Finite Group Databasebeta

← #10845959

Subgroups — #10845959

Order 768.

1116 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5114C211yesmaximal, characteristic, complemented
2C2×C8×#67C211yesmaximal, characteristic, complemented
3#82668C211yesmaximal, characteristic, complemented
4C2×#4787C211yesmaximal, characteristic, complemented
5C2×#4775C211yesmaximal, characteristic, complemented
6#73933C211yesmaximal, characteristic, complemented
7C3×#1893C211yesmaximal, characteristic, complemented
8#71684C211yesmaximal, characteristic, complemented
9#70176C211yesmaximal, characteristic, complemented
10#70158C211yesmaximal, characteristic, complemented
11#69527C211yesmaximal, characteristic, complemented
12#68887C211yesmaximal, characteristic, complemented
13#68882C211yesmaximal, characteristic, complemented
14#68797C211yesmaximal, characteristic, complemented
15#68780C211yesmaximal, characteristic, complemented
16#25388—31nomaximal, Sylow
17C23×C3×C8C2211yescharacteristic
18C2×C3×#121C2211yescharacteristic
19C2×#938C2211yescharacteristic
20C2×#936C2211yescharacteristic
21C22×#213C2211yescharacteristic
22C2×#930C2211yescharacteristic
23C2×C4×#67C2211yescharacteristic
24C2×#924C2211yescharacteristic
25C22×#204C2211yescharacteristic
26C22×D3×C8C2211yescharacteristic
27C2×#897C2211yescharacteristic
28C2×#895C2211yescharacteristic
29C2×#893C2211yescharacteristic
30C2×C3×#102C2211yescharacteristic
31C2×C3×#102C2211yescharacteristic
32C3×#380C2211yescharacteristic
33#5223—21no—
34#5221—21no—
35C2×#832C2211yescharacteristic
36C2×#830C2211yescharacteristic
37#5114—24no—
38C2×#821C2211yescharacteristic
39C8×#67—24no—
40C2×(C2×D3)⋊C8C2211yescharacteristic
41C2×#817C2211yescharacteristic
42C2×#816C2211yescharacteristic
43C2×Dic3⋊C8C2211yescharacteristic
44C2×C8×Dic3C2211yescharacteristic
45#4987C2211yescharacteristic
46#4977C2211yescharacteristic
47Dic3×C4⋊C4C2211yescharacteristic
48C2×#810C2211yescharacteristic
49C2×#810C2211yescharacteristic
50C2×#809C2211yescharacteristic
51C2×#807C2211yescharacteristic
52#4960—21no—
53#4957—21no—
54#4956—21no—
55#4949—21no—
56#4787—24no—
57#4775—24no—
58#4675—21no—
59#4665—21no—
60C3×#340C2211yescharacteristic
61C3×#340C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#466—31no—
65C2×#465—31no—
66C2×#463—31no—
67C2×C8×D4—31no—
68#2540—31no—
69#2535—31no—
70#2036—31no—
71#2034—31no—
72#2000—31no—
73#1999—31no—
74#1958—31no—
75#1949—31no—
76#1893D311yescharacteristic, complemented
77#1892—31no—
78C4×#102—31no—
79C22×C3×D4—21no—
80C22×C3×D4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C22×#67—21no—
83C22×#67—21no—
84C22×#67D411yescharacteristic
85C22×D12—21no—
86C22×D12C2311yescharacteristic
87C22×C4×D3—21no—
88C22×C4×D3C2311yescharacteristic
