Finite Group Databasebeta

← #11867144

Subgroups — #11867144

Order 1152.

1161 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#911C211yesmaximal, characteristic, complemented
2#10595301C211yesmaximal, characteristic, complemented
3D3×#938C211yesmaximal, characteristic, complemented
4C2×D3×ΓL(1,𝔽25)C211yesmaximal, characteristic, complemented
5#10592858C211yesmaximal, characteristic, complemented
6C3×#5157C211yesmaximal, characteristic, complemented
7#10591499C211yesmaximal, characteristic, complemented
8#10591498C211yesmaximal, characteristic, complemented
9#10591464C211yesmaximal, characteristic, complemented
10#10591454C211yesmaximal, characteristic, complemented
11#10591421C211yesmaximal, characteristic, complemented
12#10591414C211yesmaximal, characteristic, complemented
13#10590845C211yesmaximal, characteristic, complemented
14#10590829C211yesmaximal, characteristic, complemented
15#10590683C211yesmaximal, characteristic, complemented
16#83950—31nomaximal
17#80715—31nomaximal
18C2×C3×#237C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C2×D3×#67—21no—
21C2×C4×D32C2211yescharacteristic
22C2×C32×D8C2211yescharacteristic, complemented
23#64147C2211yescharacteristic
24#64147C2211yescharacteristic, complemented
25C2×#3743C2211yescharacteristic, complemented
26C3×#938C2211yescharacteristic
27C3×#938C2211yescharacteristic, complemented
28C2×C3×#214C2211yescharacteristic, complemented
29C2×C3×#213C2211yescharacteristic, complemented
30C3×#911—24no—
31C2×C3×#204C2211yescharacteristic, complemented
32C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
33C2×C3×D3×C8C2211yescharacteristic, complemented
34#63983—21no—
35Dic3×#67—21no—
36#63970—21no—
37#63969—21no—
38D3×#217—21no—
39#63958—21no—
40#63952—21no—
41#63916C2211yescharacteristic
42#63908C2211yescharacteristic
43D3×C4⋊Dic3C2211yescharacteristic
44#63871C2211yescharacteristic, complemented
45#63856C2211yescharacteristic, complemented
46#63841C2211yescharacteristic
47C2×#3712C2211yescharacteristic, complemented
48C2×#3711C2211yescharacteristic
49C2×D3×C3⋊C8C2211yescharacteristic, complemented
50D3×ΓL(1,𝔽25)—24no—
51#63659C2211yescharacteristic, complemented
52#63659C2211yescharacteristic, complemented
53#63644C2211yescharacteristic, complemented
54C3×#832C2211yescharacteristic, complemented
55C3×#832C2211yescharacteristic, complemented
56C3×#818C2211yescharacteristic, complemented
57#63575C2211yescharacteristic, complemented
58#63573C2211yescharacteristic, complemented
59#63566C2211yescharacteristic, complemented
60#63565C2211yescharacteristic, complemented
61#63563C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63C2×C3×AGL(1,ℤ/8)—31no—
64#5828—31no—
65C2×#938—31no—
