Finite Group Databasebeta

← #11866219

Subgroups — #11866219

Order 1152.

1122 conjugacy classes of subgroups.

The subgroup lattice has 909 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595235C211yesmaximal, characteristic, complemented
2C2×D3×#213C211yesmaximal, characteristic, complemented
3C2×#63794C211yesmaximal, characteristic, complemented
4#10594604C211yesmaximal, characteristic, complemented
5#10592485C211yesmaximal, characteristic, complemented
6C3×#4787C211yesmaximal, characteristic, complemented
7C3×#4770C211yesmaximal, characteristic, complemented
8#10591433C211yesmaximal, characteristic, complemented
9#10591432C211yesmaximal, characteristic, complemented
10#10590765C211yesmaximal, characteristic, complemented
11#10590750C211yesmaximal, characteristic, complemented
12#10590695C211yesmaximal, characteristic, complemented
13#10590610C211yesmaximal, characteristic, complemented
14#10590547C211yesmaximal, characteristic, complemented
15#10590540C211yesmaximal, characteristic, complemented
16#80536—31nomaximal
17#78944—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×D3×D12C2211yescharacteristic
20C2×#3799C2211yescharacteristic
21#64149C2211yescharacteristic, complemented
22C2×#3753C2211yescharacteristic
23C2×#3745C2211yescharacteristic, complemented
24#64102C2211yescharacteristic, complemented
25C3×#936C2211yescharacteristic, complemented
26C2×C3×#213C2211yescharacteristic
27C2×C3×#204C2211yescharacteristic, complemented
28C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
29C3×#893C2211yescharacteristic, complemented
30C3×#892C2211yescharacteristic
31#63977—21no—
32#63977—21no—
33#63958—21no—
34#63958—21no—
35D3×#213—24no—
36#63921—21no—
37D3×(C2×D3)⋊C4—21no—
38#63911C2211yescharacteristic, complemented
39C4×#626—21no—
40#63898C2211yescharacteristic, complemented
41#63894C2211yescharacteristic, complemented
42#63880—21no—
43#63863C2211yescharacteristic, complemented
44#63855C2211yescharacteristic
45C2×#3717C2211yescharacteristic, complemented
46C2×#3714C2211yescharacteristic
47C2×#3714C2211yescharacteristic, complemented
48C2×#3713C2211yescharacteristic
49C2×D3×C3⋊C8C2211yescharacteristic
50#63794—24no—
51C32×#102C2211yescharacteristic, complemented
52#63641C2211yescharacteristic, complemented
53#63636C2211yescharacteristic, complemented
54C3×#832C2211yescharacteristic, complemented
55C3×#821C2211yescharacteristic, complemented
56C3×Dic3⋊C8C2211yescharacteristic, complemented
57C3×#810C2211yescharacteristic, complemented
58C3×#809C2211yescharacteristic, complemented
59#63572C2211yescharacteristic, complemented
60Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
61#63565C2211yescharacteristic, complemented
62#63564C2211yescharacteristic, complemented
63#5805—31no—
64C22×#213—31no—
65C2×#914—31no—
66C2×D3×D8—31no—
67C2×#908—31no—
68#5674—31no—
69#5545—31no—
70#5521—31no—
71C3×#463—31no—
