Finite Group Databasebeta

← #10828748

Subgroups — #10828748

Order 768.

1354 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×#5551C211yesmaximal, characteristic
2C2×D3×#107C211yesmaximal, characteristic, complemented
3C2×#4774C211yesmaximal, characteristic, complemented
4#76231C211yesmaximal, characteristic, complemented
5C3×#1862C211yesmaximal, characteristic, complemented
6#71606C211yesmaximal, characteristic, complemented
7#70632C211yesmaximal, characteristic, complemented
8#70206C211yesmaximal, characteristic, complemented
9#70202C211yesmaximal, characteristic, complemented
10#70175C211yesmaximal, characteristic, complemented
11#69604C211yesmaximal, characteristic, complemented
12#68874C211yesmaximal, characteristic, complemented
13#68871C211yesmaximal, characteristic, complemented
14#68668C211yesmaximal, characteristic, complemented
15#68632C211yesmaximal, characteristic, complemented
16#24088—31nomaximal, Sylow
17C22×#235—21no—
18C2×C3×C4×D4C2211yescharacteristic
19C2×#938C2211yescharacteristic
20C2×#938C2211yescharacteristic
21C2×#924—21no—
22C22×D3×C8C2211yescharacteristic
23#5551—24no—
24#5551—24no—
25C2×#894—21no—
26C2×D3×C4⋊C4C2211yescharacteristic
27C2×D3×C4⋊C4C2211yescharacteristic
28C2×D3×C4⋊C4C2211yescharacteristic
29C2×#883—21no—
30C2×#883—21no—
31C2×C4×D12C2211yescharacteristic
32C2×#869C2211yescharacteristic
33C2×C3×#107C2211yescharacteristic
34C2×C3×#102C2211yescharacteristic
35C2×C3×#102C2211yescharacteristic
36C3×#389C2211yescharacteristic
37C2×#832C2211yescharacteristic
38C2×#832C2211yescharacteristic
39C2×(C2×D3)⋊C8C2211yescharacteristic
40C2×(C2×D3)⋊C8C2211yescharacteristic
41C2×(C2×D3)⋊C8C2211yescharacteristic
42C2×#818C2211yescharacteristic
43C2×#818C2211yescharacteristic
44#4987C2211yescharacteristic
45#4987C2211yescharacteristic
46#4987C2211yescharacteristic
47#4982—21no—
48C2×#807C2211yescharacteristic
49C2×#807C2211yescharacteristic
50C2×#807C2211yescharacteristic
51#4928C2211yescharacteristic
52D3×#107—24no—
53#4774—24no—
54#4675—21no—
55#4664—21no—
56C3×#340C2211yescharacteristic
57C3×#336C2211yescharacteristic
58#4551C2211yescharacteristic
59#4551C2211yescharacteristic
60#4529C2211yescharacteristic
61#4529C2211yescharacteristic
62#4529C2211yescharacteristic
63#4524C2211yescharacteristic
64C2×#547—31no—
65C2×#480—31no—
66C22×#107—31no—
67#2486—31no—
68#2057—31no—
69#2057—31no—
70#2033—31no—
71#2033—31no—
72#1893—31no—
73#1869—31no—
74#1862—31no—
75#1862D311yescharacteristic, complemented
76#1852—31no—
77#1852—31no—
78#1823—31no—
79C22×C3×D4C2311yescharacteristic
80C23×C3×C4—21no—
81C22×#67—21no—
82C22×#67—21no—
83C2×#235—28no—
84C2×#235—44no—
85C2×#235—44no—
