Finite Group Databasebeta

← #72271774

Subgroups — #72271774

Order 1536.

2234 conjugacy classes of subgroups.

The subgroup lattice has 1350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11664505C211yesmaximal, characteristic
2#10792695C211yesmaximal, characteristic, complemented
3#10792694C211yesmaximal, characteristic, complemented
4#10704133C211yesmaximal, characteristic, complemented
5#10704132C211yesmaximal, characteristic, complemented
6#10701785C211yesmaximal, characteristic
7#10701779C211yesmaximal, characteristic
8#10701613C211yesmaximal, characteristic, complemented
9#10701608C211yesmaximal, characteristic, complemented
10#10701600C211yesmaximal, characteristic, complemented
11#10701595C211yesmaximal, characteristic, complemented
12#10701591C211yesmaximal, characteristic, complemented
13#10701580C211yesmaximal, characteristic, complemented
14#10701579C211yesmaximal, characteristic, complemented
15C3×#10950C211yesmaximal, characteristic, complemented
16#375718—31nomaximal, Sylow
17C2×#5830C2211yescharacteristic
18#85725C2211yescharacteristic
19C2×C3×#421C2211yescharacteristic
20C3×#2896C2211yescharacteristic
21C3×#2879C2211yescharacteristic
22C3×#2873C2211yescharacteristic
23C2×#5240C2211yescharacteristic
24C2×#5236C2211yescharacteristic
25#84072C2211yescharacteristic
26C2×#5131C2211yescharacteristic
27C2×#5131C2211yescharacteristic
28C2×#5131C2211yescharacteristic
29C22×#823C2211yescharacteristic
30#83747C2211yescharacteristic
31#83747C2211yescharacteristic
32#83747C2211yescharacteristic
33#83747C2211yescharacteristic
34#82269C2211yescharacteristic
35C2×#5001C2211yescharacteristic
36#78954C414yescomplemented
37#78921C414yescomplemented
38#78876—24no—
39#78827—24no—
40C2×C3×#344C2211yescharacteristic
41C2×C3×#338C2211yescharacteristic
42C2×C3×H(3,ℤ/4)C2211yescharacteristic
43C2×C3⋊#338C2211yescharacteristic
44C2×#4556C2211yescharacteristic
45C2×#4557C2211yescharacteristic
46C2×#4557C2211yescharacteristic
47C2×#4557C2211yescharacteristic
48C2×#4557C2211yescharacteristic
49C2×#4557C2211yescharacteristic
50#71982C2211yescharacteristic
51#71593C2211yescharacteristic
52#71592C2211yescharacteristic
53#71578C2211yescharacteristic
54C2×#4531C2211yescharacteristic
55C2×#4531C2211yescharacteristic
56#69895—24no—
57#68717—24no—
58#60619—31no—
59#20370—31no—
60#20370—31no—
61#11389—31no—
62#11389—31no—
63#10989—31no—
64#10987—31no—
65#10953—31no—
66#10953—31no—
67#10951—31no—
68#10951—31no—
69#10950—31no—
70#10950D311yescharacteristic, complemented
71#10948—31no—
72#10948—31no—
73C22×C3×#41C2311yescharacteristic
74C23×D12C2311yescharacteristic
75C22×C3×M16C2311yescharacteristic
76C22×C3×M16C2311yescharacteristic
77C22×C3×M16C2311yescharacteristic
78C22×C3×M16C2311yescharacteristic
79C2×C3×#117C2311yescharacteristic
80C2×C3×#117C2311yescharacteristic
81#5830—22no—
82#5830—22no—
83#5830—41no—
84#5830—41no—
85C2×#947C2×C412yes—
86C2×#940C2×C412yes—
87C2×#937—41no—
88C2×#930—41no—
89C2×#926C2311yescharacteristic
90C2×#926C2311yescharacteristic
91C2×#926C2311yescharacteristic
92C2×#926C2311yescharacteristic
93C2×#926C2311yescharacteristic
94C22×#208C2311yescharacteristic
95C22×#208C2311yescharacteristic
96#5519—22no—
97#5519—41no—
98#5517—41no—
99#5517C2×C414yes—
100#5500—22no—
101#5483—41no—
102#5470—41no—
103C3×#421—22no—
104C3×#421—41no—
105C2×C3×#104—22no—
106C3×#419C2×C412yes—
107C3×#418C2×C412yes—
108C3×#417—22no—
109C3×#416—22no—
110C3×#408—22no—
111C3×#408—22no—
