Finite Group Databasebeta

← #10826281

Subgroups — #10826281

Order 768.

1734 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×#67C211yesmaximal, characteristic
2C22×D3×Q16C211yesmaximal, characteristic, complemented
3C2×C3×#451C211yesmaximal, characteristic, complemented
4C2×#5228C211yesmaximal, characteristic, complemented
5C2×#5186C211yesmaximal, characteristic, complemented
6#82751C211yesmaximal, characteristic
7#72073C211yesmaximal, characteristic, complemented
8#72065C211yesmaximal, characteristic, complemented
9#71700C211yesmaximal, characteristic, complemented
10#70283C211yesmaximal, characteristic, complemented
11#70270C211yesmaximal, characteristic, complemented
12#70266C211yesmaximal, characteristic, complemented
13#70239C211yesmaximal, characteristic, complemented
14#69964C211yesmaximal, characteristic, complemented
15#69957C211yesmaximal, characteristic
16#23856—31nomaximal, Sylow
17C23×C3×Q8C2211yescharacteristic
18C22×D3×Q8C2211yescharacteristic
19C22×D3×Q8C2211yescharacteristic
20C22×C3×Q16C2211yescharacteristic
21C22×C3×Q16C2211yescharacteristic
22C2×C3×C22⋊Q8C2211yescharacteristic
23Q8×#67—24no—
24Q8×#67—24no—
25C2×#946—21no—
26C2×#946C2211yescharacteristic
27C2×Q8×Dic3C2211yescharacteristic
28C2×#944—21no—
29C2×#944C2211yescharacteristic
30C22×#216C2211yescharacteristic
31C22×#216C2211yescharacteristic
32C22×#216C2211yescharacteristic
33C2×C4×#67—21no—
34C2×C4×#67C2211yescharacteristic
35C2×#924—21no—
36C2×#924C2211yescharacteristic
37C2×#924C2211yescharacteristic
38C2×D3×Q16—24no—
39C2×D3×Q16—24no—
40C2×D3×Q16—24no—
41C22×Dic12C2211yescharacteristic
42C22×D3×C8C2211yescharacteristic
43C3×#451—24no—
44C2×C3×#103C2211yescharacteristic
45C2×C3×#103C2211yescharacteristic
46C2×C3×C22⋊C8C2211yescharacteristic
47#5229C2211yescharacteristic
48#5228—24no—
49C2×#835C2211yescharacteristic
50C2×#835C2211yescharacteristic
51C2×#835C2211yescharacteristic
52C2×#830C2211yescharacteristic
53#5186—24no—
54C2×(C2×D3)⋊C8C2211yescharacteristic
55C2×#816C2211yescharacteristic
56C2×#816C2211yescharacteristic
57#4989—21no—
58#4987C2211yescharacteristic
59#4979—21no—
60#4973C2211yescharacteristic
61C2×#810C2211yescharacteristic
62#4956—21no—
63#4947—21no—
64#4551C2211yescharacteristic
65#4550C2211yescharacteristic
66#4550C2211yescharacteristic
67#4529C2211yescharacteristic
68C23×Q16—31no—
69C2×D4×Q8—31no—
70C2×#451—31no—
71C2×#451—31no—
72C2×#451D311yescharacteristic, complemented
73#2409—31no—
74#2016—31no—
75#2016—31no—
76#2001—31no—
77#2001—31no—
78#1892—31no—
79#1878—31no—
80#1878—31no—
81#1869—31no—
82#1787—31no—
83C22×C3×Q8—22no—
84C22×C3×Q8—22no—
85C22×C3×Q8—21no—
