Finite Group Databasebeta

← #10829225

Subgroups — #10829225

Order 768.

1400 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5507C211yesmaximal, characteristic, complemented
2#82666C211yesmaximal, characteristic, complemented
3C2×#4761C211yesmaximal, characteristic, complemented
4C2×#4785C211yesmaximal, characteristic, complemented
5C3×#1874C211yesmaximal, characteristic, complemented
6#71684C211yesmaximal, characteristic, complemented
7#71556C211yesmaximal, characteristic, complemented
8#70204C211yesmaximal, characteristic, complemented
9#70200C211yesmaximal, characteristic, complemented
10#69935C211yesmaximal, characteristic, complemented
11#69917C211yesmaximal, characteristic, complemented
12#68893C211yesmaximal, characteristic, complemented
13#68875C211yesmaximal, characteristic, complemented
14#68823C211yesmaximal, characteristic, complemented
15#68806C211yesmaximal, characteristic, complemented
16#24128—31nomaximal, Sylow
17C22×#235—21no—
18C2×C3×#121C2211yescharacteristic
19C22×C3×C4⋊C4C2211yescharacteristic
20C2×#938C2211yescharacteristic
21C2×D4×Dic3C2211yescharacteristic
22C22×#213C2211yescharacteristic
23C2×#930C2211yescharacteristic
24C2×#929—21no—
25C2×C4×#67C2211yescharacteristic
26C2×#896—21no—
27#5507—24no—
28#5507—24no—
29C2×#895C2211yescharacteristic
30C2×#894—21no—
31C2×#893C2211yescharacteristic
32C2×D3×C4⋊C4C2211yescharacteristic
33C2×#888C2211yescharacteristic
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×#817C2211yescharacteristic
47C2×#815C2211yescharacteristic
48C2×Dic3⋊C8C2211yescharacteristic
49#4987C2211yescharacteristic
50#4977C2211yescharacteristic
51C2×#809C2211yescharacteristic
52C2×#808C2211yescharacteristic
53C2×#808C2211yescharacteristic
54#4958—21no—
55#4952—21no—
56#4785—24no—
57#4761—24no—
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60#4551C2211yescharacteristic
61#4529C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#547—31no—
65C2×#476—31no—
66C2×#442—31no—
67#2535—31no—
68#2034—31no—
69#2034—31no—
70#1999—31no—
71#1999—31no—
72#1993—31no—
73#1955—31no—
74#1874—31no—
75#1874D311yescharacteristic, complemented
76#1853—31no—
77#1853—31no—
78#1804—31no—
79C22×C3×D4—21no—
80C22×C3×D4C2311yescharacteristic
81C23×C3×C4—21no—
82C23×C3×C4C2311yescharacteristic
83C22×#67—21no—
84C22×#67—21no—
85C22×#67D411yescharacteristic
86C23×Dic3—21no—
87C2×#235—28no—
88C2×#235—44no—
89C2×#235—44no—
90C22×D12—21no—
91C22×D12C2311yescharacteristic
92C22×C4×D3—21no—
93C22×C4×D3—21no—
94C22×C4×D3C2311yescharacteristic
95C22×Dic6—21no—
96C22×C3×C8C2311yescharacteristic
97C22×C3×C8C2311yescharacteristic
98C3×#121—22no—
99C3×#121—41no—
