Finite Group Databasebeta

← #10846258

Subgroups — #10846258

Order 768.

1052 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5155C211yesmaximal, characteristic, complemented
2#82647C211yesmaximal, characteristic, complemented
3#82646C211yesmaximal, characteristic, complemented
4C2×#5041C211yesmaximal, characteristic, complemented
5C2×#5041C211yesmaximal, characteristic, complemented
6C2×#4758C211yesmaximal, characteristic, complemented
7C3×#1999C211yesmaximal, characteristic
8#72037C211yesmaximal, characteristic, complemented
9#70216C211yesmaximal, characteristic, complemented
10#70189C211yesmaximal, characteristic, complemented
11#70178C211yesmaximal, characteristic, complemented
12#69964C211yesmaximal, characteristic, complemented
13#69947C211yesmaximal, characteristic, complemented
14#68908C211yesmaximal, characteristic, complemented
15#68858C211yesmaximal, characteristic, complemented
16#25411—31nomaximal, Sylow
17C22×C3×D8C2211yescharacteristic
18C2×C3×#121C2211yescharacteristic
19C2×C3×#121C2211yescharacteristic
20C2×#936C2211yescharacteristic
21C2×#936C2211yescharacteristic
22C2×D4×Dic3C2211yescharacteristic
23C22×#214C2211yescharacteristic
24C22×#214C2211yescharacteristic
25C2×#924C2211yescharacteristic
26C2×#924C2211yescharacteristic
27C23×C3⋊C8C2211yescharacteristic
28C22×Dic12C2211yescharacteristic
29C2×#887C2211yescharacteristic
30C2×C3×#102C2211yescharacteristic
31C2×C3×#102C2211yescharacteristic
32C2×C3×C22⋊C8C2211yescharacteristic
33#5222—21no—
34#5222—21no—
35#5221—21no—
36#5221C2211yescharacteristic
37#5220—21no—
38C2×#832C2211yescharacteristic
39C2×#832C2211yescharacteristic
40C4×#217C2211yescharacteristic
41#5155—24no—
42C2×#816C2211yescharacteristic
43C2×#816C2211yescharacteristic
44C2×C8×Dic3C2211yescharacteristic
45C2×C8×Dic3C2211yescharacteristic
46#5041—24no—
47#5041—24no—
48#4984C2211yescharacteristic
49#4973C2211yescharacteristic
50#4972C2211yescharacteristic
51C2×#810C2211yescharacteristic
52C2×#810C2211yescharacteristic
53C2×#808C2211yescharacteristic
54C2×#808C2211yescharacteristic
55#4952—21no—
56#4948—21no—
57#4944—21no—
58#4942—21no—
59#4758—24no—
60C3×#340C2211yescharacteristic
61#4551C2211yescharacteristic
62#4550C2211yescharacteristic
63#4550C2211yescharacteristic
64C2×#495—31no—
65C2×#465—31no—
66C2×#465—31no—
67C2×C4×SD16—31no—
68#2427—31no—
69#2426—31no—
70#2042—31no—
71#2042—31no—
72#2001—31no—
73#1999D311yescharacteristic
74#1968—31no—
75#1941—31no—
76#1879—31no—
77#1878—31no—
78C8×C22⋊C4—31no—
79C22×C3×D4—21no—
80C22×C3×D4—21no—
81C22×C3×D4C2311yescharacteristic
82C22×C3×D4C2311yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C23×Dic3—21no—
85C22×Dic6C2311yescharacteristic
86C22×Dic6C2311yescharacteristic
87C2×C3×D8—22no—
88C2×C3×D8—22no—
89C2×C3×D8—41no—
90C22×C3×C8C2311yescharacteristic
91C22×C3×C8C2311yescharacteristic
92C3×#121—22no—
93C3×#121—22no—
94C3×#121—41no—
95C3×#121—41no—
