Finite Group Databasebeta

← #11867136

Subgroups — #11867136

Order 1152.

1158 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#914C211yesmaximal, characteristic, complemented
2#10595424C211yesmaximal, characteristic, complemented
3D3×#938C211yesmaximal, characteristic, complemented
4C2×#63791C211yesmaximal, characteristic, complemented
5#10592870C211yesmaximal, characteristic, complemented
6C3×#5174C211yesmaximal, characteristic, complemented
7#10591591C211yesmaximal, characteristic, complemented
8#10591587C211yesmaximal, characteristic, complemented
9#10591550C211yesmaximal, characteristic, complemented
10#10591455C211yesmaximal, characteristic, complemented
11#10591451C211yesmaximal, characteristic, complemented
12#10591421C211yesmaximal, characteristic, complemented
13#10590844C211yesmaximal, characteristic, complemented
14#10590836C211yesmaximal, characteristic, complemented
15#10590683C211yesmaximal, characteristic, complemented
16#83950—31nomaximal
17#80805—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C2×D3×#67—21no—
21C2×C4×D32C2211yescharacteristic
22C2×C32×SD16C2211yescharacteristic, complemented
23#64155C2211yescharacteristic, complemented
24#64147C2211yescharacteristic
25C2×C8×C3⋊D3C2211yescharacteristic, complemented
26C3×#946C2211yescharacteristic, complemented
27C2×C3×#215C2211yescharacteristic, complemented
28C3×#938C2211yescharacteristic
29C2×C3×#213C2211yescharacteristic, complemented
30C3×#914—24no—
31C2×C3×D24C2211yescharacteristic, complemented
32C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
33C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
34#63970—21no—
35D3×#217—21no—
36#63958—21no—
37#63922—21no—
38#63916C2211yescharacteristic
39#63916C2211yescharacteristic, complemented
40#63908C2211yescharacteristic
41#63908C2211yescharacteristic, complemented
42#63904—21no—
43D3×C4⋊Dic3C2211yescharacteristic
44#63884—21no—
45#63879—21no—
46#63841C2211yescharacteristic
47C2×#3711C2211yescharacteristic
48C2×#3711C2211yescharacteristic, complemented
49C2×#3710C2211yescharacteristic, complemented
50#63791—24no—
51#63662C2211yescharacteristic, complemented
52#63659C2211yescharacteristic, complemented
53#63644C2211yescharacteristic, complemented
54C3×#835C2211yescharacteristic, complemented
55C3×#832C2211yescharacteristic, complemented
56C3×#818C2211yescharacteristic, complemented
57#63575C2211yescharacteristic, complemented
58#63573C2211yescharacteristic, complemented
59#63563C2211yescharacteristic, complemented
60#63563C2211yescharacteristic, complemented
