Finite Group Databasebeta

← #30623940

Subgroups — #30623940

Order 15616.

1240 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462429C211yesmaximal, characteristic, complemented
2#21462418C211yesmaximal, characteristic, complemented
3#21462082C212yesmaximal, complemented
4#21462075C212yesmaximal, complemented
5#21462074C212yesmaximal, complemented
6#21462071C212yesmaximal, complemented
7C2×#16840665C212yesmaximal, complemented
8D61⋊#352C212yesmaximal, complemented
9#21459460C211yesmaximal, characteristic
10#16840840—21no—
11#16840829—21no—
12#16840749—21no—
13#16840749C2212yes—
14#16840748—21no—
15D61⋊#100C2212yes—
16C2×#14519837—21no—
17C2×#14519837C2212yes—
18#16840742C2212yes—
19#16840741—21no—
20D61⋊#99—21no—
21D61⋊#99C2212yes—
22C2×#14519835—21no—
23C2×#14519835C2212yes—
24#16840665C2214yescomplemented
25#16840665C2214yescomplemented
26#16840664C2214yescomplemented
27#16840662C2214yescomplemented
28C2×#14519822C2211yescharacteristic
29C22×#11758224C411yescharacteristic, complemented
30#16840412—21no—
31#16840412—21no—
32#16840410—21no—
33#16840410—21no—
34#16840401—21no—
35#16840401—21no—
36#16840399—21no—
37#16840399—21no—
38#16840334C411yescharacteristic, complemented
39#16840334C2211yescharacteristic
40#16840322C411yescharacteristic, complemented
41#16840322C2211yescharacteristic
42#16840321C2211yescharacteristic
43#16840268C411yescharacteristic, complemented
44#16840268C2211yescharacteristic
45C2×#14519761C2211yescharacteristic
46C2×#14519758C411yescharacteristic, complemented
47#123×D61C411yescharacteristic, complemented
48#123×D61C2211yescharacteristic
49#16840235C411yescharacteristic, complemented
50C61×#534C411yescharacteristic, complemented
51#14519864—44no—
52D61⋊M16—22no—
53C2×#11758217—22no—
54C2×#11758217—22no—
55D4×#6923—44no—
56#14519856—22no—
57C2×C22⋊#6923—22no—
58C2×C22⋊#6923—22no—
59#14519838—22no—
60#14519837—22no—
61#14519837—22no—
62#14519837C2314yes—
63#14519836—22no—
64#14519835—22no—
65#14519835—22no—
66#14519835C2314yes—
67#14519822—44no—
68C2×#11758222D411yescharacteristic
69C2×#11758222D411yescharacteristic
70C2×#11758224—21no—
71C2×#11758224—21no—
72C2×#11758224—21no—
73C2×#11758224—21no—
74C2×#11758224—44no—
75C2×#11758224C2×C411yescharacteristic
76C2×#11758224D411yescharacteristic
77C2×#11758224D411yescharacteristic
78C2×#11758224C2311yescharacteristic
79C22×Dic122C2×C411yescharacteristic, complemented
80C22×C22⋊D61C2×C411yescharacteristic
81C22×C22⋊D61C2×C411yescharacteristic, complemented
82C22×C22⋊D61D411yescharacteristic
83C22×C22⋊D61D411yescharacteristic
84C22×C22⋊D61C2311yescharacteristic
85C2×D4×D61C2×C411yescharacteristic
86C2×D4×D61D411yescharacteristic
