Finite Group Databasebeta

← #10846071

Subgroups — #10846071

Order 768.

1118 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
1#82417C211yesmaximal, characteristic, complemented
2C2×#5016C211yesmaximal, characteristic, complemented
3C2×#4780C211yesmaximal, characteristic, complemented
4C2×#4775C211yesmaximal, characteristic, complemented
5C2×#4706C211yesmaximal, characteristic, complemented
6#73798C211yesmaximal, characteristic, complemented
7C3×#1762C211yesmaximal, characteristic, complemented
8#70205C211yesmaximal, characteristic, complemented
9#70204C211yesmaximal, characteristic, complemented
10#69821C211yesmaximal, characteristic, complemented
11#69466C211yesmaximal, characteristic, complemented
12#68885C211yesmaximal, characteristic, complemented
13#68882C211yesmaximal, characteristic, complemented
14#68825C211yesmaximal, characteristic, complemented
15#68822C211yesmaximal, characteristic, complemented
16#25397—31nomaximal, Sylow
17C2×C3×C4×D4C2211yescharacteristic
18C2×#938C2211yescharacteristic
19C2×#938C2211yescharacteristic
20C22×#214C2211yescharacteristic
21C22×#213C2211yescharacteristic
22C2×#930—21no—
23C22×ΓL(1,𝔽25)C2211yescharacteristic
24C22×D3×C8C2211yescharacteristic
25C2×#897C2211yescharacteristic
26C2×#897C2211yescharacteristic
27C2×#895C2211yescharacteristic
28C2×#895C2211yescharacteristic
29C2×#875C2211yescharacteristic
30C2×C4×D12C2211yescharacteristic
31C2×C3×#102C2211yescharacteristic
32C2×C3×#102C2211yescharacteristic
33C2×C3×#97C2211yescharacteristic
34C3×C4×C4⋊C4C2211yescharacteristic
35#5212—21no—
36C2×#821C2211yescharacteristic
37C2×#821C2211yescharacteristic
38C2×(C2×D3)⋊C8C2211yescharacteristic
39C2×(C2×D3)⋊C8C2211yescharacteristic
40C2×#816C2211yescharacteristic
41C2×#816C2211yescharacteristic
42#5016—24no—
43#4987C2211yescharacteristic
44#4987C2211yescharacteristic
45C2×#810C2211yescharacteristic
46C2×#809C2211yescharacteristic
47C2×#807C2211yescharacteristic
48C2×#807C2211yescharacteristic
49#4961—21no—
50#4961—21no—
51#4939—21no—
52#4939—21no—
53#4935C2211yescharacteristic
54C2×C4⋊(C3⋊C8)C2211yescharacteristic
55#4780—24no—
56#4775—24no—
57#4706—24no—
58#4677—21no—
59#4671—21no—
60C3×#340C2211yescharacteristic
61C3×#340C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#468—31no—
65C2×#466—31no—
66C2×#463—31no—
67C2×#435—31no—
68#2540—31no—
69#2537—31no—
70#2036—31no—
71#2033—31no—
72#2000—31no—
73#1999—31no—
74#1959—31no—
75#1947—31no—
76#1895—31no—
77#1892—31no—
78#1762D311yescharacteristic, complemented
79C22×C3×D4C2311yescharacteristic
80C23×C3×C4—21no—
81C22×#67—21no—
82C22×#67—21no—
83C22×D12—21no—
