Finite Group Databasebeta

← #11864271

Subgroups — #11864271

Order 1152.

1663 conjugacy classes of subgroups.

The subgroup lattice has 1072 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64314C211yesmaximal, characteristic, complemented
2C2×#63926C211yesmaximal, characteristic, complemented
3C2×#63798C211yesmaximal, characteristic, complemented
4#10594634C211yesmaximal, characteristic, complemented
5#10592469C211yesmaximal, characteristic, complemented
6C3×#4781C211yesmaximal, characteristic, complemented
7C3×#4773C211yesmaximal, characteristic, complemented
8#10591450C211yesmaximal, characteristic, complemented
9#10591447C211yesmaximal, characteristic, complemented
10#10590959C211yesmaximal, characteristic, complemented
11#10590944C211yesmaximal, characteristic, complemented
12#10590823C211yesmaximal, characteristic, complemented
13#10590615C211yesmaximal, characteristic, complemented
14#10590611C211yesmaximal, characteristic, complemented
15#10590595C211yesmaximal, characteristic, complemented
16#80085—31nomaximal
17#80004—31nomaximal
18C2×D4×C3⋊D3C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic, complemented
20C2×C3×D3×D4C2211yescharacteristic, complemented
21C2×#3811—21no—
22C2×D3×#67—21no—
23C22×#626—21no—
24C2×#3804—21no—
25#64314—24no—
26#64314—24no—
27C2×#3802C2211yescharacteristic, complemented
28C2×D3×D12C2211yescharacteristic, complemented
29C2×#3799C2211yescharacteristic, complemented
30C2×#3798C2211yescharacteristic
31C2×#3796C2211yescharacteristic
32C2×#3743C2211yescharacteristic, complemented
33#64101C2211yescharacteristic, complemented
34C2×C3×#213C2211yescharacteristic, complemented
35C2×C3×#213C2211yescharacteristic, complemented
36C2×C3×D24C2211yescharacteristic, complemented
37C2×C3×#204C2211yescharacteristic, complemented
38C3×#895C2211yescharacteristic, complemented
39C3×#895C2211yescharacteristic, complemented
40#63926—24no—
41#63922—21no—
42#63922—21no—
43#63915—21no—
44#63914—21no—
45#63908C2211yescharacteristic, complemented
46#63908C2211yescharacteristic, complemented
47C2×#3715C2211yescharacteristic, complemented
48C2×#3714C2211yescharacteristic, complemented
49C2×#3714C2211yescharacteristic, complemented
50C2×#3713C2211yescharacteristic, complemented
51C2×#3710C2211yescharacteristic, complemented
52#63798—24no—
53C32×#102C2211yescharacteristic, complemented
54#63659C2211yescharacteristic, complemented
55#63648C2211yescharacteristic, complemented
56#63636C2211yescharacteristic, complemented
57C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
58C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
59C3×#810C2211yescharacteristic, complemented
60C3×#809C2211yescharacteristic, complemented
61#63566C2211yescharacteristic, complemented
62#63563C2211yescharacteristic, complemented
63(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
64(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
