Finite Group Databasebeta

← #11866221

Subgroups — #11866221

Order 1152.

1114 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595233C211yesmaximal, characteristic, complemented
2C2×D3×#213C211yesmaximal, characteristic, complemented
3C2×#63795C211yesmaximal, characteristic, complemented
4#10594604C211yesmaximal, characteristic, complemented
5#10592486C211yesmaximal, characteristic, complemented
6C3×#4786C211yesmaximal, characteristic, complemented
7C3×#4770C211yesmaximal, characteristic, complemented
8#10591434C211yesmaximal, characteristic, complemented
9#10591429C211yesmaximal, characteristic, complemented
10#10590860C211yesmaximal, characteristic, complemented
11#10590749C211yesmaximal, characteristic, complemented
12#10590695C211yesmaximal, characteristic, complemented
13#10590608C211yesmaximal, characteristic, complemented
14#10590551C211yesmaximal, characteristic, complemented
15#10590530C211yesmaximal, characteristic, complemented
16#80334—31nomaximal
17#78944—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×D3×D12C2211yescharacteristic
20C2×#3795C2211yescharacteristic
21#64145C2211yescharacteristic, complemented
22C2×#3753C2211yescharacteristic
23C2×#3744C2211yescharacteristic, complemented
24#64102C2211yescharacteristic, complemented
25C3×#940C2211yescharacteristic, complemented
26C2×C3×#213C2211yescharacteristic
27C2×C3×D24C2211yescharacteristic, complemented
28C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
29C3×#893C2211yescharacteristic, complemented
30C3×#892C2211yescharacteristic
31#63976—21no—
32#63976—21no—
33#63970—21no—
34#63970—21no—
35D3×#213—24no—
36#63921—21no—
37D3×(C2×D3)⋊C4—21no—
38#63914C2211yescharacteristic, complemented
39C4×#626—21no—
40#63898C2211yescharacteristic, complemented
41#63894C2211yescharacteristic, complemented
42#63880—21no—
43#63860C2211yescharacteristic, complemented
44#63855C2211yescharacteristic
45C2×#3716C2211yescharacteristic, complemented
46C2×#3714C2211yescharacteristic
47C2×#3714C2211yescharacteristic, complemented
48C2×#3713C2211yescharacteristic
49C2×D3×C3⋊C8C2211yescharacteristic
50#63795—24no—
51C32×#102C2211yescharacteristic, complemented
52#63641C2211yescharacteristic, complemented
53#63637C2211yescharacteristic, complemented
54C3×#832C2211yescharacteristic, complemented
55C3×#821C2211yescharacteristic, complemented
56C3×Dic3⋊C8C2211yescharacteristic, complemented
57C3×#809C2211yescharacteristic, complemented
58C3×#809C2211yescharacteristic, complemented
59#63572C2211yescharacteristic, complemented
60Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
61#63567C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63#5805—31no—
64C22×#213—31no—
65C2×#911—31no—
66C2×D3×D8—31no—
67C2×#908—31no—
68#5715—31no—
69#5545—31no—
70#5521—31no—
71C3×#459—31no—
72C3×#418—31no—
