Finite Group Databasebeta

← #11885820

Subgroups — #11885820

Order 1152.

1119 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595244C211yesmaximal, characteristic, complemented
2C2×#63935C211yesmaximal, characteristic, complemented
3C2×D3×#213C211yesmaximal, characteristic, complemented
4#10594633C211yesmaximal, characteristic, complemented
5#10592455C211yesmaximal, characteristic, complemented
6C3×#4781C211yesmaximal, characteristic, complemented
7C3×#4776C211yesmaximal, characteristic, complemented
8#10591476C211yesmaximal, characteristic, complemented
9#10590942C211yesmaximal, characteristic, complemented
10#10590867C211yesmaximal, characteristic, complemented
11#10590823C211yesmaximal, characteristic, complemented
12#10590718C211yesmaximal, characteristic, complemented
13#10590540C211yesmaximal, characteristic, complemented
14#10590518C211yesmaximal, characteristic, complemented
15#10590499C211yesmaximal, characteristic, complemented
16#80168—31nomaximal
17#80101—31nomaximal
18C2×C3×#237C2211yescharacteristic, complemented
19C2×C3×D3×D4C2211yescharacteristic
20C2×D3×D12C2211yescharacteristic
21C2×#3799C2211yescharacteristic, complemented
22D4×C3⋊Dic3C2211yescharacteristic, complemented
23C2×#3753C2211yescharacteristic
24#64102C2211yescharacteristic, complemented
25C2×C3×#214C2211yescharacteristic, complemented
26C2×C3×#213C2211yescharacteristic
27C2×C3×#204C2211yescharacteristic, complemented
28C2×C3×#204C2211yescharacteristic, complemented
29C3×#897C2211yescharacteristic
30C3×#895C2211yescharacteristic, complemented
31#63980—21no—
32#63976—21no—
33#63961—21no—
34C2×(C2×D3)⋊Dic3—21no—
35#63935—24no—
36D3×#213—24no—
37#63922—21no—
38#63921—21no—
39#63916—21no—
40#63908C2211yescharacteristic, complemented
41C4×#625C2211yescharacteristic
42#63863C2211yescharacteristic, complemented
43#63863C2211yescharacteristic, complemented
44#63856C2211yescharacteristic
45#63854—21no—
46C2×#3718C2211yescharacteristic, complemented
47C2×#3717C2211yescharacteristic, complemented
48C2×#3714C2211yescharacteristic
49C2×#3713C2211yescharacteristic
50C2×D3×C3⋊C8C2211yescharacteristic
51C2×D3×C3⋊C8C2211yescharacteristic, complemented
52C32×#102C2211yescharacteristic, complemented
53#63648C2211yescharacteristic, complemented
54C8×C3⋊Dic3C2211yescharacteristic, complemented
55#63634C2211yescharacteristic, complemented
56C3×(C2×D3)⋊C8C2211yescharacteristic
57C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
58C3×#810C2211yescharacteristic, complemented
59C3×#809C2211yescharacteristic, complemented
