Finite Group Databasebeta

← #10845984

Subgroups — #10845984

Order 768.

1084 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#82998C211yesmaximal, characteristic, complemented
2C2×#5057C211yesmaximal, characteristic, complemented
3C2×#4812C211yesmaximal, characteristic, complemented
4C2×#4782C211yesmaximal, characteristic, complemented
5C2×#4688C211yesmaximal, characteristic, complemented
6#74239C211yesmaximal, characteristic, complemented
7C3×#1958C211yesmaximal, characteristic, complemented
8#70274C211yesmaximal, characteristic, complemented
9#70272C211yesmaximal, characteristic, complemented
10#70271C211yesmaximal, characteristic, complemented
11#70206C211yesmaximal, characteristic, complemented
12#70204C211yesmaximal, characteristic, complemented
13#70203C211yesmaximal, characteristic, complemented
14C4×#821C211yesmaximal, characteristic, complemented
15#69540C211yesmaximal, characteristic, complemented
16#25390—31nomaximal, Sylow
17C2×C3×#124C2211yescharacteristic
18C2×#946C2211yescharacteristic
19C2×#946C2211yescharacteristic
20C22×#215C2211yescharacteristic
21C2×#938C2211yescharacteristic
22C2×#938C2211yescharacteristic
23C22×#213C2211yescharacteristic
24C22×ΓL(1,𝔽25)C2211yescharacteristic
25C22×ΓL(1,𝔽25)C2211yescharacteristic
26C2×#895C2211yescharacteristic
27C2×#895C2211yescharacteristic
28C2×C4×D12C2211yescharacteristic
29C2×C4×D12C2211yescharacteristic
30C2×C3×#103C2211yescharacteristic
31C2×C3×#103C2211yescharacteristic
32C2×C3×#102C2211yescharacteristic
33C2×C3×#102C2211yescharacteristic
34C2×C3×C4×C8C2211yescharacteristic
35C3×#382C2211yescharacteristic
36C2×#835C2211yescharacteristic
37C2×#832C2211yescharacteristic
38C2×#821C2211yescharacteristic
39C2×#821C2211yescharacteristic
40C2×(C2×D3)⋊C8C2211yescharacteristic
41C2×(C2×D3)⋊C8C2211yescharacteristic
42#5057—24no—
43#4987C2211yescharacteristic
44#4987C2211yescharacteristic
45C2×#808C2211yescharacteristic
46C2×#807C2211yescharacteristic
47#4960—21no—
48#4957—21no—
49#4957—21no—
50#4949—21no—
51C4×C4⋊Dic3C2211yescharacteristic
52C2×C4⋊(C3⋊C8)C2211yescharacteristic
53#4812—24no—
54#4782—24no—
55#4688—24no—
56#4674—21no—
57#4671—21no—
58#4665—21no—
59#4665—21no—
60#4551C2211yescharacteristic
61#4551C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#469—31no—
65C2×#468—31no—
66C2×#463—31no—
67C2×#436—31no—
68#2540—31no—
69#2535—31no—
70#2035—31no—
71#2033—31no—
72#2000—31no—
73#1999—31no—
74#1958D311yescharacteristic, complemented
75#1949—31no—
76#1895—31no—
77#1894—31no—
78C4×#102—31no—
79C22×C3×Q8C2311yescharacteristic
80C22×C3×D4C2311yescharacteristic
81C22×#67—21no—
82C22×#67—21no—
83C22×D12—21no—
