Finite Group Databasebeta

← #11864157

Subgroups — #11864157

Order 1152.

1693 conjugacy classes of subgroups.

The subgroup lattice has 1051 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#239C211yesmaximal, characteristic, complemented
2C2×#63941C211yesmaximal, characteristic, complemented
3C2×#63798C211yesmaximal, characteristic, complemented
4#10594612C211yesmaximal, characteristic, complemented
5#10592502C211yesmaximal, characteristic, complemented
6C3×#4810C211yesmaximal, characteristic, complemented
7C3×#4806C211yesmaximal, characteristic, complemented
8#10591586C211yesmaximal, characteristic, complemented
9#10591583C211yesmaximal, characteristic, complemented
10#10590944C211yesmaximal, characteristic, complemented
11#10590937C211yesmaximal, characteristic, complemented
12#10590823C211yesmaximal, characteristic, complemented
13#10590615C211yesmaximal, characteristic, complemented
14#10590612C211yesmaximal, characteristic, complemented
15#10590595C211yesmaximal, characteristic, complemented
16#80084—31nomaximal
17#80040—31nomaximal
18C2×#3832C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic, complemented
20C2×C3×D3×Q8C2211yescharacteristic, complemented
21D3×#239—24no—
22D3×#239—24no—
23C2×#3802—21no—
24C2×#3802C2211yescharacteristic, complemented
25C2×D3×D12—21no—
26C2×D3×D12C2211yescharacteristic, complemented
27C2×C4×D32—21no—
28C2×C4×D32C2211yescharacteristic
29C2×#3799—21no—
30C2×#3799C2211yescharacteristic, complemented
31C2×#3796—21no—
32C2×#3796C2211yescharacteristic
33C2×#3743C2211yescharacteristic, complemented
34C4⋊C4×C3⋊D3C2211yescharacteristic, complemented
35C2×C3×#215C2211yescharacteristic, complemented
36C2×C3×#215C2211yescharacteristic, complemented
37C2×C3×D24C2211yescharacteristic, complemented
38C2×C3×#204C2211yescharacteristic, complemented
39C3×#895C2211yescharacteristic
40C3×#895C2211yescharacteristic, complemented
41#63941—24no—
42#63921—21no—
43#63908C2211yescharacteristic
44#63908C2211yescharacteristic, complemented
45#63885—21no—
46#63885—21no—
47C2×#3715C2211yescharacteristic, complemented
48C2×#3714C2211yescharacteristic, complemented
49C2×#3714C2211yescharacteristic, complemented
50C2×#3713C2211yescharacteristic, complemented
51C2×#3712C2211yescharacteristic, complemented
52#63798—24no—
53C32×#103C2211yescharacteristic, complemented
54#63662C2211yescharacteristic, complemented
55#63648C2211yescharacteristic, complemented
56#63636C2211yescharacteristic, complemented
57C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
58C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
59C3×#810C2211yescharacteristic, complemented
60C3×#809C2211yescharacteristic, complemented
61#63566C2211yescharacteristic, complemented
62#63563C2211yescharacteristic, complemented
63(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
