Finite Group Databasebeta

← #11902007

Subgroups — #11902007

Order 1152.

2441 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595954C211yesmaximal, characteristic, complemented
2C3×#5493C211yesmaximal, characteristic, complemented
3C2×C3×#67⋊C4C211yesmaximal, characteristic, complemented
4#10595518C212yesmaximal, complemented
5C2×Dic3×#67C212yesmaximal, complemented
6#10594977C212yesmaximal, complemented
7#10594973C212yesmaximal, complemented
8#10594949C212yesmaximal, complemented
9#10594892C212yesmaximal, complemented
10#10594238C214yesmaximal, complemented
11#10594177C214yesmaximal, complemented
12#10594131C214yesmaximal, complemented
13#10594054C214yesmaximal, complemented
14#86295—31nomaximal
15#85776—31nomaximal
16C22×C3×#67C2212yes—
17C22×C3×#67C2211yescharacteristic
18C23×C3×Dic3C2211yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic, complemented
20C22×D3×Dic3C2212yescomplemented
21C2×#3795C2212yescomplemented
22C2×C32×C22⋊C4C2211yescharacteristic
23C2×#3757C2212yes—
24#64133C2212yescomplemented
25#64133C2212yescomplemented
26#64087C2214yescomplemented
27#64087C2214yescomplemented
28C3×#930C2212yes—
29C3×#930C2212yes—
30C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
31C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
32C2×C3×C4×Dic3C2211yescharacteristic, complemented
33C3×#886C2214yescomplemented
34C3×#882C2214yescomplemented
35C3×#67⋊C4C2214yescomplemented
36C3×#67⋊C4C2214yescomplemented
37#63980C2214yes—
38#63980C2214yes—
39#63976C2214yescomplemented
40#63976C2214yescomplemented
41Dic3×#67C2214yescomplemented
42Dic3×#67C2214yescomplemented
43Dic3×#67C2214yescomplemented
44Dic3×#67C2214yescomplemented
45C2×Dic3⋊Dic3C2212yescomplemented
46#63961C2214yescomplemented
47#63961C2214yescomplemented
48C2×(C2×D3)⋊Dic3C2212yescomplemented
49C2×Dic32C2212yescomplemented
50#63913C2214yescomplemented
51#63908C2212yescomplemented
52#63905C2214yescomplemented
53#63896C2214yescomplemented
54Dic3×D12C2212yescomplemented
55#63891C2214yescomplemented
56#63885C2214yescomplemented
57#63884C2214yescomplemented
58#63879C2214yescomplemented
59#63877C2214yescomplemented
60#63869C2212yescomplemented
61#63861C2214yescomplemented
62#63860C2212yescomplemented
63#63859C2214yescomplemented
64#63858C2214yescomplemented
65#63857C2212yescomplemented
66#63847C2214yescomplemented
67#63844C2212yescomplemented
68#63841C2212yescomplemented
69C3×#534—31no—
70C2×C3×C4×D4—31no—
71#5804—32no—
