Finite Group Databasebeta

← #11904426

Subgroups — #11904426

Order 1152.

3285 conjugacy classes of subgroups.

The subgroup lattice has 1016 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64313C211yesmaximal, characteristic, complemented
2C22×#3798C211yesmaximal, characteristic, complemented
3#10596127C211yesmaximal, characteristic, complemented
4C3×D3×#123C212yesmaximal, complemented
5#10595271C211yesmaximal, characteristic, complemented
6#10595234C212yesmaximal, complemented
7D3×#929C212yesmaximal, complemented
8#10594920C211yesmaximal, characteristic, complemented
9#10594616C212yesmaximal, complemented
10#10594513C214yesmaximal, complemented
11#10594512C212yesmaximal, complemented
12#10594291C212yesmaximal, complemented
13#10594272C214yesmaximal, complemented
14#10594185C212yesmaximal, complemented
15#10594183C212yesmaximal, complemented
16#10594181C211yesmaximal, characteristic, complemented
17#10594084C211yesmaximal, characteristic, complemented
18#86012—32nomaximal
19C2×#3830C2211yescharacteristic
20C22×C4×C3⋊D3C2211yescharacteristic, complemented
21C2×C3×D3×D4C2212yes—
22C22×C3×C4×D3C2212yescomplemented
23C2×D3×#67C2212yes—
24C2×D3×#67C2212yescomplemented
25C22×#627C2211yescharacteristic, complemented
26C22×#626C2212yescomplemented
27C22×#625C2211yescharacteristic
28C22×#625C2211yescharacteristic, complemented
29C2×#3805C2211yescharacteristic
30C2×#3805C2211yescharacteristic, complemented
31#64313—28no—
32C2×#3802C2211yescharacteristic, complemented
33C2×#3798—28no—
34C2×#3798C2212yescomplemented
35C2×#3798C2212yescomplemented
36C2×#3798C2214yescomplemented
37C2×#3798C2211yescharacteristic, complemented
38C2×#3795C2212yescomplemented
39C32×#123C2211yescharacteristic, complemented
40#64146C2211yescharacteristic, complemented
41#64138C2211yescharacteristic, complemented
42#64105C2212yescomplemented
43#64102C2212yescomplemented
44#64093C2212yescomplemented
45#64091C2211yescharacteristic, complemented
46#64090C2212yescomplemented
47#64086C2211yescharacteristic, complemented
48C3×#935C2212yescomplemented
49C3×#929C2212yescomplemented
50C3×#894C2214yescomplemented
51C3×D3×C4⋊C4C2214yescomplemented
52C3×#886C2212yescomplemented
53C3×#883C2214yescomplemented
54C3×D3×C22⋊C4C2212yescomplemented
55C3×D3×C22⋊C4C2214yescomplemented
56#63982C2212yescomplemented
57#63981C2212yescomplemented
58#63977C2214yescomplemented
59#63971C2214yescomplemented
60D3×#217C2212yescomplemented
61#63966C2212yescomplemented
62#63961C2212yescomplemented
63#63957C2211yescharacteristic, complemented
64#63953C2212yescomplemented
65#63923C2214yescomplemented
66D3×(C2×D3)⋊C4C2214yescomplemented
67#63919C2212yescomplemented
68#63915C2212yescomplemented
69#63912C2212yescomplemented
70#63909C2214yescomplemented
71#63906C2214yescomplemented
