Finite Group Databasebeta

← #10829236

Subgroups — #10829236

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
2#82666C211yesmaximal, characteristic, complemented
3C2×#4759C211yesmaximal, characteristic, complemented
4C2×#4785C211yesmaximal, characteristic, complemented
5C3×#1875C211yesmaximal, characteristic, complemented
6#71684C211yesmaximal, characteristic, complemented
7#71576C211yesmaximal, characteristic, complemented
8#70204C211yesmaximal, characteristic, complemented
9#70201C211yesmaximal, characteristic, complemented
10#69934C211yesmaximal, characteristic, complemented
11#69917C211yesmaximal, characteristic, complemented
12#68893C211yesmaximal, characteristic, complemented
13#68877C211yesmaximal, characteristic, complemented
14#68822C211yesmaximal, characteristic, complemented
15#68806C211yesmaximal, characteristic, complemented
16#24129—31nomaximal, Sylow
17C2×C3×#121C2211yescharacteristic
18C2×C3×#117C2211yescharacteristic
19C2×#938C2211yescharacteristic
20C2×D4×Dic3C2211yescharacteristic
21C22×#213C2211yescharacteristic
22C2×#930C2211yescharacteristic
23C2×C4×#67C2211yescharacteristic
24#5532—24no—
25#5532—24no—
26C2×#895C2211yescharacteristic
27C2×#893C2211yescharacteristic
28C2×#892C2211yescharacteristic
29C2×#888C2211yescharacteristic
30C2×#885—21no—
31C2×#884—21no—
32C2×#875—21no—
33C2×#872—21no—
34C2×C3×#102C2211yescharacteristic
35C2×C3×#102C2211yescharacteristic
36C2×C3×C22⋊C8C2211yescharacteristic
37#5223—21no—
38#5220—21no—
39C2×#832C2211yescharacteristic
40#5212C2211yescharacteristic
41C2×#830C2211yescharacteristic
42C2×#821C2211yescharacteristic
43C2×#821C2211yescharacteristic
44C2×(C2×D3)⋊C8C2211yescharacteristic
45C2×(C2×D3)⋊C8C2211yescharacteristic
46C2×#818C2211yescharacteristic
47C2×#815C2211yescharacteristic
48C2×Dic3⋊C8C2211yescharacteristic
49#4987C2211yescharacteristic
50#4977C2211yescharacteristic
51C2×#809C2211yescharacteristic
52C2×#808C2211yescharacteristic
53C2×#807C2211yescharacteristic
54#4958—21no—
55#4952—21no—
56#4785—24no—
57#4759—24no—
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#1875D311yescharacteristic, complemented
76#1854—31no—
77#1854—31no—
78#1804—31no—
79C22×C3×D4—21no—
80C22×C3×D4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C22×#67—21no—
83C22×#67—21no—
84C22×#67D411yescharacteristic
85C23×Dic3—21no—
86C22×D12—21no—
87C22×D12C2311yescharacteristic
88C22×C4×D3—21no—
89C22×C4×D3C2311yescharacteristic
90C22×Dic6—21no—
91C22×C3×C8C2311yescharacteristic
92C22×C3×C8C2311yescharacteristic
93C3×#121—22no—
94C3×#121—41no—
95C3×#117—22no—
96C3×#117—22no—
97C2×C3×C4⋊C4C2311yescharacteristic
98C2×C3×C4⋊C4C2311yescharacteristic
99C2×C3×C4⋊C4C2311yescharacteristic
100C2×C3×C22⋊C4—21no—
101C2×C3×C22⋊C4—21no—
102C2×C3×C42—21no—
103C2×#217—21no—
104C2×#217—21no—
105C2×#217—21no—
106C2×#217D411yescharacteristic
107#938—22no—
108#938—41no—
109D4×Dic3—22no—
110D4×Dic3—22no—
111C2×#213—22no—
112C2×#213—22no—
113C2×#213—22no—
114#930—22no—
115#930—22no—
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⋊Dic3C2311yescharacteristic
125C2×C4⋊Dic3C2311yescharacteristic
126C2×C4⋊Dic3C2311yescharacteristic
127C2×Dic3⋊C4—21no—
128C2×Dic3⋊C4D411yescharacteristic
129C2×C4×Dic3—21no—
130C2×C4×Dic3C2311yescharacteristic
131C22×C3⋊C8C2311yescharacteristic
132C22×C3⋊C8C2311yescharacteristic
133#895—22no—
