Finite Group Databasebeta

← #29646204

Subgroups — #29646204

Order 15616.

1046 conjugacy classes of subgroups.

The subgroup lattice has 958 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840436C211yesmaximal, characteristic
2#21454477C211yesmaximal, characteristic, complemented
3#21444189C211yesmaximal, characteristic, complemented
4#21444186C211yesmaximal, characteristic, complemented
5#21444172C211yesmaximal, characteristic, complemented
6#21444170C211yesmaximal, characteristic, complemented
7#21444168C211yesmaximal, characteristic, complemented
8#21444165C211yesmaximal, characteristic, complemented
9#21444159C211yesmaximal, characteristic, complemented
10#21444151C211yesmaximal, characteristic, complemented
11#21444145C211yesmaximal, characteristic, complemented
12#21444139C211yesmaximal, characteristic, complemented
13#21444131C211yesmaximal, characteristic, complemented
14C2×#16839485C211yesmaximal, characteristic, complemented
15C61×#2924C211yesmaximal, characteristic, complemented
16#16840436—21no—
17#16840436—21no—
18#16840436—21no—
19#16840436—21no—
20#16840436—21no—
21#16840436—21no—
22#16840436—21no—
23#16840436—21no—
24C2×#14519772C411yescharacteristic
25C2×#14519771C2211yescharacteristic
26C2×#14519765C2211yescharacteristic
27C2×#14519762C411yescharacteristic
28C2×#14519762C411yescharacteristic
29C2×#14519760C2211yescharacteristic
30C2×#14519755C411yescharacteristic
31C2×#14519754C411yescharacteristic
32C2×#14519747C411yescharacteristic
33C2×C4×D244C2211yescharacteristic
34C2×#14519737C411yescharacteristic
35C2×#14519734C2211yescharacteristic
36C22×#11758198C2211yescharacteristic
37C2×C22⋊C4×D61C411yescharacteristic
38#16839823—21no—
39#16839823—21no—
40#16839819C2211yescharacteristic, complemented
41#16839819C2211yescharacteristic, complemented
42#16839815C2211yescharacteristic, complemented
43#16839815C2211yescharacteristic, complemented
44#16839789—21no—
45#16839726C2211yescharacteristic
46C2×C22⋊#92418C2211yescharacteristic
47#16839718—21no—
48#16839487C2211yescharacteristic, complemented
49#16839487C2211yescharacteristic, complemented
50#16839487C2211yescharacteristic, complemented
51#16839487C2211yescharacteristic, complemented
52#16839485C2211yescharacteristic
53#16839485C2211yescharacteristic
54#16839485C2211yescharacteristic
55#16839485C2211yescharacteristic
56#16839485C2211yescharacteristic
57#16839485C2211yescharacteristic
58#16839485C2211yescharacteristic
59#16839485C2211yescharacteristic
60#16839485C2211yescharacteristic, complemented
61#16839485C2211yescharacteristic, complemented
62#16839485C2211yescharacteristic, complemented
63#16839485C2211yescharacteristic, 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—
75C24×D61C2×C411yescharacteristic
