Finite Group Databasebeta

← #11864156

Subgroups — #11864156

Order 1152.

1691 conjugacy classes of subgroups.

The subgroup lattice has 1054 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64319C211yesmaximal, characteristic, complemented
2C2×#63939C211yesmaximal, characteristic, complemented
3C2×#63795C211yesmaximal, characteristic, complemented
4D3×#895C211yesmaximal, characteristic, complemented
5#10592505C211yesmaximal, characteristic, complemented
6C3×#4810C211yesmaximal, characteristic, complemented
7C3×#4803C211yesmaximal, characteristic, complemented
8#10591592C211yesmaximal, characteristic, complemented
9#10591588C211yesmaximal, characteristic, complemented
10#10590968C211yesmaximal, characteristic, complemented
11#10590945C211yesmaximal, characteristic, complemented
12#10590936C211yesmaximal, characteristic, complemented
13#10590613C211yesmaximal, characteristic, complemented
14#10590607C211yesmaximal, characteristic, complemented
15#10590598C211yesmaximal, characteristic, complemented
16#80084—31nomaximal
17#78884—31nomaximal
18C2×Q8×C3⋊D3C2211yescharacteristic, complemented
19C2×C3×#239C2211yescharacteristic
20C2×C3×#239C2211yescharacteristic, complemented
21#64319—24no—
22#64319—24no—
23C2×#3802—21no—
24C2×#3802C2211yescharacteristic, complemented
25C2×D3×D12—21no—
26C2×D3×D12C2211yescharacteristic, complemented
27C2×C4×D32—21no—
28C2×C4×D32C2211yescharacteristic
29C2×#3795—21no—
30C2×#3795—21no—
31C2×#3795C2211yescharacteristic
32C2×#3795C2211yescharacteristic, complemented
33C2×#3755C2211yescharacteristic, complemented
34C2×#3744C2211yescharacteristic, complemented
35#64104C2211yescharacteristic
36C2×C3×#215C2211yescharacteristic, complemented
37C2×C3×D24C2211yescharacteristic, complemented
38C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
39C3×#895C2211yescharacteristic, complemented
40C3×D3×C4⋊C4C2211yescharacteristic, complemented
41#63939—24no—
42D3×(C2×D3)⋊C4—21no—
43#63916C2211yescharacteristic
44#63910—21no—
45#63909C2211yescharacteristic, complemented
46#63886—21no—
47C2×#3716C2211yescharacteristic, complemented
48C2×#3714C2211yescharacteristic, complemented
49C2×#3714C2211yescharacteristic, complemented
50C2×#3713C2211yescharacteristic, complemented
51C2×#3711C2211yescharacteristic, complemented
52#63795—24no—
53C32×#103C2211yescharacteristic, complemented
54#63647C2211yescharacteristic, complemented
55#63637C2211yescharacteristic, complemented
56C3×#835C2211yescharacteristic, complemented
57C3×#821C2211yescharacteristic, complemented
58C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
59C3×#809C2211yescharacteristic, complemented
60C3×#809C2211yescharacteristic, complemented
61#63567C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, 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#4810D311yescharacteristic, complemented