73#5153—31no—
74#5150—31no—
75#5119—31no—
76#5072—31no—
77#5016—31no—
78#5002—31no—
79#4844—31no—
80#4839—31no—
81#4787—31no—
82#4787—31no—
83#4787—31no—
84#4787—31no—
85#4787—31no—
86#4787—61no—
87#4786—31no—
88#4786—31no—
89#4786—31no—
90#4786—31no—
91#4786D311yescharacteristic, complemented
92#4772—31no—
93#4770D311yescharacteristic, complemented
94C23×C3×D3—21no—
95C22×D32—21no—
96C2×C32×D4C2311yescharacteristic
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4×C3⋊D3—21no—
99C2×#634C2311yescharacteristic
100C2×C3×#67—21no—
101C2×C3×#67—21no—
102C2×C3×#67—21no—
103C3×D3×D4—22no—
104C3×D3×D4—22no—
105C2×C3×D12C2311yescharacteristic
106C2×C3×D12C2311yescharacteristic
107C2×C3×D12C2311yescharacteristic
108C2×C3×C4×D3—21no—
109C2×C3×C4×D3C2311yescharacteristic
110C2×#626—21no—
111C2×#625—21no—
112C2×#625—21no—
113C2×#625—21no—
114C2×#624—21no—
115C2×D3×Dic3—21no—
116C2×D3×Dic3—21no—
117D3×D12—22no—
118D3×D12D414yescomplemented
119#3795—22no—
120#3795—22no—
121C2×C32×C8C2311yescharacteristic
122C32×C4⋊C4C2311yescharacteristic
123#3757—21no—
124#3757—21no—
125#3753—22no—
126#3752—21no—
127C4×C3⋊Dic3C2311yescharacteristic
128C2×C3⋊(C3⋊C8)C2311yescharacteristic
129#3744—22no—
130C3×#213—22no—
131C3×(C2×D3)⋊C4—21no—
132C3×(C2×D3)⋊C4—21no—
133C3×C4⋊Dic3C2311yescharacteristic
134C3×C4×Dic3—21no—
135C3×C4×Dic3C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138C3×D24—22no—
139C3×ΓL(1,𝔽25)—22no—
140Dic3⋊Dic3D411yescharacteristic
141Dic3⋊Dic3D411yescharacteristic
142#3722—21no—
143(C2×D3)⋊Dic3—21no—
144(C2×D3)⋊Dic3—21no—
145(C2×D3)⋊Dic3—21no—
146(C2×D3)⋊Dic3D411yescharacteristic
147(C2×D3)⋊Dic3D411yescharacteristic
148#3716—22no—
149#3714—22no—
150#3714—22no—
151#3713—22no—
152D3×C3⋊C8—22no—
153#3041—91noSylow
154C22×C3×D4—31no—
155C2×#237—31no—
156C2×D3×D4—31no—
157C2×D3×D4C2×D311yescharacteristic
158C2×#235—31no—
159C22×D12—31no—
160C2×C3×D8—31no—
161C2×C3×D8—31no—
162C2×C3×M16—31no—
163C3×#127—31no—
164C3×C4×D4—31no—
165C3×#117—31no—
166#953—61no—
167#953—61no—
168#940—31no—
169#940—31no—
170#940C2×D311yescharacteristic, complemented
171#939—61no—
172#939—61no—
173#938—61no—
174#938—61no—
175#937—61no—
176#937—61no—
177#936—31no—
178#936—31no—
179#936—31no—
180#936—61no—
181D4×Dic3—31no—
182C2×#214—31no—
183C2×#213—31no—
184C2×#213—31no—
185C2×#213—31no—
186C2×#213—31no—
187C2×#213—31no—
188C2×#213—31no—
189C2×#213—61no—
190C2×#213—64no—
191C2×#213C2×D311yescharacteristic
192C4×#67—61no—
193C2×(C2×D3)⋊C4—61no—
194#926—31no—
195C22×C3⋊C8—31no—
196#911—64no—
197D3×D8—64no—
198#908—64no—
199C2×D24—31no—
200C2×D24—31no—
201C2×D24C2×D311yescharacteristic, complemented
202C2×#204—31no—
203C2×#204—31no—
204C2×#204—31no—
205C2×#204—61no—
206C2×ΓL(1,𝔽25)C2×D311yescharacteristic
207C2×D3×C8—31no—
208#893—31no—
209#893—31no—
210#893—31no—
211#893—31no—
212#893—61no—
