Finite Group Databasebeta

← #10944196

Subgroups — #10944196

Order 768.

1468 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#1009C211yesmaximal, characteristic, complemented
2#82527C211yesmaximal, characteristic, complemented
3#79058C211yesmaximal, characteristic, complemented
4C2×#4825C211yesmaximal, characteristic, complemented
5C2×#4822C211yesmaximal, characteristic
6#73801C211yesmaximal, characteristic, complemented
7C3×#1806C211yesmaximal, characteristic, complemented
8#70527C211yesmaximal, characteristic, complemented
9#70366C211yesmaximal, characteristic, complemented
10#70365C211yesmaximal, characteristic, complemented
11#69494C211yesmaximal, characteristic, complemented
12#68776C211yesmaximal, characteristic, complemented
13#68775C211yesmaximal, characteristic, complemented
14#68760C211yesmaximal, characteristic, complemented
15#68759C211yesmaximal, characteristic, complemented
16#32924—31nomaximal, Sylow
17C2×#1009C2211yescharacteristic
18C3×C4×#41C2211yescharacteristic
19#5827C2211yescharacteristic
20C2×#951C2211yescharacteristic
21C2×#949C2211yescharacteristic
22C2×#909C2211yescharacteristic
23C2×#908C2211yescharacteristic
24#5574—21no—
25C4×#239—21no—
26#5545—21no—
27#5545—22no—
28C4×D3×D4—22no—
29C4×D3×D4—21no—
30#5523—21no—
31#5523C2211yescharacteristic
32#5521—21no—
33#5521C2211yescharacteristic
34C2×#875C2211yescharacteristic
35C2×#875C2211yescharacteristic, complemented
36C2×#874C2211yescharacteristic
37C4×#235—21no—
38C4×#235C2211yescharacteristic
39C2×C4×D12—21no—
40C2×C4×D12C2211yescharacteristic
41C3×#423C2211yescharacteristic, complemented
42C2×C3×#104C2211yescharacteristic
43C2×C3×#104C2211yescharacteristic
44C3×C4×C4⋊C4C2211yescharacteristic, complemented
45#5131C2211yescharacteristic, complemented
46C2×#823C2211yescharacteristic
47C2×#823C2211yescharacteristic
48#5120C2211yescharacteristic, complemented
49#5028—21no—
50#5028—21no—
51#5016—21no—
52#5016—21no—
53#5004C2211yescharacteristic, complemented
54#5001C2211yescharacteristic, complemented
55#4991—22no—
56#4939C2211yescharacteristic, complemented
57#4929C2211yescharacteristic, complemented
58C2×#805C2211yescharacteristic
59C2×#805C2211yescharacteristic
60#4924C2211yescharacteristic, complemented
61#4845—21no—
62#4845—21no—
63#4844—21no—
64#4844—21no—
65#4825—24no—
66#4822—24no—
67#4665—22no—
68C3×#339C2211yescharacteristic, complemented
69C3×#339C2211yescharacteristic, complemented
70#4554C2211yescharacteristic, complemented
71#4554C2211yescharacteristic, complemented
