Finite Group Databasebeta

← #10829221

Subgroups — #10829221

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×#5611C211yesmaximal, characteristic, complemented
2C2×#5152C211yesmaximal, characteristic, complemented
3#82666C211yesmaximal, characteristic, complemented
4C2×#4761C211yesmaximal, characteristic, complemented
5C3×#1999C211yesmaximal, characteristic, complemented
6#72043C211yesmaximal, characteristic, complemented
7#71680C211yesmaximal, characteristic, complemented
8#71677C211yesmaximal, characteristic, complemented
9#70200C211yesmaximal, characteristic, complemented
10#70176C211yesmaximal, characteristic, complemented
11#70154C211yesmaximal, characteristic, complemented
12#69928C211yesmaximal, characteristic, complemented
13#69917C211yesmaximal, characteristic, complemented
14#68875C211yesmaximal, characteristic, complemented
15#68806C211yesmaximal, characteristic, complemented
16#24128—31nomaximal, Sylow
17C22×#237—21no—
18C22×C3×D8C2211yescharacteristic
19C2×C3×#121C2211yescharacteristic
20C2×C3×#121C2211yescharacteristic
21C2×#938C2211yescharacteristic
22C2×#938C2211yescharacteristic
23C2×#935—21no—
24C2×D4×Dic3C2211yescharacteristic
25C2×D4×Dic3C2211yescharacteristic
26C2×C4×#67C2211yescharacteristic
27C22×C4⋊Dic3C2211yescharacteristic
28#5611—24no—
29#5611—24no—
30C2×D3×C4⋊C4C2211yescharacteristic
31C2×#888C2211yescharacteristic
32C2×#883—21no—
33C2×#878—21no—
34C2×C3×#102C2211yescharacteristic
35C2×C3×#102C2211yescharacteristic
36C2×C3×C22⋊C8C2211yescharacteristic
37#5223—21no—
38#5220—21no—
39C2×#832C2211yescharacteristic
40C2×#832C2211yescharacteristic
41C2×#832C2211yescharacteristic
42C2×#832C2211yescharacteristic
43#5212C2211yescharacteristic
44C2×#830C2211yescharacteristic
45#5152—24no—
46C2×(C2×D3)⋊C8C2211yescharacteristic
47C2×(C2×D3)⋊C8C2211yescharacteristic
48C2×#817C2211yescharacteristic
49C2×#817C2211yescharacteristic
50C2×#815C2211yescharacteristic
51C2×Dic3⋊C8C2211yescharacteristic
52#4987C2211yescharacteristic
53#4977C2211yescharacteristic
54C2×#808C2211yescharacteristic
55#4958—21no—
56#4952—21no—
57#4761—24no—
58C3×#340C2211yescharacteristic
59#4551C2211yescharacteristic
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#1999D311yescharacteristic, complemented
72#1993—31no—
73#1955—31no—
74#1874—31no—
75#1874—31no—
76#1853—31no—
77#1853—31no—
78#1804—31no—
79C22×C3×D4—21no—
80C22×C3×D4—21no—
81C22×C3×D4C2311yescharacteristic
82C22×C3×D4C2311yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C22×#67—21no—
85C22×#67—21no—
86C22×#67D411yescharacteristic
87C23×Dic3—21no—
88C23×Dic3—21no—
89C23×Dic3—21no—
90C2×#237—28no—
91C2×#237—44no—
92C2×#237—44no—
93C22×C4×D3—21no—
94C22×C4×D3C2311yescharacteristic
95C22×Dic6—21no—
96C2×C3×D8—22no—
97C2×C3×D8—22no—
98C2×C3×D8—22no—
99C22×C3×C8C2311yescharacteristic
100C22×C3×C8C2311yescharacteristic
101C3×#121—22no—
102C3×#121—22no—
103C3×#121—22no—
104C3×#121—41no—
105C2×C3×C4⋊C4C2311yescharacteristic
