Finite Group Databasebeta

← #11864158

Subgroups — #11864158

Order 1152.

1693 conjugacy classes of subgroups.

The subgroup lattice has 1057 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#239C211yesmaximal, characteristic, complemented
2C2×#63939C211yesmaximal, characteristic, complemented
3C2×#63794C211yesmaximal, characteristic, complemented
4D3×#895C211yesmaximal, characteristic, complemented
5#10592509C211yesmaximal, characteristic, complemented
6C3×#4806C211yesmaximal, characteristic, complemented
7C3×#4803C211yesmaximal, characteristic, complemented
8#10591593C211yesmaximal, characteristic, complemented
9#10591584C211yesmaximal, characteristic, complemented
10#10590964C211yesmaximal, characteristic, complemented
11#10590947C211yesmaximal, characteristic, complemented
12#10590936C211yesmaximal, characteristic, complemented
13#10590617C211yesmaximal, characteristic, complemented
14#10590609C211yesmaximal, characteristic, complemented
15#10590595C211yesmaximal, characteristic, complemented
16#80040—31nomaximal
17#78884—31nomaximal
18C2×#3832C2211yescharacteristic, complemented
19C2×C3×#239C2211yescharacteristic
20C2×C3×D3×Q8C2211yescharacteristic, complemented
21D3×#239—24no—
22D3×#239—24no—
23C2×D3×D12—21no—
24C2×D3×D12—21no—
25C2×D3×D12C2211yescharacteristic, complemented
26C2×D3×D12C2211yescharacteristic, complemented
27C2×C4×D32—21no—
28C2×C4×D32C2211yescharacteristic
29C2×#3799—21no—
30C2×#3799C2211yescharacteristic
31C2×#3796—21no—
32C2×#3796C2211yescharacteristic, complemented
33C2×#3755C2211yescharacteristic, complemented
34C2×#3745C2211yescharacteristic, complemented
35#64104C2211yescharacteristic, complemented
36C2×C3×#215C2211yescharacteristic, complemented
37C2×C3×#204C2211yescharacteristic, complemented
38C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
39C3×#895C2211yescharacteristic
40C3×D3×C4⋊C4C2211yescharacteristic, complemented
41#63939—24no—
42D3×(C2×D3)⋊C4—21no—
43#63916C2211yescharacteristic, complemented
44#63910—21no—
45#63909C2211yescharacteristic
46#63886—21no—
47C2×#3717C2211yescharacteristic, complemented
48C2×#3714C2211yescharacteristic, complemented
49C2×#3714C2211yescharacteristic, complemented
50C2×#3713C2211yescharacteristic, complemented
51C2×#3711C2211yescharacteristic, complemented
52#63794—24no—
53C32×#103C2211yescharacteristic, complemented
54#63647C2211yescharacteristic, complemented
55#63636C2211yescharacteristic, complemented
56C3×#835C2211yescharacteristic, complemented
57C3×#821C2211yescharacteristic, complemented
58C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
59C3×#810C2211yescharacteristic, complemented
60C3×#809C2211yescharacteristic, complemented
61#63565C2211yescharacteristic, complemented