72#5804—32no—
73C2×D4×Dic3—32no—
74#5791—32no—
75C2×C4×#67—32no—
76#5665—34no—
77#5649—34no—
78#5617—32no—
79#5606—32no—
80#5602—32no—
81#5600—32no—
82#5593—34no—
83#5586—34no—
84#5564—34no—
85#5560—34no—
86#5547—34no—
87#5538—34no—
88#5515—32no—
89#5494—32no—
90#5493D311yescharacteristic, complemented
91C2×#67⋊C4D311yescharacteristic, complemented
92#5483—31no—
93#5483—31no—
94#5483—61no—
95#5479—32no—
96C24×C32C2311yescharacteristic
97C23×C3×D3C2312yes—
98C23×C3×D3C2311yescharacteristic
99C22×C32×C4C2311yescharacteristic
100C22×C32×C4C2311yescharacteristic
101C22×C3⋊Dic3C2312yes—
102C22×C3⋊Dic3C2312yes—
103C2×#634C2312yes—
104C2×#634C2312yes—
105C2×C3×#67—24no—
106C2×C3×#67—28no—
107C2×C3×#67C2314yes—
108C2×C3×#67C2314yes—
109C2×C3×#67C2314yes—
110C22×C3×Dic3—42no—
111C22×C3×Dic3C2312yes—
112C22×C3×Dic3C2312yes—
113C22×C3×Dic3C2311yescharacteristic
114C22×C3×Dic3C2311yescharacteristic
115C22×C3×Dic3C2312yes—
116C22×C3×Dic3C2311yescharacteristic
117C2×C3×D12C2312yes—
118C2×C3×D12C2312yes—
119C2×C3×C4×D3—42no—
120C2×C3×C4×D3C2312yes—
121C2×C3×C4×D3C2312yes—
122C2×#625C2314yes—
123C2×#625C2314yes—
124C2×D3×Dic3—44no—
125C2×D3×Dic3C2314yes—
126C2×D3×Dic3C2314yes—
127#3795—44no—
128C32×C22⋊C4C2314yes—
129#3757C2314yes—
130#3757C2314yes—
131C4⋊(C3⋊Dic3)C2312yes—
132C4⋊(C3⋊Dic3)C2312yes—
133#3750C2314yes—
134#3750C2314yes—
135C3×(C2×D3)⋊C4C2314yes—
136C3×(C2×D3)⋊C4C2314yes—
137C3×(C2×D3)⋊C4C2314yes—
138C3×C4⋊Dic3C2312yes—
139C3×C4⋊Dic3C2312yes—
140C3×Dic3⋊C4C2314yes—
141C3×C4×Dic3C2312yes—
142C3×C4×Dic3C2312yes—
143#3724C2314yes—
144#3724C2314yes—
145Dic3⋊Dic3C2314yes—
146Dic3⋊Dic3C2314yes—
147(C2×D3)⋊Dic3C2314yes—
148(C2×D3)⋊Dic3C2314yes—
149(C2×D3)⋊Dic3C2314yes—
150(C2×D3)⋊Dic3C2314yes—
151(C2×D3)⋊Dic3C2314yes—
152(C2×D3)⋊Dic3C2314yes—
153Dic32C2314yes—
154Dic32C2314yes—
155#3459—91noSylow
156C22×C3×D4—32no—
157C22×C3×D4—31no—
158C23×C3×C4—31no—
159C23×C3×C4—31no—
160C22×#67C2×D311yescharacteristic
161C22×#67C2×D312yes—
162C23×Dic3—32no—
163C23×Dic3C2×D311yescharacteristic
164C2×#237—32no—
165C2×#235—32no—
166C22×C4×D3—32no—
167C22×C4×D3C2×D311yescharacteristic, complemented
168C3×#123—34no—
169C3×#121—32no—
170C3×#121—32no—
171C3×#120—34no—
172C3×C4×D4—34no—
173C3×C4×D4—34no—
174C2×C3×C4⋊C4—31no—
175C2×C3×C22⋊C4—21no—
176C2×C3×C22⋊C4—31no—
177C2×C3×C22⋊C4C2×D311yescharacteristic
178C2×C3×C22⋊C4C2×D311yescharacteristic
179C2×C3×C42—31no—
180#953—34no—
181#953—34no—
182C2×#217—32no—