96C2×C3×C4⋊C4C2311yescharacteristic
97C2×C3×C4⋊C4C2311yescharacteristic
98C2×C3×C22⋊C4—21no—
99C2×C3×C22⋊C4—21no—
100C2×#217—21no—
101C2×#217—21no—
102C2×#217—21no—
103C2×#217—21no—
104C2×#217—21no—
105C2×#217—21no—
106C2×#217—21no—
107C2×#217—21no—
108C2×#217—21no—
109C2×#217D411yescharacteristic
110C2×#217D411yescharacteristic
111#936—22no—
112#936—22no—
113#936—41no—
114#936—41no—
115D4×Dic3—22no—
116D4×Dic3—41no—
117C2×#214—22no—
118C2×#214—22no—
119C2×#214—22no—
120C2×#214—22no—
121C2×#214—22no—
122C2×#214D414yescomplemented
123C2×C4⋊Dic3—21no—
124C2×C4⋊Dic3C2311yescharacteristic
125C2×C4⋊Dic3C2311yescharacteristic
126#924—22no—
127#924—22no—
128#924—41no—
129#924—41no—
130C2×Dic3⋊C4—21no—
131C2×Dic3⋊C4—21no—
132C2×Dic3⋊C4—21no—
133C2×Dic3⋊C4—21no—
134C2×C4×Dic3—21no—
135C2×C4×Dic3C2311yescharacteristic
136C2×C4×Dic3C2311yescharacteristic
137C22×C3⋊C8—22no—
138C22×C3⋊C8—22no—
139C22×C3⋊C8—22no—
140C22×C3⋊C8C2311yescharacteristic
141C22×C3⋊C8C2311yescharacteristic
142C2×Dic12—22no—
143C2×Dic12—22no—
144C2×Dic12—41no—
145#887—22no—
146#887—41no—
147C3×#102—22no—
148C3×#102—41no—
149C3×C22⋊C8—22no—
150#832—22no—
151#832—22no—
152C3⋊#95—21no—
153C3⋊#95—21no—
154C3⋊#95—21no—
155C3⋊#95—21no—
156C3⋊#95D411yescharacteristic
157C3⋊#95D411yescharacteristic
158#816—22no—
159#816—41no—
160C8×Dic3—22no—
161C8×Dic3—22no—
162#810—22no—
163#810—22no—
164#808—22no—
165#808D414yescomplemented
166C22×Q16—31no—
167C22×SD16—31no—
168C22×SD16—31no—
169C22×D8C2×D311yescharacteristic
170C23×C8—31no—
171C2×#124—31no—
172C2×#124—31no—
173C2×C22⋊Q8—31no—
174C2×C22⋊Q8—31no—
175C2×#121C2×D311yescharacteristic
176C2×#121C2×D311yescharacteristic
177C2×C4×Q8—31no—
178C2×C4×D4—31no—
179#495—64no—
180#465—64no—
181#465—64no—
182C4×SD16—64no—
183C2×#106—31no—
184C2×#106—31no—
185C2×#103—31no—
186C2×#103—31no—
187C2×#103—31no—
188C2×#103—31no—
189C2×#102—31no—
190C2×#102—31no—
191C2×#102C2×D311yescharacteristic
192C2×#102C2×D311yescharacteristic
193C2×C22⋊C8C2×D311yescharacteristic
194C2×C4×C8—31no—
195C2×C4×C8—31no—
196#397—61no—
197#396—61no—
198#394—61no—
199#394—61no—
200#391—31no—
201#390—31no—
202#390—61no—
203#389—31no—
204#389—31no—
205#388—61no—
206#386—61no—
207#380—61no—
208C4×C22⋊C4—31no—
209#340—31no—
210#340C2×D311yescharacteristic
211#336—31no—
212#336—31no—
213C24×C3—21no—
214C24×C3—21no—
215C24×C3C2×D411yescharacteristic
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—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×C4C2×D411yescharacteristic
243C22×C3×C4C2411yescharacteristic
244C22×Dic3—21no—
245C22×Dic3—21no—
246C22×Dic3—21no—
247C22×Dic3—21no—
248C22×Dic3—42no—
249C22×Dic3—42no—
250C22×Dic3—81no—
251C22×Dic3C2×D411yescharacteristic
252C22×Dic3C2×D411yescharacteristic
253C22×Dic3C2×D411yescharacteristic
254C22×Dic3C2×D411yescharacteristic
255C2×Dic6—21no—
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×Dic6C2×D412yes—
