic
522#405—21no—
523#387—1221no—
524#387—1221no—
525#385—1221no—
526#383—611no—
527#382—611no—
528#381—611no—
529C4×C4⋊C4—611no—
530C4×C22⋊C4—1221no—
531#376—611no—
532C2×#95—611no—
533#328—611no—
534#328—611no—
535#328—611no—
536#328—611no—
537#327—611no—
538#327—611no—
539#327—611no—
540#327—611no—
541#327—611no—
542#327—611no—
543#327—611no—
544#327—611no—
545#327—611no—
546#327—611no—
547#327—611no—
548#327—611no—
549C61#1760411yescharacteristic, complemented, Sylow
550C2×#41—611no—
551C2×#41—1221no—
552C2×#41—1221no—
553C22×D4—611no—
554C22×D4—1221no—
555C23×C4—1221no—
556C23×C4C22×D6111yescharacteristic
557C2×M16—21no—
558C22×C8—21no—
559C4⋊Q8—611no—
560C4⋊Q8—611no—
561C4⋊Q8—1221no—
562#127—611no—
563#127—611no—
564#126—1221no—
565#126—1221no—
566#126—1221no—
567#126—1221no—
568#125—611no—
569#125—611no—
570#125—1221no—
571#124—611no—
572#124—611no—
573#124—1221no—
574#124—1221no—
575#124—1221no—
576#124—1221no—
577#123—1221no—
578#123—1221no—
579#123—1221no—
580#123—1221no—
581#123—1221no—
582#123—1221no—
583#123—1221no—
584#123—1221no—
585#123—1221no—
586C22⋊Q8—611no—
587C22⋊Q8—611no—
588C22⋊Q8—1221no—
589C22⋊Q8—1221no—
590C22⋊Q8—1221no—
591C22⋊Q8—1221no—
592#121—611no—
593#121—611no—
594#121—611no—
595#121—611no—
596#121—611no—
597#121—611no—
598#121—1221no—
599#121—1221no—
600#121—1221no—
601#121—1221no—
602#121—1221no—
603#121—1221no—
604#121—1221no—
605#121—1221no—
606#121—1221no—
607#121—1221no—
608#120—1221no—
609#120—1221no—
610#120—1221no—
611C4×Q8—611no—
612C4×Q8—611no—
613C4×D4—611no—
614C4×D4—611no—
615C4×D4—611no—
616C4×D4—611no—
617C4×D4—611no—
618C4×D4—611no—
619C4×D4—1221no—
620C4×D4—1221no—
621C4×D4—1221no—
622C4×D4—1221no—
623C4×D4—1221no—
624C4×D4—1221no—
625C4×D4—1221no—
626C4×D4—1221no—
627C4×D4—1221no—
628C4×D4—1221no—
629#117—611no—
630#117—1221no—
631#117—1221no—
632#117—1221no—
633#117C4×D6111yescharacteristic
634#117C4×D6111yescharacteristic
635#117C4×D6111yescharacteristic
636#117C4×D6111yescharacteristic
637#117C22⋊D6111yescharacteristic
638#117C22⋊D6111yescharacteristic
639#117C22⋊D6111yescharacteristic
640#117C22⋊D6111yescharacteristic
641C2×C4⋊C4—611no—
642C2×C4⋊C4—1221no—
643C2×C4⋊C4—1221no—
644C2×C4⋊C4—1221no—
645C2×C4⋊C4D24411yescharacteristic
646C2×C4⋊C4D24411yescharacteristic
647C2×C22⋊C4—1221no—
648C2×C22⋊C4—1221no—
649C2×C22⋊C4—1221no—
650C2×C22⋊C4—1221no—
651C2×C22⋊C4D24411yescharacteristic
652C2×C22⋊C4D24411yescharacteristic
653C2×C42—1221no—
654C2×C42—1221no—
655C2×C42C22×D6111yescharacteristic
656C2×C42C22×D6111yescharacteristic
657C4⋊C8—21no—
658C4⋊C8—21no—
659C4⋊C8—21no—
660C4⋊C8—21no—
661C22⋊C8—21no—
662C22⋊C8—21no—
