Finite Group Databasebeta

← #11904647

Subgroups — #11904647

Order 1152.

3765 conjugacy classes of subgroups.

The subgroup lattice has 1229 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64366C211yesmaximal, characteristic, complemented
2C2×D3×#235C211yesmaximal, characteristic, complemented
3C3×#5833C211yesmaximal, characteristic, complemented
4C3×#5828C211yesmaximal, characteristic, complemented
5#10595430C212yesmaximal, complemented
6#10595404C212yesmaximal, complemented
7#10595292C214yesmaximal, complemented
8#10595282C212yesmaximal, complemented
9#10595241C212yesmaximal, complemented
10#10595163C214yesmaximal, complemented
11#10595074C212yesmaximal, complemented
12#10595045C211yesmaximal, characteristic, complemented
13#10595018C212yesmaximal, complemented
14C2×#63909C211yesmaximal, characteristic, complemented
15#10594990C211yesmaximal, characteristic, complemented
16#10594919C212yesmaximal, complemented
17#10594916C212yesmaximal, complemented
18#86379—31nomaximal
19#86041—31nomaximal
20C2×C32×#41C2211yescharacteristic, complemented
21#64366—28no—
22C2×#3832C2212yescomplemented
23C2×D4×C3⋊D3C2214yescomplemented
24C2×D4×C3⋊D3C2212yescomplemented
25C2×#3828C2211yescharacteristic
26C2×#3828C2212yescomplemented
27C22×C4⋊(C3⋊D3)C2212yescomplemented
28C22×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
29C2×C3×#235C2211yescharacteristic, complemented
30C22×C3×C4×D3C2211yescharacteristic, complemented
31C2×#3811C2214yescomplemented
32C2×D3×#67C2212yescomplemented
33C22×#626C2212yescomplemented
34C2×#3804C2212yescomplemented
35D3×#235—28no—
36C2×D3×D12C2211yescharacteristic, complemented
37C2×C4×D32C2212yescomplemented
38C2×#3799C2211yescharacteristic, complemented
39C2×#3798C2212yescomplemented
40C2×#3795C2211yescharacteristic, complemented
41C2×D3×Dic6C2211yescharacteristic, complemented
42C3×#946C2211yescharacteristic, complemented
43C3×#946C2212yescomplemented
44C3×#946C2211yescharacteristic, complemented
45C3×#939C2214yescomplemented
46C3×#938C2211yescharacteristic, complemented
47C3×#938C2211yescharacteristic, complemented
48C3×#938C2212yescomplemented
49C3×#937C2212yescomplemented
50C3×#935C2212yescomplemented
51C3×#930C2212yescomplemented
52C3×C4×#67C2212yescomplemented
53C3×C4×#67C2212yescomplemented
54C3×#926C2211yescharacteristic, complemented
55C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
56C3×#924C2212yescomplemented
57#63981C2214yescomplemented
58#63981C2214yescomplemented
59#63981C2214yescomplemented
60#63979C2214yescomplemented
61#63974C2214yescomplemented
62#63971C2214yescomplemented
63#63971C2214yescomplemented
64C2×#3722C2212yescomplemented
65#63953C2214yescomplemented
66#63952C2214yescomplemented
67#63923C2214yescomplemented
68#63912C2214yescomplemented
69#63911C2212yescomplemented
70#63910C2214yescomplemented
71#63910C2214yescomplemented
72#63909C2212yescomplemented
73#63909C2212yescomplemented
74#63909C2212yescomplemented
75#63909C2212yescomplemented
76#63909C2212yescomplemented
77#63909C2212yescomplemented
78#63900C2212yescomplemented
79#63897C2214yescomplemented
80#63894C2212yescomplemented
81#63881C2214yescomplemented
82#63881C2214yescomplemented
83#63865C2214yescomplemented
84#63864C2212yescomplemented
85#63849C2212yescomplemented
86#63844C2212yescomplemented
87C2×#1009—31no—
88C2×#1009—31no—
89C2×#1009—61no—
90C2×D3×#41—31no—
91C22×#235—31no—
92C3×#537—31no—
93C3×#525—31no—
94#5833D311yescharacteristic, complemented
95#5830—31no—
96#5828D311yescharacteristic, complemented
