Finite Group Databasebeta

← #10823408

Subgroups — #10823408

Order 768.

1508 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5548C211yesmaximal, characteristic, complemented
2C2×C3×#442C211yesmaximal, characteristic, complemented
3C4×#938C211yesmaximal, characteristic, complemented
4C2×#5014C211yesmaximal, characteristic, complemented
5#72044C211yesmaximal, characteristic, complemented
6#72043C211yesmaximal, characteristic, complemented
7#71609C211yesmaximal, characteristic, complemented
8#70581C211yesmaximal, characteristic, complemented
9#70565C211yesmaximal, characteristic, complemented
10#70211C211yesmaximal, characteristic, complemented
11#70207C211yesmaximal, characteristic, complemented
12#70204C211yesmaximal, characteristic, complemented
13#70163C211yesmaximal, characteristic, complemented
14#69812C211yesmaximal, characteristic, complemented
15#69807C211yesmaximal, characteristic, complemented
16#23573—31nomaximal, Sylow
17C22×#235—21no—
18C22×C3×D8C2211yescharacteristic
19C2×C3×C4×D4C2211yescharacteristic
20C2×C3×C4×D4C2211yescharacteristic
21C2×#940C2211yescharacteristic
22C2×#938C2211yescharacteristic
23C2×#938C2211yescharacteristic
24C22×#213C2211yescharacteristic
25C2×C4×#67—21no—
26C2×C4×#67—21no—
27#5548—24no—
28#5548—24no—
29C2×#895C2211yescharacteristic
30C2×#888C2211yescharacteristic
31C2×#885—21no—
32C2×#884—21no—
33C2×C4×D12C2211yescharacteristic
34C2×C42×D3C2211yescharacteristic
35C3×#442—24no—
36C2×C3×#106C2211yescharacteristic
37C2×C3×#102C2211yescharacteristic
38C2×C3×#102C2211yescharacteristic
39C2×C3×#97C2211yescharacteristic
40#5221C2211yescharacteristic
41C2×#832C2211yescharacteristic
42C2×#832C2211yescharacteristic
43C2×#832C2211yescharacteristic
44C4×#217—21no—
45C2×#821C2211yescharacteristic
46C2×#821C2211yescharacteristic
47C2×(C2×D3)⋊C8C2211yescharacteristic
48C2×(C2×D3)⋊C8C2211yescharacteristic
49#5014—24no—
50#4987C2211yescharacteristic
51#4972C2211yescharacteristic
52C2×#809C2211yescharacteristic
53C2×#808C2211yescharacteristic
54#4956—21no—
55#4944—21no—
56C4×C4⋊Dic3C2211yescharacteristic
57C2×#803C2211yescharacteristic
58#4551C2211yescharacteristic
59#4551C2211yescharacteristic
60#4550C2211yescharacteristic
61#4550C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#532—31no—
65C2×#442—31no—
66C2×#442D311yescharacteristic, complemented
67C4×#121—31no—
68#2058—31no—
69#2041—31no—
70#2034—31no—
71#2034—31no—
72#2023—31no—
73#2011—31no—
74#1999—31no—
75#1999—31no—
76#1762—31no—
77#1762—31no—
78#1749—31no—
79C22×C3×D4C2311yescharacteristic
80C22×C3×D4C2311yescharacteristic
81C23×C3×C4—21no—
82C23×C3×C4—21no—
83C22×#67—21no—
84C22×#67—21no—
85C22×#67—21no—
86C22×#67—21no—
87C2×#235—28no—
88C2×#235—44no—
89C2×#235—44no—
90C22×D12—21no—
91C22×D12C2311yescharacteristic
92C22×C4×D3—21no—
93C22×C4×D3D411yescharacteristic