61#63562C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63C2×C3×AGL(1,ℤ/8)—31no—
64#5828—31no—
65C2×#938—31no—
66C2×#914D311yescharacteristic, complemented
67C2×D3×M16—31no—
68C2×D3×M16—31no—
69#5627—31no—
70D3×#121—31no—
71C3×#468—31no—
72#5232—31no—
73#5215—31no—
74#5174—31no—
75#5174D311yescharacteristic, complemented
76#5171—31no—
77#5171—31no—
78#5171—31no—
79#5171—61no—
80#5159—31no—
81#5159—31no—
82#5157—31no—
83#5157—31no—
84#5135—31no—
85#5121—31no—
86#5049—31no—
87#5039—31no—
88#4883—31no—
89#4881—31no—
90#4807—31no—
91#4803—31no—
92#4775—31no—
93#4770—31no—
94C23×C3×D3—21no—
95C22×D32D411yescharacteristic
96C2×C32×Q8C2311yescharacteristic
97C2×C32×D4C2311yescharacteristic
98C2×#638—21no—
99C2×C4×C3⋊D3C2311yescharacteristic
100C2×C3×#67—21no—
101C2×C3×#67—21no—
102C3×#239—22no—
103C3×#239—22no—
104C3×D3×D4—22no—
105C3×D3×D4—22no—
106C2×C3×D12—21no—
107C2×C3×D12C2311yescharacteristic
108C2×C3×D12C2311yescharacteristic
109C2×C3×C4×D3—21no—
110C2×C3×C4×D3C2311yescharacteristic
111C2×C3×C4×D3C2311yescharacteristic
112D3×#67—44no—
113C2×#626—21no—
114C2×#626—21no—
115C2×#625—21no—
116C2×#625—21no—
117C2×#624D411yescharacteristic
118C2×D3×Dic3—21no—
119C2×D3×Dic3D411yescharacteristic
120C2×D3×Dic3D411yescharacteristic
121C4×D32—22no—
122C4×D32—22no—
123C32×SD16—22no—
124C2×C32×C8C2311yescharacteristic
125#3757—21no—
126#3752—21no—
127C4⋊(C3⋊Dic3)C2311yescharacteristic
128C4⋊(C3⋊Dic3)C2311yescharacteristic
129#3750—21no—
130C2×C3⋊(C3⋊C8)C2311yescharacteristic
131C8×C3⋊D3—22no—
132C3×#217—21no—
133C3×#215—22no—
134C3×#213—22no—
135C3×(C2×D3)⋊C4—21no—
136C3×C4⋊Dic3C2311yescharacteristic
137C3×C4⋊Dic3C2311yescharacteristic
138C3×Dic3⋊C4—21no—
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141C3×D24—22no—
142C3×ΓL(1,𝔽25)—22no—
143C3×ΓL(1,𝔽25)D414yescomplemented
144Dic3⋊Dic3—21no—
145(C2×D3)⋊Dic3—21no—
146(C2×D3)⋊Dic3—21no—
147(C2×D3)⋊Dic3—21no—
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3—21no—
150Dic32—21no—
151#3711—22no—
152#3711—22no—
153#3710—22no—
154#3055—91noSylow
155C2×C3×#41—31no—
156C22×C3×D4—31no—
157C22×#67—61no—
158C2×#239C2×D311yescharacteristic
159C2×D3×D4—61no—
160C2×D3×D4C2×D311yescharacteristic
161C22×C4×D3—31no—
162C22×C4×D3—31no—
163C3×AGL(1,ℤ/8)—64no—
164C2×C3×SD16—21no—
165C2×C3×SD16—31no—
166C2×C3×SD16C2×D311yescharacteristic, complemented
167C2×C3×SD16C2×D311yescharacteristic, complemented
168C2×C3×D8—31no—
169C2×C3×D8—31no—
170C2×C3×M16—31no—
171C2×C3×M16—31no—
172C3×C22⋊Q8—31no—
173C3×#121—31no—
174C2×#217—61no—
175#946—31no—