72#4523C2211yescharacteristic, complemented
73#4523C2211yescharacteristic, complemented
74C4×H(5,𝔽2)—31no—
75#3040—31no—
76#3040—31no—
77C2×#455—31no—
78C2×#453—31no—
79#2544—31no—
80#1887—31no—
81#1885—31no—
82#1883—31no—
83#1883—31no—
84#1882—31no—
85#1882—31no—
86#1806—31no—
87#1806D311yescharacteristic, complemented
88#1800—31no—
89C2×C3×#41C2311yescharacteristic
90#1009—22no—
91#1009—22no—
92#1009—22no—
93#1009D414yes—
94C2×#239—21no—
95C2×D3×D4—22no—
96C2×D3×D4—21no—
97C2×#235—21no—
98C2×#235C2311yescharacteristic
99C22×D12—21no—
100C22×D12—22no—
101C22×D12C2311yescharacteristic
102C22×D12C2311yescharacteristic
103C22×C4×D3—22no—
104C22×C4×D3D412yes—
105C22×Dic6C2311yescharacteristic
106C2×C3×M16C2311yescharacteristic
107C2×C3×M16C2311yescharacteristic
108C3×C4×Q8D411yescharacteristic, complemented
109C3×C4×Q8D411yescharacteristic, complemented
110C3×C4×D4—21no—
111C3×C4×D4—21no—
112C3×C4×D4D411yescharacteristic, complemented
113C3×C4×D4D411yescharacteristic, complemented
114C3×#117—21no—
115C3×#117C2311yescharacteristic
116C2×C3×C4⋊C4—21no—
117C2×C3×C42—21no—
118C2×C3×C42C2311yescharacteristic
119C2×C3×C42C2311yescharacteristic
120C2×C3×C42C2311yescharacteristic
121#951—22no—
122#951—22no—
123#949—22no—
124#949—22no—
125Q8×Dic3—21no—
126C2×#216—21no—
127C2×#215—21no—
128D4×Dic3—21no—
129D4×Dic3—22no—
130C2×#214—21no—
131C2×#213—21no—
132C4×#67—22no—
133C4×#67—22no—
134C4×#67—21no—
135C4×#67—21no—
136C2×(C2×D3)⋊C4—22no—
137C2×(C2×D3)⋊C4—22no—
138C2×(C2×D3)⋊C4—21no—
139C2×(C2×D3)⋊C4—21no—
140C2×(C2×D3)⋊C4—22no—
141C2×(C2×D3)⋊C4D412yes—
142#926—21no—
143#926C2311yescharacteristic
144C2×C4⋊Dic3—21no—
145C2×C4⋊Dic3C2311yescharacteristic
146C2×#208C2311yescharacteristic
147C2×#208C2311yescharacteristic
148#909—22no—
149#909—22no—
150#908—22no—
151#908—22no—
152C2×Dic12—21no—
153C2×D24—21no—
154C2×#204—21no—
155C2×#204—21no—
156#893—22no—
157#893—22no—
158#893—21no—
159#893—21no—
160#892—22no—
161#892—21no—
162D3×C4⋊C4—22no—
163D3×C4⋊C4—21no—
164#67⋊C4—22no—
165#67⋊C4—22no—
166#67⋊C4—22no—
167D3×C22⋊C4—22no—
168D3×C22⋊C4—22no—
169D3×C22⋊C4—22no—
170#875—22no—
171#875—22no—
172#875—21no—
173#875—21no—
174#875—21no—
175#875—21no—
176#874—22no—
177#874—22no—
178C4×D12—22no—
179C4×D12—22no—
180C4×D12—21no—
181C4×D12—21no—
182C4×D12—21no—
183C4×D12—21no—
184C4×D12—21no—
185C4×D12—21no—
186C4×D12—21no—
187C4×D12D411yescharacteristic, complemented
188C4×D12D411yescharacteristic, complemented
189#872—22no—
190#872—21no—
191C42×D3—22no—
192C42×D3—21no—
193C4×Dic6—21no—
