Finite Group Databasebeta

← #11865815

Subgroups — #11865815

Order 1152.

1048 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×#239C211yesmaximal, characteristic, complemented
2C2×#63949C211yesmaximal, characteristic, complemented
3C2×#63947C211yesmaximal, characteristic, complemented
4#10593969C211yesmaximal, characteristic, complemented
5#10592727C211yesmaximal, characteristic, complemented
6C3×#5028C211yesmaximal, characteristic, complemented
7#10591625C211yesmaximal, characteristic, complemented
8#10591617C211yesmaximal, characteristic, complemented
9#10590610C211yesmaximal, characteristic, complemented
10#10590608C211yesmaximal, characteristic, complemented
11#10590559C211yesmaximal, characteristic, complemented
12#10590547C211yesmaximal, characteristic, complemented
13#10590366C211yesmaximal, characteristic, complemented
14#10590348C211yesmaximal, characteristic, complemented
15D3×C4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
16#82525—31nomaximal
17#80597—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×#3799C2211yescharacteristic
20C2×#3795C2211yescharacteristic
21C32×C4×Q8C2211yescharacteristic
22C2×#3756C2211yescharacteristic
23C2×#3755C2211yescharacteristic
24#64084C2211yescharacteristic
25C3×Q8×Dic3C2211yescharacteristic
26C2×C3×#216C2211yescharacteristic
27C2×C3×#215C2211yescharacteristic
28C3×#893—21no—
29C3×#893C2211yescharacteristic
30C3×#892—21no—
31C3×#892C2211yescharacteristic
32C3×#875C2211yescharacteristic
33C3×C4×D12—21no—
34C3×C4×D12C2211yescharacteristic
35C3×C42×D3—21no—
36C3×C42×D3C2211yescharacteristic
37#63949—24no—
38#63947—24no—
39#63911C2211yescharacteristic
40#63906—21no—
41#63906—21no—
42#63880—21no—
43#63880—21no—
44#63866C2211yescharacteristic
45C2×#3716C2211yescharacteristic
46C2×#3715C2211yescharacteristic
47C2×#3714C2211yescharacteristic
48C2×#3713C2211yescharacteristic
49C2×D3×C3⋊C8C2211yescharacteristic
50C2×D3×C3⋊C8C2211yescharacteristic
51#63637C2211yescharacteristic
52#63636C2211yescharacteristic
53C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
54C3×#810C2211yescharacteristic
55C3×#809C2211yescharacteristic
56C3×C4⋊(C3⋊C8)C2211yescharacteristic
57Dic3⋊(C3⋊C8)C2211yescharacteristic
58Dic3⋊(C3⋊C8)C2211yescharacteristic
59#63567C2211yescharacteristic
60#63565C2211yescharacteristic
61#63564C2211yescharacteristic
62#63562C2211yescharacteristic
63C3×C4×#41—31no—
64C2×#950—31no—
65C2×#950—31no—
66C2×#919—31no—
67C2×#916—31no—
68#5668—31no—
69C4×#239D311yescharacteristic, complemented
70#5477—31no—
71C3×#464—31no—
72#5182—31no—
73#5163—31no—