84C22×D12—21no—
85C22×D12D411yescharacteristic
86C22×D12C2311yescharacteristic
87C22×C4×D3—21no—
88C22×C4×D3C2311yescharacteristic
89C22×C4×D3C2311yescharacteristic
90C22×C3×C8C2311yescharacteristic
91C22×C3×C8C2311yescharacteristic
92C3×#124—22no—
93C3×#124—22no—
94C2×C3×C4⋊C4C2311yescharacteristic
95C2×C3×C4⋊C4C2311yescharacteristic
96C2×C3×C22⋊C4—21no—
97C2×C3×C22⋊C4—21no—
98C2×C3×C42C2311yescharacteristic
99C2×#217—21no—
100C2×#217—21no—
101#946—22no—
102#946—22no—
103#946—41no—
104#946—41no—
105C2×#215—22no—
106C2×#215—22no—
107C2×#215—41no—
108#938—22no—
109#938—22no—
110#938—41no—
111#938—41no—
112C2×#213—22no—
113C2×#213—22no—
114C2×#213—41no—
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)⋊C4—21no—
122C2×(C2×D3)⋊C4D411yescharacteristic
123C2×(C2×D3)⋊C4D411yescharacteristic
124C2×C4⋊Dic3D411yescharacteristic
125C2×C4⋊Dic3C2311yescharacteristic
126C2×C4⋊Dic3C2311yescharacteristic
127C2×C4⋊Dic3C2311yescharacteristic
128C2×Dic3⋊C4—21no—
129C2×Dic3⋊C4—21no—
130C2×C4×Dic3—21no—
131C22×C3⋊C8C2311yescharacteristic
132C22×C3⋊C8C2311yescharacteristic
133C2×ΓL(1,𝔽25)—22no—
134C2×ΓL(1,𝔽25)—22no—
135C2×ΓL(1,𝔽25)—22no—
136C2×ΓL(1,𝔽25)—22no—
137C2×ΓL(1,𝔽25)—41no—
138C2×ΓL(1,𝔽25)—41no—
139#895—22no—
140#895—22no—
141#895—41no—
142#895—41no—
143C4×D12—22no—
144C4×D12—22no—
145C4×D12—22no—
146C4×D12—22no—
147C3×#103—22no—
148C3×#103—41no—
149C3×#102—22no—
150C3×#102—41no—
151C3×C4×C8—22no—
152C3×#95—21no—
153C3×#95—21no—
154#835—22no—
155#832—22no—
156C3⋊#95—21no—
157C3⋊#95—21no—
158C3⋊#95—21no—
159#821—22no—
160#821D414yescomplemented
161(C2×D3)⋊C8—22no—
162(C2×D3)⋊C8—22no—
163#808—22no—
164#807—22no—
165C4⋊(C3⋊C8)D414yescomplemented
166C22×SD16—31no—
167C22×D8—31no—
168C22×M16—31no—
169C22×M16—31no—
170C2×#124C2×D311yescharacteristic
171C2×C22⋊Q8—31no—
172C2×C22⋊Q8—31no—
173C2×#121—31no—
174C2×#121—31no—
175C2×#121—31no—
176C2×#121—31no—
177C2×C4×D4—31no—
178C2×C4×D4—31no—
179#469—64no—
180#468—64no—
181#463—64no—
182#436—64no—
183C2×#107—31no—
184C2×#106—31no—
185C2×C4⋊C8—31no—
186C2×#103—31no—
187C2×#103C2×D311yescharacteristic
188C2×#103C2×D311yescharacteristic
189C2×#102—31no—
190C2×#102—31no—
191C2×#102—31no—
192C2×#102C2×D311yescharacteristic
193C2×#102C2×D311yescharacteristic
194C2×C22⋊C8—31no—
195C2×C22⋊C8—31no—
196C2×C4×C8C2×D311yescharacteristic
197#399—61no—
198#397—61no—
199#392—61no—
200#392—61no—
201#390—61no—
202#390—61no—
203#386—61no—
204#386—61no—
205#382C2×D311yescharacteristic
206#380—31no—
207#380—31no—
208C4×C4⋊C4—31no—
209#340—31no—
210#340—31no—
211#340—31no—
212#340—31no—
213C24×C3—21no—
214C23×D3—21no—
215C23×D3C2×D411yescharacteristic
