Finite Group Databasebeta

← #29707023

Subgroups — #29707023

Order 15616.

1948 conjugacy classes of subgroups.

The subgroup lattice has 1044 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840560C211yesmaximal, characteristic, complemented
2C2×#16840560C211yesmaximal, characteristic, complemented
3C2×#16839779C211yesmaximal, characteristic, complemented
4#21454338C211yesmaximal, characteristic, complemented
5C2×#16839735C211yesmaximal, characteristic, complemented
6#21446879C214yesmaximal, complemented
7#21446872C214yesmaximal, complemented
8C2×#16839532C211yesmaximal, characteristic, complemented
9C61×#3449C211yesmaximal, characteristic, complemented
10C22×#11758222C2211yescharacteristic
11#16840560—22no—
12#16840560—22no—
13#16840560—22no—
14#16840560—22no—
15#16840560—22no—
16#16840560—22no—
17#16840560—22no—
18#16840560C2214yes—
19C2×#14519808—21no—
20C2×#14519808C2212yescomplemented
21C2×#14519807—21no—
22C2×#14519807—21no—
23C2×#14519803—21no—
24C2×#14519803C2212yescomplemented
25C2×#14519802—21no—
26C2×#14519802—21no—
27C2×#14519797—22no—
28C2×#14519797—22no—
29C22×#11758194C2211yescharacteristic
30C22×#11758194C2211yescharacteristic
31C2×#14519736C2211yescharacteristic
32#16839779—22no—
33#16839779C2214yescomplemented
34C2×#14519704—22no—
35#16839771C2212yescomplemented
36#16839767C2212yescomplemented
37#16839763—22no—
38#16839758—22no—
39#16839735—22no—
40#16839735C2214yescomplemented
41C2×#14519691—22no—
42#16839532C2214yescomplemented
43C22×#41×C61C2211yescharacteristic
44C22×#41×C61C2211yescharacteristic
45C61×#537—22no—
46C61×#536—21no—
47C61×#536C2212yescomplemented
48C61×#535—21no—
49C61×#535C2212yescomplemented
50C61×#534—22no—
51C61×#532—22no—
52C61×#525—22no—
53C61×#525—22no—
54C2×#117×C61C2211yescharacteristic
55C2×#11758222—21no—
56C2×#11758222—21no—
57C2×#11758222—21no—
58C2×#11758222—21no—
59C2×#11758222—21no—
60C2×#11758222—21no—
61C2×#11758222—21no—
62C2×#11758222—21no—
63C2×#11758222—21no—
64C2×#11758222—21no—
65C2×#11758222D412yescomplemented
66C2×#11758222C2312yes—
67C22×Dic122D411yescharacteristic, complemented
68C22×D244D411yescharacteristic, complemented
69C22×C22⋊D61—21no—
70C22×C4×D61—21no—
71#14519808—24no—
72#14519808—24no—
73#14519808—24no—
74#14519808—24no—
75#14519807—24no—
76#14519807—24no—
77#14519807—24no—
78#14519807—24no—
79#14519803—24no—
80#14519803—24no—
81#14519803—24no—
82#14519803—24no—
83#14519802—24no—
84#14519802—24no—
85#14519802—24no—
86#14519802—24no—
87#14519797—28no—
88#14519797—28no—
89#14519797—28no—
90#14519797—28no—
91C2×#11758202—22no—
92C2×#11758202—22no—
93C2×#11758200—22no—
94C2×#11758200—22no—
95C2×#11758201—22no—
96C2×#11758201—22no—
97C2×#11758199—22no—
98C2×#11758199—22no—
99C2×#11758194—21no—
100C2×#11758194—21no—
101C2×#11758194—21no—
102C2×#11758194—21no—
103C2×#11758194—21no—
104C2×#11758194—21no—
105C2×#11758194—21no—