194C4×Dic6D411yescharacteristic, complemented
195C4×Dic6D411yescharacteristic, complemented
196C3×C4⋊C8—21no—
197C3×C4⋊C8—21no—
198C3×#104—22no—
199C3×#104—22no—
200C3×#95—21no—
201C3⋊#95—22no—
202#823—22no—
203#823—22no—
204#821—21no—
205#821—21no—
206#816—21no—
207#816—21no—
208#810—21no—
209#810—21no—
210#809—21no—
211#809—21no—
212#805—22no—
213#805—22no—
214C4⋊(C3⋊C8)—21no—
215C4⋊(C3⋊C8)—21no—
216C2×H(5,𝔽2)—31no—
217C2×#137—31no—
218C2×#137—31no—
219C2×AGL(1,ℤ/8)—31no—
220C2×AGL(1,ℤ/8)—31no—
221C2×#127—31no—
222C2×#124—31no—
223C2×#124—31no—
224#520—31no—
225#520—31no—
226#520—61no—
227#520—61no—
228#518—31no—
229#518—62no—
230#518—61no—
231#518—61no—
232C4×#41—31no—
233C4×#41—61no—
234C4×#41—61no—
235C4×#41C2×D311yescharacteristic
236C2×C4×D4—31no—
237C2×C4×D4—61no—
238C2×C4×D4—62no—
239C2×C4×D4—61no—
240#464—61no—
241#464—61no—
242#464—61no—
243#464—61no—
244#463—61no—
245#463—61no—
246#463—61no—
247#463—61no—
248#455—64no—
249#453—64no—
250#423—31no—
251#423C2×D311yescharacteristic, complemented
252C2×#104—31no—
253C2×#104—31no—
254C2×#104C2×D311yescharacteristic
255C2×#104C2×D311yescharacteristic
256#419—31no—
257#419—31no—
258#418—31no—
259#418—31no—
260C2×#100—31no—
261C2×#100—31no—
262#394—62no—
263#391—31no—
264#390—31no—
265#386—62no—
266C4×C4⋊C4C2×D311yescharacteristic, complemented
267#343—31no—
268#343—31no—
269#339—31no—
270#339—31no—
271#339C2×D311yescharacteristic, complemented
272#339C2×D311yescharacteristic, complemented
273C23×D3—22no—
274C23×D3—21no—
275C23×D3C2×D412yes—
276C3×#41—21no—
277C3×#41—21no—
278C3×#41C2×D412yes—
279C3×#41#4112yes—
280C2×C3×Q8C2×D411yescharacteristic
281C2×C3×D4—21no—
282C2×C3×D4C2×D411yescharacteristic
283C22×C3×C4—21no—
284C22×C3×C4—21no—
285C22×C3×C4—21no—
286C22×C3×C4—21no—
287C22×C3×C4—21no—
288C22×C3×C4C2×D411yescharacteristic
289C22×C3×C4C2×D411yescharacteristic
290C22×C3×C4C2411yescharacteristic
291C2×#67—22no—
292C2×#67—21no—
293C22×Dic3—22no—
294C22×Dic3—21no—
295C22×Dic3C2×D412yes—
296#239—24no—
297#239—24no—
298D3×D4—28no—
299D3×D4—24no—
300D3×D4—28no—
301D3×D4—24no—
302#235—24no—
303#235—21no—
304#235—21no—
305#235—24no—
306#235C2×D412yes—
307#235#4112yes—
308C2×D12—22no—
309C2×D12—24no—
310C2×D12—21no—
311C2×D12—21no—
312C2×D12—21no—
313C2×D12—21no—
314C2×D12—24no—
315C2×D12—21no—
316C2×D12—21no—
317C2×D12—21no—
318C2×D12—21no—
319C2×D12—21no—
320C2×D12—21no—
321C2×D12—44no—
322C2×D12—44no—
323C2×D12—82no—
324C2×D12C2×D412yes—
325C2×D12C2×D411yescharacteristic
326C2×D12#4112yes—
327C2×C4×D3—22no—
328C2×C4×D3—21no—