216C23×D3C2×D411yescharacteristic
217C2×C3×Q8—21no—
218C2×C3×Q8—21no—
219C2×C3×Q8—21no—
220C2×C3×Q8—21no—
221C2×C3×Q8—21no—
222C2×C3×Q8—21no—
223C2×C3×D4—21no—
224C2×C3×D4—21no—
225C2×C3×D4—21no—
226C2×C3×D4—21no—
227C2×C3×D4—21no—
228C2×C3×D4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4C2×D411yescharacteristic
233C22×C3×C4C2×D411yescharacteristic
234C22×C3×C4C2411yescharacteristic
235C2×#67—42no—
236C2×#67—42no—
237C2×#67—42no—
238C2×#67—42no—
239C2×#67—81no—
240C2×#67—81no—
241C22×Dic3—21no—
242C22×Dic3—21no—
243C22×Dic3—21no—
244C22×Dic3C2×D411yescharacteristic
245C22×Dic3C2×D411yescharacteristic
246C2×D12—21no—
247C2×D12—21no—
248C2×D12—21no—
249C2×D12—21no—
250C2×D12—22no—
251C2×D12—21no—
252C2×D12—41no—
253C2×D12—41no—
254C2×D12—42no—
255C2×D12—42no—
256C2×D12—42no—
257C2×D12—42no—
258C2×D12—81no—
259C2×D12—81no—
260C2×D12C2×D412yes—
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×C4×D3—21no—
272C2×C4×D3—21no—
273C2×C4×D3—42no—
274C2×C4×D3—81no—
275C2×C4×D3—81no—
276C2×C3×C8—21no—
277C2×C3×C8—21no—
278C2×C3×C8—21no—
279C2×C3×C8—21no—
280C2×C3×C8—21no—
281C2×C3×C8C2×D412yes—
282C3×C4⋊C4—21no—
283C3×C4⋊C4—21no—
284C3×C4⋊C4—21no—
285C3×C4⋊C4—21no—
286C3×C22⋊C4—42no—
287C3×C22⋊C4—42no—
288C3×C42C2×D412yes—
289C3×C42#4112yes—
290#217—42no—
291#217—42no—
292#215—44no—
293#213—44no—
294(C2×D3)⋊C4—22no—
295(C2×D3)⋊C4—22no—
296(C2×D3)⋊C4—42no—
297(C2×D3)⋊C4—42no—
298(C2×D3)⋊C4—42no—
299(C2×D3)⋊C4—42no—
300(C2×D3)⋊C4—42no—
301(C2×D3)⋊C4—81no—
302(C2×D3)⋊C4—81no—
303C4⋊Dic3—22no—
304C4⋊Dic3—21no—
305C4⋊Dic3—21no—
306C4⋊Dic3—21no—
307C4⋊Dic3—21no—
308C4⋊Dic3C2×D412yes—
309C4⋊Dic3#4112yes—
310Dic3⋊C4—42no—
311Dic3⋊C4—42no—
312C4×Dic3—81no—
313C2×C3⋊C8—21no—
314C2×C3⋊C8—21no—
315C2×C3⋊C8—21no—
316C2×C3⋊C8—21no—
317C2×C3⋊C8C2×D412yes—
318C2×C3⋊C8C2×D412yes—
319ΓL(1,𝔽25)—44no—
320ΓL(1,𝔽25)—44no—
321C22×Q8C22×D311yescharacteristic
322C22×D4—31no—
323C22×D4—31no—
324C22×D4—61no—
325C22×D4—61no—
326C22×D4—61no—
327C22×D4—61no—
328C22×D4C22×D311yescharacteristic
329C23×C4—31no—
330C23×C4—31no—
331C23×C4—61no—
332C2×SD16—62no—
333C2×SD16—62no—
334C2×SD16—121no—
335C2×D8—62no—
336C2×D8—62no—
337C2×D8—121no—
338C2×M16—62no—
339C2×M16—62no—
340C2×M16—62no—
341C2×M16—62no—
342C2×M16—121no—
343C2×M16—121no—
344C22×C8—31no—
345C22×C8—31no—
346C22×C8C22×D311yescharacteristic
347C22×C8C22×D311yescharacteristic
348#124—22no—
349#124—22no—
350C22⋊Q8—62no—
351C22⋊Q8—62no—
352C22⋊Q8—121no—
353C22⋊Q8—121no—
354#121—62no—
355#121—62no—
356#121—62no—
357#121—62no—
358#121—121no—
359#121—121no—
360#121—121no—
361#121—121no—
362C4×D4—62no—
363C4×D4—62no—
364C4×D4—62no—
365C4×D4—62no—
