Finite Group Databasebeta

← #10846072

Subgroups — #10846072

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×#5174C211yesmaximal, characteristic, complemented
2C2×#5165C211yesmaximal, characteristic, complemented
3#82779C211yesmaximal, characteristic, complemented
4#82667C211yesmaximal, characteristic, complemented
5C2×#5038C211yesmaximal, characteristic, complemented
6C2×#4730C211yesmaximal, characteristic, complemented
7C3×#2000C211yesmaximal, characteristic, complemented
8#71696C211yesmaximal, characteristic, complemented
9#70275C211yesmaximal, characteristic, complemented
10#70227C211yesmaximal, characteristic, complemented
11#70204C211yesmaximal, characteristic, complemented
12#70152C211yesmaximal, characteristic, complemented
13#69934C211yesmaximal, characteristic, complemented
14#68885C211yesmaximal, characteristic, complemented
15#68795C211yesmaximal, characteristic, complemented
16#25397—31nomaximal, Sylow
17C22×C3×SD16C2211yescharacteristic
18C2×C3×C22⋊Q8C2211yescharacteristic
19C2×C3×#121C2211yescharacteristic
20C2×#947C2211yescharacteristic
21C2×#946C2211yescharacteristic
22C2×#939—21no—
23C2×#938C2211yescharacteristic
24C2×D4×Dic3C2211yescharacteristic
25C22×#213C2211yescharacteristic
26C2×#930C2211yescharacteristic
27C2×C4×#67C2211yescharacteristic
28C23×C3⋊C8C2211yescharacteristic
29C22×ΓL(1,𝔽25)C2211yescharacteristic
30C2×#895C2211yescharacteristic
31C2×C3×#103C2211yescharacteristic
32C2×C3×#102C2211yescharacteristic
33C2×C3×C22⋊C8C2211yescharacteristic
34C2×#835C2211yescharacteristic
35C2×#835C2211yescharacteristic
36#5222—21no—
37C2×#832C2211yescharacteristic
38#5212C2211yescharacteristic
39#5174—24no—
40#5165—24no—
41C2×#821C2211yescharacteristic
42C2×#821C2211yescharacteristic
43C2×(C2×D3)⋊C8C2211yescharacteristic
44C2×#818C2211yescharacteristic
45C2×#815C2211yescharacteristic
46C2×Dic3⋊C8C2211yescharacteristic
47#5038—24no—
48#4993—21no—
49#4988—21no—
50#4987C2211yescharacteristic
51#4975C2211yescharacteristic
52Dic3×C4⋊C4C2211yescharacteristic
53C2×#809C2211yescharacteristic
54C2×#807C2211yescharacteristic
55#4960—21no—
56#4959—21no—
57#4957—21no—
58#4942—21no—
59#4730—24no—
60C3×#340C2211yescharacteristic
61#4551C2211yescharacteristic
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#2000D311yescharacteristic, complemented
73#1999—31no—
74#1959—31no—
75#1947—31no—
76#1895—31no—
77#1892—31no—
78#1762—31no—
79C22×C3×Q8C2311yescharacteristic
80C22×C3×D4—21no—
81C22×C3×D4C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C22×#67—21no—
84C22×#67—21no—
85C22×#67D411yescharacteristic
86C23×Dic3—21no—
87C22×D12—21no—
88C22×D12C2311yescharacteristic
89C22×C4×D3C2311yescharacteristic
90C2×C3×SD16—22no—
91C2×C3×SD16—22no—
92C2×C3×SD16—41no—
93C22×C3×C8C2311yescharacteristic
94C22×C3×C8C2311yescharacteristic
95C3×C22⋊Q8—22no—
96C3×C22⋊Q8—41no—
97C3×#121—22no—
98C3×#121—41no—
99C2×C3×C4⋊C4—21no—
100C2×C3×C4⋊C4C2311yescharacteristic
101C2×C3×C4⋊C4C2311yescharacteristic
102C2×C3×C22⋊C4—21no—
103C2×C3×C22⋊C4—21no—
104C2×#217—21no—
105C2×#217—21no—
106C2×#217—21no—
107C2×#217D411yescharacteristic
108#947—22no—
109#947—22no—
110#946—22no—
111#946—41no—
112#939—44no—
113#938—22no—
114#938—41no—
115D4×Dic3—22no—
116D4×Dic3—22no—
117C2×#213—22no—
118C2×#213—22no—
119C2×#213—41no—
120#930—22no—
121#930—41no—
122C4×#67—22no—
123C4×#67—22no—
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×C4⋊Dic3C2311yescharacteristic
132C2×C4⋊Dic3C2311yescharacteristic
