Finite Group Databasebeta

← #30623937

Subgroups — #30623937

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#21462077C212yesmaximal, complemented
5#21462076C212yesmaximal, complemented
6#21462073C212yesmaximal, complemented
7D61⋊#352C212yesmaximal, complemented
8C2×#16840664C212yesmaximal, complemented
9#21459457C211yesmaximal, 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#16840664C2214yescomplemented
26#16840664C2214yescomplemented
27#16840663C2214yescomplemented
28C2×#14519822C2211yescharacteristic
29C22×#11758222C411yescharacteristic, complemented
30#16840413—21no—
31#16840413—21no—
32#16840410—21no—
33#16840410—21no—
34#16840404—21no—
35#16840404—21no—
36#16840402—21no—
37#16840402—21no—
38#16840334C411yescharacteristic, complemented
39#16840334C2211yescharacteristic
40#16840324C2211yescharacteristic
41#16840323C411yescharacteristic, complemented
42#16840323C2211yescharacteristic
43#16840321C411yescharacteristic, complemented
44#16840270C411yescharacteristic, complemented
45#16840270C2211yescharacteristic
46C2×#14519760C2211yescharacteristic
47#123×D61C411yescharacteristic, complemented
48#123×D61C2211yescharacteristic
49#16840235C411yescharacteristic, complemented
50C2×#123×C61C411yescharacteristic, 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×#11758222—21no—
69C2×#11758222—21no—
70C2×#11758222—21no—
71C2×#11758222—21no—
72C2×#11758222—44no—
73C2×#11758222D411yescharacteristic
74C2×#11758222D411yescharacteristic
75C2×#11758224C2×C411yescharacteristic
76C2×#11758224D411yescharacteristic
77C2×#11758224D411yescharacteristic
78C2×#11758224C2311yescharacteristic
79C22×Dic122C2×C411yescharacteristic, complemented
80C22×D244C2×C411yescharacteristic, complemented
81C22×C22⋊D61C2×C411yescharacteristic
82C22×C22⋊D61C2×C411yescharacteristic, complemented
83C22×C22⋊D61D411yescharacteristic
84C22×C22⋊D61D411yescharacteristic
85C22×C22⋊D61C2311yescharacteristic
86C2×D4×D61C2×C411yescharacteristic
87C2×D4×D61D411yescharacteristic
88C2×D4×D61D411yescharacteristic
89C2×D4×D61C2311yescharacteristic
90C22×C4×D61C2×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#14519762—21no—
99#14519762—21no—
100#14519761—21no—
101#14519761C2×C411yescharacteristic, complemented
102#14519761C2311yescharacteristic
103#14519760—21no—
104#14519760—21no—
105#14519760—21no—
106#14519760C2×C411yescharacteristic, complemented
107#14519760C2×C411yescharacteristic, complemented
108#14519760C2311yescharacteristic
109#14519760C2311yescharacteristic
110#14519759—21no—
111#14519759—21no—
112#14519758C2×C411yescharacteristic, complemented
113#14519758C2×C411yescharacteristic, complemented
114#14519755—21no—
115#14519755—21no—
116#14519755—21no—
117#14519755—21no—
118#14519754—21no—
119#14519754—21no—
120#14519752—21no—
121#14519752—21no—
122#14519751—21no—
123#14519751—21no—
124#14519750—21no—
125#14519750—21no—
126#14519750—21no—
127#14519750—21no—
128#14519749—21no—
129#14519749—21no—
130#14519747—21no—
131#14519747—21no—
132#14519747—21no—
133#14519747C2×C411yescharacteristic, complemented
134#14519747C2311yescharacteristic
135#14519746—21no—
136#14519745C2×C411yescharacteristic, complemented
137#14519745C2×C411yescharacteristic, complemented
138#14519739—21no—
139#14519739—21no—
140C4×C22⋊D61—21no—
141C4×C22⋊D61—21no—
142#14519737—21no—
143#14519737—21no—
144#14519737—21no—
145#14519737—21no—
146#14519733C2×C411yescharacteristic, complemented
147#14519733C2×C411yescharacteristic, complemented
148C2×#11758196—21no—
149C4⋊C4×D61—21no—
