Finite Group Databasebeta

← #11864055

Subgroups — #11864055

Order 1152.

1592 conjugacy classes of subgroups.

The subgroup lattice has 1013 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#237C211yesmaximal, characteristic, complemented
2C2×C3×#914C211yesmaximal, characteristic, complemented
3#10595424C211yesmaximal, characteristic, complemented
4C2×#63943C211yesmaximal, characteristic, complemented
5#10592872C211yesmaximal, characteristic, complemented
6C3×#5173C211yesmaximal, characteristic, complemented
7#10591656C211yesmaximal, characteristic, complemented
8#10591655C211yesmaximal, characteristic, complemented
9#10591457C211yesmaximal, characteristic, complemented
10#10591450C211yesmaximal, characteristic, complemented
11#10591421C211yesmaximal, characteristic, complemented
12#10590963C211yesmaximal, characteristic, complemented
13#10590962C211yesmaximal, characteristic, complemented
14#10590948C211yesmaximal, characteristic, complemented
15#10590936C211yesmaximal, characteristic, complemented
16#83945—31nomaximal
17#80227—31nomaximal
18C2×#3830C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic
20C2×C3×#237C2211yescharacteristic
21C2×C3×D3×D4C2211yescharacteristic
22C2×D3×#67—21no—
23C2×#3805—21no—
24C2×#3804—21no—
25C22×D3×Dic3—21no—
26D3×#237—24no—
27D3×#237—24no—
28C2×C4×D32C2211yescharacteristic
29C2×#3796C2211yescharacteristic
30C2×#3795C2211yescharacteristic
31C2×D3×Dic6C2211yescharacteristic
32C2×C32×SD16C2211yescharacteristic, complemented
33#64155C2211yescharacteristic, complemented
34C2×#3756C2211yescharacteristic, complemented
35C3×#946C2211yescharacteristic, complemented
36C2×C3×#216C2211yescharacteristic, complemented
37C2×C3×#215C2211yescharacteristic, complemented
38C2×C3×#213C2211yescharacteristic, complemented
39C3×#914—24no—
40C2×C3×D24C2211yescharacteristic, complemented
41C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
42#63943—24no—
43#63922—21no—
44#63916C2211yescharacteristic, complemented
45#63908C2211yescharacteristic, complemented
46#63904—21no—
47#63884—21no—
48#63879—21no—
49#63841C2211yescharacteristic
50C2×#3716C2211yescharacteristic, complemented
51C2×#3715C2211yescharacteristic, complemented
52C2×#3711C2211yescharacteristic
53#63659C2211yescharacteristic, complemented
54#63647C2211yescharacteristic, complemented
55#63643C2211yescharacteristic, complemented
56C3×#832C2211yescharacteristic, complemented
57C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
58C3×#816C2211yescharacteristic, complemented
59#63567C2211yescharacteristic, complemented
60#63566C2211yescharacteristic, complemented
61#63563C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63#63557C2211yescharacteristic, complemented