74#5057—31no—
75#5031—31no—
76#5028—31no—
77#5028—31no—
78#5028—61no—
79#5028D311yescharacteristic, complemented
80#5027—31no—
81#5019—31no—
82#5016—31no—
83#5016—31no—
84#5015—31no—
85#5002—31no—
86#5002—31no—
87C2×C4⋊(C3⋊C8)—31no—
88#4844—31no—
89D3×C4⋊C8—31no—
90#4818—31no—
91#4804—31no—
92#4786—31no—
93#4772—31no—
94C2×C32×Q8C2311yescharacteristic
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C2×#634C2311yescharacteristic
97C3×#239—22no—
98C3×#239D414yescomplemented
99C2×C3×D12—21no—
100C2×C3×D12C2311yescharacteristic
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3D411yescharacteristic
106C2×C3×C4×D3D411yescharacteristic
107C2×C3×C4×D3C2311yescharacteristic
108C2×C3×Dic6C2311yescharacteristic
109C2×#626—21no—
110C2×#626—21no—
111C2×#626—21no—
112C2×#625—21no—
113C2×#624—21no—
114C2×D3×Dic3—21no—
115#3799—22no—
116#3799—22no—
117#3795—22no—
118#3795—22no—
119C32×C4⋊C4—21no—
120C32×C4⋊C4C2311yescharacteristic
121C32×C42—21no—
122C32×C42C2311yescharacteristic
123#3756—22no—
124#3755—22no—
125#3752—21no—
126#3752—21no—
127C2×C3⋊(C3⋊C8)C2311yescharacteristic
128C2×C3⋊(C3⋊C8)C2311yescharacteristic
129C3×#216—22no—
130C3×#215—22no—
131C3×(C2×D3)⋊C4—21no—
132C3×(C2×D3)⋊C4—21no—
133C3×(C2×D3)⋊C4—21no—
134C3×(C2×D3)⋊C4—21no—
135C3×(C2×D3)⋊C4—21no—
136C3×C4⋊Dic3—21no—
137C3×C4⋊Dic3C2311yescharacteristic
138C3×C4×Dic3—21no—
139C3×C4×Dic3—21no—
140C3×C4×Dic3D411yescharacteristic
141C3×C4×Dic3D411yescharacteristic
142C3×C4×Dic3C2311yescharacteristic
143C2×C3×C3⋊C8C2311yescharacteristic
144C2×C3×C3⋊C8C2311yescharacteristic
145Dic3⋊Dic3—21no—
146Dic3⋊Dic3—21no—
147#3716—22no—
148#3715—22no—
149#3714—22no—
150#3713—22no—
151D3×C3⋊C8—22no—
152D3×C3⋊C8—22no—
153#3035—91noSylow
154C2×C3×#41—31no—
155C2×#239—31no—
156C2×#239C2×D311yescharacteristic
157C2×#237—31no—
158C2×#235—31no—
159C2×#235—31no—
160C2×C3×Q16—31no—
161C2×C3×SD16—31no—
162C3×#124—31no—
163C3×C4×Q8—21no—
164C3×C4×Q8—31no—
165C3×C4×Q8C2×D311yescharacteristic
166C3×C4×Q8C2×D311yescharacteristic
167C3×C4×D4—31no—
168C3×C4×D4—31no—
169C3×C4×D4—61no—
170C3×C4×D4—61no—
171C3×#117—31no—
172C3×#117—61no—
173C2×C3×C42—31no—
174C2×C3×C42—61no—
175#950—64no—
176#950—64no—
177Q8×Dic3C2×D311yescharacteristic
178#944—31no—
179C2×#216—31no—
180C2×#216—31no—
181C2×#216—61no—
182C2×#216C2×D311yescharacteristic
183C2×#215—31no—
184C2×#215—31no—
185C2×#215—31no—
186C2×#215—61no—
187C2×#215C2×D311yescharacteristic
188#940—31no—
189C2×#214—31no—
190C2×#214—31no—
191C2×#213—31no—
192C2×#213—31no—
193C2×#213—31no—
194#930—61no—
195#930—61no—
196C22×C3⋊C8—31no—
