Finite Group Databasebeta

← #11864210

Subgroups — #11864210

Order 1152.

1637 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#235C211yesmaximal, characteristic
2C2×#64151C211yesmaximal, characteristic, complemented
3C2×C3×#946C211yesmaximal, characteristic, complemented
4C2×C3×#942C211yesmaximal, characteristic, complemented
5#10591657C212yesmaximal, complemented
6#10591655C212yesmaximal, complemented
7#10591653C212yesmaximal, complemented
8#10591651C212yesmaximal, complemented
9#10591106C211yesmaximal, characteristic, complemented
10#10591087C211yesmaximal, characteristic, complemented
11#10591069C211yesmaximal, characteristic, complemented
12#83981—31nomaximal
13#82735—31nomaximal
14C22×C32×Q8C2211yescharacteristic, complemented
15C2×#3828C2211yescharacteristic
16C2×C3×#235C2211yescharacteristic
17C22×C3×C4×D3C2211yescharacteristic
18C2×D3×#67—21no—
19C2×#3804—21no—
20D3×#235—24no—
21D3×#235—24no—
22C2×D3×D12C2211yescharacteristic
23C2×C4×D32—21no—
24C2×#3799C2211yescharacteristic
25C2×#3798—21no—
26C2×#3795C2211yescharacteristic
27C2×D3×Dic6C2211yescharacteristic
28C2×#3756C2212yescomplemented
29#64151—24no—
30C2×#3755C2212yescomplemented
31C2×#3748C2211yescharacteristic, complemented
32C3×#946—21no—
33C3×#946—21no—
34C3×#946C2212yes—
35C3×#946C2212yescomplemented
36C2×C3×#216C2212yescomplemented
37C3×#942—24no—
38C2×C3×#215C2212yescomplemented
39C2×C3×(C2×D3)⋊C4—21no—
40C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
41C2×C3×Dic3⋊C4—21no—
42C2×C3×#208C2211yescharacteristic, complemented
43#63567C2212yescomplemented
44#63565C2212yescomplemented
45#63564C2212yescomplemented
46#63562C2212yescomplemented
47(C2×D3)⋊(C3⋊C8)C2212yes—
48(C2×D3)⋊(C3⋊C8)C2212yescomplemented
49C2×D3×#41—31no—
50C22×#235—31no—
51C2×C3×#137—31no—
52C2×C3×C22⋊Q8—31no—
53C2×#946D311yescharacteristic, complemented
54C2×#942—31no—
55C2×#942—31no—
56C2×#942—61no—
57C2×#942D311yescharacteristic, complemented
58#5232—31no—
59#5207—31no—
60#5187—32no—
61#5186—32no—
62#5173—32no—
63#5169—32no—
64#5133—31no—
65#5126—31no—
66#5050—32no—
67#5047—32no—
68#5047—32no—
69#5046—32no—
70#4966—31no—
71#4966—31no—
72C23×C3×D3D411yescharacteristic
73C22×D32—21no—
74C2×C32×Q8—21no—
75C2×C32×Q8—22no—
76C2×C32×Q8—22no—
77C2×C32×Q8C2312yes—
78C22×C32×C4—21no—
79C22×C32×C4C2311yescharacteristic
80C2×#638—21no—
81#3828—22no—
82#3828D414yes—
83C2×C4⋊(C3⋊D3)C2311yescharacteristic
84C2×C4×C3⋊D3—21no—
85C2×#634C2311yescharacteristic
86C2×C3×#67—21no—
87C22×C3×Dic3—21no—
88C22×C3×Dic3D411yescharacteristic
89C3×#235—22no—
90C3×#235D414yes—
