Finite Group Databasebeta

← #10829311

Subgroups — #10829311

Order 768.

1238 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5618C211yesmaximal, characteristic, complemented
2C2×#4891C211yesmaximal, characteristic, complemented
3C2×#4785C211yesmaximal, characteristic, complemented
4#73935C211yesmaximal, characteristic, complemented
5C3×#2033C211yesmaximal, characteristic, complemented
6#71684C211yesmaximal, characteristic, complemented
7#70633C211yesmaximal, characteristic, complemented
8#70207C211yesmaximal, characteristic, complemented
9#70204C211yesmaximal, characteristic, complemented
10#70153C211yesmaximal, characteristic, complemented
11#69932C211yesmaximal, characteristic, complemented
12#69917C211yesmaximal, characteristic, complemented
13#69505C211yesmaximal, characteristic, complemented
14#68881C211yesmaximal, characteristic, complemented
15#68805C211yesmaximal, characteristic, complemented
16#24136—31nomaximal, Sylow
17C2×C3×#121C2211yescharacteristic
18C2×#939—21no—
19C2×#938C2211yescharacteristic
20C2×D4×Dic3—21no—
21C2×D4×Dic3C2211yescharacteristic
22C22×#213C2211yescharacteristic
23C2×#930C2211yescharacteristic
24C2×C4×#67C2211yescharacteristic
25C22×C4⋊Dic3C2211yescharacteristic
26#5618—24no—
27#5618—24no—
28C2×#895C2211yescharacteristic
29C2×#893C2211yescharacteristic
30C2×#892C2211yescharacteristic
31C2×#890C2211yescharacteristic
32C2×#886—21no—
33C2×#884—21no—
34C2×#879—21no—
35C2×C3×#107C2211yescharacteristic
36C2×C3×#102C2211yescharacteristic
37C2×C3×#102C2211yescharacteristic
38C2×C3×C22⋊C8C2211yescharacteristic
39C3×#380C2211yescharacteristic
40C2×#832C2211yescharacteristic
41C2×#830C2211yescharacteristic
42C2×#821C2211yescharacteristic
43C2×#821C2211yescharacteristic
44C2×(C2×D3)⋊C8C2211yescharacteristic
45C2×(C2×D3)⋊C8C2211yescharacteristic
46C2×#815C2211yescharacteristic
47C2×Dic3⋊C8C2211yescharacteristic
48#4987C2211yescharacteristic
49#4975C2211yescharacteristic
50C2×#809C2211yescharacteristic
51C2×#808C2211yescharacteristic
52C2×#808C2211yescharacteristic
53#4959—21no—
54#4891—24no—
55#4785—24no—
56#4672—21no—
57#4667—21no—
58C3×#340C2211yescharacteristic
59#4551C2211yescharacteristic
60#4551C2211yescharacteristic
61#4529C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#553—31no—
65C2×#478—31no—
66C2×#442—31no—
67#2537—31no—
68#2034—31no—
69#2033D311yescharacteristic, complemented
70#1999—31no—
71#1999—31no—
72#1992—31no—
73#1955—31no—
74#1875—31no—
75#1874—31no—
76#1854—31no—
77#1853—31no—
78#1802—31no—
79C22×C3×D4—21no—
80C22×C3×D4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C22×#67—21no—
83C22×#67—21no—
84C22×#67D411yescharacteristic
85C23×Dic3—21no—
86C23×Dic3—21no—
