Finite Group Databasebeta

← #10848848

Subgroups — #10848848

Order 768.

1116 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5603C211yesmaximal, characteristic
2C2×#5167C211yesmaximal, characteristic, complemented
3#82786C211yesmaximal, characteristic, complemented
4C2×#4792C211yesmaximal, characteristic, complemented
5C3×#2000C211yesmaximal, characteristic
6#72047C211yesmaximal, characteristic, complemented
7#71700C211yesmaximal, characteristic, complemented
8#71685C211yesmaximal, characteristic
9#70281C211yesmaximal, characteristic, complemented
10#70171C211yesmaximal, characteristic, complemented
11#70158C211yesmaximal, characteristic, complemented
12#69964C211yesmaximal, characteristic, complemented
13#69907C211yesmaximal, characteristic, complemented
14#68908C211yesmaximal, characteristic, complemented
15#68806C211yesmaximal, characteristic, complemented
16#25613—31nomaximal, Sylow
17C22×C3×SD16C2211yescharacteristic
18C2×C3×C22⋊Q8C2211yescharacteristic
19C2×C3×#121C2211yescharacteristic
20C2×#944C2211yescharacteristic
21C22×#216C2211yescharacteristic
22C2×#936—21no—
23C2×#936C2211yescharacteristic
24C2×#935—21no—
25C2×D4×Dic3C2211yescharacteristic
26C22×#214C2211yescharacteristic
27C2×#926C2211yescharacteristic
28C2×#924C2211yescharacteristic
29C2×#924C2211yescharacteristic
30C22×Dic12C2211yescharacteristic
31#5603—24no—
32#5603—24no—
33C2×#888C2211yescharacteristic
34C2×#887C2211yescharacteristic
35C2×#879—21no—
36C2×#878—21no—
37C2×C3×#103C2211yescharacteristic
38C2×C3×#102C2211yescharacteristic
39C2×C3×C22⋊C8C2211yescharacteristic
40#5229C2211yescharacteristic
41C2×#835C2211yescharacteristic
42C2×#832C2211yescharacteristic
43C2×#830C2211yescharacteristic
44#5167—24no—
45C2×#816C2211yescharacteristic
46C2×#816C2211yescharacteristic
47C2×#815C2211yescharacteristic
48C2×C8×Dic3C2211yescharacteristic
49#4982—21no—
50#4982—21no—
51#4977C2211yescharacteristic
52#4973C2211yescharacteristic
53C2×#810C2211yescharacteristic
54C2×#810C2211yescharacteristic
55#4952—21no—
56#4952—21no—
57#4792—24no—
58C3×#340C2211yescharacteristic
59#4551C2211yescharacteristic
60#4550C2211yescharacteristic
61#4550C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#542—31no—
65C2×#497—31no—
66C2×#487—31no—
67#2621—31no—
68#2001—31no—
69#2001—31no—
70#2000—31no—
71#2000D311yescharacteristic
72#1993—31no—
73#1958—31no—
74#1878—31no—
75#1878—31no—
76#1877—31no—
77#1877—31no—
78#1750—31no—
79C22×C3×Q8C2311yescharacteristic
80C22×C3×D4—21no—
81C22×C3×D4C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C23×Dic3—21no—