72C3×#418—31no—
73#5165—31no—
74#5150—31no—
75#5119—31no—
76#5057—31no—
77#5015—31no—
78#5002—31no—
79#4843—31no—
80#4839—31no—
81#4819—31no—
82#4804—31no—
83#4787—31no—
84#4787—31no—
85#4787—31no—
86#4787D311yescharacteristic, complemented
87#4786—31no—
88#4786—31no—
89#4786—31no—
90#4786—31no—
91#4786—31no—
92#4786—61no—
93#4770D311yescharacteristic, complemented
94C23×C3×D3—21no—
95C22×D32—21no—
96C2×C32×D4C2311yescharacteristic
97C2×#638—21no—
98C2×#638—21no—
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C4⋊(C3⋊D3)C2311yescharacteristic
101C2×C4×C3⋊D3—21no—
102C2×C3×#67—21no—
103C3×D3×D4—22no—
104C3×D3×D4—22no—
105C2×C3×D12C2311yescharacteristic
106C2×C3×D12C2311yescharacteristic
107C2×C3×C4×D3—21no—
108C2×C3×C4×D3C2311yescharacteristic
109C2×C3×Dic6C2311yescharacteristic
110C2×#626—21no—
111C2×#626—21no—
112C2×#626—21no—
113C2×#626—21no—
114C2×#624—21no—
115C2×#624—21no—
116C2×D3×Dic3—21no—
117D3×D12—22no—
118D3×D12D414yescomplemented
119#3799—22no—
120#3799—22no—
121C2×C32×C8C2311yescharacteristic
122C32×C4⋊C4C2311yescharacteristic
123#3753—22no—
124#3752—21no—
125C4×C3⋊Dic3C2311yescharacteristic
126C2×C3⋊(C3⋊C8)C2311yescharacteristic
127#3745—22no—
128C3×#217—21no—
129C3×#217—21no—
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×#204—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#3717—22no—
149#3714—22no—
150#3714—22no—
151#3713—22no—
152D3×C3⋊C8—22no—
153#3041—91noSylow
154C22×C3×D4—31no—
155C2×#239—31no—
156C2×D3×D4—31no—
157C2×D3×D4C2×D311yescharacteristic
158C2×#235—31no—
159C22×D12—31no—
160C2×C3×SD16—31no—
161C2×C3×D8—31no—
162C2×C3×M16—31no—
163C3×#124—31no—
164C3×C4×D4—31no—
165C3×#117—31no—
166#953—61no—
167#953—61no—
168#947—31no—
169C2×#215—31no—
170#940—31no—
171#940—31no—
172#940—31no—
173#940—61no—
174#938—61no—
175#938—61no—
176#936—31no—
177#936C2×D311yescharacteristic, complemented
178D4×Dic3—31no—
179C2×#213—31no—
180C2×#213—31no—
181C2×#213—31no—
182C2×#213—31no—
183C2×#213—31no—
184C2×#213—31no—
185C2×#213—61no—
186C2×#213—64no—
187C2×#213C2×D311yescharacteristic
188C4×#67—61no—
189C2×(C2×D3)⋊C4—61no—
190#926—31no—
191C22×C3⋊C8—31no—
192#914—64no—
193D3×D8—64no—
194#908—64no—
195C2×D24—31no—
196C2×D24—31no—
197C2×D24—31no—
198C2×D24—31no—
199C2×D24—61no—
200C2×#204—31no—
201C2×#204C2×D311yescharacteristic, complemented
202C2×ΓL(1,𝔽25)C2×D311yescharacteristic
203C2×D3×C8—31no—
204#893—31no—
205#893—31no—
206#893—31no—
207#893—31no—
208#893—61no—
209#893C2×D311yescharacteristic, complemented
210#892C2×D311yescharacteristic
211#884—61no—
212#884—61no—
213#882—61no—
214#882—61no—
215#67⋊C4—61no—
216D3×C22⋊C4—61no—
217D3×C22⋊C4—61no—
218D3×C22⋊C4—61no—
219#874—31no—
220C4×D12—31no—
221C4×D12—61no—
222C4×D12—61no—
223#872—31no—
224C3×C4⋊C8—31no—
225C3×#103—31no—
226C3×#102—21no—
227C3×#102—31no—
228C3×#102—31no—
229C3×#102—31no—
230C3×#102C2×D311yescharacteristic, complemented