64(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
65C2×D3×#41—31no—
66C22×#239—31no—
67C2×#914—31no—
68C2×#914—31no—
69C2×#914—31no—
70C2×#911—31no—
71D3×#121—31no—
72D3×#121—31no—
73C3×#449—31no—
74C3×#448—31no—
75#5238—31no—
76#5227—31no—
77#5172—31no—
78#5172—31no—
79#5170—31no—
80#5156—31no—
81#5037—31no—
82#5036—31no—
83#4810—31no—
84#4810D311yescharacteristic, complemented
85#4806D311yescharacteristic, complemented
86#4803—31no—
87#4803—31no—
88#4803—31no—
89#4803—61no—
90#4773—31no—
91#4771—31no—
92#4734—31no—
93#4732—31no—
94#4726—31no—
95#4726—31no—
96C22×D32—21no—
97C22×D32—21no—
98C22×D32D411yescharacteristic
99C2×C32×Q8C2311yescharacteristic
100#3832—22no—
101#3832D414yescomplemented
102C2×C4⋊(C3⋊D3)—21no—
103C2×C4⋊(C3⋊D3)C2311yescharacteristic
104C2×C4×C3⋊D3—21no—
105C2×C4×C3⋊D3—21no—
106C2×C4×C3⋊D3C2311yescharacteristic
107C3×#239—22no—
108C3×#239—22no—
109C3×D3×Q8—22no—
110C3×D3×Q8—22no—
111C2×C3×D12—21no—
112C2×C3×D12—21no—
113C2×C3×D12—21no—
114C2×C3×D12C2311yescharacteristic
115C2×C3×D12C2311yescharacteristic
116C2×C3×D12C2311yescharacteristic
117C2×C3×C4×D3—21no—
118C2×C3×C4×D3—21no—
119C2×C3×C4×D3C2311yescharacteristic
120C2×C3×C4×D3C2311yescharacteristic
121C2×C3×Dic6—21no—
122C2×C3×Dic6C2311yescharacteristic
123C2×#626—21no—
124C2×#626—21no—
125C2×#626—21no—
126C2×#625—21no—
127C2×#625—21no—
128C2×#625—21no—
129C2×#624—21no—
130C2×#624D411yescharacteristic
131C2×D3×Dic3—21no—
132C2×D3×Dic3D411yescharacteristic
133C2×D3×Dic3D411yescharacteristic
134#3802—22no—
135#3802—22no—
136#3802—44no—
137D3×D12—28no—
138D3×D12—22no—
139D3×D12—22no—
140C4×D32—28no—
141C4×D32—22no—
142C4×D32—22no—
143#3799—28no—
144#3799—22no—
145#3799—22no—
146#3796—28no—
147#3796—22no—
148#3796D414yescomplemented
149C2×C32×C8C2311yescharacteristic
150C32×C4⋊C4C2311yescharacteristic
151C4⋊(C3⋊Dic3)C2311yescharacteristic
152#3750—21no—
153C2×C3⋊(C3⋊C8)C2311yescharacteristic
154#3743—22no—
155C3×#215—22no—
156C3×#215—22no—
157C3×(C2×D3)⋊C4—21no—
158C3×(C2×D3)⋊C4—21no—
159C2×C3×C3⋊C8C2311yescharacteristic
160C2×C3×C3⋊C8C2311yescharacteristic
161C3×D24—22no—
162C3×#204—22no—
163(C2×D3)⋊Dic3—21no—
164(C2×D3)⋊Dic3—21no—
165#3715—22no—
166#3714—22no—
167#3714—22no—
168#3713—22no—
169#3712—22no—
170#3006—91noSylow
171C2×C3×#41—31no—
172C22×C3×Q8—31no—
173D3×#41—64no—
174D3×#41—64no—
175C2×#239—31no—
176C2×#239—31no—
177C2×#239—31no—
178C2×#239—31no—
179C2×#239—61no—
180C2×#239—61no—
181C2×#239—61no—
182C2×#239—64no—
183C2×#239—64no—
184C2×#239C2×D311yescharacteristic, complemented
185C2×D3×Q8C2×D311yescharacteristic, complemented
186C2×#237—31no—
187C2×#237—61no—
188C2×D3×D4—31no—
189C2×D3×D4—31no—
190C2×D3×D4—31no—
191C2×D3×D4—61no—
192C2×D3×D4—61no—
193C2×D3×D4—61no—
194C2×#235—31no—
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×SD16—31no—
204C2×C3×SD16—31no—
205C2×C3×D8—31no—
206C3×#121—31no—