87C22×D12—21no—
88C22×D12C2311yescharacteristic
89C22×C4×D3—21no—
90C22×C4×D3C2311yescharacteristic
91C22×C3×C8C2311yescharacteristic
92C22×C3×C8C2311yescharacteristic
93C3×#121—22no—
94C3×#121—22no—
95C2×C3×C4⋊C4C2311yescharacteristic
96C2×C3×C4⋊C4C2311yescharacteristic
97C2×C3×C4⋊C4C2311yescharacteristic
98C2×C3×C22⋊C4—21no—
99C2×C3×C22⋊C4—21no—
100C2×#217—21no—
101C2×#217—21no—
102C2×#217D411yescharacteristic
103#939—28no—
104#938—22no—
105#938—22no—
106D4×Dic3—28no—
107D4×Dic3—22no—
108D4×Dic3D414yescomplemented
109C2×#213—22no—
110C2×#213—22no—
111C2×#213—22no—
112#930—22no—
113#930—41no—
114C4×#67—22no—
115C4×#67—22no—
116C2×(C2×D3)⋊C4—21no—
117C2×(C2×D3)⋊C4—21no—
118C2×(C2×D3)⋊C4—21no—
119C2×(C2×D3)⋊C4—21no—
120C2×(C2×D3)⋊C4—21no—
121C2×(C2×D3)⋊C4D411yescharacteristic
122C2×C4⋊Dic3—21no—
123C2×C4⋊Dic3—21no—
124C2×C4⋊Dic3—22no—
125C2×C4⋊Dic3—22no—
126C2×C4⋊Dic3C2311yescharacteristic
127C2×C4⋊Dic3C2311yescharacteristic
128C2×C4⋊Dic3C2311yescharacteristic
129C2×Dic3⋊C4—21no—
130C2×Dic3⋊C4—21no—
131C2×Dic3⋊C4—21no—
132C2×Dic3⋊C4D411yescharacteristic
133C2×C4×Dic3—21no—
134C2×C4×Dic3C2311yescharacteristic
135C22×C3⋊C8C2311yescharacteristic
136C22×C3⋊C8C2311yescharacteristic
137#895—22no—
138#895—41no—
139#893—22no—
140#893—22no—
141#892—22no—
142#892—22no—
143#890—22no—
144#890D414yescomplemented
145#886—28no—
146#884—44no—
147#879—28no—
148C3×#107—22no—
149C3×#102—22no—
150C3×#102—41no—
151C3×C22⋊C8—41no—
152C3×#95—21no—
153#832—41no—
154C3⋊#95—21no—
155#830—22no—
156#821—22no—
157#821—22no—
158(C2×D3)⋊C8—22no—
159(C2×D3)⋊C8—41no—
160#815—22no—
161Dic3⋊C8—22no—
162#809—22no—
163#808—22no—
164#808—22no—
165C22×D8—31no—
166#553—64no—
167#553—64no—
168C2×#126—61no—
169C2×#125—31no—
170C2×#123—61no—
171C2×#121—31no—
172C2×#121—31no—
173C2×#121—31no—
174C2×#121—61no—
175C2×#121—61no—
176C2×#121C2×D311yescharacteristic
177C2×C4×D4—31no—
178C2×C4×D4—31no—
179C2×C4×D4—31no—
180C2×C4×D4—61no—
181C2×#117—31no—
182C22×C4⋊C4—31no—
183#478—64no—
184#442—64no—
185C2×#107C2×D311yescharacteristic
186C2×#106—31no—
187C2×#106—31no—
188C2×C4⋊C8—31no—
189C2×#102—31no—
190C2×#102—31no—
191C2×#102—31no—
192C2×#102—31no—
193C2×#102C2×D311yescharacteristic
194C2×#102C2×D311yescharacteristic
195C2×C22⋊C8—31no—
196C2×C22⋊C8—31no—
197C2×C22⋊C8—31no—
198C2×C22⋊C8C2×D311yescharacteristic
199C2×#97—31no—
200#394—61no—
201#394—61no—
202#384—31no—
203#380—31no—
204#380—61no—
205#380C2×D311yescharacteristic
206#340—31no—
207#340—31no—
208#340—31no—
209#340—31no—
210#340—31no—
211#340C2×D311yescharacteristic
212C24×C3—21no—
213C24×C3C2×D411yescharacteristic
214C23×D3—21no—
215C23×D3C2×D411yescharacteristic
216C2×C3×D4—24no—
217C2×C3×D4—21no—
