Finite Group Databasebeta

← #11904910

Subgroups — #11904910

Order 1152.

2777 conjugacy classes of subgroups.

The subgroup lattice has 922 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595954C211yesmaximal, characteristic, complemented
2C2×C3×#882C211yesmaximal, characteristic, complemented
3C3×#5486C211yesmaximal, characteristic, complemented
4#10595518C211yesmaximal, characteristic, complemented
5C2×#63976C211yesmaximal, characteristic, complemented
6#10595506C211yesmaximal, characteristic, complemented
7C2×D3×#217C211yesmaximal, characteristic, complemented
8#10594938C214yesmaximal, complemented
9#10594886C214yesmaximal, complemented
10#10594238C214yesmaximal, complemented
11#10594184C214yesmaximal, complemented
12#10594117C214yesmaximal, complemented
13#10594054C214yesmaximal, complemented
14#85913—31nomaximal
15#85868—31nomaximal
16C24×C3×D3C2211yescharacteristic
17C22×C3×#67C2211yescharacteristic
18C22×C3×#67C2211yescharacteristic
19C22×C3×D12C2212yescomplemented
20C22×#625C2212yescomplemented
21C22×D3×Dic3C2212yescomplemented
22C2×#3795C2214yescomplemented
23C2×C32×C22⋊C4C2211yescharacteristic
24C2×#3757C2211yescharacteristic
25C2×#3757C2211yescharacteristic
26#64133C2214yescomplemented
27#64087C2214yescomplemented
28#64087C2214yescomplemented
29C2×C3×#217C2211yescharacteristic
30C3×C4×#67C2214yescomplemented
31C2×C3×(C2×D3)⋊C4C2212yescomplemented
32C3×#882C2214yes—
33C3×#882C2212yescomplemented
34C3×#882C2212yescomplemented
35C3×#67⋊C4C2214yescomplemented
36C3×D3×C22⋊C4C2212yescomplemented
37C3×#877C2212yescomplemented
38#63980C2214yescomplemented
39#63976C2214yes—
40#63976C2212yescomplemented
41#63976C2212yescomplemented
42#63976C2212yescomplemented
43#63976C2212yescomplemented
44#67⋊Dic3C2214yescomplemented
45Dic3×#67C2214yescomplemented
46D3×#217C2214yescomplemented
47D3×#217C2214yescomplemented
48D3×#217C2212yescomplemented
49#63961C2212yescomplemented
50#63961C2212yescomplemented
51C2×(C2×D3)⋊Dic3C2212yescomplemented
52C2×(C2×D3)⋊Dic3C2212yescomplemented
53#63955C2212yescomplemented
54#63913C2214yescomplemented
55#63908C2214yescomplemented
56#63905C2214yescomplemented
57#63896C2214yescomplemented
58Dic3×D12C2214yescomplemented
59#63891C2214yescomplemented
60#63885C2214yescomplemented
61#63885C2214yescomplemented
62#63884C2214yescomplemented
63#63884C2214yescomplemented
64#63879C2214yescomplemented
65#63877C2214yescomplemented
66#63861C2214yescomplemented
67#63860C2214yescomplemented
68#63859C2214yescomplemented
69C2×C3×#120—31no—
70C3×#518—31no—
71C2×#953—31no—
72C22×#217—31no—
73#5806—34no—
74#5804—31no—
75#5804—31no—
76C2×#937—31no—
77#5798—31no—
