Finite Group Databasebeta

← #10800217

Subgroups — #10800217

Order 768.

1164 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#86018C211yesmaximal, characteristic
2C2×Dic3×M16C211yesmaximal, characteristic, complemented
3#73437C211yesmaximal, characteristic, complemented
4C3×#1871C211yesmaximal, characteristic, complemented
5#71984C211yesmaximal, characteristic, complemented
6#71713C211yesmaximal, characteristic, complemented
7#70358C212yesmaximal, complemented
8#70354C212yesmaximal, complemented
9#69453C211yesmaximal, characteristic, complemented
10#68730C212yesmaximal, complemented
11#68729C212yesmaximal, complemented
12#21383—31nomaximal, Sylow
13C22×C3×M16C2211yescharacteristic
14C3×#525C2211yescharacteristic
15#5832C2211yescharacteristic
16Dic3×#41C2211yescharacteristic
17#5791C2211yescharacteristic
18C22×C4×Dic3C2211yescharacteristic
19C22×#208C2211yescharacteristic
20#5649—21no—
21#5649—21no—
22#5624C411yescharacteristic, complemented
23#5624C411yescharacteristic, complemented
24#5622C411yescharacteristic, complemented
25#5622C411yescharacteristic, complemented
26#5600C411yescharacteristic, complemented
27#5600C411yescharacteristic, complemented
28#5596C411yescharacteristic, complemented
29#5596C411yescharacteristic, complemented
30#5586—21no—
31#5586—21no—
32#5538—21no—
33#5538—21no—
34C4×#237—21no—
35C4×#237—21no—
36#5522C2211yescharacteristic
37#5517C2211yescharacteristic
38C2×C3×#104C2212yes—
39C3×C4×C22⋊C4C2211yescharacteristic
40C2×#837C2212yes—
41C4×#217C2211yescharacteristic
42C2×#825C2212yes—
43Dic3×M16—21no—
44Dic3×M16—21no—
45Dic3×M16C2212yes—
46Dic3×M16C2212yes—
47C2×#815—21no—
48C2×C8×Dic3—21no—
49#4943—21no—
50#4942—21no—
51#4932C2212yes—
52C4×Dic3⋊C4C2212yes—
53C2×#805C2212yes—
54#4651—21no—
55#4650—21no—
56C3×#339C2212yes—
57#4555C2212yes—
58#4532C2212yes—
59#4523C2212yes—
60#3444—31no—
61C2×C4×M16—31no—
62#2283—31no—
63#1986—32no—
64#1980—32no—
65#1871—31no—
66#1871—31no—
67#1871—31no—
68#1871D311yescharacteristic, complemented
69#1759—32no—
70#1759—32no—
71C2×C3×#41C2311yescharacteristic
72C23×C3×C4C2311yescharacteristic
73C23×Dic3D411yescharacteristic
74C23×Dic3D411yescharacteristic
75C2×#237—21no—
76C2×#237—21no—
77C2×#235C2311yescharacteristic
78C2×C3×M16—21no—
79C2×C3×M16—24no—
80C2×C3×M16C2312yes—
81C22×C3×C8—21no—
82C3×#123—21no—
83C3×C22⋊Q8C2×C411yescharacteristic
84C3×C22⋊Q8C2×C411yescharacteristic
85C3×#121C2×C411yescharacteristic
86C3×#121C2×C411yescharacteristic
87C3×#120—21no—
88C3×C4×D4—21no—
89C3×C4×D4—21no—
90C3×#117C2311yescharacteristic
91C2×C3×C22⋊C4—21no—
92C2×C3×C42C2312yes—
93#953—21no—