65C2×#1009—31no—
66C2×#1004—31no—
67C2×#914—31no—
68C2×#911—31no—
69C2×D3×D8—31no—
70C2×D3×D8—31no—
71#5607—31no—
72#5607—31no—
73C3×#449—31no—
74C3×#447—31no—
75#5238—31no—
76#5217—31no—
77#5172—31no—
78#5158—31no—
79#5156—31no—
80#5156—31no—
81#5037—31no—
82#5036—31no—
83#4810—31no—
84#4804—31no—
85#4781D311yescharacteristic, complemented
86#4773—31no—
87#4773D311yescharacteristic, complemented
88#4772—31no—
89#4770—31no—
90#4770—31no—
91#4770—61no—
92#4734—31no—
93#4732—31no—
94#4727—31no—
95#4727—31no—
96C23×C3⋊D3—21no—
97C23×C3×D3—21no—
98C22×D32—21no—
99C22×D32—21no—
100C2×C32×D4C2311yescharacteristic
101C2×#638—21no—
102D4×C3⋊D3—22no—
103D4×C3⋊D3D414yescomplemented
104C2×C4⋊(C3⋊D3)C2311yescharacteristic
105C2×C4×C3⋊D3C2311yescharacteristic
106C2×C3×#67—21no—
107C2×C3×#67—21no—
108C22×C3×Dic3—21no—
109C3×#237—22no—
110C3×#237—22no—
111C3×D3×D4—22no—
112C3×D3×D4—22no—
113C2×C3×D12—21no—
114C2×C3×D12—21no—
115C2×C3×D12C2311yescharacteristic
116C2×C3×D12C2311yescharacteristic
117C2×C3×D12C2311yescharacteristic
118C2×C3×C4×D3C2311yescharacteristic
119C2×C3×C4×D3C2311yescharacteristic
120C2×C3×Dic6C2311yescharacteristic
121#3811—28no—
122D3×#67—28no—
123C2×#627D411yescharacteristic
124C2×#626—28no—
125C2×#626—21no—
126C2×#626—21no—
127C2×#626—21no—
128C2×#626D411yescharacteristic
129C2×#626D411yescharacteristic
130C2×#625—21no—
131C2×#625—21no—
132C2×#625—21no—
133C2×#625D411yescharacteristic
134C2×#624—21no—
135#3804—28no—
136C2×D3×Dic3—21no—
137#3802—22no—
138#3802—22no—
139D3×D12—22no—
140D3×D12—22no—
141#3799—22no—
142#3799—22no—
143#3798—22no—
144#3798—22no—
145#3796—22no—
146#3796D414yescomplemented
147C2×C32×C8C2311yescharacteristic
148C32×C4⋊C4C2311yescharacteristic
149#3752—21no—
150C4⋊(C3⋊Dic3)C2311yescharacteristic
151C4×C3⋊Dic3—21no—
152C2×C3⋊(C3⋊C8)C2311yescharacteristic
153#3743—22no—
154C3×#213—22no—
155C3×#213—22no—
156C3×(C2×D3)⋊C4—21no—
157C3×(C2×D3)⋊C4—21no—
158C2×C3×C3⋊C8C2311yescharacteristic
159C2×C3×C3⋊C8C2311yescharacteristic
160C3×D24—22no—
161C3×#204—22no—
162(C2×D3)⋊Dic3—21no—
163(C2×D3)⋊Dic3—21no—
164#3715—22no—
165#3714—22no—
166#3714—22no—
167#3713—22no—
168#3710—22no—
169#3008—91noSylow
170C2×C3×#41—31no—
171C22×C3×D4—31no—
172C22×#67—61no—
173C22×#67—61no—
174#1009—64no—
175#1009—64no—
176C2×#239—31no—
177C2×#239—31no—
178#1004—64no—
179#1004—64no—
180C2×#237—31no—
181C2×#237—61no—
182C2×#237C2×D311yescharacteristic, complemented
183C2×D3×D4—31no—
184C2×D3×D4—31no—
185C2×D3×D4—31no—
186C2×D3×D4—31no—
187C2×D3×D4—31no—
188C2×D3×D4—61no—
189C2×D3×D4—61no—
190C2×D3×D4—61no—
191C2×D3×D4—61no—
192C2×D3×D4C2×D311yescharacteristic, complemented
193C2×#235—31no—
194C2×#235—31no—
195C2×#235—31no—
196C2×#235—61no—
197C22×D12—31no—
198C22×D12—61no—
199C2×C3×SD16—31no—
200C2×C3×D8—31no—
201C2×C3×D8—31no—
202C2×C3×D8—31no—
203C3×#121—31no—
204C3×#121—31no—
205C2×#215—31no—
206#940—61no—