94C22×C4×D3D411yescharacteristic
95C22×C4×D3C2311yescharacteristic
96C22×Dic6—21no—
97C2×C3×D8—22no—
98C2×C3×D8—22no—
99C2×C3×D8—22no—
100C22×C3×C8C2311yescharacteristic
101C22×C3×C8C2311yescharacteristic
102C3×C4×D4—22no—
103C3×C4×D4—22no—
104C3×C4×D4—22no—
105C3×C4×D4D414yescomplemented
106C2×C3×C4⋊C4C2311yescharacteristic
107C2×C3×C4⋊C4C2311yescharacteristic
108C2×C3×C22⋊C4—21no—
109C2×C3×C22⋊C4—21no—
110C2×C3×C42C2311yescharacteristic
111C2×#217—21no—
112C2×#217—21no—
113C2×#217—21no—
114C2×#217—21no—
115#940—22no—
116#940—22no—
117#938—22no—
118#938—22no—
119#938—22no—
120#938—22no—
121C2×#213—22no—
122C2×#213—22no—
123C2×#213—22no—
124C4×#67—28no—
125C4×#67—44no—
126C2×(C2×D3)⋊C4—21no—
127C2×(C2×D3)⋊C4—21no—
128C2×(C2×D3)⋊C4—21no—
129C2×C4⋊Dic3C2311yescharacteristic
130C2×C4⋊Dic3C2311yescharacteristic
131C2×C4⋊Dic3C2311yescharacteristic
132C2×Dic3⋊C4—21no—
133C2×Dic3⋊C4—21no—
134C2×C4×Dic3—21no—
135C2×C4×Dic3D411yescharacteristic
136C2×C4×Dic3D411yescharacteristic
137C2×C4×Dic3C2311yescharacteristic
138C22×C3⋊C8C2311yescharacteristic
139C22×C3⋊C8C2311yescharacteristic
140#895—22no—
141#895—22no—
142#888—22no—
143#888—22no—
144#885—28no—
145#884—28no—
146C4×D12—22no—
147C4×D12D414yescomplemented
148C42×D3—22no—
149C42×D3—22no—
150C3×#106—22no—
151C3×#102—22no—
152C3×#102—22no—
153C3×#97—22no—
154#832—22no—
155#832—22no—
156#832—22no—
157C3⋊#95—21no—
158C3⋊#95—21no—
159C3⋊#95—21no—
160#821—22no—
161#821—22no—
162(C2×D3)⋊C8—22no—
163(C2×D3)⋊C8—22no—
164#809—22no—
165#808—22no—
166#803—22no—
167C22×#41—61no—
168C22×D8—31no—
169C22×D8C2×D311yescharacteristic
170#532—64no—
171#532—64no—
172C2×C4⋊Q8—31no—
173C2×#127—31no—
174C2×#124—61no—
175C2×#121—31no—
176C2×#121—31no—
177C2×#121—31no—
178C2×#121—61no—
179C2×C4×D4—31no—
180C2×C4×D4—61no—
181C2×C4×D4—61no—
182C2×C4×D4C2×D311yescharacteristic
183C2×C4×D4C2×D311yescharacteristic
184C22×C42—31no—
185#442—24no—
186#442—64no—
187C2×#106—31no—
188C2×#106C2×D311yescharacteristic
189C2×#102—31no—
190C2×#102—31no—
191C2×#102—31no—
192C2×#102—31no—
193C2×#102—31no—
194C2×#102—31no—
195C2×#102C2×D311yescharacteristic
196C2×#102C2×D311yescharacteristic
197C2×C22⋊C8—31no—
198C2×C22⋊C8—31no—
199C2×#97—31no—
200C2×#97C2×D311yescharacteristic
201#390—31no—
202#389—31no—
203#388—61no—
204#386—61no—
205#380—31no—
206C4×C4⋊C4—31no—
207C4×C22⋊C4—61no—
208#340—31no—
209#340—31no—
210#340—31no—
211#340—31no—
212#336—31no—
213#336—31no—
214C24×C3—21no—
215C24×C3—21no—
216C23×D3—21no—
217C23×D3C2×D411yescharacteristic
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×D4C2×D412yes—
229C2×C3×D4#4112yescomplemented
230C22×C3×C4—21no—
231C22×C3×C4—24no—
232C22×C3×C4—21no—
233C22×C3×C4—42no—
234C22×C3×C4—42no—
235C22×C3×C4—42no—
236C22×C3×C4—42no—
237C22×C3×C4—42no—
238C22×C3×C4C2×D411yescharacteristic
239C22×C3×C4C2×D411yescharacteristic