84C22×D12—21no—
85C22×D12D411yescharacteristic
86C22×D12C2311yescharacteristic
87C22×C4×D3C2311yescharacteristic
88C22×C4×D3C2311yescharacteristic
89C22×Dic6C2311yescharacteristic
90C22×C3×C8C2311yescharacteristic
91C22×C3×C8C2311yescharacteristic
92C3×C4×D4—22no—
93C3×C4×D4—22no—
94C2×C3×C4⋊C4C2311yescharacteristic
95C2×C3×C4⋊C4C2311yescharacteristic
96C2×C3×C4⋊C4C2311yescharacteristic
97C2×C3×C22⋊C4—21no—
98C2×C3×C42—21no—
99C2×C3×C42C2311yescharacteristic
100C2×#217—21no—
101C2×#217—21no—
102#938—22no—
103#938—22no—
104#938—41no—
105#938—41no—
106C2×#214—22no—
107C2×#214—22no—
108C2×#214—41no—
109C2×#213—22no—
110C2×#213—22no—
111C2×#213—41no—
112#930—44no—
113C2×(C2×D3)⋊C4—21no—
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×(C2×D3)⋊C4D411yescharacteristic
123C2×C4⋊Dic3—21no—
124C2×C4⋊Dic3—21no—
125C2×C4⋊Dic3—21no—
126C2×C4⋊Dic3—21no—
127C2×C4⋊Dic3D411yescharacteristic
128C2×C4⋊Dic3C2311yescharacteristic
129C2×C4⋊Dic3C2311yescharacteristic
130C22×C3⋊C8C2311yescharacteristic
131C22×C3⋊C8C2311yescharacteristic
132C2×ΓL(1,𝔽25)—22no—
133C2×ΓL(1,𝔽25)—22no—
134C2×ΓL(1,𝔽25)—41no—
135C2×D3×C8—22no—
136C2×D3×C8—22no—
137C2×D3×C8—41no—
138#897—22no—
139#897—22no—
140#897—41no—
141#897—41no—
142#895—22no—
143#895—22no—
144#895—41no—
145#895—41no—
146#875—22no—
147#875—22no—
148C4×D12—22no—
149C4×D12—22no—
150C3×#102—22no—
151C3×#102D414yescomplemented
152C3×#97—22no—
153C3×#95—21no—
154C3⋊#95—21no—
155C3⋊#95—21no—
156#821—22no—
157#821—41no—
158(C2×D3)⋊C8—22no—
159(C2×D3)⋊C8—22no—
160#816—22no—
161#816—41no—
162#810—22no—
163#809—22no—
164#807—22no—
165#807—22no—
166C4⋊(C3⋊C8)D414yescomplemented
167C22×SD16—31no—
168C22×D8—31no—
169C22×M16—31no—
170C23×C8—31no—
171C2×#124—31no—
172C2×C22⋊Q8—31no—
173C2×C22⋊Q8—31no—
174C2×#121—31no—
175C2×#121—31no—
176C2×#121—31no—
177C2×#121—31no—
178C2×#121—61no—
179C2×C4×D4—31no—
180C2×C4×D4C2×D311yescharacteristic
181#468—64no—
182#466—64no—
183#463—64no—
184#435—64no—
185C2×#107—31no—
186C2×#107—31no—
187C2×C4⋊C8—31no—
188C2×#103—31no—
189C2×#103—31no—
190C2×#103—31no—
191C2×#102—31no—
192C2×#102—31no—
193C2×#102—31no—
194C2×#102C2×D311yescharacteristic
195C2×#102C2×D311yescharacteristic
196C2×C22⋊C8—31no—
197C2×C22⋊C8—31no—
198C2×#97C2×D311yescharacteristic
199#399—61no—
200#394—61no—
201#394—61no—
202#392—61no—
203#390—61no—
204#390—61no—
205#384—31no—
206#380—31no—
207#380—31no—
208#380—61no—
209C4×C4⋊C4C2×D311yescharacteristic
210#340—31no—
211#340—31no—
212#340C2×D311yescharacteristic
213#340C2×D311yescharacteristic
214C24×C3—21no—
215C23×D3—21no—
216C23×D3C2×D411yescharacteristic
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—21no—
