Finite Group Databasebeta

← #10847428

Subgroups — #10847428

Order 768.

1226 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5600C211yesmaximal, characteristic, complemented
2C2×C3×#466C211yesmaximal, characteristic
3#82699C211yesmaximal, characteristic, complemented
4C2×#5041C211yesmaximal, characteristic, complemented
5#72045C211yesmaximal, characteristic, complemented
6#72037C211yesmaximal, characteristic, complemented
7#71972C211yesmaximal, characteristic, complemented
8C2×#4550C211yesmaximal, characteristic, complemented
9#71681C211yesmaximal, characteristic, complemented
10#70642C211yesmaximal, characteristic, complemented
11#70618C211yesmaximal, characteristic, complemented
12#70216C211yesmaximal, characteristic, complemented
13#70213C211yesmaximal, characteristic, complemented
14#70169C211yesmaximal, characteristic, complemented
15#70164C211yesmaximal, characteristic, complemented
16#25500—31nomaximal, Sylow
17C22×C3×D8C2211yescharacteristic
18C23×C3×C8C2211yescharacteristic
19C2×C3×#121C2211yescharacteristic
20C2×C3×#121C2211yescharacteristic
21C2×#936C2211yescharacteristic
22C2×#935—21no—
23C2×#935—21no—
24C2×D4×Dic3—21no—
25C2×D4×Dic3C2211yescharacteristic
26C22×#214C2211yescharacteristic
27C2×#924C2211yescharacteristic
28C22×C4×Dic3C2211yescharacteristic
29C23×C3⋊C8C2211yescharacteristic
30#5600—24no—
31#5600—24no—
32C2×#890C2211yescharacteristic
33C2×#887C2211yescharacteristic
34C2×#879—21no—
35C2×#877—21no—
36C3×#466—24no—
37C2×C3×#107C2211yescharacteristic
38C2×C3×#102C2211yescharacteristic
39C2×C3×#102C2211yescharacteristic
40#5221C2211yescharacteristic
41#5221C2211yescharacteristic
42#5220—21no—
43C2×#832C2211yescharacteristic
44C2×#832C2211yescharacteristic
45C2×#832C2211yescharacteristic
46#5212C2211yescharacteristic
47C2×#816C2211yescharacteristic
48C2×#816C2211yescharacteristic
49#5041—24no—
50#4972C2211yescharacteristic
51#4972C2211yescharacteristic
52C2×#810C2211yescharacteristic
53C2×#808C2211yescharacteristic
54#4944—21no—
55#4944—21no—
56#4551C2211yescharacteristic
57#4551C2211yescharacteristic
58#4550C2211yescharacteristic
59#4550C2211yescharacteristic
60#4550C2211yescharacteristic
61#4550C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#529—31no—
65C2×#466D311yescharacteristic
66C2×#465—31no—
67#2854—31no—
68#2059—31no—
69#2042—31no—
70#2025—31no—
71#2012—31no—
72#1893—31no—
73#1892—31no—
74#1880—31no—
75#1879—31no—
76#1864—31no—
77#1863—31no—
78C2×#336—31no—
79C22×C3×D4—21no—
80C22×C3×D4—21no—
81C22×C3×D4C2311yescharacteristic
82C22×C3×D4C2311yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C23×Dic3—21no—
85C23×Dic3D411yescharacteristic