183C2×#217—32no—
184C2×#217—32no—
185C2×#217—62no—
186#939—34no—
187#939—34no—
188#939—34no—
189#939—34no—
190#939—34no—
191#938—32no—
192#937—34no—
193#937—34no—
194#936—32no—
195#935—34no—
196#935—34no—
197#935—34no—
198D4×Dic3—34no—
199D4×Dic3—34no—
200D4×Dic3—34no—
201D4×Dic3—34no—
202D4×Dic3—32no—
203#930—32no—
204#930C2×D312yes—
205#930C2×D312yes—
206#929—34no—
207#929—34no—
208#929—34no—
209C4×#67—34no—
210C4×#67—34no—
211C4×#67—34no—
212C4×#67—34no—
213C4×#67—34no—
214C2×(C2×D3)⋊C4—32no—
215C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
216#926—32no—
217C2×C4⋊Dic3—32no—
218#924—32no—
219#924—32no—
220#924—32no—
221#924—32no—
222#924—32no—
223#924—62no—
224#924—62no—
225C2×Dic3⋊C4—32no—
226C2×Dic3⋊C4C2×D311yescharacteristic, complemented
227C2×C4×Dic3—32no—
228C2×C4×Dic3—32no—
229C2×C4×Dic3C2×D311yescharacteristic, complemented
230#898—34no—
231#898—34no—
232#897—32no—
233#896—34no—
234#894—34no—
235#892—32no—
236#890—32no—
237#889—34no—
238#889—34no—
239#887—32no—
240#886—34no—
241#886C2×D314yescomplemented
242#885—34no—
243#885—34no—
244#884—34no—
245#883—34no—
246#883—34no—
247#882C2×D314yescomplemented
248#67⋊C4—34no—
249#67⋊C4C2×D314yescomplemented
250#67⋊C4C2×D314yescomplemented
251#879—34no—
252#879—34no—
253#879—34no—
254#878—34no—
255#878—34no—
256#878—34no—
257#878—34no—
258#878—34no—
259#878—64no—
260#878—64no—
261#877—34no—
262#876—34no—
263#875—32no—
264C4×D12—32no—
265#872—34no—
266#870—32no—
267C4×Dic6—32no—
268C23×C32—41no—
269C23×C32—41no—
270C23×C32#4114yescomplemented
271C23×C32C2411yescharacteristic
272C23×C32C2412yes—
273C22×C3×D3—22no—
274C22×C3×D3—24no—
275C22×C3×D3—41no—
276C22×C3×D3—42no—
277C22×C3×D3—42no—
278C22×C3×D3—41no—
279C22×C3×D3C2414yes—
280C22×C3×D3C2412yes—
281C2×C32×C4—41no—
282C2×C32×C4—41no—
283C2×C32×C4C2412yes—
284C2×C32×C4C2412yes—
285C2×C3⋊Dic3—42no—
286C2×C3⋊Dic3—42no—
287C2×C3⋊Dic3C2414yes—
288C2×C3⋊Dic3C2414yes—
289#634—42no—
290#634—42no—
291C3×#67—28no—
292C3×#67—28no—
293C3×#67—28no—
294C2×C3×Dic3—22no—
295C2×C3×Dic3—24no—
296C2×C3×Dic3—24no—
297C2×C3×Dic3—22no—
298C2×C3×Dic3—41no—
299C2×C3×Dic3—42no—
300C2×C3×Dic3C2414yes—
301C2×C3×Dic3C2412yes—
302C2×C3×Dic3C2411yescharacteristic
303C2×C3×Dic3C2412yes—
304C2×C3×Dic3C2411yescharacteristic
305C3×D12—42no—
306C3×D12—42no—
307C3×C4×D3—24no—
308C3×C4×D3—42no—
309#625—44no—
310#625—44no—
311D3×Dic3—28no—
312D3×Dic3—44no—
313#543—91no—
314#539—92no—
315#539—94no—
316#538—92no—
317#538—94no—
