Finite Group Databasebeta

← #11906029

Subgroups — #11906029

Order 1152.

3098 conjugacy classes of subgroups.

The subgroup lattice has 1024 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64309C212yesmaximal, complemented
2#10596026C211yesmaximal, characteristic, complemented
3C3×#5555C211yesmaximal, characteristic, complemented
4C3×C4×#237C211yesmaximal, characteristic, complemented
5#10595248C212yesmaximal, complemented
6C2×#63918C212yesmaximal, complemented
7#10594910C212yesmaximal, complemented
8#10594907C212yesmaximal, complemented
9#10594906C212yesmaximal, complemented
10#10594383C212yesmaximal, complemented
11#10594380C212yesmaximal, complemented
12#10594081C214yesmaximal, complemented
13#10594077C214yesmaximal, complemented
14#10593968C211yesmaximal, characteristic, complemented
15#10593903C211yesmaximal, characteristic, complemented
16Dic6×D12C211yesmaximal, characteristic, complemented
17D3×#869C211yesmaximal, characteristic, complemented
18#86679—31nomaximal
19#85827—31nomaximal
20C2×#3830C2212yes—
21C2×C3×#237C2212yes—
22C2×C3×#237C2211yescharacteristic
23C22×#627C2214yes—
24C2×#3805C2214yes—
25C2×#3804C2214yes—
26C2×#3804C2214yes—
27#64309—216no—
28C2×#3798C2212yes—
29C2×#3797C2212yes—
30C2×D3×Dic6C2212yes—
31C2×D3×Dic6C2212yes—
32C32×C4×D4C2211yescharacteristic
33#64139C2212yes—
34C2×C4⋊(C3⋊Dic3)C2212yes—
35#64106C2212yes—
36#64095C2214yes—
37C4×C4⋊(C3⋊D3)C2211yescharacteristic
38#64078C2211yescharacteristic
39C3×D4×Dic3C2211yescharacteristic
40C3×#930C2212yes—
41C3×C4×#67C2212yes—
42C2×C3×C4⋊Dic3C2212yes—
43C2×C3×C4×Dic3C2212yes—
44C3×#897C2212yes—
45C3×#892C2211yescharacteristic
46C3×#887C2211yescharacteristic
47C3×#886C2214yes—
48C3×#67⋊C4C2212yes—
49C3×#877C2212yes—
50C3×C4×D12C2211yescharacteristic
51C3×C42×D3C2211yescharacteristic
52C3×#869C2211yescharacteristic
53C3×C4×Dic6C2211yescharacteristic
54#63978C2214yes—
55#63966C2214yes—
56C2×Dic3⋊Dic3C2214yes—
57#63962C2214yes—
58#63918C2214yes—
59#63918C2212yes—
60#63918C2214yes—
61#63918C2212yes—
62#63918C2212yes—
63#63918C2212yes—
64#63918C2211yescharacteristic
65#63911C2211yescharacteristic
66#63909C2211yescharacteristic
67#63908C2211yescharacteristic
68#63906C2212yes—
69C4×#626C2212yes—
70#63895C2214yes—
71#63895C2214yes—
72#63894C2212yes—
73#63893C2214yes—
74#63893C2214yes—
75Dic3×D12C2212yes—
76#63891C2214yes—
77#63890C2214yes—
78D3×C4⋊Dic3C2212yes—
79D3×C4⋊Dic3C2212yes—
80#63880C2214yes—
81#63871C2212yes—
82#63866C2212yes—
83#63857C2212yes—
84#63852C2212yes—
85#63852C2214yes—
86C2×#1010—32no—
87C2×#1010—32no—
88C3×#547—31no—
89C3×C4×#41—31no—
90#5824—32no—
91#5727—31no—
92D3×C4⋊Q8—31no—
93#5655—34no—
94#5648—34no—
