Finite Group Databasebeta

← #11904778

Subgroups — #11904778

Order 1152.

3205 conjugacy classes of subgroups.

The subgroup lattice has 1155 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64306C211yesmaximal, characteristic, complemented
2C2×#64298C211yesmaximal, characteristic, complemented
3C2×#64106C211yesmaximal, characteristic, complemented
4C3×#5510C211yesmaximal, characteristic, complemented
5C3×#5504C211yesmaximal, characteristic, complemented
6#10595075C214yesmaximal, complemented
7#10595034C211yesmaximal, characteristic, complemented
8#10594907C214yesmaximal, complemented
9#10594856C211yesmaximal, characteristic, complemented
10#10594630C212yesmaximal, complemented
11#10594626C212yesmaximal, complemented
12D3×#897C212yesmaximal, complemented
13#10594522C212yesmaximal, complemented
14#10594383C212yesmaximal, complemented
15#10594382C212yesmaximal, complemented
16#10594381C212yesmaximal, complemented
17#10594380C212yesmaximal, complemented
18#86380—31nomaximal
19#85901—31nomaximal
20C22×C4×C3⋊D3C2211yescharacteristic
21C22×#634C2211yescharacteristic, complemented
22C2×C3×#235C2211yescharacteristic
23C2×C3×#235C2211yescharacteristic
24C2×C3×#235C2211yescharacteristic, complemented
25C2×#3811C2212yes—
26C2×#3805C2212yes—
27C2×#3805C2214yescomplemented
28#64306—28no—
29C2×#3802C2211yescharacteristic
30C2×C4×D32C2212yes—
31C2×#3798C2212yes—
32C2×#3797C2211yescharacteristic
33#64298—28no—
34C2×#3796C2211yescharacteristic
35C2×#3796C2211yescharacteristic
36C2×#3795C2212yescomplemented
37C2×#3795C2212yescomplemented
38C2×D3×Dic6C2212yescomplemented
39C2×D3×Dic6C2212yescomplemented
40C2×C32×C4⋊C4C2211yescharacteristic, complemented
41C2×#3752C2212yes—
42C2×C4⋊(C3⋊Dic3)C2212yescomplemented
43#64106C2212yes—
44#64106C2212yes—
45#64106C2212yescomplemented
46#64106C2212yescomplemented
47C3×#930C2214yescomplemented
48C3×C4×#67C2214yescomplemented
49C3×#926C2211yescharacteristic, complemented
50C3×#897C2212yescomplemented
51C3×#897C2212yescomplemented
52C3×#895C2212yescomplemented
53C3×#895C2212yescomplemented
54C3×#893C2212yescomplemented
55C3×#892C2212yescomplemented
56C3×D3×C4⋊C4C2212yescomplemented
57C3×#887C2212yescomplemented
58#63981C2212yes—
59#63962C2214yescomplemented
60#63962C2212yescomplemented
61#63922C2214yes—
62D3×(C2×D3)⋊C4C2214yes—
63#63918C2214yescomplemented
64#63916C2211yescharacteristic
65#63916C2211yescharacteristic, complemented
66#63908C2214yescomplemented
67#63906C2214yescomplemented
68C4×#626C2212yes—
69C4×#626C2212yescomplemented
70#63895C2214yes—
71#63893C2214yescomplemented
72#63893C2214yescomplemented
73Dic3×D12C2214yescomplemented
74#63891C2214yescomplemented
75#63891C2214yescomplemented
76#63890C2214yescomplemented
77D3×C4⋊Dic3C2214yescomplemented
78#63886C2214yescomplemented
79#63880C2214yes—
80#63871C2211yescharacteristic
81#63871C2211yescharacteristic, complemented
82#63866C2212yescomplemented
83#63860C2212yescomplemented
84#63857C2212yescomplemented
85#63857C2212yescomplemented
86#63852C2214yescomplemented
87C2×#1010—31no—
88C2×#1010—31no—
89C2×D3×#41—31no—
90C2×D3×#41—31no—
91C3×#537—31no—
92C3×#520—31no—
93#5828—31no—