86C22×C3×Q8—22no—
87C22×C3×Q8—22no—
88C22×C3×Q8—41no—
89C22×C3×Q8—41no—
90C22×C3×Q8C2311yescharacteristic
91C22×C3×Q8C2311yescharacteristic
92C22×C3×Q8C2311yescharacteristic
93C23×C3×C4—21no—
94C23×C3×C4C2311yescharacteristic
95C22×#67D411yescharacteristic
96C2×D3×Q8—22no—
97C2×D3×Q8—22no—
98C2×D3×Q8—22no—
99C2×D3×Q8—22no—
100C2×D3×Q8—22no—
101C2×D3×Q8—22no—
102C2×D3×Q8—22no—
103C2×D3×Q8—41no—
104C2×D3×Q8—41no—
105C2×D3×Q8—41no—
106C2×D3×Q8—41no—
107C2×D3×Q8D414yes—
108C22×C4×D3—21no—
109C22×C4×D3—21no—
110C22×C4×D3C2311yescharacteristic
111C22×Dic6—21no—
112C22×Dic6—21no—
113C22×Dic6C2311yescharacteristic
114C22×Dic6C2311yescharacteristic
115C2×C3×Q16—22no—
116C2×C3×Q16—22no—
117C2×C3×Q16—22no—
118C2×C3×Q16—22no—
119C2×C3×Q16—41no—
120C2×C3×Q16D414yescomplemented
121C22×C3×C8C2311yescharacteristic
122C22×C3×C8C2311yescharacteristic
123C3×C22⋊Q8—22no—
124C3×C22⋊Q8—41no—
125C2×C3×C4⋊C4—21no—
126C2×C3×C4⋊C4C2311yescharacteristic
127C2×C3×C22⋊C4—21no—
128C2×#217—21no—
129C2×#217—21no—
130C2×#217D411yescharacteristic
131#946—28no—
132#946—22no—
133#946D414yes—
134Q8×Dic3—22no—
135Q8×Dic3—22no—
136#944—28no—
137#944—22no—
138#944—22no—
139C2×#216—22no—
140C2×#216—22no—
141C2×#216—22no—
142C2×#216—22no—
143C2×#216—22no—
144C2×#216—22no—
145C2×#216—22no—
146C2×#216—41no—
147C2×#216D414yescomplemented
148C4×#67—28no—
149C4×#67—22no—
150C4×#67—22no—
151C2×(C2×D3)⋊C4—21no—
152C2×(C2×D3)⋊C4—21no—
153C2×(C2×D3)⋊C4D411yescharacteristic
154C2×C4⋊Dic3—21no—
155C2×C4⋊Dic3C2311yescharacteristic
156C2×C4⋊Dic3C2311yescharacteristic
157#924—28no—
158#924—22no—
159#924—22no—
160#924—22no—
161#924—41no—
162C2×Dic3⋊C4—21no—
163C2×Dic3⋊C4—21no—
164C2×Dic3⋊C4—21no—
165C2×Dic3⋊C4—21no—
166C2×Dic3⋊C4—21no—
167C2×Dic3⋊C4D411yescharacteristic
168C2×C4×Dic3—21no—
169C2×C4×Dic3C2311yescharacteristic
170C22×C3⋊C8C2311yescharacteristic
171C22×C3⋊C8C2311yescharacteristic
172D3×Q16—232no—
173C2×Dic12—22no—
174C2×Dic12—22no—
175C2×Dic12—22no—
176C2×D3×C8—22no—
177C2×D3×C8—22no—
178C2×D3×C8—22no—
179C3×#103—22no—
180C3×#103—22no—
181C3×C22⋊C8—22no—
182#835—22no—
183#835—22no—
184#835—22no—
185C3⋊#95—21no—
186C3⋊#95—21no—
187C3⋊#95—21no—
188C3⋊#95—21no—
189C3⋊#95—21no—
190#830—22no—
191(C2×D3)⋊C8—22no—
192#816—22no—
193#816—41no—
194#810—41no—
195C23×Q8—31no—
196C23×Q8—31no—
197C23×Q8C2×D311yescharacteristic
198C22×Q16—31no—
199C22×Q16—31no—
200C22×Q16—31no—
201C22×Q16—31no—
202C22×Q16—64no—
203C22×Q16—64no—
204C22×Q16—64no—
205C22×Q16C2×D311yescharacteristic
206C22×Q16C2×D311yescharacteristic
207C23×C8—31no—
208D4×Q8—64no—
209D4×Q8—64no—
210C2×C4⋊Q8—31no—
211C2×C4⋊Q8—61no—
212C2×C22⋊Q8—31no—