197C22×C3⋊C8—31no—
198#919—64no—
199#916—64no—
200C2×D24—31no—
201C2×#204—31no—
202C2×D3×C8—31no—
203C2×D3×C8—31no—
204#893—21no—
205#893C2×D311yescharacteristic
206#892—21no—
207#892C2×D311yescharacteristic
208#884—61no—
209#884—61no—
210#67⋊C4—61no—
211#67⋊C4—61no—
212#875—31no—
213#875—31no—
214#875—61no—
215#875C2×D311yescharacteristic
216#874—31no—
217C4×D12—21no—
218C4×D12—61no—
219C4×D12—61no—
220C4×D12C2×D311yescharacteristic
221C42×D3—21no—
222C42×D3C2×D311yescharacteristic
223#869—31no—
224C3×C4⋊C8—31no—
225C3×#103—31no—
226C3×#102—31no—
227#835—31no—
228#832—31no—
229#821—31no—
230#816—31no—
231Dic3⋊C8—31no—
232Dic3⋊C8—31no—
233#810—31no—
234#810—31no—
235#810—31no—
236#810—31no—
237#810—61no—
238#810C2×D311yescharacteristic
239#809—31no—
240#809—31no—
241#809—31no—
242#809—31no—
243#809—61no—
244#809C2×D311yescharacteristic
245C4⋊(C3⋊C8)—31no—
246C4⋊(C3⋊C8)—31no—
247C4⋊(C3⋊C8)—31no—
248C4⋊(C3⋊C8)—31no—
249C4⋊(C3⋊C8)—61no—
250C4⋊(C3⋊C8)C2×D311yescharacteristic
251C22×C3⋊D3—21no—
252C22×C3×D3—21no—
253C22×C3×D3—21no—
254C22×C3×D3C2×D411yescharacteristic
255C32×Q8—21no—
256C32×Q8C2×D412yes—
257C2×C32×C4—21no—
258C2×C32×C4—21no—
259C2×C32×C4C2×D411yescharacteristic
260C2×C32×C4C2×D411yescharacteristic
261C2×C32×C4C2411yescharacteristic
262C2×C3⋊Dic3—21no—
263C4⋊(C3⋊D3)—21no—
264C4⋊(C3⋊D3)—21no—
265#634—21no—
266#634—21no—
267C2×C3×Dic3—21no—
268C2×C3×Dic3—21no—
269C2×C3×Dic3C2×D411yescharacteristic
270C2×C3×Dic3C2×D411yescharacteristic
271C2×C3×Dic3C2×D411yescharacteristic
272C3×D12—24no—
273C3×D12—21no—
274C3×D12—21no—
275C3×D12—21no—
276C3×D12C2×D412yes—
277C3×C4×D3—24no—
278C3×C4×D3—22no—
279C3×C4×D3—41no—
280C3×C4×D3—42no—
281C3×C4×D3—42no—
282C3×C4×D3C2×D412yes—
283C3×C4×D3#4112yes—
284C3×Dic6—21no—
285C3×Dic6—21no—
286#626—42no—
287#626—42no—
288#626—42no—
289#625—42no—
290#624—42no—
291D3×Dic3—42no—
292C3⋊(C3⋊C8)—21no—
293C3⋊(C3⋊C8)—21no—
294C3×C3⋊C8—21no—
295C3×C3⋊C8—21no—
296C2×#135—91no—
297C2×#135—91no—
298#532—91no—
299C4×#41—31no—
300#464—31no—
301#464—91no—
302#463—91no—
303#463—91no—
304#462—91no—
305#461—91no—
306#460—91no—
307#459—91no—
308C2×C4⋊C8—91no—
309#416—91no—
310#416—91no—
311C3×#41—34no—
312C3×#41—62no—
313C2×C3×Q8—21no—
314C2×C3×Q8—31no—
315C2×C3×Q8C22×D311yescharacteristic
316C2×C3×Q8C22×D311yescharacteristic
317C2×C3×D4—31no—
318C2×C3×D4—31no—
319C2×C3×D4—61no—
320C22×C3×C4—31no—
321C22×C3×C4—31no—
322C22×C3×C4—31no—
323C22×C3×C4—61no—
324C22×C3×C4—61no—
325C22×C3×C4—61no—
326C2×#67—61no—
327C2×#67—61no—
328C2×#67—61no—
329C2×#67—61no—
330C2×#67—61no—