94#5825—31no—
95#5632—32no—
96#5631—32no—
97#5628—32no—
98D3×C22⋊Q8—32no—
99#5612—32no—
100#5611—34no—
101#5610—34no—
102#5608—32no—
103#5606—32no—
104#5598—32no—
105#5576—32no—
106Q8×D12—32no—
107#5555—34no—
108#5555—32no—
109#5554—34no—
110#5554—32no—
111#5526—31no—
112#5526—32no—
113#5524—31no—
114#5524—32no—
115#5510—32no—
116#5510D311yescharacteristic, complemented
117C2×#897—31no—
118C2×#897—31no—
119C2×#897—32no—
120C2×#897—61no—
121#5504D311yescharacteristic, complemented
122C23×C3⋊D3C2311yescharacteristic
123C22×D32C2312yes—
124C22×C32×C4C2312yes—
125C22×C32×C4C2311yescharacteristic
126C22×C3⋊Dic3C2311yescharacteristic
127C22×C3⋊Dic3C2312yes—
128C2×C4×C3⋊D3—24no—
129C2×C4×C3⋊D3C2311yescharacteristic
130C2×C4×C3⋊D3C2311yescharacteristic
131C2×C4×C3⋊D3C2311yescharacteristic
132C2×C4×C3⋊D3C2311yescharacteristic
133C2×#634—24no—
134C2×#634C2312yes—
135C2×#634C2312yes—
136C2×C3×#67C2312yes—
137C2×C3×#67C2312yes—
138C2×C3×#67C2312yes—
139C3×#235—24no—
140C3×#235—24no—
141C3×#235D418yescomplemented
142C2×C3×D12C2311yescharacteristic
143C2×C3×D12C2311yescharacteristic
144C2×C3×D12C2314yes—
145C2×C3×D12C2311yescharacteristic
146C2×C3×C4×D3C2312yes—
147C2×C3×C4×D3C2312yes—
148C2×C3×C4×D3C2314yes—
149C2×C3×C4×D3C2312yes—
150C2×C3×Dic6C2311yescharacteristic
151C2×C3×Dic6C2311yescharacteristic
152C2×C3×Dic6C2311yescharacteristic
153#3811—28no—
154C2×#627C2314yes—
155C2×#627C2312yes—
156C2×#626C2312yes—
157C2×#626C2312yes—
158C2×#626C2312yes—
159C2×#626C2312yes—
160C2×#625C2314yes—
161C2×#625C2312yes—
162C2×#624C2312yes—
163#3805—216no—
164#3805—28no—
165C2×D3×Dic3C2314yes—
166C2×D3×Dic3C2314yes—
167C2×D3×Dic3C2312yes—
168C2×D3×Dic3C2312yes—
169#3802—24no—
170C4×D32—28no—
171#3798—28no—
172#3797—24no—
173#3796—24no—
174#3796—24no—
175#3795—28no—
176#3795—28no—
177D3×Dic6—28no—
178D3×Dic6—28no—
179C32×C4⋊C4C2312yes—
180C32×C4⋊C4C2312yes—
181#3752C2314yes—
182#3752C2314yes—
183C4⋊(C3⋊Dic3)C2314yes—
184C4⋊(C3⋊Dic3)C2314yes—
185C3×#217C2312yes—
186C3×(C2×D3)⋊C4C2314yes—
187C3×(C2×D3)⋊C4C2314yes—
188C3×(C2×D3)⋊C4C2314yes—
189C3×C4⋊Dic3C2311yescharacteristic
190C3×C4⋊Dic3C2311yescharacteristic
191C3×C4⋊Dic3C2314yes—
192C3×Dic3⋊C4C2314yes—
193C3×C4×Dic3C2314yes—
194C3×C4×Dic3C2312yes—
195Dic3⋊Dic3C2314yes—
196Dic3⋊Dic3C2314yes—
197Dic3⋊Dic3C2312yes—
198Dic3⋊Dic3C2312yes—
199#3722C2312yes—
200#3722C2312yes—
201(C2×D3)⋊Dic3C2314yes—
202(C2×D3)⋊Dic3C2314yes—
203(C2×D3)⋊Dic3C2312yes—
204(C2×D3)⋊Dic3C2312yes—
205#3489—91noSylow
206C2×C3×#41—31no—
207C2×C3×#41—31no—
208C2×C3×#41—31no—
209#1010—68no—
210#1010—68no—
211D3×#41—68no—
212D3×#41—68no—
213C2×#239—31no—
214C2×#239—31no—
215C2×D3×Q8—32no—
216C2×D3×Q8—32no—
217C2×D3×Q8—31no—
218C2×D3×Q8—31no—
219C2×#237—32no—
220C2×#237—32no—
221C2×#237—34no—
222C2×#237—34no—
223C2×#237—32no—
224C2×#237—32no—
225C2×#237—31no—
226C2×#237—31no—
227C2×D3×D4—32no—
228C2×D3×D4—32no—
229C2×D3×D4—31no—
230C2×D3×D4—31no—
231C2×#235—32no—
232C2×#235—32no—
233C2×#235—32no—
234C2×#235—32no—
235C2×#235C2×D311yescharacteristic
236C2×#235C2×D311yescharacteristic
237C2×#235C2×D311yescharacteristic, complemented
238C22×C4×D3—31no—
239C22×C4×D3—31no—