91C2×C3×D12C2311yescharacteristic
92C2×C3×C4×D3—21no—
93C2×C3×C4×D3—22no—
94C2×C3×C4×D3—22no—
95C2×C3×C4×D3D411yescharacteristic
96C2×C3×C4×D3D411yescharacteristic
97C2×C3×C4×D3C2311yescharacteristic
98C2×C3×C4×D3C2311yescharacteristic
99C2×C3×Dic6C2311yescharacteristic
100D3×#67—28no—
101C2×#627—21no—
102C2×#626—21no—
103C2×#626—21no—
104C2×#625—21no—
105C2×#624—21no—
106#3804—28no—
107C2×D3×Dic3—21no—
108C2×D3×Dic3—21no—
109D3×D12—22no—
110D3×D12—22no—
111C4×D32—28no—
112#3799—22no—
113#3799—22no—
114#3798—28no—
115#3795—22no—
116#3795—22no—
117D3×Dic6—22no—
118D3×Dic6—22no—
119#3756—24no—
120#3755—24no—
121#3748—22no—
122C2×C3⋊(C3⋊C8)C2312yes—
123C3×#216—24no—
124C3×#215—24no—
125C3×(C2×D3)⋊C4—22no—
126C3×(C2×D3)⋊C4—22no—
127C3×C4⋊Dic3—21no—
128C3×C4⋊Dic3C2312yes—
129C3×Dic3⋊C4—22no—
130C3×Dic3⋊C4—22no—
131C3×#208—22no—
132C2×C3×C3⋊C8C2312yes—
133#3007—91noSylow
134C2×C3×#41—31no—
135C22×C3×Q8—21no—
136C22×C3×Q8C2×D311yescharacteristic, complemented
137C22×C3×Q8C2×D311yescharacteristic, complemented
138C23×C3×C4—31no—
139C22×#67—61no—
140D3×#41—64no—
141D3×#41—64no—
142C2×#239—31no—
143C2×D3×Q8—31no—
144C2×#237—31no—
145C2×#237—61no—
146C2×D3×D4—31no—
147C2×D3×D4—61no—
148C2×#235—31no—
149C2×#235—31no—
150C2×#235—31no—
151C2×#235—31no—
152C2×#235—61no—
153C2×#235—61no—
154C2×#235—64no—
155C2×#235—61no—
156C2×#235—64no—
157C2×#235—61no—
158C2×#235C2×D311yescharacteristic
159C22×D12—31no—
160C22×C4×D3—61no—
161C22×C4×D3—61no—
162C22×C4×D3C2×D311yescharacteristic
163C22×Dic6—31no—
164C3×#137—64no—
165C2×C3×Q16—32no—
166C2×C3×SD16—32no—
167C2×C3×M16—31no—
168C3×C22⋊Q8—32no—
169C3×C22⋊Q8—32no—
170C3×C22⋊Q8—61no—
171C3×C22⋊Q8—61no—
172C2×C3×C4⋊C4—31no—
173C2×C3×C4⋊C4—61no—
174C2×C3×C22⋊C4—61no—
175#946—21no—
176#946—21no—
177#946C2×D312yes—
178#946C2×D312yescomplemented
179C2×#216—32no—
180C2×#216—32no—
181C2×#216—62no—
182C2×#216C2×D312yescomplemented
183#942—24no—
184#942—64no—
185#942—64no—
186#942—68no—
187C2×#215—32no—
188C2×#215—32no—
189C2×#215—62no—
190C2×#215C2×D312yescomplemented
191C2×(C2×D3)⋊C4—21no—
192C2×C4⋊Dic3C2×D311yescharacteristic, complemented
193C2×Dic3⋊C4—21no—
194C2×#208—31no—
195C2×#208—31no—
196C2×#208—61no—
197C2×#208C2×D311yescharacteristic, complemented
198#835—32no—
199#832—32no—
200#830—32no—
201#830—32no—
202#821—32no—
203(C2×D3)⋊C8—32no—
204(C2×D3)⋊C8—32no—
205#816—32no—
206#810—32no—
207#810—32no—
208#809—32no—
209#809—32no—
210C23×C32C2×D411yescharacteristic
211C22×C3⋊D3—21no—
212C22×C3×D3—22no—
213C22×C3×D3—21no—
214C22×C3×D3—22no—
215C22×C3×D3—41no—