95#5632—32no—
96#5628—32no—
97#5611—32no—
98#5596—32no—
99Q8×D12—32no—
100Q8×D12—31no—
101Q8×D12—31no—
102#5555—32no—
103#5555—31no—
104#5555—31no—
105#5555—32no—
106#5555—32no—
107#5555—34no—
108#5555—61no—
109#5555D311yescharacteristic, complemented
110#5548—31no—
111D4×Dic6—31no—
112C4×#237D311yescharacteristic, complemented
113#5526—32no—
114#5526—34no—
115#5507—32no—
116C2×#888—32no—
117#5477—32no—
118#5477—31no—
119C2×#869—32no—
120C2×#869—31no—
121C2×C32×D4C2311yescharacteristic
122C22×C32×C4C2312yes—
123C2×#638C2314yes—
124C22×C3⋊Dic3C2314yes—
125#3830—28no—
126C2×C4⋊(C3⋊D3)C2311yescharacteristic
127C2×C4×C3⋊D3C2312yes—
128C2×#634C2312yes—
129C2×C3×#67C2314yes—
130C2×C3×#67C2312yes—
131C22×C3×Dic3C2312yes—
132C22×C3×Dic3C2314yes—
133C22×C3×Dic3C2312yes—
134C3×#237—28no—
135C3×#237D418yescomplemented
136C2×C3×D12C2311yescharacteristic
137C2×C3×C4×D3C2311yescharacteristic
138C2×C3×C4×D3C2312yes—
139C2×C3×C4×D3C2311yescharacteristic
140C2×C3×C4×D3C2311yescharacteristic
141C2×C3×Dic6C2312yes—
142C2×C3×Dic6C2311yescharacteristic
143C2×#627—216no—
144C2×#627C2314yes—
145C2×#627C2314yes—
146C2×#627C2314yes—
147C2×#627C2312yes—
148C2×#626C2312yes—
149C2×#626C2312yes—
150C2×#626C2312yes—
151C2×#625C2312yes—
152C2×#624C2314yes—
153#3805—216no—
154#3804—216no—
155#3804—216no—
156C2×D3×Dic3C2314yes—
157C2×D3×Dic3C2314yes—
158#3798—28no—
159#3797—28no—
160D3×Dic6—28no—
161D3×Dic6—28no—
162C32×C4⋊C4C2311yescharacteristic
163C32×C22⋊C4C2312yes—
164C32×C42C2311yescharacteristic
165#3752C2312yes—
166#3752C2314yes—
167C4⋊(C3⋊Dic3)C2312yes—
168C4⋊(C3⋊Dic3)C2312yes—
169C4⋊(C3⋊Dic3)C2311yescharacteristic
170C4⋊(C3⋊Dic3)C2314yes—
171C3×#217C2312yes—
172C3×(C2×D3)⋊C4C2312yes—
173C3×(C2×D3)⋊C4C2312yes—
174C3×(C2×D3)⋊C4C2314yes—
175C3×C4⋊Dic3C2312yes—
176C3×C4⋊Dic3C2314yes—
177C3×C4⋊Dic3C2311yescharacteristic
178C3×C4⋊Dic3C2311yescharacteristic
179C3×C4⋊Dic3C2312yes—
180C3×Dic3⋊C4C2312yes—
181C3×Dic3⋊C4C2312yes—
182C3×C4×Dic3C2311yescharacteristic
183C3×C4×Dic3C2312yes—
184C3×C4×Dic3C2312yes—
185C3×C4×Dic3C2311yescharacteristic
186C3×C4×Dic3C2311yescharacteristic
187C3×C4×Dic3C2312yes—
188Dic3⋊Dic3C2314yes—
189Dic3⋊Dic3C2314yes—
190Dic3⋊Dic3C2314yes—
191Dic3⋊Dic3C2314yes—
192Dic3⋊Dic3C2312yes—
193#3722C2314yes—
194#3722C2312yes—
195(C2×D3)⋊Dic3C2314yes—
196(C2×D3)⋊Dic3C2312yes—
197#3499—91noSylow
198C2×C3×#41—31no—
199C2×C3×#41—32no—
200#1010—616no—
201#1010—616no—
202C2×D3×Q8—32no—
203C2×D3×Q8—32no—
204C2×D3×Q8—32no—
205C2×D3×Q8—32no—
206C2×#237—32no—
207C2×#237—32no—
208C2×#237—34no—
209C2×#237—34no—
210C2×#237—34no—
211C2×#237—34no—
212C2×#237—62no—
213C2×#237C2×D312yes—
214C2×#237C2×D311yescharacteristic
