Finite Group Databasebeta

← #30548528

Subgroups — #30548528

Order 15616.

2074 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840385C211yesmaximal, characteristic, complemented
2#21459022C211yesmaximal, characteristic, complemented
3#21456089C214yesmaximal, complemented
4#21456082C214yesmaximal, complemented
5#21456049C214yesmaximal, complemented
6#21456004C214yesmaximal, complemented
7#21455763C211yesmaximal, characteristic, complemented
8#21455760C211yesmaximal, characteristic, complemented
9#21455630C212yesmaximal, complemented
10#21455315C212yesmaximal, complemented
11#21455071C211yesmaximal, characteristic
12#137×Dic61C212yesmaximal, complemented
13#21454632C212yesmaximal, complemented
14#21454454C211yesmaximal, characteristic, complemented
15C61×#3007C211yesmaximal, characteristic, complemented
16C2×#14519802C2212yes—
17#16840385—22no—
18#16840385—22no—
19#16840385C2214yes—
20#16840385C2214yescomplemented
21C2×#14519776C2211yescharacteristic, complemented
22C2×#14519772—21no—
23C2×#14519766C2211yescharacteristic, complemented
24C2×#14519763—21no—
25C2×#14519759—21no—
26C2×#14519757—21no—
27C2×#14519751C2211yescharacteristic
28#16840245—21no—
29#16840245—21no—
30#16840245C2212yescomplemented
31#16840245C2212yescomplemented
32#16840240C2212yescomplemented
33#16840237—21no—
34#16840237—21no—
35#16840237C2212yescomplemented
36#41×Dic61—22no—
37#41×Dic61C2212yes—
38#41×Dic61C2212yes—
39C2×Q8×Dic61C2211yescharacteristic, complemented
40C2×#14519739C2211yescharacteristic, complemented
41C2×#14519736—22no—
42C2×#14519736C2211yescharacteristic
43C2×#14519736C2211yescharacteristic
44#16840100C2214yescomplemented
45#16840095C2212yescomplemented
46#16840090C2212yescomplemented
47#16840087C2214yes—
48#16840081C2212yescomplemented
49#16840076C2212yescomplemented
50#16840055C2214yescomplemented
51#16840050C2214yescomplemented
52#16840045C2214yescomplemented
53#16840040C2214yescomplemented
54#16839986C2214yescomplemented
55#16839986C2214yescomplemented
56#16839979C2214yescomplemented
57#16839979C2214yescomplemented
58#16839907C2214yes—
59#16839901C2212yes—
60#16839896C2212yes—
61#16839871C2214yescomplemented
62#16839869C2214yescomplemented
63#16839865C2214yescomplemented
64#16839863C2214yescomplemented
65Q16×Dic61C2214yescomplemented
66SD16×Dic61C2214yescomplemented
67#16839847C2214yescomplemented
68#16839842C2214yescomplemented
69#16839820C2214yescomplemented
70#16839820C2214yescomplemented
71#16839804C2212yescomplemented
72#16839802C2212yescomplemented
73#16839785C2212yescomplemented
74#16839771C2212yescomplemented
75#16839768C2212yescomplemented
76#16839763C2212yes—
77#16839726C2211yescharacteristic
78M16×Dic61C2212yescomplemented
79C22×#41×C61C2211yescharacteristic
80C2×#137×C61C2212yes—
81C2×C22⋊Q8×C61C2211yescharacteristic
82C61×#452C2214yescomplemented
83C61×#451C2212yescomplemented
84C61×#450C2212yescomplemented
