Finite Group Databasebeta

← #11884406

Subgroups — #11884406

Order 1152.

1176 conjugacy classes of subgroups.

The subgroup lattice has 958 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596305C211yesmaximal, characteristic, complemented
2C2×C3×#949C211yesmaximal, characteristic, complemented
3C2×#63950C211yesmaximal, characteristic, complemented
4#10594889C211yesmaximal, characteristic, complemented
5C3×#5239C211yesmaximal, characteristic, complemented
6#10591612C211yesmaximal, characteristic, complemented
7#10591593C211yesmaximal, characteristic, complemented
8#10591572C211yesmaximal, characteristic, complemented
9#10591520C211yesmaximal, characteristic, complemented
10#10591475C211yesmaximal, characteristic, complemented
11#10591455C211yesmaximal, characteristic, complemented
12#10591433C211yesmaximal, characteristic, complemented
13#10591178C211yesmaximal, characteristic, complemented
14#10591162C211yesmaximal, characteristic, complemented
15#10591149C211yesmaximal, characteristic, complemented
16#83955—31nomaximal
17#80266—31nomaximal
18C2×C32×#41C2211yescharacteristic
19C2×#3832C2211yescharacteristic, complemented
20C22×C3×D12C2211yescharacteristic
21C2×#3796C2211yescharacteristic
22Q8×C3⋊Dic3C2211yescharacteristic, complemented
23#64149—21no—
24#64149C2211yescharacteristic, complemented
25#64147—21no—
26#64147C2211yescharacteristic, complemented
27#64139—21no—
28#64139C2211yescharacteristic
29C4×#638—21no—
30C4×#638C2211yescharacteristic
31C3×#949—24no—
32C2×C3×#216C2211yescharacteristic, complemented
33C2×C3×#215C2211yescharacteristic
34C2×C3×#215C2211yescharacteristic
35C2×C3×#214C2211yescharacteristic, complemented
36C2×C3×#213C2211yescharacteristic
37C2×C3×#213C2211yescharacteristic
38C3×#924C2211yescharacteristic
39C2×C3×#208C2211yescharacteristic
40#63977—21no—
41D3×#217—21no—
42#63950—24no—
43#63916C2211yescharacteristic
44#63898C2211yescharacteristic
45#63886—21no—
46#63884—21no—
47#63863C2211yescharacteristic
48C2×#3717C2211yescharacteristic, complemented
49C2×#3714C2211yescharacteristic
50C2×#3714C2211yescharacteristic
51C2×#3710C2211yescharacteristic, complemented
52C3×#835C2211yescharacteristic, complemented
53C3×#832C2211yescharacteristic, complemented
54C3×#830C2211yescharacteristic
55#63575C2211yescharacteristic, complemented
56#63572C2211yescharacteristic, complemented
57#63566C2211yescharacteristic, complemented
58#63564C2211yescharacteristic, complemented
59#63563C2211yescharacteristic
60#63563C2211yescharacteristic