83#4806—31no—
84#4806—31no—
85#4806—31no—
86#4806—61no—
87#4803D311yescharacteristic, complemented
88#4781—31no—
89#4781—31no—
90#4773—31no—
91#4773—31no—
92#4773—31no—
93#4771—31no—
94#4734—31no—
95#4726—31no—
96C22×D32—21no—
97C22×D32—21no—
98C22×D32D411yescharacteristic
99C2×C32×Q8C2311yescharacteristic
100Q8×C3⋊D3—22no—
101Q8×C3⋊D3—22no—
102C2×C4⋊(C3⋊D3)—21no—
103C2×C4⋊(C3⋊D3)C2311yescharacteristic
104C2×C4×C3⋊D3—21no—
105C2×C4×C3⋊D3C2311yescharacteristic
106C2×#634—21no—
107C2×#634C2311yescharacteristic
108C3×#239—22no—
109C3×#239—22no—
110C3×#239—22no—
111C3×#239D414yescomplemented
112C2×C3×D12—21no—
113C2×C3×D12—21no—
114C2×C3×D12—21no—
115C2×C3×D12C2311yescharacteristic
116C2×C3×D12C2311yescharacteristic
117C2×C3×D12C2311yescharacteristic
118C2×C3×C4×D3—21no—
119C2×C3×C4×D3—21no—
120C2×C3×C4×D3—21no—
121C2×C3×C4×D3C2311yescharacteristic
122C2×C3×C4×D3C2311yescharacteristic
123C2×#626—21no—
124C2×#626—21no—
125C2×#626—21no—
126C2×#625—21no—
127C2×#625—21no—
128C2×#625—21no—
129C2×#624D411yescharacteristic
130C2×D3×Dic3—21no—
131C2×D3×Dic3—21no—
132C2×D3×Dic3D411yescharacteristic
133C2×D3×Dic3D411yescharacteristic
134#3802—28no—
135#3802—22no—
136#3802—22no—
137D3×D12—22no—
138D3×D12—22no—
139D3×D12—44no—
140C4×D32—28no—
141C4×D32—22no—
142C4×D32—22no—
143#3795—28no—
144#3795—28no—
145#3795—22no—
146#3795—22no—
147#3795—22no—
148#3795D414yescomplemented
149C2×C32×C8C2311yescharacteristic
150C32×C4⋊C4C2311yescharacteristic
151#3755—22no—
152#3752—21no—
153C2×C3⋊(C3⋊C8)C2311yescharacteristic
154#3744—22no—
155C3×#215—22no—
156C3×(C2×D3)⋊C4—21no—
157C3×C4⋊Dic3C2311yescharacteristic
158C3×Dic3⋊C4—21no—
159C2×C3×C3⋊C8C2311yescharacteristic
160C2×C3×C3⋊C8C2311yescharacteristic
161C3×D24—22no—
162C3×ΓL(1,𝔽25)—22no—
163#3722—21no—
164(C2×D3)⋊Dic3—21no—
165#3716—22no—
166#3714—22no—
167#3714—22no—
168#3713—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×#239C2×D311yescharacteristic
178C2×#239C2×D311yescharacteristic, complemented
179C2×D3×Q8—31no—
180C2×D3×Q8—31no—
181C2×D3×Q8—61no—
182C2×#237—31no—
183C2×#237—31no—
184C2×#237—61no—
185C2×#237—61no—
186C2×D3×D4—31no—
187C2×D3×D4—31no—
188C2×D3×D4—31no—
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—61no—
211C2×#215C2×D311yescharacteristic, complemented
212#939—61no—
213#938—31no—
214C2×#214—31no—
215C2×#213—31no—
216C2×#213—31no—
217C2×#213—31no—
218C2×#213—31no—
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×D24C2×D311yescharacteristic, complemented
228C2×#204—31no—
229C2×#204—31no—
230C2×#204—31no—
231C2×#204—61no—
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—21no—
246C3×#103—31no—
247C3×#103C2×D311yescharacteristic, complemented
248C3×#103C2×D311yescharacteristic, complemented
249C3×#102—31no—
