Finite Group Databasebeta

← #11904423

Subgroups — #11904423

Order 1152.

3289 conjugacy classes of subgroups.

The subgroup lattice has 1066 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64330C211yesmaximal, characteristic, complemented
2C22×#3804C211yesmaximal, characteristic, complemented
3#10595957C211yesmaximal, characteristic, complemented
4C3×#5493C211yesmaximal, characteristic, complemented
5C2×C3×#886C211yesmaximal, characteristic, complemented
6#10595518C211yesmaximal, characteristic, complemented
7C2×#63961C211yesmaximal, characteristic, complemented
8#10595083C214yesmaximal, complemented
9#10594928C214yesmaximal, complemented
10#10594296C212yesmaximal, complemented
11#10594295C212yesmaximal, complemented
12#10594294C214yesmaximal, complemented
13#10594084C212yesmaximal, complemented
14#10594083C214yesmaximal, complemented
15#10594082C212yesmaximal, complemented
16#86296—31nomaximal
17#86012—31nomaximal
18C22×#638C2211yescharacteristic
19C22×C3×#67C2211yescharacteristic
20C22×C3×#67C2211yescharacteristic
21C22×C3×#67C2211yescharacteristic, complemented
22C23×C3×Dic3C2211yescharacteristic, complemented
23#64330—28no—
24C2×#3811C2212yes—
25C2×D3×#67C2212yescomplemented
26C2×D3×#67C2212yescomplemented
27C22×#627C2211yescharacteristic, complemented
28C22×#626C2211yescharacteristic, complemented
29C22×#624C2211yescharacteristic, complemented
30C2×#3805C2212yes—
31C2×#3804—28no—
32C2×#3804C2214yescomplemented
33C2×#3804C2212yescomplemented
34C2×#3804C2214yescomplemented
35C2×#3804C2212yescomplemented
36C22×D3×Dic3C2211yescharacteristic, complemented
37C2×C32×C22⋊C4C2211yescharacteristic, complemented
38C2×#3757C2211yescharacteristic, complemented
39C4×#638C2214yescomplemented
40#64090C2214yescomplemented
41C22⋊C4×C3⋊D3C2212yescomplemented
42#64086C2212yescomplemented
43C3×#930C2214yescomplemented
44C2×C3×(C2×D3)⋊C4C2212yescomplemented
45C2×C3×C4⋊Dic3C2212yescomplemented
46C3×#886C2212yescomplemented
47C3×#886C2214yescomplemented
48C3×#886C2212yescomplemented
49C3×#886C2212yescomplemented
50C3×#886C2212yescomplemented
51C3×#882C2212yescomplemented
52C3×#882C2212yescomplemented
53#63980C2214yescomplemented
54#63976C2212yescomplemented
55#63976C2212yescomplemented
56C2×#3724C2212yescomplemented
57#63961C2214yescomplemented
58#63961C2212yescomplemented
59#63961C2212yescomplemented
60#63961C2212yescomplemented
61#63961C2212yescomplemented
62C2×(C2×D3)⋊Dic3C2212yescomplemented
63#63922C2214yescomplemented
64#63921C2214yescomplemented
65#63919C2214yescomplemented
66#63916C2214yescomplemented
67#63915C2214yescomplemented
68#63912C2214yescomplemented
69#63902C2214yescomplemented
70#63900C2214yescomplemented
71#63899C2214yescomplemented
72#63899C2214yescomplemented
73#63899C2214yescomplemented
74#63898C2214yescomplemented
75#63885C2214yescomplemented
76#63854C2214yescomplemented
77#63854C2214yescomplemented
78#63854C2214yescomplemented
79C2×#1004—31no—
80C2×#1004—31no—