87C2×D4×D61D411yescharacteristic
88C2×D4×D61C2311yescharacteristic
89C23×Dic61C2×C411yescharacteristic, complemented
90C23×Dic61C2×C411yescharacteristic, complemented
91C22×C4×D61C2×C411yescharacteristic, complemented
92#14519776—21no—
93#14519776—21no—
94#14519763—21no—
95#14519763—21no—
96#14519762—21no—
97#14519762—21no—
98#14519761—21no—
99#14519761—21no—
100#14519761C2×C411yescharacteristic, complemented
101#14519761C2×C411yescharacteristic, complemented
102#14519761C2311yescharacteristic
103#14519761C2311yescharacteristic
104#14519760C2×C411yescharacteristic, complemented
105#14519760C2311yescharacteristic
106#14519759—21no—
107#14519759—21no—
108#14519759—21no—
109#14519759—21no—
110#14519758—21no—
111#14519758—21no—
112#14519758—21no—
113#14519758C2×C411yescharacteristic, complemented
114#14519758C2×C411yescharacteristic, complemented
115#14519758C2×C411yescharacteristic, complemented
116#14519758C2×C411yescharacteristic, complemented
117#14519755—21no—
118#14519755—21no—
119#14519754—21no—
120#14519754—21no—
121#14519754—21no—
122#14519754—21no—
123#14519750—21no—
124#14519750—21no—
125#14519749—21no—
126#14519749—21no—
127#14519749—21no—
128#14519749—21no—
129#14519748—21no—
130#14519748—21no—
131#14519746C2×C411yescharacteristic, complemented
132#14519746C2311yescharacteristic
133#14519745—21no—
134#14519745—21no—
135#14519745—21no—
136D4×Dic61—21no—
137D4×Dic61—21no—
138C4×C22⋊D61—21no—
139C4×C22⋊D61—21no—
140#14519737—21no—
141#14519737—21no—
142#14519737—21no—
143#14519737—21no—
144#14519733C2×C411yescharacteristic, complemented
145#14519733C2×C411yescharacteristic, complemented
146C2×C4⋊Dic61—21no—
147C2×#11758196—21no—
148C4⋊C4×D61—21no—
149C4⋊C4×D61—21no—
150C2×C22⋊Dic61—21no—
151C2×C22⋊Dic61C2×C411yescharacteristic, complemented
152C2×#11758198—21no—
153C22⋊C4×D61—21no—
154C22⋊C4×D61—21no—
155C22⋊C4×D61C2×C411yescharacteristic, complemented
156C22⋊C4×D61C2×C411yescharacteristic, complemented
157C22×D4×C61C2×C411yescharacteristic
158C22×D4×C61C2×C411yescharacteristic, complemented
159#123×C61—21no—
160#123×C61C2×C411yescharacteristic, complemented
161#123×C61C2×C411yescharacteristic, complemented
162#121×C61—21no—
163#121×C61—21no—
164#120×C61—21no—
165#120×C61C2×C411yescharacteristic, complemented
166#120×C61C2×C411yescharacteristic, complemented
167C2×C22⋊C4×C61C2×C411yescharacteristic, complemented
168C24×C61C22⋊C411yescharacteristic
169C24×C61C22×C411yescharacteristic
170C24×C61C22×C411yescharacteristic
171C23×D61C22⋊C411yescharacteristic
172C23×D61C22×C411yescharacteristic
173C23×D61C2×D411yescharacteristic
174C23×D61C2×D411yescharacteristic
175C22×#6923—42no—