97C2×#930—31no—
98#5654—34no—
99#5633—32no—
100#5630—32no—
101#5629—32no—
102#5629—32no—
103#5627—32no—
104#5627—32no—
105#5610—34no—
106#5609—34no—
107#5609—32no—
108#5607—32no—
109#5607—32no—
110D3×#121—32no—
111D3×#121—32no—
112#5599—32no—
113#5590—34no—
114#5553—32no—
115#5552—32no—
116#5550—32no—
117D4×D12—32no—
118#5525—31no—
119#5523—31no—
120C2×#895—31no—
121#5504—31no—
122C23×C3⋊D3C2312yes—
123C23×C3⋊D3C2314yes—
124C23×C3×D3C2311yescharacteristic
125C22×D32C2312yes—
126C32×#41—24no—
127C2×C32×Q8C2311yescharacteristic
128C2×C32×D4C2312yes—
129C2×C32×D4C2311yescharacteristic
130C22×C32×C4C2312yes—
131C22×C32×C4C2311yescharacteristic
132C2×#638C2314yes—
133C2×#638C2312yes—
134#3832—28no—
135D4×C3⋊D3—216no—
136D4×C3⋊D3—28no—
137#3828—28no—
138#3828D418yescomplemented
139C2×C4⋊(C3⋊D3)—24no—
140C2×C4⋊(C3⋊D3)—28no—
141C2×C4⋊(C3⋊D3)C2312yes—
142C2×C4⋊(C3⋊D3)C2314yes—
143C2×C4⋊(C3⋊D3)C2312yes—
144C2×C4⋊(C3⋊D3)C2311yescharacteristic
145C2×C4×C3⋊D3C2314yes—
146C2×C4×C3⋊D3C2312yes—
147C2×#634C2311yescharacteristic
148C2×C3×#67C2312yes—
149C2×C3×#67C2312yes—
150C2×C3×#67C2312yes—
151C2×C3×#67C2314yes—
152C22×C3×Dic3C2311yescharacteristic
153C22×C3×Dic3C2312yes—
154C3×#235—24no—
155C2×C3×D12C2311yescharacteristic
156C2×C3×C4×D3—24no—
157C2×C3×C4×D3C2311yescharacteristic
158C2×C3×C4×D3C2311yescharacteristic
159C2×C3×C4×D3C2311yescharacteristic
160C2×C3×C4×D3C2312yes—
161C2×C3×C4×D3C2311yescharacteristic
162C2×C3×Dic6C2311yescharacteristic
163#3811—48no—
164D3×#67—28no—
165C2×#627C2312yes—
166C2×#626—44no—
167C2×#626C2312yes—
168C2×#626C2312yes—
169C2×#626C2314yes—
170C2×#626C2314yes—
171C2×#626C2314yes—
172C2×#626C2314yes—
173C2×#625C2312yes—
174C2×#624C2312yes—
175C2×#624C2314yes—
176#3804—28no—
177C2×D3×Dic3C2312yes—
178C2×D3×Dic3C2312yes—
179D3×D12—24no—
180C4×D32—28no—
181#3799—24no—
182#3798—28no—
183#3795—24no—
184D3×Dic6—24no—
185C3×#217C2314yes—
186C3×#217C2312yes—
187C3×#217C2312yes—
188C3×#217C2312yes—
189C3×(C2×D3)⋊C4C2312yes—
190C3×(C2×D3)⋊C4C2312yes—
191C3×(C2×D3)⋊C4C2314yes—
192C3×C4⋊Dic3C2312yes—
193C3×C4⋊Dic3C2312yes—
194C3×C4⋊Dic3C2311yescharacteristic
195C3×C4⋊Dic3C2311yescharacteristic
196C3×Dic3⋊C4C2314yes—
197C3×Dic3⋊C4C2312yes—
198C3×Dic3⋊C4C2312yes—
199C3×C4×Dic3C2312yes—
200#3724C2314yes—
201#3722C2314yes—
202#3722C2314yes—
203#3722C2314yes—
204#3722C2314yes—
205#3722C2314yes—
206Dic32C2314yes—
207#3488—91noSylow
208C2×C3×#41—21no—
209C2×C3×#41—31no—
210C2×C3×#41C2×D311yescharacteristic, complemented
211C2×C3×#41C2×D311yescharacteristic, complemented
212C23×C3×C4—31no—
213C22×#67—32no—
214C22×#67—32no—
215#1009—68no—
216#1009—68no—
217#1009—616no—
218D3×#41—68no—
219C2×#239—32no—
220C2×#239—32no—
221C2×#239—31no—
222C2×#239—62no—
223C2×D3×Q8—31no—
224C2×#237—32no—
225C2×#237—31no—
226C2×D3×D4—32no—
227C2×D3×D4—34no—
228C2×D3×D4—32no—
229C2×D3×D4—32no—
230C2×D3×D4—34no—
231C2×D3×D4—34no—
232C2×D3×D4—34no—
233C2×D3×D4—31no—
234C2×D3×D4—62no—
235C2×D3×D4—64no—
236C2×#235—31no—
237C2×#235—31no—
238C2×#235—32no—
239C2×#235—32no—
240C2×#235—32no—
241C2×#235—31no—
242C2×#235—32no—
243C2×#235—32no—
244C2×#235—31no—
245C2×#235—61no—
246C2×#235—62no—
247C2×#235—68no—
248C2×#235C2×D311yescharacteristic, complemented
249C22×D12—31no—
250C22×D12—31no—
251C22×D12—32no—
252C22×D12—32no—
253C22×D12—32no—
254C22×D12—31no—
255C22×D12—61no—
256C22×D12—62no—
257C22×C4×D3—32no—
258C22×C4×D3—32no—
259C22×C4×D3C2×D311yescharacteristic, complemented
260C22×Dic6—31no—
261C3×#123—32no—