81C22×#237—31no—
82C22×#235—31no—
83C3×#534—31no—
84C2×C3×#123—31no—
85#5804—31no—
86#5804—31no—
87C2×#935—31no—
88C2×#929—31no—
89#5656—32no—
90#5655—34no—
91#5655—34no—
92#5654—34no—
93#5653—32no—
94D3×#123—32no—
95D3×#123—32no—
96#5648—32no—
97#5648—32no—
98#5611—34no—
99#5610—34no—
100#5591—34no—
101#5589—32no—
102#5586—32no—
103#5507—34no—
104#5493D311yescharacteristic, complemented
105C2×#886D311yescharacteristic, complemented
106#5490—34no—
107#5486—31no—
108#5486—31no—
109#5486—61no—
110C24×C32C2311yescharacteristic
111C23×C3⋊D3C2311yescharacteristic
112C23×C3×D3C2311yescharacteristic
113C23×C3×D3C2311yescharacteristic
114C23×C3×D3C2311yescharacteristic
115C22×D32C2312yes—
116C22×C32×C4C2312yes—
117C2×#638D418yescomplemented
118C2×#638C2312yes—
119C2×#638C2312yes—
120C22×C3⋊Dic3C2312yes—
121C22×C3⋊Dic3C2311yescharacteristic
122C2×C4×C3⋊D3C2314yes—
123C2×C3×#67—24no—
124C2×C3×#67—24no—
125C2×C3×#67—24no—
126C2×C3×#67C2312yes—
127C2×C3×#67C2312yes—
128C2×C3×#67C2312yes—
129C2×C3×#67C2312yes—
130C2×C3×#67C2312yes—
131C2×C3×#67C2312yes—
132C22×C3×Dic3—24no—
133C22×C3×Dic3C2311yescharacteristic
134C22×C3×Dic3C2312yes—
135C22×C3×Dic3C2311yescharacteristic
136C22×C3×Dic3C2311yescharacteristic
137C22×C3×Dic3C2311yescharacteristic
138C22×C3×Dic3C2311yescharacteristic
139C22×C3×Dic3C2312yes—
140C2×C3×D12C2314yes—
141#3811—28no—
142D3×#67—28no—
143D3×#67—28no—
144C2×#627—24no—
145C2×#627C2312yes—
146C2×#627C2314yes—
147C2×#626—24no—
148C2×#626C2314yes—
149C2×#626C2312yes—
150C2×#626C2312yes—
151C2×#625C2312yes—
152C2×#625C2314yes—
153C2×#624—24no—
154C2×#624C2314yes—
155C2×#624C2312yes—
156#3805—28no—
157#3804—216no—
158#3804—216no—
159#3804—28no—
160#3804—28no—
161C2×D3×Dic3—24no—
162C2×D3×Dic3C2314yes—
163C2×D3×Dic3C2312yes—
164C2×D3×Dic3C2312yes—
165C32×C22⋊C4C2312yes—
166C32×C22⋊C4C2312yes—
167#3757C2312yes—
168#3757C2312yes—
169#3752C2314yes—
170#3750C2314yes—
171C4×C3⋊Dic3C2314yes—
172C3×(C2×D3)⋊C4C2314yes—
173C3×(C2×D3)⋊C4C2314yes—
174C3×(C2×D3)⋊C4C2314yes—
175C3×(C2×D3)⋊C4C2314yes—
176C3×C4⋊Dic3C2314yes—
177C3×C4⋊Dic3C2314yes—
178C3×C4⋊Dic3C2314yes—
179#3724C2314yes—
180#3724C2314yes—
181#3724C2314yes—
182(C2×D3)⋊Dic3C2314yes—
183(C2×D3)⋊Dic3C2314yes—
184(C2×D3)⋊Dic3C2314yes—
185(C2×D3)⋊Dic3C2314yes—
186#3485—91noSylow
187C22×C3×D4—31no—
188C22×C3×D4—31no—
189C22×C3×D4—31no—
190C23×C3×C4—31no—
191C22×#67—31no—
192C22×#67—31no—
193C22×#67—32no—
194C22×#67—32no—
195C22×#67—31no—
196C22×#67—61no—
197C22×#67C2×D311yescharacteristic
198C22×#67C2×D311yescharacteristic
199C22×#67C2×D311yescharacteristic, complemented
200C23×Dic3—31no—
201C23×Dic3C2×D311yescharacteristic, complemented
202#1004—68no—
203#1004—68no—
204C2×#237—32no—
205C2×#237—32no—
206C2×#237—32no—
207C2×#237—34no—
208C2×#237—34no—
209C2×#237—32no—
210C2×#237—68no—
211C2×D3×D4—32no—
212C2×D3×D4—32no—
213C2×D3×D4—32no—
214C2×D3×D4—32no—
215C2×#235—34no—
216C2×#235—32no—
217C2×#235—34no—
218C2×#235—32no—
219C2×#235—68no—