64(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
65C2×D3×#41—31no—
66C22×#237—31no—
67C2×C3×AGL(1,ℤ/8)—31no—
68#5828—31no—
69C2×#951—31no—
70C2×#918—31no—
71C2×#914D311yescharacteristic, complemented
72#5627—31no—
73C3×#452—31no—
74#5238—31no—
75#5215—31no—
76#5187—31no—
77#5173—31no—
78#5173—31no—
79#5173—31no—
80#5173—31no—
81#5173—61no—
82#5173D311yescharacteristic, complemented
83#5158—31no—
84#5158—31no—
85#5158—31no—
86#5158—31no—
87#5126—31no—
88#5120—31no—
89#5047—31no—
90#4810—31no—
91#4802—31no—
92#4781—31no—
93#4770—31no—
94#4734—31no—
95#4726—31no—
96C23×C3×D3—21no—
97C22×D32D411yescharacteristic
98C2×C32×Q8C2311yescharacteristic
99C2×C32×D4C2311yescharacteristic
100C2×#638—21no—
101C22×C3⋊Dic3—21no—
102#3830—22no—
103#3830—22no—
104C2×C4×C3⋊D3C2311yescharacteristic
105C2×#634C2311yescharacteristic
106C2×C3×#67—21no—
107C2×C3×#67—21no—
108C22×C3×Dic3—21no—
109C3×#239—22no—
110C3×#239—22no—
111C3×#237—22no—
112C3×#237—22no—
113C3×D3×D4—22no—
114C3×D3×D4D414yescomplemented
115C2×C3×D12—21no—
116C2×C3×D12C2311yescharacteristic
117C2×C3×D12C2311yescharacteristic
118C2×C3×C4×D3—21no—
119C2×C3×C4×D3C2311yescharacteristic
120C2×C3×C4×D3C2311yescharacteristic
121C2×C3×Dic6C2311yescharacteristic
122D3×#67—28no—
123C2×#627—21no—
124C2×#626—21no—
125C2×#626—21no—
126C2×#625—21no—
127C2×#625—21no—
128C2×#624D411yescharacteristic
129#3805—28no—
130#3804—28no—
131C2×D3×Dic3—28no—
132C2×D3×Dic3—21no—
133C2×D3×Dic3—21no—
134C2×D3×Dic3—21no—
135C2×D3×Dic3D411yescharacteristic
136C2×D3×Dic3D411yescharacteristic
137C4×D32—22no—
138C4×D32—22no—
139#3796—22no—
140#3796—22no—
141#3795—22no—
142#3795—22no—
143D3×Dic6—22no—
144D3×Dic6D414yescomplemented
145C32×SD16—22no—
146C2×C32×C8C2311yescharacteristic
147#3756—22no—
148#3752—21no—
149C4⋊(C3⋊Dic3)C2311yescharacteristic
150#3750—21no—
151C2×C3⋊(C3⋊C8)C2311yescharacteristic
152C3×#216—22no—
153C3×#215—22no—
154C3×#213—22no—
155C3×(C2×D3)⋊C4—21no—
156C3×C4⋊Dic3C2311yescharacteristic
157C3×Dic3⋊C4—21no—
158C2×C3×C3⋊C8C2311yescharacteristic
159C2×C3×C3⋊C8C2311yescharacteristic
160C3×D24—22no—
161C3×ΓL(1,𝔽25)—22no—
162(C2×D3)⋊Dic3—21no—
163(C2×D3)⋊Dic3—21no—
164(C2×D3)⋊Dic3—21no—
165Dic32—21no—
166#3716—22no—
167#3715—22no—
168#3711—22no—
169#3005—91noSylow
170C2×C3×#41—31no—
171C2×C3×#41—31no—
172C22×C3×D4—31no—
173C22×#67—61no—
174C23×Dic3—61no—
175D3×#41—64no—
176D3×#41—64no—
177C2×#239—31no—
178C2×#239C2×D311yescharacteristic
179C2×D3×Q8—31no—
180C2×#237—31no—
181C2×#237—31no—
182C2×#237—31no—
183C2×#237—31no—
184C2×#237—61no—
185C2×#237—64no—
186C2×#237—61no—
187C2×#237—61no—
188C2×#237—64no—
189C2×#237—61no—
190C2×#237C2×D311yescharacteristic
191C2×D3×D4—61no—
192C2×D3×D4C2×D311yescharacteristic
193C2×#235—31no—
194C2×#235—61no—
