Finite Group Databasebeta

← #11864127

Subgroups — #11864127

Order 1152.

1711 conjugacy classes of subgroups.

The subgroup lattice has 1063 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64312C211yesmaximal, characteristic, complemented
2C2×#63925C211yesmaximal, characteristic, complemented
3C2×#63794C211yesmaximal, characteristic, complemented
4D3×#895C211yesmaximal, characteristic, complemented
5#10592472C211yesmaximal, characteristic, complemented
6C3×#4781C211yesmaximal, characteristic, complemented
7C3×#4771C211yesmaximal, characteristic, complemented
8#10591456C211yesmaximal, characteristic, complemented
9#10591452C211yesmaximal, characteristic, complemented
10#10590967C211yesmaximal, characteristic, complemented
11#10590936C211yesmaximal, characteristic, complemented
12#10590824C211yesmaximal, characteristic, complemented
13#10590615C211yesmaximal, characteristic, complemented
14#10590609C211yesmaximal, characteristic, complemented
15#10590606C211yesmaximal, characteristic, complemented
16#80084—31nomaximal
17#78884—31nomaximal
18C2×D4×C3⋊D3C2211yescharacteristic, complemented
19C2×C3×#237C2211yescharacteristic
20C2×C3×#237C2211yescharacteristic, complemented
21C2×#3811—21no—
22C22×#624—21no—
23C2×#3804—21no—
24C2×#3804—21no—
25#64312—24no—
26#64312—24no—
27C2×D3×D12—21no—
28C2×D3×D12C2211yescharacteristic, complemented
29C2×C4×D32C2211yescharacteristic
30C2×#3799C2211yescharacteristic
31C2×#3799C2211yescharacteristic, complemented
32C2×#3797C2211yescharacteristic, complemented
33C2×#3753C2211yescharacteristic, complemented
34C2×#3745C2211yescharacteristic, complemented
35#64104C2211yescharacteristic
36C2×C3×#213C2211yescharacteristic, complemented
37C2×C3×#204C2211yescharacteristic, complemented
38C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
39C3×#895C2211yescharacteristic, complemented
40C3×D3×C4⋊C4C2211yescharacteristic, complemented
41#63925—24no—
42D3×(C2×D3)⋊C4—21no—
43#63916C2211yescharacteristic
44#63910—21no—
45#63909C2211yescharacteristic, complemented
46#63886—21no—
47C2×#3717C2211yescharacteristic, complemented
48C2×#3717C2211yescharacteristic, complemented
49C2×#3715C2211yescharacteristic, complemented
50C2×#3714C2211yescharacteristic, complemented
51C2×#3711C2211yescharacteristic, complemented
52#63794—24no—
53C32×#102C2211yescharacteristic, complemented
54#63647C2211yescharacteristic, complemented
55#63636C2211yescharacteristic, complemented
56C3×#832C2211yescharacteristic, complemented
57C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
58C3×#816C2211yescharacteristic, complemented
59C3×#810C2211yescharacteristic, complemented
60C3×#810C2211yescharacteristic, complemented
61#63565C2211yescharacteristic, complemented
62#63564C2211yescharacteristic, complemented
63#63557C2211yescharacteristic, complemented
64(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
65C2×D3×#41—31no—
66C2×D3×#41—31no—
67C2×#949—31no—
68C2×#914—31no—