220C22×D12—31no—
221C22×C4×D3—31no—
222C22×C4×D3—31no—
223C22×C4×D3—31no—
224C22×Dic6—31no—
225C22×Dic6—31no—
226C3×#123—32no—
227C3×#123—32no—
228C3×#123—32no—
229C3×#123—34no—
230C3×#123—32no—
231C3×#121—34no—
232C3×#120—32no—
233C3×#120—32no—
234C2×C3×C4⋊C4—32no—
235C2×C3×C22⋊C4—21no—
236C2×C3×C22⋊C4—32no—
237C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
238C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
239#953—32no—
240#953—32no—
241C2×#217—31no—
242C2×#217—31no—
243C2×#217—32no—
244C2×#217—61no—
245#939—34no—
246#939—34no—
247#939—34no—
248#938—34no—
249#937—32no—
250#937—32no—
251#937—34no—
252#935—32no—
253#935—32no—
254#935—32no—
255#935—34no—
256#935—32no—
257D4×Dic3—34no—
258#930C2×D314yescomplemented
259#929—32no—
260#929—32no—
261#929—32no—
262#929—34no—
263#929—32no—
264C4×#67—34no—
265C4×#67—34no—
266C4×#67—64no—
267C2×(C2×D3)⋊C4—32no—
268C2×(C2×D3)⋊C4C2×D312yescomplemented
269C2×C4⋊Dic3C2×D312yescomplemented
270C2×Dic3⋊C4—32no—
271C2×Dic3⋊C4—32no—
272#896—34no—
273#896—34no—
274#896—34no—
275#895—34no—
276#894—34no—
277#894—34no—
278#894—34no—
279#893—34no—
280D3×C4⋊C4—34no—
281D3×C4⋊C4—34no—
282#888—34no—
283#888—34no—
284#886C2×D312yescomplemented
285#886C2×D312yescomplemented
286#886C2×D312yescomplemented
287#886C2×D312yescomplemented
288#886C2×D314yescomplemented
289#885—34no—
290#885—34no—
291#884—34no—
292#884—34no—
293#884—34no—
294#883—34no—
295#883—34no—
296#883—34no—
297#882—34no—
298#882C2×D312yescomplemented
299#882C2×D312yescomplemented
300#67⋊C4—34no—
301#67⋊C4—34no—
302#67⋊C4—34no—
303#67⋊C4—34no—
304#67⋊C4—64no—
305D3×C22⋊C4—32no—
306D3×C22⋊C4—32no—
307D3×C22⋊C4—34no—
308D3×C22⋊C4—34no—
309D3×C22⋊C4—62no—
310#878—34no—
311#878—34no—
312#878—34no—
313#877—32no—
314#877—32no—
315#877—62no—
316C23×C32—42no—
317C23×C32C2×D414yes—
318C23×C32C2411yescharacteristic
319C23×C32C2411yescharacteristic
320C23×C32C2411yescharacteristic
321C22×C3⋊D3—42no—
322C22×C3⋊D3C2×D414yes—
323C22×C3⋊D3C2412yes—
324C22×C3×D3—22no—
325C22×C3×D3—22no—
326C22×C3×D3—22no—
327C22×C3×D3—42no—
328C22×C3×D3—42no—
329C22×C3×D3—42no—
330C22×C3×D3C2412yes—
331C22×C3×D3C2412yes—
332C22×C3×D3C2412yes—
333C2×D32—24no—
334C2×D32—44no—
335C2×C32×C4—42no—
336C2×C32×C4C2414yes—
337#638C2×D418yes—
338#638C2×D418yes—
339C2×C3⋊Dic3—42no—
340C2×C3⋊Dic3C2×D414yes—
341C2×C3⋊Dic3C2414yes—
342C2×C3⋊Dic3C2412yes—
343C4×C3⋊D3—44no—
344C3×#67—24no—
345C3×#67—24no—
346C3×#67—24no—
347C3×#67—24no—
348C3×#67—24no—
349C3×#67—24no—
350C2×C3×Dic3—22no—
351C2×C3×Dic3—24no—
352C2×C3×Dic3—24no—
353C2×C3×Dic3—22no—
354C2×C3×Dic3—22no—
355C2×C3×Dic3—22no—
356C2×C3×Dic3—22no—
357C2×C3×Dic3C2412yes—
358C2×C3×Dic3C2412yes—
359C2×C3×Dic3C2412yes—
360C2×C3×Dic3C2412yes—
361C2×C3×Dic3C2412yes—
362C3×D12—44no—
363#627—24no—
364#627—28no—
365#626—28no—
366#626—24no—
367#626—24no—
368#625—24no—
369#625—44no—
370#624—28no—
371#624—24no—
372D3×Dic3—28no—
373D3×Dic3—24no—
374D3×Dic3—24no—
375C2×H(5,𝔽2)—91no—