213#893C2×D311yescharacteristic, complemented
214#892C2×D311yescharacteristic
215#67⋊C4—61no—
216D3×C22⋊C4—61no—
217D3×C22⋊C4—61no—
218D3×C22⋊C4—61no—
219#875—31no—
220C4×D12—31no—
221C4×D12—61no—
222C4×D12—61no—
223#872—31no—
224C3×C4⋊C8—31no—
225C3×#102—21no—
226C3×#102—31no—
227C3×#102—31no—
228C3×#102—31no—
229C3×#102—31no—
230C3×#102C2×D311yescharacteristic, complemented
231C3×#102C2×D311yescharacteristic, complemented
232#832—31no—
233#832C2×D311yescharacteristic, complemented
234#821C2×D311yescharacteristic, complemented
235#816—31no—
236Dic3⋊C8—31no—
237Dic3⋊C8—31no—
238Dic3⋊C8—31no—
239Dic3⋊C8—31no—
240Dic3⋊C8—31no—
241Dic3⋊C8—61no—
242Dic3⋊C8C2×D311yescharacteristic, complemented
243#810—31no—
244#810—31no—
245#810—31no—
246#810—61no—
247#809—31no—
248#809C2×D311yescharacteristic, complemented
249#809C2×D311yescharacteristic, complemented
250C4⋊(C3⋊C8)—31no—
251C23×C32—21no—
252C22×C3⋊D3—21no—
253C22×C3×D3—21no—
254C22×C3×D3—21no—
255C22×C3×D3—21no—
256C22×C3×D3—42no—
257C22×C3×D3—81no—
258C22×C3×D3—81no—
259C22×C3×D3C2×D411yescharacteristic
260C2×D32—24no—
261C2×D32—81no—
262C2×D32—81no—
263C32×D4—21no—
264C32×D4—21no—
265C2×C32×C4—21no—
266C2×C32×C4C2411yescharacteristic
267C2×C3⋊Dic3—21no—
268C2×C3⋊Dic3C2×D411yescharacteristic
269C2×C3⋊Dic3C2×D411yescharacteristic
270C4⋊(C3⋊D3)—21no—
271C4⋊(C3⋊D3)C2×D412yes—
272C4×C3⋊D3—81no—
273#634—21no—
274#634—21no—
275C3×#67—42no—
276C3×#67—81no—
277C3×#67—81no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3C2×D411yescharacteristic
280C2×C3×Dic3C2×D411yescharacteristic
281C2×C3×Dic3C2×D411yescharacteristic
282C3×D12—21no—
283C3×D12—21no—
284C3×D12—21no—
285C3×D12—21no—
286C3×D12—21no—
287C3×D12C2×D412yes—
288C3×C4×D3—81no—
289C3×C4×D3C2×D412yes—
290C3×C4×D3#4112yes—
291#626—24no—
292#625—42no—
293#625—81no—
294#625—81no—
295#624—81no—
296D3×Dic3—42no—
297D3×Dic3—81no—
298C32×C8—21no—
299C3⋊(C3⋊C8)—21no—
300C3×C3⋊C8—21no—
301C3×C3⋊C8—21no—
302C2×AGL(1,ℤ/8)—91no—
303C22×D8—91no—
304#535—91no—
305#518—91no—
306#463—91no—
307#463—91no—
308#463—91no—
309#463—91no—
310#459—31no—
311#459—91no—
312#459—91no—
313#459—91no—
314#424—91no—
315#418—31no—
316#416—91no—
317C24×C3—61no—
318C23×D3—21no—
319C23×D3—61no—
320C23×D3—61no—
321C2×C3×D4—21no—
322C2×C3×D4—31no—
323C2×C3×D4—31no—
324C2×C3×D4—31no—
325C2×C3×D4—62no—
326C2×C3×D4—62no—
327C2×C3×D4—61no—
328C2×C3×D4—61no—
329C2×C3×D4—61no—
330C2×C3×D4C22×D311yescharacteristic
331C2×C3×D4C22×D311yescharacteristic
332C22×C3×C4—31no—
333C22×C3×C4—61no—
334C2×#67—21no—
335C2×#67—21no—
336C2×#67—21no—
337C2×#67—61no—
338C2×#67—61no—
339C2×#67—61no—
340C2×#67—61no—
341C2×#67—61no—
342C2×#67—61no—
343C2×#67—61no—
344C22×Dic3—61no—
345C22×Dic3—61no—
346#237—62no—
347#237—62no—
348D3×D4—22no—
349D3×D4—22no—
350D3×D4—34no—
351D3×D4—62no—
352#235—62no—