72#63905C2214yescomplemented
73#63902C2212yescomplemented
74C4×#625C2212yescomplemented
75#63899C2214yescomplemented
76#63890C2214yescomplemented
77#63886C2214yescomplemented
78#63881C2214yescomplemented
79#63879C2214yescomplemented
80D3×Dic3⋊C4C2214yescomplemented
81#63865C2212yescomplemented
82#63865C2212yescomplemented
83#63850C2214yescomplemented
84#63850C2214yescomplemented
85#63840C2212yescomplemented
86C2×#1004—32no—
87C22×#235—32no—
88C2×C3×#123—32no—
89#5804—32no—
90C2×#929—32no—
91#5656—32no—
92#5656—32no—
93#5656—61no—
94#5655—34no—
95#5655—34no—
96#5654—34no—
97#5654—34no—
98#5653—32no—
99#5653—32no—
100D3×#123—32no—
101D3×#123D312yescomplemented
102#5648—32no—
103#5648—32no—
104#5507—34no—
105#5507—34no—
106#5493—32no—
107#5490—34no—
108#5490—34no—
109#5486—32no—
110C23×C3⋊D3C2311yescharacteristic
111C23×C3×D3C2312yes—
112C23×C3×D3C2312yes—
113C22×D32C2312yes—
114C2×C32×D4C2311yescharacteristic
115C22×C32×C4C2311yescharacteristic
116C2×#638C2311yescharacteristic
117C2×#638C2311yescharacteristic
118C2×#638C2312yes—
119C22×C3⋊Dic3C2311yescharacteristic
120C22×C3⋊Dic3C2311yescharacteristic
121#3830—24no—
122C2×C4⋊(C3⋊D3)C2312yes—
123C2×C4×C3⋊D3—24no—
124C2×C4×C3⋊D3C2312yes—
125C2×C4×C3⋊D3C2312yes—
126C2×C4×C3⋊D3C2311yescharacteristic
127C2×#634C2311yescharacteristic
128C2×C3×#67C2312yes—
129C2×C3×#67C2312yes—
130C22×C3×Dic3C2312yes—
131C3×D3×D4—28no—
132C2×C3×D12C2312yes—
133C2×C3×C4×D3—28no—
134C2×C3×C4×D3C2314yes—
135C2×C3×C4×D3C2314yes—
136C2×C3×C4×D3C2312yes—
137C2×C3×C4×D3C2314yes—
138D3×#67—28no—
139D3×#67—28no—
140C2×#627—24no—
141C2×#627C2312yes—
142C2×#627C2312yes—
143C2×#627C2311yescharacteristic
144C2×#626—28no—
145C2×#626C2314yes—
146C2×#626C2314yes—
147C2×#626C2312yes—
148C2×#626C2314yes—
149C2×#625—24no—
150C2×#625D418yescomplemented
151C2×#625C2312yes—
152C2×#625C2311yescharacteristic
153C2×#625C2312yes—
154C2×#625C2311yescharacteristic
155C2×#625C2311yescharacteristic
156#3805—24no—
157#3805—24no—
158C2×D3×Dic3C2312yes—
159C2×D3×Dic3C2312yes—
160C2×D3×Dic3C2314yes—
161#3802—24no—
162#3798—216no—
163#3798—28no—
164#3798—28no—
165#3798—24no—
166#3795—28no—
167C32×C4⋊C4C2312yes—
168C32×C22⋊C4C2312yes—
169C32×C22⋊C4C2311yescharacteristic
170#3757C2311yescharacteristic
171#3752C2312yes—
172#3752C2312yes—
173#3752C2312yes—
174#3750C2312yes—
175#3750C2312yes—
176C4×C3⋊Dic3C2312yes—
177C3×#217C2314yes—
178C3×#217C2312yes—
179C3×(C2×D3)⋊C4C2314yes—
180C3×(C2×D3)⋊C4C2314yes—
181C3×(C2×D3)⋊C4C2314yes—
182C3×C4⋊Dic3C2314yes—
183C3×Dic3⋊C4C2314yes—
184C3×Dic3⋊C4C2314yes—
185#3724C2314yes—
186#3724C2312yes—
187Dic3⋊Dic3C2314yes—
188#3722C2314yes—
189#3722C2314yes—
190(C2×D3)⋊Dic3C2314yes—
191(C2×D3)⋊Dic3C2314yes—
192Dic32C2312yes—
193#3485—91noSylow
194C22×C3×D4—32no—
195C23×C3×C4—32no—
196C22×#67—32no—