85C61×#417C2212yes—
86C61×#407C2211yescharacteristic
87C22×Dic122—21no—
88C22×D244C2311yescharacteristic
89C22×C22⋊D61—21no—
90C22×C4×D61—21no—
91#14519802—28no—
92C2×#11758201C2314yes—
93C2×#11758199C2314yes—
94C2×#11758194C2312yes—
95#14519776—22no—
96#14519776C2314yes—
97#14519772—24no—
98#14519772—24no—
99#14519766—22no—
100#14519766C2314yes—
101#14519763—24no—
102#14519763—24no—
103#14519759—24no—
104#14519759—24no—
105#14519757—24no—
106#14519757—24no—
107#14519751—21no—
108#14519751—21no—
109#14519751C2312yes—
110#14519751C2312yes—
111Q8×Dic61—22no—
112Q8×Dic61—22no—
113Q8×Dic61—22no—
114Q8×Dic61C2314yes—
115Q8×Dic61C2312yes—
116Q8×Dic61C2312yes—
117Q8×Dic61C2312yes—
118Q8×Dic61C2312yes—
119D4×Dic61—22no—
120D4×Dic61—22no—
121D4×Dic61—22no—
122D4×Dic61—22no—
123D4×Dic61—22no—
124D4×Dic61—22no—
125D4×Dic61—22no—
126D4×Dic61—22no—
127D4×Dic61—22no—
128D4×Dic61—22no—
129D4×Dic61C2312yes—
130D4×Dic61C2312yes—
131D4×Dic61C2312yes—
132D4×Dic61C2312yes—
133#14519739—22no—
134#14519739C2314yes—
135#14519736—21no—
136#14519736—21no—
137#14519736—22no—
138#14519736—22no—
139#14519736—22no—
140#14519736—22no—
141#14519736—22no—
142#14519736—22no—
143#14519736D412yes—
144#14519736D412yes—
145#14519736C2312yes—
146#14519736C2312yes—
147#14519736C2312yes—
148#14519736C2312yes—
149C2×C4⋊Dic61—21no—
150C2×C4⋊Dic61—22no—
151C2×C4⋊Dic61—22no—
152C2×C4⋊Dic61D411yescharacteristic
153C2×C4⋊Dic61D411yescharacteristic
154C2×C4⋊Dic61C2311yescharacteristic
155C2×C4⋊Dic61C2311yescharacteristic
156C2×C4⋊Dic61C2311yescharacteristic
157C2×#11758196—21no—
158C2×C22⋊Dic61—21no—
159C2×C22⋊Dic61—22no—
160C2×C22⋊Dic61—22no—
161C2×C22⋊Dic61D411yescharacteristic
162C2×C22⋊Dic61D411yescharacteristic
163C2×#11758198—21no—
164C2×#11758198—21no—
165C2×#11758198—21no—
166C2×#11758198—21no—
167C2×C4×Dic61—21no—
168C2×C4×Dic61—21no—
169C2×C4×Dic61—22no—
170C2×C4×Dic61—22no—
171C2×C4×Dic61C2311yescharacteristic
172C2×C4×Dic61C2311yescharacteristic
173#14519711C2314yes—
174#14519710C2314yes—
175#14519709C2314yes—
176#14519708C2314yes—
177#14519706C2314yes—
178#14519706C2314yes—
179#14519701C2314yes—
180#14519701C2314yes—
181#14519701C2314yes—
182#14519699C2314yes—
183#14519699C2314yes—
184#14519698C2314yes—
185C22⋊#92418C2312yes—
186C22⋊#92418C2312yes—
187#14519687C2314yes—
188C8×Dic61C2314yes—
189C2×#41×C61—28no—
190C2×#41×C61—21no—
191C2×#41×C61—21no—
192C2×#41×C61C2312yes—
193C2×#41×C61C2312yes—
194C22×Q8×C61C2311yescharacteristic
195C22×Q8×C61C2311yescharacteristic
196C22×D4×C61—21no—
197C22×D4×C61C2311yescharacteristic
198C23×C4×C61—21no—
199C23×C4×C61C2311yescharacteristic
200#137×C61—28no—
201C2×Q16×C61C2314yes—
202C2×SD16×C61C2314yes—
203C2×M16×C61C2312yes—
204C22⋊Q8×C61—21no—
205C22⋊Q8×C61—21no—
206C22⋊Q8×C61C2312yes—
207C22⋊Q8×C61C2312yes—
208C2×C4⋊C4×C61—21no—
209C2×C4⋊C4×C61C2311yescharacteristic
210C2×C22⋊C4×C61—21no—
211#103×C61C2314yes—
212#102×C61C2314yes—
