Finite Group Databasebeta

← #11904790

Subgroups — #11904790

Order 1152.

3179 conjugacy classes of subgroups.

The subgroup lattice has 1142 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×#41C211yesmaximal, characteristic, complemented
2C2×#64298C211yesmaximal, characteristic, complemented
3#10596296C211yesmaximal, characteristic, complemented
4C3×#5833C211yesmaximal, characteristic, complemented
5#10595400C212yesmaximal, complemented
6#10595357C212yesmaximal, complemented
7#10595228C212yesmaximal, complemented
8#10595157C212yesmaximal, complemented
9#10595151C214yesmaximal, complemented
10#10595150C214yesmaximal, complemented
11#10595022C211yesmaximal, characteristic, complemented
12#10595004C212yesmaximal, complemented
13#10594986C211yesmaximal, characteristic, complemented
14#10594892C212yesmaximal, complemented
15#10594884C212yesmaximal, complemented
16D3×#924C212yesmaximal, complemented
17C2×#63857C211yesmaximal, characteristic, complemented
18#87264—31nomaximal
19#86380—31nomaximal
20C2×C32×#41C2211yescharacteristic
21C22×#634C2211yescharacteristic, complemented
22C3×D3×#41—28no—
23C2×C3×#239C2211yescharacteristic
24C2×C3×D3×Q8C2211yescharacteristic
25C2×C3×#237C2212yes—
26C2×C3×#237C2211yescharacteristic
27C2×C3×D3×D4C2212yes—
28C2×C3×D3×D4C2211yescharacteristic
29C2×C3×#235C2212yes—
30C2×C3×#235C2211yescharacteristic
31C2×C3×#235C2211yescharacteristic, complemented
32C22×C3×C4×D3C2211yescharacteristic
33C22×C3×C4×D3C2212yes—
34C2×#3805C2214yescomplemented
35#64298—28no—
36C2×#3795C2212yescomplemented
37C2×#3795C2212yescomplemented
38C2×D3×Dic6C2212yescomplemented
39C2×D3×Dic6C2212yescomplemented
40#64153C2212yescomplemented
41#64145C2212yescomplemented
42#64144C2214yescomplemented
43#64135C2211yescharacteristic, complemented
44#64133C2212yescomplemented
45#64133C2212yescomplemented
46C3×#946C2212yescomplemented
47C3×#939C2214yescomplemented
48C3×#938C2212yescomplemented
49C3×#930C2212yescomplemented
50C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
51C3×#924C2212yescomplemented
52#63976C2214yes—
53#63976C2212yes—
54Dic3×#67C2214yescomplemented
55Dic3×#67C2214yescomplemented
56#63970C2214yescomplemented
57#63970C2214yescomplemented
58#63969C2214yescomplemented
59D3×#217C2214yes—
60C2×Dic3⋊Dic3C2212yescomplemented
61#63964C2214yescomplemented
62#63961C2212yescomplemented
63C2×(C2×D3)⋊Dic3C2212yes—
64#63959C2214yescomplemented
65#63908C2211yescharacteristic
66#63908C2211yescharacteristic, complemented
67#63905C2214yescomplemented
68C4×#625C2212yes—
69C4×#625C2212yescomplemented
70#63898C2212yescomplemented
71D3×C4⋊Dic3C2212yescomplemented
72#63887C2214yescomplemented
73#63885C2214yescomplemented
74#63884C2214yescomplemented
75#63879C2214yes—
76D3×Dic3⋊C4C2214yescomplemented
77#63857C2212yes—
78#63857C2212yes—
79#63857C2212yescomplemented
80#63857C2212yescomplemented
81#63856C2211yescharacteristic
82#63856C2211yescharacteristic, complemented
83#63851C2214yes—
84#63843C2212yescomplemented
85#63841C2212yescomplemented
86#63839C2214yescomplemented
87C22×C3×#41—31no—
88C2×#1010—31no—
89C2×#1010—31no—
90C2×D3×#41D311yescharacteristic, complemented
