Finite Group Databasebeta

← #10829238

Subgroups — #10829238

Order 768.

1204 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5532C211yesmaximal, characteristic, complemented
2C2×#4890C211yesmaximal, characteristic, complemented
3C2×#4869C211yesmaximal, characteristic, complemented
4#73933C211yesmaximal, characteristic, complemented
5C3×#1854C211yesmaximal, characteristic, complemented
6#71586C211yesmaximal, characteristic, complemented
7#70634C211yesmaximal, characteristic, complemented
8#70580C211yesmaximal, characteristic, complemented
9#69961C211yesmaximal, characteristic, complemented
10#69917C211yesmaximal, characteristic, complemented
11#69523C211yesmaximal, characteristic, complemented
12#68893C211yesmaximal, characteristic, complemented
13#68886C211yesmaximal, characteristic, complemented
14#68881C211yesmaximal, characteristic, complemented
15#68806C211yesmaximal, characteristic, complemented
16#24129—31nomaximal, Sylow
17C2×C3×#117C2211yescharacteristic
18C2×#930C2211yescharacteristic
19C2×#930C2211yescharacteristic
20C2×C4×#67C2211yescharacteristic
21C22×D24C2211yescharacteristic
22#5532—24no—
23#5532—24no—
24C2×#895C2211yescharacteristic
25C2×#895C2211yescharacteristic
26C2×#893C2211yescharacteristic
27C2×#893C2211yescharacteristic
28C2×#892C2211yescharacteristic
29C2×#888C2211yescharacteristic
30C2×#885—21no—
31C2×#884—21no—
32C2×#875—21no—
33C2×#872—21no—
34C2×C3×#107C2211yescharacteristic
35C2×C3×#106C2211yescharacteristic
36C2×C3×C22⋊C8C2211yescharacteristic
37C3×#380C2211yescharacteristic
38C2×#830C2211yescharacteristic
39C2×#821C2211yescharacteristic
40C2×#821C2211yescharacteristic
41C2×(C2×D3)⋊C8C2211yescharacteristic
42C2×(C2×D3)⋊C8C2211yescharacteristic
43C2×#815C2211yescharacteristic
44C2×Dic3⋊C8C2211yescharacteristic
45#4987C2211yescharacteristic
46#4977C2211yescharacteristic
47C2×#809C2211yescharacteristic
48C2×#809C2211yescharacteristic
49C2×#809C2211yescharacteristic
50C2×#809C2211yescharacteristic
51C2×#807C2211yescharacteristic
52#4960—21no—
53#4956—21no—
54#4890—24no—
55#4869—24no—
56#4675—21no—
57#4665—21no—
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60#4551C2211yescharacteristic
61#4529C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#555—31no—
65C2×#474—31no—
66C2×#442—31no—
67#2535—31no—
68#2033—31no—
69#2033—31no—
70#1999—31no—
71#1999—31no—
72#1993—31no—
73#1955—31no—
74#1875—31no—
75#1875—31no—
76#1854—31no—
77#1854D311yescharacteristic, complemented
78#1804—31no—
79C23×C3×C4C2311yescharacteristic
80C22×#67—21no—
81C22×#67—21no—
82C22×#67D411yescharacteristic
83C22×D12—21no—
84C22×D12—21no—
85C22×D12C2311yescharacteristic