231C3×#102C2×D311yescharacteristic, complemented
232#835—31no—
233#832C2×D311yescharacteristic, complemented
234#821—31no—
235#821C2×D311yescharacteristic, complemented
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#810C2×D311yescharacteristic, complemented
245#809—31no—
246#809—31no—
247#809—31no—
248#809—61no—
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
267#638—81no—
268#638—81no—
269C2×C3⋊Dic3C2×D411yescharacteristic
270C2×C3⋊Dic3C2×D411yescharacteristic
271C4⋊(C3⋊D3)—21no—
272C4⋊(C3⋊D3)—21no—
273C4⋊(C3⋊D3)—21no—
274C4⋊(C3⋊D3)C2×D412yes—
275C4×C3⋊D3—81no—
276C3×#67—42no—
277C2×C3×Dic3—21no—
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×D12C2×D412yes—
286C3×C4×D3—81no—
287C3×C4×D3C2×D412yes—
288C3×C4×D3#4112yes—
289C3×Dic6—21no—
290C3×Dic6—21no—
291#626—24no—
292#626—42no—
293#626—81no—
294#626—81no—
295#624—42no—
296#624—81no—
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—31no—
307#463—91no—
308#463—91no—
309#463—91no—
310#459—91no—
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×Q8—31no—
322C2×C3×D4—21no—
323C2×C3×D4—31no—
324C2×C3×D4—31no—
325C2×C3×D4—62no—
326C2×C3×D4—62no—
327C2×C3×D4—61no—
328C2×C3×D4C22×D311yescharacteristic
329C2×C3×D4C22×D311yescharacteristic
330C22×C3×C4—31no—
331C22×C3×C4—61no—
332C2×#67—21no—
333C2×#67—61no—
334C2×#67—61no—
335C2×#67—61no—
336C2×#67—61no—
337C2×#67—61no—
338C2×#67—61no—
339C2×#67—61no—
340C2×#67—61no—
341C2×#67—121no—
342C2×#67—121no—
343C22×Dic3—61no—
344#239—62no—
345#239—62no—
346D3×D4—22no—
347D3×D4—22no—
348D3×D4—34no—
349D3×D4—62no—
350#235—62no—
351#235—62no—
352C2×D12—31no—
353C2×D12—31no—
354C2×D12—34no—
355C2×D12—31no—
356C2×D12—31no—
357C2×D12—61no—
358C2×D12—61no—
359C2×D12—62no—
360C2×D12—61no—
361C2×D12—61no—
362C2×D12—61no—
363C2×D12—61no—
364C2×D12C22×D311yescharacteristic
365C2×D12C22×D311yescharacteristic
366C2×C4×D3—21no—
367C2×C4×D3—61no—
368C2×C4×D3—61no—
369C2×C4×D3—61no—
370C2×C4×D3—61no—
371C2×C4×D3—61no—
372C2×C4×D3—61no—
373C2×C4×D3—61no—
374C2×C4×D3—121no—
375C2×C4×D3C22×D311yescharacteristic
376C2×Dic6C22×D311yescharacteristic
377C3×SD16—62no—
378C3×D8—62no—
379C3×M16—62no—
380C2×C3×C8—21no—
381C2×C3×C8—31no—
382C2×C3×C8—31no—
383C2×C3×C8C22×D311yescharacteristic
384C2×C3×C8C22×D311yescharacteristic
385C3×C4⋊C4—21no—
386C3×C4⋊C4—31no—
387C3×C4⋊C4C22×D311yescharacteristic
388C3×C4⋊C4C22×D311yescharacteristic
389C3×C22⋊C4—61no—
390C3×C22⋊C4—61no—
391C3×C22⋊C4—61no—
392C3×C22⋊C4—61no—
393C3×C42—31no—
394C3×C42—61no—
395#217—21no—
396#217—21no—
397#217—31no—
398#217—31no—
399#217—61no—
400#217—61no—
401#217—61no—
402#215—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—62no—
440D24—62no—
441D24—62no—
442D24—62no—
443D24—122no—
444#204—22no—
445#204—62no—
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—41no—
456C2×C3⋊D3—41no—
457C2×C3⋊D3—41no—
458C2×C3×D3—21no—
459C2×C3×D3—21no—
460C2×C3×D3—22no—