366C2×C4⋊C4—31no—
367C2×C4⋊C4—31no—
368C2×C4⋊C4—31no—
369C2×C4⋊C4—31no—
370C2×C4⋊C4—61no—
371C2×C4⋊C4—61no—
372C2×C4⋊C4C22×D311yescharacteristic
373C2×C4⋊C4C22×D311yescharacteristic
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—31no—
377C2×C22⋊C4—31no—
378C2×C22⋊C4—61no—
379C2×C22⋊C4—61no—
380C2×C22⋊C4—61no—
381C2×C22⋊C4—61no—
382C2×C22⋊C4—61no—
383C2×C22⋊C4—61no—
384C2×C22⋊C4—61no—
385C2×C22⋊C4—61no—
386C2×C22⋊C4—61no—
387C2×C42—61no—
388C2×C42C22×D311yescharacteristic
389#107—62no—
390#106—62no—
391C4⋊C8—34no—
392#103—22no—
393#103—41no—
394#103—62no—
395#102—22no—
396#102—34no—
397#102—41no—
398#102—62no—
399#102—62no—
400C22⋊C8—62no—
401C22⋊C8—62no—
402C4×C8—22no—
403#95—21no—
404#95—21no—
405#95—61no—
406#95—61no—
407#95—61no—
408C23×C3—41no—
409C23×C3—41no—
410C23×C3—41no—
411C23×C3—41no—
412C23×C3—41no—
413C23×C3—41no—
414C23×C3—41no—
415C23×C3C22×D411yescharacteristic
416C22×D3—21no—
417C22×D3—21no—
418C22×D3—21no—
419C22×D3—22no—
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—41no—
432C22×D3—41no—
433C22×D3—41no—
434C22×D3—41no—
435C22×D3—41no—
436C22×D3—41no—
437C3×Q8—41no—
438C3×Q8—41no—
439C3×Q8—41no—
440C3×Q8—41no—
441C3×D4—41no—
442C3×D4—41no—
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—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—41no—
458C2×C3×C4#12112yes—
459C2×C3×C4#12112yes—
460C2×C3×C4C22×D411yescharacteristic
461C2×C3×C4C22×D411yescharacteristic
462C2×C3×C4C2×#4111yescharacteristic
463C2×C3×C4C2×#4111yescharacteristic
464C2×C3×C4H(5,𝔽2)11yescharacteristic
465C2×C3×C4H(5,𝔽2)11yescharacteristic
466#67—84no—
467#67—84no—
468C2×Dic3—21no—
469C2×Dic3—21no—
470C2×Dic3—21no—
471C2×Dic3—22no—
472C2×Dic3—21no—
473C2×Dic3—21no—
474C2×Dic3—22no—
475C2×Dic3—21no—
476C2×Dic3—41no—
477C2×Dic3—41no—
478C2×Dic3—41no—
479C2×Dic3—41no—
480C2×Dic3—41no—
481C2×Dic3—41no—
482C2×Dic3—41no—
483D12—22no—
484D12—22no—
485D12—44no—
486D12—41no—
487D12—41no—
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—
499C3×C8—22no—
500C3×C8—41no—
501C3⋊C8—22no—
502C3⋊C8—22no—
503C24—21no—
504C24—31no—
505C24—31no—
506C24—61no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—32no—
520C2×D4—62no—
521C2×D4—61no—
522C2×D4—61no—
523C2×D4—61no—
524C2×D4—61no—
525C2×D4—61no—
526C2×D4—121no—
527C2×D4—121no—
528C2×D4—122no—
529C2×D4—122no—
530C2×D4—122no—
531C2×D4—122no—
532C2×D4—122no—
533C2×D4—122no—
534C2×D4—122no—
535C2×D4—122no—
536C2×D4—241no—
537C2×D4—241no—
538C2×D4—241no—
539C2×D4—241no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—31no—
544C22×C4—31no—
545C22×C4—61no—
546C22×C4—61no—
547C22×C4—61no—
548C22×C4—61no—
549C22×C4—61no—
