Finite Group Databasebeta

← #10829227

Subgroups — #10829227

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
2C2×#4870C211yesmaximal, characteristic, complemented
3C2×#4869C211yesmaximal, characteristic, complemented
4#73933C211yesmaximal, characteristic, complemented
5C3×#1853C211yesmaximal, characteristic, complemented
6#71560C211yesmaximal, characteristic, complemented
7#70581C211yesmaximal, characteristic, complemented
8#70579C211yesmaximal, characteristic, complemented
9#69961C211yesmaximal, characteristic, complemented
10#69917C211yesmaximal, characteristic, complemented
11#69524C211yesmaximal, characteristic, complemented
12#68893C211yesmaximal, characteristic, complemented
13#68886C211yesmaximal, characteristic, complemented
14#68880C211yesmaximal, characteristic, complemented
15#68806C211yesmaximal, characteristic, complemented
16#24128—31nomaximal, Sylow
17C22×#235—21no—
18C22×C3×C4⋊C4C2211yescharacteristic
19C2×#930C2211yescharacteristic
20C2×#930C2211yescharacteristic
21C2×#929—21no—
22C2×C4×#67C2211yescharacteristic
23C22×D24C2211yescharacteristic
24C2×#896—21no—
25#5507—24no—
26#5507—24no—
27C2×#895C2211yescharacteristic
28C2×#895C2211yescharacteristic
29C2×#894—21no—
30C2×#893C2211yescharacteristic
31C2×#893C2211yescharacteristic
32C2×D3×C4⋊C4C2211yescharacteristic
33C2×#888C2211yescharacteristic
34C2×C3×#106C2211yescharacteristic
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×#808C2211yescharacteristic
52#4960—21no—
53#4956—21no—
54#4870—24no—
55#4869—24no—
56#4675—21no—
57#4665—21no—
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#1874—31no—
76#1853—31no—
77#1853D311yescharacteristic, complemented
78#1804—31no—
79C23×C3×C4—21no—
80C23×C3×C4C2311yescharacteristic
81C22×#67—21no—
82C22×#67—21no—
83C22×#67D411yescharacteristic
84C2×#235—28no—
85C2×#235—44no—
86C2×#235—44no—
87C22×D12—21no—
88C22×D12—21no—
89C22×D12C2311yescharacteristic
90C22×D12C2311yescharacteristic
91C22×C4×D3—21no—
92C22×C4×D3—21no—
93C22×C4×D3—21no—
94C22×C4×D3C2311yescharacteristic
95C22×Dic6—21no—
96C22×C3×C8C2311yescharacteristic
97C22×C3×C8C2311yescharacteristic
98C2×C3×C4⋊C4—21no—
99C2×C3×C4⋊C4—22no—
100C2×C3×C4⋊C4—22no—
101C2×C3×C4⋊C4C2311yescharacteristic
102C2×C3×C4⋊C4C2311yescharacteristic
103C2×C3×C4⋊C4C2311yescharacteristic
104C2×C3×C4⋊C4C2311yescharacteristic
105C2×C3×C22⋊C4—21no—
106C2×#217D411yescharacteristic
107#930—22no—
108#930—22no—
109#930—22no—
110#930—41no—
111#929—28no—
112C4×#67—22no—
113C4×#67—22no—
114C2×(C2×D3)⋊C4—21no—
115C2×(C2×D3)⋊C4—21no—
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⋊Dic3C2311yescharacteristic
123C2×C4⋊Dic3C2311yescharacteristic
124C2×Dic3⋊C4—21no—
125C2×Dic3⋊C4—21no—
126C2×Dic3⋊C4D411yescharacteristic
127C2×C4×Dic3C2311yescharacteristic
128C22×C3⋊C8C2311yescharacteristic
129C22×C3⋊C8C2311yescharacteristic
130C2×D24—22no—
131C2×D24—22no—
132C2×D24—22no—
133#896—28no—
134#895—22no—
135#895—22no—
136#895—22no—
137#895—41no—
138#894—28no—
139#893—22no—
140#893—22no—
141#893—22no—
142#893D414yescomplemented
143D3×C4⋊C4—22no—
144D3×C4⋊C4—22no—
145#888—22no—
146#888D414yescomplemented
147C3×#106—22no—
148C3×#106—22no—
149C3×C22⋊C8—22no—
150C3×#95—21no—
151C3⋊#95—21no—
152C3⋊#95—21no—
153C3⋊#95—21no—
154#830—41no—
155#821—22no—
156#821—41no—
157(C2×D3)⋊C8—22no—
158(C2×D3)⋊C8—41no—
159#815—22no—
160Dic3⋊C8—22no—
161#809—22no—
162#809—22no—
