Finite Group Databasebeta

← #10826296

Subgroups — #10826296

Order 768.

1852 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#550C211yesmaximal, characteristic, complemented
2C22×#950C211yesmaximal, characteristic, complemented
3C2×#5239C211yesmaximal, characteristic, complemented
4C2×#5238C211yesmaximal, characteristic, complemented
5C2×#5037C211yesmaximal, characteristic, complemented
6#82402C211yesmaximal, characteristic, complemented
7#72135C211yesmaximal, characteristic, complemented
8#71768C211yesmaximal, characteristic, complemented
9#71767C211yesmaximal, characteristic, complemented
10#71685C211yesmaximal, characteristic, complemented
11#71684C211yesmaximal, characteristic, complemented
12#71681C211yesmaximal, characteristic, complemented
13#71633C211yesmaximal, characteristic, complemented
14#71632C211yesmaximal, characteristic, complemented
15#71610C211yesmaximal, characteristic, complemented
16#23857—31nomaximal, Sylow
17C22×C3×#41C2211yescharacteristic
18C22×C3×#41C2211yescharacteristic
19C22×#235C2211yescharacteristic
20C3×#550—24no—
21C3×#550—24no—
22C2×C3×#127—21no—
23C2×C3×#127C2211yescharacteristic
24C2×C3×#121—21no—
25C2×C3×#121—21no—
26C2×C3×#121C2211yescharacteristic
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×#215C2211yescharacteristic
36C22×#214C2211yescharacteristic
37C22×#214C2211yescharacteristic
38C22×#213C2211yescharacteristic
39C22×#213C2211yescharacteristic
40C2×#930C2211yescharacteristic
41C2×#924C2211yescharacteristic
42C23×C3⋊C8C2211yescharacteristic
43#5239—24no—
44#5238—24no—
45C2×#835C2211yescharacteristic
46C2×#835C2211yescharacteristic
47#5223—21no—
48C2×#832C2211yescharacteristic
49C2×#832C2211yescharacteristic
50C2×#832C2211yescharacteristic
51C2×#832C2211yescharacteristic
52#5212C2211yescharacteristic
53C2×#830C2211yescharacteristic
54C2×#830C2211yescharacteristic
55C2×#830C2211yescharacteristic
56#5037—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×#550D311yescharacteristic, complemented
70C2×#452—31no—
71C2×#449—31no—
72C2×#449—31no—
73#2407—31no—
74#2014—31no—
75#2011—31no—
76#2000—31no—
77#1999—31no—
78#1893—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—22no—
87C2×C3×#41—22no—
88C2×C3×#41—22no—
89C2×C3×#41—22no—
90C2×C3×#41—41no—
91C2×C3×#41—41no—
92C2×C3×#41—41no—
93C2×C3×#41—41no—
94C2×C3×#41D414yescomplemented
95C22×C3×Q8C2311yescharacteristic
96C22×C3×D4—21no—
97C22×C3×D4—21no—
98C22×C3×D4—21no—
99C22×C3×D4—21no—
100C22×C3×D4—21no—
101C22×C3×D4—21no—
102C22×C3×D4D411yescharacteristic
103C22×C3×D4C2311yescharacteristic
104C22×C3×D4C2311yescharacteristic
105C23×C3×C4—21no—
106C23×C3×C4—21no—
107C23×C3×C4C2311yescharacteristic