240C22×C4×D3—32no—
241C22×C4×D3—32no—
242C22×C4×D3—61no—
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—34no—
251C3×#121—32no—
252C3×#121—32no—
253C3×C4×Q8—32no—
254C3×C4×D4—34no—
255C3×C4×D4—32no—
256C3×#117—31no—
257C3×#117—32no—
258C2×C3×C4⋊C4—21no—
259C2×C3×C4⋊C4—32no—
260C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
261C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
262#946—31no—
263#946—31no—
264#944—32no—
265#939—34no—
266#938—34no—
267#938—31no—
268#938—31no—
269#937—32no—
270#937—34no—
271#936—32no—
272#935—34no—
273#935—32no—
274D4×Dic3—34no—
275#930—34no—
276#930—34no—
277#930C2×D314yescomplemented
278C4×#67—32no—
279C4×#67—32no—
280C4×#67C2×D314yescomplemented
281C2×(C2×D3)⋊C4—32no—
282C2×(C2×D3)⋊C4—32no—
283C2×(C2×D3)⋊C4—34no—
284C2×(C2×D3)⋊C4—62no—
285#926C2×D311yescharacteristic, complemented
286C2×C4⋊Dic3—32no—
287C2×C4⋊Dic3—32no—
288C2×C4⋊Dic3—34no—
289C2×C4⋊Dic3—62no—
290#924—32no—
291#924—32no—
292#897—32no—
293#897—32no—
294#897—31no—
295#897—31no—
296#897—32no—
297#897—32no—
298#897—32no—
299#897—32no—
300#897—32no—
301#897—32no—
302#897—32no—
303#897—32no—
304#897—34no—
305#897—34no—
306#897—34no—
307#897—62no—
308#897—62no—
309#897—62no—
310#897—62no—
311#897C2×D312yescomplemented
312#897C2×D312yescomplemented
313#896—34no—
314#895—31no—
315#895—34no—
316#895—31no—
317#895C2×D312yescomplemented
318#895C2×D312yescomplemented
319#894—34no—
320#893C2×D312yescomplemented
321#892C2×D312yescomplemented
322D3×C4⋊C4—34no—
323D3×C4⋊C4C2×D312yescomplemented
324#888—34no—
325#887C2×D312yescomplemented
326#886—32no—
327#886—34no—
328#886—34no—
329#886—34no—
330#886—34no—
331#885—34no—
332#884—34no—
333#883—34no—
334#883—34no—
335#882—32no—
336#882—34no—
337#67⋊C4—34no—
338D3×C22⋊C4—34no—
339#878—34no—
340#878—34no—
341#875—32no—
342#875—34no—
343C4×D12—34no—
344C4×D12—32no—
345C4×D12—32no—
346C4×D12—34no—
347#869—32no—
348#869—34no—
349C23×C32C2411yescharacteristic
350C22×C3⋊D3—22no—
351C22×C3⋊D3—22no—
352C22×C3⋊D3—41no—
353C22×C3⋊D3C2411yescharacteristic
354C22×C3⋊D3C2411yescharacteristic
355C22×C3×D3C2412yes—
356C22×C3×D3C2412yes—
357C22×C3×D3C2412yes—
358C2×D32—24no—
359C2×D32—24no—
360C2×D32—42no—
361C2×C32×C4—42no—
362C2×C32×C4C2×D414yes—
363C2×C32×C4C2414yes—
364C2×C32×C4C2411yescharacteristic
365C2×C32×C4C2411yescharacteristic
366C2×C3⋊Dic3—24no—
367C2×C3⋊Dic3—22no—
368C2×C3⋊Dic3C2411yescharacteristic
369C2×C3⋊Dic3C2411yescharacteristic
370C2×C3⋊Dic3C2414yes—
371C4×C3⋊D3—22no—
372C4×C3⋊D3—22no—
373C4×C3⋊D3—22no—
374C4×C3⋊D3—22no—
375#634—24no—
376#634—24no—
377C3×#67—24no—
378C3×#67—24no—
379C3×#67C2×D418yes—
380C2×C3×Dic3C2412yes—
381C2×C3×Dic3C2412yes—
382C2×C3×Dic3C2412yes—
383C2×C3×Dic3C2412yes—
384C2×C3×Dic3C2412yes—
385C3×D12—22no—
386C3×D12—22no—
387C3×D12—44no—
388C3×D12C2×D414yes—
389C3×C4×D3—24no—
390C3×C4×D3—24no—
391C3×C4×D3—44no—
392C3×C4×D3C2×D418yes—
393C3×Dic6—22no—
394C3×Dic6—22no—
395C3×Dic6C2×D414yes—
396#627—28no—
397#627—24no—
398#626—24no—
399#626—24no—
400#626—24no—
401#626—42no—
402#625—28no—
403#625—24no—
404#624—24no—
405D3×Dic3—28no—
406D3×Dic3—24no—
407D3×Dic3—28no—
408D3×Dic3—24no—
409C2×2−1+4—91no—