207C3×#121—31no—
208C2×#215—31no—
209C2×#215C2×D311yescharacteristic, complemented
210C2×#215C2×D311yescharacteristic, complemented
211#939—61no—
212#939—61no—
213#938—31no—
214#938—31no—
215C2×#214—31no—
216C2×#213—31no—
217C2×#213—31no—
218C2×#213—31no—
219C2×#213—31no—
220#930—31no—
221#930—31no—
222#914—64no—
223#914—64no—
224#914—64no—
225#911—64no—
226C2×D24—31no—
227C2×D24—31no—
228C2×D24C2×D311yescharacteristic, complemented
229C2×#204C2×D311yescharacteristic, complemented
230C2×ΓL(1,𝔽25)—31no—
231C2×ΓL(1,𝔽25)—31no—
232C2×ΓL(1,𝔽25)—31no—
233C2×ΓL(1,𝔽25)—31no—
234C2×ΓL(1,𝔽25)—61no—
235#895C2×D311yescharacteristic
236#895C2×D311yescharacteristic, complemented
237D3×C4⋊C4—31no—
238D3×C4⋊C4—31no—
239D3×C4⋊C4—61no—
240#884—61no—
241#884—61no—
242D3×C22⋊C4—61no—
243D3×C22⋊C4—61no—
244C3×#103—21no—
245C3×#103—31no—
246C3×#103C2×D311yescharacteristic, complemented
247C3×#103C2×D311yescharacteristic, complemented
248C3×#102—31no—
249C3×C22⋊C8—31no—
250C3×C22⋊C8—31no—
251#835—31no—
252#835—31no—
253#835—31no—
254#835—61no—
255#832—31no—
256#830—31no—
257#830—31no—
258#821—31no—
259#821—31no—
260#821—31no—
261#821—61no—
262(C2×D3)⋊C8—31no—
263(C2×D3)⋊C8—31no—
264(C2×D3)⋊C8C2×D311yescharacteristic, complemented
265(C2×D3)⋊C8C2×D311yescharacteristic, complemented
266#816—31no—
267#810C2×D311yescharacteristic, complemented
268#809—31no—
269#809—31no—
270#809—61no—
271#809C2×D311yescharacteristic, complemented
272C22×C3⋊D3—21no—
273C22×C3⋊D3C2×D411yescharacteristic
274C22×C3×D3—21no—
275C22×C3×D3—21no—
276C22×C3×D3—21no—
277C22×C3×D3C2×D411yescharacteristic
278C22×C3×D3C2×D411yescharacteristic
279C2×D32—24no—
280C2×D32—22no—
281C2×D32—22no—
282C2×D32—41no—
283C2×D32—42no—
284C2×D32—42no—
285C2×D32—42no—
286C2×D32—42no—
287C2×D32—42no—
288C32×Q8—21no—
289C32×Q8C2×D412yescomplemented
290C2×C32×C4—21no—
291C2×C32×C4—21no—
292C2×C32×C4C2411yescharacteristic
293C2×C3⋊Dic3—21no—
294C2×C3⋊Dic3C2×D411yescharacteristic
295C4⋊(C3⋊D3)—24no—
296C4⋊(C3⋊D3)—21no—
297C4⋊(C3⋊D3)C2×D412yescomplemented
298C4×C3⋊D3—24no—
299C4×C3⋊D3—42no—
300C4×C3⋊D3C2×D412yes—
301C4×C3⋊D3C2×D412yes—
302C2×C3×Dic3—21no—
303C2×C3×Dic3C2×D411yescharacteristic
304C2×C3×Dic3C2×D411yescharacteristic
305C3×D12—24no—
306C3×D12—21no—
307C3×D12—21no—
308C3×D12—21no—
309C3×D12—21no—
310C3×D12—21no—
311C3×D12—42no—
312C3×D12—42no—
313C3×D12C2×D412yescomplemented
314C3×C4×D3—24no—
315C3×C4×D3—24no—
316C3×C4×D3—21no—
317C3×C4×D3—21no—
318C3×C4×D3—21no—
319C3×C4×D3—21no—
320C3×Dic6—24no—
321C3×Dic6—21no—
322C3×Dic6C2×D412yescomplemented
323#626—24no—
324#626—24no—
325#626—24no—
326#625—42no—
327#625—42no—
328#625—42no—
329#624—24no—
330#624—22no—
331D3×Dic3—22no—
332D3×Dic3—24no—
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—31no—
347#448—91no—
348#447—91no—
349#447—91no—
350#417—91no—
351#417—91no—
352#407—91no—
353C23×D3—31no—