66C2×#911D311yescharacteristic, complemented
67C2×D3×M16—31no—
68C22×ΓL(1,𝔽25)—31no—
69#5606—31no—
70D3×#121—31no—
71C3×#466—31no—
72#5232—31no—
73#5215—31no—
74#5174—31no—
75#5174—31no—
76#5171—31no—
77#5171—31no—
78#5159—31no—
79#5159—31no—
80#5159—31no—
81#5159—61no—
82#5157—31no—
83#5157D311yescharacteristic, complemented
84#5121—31no—
85#5114—31no—
86#5041—31no—
87#5038—31no—
88#4886—31no—
89#4881—31no—
90#4782—31no—
91#4780—31no—
92#4771—31no—
93#4770—31no—
94C23×C3×D3—21no—
95C22×D32D411yescharacteristic
96C2×C32×D4C2311yescharacteristic
97C2×C32×D4C2311yescharacteristic
98C2×#638—21no—
99C2×#638—21no—
100C2×C4×C3⋊D3C2311yescharacteristic
101C2×C3×#67—21no—
102C2×C3×#67—21no—
103C2×C3×#67—21no—
104C2×C3×#67—21no—
105C22×C3×Dic3—21no—
106C3×#237—22no—
107C3×#237—22no—
108C3×D3×D4—22no—
109C3×D3×D4—22no—
110C2×C3×D12C2311yescharacteristic
111C2×C3×C4×D3C2311yescharacteristic
112C2×C3×C4×D3C2311yescharacteristic
113C2×C3×Dic6C2311yescharacteristic
114D3×#67—44no—
115C2×#626—21no—
116C2×#625—21no—
117C2×#624D411yescharacteristic
118C2×D3×Dic3—21no—
119C2×D3×Dic3D411yescharacteristic
120C2×D3×Dic3D411yescharacteristic
121C4×D32—22no—
122C4×D32—22no—
123C32×D8—22no—
124C2×C32×C8C2311yescharacteristic
125#3757—21no—
126#3757—21no—
127C4⋊(C3⋊Dic3)C2311yescharacteristic
128C4⋊(C3⋊Dic3)C2311yescharacteristic
129C2×C3⋊(C3⋊C8)C2311yescharacteristic
130#3743—22no—
131C3×#217—21no—
132C3×#217—21no—
133C3×#214—22no—
134C3×#213—22no—
135C3×C4⋊Dic3C2311yescharacteristic
136C3×C4⋊Dic3C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C3×#204—22no—
140C3×ΓL(1,𝔽25)D414yescomplemented
141C3×D3×C8—22no—
142#3724—21no—
143Dic3⋊Dic3—21no—
144Dic3⋊Dic3—21no—
145#3722—21no—
146(C2×D3)⋊Dic3—21no—
147(C2×D3)⋊Dic3—21no—
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3—21no—
150Dic32—21no—
151#3712—22no—
152#3711—22no—
153D3×C3⋊C8—22no—
154#3055—91noSylow
155C2×C3×#41—31no—
156C22×C3×D4—31no—
157C22×#67—61no—
158C2×#237C2×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—31no—
165C2×C3×SD16—31no—
166C2×C3×D8—21no—
167C2×C3×D8—31no—
168C2×C3×D8C2×D311yescharacteristic, complemented
169C2×C3×D8C2×D311yescharacteristic, complemented
170C2×C3×M16—31no—
171C22×C3×C8—31no—
172C3×#121—31no—
173C3×#121—31no—
174C2×#217—61no—
175#946—31no—
176#946—31no—
177#939—61no—
178#938—31no—
179#938—31no—
180#938—31no—
181#938—31no—
182#938—31no—
183#938—31no—
184#938—61no—
185#938—61no—
186#938—61no—
187#938—61no—
188#938C2×D311yescharacteristic
189#938C2×D311yescharacteristic, complemented
190#937—61no—
191#937—61no—
192#935—61no—
193D4×Dic3—61no—
194C2×#214C2×D311yescharacteristic, complemented
195C2×#213C2×D311yescharacteristic, complemented
196#930—31no—