218C2×C3×D4—21no—
219C2×C3×D4—21no—
220C2×C3×D4—21no—
221C2×C3×D4—21no—
222C2×C3×D4—42no—
223C2×C3×D4—42no—
224C2×C3×D4C2×D412yes—
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×C4—21no—
234C22×C3×C4C2×D411yescharacteristic
235C22×C3×C4C2411yescharacteristic
236C2×#67—22no—
237C2×#67—24no—
238C2×#67—22no—
239C2×#67—41no—
240C2×#67—42no—
241C2×#67—42no—
242C2×#67—81no—
243C2×#67—81no—
244C2×#67—81no—
245C22×Dic3—21no—
246C22×Dic3—21no—
247C22×Dic3—24no—
248C22×Dic3—24no—
249C22×Dic3—21no—
250C22×Dic3—81no—
251C22×Dic3—81no—
252C22×Dic3—81no—
253C22×Dic3—81no—
254C22×Dic3C2×D411yescharacteristic
255C22×Dic3C2×D411yescharacteristic
256C22×Dic3C2×D411yescharacteristic
257C2×D12—21no—
258C2×D12—21no—
259C2×D12—21no—
260C2×D12—21no—
261C2×D12—21no—
262C2×D12—42no—
263C2×D12—42no—
264C2×D12—81no—
265C2×D12#4112yes—
266C2×C4×D3—21no—
267C2×C4×D3—21no—
268C2×C4×D3—21no—
269C2×C4×D3—21no—
270C2×C4×D3—21no—
271C2×C4×D3—21no—
272C2×C4×D3—42no—
273C2×C4×D3—42no—
274C2×C4×D3—42no—
275C2×C3×C8—21no—
276C2×C3×C8—21no—
277C2×C3×C8—21no—
278C2×C3×C8—21no—
279C2×C3×C8—21no—
280C2×C3×C8—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×C22⋊C4—24no—
288C3×C22⋊C4—42no—
289#217—24no—
290#217—24no—
291#217—22no—
292#213—28no—
293(C2×D3)⋊C4—24no—
294(C2×D3)⋊C4—22no—
295(C2×D3)⋊C4—42no—
296(C2×D3)⋊C4—42no—
297(C2×D3)⋊C4—42no—
298(C2×D3)⋊C4—42no—
299C4⋊Dic3—24no—
300C4⋊Dic3—21no—
301C4⋊Dic3—21no—
302C4⋊Dic3—24no—
303C4⋊Dic3—21no—
304C4⋊Dic3—21no—
305C4⋊Dic3C2×D412yes—
306C4⋊Dic3C2×D412yes—
307Dic3⋊C4—22no—
308Dic3⋊C4—24no—
309Dic3⋊C4—42no—
310Dic3⋊C4—81no—
311C4×Dic3—24no—
312C4×Dic3C2×D412yes—
313C4×Dic3C2×D412yes—
314C2×C3⋊C8—21no—
315C2×C3⋊C8—21no—
316C2×C3⋊C8—21no—
317C2×C3⋊C8—21no—
318C2×C3⋊C8—21no—
319C2×C3⋊C8#4112yes—
320C22×D4—21no—
321C22×D4—31no—
322C22×D4—31no—
323C22×D4—61no—
324C22×D4—61no—
325C22×D4—61no—
326C22×D4C22×D311yescharacteristic
327C23×C4—31no—
328C23×C4—61no—
329C23×C4—61no—
330C23×C4—61no—
331C23×C4C22×D311yescharacteristic
332C2×D8—62no—
333C2×D8—62no—
334C2×D8—62no—
335C22×C8—31no—
336C22×C8—31no—
337C22×C8C22×D311yescharacteristic
338C22×C8C22×D311yescharacteristic
339#126—68no—
340#125—34no—
341#125—62no—
342#123—68no—
343#121—22no—
344#121—22no—
345#121—62no—
346#121—68no—
347#121—62no—
348#121—62no—
349#121—62no—
350#121—124no—
351#121—121no—
352#121—121no—
353C4×D4—34no—
354C4×D4—62no—
355C4×D4—62no—
356C4×D4—62no—
357C4×D4—62no—
358C4×D4—62no—
359C4×D4—68no—
360#117—62no—
361#117—62no—
362C2×C4⋊C4—31no—
363C2×C4⋊C4—31no—
364C2×C4⋊C4—31no—
365C2×C4⋊C4—31no—
366C2×C4⋊C4—62no—
367C2×C4⋊C4—62no—
368C2×C4⋊C4—61no—
369C2×C4⋊C4—61no—
370C2×C4⋊C4—61no—
371C2×C4⋊C4—61no—
372C2×C4⋊C4—61no—
