Finite Group Databasebeta

← #10846069

Subgroups — #10846069

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
1C2×#4886C211yesmaximal, characteristic, complemented
2C2×#4883C211yesmaximal, characteristic, complemented
3C2×#4844C211yesmaximal, characteristic, complemented
4C2×#4836C211yesmaximal, characteristic, complemented
5#74368C211yesmaximal, characteristic, complemented
6#73798C211yesmaximal, characteristic, complemented
7C3×#1947C211yesmaximal, characteristic, complemented
8#70635C211yesmaximal, characteristic, complemented
9#70634C211yesmaximal, characteristic, complemented
10#69581C211yesmaximal, characteristic, complemented
11#69474C211yesmaximal, characteristic, complemented
12#68887C211yesmaximal, characteristic, complemented
13#68886C211yesmaximal, characteristic, complemented
14#68885C211yesmaximal, characteristic, complemented
15#68882C211yesmaximal, characteristic, complemented
16#25397—31nomaximal, Sylow
17C22×D24C2211yescharacteristic
18C22×#204C2211yescharacteristic
19C22×ΓL(1,𝔽25)C2211yescharacteristic
20C22×D3×C8C2211yescharacteristic
21C2×#897C2211yescharacteristic
22C2×#897C2211yescharacteristic
23C2×#895—21no—
24C2×#895C2211yescharacteristic
25C2×#895C2211yescharacteristic
26C2×#895C2211yescharacteristic
27C2×#895C2211yescharacteristic
28C2×#875C2211yescharacteristic
29C2×C4×D12C2211yescharacteristic
30C2×C4×D12C2211yescharacteristic
31C2×C3×#107C2211yescharacteristic
32C2×C3×#107C2211yescharacteristic
33C2×C3×C4⋊C8C2211yescharacteristic
34C3×#384C2211yescharacteristic
35C3×C4×C4⋊C4C2211yescharacteristic
36C2×#821C2211yescharacteristic
37C2×(C2×D3)⋊C8C2211yescharacteristic
38C2×(C2×D3)⋊C8C2211yescharacteristic
39C2×#816C2211yescharacteristic
40#4991—21no—
41#4991—21no—
42#4987—21no—
43#4987C2211yescharacteristic
44#4987C2211yescharacteristic
45C2×#810C2211yescharacteristic
46C2×#810C2211yescharacteristic
47C2×#809C2211yescharacteristic
48C2×#809C2211yescharacteristic
49C2×#809C2211yescharacteristic
50C2×#809C2211yescharacteristic
51#4939—21no—
52#4939—21no—
53C2×#803C2211yescharacteristic
54#4886—24no—
55#4883—24no—
56#4844—24no—
57#4836—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#1947D311yescharacteristic, complemented
76#1895—31no—
77#1892—31no—
78#1762—31no—
79C22×D12—21no—
80C22×D12—21no—
81C22×D12—21no—
82C22×D12—21no—
83C22×D12D411yescharacteristic
84C22×D12C2311yescharacteristic
85C22×D12C2311yescharacteristic
86C22×C4×D3—21no—
87C22×C4×D3C2311yescharacteristic
88C22×C4×D3C2311yescharacteristic
89C22×Dic6C2311yescharacteristic
90C22×C3×C8C2311yescharacteristic
91C22×C3×C8C2311yescharacteristic
92C2×C3×C4⋊C4—21no—
93C2×C3×C4⋊C4—21no—
94C2×C3×C4⋊C4C2311yescharacteristic
95C2×C3×C4⋊C4C2311yescharacteristic
96C2×C3×C4⋊C4C2311yescharacteristic
97C2×C3×C4⋊C4C2311yescharacteristic
98C2×C3×C42—21no—