216C22×C3×D3C2×D411yescharacteristic
217C22×C3×D3C2×D411yescharacteristic
218C2×D32—24no—
219C2×D32—42no—
220C2×D32—42no—
221C32×Q8—22no—
222C32×Q8—22no—
223C32×Q8—42no—
224C2×C32×C4—22no—
225C2×C32×C4—42no—
226C2×C32×C4C2×D412yes—
227C2×C32×C4C2×D411yescharacteristic
228C2×C32×C4C2×D412yes—
229C2×C32×C4C2411yescharacteristic
230#638—24no—
231C2×C3⋊Dic3—21no—
232C4⋊(C3⋊D3)—21no—
233C4⋊(C3⋊D3)C2×D412yes—
234C4×C3⋊D3—24no—
235#634—21no—
236#634C2×D412yes—
237C3×#67—24no—
238C2×C3×Dic3—22no—
239C2×C3×Dic3—21no—
240C2×C3×Dic3—22no—
241C2×C3×Dic3—42no—
242C2×C3×Dic3C2×D411yescharacteristic
243C2×C3×Dic3C2×D411yescharacteristic
244C3×D12—21no—
245C3×D12C2×D412yes—
246C3×C4×D3—22no—
247C3×C4×D3—24no—
248C3×C4×D3—22no—
249C3×C4×D3—21no—
250C3×C4×D3—21no—
251C3×C4×D3—21no—
252C3×C4×D3—21no—
253C3×Dic6—21no—
254C3×Dic6C2×D412yes—
255#627—24no—
256#626—24no—
257#626—24no—
258#625—24no—
259#624—24no—
260D3×Dic3—24no—
261D3×Dic3—24no—
262C3⋊(C3⋊C8)—22no—
263C3×C3⋊C8—22no—
264C22×#41—91no—
265C2×#137—31no—
266C2×#137—91no—
267C2×C22⋊Q8—31no—
268#452—92no—
269#452—92no—
270#451—92no—
271#450—92no—
272#417—91no—
273#417—91no—
274#407—91no—
275C24×C3—31no—
276C23×D3—61no—
277C23×D3—61no—
278C23×D3#6711yescharacteristic
279C3×#41—34no—
280C3×#41—62no—
281C2×C3×Q8—21no—
282C2×C3×Q8—21no—
283C2×C3×Q8—24no—
284C2×C3×Q8—22no—
285C2×C3×Q8—22no—
286C2×C3×Q8—22no—
287C2×C3×Q8—22no—
288C2×C3×Q8—22no—
289C2×C3×Q8—31no—
290C2×C3×Q8—41no—
291C2×C3×Q8—42no—
292C2×C3×Q8C22×D312yes—
293C2×C3×Q8C22×D312yes—
294C2×C3×D4—31no—
295C2×C3×D4—61no—
296C22×C3×C4—21no—
297C22×C3×C4—21no—
298C22×C3×C4—21no—
299C22×C3×C4—31no—
300C22×C3×C4—31no—
301C22×C3×C4—31no—
302C22×C3×C4—31no—
303C22×C3×C4—31no—
304C22×C3×C4—41no—
305C22×C3×C4—62no—
306C22×C3×C4—61no—
307C22×C3×C4—62no—
308C22×C3×C4—61no—
309C22×C3×C4C22×D311yescharacteristic
310C22×C3×C4C22×D311yescharacteristic
311C2×#67—21no—
312C2×#67—61no—
313C2×#67—68no—
314C2×#67—61no—
315C2×#67—61no—
316C2×#67—61no—
317C2×#67—61no—
318C2×#67—61no—
319C2×#67—121no—
320C22×Dic3—21no—
321C22×Dic3—61no—
322C22×Dic3—61no—
323C22×Dic3#6711yescharacteristic
324#239—62no—
325#239—62no—
326D3×Q8—62no—
327D3×Q8—62no—
328#237—62no—
329#237—62no—
330#237—68no—
331D3×D4—62no—
332D3×D4—62no—
333D3×D4—68no—
334#235—22no—
335#235—34no—
336#235—34no—
337#235—64no—
338#235—62no—
339#235—62no—
340#235—68no—
341#235—68no—
342#235—68no—
343#235—62no—
344#235—62no—
345#235—62no—
346#235—62no—
347#235—122no—
348#235#6714yes—
349C2×D12—31no—
350C2×D12—31no—
351C2×D12—61no—
352C2×D12—62no—
353C2×D12—61no—