62#63564C2211yescharacteristic, complemented
63#63557C2211yescharacteristic, complemented
64(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
65C2×D3×#41—31no—
66C22×#239—31no—
67C2×#949—31no—
68C2×#914—31no—
69C2×#914—31no—
70C2×#908—31no—
71D3×#121—31no—
72C2×#895—31no—
73C3×#448—31no—
74C3×#417—31no—
75#5227—31no—
76#5172—31no—
77#5172—31no—
78#5126—31no—
79#5036—31no—
80#4966—31no—
81#4810—31no—
82#4810—31no—
83#4810—31no—
84#4810—31no—
85#4810—61no—
86#4806—31no—
87#4806D311yescharacteristic, complemented
88#4803—31no—
89#4803D311yescharacteristic, complemented
90#4781—31no—
91#4781—31no—
92#4773—31no—
93#4773—31no—
94#4732—31no—
95#4726—31no—
96C22×D32—21no—
97C22×D32—21no—
98C22×D32D411yescharacteristic
99C2×C32×Q8C2311yescharacteristic
100#3832—22no—
101#3832—22no—
102C2×C4⋊(C3⋊D3)—21no—
103C2×C4⋊(C3⋊D3)—21no—
104C2×C4⋊(C3⋊D3)C2311yescharacteristic
105C2×C4⋊(C3⋊D3)C2311yescharacteristic
106C2×C4×C3⋊D3—21no—
107C2×C4×C3⋊D3C2311yescharacteristic
108C3×#239—22no—
109C3×#239D414yescomplemented
110C3×D3×Q8—22no—
111C3×D3×Q8—22no—
112C2×C3×D12—21no—
113C2×C3×D12—21no—
114C2×C3×D12C2311yescharacteristic
115C2×C3×D12C2311yescharacteristic
116C2×C3×C4×D3—21no—
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×#626—21no—
127C2×#626—21no—
128C2×#626—21no—
129C2×#624—21no—
130C2×#624D411yescharacteristic
131C2×D3×Dic3—21no—
132C2×D3×Dic3D411yescharacteristic
133C2×D3×Dic3D411yescharacteristic
134D3×D12—28no—
135D3×D12—22no—
136D3×D12—22no—
137D3×D12—22no—
138D3×D12—22no—
139D3×D12—44no—
140C4×D32—28no—
141C4×D32—22no—
142C4×D32—22no—
143#3799—28no—
144#3799—22no—
145#3799D414yescomplemented
146#3796—28no—
147#3796—22no—
148#3796—22no—
149C2×C32×C8C2311yescharacteristic
150C32×C4⋊C4C2311yescharacteristic
151#3755—22no—
152#3752—21no—
153C2×C3⋊(C3⋊C8)C2311yescharacteristic
154#3745—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×#204—22no—
162C3×ΓL(1,𝔽25)—22no—
163#3722—21no—
164(C2×D3)⋊Dic3—21no—
165#3717—22no—
166#3714—22no—
167#3714—22no—
168#3713—22no—
169#3711—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
185C2×D3×Q8C2×D311yescharacteristic, complemented
186C2×#237—31no—
187C2×#237—61no—
188C2×D3×D4—31no—
189C2×D3×D4—31no—
190C2×D3×D4—61no—
191C2×D3×D4—61no—
192C2×#235—31no—
193C2×#235—61no—
194C22×D12—31no—
195C22×D12—31no—
196C22×D12—61no—
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×M16—31no—
205C3×#121—31no—
206C2×C3×C4⋊C4—31no—
207#949—64no—
208C2×#215—31no—
209C2×#215—31no—
210C2×#215—31no—
211C2×#215—61no—
212C2×#215C2×D311yescharacteristic, complemented
213#939—61no—
214#938—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#914—64no—
224#908—64no—
225C2×D24—31no—
226C2×D24—31no—
227C2×D24—31no—
228C2×D24—31no—
229C2×D24—61no—
