Finite Group Databasebeta

← #11867182

Subgroups — #11867182

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
1#10595424C211yesmaximal, characteristic, complemented
2C2×#63939C211yesmaximal, characteristic, complemented
3C2×#63791C211yesmaximal, characteristic, complemented
4D3×#895C211yesmaximal, characteristic, complemented
5#10592506C211yesmaximal, characteristic, complemented
6C3×#4812C211yesmaximal, characteristic, complemented
7C3×#4803C211yesmaximal, characteristic, complemented
8#10591591C211yesmaximal, characteristic, complemented
9#10591589C211yesmaximal, characteristic, complemented
10#10590939C211yesmaximal, characteristic, complemented
11#10590839C211yesmaximal, characteristic, complemented
12#10590827C211yesmaximal, characteristic, complemented
13#10590580C211yesmaximal, characteristic, complemented
14#10590509C211yesmaximal, characteristic, complemented
15#10590504C211yesmaximal, characteristic, complemented
16#80805—31nomaximal
17#78888—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×D3×D12—21no—
20C2×D3×D12C2211yescharacteristic
21C2×C4×D32C2211yescharacteristic
22#64155C2211yescharacteristic, complemented
23C2×#3755C2211yescharacteristic, complemented
24C2×C8×C3⋊D3C2211yescharacteristic, complemented
25#64104C2211yescharacteristic
26C3×#946C2211yescharacteristic, complemented
27C2×C3×#215C2211yescharacteristic, complemented
28C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
29C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
30C3×#895C2211yescharacteristic
31C3×D3×C4⋊C4C2211yescharacteristic
32#63939—24no—
33#63922—21no—
34D3×(C2×D3)⋊C4—21no—
35#63916C2211yescharacteristic
36#63916C2211yescharacteristic, complemented
37#63910—21no—
38#63909C2211yescharacteristic
39#63908C2211yescharacteristic, complemented
40#63904—21no—
41#63886—21no—
42#63884—21no—
43#63879—21no—
44#63841C2211yescharacteristic
45C2×#3714C2211yescharacteristic, complemented
46C2×#3713C2211yescharacteristic, complemented
47C2×#3711C2211yescharacteristic
48C2×#3711C2211yescharacteristic, complemented
49C2×#3710C2211yescharacteristic, complemented
50#63791—24no—
51C32×#103C2211yescharacteristic, complemented
52#63648C2211yescharacteristic, complemented
53#63635C2211yescharacteristic, complemented
54C3×#835C2211yescharacteristic, complemented
55C3×#821C2211yescharacteristic, complemented
56C3×#821C2211yescharacteristic, complemented
57C3×#809C2211yescharacteristic, complemented
58C3×#807C2211yescharacteristic, complemented
59#63576C2211yescharacteristic, complemented
60#63573C2211yescharacteristic, complemented
61#63564C2211yescharacteristic, complemented
62#63563C2211yescharacteristic, complemented
63#5828—31no—
64C2×#949—31no—
65C2×#914—31no—
66C2×D3×M16—31no—
67C2×D3×M16—31no—