84C22×Dic6—21no—
85C22×Dic6C2311yescharacteristic
86C22×Dic6C2311yescharacteristic
87C2×C3×SD16—22no—
88C2×C3×SD16—22no—
89C2×C3×SD16—41no—
90C22×C3×C8C2311yescharacteristic
91C22×C3×C8C2311yescharacteristic
92C3×C22⋊Q8—41no—
93C3×C22⋊Q8—41no—
94C3×#121—22no—
95C3×#121—22no—
96C2×C3×C4⋊C4—21no—
97C2×C3×C4⋊C4C2311yescharacteristic
98C2×C3×C4⋊C4C2311yescharacteristic
99C2×C3×C22⋊C4—21no—
100C2×C3×C22⋊C4—21no—
101C2×#217—21no—
102C2×#217—21no—
103C2×#217—21no—
104C2×#217—21no—
105C2×#217—21no—
106C2×#217D411yescharacteristic
107C2×#217D411yescharacteristic
108#944—22no—
109#944—22no—
110C2×#216—22no—
111C2×#216—22no—
112C2×#216—41no—
113#936—28no—
114#936—22no—
115#936D414yes—
116#935—28no—
117D4×Dic3—22no—
118D4×Dic3—22no—
119C2×#214—22no—
120C2×#214—22no—
121C2×#214—41no—
122#926—22no—
123#926—22no—
124C2×C4⋊Dic3D411yescharacteristic
125C2×C4⋊Dic3D411yescharacteristic
126C2×C4⋊Dic3C2311yescharacteristic
127C2×C4⋊Dic3C2311yescharacteristic
128#924—22no—
129#924—22no—
130#924—41no—
131#924—41no—
132C2×Dic3⋊C4—21no—
133C2×Dic3⋊C4—21no—
134C2×Dic3⋊C4—21no—
135C2×Dic3⋊C4—21no—
136C2×Dic3⋊C4—21no—
137C2×Dic3⋊C4—21no—
138C2×C4×Dic3—21no—
139C2×C4×Dic3C2311yescharacteristic
140C2×C4×Dic3C2311yescharacteristic
141C22×C3⋊C8C2311yescharacteristic
142C22×C3⋊C8C2311yescharacteristic
143C2×Dic12—22no—
144C2×Dic12—22no—
145C2×Dic12—41no—
146#888—22no—
147#888D414yes—
148#887—22no—
149#887—22no—
150#879—28no—
151#878—28no—
152C3×#103—22no—
153C3×#102—41no—
154C3×C22⋊C8—22no—
155#835—22no—
156#832—41no—
157C3⋊#95—21no—
158C3⋊#95—21no—
159C3⋊#95—21no—
160C3⋊#95—21no—
161C3⋊#95—21no—
162C3⋊#95—21no—
163#830—22no—
164#816—22no—
165#816—41no—
166#815—22no—
167C8×Dic3—22no—
168#810—22no—
169#810—41no—
170C22×Q16—31no—
171C22×Q16—31no—
172C22×SD16—31no—
173C22×SD16C2×D311yescharacteristic
174#542—64no—
175#542—64no—
176C2×C4⋊Q8—31no—
177C2×C4⋊Q8—31no—
178C2×#126—61no—
179C2×#124—31no—
180C2×#124—61no—
181C2×#123—61no—
182C2×C22⋊Q8—31no—
183C2×C22⋊Q8—31no—
184C2×C22⋊Q8—61no—
185C2×C22⋊Q8C2×D311yescharacteristic
186C2×#121C2×D311yescharacteristic
187C2×C4×Q8—31no—
188C2×C4×D4—31no—
189C2×#117—31no—
190#497—64no—
191#487—64no—
192C2×#103—31no—
193C2×#103—31no—
194C2×#103—31no—
195C2×#103—31no—
196C2×#103—31no—
197C2×#103C2×D311yescharacteristic
198C2×#102—31no—
199C2×#102C2×D311yescharacteristic
200C2×C22⋊C8—31no—
201C2×C22⋊C8C2×D311yescharacteristic
202C2×#97—31no—
203C2×C4×C8—31no—
204#398—61no—
205#398—61no—
206#397—61no—
207#397—61no—
208#391—31no—
209#391—31no—
210#382—31no—
211#340—31no—
212#340—31no—
213#340—31no—
214#340C2×D311yescharacteristic
