Finite Group Databasebeta

← #11866336

Subgroups — #11866336

Order 1152.

1036 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5674C211yesmaximal, characteristic
2C2×#63943C211yesmaximal, characteristic, complemented
3C2×D3×#214C211yesmaximal, characteristic, complemented
4#10593885C211yesmaximal, characteristic, complemented
5#10592753C211yesmaximal, characteristic, complemented
6C3×#5054C211yesmaximal, characteristic, complemented
7#10591578C211yesmaximal, characteristic, complemented
8#10591577C211yesmaximal, characteristic, complemented
9#10591556C211yesmaximal, characteristic, complemented
10#10591439C211yesmaximal, characteristic, complemented
11#10591438C211yesmaximal, characteristic, complemented
12#10591421C211yesmaximal, characteristic, complemented
13#10590377C211yesmaximal, characteristic, complemented
14#10590364C211yesmaximal, characteristic, complemented
15#10590324C211yesmaximal, characteristic, complemented
16#83391—31nomaximal
17#80600—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C2×D3×Dic6C2211yescharacteristic
21C32×#124C2211yescharacteristic
22C2×#3756C2211yescharacteristic, complemented
23C2×#3754C2211yescharacteristic
24C4×#634C2211yescharacteristic, complemented
25C3×#947C2211yescharacteristic
26C2×C3×#216C2211yescharacteristic, complemented
27C3×#940C2211yescharacteristic
28C2×C3×#214C2211yescharacteristic
29C3×#884—21no—
30C3×#884—21no—
31C3×#882—21no—
32C3×#882—21no—
33C3×#874C2211yescharacteristic
34C3×#872C2211yescharacteristic
35C3×C4×Dic6C2211yescharacteristic, complemented
36#63943—24no—
37D3×#214—24no—
38#63878—21no—
39#63877—21no—
40#63844C2211yescharacteristic, complemented
41Dic3×Dic6C2211yescharacteristic, complemented
42#63841C2211yescharacteristic
43#63838—21no—
44#63837—21no—
45C2×#3716C2211yescharacteristic
46C2×#3716C2211yescharacteristic, complemented
47C2×#3715C2211yescharacteristic
48C2×#3715C2211yescharacteristic, complemented
49C2×#3711C2211yescharacteristic
50C2×D3×C3⋊C8C2211yescharacteristic
51#63662C2211yescharacteristic, complemented
52#63659C2211yescharacteristic
53C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
54C3×#835C2211yescharacteristic, complemented
55C3×#832C2211yescharacteristic
56C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
57Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
58Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
59#63563C2211yescharacteristic
60#63563C2211yescharacteristic, complemented
61#63562C2211yescharacteristic
62#63562C2211yescharacteristic, complemented
63C3×#535—31no—
64C2×#951—31no—
65C22×#214—31no—
66C2×#918—31no—
67C2×D3×SD16—31no—
68#5674D311yescharacteristic