61#63557C2211yescharacteristic, complemented
62#63555C2211yescharacteristic, complemented
63C2×C3×AGL(1,ℤ/8)—31no—
64#5834—31no—
65#5834—31no—
66#5834—61no—
67C2×#949D311yescharacteristic, complemented
68#5806—31no—
69C2×#919—31no—
70C2×#916—31no—
71#5630—31no—
72C3×#452—31no—
73#5239D311yescharacteristic, complemented
74#5217—31no—
75#5185—31no—
76#5176—31no—
77#5172—31no—
78#5172—31no—
79#5166—31no—
80#5164—31no—
81#5158—31no—
82#5157—31no—
83#5154—31no—
84#5150—31no—
85#5134—31no—
86#5127—31no—
87#5049—31no—
88#4817—31no—
89#4810—31no—
90#4786—31no—
91#4775—31no—
92#4732—31no—
93#4728—31no—
94C23×C3×D3—21no—
95C32×#41—22no—
96C32×#41—41no—
97C2×C32×Q8C2311yescharacteristic
98C2×C32×D4—21no—
99C2×C32×D4C2311yescharacteristic
100C22×C32×C4—21no—
101C22×C32×C4C2311yescharacteristic
102C2×#638—21no—
103C2×#638—21no—
104C2×#638—21no—
105C2×#638—21no—
106C2×#638D411yescharacteristic
107#3832—22no—
108#3832—41no—
109C2×C4⋊(C3⋊D3)—21no—
110C2×C4⋊(C3⋊D3)C2311yescharacteristic
111C2×C4×C3⋊D3—21no—
112C2×C4×C3⋊D3C2311yescharacteristic
113C2×C3×D12—22no—
114C2×C3×D12—21no—
115C2×C3×D12—41no—
116C2×C3×D12C2311yescharacteristic
117C2×C3×D12C2311yescharacteristic
118C2×C3×Dic6C2311yescharacteristic
119C2×#626—21no—
120C2×#626—21no—
121C2×D3×Dic3—21no—
122C2×D3×Dic3—21no—
123#3796—22no—
124#3796—41no—
125#3757—21no—
126#3757D411yescharacteristic
127#3752—21no—
128#3752D411yescharacteristic
129C4⋊(C3⋊Dic3)—21no—
130C4⋊(C3⋊Dic3)C2311yescharacteristic
131#3750D411yescharacteristic
132C4×C3⋊Dic3—21no—
133C4×C3⋊Dic3C2311yescharacteristic
134C3×#217—21no—
135C3×#216—22no—
136C3×#215—22no—
137C3×#215D414yescomplemented
138C3×#214—41no—
139C3×#213—22no—
140C3×#213—22no—
141C3×C4⋊Dic3C2311yescharacteristic
142C3×Dic3⋊C4—21no—
143C3×#208—22no—
144C2×C3×C3⋊C8C2311yescharacteristic
145C2×C3×C3⋊C8C2311yescharacteristic
146C2×C3×C3⋊C8C2311yescharacteristic
147C2×C3×C3⋊C8C2311yescharacteristic
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3—21no—
151(C2×D3)⋊Dic3—21no—
152#3717—22no—
153#3714—22no—
154#3714—41no—
155#3710—22no—
156#3268—91noSylow
157C2×C3×#41—21no—
158C2×C3×#41C2×D311yescharacteristic
159C2×C3×#41C2×D311yescharacteristic
160C22×C3×D4—31no—
161C2×#239—31no—
162C2×#239—31no—
163C2×#239—31no—
164C2×#239—61no—
165C2×#237—31no—
166C22×D12C2×D311yescharacteristic
167C3×AGL(1,ℤ/8)—64no—
168C2×C3×Q16—31no—
169C2×C3×SD16—31no—
170C2×C3×SD16—31no—
171C2×C3×SD16—31no—
172C2×C3×D8—31no—
173C2×C3×D8—31no—
174C2×C3×M16—31no—
175C3×C22⋊Q8—31no—
176#953—61no—
177C2×#217—61no—
178#949—24no—
179#947—31no—