376C22×#41—91no—
377#547—94no—
378#547—94no—
379#546—94no—
380#546—94no—
381#536—92no—
382#534—31no—
383#534—92no—
384#534—91no—
385#525—92no—
386C2×#123—31no—
387C2×#123—92no—
388C2×#123—91no—
389#518—91no—
390C24×C3—21no—
391C24×C3—31no—
392C24×C3—31no—
393C24×C3—31no—
394C24×C3C22×D311yescharacteristic
395C24×C3C22×D311yescharacteristic
396C23×D3—31no—
397C23×D3—31no—
398C23×D3—32no—
399C23×D3—32no—
400C23×D3—61no—
401C23×D3C22×D311yescharacteristic
402C23×D3C22×D311yescharacteristic
403C23×D3C22×D311yescharacteristic
404C2×C3×D4—32no—
405C2×C3×D4—32no—
406C2×C3×D4—32no—
407C2×C3×D4—32no—
408C2×C3×D4—32no—
409C2×C3×D4—32no—
410C2×C3×D4—34no—
411C2×C3×D4—64no—
412C2×C3×D4—64no—
413C2×C3×D4—64no—
414C22×C3×C4—22no—
415C22×C3×C4—31no—
416C22×C3×C4—32no—
417C22×C3×C4—32no—
418C22×C3×C4—31no—
419C22×C3×C4—31no—
420C22×C3×C4—31no—
421C22×C3×C4—31no—
422C22×C3×C4—64no—
423C22×C3×C4C22×D312yes—
424C22×C3×C4C22×D312yes—
425C2×#67—24no—
426C2×#67—24no—
427C2×#67—24no—
428C2×#67—38no—
429C2×#67—38no—
430C2×#67—32no—
431C2×#67—32no—
432C2×#67—32no—
433C2×#67—32no—
434C2×#67—32no—
435C2×#67—32no—
436C2×#67—34no—
437C2×#67—34no—
438C2×#67—32no—
439C2×#67—32no—
440C2×#67—34no—
441C2×#67—62no—
442C2×#67—62no—
443C2×#67—68no—
444C2×#67—64no—
445C2×#67—68no—
446C2×#67—68no—
447C2×#67C22×D312yes—
448C2×#67C22×D312yes—
449C2×#67C22×D312yes—
450C2×#67C22×D312yes—
451C2×#67C22×D312yes—
452C2×#67C22×D312yes—
453C22×Dic3—24no—
454C22×Dic3—31no—
455C22×Dic3—31no—
456C22×Dic3—32no—
457C22×Dic3—32no—
458C22×Dic3—32no—
459C22×Dic3—32no—
460C22×Dic3—34no—
461C22×Dic3—61no—
462C22×Dic3—62no—
463C22×Dic3—64no—
464C22×Dic3C22×D311yescharacteristic
465C22×Dic3C22×D312yes—
466C22×Dic3C22×D311yescharacteristic
467C22×Dic3C22×D311yescharacteristic
468C22×Dic3C22×D311yescharacteristic
469C22×Dic3C22×D311yescharacteristic
470C22×Dic3C22×D312yes—
471#237—616no—
472#237—616no—
473#237—68no—
474#237—68no—
475#237—68no—
476#237—68no—
477D3×D4—68no—
478D3×D4—68no—
479D3×D4—68no—
480D3×D4—68no—
481#235—616no—
482#235—616no—
483#235—68no—
484#235—68no—
485C2×D12—34no—
486C2×D12—32no—
487C2×D12—32no—
488C2×D12—64no—
489C2×D12C22×D314yes—
490C2×C4×D3—32no—
491C2×C4×D3—34no—
492C2×C4×D3—32no—
493C2×C4×D3—34no—
494C2×C4×D3—34no—
495C2×C4×D3—32no—
496C2×C4×D3—32no—
497C2×C4×D3—34no—
498C2×C4×D3—34no—
499C2×C4×D3—64no—
500C2×C4×D3—64no—
501C2×C4×D3—64no—
502C2×C4×D3—64no—
503C2×Dic6—32no—
504C2×Dic6—34no—
505C2×Dic6—34no—
506C2×Dic6—32no—
507C2×Dic6—64no—
508C2×Dic6—64no—
509C3×C4⋊C4—34no—
510C3×C4⋊C4—34no—
511C3×C4⋊C4—34no—
512C3×C22⋊C4—22no—
513C3×C22⋊C4—22no—
514C3×C22⋊C4—34no—
515C3×C22⋊C4—34no—
516C3×C22⋊C4—34no—
517C3×C22⋊C4—34no—
518C3×C22⋊C4C22×D312yes—
519C3×C22⋊C4C22×D312yes—
520C3×C22⋊C4C22×D312yes—
521C3×C22⋊C4C22×D312yes—
522#217—32no—
523#217—32no—
524#217—32no—
525#217—32no—
526#217—34no—
527#217—34no—
528#217—34no—
529#217—34no—
530#217—62no—
531#217—62no—
532(C2×D3)⋊C4—34no—
533(C2×D3)⋊C4—34no—