69C2×#911—31no—
70C2×#908—31no—
71D3×#121—31no—
72C2×#895—31no—
73C3×#449—31no—
74C3×#417—31no—
75#5238—31no—
76#5170—31no—
77#5156—31no—
78#5126—31no—
79#5037—31no—
80#4966—31no—
81#4810—31no—
82#4810—31no—
83#4806—31no—
84#4806—31no—
85#4806—31no—
86#4803—31no—
87#4781—31no—
88#4781D311yescharacteristic, complemented
89#4773—31no—
90#4773—31no—
91#4773—31no—
92#4773—61no—
93#4771D311yescharacteristic, complemented
94#4734—31no—
95#4726—31no—
96C23×C3⋊D3—21no—
97C22×D32—21no—
98C22×D32D411yescharacteristic
99C2×C32×D4C2311yescharacteristic
100C2×#638—21no—
101D4×C3⋊D3—22no—
102D4×C3⋊D3—22no—
103C2×C4⋊(C3⋊D3)—21no—
104C2×C4⋊(C3⋊D3)C2311yescharacteristic
105C2×C4⋊(C3⋊D3)C2311yescharacteristic
106C2×C4×C3⋊D3C2311yescharacteristic
107C2×C3×#67—21no—
108C2×C3×#67—21no—
109C22×C3×Dic3—21no—
110C22×C3×Dic3—21no—
111C3×#237—22no—
112C3×#237—22no—
113C3×#237—22no—
114C3×#237D414yescomplemented
115C2×C3×D12—21no—
116C2×C3×D12C2311yescharacteristic
117C2×C3×C4×D3—21no—
118C2×C3×C4×D3C2311yescharacteristic
119C2×C3×C4×D3C2311yescharacteristic
120C2×C3×Dic6C2311yescharacteristic
121C2×C3×Dic6C2311yescharacteristic
122#3811—28no—
123C2×#627—21no—
124C2×#626—21no—
125C2×#626—21no—
126C2×#626—21no—
127C2×#626—21no—
128C2×#626—21no—
129C2×#624—28no—
130C2×#624—21no—
131C2×#624—21no—
132C2×#624—21no—
133C2×#624D411yescharacteristic
134#3804—28no—
135#3804—28no—
136C2×D3×Dic3D411yescharacteristic
137C2×D3×Dic3D411yescharacteristic
138D3×D12—22no—
139D3×D12—22no—
140D3×D12—44no—
141C4×D32—22no—
142C4×D32—22no—
143#3799—22no—
144#3799—22no—
145#3799—22no—
146#3799D414yescomplemented
147#3797—22no—
148#3797—22no—
149C2×C32×C8C2311yescharacteristic
150C32×C4⋊C4C2311yescharacteristic
151#3753—22no—
152#3752—21no—
153C2×C3⋊(C3⋊C8)C2311yescharacteristic
154#3745—22no—
155C3×#213—22no—
156C3×(C2×D3)⋊C4—21no—
157C3×C4⋊Dic3C2311yescharacteristic
158C3×Dic3⋊C4—21no—
159C2×C3×C3⋊C8C2311yescharacteristic
160C2×C3×C3⋊C8C2311yescharacteristic
161C3×#204—22no—
162C3×ΓL(1,𝔽25)—22no—
163#3722—21no—
164(C2×D3)⋊Dic3—21no—
165#3717—22no—
166#3717—22no—
167#3715—22no—
168#3714—22no—
169#3711—22no—
170#3006—91noSylow
171C2×C3×#41—31no—
172C2×C3×#41—31no—
173D3×#41—64no—
174D3×#41—64no—
175D3×#41—64no—
176D3×#41—64no—
177C2×#239—31no—
178C2×#239—31no—
179C2×D3×Q8—31no—
180C2×D3×Q8—31no—
181C2×#237—61no—
182C2×#237—61no—
183C2×#237C2×D311yescharacteristic
184C2×#237C2×D311yescharacteristic, complemented
185C2×D3×D4—31no—
186C2×D3×D4—31no—
187C2×D3×D4—31no—
188C2×D3×D4—61no—
189C2×D3×D4—61no—
190C2×D3×D4—61no—
191C2×D3×D4—61no—
192C2×#235—31no—
193C2×#235—31no—
194C2×#235—61no—
195C2×#235—61no—
196C22×D12—31no—
197C22×D12—61no—
198C22×C4×D3—31no—
199C22×C4×D3—31no—
200C22×C4×D3—61no—
201C22×C4×D3—61no—
202C2×C3×SD16—31no—
203C2×C3×D8—31no—
204C2×C3×M16—31no—
205C3×#121—31no—
206C2×C3×C4⋊C4—31no—
207#949—64no—
208C2×#215—31no—
209C2×#215—31no—
210C2×#215—31no—
211#939—61no—
212#938—31no—
213C2×#214—31no—
214C2×#213—31no—