215C2×#235—34no—
216C2×#235—34no—
217C2×#235—32no—
218C2×#235—32no—
219C22×Dic6—34no—
220C22×Dic6—34no—
221C22×Dic6—32no—
222C22×Dic6—32no—
223C3×C4⋊Q8—31no—
224C3×#123—34no—
225C3×C22⋊Q8—32no—
226C3×#121—32no—
227C3×C4×Q8—31no—
228C3×C4×Q8—31no—
229C3×C4×D4—21no—
230C3×C4×D4—31no—
231C3×C4×D4—32no—
232C3×C4×D4—32no—
233C3×C4×D4—31no—
234C3×C4×D4C2×D311yescharacteristic
235C3×C4×D4C2×D311yescharacteristic
236C3×#117—31no—
237C3×#117—32no—
238C2×C3×C4⋊C4—32no—
239C2×C3×C42—32no—
240C2×C3×C42—31no—
241#946—32no—
242#944—32no—
243#940—31no—
244#939—34no—
245#938—31no—
246#935—34no—
247D4×Dic3—32no—
248D4×Dic3C2×D311yescharacteristic
249#930—32no—
250#930—32no—
251#930—34no—
252#930—31no—
253#930—32no—
254#930—31no—
255#930—62no—
256#930C2×D312yes—
257#929—34no—
258C4×#67—32no—
259C4×#67C2×D312yes—
260C2×C4⋊Dic3—32no—
261C2×C4⋊Dic3—32no—
262C2×C4⋊Dic3—34no—
263C2×C4⋊Dic3—32no—
264C2×C4⋊Dic3—32no—
265C2×C4⋊Dic3—62no—
266C2×C4⋊Dic3C2×D312yes—
267#924—32no—
268C2×Dic3⋊C4—34no—
269C2×C4×Dic3C2×D312yes—
270#897—32no—
271#897—32no—
272#897—32no—
273#897—32no—
274#897—34no—
275#897—34no—
276#897—34no—
277#897—34no—
278#897—62no—
279#897C2×D312yes—
280#896—34no—
281#896—34no—
282#895—31no—
283#894—34no—
284#893—32no—
285#892C2×D311yescharacteristic
286D3×C4⋊C4—32no—
287D3×C4⋊C4—32no—
288#888—34no—
289#888—32no—
290#888—34no—
291#888—32no—
292#888—32no—
293#888—31no—
294#888—32no—
295#887C2×D311yescharacteristic
296#886—34no—
297#886—34no—
298#886—34no—
299#886—34no—
300#886—34no—
301#886—34no—
302#886—64no—
303#886C2×D314yes—
304#885—32no—
305#885—34no—
306#884—32no—
307#883—34no—
308#67⋊C4—34no—
309#67⋊C4C2×D312yes—
310#878—34no—
311#878—34no—
312#877C2×D312yes—
313#875—34no—
314#875—32no—
315#874—31no—
316C4×D12—32no—
317C4×D12—32no—
318C4×D12—31no—
319C4×D12—31no—
320C4×D12—34no—
321C4×D12—32no—
322C4×D12—61no—
323C4×D12C2×D311yescharacteristic
324C42×D3C2×D311yescharacteristic
325#869—32no—
326#869—31no—
327#869—31no—
328#869—31no—
329#869—32no—
330#869—34no—
331#869—32no—
332#869—32no—
333#869—32no—
334#869—34no—
335#869—61no—
336#869C2×D311yescharacteristic
337C4×Dic6C2×D311yescharacteristic
338C23×C32C2412yes—
339C22×C3⋊D3C2412yes—
340C22×C3×D3C2412yes—
341C22×C3×D3C2411yescharacteristic
342C32×D4C2×D414yes—
343C2×C32×C4—24no—
344C2×C32×C4C2412yes—
345C2×C32×C4C2411yescharacteristic
346C2×C32×C4C2411yescharacteristic
347C2×C32×C4C2411yescharacteristic
348#638—28no—
349C2×C3⋊Dic3—28no—
350C2×C3⋊Dic3C2414yes—
351C2×C3⋊Dic3C2412yes—
352C4⋊(C3⋊D3)—22no—
353C4×C3⋊D3—24no—
354#634—24no—
355C3×#67—28no—
356C3×#67C2×D418yes—
357C2×C3×Dic3—28no—
358C2×C3×Dic3—24no—
359C2×C3×Dic3C2×D418yes—