76C22×Dic122C2×C411yescharacteristic
77C22×D244C2×C411yescharacteristic
78C22×D244C2×C411yescharacteristic
79C22×C22⋊D61C2×C411yescharacteristic
80C23×Dic61C2×C411yescharacteristic
81C22×C4×D61C2×C411yescharacteristic
82C22×C4×D61C2×C411yescharacteristic
83C22×C4×D61C2×C411yescharacteristic
84C2×#11758194—21no—
85C22×#92418—21no—
86#14519772—21no—
87#14519772—21no—
88#14519772—21no—
89#14519772—21no—
90#14519771—21no—
91#14519771—21no—
92#14519771—21no—
93#14519771—21no—
94#14519765—21no—
95#14519765—21no—
96#14519765—21no—
97#14519765—21no—
98#14519762—21no—
99#14519762—21no—
100#14519762—21no—
101#14519762—21no—
102#14519762—21no—
103#14519762—21no—
104#14519762—21no—
105#14519762—21no—
106#14519760—21no—
107#14519760—21no—
108#14519760—21no—
109#14519760—21no—
110#14519755—21no—
111#14519755—21no—
112#14519755—21no—
113#14519755—21no—
114#14519754—21no—
115#14519754—21no—
116#14519754—21no—
117#14519754—21no—
118#14519747—21no—
119#14519747—21no—
120#14519747—21no—
121#14519747—21no—
122C4×D244—21no—
123C4×D244—21no—
124C4×D244—21no—
125C4×D244—21no—
126#14519737—21no—
127#14519737—21no—
128#14519737—21no—
129#14519737—21no—
130#14519734—21no—
131#14519734—21no—
132#14519734—21no—
133#14519734—21no—
134C2×C4⋊Dic61C2×C411yescharacteristic
135C2×#11758196C2×C411yescharacteristic
136C2×#11758196C2×C411yescharacteristic
137C2×#11758196C2×C411yescharacteristic
138C2×#11758196C2×C411yescharacteristic
139C2×#11758196C2311yescharacteristic
140C2×C22⋊Dic61C2×C411yescharacteristic
141C2×#11758198—21no—
142C2×#11758198—21no—
143C2×#11758198—21no—
144C2×#11758198—21no—
145C2×#11758198C2×C411yescharacteristic
146C2×#11758198C2×C411yescharacteristic
147C2×#11758198C2×C411yescharacteristic
148C2×#11758198C2×C411yescharacteristic
149C2×#11758198C2×C411yescharacteristic
150C2×#11758198C2×C411yescharacteristic
151C2×#11758198C2×C411yescharacteristic
152C2×#11758198C2×C411yescharacteristic
153C2×#11758198C2311yescharacteristic
154C2×#11758198C2311yescharacteristic
155C2×#11758198C2311yescharacteristic
156C22⋊C4×D61—21no—
157C22⋊C4×D61—21no—
158C22⋊C4×D61—21no—
159C22⋊C4×D61—21no—
160C2×C4×Dic61C2×C411yescharacteristic
161C4⋊#92418—21no—
162C4⋊#92418—21no—
163C4⋊#92418—21no—
164C4⋊#92418—21no—
165C22⋊#92418—21no—
166C22⋊#92418—21no—
167C22⋊#92418C2311yescharacteristic
168C22⋊#92418C2311yescharacteristic
169C22⋊#92418C2311yescharacteristic
170C22⋊#92418C2311yescharacteristic
171#14519688—21no—
172#14519688—21no—
173C4×#92418—21no—
174C4×#92418—21no—
175C23×C4×C61C2311yescharacteristic
176C2×M16×C61—21no—
177C22×C8×C61—21no—
178#117×C61D411yescharacteristic
179#117×C61D411yescharacteristic
180#117×C61D411yescharacteristic
181#117×C61D411yescharacteristic
182#117×C61D411yescharacteristic