86C22×D12C2311yescharacteristic
87C22×C4×D3—21no—
88C22×C4×D3—21no—
89C22×C4×D3C2311yescharacteristic
90C22×Dic6—21no—
91C22×C3×C8C2311yescharacteristic
92C22×C3×C8C2311yescharacteristic
93C3×#117—22no—
94C3×#117—22no—
95C2×C3×C4⋊C4C2311yescharacteristic
96C2×C3×C4⋊C4C2311yescharacteristic
97C2×C3×C4⋊C4C2311yescharacteristic
98C2×C3×C4⋊C4C2311yescharacteristic
99C2×C3×C22⋊C4—21no—
100C2×C3×C22⋊C4—21no—
101C2×C3×C42—21no—
102C2×#217D411yescharacteristic
103#930—22no—
104#930—22no—
105#930—22no—
106#930—41no—
107C4×#67—22no—
108C4×#67—22no—
109C2×(C2×D3)⋊C4—21no—
110C2×(C2×D3)⋊C4—21no—
111C2×(C2×D3)⋊C4—21no—
112C2×(C2×D3)⋊C4—21no—
113C2×(C2×D3)⋊C4—21no—
114C2×(C2×D3)⋊C4—21no—
115C2×(C2×D3)⋊C4—21no—
116C2×(C2×D3)⋊C4—21no—
117C2×(C2×D3)⋊C4D411yescharacteristic
118C2×C4⋊Dic3C2311yescharacteristic
119C2×C4⋊Dic3C2311yescharacteristic
120C2×Dic3⋊C4—21no—
121C2×Dic3⋊C4D411yescharacteristic
122C2×C4×Dic3—21no—
123C2×C4×Dic3C2311yescharacteristic
124C22×C3⋊C8C2311yescharacteristic
125C22×C3⋊C8C2311yescharacteristic
126C2×D24—22no—
127C2×D24—22no—
128C2×D24—22no—
129#895—22no—
130#895—22no—
131#895—22no—
132#895—41no—
133#893—22no—
134#893—22no—
135#893—22no—
136#893D414yescomplemented
137#892—22no—
138#892—22no—
139#888—22no—
140#888D414yescomplemented
141#885—28no—
142#884—28no—
143#875—28no—
144#872—28no—
145C3×#107—22no—
146C3×#106—22no—
147C3×C22⋊C8—22no—
148C3×#95—21no—
149C3⋊#95—21no—
150C3⋊#95—21no—
151C3⋊#95—21no—
152#830—41no—
153#821—22no—
154#821—41no—
155(C2×D3)⋊C8—22no—
156(C2×D3)⋊C8—41no—
157#815—22no—
158Dic3⋊C8—22no—
159#809—22no—
160#809—22no—
161#809—22no—
162#809—41no—
163#807—22no—
164C22×D8—31no—
165#555—64no—
166#555—64no—
167C2×C4⋊Q8—31no—
168C2×#124—61no—
169C2×#124—61no—
170C2×#121—31no—
171C2×#121—31no—
172C2×#121—31no—
173C2×#121—31no—
174C2×#121—61no—
175C2×C4×D4—31no—
176C2×C4×D4—31no—
177C2×C4×D4—31no—
178C2×#117—31no—
179C2×#117—61no—
180C2×#117C2×D311yescharacteristic
181#474—64no—
182#442—64no—
183C2×#107—31no—
184C2×#107C2×D311yescharacteristic
185C2×#106C2×D311yescharacteristic
186C2×C4⋊C8—31no—
187C2×#102—31no—
188C2×#102—31no—
189C2×#102—31no—
190C2×#102—31no—
191C2×#102—31no—
192C2×#102—31no—
193C2×C22⋊C8—31no—
194C2×C22⋊C8—31no—
195C2×C22⋊C8—31no—
196C2×C22⋊C8C2×D311yescharacteristic
197C2×#97—31no—
198#397—61no—
199#392—61no—
200#386—61no—
201#386—61no—
202#382—31no—
203#380—31no—
204#380C2×D311yescharacteristic
205#340—31no—
206#340—31no—
207#340—31no—
208#340—31no—
209#340C2×D311yescharacteristic
210#340C2×D311yescharacteristic
211C24×C3C2×D411yescharacteristic
212C23×D3—21no—
213C23×D3—21no—
214C23×D3C2×D411yescharacteristic
215C22×C3×C4—21no—
216C22×C3×C4—21no—
217C22×C3×C4—21no—