360C2×C3×Dic3C2411yescharacteristic
361C2×C3×Dic3C2412yes—
362C2×C3×Dic3C2414yes—
363C2×C3×Dic3C2412yes—
364C2×C3×Dic3C2411yescharacteristic
365C2×C3×Dic3C2412yes—
366C2×C3×Dic3C2411yescharacteristic
367C3×D12—22no—
368C3×C4×D3—24no—
369C3×C4×D3—22no—
370C3×C4×D3—22no—
371C3×C4×D3C2×D414yes—
372C3×Dic6—24no—
373C3×Dic6C2×D414yes—
374#627—28no—
375#627—28no—
376#627—28no—
377#627—24no—
378#626—24no—
379#626—24no—
380#626—24no—
381#625—24no—
382#624—28no—
383D3×Dic3—28no—
384D3×Dic3—28no—
385C2×2−1+4—92no—
386D4×Q8—91no—
387D4×Q8—92no—
388D4×Q8—91no—
389#547—31no—
390#547—92no—
391#547—92no—
392#547—94no—
393#547—92no—
394#547—91no—
395#536—92no—
396#536—94no—
397#532—91no—
398#532—92no—
399C2×C4⋊Q8—92no—
400C2×C4⋊Q8—91no—
401C4×#41—31no—
402C3×#41—38no—
403C3×#41—68no—
404C2×C3×Q8—31no—
405C2×C3×Q8—32no—
406C2×C3×D4—21no—
407C2×C3×D4—32no—
408C2×C3×D4—34no—
409C2×C3×D4—31no—
410C2×C3×D4C22×D311yescharacteristic
411C2×C3×D4C22×D311yescharacteristic
412C22×C3×C4—22no—
413C22×C3×C4—32no—
414C22×C3×C4—31no—
415C22×C3×C4—34no—
416C22×C3×C4—32no—
417C22×C3×C4—32no—
418C22×C3×C4—31no—
419C22×C3×C4—31no—
420C22×C3×C4C22×D312yes—
421C22×C3×C4C22×D312yes—
422C2×#67—34no—
423C2×#67—34no—
424C2×#67—32no—
425C2×#67—32no—
426C2×#67—32no—
427C2×#67—32no—
428C2×#67—32no—
429C2×#67—64no—
430C2×#67C22×D314yes—
431C2×#67C22×D312yes—
432C22×Dic3—34no—
433C22×Dic3—34no—
434C22×Dic3—34no—
435C22×Dic3—34no—
436C22×Dic3—64no—
437C22×Dic3C22×D312yes—
438C22×Dic3C22×D314yes—
439C22×Dic3C22×D312yes—
440D3×Q8—68no—
441D3×Q8—68no—
442D3×Q8—68no—
443D3×Q8—68no—
444#237—28no—
445#237—616no—
446#237—616no—
447#237—68no—
448#237—68no—
449#237—616no—
450#237—616no—
451#237—128no—
452#237D1218yescomplemented
453#235—68no—
454#235—616no—
455#235—616no—
456#235—68no—
457C2×D12—32no—
458C2×D12—32no—
459C2×D12—32no—
460C2×D12—31no—
461C2×D12—31no—
462C2×D12—61no—
463C2×D12C22×D311yescharacteristic
464C2×C4×D3—34no—
465C2×C4×D3—34no—
466C2×C4×D3—32no—
467C2×C4×D3—32no—
468C2×C4×D3—34no—
469C2×C4×D3—34no—
470C2×C4×D3—62no—
471C2×C4×D3C22×D311yescharacteristic
472C2×C4×D3C22×D311yescharacteristic
473C2×C4×D3C22×D312yes—
474C2×C4×D3C22×D311yescharacteristic
475C2×Dic6—32no—
476C2×Dic6—32no—
477C2×Dic6—32no—
478C2×Dic6—34no—
479C2×Dic6—34no—
480C2×Dic6—34no—
481C2×Dic6—34no—
482C2×Dic6—34no—
483C2×Dic6—32no—
484C2×Dic6—34no—
485C2×Dic6—62no—
486C2×Dic6—68no—
487C2×Dic6—616no—
488C2×Dic6—616no—
489C2×Dic6—68no—
490C2×Dic6C22×D312yes—
491C2×Dic6C22×D311yescharacteristic
492C3×C4⋊C4—21no—
493C3×C4⋊C4—31no—
494C3×C4⋊C4—32no—
495C3×C4⋊C4—34no—
496C3×C4⋊C4—32no—
497C3×C4⋊C4—32no—
498C3×C4⋊C4—32no—
499C3×C4⋊C4—31no—
500C3×C4⋊C4C22×D311yescharacteristic