250C3×#102—31no—
251C3×#102—31no—
252C3×C22⋊C8—31no—
253#835C2×D311yescharacteristic, complemented
254#832—31no—
255#830—31no—
256#821C2×D311yescharacteristic, complemented
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#816—31no—
265#810—31no—
266#810—31no—
267#810—31no—
268#810—61no—
269#809—31no—
270#809C2×D311yescharacteristic, complemented
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)—21no—
296C4⋊(C3⋊D3)—21no—
297C4⋊(C3⋊D3)—42no—
298C4×C3⋊D3—24no—
299C4×C3⋊D3—21no—
300C4×C3⋊D3—21no—
301#634—24no—
302#634—21no—
303#634C2×D412yescomplemented
304C2×C3×Dic3—21no—
305C2×C3×Dic3C2×D411yescharacteristic
306C2×C3×Dic3C2×D411yescharacteristic
307C3×D12—24no—
308C3×D12—24no—
309C3×D12—21no—
310C3×D12—21no—
311C3×D12—21no—
312C3×D12—21no—
313C3×D12—42no—
314C3×D12C2×D412yescomplemented
315C3×D12C2×D412yescomplemented
316C3×C4×D3—24no—
317C3×C4×D3—21no—
318C3×C4×D3—21no—
319C3×C4×D3—24no—
320C3×C4×D3—42no—
321C3×C4×D3C2×D412yes—
322C3×C4×D3C2×D412yes—
323#626—42no—
324#626—42no—
325#626—42no—
326#625—24no—
327#625—24no—
328#625—24no—
329#624—22no—
330D3×Dic3—24no—
331D3×Dic3—22no—
332D3×Dic3—22no—
333D3×Dic3—24no—
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—
359C3×#41—34no—
360C3×#41—62no—
361C3×#41—62no—
362C3×#41—62no—
363C2×C3×Q8—21no—
364C2×C3×Q8C22×D311yescharacteristic
365C2×C3×Q8C22×D311yescharacteristic
366C2×C3×D4—31no—
367C2×C3×D4—31no—
368C2×C3×D4—31no—
369C2×C3×D4—61no—
370C2×C3×D4—61no—
371C2×C3×D4—61no—
372C22×C3×C4—31no—
373C22×C3×C4—31no—
374C22×C3×C4—61no—
375C22×C3×C4—61no—
376C22×C3×C4—61no—
377C2×#67—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—
386C22×Dic3—31no—
387C22×Dic3—31no—
388C22×Dic3—61no—
389C22×Dic3—61no—
390#239—22no—
391#239—22no—
392#239—22no—
393#239D1214yescomplemented
394D3×Q8—62no—
395D3×Q8—62no—
396D3×Q8—62no—
397D3×Q8—62no—
398D3×Q8—122no—
399D3×Q8—122no—
400#237—34no—
401#237—62no—
402#237—62no—
403#237—68no—
404#237—68no—
405#237—62no—
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—124no—
415#235—34no—
416#235—62no—
417#235—62no—
418#235—68no—
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—62no—
429C2×D12—61no—
430C2×D12—61no—
431C2×D12—61no—
432C2×D12—61no—
433C2×D12—61no—
434C2×D12—121no—
435C2×D12—124no—
436C2×D12C22×D311yescharacteristic
437C2×D12C22×D311yescharacteristic
438C2×D12C22×D311yescharacteristic
439C2×C4×D3—21no—
440C2×C4×D3—21no—
441C2×C4×D3—21no—
442C2×C4×D3—31no—
443C2×C4×D3—31no—
444C2×C4×D3—31no—
445C2×C4×D3—31no—
446C2×C4×D3—31no—
447C2×C4×D3—31no—
448C2×C4×D3—61no—
449C2×C4×D3—62no—
450C2×C4×D3—62no—
451C2×C4×D3—68no—
452C2×C4×D3—68no—
453C2×C4×D3—61no—
454C2×C4×D3—61no—
455C2×C4×D3—61no—
456C2×C4×D3—61no—
457C2×C4×D3—62no—
458C2×C4×D3—62no—
459C2×C4×D3—121no—
460C2×C4×D3C22×D311yescharacteristic
461C2×C4×D3C22×D311yescharacteristic