176#946—31no—
177#946—61no—
178#946C2×D311yescharacteristic, complemented
179C2×#215C2×D311yescharacteristic, complemented
180#939—61no—
181#938—31no—
182#938—31no—
183#938—31no—
184#938—31no—
185#938—31no—
186#938—31no—
187#938—61no—
188#938—61no—
189#938—61no—
190#938C2×D311yescharacteristic
191#937—61no—
192#935—61no—
193C2×#213C2×D311yescharacteristic, complemented
194#930—31no—
195#930—31no—
196C4×#67—61no—
197C4×#67—61no—
198#926—31no—
199C2×C4⋊Dic3—31no—
200C2×#208—31no—
201C2×#208—31no—
202#914—24no—
203D3×M16—64no—
204D3×M16—64no—
205C2×D24C2×D311yescharacteristic, complemented
206C2×ΓL(1,𝔽25)—31no—
207C2×ΓL(1,𝔽25)—31no—
208C2×ΓL(1,𝔽25)C2×D311yescharacteristic
209C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
210C2×D3×C8—31no—
211C2×D3×C8—31no—
212C2×D3×C8—31no—
213C2×D3×C8—31no—
214C2×D3×C8—61no—
215#895—31no—
216#895—31no—
217#894—61no—
218#893—61no—
219#892—31no—
220D3×C4⋊C4—31no—
221#884—61no—
222#882—61no—
223#67⋊C4—61no—
224D3×C22⋊C4—61no—
225C3×#107—31no—
226C3×#103—31no—
227C3×#102—31no—
228#835—31no—
229#835—31no—
230#835—61no—
231#835C2×D311yescharacteristic, complemented
232#832—31no—
233#832—31no—
234#832—31no—
235#832—31no—
236#832—31no—
237#832—31no—
238#832—61no—
239#832C2×D311yescharacteristic, complemented
240#821—31no—
241#821—31no—
242#818—31no—
243#818C2×D311yescharacteristic, complemented
244#817—31no—
245#817—31no—
246#817—31no—
247#817—61no—
248#809—31no—
249#809—31no—
250#808—31no—
251#807—31no—
252C23×C32—21no—
253C22×C3⋊D3C2×D411yescharacteristic
254C22×C3×D3—21no—
255C22×C3×D3—21no—
256C22×C3×D3—42no—
257C22×C3×D3—42no—
258C22×C3×D3—42no—
259C22×C3×D3C2×D411yescharacteristic
260C22×C3×D3C2×D411yescharacteristic
261C2×D32—22no—
262C2×D32—22no—
263C2×D32—41no—
264C32×Q8—21no—
265C32×Q8—21no—
266C32×D4—21no—
267C32×D4—21no—
268C2×C32×C4—21no—
269C2×C32×C4C2411yescharacteristic
270#638—42no—
271C2×C3⋊Dic3—21no—
272C2×C3⋊Dic3—21no—
273C2×C3⋊Dic3C2×D411yescharacteristic
274C4×C3⋊D3—21no—
275C4×C3⋊D3—21no—
276C3×#67—42no—
277C3×#67—42no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3C2×D411yescharacteristic
281C2×C3×Dic3C2×D411yescharacteristic
282C3×D12—21no—
283C3×D12—21no—
284C3×D12—21no—
285C3×D12—21no—
286C3×D12—42no—
287C3×C4×D3—21no—
288C3×C4×D3—21no—
289C3×C4×D3—42no—
290C3×C4×D3C2×D412yes—
291C3×C4×D3#4112yes—
292#626—42no—
293#626—42no—
294#625—42no—
295#625—42no—
296#624—22no—
297D3×Dic3—22no—
298D3×Dic3—22no—
299D3×Dic3—42no—
300C32×C8C2×D412yescomplemented
301C3⋊(C3⋊C8)—21no—
302C3×C3⋊C8—21no—
303C3×C3⋊C8C2×D412yescomplemented