663C22⋊C8C22×D6111yescharacteristic
664C22⋊C8C22×D6111yescharacteristic
665C22⋊C8C22×D6111yescharacteristic
666C22⋊C8C22×D6111yescharacteristic
667#97—21no—
668#97—21no—
669C4×C8—21no—
670C4×C8—21no—
671#95—611no—
672#95—611no—
673#95—611no—
674#95—611no—
675#95—1221no—
676#95—1221no—
677#95—1221no—
678#95—1221no—
679#95—1221no—
680#95—1221no—
681C24—1221no—
682C24C2×D24411yescharacteristic
683#41—4881no—
684#41—4881no—
685#41—4881no—
686#41—4881no—
687#41—2442no—
688C2×Q8—611no—
689C2×Q8—1221no—
690C2×Q8—1221no—
691C2×D4—611no—
692C2×D4—611no—
693C2×D4—611no—
694C2×D4—1221no—
695C2×D4—1221no—
696C2×D4—1221no—
697C2×D4—1221no—
698C2×D4—1221no—
699C2×D4—1221no—
700C2×D4—1221no—
701C2×D4—1221no—
702C2×D4—1221no—
703C2×D4—1221no—
704C2×D4—1221no—
705C2×D4—1221no—
706C2×D4—4881no—
707C2×D4—4881no—
708C2×D4—2442no—
709C22×C4—42no—
710C22×C4—1221no—
711C22×C4—1221no—
712C22×C4—1221no—
713C22×C4—1221no—
714C22×C4—1221no—
715C22×C4—1221no—
716C22×C4—1221no—
717C22×C4—1221no—
718C22×C4—1221no—
719C22×C4—1221no—
720C22×C4—1221no—
721C22×C4—1221no—
722C22×C4—4881no—
723C22×C4—2442no—
724C22×C4—2442no—
725C22×C4C2×C4×D6111yescharacteristic
726C22×C4C2×C4×D6111yescharacteristic
727C22×C4C2×D24411yescharacteristic
728C22×C4C2×D24411yescharacteristic
729C22×C4C2×D24411yescharacteristic
730C22×C4C2×D24411yescharacteristic
731C22×C4C2×D24411yescharacteristic
732C22×C4C2×C22⋊D6111yescharacteristic
733C22×C4C2×C22⋊D6111yescharacteristic
734C22×C4C23×D6111yescharacteristic
735M16—42no—
736C2×C8—21no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—42no—
741C4⋊C4—611no—
742C4⋊C4—611no—
743C4⋊C4—611no—
744C4⋊C4—611no—
745C4⋊C4—1221no—
746C4⋊C4—1221no—
747C4⋊C4—1221no—
748C4⋊C4—1221no—
749C4⋊C4—1221no—
750C4⋊C4—1221no—
751C4⋊C4—1221no—
752C4⋊C4—1221no—
753C4⋊C4—1221no—
754C4⋊C4—1221no—
755C4⋊C4—1221no—
756C4⋊C4—4881no—
757C4⋊C4—2442no—
758C4⋊C4#1175819811yescharacteristic
759C4⋊C4#1175819811yescharacteristic
760C4⋊C4#1175819811yescharacteristic
761C4⋊C4#1175819811yescharacteristic
762C4⋊C4#1175819811yescharacteristic
763C4⋊C4#1175819811yescharacteristic
764C4⋊C4#1175819811yescharacteristic
765C4⋊C4#1175819811yescharacteristic
766C22⋊C4—1221no—
767C22⋊C4—1221no—
768C22⋊C4—1221no—
769C22⋊C4—1221no—
770C22⋊C4—1221no—
771C22⋊C4—1221no—
772C22⋊C4—1221no—
773C22⋊C4—1221no—
774C22⋊C4—1221no—
775C22⋊C4—1221no—
776C22⋊C4—1221no—
777C22⋊C4—1221no—
778C22⋊C4—1221no—
779C22⋊C4—1221no—
780C22⋊C4—1221no—
781C22⋊C4—1221no—
782C22⋊C4—1221no—
783C22⋊C4—1221no—
784C22⋊C4—1221no—
785C22⋊C4—2442no—
786C22⋊C4#1175819811yescharacteristic
787C22⋊C4#1175819811yescharacteristic
788C22⋊C4#1175819811yescharacteristic