197C4×#67—61no—
198C4×#67—61no—
199#926—31no—
200C2×C4⋊Dic3—31no—
201#924—31no—
202C2×#208—31no—
203C22×C3⋊C8—31no—
204#911—24no—
205D3×M16—64no—
206C2×#204C2×D311yescharacteristic, complemented
207C2×ΓL(1,𝔽25)—31no—
208C2×ΓL(1,𝔽25)—31no—
209C2×ΓL(1,𝔽25)—31no—
210C2×ΓL(1,𝔽25)—31no—
211C2×ΓL(1,𝔽25)—31no—
212C2×ΓL(1,𝔽25)—61no—
213C2×ΓL(1,𝔽25)—64no—
214C2×ΓL(1,𝔽25)C2×D311yescharacteristic
215C2×D3×C8—31no—
216C2×D3×C8C2×D311yescharacteristic, complemented
217#897—31no—
218#895—31no—
219#892—31no—
220D3×C4⋊C4—31no—
221#884—61no—
222#883—61no—
223#67⋊C4—61no—
224D3×C22⋊C4—61no—
225C3×#107—31no—
226C3×#102—31no—
227C3×#102—31no—
228#835—31no—
229#835—31no—
230#832—31no—
231#832—31no—
232#832—31no—
233#832—31no—
234#832—31no—
235#832—31no—
236#832—61no—
237#832—61no—
238#832C2×D311yescharacteristic, complemented
239#832C2×D311yescharacteristic, complemented
240#821—31no—
241#818—31no—
242#818C2×D311yescharacteristic, complemented
243#817—31no—
244#817—31no—
245#817—31no—
246#817—61no—
247#816—31no—
248#810—31no—
249#809—31no—
250#808—31no—
251#807—31no—
252C23×C32—21no—
253C23×C32—21no—
254C22×C3⋊D3C2×D411yescharacteristic
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×D4—21no—
265C32×D4—21no—
266C32×D4—21no—
267C32×D4—21no—
268C2×C32×C4C2411yescharacteristic
269#638—42no—
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—
278C3×#67—42no—
279C3×#67—42no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3—42no—
284C2×C3×Dic3C2×D411yescharacteristic
285C2×C3×Dic3C2×D411yescharacteristic
286C3×D12—21no—
287C3×D12—21no—
288C3×C4×D3—21no—
289C3×C4×D3—21no—
290C3×C4×D3C2×D412yes—
291C3×C4×D3#4112yes—
292C3×Dic6—21no—
293C3×Dic6—21no—
294#626—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—91no—
311#468—91no—
312#466—31no—
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—31no—
326C2×C3×D4—21no—
327C2×C3×D4—21no—
328C2×C3×D4—31no—
329C2×C3×D4—62no—
330C2×C3×D4—62no—
331C2×C3×D4—61no—
332C2×C3×D4—61no—
333C2×C3×D4—61no—
334C2×C3×D4—61no—
335C2×C3×D4C22×D311yescharacteristic
336C2×C3×D4C22×D311yescharacteristic
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—21no—
345C2×#67—21no—
346C2×#67—61no—
347C2×#67—61no—
348C2×#67—61no—
349C2×#67—61no—
350C2×#67—61no—
351C2×#67—61no—
352C2×#67—61no—
353C2×#67—121no—
354C2×#67—121no—
355C2×#67—124no—
356C22×Dic3—21no—
357C22×Dic3—31no—
358C22×Dic3—31no—
359C22×Dic3—61no—
360#237—22no—
361#237—22no—
362D3×D4—22no—
363D3×D4—22no—
364D3×D4—124no—
365C2×D12—61no—
366C2×D12C22×D311yescharacteristic
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
381C2×Dic6C22×D311yescharacteristic
382C3×SD16—62no—
383C3×SD16—62no—
384C3×D8—22no—
385C3×D8—22no—
386C3×D8—42no—
387C3×D8—62no—
388C3×M16—34no—