534(C2×D3)⋊C4—34no—
535(C2×D3)⋊C4—34no—
536(C2×D3)⋊C4—34no—
537(C2×D3)⋊C4—34no—
538(C2×D3)⋊C4—64no—
539(C2×D3)⋊C4C22×D314yes—
540(C2×D3)⋊C4C22×D314yes—
541(C2×D3)⋊C4C22×D314yes—
542(C2×D3)⋊C4C22×D314yes—
543C4⋊Dic3C22×D314yes—
544C4⋊Dic3C22×D314yes—
545C4⋊Dic3C22×D314yes—
546Dic3⋊C4—34no—
547Dic3⋊C4—34no—
548Dic3⋊C4—34no—
549Dic3⋊C4—34no—
550Dic3⋊C4—34no—
551Dic3⋊C4—34no—
552Dic3⋊C4—34no—
553Dic3⋊C4—34no—
554Dic3⋊C4—64no—
555C4×Dic3—34no—
556C4×Dic3—34no—
557C4×Dic3—64no—
558C22×C32—22no—
559C22×C32—22no—
560C22×C32—22no—
561C22×C32—44no—
562C22×C32C22×D412yes—
563C22×C32C22×D412yes—
564C22×C32C22×D412yes—
565C22×C32C2511yescharacteristic
566C2×C3⋊D3—24no—
567C2×C3⋊D3—44no—
568C2×C3⋊D3C22×D414yes—
569C2×C3×D3—22no—
570C2×C3×D3—22no—
571C2×C3×D3—22no—
572C2×C3×D3—24no—
573C2×C3×D3—24no—
574C2×C3×D3—24no—
575C2×C3×D3—44no—
576C2×C3×D3—82no—
577C2×C3×D3—82no—
578D32—84no—
579C32×C4—24no—
580C3⋊Dic3—24no—
581C3⋊Dic3C22×D414yes—
582C3×Dic3—22no—
583C3×Dic3—22no—
584C3×Dic3—22no—
585C3×Dic3—22no—
586C3×Dic3—22no—
587H(5,𝔽2)—188no—
588C2×#41—94no—
589C2×#41—94no—
590C2×#41—92no—
591C2×#41—92no—
592C2×#41—92no—
593C2×#41—188no—
594C22×Q8—91no—
595C22×D4—31no—
596C22×D4—31no—
597C22×D4—31no—
598C22×D4—91no—
599C22×D4—92no—
600C22×D4—92no—
601C22×D4—92no—
602C22×D4—91no—
603C23×C4—31no—
604C23×C4—91no—
605C23×C4—91no—
606C4⋊Q8—94no—
607#124—94no—
608#123—32no—
609#123—32no—
610#123—34no—
611#123—32no—
612#123—32no—
613#123—94no—
614#123—94no—
615#123—94no—
616#123—92no—
617#123—92no—
618#123—92no—
619#123—94no—
620#123—92no—
621C22⋊Q8—94no—
622C22⋊Q8—94no—
623C22⋊Q8—94no—
624#121—34no—
625#121—94no—
626#121—94no—
627#121—94no—
628#121—94no—
629#120—32no—
630#120—32no—
631#120—94no—
632#120—92no—
633#120—92no—
634C4×D4—94no—
635C4×D4—94no—
636C4×D4—94no—
637C4×D4—94no—
638#117—92no—
639C2×C4⋊C4—32no—
640C2×C4⋊C4—94no—
641C2×C4⋊C4—92no—
642C2×C22⋊C4—32no—
643C2×C22⋊C4—94no—
644C2×C22⋊C4—92no—
645C2×C22⋊C4—91no—
646C2×C22⋊C4—92no—
647C2×C22⋊C4D3211yescharacteristic, complemented
648C23×C3—21no—
649C23×C3—21no—
650C23×C3—21no—
651C23×C3—24no—
652C23×C3—32no—
653C23×C3—32no—
654C23×C3—32no—
655C23×C3—42no—
656C23×C3—42no—
657C23×C3—62no—
658C23×C3—62no—
659C23×C3—62no—
660C23×C3—82no—
661C23×C3—122no—
662C23×C3—122no—
663C23×C3—122no—
664C23×C3D3×D414yes—
665C23×C3D3×D414yes—
666C23×C3C23×D311yescharacteristic
667C23×C3C23×D311yescharacteristic
668C23×C3C23×D311yescharacteristic
669C23×C3C23×D311yescharacteristic
670C23×C3C23×D311yescharacteristic
671C23×C3C23×D311yescharacteristic
672C22×D3—22no—
673C22×D3—22no—
674C22×D3—22no—
675C22×D3—32no—
676C22×D3—32no—
677C22×D3—34no—
678C22×D3—34no—
679C22×D3—42no—
680C22×D3—42no—
681C22×D3—42no—
682C22×D3—62no—
683C22×D3—64no—
684C22×D3—64no—
685C22×D3—64no—
686C22×D3—124no—
687C22×D3—124no—
688C22×D3—122no—
689C22×D3—122no—
690C22×D3—242no—
691C22×D3C23×D312yes—
692C22×D3C23×D312yes—
693C22×D3C23×D312yes—
694C3×D4—64no—
695C3×D4—64no—
696C3×D4—64no—