789C22⋊C4#1175819811yescharacteristic
790C22⋊C4#1175819811yescharacteristic
791C22⋊C4#1175819811yescharacteristic
792C22⋊C4#1175819811yescharacteristic
793C22⋊C4#1175819811yescharacteristic
794C42—1221no—
795C42—1221no—
796C42—1221no—
797C42—4881no—
798C42—2442no—
799C42C2×C4×D6111yescharacteristic
800C42C2×C4×D6111yescharacteristic
801C42C2×C4×D6111yescharacteristic
802C42C2×C4×D6111yescharacteristic
803C42C2×C22⋊D6111yescharacteristic
804C42C2×C22⋊D6111yescharacteristic
805C42C2×C22⋊D6111yescharacteristic
806C42C2×C22⋊D6111yescharacteristic
807C23—22no—
808C23—21no—
809C23—21no—
810C23—41no—
811C23—1221no—
812C23—1221no—
813C23—1221no—
814C23—4881no—
815C23—4881no—
816C23—2442no—
817C23C2×#1175819811yescharacteristic
818C23C2×#1175819811yescharacteristic
819C23C22×D24411yescharacteristic
820Q8—4881no—
821Q8—4881no—
822Q8—2441no—
823D4—4881no—
824D4—4881no—
825D4—4881no—
826D4—4881no—
827D4—4881no—
828D4—4881no—
829D4—4881no—
830D4—2441no—
831D4—2441no—
832D4—2441no—
833D4—2442no—
834D4—2442no—
835D4—2441no—
836D4—2441no—
837D4—2441no—
838D4—2441no—
839D4—2441no—
840D4—2441no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—1222no—
854C2×C4—1221no—
855C2×C4—1221no—
856C2×C4—1221no—
857C2×C4—1221no—
858C2×C4—1221no—
859C2×C4—4881no—
860C2×C4—4881no—
861C2×C4—4881no—
862C2×C4—4881no—
863C2×C4—4881no—
864C2×C4—4881no—
865C2×C4—4884no—
866C2×C4—4881no—
867C2×C4—2442no—
868C2×C4—2441no—
869C2×C4—2441no—
870C2×C4—2441no—
871C2×C4—2441no—
872C2×C4—2441no—
873C2×C4—2441no—
874C2×C4—2441no—
875C2×C4—2441no—
876C2×C4—2441no—
877C2×C4—2441no—
878C2×C4—2441no—
879C2×C4C2×#1175819811yescharacteristic
880C2×C4C2×#1175819811yescharacteristic
881C2×C4C2×#1175819811yescharacteristic
882C2×C4C2×#1175819811yescharacteristic
883C2×C4C2×#1175819811yescharacteristic
884C2×C4C2×#1175819811yescharacteristic
885C2×C4C2×#1175819811yescharacteristic
886C2×C4C2×#1175819811yescharacteristic
887C2×C4C2×#1175819811yescharacteristic
888C2×C4C2×#1175819811yescharacteristic
889C2×C4C22×C4×D6111yescharacteristic
890C2×C4C22×C22⋊D6111yescharacteristic
891C8—41no—
892C8—41no—
893C8—41no—
894C8—41no—
895C22—21no—
896C22—21no—
897C22—21no—
898C22—21no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—42no—
903C22—42no—
904C22—9762no—
905C22—2441no—
906C22—2441no—
907C22—2441no—
908C22—2441no—
909C22—2441no—
910C22—2441no—
911C22—2441no—
912C22—2441no—
913C22—2441no—
914C22#1683973512yes—
915C22C22×#1175819811yescharacteristic
916C22#1684056711yescharacteristic
917C22#1684057411yescharacteristic
918C4—21no—
919C4—21no—
920C4—21no—
921C4—21no—
922C4—21no—
923C4—21no—
924C4—21no—
