Finite Group Databasebeta

← #10826259

Subgroups — #10826259

Order 768.

1794 conjugacy classes of subgroups.

The subgroup lattice has 970 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#548C211yesmaximal, characteristic, complemented
2C22×#950C211yesmaximal, characteristic, complemented
3C2×#5228C211yesmaximal, characteristic, complemented
4C2×#5227C211yesmaximal, characteristic, complemented
5C2×#5047C211yesmaximal, characteristic, complemented
6#82402C211yesmaximal, characteristic, complemented
7#72135C211yesmaximal, characteristic, complemented
8#71729C211yesmaximal, characteristic, complemented
9#71728C211yesmaximal, characteristic, complemented
10#71696C211yesmaximal, characteristic, complemented
11#71685C211yesmaximal, characteristic, complemented
12#71684C211yesmaximal, characteristic, complemented
13#71633C211yesmaximal, characteristic, complemented
14#71632C211yesmaximal, characteristic, complemented
15#71610C211yesmaximal, characteristic, complemented
16#23854—31nomaximal, Sylow
17C22×C3×#41C2211yescharacteristic
18C23×C3×Q8C2211yescharacteristic
19C22×#235C2211yescharacteristic
20C3×#548—24no—
21C3×#548—24no—
22C2×C3×#124—21no—
23C2×C3×#124C2211yescharacteristic
24C2×C3×C22⋊Q8—21no—
25C2×C3×C22⋊Q8C2211yescharacteristic
26C2×C3×#121—21no—
27C2×C3×#121C2211yescharacteristic
28C2×C3×C4×Q8C2211yescharacteristic
29C2×C3×C4×D4—21no—
30C2×C3×C4×D4C2211yescharacteristic
31C2×#950—24no—
32C2×#950—24no—
33C2×#950—24no—
34C22×#216C2211yescharacteristic
35C22×#216C2211yescharacteristic
36C22×#215C2211yescharacteristic
37C22×#215C2211yescharacteristic
38C22×#214C2211yescharacteristic
39C22×#213C2211yescharacteristic
40C2×#930C2211yescharacteristic
41C2×#924C2211yescharacteristic
42C23×C3⋊C8C2211yescharacteristic
43#5228—24no—
44#5227—24no—
45C2×#835C2211yescharacteristic
46C2×#835C2211yescharacteristic
47C2×#835C2211yescharacteristic
48C2×#835C2211yescharacteristic
49#5223—21no—
50C2×#832C2211yescharacteristic
51C2×#832C2211yescharacteristic
52#5212C2211yescharacteristic
53C2×#830C2211yescharacteristic
54C2×#830C2211yescharacteristic
55C2×#830C2211yescharacteristic
56#5047—24no—
57#4989—21no—
58C2×#810C2211yescharacteristic
59C2×#809C2211yescharacteristic
60#4959—21no—
61#4956—21no—
62#4939C2211yescharacteristic
63#4929C2211yescharacteristic
64#4529C2211yescharacteristic
65#4529C2211yescharacteristic
66#4524C2211yescharacteristic
67#4524C2211yescharacteristic
68C22×#135—31no—
69C2×#548D311yescharacteristic, complemented
70C2×#452—31no—
71C2×#451—31no—
72C2×#448—31no—
73#2407—31no—
74#2015—31no—
75#2012—31no—
76#2000—31no—
77#1999—31no—
78#1892—31no—
79#1880—31no—
80#1878—31no—
81#1869—31no—
82#1788—31no—
83C2×C3×#41—22no—
84C2×C3×#41—22no—
85C2×C3×#41—22no—
86C2×C3×#41—41no—
87C2×C3×#41—41no—