106C2×C3×C4⋊C4C2311yescharacteristic
107C2×C3×C22⋊C4—21no—
108C2×C3×C22⋊C4—21no—
109C2×#217—21no—
110C2×#217—21no—
111C2×#217—21no—
112C2×#217—21no—
113C2×#217—21no—
114C2×#217D411yescharacteristic
115#938—22no—
116#938—22no—
117#938—22no—
118#938—41no—
119#935—28no—
120D4×Dic3—22no—
121D4×Dic3—22no—
122D4×Dic3—22no—
123D4×Dic3D414yescomplemented
124C4×#67—22no—
125C4×#67—22no—
126C2×(C2×D3)⋊C4—21no—
127C2×(C2×D3)⋊C4D411yescharacteristic
128C2×C4⋊Dic3—21no—
129C2×C4⋊Dic3—22no—
130C2×C4⋊Dic3—22no—
131C2×C4⋊Dic3C2311yescharacteristic
132C2×C4⋊Dic3C2311yescharacteristic
133C2×C4⋊Dic3C2311yescharacteristic
134C2×C4⋊Dic3C2311yescharacteristic
135C2×Dic3⋊C4—21no—
136C2×Dic3⋊C4—21no—
137C2×Dic3⋊C4D411yescharacteristic
138C2×C4×Dic3C2311yescharacteristic
139C22×C3⋊C8C2311yescharacteristic
140C22×C3⋊C8C2311yescharacteristic
141D3×C4⋊C4—22no—
142D3×C4⋊C4—22no—
143#888—22no—
144#888D414yescomplemented
145#883—28no—
146#878—28no—
147C3×#102—22no—
148C3×#102—41no—
149C3×C22⋊C8—22no—
150#832—22no—
151#832—22no—
152#832—22no—
153#832—41no—
154C3⋊#95—21no—
155C3⋊#95—21no—
156C3⋊#95—21no—
157C3⋊#95—21no—
158#830—41no—
159(C2×D3)⋊C8—22no—
160(C2×D3)⋊C8—41no—
161#817—22no—
162#817—22no—
163#815—22no—
164Dic3⋊C8—22no—
165#808—22no—
166C22×#41—61no—
167C22×D8C2×D311yescharacteristic
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×#121C2×D311yescharacteristic
177C2×#121C2×D311yescharacteristic
178C2×C4×D4—31no—
179C2×C4×D4—31no—
180C2×C4×D4—31no—
181C22×C4⋊C4—31no—
182C22×C4⋊C4—31no—
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#340—31no—
212#340C2×D311yescharacteristic
213C24×C3—21no—
214C24×C3—21no—
215C24×C3C2×D411yescharacteristic
216C23×D3C2×D411yescharacteristic
217C2×C3×D4—24no—
218C2×C3×D4—21no—
219C2×C3×D4—21no—
220C2×C3×D4—21no—
221C2×C3×D4—21no—
222C2×C3×D4—21no—
223C2×C3×D4—21no—
224C2×C3×D4—21no—
225C2×C3×D4—21no—
226C2×C3×D4—21no—
227C2×C3×D4—21no—
228C2×C3×D4—42no—
229C2×C3×D4—42no—
230C2×C3×D4—42no—
231C2×C3×D4—42no—
232C2×C3×D4—81no—
233C2×C3×D4C2×D412yes—
234C2×C3×D4#4112yescomplemented
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4C2×D411yescharacteristic
244C22×C3×C4C2411yescharacteristic
245C2×#67—22no—
246C2×#67—22no—
247C2×#67—24no—
248C2×#67—22no—
249C2×#67—42no—
250C2×#67—42no—
251C2×#67—42no—
252C2×#67—42no—
253C2×#67—81no—
254C22×Dic3—24no—
255C22×Dic3—21no—
256C22×Dic3—21no—
257C22×Dic3—24no—
258C22×Dic3—21no—
259C22×Dic3—21no—
260C22×Dic3—42no—
261C22×Dic3—42no—
262C22×Dic3—42no—
263C22×Dic3—42no—
264C22×Dic3—42no—
265C22×Dic3—81no—
266C22×Dic3—81no—
267C22×Dic3C2×D411yescharacteristic
268C22×Dic3C2×D411yescharacteristic
269C22×Dic3C2×D411yescharacteristic
270#237—432no—
271C2×C4×D3—24no—
272C2×C4×D3—21no—
273C2×C4×D3—21no—
274C2×C4×D3—21no—
275C2×C4×D3—21no—
276C2×C4×D3—21no—
277C2×C4×D3—21no—
278C2×C4×D3—42no—
279C2×C4×D3—42no—
280C2×Dic6—24no—
281C2×Dic6—42no—
282C2×Dic6—42no—
283C3×D8—28no—
284C2×C3×C8—21no—
285C2×C3×C8—21no—
286C2×C3×C8—21no—