267C3×D8—44no—
268C2×C3×C8—21no—
269C2×C3×C8—21no—
270C2×C3×C8—21no—
271C2×C3×C8—21no—
272C2×C3×C8—21no—
273C2×C3×C8#4112yes—
274C3×C4⋊C4—21no—
275C3×C4⋊C4—21no—
276C3×C4⋊C4—21no—
277C3×C4⋊C4C2×D412yes—
278C3×C22⋊C4—42no—
279C3×C22⋊C4—42no—
280#217—22no—
281#217—22no—
282#217—42no—
283#217—42no—
284#217—42no—
285#217—42no—
286#217—42no—
287#217—42no—
288#217—42no—
289#217—42no—
290#217—81no—
291#214—28no—
292#214—44no—
293C4⋊Dic3—21no—
294C4⋊Dic3—21no—
295C4⋊Dic3—21no—
296C4⋊Dic3—81no—
297C4⋊Dic3C2×D412yes—
298Dic3⋊C4—42no—
299Dic3⋊C4—42no—
300Dic3⋊C4—42no—
301Dic3⋊C4—81no—
302C4×Dic3—21no—
303C4×Dic3—21no—
304C4×Dic3—21no—
305C4×Dic3—21no—
306C4×Dic3—42no—
307C2×C3⋊C8—21no—
308C2×C3⋊C8—21no—
309C2×C3⋊C8—21no—
310C2×C3⋊C8—44no—
311C2×C3⋊C8C2×D412yes—
312C2×C3⋊C8C2×D412yes—
313C2×C3⋊C8#4112yes—
314Dic12—44no—
315C22×Q8—31no—
316C22×Q8—31no—
317C22×D4—21no—
318C22×D4—21no—
319C22×D4C22×D311yescharacteristic
320C22×D4C22×D311yescharacteristic
321C23×C4—61no—
322C23×C4C22×D311yescharacteristic
323C2×Q16—62no—
324C2×Q16—62no—
325C2×Q16—121no—
326C2×SD16—34no—
327C2×SD16—62no—
328C2×SD16—62no—
329C2×SD16—62no—
330C2×SD16—62no—
331C2×SD16—62no—
332C2×D8—22no—
333C2×D8—22no—
334C2×D8—41no—
335C22×C8—31no—
336C22×C8—31no—
337C22×C8—62no—
338C22×C8—62no—
339C22×C8—62no—
340C22×C8C22×D311yescharacteristic
341C22×C8C22×D311yescharacteristic
342#124—62no—
343#124—62no—
344#124—121no—
345#124—121no—
346C22⋊Q8—62no—
347C22⋊Q8—62no—
348C22⋊Q8—121no—
349C22⋊Q8—121no—
350#121—22no—
351#121—22no—
352#121—41no—
353#121—41no—
354C4×Q8—62no—
355C4×Q8—121no—
356C4×D4—62no—
357C4×D4—121no—
358C2×C4⋊C4—31no—
359C2×C4⋊C4—31no—
360C2×C4⋊C4—61no—
361C2×C4⋊C4—61no—
362C2×C4⋊C4—61no—
363C2×C4⋊C4—61no—
364C2×C4⋊C4—61no—
365C2×C4⋊C4C22×D311yescharacteristic
366C2×C4⋊C4C22×D311yescharacteristic
367C2×C22⋊C4—21no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—31no—
370C2×C22⋊C4—31no—
371C2×C22⋊C4—61no—
372C2×C22⋊C4—61no—
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×C42—31no—
381C2×C42—31no—
382C2×C42—61no—
383#106—34no—
384#106—62no—
385#103—62no—
386#103—62no—
387#103—62no—
388#103—121no—
389#102—22no—
390#102—41no—
391#102—62no—
392#102—62no—
393C22⋊C8—22no—
394C4×C8—62no—
395C4×C8—62no—
396#95—31no—
397#95—31no—
398#95—61no—
399#95—61no—
400#95—61no—
401#95—61no—
402C23×C3—21no—
403C23×C3—21no—
404C23×C3—21no—
405C23×C3—21no—
406C23×C3—21no—
407C23×C3—21no—
408C23×C3—22no—
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—41no—
421C23×C3—41no—
422C23×C3#13512yes—
423C23×C3C22×D411yescharacteristic
424C3×D4—22no—
425C3×D4—22no—
426C3×D4—41no—
427C3×D4—41no—
428C3×D4—41no—
429C3×D4—41no—
430C3×D4—41no—
431C3×D4—41no—
432C3×D4—84no—
433C3×D4—84no—
434C2×C3×C4—21no—
435C2×C3×C4—22no—
436C2×C3×C4—21no—
437C2×C3×C4—21no—
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×C4C22×D411yescharacteristic
448C2×C3×C4C22×D411yescharacteristic