60#63572C2211yescharacteristic, complemented
61#63566C2211yescharacteristic, complemented
62#63563C2211yescharacteristic, complemented
63#5829—31no—
64C2×#950—31no—
65#5806—31no—
66C22×#213—31no—
67C2×#916—31no—
68C2×D3×D8—31no—
69#5630—31no—
70#5612—31no—
71C3×#450—31no—
72C3×#449—31no—
73#5172—31no—
74#5169—31no—
75#5168—31no—
76#5168—31no—
77#5165—31no—
78#5153—31no—
79#5051—31no—
80#5038—31no—
81#4819—31no—
82#4813—31no—
83#4787—31no—
84#4781D311yescharacteristic, complemented
85#4776D311yescharacteristic, complemented
86#4775—31no—
87#4756—31no—
88#4756—31no—
89#4756—61no—
90#4734—31no—
91#4731—31no—
92#67⋊C8—31no—
93#67⋊C8—31no—
94C23×C3×D3—21no—
95C22×D32—21no—
96C2×C32×D4C2311yescharacteristic
97C22×C3⋊Dic3—21no—
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C4×C3⋊D3—21no—
100C2×C3×#67—21no—
101C2×C3×#67—21no—
102C22×C3×Dic3—21no—
103C3×#237—22no—
104C3×#237—41no—
105C3×D3×D4—22no—
106C3×D3×D4—41no—
107C2×C3×D12—21no—
108C2×C3×D12C2311yescharacteristic
109C2×C3×D12C2311yescharacteristic
110C2×C3×C4×D3C2311yescharacteristic
111C2×C3×C4×D3C2311yescharacteristic
112C2×C3×Dic6C2311yescharacteristic
113C2×C3×Dic6C2311yescharacteristic
114C2×#626—21no—
115C2×#626—21no—
116C2×#625—21no—
117C2×#625D411yescharacteristic
118C2×#624—21no—
119D3×D12—22no—
120D3×D12—41no—
121#3799—22no—
122#3799—41no—
123C2×C32×C8C2311yescharacteristic
124C32×C4⋊C4C2311yescharacteristic
125#3757—21no—
126#3753D414yescomplemented
127#3752—21no—
128C4⋊(C3⋊Dic3)C2311yescharacteristic
129C4×C3⋊Dic3C2311yescharacteristic
130C2×C3⋊(C3⋊C8)C2311yescharacteristic
131C3×#214—22no—
132C3×#213—22no—
133C3×(C2×D3)⋊C4—21no—
134C3×(C2×D3)⋊C4—21no—
135C3×C4⋊Dic3—21no—
136C2×C3×C3⋊C8C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138C3×#204—41no—
139C3×#204—41no—
140#3724—21no—
141#3724D411yescharacteristic
142(C2×D3)⋊Dic3—21no—
143(C2×D3)⋊Dic3—21no—
144(C2×D3)⋊Dic3—21no—
145(C2×D3)⋊Dic3—21no—
146(C2×D3)⋊Dic3—21no—
147(C2×D3)⋊Dic3—21no—
148(C2×D3)⋊Dic3D411yescharacteristic
149(C2×D3)⋊Dic3D411yescharacteristic
150#3718—22no—
151#3717—22no—
152#3714—22no—
153#3713—22no—
154D3×C3⋊C8—22no—
155D3×C3⋊C8—22no—
156#3280—91noSylow
157C2×C3×#41—31no—
158C22×C3×D4—31no—
159C2×#239—31no—
160C2×#237C2×D311yescharacteristic, complemented
161C2×D3×D4—31no—
162C2×D3×D4C2×D311yescharacteristic
163C2×#235—31no—
164C22×D12—31no—
165C2×C3×SD16—31no—
166C2×C3×SD16—31no—
167C2×C3×SD16—31no—
168C2×C3×D8—31no—
169C3×C22⋊Q8—31no—
170C3×#121—31no—
171#953—61no—
172C2×#217—61no—
173#950—64no—
174#947—31no—