197C22×#67—32no—
198C22×#67—32no—
199C22×#67—32no—
200C22×#67—32no—
201#1004—616no—
202C2×#237—32no—
203C2×#237—32no—
204C2×#237—32no—
205C2×#237—32no—
206C2×#237—61no—
207C2×D3×D4—32no—
208C2×D3×D4—32no—
209C2×D3×D4—32no—
210C2×D3×D4C2×D312yes—
211C2×#235—32no—
212C2×#235—34no—
213C2×#235—34no—
214C2×#235—34no—
215C2×#235—34no—
216C2×#235—32no—
217C2×#235—616no—
218C22×D12—32no—
219C22×C4×D3—32no—
220C22×C4×D3—61no—
221C22×C4×D3C2×D312yescomplemented
222C22×Dic6—32no—
223C3×#123—21no—
224C3×#123—32no—
225C3×#123—32no—
226C3×#123—34no—
227C3×#123—34no—
228C3×#123—32no—
229C3×#123C2×D312yescomplemented
230C2×C3×C4⋊C4—34no—
231C2×C3×C22⋊C4—32no—
232C2×C3×C22⋊C4—34no—
233#953—34no—
234C2×#217—32no—
235#939—34no—
236#939—34no—
237#937—32no—
238#937—32no—
239#937—61no—
240#935—32no—
241#935C2×D312yescomplemented
242#930—34no—
243#930—34no—
244#929—32no—
245#929—32no—
246#929—32no—
247#929—34no—
248#929—34no—
249#929—34no—
250#929—61no—
251#929C2×D312yescomplemented
252C4×#67—34no—
253C4×#67—34no—
254C2×(C2×D3)⋊C4—34no—
255C2×Dic3⋊C4—34no—
256#896—34no—
257#896—34no—
258#896—34no—
259#896—34no—
260#896—62no—
261#895—34no—
262#895—34no—
263#894—34no—
264#894—34no—
265#894—34no—
266#894C2×D314yescomplemented
267#893—34no—
268#893—34no—
269#893—62no—
270D3×C4⋊C4—34no—
271D3×C4⋊C4C2×D314yescomplemented
272#888—34no—
273#888—34no—
274#886—32no—
275#886—34no—
276#886C2×D312yescomplemented
277#885—34no—
278#885—34no—
279#884—34no—
280#884—34no—
281#884—34no—
282#884—34no—
283#884—62no—
284#883—34no—
285#883C2×D314yescomplemented
286#882—34no—
287#882—32no—
288#882—32no—
289#882—34no—
290#882—34no—
291#882—61no—
292#67⋊C4—34no—
293#67⋊C4—34no—
294#67⋊C4—34no—
295#67⋊C4—34no—
296#67⋊C4—62no—
297D3×C22⋊C4—32no—
298D3×C22⋊C4—34no—
299D3×C22⋊C4C2×D312yescomplemented
300D3×C22⋊C4C2×D314yescomplemented
301#878—34no—
302#878—34no—
303#877—32no—
304#877—32no—
305#877—61no—
306C23×C32C2411yescharacteristic
307C23×C32C2411yescharacteristic
308C22×C3⋊D3—22no—
309C22×C3⋊D3—42no—
310C22×C3⋊D3C2411yescharacteristic
311C22×C3⋊D3C2412yes—
312C22×C3×D3—24no—
313C22×C3×D3—44no—
314C22×C3×D3—44no—
315C22×C3×D3C2×D418yes—
316C22×C3×D3C2412yes—
317C22×C3×D3C2412yes—
318C22×C3×D3C2412yes—
319C2×D32—24no—
320C2×D32—44no—
321C32×D4—22no—
322C2×C32×C4—22no—
323C2×C32×C4C2411yescharacteristic
324C2×C32×C4C2412yes—
325C2×C32×C4C2412yes—
326#638—22no—
327#638—22no—
328#638—42no—
329C2×C3⋊Dic3—22no—
330C2×C3⋊Dic3C2×D414yes—
331C2×C3⋊Dic3C2412yes—
332C2×C3⋊Dic3C2411yescharacteristic
333C2×C3⋊Dic3C2411yescharacteristic
334C2×C3⋊Dic3C2411yescharacteristic
335C4⋊(C3⋊D3)—42no—
336C4×C3⋊D3—24no—
337C4×C3⋊D3—24no—
338C4×C3⋊D3—22no—
339#634—22no—
340C3×#67—24no—
341C3×#67—24no—
342C2×C3×Dic3—24no—
343C2×C3×Dic3C2414yes—
344C2×C3×Dic3C2414yes—
345C2×C3×Dic3C2412yes—