213C22⋊C8×C61C2312yes—
214C22⋊C8×C61C2312yes—
215C24×C61—21no—
216C24×C61C2×D411yescharacteristic
217C23×D61—21no—
218#41×C61—28no—
219#41×C61—28no—
220#41×C61—24no—
221#41×C61—24no—
222#41×C61—24no—
223#41×C61#4118yes—
224C2×Q8×C61—24no—
225C2×Q8×C61—21no—
226C2×Q8×C61—21no—
227C2×Q8×C61—24no—
228C2×Q8×C61C2412yes—
229C2×Q8×C61C2412yes—
230C2×D4×C61—28no—
231C2×D4×C61—22no—
232C2×D4×C61—22no—
233C2×D4×C61—24no—
234C2×D4×C61—21no—
235C2×D4×C61C2412yes—
236C22×C4×C61—28no—
237C22×C4×C61—21no—
238C22×C4×C61—22no—
239C22×C4×C61—22no—
240C22×C4×C61—24no—
241C22×C4×C61—21no—
242C22×C4×C61—21no—
243C22×C4×C61C2×D411yescharacteristic
244C22×C4×C61C2×D411yescharacteristic
245C22×C4×C61C2×D411yescharacteristic
246C22×C4×C61C2411yescharacteristic
247C22×C4×C61C2411yescharacteristic
248C22×C4×C61C2411yescharacteristic
249C2×C22⋊D61—22no—
250C2×C22⋊D61—22no—
251C2×C22⋊D61—82no—
252C22×Dic61—21no—
253C22×Dic61—21no—
254C22×Dic61—21no—
255C22×Dic61—22no—
256C22×Dic61—22no—
257C22×Dic61—22no—
258C22×Dic61—22no—
259C22×Dic61C2×D411yescharacteristic
260C22×Dic61C2×D411yescharacteristic
261C22×Dic61C2×D411yescharacteristic
262C22×Dic61C2×D411yescharacteristic
263C2×D244—24no—
264C2×D244—21no—
265C2×D244C2412yes—
266C2×C4×D61—24no—
267C2×C4×D61—82no—
268C2×Dic122—24no—
269C2×Dic122—82no—
270Q16×C61—28no—
271SD16×C61—28no—
272M16×C61—24no—
273C2×C8×C61C2414yes—
274C4⋊C4×C61—22no—
275C4⋊C4×C61—22no—
276C4⋊C4×C61—21no—
277C4⋊C4×C61C2412yes—
278C22⋊C4×C61—22no—
279C22⋊C4×C61—22no—
280C22⋊Dic61—22no—
281C22⋊Dic61—22no—
282C22⋊Dic61—22no—
283C22⋊Dic61—22no—
284C22⋊Dic61—22no—
285C22⋊Dic61—22no—
286C22⋊Dic61C2×D412yes—
287C22⋊Dic61C2×D412yes—
288C22⋊Dic61C2×D412yes—
289C22⋊Dic61C2×D412yes—
290#11758201—28no—
291#11758199—28no—
292#11758198—22no—
293#11758198—22no—
294#11758198—24no—
295#11758198—24no—
296#11758198—24no—
297C4⋊Dic61—21no—
298C4⋊Dic61—21no—
299C4⋊Dic61—21no—
300C4⋊Dic61—22no—
301C4⋊Dic61—22no—
302C4⋊Dic61—22no—
303C4⋊Dic61—22no—
304C4⋊Dic61—24no—
305C4⋊Dic61C2×D412yes—
306C4⋊Dic61C2×D412yes—
307C4⋊Dic61C2×D412yes—
308C4⋊Dic61C2×D412yes—
309C4⋊Dic61C2412yes—
310C4⋊Dic61C2412yes—
311C4⋊Dic61C2412yes—
312#11758196—24no—
313C4×Dic61—22no—
314C4×Dic61—22no—
315C4×Dic61—22no—
316C4×Dic61—22no—
317C4×Dic61—22no—
318C4×Dic61—22no—
319C4×Dic61—24no—
320C4×Dic61C2×D412yes—
321C4×Dic61C2×D412yes—
322C4×Dic61C2412yes—
323C4×Dic61C2412yes—
324#11758194—24no—
325C2×#92418C2414yes—
326C23×C61—24no—
327C23×C61—22no—
328C23×C61—22no—
329C23×C61—41no—
330C23×C61—41no—
331C23×C61—81no—
332C23×C61—81no—
333C23×C61C22×D411yescharacteristic
334C23×C61C22×D411yescharacteristic
335C23×C61C22×D411yescharacteristic
336C22×D61—22no—
337C22×D61—42no—
338C22×D61—42no—
339C22×D61—42no—
340Q8×C61—24no—
341Q8×C61—22no—
342Q8×C61—24no—
343Q8×C61—42no—
344Q8×C61C2×#4114yes—
345D4×C61—28no—
346D4×C61—24no—
347D4×C61—28no—
348D4×C61—22no—
349D4×C61C2×#4114yes—