89C22×Dic6C2311yescharacteristic
90C22×C3×C8—22no—
91C22×C3×C8—22no—
92C22×C3×C8—41no—
93C22×C3×C8C2311yescharacteristic
94C22×C3×C8C2311yescharacteristic
95C3×#121—22no—
96C3×#121—41no—
97C2×C3×C4⋊C4C2311yescharacteristic
98C2×C3×C4⋊C4C2311yescharacteristic
99C2×C3×C4⋊C4C2311yescharacteristic
100C2×C3×C22⋊C4—21no—
101C2×C3×C22⋊C4—21no—
102C2×#217—21no—
103C2×#217—21no—
104C2×#217—21no—
105C2×#217—21no—
106C2×#217D411yescharacteristic
107#938—22no—
108#938—41no—
109#936—22no—
110#936—22no—
111C2×#213—22no—
112C2×#213—22no—
113C2×#213—41no—
114#930—22no—
115#930—41no—
116C4×#67—22no—
117C4×#67—22no—
118C2×(C2×D3)⋊C4—21no—
119C2×(C2×D3)⋊C4—21no—
120C2×(C2×D3)⋊C4—21no—
121C2×(C2×D3)⋊C4—21no—
122C2×(C2×D3)⋊C4—21no—
123C2×(C2×D3)⋊C4D411yescharacteristic
124C2×C4⋊Dic3—21no—
125C2×C4⋊Dic3C2311yescharacteristic
126C2×C4⋊Dic3C2311yescharacteristic
127#924—22no—
128#924—41no—
129C2×Dic3⋊C4—21no—
130C2×Dic3⋊C4D411yescharacteristic
131C2×C4×Dic3—21no—
132C2×C4×Dic3C2311yescharacteristic
133C22×C3⋊C8C2311yescharacteristic
134C22×C3⋊C8C2311yescharacteristic
135C2×#204—22no—
136C2×#204—22no—
137C2×#204—41no—
138C2×D3×C8—22no—
139C2×D3×C8—22no—
140C2×D3×C8—41no—
141#897—22no—
142#897—41no—
143#895—22no—
144#895—41no—
145#893—22no—
146#893—22no—
147C3×#102—22no—
148C3×#102—22no—
149C3×#95—21no—
150#832—41no—
151C3⋊#95—21no—
152C3⋊#95—21no—
153C3⋊#95—21no—
154C3⋊#95—21no—
155#830—22no—
156#821D414yescomplemented
157(C2×D3)⋊C8—22no—
158#817—22no—
159#816—22no—
160Dic3⋊C8D414yescomplemented
161C8×Dic3—22no—
162#810—22no—
163#810—41no—
164#809—22no—
165#807—22no—
166C22×SD16—31no—
167C22×D8—31no—
168C23×C8—31no—
169C23×C8C2×D311yescharacteristic
170C2×#124—31no—
171C2×C22⋊Q8—31no—
172C2×C22⋊Q8—31no—
173C2×#121—31no—
174C2×#121—31no—
175C2×#121—31no—
176C2×#121C2×D311yescharacteristic
177C2×C4×D4—31no—
178C2×C4×D4—31no—
179#466—64no—
180#465—64no—
181#463—64no—
182C8×D4—64no—
183C2×#107—31no—
184C2×#106—31no—
185C2×C4⋊C8—31no—
186C2×#103—31no—
187C2×#103—31no—
188C2×#103—31no—
189C2×#102—31no—
190C2×#102—31no—
191C2×#102—31no—
192C2×#102C2×D311yescharacteristic
193C2×#102C2×D311yescharacteristic
194C2×C22⋊C8—31no—
195C2×C22⋊C8—31no—
196C2×C4×C8—31no—
197#399—61no—
198#397—61no—
199#392—61no—
200#392—61no—
201#390—61no—
202#390—61no—
203#386—61no—
204#386—61no—
205#382—31no—
206#380—31no—
207#380C2×D311yescharacteristic
208C4×C4⋊C4—31no—
209#340—31no—
210#340—31no—
211#340C2×D311yescharacteristic
212#340C2×D311yescharacteristic
213C24×C3—21no—
214C24×C3C2×D411yescharacteristic
215C23×D3—21no—
216C23×D3C2×D411yescharacteristic
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—42no—
224C2×C3×D4—42no—
225C2×C3×D4—81no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4C2×D411yescharacteristic