68#5627—31no—
69D3×#121—31no—
70C2×#895—31no—
71C3×#468—31no—
72C3×#417—31no—
73#5171—31no—
74#5135—31no—
75#5131—31no—
76#5049—31no—
77#5039—31no—
78#4964—31no—
79#4883—31no—
80#4881—31no—
81#4812—31no—
82#4812D311yescharacteristic, complemented
83#4807—31no—
84#4807—31no—
85#4807—31no—
86#4807—61no—
87#4803D311yescharacteristic, complemented
88#4782—31no—
89#4782—31no—
90#4775—31no—
91#4775—31no—
92#4775—31no—
93#4770—31no—
94C22×D32—21no—
95C22×D32D411yescharacteristic
96C2×C32×Q8C2311yescharacteristic
97C2×C4⋊(C3⋊D3)—21no—
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C4×C3⋊D3C2311yescharacteristic
100C3×#239—22no—
101C3×#239—22no—
102C2×C3×D12—21no—
103C2×C3×D12—21no—
104C2×C3×D12C2311yescharacteristic
105C2×C3×D12C2311yescharacteristic
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3—21no—
108C2×C3×C4×D3C2311yescharacteristic
109C2×C3×C4×D3C2311yescharacteristic
110C2×#626—21no—
111C2×#626—21no—
112C2×#626—21no—
113C2×#626—21no—
114C2×#625—21no—
115C2×#624D411yescharacteristic
116C2×D3×Dic3D411yescharacteristic
117C2×D3×Dic3D411yescharacteristic
118D3×D12—22no—
119D3×D12—22no—
120D3×D12—44no—
121C4×D32—22no—
122C4×D32—22no—
123C2×C32×C8C2311yescharacteristic
124C32×C4⋊C4C2311yescharacteristic
125#3755—22no—
126#3752—21no—
127#3752—21no—
128C4⋊(C3⋊Dic3)C2311yescharacteristic
129#3750—21no—
130C2×C3⋊(C3⋊C8)C2311yescharacteristic
131C8×C3⋊D3—22no—
132C3×#215—22no—
133C3×(C2×D3)⋊C4—21no—
134C3×(C2×D3)⋊C4—21no—
135C3×C4⋊Dic3C2311yescharacteristic
136C3×C4⋊Dic3C2311yescharacteristic
137C3×Dic3⋊C4—21no—
138C3×Dic3⋊C4—21no—
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141C3×ΓL(1,𝔽25)—22no—
142C3×ΓL(1,𝔽25)—22no—
143#3722—21no—
144(C2×D3)⋊Dic3—21no—
145(C2×D3)⋊Dic3—21no—
146(C2×D3)⋊Dic3—21no—
147(C2×D3)⋊Dic3—21no—
148Dic32—21no—
149#3714—22no—
150#3713—22no—
151#3711—22no—
152#3711D414yescomplemented
153#3710—22no—
154#3055—91noSylow
155C2×C3×#41—31no—
156C2×#239C2×D311yescharacteristic
157C2×D3×D4—31no—
158C2×D3×D4—61no—
159C22×D12—31no—
160C22×D12—61no—
161C22×C4×D3—31no—
162C22×C4×D3—31no—
163C2×C3×SD16—31no—
164C2×C3×M16—31no—
165C2×C3×M16—31no—
166C3×C22⋊Q8—31no—
167C3×#121—31no—
168C2×C3×C4⋊C4—31no—
169#949—64no—
170#946—31no—
171#946—31no—
172#946—61no—
173#946C2×D311yescharacteristic, complemented
174C2×#215—31no—
175C2×#215—31no—
176C2×#215—61no—
177C2×#215C2×D311yescharacteristic, complemented
178#939—61no—
179#938—31no—
180#938—31no—
181#938—31no—
182#937—61no—
183#935—61no—
184C2×#213—31no—
185C2×#213—31no—
186C2×#213—31no—
187#930—31no—
188#930—31no—
189C4×#67—61no—
190C4×#67—61no—
191C2×(C2×D3)⋊C4—61no—
192#926—31no—
193C2×#208—31no—
194C2×#208—31no—
195#914—64no—
196D3×M16—64no—
197D3×M16—64no—
198C2×D24—31no—
199C2×ΓL(1,𝔽25)—31no—