215C2×#213—31no—
216C2×#213—31no—
217C2×#213—61no—
218C2×#213C2×D311yescharacteristic, complemented
219#930—31no—
220C2×(C2×D3)⋊C4—61no—
221C2×#208—31no—
222#914—64no—
223#911—64no—
224#908—64no—
225C2×D24—31no—
226C2×D24—31no—
227C2×D24—31no—
228C2×D24—61no—
229C2×#204—31no—
230C2×#204—31no—
231C2×#204C2×D311yescharacteristic, complemented
232C2×ΓL(1,𝔽25)—31no—
233C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
234#895—31no—
235#895—31no—
236#895—31no—
237#895—31no—
238#895—61no—
239#895—61no—
240#895—61no—
241#895C2×D311yescharacteristic, complemented
242D3×C4⋊C4C2×D311yescharacteristic, complemented
243#884—61no—
244D3×C22⋊C4—61no—
245C3×#103—31no—
246C3×#103—31no—
247C3×#103—31no—
248C3×#102—21no—
249C3×#102—31no—
250C3×#102C2×D311yescharacteristic, complemented
251C3×#102C2×D311yescharacteristic, complemented
252C3×C22⋊C8—31no—
253#835—31no—
254#832C2×D311yescharacteristic, complemented
255#830—31no—
256#821—31no—
257(C2×D3)⋊C8—31no—
258(C2×D3)⋊C8—31no—
259(C2×D3)⋊C8—31no—
260(C2×D3)⋊C8—31no—
261(C2×D3)⋊C8—31no—
262(C2×D3)⋊C8—61no—
263(C2×D3)⋊C8C2×D311yescharacteristic, complemented
264#816C2×D311yescharacteristic, complemented
265#810—31no—
266#810C2×D311yescharacteristic, complemented
267#810C2×D311yescharacteristic, complemented
268#809—31no—
269#809—31no—
270#809—31no—
271#809—61no—
272C23×C32—21no—
273C22×C3⋊D3—24no—
274C22×C3⋊D3—21no—
275C22×C3⋊D3—21no—
276C22×C3⋊D3—42no—
277C22×C3⋊D3—42no—
278C22×C3⋊D3C2×D411yescharacteristic
279C22×C3×D3—21no—
280C22×C3×D3C2×D411yescharacteristic
281C22×C3×D3C2×D411yescharacteristic
282C2×D32—22no—
283C2×D32—22no—
284C2×D32—41no—
285C2×D32—42no—
286C2×D32—42no—
287C2×D32—42no—
288C32×D4—21no—
289C32×D4C2×D412yescomplemented
290C2×C32×C4—21no—
291C2×C32×C4C2411yescharacteristic
292#638—24no—
293C2×C3⋊Dic3C2×D411yescharacteristic
294C4⋊(C3⋊D3)—21no—
295C4⋊(C3⋊D3)—21no—
296C4⋊(C3⋊D3)—21no—
297C4⋊(C3⋊D3)—42no—
298C4⋊(C3⋊D3)C2×D412yescomplemented
299C4×C3⋊D3—21no—
300C4×C3⋊D3—21no—
301C3×#67—24no—
302C3×#67—24no—
303C2×C3×Dic3—24no—
304C2×C3×Dic3—21no—
305C2×C3×Dic3—21no—
306C2×C3×Dic3—24no—
307C2×C3×Dic3—21no—
308C2×C3×Dic3C2×D411yescharacteristic
309C2×C3×Dic3C2×D411yescharacteristic
310C3×D12—21no—
311C3×D12—21no—
312C3×D12—42no—
313C3×C4×D3—21no—
314C3×C4×D3—21no—
315C3×C4×D3—42no—
316C3×C4×D3C2×D412yes—
317C3×C4×D3C2×D412yes—
318C3×Dic6—21no—
319C3×Dic6—21no—
320C3×Dic6C2×D412yescomplemented
321C3×Dic6C2×D412yescomplemented
322#627—24no—
323#626—24no—
324#626—24no—
325#626—42no—
326#626—42no—
327#626—42no—
328#624—24no—
329#624—24no—
330#624—24no—
331#624—22no—
332D3×Dic3—22no—
333D3×Dic3—22no—
334C32×C8—21no—
335C3⋊(C3⋊C8)—21no—
336C3×C3⋊C8—21no—
337C3×C3⋊C8—21no—
338C22×#41—91no—
339C2×AGL(1,ℤ/8)—91no—
340C2×AGL(1,ℤ/8)—91no—
341C2×#121—91no—
342#449—31no—
343#449—91no—
344#449—91no—
345#449—91no—
346#448—91no—
347#448—91no—
348#447—91no—
349#447—91no—
350#417—31no—
351#417—91no—
352#407—91no—
353C23×D3—31no—
354C23×D3—31no—