501C3×C4⋊C4C22×D311yescharacteristic
502C3×C22⋊C4—22no—
503C3×C22⋊C4—32no—
504C3×C22⋊C4—32no—
505C3×C22⋊C4—34no—
506C3×C22⋊C4—32no—
507C3×C22⋊C4C22×D312yes—
508C3×C22⋊C4C22×D312yes—
509C3×C42—21no—
510C3×C42—31no—
511C3×C42—32no—
512C3×C42—31no—
513C3×C42—32no—
514C3×C42—32no—
515C3×C42—31no—
516C3×C42C22×D311yescharacteristic
517C3×C42C22×D311yescharacteristic
518#217—32no—
519#217—34no—
520#217C22×D312yes—
521(C2×D3)⋊C4—34no—
522(C2×D3)⋊C4—32no—
523(C2×D3)⋊C4—34no—
524(C2×D3)⋊C4—32no—
525(C2×D3)⋊C4—32no—
526(C2×D3)⋊C4—34no—
527(C2×D3)⋊C4—32no—
528(C2×D3)⋊C4—34no—
529(C2×D3)⋊C4—34no—
530(C2×D3)⋊C4—32no—
531(C2×D3)⋊C4—62no—
532(C2×D3)⋊C4—64no—
533(C2×D3)⋊C4C22×D314yes—
534(C2×D3)⋊C4C22×D312yes—
535(C2×D3)⋊C4C22×D312yes—
536C4⋊Dic3—32no—
537C4⋊Dic3—31no—
538C4⋊Dic3—34no—
539C4⋊Dic3—32no—
540C4⋊Dic3—32no—
541C4⋊Dic3—32no—
542C4⋊Dic3—31no—
543C4⋊Dic3—34no—
544C4⋊Dic3—32no—
545C4⋊Dic3—34no—
546C4⋊Dic3—34no—
547C4⋊Dic3—34no—
548C4⋊Dic3—34no—
549C4⋊Dic3—62no—
550C4⋊Dic3—62no—
551C4⋊Dic3—61no—
552C4⋊Dic3—64no—
553C4⋊Dic3C22×D311yescharacteristic
554C4⋊Dic3C22×D311yescharacteristic
555C4⋊Dic3C22×D312yes—
556C4⋊Dic3C22×D314yes—
557C4⋊Dic3C22×D312yes—
558Dic3⋊C4—34no—
559Dic3⋊C4—34no—
560Dic3⋊C4—34no—
561Dic3⋊C4—34no—
562Dic3⋊C4—32no—
563Dic3⋊C4C22×D312yes—
564Dic3⋊C4C22×D312yes—
565C4×Dic3C22×D312yes—
566C4×Dic3C22×D311yescharacteristic
567C4×Dic3C22×D311yescharacteristic
568C4×Dic3C22×D311yescharacteristic
569C4×Dic3C22×D312yes—
570C4×Dic3C22×D312yes—
571C22×C32—22no—
572C22×C32—22no—
573C22×C32C22×D414yes—
574C22×C32C2511yescharacteristic
575C2×C3⋊D3—22no—
576C2×C3⋊D3—22no—
577C2×C3⋊D3—22no—
578C2×C3×D3—21no—
579C2×C3×D3—21no—
580C2×C3×D3—22no—
581C2×C3×D3—22no—
582C2×C3×D3—22no—
583C2×C3×D3C22×D412yes—
584C32×C4—21no—
585C32×C4—22no—
586C32×C4C22×D412yes—
587C32×C42−1+412yescomplemented
588C3⋊Dic3—24no—
589C3⋊Dic3—22no—
590C3×Dic3—24no—
591C3×Dic3—22no—
592C3×Dic3—21no—
593C3×Dic3—22no—
594C3×Dic3C22×D414yes—
595C3×Dic3C22×D412yes—
596C3×Dic32−1+412yescomplemented
5972−1+4—1816no—
598C2×#41—31no—
599C2×#41—32no—
600C2×#41—92no—
601C2×#41—94no—
602C2×#41—94no—
603C2×#41—94no—
604C2×#41—92no—
605C22×Q8—94no—
606C22×Q8—92no—
607C22×Q8—92no—
608C22×Q8—92no—
609C4⋊Q8—31no—
610C4⋊Q8—91no—
611C4⋊Q8—92no—
612C4⋊Q8—94no—
613C4⋊Q8—92no—
614C4⋊Q8—92no—
615C4⋊Q8—92no—
616C4⋊Q8—94no—
617C4⋊Q8—92no—
618C4⋊Q8—91no—
619#127—91no—
620#124—92no—
621#124—94no—
622#123—34no—
623#123—94no—
624#123—94no—
625#123—94no—
626#123—94no—
627#123—94no—
628C22⋊Q8—32no—
629C22⋊Q8—94no—
630C22⋊Q8—94no—
631C22⋊Q8—94no—
632C22⋊Q8—94no—
633C22⋊Q8—92no—
634C22⋊Q8—92no—
635C22⋊Q8—92no—
636#121—32no—
637#121—92no—
638#121—91no—
639#121—91no—