318#534—31no—
319#534—92no—
320#529—92no—
321#529—94no—
322#525—94no—
323#525—92no—
324C2×C4×D4—31no—
325C2×C4×D4—92no—
326C24×C3—21no—
327C24×C3—32no—
328C24×C3—31no—
329C24×C3C22×D311yescharacteristic
330C24×C3C22×D311yescharacteristic
331C23×D3C22×D312yes—
332C23×D3C22×D311yescharacteristic
333C2×C3×D4—34no—
334C2×C3×D4—34no—
335C2×C3×D4—34no—
336C2×C3×D4—32no—
337C2×C3×D4—32no—
338C2×C3×D4—68no—
339C2×C3×D4—64no—
340C22×C3×C4—21no—
341C22×C3×C4—21no—
342C22×C3×C4—32no—
343C22×C3×C4—32no—
344C22×C3×C4—31no—
345C22×C3×C4—31no—
346C22×C3×C4—32no—
347C22×C3×C4—31no—
348C22×C3×C4—32no—
349C22×C3×C4—32no—
350C22×C3×C4—122no—
351C22×C3×C4—122no—
352C22×C3×C4C22×D311yescharacteristic
353C22×C3×C4C22×D311yescharacteristic
354C22×C3×C4C22×D311yescharacteristic
355C22×C3×C4C22×D311yescharacteristic
356C2×#67—24no—
357C2×#67—28no—
358C2×#67—34no—
359C2×#67—34no—
360C2×#67—34no—
361C2×#67—34no—
362C2×#67C22×D314yes—
363C2×#67C22×D314yes—
364C2×#67C22×D314yes—
365C22×Dic3—32no—
366C22×Dic3—32no—
367C22×Dic3—32no—
368C22×Dic3—32no—
369C22×Dic3—34no—
370C22×Dic3—34no—
371C22×Dic3—42no—
372C22×Dic3—62no—
373C22×Dic3—62no—
374C22×Dic3—124no—
375C22×Dic3C22×D312yes—
376C22×Dic3C22×D312yes—
377C22×Dic3C22×D311yescharacteristic
378C22×Dic3C22×D311yescharacteristic
379C22×Dic3C22×D312yes—
380C22×Dic3C22×D311yescharacteristic
381#237—124no—
382#235—124no—
383C2×D12C22×D312yes—
384C2×D12C22×D312yes—
385C2×C4×D3—34no—
386C2×C4×D3—34no—
387C2×C4×D3—42no—
388C2×C4×D3—124no—
389C2×C4×D3C22×D312yes—
390C2×C4×D3C22×D312yes—
391C2×Dic6—32no—
392C2×Dic6—32no—
393C2×Dic6—32no—
394C2×Dic6—32no—
395C2×Dic6—62no—
396C2×Dic6—62no—
397C3×C4⋊C4—32no—
398C3×C4⋊C4—32no—
399C3×C4⋊C4—34no—
400C3×C22⋊C4—24no—
401C3×C22⋊C4—34no—
402C3×C22⋊C4—34no—
403C3×C22⋊C4—34no—
404C3×C22⋊C4C22×D314yes—
405C3×C22⋊C4C22×D314yes—
406C3×C42—32no—
407C3×C42—32no—
408#217—34no—
409#217—34no—
410#217—34no—
411#217—34no—
412#217—34no—
413#217—34no—
414#217—34no—
415#217—34no—
416#217—34no—
417#217—34no—
418#217—64no—
419#217—64no—
420(C2×D3)⋊C4—34no—
421(C2×D3)⋊C4—34no—
422(C2×D3)⋊C4—34no—
423(C2×D3)⋊C4—34no—
424(C2×D3)⋊C4—34no—
425(C2×D3)⋊C4—34no—
426(C2×D3)⋊C4C22×D314yes—
427(C2×D3)⋊C4C22×D314yes—
428(C2×D3)⋊C4C22×D314yes—
429C4⋊Dic3—32no—
430C4⋊Dic3—32no—
431C4⋊Dic3—32no—
432C4⋊Dic3—32no—
433C4⋊Dic3—34no—
434C4⋊Dic3—34no—
435C4⋊Dic3—62no—
436C4⋊Dic3—62no—
437C4⋊Dic3C22×D312yes—
438C4⋊Dic3C22×D312yes—
439Dic3⋊C4—34no—
440Dic3⋊C4—34no—
