Finite Group Databasebeta

← #10846318

Subgroups — #10846318

Order 768.

1120 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×C3×C4×SD16C211yesmaximal, characteristic, complemented
2C2×#5174C211yesmaximal, characteristic, complemented
3C2×#5176C211yesmaximal, characteristic, complemented
4#82495C211yesmaximal, characteristic, complemented
5#82409C211yesmaximal, characteristic, complemented
6C2×#4865C211yesmaximal, characteristic, complemented
7#71633C211yesmaximal, characteristic, complemented
8#71613C211yesmaximal, characteristic, complemented
9#70562C211yesmaximal, characteristic, complemented
10#70272C211yesmaximal, characteristic, complemented
11#70245C211yesmaximal, characteristic, complemented
12#70204C211yesmaximal, characteristic, complemented
13#70177C211yesmaximal, characteristic, complemented
14#69781C211yesmaximal, characteristic, complemented
15#69776C211yesmaximal, characteristic, complemented
16#25416—31nomaximal, Sylow
17C22×C3×SD16C2211yescharacteristic
18C2×C3×C4×Q8C2211yescharacteristic
19C2×C3×C4×D4C2211yescharacteristic
20C2×#947C2211yescharacteristic
21C2×#946C2211yescharacteristic
22C22×#215C2211yescharacteristic
23C2×#940C2211yescharacteristic
24C2×#938C2211yescharacteristic
25C22×#213C2211yescharacteristic
26C2×#930—21no—
27C22×D24C2211yescharacteristic
28C22×ΓL(1,𝔽25)C2211yescharacteristic
29C2×#895C2211yescharacteristic
30C2×#895C2211yescharacteristic
31C3×C4×SD16—24no—
32C2×C3×#106C2211yescharacteristic
33C2×C3×#103C2211yescharacteristic
34C2×C3×#102C2211yescharacteristic
35C2×C3×C4×C8C2211yescharacteristic
36C2×#835C2211yescharacteristic
37C2×#832C2211yescharacteristic
38#5213—21no—
39#5176—24no—
40#5174—24no—
41C2×#821C2211yescharacteristic
42C2×#821C2211yescharacteristic
43C2×(C2×D3)⋊C8C2211yescharacteristic
44C2×#818C2211yescharacteristic
45C2×#815C2211yescharacteristic
46#4994—21no—
47#4991—21no—
48#4984C2211yescharacteristic
49#4984C2211yescharacteristic
50C2×#809C2211yescharacteristic
51C2×#809C2211yescharacteristic
52#4961—21no—
53#4960—21no—
54#4940—21no—
55#4939—21no—
56#4939C2211yescharacteristic
57#4939C2211yescharacteristic
58C4×(C2×D3)⋊C4C2211yescharacteristic
59#4865—24no—
60#4550C2211yescharacteristic
61#4529C2211yescharacteristic
62#4529C2211yescharacteristic
63#4524C2211yescharacteristic
64C2×#496—31no—
65C2×#469—31no—
66C2×#468—31no—
67C2×C4×SD16D311yescharacteristic, complemented
68#2428—31no—
69#2426—31no—
70#2042—31no—
71#2041—31no—
72#2000—31no—
73#1999—31no—
74#1970—31no—
75#1944—31no—
76#1880—31no—
77#1879—31no—
78#1753—31no—
79C22×C3×Q8C2311yescharacteristic
80C22×C3×D4C2311yescharacteristic
81C23×C3×C4—21no—
82C22×#67—21no—
83C22×#67—21no—
84C22×#67—21no—
85C22×D12—21no—