180Q8×Dic3—31no—
181Q8×Dic3—31no—
182Q8×Dic3—61no—
183C2×#216C2×D311yescharacteristic, complemented
184C2×#215—31no—
185C2×#215C2×D311yescharacteristic
186C2×#215C2×D311yescharacteristic
187#940—31no—
188#940—31no—
189#940—61no—
190#940—61no—
191#940—61no—
192#940—62no—
193#939—61no—
194#938—31no—
195#938—31no—
196#938—31no—
197#938—61no—
198#938—61no—
199#938—61no—
200#938—62no—
201#936—31no—
202#935—61no—
203D4×Dic3—31no—
204C2×#214C2×D311yescharacteristic, complemented
205C2×#213—31no—
206C2×#213—31no—
207C2×#213C2×D311yescharacteristic
208C2×#213C2×D311yescharacteristic
209#930—31no—
210#930—31no—
211#930—61no—
212#930—61no—
213#930—61no—
214#930—62no—
215C4×#67—31no—
216C4×#67—31no—
217C4×#67—61no—
218C4×#67—61no—
219C4×#67—61no—
220C4×#67—62no—
221#924C2×D311yescharacteristic
222C2×#208C2×D311yescharacteristic
223#919—64no—
224#916—64no—
225C2×D24—31no—
226C2×D24—31no—
227C2×#204—31no—
228C2×D3×C8—31no—
229C2×D3×C8—31no—
230#895—31no—
231#895—61no—
232#894—61no—
233#893—31no—
234#882—61no—
235D3×C22⋊C4—61no—
236C3×#103—31no—
237C3×#102—31no—
238C3×C22⋊C8—31no—
239#835—31no—
240#835C2×D311yescharacteristic, complemented
241#832—31no—
242#832—31no—
243#832C2×D311yescharacteristic, complemented
244#830C2×D311yescharacteristic
245#821—31no—
246#821—31no—
247#821—31no—
248(C2×D3)⋊C8—31no—
249(C2×D3)⋊C8—31no—
250#818—31no—
251#816—31no—
252#815—31no—
253#815—31no—
254Dic3⋊C8—31no—
255Dic3⋊C8—31no—
256#809—31no—
257#807—31no—
258C23×C32—21no—
259C23×C32C2×D411yescharacteristic
260C22×C3⋊D3—21no—
261C22×C3⋊D3C2×D411yescharacteristic
262C22×C3×D3—21no—
263C22×C3×D3—21no—
264C22×C3×D3—42no—
265C22×C3×D3—42no—
266C22×C3×D3—81no—
267C32×Q8—21no—
268C32×Q8C2×D412yes—
269C32×D4—21no—
270C32×D4—21no—
271C32×D4—42no—
272C2×C32×C4—21no—
273C2×C32×C4—21no—
274C2×C32×C4—21no—
275C2×C32×C4—42no—
276C2×C32×C4C2×D411yescharacteristic
277C2×C32×C4C2411yescharacteristic
278#638—41no—
279#638—42no—
280#638—81no—
281#638—81no—
282#638—81no—
283C2×C3⋊Dic3—21no—
284C2×C3⋊Dic3C2×D411yescharacteristic
285C2×C3⋊Dic3C2×D411yescharacteristic
286C2×C3⋊Dic3C2×D411yescharacteristic
287C4⋊(C3⋊D3)—21no—
288C4⋊(C3⋊D3)—21no—
289C4⋊(C3⋊D3)—42no—
290C4×C3⋊D3—21no—
291C4×C3⋊D3—21no—
292C4×C3⋊D3—42no—
293C2×C3×Dic3—21no—
294C2×C3×Dic3—21no—
295C3×D12—21no—
296C3×D12—21no—
297C3×D12—21no—
298C3×D12—42no—
299C3×D12C2×D412yes—
300C3×Dic6—21no—
301C3×Dic6—21no—
302#626—42no—
303#626—81no—
304D3×Dic3—42no—
305D3×Dic3—81no—
306C3×C3⋊C8—21no—
307C3×C3⋊C8—21no—
308C3×C3⋊C8—21no—
309C3×C3⋊C8C2×D412yes—