163#809—22no—
164#809—41no—
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×#121—31no—
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×#106C2×D311yescharacteristic
187C2×#106C2×D311yescharacteristic
188C2×C4⋊C8—31no—
189C2×#102—31no—
190C2×#102—31no—
191C2×#102—31no—
192C2×#102—31no—
193C2×#102—31no—
194C2×#102—31no—
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#380C2×D311yescharacteristic
207#340—31no—
208#340—31no—
209#340—31no—
210#340—31no—
211#340C2×D311yescharacteristic
212#340C2×D311yescharacteristic
213C24×C3C2×D411yescharacteristic
214C23×D3—21no—
215C23×D3—21no—
216C23×D3C2×D411yescharacteristic
217C22×C3×C4—24no—
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×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—42no—
229C22×C3×C4—42no—
230C22×C3×C4C2×D411yescharacteristic
231C22×C3×C4C2411yescharacteristic
232C2×#67—22no—
233C2×#67—22no—
234C2×#67—24no—
235C2×#67—22no—
236C2×#67—42no—
237C2×#67—42no—
238C2×#67—42no—
239C2×#67—42no—
240C2×#67—81no—
241C22×Dic3—21no—
242C22×Dic3—21no—
243C22×Dic3C2×D411yescharacteristic
244C22×Dic3C2×D411yescharacteristic
245C22×Dic3C2×D411yescharacteristic
246#235—432no—
247C2×D12—21no—
248C2×D12—21no—
249C2×D12—21no—
250C2×D12—21no—
251C2×D12—21no—
252C2×D12—21no—
253C2×D12—21no—
254C2×D12—21no—
255C2×D12—24no—
256C2×D12—21no—
257C2×D12—21no—
258C2×D12—42no—
259C2×D12—42no—
260C2×D12—42no—
261C2×D12—42no—
262C2×D12—81no—
263C2×D12C2×D412yes—
264C2×D12#4112yescomplemented
265C2×C4×D3—24no—
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—24no—
273C2×C4×D3—42no—
274C2×C4×D3—42no—
275C2×C4×D3—42no—
276C2×C4×D3—42no—
277C2×C4×D3—42no—
278C2×C4×D3—81no—
279C2×C4×D3—81no—
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#4112yescomplemented
289C3×C4⋊C4—24no—
290C3×C4⋊C4—21no—
291C3×C4⋊C4—21no—
292C3×C4⋊C4—21no—
293C3×C4⋊C4—21no—
294C3×C4⋊C4—21no—
295C3×C4⋊C4—21no—
296C3×C4⋊C4C2×D412yes—
297C3×C4⋊C4C2×D412yes—
298C3×C22⋊C4—81no—
299#217—22no—
300(C2×D3)⋊C4—24no—
301(C2×D3)⋊C4—24no—
302(C2×D3)⋊C4—24no—
303(C2×D3)⋊C4—22no—
304(C2×D3)⋊C4—42no—
305(C2×D3)⋊C4—42no—
306(C2×D3)⋊C4—42no—
307(C2×D3)⋊C4—81no—
308C4⋊Dic3—21no—
309C4⋊Dic3—21no—
310C4⋊Dic3—21no—
311C4⋊Dic3C2×D412yes—
312Dic3⋊C4—24no—
313Dic3⋊C4—24no—
314Dic3⋊C4—22no—
315C4×Dic3C2×D412yes—
316C4×Dic3C2×D412yes—
317C2×C3⋊C8—21no—
318C2×C3⋊C8—21no—
319C2×C3⋊C8—21no—
320C2×C3⋊C8—21no—
321C2×C3⋊C8—21no—
322C2×C3⋊C8—21no—
323D24—28no—
324C2×#41—68no—
325C2×#41—124no—
326C2×#41—124no—
327C22×Q8—61no—
328C22×D4—31no—
329C22×D4—31no—
330C22×D4—31no—
331C22×D4—61no—
332C22×D4—61no—
333C22×D4—61no—
334C22×D4—61no—
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—62no—
354#121—62no—
355#121—62no—
356#121—62no—
357#121—62no—
358#121—62no—
359#121—121no—
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—62no—
374C2×C4⋊C4—61no—
375C2×C4⋊C4—61no—
376C2×C4⋊C4—62no—
377C2×C4⋊C4C22×D311yescharacteristic
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—22no—
393#106—22no—
394#106—62no—
395C4⋊C8—62no—
396#102—62no—
397#102—62no—
398#102—62no—
399#102—62no—
400#102—121no—
401#102—121no—
402C22⋊C8—22no—
403C22⋊C8—62no—
404C22⋊C8—121no—
405C22⋊C8—121no—
406#97—62no—
407#95—21no—
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×C3AGL(1,ℤ/8)12yes—
418C23×C3C22×D411yescharacteristic
419C22×D3—21no—
420C22×D3—21no—
421C22×D3—21no—
422C22×D3—21no—
423C22×D3—21no—
424C22×D3—21no—
