Finite Group Databasebeta

← #10823445

Subgroups — #10823445

Order 768.

1424 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5548C211yesmaximal, characteristic
2C2×C3×#440C211yesmaximal, characteristic, complemented
3C4×#946C211yesmaximal, characteristic, complemented
4C2×#5026C211yesmaximal, characteristic, complemented
5#72056C211yesmaximal, characteristic, complemented
6#72054C211yesmaximal, characteristic, complemented
7#71609C211yesmaximal, characteristic, complemented
8#70634C211yesmaximal, characteristic, complemented
9#70617C211yesmaximal, characteristic, complemented
10#70272C211yesmaximal, characteristic, complemented
11#70231C211yesmaximal, characteristic, complemented
12#70211C211yesmaximal, characteristic, complemented
13#70206C211yesmaximal, characteristic, complemented
14#69812C211yesmaximal, characteristic, complemented
15#69807C211yesmaximal, characteristic, complemented
16#23576—31nomaximal, Sylow
17C22×#235—21no—
18C22×C3×SD16C2211yescharacteristic
19C2×C3×C4×Q8C2211yescharacteristic
20C2×C3×C4×D4C2211yescharacteristic
21C2×#946C2211yescharacteristic
22C22×#215C2211yescharacteristic
23C2×#940C2211yescharacteristic
24C2×#938C2211yescharacteristic
25C2×C4×#67—21no—
26#5548—24no—
27#5548—24no—
28C2×#895C2211yescharacteristic
29C2×#888C2211yescharacteristic
30C2×#885—21no—
31C2×#884—21no—
32C2×C4×D12C2211yescharacteristic
33C2×C42×D3C2211yescharacteristic
34C3×#440—24no—
35C2×C3×#107C2211yescharacteristic
36C2×C3×#103C2211yescharacteristic
37C2×C3×#102C2211yescharacteristic
38C2×C3×#97C2211yescharacteristic
39#5229C2211yescharacteristic
40C2×#835C2211yescharacteristic
41C2×#832C2211yescharacteristic
42C2×#832C2211yescharacteristic
43C2×#821C2211yescharacteristic
44C2×#821C2211yescharacteristic
45C2×(C2×D3)⋊C8C2211yescharacteristic
46C2×(C2×D3)⋊C8C2211yescharacteristic
47#5026—24no—
48#4989—21no—
49#4987C2211yescharacteristic
50#4978—21no—
51#4972C2211yescharacteristic
52C2×#809C2211yescharacteristic
53C2×#807C2211yescharacteristic
54C4×(C2×D3)⋊C4—21no—
55C4×C4⋊Dic3C2211yescharacteristic
56C4×Dic3⋊C4—21no—
57C2×#803C2211yescharacteristic
58#4551C2211yescharacteristic
59#4551C2211yescharacteristic
60#4550C2211yescharacteristic
61#4550C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#532—31no—
65C2×#440—31no—
66C2×#440D311yescharacteristic, complemented
67C4×C22⋊Q8—31no—
68#2057—31no—
69#2041—31no—
70#2033—31no—
71#2033—31no—
72#2024—31no—
73#2014—31no—
74#2000—31no—
75#2000—31no—
76#1762—31no—
77#1762—31no—
78#1749—31no—
79C22×C3×Q8C2311yescharacteristic
80C22×C3×D4C2311yescharacteristic
81C23×C3×C4—21no—
82C22×#67—21no—
83C22×#67—21no—
84C22×#67—21no—
85C2×#235—28no—
86C2×#235—44no—
87C2×#235—44no—
88C22×D12—21no—
89C22×D12C2311yescharacteristic
90C22×C4×D3—21no—