354C23×D3—31no—
355C23×D3—61no—
356C23×D3—61no—
357C23×D3—61no—
358C23×D3—61no—
359C3×#41—62no—
360C3×#41—62no—
361C2×C3×Q8—21no—
362C2×C3×Q8—31no—
363C2×C3×Q8—61no—
364C2×C3×Q8—62no—
365C2×C3×Q8—62no—
366C2×C3×Q8C22×D311yescharacteristic
367C2×C3×Q8C22×D311yescharacteristic
368C2×C3×D4—31no—
369C2×C3×D4—31no—
370C2×C3×D4—31no—
371C2×C3×D4—61no—
372C2×C3×D4—61no—
373C2×C3×D4—61no—
374C22×C3×C4—31no—
375C22×C3×C4—31no—
376C22×C3×C4—61no—
377C22×C3×C4—61no—
378C2×#67—61no—
379C2×#67—61no—
380C2×#67—61no—
381C2×#67—61no—
382C2×#67—61no—
383C2×#67—61no—
384C2×#67—61no—
385C2×#67—61no—
386C2×#67—61no—
387C22×Dic3—31no—
388C22×Dic3—31no—
389C22×Dic3—61no—
390#239—22no—
391#239—22no—
392#239—34no—
393#239—34no—
394#239—34no—
395#239—64no—
396#239—62no—
397#239—62no—
398#239—68no—
399#239—62no—
400#239—62no—
401#239—62no—
402#239—68no—
403#239—122no—
404D3×Q8—22no—
405D3×Q8—22no—
406#237—34no—
407#237—62no—
408#237—68no—
409D3×D4—62no—
410D3×D4—62no—
411D3×D4—68no—
412D3×D4—62no—
413D3×D4—62no—
414D3×D4—62no—
415D3×D4—62no—
416D3×D4—124no—
417D3×D4—124no—
418#235—62no—
419#235—68no—
420#235—62no—
421C2×D12—21no—
422C2×D12—21no—
423C2×D12—21no—
424C2×D12—31no—
425C2×D12—31no—
426C2×D12—61no—
427C2×D12—62no—
428C2×D12—68no—
429C2×D12—61no—
430C2×D12—61no—
431C2×D12—61no—
432C2×D12—61no—
433C2×D12—61no—
434C2×D12—62no—
435C2×D12—121no—
436C2×D12C22×D311yescharacteristic
437C2×D12C22×D311yescharacteristic
438C2×D12C22×D311yescharacteristic
439C2×C4×D3—21no—
440C2×C4×D3—21no—
441C2×C4×D3—31no—
442C2×C4×D3—31no—
443C2×C4×D3—31no—
444C2×C4×D3—31no—
445C2×C4×D3—31no—
446C2×C4×D3—31no—
447C2×C4×D3—61no—
448C2×C4×D3—62no—
449C2×C4×D3—62no—
450C2×C4×D3—62no—
451C2×C4×D3—62no—
452C2×C4×D3—68no—
453C2×C4×D3—68no—
454C2×C4×D3—61no—
455C2×C4×D3—61no—
456C2×C4×D3—61no—
457C2×C4×D3—61no—
458C2×C4×D3—61no—
459C2×C4×D3—61no—
460C2×C4×D3—61no—
461C2×C4×D3—121no—
462C2×C4×D3—121no—
463C2×C4×D3C22×D311yescharacteristic
464C2×C4×D3C22×D311yescharacteristic
465C2×Dic6—21no—
466C2×Dic6C22×D311yescharacteristic
467C3×SD16—62no—
468C3×SD16—62no—
469C3×SD16—62no—
470C3×D8—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⋊C4C22×D311yescharacteristic
478C3×C4⋊C4C22×D311yescharacteristic
479C3×C22⋊C4—61no—
480C3×C22⋊C4—61no—
481#217—61no—
482#217—61no—
483#215—22no—
484#215—22no—
485#215—62no—
486#214—62no—
487#213—62no—
488#213—62no—
489#213—62no—
490#213—62no—
491(C2×D3)⋊C4—21no—
492(C2×D3)⋊C4—21no—
493(C2×D3)⋊C4—61no—
494(C2×D3)⋊C4—61no—
495C4⋊Dic3—31no—
496C4⋊Dic3—31no—
497C4⋊Dic3—61no—
498Dic3⋊C4—61no—
499Dic3⋊C4—61no—
500Dic3⋊C4—121no—
501C2×C3⋊C8—31no—
502C2×C3⋊C8—31no—
503C2×C3⋊C8—61no—
504C2×C3⋊C8C22×D311yescharacteristic
505C2×C3⋊C8C22×D311yescharacteristic
506D24—22no—
507D24—62no—
508D24—62no—
509#204—22no—
510ΓL(1,𝔽25)—62no—
511ΓL(1,𝔽25)—62no—
512ΓL(1,𝔽25)—62no—
513ΓL(1,𝔽25)—62no—
514ΓL(1,𝔽25)—122no—
