Finite Group Databasebeta

← #10823421

Subgroups — #10823421

Order 768.

1228 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5578C211yesmaximal, characteristic, complemented
2C2×#5026C211yesmaximal, characteristic, complemented
3C2×#4710C211yesmaximal, characteristic, complemented
4C4×#895C211yesmaximal, characteristic
5C3×#1763C211yesmaximal, characteristic, complemented
6#70282C211yesmaximal, characteristic, complemented
7#70272C211yesmaximal, characteristic
8#70246C211yesmaximal, characteristic, complemented
9#70244C211yesmaximal, characteristic, complemented
10#69807C211yesmaximal, characteristic, complemented
11#69475C211yesmaximal, characteristic, complemented
12#68898C211yesmaximal, characteristic, complemented
13#68887C211yesmaximal, characteristic
14#68826C211yesmaximal, characteristic, complemented
15#68825C211yesmaximal, characteristic, complemented
16#23574—31nomaximal, Sylow
17C2×C3×C4×Q8C2211yescharacteristic
18C2×#946C2211yescharacteristic
19C2×#944C2211yescharacteristic
20C22×#215C2211yescharacteristic
21C22×#204C2211yescharacteristic
22#5578—24no—
23#5578—24no—
24C2×#897C2211yescharacteristic
25C2×#896—21no—
26C2×#895C2211yescharacteristic
27C2×#889—21no—
28C2×#888C2211yescharacteristic
29C2×C4×D12—21no—
30C2×C4×D12C2211yescharacteristic
31C2×#872—21no—
32C2×C42×D3C2211yescharacteristic
33C2×C4×Dic6—21no—
34C2×C4×Dic6C2211yescharacteristic
35C2×C3×#103C2211yescharacteristic
36C2×C3×#103C2211yescharacteristic
37C2×C3×#97C2211yescharacteristic
38C3×C4×C4⋊C4C2211yescharacteristic
39C2×#835C2211yescharacteristic
40C2×#821C2211yescharacteristic
41C2×(C2×D3)⋊C8C2211yescharacteristic
42C2×(C2×D3)⋊C8C2211yescharacteristic
43C2×#818C2211yescharacteristic
44C2×#816C2211yescharacteristic
45#5026—24no—
46#4988C2211yescharacteristic
47#4987C2211yescharacteristic
48#4984C2211yescharacteristic
49C2×#810C2211yescharacteristic
50C2×#810C2211yescharacteristic
51C2×#809C2211yescharacteristic
52C2×#807C2211yescharacteristic
53C4×(C2×D3)⋊C4—21no—
54C2×#803C2211yescharacteristic
55#4710—24no—
56#4670—21no—
57#4665—21no—
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60#4550C2211yescharacteristic
61#4550C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#533—31no—
65C2×#440—31no—
66C2×#440—31no—
67C4×#121—31no—
68#2057—31no—
69#2043—31no—
70#2036—31no—
71#2036—31no—
72#2023—31no—
73#2013—31no—
74#2000—31no—
75#2000—31no—
76#1763—31no—
77#1763D311yescharacteristic, complemented
78#1749—31no—
79C22×C3×Q8C2311yescharacteristic
80C22×D12—21no—
81C22×D12C2311yescharacteristic
82C22×C4×D3—21no—
83C22×C4×D3D411yescharacteristic
84C22×C4×D3D411yescharacteristic
