Finite Group Databasebeta

← #11866220

Subgroups — #11866220

Order 1152.

1147 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#10595168C211yesmaximal, characteristic, complemented
2C2×#63926C211yesmaximal, characteristic, complemented
3C2×#63798C211yesmaximal, characteristic, complemented
4#10594606C211yesmaximal, characteristic, complemented
5#10592469C211yesmaximal, characteristic, complemented
6C3×#4787C211yesmaximal, characteristic, complemented
7C3×#4786C211yesmaximal, characteristic, complemented
8#10591431C211yesmaximal, characteristic, complemented
9#10591428C211yesmaximal, characteristic, complemented
10#10590754C211yesmaximal, characteristic, complemented
11#10590753C211yesmaximal, characteristic, complemented
12#10590702C211yesmaximal, characteristic, complemented
13#10590611C211yesmaximal, characteristic, complemented
14#10590547C211yesmaximal, characteristic, complemented
15#10590534C211yesmaximal, characteristic, complemented
16#80536—31nomaximal
17#80334—31nomaximal
18C2×D4×C3⋊D3C2211yescharacteristic
19C2×#3802C2211yescharacteristic
20C2×#3796C2211yescharacteristic
21C2×#3743C2211yescharacteristic
22#64101C2211yescharacteristic
23C3×#940C2211yescharacteristic, complemented
24C3×#936C2211yescharacteristic, complemented
25C2×C3×#213C2211yescharacteristic
26C2×C3×#213C2211yescharacteristic
27C2×C3×D24C2211yescharacteristic, complemented
28C2×C3×#204C2211yescharacteristic, complemented
29C3×#893C2211yescharacteristic, complemented
30C3×#893C2211yescharacteristic, complemented
31#63981—21no—
32#63981—21no—
33#63971—21no—
34#63971—21no—
35#63926—24no—
36D3×(C2×D3)⋊C4—21no—
37D3×(C2×D3)⋊C4—21no—
38#63911C2211yescharacteristic, complemented
39#63902—21no—
40C4×#625—21no—
41Dic3×D12C2211yescharacteristic, complemented
42Dic3×D12C2211yescharacteristic, complemented
43#63874C2211yescharacteristic
44#63864C2211yescharacteristic, complemented
45C2×#3715C2211yescharacteristic, complemented
46C2×#3714C2211yescharacteristic
47C2×#3714C2211yescharacteristic
48C2×#3713C2211yescharacteristic, complemented
49C2×#3710C2211yescharacteristic
50#63798—24no—
51C32×#102C2211yescharacteristic, complemented
52#63659C2211yescharacteristic, complemented
53#63648C2211yescharacteristic, complemented
54#63636C2211yescharacteristic, complemented
55C3×Dic3⋊C8C2211yescharacteristic, complemented
56C3×Dic3⋊C8C2211yescharacteristic, complemented
57C3×#810C2211yescharacteristic, complemented
58C3×#809C2211yescharacteristic, complemented
59Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
60Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
61#63566C2211yescharacteristic, complemented
62#63563C2211yescharacteristic, complemented
63C2×#914—31no—
64C2×#911—31no—
65C2×D3×D8—31no—
66C2×D3×D8—31no—
67#5715—31no—
