Finite Group Databasebeta

← #10845978

Subgroups — #10845978

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
1C2×C3×#463C211yesmaximal, characteristic, complemented
2C2×#5174C211yesmaximal, characteristic, complemented
3C2×#5159C211yesmaximal, characteristic, complemented
4#82998C211yesmaximal, characteristic, complemented
5#82416C211yesmaximal, characteristic, complemented
6C2×#4838C211yesmaximal, characteristic, complemented
7#72054C211yesmaximal, characteristic, complemented
8#72043C211yesmaximal, characteristic, complemented
9#71725C211yesmaximal, characteristic, complemented
10C4×#832C211yesmaximal, characteristic, complemented
11#70455C211yesmaximal, characteristic, complemented
12#70271C211yesmaximal, characteristic, complemented
13#70243C211yesmaximal, characteristic, complemented
14#70203C211yesmaximal, characteristic, complemented
15#70175C211yesmaximal, characteristic, complemented
16#25390—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
27C22×ΓL(1,𝔽25)C2211yescharacteristic
28C22×ΓL(1,𝔽25)C2211yescharacteristic
29C2×C4×D12C2211yescharacteristic
30C3×#463—24no—
31C2×C3×C4⋊C8C2211yescharacteristic
32C2×C3×#103C2211yescharacteristic
33C2×C3×#102C2211yescharacteristic
34C2×#835C2211yescharacteristic
35C2×#835C2211yescharacteristic
36C2×#832C2211yescharacteristic
37C2×#832C2211yescharacteristic
38C2×#832C2211yescharacteristic
39C2×#832C2211yescharacteristic
40#5213—21no—
41#5213—21no—
42#5174—24no—
43#5159—24no—
44C2×(C2×D3)⋊C8C2211yescharacteristic
45C2×(C2×D3)⋊C8C2211yescharacteristic
46C2×#818C2211yescharacteristic
47C2×#817C2211yescharacteristic
48#4987C2211yescharacteristic
49#4987C2211yescharacteristic
50#4960—21no—
51#4960—21no—
52#4957—21no—
53#4957—21no—
54#4953—21no—
55#4949—21no—
56#4936C2211yescharacteristic
57C4×C4⋊Dic3C2211yescharacteristic
58C2×C4×C3⋊C8C2211yescharacteristic
59#4838—24no—
60#4551C2211yescharacteristic
61#4551C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#469—31no—
65C2×#468—31no—
66C2×#463D311yescharacteristic, complemented
67C2×#436—31no—
68#2540—31no—
69#2535—31no—
70#2035—31no—
71#2033—31no—
72#2000—31no—
73#1999—31no—
74#1958—31no—
75#1949—31no—
76#1895—31no—
77#1894—31no—
78C4×#102—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—
123C2×(C2×D3)⋊C4—21no—
124C2×(C2×D3)⋊C4—21no—
125C2×(C2×D3)⋊C4—21no—
126C2×(C2×D3)⋊C4—21no—
127C2×(C2×D3)⋊C4D411yescharacteristic
128C2×(C2×D3)⋊C4D411yescharacteristic
129C2×C4⋊Dic3D411yescharacteristic
130C2×C4⋊Dic3C2311yescharacteristic
131C2×C4⋊Dic3C2311yescharacteristic
132C2×C4⋊Dic3C2311yescharacteristic
133C2×C4⋊Dic3C2311yescharacteristic
134C2×Dic3⋊C4—21no—
135C2×Dic3⋊C4—21no—
136C2×C4×Dic3—21no—
137C22×C3⋊C8C2311yescharacteristic
138C22×C3⋊C8C2311yescharacteristic
139C2×ΓL(1,𝔽25)—22no—
140C2×ΓL(1,𝔽25)—22no—
141C2×ΓL(1,𝔽25)—22no—
142C2×ΓL(1,𝔽25)—22no—
143C2×ΓL(1,𝔽25)—41no—
144C2×ΓL(1,𝔽25)—41no—
145C4×D12—22no—
146C4×D12—22no—
147C3×C4⋊C8D414yescomplemented
148C3×#103—22no—
149C3×#102—22no—
150#835—22no—
151#835—41no—
152#832—22no—
153#832—22no—
154#832—41no—
155#832D414yescomplemented
156C3⋊#95—21no—
157C3⋊#95—21no—
158C3⋊#95—21no—
159C3⋊#95—21no—
160C3⋊#95—21no—
161(C2×D3)⋊C8—22no—
162(C2×D3)⋊C8—22no—
163#818—22no—
164#817—22no—
165C4×C3⋊C8—22no—