100C2×C3×C4⋊C4—21no—
101C2×C3×C4⋊C4—22no—
102C2×C3×C4⋊C4—22no—
103C2×C3×C4⋊C4C2311yescharacteristic
104C2×C3×C4⋊C4C2311yescharacteristic
105C2×C3×C4⋊C4C2311yescharacteristic
106C2×C3×C22⋊C4—21no—
107C2×#217—21no—
108C2×#217—21no—
109C2×#217—21no—
110C2×#217D411yescharacteristic
111#938—22no—
112#938—41no—
113D4×Dic3—22no—
114D4×Dic3—22no—
115C2×#213—22no—
116C2×#213—22no—
117C2×#213—22no—
118#930—22no—
119#930—22no—
120#929—28no—
121C4×#67—22no—
122C4×#67—22no—
123C2×(C2×D3)⋊C4—21no—
124C2×(C2×D3)⋊C4—21no—
125C2×(C2×D3)⋊C4—21no—
126C2×(C2×D3)⋊C4—21no—
127C2×(C2×D3)⋊C4D411yescharacteristic
128C2×C4⋊Dic3C2311yescharacteristic
129C2×C4⋊Dic3C2311yescharacteristic
130C2×C4⋊Dic3C2311yescharacteristic
131C2×Dic3⋊C4—21no—
132C2×Dic3⋊C4—21no—
133C2×Dic3⋊C4D411yescharacteristic
134C2×C4×Dic3C2311yescharacteristic
135C22×C3⋊C8C2311yescharacteristic
136C22×C3⋊C8C2311yescharacteristic
137#896—28no—
138#895—22no—
139#895—22no—
140#894—28no—
141#893—22no—
142#893D414yescomplemented
143D3×C4⋊C4—22no—
144D3×C4⋊C4—22no—
145#888—22no—
146#888D414yescomplemented
147C3×#102—22no—
148C3×#102—22no—
149C3×C22⋊C8—41no—
150#832—22no—
151C3⋊#95—21no—
152C3⋊#95—21no—
153C3⋊#95—21no—
154C3⋊#95—21no—
155#830—22no—
156#821—22no—
157#821—41no—
158(C2×D3)⋊C8—22no—
159(C2×D3)⋊C8—41no—
160#817—22no—
161#815—22no—
162Dic3⋊C8—22no—
163#809—41no—
164#808—22no—
165#808—22no—
166C22×#41—61no—
167C22×D8—31no—
168#547—64no—
169#547—64no—
170C2×C4⋊Q8—31no—
171C2×#123—61no—
172C2×#123—61no—
173C2×C22⋊Q8—61no—
174C2×#121—31no—
175C2×#121—31no—
176C2×#121—31no—
177C2×#121C2×D311yescharacteristic
178C2×C4×D4—31no—
179C2×C4×D4—31no—
180C2×C4×D4—31no—
181C22×C4⋊C4—31no—
182C22×C4⋊C4C2×D311yescharacteristic
183#476—64no—
184#442—64no—
185C2×#106—31no—
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#397—61no—
201#392—61no—
202#386—61no—
203#386—61no—
204#382—31no—
205#380—31no—
206#380—31no—
207#340—31no—
208#340—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—42no—
223C2×C3×D4—42no—
224C2×C3×D4—81no—
225C2×C3×D4#4112yescomplemented
226C22×C3×C4—24no—
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×C4—21no—
236C22×C3×C4—42no—
237C22×C3×C4—42no—
238C22×C3×C4C2×D411yescharacteristic
239C22×C3×C4C2411yescharacteristic
240C2×#67—22no—
241C2×#67—22no—
242C2×#67—24no—
243C2×#67—22no—
244C2×#67—42no—
245C2×#67—42no—
246C2×#67—42no—
247C2×#67—42no—
248C2×#67—81no—
249C22×Dic3—21no—
250C22×Dic3—21no—
251C22×Dic3—21no—
252C22×Dic3—42no—
253C22×Dic3—81no—
254C22×Dic3—81no—
255C22×Dic3C2×D411yescharacteristic
256C22×Dic3C2×D411yescharacteristic
257C22×Dic3C2×D411yescharacteristic
258#235—432no—
259C2×D12—21no—