346C3×D12—24no—
347C3×C4×D3—24no—
348C3×C4×D3—28no—
349C3×C4×D3—28no—
350C3×C4×D3—44no—
351#627—24no—
352#627—24no—
353#627—22no—
354#626—28no—
355#626—28no—
356#626—24no—
357#626—44no—
358#625—24no—
359#625—22no—
360#625C2×D418yes—
361#625C2×D414yes—
362#625C2×D414yes—
363D3×Dic3—24no—
364D3×Dic3—24no—
365D3×Dic3—44no—
366C2×H(5,𝔽2)—91no—
367C22×#41—91no—
368#547—92no—
369#547—94no—
370#547—92no—
371#546—92no—
372#546—94no—
373#546—92no—
374#536—91no—
375#536—91no—
376#534—92no—
377#534—92no—
378#525—91no—
379#525—91no—
380C2×#123—32no—
381C2×#123—92no—
382#518—91no—
383C24×C3—32no—
384C24×C3—32no—
385C23×D3—32no—
386C23×D3—32no—
387C23×D3—32no—
388C23×D3—61no—
389C23×D3C22×D312yes—
390C23×D3C22×D312yes—
391C2×C3×D4—21no—
392C2×C3×D4—32no—
393C2×C3×D4—32no—
394C2×C3×D4—32no—
395C2×C3×D4—68no—
396C2×C3×D4C22×D312yes—
397C22×C3×C4—21no—
398C22×C3×C4—32no—
399C22×C3×C4—34no—
400C22×C3×C4—34no—
401C22×C3×C4—32no—
402C22×C3×C4—34no—
403C22×C3×C4—68no—
404C22×C3×C4C22×D312yes—
405C2×#67—316no—
406C2×#67—32no—
407C2×#67—32no—
408C2×#67—32no—
409C2×#67—32no—
410C2×#67—32no—
411C2×#67—32no—
412C2×#67—32no—
413C2×#67—32no—
414C2×#67—32no—
415C2×#67—34no—
416C2×#67—34no—
417C2×#67—32no—
418C2×#67—34no—
419C2×#67—34no—
420C2×#67—62no—
421C2×#67—61no—
422C2×#67—61no—
423C2×#67—68no—
424C2×#67—68no—
425C2×#67—68no—
426C2×#67—68no—
427C2×#67C22×D312yes—
428C2×#67C22×D312yes—
429C22×Dic3—32no—
430C22×Dic3—32no—
431C22×Dic3—32no—
432C22×Dic3—32no—
433C22×Dic3—34no—
434C22×Dic3—61no—
435C22×Dic3—61no—
436C22×Dic3C22×D312yes—
437#237—68no—
438#237—68no—
439#237—68no—
440#237—68no—
441#237—124no—
442D3×D4—28no—
443D3×D4—68no—
444D3×D4—68no—
445D3×D4—68no—
446#235—616no—
447#235—616no—
448#235—616no—
449#235—616no—
450#235—68no—
451#235—68no—
452C2×D12—34no—
453C2×D12—34no—
454C2×D12—32no—
455C2×D12—34no—
456C2×D12—34no—
457C2×D12—62no—
458C2×D12—68no—
459C2×D12C22×D312yes—
460C2×C4×D3—28no—
461C2×C4×D3—32no—
462C2×C4×D3—32no—
463C2×C4×D3—34no—
464C2×C4×D3—34no—
465C2×C4×D3—32no—
466C2×C4×D3—34no—
467C2×C4×D3—62no—
468C2×C4×D3—62no—
469C2×C4×D3—61no—
470C2×C4×D3—68no—
471C2×C4×D3—124no—
472C2×C4×D3C22×D314yes—
473C2×C4×D3C22×D314yes—
474C2×C4×D3C22×D312yes—
475C2×C4×D3C22×D314yes—
476C2×Dic6—32no—
477C2×Dic6—34no—
478C2×Dic6—34no—
479C2×Dic6—32no—
480C2×Dic6—61no—
481C2×Dic6—68no—
482C3×C4⋊C4—22no—
483C3×C4⋊C4—34no—
484C3×C4⋊C4—34no—
485C3×C4⋊C4—34no—
486C3×C4⋊C4C22×D314yes—
487C3×C22⋊C4—21no—
488C3×C22⋊C4—22no—
489C3×C22⋊C4—32no—
490C3×C22⋊C4—34no—
491C3×C22⋊C4—34no—
492C3×C22⋊C4—34no—
493C3×C22⋊C4—34no—
494C3×C22⋊C4C22×D312yes—
495C3×C22⋊C4C22×D314yes—
496#217—32no—
497#217—34no—
498#217—34no—
499#217—61no—
500#217C22×D312yes—
501#217C22×D314yes—
502(C2×D3)⋊C4—34no—
503(C2×D3)⋊C4—34no—
504(C2×D3)⋊C4—34no—
505(C2×D3)⋊C4—34no—
