Finite Group Databasebeta

← #10823410

Subgroups — #10823410

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×#5014C211yesmaximal, characteristic, complemented
3C2×#4711C211yesmaximal, characteristic, complemented
4C4×#895C211yesmaximal, characteristic, complemented
5C3×#1762C211yesmaximal, characteristic, complemented
6#70209C211yesmaximal, characteristic, complemented
7#70204C211yesmaximal, characteristic, complemented
8#70177C211yesmaximal, characteristic, complemented
9#70176C211yesmaximal, characteristic, complemented
10#69807C211yesmaximal, characteristic, complemented
11#69474C211yesmaximal, characteristic, complemented
12#68898C211yesmaximal, characteristic, complemented
13#68886C211yesmaximal, characteristic, complemented
14#68827C211yesmaximal, characteristic, complemented
15#68823C211yesmaximal, characteristic, complemented
16#23573—31nomaximal, Sylow
17C22×#235—21no—
18C2×C3×C4×D4C2211yescharacteristic
19C2×#940C2211yescharacteristic
20C2×#938C2211yescharacteristic
21C22×#213C2211yescharacteristic
22C2×C4×#67—21no—
23C22×D24C2211yescharacteristic
24#5548—24no—
25#5548—24no—
26C2×#895C2211yescharacteristic
27C2×#895C2211yescharacteristic
28C2×#888C2211yescharacteristic
29C2×#885—21no—
30C2×#884—21no—
31C2×C4×D12—21no—
32C2×C4×D12C2211yescharacteristic
33C2×C4×D12C2211yescharacteristic
34C2×C42×D3C2211yescharacteristic
35C2×C3×#102C2211yescharacteristic
36C2×C3×#102C2211yescharacteristic
37C2×C3×#97C2211yescharacteristic
38C3×C4×C4⋊C4C2211yescharacteristic
39C2×#832C2211yescharacteristic
40C2×#821C2211yescharacteristic
41C2×#821C2211yescharacteristic
42C2×(C2×D3)⋊C8C2211yescharacteristic
43C2×(C2×D3)⋊C8C2211yescharacteristic
44C2×#817C2211yescharacteristic
45#5014—24no—
46#4988C2211yescharacteristic
47#4987C2211yescharacteristic
48#4984C2211yescharacteristic
49C2×#809C2211yescharacteristic
50C2×#809C2211yescharacteristic
51C2×#809C2211yescharacteristic
52C2×#808C2211yescharacteristic
53C4×(C2×D3)⋊C4—21no—
54C2×#803C2211yescharacteristic
55#4711—24no—
56#4670—21no—
57#4665—21no—
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60#4550C2211yescharacteristic
61#4550C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#532—31no—
65C2×#442—31no—
66C2×#442—31no—
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#1762D311yescharacteristic, complemented
78#1749—31no—
79C22×C3×D4C2311yescharacteristic
80C23×C3×C4—21no—
81C22×#67—21no—
82C22×#67—21no—
83C22×#67—21no—
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×D3D411yescharacteristic
94C22×C4×D3D411yescharacteristic
95C22×C4×D3C2311yescharacteristic
96C22×Dic6—21no—
97C22×C3×C8C2311yescharacteristic
98C22×C3×C8C2311yescharacteristic
99C3×C4×D4—22no—
100C3×C4×D4D414yescomplemented
101C2×C3×C4⋊C4C2311yescharacteristic
102C2×C3×C4⋊C4C2311yescharacteristic
103C2×C3×C4⋊C4C2311yescharacteristic
104C2×C3×C22⋊C4—21no—
105C2×C3×C42—21no—
106C2×C3×C42C2311yescharacteristic
107C2×#217—21no—
108#940—22no—
109#940—22no—
110#938—22no—
111#938—22no—
112C2×#213—22no—
113C2×#213—22no—
114C2×#213—22no—
115C4×#67—28no—
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)⋊C4—21no—