350C2×C4×C61—24no—
351C2×C4×C61—28no—
352C2×C4×C61—22no—
353C2×C4×C61—22no—
354C2×C4×C61—22no—
355C2×C4×C61—28no—
356C2×C4×C61—22no—
357C2×C4×C61—22no—
358C2×C4×C61—22no—
359C2×C4×C61—22no—
360C2×C4×C61—22no—
361C2×C4×C61—42no—
362C2×C4×C61—42no—
363C2×C4×C61C22×D411yescharacteristic
364C2×C4×C61C22×D411yescharacteristic
365C2×C4×C61C22×D411yescharacteristic
366C2×C4×C61C2×#4114yes—
367C2×C4×C61C2511yescharacteristic
368C22⋊D61—82no—
369C22⋊D61—82no—
370C2×Dic61—22no—
371C2×Dic61—22no—
372C2×Dic61—22no—
373C2×Dic61—41no—
374C2×Dic61—41no—
375C2×Dic61—41no—
376C2×Dic61—41no—
377C2×Dic61—42no—
378C2×Dic61—82no—
379C2×Dic61—82no—
380C2×Dic61—82no—
381C2×Dic61—82no—
382C2×Dic61—81no—
383C2×Dic61—81no—
384C2×Dic61C22×D412yes—
385C2×Dic61C22×D412yes—
386C2×Dic61C22×D412yes—
387C2×Dic61C22×D412yes—
388D244—24no—
389D244—42no—
390C4×D61—84no—
391Dic122—84no—
392C8×C61—24no—
393#92418—24no—
394#60567—611nomaximal, Sylow
395C22×C61—21no—
396C22×C61—21no—
397C22×C61—21no—
398C22×C61—21no—
399C22×C61—21no—
400C22×C61—21no—
401C22×C61—21no—
402C22×C61—21no—
403C22×C61—24no—
404C22×C61—42no—
405C22×C61—42no—
406C22×C61—82no—
407C22×C61—84no—
408C22×C61#52512yes—
409C22×C61C23×D411yescharacteristic
410C2×D61—42no—
411C2×D61—42no—
412C2×D61—42no—
413C2×D61—84no—
414C4×C61—21no—
415C4×C61—24no—
416C4×C61—21no—
417C4×C61—42no—
418C4×C61—42no—
419C4×C61#52512yes—
420C4×C61C22×#4112yes—
421Dic61—22no—
422Dic61—22no—
423Dic61—22no—
424Dic61—22no—
425Dic61—42no—
426Dic61—42no—
427Dic61—42no—
428C2×#542—611no—
429#3428—611no—
430#3125—614no—
431#3124—614no—
432#3121—614no—
433#3118—614no—
434#3095—611no—
435#3094—611no—
436#3079—612no—
437#3040—612no—
438#3007D6111yescharacteristic, complemented
439#3006—611no—
440C4×#137—612no—
441C4×AGL(1,ℤ/8)—612no—
442#2921—611no—
443C2×C61—22no—
444C2×C61—41no—
445C2×C61—41no—
446C2×C61—44no—
447C2×C61C2×#52511yescharacteristic
448C2×C61#358511yescharacteristic
449C2×C61#358611yescharacteristic
450D61—82no—
451C22×#41C2×D6111yescharacteristic
452C2×#137C2×D6112yes—
453C2×AGL(1,ℤ/8)—612no—
454#542—614no—
455#542—614no—
456#542—1222no—
457#542—1222no—
458C2×C4⋊Q8—611no—
459C2×#126—1221no—
460C2×#124—611no—
461C2×#124—1221no—
462C2×#123—1221no—
463C2×C22⋊Q8—1221no—
464C2×C22⋊Q8C2×D6111yescharacteristic
465C2×#121—611no—
466#520—612no—
467#520—612no—
468#520—1221no—
469#520—1221no—
470#519—612no—
471#518—612no—
472#518—1221no—
473#518—1221no—
474C4×#41—612no—
475C4×#41—612no—
476C4×#41—1222no—
477C2×C4×Q8—611no—
478C2×C4×D4—611no—
479C2×#117—611no—
480C2×#117—611no—
481C2×#117—1222no—
482#485—614no—
483#484—612no—
484#483—612no—
485#482—614no—
486#481—612no—
487#480—612no—
488#477—614no—
489#476—614no—
490#475—614no—
491#474—614no—
492#464—614no—
493#464—614no—
494#463—614no—
495#463—614no—
496#452C2×D6114yescomplemented
497#451C2×D6112yescomplemented
498#450C2×D6112yescomplemented
499#449—614no—
500#448—612no—