355C23×D3—61no—
356C23×D3—61no—
357C23×D3—61no—
358C23×D3—61no—
359C23×D3—121no—
360C3×#41—34no—
361C3×#41—62no—
362C3×#41—62no—
363C3×#41—62no—
364C2×C3×Q8—31no—
365C2×C3×Q8—31no—
366C2×C3×D4—21no—
367C2×C3×D4—31no—
368C2×C3×D4—61no—
369C2×C3×D4—61no—
370C2×C3×D4—61no—
371C2×C3×D4C22×D311yescharacteristic
372C2×C3×D4C22×D311yescharacteristic
373C22×C3×C4—31no—
374C22×C3×C4—31no—
375C22×C3×C4—61no—
376C22×C3×C4—61no—
377C22×C3×C4—61no—
378C2×#67—21no—
379C2×#67—21no—
380C2×#67—61no—
381C2×#67—61no—
382C2×#67—61no—
383C2×#67—61no—
384C2×#67—61no—
385C2×#67—61no—
386C2×#67—61no—
387C2×#67—121no—
388C22×Dic3—21no—
389C22×Dic3—21no—
390C22×Dic3—31no—
391C22×Dic3—31no—
392#239—34no—
393#239—62no—
394#239—62no—
395#239—62no—
396D3×Q8—62no—
397D3×Q8—62no—
398D3×Q8—62no—
399D3×Q8—62no—
400#237—22no—
401#237—22no—
402#237—22no—
403#237—68no—
404#237—68no—
405#237D1214yescomplemented
406D3×D4—62no—
407D3×D4—62no—
408D3×D4—68no—
409D3×D4—68no—
410D3×D4—62no—
411D3×D4—62no—
412D3×D4—62no—
413D3×D4—62no—
414D3×D4—122no—
415D3×D4—122no—
416D3×D4—124no—
417#235—34no—
418#235—62no—
419#235—62no—
420#235—68no—
421#235—68no—
422#235—62no—
423C2×D12—21no—
424C2×D12—31no—
425C2×D12—31no—
426C2×D12—31no—
427C2×D12—31no—
428C2×D12—61no—
429C2×D12—61no—
430C2×D12—62no—
431C2×D12—62no—
432C2×D12—61no—
433C2×D12—61no—
434C2×D12—61no—
435C2×D12—61no—
436C2×D12—61no—
437C2×D12—61no—
438C2×D12—61no—
439C2×D12—121no—
440C2×D12—124no—
441C2×D12C22×D311yescharacteristic
442C2×C4×D3—21no—
443C2×C4×D3—31no—
444C2×C4×D3—31no—
445C2×C4×D3—31no—
446C2×C4×D3—31no—
447C2×C4×D3—31no—
448C2×C4×D3—31no—
449C2×C4×D3—61no—
450C2×C4×D3—62no—
451C2×C4×D3—62no—
452C2×C4×D3—61no—
453C2×C4×D3—61no—
454C2×C4×D3—61no—
455C2×C4×D3—61no—
456C2×C4×D3—68no—
457C2×C4×D3—68no—
458C2×C4×D3—61no—
459C2×C4×D3—61no—
460C2×C4×D3—62no—
461C2×C4×D3—62no—
462C2×C4×D3C22×D311yescharacteristic
463C2×C4×D3C22×D311yescharacteristic
464C2×Dic6—61no—
465C2×Dic6—61no—
466C2×Dic6C22×D311yescharacteristic
467C2×Dic6C22×D311yescharacteristic
468C3×SD16—62no—
469C3×D8—62no—
470C3×M16—62no—
471C2×C3×C8—21no—
472C2×C3×C8—31no—
473C2×C3×C8—31no—
474C2×C3×C8C22×D311yescharacteristic
475C2×C3×C8C22×D311yescharacteristic
476C3×C4⋊C4—21no—
477C3×C4⋊C4—31no—
478C3×C4⋊C4—61no—
479C3×C4⋊C4C22×D311yescharacteristic
480C3×C4⋊C4C22×D311yescharacteristic
481C3×C22⋊C4—61no—
482#217—61no—
483#215—62no—
484#215—62no—
485#215—62no—
486#214—62no—
487#213—22no—
488#213—62no—
489#213—62no—
490#213—62no—
491#213—122no—
492(C2×D3)⋊C4—21no—
493(C2×D3)⋊C4—61no—
494(C2×D3)⋊C4—61no—
495(C2×D3)⋊C4—61no—
496(C2×D3)⋊C4—61no—
497(C2×D3)⋊C4—61no—
498(C2×D3)⋊C4—121no—
499C4⋊Dic3C22×D311yescharacteristic
500Dic3⋊C4—21no—
501#208—62no—
502C2×C3⋊C8—31no—
503C2×C3⋊C8—31no—
504C2×C3⋊C8—61no—
505C2×C3⋊C8C22×D311yescharacteristic
506C2×C3⋊C8C22×D311yescharacteristic
507D24—62no—
508D24—62no—
509D24—62no—
510D24—122no—
511#204—22no—
512#204—62no—
513#204—62no—
514ΓL(1,𝔽25)—22no—
515ΓL(1,𝔽25)—62no—