134#895—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×#102—22no—
146C3×#102—22no—
147C3×C22⋊C8—41no—
148#832—22no—
149C3⋊#95—21no—
150C3⋊#95—21no—
151C3⋊#95—21no—
152C3⋊#95—21no—
153#830—22no—
154#821—22no—
155#821—41no—
156(C2×D3)⋊C8—22no—
157(C2×D3)⋊C8—41no—
158#818—22no—
159#815—22no—
160Dic3⋊C8—22no—
161#809—41no—
162#808—22no—
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—61no—
174C2×#121C2×D311yescharacteristic
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×#107—31no—
185C2×#106—31no—
186C2×C4⋊C8—31no—
187C2×#102—31no—
188C2×#102—31no—
189C2×#102—31no—
190C2×#102—31no—
191C2×#102C2×D311yescharacteristic
192C2×#102C2×D311yescharacteristic
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#380—31no—
205#340—31no—
206#340—31no—
207#340—31no—
208#340—31no—
209#340C2×D311yescharacteristic
210#340C2×D311yescharacteristic
211C24×C3—21no—
212C24×C3C2×D411yescharacteristic
213C23×D3—21no—
214C23×D3C2×D411yescharacteristic
215C2×C3×D4—21no—
216C2×C3×D4—21no—
217C2×C3×D4—21no—
218C2×C3×D4—21no—
219C2×C3×D4—21no—
220C2×C3×D4—42no—
221C2×C3×D4—42no—
222C2×C3×D4—81no—
223C2×C3×D4#4112yes—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
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×C4C2×D411yescharacteristic
234C22×C3×C4C2411yescharacteristic
235C2×#67—24no—
236C2×#67—22no—
237C2×#67—41no—
238C2×#67—41no—
239C2×#67—42no—
240C2×#67—42no—
241C2×#67—81no—
242C2×#67—81no—
243C2×#67—81no—
244C22×Dic3—21no—
245C22×Dic3—21no—
246C22×Dic3—21no—
247C22×Dic3—42no—
248C22×Dic3—81no—
249C22×Dic3—81no—
250C22×Dic3C2×D411yescharacteristic
251C22×Dic3C2×D411yescharacteristic
252C22×Dic3C2×D411yescharacteristic
253C2×D12—21no—
254C2×D12—21no—
255C2×D12—21no—
256C2×D12—21no—
257C2×D12—21no—
258C2×D12—24no—
259C2×D12—81no—
260C2×D12—81no—
261C2×D12C2×D412yes—
262C2×C4×D3—21no—
263C2×C4×D3—21no—
264C2×C4×D3—21no—
265C2×C4×D3—21no—
266C2×C4×D3—21no—
267C2×C4×D3—21no—
268C2×C4×D3—24no—
269C2×C4×D3—42no—
270C2×C4×D3—42no—
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—21no—
280C3×C4⋊C4—21no—
281C3×C4⋊C4—21no—
282C3×C4⋊C4—21no—
283C3×C4⋊C4—21no—
284C3×C4⋊C4C2×D412yes—
285C3×C4⋊C4C2×D412yes—
286C3×C22⋊C4—24no—
287C3×C22⋊C4—42no—
288C3×C42—24no—
289#217—22no—
290#217—42no—
291#217—42no—
292#217—81no—
293#213—28no—
294(C2×D3)⋊C4—24no—
295(C2×D3)⋊C4—24no—
296(C2×D3)⋊C4—24no—
297(C2×D3)⋊C4—22no—
298(C2×D3)⋊C4—24no—
299(C2×D3)⋊C4—81no—
300C4⋊Dic3—21no—
301C4⋊Dic3—21no—
302C4⋊Dic3—21no—
303C4⋊Dic3—21no—
304C4⋊Dic3—21no—
305C4⋊Dic3C2×D412yes—
306Dic3⋊C4—22no—
307Dic3⋊C4—24no—
308C4×Dic3—24no—
309C4×Dic3C2×D412yes—
310C4×Dic3C2×D412yes—
311C2×C3⋊C8—21no—
312C2×C3⋊C8—21no—
313C2×C3⋊C8—21no—
314C2×C3⋊C8—21no—
315C2×C3⋊C8—21no—
316C2×C3⋊C8#4112yes—
317C22×Q8—61no—
318C22×D4—21no—
319C22×D4—31no—
320C22×D4—31no—
321C22×D4—61no—
322C22×D4—61no—
323C22×D4—61no—
324C22×D4C22×D311yescharacteristic
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—22no—
341#121—41no—
342#121—68no—
343#121—62no—
344#121—62no—
345#121—62no—
346#121—62no—
347#121—62no—
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—31no—
364C2×C4⋊C4—61no—
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—62no—
384#107—62no—
385#106—62no—
386C4⋊C8—62no—
387#102—22no—
388#102—22no—
389#102—62no—
390#102—62no—
391#102—121no—
392#102—121no—
393C22⋊C8—41no—
394C22⋊C8—62no—
395C22⋊C8—62no—
396C22⋊C8—121no—