389C2×C3×C8—21no—
390C2×C3×C8—31no—
391C2×C3×C8—31no—
392C2×C3×C8—62no—
393C2×C3×C8C22×D311yescharacteristic
394C2×C3×C8C22×D311yescharacteristic
395C3×C4⋊C4—31no—
396C3×C4⋊C4—31no—
397C3×C22⋊C4—61no—
398C3×C22⋊C4—61no—
399#217—21no—
400#217—21no—
401#217—61no—
402#217—61no—
403#217—61no—
404#217—61no—
405#217—61no—
406#217—61no—
407#217—61no—
408#217—61no—
409#217—121no—
410#217—121no—
411#214—22no—
412#213—22no—
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—61no—
419C4⋊Dic3—31no—
420C4⋊Dic3—31no—
421C4⋊Dic3—31no—
422C4⋊Dic3—31no—
423C4⋊Dic3—61no—
424C4⋊Dic3—61no—
425C4⋊Dic3—61no—
426C4⋊Dic3—61no—
427C4⋊Dic3C22×D311yescharacteristic
428C4⋊Dic3C22×D311yescharacteristic
429Dic3⋊C4—61no—
430Dic3⋊C4—61no—
431Dic3⋊C4—61no—
432Dic3⋊C4—61no—
433C4×Dic3—61no—
434C4×Dic3—61no—
435#208—62no—
436C2×C3⋊C8—31no—
437C2×C3⋊C8—31no—
438C2×C3⋊C8—61no—
439C2×C3⋊C8—62no—
440C2×C3⋊C8C22×D311yescharacteristic
441C2×C3⋊C8C22×D311yescharacteristic
442#204—22no—
443ΓL(1,𝔽25)—62no—
444ΓL(1,𝔽25)—62no—
445ΓL(1,𝔽25)—62no—
446ΓL(1,𝔽25)—62no—
447ΓL(1,𝔽25)—62no—
448ΓL(1,𝔽25)—122no—
449ΓL(1,𝔽25)#6714yescomplemented
450D3×C8—22no—
451D3×C8—62no—
452C22×C32—41no—
453C22×C32—41no—
454C22×C32—41no—
455C22×C32—41no—
456C22×C32—41no—
457C22×C32—41no—
458C22×C32C22×D411yescharacteristic
459C2×C3⋊D3—21no—
460C2×C3⋊D3—21no—
461C2×C3⋊D3—21no—
462C2×C3×D3—21no—
463C2×C3×D3—21no—
464C2×C3×D3—21no—
465C2×C3×D3—21no—
466C2×C3×D3—41no—
467C2×C3×D3—41no—
468C2×C3×D3—41no—
469C2×C3×D3—84no—
470C2×C3×D3#12112yes—
471C2×C3×D3AGL(1,ℤ/8)12yescomplemented
472D32—44no—
473C32×C4C22×D411yescharacteristic
474C32×C4C2×#4111yescharacteristic
475C3⋊Dic3—21no—
476C3⋊Dic3—41no—
477C3⋊Dic3—41no—
478C3×Dic3—21no—
479C3×Dic3—41no—
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×SD16—31no—
490C2×D8—31no—
491C2×D8D3211yescharacteristic, complemented
492C2×M16—31no—
493C2×M16—91no—
494C2×M16—91no—
495C2×M16—91no—
496C2×M16—184no—
497C22×C8—31no—
498C22×C8—91no—
499#123—181no—
500C22⋊Q8—91no—
501C22⋊Q8—91no—
502#121—31no—
503#121—31no—
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—91no—
521#103—91no—
522#102—31no—
523#102—31no—
524#102—91no—
525#102—91no—
526#102—91no—
527#102—91no—
528C23×C3—21no—
529C23×C3—21no—
530C23×C3—21no—
531C23×C3—21no—
532C23×C3—31no—
533C23×C3—31no—
534C23×C3—41no—
535C23×C3—41no—
536C23×C3—61no—
537C23×C3—122no—
538C23×C3—122no—
539C23×C3—122no—
540C22×D3—21no—
541C22×D3—31no—
542C22×D3—31no—
543C22×D3—42no—
544C22×D3—42no—
545C22×D3—42no—
546C22×D3—61no—
547C22×D3—62no—
548C22×D3—62no—
549C22×D3—62no—
550C22×D3—62no—
551C22×D3—121no—
552C22×D3—121no—
553C22×D3D3×D411yescharacteristic
554C22×D3D3×D411yescharacteristic
555C3×Q8—61no—
556C3×Q8—61no—