106C2×#11758194D412yescomplemented
107C2×#11758194D412yescomplemented
108C2×#11758194D412yescomplemented
109C2×#11758194C2312yes—
110C2×#11758194C2312yes—
111C22×#92418—21no—
112C22×#92418D412yescomplemented
113#14519736—21no—
114#14519736—21no—
115#14519736—21no—
116#14519736C2312yes—
117C2×C4⋊Dic61—21no—
118C2×C22⋊Dic61—21no—
119C2×C4×Dic61—21no—
120#14519704—28no—
121#14519701—24no—
122#14519698—24no—
123#14519691—28no—
124C2×#41×C61—21no—
125C2×#41×C61—21no—
126C2×#41×C61—21no—
127C2×#41×C61—21no—
128C2×#41×C61—21no—
129C2×#41×C61—21no—
130C2×#41×C61—21no—
131C2×#41×C61—21no—
132C2×#41×C61—21no—
133C2×#41×C61—21no—
134C2×#41×C61—21no—
135C2×#41×C61—21no—
136C2×#41×C61—21no—
137C2×#41×C61—21no—
138C2×#41×C61—21no—
139C2×#41×C61—21no—
140C2×#41×C61—21no—
141C2×#41×C61—21no—
142C2×#41×C61—21no—
143C2×#41×C61—21no—
144C2×#41×C61D412yes—
145C2×#41×C61D412yes—
146C2×#41×C61D412yes—
147C2×#41×C61C2312yes—
148C22×Q8×C61D411yescharacteristic
149C22×Q8×C61C2311yescharacteristic
150C22×D4×C61—21no—
151C22×D4×C61—21no—
152C22×D4×C61D411yescharacteristic
153C22×D4×C61C2311yescharacteristic
154C23×C4×C61—21no—
155C23×C4×C61—21no—
156C23×C4×C61C2311yescharacteristic
157C4⋊Q8×C61—22no—
158#127×C61—22no—
159#124×C61—22no—
160#124×C61—22no—
161#123×C61—24no—
162#123×C61—24no—
163C22⋊Q8×C61—24no—
164C22⋊Q8×C61—24no—
165#121×C61—28no—
166#121×C61—24no—
167#121×C61—24no—
168#120×C61—24no—
169#120×C61—24no—
170C4×D4×C61—28no—
171#117×C61—21no—
172#117×C61—21no—
173#117×C61D412yes—
174#117×C61C2312yes—
175C2×C4⋊C4×C61—21no—
176C2×C22⋊C4×C61D412yes—
177C2×C42×C61—21no—
178C24×C61—21no—
179C24×C61—21no—
180C24×C61C2×D411yescharacteristic
181C23×D61—21no—
182#41×C61—22no—
183#41×C61—22no—
184#41×C61—22no—
185#41×C61—22no—
186#41×C61—22no—
187#41×C61—22no—
188#41×C61—22no—
189#41×C61—22no—
190#41×C61—22no—
191#41×C61—22no—
192#41×C61—22no—
193#41×C61—22no—
194#41×C61—22no—
195#41×C61—22no—
196#41×C61—22no—
197#41×C61—22no—
198#41×C61—41no—
199#41×C61—41no—
200#41×C61—41no—
201#41×C61—41no—
202#41×C61—41no—
203#41×C61—41no—
204#41×C61—41no—
205#41×C61—41no—
206#41×C61—41no—
207#41×C61—41no—
208#41×C61—41no—
209#41×C61—41no—
210#41×C61—41no—
211#41×C61—41no—
212#41×C61—41no—
213#41×C61—41no—
214C2×Q8×C61—21no—
215C2×Q8×C61—21no—
216C2×Q8×C61—21no—
217C2×Q8×C61—21no—
218C2×Q8×C61—21no—
219C2×Q8×C61—21no—
220C2×Q8×C61—21no—
221C2×Q8×C61—21no—
222C2×Q8×C61—21no—
223C2×Q8×C61—21no—
224C2×Q8×C61C2×D412yes—
225C2×Q8×C61C2×D412yes—
226C2×D4×C61—22no—
227C2×D4×C61—22no—
228C2×D4×C61—22no—
229C2×D4×C61—22no—
230C2×D4×C61—28no—
231C2×D4×C61—21no—
232C2×D4×C61—21no—
233C2×D4×C61—21no—
234C2×D4×C61—21no—
235C2×D4×C61—21no—
236C2×D4×C61—21no—
237C2×D4×C61—21no—
238C2×D4×C61—21no—
239C2×D4×C61—21no—
240C2×D4×C61—21no—
241C2×D4×C61—41no—
242C2×D4×C61—41no—
243C2×D4×C61—41no—
244C2×D4×C61—41no—
245C2×D4×C61—41no—
246C2×D4×C61—41no—
