Finite Group Databasebeta

← #11867139

Subgroups — #11867139

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×#63795C211yesmaximal, characteristic, complemented
2C2×#63791C211yesmaximal, characteristic, complemented
3#10594626C211yesmaximal, characteristic, complemented
4D3×#895C211yesmaximal, characteristic, complemented
5#10592563C211yesmaximal, characteristic, complemented
6C3×#4865C211yesmaximal, characteristic, complemented
7C3×#4861C211yesmaximal, characteristic, complemented
8#10590844C211yesmaximal, characteristic, complemented
9#10590838C211yesmaximal, characteristic, complemented
10#10590607C211yesmaximal, characteristic, complemented
11#10590592C211yesmaximal, characteristic, complemented
12#10590588C211yesmaximal, characteristic, complemented
13#10590586C211yesmaximal, characteristic, complemented
14#10590509C211yesmaximal, characteristic, complemented
15#10590507C211yesmaximal, characteristic, complemented
16#80864—31nomaximal
17#79211—31nomaximal
18C2×D3×D12—21no—
19C2×D3×D12C2211yescharacteristic
20C2×C4×D32C2211yescharacteristic
21C2×#3795C2211yescharacteristic
22C2×#3744C2211yescharacteristic, complemented
23C2×C8×C3⋊D3C2211yescharacteristic, complemented
24#64106C2211yescharacteristic, complemented
25#64104C2211yescharacteristic
26C2×C3×D24C2211yescharacteristic, complemented
27C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
28C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
29C3×#895C2211yescharacteristic
30C3×#895C2211yescharacteristic, complemented
31C3×#892C2211yescharacteristic
32C3×D3×C4⋊C4C2211yescharacteristic
33#63922—21no—
34D3×(C2×D3)⋊C4—21no—
35#63916C2211yescharacteristic
36#63916C2211yescharacteristic, complemented
37#63910—21no—
38#63909C2211yescharacteristic
39Dic3×D12—21no—
40#63891—21no—
41#63886—21no—
42#63880—21no—
43#63857C2211yescharacteristic, complemented
44C2×#3716C2211yescharacteristic, complemented
45C2×#3714C2211yescharacteristic, complemented
46C2×#3711C2211yescharacteristic
47C2×#3711C2211yescharacteristic, complemented
48C2×#3710C2211yescharacteristic, complemented
49#63795—24no—
50#63791—24no—
51C32×#106C2211yescharacteristic, complemented
52#63637C2211yescharacteristic, complemented
53#63636C2211yescharacteristic, complemented
54C3×#818C2211yescharacteristic, complemented
55C3×#809C2211yescharacteristic, complemented
56C3×#809C2211yescharacteristic, complemented
57C3×#808C2211yescharacteristic, complemented
58C3×#807C2211yescharacteristic, complemented
59#63567C2211yescharacteristic, complemented
60#63564C2211yescharacteristic, complemented
61#63562C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63C2×#911—31no—
64C2×#908—31no—
65C2×D3×M16—31no—
66C2×D3×M16—31no—
67#5606—31no—
68D3×#121—31no—
69#5524—31no—
70C2×#895—31no—
71C3×#469—31no—
72C3×#428—31no—
73#5157—31no—
74#5134—31no—
75#5042—31no—
76#5039—31no—
77#5001—31no—
78#4966—31no—
79#4886—31no—
80#4886—31no—
81#4883—31no—
82#4883—31no—
83#4865—31no—
84#4865D311yescharacteristic, complemented
85#4864—31no—
86#4864—31no—
87#4864—31no—
88#4864—61no—
89#4861D311yescharacteristic, complemented