310C2×AGL(1,ℤ/8)—31no—
311C2×#135—91no—
312#550—91no—
313#546—91no—
314#496—91no—
315#468—91no—
316#466—91no—
317#464—91no—
318#459—91no—
319#452—31no—
320#449—91no—
321#449—91no—
322#447—91no—
323#440—91no—
324#435—91no—
325C24×C3—61no—
326C23×D3—21no—
327C3×#41—22no—
328C3×#41—22no—
329C3×#41—42no—
330C3×#41—41no—
331C3×#41—41no—
332C3×#41—42no—
333C2×C3×Q8—21no—
334C2×C3×Q8—31no—
335C2×C3×Q8C22×D311yescharacteristic
336C2×C3×Q8C22×D311yescharacteristic
337C2×C3×D4—22no—
338C2×C3×D4—21no—
339C2×C3×D4—21no—
340C2×C3×D4—21no—
341C2×C3×D4—31no—
342C2×C3×D4—31no—
343C2×C3×D4—62no—
344C2×C3×D4—61no—
345C2×C3×D4—121no—
346C2×C3×D4C22×D311yescharacteristic
347C2×C3×D4C22×D311yescharacteristic
348C22×C3×C4—22no—
349C22×C3×C4—21no—
350C22×C3×C4—21no—
351C22×C3×C4—21no—
352C22×C3×C4C22×D311yescharacteristic
353C22×C3×C4C22×D311yescharacteristic
354C2×#67—31no—
355C2×#67—31no—
356C2×#67—61no—
357C2×#67—61no—
358C2×#67—61no—
359C2×#67—61no—
360C2×#67—61no—
361C2×#67—61no—
362C2×#67—61no—
363C2×#67—62no—
364C2×#67—61no—
365C2×#67—61no—
366C2×#67—62no—
367C2×#67—62no—
368C2×#67—62no—
369C2×#67—61no—
370C2×#67—61no—
371C22×Dic3—61no—
372C22×Dic3—61no—
373#239—62no—
374#239—62no—
375#239—62no—
376#239—122no—
377#239—121no—
378#239—121no—
379#239—121no—
380#239—122no—
381#237—62no—
382#237—121no—
383C2×D12—22no—
384C2×D12—21no—
385C2×D12—31no—
386C2×D12—31no—
387C2×D12—41no—
388C2×D12—61no—
389C2×D12—61no—
390C2×D12—61no—
391C2×D12—62no—
392C2×D12—61no—
393C2×D12—61no—
394C2×D12C22×D311yescharacteristic
395C2×D12C22×D311yescharacteristic
396C2×C4×D3—31no—
397C2×C4×D3—31no—
398C2×C4×D3—61no—
399C2×C4×D3—61no—
400C2×C4×D3—61no—
401C2×C4×D3—61no—
402C2×C4×D3—62no—
403C2×C4×D3—61no—
404C2×Dic6C22×D311yescharacteristic
405C3×Q16—62no—
406C3×SD16—34no—
407C3×SD16—62no—
408C3×SD16—121no—
409C3×D8—62no—
410C3×D8—62no—
411C3×M16—62no—
412C2×C3×C8—31no—
413C2×C3×C8—31no—
414C2×C3×C8—31no—
415C2×C3×C8—31no—
416C3×C4⋊C4—31no—
417C3×C4⋊C4—61no—
418C3×C22⋊C4—61no—
419#217—21no—
420#217—31no—
421#217—31no—
422#217—61no—
423#217—61no—
424#217—61no—
425#217—61no—
426#217—61no—
427#217—61no—
428#217—61no—
429#217—62no—
430#216—22no—
431#215—22no—
432#215—62no—
433#215#6714yescomplemented
434#214—41no—
435#213—22no—
436#213—22no—
437#213—62no—
438#213—121no—
439(C2×D3)⋊C4—31no—
440(C2×D3)⋊C4—31no—
441(C2×D3)⋊C4—61no—
442(C2×D3)⋊C4—61no—
443(C2×D3)⋊C4—61no—
444(C2×D3)⋊C4—61no—
445(C2×D3)⋊C4—61no—
446(C2×D3)⋊C4—62no—
447(C2×D3)⋊C4—61no—
448(C2×D3)⋊C4—61no—
449C4⋊Dic3—31no—
450C4⋊Dic3—31no—
451C4⋊Dic3—61no—