353#235—62no—
354C2×D12—31no—
355C2×D12—31no—
356C2×D12—34no—
357C2×D12—61no—
358C2×D12—62no—
359C2×D12—61no—
360C2×D12C22×D311yescharacteristic
361C2×D12C22×D311yescharacteristic
362C2×D12C22×D311yescharacteristic
363C2×C4×D3—21no—
364C2×C4×D3—61no—
365C2×C4×D3—61no—
366C2×C4×D3—61no—
367C2×C4×D3—61no—
368C2×C4×D3—61no—
369C2×C4×D3—61no—
370C2×C4×D3—121no—
371C2×C4×D3C22×D311yescharacteristic
372C2×Dic6—31no—
373C2×Dic6—31no—
374C2×Dic6—61no—
375C3×D8—62no—
376C3×D8—62no—
377C3×M16—62no—
378C2×C3×C8—21no—
379C2×C3×C8—31no—
380C2×C3×C8—31no—
381C2×C3×C8C22×D311yescharacteristic
382C2×C3×C8C22×D311yescharacteristic
383C3×C4⋊C4—21no—
384C3×C4⋊C4—31no—
385C3×C4⋊C4C22×D311yescharacteristic
386C3×C4⋊C4C22×D311yescharacteristic
387C3×C22⋊C4—61no—
388C3×C22⋊C4—61no—
389C3×C42—31no—
390C3×C42—61no—
391#217—31no—
392#217—31no—
393#217—61no—
394#217—61no—
395#217—61no—
396#217—61no—
397#217—61no—
398#217—61no—
399#217—61no—
400#217—121no—
401#217—121no—
402#214—62no—
403#213—22no—
404#213—62no—
405#213—62no—
406#213—62no—
407#213—62no—
408#213—62no—
409#213—62no—
410#213—122no—
411(C2×D3)⋊C4—21no—
412(C2×D3)⋊C4—21no—
413(C2×D3)⋊C4—31no—
414(C2×D3)⋊C4—31no—
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—121no—
423C4⋊Dic3—31no—
424C4⋊Dic3—31no—
425C4⋊Dic3C22×D311yescharacteristic
426Dic3⋊C4—31no—
427Dic3⋊C4—31no—
428C4×Dic3—21no—
429C4×Dic3—31no—
430C4×Dic3—31no—
431C4×Dic3—61no—
432C4×Dic3C22×D311yescharacteristic
433C2×C3⋊C8—31no—
434C2×C3⋊C8—31no—
435C2×C3⋊C8—61no—
436C2×C3⋊C8—62no—
437C2×C3⋊C8C22×D311yescharacteristic
438C2×C3⋊C8C22×D311yescharacteristic
439D24—22no—
440D24—62no—
441D24—62no—
442#204—62no—
443#204—62no—
444#204—62no—
445#204—122no—
446ΓL(1,𝔽25)—22no—
447D3×C8—62no—
448C22×C32—41no—
449C22×C32—41no—
450C22×C32—41no—
451C22×C32C22×D411yescharacteristic
452C2×C3⋊D3—22no—
453C2×C3⋊D3—41no—
454C2×C3⋊D3—41no—
455C2×C3×D3—21no—
456C2×C3×D3—21no—
457C2×C3×D3—22no—
458C2×C3×D3—41no—
459C2×C3×D3—41no—
460C2×C3×D3—41no—
461C2×C3×D3—41no—
462C2×C3×D3—41no—
463C2×C3×D3—41no—
464C2×C3×D3—41no—
465C2×C3×D3—41no—
466C2×C3×D3—84no—
467C2×C3×D3#12112yes—
468D32—84no—
469C32×C4—41no—
470C32×C4C22×D411yescharacteristic
471C32×C4C2×#4111yescharacteristic
472C3⋊Dic3—21no—
473C3⋊Dic3—21no—
474C3⋊Dic3—41no—
475C3×Dic3—21no—
476C3×Dic3—21no—
477C3×Dic3—41no—
478C3×Dic3#12112yes—
479C2×#41—91no—
480C22×D4—31no—
481C22×D4—91no—
482AGL(1,ℤ/8)—184no—
483C2×SD16—91no—
484C2×SD16—91no—
485C2×D8—31no—
486C2×D8—31no—
487C2×D8—91no—
488C2×D8—91no—
489C2×D8—91no—
490C2×D8—91no—
491C2×D8—184no—
492C2×M16—31no—
493C22×C8—91no—
494#127—31no—
495#127—91no—
496#124—91no—
497#124—91no—
498#121—181no—
499#121—181no—
500#120—181no—
501#120—181no—
502C4×D4—31no—
503C4×D4—91no—
504C4×D4—91no—
505C4×D4—91no—
506C4×D4—181no—
507C4×D4—181no—
508#117—31no—
509#117—91no—
510C2×C22⋊C4—181no—