515C22×C32C22×D411yescharacteristic
516C2×C3⋊D3—21no—
517C2×C3⋊D3—21no—
518C2×C3⋊D3—22no—
519C2×C3⋊D3—41no—
520C2×C3⋊D3—41no—
521C2×C3⋊D3#12012yes—
522C2×C3×D3—21no—
523C2×C3×D3—21no—
524C2×C3×D3—21no—
525C2×C3×D3—22no—
526C2×C3×D3—21no—
527C2×C3×D3—21no—
528C2×C3×D3—41no—
529C2×C3×D3—41no—
530C2×C3×D3—41no—
531C2×C3×D3—41no—
532C2×C3×D3—41no—
533C2×C3×D3—41no—
534C2×C3×D3—41no—
535C2×C3×D3—41no—
536C2×C3×D3AGL(1,ℤ/8)12yescomplemented
537D32—44no—
538D32—48no—
539D32—84no—
540C32×C4—22no—
541C32×C4—41no—
542C32×C4C22×D411yescharacteristic
543C32×C4C22×D411yescharacteristic
544C3⋊Dic3—41no—
545C3⋊Dic3#12012yes—
546C3×Dic3—21no—
547C3×Dic3—21no—
548C3×Dic3—22no—
549C2×#41—31no—
550C2×#41—91no—
551C2×#41—91no—
552C2×#41—91no—
553C2×#41—181no—
554C2×#41—181no—
555C2×#41—184no—
556C2×#41—184no—
557C22×Q8—31no—
558C22×D4—91no—
559C22×D4—91no—
560C22×D4—181no—
561C22×D4—181no—
562C23×C4—91no—
563C23×C4—181no—
564AGL(1,ℤ/8)—184no—
565AGL(1,ℤ/8)—184no—
566C2×SD16—31no—
567C2×SD16—31no—
568C2×SD16—31no—
569C2×SD16—91no—
570C2×D8—31no—
571C2×D8—91no—
572C2×D8—91no—
573C2×D8—91no—
574C2×M16—91no—
575C2×M16—91no—
576#121—31no—
577#121—31no—
578#121—91no—
579#121—91no—
580#121—181no—
581#121—181no—
582C2×C4⋊C4—91no—
583C2×C22⋊C4—181no—
584#103—31no—
585#103—91no—
586#103—91no—
587#103D3211yescharacteristic, complemented
588#102—31no—
589#102—91no—
590#102—91no—
591#102—91no—
592C22⋊C8—31no—
593C22⋊C8—31no—
594C22⋊C8—91no—
595C22⋊C8—91no—
596C23×C3—31no—
597C23×C3—31no—
598C23×C3—61no—
599C23×C3—61no—
600C23×C3—61no—
601C22×D3—21no—
602C22×D3—21no—
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—121no—
616C22×D3—121no—
617C22×D3—121no—
618C22×D3—122no—
619C22×D3—122no—
620C22×D3—122no—
621C22×D3—122no—
622C22×D3—122no—
623C22×D3—122no—
624C22×D3—122no—
625C22×D3—122no—
626C22×D3—122no—
627C22×D3—122no—
628C22×D3D3×D411yescharacteristic
629C22×D3D3×D411yescharacteristic
630C3×Q8—21no—
631C3×Q8—21no—
632C3×Q8—22no—
633C3×Q8—32no—
634C3×Q8—41no—
635C3×Q8—64no—
636C3×Q8—61no—
637C3×Q8D3×D412yescomplemented
638C3×Q8D3×D412yescomplemented
639C3×D4—32no—
640C3×D4—64no—
641C3×D4—61no—
642C3×D4—61no—
643C3×D4—61no—
644C3×D4—61no—
645C3×D4—61no—
646C3×D4—122no—
647C3×D4—122no—
648C2×C3×C4—21no—
649C2×C3×C4—21no—
650C2×C3×C4—21no—
651C2×C3×C4—21no—
652C2×C3×C4—21no—
653C2×C3×C4—31no—
654C2×C3×C4—31no—
655C2×C3×C4—41no—
656C2×C3×C4—41no—
657C2×C3×C4—64no—
658C2×C3×C4—64no—
659C2×C3×C4—61no—
660C2×C3×C4—61no—
661C2×C3×C4—61no—
662C2×C3×C4—61no—
663C2×C3×C4—61no—
664C2×C3×C4C23×D311yescharacteristic
665C2×C3×C4C23×D311yescharacteristic
666#67—64no—
667#67—64no—
668#67—64no—
669#67—122no—
670#67—122no—
671#67—122no—
672#67—122no—
673#67—122no—
674#67—122no—
675C2×Dic3—21no—
676C2×Dic3—31no—
677C2×Dic3—31no—
678C2×Dic3—61no—
679C2×Dic3—62no—
680C2×Dic3—64no—
681C2×Dic3—62no—
682C2×Dic3—61no—
683C2×Dic3—61no—