557C3×D4—21no—
558C3×D4—21no—
559C3×D4—21no—
560C3×D4—21no—
561C3×D4—21no—
562C3×D4—21no—
563C3×D4—21no—
564C3×D4—21no—
565C3×D4—41no—
566C3×D4—41no—
567C3×D4—41no—
568C3×D4—41no—
569C3×D4—61no—
570C3×D4—61no—
571C3×D4—122no—
572C3×D4—122no—
573C3×D4—122no—
574C3×D4—122no—
575C2×C3×C4—21no—
576C2×C3×C4—31no—
577C2×C3×C4—32no—
578C2×C3×C4—32no—
579C2×C3×C4—31no—
580C2×C3×C4—61no—
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—42no—
591#67—42no—
592#67—122no—
593#67—122no—
594#67—122no—
595#67—122no—
596#67—122no—
597#67—122no—
598#67—122no—
599#67—242no—
600#67—242no—
601C2×Dic3—21no—
602C2×Dic3—21no—
603C2×Dic3—21no—
604C2×Dic3—31no—
605C2×Dic3—31no—
606C2×Dic3—42no—
607C2×Dic3—61no—
608C2×Dic3—62no—
609C2×Dic3—62no—
610C2×Dic3—61no—
611C2×Dic3—61no—
612C2×Dic3—61no—
613C2×Dic3—61no—
614C2×Dic3—121no—
615C2×Dic3—121no—
616C2×Dic3—122no—
617C2×Dic3D3×D411yescharacteristic
618C2×Dic3D3×D411yescharacteristic
619D12—21no—
620D12—21no—
621D12—122no—
622C4×D3—21no—
623C4×D3—21no—
624C4×D3—62no—
625C4×D3—62no—
626C4×D3—62no—
627C4×D3—61no—
628C4×D3—61no—
629C4×D3—61no—
630C4×D3—61no—
631C4×D3—62no—
632C4×D3—121no—
633C4×D3—121no—
634C4×D3—122no—
635C4×D3#23712yes—
636C4×D3C2×#6712yes—
637Dic6—21no—
638Dic6—21no—
639C3×C8—22no—
640C3×C8—32no—
641C3×C8—61no—
642C3×C8D3×D412yescomplemented
643C3×C8C2×#6712yescomplemented
644C3⋊C8—21no—
645C3⋊C8—61no—
646C3⋊C8—61no—
647C3⋊C8—121no—
648C3⋊C8C2×#6712yescomplemented
649C2×C32—81no—
650C2×C32—81no—
651C2×C32C2×#12111yescharacteristic
652C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
653C2×C32#57511yescharacteristic
654C3⋊D3—41no—
655C3×D3—22no—
656C3×D3—22no—
657C3×D3—81no—
658C24—61no—
659C24—91no—
660#41—62no—
661#41—62no—
662C2×Q8—31no—
663C2×D4—31no—
664C2×D4—62no—
665C2×D4—62no—
666C2×D4—61no—
667C2×D4—61no—
668C2×D4—61no—
669C2×D4—61no—
670C2×D4—181no—
671C2×D4—181no—
672C2×D4—181no—
673C2×D4—181no—
674C2×D4—364no—
675C2×D4C2×D3211yescharacteristic
676C2×D4C2×D3211yescharacteristic
677C22×C4—31no—
678C22×C4—31no—
679C22×C4—61no—
680C22×C4—91no—
681C22×C4—91no—
682C22×C4—91no—
683C22×C4—91no—
684C22×C4—182no—
685C22×C4—182no—
686C22×C4—181no—
687SD16—62no—
688SD16—62no—
689D8—22no—
690D8—62no—
691M16—34no—
692M16—182no—
693M16—182no—
694M16—182no—
695C2×C8—31no—
696C2×C8—31no—
697C2×C8—62no—
698C2×C8—91no—
699C2×C8—182no—
700C2×C8C2×D3211yescharacteristic
701C4⋊C4—31no—
702C4⋊C4—31no—
703C4⋊C4—91no—
704C4⋊C4—91no—
705C4⋊C4—181no—
706C4⋊C4—181no—
707C4⋊C4—181no—
708C22⋊C4—61no—
709C22⋊C4—61no—
710C22⋊C4—181no—
711C22⋊C4—181no—
712C22⋊C4—181no—
713C22⋊C4—181no—
714C22⋊C4—181no—
715C22⋊C4—181no—
716C22⋊C4—181no—
717C42—181no—
718C22×C3—21no—
719C22×C3—32no—
720C22×C3—32no—
721C22×C3—41no—