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
242D3×C4⋊C4C2×D311yescharacteristic, complemented
243#884—61no—
244D3×C22⋊C4—61no—
245C3×#103—21no—
246C3×#103—31no—
247C3×#103—31no—
248C3×#103C2×D311yescharacteristic, complemented
249C3×#103C2×D311yescharacteristic, complemented
250C3×#102—31no—
251C3×#102—31no—
252C3×C22⋊C8—31no—
253#835—31no—
254#835C2×D311yescharacteristic, complemented
255#830—31no—
256#821—31no—
257#821C2×D311yescharacteristic, complemented
258(C2×D3)⋊C8—31no—
259(C2×D3)⋊C8—31no—
260(C2×D3)⋊C8—31no—
261(C2×D3)⋊C8—31no—
262(C2×D3)⋊C8—31no—
263(C2×D3)⋊C8—61no—
264(C2×D3)⋊C8C2×D311yescharacteristic, complemented
265#810—31no—
266#810C2×D311yescharacteristic, complemented
267#809—31no—
268#809—31no—
269#809—31no—
270#809—61no—
271#809C2×D311yescharacteristic, complemented
272C22×C3⋊D3—21no—
273C22×C3⋊D3—21no—
274C22×C3⋊D3C2×D411yescharacteristic
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⋊Dic3C2×D411yescharacteristic
294C4⋊(C3⋊D3)—24no—
295C4⋊(C3⋊D3)—21no—
296C4⋊(C3⋊D3)—21no—
297C4⋊(C3⋊D3)—21no—
298C4⋊(C3⋊D3)—42no—
299C4⋊(C3⋊D3)C2×D412yescomplemented
300C4×C3⋊D3—24no—
301C4×C3⋊D3—21no—
302C4×C3⋊D3—21no—
303C2×C3×Dic3—21no—
304C2×C3×Dic3—21no—
305C2×C3×Dic3C2×D411yescharacteristic
306C2×C3×Dic3C2×D411yescharacteristic
307C3×D12—24no—
308C3×D12—21no—
309C3×D12—21no—
310C3×D12—21no—
311C3×D12—42no—
312C3×D12C2×D412yescomplemented
313C3×C4×D3—24no—
314C3×C4×D3—21no—
315C3×C4×D3—21no—
316C3×C4×D3—24no—
317C3×C4×D3—42no—
318C3×C4×D3C2×D412yes—
319C3×C4×D3C2×D412yes—
320C3×Dic6—24no—
321C3×Dic6—21no—
322C3×Dic6C2×D412yescomplemented
323#626—24no—
324#626—24no—
325#626—24no—
326#626—42no—
327#626—42no—
328#626—42no—
329#624—22no—
330#624—24no—
331D3×Dic3—24no—
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—91no—
343#449—91no—
344#449—91no—
345#449—91no—
346#448—31no—
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—
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—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—
383C22×Dic3—31no—
384C22×Dic3—31no—
385C22×Dic3—61no—
386#239—22no—
387#239—34no—
388#239—68no—
389#239—62no—
390#239—68no—
391#239—62no—
392#239—62no—
393#239—62no—
394#239—62no—
395#239—62no—
396#239—62no—
397#239—122no—
398#239—122no—
399#239D1214yescomplemented
400D3×Q8—22no—
401D3×Q8—22no—
402#237—62no—
403#237—68no—
404#237—62no—
405D3×D4—62no—
406D3×D4—62no—
407D3×D4—68no—
408D3×D4—62no—
409D3×D4—62no—
410D3×D4—124no—
411#235—34no—
412#235—62no—
413#235—68no—
414C2×D12—21no—
415C2×D12—21no—
416C2×D12—31no—
417C2×D12—31no—
418C2×D12—31no—
419C2×D12—31no—
420C2×D12—61no—
421C2×D12—61no—
422C2×D12—62no—
423C2×D12—68no—
424C2×D12—62no—
425C2×D12—62no—
426C2×D12—61no—
427C2×D12—61no—
428C2×D12—61no—
429C2×D12—61no—
430C2×D12—61no—