195C22×C4×D3—31no—
196C22×C4×D3—31no—
197C22×C4×D3—61no—
198C22×Dic6—31no—
199C3×AGL(1,ℤ/8)—64no—
200C2×C3×Q16—31no—
201C2×C3×SD16—21no—
202C2×C3×SD16—31no—
203C2×C3×SD16C2×D311yescharacteristic, complemented
204C2×C3×SD16C2×D311yescharacteristic, complemented
205C2×C3×D8—31no—
206C2×C3×D8—31no—
207C2×C3×M16—31no—
208C3×C22⋊Q8—31no—
209#951—64no—
210#946—31no—
211#946—31no—
212#946—61no—
213#946C2×D311yescharacteristic, complemented
214C2×#216—31no—
215C2×#216—31no—
216C2×#216—61no—
217C2×#216C2×D311yescharacteristic, complemented
218C2×#215—31no—
219C2×#215C2×D311yescharacteristic, complemented
220#938—31no—
221#938—31no—
222#937—61no—
223#935—61no—
224C2×#214—31no—
225C2×#214—31no—
226C2×#213C2×D311yescharacteristic, complemented
227#930—31no—
228C4×#67—61no—
229C4×#67—61no—
230#926—31no—
231C2×#208—31no—
232#918—64no—
233#914—24no—
234C2×D24C2×D311yescharacteristic, complemented
235C2×#204—31no—
236C2×ΓL(1,𝔽25)—31no—
237C2×ΓL(1,𝔽25)C2×D311yescharacteristic
238#895—31no—
239#894—61no—
240#893—61no—
241#892—31no—
242#882—61no—
243#67⋊C4—61no—
244C3×#103—31no—
245C3×#102—31no—
246C3×C22⋊C8—31no—
247#835—31no—
248#832—31no—
249#832—31no—
250#832—31no—
251#832—31no—
252#832—61no—
253#832C2×D311yescharacteristic, complemented
254#830—31no—
255#821—31no—
256(C2×D3)⋊C8—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—61no—
262(C2×D3)⋊C8C2×D311yescharacteristic, complemented
263#816—31no—
264#816—31no—
265#816—31no—
266#816—31no—
267#816—61no—
268#816C2×D311yescharacteristic, complemented
269#810—31no—
270#809—31no—
271C23×C32—21no—
272C22×C3⋊D3C2×D411yescharacteristic
273C22×C3×D3—21no—
274C22×C3×D3—24no—
275C22×C3×D3—21no—
276C22×C3×D3—42no—
277C22×C3×D3—42no—
278C22×C3×D3C2×D411yescharacteristic
279C22×C3×D3C2×D411yescharacteristic
280C2×D32—22no—
281C2×D32—41no—
282C2×D32—41no—
283C32×Q8—21no—
284C32×Q8—21no—
285C32×D4—21no—
286C32×D4C2×D412yes—
287C2×C32×C4—21no—
288C2×C32×C4C2411yescharacteristic
289#638—24no—
290C2×C3⋊Dic3—24no—
291C2×C3⋊Dic3—21no—
292C2×C3⋊Dic3—21no—
293C2×C3⋊Dic3C2×D411yescharacteristic
294C4×C3⋊D3—21no—
295C4×C3⋊D3—21no—
296#634—21no—
297#634C2×D412yes—
298C3×#67—24no—
299C3×#67—24no—
300C2×C3×Dic3—24no—
301C2×C3×Dic3—21no—
302C2×C3×Dic3—21no—
303C2×C3×Dic3C2×D411yescharacteristic
304C2×C3×Dic3C2×D411yescharacteristic
305C3×D12—21no—
306C3×D12—21no—
307C3×D12—21no—
308C3×D12—42no—
309C3×D12C2×D412yes—
310C3×C4×D3—21no—
311C3×C4×D3—21no—
312C3×C4×D3—42no—
313C3×C4×D3C2×D412yes—
314C3×C4×D3C2×D412yes—
315C3×Dic6—21no—
316C3×Dic6C2×D412yes—
317#627—24no—
318#626—24no—
319#626—42no—
320#625—24no—
321#625—42no—
322#624—22no—
323D3×Dic3—24no—
324D3×Dic3—24no—
325D3×Dic3—24no—
326D3×Dic3—22no—
327D3×Dic3—22no—
328C32×C8—21no—
329C3⋊(C3⋊C8)—21no—