410C22×#41—91no—
411D4×Q8—92no—
412#548—92no—
413#547—94no—
414#547—92no—
415#546—94no—
416#546—92no—
417#537—31no—
418#537—92no—
419#536—92no—
420#536—91no—
421#525—92no—
422#525—91no—
423C2×C22⋊Q8—92no—
424C2×C22⋊Q8—91no—
425#520—31no—
426C23×D3—31no—
427C23×D3—31no—
428C23×D3—32no—
429C23×D3—32no—
430C23×D3—61no—
431C3×#41—38no—
432C3×#41—64no—
433C3×#41—64no—
434C2×C3×Q8—31no—
435C2×C3×Q8—31no—
436C2×C3×Q8—31no—
437C2×C3×D4—32no—
438C2×C3×D4—32no—
439C2×C3×D4—32no—
440C2×C3×D4—31no—
441C2×C3×D4—31no—
442C2×C3×D4—31no—
443C2×C3×D4—34no—
444C22×C3×C4—21no—
445C22×C3×C4—22no—
446C22×C3×C4—32no—
447C22×C3×C4—32no—
448C22×C3×C4—32no—
449C22×C3×C4—34no—
450C22×C3×C4C22×D312yes—
451C22×C3×C4C22×D312yes—
452C22×C3×C4C22×D311yescharacteristic
453C22×C3×C4C22×D311yescharacteristic
454C2×#67—34no—
455C2×#67—32no—
456C2×#67—34no—
457C2×#67—32no—
458C2×#67—32no—
459C2×#67—32no—
460C2×#67—32no—
461C2×#67—32no—
462C2×#67C22×D312yes—
463C2×#67C22×D312yes—
464C2×#67C22×D312yes—
465C22×Dic3—31no—
466C22×Dic3—32no—
467C22×Dic3—31no—
468C22×Dic3—32no—
469C22×Dic3—32no—
470C22×Dic3—34no—
471C22×Dic3—32no—
472C22×Dic3—34no—
473C22×Dic3—61no—
474C22×Dic3—62no—
475#239—64no—
476#239—64no—
477D3×Q8—64no—
478D3×Q8—68no—
479D3×Q8—68no—
480D3×Q8—64no—
481#237—64no—
482#237—68no—
483#237—68no—
484#237—616no—
485#237—68no—
486#237—616no—
487#237—68no—
488#237—64no—
489D3×D4—64no—
490D3×D4—68no—
491D3×D4—68no—
492D3×D4—64no—
493#235—24no—
494#235—24no—
495#235—68no—
496#235—68no—
497#235—68no—
498#235—68no—
499#235D1218yescomplemented
500C2×D12—32no—
501C2×D12—32no—
502C2×D12—32no—
503C2×D12—32no—
504C2×D12C22×D311yescharacteristic
505C2×D12C22×D311yescharacteristic
506C2×D12C22×D314yes—
507C2×D12C22×D311yescharacteristic
508C2×C4×D3—34no—
509C2×C4×D3—32no—
510C2×C4×D3—34no—
511C2×C4×D3—32no—
512C2×C4×D3—31no—
513C2×C4×D3—31no—
514C2×C4×D3—31no—
515C2×C4×D3—31no—
516C2×C4×D3—31no—
517C2×C4×D3—31no—
518C2×C4×D3—31no—
519C2×C4×D3—31no—
520C2×C4×D3—32no—
521C2×C4×D3—32no—
522C2×C4×D3—61no—
523C2×C4×D3—61no—
524C2×C4×D3—61no—
525C2×C4×D3—61no—
526C2×C4×D3—68no—
527C2×C4×D3—64no—
528C2×C4×D3—64no—
529C2×C4×D3—68no—
530C2×C4×D3—124no—
531C2×C4×D3C22×D312yes—
532C2×C4×D3C22×D312yes—
533C2×C4×D3C22×D314yes—
534C2×C4×D3C22×D312yes—
535C2×Dic6—32no—
536C2×Dic6—32no—
537C2×Dic6—32no—
538C2×Dic6—32no—
539C2×Dic6—32no—
540C2×Dic6—34no—
541C2×Dic6—32no—
542C2×Dic6—34no—
543C2×Dic6—62no—
544C2×Dic6—62no—
545C2×Dic6—68no—
546C2×Dic6—64no—
547C2×Dic6—64no—
548C2×Dic6—68no—
549C2×Dic6—124no—
550C2×Dic6C22×D311yescharacteristic
551C2×Dic6C22×D311yescharacteristic
552C2×Dic6C22×D311yescharacteristic
553C3×C4⋊C4—22no—
554C3×C4⋊C4—22no—
555C3×C4⋊C4—34no—
556C3×C4⋊C4—34no—
557C3×C4⋊C4—31no—
558C3×C4⋊C4—31no—
559C3×C4⋊C4C22×D312yes—
560C3×C4⋊C4C22×D312yes—
561C3×C4⋊C4C22×D312yes—
562C3×C4⋊C4C22×D312yes—
563C3×C22⋊C4—32no—
564C3×C22⋊C4—34no—
565C3×C22⋊C4—34no—
566C3×C22⋊C4—34no—
567C3×C42—34no—
568C3×C42—32no—
569#217—32no—
570#217—34no—
571#217—32no—
572#217—34no—
573#217C22×D312yes—
574(C2×D3)⋊C4—32no—
575(C2×D3)⋊C4—34no—
576(C2×D3)⋊C4—32no—
577(C2×D3)⋊C4—34no—
578(C2×D3)⋊C4—34no—
579(C2×D3)⋊C4—34no—