236C22×C3×C4C2411yescharacteristic
237C2×#67—22no—
238C2×#67—22no—
239C2×#67—22no—
240C2×#67—42no—
241C2×#67—42no—
242C2×#67—42no—
243C2×#67—42no—
244C2×#67—81no—
245C2×#67—81no—
246C22×Dic3—21no—
247C22×Dic3—21no—
248C22×Dic3—21no—
249C22×Dic3C2×D411yescharacteristic
250C22×Dic3C2×D411yescharacteristic
251C22×Dic3C2×D411yescharacteristic
252C2×D12—21no—
253C2×D12—21no—
254C2×D12—21no—
255C2×D12—21no—
256C2×D12—21no—
257C2×D12—42no—
258C2×D12—42no—
259C2×D12—81no—
260C2×D12C2×D412yes—
261C2×C4×D3—21no—
262C2×C4×D3—21no—
263C2×C4×D3—21no—
264C2×C4×D3—21no—
265C2×C4×D3—21no—
266C2×C4×D3—21no—
267C2×C4×D3—42no—
268C2×C4×D3—81no—
269C2×C4×D3—81no—
270C2×Dic6—21no—
271C2×Dic6—21no—
272C2×Dic6—21no—
273C2×Dic6—21no—
274C2×Dic6—21no—
275C2×Dic6—21no—
276C2×C3×C8—21no—
277C2×C3×C8—21no—
278C2×C3×C8—21no—
279C2×C3×C8—21no—
280C2×C3×C8—44no—
281C2×C3×C8C2×D412yes—
282C2×C3×C8C2×D412yes—
283C3×C4⋊C4—21no—
284C3×C4⋊C4—21no—
285C3×C4⋊C4—21no—
286C3×C4⋊C4—21no—
287C3×C4⋊C4—21no—
288C3×C4⋊C4#4112yes—
289C3×C22⋊C4—42no—
290C3×C22⋊C4—81no—
291#217—22no—
292#217—42no—
293#217—42no—
294#217—42no—
295#217—42no—
296#213—44no—
297(C2×D3)⋊C4—22no—
298(C2×D3)⋊C4—42no—
299(C2×D3)⋊C4—42no—
300(C2×D3)⋊C4—42no—
301(C2×D3)⋊C4—42no—
302(C2×D3)⋊C4—81no—
303C4⋊Dic3—21no—
304C4⋊Dic3—21no—
305C4⋊Dic3—21no—
306C4⋊Dic3—42no—
307C4⋊Dic3C2×D412yes—
308Dic3⋊C4—22no—
309Dic3⋊C4—42no—
310C4×Dic3—81no—
311C4×Dic3C2×D412yes—
312C4×Dic3#4112yes—
313C2×C3⋊C8—21no—
314C2×C3⋊C8—21no—
315C2×C3⋊C8—21no—
316C2×C3⋊C8—21no—
317C2×C3⋊C8—21no—
318C2×C3⋊C8C2×D412yes—
319#204—44no—
320D3×C8—44no—
321C22×Q8—31no—
322C22×D4—21no—
323C22×D4—31no—
324C22×D4—31no—
325C22×D4—61no—
326C22×D4—61no—
327C22×D4—61no—
328C22×D4C22×D311yescharacteristic
329C23×C4—31no—
330C23×C4—61no—
331C23×C4C22×D311yescharacteristic
332C2×SD16—62no—
333C2×SD16—62no—
334C2×SD16—121no—
335C2×D8—62no—
336C2×D8—62no—
337C2×D8—121no—
338C22×C8—22no—
339C22×C8—22no—
340C22×C8—31no—
341C22×C8—31no—
342C22×C8—41no—
343C22×C8—62no—
344C22×C8—62no—
345C22×C8—121no—
346C22×C8C22×D311yescharacteristic
347C22×C8C22×D311yescharacteristic
348#124—62no—
349#124—62no—
350C22⋊Q8—62no—
351C22⋊Q8—62no—
352C22⋊Q8—121no—
353C22⋊Q8—121no—
354#121—22no—
355#121—41no—
356#121—62no—
357#121—62no—
358#121—62no—
359#121—121no—
360#121—121no—
361#121—121no—
362C4×D4—62no—
363C4×D4—62no—
364C4×D4—62no—
365C4×D4—62no—
366C2×C4⋊C4—31no—
367C2×C4⋊C4—31no—
368C2×C4⋊C4—31no—
369C2×C4⋊C4—61no—
370C2×C4⋊C4—61no—
371C2×C4⋊C4C22×D311yescharacteristic
372C2×C4⋊C4C22×D311yescharacteristic
373C2×C4⋊C4C22×D311yescharacteristic
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—31no—
377C2×C22⋊C4—31no—
378C2×C22⋊C4—61no—
379C2×C22⋊C4—61no—
380C2×C22⋊C4—61no—
381C2×C22⋊C4—61no—