200C2×ΓL(1,𝔽25)—31no—
201C2×ΓL(1,𝔽25)C2×D311yescharacteristic
202C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
203C2×D3×C8—31no—
204C2×D3×C8—31no—
205C2×D3×C8—31no—
206C2×D3×C8—31no—
207C2×D3×C8—61no—
208#895—31no—
209#895—31no—
210#895—31no—
211#895—31no—
212#895—31no—
213#895—61no—
214#895—61no—
215#895—61no—
216#895C2×D311yescharacteristic
217#894—61no—
218#893—61no—
219#892—31no—
220D3×C4⋊C4C2×D311yescharacteristic
221#884—61no—
222#882—61no—
223#67⋊C4—61no—
224D3×C22⋊C4—61no—
225C3×#107—31no—
226C3×#103—21no—
227C3×#103—31no—
228C3×#103C2×D311yescharacteristic, complemented
229C3×#103C2×D311yescharacteristic, complemented
230C3×#102—31no—
231C3×#102—31no—
232C3×#102—31no—
233#835C2×D311yescharacteristic, complemented
234#832—31no—
235#821—31no—
236#821—31no—
237#821—31no—
238#821—31no—
239#821—61no—
240#821C2×D311yescharacteristic, complemented
241#821C2×D311yescharacteristic, complemented
242#817—31no—
243#809—31no—
244#809C2×D311yescharacteristic, complemented
245#808—31no—
246#808—31no—
247#808—31no—
248#808—61no—
249#807—31no—
250#807—31no—
251#807C2×D311yescharacteristic, complemented
252C22×C3⋊D3—21no—
253C22×C3⋊D3C2×D411yescharacteristic
254C22×C3×D3—21no—
255C22×C3×D3—21no—
256C22×C3×D3C2×D411yescharacteristic
257C22×C3×D3C2×D411yescharacteristic
258C2×D32—22no—
259C2×D32—22no—
260C2×D32—41no—
261C2×D32—42no—
262C2×D32—42no—
263C2×D32—42no—
264C32×Q8—21no—
265C32×Q8—21no—
266C2×C32×C4—21no—
267C2×C32×C4—21no—
268C2×C32×C4C2411yescharacteristic
269C2×C3⋊Dic3—21no—
270C2×C3⋊Dic3C2×D411yescharacteristic
271C4⋊(C3⋊D3)—21no—
272C4⋊(C3⋊D3)—21no—
273C4⋊(C3⋊D3)—42no—
274C4×C3⋊D3—21no—
275C4×C3⋊D3—21no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3C2×D411yescharacteristic
279C2×C3×Dic3C2×D411yescharacteristic
280C3×D12—21no—
281C3×D12—21no—
282C3×D12—21no—
283C3×D12—21no—
284C3×D12—42no—
285C3×D12—42no—
286C3×C4×D3—21no—
287C3×C4×D3—21no—
288C3×C4×D3—42no—
289C3×C4×D3—42no—
290C3×C4×D3C2×D412yes—
291C3×C4×D3#4112yes—
292#626—42no—
293#626—42no—
294#626—42no—
295#626—42no—
296#625—42no—
297#624—22no—
298D3×Dic3—22no—
299D3×Dic3—22no—
300C32×C8—21no—
301C3⋊(C3⋊C8)C2×D412yescomplemented
302C3×C3⋊C8—21no—
303C3×C3⋊C8C2×D412yescomplemented
304C2×AGL(1,ℤ/8)—91no—
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—31no—
319C23×D3—31no—
320C23×D3—31no—
321C23×D3—61no—
322C23×D3—61no—
323C3×#41—62no—
324C3×#41—62no—
325C2×C3×Q8—21no—
326C2×C3×Q8C22×D311yescharacteristic
327C2×C3×Q8C22×D311yescharacteristic
328C2×C3×D4—31no—
329C2×C3×D4—31no—
330C2×C3×D4—61no—
331C2×C3×D4—61no—
332C22×C3×C4—31no—
333C22×C3×C4—31no—
334C22×C3×C4—61no—
335C22×C3×C4—61no—
336C2×#67—61no—
337C2×#67—61no—
338C2×#67—61no—
339C2×#67—61no—
340C2×#67—61no—
341C2×#67—61no—
342C22×Dic3—31no—