86C23×Dic3D411yescharacteristic
87C22×Dic6C2311yescharacteristic
88C2×C3×D8—22no—
89C2×C3×D8—22no—
90C2×C3×D8—41no—
91C22×C3×C8—22no—
92C22×C3×C8—22no—
93C22×C3×C8—41no—
94C22×C3×C8C2311yescharacteristic
95C22×C3×C8C2311yescharacteristic
96C3×#121—22no—
97C3×#121—22no—
98C3×#121—22no—
99C3×#121D414yes—
100C2×C3×C4⋊C4C2311yescharacteristic
101C2×C3×C4⋊C4C2311yescharacteristic
102C2×C3×C22⋊C4—21no—
103C2×C3×C22⋊C4—21no—
104C2×#217—21no—
105C2×#217—21no—
106C2×#217—21no—
107C2×#217—21no—
108C2×#217—21no—
109C2×#217—21no—
110C2×#217—21no—
111C2×#217—21no—
112C2×#217—21no—
113#936—22no—
114#936—22no—
115#935—28no—
116#935—44no—
117D4×Dic3—28no—
118D4×Dic3—22no—
119D4×Dic3—22no—
120C2×#214—22no—
121C2×#214—22no—
122C2×#214—41no—
123C2×C4⋊Dic3—21no—
124C2×C4⋊Dic3C2311yescharacteristic
125C2×C4⋊Dic3C2311yescharacteristic
126C2×C4⋊Dic3C2311yescharacteristic
127#924—22no—
128#924D414yes—
129C2×Dic3⋊C4—21no—
130C2×Dic3⋊C4—21no—
131C2×Dic3⋊C4—21no—
132C2×Dic3⋊C4—21no—
133C2×Dic3⋊C4—21no—
134C2×C4×Dic3—22no—
135C2×C4×Dic3—22no—
136C2×C4×Dic3—21no—
137C2×C4×Dic3D411yescharacteristic
138C2×C4×Dic3D411yescharacteristic
139C2×C4×Dic3C2311yescharacteristic
140C2×C4×Dic3C2311yescharacteristic
141C22×C3⋊C8—22no—
142C22×C3⋊C8—22no—
143C22×C3⋊C8—41no—
144C22×C3⋊C8C2311yescharacteristic
145C22×C3⋊C8C2311yescharacteristic
146#890—22no—
147#890—22no—
148#887—22no—
149#887—22no—
150#879—28no—
151#877—28no—
152C3×#107—22no—
153C3×#102—22no—
154C3×#102—22no—
155#832—22no—
156#832—22no—
157#832—41no—
158C3⋊#95—21no—
159C3⋊#95—21no—
160C3⋊#95—21no—
161#816—22no—
162#816—41no—
163#810—22no—
164#808—22no—
165C22×SD16—31no—
166C22×D8C2×D311yescharacteristic
167C23×C8—31no—
168C23×C8C2×D311yescharacteristic
169#529—64no—
170#529—64no—
171C2×#126—61no—
172C2×#125—31no—
173C2×#124—31no—
174C2×#123—61no—
175C2×#123—61no—
176C2×C22⋊Q8—31no—
177C2×#121C2×D311yescharacteristic
178C2×#121C2×D311yescharacteristic
179C2×C4×Q8—31no—
180C2×C4×D4—31no—
181C2×C4×D4—61no—
182C2×#117—61no—
183C22×C42—31no—
184#466—24no—
185#465—64no—
186C2×#107C2×D311yescharacteristic
187C2×#106—31no—
188C2×#103—31no—
189C2×#103—31no—
190C2×#103—31no—
191C2×#102—31no—
192C2×#102—31no—
193C2×#102—31no—
194C2×#102C2×D311yescharacteristic
195C2×#102C2×D311yescharacteristic
196#390—31no—
197#390—31no—
198#389—31no—
199#389—31no—
200#388—61no—
201#388—61no—
202#386—61no—
203#380—31no—
204#340—31no—
205#340—31no—
206#340—31no—
207#340—31no—
208#336—31no—
209#336—31no—
210#336—31no—
211#336—31no—
212C24×C3—21no—
213C24×C3—21no—
214C24×C3C2×D411yescharacteristic
215C2×C3×D4—24no—
216C2×C3×D4—21no—
217C2×C3×D4—21no—
218C2×C3×D4—21no—
219C2×C3×D4—21no—