516C22×C32—22no—
517C22×C32—41no—
518C22×C32—41no—
519C22×C32C22×D411yescharacteristic
520C2×C3⋊D3—21no—
521C2×C3⋊D3—21no—
522C2×C3⋊D3—22no—
523C2×C3⋊D3—48no—
524C2×C3⋊D3—41no—
525C2×C3⋊D3—41no—
526C2×C3⋊D3—41no—
527C2×C3⋊D3—41no—
528C2×C3⋊D3—41no—
529C2×C3⋊D3AGL(1,ℤ/8)12yescomplemented
530C2×C3×D3—21no—
531C2×C3×D3—21no—
532C2×C3×D3—21no—
533C2×C3×D3—21no—
534C2×C3×D3—21no—
535C2×C3×D3—41no—
536C2×C3×D3—41no—
537C2×C3×D3—41no—
538C2×C3×D3#12012yes—
539D32—44no—
540D32—84no—
541C32×C4—41no—
542C32×C4C22×D411yescharacteristic
543C32×C4C22×D411yescharacteristic
544C3⋊Dic3—21no—
545C3×Dic3—21no—
546C3×Dic3—22no—
547C3×Dic3—22no—
548C3×Dic3—41no—
549C3×Dic3#12012yes—
550C2×#41—31no—
551C2×#41—31no—
552C2×#41—91no—
553C2×#41—91no—
554C2×#41—181no—
555C2×#41—181no—
556C2×#41—184no—
557C2×#41—184no—
558C22×Q8—91no—
559C22×D4—91no—
560C22×D4—91no—
561C22×D4—181no—
562C22×D4—181no—
563C23×C4—91no—
564C23×C4—181no—
565AGL(1,ℤ/8)—184no—
566AGL(1,ℤ/8)—184no—
567C2×SD16—31no—
568C2×SD16—91no—
569C2×SD16—91no—
570C2×SD16—91no—
571C2×D8—31no—
572C2×D8—91no—
573C2×D8—91no—
574C2×D8—91no—
575C2×M16—31no—
576C2×M16—91no—
577#121—31no—
578#121—91no—
579#121—91no—
580#121—91no—
581#121—181no—
582#121—181no—
583C2×C4⋊C4—31no—
584C2×C22⋊C4—181no—
585#103—31no—
586#103—31no—
587#103—31no—
588#103—91no—
589#102—31no—
590#102—91no—
591#102—91no—
592#102D3211yescharacteristic, complemented
593C22⋊C8—31no—
594C22⋊C8—91no—
595C22⋊C8—91no—
596C22⋊C8—91no—
597C23×C3—21no—
598C23×C3—21no—
599C23×C3—31no—
600C23×C3—31no—
601C23×C3—41no—
602C23×C3—61no—
603C22×D3—21no—
604C22×D3—31no—
605C22×D3—31no—
606C22×D3—61no—
607C22×D3—62no—
608C22×D3—62no—
609C22×D3—62no—
610C22×D3—64no—
611C22×D3—64no—
612C22×D3—61no—
613C22×D3—61no—
614C22×D3—62no—
615C22×D3—61no—
616C22×D3—61no—
617C22×D3—121no—
618C22×D3—124no—
619C22×D3—121no—
620C22×D3—121no—
621C22×D3—121no—
622C22×D3—122no—
623C22×D3—122no—
624C22×D3—122no—
625C22×D3—122no—
626C22×D3—122no—
627C22×D3—122no—
628C22×D3—122no—
629C22×D3—122no—
630C22×D3—122no—
631C22×D3—122no—
632C22×D3—242no—
633C22×D3—242no—
634C22×D3D3×D411yescharacteristic
635C22×D3D3×D411yescharacteristic
636C3×Q8—32no—
637C3×Q8—32no—
638C3×Q8—61no—
639C3×Q8—61no—
640C3×D4—21no—
641C3×D4—21no—
642C3×D4—22no—
643C3×D4—41no—
644C3×D4—64no—
645C3×D4—64no—
646C3×D4—61no—
647C3×D4—61no—
648C3×D4—122no—
649C3×D4C2×D1212yescomplemented
650C3×D4D3×D412yescomplemented
651C2×C3×C4—21no—
652C2×C3×C4—21no—
653C2×C3×C4—21no—
654C2×C3×C4—31no—
655C2×C3×C4—32no—
656C2×C3×C4—32no—
657C2×C3×C4—31no—
658C2×C3×C4—41no—
659C2×C3×C4—64no—
660C2×C3×C4—64no—
661C2×C3×C4—61no—
662C2×C3×C4—61no—
663C2×C3×C4—61no—
664C2×C3×C4—61no—
665C2×C3×C4—61no—
666C2×C3×C4—122no—
667C2×C3×C4C23×D311yescharacteristic
668C2×C3×C4C23×D311yescharacteristic
669#67—24no—
670#67—24no—
671#67—64no—
672#67—64no—
673#67—64no—
674#67—64no—
675#67—124no—
676#67—122no—
677#67—122no—
678#67—122no—
679C2×Dic3—24no—
680C2×Dic3—21no—