462C2×Dic6—31no—
463C2×Dic6—31no—
464C2×Dic6—61no—
465C2×Dic6—61no—
466C2×Dic6—61no—
467C2×Dic6—121no—
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—22no—
484#215—62no—
485#215—62no—
486#215—122no—
487#214—62no—
488#213—62no—
489#213—62no—
490#213—62no—
491#213—62no—
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—22no—
508D24—62no—
509D24—62no—
510#204—62no—
511#204—62no—
512#204—62no—
513#204—122no—
514ΓL(1,𝔽25)—22no—
515ΓL(1,𝔽25)—62no—
516C22×C32C22×D411yescharacteristic
517C2×C3⋊D3—21no—
518C2×C3⋊D3—21no—
519C2×C3⋊D3—41no—
520C2×C3⋊D3—41no—
521C2×C3⋊D3—41no—
522C2×C3⋊D3AGL(1,ℤ/8)12yescomplemented
523C2×C3×D3—21no—
524C2×C3×D3—21no—
525C2×C3×D3—21no—
526C2×C3×D3—22no—
527C2×C3×D3—22no—
528C2×C3×D3—21no—
529C2×C3×D3—21no—
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×D3—41no—
537C2×C3×D3#12012yes—
538D32—44no—
539D32—48no—
540D32—84no—
541C32×C4—22no—
542C32×C4—41no—
543C32×C4C22×D411yescharacteristic
544C32×C4C22×D411yescharacteristic
545C3⋊Dic3—21no—
546C3⋊Dic3—22no—
547C3×Dic3—21no—
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—91no—
587#103—91no—
588#103D3211yescharacteristic, complemented
589#102—31no—
590#102—31no—
591#102—31no—
592#102—91no—
593C22⋊C8—31no—
594C22⋊C8—91no—
595C22⋊C8—91no—
596C22⋊C8—91no—
597C23×C3—31no—
598C23×C3—31no—
599C23×C3—61no—
600C23×C3—61no—
601C23×C3—61no—
602C22×D3—21no—
603C22×D3—21no—
604C22×D3—21no—
605C22×D3—31no—
606C22×D3—31no—
607C22×D3—61no—
608C22×D3—62no—
609C22×D3—62no—
610C22×D3—62no—
611C22×D3—64no—
612C22×D3—64no—
613C22×D3—62no—
614C22×D3—61no—
615C22×D3—61no—
616C22×D3—121no—
617C22×D3—121no—
618C22×D3—121no—
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×D3—122no—
629C22×D3D3×D411yescharacteristic
630C22×D3D3×D411yescharacteristic
631C3×Q8—21no—
632C3×Q8—21no—
633C3×Q8—22no—
634C3×Q8—41no—
635C3×Q8C2×D1212yescomplemented
636C3×Q8D3×D412yescomplemented
637C3×D4—32no—
638C3×D4—32no—
639C3×D4—64no—
640C3×D4—64no—
641C3×D4—61no—
642C3×D4—61no—
643C3×D4—61no—
644C3×D4—61no—
645C3×D4—122no—
646C2×C3×C4—21no—
647C2×C3×C4—21no—
648C2×C3×C4—21no—
649C2×C3×C4—21no—
650C2×C3×C4—21no—
651C2×C3×C4—31no—
652C2×C3×C4—32no—
653C2×C3×C4—32no—
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—122no—
663C2×C3×C4C23×D311yescharacteristic
664C2×C3×C4C23×D311yescharacteristic
665#67—64no—
666#67—64no—
667#67—64no—
668#67—64no—
669#67—64no—
670#67—64no—
671#67—122no—
672#67—122no—
673#67—122no—
674C2×Dic3—21no—
675C2×Dic3—31no—
676C2×Dic3—31no—
677C2×Dic3—61no—
678C2×Dic3—62no—
679C2×Dic3—64no—
680C2×Dic3—61no—
681C2×Dic3—61no—
682C2×Dic3—64no—
683C2×Dic3—62no—
684C2×Dic3—121no—
685C2×Dic3D3×D411yescharacteristic
686C2×Dic3D3×D411yescharacteristic
687D12—24no—
688D12—24no—
689D12—21no—
690D12—21no—
691D12—21no—
692D12—21no—
693D12—42no—
