Finite Group Databasebeta

← #10944190

Subgroups — #10944190

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
2C3×#3040C211yesmaximal, characteristic, complemented
3C2×#5202C211yesmaximal, characteristic, complemented
4C2×#5198C211yesmaximal, characteristic
5#82969C211yesmaximal, characteristic, complemented
6#82945C211yesmaximal, characteristic, complemented
7#72100C211yesmaximal, characteristic, complemented
8#72088C211yesmaximal, characteristic, complemented
9#71646C211yesmaximal, characteristic, complemented
10#70529C211yesmaximal, characteristic, complemented
11#70527C211yesmaximal, characteristic, complemented
12#70348C211yesmaximal, characteristic, complemented
13#70343C211yesmaximal, characteristic, complemented
14#70328C211yesmaximal, characteristic, complemented
15#70323C211yesmaximal, characteristic, complemented
16#32924—31nomaximal, Sylow
17C2×#1009C2211yescharacteristic
18C2×C3×#137C2211yescharacteristic
19C2×C3×AGL(1,ℤ/8)C2211yescharacteristic
20C2×C3×#124C2211yescharacteristic, complemented
21C3×C4×#41C2211yescharacteristic
22#5827C2211yescharacteristic
23C2×#947C2211yescharacteristic
24C2×#942C2211yescharacteristic
25C2×#940C2211yescharacteristic
26C2×#932C2211yescharacteristic
27#5574—21no—
28C4×#239—21no—
29#5545—21no—
30#5545—22no—
31C4×D3×D4—22no—
32C4×D3×D4—21no—
33#5523—21no—
34#5523C2211yescharacteristic
35#5521—21no—
36#5521C2211yescharacteristic
37C4×#235—21no—
38C4×#235C2211yescharacteristic
39C2×C4×D12—21no—
40C2×C4×D12C2211yescharacteristic
41C3×#464—21no—
42C3×#464—21no—
43C3×#463—21no—
44C3×#463—21no—
45C3×#423C2211yescharacteristic, complemented
46C3×#419C2211yescharacteristic, complemented
47C3×#418C2211yescharacteristic, complemented
48C2×#837C2211yescharacteristic
49C2×#837C2211yescharacteristic
50#5229C2211yescharacteristic, complemented
51#5225C2211yescharacteristic, complemented
52#5221C2211yescharacteristic, complemented
53#5215C2211yescharacteristic, complemented
54#5202—24no—
55#5198—24no—
56C2×#825C2211yescharacteristic
57C2×#825C2211yescharacteristic
58C2×#823C2211yescharacteristic
59C2×#823C2211yescharacteristic
60#5057—21no—
61#5057—21no—
62#5054—21no—
63#5054—21no—
64#4961—22no—
65#4956—22no—
66C4×C4⋊Dic3C2211yescharacteristic, complemented
67#4924C2211yescharacteristic, complemented
68#4555C2211yescharacteristic, complemented
69#4555C2211yescharacteristic, complemented
70#4554C2211yescharacteristic, complemented
71#4554C2211yescharacteristic, complemented
72#4532C2211yescharacteristic, complemented
73#4532C2211yescharacteristic, complemented
74C4×H(5,𝔽2)—31no—
75#3040—31no—