183#117×C61D411yescharacteristic
184#117×C61D411yescharacteristic
185#117×C61D411yescharacteristic
186C2×C4⋊C4×C61C2×C411yescharacteristic
187C2×C4⋊C4×C61C2×C411yescharacteristic
188C2×C22⋊C4×C61C2×C411yescharacteristic
189C2×C22⋊C4×C61C2×C411yescharacteristic
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×C61C22×C411yescharacteristic
207C23×D61—21no—
208C23×D61—21no—
209C23×D61—22no—
210C23×D61—41no—
211C23×D61—42no—
212C23×D61—81no—
213C23×D61C22×C411yescharacteristic
214C23×D61C22×C411yescharacteristic
215C23×D61C22×C411yescharacteristic
216C22×C4×C61—42no—
217C22×C4×C61C22×C411yescharacteristic
218C22×C4×C61C22×C411yescharacteristic
219C22×C4×C61C22×C411yescharacteristic
220C22×C4×C61C22×C411yescharacteristic
221C22×C4×C61C22×C411yescharacteristic
222C22×C4×C61C2×D411yescharacteristic
223C22×C4×C61C2×D411yescharacteristic
224C22×C4×C61C2×D411yescharacteristic
225C22×C4×C61C2×D411yescharacteristic
226C22×C4×C61C2411yescharacteristic
227C2×C22⋊D61—21no—
228C2×C22⋊D61—21no—
229C2×C22⋊D61—42no—
230C22×Dic61—21no—
231C22×Dic61—21no—
232C22×Dic61—81no—
233C22×Dic61C22×C411yescharacteristic
234C22×Dic61C22×C411yescharacteristic
235C22×Dic61C22×C411yescharacteristic
236C22×Dic61C22×C411yescharacteristic
237C22×Dic61C22×C411yescharacteristic
238C2×D244—22no—
239C2×D244—21no—
240C2×D244—21no—
241C2×D244—21no—
242C2×D244—21no—
243C2×D244—41no—
244C2×D244—81no—
245C2×C4×D61—22no—
246C2×C4×D61—21no—
247C2×C4×D61—21no—
248C2×C4×D61—21no—
249C2×C4×D61—21no—
250C2×C4×D61—21no—
251C2×C4×D61—21no—
252C2×C4×D61—41no—
253C2×C4×D61—81no—
254C2×C4×D61—81no—
255C2×Dic122—21no—
256C2×Dic122—21no—
257C2×Dic122—81no—
258M16×C61—42no—
259C2×C8×C61—21no—
260C2×C8×C61—21no—
261C2×C8×C61—21no—
262C2×C8×C61—21no—
263C2×C8×C61—42no—
264C4⋊C4×C61C22⋊C411yescharacteristic
265C4⋊C4×C61C22⋊C411yescharacteristic
266C4⋊C4×C61C22⋊C411yescharacteristic
267C4⋊C4×C61C22⋊C411yescharacteristic
268C4⋊C4×C61C22⋊C411yescharacteristic
269C4⋊C4×C61C22⋊C411yescharacteristic
270C4⋊C4×C61C22⋊C411yescharacteristic
271C4⋊C4×C61C22⋊C411yescharacteristic
272C22⋊C4×C61C22⋊C411yescharacteristic
273C22⋊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
280C42×C61C2×D411yescharacteristic
281C42×C61C2×D411yescharacteristic
282C42×C61C2×D411yescharacteristic
283C42×C61C2×D411yescharacteristic
284C42×C61C2×D411yescharacteristic
285C42×C61C2×D411yescharacteristic
286C42×C61C2×D411yescharacteristic
287C42×C61C2×D411yescharacteristic
288C22⋊Dic61—21no—
289C22⋊Dic61—21no—
290#11758198—21no—
291#11758198—21no—
292#11758198—21no—
293#11758198—21no—
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—
310#11758198—21no—
311#11758198—21no—
312C4⋊Dic61—21no—
313C4⋊Dic61—21no—
314#11758196—21no—
315#11758196—21no—
316#11758196—21no—
