Finite Group Databasebeta

← #10845938

Subgroups — #10845938

Order 768.

1154 conjugacy classes of subgroups.

The subgroup lattice has 840 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×C8×#67C211yesmaximal, characteristic, complemented
4#82778C211yesmaximal, characteristic, complemented
5#82669C211yesmaximal, characteristic
6C2×#4807C211yesmaximal, characteristic, complemented
7#72054C211yesmaximal, characteristic, complemented
8#71973C211yesmaximal, characteristic, complemented
9#71699C211yesmaximal, characteristic, complemented
10#71680C211yesmaximal, characteristic, complemented
11#70581C211yesmaximal, characteristic, complemented
12#70563C211yesmaximal, characteristic, complemented
13Dic3×#103C211yesmaximal, characteristic, complemented
14#70202C211yesmaximal, characteristic, complemented
15#70157C211yesmaximal, characteristic, complemented
16#25387—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×D3×C8C2211yescharacteristic
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
44C8×#67—24no—
45C2×(C2×D3)⋊C8C2211yescharacteristic
46C2×Dic3⋊C8C2211yescharacteristic
47C2×C8×Dic3C2211yescharacteristic
48#4994—21no—
49#4987C2211yescharacteristic
50#4976—21no—
51#4975C2211yescharacteristic
52Dic3×C4⋊C4C2211yescharacteristic
53C2×#809C2211yescharacteristic
54C2×#808C2211yescharacteristic
55#4960—21no—
56#4957—21no—
57#4957—21no—
58#4948—21no—
59#4807—24no—
60#4551C2211yescharacteristic
61#4551C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#465—31no—
65C2×#465D311yescharacteristic, complemented
66C2×#460—31no—
67C2×C8×D4—31no—
68#2541—31no—
69#2538—31no—
70#2034—31no—
71#2034—31no—
72#2000—31no—
73#2000—31no—
74#1957—31no—
75#1948—31no—
76#1893—31no—
77#1893—31no—
78C4×#103—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⋊C4—21no—
138C2×Dic3⋊C4—21no—
139C2×Dic3⋊C4D411yescharacteristic
140C2×C4×Dic3—21no—
141C2×C4×Dic3—21no—
142C2×C4×Dic3C2311yescharacteristic
143C22×C3⋊C8C2311yescharacteristic
144C22×C3⋊C8C2311yescharacteristic
145C2×D3×C8—22no—
146C2×D3×C8—22no—
147C2×D3×C8—41no—
148#895—22no—
149#895—41no—
150C3×#106—22no—
151C3×#103D414yescomplemented
152C3×#102—22no—
153#835—22no—
154#832—22no—
155#832—41no—
156C3⋊#95—21no—
157C3⋊#95—21no—
158C3⋊#95—21no—
159#830—22no—
160#821—22no—
161#821—22no—
162(C2×D3)⋊C8—22no—
163Dic3⋊C8D414yescomplemented
164C8×Dic3—22no—
165#809—41no—
166#808—22no—
167C22×SD16—31no—
168C22×SD16C2×D311yescharacteristic
169C23×C8—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#465—24no—
182#465—64no—
183#460—64no—
184C8×D4—64no—
185C2×#106—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×C4×C8—31no—
199#396—61no—
200#396—61no—
201#392—61no—
202#392—61no—
203#390—61no—
204#390—61no—
205#389—61no—
206#384—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—42no—
247C2×#67—42no—
248C2×#67—42no—
249C2×#67—42no—
250C2×#67—42no—
251C2×#67—42no—
252C2×#67—42no—
253C2×#67—42no—
254C2×#67—81no—
255C2×#67—81no—
256C2×#67—81no—
257C2×#67—81no—
258C2×#67SD1614yescomplemented
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—81no—
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—81no—