449C2×C3×C4C2×#4111yescharacteristic
450C2×C3×C4C2×#4111yescharacteristic
451C2×C3×C4H(5,𝔽2)11yescharacteristic
452C2×C3×C4H(5,𝔽2)11yescharacteristic
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—41no—
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—84no—
477C2×Dic3#13512yes—
478Dic6—22no—
479Dic6—22no—
480Dic6—41no—
481Dic6—41no—
482Dic6—41no—
483Dic6—41no—
484Dic6—41no—
485Dic6—41no—
486C3×C8—22no—
487C3×C8—41no—
488C3⋊C8—41no—
489C3⋊C8#12114yes—
490C24—21no—
491C24—21no—
492C24D3×D411yescharacteristic
493C2×Q8—32no—
494C2×Q8—61no—
495C2×Q8—61no—
496C2×Q8—61no—
497C2×Q8—61no—
498C2×Q8—61no—
499C2×Q8—61no—
500C2×Q8—61no—
501C2×Q8—61no—
502C2×Q8—61no—
503C2×Q8—61no—
504C2×Q8—61no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—42no—
517C2×D4—42no—
518C2×D4—42no—
519C2×D4—42no—
520C2×D4—81no—
521C2×D4—81no—
522C2×D4D3×D412yes—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—31no—
532C22×C4—31no—
533C22×C4—31no—
534C22×C4—31no—
535C22×C4—61no—
536C22×C4—61no—
537C22×C4—61no—
538C22×C4—61no—
539C22×C4—122no—
540C22×C4—122no—
541C22×C4—241no—
542C22×C4D3×D411yescharacteristic
543C22×C4C23×D311yescharacteristic
544Q16—124no—
545SD16—68no—
546SD16—124no—
547D8—44no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—32no—
554C2×C8—32no—
555C2×C8—32no—
556C2×C8—61no—
557C2×C8—61no—
558C2×C8—61no—
559C2×C8—124no—
560C2×C8#23712yes—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—32no—
565C4⋊C4—61no—
566C4⋊C4—61no—
567C4⋊C4—61no—
568C4⋊C4—122no—
569C4⋊C4—122no—
570C4⋊C4—122no—
571C4⋊C4—241no—
572C4⋊C4—241no—
573C4⋊C4D3×D412yes—
574C22⋊C4—42no—
575C22⋊C4—42no—
576C22⋊C4—62no—
577C22⋊C4—62no—
578C22⋊C4—122no—
579C22⋊C4—122no—
580C22⋊C4—122no—
581C22⋊C4—122no—
582C22⋊C4—122no—
583C22⋊C4—122no—
584C22⋊C4—122no—
585C22⋊C4—122no—
586C22⋊C4—241no—
587C42—61no—
588C42—61no—
589C42—61no—
590C42—61no—
591C42—122no—
592C22×C3—22no—
593C22×C3—22no—
594C22×C3—22no—
595C22×C3—41no—
596C22×C3—41no—
597C22×C3—41no—
598C22×C3—41no—
599C22×C3—42no—
600C22×C3—42no—
601C22×C3—42no—
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—81no—
613C22×C3#53211yescharacteristic
614C22×C3D4211yescharacteristic
615C22×C3D4211yescharacteristic
616C22×C3C2×#13511yescharacteristic
617C22×C3C2×#13511yescharacteristic
618C22×C3#57711yescharacteristic
619C22×C3#57711yescharacteristic
620C3×C4—41no—
621C3×C4—42no—
622C3×C4—81no—
623C3×C4C2×#12111yescharacteristic
624C3×C4#54011yescharacteristic
625C3×C4#54611yescharacteristic
626C3×C4#55011yescharacteristic
627Dic3—22no—
628Dic3—42no—
629Dic3—41no—
630Dic3—41no—
631Dic3—42no—
632Dic3—41no—
633Dic3—81no—
634Dic3—81no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—22no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23#91212yes—
656C23C2×D3×D411yescharacteristic
657Q8—62no—
658Q8—62no—
659Q8—121no—
660Q8—121no—
661Q8—121no—
662Q8—121no—
663Q8—121no—
664Q8—121no—
665D4—22no—
666D4—22no—
667D4—41no—