240C22×C3×C4C2411yescharacteristic
241C2×#67—24no—
242C2×#67—24no—
243C2×#67—24no—
244C2×#67—24no—
245C2×#67—42no—
246C2×#67—42no—
247C2×#67—42no—
248C2×#67—42no—
249C2×#67—42no—
250C2×#67—42no—
251C2×#67—42no—
252C2×#67—42no—
253C22×Dic3—21no—
254C22×Dic3—21no—
255C22×Dic3—21no—
256C22×Dic3C2×D411yescharacteristic
257C22×Dic3C2×D411yescharacteristic
258C22×Dic3C2×D411yescharacteristic
259#235—432no—
260C2×D12—21no—
261C2×D12—21no—
262C2×D12—21no—
263C2×D12—21no—
264C2×D12—24no—
265C2×D12—21no—
266C2×D12—42no—
267C2×D12—42no—
268C2×D12C2×D412yes—
269C2×C4×D3—22no—
270C2×C4×D3—22no—
271C2×C4×D3—22no—
272C2×C4×D3—22no—
273C2×C4×D3—24no—
274C2×C4×D3—21no—
275C2×C4×D3—21no—
276C2×C4×D3—21no—
277C2×C4×D3—21no—
278C2×C4×D3—21no—
279C2×C4×D3—21no—
280C2×C4×D3—22no—
281C2×C4×D3—41no—
282C2×C4×D3—42no—
283C2×C4×D3—42no—
284C2×Dic6—24no—
285C2×Dic6—42no—
286C2×Dic6—42no—
287C3×D8—28no—
288C2×C3×C8—21no—
289C2×C3×C8—21no—
290C2×C3×C8—21no—
291C2×C3×C8—21no—
292C2×C3×C8—21no—
293C2×C3×C8#4112yescomplemented
294C3×C4⋊C4—21no—
295C3×C4⋊C4—21no—
296C3×C4⋊C4—21no—
297C3×C4⋊C4C2×D412yes—
298C3×C22⋊C4—24no—
299C3×C22⋊C4—42no—
300C3×C42C2×D412yes—
301C3×C42C2×D412yes—
302#217—24no—
303#217—24no—
304#217—42no—
305#217—42no—
306#213—28no—
307(C2×D3)⋊C4—24no—
308(C2×D3)⋊C4—24no—
309(C2×D3)⋊C4—42no—
310C4⋊Dic3—21no—
311C4⋊Dic3—21no—
312C4⋊Dic3—21no—
313C4⋊Dic3—21no—
314C4⋊Dic3C2×D412yes—
315C4⋊Dic3#4112yescomplemented
316Dic3⋊C4—24no—
317Dic3⋊C4—42no—
318C4×Dic3—22no—
319C4×Dic3—22no—
320C4×Dic3—21no—
321C4×Dic3—21no—
322C4×Dic3—42no—
323C2×C3⋊C8—21no—
324C2×C3⋊C8—21no—
325C2×C3⋊C8—21no—
326C2×C3⋊C8—21no—
327C2×C3⋊C8—21no—
328C2×C3⋊C8#4112yescomplemented
329C2×#41—68no—
330C2×#41—124no—
331C2×#41—124no—
332C22×Q8—61no—
333C22×D4—31no—
334C22×D4—61no—
335C22×D4—61no—
336C22×D4—61no—
337C22×D4—61no—
338C22×D4—61no—
339C22×D4C22×D311yescharacteristic
340C22×D4C22×D311yescharacteristic
341C23×C4—21no—
342C23×C4—21no—
343C23×C4—31no—
344C23×C4—31no—
345C23×C4—31no—
346C23×C4—61no—
347C2×D8—22no—
348C2×D8—22no—
349C2×D8—22no—
350C2×D8—62no—
351C2×D8—62no—
352C2×D8—62no—
353C22×C8—31no—
354C22×C8—31no—
355C22×C8C22×D311yescharacteristic
356C22×C8C22×D311yescharacteristic
357C4⋊Q8—62no—
358C4⋊Q8—62no—
359#127—62no—
360#127—62no—
361#124—68no—
362#121—68no—
363#121—62no—
364#121—62no—
365#121—62no—
366#121—62no—
367#121—62no—
368#121—62no—
369C4×D4—22no—
370C4×D4—22no—
371C4×D4—22no—
372C4×D4—34no—
373C4×D4—68no—
374C4×D4—62no—
375C4×D4—124no—
376C4×D4#6714yescomplemented
377C2×C4⋊C4—31no—
378C2×C4⋊C4—31no—
379C2×C4⋊C4—31no—
380C2×C4⋊C4—61no—
381C2×C4⋊C4—61no—
382C2×C4⋊C4C22×D311yescharacteristic
383C2×C4⋊C4C22×D311yescharacteristic
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—61no—
387C2×C22⋊C4—61no—
388C2×C22⋊C4—61no—
389C2×C22⋊C4—61no—
390C2×C22⋊C4—61no—
391C2×C22⋊C4—61no—
392C2×C22⋊C4—61no—