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—
313Dic3⋊C4—42no—
314Dic3⋊C4—81no—
315C4×Dic3—42no—
316C4×Dic3—42no—
317C4×Dic3C2×D412yes—
318C4×Dic3#4112yes—
319C2×C3⋊C8—21no—
320C2×C3⋊C8—21no—
321C2×C3⋊C8—21no—
322C2×C3⋊C8—21no—
323C2×C3⋊C8—21no—
324C2×C3⋊C8C2×D412yes—
325D3×C8—44no—
326C22×Q8C22×D311yescharacteristic
327C22×D4—21no—
328C22×D4—31no—
329C22×D4—31no—
330C22×D4—61no—
331C22×D4—61no—
332C22×D4—61no—
333C22×D4—61no—
334C22×D4—61no—
335C22×D4C22×D311yescharacteristic
336C23×C4—31no—
337C23×C4C22×D311yescharacteristic
338C2×SD16—22no—
339C2×SD16—22no—
340C2×SD16—41no—
341C2×SD16—62no—
342C2×SD16—62no—
343C2×SD16—121no—
344C22×C8—22no—
345C22×C8—22no—
346C22×C8—31no—
347C22×C8—31no—
348C22×C8—41no—
349C22×C8—62no—
350C22×C8—62no—
351C22×C8—121no—
352C22×C8C22×D311yescharacteristic
353C22×C8C22×D311yescharacteristic
354#127—62no—
355#127—62no—
356#127—124no—
357C22⋊Q8—22no—
358C22⋊Q8—41no—
359C22⋊Q8—62no—
360C22⋊Q8—121no—
361#121—22no—
362#121—41no—
363#121—62no—
364#121—62no—
365#121—62no—
366#121—121no—
367#121—121no—
368#121—121no—
369C4×Q8—62no—
370C4×Q8—62no—
371C4×D4—62no—
372C4×D4—62no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—31no—
375C2×C4⋊C4—31no—
376C2×C4⋊C4—31no—
377C2×C4⋊C4—31no—
378C2×C4⋊C4—61no—
379C2×C4⋊C4—61no—
380C2×C4⋊C4—61no—
381C2×C4⋊C4—61no—
382C2×C4⋊C4C22×D311yescharacteristic
383C2×C4⋊C4C22×D311yescharacteristic
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—31no—
387C2×C22⋊C4—31no—
388C2×C22⋊C4—61no—
389C2×C22⋊C4—61no—
390C2×C22⋊C4—61no—
391C2×C22⋊C4—61no—
392C2×C22⋊C4—61no—
393C2×C22⋊C4—61no—
394C2×C42—31no—
395C2×C42—61no—
396C2×C42—61no—
397#106—22no—
398#106—62no—
399C4⋊C8—34no—
400#103—62no—
401#103#6714yescomplemented
402#102—22no—
403#102—62no—
404#102—62no—
405#102—62no—
406#102—121no—
407#102—121no—
408C22⋊C8—62no—
409C22⋊C8—62no—
410C4×C8—62no—
411#95—61no—
412#95—61no—
413#95—61no—
414C23×C3—21no—
415C23×C3—21no—
416C23×C3—21no—
417C23×C3—21no—
418C23×C3—21no—
419C23×C3—21no—
420C23×C3—41no—
421C23×C3—41no—
422C23×C3—41no—
423C23×C3—41no—
424C23×C3—41no—
425C23×C3—41no—
426C23×C3—41no—
427C23×C3C2×SD1612yes—
428C23×C3C22×D411yescharacteristic
429C22×D3—21no—
430C22×D3—21no—
431C22×D3—21no—
432C22×D3—21no—
433C22×D3—21no—
434C22×D3—21no—
435C22×D3—41no—
436C22×D3—41no—
437C22×D3—41no—
438C22×D3—41no—
439C22×D3—41no—
440C22×D3—41no—
441C22×D3—41no—
442C22×D3C2×SD1612yes—
443C3×Q8—22no—
444C3×Q8—22no—
445C3×Q8—41no—
446C3×Q8—41no—
447C3×D4—41no—
448C3×D4—41no—
449C3×D4—41no—
450C3×D4—41no—
451C3×D4—84no—
452C2×C3×C4—21no—
453C2×C3×C4—22no—
454C2×C3×C4—22no—
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—41no—
464C2×C3×C4—41no—
465C2×C3×C4—41no—
466C2×C3×C4—41no—
467C2×C3×C4—41no—
468C2×C3×C4C22×D411yescharacteristic
469C2×C3×C4C22×D411yescharacteristic
470C2×C3×C4C2×#4111yescharacteristic
471C2×C3×C4C2×#4111yescharacteristic
472C2×C3×C4H(5,𝔽2)11yescharacteristic
473C2×C3×C4H(5,𝔽2)11yescharacteristic
474#67—28no—
475#67—84no—
476#67—84no—
477#67—84no—
478#67—84no—
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—
495C2×Dic3C2×SD1612yes—
496C2×Dic3#13512yes—
497D12—41no—