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—122no—
561C22×C4—241no—
562C22×C4—241no—
563C22×C4D3×D411yescharacteristic
564C22×C4D3×D411yescharacteristic
565C22×C4C23×D311yescharacteristic
566SD16—124no—
567D8—124no—
568M16—124no—
569M16—124no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—32no—
576C2×C8—32no—
577C2×C8—61no—
578C2×C8—61no—
579C2×C8—61no—
580C2×C8—61no—
581C2×C8D3×D412yes—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—32no—
587C4⋊C4—32no—
588C4⋊C4—62no—
589C4⋊C4—61no—
590C4⋊C4—61no—
591C4⋊C4—61no—
592C4⋊C4—61no—
593C4⋊C4—122no—
594C4⋊C4—122no—
595C22⋊C4—42no—
596C22⋊C4—42no—
597C22⋊C4—62no—
598C22⋊C4—62no—
599C22⋊C4—122no—
600C22⋊C4—122no—
601C22⋊C4—122no—
602C22⋊C4—122no—
603C22⋊C4—122no—
604C22⋊C4—122no—
605C22⋊C4—122no—
606C22⋊C4—241no—
607C22⋊C4—241no—
608C42—241no—
609C42#23512yes—
610C42D3×D412yes—
611C22×C3—81no—
612C22×C3—81no—
613C22×C3—81no—
614C22×C3—81no—
615C22×C3—81no—
616C22×C3—81no—
617C22×C3—81no—
618C22×C3C2×#12111yescharacteristic
619C22×C3D4211yescharacteristic
620C22×C3#54611yescharacteristic
621C22×C3#57511yescharacteristic
622C22×C3#57511yescharacteristic
623C22×C3#57611yescharacteristic
624C22×C3#57711yescharacteristic
625C2×D3—41no—
626C2×D3—41no—
627C2×D3—42no—
628C2×D3—41no—
629C2×D3—42no—
630C2×D3—41no—
631C2×D3—41no—
632C2×D3—42no—
633C2×D3—41no—
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—81no—
643C2×D3—81no—
644C2×D3—81no—
645C2×D3—81no—
646C3×C4—22no—
647C3×C4—22no—
648C3×C4—81no—
649C3×C4—81no—
650C3×C4—81no—
651C3×C4#53211yescharacteristic
652C3×C4#54011yescharacteristic
653C3×C4D4211yescharacteristic
654C3×C4#55011yescharacteristic
655Dic3—41no—
656Dic3—41no—
657Dic3—42no—
658Dic3—42no—
659Dic3—81no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—61no—
668C23—61no—
669C23—61no—
670C23—62no—
671C23—61no—
672C23—61no—
673C23—61no—
674C23—61no—
675C23—61no—
676C23—61no—
677C23—61no—
678C23—61no—
679C23—61no—
680C23—61no—
681C23—61no—
682C23—121no—
683C23—121no—
684C23—121no—
685C23—121no—
686C23—121no—
687C23—121no—
688C23C2×D3×D411yescharacteristic
689Q8—41no—
690Q8—41no—
691Q8—41no—
692Q8—41no—
693D4—41no—
694D4—41no—
695D4—41no—
696D4—41no—
697D4—62no—
698D4—62no—
699D4—124no—
700D4—121no—
701D4—121no—
702D4—244no—
703D4—244no—
704D4—244no—
705D4—244no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—62no—
720C2×C4—61no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—62no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—121no—
728C2×C4—121no—
729C2×C4—121no—
730C2×C4—121no—
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—244no—
743C2×C4#88412yes—
744C2×C4#88412yes—