207#940—61no—
208#938—31no—
209#938—31no—
210#937—61no—
211#937—61no—
212C2×#214—31no—
213C2×#213—31no—
214C2×#213—31no—
215C2×#213—31no—
216C2×#213—31no—
217C2×#213C2×D311yescharacteristic, complemented
218C2×#213C2×D311yescharacteristic, complemented
219#930—31no—
220#930—31no—
221#914—64no—
222#911—64no—
223D3×D8—64no—
224D3×D8—64no—
225C2×D24—31no—
226C2×D24—31no—
227C2×D24C2×D311yescharacteristic, complemented
228C2×#204C2×D311yescharacteristic, complemented
229C2×ΓL(1,𝔽25)—31no—
230C2×ΓL(1,𝔽25)—31no—
231C2×ΓL(1,𝔽25)—61no—
232C2×D3×C8—31no—
233C2×D3×C8—31no—
234#895C2×D311yescharacteristic, complemented
235#895C2×D311yescharacteristic, complemented
236#892—31no—
237#892—31no—
238#892—61no—
239#885—61no—
240#885—61no—
241#882—61no—
242#882—61no—
243C3×#103—31no—
244C3×#102—21no—
245C3×#102—31no—
246C3×#102C2×D311yescharacteristic, complemented
247C3×#102C2×D311yescharacteristic, complemented
248C3×C22⋊C8—31no—
249C3×C22⋊C8—31no—
250#835—31no—
251#832—31no—
252#832—31no—
253#832—31no—
254#832—61no—
255#830—31no—
256#830—31no—
257#821—31no—
258#821—31no—
259#821—31no—
260#821—61no—
261(C2×D3)⋊C8—31no—
262(C2×D3)⋊C8—31no—
263(C2×D3)⋊C8C2×D311yescharacteristic, complemented
264(C2×D3)⋊C8C2×D311yescharacteristic, complemented
265#816—31no—
266#810C2×D311yescharacteristic, complemented
267#809—31no—
268#809—31no—
269#809—61no—
270#809C2×D311yescharacteristic, complemented
271C23×C32—21no—
272C22×C3⋊D3—21no—
273C22×C3⋊D3—24no—
274C22×C3⋊D3—81no—
275C22×C3⋊D3—81no—
276C22×C3⋊D3C2×D411yescharacteristic
277C22×C3×D3—21no—
278C22×C3×D3—24no—
279C22×C3×D3—21no—
280C22×C3×D3—21no—
281C22×C3×D3—81no—
282C22×C3×D3—81no—
283C22×C3×D3C2×D411yescharacteristic
284C22×C3×D3C2×D411yescharacteristic
285C2×D32—24no—
286C2×D32—42no—
287C2×D32—81no—
288C2×D32—81no—
289C2×D32—81no—
290C2×D32—81no—
291C32×D4—21no—
292C32×D4C2×D412yes—
293C2×C32×C4—21no—
294C2×C32×C4C2411yescharacteristic
295#638—24no—
296C2×C3⋊Dic3—21no—
297C2×C3⋊Dic3C2×D411yescharacteristic
298C4⋊(C3⋊D3)—21no—
299C4⋊(C3⋊D3)C2×D412yes—
300C4×C3⋊D3C2×D412yes—
301C4×C3⋊D3C2×D412yes—
302C3×#67—24no—
303C3×#67—24no—
304C2×C3×Dic3—24no—
305C2×C3×Dic3—21no—
306C2×C3×Dic3C2×D411yescharacteristic
307C2×C3×Dic3C2×D411yescharacteristic
308C3×D12—21no—
309C3×D12—21no—
310C3×D12—21no—
311C3×D12—21no—
312C3×D12—21no—
313C3×D12—81no—
314C3×D12—81no—
315C3×D12C2×D412yes—
316C3×C4×D3—21no—
317C3×C4×D3—21no—
318C3×C4×D3—21no—
319C3×C4×D3—21no—
320C3×Dic6—21no—
321C3×Dic6C2×D412yes—
322#627—22no—
323#626—24no—
324#626—24no—
325#626—24no—
326#626—22no—
327#626—22no—
328#625—22no—
329#625—42no—
330#625—81no—
331#625—81no—
332#624—24no—
333D3×Dic3—24no—
334C32×C8—21no—
335C3⋊(C3⋊C8)—21no—
336C3×C3⋊C8—21no—
337C3×C3⋊C8—21no—
338C2×H(5,𝔽2)—91no—
339C2×AGL(1,ℤ/8)—91no—
340C22×D8—91no—
341#535—91no—
342#449—31no—
343#449—91no—
344#449—91no—
345#449—91no—
346#447—31no—
347#447—91no—
348#447—91no—
349#447—91no—