112C3×#407—41no—
113C3×#405—22no—
114C3×#405—22no—
115C3×C4×M16—22no—
116#5240—22no—
117#5240—22no—
118#5236—22no—
119#5236—41no—
120C2×#837—22no—
121#5233—22no—
122#5232—22no—
123#5225C2×C412yes—
124C2×#834—41no—
125#5215C2×C412yes—
126#5131—22no—
127#5131—22no—
128#5131—22no—
129#5131—41no—
130#5131—41no—
131#5131C2×C414yes—
132C2×#823—22no—
133C2×#823—22no—
134C2×#823—41no—
135#5122—22no—
136#5122—22no—
137#5122—22no—
138#5122D414yes—
139Dic3×M16—22no—
140Dic3×M16—22no—
141Dic3×M16—22no—
142Dic3×M16C2×C414yes—
143C2×#821—22no—
144C2×#821—22no—
145C2×#821—22no—
146#5101—22no—
147#5101—22no—
148#5101—22no—
149#5101D414yes—
150#5001—22no—
151#5001C2×C414yes—
152#4988—22no—
153C2×#809—22no—
154#4955—41no—
155#4939—22no—
156#4800—28no—
157#4794—28no—
158#4764—28no—
159#4760—28no—
160C3×#344—41no—
161C3×#338—22no—
162C3×H(3,ℤ/4)—41no—
163C3⋊#338—22no—
164#4557—22no—
165#4557—22no—
166#4557—22no—
167#4557—22no—
168#4557—41no—
169#4556—41no—
170#4555—41no—
171#4531—22no—
172#4531—22no—
173#4527—41no—
174#4526—41no—
175#4523—41no—
176#3458—31no—
177C2×#535—31no—
178#3140—34no—
179#3138—34no—
180#3136—64no—
181#3136—64no—
182C2×#421—31no—
183C2×#421C2×D311yescharacteristic
184#2896—31no—
185#2896C2×D311yescharacteristic
186C2×#418—31no—
187C2×#418—31no—
188C2×#418—31no—
189C2×#418—31no—
190C22×#100—31no—
191C2×#410—31no—
192#2879C2×D311yescharacteristic
193#2873—31no—
194#2873—31no—
195#2873—31no—
196#2873—31no—
197#2873C2×D311yescharacteristic
198#2309—31no—
199#1747—64no—
200#1747—64no—
201C2×#344—31no—
202C2×#344C2×D311yescharacteristic
203#1740—31no—
204#1740—31no—
205#1733—31no—
206#1733—31no—
207C2×#338—31no—
208C2×#338C2×D311yescharacteristic
209C2×H(3,ℤ/4)—31no—
210C2×H(3,ℤ/4)—31no—
211C2×H(3,ℤ/4)—31no—
212C2×H(3,ℤ/4)—31no—
213C2×H(3,ℤ/4)—31no—
214C2×H(3,ℤ/4)—31no—
215C2×H(3,ℤ/4)—31no—
216C2×H(3,ℤ/4)C2×D311yescharacteristic
217C24×D3—21no—
218C2×C3×#41—21no—
219C2×C3×#41—21no—
220C2×C3×#41—21no—
221C2×C3×#41—21no—
222C2×C3×#41—21no—
223C2×C3×#41—21no—
224C2×C3×#41—21no—
225C2×C3×#41—21no—
226C2×C3×#41—21no—
227C2×C3×#41—21no—
228C2×C3×#41—21no—
229C2×C3×#41—21no—
230C22×C3×Q8C22×C411yescharacteristic
231C22×C3×D4—21no—
232C22×C3×D4C22×C411yescharacteristic
233C23×C3×C4—21no—
234C23×C3×C4C2411yescharacteristic
235C22×#67—42no—
236C22×D12—21no—
237C22×D12—21no—
238C22×D12—21no—
239C22×D12—21no—
240C22×D12—21no—
241C22×D12—21no—
242C22×D12—21no—
243C22×D12—21no—
244C22×D12—21no—
245C22×D12—21no—
246C22×D12—21no—
247C22×D12—21no—
248C22×D12—21no—
249C22×D12C22×C412yes—
250C2×C3×M16—21no—
251C2×C3×M16—21no—
252C2×C3×M16—21no—
253C2×C3×M16—21no—
254C2×C3×M16—21no—
255C2×C3×M16—21no—
256C2×C3×M16—21no—
257C2×C3×M16—21no—
258C2×C3×M16—21no—
259C2×C3×M16—21no—
260C2×C3×M16—21no—
261C2×C3×M16—21no—
262C2×C3×M16—21no—
263C2×C3×M16—21no—
264C2×C3×M16—21no—
265C2×C3×M16—21no—
266C2×C3×M16—21no—
267C2×C3×M16—21no—
268C2×C3×M16—21no—
269C2×C3×M16—21no—
270C2×C3×M16—21no—
271C2×C3×M16C22×C412yes—
272C2×C3×M16C2×D412yes—
273C2×C3×M16#4112yes—
274C22×C3×C8—21no—
275C22×C3×C8C2×D412yes—
276C22×C3×C8#4112yes—
277C22×C3×C8#4112yes—
278C3×#117—21no—
279C3×#117—21no—
280C3×#117—21no—
281C3×#117—21no—
282C3×#117—21no—
283C3×#117—21no—
284C3×#117—21no—
285C3×#117C22×C412yes—
286C2×C3×C4⋊C4—21no—
287C2×C3×C4⋊C4—21no—
288C2×C3×C22⋊C4—21no—
289C2×C3×C22⋊C4—21no—
290C2×C3×C42—21no—
291C2×C3×C42#4112yes—
292C2×#217—21no—
293C2×#217—21no—
294C2×#217—21no—
295C2×#217—21no—
296C2×#217—21no—