697C3×D4—64no—
698C3×D4—64no—
699C3×D4—64no—
700C3×D4—124no—
701C2×C3×C4—24no—
702C2×C3×C4—32no—
703C2×C3×C4—32no—
704C2×C3×C4—32no—
705C2×C3×C4—32no—
706C2×C3×C4—32no—
707C2×C3×C4—42no—
708C2×C3×C4—42no—
709C2×C3×C4—62no—
710C2×C3×C4—62no—
711C2×C3×C4—62no—
712C2×C3×C4—64no—
713C2×C3×C4—64no—
714C2×C3×C4—62no—
715C2×C3×C4—62no—
716C2×C3×C4—82no—
717C2×C3×C4C23×D314yes—
718C2×C3×C4C23×D314yes—
719#67—24no—
720#67—24no—
721#67—24no—
722#67—24no—
723#67—24no—
724#67—24no—
725#67—38no—
726#67—38no—
727#67—38no—
728#67—38no—
729#67—68no—
730#67—68no—
731#67—64no—
732#67—64no—
733#67—68no—
734#67—64no—
735#67—64no—
736#67—124no—
737#67—124no—
738C2×Dic3—22no—
739C2×Dic3—22no—
740C2×Dic3—22no—
741C2×Dic3—24no—
742C2×Dic3—24no—
743C2×Dic3—22no—
744C2×Dic3—22no—
745C2×Dic3—34no—
746C2×Dic3—34no—
747C2×Dic3—32no—
748C2×Dic3—32no—
749C2×Dic3—34no—
750C2×Dic3—34no—
751C2×Dic3—64no—
752C2×Dic3—62no—
753C2×Dic3—64no—
754C2×Dic3—68no—
755C2×Dic3—64no—
756C2×Dic3—64no—
757C2×Dic3—122no—
758C2×Dic3—122no—
759C2×Dic3—242no—
760C2×Dic3C23×D312yes—
761C2×Dic3C23×D312yes—
762C2×Dic3C23×D312yes—
763C2×Dic3C23×D312yes—
764C2×Dic3C23×D312yes—
765D12—44no—
766D12—68no—
767D12—64no—
768D12—64no—
769C4×D3—68no—
770C4×D3—68no—
771C4×D3—64no—
772C4×D3—64no—
773C4×D3—68no—
774C4×D3—64no—
775C4×D3—64no—
776C4×D3—124no—
777C4×D3—124no—
778C4×D3—244no—
779Dic6—68no—
780Dic6—68no—
781Dic6—64no—
782Dic6—64no—
783C2×C32—22no—
784C2×C32—22no—
785C2×C32—22no—
786C2×C32C23×D411yescharacteristic
787C2×C32#58512yes—
788C3⋊D3—24no—
789C3×D3—42no—
790C3×D3—42no—
791C3×D3—42no—
792C24—31no—
793C24—31no—
794C24—31no—
795C24—92no—
796C24—91no—
797C24C2×D3211yescharacteristic
798#41—1816no—
799#41—1816no—
800#41—188no—
801#41—188no—
802#41—188no—
803C2×Q8—94no—
804C2×Q8—92no—
805C2×Q8—184no—
806C2×D4—32no—
807C2×D4—32no—
808C2×D4—32no—
809C2×D4—32no—
810C2×D4—32no—
811C2×D4—32no—
812C2×D4—34no—
813C2×D4—64no—
814C2×D4—64no—
815C2×D4—64no—
816C2×D4—94no—
817C2×D4—92no—
818C2×D4—92no—
819C2×D4—92no—
820C2×D4—92no—
821C2×D4—98no—
822C2×D4—92no—
823C2×D4—94no—
824C2×D4—184no—
825C2×D4—188no—
826C2×D4—188no—
827C2×D4—188no—
828C22×C4—32no—
829C22×C4—32no—
830C22×C4—31no—
831C22×C4—31no—
832C22×C4—31no—
833C22×C4—31no—
834C22×C4—31no—
835C22×C4—64no—
836C22×C4—94no—
837C22×C4—92no—
838C22×C4—94no—
839C22×C4—92no—
840C22×C4—92no—
841C22×C4—91no—
842C22×C4—92no—
843C22×C4—94no—
844C22×C4—184no—
845C22×C4—184no—
846C22×C4C2×D3212yes—
847C4⋊C4—34no—
848C4⋊C4—34no—
849C4⋊C4—34no—
850C4⋊C4—94no—
851C4⋊C4—94no—
852C4⋊C4—94no—
853C4⋊C4—94no—
854C22⋊C4—34no—
855C22⋊C4—34no—
856C22⋊C4—34no—
857C22⋊C4—34no—
858C22⋊C4—94no—
859C22⋊C4—94no—
860C22⋊C4—94no—
861C22⋊C4—94no—
862C22⋊C4—92no—
863C22⋊C4—92no—
864C22⋊C4—94no—
865C22⋊C4C2×D3212yes—
866C22⋊C4C2×D3212yes—
867C42—94no—
868C22×C3—22no—
869C22×C3—22no—
870C22×C3—22no—
871C22×C3—22no—
872C22×C3—22no—
873C22×C3—22no—
874C22×C3—22no—
875C22×C3—22no—
876C22×C3—22no—
877C22×C3—21no—
878C22×C3—42no—