506(C2×D3)⋊C4—34no—
507(C2×D3)⋊C4—34no—
508(C2×D3)⋊C4—34no—
509(C2×D3)⋊C4—34no—
510(C2×D3)⋊C4—34no—
511(C2×D3)⋊C4—62no—
512(C2×D3)⋊C4—62no—
513(C2×D3)⋊C4—62no—
514(C2×D3)⋊C4C22×D314yes—
515(C2×D3)⋊C4C22×D314yes—
516(C2×D3)⋊C4C22×D314yes—
517C4⋊Dic3—34no—
518C4⋊Dic3C22×D314yes—
519Dic3⋊C4—34no—
520Dic3⋊C4—34no—
521Dic3⋊C4—34no—
522Dic3⋊C4—34no—
523Dic3⋊C4—34no—
524Dic3⋊C4—34no—
525Dic3⋊C4—62no—
526Dic3⋊C4—62no—
527Dic3⋊C4C22×D314yes—
528Dic3⋊C4C22×D314yes—
529C4×Dic3—34no—
530C4×Dic3—34no—
531C4×Dic3—62no—
532C22×C32—22no—
533C22×C32—21no—
534C22×C32—22no—
535C22×C32C22×D412yes—
536C22×C32C2511yescharacteristic
537C2×C3⋊D3—22no—
538C2×C3⋊D3—22no—
539C2×C3⋊D3—21no—
540C2×C3⋊D3—22no—
541C2×C3⋊D3—22no—
542C2×C3⋊D3—44no—
543C2×C3×D3—24no—
544C2×C3×D3—24no—
545C2×C3×D3—22no—
546C2×C3×D3—24no—
547C2×C3×D3—48no—
548C2×C3×D3—84no—
549C2×C3×D3C22×D414yes—
550C2×C3×D3C22×D414yes—
551D32—84no—
552C32×C4—22no—
553C32×C4—21no—
554C32×C4—22no—
555C3⋊Dic3—21no—
556C3⋊Dic3—22no—
557C3⋊Dic3C22×D412yes—
558C3⋊Dic3C22×D412yes—
559C3×Dic3—22no—
560C3×Dic3—24no—
561C3×Dic3—24no—
562H(5,𝔽2)—188no—
563C2×#41—92no—
564C2×#41—94no—
565C2×#41—92no—
566C2×#41—91no—
567C2×#41—92no—
568C2×#41—91no—
569C2×#41—91no—
570C2×#41—91no—
571C2×#41—188no—
572C22×Q8—91no—
573C22×D4—32no—
574C22×D4—92no—
575C22×D4—91no—
576C22×D4—92no—
577C22×D4—92no—
578C22×D4—91no—
579C22×D4—91no—
580C23×C4—32no—
581C23×C4—91no—
582C4⋊Q8—92no—
583C4⋊Q8—92no—
584#124—92no—
585#124—92no—
586#123—32no—
587#123—32no—
588#123—34no—
589#123—32no—
590#123—34no—
591#123—94no—
592#123—92no—
593#123—94no—
594#123—94no—
595#123—94no—
596#123—92no—
597#123—91no—
598#123D3211yescharacteristic, complemented
599C22⋊Q8—92no—
600C22⋊Q8—94no—
601C22⋊Q8—92no—
602C22⋊Q8—92no—
603C22⋊Q8—92no—
604#121—92no—
605#121—94no—
606#121—94no—
607#121—94no—
608#121—94no—
609#121—92no—
610#120—94no—
611#120—92no—
612#120—94no—
613#120—91no—
614#120—91no—
615C4×D4—92no—
616C4×D4—94no—
617C4×D4—94no—
618C4×D4—92no—
619C4×D4—92no—
620C4×D4—92no—
621#117—91no—
622#117—91no—
623C2×C4⋊C4—34no—
624C2×C4⋊C4—94no—
625C2×C22⋊C4—32no—
626C2×C22⋊C4—34no—
627C2×C22⋊C4—94no—
628C2×C22⋊C4—92no—
629C23×C3—21no—
630C23×C3—21no—
631C23×C3—32no—
632C23×C3—32no—
633C23×C3—38no—
634C23×C3—32no—
635C23×C3—64no—
636C23×C3—124no—
637C23×C3—124no—
638C23×C3C23×D312yes—
639C23×C3C23×D312yes—
640C22×D3—24no—
641C22×D3—32no—
642C22×D3—34no—
643C22×D3—44no—
644C22×D3—44no—
645C22×D3—62no—
646C22×D3—61no—
647C22×D3—64no—
648C22×D3—64no—
649C22×D3—64no—
650C22×D3—122no—
651C22×D3—124no—
652C22×D3—124no—
653C22×D3—124no—
654C22×D3—124no—
655C22×D3D3×D418yes—
656C22×D3C23×D312yes—
657C22×D3C23×D312yes—
658C22×D3C23×D312yes—
659C3×D4—24no—
660C3×D4—42no—
661C3×D4—64no—
662C3×D4—64no—
663C3×D4—64no—
664C2×C3×C4—24no—
665C2×C3×C4—22no—