218C22×C3×C4—21no—
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4C2×D411yescharacteristic
226C22×C3×C4C2411yescharacteristic
227C2×#67—24no—
228C2×#67—22no—
229C2×#67—41no—
230C2×#67—41no—
231C2×#67—42no—
232C2×#67—42no—
233C2×#67—81no—
234C2×#67—81no—
235C2×#67—81no—
236C22×Dic3—21no—
237C22×Dic3—21no—
238C22×Dic3C2×D411yescharacteristic
239C22×Dic3C2×D411yescharacteristic
240C22×Dic3C2×D411yescharacteristic
241C2×D12—21no—
242C2×D12—21no—
243C2×D12—21no—
244C2×D12—21no—
245C2×D12—21no—
246C2×D12—21no—
247C2×D12—21no—
248C2×D12—21no—
249C2×D12—21no—
250C2×D12—21no—
251C2×D12—24no—
252C2×D12—42no—
253C2×D12—42no—
254C2×D12—81no—
255C2×D12—81no—
256C2×D12—81no—
257C2×D12C2×D412yes—
258C2×D12#4112yes—
259C2×C4×D3—21no—
260C2×C4×D3—21no—
261C2×C4×D3—21no—
262C2×C4×D3—21no—
263C2×C4×D3—21no—
264C2×C4×D3—21no—
265C2×C4×D3—24no—
266C2×C4×D3—42no—
267C2×C4×D3—42no—
268C2×C4×D3—42no—
269C2×C4×D3—81no—
270C2×C4×D3—81no—
271C2×Dic6—24no—
272C2×Dic6—81no—
273C2×Dic6—81no—
274C2×C3×C8—21no—
275C2×C3×C8—21no—
276C2×C3×C8—21no—
277C2×C3×C8—21no—
278C2×C3×C8—21no—
279C2×C3×C8#4112yes—
280C3×C4⋊C4—21no—
281C3×C4⋊C4—21no—
282C3×C4⋊C4—21no—
283C3×C4⋊C4—21no—
284C3×C4⋊C4—21no—
285C3×C4⋊C4—21no—
286C3×C4⋊C4C2×D412yes—
287C3×C4⋊C4C2×D412yes—
288C3×C22⋊C4—24no—
289C3×C22⋊C4—81no—
290C3×C42—24no—
291#217—22no—
292(C2×D3)⋊C4—24no—
293(C2×D3)⋊C4—24no—
294(C2×D3)⋊C4—24no—
295(C2×D3)⋊C4—22no—
296(C2×D3)⋊C4—24no—
297(C2×D3)⋊C4—42no—
298(C2×D3)⋊C4—42no—
299(C2×D3)⋊C4—42no—
300(C2×D3)⋊C4—81no—
301C4⋊Dic3—21no—
302C4⋊Dic3—21no—
303C4⋊Dic3—21no—
304C4⋊Dic3C2×D412yes—
305Dic3⋊C4—22no—
306Dic3⋊C4—24no—
307C4×Dic3—24no—
308C4×Dic3C2×D412yes—
309C4×Dic3C2×D412yes—
310C2×C3⋊C8—21no—
311C2×C3⋊C8—21no—
312C2×C3⋊C8—21no—
313C2×C3⋊C8—21no—
314C2×C3⋊C8—21no—
315C2×C3⋊C8—21no—
316D24—28no—
317C22×Q8—61no—
318C22×D4—31no—
319C22×D4—31no—
320C22×D4—31no—
321C22×D4—61no—
322C22×D4—61no—
323C22×D4—61no—
324C22×D4—61no—
325C23×C4—31no—
326C23×C4—61no—
327C23×C4—61no—
328C23×C4C22×D311yescharacteristic
329C2×D8—62no—
330C2×D8—62no—
331C2×D8—62no—
332C22×C8—31no—
333C22×C8—31no—
334C22×C8C22×D311yescharacteristic
335C22×C8C22×D311yescharacteristic
336C4⋊Q8—34no—
337C4⋊Q8—62no—
338#124—68no—
339#124—68no—
340#121—68no—
341#121—62no—
342#121—62no—
343#121—62no—
344#121—62no—
345#121—62no—
346#121—62no—
347#121—121no—
348#121—121no—
349C4×D4—34no—
350C4×D4—62no—
351C4×D4—62no—
352C4×D4—62no—
353C4×D4—62no—
354C4×D4—62no—
355#117—22no—
356#117—22no—
357#117—68no—
358#117—62no—
359#117—62no—
360C2×C4⋊C4—31no—
361C2×C4⋊C4—31no—
362C2×C4⋊C4—31no—
363C2×C4⋊C4—61no—
364C2×C4⋊C4C22×D311yescharacteristic
365C2×C4⋊C4C22×D311yescharacteristic