694D12—61no—
695D12—61no—
696D12—61no—
697D12—61no—
698D12—121no—
699D12—121no—
700D12—122no—
701D12—122no—
702D12—122no—
703D12—122no—
704D12—122no—
705D12—242no—
706D12C2×D1212yescomplemented
707D12D3×D412yescomplemented
708C4×D3—24no—
709C4×D3—21no—
710C4×D3—21no—
711C4×D3—24no—
712C4×D3—42no—
713C4×D3—62no—
714C4×D3—64no—
715C4×D3—64no—
716C4×D3—62no—
717C4×D3—64no—
718C4×D3—64no—
719C4×D3—62no—
720C4×D3—61no—
721C4×D3—61no—
722C4×D3—61no—
723C4×D3—61no—
724C4×D3—62no—
725C4×D3—121no—
726C4×D3—121no—
727C4×D3—124no—
728C4×D3C2×D1212yes—
729C4×D3D3×D412yes—
730Dic6—32no—
731Dic6—32no—
732Dic6—62no—
733Dic6—64no—
734Dic6—64no—
735Dic6—61no—
736Dic6—61no—
737Dic6—121no—
738Dic6—124no—
739C3×C8—21no—
740C3×C8—21no—
741C3×C8—41no—
742C3×C8—61no—
743C3×C8—61no—
744C3⋊C8—21no—
745C3⋊C8—21no—
746C3⋊C8—61no—
747C3⋊C8—61no—
748C3⋊C8—121no—
749C2×C32C2×#12011yescharacteristic
750C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
751C2×C32#57511yescharacteristic
752C3⋊D3—22no—
753C3⋊D3—81no—
754C3×D3—22no—
755C3×D3—41no—
756C3×D3—42no—
757C3×D3—42no—
758C3×D3—81no—
759C24—91no—
760C24—181no—
761C24—181no—
762#41—34no—
763#41—62no—
764#41—62no—
765#41—62no—
766#41—94no—
767#41—182no—
768#41—182no—
769#41—182no—
770#41—188no—
771#41—188no—
772C2×Q8—91no—
773C2×Q8—181no—
774C2×Q8—182no—
775C2×Q8—182no—
776C2×Q8C2×D3211yescharacteristic
777C2×D4—31no—
778C2×D4—31no—
779C2×D4—31no—
780C2×D4—61no—
781C2×D4—61no—
782C2×D4—61no—
783C2×D4—91no—
784C2×D4—181no—
785C2×D4—182no—
786C2×D4—182no—
787C2×D4—181no—
788C2×D4—181no—
789C2×D4—181no—
790C2×D4—181no—
791C2×D4—182no—
792C2×D4—182no—
793C2×D4—188no—
794C2×D4—181no—
795C2×D4—181no—
796C2×D4—364no—
797C22×C4—31no—
798C22×C4—31no—
799C22×C4—61no—
800C22×C4—61no—
801C22×C4—61no—
802C22×C4—91no—
803C22×C4—91no—
804C22×C4—91no—
805C22×C4—91no—
806C22×C4—181no—
807C22×C4—182no—
808C22×C4—182no—
809C22×C4—181no—
810C22×C4—181no—
811C22×C4—188no—
812SD16—62no—
813SD16—182no—
814SD16—182no—
815SD16—182no—
816D8—62no—
817D8—182no—
818D8—182no—
819D8—182no—
820M16—62no—
821M16—182no—
822C2×C8—31no—
823C2×C8—31no—
824C2×C8—91no—
825C2×C8C2×D3211yescharacteristic
826C4⋊C4—31no—
827C4⋊C4—61no—
828C4⋊C4C2×D3211yescharacteristic
829C22⋊C4—61no—
830C22⋊C4—181no—
831C22⋊C4—181no—
832C22⋊C4—181no—
833C22×C3—21no—
834C22×C3—32no—
835C22×C3—61no—
836C22×C3—61no—
837C22×C3—62no—
838C22×C3—61no—
839C22×C3—61no—
840C22×C3—61no—
841C22×C3—62no—
842C22×C3—121no—
843C22×C3—121no—
844C22×C3—121no—
845C22×C3—121no—
846C22×C3—121no—
847C22×C3—121no—
848C22×C3—121no—
849C22×C3C2×D3×D411yescharacteristic
850C22×C3C2×D3×D411yescharacteristic
851C2×D3—21no—
852C2×D3—21no—
853C2×D3—22no—
854C2×D3—21no—
855C2×D3—21no—
856C2×D3—21no—
857C2×D3—22no—
858C2×D3—32no—
859C2×D3—32no—
860C2×D3—41no—
861C2×D3—41no—
862C2×D3—41no—