69#5572—31no—
70#5516—31no—
71C3×#464—31no—
72#5233—31no—
73#5215—31no—
74#5185—31no—
75#5163—31no—
76#5075—31no—
77#5075—31no—
78#5075—31no—
79#5075—31no—
80#5054—31no—
81#5054—31no—
82#5054—31no—
83#5054—31no—
84#5054—61no—
85#5054D311yescharacteristic, complemented
86#5027—31no—
87#4999—31no—
88#4848—31no—
89#4839—31no—
90#4804—31no—
91#4798—31no—
92#4770—31no—
93#4762—31no—
94C23×C3×D3—21no—
95C2×C32×Q8C2311yescharacteristic
96C2×C32×D4C2311yescharacteristic
97C2×#634C2311yescharacteristic
98C2×C3×#67—21no—
99C2×C3×#67—21no—
100C2×C3×#67—21no—
101C3×#239—22no—
102C3×#239—22no—
103C3×D3×D4—22no—
104C3×D3×D4—22no—
105C2×C3×D12—21no—
106C2×C3×D12—21no—
107C2×C3×D12—21no—
108C2×C3×D12C2311yescharacteristic
109C2×C3×D12C2311yescharacteristic
110C2×C3×C4×D3—21no—
111C2×C3×C4×D3C2311yescharacteristic
112C2×C3×Dic6C2311yescharacteristic
113C2×#627—21no—
114C2×D3×Dic3—21no—
115D3×Dic6—22no—
116D3×Dic6D414yescomplemented
117C32×C22⋊C4—21no—
118C32×C22⋊C4—21no—
119C32×C42C2311yescharacteristic
120#3756—22no—
121#3754—22no—
122C4⋊(C3⋊Dic3)C2311yescharacteristic
123#3750—21no—
124C4×C3⋊Dic3—21no—
125C2×C3⋊(C3⋊C8)C2311yescharacteristic
126C2×C3⋊(C3⋊C8)C2311yescharacteristic
127C3×#216—22no—
128C3×#214—22no—
129C3×(C2×D3)⋊C4—21no—
130C3×(C2×D3)⋊C4—21no—
131C3×(C2×D3)⋊C4D411yescharacteristic
132C3×(C2×D3)⋊C4D411yescharacteristic
133C3×C4⋊Dic3C2311yescharacteristic
134C3×Dic3⋊C4—21no—
135C3×Dic3⋊C4D411yescharacteristic
136C3×Dic3⋊C4D411yescharacteristic
137C3×C4×Dic3—21no—
138C3×C4×Dic3C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141#3724—21no—
142Dic3⋊Dic3—21no—
143(C2×D3)⋊Dic3—21no—
144Dic32—21no—
145Dic32—21no—
146Dic32—21no—
147#3716—22no—
148#3716—22no—
149#3715—22no—
150#3715—22no—
151#3711—22no—
152D3×C3⋊C8—22no—
153#3043—91noSylow
154C2×C3×#41—31no—
155C22×C3×D4—31no—
156C2×#239C2×D311yescharacteristic
157C2×D3×Q8—31no—
158C2×D3×D4C2×D311yescharacteristic
159C22×Dic6—31no—
160C2×C3×Q16—31no—
161C2×C3×SD16—31no—
162C3×#127—31no—
163C3×#127—31no—
164C3×#124—21no—
165C3×#124—31no—
166C3×#124C2×D311yescharacteristic
167C3×#124C2×D311yescharacteristic
168C3×#121—61no—
169C3×#121—61no—
170C3×#120—61no—
171C3×#120—61no—
172C3×C4×Q8—31no—
173C3×#117—31no—
174#951—64no—
175#947C2×D311yescharacteristic
176Q8×Dic3—31no—
177C2×#216—31no—
178C2×#216—31no—
179C2×#216—61no—
180C2×#216C2×D311yescharacteristic, complemented
181C2×#215—31no—
182C2×#215—31no—
183#940C2×D311yescharacteristic
184C2×#214—31no—
185C2×#214—31no—
186C2×#214—31no—
187C2×#214—31no—
188C2×#214—31no—
189C2×#214—31no—
190C2×#214—61no—
191C2×#214—64no—
192C2×#214C2×D311yescharacteristic
193#926—31no—
194C2×#208—31no—