511C2×C22⋊C4—181no—
512C4⋊C8—31no—
513C4⋊C8—91no—
514C4⋊C8—91no—
515C4⋊C8—91no—
516#103—91no—
517#103—91no—
518#102—31no—
519#102—31no—
520#102—31no—
521#102—31no—
522#102—91no—
523#102D3211yescharacteristic, complemented
524C23×C3—21no—
525C23×C3—21no—
526C23×C3—31no—
527C23×C3—41no—
528C23×C3—61no—
529C23×C3—61no—
530C23×C3—61no—
531C23×C3—122no—
532C23×C3—241no—
533C23×C3—241no—
534C22×D3—21no—
535C22×D3—21no—
536C22×D3—21no—
537C22×D3—42no—
538C22×D3—64no—
539C22×D3—61no—
540C22×D3—61no—
541C22×D3—64no—
542C22×D3—81no—
543C22×D3—81no—
544C22×D3—121no—
545C22×D3—241no—
546C22×D3—241no—
547C22×D3—241no—
548C22×D3—241no—
549C22×D3D3×D411yescharacteristic
550C3×D4—21no—
551C3×D4—21no—
552C3×D4—21no—
553C3×D4—21no—
554C3×D4—32no—
555C3×D4—41no—
556C3×D4—41no—
557C3×D4—61no—
558C3×D4—61no—
559C3×D4—61no—
560C3×D4—61no—
561C3×D4—61no—
562C3×D4—122no—
563C3×D4—241no—
564C3×D4—241no—
565C2×C3×C4—21no—
566C2×C3×C4—21no—
567C2×C3×C4—21no—
568C2×C3×C4—31no—
569C2×C3×C4—32no—
570C2×C3×C4—32no—
571C2×C3×C4—31no—
572C2×C3×C4—31no—
573C2×C3×C4—41no—
574C2×C3×C4—61no—
575C2×C3×C4—241no—
576C2×C3×C4C23×D311yescharacteristic
577C2×C3×C4C23×D311yescharacteristic
578#67—42no—
579#67—64no—
580#67—81no—
581#67—81no—
582#67—122no—
583#67—122no—
584#67—241no—
585#67—241no—
586#67—241no—
587#67—241no—
588C2×Dic3—21no—
589C2×Dic3—31no—
590C2×Dic3—31no—
591C2×Dic3—31no—
592C2×Dic3—31no—
593C2×Dic3—61no—
594C2×Dic3—61no—
595C2×Dic3—61no—
596C2×Dic3—61no—
597C2×Dic3—121no—
598C2×Dic3—122no—
599C2×Dic3—241no—
600C2×Dic3D3×D411yescharacteristic
601C2×Dic3D3×D411yescharacteristic
602C2×Dic3D3×D411yescharacteristic
603D12—21no—
604D12—21no—
605D12—21no—
606D12—21no—
607D12—21no—
608D12—32no—
609D12—32no—
610D12—62no—
611D12—64no—
612D12—61no—
613D12—61no—
614D12—121no—
615D12D3×D412yes—
616C4×D3—81no—
617C4×D3—122no—
618C4×D3—241no—
619C4×D3—241no—
620C4×D3—241no—
621C4×D3—241no—
622C4×D3—241no—
623C4×D3—242no—
624C4×D3#23512yes—
625C4×D3D3×D412yes—
626Dic6—61no—
627Dic6—61no—
628Dic6—61no—
629Dic6—61no—
630Dic6—121no—
631Dic6—121no—
632C3×C8—21no—
633C3×C8—21no—
634C3×C8—41no—
635C3×C8—61no—
636C3×C8—61no—
637C3⋊C8—21no—
638C3⋊C8—21no—
639C3⋊C8—61no—
640C3⋊C8—61no—
641C3⋊C8—121no—
642C2×C32—81no—
643C2×C32C2×#12111yescharacteristic
644C2×C32#57611yescharacteristic
645C2×C32#57611yescharacteristic
646C3⋊D3—42no—
647C3×D3—22no—
648C3×D3—42no—
649C3×D3—81no—
650C3×D3—81no—
651C24—61no—
652C24—181no—
653#41—182no—
654#41—182no—
655C2×Q8—91no—
656C2×D4—31no—
657C2×D4—31no—
658C2×D4—31no—
659C2×D4—62no—
660C2×D4—62no—
661C2×D4—61no—
662C2×D4—61no—
663C2×D4—61no—
664C2×D4—94no—
665C2×D4—91no—
666C2×D4—182no—
667C2×D4—181no—
668C2×D4—181no—
669C2×D4—181no—
670C2×D4—181no—
671C2×D4C2×D3211yescharacteristic
672C22×C4—31no—
673C22×C4—61no—
674C22×C4—181no—
675C22×C4—181no—