175#947—31no—
176#946—31no—
177C2×#216—31no—
178C2×#216—31no—
179C2×#215—31no—
180#939—61no—
181#939—61no—
182#938—31no—
183#938—61no—
184#937—61no—
185#937—61no—
186#936—31no—
187#936—31no—
188#935—61no—
189D4×Dic3—31no—
190D4×Dic3—31no—
191D4×Dic3—61no—
192C2×#214C2×D311yescharacteristic, complemented
193C2×#213—31no—
194C2×#213—31no—
195C2×#213—31no—
196C2×#213—31no—
197C2×#213—31no—
198C2×#213—61no—
199C2×#213—64no—
200C2×#213C2×D311yescharacteristic
201#930—31no—
202#929—61no—
203C4×#67—31no—
204C4×#67—31no—
205C2×(C2×D3)⋊C4—61no—
206#924—31no—
207C22×C3⋊C8—31no—
208C22×C3⋊C8—31no—
209#916—64no—
210D3×D8—64no—
211C2×D24—31no—
212C2×#204—31no—
213C2×#204C2×D311yescharacteristic, complemented
214C2×#204C2×D311yescharacteristic, complemented
215C2×D3×C8—31no—
216C2×D3×C8—31no—
217#897C2×D311yescharacteristic
218#895—61no—
219#895C2×D311yescharacteristic, complemented
220#894—61no—
221#893—31no—
222#893—31no—
223#893—61no—
224#883—61no—
225#882—61no—
226D3×C22⋊C4—61no—
227D3×C22⋊C4—61no—
228C3×#103—31no—
229C3×#102—21no—
230C3×#102—31no—
231C3×#102C2×D311yescharacteristic, complemented
232C3×#102C2×D311yescharacteristic, complemented
233C3×C22⋊C8—31no—
234C3×C22⋊C8—31no—
235#835—31no—
236#832—31no—
237#821—31no—
238#821—31no—
239#821—31no—
240#821—61no—
241(C2×D3)⋊C8C2×D311yescharacteristic
242(C2×D3)⋊C8C2×D311yescharacteristic, complemented
243#816—31no—
244Dic3⋊C8—31no—
245Dic3⋊C8—31no—
246C8×Dic3—31no—
247C8×Dic3—31no—
248C8×Dic3—61no—
249#810C2×D311yescharacteristic, complemented
250#809C2×D311yescharacteristic, complemented
251#807—31no—
252#807—31no—
253#807—61no—
254C23×C32—21no—
255C22×C3⋊D3—21no—
256C22×C3×D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3—42no—
259C22×C3×D3—42no—
260C22×C3×D3—81no—
261C22×C3×D3C2×D411yescharacteristic
262C22×C3×D3C2×D411yescharacteristic
263C2×D32—42no—
264C2×D32—42no—
265C2×D32—81no—
266C32×D4—21no—
267C32×D4C2×D412yes—
268C2×C32×C4—21no—
269C2×C32×C4C2411yescharacteristic
270C2×C3⋊Dic3—21no—
271C2×C3⋊Dic3—81no—
272C2×C3⋊Dic3C2×D411yescharacteristic
273C2×C3⋊Dic3C2×D411yescharacteristic
274C4⋊(C3⋊D3)—21no—
275C4⋊(C3⋊D3)C2×D412yes—
276C4×C3⋊D3—81no—
277C3×#67—42no—
278C3×#67—42no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—42no—
282C2×C3×Dic3C2×D411yescharacteristic
283C2×C3×Dic3C2×D411yescharacteristic
284C3×D12—21no—
285C3×D12—21no—
286C3×D12—21no—
287C3×D12—21no—
288C3×D12—81no—
289C3×C4×D3—21no—
290C3×C4×D3—21no—
291C3×C4×D3—21no—
292C3×C4×D3—21no—
293C3×Dic6—21no—
294C3×Dic6—21no—
295C3×Dic6—21no—
296C3×Dic6—21no—