195C22×C3⋊C8—31no—
196#918—64no—
197D3×SD16—64no—
198C2×#204—31no—
199C2×#204—31no—
200C2×ΓL(1,𝔽25)—31no—
201C2×D3×C8—31no—
202#892—31no—
203#892—61no—
204#887—31no—
205#887—61no—
206#887—61no—
207#887—61no—
208#884—21no—
209#884—21no—
210#882—21no—
211#882—21no—
212#877—61no—
213#877—61no—
214#874C2×D311yescharacteristic
215#872—61no—
216#872C2×D311yescharacteristic
217C4×Dic6—31no—
218C4×Dic6—31no—
219C4×Dic6—31no—
220C4×Dic6—31no—
221C4×Dic6—61no—
222C4×Dic6—61no—
223C4×Dic6C2×D311yescharacteristic, complemented
224C3×C4⋊C8—31no—
225C3×#103—31no—
226C3×#102—31no—
227#835—31no—
228#835—31no—
229#835—61no—
230#835C2×D311yescharacteristic, complemented
231#832—31no—
232#832—31no—
233#832—31no—
234#832—31no—
235#832—31no—
236#832—31no—
237#832—61no—
238#832C2×D311yescharacteristic
239#821—31no—
240#821—31no—
241Dic3⋊C8—31no—
242Dic3⋊C8—31no—
243#809—31no—
244#809—31no—
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, complemented
251C23×C32—21no—
252C22×C3×D3—21no—
253C22×C3×D3—21no—
254C22×C3×D3—42no—
255C22×C3×D3—81no—
256C22×C3×D3—81no—
257C22×C3×D3C2×D411yescharacteristic
258C32×Q8—21no—
259C32×Q8—21no—
260C32×D4—21no—
261C32×D4—21no—
262C2×C32×C4—21no—
263C2×C32×C4C2×D411yescharacteristic
264C2×C32×C4C2×D411yescharacteristic
265C2×C32×C4C2411yescharacteristic
266C2×C3⋊Dic3—21no—
267C2×C3⋊Dic3—21no—
268#634—21no—
269#634C2×D412yes—
270C3×#67—42no—
271C3×#67—81no—
272C3×#67—81no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3C2×D411yescharacteristic
276C2×C3×Dic3C2×D411yescharacteristic
277C2×C3×Dic3C2×D411yescharacteristic
278C3×D12—21no—
279C3×D12—21no—
280C3×D12—21no—
281C3×D12—21no—
282C3×D12—42no—
283C3×D12—81no—
284C3×D12—81no—
285C3×C4×D3—42no—
286C3×C4×D3C2×D412yes—
287C3×C4×D3#4112yes—
288C3×Dic6—21no—
289C3×Dic6C2×D412yes—
290#627—24no—
291D3×Dic3—24no—
292C3⋊(C3⋊C8)—21no—
293C3⋊(C3⋊C8)—21no—
294C3×C3⋊C8—21no—
295C3×C3⋊C8—21no—
296C2×#137—91no—
297C22×SD16—91no—
298#535—31no—
299#519—91no—
300#464—31no—
301#464—91no—
302#464—91no—
303#464—91no—
304#460—91no—
305#460—91no—
306#460—91no—
307#460—91no—
308#424—91no—
309#418—91no—
310#416—91no—
311C24×C3—61no—
312C23×D3—21no—
313C3×#41—62no—
314C3×#41—62no—
315C2×C3×Q8—21no—
316C2×C3×Q8—31no—
317C2×C3×Q8C22×D311yescharacteristic
318C2×C3×Q8C22×D311yescharacteristic
319C2×C3×D4—21no—
320C2×C3×D4—31no—
321C2×C3×D4—31no—
322C2×C3×D4—61no—
323C2×C3×D4—62no—
324C2×C3×D4—62no—
325C2×C3×D4—61no—
326C2×C3×D4—61no—
327C2×C3×D4—61no—
328C2×C3×D4—61no—
329C2×C3×D4—61no—
330C2×C3×D4C22×D311yescharacteristic
331C2×C3×D4C22×D311yescharacteristic
332C22×C3×C4—31no—
333C22×C3×C4—61no—
334C2×#67—21no—
335C2×#67—21no—
336C2×#67—21no—