287C2×C3×C8—21no—
288C2×C3×C8—21no—
289C2×C3×C8#4112yescomplemented
290C3×C4⋊C4—21no—
291C3×C4⋊C4—21no—
292C3×C4⋊C4—21no—
293C3×C4⋊C4C2×D412yes—
294C3×C22⋊C4—24no—
295C3×C22⋊C4—42no—
296#217—24no—
297#217—24no—
298#217—22no—
299#217—42no—
300#217—42no—
301#217—81no—
302(C2×D3)⋊C4—22no—
303(C2×D3)⋊C4—81no—
304C4⋊Dic3—24no—
305C4⋊Dic3—21no—
306C4⋊Dic3—21no—
307C4⋊Dic3—21no—
308C4⋊Dic3—21no—
309C4⋊Dic3—21no—
310C4⋊Dic3—21no—
311C4⋊Dic3C2×D412yes—
312C4⋊Dic3C2×D412yes—
313Dic3⋊C4—24no—
314Dic3⋊C4—22no—
315Dic3⋊C4—24no—
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—21no—
324C2×#41—68no—
325C2×#41—124no—
326C2×#41—124no—
327C22×Q8—61no—
328C22×D4—21no—
329C22×D4—21no—
330C22×D4—31no—
331C22×D4—61no—
332C22×D4—61no—
333C22×D4C22×D311yescharacteristic
334C22×D4C22×D311yescharacteristic
335C23×C4—31no—
336C23×C4—61no—
337C23×C4—61no—
338C23×C4—61no—
339C23×C4—61no—
340C23×C4C22×D311yescharacteristic
341C2×D8—22no—
342C2×D8—22no—
343C2×D8—22no—
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—22no—
355#121—22no—
356#121—41no—
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—31no—
368C2×C4⋊C4—31no—
369C2×C4⋊C4—31no—
370C2×C4⋊C4—31no—
371C2×C4⋊C4—31no—
372C2×C4⋊C4—62no—
373C2×C4⋊C4—62no—
374C2×C4⋊C4—62no—
375C2×C4⋊C4—61no—
376C2×C4⋊C4—61no—
377C2×C4⋊C4—61no—
378C2×C4⋊C4—62no—
379C2×C4⋊C4C22×D311yescharacteristic
380C2×C4⋊C4C22×D311yescharacteristic
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—31no—
384C2×C22⋊C4—31no—
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—41no—
398#102—62no—
399#102—62no—
400#102—62no—
401#102—121no—
402C22⋊C8—22no—
403C22⋊C8—62no—
404C22⋊C8—121no—
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—22no—
419C23×C3—41no—
420C23×C3—41no—
421C23×C3—41no—
422C23×C3—41no—
423C23×C3—41no—
424C23×C3—41no—
425C23×C3—41no—
426C23×C3—41no—
427C23×C3—41no—
428C23×C3—41no—
429C23×C3—41no—
430C23×C3—41no—
431C23×C3AGL(1,ℤ/8)12yes—
432C23×C3C22×D411yescharacteristic
433C22×D3—21no—
434C22×D3—21no—
435C22×D3—21no—
436C22×D3—21no—
437C22×D3—21no—
438C22×D3—21no—
439C22×D3AGL(1,ℤ/8)12yes—
440C3×D4—22no—
441C3×D4—22no—
442C3×D4—22no—
443C3×D4—22no—
444C3×D4—48no—
445C3×D4—41no—
446C3×D4—41no—
447C3×D4—41no—
448C3×D4—41no—
449C3×D4—84no—
450C2×C3×C4—22no—
451C2×C3×C4—21no—
452C2×C3×C4—21no—
453C2×C3×C4—21no—
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×C4—41no—
463C2×C3×C4C22×D411yescharacteristic
464C2×C3×C4C22×D411yescharacteristic
465C2×C3×C4C2×#4111yescharacteristic
466C2×C3×C4C2×#4111yescharacteristic
467C2×C3×C4H(5,𝔽2)11yescharacteristic
468C2×C3×C42−1+411yescharacteristic
469#67—28no—
470#67—48no—
471#67—84no—
472C2×Dic3—21no—
473C2×Dic3—21no—
474C2×Dic3—21no—
475C2×Dic3—21no—
476C2×Dic3—21no—
477C2×Dic3—22no—
478C2×Dic3—22no—
479C2×Dic3—21no—
480C2×Dic3—21no—
481C2×Dic3—48no—
482C2×Dic3—48no—
483C2×Dic3—41no—
484C2×Dic3—41no—
485C2×Dic3—41no—
486C2×Dic3—41no—
487C2×Dic3—41no—
488C2×Dic3—41no—
489C2×Dic3—41no—
490C2×Dic3—41no—
