Finite Group Databasebeta

← D3×#5523 #11900080

Subgroups — D3×#5523 #11900080

Order 1152.

3427 conjugacy classes of subgroups.

The subgroup lattice has 1080 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#235C211yesmaximal, characteristic
2#10595994C211yesmaximal, characteristic, complemented
3C3×#5523C211yesmaximal, characteristic, complemented
4C3×D3×#117C211yesmaximal, characteristic, complemented
5#10594992C211yesmaximal, characteristic, complemented
6#10594990C211yesmaximal, characteristic, complemented
7C2×D3×C4⋊Dic3C211yesmaximal, characteristic, complemented
8D3×#892C212yesmaximal, complemented
9D32×C4⋊C4C212yesmaximal, complemented
10#10594511C212yesmaximal, complemented
11#10594510C212yesmaximal, complemented
12D3×#67⋊C4C214yesmaximal, complemented
13#10594049C214yesmaximal, complemented
14C4×D3×D12C212yesmaximal, complemented
15#10593890C212yesmaximal, complemented
16#10593887C212yesmaximal, complemented
17C4×D3×Dic6C212yesmaximal, complemented
18D3×#520—31nomaximal
19C2×#5523—31nomaximal
20C2×#3828C2211yescharacteristic
21C2×C3×#235C2211yescharacteristic
22C22×C3×C4×D3C2211yescharacteristic
23C2×D3×#67C2212yes—
24C2×#3804C2212yes—
25C22×D3×Dic3C2212yes—
26D3×#235C4116yescomplemented
27C2×D3×D12C2211yescharacteristic
28C2×C4×D32C2214yes—
29C2×C4×D32C2212yes—
30C2×#3799C2211yescharacteristic
31C2×#3798C2212yes—
32C2×#3795C2211yescharacteristic
33C2×D3×Dic6C2211yescharacteristic
34C32×#117C2211yescharacteristic, complemented
35C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
36#64101C2212yescomplemented
37C4⋊C4×C3⋊D3C2212yescomplemented
38#64090C2214yescomplemented
39C4×C4⋊(C3⋊D3)C2212yescomplemented
40C4×#634C2212yescomplemented
41C3×#926C2211yescharacteristic, complemented
42C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
43C3×#892C2211yescharacteristic, complemented
44C3×#892C2211yescharacteristic, complemented
45C3×#892C2212yescomplemented
46C3×D3×C4⋊C4C2211yescharacteristic
47C3×D3×C4⋊C4C2211yescharacteristic
48C3×D3×C4⋊C4C2212yescomplemented
49C3×#67⋊C4C2214yescomplemented
50C3×D3×C22⋊C4C2212yes—
51C3×#877C2212yescomplemented
52C3×C4×D12C2212yescomplemented
53C3×#872C2212yescomplemented
54C3×C42×D3C2212yes—
55C3×C4×Dic6C2212yescomplemented
56#67⋊Dic3C2214yescomplemented
57C2×Dic3⋊Dic3C2212yescomplemented
58#63952C2214yescomplemented
59D3×(C2×D3)⋊C4C2214yes—
60C4×#627C2214yescomplemented
61C4×#626C2214yescomplemented
62#63902C2214yescomplemented
63#63900C2212yescomplemented
64#63894C2212yescomplemented
65Dic3×D12C2212yescomplemented
66D3×C4⋊Dic3C2212yes—
67D3×C4⋊Dic3C2212yes—
68D3×C4⋊Dic3C2212yescomplemented
69D3×C4⋊Dic3C2212yescomplemented
70D3×C4⋊Dic3C2212yescomplemented