85C22×C4×D3C2311yescharacteristic
86C22×Dic6—21no—
87C22×Dic6C2311yescharacteristic
88C22×C3×C8C2311yescharacteristic
89C22×C3×C8C2311yescharacteristic
90C3×C4×Q8—22no—
91C3×C4×Q8D414yescomplemented
92C2×C3×C4⋊C4—21no—
93C2×C3×C4⋊C4C2311yescharacteristic
94C2×C3×C4⋊C4C2311yescharacteristic
95C2×C3×C4⋊C4C2311yescharacteristic
96C2×C3×C42—21no—
97C2×C3×C42—21no—
98C2×C3×C42C2311yescharacteristic
99#946—22no—
100#946—22no—
101#944—22no—
102#944—22no—
103C2×#215—22no—
104C2×#215—22no—
105C2×#215—22no—
106C2×(C2×D3)⋊C4—21no—
107C2×(C2×D3)⋊C4—21no—
108C2×(C2×D3)⋊C4—21no—
109C2×(C2×D3)⋊C4—21no—
110C2×(C2×D3)⋊C4—21no—
111C2×(C2×D3)⋊C4—21no—
112C2×(C2×D3)⋊C4—21no—
113C2×C4⋊Dic3—21no—
114C2×C4⋊Dic3—21no—
115C2×C4⋊Dic3C2311yescharacteristic
116C2×C4⋊Dic3C2311yescharacteristic
117C2×Dic3⋊C4—21no—
118C2×Dic3⋊C4—21no—
119C2×Dic3⋊C4—21no—
120C2×Dic3⋊C4—21no—
121C2×Dic3⋊C4—21no—
122C2×C4×Dic3—21no—
123C2×C4×Dic3D411yescharacteristic
124C2×C4×Dic3D411yescharacteristic
125C2×C4×Dic3C2311yescharacteristic
126C22×C3⋊C8C2311yescharacteristic
127C22×C3⋊C8C2311yescharacteristic
128C2×#204—22no—
129C2×#204—22no—
130C2×#204—22no—
131#897—22no—
132#897—22no—
133#896—28no—
134#895—22no—
135#895—22no—
136#889—28no—
137#888—22no—
138#888—22no—
139C4×D12—22no—
140C4×D12—22no—
141C4×D12—44no—
142#872—28no—
143C42×D3—22no—
144C42×D3—22no—
145C4×Dic6—28no—
146C4×Dic6—22no—
147C4×Dic6D414yescomplemented
148C3×#103—22no—
149C3×#103—22no—
150C3×#97—22no—
151C3×#95—21no—
152#835—22no—
153C3⋊#95—21no—
154C3⋊#95—21no—
155#821—22no—
156(C2×D3)⋊C8—22no—
157(C2×D3)⋊C8—22no—
158#818—22no—
159#816—22no—
160#810—22no—
161#810—22no—
162#809—22no—
163#807—22no—
164#803—22no—
165C22×SD16—31no—
166C22×SD16—31no—
167#533—64no—
168#533—64no—
169C2×C4⋊Q8—31no—
170C2×C4⋊Q8—31no—
171C2×#125—61no—
172C2×C22⋊Q8—31no—
173C2×C22⋊Q8—31no—
174C2×C22⋊Q8—61no—
175C2×#121—31no—
176C2×C4×Q8—31no—
177C2×C4×Q8—61no—
178C2×C4×Q8C2×D311yescharacteristic
179C2×C4×D4—31no—
180C2×C4×D4—61no—
181C2×#117—61no—
182C22×C42—31no—
183#440—64no—
184#440—64no—
185C2×#107—31no—
186C2×#107—31no—
187C2×#103—31no—
188C2×#103—31no—
189C2×#103—31no—
190C2×#103—31no—
191C2×#103C2×D311yescharacteristic
192C2×#103C2×D311yescharacteristic
193C2×#102—31no—
194C2×#102—31no—
195C2×C22⋊C8—31no—
196C2×C22⋊C8—31no—
197C2×#97—31no—
198C2×#97C2×D311yescharacteristic
199#390—31no—
200#389—31no—
201#388—61no—
202#386—61no—
203#380—31no—
204C4×C4⋊C4C2×D311yescharacteristic
205C4×C22⋊C4—61no—
206#340—31no—
207#340—31no—
208#340C2×D311yescharacteristic
209#340C2×D311yescharacteristic
210#336—31no—
211#336—31no—
212C23×D3—21no—
213C23×D3C2×D411yescharacteristic
214C2×C3×Q8—21no—
215C2×C3×Q8—21no—