331C22×Dic3—61no—
332#239—22no—
333#239—62no—
334#239—62no—
335#239D1214yescomplemented
336#237—62no—
337#237—62no—
338#235—62no—
339#235—62no—
340#235—62no—
341#235—62no—
342C2×D12—21no—
343C2×D12—31no—
344C2×D12—31no—
345C2×D12—61no—
346C2×D12—61no—
347C2×D12—61no—
348C2×D12—61no—
349C2×D12C22×D311yescharacteristic
350C2×D12C22×D311yescharacteristic
351C2×C4×D3—21no—
352C2×C4×D3—21no—
353C2×C4×D3—21no—
354C2×C4×D3—61no—
355C2×C4×D3—61no—
356C2×C4×D3—61no—
357C2×C4×D3#6711yescharacteristic
358C2×C4×D3#6711yescharacteristic
359C2×C4×D3C22×D311yescharacteristic
360C2×Dic6—31no—
361C2×Dic6—31no—
362C2×Dic6—61no—
363C2×Dic6C22×D311yescharacteristic
364C3×Q16—62no—
365C3×SD16—62no—
366C2×C3×C8—31no—
367C2×C3×C8—31no—
368C3×C4⋊C4—21no—
369C3×C4⋊C4—21no—
370C3×C4⋊C4—21no—
371C3×C4⋊C4—31no—
372C3×C4⋊C4—41no—
373C3×C4⋊C4—61no—
374C3×C4⋊C4C22×D311yescharacteristic
375C3×C4⋊C4C22×D311yescharacteristic
376C3×C22⋊C4—61no—
377C3×C22⋊C4—61no—
378C3×C22⋊C4—61no—
379C3×C22⋊C4—61no—
380C3×C22⋊C4—61no—
381C3×C42—21no—
382C3×C42—21no—
383C3×C42—21no—
384C3×C42—31no—
385C3×C42—31no—
386C3×C42—31no—
387C3×C42—41no—
388C3×C42—61no—
389C3×C42—61no—
390C3×C42C22×D311yescharacteristic
391C3×C42C22×D311yescharacteristic
392#216—22no—
393#216—62no—
394#216—62no—
395#216—122no—
396#215—22no—
397#215—62no—
398#215—62no—
399#215—62no—
400#215—122no—
401#214—62no—
402#214—62no—
403#213—62no—
404#213—62no—
405#213—62no—
406(C2×D3)⋊C4—21no—
407(C2×D3)⋊C4—21no—
408(C2×D3)⋊C4—21no—
409(C2×D3)⋊C4—21no—
410(C2×D3)⋊C4—21no—
411(C2×D3)⋊C4—61no—
412(C2×D3)⋊C4—61no—
413(C2×D3)⋊C4—61no—
414(C2×D3)⋊C4—61no—
415(C2×D3)⋊C4—121no—
416(C2×D3)⋊C4—121no—
417C4⋊Dic3—21no—
418C4⋊Dic3—61no—
419C4⋊Dic3—61no—
420C4⋊Dic3C22×D311yescharacteristic
421Dic3⋊C4—61no—
422Dic3⋊C4—61no—
423C4×Dic3—21no—
424C4×Dic3—21no—
425C4×Dic3#6711yescharacteristic
426C4×Dic3#6711yescharacteristic
427C4×Dic3C22×D311yescharacteristic
428C2×C3⋊C8—31no—
429C2×C3⋊C8—31no—
430C2×C3⋊C8—31no—
431C2×C3⋊C8—31no—
432C2×C3⋊C8—61no—
433C2×C3⋊C8—61no—
434C2×C3⋊C8—62no—
435C2×C3⋊C8—62no—
436C2×C3⋊C8C22×D311yescharacteristic
437C2×C3⋊C8C22×D311yescharacteristic
438D24—62no—
439#204—62no—
440D3×C8—62no—
441D3×C8—62no—
442C22×C32C22×D411yescharacteristic
443C2×C3⋊D3—41no—
444C2×C3⋊D3—41no—
445C2×C3⋊D3—41no—
446C2×C3×D3—21no—
447C2×C3×D3—21no—
448C2×C3×D3—22no—
449C2×C3×D3—41no—
450C2×C3×D3—41no—
451C2×C3×D3—41no—
452C2×C3×D3—41no—
453C2×C3×D3—41no—
454C2×C3×D3#12112yes—
455C32×C4—22no—
456C32×C4—21no—
457C32×C4—21no—
458C32×C4—41no—
459C32×C4C22×D411yescharacteristic
460C32×C4C2×#4111yescharacteristic