99C2×C3×C42C2311yescharacteristic
100C2×(C2×D3)⋊C4—21no—
101C2×(C2×D3)⋊C4—21no—
102C2×(C2×D3)⋊C4—21no—
103C2×(C2×D3)⋊C4—21no—
104C2×(C2×D3)⋊C4—21no—
105C2×(C2×D3)⋊C4—21no—
106C2×(C2×D3)⋊C4—21no—
107C2×(C2×D3)⋊C4—21no—
108C2×(C2×D3)⋊C4—21no—
109C2×(C2×D3)⋊C4—21no—
110C2×(C2×D3)⋊C4—21no—
111C2×(C2×D3)⋊C4D411yescharacteristic
112C2×(C2×D3)⋊C4D411yescharacteristic
113C2×C4⋊Dic3—21no—
114C2×C4⋊Dic3—21no—
115C2×C4⋊Dic3D411yescharacteristic
116C2×C4⋊Dic3C2311yescharacteristic
117C22×C3⋊C8C2311yescharacteristic
118C22×C3⋊C8C2311yescharacteristic
119C2×D24—22no—
120C2×D24—22no—
121C2×D24—41no—
122C2×#204—22no—
123C2×#204—22no—
124C2×#204—41no—
125C2×ΓL(1,𝔽25)—22no—
126C2×ΓL(1,𝔽25)—22no—
127C2×ΓL(1,𝔽25)—41no—
128C2×D3×C8—22no—
129C2×D3×C8—22no—
130C2×D3×C8—41no—
131#897—22no—
132#897—22no—
133#897—41no—
134#897—41no—
135#895—22no—
136#895—22no—
137#895—22no—
138#895—22no—
139#895—41no—
140#895—41no—
141#895—41no—
142#895—41no—
143#895—44no—
144#875—22no—
145#875—22no—
146C4×D12—22no—
147C4×D12—22no—
148C4×D12—22no—
149C4×D12—22no—
150C3×#107—22no—
151C3×#107—22no—
152C3×C4⋊C8D414yescomplemented
153C3×#95—21no—
154C3⋊#95—21no—
155C3⋊#95—21no—
156#821—22no—
157(C2×D3)⋊C8—22no—
158(C2×D3)⋊C8—22no—
159#816—22no—
160#810—22no—
161#810—41no—
162#809—22no—
163#809—22no—
164#809—41no—
165#809D414yescomplemented
166#803—22no—
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×D4—31no—
181#468—64no—
182#466—64no—
183#463—64no—
184#435—64no—
185C2×#107C2×D311yescharacteristic
186C2×#107C2×D311yescharacteristic
187C2×C4⋊C8C2×D311yescharacteristic
188C2×#103—31no—
189C2×#103—31no—
190C2×#103—31no—
191C2×#102—31no—
192C2×#102—31no—
193C2×#102—31no—
194C2×#102—31no—
195C2×#102—31no—
196C2×C22⋊C8—31no—
197C2×C22⋊C8—31no—
198C2×#97—31no—
199#399—61no—
200#394—61no—
201#394—61no—
202#392—61no—
203#390—61no—
204#390—61no—
205#384C2×D311yescharacteristic
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
214C23×D3—21no—
215C23×D3—21no—
216C23×D3C2×D411yescharacteristic
217C23×D3C2×D411yescharacteristic
218C22×C3×C4—21no—
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4C2×D411yescharacteristic
223C22×C3×C4C2×D411yescharacteristic
224C22×C3×C4C2411yescharacteristic
225C22×Dic3—21no—
226C22×Dic3—21no—
227C22×Dic3C2×D411yescharacteristic
228C22×Dic3C2×D411yescharacteristic
229C2×D12—21no—
230C2×D12—21no—
231C2×D12—21no—
232C2×D12—21no—
233C2×D12—22no—
234C2×D12—22no—
235C2×D12—21no—
236C2×D12—21no—
237C2×D12—21no—
238C2×D12—21no—
239C2×D12—21no—
240C2×D12—21no—
241C2×D12—21no—
242C2×D12—41no—
243C2×D12—42no—
244C2×D12—42no—
245C2×D12—42no—
246C2×D12—42no—
247C2×D12—42no—
248C2×D12—42no—
249C2×D12—42no—
250C2×D12—42no—
251C2×D12—81no—
252C2×D12—81no—
253C2×D12—81no—
254C2×D12—81no—
255C2×D12C2×D412yes—
256C2×C4×D3—21no—
257C2×C4×D3—21no—
258C2×C4×D3—21no—
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—42no—