262C3×C22⋊Q8—31no—
263C3×C22⋊Q8—31no—
264C3×C22⋊Q8—32no—
265C3×C22⋊Q8—32no—
266C3×#121—31no—
267C3×#121—31no—
268C3×#121—32no—
269C3×#121—34no—
270C3×#121—32no—
271C3×#120—32no—
272C3×C4×D4—32no—
273C3×C4×D4—32no—
274C3×#117—31no—
275C2×C3×C4⋊C4—31no—
276#947—32no—
277#946C2×D311yescharacteristic, complemented
278#946C2×D311yescharacteristic, complemented
279#946C2×D312yescomplemented
280#940—34no—
281#940—34no—
282#940—32no—
283#939—34no—
284#939—34no—
285#939C2×D314yescomplemented
286#938C2×D311yescharacteristic, complemented
287#938C2×D311yescharacteristic, complemented
288#938C2×D312yescomplemented
289#937—34no—
290#937—34no—
291#937—34no—
292#937C2×D312yescomplemented
293#935C2×D312yescomplemented
294#930—32no—
295#930—32no—
296#930—32no—
297#930—32no—
298#930—32no—
299#930—32no—
300#930C2×D312yescomplemented
301C4×#67—34no—
302C4×#67C2×D312yescomplemented
303C4×#67C2×D312yescomplemented
304C2×(C2×D3)⋊C4—32no—
305C2×(C2×D3)⋊C4—32no—
306#926C2×D311yescharacteristic, complemented
307C2×C4⋊Dic3C2×D311yescharacteristic, complemented
308#924C2×D312yescomplemented
309#896—34no—
310#896—34no—
311#895—32no—
312#895—32no—
313#895—32no—
314#895—32no—
315#895—32no—
316#895—32no—
317#895—34no—
318#895—34no—
319#894—34no—
320#894—34no—
321#893—34no—
322#893—34no—
323#893—32no—
324#892—32no—
325#892—32no—
326D3×C4⋊C4—32no—
327D3×C4⋊C4—32no—
328#887—32no—
329#885—34no—
330#885—34no—
331#884—34no—
332#884—34no—
333#884—34no—
334#884—34no—
335#884—34no—
336#884—34no—
337#882—34no—
338#882—34no—
339#882—34no—
340#882—34no—
341#882—34no—
342#67⋊C4—34no—
343#67⋊C4—34no—
344#67⋊C4—34no—
345D3×C22⋊C4—34no—
346D3×C22⋊C4—34no—
347#875—32no—
348#874—32no—
349C4×D12—32no—
350C4×Dic6—32no—
351C23×C32C2412yes—
352C23×C32C2411yescharacteristic
353C22×C3⋊D3—24no—
354C22×C3⋊D3—28no—
355C22×C3⋊D3—44no—
356C22×C3⋊D3—42no—
357C22×C3⋊D3—42no—
358C22×C3⋊D3—44no—
359C22×C3⋊D3C2414yes—
360C22×C3⋊D3C2412yes—
361C22×C3×D3—22no—
362C22×C3×D3—22no—
363C22×C3×D3—41no—
364C22×C3×D3C2412yes—
365C22×C3×D3C2411yescharacteristic
366C22×C3×D3C2411yescharacteristic
367C2×D32—24no—
368C2×D32—24no—
369C2×D32—42no—
370C32×Q8—22no—
371C32×D4—24no—
372C32×D4—22no—
373C2×C32×C4—24no—
374C2×C32×C4C2×D414yescomplemented
375C2×C32×C4C2412yes—
376C2×C32×C4C2411yescharacteristic
377C2×C32×C4C2411yescharacteristic
378#638—28no—
379#638C2×D418yescomplemented
380C2×C3⋊Dic3C2412yes—
381C4⋊(C3⋊D3)—28no—
382C4⋊(C3⋊D3)—24no—
383C4⋊(C3⋊D3)—24no—
384C4⋊(C3⋊D3)C2×D414yescomplemented
385C4×C3⋊D3—28no—
386C4×C3⋊D3C2×D418yescomplemented
387#634C2×D414yescomplemented
388C3×#67—24no—
389C3×#67—24no—
390C3×#67—44no—
391C3×#67—42no—
392C2×C3×Dic3—22no—
393C2×C3×Dic3—42no—
394C2×C3×Dic3C2412yes—
395C2×C3×Dic3C2414yes—
396C2×C3×Dic3C2411yescharacteristic
397C2×C3×Dic3C2412yes—
398C2×C3×Dic3C2411yescharacteristic
399C2×C3×Dic3C2412yes—
400C3×D12—22no—
401C3×C4×D3—22no—
402C3×C4×D3—22no—
403C3×C4×D3—22no—
404C3×C4×D3—24no—
405C3×C4×D3—22no—
406C3×Dic6—22no—
407#627—24no—
408#626—24no—
409#626—24no—
410#626—28no—
411#626—44no—
412#626—44no—
413#626—44no—
414#625—24no—
415#624—24no—
416#624—44no—
417D3×Dic3—24no—
418D3×Dic3—24no—
419C2×H(5,𝔽2)—91no—
420C22×#41—91no—
421#550—92no—
422#548—92no—
423#546—92no—
424#546—94no—
425D42—92no—
426D42—94no—
427#537—31no—
428#537—92no—
429#535—91no—
430#535—92no—
431#525—31no—
432#525—92no—
433C2×#121—91no—
434C2×#121—92no—
435#520—91no—
436C24×C3—31no—
437C23×D3—34no—
438C23×D3—34no—
439C23×D3—32no—
440C23×D3—32no—
441C23×D3—32no—
442C23×D3—32no—