317#11758196—21no—
318#11758196—21no—
319#11758196—21no—
320#11758196—21no—
321#11758196—21no—
322#11758196—21no—
323#11758196—21no—
324C4×Dic61—21no—
325C4×Dic61—21no—
326#11758194—42no—
327C2×#92418—21no—
328C2×#92418—21no—
329C2×#92418—21no—
330C2×#92418—21no—
331C2×#92418—42no—
332C23×C61—21no—
333C23×C61—21no—
334C23×C61—22no—
335C23×C61—41no—
336C23×C61C2×C22⋊C411yescharacteristic
337C23×C61C2×C22⋊C411yescharacteristic
338C23×C61C23×C411yescharacteristic
339C22×D61—21no—
340C22×D61—21no—
341C22×D61—21no—
342C22×D61—21no—
343C22×D61—21no—
344C22×D61—21no—
345C22×D61—21no—
346C22×D61—21no—
347C22×D61—42no—
348C22×D61—42no—
349C22×D61—41no—
350C22×D61—41no—
351C22×D61—42no—
352C22×D61—42no—
353C22×D61—41no—
354C22×D61—41no—
355C22×D61—41no—
356C22×D61—41no—
357C22×D61—81no—
358C22×D61—81no—
359C22×D61—84no—
360C22×D61—84no—
361C22×D61#13112yes—
362C2×C4×C61—21no—
363C2×C4×C61—21no—
364C2×C4×C61—21no—
365C2×C4×C61—21no—
366C2×C4×C61—22no—
367C2×C4×C61—22no—
368C2×C4×C61—41no—
369C2×C4×C61—41no—
370C2×C4×C61—41no—
371C2×C4×C61—41no—
372C2×C4×C61—41no—
373C2×C4×C61—41no—
374C2×C4×C61C2×C22⋊C411yescharacteristic
375C2×C4×C61C2×C22⋊C411yescharacteristic
376C2×C4×C61C2×C22⋊C411yescharacteristic
377C2×C4×C61C2×C22⋊C411yescharacteristic
378C2×C4×C61C2×C22⋊C411yescharacteristic
379C2×C4×C61C2×C22⋊C411yescharacteristic
380C2×C4×C61C2×C22⋊C411yescharacteristic
381C2×C4×C61C2×C22⋊C411yescharacteristic
382C2×C4×C61C2×C22⋊C411yescharacteristic
383C2×C4×C61C2×C22⋊C411yescharacteristic
384C2×C4×C61C22×D411yescharacteristic
385C2×C4×C61C22×D411yescharacteristic
386C22⋊D61—42no—
387C22⋊D61—42no—
388C2×Dic61—21no—
389C2×Dic61—21no—
390C2×Dic61—21no—
391C2×Dic61—21no—
392C2×Dic61—21no—
393C2×Dic61—21no—
394C2×Dic61—21no—
395C2×Dic61—41no—
396C2×Dic61—41no—
397C2×Dic61—41no—
398C2×Dic61—41no—
399C2×Dic61—81no—
400C2×Dic61—81no—
401D244—42no—
402D244—42no—
403D244—81no—
404D244—81no—
405C4×D61—42no—
406C4×D61—42no—
407C4×D61—81no—
408C4×D61—81no—
409C4×D61—81no—
410C4×D61—81no—
411Dic122—81no—
412Dic122—81no—
413C8×C61—41no—
414C8×C61—41no—
415C8×C61—41no—
416C8×C61—41no—
417#92418—41no—
418#92418—41no—
419#92418—41no—
420#92418—41no—
421#17412—611nomaximal, Sylow
422C22×C61—21no—
423C22×C61—21no—
424C22×C61—21no—
425C22×C61—21no—
426C22×C61—21no—
427C22×C61—21no—
428C22×C61—21no—
429C22×C61—42no—
430C22×C61—42no—
431C22×C61#41012yes—
432C22×C61C22×C22⋊C411yescharacteristic
433C22×C61C2×#13111yescharacteristic
434C22×C61#56811yescharacteristic
435C2×D61—22no—
436C2×D61—42no—
437C2×D61—41no—
438C2×D61—41no—
439C2×D61—42no—
440C2×D61—41no—
441C2×D61—41no—
442C2×D61—41no—
443C2×D61—41no—
444C2×D61—41no—
445C2×D61—41no—
446C2×D61—84no—
447C2×D61—84no—
448C2×D61—81no—
449C2×D61—81no—
450C2×D61—81no—