269C2×C4×D3—42no—
270C2×C4×D3—42no—
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×C8C2×D412yes—
282C2×C3×C8C2×D412yes—
283C3×C4⋊C4—21no—
284C3×C4⋊C4—21no—
285C3×C4⋊C4—21no—
286C3×C4⋊C4—21no—
287C3×C4⋊C4—21no—
288C3×C4⋊C4—21no—
289C3×C4⋊C4—42no—
290C3×C4⋊C4—81no—
291C3×C4⋊C4C2×D412yes—
292C3×C4⋊C4#4112yes—
293C3×C42—81no—
294C3×C42C2×D412yes—
295C3×C42#4112yes—
296(C2×D3)⋊C4—22no—
297(C2×D3)⋊C4—22no—
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—42no—
306(C2×D3)⋊C4—42no—
307(C2×D3)⋊C4—42no—
308(C2×D3)⋊C4—42no—
309C4⋊Dic3—22no—
310C4⋊Dic3—21no—
311C4⋊Dic3—21no—
312C4⋊Dic3—42no—
313C4⋊Dic3—42no—
314C2×C3⋊C8—21no—
315C2×C3⋊C8—21no—
316C2×C3⋊C8—21no—
317C2×C3⋊C8—21no—
318C2×C3⋊C8—21no—
319C2×C3⋊C8C2×D412yes—
320D24—44no—
321#204—44no—
322ΓL(1,𝔽25)—44no—
323D3×C8—44no—
324C22×Q8—31no—
325C22×D4—31no—
326C22×D4—31no—
327C22×D4—31no—
328C22×D4—61no—
329C22×D4—61no—
330C22×D4—61no—
331C22×D4—61no—
332C23×C4—31no—
333C23×C4—31no—
334C23×C4—61no—
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—62no—
367C4×D4—62no—
368C4×D4—62no—
369C4×D4—62no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—31no—
373C2×C4⋊C4—31no—
374C2×C4⋊C4—61no—
375C2×C4⋊C4—61no—
376C2×C4⋊C4C22×D311yescharacteristic
377C2×C4⋊C4C22×D311yescharacteristic
378C2×C4⋊C4C22×D311yescharacteristic
379C2×C4⋊C4C22×D311yescharacteristic
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×C22⋊C4—61no—
393C2×C42—21no—
394C2×C42C22×D311yescharacteristic
395#107—22no—
396#107—22no—
397C4⋊C8D1214yescomplemented
398#103—62no—
399#103—62no—
400#103—121no—
401#102—34no—
402#102—62no—
403#102—62no—
404#102—62no—
405#102—121no—
406C22⋊C8—62no—
407C22⋊C8—62no—
408#97—62no—
409#95—21no—
410#95—61no—
411#95—61no—
412C23×C3C22×D411yescharacteristic
413C22×D3—21no—
414C22×D3—21no—
415C22×D3—21no—
416C22×D3—21no—
417C22×D3—21no—
418C22×D3—21no—
419C22×D3—21no—
420C22×D3—21no—
421C22×D3—22no—
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×D3AGL(1,ℤ/8)12yes—
441C2×C3×C4—21no—
442C2×C3×C4—21no—
443C2×C3×C4—21no—
444C2×C3×C4—21no—
445C2×C3×C4—22no—
446C2×C3×C4—22no—
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—41no—
454C2×C3×C4—41no—
455C2×C3×C4—41no—
456C2×C3×C4—41no—
457C2×C3×C4#12112yes—
458C2×C3×C4#12112yes—
459C2×C3×C4C22×D411yescharacteristic
460C2×C3×C4C22×D411yescharacteristic
461C2×C3×C4C2×#4111yescharacteristic
462C2×C3×C4C2×#4111yescharacteristic
463C2×C3×C4H(5,𝔽2)11yescharacteristic
464C2×C3×C4H(5,𝔽2)11yescharacteristic
465C2×Dic3—21no—
466C2×Dic3—21no—
467C2×Dic3—21no—
468C2×Dic3—21no—
469C2×Dic3—21no—
470C2×Dic3—21no—
471C2×Dic3—41no—
472C2×Dic3—41no—
473C2×Dic3—41no—
474C2×Dic3—41no—
475C2×Dic3—41no—
476C2×Dic3—41no—
477D12—22no—
478D12—22no—
479D12—44no—
480D12—41no—
481D12—41no—
482D12—41no—
483D12—41no—
484D12—41no—
485D12—41no—
