Finite Group Databasebeta

← #10846067

Subgroups — #10846067

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×C3×#463C211yesmaximal, characteristic, complemented
2C2×#5174C211yesmaximal, characteristic, complemented
3C2×#5157C211yesmaximal, characteristic, complemented
4#82998C211yesmaximal, characteristic, complemented
5#82417C211yesmaximal, characteristic, complemented
6C2×#4836C211yesmaximal, characteristic, complemented
7#72054C211yesmaximal, characteristic, complemented
8#72043C211yesmaximal, characteristic, complemented
9#71726C211yesmaximal, characteristic, complemented
10#71609C211yesmaximal, characteristic, complemented
11#70453C211yesmaximal, characteristic, complemented
12#70270C211yesmaximal, characteristic, complemented
13#70244C211yesmaximal, characteristic, complemented
14#70203C211yesmaximal, characteristic, complemented
15#70175C211yesmaximal, characteristic, complemented
16#25397—31nomaximal, Sylow
17C22×C3×SD16C2211yescharacteristic
18C22×C3×D8C2211yescharacteristic
19C2×C3×#124C2211yescharacteristic
20C2×C3×C4×D4C2211yescharacteristic
21C2×#946C2211yescharacteristic
22C2×#946C2211yescharacteristic
23C2×#938C2211yescharacteristic
24C2×#938C2211yescharacteristic
25C2×#938C2211yescharacteristic
26C2×#938C2211yescharacteristic
27C2×#930—21no—
28C22×ΓL(1,𝔽25)C2211yescharacteristic
29C22×D3×C8C2211yescharacteristic
30C2×C4×D12C2211yescharacteristic
31C3×#463—24no—
32C2×C3×C4⋊C8C2211yescharacteristic
33C2×C3×#103C2211yescharacteristic
34C2×C3×#102C2211yescharacteristic
35C2×#835C2211yescharacteristic
36C2×#835C2211yescharacteristic
37C2×#832C2211yescharacteristic
38C2×#832C2211yescharacteristic
39C2×#832C2211yescharacteristic
40C2×#832C2211yescharacteristic
41#5212—21no—
42#5174—24no—
43#5157—24no—
44C2×(C2×D3)⋊C8C2211yescharacteristic
45C2×(C2×D3)⋊C8C2211yescharacteristic
46C2×#818C2211yescharacteristic
47C2×#818C2211yescharacteristic
48#4987C2211yescharacteristic
49#4987C2211yescharacteristic
50#4961—21no—
51#4961—21no—
52#4960—21no—
53#4957—21no—
54#4957—21no—
55#4949—21no—
56#4935C2211yescharacteristic
57C4×C4⋊Dic3C2211yescharacteristic
58C2×#803C2211yescharacteristic
59#4836—24no—
60#4551C2211yescharacteristic
61#4551C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#468—31no—
65C2×#466—31no—
66C2×#463D311yescharacteristic, complemented
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#1762—31no—
79C22×C3×Q8C2311yescharacteristic
80C22×C3×D4C2311yescharacteristic
81C22×C3×D4C2311yescharacteristic
82C23×C3×C4—21no—
83C22×#67—21no—
84C22×#67—21no—
85C22×#67—21no—
86C22×#67—21no—
87C22×D12D411yescharacteristic
88C22×C4×D3C2311yescharacteristic
89C22×C4×D3C2311yescharacteristic
90C2×C3×SD16—22no—
91C2×C3×SD16—22no—
92C2×C3×SD16—41no—
93C2×C3×D8—22no—
94C2×C3×D8—22no—
95C2×C3×D8—41no—
96C22×C3×C8C2311yescharacteristic
97C22×C3×C8C2311yescharacteristic
98C3×#124—22no—
99C3×#124—22no—
100C3×C4×D4—22no—
101C3×C4×D4—22no—