668D4—41no—
669D4—41no—
670D4—41no—
671D4—41no—
672D4—41no—
673D4—84no—
674D4—84no—
675C2×C4—22no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—32no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—61no—
690C2×C4—61no—
691C2×C4—61no—
692C2×C4—61no—
693C2×C4—61no—
694C2×C4—61no—
695C2×C4—61no—
696C2×C4—61no—
697C2×C4—61no—
698C2×C4—61no—
699C2×C4—61no—
700C2×C4—62no—
701C2×C4—62no—
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—121no—
711C2×C4—121no—
712C2×C4—244no—
713C2×C4C2×D3×D411yescharacteristic
714C2×C4C2×D3×D411yescharacteristic
715C2×C4C2×#23711yescharacteristic
716C2×C4#100411yescharacteristic
717C2×C4#100411yescharacteristic
718C2×C4D3×#4111yescharacteristic
719C8—22no—
720C8—34no—
721C8—41no—
722C8—121no—
723C2×C3—42no—
724C2×C3—82no—
725C2×C3—161no—
726C2×C3#242811yescharacteristic
727C2×C3#316811yescharacteristic
728C2×C3#317311yescharacteristic
729C2×C3#328211yescharacteristic
730C2×C3#328211yescharacteristic
731C2×C3#328211yescharacteristic
732C2×C3#328411yescharacteristic
733C22—22no—
734C22—22no—
735C22—22no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—81no—
744C22—81no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22—81no—
752C22—81no—
753C22—81no—
754C22#559011yescharacteristic
755C22#559011yescharacteristic
756C22#559611yescharacteristic
757C22C2×#91211yescharacteristic
758C22D3×#13511yescharacteristic
759C22#577511yescharacteristic
760C22#577511yescharacteristic
761C4—41no—
762C4—42no—
763C4—62no—
764C4—81no—
765C4—121no—
766C4—122no—
767C4—121no—
768C4—121no—
769C4—122no—
770C4—241no—
771C4—241no—
772C4#559111yescharacteristic
773C4D3×#12111yescharacteristic
774C4#561511yescharacteristic
775C4#571811yescharacteristic
776C3#2541111yescharacteristic, complemented, Sylow
777C2—42no—
778C2—82no—
779C2—161no—
780C2#7667111yescharacteristic
781C2#8002711yescharacteristic
782C2#8002711yescharacteristic
783C2#8012611yescharacteristic
784C2#8013011yescharacteristic
785C2#8069611yescharacteristic
786C2#8084911yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
Fitting, prime radicalC3×#1999C2
socleC23×C3C22×D4
hypercenter#1999D3
hypocenterC3#25411
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1999

Complements

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

NH ≅ G/Ntype
1. C2×#5155C2semidirect
2. #82647C2semidirect
3. #82646C2semidirect
4. C2×#5041C2semidirect
5. C2×#5041C2semidirect
6. C2×#4758C2semidirect
8. #72037C2semidirect
9. #70216C2semidirect
10. #70189C2semidirect
11. #70178C2semidirect
12. #69964C2semidirect
13. #69947C2semidirect
14. #68908C2semidirect
15. #68858C2semidirect
122. C2×#214D4semidirect
165. #808D4semidirect
776. C3#25411semidirect

Maximal subgroups

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

subgroupindex
C2×#51552
#826472
#826462
C2×#50412
C2×#47582
C3×#19992
#720372
#702162
#701892
#701782
#699642
#699472
#689082
#688582
#254113