78#5593—34no—
79#5591—34no—
80#5587—34no—
81#5586—34no—
82#5560—34no—
83#5556—34no—
84#5550—34no—
85#5547—34no—
86#5527—34no—
87#5495—34no—
88#5490—34no—
89C2×#882D311yescharacteristic, complemented
90#5486—31no—
91#5486D311yescharacteristic, complemented
92C2×D3×C22⋊C4—31no—
93#5483—31no—
94#5483—31no—
95#5483—61no—
96C24×C32C2311yescharacteristic
97C23×C3×D3—24no—
98C23×C3×D3—44no—
99C23×C3×D3C2311yescharacteristic
100C23×C3×D3C2312yes—
101C23×C3×D3C2312yes—
102C23×C3×D3C2311yescharacteristic
103C23×C3×D3C2311yescharacteristic
104C23×C3×D3C2311yescharacteristic
105C22×C32×C4C2312yes—
106C22×C3⋊Dic3C2312yes—
107C22×C3⋊Dic3C2312yes—
108C2×#634C2314yescomplemented
109C2×C3×#67—24no—
110C2×C3×#67—24no—
111C2×C3×#67C2312yes—
112C2×C3×#67C2312yes—
113C2×C3×#67C2312yes—
114C2×C3×#67C2312yes—
115C22×C3×Dic3C2311yescharacteristic
116C22×C3×Dic3C2311yescharacteristic
117C22×C3×Dic3C2312yes—
118C2×C3×D12—44no—
119C2×C3×D12C2314yes—
120C2×C3×D12C2314yes—
121C2×C3×C4×D3C2314yescomplemented
122C2×#625—44no—
123C2×#625C2314yes—
124C2×#625C2314yes—
125C2×#625C2314yescomplemented
126C2×D3×Dic3—44no—
127C2×D3×Dic3C2314yes—
128C2×D3×Dic3C2314yes—
129C2×D3×Dic3C2314yescomplemented
130#3795—48no—
131C32×C22⋊C4C2312yes—
132C32×C22⋊C4C2312yes—
133#3757C2312yes—
134#3757C2312yes—
135#3757C2312yes—
136#3757C2312yes—
137C4⋊(C3⋊Dic3)C2314yescomplemented
138#3750C2314yescomplemented
139#3750C2314yescomplemented
140C3×#217C2312yes—
141C3×#217C2312yes—
142C3×(C2×D3)⋊C4C2314yes—
143C3×(C2×D3)⋊C4C2314yes—
144C3×(C2×D3)⋊C4C2314yescomplemented
145C3×Dic3⋊C4C2314yescomplemented
146C3×C4×Dic3C2314yescomplemented
147#3724C2314yescomplemented
148Dic3⋊Dic3C2314yescomplemented
149(C2×D3)⋊Dic3C2314yes—
150(C2×D3)⋊Dic3C2314yes—
151(C2×D3)⋊Dic3C2314yes—
152(C2×D3)⋊Dic3C2314yes—
153(C2×D3)⋊Dic3C2314yescomplemented
154(C2×D3)⋊Dic3C2314yescomplemented
155(C2×D3)⋊Dic3C2314yescomplemented
156Dic32C2314yescomplemented
157#3490—91noSylow
158C25×C3—31no—
159C24×D3C2×D311yescharacteristic
160C22×C3×D4—31no—
161C22×C3×D4—31no—
162C22×C3×D4—32no—
163C22×#67—32no—
164C22×#67—32no—
165C22×#67C2×D311yescharacteristic
166C22×#67C2×D311yescharacteristic
167C23×Dic3—32no—
168C2×#237—34no—
169C2×#235—34no—
170C22×D12C2×D312yescomplemented
171C22×C4×D3—32no—
172C3×#120—34no—
173C3×#120—32no—
174C3×#120—32no—
175C3×C4×D4—34no—
176C3×C4×D4—34no—
177C3×#117—32no—
178C2×C3×C22⋊C4—21no—
179C2×C3×C22⋊C4—31no—
180C2×C3×C22⋊C4—32no—
181C2×C3×C22⋊C4—32no—
182C2×C3×C22⋊C4C2×D311yescharacteristic
183C2×C3×C22⋊C4C2×D311yescharacteristic
184#953—32no—
185#953—34no—
186#953—32no—
187#953—32no—
188#953—32no—
189C2×#217—31no—
190C2×#217—31no—