122C2×(C2×D3)⋊C4—21no—
123C2×C4⋊Dic3—21no—
124C2×C4⋊Dic3C2311yescharacteristic
125C2×C4⋊Dic3C2311yescharacteristic
126C2×Dic3⋊C4—21no—
127C2×C4×Dic3D411yescharacteristic
128C2×C4×Dic3D411yescharacteristic
129C2×C4×Dic3C2311yescharacteristic
130C22×C3⋊C8C2311yescharacteristic
131C22×C3⋊C8C2311yescharacteristic
132C2×D24—22no—
133C2×D24—22no—
134C2×D24—22no—
135#895—22no—
136#895—22no—
137#895—22no—
138#895—22no—
139#888—22no—
140#888—22no—
141#885—28no—
142#884—28no—
143C4×D12—22no—
144C4×D12—22no—
145C4×D12—22no—
146C4×D12—44no—
147C4×D12D414yescomplemented
148C42×D3—22no—
149C42×D3—22no—
150C3×#102—22no—
151C3×#102—22no—
152C3×#97—22no—
153C3×#95—21no—
154#832—22no—
155C3⋊#95—21no—
156C3⋊#95—21no—
157#821—22no—
158#821—22no—
159(C2×D3)⋊C8—22no—
160(C2×D3)⋊C8—22no—
161#817—22no—
162#809—22no—
163#809—22no—
164#809—22no—
165#808—22no—
166#803—22no—
167C22×#41—61no—
168C22×D8—31no—
169C22×D8—31no—
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—31no—
181C2×C4×D4—61no—
182C2×C4×D4—61no—
183C2×C4×D4C2×D311yescharacteristic
184C22×C42—31no—
185#442—64no—
186#442—64no—
187C2×#106—31no—
188C2×#106—31no—
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⋊C4C2×D311yescharacteristic
207C4×C22⋊C4—61no—
208#340—31no—
209#340—31no—
210#340C2×D311yescharacteristic
211#340C2×D311yescharacteristic
212#336—31no—
213#336—31no—
214C24×C3—21no—
215C23×D3—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×D4C2×D412yes—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—24no—
227C22×C3×C4—21no—
228C22×C3×C4—42no—
229C22×C3×C4—42no—
230C22×C3×C4C2×D411yescharacteristic
231C22×C3×C4C2×D411yescharacteristic
232C22×C3×C4C2411yescharacteristic
233C2×#67—24no—
234C2×#67—24no—
235C2×#67—24no—
236C2×#67—42no—
237C2×#67—42no—
238C2×#67—42no—
239C2×#67—42no—
240C2×#67—42no—
241C2×#67—42no—
242C22×Dic3—21no—
243C22×Dic3—21no—
244C22×Dic3C2×D411yescharacteristic
245C22×Dic3C2×D411yescharacteristic
246C22×Dic3C2×D411yescharacteristic
247#235—432no—
248C2×D12—21no—
249C2×D12—21no—
250C2×D12—21no—
251C2×D12—21no—
252C2×D12—21no—
253C2×D12—21no—
254C2×D12—21no—
255C2×D12—21no—
256C2×D12—24no—
257C2×D12—24no—
258C2×D12—21no—
259C2×D12—21no—
260C2×D12—42no—
261C2×D12—42no—
262C2×D12—42no—
263C2×D12—42no—
264C2×D12C2×D412yes—
265C2×D12#4112yescomplemented
266C2×C4×D3—22no—
267C2×C4×D3—22no—
268C2×C4×D3—22no—
269C2×C4×D3—22no—
270C2×C4×D3—24no—
271C2×C4×D3—21no—
272C2×C4×D3—21no—
273C2×C4×D3—21no—
274C2×C4×D3—21no—
275C2×C4×D3—21no—
276C2×C4×D3—21no—
277C2×C4×D3—22no—
278C2×C4×D3—41no—
279C2×C4×D3—42no—
280C2×C4×D3—42no—
281C2×C4×D3—42no—
282C2×C4×D3—42no—
283C2×C4×D3—42no—
284C2×Dic6—24no—
285C2×Dic6—42no—
286C2×Dic6—42no—
287C2×C3×C8—21no—
288C2×C3×C8—21no—
289C2×C3×C8—21no—
290C2×C3×C8—21no—
291C2×C3×C8—21no—
292C2×C3×C8#4112yescomplemented
293C3×C4⋊C4—21no—
294C3×C4⋊C4—21no—
295C3×C4⋊C4—21no—
296C3×C4⋊C4—21no—
297C3×C4⋊C4C2×D412yes—
298C3×C4⋊C4#4112yescomplemented
299C3×C22⋊C4—24no—
300C3×C42—42no—
301C3×C42C2×D412yes—
302C3×C42C2×D412yes—
303#217—24no—
304#213—28no—
305(C2×D3)⋊C4—24no—
306(C2×D3)⋊C4—24no—