215#336—31no—
216#336—31no—
217C24×C3—21no—
218C24×C3C2×D411yescharacteristic
219C2×C3×Q8—21no—
220C2×C3×Q8—21no—
221C2×C3×Q8—21no—
222C2×C3×Q8—21no—
223C2×C3×Q8—21no—
224C2×C3×Q8—21no—
225C2×C3×D4—24no—
226C2×C3×D4—21no—
227C2×C3×D4—21no—
228C2×C3×D4—21no—
229C2×C3×D4—21no—
230C2×C3×D4—21no—
231C2×C3×D4—81no—
232C2×C3×D4—81no—
233C2×C3×D4C2×D412yes—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4C2×D411yescharacteristic
244C22×C3×C4C2411yescharacteristic
245C22×Dic3—21no—
246C22×Dic3—21no—
247C22×Dic3—24no—
248C22×Dic3—21no—
249C22×Dic3—21no—
250C22×Dic3—81no—
251C22×Dic3—81no—
252C22×Dic3C2×D411yescharacteristic
253C22×Dic3C2×D411yescharacteristic
254C22×Dic3C2×D411yescharacteristic
255C22×Dic3C2×D411yescharacteristic
256C2×Dic6—21no—
257C2×Dic6—21no—
258C2×Dic6—21no—
259C2×Dic6—21no—
260C2×Dic6—21no—
261C2×Dic6—21no—
262C2×Dic6—21no—
263C2×Dic6—21no—
264C2×Dic6—21no—
265C2×Dic6—21no—
266C2×Dic6—21no—
267C2×Dic6—24no—
268C2×Dic6—81no—
269C2×Dic6—81no—
270C2×Dic6C2×D412yes—
271C3×SD16—44no—
272C2×C3×C8—21no—
273C2×C3×C8—21no—
274C2×C3×C8—21no—
275C2×C3×C8—21no—
276C2×C3×C8—21no—
277C2×C3×C8#4112yes—
278C3×C4⋊C4—21no—
279C3×C4⋊C4—21no—
280C3×C4⋊C4—21no—
281C3×C4⋊C4—42no—
282C3×C4⋊C4C2×D412yes—
283C3×C22⋊C4—24no—
284C3×C22⋊C4—42no—
285#217—24no—
286#217—24no—
287#217—24no—
288#217—24no—
289#217—22no—
290#217—22no—
291#217—42no—
292#216—44no—
293#214—44no—
294C4⋊Dic3—21no—
295C4⋊Dic3—22no—
296C4⋊Dic3—22no—
297C4⋊Dic3—21no—
298C4⋊Dic3—21no—
299C4⋊Dic3C2×D412yes—
300Dic3⋊C4—24no—
301Dic3⋊C4—24no—
302Dic3⋊C4—24no—
303Dic3⋊C4—42no—
304Dic3⋊C4—42no—
305Dic3⋊C4—42no—
306C4×Dic3—24no—
307C4×Dic3—21no—
308C4×Dic3—21no—
309C4×Dic3C2×D412yes—
310C4×Dic3C2×D412yes—
311C2×C3⋊C8—21no—
312C2×C3⋊C8—21no—
313C2×C3⋊C8—21no—
314C2×C3⋊C8—21no—
315C2×C3⋊C8—21no—
316C2×C3⋊C8#4112yes—
317Dic12—44no—
318C22×Q8—31no—
319C22×Q8—31no—
320C22×Q8—61no—
321C22×Q8C22×D311yescharacteristic
322C22×D4—21no—
323C22×D4C22×D311yescharacteristic
324C23×C4—61no—
325C23×C4C22×D311yescharacteristic
326C2×Q16—62no—
327C2×Q16—62no—
328C2×Q16—62no—
329C2×Q16—62no—
330C2×Q16—121no—
331C2×Q16—121no—
332C2×SD16—22no—
333C2×SD16—22no—
334C2×SD16—41no—
335C2×SD16—62no—
336C2×SD16—62no—
337C2×SD16—121no—
338C22×C8—31no—
339C22×C8—31no—
340C22×C8C22×D311yescharacteristic
341C22×C8C22×D311yescharacteristic
342C4⋊Q8—34no—
343C4⋊Q8—62no—
344C4⋊Q8—62no—
345C4⋊Q8—62no—
346#126—68no—
347#124—34no—
348#124—62no—
349#124—68no—
350#123—68no—
351C22⋊Q8—41no—
352C22⋊Q8—41no—
353C22⋊Q8—68no—
354C22⋊Q8—62no—
355C22⋊Q8—62no—
356C22⋊Q8—121no—
357C22⋊Q8—121no—