191C2×#217—31no—
192C2×#217—31no—
193C2×#217—32no—
194C2×#217—32no—
195C2×#217—34no—
196C2×#217—32no—
197C2×#217—34no—
198C2×#217—61no—
199C2×#217—61no—
200C2×#217C2×D311yescharacteristic
201#939—34no—
202#939—34no—
203#939—34no—
204#939—34no—
205#938—34no—
206#937—32no—
207#937—34no—
208#937—32no—
209#937—32no—
210#937—32no—
211#936—34no—
212#935—32no—
213#935—32no—
214#935—34no—
215#935—34no—
216D4×Dic3—34no—
217D4×Dic3—34no—
218D4×Dic3—34no—
219#930—34no—
220#929—32no—
221#929—32no—
222#929—34no—
223C4×#67—34no—
224C4×#67—34no—
225C4×#67C2×D314yescomplemented
226C2×(C2×D3)⋊C4—32no—
227C2×(C2×D3)⋊C4—32no—
228C2×(C2×D3)⋊C4C2×D312yescomplemented
229#926—32no—
230#924—34no—
231#924—34no—
232#924—64no—
233#898—34no—
234#896—34no—
235#894—34no—
236#894—34no—
237#886—34no—
238#885—34no—
239#885—34no—
240#884—34no—
241#884—34no—
242#883—34no—
243#883—34no—
244#882C2×D314yes—
245#882C2×D312yescomplemented
246#882C2×D312yescomplemented
247#67⋊C4—34no—
248#67⋊C4—34no—
249#67⋊C4C2×D314yescomplemented
250D3×C22⋊C4—34no—
251D3×C22⋊C4—34no—
252D3×C22⋊C4—32no—
253D3×C22⋊C4C2×D312yescomplemented
254#879—34no—
255#879—34no—
256#878—34no—
257#878—34no—
258#878—34no—
259#878—34no—
260#878—34no—
261#878—64no—
262#878—64no—
263#877—32no—
264#877—34no—
265#877C2×D312yescomplemented
266#876—34no—
267#875—34no—
268C4×D12—34no—
269#872—34no—
270C23×C32—42no—
271C23×C32#4114yescomplemented
272C23×C32C2411yescharacteristic
273C23×C32C2411yescharacteristic
274C23×C32C2411yescharacteristic
275C22×C3×D3—22no—
276C22×C3×D3—24no—
277C22×C3×D3—24no—
278C22×C3×D3—24no—
279C22×C3×D3—22no—
280C22×C3×D3—22no—
281C22×C3×D3—22no—
282C22×C3×D3—24no—
283C22×C3×D3—24no—
284C22×C3×D3—42no—
285C22×C3×D3—42no—
286C22×C3×D3—42no—
287C22×C3×D3—42no—
288C22×C3×D3—42no—
289C22×C3×D3—416no—
290C22×C3×D3C2412yes—
291C22×C3×D3C2412yes—
292C22×C3×D3C2412yes—
293C22×C3×D3C2412yes—
294C2×C32×C4—42no—
295C2×C32×C4C2414yes—
296C2×C3⋊Dic3—42no—
297C2×C3⋊Dic3—42no—
298C2×C3⋊Dic3C2414yes—
299C2×C3⋊Dic3C2414yes—
300#634—44no—
301C3×#67—24no—
302C3×#67—24no—
303C3×#67—24no—
304C3×#67—24no—
305C2×C3×Dic3—22no—
306C2×C3×Dic3—22no—
307C2×C3×Dic3—42no—
308C2×C3×Dic3C2412yes—
309C2×C3×Dic3C2414yes—
310C2×C3×Dic3C2412yes—
311C3×D12—28no—
312C3×D12—44no—
313C3×C4×D3—44no—
314#625—28no—
315#625—44no—
316#625—44no—
317D3×Dic3—28no—
318D3×Dic3—44no—
319D3×Dic3—44no—
320#551—94no—
321#551—94no—
322#546—94no—
323#546—94no—
324#543—91no—
325#538—94no—
326#534—91no—
327#525—94no—
328C2×#120—31no—
329C2×#120—91no—
330#518—31no—
331#518—91no—
332C22×C22⋊C4—91no—
333C24×C3—21no—
334C24×C3—31no—
335C24×C3—32no—
336C24×C3—32no—
337C24×C3—31no—