366C2×C4⋊C4C22×D311yescharacteristic
367C2×C4⋊C4C22×D311yescharacteristic
368C2×C22⋊C4—21no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—31no—
371C2×C22⋊C4—31no—
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—21no—
381C2×C42—31no—
382C2×C42—61no—
383#107—22no—
384#107—62no—
385#106—22no—
386C4⋊C8—62no—
387#102—62no—
388#102—62no—
389#102—62no—
390#102—62no—
391#102—121no—
392#102—121no—
393C22⋊C8—22no—
394C22⋊C8—62no—
395C22⋊C8—121no—
396C22⋊C8—121no—
397#97—62no—
398#95—21no—
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—21no—
409C23×C3C22×D411yescharacteristic
410C22×D3—21no—
411C22×D3—22no—
412C22×D3—22no—
413C22×D3—21no—
414C22×D3—21no—
415C22×D3—21no—
416C22×D3—21no—
417C22×D3—21no—
418C22×D3—21no—
419C22×D3—41no—
420C22×D3—41no—
421C22×D3—41no—
422C22×D3—41no—
423C22×D3—41no—
424C22×D3—41no—
425C22×D3—41no—
426C22×D3—41no—
427C22×D3—41no—
428C22×D3—41no—
429C22×D3—41no—
430C22×D3—41no—
431C2×C3×C4—22no—
432C2×C3×C4—21no—
433C2×C3×C4—22no—
434C2×C3×C4—21no—
435C2×C3×C4—21no—
436C2×C3×C4—41no—
437C2×C3×C4—41no—
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×C4—41no—
448C2×C3×C4—41no—
449C2×C3×C4—41no—
450C2×C3×C4C22×D411yescharacteristic
451C2×C3×C4C22×D411yescharacteristic
452C2×C3×C4C2×#4111yescharacteristic
453C2×C3×C4C2×#4111yescharacteristic
454C2×C3×C4H(5,𝔽2)11yescharacteristic
455C2×C3×C42−1+411yescharacteristic
456#67—44no—
457#67—84no—
458#67—84no—
459C2×Dic3—21no—
460C2×Dic3—21no—
461C2×Dic3—21no—
462C2×Dic3—21no—
463C2×Dic3—21no—
464C2×Dic3—22no—
465C2×Dic3—21no—
466C2×Dic3—21no—
467C2×Dic3—41no—
468C2×Dic3—41no—
469C2×Dic3—41no—
470C2×Dic3—41no—
471C2×Dic3—41no—
472C2×Dic3#12012yes—
473C2×Dic3#12012yes—
474D12—22no—
475D12—22no—
476D12—22no—
477D12—22no—
478D12—41no—
479D12—41no—
480D12—41no—
481D12—41no—
482D12—84no—
483D12—84no—
484C4×D3—48no—
485C4×D3—41no—
486C4×D3—41no—
487C4×D3—41no—
488C4×D3—41no—
489C4×D3—84no—
490Dic6—84no—
491C3×C8—22no—
492C3×C8—41no—
493C3⋊C8—41no—
494C3⋊C8—41no—
495C24—31no—
496C24—61no—
497C24—61no—
498C24D3×D411yescharacteristic
499C2×Q8—64no—
500C2×Q8—241no—
501C2×Q8—241no—
502C2×D4—32no—
503C2×D4—32no—
504C2×D4—64no—
505C2×D4—62no—
506C2×D4—64no—
507C2×D4—61no—
508C2×D4—61no—
509C2×D4—61no—
510C2×D4—61no—
511C2×D4—61no—
512C2×D4—61no—
513C2×D4—61no—
514C2×D4—61no—
515C2×D4—61no—
516C2×D4—61no—
517C2×D4—122no—
518C2×D4—122no—
519C2×D4—121no—
520C2×D4—121no—
521C2×D4—122no—
522C2×D4—122no—
523C2×D4—241no—
524C2×D4—241no—
525C2×D4—241no—
526C2×D4—241no—
527C2×D4—241no—
528C2×D4—241no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—31no—
540C22×C4—31no—
541C22×C4—31no—
542C22×C4—64no—
543C22×C4—61no—
544C22×C4—61no—