580(C2×D3)⋊C4—34no—
581(C2×D3)⋊C4—34no—
582(C2×D3)⋊C4—32no—
583(C2×D3)⋊C4—32no—
584(C2×D3)⋊C4—32no—
585(C2×D3)⋊C4—32no—
586(C2×D3)⋊C4—64no—
587(C2×D3)⋊C4—64no—
588(C2×D3)⋊C4C22×D314yes—
589(C2×D3)⋊C4C22×D314yes—
590(C2×D3)⋊C4C22×D314yes—
591C4⋊Dic3—34no—
592C4⋊Dic3—34no—
593C4⋊Dic3—34no—
594C4⋊Dic3—34no—
595C4⋊Dic3—32no—
596C4⋊Dic3—34no—
597C4⋊Dic3—34no—
598C4⋊Dic3—32no—
599C4⋊Dic3—64no—
600C4⋊Dic3—64no—
601C4⋊Dic3C22×D314yes—
602C4⋊Dic3C22×D311yescharacteristic
603C4⋊Dic3C22×D311yescharacteristic
604Dic3⋊C4—32no—
605Dic3⋊C4—34no—
606Dic3⋊C4—34no—
607Dic3⋊C4—32no—
608Dic3⋊C4C22×D314yes—
609C4×Dic3C22×D314yes—
610C4×Dic3C22×D312yes—
611C22×C32—21no—
612C22×C32—21no—
613C22×C32C22×D412yes—
614C22×C32C2511yescharacteristic
615C2×C3⋊D3—21no—
616C2×C3⋊D3—21no—
617C2×C3⋊D3—21no—
618C2×C3⋊D3—21no—
619C2×C3⋊D3—21no—
620C2×C3⋊D3—44no—
621C2×C3⋊D32−1+412yescomplemented
622C2×C3×D3—22no—
623C2×C3×D3—22no—
624C2×C3×D3—22no—
625C2×C3×D3—22no—
626C2×C3×D3—22no—
627C2×C3×D3—22no—
628C2×C3×D3—22no—
629C2×C3×D3—22no—
630C2×C3×D3C22×D414yes—
631D32—48no—
632C32×C4—24no—
633C32×C4C22×D412yes—
634C32×C4C22×D412yes—
635C3⋊Dic3—21no—
636C3⋊Dic3—24no—
637C3⋊Dic3—21no—
638C3×Dic3—22no—
639C3×Dic3—22no—
640C3×Dic3—22no—
641C3×Dic3—22no—
642C3×Dic3C22×D414yes—
6432−1+4—188no—
644C2×#41—31no—
645C2×#41—31no—
646C2×#41—31no—
647C2×#41—92no—
648C2×#41—92no—
649C2×#41—92no—
650C2×#41—94no—
651C2×#41—92no—
652C2×#41—91no—
653C2×#41—91no—
654C2×#41—188no—
655C22×Q8—92no—
656C22×Q8—92no—
657C22×Q8—91no—
658C22×Q8—91no—
659C22×D4—92no—
660C22×D4—91no—
661C23×C4—92no—
662C23×C4—91no—
663C4⋊Q8—94no—
664C4⋊Q8—92no—
665#124—94no—
666#124—92no—
667#123—94no—
668#123—94no—
669#123—94no—
670#123—92no—
671#123—94no—
672C22⋊Q8—32no—
673C22⋊Q8—32no—
674C22⋊Q8—94no—
675C22⋊Q8—94no—
676C22⋊Q8—94no—
677C22⋊Q8—92no—
678C22⋊Q8—92no—
679C22⋊Q8—91no—
680C22⋊Q8—91no—
681C22⋊Q8—92no—
682C22⋊Q8—92no—
683C22⋊Q8—92no—
684C22⋊Q8—92no—
685#121—34no—
686#121—32no—
687#121—32no—
688#121—94no—
689#121—91no—
690#121—91no—
691#121—94no—
692#121—94no—
693#120—92no—
694#120—94no—
695C4×Q8—32no—
696C4×D4—34no—
697C4×D4—32no—
698C4×D4—94no—
699C4×D4—92no—
700C4×D4—92no—
701C4×D4—94no—
702#117—31no—
703#117—32no—
704C2×C4⋊C4—32no—
705C2×C4⋊C4—94no—
706C2×C4⋊C4—92no—
707C2×C4⋊C4D3211yescharacteristic, complemented
708C2×C22⋊C4—94no—
709C2×C22⋊C4—92no—
710C23×C3—21no—
711C23×C3—32no—
712C23×C3—32no—
713C23×C3—32no—
714C23×C3C23×D311yescharacteristic
715C23×C3C23×D311yescharacteristic
716C22×D3—31no—
717C22×D3—31no—
718C22×D3—31no—
719C22×D3—31no—
720C22×D3—61no—
721C22×D3—61no—
722C22×D3—64no—
723C22×D3—64no—
724C22×D3—64no—
725C22×D3—62no—
726C22×D3—62no—
727C22×D3—64no—
728C22×D3—62no—
729C22×D3—62no—
730C22×D3—64no—
731C22×D3—122no—
732C22×D3—122no—
733C22×D3—122no—
734C22×D3—121no—
735C22×D3—121no—
736C22×D3—122no—
737C22×D3C23×D312yes—
738C22×D3C23×D312yes—
739C22×D3C23×D312yes—
740C3×Q8—34no—
741C3×Q8—62no—
742C3×Q8—62no—
743C3×D4—38no—
744C3×D4—34no—
745C3×D4—64no—
746C3×D4—64no—
747C3×D4—62no—
748C3×D4—62no—
749C3×D4—124no—
750C2×C3×C4—21no—
751C2×C3×C4—21no—
752C2×C3×C4—24no—
753C2×C3×C4—24no—
754C2×C3×C4—32no—
755C2×C3×C4—38no—