431C2×D12—62no—
432C2×D12—61no—
433C2×D12—61no—
434C2×D12—61no—
435C2×D12—61no—
436C2×D12—61no—
437C2×D12—121no—
438C2×D12—121no—
439C2×D12—124no—
440C2×D12C22×D311yescharacteristic
441C2×D12C22×D311yescharacteristic
442C2×C4×D3—21no—
443C2×C4×D3—21no—
444C2×C4×D3—21no—
445C2×C4×D3—31no—
446C2×C4×D3—31no—
447C2×C4×D3—31no—
448C2×C4×D3—31no—
449C2×C4×D3—31no—
450C2×C4×D3—31no—
451C2×C4×D3—61no—
452C2×C4×D3—62no—
453C2×C4×D3—62no—
454C2×C4×D3—68no—
455C2×C4×D3—68no—
456C2×C4×D3—61no—
457C2×C4×D3—61no—
458C2×C4×D3—61no—
459C2×C4×D3—61no—
460C2×C4×D3—61no—
461C2×C4×D3—62no—
462C2×C4×D3—62no—
463C2×C4×D3—121no—
464C2×C4×D3C22×D311yescharacteristic
465C2×C4×D3C22×D311yescharacteristic
466C2×Dic6—21no—
467C2×Dic6C22×D311yescharacteristic
468C3×SD16—62no—
469C3×SD16—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—62no—
487#215—122no—
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—62no—
508D24—62no—
509D24—62no—
510D24—62no—
511D24—122no—
512#204—22no—
513#204—62no—
514ΓL(1,𝔽25)—22no—
515ΓL(1,𝔽25)—62no—
516C22×C32C22×D411yescharacteristic
517C2×C3⋊D3—21no—
518C2×C3⋊D3—22no—
519C2×C3⋊D3—21no—
520C2×C3⋊D3—21no—
521C2×C3⋊D3—41no—
522C2×C3⋊D3—41no—
523C2×C3⋊D3—41no—
524C2×C3⋊D3—41no—
525C2×C3⋊D3—41no—
526C2×C3×D3—21no—
527C2×C3×D3—21no—
528C2×C3×D3—21no—
529C2×C3×D3—21no—
530C2×C3×D3—22no—
531C2×C3×D3—41no—
532C2×C3×D3—41no—
533C2×C3×D3—41no—
534C2×C3×D3—41no—
535C2×C3×D3—41no—
536C2×C3×D3#12012yes—
537C2×C3×D3AGL(1,ℤ/8)12yescomplemented
538D32—44no—
539D32—48no—
540D32—84no—
541C32×C4—22no—
542C32×C4—41no—
543C32×C4C22×D411yescharacteristic
544C32×C4C22×D411yescharacteristic
545C3⋊Dic3—21no—
546C3×Dic3—21no—
547C3×Dic3—22no—
548C3×Dic3—41no—
549C3×Dic3#12012yes—
550C2×#41—31no—
551C2×#41—91no—
552C2×#41—91no—
553C2×#41—91no—
554C2×#41—181no—
555C2×#41—181no—
556C2×#41—184no—
557C2×#41—184no—
558C22×Q8—31no—
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—31no—
569C2×SD16—91no—
570C2×SD16—91no—
571C2×D8—91no—
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—91no—
588#103D3211yescharacteristic, complemented
589#102—31no—
590#102—31no—
591#102—91no—
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—
601C22×D3—21no—
602C22×D3—21no—
603C22×D3—31no—
604C22×D3—31no—
605C22×D3—61no—
606C22×D3—62no—
607C22×D3—62no—
608C22×D3—64no—
609C22×D3—64no—
610C22×D3—61no—
611C22×D3—61no—
612C22×D3—62no—
613C22×D3—62no—
614C22×D3—61no—
615C22×D3—61no—
616C22×D3—121no—
617C22×D3—121no—
618C22×D3—121no—
619C22×D3—121no—
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×D3—122no—
630C22×D3D3×D411yescharacteristic
631C22×D3D3×D411yescharacteristic
632C3×Q8—21no—
633C3×Q8—21no—
634C3×Q8—22no—
635C3×Q8—32no—
636C3×Q8—41no—
637C3×Q8—64no—
638C3×Q8—61no—
639C3×Q8C2×D1212yescomplemented