247C2×D4×C61—41no—
248C2×D4×C61—41no—
249C2×D4×C61C2×D412yes—
250C2×D4×C61C2×D412yes—
251C22×C4×C61—21no—
252C22×C4×C61—21no—
253C22×C4×C61—22no—
254C22×C4×C61—22no—
255C22×C4×C61—22no—
256C22×C4×C61—22no—
257C22×C4×C61—22no—
258C22×C4×C61—41no—
259C22×C4×C61—41no—
260C22×C4×C61—41no—
261C22×C4×C61—41no—
262C22×C4×C61—41no—
263C22×C4×C61—41no—
264C22×C4×C61—41no—
265C22×C4×C61—41no—
266C22×C4×C61C2×D411yescharacteristic
267C22×C4×C61C2×D411yescharacteristic
268C22×C4×C61C2×D411yescharacteristic
269C22×C4×C61C2×D411yescharacteristic
270C22×C4×C61C2×D411yescharacteristic
271C22×C4×C61C2×D411yescharacteristic
272C22×C4×C61C2×D411yescharacteristic
273C22×C4×C61C2×D411yescharacteristic
274C22×C4×C61C2×D411yescharacteristic
275C22×C4×C61C2×D411yescharacteristic
276C22×C4×C61C2×D411yescharacteristic
277C22×C4×C61#4111yescharacteristic
278C22×C4×C61#4111yescharacteristic
279C22×C4×C61C2411yescharacteristic
280C2×C22⋊D61—22no—
281C2×C22⋊D61—22no—
282C2×C22⋊D61—41no—
283C2×C22⋊D61—41no—
284C2×C22⋊D61—41no—
285C2×C22⋊D61—41no—
286C22×Dic61—21no—
287C22×Dic61—41no—
288#11758222—22no—
289#11758222—22no—
290#11758222—22no—
291#11758222—22no—
292#11758222—22no—
293#11758222—22no—
294#11758222—22no—
295#11758222—22no—
296#11758222—41no—
297#11758222—41no—
298#11758222—41no—
299#11758222—41no—
300#11758222—41no—
301#11758222—41no—
302#11758222—41no—
303#11758222—41no—
304C2×D244—21no—
305C2×D244—21no—
306C2×D244—21no—
307C2×D244—21no—
308C2×D244—21no—
309C2×D244C2×D412yes—
310C2×C4×D61—22no—
311C2×C4×D61—22no—
312C2×C4×D61—41no—
313C2×C4×D61—41no—
314C2×C4×D61—41no—
315C2×C4×D61—41no—
316C2×Dic122—21no—
317C2×Dic122—21no—
318C2×Dic122—21no—
319C2×Dic122—21no—
320C2×Dic122—21no—
321C2×Dic122C2×D412yes—
322C4⋊C4×C61—28no—
323C4⋊C4×C61—22no—
324C4⋊C4×C61—22no—
325C22⋊C4×C61—28no—
326C22⋊C4×C61—28no—
327C22⋊C4×C61—22no—
328C22⋊C4×C61C2×D414yes—
329C42×C61—22no—
330C42×C61—22no—
331C22⋊Dic61—22no—
332C22⋊Dic61—41no—
333#11758202—28no—
334#11758202—28no—
335#11758201—28no—
336#11758201—28no—
337#11758200—28no—
338#11758200—28no—
339#11758199—28no—
340#11758199—28no—
341C4⋊Dic61—22no—
342C4⋊Dic61—41no—
343C4×Dic61—22no—
344C4×Dic61—41no—
345#11758194—22no—
346#11758194—22no—
347#11758194—22no—
348#11758194—22no—
349#11758194—22no—
350#11758194—22no—
351#11758194—22no—
352#11758194C2×D414yes—
353C2×#92418—22no—
354C2×#92418—22no—
355C2×#92418—22no—
356C2×#92418—22no—
357C2×#92418—22no—
358C2×#92418C2×D414yes—
359C23×C61—22no—
360C23×C61—22no—
361C23×C61—41no—
362C23×C61—41no—
363C23×C61—41no—
364C23×C61—41no—
365C23×C61—81no—
366C23×C61—82no—
367C23×C61—82no—
368C23×C61#12011yescharacteristic
369C23×C61#12011yescharacteristic
370C23×C61#12111yescharacteristic
371C23×C61#12111yescharacteristic
372C23×C61#12711yescharacteristic
373C23×C61#12711yescharacteristic
374C23×C61C22×D411yescharacteristic
375C22×D61—22no—