330C3×C3⋊C8—21no—
331C3×C3⋊C8—21no—
332C22×#41—91no—
333C2×#137—91no—
334C2×AGL(1,ℤ/8)—31no—
335#525—91no—
336#452—31no—
337#452—91no—
338#452—91no—
339#452—91no—
340#449—91no—
341#449—91no—
342#449—91no—
343#449—91no—
344#419—91no—
345#418—91no—
346#407—91no—
347C24×C3—61no—
348C23×D3—21no—
349C23×D3—31no—
350C23×D3—31no—
351C3×#41—62no—
352C3×#41—62no—
353C3×#41—62no—
354C3×#41—62no—
355C2×C3×Q8—21no—
356C2×C3×Q8—31no—
357C2×C3×Q8C22×D311yescharacteristic
358C2×C3×Q8C22×D311yescharacteristic
359C2×C3×D4—21no—
360C2×C3×D4—34no—
361C2×C3×D4—31no—
362C2×C3×D4—31no—
363C2×C3×D4—61no—
364C2×C3×D4—62no—
365C2×C3×D4—61no—
366C2×C3×D4—61no—
367C2×C3×D4C22×D311yescharacteristic
368C2×C3×D4C22×D311yescharacteristic
369C22×C3×C4—31no—
370C22×C3×C4—31no—
371C22×C3×C4—61no—
372C22×C3×C4—61no—
373C2×#67—21no—
374C2×#67—21no—
375C2×#67—61no—
376C2×#67—61no—
377C2×#67—68no—
378C2×#67—61no—
379C2×#67—61no—
380C2×#67—61no—
381C2×#67—61no—
382C2×#67—61no—
383C2×#67—61no—
384C2×#67—121no—
385C22×Dic3—21no—
386C22×Dic3—31no—
387C22×Dic3—31no—
388C22×Dic3—61no—
389C22×Dic3—61no—
390C22×Dic3—68no—
391C22×Dic3—61no—
392C22×Dic3—61no—
393C22×Dic3—61no—
394C22×Dic3—121no—
395#239—22no—
396#239—22no—
397#239—62no—
398#239—62no—
399D3×Q8—34no—
400D3×Q8—62no—
401#237—22no—
402#237—22no—
403#237—62no—
404#237—62no—
405#237—62no—
406#237—62no—
407#237—62no—
408#237—68no—
409#237—68no—
410#237—68no—
411#237—62no—
412#237—62no—
413#237—62no—
414#237—122no—
415#237—122no—
416D3×D4—22no—
417D3×D4—68no—
418D3×D4#6714yescomplemented
419#235—62no—
420#235—68no—
421#235—62no—
422C2×D12—21no—
423C2×D12—61no—
424C2×D12—61no—
425C2×D12C22×D311yescharacteristic
426C2×D12C22×D311yescharacteristic
427C2×C4×D3—21no—
428C2×C4×D3—31no—
429C2×C4×D3—31no—
430C2×C4×D3—31no—
431C2×C4×D3—31no—
432C2×C4×D3—31no—
433C2×C4×D3—31no—
434C2×C4×D3—61no—
435C2×C4×D3—62no—
436C2×C4×D3—62no—
437C2×C4×D3—61no—
438C2×C4×D3—61no—
439C2×C4×D3—68no—
440C2×C4×D3—61no—
441C2×C4×D3—62no—
442C2×C4×D3—62no—
443C2×C4×D3C22×D311yescharacteristic
444C2×C4×D3C22×D311yescharacteristic
445C2×Dic6—31no—
446C2×Dic6—31no—
447C2×Dic6—34no—
448C2×Dic6—61no—
449C2×Dic6—62no—
450C2×Dic6—61no—
451C2×Dic6—61no—
452C2×Dic6C22×D311yescharacteristic
453C3×Q16—62no—
454C3×SD16—22no—
455C3×SD16—22no—
456C3×SD16—42no—
457C3×SD16—62no—
458C3×D8—62no—
459C3×D8—62no—
460C3×M16—62no—
461C2×C3×C8—21no—
462C2×C3×C8—31no—
463C2×C3×C8—31no—
464C2×C3×C8C22×D311yescharacteristic
465C2×C3×C8C22×D311yescharacteristic
466C3×C4⋊C4—31no—
467C3×C4⋊C4—61no—
468C3×C22⋊C4—61no—
469#217—61no—
470#217—61no—
471#217—61no—
472#216—22no—
473#216—62no—
474#216—62no—
475#216—122no—
476#215—22no—
477#215—62no—
478#214—62no—
479#214—62no—
480#213—22no—
481(C2×D3)⋊C4—21no—