501#447—612no—
502#442—614no—
503#441—614no—
504#440—614no—
505#440—614no—
506C4×Q16—614no—
507C4×SD16—614no—
508C4×SD16—614no—
509C4×D8—614no—
510#433—614no—
511#433—614no—
512#428—612no—
513#428—612no—
514#423—612no—
515#419—612no—
516#418—612no—
517#417—612no—
518#417C2×D6112yes—
519#407—611no—
520#407C2×D6111yescharacteristic
521C4×M16—612no—
522C61#6056711yescharacteristic, complemented, Sylow
523C2×#41—28no—
524C2×#41—21no—
525C2×#41—21no—
526C2×#41C22×D6112yes—
527C2×#41C22×D6112yes—
528C22×Q8—1221no—
529C22×Q8C22×D6111yescharacteristic
530C22×Q8C22×D6111yescharacteristic
531C22×D4—21no—
532C22×D4—611no—
533C22×D4—1221no—
534C22×D4C22×D6111yescharacteristic
535C23×C4—21no—
536C23×C4—1221no—
537C23×C4C22×D6111yescharacteristic
538#137—28no—
539AGL(1,ℤ/8)—1228no—
540C2×Q16C22×D6114yes—
541C2×SD16—614no—
542C2×SD16C22×D6114yes—
543C2×D8—614no—
544C2×M16—612no—
545C2×M16C22×D6112yes—
546C4⋊Q8—614no—
547C4⋊Q8—1222no—
548#126—1224no—
549#126—1224no—
550#124—614no—
551#124—1222no—
552#124—1224no—
553#124—1224no—
554#123—1224no—
555#123—1224no—
556C22⋊Q8—21no—
557C22⋊Q8—21no—
558C22⋊Q8—1224no—
559C22⋊Q8—1224no—
560C22⋊Q8C22×D6112yes—
561C22⋊Q8C22×D6112yes—
562#121—612no—
563#121—612no—
564#121—1221no—
565#121—1221no—
566C4×Q8—614no—
567C4×Q8—612no—
568C4×Q8—612no—
569C4×Q8—612no—
570C4×Q8—612no—
571C4×Q8—1222no—
572C4×Q8—1222no—
573C4×Q8—1222no—
574C4×D4—612no—
575C4×D4—612no—
576C4×D4—612no—
577C4×D4—612no—
578C4×D4—614no—
579C4×D4—1222no—
580C4×D4—1222no—
581C4×D4—1222no—
582C4×D4—1222no—
583C4×D4—1222no—
584C4×D4—1222no—
585C4×D4—1222no—
586C4×D4—1222no—
587C4×D4—1222no—
588C4×D4—1222no—
589C4×D4—1222no—
590#117—612no—
591#117—612no—
592#117—612no—
593#117—612no—
594#117—612no—
595#117—612no—
596#117—1222no—
597#117—1222no—
598#117—1222no—
599#117—1222no—
600#117—1222no—
601#117—1222no—
602#117—1221no—
603#117—1221no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—611no—
606C2×C4⋊C4—611no—
607C2×C4⋊C4—611no—
608C2×C4⋊C4—611no—
609C2×C4⋊C4—611no—
610C2×C4⋊C4—1222no—
611C2×C4⋊C4—1222no—
612C2×C4⋊C4—1221no—
613C2×C4⋊C4—1221no—
614C2×C4⋊C4C22×D6111yescharacteristic
615C2×C22⋊C4—21no—
616C2×C22⋊C4—611no—
617C2×C22⋊C4—611no—
618C2×C22⋊C4—1222no—
619C2×C22⋊C4—1222no—
620C2×C22⋊C4—1221no—
621C2×C22⋊C4—1221no—
622C2×C22⋊C4—1221no—
623C2×C22⋊C4—1221no—
624C2×C22⋊C4—1221no—
625C2×C42—611no—
626C2×C42—611no—
627C2×C42—1222no—
628C2×C42—1222no—
629C2×C42—1221no—
630C2×C42—1221no—
631#107—614no—
632#107—614no—
633#106—614no—
634#106—614no—
635C4⋊C8—614no—
636C4⋊C8—614no—
637#103—614no—
638#103—614no—
639#103—614no—
640#103C22×D6114yes—
641#102—614no—
642#102—614no—
643#102—614no—
644#102C22×D6114yes—
645C22⋊C8—612no—
646C22⋊C8—612no—
647C22⋊C8C22×D6112yes—
648C22⋊C8C22×D6112yes—
649#97—614no—
650C4×C8—614no—
651C24—21no—
652C24—1221no—
653C24D4×D6111yescharacteristic
654#41—28no—
655#41—28no—
656#41—24no—
657#41—24no—
658#41—24no—