90#4778—31no—
91#4775—31no—
92#4771—31no—
93#4770—31no—
94C22×D32—21no—
95C22×D32D411yescharacteristic
96C2×C4⋊(C3⋊D3)—21no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4×C3⋊D3C2311yescharacteristic
99C2×#634C2311yescharacteristic
100C2×C3×D12—21no—
101C2×C3×D12—21no—
102C2×C3×D12C2311yescharacteristic
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3C2311yescharacteristic
106C2×C3×C4×D3C2311yescharacteristic
107C2×#626—21no—
108C2×#626—21no—
109C2×#626—21no—
110C2×#626—21no—
111C2×#625—21no—
112C2×#624D411yescharacteristic
113C2×D3×Dic3—21no—
114C2×D3×Dic3D411yescharacteristic
115C2×D3×Dic3D411yescharacteristic
116D3×D12—22no—
117D3×D12—22no—
118D3×D12—44no—
119C4×D32—22no—
120C4×D32—22no—
121#3795—22no—
122#3795—22no—
123C2×C32×C8C2311yescharacteristic
124C32×C4⋊C4C2311yescharacteristic
125C32×C4⋊C4C2311yescharacteristic
126#3752—21no—
127#3752—21no—
128C4⋊(C3⋊Dic3)—21no—
129C2×C3⋊(C3⋊C8)C2311yescharacteristic
130#3744—22no—
131C8×C3⋊D3—22no—
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×C4×Dic3—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#3722—21no—
146(C2×D3)⋊Dic3—21no—
147(C2×D3)⋊Dic3—21no—
148(C2×D3)⋊Dic3—21no—
149#3716—22no—
150#3714—22no—
151#3711—22no—
152#3711—22no—
153#3710—22no—
154#3055—91noSylow
155C2×#237—31no—
156C2×D3×D4—31no—
157C2×D3×D4—61no—
158C2×#235—31no—
159C22×D12—31no—
160C22×D12—61no—
161C22×C4×D3—31no—
162C22×C4×D3—31no—
163C2×C3×D8—31no—
164C2×C3×M16—31no—
165C2×C3×M16—31no—
166C3×#121—31no—
167C3×#121—31no—
168C3×#117—31no—
169C2×C3×C4⋊C4—31no—
170#939—61no—
171#938—31no—
172#938—31no—
173#937—61no—
174D4×Dic3—61no—
175C2×#214—31no—
176C2×#213—31no—
177#930—31no—
178C2×(C2×D3)⋊C4—61no—
179#924—31no—
180C2×#208—31no—
181C2×#208—31no—
182#911—64no—
183#908—64no—
184D3×M16—64no—
185D3×M16—64no—
186C2×D24—31no—
187C2×D24C2×D311yescharacteristic, complemented
188C2×#204—31no—
189C2×#204—31no—
190C2×#204—31no—
191C2×#204—61no—
192C2×ΓL(1,𝔽25)—31no—
193C2×ΓL(1,𝔽25)—31no—
194C2×ΓL(1,𝔽25)C2×D311yescharacteristic
195C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
196C2×D3×C8—31no—
197C2×D3×C8—31no—
198C2×D3×C8—31no—
199C2×D3×C8—31no—
200C2×D3×C8—61no—
201#897—31no—
202#897—31no—
203#897—31no—
204#897—61no—
205#895—31no—
206#895—31no—
207#895—31no—
208#895—31no—
209#895—31no—
210#895—61no—
211#895—61no—
212#895—61no—
213#895C2×D311yescharacteristic
214#895C2×D311yescharacteristic, complemented
215#892C2×D311yescharacteristic
216D3×C4⋊C4C2×D311yescharacteristic
217#886—61no—
218#884—61no—
219#883—61no—
220#882—61no—
221#67⋊C4—61no—
222D3×C22⋊C4—61no—
223C4×D12—61no—
224C4×D12—61no—
225C3×#107—31no—
226C3×#107—31no—
227C3×#106—21no—
228C3×#106—31no—
229C3×#106C2×D311yescharacteristic, complemented
230C3×#106C2×D311yescharacteristic, complemented
231C3×#102—31no—
232C3×#102—31no—
233#832—31no—
234#832—31no—
235#821—31no—
236#818C2×D311yescharacteristic, complemented
237#816—31no—
238#810—31no—
239#810—31no—
240#810—31no—
241#810—61no—
242#809—31no—
243#809—31no—
244#809—31no—
245#809—31no—
246#809—31no—
247#809—61no—
248#809C2×D311yescharacteristic, complemented