452C4⋊Dic3—61no—
453C4⋊Dic3—61no—
454C4⋊Dic3—62no—
455C4⋊Dic3C22×D311yescharacteristic
456Dic3⋊C4—21no—
457Dic3⋊C4—31no—
458Dic3⋊C4—31no—
459Dic3⋊C4—61no—
460C4×Dic3—31no—
461C4×Dic3—31no—
462C4×Dic3—61no—
463C4×Dic3—61no—
464C4×Dic3—61no—
465C4×Dic3—62no—
466#208—22no—
467C2×C3⋊C8C22×D311yescharacteristic
468C2×C3⋊C8C22×D311yescharacteristic
469C2×C3⋊C8C22×D311yescharacteristic
470C2×C3⋊C8C22×D311yescharacteristic
471D24—62no—
472D24—121no—
473#204—62no—
474D3×C8—62no—
475D3×C8—62no—
476C22×C32—21no—
477C22×C32—21no—
478C22×C32—21no—
479C22×C32—41no—
480C22×C32—41no—
481C22×C32—41no—
482C22×C32C22×D411yescharacteristic
483C2×C3⋊D3—21no—
484C2×C3⋊D3—21no—
485C2×C3⋊D3—21no—
486C2×C3⋊D3—41no—
487C2×C3⋊D3—41no—
488C2×C3⋊D3—41no—
489C2×C3×D3—22no—
490C2×C3×D3—41no—
491C2×C3×D3—41no—
492C2×C3×D3—41no—
493C2×C3×D3—41no—
494C2×C3×D3—41no—
495C2×C3×D3—84no—
496C32×C4—22no—
497C32×C4—21no—
498C32×C4C22×D411yescharacteristic
499C32×C4H(5,𝔽2)11yescharacteristic
500C3⋊Dic3—21no—
501C3⋊Dic3—21no—
502C3⋊Dic3—21no—
503C3⋊Dic3—41no—
504C3×Dic3—41no—
505C3×Dic3—41no—
506C2×#41—91no—
507C2×#41—91no—
508C2×#41D3211yescharacteristic
509C22×D4—31no—
510AGL(1,ℤ/8)—64no—
511#135—184no—
512C2×Q16—31no—
513C2×SD16—31no—
514C2×SD16—31no—
515C2×SD16—31no—
516C2×SD16—91no—
517C2×D8—31no—
518C2×D8—31no—
519C2×D8—91no—
520C2×D8—91no—
521C2×M16—31no—
522C22×C8—91no—
523#127—91no—
524#127—181no—
525#124—91no—
526#123—181no—
527C22⋊Q8—31no—
528#121—91no—
529#121—91no—
530#121—91no—
531#121—181no—
532#121—181no—
533#121—181no—
534#120—181no—
535C4×Q8—91no—
536C4×D4—91no—
537C4×D4—91no—
538C4×D4—181no—
539C2×C22⋊C4—181no—
540#107—91no—
541C4⋊C8—91no—
542#103—31no—
543#103—91no—
544#102—31no—
545#102—91no—
546#102—91no—
547#102—91no—
548C22⋊C8—31no—
549C22⋊C8—91no—
550#97—91no—
551C23×C3—22no—
552C23×C3—21no—
553C23×C3—21no—
554C23×C3—21no—
555C23×C3—61no—
556C23×C3—61no—
557C23×C3—122no—
558C23×C3—122no—
559C23×C3—241no—
560C23×C3D3×D411yescharacteristic
561C23×C3D3×D411yescharacteristic
562C22×D3—21no—
563C22×D3—21no—
564C22×D3—31no—
565C22×D3—31no—
566C22×D3—42no—
567C22×D3—42no—
568C22×D3—61no—
569C22×D3—62no—
570C22×D3—61no—
571C22×D3—61no—
572C22×D3—81no—
573C3×Q8—22no—
574C3×Q8—21no—
575C3×Q8—21no—
576C3×Q8—22no—
577C3×Q8—61no—
578C3×Q8—61no—
579C3×Q8D3×D412yes—
580C3×Q8C2×#6712yes—
581C3×D4—21no—
582C3×D4—21no—
583C3×D4—21no—
584C3×D4—21no—
585C3×D4—32no—
586C3×D4—41no—
587C3×D4—41no—
588C3×D4—42no—
589C3×D4—42no—
590C3×D4—44no—
591C3×D4—61no—
592C3×D4—61no—
593C3×D4—61no—
594C3×D4—122no—