756C2×C3×C4—32no—
757C2×C3×C4—32no—
758C2×C3×C4—32no—
759C2×C3×C4—32no—
760C2×C3×C4—42no—
761C2×C3×C4—42no—
762C2×C3×C4—44no—
763C2×C3×C4—64no—
764C2×C3×C4—64no—
765C2×C3×C4—124no—
766C2×C3×C4C2×D1214yes—
767C2×C3×C4D3×D414yes—
768C2×C3×C4C23×D314yes—
769C2×C3×C4C23×D314yes—
770C2×C3×C4C23×D311yescharacteristic
771C2×C3×C4C23×D311yescharacteristic
772C2×C3×C4C23×D311yescharacteristic
773C2×C3×C4C23×D311yescharacteristic
774#67—24no—
775#67—24no—
776#67—64no—
777#67—64no—
778#67—64no—
779#67—68no—
780#67—64no—
781#67—68no—
782#67—64no—
783#67—122no—
784#67C2×D1218yes—
785C2×Dic3—31no—
786C2×Dic3—31no—
787C2×Dic3—34no—
788C2×Dic3—31no—
789C2×Dic3—31no—
790C2×Dic3—34no—
791C2×Dic3—61no—
792C2×Dic3—61no—
793C2×Dic3—64no—
794C2×Dic3—68no—
795C2×Dic3—64no—
796C2×Dic3—64no—
797C2×Dic3—62no—
798C2×Dic3—64no—
799C2×Dic3—62no—
800C2×Dic3—68no—
801C2×Dic3—64no—
802C2×Dic3—124no—
803C2×Dic3—122no—
804C2×Dic3C23×D312yes—
805C2×Dic3C23×D312yes—
806C2×Dic3C23×D312yes—
807C2×Dic3C23×D312yes—
808C2×Dic3C23×D312yes—
809D12—22no—
810D12—22no—
811D12—44no—
812D12—64no—
813D12—64no—
814D12—64no—
815D12—122no—
816D12C2×D1214yes—
817C4×D3—24no—
818C4×D3—24no—
819C4×D3—44no—
820C4×D3—64no—
821C4×D3—64no—
822C4×D3—68no—
823C4×D3—64no—
824C4×D3—68no—
825C4×D3—62no—
826C4×D3—62no—
827C4×D3—62no—
828C4×D3—62no—
829C4×D3—62no—
830C4×D3—62no—
831C4×D3—62no—
832C4×D3—62no—
833C4×D3—64no—
834C4×D3—122no—
835C4×D3—122no—
836C4×D3—122no—
837C4×D3—122no—
838C4×D3C2×D1218yes—
839Dic6—22no—
840Dic6—22no—
841Dic6—68no—
842Dic6—64no—
843Dic6—64no—
844Dic6—64no—
845Dic6—64no—
846Dic6—64no—
847Dic6—68no—
848Dic6—64no—
849Dic6—124no—
850Dic6—124no—
851Dic6C2×D1214yes—
852C2×C32—22no—
853C2×C32C23×D411yescharacteristic
854C2×C32C2×2−1+411yescharacteristic
855C2×C32#58511yescharacteristic
856C3⋊D3—22no—
857C3⋊D3—41no—
858C3×D3—24no—
859C3×D3—42no—
860C3×D3—42no—
861C24—92no—
862C24—91no—
863#41—38no—
864#41—64no—
865#41—64no—
866#41—188no—
867#41—188no—
868#41—188no—
869#41—188no—
870#41—1816no—
871#41—184no—
872#41—184no—
873C2×Q8—31no—
874C2×Q8—31no—
875C2×Q8—31no—
876C2×Q8—94no—
877C2×Q8—92no—
878C2×Q8—92no—
879C2×Q8—92no—
880C2×Q8—188no—
881C2×Q8—188no—
882C2×Q8—184no—
883C2×Q8—184no—
884C2×D4—32no—
885C2×D4—32no—
886C2×D4—32no—
887C2×D4—31no—
888C2×D4—31no—
889C2×D4—31no—
890C2×D4—34no—
891C2×D4—92no—
892C2×D4—92no—
893C2×D4—92no—
894C2×D4—92no—
895C2×D4—94no—
896C2×D4—92no—
897C2×D4—188no—
898C2×D4—184no—
899C22×C4—32no—
900C22×C4—32no—
901C22×C4—32no—
902C22×C4—34no—
903C22×C4—92no—
904C22×C4—94no—
905C22×C4—92no—
906C22×C4—94no—
907C22×C4—92no—
908C22×C4—92no—
909C22×C4—91no—
910C22×C4—91no—
911C22×C4—91no—
912C22×C4—91no—
913C22×C4—91no—
914C22×C4—188no—
915C22×C4—184no—
916C22×C4C2×D3212yes—
917C22×C4C2×D3211yescharacteristic
918C4⋊C4—31no—
919C4⋊C4—34no—
920C4⋊C4—34no—
921C4⋊C4—31no—
922C4⋊C4—92no—
923C4⋊C4—94no—
924C4⋊C4—92no—
925C4⋊C4—94no—
926C4⋊C4—94no—
927C4⋊C4—94no—
928C4⋊C4C2×D3212yes—
929C4⋊C4C2×D3212yes—
930C22⋊C4—32no—
931C22⋊C4—34no—
932C22⋊C4—34no—
933C22⋊C4—34no—
934C22⋊C4—92no—
935C22⋊C4—92no—
936C22⋊C4—94no—
937C22⋊C4—92no—
938C22⋊C4—94no—
939C22⋊C4—92no—
940C22⋊C4—94no—