297#626—42no—
298#626—42no—
299#625—22no—
300#625—81no—
301#624—42no—
302C32×C8—21no—
303C3⋊(C3⋊C8)C2×D412yes—
304C3×C3⋊C8—21no—
305C3×C3⋊C8—21no—
306C2×#135—91no—
307C22×D8—91no—
308#546—91no—
309#546—91no—
310#495—91no—
311#467—91no—
312#466—91no—
313#463—91no—
314#463—91no—
315#450—31no—
316#450—91no—
317#449—31no—
318#449—91no—
319C4×D8—91no—
320C8×D4—91no—
321C24×C3—61no—
322C23×D3—21no—
323C23×D3—61no—
324C23×D3—61no—
325C3×#41—62no—
326C3×#41—121no—
327C2×C3×Q8—31no—
328C2×C3×Q8—31no—
329C2×C3×D4—21no—
330C2×C3×D4—31no—
331C2×C3×D4—31no—
332C2×C3×D4—61no—
333C2×C3×D4—61no—
334C2×C3×D4—62no—
335C2×C3×D4—61no—
336C2×C3×D4—121no—
337C2×C3×D4C22×D311yescharacteristic
338C2×C3×D4C22×D311yescharacteristic
339C22×C3×C4—31no—
340C22×C3×C4—31no—
341C22×C3×C4—61no—
342C2×#67—21no—
343C2×#67—21no—
344C2×#67—31no—
345C2×#67—31no—
346C2×#67—61no—
347C2×#67—61no—
348C2×#67—61no—
349C2×#67—61no—
350C22×Dic3—21no—
351C22×Dic3—61no—
352C22×Dic3—61no—
353C22×Dic3—121no—
354#239—62no—
355#239—121no—
356#237—22no—
357#237—41no—
358D3×D4—22no—
359D3×D4—41no—
360D3×D4—62no—
361D3×D4—121no—
362#235—62no—
363#235—121no—
364C2×D12—21no—
365C2×D12—31no—
366C2×D12—31no—
367C2×D12—61no—
368C2×D12—62no—
369C2×D12—61no—
370C2×D12—61no—
371C2×D12—121no—
372C2×D12C22×D311yescharacteristic
373C2×D12C22×D311yescharacteristic
374C2×C4×D3—61no—
375C2×C4×D3—61no—
376C2×C4×D3—61no—
377C2×C4×D3—61no—
378C2×C4×D3—121no—
379C2×C4×D3C22×D311yescharacteristic
380C2×C4×D3C22×D311yescharacteristic
381C2×Dic6C22×D311yescharacteristic
382C2×Dic6C22×D311yescharacteristic
383C3×SD16—62no—
384C3×SD16—121no—
385C3×SD16—121no—
386C3×D8—62no—
387C2×C3×C8—21no—
388C2×C3×C8—31no—
389C2×C3×C8—31no—
390C2×C3×C8C22×D311yescharacteristic
391C2×C3×C8C22×D311yescharacteristic
392C3×C4⋊C4—21no—
393C3×C4⋊C4—61no—
394C3×C4⋊C4C22×D311yescharacteristic
395C3×C4⋊C4C22×D311yescharacteristic
396C3×C22⋊C4—61no—
397C3×C22⋊C4—61no—
398#217—31no—
399#217—31no—
400#217—61no—
401#217—61no—
402#217—61no—
403#217—61no—
404#217—61no—
405#217—61no—
406#217—61no—
407#217—61no—
408#217—121no—
409#216—62no—
410#216—62no—
411#215—62no—
412#214—22no—
413#213—22no—
414#213—34no—
415#213—34no—
416#213—64no—
417#213—62no—
418#213—62no—
419#213—62no—
420(C2×D3)⋊C4—21no—
421(C2×D3)⋊C4—21no—
422(C2×D3)⋊C4—31no—
423(C2×D3)⋊C4—31no—
424(C2×D3)⋊C4—61no—
425(C2×D3)⋊C4—61no—
426(C2×D3)⋊C4—61no—
427(C2×D3)⋊C4—61no—
428(C2×D3)⋊C4—61no—
429(C2×D3)⋊C4—61no—
430(C2×D3)⋊C4—61no—
431(C2×D3)⋊C4—61no—
432(C2×D3)⋊C4—121no—
433C4⋊Dic3—21no—
434C4⋊Dic3—31no—
435C4⋊Dic3—31no—