666C2×C3×C4—22no—
667C2×C3×C4—21no—
668C2×C3×C4—34no—
669C2×C3×C4—34no—
670C2×C3×C4—32no—
671C2×C3×C4—42no—
672C2×C3×C4—68no—
673C2×C3×C4—68no—
674C2×C3×C4—64no—
675C2×C3×C4—64no—
676C2×C3×C4—124no—
677C2×C3×C4C23×D314yes—
678C2×C3×C4C23×D314yes—
679C2×C3×C4C23×D312yes—
680#67—24no—
681#67—24no—
682#67—38no—
683#67—38no—
684#67—38no—
685#67—38no—
686#67—68no—
687#67—68no—
688#67—64no—
689#67—64no—
690#67—64no—
691#67—64no—
692#67—64no—
693#67—64no—
694#67—122no—
695#67—122no—
696#67—124no—
697#67—124no—
698#67—124no—
699C2×Dic3—24no—
700C2×Dic3—38no—
701C2×Dic3—32no—
702C2×Dic3—32no—
703C2×Dic3—34no—
704C2×Dic3—32no—
705C2×Dic3—64no—
706C2×Dic3—61no—
707C2×Dic3—61no—
708C2×Dic3—62no—
709C2×Dic3—61no—
710C2×Dic3—64no—
711C2×Dic3—64no—
712C2×Dic3—64no—
713C2×Dic3—122no—
714C2×Dic3—124no—
715C2×Dic3C23×D314yes—
716C2×Dic3C23×D312yes—
717C2×Dic3C23×D314yes—
718D12—24no—
719D12—68no—
720D12—68no—
721D12—64no—
722D12—124no—
723D12—124no—
724D12—124no—
725C4×D3—28no—
726C4×D3—28no—
727C4×D3—24no—
728C4×D3—44no—
729C4×D3—68no—
730C4×D3—68no—
731C4×D3—64no—
732C4×D3—64no—
733C4×D3—64no—
734C4×D3—124no—
735C4×D3—124no—
736C4×D3—122no—
737C4×D3—124no—
738Dic6—68no—
739Dic6—68no—
740Dic6—64no—
741Dic6—64no—
742Dic6—122no—
743C2×C32—22no—
744C2×C32—41no—
745C2×C32C23×D411yescharacteristic
746C2×C32#58512yes—
747C3⋊D3—42no—
748C3⋊D3—41no—
749C3×D3—24no—
750C3×D3—24no—
751C3×D3—42no—
752C24—32no—
753C24—32no—
754C24—92no—
755C24—91no—
756#41—188no—
757#41—1816no—
758#41—188no—
759#41—184no—
760#41—188no—
761#41—184no—
762#41—184no—
763#41—184no—
764C2×Q8—92no—
765C2×Q8—92no—
766C2×Q8—91no—
767C2×Q8—91no—
768C2×Q8—184no—
769C2×D4—32no—
770C2×D4—32no—
771C2×D4—32no—
772C2×D4—68no—
773C2×D4—94no—
774C2×D4—94no—
775C2×D4—92no—
776C2×D4—94no—
777C2×D4—91no—
778C2×D4—92no—
779C2×D4—91no—
780C2×D4—98no—
781C2×D4—92no—
782C2×D4—91no—
783C2×D4—91no—
784C2×D4—91no—
785C2×D4—92no—
786C2×D4—92no—
787C2×D4—188no—
788C2×D4—184no—
789C2×D4—188no—
790C2×D4—188no—
791C2×D4—184no—
792C2×D4C2×D3211yescharacteristic
793C22×C4—32no—
794C22×C4—34no—
795C22×C4—34no—
796C22×C4—32no—
797C22×C4—34no—
798C22×C4—68no—
799C22×C4—92no—
800C22×C4—92no—
801C22×C4—94no—
802C22×C4—91no—
803C22×C4—91no—
804C22×C4—92no—
805C22×C4—92no—
806C22×C4—91no—
807C22×C4—184no—
808C22×C4C2×D3211yescharacteristic
809C4⋊C4—34no—
810C4⋊C4—34no—
811C4⋊C4—34no—
812C4⋊C4—94no—
813C4⋊C4—94no—
814C4⋊C4—92no—
815C4⋊C4—92no—
816C4⋊C4—92no—
817C4⋊C4C2×D3212yes—
818C22⋊C4—32no—
819C22⋊C4—34no—
820C22⋊C4—34no—
821C22⋊C4—34no—
822C22⋊C4—34no—
823C22⋊C4—94no—
824C22⋊C4—94no—
825C22⋊C4—94no—
826C22⋊C4—94no—
827C22⋊C4—91no—
828C22⋊C4—92no—
829C22⋊C4—92no—
830C22⋊C4—92no—
831C22⋊C4C2×D3211yescharacteristic
832C22⋊C4C2×D3212yes—
833C42—92no—
834C42—92no—
835C22×C3—24no—
836C22×C3—22no—