451C2×D61—81no—
452C4×C61—21no—
453C4×C61—21no—
454C4×C61—21no—
455C4×C61—21no—
456C4×C61—21no—
457C4×C61—21no—
458C4×C61—21no—
459C4×C61—21no—
460C4×C61—21no—
461C4×C61—21no—
462C4×C61—21no—
463C4×C61—21no—
464Dic61—41no—
465Dic61—41no—
466Dic61—41no—
467Dic61—41no—
468Dic61—41no—
469C2×#551—611no—
470#2924—611no—
471#2924D6111yescharacteristic, complemented
472#1473—611no—
473#1473—611no—
474#1469—611no—
475#1469—611no—
476#1468—611no—
477#1468—611no—
478#1466—611no—
479#1464—611no—
480#1462—611no—
481#1460—611no—
482#1458—611no—
483C2×#323—611no—
484C2×C61—21no—
485C2×C61—21no—
486C2×C61—22no—
487C2×C61—41no—
488C2×C61#288011yescharacteristic
489C2×C61C2×#41011yescharacteristic
490C2×C61#288811yescharacteristic
491D61—42no—
492D61—81no—
493D61—81no—
494#551—1221no—
495#551—1221no—
496#551—1221no—
497#551—1221no—
498#551—1221no—
499#551—1221no—
500#551—1221no—
501#551—1221no—
502C2×#126—611no—
503C2×#126—611no—
504C2×#124—611no—
505C2×#123—611no—
506C2×#123—611no—
507C2×#123—611no—
508C2×C22⋊Q8—611no—
509C2×C22⋊Q8—611no—
510C2×#120—611no—
511C2×C4×D4—611no—
512C2×C4×D4—611no—
513C2×#117—611no—
514C2×#117C2×D6111yescharacteristic
515C22×C22⋊C4—611no—
516C22×C22⋊C4—611no—
517#433—21no—
518#433—21no—
519#433—1221no—
520#433—1221no—
521#432—611no—
522#432—611no—
523#432C2×D6111yescharacteristic, complemented
524#432C2×D6111yescharacteristic, complemented
525#431—611no—
526#431—611no—
527#431C2×D6111yescharacteristic, complemented
528#431C2×D6111yescharacteristic, complemented
529#424—21no—
530#424—1221no—
531#407—611no—
532#407C2×D6111yescharacteristic
533C2×C22⋊C8—611no—
534C2×C22⋊C8C2×D6111yescharacteristic
535#405—21no—
536#405—1221no—
537#324—611no—
538#324—611no—
539#324—611no—
540#324—611no—
541#323—611no—
542#323—611no—
543#323—611no—
544#323—611no—
545#323—611no—
546#323—611no—
547#323—611no—
548#323—611no—
549#323—611no—
550#323—611no—
551#323—611no—
552#323—611no—
553C61#1741211yescharacteristic, complemented, Sylow
554C25—611no—
555C22×Q8—611no—
556C22×D4—611no—
557C22×D4—611no—
558C22×D4—611no—
559C23×C4—611no—
560C23×C4—611no—
561C23×C4—611no—
562C23×C4—611no—
563C23×C4C22×D6111yescharacteristic
564C2×M16—21no—
565C2×M16—1221no—
566C22×C8—21no—
567C22×C8—1221no—
568#126—1221no—
569#126—1221no—
570#126—1221no—
571#126—1221no—
572#126—1221no—
573#126—1221no—
574#126—1221no—
575#126—1221no—
576#124—1221no—
577#124—1221no—
578#124—1221no—
579#124—1221no—
580#123—1221no—
581#123—1221no—
582#123—1221no—
583#123—1221no—
584#123—1221no—
585#123—1221no—
586#123—1221no—
587#123—1221no—
588#123—1221no—
589#123—1221no—
590#123—1221no—
591#123—1221no—
592C22⋊Q8—1221no—
593C22⋊Q8—1221no—
594C22⋊Q8—1221no—
595C22⋊Q8—1221no—
596C22⋊Q8—1221no—
597C22⋊Q8—1221no—
598C22⋊Q8—1221no—