307(C2×D3)⋊C4—24no—
308(C2×D3)⋊C4—42no—
309(C2×D3)⋊C4—42no—
310(C2×D3)⋊C4—42no—
311(C2×D3)⋊C4—42no—
312C4⋊Dic3—21no—
313C4⋊Dic3—21no—
314C4⋊Dic3—21no—
315C4⋊Dic3—42no—
316C4⋊Dic3C2×D412yes—
317Dic3⋊C4—24no—
318C4×Dic3—22no—
319C4×Dic3—22no—
320C4×Dic3—21no—
321C4×Dic3—21no—
322C2×C3⋊C8—21no—
323C2×C3⋊C8—21no—
324C2×C3⋊C8—21no—
325C2×C3⋊C8—21no—
326C2×C3⋊C8—21no—
327C2×C3⋊C8#4112yescomplemented
328D24—28no—
329C2×#41—68no—
330C2×#41—124no—
331C2×#41—124no—
332C22×Q8—61no—
333C22×D4—31no—
334C22×D4—31no—
335C22×D4—61no—
336C22×D4—61no—
337C22×D4—61no—
338C22×D4—61no—
339C22×D4—61no—
340C22×D4C22×D311yescharacteristic
341C23×C4—21no—
342C23×C4—31no—
343C23×C4—31no—
344C23×C4—31no—
345C23×C4—61no—
346C23×C4—61no—
347C2×D8—62no—
348C2×D8—62no—
349C2×D8—62no—
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—34no—
371C4×D4—68no—
372C4×D4—62no—
373C4×D4—62no—
374C4×D4—62no—
375C4×D4—124no—
376C4×D4D1214yescomplemented
377C2×C4⋊C4—31no—
378C2×C4⋊C4—31no—
379C2×C4⋊C4—61no—
380C2×C4⋊C4—61no—
381C2×C4⋊C4C22×D311yescharacteristic
382C2×C4⋊C4C22×D311yescharacteristic
383C2×C4⋊C4C22×D311yescharacteristic
384C2×C22⋊C4—21no—
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×C22⋊C4—61no—
392C2×C22⋊C4—61no—
393C2×C42—21no—
394C2×C42—31no—
395C2×C42—31no—
396C2×C42—31no—
397C2×C42—62no—
398C2×C42—62no—
399C2×C42C22×D311yescharacteristic
400#106—62no—
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—21no—
415#95—61no—
416#95—61no—
417C23×C3—22no—
418C23×C3—41no—
419C23×C3—41no—
420C23×C3—41no—
421C23×C3—41no—
422C23×C3—41no—
423C23×C3—41no—
424C23×C3C22×D411yescharacteristic
425C22×D3—21no—
426C22×D3—21no—
427C22×D3—21no—
428C22×D3—21no—
429C22×D3—21no—
430C22×D3—21no—
431C22×D3—22no—
432C22×D3—22no—
433C22×D3—41no—
434C22×D3—41no—
435C22×D3—41no—
436C22×D3—41no—
437C22×D3—41no—
438C22×D3—41no—
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—41no—
449C3×D4—41no—
450C2×C3×C4—21no—
451C2×C3×C4—21no—
452C2×C3×C4—21no—
453C2×C3×C4—21no—
454C2×C3×C4—22no—
455C2×C3×C4—22no—
456C2×C3×C4—48no—
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×C4—41no—
464C2×C3×C4#12012yes—
465C2×C3×C4#12012yes—
466C2×C3×C4C22×D411yescharacteristic
467C2×C3×C4C22×D411yescharacteristic
468C2×C3×C4C2×#4111yescharacteristic
469C2×C3×C4C2×#4111yescharacteristic
470C2×C3×C4C2×#4111yescharacteristic
471C2×C3×C4C2×#4111yescharacteristic
472#67—48no—
473#67—48no—
474#67—48no—
475C2×Dic3—21no—
476C2×Dic3—21no—
477C2×Dic3—21no—
478C2×Dic3—21no—
479C2×Dic3—21no—
480C2×Dic3—22no—
481C2×Dic3—21no—
482C2×Dic3—21no—
483C2×Dic3—41no—
484C2×Dic3—41no—
485C2×Dic3—41no—
486C2×Dic3—41no—
487C2×Dic3—41no—
488C2×Dic3AGL(1,ℤ/8)12yes—
489C2×Dic3AGL(1,ℤ/8)12yes—
490D12—22no—
491D12—22no—
492D12—22no—
493D12—22no—
494D12—48no—
495D12—48no—
496D12—41no—
497D12—41no—
498D12—41no—
499D12—41no—
500C4×D3—28no—
501C4×D3—44no—
502C4×D3—48no—
503C4×D3—41no—
504C4×D3—41no—
505C4×D3—41no—
506C4×D3—41no—
507C4×D3—84no—
508Dic6—48no—
509C3×C8—22no—
510C3×C8—41no—
511C3⋊C8—22no—
512C3⋊C8—41no—
513C24—21no—
514C24—31no—
515C24—61no—
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—32no—