436C4⋊Dic3—61no—
437Dic3⋊C4—31no—
438Dic3⋊C4—31no—
439Dic3⋊C4—61no—
440Dic3⋊C4—61no—
441C4×Dic3—31no—
442C4×Dic3—31no—
443C4×Dic3—61no—
444C2×C3⋊C8—31no—
445C2×C3⋊C8—31no—
446C2×C3⋊C8—61no—
447C2×C3⋊C8—62no—
448C2×C3⋊C8—62no—
449C2×C3⋊C8C22×D311yescharacteristic
450C2×C3⋊C8C22×D311yescharacteristic
451D24—62no—
452#204—41no—
453#204—41no—
454#204—62no—
455D3×C8—62no—
456D3×C8—62no—
457C22×C32—22no—
458C22×C32—41no—
459C22×C32—41no—
460C22×C32C22×D411yescharacteristic
461C2×C3⋊D3—22no—
462C2×C3⋊D3—41no—
463C2×C3⋊D3—41no—
464C2×C3×D3—21no—
465C2×C3×D3—21no—
466C2×C3×D3—21no—
467C2×C3×D3—21no—
468C2×C3×D3—21no—
469C2×C3×D3—41no—
470C2×C3×D3—41no—
471C2×C3×D3—41no—
472C2×C3×D3—41no—
473C2×C3×D3—41no—
474C2×C3×D3—41no—
475C2×C3×D3—84no—
476C2×C3×D3#13512yescomplemented
477D32—84no—
478C32×C4—41no—
479C32×C4C22×D411yescharacteristic
480C32×C4H(5,𝔽2)11yescharacteristic
481C3⋊Dic3—21no—
482C3⋊Dic3—21no—
483C3⋊Dic3—41no—
484C3×Dic3—21no—
485C3×Dic3—21no—
486C3×Dic3—41no—
487C3×Dic3—41no—
488C2×#41—31no—
489C2×#41—91no—
490C22×D4—31no—
491C22×D4—91no—
492#135—184no—
493C2×Q16—91no—
494C2×SD16—31no—
495C2×SD16—31no—
496C2×SD16—31no—
497C2×SD16—91no—
498C2×D8—31no—
499C2×D8—91no—
500C2×D8—91no—
501C2×D8—91no—
502C2×D8—184no—
503C22×C8—91no—
504C22×C8—91no—
505#124—91no—
506#124—91no—
507#123—181no—
508#123—181no—
509C22⋊Q8—31no—
510C22⋊Q8—91no—
511#121—31no—
512#121—91no—
513#121—181no—
514#121—181no—
515#120—181no—
516#120—181no—
517C4×D4—91no—
518C4×D4—91no—
519C4×D4—91no—
520C2×C22⋊C4—181no—
521C2×C22⋊C4—181no—
522#107—91no—
523C4⋊C8—91no—
524#103—31no—
525#103—91no—
526#102—31no—
527#102—91no—
528#102—91no—
529#102D3211yescharacteristic, complemented
530C22⋊C8—31no—
531C22⋊C8—31no—
532C4×C8—91no—
533C23×C3—21no—
534C23×C3—21no—
535C23×C3—31no—
536C23×C3—31no—
537C23×C3—41no—
538C23×C3—61no—
539C23×C3—61no—
540C23×C3—122no—
541C23×C3—122no—
542C23×C3—241no—
543C22×D3—21no—
544C22×D3—21no—
545C22×D3—42no—
546C22×D3—42no—
547C22×D3—61no—
548C22×D3—61no—
549C22×D3—81no—
550C22×D3—121no—
551C22×D3—122no—
552C22×D3—122no—
553C22×D3—122no—
554C22×D3—122no—
555C22×D3—241no—
556C22×D3—241no—
557C22×D3D3×D411yescharacteristic
558C22×D3D3×D411yescharacteristic
559C3×Q8—61no—
560C3×Q8—61no—
561C3×Q8—61no—
562C3×Q8—61no—
563C3×D4—21no—
564C3×D4—21no—
565C3×D4—22no—
566C3×D4—41no—
567C3×D4—61no—
568C3×D4—61no—
569C3×D4—61no—
570C3×D4—61no—
571C3×D4—122no—
572C3×D4—122no—
573C3×D4—241no—
574C3×D4D3×D412yes—
575C3×D4D3×D412yes—
576C2×C3×C4—21no—
577C2×C3×C4—21no—
578C2×C3×C4—21no—