443C23×D3—62no—
444C23×D3—64no—
445C23×D3C22×D311yescharacteristic
446C3×#41—28no—
447C3×#41—24no—
448C3×#41—24no—
449C3×#41—64no—
450C2×C3×Q8—21no—
451C2×C3×Q8—31no—
452C2×C3×Q8C22×D311yescharacteristic
453C2×C3×Q8C22×D311yescharacteristic
454C2×C3×D4—22no—
455C2×C3×D4—21no—
456C2×C3×D4—32no—
457C2×C3×D4—32no—
458C2×C3×D4—32no—
459C2×C3×D4—34no—
460C2×C3×D4—31no—
461C2×C3×D4C22×D312yes—
462C2×C3×D4C22×D311yescharacteristic
463C2×C3×D4C22×D311yescharacteristic
464C2×C3×D4C22×D312yes—
465C22×C3×C4—22no—
466C22×C3×C4—21no—
467C22×C3×C4—31no—
468C22×C3×C4—32no—
469C22×C3×C4—31no—
470C22×C3×C4—31no—
471C22×C3×C4—31no—
472C22×C3×C4—32no—
473C22×C3×C4—31no—
474C22×C3×C4—64no—
475C22×C3×C4C22×D312yes—
476C22×C3×C4C22×D312yes—
477C22×C3×C4C22×D311yescharacteristic
478C22×C3×C4C22×D311yescharacteristic
479C2×#67—32no—
480C2×#67—32no—
481C2×#67—34no—
482C2×#67—34no—
483C2×#67—32no—
484C2×#67—32no—
485C2×#67—34no—
486C2×#67—32no—
487C2×#67—32no—
488C2×#67—34no—
489C2×#67—34no—
490C2×#67—34no—
491C2×#67—62no—
492C2×#67—64no—
493C2×#67—68no—
494C2×#67—124no—
495C2×#67C22×D312yes—
496C2×#67C22×D312yes—
497C2×#67C22×D312yes—
498C2×#67C22×D314yes—
499C22×Dic3—32no—
500C22×Dic3—32no—
501C22×Dic3C22×D311yescharacteristic
502C22×Dic3C22×D312yes—
503#239—64no—
504#239—68no—
505#239—68no—
506#239—616no—
507D3×Q8—64no—
508#237—64no—
509#237—68no—
510D3×D4—64no—
511D3×D4—68no—
512D3×D4—68no—
513D3×D4—616no—
514D3×D4—616no—
515D3×D4—68no—
516D3×D4—616no—
517D3×D4—632no—
518D3×D4—128no—
519D3×D4—128no—
520#235—24no—
521#235—38no—
522#235—38no—
523#235—68no—
524#235—64no—
525#235—64no—
526#235—68no—
527#235—68no—
528#235—68no—
529#235—68no—
530#235—68no—
531#235—616no—
532C2×D12—31no—
533C2×D12—31no—
534C2×D12—32no—
535C2×D12—32no—
536C2×D12—34no—
537C2×D12—32no—
538C2×D12—34no—
539C2×D12—34no—
540C2×D12—32no—
541C2×D12—32no—
542C2×D12—32no—
543C2×D12—34no—
544C2×D12—34no—
545C2×D12—34no—
546C2×D12—61no—
547C2×D12—62no—
548C2×D12—64no—
549C2×D12—62no—
550C2×D12—64no—
551C2×D12—68no—
552C2×D12—68no—
553C2×D12—616no—
554C2×D12—68no—
555C2×D12—64no—
556C2×D12—64no—
557C2×D12—124no—
558C2×D12C22×D311yescharacteristic
559C2×C4×D3—24no—
560C2×C4×D3—32no—
561C2×C4×D3—32no—
562C2×C4×D3—32no—
563C2×C4×D3—32no—
564C2×C4×D3—34no—
565C2×C4×D3—34no—
566C2×C4×D3—32no—
567C2×C4×D3—32no—
568C2×C4×D3—34no—
569C2×C4×D3—34no—
570C2×C4×D3—62no—
571C2×C4×D3—64no—
572C2×C4×D3—68no—
573C2×C4×D3—68no—
574C2×C4×D3C22×D311yescharacteristic
575C2×C4×D3C22×D311yescharacteristic
576C2×C4×D3C22×D311yescharacteristic
577C2×C4×D3C22×D312yes—
578C2×C4×D3C22×D311yescharacteristic
579C2×Dic6—31no—
580C2×Dic6—31no—
581C2×Dic6—32no—
582C2×Dic6—32no—
583C2×Dic6—61no—
584C2×Dic6—64no—
585C2×Dic6C22×D311yescharacteristic
586C3×C4⋊C4—32no—
587C3×C4⋊C4—31no—
588C3×C4⋊C4—32no—
589C3×C4⋊C4—31no—
590C3×C4⋊C4—32no—
591C3×C4⋊C4—34no—
592C3×C4⋊C4—32no—
593C3×C22⋊C4—32no—
594C3×C22⋊C4—34no—
595C3×C22⋊C4—32no—
596C3×C22⋊C4—32no—
597C3×C22⋊C4—32no—
598C3×C22⋊C4—34no—
599C3×C22⋊C4—32no—
600C3×C42—32no—
601#217C22×D312yes—
602#217C22×D314yes—
603#217C22×D312yes—
604#217C22×D312yes—
605(C2×D3)⋊C4—34no—
606(C2×D3)⋊C4—34no—
607(C2×D3)⋊C4—34no—
608(C2×D3)⋊C4—34no—
609(C2×D3)⋊C4—34no—
610(C2×D3)⋊C4—34no—
611(C2×D3)⋊C4—34no—
612(C2×D3)⋊C4—34no—
613(C2×D3)⋊C4—34no—
614(C2×D3)⋊C4—34no—
615(C2×D3)⋊C4C22×D312yes—
616(C2×D3)⋊C4C22×D314yes—
617(C2×D3)⋊C4C22×D312yes—
618C4⋊Dic3C22×D312yes—
619C4⋊Dic3C22×D311yescharacteristic
620C4⋊Dic3C22×D312yes—
621C4⋊Dic3C22×D311yescharacteristic
622Dic3⋊C4—34no—