745C2×C4C2×#23511yescharacteristic
746C2×C4C2×D3×D411yescharacteristic
747C2×C4C2×D3×D411yescharacteristic
748C2×C4#100411yescharacteristic
749C2×C4D3×#4111yescharacteristic
750C2×C4#100911yescharacteristic
751C8—22no—
752C8—41no—
753C8—62no—
754C8—62no—
755C2×C3—161no—
756C2×C3#242811yescharacteristic
757C2×C3#305411yescharacteristic
758C2×C3#306211yescharacteristic
759C2×C3#327311yescharacteristic
760C2×C3#327511yescharacteristic
761C2×C3#332211yescharacteristic
762C2×C3#332611yescharacteristic
763D3—81no—
764D3—81no—
765D3—82no—
766C22—81no—
767C22—81no—
768C22—81no—
769C22—81no—
770C22—81no—
771C22—81no—
772C22—81no—
773C22—121no—
774C22—121no—
775C22—122no—
776C22—121no—
777C22—121no—
778C22—122no—
779C22—121no—
780C22—122no—
781C22—121no—
782C22—121no—
783C22—121no—
784C22—121no—
785C22—121no—
786C22—121no—
787C22—121no—
788C22—121no—
789C22—121no—
790C22—241no—
791C22—241no—
792C22—241no—
793C22—241no—
794C22C2×#88411yescharacteristic
795C22#567611yescharacteristic
796C22#571711yescharacteristic
797C22#576811yescharacteristic
798C22#576811yescharacteristic
799C22#576911yescharacteristic
800C22#577011yescharacteristic
801C4—22no—
802C4—22no—
803C4—81no—
804C4—81no—
805C4—81no—
806C4—121no—
807C4—121no—
808C4—122no—
809C4—122no—
810C4—241no—
811C4#554811yescharacteristic
812C4#556211yescharacteristic
813C4#559911yescharacteristic
814C4#560911yescharacteristic
815C3#2539011yescharacteristic, complemented, Sylow
816C2—161no—
817C2—241no—
818C2—241no—
819C2—242no—
820C2#7644411yescharacteristic
821C2#7883911yescharacteristic
822C2#7884011yescharacteristic
823C2#8165611yescharacteristic
824C2#8165811yescharacteristic
825C2#8182911yescharacteristic
826C2#8183011yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1958C2
socleC23×C3C22×D4
hypercenter#1958D3
hypocenterC3#25390
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1958

Complements

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

NH ≅ G/Ntype
1. #82998C2semidirect
2. C2×#5057C2semidirect
3. C2×#4812C2semidirect
4. C2×#4782C2semidirect
5. C2×#4688C2semidirect
6. #74239C2semidirect
7. C3×#1958C2semidirect
8. #70274C2semidirect
9. #70272C2semidirect
10. #70271C2semidirect
11. #70206C2semidirect
12. #70204C2semidirect
13. #70203C2semidirect
14. C4×#821C2semidirect
15. #69540C2semidirect
74. #1958D3semidirect
160. #821D4semidirect
165. C4⋊(C3⋊C8)D4semidirect
815. C3#25390semidirect

Maximal subgroups

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

subgroupindex
#829982
C2×#50572
C2×#48122
C2×#47822
C2×#46882
#742392
C3×#19582
#702742
#702722
#702712
#702062
#702042
#702032
C4×#8212
#695402
#253903