249#809C2×D311yescharacteristic, complemented
250#808C2×D311yescharacteristic, complemented
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—
264C2×C32×C4—21no—
265C2×C32×C4—21no—
266C2×C32×C4C2411yescharacteristic
267C2×C3⋊Dic3—21no—
268C2×C3⋊Dic3C2×D411yescharacteristic
269C4⋊(C3⋊D3)—21no—
270C4⋊(C3⋊D3)—21no—
271C4⋊(C3⋊D3)—42no—
272C4×C3⋊D3—21no—
273C4×C3⋊D3—21no—
274#634—21no—
275#634—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×D3C2×D412yes—
290C3×C4×D3#4112yes—
291#626—42no—
292#626—42no—
293#626—42no—
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)—91no—
305C22×M16—91no—
306#525—91no—
307C2×#121—91no—
308#469—31no—
309#469—91no—
310#468—91no—
311#468—91no—
312#466—91no—
313#466—91no—
314#465—91no—
315#465—91no—
316#428—31no—
317#418—91no—
318#417—91no—
319C23×D3—31no—
320C23×D3—31no—
321C23×D3—61no—
322C23×D3—61no—
323C2×C3×D4—31no—
324C2×C3×D4—31no—
325C2×C3×D4—61no—
326C2×C3×D4—61no—
327C22×C3×C4—31no—
328C22×C3×C4—31no—
329C22×C3×C4—61no—
330C2×#67—61no—
331C2×#67—61no—
332C2×#67—61no—
333C2×#67—61no—
334C2×#67—61no—
335C2×#67—61no—
336C22×Dic3—31no—
337C22×Dic3—31no—
338C22×Dic3—61no—
339#237—62no—
340#237—62no—
341D3×D4—62no—
342D3×D4—62no—
343D3×D4—124no—
344#235—62no—
345#235—62no—
346C2×D12—21no—
347C2×D12—21no—
348C2×D12—31no—
349C2×D12—31no—
350C2×D12—61no—
351C2×D12—62no—
352C2×D12—62no—
353C2×D12—61no—
354C2×D12—61no—
355C2×D12—61no—
356C2×D12—61no—
357C2×D12—61no—
358C2×D12—61no—
359C2×D12—121no—
360C2×D12—124no—
361C2×D12C22×D311yescharacteristic
362C2×D12C22×D311yescharacteristic
363C2×C4×D3—21no—
364C2×C4×D3—31no—
365C2×C4×D3—31no—
366C2×C4×D3—31no—
367C2×C4×D3—31no—
368C2×C4×D3—31no—
369C2×C4×D3—31no—
370C2×C4×D3—61no—
371C2×C4×D3—62no—
372C2×C4×D3—62no—
373C2×C4×D3—62no—
374C2×C4×D3—62no—
375C2×C4×D3—61no—
376C2×C4×D3C22×D311yescharacteristic
377C2×C4×D3C22×D311yescharacteristic
378C2×Dic6—31no—
379C2×Dic6—31no—
380C2×Dic6—61no—
381C3×D8—62no—
382C3×M16—34no—
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—21no—
391C3×C4⋊C4—31no—
392C3×C4⋊C4—31no—
393C3×C4⋊C4—61no—
394C3×C4⋊C4C22×D311yescharacteristic
395C3×C4⋊C4C22×D311yescharacteristic
396C3×C4⋊C4C22×D311yescharacteristic
397C3×C4⋊C4C22×D311yescharacteristic
398C3×C22⋊C4—61no—
399C3×C22⋊C4—61no—
400C3×C22⋊C4—61no—
401C3×C42—61no—
402#217—61no—
403#217—61no—
404#217—61no—
405#214—62no—
406#213—62no—
407(C2×D3)⋊C4—21no—
408(C2×D3)⋊C4—21no—
409(C2×D3)⋊C4—21no—
410(C2×D3)⋊C4—61no—
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—121no—
420(C2×D3)⋊C4—121no—
421C4⋊Dic3—61no—
422C4⋊Dic3—61no—
423C4⋊Dic3—61no—
424C4⋊Dic3—121no—
425C4⋊Dic3C22×D311yescharacteristic
426C4⋊Dic3C22×D311yescharacteristic
427Dic3⋊C4—21no—
428Dic3⋊C4—61no—
429C4×Dic3—21no—
430#208—62no—
431#208—62no—
432C2×C3⋊C8—31no—
433C2×C3⋊C8—31no—
434C2×C3⋊C8—61no—
435C2×C3⋊C8C22×D311yescharacteristic
436C2×C3⋊C8C22×D311yescharacteristic
437D24—22no—
438D24—62no—
439#204—62no—
440#204—62no—
441#204—62no—
442#204—122no—
443ΓL(1,𝔽25)—22no—
444ΓL(1,𝔽25)—62no—
445ΓL(1,𝔽25)—62no—
446ΓL(1,𝔽25)D1214yescomplemented
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—91no—