684C2×Dic3—121no—
685C2×Dic3D3×D411yescharacteristic
686C2×Dic3D3×D411yescharacteristic
687D12—24no—
688D12—21no—
689D12—21no—
690D12—21no—
691D12—21no—
692D12—21no—
693D12—32no—
694D12—32no—
695D12—42no—
696D12—42no—
697D12—62no—
698D12—64no—
699D12—64no—
700D12—64no—
701D12—64no—
702D12—64no—
703D12—61no—
704D12—61no—
705D12—121no—
706D12—124no—
707D12D3×D412yescomplemented
708C4×D3—24no—
709C4×D3—24no—
710C4×D3—21no—
711C4×D3—21no—
712C4×D3—21no—
713C4×D3—21no—
714C4×D3—32no—
715C4×D3—32no—
716C4×D3—32no—
717C4×D3—32no—
718C4×D3—62no—
719C4×D3—62no—
720C4×D3—62no—
721C4×D3—62no—
722C4×D3—64no—
723C4×D3—64no—
724C4×D3—64no—
725C4×D3—64no—
726C4×D3—62no—
727C4×D3—62no—
728C4×D3—64no—
729C4×D3—124no—
730C4×D3—122no—
731C4×D3—122no—
732C4×D3—242no—
733Dic6—24no—
734Dic6—21no—
735Dic6D3×D412yescomplemented
736C3×C8—21no—
737C3×C8—21no—
738C3×C8—41no—
739C3×C8—61no—
740C3×C8—61no—
741C3⋊C8—21no—
742C3⋊C8—21no—
743C3⋊C8—61no—
744C3⋊C8—61no—
745C3⋊C8—121no—
746C2×C32C2×#12011yescharacteristic
747C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
748C2×C32#57511yescharacteristic
749C3⋊D3—22no—
750C3⋊D3—42no—
751C3×D3—22no—
752C3×D3—41no—
753C3×D3—42no—
754C3×D3—81no—
755C3×D3—81no—
756C24—91no—
757C24—181no—
758C24—181no—
759#41—62no—
760#41—62no—
761#41—94no—
762#41—94no—
763#41—182no—
764#41—182no—
765#41—188no—
766#41—182no—
767#41—182no—
768#41—188no—
769C2×Q8—31no—
770C2×Q8—61no—
771C2×Q8—62no—
772C2×Q8—62no—
773C2×Q8C2×D3211yescharacteristic
774C2×D4—31no—
775C2×D4—31no—
776C2×D4—31no—
777C2×D4—61no—
778C2×D4—61no—
779C2×D4—61no—
780C2×D4—91no—
781C2×D4—181no—
782C2×D4—181no—
783C2×D4—182no—
784C2×D4—182no—
785C2×D4—188no—
786C2×D4—181no—
787C2×D4—181no—
788C2×D4—182no—
789C2×D4—182no—
790C2×D4—181no—
791C2×D4—181no—
792C2×D4—181no—
793C2×D4—364no—
794C22×C4—31no—
795C22×C4—31no—
796C22×C4—61no—
797C22×C4—61no—
798C22×C4—91no—
799C22×C4—91no—
800C22×C4—91no—
801C22×C4—91no—
802C22×C4—181no—
803C22×C4—181no—
804C22×C4—181no—
805C22×C4—182no—
806C22×C4—182no—
807C22×C4—188no—
808C22×C4—181no—
809SD16—62no—
810SD16—62no—
811SD16—62no—
812SD16—182no—
813D8—62no—
814D8—182no—
815D8—182no—
816D8—182no—
817M16—182no—
818M16—182no—
819C2×C8—31no—
820C2×C8—31no—
821C2×C8—91no—
822C2×C8C2×D3211yescharacteristic
823C4⋊C4—91no—
824C4⋊C4—181no—
825C4⋊C4C2×D3211yescharacteristic
826C22⋊C4—61no—
827C22⋊C4—61no—
828C22⋊C4—181no—
829C22⋊C4—181no—
830C22×C3—21no—
831C22×C3—32no—
832C22×C3—61no—
833C22×C3—61no—
834C22×C3—61no—
835C22×C3—61no—
836C22×C3—62no—
837C22×C3—61no—
838C22×C3—121no—
839C22×C3—121no—
840C22×C3—121no—
841C22×C3—121no—
842C22×C3—121no—
843C22×C3—121no—
844C22×C3—121no—
845C22×C3—121no—
846C22×C3C2×D3×D411yescharacteristic
847C22×C3C2×D3×D411yescharacteristic
848C2×D3—21no—
849C2×D3—21no—
850C2×D3—21no—
851C2×D3—21no—
852C2×D3—21no—
853C2×D3—22no—
854C2×D3—32no—
855C2×D3—32no—