94C2×#217—21no—
95#947C2×C411yescharacteristic
96Q8×Dic3C2×C411yescharacteristic
97Q8×Dic3C2×C411yescharacteristic
98#944C2×C411yescharacteristic
99#940C2×C411yescharacteristic
100#939—21no—
101#939—21no—
102#939—21no—
103#939—21no—
104#936C2×C411yescharacteristic
105#935—21no—
106#935—21no—
107D4×Dic3—21no—
108D4×Dic3—21no—
109D4×Dic3—21no—
110D4×Dic3—21no—
111D4×Dic3C2×C411yescharacteristic
112D4×Dic3C2×C411yescharacteristic
113#930C2×C411yescharacteristic
114#930C2×C411yescharacteristic
115#929—21no—
116C4×#67—21no—
117C4×#67—21no—
118C4×#67—21no—
119C4×#67—21no—
120#926—21no—
121#926C2311yescharacteristic
122#924C2×C411yescharacteristic
123#924C2×C411yescharacteristic
124C2×Dic3⋊C4—22no—
125C2×C4×Dic3—21no—
126C2×C4×Dic3C2×C411yescharacteristic
127C2×C4×Dic3C2×C411yescharacteristic
128C2×C4×Dic3C2×C411yescharacteristic
129C2×C4×Dic3C2×C411yescharacteristic
130C2×C4×Dic3D411yescharacteristic
131C2×C4×Dic3D411yescharacteristic
132C2×C4×Dic3D411yescharacteristic
133C2×C4×Dic3D411yescharacteristic
134C2×C4×Dic3D411yescharacteristic
135C2×C4×Dic3D411yescharacteristic
136C2×C4×Dic3C2312yes—
137C2×C4×Dic3C2311yescharacteristic
138C2×C4×Dic3C2311yescharacteristic
139C2×#208—21no—
140C2×#208—24no—
141C2×#208C2312yes—
142C22×C3⋊C8—21no—
143#898—21no—
144#898—21no—
145#893C2×C411yescharacteristic
146#893C2×C411yescharacteristic
147#892—21no—
148#892—21no—
149#890C2×C411yescharacteristic
150#890C2×C411yescharacteristic
151#889—21no—
152#889—21no—
153#888C2×C411yescharacteristic
154#888C2×C411yescharacteristic
155#887—21no—
156#887—21no—
157#887C2×C411yescharacteristic
158#887C2×C411yescharacteristic
159#886—21no—
160#886—21no—
161#885—21no—
162#885—21no—
163#67⋊C4—21no—
164#67⋊C4—21no—
165#67⋊C4—21no—
166#67⋊C4—21no—
167#67⋊C4—21no—
168#67⋊C4—21no—
169#879—21no—
170#879—21no—
171#878—21no—
172#878—21no—
173#878—21no—
174#878—21no—
175#877—21no—
176#877—21no—
177#877—21no—
178#877—21no—
179#872—21no—
180C42×D3—21no—
181C4×Dic6—21no—
182C4×Dic6—21no—
183C3×#104—24no—
184C3×#95—21no—
185#837—24no—
186C3⋊#95—21no—
187C3⋊#95—22no—
188C3⋊#95—22no—
189C3⋊#95—22no—
190#825—24no—
191#815—22no—
192#815—22no—
193C8×Dic3—22no—
194C8×Dic3—22no—
195#805—24no—
196C22×M16—31no—
197C22×M16C2×D311yescharacteristic
198#533—31no—
199#533—31no—
200#533—31no—
201#532—31no—
202#532—31no—
203#532—31no—
204#529—31no—
205#529—31no—
206#529—31no—
207#529—31no—
208#529—61no—
209#529—61no—
210#529—61no—
211#529—61no—
212#525—31no—
213#525—61no—
214#525—61no—
215#525C2×D311yescharacteristic
216C4×#41—31no—
217C4×#41—31no—
218C4×#41—61no—
219C4×#41—61no—
220C22×C42—31no—