376C22×D61—41no—
377C22×D61—41no—
378C22×D61—82no—
379Q8×C61—22no—
380Q8×C61—22no—
381Q8×C61—22no—
382Q8×C61—22no—
383Q8×C61—41no—
384Q8×C61—41no—
385Q8×C61—41no—
386Q8×C61—41no—
387D4×C61—22no—
388D4×C61—22no—
389D4×C61—22no—
390D4×C61—22no—
391D4×C61—42no—
392D4×C61—42no—
393D4×C61—42no—
394D4×C61—42no—
395D4×C61—42no—
396D4×C61—42no—
397D4×C61—42no—
398D4×C61—42no—
399D4×C61—41no—
400D4×C61—41no—
401D4×C61—41no—
402D4×C61—41no—
403D4×C61—88no—
404C2×C4×C61—24no—
405C2×C4×C61—22no—
406C2×C4×C61—22no—
407C2×C4×C61—41no—
408C2×C4×C61—41no—
409C2×C4×C61—41no—
410C2×C4×C61—41no—
411C2×C4×C61—42no—
412C2×C4×C61—42no—
413C2×C4×C61—42no—
414C2×C4×C61—42no—
415C2×C4×C61—42no—
416C2×C4×C61—42no—
417C2×C4×C61—42no—
418C2×C4×C61—42no—
419C2×C4×C61—82no—
420C2×C4×C61#12011yescharacteristic
421C2×C4×C61#12011yescharacteristic
422C2×C4×C61#12011yescharacteristic
423C2×C4×C61#12011yescharacteristic
424C2×C4×C61#12011yescharacteristic
425C2×C4×C61#12011yescharacteristic
426C2×C4×C61#12011yescharacteristic
427C2×C4×C61#12011yescharacteristic
428C2×C4×C61#12011yescharacteristic
429C2×C4×C61#12011yescharacteristic
430C2×C4×C61#12111yescharacteristic
431C2×C4×C61#12111yescharacteristic
432C2×C4×C61#12111yescharacteristic
433C2×C4×C61#12111yescharacteristic
434C2×C4×C61#12111yescharacteristic
435C2×C4×C61#12111yescharacteristic
436C2×C4×C61#12111yescharacteristic
437C2×C4×C61#12111yescharacteristic
438C2×C4×C61#12111yescharacteristic
439C2×C4×C61#12111yescharacteristic
440C2×C4×C61#12711yescharacteristic
441C2×C4×C61#12711yescharacteristic
442C2×C4×C61C22×D411yescharacteristic
443C2×C4×C61C22×D411yescharacteristic
444C2×C4×C61C22×D411yescharacteristic
445C2×C4×C61C22×D411yescharacteristic
446C2×C4×C61C22×D411yescharacteristic
447C2×C4×C61C2×#4111yescharacteristic
448C22⋊D61—42no—
449C22⋊D61—42no—
450C22⋊D61—42no—
451C22⋊D61—42no—
452C2×Dic61—22no—
453C2×Dic61—41no—
454C2×Dic61—41no—
455C2×Dic61—42no—
456C2×Dic61—82no—
457D244—22no—
458D244—22no—
459D244—41no—
460D244—41no—
461C4×D61—42no—
462C4×D61—42no—
463C4×D61—42no—
464C4×D61—42no—
465Dic122—22no—
466Dic122—22no—
467Dic122—41no—
468Dic122—41no—
469#92418—24no—
470#92418—24no—
471#23412—611nomaximal, Sylow
472C22×C61—41no—
473C22×C61—41no—
474C22×C61—41no—
475C22×C61—41no—
476C22×C61—41no—
477C22×C61—41no—
478C22×C61—41no—
479C22×C61—44no—
480C22×C61—44no—
481C22×C61—42no—
482C22×C61—42no—
483C22×C61—82no—
484C22×C61—82no—
485C22×C61—82no—
486C22×C61—82no—
487C22×C61#39211yescharacteristic
488C22×C61#39211yescharacteristic
489C22×C61#39211yescharacteristic
490C22×C61#39211yescharacteristic
491C22×C61C2×#12011yescharacteristic
492C22×C61C2×#12111yescharacteristic
493C22×C61C2×#12711yescharacteristic
494C2×D61—42no—
495C2×D61—82no—
496C2×D61—82no—
497C2×D61—82no—
498C4×C61—44no—
499C4×C61—42no—
500C4×C61—42no—
501C4×C61#39211yescharacteristic
502C4×C61#39211yescharacteristic
