Finite Group Databasebeta

← #11904447

Subgroups — #11904447

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
1C22×#3805C211yesmaximal, characteristic, complemented
2C2×#64313C211yesmaximal, characteristic, complemented
3#10596057C211yesmaximal, characteristic, complemented
4C3×#5589C212yesmaximal, complemented
5#10595524C212yesmaximal, complemented
6#10595501C211yesmaximal, characteristic, complemented
7#10595290C214yesmaximal, complemented
8#10595271C211yesmaximal, characteristic, complemented
9#10595225C212yesmaximal, complemented
10D3×#935C212yesmaximal, complemented
11#10595134C212yesmaximal, complemented
12D3×#886C212yesmaximal, complemented
13#10594276C212yesmaximal, complemented
14#10594185C212yesmaximal, complemented
15#10594181C211yesmaximal, characteristic, complemented
16#10594084C211yesmaximal, characteristic, complemented
17#10594062C214yesmaximal, complemented
18#86296—32nomaximal
19C23×C3⋊Dic3C2211yescharacteristic, complemented
20C2×#3830C2211yescharacteristic
21C22×C3×#67C2212yescomplemented
22C2×C3×D3×D4C2212yes—
23C2×D3×#67C2212yes—
24C2×D3×#67C2212yescomplemented
25C22×#627C2211yescharacteristic, complemented
26C22×#625C2211yescharacteristic
27C22×#625C2211yescharacteristic, complemented
28C2×#3805—28no—
29C2×#3805C2211yescharacteristic
30C2×#3805C2214yescomplemented
31C2×#3805C2211yescharacteristic, complemented
32C2×#3805C2212yescomplemented
33C2×#3805C2212yescomplemented
34C22×D3×Dic3C2212yescomplemented
35#64313—28no—
36C2×#3802C2211yescharacteristic, complemented
37C2×#3798C2211yescharacteristic, complemented
38C2×#3795C2212yescomplemented
39C32×#120C2211yescharacteristic, complemented
40#64162C2211yescharacteristic, complemented
41#64148C2212yescomplemented
42#64144C2211yescharacteristic, complemented
43D4×C3⋊Dic3C2212yescomplemented
44#64095C2211yescharacteristic, complemented
45#64090C2212yescomplemented
46#64087C2212yescomplemented
47#64086C2211yescharacteristic, complemented
48C3×#953C2212yescomplemented
49C3×#938C2214yescomplemented
50C3×#937C2214yescomplemented
51C3×#935C2212yescomplemented
52C3×#886C2212yescomplemented
53C3×#884C2214yescomplemented
54C3×#883C2214yescomplemented
55C3×D3×C22⋊C4C2212yescomplemented
56#63983C2214yescomplemented
57#63982C2212yescomplemented
58#63982C2212yescomplemented
59#63980C2212yescomplemented
60#67⋊Dic3C2214yescomplemented
61#63971C2214yescomplemented
62#63970C2214yescomplemented
63#63969C2214yescomplemented
64#63969C2214yescomplemented
65D3×#217C2212yescomplemented
66D3×#217C2214yescomplemented
67#63966C2212yescomplemented
68#63962C2212yescomplemented
69#63961C2212yescomplemented