484C22×D4—91no—
485C22×D4—181no—
486C23×C4—91no—
487AGL(1,ℤ/8)—184no—
488C2×SD16—91no—
489C2×SD16—91no—
490C2×D8—31no—
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—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—31no—
514C2×C4⋊C4—31no—
515C2×C22⋊C4—181no—
516#107—31no—
517#107—31no—
518#106—31no—
519#106D3211yescharacteristic, complemented
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—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×D4—61no—
555C3×D4—61no—
556C3×D4—61no—
557C3×D4—61no—
558C3×D4—122no—
559C3×D4—122no—
560C2×C3×C4—21no—
561C2×C3×C4—21no—
562C2×C3×C4—21no—
563C2×C3×C4—21no—
564C2×C3×C4—21no—
565C2×C3×C4—31no—
566C2×C3×C4—32no—
567C2×C3×C4—32no—
568C2×C3×C4—31no—
569C2×C3×C4—41no—
570C2×C3×C4—41no—
571C2×C3×C4—61no—
572C2×C3×C4—61no—
573C2×C3×C4—61no—
574C2×C3×C4—61no—
575C2×C3×C4—122no—
576C2×C3×C4C23×D311yescharacteristic
577C2×C3×C4C23×D311yescharacteristic
578#67—122no—
579#67—122no—
580#67—122no—
581#67—122no—
582#67—122no—
583#67—122no—
584C2×Dic3—21no—
585C2×Dic3—21no—
586C2×Dic3—31no—
587C2×Dic3—31no—
588C2×Dic3—61no—
589C2×Dic3—62no—
590C2×Dic3—62no—
591C2×Dic3—61no—
592C2×Dic3—61no—
593C2×Dic3—121no—
594C2×Dic3—122no—
595C2×Dic3D3×D411yescharacteristic
596C2×Dic3D3×D411yescharacteristic
597D12—21no—
598D12—21no—
599D12—21no—
600D12—21no—
601D12—42no—
602D12—42no—
603D12—61no—
604D12—61no—
605D12—61no—
606D12—61no—
607D12—121no—
608D12—121no—
609D12—122no—
610D12—122no—
611D12—122no—
612D12—122no—
613D12—122no—
614D12—122no—
615D12—242no—
616C4×D3—21no—
617C4×D3—21no—
618C4×D3—42no—
619C4×D3—62no—
620C4×D3—62no—
621C4×D3—62no—
622C4×D3—61no—
623C4×D3—61no—
624C4×D3—61no—
625C4×D3—61no—
626C4×D3—62no—
627C4×D3—121no—
628C4×D3—121no—
629C4×D3—122no—
630C4×D3C2×D1212yes—
631C4×D3#23912yes—
632Dic6—61no—
633Dic6—61no—
634Dic6—61no—
635Dic6—61no—
636Dic6—121no—
637Dic6—121no—
638C3×C8—22no—
639C3×C8—32no—
640C3×C8—61no—
641C3×C8C2×D1212yescomplemented
642C3×C8D3×D412yescomplemented
643C3⋊C8—21no—
644C3⋊C8—61no—
645C3⋊C8—61no—
646C3⋊C8—121no—
647C3⋊C8C2×D1212yescomplemented
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—182no—
660#41—182no—
661C2×Q8—91no—
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—91no—
680C22×C4—91no—
681C22×C4—91no—
682C22×C4—91no—
683C22×C4—182no—
684C22×C4—182no—
685C22×C4—181no—
686SD16—182no—
687SD16—182no—
688D8—62no—
689D8—182no—
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—181no—
704C4⋊C4—181no—
705C4⋊C4C2×D3211yescharacteristic
706C4⋊C4C2×D3211yescharacteristic
707C22⋊C4—61no—
708C22⋊C4—61no—
709C22⋊C4—61no—
710C22⋊C4—181no—
711C22⋊C4—181no—
712C22⋊C4—181no—
713C22⋊C4—181no—
714C22⋊C4—181no—
715C22⋊C4—181no—
716C42—61no—
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#89512yes—
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×C4C22×D1211yescharacteristic
779C3×C4C2×D3×D411yescharacteristic
780C3×C4C2×#23911yescharacteristic
781C3×C4D3×#4111yescharacteristic
782Dic3—21no—
783Dic3—41no—
784Dic3—41no—
785Dic3—61no—
786Dic3—61no—
787Dic3—121no—
788Dic3—121no—
789Dic3—121no—
790Dic3—241no—
791Dic3#89512yes—