623Dic3⋊C4—34no—
624Dic3⋊C4C22×D312yes—
625Dic3⋊C4C22×D314yes—
626Dic3⋊C4C22×D312yes—
627C4×Dic3—34no—
628C4×Dic3—34no—
629C4×Dic3C22×D312yes—
630C22×C32—22no—
631C22×C32—21no—
632C22×C32—21no—
633C22×C32—22no—
634C22×C32—22no—
635C22×C32C22×D412yes—
636C22×C32C2511yescharacteristic
637C2×C3⋊D3—24no—
638C2×C3⋊D3—22no—
639C2×C3⋊D3—22no—
640C2×C3⋊D3—24no—
641C2×C3⋊D3—24no—
642C2×C3⋊D3—88no—
643C2×C3⋊D3—84no—
644C2×C3⋊D3C22×D414yes—
645C2×C3×D3—21no—
646C2×C3×D3—21no—
647C2×C3×D3—22no—
648C2×C3×D3—21no—
649C2×C3×D3—21no—
650C2×C3×D3—22no—
651C2×C3×D3—22no—
652C2×C3×D3—21no—
653C2×C3×D3—44no—
654C2×C3×D3H(5,𝔽2)12yescomplemented
655D32—48no—
656C32×C4—22no—
657C32×C4C22×D412yes—
658C32×C4C22×D412yes—
659C3⋊Dic3C22×D414yes—
660C3×Dic3—21no—
661C3×Dic3—22no—
662C3×Dic3—21no—
663C3×Dic3—22no—
664C3×Dic3—24no—
665C3×Dic3—22no—
666H(5,𝔽2)—188no—
667C2×#41—31no—
668C2×#41—92no—
669C2×#41—92no—
670C2×#41—91no—
671C2×#41—91no—
672C2×#41—92no—
673C2×#41—91no—
674C2×#41—92no—
675C2×#41—188no—
676C2×#41D3211yescharacteristic, complemented
677C22×Q8—91no—
678C22×D4—91no—
679C22×D4—92no—
680C22×D4—94no—
681C22×D4—92no—
682C22×D4—92no—
683C22×D4—94no—
684C22×D4—91no—
685C22×D4—92no—
686C23×C4—31no—
687C23×C4—92no—
688#127—92no—
689#127—94no—
690#124—92no—
691#124—94no—
692#123—32no—
693#123—94no—
694C22⋊Q8—31no—
695C22⋊Q8—31no—
696C22⋊Q8—32no—
697C22⋊Q8—32no—
698C22⋊Q8—94no—
699#121—31no—
700#121—32no—
701#121—31no—
702#121—34no—
703#121—32no—
704#121—94no—
705#121—94no—
706#121—94no—
707#121—94no—
708#121—94no—
709#121—92no—
710#121—92no—
711#121—92no—
712#121—92no—
713#121—92no—
714#121—92no—
715#120—32no—
716#120—94no—
717#120—94no—
718#120—94no—
719#120—94no—
720C4×Q8—92no—
721C4×D4—32no—
722C4×D4—32no—
723C4×D4—92no—
724C4×D4—94no—
725C4×D4—94no—
726C4×D4—94no—
727#117—31no—
728#117—92no—
729C2×C4⋊C4—31no—
730C2×C4⋊C4—92no—
731C2×C22⋊C4—94no—
732C2×C22⋊C4—92no—
733C23×C3—22no—
734C23×C3—21no—
735C23×C3—31no—
736C23×C3—32no—
737C23×C3—31no—
738C23×C3—62no—
739C23×C3—62no—
740C23×C3—121no—
741C23×C3C23×D312yes—
742C23×C3C23×D312yes—
743C23×C3C23×D311yescharacteristic
744C23×C3C23×D311yescharacteristic
745C22×D3—22no—
746C22×D3—22no—
747C22×D3—32no—
748C22×D3—32no—
749C22×D3—34no—
750C22×D3—34no—
751C22×D3—41no—
752C22×D3—62no—
753C22×D3—64no—
754C22×D3—64no—
755C22×D3—64no—
756C22×D3—64no—
757C22×D3—68no—
758C22×D3—68no—
759C22×D3—616no—
760C22×D3—68no—
761C22×D3—64no—
762C22×D3—64no—
763C22×D3—64no—
764C22×D3—122no—
765C22×D3—122no—
766C22×D3—122no—
767C22×D3—124no—
768C22×D3—124no—
769C22×D3—122no—
770C22×D3—124no—
771C22×D3—124no—
772C22×D3—122no—
773C22×D3—122no—
774C22×D3—242no—
775C22×D3—244no—
776C22×D3—242no—
777C22×D3—244no—
778C22×D3C23×D312yes—
779C22×D3C23×D311yescharacteristic
780C22×D3C23×D311yescharacteristic
781C3×Q8—24no—
782C3×Q8—22no—
783C3×Q8—22no—
784C3×Q8—62no—
785C3×D4—28no—
786C3×D4—24no—
787C3×D4—24no—
788C3×D4—24no—
789C3×D4—22no—
790C3×D4—22no—
791C3×D4—64no—
792C3×D4—64no—
793C3×D4—62no—
794C3×D4—124no—
795C3×D4—122no—
796C2×C3×C4—28no—
797C2×C3×C4—24no—
798C2×C3×C4—24no—
799C2×C3×C4—21no—
800C2×C3×C4—22no—
801C2×C3×C4—21no—
802C2×C3×C4—24no—
803C2×C3×C4—32no—
804C2×C3×C4—34no—
805C2×C3×C4—32no—
806C2×C3×C4—31no—
807C2×C3×C4—32no—
808C2×C3×C4—31no—
809C2×C3×C4—62no—
810C2×C3×C4—62no—
811C2×C3×C4—62no—
812C2×C3×C4—64no—
813C2×C3×C4—62no—
814C2×C3×C4—62no—
815C2×C3×C4—122no—
816C2×C3×C4D3×D414yescomplemented
817C2×C3×C4D3×D414yescomplemented
818C2×C3×C4C23×D312yes—
819C2×C3×C4C23×D312yes—