329C2×C4×D3—22no—
330C2×C4×D3—21no—
331C2×C4×D3—22no—
332C2×C4×D3—22no—
333C2×C4×D3—22no—
334C2×C4×D3—21no—
335C2×C4×D3—22no—
336C2×C4×D3—84no—
337C2×C4×D3—82no—
338C2×Dic6—21no—
339C2×Dic6—21no—
340C2×Dic6—21no—
341C2×Dic6—21no—
342C2×Dic6—21no—
343C2×Dic6—21no—
344C2×Dic6C2×D411yescharacteristic
345C3×M16—21no—
346C3×M16—21no—
347C3×M16—21no—
348C3×M16—21no—
349C2×C3×C8—21no—
350C2×C3×C8—21no—
351C3×C4⋊C4—21no—
352C3×C4⋊C4—21no—
353C3×C4⋊C4—42no—
354C3×C4⋊C4C2×D411yescharacteristic
355C3×C4⋊C4C2×D411yescharacteristic
356C3×C22⋊C4—21no—
357C3×C22⋊C4—21no—
358C3×C22⋊C4—21no—
359C3×C42—21no—
360C3×C42—21no—
361C3×C42—21no—
362C3×C42—21no—
363C3×C42—21no—
364C3×C42—21no—
365C3×C42—21no—
366C3×C42C2×D411yescharacteristic
367C3×C42C2×D411yescharacteristic
368C3×C42C2×D411yescharacteristic
369C3×C42C2×D411yescharacteristic
370#217—22no—
371#217—21no—
372#216—42no—
373#215—42no—
374#214—42no—
375#213—42no—
376(C2×D3)⋊C4—22no—
377(C2×D3)⋊C4—22no—
378(C2×D3)⋊C4—22no—
379(C2×D3)⋊C4—22no—
380(C2×D3)⋊C4—21no—
381(C2×D3)⋊C4—21no—
382(C2×D3)⋊C4—22no—
383(C2×D3)⋊C4—44no—
384(C2×D3)⋊C4—41no—
385(C2×D3)⋊C4—41no—
386(C2×D3)⋊C4—41no—
387(C2×D3)⋊C4—41no—
388(C2×D3)⋊C4—82no—
389C4⋊Dic3—22no—
390C4⋊Dic3—21no—
391C4⋊Dic3—21no—
392C4⋊Dic3C2×D411yescharacteristic
393C4⋊Dic3C2×D411yescharacteristic
394Dic3⋊C4—22no—
395Dic3⋊C4—21no—
396Dic3⋊C4—21no—
397C4×Dic3—22no—
398C4×Dic3—22no—
399C4×Dic3—21no—
400C4×Dic3—21no—
401C4×Dic3—21no—
402#208—21no—
403#208—21no—
404#208—21no—
405#208—21no—
406C2×C3⋊C8—21no—
407C2×C3⋊C8—21no—
408Dic12—42no—
409D24—42no—
410#204—42no—
411#204—42no—
412H(5,𝔽2)—34no—
413H(5,𝔽2)—62no—
414H(5,𝔽2)—62no—
415H(5,𝔽2)—62no—
416C2×#41—31no—
417C2×#41—61no—
418C2×#41—61no—
419C2×#41C22×D311yescharacteristic
420C22×Q8—31no—
421C22×D4—31no—
422C22×D4—31no—
423C22×D4—61no—
424C22×D4—62no—
425C22×D4—62no—
426C22×D4—61no—
427C23×C4—32no—
428C23×C4—62no—
429#137—62no—
430#137—62no—
431#137—62no—
432#137—62no—
433AGL(1,ℤ/8)—62no—
434AGL(1,ℤ/8)—62no—
435AGL(1,ℤ/8)—62no—
436AGL(1,ℤ/8)—62no—
437C2×Q16—61no—
438C2×Q16—61no—
439C2×SD16—61no—
440C2×SD16—61no—
441C2×SD16—61no—
442C2×SD16—61no—
443C2×D8—61no—
444C2×D8—61no—
445C2×M16—31no—
446C2×M16—31no—
447C2×M16C22×D311yescharacteristic
448C2×M16C22×D311yescharacteristic
449#127—62no—
450#127—62no—
451#124—62no—
452#124—62no—
453#124—61no—
454#124—61no—
455#124—61no—
456#124—61no—
457C4×Q8—31no—
458C4×Q8—31no—
459C4×Q8—61no—
460C4×Q8—61no—
461C4×Q8D1211yescharacteristic, complemented
462C4×Q8D1211yescharacteristic, complemented
463C4×D4—21no—