227C22×C3×C4—42no—
228C22×C3×C4—42no—
229C22×C3×C4—42no—
230C22×C3×C4C2×D411yescharacteristic
231C22×C3×C4C2×D411yescharacteristic
232C22×C3×C4C2411yescharacteristic
233C2×#67—42no—
234C2×#67—42no—
235C2×#67—42no—
236C2×#67—42no—
237C2×#67—81no—
238C2×#67—81no—
239C22×Dic3—21no—
240C22×Dic3—21no—
241C22×Dic3—21no—
242C22×Dic3C2×D411yescharacteristic
243C22×Dic3C2×D411yescharacteristic
244C2×D12—22no—
245C2×D12—22no—
246C2×D12—21no—
247C2×D12—21no—
248C2×D12—21no—
249C2×D12—21no—
250C2×D12—21no—
251C2×D12—21no—
252C2×D12—41no—
253C2×D12—42no—
254C2×D12—42no—
255C2×D12—42no—
256C2×D12—42no—
257C2×D12—81no—
258C2×D12—81no—
259C2×C4×D3—21no—
260C2×C4×D3—21no—
261C2×C4×D3—21no—
262C2×C4×D3—21no—
263C2×C4×D3—21no—
264C2×C4×D3—21no—
265C2×C4×D3—21no—
266C2×C4×D3—21no—
267C2×C4×D3—21no—
268C2×C4×D3—21no—
269C2×C4×D3—21no—
270C2×C4×D3—21no—
271C2×Dic6—21no—
272C2×Dic6—21no—
273C2×Dic6—21no—
274C2×Dic6—21no—
275C2×Dic6—21no—
276C2×Dic6—21no—
277C2×C3×C8—21no—
278C2×C3×C8—21no—
279C2×C3×C8—21no—
280C2×C3×C8—21no—
281C2×C3×C8—21no—
282C2×C3×C8C2×D412yes—
283C3×C4⋊C4—21no—
284C3×C4⋊C4—21no—
285C3×C4⋊C4—21no—
286C3×C4⋊C4—21no—
287C3×C4⋊C4C2×D412yes—
288C3×C4⋊C4#4112yes—
289C3×C22⋊C4—42no—
290C3×C42—81no—
291C3×C42C2×D412yes—
292C3×C42#4112yes—
293#217—42no—
294#217—42no—
295#214—44no—
296#213—44no—
297(C2×D3)⋊C4—22no—
298(C2×D3)⋊C4—22no—
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—42no—
306(C2×D3)⋊C4—42no—
307C4⋊Dic3—22no—
308C4⋊Dic3—21no—
309C4⋊Dic3—21no—
310C4⋊Dic3—21no—
311C4⋊Dic3—21no—
312C4⋊Dic3—42no—
313C4⋊Dic3—42no—
314C4⋊Dic3—42no—
315C4⋊Dic3—81no—
316C2×C3⋊C8—21no—
317C2×C3⋊C8—21no—
318C2×C3⋊C8—21no—
319C2×C3⋊C8—21no—
320C2×C3⋊C8C2×D412yes—
321C2×C3⋊C8C2×D412yes—
322ΓL(1,𝔽25)—44no—
323D3×C8—44no—
324C22×Q8—31no—
325C22×D4—31no—
326C22×D4—31no—
327C22×D4—61no—
328C22×D4—61no—
329C22×D4—61no—
330C22×D4—61no—
331C22×D4C22×D311yescharacteristic
332C23×C4—21no—
333C23×C4—31no—
334C23×C4—31no—
335C2×SD16—62no—
336C2×SD16—62no—
337C2×SD16—121no—
338C2×D8—62no—
339C2×D8—62no—
340C2×D8—121no—
341C2×M16—62no—
342C2×M16—62no—
343C2×M16—121no—
344C22×C8—31no—
345C22×C8—31no—
346C22×C8—62no—
347C22×C8—62no—
348C22×C8—121no—
349C22×C8C22×D311yescharacteristic
350C22×C8C22×D311yescharacteristic
351#124—62no—
352#124—62no—
353C22⋊Q8—62no—
354C22⋊Q8—62no—
355C22⋊Q8—121no—
356C22⋊Q8—121no—
357#121—62no—
358#121—62no—
359#121—62no—
360#121—62no—
361#121—121no—
362#121—121no—
363#121—121no—
364#121—121no—
365#121—124no—
366C4×D4—22no—
367C4×D4—22no—
368C4×D4—62no—
369C4×D4—62no—
370C2×C4⋊C4—31no—
371C2×C4⋊C4—31no—
372C2×C4⋊C4—31no—
373C2×C4⋊C4—61no—