108C23×C3×C4C2311yescharacteristic
109C22×#67—21no—
110C22×#67—21no—
111C2×#235—22no—
112C2×#235—22no—
113C2×#235—22no—
114C2×#235—22no—
115C2×#235—41no—
116C2×#235—41no—
117C22×D12C2311yescharacteristic
118C22×C4×D3—21no—
119C22×Dic6C2311yescharacteristic
120C3×#127—28no—
121C3×#127—22no—
122C3×#127—22no—
123C3×#121—28no—
124C3×#121—28no—
125C3×#121—22no—
126C3×#121—22no—
127C3×#121—22no—
128C3×#121D414yescomplemented
129C3×C4×Q8—22no—
130C3×C4×Q8—22no—
131C3×C4×D4—28no—
132C3×C4×D4—22no—
133C3×C4×D4—22no—
134C2×C3×C4⋊C4—21no—
135C2×C3×C4⋊C4D411yescharacteristic
136C2×C3×C4⋊C4C2311yescharacteristic
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×#216D414yescomplemented
149C2×#215—22no—
150C2×#215—22no—
151C2×#215D414yescomplemented
152C2×#214—22no—
153C2×#214—22no—
154C2×#214—22no—
155C2×#214—22no—
156C2×#214—22no—
157C2×#214—41no—
158C2×#213—22no—
159C2×#213—22no—
160C2×#213—22no—
161C2×#213—22no—
162C2×#213—22no—
163C2×#213—41no—
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#832—22no—
184#832—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
197C22×#41C2×D311yescharacteristic
198C2×#135—64no—
199C2×#135—64no—
200C2×#135—64no—
201C22×Q16—31no—
202C22×SD16—31no—
203C22×SD16—31no—
204C22×SD16—31no—
205C22×D8—31no—
206C22×D8—31no—
207C23×C8—31no—
208#550—24no—
209#550—24no—
210C2×#127—21no—
211C2×#127C2×D311yescharacteristic
212C2×C22⋊Q8—31no—
213C2×#121—21no—
214C2×#121—21no—
215C2×#121—31no—
216C2×#121C2×D311yescharacteristic
217C2×#121C2×D311yescharacteristic
218C2×C4×Q8C2×D311yescharacteristic
219C2×C4×D4—21no—
220C2×C4×D4C2×D311yescharacteristic
221#452—64no—
222#449—64no—
223#449—64no—
224C2×#103—31no—
225C2×#103—31no—
226C2×#103—31no—
227C2×#102—31no—
228C2×#102—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×C3—21no—
248C24×C3C2×D411yescharacteristic
249C24×C3C2×D411yescharacteristic
250C23×D3—21no—
251C3×#41—28no—
252C3×#41—44no—
253C3×#41—44no—
254C3×#41—44no—
255C3×#41—44no—
256C3×#41—44no—
257C3×#41—44no—
258C3×#41—44no—
259C2×C3×Q8—21no—
260C2×C3×Q8—21no—
261C2×C3×Q8—21no—
262C2×C3×Q8C2×D412yes—
263C2×C3×Q8C2×D412yes—
264C2×C3×Q8C2×D412yes—
265C2×C3×D4—24no—
266C2×C3×D4—24no—
267C2×C3×D4—22no—
268C2×C3×D4—24no—
269C2×C3×D4—24no—
270C2×C3×D4—24no—
271C2×C3×D4—24no—
272C2×C3×D4—22no—
273C2×C3×D4—21no—
274C2×C3×D4—21no—
275C2×C3×D4—21no—
276C2×C3×D4—21no—
277C2×C3×D4—21no—
278C2×C3×D4—21no—
279C2×C3×D4—21no—
280C2×C3×D4—21no—
281C2×C3×D4—21no—
282C2×C3×D4—21no—
283C2×C3×D4—41no—
284C2×C3×D4—42no—
285C2×C3×D4—42no—
286C2×C3×D4—42no—
287C2×C3×D4—42no—
288C2×C3×D4—42no—
289C2×C3×D4—42no—
290C2×C3×D4—81no—
291C2×C3×D4—81no—
292C2×C3×D4—81no—
293C2×C3×D4—81no—
294C2×C3×D4—81no—