88C2×C3×#41D414yescomplemented
89C22×C3×Q8—22no—
90C22×C3×Q8—22no—
91C22×C3×Q8—21no—
92C22×C3×Q8—22no—
93C22×C3×Q8—22no—
94C22×C3×Q8—41no—
95C22×C3×Q8—41no—
96C22×C3×Q8C2311yescharacteristic
97C22×C3×Q8C2311yescharacteristic
98C22×C3×D4—21no—
99C22×C3×D4—21no—
100C22×C3×D4D411yescharacteristic
101C22×C3×D4C2311yescharacteristic
102C23×C3×C4—21no—
103C23×C3×C4—21no—
104C23×C3×C4C2311yescharacteristic
105C23×C3×C4C2311yescharacteristic
106C22×#67—21no—
107C22×#67—21no—
108C2×#235—22no—
109C2×#235—22no—
110C2×#235—22no—
111C2×#235—22no—
112C2×#235—41no—
113C2×#235—41no—
114C22×D12C2311yescharacteristic
115C22×C4×D3—21no—
116C22×Dic6C2311yescharacteristic
117C3×#124—28no—
118C3×#124—22no—
119C3×#124—22no—
120C3×C22⋊Q8—28no—
121C3×C22⋊Q8—22no—
122C3×C22⋊Q8D414yescomplemented
123C3×#121—28no—
124C3×#121—22no—
125C3×#121—22no—
126C3×C4×Q8—22no—
127C3×C4×Q8—22no—
128C3×C4×D4—28no—
129C3×C4×D4—22no—
130C3×C4×D4—22no—
131C2×C3×C4⋊C4—21no—
132C2×C3×C4⋊C4—21no—
133C2×C3×C4⋊C4D411yescharacteristic
134C2×C3×C4⋊C4C2311yescharacteristic
135C2×C3×C22⋊C4—21no—
136C2×C3×C22⋊C4—21no—
137C2×C3×C22⋊C4—21no—
138C2×C3×C22⋊C4—21no—
139C2×C3×C22⋊C4D411yescharacteristic
140C2×C3×C22⋊C4D411yescharacteristic
141C2×C3×C42—21no—
142C2×C3×C42C2311yescharacteristic
143C2×#217—21no—
144C2×#217—21no—
145#950—232no—
146C2×#216—22no—
147C2×#216—22no—
148C2×#216—22no—
149C2×#216—22no—
150C2×#216—41no—
151C2×#216D414yescomplemented
152C2×#215—22no—
153C2×#215—22no—
154C2×#215—22no—
155C2×#215—22no—
156C2×#215—41no—
157C2×#215D414yescomplemented
158C2×#214—22no—
159C2×#214—22no—
160C2×#214—22no—
161C2×#213—22no—
162C2×#213—22no—
163C2×#213—22no—
164#930—22no—
165#930—41no—
166C2×(C2×D3)⋊C4—21no—
167C2×(C2×D3)⋊C4—21no—
168C2×(C2×D3)⋊C4—21no—
169C2×C4⋊Dic3C2311yescharacteristic
170C2×C4⋊Dic3C2311yescharacteristic
171#924—22no—
172#924—41no—
173C2×Dic3⋊C4—21no—
174C22×C3⋊C8—22no—
175C22×C3⋊C8—22no—
176C22×C3⋊C8—22no—
177C22×C3⋊C8C2311yescharacteristic
178C22×C3⋊C8C2311yescharacteristic
179C22×C3⋊C8C2311yescharacteristic
180C22×C3⋊C8C2311yescharacteristic
181#835—22no—
182#835—22no—
183#835—22no—
184#835—22no—
185#832—41no—
186#832—41no—
187C3⋊#95—21no—
188C3⋊#95—21no—
189C3⋊#95—21no—
190#830—22no—
191#830—22no—
192#830—22no—
193#810—22no—
194#809—22no—
195C22×#41—31no—
196C22×#41C2×D311yescharacteristic
197C23×Q8C2×D311yescharacteristic
198C2×#135—64no—
199C2×#135—64no—
200C2×#135—64no—
201C22×Q16—31no—
202C22×Q16—31no—
203C22×SD16—31no—
204C22×SD16—31no—
205C22×SD16—31no—
206C22×D8—31no—
207C23×C8—31no—
208#548—24no—
209#548—24no—
210C2×#124—21no—
211C2×#124C2×D311yescharacteristic
212C2×C22⋊Q8—21no—
213C2×C22⋊Q8—31no—
214C2×C22⋊Q8C2×D311yescharacteristic
215C2×#121—21no—
216C2×#121—31no—
217C2×#121C2×D311yescharacteristic