441Dic3⋊C4—34no—
442Dic3⋊C4—34no—
443Dic3⋊C4—34no—
444Dic3⋊C4—34no—
445Dic3⋊C4—34no—
446Dic3⋊C4—34no—
447Dic3⋊C4—34no—
448Dic3⋊C4—34no—
449Dic3⋊C4—64no—
450Dic3⋊C4—64no—
451Dic3⋊C4C22×D314yes—
452C4×Dic3—34no—
453C4×Dic3—34no—
454C4×Dic3—34no—
455C4×Dic3—34no—
456C4×Dic3C22×D312yes—
457C4×Dic3C22×D312yes—
458C22×C32—22no—
459C22×C32—21no—
460C22×C32—22no—
461C22×C32—21no—
462C22×C32—44no—
463C22×C32C2×#4112yes—
464C22×C32C2×#4114yes—
465C22×C32C2511yescharacteristic
466C2×C3×D3—22no—
467C2×C3×D3—24no—
468C2×C3×D3—24no—
469C2×C3×D3—22no—
470C2×C3×D3—22no—
471C2×C3×D3—24no—
472C2×C3×D3—48no—
473C2×C3×D3—44no—
474C32×C4—22no—
475C32×C4—22no—
476C3⋊Dic3—24no—
477C3⋊Dic3—24no—
478C3×Dic3—22no—
479C3×Dic3—24no—
480C3×Dic3—22no—
481C3×Dic3—21no—
482C3×Dic3H(5,𝔽2)12yes—
483C2×#41—92no—
484C22×D4—31no—
485C22×D4—32no—
486C23×C4—31no—
487C23×C4—31no—
488C23×C4—92no—
489#126—94no—
490#126—94no—
491#126—94no—
492#125—92no—
493#125—94no—
494#124—92no—
495#124—94no—
496#123—34no—
497#123—94no—
498#123—94no—
499#123—94no—
500#123—94no—
501#123—94no—
502C22⋊Q8—94no—
503C22⋊Q8—92no—
504C22⋊Q8—92no—
505C22⋊Q8—92no—
506C22⋊Q8—94no—
507C22⋊Q8—94no—
508#121—32no—
509#121—32no—
510#121—94no—
511#121—92no—
512#121—94no—
513#121—94no—
514#120—34no—
515#120—94no—
516#120—94no—
517C4×Q8—92no—
518C4×D4—34no—
519C4×D4—34no—
520C4×D4—92no—
521C4×D4—94no—
522C4×D4—94no—
523C4×D4—94no—
524C4×D4—94no—
525C4×D4—94no—
526#117—94no—
527#117—92no—
528C2×C4⋊C4—31no—
529C2×C4⋊C4—92no—
530C2×C22⋊C4—31no—
531C2×C22⋊C4—92no—
532C2×C22⋊C4—92no—
533C2×C22⋊C4D3211yescharacteristic
534C2×C42—31no—
535C2×C42—92no—
536C23×C3—21no—
537C23×C3—22no—
538C23×C3—24no—
539C23×C3—34no—
540C23×C3—32no—
541C23×C3—41no—
542C23×C3—41no—
543C23×C3—41no—
544C23×C3—41no—
545C23×C3—64no—
546C23×C3—62no—
547C23×C3—81no—
548C23×C3—81no—
549C23×C3—122no—
550C23×C3—121no—
551C23×C3—122no—
552C23×C3—121no—
553C23×C3#23514yescomplemented
554C23×C3#23714yescomplemented
555C23×C3C23×D311yescharacteristic
556C23×C3C23×D312yes—
557C23×C3C23×D311yescharacteristic
558C23×C3C23×D312yes—
559C22×D3—22no—
560C22×D3—24no—
561C22×D3—41no—
562C22×D3—42no—
563C22×D3—41no—
564C22×D3—42no—
565C22×D3C23×D314yes—
566C22×D3C23×D312yes—
567C3×D4—68no—
568C3×D4—68no—
569C3×D4—68no—
570C3×D4—122no—
571C3×D4—122no—
572C2×C3×C4—22no—
573C2×C3×C4—22no—
574C2×C3×C4—31no—
575C2×C3×C4—34no—
576C2×C3×C4—32no—
577C2×C3×C4—32no—
578C2×C3×C4—31no—
579C2×C3×C4—41no—
580C2×C3×C4—41no—
