Finite Group Databasebeta

← #10846143

Subgroups — #10846143

Order 768.

1120 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#465C211yesmaximal, characteristic, complemented
2C2×#5163C211yesmaximal, characteristic, complemented
3C2×#5111C211yesmaximal, characteristic, complemented
4#82777C211yesmaximal, characteristic, complemented
5#82669C211yesmaximal, characteristic
6C2×#4812C211yesmaximal, characteristic, complemented
7#72054C211yesmaximal, characteristic, complemented
8#71973C211yesmaximal, characteristic, complemented
9#71699C211yesmaximal, characteristic, complemented
10#71679C211yesmaximal, characteristic, complemented
11#70581C211yesmaximal, characteristic, complemented
12#70564C211yesmaximal, characteristic, complemented
13#70220C211yesmaximal, characteristic, complemented
14#70203C211yesmaximal, characteristic, complemented
15#70160C211yesmaximal, characteristic, complemented
16#25402—31nomaximal, Sylow
17C22×C3×SD16C2211yescharacteristic
18C23×C3×C8C2211yescharacteristic
19C2×C3×C22⋊Q8C2211yescharacteristic
20C2×C3×#121C2211yescharacteristic
21C2×#946C2211yescharacteristic
22C2×Q8×Dic3C2211yescharacteristic
23C22×#215C2211yescharacteristic
24C2×#940—21no—
25C2×#940C2211yescharacteristic
26C2×#938C2211yescharacteristic
27C2×#930C2211yescharacteristic
28C2×C4×#67C2211yescharacteristic
29C22×ΓL(1,𝔽25)C2211yescharacteristic
30C2×#895C2211yescharacteristic
31C3×#465—24no—
32C2×C3×#106C2211yescharacteristic
33C2×C3×#103C2211yescharacteristic
34C2×C3×#102C2211yescharacteristic
35C2×#835C2211yescharacteristic
36#5223—21no—
37C2×#832C2211yescharacteristic
38C2×#832C2211yescharacteristic
39#5212C2211yescharacteristic
40C2×#830C2211yescharacteristic
41#5163—24no—
42C2×#821C2211yescharacteristic
43C2×#821C2211yescharacteristic
44#5111—24no—
45C2×(C2×D3)⋊C8C2211yescharacteristic
46C2×#815C2211yescharacteristic
47C2×Dic3⋊C8C2211yescharacteristic
48#4990—21no—
49#4987C2211yescharacteristic
50#4982—21no—
51#4977C2211yescharacteristic
52Dic3×C4⋊C4C2211yescharacteristic
53C2×#809C2211yescharacteristic
54C2×#807C2211yescharacteristic
55#4961—21no—
56#4960—21no—
57#4957—21no—
58#4945—21no—
59#4812—24no—
60#4551C2211yescharacteristic
61#4551C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#468—31no—
65C2×#465D311yescharacteristic, complemented
66C2×#460—31no—
67C2×#435—31no—
68#2541—31no—
69#2536—31no—
70#2034—31no—
71#2033—31no—
72#2000—31no—
73#2000—31no—
74#1961—31no—
75#1949—31no—
76#1895—31no—
77#1893—31no—
78#1763—31no—
79C22×C3×Q8C2311yescharacteristic
80C22×C3×D4—21no—
81C22×C3×D4C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C22×#67—21no—
84C22×#67—21no—
85C22×#67—21no—
86C22×#67—21no—
87C22×#67D411yescharacteristic
88C22×D12—21no—
89C22×D12C2311yescharacteristic
90C22×C4×D3C2311yescharacteristic
91C2×C3×SD16—22no—
92C2×C3×SD16—22no—
93C2×C3×SD16—41no—
94C22×C3×C8—22no—
95C22×C3×C8—22no—
96C22×C3×C8—41no—
97C22×C3×C8C2311yescharacteristic