393C2×C42—31no—
394C2×C42—31no—
395C2×C42—31no—
396C2×C42—62no—
397C2×C42—62no—
398C2×C42—61no—
399C2×C42C22×D311yescharacteristic
400#106—22no—
401#106—62no—
402#102—22no—
403#102—22no—
404#102—62no—
405#102—62no—
406#102—62no—
407#102—62no—
408#102—62no—
409#102—62no—
410C22⋊C8—62no—
411C22⋊C8—62no—
412#97—22no—
413#97—62no—
414#95—61no—
415#95—61no—
416#95—61no—
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×C3C22×D411yescharacteristic
432C22×D3—21no—
433C22×D3—21no—
434C22×D3—21no—
435C22×D3—21no—
436C22×D3—21no—
437C22×D3—21no—
438C22×D3—22no—
439C22×D3—41no—
440C22×D3—41no—
441C22×D3—41no—
442C22×D3—41no—
443C22×D3—41no—
444C22×D3—41no—
445C22×D3AGL(1,ℤ/8)12yes—
446C3×D4—22no—
447C3×D4—22no—
448C3×D4—22no—
449C3×D4—22no—
450C3×D4—41no—
451C3×D4—41no—
452C3×D4—41no—
453C3×D4—41no—
454C2×C3×C4—21no—
455C2×C3×C4—21no—
456C2×C3×C4—21no—
457C2×C3×C4—21no—
458C2×C3×C4—22no—
459C2×C3×C4—48no—
460C2×C3×C4—41no—
461C2×C3×C4—41no—
462C2×C3×C4—41no—
463C2×C3×C4—41no—
464C2×C3×C4—41no—
465C2×C3×C4—84no—
466C2×C3×C4#12012yes—
467C2×C3×C4#12012yes—
468C2×C3×C4C22×D411yescharacteristic
469C2×C3×C4C22×D411yescharacteristic
470C2×C3×C4C2×#4111yescharacteristic
471C2×C3×C4C2×#4111yescharacteristic
472C2×C3×C4C2×#4111yescharacteristic
473C2×C3×C4C2×#4111yescharacteristic
474#67—48no—
475#67—48no—
476#67—48no—
477#67—48no—
478C2×Dic3—21no—
479C2×Dic3—21no—
480C2×Dic3—21no—
481C2×Dic3—21no—
482C2×Dic3—21no—
483C2×Dic3—22no—
484C2×Dic3—22no—
485C2×Dic3—21no—
486C2×Dic3—21no—
487C2×Dic3—41no—
488C2×Dic3—41no—
489C2×Dic3—41no—
490C2×Dic3—41no—
491C2×Dic3—41no—
492C2×Dic3—41no—
493C2×Dic3—41no—
494C2×Dic3AGL(1,ℤ/8)12yes—
495C2×Dic3AGL(1,ℤ/8)12yes—
496D12—22no—
497D12—22no—
498D12—48no—
499D12—41no—
500D12—41no—
501C4×D3—28no—
502C4×D3—44no—
503C4×D3—48no—
504C4×D3—41no—
505C4×D3—41no—
506C4×D3—41no—
507C4×D3—41no—
508Dic6—48no—
509C3×C8—22no—
510C3×C8—41no—
511C3⋊C8—22no—
512C3⋊C8—41no—
513C24—21no—
514C24—21no—
515C24—31no—
516C24—61no—
517#41—1232no—
518C2×Q8—64no—
519C2×Q8—122no—
520C2×Q8—122no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—32no—
532C2×D4—64no—
533C2×D4—64no—
534C2×D4—64no—
535C2×D4—64no—
536C2×D4—64no—
537C2×D4—61no—
538C2×D4—61no—
539C2×D4—61no—
540C2×D4—61no—
541C2×D4—61no—
542C2×D4—122no—
543C2×D4—122no—
544C2×D4—122no—
545C2×D4—122no—
546C2×D4—122no—
547C2×D4—122no—
548C2×D4—122no—
549C2×D4—122no—
550C2×D4—122no—
551C2×D4—122no—
552C2×D4#23512yescomplemented
553C2×D4C2×#6712yes—
554C22×C4—21no—
555C22×C4—24no—
556C22×C4—21no—
557C22×C4—31no—
558C22×C4—31no—
559C22×C4—31no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—62no—
566C22×C4—62no—
567C22×C4—62no—
568C22×C4—62no—
569C22×C4—61no—
570C22×C4—61no—
571C22×C4—62no—
572C22×C4—64no—
573C22×C4—61no—
574C22×C4—61no—
575C22×C4—61no—
576C22×C4—61no—
577C22×C4—61no—
578C22×C4—61no—
579C22×C4—61no—