91C22×C4×D3D411yescharacteristic
92C22×C4×D3D411yescharacteristic
93C22×C4×D3C2311yescharacteristic
94C22×Dic6—21no—
95C2×C3×SD16—22no—
96C2×C3×SD16—22no—
97C2×C3×SD16—22no—
98C22×C3×C8C2311yescharacteristic
99C22×C3×C8C2311yescharacteristic
100C3×C4×Q8—22no—
101C3×C4×Q8—22no—
102C3×C4×D4—22no—
103C3×C4×D4D414yes—
104C2×C3×C4⋊C4—21no—
105C2×C3×C4⋊C4C2311yescharacteristic
106C2×C3×C4⋊C4C2311yescharacteristic
107C2×C3×C22⋊C4—21no—
108C2×C3×C42—21no—
109C2×C3×C42C2311yescharacteristic
110C2×#217—21no—
111#946—22no—
112#946—22no—
113C2×#215—22no—
114C2×#215—22no—
115C2×#215—22no—
116#940—22no—
117#940—22no—
118#938—22no—
119#938—22no—
120C4×#67—28no—
121C2×(C2×D3)⋊C4—21no—
122C2×(C2×D3)⋊C4—21no—
123C2×(C2×D3)⋊C4—21no—
124C2×(C2×D3)⋊C4—21no—
125C2×C4⋊Dic3C2311yescharacteristic
126C2×C4⋊Dic3C2311yescharacteristic
127C2×C4⋊Dic3C2311yescharacteristic
128C2×Dic3⋊C4—21no—
129C2×Dic3⋊C4—21no—
130C2×Dic3⋊C4—21no—
131C2×C4×Dic3—21no—
132C2×C4×Dic3D411yescharacteristic
133C2×C4×Dic3D411yescharacteristic
134C2×C4×Dic3C2311yescharacteristic
135C22×C3⋊C8C2311yescharacteristic
136C22×C3⋊C8C2311yescharacteristic
137#895—22no—
138#895—22no—
139#888—22no—
140#888—22no—
141#885—28no—
142#884—28no—
143C4×D12—22no—
144C4×D12D414yes—
145C42×D3—22no—
146C42×D3—22no—
147C3×#107—22no—
148C3×#103—22no—
149C3×#102—22no—
150C3×#97—22no—
151#835—22no—
152#832—22no—
153#832—22no—
154C3⋊#95—21no—
155C3⋊#95—21no—
156C3⋊#95—21no—
157C3⋊#95—21no—
158C3⋊#95—21no—
159#821—22no—
160#821—22no—
161(C2×D3)⋊C8—22no—
162(C2×D3)⋊C8—22no—
163#809—22no—
164#807—22no—
165#803—22no—
166C22×#41—61no—
167C22×SD16—31no—
168C22×SD16C2×D311yescharacteristic
169#532—64no—
170#532—64no—
171C2×C4⋊Q8—31no—
172C2×#127—31no—
173C2×#124—61no—
174C2×C22⋊Q8—31no—
175C2×#121—31no—
176C2×#121—31no—
177C2×#121—61no—
178C2×C4×Q8C2×D311yescharacteristic
179C2×C4×D4—31no—
180C2×C4×D4—61no—
181C2×C4×D4C2×D311yescharacteristic
182C22×C42—31no—
183#440—24no—
184#440—64no—
185C2×#107—31no—
186C2×#107C2×D311yescharacteristic
187C2×#103—31no—
188C2×#103C2×D311yescharacteristic
189C2×#102—31no—
190C2×#102—31no—
191C2×#102—31no—
192C2×#102—31no—
193C2×#102—31no—
194C2×#102C2×D311yescharacteristic
195C2×C22⋊C8—31no—
196C2×C22⋊C8—31no—
197C2×#97—31no—
198C2×#97C2×D311yescharacteristic
199#391—31no—
200#389—31no—
201#387—61no—
202#385—61no—
203#380—31no—
204C4×C4⋊C4—31no—
205C4×C4⋊C4—61no—
206C4×C22⋊C4—61no—
207#340—31no—
208#340—31no—
209#340—31no—
210#340—31no—
211#336—31no—
212#336—31no—
213C24×C3—21no—
214C23×D3—21no—
215C23×D3C2×D411yescharacteristic
216C2×C3×Q8—21no—
217C2×C3×Q8—21no—
218C2×C3×Q8—21no—
219C2×C3×Q8—21no—
220C2×C3×Q8—21no—
221C2×C3×Q8#4112yescomplemented
222C2×C3×D4—21no—
223C2×C3×D4—21no—
224C2×C3×D4—21no—
225C2×C3×D4—21no—
226C2×C3×D4—21no—