86C22×D12—21no—
87C22×D12C2311yescharacteristic
88C22×D12C2311yescharacteristic
89C22×C4×D3C2311yescharacteristic
90C2×C3×SD16—22no—
91C2×C3×SD16—22no—
92C2×C3×SD16D414yescomplemented
93C22×C3×C8C2311yescharacteristic
94C22×C3×C8C2311yescharacteristic
95C3×C4×Q8—22no—
96C3×C4×Q8—41no—
97C3×C4×D4—22no—
98C3×C4×D4—41no—
99C2×C3×C4⋊C4—21no—
100C2×C3×C4⋊C4C2311yescharacteristic
101C2×C3×C4⋊C4C2311yescharacteristic
102C2×C3×C22⋊C4—21no—
103C2×C3×C42—21no—
104C2×C3×C42C2311yescharacteristic
105C2×#217—21no—
106#947—22no—
107#947—41no—
108#946—22no—
109#946—41no—
110C2×#215—22no—
111C2×#215—22no—
112C2×#215—41no—
113#940—22no—
114#940—41no—
115#938—22no—
116#938—41no—
117C2×#213—22no—
118C2×#213—22no—
119C2×#213—41no—
120#930—44no—
121C2×(C2×D3)⋊C4—21no—
122C2×(C2×D3)⋊C4—21no—
123C2×(C2×D3)⋊C4—21no—
124C2×(C2×D3)⋊C4—21no—
125C2×(C2×D3)⋊C4—21no—
126C2×(C2×D3)⋊C4—21no—
127C2×(C2×D3)⋊C4—21no—
128C2×(C2×D3)⋊C4—21no—
129C2×(C2×D3)⋊C4—21no—
130C2×(C2×D3)⋊C4D411yescharacteristic
131C2×(C2×D3)⋊C4D411yescharacteristic
132C2×C4⋊Dic3—21no—
133C2×C4⋊Dic3—21no—
134C2×C4⋊Dic3C2311yescharacteristic
135C2×C4⋊Dic3C2311yescharacteristic
136C2×Dic3⋊C4—21no—
137C2×C4×Dic3C2311yescharacteristic
138C22×C3⋊C8C2311yescharacteristic
139C22×C3⋊C8C2311yescharacteristic
140C2×D24—22no—
141C2×D24—22no—
142C2×D24—22no—
143C2×ΓL(1,𝔽25)—22no—
144C2×ΓL(1,𝔽25)—22no—
145C2×ΓL(1,𝔽25)—22no—
146#895—22no—
147#895—22no—
148#895—41no—
149#895—41no—
150C3×#106D414yescomplemented
151C3×#103—22no—
152C3×#102—22no—
153C3×C4×C8—22no—
154#835—22no—
155#832—22no—
156C3⋊#95—21no—
157C3⋊#95—21no—
158C3⋊#95D411yescharacteristic
159C3⋊#95D411yescharacteristic
160#821—41no—
161#821—41no—
162(C2×D3)⋊C8—22no—
163#818—22no—
164#815—22no—
165#809—22no—
166#809—22no—
167C22×SD16—31no—
168C22×SD16C2×D311yescharacteristic
169C22×D8—31no—
170C22×D8—31no—
171C22×M16—31no—
172C2×#127—31no—
173C2×#124—31no—
174C2×C22⋊Q8—31no—
175C2×#121—31no—
176C2×#121—31no—
177C2×#121—31no—
178C2×#121—61no—
179C2×C4×Q8C2×D311yescharacteristic
180C2×C4×D4C2×D311yescharacteristic
181#496—64no—
182#469—64no—
183#468—64no—
184C4×SD16—24no—
185C2×#107—31no—
186C2×#106C2×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×#97—31no—
197C2×C4×C8C2×D311yescharacteristic
198#396—61no—
199#394—61no—
200#394—61no—
201#392—61no—
202#390—31no—
203#390—31no—
204#390—61no—
205#389—31no—
206#389—31no—
207#388—61no—
208#386—61no—
209C4×C22⋊C4—31no—
210#340—31no—
211#340—31no—
212#336—31no—
213#336—31no—
214C24×C3—21no—
215C23×D3—21no—
216C23×D3—21no—
217C23×D3C2×D411yescharacteristic
218C2×C3×Q8—21no—
219C2×C3×Q8—21no—
220C2×C3×Q8—21no—
221C2×C3×Q8—21no—
222C2×C3×Q8—21no—
223C2×C3×Q8C2×D412yes—
224C2×C3×D4—21no—
225C2×C3×D4—21no—
226C2×C3×D4—21no—