221C2×#104—32no—
222C2×#104—32no—
223C2×#104—32no—
224C2×#104C2×D312yes—
225C4×M16—32no—
226C4×M16—32no—
227C4×M16—61no—
228C4×M16—61no—
229C2×#97—61no—
230C2×C4×C8—61no—
231#383—61no—
232#382—61no—
233#381—61no—
234#380—61no—
235C4×C4⋊C4—32no—
236C4×C22⋊C4—31no—
237C4×C22⋊C4C2×D311yescharacteristic
238#376—32no—
239#339—32no—
240#339—32no—
241#339—32no—
242#339C2×D312yes—
243C24×C3C2×D411yescharacteristic
244C3×#41—22no—
245C3×#41—22no—
246C2×C3×Q8C22×C411yescharacteristic
247C2×C3×D4—21no—
248C2×C3×D4—21no—
249C2×C3×D4—21no—
250C2×C3×D4C22×C411yescharacteristic
251C22×C3×C4—22no—
252C22×C3×C4—22no—
253C22×C3×C4—21no—
254C22×C3×C4—22no—
255C22×C3×C4C22×C411yescharacteristic
256C22×C3×C4C22×C411yescharacteristic
257C22×C3×C4C2×D411yescharacteristic
258C22×C3×C4C2×D411yescharacteristic
259C22×C3×C4C2×D411yescharacteristic
260C22×C3×C4C2411yescharacteristic
261C2×#67—21no—
262C2×#67—21no—
263C2×#67—21no—
264C2×#67—21no—
265C2×#67—21no—
266C22×Dic3—21no—
267C22×Dic3—21no—
268C22×Dic3—22no—
269C22×Dic3—42no—
270C22×Dic3—42no—
271C22×Dic3C22⋊C411yescharacteristic
272C22×Dic3C22⋊C411yescharacteristic
273C22×Dic3C22⋊C411yescharacteristic
274C22×Dic3C22⋊C411yescharacteristic
275C22×Dic3C22⋊C411yescharacteristic
276C22×Dic3C22⋊C411yescharacteristic
277C22×Dic3C22⋊C411yescharacteristic
278C22×Dic3C22⋊C411yescharacteristic
279C22×Dic3C2×D411yescharacteristic
280C22×Dic3C2×D411yescharacteristic
281C22×Dic3C2×D411yescharacteristic
282C22×Dic3C2×D411yescharacteristic
283#237—44no—
284#237—44no—
285#235—22no—
286#235—22no—
287C2×D12C22×C411yescharacteristic
288C2×C4×D3—21no—
289C2×C4×D3—21no—
290C2×C4×D3—21no—
291C2×Dic6—21no—
292C2×Dic6—21no—
293C2×Dic6C22×C411yescharacteristic
294C3×M16—24no—
295C3×M16—22no—
296C3×M16#4114yescomplemented
297C2×C3×C8—24no—
298C2×C3×C8—22no—
299C3×C4⋊C4—21no—
300C3×C4⋊C4—21no—
301C3×C4⋊C4C22×C411yescharacteristic
302C3×C4⋊C4C22×C411yescharacteristic
303C3×C22⋊C4—21no—
304C3×C22⋊C4—21no—
305C3×C22⋊C4—21no—
306C3×C22⋊C4—21no—
307C3×C22⋊C4—21no—
308C3×C22⋊C4—42no—
309C3×C42—21no—
310C3×C42—22no—
311C3×C42—22no—
312#217—21no—
313#217—21no—
314#217—21no—
315#217—21no—
316#217—21no—
317#217—21no—
318#217—21no—
319#217—42no—
320(C2×D3)⋊C4—21no—
321(C2×D3)⋊C4—21no—
322(C2×D3)⋊C4—21no—
323(C2×D3)⋊C4—21no—
324(C2×D3)⋊C4—21no—
325(C2×D3)⋊C4—21no—
326C4⋊Dic3—21no—
327C4⋊Dic3—21no—
328C4⋊Dic3—21no—
329C4⋊Dic3—21no—
330C4⋊Dic3C22×C411yescharacteristic
331C4⋊Dic3C22×C411yescharacteristic
332Dic3⋊C4—21no—
333Dic3⋊C4—21no—
334Dic3⋊C4—21no—
335Dic3⋊C4—21no—
336Dic3⋊C4—21no—
337Dic3⋊C4—21no—
338Dic3⋊C4—21no—
339Dic3⋊C4—21no—
340Dic3⋊C4—21no—