91C3×#537—31no—
92#5833—32no—
93#5833D311yescharacteristic, complemented
94#5831—32no—
95#5828—31no—
96#5827—31no—
97#5825—31no—
98#5825—31no—
99#5825—32no—
100#5825—61no—
101#5824—32no—
102#5824—34no—
103Q8×#67—32no—
104#5806—34no—
105#5806—32no—
106#5791—31no—
107#5791—32no—
108C2×#924—31no—
109C2×#924—32no—
110#5632—32no—
111#5631—32no—
112#5628—32no—
113D3×C22⋊Q8—32no—
114#5612—32no—
115#5611—34no—
116#5610—34no—
117#5608—32no—
118#5606—32no—
119#5598—32no—
120C2×#897—31no—
121#5504—31no—
122C23×C3×D3C2311yescharacteristic
123C23×C3×D3C2312yes—
124C32×#41—24no—
125C2×C32×Q8C2311yescharacteristic
126C2×C32×D4C2311yescharacteristic
127C2×C32×D4C2312yes—
128C22×C32×C4C2312yes—
129C22×C32×C4C2311yescharacteristic
130C22×C3⋊Dic3C2312yes—
131C2×#634—24no—
132C2×#634C2312yes—
133C2×#634C2312yes—
134C2×C3×#67C2312yes—
135C2×C3×#67C2312yes—
136C2×C3×#67C2312yes—
137C2×C3×#67C2314yes—
138C2×C3×#67C2312yes—
139C22×C3×Dic3C2311yescharacteristic
140C22×C3×Dic3C2312yes—
141C22×C3×Dic3C2312yes—
142C3×#239—24no—
143C3×D3×Q8—24no—
144C3×#237—28no—
145C3×#237—24no—
146C3×D3×D4—28no—
147C3×D3×D4—24no—
148C3×#235—24no—
149C3×#235—28no—
150C3×#235D418yescomplemented
151C2×C3×D12C2311yescharacteristic
152C2×C3×D12C2312yes—
153C2×C3×D12C2311yescharacteristic
154C2×C3×C4×D3—24no—
155C2×C3×C4×D3—28no—
156C2×C3×C4×D3C2312yes—
157C2×C3×C4×D3C2311yescharacteristic
158C2×C3×C4×D3C2311yescharacteristic
159C2×C3×C4×D3C2312yes—
160C2×C3×C4×D3C2311yescharacteristic
161C2×C3×C4×D3C2311yescharacteristic
162C2×C3×C4×D3C2312yes—
163C2×C3×C4×D3C2312yes—
164C2×C3×Dic6C2311yescharacteristic
165C2×C3×Dic6C2312yes—
166C2×C3×Dic6C2311yescharacteristic
167C2×#627C2314yes—
168C2×#625C2314yes—
169C2×#625C2312yes—
170C2×#625C2312yes—
171#3805—216no—
172C2×D3×Dic3C2314yes—
173C2×D3×Dic3C2314yes—
174C2×D3×Dic3C2314yes—
175#3795—28no—
176#3795—28no—
177D3×Dic6—28no—
178D3×Dic6—28no—
179#3757C2314yes—
180#3757C2314yes—
181#3757C2312yes—
182C4⋊(C3⋊Dic3)C2311yescharacteristic
183C4⋊(C3⋊Dic3)C2311yescharacteristic
184#3750C2314yes—
185#3750C2314yes—
186C4×C3⋊Dic3C2312yes—
187C3×#217C2314yes—
188C3×(C2×D3)⋊C4C2314yes—
189C3×C4⋊Dic3C2312yes—
190C3×C4⋊Dic3C2312yes—
191C3×Dic3⋊C4C2314yes—
192#3724C2312yes—
193#3724C2312yes—
194Dic3⋊Dic3C2314yes—
195Dic3⋊Dic3C2314yes—
196Dic3⋊Dic3C2314yes—
197(C2×D3)⋊Dic3C2314yes—
198(C2×D3)⋊Dic3C2312yes—
199(C2×D3)⋊Dic3C2314yes—
200(C2×D3)⋊Dic3C2312yes—
201(C2×D3)⋊Dic3C2314yes—
202(C2×D3)⋊Dic3C2312yes—
203(C2×D3)⋊Dic3C2312yes—
204Dic32C2314yes—
205#3489—91noSylow
206C2×C3×#41—21no—
207C2×C3×#41—31no—
208C2×C3×#41—32no—
209C2×C3×#41—31no—
210C2×C3×#41—31no—
211C2×C3×#41—31no—
212C2×C3×#41—32no—
213C2×C3×#41—68no—
214C2×C3×#41C2×D311yescharacteristic
215C2×C3×#41C2×D311yescharacteristic
216C22×C3×Q8—31no—
217C22×C3×D4—32no—
218C22×C3×D4—31no—
219C23×C3×C4—32no—
220C23×C3×C4—31no—
221#1010—68no—
222#1010—68no—
223D3×#41—28no—
224C2×#239C2×D311yescharacteristic
225C2×D3×Q8—32no—
226C2×D3×Q8—32no—
227C2×D3×Q8C2×D311yescharacteristic
228C2×#237—34no—
229C2×#237—34no—
230C2×#237—32no—
231C2×#237—32no—
232C2×#237C2×D311yescharacteristic