350#418—91no—
351#416—91no—
352#408—91no—
353C24×C3—61no—
354C23×D3—21no—
355C23×D3—61no—
356C23×D3—61no—
357C23×D3—61no—
358C23×D3—61no—
359C23×D3—61no—
360C23×D3—61no—
361C23×D3—121no—
362C3×#41—62no—
363C3×#41—62no—
364C2×C3×Q8—31no—
365C2×C3×D4—21no—
366C2×C3×D4—31no—
367C2×C3×D4—31no—
368C2×C3×D4—31no—
369C2×C3×D4—61no—
370C2×C3×D4—61no—
371C2×C3×D4—61no—
372C2×C3×D4—62no—
373C2×C3×D4—61no—
374C2×C3×D4—62no—
375C2×C3×D4C22×D311yescharacteristic
376C2×C3×D4C22×D311yescharacteristic
377C22×C3×C4—31no—
378C22×C3×C4—31no—
379C22×C3×C4—61no—
380C2×#67—21no—
381C2×#67—21no—
382C2×#67—31no—
383C2×#67—31no—
384C2×#67—31no—
385C2×#67—31no—
386C2×#67—61no—
387C2×#67—61no—
388C2×#67—68no—
389C2×#67—61no—
390C2×#67—61no—
391C2×#67—61no—
392C2×#67—61no—
393C2×#67—68no—
394C2×#67—61no—
395C2×#67—61no—
396C2×#67—61no—
397C2×#67—61no—
398C2×#67—61no—
399C2×#67—121no—
400C22×Dic3—21no—
401C22×Dic3—61no—
402#239—34no—
403#239—62no—
404#239—62no—
405#239—62no—
406#237—22no—
407#237—22no—
408#237—34no—
409#237—62no—
410#237—68no—
411D3×D4—22no—
412D3×D4—22no—
413D3×D4—34no—
414D3×D4—34no—
415D3×D4—64no—
416D3×D4—62no—
417D3×D4—62no—
418D3×D4—62no—
419D3×D4—62no—
420D3×D4—62no—
421D3×D4—62no—
422D3×D4—62no—
423D3×D4—62no—
424D3×D4—68no—
425D3×D4—68no—
426D3×D4—68no—
427D3×D4—122no—
428#235—62no—
429#235—62no—
430#235—62no—
431#235—62no—
432#235—62no—
433#235—68no—
434#235—62no—
435C2×D12—21no—
436C2×D12—21no—
437C2×D12—31no—
438C2×D12—31no—
439C2×D12—31no—
440C2×D12—31no—
441C2×D12—61no—
442C2×D12—62no—
443C2×D12—61no—
444C2×D12—61no—
445C2×D12—68no—
446C2×D12—61no—
447C2×D12—62no—
448C2×D12C22×D311yescharacteristic
449C2×D12C22×D311yescharacteristic
450C2×D12C22×D311yescharacteristic
451C2×C4×D3—31no—
452C2×C4×D3—31no—
453C2×C4×D3—61no—
454C2×C4×D3—61no—
455C2×C4×D3—61no—
456C2×C4×D3—61no—
457C2×C4×D3C22×D311yescharacteristic
458C2×C4×D3C22×D311yescharacteristic
459C2×Dic6—31no—
460C2×Dic6—31no—
461C2×Dic6C22×D311yescharacteristic
462C3×SD16—62no—
463C3×D8—62no—
464C3×D8—62no—
465C3×D8—62no—
466C2×C3×C8—21no—
467C2×C3×C8—31no—
468C2×C3×C8—31no—
469C2×C3×C8C22×D311yescharacteristic
470C2×C3×C8C22×D311yescharacteristic
471C3×C4⋊C4—21no—
472C3×C4⋊C4C22×D311yescharacteristic
473C3×C4⋊C4C22×D311yescharacteristic
474C3×C22⋊C4—61no—
475C3×C22⋊C4—61no—
476#217—61no—
477#217—61no—
478#215—62no—
479#214—62no—
480#213—22no—
481#213—22no—
482#213—62no—
483#213—62no—
484#213—62no—
485#213—62no—
486(C2×D3)⋊C4—21no—
487(C2×D3)⋊C4—21no—
488(C2×D3)⋊C4—61no—
489(C2×D3)⋊C4—61no—
490(C2×D3)⋊C4—61no—
491(C2×D3)⋊C4—61no—
492(C2×D3)⋊C4—121no—
493C4⋊Dic3—31no—
494C4⋊Dic3—31no—
495C4⋊Dic3—61no—
496C4×Dic3—61no—
497C4×Dic3—61no—
498C4×Dic3—121no—
499C2×C3⋊C8—31no—
500C2×C3⋊C8—31no—
501C2×C3⋊C8—61no—
502C2×C3⋊C8C22×D311yescharacteristic
503C2×C3⋊C8C22×D311yescharacteristic
504D24—22no—
505D24—62no—
506D24—62no—
507#204—22no—
508ΓL(1,𝔽25)—62no—
509ΓL(1,𝔽25)—62no—