491C2×Dic3—41no—
492C2×Dic3—41no—
493C2×Dic3—84no—
494C2×Dic3#12012yes—
495C2×Dic3#12012yes—
496C4×D3—48no—
497C4×D3—41no—
498C4×D3—41no—
499C4×D3—41no—
500C4×D3—41no—
501Dic6—48no—
502C3×C8—22no—
503C3×C8—41no—
504C3⋊C8—41no—
505C3⋊C8—41no—
506C24—21no—
507C24—21no—
508C24—31no—
509C24D3×D411yescharacteristic
510#41—1232no—
511C2×Q8—64no—
512C2×Q8—122no—
513C2×Q8—122no—
514C2×D4—24no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—42no—
526C2×D4—42no—
527C2×D4—42no—
528C2×D4—42no—
529C2×D4—62no—
530C2×D4—62no—
531C2×D4—62no—
532C2×D4—64no—
533C2×D4—81no—
534C2×D4—122no—
535C2×D4—122no—
536C2×D4—122no—
537C2×D4—122no—
538C2×D4—241no—
539C2×D4D3×D412yes—
540C2×D4#23712yescomplemented
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—64no—
553C22×C4—64no—
554C22×C4—64no—
555C22×C4—61no—
556C22×C4—61no—
557C22×C4—61no—
558C22×C4—61no—
559C22×C4—61no—
560C22×C4—61no—
561C22×C4—61no—
562C22×C4—61no—
563C22×C4—61no—
564C22×C4—61no—
565C22×C4—122no—
566C22×C4—122no—
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—28no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—61no—
583C2×C8—61no—
584C2×C8—61no—
585C2×C8—61no—
586C2×C8—61no—
587C2×C8—61no—
588C2×C8#23712yescomplemented
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—32no—
593C4⋊C4—32no—
594C4⋊C4—62no—
595C4⋊C4—64no—
596C4⋊C4—64no—
597C4⋊C4—64no—
598C4⋊C4—61no—
599C4⋊C4—61no—
600C4⋊C4—61no—
601C4⋊C4—61no—
602C4⋊C4—61no—
603C4⋊C4—61no—
604C4⋊C4D3×D412yes—
605C22⋊C4—24no—
606C22⋊C4—42no—
607C22⋊C4—62no—
608C22⋊C4—62no—
609C22⋊C4—64no—
610C22⋊C4—64no—
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—42no—
628C22×C3—42no—
629C22×C3—42no—
630C22×C3—81no—
631C22×C3—81no—
632C22×C3—81no—
633C22×C3—81no—
634C22×C3—81no—
635C22×C3—81no—
636C22×C3—81no—
637C22×C3—81no—
638C22×C3C2×#12011yescharacteristic
639C22×C3#54611yescharacteristic
640C22×C3#54711yescharacteristic
641C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
642C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
643C22×C3#57711yescharacteristic
644C22×C3#57711yescharacteristic
645C2×D3—22no—
646C2×D3—22no—
647C2×D3—22no—
648C2×D3—41no—
649C2×D3—41no—
650C2×D3—41no—
651C2×D3—41no—
652C3×C4—41no—
653C3×C4—42no—
654C3×C4—81no—
655C3×C4#52511yescharacteristic
656C3×C4#53711yescharacteristic
657C3×C4#54811yescharacteristic
658C3×C4#55011yescharacteristic
659Dic3—22no—
660Dic3—22no—
661Dic3—41no—
662Dic3—42no—
663Dic3—42no—
664Dic3—81no—
665Dic3—81no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—22no—
673C23—22no—
674C23—32no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—61no—
688C23—61no—
689C23—61no—
690C23—61no—
691C23—61no—
692C23—61no—
693C23#91112yes—
694C23C2×D3×D411yescharacteristic
695Q8—128no—
696D4—22no—
697D4—22no—
698D4—22no—
699D4—22no—
700D4—48no—
701D4—41no—
702D4—41no—
703D4—41no—
704D4—41no—
705D4—68no—
706D4—84no—
707D4—128no—
708D4—244no—
709C2×C4—21no—
710C2×C4—22no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—32no—