856C2×D3—41no—
857C2×D3—41no—
858C2×D3—41no—
859C2×D3—41no—
860C2×D3—41no—
861C2×D3—41no—
862C2×D3—41no—
863C2×D3—41no—
864C2×D3—62no—
865C2×D3—61no—
866C2×D3—61no—
867C2×D3—61no—
868C2×D3—61no—
869C2×D3—62no—
870C2×D3—62no—
871C2×D3—121no—
872C2×D3—121no—
873C2×D3—122no—
874C2×D3—124no—
875C2×D3—128no—
876C2×D3—124no—
877C2×D3—128no—
878C2×D3—121no—
879C2×D3—121no—
880C2×D3—121no—
881C2×D3—121no—
882C2×D3—241no—
883C2×D3—241no—
884C2×D3—244no—
885C2×D3—244no—
886C2×D3#91412yescomplemented
887C3×C4—22no—
888C3×C4—22no—
889C3×C4—21no—
890C3×C4—21no—
891C3×C4—42no—
892C3×C4—41no—
893C3×C4—41no—
894C3×C4—61no—
895C3×C4—61no—
896C3×C4—62no—
897C3×C4—81no—
898C3×C4C2×D3×D411yescharacteristic
899C3×C4C2×D3×D411yescharacteristic
900C3×C4C2×D3×D411yescharacteristic
901C3×C4C2×D3×D411yescharacteristic
902Dic3—21no—
903Dic3—22no—
904Dic3—21no—
905Dic3—32no—
906Dic3—32no—
907Dic3—62no—
908Dic3—121no—
909Dic3—121no—
910Dic3—241no—
911C32#300611yescharacteristic, complemented, Sylow
912C23—31no—
913C23—31no—
914C23—61no—
915C23—61no—
916C23—61no—
917C23—91no—
918C23—182no—
919C23—182no—
920C23—184no—
921C23—181no—
922C23—362no—
923C23—361no—
924C23—362no—
925C23—362no—
926C23—362no—
927C23—362no—
928Q8—21no—
929Q8—32no—
930Q8—64no—
931Q8—61no—
932Q8#380212yescomplemented
933D4—32no—
934D4—64no—
935D4—61no—
936D4—61no—
937D4—61no—
938D4—61no—
939D4—61no—
940D4—92no—
941D4—122no—
942D4—122no—
943D4—184no—
944D4—184no—
945D4—184no—
946D4—184no—
947D4—181no—
948D4—362no—
949D4—362no—
950D4—362no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—31no—
954C2×C4—31no—
955C2×C4—64no—
956C2×C4—64no—
957C2×C4—61no—
958C2×C4—61no—
959C2×C4—61no—
960C2×C4—61no—
961C2×C4—61no—
962C2×C4—91no—
963C2×C4—92no—
964C2×C4—92no—
965C2×C4—184no—
966C2×C4—182no—
967C2×C4—184no—
968C2×C4—182no—
969C2×C4—182no—
970C2×C4—184no—
971C2×C4—181no—
972C2×C4—362no—
973C2×C4C22×D3211yescharacteristic
974C8—21no—
975C8—61no—
976C8—61no—
977C8—181no—
978C2×C3—21no—
979C2×C3—21no—
980C2×C3—21no—
981C2×C3—62no—
982C2×C3—121no—
983C2×C3—122no—
984C2×C3—241no—
985C2×C3—241no—
986C2×C3D3×#12011yescharacteristic
987C2×C3D3×#12011yescharacteristic
988C2×C3C2×#91411yescharacteristic
989C2×C3#576811yescharacteristic
990C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
991C2×C3#577711yescharacteristic
992D3—22no—
993D3—41no—
994D3—42no—
995D3—62no—
996D3—62no—
997D3—81no—
998D3—81no—
999D3—122no—
1000D3—122no—
1001D3—122no—
1002D3—242no—
1003C22—32no—
1004C22—61no—
1005C22—61no—
1006C22—61no—
1007C22—61no—
1008C22—62no—
1009C22—61no—
1010C22—92no—
1011C22—121no—
1012C22—121no—
1013C22—121no—
1014C22—121no—
1015C22—121no—
1016C22—121no—
1017C22—121no—
1018C22—121no—
1019C22—181no—
1020C22—181no—
1021C22—182no—
1022C22—364no—
1023C22—368no—
1024C22—361no—
1025C22—361no—
1026C22—724no—
1027C22D32×D411yescharacteristic
1028C4—22no—