461C3⋊Dic3—41no—
462C3×Dic3—21no—
463C3×Dic3—41no—
464C3×Dic3—41no—
465C3×Dic3#12112yes—
466C3×Dic3#13512yescomplemented
467C2×#41—31no—
468C2×#41—91no—
469C2×#41—91no—
470#135—184no—
471#135—184no—
472C2×Q16—31no—
473C2×Q16—91no—
474C2×SD16—31no—
475C2×SD16—91no—
476C2×SD16—91no—
477C2×SD16—91no—
478C2×D8—91no—
479C2×D8—91no—
480C22×C8—91no—
481C22×C8—91no—
482C4⋊Q8—91no—
483#127—91no—
484#124—31no—
485#124—91no—
486#121—181no—
487#121—181no—
488C4×Q8—31no—
489C4×Q8D3211yescharacteristic
490C4×D4—31no—
491C4×D4—31no—
492C4×D4—61no—
493C4×D4—61no—
494C4×D4—181no—
495C4×D4—181no—
496#117—31no—
497#117—61no—
498C2×C42—31no—
499C2×C42—61no—
500C4⋊C8—31no—
501C4⋊C8—91no—
502C4⋊C8—91no—
503C4⋊C8—91no—
504#103—31no—
505#103—91no—
506#103—91no—
507#103—91no—
508#102—31no—
509#102—91no—
510#102—91no—
511#102—91no—
512C23×C3—31no—
513C23×C3—61no—
514C23×C3—61no—
515C22×D3—21no—
516C22×D3—21no—
517C22×D3—61no—
518C22×D3—61no—
519C22×D3—121no—
520C22×D3C2×#6711yescharacteristic
521C3×Q8—21no—
522C3×Q8—21no—
523C3×Q8—22no—
524C3×Q8—41no—
525C3×Q8—61no—
526C3×Q8—61no—
527C3×Q8C2×D1212yes—
528C3×Q8D3×D412yes—
529C3×D4—32no—
530C3×D4—64no—
531C3×D4—61no—
532C3×D4—61no—
533C3×D4—61no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—21no—
538C2×C3×C4—21no—
539C2×C3×C4—21no—
540C2×C3×C4—21no—
541C2×C3×C4—31no—
542C2×C3×C4—31no—
543C2×C3×C4—32no—
544C2×C3×C4—32no—
545C2×C3×C4—31no—
546C2×C3×C4—41no—
547C2×C3×C4—41no—
548C2×C3×C4—62no—
549C2×C3×C4—64no—
550C2×C3×C4—61no—
551C2×C3×C4—61no—
552C2×C3×C4—121no—
553C2×C3×C4—122no—
554C2×C3×C4—122no—
555C2×C3×C4D3×D411yescharacteristic
556C2×C3×C4D3×D411yescharacteristic
557C2×C3×C4C2×#6711yescharacteristic
558C2×C3×C4C2×#6711yescharacteristic
559C2×C3×C4C23×D311yescharacteristic
560C2×C3×C4C23×D311yescharacteristic
561#67—122no—
562#67—122no—
563#67—122no—
564#67—122no—
565#67—122no—
566C2×Dic3—21no—
567C2×Dic3—21no—
568C2×Dic3—61no—
569C2×Dic3—61no—
570C2×Dic3—121no—
571C2×Dic3—122no—
572C2×Dic3C2×#6711yescharacteristic
573C2×Dic3C2×#6711yescharacteristic
574C2×Dic3C2×#6711yescharacteristic
575D12—24no—
576D12—21no—
577D12—21no—
578D12—21no—
579D12—61no—
580D12—61no—
581D12—61no—
582D12—61no—
583D12—121no—
584D12—121no—
585D12—122no—
586D12—122no—
587D12—122no—
588D12C2×D1212yes—
589C4×D3—24no—
590C4×D3—22no—
591C4×D3—41no—
592C4×D3—42no—
593C4×D3—42no—
594C4×D3—122no—
595C4×D3—122no—
596C4×D3—122no—
597C4×D3C2×D1212yes—
598C4×D3#23512yes—
599Dic6—21no—
600Dic6—21no—
601Dic6—61no—
602Dic6—61no—
603Dic6—61no—
604Dic6—61no—
605Dic6—121no—
606Dic6—121no—
607C3×C8—61no—