581C2×C3×C4—41no—
582C2×C3×C4—41no—
583C2×C3×C4—64no—
584C2×C3×C4—64no—
585C2×C3×C4—62no—
586C2×C3×C4—64no—
587C2×C3×C4—62no—
588C2×C3×C4—81no—
589C2×C3×C4—81no—
590C2×C3×C4—122no—
591C2×C3×C4—121no—
592C2×C3×C4—122no—
593C2×C3×C4C23×D312yes—
594C2×C3×C4C23×D312yes—
595C2×C3×C4C23×D312yes—
596C2×C3×C4C23×D312yes—
597#67—28no—
598#67—28no—
599#67—28no—
600#67—124no—
601#67—124no—
602#67—124no—
603#67—124no—
604C2×Dic3—22no—
605C2×Dic3—24no—
606C2×Dic3—22no—
607C2×Dic3—24no—
608C2×Dic3—34no—
609C2×Dic3—34no—
610C2×Dic3—34no—
611C2×Dic3—34no—
612C2×Dic3—42no—
613C2×Dic3—41no—
614C2×Dic3—64no—
615C2×Dic3—64no—
616C2×Dic3—68no—
617C2×Dic3—124no—
618C2×Dic3—122no—
619C2×Dic3—122no—
620C2×Dic3—122no—
621C2×Dic3—122no—
622C2×Dic3—242no—
623C2×Dic3—242no—
624C2×Dic3C23×D314yes—
625C2×Dic3C23×D312yes—
626C2×Dic3C23×D312yes—
627C2×Dic3C23×D311yescharacteristic
628C2×Dic3C23×D311yescharacteristic
629D12—42no—
630D12—42no—
631C4×D3—24no—
632C4×D3—42no—
633C4×D3—68no—
634C4×D3—124no—
635Dic6—122no—
636Dic6—122no—
637Dic6—122no—
638Dic6—122no—
639Dic6—242no—
640Dic6—242no—
641C2×C32—22no—
642C2×C32—24no—
643C2×C32C22×#4111yescharacteristic
644C2×C32C2×H(5,𝔽2)11yescharacteristic
645C2×C32#58511yescharacteristic
646C3×D3—42no—
647C3×D3—44no—
648C24—31no—
649C24—32no—
650C24C2×D3211yescharacteristic
651#41—364no—
652C2×Q8—92no—
653C2×Q8—92no—
654C2×D4—34no—
655C2×D4—34no—
656C2×D4—34no—
657C2×D4—32no—
658C2×D4—32no—
659C2×D4—64no—
660C2×D4—68no—
661C2×D4—94no—
662C2×D4—94no—
663C22×C4—31no—
664C22×C4—31no—
665C22×C4—32no—
666C22×C4—32no—
667C22×C4—31no—
668C22×C4—32no—
669C22×C4—32no—
670C22×C4—32no—
671C22×C4—94no—
672C22×C4—94no—
673C22×C4—92no—
674C22×C4—92no—
675C22×C4—122no—
676C22×C4—122no—
677C22×C4—364no—
678C22×C4C2×D3211yescharacteristic
679C22×C4C2×D3211yescharacteristic
680C4⋊C4—34no—
681C4⋊C4—32no—
682C4⋊C4—32no—
683C4⋊C4—94no—
684C4⋊C4—94no—
685C4⋊C4—94no—
686C4⋊C4—94no—
687C4⋊C4—94no—
688C4⋊C4—92no—
689C4⋊C4—94no—
690C4⋊C4—92no—
691C22⋊C4—34no—
692C22⋊C4—34no—
693C22⋊C4—34no—
694C22⋊C4—94no—
695C22⋊C4—94no—
696C22⋊C4—94no—
697C22⋊C4—94no—
698C22⋊C4—94no—
699C22⋊C4—94no—
700C22⋊C4—94no—
701C22⋊C4—94no—
702C22⋊C4C2×D3214yes—
703C42—32no—
704C42—32no—
705C42—94no—
706C42—94no—
707C22×C3—22no—
708C22×C3—21no—
709C22×C3—22no—
710C22×C3—21no—
711C22×C3—22no—
712C22×C3—21no—
713C22×C3—22no—
714C22×C3—21no—
715C22×C3—22no—
716C22×C3—24no—
717C22×C3—21no—
718C22×C3—42no—
719C22×C3—42no—
720C22×C3—41no—