595C2×C3×C4—22no—
596C2×C3×C4—21no—
597C2×C3×C4—21no—
598C2×C3×C4—21no—
599C2×C3×C4—21no—
600C2×C3×C4—21no—
601C2×C3×C4—21no—
602C2×C3×C4—21no—
603C2×C3×C4—21no—
604C2×C3×C4—41no—
605C2×C3×C4—41no—
606C2×C3×C4—42no—
607C2×C3×C4—42no—
608C2×C3×C4—44no—
609C2×C3×C4—61no—
610C2×C3×C4—61no—
611C2×C3×C4D3×D411yescharacteristic
612C2×C3×C4D3×D411yescharacteristic
613C2×C3×C4C23×D311yescharacteristic
614C2×C3×C4C23×D311yescharacteristic
615#67—122no—
616#67—121no—
617#67—121no—
618#67—122no—
619#67—124no—
620#67—122no—
621#67—122no—
622#67—241no—
623#67—241no—
624#67—241no—
625#67—241no—
626#67—241no—
627#67—241no—
628#67—241no—
629#67—242no—
630#67—242no—
631#67—242no—
632C2×Dic3—21no—
633C2×Dic3—21no—
634C2×Dic3—31no—
635C2×Dic3—31no—
636C2×Dic3—31no—
637C2×Dic3—31no—
638C2×Dic3—31no—
639C2×Dic3—31no—
640C2×Dic3—61no—
641C2×Dic3—61no—
642C2×Dic3—61no—
643C2×Dic3—62no—
644C2×Dic3—61no—
645C2×Dic3—61no—
646C2×Dic3—122no—
647C2×Dic3—241no—
648D12—21no—
649D12—21no—
650D12—21no—
651D12—42no—
652D12—61no—
653D12—61no—
654D12—61no—
655D12—61no—
656D12—121no—
657D12—121no—
658D12—122no—
659D12—122no—
660D12—124no—
661D12—122no—
662D12—241no—
663D12C2×#6712yes—
664C4×D3—61no—
665C4×D3—61no—
666C4×D3—61no—
667C4×D3—61no—
668C4×D3—121no—
669C4×D3—121no—
670C4×D3—122no—
671C4×D3—122no—
672C4×D3—122no—
673C4×D3—124no—
674C4×D3—241no—
675Dic6—21no—
676Dic6—21no—
677C3×C8—32no—
678C3×C8—61no—
679C3×C8—61no—
680C3×C8—61no—
681C3⋊C8—21no—
682C3⋊C8—21no—
683C3⋊C8—21no—
684C3⋊C8C2×#6712yes—
685C2×C32—41no—
686C2×C32—81no—
687C2×C32D4211yescharacteristic
688C2×C32#57511yescharacteristic
689C2×C32#57611yescharacteristic
690C3⋊D3—41no—
691C3⋊D3—81no—
692C3×D3—42no—
693C3×D3—81no—
694C24—61no—
695#41—22no—
696#41—41no—
697#41—182no—
698#41—182no—
699#41—361no—
700#41—361no—
701C2×Q8—31no—
702C2×Q8C2×D3211yescharacteristic
703C2×D4—21no—
704C2×D4—31no—
705C2×D4—31no—
706C2×D4—62no—
707C2×D4—61no—
708C2×D4—91no—
709C2×D4—91no—
710C2×D4—121no—
711C2×D4—181no—
712C2×D4—181no—
713C2×D4—181no—
714C2×D4—181no—
715C2×D4—181no—
716C2×D4—181no—
717C2×D4—181no—
718C2×D4C2×D3211yescharacteristic
719C22×C4—21no—
720C22×C4—91no—
721C22×C4—181no—
722C22×C4—181no—
723C22×C4—181no—
724C22×C4C2×D3211yescharacteristic
725Q16—62no—
726SD16—34no—
727SD16—62no—
728SD16—121no—
729SD16—182no—
730D8—62no—
731D8—62no—
732D8—182no—
733D8—361no—
734M16—62no—
735C2×C8—31no—
736C2×C8—31no—
737C2×C8—31no—
738C2×C8—31no—
739C2×C8—182no—
740C4⋊C4—31no—
741C4⋊C4—61no—
742C4⋊C4—91no—
743C4⋊C4—91no—
744C4⋊C4—181no—
745C22⋊C4—61no—