580C22×C4—121no—
581C22×C4—122no—
582C22×C4—122no—
583C22×C4D3×D411yescharacteristic
584C22×C4D3×D411yescharacteristic
585C22×C4C23×D311yescharacteristic
586D8—28no—
587D8—68no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—32no—
594C2×C8—61no—
595C2×C8—61no—
596C2×C8—61no—
597C2×C8—61no—
598C2×C8—61no—
599C2×C8#23512yescomplemented
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—32no—
604C4⋊C4—32no—
605C4⋊C4—64no—
606C4⋊C4—61no—
607C4⋊C4—61no—
608C4⋊C4—61no—
609C4⋊C4—61no—
610C4⋊C4—122no—
611C4⋊C4C2×#6712yes—
612C22⋊C4—24no—
613C22⋊C4—42no—
614C22⋊C4—64no—
615C22⋊C4—64no—
616C22⋊C4—64no—
617C22⋊C4—64no—
618C22⋊C4—122no—
619C22⋊C4—122no—
620C22⋊C4—122no—
621C42—62no—
622C42—62no—
623C42—61no—
624C42—61no—
625C42—122no—
626C42D3×D412yes—
627C42C2×#6712yes—
628C22×C3—42no—
629C22×C3—42no—
630C22×C3—42no—
631C22×C3—42no—
632C22×C3—42no—
633C22×C3—42no—
634C22×C3—81no—
635C22×C3—81no—
636C22×C3—81no—
637C22×C3—81no—
638C22×C3—81no—
639C22×C3—81no—
640C22×C3—81no—
641C22×C3—81no—
642C22×C3C2×#12011yescharacteristic
643C22×C3#52511yescharacteristic
644C22×C3#53211yescharacteristic
645C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
646C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
647C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
648C22×C3#57511yescharacteristic
649C2×D3—22no—
650C2×D3—22no—
651C2×D3—22no—
652C2×D3—41no—
653C2×D3—41no—
654C2×D3—41no—
655C2×D3—41no—
656C2×D3—42no—
657C2×D3—42no—
658C2×D3—42no—
659C2×D3—81no—
660C2×D3—81no—
661C2×D3—81no—
662C2×D3—81no—
663C3×C4—22no—
664C3×C4—22no—
665C3×C4—42no—
666C3×C4—81no—
667C3×C4#52511yescharacteristic
668C3×C4#52511yescharacteristic
669C3×C4#53211yescharacteristic
670C3×C4#53211yescharacteristic
671Dic3—22no—
672Dic3—22no—
673Dic3—42no—
674Dic3—41no—
675Dic3—42no—
676Dic3—81no—
677C23—22no—
678C23—22no—
679C23—32no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—61no—
693C23—61no—
694C23—61no—
695C23—61no—
696C23—61no—
697C23—61no—
698C23—62no—
699C23—121no—
700C23—121no—
701C23—121no—
702C23—121no—
703C23—121no—
704C23—121no—
705C23C2×D3×D411yescharacteristic
706Q8—128no—
707D4—22no—
708D4—22no—
709D4—22no—
710D4—22no—
711D4—41no—
712D4—41no—
713D4—41no—
714D4—41no—
715D4—62no—
716D4—62no—
717D4—128no—
718D4—128no—
719D4—128no—
720D4—128no—
721D4—128no—
722D4—121no—
723D4—121no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—32no—
730C2×C4—32no—
731C2×C4—48no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—68no—
738C2×C4—61no—
739C2×C4—61no—
740C2×C4—61no—
741C2×C4—61no—
742C2×C4—61no—
743C2×C4—62no—
744C2×C4—61no—
745C2×C4—62no—
746C2×C4—61no—
747C2×C4—84no—
748C2×C4—124no—
749C2×C4—128no—
750C2×C4—121no—
751C2×C4—121no—
752C2×C4—121no—
753C2×C4—121no—
754C2×C4—121no—
755C2×C4—121no—
756C2×C4—121no—
757C2×C4—121no—
758C2×C4—121no—
759C2×C4—121no—
760C2×C4—121no—
