Finite Group Databasebeta

← #11867183

Subgroups — #11867183

Order 1152.

1177 conjugacy classes of subgroups.

The subgroup lattice has 915 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595430C211yesmaximal, characteristic, complemented
2C2×#63941C211yesmaximal, characteristic, complemented
3C2×D3×ΓL(1,𝔽25)C211yesmaximal, characteristic, complemented
4#10594612C211yesmaximal, characteristic, complemented
5#10592502C211yesmaximal, characteristic, complemented
6C3×#4812C211yesmaximal, characteristic, complemented
7C3×#4807C211yesmaximal, characteristic, complemented
8#10591634C211yesmaximal, characteristic, complemented
9#10591587C211yesmaximal, characteristic, complemented
10#10590941C211yesmaximal, characteristic, complemented
11#10590827C211yesmaximal, characteristic, complemented
12#10590826C211yesmaximal, characteristic, complemented
13#10590586C211yesmaximal, characteristic, complemented
14#10590583C211yesmaximal, characteristic, complemented
15#10590576C211yesmaximal, characteristic, complemented
16#80805—31nomaximal
17#80657—31nomaximal
18C2×#3832C2211yescharacteristic
19C2×#3802—21no—
20C2×#3802C2211yescharacteristic
21C2×C4×D32C2211yescharacteristic
22C2×#3743C2211yescharacteristic
23C4⋊C4×C3⋊D3C2211yescharacteristic
24C3×#946C2211yescharacteristic, complemented
25C3×#946C2211yescharacteristic, complemented
26C2×C3×#215C2211yescharacteristic, complemented
27C2×C3×#215C2211yescharacteristic, complemented
28C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
29C2×C3×D3×C8C2211yescharacteristic, complemented
30C3×#895C2211yescharacteristic
31C3×#895C2211yescharacteristic
32#63941—24no—
33#63923—21no—
34#63921—21no—
35#63909C2211yescharacteristic, complemented
36#63909C2211yescharacteristic, complemented
37#63908C2211yescharacteristic
38#63908C2211yescharacteristic
39#63897—21no—
40#63885—21no—
41#63885—21no—
42#63881—21no—
43#63881—21no—
44#63849C2211yescharacteristic
45C2×#3714C2211yescharacteristic, complemented
46C2×#3714C2211yescharacteristic, complemented
47C2×#3712C2211yescharacteristic
48C2×#3711C2211yescharacteristic, complemented
49C2×D3×C3⋊C8C2211yescharacteristic, complemented
50D3×ΓL(1,𝔽25)—24no—
51C32×#103C2211yescharacteristic, complemented
52#63662C2211yescharacteristic, complemented
53#63648C2211yescharacteristic, complemented
54#63636C2211yescharacteristic, complemented
55C3×#821C2211yescharacteristic, complemented
56C3×#821C2211yescharacteristic, complemented
57C3×#808C2211yescharacteristic, complemented
58C3×#807C2211yescharacteristic, complemented
59#63575C2211yescharacteristic, complemented
60#63573C2211yescharacteristic, complemented
61#63562C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63C2×#914—31no—