76#3040D311yescharacteristic, complemented
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#1806—31no—
88#1800—31no—
89C2×C3×#41C2311yescharacteristic
90C22×C3×Q8C2311yescharacteristic
91C22×C3×D4C2311yescharacteristic
92C22×#67—22no—
93#1009—22no—
94#1009—22no—
95#1009—22no—
96#1009D414yes—
97C2×#239—21no—
98C2×D3×D4—22no—
99C2×D3×D4—21no—
100C2×#235—21no—
101C2×#235C2311yescharacteristic
102C22×D12—21no—
103C22×D12C2311yescharacteristic
104C22×C4×D3—22no—
105C22×C4×D3D412yes—
106C3×#137—22no—
107C3×#137—22no—
108C3×AGL(1,ℤ/8)—22no—
109C3×AGL(1,ℤ/8)—22no—
110C2×C3×Q16—21no—
111C2×C3×SD16—21no—
112C2×C3×SD16—21no—
113C2×C3×D8—21no—
114C2×C3×M16C2311yescharacteristic
115C2×C3×M16C2311yescharacteristic
116C3×#124—21no—
117C3×#124—21no—
118C3×#124—21no—
119C3×#124—21no—
120C3×C4×Q8D411yescharacteristic, complemented
121C3×C4×Q8D411yescharacteristic, complemented
122C3×C4×D4—21no—
123C3×C4×D4—21no—
124C3×C4×D4D411yescharacteristic, complemented
125C3×C4×D4D411yescharacteristic, complemented
126C3×#117—21no—
127C3×#117C2311yescharacteristic
128C2×C3×C22⋊C4—21no—
129C2×C3×C22⋊C4—21no—
130C2×C3×C42—21no—
131C2×C3×C42C2311yescharacteristic
132C2×#217—22no—
133#947—22no—
134#947—22no—
135Q8×Dic3—21no—
136C2×#216—21no—
137#942—22no—
138#942—22no—
139C2×#215—21no—
140#940—22no—
141#940—22no—
142D4×Dic3—21no—
143D4×Dic3—22no—
144C2×#214—21no—
145#932—22no—
146#932—22no—
147C2×#213—21no—
148C4×#67—22no—
149C4×#67—22no—
150C4×#67—21no—
151C4×#67—21no—
152C2×(C2×D3)⋊C4—22no—
153C2×(C2×D3)⋊C4—22no—
154C2×(C2×D3)⋊C4D412yes—
155#926—21no—
156#926C2311yescharacteristic
157C2×C4⋊Dic3—21no—
158C2×C4⋊Dic3—21no—
159C2×C4⋊Dic3C2311yescharacteristic
160C2×C4×Dic3C2311yescharacteristic
161C2×C4×Dic3C2311yescharacteristic
162C2×#208C2311yescharacteristic
163C2×#208C2311yescharacteristic
164#893—22no—
165#893—22no—
166#893—21no—
167#893—21no—
168#892—22no—
169#892—21no—
170D3×C4⋊C4—22no—
171D3×C4⋊C4—21no—
172#67⋊C4—22no—
173#67⋊C4—22no—
174#67⋊C4—22no—
175D3×C22⋊C4—22no—
176D3×C22⋊C4—22no—
177D3×C22⋊C4—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×#103—21no—
199C3×#103—21no—
200C3×#102—21no—
201C3×#102—21no—
202#837—22no—
203#837—22no—
204#835—21no—
205#835—21no—
206#832—21no—
207#832—21no—
208C3⋊#95—21no—
209C3⋊#95—22no—
210#825—22no—
211#825—22no—
212#823—22no—
213#823—22no—
214C4⋊(C3⋊C8)—21no—
215C4⋊(C3⋊C8)—21no—
216C2×H(5,𝔽2)—31no—
217C2×#137—31no—
218C2×#137C2×D311yescharacteristic
219C2×AGL(1,ℤ/8)—31no—
220C2×AGL(1,ℤ/8)C2×D311yescharacteristic
221C2×#127—31no—
222C2×#124—31no—
223C2×#124C2×D311yescharacteristic, complemented