176C22×#6923—42no—
177C2×D4×C61—21no—
178C2×D4×C61—21no—
179C2×D4×C61—21no—
180C2×D4×C61—21no—
181C2×D4×C61—42no—
182C2×D4×C61—42no—
183C2×D4×C61C22⋊C411yescharacteristic
184C2×D4×C61C22⋊C411yescharacteristic
185C2×D4×C61C22×C411yescharacteristic
186C2×D4×C61C22×C411yescharacteristic
187C22×C4×C61—21no—
188C22×C4×C61C22⋊C411yescharacteristic
189C22×C4×C61C22×C411yescharacteristic
190C2×C22⋊D61—24no—
191C2×C22⋊D61—21no—
192C2×C22⋊D61—21no—
193C2×C22⋊D61—21no—
194C2×C22⋊D61—21no—
195C2×C22⋊D61—42no—
196C2×C22⋊D61—42no—
197C2×C22⋊D61—42no—
198C2×C22⋊D61—42no—
199C2×C22⋊D61C22⋊C411yescharacteristic
200C2×C22⋊D61C22⋊C411yescharacteristic
201C2×C22⋊D61C22⋊C411yescharacteristic
202C2×C22⋊D61C22⋊C411yescharacteristic
203C2×C22⋊D61C22⋊C411yescharacteristic
204C2×C22⋊D61C22⋊C411yescharacteristic
205C2×C22⋊D61C22×C411yescharacteristic
206C2×C22⋊D61C2×D411yescharacteristic
207C2×C22⋊D61C2×D411yescharacteristic
208C2×C22⋊D61C2×D411yescharacteristic
209C2×C22⋊D61C2×D411yescharacteristic
210C2×C22⋊D61C2411yescharacteristic
211C22×Dic61—21no—
212C22×Dic61—21no—
213C22×Dic61—21no—
214C22×Dic61—21no—
215C22×Dic61—21no—
216C22×Dic61—42no—
217C22×Dic61—42no—
218C22×Dic61C22⋊C411yescharacteristic
219C22×Dic61C22×C411yescharacteristic
220C22×Dic61C22×C411yescharacteristic
221C22×Dic61C22×C411yescharacteristic
222C22×Dic61C2×D411yescharacteristic
223C22×Dic61C2×D411yescharacteristic
224#11758224—24no—
225#11758224—42no—
226#11758224—42no—
227#11758224—42no—
228#11758224—44no—
229#11758224—44no—
230#11758224—44no—
231#11758224—44no—
232D4×D61—24no—
233D4×D61—42no—
234D4×D61—42no—
235D4×D61—42no—
236#11758222—42no—
237#11758222—42no—
238C2×D244C22⋊C411yescharacteristic
239C2×D244C2×D411yescharacteristic
240C2×C4×D61—21no—
241C2×C4×D61—21no—
242C2×C4×D61—21no—
243C2×C4×D61—21no—
244C2×C4×D61—42no—
245C2×C4×D61C22⋊C411yescharacteristic
246C2×C4×D61C22⋊C411yescharacteristic
247C2×C4×D61C2×D411yescharacteristic
248C2×C4×D61C2×D411yescharacteristic
249C2×Dic122—21no—
250C2×Dic122—21no—
251C2×Dic122—42no—
252C2×Dic122C22⋊C411yescharacteristic
253C2×Dic122C2×D411yescharacteristic
254C22⋊#6923—24no—
255C22⋊#6923—42no—
256C22⋊#6923—42no—
257#11758217—24no—
258#11758217—42no—
259#11758217—42no—
260C2×#92420—42no—
261C2×#92420—42no—
262C4⋊#6923—42no—
263C4×#6923—42no—
264#11758213—42no—
265D61⋊C8—42no—
266C4⋊C4×C61—21no—
267C4⋊C4×C61—21no—
268C22⋊C4×C61—21no—
269C22⋊C4×C61—21no—
270C22⋊C4×C61—21no—
271C22⋊C4×C61—21no—
272C22⋊C4×C61—21no—
273C22⋊C4×C61C22×C411yescharacteristic
274C22⋊C4×C61C22×C411yescharacteristic
275C22⋊Dic61—21no—
276C22⋊Dic61—21no—
277C22⋊Dic61—21no—
278C22⋊Dic61—21no—
279C22⋊Dic61—21no—
280C22⋊Dic61—21no—
281C22⋊Dic61—21no—