358#121—22no—
359#121—22no—
360C4×Q8—62no—
361C4×Q8—62no—
362C4×D4—62no—
363C4×D4—62no—
364#117—62no—
365#117—62no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—31no—
368C2×C4⋊C4—31no—
369C2×C4⋊C4—31no—
370C2×C4⋊C4—31no—
371C2×C4⋊C4—61no—
372C2×C4⋊C4—61no—
373C2×C4⋊C4—61no—
374C2×C4⋊C4—61no—
375C2×C4⋊C4—61no—
376C2×C4⋊C4—61no—
377C2×C4⋊C4C22×D311yescharacteristic
378C2×C4⋊C4C22×D311yescharacteristic
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—31no—
382C2×C22⋊C4—31no—
383C2×C22⋊C4—61no—
384C2×C22⋊C4—61no—
385C2×C22⋊C4—61no—
386C2×C22⋊C4—61no—
387C2×C22⋊C4—61no—
388C2×C42—31no—
389C2×C42—31no—
390C2×C42—61no—
391#103—22no—
392#103—62no—
393#103—62no—
394#103—62no—
395#103—121no—
396#103—121no—
397#102—41no—
398#102—121no—
399C22⋊C8—22no—
400C22⋊C8—62no—
401#97—62no—
402C4×C8—62no—
403#95—61no—
404#95—61no—
405#95—61no—
406#95—61no—
407#95—61no—
408#95—61no—
409C23×C3—21no—
410C23×C3—22no—
411C23×C3—21no—
412C23×C3—21no—
413C23×C3—21no—
414C23×C3—21no—
415C23×C3—21no—
416C23×C3—21no—
417C23×C3—41no—
418C23×C3—41no—
419C23×C3—41no—
420C23×C3—41no—
421C23×C3—41no—
422C23×C3—41no—
423C23×C3C22×D411yescharacteristic
424C3×Q8—41no—
425C3×Q8—41no—
426C3×Q8—41no—
427C3×Q8—41no—
428C3×D4—22no—
429C3×D4—22no—
430C3×D4—41no—
431C3×D4—41no—
432C3×D4—84no—
433C2×C3×C4—22no—
434C2×C3×C4—21no—
435C2×C3×C4—21no—
436C2×C3×C4—21no—
437C2×C3×C4—41no—
438C2×C3×C4—41no—
439C2×C3×C4—41no—
440C2×C3×C4—41no—
441C2×C3×C4—41no—
442C2×C3×C4—41no—
443C2×C3×C4—41no—
444C2×C3×C4—41no—
445C2×C3×C4—41no—
446C2×C3×C4—41no—
447C2×C3×C4—41no—
448C2×C3×C4—41no—
449C2×C3×C4C22×D411yescharacteristic
450C2×C3×C4C22×D411yescharacteristic
451C2×C3×C4C2×#4111yescharacteristic
452C2×C3×C4C2×#4111yescharacteristic
453C2×C3×C4H(5,𝔽2)11yescharacteristic
454C2×C3×C4H(5,𝔽2)11yescharacteristic
455C2×Dic3—21no—
456C2×Dic3—21no—
457C2×Dic3—21no—
458C2×Dic3—21no—
459C2×Dic3—21no—
460C2×Dic3—21no—
461C2×Dic3—22no—
462C2×Dic3—22no—
463C2×Dic3—21no—
464C2×Dic3—21no—
465C2×Dic3—21no—
466C2×Dic3—21no—
467C2×Dic3—41no—
468C2×Dic3—41no—
469C2×Dic3—41no—
470C2×Dic3—41no—
471C2×Dic3—41no—
472C2×Dic3—41no—
473C2×Dic3—41no—
474C2×Dic3—41no—
475C2×Dic3—41no—
476C2×Dic3—41no—
477C2×Dic3—84no—
478C2×Dic3#12012yes—
479C2×Dic3#12012yes—
480Dic6—22no—
481Dic6—22no—
482Dic6—41no—
483Dic6—41no—
484Dic6—41no—
485Dic6—41no—
486Dic6—41no—
487Dic6—41no—
488Dic6—84no—
489C3×C8—22no—
490C3×C8—41no—
491C3⋊C8—22no—
492C3⋊C8—41no—
493C24—21no—
494C24D3×D411yescharacteristic
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—32no—
502C2×Q8—64no—
503C2×Q8—61no—
504C2×Q8—61no—