354C2×D12—61no—
355C2×D12—62no—
356C2×D12C22×D311yescharacteristic
357C2×C4×D3—21no—
358C2×C4×D3—22no—
359C2×C4×D3—22no—
360C2×C4×D3—68no—
361C2×C4×D3—68no—
362C2×C4×D3—61no—
363C2×C4×D3—61no—
364C2×C4×D3—61no—
365C2×C4×D3—61no—
366C2×C4×D3—61no—
367C2×C4×D3—61no—
368C2×C4×D3—121no—
369C2×C4×D3#6711yescharacteristic
370C2×C4×D3#6711yescharacteristic
371C2×C4×D3C22×D311yescharacteristic
372C2×C4×D3C22×D311yescharacteristic
373C2×Dic6—31no—
374C2×Dic6—31no—
375C2×Dic6—61no—
376C2×Dic6—62no—
377C2×Dic6—61no—
378C2×Dic6—61no—
379C2×Dic6—62no—
380C2×Dic6C22×D311yescharacteristic
381C3×Q16—64no—
382C3×SD16—64no—
383C3×M16—62no—
384C2×C3×C8—32no—
385C3×C4⋊C4—32no—
386C3×C4⋊C4—62no—
387C3×C4⋊C4—62no—
388C3×C4⋊C4—61no—
389C3×C22⋊C4—62no—
390C3×C22⋊C4—62no—
391#216—24no—
392#216—64no—
393#216—64no—
394#216—68no—
395#215—24no—
396#215—64no—
397#215—64no—
398#215—68no—
399(C2×D3)⋊C4—22no—
400(C2×D3)⋊C4—22no—
401C4⋊Dic3—21no—
402C4⋊Dic3C22×D312yes—
403Dic3⋊C4—22no—
404Dic3⋊C4—22no—
405#208—22no—
406#208—64no—
407#208—62no—
408#208—62no—
409C2×C3⋊C8—32no—
410C2×C3⋊C8—32no—
411C2×C3⋊C8—62no—
412C2×C3⋊C8C22×D312yes—
413C22×C32—21no—
414C22×C32—21no—
415C22×C32#12012yes—
416C22×C32C22×D411yescharacteristic
417C2×C3⋊D3—22no—
418C2×C3⋊D3—41no—
419C2×C3⋊D3—41no—
420C2×C3×D3—21no—
421C2×C3×D3—21no—
422C2×C3×D3—22no—
423C2×C3×D3—21no—
424C2×C3×D3—21no—
425C2×C3×D3—21no—
426C2×C3×D3—44no—
427C2×C3×D3—41no—
428C2×C3×D3—41no—
429C2×C3×D3#13712yescomplemented
430D32—48no—
431C32×C4—42no—
432C32×C4#12012yes—
433C32×C4C22×D411yescharacteristic
434C32×C4C22×D411yescharacteristic
435C3⋊Dic3—22no—
436C3×Dic3—21no—
437C3×Dic3—22no—
438C3×Dic3—21no—
439C3×Dic3—42no—
440C2×#41—31no—
441C2×#41—91no—
442C2×#41—91no—
443C2×#41—91no—
444C2×#41—181no—
445C2×#41—181no—
446C2×#41—184no—
447C2×#41—184no—
448C22×Q8—91no—
449C22×Q8D3211yescharacteristic, complemented
450C22×D4—91no—
451C22×D4—181no—
452C23×C4—31no—
453C23×C4—181no—
454#137—64no—
455#137—184no—
456C2×Q16—32no—
457C2×Q16—92no—
458C2×SD16—32no—
459C2×SD16—92no—
460C2×M16—31no—
461C2×M16—91no—
462C22⋊Q8—32no—
463C22⋊Q8—32no—
464C22⋊Q8—61no—
465C22⋊Q8—61no—
466C2×C4⋊C4—31no—
467C2×C4⋊C4—61no—
468C2×C22⋊C4—61no—
469#103—92no—
470#103—92no—
471#102—92no—
472#102—92no—
473C22⋊C8—92no—
474C22⋊C8—92no—
475C23×C3—21no—
476C23×C3—31no—
477C23×C3—31no—
478C23×C3—62no—
479C23×C3—62no—
480C23×C3—61no—
481C23×C3—121no—
482C23×C3D3×D411yescharacteristic
483C23×C3C2×#6711yescharacteristic
484C22×D3—22no—
485C22×D3—21no—
486C22×D3—22no—
487C22×D3—41no—
488C22×D3—64no—
489C22×D3—64no—
490C22×D3—61no—