166C22×SD16C2×D311yescharacteristic
167C22×D8C2×D311yescharacteristic
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×D4C2×D311yescharacteristic
179#469—64no—
180#468—64no—
181#463—24no—
182#436—64no—
183C2×#107—31no—
184C2×#106—31no—
185C2×C4⋊C8C2×D311yescharacteristic
186C2×#103—31no—
187C2×#103—31no—
188C2×#103C2×D311yescharacteristic
189C2×#102—31no—
190C2×#102—31no—
191C2×#102—31no—
192C2×#102—31no—
193C2×#102C2×D311yescharacteristic
194C2×C22⋊C8—31no—
195C2×C22⋊C8—31no—
196C2×C4×C8—31no—
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#382—31no—
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—
214C24×C3—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—
229C2×C3×D4—21no—
230C2×C3×D4—21no—
231C2×C3×D4—21no—
232C2×C3×D4—21no—
233C2×C3×D4—21no—
234C2×C3×D4C2×D412yes—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—42no—
238C22×C3×C4—81no—
239C22×C3×C4—81no—
240C22×C3×C4C2×D411yescharacteristic
241C22×C3×C4C2×D411yescharacteristic
242C22×C3×C4C2411yescharacteristic
243C2×#67—42no—
244C2×#67—42no—
245C2×#67—42no—
246C2×#67—42no—
247C2×#67—42no—
248C2×#67—42no—
249C2×#67—42no—
250C2×#67—42no—
251C2×#67—81no—
252C2×#67—81no—
253C2×#67—81no—
254C2×#67—81no—
255C22×Dic3—21no—
256C22×Dic3—21no—
257C22×Dic3—21no—
258C22×Dic3—21no—
259C22×Dic3C2×D411yescharacteristic
260C22×Dic3C2×D411yescharacteristic
261C2×D12—22no—
262C2×D12—41no—
263C2×D12—41no—
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—21no—
274C2×C4×D3—21no—
275C2×C4×D3—21no—
276C3×SD16—44no—
277C3×D8—44no—
278C2×C3×C8—21no—
279C2×C3×C8—21no—
280C2×C3×C8—21no—
281C2×C3×C8—21no—
282C2×C3×C8C2×D412yes—
283C2×C3×C8C2×D412yes—
284C3×C4⋊C4—21no—
285C3×C4⋊C4—21no—
286C3×C22⋊C4—42no—
287C3×C22⋊C4—42no—
288C3×C22⋊C4—42no—
289C3×C42C2×D412yes—
290C3×C42#4112yes—
291#217—42no—
292#217—42no—
293#217—42no—
294#217—42no—
295(C2×D3)⋊C4—22no—
296(C2×D3)⋊C4—22no—
297(C2×D3)⋊C4—42no—
298(C2×D3)⋊C4—42no—
299(C2×D3)⋊C4—81no—
300(C2×D3)⋊C4—81no—
301C4⋊Dic3—22no—
302C4⋊Dic3—21no—
303C4⋊Dic3—21no—
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⋊C8—21no—
318C2×C3⋊C8C2×D412yes—
319ΓL(1,𝔽25)—44no—
320ΓL(1,𝔽25)—44no—
321C22×Q8C22×D311yescharacteristic
322C22×D4—31no—
323C22×D4—61no—
324C22×D4—61no—
325C22×D4—61no—
326C22×D4—61no—
327C22×D4C22×D311yescharacteristic
328C22×D4C22×D311yescharacteristic
329C23×C4—21no—
330C23×C4—31no—
331C23×C4—31no—
332C2×SD16—22no—
333C2×SD16—22no—
334C2×SD16—41no—
335C2×D8—22no—
336C2×D8—22no—
337C2×D8—41no—
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—22no—
363C4×D4—22no—
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—31no—
371C2×C4⋊C4—61no—
372C2×C4⋊C4—61no—
373C2×C4⋊C4C22×D311yescharacteristic
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—31no—
378C2×C22⋊C4—31no—
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#6714yescomplemented
392#103—22no—
393#103—62no—
394#103—121no—
395#102—22no—
396#102—34no—
397#102—62no—
398#102—62no—
399#102—121no—
400C22⋊C8—62no—
401C22⋊C8—62no—
402C4×C8—62no—
403#95—61no—
404#95—61no—
405#95—61no—
406#95—61no—
407#95—61no—
408C23×C3—22no—
409C23×C3—41no—
410C23×C3—41no—
411C23×C3—41no—
412C23×C3—41no—
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×C3C22×D411yescharacteristic