486D12—84no—
487D12—84no—
488D12—84no—
489D12—84no—
490C4×D3—41no—
491C4×D3—41no—
492C4×D3—41no—
493C4×D3—41no—
494C4×D3—41no—
495C4×D3—41no—
496C4×D3—41no—
497C4×D3—41no—
498C4×D3—84no—
499Dic6—41no—
500Dic6—41no—
501Dic6—41no—
502Dic6—41no—
503C3×C8—22no—
504C3×C8—22no—
505C3⋊C8—22no—
506C3⋊C8—41no—
507C24—31no—
508C24—31no—
509C24—61no—
510C24—61no—
511C2×Q8—61no—
512C2×Q8—61no—
513C2×Q8—61no—
514C2×Q8—61no—
515C2×Q8—61no—
516C2×Q8—61no—
517C2×D4—32no—
518C2×D4—62no—
519C2×D4—62no—
520C2×D4—61no—
521C2×D4—61no—
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—121no—
532C2×D4—122no—
533C2×D4—122no—
534C2×D4—122no—
535C2×D4—122no—
536C2×D4—122no—
537C2×D4—122no—
538C2×D4—122no—
539C2×D4—122no—
540C2×D4—241no—
541C2×D4—241no—
542C2×D4—241no—
543C2×D4—241no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—31no—
549C22×C4—31no—
550C22×C4—61no—
551C22×C4—61no—
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—122no—
565C22×C4—122no—
566C22×C4—122no—
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—32no—
578C2×C8—61no—
579C2×C8—61no—
580C2×C8—61no—
581C2×C8—61no—
582C2×C8—61no—
583C2×C8—124no—
584C2×C8C2×D1212yes—
585C2×C8C2×D1212yes—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—42no—
593C4⋊C4—62no—
594C4⋊C4—61no—
595C4⋊C4—61no—
596C4⋊C4—81no—
597C4⋊C4—122no—
598C4⋊C4—122no—
599C4⋊C4D3×D412yes—
600C4⋊C4#23912yes—
601C22⋊C4—62no—
602C22⋊C4—62no—
603C22⋊C4—122no—
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—
615C42C2×D1212yes—
616C42#23912yes—
617C22×C3C2×#12111yescharacteristic
618C22×C3D4211yescharacteristic
619C22×C3#54611yescharacteristic
620C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
621C22×C3#57511yescharacteristic
622C22×C3#57611yescharacteristic
623C22×C3#57811yescharacteristic
624C2×D3—22no—
625C2×D3—22no—
626C2×D3—22no—
627C2×D3—41no—
628C2×D3—41no—
629C2×D3—41no—
630C2×D3—41no—
631C2×D3—41no—
632C2×D3—42no—
633C2×D3—41no—
634C2×D3—42no—
635C2×D3—41no—
636C2×D3—42no—
637C2×D3—41no—
638C2×D3—41no—
639C2×D3—41no—
640C2×D3—41no—
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—22no—
654C3×C4—42no—
655C3×C4—42no—
656C3×C4—81no—
657C3×C4—81no—
658C3×C4#53211yescharacteristic
659C3×C4#54011yescharacteristic
660C3×C4D4211yescharacteristic
661C3×C4#55011yescharacteristic
662Dic3—41no—
663Dic3—41no—
664Dic3—81no—
665Dic3—81no—
666C23—32no—
667C23—61no—
668C23—61no—
669C23—61no—
670C23—61no—
671C23—61no—
672C23—61no—
673C23—61no—
674C23—61no—
675C23—61no—
676C23—61no—
677C23—61no—
678C23—61no—
679C23—62no—
680C23—61no—
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—121no—
696Q8—121no—
697Q8—121no—
698Q8—121no—
699D4—62no—
700D4—62no—
701D4—124no—
702D4—121no—
703D4—121no—
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—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—61no—
729C2×C4—61no—