341Dic3⋊C4—21no—
342Dic3⋊C4—44no—
343C4×Dic3—21no—
344C4×Dic3—21no—
345C4×Dic3—21no—
346C4×Dic3—21no—
347C4×Dic3—21no—
348C4×Dic3—22no—
349C4×Dic3—22no—
350C4×Dic3C22⋊C411yescharacteristic
351C4×Dic3C22⋊C411yescharacteristic
352C4×Dic3C22⋊C411yescharacteristic
353C4×Dic3C22⋊C411yescharacteristic
354C4×Dic3C22⋊C411yescharacteristic
355C4×Dic3C22⋊C411yescharacteristic
356C4×Dic3C22⋊C411yescharacteristic
357C4×Dic3C22⋊C411yescharacteristic
358C4×Dic3C22×C411yescharacteristic
359C4×Dic3C22×C411yescharacteristic
360C4×Dic3C22×C411yescharacteristic
361C4×Dic3C22×C411yescharacteristic
362C4×Dic3C2×D411yescharacteristic
363C4×Dic3C2×D411yescharacteristic
364C4×Dic3C2×D411yescharacteristic
365C4×Dic3C2×D411yescharacteristic
366#208—24no—
367#208—22no—
368#208#4114yescomplemented
369C2×C3⋊C8—24no—
370C2×C3⋊C8—22no—
371C2×#41—31no—
372C2×#41—61no—
373C2×#41—61no—
374C2×#41C22×D311yescharacteristic
375C23×C4—31no—
376C23×C4—31no—
377C23×C4C22×D311yescharacteristic
378C2×M16—21no—
379C2×M16—24no—
380C2×M16—32no—
381C2×M16—64no—
382C2×M16—61no—
383C2×M16C22×D312yes—
384C22×C8—21no—
385C22×C8—61no—
386C4⋊Q8—31no—
387C4⋊Q8—31no—
388C4⋊Q8—31no—
389#127—31no—
390#126—61no—
391#126—61no—
392#126—61no—
393#126—61no—
394#125—31no—
395#125—31no—
396#125—61no—
397#125—61no—
398#124—31no—
399#124—31no—
400#124—61no—
401#124—61no—
402#123—21no—
403#123—61no—
404#123—61no—
405#123—61no—
406#123—61no—
407#123—61no—
408C22⋊Q8—31no—
409C22⋊Q8—31no—
410C22⋊Q8—61no—
411C22⋊Q8—61no—
412C22⋊Q8—61no—
413C22⋊Q8—61no—
414C22⋊Q8C4×D311yescharacteristic
415C22⋊Q8C4×D311yescharacteristic
416#121—31no—
417#121—31no—
418#121—61no—
419#121—61no—
420#121—61no—
421#121—61no—
422#121C4×D311yescharacteristic
423#121C4×D311yescharacteristic
424#120—21no—
425#120—61no—
426C4×Q8—31no—
427C4×Q8—31no—
428C4×Q8—31no—
429C4×Q8—31no—
430C4×Q8—61no—
431C4×Q8—61no—
432C4×Q8—61no—
433C4×Q8—61no—
434C4×D4—21no—
435C4×D4—21no—
436C4×D4—31no—
437C4×D4—31no—
438C4×D4—31no—
439C4×D4—31no—
440C4×D4—61no—
441C4×D4—61no—
442C4×D4—61no—
443C4×D4—61no—
444C4×D4—61no—
445C4×D4—61no—
446C4×D4—61no—
447C4×D4—61no—
448C4×D4—61no—
449C4×D4—61no—
450C4×D4—61no—
451C4×D4—61no—
452C4×D4—61no—
453C4×D4—61no—
454#117—31no—
455#117—61no—
456#117—61no—
457#117—61no—
458#117—61no—
459#117—61no—
460#117—61no—
461#117—61no—
462#117—61no—
463#117C22×D311yescharacteristic
464C2×C4⋊C4—62no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—61no—
467C2×C42—31no—
468C2×C42—31no—
469C2×C42—31no—
470C2×C42—31no—
471C2×C42—31no—
472C2×C42—31no—
473C2×C42—31no—
474C2×C42—31no—
475C2×C42—31no—
476C2×C42—31no—
477C2×C42—31no—