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—21no—
434C22×D3—21no—
435C22×D3—21no—
436C22×D3—21no—
437C3×Q8—41no—
438C3×Q8—41no—
439C3×Q8—41no—
440C3×Q8—41no—
441C3×D4—22no—
442C3×D4—22no—
443C3×D4—41no—
444C3×D4—41no—
445C3×D4—41no—
446C3×D4—41no—
447C3×D4—41no—
448C3×D4—41no—
449C2×C3×C4—21no—
450C2×C3×C4—21no—
451C2×C3×C4—21no—
452C2×C3×C4—21no—
453C2×C3×C4—41no—
454C2×C3×C4—41no—
455C2×C3×C4—41no—
456C2×C3×C4—41no—
457C2×C3×C4—41no—
458C2×C3×C4—41no—
459C2×C3×C4—84no—
460C2×C3×C4#12112yes—
461C2×C3×C4#12112yes—
462C2×C3×C4C22×D411yescharacteristic
463C2×C3×C4C22×D411yescharacteristic
464C2×C3×C4C2×#4111yescharacteristic
465C2×C3×C4C2×#4111yescharacteristic
466C2×C3×C4H(5,𝔽2)11yescharacteristic
467C2×C3×C4H(5,𝔽2)11yescharacteristic
468#67—84no—
469#67—84no—
470#67—84no—
471#67—84no—
472C2×Dic3—21no—
473C2×Dic3—21no—
474C2×Dic3—21no—
475C2×Dic3—22no—
476C2×Dic3—21no—
477C2×Dic3—21no—
478C2×Dic3—22no—
479C2×Dic3—21no—
480C2×Dic3—41no—
481C2×Dic3—41no—
482C2×Dic3—41no—
483C2×Dic3—41no—
484C2×Dic3—41no—
485C2×Dic3—41no—
486C2×Dic3—41no—
487C2×Dic3—41no—
488C2×Dic3—41no—
489C2×Dic3—41no—
490D12—44no—
491C4×D3—41no—
492C4×D3—41no—
493C4×D3—41no—
494C4×D3—41no—
495C4×D3—41no—
496C4×D3—41no—
497C4×D3—41no—
498C4×D3—41no—
499C3×C8—22no—
500C3×C8—22no—
501C3⋊C8—22no—
502C3⋊C8—41no—
503C24—21no—
504C24—21no—
505C24—31no—
506C24—31no—
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—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—62no—
525C2×D4—121no—
526C2×D4—121no—
527C2×D4—122no—
528C2×D4—122no—
529C2×D4—122no—
530C2×D4—122no—
531C2×D4—122no—
532C2×D4—122no—
533C2×D4—122no—
534C2×D4—122no—
535C2×D4—241no—
536C2×D4—241no—
537C2×D4—241no—
538C2×D4—241no—
539C2×D4D3×D412yes—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—31no—
543C22×C4—31no—
544C22×C4—42no—
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—61no—
561C22×C4—81no—
562C22×C4—81no—
563C22×C4D3×D411yescharacteristic
564C22×C4D3×D411yescharacteristic
565C22×C4C23×D311yescharacteristic
566SD16—44no—
567D8—44no—
568M16—124no—
569M16—124no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—32no—
575C2×C8—61no—
576C2×C8—61no—
577C2×C8—61no—
578C2×C8—61no—
579C2×C8—61no—
580C2×C8C2×#6712yes—
581C2×C8C2×#6712yes—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—32no—
585C4⋊C4—32no—
586C4⋊C4—62no—
587C4⋊C4—61no—
588C4⋊C4—61no—
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—42no—
598C22⋊C4—62no—
599C22⋊C4—62no—
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#23712yes—
610C42C2×#6712yes—
611C22×C3—42no—
612C22×C3—42no—
613C22×C3—42no—
614C22×C3—81no—
615C22×C3—81no—
616C22×C3—81no—
617C22×C3—81no—
618C22×C3—81no—
619C22×C3—81no—
620C22×C3—81no—
621C22×C3—81no—
622C22×C3—81no—
623C22×C3—81no—
624C22×C3—81no—
625C22×C3C2×#12111yescharacteristic
626C22×C3D4211yescharacteristic
627C22×C3#54611yescharacteristic
628C22×C3#57511yescharacteristic
629C22×C3#57511yescharacteristic
630C22×C3#57611yescharacteristic
631C22×C3#57711yescharacteristic
632C2×D3—41no—
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—41no—
643C2×D3—41no—
644C2×D3—41no—
645C2×D3—41no—
646C3×C4—22no—
647C3×C4—22no—
648C3×C4—81no—
649C3×C4—81no—
650C3×C4#53211yescharacteristic