133C2×C4⋊Dic3C2311yescharacteristic
134C2×Dic3⋊C4—21no—
135C2×Dic3⋊C4—21no—
136C2×Dic3⋊C4—21no—
137C2×Dic3⋊C4D411yescharacteristic
138C2×C4×Dic3—21no—
139C2×C4×Dic3C2311yescharacteristic
140C22×C3⋊C8—22no—
141C22×C3⋊C8—22no—
142C22×C3⋊C8—41no—
143C22×C3⋊C8C2311yescharacteristic
144C22×C3⋊C8C2311yescharacteristic
145C2×ΓL(1,𝔽25)—22no—
146C2×ΓL(1,𝔽25)—22no—
147C2×ΓL(1,𝔽25)—41no—
148#895—22no—
149#895—41no—
150C3×#103—41no—
151C3×#102—22no—
152C3×C22⋊C8—22no—
153#835—22no—
154#835—22no—
155#832D414yescomplemented
156C3⋊#95—21no—
157C3⋊#95—21no—
158C3⋊#95—21no—
159#821—22no—
160#821—41no—
161(C2×D3)⋊C8—22no—
162#818—22no—
163#815—22no—
164Dic3⋊C8D414yescomplemented
165#809—22no—
166#807—22no—
167C22×SD16C2×D311yescharacteristic
168C22×D8—31no—
169C22×M16—31no—
170C23×C8—31no—
171C2×#124—31no—
172C2×C22⋊Q8—31no—
173C2×C22⋊Q8C2×D311yescharacteristic
174C2×#121—31no—
175C2×#121—31no—
176C2×#121—31no—
177C2×#121—61no—
178C2×#121C2×D311yescharacteristic
179C2×C4×D4—31no—
180C2×C4×D4—31no—
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×#103C2×D311yescharacteristic
191C2×#102—31no—
192C2×#102—31no—
193C2×#102—31no—
194C2×#102—31no—
195C2×#102C2×D311yescharacteristic
196C2×C22⋊C8—31no—
197C2×C22⋊C8C2×D311yescharacteristic
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#340C2×D311yescharacteristic
214C24×C3—21no—
215C24×C3C2×D411yescharacteristic
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×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—42no—
230C2×C3×D4—42no—
231C2×C3×D4—81no—
232C2×C3×D4C2×D412yes—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4C2×D411yescharacteristic
243C22×C3×C4C2411yescharacteristic
244C2×#67—22no—
245C2×#67—22no—
246C2×#67—41no—
247C2×#67—42no—
248C2×#67—42no—
249C2×#67—42no—
250C2×#67—42no—
251C2×#67—81no—
252C2×#67—81no—
253C22×Dic3—21no—
254C22×Dic3—21no—
255C22×Dic3—21no—
256C22×Dic3—42no—
257C22×Dic3—42no—
258C22×Dic3—42no—
259C22×Dic3C2×D411yescharacteristic
260C22×Dic3C2×D411yescharacteristic
261C22×Dic3C2×D411yescharacteristic
262C2×D12—21no—
263C2×D12—21no—
264C2×D12—21no—
265C2×D12—21no—
266C2×D12—21no—
267C2×D12—21no—
268C2×D12—42no—
269C2×D12—42no—
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—44no—
278C2×C3×C8—21no—
279C2×C3×C8—21no—
280C2×C3×C8—21no—
281C2×C3×C8—21no—
282C2×C3×C8—21no—
283C2×C3×C8C2×D412yes—
284C3×C4⋊C4—21no—
285C3×C4⋊C4—21no—
286C3×C4⋊C4—21no—
287C3×C4⋊C4—42no—
288C3×C4⋊C4#4112yes—
289C3×C22⋊C4—42no—
290C3×C22⋊C4—42no—
291#217—22no—
292#217—42no—
293#217—42no—
294#217—42no—
295#213—44no—
296(C2×D3)⋊C4—22no—
297(C2×D3)⋊C4—42no—
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—
303C4⋊Dic3—21no—
304C4⋊Dic3—21no—
305C4⋊Dic3—21no—
306C4⋊Dic3—21no—
307C4⋊Dic3—21no—
308C4⋊Dic3C2×D412yes—
309Dic3⋊C4—22no—
310Dic3⋊C4—42no—
311Dic3⋊C4—42no—
312Dic3⋊C4—81no—
313C4×Dic3—81no—
314C4×Dic3C2×D412yes—
315C4×Dic3#4112yes—
316C2×C3⋊C8—21no—
317C2×C3⋊C8—21no—
318C2×C3⋊C8—21no—
319C2×C3⋊C8—21no—
320C2×C3⋊C8—44no—
321C2×C3⋊C8C2×D412yes—
322C2×C3⋊C8C2×D412yes—
323ΓL(1,𝔽25)—44no—
324C22×Q8C22×D311yescharacteristic
325C22×D4—21no—
326C22×D4—31no—
327C22×D4—31no—
328C22×D4—61no—
329C22×D4—61no—
330C22×D4—61no—
331C22×D4C22×D311yescharacteristic
332C23×C4—31no—
333C23×C4—61no—
334C23×C4C22×D311yescharacteristic
335C2×SD16—22no—
336C2×SD16—22no—
337C2×SD16—41no—
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—22no—
354C22⋊Q8—41no—
355C22⋊Q8—62no—
356C22⋊Q8—121no—
357#121—22no—
358#121—41no—