260C2×D12—21no—
261C2×D12—21no—
262C2×D12—21no—
263C2×D12—24no—
264C2×D12—21no—
265C2×D12—42no—
266C2×D12—42no—
267C2×D12C2×D412yes—
268C2×C4×D3—24no—
269C2×C4×D3—21no—
270C2×C4×D3—21no—
271C2×C4×D3—21no—
272C2×C4×D3—21no—
273C2×C4×D3—21no—
274C2×C4×D3—21no—
275C2×C4×D3—24no—
276C2×C4×D3—42no—
277C2×C4×D3—42no—
278C2×C4×D3—42no—
279C2×C4×D3—42no—
280C2×Dic6—24no—
281C2×Dic6—42no—
282C2×Dic6—42no—
283C2×C3×C8—21no—
284C2×C3×C8—21no—
285C2×C3×C8—21no—
286C2×C3×C8—21no—
287C2×C3×C8—21no—
288C2×C3×C8—21no—
289C3×C4⋊C4—24no—
290C3×C4⋊C4—21no—
291C3×C4⋊C4—21no—
292C3×C4⋊C4—21no—
293C3×C4⋊C4—21no—
294C3×C4⋊C4C2×D412yes—
295C3×C4⋊C4C2×D412yes—
296C3×C22⋊C4—42no—
297#217—22no—
298#217—42no—
299#217—42no—
300#217—81no—
301#213—28no—
302(C2×D3)⋊C4—24no—
303(C2×D3)⋊C4—24no—
304(C2×D3)⋊C4—24no—
305(C2×D3)⋊C4—22no—
306(C2×D3)⋊C4—81no—
307C4⋊Dic3—21no—
308C4⋊Dic3—21no—
309C4⋊Dic3—21no—
310C4⋊Dic3—21no—
311C4⋊Dic3—21no—
312C4⋊Dic3C2×D412yes—
313Dic3⋊C4—24no—
314Dic3⋊C4—24no—
315Dic3⋊C4—22no—
316C4×Dic3C2×D412yes—
317C4×Dic3C2×D412yes—
318C2×C3⋊C8—21no—
319C2×C3⋊C8—21no—
320C2×C3⋊C8—21no—
321C2×C3⋊C8—21no—
322C2×C3⋊C8—21no—
323C2×C3⋊C8#4112yescomplemented
324C2×#41—68no—
325C2×#41—124no—
326C2×#41—124no—
327C22×Q8—61no—
328C22×D4—21no—
329C22×D4—31no—
330C22×D4—31no—
331C22×D4—61no—
332C22×D4—61no—
333C22×D4—61no—
334C22×D4C22×D311yescharacteristic
335C23×C4—21no—
336C23×C4—31no—
337C23×C4—61no—
338C23×C4—61no—
339C23×C4—61no—
340C23×C4C22×D311yescharacteristic
341C2×D8—62no—
342C2×D8—62no—
343C2×D8—62no—
344C22×C8—31no—
345C22×C8—31no—
346C22×C8C22×D311yescharacteristic
347C22×C8C22×D311yescharacteristic
348C4⋊Q8—34no—
349C4⋊Q8—62no—
350#123—68no—
351#123—68no—
352C22⋊Q8—68no—
353#121—22no—
354#121—41no—
355#121—62no—
356#121—62no—
357#121—62no—
358#121—62no—
359#121—62no—
360#121—121no—
361C4×D4—34no—
362C4×D4—62no—
363C4×D4—62no—
364C4×D4—62no—
365C4×D4—62no—
366C4×D4—62no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—31no—
371C2×C4⋊C4—31no—
372C2×C4⋊C4—31no—
373C2×C4⋊C4—31no—
374C2×C4⋊C4—62no—
375C2×C4⋊C4—61no—
376C2×C4⋊C4—61no—
377C2×C4⋊C4—62no—
378C2×C4⋊C4C22×D311yescharacteristic
379C2×C4⋊C4C22×D311yescharacteristic
380C2×C4⋊C4C22×D311yescharacteristic
381C2×C22⋊C4—21no—
382C2×C22⋊C4—31no—
383C2×C22⋊C4—31no—
384C2×C22⋊C4—61no—
385C2×C22⋊C4—61no—
386C2×C22⋊C4—61no—
387C2×C22⋊C4—61no—
388C2×C22⋊C4—61no—
389C2×C22⋊C4—61no—
390C2×C22⋊C4—61no—
391C2×C42—31no—
392#106—62no—
393#106—62no—
394#106—62no—
395C4⋊C8—62no—
396#102—22no—
397#102—22no—
398#102—62no—
399#102—62no—
400#102—121no—
401#102—121no—
402C22⋊C8—41no—
403C22⋊C8—62no—
404C22⋊C8—62no—
405C22⋊C8—121no—
406#97—62no—