397#97—62no—
398#95—61no—
399#95—61no—
400#95—61no—
401#95—61no—
402C23×C3—21no—
403C23×C3—22no—
404C23×C3—21no—
405C23×C3—21no—
406C23×C3—21no—
407C23×C3—21no—
408C23×C3—21no—
409C23×C3—21no—
410C23×C3—41no—
411C23×C3—41no—
412C23×C3—41no—
413C23×C3—41no—
414C23×C3—41no—
415C23×C3—41no—
416C23×C3C22×D411yescharacteristic
417C22×D3—21no—
418C22×D3—22no—
419C22×D3—21no—
420C22×D3—21no—
421C22×D3—21no—
422C22×D3—21no—
423C22×D3—21no—
424C22×D3—21no—
425C22×D3—41no—
426C22×D3—41no—
427C22×D3—41no—
428C22×D3—41no—
429C22×D3—41no—
430C22×D3—41no—
431C3×D4—22no—
432C3×D4—22no—
433C3×D4—41no—
434C3×D4—41no—
435C3×D4—84no—
436C2×C3×C4—22no—
437C2×C3×C4—21no—
438C2×C3×C4—22no—
439C2×C3×C4—21no—
440C2×C3×C4—21no—
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×C4—41no—
451C2×C3×C4—41no—
452C2×C3×C4C22×D411yescharacteristic
453C2×C3×C4C22×D411yescharacteristic
454C2×C3×C4C2×#4111yescharacteristic
455C2×C3×C4C2×#4111yescharacteristic
456C2×C3×C4H(5,𝔽2)11yescharacteristic
457C2×C3×C42−1+411yescharacteristic
458#67—44no—
459#67—84no—
460#67—84no—
461C2×Dic3—21no—
462C2×Dic3—21no—
463C2×Dic3—21no—
464C2×Dic3—21no—
465C2×Dic3—21no—
466C2×Dic3—22no—
467C2×Dic3—21no—
468C2×Dic3—21no—
469C2×Dic3—41no—
470C2×Dic3—41no—
471C2×Dic3—41no—
472C2×Dic3—41no—
473C2×Dic3—41no—
474C2×Dic3—41no—
475C2×Dic3—41no—
476C2×Dic3—41no—
477C2×Dic3—84no—
478C2×Dic3#12012yes—
479C2×Dic3#12012yes—
480D12—22no—
481D12—22no—
482D12—41no—
483D12—41no—
484D12—84no—
485C4×D3—48no—
486C4×D3—41no—
487C4×D3—41no—
488C4×D3—41no—
489C4×D3—41no—
490Dic6—84no—
491C3×C8—41no—
492C3×C8—41no—
493C3⋊C8—22no—
494C3⋊C8—41no—
495C24—21no—
496C24—31no—
497C24—61no—
498C24D3×D411yescharacteristic
499C2×Q8—64no—
500C2×Q8—241no—
501C2×Q8—241no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—32no—
508C2×D4—42no—
509C2×D4—42no—
510C2×D4—64no—
511C2×D4—62no—
512C2×D4—64no—
513C2×D4—61no—
514C2×D4—61no—
515C2×D4—61no—
516C2×D4—61no—
517C2×D4—61no—
518C2×D4—81no—
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#23512yes—
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—31no—
539C22×C4—31no—
540C22×C4—31no—
541C22×C4—64no—
542C22×C4—61no—
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—21no—
565C2×C8—32no—
566C2×C8—61no—
567C2×C8—61no—
568C2×C8—61no—
569C2×C8—61no—
570C2×C8—61no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—32no—
576C4⋊C4—62no—
577C4⋊C4—64no—
578C4⋊C4—61no—
579C4⋊C4—61no—
580C4⋊C4—61no—
581C4⋊C4—61no—
582C4⋊C4—61no—
583C4⋊C4D3×D412yes—
584C4⋊C4D3×D412yes—
585C22⋊C4—24no—
586C22⋊C4—42no—
587C22⋊C4—62no—
588C22⋊C4—64no—
589C22⋊C4—64no—
590C22⋊C4—64no—
591C22⋊C4—64no—
592C22⋊C4—62no—
593C22⋊C4—122no—
594C22⋊C4—122no—
595C22⋊C4—241no—
596C22⋊C4—241no—
597C42—24no—
598C42—32no—
599C42—32no—
600C42—64no—
601C22×C3—41no—
602C22×C3—41no—
603C22×C3—41no—
604C22×C3—42no—
605C22×C3—41no—
606C22×C3—41no—
607C22×C3—42no—
608C22×C3—41no—
609C22×C3—42no—
610C22×C3—41no—
611C22×C3—81no—
612C22×C3—81no—
613C22×C3—81no—
614C22×C3—81no—
615C22×C3C2×#12011yescharacteristic
616C22×C3#54611yescharacteristic
617C22×C3#54711yescharacteristic
618C22×C3#57511yescharacteristic
619C22×C3#57511yescharacteristic
620C22×C3#57611yescharacteristic
621C22×C3#57611yescharacteristic
622C2×D3—41no—
623C2×D3—41no—
624C2×D3—41no—
625C2×D3—42no—
626C2×D3—42no—
627C2×D3—41no—
628C2×D3—41no—
629C2×D3—42no—