216C2×C3×Q8—21no—
217C2×C3×Q8—21no—
218C2×C3×Q8—21no—
219C2×C3×Q8C2×D412yes—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4C2×D411yescharacteristic
225C22×C3×C4C2×D411yescharacteristic
226C22×C3×C4C2411yescharacteristic
227C22×Dic3—21no—
228C22×Dic3—21no—
229C22×Dic3—21no—
230C22×Dic3C2×D411yescharacteristic
231C22×Dic3C2×D411yescharacteristic
232C22×Dic3C2×D411yescharacteristic
233C2×D12—21no—
234C2×D12—21no—
235C2×D12—21no—
236C2×D12—21no—
237C2×D12—24no—
238C2×D12—21no—
239C2×D12—42no—
240C2×D12—42no—
241C2×D12#4112yes—
242C2×C4×D3—22no—
243C2×C4×D3—22no—
244C2×C4×D3—22no—
245C2×C4×D3—22no—
246C2×C4×D3—21no—
247C2×C4×D3—21no—
248C2×C4×D3—21no—
249C2×C4×D3—21no—
250C2×C4×D3—21no—
251C2×C4×D3—21no—
252C2×C4×D3—22no—
253C2×C4×D3—41no—
254C2×C4×D3—42no—
255C2×C4×D3—42no—
256C2×C4×D3—42no—
257C2×Dic6—21no—
258C2×Dic6—21no—
259C2×Dic6—21no—
260C2×Dic6—21no—
261C2×Dic6—24no—
262C2×Dic6—21no—
263C2×Dic6—42no—
264C2×Dic6—42no—
265C2×Dic6C2×D412yes—
266C2×C3×C8—21no—
267C2×C3×C8—21no—
268C2×C3×C8—21no—
269C2×C3×C8—21no—
270C2×C3×C8—21no—
271C2×C3×C8#4112yes—
272C3×C4⋊C4—24no—
273C3×C4⋊C4—21no—
274C3×C4⋊C4—21no—
275C3×C4⋊C4—21no—
276C3×C4⋊C4—21no—
277C3×C4⋊C4C2×D412yes—
278C3×C4⋊C4#4112yes—
279C3×C42—24no—
280C3×C42—42no—
281C3×C42C2×D412yes—
282C3×C42C2×D412yes—
283#215—28no—
284(C2×D3)⋊C4—24no—
285(C2×D3)⋊C4—24no—
286(C2×D3)⋊C4—24no—
287(C2×D3)⋊C4—42no—
288(C2×D3)⋊C4—42no—
289(C2×D3)⋊C4—42no—
290(C2×D3)⋊C4—42no—
291C4⋊Dic3—24no—
292C4⋊Dic3—21no—
293C4⋊Dic3—21no—
294C4⋊Dic3—21no—
295C4⋊Dic3—42no—
296C4⋊Dic3C2×D412yes—
297Dic3⋊C4—24no—
298Dic3⋊C4—24no—
299Dic3⋊C4—24no—
300Dic3⋊C4—24no—
301Dic3⋊C4—24no—
302C4×Dic3—22no—
303C4×Dic3—24no—
304C4×Dic3—22no—
305C4×Dic3—21no—
306C4×Dic3—21no—
307C2×C3⋊C8—21no—
308C2×C3⋊C8—21no—
309C2×C3⋊C8—21no—
310C2×C3⋊C8—21no—
311C2×C3⋊C8—21no—
312C2×C3⋊C8#4112yes—
313#204—28no—
314C22×Q8—31no—
315C22×Q8—61no—
316C22×Q8C22×D311yescharacteristic
317C22×D4—31no—
318C22×D4—61no—
319C23×C4—31no—
320C23×C4—31no—
321C23×C4—31no—
322C23×C4—61no—
323C2×SD16—62no—
324C2×SD16—62no—
325C2×SD16—62no—
326C2×SD16—62no—
327C2×SD16—62no—
328C2×SD16—62no—
329C22×C8—31no—
330C22×C8—31no—
331C22×C8C22×D311yescharacteristic
332C22×C8C22×D311yescharacteristic
333C4⋊Q8—62no—
334C4⋊Q8—62no—
335C4⋊Q8—62no—
336C4⋊Q8—62no—
337#125—68no—
338C22⋊Q8—62no—
339C22⋊Q8—68no—
340C22⋊Q8—62no—
341C22⋊Q8—62no—
342C22⋊Q8—62no—
343#121—62no—
344#121—62no—
345C4×Q8—22no—
346C4×Q8—34no—
347C4×Q8—68no—
348C4×Q8—62no—
349C4×Q8D1214yescomplemented
350C4×D4—62no—
351C4×D4—62no—
352C4×D4—124no—
353#117—68no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—31no—
356C2×C4⋊C4—31no—