482(C2×D3)⋊C4—61no—
483(C2×D3)⋊C4—61no—
484(C2×D3)⋊C4—61no—
485(C2×D3)⋊C4—61no—
486(C2×D3)⋊C4—61no—
487(C2×D3)⋊C4—121no—
488C4⋊Dic3—31no—
489C4⋊Dic3—31no—
490C4⋊Dic3—61no—
491C4⋊Dic3C22×D311yescharacteristic
492Dic3⋊C4—21no—
493Dic3⋊C4—61no—
494Dic3⋊C4—61no—
495Dic3⋊C4—121no—
496C4×Dic3—61no—
497C4×Dic3—61no—
498#208—62no—
499C2×C3⋊C8—31no—
500C2×C3⋊C8—31no—
501C2×C3⋊C8—61no—
502C2×C3⋊C8C22×D311yescharacteristic
503C2×C3⋊C8C22×D311yescharacteristic
504D24—22no—
505#204—62no—
506ΓL(1,𝔽25)—22no—
507ΓL(1,𝔽25)—62no—
508C22×C32—22no—
509C22×C32—41no—
510C22×C32—41no—
511C22×C32C22×D411yescharacteristic
512C2×C3⋊D3—21no—
513C2×C3⋊D3—21no—
514C2×C3⋊D3—21no—
515C2×C3×D3—21no—
516C2×C3×D3—21no—
517C2×C3×D3—22no—
518C2×C3×D3—21no—
519C2×C3×D3—21no—
520C2×C3×D3—21no—
521C2×C3×D3—48no—
522C2×C3×D3—41no—
523C2×C3×D3—41no—
524C2×C3×D3—41no—
525C2×C3×D3—41no—
526C2×C3×D3—41no—
527C2×C3×D3#12012yes—
528D32—44no—
529C32×C4—41no—
530C32×C4C22×D411yescharacteristic
531C32×C4C22×D411yescharacteristic
532C3⋊Dic3—21no—
533C3⋊Dic3—22no—
534C3⋊Dic3—41no—
535C3×Dic3—21no—
536C3×Dic3—22no—
537C3×Dic3—41no—
538C3×Dic3#12012yes—
539C2×#41—31no—
540C2×#41—31no—
541C2×#41—91no—
542C2×#41—91no—
543C2×#41—91no—
544C2×#41—181no—
545C2×#41—181no—
546C2×#41—184no—
547C2×#41—184no—
548C22×Q8—91no—
549C22×D4—31no—
550C22×D4—181no—
551C23×C4—91no—
552C23×C4—181no—
553#137—184no—
554AGL(1,ℤ/8)—64no—
555C2×Q16—31no—
556C2×Q16—91no—
557C2×SD16—31no—
558C2×SD16—91no—
559C2×SD16—91no—
560C2×SD16D3211yescharacteristic, complemented
561C2×D8—31no—
562C2×D8—31no—
563C2×M16—31no—
564C2×M16—91no—
565#123—181no—
566C22⋊Q8—31no—
567C22⋊Q8—91no—
568#121—91no—
569#121—91no—
570#120—181no—
571C4×D4—181no—
572C4×D4—181no—
573#117—91no—
574#103—31no—
575#103—91no—
576#103—91no—
577#103—91no—
578#102—31no—
579#102—91no—
580#102—91no—
581#102—91no—
582C22⋊C8—31no—
583C22⋊C8—91no—
584C22⋊C8—91no—
585C22⋊C8—91no—
586C23×C3—21no—
587C23×C3—21no—
588C23×C3—31no—
589C23×C3—31no—
590C23×C3—41no—
591C23×C3—64no—
592C23×C3—61no—
593C23×C3—61no—
594C23×C3—122no—
595C23×C3—122no—
596C22×D3—21no—
597C22×D3—24no—
598C22×D3—21no—
599C22×D3—31no—
600C22×D3—31no—
601C22×D3—42no—
602C22×D3—42no—
603C22×D3—61no—
604C22×D3—62no—
605C22×D3—62no—
606C22×D3—121no—
607C22×D3—121no—
608C22×D3—121no—
609C22×D3—121no—
610C22×D3D3×D411yescharacteristic
611C22×D3D3×D411yescharacteristic
612C3×Q8—21no—
613C3×Q8—21no—
614C3×Q8—21no—
615C3×Q8—21no—
616C3×Q8—32no—
617C3×Q8—41no—
618C3×Q8—41no—
619C3×Q8—61no—
620C3×D4—21no—
621C3×D4—21no—
622C3×D4—22no—
623C3×D4—32no—
624C3×D4—41no—
625C3×D4—64no—
626C3×D4—64no—
627C3×D4—61no—
628C3×D4—61no—
629C3×D4—61no—
630C3×D4—122no—
631C3×D4D3×D412yes—
632C3×D4C2×#6712yes—
633C2×C3×C4—21no—
634C2×C3×C4—21no—