722C22×C3—41no—
723C22×C3—41no—
724C22×C3—41no—
725C22×C3—41no—
726C22×C3—41no—
727C22×C3—41no—
728C22×C3—41no—
729C22×C3—41no—
730C22×C3—41no—
731C22×C3—41no—
732C22×C3—41no—
733C22×C3—61no—
734C22×C3—61no—
735C22×C3—61no—
736C22×C3—61no—
737C22×C3—81no—
738C22×C3—81no—
739C22×C3—81no—
740C22×C3—81no—
741C22×C3—81no—
742C22×C3—81no—
743C22×C3—121no—
744C22×C3—121no—
745C22×C3—121no—
746C22×C3—244no—
747C22×C3C2×D3×D411yescharacteristic
748C22×C3C2×D3×D411yescharacteristic
749C2×D3—21no—
750C2×D3—21no—
751C2×D3—21no—
752C2×D3—21no—
753C2×D3—41no—
754C2×D3—41no—
755C2×D3—41no—
756C2×D3—61no—
757C2×D3—61no—
758C2×D3—61no—
759C2×D3—61no—
760C2×D3—61no—
761C2×D3—61no—
762C2×D3—84no—
763C2×D3—121no—
764C2×D3—121no—
765C2×D3—121no—
766C2×D3—124no—
767C2×D3—124no—
768C2×D3#91112yescomplemented
769C2×D3#93812yes—
770C3×C4—21no—
771C3×C4—21no—
772C3×C4—32no—
773C3×C4—61no—
774C3×C4—121no—
775C3×C4—121no—
776C3×C4—121no—
777C3×C4C2×D3×D411yescharacteristic
778C3×C4C2×#23711yescharacteristic
779C3×C4D3×#4111yescharacteristic
780C3×C4C22×#6711yescharacteristic
781Dic3—21no—
782Dic3—41no—
783Dic3—41no—
784Dic3—41no—
785Dic3—61no—
786Dic3—61no—
787Dic3—121no—
788Dic3—121no—
789Dic3—121no—
790Dic3—121no—
791Dic3—121no—
792Dic3—241no—
793Dic3—241no—
794Dic3#93812yes—
795C32#305511yescharacteristic, complemented, Sylow
796C23—21no—
797C23—21no—
798C23—31no—
799C23—31no—
800C23—61no—
801C23—91no—
802C23—122no—
803C23—122no—
804C23—122no—
805C23—182no—
806C23—182no—
807C23—361no—
808Q8—61no—
809Q8—61no—
810D4—21no—
811D4—21no—
812D4—21no—
813D4—21no—
814D4—61no—
815D4—61no—
816D4—122no—
817D4—122no—
818D4—122no—
819D4—122no—
820D4—362no—
821D4—362no—
822D4—362no—
823D4—362no—
824C2×C4—31no—
825C2×C4—32no—
826C2×C4—32no—
827C2×C4—31no—
828C2×C4—61no—
829C2×C4—61no—
830C2×C4—61no—
831C2×C4—61no—
832C2×C4—61no—
833C2×C4—91no—
834C2×C4—122no—
835C2×C4—182no—
836C2×C4—182no—
837C2×C4—182no—
838C2×C4—181no—
839C2×C4—181no—
840C2×C4—181no—
841C2×C4—181no—
842C2×C4—362no—
843C2×C4C22×D3211yescharacteristic
844C8—32no—
845C8—61no—
846C8—181no—
847C8D3×#6712yescomplemented
848C2×C3—21no—
849C2×C3—21no—
850C2×C3—21no—
851C2×C3—62no—
852C2×C3—62no—
853C2×C3—81no—
854C2×C3—81no—
855C2×C3—81no—
856C2×C3—81no—
857C2×C3—161no—
858C2×C3—161no—
859C2×C3—241no—
860C2×C3D3×#12111yescharacteristic
861C2×C3C2×#91111yescharacteristic
862C2×C3#576811yescharacteristic
863C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
864C2×C3#577311yescharacteristic
865C2×C3C2×#93811yescharacteristic
866D3—22no—
867D3—22no—
868D3—81no—
869D3—121no—
870D3—121no—
871D3—241no—
872C22—32no—
873C22—32no—
874C22—41no—
875C22—41no—
876C22—41no—
877C22—41no—
878C22—41no—
879C22—41no—
880C22—61no—