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—21no—
241#464—21no—
242#464—61no—
243#464—61no—
244#463—21no—
245#463—21no—
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×#104—31no—
255C2×#104—31no—
256#419—31no—
257#419C2×D311yescharacteristic, complemented
258#418—31no—
259#418C2×D311yescharacteristic, complemented
260C2×#100—31no—
261C2×#100—31no—
262#394—62no—
263#391—31no—
264#390—31no—
265#386—62no—
266C4×C4⋊C4—31no—
267#343—31no—
268#343—31no—
269#339—31no—
270#339—31no—
271#339—31no—
272#339—31no—
273C24×C3—21no—
274C23×D3—22no—
275C23×D3C2×D412yes—
276C3×#41—21no—
277C3×#41—21no—
278C3×#41C2×D412yes—
279C3×#41#4112yes—
280C2×C3×Q8—21no—
281C2×C3×Q8—21no—
282C2×C3×Q8—21no—
283C2×C3×Q8—21no—
284C2×C3×Q8—21no—
285C2×C3×Q8—21no—
286C2×C3×Q8C2×D411yescharacteristic
287C2×C3×D4—21no—
288C2×C3×D4—21no—
289C2×C3×D4—21no—
290C2×C3×D4—21no—
291C2×C3×D4—21no—
292C2×C3×D4—21no—
293C2×C3×D4—21no—
294C2×C3×D4C2×D411yescharacteristic
295C22×C3×C4—21no—
296C22×C3×C4—21no—
297C22×C3×C4—21no—
298C22×C3×C4—21no—
299C22×C3×C4C2×D411yescharacteristic
300C22×C3×C4C2×D411yescharacteristic
301C22×C3×C4C2411yescharacteristic
302C2×#67—22no—
303C2×#67—21no—
304C2×#67—44no—
305C2×#67—44no—
306C2×#67—82no—
307C22×Dic3—21no—
308C22×Dic3—22no—
309C22×Dic3—21no—
310C22×Dic3C2×D412yes—
311#239—24no—
312#239—24no—
313D3×D4—28no—
314D3×D4—24no—
315D3×D4—28no—
316D3×D4—24no—
317#235—24no—
318#235—21no—
319#235—21no—
320#235—24no—
321#235C2×D412yes—
322#235#4112yes—
323C2×D12—22no—
324C2×D12—24no—
325C2×D12—21no—
326C2×D12—21no—
327C2×D12—21no—
328C2×D12—21no—
329C2×D12—24no—
330C2×D12C2×D412yes—
331C2×D12C2×D411yescharacteristic
332C2×D12#4112yes—
333C2×C4×D3—22no—
334C2×C4×D3—21no—
335C2×C4×D3—22no—
336C2×C4×D3—21no—
337C2×C4×D3—22no—
338C2×C4×D3—22no—
339C2×C4×D3—22no—
340C2×C4×D3—21no—
341C2×C4×D3—22no—
342C2×C4×D3—84no—
343C2×C4×D3—82no—
344C2×Dic6C2×D411yescharacteristic
345C3×Q16—42no—
346C3×SD16—42no—
347C3×SD16—42no—
348C3×D8—42no—
349C3×M16—21no—
350C3×M16—21no—
351C3×M16—21no—
352C3×M16—21no—
353C2×C3×C8—21no—
354C2×C3×C8—21no—
355C3×C4⋊C4—21no—
356C3×C4⋊C4—21no—
357C3×C4⋊C4C2×D411yescharacteristic
358C3×C4⋊C4C2×D411yescharacteristic
359C3×C22⋊C4—21no—
360C3×C22⋊C4—21no—
361C3×C22⋊C4—21no—
362C3×C22⋊C4—41no—
363C3×C22⋊C4—41no—
364C3×C22⋊C4—41no—
365C3×C22⋊C4—41no—
366C3×C42—21no—
367C3×C42—21no—
368C3×C42—21no—
369C3×C42C2×D411yescharacteristic
370C3×C42C2×D411yescharacteristic
371C3×C42C2×D411yescharacteristic
372C3×C42C2×D411yescharacteristic
373#217—22no—
374#217—21no—
375#217—82no—
376#216—42no—
377#215—42no—
378#214—42no—