373C2×C4⋊C4C22×D311yescharacteristic
374C2×C4⋊C4C22×D311yescharacteristic
375C2×C4⋊C4C22×D311yescharacteristic
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—31no—
379C2×C22⋊C4—31no—
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—22no—
390#106—62no—
391#106—62no—
392C4⋊C8—62no—
393#102—22no—
394#102—41no—
395#102—62no—
396#102—62no—
397#102—62no—
398#102—121no—
399C22⋊C8—41no—
400C22⋊C8—62no—
401C22⋊C8—62no—
402C22⋊C8—121no—
403#97—62no—
404#95—21no—
405#95—61no—
406C23×C3—21no—
407C23×C3—21no—
408C23×C3—21no—
409C23×C3—21no—
410C23×C3—21no—
411C23×C3—21no—
412C23×C3—22no—
413C23×C3—41no—
414C23×C3—41no—
415C23×C3—41no—
416C23×C3—41no—
417C23×C3—41no—
418C23×C3—41no—
419C23×C3AGL(1,ℤ/8)12yes—
420C23×C3C22×D411yescharacteristic
421C22×D3—21no—
422C22×D3—22no—
423C22×D3—21no—
424C22×D3—21no—
425C22×D3—21no—
426C22×D3—21no—
427C22×D3—21no—
428C22×D3—21no—
429C22×D3—41no—
430C22×D3—41no—
431C22×D3—41no—
432C22×D3—41no—
433C22×D3—41no—
434C22×D3—41no—
435C3×D4—22no—
436C3×D4—22no—
437C3×D4—48no—
438C3×D4—41no—
439C3×D4—41no—
440C2×C3×C4—22no—
441C2×C3×C4—21no—
442C2×C3×C4—21no—
443C2×C3×C4—21no—
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×C4—41no—
453C2×C3×C4—41no—
454C2×C3×C4—41no—
455C2×C3×C4—41no—
456C2×C3×C4C22×D411yescharacteristic
457C2×C3×C4C22×D411yescharacteristic
458C2×C3×C4C2×#4111yescharacteristic
459C2×C3×C4C2×#4111yescharacteristic
460C2×C3×C4H(5,𝔽2)11yescharacteristic
461C2×C3×C42−1+411yescharacteristic
462#67—44no—
463#67—84no—
464#67—84no—
465C2×Dic3—21no—
466C2×Dic3—21no—
467C2×Dic3—21no—
468C2×Dic3—21no—
469C2×Dic3—21no—
470C2×Dic3—22no—
471C2×Dic3—22no—
472C2×Dic3—21no—
473C2×Dic3—21no—
474C2×Dic3—41no—
475C2×Dic3—41no—
476C2×Dic3—41no—
477C2×Dic3—41no—
478C2×Dic3—41no—
479C2×Dic3—41no—
480C2×Dic3—41no—
481C2×Dic3—84no—
482C2×Dic3—84no—
483C2×Dic3#12012yes—
484C2×Dic3#12012yes—
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—
495C3×C8—41no—
496C3×C8—41no—
497C3⋊C8—22no—
498C3⋊C8—41no—
499C24—21no—
500C24—31no—
501C24—61no—
502C24D3×D411yescharacteristic
503C2×D4—24no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—32no—
510C2×D4—42no—
511C2×D4—42no—
512C2×D4—62no—
513C2×D4—62no—
514C2×D4—64no—
515C2×D4—61no—
516C2×D4—61no—
517C2×D4—61no—
518C2×D4—61no—
519C2×D4—61no—
520C2×D4—122no—
521C2×D4—122no—
522C2×D4—121no—
523C2×D4—122no—
524C2×D4—122no—
525C2×D4—241no—
526C2×D4—241no—
527C2×D4—241no—
528C2×D4—241no—
529C2×D4D3×D412yes—
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—64no—
546C22×C4—61no—
547C22×C4—61no—
548C22×C4—61no—
549C22×C4—61no—
550C22×C4—61no—
551C22×C4—61no—
552C22×C4—61no—
553C22×C4—122no—
554C22×C4—122no—
555C22×C4—122no—
556C22×C4—241no—