608C3×C8—61no—
609C3⋊C8—21no—
610C3⋊C8—21no—
611C3⋊C8—61no—
612C3⋊C8—61no—
613C3⋊C8—61no—
614C3⋊C8—61no—
615C3⋊C8—121no—
616C3⋊C8—121no—
617C2×C32C2×#12111yescharacteristic
618C2×C32C2×#13511yescharacteristic
619C2×C32#57511yescharacteristic
620C3⋊D3—81no—
621C3×D3—22no—
622C3×D3—42no—
623C3×D3—81no—
624#41—34no—
625#41—62no—
626#41—182no—
627#41—182no—
628#41—182no—
629#41—182no—
630C2×Q8—31no—
631C2×Q8—91no—
632C2×Q8C2×D3211yescharacteristic
633C2×D4—31no—
634C2×D4—31no—
635C2×D4—61no—
636C2×D4—91no—
637C2×D4—181no—
638C2×D4—181no—
639C2×D4—181no—
640C2×D4—181no—
641C22×C4—31no—
642C22×C4—31no—
643C22×C4—31no—
644C22×C4—61no—
645C22×C4—61no—
646C22×C4—61no—
647C22×C4—181no—
648C22×C4—181no—
649Q16—62no—
650Q16—182no—
651SD16—62no—
652SD16—182no—
653SD16—182no—
654SD16—182no—
655D8—182no—
656D8—182no—
657C2×C8—31no—
658C2×C8—31no—
659C2×C8—91no—
660C2×C8—91no—
661C2×C8—182no—
662C2×C8—182no—
663C4⋊C4—21no—
664C4⋊C4—31no—
665C4⋊C4—61no—
666C4⋊C4—181no—
667C4⋊C4—181no—
668C4⋊C4C2×D3211yescharacteristic
669C22⋊C4—61no—
670C22⋊C4—61no—
671C22⋊C4—61no—
672C22⋊C4—61no—
673C22⋊C4—61no—
674C22⋊C4—181no—
675C22⋊C4—181no—
676C42—21no—
677C42—31no—
678C42—31no—
679C42—31no—
680C42—61no—
681C42—61no—
682C42C2×D3211yescharacteristic
683C22×C3—21no—
684C22×C3—32no—
685C22×C3—61no—
686C22×C3—61no—
687C22×C3—62no—
688C22×C3—121no—
689C22×C3—121no—
690C22×C3—121no—
691C22×C3—121no—
692C22×C3—121no—
693C22×C3C2×D3×D411yescharacteristic
694C22×C3C22×#6711yescharacteristic
695C2×D3—21no—
696C2×D3—21no—
697C2×D3—22no—
698C2×D3—41no—
699C2×D3—41no—
700C2×D3—41no—
701C2×D3—41no—
702C2×D3—41no—
703C2×D3—121no—
704C2×D3—121no—
705C2×D3—121no—
706C2×D3—121no—
707C2×D3—121no—
708C2×D3—121no—
709C2×D3—241no—
710C2×D3—241no—
711C2×D3—241no—
712C2×D3#93012yes—
713C3×C4—21no—
714C3×C4—21no—
715C3×C4—22no—
716C3×C4—21no—
717C3×C4—21no—
718C3×C4—22no—
719C3×C4—21no—
720C3×C4—21no—
721C3×C4—32no—
722C3×C4—32no—
723C3×C4—41no—
724C3×C4—41no—
725C3×C4—42no—
726C3×C4—41no—
727C3×C4—41no—
728C3×C4—61no—
729C3×C4—81no—
730C3×C4—121no—
731C3×C4—121no—
732C3×C4C22×D1211yescharacteristic
733C3×C4C2×#23511yescharacteristic
734C3×C4C2×D3×D411yescharacteristic
735C3×C4D3×#4111yescharacteristic
736Dic3—21no—
737Dic3—41no—
738Dic3—41no—
739Dic3—121no—
740Dic3—121no—
741Dic3—241no—
742Dic3#93012yes—
743Dic3#95012yescomplemented
744C32#303511yescharacteristic, complemented, Sylow
745C23—31no—
746C23—61no—
747C23—61no—
748C23—181no—
749Q8—21no—
750Q8—61no—
751Q8—61no—
752Q8—181no—
753Q8—181no—
754Q8D3×D1212yes—
755D4—32no—
756D4—64no—
757D4—61no—