150C4⋊C4×D61—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
158C23×C4×C61C2×C411yescharacteristic, complemented
159#123×C61—21no—
160#123×C61—21no—
161#123×C61C2×C411yescharacteristic, complemented
162#123×C61C2×C411yescharacteristic, complemented
163#123×C61C2×C411yescharacteristic, complemented
164#123×C61C2×C411yescharacteristic, complemented
165C2×C4⋊C4×C61—21no—
166C2×C22⋊C4×C61—21no—
167C2×C22⋊C4×C61C2×C411yescharacteristic, complemented
168C24×C61C22⋊C411yescharacteristic
169C24×C61C22×C411yescharacteristic
170C23×D61C22⋊C411yescharacteristic
171C23×D61C22×C411yescharacteristic
172C23×D61C22×C411yescharacteristic
173C23×D61C2×D411yescharacteristic
174C23×D61C2×D411yescharacteristic
175C22×#6923—42no—
176C22×#6923—42no—
177C2×D4×C61—42no—
178C2×D4×C61C22⋊C411yescharacteristic
179C2×D4×C61C22⋊C411yescharacteristic
180C2×D4×C61C22×C411yescharacteristic
181C2×D4×C61C22×C411yescharacteristic
182C22×C4×C61—21no—
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61—42no—
186C22×C4×C61C22⋊C411yescharacteristic
187C22×C4×C61C22×C411yescharacteristic
188C22×C4×C61C22×C411yescharacteristic
189C2×C22⋊D61—24no—
190C2×C22⋊D61—21no—
191C2×C22⋊D61—21no—
192C2×C22⋊D61—21no—
193C2×C22⋊D61—21no—
194C2×C22⋊D61—42no—
195C2×C22⋊D61—42no—
196C2×C22⋊D61—42no—
197C2×C22⋊D61—42no—
198C2×C22⋊D61C22⋊C411yescharacteristic
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⋊D61C2×D411yescharacteristic
206C2×C22⋊D61C2×D411yescharacteristic
207C2×C22⋊D61C2×D411yescharacteristic
208C2×C22⋊D61C2×D411yescharacteristic
209C2×C22⋊D61C2411yescharacteristic
210C22×Dic61—21no—
211C22×Dic61C22⋊C411yescharacteristic
212C22×Dic61C22×C411yescharacteristic
213C22×Dic61C22×C411yescharacteristic
214C22×Dic61C2×D411yescharacteristic
215C22×Dic61C2×D411yescharacteristic
216#11758224—24no—
217#11758224—42no—
218#11758224—42no—
219#11758224—42no—
220D4×D61—24no—
221D4×D61—42no—
222D4×D61—42no—
223D4×D61—42no—
224#11758222—42no—
225#11758222—42no—
226#11758222—44no—
227#11758222—44no—
228#11758222—44no—
229#11758222—44no—
230C2×D244—21no—
231C2×D244—21no—
232C2×D244—21no—
233C2×D244—21no—
234C2×D244—42no—
235C2×D244C22⋊C411yescharacteristic
236C2×D244C2×D411yescharacteristic
237C2×C4×D61—21no—
238C2×C4×D61—21no—
239C2×C4×D61—21no—
240C2×C4×D61—21no—
241C2×C4×D61—21no—
242C2×C4×D61—21no—
243C2×C4×D61—42no—
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—
268C4⋊C4×C61—21no—
269C4⋊C4×C61—21no—
270C22⋊C4×C61—21no—
271C22⋊C4×C61—21no—
272C22⋊C4×C61—21no—
273C22⋊C4×C61—21no—
274C22⋊C4×C61—21no—
275C22⋊C4×C61C22×C411yescharacteristic
276C22⋊C4×C61C22×C411yescharacteristic
277C22⋊Dic61—21no—
278C22⋊Dic61—21no—
279C22⋊Dic61—21no—
280C22⋊Dic61C22×C411yescharacteristic
281C22⋊Dic61C22×C411yescharacteristic
282#11758198—21no—
283#11758198—21no—
284#11758198—21no—
285#11758198—21no—
286#11758198—21no—
287#11758198—21no—
288#11758198—21no—
289#11758198—21no—
290#11758198—21no—
291#11758198—21no—
292#11758198—21no—
293#11758198—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—41no—
308C23×C61—81no—
309C23×C61—81no—
310C23×C61C2×C22⋊C411yescharacteristic
311C23×C61C2×C22⋊C411yescharacteristic
312C23×C61C2×C22⋊C411yescharacteristic
313C23×C61C2×C22⋊C411yescharacteristic
314C23×C61C23×C411yescharacteristic
315C22×D61—22no—
316C22×D61—22no—
317C22×D61—22no—
318C22×D61—21no—
319C22×D61—41no—
320C22×D61—41no—
321C22×D61—81no—
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—
337C2×C4×C61—21no—
338C2×C4×C61—21no—
339C2×C4×C61—21no—
340C2×C4×C61—21no—
341C2×C4×C61—41no—