714C2×C4—32no—
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—62no—
730C2×C4—62no—
731C2×C4—61no—
732C2×C4—61no—
733C2×C4—128no—
734C2×C4—128no—
735C2×C4—128no—
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—121no—
745C2×C4—121no—
746C2×C4—121no—
747C2×C4—121no—
748C2×C4—121no—
749C2×C4—121no—
750C2×C4—244no—
751C2×C4C2×D3×D411yescharacteristic
752C2×C4C2×D3×D411yescharacteristic
753C2×C4C2×#23711yescharacteristic
754C2×C4C2×#23711yescharacteristic
755C2×C4#100411yescharacteristic
756C2×C4#101011yescharacteristic
757C8—22no—
758C8—41no—
759C8—121no—
760C8—121no—
761C2×C3—42no—
762C2×C3—82no—
763C2×C3—82no—
764C2×C3#240711yescharacteristic
765C2×C3#300311yescharacteristic
766C2×C3#301011yescharacteristic
767C2×C3#330611yescharacteristic
768C2×C3#330611yescharacteristic
769C2×C3#334511yescharacteristic
770C2×C3#334511yescharacteristic
771D3—42no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—62no—
786C22—62no—
787C22—62no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22—81no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22—81no—
796C22—121no—
797C22—121no—
798C22—121no—
799C22—121no—
800C22D3×#12011yescharacteristic
801C22#559111yescharacteristic
802C22#561111yescharacteristic
803C22C2×#91111yescharacteristic
804C22#577011yescharacteristic
805C22D3×AGL(1,ℤ/8)11yescharacteristic
806C22#577511yescharacteristic
807C4—41no—
808C4—42no—
809C4—62no—
810C4—62no—
811C4—81no—
812C4—121no—
813C4—122no—
814C4—122no—
815C4—241no—
816C4—241no—
817C4#558611yescharacteristic
818C4#559711yescharacteristic
819C4#559811yescharacteristic
820C4#571811yescharacteristic
821C3#2412811yescharacteristic, complemented, Sylow
822C2—42no—
823C2—82no—
824C2—82no—
825C2—122no—
826C2#7666811yescharacteristic
827C2#8000211yescharacteristic
828C2#8001611yescharacteristic
829C2#8008611yescharacteristic
830C2#8010611yescharacteristic
831C2#8071111yescharacteristic
832C2#8087911yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1999C2
socleC23×C3C22×D4
hypercenter#1999D3
hypocenterC3#24128
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1999

Complements

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

NH ≅ G/Ntype
1. C2×#5611C2semidirect
2. C2×#5152C2semidirect
3. #82666C2semidirect
4. C2×#4761C2semidirect
5. C3×#1999C2semidirect
6. #72043C2semidirect
7. #71680C2semidirect
8. #71677C2semidirect
9. #70200C2semidirect
10. #70176C2semidirect
11. #70154C2semidirect
12. #69928C2semidirect
13. #69917C2semidirect
14. #68875C2semidirect
15. #68806C2semidirect
71. #1999D3semidirect
123. D4×Dic3D4semidirect
144. #888D4semidirect
234. C2×C3×D4#41semidirect
289. C2×C3×C8#41semidirect
540. C2×D4#237semidirect
588. C2×C8#237semidirect
821. C3#24128semidirect

Maximal subgroups

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

subgroupindex
C2×#56112
C2×#51522
#826662
C2×#47612
C3×#19992
#720432
#716802
#716772
#702002
#701762
#701542
#699282
#699172
#688752
#688062
#241283