68#5674—31no—
69#5545—31no—
70#5545—31no—
71C3×#463—31no—
72C3×#459—31no—
73#5165—31no—
74#5153—31no—
75#5150—31no—
76#5150—31no—
77#5072—31no—
78#5057—31no—
79#5016—31no—
80#5015—31no—
81#4844—31no—
82#4843—31no—
83#4839—31no—
84#4839—31no—
85#4819—31no—
86#4804—31no—
87#4787D311yescharacteristic, complemented
88#4786—31no—
89#4786D311yescharacteristic, complemented
90#4772—31no—
91#4770—31no—
92#4770—31no—
93#4770—61no—
94C23×C3⋊D3—21no—
95C22×D32—21no—
96C2×C32×D4C2311yescharacteristic
97C2×#638—21no—
98D4×C3⋊D3—22no—
99D4×C3⋊D3—22no—
100C2×C4⋊(C3⋊D3)C2311yescharacteristic
101C2×C4×C3⋊D3C2311yescharacteristic
102C2×C3×#67—21no—
103C2×C3×#67—21no—
104C2×C3×D12C2311yescharacteristic
105C2×C3×D12C2311yescharacteristic
106C2×C3×D12C2311yescharacteristic
107C2×C3×C4×D3—21no—
108C2×C3×C4×D3—21no—
109C2×C3×Dic6C2311yescharacteristic
110C2×#626—21no—
111C2×#626—21no—
112C2×#626—21no—
113C2×#625—21no—
114C2×D3×Dic3—21no—
115C2×D3×Dic3—21no—
116C2×D3×Dic3—21no—
117#3802—22no—
118#3802D414yescomplemented
119#3796—22no—
120#3796—22no—
121C2×C32×C8C2311yescharacteristic
122C32×C4⋊C4C2311yescharacteristic
123#3752—21no—
124C4⋊(C3⋊Dic3)C2311yescharacteristic
125C4×C3⋊Dic3—21no—
126C2×C3⋊(C3⋊C8)C2311yescharacteristic
127#3743—22no—
128C3×#217—21no—
129C3×#217—21no—
130C3×#213—22no—
131C3×#213—22no—
132C3×(C2×D3)⋊C4—21no—
133C3×(C2×D3)⋊C4—21no—
134C3×C4×Dic3C2311yescharacteristic
135C3×C4×Dic3C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138C3×D24—22no—
139C3×#204—22no—
140#3724D411yescharacteristic
141#3724D411yescharacteristic
142#3722—21no—
143#3722—21no—
144#3722D411yescharacteristic
145#3722D411yescharacteristic
146(C2×D3)⋊Dic3—21no—
147(C2×D3)⋊Dic3—21no—
148#3715—22no—
149#3714—22no—
150#3714—22no—
151#3713—22no—
152#3710—22no—
153#3041—91noSylow
154C2×#239—31no—
155C2×#237—31no—
156C2×D3×D4—31no—
157C2×D3×D4—31no—
158C2×D3×D4—31no—
159C2×D3×D4—31no—
160C2×D3×D4—61no—
161C2×C3×SD16—31no—
162C2×C3×D8—31no—
163C2×C3×D8—31no—
164C2×C3×D8—31no—
165C3×#127—31no—
166C3×#124—31no—
167C3×C4×D4—31no—
168C3×C4×D4—31no—
169#947—31no—
170C2×#215—31no—
171#940—31no—
172#940C2×D311yescharacteristic, complemented
173#939—61no—
174#939—61no—
175#937—61no—
176#937—61no—
177#936C2×D311yescharacteristic, complemented
178D4×Dic3—31no—
179D4×Dic3—31no—
180C2×#214—31no—
181C2×#213—31no—
182C2×#213—31no—
183C2×#213—31no—
184C2×#213—31no—
185C2×#213C2×D311yescharacteristic
186C2×#213C2×D311yescharacteristic
187C4×#67—61no—
188C4×#67—61no—
189C2×(C2×D3)⋊C4—61no—
190C2×(C2×D3)⋊C4—61no—
191#914—64no—
192#911—64no—
193D3×D8—64no—
194D3×D8—64no—
195C2×D24—31no—
196C2×D24—31no—
197C2×D24C2×D311yescharacteristic, complemented
198C2×#204C2×D311yescharacteristic, complemented
199C2×ΓL(1,𝔽25)—31no—
200C2×ΓL(1,𝔽25)—31no—