491C22×D3—61no—
492C22×D3—121no—
493C22×D3—122no—
494C22×D3—122no—
495C22×D3—122no—
496C22×D3—122no—
497C22×D3C2×#6711yescharacteristic
498C22×D3C2×#6711yescharacteristic
499C3×Q8—24no—
500C3×Q8—22no—
501C3×Q8—22no—
502C3×Q8—22no—
503C3×Q8—22no—
504C3×Q8—32no—
505C3×Q8—42no—
506C3×Q8—44no—
507C3×Q8—42no—
508C3×Q8—42no—
509C3×Q8—61no—
510C3×D4—32no—
511C3×D4—64no—
512C3×D4—61no—
513C2×C3×C4—22no—
514C2×C3×C4—22no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—22no—
518C2×C3×C4—22no—
519C2×C3×C4—31no—
520C2×C3×C4—31no—
521C2×C3×C4—42no—
522C2×C3×C4—44no—
523C2×C3×C4—42no—
524C2×C3×C4—42no—
525C2×C3×C4—62no—
526C2×C3×C4—61no—
527C2×C3×C4—62no—
528C2×C3×C4—64no—
529C2×C3×C4—62no—
530C2×C3×C4—61no—
531C2×C3×C4—61no—
532C2×C3×C4—61no—
533C2×C3×C4—61no—
534C2×C3×C4—62no—
535C2×C3×C4—122no—
536C2×C3×C4D3×D411yescharacteristic
537C2×C3×C4D3×D412yes—
538C2×C3×C4D3×D412yes—
539C2×C3×C4D3×D412yes—
540C2×C3×C4C2×#6711yescharacteristic
541C2×C3×C4C2×#6712yes—
542C2×C3×C4C23×D311yescharacteristic
543C2×C3×C4C23×D311yescharacteristic
544#67—24no—
545#67—64no—
546#67—64no—
547#67—64no—
548#67—64no—
549#67—64no—
550#67—64no—
551#67—124no—
552C2×Dic3—22no—
553C2×Dic3—21no—
554C2×Dic3—22no—
555C2×Dic3—42no—
556C2×Dic3—64no—
557C2×Dic3—64no—
558C2×Dic3—61no—
559C2×Dic3—61no—
560C2×Dic3—121no—
561C2×Dic3C2×#6711yescharacteristic
562C2×Dic3C2×#6711yescharacteristic
563D12—21no—
564D12—32no—
565D12—32no—
566D12—62no—
567D12—64no—
568D12—64no—
569D12—61no—
570D12—61no—
571D12—121no—
572D12C2×#6712yes—
573C4×D3—22no—
574C4×D3—22no—
575C4×D3—24no—
576C4×D3—21no—
577C4×D3—21no—
578C4×D3—21no—
579C4×D3—21no—
580C4×D3—64no—
581C4×D3—64no—
582C4×D3—64no—
583C4×D3—64no—
584C4×D3—64no—
585C4×D3—64no—
586C4×D3—124no—
587Dic6—21no—
588Dic6—32no—
589Dic6—32no—
590Dic6—62no—
591Dic6—64no—
592Dic6—64no—
593Dic6—61no—
594Dic6—61no—
595Dic6—121no—
596Dic6C2×#6712yes—
597C3×C8—62no—
598C3⋊C8—22no—
599C3⋊C8—64no—
600C3⋊C8—62no—
601C3⋊C8—62no—
602C2×C32—22no—
603C2×C32C2×#12011yescharacteristic
604C2×C32C2×#13711yescharacteristic
605C2×C32#57511yescharacteristic
606C3⋊D3—42no—
607C3×D3—22no—
608C3×D3—42no—
609C3×D3—41no—
610C24—31no—
611C24—181no—
612#41—34no—
613#41—62no—
614#41—94no—
615#41—188no—
616#41—182no—
617#41—182no—
618#41—188no—
619#41—182no—
620#41—182no—
621#41—182no—
622C2×Q8—21no—
623C2×Q8—22no—
624C2×Q8—22no—
625C2×Q8—31no—
626C2×Q8—91no—
627C2×Q8—181no—
628C2×Q8—182no—
629C2×Q8—182no—
630C2×Q8C2×D3212yes—
631C2×D4—31no—
632C2×D4—61no—
633C2×D4—91no—
634C2×D4—181no—
635C2×D4—182no—
636C2×D4—182no—