863C2×D3—41no—
864C2×D3—41no—
865C2×D3—41no—
866C2×D3—41no—
867C2×D3—62no—
868C2×D3—61no—
869C2×D3—61no—
870C2×D3—61no—
871C2×D3—61no—
872C2×D3—121no—
873C2×D3—121no—
874C2×D3—124no—
875C2×D3—124no—
876C2×D3—128no—
877C2×D3—128no—
878C2×D3—121no—
879C2×D3—121no—
880C2×D3—121no—
881C2×D3—121no—
882C2×D3—121no—
883C2×D3—121no—
884C2×D3—241no—
885C2×D3—241no—
886C2×D3—241no—
887C2×D3—244no—
888C2×D3—244no—
889C2×D3#88212yes—
890C3×C4—22no—
891C3×C4—22no—
892C3×C4—21no—
893C3×C4—21no—
894C3×C4—32no—
895C3×C4—42no—
896C3×C4—41no—
897C3×C4—41no—
898C3×C4—61no—
899C3×C4—81no—
900C3×C4—121no—
901C3×C4C22×D1211yescharacteristic
902C3×C4C2×D3×D411yescharacteristic
903C3×C4C2×D3×D411yescharacteristic
904C3×C4C2×D3×D411yescharacteristic
905Dic3—21no—
906Dic3—41no—
907Dic3—62no—
908Dic3—61no—
909Dic3—62no—
910Dic3—61no—
911Dic3—122no—
912Dic3—121no—
913Dic3#88212yes—
914C32#300611yescharacteristic, complemented, Sylow
915C23—31no—
916C23—31no—
917C23—61no—
918C23—61no—
919C23—61no—
920C23—91no—
921C23—182no—
922C23—182no—
923C23—184no—
924C23—181no—
925C23—362no—
926C23—361no—
927C23—362no—
928C23—362no—
929C23—362no—
930C23—362no—
931Q8—21no—
932Q8—92no—
933Q8—184no—
934Q8—181no—
935Q8D3×D1212yescomplemented
936D4—32no—
937D4—32no—
938D4—64no—
939D4—64no—
940D4—61no—
941D4—61no—
942D4—61no—
943D4—61no—
944D4—122no—
945D4—184no—
946D4—184no—
947D4—184no—
948D4—181no—
949D4—181no—
950D4—362no—
951D4—362no—
952D4—362no—
953D4—362no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—31no—
957C2×C4—32no—
958C2×C4—32no—
959C2×C4—31no—
960C2×C4—64no—
961C2×C4—64no—
962C2×C4—61no—
963C2×C4—61no—
964C2×C4—61no—
965C2×C4—91no—
966C2×C4—122no—
967C2×C4—184no—
968C2×C4—182no—
969C2×C4—182no—
970C2×C4—184no—
971C2×C4—182no—
972C2×C4—184no—
973C2×C4—181no—
974C2×C4—181no—
975C2×C4—181no—
976C2×C4C22×D3211yescharacteristic
977C8—21no—
978C8—61no—
979C8—61no—
980C8—181no—
981C2×C3—21no—
982C2×C3—21no—
983C2×C3—21no—
984C2×C3—62no—
985C2×C3—121no—
986C2×C3—122no—
987C2×C3—122no—
988C2×C3—241no—
989C2×C3C2×#88211yescharacteristic
990C2×C3D3×#12011yescharacteristic
991C2×C3#576811yescharacteristic
992C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
993C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
994C2×C3#577711yescharacteristic
995D3—22no—
996D3—42no—
997D3—41no—
998D3—42no—
999D3—62no—
1000D3—62no—
1001D3—81no—
1002D3—122no—
1003D3—241no—
1004D3—241no—
1005D3—481no—
1006C22—32no—
1007C22—61no—
1008C22—61no—
1009C22—61no—
1010C22—61no—
1011C22—62no—
1012C22—62no—
1013C22—61no—
1014C22—92no—
1015C22—121no—
1016C22—121no—
1017C22—121no—
1018C22—121no—
1019C22—121no—
1020C22—121no—
1021C22—121no—
1022C22—181no—
1023C22—181no—
1024C22—364no—
1025C22—368no—
1026C22—361no—
1027C22—361no—
1028C22—361no—
1029C22—724no—
1030C22D32×D411yescharacteristic