70#63957C2211yescharacteristic, complemented
71#63953C2212yescomplemented
72D3×(C2×D3)⋊C4C2214yescomplemented
73#63919C2212yescomplemented
74#63915C2212yescomplemented
75#63902C2212yescomplemented
76C4×#625C2212yescomplemented
77#63899C2214yescomplemented
78#63891C2214yescomplemented
79#63890C2214yescomplemented
80D3×C4⋊Dic3C2214yescomplemented
81#63884C2214yescomplemented
82#63879C2214yescomplemented
83D3×Dic3⋊C4C2214yescomplemented
84#63865C2212yescomplemented
85#63840C2212yescomplemented
86C2×#1004—32no—
87C22×#237—32no—
88C3×#534—32no—
89#5804—32no—
90C2×#935—32no—
91#5655—34no—
92#5655—34no—
93D3×#123—32no—
94D3×#123—32no—
95#5648—32no—
96#5648—32no—
97#5611—34no—
98#5611—34no—
99#5610—34no—
100#5610—34no—
101#5591—34no—
102#5591—34no—
103#5589—32no—
104#5589D312yescomplemented
105#5586—32no—
106#5586—32no—
107#5586—61no—
108C2×#886—32no—
109#5486—32no—
110C24×C32C2311yescharacteristic
111C23×C3×D3C2312yes—
112C23×C3×D3C2312yes—
113C22×D32C2312yes—
114C2×C32×D4C2311yescharacteristic
115C2×C32×D4C2312yes—
116C2×#638C2311yescharacteristic
117C2×#638C2311yescharacteristic
118C2×#638C2312yes—
119C22×C3⋊Dic3—24no—
120C22×C3⋊Dic3C2311yescharacteristic
121C22×C3⋊Dic3C2312yes—
122C22×C3⋊Dic3C2312yes—
123C22×C3⋊Dic3C2311yescharacteristic
124C22×C3⋊Dic3C2311yescharacteristic
125#3830—24no—
126C2×C4×C3⋊D3C2311yescharacteristic
127C2×#634C2311yescharacteristic
128C2×C3×#67—28no—
129C2×C3×#67C2314yes—
130C2×C3×#67C2314yes—
131C2×C3×#67C2312yes—
132C2×C3×#67C2312yes—
133C2×C3×#67C2314yes—
134C22×C3×Dic3C2312yes—
135C3×D3×D4—28no—
136C2×C3×D12C2312yes—
137C2×C3×C4×D3C2312yes—
138C2×C3×C4×D3C2314yes—
139D3×#67—28no—
140D3×#67—28no—
141C2×#627—24no—
142C2×#627C2311yescharacteristic
143C2×#627C2312yes—
144C2×#627C2312yes—
145C2×#626C2312yes—
146C2×#625—24no—
147C2×#625D418yescomplemented
148C2×#625C2312yes—
149C2×#625C2311yescharacteristic
150C2×#625C2312yes—
151C2×#625C2311yescharacteristic
152C2×#625C2311yescharacteristic
153#3805—24no—
154#3805—24no—
155#3805—216no—
156#3805—28no—
157#3805—28no—
158C2×D3×Dic3—28no—
159C2×D3×Dic3C2312yes—
160C2×D3×Dic3C2312yes—
161C2×D3×Dic3C2314yes—
162C2×D3×Dic3C2314yes—
163C2×D3×Dic3C2314yes—
164#3802—24no—
165#3798—24no—
166#3795—28no—
167C32×C22⋊C4C2311yescharacteristic
168C32×C22⋊C4C2312yes—
169#3757C2311yescharacteristic
170#3757C2312yes—
171#3757C2312yes—
172#3752C2312yes—
173C4⋊(C3⋊Dic3)C2312yes—
174#3750C2312yes—
175#3750C2312yes—
176C4×C3⋊Dic3C2312yes—
177C3×#217C2312yes—
178C3×#217C2314yes—
179C3×#217C2314yes—
180C3×(C2×D3)⋊C4C2314yes—
181C3×(C2×D3)⋊C4C2314yes—
182C3×C4⋊Dic3C2314yes—
183C3×Dic3⋊C4C2314yes—
184#3724C2312yes—
185#3724C2314yes—