218C2×C4×Q8C2×D311yescharacteristic
219C2×C4×D4—21no—
220C2×C4×D4C2×D311yescharacteristic
221#452—64no—
222#451—64no—
223#448—64no—
224C2×#103—31no—
225C2×#103—31no—
226C2×#103—31no—
227C2×#103—31no—
228C2×#103—31no—
229C2×#102—31no—
230C2×#102—31no—
231C2×#102—31no—
232C2×C22⋊C8—31no—
233C2×C22⋊C8—31no—
234C2×C22⋊C8—31no—
235#394—61no—
236#392—61no—
237#391—31no—
238#390—31no—
239#386—61no—
240#385—61no—
241#380—31no—
242#340—31no—
243#340—31no—
244#336—31no—
245#336—31no—
246C24×C3—21no—
247C24×C3C2×D411yescharacteristic
248C24×C3C2×D411yescharacteristic
249C23×D3—21no—
250C3×#41—28no—
251C3×#41—44no—
252C3×#41—44no—
253C3×#41—44no—
254C2×C3×Q8—24no—
255C2×C3×Q8—21no—
256C2×C3×Q8—21no—
257C2×C3×Q8—21no—
258C2×C3×Q8—21no—
259C2×C3×Q8—21no—
260C2×C3×Q8—21no—
261C2×C3×Q8—21no—
262C2×C3×Q8—21no—
263C2×C3×Q8—42no—
264C2×C3×Q8—42no—
265C2×C3×Q8—44no—
266C2×C3×Q8—44no—
267C2×C3×Q8—44no—
268C2×C3×Q8—44no—
269C2×C3×Q8C2×D412yes—
270C2×C3×Q8C2×D412yes—
271C2×C3×Q8C2×D412yes—
272C2×C3×Q8C2×D412yes—
273C2×C3×D4—24no—
274C2×C3×D4—22no—
275C2×C3×D4—24no—
276C2×C3×D4—22no—
277C2×C3×D4—21no—
278C2×C3×D4—21no—
279C2×C3×D4—21no—
280C2×C3×D4—21no—
281C2×C3×D4—21no—
282C2×C3×D4—41no—
283C2×C3×D4—42no—
284C2×C3×D4—42no—
285C2×C3×D4—42no—
286C2×C3×D4—42no—
287C2×C3×D4C2×D412yes—
288C22×C3×C4—21no—
289C22×C3×C4—21no—
290C22×C3×C4—21no—
291C22×C3×C4—21no—
292C22×C3×C4—21no—
293C22×C3×C4—24no—
294C22×C3×C4—21no—
295C22×C3×C4—21no—
296C22×C3×C4—24no—
297C22×C3×C4—21no—
298C22×C3×C4—21no—
299C22×C3×C4—21no—
300C22×C3×C4—21no—
301C22×C3×C4—21no—
302C22×C3×C4—21no—
303C22×C3×C4—42no—
304C22×C3×C4—42no—
305C22×C3×C4—42no—
306C22×C3×C4—42no—
307C22×C3×C4C2×D411yescharacteristic
308C22×C3×C4C2×D411yescharacteristic
309C22×C3×C4C2×D411yescharacteristic
310C22×C3×C4C2×D411yescharacteristic
311C22×C3×C4C2×D412yes—
312C22×C3×C4C2×D412yes—
313C22×C3×C4C2411yescharacteristic
314C2×#67—42no—
315C2×#67—42no—
316C2×#67—42no—
317C2×#67—42no—
318C2×#67—42no—
319C2×#67—81no—
320C22×Dic3—21no—
321C22×Dic3—21no—
322C22×Dic3—21no—
323#235—28no—
324#235—44no—
325#235—44no—
326#235—44no—
327C2×D12—21no—
328C2×D12—21no—
329C2×D12—21no—
330C2×D12—21no—
331C2×D12—21no—
332C2×D12C2×D412yes—
333C2×C4×D3—42no—
334C2×C4×D3—42no—
335C2×C4×D3—42no—
336C2×Dic6—21no—
337C2×Dic6—21no—
338C2×Dic6—21no—
339C2×Dic6—21no—
340C2×Dic6—21no—
341C2×Dic6C2×D412yes—
342C3×C4⋊C4—24no—
343C3×C4⋊C4—24no—
344C3×C4⋊C4—22no—
345C3×C4⋊C4—21no—
346C3×C4⋊C4C2×D412yes—
347C3×C22⋊C4—24no—
348C3×C22⋊C4—24no—
349C3×C22⋊C4—24no—
350C3×C22⋊C4—24no—
351C3×C22⋊C4—22no—
352C3×C22⋊C4—22no—
353C3×C42—24no—
354C3×C42—21no—
355C3×C42—21no—
356#217—42no—
357#217—81no—
358#216—28no—
359#216—44no—
360#215—28no—
361#215—44no—
362#214—28no—
363#213—28no—
364(C2×D3)⋊C4—42no—
365(C2×D3)⋊C4—42no—
366(C2×D3)⋊C4—81no—