86C22×D12D411yescharacteristic
87C22×C4×D3—21no—
88C22×C4×D3—21no—
89C22×C4×D3—21no—
90C22×C4×D3C2311yescharacteristic
91C22×C4×D3C2311yescharacteristic
92C22×Dic6—21no—
93C22×C3×C8C2311yescharacteristic
94C22×C3×C8C2311yescharacteristic
95C3×C4×D4—22no—
96C3×C4×D4—22no—
97C2×C3×C4⋊C4—21no—
98C2×C3×C4⋊C4C2311yescharacteristic
99C2×C3×C4⋊C4C2311yescharacteristic
100C2×C3×C4⋊C4C2311yescharacteristic
101C2×C3×C22⋊C4—21no—
102C2×C3×C42C2311yescharacteristic
103C2×#217—21no—
104C2×#217—21no—
105#938—22no—
106#938—22no—
107#938—22no—
108#938D414yes—
109C2×(C2×D3)⋊C4—21no—
110C2×(C2×D3)⋊C4—21no—
111C2×(C2×D3)⋊C4—21no—
112C2×(C2×D3)⋊C4D411yescharacteristic
113C2×(C2×D3)⋊C4D411yescharacteristic
114C2×C4⋊Dic3—21no—
115C2×C4⋊Dic3D411yescharacteristic
116C2×C4⋊Dic3C2311yescharacteristic
117C2×C4⋊Dic3C2311yescharacteristic
118C2×C4⋊Dic3C2311yescharacteristic
119C2×C4⋊Dic3C2311yescharacteristic
120#924—28no—
121C2×Dic3⋊C4—21no—
122C2×Dic3⋊C4—21no—
123C2×Dic3⋊C4—21no—
124C2×Dic3⋊C4—21no—
125C22×C3⋊C8C2311yescharacteristic
126C22×C3⋊C8C2311yescharacteristic
127C2×D3×C8—22no—
128C2×D3×C8—22no—
129C2×D3×C8—22no—
130#894—44no—
131D3×C4⋊C4—22no—
132D3×C4⋊C4—22no—
133D3×C4⋊C4—22no—
134D3×C4⋊C4—22no—
135D3×C4⋊C4—22no—
136D3×C4⋊C4D414yes—
137#883—28no—
138#883—28no—
139C4×D12—22no—
140C4×D12—22no—
141#869—22no—
142#869—22no—
143C3×#107—22no—
144C3×#102—22no—
145C3×#102—22no—
146C3×#95—21no—
147#832—22no—
148#832—22no—
149C3⋊#95—21no—
150C3⋊#95—21no—
151C3⋊#95—21no—
152C3⋊#95—21no—
153(C2×D3)⋊C8—22no—
154(C2×D3)⋊C8—22no—
155(C2×D3)⋊C8—22no—
156#818—22no—
157#818—22no—
158#807—22no—
159#807—22no—
160#807—22no—
161C22×#41—61no—
162C23×C8—31no—
163#547—64no—
164#547—64no—
165C2×C4⋊Q8—31no—
166C2×#123—61no—
167C2×#123—61no—
168C2×#123—61no—
169C2×C22⋊Q8—61no—
170C2×#121—31no—
171C2×#121—31no—
172C2×C4×D4—31no—
173C2×C4×D4C2×D311yescharacteristic
174C22×C4⋊C4—31no—
175C22×C4⋊C4—31no—
176C22×C4⋊C4—31no—
177#480—64no—
178C2×#107—31no—
179C2×#107—31no—
180C2×#107—31no—
181C2×#107—31no—
182C2×#107—31no—
183C2×#107—64no—
184C2×#107C2×D311yescharacteristic
185C2×#102—31no—
186C2×#102—31no—
187C2×#102C2×D311yescharacteristic
188C2×#102C2×D311yescharacteristic
189C2×C22⋊C8—31no—
190C2×C22⋊C8—31no—
191C2×C22⋊C8—31no—
192#398—61no—
193#397—61no—
194#389—31no—
195#389C2×D311yescharacteristic
196#381—61no—
197#380—31no—
198#380—31no—
199#380—31no—
200#340—31no—
201#340—31no—
202#340—31no—
203#340—31no—
204#340—31no—
205#340C2×D311yescharacteristic
206#336—31no—
207#336C2×D311yescharacteristic
208C24×C3—21no—
209C23×D3C2×D411yescharacteristic
210C23×D3C2×D411yescharacteristic
211C2×C3×D4—21no—
212C2×C3×D4—21no—
213C2×C3×D4—21no—
214C2×C3×D4—21no—
215C2×C3×D4—21no—