337C22×Dic3—61no—
338#239—22no—
339#239—22no—
340D3×Q8—34no—
341D3×Q8—62no—
342D3×D4—22no—
343D3×D4—22no—
344C2×D12—21no—
345C2×D12—21no—
346C2×D12—21no—
347C2×D12C22×D311yescharacteristic
348C2×D12C22×D311yescharacteristic
349C2×C4×D3—21no—
350C2×C4×D3—61no—
351C2×C4×D3C22×D311yescharacteristic
352C2×Dic6—31no—
353C2×Dic6—31no—
354C2×Dic6—34no—
355C2×Dic6—61no—
356C2×Dic6—62no—
357C2×Dic6—61no—
358C2×Dic6—61no—
359C2×Dic6C22×D311yescharacteristic
360C3×Q16—62no—
361C3×SD16—62no—
362C2×C3×C8—31no—
363C2×C3×C8—31no—
364C3×C4⋊C4—31no—
365C3×C4⋊C4—31no—
366C3×C4⋊C4—31no—
367C3×C4⋊C4—61no—
368C3×C22⋊C4—21no—
369C3×C22⋊C4—21no—
370C3×C22⋊C4—21no—
371C3×C22⋊C4—21no—
372C3×C22⋊C4—31no—
373C3×C22⋊C4—31no—
374C3×C22⋊C4—41no—
375C3×C22⋊C4—41no—
376C3×C22⋊C4—61no—
377C3×C22⋊C4—61no—
378C3×C42—21no—
379C3×C42—31no—
380C3×C42—61no—
381C3×C42C22×D311yescharacteristic
382C3×C42C22×D311yescharacteristic
383#217—61no—
384#216—22no—
385#216—62no—
386#216—62no—
387#216—122no—
388#215—62no—
389#215—62no—
390#214—22no—
391#214—62no—
392#214—62no—
393#214—62no—
394#214—62no—
395#214—62no—
396#214—62no—
397#214—122no—
398(C2×D3)⋊C4—21no—
399(C2×D3)⋊C4—21no—
400(C2×D3)⋊C4—61no—
401(C2×D3)⋊C4#6711yescharacteristic
402(C2×D3)⋊C4#6711yescharacteristic
403C4⋊Dic3—31no—
404C4⋊Dic3—31no—
405C4⋊Dic3—61no—
406C4⋊Dic3—61no—
407C4⋊Dic3C22×D311yescharacteristic
408Dic3⋊C4—21no—
409Dic3⋊C4—61no—
410Dic3⋊C4—61no—
411Dic3⋊C4—61no—
412Dic3⋊C4—61no—
413Dic3⋊C4—61no—
414Dic3⋊C4—121no—
415Dic3⋊C4#6711yescharacteristic
416Dic3⋊C4#6711yescharacteristic
417C4×Dic3—21no—
418C4×Dic3—61no—
419C4×Dic3—61no—
420C4×Dic3—61no—
421C4×Dic3—61no—
422C4×Dic3—61no—
423C4×Dic3—61no—
424C4×Dic3—61no—
425C4×Dic3—61no—
426C4×Dic3—121no—
427C4×Dic3C22×D311yescharacteristic
428#208—62no—
429C2×C3⋊C8—31no—
430C2×C3⋊C8—31no—
431C2×C3⋊C8—31no—
432C2×C3⋊C8—31no—
433C2×C3⋊C8—61no—
434C2×C3⋊C8—61no—
435C2×C3⋊C8—62no—
436C2×C3⋊C8C22×D311yescharacteristic
437C2×C3⋊C8C22×D311yescharacteristic
438#204—62no—
439#204—62no—
440ΓL(1,𝔽25)—62no—
441D3×C8—62no—
442C22×C32—41no—
443C22×C32—41no—
444C22×C32—41no—
445C22×C32C22×D411yescharacteristic
446C2×C3×D3—21no—
447C2×C3×D3—21no—
448C2×C3×D3—41no—
449C2×C3×D3—41no—
450C2×C3×D3—41no—
451C2×C3×D3—41no—
452C2×C3×D3—41no—
453C2×C3×D3—41no—
454C2×C3×D3—84no—
455C2×C3×D3#12112yes—
456C32×C4—21no—
457C32×C4—21no—
458C32×C4—41no—
459C32×C4C22×D411yescharacteristic
460C32×C4C2×#4111yescharacteristic
461C3⋊Dic3—22no—
462C3⋊Dic3—41no—
463C3×Dic3—22no—
464C3×Dic3—21no—
465C3×Dic3—21no—
466C3×Dic3—41no—
467C3×Dic3#12112yes—
468C2×#41—31no—
469C22×Q8—91no—
470C22×D4—31no—
471#137—184no—
472C2×Q16—31no—
473C2×Q16—91no—