295C2×C3×D4—81no—
296C2×C3×D4C2×D412yes—
297C2×C3×D4C2×D412yes—
298C22×C3×C4—21no—
299C22×C3×C4—21no—
300C22×C3×C4—21no—
301C22×C3×C4—21no—
302C22×C3×C4—21no—
303C22×C3×C4—24no—
304C22×C3×C4—21no—
305C22×C3×C4—24no—
306C22×C3×C4—21no—
307C22×C3×C4—21no—
308C22×C3×C4—21no—
309C22×C3×C4—21no—
310C22×C3×C4—21no—
311C22×C3×C4—21no—
312C22×C3×C4—42no—
313C22×C3×C4—42no—
314C22×C3×C4—42no—
315C22×C3×C4—42no—
316C22×C3×C4C2×D411yescharacteristic
317C22×C3×C4C2×D411yescharacteristic
318C22×C3×C4C2×D411yescharacteristic
319C22×C3×C4C2×D412yes—
320C22×C3×C4C2×D412yes—
321C22×C3×C4C2×D411yescharacteristic
322C22×C3×C4C2411yescharacteristic
323C2×#67—42no—
324C2×#67—42no—
325C2×#67—42no—
326C2×#67—42no—
327C2×#67—42no—
328C2×#67—81no—
329C22×Dic3—21no—
330C22×Dic3—21no—
331C22×Dic3—21no—
332#235—28no—
333#235—44no—
334#235—44no—
335#235—44no—
336C2×D12—21no—
337C2×D12—21no—
338C2×D12—21no—
339C2×D12—21no—
340C2×D12—21no—
341C2×D12C2×D412yes—
342C2×C4×D3—42no—
343C2×C4×D3—42no—
344C2×C4×D3—42no—
345C2×Dic6—21no—
346C2×Dic6—21no—
347C2×Dic6—21no—
348C2×Dic6—21no—
349C2×Dic6—21no—
350C2×Dic6C2×D412yes—
351C3×C4⋊C4—24no—
352C3×C4⋊C4—22no—
353C3×C4⋊C4—21no—
354C3×C4⋊C4C2×D412yes—
355C3×C22⋊C4—24no—
356C3×C22⋊C4—22no—
357C3×C22⋊C4—24no—
358C3×C22⋊C4—22no—
359C3×C42—24no—
360C3×C42—21no—
361C3×C42—21no—
362#217—42no—
363#217—81no—
364#216—28no—
365#215—28no—
366#214—28no—
367#214—44no—
368#213—28no—
369#213—44no—
370(C2×D3)⋊C4—42no—
371(C2×D3)⋊C4—42no—
372(C2×D3)⋊C4—81no—
373C4⋊Dic3—21no—
374C4⋊Dic3—21no—
375C4⋊Dic3—21no—
376C4⋊Dic3—21no—
377Dic3⋊C4—42no—
378C2×C3⋊C8—28no—
379C2×C3⋊C8—21no—
380C2×C3⋊C8—21no—
381C2×C3⋊C8—21no—
382C2×C3⋊C8—21no—
383C2×C3⋊C8—21no—
384C2×C3⋊C8—21no—
385C2×C3⋊C8—21no—
386C2×C3⋊C8—21no—
387C2×C3⋊C8—21no—
388C2×C3⋊C8—21no—
389C2×C3⋊C8C2×D412yes—
390C2×C3⋊C8C2×D412yes—
391C2×#41—22no—
392C2×#41—22no—
393C2×#41—22no—
394C2×#41—22no—
395C2×#41—22no—
396C2×#41—22no—
397C2×#41—22no—
398C2×#41—41no—
399C2×#41—41no—
400C2×#41—41no—
401C2×#41—41no—
402C2×#41—62no—
403C2×#41—62no—
404C2×#41—62no—
405C2×#41—62no—
406C2×#41—121no—
407C2×#41—121no—
408C2×#41#6714yescomplemented
409C22×Q8—31no—
410C22×Q8C22×D311yescharacteristic
411C22×D4—21no—
412C22×D4—21no—
413C22×D4—21no—
414C22×D4—21no—
415C22×D4—21no—
416C22×D4—21no—
417C22×D4—31no—
418C22×D4—61no—
419C22×D4—61no—
420C22×D4#6711yescharacteristic
421C22×D4C22×D311yescharacteristic
422C22×D4C22×D311yescharacteristic
423C23×C4—21no—
424C23×C4—21no—
425C23×C4—61no—
426C23×C4C22×D311yescharacteristic
427C23×C4C22×D311yescharacteristic
428#135—632no—
429C2×Q16—34no—
430C2×Q16—62no—
431C2×Q16—62no—
432C2×SD16—34no—
433C2×SD16—62no—
434C2×SD16—62no—
435C2×SD16—62no—