407#95—61no—
408#95—61no—
409#95—61no—
410#95—61no—
411C23×C3—21no—
412C23×C3—21no—
413C23×C3—21no—
414C23×C3—21no—
415C23×C3—21no—
416C23×C3—21no—
417C23×C3—22no—
418C23×C3—41no—
419C23×C3—41no—
420C23×C3—41no—
421C23×C3—41no—
422C23×C3—41no—
423C23×C3—41no—
424C23×C3AGL(1,ℤ/8)12yes—
425C23×C3C22×D411yescharacteristic
426C22×D3—21no—
427C22×D3—21no—
428C22×D3—21no—
429C22×D3—21no—
430C22×D3—21no—
431C22×D3—21no—
432C22×D3—22no—
433C22×D3—41no—
434C22×D3—41no—
435C22×D3—41no—
436C22×D3—41no—
437C22×D3—41no—
438C22×D3—41no—
439C22×D3AGL(1,ℤ/8)12yes—
440C3×D4—22no—
441C3×D4—22no—
442C3×D4—41no—
443C3×D4—41no—
444C3×D4—84no—
445C2×C3×C4—21no—
446C2×C3×C4—22no—
447C2×C3×C4—22no—
448C2×C3×C4—21no—
449C2×C3×C4—21no—
450C2×C3×C4—48no—
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×C4—41no—
459C2×C3×C4—41no—
460C2×C3×C4—41no—
461C2×C3×C4—41no—
462C2×C3×C4C22×D411yescharacteristic
463C2×C3×C4C22×D411yescharacteristic
464C2×C3×C4C2×#4111yescharacteristic
465C2×C3×C4C2×#4111yescharacteristic
466C2×C3×C4H(5,𝔽2)11yescharacteristic
467C2×C3×C42−1+411yescharacteristic
468#67—28no—
469#67—48no—
470#67—84no—
471C2×Dic3—21no—
472C2×Dic3—21no—
473C2×Dic3—21no—
474C2×Dic3—21no—
475C2×Dic3—21no—
476C2×Dic3—22no—
477C2×Dic3—21no—
478C2×Dic3—21no—
479C2×Dic3—41no—
480C2×Dic3—41no—
481C2×Dic3—41no—
482C2×Dic3—41no—
483C2×Dic3—41no—
484C2×Dic3—41no—
485C2×Dic3—41no—
486C2×Dic3—41no—
487C2×Dic3—84no—
488C2×Dic3#12012yes—
489C2×Dic3#12012yes—
490D12—22no—
491D12—22no—
492D12—48no—
493D12—41no—
494D12—41no—
495C4×D3—48no—
496C4×D3—48no—
497C4×D3—41no—
498C4×D3—41no—
499C4×D3—41no—
500C4×D3—41no—
501Dic6—48no—
502C3×C8—41no—
503C3×C8—41no—
504C3⋊C8—22no—
505C3⋊C8—41no—
506C24—21no—
507C24—31no—
508C24—61no—
509C24D3×D411yescharacteristic
510#41—1232no—
511C2×Q8—64no—
512C2×Q8—122no—
513C2×Q8—122no—
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—64no—
523C2×D4—62no—
524C2×D4—62no—
525C2×D4—62no—
526C2×D4—64no—
527C2×D4—61no—
528C2×D4—61no—
529C2×D4—61no—
530C2×D4—61no—
531C2×D4—61no—
532C2×D4—81no—
533C2×D4—122no—
534C2×D4—122no—
535C2×D4—122no—
536C2×D4—122no—
537C2×D4—122no—
538C2×D4—122no—
539C2×D4—241no—
540C2×D4#23512yescomplemented
541C22×C4—24no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—31no—
552C22×C4—31no—
553C22×C4—31no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—64no—
557C22×C4—64no—
558C22×C4—61no—
559C22×C4—61no—
560C22×C4—61no—
561C22×C4—61no—
562C22×C4—61no—
563C22×C4—61no—
564C22×C4—61no—
565C22×C4—61no—
566C22×C4—61no—
567C22×C4—122no—
568C22×C4—122no—
569C22×C4—122no—
570C22×C4—122no—
571C22×C4—122no—
572C22×C4—241no—
573C22×C4—241no—