837C22×C3—24no—
838C22×C3—22no—
839C22×C3—21no—
840C22×C3—34no—
841C22×C3—34no—
842C22×C3—42no—
843C22×C3—41no—
844C22×C3—42no—
845C22×C3—64no—
846C22×C3—64no—
847C22×C3—62no—
848C22×C3—64no—
849C22×C3—128no—
850C22×C3—244no—
851C22×C3C2×D3×D414yes—
852C22×C3C24×D312yes—
853C2×D3—24no—
854C2×D3—24no—
855C2×D3—22no—
856C2×D3—24no—
857C2×D3—48no—
858C2×D3—64no—
859C2×D3—64no—
860C2×D3—62no—
861C2×D3—64no—
862C2×D3—64no—
863C2×D3—64no—
864C2×D3—84no—
865C2×D3—122no—
866C2×D3—122no—
867C2×D3—121no—
868C2×D3—122no—
869C2×D3—128no—
870C2×D3—128no—
871C2×D3—244no—
872C2×D3—244no—
873C2×D3C2×D3×D414yes—
874C2×D3C2×D3×D414yes—
875C3×C4—22no—
876C3×C4—24no—
877C3×C4—24no—
878C3×C4—41no—
879C3×C4—42no—
880C3×C4—42no—
881C3×C4—64no—
882C3×C4—62no—
883C3×C4—64no—
884Dic3—24no—
885Dic3—22no—
886Dic3—24no—
887Dic3—34no—
888Dic3—34no—
889Dic3—62no—
890Dic3—62no—
891Dic3—62no—
892Dic3—64no—
893Dic3—121no—
894Dic3—122no—
895C32#348511yescharacteristic, complemented, Sylow
896C23—32no—
897C23—32no—
898C23—38no—
899C23—32no—
900C23—64no—
901C23—91no—
902C23—92no—
903C23—124no—
904C23—124no—
905C23—184no—
906C23—182no—
907C23—362no—
908C23—364no—
909C23C22×D3211yescharacteristic
910C23C22×D3211yescharacteristic
911Q8—182no—
912Q8—184no—
913Q8—184no—
914Q8—182no—
915D4—22no—
916D4—64no—
917D4—64no—
918D4—64no—
919D4—94no—
920D4—98no—
921D4—94no—
922D4—184no—
923D4—188no—
924D4—188no—
925D4—182no—
926D4—182no—
927D4—184no—
928D4—182no—
929D4—362no—
930D4—364no—
931D4—362no—
932C2×C4—22no—
933C2×C4—34no—
934C2×C4—34no—
935C2×C4—32no—
936C2×C4—68no—
937C2×C4—68no—
938C2×C4—64no—
939C2×C4—64no—
940C2×C4—94no—
941C2×C4—91no—
942C2×C4—91no—
943C2×C4—92no—
944C2×C4—91no—
945C2×C4—124no—
946C2×C4—184no—
947C2×C4—184no—
948C2×C4—182no—
949C2×C4—184no—
950C2×C4—184no—
951C2×C4—182no—
952C2×C4—364no—
953C2×C4C22×D3212yes—
954C2×C4C22×D3212yes—
955C2×C4C22×D3211yescharacteristic
956C2×C3—24no—
957C2×C3—21no—
958C2×C3—22no—
959C2×C3—42no—
960C2×C3—42no—
961C2×C3—64no—
962C2×C3—64no—
963C2×C3—81no—
964C2×C3—122no—
965C2×C3C22×D3×D412yes—
966C2×C3#596414yes—
967D3—24no—
968D3—24no—
969D3—42no—
970D3—124no—
971D3—124no—
972D3—122no—
973D3—241no—
974C22—22no—
975C22—21no—
976C22—22no—
977C22—34no—
978C22—34no—
979C22—64no—
980C22—64no—
981C22—62no—
982C22—64no—
983C22—128no—
984C22—182no—
985C22—181no—
986C22—182no—
987C22—182no—
988C22—182no—
989C22—244no—
990C22—364no—
991C22—724no—
992C22D32×D412yes—
993C22C23×D3211yescharacteristic
994C4—22no—
995C4—21no—
996C4—22no—
997C4—64no—
998C4—62no—
999C4—64no—
1000C4—92no—
1001C4—92no—
1002C4—181no—
1003C4—182no—
1004C3—21no—
1005C3#8601212yescomplemented
1006C2—22no—
1007C2—41no—
1008C2—64no—
1009C2—64no—
1010C2—122no—
1011C2—362no—
1012C2—361no—
1013C2C2×D32×D411yescharacteristic
1014C2#1059669512yes—