304C2×AGL(1,ℤ/8)—31no—
305C22×M16—91no—
306#525—91no—
307C2×#121—91no—
308#469—91no—
309#469—91no—
310#468—31no—
311#468—91no—
312#466—91no—
313#466—91no—
314#465—91no—
315#465—91no—
316#428—91no—
317#418—91no—
318#417—91no—
319C24×C3—61no—
320C23×D3—21no—
321C23×D3—31no—
322C23×D3—31no—
323C3×#41—62no—
324C3×#41—62no—
325C2×C3×Q8—21no—
326C2×C3×Q8C22×D311yescharacteristic
327C2×C3×Q8C22×D311yescharacteristic
328C2×C3×D4—21no—
329C2×C3×D4—31no—
330C2×C3×D4—31no—
331C2×C3×D4—61no—
332C2×C3×D4—62no—
333C2×C3×D4—62no—
334C2×C3×D4—61no—
335C2×C3×D4—61no—
336C2×C3×D4C22×D311yescharacteristic
337C2×C3×D4C22×D311yescharacteristic
338C22×C3×C4—31no—
339C22×C3×C4—31no—
340C22×C3×C4—61no—
341C2×#67—21no—
342C2×#67—21no—
343C2×#67—61no—
344C2×#67—61no—
345C2×#67—61no—
346C2×#67—61no—
347C2×#67—61no—
348C2×#67—61no—
349C2×#67—61no—
350C2×#67—61no—
351C2×#67—121no—
352C2×#67—124no—
353C22×Dic3—31no—
354C22×Dic3—31no—
355C22×Dic3—61no—
356#239—22no—
357#239—22no—
358D3×D4—22no—
359D3×D4—22no—
360D3×D4—124no—
361C2×D12—21no—
362C2×D12—61no—
363C2×D12—61no—
364C2×D12C22×D311yescharacteristic
365C2×D12C22×D311yescharacteristic
366C2×C4×D3—21no—
367C2×C4×D3—31no—
368C2×C4×D3—31no—
369C2×C4×D3—31no—
370C2×C4×D3—31no—
371C2×C4×D3—31no—
372C2×C4×D3—31no—
373C2×C4×D3—61no—
374C2×C4×D3—62no—
375C2×C4×D3—62no—
376C2×C4×D3—62no—
377C2×C4×D3—62no—
378C2×C4×D3—61no—
379C2×C4×D3C22×D311yescharacteristic
380C2×C4×D3C22×D311yescharacteristic
381C3×SD16—22no—
382C3×SD16—22no—
383C3×SD16—42no—
384C3×SD16—62no—
385C3×D8—62no—
386C3×D8—62no—
387C3×M16—34no—
388C3×M16—62no—
389C2×C3×C8—21no—
390C2×C3×C8—31no—
391C2×C3×C8—31no—
392C2×C3×C8C22×D311yescharacteristic
393C2×C3×C8C22×D311yescharacteristic
394C3×C4⋊C4—31no—
395C3×C4⋊C4—31no—
396C3×C4⋊C4—61no—
397C3×C22⋊C4—61no—
398C3×C22⋊C4—61no—
399#217—21no—
400#217—61no—
401#217—61no—
402#217—61no—
403#217—61no—
404#217—61no—
405#217—61no—
406#217—61no—
407#217—121no—
408#215—22no—
409#213—22no—
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—61no—
416(C2×D3)⋊C4—61no—
417(C2×D3)⋊C4—61no—
418(C2×D3)⋊C4—121no—
419C4⋊Dic3—31no—
420C4⋊Dic3—31no—
421C4⋊Dic3—31no—
422C4⋊Dic3—31no—
423C4⋊Dic3—61no—
424C4⋊Dic3—61no—
425C4⋊Dic3—61no—
426C4⋊Dic3C22×D311yescharacteristic
427C4⋊Dic3C22×D311yescharacteristic
428Dic3⋊C4—21no—
429Dic3⋊C4—61no—
430Dic3⋊C4—61no—
431Dic3⋊C4—61no—
432Dic3⋊C4—121no—
433C4×Dic3—61no—
434C4×Dic3—61no—
435#208—62no—
436#208—62no—
437C2×C3⋊C8—31no—
438C2×C3⋊C8—31no—
439C2×C3⋊C8—61no—
440C2×C3⋊C8C22×D311yescharacteristic
441C2×C3⋊C8C22×D311yescharacteristic