579C2×C3×C4—31no—
580C2×C3×C4—31no—
581C2×C3×C4—41no—
582C2×C3×C4—61no—
583C2×C3×C4—61no—
584C2×C3×C4—61no—
585C2×C3×C4—61no—
586C2×C3×C4—61no—
587C2×C3×C4—61no—
588C2×C3×C4—122no—
589C2×C3×C4C23×D311yescharacteristic
590C2×C3×C4C23×D311yescharacteristic
591#67—42no—
592#67—42no—
593#67—62no—
594#67—62no—
595#67—122no—
596#67—122no—
597#67—241no—
598#67—241no—
599C2×Dic3—21no—
600C2×Dic3—21no—
601C2×Dic3—31no—
602C2×Dic3—31no—
603C2×Dic3—31no—
604C2×Dic3—31no—
605C2×Dic3—42no—
606C2×Dic3—61no—
607C2×Dic3—61no—
608C2×Dic3—61no—
609C2×Dic3—61no—
610C2×Dic3—121no—
611C2×Dic3—241no—
612C2×Dic3—241no—
613C2×Dic3—242no—
614C2×Dic3D3×D411yescharacteristic
615C2×Dic3D3×D411yescharacteristic
616D12—21no—
617D12—21no—
618D12—21no—
619D12—21no—
620D12—32no—
621D12—32no—
622D12—62no—
623D12—61no—
624D12—61no—
625D12—81no—
626D12—121no—
627D12—122no—
628D12—122no—
629C4×D3—21no—
630C4×D3—21no—
631C4×D3—21no—
632C4×D3—21no—
633C4×D3—122no—
634C4×D3—122no—
635C4×D3—241no—
636C4×D3—241no—
637C4×D3—242no—
638Dic6—21no—
639Dic6—21no—
640Dic6—21no—
641Dic6—21no—
642C3×C8—21no—
643C3×C8—21no—
644C3×C8—41no—
645C3×C8—61no—
646C3×C8—61no—
647C3⋊C8—21no—
648C3⋊C8—21no—
649C3⋊C8—32no—
650C3⋊C8—32no—
651C3⋊C8—62no—
652C2×C32—42no—
653C2×C32D4211yescharacteristic
654C2×C32C2×#13511yescharacteristic
655C2×C32#57611yescharacteristic
656C3⋊D3—42no—
657C3×D3—22no—
658C3×D3—41no—
659C3×D3—81no—
660C3×D3—81no—
661C24—61no—
662C24—181no—
663#41—62no—
664#41—121no—
665#41—182no—
666#41—361no—
667C2×Q8—31no—
668C2×Q8—31no—
669C2×D4—31no—
670C2×D4—31no—
671C2×D4—61no—
672C2×D4—61no—
673C2×D4—62no—
674C2×D4—61no—
675C2×D4—91no—
676C2×D4—91no—
677C2×D4—121no—
678C2×D4—181no—
679C2×D4—182no—
680C2×D4—181no—
681C2×D4—181no—
682C2×D4—361no—
683C2×D4C2×D3211yescharacteristic
684C22×C4—31no—
685C22×C4—31no—
686C22×C4—61no—
687C22×C4—181no—
688C22×C4—181no—
689C22×C4—181no—
690Q16—182no—
691SD16—62no—
692SD16—121no—
693SD16—121no—
694SD16—182no—
695D8—62no—
696D8—94no—
697D8—182no—
698D8—182no—
699C2×C8—31no—
700C2×C8—31no—
701C2×C8—91no—
702C2×C8—182no—
703C2×C8—182no—
704C2×C8C2×D3211yescharacteristic
705C4⋊C4—61no—
706C4⋊C4—91no—
707C4⋊C4—91no—
708C4⋊C4—181no—
709C4⋊C4C2×D3211yescharacteristic
710C22⋊C4—61no—
711C22⋊C4—61no—
712C22⋊C4—91no—
713C22⋊C4—91no—
714C22⋊C4—181no—
715C22⋊C4—181no—
716C22⋊C4—181no—
717C22⋊C4—181no—
718C22⋊C4—181no—
719C22⋊C4—181no—
720C22⋊C4—181no—
721C22⋊C4—181no—
722C42—91no—
723C22×C3—22no—
724C22×C3—22no—
725C22×C3—21no—
726C22×C3—32no—
727C22×C3—42no—
728C22×C3—41no—
729C22×C3—41no—