233C2×#237C2×D312yes—
234C2×D3×D4C2×D312yes—
235C2×D3×D4C2×D311yescharacteristic
236C2×#235—32no—
237C2×#235—32no—
238C2×#235C2×D312yes—
239C2×#235C2×D311yescharacteristic
240C2×#235C2×D311yescharacteristic, complemented
241C22×C4×D3C2×D311yescharacteristic
242C22×C4×D3C2×D312yes—
243C22×Dic6—31no—
244C22×Dic6—31no—
245C22×Dic6—32no—
246C22×Dic6—32no—
247C22×Dic6—61no—
248C3×C22⋊Q8—32no—
249C3×C22⋊Q8—32no—
250C3×#121—32no—
251C3×#121—34no—
252C3×#121—32no—
253C2×C3×C4⋊C4—31no—
254#953—34no—
255#953—32no—
256C2×#217—32no—
257C2×#217—34no—
258#946—31no—
259#946—31no—
260#946—34no—
261#946C2×D312yescomplemented
262Q8×Dic3—32no—
263#944—32no—
264#944—32no—
265#944—34no—
266#944—62no—
267#939—34no—
268#939—34no—
269#939—34no—
270#939C2×D314yescomplemented
271#938—34no—
272#938—34no—
273#938—31no—
274#938—31no—
275#938C2×D312yescomplemented
276#937—32no—
277#937—34no—
278#936—32no—
279#936—32no—
280#936—34no—
281#936—62no—
282#935—34no—
283#935—34no—
284#935—32no—
285#935—34no—
286#935—34no—
287#935—64no—
288D4×Dic3—34no—
289D4×Dic3—34no—
290D4×Dic3—32no—
291#930—31no—
292#930—31no—
293#930C2×D312yescomplemented
294#929—32no—
295#929—34no—
296C4×#67—34no—
297C4×#67—34no—
298C4×#67—32no—
299C4×#67—32no—
300C4×#67—32no—
301C4×#67—32no—
302C4×#67—34no—
303C2×(C2×D3)⋊C4—32no—
304#926—31no—
305#926—31no—
306#926—32no—
307#926—61no—
308C2×C4⋊Dic3—32no—
309C2×C4⋊Dic3—32no—
310C2×C4⋊Dic3C2×D311yescharacteristic, complemented
311#924—32no—
312#924—32no—
313#924—32no—
314#924—32no—
315#924—31no—
316#924—31no—
317#924—34no—
318#924—32no—
319#924—32no—
320#924—32no—
321#924—32no—
322#924—34no—
323#924—62no—
324#924—62no—
325#924C2×D312yescomplemented
326C2×Dic3⋊C4—32no—
327C2×Dic3⋊C4—34no—
328#897—32no—
329#897—32no—
330#897—32no—
331#897—32no—
332#896—34no—
333#894—34no—
334#893—32no—
335#892—32no—
336D3×C4⋊C4—32no—
337D3×C4⋊C4—34no—
338#888—34no—
339#887—32no—
340#885—34no—
341#884—34no—
342#883—34no—
343#883—34no—
344#67⋊C4—34no—
345D3×C22⋊C4—34no—
346#878—34no—
347#878—34no—
348C23×C32C2412yes—
349C23×C32C2411yescharacteristic
350C22×C3×D3—22no—
351C22×C3×D3—24no—
352C22×C3×D3—24no—
353C22×C3×D3—22no—
354C22×C3×D3—42no—
355C22×C3×D3—41no—
356C22×C3×D3C2411yescharacteristic
357C22×C3×D3C2412yes—
358C22×C3×D3C2412yes—
359C22×C3×D3C2411yescharacteristic
360C32×Q8—22no—
361C32×D4—24no—
362C32×D4—22no—
363C2×C32×C4—24no—
364C2×C32×C4C2×D414yes—
365C2×C32×C4C2412yes—
366C2×C32×C4C2411yescharacteristic
367C2×C32×C4C2411yescharacteristic
368C2×C3⋊Dic3—24no—
369C2×C3⋊Dic3C2412yes—
370C2×C3⋊Dic3C2412yes—
371C2×C3⋊Dic3C2414yes—
372#634—24no—
373#634—24no—
374C3×#67—24no—
375C3×#67—24no—
376C3×#67—24no—
377C3×#67—44no—
378C3×#67C2×D418yes—
379C2×C3×Dic3—22no—
380C2×C3×Dic3—24no—
381C2×C3×Dic3—42no—
382C2×C3×Dic3C2414yes—
383C2×C3×Dic3C2411yescharacteristic
384C2×C3×Dic3C2411yescharacteristic
385C2×C3×Dic3C2412yes—
386C2×C3×Dic3C2412yes—
387C3×D12—24no—
388C3×D12—22no—
389C3×D12C2×D414yes—
390C3×C4×D3—24no—
391C3×C4×D3—24no—
392C3×C4×D3—22no—
393C3×C4×D3—22no—
394C3×C4×D3—22no—
395C3×C4×D3—22no—
396C3×C4×D3—24no—
397C3×C4×D3C2×D418yes—
398C3×Dic6—22no—
399C3×Dic6—24no—