297#947—24no—
298#947—42no—
299#940—24no—
300#940—42no—
301#937—44no—
302#937—44no—
303#930—44no—
304#930—44no—
305C2×(C2×D3)⋊C4—42no—
306C2×(C2×D3)⋊C4—44no—
307#926—21no—
308#926—21no—
309#926—21no—
310#926—21no—
311#926—21no—
312#926—21no—
313#926—21no—
314#926—21no—
315#926—21no—
316#926—21no—
317#926—21no—
318#926—21no—
319#926—21no—
320#926—21no—
321#926—21no—
322#926C22×C412yes—
323#926C2×D412yes—
324#926C2×D412yes—
325#926#4112yes—
326#926#4112yes—
327C2×C4⋊Dic3—21no—
328C2×C4⋊Dic3—21no—
329C2×C4⋊Dic3—21no—
330C2×C4⋊Dic3—21no—
331C2×C4⋊Dic3—21no—
332#924—44no—
333C2×C4×Dic3—21no—
334C2×C4×Dic3—21no—
335C2×C4×Dic3—21no—
336C2×C4×Dic3C22×C412yes—
337C2×C4×Dic3#4112yes—
338C2×#208—21no—
339C2×#208—21no—
340C2×#208—21no—
341C2×#208—21no—
342C2×#208—21no—
343C2×#208—21no—
344C2×#208—21no—
345C2×#208—21no—
346C2×#208—21no—
347C2×#208C22×C412yes—
348C2×#208C2×D412yes—
349C2×#208#4112yes—
350C22×C3⋊C8—21no—
351C22×C3⋊C8C2×D412yes—
352#890—24no—
353#890—42no—
354#888—24no—
355#888—42no—
356#878—44no—
357#878—44no—
358#870—42no—
359#869—42no—
360C4×Dic6—44no—
361C3×#104—44no—
362C3×#103—24no—
363C3×#102—24no—
364C3×C22⋊C8—44no—
365C3×#97—24no—
366C3×C4×C8—24no—
367#837—44no—
368#835—24no—
369#834—44no—
370#832—24no—
371#823—44no—
372#821—28no—
373#821—44no—
374#821—44no—
375#815—24no—
376#815—24no—
377#815—24no—
378#815C22⋊C418yescomplemented
379C8×Dic3—24no—
380C8×Dic3—24no—
381C8×Dic3—24no—
382C8×Dic3C22⋊C418yescomplemented
383#809—28no—
384C22×#41C22×D311yescharacteristic
385C23×D4—31no—
386C22×M16—31no—
387C22×M16—31no—
388C22×M16C22×D311yescharacteristic
389C22×M16C22×D311yescharacteristic
390C22×M16C22×D311yescharacteristic
391C22×M16C22×D311yescharacteristic
392#544—62no—
393#544—62no—
394#544—121no—
395#543—121no—
396#535—62no—
397#535—62no—
398#535—121no—
399#535—121no—
400#533—34no—
401#533—121no—
402#533—121no—
403C2×#127—32no—
404C2×#124—32no—
405C2×#121—121no—
406C2×#120—121no—
407C2×#117—31no—
408C2×#117—31no—
409C2×#117—31no—
410C2×#117—31no—
411C2×#117—31no—
412C2×#117C22×D311yescharacteristic
413C2×#117C22×D311yescharacteristic
414#490—68no—
415#489—68no—
416#488—68no—
417#486—68no—
418#421—22no—
419#421—41no—
420#421—62no—
421#421—121no—
422C2×#104—22no—
423C2×#104—62no—
424#419—32no—
425#419C4×D312yes—
426#418—32no—
427#418—34no—
428#418—34no—
429#418—62no—
430#418—62no—
431#418—62no—
432#418—62no—
433#418—121no—
434#418—121no—
435#418C4×D312yes—
436#417—22no—
437#417—62no—
438#416—22no—
439#416—62no—
440C2×#102—62no—
441C2×#102—62no—
442C2×#102—62no—
443C2×#102—62no—
444C2×#100—62no—
445C2×#100—62no—
446C2×#100—121no—
447#410—62no—
448#410—62no—
449C2×#99—121no—
450#408—22no—
451#408—22no—
452#407—41no—
453#405—22no—
454#405—22no—
455#405—34no—
456#405—34no—
457#405—62no—
458#405—62no—
459#405—62no—
460#405—62no—
461#405—62no—
462#405—62no—
463C4×M16—22no—
464C4×M16—34no—
465C4×M16—62no—
466C4×M16—62no—
467C4×M16—62no—
468#390—62no—
469#390—62no—
470#379—121no—
471#344—41no—
472#344—121no—
473#342—121no—
474#342—121no—
475#339—121no—
476#339—121no—
477#338—22no—
478#338—62no—
479H(3,ℤ/4)—41no—
480H(3,ℤ/4)—62no—
481H(3,ℤ/4)—62no—
482H(3,ℤ/4)—62no—
483H(3,ℤ/4)—62no—
484H(3,ℤ/4)—62no—
485H(3,ℤ/4)—62no—
486H(3,ℤ/4)—121no—
487C24×C3—21no—
488C24×C3H(5,𝔽2)11yescharacteristic
489C23×D3—22no—
490C23×D3—41no—
491C23×D3—41no—
492C23×D3—41no—
493C23×D3—41no—
494C23×D3—41no—
495C23×D3—41no—
496C23×D3—162no—
497C3×#41—41no—
498C3×#41—41no—
499C3×#41—41no—