498D12—41no—
499D12—41no—
500D12—41no—
501D12—84no—
502C4×D3—41no—
503C4×D3—41no—
504C4×D3—41no—
505C4×D3—41no—
506C3×C8—22no—
507C3×C8—22no—
508C3⋊C8—22no—
509C3⋊C8—41no—
510C24—21no—
511C24—31no—
512C24—61no—
513C24D3×D411yescharacteristic
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—21no—
519C2×Q8C2×#6712yes—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—34no—
527C2×D4—42no—
528C2×D4—42no—
529C2×D4—62no—
530C2×D4—62no—
531C2×D4—61no—
532C2×D4—61no—
533C2×D4—61no—
534C2×D4—61no—
535C2×D4—61no—
536C2×D4—61no—
537C2×D4—81no—
538C2×D4—122no—
539C2×D4—122no—
540C2×D4—122no—
541C2×D4—122no—
542C2×D4—122no—
543C2×D4—122no—
544C2×D4—122no—
545C2×D4—122no—
546C2×D4—122no—
547C2×D4—122no—
548C2×D4—241no—
549C2×D4—241no—
550C2×D4—241no—
551C2×D4—241no—
552C2×D4—241no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—31no—
563C22×C4—31no—
564C22×C4—31no—
565C22×C4—61no—
566C22×C4—61no—
567C22×C4—61no—
568C22×C4—61no—
569C22×C4—61no—
570C22×C4—61no—
571C22×C4—61no—
572C22×C4—61no—
573C22×C4—61no—
574C22×C4D3×D411yescharacteristic
575C22×C4C23×D311yescharacteristic
576SD16—44no—
577SD16—124no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—32no—
583C2×C8—44no—
584C2×C8—61no—
585C2×C8—61no—
586C2×C8—61no—
587C2×C8—61no—
588C2×C8—61no—
589C2×C8—124no—
590C2×C8D3×D412yes—
591C2×C8C2×#6712yes—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—32no—
596C4⋊C4—42no—
597C4⋊C4—62no—
598C4⋊C4—61no—
599C4⋊C4—61no—
600C4⋊C4—61no—
601C4⋊C4—61no—
602C4⋊C4—61no—
603C4⋊C4—122no—
604C4⋊C4—122no—
605C4⋊C4—122no—
606C4⋊C4—241no—
607C4⋊C4C2×#6712yes—
608C22⋊C4—42no—
609C22⋊C4—42no—
610C22⋊C4—62no—
611C22⋊C4—62no—
612C22⋊C4—122no—
613C22⋊C4—122no—
614C22⋊C4—122no—
615C22⋊C4—122no—
616C22⋊C4—241no—
617C22⋊C4—241no—
618C42—32no—
619C42—32no—
620C42—122no—
621C42—122no—
622C22×C3—22no—
623C22×C3—22no—
624C22×C3—22no—
625C22×C3—41no—
626C22×C3—41no—
627C22×C3—41no—
628C22×C3—41no—
629C22×C3—81no—
630C22×C3—81no—
631C22×C3—81no—
632C22×C3—81no—
633C22×C3—81no—
634C22×C3—81no—
635C22×C3—81no—
636C22×C3C2×#12111yescharacteristic
637C22×C3D4211yescharacteristic
638C22×C3#54611yescharacteristic
639C22×C3C22×SD1611yescharacteristic
640C22×C3C2×#13511yescharacteristic
641C22×C3#57611yescharacteristic
642C22×C3#57711yescharacteristic
643C2×D3—22no—
644C2×D3—22no—
645C2×D3—22no—
646C2×D3—41no—
647C2×D3—41no—
648C2×D3—41no—
649C2×D3—41no—
650C2×D3—81no—
651C2×D3—81no—
652C2×D3—81no—
653C2×D3—81no—
654C2×D3—81no—
655C2×D3—81no—
656C2×D3—81no—
657C3×C4—41no—
658C3×C4—42no—
659C3×C4—42no—
660C3×C4—81no—
661C3×C4#53211yescharacteristic
662C3×C4#54011yescharacteristic
663C3×C4D4211yescharacteristic
664C3×C4#55011yescharacteristic
665Dic3—22no—
666Dic3—41no—
667Dic3—42no—
668Dic3—81no—
669Dic3—81no—
670Dic3#46514yescomplemented
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—32no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—61no—
686C23—61no—
687C23—61no—
688C23—61no—
689C23—61no—
690C23—61no—
691C23—121no—
692C23—121no—
693C23—121no—
694C23—121no—
695C23—121no—
696C23—121no—
697C23—121no—
698C23D3×SD1612yes—
699C23C2×D3×D411yescharacteristic
700Q8—22no—
701Q8—22no—