282C22⋊Dic61C22×C411yescharacteristic
283C22⋊Dic61C22×C411yescharacteristic
284#11758198—21no—
285#11758198—21no—
286#11758198—21no—
287#11758198—21no—
288#11758198—21no—
289#11758198—21no—
290#11758198—21no—
291#11758198—21no—
292C4⋊Dic61—21no—
293C4⋊Dic61—21no—
294C4⋊Dic61—21no—
295C4⋊Dic61—21no—
296#11758196—21no—
297#11758196—21no—
298#11758196—21no—
299#11758196—21no—
300#11758196—21no—
301#11758196—21no—
302#11758196—21no—
303#11758196—21no—
304C4×Dic61—21no—
305C4×Dic61—21no—
306C23×C61—22no—
307C23×C61—21no—
308C23×C61—41no—
309C23×C61—41no—
310C23×C61—81no—
311C23×C61—81no—
312C23×C61—81no—
313C23×C61C2×C22⋊C411yescharacteristic
314C23×C61C2×C22⋊C411yescharacteristic
315C23×C61C2×C22⋊C411yescharacteristic
316C23×C61C2×C22⋊C411yescharacteristic
317C23×C61C23×C411yescharacteristic
318C22×D61—22no—
319C22×D61—22no—
320C22×D61—22no—
321C22×D61—41no—
322C22×D61—81no—
323C22×D61—81no—
324C22×D61—81no—
325C22×D61—81no—
326C22×D61C2×C22⋊C411yescharacteristic
327C22×D61C2×C22⋊C411yescharacteristic
328C22×D61C2×C22⋊C411yescharacteristic
329C22×D61C22×D411yescharacteristic
330C2×#6923—44no—
331C2×#6923—162no—
332C2×#6923—162no—
333D4×C61—22no—
334D4×C61—22no—
335D4×C61—41no—
336D4×C61—41no—
337D4×C61—42no—
338D4×C61—42no—
339D4×C61—81no—
340D4×C61—81no—
341C2×C4×C61—21no—
342C2×C4×C61—21no—
343C2×C4×C61—21no—
344C2×C4×C61—41no—
345C2×C4×C61—41no—
346C2×C4×C61—81no—
347C2×C4×C61C2×C22⋊C411yescharacteristic
348C2×C4×C61C2×C22⋊C411yescharacteristic
349C22⋊D61—22no—
350C22⋊D61—22no—
351C22⋊D61—22no—
352C22⋊D61—22no—
353C22⋊D61—22no—
354C22⋊D61—41no—
355C22⋊D61—41no—
356C22⋊D61—41no—
357C22⋊D61—41no—
358C22⋊D61—41no—
359C22⋊D61—41no—
360C22⋊D61—42no—
361C22⋊D61—42no—
362C22⋊D61—81no—
363C22⋊D61—81no—
364C22⋊D61#9914yes—
365C2×Dic61—22no—
366C2×Dic61—22no—
367C2×Dic61—22no—
368C2×Dic61—21no—
369C2×Dic61—21no—
370C2×Dic61—21no—
371C2×Dic61—21no—
372C2×Dic61—41no—
373C2×Dic61—42no—
374C2×Dic61—42no—
375C2×Dic61—42no—
376C2×Dic61—42no—
377C2×Dic61—41no—
378C2×Dic61—41no—
379C2×Dic61—81no—
380C2×Dic61C2×C22⋊C411yescharacteristic
381C2×Dic61C2×C22⋊C411yescharacteristic
382C2×Dic61C2×C22⋊C411yescharacteristic
383C2×Dic61C22×D411yescharacteristic
384D244—22no—
385D244—41no—
386C4×D61—22no—
387C4×D61—22no—
388C4×D61—41no—
389C4×D61—41no—
390C4×D61—42no—
391C4×D61—42no—
392C4×D61—81no—
393C4×D61—81no—
394Dic122—22no—
395Dic122—41no—
396Dic122—42no—
397Dic122—42no—
398#92420—44no—
399#33350—611nomaximal, Sylow
400C22×C61—21no—
401C22×C61—21no—
402C22×C61—21no—
403C22×C61—21no—
404C22×C61—41no—
405C22×C61—41no—
406C22×C61—41no—
407C22×C61—41no—
408C22×C61—41no—
409C22×C61—41no—
410C22×C61—41no—
411C22×C61—41no—