425C22×D3—22no—
426C22×D3—22no—
427C22×D3—41no—
428C22×D3—41no—
429C22×D3—41no—
430C22×D3—41no—
431C22×D3—41no—
432C22×D3—41no—
433C22×D3—41no—
434C22×D3—41no—
435C22×D3—41no—
436C22×D3—41no—
437C22×D3—41no—
438C22×D3—41no—
439C22×D3AGL(1,ℤ/8)12yes—
440C2×C3×C4—21no—
441C2×C3×C4—22no—
442C2×C3×C4—22no—
443C2×C3×C4—21no—
444C2×C3×C4—21no—
445C2×C3×C4—48no—
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×C4—41no—
457C2×C3×C4—41no—
458C2×C3×C4—41no—
459C2×C3×C4—41no—
460C2×C3×C4C22×D411yescharacteristic
461C2×C3×C4C22×D411yescharacteristic
462C2×C3×C4C2×#4111yescharacteristic
463C2×C3×C4C2×#4111yescharacteristic
464C2×C3×C4H(5,𝔽2)11yescharacteristic
465C2×C3×C42−1+411yescharacteristic
466#67—28no—
467#67—48no—
468#67—84no—
469C2×Dic3—21no—
470C2×Dic3—21no—
471C2×Dic3—21no—
472C2×Dic3—21no—
473C2×Dic3—21no—
474C2×Dic3—22no—
475C2×Dic3—21no—
476C2×Dic3—21no—
477C2×Dic3—41no—
478C2×Dic3—41no—
479C2×Dic3—41no—
480C2×Dic3—41no—
481C2×Dic3—41no—
482C2×Dic3#12012yes—
483C2×Dic3#12012yes—
484D12—22no—
485D12—22no—
486D12—22no—
487D12—22no—
488D12—48no—
489D12—41no—
490D12—41no—
491D12—41no—
492D12—41no—
493D12—84no—
494C4×D3—48no—
495C4×D3—48no—
496C4×D3—41no—
497C4×D3—41no—
498C4×D3—41no—
499C4×D3—41no—
500C4×D3—84no—
501Dic6—48no—
502C3×C8—22no—
503C3×C8—41no—
504C3⋊C8—41no—
505C3⋊C8—41no—
506C24—31no—
507C24—61no—
508C24—61no—
509C24D3×D411yescharacteristic
510#41—1232no—
511C2×Q8—64no—
512C2×Q8—122no—
513C2×Q8—122no—
514C2×D4—32no—
515C2×D4—32no—
516C2×D4—64no—
517C2×D4—62no—
518C2×D4—62no—
519C2×D4—62no—
520C2×D4—64no—
521C2×D4—61no—
522C2×D4—61no—
523C2×D4—61no—
524C2×D4—61no—
525C2×D4—61no—
526C2×D4—61no—
527C2×D4—61no—
528C2×D4—61no—
529C2×D4—61no—
530C2×D4—61no—
531C2×D4—122no—
532C2×D4—122no—
533C2×D4—122no—
534C2×D4—122no—
535C2×D4—122no—
536C2×D4—122no—
537C2×D4—122no—
538C2×D4—122no—
539C2×D4—241no—
540C2×D4—241no—
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—21no—
552C22×C4—31no—
553C22×C4—31no—
554C22×C4—31no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—64no—
558C22×C4—64no—
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—61no—
583C2×C8—61no—
584C2×C8—61no—
585C2×C8—61no—
586C2×C8—61no—
587C2×C8—61no—
588C2×C8#23512yescomplemented
589C4⋊C4—24no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—32no—
597C4⋊C4—62no—
598C4⋊C4—64no—
599C4⋊C4—64no—
600C4⋊C4—61no—
601C4⋊C4—61no—
602C4⋊C4—61no—
603C4⋊C4D3×D412yes—
604C4⋊C4D3×D412yes—
605C22⋊C4—62no—
606C22⋊C4—64no—
607C22⋊C4—64no—
608C22⋊C4—64no—
609C22⋊C4—62no—
610C22⋊C4—81no—
611C22⋊C4—122no—
612C22⋊C4—122no—
613C22⋊C4—122no—
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×C3C2×#12011yescharacteristic
625C22×C3#54611yescharacteristic
626C22×C3#54711yescharacteristic
627C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
628C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
629C22×C3#57711yescharacteristic
630C22×C3#57711yescharacteristic
631C2×D3—22no—
632C2×D3—22no—
633C2×D3—22no—
634C2×D3—41no—
635C2×D3—41no—
636C2×D3—41no—
637C2×D3—41no—
638C2×D3—42no—
639C2×D3—42no—
640C2×D3—42no—
641C2×D3—42no—
642C2×D3—42no—
643C2×D3—42no—
644C2×D3—81no—
645C2×D3—81no—
646C2×D3—81no—
647C2×D3—81no—
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—81no—
657C3×C4#52511yescharacteristic
658C3×C4#53711yescharacteristic
659C3×C4#54811yescharacteristic
660C3×C4#55011yescharacteristic
661Dic3—22no—
662Dic3—22no—