186Dic3⋊Dic3C2314yes—
187Dic3⋊Dic3C2314yes—
188#3722C2314yes—
189(C2×D3)⋊Dic3C2314yes—
190(C2×D3)⋊Dic3C2314yes—
191(C2×D3)⋊Dic3C2314yes—
192Dic32C2312yes—
193#3485—91noSylow
194C22×C3×D4—32no—
195C22×C3×D4—32no—
196C22×#67—32no—
197C22×#67—32no—
198C22×#67—32no—
199C22×#67—32no—
200C22×#67C2×D312yescomplemented
201C23×Dic3—32no—
202C23×Dic3—32no—
203C23×Dic3—61no—
204#1004—616no—
205C2×#237—32no—
206C2×#237—32no—
207C2×#237—34no—
208C2×#237—34no—
209C2×#237—34no—
210C2×#237—34no—
211C2×#237—32no—
212C2×#237—32no—
213C2×#237—61no—
214C2×#237—616no—
215C2×D3×D4—32no—
216C2×D3×D4—32no—
217C2×D3×D4—32no—
218C2×D3×D4C2×D312yes—
219C2×#235—32no—
220C2×#235—32no—
221C22×C4×D3—32no—
222C22×Dic6—32no—
223C3×#123—32no—
224C3×#123—34no—
225C3×#123—32no—
226C3×#121—34no—
227C3×#121—34no—
228C3×#120—21no—
229C3×#120—32no—
230C3×#120—34no—
231C3×#120C2×D312yescomplemented
232C2×C3×C22⋊C4—32no—
233#953—32no—
234#953—61no—
235#953C2×D312yescomplemented
236C2×#217—32no—
237C2×#217—34no—
238#939—34no—
239#939—34no—
240#939—34no—
241#939—34no—
242#939—62no—
243#938—34no—
244#938C2×D314yescomplemented
245#937—34no—
246#937—34no—
247#937C2×D314yescomplemented
248#935—32no—
249#935—32no—
250#935—32no—
251#935—34no—
252#935—34no—
253#935—34no—
254#935—61no—
255#935C2×D312yescomplemented
256D4×Dic3—34no—
257D4×Dic3—34no—
258D4×Dic3—62no—
259#929—32no—
260#929—32no—
261C4×#67—34no—
262C4×#67—34no—
263C2×(C2×D3)⋊C4—34no—
264C2×C4⋊Dic3—34no—
265C2×Dic3⋊C4—34no—
266#896—34no—
267#896—34no—
268#894—34no—
269#894—34no—
270D3×C4⋊C4—34no—
271D3×C4⋊C4—34no—
272#888—34no—
273#888—34no—
274#886—32no—
275#886—32no—
276#886—32no—
277#886—34no—
278#886—34no—
279#886—61no—
280#886C2×D312yescomplemented
281#885—34no—
282#885—34no—
283#884—34no—
284#884C2×D314yescomplemented
285#883—34no—
286#883—34no—
287#883—34no—
288#883C2×D314yescomplemented
289#67⋊C4—34no—
290#67⋊C4—34no—
291#67⋊C4—34no—
292#67⋊C4—34no—
293#67⋊C4—62no—
294D3×C22⋊C4—32no—
295D3×C22⋊C4—34no—
296D3×C22⋊C4—34no—
297D3×C22⋊C4C2×D312yescomplemented
298#878—34no—
299#878—34no—
300#878—34no—
301#878—34no—
302#878—62no—
303#877—32no—
304#877—32no—
305#877—61no—
306C23×C32—22no—
307C23×C32—42no—
308C23×C32C2411yescharacteristic
309C23×C32C2412yes—
310C23×C32C2411yescharacteristic
311C22×C3⋊D3C2411yescharacteristic
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—
322C32×D4—42no—
323C2×C32×C4C2411yescharacteristic
324C2×C32×C4C2412yes—
325#638—22no—
326#638—22no—
327#638—42no—
328C2×C3⋊Dic3—22no—
329C2×C3⋊Dic3—24no—
330C2×C3⋊Dic3—24no—
331C2×C3⋊Dic3—22no—
332C2×C3⋊Dic3C2×D414yes—
333C2×C3⋊Dic3C2412yes—
334C2×C3⋊Dic3C2412yes—