374C2×C4⋊C4—61no—
375C2×C4⋊C4—61no—
376C2×C4⋊C4—61no—
377C2×C4⋊C4C22×D311yescharacteristic
378C2×C4⋊C4C22×D311yescharacteristic
379C2×C4⋊C4C22×D311yescharacteristic
380C2×C22⋊C4—21no—
381C2×C22⋊C4—31no—
382C2×C22⋊C4—31no—
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×C22⋊C4—61no—
393C2×C42—21no—
394C2×C42C22×D311yescharacteristic
395#107—62no—
396#107—62no—
397C4⋊C8—34no—
398#103—62no—
399#103—62no—
400#103—121no—
401#102—22no—
402#102—62no—
403#102—62no—
404#102—121no—
405#102D1214yescomplemented
406C22⋊C8—62no—
407C22⋊C8—62no—
408#97—22no—
409#95—21no—
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—21no—
428C22×D3—21no—
429C22×D3—21no—
430C22×D3—21no—
431C22×D3—21no—
432C22×D3—21no—
433C22×D3—41no—
434C22×D3—41no—
435C22×D3—41no—
436C22×D3—41no—
437C22×D3—41no—
438C22×D3—41no—
439C22×D3—41no—
440C22×D3AGL(1,ℤ/8)12yes—
441C3×D4—22no—
442C3×D4—22no—
443C3×D4—41no—
444C3×D4—41no—
445C2×C3×C4—21no—
446C2×C3×C4—21no—
447C2×C3×C4—21no—
448C2×C3×C4—21no—
449C2×C3×C4—22no—
450C2×C3×C4—22no—
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—84no—
459C2×C3×C4#12112yes—
460C2×C3×C4#12112yes—
461C2×C3×C4C22×D411yescharacteristic
462C2×C3×C4C22×D411yescharacteristic
463C2×C3×C4C2×#4111yescharacteristic
464C2×C3×C4C2×#4111yescharacteristic
465C2×C3×C4H(5,𝔽2)11yescharacteristic
466C2×C3×C4H(5,𝔽2)11yescharacteristic
467#67—84no—
468#67—84no—
469C2×Dic3—21no—
470C2×Dic3—21no—
471C2×Dic3—21no—
472C2×Dic3—21no—
473C2×Dic3—21no—
474C2×Dic3—21no—
475C2×Dic3—41no—
476C2×Dic3—41no—
477C2×Dic3—41no—
478C2×Dic3—41no—
479C2×Dic3—41no—
480C2×Dic3—41no—
481C2×Dic3—41no—
482C2×Dic3—41no—
483C2×Dic3—41no—
484D12—44no—
485D12—41no—
486D12—41no—
487D12—41no—
488D12—41no—
489D12—84no—
490D12—84no—
491C4×D3—41no—
492C4×D3—41no—
493C4×D3—41no—
494C4×D3—41no—
495C4×D3—41no—
496C4×D3—41no—
497C4×D3—41no—
498C4×D3—41no—
499Dic6—41no—
500Dic6—41no—
501Dic6—41no—
502Dic6—41no—
503C3×C8—22no—
504C3×C8—41no—
505C3⋊C8—22no—
506C3⋊C8—22no—
507C24—21no—
508C24—31no—
509C24—31no—
510C24—61no—
511C2×Q8—61no—
512C2×Q8—61no—
513C2×Q8—61no—
514C2×Q8—61no—
515C2×Q8—61no—
516C2×Q8—61no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—62no—
523C2×D4—62no—
524C2×D4—61no—
525C2×D4—61no—
526C2×D4—61no—
527C2×D4—61no—
528C2×D4—61no—
529C2×D4—61no—
530C2×D4—121no—
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—
541C2×D4—241no—
542C2×D4—241no—
543C2×D4C2×D1212yes—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—31no—
548C22×C4—31no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—61no—
553C22×C4—61no—
554C22×C4—61no—
555C22×C4—61no—
556C22×C4—61no—
557C22×C4—61no—