881C22—61no—
882C22—61no—
883C22—61no—
884C22—121no—
885C22—121no—
886C22—121no—
887C22—181no—
888C22—181no—
889C22—181no—
890C22—244no—
891C22—364no—
892C22D32×D411yescharacteristic
893C4—32no—
894C4—61no—
895C4—121no—
896C4—121no—
897C4—121no—
898C4—181no—
899C4—361no—
900C4—361no—
901C4D3×#23711yescharacteristic
902C4C2×D3×#6711yescharacteristic
903C3—21no—
904C3#8071511yescharacteristic, complemented
905C3#8395011yescharacteristic, complemented
906C2—62no—
907C2—62no—
908C2—81no—
909C2—81no—
910C2—241no—
911C2—361no—
912C2D3×#91111yescharacteristic
913C2#1059472911yescharacteristic
914C2D3×#93811yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×D8C22
socleC22×C32C22×D4
hypercenterC2×D8D32
hypocenterC32#3055
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. C2×C3×#911C2semidirect
2. #10595301C2semidirect
3. D3×#938C2semidirect
4. C2×D3×ΓL(1,𝔽25)C2semidirect
5. #10592858C2semidirect
6. C3×#5157C2semidirect
7. #10591499C2semidirect
8. #10591498C2semidirect
9. #10591464C2semidirect
10. #10591454C2semidirect
11. #10591421C2semidirect
12. #10591414C2semidirect
13. #10590845C2semidirect
14. #10590829C2semidirect
15. #10590683C2semidirect
22. C2×C32×D8C22semidirect
24. #64147C22semidirect
25. C2×#3743C22semidirect
27. C3×#938C22semidirect
28. C2×C3×#214C22semidirect
29. C2×C3×#213C22semidirect
31. C2×C3×#204C22semidirect
33. C2×C3×D3×C8C22semidirect
44. #63871C22semidirect
45. #63856C22semidirect
47. C2×#3712C22semidirect
49. C2×D3×C3⋊C8C22semidirect
51. #63659C22semidirect
52. #63659C22semidirect
53. #63644C22semidirect
54. C3×#832C22semidirect
55. C3×#832C22semidirect
56. C3×#818C22semidirect
57. #63575C22semidirect
58. #63573C22semidirect
59. #63566C22semidirect
60. #63565C22semidirect
61. #63563C22semidirect
62. #63562C22semidirect
66. C2×#911D3semidirect
83. #5157D3semidirect
140. C3×ΓL(1,𝔽25)D4semidirect
168. C2×C3×D8C2×D3semidirect
169. C2×C3×D8C2×D3semidirect
189. #938C2×D3semidirect
194. C2×#214C2×D3semidirect
195. C2×#213C2×D3semidirect
206. C2×#204C2×D3semidirect
216. C2×D3×C8C2×D3semidirect
238. #832C2×D3semidirect
239. #832C2×D3semidirect
242. #818C2×D3semidirect
300. C32×C8C2×D4semidirect
303. C3×C3⋊C8C2×D4semidirect
449. ΓL(1,𝔽25)#67semidirect
471. C2×C3×D3AGL(1,ℤ/8)semidirect
491. C2×D8D32semidirect
642. C3×C8D3×D4semidirect
643. C3×C8C2×#67semidirect
648. C3⋊C8C2×#67semidirect
768. C2×D3#911semidirect
795. C32#3055semidirect
847. C8D3×#67semidirect
904. C3#80715semidirect
905. C3#83950semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9112
#105953012
D3×#9382
C2×D3×ΓL(1,𝔽25)2
#105928582
C3×#51572
#105914992
#105914982
#105914642
#105914542
#105914212
#105914142
#105908452
#105908292
#105906832
#839503
#807153