676C22×C4—181no—
677C22×C4—181no—
678SD16—182no—
679SD16—182no—
680D8—62no—
681D8—62no—
682D8—182no—
683D8—182no—
684D8—182no—
685D8—182no—
686M16—62no—
687C2×C8—31no—
688C2×C8—31no—
689C2×C8—91no—
690C2×C8—182no—
691C2×C8C2×D3211yescharacteristic
692C4⋊C4—31no—
693C4⋊C4—91no—
694C4⋊C4—91no—
695C4⋊C4C2×D3211yescharacteristic
696C22⋊C4—61no—
697C22⋊C4—61no—
698C22⋊C4—91no—
699C22⋊C4—91no—
700C22⋊C4—181no—
701C22⋊C4—181no—
702C22⋊C4—181no—
703C22⋊C4—181no—
704C22⋊C4—181no—
705C22⋊C4—181no—
706C22⋊C4—181no—
707C42—31no—
708C42—61no—
709C42—91no—
710C22×C3—21no—
711C22×C3—32no—
712C22×C3—41no—
713C22×C3—41no—
714C22×C3—41no—
715C22×C3—41no—
716C22×C3—41no—
717C22×C3—41no—
718C22×C3—61no—
719C22×C3—61no—
720C22×C3—62no—
721C22×C3—81no—
722C22×C3—81no—
723C22×C3—81no—
724C22×C3—121no—
725C22×C3—121no—
726C22×C3—121no—
727C22×C3—121no—
728C22×C3—121no—
729C22×C3—121no—
730C22×C3—121no—
731C22×C3—121no—
732C22×C3—244no—
733C22×C3C2×D3×D411yescharacteristic
734C22×C3C2×D3×D411yescharacteristic
735C2×D3—21no—
736C2×D3—21no—
737C2×D3—22no—
738C2×D3—41no—
739C2×D3—41no—
740C2×D3—41no—
741C2×D3—41no—
742C2×D3—41no—
743C2×D3—41no—
744C2×D3—41no—
745C2×D3—41no—
746C2×D3—62no—
747C2×D3—62no—
748C2×D3—84no—
749C2×D3—122no—
750C2×D3—121no—
751C2×D3—121no—
752C2×D3—121no—
753C2×D3—121no—
754C2×D3—241no—
755C2×D3—241no—
756C2×D3—244no—
757C2×D3—244no—
758C2×D3#88412yes—
759C3×C4—21no—
760C3×C4—21no—
761C3×C4—32no—
762C3×C4—41no—
763C3×C4—41no—
764C3×C4—61no—
765C3×C4—61no—
766C3×C4—81no—
767C3×C4—121no—
768C3×C4C2×#23511yescharacteristic
769C3×C4C2×D3×D411yescharacteristic
770C3×C4C2×D3×D411yescharacteristic
771C3×C4D3×#4111yescharacteristic
772Dic3—21no—
773Dic3—21no—
774Dic3—41no—
775Dic3—61no—
776Dic3—61no—
777Dic3—61no—
778Dic3—61no—
779Dic3—121no—
780Dic3—121no—
781Dic3—121no—
782Dic3—121no—
783Dic3—241no—
784Dic3#88412yes—
785C32#304111yescharacteristic, complemented, Sylow
786C23—21no—
787C23—31no—
788C23—61no—
789C23—61no—
790C23—61no—
791C23—122no—
792C23—184no—
793C23—181no—
794C23—241no—
795C23—241no—
796C23—721no—
797C23—721no—
798Q8—181no—
799Q8—181no—
800D4—21no—
801D4—21no—
802D4—32no—
803D4—61no—
804D4—61no—
805D4—61no—
806D4—61no—
807D4—61no—
808D4—92no—
809D4—122no—
810D4—184no—
811D4—181no—
812D4—241no—
813D4—241no—
814D4—362no—
815D4—721no—
816D4—721no—
817C2×C4—21no—
818C2×C4—31no—
819C2×C4—32no—
820C2×C4—32no—
821C2×C4—31no—
822C2×C4—31no—
823C2×C4—61no—
824C2×C4—91no—
825C2×C4—91no—
826C2×C4—181no—
827C2×C4—241no—
828C2×C4—362no—
829C2×C4—721no—
830C2×C4—721no—
831C2×C4—721no—
832C2×C4C22×D3211yescharacteristic
833C8—21no—
834C8—61no—
835C8—61no—
836C8—181no—
837C2×C3—21no—
838C2×C3—21no—
839C2×C3—21no—
840C2×C3—62no—
841C2×C3—81no—
842C2×C3—81no—
843C2×C3—122no—
844C2×C3—161no—
845C2×C3—241no—
846C2×C3—241no—
847C2×C3C2×#88411yescharacteristic