1031C4—22no—
1032C4—32no—
1033C4—41no—
1034C4—61no—
1035C4—121no—
1036C4—181no—
1037C4—182no—
1038C4C2×D3×D1211yescharacteristic
1039C4D32×D411yescharacteristic
1040C3—21no—
1041C3#7888411yescharacteristic, complemented
1042C3#8008411yescharacteristic, complemented
1043C2—62no—
1044C2—121no—
1045C2—122no—
1046C2—122no—
1047C2—182no—
1048C2—241no—
1049C2—721no—
1050C2D3×#88211yescharacteristic
1051C2#1059474011yescharacteristic
1052C2#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×#64319C2semidirect
2. C2×#63939C2semidirect
3. C2×#63795C2semidirect
4. D3×#895C2semidirect
5. #10592505C2semidirect
6. C3×#4810C2semidirect
7. C3×#4803C2semidirect
8. #10591592C2semidirect
9. #10591588C2semidirect
10. #10590968C2semidirect
11. #10590945C2semidirect
12. #10590936C2semidirect
13. #10590613C2semidirect
14. #10590607C2semidirect
15. #10590598C2semidirect
18. C2×Q8×C3⋊D3C22semidirect
20. C2×C3×#239C22semidirect
24. C2×#3802C22semidirect
26. C2×D3×D12C22semidirect
32. C2×#3795C22semidirect
33. C2×#3755C22semidirect
34. C2×#3744C22semidirect
36. C2×C3×#215C22semidirect
37. C2×C3×D24C22semidirect
38. C2×C3×ΓL(1,𝔽25)C22semidirect
39. C3×#895C22semidirect
40. C3×D3×C4⋊C4C22semidirect
45. #63909C22semidirect
47. C2×#3716C22semidirect
48. C2×#3714C22semidirect
49. C2×#3714C22semidirect
50. C2×#3713C22semidirect
51. C2×#3711C22semidirect
53. C32×#103C22semidirect
54. #63647C22semidirect
55. #63637C22semidirect
56. C3×#835C22semidirect
57. C3×#821C22semidirect
58. C3×(C2×D3)⋊C8C22semidirect
59. C3×#809C22semidirect
60. C3×#809C22semidirect
61. #63567C22semidirect
62. #63562C22semidirect
63. #63557C22semidirect
64. (C2×D3)⋊(C3⋊C8)C22semidirect
82. #4810D3semidirect
87. #4803D3semidirect
111. C3×#239D4semidirect
148. #3795D4semidirect
178. C2×#239C2×D3semidirect
211. C2×#215C2×D3semidirect
227. C2×D24C2×D3semidirect
233. C2×ΓL(1,𝔽25)C2×D3semidirect
241. #895C2×D3semidirect
242. D3×C4⋊C4C2×D3semidirect
247. C3×#103C2×D3semidirect
248. C3×#103C2×D3semidirect
253. #835C2×D3semidirect
256. #821C2×D3semidirect
263. (C2×D3)⋊C8C2×D3semidirect
270. #809C2×D3semidirect
271. #809C2×D3semidirect
289. C32×Q8C2×D4semidirect
303. #634C2×D4semidirect
314. C3×D12C2×D4semidirect
315. C3×D12C2×D4semidirect
393. #239D12semidirect
522. C2×C3⋊D3AGL(1,ℤ/8)semidirect
588. #103D32semidirect
635. C3×Q8C2×D12semidirect
636. C3×Q8D3×D4semidirect
706. D12C2×D12semidirect
707. D12D3×D4semidirect
914. C32#3006semidirect
935. Q8D3×D12semidirect
1041. C3#78884semidirect
1042. C3#80084semidirect

Maximal subgroups

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

subgroupindex
C2×#643192
C2×#639392
C2×#637952
D3×#8952
#105925052
C3×#48102
C3×#48032
#105915922
#105915882
#105909682
#105909452
#105909362
#105906132
#105906072
#105905982
#800843
#788843