220C2×C3×D4—21no—
221C2×C3×D4—21no—
222C2×C3×D4—21no—
223C2×C3×D4—21no—
224C2×C3×D4—21no—
225C2×C3×D4—21no—
226C2×C3×D4—21no—
227C2×C3×D4—42no—
228C2×C3×D4—42no—
229C2×C3×D4—42no—
230C2×C3×D4—42no—
231C2×C3×D4—42no—
232C2×C3×D4C2×D412yes—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4C2×D411yescharacteristic
240C22×C3×C4C2×D412yes—
241C22×C3×C4C2×D412yes—
242C22×C3×C4C2411yescharacteristic
243C22×Dic3—24no—
244C22×Dic3—22no—
245C22×Dic3—22no—
246C22×Dic3—22no—
247C22×Dic3—22no—
248C22×Dic3—21no—
249C22×Dic3—21no—
250C22×Dic3—22no—
251C22×Dic3—21no—
252C22×Dic3—21no—
253C22×Dic3—41no—
254C22×Dic3—42no—
255C22×Dic3—42no—
256C22×Dic3C2×D411yescharacteristic
257C22×Dic3C2×D411yescharacteristic
258C22×Dic3C2×D411yescharacteristic
259C22×Dic3C2×D411yescharacteristic
260C2×Dic6—21no—
261C2×Dic6—21no—
262C2×Dic6—21no—
263C2×Dic6—21no—
264C2×Dic6—21no—
265C2×Dic6C2×D412yes—
266C3×D8—44no—
267C2×C3×C8—21no—
268C2×C3×C8—21no—
269C2×C3×C8—21no—
270C2×C3×C8—21no—
271C2×C3×C8—21no—
272C2×C3×C8—44no—
273C2×C3×C8#4112yes—
274C3×C4⋊C4—21no—
275C3×C4⋊C4—21no—
276C3×C4⋊C4—21no—
277C3×C4⋊C4C2×D412yes—
278C3×C22⋊C4—24no—
279C3×C22⋊C4—42no—
280#217—24no—
281#217—24no—
282#217—24no—
283#217—24no—
284#217—42no—
285#217—42no—
286#217—42no—
287#217—42no—
288#217—42no—
289#214—44no—
290C4⋊Dic3—24no—
291C4⋊Dic3—21no—
292C4⋊Dic3—21no—
293C4⋊Dic3—21no—
294C4⋊Dic3—21no—
295C4⋊Dic3—21no—
296C4⋊Dic3C2×D412yes—
297Dic3⋊C4—24no—
298Dic3⋊C4—24no—
299Dic3⋊C4—24no—
300Dic3⋊C4—42no—
301Dic3⋊C4—42no—
302C4×Dic3—24no—
303C4×Dic3—22no—
304C4×Dic3—22no—
305C4×Dic3—21no—
306C4×Dic3—21no—
307C4×Dic3—21no—
308C4×Dic3—21no—
309C2×C3⋊C8—21no—
310C2×C3⋊C8—21no—
311C2×C3⋊C8—21no—
312C2×C3⋊C8—21no—
313C2×C3⋊C8—21no—
314C2×C3⋊C8—44no—
315C2×C3⋊C8#4112yes—
316C22×Q8—31no—
317C22×D4—21no—
318C22×D4—21no—
319C22×D4C22×D311yescharacteristic
320C22×D4C22×D311yescharacteristic
321C23×C4—31no—
322C23×C4—31no—
323C23×C4—61no—
324C23×C4C22×D311yescharacteristic
325C2×SD16—62no—
326C2×SD16—62no—
327C2×SD16—121no—
328C2×D8—22no—
329C2×D8—22no—
330C2×D8—41no—
331C22×C8—22no—
332C22×C8—22no—
333C22×C8—31no—
334C22×C8—31no—
335C22×C8—41no—
336C22×C8—62no—
337C22×C8—62no—
338C22×C8—121no—
339C22×C8C22×D311yescharacteristic
340C22×C8C22×D311yescharacteristic
341#126—68no—
342#125—62no—
343#125—62no—
344#124—62no—
345#124—62no—
346#123—68no—
347#123—124no—
348C22⋊Q8—34no—
349C22⋊Q8—62no—
350#121—22no—
351#121—22no—
352#121—22no—
353#121#6714yes—
354C4×Q8—62no—
355C4×Q8—62no—
356C4×D4—62no—
357C4×D4—68no—
358C4×D4—62no—
359#117—68no—
360C2×C4⋊C4—31no—
361C2×C4⋊C4—31no—
362C2×C4⋊C4—31no—
363C2×C4⋊C4—61no—
364C2×C4⋊C4—61no—
365C2×C4⋊C4—61no—