681C2×Dic3—21no—
682C2×Dic3—24no—
683C2×Dic3—21no—
684C2×Dic3—31no—
685C2×Dic3—31no—
686C2×Dic3—61no—
687C2×Dic3—62no—
688C2×Dic3—62no—
689C2×Dic3D3×D411yescharacteristic
690C2×Dic3D3×D411yescharacteristic
691D12—21no—
692D12—21no—
693D12—32no—
694D12—32no—
695D12—42no—
696D12—62no—
697D12—64no—
698D12—64no—
699D12—61no—
700D12—61no—
701D12—61no—
702D12—61no—
703D12—61no—
704D12—61no—
705D12—121no—
706D12—121no—
707D12—121no—
708D12—122no—
709D12—122no—
710D12—122no—
711D12—122no—
712D12—122no—
713D12—242no—
714C4×D3—21no—
715C4×D3—21no—
716C4×D3—42no—
717C4×D3—62no—
718C4×D3—64no—
719C4×D3—64no—
720C4×D3—64no—
721C4×D3—64no—
722C4×D3—64no—
723C4×D3—62no—
724C4×D3—62no—
725C4×D3—61no—
726C4×D3—61no—
727C4×D3—61no—
728C4×D3—61no—
729C4×D3—62no—
730C4×D3—64no—
731C4×D3—121no—
732C4×D3—121no—
733C4×D3C2×D1212yes—
734C4×D3D3×D412yes—
735Dic6—21no—
736Dic6—21no—
737Dic6—64no—
738Dic6—64no—
739Dic6C2×D1212yescomplemented
740Dic6D3×D412yescomplemented
741C3×C8—21no—
742C3×C8—21no—
743C3×C8—41no—
744C3×C8—61no—
745C3×C8—61no—
746C3⋊C8—21no—
747C3⋊C8—21no—
748C3⋊C8—61no—
749C3⋊C8—61no—
750C3⋊C8—121no—
751C2×C32—42no—
752C2×C32C2×#12011yescharacteristic
753C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
754C2×C32#57511yescharacteristic
755C3⋊D3—22no—
756C3⋊D3—42no—
757C3⋊D3—81no—
758C3×D3—22no—
759C3×D3—41no—
760C3×D3—81no—
761C24—91no—
762C24—181no—
763C24—181no—
764#41—34no—
765#41—62no—
766#41—62no—
767#41—62no—
768#41—94no—
769#41—182no—
770#41—188no—
771#41—188no—
772#41—182no—
773#41—182no—
774C2×Q8—31no—
775C2×Q8—31no—
776C2×Q8—181no—
777C2×Q8—182no—
778C2×Q8—182no—
779C2×D4—31no—
780C2×D4—61no—
781C2×D4—61no—
782C2×D4—61no—
783C2×D4—91no—
784C2×D4—91no—
785C2×D4—181no—
786C2×D4—182no—
787C2×D4—182no—
788C2×D4—181no—
789C2×D4—181no—
790C2×D4—181no—
791C2×D4—181no—
792C2×D4—181no—
793C2×D4—181no—
794C2×D4—182no—
795C2×D4—188no—
796C2×D4—182no—
797C2×D4—364no—
798C2×D4C2×D3211yescharacteristic
799C22×C4—31no—
800C22×C4—31no—
801C22×C4—61no—
802C22×C4—61no—
803C22×C4—61no—
804C22×C4—91no—
805C22×C4—91no—
806C22×C4—91no—
807C22×C4—91no—
808C22×C4—182no—
809C22×C4—182no—
810C22×C4—181no—
811C22×C4—181no—
812C22×C4—181no—
813C22×C4—188no—
814SD16—62no—
815SD16—182no—
816SD16—182no—
817SD16—182no—
818D8—62no—
819D8—182no—
820D8—182no—
821D8—182no—
822M16—62no—
823M16—182no—
824C2×C8—31no—
825C2×C8—31no—
826C2×C8—91no—
827C2×C8C2×D3211yescharacteristic
828C4⋊C4—31no—
829C4⋊C4—61no—
830C4⋊C4C2×D3211yescharacteristic
831C22⋊C4—61no—
832C22⋊C4—181no—
833C22⋊C4—181no—
834C22⋊C4—181no—
835C22×C3—22no—
836C22×C3—22no—
837C22×C3—21no—
838C22×C3—32no—
839C22×C3—42no—
840C22×C3—41no—
841C22×C3—41no—
842C22×C3—41no—
843C22×C3—41no—
844C22×C3—61no—
845C22×C3—61no—
846C22×C3—61no—
847C22×C3—61no—
848C22×C3—61no—
849C22×C3—81no—
850C22×C3—81no—
851C22×C3—121no—
852C22×C3—121no—
853C22×C3—121no—
854C22×C3C2×D3×D411yescharacteristic
855C22×C3C2×D3×D411yescharacteristic
856C2×D3—21no—
857C2×D3—21no—