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—21no—
475C3×Dic3—21no—
476C3×Dic3—41no—
477C3×Dic3—41no—
478C3×Dic3#12112yes—
479C2×#41—91no—
480C22×D4—31no—
481C22×D4—91no—
482AGL(1,ℤ/8)—184no—
483C2×SD16—31no—
484C2×SD16—91no—
485C2×D8—31no—
486C2×D8—91no—
487C2×D8—91no—
488C2×D8—91no—
489C2×D8—91no—
490C2×D8—91no—
491C2×D8—184no—
492C2×M16—31no—
493C22×C8—91no—
494#127—91no—
495#127—91no—
496#124—31no—
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—31no—
517#103—91no—
518#102—31no—
519#102—31no—
520#102—31no—
521#102—91no—
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—122no—
531C23×C3—241no—
532C23×C3—241no—
533C22×D3—21no—
534C22×D3—21no—
535C22×D3—42no—
536C22×D3—64no—
537C22×D3—61no—
538C22×D3—61no—
539C22×D3—64no—
540C22×D3—61no—
541C22×D3—61no—
542C22×D3—81no—
543C22×D3—81no—
544C22×D3—121no—
545C22×D3—121no—
546C22×D3—241no—
547C22×D3—241no—
548C22×D3—241no—
549C22×D3—241no—
550C22×D3D3×D411yescharacteristic
551C3×Q8—61no—
552C3×Q8—61no—
553C3×D4—21no—
554C3×D4—21no—
555C3×D4—21no—
556C3×D4—21no—
557C3×D4—32no—
558C3×D4—41no—
559C3×D4—41no—
560C3×D4—61no—
561C3×D4—61no—
562C3×D4—61no—
563C3×D4—122no—
564C2×C3×C4—21no—
565C2×C3×C4—21no—
566C2×C3×C4—21no—
567C2×C3×C4—31no—
568C2×C3×C4—32no—
569C2×C3×C4—32no—
570C2×C3×C4—31no—
571C2×C3×C4—31no—
572C2×C3×C4—41no—
573C2×C3×C4—61no—
574C2×C3×C4—61no—
575C2×C3×C4—241no—
576C2×C3×C4C23×D311yescharacteristic
577C2×C3×C4C23×D311yescharacteristic
578#67—42no—
579#67—64no—
580#67—122no—
581#67—241no—
582#67—241no—
583#67—241no—
584#67—241no—
585#67—241no—
586#67—241no—
587#67—242no—
588#67—242no—
589C2×Dic3—21no—
590C2×Dic3—21no—
591C2×Dic3—31no—
592C2×Dic3—31no—
593C2×Dic3—31no—
594C2×Dic3—31no—
595C2×Dic3—61no—
596C2×Dic3—61no—
597C2×Dic3—241no—
598C2×Dic3D3×D411yescharacteristic
599C2×Dic3D3×D411yescharacteristic
600C2×Dic3D3×D411yescharacteristic
601D12—21no—
602D12—21no—
603D12—21no—
604D12—32no—
605D12—32no—
606D12—62no—
607D12—64no—
608D12—61no—
609D12—61no—
610D12—61no—
611D12—61no—
612D12—61no—
613D12—61no—
614D12—121no—
615D12—121no—
616D12—121no—
617D12—122no—
618D12—241no—
619D12—241no—
620D12D3×D412yes—
621C4×D3—81no—
622C4×D3—122no—
623C4×D3—122no—
624C4×D3—241no—
625C4×D3—241no—
626C4×D3—241no—
627C4×D3—241no—
628C4×D3—242no—
629C4×D3—241no—
630C4×D3#23512yes—
631C4×D3D3×D412yes—
632Dic6—21no—
633Dic6—21no—
634C3×C8—21no—
635C3×C8—21no—
636C3×C8—41no—
637C3×C8—61no—
638C3×C8—61no—
639C3⋊C8—21no—
640C3⋊C8—21no—
641C3⋊C8—61no—
642C3⋊C8—61no—
643C3⋊C8—121no—
644C2×C32—81no—
645C2×C32C2×#12111yescharacteristic
646C2×C32#57611yescharacteristic
647C2×C32#57611yescharacteristic
648C3⋊D3—42no—
649C3⋊D3—81no—
650C3×D3—22no—
651C3×D3—42no—
652C3×D3—81no—
653C24—61no—
654C24—181no—
655#41—182no—
656#41—182no—
657C2×Q8—31no—
658C2×D4—31no—
659C2×D4—31no—
660C2×D4—62no—
661C2×D4—62no—
662C2×D4—61no—
663C2×D4—94no—
664C2×D4—91no—
665C2×D4—91no—
666C2×D4—182no—
667C2×D4—181no—