102C2×C3×C4⋊C4C2311yescharacteristic
103C2×C3×C22⋊C4—21no—
104C2×C3×C22⋊C4—21no—
105C2×C3×C22⋊C4—21no—
106C2×C3×C42C2311yescharacteristic
107C2×#217—21no—
108C2×#217—21no—
109C2×#217—21no—
110C2×#217—21no—
111#946—22no—
112#946—22no—
113#946—41no—
114#946—41no—
115#938—22no—
116#938—22no—
117#938—22no—
118#938—22no—
119#938—41no—
120#938—41no—
121#938—41no—
122#938—41no—
123#930—44no—
124C2×(C2×D3)⋊C4—21no—
125C2×(C2×D3)⋊C4—21no—
126C2×(C2×D3)⋊C4—21no—
127C2×(C2×D3)⋊C4—21no—
128C2×(C2×D3)⋊C4D411yescharacteristic
129C2×(C2×D3)⋊C4D411yescharacteristic
130C2×C4⋊Dic3—21no—
131C2×C4⋊Dic3—21no—
132C2×C4⋊Dic3D411yescharacteristic
133C2×C4⋊Dic3C2311yescharacteristic
134C2×C4⋊Dic3C2311yescharacteristic
135C2×C4⋊Dic3C2311yescharacteristic
136C2×C4⋊Dic3C2311yescharacteristic
137C2×Dic3⋊C4—21no—
138C2×Dic3⋊C4—21no—
139C2×C4×Dic3—21no—
140C22×C3⋊C8C2311yescharacteristic
141C22×C3⋊C8C2311yescharacteristic
142C2×ΓL(1,𝔽25)—22no—
143C2×ΓL(1,𝔽25)—22no—
144C2×ΓL(1,𝔽25)—41no—
145C2×D3×C8—22no—
146C2×D3×C8—22no—
147C2×D3×C8—41no—
148C4×D12—22no—
149C4×D12—22no—
150C3×C4⋊C8D414yescomplemented
151C3×#103—22no—
152C3×#102—22no—
153#835—22no—
154#835—41no—
155#832—22no—
156#832—22no—
157#832—41no—
158#832D414yescomplemented
159C3⋊#95—21no—
160C3⋊#95—21no—
161C3⋊#95—21no—
162(C2×D3)⋊C8—22no—
163(C2×D3)⋊C8—22no—
164#818—22no—
165#818—22no—
166#803—22no—
167C22×SD16C2×D311yescharacteristic
168C22×D8C2×D311yescharacteristic
169C22×M16—31no—
170C23×C8—31no—
171C2×#124C2×D311yescharacteristic
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—24no—
184#435—64no—
185C2×#107—31no—
186C2×#107—31no—
187C2×C4⋊C8C2×D311yescharacteristic
188C2×#103—31no—
189C2×#103—31no—
190C2×#103C2×D311yescharacteristic
191C2×#102—31no—
192C2×#102—31no—
193C2×#102—31no—
194C2×#102—31no—
195C2×#102C2×D311yescharacteristic
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#384—31no—
206#380—31no—
207#380—31no—
208#380—61no—
209C4×C4⋊C4—31no—
210#340—31no—
211#340—31no—
212#340—31no—
213#340—31no—
214C24×C3—21no—
215C24×C3—21no—
216C23×D3C2×D411yescharacteristic
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×Q8—21no—
224C2×C3×D4—21no—
225C2×C3×D4—21no—
226C2×C3×D4—21no—
227C2×C3×D4—21no—
228C2×C3×D4—21no—
229C2×C3×D4—21no—
230C2×C3×D4—21no—
231C2×C3×D4—21no—
232C2×C3×D4—21no—
233C2×C3×D4—21no—
234C2×C3×D4—21no—
235C2×C3×D4C2×D412yes—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—42no—
239C22×C3×C4—42no—
240C22×C3×C4—42no—
241C22×C3×C4C2×D411yescharacteristic
242C22×C3×C4C2×D411yescharacteristic
243C22×C3×C4C2411yescharacteristic
244C2×#67—42no—
245C2×#67—42no—
246C2×#67—42no—
247C2×#67—42no—
248C2×#67—42no—
249C2×#67—42no—
250C2×#67—42no—
251C2×#67—42no—
252C2×#67—81no—
253C2×#67—81no—
254C2×#67—81no—
255C2×#67—81no—
256C22×Dic3—21no—
257C22×Dic3—21no—
258C22×Dic3—21no—
259C22×Dic3—21no—
260C22×Dic3C2×D411yescharacteristic
261C22×Dic3C2×D411yescharacteristic
262C2×D12—22no—