879C22×C3—42no—
880C22×C3—42no—
881C22×C3—44no—
882C22×C3—44no—
883C22×C3—62no—
884C22×C3—62no—
885C22×C3—62no—
886C22×C3—64no—
887C22×C3—64no—
888C22×C3—64no—
889C22×C3—84no—
890C22×C3—124no—
891C22×C3—242no—
892C22×C3—242no—
893C22×C3C2×D3×D412yes—
894C22×C3C2×D3×D412yes—
895C22×C3C2×D3×D412yes—
896C22×C3C2×D3×D412yes—
897C22×C3C2×D3×D412yes—
898C22×C3C2×D3×D412yes—
899C22×C3C24×D311yescharacteristic
900C22×C3C24×D311yescharacteristic
901C2×D3—22no—
902C2×D3—22no—
903C2×D3—22no—
904C2×D3—24no—
905C2×D3—24no—
906C2×D3—24no—
907C2×D3—34no—
908C2×D3—34no—
909C2×D3—44no—
910C2×D3—64no—
911C2×D3—64no—
912C2×D3—64no—
913C2×D3—82no—
914C2×D3—82no—
915C2×D3—124no—
916C2×D3—124no—
917C2×D3—124no—
918C2×D3—244no—
919C2×D3—244no—
920C2×D3—244no—
921C3×C4—24no—
922C3×C4—24no—
923C3×C4—44no—
924C3×C4—62no—
925C3×C4—62no—
926C3×C4—62no—
927C3×C4—62no—
928C3×C4—62no—
929Dic3—22no—
930Dic3—22no—
931Dic3—22no—
932Dic3—22no—
933Dic3—22no—
934Dic3—34no—
935Dic3—34no—
936Dic3—64no—
937Dic3—64no—
938Dic3—64no—
939Dic3—124no—
940C32#348511yescharacteristic, complemented, Sylow
941C23—32no—
942C23—32no—
943C23—32no—
944C23—42no—
945C23—62no—
946C23—62no—
947C23—62no—
948C23—92no—
949C23—94no—
950C23—122no—
951C23—122no—
952C23—122no—
953C23—184no—
954C23—362no—
955C23—364no—
956C23#380214yes—
957C23C22×D3211yescharacteristic
958C23C22×D3211yescharacteristic
959C23C22×D3211yescharacteristic
960Q8—188no—
961Q8—184no—
962D4—64no—
963D4—64no—
964D4—64no—
965D4—64no—
966D4—64no—
967D4—64no—
968D4—98no—
969D4—98no—
970D4—124no—
971D4—184no—
972D4—184no—
973D4—188no—
974D4—184no—
975D4—364no—
976C2×C4—32no—
977C2×C4—32no—
978C2×C4—32no—
979C2×C4—32no—
980C2×C4—32no—
981C2×C4—42no—
982C2×C4—62no—
983C2×C4—62no—
984C2×C4—64no—
985C2×C4—64no—
986C2×C4—62no—
987C2×C4—62no—
988C2×C4—62no—
989C2×C4—94no—
990C2×C4—92no—
991C2×C4—94no—
992C2×C4—188no—
993C2×C4—184no—
994C2×C4—188no—
995C2×C4—184no—
996C2×C4—184no—
997C2×C4—364no—
998C2×C4—362no—
999C2×C4C22×D3214yes—
1000C2×C3—22no—
1001C2×C3—22no—
1002C2×C3—22no—
1003C2×C3—22no—
1004C2×C3—22no—
1005C2×C3—22no—
1006C2×C3—21no—
1007C2×C3—22no—
1008C2×C3—42no—
1009C2×C3—42no—
1010C2×C3—42no—
1011C2×C3—122no—
1012C2×C3—122no—
1013C2×C3—122no—
1014C2×C3C22×D3×D411yescharacteristic
1015C2×C3C22×D3×D411yescharacteristic
1016C2×C3#596412yes—
1017C2×C3#596612yes—
1018D3—42no—
1019D3—42no—
1020D3—42no—
1021D3—64no—
1022D3—64no—
1023D3—124no—
1024C22—22no—
1025C22—22no—
1026C22—22no—
1027C22—44no—
1028C22—62no—
1029C22—62no—
1030C22—62no—
1031C22—64no—
1032C22—64no—
1033C22—64no—
1034C22—94no—
1035C22—124no—
1036C22—184no—
1037C22—242no—
1038C22—242no—
1039C22—364no—
1040C22—724no—
1041C22C2×#380212yes—
1042C22C2×#380212yes—
1043C22C2×#380212yes—
1044C22C23×D3211yescharacteristic
1045C4—24no—
1046C4—62no—
1047C4—62no—
1048C4—62no—
1049C4—62no—
1050C4—62no—
1051C4—94no—
1052C4—184no—
1053C3—21no—
1054C3#8601211yescharacteristic, complemented
1055C3#8629611yescharacteristic, complemented