366C2×C4⋊C4—61no—
367C2×C4⋊C4—61no—
368C2×C4⋊C4—61no—
369C2×C4⋊C4C22×D311yescharacteristic
370C2×C4⋊C4C22×D311yescharacteristic
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—61no—
374C2×C22⋊C4—61no—
375C2×C22⋊C4—61no—
376C2×C22⋊C4—61no—
377C2×C22⋊C4—61no—
378C2×C22⋊C4—61no—
379C2×C22⋊C4—61no—
380C2×C22⋊C4—61no—
381C2×C22⋊C4—61no—
382C2×C42—31no—
383C2×C42—31no—
384C2×C42—31no—
385C2×C42—31no—
386C2×C42—61no—
387C2×C42—62no—
388C2×C42—62no—
389#107—22no—
390#106—62no—
391#103—62no—
392#103—62no—
393#103—121no—
394#102—22no—
395#102—22no—
396#102—62no—
397#102—62no—
398#102—121no—
399#95—61no—
400#95—61no—
401#95—61no—
402C23×C3—21no—
403C23×C3—21no—
404C23×C3—21no—
405C23×C3—21no—
406C23×C3—22no—
407C23×C3—41no—
408C23×C3—41no—
409C23×C3—41no—
410C23×C3—41no—
411C23×C3—41no—
412C23×C3—41no—
413C23×C3—41no—
414C23×C3—41no—
415C23×C3—41no—
416C23×C3—41no—
417C23×C3—41no—
418C23×C3—41no—
419C23×C3—41no—
420C23×C3#12012yes—
421C23×C3#13512yes—
422C23×C3AGL(1,ℤ/8)12yes—
423C23×C3C22×D411yescharacteristic
424C3×D4—22no—
425C3×D4—22no—
426C3×D4—48no—
427C3×D4—41no—
428C3×D4—41no—
429C3×D4—41no—
430C3×D4—41no—
431C3×D4—41no—
432C3×D4—41no—
433C3×D4—84no—
434C2×C3×C4—21no—
435C2×C3×C4—21no—
436C2×C3×C4—22no—
437C2×C3×C4—22no—
438C2×C3×C4—22no—
439C2×C3×C4—22no—
440C2×C3×C4—22no—
441C2×C3×C4—41no—
442C2×C3×C4—41no—
443C2×C3×C4—41no—
444C2×C3×C4—41no—
445C2×C3×C4—41no—
446C2×C3×C4#12012yes—
447C2×C3×C4C22×D411yescharacteristic
448C2×C3×C4C22×D411yescharacteristic
449C2×C3×C4C2×#4111yescharacteristic
450C2×C3×C4C2×#4111yescharacteristic
451C2×C3×C4H(5,𝔽2)11yescharacteristic
452C2×C3×C42−1+411yescharacteristic
453C2×Dic3—21no—
454C2×Dic3—21no—
455C2×Dic3—21no—
456C2×Dic3—21no—
457C2×Dic3—21no—
458C2×Dic3—22no—
459C2×Dic3—22no—
460C2×Dic3—21no—
461C2×Dic3—21no—
462C2×Dic3—21no—
463C2×Dic3—21no—
464C2×Dic3—21no—
465C2×Dic3—21no—
466C2×Dic3—44no—
467C2×Dic3—48no—
468C2×Dic3—41no—
469C2×Dic3—41no—
470C2×Dic3—41no—
471C2×Dic3—41no—
472C2×Dic3—44no—
473C2×Dic3—41no—
474C2×Dic3—41no—
475C2×Dic3—41no—
476C2×Dic3—41no—
477C2×Dic3—41no—
478C2×Dic3—41no—
479C2×Dic3#13512yes—
480Dic6—22no—
481Dic6—22no—
482Dic6—41no—
483Dic6—41no—
484C3×C8—22no—
485C3×C8—41no—
486C3⋊C8—22no—
487C3⋊C8—41no—
488C24—21no—
489C24—21no—
490C24D3×D411yescharacteristic
491C2×Q8—32no—
492C2×Q8—61no—
493C2×Q8—61no—
494C2×Q8—61no—
495C2×Q8—61no—
496C2×Q8—61no—
497C2×D4—24no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—42no—
510C2×D4—42no—
511C2×D4—42no—
512C2×D4—42no—
513C2×D4—42no—
514C2×D4C2×#6712yes—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—31no—
522C22×C4—31no—
523C22×C4—31no—
524C22×C4—31no—