216C2×C3×D4C2×D412yes—
217C22×C3×C4—24no—
218C22×C3×C4—21no—
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C22×C3×C4—42no—
222C22×C3×C4—42no—
223C22×C3×C4C2×D411yescharacteristic
224C22×C3×C4C2×D411yescharacteristic
225C22×C3×C4C2411yescharacteristic
226C2×#67—24no—
227C2×#67—24no—
228C2×#67—42no—
229C2×#67—42no—
230C2×#67—42no—
231C2×#67—42no—
232C22×Dic3—21no—
233C22×Dic3—21no—
234C22×Dic3—21no—
235C22×Dic3—21no—
236C22×Dic3C2×D411yescharacteristic
237C22×Dic3C2×D411yescharacteristic
238#235—432no—
239C2×D12—22no—
240C2×D12—22no—
241C2×D12D814yes—
242C2×C4×D3—21no—
243C2×C4×D3—21no—
244C2×C4×D3—21no—
245C2×C4×D3—21no—
246C2×C4×D3—24no—
247C2×C4×D3—24no—
248C2×C4×D3—21no—
249C2×C4×D3—21no—
250C2×C4×D3—21no—
251C2×C4×D3—21no—
252C2×C4×D3—21no—
253C2×C4×D3—21no—
254C2×C4×D3—42no—
255C2×C4×D3—42no—
256C2×C4×D3—42no—
257C2×C4×D3—42no—
258C2×C4×D3—42no—
259C2×C4×D3—42no—
260C2×C4×D3—42no—
261C2×C4×D3C2×D412yes—
262C2×C4×D3C2×D412yes—
263C2×Dic6—24no—
264C2×Dic6—42no—
265C2×Dic6—42no—
266C2×C3×C8—21no—
267C2×C3×C8—21no—
268C2×C3×C8—21no—
269C2×C3×C8—21no—
270C2×C3×C8—21no—
271C2×C3×C8#4112yescomplemented
272C3×C4⋊C4—21no—
273C3×C4⋊C4—21no—
274C3×C4⋊C4—21no—
275C3×C4⋊C4—21no—
276C3×C4⋊C4—21no—
277C3×C4⋊C4—42no—
278C3×C4⋊C4C2×D412yes—
279C3×C22⋊C4—24no—
280C3×C42—21no—
281C3×C42—21no—
282#217—24no—
283#217—24no—
284(C2×D3)⋊C4—22no—
285(C2×D3)⋊C4—22no—
286(C2×D3)⋊C4—42no—
287(C2×D3)⋊C4—42no—
288(C2×D3)⋊C4—42no—
289C4⋊Dic3—24no—
290C4⋊Dic3—21no—
291C4⋊Dic3—21no—
292C4⋊Dic3—22no—
293C4⋊Dic3—21no—
294C4⋊Dic3—21no—
295C4⋊Dic3—21no—
296C4⋊Dic3—21no—
297C4⋊Dic3C2×D412yes—
298C4⋊Dic3C2×D412yes—
299Dic3⋊C4—24no—
300Dic3⋊C4—24no—
301Dic3⋊C4—42no—
302Dic3⋊C4—42no—
303C2×C3⋊C8—21no—
304C2×C3⋊C8—21no—
305C2×C3⋊C8—21no—
306C2×C3⋊C8—21no—
307C2×C3⋊C8—21no—
308C2×C3⋊C8#4112yescomplemented
309D3×C8—28no—
310C2×#41—68no—
311C2×#41—124no—
312C2×#41—124no—
313C22×Q8—61no—
314C22×D4—31no—
315C22×D4—61no—
316C22×D4—61no—
317C22×D4C22×D311yescharacteristic
318C23×C4—21no—
319C23×C4—31no—
320C23×C4—31no—
321C23×C4—61no—
322C23×C4—61no—
323C23×C4—61no—
324C22×C8—31no—
325C22×C8—31no—
326C22×C8—62no—
327C22×C8—62no—
328C22×C8—62no—
329C22×C8C22×D311yescharacteristic
330C22×C8C22×D311yescharacteristic
331C4⋊Q8—62no—
332C4⋊Q8—62no—
333#123—68no—
334#123—68no—
335#123—124no—
336C22⋊Q8—68no—
337#121—34no—
338#121—62no—
339#121—62no—
340#121—62no—
341C4×D4—22no—
342C4×D4—22no—
343C4×D4—62no—
344C4×D4—62no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—31no—
347C2×C4⋊C4—31no—
348C2×C4⋊C4—34no—
349C2×C4⋊C4—31no—
350C2×C4⋊C4—31no—
351C2×C4⋊C4—31no—
352C2×C4⋊C4—62no—
353C2×C4⋊C4—62no—
354C2×C4⋊C4—62no—
355C2×C4⋊C4—62no—