545C22×C4—61no—
546C22×C4—61no—
547C22×C4—61no—
548C22×C4—61no—
549C22×C4—61no—
550C22×C4—61no—
551C22×C4—122no—
552C22×C4—122no—
553C22×C4—122no—
554C22×C4—241no—
555C22×C4—241no—
556C22×C4D3×D411yescharacteristic
557C22×C4C23×D311yescharacteristic
558D8—68no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—61no—
565C2×C8—61no—
566C2×C8—61no—
567C2×C8—61no—
568C2×C8—61no—
569C2×C8—61no—
570C2×C8#23512yes—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—32no—
578C4⋊C4—62no—
579C4⋊C4—64no—
580C4⋊C4—61no—
581C4⋊C4—61no—
582C4⋊C4—61no—
583C4⋊C4D3×D412yes—
584C4⋊C4D3×D412yes—
585C22⋊C4—24no—
586C22⋊C4—62no—
587C22⋊C4—64no—
588C22⋊C4—64no—
589C22⋊C4—64no—
590C22⋊C4—64no—
591C22⋊C4—62no—
592C22⋊C4—81no—
593C22⋊C4—122no—
594C22⋊C4—122no—
595C22⋊C4—122no—
596C22⋊C4—241no—
597C42—24no—
598C42—32no—
599C42—32no—
600C42—64no—
601C22×C3—41no—
602C22×C3—41no—
603C22×C3—41no—
604C22×C3—41no—
605C22×C3—41no—
606C22×C3—41no—
607C22×C3—41no—
608C22×C3C2×#12011yescharacteristic
609C22×C3#54611yescharacteristic
610C22×C3#54711yescharacteristic
611C22×C3#57511yescharacteristic
612C22×C3#57511yescharacteristic
613C22×C3#57611yescharacteristic
614C22×C3#57611yescharacteristic
615C2×D3—41no—
616C2×D3—41no—
617C2×D3—41no—
618C2×D3—42no—
619C2×D3—42no—
620C2×D3—42no—
621C2×D3—41no—
622C2×D3—41no—
623C2×D3—42no—
624C2×D3—41no—
625C2×D3—42no—
626C2×D3—42no—
627C2×D3—41no—
628C2×D3—81no—
629C2×D3—81no—
630C2×D3—81no—
631C2×D3—81no—
632C2×D3—81no—
633C2×D3—81no—
634C2×D3—81no—
635C2×D3—81no—
636C3×C4—41no—
637C3×C4—42no—
638C3×C4—42no—
639C3×C4—81no—
640C3×C4—81no—
641C3×C4#52511yescharacteristic
642C3×C4#53711yescharacteristic
643C3×C4#54811yescharacteristic
644C3×C4#55011yescharacteristic
645Dic3—22no—
646Dic3—22no—
647Dic3—41no—
648Dic3—42no—
649Dic3—81no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—62no—
658C23—61no—
659C23—61no—
660C23—61no—
661C23—61no—
662C23—61no—
663C23—61no—
664C23—62no—
665C23—61no—
666C23—121no—
667C23—121no—
668C23—121no—
669C23—121no—
670C23—121no—
671C23—121no—
672C23—121no—
673C23—121no—
674C23—121no—
675C23—121no—
676C23—121no—
677C23—121no—
678C23C2×D3×D411yescharacteristic
679Q8—244no—
680D4—62no—
681D4—62no—
682D4—62no—
683D4—62no—
684D4—124no—
685D4—121no—
686D4—121no—
687D4—121no—
688D4—121no—
689D4—244no—
690D4—244no—
691D4—244no—
692D4—244no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—32no—
699C2×C4—32no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—61no—
715C2×C4—61no—
716C2×C4—61no—
717C2×C4—61no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—62no—
722C2×C4—128no—
723C2×C4—121no—
724C2×C4—121no—
725C2×C4—121no—
726C2×C4—121no—
727C2×C4—121no—