941C22⋊C4—94no—
942C42—34no—
943C42—32no—
944C22×C3—22no—
945C22×C3—22no—
946C22×C3—21no—
947C22×C3—21no—
948C22×C3—21no—
949C22×C3—21no—
950C22×C3—22no—
951C22×C3—21no—
952C22×C3—34no—
953C22×C3—62no—
954C22×C3—62no—
955C22×C3—62no—
956C22×C3—62no—
957C22×C3—62no—
958C22×C3—62no—
959C22×C3—62no—
960C22×C3—62no—
961C22×C3C22×D1212yes—
962C22×C3C2×D3×D412yes—
963C22×C3C24×D311yescharacteristic
964C22×C3C24×D311yescharacteristic
965C2×D3—22no—
966C2×D3—22no—
967C2×D3—22no—
968C2×D3—22no—
969C2×D3—22no—
970C2×D3—22no—
971C2×D3—22no—
972C2×D3—22no—
973C2×D3—32no—
974C2×D3—32no—
975C2×D3—62no—
976C2×D3—61no—
977C2×D3—61no—
978C2×D3—61no—
979C2×D3—61no—
980C2×D3—62no—
981C2×D3—61no—
982C2×D3—61no—
983C2×D3—61no—
984C2×D3—61no—
985C2×D3—61no—
986C2×D3—61no—
987C2×D3—121no—
988C2×D3—121no—
989C2×D3—121no—
990C2×D3—121no—
991C2×D3—128no—
992C2×D3—128no—
993C2×D3—124no—
994C2×D3—124no—
995C2×D3—128no—
996C2×D3C22×D1214yes—
997C3×C4—24no—
998C3×C4—24no—
999C3×C4—22no—
1000C3×C4—22no—
1001C3×C4—34no—
1002C3×C4—44no—
1003C3×C4—62no—
1004C3×C4—62no—
1005C3×C4—62no—
1006C3×C4—62no—
1007C3×C4C22×D1212yes—
1008C3×C4C22×D1212yes—
1009C3×C4C2×D3×D412yes—
1010C3×C4C2×D3×D412yes—
1011Dic3—22no—
1012Dic3—22no—
1013Dic3—22no—
1014Dic3—22no—
1015Dic3—64no—
1016Dic3—61no—
1017Dic3—61no—
1018Dic3—64no—
1019Dic3—61no—
1020Dic3—61no—
1021Dic3—124no—
1022Dic3—121no—
1023Dic3—121no—
1024Dic3C22×D1214yes—
1025C32#348911yescharacteristic, complemented, Sylow
1026C23—32no—
1027C23—32no—
1028C23—32no—
1029C23—91no—
1030C23—91no—
1031C23—182no—
1032C23—184no—
1033C23—184no—
1034C23—182no—
1035C23—361no—
1036C23—362no—
1037C23C22×D3211yescharacteristic
1038Q8—34no—
1039Q8—62no—
1040Q8—62no—
1041Q8—188no—
1042Q8—184no—
1043Q8—184no—
1044Q8—184no—
1045D4—38no—
1046D4—34no—
1047D4—64no—
1048D4—64no—
1049D4—62no—
1050D4—62no—
1051D4—124no—
1052D4—184no—
1053D4—184no—
1054D4—184no—
1055D4—184no—
1056D4—188no—
1057D4—362no—
1058C2×C4—32no—
1059C2×C4—38no—
1060C2×C4—32no—
1061C2×C4—32no—
1062C2×C4—32no—
1063C2×C4—32no—
1064C2×C4—42no—
1065C2×C4—64no—
1066C2×C4—64no—
1067C2×C4—94no—
1068C2×C4—91no—
1069C2×C4—91no—
1070C2×C4—124no—
1071C2×C4—184no—
1072C2×C4—184no—
1073C2×C4—188no—
1074C2×C4—184no—
1075C2×C4—188no—
1076C2×C4—182no—
1077C2×C4—184no—
1078C2×C4—182no—
1079C2×C4—182no—
1080C2×C4—182no—
1081C2×C4—182no—
1082C2×C4D3×D1214yes—
1083C2×C4C22×D3214yes—
1084C2×C4C22×D3211yescharacteristic
1085C2×C4C22×D3211yescharacteristic
1086C2×C3—24no—
1087C2×C3—22no—
1088C2×C3—22no—
1089C2×C3—21no—
1090C2×C3—21no—
1091C2×C3—21no—
1092C2×C3—64no—
1093C2×C3—122no—
1094C2×C3—122no—
1095C2×C3C23×D1211yescharacteristic
1096C2×C3C22×D3×D411yescharacteristic
1097C2×C3#596611yescharacteristic
1098C2×C3#596611yescharacteristic
1099C2×C3D3×2−1+411yescharacteristic
1100C2×C3D3×2−1+411yescharacteristic
1101D3—24no—
1102D3—42no—
1103D3—42no—
1104D3—62no—
1105D3—62no—
1106D3—122no—
1107D3—122no—
1108D3—121no—
1109D3—121no—
1110C22—21no—
1111C22—21no—
1112C22—34no—
1113C22—62no—
1114C22—62no—
1115C22—62no—
1116C22—62no—
1117C22—62no—
1118C22—62no—
1119C22—62no—
1120C22—62no—
1121C22—92no—
1122C22—181no—
1123C22—181no—
1124C22—181no—