342C2×C4×C61—42no—
343C2×C4×C61—42no—
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—41no—
372C2×Dic61—41no—
373C2×Dic61—81no—
374C2×Dic61C2×C22⋊C411yescharacteristic
375C2×Dic61C2×C22⋊C411yescharacteristic
376C2×Dic61C2×C22⋊C411yescharacteristic
377C2×Dic61C22×D411yescharacteristic
378D244—22no—
379D244—41no—
380D244—42no—
381D244—42no—
382D244—81no—
383D244—81no—
384C4×D61—22no—
385C4×D61—22no—
386C4×D61—41no—
387C4×D61—41no—
388C4×D61—42no—
389C4×D61—42no—
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—82no—
410C22×C61—161no—
411C22×C61C2×#9912yes—
412C22×C61C22×C22⋊C411yescharacteristic
413C2×D61—21no—
414C2×D61—21no—
415C2×D61—21no—
416C2×D61—41no—
417C2×D61—41no—
418C2×D61—41no—
419C2×D61—41no—
420C2×D61—41no—
421C2×D61—41no—
422C2×D61—41no—
423C2×D61—82no—
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—
435C4×C61—41no—
436Dic61—21no—
437Dic61—21no—
438Dic61—21no—
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×C61C22×#9911yescharacteristic
459D61—22no—
460D61—41no—
461D61—41no—
462D61—41no—
463D61—81no—
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—611no—
481#525—611no—
482#525—611no—
483C2×#123—611no—
484C2×#123—611no—
485C2×#123—611no—
486C2×#123#692311yescharacteristic, complemented
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×D4—611no—
529C22×D4C2×#692311yescharacteristic
530C23×C4—611no—
531C23×C4—611no—
532C23×C4C2×#692311yescharacteristic, complemented
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—21no—
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—1221no—
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#123C2×#692311yescharacteristic, complemented
562#123C2×#692311yescharacteristic, complemented
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—1221no—
572#121—1221no—
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—611no—
582#120—611no—
583#120—611no—
584#120—611no—
585#120—1221no—
586#120—1221no—
587#120—1221no—
588#120—1221no—
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—21no—
602C2×C4⋊C4—1221no—
603C2×C4⋊C4—1221no—
604C2×C4⋊C4—1221no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—611no—
607C2×C22⋊C4—611no—
608C2×C22⋊C4—611no—
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—
627C24—611no—
628C24C22⋊#692311yescharacteristic
629C24C22×#692311yescharacteristic
630#41—1224no—
631#41—2442no—
632#41—2442no—
633#41—2444no—
634#41—2444no—
635#41—2444no—
636#41—2444no—
637#41—2442no—
638#41—2442no—
639#41—2442no—
640C2×Q8—611no—
641C2×Q8—611no—
642C2×Q8—1221no—
643C2×Q8—1221no—
644C2×Q8—2442no—
645C2×D4—42no—
646C2×D4—611no—
647C2×D4—611no—
648C2×D4—611no—
649C2×D4—611no—
650C2×D4—611no—
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—1221no—
661C2×D4—1221no—
662C2×D4—1221no—
663C2×D4—1221no—
664C2×D4—1224no—
665C2×D4—1224no—
666C2×D4—1221no—
667C2×D4—1221no—
668C2×D4—1221no—
669C2×D4—1221no—
670C2×D4—2442no—
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—21no—
684C22×C4—21no—
685C22×C4—42no—
686C22×C4—611no—
687C22×C4—611no—
688C22×C4—611no—
689C22×C4—611no—
690C22×C4—611no—
691C22×C4—611no—
692C22×C4—611no—
693C22×C4—611no—
694C22×C4—611no—
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×C4C22⋊#692311yescharacteristic
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—21no—
719C4⋊C4—21no—
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—41no—
763C23—81no—
764C23—81no—
765C23—611no—
766C23—611no—
767C23—611no—
768C23—611no—
769C23—1222no—
770C23—1222no—
771C23—1222no—
772C23—1221no—
773C23—4881no—