382C2×C22⋊C4—61no—
383C2×C22⋊C4—61no—
384C2×C22⋊C4—61no—
385C2×C22⋊C4—61no—
386C2×C22⋊C4—61no—
387C2×C42—31no—
388C2×C42—61no—
389#107—62no—
390#106—62no—
391C4⋊C8—34no—
392#103—62no—
393#103—62no—
394#103—121no—
395#102—22no—
396#102—22no—
397#102—34no—
398#102—62no—
399#102—121no—
400C22⋊C8—62no—
401C22⋊C8—62no—
402C4×C8—62no—
403#95—21no—
404#95—61no—
405#95—61no—
406#95—61no—
407#95—61no—
408C23×C3—21no—
409C23×C3—21no—
410C23×C3—21no—
411C23×C3—21no—
412C23×C3—21no—
413C23×C3—21no—
414C23×C3—41no—
415C23×C3—41no—
416C23×C3—41no—
417C23×C3—41no—
418C23×C3—41no—
419C23×C3—41no—
420C23×C3—41no—
421C23×C3#13512yes—
422C23×C3C22×D411yescharacteristic
423C22×D3—21no—
424C22×D3—21no—
425C22×D3—21no—
426C22×D3—21no—
427C22×D3—21no—
428C22×D3—21no—
429C22×D3—22no—
430C22×D3—41no—
431C22×D3—41no—
432C22×D3—41no—
433C22×D3—41no—
434C22×D3—41no—
435C22×D3—41no—
436C22×D3#13512yes—
437C3×D4—41no—
438C3×D4—41no—
439C3×D4—41no—
440C3×D4—41no—
441C3×D4—84no—
442C2×C3×C4—21no—
443C2×C3×C4—21no—
444C2×C3×C4—22no—
445C2×C3×C4—21no—
446C2×C3×C4—41no—
447C2×C3×C4—41no—
448C2×C3×C4—41no—
449C2×C3×C4—41no—
450C2×C3×C4—41no—
451C2×C3×C4—41no—
452C2×C3×C4—41no—
453C2×C3×C4—41no—
454C2×C3×C4—41no—
455C2×C3×C4—41no—
456C2×C3×C4—41no—
457C2×C3×C4—41no—
458C2×C3×C4C22×D411yescharacteristic
459C2×C3×C4C22×D411yescharacteristic
460C2×C3×C4C2×#4111yescharacteristic
461C2×C3×C4C2×#4111yescharacteristic
462C2×C3×C4H(5,𝔽2)11yescharacteristic
463C2×C3×C4H(5,𝔽2)11yescharacteristic
464#67—28no—
465#67—84no—
466#67—84no—
467C2×Dic3—21no—
468C2×Dic3—21no—
469C2×Dic3—21no—
470C2×Dic3—21no—
471C2×Dic3—21no—
472C2×Dic3—22no—
473C2×Dic3—21no—
474C2×Dic3—21no—
475C2×Dic3—41no—
476C2×Dic3—41no—
477C2×Dic3—41no—
478C2×Dic3—41no—
479C2×Dic3—41no—
480C2×Dic3—41no—
481C2×Dic3—41no—
482C2×Dic3—41no—
483C2×Dic3#12112yes—
484C2×Dic3#12112yes—
485D12—22no—
486D12—22no—
487D12—41no—
488D12—41no—
489D12—84no—
490C4×D3—41no—
491C4×D3—41no—
492C4×D3—41no—
493C4×D3—41no—
494C4×D3—84no—
495Dic6—41no—
496Dic6—41no—
497Dic6—41no—
498Dic6—41no—
499C3×C8—22no—
500C3×C8—22no—
501C3⋊C8—22no—
502C3⋊C8—41no—
503C24—21no—
504C24—31no—
505C24—61no—
506C24D3×D411yescharacteristic
507C2×Q8—61no—
508C2×Q8—61no—
509C2×Q8—61no—
510C2×Q8—61no—
511C2×Q8—61no—
512C2×Q8—61no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—32no—
520C2×D4—42no—
521C2×D4—42no—
522C2×D4—62no—
523C2×D4—62no—
524C2×D4—62no—
525C2×D4—61no—
526C2×D4—61no—
527C2×D4—61no—
528C2×D4—61no—
529C2×D4—61no—
530C2×D4—81no—
531C2×D4—122no—
532C2×D4—122no—
533C2×D4—122no—
534C2×D4—122no—
535C2×D4—122no—
536C2×D4—122no—
537C2×D4—241no—
538C2×D4—241no—
539C2×D4—241no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—31no—
550C22×C4—31no—
551C22×C4—31no—
552C22×C4—61no—