367C4⋊Dic3—21no—
368C4⋊Dic3—21no—
369C4⋊Dic3—21no—
370C4⋊Dic3—21no—
371Dic3⋊C4—42no—
372C2×C3⋊C8—28no—
373C2×C3⋊C8—21no—
374C2×C3⋊C8—21no—
375C2×C3⋊C8—21no—
376C2×C3⋊C8—21no—
377C2×C3⋊C8—21no—
378C2×C3⋊C8—21no—
379C2×C3⋊C8—21no—
380C2×C3⋊C8—21no—
381C2×C3⋊C8—21no—
382C2×C3⋊C8—21no—
383C2×C3⋊C8C2×D412yes—
384C2×C3⋊C8C2×D412yes—
385C2×#41—22no—
386C2×#41—22no—
387C2×#41—22no—
388C2×#41—41no—
389C2×#41—41no—
390C2×#41—62no—
391C2×#41—62no—
392C2×#41—62no—
393C2×#41—62no—
394C2×#41—121no—
395C2×#41—121no—
396C2×#41#6714yescomplemented
397C22×Q8—22no—
398C22×Q8—22no—
399C22×Q8—21no—
400C22×Q8—22no—
401C22×Q8—22no—
402C22×Q8—31no—
403C22×Q8—41no—
404C22×Q8—41no—
405C22×Q8C22×D311yescharacteristic
406C22×Q8C22×D311yescharacteristic
407C22×D4—21no—
408C22×D4—21no—
409C22×D4—31no—
410C22×D4—61no—
411C22×D4—61no—
412C22×D4#6711yescharacteristic
413C22×D4C22×D311yescharacteristic
414C23×C4—21no—
415C23×C4—21no—
416C23×C4—61no—
417C23×C4C22×D311yescharacteristic
418C23×C4C22×D311yescharacteristic
419#135—632no—
420C2×Q16—34no—
421C2×Q16—62no—
422C2×Q16—62no—
423C2×Q16—62no—
424C2×Q16—62no—
425C2×Q16—121no—
426C2×SD16—34no—
427C2×SD16—62no—
428C2×SD16—62no—
429C2×SD16—62no—
430C2×SD16—62no—
431C2×SD16—62no—
432C2×SD16—62no—
433C2×SD16—62no—
434C2×SD16—121no—
435C2×D8—62no—
436C2×D8—62no—
437C2×D8—62no—
438C22×C8—31no—
439C22×C8—31no—
440C22×C8—31no—
441C22×C8—31no—
442C22×C8—62no—
443C22×C8—62no—
444C22×C8—62no—
445#124—28no—
446#124—22no—
447#124—22no—
448C22⋊Q8—28no—
449C22⋊Q8—22no—
450C22⋊Q8—62no—
451C22⋊Q8—121no—
452C22⋊Q8#6714yescomplemented
453#121—28no—
454#121—22no—
455#121—22no—
456#121—62no—
457#121—121no—
458C4×Q8—22no—
459C4×Q8—22no—
460C4×D4—28no—
461C4×D4—22no—
462C4×D4—22no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—31no—
466C2×C4⋊C4—31no—
467C2×C4⋊C4—61no—
468C2×C4⋊C4#6711yescharacteristic
469C2×C4⋊C4C22×D311yescharacteristic
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—61no—
475C2×C22⋊C4—61no—
476C2×C22⋊C4—61no—
477C2×C22⋊C4—61no—
478C2×C22⋊C4—61no—
479C2×C22⋊C4#6711yescharacteristic
480C2×C22⋊C4#6711yescharacteristic
481C2×C42—21no—
482C2×C42C22×D311yescharacteristic
483#103—62no—
484#103—62no—
485#103—62no—
486#103—62no—
487#103—62no—
488#102—62no—
489#102—121no—
490#102—121no—
491C22⋊C8—62no—
492C22⋊C8—62no—
493C22⋊C8—62no—
494#95—61no—
495#95—61no—
496#95—61no—
497C23×C3—21no—
498C23×C3—21no—
499C23×C3—21no—
500C23×C3—21no—
501C23×C3—21no—
502C23×C3—21no—
503C23×C3—21no—
504C23×C3—21no—
505C23×C3—21no—
506C23×C3—21no—
507C23×C3—21no—
508C23×C3—21no—
509C23×C3—22no—
510C23×C3—41no—
511C23×C3—41no—
512C23×C3—41no—
513C23×C3—41no—
514C23×C3—41no—
515C23×C3—41no—
516C23×C3#12012yes—
517C23×C3#13512yescomplemented
518C23×C3C22×D411yescharacteristic
519C22×D3—22no—
520C22×D3—41no—