758D4—61no—
759D4—61no—
760D4—181no—
761D4—181no—
762D4—362no—
763D4—362no—
764D4—362no—
765D4—362no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—31no—
769C2×C4—31no—
770C2×C4—32no—
771C2×C4—32no—
772C2×C4—31no—
773C2×C4—62no—
774C2×C4—64no—
775C2×C4—61no—
776C2×C4—61no—
777C2×C4—121no—
778C2×C4—122no—
779C2×C4—122no—
780C2×C4—181no—
781C2×C4—362no—
782C2×C4—362no—
783C2×C4D3×#6711yescharacteristic
784C2×C4D3×#6711yescharacteristic
785C2×C4C22×D3211yescharacteristic
786C8—61no—
787C8—61no—
788C8—181no—
789C8—181no—
790C2×C3—21no—
791C2×C3—21no—
792C2×C3—21no—
793C2×C3—62no—
794C2×C3—122no—
795C2×C3—241no—
796C2×C3D3×#12111yescharacteristic
797C2×C3D3×#13511yescharacteristic
798C2×C3#577711yescharacteristic
799C2×C3C2×#93011yescharacteristic
800C2×C3C2×#95011yescharacteristic
801C2×C3#582211yescharacteristic
802D3—22no—
803D3—42no—
804D3—81no—
805D3—241no—
806D3—241no—
807D3—481no—
808C22—32no—
809C22—61no—
810C22—61no—
811C22—62no—
812C22—121no—
813C22—121no—
814C22—121no—
815C22—121no—
816C22—121no—
817C22—361no—
818C22—361no—
819C22—361no—
820C22C2×D3×#6711yescharacteristic
821C4—21no—
822C4—21no—
823C4—22no—
824C4—32no—
825C4—32no—
826C4—41no—
827C4—61no—
828C4—121no—
829C4—121no—
830C4—361no—
831C4C2×D3×D1211yescharacteristic
832C4D3×#23511yescharacteristic
833C3—21no—
834C3#8059711yescharacteristic, complemented
835C3#8252511yescharacteristic, complemented
836C2—62no—
837C2—122no—
838C2—241no—
839C2—721no—
840C2D3×#93011yescharacteristic
841C2#1059531711yescharacteristic
842C2D3×#95011yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
hypercenterC4×Q8D32
hypocenterC32#3035
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C3×C4×#239C2semidirect
2. C2×#63949C2semidirect
3. C2×#63947C2semidirect
4. #10593969C2semidirect
5. #10592727C2semidirect
6. C3×#5028C2semidirect
7. #10591625C2semidirect
8. #10591617C2semidirect
9. #10590610C2semidirect
10. #10590608C2semidirect
11. #10590559C2semidirect
12. #10590547C2semidirect
13. #10590366C2semidirect
14. #10590348C2semidirect
15. D3×C4⋊(C3⋊C8)C2semidirect
69. C4×#239D3semidirect
79. #5028D3semidirect
98. C3×#239D4semidirect
335. #239D12semidirect
466. C3×Dic3#135semidirect
743. Dic3#950semidirect
744. C32#3035semidirect
834. C3#80597semidirect
835. C3#82525semidirect

Maximal subgroups

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

subgroupindex
C3×C4×#2392
C2×#639492
C2×#639472
#105939692
#105927272
C3×#50282
#105916252
#105916172
#105906102
#105906082
#105905592
#105905472
#105903662
#105903482
D3×C4⋊(C3⋊C8)2
#825253
#805973