379#213—42no—
380(C2×D3)⋊C4—22no—
381(C2×D3)⋊C4—22no—
382(C2×D3)⋊C4—22no—
383(C2×D3)⋊C4—22no—
384(C2×D3)⋊C4—21no—
385(C2×D3)⋊C4—21no—
386(C2×D3)⋊C4—22no—
387(C2×D3)⋊C4—44no—
388C4⋊Dic3—22no—
389C4⋊Dic3—21no—
390C4⋊Dic3—21no—
391C4⋊Dic3—42no—
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—
402C4×Dic3—21no—
403C4×Dic3—21no—
404C4×Dic3—21no—
405C4×Dic3—21no—
406#208—21no—
407#208—21no—
408#208—21no—
409#208—21no—
410C2×C3⋊C8—21no—
411C2×C3⋊C8—21no—
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×Q8C22×D311yescharacteristic
421C22×D4—31no—
422C22×D4—61no—
423C22×D4—62no—
424C22×D4—61no—
425C22×D4—62no—
426C22×D4C22×D311yescharacteristic
427C23×C4—32no—
428C23×C4—62no—
429#137—22no—
430#137—22no—
431#137—62no—
432#137—62no—
433AGL(1,ℤ/8)—22no—
434AGL(1,ℤ/8)—22no—
435AGL(1,ℤ/8)—62no—
436AGL(1,ℤ/8)—62no—
437C2×Q16—21no—
438C2×Q16—61no—
439C2×SD16—21no—
440C2×SD16—21no—
441C2×SD16—61no—
442C2×SD16—61no—
443C2×D8—21no—
444C2×D8—61no—
445C2×M16—31no—
446C2×M16—31no—
447C2×M16C22×D311yescharacteristic
448C2×M16C22×D311yescharacteristic
449#127—62no—
450#127—62no—
451#124—21no—
452#124—21no—
453#124—21no—
454#124—21no—
455#124—62no—
456#124—62no—
457C4×Q8—31no—
458C4×Q8—31no—
459C4×Q8—61no—
460C4×Q8—61no—
461C4×Q8#6711yescharacteristic, complemented
462C4×Q8#6711yescharacteristic, 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×D4#6711yescharacteristic, complemented
490C4×D4#6711yescharacteristic, 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—31no—
500C2×C4⋊C4—62no—
501C2×C4⋊C4—61no—
502C2×C4⋊C4—61no—
503C2×C4⋊C4—61no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—32no—
507C2×C22⋊C4—62no—
508C2×C22⋊C4—62no—
509C2×C22⋊C4—62no—
510C2×C22⋊C4—62no—
511C2×C22⋊C4—62no—
512C2×C22⋊C4—62no—
513C2×C42—21no—
514C2×C42—31no—
515C2×C42—31no—
516C2×C42—62no—
517C2×C42—61no—
518C2×C42C22×D311yescharacteristic
519C4⋊C8—21no—
520C4⋊C8—21no—
521C4⋊C8—61no—
522C4⋊C8—61no—
523#104—62no—
524#104—62no—
525#104—62no—
526#104—62no—
527#103—21no—
528#103—21no—
529#103—61no—
530#103—61no—
531#102—21no—
532#102—21no—
533#102—61no—
534#102—61no—
535#100—62no—
536#100—62no—
537#95—62no—
538#95—61no—
539C23×C3—21no—
540C23×C3—42no—
541C23×C3—42no—
542C23×C3—41no—
543C23×C3—41no—
544C23×C3—41no—
545C23×C3C22×D411yescharacteristic
546C22×D3—22no—
547C22×D3—21no—
548C22×D3—28no—
549C22×D3—22no—
550C22×D3—42no—
551C22×D3—42no—
552C22×D3—82no—
553C22×D3—82no—
554C22×D3#12114yes—
555C3×Q8—21no—
556C3×Q8—41no—
557C3×Q8—41no—
558C3×Q8—41no—
559C3×Q8—41no—
560C3×Q8#12112yes—
561C3×D4—22no—
562C3×D4—22no—
563C3×D4—21no—
564C3×D4—41no—