442D24—22no—
443ΓL(1,𝔽25)—22no—
444ΓL(1,𝔽25)—62no—
445ΓL(1,𝔽25)—62no—
446ΓL(1,𝔽25)#6714yescomplemented
447D3×C8—62no—
448D3×C8—62no—
449D3×C8—62no—
450D3×C8—62no—
451D3×C8—122no—
452C22×C32—41no—
453C22×C32—41no—
454C22×C32—41no—
455C22×C32C22×D411yescharacteristic
456C2×C3⋊D3—21no—
457C2×C3⋊D3—21no—
458C2×C3⋊D3AGL(1,ℤ/8)12yescomplemented
459C2×C3×D3—21no—
460C2×C3×D3—21no—
461C2×C3×D3—21no—
462C2×C3×D3—21no—
463C2×C3×D3—21no—
464C2×C3×D3—41no—
465C2×C3×D3—41no—
466C2×C3×D3—41no—
467C2×C3×D3—41no—
468C2×C3×D3—41no—
469C2×C3×D3—41no—
470C2×C3×D3—84no—
471C2×C3×D3#12112yes—
472D32—44no—
473C32×C4—41no—
474C32×C4C22×D411yescharacteristic
475C32×C4C2×#4111yescharacteristic
476C3⋊Dic3—21no—
477C3⋊Dic3—41no—
478C3⋊Dic3—41no—
479C3×Dic3—21no—
480C3×Dic3—41no—
481C3×Dic3—41no—
482C3×Dic3#12112yes—
483C2×#41—31no—
484C22×D4—31no—
485C22×D4—181no—
486C23×C4—91no—
487AGL(1,ℤ/8)—64no—
488C2×SD16—31no—
489C2×SD16D3211yescharacteristic, complemented
490C2×D8—31no—
491C2×D8—31no—
492C2×M16—31no—
493C2×M16—31no—
494C2×M16—91no—
495C2×M16—91no—
496C2×M16—184no—
497C22×C8—91no—
498C22×C8—91no—
499#123—181no—
500C22⋊Q8—31no—
501C22⋊Q8—91no—
502#121—31no—
503#121—91no—
504#121—91no—
505#121—91no—
506#121—91no—
507#121—91no—
508#121—181no—
509#121—181no—
510#120—181no—
511C4×D4—181no—
512C4×D4—181no—
513#117—91no—
514C2×C4⋊C4—91no—
515C2×C22⋊C4—181no—
516#107—31no—
517#107—91no—
518#106—91no—
519#106—91no—
520#103—31no—
521#103—91no—
522#102—31no—
523#102—91no—
524#102—91no—
525#102—91no—
526#102—91no—
527#102—91no—
528C23×C3—21no—
529C23×C3—21no—
530C23×C3—31no—
531C23×C3—31no—
532C23×C3—41no—
533C23×C3—61no—
534C23×C3—61no—
535C23×C3—122no—
536C23×C3—122no—
537C23×C3—122no—
538C22×D3—21no—
539C22×D3—21no—
540C22×D3—31no—
541C22×D3—31no—
542C22×D3—42no—
543C22×D3—42no—
544C22×D3—42no—
545C22×D3—61no—
546C22×D3—62no—
547C22×D3—62no—
548C22×D3—62no—
549C22×D3—62no—
550C22×D3—121no—
551C22×D3—121no—
552C22×D3D3×D411yescharacteristic
553C22×D3D3×D411yescharacteristic
554C3×Q8—21no—
555C3×Q8—21no—
556C3×Q8—21no—
557C3×Q8—21no—
558C3×Q8—41no—
559C3×Q8—41no—
560C3×D4—21no—
561C3×D4—21no—
562C3×D4—21no—
563C3×D4—21no—
564C3×D4—41no—
565C3×D4—41no—
566C3×D4—61no—
567C3×D4—61no—
568C3×D4—61no—
569C3×D4—61no—
570C3×D4—122no—
571C3×D4—122no—
572C3×D4—122no—
573C2×C3×C4—21no—
574C2×C3×C4—21no—
575C2×C3×C4—21no—
576C2×C3×C4—31no—
577C2×C3×C4—32no—
578C2×C3×C4—32no—
579C2×C3×C4—31no—
580C2×C3×C4—41no—
581C2×C3×C4—61no—
582C2×C3×C4—61no—
583C2×C3×C4—61no—
584C2×C3×C4—61no—
585C2×C3×C4—122no—
586C2×C3×C4C23×D311yescharacteristic