659#41#1175822418yes—
660C2×Q8—24no—
661C2×Q8—21no—
662C2×Q8—21no—
663C2×Q8—24no—
664C2×Q8—1224no—
665C2×Q8—4882no—
666C2×Q8C23×D6112yes—
667C2×Q8C23×D6112yes—
668C2×D4—28no—
669C2×D4—22no—
670C2×D4—22no—
671C2×D4—24no—
672C2×D4—21no—
673C2×D4—612no—
674C2×D4—1222no—
675C2×D4—1222no—
676C2×D4—1221no—
677C2×D4—1224no—
678C2×D4—4882no—
679C2×D4C23×D6112yes—
680C22×C4—28no—
681C22×C4—21no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—24no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—611no—
688C22×C4—611no—
689C22×C4—611no—
690C22×C4—611no—
691C22×C4—1224no—
692C22×C4—1222no—
693C22×C4—1222no—
694C22×C4—1222no—
695C22×C4—1222no—
696C22×C4—1221no—
697C22×C4—1221no—
698C22×C4—1221no—
699C22×C4—4882no—
700C22×C4D4×D6111yescharacteristic
701C22×C4D4×D6111yescharacteristic
702C22×C4D4×D6111yescharacteristic
703C22×C4C23×D6111yescharacteristic
704C22×C4C23×D6111yescharacteristic
705C22×C4C23×D6111yescharacteristic
706Q16—28no—
707SD16—28no—
708SD16—1228no—
709D8—1228no—
710M16—24no—
711M16—1224no—
712C2×C8—614no—
713C2×C8C23×D6114yes—
714C4⋊C4—22no—
715C4⋊C4—22no—
716C4⋊C4—21no—
717C4⋊C4—612no—
718C4⋊C4—612no—
719C4⋊C4—612no—
720C4⋊C4—612no—
721C4⋊C4—612no—
722C4⋊C4—612no—
723C4⋊C4—612no—
724C4⋊C4—1224no—
725C4⋊C4—1222no—
726C4⋊C4—1222no—
727C4⋊C4—1222no—
728C4⋊C4—1222no—
729C4⋊C4—1224no—
730C4⋊C4—1221no—
731C4⋊C4—1221no—
732C4⋊C4—1221no—
733C4⋊C4C23×D6112yes—
734C22⋊C4—22no—
735C22⋊C4—22no—
736C22⋊C4—612no—
737C22⋊C4—612no—
738C22⋊C4—612no—
739C22⋊C4—612no—
740C22⋊C4—1224no—
741C22⋊C4—1224no—
742C22⋊C4—1224no—
743C22⋊C4—1222no—
744C22⋊C4—1222no—
745C22⋊C4—1222no—
746C22⋊C4—1222no—
747C22⋊C4—1222no—
748C22⋊C4—1222no—
749C22⋊C4—1222no—
750C22⋊C4—1222no—
751C42—612no—
752C42—612no—
753C42—612no—
754C42—612no—
755C42—1222no—
756C42—1222no—
757C42—1222no—
758C42—1222no—
759C42—1224no—
760C42—1222no—
761C42—1222no—
762C23—24no—
763C23—22no—
764C23—22no—
765C23—41no—
766C23—41no—
767C23—81no—
768C23—81no—
769C23—1222no—
770C23—2442no—
771C23—2442no—
772C23—2442no—
773C23C2×D4×D6111yescharacteristic
774C23C2×D4×D6111yescharacteristic
775C23C2×D4×D6111yescharacteristic
776Q8—24no—
777Q8—22no—
778Q8—24no—
779Q8—42no—
780Q8—4884no—
781Q8C2×#1175822414yes—
782D4—28no—
783D4—24no—
784D4—28no—
785D4—22no—
786D4—1224no—
787D4—4882no—
788D4—4882no—
789D4—2442no—
790D4C2×#1175822414yes—
791C2×C4—24no—
792C2×C4—28no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—28no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—612no—
805C2×C4—612no—
806C2×C4—612no—
807C2×C4—612no—
808C2×C4—1222no—
809C2×C4—1222no—
810C2×C4—1222no—
811C2×C4—4884no—
812C2×C4—4882no—
813C2×C4—4882no—
814C2×C4—4882no—
815C2×C4—4882no—
816C2×C4—4881no—
817C2×C4—4881no—
818C2×C4—2441no—
819C2×C4—2441no—
820C2×C4—2441no—
821C2×C4—2441no—
822C2×C4—2442no—
823C2×C4C2×D4×D6111yescharacteristic
824C2×C4C2×D4×D6111yescharacteristic
825C2×C4C2×D4×D6111yescharacteristic