412C22×C61—82no—
413C22×C61—82no—
414C22×C61—161no—
415C22×C61C2×#9912yes—
416C22×C61C22×C22⋊C411yescharacteristic
417C2×D61—21no—
418C2×D61—21no—
419C2×D61—21no—
420C2×D61—41no—
421C2×D61—41no—
422C2×D61—41no—
423C2×D61—41no—
424C2×D61—82no—
425C2×D61—82no—
426C2×D61—82no—
427C2×D61—161no—
428C2×D61C2×#9912yes—
429#6923—84no—
430C4×C61—21no—
431C4×C61—21no—
432C4×C61—41no—
433C4×C61—41no—
434C4×C61—41no—
435Dic61—21no—
436Dic61—21no—
437Dic61—21no—
438Dic61—41no—
439Dic61—41no—
440Dic61—41no—
441Dic61—41no—
442Dic61C2×#9912yes—
443#3485—611no—
444#2888—611no—
445#2883—611no—
446#2123—612no—
447#2121—612no—
448#2121—612no—
449#2120—612no—
450C2×#352—612no—
451C2×#352—612no—
452C2×C61—21no—
453C2×C61—22no—
454C2×C61—41no—
455C2×C61—41no—
456C2×C61—41no—
457C2×C61—41no—
458C2×C61—81no—
459C2×C61C22×#9911yescharacteristic
460D61—22no—
461D61—41no—
462D61—41no—
463D61—41no—
464C2×H(5,𝔽2)—611no—
465C22×#41—611no—
466#568—1221no—
467#547—1221no—
468#547—1221no—
469#547—1221no—
470#547—1221no—
471#546—1221no—
472#546—1221no—
473#546—1221no—
474#546—1221no—
475#536—611no—
476#536—611no—
477#534—611no—
478#534—611no—
479#534—611no—
480#534#692311yescharacteristic, complemented
481#525—611no—
482#525—611no—
483C2×#123—611no—
484C2×#123—611no—
485C2×#123—611no—
486C2×#123—611no—
487#518—611no—
488#518—1221no—
489#413—612no—
490#413—1221no—
491#413—1221no—
492C2×#100—612no—
493C2×#100—612no—
494C2×#100—1221no—
495#410—612no—
496#410—1221no—
497C2×#99—612no—
498C2×#99—612no—
499C2×#99—1221no—
500C2×#99—1221no—
501#352—614no—
502#352—614no—
503#352—614no—
504AΣL(1,𝔽16)—614no—
505C61#3335011yescharacteristic, complemented, Sylow
506H(5,𝔽2)—2444no—
507C2×#41—611no—
508C2×#41—611no—
509C2×#41—611no—
510C2×#41—611no—
511C2×#41—611no—
512C2×#41—611no—
513C2×#41—1221no—
514C2×#41—1221no—
515C2×#41—1221no—
516C2×#41—1221no—
517C2×#41—2444no—
518C22×Q8—611no—
519C22×D4—611no—
520C22×D4—611no—
521C22×D4—611no—
522C22×D4—611no—
523C22×D4—611no—
524C22×D4—611no—
525C22×D4—611no—
526C22×D4—611no—
527C22×D4—611no—
528C22×D4C2×#692311yescharacteristic
529C22×D4C2×#692311yescharacteristic, complemented
530C23×C4—611no—
531C23×C4—611no—
532C23×C4—611no—
533#131—2444no—
534C2×M16—1222no—
535C2×M16—1222no—
536C2×M16—1222no—
537C4⋊Q8—1221no—
538C4⋊Q8—1221no—
539#124—1221no—
540#124—1221no—
541#123—21no—
542#123—611no—
543#123—611no—
544#123—611no—
545#123—611no—
546#123—611no—
547#123—611no—
548#123—611no—
549#123—611no—
550#123—611no—
551#123—611no—
552#123—1221no—
553#123—1221no—
554#123—1221no—
555#123—1221no—
556#123—1221no—
557#123—1221no—
558#123—1221no—
559#123—1221no—
560#123—1221no—
561#123—1221no—
562#123—1221no—