510ΓL(1,𝔽25)—122no—
511D3×C8—62no—
512D3×C8—62no—
513C22×C32—22no—
514C22×C32—41no—
515C22×C32—41no—
516C22×C32C22×D411yescharacteristic
517C2×C3⋊D3—21no—
518C2×C3⋊D3—21no—
519C2×C3⋊D3—22no—
520C2×C3⋊D3—41no—
521C2×C3⋊D3—41no—
522C2×C3⋊D3—84no—
523C2×C3⋊D3#12012yes—
524C2×C3×D3—22no—
525C2×C3×D3—21no—
526C2×C3×D3—21no—
527C2×C3×D3—21no—
528C2×C3×D3—21no—
529C2×C3×D3—21no—
530C2×C3×D3—21no—
531C2×C3×D3—41no—
532C2×C3×D3—41no—
533C2×C3×D3—41no—
534C2×C3×D3—41no—
535C2×C3×D3—41no—
536C2×C3×D3—41no—
537C2×C3×D3—41no—
538C2×C3×D3—41no—
539C2×C3×D3—84no—
540D32—84no—
541D32—84no—
542C32×C4—41no—
543C32×C4C22×D411yescharacteristic
544C32×C4C22×D411yescharacteristic
545C3⋊Dic3—41no—
546C3⋊Dic3#12012yes—
547C3×Dic3—22no—
548C3×Dic3—21no—
549C3×Dic3—21no—
550H(5,𝔽2)—184no—
551H(5,𝔽2)—184no—
552C2×#41—31no—
553C2×#41—91no—
554C2×#41—91no—
555C2×#41—91no—
556C2×#41—181no—
557C22×D4—31no—
558C22×D4—91no—
559C22×D4—91no—
560C22×D4—91no—
561C22×D4—181no—
562C22×D4—181no—
563C22×D4—181no—
564AGL(1,ℤ/8)—184no—
565C2×SD16—31no—
566C2×SD16—91no—
567C2×D8—31no—
568C2×D8—31no—
569C2×D8—31no—
570C2×D8—91no—
571C2×D8—91no—
572C2×D8—91no—
573C2×D8—184no—
574C2×M16—91no—
575C22×C8—91no—
576#127—181no—
577#124—181no—
578#121—31no—
579#121—31no—
580#121—91no—
581#121—91no—
582#120—181no—
583#120—181no—
584#117—91no—
585#103—31no—
586#103—91no—
587#102—31no—
588#102—91no—
589#102—91no—
590#102—91no—
591#102—91no—
592#102D3211yescharacteristic, complemented
593C22⋊C8—31no—
594C22⋊C8—31no—
595C22⋊C8—91no—
596C22⋊C8—91no—
597C23×C3—21no—
598C23×C3—21no—
599C23×C3—31no—
600C23×C3—31no—
601C23×C3—41no—
602C23×C3—64no—
603C23×C3—61no—
604C23×C3—61no—
605C23×C3—61no—
606C23×C3—241no—
607C23×C3—241no—
608C22×D3—21no—
609C22×D3—24no—
610C22×D3—21no—
611C22×D3—21no—
612C22×D3—31no—
613C22×D3—31no—
614C22×D3—61no—
615C22×D3—64no—
616C22×D3—64no—
617C22×D3—64no—
618C22×D3—64no—
619C22×D3—61no—
620C22×D3—61no—
621C22×D3—81no—
622C22×D3—81no—
623C22×D3—124no—
624C22×D3—121no—
625C22×D3—122no—
626C22×D3—122no—
627C22×D3—241no—
628C22×D3—241no—
629C22×D3—241no—
630C22×D3—241no—
631C22×D3—241no—
632C22×D3—241no—
633C22×D3—241no—
634C22×D3—241no—
635C22×D3—241no—
636C22×D3—241no—
637C22×D3—241no—
638C22×D3—241no—
639C22×D3—242no—
640C22×D3—242no—
641C22×D3D3×D411yescharacteristic
642C22×D3D3×D411yescharacteristic
643C3×Q8—32no—
644C3×Q8—61no—
645C3×D4—21no—
646C3×D4—21no—
647C3×D4—22no—
648C3×D4—32no—
649C3×D4—41no—
650C3×D4—64no—
651C3×D4—64no—
652C3×D4—61no—
653C3×D4—61no—
654C3×D4—61no—
655C3×D4—61no—
656C3×D4—61no—
657C3×D4—241no—
658C3×D4—241no—
659C3×D4D3×D412yes—
660C3×D4D3×D412yes—
661C2×C3×C4—21no—
662C2×C3×C4—21no—
663C2×C3×C4—21no—
664C2×C3×C4—31no—
665C2×C3×C4—31no—
666C2×C3×C4—41no—
667C2×C3×C4—64no—
668C2×C3×C4—61no—
669C2×C3×C4—61no—
670C2×C3×C4—61no—
671C2×C3×C4—61no—
672C2×C3×C4—61no—
673C2×C3×C4C23×D311yescharacteristic
674C2×C3×C4C23×D311yescharacteristic