64C2×#914—31no—
65C2×D3×M16—31no—
66C22×ΓL(1,𝔽25)—31no—
67#5627—31no—
68#5627—31no—
69D3×#121—31no—
70D3×#121—31no—
71C3×#468—31no—
72C3×#465—31no—
73#5174—31no—
74#5171—31no—
75#5135—31no—
76#5115—31no—
77#5049—31no—
78#5048—31no—
79#5039—31no—
80#5038—31no—
81#4883—31no—
82#4881—31no—
83#4865—31no—
84#4861—31no—
85#4812D311yescharacteristic, complemented
86#4807D311yescharacteristic, complemented
87#4803—31no—
88#4803—31no—
89#4803—61no—
90#4782—31no—
91#4775—31no—
92#4770—31no—
93#4770—31no—
94C22×D32—21no—
95C22×D32D411yescharacteristic
96C2×C32×Q8C2311yescharacteristic
97#3832—22no—
98#3832—22no—
99C2×C4⋊(C3⋊D3)—21no—
100C2×C4⋊(C3⋊D3)C2311yescharacteristic
101C2×C4×C3⋊D3—21no—
102C2×C4×C3⋊D3—21no—
103C2×C4×C3⋊D3C2311yescharacteristic
104C2×C3×D12—21no—
105C2×C3×D12—21no—
106C2×C3×D12C2311yescharacteristic
107C2×C3×D12C2311yescharacteristic
108C2×C3×C4×D3C2311yescharacteristic
109C2×C3×C4×D3C2311yescharacteristic
110C2×#626—21no—
111C2×#626—21no—
112C2×#625—21no—
113C2×#625—21no—
114C2×#625—21no—
115C2×#624D411yescharacteristic
116C2×D3×Dic3D411yescharacteristic
117C2×D3×Dic3D411yescharacteristic
118#3802—22no—
119#3802—22no—
120#3802—44no—
121C4×D32—22no—
122C4×D32—22no—
123C2×C32×C8C2311yescharacteristic
124C32×C4⋊C4C2311yescharacteristic
125C4⋊(C3⋊Dic3)C2311yescharacteristic
126#3750—21no—
127C2×C3⋊(C3⋊C8)C2311yescharacteristic
128#3743—22no—
129C3×#215—22no—
130C3×#215—22no—
131C3×(C2×D3)⋊C4—21no—
132C3×(C2×D3)⋊C4—21no—
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×D3×C8—22no—
143#3722—21no—
144#3722—21no—
145#3722—21no—
146(C2×D3)⋊Dic3—21no—
147(C2×D3)⋊Dic3—21no—
148Dic32—21no—
149#3714—22no—
150#3714—22no—
151#3712D414yescomplemented
152#3711—22no—
153D3×C3⋊C8—22no—
154#3055—91noSylow
155C2×#239—31no—
156C2×#239—31no—
157C2×#239—61no—
158C2×D3×D4—31no—
159C2×D3×D4—31no—
160C2×D3×D4—61no—
161C2×D3×D4—61no—
162C22×C4×D3—31no—
163C22×C4×D3—31no—
164C2×C3×SD16—31no—
165C2×C3×SD16—31no—
166C2×C3×M16—31no—
167C22×C3×C8—31no—
168C3×C22⋊Q8—31no—
169C3×C22⋊Q8—31no—
170C3×#121—31no—
171C3×#121—31no—
172#946C2×D311yescharacteristic, complemented
173#946C2×D311yescharacteristic, complemented
174C2×#215C2×D311yescharacteristic, complemented
175C2×#215C2×D311yescharacteristic, complemented
176#939—61no—
177#939—61no—
178#938—31no—
179#938—31no—
180C2×#213—31no—
181C2×#213—31no—
182#930—31no—
183#930—31no—
184#930—31no—
185#930—31no—
186C2×#208—31no—
187C22×C3⋊C8—31no—
188#914—64no—
189#914—64no—
190D3×M16—64no—
191C2×D24—31no—
192C2×D24—31no—
193C2×ΓL(1,𝔽25)—31no—
194C2×ΓL(1,𝔽25)—31no—
195C2×ΓL(1,𝔽25)—31no—
196C2×ΓL(1,𝔽25)—31no—
197C2×ΓL(1,𝔽25)—31no—
198C2×ΓL(1,𝔽25)—61no—
199C2×ΓL(1,𝔽25)—64no—