338C24×C3—31no—
339C24×C3—31no—
340C24×C3—64no—
341C24×C3—124no—
342C24×C3C22×D311yescharacteristic
343C24×C3C22×D311yescharacteristic
344C23×D3—24no—
345C23×D3—44no—
346C23×D3C22×D311yescharacteristic
347C23×D3C22×D312yes—
348C23×D3C22×D312yes—
349C23×D3C22×D311yescharacteristic
350C23×D3C22×D311yescharacteristic
351C23×D3C22×D311yescharacteristic
352C2×C3×D4—32no—
353C2×C3×D4—32no—
354C2×C3×D4—32no—
355C2×C3×D4—32no—
356C2×C3×D4—34no—
357C2×C3×D4—34no—
358C2×C3×D4—64no—
359C2×C3×D4—64no—
360C2×C3×D4—124no—
361C22×C3×C4—22no—
362C22×C3×C4—31no—
363C22×C3×C4—31no—
364C22×C3×C4—32no—
365C22×C3×C4—34no—
366C22×C3×C4C22×D312yes—
367C22×C3×C4C22×D312yes—
368C2×#67—24no—
369C2×#67—24no—
370C2×#67—34no—
371C2×#67—34no—
372C2×#67—34no—
373C2×#67—34no—
374C2×#67—34no—
375C2×#67—34no—
376C2×#67—124no—
377C2×#67—124no—
378C2×#67C22×D312yes—
379C2×#67C22×D312yes—
380C2×#67C22×D312yes—
381C2×#67C22×D312yes—
382C22×Dic3—32no—
383C22×Dic3—32no—
384C22×Dic3—32no—
385C22×Dic3—32no—
386C22×Dic3—34no—
387C22×Dic3—34no—
388C22×Dic3—34no—
389C22×Dic3—62no—
390C22×Dic3—62no—
391C22×Dic3—124no—
392C22×Dic3C22×D311yescharacteristic
393C22×Dic3C22×D311yescharacteristic
394C22×Dic3C22×D312yes—
395#237—128no—
396#235—128no—
397C2×D12—44no—
398C2×D12C22×D314yes—
399C2×D12C22×D314yes—
400C2×C4×D3—34no—
401C2×C4×D3—34no—
402C2×C4×D3—34no—
403C2×C4×D3—124no—
404C2×C4×D3C22×D314yescomplemented
405C2×Dic6—34no—
406C2×Dic6—34no—
407C2×Dic6—64no—
408C3×C4⋊C4—34no—
409C3×C22⋊C4—22no—
410C3×C22⋊C4—22no—
411C3×C22⋊C4—32no—
412C3×C22⋊C4—32no—
413C3×C22⋊C4—34no—
414C3×C22⋊C4—34no—
415C3×C22⋊C4—34no—
416C3×C22⋊C4C22×D312yes—
417C3×C22⋊C4C22×D312yes—
418C3×C22⋊C4C22×D312yes—
419C3×C22⋊C4C22×D312yes—
420C3×C42—34no—
421#217—32no—
422#217—32no—
423#217—32no—
424#217—32no—
425#217—32no—
426#217—32no—
427#217—32no—
428#217—32no—
429#217—34no—
430#217—34no—
431#217—34no—
432#217—34no—
433#217—34no—
434#217—34no—
435#217—34no—
436#217—62no—
437#217—62no—
438#217—62no—
439#217—62no—
440#217C22×D312yes—
441#217C22×D312yes—
442(C2×D3)⋊C4—34no—
443(C2×D3)⋊C4—34no—
444(C2×D3)⋊C4—34no—
445(C2×D3)⋊C4—34no—
446(C2×D3)⋊C4—34no—
447(C2×D3)⋊C4—34no—
448(C2×D3)⋊C4—34no—
449(C2×D3)⋊C4C22×D314yes—
450(C2×D3)⋊C4C22×D314yes—
451(C2×D3)⋊C4C22×D314yescomplemented
452C4⋊Dic3—34no—
453C4⋊Dic3—34no—
454C4⋊Dic3—34no—
455C4⋊Dic3—64no—
456Dic3⋊C4—34no—
457Dic3⋊C4—34no—
458Dic3⋊C4—34no—
459Dic3⋊C4—34no—
460Dic3⋊C4—34no—
461Dic3⋊C4—34no—
462Dic3⋊C4—34no—
463Dic3⋊C4—64no—
464Dic3⋊C4—64no—
465Dic3⋊C4C22×D314yescomplemented
466C4×Dic3—34no—
467C4×Dic3—34no—
468C4×Dic3C22×D314yescomplemented
469C22×C32—22no—
470C22×C32—22no—
471C22×C32—22no—