553C22×C4—61no—
554C22×C4—61no—
555C22×C4—61no—
556C22×C4—61no—
557C22×C4—61no—
558C22×C4—61no—
559C22×C4—61no—
560C22×C4—61no—
561C22×C4—122no—
562C22×C4—241no—
563C22×C4—241no—
564C22×C4D3×D411yescharacteristic
565C22×C4C23×D311yescharacteristic
566SD16—124no—
567D8—124no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—32no—
573C2×C8—44no—
574C2×C8—61no—
575C2×C8—61no—
576C2×C8—61no—
577C2×C8—61no—
578C2×C8—61no—
579C2×C8—124no—
580C2×C8D3×D412yes—
581C2×C8D3×D412yes—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—32no—
588C4⋊C4—62no—
589C4⋊C4—61no—
590C4⋊C4—61no—
591C4⋊C4—61no—
592C4⋊C4—122no—
593C4⋊C4—122no—
594C4⋊C4#23512yes—
595C22⋊C4—42no—
596C22⋊C4—62no—
597C22⋊C4—62no—
598C22⋊C4—81no—
599C22⋊C4—122no—
600C22⋊C4—122no—
601C22⋊C4—122no—
602C22⋊C4—122no—
603C22⋊C4—122no—
604C22⋊C4—122no—
605C22⋊C4—122no—
606C22⋊C4—122no—
607C22⋊C4—241no—
608C42—32no—
609C42—32no—
610C42—241no—
611C22×C3—22no—
612C22×C3—22no—
613C22×C3—22no—
614C22×C3—41no—
615C22×C3—41no—
616C22×C3—41no—
617C22×C3—41no—
618C22×C3—81no—
619C22×C3—81no—
620C22×C3—81no—
621C22×C3—81no—
622C22×C3—81no—
623C22×C3—81no—
624C22×C3—81no—
625C22×C3C2×#12111yescharacteristic
626C22×C3D4211yescharacteristic
627C22×C3#54611yescharacteristic
628C22×C3C2×#13511yescharacteristic
629C22×C3C2×#13511yescharacteristic
630C22×C3#57611yescharacteristic
631C22×C3#57711yescharacteristic
632C2×D3—22no—
633C2×D3—22no—
634C2×D3—22no—
635C2×D3—41no—
636C2×D3—41no—
637C2×D3—41no—
638C2×D3—41no—
639C2×D3—42no—
640C2×D3—42no—
641C2×D3—42no—
642C2×D3—81no—
643C2×D3—81no—
644C2×D3—81no—
645C2×D3—81no—
646C3×C4—41no—
647C3×C4—42no—
648C3×C4—81no—
649C3×C4—81no—
650C3×C4#53211yescharacteristic
651C3×C4#54011yescharacteristic
652C3×C4D4211yescharacteristic
653C3×C4#55011yescharacteristic
654Dic3—22no—
655Dic3—22no—
656Dic3—41no—
657Dic3—42no—
658Dic3—81no—
659Dic3—81no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—32no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—61no—
675C23—61no—
676C23—61no—
677C23—61no—
678C23—61no—
679C23—61no—
680C23—62no—
681C23—121no—
682C23—121no—
683C23—121no—
684C23—121no—
685C23—121no—
686C23—121no—
687C23#91612yes—
688C23C2×D3×D411yescharacteristic
689Q8—121no—
690Q8—121no—
691Q8—121no—
692Q8—121no—
693D4—41no—
694D4—41no—
695D4—41no—
696D4—41no—
697D4—68no—
698D4—62no—
699D4—62no—
700D4—84no—
701D4—121no—
702D4—121no—
703D4—244no—
704D4—244no—
705D4—244no—
706C2×C4—21no—
707C2×C4—22no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—32no—
711C2×C4—32no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—61no—
728C2×C4—61no—
729C2×C4—61no—
730C2×C4—61no—
731C2×C4—62no—
732C2×C4—121no—
733C2×C4—121no—
734C2×C4—121no—
735C2×C4—121no—
736C2×C4—121no—
737C2×C4—121no—
738C2×C4—121no—