635C2×C3×C4—21no—
636C2×C3×C4—31no—
637C2×C3×C4—32no—
638C2×C3×C4—32no—
639C2×C3×C4—31no—
640C2×C3×C4—41no—
641C2×C3×C4—64no—
642C2×C3×C4—61no—
643C2×C3×C4—61no—
644C2×C3×C4—61no—
645C2×C3×C4—61no—
646C2×C3×C4—122no—
647C2×C3×C4C23×D311yescharacteristic
648C2×C3×C4C23×D311yescharacteristic
649#67—24no—
650#67—24no—
651#67—64no—
652#67—64no—
653#67—64no—
654#67—64no—
655#67—64no—
656#67—124no—
657#67—122no—
658#67—122no—
659#67—122no—
660C2×Dic3—24no—
661C2×Dic3—21no—
662C2×Dic3—21no—
663C2×Dic3—31no—
664C2×Dic3—31no—
665C2×Dic3—61no—
666C2×Dic3—64no—
667C2×Dic3—62no—
668C2×Dic3—64no—
669C2×Dic3—64no—
670C2×Dic3—64no—
671C2×Dic3—64no—
672C2×Dic3—61no—
673C2×Dic3—61no—
674C2×Dic3—62no—
675C2×Dic3—61no—
676C2×Dic3—61no—
677C2×Dic3—121no—
678C2×Dic3—124no—
679C2×Dic3—121no—
680C2×Dic3D3×D411yescharacteristic
681C2×Dic3D3×D411yescharacteristic
682D12—21no—
683D12—21no—
684D12—21no—
685D12—42no—
686D12—64no—
687D12—122no—
688D12C2×#6712yes—
689C4×D3—21no—
690C4×D3—21no—
691C4×D3—42no—
692C4×D3—62no—
693C4×D3—62no—
694C4×D3—64no—
695C4×D3—64no—
696C4×D3—62no—
697C4×D3—64no—
698C4×D3—61no—
699C4×D3—61no—
700C4×D3—61no—
701C4×D3—61no—
702C4×D3—62no—
703C4×D3—121no—
704C4×D3—121no—
705C4×D3D3×D412yes—
706C4×D3C2×#6712yes—
707Dic6—21no—
708Dic6—32no—
709Dic6—32no—
710Dic6—62no—
711Dic6—64no—
712Dic6—61no—
713Dic6—61no—
714Dic6—64no—
715Dic6—121no—
716Dic6D3×D412yes—
717C3×C8—21no—
718C3×C8—21no—
719C3×C8—41no—
720C3×C8—61no—
721C3×C8—61no—
722C3⋊C8—21no—
723C3⋊C8—21no—
724C3⋊C8—61no—
725C3⋊C8—61no—
726C3⋊C8—121no—
727C2×C32—42no—
728C2×C32C2×#12011yescharacteristic
729C2×C32#57511yescharacteristic
730C2×C32#57511yescharacteristic
731C3⋊D3—41no—
732C3×D3—22no—
733C3×D3—41no—
734C3×D3—42no—
735C3×D3—81no—
736C24—61no—
737C24—91no—
738#41—62no—
739#41—62no—
740#41—62no—
741#41—62no—
742#41—182no—
743#41—182no—
744#41—188no—
745#41—182no—
746#41—182no—
747#41—188no—
748#41—182no—
749#41—182no—
750C2×Q8—31no—
751C2×Q8—94no—
752C2×Q8—91no—
753C2×Q8—181no—
754C2×Q8—182no—
755C2×Q8C2×D3211yescharacteristic
756C2×D4—34no—
757C2×D4—31no—
758C2×D4—31no—
759C2×D4—61no—
760C2×D4—62no—
761C2×D4—61no—
762C2×D4—61no—
763C2×D4—181no—
764C2×D4—181no—
765C2×D4—188no—
766C2×D4—181no—
767C2×D4—181no—
768C2×D4—181no—
769C2×D4C2×D3211yescharacteristic
770C22×C4—31no—
771C22×C4—31no—
772C22×C4—61no—
773C22×C4—61no—
774C22×C4—91no—
775C22×C4—91no—
776C22×C4—91no—
777C22×C4—91no—
778C22×C4—182no—
779C22×C4—182no—
780C22×C4—181no—
781C22×C4—181no—
782C22×C4—181no—
783C22×C4—188no—
784C22×C4—181no—
785Q16—62no—
786Q16—182no—
787SD16—22no—
788SD16—62no—
789SD16—182no—
790SD16—182no—
791D8—62no—
792D8—62no—
793M16—62no—
794M16—182no—
795C2×C8—31no—
796C2×C8—31no—
797C2×C8—91no—
798C2×C8C2×D3211yescharacteristic