640#121—94no—
641#121—92no—
642C4×Q8—31no—
643C4×Q8—31no—
644C4×D4—31no—
645C4×D4—32no—
646C4×D4—32no—
647C4×D4—31no—
648C4×D4—94no—
649C4×D4—92no—
650C4×D4—92no—
651C4×D4—92no—
652C4×D4—91no—
653C4×D4D3211yescharacteristic
654#117—31no—
655#117—32no—
656C2×C4⋊C4—32no—
657C2×C4⋊C4—92no—
658C2×C4⋊C4—92no—
659C2×C4⋊C4—94no—
660C2×C4⋊C4—92no—
661C2×C42—32no—
662C2×C42—31no—
663C23×C3—22no—
664C23×C3—31no—
665C23×C3—32no—
666C23×C3C23×D312yes—
667C23×C3C23×D312yes—
668C22×D3—32no—
669C22×D3—32no—
670C22×D3—62no—
671C22×D3C23×D312yes—
672C22×D3C23×D311yescharacteristic
673C3×Q8—34no—
674C3×Q8—64no—
675C3×D4—24no—
676C3×D4—38no—
677C3×D4—68no—
678C3×D4—62no—
679C3×D4C2×D1214yes—
680C3×D4D3×D414yes—
681C2×C3×C4—24no—
682C2×C3×C4—24no—
683C2×C3×C4—21no—
684C2×C3×C4—21no—
685C2×C3×C4—21no—
686C2×C3×C4—22no—
687C2×C3×C4—38no—
688C2×C3×C4—31no—
689C2×C3×C4—31no—
690C2×C3×C4—32no—
691C2×C3×C4—34no—
692C2×C3×C4—32no—
693C2×C3×C4—34no—
694C2×C3×C4—31no—
695C2×C3×C4—32no—
696C2×C3×C4—44no—
697C2×C3×C4—62no—
698C2×C3×C4—64no—
699C2×C3×C4—68no—
700C2×C3×C4—64no—
701C2×C3×C4—62no—
702C2×C3×C4C23×D312yes—
703C2×C3×C4C23×D311yescharacteristic
704C2×C3×C4C23×D312yes—
705C2×C3×C4C23×D311yescharacteristic
706C2×C3×C4C23×D311yescharacteristic
707C2×C3×C4C23×D311yescharacteristic
708C2×C3×C4C23×D311yescharacteristic
709C2×C3×C4C23×D311yescharacteristic
710#67—28no—
711#67—64no—
712#67—64no—
713#67—68no—
714#67—68no—
715#67—64no—
716#67—64no—
717#67—64no—
718#67—128no—
719#67C2×D1218yes—
720C2×Dic3—28no—
721C2×Dic3—24no—
722C2×Dic3—34no—
723C2×Dic3—32no—
724C2×Dic3—34no—
725C2×Dic3—32no—
726C2×Dic3—64no—
727C2×Dic3—62no—
728C2×Dic3—68no—
729C2×Dic3—68no—
730C2×Dic3—68no—
731C2×Dic3—68no—
732C2×Dic3—128no—
733C2×Dic3C2×D1218yes—
734C2×Dic3C23×D311yescharacteristic
735C2×Dic3C23×D312yes—
736C2×Dic3C23×D312yes—
737C2×Dic3C23×D314yes—
738C2×Dic3C23×D311yescharacteristic
739C2×Dic3C23×D312yes—
740C2×Dic3C23×D311yescharacteristic
741D12—22no—
742D12—64no—
743D12—64no—
744D12—64no—
745D12—62no—
746D12—62no—
747D12—122no—
748C4×D3—24no—
749C4×D3—22no—
750C4×D3—22no—
751C4×D3—68no—
752C4×D3—68no—
753C4×D3—68no—
754C4×D3—64no—
755C4×D3—64no—
756C4×D3—68no—
757C4×D3—124no—
758C4×D3C2×D1214yes—
759Dic6—24no—
760Dic6—68no—
761Dic6—64no—
762Dic6—68no—
763Dic6—68no—
764Dic6—64no—
765Dic6—64no—
766Dic6—64no—
767Dic6—68no—
768Dic6—68no—
769Dic6—68no—
770Dic6—124no—
771Dic6C2×D1214yes—
772C2×C32—24no—
773C2×C32C23×D411yescharacteristic
774C2×C32C2×2−1+411yescharacteristic
775C2×C32C2×2−1+411yescharacteristic
776C3⋊D3—42no—
777C3×D3—22no—
778C3×D3—42no—
779#41—38no—
780#41—68no—
781#41—188no—
782#41—1816no—
783#41—1816no—
784#41—1816no—