478C2×C42—31no—
479C2×C42—32no—
480C2×C42—61no—
481C2×C42—61no—
482C2×C42C22×D312yes—
483#104—24no—
484#104—64no—
485#104—64no—
486#104—64no—
487#97—62no—
488#97—62no—
489C4×C8—62no—
490C4×C8—62no—
491#95—21no—
492#95—62no—
493#95—62no—
494#95—62no—
495#95—61no—
496C23×C3—22no—
497C23×C3—22no—
498C23×C3—21no—
499C23×C3—41no—
500C23×C3C2×C22⋊C411yescharacteristic
501C23×C3C2×C22⋊C411yescharacteristic
502C23×C3C22×D411yescharacteristic
503C22×D3—21no—
504C3×Q8—22no—
505C3×D4—22no—
506C3×D4—42no—
507C3×D4—42no—
508C3×D4—42no—
509C2×C3×C4—22no—
510C2×C3×C4—22no—
511C2×C3×C4—22no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—41no—
520C2×C3×C4—41no—
521C2×C3×C4—42no—
522C2×C3×C4—42no—
523C2×C3×C4—42no—
524C2×C3×C4C2×C22⋊C411yescharacteristic
525C2×C3×C4C2×C22⋊C411yescharacteristic
526C2×C3×C4C23×C411yescharacteristic
527C2×C3×C4C22×D411yescharacteristic
528C2×C3×C4C2×#4112yes—
529C2×C3×C4C2×#4112yes—
530#67—42no—
531#67—42no—
532#67—42no—
533#67—42no—
534#67—42no—
535C2×Dic3—22no—
536C2×Dic3—22no—
537C2×Dic3—22no—
538C2×Dic3—22no—
539C2×Dic3—22no—
540C2×Dic3—21no—
541C2×Dic3—21no—
542C2×Dic3—21no—
543C2×Dic3—41no—
544C2×Dic3—41no—
545C2×Dic3—41no—
546C2×Dic3—41no—
547C2×Dic3—41no—
548C2×Dic3—41no—
549C2×Dic3—41no—
550C2×Dic3—42no—
551C2×Dic3—42no—
552C2×Dic3—42no—
553C2×Dic3—42no—
554C2×Dic3—42no—
555C2×Dic3C2×C22⋊C411yescharacteristic
556C2×Dic3C2×C22⋊C411yescharacteristic
557C2×Dic3C2×C22⋊C411yescharacteristic
558C2×Dic3C2×C22⋊C411yescharacteristic
559C2×Dic3C2×C22⋊C411yescharacteristic
560C2×Dic3C2×C22⋊C411yescharacteristic
561C2×Dic3C2×C22⋊C411yescharacteristic
562C2×Dic3C2×C22⋊C411yescharacteristic
563D12—22no—
564C4×D3—42no—
565C4×D3—42no—
566C4×D3—41no—
567C4×D3—41no—
568Dic6—22no—
569Dic6—42no—
570Dic6—42no—
571C3×C8—24no—
572C3⋊C8—24no—
573C24D3×D411yescharacteristic
574#41—22no—
575#41—22no—
576#41—62no—
577#41—62no—
578#41—124no—
579#41—124no—
580C2×Q8—31no—
581C2×Q8—61no—
582C2×Q8—61no—
583C2×Q8C2×C4×D311yescharacteristic
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—31no—
588C2×D4—61no—
589C2×D4—61no—
590C2×D4—61no—
591C2×D4—61no—
592C2×D4—61no—
593C2×D4C2×C4×D311yescharacteristic
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—21no—
597C22×C4—22no—
598C22×C4—31no—
599C22×C4—31no—
600C22×C4—31no—
601C22×C4—31no—
602C22×C4—31no—
603C22×C4—31no—
604C22×C4—31no—
605C22×C4—31no—
606C22×C4—31no—
607C22×C4—31no—
608C22×C4—31no—
609C22×C4—31no—
610C22×C4—61no—
611C22×C4—61no—
612C22×C4—61no—
613C22×C4—61no—
614C22×C4—61no—
615C22×C4—62no—
616C22×C4—122no—
617C22×C4—122no—
618C22×C4C2×C4×D311yescharacteristic