503C4×C61#39211yescharacteristic
504C4×C61#39211yescharacteristic
505C4×C61C2×#12011yescharacteristic
506C4×C61C2×#12011yescharacteristic
507C4×C61C2×#12111yescharacteristic
508C4×C61C2×#12111yescharacteristic
509Dic61—42no—
510Dic61—82no—
511C2×#575—611no—
512C2×#575—611no—
513#3449D6111yescharacteristic, complemented
514C2×#421—611no—
515#2896—611no—
516C2×#410—611no—
517#2009—614no—
518#2008—614no—
519C2×#344—611no—
520C2×C61—21no—
521C2×C61—21no—
522C2×C61—21no—
523C2×C61—21no—
524C2×C61—21no—
525C2×C61—21no—
526C2×C61—21no—
527C2×C61—82no—
528C2×C61—82no—
529C2×C61C2×#39211yescharacteristic
530D61—82no—
531C22×#41—611no—
532C22×#41C2×D6111yescharacteristic
533C22×#41C2×D6111yescharacteristic
534#575—614no—
535#575—1222no—
536#575—1222no—
537#575—1222no—
538#575—1222no—
539#575—1222no—
540#575—1222no—
541#575—1222no—
542C2×#137—612no—
543C2×#137—1221no—
544C2×#137—1221no—
545C2×#137—1221no—
546C2×AGL(1,ℤ/8)—612no—
547C2×AGL(1,ℤ/8)—1221no—
548C2×AGL(1,ℤ/8)—1221no—
549C2×AGL(1,ℤ/8)—1221no—
550C2×#135—1222no—
551C2×#135—1222no—
552C22×M16—611no—
553C22×M16—611no—
554#537—22no—
555#536—21no—
556#536C2×D6112yescomplemented
557#535—21no—
558#535C2×D6112yescomplemented
559#534—22no—
560#532—22no—
561#525—22no—
562#525—22no—
563C2×#117—611no—
564C2×#117C2×D6111yescharacteristic
565#421—614no—
566#421—1222no—
567C2×#104—1222no—
568#419—612no—
569#418—612no—
570#417—1222no—
571#416—1222no—
572#410—614no—
573#410—1222no—
574C2×#99—1222no—
575#344—614no—
576C61#2341211yescharacteristic, complemented, Sylow
577C2×#41—21no—
578C2×#41—21no—
579C2×#41—21no—
580C2×#41—21no—
581C2×#41—21no—
582C2×#41—21no—
583C2×#41—21no—
584C2×#41—21no—
585C2×#41—21no—
586C2×#41—21no—
587C2×#41—21no—
588C2×#41—21no—
589C2×#41—21no—
590C2×#41—21no—
591C2×#41—21no—
592C2×#41—21no—
593C2×#41—21no—
594C2×#41—21no—
595C2×#41—21no—
596C2×#41—21no—
597C2×#41—612no—
598C2×#41—612no—
599C2×#41—1221no—
600C2×#41—1221no—
601C2×#41—1221no—
602C2×#41—1221no—
603C2×#41—1221no—
604C2×#41—1221no—
605C2×#41—1221no—
606C2×#41—1221no—
607C2×#41—1221no—
608C2×#41—1221no—
609C2×#41C22⋊D6112yes—
610C2×#41C22⋊D6112yes—
611C2×#41C22⋊D6112yes—
612C2×#41C22×D6112yes—
613C22×Q8—611no—
614C22×Q8C22⋊D6111yescharacteristic
615C22×Q8C22×D6111yescharacteristic
616C22×D4—21no—
617C22×D4—21no—
618C22×D4—611no—
619C22×D4—1221no—
620C22×D4C22⋊D6111yescharacteristic
621C22×D4C22×D6111yescharacteristic
622C23×C4—21no—
623C23×C4—21no—
624C23×C4—1221no—
625C23×C4C22×D6111yescharacteristic
626#137—1224no—
627#137—1224no—
628#137—1224no—
629#137—1224no—
630#137—1224no—
631#137—1224no—
632#137—1224no—
633#137—1224no—
634AGL(1,ℤ/8)—1224no—
635AGL(1,ℤ/8)—1224no—
636AGL(1,ℤ/8)—1224no—
637AGL(1,ℤ/8)—1224no—
638AGL(1,ℤ/8)—1224no—
639AGL(1,ℤ/8)—1224no—
640AGL(1,ℤ/8)—1224no—
641AGL(1,ℤ/8)—1224no—
642#135—1228no—
643#135—1228no—
644#135—1228no—
645#135—1228no—