663Dic3—41no—
664Dic3—42no—
665Dic3—81no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—32no—
673C23—61no—
674C23—61no—
675C23—61no—
676C23—61no—
677C23—61no—
678C23—61no—
679C23—62no—
680C23—62no—
681C23—121no—
682C23—121no—
683C23—121no—
684C23—121no—
685C23—121no—
686C23—121no—
687C23—121no—
688C23—121no—
689C23—121no—
690C23—121no—
691C23—121no—
692C23—121no—
693C23#91412yes—
694C23C2×D3×D411yescharacteristic
695Q8—128no—
696D4—68no—
697D4—62no—
698D4—62no—
699D4—62no—
700D4—62no—
701D4—128no—
702D4—128no—
703D4—121no—
704D4—121no—
705D4—121no—
706D4—121no—
707D4—244no—
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—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—61no—
732C2×C4—61no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—61no—
736C2×C4—61no—
737C2×C4—61no—
738C2×C4—62no—
739C2×C4—128no—
740C2×C4—128no—
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#100711yescharacteristic
755C2×C4D3×#4111yescharacteristic
756C2×C4#100911yescharacteristic
757C8—22no—
758C8—41no—
759C8—121no—
760C8—121no—
761C2×C3—42no—
762C2×C3#240711yescharacteristic
763C2×C3#300311yescharacteristic
764C2×C3#301011yescharacteristic
765C2×C3#330611yescharacteristic
766C2×C3#330611yescharacteristic
767C2×C3#334511yescharacteristic
768C2×C3#334511yescharacteristic
769D3—42no—
770D3—82no—
771D3—82no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—62no—
780C22—62no—
781C22—62no—
782C22—121no—
783C22—121no—
784C22—121no—
785C22—121no—
786C22—122no—
787C22—122no—
788C22—122no—
789C22—122no—
790C22—122no—
791C22—122no—
792C22—241no—
793C22—241no—
794C22—241no—
795C22—241no—
796C22—241no—
797C22—241no—
798C22—241no—
799C22—241no—
800C22#550711yescharacteristic
801C22D3×#12011yescharacteristic
802C22#565411yescharacteristic
803C22C2×#91411yescharacteristic
804C22#576211yescharacteristic
805C22D3×AGL(1,ℤ/8)11yescharacteristic
806C22#577811yescharacteristic
807C4—42no—
808C4—42no—
809C4—41no—
810C4—62no—
811C4—62no—
812C4—81no—
813C4—81no—
814C4—122no—
815C4—121no—
816C4—241no—
817C4#554711yescharacteristic
818C4#555311yescharacteristic
819C4#562911yescharacteristic
820C4#563311yescharacteristic
821C3#2412811yescharacteristic, complemented, Sylow
822C2—42no—
823C2—122no—
824C2—242no—
825C2—242no—
826C2#7440411yescharacteristic
827C2#7912711yescharacteristic
828C2#7922511yescharacteristic
829C2#8004111yescharacteristic
830C2#8014611yescharacteristic
831C2#8133111yescharacteristic
832C2#8144611yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1853C2
socleC23×C3C22×D4
hypercenter#1853D3
hypocenterC3#24128
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1853

Complements

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

NH ≅ G/Ntype
1. C2×#5507C2semidirect
2. C2×#4870C2semidirect
3. C2×#4869C2semidirect
4. #73933C2semidirect
5. C3×#1853C2semidirect
6. #71560C2semidirect
7. #70581C2semidirect
8. #70579C2semidirect
9. #69961C2semidirect
10. #69917C2semidirect
11. #69524C2semidirect
12. #68893C2semidirect
13. #68886C2semidirect
14. #68880C2semidirect
15. #68806C2semidirect
77. #1853D3semidirect
142. #893D4semidirect
146. #888D4semidirect
264. C2×D12#41semidirect
288. C2×C3×C8#41semidirect
588. C2×C8#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
C2×#48702
C2×#48692
#739332
C3×#18532
#715602
#705812
#705792
#699612
#699172
#695242
#688932
#688862
#688802
#688062
#241283