500C3×#41—41no—
501C3×#41—41no—
502C3×#41—41no—
503C3×#41—41no—
504C3×#41—41no—
505C3×#41—41no—
506C3×#41—41no—
507C3×#41—41no—
508C3×#41—41no—
509C3×#41—41no—
510C3×#41—41no—
511C3×#41—41no—
512C3×#41—41no—
513C2×C3×Q8—21no—
514C2×C3×Q8—21no—
515C2×C3×Q8—21no—
516C2×C3×Q8—21no—
517C2×C3×Q8—21no—
518C2×C3×Q8—21no—
519C2×C3×D4—21no—
520C2×C3×D4—21no—
521C2×C3×D4—21no—
522C2×C3×D4—21no—
523C2×C3×D4—21no—
524C2×C3×D4—21no—
525C2×C3×D4—41no—
526C2×C3×D4—41no—
527C2×C3×D4—41no—
528C2×C3×D4—41no—
529C2×C3×D4—41no—
530C2×C3×D4—41no—
531C22×C3×C4—21no—
532C22×C3×C4—22no—
533C22×C3×C4—41no—
534C22×C3×C4—41no—
535C22×C3×C4—41no—
536C22×C3×C4—41no—
537C22×C3×C4—41no—
538C22×C3×C4—41no—
539C22×C3×C4—41no—
540C22×C3×C4C23×C411yescharacteristic
541C22×C3×C4C22×D411yescharacteristic
542C22×C3×C4C22×D411yescharacteristic
543C22×C3×C4C2×#4111yescharacteristic
544C22×C3×C4C2×#4111yescharacteristic
545C22×C3×C4C2×#4111yescharacteristic
546C22×C3×C4C2×#4111yescharacteristic
547C22×C3×C4C2×#4111yescharacteristic
548C22×C3×C4C2×#4111yescharacteristic
549C22×C3×C4C2×#4111yescharacteristic
550C22×C3×C4C2×#4111yescharacteristic
551C22×C3×C4H(5,𝔽2)11yescharacteristic
552C22×C3×C4H(5,𝔽2)11yescharacteristic
553C22×C3×C4H(5,𝔽2)11yescharacteristic
554C2×#67—48no—
555C2×#67—164no—
556C22×Dic3—22no—
557C22×Dic3—22no—
558C22×Dic3—41no—
559C22×Dic3—41no—
560C22×Dic3—41no—
561C2×D12—22no—
562C2×D12—22no—
563C2×D12—22no—
564C2×D12—22no—
565C2×D12—22no—
566C2×D12—22no—
567C2×D12—41no—
568C2×D12—41no—
569C2×D12—41no—
570C2×D12—41no—
571C2×D12—41no—
572C2×D12—41no—
573C2×D12—41no—
574C2×D12—41no—
575C2×D12—41no—
576C2×D12—41no—
577C2×D12—41no—
578C2×D12—41no—
579C2×D12—41no—
580C2×D12—41no—
581C2×D12—41no—
582C2×D12—41no—
583C2×D12—41no—
584C2×D12—41no—
585C2×D12—41no—
586C2×D12—41no—
587C2×D12—41no—
588C2×D12—41no—
589C2×Dic6—44no—
590C3×M16—22no—
591C3×M16—22no—
592C3×M16—22no—
593C3×M16—22no—
594C3×M16—22no—
595C3×M16—22no—
596C3×M16—41no—
597C3×M16—41no—
598C3×M16—41no—
599C3×M16—41no—
600C3×M16—41no—
601C3×M16—41no—
602C3×M16—41no—
603C3×M16—41no—
604C3×M16—41no—
605C3×M16—41no—
606C2×C3×C8—22no—
607C2×C3×C8—22no—
608C2×C3×C8—22no—
609C2×C3×C8—22no—
610C2×C3×C8—22no—
611C2×C3×C8—22no—
612C2×C3×C8—22no—
613C2×C3×C8—22no—
614C2×C3×C8—22no—
615C2×C3×C8—41no—
616C2×C3×C8—41no—
617C2×C3×C8C2×C22⋊C414yes—
618C3×C4⋊C4—22no—
619C3×C4⋊C4—41no—
620C3×C4⋊C4—41no—
621C3×C4⋊C4—41no—
622C3×C22⋊C4—22no—
623C3×C22⋊C4—41no—
624C3×C22⋊C4—41no—
625C3×C22⋊C4—41no—
626C3×C42—22no—
627C3×C42—22no—
628C3×C42—22no—
629C3×C42—41no—
630#217—22no—
631#217—22no—
632#217—22no—
633#217—22no—
634#217—22no—
635#217—41no—
636#217—41no—
637#217—41no—
638#217—41no—
639#217—41no—
640(C2×D3)⋊C4—48no—
641(C2×D3)⋊C4—164no—
642C4⋊Dic3—22no—
643C4⋊Dic3—22no—
644C4⋊Dic3—22no—
645C4⋊Dic3—22no—
646C4⋊Dic3—22no—
647C4⋊Dic3—44no—
648C4⋊Dic3—41no—
649C4⋊Dic3—41no—
650C4⋊Dic3—41no—
651C4⋊Dic3—41no—
652C4⋊Dic3—41no—
653Dic3⋊C4—44no—
654Dic3⋊C4—44no—
655C4×Dic3—22no—
656C4×Dic3—22no—
657C4×Dic3—22no—
658C4×Dic3—22no—
659C4×Dic3—22no—
660C4×Dic3—22no—
661C4×Dic3—41no—
662C4×Dic3—41no—
663C4×Dic3—41no—
664C4×Dic3C2×C22⋊C414yes—
665#208—22no—
666#208—22no—
667#208—22no—
668#208—22no—
669#208—22no—
670#208—22no—
671#208—41no—
672#208—41no—
673C2×C3⋊C8—22no—
674C2×C3⋊C8—22no—
675C2×C3⋊C8—22no—
676C2×C3⋊C8—41no—
677C2×C3⋊C8—41no—
678C2×C3⋊C8C2×C22⋊C414yes—
679C25—61no—
680C2×#41—21no—
681C2×#41—21no—
682C2×#41—21no—
683C2×#41—21no—
684C2×#41—21no—