343C22×Dic3—31no—
344#239—22no—
345#239—22no—
346D3×D4—62no—
347D3×D4—62no—
348D3×D4—124no—
349C2×D12—21no—
350C2×D12—21no—
351C2×D12—31no—
352C2×D12—31no—
353C2×D12—61no—
354C2×D12—62no—
355C2×D12—62no—
356C2×D12—61no—
357C2×D12—61no—
358C2×D12—61no—
359C2×D12—61no—
360C2×D12—61no—
361C2×D12—61no—
362C2×D12—121no—
363C2×D12—124no—
364C2×D12C22×D311yescharacteristic
365C2×D12C22×D311yescharacteristic
366C2×C4×D3—21no—
367C2×C4×D3—21no—
368C2×C4×D3—31no—
369C2×C4×D3—31no—
370C2×C4×D3—31no—
371C2×C4×D3—31no—
372C2×C4×D3—31no—
373C2×C4×D3—31no—
374C2×C4×D3—61no—
375C2×C4×D3—62no—
376C2×C4×D3—62no—
377C2×C4×D3—62no—
378C2×C4×D3—62no—
379C2×C4×D3C22×D311yescharacteristic
380C2×C4×D3C22×D311yescharacteristic
381C3×SD16—62no—
382C3×M16—62no—
383C3×M16—62no—
384C2×C3×C8—21no—
385C2×C3×C8—31no—
386C2×C3×C8—31no—
387C2×C3×C8C22×D311yescharacteristic
388C2×C3×C8C22×D311yescharacteristic
389C3×C4⋊C4—21no—
390C3×C4⋊C4—31no—
391C3×C4⋊C4—31no—
392C3×C4⋊C4—61no—
393C3×C4⋊C4—61no—
394C3×C4⋊C4C22×D311yescharacteristic
395C3×C4⋊C4C22×D311yescharacteristic
396C3×C22⋊C4—61no—
397C3×C22⋊C4—61no—
398#217—61no—
399#217—61no—
400#217—61no—
401#217—61no—
402#215—22no—
403#215—62no—
404#215—62no—
405#215—122no—
406#213—62no—
407#213—62no—
408#213—62no—
409(C2×D3)⋊C4—21no—
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—61no—
419(C2×D3)⋊C4—61no—
420(C2×D3)⋊C4—61no—
421(C2×D3)⋊C4—121no—
422(C2×D3)⋊C4—121no—
423C4⋊Dic3—31no—
424C4⋊Dic3—31no—
425C4⋊Dic3—61no—
426C4⋊Dic3C22×D311yescharacteristic
427C4⋊Dic3C22×D311yescharacteristic
428Dic3⋊C4—21no—
429Dic3⋊C4—21no—
430Dic3⋊C4—61no—
431Dic3⋊C4—61no—
432Dic3⋊C4—121no—
433C4×Dic3—61no—
434C4×Dic3—61no—
435#208—34no—
436#208—62no—
437C2×C3⋊C8—31no—
438C2×C3⋊C8—31no—
439C2×C3⋊C8—61no—
440C2×C3⋊C8C22×D311yescharacteristic
441C2×C3⋊C8C22×D311yescharacteristic
442D24—62no—
443ΓL(1,𝔽25)—22no—
444ΓL(1,𝔽25)—22no—
445ΓL(1,𝔽25)—34no—
446ΓL(1,𝔽25)—62no—
447D3×C8—62no—
448D3×C8—62no—
449D3×C8—62no—
450D3×C8—62no—
451D3×C8—122no—
452C22×C32C22×D411yescharacteristic
453C2×C3⋊D3—21no—
454C2×C3⋊D3—21no—
455C2×C3⋊D3—41no—
456C2×C3⋊D3—41no—
457C2×C3⋊D3—41no—
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#12112yes—
471D32—44no—
472D32—84no—
473C32×C4—41no—
474C32×C4—41no—
475C32×C4C22×D411yescharacteristic
476C32×C4C2×#4111yescharacteristic
477C3⋊Dic3—21no—
478C3⋊Dic3—41no—
479C3×Dic3—21no—
480C3×Dic3—41no—
481C3×Dic3—41no—
482C3×Dic3#12112yes—
483C2×#41—31no—
484C22×D4—91no—
485C22×D4—181no—
486C23×C4—91no—
487AGL(1,ℤ/8)—184no—
488C2×SD16—31no—
489C2×SD16—91no—
490C2×D8—91no—
491C2×D8—91no—
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—31no—
515C2×C22⋊C4—181no—
516#107—31no—
517#107—91no—
518#106—91no—
519#106—91no—
520#103—31no—
521#103D3211yescharacteristic, complemented