98C22×C3×C8C2311yescharacteristic
99C3×C22⋊Q8—22no—
100C3×C22⋊Q8—41no—
101C3×#121—22no—
102C3×#121—41no—
103C2×C3×C4⋊C4—21no—
104C2×C3×C4⋊C4C2311yescharacteristic
105C2×C3×C4⋊C4C2311yescharacteristic
106C2×C3×C22⋊C4—21no—
107C2×C3×C22⋊C4—21no—
108C2×#217—21no—
109C2×#217—21no—
110C2×#217D411yescharacteristic
111#946—22no—
112#946—41no—
113Q8×Dic3—22no—
114Q8×Dic3—22no—
115C2×#215—22no—
116C2×#215—22no—
117C2×#215—41no—
118#940—22no—
119#940—22no—
120#940—44no—
121#938—22no—
122#938—41no—
123#930—22no—
124#930—41no—
125C4×#67—22no—
126C4×#67—22no—
127C2×(C2×D3)⋊C4—21no—
128C2×(C2×D3)⋊C4—21no—
129C2×(C2×D3)⋊C4—21no—
130C2×(C2×D3)⋊C4—21no—
131C2×(C2×D3)⋊C4D411yescharacteristic
132C2×C4⋊Dic3—21no—
133C2×C4⋊Dic3C2311yescharacteristic
134C2×C4⋊Dic3C2311yescharacteristic
135C2×C4⋊Dic3C2311yescharacteristic
136C2×Dic3⋊C4—21no—
137C2×Dic3⋊C4D411yescharacteristic
138C2×C4×Dic3—21no—
139C2×C4×Dic3—21no—
140C2×C4×Dic3C2311yescharacteristic
141C22×C3⋊C8C2311yescharacteristic
142C22×C3⋊C8C2311yescharacteristic
143C2×ΓL(1,𝔽25)—22no—
144C2×ΓL(1,𝔽25)—22no—
145C2×ΓL(1,𝔽25)—41no—
146#895—22no—
147#895—41no—
148C3×#106—22no—
149C3×#103D414yescomplemented
150C3×#102—22no—
151#835—22no—
152#832—22no—
153#832—41no—
154C3⋊#95—21no—
155C3⋊#95—21no—
156C3⋊#95—21no—
157C3⋊#95—21no—
158C3⋊#95—21no—
159#830—22no—
160#821—22no—
161#821—22no—
162(C2×D3)⋊C8—22no—
163#815—22no—
164Dic3⋊C8D414yescomplemented
165#809—41no—
166#807—22no—
167C22×SD16—31no—
168C22×SD16C2×D311yescharacteristic
169C22×M16—31no—
170C23×C8C2×D311yescharacteristic
171C2×#127—31no—
172C2×#127—61no—
173C2×C22⋊Q8—31no—
174C2×C22⋊Q8C2×D311yescharacteristic
175C2×#121—31no—
176C2×#121—31no—
177C2×#121—31no—
178C2×#121C2×D311yescharacteristic
179C2×C4×Q8—31no—
180C2×C4×D4—31no—
181#468—64no—
182#465—24no—
183#460—64no—
184#435—64no—
185C2×#107—31no—
186C2×#106C2×D311yescharacteristic
187C2×C4⋊C8—31no—
188C2×#103—31no—
189C2×#103C2×D311yescharacteristic
190C2×#102—31no—
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#398—61no—
200#394—61no—
201#392—61no—
202#392—61no—
203#390—61no—
204#388—61no—
205#388—61no—
206#382—31no—
207#380—31no—
208#380—31no—
209C4×C4⋊C4—31no—
210#340—31no—
211#340—31no—
212#340—31no—
213#340—31no—
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×Q8C2×D412yes—
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—42no—
231C2×C3×D4—42no—
232C2×C3×D4—81no—
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—42no—
252C2×#67—42no—
253C2×#67—42no—
254C2×#67—42no—
255C2×#67—81no—
256C2×#67—81no—
257C2×#67—81no—
258C2×#67—81no—
259C22×Dic3—21no—
260C22×Dic3—21no—
261C22×Dic3—21no—
262C22×Dic3C2×D411yescharacteristic
263C22×Dic3C2×D411yescharacteristic
264C22×Dic3C2×D411yescharacteristic
265C2×D12—21no—
266C2×D12—21no—
267C2×D12—21no—
268C2×D12—21no—
269C2×D12—21no—
270C2×D12—21no—
271C2×D12—42no—
272C2×D12—42no—
273C2×D12—81no—
274C2×C4×D3—21no—
275C2×C4×D3—21no—
276C2×C4×D3—21no—
277C2×C4×D3—21no—
278C2×C4×D3—21no—