774C23—4881no—
775C23—4881no—
776C23—4881no—
777C23—4881no—
778C23—2441no—
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—614no—
794D4—1222no—
795D4—1222no—
796D4—1222no—
797D4—1222no—
798D4—1222no—
799D4—1222no—
800D4—4881no—
801D4—4881no—
802D4—4881no—
803D4—4881no—
804D4—2441no—
805D4—2442no—
806D4—2442no—
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—21no—
819C2×C4—41no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—81no—
825C2×C4—611no—
826C2×C4—611no—
827C2×C4—611no—
828C2×C4—611no—
829C2×C4—1222no—
830C2×C4—1222no—
831C2×C4—1222no—
832C2×C4—1222no—
833C2×C4—1222no—
834C2×C4—1221no—
835C2×C4—1221no—
836C2×C4—1221no—
837C2×C4—9762no—
838C2×C4—9762no—
839C2×C4—4881no—
840C2×C4—4881no—
841C2×C4—4881no—
842C2×C4—2441no—
843C2×C4—2441no—
844C2×C4—2442no—
845C2×C4—2442no—
846C2×C4—2442no—
847C2×C4—2442no—
848C2×C4—2441no—
849C2×C4—2444no—
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—82no—
864C22—161no—
865C22—612no—
866C22—1221no—
867C22—1221no—
868C22—1221no—
869C22—9761no—
870C22—4882no—
871C22—4882no—
872C22—4882no—
873C22—4882no—
874C22—2441no—
875C22—2441no—
876C22—2441no—
877C22—2441no—
878C22—2441no—
879C22—2441no—
880C22—2441no—
881C22D61⋊#9912yes—
882C22C22×C22⋊#692311yescharacteristic
883C4—21no—
884C4—21no—
885C4—41no—
886C4—41no—
887C4—41no—
888C4—41no—
889C4—612no—
890C4—1221no—
891C4—1221no—
892C4—1221no—
893C4—4884no—
894C4—2441no—
895C4—2441no—
896C4—2441no—
897C2—21no—
898C2—22no—
899C2—41no—
900C2—41no—
901C2—41no—
902C2—41no—
903C2—1222no—
904C2—4881no—
905C2—2441no—
906C2—2441no—
907C2—2441no—
908C2C2×D61⋊#9911yescharacteristic
subgroupG/H
centerC2C2×D61⋊#99
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC2×#123×C61C4
socleC2×C61C22×#99
prime radical#21459457C2
cosocleC2×C22⋊D61C24
hypercenterC2×#123#6923
hypocenterC61#33350
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C23 ◁ C22×D4 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. #21462429C2semidirect
2. #21462418C2semidirect
3. #21462082C2semidirect
4. #21462077C2semidirect
5. #21462076C2semidirect
6. #21462073C2semidirect
7. D61⋊#352C2semidirect
8. C2×#16840664C2semidirect
24. #16840665C22semidirect
25. #16840664C22semidirect
26. #16840664C22semidirect
27. #16840663C22semidirect
29. C22×#11758222C4semidirect
38. #16840334C4semidirect
41. #16840323C4semidirect
43. #16840321C4semidirect
44. #16840270C4semidirect
47. #123×D61C4semidirect
49. #16840235C4semidirect
50. C2×#123×C61C4semidirect
79. C22×Dic122C2×C4semidirect
80. C22×D244C2×C4semidirect
82. C22×C22⋊D61C2×C4semidirect
90. C22×C4×D61C2×C4semidirect
91. C22×C4×D61C2×C4semidirect
101. #14519761C2×C4semidirect
106. #14519760C2×C4semidirect
107. #14519760C2×C4semidirect
112. #14519758C2×C4semidirect
113. #14519758C2×C4semidirect
133. #14519747C2×C4semidirect
136. #14519745C2×C4semidirect
137. #14519745C2×C4semidirect
146. #14519733C2×C4semidirect
147. #14519733C2×C4semidirect
151. C2×C22⋊Dic61C2×C4semidirect
155. C22⋊C4×D61C2×C4semidirect
156. C22⋊C4×D61C2×C4semidirect
158. C23×C4×C61C2×C4semidirect
161. #123×C61C2×C4semidirect
162. #123×C61C2×C4semidirect
163. #123×C61C2×C4semidirect
164. #123×C61C2×C4semidirect
167. C2×C22⋊C4×C61C2×C4semidirect
486. C2×#123#6923semidirect
505. C61#33350semidirect
532. C23×C4C2×#6923semidirect
561. #123C2×#6923semidirect
562. #123C2×#6923semidirect
563. #123C2×#6923semidirect
564. #123C2×#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
#214620772
#214620762
#214620732
D61⋊#3522
C2×#168406642
#214594572
#3335061