201C2×ΓL(1,𝔽25)—61no—
202C2×D3×C8—31no—
203C2×D3×C8—31no—
204#893C2×D311yescharacteristic, complemented
205#893C2×D311yescharacteristic, complemented
206#892—31no—
207#892—31no—
208#892—61no—
209#884—61no—
210#884—61no—
211#882—61no—
212#882—61no—
213#67⋊C4—61no—
214#67⋊C4—61no—
215D3×C22⋊C4—61no—
216D3×C22⋊C4—61no—
217#875—31no—
218#874—31no—
219C4×D12—31no—
220C4×D12—31no—
221#872—31no—
222#872—31no—
223C3×C4⋊C8—31no—
224C3×C4⋊C8—31no—
225C3×#103—31no—
226C3×#102—21no—
227C3×#102—31no—
228C3×#102C2×D311yescharacteristic, complemented
229C3×#102C2×D311yescharacteristic, complemented
230#835—31no—
231#832—31no—
232#832—31no—
233#832—31no—
234#832—61no—
235#821—31no—
236#821—31no—
237#821—31no—
238#821—61no—
239#816—31no—
240Dic3⋊C8—31no—
241Dic3⋊C8—31no—
242Dic3⋊C8C2×D311yescharacteristic, complemented
243Dic3⋊C8C2×D311yescharacteristic, complemented
244#810C2×D311yescharacteristic, complemented
245#809—31no—
246#809—31no—
247#809—61no—
248#809C2×D311yescharacteristic, complemented
249C4⋊(C3⋊C8)—31no—
250C4⋊(C3⋊C8)—31no—
251C23×C32—21no—
252C22×C3⋊D3—21no—
253C22×C3⋊D3—42no—
254C22×C3⋊D3—81no—
255C22×C3⋊D3—81no—
256C22×C3⋊D3C2×D411yescharacteristic
257C22×C3×D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3—21no—
260C2×D32—24no—
261C2×D32—81no—
262C2×D32—81no—
263C32×D4—21no—
264C32×D4—21no—
265C2×C32×C4—21no—
266C2×C32×C4C2411yescharacteristic
267#638—42no—
268C2×C3⋊Dic3—21no—
269C2×C3⋊Dic3C2×D411yescharacteristic
270C4⋊(C3⋊D3)—21no—
271C4⋊(C3⋊D3)—21no—
272C4×C3⋊D3C2×D412yes—
273C4×C3⋊D3#4112yes—
274C3×#67—81no—
275C3×#67—81no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3C2×D411yescharacteristic
278C2×C3×Dic3C2×D411yescharacteristic
279C2×C3×Dic3C2×D411yescharacteristic
280C2×C3×Dic3C2×D411yescharacteristic
281C3×D12—21no—
282C3×D12—21no—
283C3×D12—21no—
284C3×D12—21no—
285C3×D12C2×D412yes—
286C3×D12C2×D412yes—
287C3×C4×D3—81no—
288C3×C4×D3—81no—
289C3×Dic6—21no—
290C3×Dic6—21no—
291#626—42no—
292#626—81no—
293#626—81no—
294#625—24no—
295D3×Dic3—42no—
296D3×Dic3—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—31no—
311#459—91no—
312#459—91no—
313#459—91no—
314#424—91no—
315#418—91no—
316#416—91no—
317C23×D3—61no—
318C23×D3—61no—
319C23×D3—61no—
320C23×D3—61no—
321C23×D3—121no—
322C2×C3×Q8—31no—
323C2×C3×D4—21no—
324C2×C3×D4—31no—
325C2×C3×D4—31no—
326C2×C3×D4—31no—
327C2×C3×D4—61no—
328C2×C3×D4—61no—
329C2×C3×D4C22×D311yescharacteristic
330C2×C3×D4C22×D311yescharacteristic
331C22×C3×C4—61no—
332C22×C3×C4—61no—
333C2×#67—21no—
334C2×#67—21no—
335C2×#67—61no—
336C2×#67—61no—
337C2×#67—61no—
338C2×#67—61no—
339C2×#67—61no—
340C2×#67—61no—
341C2×#67—61no—
342C2×#67—121no—
343C22×Dic3—61no—
344C22×Dic3—61no—
345C22×Dic3—61no—
346#239—62no—
347#239—62no—
348#237—62no—
349#237—62no—