521C22×D3—41no—
522C22×D3—41no—
523C22×D3—41no—
524C22×D3—41no—
525C22×D3—41no—
526C3×Q8—22no—
527C3×Q8—22no—
528C3×Q8—22no—
529C3×Q8—22no—
530C3×Q8—22no—
531C3×Q8—48no—
532C3×Q8—41no—
533C3×Q8—41no—
534C3×Q8#12014yes—
535C3×D4—22no—
536C3×D4—22no—
537C3×D4—48no—
538C3×D4—44no—
539C3×D4—48no—
540C3×D4—41no—
541C3×D4—41no—
542C2×C3×C4—22no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—22no—
546C2×C3×C4—22no—
547C2×C3×C4—22no—
548C2×C3×C4—22no—
549C2×C3×C4—22no—
550C2×C3×C4—22no—
551C2×C3×C4—21no—
552C2×C3×C4—21no—
553C2×C3×C4—22no—
554C2×C3×C4—22no—
555C2×C3×C4—21no—
556C2×C3×C4—21no—
557C2×C3×C4—21no—
558C2×C3×C4—21no—
559C2×C3×C4—21no—
560C2×C3×C4—21no—
561C2×C3×C4—21no—
562C2×C3×C4—48no—
563C2×C3×C4—48no—
564C2×C3×C4—41no—
565C2×C3×C4—41no—
566C2×C3×C4—41no—
567C2×C3×C4—41no—
568C2×C3×C4—41no—
569C2×C3×C4—41no—
570C2×C3×C4—41no—
571C2×C3×C4—41no—
572C2×C3×C4#12012yes—
573C2×C3×C4C22×D411yescharacteristic
574C2×C3×C4C22×D411yescharacteristic
575C2×C3×C4C22×D411yescharacteristic
576C2×C3×C4C22×D411yescharacteristic
577C2×C3×C4H(5,𝔽2)11yescharacteristic
578C2×C3×C4H(5,𝔽2)11yescharacteristic
579#67—48no—
580#67—84no—
581C2×Dic3—22no—
582C2×Dic3—41no—
583C2×Dic3—41no—
584C2×Dic3—41no—
585C2×Dic3—41no—
586C2×Dic3—41no—
587C2×Dic3—41no—
588C2×Dic3—41no—
589C2×Dic3—41no—
590D12—22no—
591D12—22no—
592D12—41no—
593D12—41no—
594C4×D3—48no—
595Dic6—22no—
596Dic6—22no—
597Dic6—41no—
598Dic6—41no—
599C3⋊C8—22no—
600C3⋊C8—22no—
601C3⋊C8—41no—
602C3⋊C8—41no—
603C24—21no—
604C24—61no—
605C24C2×#6711yescharacteristic
606C24C2×#6711yescharacteristic
607#41—28no—
608#41—44no—
609#41—44no—
610#41—44no—
611#41—68no—
612#41—124no—
613#41—124no—
614#41—124no—
615C2×Q8—24no—
616C2×Q8—21no—
617C2×Q8—21no—
618C2×Q8—21no—
619C2×Q8—21no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8—32no—
625C2×Q8—42no—
626C2×Q8—42no—
627C2×Q8—44no—
628C2×Q8—44no—
629C2×Q8—44no—
630C2×Q8—44no—
631C2×Q8—61no—
632C2×Q8—61no—
633C2×Q8—61no—
634C2×Q8—61no—
635C2×Q8—61no—
636C2×Q8D3×D412yes—
637C2×Q8D3×D412yes—
638C2×Q8C2×#6712yes—
639C2×Q8C2×#6712yes—
640C2×D4—24no—
641C2×D4—22no—
642C2×D4—22no—
643C2×D4—24no—
644C2×D4—21no—
645C2×D4—21no—
646C2×D4—21no—
647C2×D4—21no—
648C2×D4—21no—
649C2×D4—32no—
650C2×D4—41no—
651C2×D4—42no—
652C2×D4—42no—
653C2×D4—42no—
654C2×D4—42no—
655C2×D4—61no—
656C2×D4—61no—
657C2×D4—61no—
658C2×D4—61no—
659C2×D4—61no—
660C2×D4—122no—
661C2×D4—122no—
662C2×D4—122no—
663C2×D4—122no—
664C2×D4—122no—
665C2×D4—241no—
666C2×D4C2×#6712yes—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—24no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—24no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—42no—
683C22×C4—42no—
684C22×C4—42no—
685C22×C4—42no—
686C22×C4—61no—
687C22×C4—61no—
688C22×C4—61no—