400C3×Dic6C2×D414yes—
401#627—28no—
402#625—28no—
403#625—24no—
404#625—42no—
405D3×Dic3—28no—
406D3×Dic3—28no—
407D3×Dic3—44no—
408C2×2−1+4—91no—
409C22×#41—31no—
410D4×Q8—92no—
411#548—92no—
412#547—94no—
413#547—92no—
414#546—94no—
415#546—92no—
416#537—31no—
417#537—92no—
418#536—92no—
419#536—91no—
420#525—92no—
421#525—91no—
422C2×C22⋊Q8—91no—
423C2×C22⋊Q8—92no—
424#520—91no—
425C24×C3—32no—
426C24×C3—31no—
427C23×D3C22×D312yes—
428C23×D3C22×D311yescharacteristic
429C3×#41—24no—
430C3×#41—24no—
431C3×#41—38no—
432C3×#41—44no—
433C3×#41—68no—
434C3×#41—68no—
435C3×#41—64no—
436C3×#41—64no—
437C3×#41—64no—
438C2×C3×Q8—21no—
439C2×C3×Q8—31no—
440C2×C3×Q8—32no—
441C2×C3×Q8—31no—
442C2×C3×Q8—64no—
443C2×C3×Q8C22×D311yescharacteristic
444C2×C3×Q8C22×D311yescharacteristic
445C2×C3×D4—22no—
446C2×C3×D4—21no—
447C2×C3×D4—32no—
448C2×C3×D4—32no—
449C2×C3×D4—32no—
450C2×C3×D4—32no—
451C2×C3×D4—34no—
452C2×C3×D4—31no—
453C2×C3×D4—32no—
454C2×C3×D4—31no—
455C2×C3×D4—68no—
456C2×C3×D4—64no—
457C2×C3×D4C22×D312yes—
458C2×C3×D4C22×D312yes—
459C2×C3×D4C22×D311yescharacteristic
460C2×C3×D4C22×D311yescharacteristic
461C22×C3×C4—21no—
462C22×C3×C4—22no—
463C22×C3×C4—32no—
464C22×C3×C4—31no—
465C22×C3×C4—32no—
466C22×C3×C4—32no—
467C22×C3×C4—32no—
468C22×C3×C4—31no—
469C22×C3×C4—31no—
470C22×C3×C4—32no—
471C22×C3×C4—31no—
472C22×C3×C4—31no—
473C22×C3×C4—32no—
474C22×C3×C4—68no—
475C22×C3×C4—64no—
476C22×C3×C4C22×D312yes—
477C22×C3×C4C22×D312yes—
478C22×C3×C4C22×D311yescharacteristic
479C22×C3×C4C22×D311yescharacteristic
480C2×#67—32no—
481C2×#67—34no—
482C2×#67—32no—
483C2×#67—34no—
484C2×#67—32no—
485C2×#67—32no—
486C2×#67C22×D312yes—
487C2×#67C22×D312yes—
488C2×#67C22×D312yes—
489C2×#67C22×D314yes—
490C2×#67C22×D312yes—
491C22×Dic3—32no—
492C22×Dic3—32no—
493C22×Dic3—34no—
494C22×Dic3—34no—
495C22×Dic3—34no—
496C22×Dic3—62no—
497C22×Dic3C22×D312yes—
498C22×Dic3C22×D311yescharacteristic
499C22×Dic3C22×D312yes—
500#239—24no—
501D3×Q8—24no—
502D3×Q8—68no—
503D3×Q8—68no—
504#237—28no—
505#237—24no—
506#237—68no—
507#237—616no—
508#237—616no—
509#237—68no—
510D3×D4—28no—
511D3×D4—24no—
512#235—24no—
513#235—28no—
514#235—68no—
515#235—68no—
516#235#6718yescomplemented
517C2×D12C22×D312yes—
518C2×D12C22×D311yescharacteristic
519C2×D12C22×D311yescharacteristic
520C2×C4×D3—24no—
521C2×C4×D3—28no—
522C2×C4×D3—34no—
523C2×C4×D3—34no—
524C2×C4×D3—34no—
525C2×C4×D3C22×D312yes—
526C2×C4×D3C22×D312yes—
527C2×C4×D3C22×D311yescharacteristic
528C2×C4×D3C22×D311yescharacteristic
529C2×C4×D3C22×D311yescharacteristic
530C2×C4×D3C22×D311yescharacteristic
531C2×C4×D3C22×D312yes—
532C2×C4×D3C22×D312yes—
533C2×Dic6—32no—
534C2×Dic6—32no—
535C2×Dic6—32no—
536C2×Dic6—32no—
537C2×Dic6—34no—
538C2×Dic6—34no—
539C2×Dic6—62no—
540C2×Dic6—62no—
541C2×Dic6—68no—
542C2×Dic6—64no—
543C2×Dic6—64no—
544C2×Dic6—68no—
545C2×Dic6—124no—
546C2×Dic6C22×D312yes—
547C2×Dic6C22×D311yescharacteristic
548C2×Dic6C22×D311yescharacteristic
549C3×C4⋊C4—32no—
550C3×C4⋊C4—34no—
551C3×C4⋊C4—32no—
552C3×C22⋊C4—34no—
553C3×C22⋊C4—34no—
554#217—34no—
555#217—34no—
556#217—34no—
557#217—34no—
558#217—32no—
559#217—32no—