227C2×C3×D4C2×D412yes—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—24no—
231C22×C3×C4—21no—
232C22×C3×C4—42no—
233C22×C3×C4—42no—
234C22×C3×C4C2×D411yescharacteristic
235C22×C3×C4C2×D411yescharacteristic
236C22×C3×C4C2411yescharacteristic
237C2×#67—24no—
238C2×#67—24no—
239C2×#67—24no—
240C2×#67—42no—
241C2×#67—42no—
242C2×#67—42no—
243C2×#67—42no—
244C2×#67—42no—
245C2×#67—42no—
246C22×Dic3—21no—
247C22×Dic3—21no—
248C22×Dic3—21no—
249C22×Dic3C2×D411yescharacteristic
250C22×Dic3C2×D411yescharacteristic
251C22×Dic3C2×D411yescharacteristic
252#235—432no—
253C2×D12—21no—
254C2×D12—21no—
255C2×D12—21no—
256C2×D12—21no—
257C2×D12—24no—
258C2×D12—21no—
259C2×D12—42no—
260C2×D12—42no—
261C2×D12C2×D412yes—
262C2×C4×D3—22no—
263C2×C4×D3—22no—
264C2×C4×D3—22no—
265C2×C4×D3—22no—
266C2×C4×D3—24no—
267C2×C4×D3—21no—
268C2×C4×D3—21no—
269C2×C4×D3—21no—
270C2×C4×D3—21no—
271C2×C4×D3—21no—
272C2×C4×D3—21no—
273C2×C4×D3—22no—
274C2×C4×D3—41no—
275C2×C4×D3—42no—
276C2×C4×D3—42no—
277C2×Dic6—24no—
278C2×Dic6—42no—
279C2×Dic6—42no—
280C3×SD16—28no—
281C2×C3×C8—21no—
282C2×C3×C8—21no—
283C2×C3×C8—21no—
284C2×C3×C8—21no—
285C2×C3×C8—21no—
286C2×C3×C8#4112yescomplemented
287C3×C4⋊C4—21no—
288C3×C4⋊C4—21no—
289C3×C4⋊C4—21no—
290C3×C4⋊C4—42no—
291C3×C4⋊C4C2×D412yes—
292C3×C22⋊C4—24no—
293C3×C42—42no—
294C3×C42C2×D412yes—
295C3×C42C2×D412yes—
296#217—24no—
297#215—28no—
298(C2×D3)⋊C4—24no—
299(C2×D3)⋊C4—24no—
300(C2×D3)⋊C4—24no—
301(C2×D3)⋊C4—42no—
302C4⋊Dic3—21no—
303C4⋊Dic3—21no—
304C4⋊Dic3—21no—
305C4⋊Dic3—21no—
306C4⋊Dic3C2×D412yes—
307C4⋊Dic3#4112yescomplemented
308Dic3⋊C4—24no—
309Dic3⋊C4—24no—
310Dic3⋊C4—42no—
311C4×Dic3—22no—
312C4×Dic3—22no—
313C4×Dic3—21no—
314C4×Dic3—21no—
315C4×Dic3—42no—
316C2×C3⋊C8—21no—
317C2×C3⋊C8—21no—
318C2×C3⋊C8—21no—
319C2×C3⋊C8—21no—
320C2×C3⋊C8—21no—
321C2×C3⋊C8#4112yescomplemented
322C2×#41—68no—
323C2×#41—124no—
324C2×#41—124no—
325C22×Q8—61no—
326C22×Q8C22×D311yescharacteristic
327C22×D4—31no—
328C22×D4—61no—
329C22×D4—61no—
330C22×D4—61no—
331C22×D4—61no—
332C22×D4C22×D311yescharacteristic
333C23×C4—21no—
334C23×C4—31no—
335C23×C4—31no—
336C23×C4—31no—
337C23×C4—61no—
338C2×SD16—22no—
339C2×SD16—22no—
340C2×SD16—22no—
341C2×SD16—62no—
342C2×SD16—62no—
343C2×SD16—62no—
344C22×C8—31no—
345C22×C8—31no—
346C22×C8C22×D311yescharacteristic
347C22×C8C22×D311yescharacteristic
348C4⋊Q8—62no—
349C4⋊Q8—62no—
350#127—62no—
351#127—62no—
352#124—68no—
353C22⋊Q8—62no—
354C22⋊Q8—62no—
355#121—68no—
356#121—62no—
357#121—62no—
358#121—62no—
359#121—62no—
360C4×Q8—22no—
361C4×Q8—22no—
362C4×D4—22no—
363C4×D4—34no—
364C4×D4—68no—
365C4×D4—62no—
366C4×D4#6714yes—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—31no—
369C2×C4⋊C4—31no—
370C2×C4⋊C4—31no—
371C2×C4⋊C4—61no—
372C2×C4⋊C4—61no—
373C2×C4⋊C4—61no—