350D3×D4—34no—
351D3×D4—34no—
352D3×D4—62no—
353D3×D4—62no—
354D3×D4—62no—
355D3×D4—62no—
356D3×D4—62no—
357D3×D4—62no—
358D3×D4—64no—
359D3×D4—122no—
360C2×D12—31no—
361C2×D12—31no—
362C2×D12—61no—
363C2×D12—61no—
364C2×D12—61no—
365C2×D12—61no—
366C2×D12C22×D311yescharacteristic
367C2×D12C22×D311yescharacteristic
368C2×D12C22×D311yescharacteristic
369C2×C4×D3—21no—
370C2×C4×D3—21no—
371C2×C4×D3—31no—
372C2×C4×D3—31no—
373C2×C4×D3—61no—
374C2×C4×D3—61no—
375C2×C4×D3—61no—
376C2×C4×D3—61no—
377C2×Dic6C22×D311yescharacteristic
378C3×SD16—62no—
379C3×D8—62no—
380C3×D8—62no—
381C3×D8—62no—
382C2×C3×C8—21no—
383C2×C3×C8—31no—
384C2×C3×C8—31no—
385C2×C3×C8C22×D311yescharacteristic
386C2×C3×C8C22×D311yescharacteristic
387C3×C4⋊C4—21no—
388C3×C4⋊C4C22×D311yescharacteristic
389C3×C4⋊C4C22×D311yescharacteristic
390C3×C22⋊C4—61no—
391C3×C22⋊C4—61no—
392C3×C22⋊C4—61no—
393C3×C22⋊C4—61no—
394C3×C42—31no—
395C3×C42—31no—
396#217—21no—
397#217—21no—
398#217—61no—
399#217—61no—
400#215—62no—
401#214—62no—
402#213—22no—
403#213—22no—
404#213—62no—
405#213—62no—
406#213—62no—
407#213—62no—
408(C2×D3)⋊C4—21no—
409(C2×D3)⋊C4—21no—
410(C2×D3)⋊C4—31no—
411(C2×D3)⋊C4—31no—
412(C2×D3)⋊C4—31no—
413(C2×D3)⋊C4—31no—
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—61no—
422(C2×D3)⋊C4—121no—
423C4⋊Dic3—31no—
424C4⋊Dic3—31no—
425C4⋊Dic3—61no—
426Dic3⋊C4—31no—
427Dic3⋊C4—31no—
428Dic3⋊C4—31no—
429Dic3⋊C4—31no—
430C4×Dic3—61no—
431C4×Dic3—61no—
432C4×Dic3—121no—
433C4×Dic3C22×D311yescharacteristic
434C4×Dic3C22×D311yescharacteristic
435C2×C3⋊C8—31no—
436C2×C3⋊C8—31no—
437C2×C3⋊C8—61no—
438C2×C3⋊C8C22×D311yescharacteristic
439C2×C3⋊C8C22×D311yescharacteristic
440D24—22no—
441D24—62no—
442D24—62no—
443#204—22no—
444ΓL(1,𝔽25)—62no—
445ΓL(1,𝔽25)—62no—
446ΓL(1,𝔽25)—122no—
447D3×C8—62no—
448D3×C8—62no—
449C22×C32—41no—
450C22×C32—41no—
451C22×C32—41no—
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⋊D3—84no—
459C2×C3⋊D3#12112yes—
460C2×C3×D3—22no—
461C2×C3×D3—22no—
462C2×C3×D3—41no—
463C2×C3×D3—41no—
464C2×C3×D3—41no—
465C2×C3×D3—41no—
466C2×C3×D3—41no—
467C2×C3×D3—41no—
468C2×C3×D3—41no—
469D32—84no—
470C32×C4—41no—
471C32×C4C22×D411yescharacteristic
472C32×C4C2×#4111yescharacteristic
473C3⋊Dic3—41no—
474C3⋊Dic3#12112yes—
475C3×Dic3—21no—
476C3×Dic3—21no—
477C3×Dic3—21no—
478C3×Dic3—21no—
479C3×Dic3—41no—
480C2×#41—91no—
481C22×D4—91no—
482C22×D4—91no—
483AGL(1,ℤ/8)—184no—
484C2×SD16—31no—
485C2×SD16—91no—
486C2×D8—31no—
487C2×D8—31no—
488C2×D8—31no—
489C2×D8—91no—
490C2×D8—91no—
491C2×D8—91no—
492C2×D8—184no—
493C2×M16—91no—
494C22×C8—91no—
495#127—31no—
496#127—91no—
497#124—31no—
498#124—91no—
499#121—181no—
500#121—181no—
501#120—181no—
502#120—181no—
503C4×D4—31no—
504C4×D4—31no—
505C4×D4—91no—
506C4×D4—91no—