557C22×C4—241no—
558C22×C4—241no—
559C22×C4—241no—
560C22×C4D3×D411yescharacteristic
561C22×C4C23×D311yescharacteristic
562D8—68no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—32no—
570C2×C8—61no—
571C2×C8—61no—
572C2×C8—61no—
573C2×C8—61no—
574C2×C8—61no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—32no—
581C4⋊C4—32no—
582C4⋊C4—62no—
583C4⋊C4—64no—
584C4⋊C4—64no—
585C4⋊C4—64no—
586C4⋊C4—61no—
587C4⋊C4—61no—
588C4⋊C4—61no—
589C4⋊C4—61no—
590C4⋊C4—122no—
591C4⋊C4—241no—
592C4⋊C4D3×D412yes—
593C22⋊C4—24no—
594C22⋊C4—42no—
595C22⋊C4—62no—
596C22⋊C4—64no—
597C22⋊C4—62no—
598C22⋊C4—64no—
599C22⋊C4—64no—
600C22⋊C4—122no—
601C22⋊C4—122no—
602C22⋊C4—122no—
603C22⋊C4—122no—
604C42—32no—
605C42—32no—
606C42—64no—
607C22×C3—22no—
608C22×C3—22no—
609C22×C3—22no—
610C22×C3—41no—
611C22×C3—41no—
612C22×C3—41no—
613C22×C3—41no—
614C22×C3—42no—
615C22×C3—42no—
616C22×C3—42no—
617C22×C3—81no—
618C22×C3—81no—
619C22×C3—81no—
620C22×C3—81no—
621C22×C3C2×#12011yescharacteristic
622C22×C3#54611yescharacteristic
623C22×C3#54711yescharacteristic
624C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
625C22×C3#57511yescharacteristic
626C22×C3#57611yescharacteristic
627C22×C3#57711yescharacteristic
628C2×D3—41no—
629C2×D3—41no—
630C2×D3—41no—
631C2×D3—42no—
632C2×D3—41no—
633C2×D3—41no—
634C2×D3—41no—
635C2×D3—42no—
636C2×D3—41no—
637C2×D3—42no—
638C2×D3—81no—
639C2×D3—81no—
640C2×D3—81no—
641C2×D3—81no—
642C3×C4—41no—
643C3×C4—42no—
644C3×C4—81no—
645C3×C4—81no—
646C3×C4#52511yescharacteristic
647C3×C4#53711yescharacteristic
648C3×C4#54811yescharacteristic
649C3×C4#55011yescharacteristic
650Dic3—22no—
651Dic3—22no—
652Dic3—41no—
653Dic3—42no—
654Dic3—42no—
655Dic3—81no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—22no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—61no—
670C23—61no—
671C23—61no—
672C23—61no—
673C23—61no—
674C23—61no—
675C23—62no—
676C23—61no—
677C23—121no—
678C23—121no—
679C23—121no—
680C23—121no—
681C23—121no—
682C23—121no—
683C23#91112yes—
684C23C2×D3×D411yescharacteristic
685D4—22no—
686D4—22no—
687D4—48no—
688D4—41no—
689D4—41no—
690D4—62no—
691D4—62no—
692D4—124no—
693D4—121no—
694D4—121no—
695D4—244no—
696D4—244no—
697D4—244no—
698C2×C4—21no—
699C2×C4—22no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—32no—
703C2×C4—32no—
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—41no—
715C2×C4—41no—
716C2×C4—61no—
717C2×C4—61no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—61no—
722C2×C4—62no—
723C2×C4—62no—
724C2×C4—61no—
725C2×C4—121no—
726C2×C4—121no—
727C2×C4—121no—
728C2×C4—121no—
729C2×C4—121no—
730C2×C4—121no—
731C2×C4—121no—
732C2×C4—121no—
733C2×C4—121no—
734C2×C4—121no—