630C2×D3—41no—
631C2×D3—41no—
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#52511yescharacteristic
641C3×C4#53711yescharacteristic
642C3×C4#54811yescharacteristic
643C3×C4#55011yescharacteristic
644Dic3—22no—
645Dic3—22no—
646Dic3—41no—
647Dic3—42no—
648Dic3—81no—
649Dic3—81no—
650C23—21no—
651C23—22no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—61no—
665C23—61no—
666C23—61no—
667C23—61no—
668C23—61no—
669C23—61no—
670C23—62no—
671C23—61no—
672C23—121no—
673C23—121no—
674C23—121no—
675C23—121no—
676C23—121no—
677C23—121no—
678C23C2×D3×D411yescharacteristic
679Q8—244no—
680D4—22no—
681D4—22no—
682D4—41no—
683D4—41no—
684D4—62no—
685D4—62no—
686D4—84no—
687D4—124no—
688D4—121no—
689D4—121no—
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—61no—
712C2×C4—61no—
713C2×C4—61no—
714C2×C4—61no—
715C2×C4—61no—
716C2×C4—61no—
717C2×C4—61no—
718C2×C4—62no—
719C2×C4—128no—
720C2×C4—121no—
721C2×C4—121no—
722C2×C4—121no—
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#100411yescharacteristic
737C2×C4D3×#4111yescharacteristic
738C2×C4#101011yescharacteristic
739C8—41no—
740C8—41no—
741C8—62no—
742C8—121no—
743C2×C3—81no—
744C2×C3—82no—
745C2×C3#240711yescharacteristic
746C2×C3#300511yescharacteristic
747C2×C3#300811yescharacteristic
748C2×C3#331911yescharacteristic
749C2×C3#331911yescharacteristic
750C2×C3#334711yescharacteristic
751C2×C3#334711yescharacteristic
752D3—81no—
753D3—82no—
754C22—42no—
755C22—41no—
756C22—41no—
757C22—42no—
758C22—41no—
759C22—42no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22—81no—
768C22—121no—
769C22—121no—
770C22—121no—
771C22—122no—
772C22—122no—
773C22—121no—
774C22—121no—
775C22—122no—
776C22—121no—
777C22—121no—
778C22—241no—
779C22—241no—
780C22—241no—
781C22—241no—
782C22#549011yescharacteristic
783C22D3×#12011yescharacteristic
784C22#565511yescharacteristic
785C22#576811yescharacteristic
786C22#576911yescharacteristic
787C22#577311yescharacteristic
788C22#577411yescharacteristic
789C4—41no—
790C4—42no—
791C4—42no—
792C4—62no—
793C4—62no—
794C4—81no—
795C4—121no—
796C4—122no—
797C4—241no—
798C4—241no—
799C4#554711yescharacteristic
800C4#555211yescharacteristic
801C4#559911yescharacteristic
802C4#560811yescharacteristic
803C3#2412911yescharacteristic, complemented, Sylow
804C2—81no—
805C2—82no—
806C2—241no—
807C2—242no—
808C2#7468811yescharacteristic
809C2#7885911yescharacteristic
810C2#7893711yescharacteristic
811C2#8008311yescharacteristic
812C2#8008511yescharacteristic
813C2#8139211yescharacteristic
814C2#8139311yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1875C2
socleC23×C3C22×D4
hypercenter#1875D3
hypocenterC3#24129
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1875

Complements

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

NH ≅ G/Ntype
1. C2×#5532C2semidirect
2. #82666C2semidirect
3. C2×#4759C2semidirect
4. C2×#4785C2semidirect
5. C3×#1875C2semidirect
6. #71684C2semidirect
7. #71576C2semidirect
8. #70204C2semidirect
9. #70201C2semidirect
10. #69934C2semidirect
11. #69917C2semidirect
12. #68893C2semidirect
13. #68877C2semidirect
14. #68822C2semidirect
15. #68806C2semidirect
75. #1875D3semidirect
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
#826662
C2×#47592
C2×#47852
C3×#18752
#716842
#715762
#702042
#702012
#699342
#699172
#688932
#688772
#688222
#688062
#241293