746C22⋊C4—91no—
747C22⋊C4—91no—
748C22⋊C4—181no—
749C22⋊C4—181no—
750C22⋊C4—181no—
751C22⋊C4—181no—
752C22⋊C4—181no—
753C22⋊C4—181no—
754C42—91no—
755C42—181no—
756C22×C3—21no—
757C22×C3—21no—
758C22×C3—21no—
759C22×C3—21no—
760C22×C3—21no—
761C22×C3—21no—
762C22×C3—21no—
763C22×C3—41no—
764C22×C3—41no—
765C22×C3—41no—
766C22×C3—42no—
767C22×C3—42no—
768C22×C3—42no—
769C22×C3—41no—
770C22×C3—41no—
771C22×C3—41no—
772C22×C3—41no—
773C22×C3—41no—
774C22×C3—41no—
775C22×C3—62no—
776C22×C3—121no—
777C22×C3—121no—
778C22×C3—121no—
779C22×C3—121no—
780C22×C3—121no—
781C22×C3—244no—
782C22×C3C2×D3×D411yescharacteristic
783C22×C3C2×D3×D411yescharacteristic
784C2×D3—22no—
785C2×D3—41no—
786C2×D3—41no—
787C2×D3—41no—
788C2×D3—41no—
789C2×D3—41no—
790C2×D3—61no—
791C2×D3—61no—
792C2×D3—61no—
793C2×D3—61no—
794C2×D3—61no—
795C2×D3—61no—
796C2×D3—84no—
797C2×D3—121no—
798C2×D3—121no—
799C2×D3—121no—
800C2×D3—122no—
801C2×D3—122no—
802C2×D3—122no—
803C2×D3—121no—
804C2×D3—121no—
805C2×D3—121no—
806C2×D3—121no—
807C2×D3—121no—
808C2×D3—121no—
809C3×C4—24no—
810C3×C4—22no—
811C3×C4—21no—
812C3×C4—22no—
813C3×C4—21no—
814C3×C4—21no—
815C3×C4—21no—
816C3×C4—41no—
817C3×C4—121no—
818C3×C4—121no—
819C3×C4C2×D3×D411yescharacteristic
820C3×C4#100411yescharacteristic
821C3×C4#100411yescharacteristic
822C3×C4C22×#6711yescharacteristic
823Dic3—41no—
824Dic3—41no—
825Dic3—62no—
826Dic3—61no—
827Dic3—61no—
828Dic3—61no—
829Dic3—61no—
830Dic3—61no—
831Dic3—61no—
832Dic3—121no—
833Dic3—121no—
834Dic3—122no—
835Dic3—121no—
836Dic3—121no—
837C32#326811yescharacteristic, complemented, Sylow
838C23—21no—
839C23—61no—
840C23—61no—
841C23—91no—
842C23—122no—
843C23—122no—
844C23—181no—
845C23—241no—
846C23#381111yescharacteristic
847Q8—21no—
848Q8—61no—
849Q8—61no—
850Q8D3×#6712yes—
851D4—21no—
852D4—21no—
853D4—32no—
854D4—42no—
855D4—61no—
856D4—61no—
857D4—61no—
858D4—122no—
859D4—181no—
860D4—181no—
861D4—362no—
862D4—362no—
863D4—361no—
864D4—362no—
865D4—721no—
866D4—721no—
867D4—721no—
868D4—721no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—42no—
873C2×C4—61no—
874C2×C4—61no—
875C2×C4—91no—
876C2×C4—91no—
877C2×C4—91no—
878C2×C4—181no—
879C2×C4—181no—
880C2×C4—181no—
881C2×C4—362no—
882C2×C4—362no—
883C2×C4—721no—
884C2×C4#381111yescharacteristic
885C2×C4C22×D3211yescharacteristic
886C8—32no—
887C8—61no—
888C8—61no—
889C8—61no—
890C2×C3—21no—
891C2×C3—21no—
892C2×C3—21no—
893C2×C3—41no—
894C2×C3—41no—
895C2×C3—81no—
896C2×C3—82no—
897C2×C3—81no—
898C2×C3—81no—
899C2×C3—122no—