721C22×C3—41no—
722C22×C3—44no—
723C22×C3—44no—
724C22×C3—64no—
725C22×C3—62no—
726C22×C3—64no—
727C22×C3—64no—
728C22×C3—62no—
729C22×C3—62no—
730C22×C3—84no—
731C22×C3—128no—
732C22×C3—124no—
733C22×C3C2×#23512yes—
734C22×C3C2×#23514yes—
735C22×C3C2×#23714yes—
736C22×C3C2×#23712yes—
737C22×C3C24×D311yescharacteristic
738C22×C3C24×D311yescharacteristic
739C2×D3—22no—
740C2×D3—24no—
741C2×D3—22no—
742C2×D3—22no—
743C2×D3—24no—
744C2×D3—24no—
745C2×D3—44no—
746C2×D3—48no—
747C3×C4—22no—
748C3×C4—22no—
749C3×C4—22no—
750C3×C4—22no—
751C3×C4—32no—
752C3×C4—42no—
753C3×C4—42no—
754C3×C4—64no—
755C3×C4—62no—
756C3×C4—62no—
757C3×C4—61no—
758Dic3—22no—
759Dic3—24no—
760Dic3—21no—
761Dic3—22no—
762Dic3—64no—
763Dic3—64no—
764Dic3—64no—
765Dic3—64no—
766Dic3—124no—
767Dic3—124no—
768Dic3#100412yes—
769C32#345911yescharacteristic, complemented, Sylow
770C23—32no—
771C23—34no—
772C23—41no—
773C23—41no—
774C23—62no—
775C23—64no—
776C23—121no—
777C23—122no—
778C23—121no—
779C23—122no—
780C23#379514yescomplemented
781C23C22×D3211yescharacteristic
782C23C22×D3212yes—
783Q8—362no—
784Q8—362no—
785D4—68no—
786D4—68no—
787D4—68no—
788D4—122no—
789D4—122no—
790D4—364no—
791D4—364no—
792C2×C4—31no—
793C2×C4—32no—
794C2×C4—31no—
795C2×C4—34no—
796C2×C4—32no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—64no—
800C2×C4—62no—
801C2×C4—64no—
802C2×C4—62no—
803C2×C4—64no—
804C2×C4—94no—
805C2×C4—94no—
806C2×C4—122no—
807C2×C4—122no—
808C2×C4—121no—
809C2×C4—188no—
810C2×C4—364no—
811C2×C4—362no—
812C2×C4—362no—
813C2×C4C22×D3212yes—
814C2×C4C22×D3212yes—
815C2×C3—22no—
816C2×C3—24no—
817C2×C3—24no—
818C2×C3—22no—
819C2×C3—21no—
820C2×C3—21no—
821C2×C3—21no—
822C2×C3—44no—
823C2×C3—42no—
824C2×C3—124no—
825C2×C3—122no—
826C2×C3C22×#23511yescharacteristic
827C2×C3C22×#23711yescharacteristic
828C2×C3C2×#100411yescharacteristic
829C2×C3#596411yescharacteristic
830C2×C3D3×H(5,𝔽2)11yescharacteristic
831C2×C3#596611yescharacteristic
832D3—42no—
833D3—44no—
834C22—21no—
835C22—22no—
836C22—21no—
837C22—22no—
838C22—44no—
839C22—62no—
840C22—64no—
841C22—62no—
842C22—64no—
843C22—64no—
844C22—62no—
845C22—124no—
846C22—128no—
847C22C2×#379512yes—
848C22C2×#379514yes—
849C22C23×D3211yescharacteristic
850C4—22no—
851C4—22no—
852C4—32no—
853C4—62no—
854C4—64no—
855C4—61no—
856C4—62no—
857C4—184no—
858C4—184no—
859C3—21no—
860C3#8577611yescharacteristic, complemented
861C3#8629511yescharacteristic, complemented
862C2—22no—