1029C4—41no—
1030C4—61no—
1031C4—61no—
1032C4—62no—
1033C4—92no—
1034C4—361no—
1035C4C2×#380211yescharacteristic
1036C4D32×D411yescharacteristic
1037C3—21no—
1038C3#8004011yescharacteristic, complemented
1039C3#8008411yescharacteristic, complemented
1040C2—62no—
1041C2—121no—
1042C2—122no—
1043C2—182no—
1044C2—241no—
1045C2—241no—
1046C2—362no—
1047C2#1059425811yescharacteristic
1048C2D3×#91411yescharacteristic
1049C2#1059476311yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
hypercenter#103D32
hypocenterC32#3006
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
1. C2×D3×#239C2semidirect
2. C2×#63941C2semidirect
3. C2×#63798C2semidirect
4. #10594612C2semidirect
5. #10592502C2semidirect
6. C3×#4810C2semidirect
7. C3×#4806C2semidirect
8. #10591586C2semidirect
9. #10591583C2semidirect
10. #10590944C2semidirect
11. #10590937C2semidirect
12. #10590823C2semidirect
13. #10590615C2semidirect
14. #10590612C2semidirect
15. #10590595C2semidirect
19. C2×C3×#239C22semidirect
20. C2×C3×D3×Q8C22semidirect
24. C2×#3802C22semidirect
26. C2×D3×D12C22semidirect
30. C2×#3799C22semidirect
33. C2×#3743C22semidirect
34. C4⋊C4×C3⋊D3C22semidirect
35. C2×C3×#215C22semidirect
36. C2×C3×#215C22semidirect
37. C2×C3×D24C22semidirect
38. C2×C3×#204C22semidirect
40. C3×#895C22semidirect
44. #63908C22semidirect
47. C2×#3715C22semidirect
48. C2×#3714C22semidirect
49. C2×#3714C22semidirect
50. C2×#3713C22semidirect
51. C2×#3712C22semidirect
53. C32×#103C22semidirect
54. #63662C22semidirect
55. #63648C22semidirect
56. #63636C22semidirect
57. C3×(C2×D3)⋊C8C22semidirect
58. C3×(C2×D3)⋊C8C22semidirect
59. C3×#810C22semidirect
60. C3×#809C22semidirect
61. #63566C22semidirect
62. #63563C22semidirect
63. (C2×D3)⋊(C3⋊C8)C22semidirect
64. (C2×D3)⋊(C3⋊C8)C22semidirect
84. #4810D3semidirect
85. #4806D3semidirect
101. #3832D4semidirect
148. #3796D4semidirect
184. C2×#239C2×D3semidirect
185. C2×D3×Q8C2×D3semidirect
209. C2×#215C2×D3semidirect
210. C2×#215C2×D3semidirect
228. C2×D24C2×D3semidirect
229. C2×#204C2×D3semidirect
236. #895C2×D3semidirect
246. C3×#103C2×D3semidirect
247. C3×#103C2×D3semidirect
264. (C2×D3)⋊C8C2×D3semidirect
265. (C2×D3)⋊C8C2×D3semidirect
267. #810C2×D3semidirect
271. #809C2×D3semidirect
289. C32×Q8C2×D4semidirect
297. C4⋊(C3⋊D3)C2×D4semidirect
313. C3×D12C2×D4semidirect
322. C3×Dic6C2×D4semidirect
536. C2×C3×D3AGL(1,ℤ/8)semidirect
587. #103D32semidirect
637. C3×Q8D3×D4semidirect
638. C3×Q8D3×D4semidirect
707. D12D3×D4semidirect
735. Dic6D3×D4semidirect
886. C2×D3#914semidirect
911. C32#3006semidirect
932. Q8#3802semidirect
1038. C3#80040semidirect
1039. C3#80084semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#2392
C2×#639412
C2×#637982
#105946122
#105925022
C3×#48102
C3×#48062
#105915862
#105915832
#105909442
#105909372
#105908232
#105906152
#105906122
#105905952
#800843
#800403