799C4⋊C4—31no—
800C4⋊C4—61no—
801C4⋊C4—91no—
802C4⋊C4—181no—
803C22⋊C4—61no—
804C22⋊C4—181no—
805C22⋊C4—181no—
806C22⋊C4—181no—
807C22⋊C4—181no—
808C42—181no—
809C22×C3—22no—
810C22×C3—22no—
811C22×C3—21no—
812C22×C3—32no—
813C22×C3—42no—
814C22×C3—41no—
815C22×C3—41no—
816C22×C3—41no—
817C22×C3—41no—
818C22×C3—61no—
819C22×C3—61no—
820C22×C3—61no—
821C22×C3—61no—
822C22×C3—61no—
823C22×C3—62no—
824C22×C3—81no—
825C22×C3—81no—
826C22×C3—128no—
827C22×C3—121no—
828C22×C3—121no—
829C22×C3—121no—
830C22×C3—121no—
831C22×C3—121no—
832C22×C3C2×D3×D411yescharacteristic
833C22×C3C2×D3×D411yescharacteristic
834C2×D3—21no—
835C2×D3—21no—
836C2×D3—21no—
837C2×D3—21no—
838C2×D3—22no—
839C2×D3—21no—
840C2×D3—48no—
841C2×D3—41no—
842C2×D3—41no—
843C2×D3—41no—
844C2×D3—41no—
845C2×D3—41no—
846C2×D3—61no—
847C2×D3—61no—
848C2×D3—61no—
849C2×D3—61no—
850C2×D3—61no—
851C2×D3—61no—
852C2×D3—121no—
853C2×D3—121no—
854C2×D3—121no—
855C2×D3—124no—
856C2×D3—124no—
857C2×D3#93712yes—
858C3×C4—21no—
859C3×C4—21no—
860C3×C4—32no—
861C3×C4—41no—
862C3×C4—41no—
863C3×C4—62no—
864C3×C4—61no—
865C3×C4—81no—
866C3×C4—121no—
867C3×C4C2×D3×D411yescharacteristic
868C3×C4C2×D3×D411yescharacteristic
869C3×C4C2×D3×D411yescharacteristic
870C3×C4C22×#6711yescharacteristic
871Dic3—22no—
872Dic3—21no—
873Dic3—41no—
874Dic3—62no—
875Dic3—61no—
876Dic3—62no—
877Dic3—61no—
878Dic3—122no—
879Dic3—121no—
880Dic3—121no—
881Dic3—121no—
882Dic3—241no—
883Dic3#93712yes—
884C32#300511yescharacteristic, complemented, Sylow
885C23—21no—
886C23—31no—
887C23—31no—
888C23—64no—
889C23—61no—
890C23—61no—
891C23—91no—
892C23—122no—
893C23—122no—
894C23—182no—
895C23—361no—
896C23—361no—
897Q8—21no—
898Q8—21no—
899Q8—32no—
900Q8—61no—
901Q8—92no—
902Q8—184no—
903Q8—181no—
904D4—21no—
905D4—32no—
906D4—64no—
907D4—64no—
908D4—61no—
909D4—61no—
910D4—61no—
911D4—122no—
912D4—184no—
913D4—184no—
914D4—184no—
915D4—362no—
916D4—362no—
917D4D3×#6712yes—
918C2×C4—21no—
919C2×C4—31no—
920C2×C4—32no—
921C2×C4—32no—
922C2×C4—31no—
923C2×C4—64no—
924C2×C4—61no—
925C2×C4—61no—
926C2×C4—61no—
927C2×C4—61no—
928C2×C4—91no—
929C2×C4—122no—
930C2×C4—182no—
931C2×C4—182no—
932C2×C4—182no—
933C2×C4—184no—
934C2×C4—184no—
935C2×C4—184no—
936C2×C4—184no—
937C2×C4—181no—
938C2×C4—181no—
939C2×C4—181no—
940C2×C4—181no—
941C2×C4C22×D3211yescharacteristic
942C8—21no—
943C8—61no—
944C8—61no—
945C8—181no—
946C2×C3—21no—
947C2×C3—21no—
948C2×C3—21no—
949C2×C3—42no—
950C2×C3—42no—
951C2×C3—62no—
952C2×C3—82no—
953C2×C3—122no—
954C2×C3—121no—
955C2×C3—241no—
956C2×C3D3×#12011yescharacteristic
957C2×C3#576811yescharacteristic
958C2×C3#577311yescharacteristic
959C2×C3#577311yescharacteristic
960C2×C3#577711yescharacteristic
961C2×C3C2×#93711yescharacteristic