525C22×C4—62no—
526C22×C4—64no—
527C22×C4—62no—
528C22×C4—62no—
529C22×C4—62no—
530C22×C4—62no—
531C22×C4—61no—
532C22×C4—61no—
533C22×C4—61no—
534C22×C4—61no—
535C22×C4—122no—
536C22×C4—121no—
537C22×C4—122no—
538C22×C4D3×D411yescharacteristic
539C22×C4D3×D412yes—
540C22×C4C2×#6712yes—
541C22×C4C23×D311yescharacteristic
542SD16—124no—
543D8—44no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—32no—
550C2×C8—44no—
551C2×C8—61no—
552C2×C8—61no—
553C2×C8—61no—
554C2×C8—61no—
555C2×C8—61no—
556C2×C8—124no—
557C2×C8#23712yes—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—32no—
562C4⋊C4—64no—
563C4⋊C4—64no—
564C4⋊C4—64no—
565C4⋊C4—64no—
566C4⋊C4—61no—
567C4⋊C4—61no—
568C4⋊C4—61no—
569C4⋊C4—61no—
570C4⋊C4—61no—
571C4⋊C4—122no—
572C4⋊C4—122no—
573C4⋊C4C2×#6712yes—
574C22⋊C4—24no—
575C22⋊C4—42no—
576C22⋊C4—64no—
577C22⋊C4—64no—
578C22⋊C4—64no—
579C22⋊C4—64no—
580C22⋊C4—122no—
581C22⋊C4—122no—
582C22⋊C4—122no—
583C22⋊C4—122no—
584C22⋊C4—122no—
585C42—64no—
586C42—62no—
587C42—62no—
588C42—61no—
589C42—61no—
590C42—61no—
591C42—61no—
592C22×C3—22no—
593C22×C3—22no—
594C22×C3—22no—
595C22×C3—22no—
596C22×C3—22no—
597C22×C3—22no—
598C22×C3—42no—
599C22×C3—42no—
600C22×C3—42no—
601C22×C3—81no—
602C22×C3—81no—
603C22×C3—81no—
604C22×C3—81no—
605C22×C3—81no—
606C22×C3—81no—
607C22×C3—81no—
608C22×C3—81no—
609C22×C3—81no—
610C22×C3—81no—
611C22×C3—81no—
612C22×C3#44914yes—
613C22×C3C2×#12011yescharacteristic
614C22×C3#53211yescharacteristic
615C22×C3#53711yescharacteristic
616C22×C3C2×#13511yescharacteristic
617C22×C3C2×#13511yescharacteristic
618C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
619C22×C3#57511yescharacteristic
620C3×C4—22no—
621C3×C4—42no—
622C3×C4—81no—
623C3×C4#54611yescharacteristic
624C3×C4#54611yescharacteristic
625C3×C4#54711yescharacteristic
626C3×C4#54711yescharacteristic
627Dic3—22no—
628Dic3—42no—
629Dic3—41no—
630Dic3—41no—
631Dic3—41no—
632Dic3—42no—
633Dic3—81no—
634Dic3—81no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—22no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23#91112yes—
654C23#91212yes—
655C23#93712yes—
656C23C2×D3×D411yescharacteristic
657Q8—62no—
658Q8—62no—
659Q8—121no—
660Q8—121no—
661D4—22no—
662D4—22no—
663D4—48no—
664D4—41no—
665D4—41no—
666D4—41no—
667D4—41no—
668D4—41no—
669D4—41no—
670D4—84no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—32no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—61no—
685C2×C4—61no—
686C2×C4—61no—
687C2×C4—61no—
688C2×C4—61no—
689C2×C4—61no—
690C2×C4—61no—
691C2×C4—61no—
692C2×C4—61no—
693C2×C4—61no—
694C2×C4—61no—
695C2×C4—62no—
696C2×C4—62no—
697C2×C4—124no—