200C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
201C2×D3×C8—31no—
202C2×D3×C8C2×D311yescharacteristic, complemented
203#895—31no—
204#895—31no—
205#895C2×D311yescharacteristic
206#895C2×D311yescharacteristic
207#894—61no—
208#894—61no—
209#893—61no—
210#893—61no—
211#892—31no—
212#892—31no—
213D3×C4⋊C4—31no—
214D3×C4⋊C4—31no—
215D3×C4⋊C4—61no—
216#884—61no—
217#884—61no—
218#882—61no—
219#882—61no—
220#67⋊C4—61no—
221#67⋊C4—61no—
222D3×C22⋊C4—61no—
223D3×C22⋊C4—61no—
224C3×#107—31no—
225C3×#106—31no—
226C3×#103—21no—
227C3×#103C2×D311yescharacteristic, complemented
228C3×#103C2×D311yescharacteristic, complemented
229C3×#102—31no—
230C3×#102—31no—
231#835—31no—
232#835—31no—
233#835—61no—
234#832—31no—
235#832—31no—
236#821—31no—
237#821—31no—
238#821—61no—
239#821C2×D311yescharacteristic, complemented
240#821C2×D311yescharacteristic, complemented
241#818—31no—
242#817—31no—
243#809—31no—
244#809—31no—
245#809—31no—
246#809—31no—
247#809—61no—
248#808—31no—
249#808C2×D311yescharacteristic, complemented
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—42no—
275C4×C3⋊D3—42no—
276C4×C3⋊D3C2×D412yes—
277C4×C3⋊D3#4112yes—
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×D12—42no—
288C3×C4×D3—21no—
289C3×C4×D3—21no—
290C3×C4×D3—21no—
291C3×C4×D3—21no—
292#626—42no—
293#626—42no—
294#625—42no—
295#625—42no—
296#625—42no—
297#624—22no—
298D3×Dic3—22no—
299D3×Dic3—22no—
300C32×C8—21no—
301C3⋊(C3⋊C8)—21no—
302C3×C3⋊C8C2×D412yescomplemented
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—31no—
315#465—91no—
316#428—91no—
317#418—91no—
318#417—91no—
319C23×D3—31no—
320C23×D3—31no—
321C23×D3—61no—
322C23×D3—61no—
323C2×C3×Q8—21no—
324C2×C3×Q8C22×D311yescharacteristic
325C2×C3×Q8C22×D311yescharacteristic
326C2×C3×D4—31no—
327C2×C3×D4—31no—
328C2×C3×D4—61no—
329C2×C3×D4—61no—
330C22×C3×C4—31no—
331C22×C3×C4—31no—
332C2×#67—61no—
333C2×#67—61no—
334C2×#67—61no—
335C2×#67—61no—
336C2×#67—61no—
337C2×#67—61no—
338C2×#67—61no—
339C2×#67—61no—
340C22×Dic3—31no—
341C22×Dic3—31no—
342#239—62no—
343#239—62no—
344#239—62no—
345#239—62no—
346#239—64no—
347#239—122no—
348D3×D4—62no—
349D3×D4—62no—
350D3×D4—62no—
351D3×D4—62no—
352D3×D4—124no—
353D3×D4—124no—
354C2×D12—21no—
355C2×D12—21no—
356C2×D12—31no—
357C2×D12—31no—
358C2×D12—61no—
359C2×D12—61no—
360C2×D12—61no—
361C2×D12—61no—
362C2×D12—61no—
363C2×D12—121no—
364C2×D12C22×D311yescharacteristic
365C2×D12C22×D311yescharacteristic
366C2×C4×D3—31no—
367C2×C4×D3—31no—
368C2×C4×D3—31no—
369C2×C4×D3—31no—
370C2×C4×D3—31no—
371C2×C4×D3—31no—
372C2×C4×D3—61no—
373C2×C4×D3—62no—
374C2×C4×D3—62no—
375C2×C4×D3—62no—
376C2×C4×D3—62no—
377C2×C4×D3—61no—
378C2×C4×D3—61no—
379C2×C4×D3—61no—