374C2×C4⋊C4C22×D311yescharacteristic
375C2×C4⋊C4C22×D311yescharacteristic
376C2×C22⋊C4—21no—
377C2×C22⋊C4—61no—
378C2×C22⋊C4—61no—
379C2×C22⋊C4—61no—
380C2×C22⋊C4—61no—
381C2×C22⋊C4—61no—
382C2×C42—21no—
383C2×C42—31no—
384C2×C42—31no—
385C2×C42—31no—
386C2×C42—62no—
387C2×C42—62no—
388C2×C42—61no—
389C2×C42C22×D311yescharacteristic
390#107—22no—
391#107—62no—
392#103—22no—
393#103—62no—
394#102—22no—
395#102—62no—
396#102—62no—
397#102—62no—
398#102—62no—
399#102—62no—
400C22⋊C8—62no—
401C22⋊C8—62no—
402#97—22no—
403#97—62no—
404#95—61no—
405#95—61no—
406#95—61no—
407#95—61no—
408#95—61no—
409C23×C3—22no—
410C23×C3—41no—
411C23×C3—41no—
412C23×C3—41no—
413C23×C3—41no—
414C23×C3—41no—
415C23×C3—41no—
416C23×C3C22×D411yescharacteristic
417C22×D3—21no—
418C22×D3—21no—
419C22×D3—21no—
420C22×D3—21no—
421C22×D3—21no—
422C22×D3—21no—
423C22×D3—22no—
424C22×D3—41no—
425C22×D3—41no—
426C22×D3—41no—
427C22×D3—41no—
428C22×D3—41no—
429C22×D3—41no—
430C22×D3AGL(1,ℤ/8)12yes—
431C3×Q8—22no—
432C3×Q8—22no—
433C3×Q8—41no—
434C3×Q8—41no—
435C3×D4—22no—
436C3×D4—22no—
437C3×D4—41no—
438C3×D4—41no—
439C2×C3×C4—21no—
440C2×C3×C4—21no—
441C2×C3×C4—21no—
442C2×C3×C4—21no—
443C2×C3×C4—22no—
444C2×C3×C4—22no—
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#12012yes—
454C2×C3×C4#12012yes—
455C2×C3×C4C22×D411yescharacteristic
456C2×C3×C4C22×D411yescharacteristic
457C2×C3×C4C2×#4111yescharacteristic
458C2×C3×C4C2×#4111yescharacteristic
459C2×C3×C4C2×#4111yescharacteristic
460C2×C3×C4C2×#4111yescharacteristic
461#67—48no—
462#67—48no—
463#67—48no—
464C2×Dic3—21no—
465C2×Dic3—21no—
466C2×Dic3—21no—
467C2×Dic3—21no—
468C2×Dic3—21no—
469C2×Dic3—22no—
470C2×Dic3—21no—
471C2×Dic3—22no—
472C2×Dic3—21no—
473C2×Dic3—41no—
474C2×Dic3—41no—
475C2×Dic3—41no—
476C2×Dic3—41no—
477C2×Dic3—41no—
478C2×Dic3—41no—
479C2×Dic3—41no—
480C2×Dic3AGL(1,ℤ/8)12yes—
481C2×Dic3#13712yes—
482D12—22no—
483D12—22no—
484D12—48no—
485D12—41no—
486D12—41no—
487C4×D3—28no—
488C4×D3—44no—
489C4×D3—48no—
490C4×D3—41no—
491C4×D3—41no—
492C4×D3—41no—
493C4×D3—41no—
494Dic6—48no—
495C3×C8—22no—
496C3×C8—41no—
497C3⋊C8—22no—
498C3⋊C8—41no—
499C24—21no—
500C24—31no—
501C24—61no—
502#41—1232no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—64no—
509C2×Q8—122no—
510C2×Q8—122no—
511C2×Q8#23512yescomplemented
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—32no—
518C2×D4—64no—
519C2×D4—64no—
520C2×D4—64no—
521C2×D4—64no—
522C2×D4—61no—
523C2×D4—61no—
524C2×D4—61no—
525C2×D4—61no—
526C2×D4—61no—
527C2×D4—122no—
528C2×D4—122no—
529C2×D4—122no—
530C2×D4—122no—
531C2×D4—122no—
532C2×D4—122no—
533C2×D4—122no—
534C2×D4—122no—
535C2×D4C2×#6712yes—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—24no—
539C22×C4—21no—
540C22×C4—31no—
541C22×C4—31no—
542C22×C4—31no—
543C22×C4—42no—