637C2×D4—181no—
638C2×D4—188no—
639C2×D4—181no—
640C2×D4—181no—
641C22×C4—21no—
642C22×C4—31no—
643C22×C4—31no—
644C22×C4—31no—
645C22×C4—31no—
646C22×C4—31no—
647C22×C4—62no—
648C22×C4—61no—
649C22×C4—62no—
650C22×C4—61no—
651C22×C4—181no—
652C22×C4—181no—
653C22×C4—188no—
654C22×C4—181no—
655C22×C4—181no—
656C22×C4C2×D3211yescharacteristic
657Q16—64no—
658Q16—184no—
659SD16—64no—
660SD16—184no—
661M16—62no—
662M16—182no—
663C2×C8—32no—
664C2×C8—92no—
665C4⋊C4—32no—
666C4⋊C4—62no—
667C4⋊C4—62no—
668C4⋊C4—61no—
669C22⋊C4—62no—
670C22⋊C4—62no—
671C22×C3—21no—
672C22×C3—21no—
673C22×C3—21no—
674C22×C3—21no—
675C22×C3—21no—
676C22×C3—22no—
677C22×C3—32no—
678C22×C3—41no—
679C22×C3—41no—
680C22×C3—61no—
681C22×C3—61no—
682C22×C3—61no—
683C22×C3—61no—
684C22×C3—62no—
685C22×C3—61no—
686C22×C3—124no—
687C22×C3—121no—
688C22×C3—121no—
689C22×C3#93712yes—
690C22×C3#93712yes—
691C22×C3C2×D3×D411yescharacteristic
692C22×C3C22×#6711yescharacteristic
693C2×D3—21no—
694C2×D3—21no—
695C2×D3—21no—
696C2×D3—22no—
697C2×D3—21no—
698C2×D3—21no—
699C2×D3—44no—
700C2×D3—41no—
701C2×D3—41no—
702C2×D3—62no—
703C2×D3—62no—
704C2×D3—122no—
705C2×D3—128no—
706C2×D3—128no—
707C2×D3—121no—
708C2×D3—121no—
709C2×D3—121no—
710C2×D3—121no—
711C2×D3—241no—
712C2×D3—241no—
713C2×D3#94212yescomplemented
714C3×C4—21no—
715C3×C4—21no—
716C3×C4—22no—
717C3×C4—44no—
718C3×C4—42no—
719C3×C4—42no—
720C3×C4—61no—
721C3×C4—62no—
722C3×C4—61no—
723C3×C4—122no—
724C3×C4#93712yes—
725C3×C4#93712yes—
726C3×C4C2×D3×D411yescharacteristic
727C3×C4C2×D3×D411yescharacteristic
728C3×C4C2×D3×D411yescharacteristic
729C3×C4C22×#6711yescharacteristic
730Dic3—22no—
731Dic3—21no—
732Dic3—21no—
733Dic3—42no—
734Dic3—62no—
735Dic3—62no—
736Dic3—122no—
737C32#300711yescharacteristic, complemented, Sylow
738C23—31no—
739C23—31no—
740C23—62no—
741C23—61no—
742C23—62no—
743C23—121no—
744C23—184no—
745C23—181no—
746C23—362no—
747C23—362no—
748C23D3×#6711yescharacteristic
749Q8—22no—
750Q8—22no—
751Q8—32no—
752Q8—42no—
753Q8—61no—
754Q8—92no—
755Q8—184no—
756Q8—181no—
757D4—32no—
758D4—64no—
759D4—61no—
760D4—92no—
761D4—184no—
762D4—184no—
763D4—184no—
764D4—184no—
765D4—181no—
766C2×C4—22no—
767C2×C4—31no—
768C2×C4—31no—
769C2×C4—42no—
770C2×C4—61no—
771C2×C4—62no—
772C2×C4—61no—
773C2×C4—61no—
774C2×C4—61no—
775C2×C4—61no—
776C2×C4—62no—
777C2×C4—62no—
778C2×C4—64no—
779C2×C4—62no—
780C2×C4—122no—
781C2×C4—184no—
782C2×C4—184no—
783C2×C4—184no—
784C2×C4—181no—
785C2×C4—184no—
786C2×C4D3×#6712yes—
787C2×C4D3×#6711yescharacteristic
788C2×C4#381112yes—