507C4×D4—181no—
508C4×D4—181no—
509#117—91no—
510#117—91no—
511C2×C22⋊C4—181no—
512C2×C22⋊C4—181no—
513C4⋊C8—31no—
514C4⋊C8—31no—
515C4⋊C8—91no—
516C4⋊C8—91no—
517#103—31no—
518#103—91no—
519#102—31no—
520#102—91no—
521#102—91no—
522#102—91no—
523#102—91no—
524#102D3211yescharacteristic, complemented
525C23×C3—21no—
526C23×C3—21no—
527C23×C3—41no—
528C23×C3—61no—
529C23×C3—61no—
530C23×C3—61no—
531C22×D3—21no—
532C22×D3—21no—
533C22×D3—21no—
534C22×D3—31no—
535C22×D3—31no—
536C22×D3—61no—
537C22×D3—64no—
538C22×D3—64no—
539C22×D3—61no—
540C22×D3—61no—
541C22×D3—121no—
542C22×D3—122no—
543C22×D3—122no—
544C22×D3—124no—
545C22×D3—241no—
546C22×D3—241no—
547C22×D3—241no—
548C22×D3—241no—
549C22×D3—241no—
550C22×D3—241no—
551C22×D3—241no—
552C22×D3—241no—
553C22×D3—242no—
554C22×D3—242no—
555C3×Q8—61no—
556C3×Q8—61no—
557C3×D4—22no—
558C3×D4—21no—
559C3×D4—21no—
560C3×D4—21no—
561C3×D4—21no—
562C3×D4—32no—
563C3×D4—32no—
564C3×D4—41no—
565C3×D4—61no—
566C3×D4—61no—
567C3×D4—61no—
568C3×D4—61no—
569C3×D4—241no—
570C3×D4—241no—
571C2×C3×C4—21no—
572C2×C3×C4—21no—
573C2×C3×C4—21no—
574C2×C3×C4—31no—
575C2×C3×C4—31no—
576C2×C3×C4—31no—
577C2×C3×C4—31no—
578C2×C3×C4—41no—
579C2×C3×C4—61no—
580C2×C3×C4—241no—
581C2×C3×C4—241no—
582C2×C3×C4C23×D311yescharacteristic
583C2×C3×C4C23×D311yescharacteristic
584#67—64no—
585#67—64no—
586#67—81no—
587#67—81no—
588#67—122no—
589#67—122no—
590#67—122no—
591#67—124no—
592#67—241no—
593#67—241no—
594C2×Dic3—21no—
595C2×Dic3—31no—
596C2×Dic3—31no—
597C2×Dic3—61no—
598C2×Dic3—61no—
599C2×Dic3—61no—
600C2×Dic3—121no—
601C2×Dic3—122no—
602C2×Dic3—241no—
603C2×Dic3—241no—
604C2×Dic3D3×D411yescharacteristic
605C2×Dic3D3×D411yescharacteristic
606C2×Dic3D3×D411yescharacteristic
607C2×Dic3D3×D411yescharacteristic
608D12—21no—
609D12—21no—
610D12—21no—
611D12—21no—
612D12—62no—
613D12—61no—
614D12—61no—
615D12—61no—
616D12—61no—
617D12—121no—
618D12—122no—
619D12—241no—
620D12—241no—
621D12D3×D412yes—
622D12D3×D412yes—
623C4×D3—32no—
624C4×D3—32no—
625C4×D3—32no—
626C4×D3—32no—
627C4×D3—62no—
628C4×D3—62no—
629C4×D3—81no—
630C4×D3—81no—
631C4×D3—122no—
632C4×D3—241no—
633C4×D3—241no—
634Dic6—21no—
635Dic6—21no—
636C3×C8—21no—
637C3×C8—21no—
638C3×C8—41no—
639C3×C8—61no—
640C3×C8—61no—
641C3⋊C8—21no—
642C3⋊C8—21no—
643C3⋊C8—61no—
644C3⋊C8—61no—
645C3⋊C8—121no—
646C2×C32—81no—
647C2×C32C2×#12111yescharacteristic
648C2×C32#57611yescharacteristic
649C2×C32#57611yescharacteristic
650C3⋊D3—22no—
651C3⋊D3—81no—
652C3×D3—42no—
653C3×D3—42no—
654C3×D3—81no—
655C24—181no—
656C24—181no—
657#41—182no—
658#41—182no—
659C2×Q8—31no—
660C2×D4—31no—
661C2×D4—31no—
662C2×D4—31no—
663C2×D4—61no—
664C2×D4—61no—
665C2×D4—94no—
666C2×D4—91no—
667C2×D4—181no—
668C2×D4—181no—
669C2×D4—181no—
670C2×D4—182no—