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—61no—
567C22×C4D3×D411yescharacteristic
568C22×C4D3×D411yescharacteristic
569C22×C4C23×D311yescharacteristic
570SD16—124no—
571D8—124no—
572M16—124no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—32no—
579C2×C8—32no—
580C2×C8—61no—
581C2×C8—61no—
582C2×C8—61no—
583C2×C8—61no—
584C2×C8—124no—
585C2×C8C2×D1212yes—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—62no—
591C4⋊C4—61no—
592C4⋊C4—61no—
593C4⋊C4—61no—
594C4⋊C4—61no—
595C4⋊C4—122no—
596C4⋊C4—122no—
597C4⋊C4—122no—
598C4⋊C4—241no—
599C4⋊C4C2×D1212yes—
600C4⋊C4#23512yes—
601C22⋊C4—42no—
602C22⋊C4—62no—
603C22⋊C4—62no—
604C22⋊C4—122no—
605C22⋊C4—122no—
606C22⋊C4—122no—
607C22⋊C4—122no—
608C22⋊C4—122no—
609C22⋊C4—122no—
610C22⋊C4—122no—
611C22⋊C4—122no—
612C22⋊C4—122no—
613C22⋊C4—122no—
614C42—81no—
615C42#23512yes—
616C42D3×D412yes—
617C22×C3—42no—
618C22×C3—42no—
619C22×C3—42no—
620C22×C3—81no—
621C22×C3—81no—
622C22×C3—81no—
623C22×C3—81no—
624C22×C3C2×#12111yescharacteristic
625C22×C3D4211yescharacteristic
626C22×C3#54611yescharacteristic
627C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
628C22×C3#57511yescharacteristic
629C22×C3#57611yescharacteristic
630C22×C3#57811yescharacteristic
631C2×D3—22no—
632C2×D3—22no—
633C2×D3—22no—
634C2×D3—41no—
635C2×D3—41no—
636C2×D3—41no—
637C2×D3—41no—
638C2×D3—41no—
639C2×D3—41no—
640C2×D3—41no—
641C2×D3—41no—
642C2×D3—41no—
643C2×D3—41no—
644C2×D3—41no—
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—22no—
654C3×C4—42no—
655C3×C4—42no—
656C3×C4—81no—
657C3×C4#53211yescharacteristic
658C3×C4#54011yescharacteristic
659C3×C4D4211yescharacteristic
660C3×C4#55011yescharacteristic
661Dic3—41no—
662Dic3—41no—
663Dic3—81no—
664Dic3—81no—
665Dic3—81no—
666C23—22no—
667C23—32no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—61no—
675C23—61no—
676C23—61no—
677C23—61no—
678C23—61no—
679C23—61no—
680C23—61no—
681C23—61no—
682C23—61no—
683C23—61no—
684C23—61no—
685C23—61no—
686C23—61no—
687C23—121no—
688C23—121no—
689C23—121no—
690C23—121no—
691C23—121no—
692C23—121no—
693C23—121no—
694C23C2×D3×D411yescharacteristic
695Q8—121no—
696Q8—121no—
697Q8—121no—
698Q8—121no—
699D4—22no—
700D4—22no—
701D4—41no—
702D4—41no—
703D4—124no—
704D4—121no—
705D4—121no—
706D4—121no—
707D4—121no—
708D4—244no—
709D4—244no—
710D4—244no—
711D4—244no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—61no—
728C2×C4—61no—
729C2×C4—61no—
730C2×C4—61no—
731C2×C4—84no—
732C2×C4—121no—
733C2×C4—121no—
734C2×C4—121no—
735C2×C4—121no—
736C2×C4—121no—
737C2×C4—121no—
738C2×C4—121no—
739C2×C4—121no—
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#88412yes—