789C2×C4C22×D3211yescharacteristic
790C8—62no—
791C8—182no—
792C2×C3—22no—
793C2×C3—22no—
794C2×C3—21no—
795C2×C3—21no—
796C2×C3—21no—
797C2×C3—42no—
798C2×C3—62no—
799C2×C3—121no—
800C2×C3—122no—
801C2×C3D3×#13711yescharacteristic
802C2×C3#577711yescharacteristic
803C2×C3C2×#93711yescharacteristic
804C2×C3C2×#93711yescharacteristic
805C2×C3C2×#94211yescharacteristic
806C2×C3#582211yescharacteristic
807D3—22no—
808D3—42no—
809D3—41no—
810D3—122no—
811D3—122no—
812D3—242no—
813C22—21no—
814C22—21no—
815C22—32no—
816C22—61no—
817C22—61no—
818C22—61no—
819C22—62no—
820C22—61no—
821C22—61no—
822C22—124no—
823C22—121no—
824C22—121no—
825C22—182no—
826C22—368no—
827C22—361no—
828C22—361no—
829C22#6398312yes—
830C22C2×D3×#6711yescharacteristic
831C4—42no—
832C4—61no—
833C4—61no—
834C4—62no—
835C4—122no—
836C4—182no—
837C4#6398312yes—
838C4C2×D3×#6711yescharacteristic
839C4C2×#381111yescharacteristic
840C3—21no—
841C3#8273511yescharacteristic, complemented
842C3#8398111yescharacteristic, complemented
843C2—22no—
844C2—62no—
845C2—121no—
846C2—122no—
847C2—362no—
848C2D3×#94211yescharacteristic
849C2#1059531711yescharacteristic
850C2C2×#6398311yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC22×C32C22×D4
prime radicalC2×D3×#235C2
hypercenterC22×Q8D32
hypocenterC32#3007
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. C2×#64151C2semidirect
3. C2×C3×#946C2semidirect
4. C2×C3×#942C2semidirect
5. #10591657C2semidirect
6. #10591655C2semidirect
7. #10591653C2semidirect
8. #10591651C2semidirect
9. #10591106C2semidirect
10. #10591087C2semidirect
11. #10591069C2semidirect
14. C22×C32×Q8C22semidirect
28. C2×#3756C22semidirect
30. C2×#3755C22semidirect
31. C2×#3748C22semidirect
35. C3×#946C22semidirect
36. C2×C3×#216C22semidirect
38. C2×C3×#215C22semidirect
40. C2×C3×C4⋊Dic3C22semidirect
42. C2×C3×#208C22semidirect
43. #63567C22semidirect
44. #63565C22semidirect
45. #63564C22semidirect
46. #63562C22semidirect
48. (C2×D3)⋊(C3⋊C8)C22semidirect
53. C2×#946D3semidirect
57. C2×#942D3semidirect
136. C22×C3×Q8C2×D3semidirect
137. C22×C3×Q8C2×D3semidirect
178. #946C2×D3semidirect
182. C2×#216C2×D3semidirect
190. C2×#215C2×D3semidirect
192. C2×C4⋊Dic3C2×D3semidirect
197. C2×#208C2×D3semidirect
429. C2×C3×D3#137semidirect
449. C22×Q8D32semidirect
713. C2×D3#942semidirect
737. C32#3007semidirect
841. C3#82735semidirect
842. C3#83981semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#2352
C2×#641512
C2×C3×#9462
C2×C3×#9422
#105916572
#105916552
#105916532
#105916512
#105911062
#105910872
#105910692
#839813
#827353