619C22×C4C2×C4×D311yescharacteristic
620C22×C4D3×D411yescharacteristic
621C22×C4D3×D411yescharacteristic
622C22×C4D3×D411yescharacteristic
623C22×C4C23×D311yescharacteristic
624M16—24no—
625M16—22no—
626M16—34no—
627M16—64no—
628M16—62no—
629M16#23714yescomplemented
630C2×C8—24no—
631C2×C8—22no—
632C2×C8—64no—
633C2×C8—62no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—31no—
637C4⋊C4—31no—
638C4⋊C4—61no—
639C4⋊C4—61no—
640C4⋊C4—61no—
641C4⋊C4—61no—
642C4⋊C4—61no—
643C4⋊C4—61no—
644C4⋊C4—61no—
645C4⋊C4—61no—
646C4⋊C4—61no—
647C4⋊C4—61no—
648C4⋊C4—61no—
649C4⋊C4—61no—
650C4⋊C4—61no—
651C4⋊C4—61no—
652C4⋊C4—124no—
653C4⋊C4C2×C4×D311yescharacteristic
654C4⋊C4C2×C4×D311yescharacteristic
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—21no—
658C22⋊C4—21no—
659C22⋊C4—21no—
660C22⋊C4—42no—
661C22⋊C4—61no—
662C22⋊C4—61no—
663C22⋊C4—61no—
664C22⋊C4—61no—
665C22⋊C4—61no—
666C22⋊C4—61no—
667C22⋊C4—61no—
668C22⋊C4—61no—
669C22⋊C4—61no—
670C22⋊C4—61no—
671C22⋊C4—61no—
672C22⋊C4—61no—
673C22⋊C4—61no—
674C22⋊C4—122no—
675C42—21no—
676C42—22no—
677C42—22no—
678C42—31no—
679C42—31no—
680C42—31no—
681C42—31no—
682C42—31no—
683C42—31no—
684C42—31no—
685C42—31no—
686C42—31no—
687C42—31no—
688C42—31no—
689C42—31no—
690C42—31no—
691C42—31no—
692C42—31no—
693C42—31no—
694C42—61no—
695C42—61no—
696C42—61no—
697C42—61no—
698C42—61no—
699C42—62no—
700C42—62no—
701C22×C3—21no—
702C22×C3—21no—
703C22×C3—21no—
704C22×C3—21no—
705C22×C3—21no—
706C22×C3—21no—
707C22×C3—21no—
708C22×C3—44no—
709C22×C3—41no—
710C22×C3—41no—
711C22×C3—41no—
712C22×C3#42112yes—
713C22×C3C22×C22⋊C411yescharacteristic
714C22×C3#53212yes—
715C2×D3—41no—
716C2×D3—41no—
717C2×D3—41no—
718C3×C4—21no—
719C3×C4—21no—
720C3×C4—41no—
721C3×C4—41no—
722C3×C4—41no—
723C3×C4—82no—
724C3×C4C4×#4112yes—
725C3×C4#52511yescharacteristic
726C3×C4#52511yescharacteristic
727Dic3—21no—
728Dic3—21no—
729Dic3—21no—
730Dic3—21no—
731Dic3—21no—
732Dic3—21no—
733Dic3—21no—
734Dic3—41no—
735Dic3—41no—
736Dic3—41no—
737Dic3—82no—
738Dic3#42112yes—
739C23—22no—
740C23—22no—
741C23—21no—
742C23—41no—
743C23—61no—
744C23D3×C22⋊C411yescharacteristic
745C23D3×C22⋊C411yescharacteristic
746C23C2×D3×D411yescharacteristic
747Q8—22no—
748Q8—62no—
749Q8—122no—
750Q8—122no—
751D4—22no—
752D4—42no—
753D4—42no—
754D4—42no—
755D4—62no—
756D4—122no—
757D4—122no—
758D4—122no—
759D4—122no—
760D4—122no—
761C2×C4—22no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—31no—
772C2×C4—31no—
773C2×C4—31no—
774C2×C4—31no—
775C2×C4—31no—
776C2×C4—31no—
777C2×C4—31no—
778C2×C4—31no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—62no—