702Q8—41no—
703Q8—41no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—41no—
708D4—68no—
709D4—84no—
710D4—121no—
711D4—121no—
712D4—121no—
713D4—121no—
714D4—244no—
715D4—244no—
716D4—244no—
717D4—244no—
718D4—244no—
719C2×C4—21no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—32no—
725C2×C4—32no—
726C2×C4—32no—
727C2×C4—32no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—61no—
740C2×C4—61no—
741C2×C4—61no—
742C2×C4—61no—
743C2×C4—62no—
744C2×C4—61no—
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×C4—121no—
754C2×C4—121no—
755C2×C4—121no—
756C2×C4—121no—
757C2×C4C2×D3×D411yescharacteristic
758C2×C4#100411yescharacteristic
759C2×C4#100411yescharacteristic
760C2×C4D3×#4111yescharacteristic
761C2×C4D3×#4111yescharacteristic
762C2×C4C22×#6711yescharacteristic
763C8—22no—
764C8—22no—
765C8—62no—
766C8—121no—
767C2×C3—42no—
768C2×C3—161no—
769C2×C3#242811yescharacteristic
770C2×C3C2×#46511yescharacteristic
771C2×C3#306211yescharacteristic
772C2×C3D4×SD1611yescharacteristic
773C2×C3#328711yescharacteristic
774C2×C3#329511yescharacteristic
775C2×C3#330411yescharacteristic
776D3—42no—
777D3—161no—
778C22—22no—
779C22—22no—
780C22—22no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—62no—
786C22—62no—
787C22—62no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22—81no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22—121no—
796C22—121no—
797C22—121no—
798C22—121no—
799C22—241no—
800C22—241no—
801C22—241no—
802C22—241no—
803C22—241no—
804C22—241no—
805C22—241no—
806C22D3×#12111yescharacteristic
807C22#561011yescharacteristic
808C22C2×D3×SD1611yescharacteristic
809C22#576211yescharacteristic
810C22D3×#13511yescharacteristic
811C22#576911yescharacteristic
812C22D4×#6711yescharacteristic
813C4—34no—
814C4—42no—
815C4—41no—
816C4—42no—
817C4—62no—
818C4—81no—
819C4—122no—
820C4—121no—
821C4—241no—
822C4—241no—
823C4#559911yescharacteristic
824C4#561511yescharacteristic
825C4D4×#6711yescharacteristic
826C4#583211yescharacteristic
827C3#2538711yescharacteristic, complemented, Sylow
828C2—42no—
829C2—122no—
830C2—161no—
831C2—481no—
832C2D3×#46511yescharacteristic
833C2#8066111yescharacteristic
834C2#8068011yescharacteristic
835C2#8069111yescharacteristic
836C2#8265011yescharacteristic
837C2SD16×#6711yescharacteristic
838C2#8392411yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#465C2
socleC23×C3C22×D4
prime radical#82669C2
hypercenterC2×#465D3
hypocenterC3#25387
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×C8×#67C2semidirect
4. #82778C2semidirect
6. C2×#4807C2semidirect
7. #72054C2semidirect
8. #71973C2semidirect
9. #71699C2semidirect
10. #71680C2semidirect
11. #70581C2semidirect
12. #70563C2semidirect
13. Dic3×#103C2semidirect
14. #70202C2semidirect
15. #70157C2semidirect
65. C2×#465D3semidirect
151. C3×#103D4semidirect
163. Dic3⋊C8D4semidirect
258. C2×#67SD16semidirect
401. #103#67semidirect
670. Dic3#465semidirect
827. C3#25387semidirect

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×C8×#672
#827782
#826692
C2×#48072
#720542
#719732
#716992
#716802
#705812
#705632
Dic3×#1032
#702022
#701572
#253873