675#67—24no—
676#67—24no—
677#67—62no—
678#67—62no—
679#67—64no—
680#67—64no—
681#67—64no—
682#67—62no—
683#67—62no—
684#67—64no—
685#67—64no—
686#67—124no—
687#67—122no—
688#67—122no—
689#67—241no—
690#67—241no—
691#67—241no—
692#67—241no—
693C2×Dic3—24no—
694C2×Dic3—21no—
695C2×Dic3—31no—
696C2×Dic3—31no—
697C2×Dic3—61no—
698C2×Dic3—64no—
699C2×Dic3—61no—
700C2×Dic3—61no—
701C2×Dic3—121no—
702C2×Dic3D3×D411yescharacteristic
703C2×Dic3D3×D411yescharacteristic
704D12—21no—
705D12—21no—
706D12—21no—
707D12—21no—
708D12—21no—
709D12—32no—
710D12—32no—
711D12—62no—
712D12—62no—
713D12—62no—
714D12—64no—
715D12—64no—
716D12—64no—
717D12—61no—
718D12—61no—
719D12—81no—
720D12—81no—
721D12—121no—
722D12D3×D412yes—
723C4×D3—21no—
724C4×D3—21no—
725C4×D3—21no—
726C4×D3—21no—
727C4×D3—32no—
728C4×D3—32no—
729C4×D3—32no—
730C4×D3—32no—
731C4×D3—62no—
732C4×D3—62no—
733C4×D3—64no—
734C4×D3—64no—
735C4×D3—64no—
736Dic6—21no—
737Dic6—62no—
738Dic6—62no—
739Dic6D3×D412yes—
740C3×C8—21no—
741C3×C8—21no—
742C3×C8—41no—
743C3×C8—61no—
744C3×C8—61no—
745C3⋊C8—21no—
746C3⋊C8—21no—
747C3⋊C8—61no—
748C3⋊C8—61no—
749C3⋊C8—121no—
750C2×C32—42no—
751C2×C32C2×#12011yescharacteristic
752C2×C32#57611yescharacteristic
753C2×C32#57611yescharacteristic
754C3⋊D3—22no—
755C3⋊D3—42no—
756C3×D3—41no—
757C3×D3—42no—
758C3×D3—41no—
759C3×D3—81no—
760C3×D3—81no—
761C24—61no—
762C24—181no—
763C24—181no—
764C24—181no—
765#41—62no—
766#41—62no—
767#41—94no—
768#41—182no—
769#41—182no—
770#41—188no—
771#41—182no—
772#41—182no—
773#41—182no—
774C2×Q8—31no—
775C2×Q8—91no—
776C2×D4—31no—
777C2×D4—31no—
778C2×D4—31no—
779C2×D4—61no—
780C2×D4—61no—
781C2×D4—61no—
782C2×D4—62no—
783C2×D4—61no—
784C2×D4—62no—
785C2×D4—91no—
786C2×D4—91no—
787C2×D4—94no—
788C2×D4—91no—
789C2×D4—91no—
790C2×D4—181no—
791C2×D4—182no—
792C2×D4—182no—
793C2×D4—181no—
794C2×D4—181no—
795C2×D4—188no—
796C2×D4—182no—
797C2×D4—182no—
798C2×D4—182no—
799C2×D4—181no—
800C2×D4—181no—
801C2×D4—188no—
802C2×D4—188no—
803C2×D4—181no—
804C2×D4—181no—
805C2×D4C2×D3211yescharacteristic
806C22×C4—31no—
807C22×C4—31no—
808C22×C4—61no—
809C22×C4—91no—
810C22×C4—181no—
811C22×C4—181no—
812SD16—62no—
813SD16—182no—
814D8—62no—
815D8—62no—
816D8—62no—
817D8—182no—
818D8—182no—
819D8—182no—
820M16—182no—
821C2×C8—31no—
822C2×C8—31no—
823C2×C8—91no—
824C2×C8—182no—
825C2×C8C2×D3211yescharacteristic
826C4⋊C4—91no—
827C4⋊C4C2×D3211yescharacteristic
828C22⋊C4—61no—
829C22⋊C4—61no—
830C22⋊C4—181no—
831C22⋊C4—181no—
832C22⋊C4—181no—
833C42—181no—
834C22×C3—22no—
835C22×C3—22no—
836C22×C3—21no—
837C22×C3—42no—
838C22×C3—41no—
839C22×C3—41no—
840C22×C3—41no—
841C22×C3—41no—
842C22×C3—61no—
843C22×C3—61no—
844C22×C3—61no—
845C22×C3—61no—
846C22×C3—62no—
847C22×C3—61no—
848C22×C3—61no—
849C22×C3—81no—
850C22×C3—81no—
851C22×C3—121no—
852C22×C3—121no—
853C22×C3—121no—
854C22×C3—121no—
855C22×C3—121no—
856C22×C3—121no—
857C22×C3—121no—