671C2×D4—182no—
672C2×D4—182no—
673C2×D4—181no—
674C2×D4—181no—
675C2×D4C2×D3211yescharacteristic
676C22×C4—61no—
677C22×C4—61no—
678C22×C4—91no—
679C22×C4—181no—
680C22×C4—181no—
681C22×C4—181no—
682SD16—62no—
683SD16—182no—
684D8—62no—
685D8—62no—
686D8—62no—
687D8—182no—
688D8—182no—
689D8—182no—
690M16—182no—
691C2×C8—31no—
692C2×C8—31no—
693C2×C8—91no—
694C2×C8—182no—
695C2×C8C2×D3211yescharacteristic
696C4⋊C4—91no—
697C4⋊C4—91no—
698C4⋊C4—91no—
699C4⋊C4C2×D3211yescharacteristic
700C22⋊C4—61no—
701C22⋊C4—61no—
702C22⋊C4—61no—
703C22⋊C4—61no—
704C22⋊C4—91no—
705C22⋊C4—91no—
706C22⋊C4—181no—
707C22⋊C4—181no—
708C22⋊C4—181no—
709C22⋊C4—181no—
710C22⋊C4—181no—
711C42—31no—
712C42—31no—
713C42—181no—
714C22×C3—21no—
715C22×C3—42no—
716C22×C3—41no—
717C22×C3—41no—
718C22×C3—41no—
719C22×C3—41no—
720C22×C3—41no—
721C22×C3—41no—
722C22×C3—62no—
723C22×C3—62no—
724C22×C3—81no—
725C22×C3—81no—
726C22×C3—121no—
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—22no—
736C2×D3—22no—
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—41no—
746C2×D3—62no—
747C2×D3—61no—
748C2×D3—61no—
749C2×D3—61no—
750C2×D3—61no—
751C2×D3—121no—
752C2×D3—121no—
753C2×D3—122no—
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—244no—
763C2×D3—244no—
764C2×D3—244no—
765C2×D3—244no—
766C2×D3—248no—
767C3×C4—21no—
768C3×C4—21no—
769C3×C4—41no—
770C3×C4—41no—
771C3×C4—61no—
772C3×C4—61no—
773C3×C4—61no—
774C3×C4—61no—
775C3×C4—81no—
776C3×C4—121no—
777C3×C4C2×D3×D411yescharacteristic
778C3×C4C2×D3×D411yescharacteristic
779C3×C4D3×#4111yescharacteristic
780C3×C4D3×#4111yescharacteristic
781Dic3—21no—
782Dic3—21no—
783Dic3—21no—
784Dic3—21no—
785Dic3—32no—
786Dic3—32no—
787Dic3—41no—
788Dic3—62no—
789Dic3—121no—
790Dic3—121no—
791Dic3—241no—
792C32#304111yescharacteristic, complemented, Sylow
793C23—21no—
794C23—61no—
795C23—61no—
796C23—61no—
797C23—91no—
798C23—184no—
799C23—181no—
800C23—362no—
801C23—721no—
802C23—721no—
803C23—721no—
804C23—721no—
805Q8—61no—
806Q8—61no—
807D4—21no—
808D4—21no—
809D4—32no—
810D4—32no—
811D4—61no—
812D4—61no—
813D4—61no—
814D4—61no—
815D4—184no—
816D4—181no—
817D4—181no—
818D4—241no—
819D4—241no—
820D4—362no—
821D4—362no—
822D4—721no—
823D4—721no—
824C2×C4—21no—
825C2×C4—31no—
826C2×C4—31no—
827C2×C4—31no—
828C2×C4—31no—
829C2×C4—61no—
830C2×C4—91no—
831C2×C4—92no—
832C2×C4—92no—
833C2×C4—181no—
834C2×C4—241no—
835C2×C4—241no—
836C2×C4—362no—
837C2×C4—721no—
838C2×C4—721no—
839C2×C4C22×D3211yescharacteristic
840C8—21no—
841C8—61no—
842C8—61no—
843C8—181no—
844C2×C3—21no—
845C2×C3—21no—
846C2×C3—21no—
847C2×C3—82no—
848C2×C3—81no—
849C2×C3—81no—
850C2×C3—122no—
851C2×C3—122no—
852C2×C3—241no—
853C2×C3D3×#12111yescharacteristic
854C2×C3D3×#12111yescharacteristic