785C2×C4—62no—
786C2×C4—62no—
787C2×C4—62no—
788C2×C4—62no—
789C2×C4—61no—
790C2×C4—61no—
791C2×C4—61no—
792C2×C4—122no—
793C2×C4—122no—
794C2×C4—121no—
795C2×C4—121no—
796C2×C4—121no—
797C2×C4—121no—
798C2×C4—121no—
799C2×C4—121no—
800C2×C4—121no—
801C2×C4—122no—
802C2×C4—122no—
803C2×C4—121no—
804C2×C4—121no—
805C2×C4—122no—
806C2×C4—122no—
807C2×C4—122no—
808C2×C4D3×C22⋊C411yescharacteristic
809C2×C4D3×C22⋊C411yescharacteristic
810C2×C4C22×C4×D311yescharacteristic
811C2×C4C2×D3×D411yescharacteristic
812C2×C4C2×#23712yes—
813C2×C4D3×#4112yes—
814C8—24no—
815C8—64no—
816C2×C3—22no—
817C2×C3—22no—
818C2×C3—41no—
819C2×C3—81no—
820C2×C3#229711yescharacteristic
821C2×C3C2×#42111yescharacteristic
822C2×C3C2×#42111yescharacteristic
823D3—81no—
824C22—21no—
825C22—21no—
826C22—21no—
827C22—21no—
828C22—21no—
829C22—21no—
830C22—21no—
831C22—44no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—121no—
836C22—121no—
837C22—121no—
838C22#482112yes—
839C22C2×D3×C22⋊C411yescharacteristic
840C22#559612yes—
841C4—21no—
842C4—21no—
843C4—32no—
844C4—41no—
845C4—41no—
846C4—41no—
847C4—61no—
848C4—61no—
849C4—61no—
850C4—61no—
851C4—61no—
852C4—61no—
853C4—61no—
854C4—82no—
855C4—121no—
856C4—121no—
857C4—121no—
858C4—242no—
859C4C4×#23712yes—
860C4#558611yescharacteristic
861C4#565611yescharacteristic
862C3#2138311yescharacteristic, complemented, Sylow
863C2—22no—
864C2—22no—
865C2—41no—
866C2—81no—
867C2—241no—
868C2#7465811yescharacteristic
869C2C2×#482111yescharacteristic
870C2D3×#42111yescharacteristic
subgroupG/H
centerC2×C4C2×D3×D4
commutatorC2×C3×C4C23×C4
FrattiniC22×C4C23×D3
FittingC3×#1871C2
socleC22×C3C22×C22⋊C4
prime radical#86018C2
cosocleC22×C3×C4C24
hypercenter#1871D3
hypocenterC3#21383
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1871

Complements

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

NH ≅ G/Ntype
2. C2×Dic3×M16C2semidirect
3. #73437C2semidirect
4. C3×#1871C2semidirect
5. #71984C2semidirect
6. #71713C2semidirect
7. #70358C2semidirect
8. #70354C2semidirect
9. #69453C2semidirect
10. #68730C2semidirect
11. #68729C2semidirect
22. #5624C4semidirect
23. #5624C4semidirect
24. #5622C4semidirect
25. #5622C4semidirect
26. #5600C4semidirect
27. #5600C4semidirect
28. #5596C4semidirect
29. #5596C4semidirect
68. #1871D3semidirect
296. C3×M16#41semidirect
368. #208#41semidirect
629. M16#237semidirect
862. C3#21383semidirect

Maximal subgroups

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

subgroupindex
#860182
C2×Dic3×M162
#734372
C3×#18712
#719842
#717132
#703582
#703542
#694532
#687302
#687292
#213833