668C2×D4—181no—
669C2×D4—181no—
670C2×D4—181no—
671C2×D4—181no—
672C2×D4—181no—
673C2×D4C2×D3211yescharacteristic
674C22×C4—31no—
675C22×C4—61no—
676C22×C4—181no—
677C22×C4—181no—
678C22×C4—181no—
679C22×C4—181no—
680SD16—62no—
681SD16—182no—
682D8—62no—
683D8—182no—
684D8—182no—
685D8—182no—
686D8—182no—
687D8—182no—
688M16—62no—
689C2×C8—31no—
690C2×C8—31no—
691C2×C8—91no—
692C2×C8—182no—
693C2×C8C2×D3211yescharacteristic
694C4⋊C4—31no—
695C4⋊C4—91no—
696C4⋊C4—91no—
697C4⋊C4C2×D3211yescharacteristic
698C22⋊C4—61no—
699C22⋊C4—61no—
700C22⋊C4—61no—
701C22⋊C4—61no—
702C22⋊C4—91no—
703C22⋊C4—91no—
704C22⋊C4—181no—
705C22⋊C4—181no—
706C22⋊C4—181no—
707C22⋊C4—181no—
708C22⋊C4—181no—
709C42—31no—
710C42—61no—
711C42—91no—
712C22×C3—21no—
713C22×C3—32no—
714C22×C3—41no—
715C22×C3—41no—
716C22×C3—41no—
717C22×C3—41no—
718C22×C3—41no—
719C22×C3—41no—
720C22×C3—61no—
721C22×C3—61no—
722C22×C3—62no—
723C22×C3—81no—
724C22×C3—81no—
725C22×C3—81no—
726C22×C3—121no—
727C22×C3—121no—
728C22×C3—121no—
729C22×C3—121no—
730C22×C3—121no—
731C22×C3—244no—
732C22×C3C2×D3×D411yescharacteristic
733C22×C3C2×D3×D411yescharacteristic
734C2×D3—21no—
735C2×D3—21no—
736C2×D3—22no—
737C2×D3—41no—
738C2×D3—41no—
739C2×D3—41no—
740C2×D3—41no—
741C2×D3—41no—
742C2×D3—62no—
743C2×D3—62no—
744C2×D3—84no—
745C2×D3—122no—
746C2×D3—121no—
747C2×D3—121no—
748C2×D3—121no—
749C2×D3—121no—
750C2×D3—121no—
751C2×D3—121no—
752C2×D3—121no—
753C2×D3—121no—
754C2×D3—121no—
755C2×D3—121no—
756C2×D3—241no—
757C2×D3—241no—
758C2×D3—241no—
759C2×D3—241no—
760C2×D3—241no—
761C2×D3—244no—
762C2×D3—244no—
763C2×D3#88412yes—
764C3×C4—21no—
765C3×C4—21no—
766C3×C4—32no—
767C3×C4—41no—
768C3×C4—41no—
769C3×C4—61no—
770C3×C4—61no—
771C3×C4—81no—
772C3×C4—121no—
773C3×C4—121no—
774C3×C4C2×#23511yescharacteristic
775C3×C4C2×D3×D411yescharacteristic
776C3×C4C2×D3×D411yescharacteristic
777C3×C4D3×#4111yescharacteristic
778Dic3—21no—
779Dic3—21no—
780Dic3—41no—
781Dic3—41no—
782Dic3—62no—
783Dic3—61no—
784Dic3—61no—
785Dic3—61no—
786Dic3—61no—
787Dic3—121no—
788Dic3#88412yes—
789C32#304111yescharacteristic, complemented, Sylow
790C23—21no—
791C23—31no—
792C23—61no—
793C23—61no—
794C23—122no—
795C23—184no—
796C23—181no—
797C23—181no—
798C23—241no—
799C23—241no—
800C23—721no—
801C23—721no—
802Q8—61no—
803Q8—61no—
804D4—21no—
805D4—21no—
806D4—32no—
807D4—61no—
808D4—61no—
809D4—61no—
810D4—92no—
811D4—122no—
812D4—184no—
813D4—181no—
814D4—181no—
815D4—181no—
816D4—362no—
817D4—721no—
818D4—721no—
819D4—721no—
820D4—721no—
821C2×C4—21no—
822C2×C4—31no—
823C2×C4—32no—
824C2×C4—32no—
825C2×C4—31no—
826C2×C4—31no—
827C2×C4—61no—
828C2×C4—61no—
829C2×C4—91no—
830C2×C4—91no—
831C2×C4—241no—
832C2×C4—362no—
833C2×C4—721no—
834C2×C4—721no—
835C2×C4—721no—
836C2×C4C22×D3211yescharacteristic
837C8—21no—
838C8—61no—
839C8—61no—
840C8—181no—
841C2×C3—21no—
842C2×C3—21no—
843C2×C3—21no—
844C2×C3—62no—