563#123C2×#692311yescharacteristic, complemented
564#123C2×#692311yescharacteristic, complemented
565C22⋊Q8—1221no—
566C22⋊Q8—1221no—
567C22⋊Q8—1221no—
568C22⋊Q8—1221no—
569C22⋊Q8—1221no—
570C22⋊Q8—1221no—
571#121—21no—
572#121—21no—
573#121—1221no—
574#121—1221no—
575#121—1221no—
576#121—1221no—
577#121—1221no—
578#121—1221no—
579#121—1221no—
580#121—1221no—
581#120—21no—
582#120—611no—
583#120—611no—
584#120—1221no—
585#120—1221no—
586#120—1221no—
587#120C2×#692311yescharacteristic, complemented
588#120C2×#692311yescharacteristic, complemented
589C4×D4—1221no—
590C4×D4—1221no—
591C4×D4—1221no—
592C4×D4—1221no—
593C4×D4—1221no—
594C4×D4—1221no—
595C4×D4—1221no—
596C4×D4—1221no—
597C4×D4—2444no—
598#117—611no—
599#117—611no—
600#117—1222no—
601C2×C4⋊C4—1221no—
602C2×C4⋊C4—1221no—
603C2×C4⋊C4—1221no—
604C2×C4⋊C4—1221no—
605C2×C22⋊C4—611no—
606C2×C22⋊C4—611no—
607C2×C22⋊C4—611no—
608C2×C22⋊C4—1221no—
609C2×C22⋊C4—1221no—
610C2×C22⋊C4—1221no—
611C2×C22⋊C4—1221no—
612C2×C22⋊C4—1222no—
613C2×C22⋊C4—1222no—
614C2×C22⋊C4C2×#692311yescharacteristic, complemented
615#101—1222no—
616#100—614no—
617#100—1222no—
618#100—1222no—
619#99—614no—
620#99—1222no—
621#99—1222no—
622#99—1222no—
623C24—611no—
624C24—611no—
625C24—611no—
626C24—611no—
627C24C22⋊#692311yescharacteristic
628C24C22×#692311yescharacteristic
629C24C22×#692311yescharacteristic
630#41—1224no—
631#41—2442no—
632#41—2442no—
633#41—2442no—
634#41—2442no—
635#41—2442no—
636#41—2444no—
637#41—2444no—
638#41—2444no—
639#41—2444no—
640C2×Q8—611no—
641C2×Q8—611no—
642C2×Q8—1221no—
643C2×Q8—1221no—
644C2×Q8—2442no—
645C2×D4—21no—
646C2×D4—21no—
647C2×D4—21no—
648C2×D4—21no—
649C2×D4—42no—
650C2×D4—42no—
651C2×D4—611no—
652C2×D4—611no—
653C2×D4—611no—
654C2×D4—611no—
655C2×D4—611no—
656C2×D4—611no—
657C2×D4—611no—
658C2×D4—611no—
659C2×D4—611no—
660C2×D4—611no—
661C2×D4—611no—
662C2×D4—611no—
663C2×D4—611no—
664C2×D4—611no—
665C2×D4—1224no—
666C2×D4—1224no—
667C2×D4—1221no—
668C2×D4—1221no—
669C2×D4—1221no—
670C2×D4—1221no—
671C2×D4—2442no—
672C2×D4—2442no—
673C2×D4—2442no—
674C2×D4—2442no—
675C2×D4—2442no—
676C2×D4—2442no—
677C2×D4—2442no—
678C2×D4C22⋊#692311yescharacteristic
679C2×D4C22⋊#692311yescharacteristic
680C2×D4C22×#692311yescharacteristic
681C2×D4C22×#692311yescharacteristic
682C22×C4—21no—
683C22×C4—611no—
684C22×C4—611no—
685C22×C4—611no—
686C22×C4—611no—
687C22×C4—611no—
688C22×C4—611no—
689C22×C4—611no—
690C22×C4—611no—
691C22×C4—611no—
692C22×C4—611no—
693C22×C4—1221no—
694C22×C4—1221no—
695C22×C4—1221no—
696C22×C4—1221no—
697C22×C4—1221no—
698C22×C4—1221no—
699C22×C4—1221no—
700C22×C4—1221no—
701C22×C4—1221no—
702C22×C4—2442no—
703C22×C4—2442no—