279C2×C4×D3—21no—
280C3×SD16—44no—
281C2×C3×C8—21no—
282C2×C3×C8—21no—
283C2×C3×C8—21no—
284C2×C3×C8—21no—
285C2×C3×C8—44no—
286C2×C3×C8C2×D412yes—
287C2×C3×C8C2×D412yes—
288C3×C4⋊C4—21no—
289C3×C4⋊C4—21no—
290C3×C4⋊C4—21no—
291C3×C4⋊C4—42no—
292C3×C4⋊C4C2×D412yes—
293C3×C22⋊C4—42no—
294C3×C22⋊C4—42no—
295#217—22no—
296#217—42no—
297#217—42no—
298#215—44no—
299(C2×D3)⋊C4—22no—
300(C2×D3)⋊C4—42no—
301(C2×D3)⋊C4—42no—
302(C2×D3)⋊C4—42no—
303(C2×D3)⋊C4—42no—
304C4⋊Dic3—21no—
305C4⋊Dic3—21no—
306C4⋊Dic3—21no—
307C4⋊Dic3—21no—
308C4⋊Dic3—21no—
309C4⋊Dic3—42no—
310C4⋊Dic3#4112yes—
311Dic3⋊C4—22no—
312Dic3⋊C4—42no—
313C4×Dic3—42no—
314C4×Dic3—42no—
315C4×Dic3C2×D412yes—
316C4×Dic3#4112yes—
317C2×C3⋊C8—21no—
318C2×C3⋊C8—21no—
319C2×C3⋊C8—21no—
320C2×C3⋊C8—21no—
321C2×C3⋊C8—21no—
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×D4—61no—
332C22×D4—61no—
333C22×D4C22×D311yescharacteristic
334C23×C4—31no—
335C23×C4C22×D311yescharacteristic
336C2×SD16—22no—
337C2×SD16—22no—
338C2×SD16—41no—
339C2×SD16—62no—
340C2×SD16—62no—
341C2×SD16—121no—
342C2×M16—62no—
343C2×M16—62no—
344C2×M16—121no—
345C22×C8—22no—
346C22×C8—22no—
347C22×C8—31no—
348C22×C8—31no—
349C22×C8—41no—
350C22×C8C22×D311yescharacteristic
351C22×C8C22×D311yescharacteristic
352#127—62no—
353#127—62no—
354#127—124no—
355C22⋊Q8—22no—
356C22⋊Q8—41no—
357C22⋊Q8—62no—
358C22⋊Q8—121no—
359#121—22no—
360#121—41no—
361#121—62no—
362#121—62no—
363#121—62no—
364#121—121no—
365#121—121no—
366#121—121no—
367C4×Q8—62no—
368C4×Q8—62no—
369C4×D4—62no—
370C4×D4—62no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—31no—
373C2×C4⋊C4—31no—
374C2×C4⋊C4—31no—
375C2×C4⋊C4—31no—
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×C42—31no—
391C2×C42—61no—
392C2×C42—61no—
393#107—62no—
394#106—22no—
395C4⋊C8—34no—
396#103—62no—
397#103#6714yescomplemented
398#102—22no—
399#102—62no—
400#102—62no—
401#102—62no—
402#102—121no—
403#102—121no—
404C22⋊C8—62no—
405C22⋊C8—62no—
406#97—62no—
407#95—61no—
408#95—61no—
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—41no—
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—22no—
442C3×Q8—22no—
443C3×Q8—41no—
444C3×Q8—41no—
445C3×D4—41no—
446C3×D4—41no—
447C3×D4—41no—
448C3×D4—41no—
449C3×D4—84no—
450C2×C3×C4—21no—
451C2×C3×C4—22no—
452C2×C3×C4—22no—
453C2×C3×C4—21no—
454C2×C3×C4—21no—
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—
475#67—84no—
476#67—84no—
477C2×Dic3—21no—
478C2×Dic3—21no—
479C2×Dic3—21no—
480C2×Dic3—21no—
481C2×Dic3—21no—
482C2×Dic3—21no—
483C2×Dic3—22no—
484C2×Dic3—21no—
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#12112yes—
494C2×Dic3#12112yes—
495D12—41no—
496D12—41no—
497D12—41no—
498D12—41no—
499D12—84no—
500C4×D3—41no—
501C4×D3—41no—
502C4×D3—41no—
503C4×D3—41no—
504C3×C8—22no—
505C3×C8—22no—
506C3⋊C8—22no—
507C3⋊C8—41no—
508C24—21no—
509C24—31no—
510C24—61no—
511C24D3×D411yescharacteristic