464C4×D4—21no—
465C4×D4—31no—
466C4×D4—31no—
467C4×D4—61no—
468C4×D4—61no—
469C4×D4—61no—
470C4×D4—62no—
471C4×D4—62no—
472C4×D4—62no—
473C4×D4—62no—
474C4×D4—62no—
475C4×D4—62no—
476C4×D4—62no—
477C4×D4—62no—
478C4×D4—62no—
479C4×D4—62no—
480C4×D4—61no—
481C4×D4—61no—
482C4×D4—61no—
483C4×D4—61no—
484C4×D4—61no—
485C4×D4—61no—
486C4×D4—61no—
487C4×D4—61no—
488C4×D4—61no—
489C4×D4D1211yescharacteristic, complemented
490C4×D4D1211yescharacteristic, complemented
491#117—21no—
492#117—31no—
493#117—62no—
494#117—62no—
495#117—61no—
496#117—61no—
497#117—61no—
498#117C22×D311yescharacteristic
499C2×C4⋊C4—21no—
500C2×C4⋊C4—31no—
501C2×C4⋊C4—62no—
502C2×C4⋊C4—61no—
503C2×C4⋊C4—61no—
504C2×C22⋊C4—32no—
505C2×C22⋊C4—62no—
506C2×C22⋊C4—62no—
507C2×C22⋊C4—62no—
508C2×C22⋊C4—62no—
509C2×C22⋊C4—62no—
510C2×C22⋊C4—61no—
511C2×C22⋊C4—61no—
512C2×C22⋊C4—62no—
513C2×C42—21no—
514C2×C42—62no—
515C2×C42—61no—
516C2×C42C22×D311yescharacteristic
517C2×C42C22×D311yescharacteristic
518C2×C42C22×D311yescharacteristic
519C4⋊C8—21no—
520C4⋊C8—21no—
521C4⋊C8—61no—
522C4⋊C8—61no—
523#104—22no—
524#104—22no—
525#104—62no—
526#104—62no—
527#103—61no—
528#103—61no—
529#103—61no—
530#103—61no—
531#102—61no—
532#102—61no—
533#102—61no—
534#102—61no—
535#100—62no—
536#100—62no—
537#95—21no—
538#95—62no—
539C23×C3—21no—
540C23×C3C22×D411yescharacteristic
541C22×D3—22no—
542C22×D3—21no—
543C22×D3—28no—
544C22×D3—22no—
545C22×D3—42no—
546C22×D3—42no—
547C22×D3—42no—
548C22×D3—42no—
549C22×D3—41no—
550C22×D3—41no—
551C22×D3—41no—
552C22×D3—82no—
553C22×D3—82no—
554C22×D3#12114yes—
555C3×Q8—21no—
556C3×Q8#12112yes—
557C3×D4—22no—
558C3×D4—22no—
559C3×D4—21no—
560C3×D4#12112yes—
561C2×C3×C4—21no—
562C2×C3×C4—22no—
563C2×C3×C4—22no—
564C2×C3×C4—22no—
565C2×C3×C4—21no—
566C2×C3×C4—21no—
567C2×C3×C4—41no—
568C2×C3×C4—41no—
569C2×C3×C4—42no—
570C2×C3×C4—41no—
571C2×C3×C4—41no—
572C2×C3×C4—41no—
573C2×C3×C4—41no—
574C2×C3×C4—41no—
575C2×C3×C4—81no—
576C2×C3×C4#12011yescharacteristic
577C2×C3×C4#12011yescharacteristic
578C2×C3×C4#12011yescharacteristic
579C2×C3×C4#12011yescharacteristic
580C2×C3×C4C22×D411yescharacteristic
581C2×C3×C4C22×D411yescharacteristic
582C2×C3×C4C22×D411yescharacteristic
583C2×C3×C4C2×#4111yescharacteristic
584C2×C3×C4C2×#4111yescharacteristic
585C2×C3×C4C2×#4111yescharacteristic
586#67—28no—
587#67—22no—
588#67—22no—
589C2×Dic3—21no—
590C2×Dic3—21no—
591C2×Dic3—22no—
592C2×Dic3—21no—
593C2×Dic3—42no—
594C2×Dic3—41no—
595C2×Dic3—41no—
596C2×Dic3—41no—
597C2×Dic3—82no—
598D12—28no—