651C3×C4#54011yescharacteristic
652C3×C4D4211yescharacteristic
653C3×C4#55011yescharacteristic
654Dic3—41no—
655Dic3—41no—
656Dic3—42no—
657Dic3—42no—
658Dic3—81no—
659Dic3—81no—
660C23—22no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
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—61no—
688C23C2×D3×D411yescharacteristic
689Q8—41no—
690Q8—41no—
691Q8—41no—
692Q8—41no—
693D4—22no—
694D4—22no—
695D4—41no—
696D4—41no—
697D4—41no—
698D4—41no—
699D4—41no—
700D4—41no—
701D4—124no—
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—61no—
717C2×C4—61no—
718C2×C4—61no—
719C2×C4—62no—
720C2×C4—61no—
721C2×C4—62no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—84no—
725C2×C4—121no—
726C2×C4—121no—
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—121no—
743C2×C4#93812yes—
744C2×C4#93812yes—
745C2×C4C2×D3×D411yescharacteristic
746C2×C4C2×#23711yescharacteristic
747C2×C4#100411yescharacteristic
748C2×C4D3×#4111yescharacteristic
749C2×C4#100911yescharacteristic
750C2×C4C22×#6711yescharacteristic
751C8—22no—
752C8—22no—
753C8—62no—
754C8—121no—
755C2×C3—82no—
756C2×C3—161no—
757C2×C3#242811yescharacteristic
758C2×C3#305411yescharacteristic
759C2×C3#306211yescharacteristic
760C2×C3#327311yescharacteristic
761C2×C3#327511yescharacteristic
762C2×C3#332211yescharacteristic
763C2×C3#332611yescharacteristic
764D3—81no—
765D3—81no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22—81no—
770C22—81no—
771C22—81no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22—81no—
780C22—121no—
781C22—121no—
782C22—121no—
783C22—121no—
784C22—121no—
785C22—121no—
786C22—121no—
787C22—121no—
788C22—121no—
789C22—121no—
790C22—121no—
791C22—121no—
792C22—121no—
793C22—121no—
794C22#560911yescharacteristic
795C22#561211yescharacteristic
796C22#576811yescharacteristic
797C22#576811yescharacteristic
798C22#577411yescharacteristic
799C22#577511yescharacteristic
800C22C2×#93811yescharacteristic
801C4—22no—
802C4—22no—
803C4—81no—
804C4—81no—
805C4—122no—
806C4—122no—
807C4—121no—
808C4—121no—
809C4—241no—
810C4—241no—
811C4#559611yescharacteristic
812C4#561911yescharacteristic
813C4D4×#6711yescharacteristic
814C4#583411yescharacteristic
815C3#2539011yescharacteristic, complemented, Sylow
816C2—82no—
817C2—161no—
818C2—241no—
819C2—241no—
820C2#8055511yescharacteristic
821C2#8055611yescharacteristic
822C2#8056511yescharacteristic
823C2#8056611yescharacteristic
824C2#8264811yescharacteristic
825C2#8391511yescharacteristic
826C2#8395111yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#463C2
socleC23×C3C22×D4
hypercenterC2×#463D3
hypocenterC3#25390
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×#5159C2semidirect
4. #82998C2semidirect
5. #82416C2semidirect
6. C2×#4838C2semidirect
7. #72054C2semidirect
8. #72043C2semidirect
9. #71725C2semidirect
10. C4×#832C2semidirect
11. #70455C2semidirect
12. #70271C2semidirect
13. #70243C2semidirect
14. #70203C2semidirect
15. #70175C2semidirect
66. C2×#463D3semidirect
147. C3×C4⋊C8D4semidirect
155. #832D4semidirect
391. C4⋊C8#67semidirect
815. C3#25390semidirect

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×#51592
#829982
#824162
C2×#48382
#720542
#720432
#717252
C4×#8322
#704552
#702712
#702432
#702032
#701752
#253903