587C2×C3×C4C23×D311yescharacteristic
588#67—42no—
589#67—42no—
590#67—122no—
591#67—122no—
592#67—122no—
593#67—122no—
594#67—122no—
595#67—122no—
596#67—122no—
597#67—122no—
598#67—242no—
599C2×Dic3—21no—
600C2×Dic3—21no—
601C2×Dic3—31no—
602C2×Dic3—31no—
603C2×Dic3—61no—
604C2×Dic3—62no—
605C2×Dic3—62no—
606C2×Dic3—61no—
607C2×Dic3—61no—
608C2×Dic3—61no—
609C2×Dic3—61no—
610C2×Dic3—121no—
611C2×Dic3—121no—
612C2×Dic3—122no—
613C2×Dic3D3×D411yescharacteristic
614C2×Dic3D3×D411yescharacteristic
615D12—21no—
616D12—21no—
617D12—21no—
618D12—21no—
619D12—42no—
620D12—122no—
621D12—122no—
622C4×D3—21no—
623C4×D3—21no—
624C4×D3—42no—
625C4×D3—62no—
626C4×D3—62no—
627C4×D3—62no—
628C4×D3—61no—
629C4×D3—61no—
630C4×D3—61no—
631C4×D3—61no—
632C4×D3—62no—
633C4×D3—121no—
634C4×D3—121no—
635C4×D3—122no—
636C4×D3#23712yes—
637C4×D3C2×#6712yes—
638C3×C8—22no—
639C3×C8—32no—
640C3×C8—61no—
641C3×C8D3×D412yescomplemented
642C3×C8C2×#6712yescomplemented
643C3⋊C8—21no—
644C3⋊C8—61no—
645C3⋊C8—61no—
646C3⋊C8—121no—
647C3⋊C8C2×#6712yescomplemented
648C2×C32—81no—
649C2×C32C2×#12111yescharacteristic
650C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
651C2×C32#57511yescharacteristic
652C3⋊D3—22no—
653C3×D3—22no—
654C3×D3—41no—
655C3×D3—81no—
656C3×D3—81no—
657C24—61no—
658C24—91no—
659#41—62no—
660#41—62no—
661C2×Q8C2×D3211yescharacteristic
662C2×D4—31no—
663C2×D4—31no—
664C2×D4—61no—
665C2×D4—62no—
666C2×D4—62no—
667C2×D4—61no—
668C2×D4—61no—
669C2×D4—181no—
670C2×D4—181no—
671C2×D4—181no—
672C2×D4—181no—
673C2×D4—181no—
674C2×D4—364no—
675C2×D4C2×D3211yescharacteristic
676C22×C4—31no—
677C22×C4—31no—
678C22×C4—61no—
679C22×C4—91no—
680C22×C4—91no—
681C22×C4—91no—
682C22×C4—91no—
683C22×C4—182no—
684C22×C4—182no—
685C22×C4—181no—
686SD16—22no—
687SD16—62no—
688D8—62no—
689D8—62no—
690M16—34no—
691M16—62no—
692M16—182no—
693M16—182no—
694C2×C8—31no—
695C2×C8—31no—
696C2×C8—91no—
697C2×C8—182no—
698C2×C8—182no—
699C2×C8C2×D3211yescharacteristic
700C4⋊C4—31no—
701C4⋊C4—31no—
702C4⋊C4—61no—
703C4⋊C4—91no—
704C4⋊C4—91no—
705C4⋊C4—181no—
706C4⋊C4—181no—
707C22⋊C4—61no—
708C22⋊C4—61no—
709C22⋊C4—181no—
710C22⋊C4—181no—
711C22⋊C4—181no—
712C22⋊C4—181no—
713C22⋊C4—181no—
714C22⋊C4—181no—
715C22⋊C4—181no—
716C42—181no—
717C22×C3—21no—
718C22×C3—32no—
719C22×C3—41no—
720C22×C3—41no—
721C22×C3—41no—
722C22×C3—41no—
723C22×C3—41no—
724C22×C3—41no—
725C22×C3—61no—
726C22×C3—61no—
727C22×C3—61no—
728C22×C3—61no—
729C22×C3—61no—
730C22×C3—81no—
731C22×C3—81no—
732C22×C3—81no—
733C22×C3—121no—
734C22×C3—121no—