357C2×C4⋊C4—61no—
358C2×C4⋊C4—61no—
359C2×C4⋊C4—61no—
360C2×C4⋊C4—61no—
361C2×C4⋊C4—61no—
362C2×C4⋊C4—61no—
363C2×C4⋊C4—61no—
364C2×C4⋊C4C22×D311yescharacteristic
365C2×C4⋊C4C22×D311yescharacteristic
366C2×C4⋊C4C22×D311yescharacteristic
367C2×C22⋊C4—61no—
368C2×C22⋊C4—61no—
369C2×C22⋊C4—61no—
370C2×C22⋊C4—61no—
371C2×C22⋊C4—61no—
372C2×C22⋊C4—61no—
373C2×C22⋊C4—61no—
374C2×C42—21no—
375C2×C42—21no—
376C2×C42—31no—
377C2×C42—31no—
378C2×C42—31no—
379C2×C42—61no—
380C2×C42—62no—
381C2×C42—62no—
382C2×C42C22×D311yescharacteristic
383#107—62no—
384#107—62no—
385#103—22no—
386#103—22no—
387#103—62no—
388#103—62no—
389#103—62no—
390#103—62no—
391#102—62no—
392#102—62no—
393C22⋊C8—62no—
394C22⋊C8—62no—
395#97—22no—
396#97—62no—
397#95—21no—
398#95—61no—
399#95—61no—
400C23×C3C22×D411yescharacteristic
401C22×D3—21no—
402C22×D3—21no—
403C22×D3—21no—
404C22×D3—21no—
405C22×D3—21no—
406C22×D3—21no—
407C22×D3—22no—
408C22×D3—41no—
409C22×D3—41no—
410C22×D3—41no—
411C22×D3—41no—
412C22×D3—41no—
413C22×D3—41no—
414C22×D3#13712yes—
415C3×Q8—22no—
416C3×Q8—22no—
417C3×Q8—41no—
418C3×Q8—41no—
419C2×C3×C4—21no—
420C2×C3×C4—21no—
421C2×C3×C4—21no—
422C2×C3×C4—21no—
423C2×C3×C4—22no—
424C2×C3×C4—22no—
425C2×C3×C4—22no—
426C2×C3×C4—41no—
427C2×C3×C4—41no—
428C2×C3×C4—41no—
429C2×C3×C4—41no—
430C2×C3×C4—41no—
431C2×C3×C4—41no—
432C2×C3×C4—41no—
433C2×C3×C4—41no—
434C2×C3×C4—41no—
435C2×C3×C4#12012yes—
436C2×C3×C4#12012yes—
437C2×C3×C4C22×D411yescharacteristic
438C2×C3×C4C22×D411yescharacteristic
439C2×C3×C4C2×#4111yescharacteristic
440C2×C3×C4C2×#4111yescharacteristic
441C2×C3×C4C2×#4111yescharacteristic
442C2×C3×C4C2×#4111yescharacteristic
443C2×Dic3—21no—
444C2×Dic3—21no—
445C2×Dic3—21no—
446C2×Dic3—21no—
447C2×Dic3—21no—
448C2×Dic3—22no—
449C2×Dic3—22no—
450C2×Dic3—21no—
451C2×Dic3—21no—
452C2×Dic3—41no—
453C2×Dic3—41no—
454C2×Dic3—41no—
455C2×Dic3—41no—
456C2×Dic3—41no—
457C2×Dic3—41no—
458C2×Dic3—41no—
459C2×Dic3AGL(1,ℤ/8)12yes—
460C2×Dic3#13712yes—
461D12—22no—
462D12—22no—
463D12—48no—
464D12—41no—
465D12—41no—
466C4×D3—28no—
467C4×D3—44no—
468C4×D3—41no—
469C4×D3—41no—
470C4×D3—41no—
471C4×D3—41no—
472C4×D3—84no—
473Dic6—22no—
474Dic6—22no—
475Dic6—48no—
476Dic6—41no—
477Dic6—41no—
478C3×C8—22no—
479C3×C8—41no—
480C3⋊C8—22no—
481C3⋊C8—41no—
482C24—31no—
483C24—61no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—32no—
490C2×Q8—64no—
491C2×Q8—61no—
492C2×Q8—61no—
493C2×Q8—61no—
494C2×Q8—61no—
495C2×Q8—61no—
496C2×Q8—122no—
497C2×Q8—122no—
498C2×Q8C2×D1212yes—
499C2×D4—32no—
500C2×D4—64no—
501C2×D4—61no—
502C2×D4—61no—
503C2×D4—61no—
504C2×D4—61no—
505C2×D4—61no—
506C2×D4—122no—