685C2×#41—21no—
686C2×#41—21no—
687C2×#41—21no—
688C2×#41—21no—
689C2×#41—21no—
690C2×#41—21no—
691C2×#41—21no—
692C22×Q8C2×C4×D311yescharacteristic
693C22×D4—21no—
694C22×D4—32no—
695C22×D4—61no—
696C22×D4—61no—
697C22×D4—61no—
698C22×D4—61no—
699C22×D4—61no—
700C22×D4—61no—
701C22×D4—61no—
702C22×D4—61no—
703C22×D4—61no—
704C22×D4—61no—
705C22×D4—61no—
706C22×D4—61no—
707C22×D4—61no—
708C22×D4—122no—
709C22×D4C2×C4×D311yescharacteristic
710C23×C4—21no—
711C23×C4C23×D311yescharacteristic
712C2×M16—21no—
713C2×M16—21no—
714C2×M16—21no—
715C2×M16—21no—
716C2×M16—21no—
717C2×M16—21no—
718C2×M16—21no—
719C2×M16—21no—
720C2×M16—21no—
721C2×M16—21no—
722C2×M16—21no—
723C2×M16—21no—
724C2×M16—21no—
725C2×M16—21no—
726C2×M16—21no—
727C2×M16—21no—
728C2×M16—21no—
729C2×M16—21no—
730C2×M16—21no—
731C2×M16—21no—
732C2×M16—21no—
733C2×M16—32no—
734C2×M16—32no—
735C2×M16—32no—
736C2×M16—61no—
737C2×M16—61no—
738C2×M16—61no—
739C2×M16—61no—
740C2×M16—61no—
741C2×M16—61no—
742C2×M16—61no—
743C2×M16—61no—
744C2×M16—61no—
745C2×M16C2×C4×D312yes—
746C2×M16#23512yes—
747C2×M16D3×D412yes—
748C22×C8—21no—
749C22×C8—32no—
750C22×C8—61no—
751C22×C8#23512yes—
752C22×C8D3×D412yes—
753C22×C8#23712yes—
754C4⋊Q8—64no—
755C4⋊Q8—122no—
756C4⋊Q8—122no—
757#127—64no—
758#127—122no—
759#125—64no—
760#125—122no—
761#125—122no—
762#124—64no—
763#124—122no—
764C22⋊Q8—124no—
765C22⋊Q8—124no—
766C22⋊Q8—124no—
767#121—124no—
768#121—124no—
769#120—124no—
770#120—124no—
771C4×Q8—124no—
772#117—21no—
773#117—21no—
774#117—21no—
775#117—21no—
776#117—21no—
777#117—21no—
778#117—21no—
779#117—32no—
780#117—32no—
781#117—32no—
782#117—32no—
783#117—32no—
784#117—61no—
785#117—61no—
786#117—61no—
787#117—61no—
788#117—61no—
789#117—61no—
790#117—61no—
791#117—61no—
792#117—61no—
793#117—61no—
794#117—61no—
795#117—61no—
796#117—61no—
797#117—61no—
798#117—61no—
799#117C2×C4×D312yes—
800C2×C4⋊C4—21no—
801C2×C4⋊C4—21no—
802C2×C4⋊C4—61no—
803C2×C4⋊C4—61no—
804C2×C4⋊C4—61no—
805C2×C4⋊C4—61no—
806C2×C4⋊C4—61no—
807C2×C22⋊C4—21no—
808C2×C22⋊C4—21no—
809C2×C22⋊C4—61no—
810C2×C22⋊C4—61no—
811C2×C22⋊C4—61no—
812C2×C22⋊C4—61no—
813C2×C22⋊C4—61no—
814C2×C22⋊C4—122no—
815C2×C22⋊C4—124no—
816C2×C42—21no—
817C2×C42—32no—
818C2×C42—32no—
819C2×C42—61no—
820C2×C42—61no—
821C2×C42—61no—
822C2×C42#23712yes—
823#104—44no—
824#104—124no—
825#103—24no—
826#103—64no—
827#102—24no—
828#102—68no—
829#102—64no—
830#102—68no—
831#102—124no—
832#102—124no—
833#100—124no—
834#99—124no—
835C22⋊C8—44no—
836#97—24no—
837#97—38no—
838#97—64no—
839#97—64no—
840#97—64no—
841C4×C8—24no—
842C4×C8—38no—
843C4×C8—64no—
844C4×C8—64no—
845C4×C8—64no—
846C23×C3—41no—
847C23×C3—41no—
848C23×C3—41no—
849C23×C3—81no—
850C23×C3—82no—
851C23×C3#51811yescharacteristic
852C23×C3#53511yescharacteristic
853C23×C3#53511yescharacteristic
854C23×C3#55111yescharacteristic
855C23×C3#55111yescharacteristic
856C23×C3#55511yescharacteristic
857C23×C3#55511yescharacteristic
858C22×D3—42no—
859C22×D3—42no—
860C22×D3—42no—
861C22×D3—84no—
862C22×D3—84no—
863C22×D3—81no—
864C22×D3—81no—
865C22×D3—81no—
866C22×D3—81no—
867C22×D3—162no—
868C22×D3—162no—
869C22×D3—162no—
870C22×D3—162no—
871C22×D3—162no—
872C3×Q8—41no—
873C3×Q8—41no—
874C3×Q8—41no—
875C3×Q8—41no—
876C3×D4—41no—
877C3×D4—41no—
878C3×D4—41no—
879C3×D4—41no—
880C3×D4—81no—
881C3×D4—81no—
882C3×D4—81no—
883C3×D4—81no—
884C2×C3×C4—42no—
885C2×C3×C4—41no—
886C2×C3×C4—42no—
887C2×C3×C4—41no—
888C2×C3×C4—41no—