227C2×C3×D4—21no—
228C2×C3×D4—21no—
229C2×C3×D4C2×D412yes—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—42no—
234C22×C3×C4—42no—
235C22×C3×C4—81no—
236C22×C3×C4C2×D411yescharacteristic
237C22×C3×C4C2×D411yescharacteristic
238C22×C3×C4C2411yescharacteristic
239C2×#67—42no—
240C2×#67—42no—
241C2×#67—42no—
242C2×#67—42no—
243C2×#67—42no—
244C2×#67—42no—
245C2×#67—81no—
246C2×#67—81no—
247C2×#67—81no—
248C22×Dic3—21no—
249C22×Dic3—21no—
250C22×Dic3C2×D411yescharacteristic
251C22×Dic3C2×D411yescharacteristic
252C22×Dic3C2×D411yescharacteristic
253C2×D12—21no—
254C2×D12—21no—
255C2×D12—21no—
256C2×D12—21no—
257C2×D12—21no—
258C2×D12—21no—
259C2×D12—21no—
260C2×D12—21no—
261C2×D12—21no—
262C2×D12—21no—
263C2×D12—21no—
264C2×D12—21no—
265C2×D12—42no—
266C2×D12—42no—
267C2×D12—42no—
268C2×D12—42no—
269C2×D12—81no—
270C2×D12—81no—
271C2×C4×D3—21no—
272C2×C4×D3—21no—
273C2×C4×D3—21no—
274C2×C4×D3—21no—
275C2×C4×D3—21no—
276C2×C4×D3—21no—
277C3×SD16—28no—
278C2×C3×C8—21no—
279C2×C3×C8—21no—
280C2×C3×C8—21no—
281C2×C3×C8C2×D412yes—
282C2×C3×C8C2×D412yes—
283C2×C3×C8#4112yes—
284C3×C4⋊C4—21no—
285C3×C4⋊C4—21no—
286C3×C4⋊C4—42no—
287C3×C4⋊C4C2×D412yes—
288C3×C4⋊C4C2×D412yes—
289C3×C22⋊C4—42no—
290C3×C42—21no—
291C3×C42—21no—
292C3×C42—42no—
293#217—42no—
294#215—44no—
295#213—44no—
296(C2×D3)⋊C4—22no—
297(C2×D3)⋊C4—41no—
298(C2×D3)⋊C4—42no—
299(C2×D3)⋊C4—42no—
300(C2×D3)⋊C4—42no—
301(C2×D3)⋊C4—42no—
302(C2×D3)⋊C4—42no—
303(C2×D3)⋊C4—42no—
304(C2×D3)⋊C4—42no—
305(C2×D3)⋊C4—81no—
306(C2×D3)⋊C4—81no—
307C4⋊Dic3—21no—
308C4⋊Dic3—21no—
309C4⋊Dic3—21no—
310C4⋊Dic3—21no—
311C4⋊Dic3—42no—
312C4⋊Dic3—81no—
313Dic3⋊C4—42no—
314C4×Dic3—21no—
315C4×Dic3—21no—
316C2×C3⋊C8—21no—
317C2×C3⋊C8—21no—
318C2×C3⋊C8—21no—
319C2×C3⋊C8—21no—
320C2×C3⋊C8—21no—
321C2×C3⋊C8#4112yes—
322D24—44no—
323ΓL(1,𝔽25)—44no—
324C22×Q8C22×D311yescharacteristic
325C22×D4—31no—
326C22×D4—31no—
327C22×D4—61no—
328C22×D4—61no—
329C22×D4—61no—
330C22×D4—61no—
331C22×D4—61no—
332C22×D4C22×D311yescharacteristic
333C23×C4—21no—
334C23×C4—31no—
335C2×SD16—22no—
336C2×SD16—22no—
337C2×SD16—62no—
338C2×SD16—62no—
339C2×SD16—121no—
340C2×SD16D1214yescomplemented
341C2×D8—62no—
342C2×D8—62no—
343C2×D8—62no—
344C2×D8—62no—
345C2×D8—62no—
346C2×D8—121no—
347C2×M16—62no—
348C2×M16—62no—
349C2×M16—62no—
350C22×C8—31no—
351C22×C8—31no—
352C22×C8C22×D311yescharacteristic
353C22×C8C22×D311yescharacteristic
354#127—62no—
355#127—121no—
356#124—62no—
357#124—121no—
358C22⋊Q8—62no—
359C22⋊Q8—121no—
360#121—62no—
361#121—62no—
362#121—62no—
363#121—124no—
364#121—121no—
365#121—121no—
366#121—121no—
367C4×Q8—22no—
368C4×Q8—41no—
369C4×D4—22no—
370C4×D4—41no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—31no—