599C22⋊Q8—1221no—
600#120—1221no—
601#120—1221no—
602#120—1221no—
603#120—1221no—
604C4×D4—1221no—
605C4×D4—1221no—
606C4×D4—1221no—
607C4×D4—1221no—
608C4×D4—1221no—
609C4×D4—1221no—
610C4×D4—1221no—
611C4×D4—1221no—
612#117—1221no—
613#117—1221no—
614#117—1221no—
615#117—1221no—
616#117D24411yescharacteristic
617#117D24411yescharacteristic
618#117D24411yescharacteristic
619#117D24411yescharacteristic
620#117C22⋊D6111yescharacteristic
621#117C22⋊D6111yescharacteristic
622#117C22⋊D6111yescharacteristic
623#117C22⋊D6111yescharacteristic
624C2×C4⋊C4—611no—
625C2×C4⋊C4—611no—
626C2×C4⋊C4—611no—
627C2×C4⋊C4—611no—
628C2×C4⋊C4—611no—
629C2×C4⋊C4—611no—
630C2×C4⋊C4C4×D6111yescharacteristic
631C2×C4⋊C4C4×D6111yescharacteristic
632C2×C22⋊C4—611no—
633C2×C22⋊C4—611no—
634C2×C22⋊C4—611no—
635C2×C22⋊C4—611no—
636C2×C22⋊C4—611no—
637C2×C22⋊C4—611no—
638C2×C22⋊C4—611no—
639C2×C22⋊C4—611no—
640C2×C22⋊C4—611no—
641C2×C22⋊C4—611no—
642C2×C22⋊C4—611no—
643C2×C22⋊C4—611no—
644C2×C22⋊C4—1221no—
645C2×C22⋊C4—1221no—
646C2×C22⋊C4—1221no—
647C2×C22⋊C4—1221no—
648C2×C22⋊C4—1221no—
649C2×C22⋊C4—1221no—
650C2×C22⋊C4—1221no—
651C2×C22⋊C4—1221no—
652C2×C22⋊C4C4×D6111yescharacteristic
653C2×C22⋊C4C4×D6111yescharacteristic
654C2×C42—611no—
655C2×C42C22×D6111yescharacteristic
656C2×C42C22×D6111yescharacteristic
657C4⋊C8—21no—
658C4⋊C8—21no—
659C4⋊C8—21no—
660C4⋊C8—21no—
661C4⋊C8—1221no—
662C4⋊C8—1221no—
663C4⋊C8—1221no—
664C4⋊C8—1221no—
665C22⋊C8—21no—
666C22⋊C8—21no—
667C22⋊C8—611no—
668C22⋊C8—611no—
669C22⋊C8—611no—
670C22⋊C8—611no—
671C22⋊C8—1221no—
672C22⋊C8—1221no—
673C22⋊C8C22×D6111yescharacteristic
674C22⋊C8C22×D6111yescharacteristic
675C22⋊C8C22×D6111yescharacteristic
676C22⋊C8C22×D6111yescharacteristic
677#97—21no—
678#97—21no—
679#97—1221no—
680#97—1221no—
681C4×C8—21no—
682C4×C8—21no—
683C4×C8—1221no—
684C4×C8—1221no—
685C24—611no—
686C24—611no—
687C24—611no—
688C24—1222no—
689C24—1221no—
690C24—1221no—
691C24—4881no—
692C24—2441no—
693C24—2442no—
694C24C2×C4×D6111yescharacteristic
695C2×Q8—1221no—
696C2×Q8—1221no—
697C2×Q8—4881no—
698C2×D4—1222no—
699C2×D4—1221no—
700C2×D4—1221no—
701C2×D4—1221no—
702C2×D4—1221no—
703C2×D4—1221no—
704C2×D4—1221no—
705C2×D4—4881no—
706C2×D4—2441no—
707C2×D4—2442no—
708C22×C4—42no—
709C22×C4—611no—
710C22×C4—611no—
711C22×C4—611no—
712C22×C4—611no—
713C22×C4—611no—
714C22×C4—1222no—
715C22×C4—1221no—
716C22×C4—1221no—
717C22×C4—1221no—
718C22×C4—1221no—
719C22×C4—1221no—
720C22×C4—1221no—
721C22×C4—1221no—
722C22×C4—1221no—
723C22×C4—4881no—
724C22×C4—4881no—
725C22×C4—4881no—
726C22×C4—2441no—
727C22×C4C2×C4×D6111yescharacteristic
728C22×C4C2×C4×D6111yescharacteristic
729C22×C4C2×C4×D6111yescharacteristic
730C22×C4C2×C4×D6111yescharacteristic