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#123C22
hypercenter#123D32
hypocenterC32#3485
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
1. C2×#64313C2semidirect
2. C22×#3798C2semidirect
3. #10596127C2semidirect
4. C3×D3×#123C2semidirect
5. #10595271C2semidirect
6. #10595234C2semidirect
7. D3×#929C2semidirect
8. #10594920C2semidirect
9. #10594616C2semidirect
10. #10594513C2semidirect
11. #10594512C2semidirect
12. #10594291C2semidirect
13. #10594272C2semidirect
14. #10594185C2semidirect
15. #10594183C2semidirect
16. #10594181C2semidirect
17. #10594084C2semidirect
20. C22×C4×C3⋊D3C22semidirect
22. C22×C3×C4×D3C22semidirect
24. C2×D3×#67C22semidirect
25. C22×#627C22semidirect
26. C22×#626C22semidirect
28. C22×#625C22semidirect
30. C2×#3805C22semidirect
32. C2×#3802C22semidirect
34. C2×#3798C22semidirect
35. C2×#3798C22semidirect
36. C2×#3798C22semidirect
37. C2×#3798C22semidirect
38. C2×#3795C22semidirect
39. C32×#123C22semidirect
40. #64146C22semidirect
41. #64138C22semidirect
42. #64105C22semidirect
43. #64102C22semidirect
44. #64093C22semidirect
45. #64091C22semidirect
46. #64090C22semidirect
47. #64086C22semidirect
48. C3×#935C22semidirect
49. C3×#929C22semidirect
50. C3×#894C22semidirect
51. C3×D3×C4⋊C4C22semidirect
52. C3×#886C22semidirect
53. C3×#883C22semidirect
54. C3×D3×C22⋊C4C22semidirect
55. C3×D3×C22⋊C4C22semidirect
56. #63982C22semidirect
57. #63981C22semidirect
58. #63977C22semidirect
59. #63971C22semidirect
60. D3×#217C22semidirect
61. #63966C22semidirect
62. #63961C22semidirect
63. #63957C22semidirect
64. #63953C22semidirect
65. #63923C22semidirect
66. D3×(C2×D3)⋊C4C22semidirect
67. #63919C22semidirect
68. #63915C22semidirect
69. #63912C22semidirect
70. #63909C22semidirect
71. #63906C22semidirect
72. #63905C22semidirect
73. #63902C22semidirect
74. C4×#625C22semidirect
75. #63899C22semidirect
76. #63890C22semidirect
77. #63886C22semidirect
78. #63881C22semidirect
79. #63879C22semidirect
80. D3×Dic3⋊C4C22semidirect
81. #63865C22semidirect
82. #63865C22semidirect
83. #63850C22semidirect
84. #63850C22semidirect
85. #63840C22semidirect
101. D3×#123D3semidirect
150. C2×#625D4semidirect
221. C22×C4×D3C2×D3semidirect
229. C3×#123C2×D3semidirect
241. #935C2×D3semidirect
251. #929C2×D3semidirect
266. #894C2×D3semidirect
271. D3×C4⋊C4C2×D3semidirect
276. #886C2×D3semidirect
285. #883C2×D3semidirect
299. D3×C22⋊C4C2×D3semidirect
300. D3×C22⋊C4C2×D3semidirect
598. #123D32semidirect
895. C32#3485semidirect
1005. C3#86012semidirect

Maximal subgroups

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

subgroupindex
C2×#643132
C22×#37982
#105961272
C3×D3×#1232
#105952712
#105952342
D3×#9292
#105949202
#105946162
#105945132
#105945122
#105942912
#105942722
#105941852
#105941832
#105941812
#105940842
#860123