560#217—32no—
561#217—32no—
562#217—32no—
563#217—34no—
564#217—34no—
565#217—32no—
566#217—34no—
567#217—64no—
568#217—64no—
569#217—62no—
570#217C22×D314yes—
571(C2×D3)⋊C4—32no—
572(C2×D3)⋊C4—34no—
573(C2×D3)⋊C4—34no—
574(C2×D3)⋊C4—34no—
575(C2×D3)⋊C4—32no—
576(C2×D3)⋊C4—32no—
577(C2×D3)⋊C4—32no—
578(C2×D3)⋊C4C22×D314yes—
579C4⋊Dic3—31no—
580C4⋊Dic3—31no—
581C4⋊Dic3—31no—
582C4⋊Dic3—31no—
583C4⋊Dic3—34no—
584C4⋊Dic3—34no—
585C4⋊Dic3—34no—
586C4⋊Dic3—61no—
587C4⋊Dic3—61no—
588C4⋊Dic3C22×D312yes—
589C4⋊Dic3C22×D312yes—
590Dic3⋊C4—34no—
591Dic3⋊C4—34no—
592Dic3⋊C4—34no—
593Dic3⋊C4—34no—
594Dic3⋊C4—34no—
595Dic3⋊C4—32no—
596Dic3⋊C4—32no—
597Dic3⋊C4—34no—
598Dic3⋊C4—34no—
599Dic3⋊C4—32no—
600Dic3⋊C4—32no—
601Dic3⋊C4—64no—
602Dic3⋊C4—64no—
603Dic3⋊C4C22×D314yes—
604C4×Dic3—32no—
605C4×Dic3—32no—
606C4×Dic3—34no—
607C4×Dic3—34no—
608C4×Dic3—62no—
609C22×C32—21no—
610C22×C32—21no—
611C22×C32—22no—
612C22×C32—22no—
613C22×C32—22no—
614C22×C32C22×D412yes—
615C22×C32C2511yescharacteristic
616C2×C3×D3—21no—
617C2×C3×D3—22no—
618C2×C3×D3—22no—
619C2×C3×D3—21no—
620C2×C3×D3—22no—
621C2×C3×D3—21no—
622C2×C3×D3—22no—
623C2×C3×D3—21no—
624C2×C3×D3—21no—
625C2×C3×D3—22no—
626C2×C3×D3—48no—
627C2×C3×D3—44no—
628C2×C3×D3C22×D414yes—
629C2×C3×D32−1+412yescomplemented
630C32×C4—22no—
631C32×C4C22×D412yes—
632C32×C4C22×D412yes—
633C3⋊Dic3—24no—
634C3⋊Dic3—22no—
635C3⋊Dic3—22no—
636C3×Dic3—22no—
637C3×Dic3—21no—
638C3×Dic3—21no—
639C3×Dic3—24no—
640C3×Dic3C22×D414yes—
6412−1+4—188no—
642C2×#41—31no—
643C2×#41—32no—
644C2×#41—31no—
645C2×#41—31no—
646C2×#41—31no—
647C2×#41—32no—
648C2×#41—68no—
649C2×#41—92no—
650C2×#41—92no—
651C2×#41—94no—
652C2×#41D3211yescharacteristic
653C22×Q8—31no—
654C22×Q8—92no—
655C22×Q8—92no—
656C22×Q8—91no—
657C22×D4—32no—
658C22×D4—31no—
659C23×C4—32no—
660C23×C4—31no—
661C4⋊Q8—94no—
662C4⋊Q8—92no—
663#124—94no—
664#124—92no—
665#123—94no—
666#123—94no—
667#123—94no—
668#123—92no—
669#123—94no—
670C22⋊Q8—32no—
671C22⋊Q8—32no—
672C22⋊Q8—94no—
673C22⋊Q8—94no—
674C22⋊Q8—92no—
675C22⋊Q8—92no—
676C22⋊Q8—94no—
677C22⋊Q8—92no—
678C22⋊Q8—92no—
679C22⋊Q8—91no—
680C22⋊Q8—91no—
681C22⋊Q8—92no—
682C22⋊Q8—92no—
683#121—34no—
684#121—32no—
685#121—32no—
686#121—94no—
687#121—91no—
688#121—91no—
689#121—94no—
690#121—94no—
691#120—94no—
692#120—92no—
693C4×Q8—92no—
694C4×D4—94no—
695C4×D4—92no—
696C4×D4—92no—
697C4×D4—92no—
698C4×D4—94no—
699C4×D4—94no—
700#117—92no—
701#117—91no—
702C2×C4⋊C4—31no—
703C2×C4⋊C4—92no—
704C2×C4⋊C4—94no—
705C2×C4⋊C4—92no—
706C2×C22⋊C4—94no—
707C2×C22⋊C4—92no—
708C23×C3—21no—
709C23×C3—22no—
710C23×C3—31no—
711C23×C3—32no—
712C23×C3—31no—
713C23×C3—32no—
714C23×C3—64no—
715C23×C3—62no—
716C23×C3—64no—
717C23×C3—62no—
718C23×C3—121no—
719C23×C3—122no—
720C23×C3C23×D312yes—
721C23×C3C23×D312yes—
722C23×C3C23×D311yescharacteristic
723C23×C3C23×D311yescharacteristic
724C22×D3—22no—
725C22×D3—24no—
726C22×D3—22no—
727C22×D3—24no—
728C22×D3—42no—
729C22×D3—41no—
730C22×D3C23×D311yescharacteristic
731C22×D3C23×D312yes—
732C22×D3C23×D311yescharacteristic
733C22×D3C23×D312yes—
734C3×Q8—22no—
735C3×Q8—22no—
736C3×Q8—34no—