213C2×C22⋊Q8—31no—
214C2×C22⋊Q8—31no—
215C2×C22⋊Q8—61no—
216C2×C22⋊Q8—61no—
217C2×C22⋊Q8C2×D311yescharacteristic
218C2×C4×Q8—31no—
219C2×C4×D4—31no—
220C2×C4×D4—61no—
221#451—24no—
222#451—64no—
223#451—64no—
224C2×#103—31no—
225C2×#103—31no—
226C2×#103—31no—
227C2×#103—31no—
228C2×#103—31no—
229C2×#103—31no—
230C2×#103C2×D311yescharacteristic
231C2×#103C2×D311yescharacteristic
232C2×C22⋊C8—31no—
233C2×C22⋊C8—31no—
234C2×C22⋊C8C2×D311yescharacteristic
235#395—61no—
236#393—61no—
237#391—31no—
238#391—31no—
239#386—61no—
240#385—61no—
241#380—31no—
242#340—31no—
243#340—31no—
244#336—31no—
245#336—31no—
246C24×C3C2×D411yescharacteristic
247C23×D3C2×D411yescharacteristic
248C2×C3×Q8—24no—
249C2×C3×Q8—21no—
250C2×C3×Q8—21no—
251C2×C3×Q8—21no—
252C2×C3×Q8—21no—
253C2×C3×Q8—21no—
254C2×C3×Q8—21no—
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—42no—
263C2×C3×Q8—42no—
264C2×C3×Q8—44no—
265C2×C3×Q8—44no—
266C2×C3×Q8—44no—
267C2×C3×Q8—44no—
268C2×C3×Q8C2×D412yes—
269C2×C3×Q8C2×D412yes—
270C2×C3×Q8C2×D412yes—
271C2×C3×Q8C2×D412yes—
272C2×C3×Q8C2×D412yes—
273C22×C3×C4—21no—
274C22×C3×C4—24no—
275C22×C3×C4—21no—
276C22×C3×C4—21no—
277C22×C3×C4—21no—
278C22×C3×C4—21no—
279C22×C3×C4—21no—
280C22×C3×C4—21no—
281C22×C3×C4—21no—
282C22×C3×C4—21no—
283C22×C3×C4—21no—
284C22×C3×C4—42no—
285C22×C3×C4—42no—
286C22×C3×C4C2×D411yescharacteristic
287C22×C3×C4C2411yescharacteristic
288C2×#67—22no—
289C2×#67—22no—
290C2×#67Q1614yescomplemented
291C22×Dic3—21no—
292C22×Dic3—21no—
293C22×Dic3—21no—
294C22×Dic3—21no—
295C22×Dic3C2×D411yescharacteristic
296C22×Dic3C2×D411yescharacteristic
297C22×Dic3C2×D411yescharacteristic
298D3×Q8—28no—
299D3×Q8—28no—
300D3×Q8—44no—
301D3×Q8—44no—
302D3×Q8—44no—
303D3×Q8—44no—
304D3×Q8—44no—
305D3×Q8—44no—
306C2×C4×D3—21no—
307C2×C4×D3—21no—
308C2×C4×D3—21no—
309C2×C4×D3—21no—
310C2×C4×D3—24no—
311C2×C4×D3—42no—
312C2×C4×D3—42no—
313C2×C4×D3—42no—
314C2×C4×D3—42no—
315C2×C4×D3—42no—
316C2×C4×D3C2×D412yes—
317C2×C4×D3C2×D412yes—
318C2×Dic6—21no—
319C2×Dic6—21no—
320C2×Dic6—21no—
321C2×Dic6—21no—
322C2×Dic6—21no—
323C2×Dic6—21no—
324C2×Dic6—21no—
325C2×Dic6—21no—
326C2×Dic6—21no—
327C2×Dic6—21no—
328C2×Dic6—24no—
329C2×Dic6—42no—
330C2×Dic6—42no—
331C2×Dic6—42no—
332C2×Dic6—42no—
333C2×Dic6—42no—
334C2×Dic6C2×D412yes—
335C2×Dic6C2×D412yes—
336C3×Q16—28no—
337C3×Q16—44no—
338C2×C3×C8—21no—
339C2×C3×C8—21no—
340C2×C3×C8—21no—
341C2×C3×C8—21no—
342C2×C3×C8—21no—
343C2×C3×C8C2×D412yes—
344C3×C4⋊C4—21no—
345C3×C4⋊C4—21no—
346C3×C4⋊C4—42no—
347C3×C22⋊C4—42no—
348#217—24no—
349#217—22no—
350#217—42no—
351#216—28no—
352#216—28no—
353#216—44no—
354(C2×D3)⋊C4—24no—