522#102—31no—
523#102—31no—
524#102—31no—
525#102—91no—
526#102—91no—
527#102—91no—
528C23×C3—31no—
529C23×C3—31no—
530C23×C3—61no—
531C23×C3—61no—
532C22×D3—21no—
533C22×D3—21no—
534C22×D3—31no—
535C22×D3—31no—
536C22×D3—61no—
537C22×D3—62no—
538C22×D3—62no—
539C22×D3—62no—
540C22×D3—62no—
541C22×D3—61no—
542C22×D3—61no—
543C22×D3—121no—
544C22×D3—121no—
545C22×D3—121no—
546C22×D3—122no—
547C22×D3—122no—
548C22×D3—122no—
549C22×D3—122no—
550C22×D3—122no—
551C22×D3—122no—
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—61no—
561C3×D4—61no—
562C3×D4—61no—
563C3×D4—61no—
564C3×D4—122no—
565C3×D4—122no—
566C2×C3×C4—21no—
567C2×C3×C4—21no—
568C2×C3×C4—21no—
569C2×C3×C4—21no—
570C2×C3×C4—21no—
571C2×C3×C4—31no—
572C2×C3×C4—32no—
573C2×C3×C4—32no—
574C2×C3×C4—31no—
575C2×C3×C4—41no—
576C2×C3×C4—41no—
577C2×C3×C4—61no—
578C2×C3×C4—61no—
579C2×C3×C4—61no—
580C2×C3×C4—61no—
581C2×C3×C4—122no—
582C2×C3×C4—122no—
583C2×C3×C4C23×D311yescharacteristic
584C2×C3×C4C23×D311yescharacteristic
585#67—122no—
586#67—122no—
587#67—122no—
588#67—122no—
589#67—122no—
590#67—122no—
591C2×Dic3—21no—
592C2×Dic3—21no—
593C2×Dic3—31no—
594C2×Dic3—31no—
595C2×Dic3—61no—
596C2×Dic3—62no—
597C2×Dic3—62no—
598C2×Dic3—61no—
599C2×Dic3—61no—
600C2×Dic3—121no—
601C2×Dic3D3×D411yescharacteristic
602C2×Dic3D3×D411yescharacteristic
603D12—21no—
604D12—21no—
605D12—21no—
606D12—21no—
607D12—42no—
608D12—42no—
609D12—61no—
610D12—61no—
611D12—61no—
612D12—61no—
613D12—121no—
614D12—121no—
615D12—122no—
616D12—122no—
617D12—122no—
618D12—122no—
619D12—122no—
620D12—122no—
621D12—242no—
622C4×D3—21no—
623C4×D3—21no—
624C4×D3—42no—
625C4×D3—42no—
626C4×D3—62no—
627C4×D3—62no—
628C4×D3—62no—
629C4×D3—61no—
630C4×D3—61no—
631C4×D3—61no—
632C4×D3—61no—
633C4×D3—62no—
634C4×D3—121no—
635C4×D3—121no—
636C4×D3#23512yes—
637C4×D3D3×D412yes—
638C3×C8—21no—
639C3×C8—21no—
640C3×C8—32no—
641C3×C8—41no—
642C3×C8—61no—
643C3⋊C8—21no—
644C3⋊C8—32no—
645C3⋊C8—32no—
646C3⋊C8—62no—
647C3⋊C8D3×D412yescomplemented
648C2×C32C2×#12111yescharacteristic
649C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
650C2×C32#57511yescharacteristic
651C3⋊D3—22no—
652C3⋊D3—81no—
653C3×D3—22no—
654C3×D3—41no—
655C3×D3—81no—
656C3×D3—81no—
657C24—91no—
658C24—181no—
659#41—62no—
660#41—62no—
661C2×Q8C2×D3211yescharacteristic
662C2×D4—31no—
663C2×D4—31no—
664C2×D4—61no—
665C2×D4—61no—
666C2×D4—91no—
667C2×D4—181no—
668C2×D4—182no—
669C2×D4—182no—
670C2×D4—181no—
671C2×D4—181no—
672C2×D4—181no—
673C2×D4—181no—
674C2×D4—181no—
675C2×D4—364no—
676C22×C4—31no—
677C22×C4—31no—
678C22×C4—61no—
679C22×C4—61no—
680C22×C4—91no—
681C22×C4—91no—
682C22×C4—91no—
683C22×C4—91no—
684C22×C4—182no—
685C22×C4—182no—
686SD16—62no—
687SD16—182no—
688D8—182no—