505C2×Q8—61no—
506C2×Q8—61no—
507C2×Q8—61no—
508C2×Q8—61no—
509C2×Q8—61no—
510C2×Q8—61no—
511C2×Q8—61no—
512C2×Q8—61no—
513C2×Q8—61no—
514C2×Q8—241no—
515C2×Q8—241no—
516C2×D4—24no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—81no—
523C2×D4—81no—
524C2×D4D3×D412yes—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—31no—
535C22×C4—31no—
536C22×C4—31no—
537C22×C4—31no—
538C22×C4—61no—
539C22×C4—61no—
540C22×C4—64no—
541C22×C4—61no—
542C22×C4—61no—
543C22×C4—241no—
544C22×C4—241no—
545C22×C4D3×D411yescharacteristic
546C22×C4C23×D311yescharacteristic
547Q16—124no—
548Q16—124no—
549SD16—44no—
550SD16—124no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—32no—
557C2×C8—61no—
558C2×C8—61no—
559C2×C8—61no—
560C2×C8—61no—
561C2×C8—61no—
562C2×C8#23712yes—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—32no—
567C4⋊C4—42no—
568C4⋊C4—62no—
569C4⋊C4—62no—
570C4⋊C4—64no—
571C4⋊C4—64no—
572C4⋊C4—64no—
573C4⋊C4—61no—
574C4⋊C4—61no—
575C4⋊C4—61no—
576C4⋊C4—122no—
577C4⋊C4—122no—
578C4⋊C4—122no—
579C4⋊C4D3×D412yes—
580C22⋊C4—24no—
581C22⋊C4—42no—
582C22⋊C4—62no—
583C22⋊C4—62no—
584C22⋊C4—64no—
585C22⋊C4—64no—
586C22⋊C4—64no—
587C22⋊C4—64no—
588C22⋊C4—122no—
589C42—32no—
590C42—32no—
591C42—64no—
592C42—61no—
593C42—61no—
594C22×C3—41no—
595C22×C3—41no—
596C22×C3—41no—
597C22×C3—42no—
598C22×C3—41no—
599C22×C3—41no—
600C22×C3—42no—
601C22×C3—41no—
602C22×C3—41no—
603C22×C3—42no—
604C22×C3—81no—
605C22×C3—81no—
606C22×C3—81no—
607C22×C3—81no—
608C22×C3C2×#12011yescharacteristic
609C22×C3#53211yescharacteristic
610C22×C3#53511yescharacteristic
611C22×C3#57711yescharacteristic
612C22×C3#57711yescharacteristic
613C22×C3#57811yescharacteristic
614C22×C3#57811yescharacteristic
615C3×C4—41no—
616C3×C4—42no—
617C3×C4—81no—
618C3×C4—81no—
619C3×C4#54611yescharacteristic
620C3×C4#54611yescharacteristic
621C3×C4#55011yescharacteristic
622C3×C4#55011yescharacteristic
623Dic3—22no—
624Dic3—22no—
625Dic3—42no—
626Dic3—42no—
627Dic3—41no—
628Dic3—41no—
629Dic3—81no—
630Dic3—81no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—22no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23C2×D3×D411yescharacteristic
646Q8—41no—
647Q8—41no—
648Q8—41no—
649Q8—41no—
650Q8—62no—
651Q8—62no—
652Q8—121no—
653Q8—121no—
654Q8—121no—
655Q8—121no—
656Q8—121no—
657Q8—121no—
658Q8—244no—
659D4—22no—
660D4—22no—
661D4—41no—
662D4—41no—
663D4—84no—
664C2×C4—22no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—32no—
669C2×C4—32no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—61no—
683C2×C4—61no—
684C2×C4—61no—
685C2×C4—61no—