472C22×C32—44no—
473C22×C32C2×#4112yes—
474C22×C32C2×#4112yes—
475C22×C32C2×#4112yes—
476C22×C32C2511yescharacteristic
477C2×C3×D3—28no—
478C2×C3×D3—22no—
479C2×C3×D3—22no—
480C2×C3×D3—22no—
481C2×C3×D3—22no—
482C2×C3×D3—22no—
483C2×C3×D3—24no—
484C2×C3×D3—24no—
485C2×C3×D3—22no—
486C2×C3×D3—22no—
487C2×C3×D3—48no—
488C2×C3×D3—48no—
489C2×C3×D3—44no—
490C2×C3×D3—82no—
491C2×C3×D3—82no—
492C2×C3×D3H(5,𝔽2)14yes—
493C32×C4—24no—
494C3⋊Dic3—24no—
495C3⋊Dic3—24no—
496C3×Dic3—22no—
497C3×Dic3—22no—
498C3×Dic3—24no—
499C25—31no—
500C2×#41—94no—
501C22×D4—31no—
502C22×D4—31no—
503C22×D4—32no—
504C22×D4—92no—
505C23×C4—92no—
506#126—94no—
507#126—94no—
508#124—94no—
509#124—94no—
510#123—94no—
511#123—94no—
512#123—94no—
513#123—94no—
514#123—92no—
515#123—92no—
516C22⋊Q8—94no—
517C22⋊Q8—94no—
518C22⋊Q8—94no—
519C22⋊Q8—94no—
520#121—94no—
521#121—94no—
522#121—94no—
523#121—94no—
524#120—32no—
525#120—32no—
526#120—34no—
527#120—92no—
528#120—92no—
529#120—94no—
530#120—92no—
531#120—92no—
532C4×D4—34no—
533C4×D4—34no—
534C4×D4—94no—
535C4×D4—94no—
536C4×D4—94no—
537C4×D4—94no—
538#117—32no—
539#117—94no—
540#117—92no—
541C2×C22⋊C4—31no—
542C2×C22⋊C4—32no—
543C2×C22⋊C4—32no—
544C2×C22⋊C4—94no—
545C2×C22⋊C4—94no—
546C2×C22⋊C4—92no—
547C2×C22⋊C4—92no—
548C2×C22⋊C4—92no—
549C2×C22⋊C4—91no—
550C2×C22⋊C4—91no—
551C2×C22⋊C4D3211yescharacteristic
552C23×C3—21no—
553C23×C3—21no—
554C23×C3—21no—
555C23×C3—24no—
556C23×C3—32no—
557C23×C3—32no—
558C23×C3—32no—
559C23×C3—32no—
560C23×C3—42no—
561C23×C3—42no—
562C23×C3—64no—
563C23×C3—64no—
564C23×C3—64no—
565C23×C3—62no—
566C23×C3—64no—
567C23×C3—64no—
568C23×C3—62no—
569C23×C3—62no—
570C23×C3—62no—
571C23×C3—82no—
572C23×C3—122no—
573C23×C3—122no—
574C23×C3—122no—
575C23×C3—122no—
576C23×C3—122no—
577C23×C3—1216no—
578C23×C3#23514yescomplemented
579C23×C3#23714yescomplemented
580C23×C3C23×D311yescharacteristic
581C23×C3C23×D311yescharacteristic
582C23×C3C23×D311yescharacteristic
583C23×C3C23×D311yescharacteristic
584C23×C3C23×D311yescharacteristic
585C23×C3C23×D311yescharacteristic
586C22×D3—22no—
587C22×D3—24no—
588C22×D3—24no—
589C22×D3—24no—
590C22×D3—22no—
591C22×D3—22no—
592C22×D3—22no—
593C22×D3—24no—
594C22×D3—24no—
595C22×D3—42no—
596C22×D3—42no—
597C22×D3—42no—
598C22×D3—42no—
599C22×D3—42no—
600C22×D3—416no—
601C22×D3C23×D312yes—
602C22×D3C23×D312yes—
603C22×D3C23×D312yes—
604C22×D3C23×D312yes—
605C3×D4—68no—
606C3×D4—64no—
607C3×D4—64no—
608C3×D4—64no—
609C3×D4—64no—
610C3×D4—124no—
611C2×C3×C4—24no—
612C2×C3×C4—32no—
613C2×C3×C4—34no—
614C2×C3×C4—32no—
615C2×C3×C4—42no—
616C2×C3×C4—42no—
617C2×C3×C4—62no—
618C2×C3×C4—62no—