263C2×D12—22no—
264C2×D12—41no—
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×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—44no—
278C3×D8—44no—
279C2×C3×C8—21no—
280C2×C3×C8—21no—
281C2×C3×C8—21no—
282C2×C3×C8—21no—
283C2×C3×C8C2×D412yes—
284C2×C3×C8C2×D412yes—
285C3×C4⋊C4—21no—
286C3×C4⋊C4—21no—
287C3×C22⋊C4—42no—
288C3×C22⋊C4—42no—
289C3×C22⋊C4—42no—
290C3×C42C2×D412yes—
291C3×C42#4112yes—
292#217—42no—
293#217—42no—
294#217—42no—
295#217—42no—
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—
302C4⋊Dic3—22no—
303C4⋊Dic3—21no—
304C4⋊Dic3—21no—
305C4⋊Dic3—21no—
306C4⋊Dic3—21no—
307C4⋊Dic3—21no—
308C4⋊Dic3—21no—
309C4⋊Dic3—42no—
310C4⋊Dic3—81no—
311C4⋊Dic3C2×D412yes—
312C4⋊Dic3#4112yes—
313Dic3⋊C4—42no—
314Dic3⋊C4—42no—
315C4×Dic3—81no—
316C2×C3⋊C8—21no—
317C2×C3⋊C8—21no—
318C2×C3⋊C8—21no—
319C2×C3⋊C8—21no—
320C2×C3⋊C8—21no—
321C2×C3⋊C8C2×D412yes—
322ΓL(1,𝔽25)—44no—
323D3×C8—44no—
324C22×Q8C22×D311yescharacteristic
325C22×D4—31no—
326C22×D4—61no—
327C22×D4—61no—
328C22×D4—61no—
329C22×D4—61no—
330C22×D4C22×D311yescharacteristic
331C22×D4C22×D311yescharacteristic
332C23×C4—21no—
333C23×C4—31no—
334C23×C4—31no—
335C2×SD16—22no—
336C2×SD16—22no—
337C2×SD16—41no—
338C2×D8—22no—
339C2×D8—22no—
340C2×D8—41no—
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—22no—
352#124—22no—
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—31no—
374C2×C4⋊C4—31no—
375C2×C4⋊C4—61no—
376C2×C4⋊C4—61no—
377C2×C4⋊C4—61no—
378C2×C4⋊C4—61no—
379C2×C4⋊C4C22×D311yescharacteristic
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—31no—
384C2×C22⋊C4—31no—
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—61no—
394C2×C42C22×D311yescharacteristic
395#107—62no—
396#107—62no—
397C4⋊C8#6714yescomplemented
398#103—22no—
399#103—62no—
400#103—121no—
401#102—22no—
402#102—34no—
403#102—62no—
404#102—62no—
405#102—121no—
406C22⋊C8—62no—
407C22⋊C8—62no—
408#97—62no—
409#95—61no—
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×C3—41no—
420C23×C3—41no—
421C23×C3—41no—
422C23×C3—41no—
423C23×C3—41no—
424C23×C3—41no—
425C23×C3—41no—
426C23×C3C22×D411yescharacteristic
427C22×D3—21no—
428C22×D3—21no—
429C22×D3—21no—
430C22×D3—21no—
431C22×D3—21no—
432C22×D3—21no—
433C22×D3—21no—
434C22×D3—21no—
435C22×D3—21no—
436C22×D3—21no—
437C22×D3—21no—
438C22×D3—21no—
439C22×D3—21no—
440C22×D3AGL(1,ℤ/8)12yes—
441C3×Q8—41no—
442C3×Q8—41no—
443C3×Q8—41no—
444C3×Q8—41no—
445C3×D4—22no—
446C3×D4—22no—
447C3×D4—41no—
448C3×D4—41no—
449C3×D4—41no—
450C3×D4—41no—
451C3×D4—41no—
452C3×D4—41no—
453C2×C3×C4—21no—
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×C4#12112yes—
465C2×C3×C4#12112yes—
466C2×C3×C4C22×D411yescharacteristic
467C2×C3×C4C22×D411yescharacteristic
468C2×C3×C4C2×#4111yescharacteristic
469C2×C3×C4C2×#4111yescharacteristic
470C2×C3×C4H(5,𝔽2)11yescharacteristic
471C2×C3×C4H(5,𝔽2)11yescharacteristic
472#67—84no—
473#67—84no—
474#67—84no—