730C22×C3—41no—
731C22×C3—41no—
732C22×C3—61no—
733C22×C3—61no—
734C22×C3—61no—
735C22×C3—61no—
736C22×C3—61no—
737C22×C3—81no—
738C22×C3—81no—
739C22×C3—121no—
740C22×C3—121no—
741C22×C3—121no—
742C22×C3—121no—
743C22×C3—121no—
744C22×C3—121no—
745C22×C3—244no—
746C22×C3C2×D3×D411yescharacteristic
747C22×C3C2×D3×D411yescharacteristic
748C2×D3—21no—
749C2×D3—21no—
750C2×D3—21no—
751C2×D3—21no—
752C2×D3—21no—
753C2×D3—41no—
754C2×D3—41no—
755C2×D3—41no—
756C2×D3—41no—
757C2×D3—41no—
758C2×D3—41no—
759C2×D3—62no—
760C2×D3—62no—
761C2×D3—84no—
762C2×D3—122no—
763C2×D3—121no—
764C2×D3—121no—
765C2×D3—121no—
766C2×D3—121no—
767C2×D3—241no—
768C2×D3—241no—
769C2×D3—244no—
770C2×D3—244no—
771C2×D3#91612yescomplemented
772C3×C4—21no—
773C3×C4—21no—
774C3×C4—41no—
775C3×C4—41no—
776C3×C4—61no—
777C3×C4—61no—
778C3×C4—81no—
779C3×C4—121no—
780C3×C4—121no—
781C3×C4C2×D3×D411yescharacteristic
782C3×C4C2×D3×D411yescharacteristic
783C3×C4#100411yescharacteristic
784C3×C4#100411yescharacteristic
785Dic3—21no—
786Dic3—21no—
787Dic3—41no—
788Dic3—41no—
789Dic3—62no—
790Dic3—61no—
791Dic3—61no—
792Dic3—61no—
793Dic3—61no—
794Dic3—121no—
795Dic3—121no—
796Dic3—121no—
797Dic3—241no—
798C32#328011yescharacteristic, complemented, Sylow
799C23—21no—
800C23—31no—
801C23—31no—
802C23—61no—
803C23—61no—
804C23—122no—
805C23—122no—
806C23—181no—
807C23—241no—
808C23—362no—
809C23—362no—
810C23—721no—
811Q8—61no—
812Q8—61no—
813Q8—61no—
814Q8—61no—
815D4—21no—
816D4—61no—
817D4—61no—
818D4—61no—
819D4—61no—
820D4—92no—
821D4—122no—
822D4—122no—
823D4—182no—
824D4—181no—
825D4—241no—
826D4—362no—
827D4—362no—
828D4—721no—
829D4#380212yes—
830C2×C4—21no—
831C2×C4—31no—
832C2×C4—31no—
833C2×C4—61no—
834C2×C4—61no—
835C2×C4—61no—
836C2×C4—61no—
837C2×C4—61no—
838C2×C4—61no—
839C2×C4—91no—
840C2×C4—91no—
841C2×C4—122no—
842C2×C4—181no—
843C2×C4—362no—
844C2×C4—721no—
845C2×C4—721no—
846C2×C4C22×D3211yescharacteristic
847C8—21no—
848C8—61no—
849C8—61no—
850C8—92no—
851C2×C3—21no—
852C2×C3—21no—
853C2×C3—21no—
854C2×C3—42no—
855C2×C3—42no—
856C2×C3—62no—
857C2×C3—82no—
858C2×C3—121no—
859C2×C3—241no—
860C2×C3—241no—
861C2×C3#559011yescharacteristic
862C2×C3#559011yescharacteristic
863C2×C3C2×#91611yescharacteristic
864C2×C3D3×#13511yescharacteristic
865C2×C3#577411yescharacteristic
866C2×C3#577411yescharacteristic
867D3—22no—
868D3—41no—
869D3—81no—
870D3—81no—
871D3—122no—
872D3—122no—
873D3—242no—
874C22—22no—
875C22—32no—
876C22—41no—
877C22—41no—
878C22—61no—
879C22—61no—
880C22—61no—
881C22—61no—
882C22—61no—