574C22×C4D3×D411yescharacteristic
575C22×C4C23×D311yescharacteristic
576D8—68no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—32no—
584C2×C8—61no—
585C2×C8—61no—
586C2×C8—61no—
587C2×C8—61no—
588C2×C8—61no—
589C4⋊C4—24no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—32no—
595C4⋊C4—62no—
596C4⋊C4—64no—
597C4⋊C4—64no—
598C4⋊C4—61no—
599C4⋊C4—61no—
600C4⋊C4—61no—
601C4⋊C4—61no—
602C4⋊C4—61no—
603C4⋊C4D3×D412yes—
604C4⋊C4D3×D412yes—
605C22⋊C4—42no—
606C22⋊C4—62no—
607C22⋊C4—64no—
608C22⋊C4—64no—
609C22⋊C4—64no—
610C22⋊C4—62no—
611C22⋊C4—122no—
612C22⋊C4—122no—
613C22⋊C4—241no—
614C22⋊C4—241no—
615C42—32no—
616C42—32no—
617C22×C3—22no—
618C22×C3—22no—
619C22×C3—22no—
620C22×C3—41no—
621C22×C3—41no—
622C22×C3—41no—
623C22×C3—41no—
624C22×C3—42no—
625C22×C3—42no—
626C22×C3—42no—
627C22×C3—81no—
628C22×C3—81no—
629C22×C3—81no—
630C22×C3—81no—
631C22×C3C2×#12011yescharacteristic
632C22×C3#54611yescharacteristic
633C22×C3#54711yescharacteristic
634C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
635C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
636C22×C3#57711yescharacteristic
637C22×C3#57711yescharacteristic
638C2×D3—22no—
639C2×D3—22no—
640C2×D3—22no—
641C2×D3—41no—
642C2×D3—41no—
643C2×D3—41no—
644C2×D3—41no—
645C2×D3—42no—
646C2×D3—42no—
647C2×D3—42no—
648C2×D3—81no—
649C2×D3—81no—
650C2×D3—81no—
651C2×D3—81no—
652C3×C4—41no—
653C3×C4—42no—
654C3×C4—42no—
655C3×C4—81no—
656C3×C4#52511yescharacteristic
657C3×C4#53711yescharacteristic
658C3×C4#54811yescharacteristic
659C3×C4#55011yescharacteristic
660Dic3—22no—
661Dic3—22no—
662Dic3—41no—
663Dic3—42no—
664Dic3—81no—
665Dic3—81no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—22no—
673C23—32no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—61no—
681C23—61no—
682C23—61no—
683C23—61no—
684C23—61no—
685C23—61no—
686C23—62no—
687C23—121no—
688C23—121no—
689C23—121no—
690C23—121no—
691C23—121no—
692C23—121no—
693C23#91112yes—
694C23C2×D3×D411yescharacteristic
695Q8—128no—
696D4—22no—
697D4—22no—
698D4—41no—
699D4—41no—
700D4—68no—
701D4—62no—
702D4—62no—
703D4—84no—
704D4—128no—
705D4—128no—
706D4—121no—
707D4—121no—
708D4—244no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—32no—
715C2×C4—32no—
716C2×C4—48no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—61no—
729C2×C4—61no—
730C2×C4—61no—
731C2×C4—61no—
732C2×C4—61no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—62no—
736C2×C4—128no—
737C2×C4—128no—
738C2×C4—121no—
739C2×C4—121no—
740C2×C4—121no—
741C2×C4—121no—
742C2×C4—121no—
743C2×C4—121no—
744C2×C4—121no—
745C2×C4—121no—
746C2×C4—121no—
747C2×C4—121no—
748C2×C4—121no—
749C2×C4—121no—