599D12—22no—
600D12—22no—
601D12—21no—
602D12—22no—
603D12—22no—
604D12—41no—
605D12—41no—
606D12—41no—
607D12—41no—
608D12—88no—
609D12#12112yes—
610C4×D3—28no—
611C4×D3—22no—
612C4×D3—22no—
613C4×D3—44no—
614C4×D3—42no—
615C4×D3—81no—
616C4×D3—82no—
617C4×D3—82no—
618C4×D3—82no—
619C4×D3—82no—
620Dic6—21no—
621Dic6—41no—
622Dic6—41no—
623Dic6—41no—
624Dic6—41no—
625Dic6#12112yes—
626C3×C8—41no—
627C3×C8—41no—
628C3⋊C8—41no—
629C3⋊C8—41no—
630C24—32no—
631C24—62no—
632C24—61no—
633#41—21no—
634#41—21no—
635#41—32no—
636#41—32no—
637#41—64no—
638#41—64no—
639#41—64no—
640#41—64no—
641#41—61no—
642#41—61no—
643#41D3×D412yes—
644#41#23912yes—
645C2×Q8—31no—
646C2×Q8—61no—
647C2×Q8—61no—
648C2×Q8—61no—
649C2×Q8—61no—
650C2×Q8—61no—
651C2×Q8—61no—
652C2×Q8C2×D1211yescharacteristic
653C2×D4—21no—
654C2×D4—31no—
655C2×D4—32no—
656C2×D4—32no—
657C2×D4—64no—
658C2×D4—62no—
659C2×D4—64no—
660C2×D4—68no—
661C2×D4—68no—
662C2×D4—64no—
663C2×D4—62no—
664C2×D4—61no—
665C2×D4—64no—
666C2×D4—61no—
667C2×D4—61no—
668C2×D4—61no—
669C2×D4—61no—
670C2×D4—61no—
671C2×D4—61no—
672C2×D4—61no—
673C2×D4—61no—
674C2×D4—61no—
675C2×D4—61no—
676C2×D4—124no—
677C2×D4—124no—
678C2×D4—242no—
679C2×D4C2×D1211yescharacteristic
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—32no—
686C22×C4—62no—
687C22×C4—62no—
688C22×C4—62no—
689C22×C4—62no—
690C22×C4—61no—
691C22×C4—62no—
692C22×C4—61no—
693C22×C4—62no—
694C22×C4—61no—
695C22×C4—62no—
696C22×C4—61no—
697C22×C4—242no—
698C22×C4—244no—
699C22×C4D3×D411yescharacteristic
700C22×C4D3×D411yescharacteristic
701C22×C4C23×D311yescharacteristic
702Q16—122no—
703Q16—122no—
704SD16—122no—
705SD16—122no—
706SD16—122no—
707SD16—122no—
708D8—122no—
709D8—122no—
710M16—21no—
711M16—21no—
712M16—21no—
713M16—21no—
714M16—61no—
715M16—61no—
716M16—61no—
717M16—61no—
718C2×C8—21no—
719C2×C8—21no—
720C2×C8—61no—
721C2×C8—61no—
722C4⋊C4—21no—
723C4⋊C4—21no—
724C4⋊C4—31no—
725C4⋊C4—31no—
726C4⋊C4—42no—
727C4⋊C4—62no—
728C4⋊C4—62no—
729C4⋊C4—61no—
730C4⋊C4—61no—
731C4⋊C4—61no—
732C4⋊C4—61no—
733C4⋊C4C2×D1211yescharacteristic
734C4⋊C4C2×D1211yescharacteristic
735C22⋊C4—21no—
736C22⋊C4—21no—
737C22⋊C4—21no—
738C22⋊C4—62no—
739C22⋊C4—62no—
740C22⋊C4—62no—
741C22⋊C4—62no—
742C22⋊C4—61no—
743C22⋊C4—62no—
744C22⋊C4—62no—
745C22⋊C4—61no—
746C22⋊C4—61no—
747C22⋊C4—124no—
748C22⋊C4—121no—
749C22⋊C4—121no—
750C22⋊C4—121no—
751C22⋊C4—121no—
752C22⋊C4—242no—
753C42—21no—
754C42—21no—
755C42—21no—
756C42—21no—
757C42—21no—
758C42—21no—
759C42—21no—
760C42—62no—
761C42—62no—
762C42—61no—