858C2×D3—21no—
859C2×D3—21no—
860C2×D3—21no—
861C2×D3—32no—
862C2×D3—32no—
863C2×D3—41no—
864C2×D3—41no—
865C2×D3—41no—
866C2×D3—62no—
867C2×D3—61no—
868C2×D3—61no—
869C2×D3—61no—
870C2×D3—61no—
871C2×D3—62no—
872C2×D3—62no—
873C2×D3—121no—
874C2×D3—121no—
875C2×D3—122no—
876C2×D3—124no—
877C2×D3—124no—
878C2×D3—128no—
879C2×D3—128no—
880C2×D3—121no—
881C2×D3—121no—
882C2×D3—121no—
883C2×D3—121no—
884C2×D3—121no—
885C2×D3—121no—
886C2×D3—121no—
887C2×D3—121no—
888C2×D3—121no—
889C2×D3—121no—
890C2×D3—248no—
891C2×D3—241no—
892C2×D3—241no—
893C2×D3—241no—
894C2×D3—241no—
895C2×D3—241no—
896C2×D3—244no—
897C2×D3—244no—
898C2×D3#88212yes—
899C3×C4—21no—
900C3×C4—21no—
901C3×C4—32no—
902C3×C4—41no—
903C3×C4—41no—
904C3×C4—62no—
905C3×C4—61no—
906C3×C4—62no—
907C3×C4—81no—
908C3×C4—121no—
909C3×C4C22×D1211yescharacteristic
910C3×C4C2×D3×D411yescharacteristic
911C3×C4C2×D3×D411yescharacteristic
912C3×C4C2×D3×D411yescharacteristic
913Dic3—22no—
914Dic3—22no—
915Dic3—21no—
916Dic3—41no—
917Dic3—61no—
918Dic3—61no—
919Dic3—121no—
920Dic3#88212yes—
921C32#300611yescharacteristic, complemented, Sylow
922C23—21no—
923C23—31no—
924C23—31no—
925C23—61no—
926C23—91no—
927C23—184no—
928C23—182no—
929C23—182no—
930C23—181no—
931C23—181no—
932C23—362no—
933C23—362no—
934C23—362no—
935C23—361no—
936C23—362no—
937C23—362no—
938Q8—32no—
939Q8—32no—
940Q8—61no—
941Q8—61no—
942Q8—184no—
943D4—21no—
944D4—64no—
945D4—64no—
946D4—61no—
947D4—61no—
948D4—92no—
949D4—122no—
950D4—184no—
951D4—184no—
952D4—184no—
953D4—181no—
954D4—181no—
955D4—181no—
956D4—362no—
957D4—362no—
958D4—362no—
959D4—362no—
960D4D3×D1212yescomplemented
961C2×C4—21no—
962C2×C4—31no—
963C2×C4—32no—
964C2×C4—32no—
965C2×C4—31no—
966C2×C4—64no—
967C2×C4—64no—
968C2×C4—61no—
969C2×C4—61no—
970C2×C4—61no—
971C2×C4—61no—
972C2×C4—61no—
973C2×C4—91no—
974C2×C4—122no—
975C2×C4—182no—
976C2×C4—184no—
977C2×C4—182no—
978C2×C4—184no—
979C2×C4—184no—
980C2×C4—182no—
981C2×C4—181no—
982C2×C4—181no—
983C2×C4C22×D3211yescharacteristic
984C8—21no—
985C8—61no—
986C8—61no—
987C8—181no—
988C2×C3—21no—
989C2×C3—21no—
990C2×C3—21no—
991C2×C3—42no—
992C2×C3—42no—
993C2×C3—62no—
994C2×C3—82no—
995C2×C3—121no—
996C2×C3—241no—
997C2×C3C2×#88211yescharacteristic
998C2×C3D3×#12011yescharacteristic
999C2×C3#576811yescharacteristic
1000C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
1001C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
1002C2×C3#577711yescharacteristic
1003D3—22no—
1004D3—41no—
1005D3—62no—
1006D3—62no—
1007D3—81no—
1008D3—122no—
1009D3—122no—
1010D3—122no—
1011D3—242no—
1012D3—241no—
1013D3—241no—
1014D3—481no—
1015C22—22no—
1016C22—32no—
1017C22—41no—
1018C22—41no—
1019C22—61no—
1020C22—61no—
1021C22—61no—
1022C22—61no—
1023C22—61no—
1024C22—92no—
1025C22—121no—
1026C22—121no—
1027C22—121no—
1028C22—181no—
1029C22—181no—
1030C22—182no—
1031C22—368no—
1032C22—364no—
1033C22—361no—
1034C22—361no—
1035C22—361no—
1036C22—361no—