373C2×C4⋊C4—31no—
374C2×C4⋊C4—61no—
375C2×C4⋊C4—61no—
376C2×C4⋊C4—61no—
377C2×C4⋊C4C22×D311yescharacteristic
378C2×C4⋊C4C22×D311yescharacteristic
379C2×C22⋊C4—21no—
380C2×C22⋊C4—31no—
381C2×C22⋊C4—31no—
382C2×C22⋊C4—61no—
383C2×C22⋊C4—61no—
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×C22⋊C4—61no—
392C2×C42—21no—
393C2×C42—31no—
394C2×C42C22×D311yescharacteristic
395#107—62no—
396#106#6714yescomplemented
397#103—22no—
398#103—62no—
399#102—22no—
400#102—62no—
401#102—62no—
402#102—62no—
403#102—121no—
404#102—121no—
405C22⋊C8—62no—
406#97—62no—
407C4×C8—22no—
408#95—31no—
409#95—31no—
410#95—61no—
411#95—61no—
412C23×C3—22no—
413C23×C3—41no—
414C23×C3—41no—
415C23×C3—41no—
416C23×C3—41no—
417C23×C3—41no—
418C23×C3—41no—
419C23×C3C22×D411yescharacteristic
420C22×D3—21no—
421C22×D3—21no—
422C22×D3—21no—
423C22×D3—21no—
424C22×D3—21no—
425C22×D3—21no—
426C22×D3—21no—
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×D3—41no—
440C22×D3—41no—
441C3×Q8—22no—
442C3×Q8—22no—
443C3×Q8—41no—
444C3×Q8—41no—
445C3×D4—22no—
446C3×D4—22no—
447C3×D4—41no—
448C3×D4—41no—
449C2×C3×C4—21no—
450C2×C3×C4—21no—
451C2×C3×C4—22no—
452C2×C3×C4—22no—
453C2×C3×C4—22no—
454C2×C3×C4—21no—
455C2×C3×C4—21no—
456C2×C3×C4—21no—
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—84no—
464C2×C3×C4AGL(1,ℤ/8)12yes—
465C2×C3×C4C22×D411yescharacteristic
466C2×C3×C4C22×D411yescharacteristic
467C2×C3×C4C2×#4111yescharacteristic
468C2×C3×C4C2×#4111yescharacteristic
469C2×C3×C4H(5,𝔽2)11yescharacteristic
470C2×C3×C4H(5,𝔽2)11yescharacteristic
471#67—84no—
472#67—84no—
473#67—84no—
474C2×Dic3—21no—
475C2×Dic3—21no—
476C2×Dic3—21no—
477C2×Dic3—21no—
478C2×Dic3—21no—
479C2×Dic3—21no—
480C2×Dic3—21no—
481C2×Dic3—21no—
482C2×Dic3—21no—
483C2×Dic3—41no—
484C2×Dic3—41no—
485C2×Dic3—41no—
486C2×Dic3—41no—
487C2×Dic3—41no—
488C2×Dic3—41no—
489D12—41no—
490D12—41no—
491D12—41no—
492D12—41no—
493D12—41no—
494D12—41no—
495D12—41no—
496D12—41no—
497D12—84no—
498D12—84no—
499C4×D3—41no—
500C4×D3—41no—
501C4×D3—41no—
502C4×D3—41no—
503C3×C8—41no—
504C3×C8#12114yescomplemented
505C3⋊C8—22no—
506C3⋊C8—41no—
507C24—21no—
508C24—31no—
509C24—61no—
510C24—61no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8C2×D1212yes—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
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—61no—
532C2×D4—61no—
533C2×D4—61no—
534C2×D4—122no—
535C2×D4—122no—
536C2×D4—122no—
537C2×D4—122no—
538C2×D4—122no—
539C2×D4—122no—
540C2×D4—122no—
541C2×D4—122no—
542C2×D4—122no—
543C2×D4—122no—
544C2×D4—241no—
545C2×D4—241no—
546C2×D4—241no—
547C2×D4—241no—
548C2×D4—241no—
549C2×D4C2×D1212yes—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—31no—