962D3—22no—
963D3—41no—
964D3—42no—
965D3—81no—
966D3—121no—
967D3—121no—
968D3—241no—
969C22—22no—
970C22—32no—
971C22—41no—
972C22—41no—
973C22—61no—
974C22—61no—
975C22—61no—
976C22—61no—
977C22—61no—
978C22—62no—
979C22—128no—
980C22—121no—
981C22—121no—
982C22—121no—
983C22—121no—
984C22—121no—
985C22—181no—
986C22—181no—
987C22—181no—
988C22—364no—
989C22D32×D411yescharacteristic
990C4—32no—
991C4—41no—
992C4—61no—
993C4—62no—
994C4—121no—
995C4—181no—
996C4—182no—
997C4—361no—
998C4D32×D411yescharacteristic
999C4C2×D3×#6711yescharacteristic
1000C3—21no—
1001C3#8022711yescharacteristic, complemented
1002C3#8394511yescharacteristic, complemented
1003C2—42no—
1004C2—62no—
1005C2—121no—
1006C2—122no—
1007C2—241no—
1008C2—361no—
1009C2#1059474411yescharacteristic
1010C2#1059474511yescharacteristic
1011C2D3×#93711yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
hypercenterC2×SD16D32
hypocenterC32#3005
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C2×D3×#237C2semidirect
2. C2×C3×#914C2semidirect
3. #10595424C2semidirect
4. C2×#63943C2semidirect
5. #10592872C2semidirect
6. C3×#5173C2semidirect
7. #10591656C2semidirect
8. #10591655C2semidirect
9. #10591457C2semidirect
10. #10591450C2semidirect
11. #10591421C2semidirect
12. #10590963C2semidirect
13. #10590962C2semidirect
14. #10590948C2semidirect
15. #10590936C2semidirect
32. C2×C32×SD16C22semidirect
33. #64155C22semidirect
34. C2×#3756C22semidirect
35. C3×#946C22semidirect
36. C2×C3×#216C22semidirect
37. C2×C3×#215C22semidirect
38. C2×C3×#213C22semidirect
40. C2×C3×D24C22semidirect
44. #63916C22semidirect
45. #63908C22semidirect
50. C2×#3716C22semidirect
51. C2×#3715C22semidirect
53. #63659C22semidirect
54. #63647C22semidirect
55. #63643C22semidirect
56. C3×#832C22semidirect
57. C3×(C2×D3)⋊C8C22semidirect
58. C3×#816C22semidirect
59. #63567C22semidirect
60. #63566C22semidirect
61. #63563C22semidirect
62. #63562C22semidirect
63. #63557C22semidirect
64. (C2×D3)⋊(C3⋊C8)C22semidirect
71. C2×#914D3semidirect
82. #5173D3semidirect
114. C3×D3×D4D4semidirect
144. D3×Dic6D4semidirect
203. C2×C3×SD16C2×D3semidirect
204. C2×C3×SD16C2×D3semidirect
213. #946C2×D3semidirect
217. C2×#216C2×D3semidirect
219. C2×#215C2×D3semidirect
226. C2×#213C2×D3semidirect
234. C2×D24C2×D3semidirect
253. #832C2×D3semidirect
262. (C2×D3)⋊C8C2×D3semidirect
268. #816C2×D3semidirect
418. D3×D4#67semidirect
560. C2×SD16D32semidirect
884. C32#3005semidirect
1001. C3#80227semidirect
1002. C3#83945semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#2372
C2×C3×#9142
#105954242
C2×#639432
#105928722
C3×#51732
#105916562
#105916552
#105914572
#105914502
#105914212
#105909632
#105909622
#105909482
#105909362
#839453
#802273