640C3×Q8D3×D412yescomplemented
641C3×D4—32no—
642C3×D4—64no—
643C3×D4—61no—
644C3×D4—61no—
645C3×D4—61no—
646C3×D4—122no—
647C2×C3×C4—21no—
648C2×C3×C4—21no—
649C2×C3×C4—21no—
650C2×C3×C4—21no—
651C2×C3×C4—21no—
652C2×C3×C4—31no—
653C2×C3×C4—32no—
654C2×C3×C4—32no—
655C2×C3×C4—31no—
656C2×C3×C4—41no—
657C2×C3×C4—41no—
658C2×C3×C4—64no—
659C2×C3×C4—64no—
660C2×C3×C4—61no—
661C2×C3×C4—61no—
662C2×C3×C4—61no—
663C2×C3×C4—61no—
664C2×C3×C4—122no—
665C2×C3×C4C23×D311yescharacteristic
666C2×C3×C4C23×D311yescharacteristic
667#67—64no—
668#67—64no—
669#67—64no—
670#67—122no—
671#67—122no—
672#67—122no—
673C2×Dic3—21no—
674C2×Dic3—21no—
675C2×Dic3—31no—
676C2×Dic3—31no—
677C2×Dic3—61no—
678C2×Dic3—62no—
679C2×Dic3—64no—
680C2×Dic3—62no—
681C2×Dic3D3×D411yescharacteristic
682C2×Dic3D3×D411yescharacteristic
683D12—24no—
684D12—21no—
685D12—21no—
686D12—21no—
687D12—32no—
688D12—32no—
689D12—42no—
690D12—62no—
691D12—64no—
692D12—64no—
693D12—64no—
694D12—64no—
695D12—64no—
696D12—61no—
697D12—61no—
698D12—61no—
699D12—61no—
700D12—61no—
701D12—61no—
702D12—121no—
703D12—121no—
704D12—121no—
705D12—124no—
706D12—122no—
707D12—122no—
708D12—122no—
709D12—122no—
710D12—122no—
711D12—242no—
712D12C2×D1212yescomplemented
713C4×D3—24no—
714C4×D3—21no—
715C4×D3—21no—
716C4×D3—24no—
717C4×D3—42no—
718C4×D3—62no—
719C4×D3—64no—
720C4×D3—64no—
721C4×D3—64no—
722C4×D3—62no—
723C4×D3—64no—
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×D3—124no—
734C4×D3C2×D1212yes—
735C4×D3D3×D412yes—
736Dic6—24no—
737Dic6—21no—
738Dic6D3×D412yescomplemented
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—41no—
753C3⋊D3—42no—
754C3⋊D3—81no—
755C3×D3—22no—
756C3×D3—22no—
757C3×D3—42no—
758C3×D3—81no—
759C24—91no—
760C24—181no—
761C24—181no—
762#41—34no—
763#41—62no—
764#41—94no—
765#41—182no—
766#41—188no—
767#41—182no—
768#41—182no—
769#41—188no—
770#41—182no—
771#41—182no—
772C2×Q8—31no—
773C2×Q8—61no—
774C2×Q8—62no—
775C2×Q8—62no—
776C2×Q8C2×D3211yescharacteristic
777C2×D4—31no—
778C2×D4—31no—
779C2×D4—61no—
780C2×D4—61no—
781C2×D4—91no—
782C2×D4—91no—
783C2×D4—181no—
784C2×D4—181no—
785C2×D4—182no—
786C2×D4—182no—
787C2×D4—181no—
788C2×D4—181no—
789C2×D4—182no—
790C2×D4—182no—
791C2×D4—188no—
792C2×D4—181no—
793C2×D4—181no—
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—188no—
811C22×C4—181no—
812SD16—62no—
813SD16—62no—
814SD16—182no—
815SD16—182no—
816D8—182no—
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—32no—
836C22×C3—61no—
837C22×C3—61no—
838C22×C3—61no—
839C22×C3—61no—
840C22×C3—62no—
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—22no—
853C2×D3—41no—
854C2×D3—41no—
855C2×D3—41no—
856C2×D3—41no—
857C2×D3—41no—
858C2×D3—62no—
859C2×D3—61no—
860C2×D3—61no—
861C2×D3—61no—