565C3×D4—41no—
566C3×D4—41no—
567C3×D4—41no—
568C3×D4#12112yes—
569C2×C3×C4—21no—
570C2×C3×C4—22no—
571C2×C3×C4—22no—
572C2×C3×C4—21no—
573C2×C3×C4—21no—
574C2×C3×C4—41no—
575C2×C3×C4—41no—
576C2×C3×C4—42no—
577C2×C3×C4—41no—
578C2×C3×C4—41no—
579C2×C3×C4—41no—
580C2×C3×C4—81no—
581C2×C3×C4#12011yescharacteristic
582C2×C3×C4#12011yescharacteristic
583C2×C3×C4#12011yescharacteristic
584C2×C3×C4#12011yescharacteristic
585C2×C3×C4C22×D411yescharacteristic
586C2×C3×C4C22×D411yescharacteristic
587C2×C3×C4C22×D411yescharacteristic
588C2×C3×C4C2×#4111yescharacteristic
589C2×C3×C4C2×#4111yescharacteristic
590C2×C3×C4C2×#4111yescharacteristic
591#67—28no—
592#67—22no—
593#67—22no—
594#67—88no—
595C2×Dic3—21no—
596C2×Dic3—22no—
597C2×Dic3—21no—
598C2×Dic3—22no—
599C2×Dic3—21no—
600C2×Dic3—41no—
601C2×Dic3—41no—
602C2×Dic3—42no—
603C2×Dic3—41no—
604C2×Dic3—41no—
605C2×Dic3—41no—
606C2×Dic3—82no—
607D12—28no—
608D12—22no—
609D12—22no—
610D12—21no—
611D12—22no—
612D12—22no—
613D12#12112yes—
614C4×D3—28no—
615C4×D3—22no—
616C4×D3—22no—
617C4×D3—44no—
618C4×D3—42no—
619C4×D3—81no—
620C4×D3—82no—
621C4×D3—82no—
622C4×D3—82no—
623C4×D3—82no—
624Dic6—21no—
625Dic6#12112yes—
626C3×C8—41no—
627C3×C8—41no—
628C3⋊C8—41no—
629C3⋊C8—41no—
630C24—21no—
631C24—32no—
632C24—62no—
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#23712yes—
645C2×Q8—21no—
646C2×Q8—21no—
647C2×Q8—21no—
648C2×Q8—21no—
649C2×Q8—21no—
650C2×Q8—21no—
651C2×Q8—31no—
652C2×Q8C2×#6711yescharacteristic
653C2×D4—21no—
654C2×D4—21no—
655C2×D4—21no—
656C2×D4—21no—
657C2×D4—21no—
658C2×D4—21no—
659C2×D4—21no—
660C2×D4—31no—
661C2×D4—32no—
662C2×D4—32no—
663C2×D4—64no—
664C2×D4—62no—
665C2×D4—64no—
666C2×D4—68no—
667C2×D4—68no—
668C2×D4—64no—
669C2×D4—62no—
670C2×D4—61no—
671C2×D4—64no—
672C2×D4—61no—
673C2×D4—61no—
674C2×D4—61no—
675C2×D4—61no—
676C2×D4—124no—
677C2×D4—124no—
678C2×D4—242no—
679C2×D4C2×#6711yescharacteristic
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—32no—
685C22×C4—62no—
686C22×C4—62no—
687C22×C4—62no—
688C22×C4—62no—
689C22×C4—61no—
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—42no—
703Q16—122no—
704SD16—42no—
705SD16—42no—
706SD16—122no—
707SD16—122no—
708D8—42no—
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—62no—
727C4⋊C4—62no—
728C4⋊C4—61no—
729C4⋊C4—61no—
730C4⋊C4—61no—
731C4⋊C4—61no—
732C4⋊C4—122no—
733C4⋊C4C2×#6711yescharacteristic
734C4⋊C4C2×#6711yescharacteristic
735C22⋊C4—21no—
736C22⋊C4—21no—
737C22⋊C4—21no—
738C22⋊C4—41no—
739C22⋊C4—41no—
740C22⋊C4—41no—
741C22⋊C4—41no—
742C22⋊C4—62no—
743C22⋊C4—62no—
744C22⋊C4—62no—