436C2×SD16—62no—
437C2×SD16—62no—
438C2×SD16—62no—
439C2×SD16—62no—
440C2×SD16—121no—
441C2×D8—62no—
442C2×D8—62no—
443C2×D8—62no—
444C2×D8—62no—
445C2×D8—62no—
446C2×D8—121no—
447C22×C8—31no—
448C22×C8—31no—
449C22×C8—31no—
450C22×C8—31no—
451C22×C8—62no—
452C22×C8—62no—
453C22×C8—62no—
454#127—28no—
455#127—22no—
456#127—22no—
457C22⋊Q8—62no—
458C22⋊Q8—121no—
459#121—28no—
460#121—28no—
461#121—22no—
462#121—22no—
463#121—22no—
464#121—62no—
465#121—121no—
466#121#6714yescomplemented
467C4×Q8—22no—
468C4×Q8—22no—
469C4×D4—28no—
470C4×D4—22no—
471C4×D4—22no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—31no—
474C2×C4⋊C4—31no—
475C2×C4⋊C4—61no—
476C2×C4⋊C4#6711yescharacteristic
477C2×C4⋊C4C22×D311yescharacteristic
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—61no—
481C2×C22⋊C4—61no—
482C2×C22⋊C4—61no—
483C2×C22⋊C4—61no—
484C2×C22⋊C4—61no—
485C2×C22⋊C4#6711yescharacteristic
486C2×C22⋊C4#6711yescharacteristic
487C2×C42—21no—
488C2×C42C22×D311yescharacteristic
489#103—62no—
490#103—62no—
491#103—62no—
492#102—62no—
493#102—62no—
494#102—62no—
495#102—121no—
496#102—121no—
497C22⋊C8—62no—
498C22⋊C8—62no—
499C22⋊C8—62no—
500#95—61no—
501#95—61no—
502#95—61no—
503C23×C3—21no—
504C23×C3—21no—
505C23×C3—21no—
506C23×C3—21no—
507C23×C3—21no—
508C23×C3—21no—
509C23×C3—21no—
510C23×C3—22no—
511C23×C3—22no—
512C23×C3—21no—
513C23×C3—21no—
514C23×C3—21no—
515C23×C3—21no—
516C23×C3—21no—
517C23×C3—21no—
518C23×C3—41no—
519C23×C3—41no—
520C23×C3—41no—
521C23×C3—41no—
522C23×C3—41no—
523C23×C3—41no—
524C23×C3—41no—
525C23×C3—41no—
526C23×C3—41no—
527C23×C3—41no—
528C23×C3—41no—
529C23×C3—41no—
530C23×C3#12012yes—
531C23×C3C22×D411yescharacteristic
532C22×D3—22no—
533C22×D3—41no—
534C22×D3—41no—
535C22×D3—41no—
536C22×D3—41no—
537C22×D3—41no—
538C22×D3—41no—
539C3×Q8—22no—
540C3×Q8—22no—
541C3×Q8—22no—
542C3×Q8#12014yes—
543C3×D4—22no—
544C3×D4—22no—
545C3×D4—22no—
546C3×D4—22no—
547C3×D4—44no—
548C3×D4—48no—
549C3×D4—48no—
550C3×D4—48no—
551C3×D4—41no—
552C3×D4—41no—
553C3×D4—41no—
554C3×D4—41no—
555C3×D4—84no—
556C3×D4—84no—
557C3×D4—84no—
558C2×C3×C4—21no—
559C2×C3×C4—22no—
560C2×C3×C4—21no—
561C2×C3×C4—21no—
562C2×C3×C4—22no—
563C2×C3×C4—22no—
564C2×C3×C4—21no—
565C2×C3×C4—22no—
566C2×C3×C4—22no—
567C2×C3×C4—22no—
568C2×C3×C4—22no—
569C2×C3×C4—21no—
570C2×C3×C4—22no—
571C2×C3×C4—21no—
572C2×C3×C4—21no—
573C2×C3×C4—21no—
574C2×C3×C4—21no—
575C2×C3×C4—21no—
576C2×C3×C4—48no—
577C2×C3×C4—48no—
578C2×C3×C4—41no—
579C2×C3×C4—41no—
580C2×C3×C4—41no—
581C2×C3×C4—41no—
582C2×C3×C4—41no—
583C2×C3×C4—41no—
584C2×C3×C4#12012yes—
585C2×C3×C4#13512yescomplemented
586C2×C3×C4C22×D411yescharacteristic