380C2×C4×D3—61no—
381C2×C4×D3—121no—
382C2×C4×D3—121no—
383C2×C4×D3C22×D311yescharacteristic
384C2×C4×D3C22×D311yescharacteristic
385C3×SD16—62no—
386C3×SD16—62no—
387C3×M16—62no—
388C2×C3×C8—21no—
389C2×C3×C8—31no—
390C2×C3×C8—31no—
391C2×C3×C8—62no—
392C2×C3×C8C22×D311yescharacteristic
393C2×C3×C8C22×D311yescharacteristic
394C3×C4⋊C4—21no—
395C3×C4⋊C4—31no—
396C3×C4⋊C4—31no—
397C3×C4⋊C4—61no—
398C3×C4⋊C4—61no—
399C3×C4⋊C4C22×D311yescharacteristic
400C3×C4⋊C4C22×D311yescharacteristic
401C3×C22⋊C4—61no—
402C3×C22⋊C4—61no—
403C3×C22⋊C4—61no—
404C3×C22⋊C4—61no—
405#217—61no—
406#217—61no—
407#215—22no—
408#215—22no—
409#213—62no—
410#213—62no—
411(C2×D3)⋊C4—21no—
412(C2×D3)⋊C4—21no—
413(C2×D3)⋊C4—21no—
414(C2×D3)⋊C4—21no—
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—61no—
422(C2×D3)⋊C4—61no—
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—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
442D24—62no—
443D24—62no—
444ΓL(1,𝔽25)—22no—
445ΓL(1,𝔽25)—34no—
446ΓL(1,𝔽25)—34no—
447ΓL(1,𝔽25)—62no—
448ΓL(1,𝔽25)—62no—
449ΓL(1,𝔽25)—62no—
450ΓL(1,𝔽25)—122no—
451D3×C8—22no—
452D3×C8—62no—
453C22×C32C22×D411yescharacteristic
454C2×C3⋊D3—21no—
455C2×C3⋊D3—21no—
456C2×C3⋊D3—41no—
457C2×C3⋊D3—41no—
458C2×C3⋊D3—41no—
459C2×C3⋊D3#12112yes—
460C2×C3×D3—21no—
461C2×C3×D3—21no—
462C2×C3×D3—21no—
463C2×C3×D3—21no—
464C2×C3×D3—21no—
465C2×C3×D3—41no—
466C2×C3×D3—41no—
467C2×C3×D3—41no—
468C2×C3×D3—41no—
469C2×C3×D3—41no—
470C2×C3×D3—41no—
471C2×C3×D3AGL(1,ℤ/8)12yescomplemented
472D32—44no—
473D32—84no—
474C32×C4—41no—
475C32×C4—41no—
476C32×C4C22×D411yescharacteristic
477C32×C4C2×#4111yescharacteristic
478C3⋊Dic3—41no—
479C3⋊Dic3#12112yes—
480C3×Dic3—21no—
481C3×Dic3—21no—
482C3×Dic3—41no—
483C3×Dic3—41no—
484C2×#41—91no—
485C22×D4—91no—
486C22×D4—181no—
487C23×C4—91no—
488AGL(1,ℤ/8)—184no—
489C2×SD16—31no—
490C2×SD16—31no—
491C2×D8—91no—
492C2×D8—91no—
493C2×M16—31no—
494C2×M16—91no—
495C2×M16—91no—
496C2×M16—91no—
497C2×M16—184no—
498C22×C8—31no—
499C22×C8—91no—
500#123—181no—
501C22⋊Q8—31no—
502C22⋊Q8—31no—
503#121—31no—
504#121—31no—
505#121—91no—
506#121—91no—
507#121—91no—
508#121—91no—
509#121—181no—
510#121—181no—
511#120—181no—
512C4×D4—181no—
513C4×D4—181no—
514#117—91no—
515C2×C4⋊C4—91no—
516C2×C22⋊C4—181no—
517#107—31no—
518#107—91no—
519#106—31no—
520#106—91no—
521#103—91no—
522#103D3211yescharacteristic, complemented
523#102—31no—
524#102—31no—
525#102—91no—
526#102—91no—
527#102—91no—
528#102—91no—
529C23×C3—31no—
530C23×C3—31no—
531C23×C3—61no—
532C23×C3—61no—
533C22×D3—21no—
534C22×D3—21no—
535C22×D3—31no—
536C22×D3—31no—
537C22×D3—61no—
538C22×D3—62no—
539C22×D3—62no—
540C22×D3—62no—
541C22×D3—62no—
542C22×D3—61no—
543C22×D3—61no—