554C22×C4—31no—
555C22×C4—31no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—61no—
559C22×C4—61no—
560C22×C4—61no—
561C22×C4—61no—
562C22×C4—61no—
563C22×C4—61no—
564C22×C4—61no—
565C22×C4—61no—
566C22×C4—81no—
567C22×C4D3×D411yescharacteristic
568C22×C4D3×D411yescharacteristic
569C22×C4C23×D311yescharacteristic
570SD16—28no—
571SD16—124no—
572D8—124no—
573D8—124no—
574M16—124no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—32no—
579C2×C8—61no—
580C2×C8—61no—
581C2×C8—61no—
582C2×C8—61no—
583C2×C8—61no—
584C2×C8C2×D1212yes—
585C2×C8#23512yes—
586C2×C8C2×#6712yes—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—42no—
590C4⋊C4—61no—
591C4⋊C4—61no—
592C4⋊C4—61no—
593C4⋊C4—61no—
594C4⋊C4—122no—
595C4⋊C4—122no—
596C4⋊C4—241no—
597C4⋊C4C2×#6712yes—
598C4⋊C4C2×#6712yes—
599C22⋊C4—42no—
600C22⋊C4—62no—
601C22⋊C4—121no—
602C22⋊C4—122no—
603C22⋊C4—122no—
604C22⋊C4—122no—
605C22⋊C4—122no—
606C22⋊C4—122no—
607C22⋊C4—122no—
608C22⋊C4—122no—
609C22⋊C4—122no—
610C22⋊C4—241no—
611C22⋊C4—241no—
612C42—21no—
613C42—21no—
614C42—42no—
615C42—61no—
616C42—61no—
617C22×C3—42no—
618C22×C3—42no—
619C22×C3—42no—
620C22×C3—81no—
621C22×C3—81no—
622C22×C3—81no—
623C22×C3—81no—
624C22×C3#53211yescharacteristic
625C22×C3D4211yescharacteristic
626C22×C3D4211yescharacteristic
627C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
628C22×C3#57511yescharacteristic
629C22×C3#57611yescharacteristic
630C22×C3#57711yescharacteristic
631C2×D3—41no—
632C2×D3—41no—
633C2×D3—41no—
634C2×D3—41no—
635C2×D3—41no—
636C2×D3—41no—
637C2×D3—41no—
638C2×D3—81no—
639C2×D3—81no—
640C2×D3—81no—
641C2×D3—81no—
642C2×D3—81no—
643C2×D3—81no—
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—22no—
653C3×C4—42no—
654C3×C4—42no—
655C3×C4—42no—
656C3×C4—41no—
657C3×C4C2×#12111yescharacteristic
658C3×C4#54011yescharacteristic
659C3×C4#54611yescharacteristic
660C3×C4#55011yescharacteristic
661Dic3—41no—
662Dic3—41no—
663Dic3—41no—
664Dic3—81no—
665Dic3—81no—
666C23—22no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—61no—
674C23—61no—
675C23—61no—
676C23—61no—
677C23—61no—
678C23—61no—
679C23—61no—
680C23—121no—
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—121no—
694C23C2×D3×D411yescharacteristic
695Q8—22no—
696Q8—22no—
697Q8—41no—
698Q8—41no—
699D4—22no—
700D4—22no—
701D4—41no—
702D4—41no—
703D4—121no—
704D4—121no—
705D4—121no—
706D4—121no—
707D4—121no—
708D4—121no—
709D4—121no—
710D4—121no—
711D4—244no—
712D4—244no—
713D4—244no—
714D4—244no—
715D4—244no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—61no—
731C2×C4—61no—
732C2×C4—61no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—61no—
736C2×C4—61no—
737C2×C4—61no—
738C2×C4—61no—