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8C2×#6712yes—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—42no—
525C2×D4—42no—
526C2×D4—62no—
527C2×D4—62no—
528C2×D4—61no—
529C2×D4—61no—
530C2×D4—61no—
531C2×D4—61no—
532C2×D4—61no—
533C2×D4—61no—
534C2×D4—81no—
535C2×D4—122no—
536C2×D4—122no—
537C2×D4—122no—
538C2×D4—122no—
539C2×D4—121no—
540C2×D4—122no—
541C2×D4—122no—
542C2×D4—122no—
543C2×D4—122no—
544C2×D4—122no—
545C2×D4—122no—
546C2×D4—241no—
547C2×D4—241no—
548C2×D4—241no—
549C2×D4—241no—
550C2×D4—241no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—31no—
561C22×C4—31no—
562C22×C4—31no—
563C22×C4—61no—
564C22×C4—61no—
565C22×C4—61no—
566C22×C4—61no—
567C22×C4—61no—
568C22×C4—61no—
569C22×C4—61no—
570C22×C4—61no—
571C22×C4—61no—
572C22×C4D3×D411yescharacteristic
573C22×C4C23×D311yescharacteristic
574SD16—44no—
575SD16—124no—
576M16—124no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—32no—
582C2×C8—44no—
583C2×C8—61no—
584C2×C8—61no—
585C2×C8—61no—
586C2×C8—61no—
587C2×C8—61no—
588C2×C8D3×D412yes—
589C2×C8C2×#6712yes—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—32no—
594C4⋊C4—42no—
595C4⋊C4—62no—
596C4⋊C4—61no—
597C4⋊C4—61no—
598C4⋊C4—61no—
599C4⋊C4—61no—
600C4⋊C4—61no—
601C4⋊C4—122no—
602C4⋊C4—122no—
603C4⋊C4C2×#6712yes—
604C22⋊C4—42no—
605C22⋊C4—42no—
606C22⋊C4—62no—
607C22⋊C4—62no—
608C22⋊C4—122no—
609C22⋊C4—122no—
610C22⋊C4—122no—
611C22⋊C4—122no—
612C22⋊C4—122no—
613C22⋊C4—122no—
614C42—32no—
615C42—32no—
616C42—122no—
617C42—122no—
618C22×C3—22no—
619C22×C3—22no—
620C22×C3—22no—
621C22×C3—41no—
622C22×C3—41no—
623C22×C3—41no—
624C22×C3—41no—
625C22×C3—81no—
626C22×C3—81no—
627C22×C3—81no—
628C22×C3—81no—
629C22×C3—81no—
630C22×C3—81no—
631C22×C3—81no—
632C22×C3C2×#12111yescharacteristic
633C22×C3D4211yescharacteristic
634C22×C3#54611yescharacteristic
635C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
636C22×C3#57511yescharacteristic
637C22×C3#57711yescharacteristic
638C22×C3#57711yescharacteristic
639C2×D3—41no—
640C2×D3—41no—
641C2×D3—41no—
642C2×D3—41no—
643C2×D3—41no—
644C2×D3—41no—
645C2×D3—41no—
646C2×D3—81no—
647C2×D3—81no—
648C2×D3—81no—
649C2×D3—81no—
650C2×D3—81no—
651C2×D3—81no—
652C2×D3—81no—
653C3×C4—41no—
654C3×C4—42no—
655C3×C4—42no—
656C3×C4—81no—
657C3×C4#53211yescharacteristic
658C3×C4#54011yescharacteristic
659C3×C4D4211yescharacteristic
660C3×C4#55011yescharacteristic
661Dic3—22no—
662Dic3—22no—
663Dic3—41no—
664Dic3—42no—
665Dic3—81no—
666Dic3—81no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—61no—
681C23—61no—
682C23—61no—
683C23—61no—
684C23—61no—
685C23—61no—
686C23—61no—
687C23—121no—
688C23—121no—
689C23—121no—
690C23—121no—
691C23—121no—
692C23—121no—
693C23—121no—
694C23#91412yes—
695C23C2×D3×D411yescharacteristic
696Q8—22no—
697Q8—22no—
698Q8—41no—
699Q8—41no—
700D4—41no—
701D4—41no—
702D4—41no—
703D4—41no—
704D4—84no—
705D4—124no—
706D4—121no—
707D4—121no—
708D4—121no—
709D4—121no—
710D4—244no—
711D4—244no—
712D4—244no—