474C2×SD16—31no—
475C2×SD16—91no—
476C2×SD16—91no—
477C2×SD16—91no—
478C2×SD16—91no—
479C2×SD16—91no—
480C2×SD16—184no—
481C2×M16—91no—
482C22×C8—91no—
483#127—31no—
484#127—31no—
485#124—31no—
486#124D3211yescharacteristic
487#121—61no—
488#121—61no—
489#120—61no—
490#120—61no—
491C4×Q8—31no—
492C4×Q8—91no—
493C4×Q8—91no—
494C4×Q8—91no—
495C4×Q8—181no—
496C4×Q8—181no—
497#117—31no—
498#117—91no—
499#117—181no—
500#117—181no—
501C4⋊C8—31no—
502C4⋊C8—91no—
503C4⋊C8—91no—
504C4⋊C8—91no—
505#103—31no—
506#103—91no—
507#102—31no—
508#102—91no—
509#102—91no—
510#102—91no—
511#102—91no—
512#102—91no—
513C23×C3—21no—
514C23×C3—21no—
515C23×C3—31no—
516C23×C3—41no—
517C23×C3—61no—
518C23×C3—61no—
519C23×C3—122no—
520C23×C3—241no—
521C23×C3—241no—
522C22×D3—21no—
523C22×D3—21no—
524C22×D3—42no—
525C22×D3—81no—
526C22×D3—81no—
527C22×D3C2×#6711yescharacteristic
528C3×Q8—21no—
529C3×Q8—21no—
530C3×Q8—21no—
531C3×Q8—21no—
532C3×Q8—32no—
533C3×Q8—41no—
534C3×Q8—41no—
535C3×Q8—61no—
536C3×D4—21no—
537C3×D4—21no—
538C3×D4—21no—
539C3×D4—21no—
540C3×D4—41no—
541C3×D4—41no—
542C3×D4—61no—
543C3×D4—61no—
544C3×D4—61no—
545C3×D4—61no—
546C3×D4—122no—
547C3×D4—122no—
548C3×D4—241no—
549C3×D4—241no—
550C3×D4—241no—
551C3×D4—241no—
552C2×C3×C4—21no—
553C2×C3×C4—21no—
554C2×C3×C4—21no—
555C2×C3×C4—21no—
556C2×C3×C4—21no—
557C2×C3×C4—31no—
558C2×C3×C4—32no—
559C2×C3×C4—32no—
560C2×C3×C4—31no—
561C2×C3×C4—31no—
562C2×C3×C4—41no—
563C2×C3×C4—61no—
564C2×C3×C4—61no—
565C2×C3×C4—122no—
566C2×C3×C4D3×D411yescharacteristic
567C2×C3×C4D3×D411yescharacteristic
568C2×C3×C4C2×#6711yescharacteristic
569C2×C3×C4C2×#6711yescharacteristic
570C2×C3×C4C23×D311yescharacteristic
571C2×C3×C4C23×D311yescharacteristic
572#67—42no—
573#67—81no—
574#67—81no—
575C2×Dic3—21no—
576C2×Dic3—21no—
577C2×Dic3—64no—
578C2×Dic3—61no—
579C2×Dic3—61no—
580C2×Dic3—61no—
581C2×Dic3—61no—
582C2×Dic3—121no—
583C2×Dic3—121no—
584C2×Dic3C2×#6711yescharacteristic
585C2×Dic3C2×#6711yescharacteristic
586C2×Dic3C2×#6711yescharacteristic
587D12—21no—
588D12—21no—
589D12—21no—
590D12—21no—
591D12—42no—
592D12—81no—
593D12—81no—
594C4×D3—42no—
595C4×D3—64no—
596C4×D3D3×D412yes—
597C4×D3#23712yes—
598Dic6—21no—
599Dic6—32no—
600Dic6—32no—
601Dic6—62no—
602Dic6—64no—
603Dic6—61no—
604Dic6—61no—
605Dic6—64no—
606Dic6—121no—
607Dic6D3×D412yes—
608C3×C8—61no—
609C3×C8—61no—
610C3⋊C8—21no—
611C3⋊C8—21no—
612C3⋊C8—61no—
613C3⋊C8—61no—
614C3⋊C8—61no—
615C3⋊C8—61no—
616C3⋊C8—121no—
617C3⋊C8—121no—
618C2×C32—81no—
619C2×C32C2×#12111yescharacteristic
620C2×C32#57711yescharacteristic
621C2×C32#57711yescharacteristic
622C3×D3—22no—
623C3×D3—81no—
624C3×D3—81no—