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—181no—
806Q8—181no—
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—182no—
834C2×C4—182no—
835C2×C4—182no—
836C2×C4—181no—
837C2×C4—181no—
838C2×C4—181no—
839C2×C4—362no—
840C2×C4C22×D3211yescharacteristic
841C8—32no—
842C8—61no—
843C8—181no—
844C8D3×D1212yescomplemented
845C2×C3—21no—
846C2×C3—21no—
847C2×C3—21no—
848C2×C3—62no—
849C2×C3—121no—
850C2×C3—241no—
851C2×C3—241no—
852C2×C3C2×#89511yescharacteristic
853C2×C3D3×#12111yescharacteristic
854C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
855C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
856C2×C3#577311yescharacteristic
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—
897C4C2×D3×D1211yescharacteristic
898C4D3×#23911yescharacteristic
899C3—21no—
900C3#7921111yescharacteristic, complemented
901C3#8086411yescharacteristic, complemented
902C2—62no—
903C2—121no—
904C2—182no—
905C2—241no—
906C2—241no—
907C2—721no—
908C2D3×#89511yescharacteristic
909C2#1059474011yescharacteristic
910C2#1059474411yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
hypercenter#106D32
hypocenterC32#3055
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
1. C2×#63795C2semidirect
2. C2×#63791C2semidirect
3. #10594626C2semidirect
4. D3×#895C2semidirect
5. #10592563C2semidirect
6. C3×#4865C2semidirect
7. C3×#4861C2semidirect
8. #10590844C2semidirect
9. #10590838C2semidirect
10. #10590607C2semidirect
11. #10590592C2semidirect
12. #10590588C2semidirect
13. #10590586C2semidirect
14. #10590509C2semidirect
15. #10590507C2semidirect
22. C2×#3744C22semidirect
23. C2×C8×C3⋊D3C22semidirect
24. #64106C22semidirect
26. C2×C3×D24C22semidirect
28. C2×C3×ΓL(1,𝔽25)C22semidirect
30. C3×#895C22semidirect
36. #63916C22semidirect
43. #63857C22semidirect
44. C2×#3716C22semidirect
45. C2×#3714C22semidirect
47. C2×#3711C22semidirect
48. C2×#3710C22semidirect
51. C32×#106C22semidirect
52. #63637C22semidirect
53. #63636C22semidirect
54. C3×#818C22semidirect
55. C3×#809C22semidirect
56. C3×#809C22semidirect
57. C3×#808C22semidirect
58. C3×#807C22semidirect
59. #63567C22semidirect
60. #63564C22semidirect
61. #63562C22semidirect
62. #63562C22semidirect
84. #4865D3semidirect
89. #4861D3semidirect
143. C3×ΓL(1,𝔽25)D4semidirect
187. C2×D24C2×D3semidirect
195. C2×ΓL(1,𝔽25)C2×D3semidirect
214. #895C2×D3semidirect
229. C3×#106C2×D3semidirect
230. C3×#106C2×D3semidirect
236. #818C2×D3semidirect
248. #809C2×D3semidirect
249. #809C2×D3semidirect
250. #808C2×D3semidirect
251. #807C2×D3semidirect
300. C32×C8C2×D4semidirect
303. C3×C3⋊C8C2×D4semidirect
446. ΓL(1,𝔽25)D12semidirect
458. C2×C3⋊D3AGL(1,ℤ/8)semidirect
519. #106D32semidirect
641. C3×C8C2×D12semidirect
642. C3×C8D3×D4semidirect
647. C3⋊C8C2×D12semidirect
792. C32#3055semidirect
844. C8D3×D12semidirect
900. C3#79211semidirect
901. C3#80864semidirect

Maximal subgroups

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

subgroupindex
C2×#637952
C2×#637912
#105946262
D3×#8952
#105925632
C3×#48652
C3×#48612
#105908442
#105908382
#105906072
#105905922
#105905882
#105905862
#105905092
#105905072
#808643
#792113