713D4—244no—
714D4—244no—
715C2×C4—21no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—32no—
721C2×C4—32no—
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—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—61no—
736C2×C4—61no—
737C2×C4—61no—
738C2×C4—61no—
739C2×C4—62no—
740C2×C4—61no—
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—121no—
751C2×C4—121no—
752C2×C4—121no—
753C2×C4C2×D3×D411yescharacteristic
754C2×C4#100411yescharacteristic
755C2×C4#100411yescharacteristic
756C2×C4D3×#4111yescharacteristic
757C2×C4D3×#4111yescharacteristic
758C2×C4C22×#6711yescharacteristic
759C8—22no—
760C8—22no—
761C8—62no—
762C8—121no—
763C2×C3—42no—
764C2×C3—161no—
765C2×C3#242811yescharacteristic
766C2×C3#305511yescharacteristic
767C2×C3#305711yescharacteristic
768C2×C3#326511yescharacteristic
769C2×C3#327111yescharacteristic
770C2×C3#331011yescharacteristic
771C2×C3#331711yescharacteristic
772D3—81no—
773D3—161no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—81no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—81no—
788C22—121no—
789C22—121no—
790C22—121no—
791C22—121no—
792C22—121no—
793C22—121no—
794C22—121no—
795C22—241no—
796C22—241no—
797C22—241no—
798C22—241no—
799C22—241no—
800C22—241no—
801C22—241no—
802C22D3×#12111yescharacteristic
803C22#561011yescharacteristic
804C22C2×#91411yescharacteristic
805C22#576211yescharacteristic
806C22#576811yescharacteristic
807C22#577011yescharacteristic
808C22D4×#6711yescharacteristic
809C4—42no—
810C4—41no—
811C4—42no—
812C4—62no—
813C4—62no—
814C4—81no—
815C4—122no—
816C4—121no—
817C4—241no—
818C4—241no—
819C4#559911yescharacteristic
820C4#561511yescharacteristic
821C4D4×#6711yescharacteristic
822C4#583211yescharacteristic
823C3#2540211yescharacteristic, complemented, Sylow
824C2—42no—
825C2—161no—
826C2—241no—
827C2—481no—
828C2#8065711yescharacteristic
829C2#8065911yescharacteristic
830C2#8068511yescharacteristic
831C2#8069311yescharacteristic
832C2#8265011yescharacteristic
833C2#8386411yescharacteristic
834C2#8392311yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#465C2
socleC23×C3C22×D4
prime radical#82669C2
hypercenterC2×#465D3
hypocenterC3#25402
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#465

Complements

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

NH ≅ G/Ntype
1. C2×C3×#465C2semidirect
2. C2×#5163C2semidirect
3. C2×#5111C2semidirect
4. #82777C2semidirect
6. C2×#4812C2semidirect
7. #72054C2semidirect
8. #71973C2semidirect
9. #71699C2semidirect
10. #71679C2semidirect
11. #70581C2semidirect
12. #70564C2semidirect
13. #70220C2semidirect
14. #70203C2semidirect
15. #70160C2semidirect
65. C2×#465D3semidirect
149. C3×#103D4semidirect
164. Dic3⋊C8D4semidirect
397. #103#67semidirect
823. C3#25402semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#4652
C2×#51632
C2×#51112
#827772
#826692
C2×#48122
#720542
#719732
#716992
#716792
#705812
#705642
#702202
#702032
#701602
#254023