731C22×C4C2×C4×D6111yescharacteristic
732C22×C4C2×D24411yescharacteristic
733C22×C4C2×D24411yescharacteristic
734C22×C4C2×C22⋊D6111yescharacteristic
735C22×C4C2×C22⋊D6111yescharacteristic
736C22×C4C23×D6111yescharacteristic
737M16—42no—
738M16—2442no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—21no—
742C2×C8—21no—
743C2×C8—42no—
744C2×C8—1221no—
745C2×C8—1221no—
746C2×C8—1221no—
747C2×C8—1221no—
748C2×C8—2442no—
749C4⋊C4—1221no—
750C4⋊C4—1221no—
751C4⋊C4—1221no—
752C4⋊C4—1221no—
753C4⋊C4—1221no—
754C4⋊C4—1221no—
755C4⋊C4—1221no—
756C4⋊C4—1221no—
757C4⋊C4—1221no—
758C4⋊C4—1221no—
759C4⋊C4—1221no—
760C4⋊C4—1221no—
761C4⋊C4#1175819811yescharacteristic
762C4⋊C4#1175819811yescharacteristic
763C4⋊C4#1175819811yescharacteristic
764C4⋊C4#1175819811yescharacteristic
765C4⋊C4#1175819811yescharacteristic
766C4⋊C4#1175819811yescharacteristic
767C4⋊C4#1175819811yescharacteristic
768C4⋊C4#1175819811yescharacteristic
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—1221no—
786C22⋊C4—1221no—
787C22⋊C4—1221no—
788C22⋊C4—1221no—
789C22⋊C4—1221no—
790C22⋊C4—1221no—
791C22⋊C4—1221no—
792C22⋊C4—1221no—
793C22⋊C4#1175819811yescharacteristic
794C22⋊C4#1175819811yescharacteristic
795C22⋊C4#1175819811yescharacteristic
796C22⋊C4#1175819811yescharacteristic
797C22⋊C4#1175819811yescharacteristic
798C22⋊C4#1175819811yescharacteristic
799C22⋊C4#1175819811yescharacteristic
800C22⋊C4#1175819811yescharacteristic
801C42—1221no—
802C42—1221no—
803C42C2×D24411yescharacteristic
804C42C2×D24411yescharacteristic
805C42C2×D24411yescharacteristic
806C42C2×D24411yescharacteristic
807C42C2×C22⋊D6111yescharacteristic
808C42C2×C22⋊D6111yescharacteristic
809C42C2×C22⋊D6111yescharacteristic
810C42C2×C22⋊D6111yescharacteristic
811C23—22no—
812C23—21no—
813C23—21no—
814C23—41no—
815C23—612no—
816C23—1221no—
817C23—1221no—
818C23—1221no—
819C23—1221no—
820C23—1221no—
821C23—1221no—
822C23—1221no—
823C23—1221no—
824C23—4881no—
825C23—4881no—
826C23—4884no—
827C23—4884no—
828C23—2442no—
829C23—2442no—
830C23—2441no—
831C23—2441no—
832C23—2441no—
833C23—2441no—
834C23—2442no—
835C23—2441no—
836C23—2441no—
837C23—2442no—
838C23C2×#1175819811yescharacteristic
839C23C2×#1175819811yescharacteristic
840C23C22×C4×D6111yescharacteristic
841Q8—4881no—
842Q8—4881no—
843D4—4881no—
844D4—4881no—
845D4—2442no—
846D4—2442no—
847D4—2442no—
848D4—2442no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—1221no—
862C2×C4—1221no—
863C2×C4—1221no—
864C2×C4—1221no—
865C2×C4—1221no—
866C2×C4—1221no—
867C2×C4—1221no—
868C2×C4—4881no—
869C2×C4—4881no—
870C2×C4—4881no—
871C2×C4—4881no—
872C2×C4—4881no—
873C2×C4—4881no—
874C2×C4—2442no—
875C2×C4—2442no—
876C2×C4—2441no—
877C2×C4—2441no—
878C2×C4—2441no—
879C2×C4—2441no—