619C2×C3×C4—82no—
620C2×C3×C4—124no—
621C2×C3×C4—122no—
622C2×C3×C4C23×D314yes—
623C2×C3×C4C23×D314yes—
624#67—24no—
625#67—24no—
626#67—24no—
627#67—24no—
628#67—68no—
629#67—68no—
630#67—124no—
631#67—124no—
632#67—124no—
633#67—124no—
634C2×Dic3—22no—
635C2×Dic3—22no—
636C2×Dic3—34no—
637C2×Dic3—34no—
638C2×Dic3—34no—
639C2×Dic3—34no—
640C2×Dic3—42no—
641C2×Dic3—64no—
642C2×Dic3—64no—
643C2×Dic3—68no—
644C2×Dic3—124no—
645C2×Dic3—124no—
646C2×Dic3—122no—
647C2×Dic3—122no—
648C2×Dic3—122no—
649C2×Dic3—122no—
650C2×Dic3—242no—
651C2×Dic3—242no—
652C2×Dic3C23×D312yes—
653C2×Dic3C23×D314yes—
654C2×Dic3C23×D312yes—
655D12—28no—
656D12—44no—
657C4×D3—44no—
658C4×D3—68no—
659C4×D3—124no—
660C4×D3—124no—
661Dic6—124no—
662Dic6—124no—
663Dic6—244no—
664C2×C32—22no—
665C2×C32—22no—
666C2×C32—22no—
667C2×C32C22×#4111yescharacteristic
668C2×C32C2×H(5,𝔽2)12yes—
669C3×D3—24no—
670C3×D3—42no—
671C3×D3—42no—
672C3×D3—42no—
673C24—31no—
674C24—32no—
675C24—32no—
676C24—31no—
677C24—31no—
678C24—31no—
679C24—64no—
680C24—124no—
681C24C2×D3211yescharacteristic
682#41—368no—
683C2×Q8—94no—
684C2×D4—32no—
685C2×D4—32no—
686C2×D4—32no—
687C2×D4—32no—
688C2×D4—34no—
689C2×D4—34no—
690C2×D4—64no—
691C2×D4—64no—
692C2×D4—94no—
693C2×D4—94no—
694C2×D4—94no—
695C2×D4—124no—
696C2×D4—364no—
697C22×C4—31no—
698C22×C4—31no—
699C22×C4—32no—
700C22×C4—34no—
701C22×C4—94no—
702C22×C4—94no—
703C22×C4—94no—
704C22×C4—92no—
705C22×C4—92no—
706C22×C4—364no—
707C22×C4C2×D3212yes—
708C4⋊C4—34no—
709C4⋊C4—94no—
710C4⋊C4—94no—
711C4⋊C4—94no—
712C4⋊C4—94no—
713C4⋊C4—94no—
714C22⋊C4—32no—
715C22⋊C4—32no—
716C22⋊C4—34no—
717C22⋊C4—34no—
718C22⋊C4—34no—
719C22⋊C4—94no—
720C22⋊C4—94no—
721C22⋊C4—94no—
722C22⋊C4—94no—
723C22⋊C4—94no—
724C22⋊C4—94no—
725C22⋊C4—94no—
726C22⋊C4—92no—
727C22⋊C4—92no—
728C22⋊C4—92no—
729C22⋊C4—92no—
730C22⋊C4C2×D3212yes—
731C22⋊C4C2×D3212yes—
732C42—34no—
733C42—94no—
734C22×C3—22no—
735C22×C3—22no—
736C22×C3—22no—
737C22×C3—22no—
738C22×C3—22no—
739C22×C3—22no—
740C22×C3—22no—
741C22×C3—22no—
742C22×C3—22no—
743C22×C3—21no—
744C22×C3—34no—
745C22×C3—42no—
746C22×C3—42no—
747C22×C3—42no—
748C22×C3—44no—
749C22×C3—44no—
750C22×C3—68no—
751C22×C3—62no—
752C22×C3—62no—
753C22×C3—62no—
754C22×C3—62no—
755C22×C3—62no—
756C22×C3—64no—
757C22×C3—64no—
758C22×C3—62no—
759C22×C3—62no—
760C22×C3—84no—
761C22×C3—128no—
762C22×C3—128no—
763C22×C3—124no—
764C22×C3—242no—
765C22×C3—242no—
766C22×C3C2×#23512yes—
767C22×C3C2×#23512yes—
768C22×C3C2×#23512yes—
769C22×C3C2×#23712yes—
770C22×C3C2×#23712yes—
771C22×C3C2×#23712yes—
772C22×C3C24×D311yescharacteristic
773C22×C3C24×D311yescharacteristic