820C2×C3×C4C23×D311yescharacteristic
821C2×C3×C4C23×D311yescharacteristic
822C2×C3×C4C23×D311yescharacteristic
823C2×C3×C4C23×D311yescharacteristic
824#67—24no—
825#67—24no—
826#67—38no—
827#67—38no—
828#67—44no—
829#67—42no—
830#67—68no—
831#67—64no—
832#67—64no—
833#67—68no—
834#67—64no—
835#67—64no—
836#67—68no—
837#67—68no—
838#67—616no—
839#67—124no—
840#67—124no—
841#67—124no—
842C2×Dic3—22no—
843C2×Dic3—32no—
844C2×Dic3—32no—
845C2×Dic3—42no—
846C2×Dic3—62no—
847C2×Dic3—64no—
848C2×Dic3—64no—
849C2×Dic3C23×D312yes—
850C2×Dic3C23×D314yes—
851C2×Dic3C23×D312yes—
852C2×Dic3C23×D311yescharacteristic
853C2×Dic3C23×D312yes—
854C2×Dic3C23×D311yescharacteristic
855D12—22no—
856D12—34no—
857D12—34no—
858D12—64no—
859D12—68no—
860D12—68no—
861D12—68no—
862D12—616no—
863D12—68no—
864D12—64no—
865D12—64no—
866D12—68no—
867D12—64no—
868D12—64no—
869D12—64no—
870D12—64no—
871D12—124no—
872D12—124no—
873D12—124no—
874C4×D3—22no—
875C4×D3—22no—
876C4×D3—22no—
877C4×D3—22no—
878C4×D3—24no—
879C4×D3—38no—
880C4×D3—38no—
881C4×D3—68no—
882C4×D3—64no—
883C4×D3—64no—
884C4×D3—68no—
885C4×D3—68no—
886C4×D3—64no—
887C4×D3—64no—
888C4×D3—616no—
889C4×D3—124no—
890C4×D3—124no—
891Dic6—22no—
892Dic6—34no—
893Dic6—34no—
894Dic6—64no—
895Dic6—64no—
896Dic6—64no—
897C2×C32—22no—
898C2×C32—42no—
899C2×C32C23×D411yescharacteristic
900C2×C32C2×H(5,𝔽2)11yescharacteristic
901C2×C32#58511yescharacteristic
902C3⋊D3—24no—
903C3⋊D3—44no—
904C3×D3—22no—
905C3×D3—42no—
906C3×D3—41no—
907C24—31no—
908C24—92no—
909C24—94no—
910C24—92no—
911#41—24no—
912#41—64no—
913#41—98no—
914#41—188no—
915#41—188no—
916#41—188no—
917#41—184no—
918#41—184no—
919#41—188no—
920C2×Q8—31no—
921C2×Q8—92no—
922C2×Q8—91no—
923C2×Q8—184no—
924C2×Q8C2×D3211yescharacteristic
925C2×D4—32no—
926C2×D4—32no—
927C2×D4—32no—
928C2×D4—34no—
929C2×D4—31no—
930C2×D4—94no—
931C2×D4—92no—
932C2×D4—92no—
933C2×D4—94no—
934C2×D4—94no—
935C2×D4—94no—
936C2×D4—92no—
937C2×D4—92no—
938C2×D4—94no—
939C2×D4—91no—
940C2×D4—94no—
941C2×D4—92no—
942C2×D4—92no—
943C2×D4—188no—
944C2×D4—184no—
945C2×D4—188no—
946C2×D4—1816no—
947C2×D4—188no—
948C2×D4—184no—
949C2×D4—364no—
950C2×D4—368no—
951C2×D4C2×D3212yes—
952C2×D4C2×D3211yescharacteristic
953C22×C4—31no—
954C22×C4—32no—
955C22×C4—31no—
956C22×C4—31no—
957C22×C4—31no—
958C22×C4—31no—
959C22×C4—32no—
960C22×C4—64no—
961C22×C4—92no—
962C22×C4—94no—
963C22×C4—92no—
964C22×C4—92no—
965C22×C4—92no—
966C22×C4—94no—
967C22×C4—188no—
968C22×C4C2×D3212yes—
969C22×C4C2×D3211yescharacteristic
970C4⋊C4—32no—
971C4⋊C4—32no—
972C4⋊C4—31no—
973C4⋊C4—31no—
974C4⋊C4—32no—
975C4⋊C4—32no—
976C4⋊C4—34no—
977C4⋊C4—94no—
978C22⋊C4—32no—
979C22⋊C4—34no—
980C22⋊C4—32no—
981C22⋊C4—32no—
982C22⋊C4—32no—
983C22⋊C4—32no—
984C22⋊C4—34no—
985C22⋊C4—94no—
986C22⋊C4—94no—
987C22⋊C4—94no—
988C22⋊C4—94no—
989C22⋊C4—94no—
990C42—32no—
991C42—94no—
992C22×C3—21no—
993C22×C3—21no—
994C22×C3—21no—
995C22×C3—21no—
996C22×C3—24no—
997C22×C3—22no—
998C22×C3—22no—
999C22×C3—22no—
1000C22×C3—22no—
1001C22×C3—22no—
1002C22×C3—22no—
1003C22×C3—22no—
1004C22×C3—21no—
1005C22×C3—32no—
1006C22×C3—41no—
1007C22×C3—41no—
1008C22×C3—42no—
1009C22×C3—42no—
1010C22×C3—61no—
1011C22×C3—61no—
1012C22×C3—62no—
1013C22×C3—61no—
1014C22×C3—62no—
1015C22×C3—62no—
1016C22×C3—61no—
1017C22×C3—61no—
1018C22×C3—124no—
1019C22×C3C2×D3×D412yes—
1020C22×C3C2×D3×D412yes—
1021C22×C3C24×D311yescharacteristic
1022C22×C3C24×D311yescharacteristic
1023C2×D3—21no—
1024C2×D3—21no—
1025C2×D3—21no—
1026C2×D3—22no—