689D8—182no—
690M16—62no—
691M16—62no—
692M16—94no—
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—61no—
704C4⋊C4—91no—
705C4⋊C4—181no—
706C4⋊C4C2×D3211yescharacteristic
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—61no—
720C22×C3—61no—
721C22×C3—61no—
722C22×C3—61no—
723C22×C3—61no—
724C22×C3—121no—
725C22×C3—121no—
726C22×C3—121no—
727C22×C3—121no—
728C22×C3—121no—
729C22×C3—121no—
730C22×C3C2×D3×D411yescharacteristic
731C22×C3C2×D3×D411yescharacteristic
732C2×D3—21no—
733C2×D3—21no—
734C2×D3—21no—
735C2×D3—21no—
736C2×D3—21no—
737C2×D3—32no—
738C2×D3—32no—
739C2×D3—41no—
740C2×D3—41no—
741C2×D3—41no—
742C2×D3—41no—
743C2×D3—41no—
744C2×D3—41no—
745C2×D3—62no—
746C2×D3—61no—
747C2×D3—61no—
748C2×D3—61no—
749C2×D3—61no—
750C2×D3—121no—
751C2×D3—121no—
752C2×D3—124no—
753C2×D3—124no—
754C2×D3—121no—
755C2×D3—121no—
756C2×D3—121no—
757C2×D3—121no—
758C2×D3—121no—
759C2×D3—121no—
760C2×D3—241no—
761C2×D3—241no—
762C2×D3—241no—
763C2×D3—244no—
764C2×D3—244no—
765C2×D3#88412yes—
766C3×C4—21no—
767C3×C4—21no—
768C3×C4—32no—
769C3×C4—41no—
770C3×C4—41no—
771C3×C4—41no—
772C3×C4—41no—
773C3×C4—61no—
774C3×C4—81no—
775C3×C4—81no—
776C3×C4—121no—
777C3×C4—121no—
778C3×C4C2×#23511yescharacteristic
779C3×C4C2×D3×D411yescharacteristic
780C3×C4C2×D3×D411yescharacteristic
781C3×C4D3×#4111yescharacteristic
782Dic3—21no—
783Dic3—41no—
784Dic3—41no—
785Dic3—61no—
786Dic3—61no—
787Dic3—121no—
788Dic3—121no—
789Dic3—121no—
790Dic3—241no—
791Dic3#88412yes—
792C32#305511yescharacteristic, complemented, Sylow
793C23—31no—
794C23—31no—
795C23—61no—
796C23—61no—
797C23—91no—
798C23—182no—
799C23—182no—
800C23—181no—
801C23—362no—
802C23—361no—
803C23—362no—
804C23—362no—
805Q8—21no—
806Q8—21no—
807D4—61no—
808D4—61no—
809D4—61no—
810D4—61no—
811D4—122no—
812D4—122no—
813D4—181no—
814D4—181no—
815D4—362no—
816D4—362no—
817D4—362no—
818D4—362no—
819D4—362no—
820D4—362no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—31no—
824C2×C4—32no—
825C2×C4—32no—
826C2×C4—31no—
827C2×C4—61no—
828C2×C4—61no—
829C2×C4—61no—
830C2×C4—61no—
831C2×C4—91no—
832C2×C4—122no—
833C2×C4—122no—
834C2×C4—182no—
835C2×C4—182no—
836C2×C4—182no—
837C2×C4—181no—
838C2×C4—181no—
839C2×C4—181no—
840C2×C4C22×D3211yescharacteristic
841C8—21no—
842C8—32no—
843C8—61no—
844C8—92no—
845C2×C3—21no—
846C2×C3—21no—
847C2×C3—21no—
848C2×C3—62no—
849C2×C3—121no—
850C2×C3—241no—
851C2×C3—241no—
852C2×C3C2×#88411yescharacteristic
853C2×C3D3×#12111yescharacteristic
854C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
855C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
856C2×C3#577711yescharacteristic
857C2×C3#577711yescharacteristic
858D3—22no—
859D3—41no—
860D3—62no—
861D3—62no—
862D3—81no—
863D3—81no—