1037C22—361no—
1038C22—724no—
1039C22D32×D411yescharacteristic
1040C4—32no—
1041C4—41no—
1042C4—61no—
1043C4—62no—
1044C4—62no—
1045C4—121no—
1046C4—181no—
1047C4C2×D3×D1211yescharacteristic
1048C4D32×D411yescharacteristic
1049C3—21no—
1050C3#7888411yescharacteristic, complemented
1051C3#8008411yescharacteristic, complemented
1052C2—42no—
1053C2—62no—
1054C2—121no—
1055C2—182no—
1056C2—241no—
1057C2—362no—
1058C2—721no—
1059C2D3×#88211yescharacteristic
1060C2#1059472611yescharacteristic
1061C2#1059474611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
hypercenter#102D32
hypocenterC32#3006
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. C2×#64312C2semidirect
2. C2×#63925C2semidirect
3. C2×#63794C2semidirect
4. D3×#895C2semidirect
5. #10592472C2semidirect
6. C3×#4781C2semidirect
7. C3×#4771C2semidirect
8. #10591456C2semidirect
9. #10591452C2semidirect
10. #10590967C2semidirect
11. #10590936C2semidirect
12. #10590824C2semidirect
13. #10590615C2semidirect
14. #10590609C2semidirect
15. #10590606C2semidirect
18. C2×D4×C3⋊D3C22semidirect
20. C2×C3×#237C22semidirect
28. C2×D3×D12C22semidirect
31. C2×#3799C22semidirect
32. C2×#3797C22semidirect
33. C2×#3753C22semidirect
34. C2×#3745C22semidirect
36. C2×C3×#213C22semidirect
37. C2×C3×#204C22semidirect
38. C2×C3×ΓL(1,𝔽25)C22semidirect
39. C3×#895C22semidirect
40. C3×D3×C4⋊C4C22semidirect
45. #63909C22semidirect
47. C2×#3717C22semidirect
48. C2×#3717C22semidirect
49. C2×#3715C22semidirect
50. C2×#3714C22semidirect
51. C2×#3711C22semidirect
53. C32×#102C22semidirect
54. #63647C22semidirect
55. #63636C22semidirect
56. C3×#832C22semidirect
57. C3×(C2×D3)⋊C8C22semidirect
58. C3×#816C22semidirect
59. C3×#810C22semidirect
60. C3×#810C22semidirect
61. #63565C22semidirect
62. #63564C22semidirect
63. #63557C22semidirect
64. (C2×D3)⋊(C3⋊C8)C22semidirect
88. #4781D3semidirect
93. #4771D3semidirect
114. C3×#237D4semidirect
146. #3799D4semidirect
184. C2×#237C2×D3semidirect
218. C2×#213C2×D3semidirect
231. C2×#204C2×D3semidirect
233. C2×ΓL(1,𝔽25)C2×D3semidirect
241. #895C2×D3semidirect
242. D3×C4⋊C4C2×D3semidirect
250. C3×#102C2×D3semidirect
251. C3×#102C2×D3semidirect
254. #832C2×D3semidirect
263. (C2×D3)⋊C8C2×D3semidirect
264. #816C2×D3semidirect
266. #810C2×D3semidirect
267. #810C2×D3semidirect
289. C32×D4C2×D4semidirect
298. C4⋊(C3⋊D3)C2×D4semidirect
320. C3×Dic6C2×D4semidirect
321. C3×Dic6C2×D4semidirect
405. #237D12semidirect
529. C2×C3⋊D3AGL(1,ℤ/8)semidirect
592. #102D32semidirect
649. C3×D4C2×D12semidirect
650. C3×D4D3×D4semidirect
739. Dic6C2×D12semidirect
740. Dic6D3×D4semidirect
921. C32#3006semidirect
960. D4D3×D12semidirect
1050. C3#78884semidirect
1051. C3#80084semidirect

Maximal subgroups

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

subgroupindex
C2×#643122
C2×#639252
C2×#637942
D3×#8952
#105924722
C3×#47812
C3×#47712
#105914562
#105914522
#105909672
#105909362
#105908242
#105906152
#105906092
#105906062
#800843
#788843