544C22×D3—121no—
545C22×D3—121no—
546C22×D3—121no—
547C22×D3—122no—
548C22×D3—122no—
549C22×D3—122no—
550C22×D3—122no—
551C22×D3—122no—
552C22×D3—122no—
553C22×D3D3×D411yescharacteristic
554C22×D3D3×D411yescharacteristic
555C3×Q8—22no—
556C3×Q8—21no—
557C3×Q8—21no—
558C3×Q8—21no—
559C3×Q8—21no—
560C3×Q8—41no—
561C3×D4—61no—
562C3×D4—61no—
563C3×D4—61no—
564C3×D4—61no—
565C3×D4—122no—
566C3×D4—122no—
567C2×C3×C4—21no—
568C2×C3×C4—21no—
569C2×C3×C4—21no—
570C2×C3×C4—21no—
571C2×C3×C4—21no—
572C2×C3×C4—31no—
573C2×C3×C4—31no—
574C2×C3×C4—41no—
575C2×C3×C4—41no—
576C2×C3×C4—61no—
577C2×C3×C4—61no—
578C2×C3×C4—61no—
579C2×C3×C4—61no—
580C2×C3×C4—61no—
581C2×C3×C4—61no—
582C2×C3×C4C23×D311yescharacteristic
583C2×C3×C4C23×D311yescharacteristic
584#67—122no—
585#67—122no—
586#67—122no—
587#67—122no—
588#67—122no—
589#67—122no—
590#67—122no—
591#67—122no—
592C2×Dic3—21no—
593C2×Dic3—21no—
594C2×Dic3—31no—
595C2×Dic3—31no—
596C2×Dic3—61no—
597C2×Dic3—62no—
598C2×Dic3—62no—
599C2×Dic3—61no—
600C2×Dic3—61no—
601C2×Dic3—121no—
602C2×Dic3D3×D411yescharacteristic
603C2×Dic3D3×D411yescharacteristic
604D12—21no—
605D12—21no—
606D12—21no—
607D12—21no—
608D12—42no—
609D12—42no—
610D12—62no—
611D12—61no—
612D12—61no—
613D12—61no—
614D12—61no—
615D12—121no—
616D12—122no—
617D12—122no—
618D12—124no—
619D12—122no—
620D12—122no—
621C4×D3—21no—
622C4×D3—21no—
623C4×D3—21no—
624C4×D3—21no—
625C4×D3—32no—
626C4×D3—32no—
627C4×D3—32no—
628C4×D3—32no—
629C4×D3—62no—
630C4×D3—62no—
631C4×D3—62no—
632C4×D3—62no—
633C4×D3—62no—
634C4×D3—62no—
635C4×D3—122no—
636C4×D3—122no—
637C4×D3—124no—
638C4×D3—122no—
639C4×D3—122no—
640C4×D3—242no—
641C3×C8—21no—
642C3×C8—21no—
643C3×C8—32no—
644C3×C8—32no—
645C3×C8—41no—
646C3⋊C8—61no—
647C3⋊C8—61no—
648C3⋊C8—121no—
649C3⋊C8D3×D412yescomplemented
650C3⋊C8D3×D412yescomplemented
651C2×C32C2×#12111yescharacteristic
652C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
653C2×C32#57511yescharacteristic
654C3⋊D3—22no—
655C3⋊D3—81no—
656C3×D3—22no—
657C3×D3—41no—
658C3×D3—81no—
659C3×D3—81no—
660C24—91no—
661C24—181no—
662#41—182no—
663#41—182no—
664C2×Q8C2×D3211yescharacteristic
665C2×D4—31no—
666C2×D4—31no—
667C2×D4—61no—
668C2×D4—61no—
669C2×D4—91no—
670C2×D4—181no—
671C2×D4—181no—
672C2×D4—181no—
673C2×D4—182no—
674C2×D4—182no—
675C2×D4—181no—
676C2×D4—181no—
677C2×D4—181no—
678C2×D4—364no—
679C22×C4—31no—
680C22×C4—31no—
681C22×C4—91no—
682C22×C4—91no—
683C22×C4—91no—
684C22×C4—91no—
685C22×C4—181no—
686C22×C4—181no—
687C22×C4—182no—
688C22×C4—182no—
689SD16—62no—
690SD16—62no—
691D8—182no—
692D8—182no—
693M16—62no—
694M16—94no—
695M16—182no—
696M16—182no—
697C2×C8—31no—
698C2×C8—31no—
699C2×C8—62no—
700C2×C8—91no—