686C2×C4—61no—
687C2×C4—61no—
688C2×C4—61no—
689C2×C4—61no—
690C2×C4—61no—
691C2×C4—62no—
692C2×C4—61no—
693C2×C4—62no—
694C2×C4—121no—
695C2×C4—121no—
696C2×C4—121no—
697C2×C4—121no—
698C2×C4—121no—
699C2×C4—121no—
700C2×C4—121no—
701C2×C4—121no—
702C2×C4—121no—
703C2×C4—121no—
704C2×C4—244no—
705C2×C4C2×D3×D411yescharacteristic
706C2×C4C2×D3×D411yescharacteristic
707C2×C4C2×#23711yescharacteristic
708C2×C4#100411yescharacteristic
709C2×C4#100411yescharacteristic
710C2×C4D3×#4111yescharacteristic
711C8—22no—
712C8—41no—
713C8—62no—
714C8—121no—
715C2×C3—81no—
716C2×C3—82no—
717C2×C3#243111yescharacteristic
718C2×C3#300911yescharacteristic
719C2×C3#301111yescharacteristic
720C2×C3#317811yescharacteristic
721C2×C3#317811yescharacteristic
722C2×C3#322511yescharacteristic
723C2×C3#322511yescharacteristic
724C22—42no—
725C22—41no—
726C22—41no—
727C22—42no—
728C22—41no—
729C22—42no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—81no—
735C22—81no—
736C22—81no—
737C22—81no—
738C22D3×#12011yescharacteristic
739C22#559211yescharacteristic
740C22#559611yescharacteristic
741C22#576211yescharacteristic
742C22#577111yescharacteristic
743C22#577511yescharacteristic
744C22#577911yescharacteristic
745C4—42no—
746C4—41no—
747C4—62no—
748C4—62no—
749C4—81no—
750C4—81no—
751C4—121no—
752C4—122no—
753C4—121no—
754C4—122no—
755C4—241no—
756C4—241no—
757C4#559111yescharacteristic
758C4#559911yescharacteristic
759C4#561011yescharacteristic
760C4#571811yescharacteristic
761C3#2561311yescharacteristic, complemented, Sylow
762C2—81no—
763C2—82no—
764C2#7667211yescharacteristic
765C2#8005911yescharacteristic
766C2#8008011yescharacteristic
767C2#8014811yescharacteristic
768C2#8023011yescharacteristic
769C2#8063611yescharacteristic
770C2#8078811yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2000C2
socleC23×C3C22×D4
prime radicalC2×C3×#121C22
hypercenter#2000D3
hypocenterC3#25613
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2000

Complements

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

NH ≅ G/Ntype
2. C2×#5167C2semidirect
3. #82786C2semidirect
4. C2×#4792C2semidirect
6. #72047C2semidirect
7. #71700C2semidirect
9. #70281C2semidirect
10. #70171C2semidirect
11. #70158C2semidirect
12. #69964C2semidirect
13. #69907C2semidirect
14. #68908C2semidirect
15. #68806C2semidirect
761. C3#25613semidirect

Maximal subgroups

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

subgroupindex
C2×#56032
C2×#51672
#827862
C2×#47922
C3×#20002
#720472
#717002
#716852
#702812
#701712
#701582
#699642
#699072
#689082
#688062
#256133