71#63883C2214yescomplemented
72#63881C2214yescomplemented
73#63880C2214yescomplemented
74#63880C2214yescomplemented
75#63879C2214yescomplemented
76#63878C2214yescomplemented
77D3×Dic3⋊C4C2214yes—
78D3×Dic3⋊C4C2214yescomplemented
79C4×D3×Dic3C2214yes—
80#63849C2212yescomplemented
81#63844C2212yescomplemented
82Dic3×Dic6C2212yescomplemented
83#63841C2212yescomplemented
84#63837C2214yescomplemented
85#63836C2214yescomplemented
86C2×D3×#41—31no—
87C22×#235—31no—
88C3×#520—31no—
89C2×C3×#117—31no—
90#5827—31no—
91C22×C4⋊Dic3—31no—
92#5574—32no—
93C4×D3×Q8—32no—
94#5546—34no—
95#5546—32no—
96C4×D3×D4—34no—
97C4×D3×D4—32no—
98#5523—31no—
99#5523—31no—
100#5523—31no—
101#5523—31no—
102#5523—32no—
103#5523—32no—
104#5523—32no—
105#5523—34no—
106#5523—32no—
107#5523—32no—
108#5523—61no—
109#5523D311yescharacteristic, direct product factor
110D3×#117—32no—
111D3×#117D311yescharacteristic, complemented
112#5504—31no—
113#5504—32no—
114C2×#892—32no—
115C2×D3×C4⋊C4—31no—
116C2×D3×C4⋊C4—32no—
117C2×D3×C4⋊C4—32no—
118C2×#67⋊C4—34no—
119C2×C4×D12—32no—
120C2×C4×Dic6—32no—
121C23×C3×D3C2311yescharacteristic
122C22×D32C2312yes—
123C22×C32×C4C2311yescharacteristic
124C2×#638C2312yes—
125C22×C3⋊Dic3C2312yes—
126#3828C2×C418yescomplemented
127C2×C4⋊(C3⋊D3)C2311yescharacteristic
128C2×C4×C3⋊D3C2314yes—
129C2×C4×C3⋊D3C2312yes—
130C2×#634C2311yescharacteristic
131C2×C3×#67C2312yes—
132C22×C3×Dic3C2312yes—
133C22×C3×Dic3C2311yescharacteristic
134C3×#235C2×C418yescomplemented
135C2×C3×D12C2311yescharacteristic
136C2×C3×C4×D3C2×C418yescomplemented
137C2×C3×C4×D3C2312yes—
138C2×C3×C4×D3C2312yes—
139C2×C3×C4×D3C2314yes—
140C2×C3×C4×D3C2311yescharacteristic
141C2×C3×C4×D3C2311yescharacteristic
142C2×C3×C4×D3C2312yes—
143C2×C3×C4×D3C2311yescharacteristic
144C2×C3×C4×D3C2311yescharacteristic
145C2×C3×Dic6C2311yescharacteristic
146D3×#67C2×C4116yescomplemented
147C2×#627C2312yes—
148C2×#626C2312yes—
149C2×#626C2312yes—
150C2×#625C2312yes—
151C2×#624C2314yes—
152C2×#624C2312yes—
153#3804C2×C4116yescomplemented
154C2×D3×Dic3—44no—
155C2×D3×Dic3C2314yes—
156C2×D3×Dic3C2314yes—
157C2×D3×Dic3C2314yes—
158C2×D3×Dic3C2312yes—
159C2×D3×Dic3C2312yes—
160D3×D12C2×C418yescomplemented
161C4×D32—48no—
162C4×D32C2×C4116yescomplemented
163#3799C2×C418yescomplemented
164#3798C2×C4116yescomplemented
165#3795C2×C418yescomplemented
166D3×Dic6C2×C418yescomplemented
167C32×C4⋊C4C2311yescharacteristic
168C32×C4⋊C4C2311yescharacteristic
169C32×C22⋊C4C2312yes—
170C32×C42C2312yes—
171#3752C2314yes—
172C4⋊(C3⋊Dic3)C2312yes—
173C4⋊(C3⋊Dic3)C2312yes—
174#3750C2314yes—
175C4×C3⋊Dic3C2314yes—
176C3×#217C2312yes—
177C3×(C2×D3)⋊C4C2312yes—
178C3×(C2×D3)⋊C4C2312yes—
179C3×(C2×D3)⋊C4C2314yes—