863C2—24no—
864C2—122no—
865C2—124no—
866C2C22×#379511yescharacteristic
867C2D3×#100411yescharacteristic
868C2#1059667811yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC2×C32×C22⋊C4C22
hypercenterC2×C22⋊C4D32
hypocenterC32#3459
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. C3×#5493C2semidirect
3. C2×C3×#67⋊C4C2semidirect
4. #10595518C2semidirect
5. C2×Dic3×#67C2semidirect
6. #10594977C2semidirect
7. #10594973C2semidirect
8. #10594949C2semidirect
9. #10594892C2semidirect
10. #10594238C2semidirect
11. #10594177C2semidirect
12. #10594131C2semidirect
13. #10594054C2semidirect
19. C22×C3×C4×D3C22semidirect
20. C22×D3×Dic3C22semidirect
21. C2×#3795C22semidirect
24. #64133C22semidirect
25. #64133C22semidirect
26. #64087C22semidirect
27. #64087C22semidirect
30. C2×C3×(C2×D3)⋊C4C22semidirect
31. C2×C3×Dic3⋊C4C22semidirect
32. C2×C3×C4×Dic3C22semidirect
33. C3×#886C22semidirect
34. C3×#882C22semidirect
35. C3×#67⋊C4C22semidirect
36. C3×#67⋊C4C22semidirect
39. #63976C22semidirect
40. #63976C22semidirect
41. Dic3×#67C22semidirect
42. Dic3×#67C22semidirect
43. Dic3×#67C22semidirect
44. Dic3×#67C22semidirect
45. C2×Dic3⋊Dic3C22semidirect
46. #63961C22semidirect
47. #63961C22semidirect
48. C2×(C2×D3)⋊Dic3C22semidirect
49. C2×Dic32C22semidirect
50. #63913C22semidirect
51. #63908C22semidirect
52. #63905C22semidirect
53. #63896C22semidirect
54. Dic3×D12C22semidirect
55. #63891C22semidirect
56. #63885C22semidirect
57. #63884C22semidirect
58. #63879C22semidirect
59. #63877C22semidirect
60. #63869C22semidirect
61. #63861C22semidirect
62. #63860C22semidirect
63. #63859C22semidirect
64. #63858C22semidirect
65. #63857C22semidirect
66. #63847C22semidirect
67. #63844C22semidirect
68. #63841C22semidirect
90. #5493D3semidirect
91. C2×#67⋊C4D3semidirect
167. C22×C4×D3C2×D3semidirect
215. C2×(C2×D3)⋊C4C2×D3semidirect
226. C2×Dic3⋊C4C2×D3semidirect
229. C2×C4×Dic3C2×D3semidirect
241. #886C2×D3semidirect
247. #882C2×D3semidirect
249. #67⋊C4C2×D3semidirect
250. #67⋊C4C2×D3semidirect
270. C23×C32#41semidirect
553. C23×C3#235semidirect
554. C23×C3#237semidirect
769. C32#3459semidirect
780. C23#3795semidirect
860. C3#85776semidirect
861. C3#86295semidirect

Maximal subgroups

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

subgroupindex
#105959542
C3×#54932
C2×C3×#67⋊C42
#105955182
C2×Dic3×#672
#105949772
#105949732
#105949492
#105948922
#105942382
#105941772
#105941312
#105940542
#862953
#857763