889C2×C3×C4—81no—
890C2×C3×C4—81no—
891C2×C3×C4—81no—
892C2×C3×C4—81no—
893C2×C3×C4—82no—
894C2×C3×C4—161no—
895C2×C3×C4C22×C22⋊C411yescharacteristic
896C2×C3×C4C4×#4111yescharacteristic
897C2×C3×C4C4×#4111yescharacteristic
898C2×C3×C4C4×#4111yescharacteristic
899C2×C3×C4C4×#4111yescharacteristic
900C2×C3×C4#51811yescharacteristic
901C2×C3×C4#52511yescharacteristic
902C2×C3×C4#52511yescharacteristic
903C2×C3×C4#52511yescharacteristic
904C2×C3×C4#52511yescharacteristic
905C2×C3×C4#53211yescharacteristic
906C2×C3×C4#53211yescharacteristic
907C2×C3×C4#53211yescharacteristic
908C2×C3×C4#53211yescharacteristic
909C2×C3×C4#53511yescharacteristic
910C2×C3×C4#53511yescharacteristic
911C2×C3×C4#55111yescharacteristic
912C2×C3×C4#55111yescharacteristic
913C2×C3×C4#55111yescharacteristic
914C2×C3×C4#55111yescharacteristic
915C2×C3×C4#55111yescharacteristic
916C2×C3×C4#55111yescharacteristic
917C2×C3×C4#55511yescharacteristic
918C2×C3×C4#55511yescharacteristic
919C2×C3×C4#55511yescharacteristic
920C2×C3×C4#55511yescharacteristic
921C2×C3×C4#55511yescharacteristic
922C2×C3×C4#55511yescharacteristic
923#67—168no—
924C2×Dic3—24no—
925C2×Dic3—42no—
926C2×Dic3—42no—
927C2×Dic3—42no—
928C2×Dic3—42no—
929C2×Dic3—82no—
930C2×Dic3—82no—
931C2×Dic3—161no—
932C2×Dic3—161no—
933C2×Dic3—161no—
934D12—42no—
935D12—42no—
936D12—42no—
937D12—42no—
938D12—81no—
939D12—81no—
940D12—81no—
941D12—81no—
942Dic6—164no—
943C3×C8—24no—
944C3×C8—42no—
945C3×C8—42no—
946C3×C8—42no—
947C3⋊C8—24no—
948C3⋊C8—42no—
949C24—21no—
950C24—62no—
951C24—121no—
952C24—121no—
953C24—121no—
954C24—121no—
955C24—121no—
956C24—121no—
957C24—482no—
958C24#100911yescharacteristic
959#41—41no—
960#41—41no—
961#41—41no—
962#41—41no—
963#41—41no—
964#41—41no—
965#41—41no—
966#41—41no—
967#41—41no—
968#41—41no—
969#41—41no—
970#41—41no—
971#41—41no—
972#41—41no—
973#41—41no—
974#41—41no—
975C2×Q8—21no—
976C2×Q8—21no—
977C2×Q8—21no—
978C2×Q8—21no—
979C2×Q8—21no—
980C2×Q8—21no—
981C2×Q8—124no—
982C2×D4—21no—
983C2×D4—21no—
984C2×D4—21no—
985C2×D4—21no—
986C2×D4—21no—
987C2×D4—21no—
988C2×D4—41no—
989C2×D4—41no—
990C2×D4—41no—
991C2×D4—41no—
992C2×D4—41no—
993C2×D4—41no—
994C2×D4—62no—
995C2×D4—62no—
996C2×D4—62no—
997C2×D4—62no—
998C2×D4—62no—
999C2×D4—62no—
1000C2×D4—128no—
1001C2×D4—121no—
1002C2×D4—121no—
1003C2×D4—121no—
1004C2×D4—121no—
1005C2×D4—121no—
1006C2×D4—121no—
1007C2×D4—121no—
1008C2×D4—121no—
1009C2×D4—121no—
1010C2×D4—121no—
1011C2×D4—121no—
1012C2×D4—121no—
1013C2×D4—121no—
1014C2×D4—121no—
1015C2×D4—121no—
1016C2×D4—121no—
1017C2×D4—121no—
1018C2×D4—121no—
1019C2×D4—121no—
1020C2×D4—121no—
1021C2×D4—121no—
1022C2×D4—121no—
1023C2×D4—484no—
1024C22×C4—21no—
1025C22×C4—22no—
1026C22×C4—41no—
1027C22×C4—41no—
1028C22×C4—41no—
1029C22×C4—41no—
1030C22×C4—41no—
1031C22×C4—41no—
1032C22×C4—41no—
1033C22×C4—62no—
1034C22×C4—62no—
1035C22×C4—121no—
1036C22×C4—121no—
1037C22×C4—121no—
1038C22×C4C22×C4×D311yescharacteristic
1039C22×C4C2×#23511yescharacteristic
1040C22×C4C2×#23511yescharacteristic
1041C22×C4C2×D3×D411yescharacteristic
1042C22×C4C2×D3×D411yescharacteristic
1043C22×C4C2×#23711yescharacteristic
1044C22×C4C2×#23711yescharacteristic
1045C22×C4#100411yescharacteristic
1046C22×C4#100411yescharacteristic
1047C22×C4D3×#4111yescharacteristic
1048C22×C4D3×#4111yescharacteristic
1049C22×C4D3×#4111yescharacteristic
1050C22×C4D3×#4111yescharacteristic
1051C22×C4#100911yescharacteristic
1052M16—22no—
1053M16—22no—