862C2×D3—61no—
863C2×D3—61no—
864C2×D3—62no—
865C2×D3—61no—
866C2×D3—122no—
867C2×D3—121no—
868C2×D3—121no—
869C2×D3—121no—
870C2×D3—124no—
871C2×D3—124no—
872C2×D3—128no—
873C2×D3—128no—
874C2×D3—121no—
875C2×D3—121no—
876C2×D3—121no—
877C2×D3—121no—
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—241no—
888C2×D3—241no—
889C2×D3—244no—
890C2×D3—244no—
891C2×D3#88212yes—
892C2×D3#91412yescomplemented
893C3×C4—22no—
894C3×C4—22no—
895C3×C4—21no—
896C3×C4—21no—
897C3×C4—32no—
898C3×C4—42no—
899C3×C4—41no—
900C3×C4—41no—
901C3×C4—61no—
902C3×C4—62no—
903C3×C4—81no—
904C3×C4—121no—
905C3×C4C22×D1211yescharacteristic
906C3×C4C2×D3×D411yescharacteristic
907C3×C4C2×D3×D411yescharacteristic
908C3×C4C2×D3×D411yescharacteristic
909Dic3—21no—
910Dic3—22no—
911Dic3—41no—
912Dic3—61no—
913Dic3—61no—
914Dic3—121no—
915Dic3#88212yes—
916C32#300611yescharacteristic, complemented, Sylow
917C23—31no—
918C23—31no—
919C23—61no—
920C23—61no—
921C23—91no—
922C23—182no—
923C23—182no—
924C23—184no—
925C23—181no—
926C23—181no—
927C23—362no—
928C23—362no—
929C23—361no—
930C23—362no—
931C23—362no—
932C23—362no—
933Q8—21no—
934Q8—32no—
935Q8—64no—
936Q8—61no—
937Q8D3×D1212yescomplemented
938D4—32no—
939D4—64no—
940D4—61no—
941D4—61no—
942D4—61no—
943D4—92no—
944D4—122no—
945D4—184no—
946D4—184no—
947D4—184no—
948D4—184no—
949D4—181no—
950D4—181no—
951D4—181no—
952D4—362no—
953D4—362no—
954D4—362no—
955D4—362no—
956C2×C4—21no—
957C2×C4—21no—
958C2×C4—31no—
959C2×C4—32no—
960C2×C4—32no—
961C2×C4—31no—
962C2×C4—64no—
963C2×C4—64no—
964C2×C4—61no—
965C2×C4—61no—
966C2×C4—61no—
967C2×C4—61no—
968C2×C4—91no—
969C2×C4—122no—
970C2×C4—184no—
971C2×C4—182no—
972C2×C4—184no—
973C2×C4—182no—
974C2×C4—182no—
975C2×C4—184no—
976C2×C4—181no—
977C2×C4—181no—
978C2×C4C22×D3211yescharacteristic
979C8—21no—
980C8—61no—
981C8—61no—
982C8—181no—
983C2×C3—21no—
984C2×C3—21no—
985C2×C3—21no—
986C2×C3—62no—
987C2×C3—62no—
988C2×C3—122no—
989C2×C3—241no—
990C2×C3C2×#88211yescharacteristic
991C2×C3D3×#12011yescharacteristic
992C2×C3C2×#91411yescharacteristic
993C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
994C2×C3#577711yescharacteristic
995C2×C3#577711yescharacteristic
996D3—22no—
997D3—22no—
998D3—42no—
999D3—81no—
1000D3—121no—
1001D3—122no—
1002D3—121no—
1003D3—122no—
1004D3—241no—
1005D3—242no—
1006D3—241no—
1007D3—241no—
1008D3—481no—
1009C22—32no—
1010C22—32no—
1011C22—61no—
1012C22—61no—
1013C22—61no—
1014C22—61no—
1015C22—62no—
1016C22—121no—
1017C22—121no—
1018C22—121no—
1019C22—121no—
1020C22—121no—
1021C22—181no—
1022C22—181no—
1023C22—182no—
1024C22—181no—
1025C22—364no—
1026C22—368no—
1027C22—361no—
1028C22—361no—
1029C22—361no—
1030C22—361no—
1031C22—361no—
1032C22—724no—
1033C22D32×D411yescharacteristic