646C2×Q16—1222no—
647C2×Q16—1222no—
648C2×SD16—1222no—
649C2×SD16—1222no—
650C2×SD16—1222no—
651C2×SD16—1222no—
652C2×D8—1222no—
653C2×D8—1222no—
654C2×M16—612no—
655C2×M16—612no—
656C2×M16—612no—
657C2×M16—612no—
658C2×M16—612no—
659C2×M16—1221no—
660C2×M16—1221no—
661C2×M16—1221no—
662C2×M16—1221no—
663C2×M16—1221no—
664C2×M16—1221no—
665C2×M16—1221no—
666C22×C8—612no—
667C22×C8—1221no—
668C4⋊Q8—22no—
669#127—22no—
670#124—22no—
671#124—22no—
672#123—24no—
673#123—24no—
674C22⋊Q8—24no—
675C22⋊Q8—24no—
676#121—24no—
677#121—28no—
678#121—24no—
679#120—24no—
680#120—24no—
681C4×D4—28no—
682#117—21no—
683#117—21no—
684#117—612no—
685#117—1221no—
686#117—1221no—
687#117—1221no—
688#117C22⋊D6112yes—
689#117C22×D6112yes—
690C2×C4⋊C4—21no—
691C2×C4⋊C4—1221no—
692C2×C22⋊C4—1221no—
693C2×C22⋊C4C22⋊D6112yes—
694C2×C42—21no—
695C2×C42—1221no—
696#104—1228no—
697#103—1224no—
698#102—1224no—
699#99—1228no—
700C24—21no—
701C24—21no—
702C24—1221no—
703C24C2×C22⋊D6111yescharacteristic
704#41—22no—
705#41—22no—
706#41—22no—
707#41—22no—
708#41—22no—
709#41—22no—
710#41—22no—
711#41—22no—
712#41—22no—
713#41—22no—
714#41—22no—
715#41—22no—
716#41—22no—
717#41—22no—
718#41—22no—
719#41—22no—
720#41—41no—
721#41—41no—
722#41—41no—
723#41—41no—
724#41—41no—
725#41—41no—
726#41—41no—
727#41—41no—
728#41—41no—
729#41—41no—
730#41—41no—
731#41—41no—
732#41—41no—
733#41—41no—
734#41—41no—
735#41—41no—
736#41—1222no—
737#41—1222no—
738#41—1222no—
739#41—1222no—
740#41—1222no—
741#41—1222no—
742#41—1222no—
743#41—1222no—
744#41—2441no—
745#41—2441no—
746#41—2441no—
747#41—2441no—
748#41—2441no—
749#41—2441no—
750#41—2441no—
751#41—2441no—
752C2×Q8—21no—
753C2×Q8—21no—
754C2×Q8—21no—
755C2×Q8—21no—
756C2×Q8—21no—
757C2×Q8—21no—
758C2×Q8—21no—
759C2×Q8—21no—
760C2×Q8—21no—
761C2×Q8—21no—
762C2×Q8—612no—
763C2×Q8—1221no—
764C2×Q8—1221no—
765C2×Q8—1221no—
766C2×Q8—1221no—
767C2×Q8—1221no—
768C2×Q8C2×C22⋊D6112yes—
769C2×Q8C2×C22⋊D6112yes—
770C2×D4—22no—
771C2×D4—22no—
772C2×D4—22no—
773C2×D4—22no—
774C2×D4—28no—
775C2×D4—21no—
776C2×D4—21no—
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—41no—
786C2×D4—41no—
787C2×D4—41no—
788C2×D4—41no—
789C2×D4—41no—
790C2×D4—41no—
791C2×D4—41no—
792C2×D4—41no—
793C2×D4—612no—
794C2×D4—1222no—
795C2×D4—1222no—
796C2×D4—1221no—
797C2×D4—1221no—
798C2×D4—1221no—
799C2×D4—1221no—
800C2×D4—1221no—
801C2×D4—2441no—
802C2×D4—2441no—
803C2×D4—2441no—
804C2×D4—2441no—
805C2×D4C2×C22⋊D6112yes—
806C2×D4C2×C22⋊D6112yes—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—41no—
815C22×C4—41no—
816C22×C4—41no—
817C22×C4—41no—
818C22×C4—41no—
819C22×C4—41no—
820C22×C4—41no—
821C22×C4—41no—
822C22×C4—1221no—
823C22×C4—1222no—
824C22×C4—1222no—
825C22×C4—2441no—
826C22×C4—2441no—
827C22×C4—2441no—
828C22×C4—2441no—
829C22×C4—2441no—
830C22×C4D4×D6111yescharacteristic
831C22×C4D4×D6111yescharacteristic