180C3×C4⋊Dic3C2311yescharacteristic
181C3×C4⋊Dic3C2311yescharacteristic
182C3×C4⋊Dic3C2312yes—
183C3×C4⋊Dic3C2312yes—
184C3×Dic3⋊C4C2312yes—
185C3×Dic3⋊C4C2312yes—
186C3×Dic3⋊C4C2314yes—
187C3×C4×Dic3C2312yes—
188C3×C4×Dic3C2312yes—
189C3×C4×Dic3C2314yes—
190C3×C4×Dic3C2312yes—
191#3724C2314yes—
192Dic3⋊Dic3C2314yes—
193Dic3⋊Dic3C2314yes—
194Dic3⋊Dic3C2314yes—
195#3722C2314yes—
196(C2×D3)⋊Dic3C2314yes—
197Dic32C2314yes—
198Dic32C2314yes—
199C2×#520—91noSylow
200C2×C3×#41—31no—
201C23×C3×C4—31no—
202C22×#67—32no—
203C23×Dic3—32no—
204D3×#41—316no—
205C2×#239—31no—
206C2×D3×Q8—31no—
207C2×#237—32no—
208C2×#237—31no—
209C2×D3×D4—32no—
210C2×D3×D4—31no—
211C2×#235—31no—
212C2×#235—31no—
213C2×#235—32no—
214C2×#235—316no—
215C2×#235—31no—
216C2×#235—32no—
217C2×#235—32no—
218C2×#235—31no—
219C2×#235—61no—
220C2×#235C2×D311yescharacteristic
221C22×D12—31no—
222C22×C4×D3—32no—
223C22×C4×D3—32no—
224C22×C4×D3—32no—
225C22×C4×D3—34no—
226C22×C4×D3—34no—
227C22×C4×D3C2×D311yescharacteristic
228C22×Dic6—31no—
229C3×C4×Q8—32no—
230C3×C4×D4—34no—
231C3×C4×D4—32no—
232C3×#117—21no—
233C3×#117—31no—
234C3×#117—32no—
235C3×#117—31no—
236C3×#117—31no—
237C3×#117—32no—
238C3×#117—32no—
239C3×#117C2×D311yescharacteristic, complemented
240C3×#117C2×D311yescharacteristic, complemented
241C2×C3×C4⋊C4—31no—
242C2×C3×C4⋊C4—31no—
243C2×C3×C4⋊C4—31no—
244C2×C3×C4⋊C4—32no—
245C2×C3×C22⋊C4—32no—
246C2×C3×C42—32no—
247Q8×Dic3—32no—
248D4×Dic3—34no—
249D4×Dic3—32no—
250C4×#67—34no—
251C4×#67—34no—
252C4×#67—34no—
253C2×(C2×D3)⋊C4—34no—
254#926—32no—
255#926C2×D311yescharacteristic, complemented
256C2×C4⋊Dic3—31no—
257C2×C4⋊Dic3—31no—
258C2×C4⋊Dic3—32no—
259C2×C4⋊Dic3—32no—
260C2×C4⋊Dic3—32no—
261C2×C4⋊Dic3—32no—
262C2×C4⋊Dic3—32no—
263C2×C4⋊Dic3—32no—
264C2×C4⋊Dic3—61no—
265C2×C4⋊Dic3C2×D311yescharacteristic, complemented
266C2×Dic3⋊C4—32no—
267C2×Dic3⋊C4—34no—
268C2×Dic3⋊C4—34no—
269C2×C4×Dic3—34no—
270#893—34no—
271#893—32no—
272#892—32no—
273#892—32no—
274#892—32no—
275#892—34no—
276#892—32no—
277#892—32no—
278#892—34no—
279#892—62no—
280#892C2×D312yescomplemented
281#892C2×D311yescharacteristic, complemented
282#892C2×D311yescharacteristic, complemented
283D3×C4⋊C4—32no—
284D3×C4⋊C4—32no—
285D3×C4⋊C4—34no—
286D3×C4⋊C4—34no—
287D3×C4⋊C4—32no—
288D3×C4⋊C4—32no—
289D3×C4⋊C4—32no—
290D3×C4⋊C4—32no—
291D3×C4⋊C4—32no—
292D3×C4⋊C4—32no—
293D3×C4⋊C4—32no—
294D3×C4⋊C4—34no—
295D3×C4⋊C4—34no—
296D3×C4⋊C4—62no—
297D3×C4⋊C4C2×D311yescharacteristic
298D3×C4⋊C4C2×D311yescharacteristic
299D3×C4⋊C4C2×D312yescomplemented
300#887—34no—
301#887—32no—
302#67⋊C4—34no—
303#67⋊C4—34no—
304#67⋊C4—34no—
305#67⋊C4—34no—
306#67⋊C4—34no—
307#67⋊C4—34no—
308#67⋊C4—34no—