356C2×C4⋊C4—61no—
357C2×C4⋊C4—61no—
358C2×C4⋊C4—61no—
359C2×C4⋊C4—62no—
360C2×C4⋊C4—61no—
361C2×C4⋊C4—61no—
362C2×C4⋊C4C22×D311yescharacteristic
363C2×C4⋊C4C22×D311yescharacteristic
364C2×C4⋊C4C22×D311yescharacteristic
365C2×C22⋊C4—21no—
366C2×C22⋊C4—31no—
367C2×C22⋊C4—31no—
368C2×C22⋊C4—61no—
369C2×C22⋊C4—61no—
370C2×C22⋊C4—61no—
371C2×C22⋊C4—61no—
372C2×C22⋊C4—61no—
373C2×C42C22×D311yescharacteristic
374#107—22no—
375#107—62no—
376#107—62no—
377#107—62no—
378#107—62no—
379#107—62no—
380#102—22no—
381#102—22no—
382#102—62no—
383#102—62no—
384C22⋊C8—62no—
385C22⋊C8—62no—
386C22⋊C8—62no—
387#95—21no—
388#95—61no—
389#95—61no—
390#95—61no—
391#95—61no—
392C23×C3—22no—
393C23×C3—41no—
394C23×C3—41no—
395C23×C3—41no—
396C23×C3—41no—
397C23×C3—41no—
398C23×C3—41no—
399C23×C3C22×D411yescharacteristic
400C22×D3—21no—
401C22×D3—21no—
402C22×D3—21no—
403C22×D3—21no—
404C22×D3—21no—
405C22×D3—21no—
406C22×D3—21no—
407C22×D3—21no—
408C22×D3—21no—
409C22×D3—21no—
410C22×D3#12012yes—
411C22×D3C2×D812yes—
412C22×D3C2×D812yes—
413C22×D3AGL(1,ℤ/8)12yes—
414C3×D4—22no—
415C3×D4—22no—
416C3×D4—41no—
417C3×D4—41no—
418C2×C3×C4—21no—
419C2×C3×C4—21no—
420C2×C3×C4—22no—
421C2×C3×C4—21no—
422C2×C3×C4—21no—
423C2×C3×C4—21no—
424C2×C3×C4—48no—
425C2×C3×C4—41no—
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×C4C2×D812yes—
434C2×C3×C4C22×D411yescharacteristic
435C2×C3×C4C22×D411yescharacteristic
436C2×C3×C4C2×#4111yescharacteristic
437C2×C3×C4C2×#4111yescharacteristic
438C2×C3×C42−1+411yescharacteristic
439C2×C3×C42−1+411yescharacteristic
440#67—48no—
441#67—48no—
442C2×Dic3—21no—
443C2×Dic3—21no—
444C2×Dic3—21no—
445C2×Dic3—22no—
446C2×Dic3—22no—
447C2×Dic3—21no—
448C2×Dic3—21no—
449C2×Dic3—41no—
450C2×Dic3—41no—
451C2×Dic3—41no—
452C2×Dic3—41no—
453C2×Dic3—41no—
454C2×Dic3—41no—
455C2×Dic3—41no—
456C2×Dic3—41no—
457C2×Dic3—41no—
458C2×Dic3—41no—
459C2×Dic3#12012yes—
460D12—28no—
461C4×D3—22no—
462C4×D3—22no—
463C4×D3—22no—
464C4×D3—22no—
465C4×D3—48no—
466C4×D3—48no—
467C4×D3—41no—
468C4×D3—41no—
469C4×D3—41no—
470C4×D3—41no—
471C4×D3—84no—
472Dic6—48no—
473C3×C8—22no—
474C3×C8—41no—
475C3⋊C8—22no—
476C3⋊C8—41no—
477C24—21no—
478C24—31no—
479C24—31no—
480#41—1232no—
481C2×Q8—64no—
482C2×Q8—122no—
483C2×Q8—122no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—34no—
490C2×D4—62no—
491C2×D4—62no—
492C2×D4—64no—
493C2×D4—64no—
494C2×D4—122no—
495C2×D4—122no—
496C2×D4—122no—
497C2×D4—122no—
498C2×D4D3×D412yes—
499C22×C4—24no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—31no—
504C22×C4—32no—
505C22×C4—32no—
506C22×C4—31no—
507C22×C4—42no—
508C22×C4—42no—
509C22×C4—64no—
510C22×C4—64no—
511C22×C4—61no—
512C22×C4—61no—