739C2×C4—121no—
740C2×C4—121no—
741C2×C4—121no—
742C2×C4—121no—
743C2×C4—121no—
744C2×C4—244no—
745C2×C4C2×#23511yescharacteristic
746C2×C4C2×D3×D411yescharacteristic
747C2×C4C2×D3×D411yescharacteristic
748C2×C4#100411yescharacteristic
749C2×C4D3×#4111yescharacteristic
750C2×C4#100911yescharacteristic
751C8—22no—
752C8—22no—
753C8—62no—
754C8—121no—
755C2×C3—42no—
756C2×C3—161no—
757C2×C3#242811yescharacteristic
758C2×C3#305011yescharacteristic
759C2×C3#306211yescharacteristic
760C2×C3#328011yescharacteristic
761C2×C3#328211yescharacteristic
762C2×C3#329711yescharacteristic
763C2×C3#330111yescharacteristic
764D3—42no—
765D3—82no—
766C22—22no—
767C22—22no—
768C22—22no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—62no—
774C22—62no—
775C22—62no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22—81no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22—121no—
784C22—121no—
785C22—121no—
786C22—121no—
787C22—122no—
788C22—122no—
789C22—122no—
790C22—241no—
791C22—241no—
792C22—241no—
793C22—241no—
794C22#549011yescharacteristic
795C22D3×#12111yescharacteristic
796C22#560911yescharacteristic
797C22#575711yescharacteristic
798C22C2×#91611yescharacteristic
799C22D3×#13511yescharacteristic
800C22#577011yescharacteristic
801C4—42no—
802C4—41no—
803C4—62no—
804C4—62no—
805C4—81no—
806C4—81no—
807C4—122no—
808C4—121no—
809C4—241no—
810C4—241no—
811C4#554811yescharacteristic
812C4#555311yescharacteristic
813C4#559011yescharacteristic
814C4#566311yescharacteristic
815C3#2538811yescharacteristic, complemented, Sylow
816C2—42no—
817C2—122no—
818C2—161no—
819C2—242no—
820C2#7469811yescharacteristic
821C2#7876011yescharacteristic
822C2#7884811yescharacteristic
823C2#8065611yescharacteristic
824C2#8067711yescharacteristic
825C2#8071811yescharacteristic
826C2#8073011yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1893C2
socleC23×C3C22×D4
hypercenter#1893D3
hypocenterC3#25388
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1893

Complements

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

NH ≅ G/Ntype
1. C2×#5114C2semidirect
2. C2×C8×#67C2semidirect
3. #82668C2semidirect
4. C2×#4787C2semidirect
5. C2×#4775C2semidirect
6. #73933C2semidirect
7. C3×#1893C2semidirect
8. #71684C2semidirect
9. #70176C2semidirect
10. #70158C2semidirect
11. #69527C2semidirect
12. #68887C2semidirect
13. #68882C2semidirect
14. #68797C2semidirect
15. #68780C2semidirect
76. #1893D3semidirect
156. #821D4semidirect
160. Dic3⋊C8D4semidirect
815. C3#25388semidirect

Maximal subgroups

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

subgroupindex
C2×#51142
C2×C8×#672
#826682
C2×#47872
C2×#47752
#739332
C3×#18932
#716842
#701762
#701582
#695272
#688872
#688822
#687972
#687802
#253883