761C2×C4#93712yes—
762C2×C4#93712yes—
763C2×C4C2×#23511yescharacteristic
764C2×C4C2×#23511yescharacteristic
765C2×C4C2×D3×D411yescharacteristic
766C2×C4D3×#4111yescharacteristic
767C2×C4D3×#4111yescharacteristic
768C2×C4C22×#6711yescharacteristic
769C8—22no—
770C8—41no—
771C8—62no—
772C8—121no—
773C2×C3—82no—
774C2×C3—82no—
775C2×C3#238811yescharacteristic
776C2×C3#300311yescharacteristic
777C2×C3#300611yescharacteristic
778C2×C3#310911yescharacteristic
779C2×C3#311511yescharacteristic
780C2×C3#318011yescharacteristic
781C2×C3#318411yescharacteristic
782D3—42no—
783D3—82no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—62no—
791C22—62no—
792C22—62no—
793C22—81no—
794C22—81no—
795C22—81no—
796C22—81no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22—121no—
802C22—121no—
803C22—121no—
804C22—121no—
805C22—122no—
806C22—122no—
807C22—122no—
808C22—241no—
809C22—241no—
810C22—241no—
811C22—241no—
812C22#554711yescharacteristic
813C22#554811yescharacteristic
814C22D3×AGL(1,ℤ/8)11yescharacteristic
815C22D3×AGL(1,ℤ/8)11yescharacteristic
816C22D3×AGL(1,ℤ/8)11yescharacteristic
817C22#577311yescharacteristic
818C22C2×#93711yescharacteristic
819C4—22no—
820C4—22no—
821C4—42no—
822C4—62no—
823C4—62no—
824C4—81no—
825C4—121no—
826C4—122no—
827C4—122no—
828C4—241no—
829C4#554711yescharacteristic
830C4#554811yescharacteristic
831C4#579111yescharacteristic
832C4#583211yescharacteristic
833C3#2357311yescharacteristic, complemented, Sylow
834C2—82no—
835C2—82no—
836C2—122no—
837C2—242no—
838C2#7986911yescharacteristic
839C2#7987211yescharacteristic
840C2#7987611yescharacteristic
841C2#7987711yescharacteristic
842C2#8240011yescharacteristic
843C2#8394411yescharacteristic
844C2#8394611yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#442C2
socleC23×C3C22×D4
hypercenterC2×#442D3
hypocenterC3#23573
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#442

Complements

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

NH ≅ G/Ntype
1. C2×#5548C2semidirect
2. C2×C3×#442C2semidirect
3. C4×#938C2semidirect
4. C2×#5014C2semidirect
5. #72044C2semidirect
6. #72043C2semidirect
7. #71609C2semidirect
8. #70581C2semidirect
9. #70565C2semidirect
10. #70211C2semidirect
11. #70207C2semidirect
12. #70204C2semidirect
13. #70163C2semidirect
14. #69812C2semidirect
15. #69807C2semidirect
66. C2×#442D3semidirect
105. C3×C4×D4D4semidirect
147. C4×D12D4semidirect
229. C2×C3×D4#41semidirect
293. C2×C3×C8#41semidirect
315. C4⋊Dic3#41semidirect
328. C2×C3⋊C8#41semidirect
376. C4×D4#67semidirect
552. C2×D4#235semidirect
599. C2×C8#235semidirect
833. C3#23573semidirect

Maximal subgroups

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

subgroupindex
C2×#55482
C2×C3×#4422
C4×#9382
C2×#50142
#720442
#720432
#716092
#705812
#705652
#702112
#702072
#702042
#701632
#698122
#698072
#235733