826C2×C4C2×#1175822414yes—
827C2×C4C24×D6111yescharacteristic
828C8—24no—
829C8—1224no—
830C22—21no—
831C22—21no—
832C22—21no—
833C22—21no—
834C22—24no—
835C22—21no—
836C22—21no—
837C22—21no—
838C22—21no—
839C22—42no—
840C22—42no—
841C22—82no—
842C22—84no—
843C22—4884no—
844C22—2442no—
845C22—2442no—
846C22—2442no—
847C22#1684026812yes—
848C22C22×D4×D6111yescharacteristic
849C4—21no—
850C4—24no—
851C4—21no—
852C4—42no—
853C4—42no—
854C4—1222no—
855C4—1222no—
856C4—1222no—
857C4—1222no—
858C4—2442no—
859C4—2442no—
860C4—2442no—
861C4#1684026812yes—
862C4C22×#1175822412yes—
863C2—22no—
864C2—41no—
865C2—41no—
866C2—44no—
867C2—4882no—
868C2C2×#1684026811yescharacteristic
869C2#2146059611yescharacteristic
870C2#2146060211yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3007C2
socleC22×C61C23×D4
prime radical#21455071C2
hypercenter#3007D61
hypocenterC61#60567
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3007

Complements

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

NH ≅ G/Ntype
1. C2×#16840385C2semidirect
2. #21459022C2semidirect
3. #21456089C2semidirect
4. #21456082C2semidirect
5. #21456049C2semidirect
6. #21456004C2semidirect
7. #21455763C2semidirect
8. #21455760C2semidirect
9. #21455630C2semidirect
10. #21455315C2semidirect
12. #137×Dic61C2semidirect
13. #21454632C2semidirect
14. #21454454C2semidirect
15. C61×#3007C2semidirect
20. #16840385C22semidirect
21. C2×#14519776C22semidirect
23. C2×#14519766C22semidirect
30. #16840245C22semidirect
31. #16840245C22semidirect
32. #16840240C22semidirect
35. #16840237C22semidirect
39. C2×Q8×Dic61C22semidirect
40. C2×#14519739C22semidirect
44. #16840100C22semidirect
45. #16840095C22semidirect
46. #16840090C22semidirect
48. #16840081C22semidirect
49. #16840076C22semidirect
50. #16840055C22semidirect
51. #16840050C22semidirect
52. #16840045C22semidirect
53. #16840040C22semidirect
54. #16839986C22semidirect
55. #16839986C22semidirect
56. #16839979C22semidirect
57. #16839979C22semidirect
61. #16839871C22semidirect
62. #16839869C22semidirect
63. #16839865C22semidirect
64. #16839863C22semidirect
65. Q16×Dic61C22semidirect
66. SD16×Dic61C22semidirect
67. #16839847C22semidirect
68. #16839842C22semidirect
69. #16839820C22semidirect
70. #16839820C22semidirect
71. #16839804C22semidirect
72. #16839802C22semidirect
73. #16839785C22semidirect
74. #16839771C22semidirect
75. #16839768C22semidirect
78. M16×Dic61C22semidirect
82. C61×#452C22semidirect
83. C61×#451C22semidirect
84. C61×#450C22semidirect
438. #3007D61semidirect
496. #452C2×D61semidirect
497. #451C2×D61semidirect
498. #450C2×D61semidirect
522. C61#60567semidirect

Maximal subgroups

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

subgroupindex
C2×#168403852
#214590222
#214560892
#214560822
#214560492
#214560042
#214557632
#214557602
#214556302
#214553152
#214550712
#137×Dic612
#214546322
#214544542
C61×#30072
#6056761