1034C4—22no—
1035C4—32no—
1036C4—41no—
1037C4—61no—
1038C4—62no—
1039C4—121no—
1040C4—181no—
1041C4C2×D3×D1211yescharacteristic
1042C4D32×D411yescharacteristic
1043C3—21no—
1044C3#7888411yescharacteristic, complemented
1045C3#8004011yescharacteristic, complemented
1046C2—62no—
1047C2—62no—
1048C2—122no—
1049C2—241no—
1050C2—361no—
1051C2—362no—
1052C2—721no—
1053C2D3×#88211yescharacteristic
1054C2D3×#91411yescharacteristic
1055C2#1059476211yescharacteristic
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×#63939C2semidirect
3. C2×#63794C2semidirect
4. D3×#895C2semidirect
5. #10592509C2semidirect
6. C3×#4806C2semidirect
7. C3×#4803C2semidirect
8. #10591593C2semidirect
9. #10591584C2semidirect
10. #10590964C2semidirect
11. #10590947C2semidirect
12. #10590936C2semidirect
13. #10590617C2semidirect
14. #10590609C2semidirect
15. #10590595C2semidirect
18. C2×#3832C22semidirect
20. C2×C3×D3×Q8C22semidirect
25. C2×D3×D12C22semidirect
26. C2×D3×D12C22semidirect
32. C2×#3796C22semidirect
33. C2×#3755C22semidirect
34. C2×#3745C22semidirect
35. #64104C22semidirect
36. C2×C3×#215C22semidirect
37. C2×C3×#204C22semidirect
38. C2×C3×ΓL(1,𝔽25)C22semidirect
40. C3×D3×C4⋊C4C22semidirect
43. #63916C22semidirect
47. C2×#3717C22semidirect
48. C2×#3714C22semidirect
49. C2×#3714C22semidirect
50. C2×#3713C22semidirect
51. C2×#3711C22semidirect
53. C32×#103C22semidirect
54. #63647C22semidirect
55. #63636C22semidirect
56. C3×#835C22semidirect
57. C3×#821C22semidirect
58. C3×(C2×D3)⋊C8C22semidirect
59. C3×#810C22semidirect
60. C3×#809C22semidirect
61. #63565C22semidirect
62. #63564C22semidirect
63. #63557C22semidirect
64. (C2×D3)⋊(C3⋊C8)C22semidirect
87. #4806D3semidirect
89. #4803D3semidirect
109. C3×#239D4semidirect
145. #3799D4semidirect
185. C2×D3×Q8C2×D3semidirect
212. C2×#215C2×D3semidirect
231. C2×#204C2×D3semidirect
233. C2×ΓL(1,𝔽25)C2×D3semidirect
242. D3×C4⋊C4C2×D3semidirect
248. C3×#103C2×D3semidirect
249. C3×#103C2×D3semidirect
254. #835C2×D3semidirect
257. #821C2×D3semidirect
264. (C2×D3)⋊C8C2×D3semidirect
266. #810C2×D3semidirect
271. #809C2×D3semidirect
289. C32×Q8C2×D4semidirect
299. C4⋊(C3⋊D3)C2×D4semidirect
312. C3×D12C2×D4semidirect
322. C3×Dic6C2×D4semidirect
399. #239D12semidirect
537. C2×C3×D3AGL(1,ℤ/8)semidirect
588. #103D32semidirect
639. C3×Q8C2×D12semidirect
640. C3×Q8D3×D4semidirect
712. D12C2×D12semidirect
738. Dic6D3×D4semidirect
892. C2×D3#914semidirect
916. C32#3006semidirect
937. Q8D3×D12semidirect
1044. C3#78884semidirect
1045. C3#80040semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#2392
C2×#639392
C2×#637942
D3×#8952
#105925092
C3×#48062
C3×#48032
#105915932
#105915842
#105909642
#105909472
#105909362
#105906172
#105906092
#105905952
#800403
#788843