475#67—84no—
476C2×Dic3—21no—
477C2×Dic3—21no—
478C2×Dic3—21no—
479C2×Dic3—22no—
480C2×Dic3—21no—
481C2×Dic3—21no—
482C2×Dic3—22no—
483C2×Dic3—21no—
484C2×Dic3—41no—
485C2×Dic3—41no—
486C2×Dic3—41no—
487C2×Dic3—41no—
488C2×Dic3—41no—
489C2×Dic3—41no—
490C2×Dic3—41no—
491C2×Dic3—41no—
492C2×Dic3—41no—
493C2×Dic3—41no—
494D12—44no—
495C4×D3—41no—
496C4×D3—41no—
497C4×D3—41no—
498C4×D3—41no—
499C4×D3—41no—
500C4×D3—41no—
501C4×D3—41no—
502C4×D3—41no—
503C3×C8—22no—
504C3×C8—22no—
505C3⋊C8—22no—
506C3⋊C8—41no—
507C24—21no—
508C24—21no—
509C24—31no—
510C24—31no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—62no—
529C2×D4—62no—
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×D4D3×D412yes—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—31no—
547C22×C4—31no—
548C22×C4—42no—
549C22×C4—42no—
550C22×C4—42no—
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—61no—
565C22×C4—61no—
566C22×C4—61no—
567C22×C4D3×D411yescharacteristic
568C22×C4D3×D411yescharacteristic
569C22×C4C23×D311yescharacteristic
570SD16—44no—
571D8—44no—
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×#6712yes—
585C2×C8C2×#6712yes—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—32no—
589C4⋊C4—32no—
590C4⋊C4—62no—
591C4⋊C4—61no—
592C4⋊C4—61no—
593C4⋊C4—61no—
594C4⋊C4—61no—
595C4⋊C4—61no—
596C4⋊C4—61no—
597C4⋊C4—122no—
598C4⋊C4—122no—
599C4⋊C4—122no—
600C4⋊C4—241no—
601C22⋊C4—42no—
602C22⋊C4—42no—
603C22⋊C4—42no—
604C22⋊C4—62no—
605C22⋊C4—62no—
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—241no—
615C42#23712yes—
616C42C2×#6712yes—
617C22×C3—42no—
618C22×C3—42no—
619C22×C3—42no—
620C22×C3—81no—
621C22×C3—81no—
622C22×C3—81no—
623C22×C3—81no—
624C22×C3—81no—
625C22×C3—81no—
626C22×C3—81no—
627C22×C3—81no—
628C22×C3—81no—
629C22×C3—81no—
630C22×C3—81no—
631C22×C3C2×#12111yescharacteristic
632C22×C3D4211yescharacteristic
633C22×C3#54611yescharacteristic
634C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
635C22×C3#57511yescharacteristic
636C22×C3#57611yescharacteristic
637C22×C3#57811yescharacteristic
638C2×D3—22no—
639C2×D3—22no—
640C2×D3—22no—
641C2×D3—41no—
642C2×D3—41no—
643C2×D3—41no—
644C2×D3—41no—
645C2×D3—41no—
646C2×D3—41no—
647C2×D3—41no—
648C2×D3—41no—
649C2×D3—41no—
650C2×D3—41no—
651C2×D3—41no—
652C3×C4—22no—
653C3×C4—22no—
654C3×C4—81no—
655C3×C4—81no—
656C3×C4#53211yescharacteristic
657C3×C4#54011yescharacteristic
658C3×C4D4211yescharacteristic
659C3×C4#55011yescharacteristic
660Dic3—41no—
661Dic3—41no—
662Dic3—42no—
663Dic3—42no—
664Dic3—81no—
665Dic3—81no—
666C23—22no—
667C23—32no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—61no—
682C23—61no—
683C23—61no—
684C23—61no—
685C23—61no—
686C23—61no—
687C23—61no—
688C23—61no—
689C23—61no—
690C23—61no—
691C23—61no—
692C23—61no—
693C23—61no—
694C23C2×D3×D411yescharacteristic
695Q8—41no—
696Q8—41no—
697Q8—41no—
698Q8—41no—
699D4—22no—
700D4—22no—
701D4—41no—