883C22—121no—
884C22—121no—
885C22—121no—
886C22—121no—
887C22—121no—
888C22—121no—
889C22—182no—
890C22—244no—
891C22—361no—
892C22—361no—
893C22—724no—
894C22D32×D411yescharacteristic
895C4—41no—
896C4—61no—
897C4—61no—
898C4—121no—
899C4—121no—
900C4—181no—
901C4—181no—
902C4—361no—
903C4C2×#380211yescharacteristic
904C4#6431311yescharacteristic
905C3—21no—
906C3#8010111yescharacteristic, complemented
907C3#8016811yescharacteristic, complemented
908C2—42no—
909C2—62no—
910C2—121no—
911C2—241no—
912C2—241no—
913C2—362no—
914C2#1059427111yescharacteristic
915C2#1059473511yescharacteristic
916C2D3×#91611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
hypercenter#102D32
hypocenterC32#3280
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. #10595244C2semidirect
2. C2×#63935C2semidirect
3. C2×D3×#213C2semidirect
4. #10594633C2semidirect
5. #10592455C2semidirect
6. C3×#4781C2semidirect
7. C3×#4776C2semidirect
8. #10591476C2semidirect
9. #10590942C2semidirect
10. #10590867C2semidirect
11. #10590823C2semidirect
12. #10590718C2semidirect
13. #10590540C2semidirect
14. #10590518C2semidirect
15. #10590499C2semidirect
18. C2×C3×#237C22semidirect
21. C2×#3799C22semidirect
22. D4×C3⋊Dic3C22semidirect
24. #64102C22semidirect
25. C2×C3×#214C22semidirect
27. C2×C3×#204C22semidirect
28. C2×C3×#204C22semidirect
30. C3×#895C22semidirect
40. #63908C22semidirect
42. #63863C22semidirect
43. #63863C22semidirect
46. C2×#3718C22semidirect
47. C2×#3717C22semidirect
51. C2×D3×C3⋊C8C22semidirect
52. C32×#102C22semidirect
53. #63648C22semidirect
54. C8×C3⋊Dic3C22semidirect
55. #63634C22semidirect
57. C3×(C2×D3)⋊C8C22semidirect
58. C3×#810C22semidirect
59. C3×#809C22semidirect
60. #63572C22semidirect
61. #63566C22semidirect
62. #63563C22semidirect
84. #4781D3semidirect
85. #4776D3semidirect
126. #3753D4semidirect
160. C2×#237C2×D3semidirect
192. C2×#214C2×D3semidirect
213. C2×#204C2×D3semidirect
214. C2×#204C2×D3semidirect
219. #895C2×D3semidirect
231. C3×#102C2×D3semidirect
232. C3×#102C2×D3semidirect
242. (C2×D3)⋊C8C2×D3semidirect
249. #810C2×D3semidirect
250. #809C2×D3semidirect
476. C2×C3×D3#135semidirect
529. #102D32semidirect
771. C2×D3#916semidirect
798. C32#3280semidirect
906. C3#80101semidirect
907. C3#80168semidirect

Maximal subgroups

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

subgroupindex
#105952442
C2×#639352
C2×D3×#2132
#105946332
#105924552
C3×#47812
C3×#47762
#105914762
#105909422
#105908672
#105908232
#105907182
#105905402
#105905182
#105904992
#801683
#801013