704C22×C4—2442no—
705C22×C4—2442no—
706C22×C4—2442no—
707C22×C4C22⋊#692311yescharacteristic
708C22×C4C22×#692311yescharacteristic
709M16—1224no—
710M16—2442no—
711M16—2442no—
712M16—2442no—
713C2×C8—2442no—
714C2×C8—2442no—
715C2×C8—2442no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—1221no—
719C4⋊C4—1221no—
720C4⋊C4—1221no—
721C4⋊C4—1221no—
722C4⋊C4—1221no—
723C4⋊C4—1221no—
724C4⋊C4—1221no—
725C4⋊C4—1221no—
726C4⋊C4—1221no—
727C4⋊C4—1221no—
728C4⋊C4—1221no—
729C4⋊C4—1221no—
730C4⋊C4—2442no—
731C22⋊C4—21no—
732C22⋊C4—21no—
733C22⋊C4—21no—
734C22⋊C4—21no—
735C22⋊C4—21no—
736C22⋊C4—611no—
737C22⋊C4—611no—
738C22⋊C4—1221no—
739C22⋊C4—1221no—
740C22⋊C4—1221no—
741C22⋊C4—1221no—
742C22⋊C4—1221no—
743C22⋊C4—1221no—
744C22⋊C4—1221no—
745C22⋊C4—1221no—
746C22⋊C4—1221no—
747C22⋊C4—1221no—
748C22⋊C4—1221no—
749C22⋊C4—1221no—
750C22⋊C4—1221no—
751C22⋊C4—1221no—
752C22⋊C4—1221no—
753C22⋊C4—1224no—
754C22⋊C4—2442no—
755C22⋊C4—2442no—
756C22⋊C4C22×#692311yescharacteristic
757C22⋊C4C22×#692311yescharacteristic
758C42—1221no—
759C42—1221no—
760C42—2442no—
761C23—22no—
762C23—21no—
763C23—41no—
764C23—41no—
765C23—81no—
766C23—81no—
767C23—81no—
768C23—611no—
769C23—611no—
770C23—611no—
771C23—611no—
772C23—1222no—
773C23—1222no—
774C23—1222no—
775C23—4881no—
776C23—4881no—
777C23—4881no—
778C23—4881no—
779C23—2441no—
780C23C2×C22⋊#692311yescharacteristic
781C23C2×C22⋊#692311yescharacteristic
782C23C2×C22⋊#692311yescharacteristic
783C23C2×C22⋊#692311yescharacteristic
784C23C23×#692311yescharacteristic
785Q8—1222no—
786Q8—2441no—
787Q8—2442no—
788Q8—2442no—
789D4—22no—
790D4—22no—
791D4—41no—
792D4—41no—
793D4—42no—
794D4—42no—
795D4—81no—
796D4—81no—
797D4—614no—
798D4—1222no—
799D4—1222no—
800D4—1222no—
801D4—1222no—
802D4—1222no—
803D4—1222no—
804D4—4881no—
805D4—4881no—
806D4—2441no—
807D4—2441no—
808D4—2441no—
809D4—2441no—
810D4—2441no—
811D4—2441no—
812D4—2441no—
813D4—2442no—
814D4—2442no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—81no—
821C2×C4—611no—
822C2×C4—611no—
823C2×C4—611no—
824C2×C4—611no—
825C2×C4—1222no—
826C2×C4—1222no—
827C2×C4—1222no—
828C2×C4—1222no—
829C2×C4—1222no—
830C2×C4—1221no—
831C2×C4—1221no—
832C2×C4—1221no—
833C2×C4—1221no—
834C2×C4—9762no—
835C2×C4—9762no—
836C2×C4—4881no—
837C2×C4—4881no—
838C2×C4—4881no—
839C2×C4—2441no—
840C2×C4—2441no—
841C2×C4—2442no—
842C2×C4—2442no—
843C2×C4—2442no—
844C2×C4—2441no—
845C2×C4—2442no—
846C2×C4—2444no—
847C2×C4—2442no—
848C2×C4—2442no—
849C2×C4—2441no—
850C2×C4—2441no—
851C2×C4C2×C22⋊#692311yescharacteristic
852C2×C4C2×C22⋊#692311yescharacteristic
853C8—2444no—
854C22—21no—
855C22—21no—
856C22—21no—