845C2×C3—81no—
846C2×C3—81no—
847C2×C3—122no—
848C2×C3—161no—
849C2×C3—241no—
850C2×C3C2×#88411yescharacteristic
851C2×C3D3×#12111yescharacteristic
852C2×C3#576911yescharacteristic
853C2×C3#577411yescharacteristic
854C2×C3#577411yescharacteristic
855C2×C3#577411yescharacteristic
856D3—22no—
857D3—42no—
858D3—81no—
859D3—122no—
860D3—122no—
861D3—242no—
862D3—241no—
863D3—241no—
864D3—481no—
865C22—32no—
866C22—41no—
867C22—41no—
868C22—41no—
869C22—61no—
870C22—61no—
871C22—62no—
872C22—121no—
873C22—121no—
874C22—121no—
875C22—121no—
876C22—121no—
877C22—182no—
878C22—244no—
879C22—361no—
880C22—361no—
881C22—361no—
882C22—361no—
883C22—361no—
884C22—724no—
885C22D32×D411yescharacteristic
886C4—32no—
887C4—41no—
888C4—61no—
889C4—61no—
890C4—121no—
891C4—121no—
892C4—181no—
893C4—181no—
894C4D3×#23511yescharacteristic
895C4D32×D411yescharacteristic
896C3—21no—
897C3#7894411yescharacteristic, complemented
898C3#8053611yescharacteristic, complemented
899C2—62no—
900C2—81no—
901C2—122no—
902C2—241no—
903C2—362no—
904C2—721no—
905C2D3×#88411yescharacteristic
906C2#1059473511yescharacteristic
907C2#1059475511yescharacteristic
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. #10595235C2semidirect
2. C2×D3×#213C2semidirect
3. C2×#63794C2semidirect
4. #10594604C2semidirect
5. #10592485C2semidirect
6. C3×#4787C2semidirect
7. C3×#4770C2semidirect
8. #10591433C2semidirect
9. #10591432C2semidirect
10. #10590765C2semidirect
11. #10590750C2semidirect
12. #10590695C2semidirect
13. #10590610C2semidirect
14. #10590547C2semidirect
15. #10590540C2semidirect
21. #64149C22semidirect
23. C2×#3745C22semidirect
24. #64102C22semidirect
25. C3×#936C22semidirect
27. C2×C3×#204C22semidirect
29. C3×#893C22semidirect
38. #63911C22semidirect
40. #63898C22semidirect
41. #63894C22semidirect
43. #63863C22semidirect
45. C2×#3717C22semidirect
47. C2×#3714C22semidirect
51. C32×#102C22semidirect
52. #63641C22semidirect
53. #63636C22semidirect
54. C3×#832C22semidirect
55. C3×#821C22semidirect
56. C3×Dic3⋊C8C22semidirect
57. C3×#810C22semidirect
58. C3×#809C22semidirect
59. #63572C22semidirect
60. Dic3⋊(C3⋊C8)C22semidirect
61. #63565C22semidirect
62. #63564C22semidirect
86. #4787D3semidirect
93. #4770D3semidirect
118. D3×D12D4semidirect
177. #936C2×D3semidirect
201. C2×#204C2×D3semidirect
209. #893C2×D3semidirect
230. C3×#102C2×D3semidirect
231. C3×#102C2×D3semidirect
233. #832C2×D3semidirect
235. #821C2×D3semidirect
242. Dic3⋊C8C2×D3semidirect
244. #810C2×D3semidirect
249. #809C2×D3semidirect
523. #102D32semidirect
789. C32#3041semidirect
897. C3#78944semidirect
898. C3#80536semidirect

Maximal subgroups

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

subgroupindex
#105952352
C2×D3×#2132
C2×#637942
#105946042
#105924852
C3×#47872
C3×#47702
#105914332
#105914322
#105907652
#105907502
#105906952
#105906102
#105905472
#105905402
#805363
#789443