507C2×D4—122no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—31no—
513C22×C4—31no—
514C22×C4—31no—
515C22×C4—62no—
516C22×C4—62no—
517C22×C4—62no—
518C22×C4—62no—
519C22×C4—61no—
520C22×C4—61no—
521C22×C4—62no—
522C22×C4—61no—
523C22×C4—61no—
524C22×C4—61no—
525C22×C4—61no—
526C22×C4—61no—
527C22×C4—61no—
528C22×C4—61no—
529C22×C4—121no—
530C22×C4—122no—
531C22×C4—122no—
532C22×C4—122no—
533C22×C4D3×D411yescharacteristic
534C22×C4D3×D411yescharacteristic
535C22×C4C23×D311yescharacteristic
536SD16—68no—
537SD16—68no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—32no—
544C2×C8—61no—
545C2×C8—61no—
546C2×C8—61no—
547C2×C8—61no—
548C2×C8—61no—
549C2×C8#23512yes—
550C4⋊C4—24no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—32no—
556C4⋊C4—64no—
557C4⋊C4—64no—
558C4⋊C4—64no—
559C4⋊C4—64no—
560C4⋊C4—64no—
561C4⋊C4—64no—
562C4⋊C4—61no—
563C4⋊C4—61no—
564C4⋊C4—61no—
565C4⋊C4—122no—
566C4⋊C4C2×D1212yes—
567C4⋊C4#23512yes—
568C22⋊C4—64no—
569C22⋊C4—64no—
570C22⋊C4—64no—
571C22⋊C4—122no—
572C22⋊C4—122no—
573C22⋊C4—122no—
574C22⋊C4—122no—
575C42—24no—
576C42—42no—
577C42—62no—
578C42—62no—
579C42—64no—
580C42—61no—
581C42—61no—
582C42C2×D1212yes—
583C42D3×D412yes—
584C22×C3C2×#12011yescharacteristic
585C22×C3#52511yescharacteristic
586C22×C3#53211yescharacteristic
587C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
588C22×C3C2×#13711yescharacteristic
589C22×C3C2×#13711yescharacteristic
590C22×C3#57511yescharacteristic
591C2×D3—22no—
592C2×D3—22no—
593C2×D3—22no—
594C2×D3—41no—
595C2×D3—41no—
596C2×D3—41no—
597C2×D3—41no—
598C2×D3—42no—
599C2×D3—42no—
600C2×D3—42no—
601C2×D3—81no—
602C2×D3—81no—
603C2×D3—81no—
604C2×D3—81no—
605C3×C4—22no—
606C3×C4—22no—
607C3×C4—42no—
608C3×C4—42no—
609C3×C4—42no—
610C3×C4—81no—
611C3×C4#52511yescharacteristic
612C3×C4#52511yescharacteristic
613C3×C4#53211yescharacteristic
614C3×C4#53211yescharacteristic
615Dic3—22no—
616Dic3—22no—
617Dic3—42no—
618Dic3—41no—
619Dic3—42no—
620Dic3—81no—
621C23—32no—
622C23—61no—
623C23—61no—
624C23—61no—
625C23—61no—
626C23—61no—
627C23—61no—
628C23—62no—
629C23—121no—
630C23—121no—
631C23—121no—
632C23—121no—
633C23—121no—
634C23—121no—
635C23C2×D3×D411yescharacteristic
636Q8—22no—
637Q8—22no—
638Q8—41no—
639Q8—41no—
640Q8—62no—
641Q8—62no—
642Q8—128no—
643Q8—121no—
644Q8—121no—
645D4—62no—
646D4—62no—
647D4—128no—
648D4—121no—
649D4—121no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—32no—
658C2×C4—32no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—68no—
669C2×C4—61no—
670C2×C4—61no—
671C2×C4—61no—
672C2×C4—61no—
673C2×C4—61no—
674C2×C4—62no—
675C2×C4—62no—
676C2×C4—61no—
677C2×C4—61no—