737C3×Q8—42no—
738C3×Q8—64no—
739C3×Q8—62no—
740C3×D4—24no—
741C3×D4—24no—
742C3×D4—22no—
743C3×D4—22no—
744C3×D4—38no—
745C3×D4—34no—
746C3×D4—42no—
747C3×D4—44no—
748C3×D4—64no—
749C3×D4—64no—
750C3×D4—64no—
751C3×D4—64no—
752C3×D4—62no—
753C3×D4—124no—
754C2×C3×C4—24no—
755C2×C3×C4—24no—
756C2×C3×C4—21no—
757C2×C3×C4—21no—
758C2×C3×C4—22no—
759C2×C3×C4—24no—
760C2×C3×C4—32no—
761C2×C3×C4—38no—
762C2×C3×C4—34no—
763C2×C3×C4—31no—
764C2×C3×C4—31no—
765C2×C3×C4—32no—
766C2×C3×C4—44no—
767C2×C3×C4—64no—
768C2×C3×C4—64no—
769C2×C3×C4—64no—
770C2×C3×C4—62no—
771C2×C3×C4—62no—
772C2×C3×C4—62no—
773C2×C3×C4—62no—
774C2×C3×C4—62no—
775C2×C3×C4—64no—
776C2×C3×C4—122no—
777C2×C3×C4D3×D414yes—
778C2×C3×C4C2×#6714yes—
779C2×C3×C4C23×D312yes—
780C2×C3×C4C23×D312yes—
781C2×C3×C4C23×D311yescharacteristic
782C2×C3×C4C23×D311yescharacteristic
783C2×C3×C4C23×D311yescharacteristic
784C2×C3×C4C23×D311yescharacteristic
785#67—24no—
786#67—24no—
787#67—24no—
788#67—44no—
789#67—68no—
790#67—64no—
791#67—64no—
792#67—68no—
793#67—122no—
794#67—122no—
795#67C2×#6718yes—
796C2×Dic3—22no—
797C2×Dic3—24no—
798C2×Dic3—32no—
799C2×Dic3—32no—
800C2×Dic3—32no—
801C2×Dic3—32no—
802C2×Dic3—34no—
803C2×Dic3—34no—
804C2×Dic3—42no—
805C2×Dic3—62no—
806C2×Dic3—62no—
807C2×Dic3—64no—
808C2×Dic3—68no—
809C2×Dic3—64no—
810C2×Dic3—64no—
811C2×Dic3—68no—
812C2×Dic3—124no—
813C2×Dic3—124no—
814C2×Dic3C23×D314yes—
815C2×Dic3C23×D312yes—
816C2×Dic3C23×D311yescharacteristic
817C2×Dic3C23×D311yescharacteristic
818C2×Dic3C23×D312yes—
819D12—24no—
820D12—22no—
821D12C2×#6714yes—
822C4×D3—24no—
823C4×D3—24no—
824C4×D3—22no—
825C4×D3—22no—
826C4×D3—22no—
827C4×D3—22no—
828C4×D3—24no—
829C4×D3—68no—
830C4×D3—68no—
831C4×D3—124no—
832C4×D3C2×#6718yes—
833Dic6—22no—
834Dic6—24no—
835Dic6—68no—
836Dic6—64no—
837Dic6—64no—
838Dic6—64no—
839Dic6—64no—
840Dic6—68no—
841Dic6—124no—
842Dic6—124no—
843Dic6C2×#6714yes—
844C2×C32—22no—
845C2×C32—42no—
846C2×C32C23×D411yescharacteristic
847C2×C32C2×2−1+411yescharacteristic
848C2×C32#58511yescharacteristic
849C3×D3—22no—
850C3×D3—24no—
851C3×D3—42no—
852C3×D3—41no—
853C24—32no—
854C24—31no—
855#41—24no—
856#41—38no—
857#41—68no—
858#41—68no—
859#41—64no—
860#41—64no—
861#41—64no—
862#41—188no—
863#41—188no—
864#41—1816no—
865C2×Q8—31no—
866C2×Q8—31no—
867C2×Q8—32no—
868C2×Q8—64no—
869C2×Q8—94no—
870C2×Q8—92no—
871C2×Q8—92no—
872C2×Q8—188no—
873C2×Q8—188no—
874C2×Q8—184no—
875C2×Q8C2×D3211yescharacteristic
876C2×D4—32no—
877C2×D4—32no—
878C2×D4—32no—
879C2×D4—32no—
880C2×D4—34no—
881C2×D4—31no—
882C2×D4—31no—
883C2×D4—32no—
884C2×D4—68no—
885C2×D4—64no—
886C2×D4—92no—
887C2×D4—94no—
888C2×D4—92no—
889C2×D4C2×D3212yes—
890C2×D4C2×D3211yescharacteristic
891C22×C4—32no—
892C22×C4—31no—
893C22×C4—32no—
894C22×C4—32no—
895C22×C4—32no—
896C22×C4—32no—
897C22×C4—32no—
898C22×C4—31no—
899C22×C4—31no—
900C22×C4—31no—
901C22×C4—31no—
902C22×C4—68no—
903C22×C4—64no—
904C22×C4—94no—
905C22×C4—94no—
906C22×C4—94no—
907C22×C4—92no—
908C22×C4C2×D3212yes—
909C22×C4C2×D3211yescharacteristic
910C4⋊C4—32no—
911C4⋊C4—32no—
912C4⋊C4—34no—
913C4⋊C4—92no—
914C4⋊C4—94no—
915C4⋊C4—94no—