355(C2×D3)⋊C4—22no—
356(C2×D3)⋊C4—42no—
357C4⋊Dic3—24no—
358C4⋊Dic3—21no—
359C4⋊Dic3—21no—
360C4⋊Dic3—21no—
361C4⋊Dic3C2×D412yes—
362Dic3⋊C4—24no—
363Dic3⋊C4—24no—
364Dic3⋊C4—24no—
365Dic3⋊C4—24no—
366Dic3⋊C4—22no—
367Dic3⋊C4—42no—
368C4×Dic3—24no—
369C4×Dic3—21no—
370C4×Dic3—21no—
371C2×C3⋊C8—21no—
372C2×C3⋊C8—21no—
373C2×C3⋊C8—21no—
374C2×C3⋊C8—21no—
375C2×C3⋊C8—21no—
376C2×C3⋊C8C2×D412yes—
377Dic12—28no—
378D3×C8—28no—
379C22×Q8—22no—
380C22×Q8—22no—
381C22×Q8—21no—
382C22×Q8—22no—
383C22×Q8—22no—
384C22×Q8—34no—
385C22×Q8—31no—
386C22×Q8—31no—
387C22×Q8—41no—
388C22×Q8—41no—
389C22×Q8—61no—
390C22×Q8—61no—
391C22×Q8—62no—
392C22×Q8—62no—
393C22×Q8—62no—
394C22×Q8—62no—
395C22×Q8—62no—
396C22×Q8—62no—
397C22×Q8—62no—
398C22×Q8—121no—
399C22×Q8—121no—
400C22×Q8—121no—
401C22×Q8—121no—
402C22×Q8C22×D311yescharacteristic
403C22×Q8C22×D311yescharacteristic
404C22×Q8C22×D311yescharacteristic
405C22×D4—31no—
406C23×C4—21no—
407C23×C4—31no—
408C23×C4—61no—
409C23×C4—61no—
410C23×C4C22×D311yescharacteristic
411C2×Q16—22no—
412C2×Q16—22no—
413C2×Q16—22no—
414C2×Q16—22no—
415C2×Q16—34no—
416C2×Q16—41no—
417C2×Q16—62no—
418C2×Q16—62no—
419C2×Q16—62no—
420C2×Q16—632no—
421C2×Q16—62no—
422C2×Q16—62no—
423C2×Q16—62no—
424C2×Q16—62no—
425C2×Q16—62no—
426C2×Q16—62no—
427C2×Q16—62no—
428C2×Q16—121no—
429C2×Q16#6714yescomplemented
430C22×C8—31no—
431C22×C8—31no—
432C22×C8—62no—
433C22×C8—62no—
434C22×C8—62no—
435C22×C8C22×D311yescharacteristic
436C22×C8C22×D311yescharacteristic
437C4⋊Q8—62no—
438C4⋊Q8—68no—
439C4⋊Q8—62no—
440C22⋊Q8—22no—
441C22⋊Q8—34no—
442C22⋊Q8—41no—
443C22⋊Q8—62no—
444C22⋊Q8—62no—
445C22⋊Q8—68no—
446C22⋊Q8—62no—
447C22⋊Q8—68no—
448C22⋊Q8—62no—
449C22⋊Q8—121no—
450C4×Q8—62no—
451C4×Q8—62no—
452C4×D4—62no—
453C4×D4—62no—
454C4×D4—68no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—31no—
457C2×C4⋊C4—31no—
458C2×C4⋊C4—31no—
459C2×C4⋊C4—61no—
460C2×C4⋊C4—61no—
461C2×C4⋊C4—61no—
462C2×C4⋊C4—61no—
463C2×C4⋊C4—61no—
464C2×C4⋊C4—61no—
465C2×C4⋊C4C22×D311yescharacteristic
466C2×C22⋊C4—21no—
467C2×C22⋊C4—31no—
468C2×C22⋊C4—31no—
469C2×C22⋊C4—61no—
470C2×C22⋊C4—61no—
471C2×C22⋊C4—61no—
472C2×C22⋊C4—61no—
473C2×C42—31no—
474C2×C42—61no—
475#103—22no—
476#103—22no—
477#103—62no—
478#103—62no—
479#103—62no—
480#103—62no—
481#103—121no—
482#103—121no—
483C22⋊C8—22no—
484C22⋊C8—62no—
485C22⋊C8—62no—
486#95—61no—
487#95—61no—
488#95—61no—
489#95—61no—
490#95—61no—
491C23×C3—21no—
492C23×C3—21no—
493C23×C3—21no—
494C23×C3—21no—
495C23×C3—21no—
496C23×C3—21no—
497C23×C3C2×Q1612yescomplemented
498C23×C3C22×D411yescharacteristic
499C22×D3—21no—
500C22×D3—21no—
501C22×D3—21no—