625C24—61no—
626#41—62no—
627#41—62no—
628C2×Q8—31no—
629C2×Q8—94no—
630C2×Q8—91no—
631C2×Q8—181no—
632C2×Q8—182no—
633C2×Q8C2×D3211yescharacteristic
634C2×D4—31no—
635C2×D4—31no—
636C2×D4—61no—
637C2×D4—62no—
638C2×D4—62no—
639C2×D4—61no—
640C2×D4—61no—
641C2×D4—61no—
642C2×D4—61no—
643C2×D4—61no—
644C2×D4C2×D3211yescharacteristic
645C22×C4—31no—
646C22×C4—61no—
647C22×C4—181no—
648Q16—62no—
649Q16—182no—
650SD16—62no—
651SD16—182no—
652SD16—182no—
653SD16—182no—
654SD16—182no—
655SD16—182no—
656M16—182no—
657C2×C8—31no—
658C2×C8—31no—
659C2×C8—91no—
660C2×C8—91no—
661C2×C8—182no—
662C4⋊C4—31no—
663C4⋊C4—31no—
664C4⋊C4—31no—
665C4⋊C4—61no—
666C4⋊C4—91no—
667C4⋊C4—181no—
668C4⋊C4—181no—
669C4⋊C4—181no—
670C22⋊C4—21no—
671C22⋊C4—21no—
672C22⋊C4—31no—
673C22⋊C4—31no—
674C22⋊C4—61no—
675C22⋊C4—61no—
676C22⋊C4—181no—
677C42—31no—
678C42—61no—
679C42—181no—
680C42—181no—
681C42—181no—
682C42—181no—
683C42C2×D3211yescharacteristic
684C22×C3—21no—
685C22×C3—32no—
686C22×C3—41no—
687C22×C3—41no—
688C22×C3—41no—
689C22×C3—41no—
690C22×C3—41no—
691C22×C3—41no—
692C22×C3—61no—
693C22×C3—61no—
694C22×C3—81no—
695C22×C3—81no—
696C22×C3—81no—
697C22×C3—121no—
698C22×C3—121no—
699C22×C3—121no—
700C22×C3—121no—
701C22×C3—121no—
702C22×C3—121no—
703C22×C3—244no—
704C22×C3C2×D3×D411yescharacteristic
705C22×C3C22×#6711yescharacteristic
706C2×D3—21no—
707C2×D3—21no—
708C2×D3—41no—
709C2×D3—41no—
710C2×D3—41no—
711C2×D3—41no—
712C2×D3—41no—
713C2×D3—41no—
714C2×D3—84no—
715C2×D3#93812yes—
716C3×C4—21no—
717C3×C4—21no—
718C3×C4—21no—
719C3×C4—21no—
720C3×C4—21no—
721C3×C4—21no—
722C3×C4—32no—
723C3×C4—41no—
724C3×C4—41no—
725C3×C4—41no—
726C3×C4—41no—
727C3×C4—61no—
728C3×C4—61no—
729C3×C4—62no—
730C3×C4—81no—
731C3×C4—121no—
732C3×C4C2×D3×D411yescharacteristic
733C3×C4C2×D3×D411yescharacteristic
734C3×C4C2×#23711yescharacteristic
735C3×C4D3×#4111yescharacteristic
736Dic3—21no—
737Dic3—21no—
738Dic3—22no—
739Dic3—41no—
740Dic3—62no—
741Dic3—62no—
742Dic3—122no—
743Dic3—121no—
744Dic3—121no—
745Dic3—241no—
746Dic3#93812yes—
747C32#304311yescharacteristic, complemented, Sylow
748C23—21no—
749C23—31no—
750C23—61no—
751C23—61no—
752C23—122no—
753C23—241no—
754C23—241no—
755Q8—21no—
756Q8—21no—
757Q8—32no—
758Q8—61no—
759Q8—92no—
760Q8—184no—
761Q8—181no—
762D4—21no—
763D4—21no—
764D4—61no—
765D4—61no—
766D4—61no—
767D4—61no—
768D4—122no—
769D4—122no—
770D4—241no—
771D4—241no—
772D4—241no—
773D4—241no—
774C2×C4—21no—
775C2×C4—31no—
776C2×C4—32no—
777C2×C4—32no—
778C2×C4—31no—
779C2×C4—31no—
780C2×C4—61no—
781C2×C4—61no—
782C2×C4—122no—
783C2×C4—184no—
784C2×C4—181no—
785C2×C4—181no—
786C2×C4D3×#6711yescharacteristic