1056C2—22no—
1057C2—22no—
1058C2—22no—
1059C2—122no—
1060C2—122no—
1061C2—122no—
1062C2—184no—
1063C2C22×#380211yescharacteristic
1064C2#1059667812yes—
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC2×C32×C22⋊C4C22
hypercenterC2×C22⋊C4D32
hypocenterC32#3485
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64330C2semidirect
2. C22×#3804C2semidirect
3. #10595957C2semidirect
4. C3×#5493C2semidirect
5. C2×C3×#886C2semidirect
6. #10595518C2semidirect
7. C2×#63961C2semidirect
8. #10595083C2semidirect
9. #10594928C2semidirect
10. #10594296C2semidirect
11. #10594295C2semidirect
12. #10594294C2semidirect
13. #10594084C2semidirect
14. #10594083C2semidirect
15. #10594082C2semidirect
21. C22×C3×#67C22semidirect
22. C23×C3×Dic3C22semidirect
25. C2×D3×#67C22semidirect
26. C2×D3×#67C22semidirect
27. C22×#627C22semidirect
28. C22×#626C22semidirect
29. C22×#624C22semidirect
32. C2×#3804C22semidirect
33. C2×#3804C22semidirect
34. C2×#3804C22semidirect
35. C2×#3804C22semidirect
36. C22×D3×Dic3C22semidirect
37. C2×C32×C22⋊C4C22semidirect
38. C2×#3757C22semidirect
39. C4×#638C22semidirect
40. #64090C22semidirect
41. C22⋊C4×C3⋊D3C22semidirect
42. #64086C22semidirect
43. C3×#930C22semidirect
44. C2×C3×(C2×D3)⋊C4C22semidirect
45. C2×C3×C4⋊Dic3C22semidirect
46. C3×#886C22semidirect
47. C3×#886C22semidirect
48. C3×#886C22semidirect
49. C3×#886C22semidirect
50. C3×#886C22semidirect
51. C3×#882C22semidirect
52. C3×#882C22semidirect
53. #63980C22semidirect
54. #63976C22semidirect
55. #63976C22semidirect
56. C2×#3724C22semidirect
57. #63961C22semidirect
58. #63961C22semidirect
59. #63961C22semidirect
60. #63961C22semidirect
61. #63961C22semidirect
62. C2×(C2×D3)⋊Dic3C22semidirect
63. #63922C22semidirect
64. #63921C22semidirect
65. #63919C22semidirect
66. #63916C22semidirect
67. #63915C22semidirect
68. #63912C22semidirect
69. #63902C22semidirect
70. #63900C22semidirect
71. #63899C22semidirect
72. #63899C22semidirect
73. #63899C22semidirect
74. #63898C22semidirect
75. #63885C22semidirect
76. #63854C22semidirect
77. #63854C22semidirect
78. #63854C22semidirect
104. #5493D3semidirect
105. C2×#886D3semidirect
117. C2×#638D4semidirect
199. C22×#67C2×D3semidirect
201. C23×Dic3C2×D3semidirect
237. C2×C3×C22⋊C4C2×D3semidirect
238. C2×C3×C22⋊C4C2×D3semidirect
258. #930C2×D3semidirect
268. C2×(C2×D3)⋊C4C2×D3semidirect
269. C2×C4⋊Dic3C2×D3semidirect
284. #886C2×D3semidirect
285. #886C2×D3semidirect
286. #886C2×D3semidirect
287. #886C2×D3semidirect
288. #886C2×D3semidirect
298. #882C2×D3semidirect
299. #882C2×D3semidirect
647. C2×C22⋊C4D32semidirect
940. C32#3485semidirect
1054. C3#86012semidirect
1055. C3#86296semidirect

Maximal subgroups

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

subgroupindex
C2×#643302
C22×#38042
#105959572
C3×#54932
C2×C3×#8862
#105955182
C2×#639612
#105950832
#105949282
#105942962
#105942952
#105942942
#105940842
#105940832
#105940822
#862963
#860123