739C2×C4—84no—
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#91412yes—
751C2×C4C22×D1211yescharacteristic
752C2×C4C2×#23511yescharacteristic
753C2×C4#100411yescharacteristic
754C2×C4D3×#4111yescharacteristic
755C2×C4#100911yescharacteristic
756C2×C4C22×#6711yescharacteristic
757C8—41no—
758C8—62no—
759C8—121no—
760C8#93014yescomplemented
761C2×C3—82no—
762C2×C3#242811yescharacteristic
763C2×C3#317111yescharacteristic
764C2×C3#317911yescharacteristic
765C2×C3#326511yescharacteristic
766C2×C3#326811yescharacteristic
767C2×C3#327411yescharacteristic
768C2×C3#327511yescharacteristic
769D3—81no—
770D3—161no—
771D3—161no—
772C22—42no—
773C22—42no—
774C22—42no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22—121no—
780C22—121no—
781C22—121no—
782C22—121no—
783C22—121no—
784C22—121no—
785C22—121no—
786C22—241no—
787C22—241no—
788C22—241no—
789C22—241no—
790C22—241no—
791C22—241no—
792C22—241no—
793C22—241no—
794C22—241no—
795C22—241no—
796C22—241no—
797C22—241no—
798C22—241no—
799C22—241no—
800C22#554811yescharacteristic
801C22D4×D1211yescharacteristic
802C22C2×#91411yescharacteristic
803C22#576211yescharacteristic
804C22#576811yescharacteristic
805C22#576911yescharacteristic
806C22D4×#6711yescharacteristic
807C4—22no—
808C4—42no—
809C4—41no—
810C4—42no—
811C4—42no—
812C4—121no—
813C4—121no—
814C4—121no—
815C4—241no—
816C4—241no—
817C4#555411yescharacteristic
818C4#556211yescharacteristic
819C4C2×#93011yescharacteristic
820C4#583411yescharacteristic
821C3#2541611yescharacteristic, complemented, Sylow
822C2—82no—
823C2—241no—
824C2—481no—
825C2—481no—
826C2#7966411yescharacteristic
827C2#7966911yescharacteristic
828C2#7967011yescharacteristic
829C2#7967111yescharacteristic
830C2#8240911yescharacteristic
831C2#8386411yescharacteristic
832C2#8392211yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×C4×SD16C2
socleC23×C3C22×D4
hypercenterC2×C4×SD16D3
hypocenterC3#25416
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
1. C2×C3×C4×SD16C2semidirect
2. C2×#5174C2semidirect
3. C2×#5176C2semidirect
4. #82495C2semidirect
5. #82409C2semidirect
6. C2×#4865C2semidirect
7. #71633C2semidirect
8. #71613C2semidirect
9. #70562C2semidirect
10. #70272C2semidirect
11. #70245C2semidirect
12. #70204C2semidirect
13. #70177C2semidirect
14. #69781C2semidirect
15. #69776C2semidirect
67. C2×C4×SD16D3semidirect
92. C2×C3×SD16D4semidirect
150. C3×#106D4semidirect
340. C2×SD16D12semidirect
396. #106#67semidirect
504. C3×C8#121semidirect
760. C8#930semidirect
821. C3#25416semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×SD162
C2×#51742
C2×#51762
#824952
#824092
C2×#48652
#716332
#716132
#705622
#702722
#702452
#702042
#701772
#697812
#697762
#254163