335C2×C3⋊Dic3C2411yescharacteristic
336C2×C3⋊Dic3C2411yescharacteristic
337C2×C3⋊Dic3C2411yescharacteristic
338C4×C3⋊D3—22no—
339#634—22no—
340C3×#67—24no—
341C3×#67—28no—
342C3×#67—28no—
343C3×#67—24no—
344C3×#67—44no—
345C2×C3×Dic3—24no—
346C2×C3×Dic3C2414yes—
347C2×C3×Dic3C2414yes—
348C2×C3×Dic3C2412yes—
349C3×D12—24no—
350C3×C4×D3—24no—
351C3×C4×D3—44no—
352#627—22no—
353#627—24no—
354#627—24no—
355#626—24no—
356#625—24no—
357#625—22no—
358#625C2×D418yes—
359#625C2×D414yes—
360#625C2×D414yes—
361D3×Dic3—24no—
362D3×Dic3—28no—
363D3×Dic3—28no—
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—32no—
377#534—92no—
378#525—91no—
379#525—91no—
380C2×#123—92no—
381C2×#123—92no—
382#518—91no—
383C24×C3—21no—
384C24×C3—32no—
385C24×C3—32no—
386C24×C3C22×D312yes—
387C23×D3—32no—
388C23×D3—32no—
389C23×D3C22×D312yes—
390C23×D3C22×D312yes—
391C2×C3×D4—22no—
392C2×C3×D4—21no—
393C2×C3×D4—32no—
394C2×C3×D4—32no—
395C2×C3×D4—34no—
396C2×C3×D4—34no—
397C2×C3×D4—34no—
398C2×C3×D4—32no—
399C2×C3×D4—68no—
400C2×C3×D4—68no—
401C2×C3×D4C22×D312yes—
402C2×C3×D4C22×D314yes—
403C22×C3×C4—32no—
404C22×C3×C4—32no—
405C22×C3×C4—34no—
406C2×#67—28no—
407C2×#67—316no—
408C2×#67—32no—
409C2×#67—32no—
410C2×#67—32no—
411C2×#67—32no—
412C2×#67—32no—
413C2×#67—32no—
414C2×#67—32no—
415C2×#67—32no—
416C2×#67—32no—
417C2×#67—34no—
418C2×#67—32no—
419C2×#67—62no—
420C2×#67—61no—
421C2×#67—61no—
422C2×#67—68no—
423C2×#67—68no—
424C2×#67—68no—
425C2×#67C22×D312yes—
426C2×#67C22×D314yes—
427C2×#67C22×D314yes—
428C2×#67C22×D312yes—
429C2×#67C22×D314yes—
430C22×Dic3—32no—
431C22×Dic3—32no—
432C22×Dic3—34no—
433C22×Dic3—34no—
434C22×Dic3—32no—
435C22×Dic3—32no—
436C22×Dic3—34no—
437C22×Dic3—32no—
438C22×Dic3—34no—
439C22×Dic3—34no—
440C22×Dic3—61no—
441C22×Dic3—62no—
442C22×Dic3—62no—
443C22×Dic3—61no—
444C22×Dic3—61no—
445C22×Dic3—68no—
446C22×Dic3—68no—
447C22×Dic3—124no—
448C22×Dic3C22×D312yes—
449#237—68no—
450#237—68no—
451#237—68no—
452#237—616no—
453#237—616no—
454#237—616no—
455#237—616no—
456#237—68no—
457#237—124no—
458D3×D4—28no—
459D3×D4—68no—
460D3×D4—68no—
461D3×D4—68no—
462#235—68no—
463#235—68no—
464C2×D12—32no—
465C2×D12C22×D312yes—
466C2×C4×D3—34no—
467C2×C4×D3—34no—
468C2×C4×D3—32no—
469C2×C4×D3—32no—
470C2×C4×D3—32no—
471C2×C4×D3—34no—
472C2×C4×D3—61no—
473C2×C4×D3—68no—
474C2×C4×D3C22×D312yes—
475C2×C4×D3C22×D314yes—
476C2×Dic6—32no—
477C2×Dic6—32no—
478C2×Dic6—34no—
479C2×Dic6—34no—
480C2×Dic6—61no—
481C2×Dic6—68no—
482C3×C4⋊C4—34no—
483C3×C4⋊C4—34no—
484C3×C22⋊C4—21no—
485C3×C22⋊C4—22no—
486C3×C22⋊C4—32no—
487C3×C22⋊C4—34no—
488C3×C22⋊C4—34no—
489C3×C22⋊C4—34no—
490C3×C22⋊C4—34no—