1027C2×D3—21no—
1028C2×D3—21no—
1029C2×D3—22no—
1030C2×D3—22no—
1031C2×D3—34no—
1032C2×D3—34no—
1033C2×D3—44no—
1034C2×D3—64no—
1035C2×D3—62no—
1036C2×D3—62no—
1037C2×D3—62no—
1038C2×D3—62no—
1039C2×D3—68no—
1040C2×D3—64no—
1041C2×D3—64no—
1042C2×D3—64no—
1043C2×D3—64no—
1044C2×D3—64no—
1045C2×D3—64no—
1046C2×D3—122no—
1047C2×D3—122no—
1048C2×D3—124no—
1049C2×D3—124no—
1050C2×D3—128no—
1051C2×D3—128no—
1052C2×D3—248no—
1053C2×D3—248no—
1054C2×D3—244no—
1055C2×D3—244no—
1056C2×D3—248no—
1057C2×D3—2416no—
1058C2×D3#100912yescomplemented
1059C3×C4—24no—
1060C3×C4—22no—
1061C3×C4—22no—
1062C3×C4—22no—
1063C3×C4—22no—
1064C3×C4—61no—
1065C3×C4—62no—
1066C3×C4—61no—
1067C3×C4—64no—
1068C3×C4—62no—
1069C3×C4—62no—
1070C3×C4C2×D3×D412yes—
1071C3×C4C2×D3×D412yes—
1072C3×C4C2×D3×D412yes—
1073C3×C4C2×D3×D412yes—
1074Dic3—22no—
1075Dic3—21no—
1076Dic3—21no—
1077Dic3—22no—
1078Dic3—22no—
1079Dic3—24no—
1080Dic3—34no—
1081Dic3—34no—
1082Dic3—64no—
1083C32#348811yescharacteristic, complemented, Sylow
1084C23—31no—
1085C23—31no—
1086C23—32no—
1087C23—62no—
1088C23—62no—
1089C23—92no—
1090C23—94no—
1091C23—121no—
1092C23—188no—
1093C23—184no—
1094C23—184no—
1095C23—184no—
1096C23—362no—
1097C23—364no—
1098C23—362no—
1099C23—364no—
1100C23—362no—
1101C23C22×D3212yes—
1102C23C22×D3211yescharacteristic
1103Q8—22no—
1104Q8—62no—
1105Q8—94no—
1106Q8—184no—
1107D4—24no—
1108D4—22no—
1109D4—64no—
1110D4—64no—
1111D4—62no—
1112D4—98no—
1113D4—94no—
1114D4—124no—
1115D4—122no—
1116D4—188no—
1117D4—188no—
1118D4—184no—
1119D4—184no—
1120D4—188no—
1121D4—184no—
1122D4—184no—
1123D4—184no—
1124D4—364no—
1125D4—364no—
1126D4—364no—
1127C2×C4—24no—
1128C2×C4—32no—
1129C2×C4—32no—
1130C2×C4—34no—
1131C2×C4—31no—
1132C2×C4—31no—
1133C2×C4—32no—
1134C2×C4—62no—
1135C2×C4—62no—
1136C2×C4—62no—
1137C2×C4—62no—
1138C2×C4—62no—
1139C2×C4—64no—
1140C2×C4—92no—
1141C2×C4—98no—
1142C2×C4—122no—
1143C2×C4—188no—
1144C2×C4—184no—
1145C2×C4—184no—
1146C2×C4—184no—
1147C2×C4—364no—
1148C2×C4#381114yescomplemented
1149C2×C4C22×D3212yes—
1150C2×C4C22×D3211yescharacteristic
1151C2×C4C22×D3211yescharacteristic
1152C2×C3—22no—
1153C2×C3—22no—
1154C2×C3—21no—
1155C2×C3—21no—
1156C2×C3—21no—
1157C2×C3—42no—
1158C2×C3—44no—
1159C2×C3—42no—
1160C2×C3—42no—
1161C2×C3—62no—
1162C2×C3—122no—
1163C2×C3—121no—
1164C2×C3C22×D3×D411yescharacteristic
1165C2×C3C22×D3×D411yescharacteristic
1166C2×C3C2×#100911yescharacteristic
1167C2×C3#596411yescharacteristic
1168C2×C3D3×H(5,𝔽2)11yescharacteristic
1169C2×C3#596811yescharacteristic
1170D3—22no—
1171D3—41no—
1172D3—42no—
1173D3—64no—
1174D3—64no—
1175D3—124no—
1176D3—128no—
1177D3—124no—
1178D3—124no—
1179C22—21no—
1180C22—21no—
1181C22—22no—
1182C22—22no—
1183C22—22no—
1184C22—32no—
1185C22—61no—
1186C22—61no—
1187C22—62no—
1188C22—61no—
1189C22—61no—
1190C22—62no—
1191C22—61no—
1192C22—62no—
1193C22—94no—
1194C22—124no—
1195C22—182no—
1196C22—182no—
1197C22—184no—
1198C22—184no—
1199C22—184no—
1200C22—368no—
1201C22—724no—
1202C22—728no—
1203C22C2×#381112yes—
1204C22C23×D3211yescharacteristic
1205C4—22no—
1206C4—64no—
1207C4—62no—
1208C4—62no—
1209C4—61no—
1210C4—61no—
1211C4—62no—
1212C4—94no—
1213C4C2×#381112yes—
1214C4C2×#381112yes—
1215C3—21no—
1216C3#8604111yescharacteristic, complemented
1217C3#8637911yescharacteristic, complemented
1218C2—22no—
1219C2—42no—
1220C2—62no—
1221C2—121no—
1222C2—122no—
1223C2—184no—
1224C2—364no—
1225C2D3×#100911yescharacteristic
1226C2#1059669711yescharacteristic