527C2×D4—32no—
528C2×D4—64no—
529C2×D4—64no—
530C2×D4—64no—
531C2×D4—64no—
532C2×D4—64no—
533C2×D4—61no—
534C2×D4—61no—
535C2×D4—61no—
536C2×D4—61no—
537C2×D4—61no—
538C2×D4—61no—
539C2×D4—61no—
540C2×D4—61no—
541C2×D4—61no—
542C2×D4—61no—
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—122no—
553C2×D4C2×D1212yes—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—24no—
557C22×C4—21no—
558C22×C4—31no—
559C22×C4—31no—
560C22×C4—31no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—62no—
564C22×C4—62no—
565C22×C4—62no—
566C22×C4—62no—
567C22×C4—61no—
568C22×C4—62no—
569C22×C4—64no—
570C22×C4—61no—
571C22×C4—61no—
572C22×C4—61no—
573C22×C4—61no—
574C22×C4—61no—
575C22×C4—61no—
576C22×C4—61no—
577C22×C4—121no—
578C22×C4—122no—
579C22×C4—122no—
580C22×C4—122no—
581C22×C4—122no—
582C22×C4—122no—
583C22×C4D3×D411yescharacteristic
584C22×C4D3×D411yescharacteristic
585C22×C4C23×D311yescharacteristic
586D8—68no—
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—21no—
604C4⋊C4—32no—
605C4⋊C4—64no—
606C4⋊C4—61no—
607C4⋊C4—61no—
608C4⋊C4—61no—
609C4⋊C4—122no—
610C4⋊C4C2×D1212yes—
611C4⋊C4#23512yescomplemented
612C22⋊C4—24no—
613C22⋊C4—64no—
614C22⋊C4—64no—
615C22⋊C4—64no—
616C22⋊C4—64no—
617C22⋊C4—122no—
618C22⋊C4—122no—
619C22⋊C4—122no—
620C22⋊C4—122no—
621C42—42no—
622C42—62no—
623C42—62no—
624C42—61no—
625C42—61no—
626C42C2×D1212yes—
627C42D3×D412yes—
628C22×C3—42no—
629C22×C3—42no—
630C22×C3—42no—
631C22×C3—81no—
632C22×C3—81no—
633C22×C3—81no—
634C22×C3—81no—
635C22×C3C2×#12011yescharacteristic
636C22×C3#52511yescharacteristic
637C22×C3#53211yescharacteristic
638C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
639C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
640C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
641C22×C3#57511yescharacteristic
642C2×D3—22no—
643C2×D3—22no—
644C2×D3—22no—
645C2×D3—41no—
646C2×D3—41no—
647C2×D3—41no—
648C2×D3—41no—
649C2×D3—42no—
650C2×D3—42no—
651C2×D3—42no—
652C2×D3—42no—
653C2×D3—42no—
654C2×D3—42no—
655C2×D3—81no—
656C2×D3—81no—
657C2×D3—81no—
658C2×D3—81no—
659C2×D3—81no—
660C2×D3—81no—
661C2×D3—81no—
662C2×D3—81no—
663C3×C4—22no—
664C3×C4—22no—
665C3×C4—42no—
666C3×C4—42no—
667C3×C4—81no—
668C3×C4#52511yescharacteristic
669C3×C4#52511yescharacteristic
670C3×C4#53211yescharacteristic
671C3×C4#53211yescharacteristic
672Dic3—22no—
673Dic3—22no—
674Dic3—41no—
675Dic3—42no—
676Dic3—81no—
677C23—22no—
678C23—32no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—61no—
686C23—61no—
687C23—61no—
688C23—61no—
689C23—61no—
690C23—61no—
691C23—62no—
692C23—62no—
693C23—121no—
694C23—121no—
695C23—121no—
696C23—121no—
697C23—121no—
698C23—121no—
699C23—121no—
700C23—121no—
701C23—121no—
702C23—121no—
703C23—121no—
704C23—121no—
705C23C2×D3×D411yescharacteristic
706Q8—128no—
707D4—22no—
708D4—22no—
709D4—41no—
710D4—41no—
711D4—62no—
712D4—62no—
713D4—62no—
714D4—62no—
715D4—128no—
716D4—128no—
717D4—128no—
718D4—128no—
719D4—128no—
720D4—121no—
721D4—121no—
722D4—121no—
723D4—121no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—32no—