689C22×C4—122no—
690C22×C4—122no—
691C22×C4—122no—
692C22×C4C2×#6711yescharacteristic
693C22×C4C2×#6711yescharacteristic
694C22×C4C2×#6711yescharacteristic
695C22×C4C2×#6711yescharacteristic
696C22×C4C2×#6712yes—
697C22×C4C2×#6712yes—
698C22×C4C23×D311yescharacteristic
699Q16—68no—
700Q16—124no—
701SD16—68no—
702SD16—68no—
703SD16—124no—
704D8—68no—
705C2×C8—32no—
706C2×C8—32no—
707C2×C8—68no—
708C2×C8—61no—
709C2×C8—61no—
710C2×C8—61no—
711C2×C8—61no—
712C2×C8—61no—
713C2×C8—61no—
714C2×C8—61no—
715C2×C8—61no—
716C2×C8—61no—
717C2×C8—61no—
718C4⋊C4—24no—
719C4⋊C4—24no—
720C4⋊C4—22no—
721C4⋊C4—21no—
722C4⋊C4—61no—
723C4⋊C4—61no—
724C4⋊C4—61no—
725C4⋊C4—61no—
726C4⋊C4—122no—
727C4⋊C4C2×#6712yes—
728C22⋊C4—24no—
729C22⋊C4—24no—
730C22⋊C4—24no—
731C22⋊C4—24no—
732C22⋊C4—22no—
733C22⋊C4—22no—
734C22⋊C4—122no—
735C22⋊C4—122no—
736C22⋊C4—122no—
737C22⋊C4—241no—
738C22⋊C4—241no—
739C42—24no—
740C42—21no—
741C42—21no—
742C22×C3—22no—
743C22×C3—22no—
744C22×C3—22no—
745C22×C3—22no—
746C22×C3—22no—
747C22×C3—22no—
748C22×C3—41no—
749C22×C3—41no—
750C22×C3—41no—
751C22×C3—41no—
752C22×C3—41no—
753C22×C3—41no—
754C22×C3—41no—
755C22×C3—41no—
756C22×C3—42no—
757C22×C3—42no—
758C22×C3—42no—
759C22×C3—81no—
760C22×C3—81no—
761C22×C3—81no—
762C22×C3—81no—
763C22×C3C2×#12011yescharacteristic
764C22×C3D4211yescharacteristic
765C22×C3D4211yescharacteristic
766C22×C3C2×#13511yescharacteristic
767C22×C3#57511yescharacteristic
768C22×C3#57711yescharacteristic
769C22×C3#57811yescharacteristic
770C2×D3—42no—
771C2×D3—42no—
772C2×D3—42no—
773C2×D3—81no—
774C2×D3—81no—
775C2×D3—81no—
776C2×D3—81no—
777C3×C4—22no—
778C3×C4—24no—
779C3×C4—41no—
780C3×C4—42no—
781C3×C4—41no—
782C3×C4—42no—
783C3×C4—41no—
784C3×C4C2×#12011yescharacteristic
785C3×C4#53411yescharacteristic
786C3×C4D4211yescharacteristic
787C3×C4D4211yescharacteristic
788Dic3—42no—
789Dic3—81no—
790Dic3—81no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—21no—
795C23—21no—
796C23—21no—
797C23—21no—
798C23—21no—
799C23—21no—
800C23—21no—
801C23—21no—
802C23—21no—
803C23—22no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—62no—
811C23—121no—
812C23—121no—
813C23—121no—
814C23—121no—
815C23—121no—
816C23—121no—
817C23#95012yescomplemented
818C23#95312yes—
819C23C22×#6711yescharacteristic
820Q8—22no—
821Q8—22no—
822Q8—22no—
823Q8—22no—
824Q8—22no—
825Q8—48no—
826Q8—41no—
827Q8—41no—
828Q8—62no—
829Q8—62no—
830Q8—121no—
831Q8—121no—
832Q8#93714yes—
833D4—22no—
834D4—22no—
835D4—48no—
836D4—44no—
837D4—48no—
838D4—41no—
839D4—41no—
840D4—62no—
841D4—62no—
842D4—128no—
843D4—121no—
844D4—121no—
845D4—244no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—21no—
866C2×C4—48no—
867C2×C4—48no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—62no—
877C2×C4—128no—