544C22×C4—42no—
545C22×C4—62no—
546C22×C4—62no—
547C22×C4—62no—
548C22×C4—62no—
549C22×C4—61no—
550C22×C4—61no—
551C22×C4—62no—
552C22×C4—64no—
553C22×C4—61no—
554C22×C4—61no—
555C22×C4—61no—
556C22×C4—61no—
557C22×C4—61no—
558C22×C4—61no—
559C22×C4—61no—
560C22×C4—121no—
561C22×C4—122no—
562C22×C4—122no—
563C22×C4D3×D411yescharacteristic
564C22×C4D3×D411yescharacteristic
565C22×C4C23×D311yescharacteristic
566SD16—28no—
567SD16—68no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—32no—
574C2×C8—61no—
575C2×C8—61no—
576C2×C8—61no—
577C2×C8—61no—
578C2×C8—61no—
579C2×C8#23512yescomplemented
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—32no—
584C4⋊C4—32no—
585C4⋊C4—42no—
586C4⋊C4—64no—
587C4⋊C4—64no—
588C4⋊C4—61no—
589C4⋊C4—61no—
590C4⋊C4—61no—
591C4⋊C4—61no—
592C4⋊C4—122no—
593C4⋊C4C2×#6712yes—
594C22⋊C4—24no—
595C22⋊C4—64no—
596C22⋊C4—64no—
597C22⋊C4—64no—
598C22⋊C4—64no—
599C22⋊C4—122no—
600C42—42no—
601C42—62no—
602C42—62no—
603C42—61no—
604C42—61no—
605C42—122no—
606C42D3×D412yes—
607C42C2×#6712yes—
608C22×C3—42no—
609C22×C3—42no—
610C22×C3—42no—
611C22×C3—81no—
612C22×C3—81no—
613C22×C3—81no—
614C22×C3—81no—
615C22×C3C2×#12011yescharacteristic
616C22×C3#52511yescharacteristic
617C22×C3#53211yescharacteristic
618C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
619C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
620C22×C3C2×#13711yescharacteristic
621C22×C3#57511yescharacteristic
622C2×D3—22no—
623C2×D3—22no—
624C2×D3—22no—
625C2×D3—41no—
626C2×D3—41no—
627C2×D3—41no—
628C2×D3—41no—
629C2×D3—42no—
630C2×D3—42no—
631C2×D3—42no—
632C2×D3—81no—
633C2×D3—81no—
634C2×D3—81no—
635C2×D3—81no—
636C3×C4—22no—
637C3×C4—22no—
638C3×C4—42no—
639C3×C4—42no—
640C3×C4—81no—
641C3×C4#52511yescharacteristic
642C3×C4#52511yescharacteristic
643C3×C4#53211yescharacteristic
644C3×C4#53211yescharacteristic
645Dic3—22no—
646Dic3—22no—
647Dic3—42no—
648Dic3—41no—
649Dic3—42no—
650Dic3—81no—
651C23—22no—
652C23—32no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—61no—
660C23—61no—
661C23—61no—
662C23—61no—
663C23—61no—
664C23—61no—
665C23—62no—
666C23—121no—
667C23—121no—
668C23—121no—
669C23—121no—
670C23—121no—
671C23—121no—
672C23C2×D3×D411yescharacteristic
673Q8—22no—
674Q8—22no—
675Q8—41no—
676Q8—41no—
677Q8—128no—
678D4—22no—
679D4—22no—
680D4—41no—
681D4—41no—
682D4—62no—
683D4—62no—
684D4—128no—
685D4—128no—
686D4—128no—
687D4—128no—
688D4—121no—
689D4—121no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—32no—
697C2×C4—32no—
698C2×C4—48no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—68no—
707C2×C4—61no—
708C2×C4—61no—
709C2×C4—61no—
710C2×C4—61no—
711C2×C4—61no—
712C2×C4—62no—
713C2×C4—62no—
714C2×C4—61no—
715C2×C4—61no—
716C2×C4—124no—
717C2×C4—128no—
718C2×C4—121no—