750C2×C4#88412yes—
751C2×C4C22×D1211yescharacteristic
752C2×C4C2×#23511yescharacteristic
753C2×C4C2×#23511yescharacteristic
754C2×C4C2×D3×D411yescharacteristic
755C2×C4#100911yescharacteristic
756C2×C4#100911yescharacteristic
757C8—22no—
758C8—41no—
759C8—62no—
760C8—62no—
761C2×C3—82no—
762C2×C3#242811yescharacteristic
763C2×C3#305511yescharacteristic
764C2×C3#306111yescharacteristic
765C2×C3#326411yescharacteristic
766C2×C3#326911yescharacteristic
767C2×C3#330811yescharacteristic
768C2×C3#331911yescharacteristic
769D3—42no—
770D3—81no—
771D3—161no—
772C22—42no—
773C22—42no—
774C22—42no—
775C22—62no—
776C22—62no—
777C22—62no—
778C22—81no—
779C22—81no—
780C22—81no—
781C22—81no—
782C22—121no—
783C22—121no—
784C22—121no—
785C22—121no—
786C22—121no—
787C22—121no—
788C22—121no—
789C22—121no—
790C22—121no—
791C22—121no—
792C22—121no—
793C22—241no—
794C22—241no—
795C22—241no—
796C22—241no—
797C22—241no—
798C22—241no—
799C22—241no—
800C22C2×#88411yescharacteristic
801C22D4×D1211yescharacteristic
802C22#555011yescharacteristic
803C22D3×AGL(1,ℤ/8)11yescharacteristic
804C22#577311yescharacteristic
805C22#577411yescharacteristic
806C22#577911yescharacteristic
807C4—22no—
808C4—22no—
809C4—42no—
810C4—42no—
811C4—81no—
812C4—121no—
813C4—121no—
814C4—241no—
815C4—241no—
816C4—241no—
817C4#547711yescharacteristic
818C4#553511yescharacteristic
819C4D4×D1211yescharacteristic
820C4#555311yescharacteristic
821C3#2539711yescharacteristic, complemented, Sylow
822C2—82no—
823C2—122no—
824C2—241no—
825C2—481no—
826C2#7348711yescharacteristic
827C2#7889111yescharacteristic
828C2#7893011yescharacteristic
829C2#7979711yescharacteristic
830C2#7979811yescharacteristic
831C2#7987811yescharacteristic
832C2#7988311yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1762C2
socleC23×C3C22×D4
hypercenter#1762D3
hypocenterC3#25397
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. #82417C2semidirect
2. C2×#5016C2semidirect
3. C2×#4780C2semidirect
4. C2×#4775C2semidirect
5. C2×#4706C2semidirect
6. #73798C2semidirect
7. C3×#1762C2semidirect
8. #70205C2semidirect
9. #70204C2semidirect
10. #69821C2semidirect
11. #69466C2semidirect
12. #68885C2semidirect
13. #68882C2semidirect
14. #68825C2semidirect
15. #68822C2semidirect
78. #1762D3semidirect
151. C3×#102D4semidirect
166. C4⋊(C3⋊C8)D4semidirect
405. #102D12semidirect
821. C3#25397semidirect

Maximal subgroups

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

subgroupindex
#824172
C2×#50162
C2×#47802
C2×#47752
C2×#47062
#737982
C3×#17622
#702052
#702042
#698212
#694662
#688852
#688822
#688252
#688222
#253973