678C2×C4—124no—
679C2×C4—121no—
680C2×C4—121no—
681C2×C4—121no—
682C2×C4—121no—
683C2×C4—121no—
684C2×C4—121no—
685C2×C4—121no—
686C2×C4—121no—
687C2×C4—121no—
688C2×C4—121no—
689C2×C4—121no—
690C2×C4—244no—
691C2×C4#88212yes—
692C2×C4#88212yes—
693C2×C4C22×D1211yescharacteristic
694C2×C4C2×#23511yescharacteristic
695C2×C4C2×#23511yescharacteristic
696C2×C4C2×D3×D411yescharacteristic
697C2×C4D3×#4111yescharacteristic
698C2×C4D3×#4111yescharacteristic
699C8—22no—
700C8—41no—
701C8—62no—
702C8—121no—
703C2×C3#238811yescharacteristic
704C2×C3#300411yescharacteristic
705C2×C3#300611yescharacteristic
706C2×C3#311011yescharacteristic
707C2×C3#311611yescharacteristic
708C2×C3#318111yescharacteristic
709C2×C3#318211yescharacteristic
710D3—42no—
711D3—82no—
712C22—62no—
713C22—62no—
714C22—62no—
715C22—121no—
716C22—121no—
717C22—121no—
718C22—121no—
719C22—122no—
720C22—122no—
721C22—122no—
722C22—241no—
723C22—241no—
724C22—241no—
725C22—241no—
726C22C2×#88211yescharacteristic
727C22#554711yescharacteristic
728C22#554811yescharacteristic
729C22D3×AGL(1,ℤ/8)11yescharacteristic
730C22D3×#13711yescharacteristic
731C22D3×#13711yescharacteristic
732C22#577711yescharacteristic
733C4—22no—
734C4—22no—
735C4—42no—
736C4—42no—
737C4—42no—
738C4—62no—
739C4—62no—
740C4—81no—
741C4—122no—
742C4—121no—
743C4—122no—
744C4—241no—
745C4#547711yescharacteristic
746C4#552411yescharacteristic
747C4#554711yescharacteristic
748C4#554811yescharacteristic
749C3#2357411yescharacteristic, complemented, Sylow
750C2—122no—
751C2—242no—
752C2#7358011yescharacteristic
753C2#7888411yescharacteristic
754C2#7895811yescharacteristic
755C2#7977911yescharacteristic
756C2#7979211yescharacteristic
757C2#7983711yescharacteristic
758C2#7984811yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1763C2
socleC23×C3C22×D4
prime radicalC2×#895C22
hypercenter#1763D3
hypocenterC3#23574
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1763

Complements

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

NH ≅ G/Ntype
1. C2×#5578C2semidirect
2. C2×#5026C2semidirect
3. C2×#4710C2semidirect
5. C3×#1763C2semidirect
6. #70282C2semidirect
8. #70246C2semidirect
9. #70244C2semidirect
10. #69807C2semidirect
11. #69475C2semidirect
12. #68898C2semidirect
14. #68826C2semidirect
15. #68825C2semidirect
77. #1763D3semidirect
91. C3×C4×Q8D4semidirect
147. C4×Dic6D4semidirect
349. C4×Q8D12semidirect
749. C3#23574semidirect

Maximal subgroups

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

subgroupindex
C2×#55782
C2×#50262
C2×#47102
C4×#8952
C3×#17632
#702822
#702722
#702462
#702442
#698072
#694752
#688982
#688872
#688262
#688252
#235743