916C4⋊C4—94no—
917C4⋊C4—92no—
918C4⋊C4—91no—
919C4⋊C4—94no—
920C4⋊C4—91no—
921C4⋊C4—94no—
922C22⋊C4—34no—
923C22⋊C4—34no—
924C22⋊C4—94no—
925C22⋊C4—92no—
926C22⋊C4—94no—
927C22⋊C4—94no—
928C22⋊C4—92no—
929C22⋊C4—92no—
930C22⋊C4—92no—
931C22⋊C4—94no—
932C22⋊C4—92no—
933C22⋊C4—94no—
934C42—94no—
935C42—92no—
936C22×C3—21no—
937C22×C3—21no—
938C22×C3—21no—
939C22×C3—21no—
940C22×C3—22no—
941C22×C3—22no—
942C22×C3—22no—
943C22×C3—22no—
944C22×C3—22no—
945C22×C3—22no—
946C22×C3—22no—
947C22×C3—21no—
948C22×C3—34no—
949C22×C3—32no—
950C22×C3—41no—
951C22×C3—41no—
952C22×C3—42no—
953C22×C3—42no—
954C22×C3—42no—
955C22×C3—61no—
956C22×C3—62no—
957C22×C3—61no—
958C22×C3—62no—
959C22×C3—61no—
960C22×C3—62no—
961C22×C3—62no—
962C22×C3—61no—
963C22×C3—61no—
964C22×C3—62no—
965C22×C3—124no—
966C22×C3—128no—
967C22×C3C2×D3×D412yes—
968C22×C3C22×#6712yes—
969C22×C3C24×D311yescharacteristic
970C22×C3C24×D311yescharacteristic
971C2×D3—22no—
972C2×D3—22no—
973C2×D3—21no—
974C2×D3—21no—
975C2×D3—22no—
976C2×D3—21no—
977C2×D3—21no—
978C2×D3—22no—
979C2×D3—22no—
980C2×D3—21no—
981C2×D3—48no—
982C2×D3—44no—
983C2×D3#101012yescomplemented
984C2×D3C22×#6714yes—
985C3×C4—22no—
986C3×C4—22no—
987C3×C4—22no—
988C3×C4—22no—
989C3×C4—34no—
990C3×C4—42no—
991C3×C4—61no—
992C3×C4—61no—
993C3×C4—64no—
994C3×C4—62no—
995C3×C4C2×D3×D412yes—
996C3×C4C2×D3×D412yes—
997C3×C4C22×#6712yes—
998C3×C4C22×#6712yes—
999Dic3—22no—
1000Dic3—24no—
1001Dic3—21no—
1002Dic3—21no—
1003Dic3—64no—
1004Dic3—62no—
1005Dic3—62no—
1006Dic3—62no—
1007Dic3—62no—
1008Dic3—64no—
1009Dic3—124no—
1010Dic3—122no—
1011Dic3—122no—
1012Dic3C22×#6714yes—
1013C32#348911yescharacteristic, complemented, Sylow
1014C23—31no—
1015C23—32no—
1016C23—32no—
1017C23—31no—
1018C23—64no—
1019C23—62no—
1020C23—64no—
1021C23—62no—
1022C23—121no—
1023C23—122no—
1024C23C22×D3212yes—
1025C23C22×D3211yescharacteristic
1026Q8—22no—
1027Q8—34no—
1028Q8—64no—
1029Q8—62no—
1030Q8—188no—
1031Q8—184no—
1032Q8—184no—
1033D4—24no—
1034D4—22no—
1035D4—38no—
1036D4—34no—
1037D4—64no—
1038D4—64no—
1039D4—64no—
1040D4—64no—
1041D4—62no—
1042D4—124no—
1043D4—188no—
1044D4—184no—
1045D4—362no—
1046C2×C4—24no—
1047C2×C4—32no—
1048C2×C4—38no—
1049C2×C4—34no—
1050C2×C4—32no—
1051C2×C4—31no—
1052C2×C4—31no—
1053C2×C4—64no—
1054C2×C4—64no—
1055C2×C4—64no—
1056C2×C4—62no—
1057C2×C4—62no—
1058C2×C4—62no—
1059C2×C4—62no—
1060C2×C4—62no—
1061C2×C4—64no—
1062C2×C4—92no—
1063C2×C4—92no—
1064C2×C4—94no—
1065C2×C4—122no—
1066C2×C4—188no—
1067C2×C4—188no—
1068C2×C4—184no—
1069C2×C4—364no—
1070C2×C4D3×#6714yes—
1071C2×C4C22×D3212yes—
1072C2×C4C22×D3211yescharacteristic
1073C2×C4C22×D3211yescharacteristic
1074C2×C3—22no—
1075C2×C3—22no—
1076C2×C3—21no—
1077C2×C3—21no—
1078C2×C3—21no—
1079C2×C3—42no—
1080C2×C3—42no—
1081C2×C3—42no—
1082C2×C3—62no—
1083C2×C3—64no—
1084C2×C3—82no—
1085C2×C3—121no—
1086C2×C3—122no—
1087C2×C3C22×D3×D411yescharacteristic
1088C2×C3C2×#101011yescharacteristic
1089C2×C3#596411yescharacteristic
1090C2×C3#596611yescharacteristic
1091C2×C3D3×2−1+411yescharacteristic
1092C2×C3C23×#6711yescharacteristic
1093D3—22no—
1094D3—24no—