848C2×C3D3×#12111yescharacteristic
849C2×C3#575711yescharacteristic
850C2×C3#577411yescharacteristic
851C2×C3#577411yescharacteristic
852C2×C3#577411yescharacteristic
853D3—22no—
854D3—42no—
855D3—81no—
856D3—81no—
857D3—122no—
858D3—122no—
859D3—242no—
860C22—32no—
861C22—41no—
862C22—41no—
863C22—41no—
864C22—61no—
865C22—61no—
866C22—62no—
867C22—121no—
868C22—121no—
869C22—121no—
870C22—121no—
871C22—121no—
872C22—121no—
873C22—121no—
874C22—121no—
875C22—182no—
876C22—244no—
877C22—361no—
878C22—361no—
879C22—724no—
880C22D32×D411yescharacteristic
881C4—32no—
882C4—41no—
883C4—61no—
884C4—61no—
885C4—121no—
886C4—181no—
887C4—181no—
888C4—361no—
889C4D3×#23511yescharacteristic
890C4D32×D411yescharacteristic
891C3—21no—
892C3#7894411yescharacteristic, complemented
893C3#8033411yescharacteristic, complemented
894C2—62no—
895C2—81no—
896C2—122no—
897C2—241no—
898C2—241no—
899C2—362no—
900C2D3×#88411yescharacteristic
901C2#1059473211yescharacteristic
902C2#1059475011yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
hypercenter#102D32
hypocenterC32#3041
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
1. #10595233C2semidirect
2. C2×D3×#213C2semidirect
3. C2×#63795C2semidirect
4. #10594604C2semidirect
5. #10592486C2semidirect
6. C3×#4786C2semidirect
7. C3×#4770C2semidirect
8. #10591434C2semidirect
9. #10591429C2semidirect
10. #10590860C2semidirect
11. #10590749C2semidirect
12. #10590695C2semidirect
13. #10590608C2semidirect
14. #10590551C2semidirect
15. #10590530C2semidirect
21. #64145C22semidirect
23. C2×#3744C22semidirect
24. #64102C22semidirect
25. C3×#940C22semidirect
27. C2×C3×D24C22semidirect
29. C3×#893C22semidirect
38. #63914C22semidirect
40. #63898C22semidirect
41. #63894C22semidirect
43. #63860C22semidirect
45. C2×#3716C22semidirect
47. C2×#3714C22semidirect
51. C32×#102C22semidirect
52. #63641C22semidirect
53. #63637C22semidirect
54. C3×#832C22semidirect
55. C3×#821C22semidirect
56. C3×Dic3⋊C8C22semidirect
57. C3×#809C22semidirect
58. C3×#809C22semidirect
59. #63572C22semidirect
60. Dic3⋊(C3⋊C8)C22semidirect
61. #63567C22semidirect
62. #63562C22semidirect
91. #4786D3semidirect
93. #4770D3semidirect
118. D3×D12D4semidirect
170. #940C2×D3semidirect
201. C2×D24C2×D3semidirect
213. #893C2×D3semidirect
230. C3×#102C2×D3semidirect
231. C3×#102C2×D3semidirect
233. #832C2×D3semidirect
234. #821C2×D3semidirect
242. Dic3⋊C8C2×D3semidirect
248. #809C2×D3semidirect
249. #809C2×D3semidirect
523. #102D32semidirect
785. C32#3041semidirect
892. C3#78944semidirect
893. C3#80334semidirect

Maximal subgroups

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

subgroupindex
#105952332
C2×D3×#2132
C2×#637952
#105946042
#105924862
C3×#47862
C3×#47702
#105914342
#105914292
#105908602
#105907492
#105906952
#105906082
#105905512
#105905302
#803343
#789443