785#41—188no—
786C2×Q8—31no—
787C2×Q8—32no—
788C2×Q8—94no—
789C2×Q8—94no—
790C2×Q8—92no—
791C2×Q8—94no—
792C2×Q8—92no—
793C2×Q8—1816no—
794C2×Q8—188no—
795C2×Q8—188no—
796C2×Q8—188no—
797C2×D4—32no—
798C2×D4—34no—
799C2×D4—31no—
800C2×D4—92no—
801C2×D4—92no—
802C2×D4—92no—
803C2×D4—92no—
804C2×D4—94no—
805C2×D4—91no—
806C2×D4C2×D3211yescharacteristic
807C22×C4—32no—
808C22×C4—31no—
809C22×C4—32no—
810C22×C4—34no—
811C22×C4—31no—
812C22×C4—31no—
813C22×C4—32no—
814C22×C4—94no—
815C22×C4—94no—
816C22×C4—94no—
817C22×C4—94no—
818C22×C4—92no—
819C22×C4C2×D3212yes—
820C4⋊C4—31no—
821C4⋊C4—32no—
822C4⋊C4—34no—
823C4⋊C4—32no—
824C4⋊C4—32no—
825C4⋊C4—32no—
826C4⋊C4—31no—
827C4⋊C4—92no—
828C4⋊C4—94no—
829C4⋊C4—94no—
830C4⋊C4—94no—
831C4⋊C4—94no—
832C4⋊C4—92no—
833C4⋊C4—91no—
834C4⋊C4—94no—
835C4⋊C4—92no—
836C4⋊C4C2×D3211yescharacteristic
837C22⋊C4—32no—
838C22⋊C4—32no—
839C22⋊C4—32no—
840C22⋊C4—34no—
841C22⋊C4—92no—
842C22⋊C4—94no—
843C22⋊C4—92no—
844C22⋊C4—94no—
845C22⋊C4—94no—
846C22⋊C4—92no—
847C22⋊C4C2×D3212yes—
848C42—31no—
849C42—32no—
850C42—31no—
851C42—32no—
852C42—31no—
853C42—32no—
854C42C2×D3211yescharacteristic
855C22×C3—22no—
856C22×C3—22no—
857C22×C3—22no—
858C22×C3—22no—
859C22×C3—24no—
860C22×C3—21no—
861C22×C3—32no—
862C22×C3—42no—
863C22×C3—42no—
864C22×C3—61no—
865C22×C3—61no—
866C22×C3—62no—
867C22×C3—62no—
868C22×C3—62no—
869C22×C3C22×D1214yes—
870C22×C3C2×D3×D414yes—
871C22×C3C24×D311yescharacteristic
872C22×C3C24×D311yescharacteristic
873C2×D3—21no—
874C2×D3—21no—
875C2×D3—22no—
876C2×D3—22no—
877C2×D3—22no—
878C2×D3—62no—
879C2×D3—62no—
880C2×D3—62no—
881C2×D3—62no—
882C2×D3—62no—
883C2×D3—62no—
884C2×D3—122no—
885C2×D3—122no—
886C2×D3—122no—
887C2×D3C22×D1212yes—
888C3×C4—21no—
889C3×C4—22no—
890C3×C4—22no—
891C3×C4—21no—
892C3×C4—22no—
893C3×C4—22no—
894C3×C4—32no—
895C3×C4—34no—
896C3×C4—32no—
897C3×C4—42no—
898C3×C4—41no—
899C3×C4—62no—
900C3×C4—64no—
901C3×C4—61no—
902C3×C4—62no—
903C3×C4C22×D1212yes—
904C3×C4C2×D3×D412yes—
905C3×C4#101012yescomplemented
906C3×C4#101012yescomplemented
907Dic3—24no—
908Dic3—22no—
909Dic3—21no—
910Dic3—22no—
911Dic3—64no—
912Dic3—62no—
913Dic3—62no—
914Dic3—64no—
915Dic3—124no—
916Dic3—122no—
917Dic3C22×D1212yes—
918Dic3C22×D1214yes—
919Dic3#101012yescomplemented
920C32#349911yescharacteristic, complemented, Sylow
921C23—31no—
922C23—32no—
923C23—92no—
924C23C22×D3212yes—
925Q8—34no—
926Q8—64no—
927Q8—184no—
928Q8—188no—
929Q8—188no—
930Q8—188no—
931Q8—184no—
932D4—38no—
933D4—68no—
934D4—62no—
935D4—184no—
936D4—184no—
937D4—184no—
938D4—184no—
939D4—188no—
940D4—182no—
941D4D3×D1214yes—
942C2×C4—24no—
943C2×C4—38no—
944C2×C4—31no—
945C2×C4—31no—