774C2×D3—28no—
775C2×D3—22no—
776C2×D3—22no—
777C2×D3—22no—
778C2×D3—22no—
779C2×D3—22no—
780C2×D3—24no—
781C2×D3—22no—
782C2×D3—22no—
783C2×D3—24no—
784C2×D3—48no—
785C2×D3—48no—
786C2×D3—44no—
787C2×D3—82no—
788C2×D3—82no—
789C2×D3#100414yes—
790C3×C4—24no—
791C3×C4—24no—
792C3×C4—44no—
793C3×C4—62no—
794C3×C4—62no—
795C3×C4—64no—
796Dic3—22no—
797Dic3—22no—
798Dic3—24no—
799Dic3—64no—
800Dic3—64no—
801Dic3—64no—
802Dic3—64no—
803Dic3—124no—
804Dic3—124no—
805C32#349011yescharacteristic, complemented, Sylow
806C23—32no—
807C23—32no—
808C23—32no—
809C23—32no—
810C23—42no—
811C23—64no—
812C23—64no—
813C23—64no—
814C23—62no—
815C23—64no—
816C23—64no—
817C23—62no—
818C23—62no—
819C23—62no—
820C23—122no—
821C23—122no—
822C23—122no—
823C23—122no—
824C23—122no—
825C23—1216no—
826C23#379514yescomplemented
827C23C22×D3211yescharacteristic
828C23C22×D3211yescharacteristic
829C23C22×D3211yescharacteristic
830Q8—364no—
831D4—68no—
832D4—64no—
833D4—64no—
834D4—64no—
835D4—64no—
836D4—124no—
837D4—188no—
838D4—364no—
839D4—364no—
840C2×C4—32no—
841C2×C4—34no—
842C2×C4—32no—
843C2×C4—42no—
844C2×C4—62no—
845C2×C4—62no—
846C2×C4—94no—
847C2×C4—94no—
848C2×C4—124no—
849C2×C4—122no—
850C2×C4—188no—
851C2×C4—364no—
852C2×C4—364no—
853C2×C4—362no—
854C2×C4—362no—
855C2×C4C22×D3214yes—
856C2×C3—22no—
857C2×C3—22no—
858C2×C3—22no—
859C2×C3—22no—
860C2×C3—22no—
861C2×C3—22no—
862C2×C3—21no—
863C2×C3—22no—
864C2×C3—42no—
865C2×C3—42no—
866C2×C3—42no—
867C2×C3—64no—
868C2×C3—122no—
869C2×C3—122no—
870C2×C3—122no—
871C2×C3C22×#23511yescharacteristic
872C2×C3C22×#23711yescharacteristic
873C2×C3C2×#100412yes—
874C2×C3D3×H(5,𝔽2)12yes—
875D3—24no—
876D3—42no—
877D3—42no—
878D3—42no—
879C22—22no—
880C22—22no—
881C22—22no—
882C22—34no—
883C22—44no—
884C22—68no—
885C22—62no—
886C22—62no—
887C22—62no—
888C22—62no—
889C22—62no—
890C22—64no—
891C22—64no—
892C22—62no—
893C22—62no—
894C22—128no—
895C22—128no—
896C22—124no—
897C22—242no—
898C22—242no—
899C22C2×#379512yes—
900C22C2×#379512yes—
901C22C2×#379512yes—
902C22C23×D3211yescharacteristic
903C4—24no—
904C4—62no—
905C4—62no—
906C4—64no—
907C4—184no—
908C4—184no—
909C3—21no—
910C3#8586811yescharacteristic, complemented
911C3#8591311yescharacteristic, complemented
912C2—22no—
913C2—22no—
914C2—22no—
915C2—64no—
916C2—122no—
917C2—122no—
918C2—122no—
919C2C22×#379511yescharacteristic
920C2D3×#100412yes—
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC2×C32×C22⋊C4C22
hypercenterC2×C22⋊C4D32
hypocenterC32#3490
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #10595954C2semidirect
2. C2×C3×#882C2semidirect
3. C3×#5486C2semidirect
4. #10595518C2semidirect