832C22×C4D4×D6111yescharacteristic
833C22×C4D4×D6111yescharacteristic
834C22×C4D4×D6111yescharacteristic
835C22×C4D4×D6111yescharacteristic
836C22×C4#1175822411yescharacteristic
837C22×C4#1175822411yescharacteristic
838C22×C4C2×C22⋊D6111yescharacteristic
839C22×C4C2×C22⋊D6111yescharacteristic
840C22×C4C2×C22⋊D6111yescharacteristic
841C22×C4C2×C22⋊D6111yescharacteristic
842C22×C4C2×C22⋊D6111yescharacteristic
843C22×C4C23×D6111yescharacteristic
844Q16—1228no—
845Q16—1228no—
846SD16—1228no—
847SD16—1228no—
848SD16—1228no—
849SD16—1228no—
850D8—1228no—
851D8—1228no—
852M16—614no—
853M16—1222no—
854M16—1222no—
855M16—1222no—
856M16—1222no—
857M16—1222no—
858M16—1222no—
859M16—1222no—
860C2×C8—614no—
861C2×C8—1222no—
862C2×C8—1222no—
863C2×C8—1222no—
864C2×C8—1222no—
865C2×C8—1222no—
866C4⋊C4—28no—
867C4⋊C4—22no—
868C4⋊C4—22no—
869C4⋊C4—1222no—
870C4⋊C4—2441no—
871C22⋊C4—28no—
872C22⋊C4—28no—
873C22⋊C4—22no—
874C22⋊C4—1222no—
875C22⋊C4—2441no—
876C22⋊C4C2×C22⋊D6114yes—
877C42—22no—
878C42—22no—
879C42—1222no—
880C42—2441no—
881C23—22no—
882C23—22no—
883C23—41no—
884C23—41no—
885C23—41no—
886C23—41no—
887C23—81no—
888C23—82no—
889C23—82no—
890C23—1222no—
891C23—4882no—
892C23—2441no—
893C23—2441no—
894C23#1451974611yescharacteristic
895C23#1451974611yescharacteristic
896C23#1451974811yescharacteristic
897C23#1451974811yescharacteristic
898C23#1451977311yescharacteristic
899C23#1451977311yescharacteristic
900C23C22×C22⋊D6111yescharacteristic
901Q8—22no—
902Q8—22no—
903Q8—22no—
904Q8—22no—
905Q8—41no—
906Q8—41no—
907Q8—41no—
908Q8—41no—
909Q8—1222no—
910Q8—1222no—
911Q8—2441no—
912Q8—2441no—
913D4—22no—
914D4—22no—
915D4—22no—
916D4—22no—
917D4—42no—
918D4—42no—
919D4—42no—
920D4—42no—
921D4—42no—
922D4—42no—
923D4—42no—
924D4—42no—
925D4—41no—
926D4—41no—
927D4—41no—
928D4—41no—
929D4—88no—
930D4—1222no—
931D4—1222no—
932D4—2442no—
933D4—2442no—
934D4—2442no—
935D4—2442no—
936D4—2441no—
937D4—2441no—
938C2×C4—24no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—42no—
946C2×C4—42no—
947C2×C4—42no—
948C2×C4—42no—
949C2×C4—42no—
950C2×C4—42no—
951C2×C4—42no—
952C2×C4—42no—
953C2×C4—82no—
954C2×C4—1222no—
955C2×C4—4882no—
956C2×C4—2442no—
957C2×C4—2441no—
958C2×C4—2441no—
959C2×C4—2442no—
960C2×C4—2442no—
961C2×C4—2442no—
962C2×C4—2442no—
963C2×C4#1451974511yescharacteristic
964C2×C4#1451974511yescharacteristic
965C2×C4#1451974511yescharacteristic
966C2×C4#1451974511yescharacteristic
967C2×C4#1451974511yescharacteristic
968C2×C4#1451974511yescharacteristic
969C2×C4#1451974511yescharacteristic
970C2×C4#1451974511yescharacteristic
971C2×C4#1451974611yescharacteristic
972C2×C4#1451974611yescharacteristic
973C2×C4#1451974811yescharacteristic
974C2×C4#1451974811yescharacteristic
975C2×C4#1451974911yescharacteristic
976C2×C4#1451974911yescharacteristic
977C2×C4#1451974911yescharacteristic