900C2×C3—241no—
901C2×C3#559011yescharacteristic
902C2×C3#576911yescharacteristic
903C2×C3#577311yescharacteristic
904C2×C3#577411yescharacteristic
905C2×C3#577711yescharacteristic
906C2×C3D4×#6711yescharacteristic
907D3—42no—
908D3—81no—
909D3—121no—
910D3—121no—
911D3—241no—
912D3—242no—
913D3—241no—
914D3—241no—
915C22—21no—
916C22—21no—
917C22—21no—
918C22—41no—
919C22—41no—
920C22—41no—
921C22—62no—
922C22—121no—
923C22—121no—
924C22—121no—
925C22—121no—
926C22—121no—
927C22—181no—
928C22—181no—
929C22—181no—
930C22—244no—
931C22—361no—
932C22—361no—
933C22—361no—
934C22C2×#381111yescharacteristic
935C4—21no—
936C4—22no—
937C4—121no—
938C4—121no—
939C4—181no—
940C4—181no—
941C4—181no—
942C4—361no—
943C4C2×D3×#6711yescharacteristic
944C4#6433011yescharacteristic
945C3—21no—
946C3#8026611yescharacteristic, complemented
947C3#8395511yescharacteristic, complemented
948C2—41no—
949C2—81no—
950C2—122no—
951C2—241no—
952C2—361no—
953C2—721no—
954C2#1059546111yescharacteristic
955C2#1059547111yescharacteristic
956C2#1059552611yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
hypercenterC2×#41D32
hypocenterC32#3268
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #10596305C2semidirect
2. C2×C3×#949C2semidirect
3. C2×#63950C2semidirect
4. #10594889C2semidirect
5. C3×#5239C2semidirect
6. #10591612C2semidirect
7. #10591593C2semidirect
8. #10591572C2semidirect
9. #10591520C2semidirect
10. #10591475C2semidirect
11. #10591455C2semidirect
12. #10591433C2semidirect
13. #10591178C2semidirect
14. #10591162C2semidirect
15. #10591149C2semidirect
19. C2×#3832C22semidirect
22. Q8×C3⋊Dic3C22semidirect
24. #64149C22semidirect
26. #64147C22semidirect
32. C2×C3×#216C22semidirect
35. C2×C3×#214C22semidirect
48. C2×#3717C22semidirect
51. C2×#3710C22semidirect
52. C3×#835C22semidirect
53. C3×#832C22semidirect
55. #63575C22semidirect
56. #63572C22semidirect
57. #63566C22semidirect
58. #63564C22semidirect
61. #63557C22semidirect
62. #63555C22semidirect
67. C2×#949D3semidirect
73. #5239D3semidirect
137. C3×#215D4semidirect
183. C2×#216C2×D3semidirect
204. C2×#214C2×D3semidirect
240. #835C2×D3semidirect
243. #832C2×D3semidirect
433. #215#67semidirect
837. C32#3268semidirect
946. C3#80266semidirect
947. C3#83955semidirect

Maximal subgroups

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

subgroupindex
#105963052
C2×C3×#9492
C2×#639502
#105948892
C3×#52392
#105916122
#105915932
#105915722
#105915202
#105914752
#105914552
#105914332
#105911782
#105911622
#105911492
#839553
#802663