728C2×C4—121no—
729C2×C4—121no—
730C2×C4—121no—
731C2×C4—121no—
732C2×C4—244no—
733C2×C4C2×#23511yescharacteristic
734C2×C4C2×D3×D411yescharacteristic
735C2×C4C2×D3×D411yescharacteristic
736C2×C4#100711yescharacteristic
737C2×C4D3×#4111yescharacteristic
738C2×C4#100911yescharacteristic
739C8—22no—
740C8—41no—
741C8—121no—
742C8—121no—
743C2×C3—81no—
744C2×C3#240711yescharacteristic
745C2×C3#300511yescharacteristic
746C2×C3#300811yescharacteristic
747C2×C3#331911yescharacteristic
748C2×C3#331911yescharacteristic
749C2×C3#334711yescharacteristic
750C2×C3#334711yescharacteristic
751D3—81no—
752D3—82no—
753D3—82no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—121no—
762C22—122no—
763C22—121no—
764C22—122no—
765C22—121no—
766C22—121no—
767C22—121no—
768C22—122no—
769C22—122no—
770C22—121no—
771C22—122no—
772C22—121no—
773C22—122no—
774C22—241no—
775C22—241no—
776C22—241no—
777C22—241no—
778C22—241no—
779C22—241no—
780C22—241no—
781C22—241no—
782C22#550711yescharacteristic
783C22D3×#12011yescharacteristic
784C22#565411yescharacteristic
785C22#576811yescharacteristic
786C22#576911yescharacteristic
787C22#577411yescharacteristic
788C22#577711yescharacteristic
789C4—42no—
790C4—41no—
791C4—42no—
792C4—62no—
793C4—62no—
794C4—81no—
795C4—81no—
796C4—121no—
797C4—122no—
798C4—241no—
799C4#554711yescharacteristic
800C4#555311yescharacteristic
801C4#562911yescharacteristic
802C4#563311yescharacteristic
803C3#2412911yescharacteristic, complemented, Sylow
804C2—81no—
805C2—241no—
806C2—242no—
807C2—242no—
808C2#7440411yescharacteristic
809C2#7919211yescharacteristic
810C2#7922711yescharacteristic
811C2#8008511yescharacteristic
812C2#8022711yescharacteristic
813C2#8140211yescharacteristic
814C2#8152811yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1854C2
socleC23×C3C22×D4
hypercenter#1854D3
hypocenterC3#24129
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1854

Complements

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

NH ≅ G/Ntype
1. C2×#5532C2semidirect
2. C2×#4890C2semidirect
3. C2×#4869C2semidirect
4. #73933C2semidirect
5. C3×#1854C2semidirect
6. #71586C2semidirect
7. #70634C2semidirect
8. #70580C2semidirect
9. #69961C2semidirect
10. #69917C2semidirect
11. #69523C2semidirect
12. #68893C2semidirect
13. #68886C2semidirect
14. #68881C2semidirect
15. #68806C2semidirect
77. #1854D3semidirect
136. #893D4semidirect
140. #888D4semidirect
803. C3#24129semidirect

Maximal subgroups

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

subgroupindex
C2×#55322
C2×#48902
C2×#48692
#739332
C3×#18542
#715862
#706342
#705802
#699612
#699172
#695232
#688932
#688862
#688812
#688062
#241293