730C2×C4—61no—
731C2×C4—61no—
732C2×C4—61no—
733C2×C4—61no—
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—244no—
749C2×C4#89512yes—
750C2×C4#89512yes—
751C2×C4C22×D1211yescharacteristic
752C2×C4C2×D3×D411yescharacteristic
753C2×C4C2×#23911yescharacteristic
754C2×C4C2×#23911yescharacteristic
755C2×C4#100911yescharacteristic
756C2×C4#100911yescharacteristic
757C8—22no—
758C8—22no—
759C8—62no—
760C8—121no—
761C2×C3#242811yescharacteristic
762C2×C3#305511yescharacteristic
763C2×C3#306111yescharacteristic
764C2×C3#326411yescharacteristic
765C2×C3#326911yescharacteristic
766C2×C3#330811yescharacteristic
767C2×C3#331911yescharacteristic
768D3—42no—
769D3—81no—
770D3—82no—
771D3—161no—
772C22—62no—
773C22—62no—
774C22—62no—
775C22—121no—
776C22—121no—
777C22—121no—
778C22—121no—
779C22—121no—
780C22—121no—
781C22—121no—
782C22—121no—
783C22—122no—
784C22—121no—
785C22—122no—
786C22—121no—
787C22—121no—
788C22—122no—
789C22—241no—
790C22—241no—
791C22—241no—
792C22—241no—
793C22—241no—
794C22—241no—
795C22—241no—
796C22—241no—
797C22—241no—
798C22—241no—
799C22—241no—
800C22C2×#89511yescharacteristic
801C22#560911yescharacteristic
802C22#563011yescharacteristic
803C22#575711yescharacteristic
804C22#576611yescharacteristic
805C22D3×AGL(1,ℤ/8)11yescharacteristic
806C22#577711yescharacteristic
807C4—22no—
808C4—22no—
809C4—42no—
810C4—42no—
811C4—81no—
812C4—81no—
813C4—121no—
814C4—121no—
815C4—241no—
816C4—241no—
817C4D4×D1211yescharacteristic
818C4#557711yescharacteristic
819C4#569711yescharacteristic
820C4#572511yescharacteristic
821C3#2539711yescharacteristic, complemented, Sylow
822C2—122no—
823C2—241no—
824C2—242no—
825C2—481no—
826C2#7622011yescharacteristic
827C2#7915011yescharacteristic
828C2#7921111yescharacteristic
829C2#8035811yescharacteristic
830C2#8050011yescharacteristic
831C2#8098311yescharacteristic
832C2#8112111yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1947C2
socleC23×C3C22×D4
hypercenter#1947D3
hypocenterC3#25397
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1947

Complements

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

NH ≅ G/Ntype
1. C2×#4886C2semidirect
2. C2×#4883C2semidirect
3. C2×#4844C2semidirect
4. C2×#4836C2semidirect
5. #74368C2semidirect
6. #73798C2semidirect
7. C3×#1947C2semidirect
8. #70635C2semidirect
9. #70634C2semidirect
10. #69581C2semidirect
11. #69474C2semidirect
12. #68887C2semidirect
13. #68886C2semidirect
14. #68885C2semidirect
15. #68882C2semidirect
75. #1947D3semidirect
152. C3×C4⋊C8D4semidirect
165. #809D4semidirect
397. C4⋊C8D12semidirect
821. C3#25397semidirect

Maximal subgroups

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

subgroupindex
C2×#48862
C2×#48832
C2×#48442
C2×#48362
#743682
#737982
C3×#19472
#706352
#706342
#695812
#694742
#688872
#688862
#688852
#688822
#253973