1227C2C22×#381111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC2×C32×#41C22
hypercenterC2×#41D32
hypocenterC32#3488
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#64366C2semidirect
2. C2×D3×#235C2semidirect
3. C3×#5833C2semidirect
4. C3×#5828C2semidirect
5. #10595430C2semidirect
6. #10595404C2semidirect
7. #10595292C2semidirect
8. #10595282C2semidirect
9. #10595241C2semidirect
10. #10595163C2semidirect
11. #10595074C2semidirect
12. #10595045C2semidirect
13. #10595018C2semidirect
14. C2×#63909C2semidirect
15. #10594990C2semidirect
16. #10594919C2semidirect
17. #10594916C2semidirect
20. C2×C32×#41C22semidirect
22. C2×#3832C22semidirect
23. C2×D4×C3⋊D3C22semidirect
24. C2×D4×C3⋊D3C22semidirect
26. C2×#3828C22semidirect
27. C22×C4⋊(C3⋊D3)C22semidirect
28. C22×C4⋊(C3⋊D3)C22semidirect
29. C2×C3×#235C22semidirect
30. C22×C3×C4×D3C22semidirect
31. C2×#3811C22semidirect
32. C2×D3×#67C22semidirect
33. C22×#626C22semidirect
34. C2×#3804C22semidirect
36. C2×D3×D12C22semidirect
37. C2×C4×D32C22semidirect
38. C2×#3799C22semidirect
39. C2×#3798C22semidirect
40. C2×#3795C22semidirect
41. C2×D3×Dic6C22semidirect
42. C3×#946C22semidirect
43. C3×#946C22semidirect
44. C3×#946C22semidirect
45. C3×#939C22semidirect
46. C3×#938C22semidirect
47. C3×#938C22semidirect
48. C3×#938C22semidirect
49. C3×#937C22semidirect
50. C3×#935C22semidirect
51. C3×#930C22semidirect
52. C3×C4×#67C22semidirect
53. C3×C4×#67C22semidirect
54. C3×#926C22semidirect
55. C2×C3×C4⋊Dic3C22semidirect
56. C3×#924C22semidirect
57. #63981C22semidirect
58. #63981C22semidirect
59. #63981C22semidirect
60. #63979C22semidirect
61. #63974C22semidirect
62. #63971C22semidirect
63. #63971C22semidirect
64. C2×#3722C22semidirect
65. #63953C22semidirect
66. #63952C22semidirect
67. #63923C22semidirect
68. #63912C22semidirect
69. #63911C22semidirect
70. #63910C22semidirect
71. #63910C22semidirect
72. #63909C22semidirect
73. #63909C22semidirect
74. #63909C22semidirect
75. #63909C22semidirect
76. #63909C22semidirect
77. #63909C22semidirect
78. #63900C22semidirect
79. #63897C22semidirect
80. #63894C22semidirect
81. #63881C22semidirect
82. #63881C22semidirect
83. #63865C22semidirect
84. #63864C22semidirect
85. #63849C22semidirect
86. #63844C22semidirect
94. #5833D3semidirect
96. #5828D3semidirect
138. #3828D4semidirect
210. C2×C3×#41C2×D3semidirect
211. C2×C3×#41C2×D3semidirect
248. C2×#235C2×D3semidirect
259. C22×C4×D3C2×D3semidirect
277. #946C2×D3semidirect
278. #946C2×D3semidirect
279. #946C2×D3semidirect
285. #939C2×D3semidirect
286. #938C2×D3semidirect
287. #938C2×D3semidirect
288. #938C2×D3semidirect
292. #937C2×D3semidirect
293. #935C2×D3semidirect
300. #930C2×D3semidirect
302. C4×#67C2×D3semidirect
303. C4×#67C2×D3semidirect
306. #926C2×D3semidirect
307. C2×C4⋊Dic3C2×D3semidirect
308. #924C2×D3semidirect
374. C2×C32×C4C2×D4semidirect
379. #638C2×D4semidirect
384. C4⋊(C3⋊D3)C2×D4semidirect
386. C4×C3⋊D3C2×D4semidirect
387. #634C2×D4semidirect
654. C2×C3×D3H(5,𝔽2)semidirect
676. C2×#41D32semidirect
816. C2×C3×C4D3×D4semidirect
817. C2×C3×C4D3×D4semidirect
1058. C2×D3#1009semidirect
1083. C32#3488semidirect
1148. C2×C4#3811semidirect
1216. C3#86041semidirect
1217. C3#86379semidirect

Maximal subgroups

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

subgroupindex
C2×#643662
C2×D3×#2352
C3×#58332
C3×#58282
#105954302
#105954042
#105952922
#105952822
#105952412
#105951632
#105950742
#105950452
#105950182
C2×#639092
#105949902
#105949192
#105949162
#863793
#860413