731C2×C4—32no—
732C2×C4—48no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—68no—
741C2×C4—61no—
742C2×C4—61no—
743C2×C4—61no—
744C2×C4—61no—
745C2×C4—61no—
746C2×C4—62no—
747C2×C4—61no—
748C2×C4—61no—
749C2×C4—124no—
750C2×C4—128no—
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—244no—
761C2×C4#88212yes—
762C2×C4#88212yes—
763C2×C4C22×D1211yescharacteristic
764C2×C4C2×#23511yescharacteristic
765C2×C4C2×#23511yescharacteristic
766C2×C4C2×D3×D411yescharacteristic
767C2×C4D3×#4111yescharacteristic
768C2×C4D3×#4111yescharacteristic
769C8—22no—
770C8—41no—
771C8—62no—
772C8—121no—
773C2×C3—82no—
774C2×C3#238811yescharacteristic
775C2×C3#300311yescharacteristic
776C2×C3#300611yescharacteristic
777C2×C3#310911yescharacteristic
778C2×C3#311511yescharacteristic
779C2×C3#318011yescharacteristic
780C2×C3#318411yescharacteristic
781D3—42no—
782D3—82no—
783D3—82no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—62no—
788C22—62no—
789C22—62no—
790C22—81no—
791C22—81no—
792C22—81no—
793C22—81no—
794C22—121no—
795C22—121no—
796C22—121no—
797C22—121no—
798C22—122no—
799C22—122no—
800C22—122no—
801C22—122no—
802C22—122no—
803C22—122no—
804C22—241no—
805C22—241no—
806C22—241no—
807C22—241no—
808C22—241no—
809C22—241no—
810C22—241no—
811C22—241no—
812C22C2×#88211yescharacteristic
813C22#554711yescharacteristic
814C22#554811yescharacteristic
815C22D3×AGL(1,ℤ/8)11yescharacteristic
816C22D3×AGL(1,ℤ/8)11yescharacteristic
817C22D3×AGL(1,ℤ/8)11yescharacteristic
818C22#577711yescharacteristic
819C4—22no—
820C4—22no—
821C4—42no—
822C4—42no—
823C4—62no—
824C4—62no—
825C4—81no—
826C4—122no—
827C4—121no—
828C4—241no—
829C4#547711yescharacteristic
830C4#552411yescharacteristic
831C4#554711yescharacteristic
832C4#554811yescharacteristic
833C3#2357311yescharacteristic, complemented, Sylow
834C2—82no—
835C2—122no—
836C2—242no—
837C2—242no—
838C2#7358011yescharacteristic
839C2#7888411yescharacteristic
840C2#7892611yescharacteristic
841C2#7979011yescharacteristic
842C2#7981111yescharacteristic
843C2#7986911yescharacteristic
844C2#7987711yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1762C2
socleC23×C3C22×D4
hypercenter#1762D3
hypocenterC3#23573
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1762

Complements

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

NH ≅ G/Ntype
1. C2×#5548C2semidirect
2. C2×#5014C2semidirect
3. C2×#4711C2semidirect
4. C4×#895C2semidirect
5. C3×#1762C2semidirect
6. #70209C2semidirect
7. #70204C2semidirect
8. #70177C2semidirect
9. #70176C2semidirect
10. #69807C2semidirect
11. #69474C2semidirect
12. #68898C2semidirect
13. #68886C2semidirect
14. #68827C2semidirect
15. #68823C2semidirect
77. #1762D3semidirect
100. C3×C4×D4D4semidirect
147. C4×D12D4semidirect
265. C2×D12#41semidirect
292. C2×C3×C8#41semidirect
298. C3×C4⋊C4#41semidirect
327. C2×C3⋊C8#41semidirect
376. C4×D4D12semidirect
599. C2×C8#235semidirect
611. C4⋊C4#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×#50142
C2×#47112
C4×#8952
C3×#17622
#702092
#702042
#701772
#701762
#698072
#694742
#688982
#688862
#688272
#688232
#235733