1054M16—22no—
1055M16—22no—
1056M16—22no—
1057M16—22no—
1058M16—41no—
1059M16—41no—
1060M16—41no—
1061M16—41no—
1062M16—41no—
1063M16—41no—
1064M16—41no—
1065M16—41no—
1066M16—41no—
1067M16—41no—
1068M16—62no—
1069M16—62no—
1070M16—62no—
1071M16—62no—
1072M16—62no—
1073M16—62no—
1074M16—121no—
1075M16—121no—
1076C2×C8—22no—
1077C2×C8—22no—
1078C2×C8—22no—
1079C2×C8—22no—
1080C2×C8—22no—
1081C2×C8—22no—
1082C2×C8—22no—
1083C2×C8—22no—
1084C2×C8—22no—
1085C2×C8—34no—
1086C2×C8—41no—
1087C2×C8—41no—
1088C2×C8—62no—
1089C2×C8—62no—
1090C2×C8—62no—
1091C2×C8—121no—
1092C2×C8—121no—
1093C2×C8D3×C22⋊C414yes—
1094C4⋊C4—22no—
1095C4⋊C4—41no—
1096C4⋊C4—41no—
1097C4⋊C4—41no—
1098C4⋊C4—62no—
1099C4⋊C4—62no—
1100C4⋊C4—62no—
1101C4⋊C4—62no—
1102C4⋊C4—62no—
1103C4⋊C4—124no—
1104C4⋊C4—124no—
1105C4⋊C4—124no—
1106C4⋊C4—121no—
1107C4⋊C4—121no—
1108C4⋊C4—121no—
1109C4⋊C4—121no—
1110C4⋊C4—121no—
1111C22⋊C4—22no—
1112C22⋊C4—41no—
1113C22⋊C4—41no—
1114C22⋊C4—41no—
1115C22⋊C4—62no—
1116C22⋊C4—62no—
1117C22⋊C4—62no—
1118C22⋊C4—62no—
1119C22⋊C4—62no—
1120C22⋊C4—128no—
1121C22⋊C4—121no—
1122C22⋊C4—121no—
1123C22⋊C4—121no—
1124C22⋊C4—121no—
1125C22⋊C4—121no—
1126C22⋊C4—484no—
1127C42—22no—
1128C42—22no—
1129C42—22no—
1130C42—34no—
1131C42—41no—
1132C42—62no—
1133C42—62no—
1134C42—62no—
1135C42—62no—
1136C42—62no—
1137C42—62no—
1138C42—121no—
1139C42—121no—
1140C42—121no—
1141C22×C3—41no—
1142C22×C3—41no—
1143C22×C3—41no—
1144C22×C3—41no—
1145C22×C3—41no—
1146C22×C3—41no—
1147C22×C3—41no—
1148C22×C3—82no—
1149C22×C3—82no—
1150C22×C3—81no—
1151C22×C3—161no—
1152C22×C3#230911yescharacteristic
1153C22×C3#237211yescharacteristic
1154C22×C3#237211yescharacteristic
1155C22×C3#261011yescharacteristic
1156C22×C3#261011yescharacteristic
1157C22×C3#261011yescharacteristic
1158C22×C3#261011yescharacteristic
1159C2×D3—84no—
1160C2×D3—84no—
1161C2×D3—82no—
1162C2×D3—162no—
1163C2×D3—162no—
1164C2×D3—162no—
1165C2×D3—162no—
1166C2×D3—162no—
1167C3×C4—82no—
1168C3×C4—82no—
1169C3×C4—81no—
1170C3×C4#229711yescharacteristic
1171C3×C4#229711yescharacteristic
1172C3×C4#237211yescharacteristic
1173C3×C4#237211yescharacteristic
1174C3×C4#261011yescharacteristic
1175C3×C4#261011yescharacteristic
1176C3×C4#261011yescharacteristic
1177C3×C4#261011yescharacteristic
1178Dic3—44no—
1179Dic3—82no—
1180Dic3—82no—
1181Dic3—82no—
1182Dic3—82no—
1183C23—41no—
1184C23—41no—
1185C23—41no—
1186C23—81no—
1187C23—82no—
1188C23—122no—
1189C23—122no—
1190C23—122no—
1191C23—244no—
1192C23—244no—
1193C23—241no—
1194C23—241no—
1195C23—241no—
1196C23—241no—
1197C23—482no—
1198C23—482no—
1199C23—482no—
1200C23—482no—
1201C23—482no—
1202C23#553211yescharacteristic
1203C23#554511yescharacteristic
1204C23#556311yescharacteristic
1205C23#560711yescharacteristic
1206C23#565811yescharacteristic
1207C23#567411yescharacteristic
1208C23#570511yescharacteristic
1209Q8—41no—
1210Q8—41no—
1211Q8—41no—
1212Q8—41no—
1213Q8—484no—
1214D4—41no—
1215D4—41no—
1216D4—41no—
1217D4—41no—
1218D4—81no—
1219D4—81no—
1220D4—81no—
1221D4—81no—
1222D4—122no—
1223D4—122no—
1224D4—122no—
1225D4—122no—
1226D4—241no—
1227D4—241no—
1228D4—241no—
1229D4—241no—
1230D4—488no—
1231C2×C4—41no—
1232C2×C4—42no—
1233C2×C4—42no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—64no—
1237C2×C4—81no—
1238C2×C4—81no—
1239C2×C4—81no—
1240C2×C4—81no—
1241C2×C4—82no—
1242C2×C4—122no—
1243C2×C4—122no—
1244C2×C4—122no—
1245C2×C4—122no—
1246C2×C4—161no—
1247C2×C4—242no—
1248C2×C4—242no—