513C22×C4—61no—
514C22×C4—61no—
515C22×C4—61no—
516C22×C4—61no—
517C22×C4—61no—
518C22×C4—61no—
519C22×C4—61no—
520C22×C4—61no—
521C22×C4—61no—
522C22×C4—61no—
523C22×C4—61no—
524C22×C4—61no—
525C22×C4—122no—
526C22×C4—122no—
527C22×C4—122no—
528C22×C4—122no—
529C22×C4—122no—
530C22×C4—122no—
531C22×C4—122no—
532C22×C4D3×D411yescharacteristic
533C22×C4D3×D411yescharacteristic
534C22×C4C23×D311yescharacteristic
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—32no—
541C2×C8—68no—
542C2×C8—61no—
543C2×C8—61no—
544C2×C8—61no—
545C2×C8—61no—
546C2×C8—61no—
547C2×C8#23512yescomplemented
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—32no—
554C4⋊C4—32no—
555C4⋊C4—42no—
556C4⋊C4—64no—
557C4⋊C4—62no—
558C4⋊C4—64no—
559C4⋊C4—64no—
560C4⋊C4—61no—
561C4⋊C4—61no—
562C4⋊C4—61no—
563C4⋊C4—61no—
564C4⋊C4—61no—
565C4⋊C4—61no—
566C4⋊C4—122no—
567C4⋊C4—122no—
568C4⋊C4D3×D412yes—
569C22⋊C4—24no—
570C22⋊C4—62no—
571C22⋊C4—62no—
572C22⋊C4—64no—
573C22⋊C4—64no—
574C22⋊C4—122no—
575C22⋊C4—122no—
576C22⋊C4—122no—
577C42—21no—
578C42—21no—
579C22×C3—42no—
580C22×C3—42no—
581C22×C3—42no—
582C22×C3—81no—
583C22×C3—81no—
584C22×C3—81no—
585C22×C3—81no—
586C22×C3C2×#12011yescharacteristic
587C22×C3#54711yescharacteristic
588C22×C3#54711yescharacteristic
589C22×C3C22×D811yescharacteristic
590C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
591C22×C3#57811yescharacteristic
592C22×C3#57811yescharacteristic
593C2×D3—22no—
594C2×D3—22no—
595C2×D3—22no—
596C2×D3—22no—
597C2×D3—22no—
598C2×D3—22no—
599C2×D3—22no—
600C2×D3—22no—
601C2×D3—22no—
602C2×D3—41no—
603C2×D3—41no—
604C2×D3—41no—
605C2×D3—41no—
606C2×D3#44714yes—
607C3×C4—22no—
608C3×C4—42no—
609C3×C4—41no—
610C3×C4—81no—
611C3×C4—81no—
612C3×C4#52511yescharacteristic
613C3×C4#53611yescharacteristic
614C3×C4#54711yescharacteristic
615C3×C4#54711yescharacteristic
616Dic3—22no—
617Dic3—41no—
618Dic3—42no—
619Dic3—42no—
620Dic3—81no—
621Dic3—81no—
622C23—22no—
623C23—32no—
624C23—32no—
625C23—32no—
626C23—32no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—61no—
634C23—61no—
635C23—61no—
636C23—61no—
637C23—61no—
638C23—61no—
639C23—61no—
640C23—61no—
641C23—61no—
642C23—61no—
643C23C2×D3×D411yescharacteristic
644Q8—128no—
645D4—22no—
646D4—22no—
647D4—41no—
648D4—41no—
649D4—68no—
650D4—128no—
651D4—128no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—22no—
658C2×C4—32no—
659C2×C4—48no—
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—61no—
669C2×C4—61no—
670C2×C4—62no—
671C2×C4—62no—
672C2×C4—62no—
673C2×C4—62no—
674C2×C4—61no—
675C2×C4—61no—
676C2×C4—62no—
677C2×C4—62no—
678C2×C4—61no—
679C2×C4—128no—
680C2×C4—128no—
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—121no—