491C3×C22⋊C4C22×D312yes—
492C3×C22⋊C4C22×D314yes—
493#217—32no—
494#217—34no—
495#217—34no—
496#217—34no—
497#217—34no—
498#217—34no—
499#217—61no—
500#217—62no—
501#217—62no—
502#217C22×D312yes—
503#217C22×D314yes—
504#217C22×D314yes—
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)⋊C4C22×D314yes—
513(C2×D3)⋊C4C22×D314yes—
514C4⋊Dic3—34no—
515C4⋊Dic3—34no—
516C4⋊Dic3—34no—
517C4⋊Dic3—62no—
518C4⋊Dic3C22×D314yes—
519Dic3⋊C4—34no—
520Dic3⋊C4—34no—
521Dic3⋊C4—34no—
522Dic3⋊C4—34no—
523Dic3⋊C4—34no—
524Dic3⋊C4—34no—
525Dic3⋊C4—34no—
526Dic3⋊C4—62no—
527Dic3⋊C4—62no—
528Dic3⋊C4C22×D314yes—
529C4×Dic3—34no—
530C4×Dic3—34no—
531C4×Dic3—62no—
532C22×C32—22no—
533C22×C32—22no—
534C22×C32—22no—
535C22×C32—21no—
536C22×C32—22no—
537C22×C32—22no—
538C22×C32—44no—
539C22×C32C22×D412yes—
540C22×C32C2511yescharacteristic
541C2×C3⋊D3—21no—
542C2×C3⋊D3—22no—
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—21no—
553C32×C4—22no—
554C3⋊Dic3—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—91no—
564C2×#41—92no—
565C2×#41—91no—
566C2×#41—92no—
567C2×#41—94no—
568C2×#41—92no—
569C2×#41—91no—
570C2×#41—91no—
571C2×#41—188no—
572C22×Q8—91no—
573C22×D4—32no—
574C22×D4—32no—
575C22×D4—91no—
576C22×D4—92no—
577C22×D4—92no—
578C22×D4—91no—
579C22×D4—91no—
580C23×C4—92no—
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—94no—
590#123—94no—
591#123—92no—
592#123—92no—
593#123—94no—
594#123—94no—
595#123—94no—
596#123—92no—
597#123—91no—
598#123—91no—
599C22⋊Q8—92no—
600C22⋊Q8—92no—
601C22⋊Q8—94no—
602C22⋊Q8—92no—
603C22⋊Q8—92no—
604#121—34no—
605#121—34no—
606#121—94no—
607#121—92no—
608#121—94no—
609#121—92no—
610#120—32no—
611#120—34no—
612#120—94no—
613#120—91no—
614#120D3211yescharacteristic, complemented
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—94no—
624C2×C4⋊C4—94no—
625C2×C22⋊C4—32no—
626C2×C22⋊C4—94no—
627C2×C22⋊C4—92no—
628C2×C22⋊C4—94no—
629C23×C3—24no—
630C23×C3—22no—
631C23×C3—21no—
632C23×C3—21no—
633C23×C3—32no—
634C23×C3—32no—
635C23×C3—38no—
636C23×C3—32no—
637C23×C3—42no—
638C23×C3—44no—
639C23×C3—44no—
640C23×C3—64no—
641C23×C3—124no—
642C23×C3—124no—
643C23×C3C23×D312yes—
644C23×C3C23×D314yes—
645C23×C3C23×D312yes—
646C22×D3—24no—
647C22×D3—32no—
648C22×D3—44no—
649C22×D3—44no—
650C22×D3—61no—
651C22×D3—64no—
652C22×D3—64no—
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—44no—
662C3×D4—44no—
663C3×D4—64no—
664C3×D4—64no—
665C3×D4—68no—
666C3×D4—68no—
667C3×D4—64no—
668C3×D4—124no—
669C2×C3×C4—22no—
670C2×C3×C4—21no—
671C2×C3×C4—34no—
672C2×C3×C4—32no—
673C2×C3×C4—34no—
674C2×C3×C4—64no—
675C2×C3×C4—64no—
676C2×C3×C4—124no—