502C22×D3—21no—
503C22×D3#12012yes—
504C22×D3C2×Q1612yes—
505C22×D3#13712yes—
506C3×Q8—22no—
507C3×Q8—22no—
508C3×Q8—22no—
509C3×Q8—22no—
510C3×Q8—22no—
511C3×Q8—22no—
512C3×Q8—22no—
513C3×Q8—48no—
514C3×Q8—41no—
515C3×Q8—41no—
516C3×Q8—41no—
517C3×Q8—41no—
518C3×Q8#12014yes—
519C2×C3×C4—22no—
520C2×C3×C4—22no—
521C2×C3×C4—22no—
522C2×C3×C4—22no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—22no—
526C2×C3×C4—21no—
527C2×C3×C4—48no—
528C2×C3×C4—41no—
529C2×C3×C4—41no—
530C2×C3×C4—41no—
531C2×C3×C4—41no—
532C2×C3×C4—41no—
533C2×C3×C4—41no—
534C2×C3×C4—41no—
535C2×C3×C4—41no—
536C2×C3×C4—41no—
537C2×C3×C4—41no—
538C2×C3×C4—41no—
539C2×C3×C4C22×D411yescharacteristic
540C2×C3×C4C22×D411yescharacteristic
541C2×C3×C4C22×D411yescharacteristic
542C2×C3×C4C22×D411yescharacteristic
543C2×C3×C4H(5,𝔽2)11yescharacteristic
544C2×C3×C4H(5,𝔽2)11yescharacteristic
545#67—28no—
546C2×Dic3—21no—
547C2×Dic3—21no—
548C2×Dic3—21no—
549C2×Dic3—21no—
550C2×Dic3—21no—
551C2×Dic3—22no—
552C2×Dic3—22no—
553C2×Dic3—22no—
554C2×Dic3—21no—
555C2×Dic3—21no—
556C2×Dic3—41no—
557C2×Dic3—41no—
558C2×Dic3—41no—
559C2×Dic3—41no—
560C2×Dic3—41no—
561C2×Dic3—41no—
562C2×Dic3—41no—
563C2×Dic3—41no—
564C2×Dic3—41no—
565C2×Dic3#12012yes—
566C2×Dic3C2×Q1612yescomplemented
567C4×D3—22no—
568C4×D3—22no—
569C4×D3—22no—
570C4×D3—22no—
571C4×D3—48no—
572C4×D3—48no—
573Dic6—22no—
574Dic6—22no—
575Dic6—22no—
576Dic6—22no—
577Dic6—48no—
578Dic6—48no—
579Dic6—41no—
580Dic6—41no—
581Dic6—41no—
582Dic6—41no—
583C3×C8—22no—
584C3×C8—41no—
585C3⋊C8—22no—
586C3⋊C8—41no—
587C24—31no—
588C24D3×D411yescharacteristic
589C2×Q8—24no—
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×Q8—21no—
598C2×Q8—21no—
599C2×Q8—21no—
600C2×Q8—21no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×Q8—32no—
604C2×Q8—32no—
605C2×Q8—42no—
606C2×Q8—42no—
607C2×Q8—44no—
608C2×Q8—44no—
609C2×Q8—44no—
610C2×Q8—44no—
611C2×Q8—64no—
612C2×Q8—61no—
613C2×Q8—61no—
614C2×Q8—68no—
615C2×Q8—68no—
616C2×Q8—61no—
617C2×Q8—61no—
618C2×Q8—61no—
619C2×Q8—61no—
620C2×Q8—61no—
621C2×Q8—61no—
622C2×Q8—61no—
623C2×Q8—61no—
624C2×Q8—122no—
625C2×Q8—122no—
626C2×Q8—122no—
627C2×Q8—122no—
628C2×Q8—122no—
629C2×Q8—124no—
630C2×Q8—124no—
631C2×Q8—124no—
632C2×Q8—124no—
633C2×Q8—124no—
634C2×Q8—124no—
635C2×Q8D3×D412yes—
636C2×Q8D3×D412yes—
637C2×Q8D3×D412yes—
638C2×Q8C2×#6712yes—
639C2×Q8C2×#6712yes—
640C2×D4—34no—
641C2×D4—62no—
642C2×D4—62no—
643C22×C4—21no—
644C22×C4—24no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—31no—
655C22×C4—31no—
656C22×C4—32no—
657C22×C4—32no—
658C22×C4—31no—
659C22×C4—42no—
660C22×C4—42no—
661C22×C4—64no—
662C22×C4—61no—