1249C2×C4—481no—
1250C2×C4—481no—
1251C2×C4—481no—
1252C2×C4C4×#23511yescharacteristic
1253C2×C4C2×D3×C22⋊C411yescharacteristic
1254C2×C4#549511yescharacteristic
1255C2×C4#549511yescharacteristic
1256C2×C4#552211yescharacteristic
1257C2×C4#553211yescharacteristic
1258C2×C4C4×#23711yescharacteristic
1259C2×C4C4×#23711yescharacteristic
1260C2×C4#554511yescharacteristic
1261C2×C4#554711yescharacteristic
1262C2×C4#554711yescharacteristic
1263C2×C4#554811yescharacteristic
1264C2×C4#554811yescharacteristic
1265C2×C4#555611yescharacteristic
1266C2×C4#555611yescharacteristic
1267C2×C4#556311yescharacteristic
1268C2×C4#558611yescharacteristic
1269C2×C4#559611yescharacteristic
1270C2×C4#559611yescharacteristic
1271C2×C4#560711yescharacteristic
1272C2×C4#561611yescharacteristic
1273C2×C4#561611yescharacteristic
1274C2×C4#565611yescharacteristic
1275C2×C4#565811yescharacteristic
1276C2×C4#567011yescharacteristic
1277C2×C4#567011yescharacteristic
1278C2×C4#570511yescharacteristic
1279C2×C4#571511yescharacteristic
1280C8—24no—
1281C8—42no—
1282C8—42no—
1283C8—42no—
1284C8—64no—
1285C8—122no—
1286C2×C3—21no—
1287C2×C3—21no—
1288C2×C3—21no—
1289C2×C3—21no—
1290C2×C3—21no—
1291C2×C3—21no—
1292C2×C3—21no—
1293C2×C3—161no—
1294C2×C3#1416911yescharacteristic
1295D3—162no—
1296C22—41no—
1297C22—41no—
1298C22—41no—
1299C22—41no—
1300C22—41no—
1301C22—41no—
1302C22—41no—
1303C22—82no—
1304C22—82no—
1305C22—81no—
1306C22—161no—
1307C22—244no—
1308C22—244no—
1309C22—242no—
1310C22—482no—
1311C22—482no—
1312C22—482no—
1313C22—482no—
1314C22—482no—
1315C22#7347511yescharacteristic
1316C22#7478011yescharacteristic
1317C22#7548311yescharacteristic
1318C22#7565011yescharacteristic
1319C22#7565011yescharacteristic
1320C22#7590011yescharacteristic
1321C22#7642811yescharacteristic
1322C4—82no—
1323C4—82no—
1324C4—81no—
1325C4—124no—
1326C4—242no—
1327C4—242no—
1328C4—242no—
1329C4—242no—
1330C4#7347511yescharacteristic
1331C4#7356311yescharacteristic
1332C4#7465811yescharacteristic
1333C4#7478011yescharacteristic
1334C4#7548311yescharacteristic
1335C4#7590011yescharacteristic
1336C4#7637211yescharacteristic
1337C4#7637211yescharacteristic
1338C3#37571811yescharacteristic, complemented, Sylow
1339C2—21no—
1340C2—21no—
1341C2—21no—
1342C2—21no—
1343C2—21no—
1344C2—21no—
1345C2—21no—
1346C2—161no—
1347C2—482no—
1348C2#1072046611yescharacteristic
subgroupG/H
centerC2#10720466
commutatorC22×C3×C4C23×C4
FrattiniC23×C4C23×D3
FittingC3×#10950C2
socleC2×C3#14169
prime radicalC2×#5830C22
cosocleC23×C3×C4C24
hypercenter#10950D3
hypocenterC3#375718
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2 ◁ C23×C4 ◁ #10950

Complements

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

NH ≅ G/Ntype
2. #10792695C2semidirect
3. #10792694C2semidirect
4. #10704133C2semidirect
5. #10704132C2semidirect
8. #10701613C2semidirect
9. #10701608C2semidirect
10. #10701600C2semidirect
11. #10701595C2semidirect
12. #10701591C2semidirect
13. #10701580C2semidirect
14. #10701579C2semidirect
15. C3×#10950C2semidirect
36. #78954C4semidirect
37. #78921C4semidirect
70. #10950D3semidirect
378. #815C22⋊C4semidirect
382. C8×Dic3C22⋊C4semidirect
1338. C3#375718semidirect

Maximal subgroups

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

subgroupindex
#116645052
#107926952
#107926942
#107041332
#107041322
#107017852
#107017792
#107016132
#107016082
#107016002
#107015952
#107015912
#107015802
#107015792
C3×#109502
#3757183