359#121—62no—
360#121—62no—
361#121—62no—
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—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⋊C4C22×D311yescharacteristic
379C2×C4⋊C4C22×D311yescharacteristic
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—31no—
383C2×C22⋊C4—31no—
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—31no—
394C2×C42—61no—
395#107—62no—
396#107—62no—
397C4⋊C8—34no—
398#103—41no—
399#103—62no—
400#103—62no—
401#102—22no—
402#102—34no—
403#102—62no—
404#102—62no—
405#102—121no—
406C22⋊C8—22no—
407C22⋊C8—62no—
408#97—62no—
409#95—61no—
410#95—61no—
411#95—61no—
412C23×C3—21no—
413C23×C3—21no—
414C23×C3—21no—
415C23×C3—21no—
416C23×C3—21no—
417C23×C3—21no—
418C23×C3—22no—
419C23×C3—41no—
420C23×C3—41no—
421C23×C3—41no—
422C23×C3—41no—
423C23×C3—41no—
424C23×C3—41no—
425C23×C3AGL(1,ℤ/8)12yes—
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—41no—
435C22×D3—41no—
436C22×D3—41no—
437C22×D3—41no—
438C22×D3—41no—
439C22×D3—41no—
440C22×D3—41no—
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—84no—
450C2×C3×C4—21no—
451C2×C3×C4—21no—
452C2×C3×C4—22no—
453C2×C3×C4—21no—
454C2×C3×C4—41no—
455C2×C3×C4—41no—
456C2×C3×C4—41no—
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—41no—
464C2×C3×C4—41no—
465C2×C3×C4—41no—
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—44no—
473#67—84no—
474#67—84no—
475C2×Dic3—21no—
476C2×Dic3—21no—
477C2×Dic3—21no—
478C2×Dic3—21no—
479C2×Dic3—21no—
480C2×Dic3—21no—
481C2×Dic3—22no—
482C2×Dic3—21no—
483C2×Dic3—41no—
484C2×Dic3—41no—
485C2×Dic3—41no—
486C2×Dic3—41no—
487C2×Dic3—41no—
488C2×Dic3—41no—
489C2×Dic3—41no—
490C2×Dic3—41no—
491C2×Dic3—84no—
492C2×Dic3#12112yes—
493C2×Dic3#12112yes—
494D12—41no—
495D12—41no—
496D12—41no—
497D12—41no—
498D12—84no—
499C4×D3—41no—
500C4×D3—41no—
501C4×D3—41no—
502C4×D3—41no—
503C3×C8—22no—
504C3×C8—41no—
505C3⋊C8—22no—
506C3⋊C8—22no—
507C24—21no—
508C24—31no—
509C24—61no—
510C24D3×D411yescharacteristic
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—42no—
523C2×D4—42no—
524C2×D4—62no—
525C2×D4—62no—
526C2×D4—61no—
527C2×D4—61no—
528C2×D4—61no—
529C2×D4—61no—
530C2×D4—61no—
531C2×D4—61no—
532C2×D4—81no—
533C2×D4—122no—
534C2×D4—122no—
535C2×D4—121no—
536C2×D4—122no—
537C2×D4—122no—
538C2×D4—122no—
539C2×D4—122no—
540C2×D4—241no—
541C2×D4—241no—
542C2×D4—241no—
543C2×D4D3×D412yes—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—31no—
554C22×C4—31no—
555C22×C4—31no—
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—122no—
566C22×C4—122no—
567C22×C4—122no—
568C22×C4D3×D411yescharacteristic
569C22×C4C23×D311yescharacteristic
570SD16—44no—
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×C8D3×D412yes—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—32no—
590C4⋊C4—42no—
591C4⋊C4—62no—
592C4⋊C4—61no—
593C4⋊C4—61no—
594C4⋊C4—61no—
595C4⋊C4—61no—
596C4⋊C4—61no—
597C4⋊C4—122no—
598C4⋊C4—122no—
599C4⋊C4—241no—
600C4⋊C4#23712yes—
601C22⋊C4—42no—
602C22⋊C4—42no—
603C22⋊C4—62no—
604C22⋊C4—62no—
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—32no—
615C42—32no—
616C42—241no—
617C22×C3—22no—
618C22×C3—22no—
619C22×C3—22no—
620C22×C3—41no—
621C22×C3—41no—
622C22×C3—41no—
623C22×C3—41no—
624C22×C3—42no—
625C22×C3—42no—
626C22×C3—42no—
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—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—41no—
653C3×C4—42no—
654C3×C4—81no—
655C3×C4—81no—
656C3×C4#53211yescharacteristic
657C3×C4#54011yescharacteristic