750C2×C4—244no—
751C2×C4C2×#23511yescharacteristic
752C2×C4C2×D3×D411yescharacteristic
753C2×C4C2×D3×D411yescharacteristic
754C2×C4#100411yescharacteristic
755C2×C4D3×#4111yescharacteristic
756C2×C4#101011yescharacteristic
757C8—41no—
758C8—41no—
759C8—62no—
760C8—121no—
761C2×C3—42no—
762C2×C3—82no—
763C2×C3#240711yescharacteristic
764C2×C3#300311yescharacteristic
765C2×C3#301011yescharacteristic
766C2×C3#330611yescharacteristic
767C2×C3#330611yescharacteristic
768C2×C3#334511yescharacteristic
769C2×C3#334511yescharacteristic
770D3—42no—
771D3—82no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—62no—
783C22—62no—
784C22—62no—
785C22—81no—
786C22—81no—
787C22—81no—
788C22—81no—
789C22—121no—
790C22—121no—
791C22—121no—
792C22—121no—
793C22—122no—
794C22—122no—
795C22—122no—
796C22—241no—
797C22—241no—
798C22—241no—
799C22—241no—
800C22#549011yescharacteristic
801C22D3×#12011yescharacteristic
802C22#565511yescharacteristic
803C22C2×#91111yescharacteristic
804C22#576211yescharacteristic
805C22D3×AGL(1,ℤ/8)11yescharacteristic
806C22#577811yescharacteristic
807C4—42no—
808C4—42no—
809C4—41no—
810C4—62no—
811C4—62no—
812C4—81no—
813C4—122no—
814C4—121no—
815C4—241no—
816C4—241no—
817C4#554711yescharacteristic
818C4#555211yescharacteristic
819C4#559911yescharacteristic
820C4#560811yescharacteristic
821C3#2412811yescharacteristic, complemented, Sylow
822C2—42no—
823C2—82no—
824C2—122no—
825C2—242no—
826C2#7468811yescharacteristic
827C2#7876111yescharacteristic
828C2#7889411yescharacteristic
829C2#8000211yescharacteristic
830C2#8004111yescharacteristic
831C2#8129411yescharacteristic
832C2#8133511yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1874C2
socleC23×C3C22×D4
hypercenter#1874D3
hypocenterC3#24128
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1874

Complements

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

NH ≅ G/Ntype
1. C2×#5507C2semidirect
2. #82666C2semidirect
3. C2×#4761C2semidirect
4. C2×#4785C2semidirect
5. C3×#1874C2semidirect
6. #71684C2semidirect
7. #71556C2semidirect
8. #70204C2semidirect
9. #70200C2semidirect
10. #69935C2semidirect
11. #69917C2semidirect
12. #68893C2semidirect
13. #68875C2semidirect
14. #68823C2semidirect
15. #68806C2semidirect
75. #1874D3semidirect
142. #893D4semidirect
146. #888D4semidirect
225. C2×C3×D4#41semidirect
323. C2×C3⋊C8#41semidirect
540. C2×D4#235semidirect
821. C3#24128semidirect

Maximal subgroups

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

subgroupindex
C2×#55072
#826662
C2×#47612
C2×#47852
C3×#18742
#716842
#715562
#702042
#702002
#699352
#699172
#688932
#688752
#688232
#688062
#241283