858C22×C3—121no—
859C22×C3—244no—
860C22×C3C2×D3×D411yescharacteristic
861C22×C3C2×D3×D411yescharacteristic
862C2×D3—21no—
863C2×D3—21no—
864C2×D3—21no—
865C2×D3—21no—
866C2×D3—21no—
867C2×D3—21no—
868C2×D3—22no—
869C2×D3—32no—
870C2×D3—32no—
871C2×D3—41no—
872C2×D3—41no—
873C2×D3—41no—
874C2×D3—41no—
875C2×D3—41no—
876C2×D3—41no—
877C2×D3—41no—
878C2×D3—41no—
879C2×D3—62no—
880C2×D3—61no—
881C2×D3—61no—
882C2×D3—61no—
883C2×D3—61no—
884C2×D3—62no—
885C2×D3—62no—
886C2×D3—84no—
887C2×D3—121no—
888C2×D3—121no—
889C2×D3—122no—
890C2×D3—121no—
891C2×D3—121no—
892C2×D3—121no—
893C2×D3—121no—
894C2×D3—241no—
895C2×D3—241no—
896C2×D3—244no—
897C2×D3—244no—
898C2×D3—244no—
899C2×D3—244no—
900C2×D3—244no—
901C2×D3—244no—
902C2×D3—248no—
903C3×C4—21no—
904C3×C4—21no—
905C3×C4—41no—
906C3×C4—41no—
907C3×C4—61no—
908C3×C4—61no—
909C3×C4—62no—
910C3×C4—81no—
911C3×C4C2×D3×D411yescharacteristic
912C3×C4C2×D3×D411yescharacteristic
913C3×C4C2×D3×D411yescharacteristic
914C3×C4C2×D3×D411yescharacteristic
915Dic3—22no—
916Dic3—21no—
917Dic3—21no—
918Dic3—32no—
919Dic3—32no—
920Dic3—62no—
921Dic3—121no—
922Dic3—121no—
923Dic3—241no—
924C32#300811yescharacteristic, complemented, Sylow
925C23—21no—
926C23—31no—
927C23—31no—
928C23—64no—
929C23—61no—
930C23—61no—
931C23—61no—
932C23—91no—
933C23—184no—
934C23—184no—
935C23—181no—
936C23—241no—
937C23—241no—
938C23—362no—
939C23—721no—
940C23—721no—
941C23—721no—
942C23—721no—
943C23—721no—
944C23—721no—
945Q8—32no—
946Q8—61no—
947Q8—182no—
948D4—21no—
949D4—32no—
950D4—64no—
951D4—64no—
952D4—61no—
953D4—61no—
954D4—61no—
955D4—61no—
956D4—61no—
957D4—92no—
958D4—182no—
959D4—182no—
960D4—184no—
961D4—184no—
962D4—184no—
963D4—184no—
964D4—182no—
965D4—181no—
966D4—241no—
967D4—241no—
968D4—362no—
969D4—721no—
970D4—721no—
971D4#380212yes—
972C2×C4—21no—
973C2×C4—31no—
974C2×C4—31no—
975C2×C4—64no—
976C2×C4—61no—
977C2×C4—61no—
978C2×C4—61no—
979C2×C4—61no—
980C2×C4—61no—
981C2×C4—91no—
982C2×C4—92no—
983C2×C4—92no—
984C2×C4—184no—
985C2×C4—184no—
986C2×C4—181no—
987C2×C4C22×D3211yescharacteristic
988C8—21no—
989C8—61no—
990C8—61no—
991C8—181no—
992C2×C3—21no—
993C2×C3—21no—
994C2×C3—21no—
995C2×C3—42no—
996C2×C3—42no—
997C2×C3—82no—
998C2×C3—121no—
999C2×C3—122no—
1000C2×C3—121no—
1001C2×C3—241no—
1002C2×C3—241no—
1003C2×C3D3×#12011yescharacteristic
1004C2×C3D3×#12011yescharacteristic
1005C2×C3#575711yescharacteristic
1006C2×C3#576911yescharacteristic
1007C2×C3#577411yescharacteristic
1008C2×C3#577411yescharacteristic
1009D3—41no—
1010D3—42no—
1011D3—41no—
1012D3—62no—
1013D3—62no—
1014D3—81no—
1015D3—81no—
1016D3—122no—
1017D3—122no—
1018D3—122no—
1019D3—242no—
1020C22—22no—
1021C22—41no—
1022C22—41no—
1023C22—61no—
1024C22—61no—
1025C22—61no—
1026C22—61no—
1027C22—61no—
1028C22—61no—
1029C22—62no—
1030C22—92no—
1031C22—121no—
1032C22—121no—
1033C22—121no—
1034C22—121no—
1035C22—121no—