677C2×C3×C4C23×D314yes—
678C2×C3×C4C23×D312yes—
679#67—24no—
680#67—24no—
681#67—28no—
682#67—28no—
683#67—38no—
684#67—38no—
685#67—38no—
686#67—38no—
687#67—44no—
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—
698C2×Dic3—24no—
699C2×Dic3—38no—
700C2×Dic3—32no—
701C2×Dic3—32no—
702C2×Dic3—34no—
703C2×Dic3—32no—
704C2×Dic3—34no—
705C2×Dic3—64no—
706C2×Dic3—61no—
707C2×Dic3—61no—
708C2×Dic3—62no—
709C2×Dic3—62no—
710C2×Dic3—61no—
711C2×Dic3—64no—
712C2×Dic3—68no—
713C2×Dic3—68no—
714C2×Dic3—64no—
715C2×Dic3—68no—
716C2×Dic3—68no—
717C2×Dic3—64no—
718C2×Dic3—64no—
719C2×Dic3—122no—
720C2×Dic3—124no—
721C2×Dic3—124no—
722C2×Dic3—122no—
723C2×Dic3—124no—
724C2×Dic3C23×D314yes—
725C2×Dic3C23×D312yes—
726C2×Dic3C23×D314yes—
727D12—24no—
728D12—64no—
729C4×D3—24no—
730C4×D3—44no—
731C4×D3—64no—
732C4×D3—64no—
733C4×D3—68no—
734C4×D3—68no—
735C4×D3—64no—
736C4×D3—122no—
737C4×D3—124no—
738Dic6—68no—
739Dic6—68no—
740Dic6—64no—
741Dic6—64no—
742Dic6—122no—
743C2×C32—22no—
744C2×C32—42no—
745C2×C32—41no—
746C2×C32C23×D411yescharacteristic
747C2×C32#58512yes—
748C3⋊D3—41no—
749C3×D3—24no—
750C3×D3—24no—
751C3×D3—42no—
752C24—32no—
753C24—32no—
754C24—92no—
755C24C2×D3211yescharacteristic
756#41—184no—
757#41—188no—
758#41—184no—
759#41—184no—
760#41—188no—
761#41—1816no—
762#41—188no—
763#41—184no—
764C2×Q8—92no—
765C2×Q8—92no—
766C2×Q8—91no—
767C2×Q8—91no—
768C2×Q8—184no—
769C2×D4—34no—
770C2×D4—32no—
771C2×D4—34no—
772C2×D4—32no—
773C2×D4—34no—
774C2×D4—32no—
775C2×D4—68no—
776C2×D4—68no—
777C2×D4—92no—
778C2×D4—91no—
779C2×D4—92no—
780C2×D4—91no—
781C2×D4—98no—
782C2×D4—92no—
783C2×D4—91no—
784C2×D4—91no—
785C2×D4—91no—
786C2×D4—92no—
787C2×D4—184no—
788C2×D4—188no—
789C2×D4—188no—
790C2×D4—184no—
791C2×D4C2×D3211yescharacteristic
792C2×D4C2×D3212yes—
793C22×C4—32no—
794C22×C4—32no—
795C22×C4—34no—
796C22×C4—94no—
797C22×C4—94no—
798C22×C4—92no—
799C22×C4—92no—
800C22×C4—94no—
801C22×C4—91no—
802C22×C4—92no—
803C22×C4—92no—
804C22×C4—91no—
805C22×C4—91no—
806C22×C4—91no—
807C22×C4—188no—
808C22×C4—184no—
809C4⋊C4—34no—
810C4⋊C4—34no—
811C4⋊C4—94no—
812C4⋊C4—94no—
813C4⋊C4—94no—
814C4⋊C4—92no—
815C4⋊C4—92no—
816C4⋊C4—92no—
817C4⋊C4—92no—
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—24no—
837C22×C3—24no—
838C22×C3—22no—
839C22×C3—24no—
840C22×C3—24no—
841C22×C3—24no—
842C22×C3—22no—
843C22×C3—21no—
844C22×C3—34no—
845C22×C3—34no—
846C22×C3—42no—
847C22×C3—42no—
848C22×C3—42no—
849C22×C3—41no—
850C22×C3—42no—
851C22×C3—48no—
852C22×C3—48no—
853C22×C3—64no—
854C22×C3—64no—
855C22×C3—62no—
856C22×C3—64no—
857C22×C3—128no—
858C22×C3—244no—
859C22×C3C2×D3×D414yes—