663C22×C4—61no—
664C22×C4—61no—
665C22×C4—61no—
666C22×C4—61no—
667C22×C4—61no—
668C22×C4—61no—
669C22×C4—61no—
670C22×C4—122no—
671C22×C4—122no—
672C22×C4—122no—
673C22×C4—122no—
674C22×C4—122no—
675C22×C4D3×D411yescharacteristic
676C22×C4C23×D311yescharacteristic
677Q16—28no—
678Q16—44no—
679Q16—68no—
680Q16—68no—
681Q16—68no—
682Q16—124no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—32no—
689C2×C8—68no—
690C2×C8—61no—
691C2×C8—61no—
692C2×C8—61no—
693C2×C8—61no—
694C2×C8—61no—
695C2×C8C2×#6712yes—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—32no—
699C4⋊C4—42no—
700C4⋊C4—62no—
701C4⋊C4—64no—
702C4⋊C4—64no—
703C4⋊C4—64no—
704C4⋊C4—64no—
705C4⋊C4—64no—
706C4⋊C4—61no—
707C4⋊C4—61no—
708C4⋊C4—61no—
709C4⋊C4—122no—
710C22⋊C4—42no—
711C22⋊C4—62no—
712C22⋊C4—64no—
713C22⋊C4—62no—
714C22⋊C4—64no—
715C22⋊C4—122no—
716C22⋊C4—122no—
717C42—64no—
718C42—61no—
719C42—61no—
720C22×C3—22no—
721C22×C3—22no—
722C22×C3—22no—
723C22×C3—41no—
724C22×C3—41no—
725C22×C3—41no—
726C22×C3—41no—
727C22×C3C2×#12011yescharacteristic
728C22×C3D4211yescharacteristic
729C22×C3D4211yescharacteristic
730C22×C3C22×Q1611yescharacteristic
731C22×C3C2×#13711yescharacteristic
732C22×C3#57811yescharacteristic
733C22×C3#57811yescharacteristic
734C2×D3—22no—
735C2×D3—22no—
736C2×D3—22no—
737C2×D3—22no—
738C2×D3—22no—
739C2×D3—22no—
740C2×D3#45114yescomplemented
741C3×C4—24no—
742C3×C4—42no—
743C3×C4—41no—
744C3×C4—42no—
745C3×C4—81no—
746C3×C4C2×#12011yescharacteristic
747C3×C4#53411yescharacteristic
748C3×C4D4211yescharacteristic
749C3×C4D4211yescharacteristic
750Dic3—22no—
751Dic3—22no—
752Dic3—42no—
753Dic3—42no—
754Dic3—41no—
755Dic3—42no—
756Dic3—81no—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—32no—
764C23—32no—
765C23—32no—
766C23—61no—
767C23—61no—
768C23—61no—
769C23—61no—
770C23D3×Q1612yescomplemented
771C23C2×D3×D411yescharacteristic
772Q8—22no—
773Q8—22no—
774Q8—22no—
775Q8—22no—
776Q8—22no—
777Q8—22no—
778Q8—22no—
779Q8—48no—
780Q8—41no—
781Q8—41no—
782Q8—41no—
783Q8—41no—
784Q8—62no—
785Q8—62no—
786Q8—62no—
787Q8—62no—
788Q8—128no—
789Q8—128no—
790Q8—121no—
791Q8—121no—
792Q8—121no—
793Q8—121no—
794Q8#93714yes—
795D4—68no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—21no—
801C2×C4—22no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—32no—
805C2×C4—32no—
806C2×C4—48no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—61no—
819C2×C4—61no—
820C2×C4—61no—
821C2×C4—61no—
822C2×C4—62no—
823C2×C4—62no—
824C2×C4—62no—
825C2×C4—62no—
826C2×C4—61no—
827C2×C4—61no—
828C2×C4—62no—
829C2×C4—61no—
830C2×C4—62no—
831C2×C4—62no—
832C2×C4—128no—
833C2×C4—128no—
834C2×C4—121no—