735C2×C4—121no—
736C2×C4—244no—
737C2×C4—244no—
738C2×C4—244no—
739C2×C4C2×D3×D411yescharacteristic
740C2×C4C2×D3×D411yescharacteristic
741C2×C4#100411yescharacteristic
742C2×C4D3×#4111yescharacteristic
743C2×C4D3×#4111yescharacteristic
744C2×C4#101011yescharacteristic
745C8—41no—
746C8—41no—
747C8—62no—
748C8—121no—
749C2×C3—42no—
750C2×C3—82no—
751C2×C3#240711yescharacteristic
752C2×C3#300611yescharacteristic
753C2×C3#301211yescharacteristic
754C2×C3#330711yescharacteristic
755C2×C3#331811yescharacteristic
756C2×C3#334511yescharacteristic
757C2×C3#334711yescharacteristic
758D3—81no—
759D3—82no—
760C22—22no—
761C22—22no—
762C22—22no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—42no—
768C22—42no—
769C22—42no—
770C22—81no—
771C22—81no—
772C22—81no—
773C22—81no—
774C22—121no—
775C22—122no—
776C22—121no—
777C22—122no—
778C22—121no—
779C22—121no—
780C22—121no—
781C22—121no—
782C22—122no—
783C22—121no—
784C22—241no—
785C22—241no—
786C22—241no—
787C22—241no—
788C22D3×#12011yescharacteristic
789C22#561011yescharacteristic
790C22#565511yescharacteristic
791C22C2×#91111yescharacteristic
792C22#576911yescharacteristic
793C22#577311yescharacteristic
794C22#577811yescharacteristic
795C4—41no—
796C4—42no—
797C4—62no—
798C4—62no—
799C4—81no—
800C4—81no—
801C4—121no—
802C4—122no—
803C4—122no—
804C4—241no—
805C4#559711yescharacteristic
806C4#559911yescharacteristic
807C4#565611yescharacteristic
808C4#567711yescharacteristic
809C3#2413611yescharacteristic, complemented, Sylow
810C2—42no—
811C2—82no—
812C2—241no—
813C2—242no—
814C2#7689411yescharacteristic
815C2#8000311yescharacteristic
816C2#8023111yescharacteristic
817C2#8073211yescharacteristic
818C2#8081911yescharacteristic
819C2#8129411yescharacteristic
820C2#8139311yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2033C2
socleC23×C3C22×D4
hypercenter#2033D3
hypocenterC3#24136
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2033

Complements

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

NH ≅ G/Ntype
1. C2×#5618C2semidirect
2. C2×#4891C2semidirect
3. C2×#4785C2semidirect
4. #73935C2semidirect
5. C3×#2033C2semidirect
6. #71684C2semidirect
7. #70633C2semidirect
8. #70207C2semidirect
9. #70204C2semidirect
10. #70153C2semidirect
11. #69932C2semidirect
12. #69917C2semidirect
13. #69505C2semidirect
14. #68881C2semidirect
15. #68805C2semidirect
69. #2033D3semidirect
108. D4×Dic3D4semidirect
144. #890D4semidirect
809. C3#24136semidirect

Maximal subgroups

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

subgroupindex
C2×#56182
C2×#48912
C2×#47852
#739352
C3×#20332
#716842
#706332
#702072
#702042
#701532
#699322
#699172
#695052
#688812
#688052
#241363