702D4—41no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—124no—
708D4—244no—
709D4—244no—
710D4—244no—
711D4—244no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—62no—
726C2×C4—61no—
727C2×C4—62no—
728C2×C4—61no—
729C2×C4—61no—
730C2×C4—84no—
731C2×C4—121no—
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#93812yes—
750C2×C4#93812yes—
751C2×C4C2×D3×D411yescharacteristic
752C2×C4C2×#23711yescharacteristic
753C2×C4#100411yescharacteristic
754C2×C4D3×#4111yescharacteristic
755C2×C4#100911yescharacteristic
756C2×C4C22×#6711yescharacteristic
757C8—22no—
758C8—22no—
759C8—62no—
760C8—121no—
761C2×C3—82no—
762C2×C3—161no—
763C2×C3#242811yescharacteristic
764C2×C3#305511yescharacteristic
765C2×C3#306111yescharacteristic
766C2×C3#326411yescharacteristic
767C2×C3#326911yescharacteristic
768C2×C3#330811yescharacteristic
769C2×C3#331911yescharacteristic
770D3—42no—
771D3—81no—
772C22—42no—
773C22—42no—
774C22—42no—
775C22—62no—
776C22—62no—
777C22—62no—
778C22—81no—
779C22—81no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—81no—
788C22—81no—
789C22—121no—
790C22—121no—
791C22—121no—
792C22—121no—
793C22—121no—
794C22—121no—
795C22—121no—
796C22—121no—
797C22—121no—
798C22—121no—
799C22—121no—
800C22#560911yescharacteristic
801C22#561211yescharacteristic
802C22#576911yescharacteristic
803C22#577111yescharacteristic
804C22D3×AGL(1,ℤ/8)11yescharacteristic
805C22#577311yescharacteristic
806C22C2×#93811yescharacteristic
807C4—22no—
808C4—22no—
809C4—81no—
810C4—81no—
811C4—122no—
812C4—122no—
813C4—121no—
814C4—121no—
815C4—241no—
816C4—241no—
817C4#559611yescharacteristic
818C4#561911yescharacteristic
819C4D4×#6711yescharacteristic
820C4#583411yescharacteristic
821C3#2539711yescharacteristic, complemented, Sylow
822C2—82no—
823C2—122no—
824C2—161no—
825C2—241no—
826C2#8055211yescharacteristic
827C2#8055411yescharacteristic
828C2#8056211yescharacteristic
829C2#8056311yescharacteristic
830C2#8264811yescharacteristic
831C2#8391711yescharacteristic
832C2#8395011yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#463C2
socleC23×C3C22×D4
hypercenterC2×#463D3
hypocenterC3#25397
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#463

Complements

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

NH ≅ G/Ntype
1. C2×C3×#463C2semidirect
2. C2×#5174C2semidirect
3. C2×#5157C2semidirect
4. #82998C2semidirect
5. #82417C2semidirect
6. C2×#4836C2semidirect
7. #72054C2semidirect
8. #72043C2semidirect
9. #71726C2semidirect
10. #71609C2semidirect
11. #70453C2semidirect
12. #70270C2semidirect
13. #70244C2semidirect
14. #70203C2semidirect
15. #70175C2semidirect
66. C2×#463D3semidirect
150. C3×C4⋊C8D4semidirect
158. #832D4semidirect
397. C4⋊C8#67semidirect
821. C3#25397semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#4632
C2×#51742
C2×#51572
#829982
#824172
C2×#48362
#720542
#720432
#717262
#716092
#704532
#702702
#702442
#702032
#701752
#253973