763C42—61no—
764C42—61no—
765C42C2×D1211yescharacteristic
766C42C2×D1211yescharacteristic
767C42D3×D411yescharacteristic
768C42D3×D411yescharacteristic
769C22×C3—21no—
770C22×C3—21no—
771C22×C3—22no—
772C22×C3—41no—
773C22×C3—41no—
774C22×C3C2×#12011yescharacteristic
775C22×C3C2×#12111yescharacteristic
776C22×C3#52511yescharacteristic
777C2×D3—24no—
778C2×D3—22no—
779C2×D3—42no—
780C2×D3—41no—
781C2×D3—42no—
782C2×D3—41no—
783C2×D3—44no—
784C2×D3—82no—
785C2×D3—88no—
786C2×D3—82no—
787C2×D3—82no—
788C2×D3—81no—
789C2×D3—81no—
790C2×D3—81no—
791C3×C4—22no—
792C3×C4—21no—
793C3×C4—21no—
794C3×C4—21no—
795C3×C4—21no—
796C3×C4—42no—
797C3×C4—41no—
798C3×C4—41no—
799C3×C4—81no—
800C3×C4C2×#12111yescharacteristic
801C3×C4C2×#12111yescharacteristic
802C3×C4#52511yescharacteristic
803C3×C4#52511yescharacteristic
804Dic3—22no—
805Dic3—41no—
806Dic3—42no—
807Dic3—41no—
808Dic3—81no—
809C23—21no—
810C23—34no—
811C23—68no—
812C23—61no—
813C23—62no—
814C23—62no—
815C23—122no—
816C23—122no—
817C23—122no—
818C23—122no—
819C23—121no—
820C23—121no—
821C23—121no—
822C23—242no—
823C23—242no—
824C23C2×D3×D411yescharacteristic
825Q8—21no—
826Q8—32no—
827Q8—61no—
828Q8—121no—
829Q8—121no—
830Q8—121no—
831Q8—121no—
832Q8#89512yes—
833D4—22no—
834D4—22no—
835D4—21no—
836D4—32no—
837D4—68no—
838D4—68no—
839D4—62no—
840D4—62no—
841D4—62no—
842D4—62no—
843D4—62no—
844D4—61no—
845D4—62no—
846D4—121no—
847D4—121no—
848D4—121no—
849D4—121no—
850D4—248no—
851D4#89512yes—
852C2×C4—21no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—42no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—68no—
867C2×C4—61no—
868C2×C4—62no—
869C2×C4—62no—
870C2×C4—61no—
871C2×C4—61no—
872C2×C4—62no—
873C2×C4—81no—
874C2×C4—124no—
875C2×C4—122no—
876C2×C4—122no—
877C2×C4—121no—
878C2×C4—121no—
879C2×C4—121no—
880C2×C4—242no—
881C2×C4—241no—
882C2×C4—242no—
883C2×C4—242no—
884C2×C4—242no—
885C2×C4—242no—
886C2×C4#88211yescharacteristic
887C2×C4#88211yescharacteristic
888C2×C4#88211yescharacteristic
889C2×C4#88211yescharacteristic
890C2×C4C22×D1211yescharacteristic
891C2×C4C2×D3×D411yescharacteristic
892C2×C4C2×D3×D411yescharacteristic
893C2×C4C2×#23911yescharacteristic
894C2×C4D3×#4111yescharacteristic
895C2×C4D3×#4111yescharacteristic
896C8—41no—
897C8—41no—
898C8—121no—
899C8—121no—
900C2×C3—21no—
901C2×C3—21no—
902C2×C3—42no—
903C2×C3#284711yescharacteristic
904C2×C3#301811yescharacteristic
905C2×C3#301911yescharacteristic
906D3—44no—
907D3—42no—
908D3—161no—
909C22—21no—
910C22—21no—
911C22—22no—