946C2×C4—32no—
947C2×C4—34no—
948C2×C4—31no—
949C2×C4—32no—
950C2×C4—32no—
951C2×C4—34no—
952C2×C4—62no—
953C2×C4—64no—
954C2×C4—68no—
955C2×C4—64no—
956C2×C4—62no—
957C2×C4—94no—
958C2×C4—92no—
959C2×C4—188no—
960C2×C4—188no—
961C2×C4—188no—
962C2×C4—188no—
963C2×C4—184no—
964C2×C4C22×D3212yes—
965C2×C4C22×D3211yescharacteristic
966C2×C4C22×D3211yescharacteristic
967C2×C4C22×D3211yescharacteristic
968C2×C3—24no—
969C2×C3—24no—
970C2×C3—21no—
971C2×C3—21no—
972C2×C3—21no—
973C2×C3—44no—
974C2×C3—62no—
975C2×C3—122no—
976C2×C3C23×D1211yescharacteristic
977C2×C3C22×D3×D411yescharacteristic
978C2×C3C2×#101011yescharacteristic
979C2×C3C2×#101011yescharacteristic
980C2×C3C2×#101011yescharacteristic
981C2×C3D3×2−1+411yescharacteristic
982D3—22no—
983D3—42no—
984D3—122no—
985D3—122no—
986D3—242no—
987C22—22no—
988C22—22no—
989C22—32no—
990C22—61no—
991C22—61no—
992C22—62no—
993C22—62no—
994C22—62no—
995C22—182no—
996C22—182no—
997C22—182no—
998C22C2×D3×D1214yes—
999C22C23×D3211yescharacteristic
1000C4—22no—
1001C4—21no—
1002C4—32no—
1003C4—34no—
1004C4—32no—
1005C4—62no—
1006C4—64no—
1007C4—61no—
1008C4—62no—
1009C4—184no—
1010C4—182no—
1011C4C2×D3×D1212yes—
1012C4#6430912yescomplemented
1013C3—21no—
1014C3#8582711yescharacteristic, complemented
1015C3#8667911yescharacteristic, complemented
1016C2—24no—
1017C2—62no—
1018C2—122no—
1019C2—362no—
1020C2C22×D3×D1211yescharacteristic
1021C2C2×#6430911yescharacteristic
1022C2D3×#101011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×D4C22
hypercenterC4×D4D32
hypocenterC32#3499
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×#64309C2semidirect
2. #10596026C2semidirect
3. C3×#5555C2semidirect
4. C3×C4×#237C2semidirect
5. #10595248C2semidirect
6. C2×#63918C2semidirect
7. #10594910C2semidirect
8. #10594907C2semidirect
9. #10594906C2semidirect
10. #10594383C2semidirect
11. #10594380C2semidirect
12. #10594081C2semidirect
13. #10594077C2semidirect
14. #10593968C2semidirect
15. #10593903C2semidirect
16. Dic6×D12C2semidirect
17. D3×#869C2semidirect
109. #5555D3semidirect
112. C4×#237D3semidirect
135. C3×#237D4semidirect
452. #237D12semidirect
587. C32×C42−1+4semidirect
596. C3×Dic32−1+4semidirect
905. C3×C4#1010semidirect
906. C3×C4#1010semidirect
919. Dic3#1010semidirect
920. C32#3499semidirect
1012. C4#64309semidirect
1014. C3#85827semidirect
1015. C3#86679semidirect

Maximal subgroups

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

subgroupindex
C2×#643092
#105960262
C3×#55552
C3×C4×#2372
#105952482
C2×#639182
#105949102
#105949072
#105949062
#105943832
#105943802
#105940812
#105940772
#105939682
#105939032
Dic6×D122
D3×#8692
#866793
#858273