857C22—21no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22—82no—
867C22—82no—
868C22—161no—
869C22—612no—
870C22—1221no—
871C22—1221no—
872C22—1221no—
873C22—9761no—
874C22—4882no—
875C22—4882no—
876C22—4882no—
877C22—2441no—
878C22—2441no—
879C22—2441no—
880C22—2441no—
881C22D61⋊#9912yes—
882C22C22×C22⋊#692311yescharacteristic
883C4—21no—
884C4—21no—
885C4—41no—
886C4—41no—
887C4—41no—
888C4—612no—
889C4—1221no—
890C4—1221no—
891C4—1221no—
892C4—4884no—
893C4—2441no—
894C4—2441no—
895C4—2441no—
896C4—2441no—
897C2—21no—
898C2—22no—
899C2—41no—
900C2—41no—
901C2—41no—
902C2—41no—
903C2—81no—
904C2—1222no—
905C2—2441no—
906C2—2441no—
907C2—2441no—
908C2C2×D61⋊#9911yescharacteristic
subgroupG/H
centerC2C2×D61⋊#99
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC61×#534C4
socleC2×C61C22×#99
prime radical#21459460C2
cosocleC2×C22⋊D61C24
hypercenter#534#6923
hypocenterC61#33350
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C23 ◁ C22×D4 ◁ #534

Complements

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

NH ≅ G/Ntype
1. #21462429C2semidirect
2. #21462418C2semidirect
3. #21462082C2semidirect
4. #21462075C2semidirect
5. #21462074C2semidirect
6. #21462071C2semidirect
7. C2×#16840665C2semidirect
8. D61⋊#352C2semidirect
24. #16840665C22semidirect
25. #16840665C22semidirect
26. #16840664C22semidirect
27. #16840662C22semidirect
29. C22×#11758224C4semidirect
38. #16840334C4semidirect
40. #16840322C4semidirect
43. #16840268C4semidirect
46. C2×#14519758C4semidirect
47. #123×D61C4semidirect
49. #16840235C4semidirect
50. C61×#534C4semidirect
79. C22×Dic122C2×C4semidirect
81. C22×C22⋊D61C2×C4semidirect
89. C23×Dic61C2×C4semidirect
90. C23×Dic61C2×C4semidirect
91. C22×C4×D61C2×C4semidirect
100. #14519761C2×C4semidirect
101. #14519761C2×C4semidirect
104. #14519760C2×C4semidirect
113. #14519758C2×C4semidirect
114. #14519758C2×C4semidirect
115. #14519758C2×C4semidirect
116. #14519758C2×C4semidirect
131. #14519746C2×C4semidirect
144. #14519733C2×C4semidirect
145. #14519733C2×C4semidirect
151. C2×C22⋊Dic61C2×C4semidirect
155. C22⋊C4×D61C2×C4semidirect
156. C22⋊C4×D61C2×C4semidirect
158. C22×D4×C61C2×C4semidirect
160. #123×C61C2×C4semidirect
161. #123×C61C2×C4semidirect
165. #120×C61C2×C4semidirect
166. #120×C61C2×C4semidirect
167. C2×C22⋊C4×C61C2×C4semidirect
480. #534#6923semidirect
505. C61#33350semidirect
529. C22×D4C2×#6923semidirect
563. #123C2×#6923semidirect
564. #123C2×#6923semidirect
587. #120C2×#6923semidirect
588. #120C2×#6923semidirect
614. C2×C22⋊C4C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214624292
#214624182
#214620822
#214620752
#214620742
#214620712
C2×#168406652
D61⋊#3522
#214594602
#3335061