698C2×C4—128no—
699C2×C4—124no—
700C2×C4—121no—
701C2×C4—121no—
702C2×C4—121no—
703C2×C4—121no—
704C2×C4—121no—
705C2×C4—121no—
706C2×C4—121no—
707C2×C4—121no—
708C2×C4—121no—
709C2×C4—121no—
710C2×C4#93712yes—
711C2×C4C2×D3×D411yescharacteristic
712C2×C4C2×#23711yescharacteristic
713C2×C4#100411yescharacteristic
714C2×C4D3×#4111yescharacteristic
715C2×C4#101011yescharacteristic
716C2×C4C22×#6711yescharacteristic
717C8—22no—
718C8—41no—
719C8—62no—
720C8—121no—
721C2×C3—24no—
722C2×C3—82no—
723C2×C3—161no—
724C2×C3#243011yescharacteristic
725C2×C3C2×#44911yescharacteristic
726C2×C3#300211yescharacteristic
727C2×C3#316811yescharacteristic
728C2×C3#318011yescharacteristic
729C2×C3#324711yescharacteristic
730C2×C3#325011yescharacteristic
731C22—22no—
732C22—22no—
733C22—22no—
734C22—22no—
735C22—22no—
736C22—22no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—81no—
741C22—81no—
742C22—81no—
743C22—81no—
744C22—81no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22#515814yes—
752C22#559611yescharacteristic
753C22#559711yescharacteristic
754C22C2×#91111yescharacteristic
755C22C2×#91211yescharacteristic
756C22D3×#13511yescharacteristic
757C22#576811yescharacteristic
758C22C2×#93711yescharacteristic
759C4—22no—
760C4—42no—
761C4—62no—
762C4—81no—
763C4—121no—
764C4—121no—
765C4—121no—
766C4—122no—
767C4—122no—
768C4—241no—
769C4—241no—
770C4#561011yescharacteristic
771C4#561111yescharacteristic
772C4#580611yescharacteristic
773C4#582411yescharacteristic
774C3#2550011yescharacteristic, complemented, Sylow
775C2—24no—
776C2—82no—
777C2—161no—
778C2#8069611yescharacteristic
779C2#8070111yescharacteristic
780C2#8070311yescharacteristic
781C2#8070411yescharacteristic
782C2#8265111yescharacteristic
783C2C2×#515811yescharacteristic
784C2#8391111yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
Fitting, prime radicalC2×C3×#466C2
socleC23×C3C22×D4
hypercenterC2×#466D3
hypocenterC3#25500
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#466

Complements

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

NH ≅ G/Ntype
1. C2×#5600C2semidirect
3. #82699C2semidirect
4. C2×#5041C2semidirect
5. #72045C2semidirect
6. #72037C2semidirect
7. #71972C2semidirect
8. C2×#4550C2semidirect
9. #71681C2semidirect
10. #70642C2semidirect
11. #70618C2semidirect
12. #70216C2semidirect
13. #70213C2semidirect
14. #70169C2semidirect
15. #70164C2semidirect
774. C3#25500semidirect

Maximal subgroups

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

subgroupindex
C2×#56002
C2×C3×#4662
#826992
C2×#50412
#720452
#720372
#719722
C2×#45502
#716812
#706422
#706182
#702162
#702132
#701692
#701642
#255003