587C2×C3×C4C22×D411yescharacteristic
588C2×C3×C4C22×D411yescharacteristic
589C2×C3×C4C22×D411yescharacteristic
590C2×C3×C4H(5,𝔽2)11yescharacteristic
591C2×C3×C4H(5,𝔽2)11yescharacteristic
592#67—48no—
593#67—84no—
594C2×Dic3—22no—
595C2×Dic3—41no—
596C2×Dic3—41no—
597C2×Dic3—41no—
598C2×Dic3—41no—
599C2×Dic3—41no—
600C2×Dic3—41no—
601C2×Dic3—41no—
602C2×Dic3—41no—
603D12—22no—
604D12—22no—
605D12—41no—
606D12—41no—
607C4×D3—48no—
608Dic6—22no—
609Dic6—22no—
610Dic6—41no—
611Dic6—41no—
612C3⋊C8—22no—
613C3⋊C8—22no—
614C3⋊C8—41no—
615C3⋊C8—41no—
616C24—21no—
617C24—21no—
618C24—61no—
619C24C2×#6711yescharacteristic
620C24C2×#6711yescharacteristic
621#41—28no—
622#41—44no—
623#41—44no—
624#41—44no—
625#41—44no—
626#41—44no—
627#41—44no—
628#41—44no—
629#41—68no—
630#41—124no—
631#41—124no—
632#41—124no—
633C2×Q8—21no—
634C2×Q8—21no—
635C2×Q8—21no—
636C2×Q8—32no—
637C2×Q8—61no—
638C2×Q8—61no—
639C2×Q8—61no—
640C2×Q8—61no—
641C2×Q8—61no—
642C2×Q8D3×D412yes—
643C2×Q8D3×D412yes—
644C2×Q8C2×#6712yes—
645C2×D4—24no—
646C2×D4—24no—
647C2×D4—22no—
648C2×D4—24no—
649C2×D4—24no—
650C2×D4—24no—
651C2×D4—24no—
652C2×D4—22no—
653C2×D4—21no—
654C2×D4—21no—
655C2×D4—21no—
656C2×D4—21no—
657C2×D4—21no—
658C2×D4—21no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—32no—
664C2×D4—41no—
665C2×D4—42no—
666C2×D4—42no—
667C2×D4—42no—
668C2×D4—42no—
669C2×D4—42no—
670C2×D4—42no—
671C2×D4—61no—
672C2×D4—61no—
673C2×D4—61no—
674C2×D4—61no—
675C2×D4—61no—
676C2×D4—81no—
677C2×D4—81no—
678C2×D4—81no—
679C2×D4—81no—
680C2×D4—81no—
681C2×D4—81no—
682C2×D4—122no—
683C2×D4—122no—
684C2×D4—122no—
685C2×D4—122no—
686C2×D4—122no—
687C2×D4—241no—
688C2×D4C2×#6712yes—
689C2×D4C2×#6712yes—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—24no—
696C22×C4—21no—
697C22×C4—24no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—42no—
705C22×C4—42no—
706C22×C4—42no—
707C22×C4—42no—
708C22×C4—61no—
709C22×C4—61no—
710C22×C4—61no—
711C22×C4—122no—
712C22×C4—122no—
713C22×C4—122no—
714C22×C4C2×#6711yescharacteristic
715C22×C4C2×#6711yescharacteristic
716C22×C4C2×#6711yescharacteristic
717C22×C4C2×#6711yescharacteristic
718C22×C4C2×#6712yes—
719C22×C4C2×#6712yes—
720C22×C4C23×D311yescharacteristic
721Q16—68no—
722SD16—68no—
723SD16—68no—
724SD16—124no—
725D8—68no—
726D8—124no—
727C2×C8—32no—
728C2×C8—32no—
729C2×C8—68no—
730C2×C8—61no—
731C2×C8—61no—
732C2×C8—61no—
733C2×C8—61no—
734C2×C8—61no—
735C2×C8—61no—
736C2×C8—61no—
737C2×C8—61no—
738C2×C8—61no—
739C2×C8—61no—
740C4⋊C4—24no—
741C4⋊C4—22no—
742C4⋊C4—21no—
743C4⋊C4—61no—
744C4⋊C4—61no—
745C4⋊C4—61no—
746C4⋊C4—61no—
747C4⋊C4—122no—
748C4⋊C4C2×#6712yes—
749C22⋊C4—24no—
750C22⋊C4—22no—
751C22⋊C4—24no—