658C3×C4D4211yescharacteristic
659C3×C4#55011yescharacteristic
660Dic3—22no—
661Dic3—22no—
662Dic3—41no—
663Dic3—42no—
664Dic3—81no—
665Dic3—81no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—22no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—61no—
680C23—61no—
681C23—61no—
682C23—61no—
683C23—61no—
684C23—61no—
685C23—61no—
686C23—121no—
687C23—121no—
688C23—121no—
689C23—121no—
690C23—121no—
691C23—121no—
692C23—121no—
693C23#91412yes—
694C23C2×D3×D411yescharacteristic
695Q8—41no—
696Q8—41no—
697Q8—41no—
698Q8—41no—
699D4—22no—
700D4—22no—
701D4—41no—
702D4—41no—
703D4—84no—
704D4—124no—
705D4—121no—
706D4—121no—
707D4—121no—
708D4—121no—
709D4—244no—
710D4—244no—
711D4—244no—
712C2×C4—21no—
713C2×C4—22no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—32no—
717C2×C4—32no—
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—41no—
729C2×C4—41no—
730C2×C4—61no—
731C2×C4—61no—
732C2×C4—61no—
733C2×C4—61no—
734C2×C4—62no—
735C2×C4—61no—
736C2×C4—61no—
737C2×C4—61no—
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—121no—
750C2×C4—244no—
751C2×C4C2×D3×D411yescharacteristic
752C2×C4C2×D3×D411yescharacteristic
753C2×C4C2×#23711yescharacteristic
754C2×C4#100411yescharacteristic
755C2×C4#100411yescharacteristic
756C2×C4D3×#4111yescharacteristic
757C8—22no—
758C8—41no—
759C8—62no—
760C8—62no—
761C2×C3—42no—
762C2×C3—82no—
763C2×C3#242811yescharacteristic
764C2×C3#305511yescharacteristic
765C2×C3#306111yescharacteristic
766C2×C3#326411yescharacteristic
767C2×C3#326911yescharacteristic
768C2×C3#330811yescharacteristic
769C2×C3#331911yescharacteristic
770D3—81no—
771D3—161no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22—81no—
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—
800C22#559011yescharacteristic
801C22#559111yescharacteristic
802C22D3×#12111yescharacteristic
803C22C2×#91411yescharacteristic
804C22#576811yescharacteristic
805C22#577411yescharacteristic
806C22#577911yescharacteristic
807C4—41no—
808C4—42no—
809C4—62no—
810C4—62no—
811C4—81no—
812C4—81no—
813C4—122no—
814C4—121no—
815C4—241no—
816C4—241no—
817C4#559011yescharacteristic
818C4#559611yescharacteristic
819C4#561511yescharacteristic
820C4#571811yescharacteristic
821C3#2539711yescharacteristic, complemented, Sylow
822C2—42no—
823C2—82no—
824C2—241no—
825C2—481no—
826C2#7667111yescharacteristic
827C2#8005111yescharacteristic
828C2#8011211yescharacteristic
829C2#8016611yescharacteristic
830C2#8027211yescharacteristic
831C2#8065711yescharacteristic
832C2#8080811yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2000C2
socleC23×C3C22×D4
hypercenter#2000D3
hypocenterC3#25397
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2000

Complements

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

NH ≅ G/Ntype
1. C2×#5174C2semidirect
2. C2×#5165C2semidirect
3. #82779C2semidirect
4. #82667C2semidirect
5. C2×#5038C2semidirect
6. C2×#4730C2semidirect
7. C3×#2000C2semidirect
8. #71696C2semidirect
9. #70275C2semidirect
10. #70227C2semidirect
11. #70204C2semidirect
12. #70152C2semidirect
13. #69934C2semidirect
14. #68885C2semidirect
15. #68795C2semidirect
72. #2000D3semidirect
155. #832D4semidirect
164. Dic3⋊C8D4semidirect
821. C3#25397semidirect

Maximal subgroups

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

subgroupindex
C2×#51742
C2×#51652
#827792
#826672
C2×#50382
C2×#47302
C3×#20002
#716962
#702752
#702272
#702042
#701522
#699342
#688852
#687952
#253973