978C2×C4#1451974911yescharacteristic
979C2×C4#1451974911yescharacteristic
980C2×C4#1451974911yescharacteristic
981C2×C4#1451974911yescharacteristic
982C2×C4#1451974911yescharacteristic
983C2×C4#1451977311yescharacteristic
984C2×C4#1451977311yescharacteristic
985C2×C4C2×D4×D6111yescharacteristic
986C2×C4C2×D4×D6111yescharacteristic
987C2×C4C2×D4×D6111yescharacteristic
988C2×C4C22×C22⋊D6111yescharacteristic
989C2×C4C22×C22⋊D6111yescharacteristic
990C2×C4C2×#1175822411yescharacteristic
991C8—1224no—
992C8—1224no—
993C22—41no—
994C22—41no—
995C22—41no—
996C22—41no—
997C22—41no—
998C22—41no—
999C22—41no—
1000C22—44no—
1001C22—44no—
1002C22—42no—
1003C22—42no—
1004C22—82no—
1005C22—82no—
1006C22—82no—
1007C22—82no—
1008C22—4882no—
1009C22—4882no—
1010C22—4882no—
1011C22—2442no—
1012C22#1683967011yescharacteristic
1013C22#1683967011yescharacteristic
1014C22#1683967011yescharacteristic
1015C22#1683967011yescharacteristic
1016C22C2×#1451974611yescharacteristic
1017C22C2×#1451974811yescharacteristic
1018C22C2×#1451977311yescharacteristic
1019C4—44no—
1020C4—42no—
1021C4—42no—
1022C4—4882no—
1023C4—2442no—
1024C4#1683967011yescharacteristic
1025C4#1683967011yescharacteristic
1026C4#1683967011yescharacteristic
1027C4#1683967011yescharacteristic
1028C4C2×#1451974511yescharacteristic
1029C4C2×#1451974511yescharacteristic
1030C4C2×#1451974911yescharacteristic
1031C4C2×#1451974911yescharacteristic
1032C2—21no—
1033C2—21no—
1034C2—21no—
1035C2—21no—
1036C2—21no—
1037C2—21no—
1038C2—21no—
1039C2—82no—
1040C2—82no—
1041C2—4882no—
1042C2C2×#1683967011yescharacteristic
subgroupG/H
centerC4#16839670
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#3449C2
socleC2×C61C2×#392
hypercenter#3449D61
hypocenterC61#23412
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C23×C4 ◁ #3449

Complements

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

NH ≅ G/Ntype
1. C2×#16840560C2semidirect
2. C2×#16840560C2semidirect
3. C2×#16839779C2semidirect
4. #21454338C2semidirect
5. C2×#16839735C2semidirect
6. #21446879C2semidirect
7. #21446872C2semidirect
8. C2×#16839532C2semidirect
9. C61×#3449C2semidirect
20. C2×#14519808C22semidirect
24. C2×#14519803C22semidirect
33. #16839779C22semidirect
35. #16839771C22semidirect
36. #16839767C22semidirect
40. #16839735C22semidirect
42. #16839532C22semidirect
47. C61×#536C22semidirect
49. C61×#535C22semidirect
65. C2×#11758222D4semidirect
67. C22×Dic122D4semidirect
68. C22×D244D4semidirect
106. C2×#11758194D4semidirect
107. C2×#11758194D4semidirect
108. C2×#11758194D4semidirect
112. C22×#92418D4semidirect
513. #3449D61semidirect
556. #536C2×D61semidirect
558. #535C2×D61semidirect
576. C61#23412semidirect

Maximal subgroups

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

subgroupindex
C2×#168405602
C2×#168397792
#214543382
C2×#168397352
#214468792
#214468722
C2×#168395322
C61×#34492
#2341261