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×C4C2×#1175819811yescharacteristic
890C2×C4C22×C22⋊D6111yescharacteristic
891C2×C4C22×D24411yescharacteristic
892C8—41no—
893C8—41no—
894C8—41no—
895C8—41no—
896C8—2441no—
897C8—2441no—
898C8—2441no—
899C8—2441no—
900C22—21no—
901C22—21no—
902C22—21no—
903C22—21no—
904C22—21no—
905C22—21no—
906C22—21no—
907C22—42no—
908C22—42no—
909C22—1222no—
910C22—4881no—
911C22—4881no—
912C22—4881no—
913C22—4881no—
914C22—4884no—
915C22—4884no—
916C22—2442no—
917C22—2442no—
918C22—2441no—
919C22—2441no—
920C22—2441no—
921C22—2441no—
922C22—2441no—
923C22—2441no—
924C22—2441no—
925C22—2441no—
926C22#1683973512yes—
927C22C22×#1175819811yescharacteristic
928C22#131×D6111yescharacteristic
929C22#1684052711yescharacteristic
930C4—21no—
931C4—21no—
932C4—21no—
933C4—21no—
934C4—21no—
935C4—21no—
936C4—21no—
937C4—21no—
938C4—21no—
939C4—21no—
940C4—21no—
941C4—21no—
942C4—2441no—
943C4—2441no—
944C4—2441no—
945C4—2441no—
946C4—2441no—
947C2—21no—
948C2—21no—
949C2—22no—
950C2—41no—
951C2—4881no—
952C2—4881no—
953C2—2442no—
954C2#2145426611yescharacteristic
955C2C2×#1683973511yescharacteristic
956C2#2145429711yescharacteristic
subgroupG/H
centerC22C22×#11758198
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#2924C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#14519747C4
cosocleC22×C4×C61C24
hypercenter#2924D61
hypocenterC61#17412
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×#117 ◁ #2924

Complements

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

NH ≅ G/Ntype
2. #21454477C2semidirect
3. #21444189C2semidirect
4. #21444186C2semidirect
5. #21444172C2semidirect
6. #21444170C2semidirect
7. #21444168C2semidirect
8. #21444165C2semidirect
9. #21444159C2semidirect
10. #21444151C2semidirect
11. #21444145C2semidirect
12. #21444139C2semidirect
13. #21444131C2semidirect
14. C2×#16839485C2semidirect
15. C61×#2924C2semidirect
40. #16839819C22semidirect
41. #16839819C22semidirect
42. #16839815C22semidirect
43. #16839815C22semidirect
48. #16839487C22semidirect
49. #16839487C22semidirect
50. #16839487C22semidirect
51. #16839487C22semidirect
60. #16839485C22semidirect
61. #16839485C22semidirect
62. #16839485C22semidirect
63. #16839485C22semidirect
67. C61×#432C22semidirect
68. C61×#432C22semidirect
69. C61×#431C22semidirect
70. C61×#431C22semidirect
471. #2924D61semidirect
523. #432C2×D61semidirect
524. #432C2×D61semidirect
527. #431C2×D61semidirect
528. #431C2×D61semidirect
553. C61#17412semidirect

Maximal subgroups

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

subgroupindex
C2×#168404362
#214544772
#214441892
#214441862
#214441722
#214441702
#214441682
#214441652
#214441592
#214441512
#214441452
#214441392
#214441312
C2×#168394852
C61×#29242
#1741261