878C2×C4—121no—
879C2×C4—121no—
880C2×C4—121no—
881C2×C4—121no—
882C2×C4—121no—
883C2×C4—121no—
884C2×C4—121no—
885C2×C4—121no—
886C2×C4#95312yes—
887C2×C4C2×D3×D411yescharacteristic
888C2×C4C2×D3×D411yescharacteristic
889C2×C4#100411yescharacteristic
890C2×C4#100411yescharacteristic
891C2×C4C22×#6711yescharacteristic
892C2×C4C22×#6711yescharacteristic
893C8—62no—
894C8—62no—
895C8—121no—
896C8—121no—
897C2×C3—42no—
898C2×C3—42no—
899C2×C3—82no—
900C2×C3#240311yescharacteristic
901C2×C3#300211yescharacteristic
902C2×C3#301311yescharacteristic
903C2×C3#326911yescharacteristic
904C2×C3#327111yescharacteristic
905C2×C3#328211yescharacteristic
906C2×C3#328511yescharacteristic
907D3—82no—
908C22—22no—
909C22—22no—
910C22—22no—
911C22—22no—
912C22—22no—
913C22—22no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—41no—
921C22—41no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—122no—
930C22—122no—
931C22—122no—
932C22—241no—
933C22—241no—
934C22—241no—
935C22—241no—
936C22D4×#6711yescharacteristic
937C22D4×#6711yescharacteristic
938C22C2×#95011yescharacteristic
939C22#582211yescharacteristic
940C22#583711yescharacteristic
941C22#583811yescharacteristic
942C22C2×#95311yescharacteristic
943C4—22no—
944C4—24no—
945C4—41no—
946C4—42no—
947C4—41no—
948C4—42no—
949C4—41no—
950C4—122no—
951C4—241no—
952C4—241no—
953C4C2×#93711yescharacteristic
954C4D4×#6711yescharacteristic
955C4D4×#6711yescharacteristic
956C4#580411yescharacteristic
957C3#2385411yescharacteristic, complemented, Sylow
958C2—42no—
959C2—42no—
960C2—82no—
961C2—242no—
962C2#8354311yescharacteristic
963C2#8354511yescharacteristic
964C2#8354711yescharacteristic
965C2#8354911yescharacteristic
966C2#8405211yescharacteristic
967C2#8408011yescharacteristic
968C2#8411411yescharacteristic
subgroupG/H
centerC23C22×#67
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#548C2
socleC23×C3C22×D4
hypercenterC2×#548D3
hypocenterC3#23854
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C2×C3×#548C2semidirect
2. C22×#950C2semidirect
3. C2×#5228C2semidirect
4. C2×#5227C2semidirect
5. C2×#5047C2semidirect
6. #82402C2semidirect
7. #72135C2semidirect
8. #71729C2semidirect
9. #71728C2semidirect
10. #71696C2semidirect
11. #71685C2semidirect
12. #71684C2semidirect
13. #71633C2semidirect
14. #71632C2semidirect
15. #71610C2semidirect
69. C2×#548D3semidirect
88. C2×C3×#41D4semidirect
122. C3×C22⋊Q8D4semidirect
151. C2×#216D4semidirect
157. C2×#215D4semidirect
396. C2×#41#67semidirect
452. C22⋊Q8#67semidirect
517. C23×C3#135semidirect
817. C23#950semidirect
957. C3#23854semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#5482
C22×#9502
C2×#52282
C2×#52272
C2×#50472
#824022
#721352
#717292
#717282
#716962
#716852
#716842
#716332
#716322
#716102
#238543