691C2×C4—121no—
692C2×C4—121no—
693C2×C4—121no—
694C2×C4—121no—
695C2×C4—244no—
696C2×C4D3×D812yes—
697C2×C4C2×#23511yescharacteristic
698C2×C4C2×D3×D411yescharacteristic
699C2×C4C2×D3×D411yescharacteristic
700C2×C4#100711yescharacteristic
701C2×C4D3×#4111yescharacteristic
702C2×C4#101011yescharacteristic
703C8—22no—
704C8—41no—
705C8—62no—
706C8—121no—
707C2×C3—82no—
708C2×C3#240611yescharacteristic
709C2×C3C2×#44711yescharacteristic
710C2×C3#301111yescharacteristic
711C2×C3#333411yescharacteristic
712C2×C3#333411yescharacteristic
713C2×C3#334311yescharacteristic
714C2×C3#334311yescharacteristic
715D3—24no—
716D3—42no—
717C22—34no—
718C22—42no—
719C22—42no—
720C22—42no—
721C22—62no—
722C22—62no—
723C22—62no—
724C22—62no—
725C22—62no—
726C22—62no—
727C22—62no—
728C22—62no—
729C22—62no—
730C22—81no—
731C22—81no—
732C22—81no—
733C22—81no—
734C22—121no—
735C22—121no—
736C22—121no—
737C22—121no—
738C22#555111yescharacteristic
739C22D3×#12011yescharacteristic
740C22#563111yescharacteristic
741C22C2×D3×D811yescharacteristic
742C22#577111yescharacteristic
743C22D3×AGL(1,ℤ/8)11yescharacteristic
744C22#577911yescharacteristic
745C4—22no—
746C4—41no—
747C4—42no—
748C4—62no—
749C4—81no—
750C4—81no—
751C4—121no—
752C4—122no—
753C4—122no—
754C4—241no—
755C4—241no—
756C4#550711yescharacteristic
757C4#554711yescharacteristic
758C4#562811yescharacteristic
759C4#565511yescharacteristic
760C3#2408811yescharacteristic, complemented, Sylow
761C2—64no—
762C2—82no—
763C2—122no—
764C2#7460011yescharacteristic
765C2#7961411yescharacteristic
766C2#7980611yescharacteristic
767C2D3×#44711yescharacteristic
768C2#8023011yescharacteristic
769C2#8098611yescharacteristic
770C2#8119611yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1862C2
socleC23×C3C22×D4
prime radicalC2×#5551C2
hypercenter#1862D3
hypocenterC3#24088
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1862

Complements

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

NH ≅ G/Ntype
2. C2×D3×#107C2semidirect
3. C2×#4774C2semidirect
4. #76231C2semidirect
5. C3×#1862C2semidirect
6. #71606C2semidirect
7. #70632C2semidirect
8. #70206C2semidirect
9. #70202C2semidirect
10. #70175C2semidirect
11. #69604C2semidirect
12. #68874C2semidirect
13. #68871C2semidirect
14. #68668C2semidirect
15. #68632C2semidirect
75. #1862D3semidirect
271. C2×C3×C8#41semidirect
308. C2×C3⋊C8#41semidirect
547. C2×C8#235semidirect
760. C3#24088semidirect

Maximal subgroups

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

subgroupindex
C2×#55512
C2×D3×#1072
C2×#47742
#762312
C3×#18622
#716062
#706322
#702062
#702022
#701752
#696042
#688742
#688712
#686682
#686322
#240883