925C4—21no—
926C4—21no—
927C4—21no—
928C4—21no—
929C4—21no—
930C4—4881no—
931C4—4881no—
932C4—4881no—
933C4—2442no—
934C4—2441no—
935C4—2441no—
936C4—2441no—
937C4—2441no—
938C4—2441no—
939C2—21no—
940C2—21no—
941C2—22no—
942C2—41no—
943C2—4881no—
944C2—4881no—
945C2—4881no—
946C2C2×#1683973511yescharacteristic
947C2#2145434611yescharacteristic
948C2#2145436411yescharacteristic
subgroupG/H
centerC22C22×#11758198
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#2924C2
socleC22×C61C22×C22⋊C4
prime radical#21459554C2
cosocleC22×C4×C61C24
hypercenter#2924D61
hypocenterC61#17604
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×#117 ◁ #2924

Complements

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

NH ≅ G/Ntype
2. #21448679C2semidirect
3. #21444397C2semidirect
4. #21444380C2semidirect
5. #21444376C2semidirect
6. #21444367C2semidirect
7. #21444358C2semidirect
8. #21444349C2semidirect
9. #21444345C2semidirect
10. #21444328C2semidirect
11. #21444324C2semidirect
12. #21444315C2semidirect
13. #21444306C2semidirect
14. C2×#16839497C2semidirect
15. C61×#2924C2semidirect
24. #16840390C4semidirect
25. #16840383C4semidirect
26. #16840383C4semidirect
27. #16840367C4semidirect
28. #16840367C4semidirect
29. #16840331C4semidirect
36. #16840242C4semidirect
37. #16840236C4semidirect
41. #16839630C22semidirect
42. #16839628C22semidirect
44. C4×C4⋊Dic61C22semidirect
46. #16839608C22semidirect
48. #16839500C22semidirect
49. #16839500C22semidirect
50. #16839500C22semidirect
51. #16839500C22semidirect
60. #16839497C22semidirect
61. #16839497C22semidirect
62. #16839497C22semidirect
63. #16839497C22semidirect
67. C61×#432C22semidirect
68. C61×#432C22semidirect
69. C61×#431C22semidirect
70. C61×#431C22semidirect
81. #14519777C2×C4semidirect
82. #14519777C2×C4semidirect
84. #14519774C2×C4semidirect
85. #14519774C2×C4semidirect
90. #14519769C2×C4semidirect
91. #14519769C2×C4semidirect
95. #14519765C2×C4semidirect
96. #14519765C2×C4semidirect
133. C4×Dic122C2×C4semidirect
134. C4×Dic122C2×C4semidirect
137. C4×D244C2×C4semidirect
138. C4×D244C2×C4semidirect
139. C4×D244C2×C4semidirect
140. C4×D244C2×C4semidirect
141. C4×D244C2×C4semidirect
142. C4×D244C2×C4semidirect
466. #2924D61semidirect
515. #432C2×D61semidirect
516. #432C2×D61semidirect
517. #431C2×D61semidirect
518. #431C2×D61semidirect
549. C61#17604semidirect

Maximal subgroups

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

subgroupindex
#214595542
#214486792
#214443972
#214443802
#214443762
#214443672
#214443582
#214443492
#214443452
#214443282
#214443242
#214443152
#214443062
C2×#168394972
C61×#29242
#1760461