745C22⋊C4—62no—
746C22⋊C4—61no—
747C22⋊C4—62no—
748C22⋊C4—62no—
749C22⋊C4—61no—
750C22⋊C4—61no—
751C22⋊C4—124no—
752C22⋊C4—242no—
753C42—21no—
754C42—21no—
755C42—21no—
756C42—62no—
757C42—62no—
758C42—61no—
759C42—61no—
760C42—61no—
761C42—61no—
762C42—61no—
763C42—61no—
764C42—61no—
765C42D3×D411yescharacteristic
766C42D3×D411yescharacteristic
767C42C2×#6711yescharacteristic
768C42C2×#6711yescharacteristic
769C22×C3—21no—
770C22×C3—21no—
771C22×C3—22no—
772C22×C3—41no—
773C22×C3—41no—
774C22×C3—82no—
775C22×C3—82no—
776C22×C3—81no—
777C22×C3—81no—
778C22×C3—81no—
779C22×C3C2×#12011yescharacteristic
780C22×C3C2×#12111yescharacteristic
781C22×C3#52511yescharacteristic
782C2×D3—24no—
783C2×D3—22no—
784C2×D3—42no—
785C2×D3—41no—
786C2×D3—42no—
787C2×D3—41no—
788C2×D3—44no—
789C2×D3—82no—
790C2×D3—88no—
791C3×C4—22no—
792C3×C4—21no—
793C3×C4—21no—
794C3×C4—21no—
795C3×C4—21no—
796C3×C4—41no—
797C3×C4—41no—
798C3×C4—81no—
799C3×C4C2×#12111yescharacteristic
800C3×C4C2×#12111yescharacteristic
801C3×C4#52511yescharacteristic
802C3×C4#52511yescharacteristic
803Dic3—22no—
804Dic3—42no—
805Dic3—41no—
806Dic3—42no—
807Dic3—41no—
808Dic3—81no—
809C23—21no—
810C23—34no—
811C23—42no—
812C23—42no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—68no—
817C23—61no—
818C23—62no—
819C23—62no—
820C23—122no—
821C23—122no—
822C23—242no—
823C23—242no—
824C23C2×D3×D411yescharacteristic
825Q8—21no—
826Q8—32no—
827Q8—41no—
828Q8—41no—
829Q8—41no—
830Q8—41no—
831Q8—61no—
832Q8#93812yes—
833D4—22no—
834D4—22no—
835D4—21no—
836D4—32no—
837D4—41no—
838D4—41no—
839D4—41no—
840D4—41no—
841D4—68no—
842D4—68no—
843D4—62no—
844D4—62no—
845D4—62no—
846D4—62no—
847D4—62no—
848D4—61no—
849D4—62no—
850D4—248no—
851D4#93812yes—
852C2×C4—21no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—42no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—68no—
864C2×C4—61no—
865C2×C4—62no—
866C2×C4—62no—
867C2×C4—62no—
868C2×C4—61no—
869C2×C4—61no—
870C2×C4—62no—
871C2×C4—81no—
872C2×C4—124no—
873C2×C4—122no—
874C2×C4—121no—
875C2×C4—121no—
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#93711yescharacteristic
887C2×C4#93711yescharacteristic
888C2×C4#93711yescharacteristic
889C2×C4#93711yescharacteristic
890C2×C4C2×D3×D411yescharacteristic
891C2×C4C2×D3×D411yescharacteristic
892C2×C4C2×#23711yescharacteristic
893C2×C4D3×#4111yescharacteristic
894C2×C4D3×#4111yescharacteristic
895C2×C4C22×#6711yescharacteristic
896C8—41no—
897C8—41no—
898C8—121no—
899C8—121no—
900C2×C3—21no—
901C2×C3—21no—
902C2×C3—42no—
903C2×C3—161no—
904C2×C3#284711yescharacteristic