835C2×C4—121no—
836C2×C4—121no—
837C2×C4—121no—
838C2×C4—121no—
839C2×C4—121no—
840C2×C4—121no—
841C2×C4—121no—
842C2×C4—121no—
843C2×C4C2×D3×D411yescharacteristic
844C2×C4C2×D3×D411yescharacteristic
845C2×C4C2×D3×D411yescharacteristic
846C2×C4#100411yescharacteristic
847C2×C4#100411yescharacteristic
848C2×C4C22×#6711yescharacteristic
849C8—22no—
850C8—41no—
851C8—62no—
852C8—121no—
853C2×C3—42no—
854C2×C3#240311yescharacteristic
855C2×C3C2×#45111yescharacteristic
856C2×C3#301111yescharacteristic
857C2×C3#327011yescharacteristic
858C2×C3#327011yescharacteristic
859C2×C3D4×Q1611yescharacteristic
860C2×C3D4×Q1611yescharacteristic
861D3—24no—
862C22—22no—
863C22—22no—
864C22—22no—
865C22—34no—
866C22—41no—
867C22—41no—
868C22—41no—
869C22—41no—
870C22—62no—
871C22—62no—
872C22—62no—
873C22—62no—
874C22—62no—
875C22—62no—
876C22D3×#12011yescharacteristic
877C22#559011yescharacteristic
878C22C2×D3×Q1611yescharacteristic
879C22#576611yescharacteristic
880C22D3×#13711yescharacteristic
881C22#577911yescharacteristic
882C22D4×#6711yescharacteristic
883C4—24no—
884C4—41no—
885C4—42no—
886C4—42no—
887C4—62no—
888C4—62no—
889C4—81no—
890C4—121no—
891C4—122no—
892C4—122no—
893C4—122no—
894C4—241no—
895C4#558911yescharacteristic
896C4#559011yescharacteristic
897C4C2×#93711yescharacteristic
898C4D4×#6711yescharacteristic
899C3#2385611yescharacteristic, complemented, Sylow
900C2—42no—
901C2—64no—
902C2D3×#45111yescharacteristic
903C2#8018511yescharacteristic
904C2#8020911yescharacteristic
905C2#8021111yescharacteristic
906C2#8260411yescharacteristic
907C2Q16×#6711yescharacteristic
908C2#8398911yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#451C2
socleC23×C3C22×D4
prime radicalC22×#67D4
hypercenterC2×#451D3
hypocenterC3#23856
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#451

Complements

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

NH ≅ G/Ntype
2. C22×D3×Q16C2semidirect
3. C2×C3×#451C2semidirect
4. C2×#5228C2semidirect
5. C2×#5186C2semidirect
7. #72073C2semidirect
8. #72065C2semidirect
9. #71700C2semidirect
10. #70283C2semidirect
11. #70270C2semidirect
12. #70266C2semidirect
13. #70239C2semidirect
14. #69964C2semidirect
72. C2×#451D3semidirect
120. C2×C3×Q16D4semidirect
147. C2×#216D4semidirect
290. C2×#67Q16semidirect
429. C2×Q16#67semidirect
497. C23×C3C2×Q16semidirect
566. C2×Dic3C2×Q16semidirect
740. C2×D3#451semidirect
770. C23D3×Q16semidirect
899. C3#23856semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×#672
C22×D3×Q162
C2×C3×#4512
C2×#52282
C2×#51862
#827512
#720732
#720652
#717002
#702832
#702702
#702662
#702392
#699642
#699572
#238563