1036C22—121no—
1037C22—121no—
1038C22—121no—
1039C22—181no—
1040C22—181no—
1041C22—182no—
1042C22—244no—
1043C22—361no—
1044C22—361no—
1045C22—724no—
1046C22—724no—
1047C22—724no—
1048C22D32×D411yescharacteristic
1049C4—41no—
1050C4—61no—
1051C4—61no—
1052C4—62no—
1053C4—92no—
1054C4—361no—
1055C4C2×#380211yescharacteristic
1056C4D32×D411yescharacteristic
1057C3—21no—
1058C3#8000411yescharacteristic, complemented
1059C3#8008511yescharacteristic, complemented
1060C2—42no—
1061C2—121no—
1062C2—121no—
1063C2—122no—
1064C2—182no—
1065C2—241no—
1066C2—241no—
1067C2—362no—
1068C2#1059425811yescharacteristic
1069C2#1059473211yescharacteristic
1070C2#1059475511yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
hypercenter#102D32
hypocenterC32#3008
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
1. C2×#64314C2semidirect
2. C2×#63926C2semidirect
3. C2×#63798C2semidirect
4. #10594634C2semidirect
5. #10592469C2semidirect
6. C3×#4781C2semidirect
7. C3×#4773C2semidirect
8. #10591450C2semidirect
9. #10591447C2semidirect
10. #10590959C2semidirect
11. #10590944C2semidirect
12. #10590823C2semidirect
13. #10590615C2semidirect
14. #10590611C2semidirect
15. #10590595C2semidirect
19. C2×C3×#237C22semidirect
20. C2×C3×D3×D4C22semidirect
27. C2×#3802C22semidirect
28. C2×D3×D12C22semidirect
29. C2×#3799C22semidirect
32. C2×#3743C22semidirect
33. #64101C22semidirect
34. C2×C3×#213C22semidirect
35. C2×C3×#213C22semidirect
36. C2×C3×D24C22semidirect
37. C2×C3×#204C22semidirect
38. C3×#895C22semidirect
39. C3×#895C22semidirect
45. #63908C22semidirect
46. #63908C22semidirect
47. C2×#3715C22semidirect
48. C2×#3714C22semidirect
49. C2×#3714C22semidirect
50. C2×#3713C22semidirect
51. C2×#3710C22semidirect
53. C32×#102C22semidirect
54. #63659C22semidirect
55. #63648C22semidirect
56. #63636C22semidirect
57. C3×(C2×D3)⋊C8C22semidirect
58. C3×(C2×D3)⋊C8C22semidirect
59. C3×#810C22semidirect
60. C3×#809C22semidirect
61. #63566C22semidirect
62. #63563C22semidirect
63. (C2×D3)⋊(C3⋊C8)C22semidirect
64. (C2×D3)⋊(C3⋊C8)C22semidirect
85. #4781D3semidirect
87. #4773D3semidirect
103. D4×C3⋊D3D4semidirect
146. #3796D4semidirect
182. C2×#237C2×D3semidirect
192. C2×D3×D4C2×D3semidirect
217. C2×#213C2×D3semidirect
218. C2×#213C2×D3semidirect
227. C2×D24C2×D3semidirect
228. C2×#204C2×D3semidirect
234. #895C2×D3semidirect
235. #895C2×D3semidirect
246. C3×#102C2×D3semidirect
247. C3×#102C2×D3semidirect
263. (C2×D3)⋊C8C2×D3semidirect
264. (C2×D3)⋊C8C2×D3semidirect
266. #810C2×D3semidirect
270. #809C2×D3semidirect
592. #102D32semidirect
924. C32#3008semidirect
1058. C3#80004semidirect
1059. C3#80085semidirect

Maximal subgroups

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

subgroupindex
C2×#643142
C2×#639262
C2×#637982
#105946342
#105924692
C3×#47812
C3×#47732
#105914502
#105914472
#105909592
#105909442
#105908232
#105906152
#105906112
#105905952
#800853
#800043