735C22×C3—121no—
736C22×C3—121no—
737C22×C3—121no—
738C22×C3—121no—
739C22×C3—244no—
740C22×C3C2×D3×D411yescharacteristic
741C22×C3C2×D3×D411yescharacteristic
742C2×D3—21no—
743C2×D3—21no—
744C2×D3—21no—
745C2×D3—21no—
746C2×D3—21no—
747C2×D3—32no—
748C2×D3—32no—
749C2×D3—41no—
750C2×D3—41no—
751C2×D3—41no—
752C2×D3—41no—
753C2×D3—41no—
754C2×D3—41no—
755C2×D3—62no—
756C2×D3—61no—
757C2×D3—61no—
758C2×D3—61no—
759C2×D3—61no—
760C2×D3—84no—
761C2×D3—121no—
762C2×D3—121no—
763C2×D3—124no—
764C2×D3—124no—
765C2×D3#93812yes—
766C3×C4—21no—
767C3×C4—21no—
768C3×C4—32no—
769C3×C4—41no—
770C3×C4—41no—
771C3×C4—61no—
772C3×C4—81no—
773C3×C4—121no—
774C3×C4—121no—
775C3×C4C2×D3×D411yescharacteristic
776C3×C4C2×#23711yescharacteristic
777C3×C4D3×#4111yescharacteristic
778C3×C4C22×#6711yescharacteristic
779Dic3—21no—
780Dic3—41no—
781Dic3—41no—
782Dic3—61no—
783Dic3—61no—
784Dic3—121no—
785Dic3—121no—
786Dic3—121no—
787Dic3—121no—
788Dic3—121no—
789Dic3—241no—
790Dic3—241no—
791Dic3#93812yes—
792C32#305511yescharacteristic, complemented, Sylow
793C23—21no—
794C23—31no—
795C23—31no—
796C23—61no—
797C23—61no—
798C23—91no—
799C23—122no—
800C23—122no—
801C23—122no—
802C23—182no—
803C23—182no—
804C23—361no—
805Q8—21no—
806Q8—21no—
807D4—21no—
808D4—21no—
809D4—61no—
810D4—61no—
811D4—61no—
812D4—61no—
813D4—122no—
814D4—122no—
815D4—122no—
816D4—362no—
817D4—362no—
818D4—362no—
819D4—362no—
820D4—362no—
821C2×C4—21no—
822C2×C4—31no—
823C2×C4—32no—
824C2×C4—32no—
825C2×C4—31no—
826C2×C4—61no—
827C2×C4—61no—
828C2×C4—61no—
829C2×C4—61no—
830C2×C4—91no—
831C2×C4—122no—
832C2×C4—182no—
833C2×C4—182no—
834C2×C4—182no—
835C2×C4—181no—
836C2×C4—181no—
837C2×C4—181no—
838C2×C4—181no—
839C2×C4—362no—
840C2×C4C22×D3211yescharacteristic
841C8—32no—
842C8—61no—
843C8—181no—
844C8D3×#6712yescomplemented
845C2×C3—21no—
846C2×C3—21no—
847C2×C3—21no—
848C2×C3—62no—
849C2×C3—81no—
850C2×C3—81no—
851C2×C3—121no—
852C2×C3—161no—
853C2×C3—241no—
854C2×C3—241no—
855C2×C3D3×#12111yescharacteristic
856C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
857C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
858C2×C3#577311yescharacteristic
859C2×C3#577711yescharacteristic
860C2×C3C2×#93811yescharacteristic
861D3—22no—
862D3—41no—
863D3—62no—
864D3—62no—
865D3—81no—
866D3—81no—
867D3—122no—
868C22—32no—
869C22—41no—
870C22—41no—
871C22—41no—
872C22—61no—
873C22—61no—
874C22—61no—
875C22—61no—
876C22—61no—
877C22—92no—
878C22—121no—
879C22—121no—
880C22—121no—
881C22—121no—
882C22—121no—
883C22—121no—
884C22—181no—