855C2×C3#575711yescharacteristic
856C2×C3#576911yescharacteristic
857C2×C3#577411yescharacteristic
858C2×C3#577411yescharacteristic
859D3—42no—
860D3—42no—
861D3—62no—
862D3—62no—
863D3—81no—
864D3—122no—
865D3—242no—
866D3—241no—
867D3—241no—
868C22—41no—
869C22—41no—
870C22—41no—
871C22—62no—
872C22—62no—
873C22—92no—
874C22—121no—
875C22—121no—
876C22—121no—
877C22—121no—
878C22—121no—
879C22—121no—
880C22—121no—
881C22—181no—
882C22—181no—
883C22—361no—
884C22—361no—
885C22—361no—
886C22—724no—
887C22—724no—
888C22D32×D411yescharacteristic
889C4—41no—
890C4—61no—
891C4—61no—
892C4—61no—
893C4—61no—
894C4—92no—
895C4—121no—
896C4—361no—
897C4#6430611yescharacteristic
898C4D32×D411yescharacteristic
899C3—21no—
900C3#8033411yescharacteristic, complemented
901C3#8053611yescharacteristic, complemented
902C2—81no—
903C2—122no—
904C2—122no—
905C2—182no—
906C2—241no—
907C2—721no—
908C2#1059426511yescharacteristic
909C2#1059473211yescharacteristic
910C2#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. #10595168C2semidirect
2. C2×#63926C2semidirect
3. C2×#63798C2semidirect
4. #10594606C2semidirect
5. #10592469C2semidirect
6. C3×#4787C2semidirect
7. C3×#4786C2semidirect
8. #10591431C2semidirect
9. #10591428C2semidirect
10. #10590754C2semidirect
11. #10590753C2semidirect
12. #10590702C2semidirect
13. #10590611C2semidirect
14. #10590547C2semidirect
15. #10590534C2semidirect
23. C3×#940C22semidirect
24. C3×#936C22semidirect
27. C2×C3×D24C22semidirect
28. C2×C3×#204C22semidirect
29. C3×#893C22semidirect
30. C3×#893C22semidirect
38. #63911C22semidirect
41. Dic3×D12C22semidirect
42. Dic3×D12C22semidirect
44. #63864C22semidirect
45. C2×#3715C22semidirect
48. C2×#3713C22semidirect
51. C32×#102C22semidirect
52. #63659C22semidirect
53. #63648C22semidirect
54. #63636C22semidirect
55. C3×Dic3⋊C8C22semidirect
56. C3×Dic3⋊C8C22semidirect
57. C3×#810C22semidirect
58. C3×#809C22semidirect
59. Dic3⋊(C3⋊C8)C22semidirect
60. Dic3⋊(C3⋊C8)C22semidirect
61. #63566C22semidirect
62. #63563C22semidirect
87. #4787D3semidirect
89. #4786D3semidirect
118. #3802D4semidirect
172. #940C2×D3semidirect
177. #936C2×D3semidirect
197. C2×D24C2×D3semidirect
198. C2×#204C2×D3semidirect
204. #893C2×D3semidirect
205. #893C2×D3semidirect
228. C3×#102C2×D3semidirect
229. C3×#102C2×D3semidirect
242. Dic3⋊C8C2×D3semidirect
243. Dic3⋊C8C2×D3semidirect
244. #810C2×D3semidirect
248. #809C2×D3semidirect
524. #102D32semidirect
792. C32#3041semidirect
900. C3#80334semidirect
901. C3#80536semidirect

Maximal subgroups

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

subgroupindex
#105951682
C2×#639262
C2×#637982
#105946062
#105924692
C3×#47872
C3×#47862
#105914312
#105914282
#105907542
#105907532
#105907022
#105906112
#105905472
#105905342
#805363
#803343