860C22×C3C24×D312yes—
861C2×D3—24no—
862C2×D3—24no—
863C2×D3—22no—
864C2×D3—24no—
865C2×D3—48no—
866C2×D3—62no—
867C2×D3—64no—
868C2×D3—84no—
869C2×D3—121no—
870C2×D3—122no—
871C2×D3—244no—
872C2×D3—244no—
873C2×D3C2×D3×D414yes—
874C2×D3C2×D3×D414yes—
875C3×C4—22no—
876C3×C4—24no—
877C3×C4—41no—
878C3×C4—42no—
879C3×C4—64no—
880C3×C4—62no—
881C3×C4—64no—
882Dic3—24no—
883Dic3—22no—
884Dic3—24no—
885Dic3—34no—
886Dic3—34no—
887Dic3—62no—
888Dic3—62no—
889Dic3—62no—
890Dic3—64no—
891Dic3—64no—
892Dic3—121no—
893Dic3—122no—
894Dic3—122no—
895C32#348511yescharacteristic, complemented, Sylow
896C23—22no—
897C23—32no—
898C23—32no—
899C23—38no—
900C23—32no—
901C23—42no—
902C23—64no—
903C23—91no—
904C23—124no—
905C23—124no—
906C23—184no—
907C23—364no—
908C23C22×D3211yescharacteristic
909C23C22×D3212yes—
910C23C22×D3211yescharacteristic
911Q8—182no—
912Q8—184no—
913Q8—184no—
914Q8—182no—
915D4—22no—
916D4—42no—
917D4—64no—
918D4—64no—
919D4—68no—
920D4—68no—
921D4—64no—
922D4—94no—
923D4—98no—
924D4—94no—
925D4—124no—
926D4—184no—
927D4—182no—
928D4—182no—
929D4—184no—
930D4—182no—
931D4—362no—
932C2×C4—34no—
933C2×C4—34no—
934C2×C4—32no—
935C2×C4—64no—
936C2×C4—64no—
937C2×C4—94no—
938C2×C4—91no—
939C2×C4—91no—
940C2×C4—92no—
941C2×C4—92no—
942C2×C4—91no—
943C2×C4—124no—
944C2×C4—182no—
945C2×C4—184no—
946C2×C4—188no—
947C2×C4—188no—
948C2×C4—184no—
949C2×C4—184no—
950C2×C4—184no—
951C2×C4—182no—
952C2×C4—182no—
953C2×C4—364no—
954C2×C4C22×D3212yes—
955C2×C4C22×D3211yescharacteristic
956C2×C3—24no—
957C2×C3—21no—
958C2×C3—22no—
959C2×C3—42no—
960C2×C3—44no—
961C2×C3—42no—
962C2×C3—44no—
963C2×C3—64no—
964C2×C3—64no—
965C2×C3—81no—
966C2×C3—122no—
967C2×C3C22×D3×D412yes—
968C2×C3#596614yes—
969D3—24no—
970D3—24no—
971D3—42no—
972D3—122no—
973D3—241no—
974C22—22no—
975C22—22no—
976C22—21no—
977C22—22no—
978C22—22no—
979C22—22no—
980C22—34no—
981C22—34no—
982C22—44no—
983C22—64no—
984C22—64no—
985C22—62no—
986C22—64no—
987C22—128no—
988C22—181no—
989C22—182no—
990C22—244no—
991C22—724no—
992C22D32×D412yes—
993C22C23×D3211yescharacteristic
994C4—21no—
995C4—22no—
996C4—62no—
997C4—64no—
998C4—64no—
999C4—92no—
1000C4—92no—
1001C4—182no—
1002C4—181no—
1003C4—182no—
1004C3—21no—
1005C3#8629612yescomplemented
1006C2—22no—
1007C2—42no—
1008C2—41no—
1009C2—64no—
1010C2—64no—
1011C2—122no—
1012C2—361no—
1013C2C2×D32×D411yescharacteristic
1014C2#1059667912yes—
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#120C22
hypercenter#120D32
hypocenterC32#3485
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #120

Complements

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