1095D3—42no—
1096D3—41no—
1097C22—21no—
1098C22—21no—
1099C22—22no—
1100C22—22no—
1101C22—22no—
1102C22—32no—
1103C22—34no—
1104C22—62no—
1105C22—62no—
1106C22—61no—
1107C22—61no—
1108C22—62no—
1109C22—61no—
1110C22—62no—
1111C22—61no—
1112C22—61no—
1113C22—62no—
1114C22—124no—
1115C22—128no—
1116C22C2×D3×#6712yes—
1117C22C23×D3211yescharacteristic
1118C4—22no—
1119C4—34no—
1120C4—64no—
1121C4—61no—
1122C4—61no—
1123C4—62no—
1124C4—182no—
1125C4—182no—
1126C4—184no—
1127C4C2×D3×#6712yes—
1128C4C2×D3×#6712yes—
1129C3—21no—
1130C3#8638011yescharacteristic, complemented
1131C3#8726411yescharacteristic, complemented
1132C2—22no—
1133C2—42no—
1134C2—62no—
1135C2—64no—
1136C2—121no—
1137C2—122no—
1138C2D3×#101011yescharacteristic
1139C2#1059669611yescharacteristic
1140C2C22×D3×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC2×C32×#41C22
hypercenterC2×#41D32
hypocenterC32#3489
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×C3×D3×#41C2semidirect
2. C2×#64298C2semidirect
3. #10596296C2semidirect
4. C3×#5833C2semidirect
5. #10595400C2semidirect
6. #10595357C2semidirect
7. #10595228C2semidirect
8. #10595157C2semidirect
9. #10595151C2semidirect
10. #10595150C2semidirect
11. #10595022C2semidirect
12. #10595004C2semidirect
13. #10594986C2semidirect
14. #10594892C2semidirect
15. #10594884C2semidirect
16. D3×#924C2semidirect
17. C2×#63857C2semidirect
21. C22×#634C22semidirect
31. C2×C3×#235C22semidirect
34. C2×#3805C22semidirect
36. C2×#3795C22semidirect
37. C2×#3795C22semidirect
38. C2×D3×Dic6C22semidirect
39. C2×D3×Dic6C22semidirect
40. #64153C22semidirect
41. #64145C22semidirect
42. #64144C22semidirect
43. #64135C22semidirect
44. #64133C22semidirect
45. #64133C22semidirect
46. C3×#946C22semidirect
47. C3×#939C22semidirect
48. C3×#938C22semidirect
49. C3×#930C22semidirect
50. C2×C3×C4⋊Dic3C22semidirect
51. C3×#924C22semidirect
54. Dic3×#67C22semidirect
55. Dic3×#67C22semidirect
56. #63970C22semidirect
57. #63970C22semidirect
58. #63969C22semidirect
60. C2×Dic3⋊Dic3C22semidirect
61. #63964C22semidirect
62. #63961C22semidirect
64. #63959C22semidirect
66. #63908C22semidirect
67. #63905C22semidirect
69. C4×#625C22semidirect
70. #63898C22semidirect
71. D3×C4⋊Dic3C22semidirect
72. #63887C22semidirect
73. #63885C22semidirect
74. #63884C22semidirect
76. D3×Dic3⋊C4C22semidirect
79. #63857C22semidirect
80. #63857C22semidirect
82. #63856C22semidirect
84. #63843C22semidirect
85. #63841C22semidirect
86. #63839C22semidirect
90. C2×D3×#41D3semidirect
93. #5833D3semidirect
150. C3×#235D4semidirect
240. C2×#235C2×D3semidirect
261. #946C2×D3semidirect
270. #939C2×D3semidirect
275. #938C2×D3semidirect
293. #930C2×D3semidirect
310. C2×C4⋊Dic3C2×D3semidirect
325. #924C2×D3semidirect
516. #235#67semidirect
629. C2×C3×D32−1+4semidirect
983. C2×D3#1010semidirect
1013. C32#3489semidirect
1130. C3#86380semidirect
1131. C3#87264semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×#412
C2×#642982
#105962962
C3×#58332
#105954002
#105953572
#105952282
#105951572
#105951512
#105951502
#105950222
#105950042
#105949862
#105948922
#105948842
D3×#9242
C2×#638572
#872643
#863803