787C2×C4D3×#6711yescharacteristic
788C2×C4C22×D3211yescharacteristic
789C8—61no—
790C8—61no—
791C8—181no—
792C8—181no—
793C2×C3—21no—
794C2×C3—21no—
795C2×C3—21no—
796C2×C3—62no—
797C2×C3—81no—
798C2×C3—81no—
799C2×C3—161no—
800C2×C3—241no—
801C2×C3—241no—
802C2×C3D3×#12111yescharacteristic
803C2×C3#577011yescharacteristic
804C2×C3#577811yescharacteristic
805C2×C3C2×#93811yescharacteristic
806C2×C3#583611yescharacteristic
807C2×C3#583611yescharacteristic
808D3—22no—
809D3—81no—
810D3—81no—
811C22—32no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—61no—
816C22—61no—
817C22—121no—
818C22—121no—
819C22—121no—
820C22—121no—
821C22—121no—
822C22—121no—
823C22—244no—
824C22C2×D3×#6711yescharacteristic
825C4—21no—
826C4—21no—
827C4—32no—
828C4—41no—
829C4—61no—
830C4—61no—
831C4—62no—
832C4—121no—
833C4—182no—
834C4—361no—
835C4D32×D411yescharacteristic
836C4D3×#23711yescharacteristic
837C3—21no—
838C3#8060011yescharacteristic, complemented
839C3#8339111yescharacteristic, complemented
840C2—62no—
841C2—81no—
842C2—241no—
843C2—241no—
844C2D3×#93811yescharacteristic
845C2#1059546411yescharacteristic
846C2#1059546611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#124C22
socleC22×C32C22×D4
prime radicalC3×#5674C2
hypercenter#124D32
hypocenterC32#3043
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
2. C2×#63943C2semidirect
3. C2×D3×#214C2semidirect
4. #10593885C2semidirect
5. #10592753C2semidirect
6. C3×#5054C2semidirect
7. #10591578C2semidirect
8. #10591577C2semidirect
9. #10591556C2semidirect
10. #10591439C2semidirect
11. #10591438C2semidirect
12. #10591421C2semidirect
13. #10590377C2semidirect
14. #10590364C2semidirect
15. #10590324C2semidirect
22. C2×#3756C22semidirect
24. C4×#634C22semidirect
26. C2×C3×#216C22semidirect
35. C3×C4×Dic6C22semidirect
40. #63844C22semidirect
41. Dic3×Dic6C22semidirect
46. C2×#3716C22semidirect
48. C2×#3715C22semidirect
51. #63662C22semidirect
53. C4⋊(C3⋊(C3⋊C8))C22semidirect
54. C3×#835C22semidirect
56. C3×C4⋊(C3⋊C8)C22semidirect
57. Dic3⋊(C3⋊C8)C22semidirect
58. Dic3⋊(C3⋊C8)C22semidirect
60. #63563C22semidirect
62. #63562C22semidirect
85. #5054D3semidirect
116. D3×Dic6D4semidirect
180. C2×#216C2×D3semidirect
223. C4×Dic6C2×D3semidirect
230. #835C2×D3semidirect
250. C4⋊(C3⋊C8)C2×D3semidirect
747. C32#3043semidirect
838. C3#80600semidirect
839. C3#83391semidirect

Maximal subgroups

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

subgroupindex
C3×#56742
C2×#639432
C2×D3×#2142
#105938852
#105927532
C3×#50542
#105915782
#105915772
#105915562
#105914392
#105914382
#105914212
#105903772
#105903642
#105903242
#833913
#806003