NH ≅ G/Ntype
1. C22×#3805C2semidirect
2. C2×#64313C2semidirect
3. #10596057C2semidirect
4. C3×#5589C2semidirect
5. #10595524C2semidirect
6. #10595501C2semidirect
7. #10595290C2semidirect
8. #10595271C2semidirect
9. #10595225C2semidirect
10. D3×#935C2semidirect
11. #10595134C2semidirect
12. D3×#886C2semidirect
13. #10594276C2semidirect
14. #10594185C2semidirect
15. #10594181C2semidirect
16. #10594084C2semidirect
17. #10594062C2semidirect
19. C23×C3⋊Dic3C22semidirect
21. C22×C3×#67C22semidirect
24. C2×D3×#67C22semidirect
25. C22×#627C22semidirect
27. C22×#625C22semidirect
30. C2×#3805C22semidirect
31. C2×#3805C22semidirect
32. C2×#3805C22semidirect
33. C2×#3805C22semidirect
34. C22×D3×Dic3C22semidirect
36. C2×#3802C22semidirect
37. C2×#3798C22semidirect
38. C2×#3795C22semidirect
39. C32×#120C22semidirect
40. #64162C22semidirect
41. #64148C22semidirect
42. #64144C22semidirect
43. D4×C3⋊Dic3C22semidirect
44. #64095C22semidirect
45. #64090C22semidirect
46. #64087C22semidirect
47. #64086C22semidirect
48. C3×#953C22semidirect
49. C3×#938C22semidirect
50. C3×#937C22semidirect
51. C3×#935C22semidirect
52. C3×#886C22semidirect
53. C3×#884C22semidirect
54. C3×#883C22semidirect
55. C3×D3×C22⋊C4C22semidirect
56. #63983C22semidirect
57. #63982C22semidirect
58. #63982C22semidirect
59. #63980C22semidirect
60. #67⋊Dic3C22semidirect
61. #63971C22semidirect
62. #63970C22semidirect
63. #63969C22semidirect
64. #63969C22semidirect
65. D3×#217C22semidirect
66. D3×#217C22semidirect
67. #63966C22semidirect
68. #63962C22semidirect
69. #63961C22semidirect
70. #63957C22semidirect
71. #63953C22semidirect
72. D3×(C2×D3)⋊C4C22semidirect
73. #63919C22semidirect
74. #63915C22semidirect
75. #63902C22semidirect
76. C4×#625C22semidirect
77. #63899C22semidirect
78. #63891C22semidirect
79. #63890C22semidirect
80. D3×C4⋊Dic3C22semidirect
81. #63884C22semidirect
82. #63879C22semidirect
83. D3×Dic3⋊C4C22semidirect
84. #63865C22semidirect
85. #63840C22semidirect
104. #5589D3semidirect
147. C2×#625D4semidirect
200. C22×#67C2×D3semidirect
231. C3×#120C2×D3semidirect
235. #953C2×D3semidirect
244. #938C2×D3semidirect
247. #937C2×D3semidirect
255. #935C2×D3semidirect
280. #886C2×D3semidirect
284. #884C2×D3semidirect
288. #883C2×D3semidirect
297. D3×C22⋊C4C2×D3semidirect
614. #120D32semidirect
895. C32#3485semidirect
1005. C3#86296semidirect

Maximal subgroups

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

subgroupindex
C22×#38052
C2×#643132
#105960572
C3×#55892
#105955242
#105955012
#105952902
#105952712
#105952252
D3×#9352
#105951342
D3×#8862
#105942762
#105941852
#105941812
#105940842
#105940622
#862963