752C22⋊C4—22no—
753C22⋊C4—122no—
754C22⋊C4—122no—
755C22⋊C4—122no—
756C22⋊C4—241no—
757C22⋊C4—241no—
758C42—24no—
759C42—21no—
760C42—21no—
761C22×C3—22no—
762C22×C3—22no—
763C22×C3—22no—
764C22×C3—41no—
765C22×C3—41no—
766C22×C3—41no—
767C22×C3—41no—
768C22×C3—42no—
769C22×C3—42no—
770C22×C3—41no—
771C22×C3—41no—
772C22×C3—42no—
773C22×C3—42no—
774C22×C3—41no—
775C22×C3—42no—
776C22×C3—42no—
777C22×C3—41no—
778C22×C3—41no—
779C22×C3—41no—
780C22×C3—41no—
781C22×C3—81no—
782C22×C3—81no—
783C22×C3—81no—
784C22×C3—81no—
785C22×C3—81no—
786C22×C3—81no—
787C22×C3—81no—
788C22×C3—81no—
789C22×C3C2×#12011yescharacteristic
790C22×C3D4211yescharacteristic
791C22×C3D4211yescharacteristic
792C22×C3C2×#13511yescharacteristic
793C22×C3#57511yescharacteristic
794C22×C3#57611yescharacteristic
795C22×C3#57711yescharacteristic
796C2×D3—42no—
797C2×D3—42no—
798C2×D3—42no—
799C2×D3—81no—
800C2×D3—81no—
801C2×D3—81no—
802C2×D3—81no—
803C3×C4—22no—
804C3×C4—24no—
805C3×C4—22no—
806C3×C4—41no—
807C3×C4—41no—
808C3×C4—42no—
809C3×C4C2×#12011yescharacteristic
810C3×C4#53411yescharacteristic
811C3×C4D4211yescharacteristic
812C3×C4D4211yescharacteristic
813Dic3—42no—
814Dic3—81no—
815Dic3—81no—
816C23—21no—
817C23—21no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—21no—
822C23—21no—
823C23—21no—
824C23—21no—
825C23—21no—
826C23—21no—
827C23—21no—
828C23—21no—
829C23—22no—
830C23—22no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23—41no—
842C23—41no—
843C23—62no—
844C23—121no—
845C23—121no—
846C23—121no—
847C23—121no—
848C23—121no—
849C23—121no—
850C23#95312yes—
851C23C22×#6711yescharacteristic
852Q8—22no—
853Q8—22no—
854Q8—22no—
855Q8—62no—
856Q8—62no—
857Q8—121no—
858Q8—121no—
859Q8#93714yes—
860D4—22no—
861D4—22no—
862D4—22no—
863D4—22no—
864D4—44no—
865D4—48no—
866D4—48no—
867D4—48no—
868D4—41no—
869D4—41no—
870D4—41no—
871D4—41no—
872D4—62no—
873D4—62no—
874D4—84no—
875D4—84no—
876D4—84no—
877D4—128no—
878D4—121no—
879D4—121no—
880D4—244no—
881C2×C4—21no—
882C2×C4—21no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—21no—
886C2×C4—21no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—21no—
893C2×C4—21no—
894C2×C4—21no—
895C2×C4—21no—
896C2×C4—21no—
897C2×C4—22no—
898C2×C4—21no—
899C2×C4—48no—
900C2×C4—48no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—62no—
908C2×C4—128no—
909C2×C4—121no—
910C2×C4—121no—
911C2×C4—121no—
912C2×C4—121no—
913C2×C4—121no—
914C2×C4—121no—
915C2×C4—121no—
916C2×C4—121no—
917C2×C4#95012yescomplemented
918C2×C4#95312yes—
919C2×C4C2×D3×D411yescharacteristic
920C2×C4C2×D3×D411yescharacteristic
921C2×C4#100411yescharacteristic
922C2×C4#100411yescharacteristic