701C2×C8—182no—
702C2×C8C2×D3211yescharacteristic
703C4⋊C4—31no—
704C4⋊C4—31no—
705C4⋊C4—61no—
706C4⋊C4—61no—
707C4⋊C4—91no—
708C4⋊C4—181no—
709C4⋊C4C2×D3211yescharacteristic
710C22⋊C4—61no—
711C22⋊C4—61no—
712C22⋊C4—61no—
713C22⋊C4—61no—
714C22⋊C4—181no—
715C22⋊C4—181no—
716C22⋊C4—181no—
717C22⋊C4—181no—
718C22⋊C4—181no—
719C42—181no—
720C22×C3—21no—
721C22×C3—32no—
722C22×C3—61no—
723C22×C3—61no—
724C22×C3—61no—
725C22×C3—61no—
726C22×C3—61no—
727C22×C3—121no—
728C22×C3—121no—
729C22×C3—121no—
730C22×C3—121no—
731C22×C3—121no—
732C22×C3—121no—
733C22×C3C2×D3×D411yescharacteristic
734C22×C3C2×D3×D411yescharacteristic
735C2×D3—21no—
736C2×D3—21no—
737C2×D3—21no—
738C2×D3—21no—
739C2×D3—21no—
740C2×D3—32no—
741C2×D3—32no—
742C2×D3—41no—
743C2×D3—41no—
744C2×D3—41no—
745C2×D3—41no—
746C2×D3—41no—
747C2×D3—41no—
748C2×D3—62no—
749C2×D3—61no—
750C2×D3—61no—
751C2×D3—61no—
752C2×D3—61no—
753C2×D3—121no—
754C2×D3—121no—
755C2×D3—124no—
756C2×D3—124no—
757C2×D3—122no—
758C2×D3—121no—
759C2×D3—121no—
760C2×D3—121no—
761C2×D3—121no—
762C2×D3—121no—
763C2×D3—121no—
764C2×D3—241no—
765C2×D3—241no—
766C2×D3—244no—
767C2×D3—244no—
768C2×D3#91412yescomplemented
769C3×C4—21no—
770C3×C4—21no—
771C3×C4—42no—
772C3×C4—41no—
773C3×C4—41no—
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×C4D3×#4111yescharacteristic
784C3×C4D3×#4111yescharacteristic
785Dic3—21no—
786Dic3—21no—
787Dic3—32no—
788Dic3—32no—
789Dic3—41no—
790Dic3—41no—
791Dic3—62no—
792Dic3—121no—
793Dic3—121no—
794Dic3—241no—
795C32#305511yescharacteristic, complemented, Sylow
796C23—31no—
797C23—31no—
798C23—61no—
799C23—61no—
800C23—91no—
801C23—182no—
802C23—182no—
803C23—181no—
804C23—361no—
805C23—362no—
806C23—362no—
807C23—362no—
808Q8—21no—
809Q8—21no—
810D4—61no—
811D4—61no—
812D4—61no—
813D4—61no—
814D4—122no—
815D4—122no—
816D4—181no—
817D4—181no—
818D4—362no—
819D4—362no—
820D4—362no—
821D4—362no—
822D4—362no—
823D4—362no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—31no—
827C2×C4—31no—
828C2×C4—61no—
829C2×C4—61no—
830C2×C4—61no—
831C2×C4—61no—
832C2×C4—61no—
833C2×C4—61no—
834C2×C4—91no—
835C2×C4—92no—
836C2×C4—92no—
837C2×C4—182no—
838C2×C4—182no—
839C2×C4—182no—
840C2×C4—181no—
841C2×C4—362no—
842C2×C4—362no—
843C2×C4C22×D3211yescharacteristic
844C8—21no—
845C8—32no—
846C8—32no—
847C8—181no—
848C2×C3—21no—
849C2×C3—21no—
850C2×C3—21no—
851C2×C3—62no—
852C2×C3—121no—
853C2×C3—241no—
854C2×C3—241no—
855C2×C3D3×#12111yescharacteristic
856C2×C3D3×#12111yescharacteristic
857C2×C3C2×#91411yescharacteristic
858C2×C3#576811yescharacteristic
859C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
860C2×C3#577711yescharacteristic
861D3—22no—
862D3—41no—
863D3—62no—