5. C2×#63976C2semidirect
6. #10595506C2semidirect
7. C2×D3×#217C2semidirect
8. #10594938C2semidirect
9. #10594886C2semidirect
10. #10594238C2semidirect
11. #10594184C2semidirect
12. #10594117C2semidirect
13. #10594054C2semidirect
19. C22×C3×D12C22semidirect
20. C22×#625C22semidirect
21. C22×D3×Dic3C22semidirect
22. C2×#3795C22semidirect
26. #64133C22semidirect
27. #64087C22semidirect
28. #64087C22semidirect
30. C3×C4×#67C22semidirect
31. C2×C3×(C2×D3)⋊C4C22semidirect
33. C3×#882C22semidirect
34. C3×#882C22semidirect
35. C3×#67⋊C4C22semidirect
36. C3×D3×C22⋊C4C22semidirect
37. C3×#877C22semidirect
38. #63980C22semidirect
40. #63976C22semidirect
41. #63976C22semidirect
42. #63976C22semidirect
43. #63976C22semidirect
44. #67⋊Dic3C22semidirect
45. Dic3×#67C22semidirect
46. D3×#217C22semidirect
47. D3×#217C22semidirect
48. D3×#217C22semidirect
49. #63961C22semidirect
50. #63961C22semidirect
51. C2×(C2×D3)⋊Dic3C22semidirect
52. C2×(C2×D3)⋊Dic3C22semidirect
53. #63955C22semidirect
54. #63913C22semidirect
55. #63908C22semidirect
56. #63905C22semidirect
57. #63896C22semidirect
58. Dic3×D12C22semidirect
59. #63891C22semidirect
60. #63885C22semidirect
61. #63885C22semidirect
62. #63884C22semidirect
63. #63884C22semidirect
64. #63879C22semidirect
65. #63877C22semidirect
66. #63861C22semidirect
67. #63860C22semidirect
68. #63859C22semidirect
89. C2×#882D3semidirect
91. #5486D3semidirect
108. C2×#634C23semidirect
121. C2×C3×C4×D3C23semidirect
125. C2×#625C23semidirect
129. C2×D3×Dic3C23semidirect
137. C4⋊(C3⋊Dic3)C23semidirect
138. #3750C23semidirect
139. #3750C23semidirect
144. C3×(C2×D3)⋊C4C23semidirect
145. C3×Dic3⋊C4C23semidirect
146. C3×C4×Dic3C23semidirect
147. #3724C23semidirect
148. Dic3⋊Dic3C23semidirect
153. (C2×D3)⋊Dic3C23semidirect
154. (C2×D3)⋊Dic3C23semidirect
155. (C2×D3)⋊Dic3C23semidirect
156. Dic32C23semidirect
170. C22×D12C2×D3semidirect
225. C4×#67C2×D3semidirect
228. C2×(C2×D3)⋊C4C2×D3semidirect
245. #882C2×D3semidirect
246. #882C2×D3semidirect
249. #67⋊C4C2×D3semidirect
253. D3×C22⋊C4C2×D3semidirect
265. #877C2×D3semidirect
271. C23×C32#41semidirect
404. C2×C4×D3C22×D3semidirect
451. (C2×D3)⋊C4C22×D3semidirect
465. Dic3⋊C4C22×D3semidirect
468. C4×Dic3C22×D3semidirect
578. C23×C3#235semidirect
579. C23×C3#237semidirect
805. C32#3490semidirect
826. C23#3795semidirect
910. C3#85868semidirect
911. C3#85913semidirect

Maximal subgroups

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

subgroupindex
#105959542
C2×C3×#8822
C3×#54862
#105955182
C2×#639762
#105955062
C2×D3×#2172
#105949382
#105948862
#105942382
#105941842
#105941172
#105940542
#859133
#858683