719C2×C4—121no—
720C2×C4—121no—
721C2×C4—121no—
722C2×C4—121no—
723C2×C4—121no—
724C2×C4—121no—
725C2×C4—121no—
726C2×C4—121no—
727C2×C4—121no—
728C2×C4—121no—
729C2×C4#93712yes—
730C2×C4#93712yes—
731C2×C4C2×#23511yescharacteristic
732C2×C4C2×#23511yescharacteristic
733C2×C4C2×D3×D411yescharacteristic
734C2×C4D3×#4111yescharacteristic
735C2×C4D3×#4111yescharacteristic
736C2×C4C22×#6711yescharacteristic
737C8—22no—
738C8—41no—
739C8—62no—
740C8—121no—
741C2×C3—82no—
742C2×C3#238811yescharacteristic
743C2×C3#300311yescharacteristic
744C2×C3#300711yescharacteristic
745C2×C3#311211yescharacteristic
746C2×C3#311511yescharacteristic
747C2×C3#318011yescharacteristic
748C2×C3#318211yescharacteristic
749D3—42no—
750D3—82no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—62no—
755C22—62no—
756C22—62no—
757C22—81no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—121no—
762C22—121no—
763C22—121no—
764C22—121no—
765C22—122no—
766C22—122no—
767C22—122no—
768C22—241no—
769C22—241no—
770C22—241no—
771C22—241no—
772C22#554711yescharacteristic
773C22#554811yescharacteristic
774C22D3×AGL(1,ℤ/8)11yescharacteristic
775C22D3×AGL(1,ℤ/8)11yescharacteristic
776C22D3×#13711yescharacteristic
777C22#577711yescharacteristic
778C22C2×#93711yescharacteristic
779C4—22no—
780C4—22no—
781C4—42no—
782C4—42no—
783C4—62no—
784C4—62no—
785C4—81no—
786C4—122no—
787C4—121no—
788C4—122no—
789C4—241no—
790C4#554711yescharacteristic
791C4#554811yescharacteristic
792C4#579111yescharacteristic
793C4#583211yescharacteristic
794C3#2357611yescharacteristic, complemented, Sylow
795C2—82no—
796C2—122no—
797C2—242no—
798C2#7978111yescharacteristic
799C2#7979011yescharacteristic
800C2#7979211yescharacteristic
801C2#7981111yescharacteristic
802C2#8240011yescharacteristic
803C2#8394411yescharacteristic
804C2#8398111yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#440C2
socleC23×C3C22×D4
prime radicalC2×#5548C2
hypercenterC2×#440D3
hypocenterC3#23576
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
2. C2×C3×#440C2semidirect
3. C4×#946C2semidirect
4. C2×#5026C2semidirect
5. #72056C2semidirect
6. #72054C2semidirect
7. #71609C2semidirect
8. #70634C2semidirect
9. #70617C2semidirect
10. #70272C2semidirect
11. #70231C2semidirect
12. #70211C2semidirect
13. #70206C2semidirect
14. #69812C2semidirect
15. #69807C2semidirect
66. C2×#440D3semidirect
221. C2×C3×Q8#41semidirect
286. C2×C3×C8#41semidirect
307. C4⋊Dic3#41semidirect
321. C2×C3⋊C8#41semidirect
511. C2×Q8#235semidirect
579. C2×C8#235semidirect
794. C3#23576semidirect

Maximal subgroups

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

subgroupindex
C2×#55482
C2×C3×#4402
C4×#9462
C2×#50262
#720562
#720542
#716092
#706342
#706172
#702722
#702312
#702112
#702062
#698122
#698072
#235763