905C2×C3#301811yescharacteristic
906C2×C3#301911yescharacteristic
907D3—44no—
908D3—42no—
909C22—21no—
910C22—21no—
911C22—22no—
912C22—41no—
913C22—41no—
914C22—62no—
915C22—64no—
916C22—82no—
917C22—82no—
918C22—81no—
919C22—81no—
920C22—81no—
921C22—124no—
922C22—122no—
923C22—121no—
924C22—122no—
925C22—121no—
926C22—242no—
927C22—248no—
928C22D3×#12111yescharacteristic
929C22#560611yescharacteristic
930C22C2×#93711yescharacteristic
931C4—22no—
932C4—21no—
933C4—21no—
934C4—21no—
935C4—21no—
936C4—41no—
937C4—41no—
938C4—62no—
939C4—81no—
940C4—122no—
941C4—121no—
942C4—122no—
943C4—121no—
944C4—241no—
945C4D3×#12111yescharacteristic
946C4#560611yescharacteristic
947C4C2×#93811yescharacteristic
948C4#582811yescharacteristic
949C3#3292411yescharacteristic, complemented, Sylow
950C2—21no—
951C2—21no—
952C2—42no—
953C2—124no—
954C2—122no—
955C2—161no—
956C2#8272311yescharacteristic
957C2#8400411yescharacteristic
958C2#8400511yescharacteristic
subgroupG/H
centerC22C2×#937
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#3040C2
socleC22×C3C2×#120
prime radicalC2×#5198C2
hypercenter#3040D3
hypocenterC3#32924
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3040

Complements

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

NH ≅ G/Ntype
1. C4×#1009C2semidirect
2. C3×#3040C2semidirect
3. C2×#5202C2semidirect
5. #82969C2semidirect
6. #82945C2semidirect
7. #72100C2semidirect
8. #72088C2semidirect
9. #71646C2semidirect
10. #70529C2semidirect
11. #70527C2semidirect
12. #70348C2semidirect
13. #70343C2semidirect
14. #70328C2semidirect
15. #70323C2semidirect
20. C2×C3×#124C22semidirect
45. C3×#423C22semidirect
46. C3×#419C22semidirect
47. C3×#418C22semidirect
50. #5229C22semidirect
51. #5225C22semidirect
52. #5221C22semidirect
53. #5215C22semidirect
66. C4×C4⋊Dic3C22semidirect
67. #4924C22semidirect
68. #4555C22semidirect
69. #4555C22semidirect
70. #4554C22semidirect
71. #4554C22semidirect
72. #4532C22semidirect
73. #4532C22semidirect
76. #3040D3semidirect
120. C3×C4×Q8D4semidirect
121. C3×C4×Q8D4semidirect
124. C3×C4×D4D4semidirect
125. C3×C4×D4D4semidirect
187. C4×D12D4semidirect
188. C4×D12D4semidirect
194. C4×Dic6D4semidirect
195. C4×Dic6D4semidirect
223. C2×#124C2×D3semidirect
251. #423C2×D3semidirect
257. #419C2×D3semidirect
259. #418C2×D3semidirect
461. C4×Q8#67semidirect
462. C4×Q8#67semidirect
489. C4×D4#67semidirect
490. C4×D4#67semidirect
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
C3×#30402
C2×#52022
C2×#51982
#829692
#829452
#721002
#720882
#716462
#705292
#705272
#703482
#703432
#703282
#703232
#329243