864D3—62no—
865D3—81no—
866D3—81no—
867D3—122no—
868D3—242no—
869D3—241no—
870D3—241no—
871C22—32no—
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—364no—
887C22—361no—
888C22—361no—
889C22—361no—
890C22—724no—
891C22D32×D411yescharacteristic
892C4—41no—
893C4—41no—
894C4—61no—
895C4—61no—
896C4—92no—
897C4—121no—
898C4—121no—
899C4—361no—
900C4#6430611yescharacteristic
901C4D32×D411yescharacteristic
902C3—21no—
903C3#8065711yescharacteristic, complemented
904C3#8080511yescharacteristic, complemented
905C2—62no—
906C2—121no—
907C2—182no—
908C2—241no—
909C2—241no—
910C2—721no—
911C2#1059426511yescharacteristic
912C2D3×#91411yescharacteristic
913C2#1059476311yescharacteristic
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. #10595430C2semidirect
2. C2×#63941C2semidirect
3. C2×D3×ΓL(1,𝔽25)C2semidirect
4. #10594612C2semidirect
5. #10592502C2semidirect
6. C3×#4812C2semidirect
7. C3×#4807C2semidirect
8. #10591634C2semidirect
9. #10591587C2semidirect
10. #10590941C2semidirect
11. #10590827C2semidirect
12. #10590826C2semidirect
13. #10590586C2semidirect
14. #10590583C2semidirect
15. #10590576C2semidirect
24. C3×#946C22semidirect
25. C3×#946C22semidirect
26. C2×C3×#215C22semidirect
27. C2×C3×#215C22semidirect
28. C2×C3×ΓL(1,𝔽25)C22semidirect
29. C2×C3×D3×C8C22semidirect
35. #63909C22semidirect
36. #63909C22semidirect
45. C2×#3714C22semidirect
46. C2×#3714C22semidirect
48. C2×#3711C22semidirect
49. C2×D3×C3⋊C8C22semidirect
51. C32×#103C22semidirect
52. #63662C22semidirect
53. #63648C22semidirect
54. #63636C22semidirect
55. C3×#821C22semidirect
56. C3×#821C22semidirect
57. C3×#808C22semidirect
58. C3×#807C22semidirect
59. #63575C22semidirect
60. #63573C22semidirect
61. #63562C22semidirect
62. #63562C22semidirect
85. #4812D3semidirect
86. #4807D3semidirect
151. #3712D4semidirect
172. #946C2×D3semidirect
173. #946C2×D3semidirect
174. C2×#215C2×D3semidirect
175. C2×#215C2×D3semidirect
200. C2×ΓL(1,𝔽25)C2×D3semidirect
202. C2×D3×C8C2×D3semidirect
227. C3×#103C2×D3semidirect
228. C3×#103C2×D3semidirect
239. #821C2×D3semidirect
240. #821C2×D3semidirect
249. #808C2×D3semidirect
251. #807C2×D3semidirect
302. C3×C3⋊C8C2×D4semidirect
303. C3×C3⋊C8C2×D4semidirect
471. C2×C3×D3AGL(1,ℤ/8)semidirect
522. #103D32semidirect
649. C3⋊C8D3×D4semidirect
650. C3⋊C8D3×D4semidirect
768. C2×D3#914semidirect
795. C32#3055semidirect
903. C3#80657semidirect
904. C3#80805semidirect

Maximal subgroups

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

subgroupindex
#105954302
C2×#639412
C2×D3×ΓL(1,𝔽25)2
#105946122
#105925022
C3×#48122
C3×#48072
#105916342
#105915872
#105909412
#105908272
#105908262
#105905862
#105905832
#105905762
#808053
#806573