912C22—41no—
913C22—41no—
914C22—62no—
915C22—64no—
916C22—124no—
917C22—122no—
918C22—121no—
919C22—122no—
920C22—121no—
921C22—242no—
922C22—242no—
923C22—242no—
924C22—248no—
925C22—241no—
926C22—241no—
927C22—241no—
928C22C2×#88211yescharacteristic
929C22D3×#12111yescharacteristic
930C22#562711yescharacteristic
931C4—22no—
932C4—21no—
933C4—21no—
934C4—21no—
935C4—21no—
936C4—42no—
937C4—41no—
938C4—41no—
939C4—62no—
940C4—81no—
941C4—121no—
942C4—122no—
943C4—121no—
944C4—241no—
945C4C2×#89511yescharacteristic
946C4#552411yescharacteristic
947C4D3×#12111yescharacteristic
948C4#562711yescharacteristic
949C3#3292411yescharacteristic, complemented, Sylow
950C2—21no—
951C2—21no—
952C2—42no—
953C2—124no—
954C2—122no—
955C2—481no—
956C2#7404811yescharacteristic
957C2#7898611yescharacteristic
958C2#7899311yescharacteristic
subgroupG/H
centerC22C2×#882
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1806C2
socleC22×C3C2×#120
prime radicalC2×#4822C2
hypercenter#1806D3
hypocenterC3#32924
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1806

Complements

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

NH ≅ G/Ntype
1. C4×#1009C2semidirect
2. #82527C2semidirect
3. #79058C2semidirect
4. C2×#4825C2semidirect
6. #73801C2semidirect
7. C3×#1806C2semidirect
8. #70527C2semidirect
9. #70366C2semidirect
10. #70365C2semidirect
11. #69494C2semidirect
12. #68776C2semidirect
13. #68775C2semidirect
14. #68760C2semidirect
15. #68759C2semidirect
35. C2×#875C22semidirect
41. C3×#423C22semidirect
44. C3×C4×C4⋊C4C22semidirect
45. #5131C22semidirect
48. #5120C22semidirect
53. #5004C22semidirect
54. #5001C22semidirect
56. #4939C22semidirect
57. #4929C22semidirect
60. #4924C22semidirect
68. C3×#339C22semidirect
69. C3×#339C22semidirect
70. #4554C22semidirect
71. #4554C22semidirect
72. #4523C22semidirect
73. #4523C22semidirect
87. #1806D3semidirect
108. C3×C4×Q8D4semidirect
109. C3×C4×Q8D4semidirect
112. C3×C4×D4D4semidirect
113. C3×C4×D4D4semidirect
187. C4×D12D4semidirect
188. C4×D12D4semidirect
194. C4×Dic6D4semidirect
195. C4×Dic6D4semidirect
251. #423C2×D3semidirect
266. C4×C4⋊C4C2×D3semidirect
271. #339C2×D3semidirect
272. #339C2×D3semidirect
461. C4×Q8D12semidirect
462. C4×Q8D12semidirect
489. C4×D4D12semidirect
490. C4×D4D12semidirect
949. C3#32924semidirect

Maximal subgroups

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

subgroupindex
C4×#10092
#825272
#790582
C2×#48252
C2×#48222
#738012
C3×#18062
#705272
#703662
#703652
#694942
#687762
#687752
#687602
#687592
#329243