885C22—181no—
886C22—244no—
887C22—364no—
888C22D32×D411yescharacteristic
889C4—32no—
890C4—41no—
891C4—61no—
892C4—121no—
893C4—121no—
894C4—181no—
895C4—361no—
896C4—361no—
897C4D3×#23711yescharacteristic
898C4C2×D3×#6711yescharacteristic
899C3—21no—
900C3#8080511yescharacteristic, complemented
901C3#8395011yescharacteristic, complemented
902C2—62no—
903C2—81no—
904C2—121no—
905C2—182no—
906C2—241no—
907C2—241no—
908C2#1059474011yescharacteristic
909C2#1059474411yescharacteristic
910C2D3×#93811yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
hypercenterC2×SD16D32
hypocenterC32#3055
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C2×C3×#914C2semidirect
2. #10595424C2semidirect
3. D3×#938C2semidirect
4. C2×#63791C2semidirect
5. #10592870C2semidirect
6. C3×#5174C2semidirect
7. #10591591C2semidirect
8. #10591587C2semidirect
9. #10591550C2semidirect
10. #10591455C2semidirect
11. #10591451C2semidirect
12. #10591421C2semidirect
13. #10590844C2semidirect
14. #10590836C2semidirect
15. #10590683C2semidirect
22. C2×C32×SD16C22semidirect
23. #64155C22semidirect
25. C2×C8×C3⋊D3C22semidirect
26. C3×#946C22semidirect
27. C2×C3×#215C22semidirect
29. C2×C3×#213C22semidirect
31. C2×C3×D24C22semidirect
33. C2×C3×ΓL(1,𝔽25)C22semidirect
39. #63916C22semidirect
41. #63908C22semidirect
48. C2×#3711C22semidirect
49. C2×#3710C22semidirect
51. #63662C22semidirect
52. #63659C22semidirect
53. #63644C22semidirect
54. C3×#835C22semidirect
55. C3×#832C22semidirect
56. C3×#818C22semidirect
57. #63575C22semidirect
58. #63573C22semidirect
59. #63563C22semidirect
60. #63563C22semidirect
61. #63562C22semidirect
62. #63562C22semidirect
66. C2×#914D3semidirect
75. #5174D3semidirect
143. C3×ΓL(1,𝔽25)D4semidirect
166. C2×C3×SD16C2×D3semidirect
167. C2×C3×SD16C2×D3semidirect
178. #946C2×D3semidirect
179. C2×#215C2×D3semidirect
193. C2×#213C2×D3semidirect
205. C2×D24C2×D3semidirect
209. C2×ΓL(1,𝔽25)C2×D3semidirect
231. #835C2×D3semidirect
239. #832C2×D3semidirect
243. #818C2×D3semidirect
300. C32×C8C2×D4semidirect
303. C3×C3⋊C8C2×D4semidirect
446. ΓL(1,𝔽25)#67semidirect
458. C2×C3⋊D3AGL(1,ℤ/8)semidirect
489. C2×SD16D32semidirect
641. C3×C8D3×D4semidirect
642. C3×C8C2×#67semidirect
647. C3⋊C8C2×#67semidirect
792. C32#3055semidirect
844. C8D3×#67semidirect
900. C3#80805semidirect
901. C3#83950semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9142
#105954242
D3×#9382
C2×#637912
#105928702
C3×#51742
#105915912
#105915872
#105915502
#105914552
#105914512
#105914212
#105908442
#105908362
#105906832
#839503
#808053