864D3—122no—
865D3—241no—
866D3—241no—
867D3—481no—
868C22—32no—
869C22—61no—
870C22—61no—
871C22—61no—
872C22—61no—
873C22—61no—
874C22—92no—
875C22—121no—
876C22—121no—
877C22—121no—
878C22—121no—
879C22—121no—
880C22—121no—
881C22—181no—
882C22—181no—
883C22—364no—
884C22—361no—
885C22—361no—
886C22—361no—
887C22—724no—
888C22D32×D411yescharacteristic
889C4—32no—
890C4—41no—
891C4—41no—
892C4—61no—
893C4—121no—
894C4—121no—
895C4—181no—
896C4—361no—
897C4D3×#23511yescharacteristic
898C4D32×D411yescharacteristic
899C3—21no—
900C3#7888811yescharacteristic, complemented
901C3#8080511yescharacteristic, complemented
902C2—62no—
903C2—121no—
904C2—182no—
905C2—241no—
906C2—241no—
907C2—721no—
908C2D3×#88411yescharacteristic
909C2#1059474011yescharacteristic
910C2#1059476211yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
hypercenter#103D32
hypocenterC32#3055
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
1. #10595424C2semidirect
2. C2×#63939C2semidirect
3. C2×#63791C2semidirect
4. D3×#895C2semidirect
5. #10592506C2semidirect
6. C3×#4812C2semidirect
7. C3×#4803C2semidirect
8. #10591591C2semidirect
9. #10591589C2semidirect
10. #10590939C2semidirect
11. #10590839C2semidirect
12. #10590827C2semidirect
13. #10590580C2semidirect
14. #10590509C2semidirect
15. #10590504C2semidirect
22. #64155C22semidirect
23. C2×#3755C22semidirect
24. C2×C8×C3⋊D3C22semidirect
26. C3×#946C22semidirect
27. C2×C3×#215C22semidirect
29. C2×C3×ΓL(1,𝔽25)C22semidirect
36. #63916C22semidirect
39. #63908C22semidirect
45. C2×#3714C22semidirect
46. C2×#3713C22semidirect
48. C2×#3711C22semidirect
49. C2×#3710C22semidirect
51. C32×#103C22semidirect
52. #63648C22semidirect
53. #63635C22semidirect
54. C3×#835C22semidirect
55. C3×#821C22semidirect
56. C3×#821C22semidirect
57. C3×#809C22semidirect
58. C3×#807C22semidirect
59. #63576C22semidirect
60. #63573C22semidirect
61. #63564C22semidirect
62. #63563C22semidirect
82. #4812D3semidirect
87. #4803D3semidirect
152. #3711D4semidirect
173. #946C2×D3semidirect
177. C2×#215C2×D3semidirect
202. C2×ΓL(1,𝔽25)C2×D3semidirect
228. C3×#103C2×D3semidirect
229. C3×#103C2×D3semidirect
233. #835C2×D3semidirect
240. #821C2×D3semidirect
241. #821C2×D3semidirect
244. #809C2×D3semidirect
251. #807C2×D3semidirect
301. C3⋊(C3⋊C8)C2×D4semidirect
303. C3×C3⋊C8C2×D4semidirect
458. C2×C3⋊D3AGL(1,ℤ/8)semidirect
521. #103D32semidirect
647. C3⋊C8D3×D4semidirect
792. C32#3055semidirect
900. C3#78888semidirect
901. C3#80805semidirect

Maximal subgroups

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

subgroupindex
#105954242
C2×#639392
C2×#637912
D3×#8952
#105925062
C3×#48122
C3×#48032
#105915912
#105915892
#105909392
#105908392
#105908272
#105905802
#105905092
#105905042
#808053
#788883