923C2×C4C22×#6711yescharacteristic
924C2×C4C22×#6711yescharacteristic
925C8—62no—
926C8—62no—
927C8—121no—
928C8—121no—
929C2×C3—42no—
930C2×C3—81no—
931C2×C3—82no—
932C2×C3—82no—
933C2×C3#240311yescharacteristic
934C2×C3#300211yescharacteristic
935C2×C3#301211yescharacteristic
936C2×C3#326811yescharacteristic
937C2×C3#327111yescharacteristic
938C2×C3#328411yescharacteristic
939C2×C3#328711yescharacteristic
940D3—82no—
941C22—22no—
942C22—22no—
943C22—22no—
944C22—41no—
945C22—41no—
946C22—41no—
947C22—41no—
948C22—42no—
949C22—42no—
950C22—41no—
951C22—41no—
952C22—42no—
953C22—42no—
954C22—41no—
955C22—41no—
956C22—41no—
957C22—41no—
958C22—41no—
959C22—42no—
960C22—42no—
961C22—81no—
962C22—81no—
963C22—81no—
964C22—81no—
965C22—81no—
966C22—81no—
967C22—81no—
968C22—81no—
969C22—122no—
970C22—122no—
971C22—122no—
972C22—241no—
973C22—241no—
974C22—241no—
975C22—241no—
976C22D4×#6711yescharacteristic
977C22D4×#6711yescharacteristic
978C22C2×#95011yescharacteristic
979C22#582211yescharacteristic
980C22#583511yescharacteristic
981C22#583611yescharacteristic
982C22C2×#95311yescharacteristic
983C4—22no—
984C4—24no—
985C4—22no—
986C4—41no—
987C4—41no—
988C4—42no—
989C4—122no—
990C4—241no—
991C4—241no—
992C4C2×#93711yescharacteristic
993C4D4×#6711yescharacteristic
994C4D4×#6711yescharacteristic
995C4#580411yescharacteristic
996C3#2385711yescharacteristic, complemented, Sylow
997C2—42no—
998C2—81no—
999C2—82no—
1000C2—82no—
1001C2—242no—
1002C2#8357711yescharacteristic
1003C2#8357911yescharacteristic
1004C2#8358311yescharacteristic
1005C2#8358511yescharacteristic
1006C2#8405211yescharacteristic
1007C2#8408011yescharacteristic
1008C2#8410211yescharacteristic
subgroupG/H
centerC23C22×#67
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#550C2
socleC23×C3C22×D4
hypercenterC2×#550D3
hypocenterC3#23857
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
1. C2×C3×#550C2semidirect
2. C22×#950C2semidirect
3. C2×#5239C2semidirect
4. C2×#5238C2semidirect
5. C2×#5037C2semidirect
6. #82402C2semidirect
7. #72135C2semidirect
8. #71768C2semidirect
9. #71767C2semidirect
10. #71685C2semidirect
11. #71684C2semidirect
12. #71681C2semidirect
13. #71633C2semidirect
14. #71632C2semidirect
15. #71610C2semidirect
69. C2×#550D3semidirect
94. C2×C3×#41D4semidirect
128. C3×#121D4semidirect
148. C2×#216D4semidirect
151. C2×#215D4semidirect
408. C2×#41#67semidirect
466. #121#67semidirect
585. C2×C3×C4#135semidirect
917. C2×C4#950semidirect
996. C3#23857semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#5502
C22×#9502
C2×#52392
C2×#52382
C2×#50372
#824022
#721352
#717682
#717672
#716852
#716842
#716812
#716332
#716322
#716102
#238573