1125C22—181no—
1126C22—181no—
1127C22—364no—
1128C22—368no—
1129C22C2×D3×D1212yes—
1130C22C23×D3211yescharacteristic
1131C4—24no—
1132C4—34no—
1133C4—62no—
1134C4—62no—
1135C4—62no—
1136C4—62no—
1137C4—181no—
1138C4—181no—
1139C4—184no—
1140C4C2×D3×D1212yes—
1141C4C2×D3×D1212yes—
1142C3—21no—
1143C3#8590111yescharacteristic, complemented
1144C3#8638011yescharacteristic, complemented
1145C2—22no—
1146C2—64no—
1147C2—122no—
1148C2—122no—
1149C2—182no—
1150C2—361no—
1151C2C22×D3×D1211yescharacteristic
1152C2#1059667911yescharacteristic
1153C2#1059668711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC2×C32×C4⋊C4C22
hypercenterC2×C4⋊C4D32
hypocenterC32#3489
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64306C2semidirect
2. C2×#64298C2semidirect
3. C2×#64106C2semidirect
4. C3×#5510C2semidirect
5. C3×#5504C2semidirect
6. #10595075C2semidirect
7. #10595034C2semidirect
8. #10594907C2semidirect
9. #10594856C2semidirect
10. #10594630C2semidirect
11. #10594626C2semidirect
12. D3×#897C2semidirect
13. #10594522C2semidirect
14. #10594383C2semidirect
15. #10594382C2semidirect
16. #10594381C2semidirect
17. #10594380C2semidirect
21. C22×#634C22semidirect
24. C2×C3×#235C22semidirect
27. C2×#3805C22semidirect
36. C2×#3795C22semidirect
37. C2×#3795C22semidirect
38. C2×D3×Dic6C22semidirect
39. C2×D3×Dic6C22semidirect
40. C2×C32×C4⋊C4C22semidirect
42. C2×C4⋊(C3⋊Dic3)C22semidirect
45. #64106C22semidirect
46. #64106C22semidirect
47. C3×#930C22semidirect
48. C3×C4×#67C22semidirect
49. C3×#926C22semidirect
50. C3×#897C22semidirect
51. C3×#897C22semidirect
52. C3×#895C22semidirect
53. C3×#895C22semidirect
54. C3×#893C22semidirect
55. C3×#892C22semidirect
56. C3×D3×C4⋊C4C22semidirect
57. C3×#887C22semidirect
59. #63962C22semidirect
60. #63962C22semidirect
63. #63918C22semidirect
65. #63916C22semidirect
66. #63908C22semidirect
67. #63906C22semidirect
69. C4×#626C22semidirect
71. #63893C22semidirect
72. #63893C22semidirect
73. Dic3×D12C22semidirect
74. #63891C22semidirect
75. #63891C22semidirect
76. #63890C22semidirect
77. D3×C4⋊Dic3C22semidirect
78. #63886C22semidirect
81. #63871C22semidirect
82. #63866C22semidirect
83. #63860C22semidirect
84. #63857C22semidirect
85. #63857C22semidirect
86. #63852C22semidirect
116. #5510D3semidirect
121. #5504D3semidirect
141. C3×#235D4semidirect
237. C2×#235C2×D3semidirect
260. C2×C3×C4⋊C4C2×D3semidirect
261. C2×C3×C4⋊C4C2×D3semidirect
277. #930C2×D3semidirect
280. C4×#67C2×D3semidirect
285. #926C2×D3semidirect
311. #897C2×D3semidirect
312. #897C2×D3semidirect
317. #895C2×D3semidirect
318. #895C2×D3semidirect
320. #893C2×D3semidirect
321. #892C2×D3semidirect
323. D3×C4⋊C4C2×D3semidirect
325. #887C2×D3semidirect
499. #235D12semidirect
621. C2×C3⋊D32−1+4semidirect
707. C2×C4⋊C4D32semidirect
1025. C32#3489semidirect
1143. C3#85901semidirect
1144. C3#86380semidirect

Maximal subgroups

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

subgroupindex
C2×#643062
C2×#642982
C2×#641062
C3×#55102
C3×#55042
#105950752
#105950342
#105949072
#105948562
#105946302
#105946262
D3×#8972
#105945222
#105943832
#105943822
#105943812
#105943802
#863803
#859013