309#67⋊C4—34no—
310#67⋊C4—34no—
311#67⋊C4—34no—
312#67⋊C4—64no—
313#67⋊C4C2×D314yescomplemented
314D3×C22⋊C4—34no—
315D3×C22⋊C4C2×D312yes—
316#877—34no—
317#877C2×D312yescomplemented
318C4×D12—32no—
319C4×D12—34no—
320C4×D12—32no—
321C4×D12—32no—
322C4×D12—34no—
323C4×D12—34no—
324C4×D12—32no—
325C4×D12—62no—
326C4×D12C2×D312yescomplemented
327#872—34no—
328#872C2×D312yescomplemented
329C42×D3—34no—
330C42×D3C2×D312yes—
331C4×Dic6—32no—
332C4×Dic6—32no—
333C4×Dic6—32no—
334C4×Dic6—32no—
335C4×Dic6—34no—
336C4×Dic6—34no—
337C4×Dic6—34no—
338C4×Dic6—62no—
339C4×Dic6C2×D312yescomplemented
340C23×C32C2411yescharacteristic
341C22×C3⋊D3C2412yes—
342C22×C3×D3—22no—
343C22×C3×D3—22no—
344C22×C3×D3C22×C414yes—
345C22×C3×D3C2412yes—
346C22×C3×D3C2411yescharacteristic
347C22×C3×D3C2411yescharacteristic
348C2×D32—24no—
349C2×D32—24no—
350C2×D32C22×C418yes—
351C2×C32×C4C22×C414yescomplemented
352C2×C32×C4C2412yes—
353C2×C32×C4C2412yes—
354C2×C32×C4C2411yescharacteristic
355C2×C32×C4C2411yescharacteristic
356#638C22×C418yescomplemented
357C2×C3⋊Dic3—42no—
358C2×C3⋊Dic3C2414yes—
359C2×C3⋊Dic3C2412yes—
360C4⋊(C3⋊D3)C22×C414yescomplemented
361C4×C3⋊D3—44no—
362C4×C3⋊D3C22×C418yescomplemented
363#634C22×C414yescomplemented
364C3×#67C22×C418yescomplemented
365C2×C3×Dic3—42no—
366C2×C3×Dic3C22×C414yescomplemented
367C2×C3×Dic3C2412yes—
368C2×C3×Dic3C2414yes—
369C2×C3×Dic3C2412yes—
370C2×C3×Dic3C2412yes—
371C2×C3×Dic3C2411yescharacteristic
372C2×C3×Dic3C2411yescharacteristic
373C3×D12C22×C414yescomplemented
374C3×C4×D3—24no—
375C3×C4×D3—24no—
376C3×C4×D3—44no—
377C3×C4×D3C22×C414yes—
378C3×C4×D3C22×C414yes—
379C3×C4×D3C22×C414yescomplemented
380C3×C4×D3C22×C414yescomplemented
381C3×C4×D3C22×C418yescomplemented
382C3×Dic6C22×C414yescomplemented
383#627C22×C418yescomplemented
384#626C22×C418yescomplemented
385#626C22×C418yescomplemented
386#625C22×C418yescomplemented
387#624—44no—
388#624C22×C418yescomplemented
389D3×Dic3—28no—
390D3×Dic3—44no—
391D3×Dic3—44no—
392D3×Dic3C22×C418yes—
393D3×Dic3C22×C418yescomplemented
394C22×#41—91no—
395#520—31no—
396#520—91no—
397#520—92no—
398#520—92no—
399#520—94no—
400#520—92no—
401#520—92no—
402#520—91no—
403#520—91no—
404C2×C4×Q8—92no—
405C2×C4×D4—92no—
406C2×C4×D4—94no—
407C2×#117—31no—
408C2×#117—92no—
409C22×C4⋊C4—92no—
410C22×C4⋊C4—91no—
411C24×C3—31no—
412C23×D3—32no—
413C23×D3—32no—
414C23×D3C22×D311yescharacteristic
415C3×#41—38no—
416C2×C3×Q8—31no—
417C2×C3×D4—32no—
418C2×C3×D4—31no—
419C22×C3×C4—21no—
420C22×C3×C4—31no—
421C22×C3×C4—38no—
422C22×C3×C4—31no—
423C22×C3×C4—31no—
424C22×C3×C4—31no—
425C22×C3×C4—31no—
426C22×C3×C4—32no—
427C22×C3×C4—32no—
428C22×C3×C4—32no—
429C22×C3×C4—32no—
430C22×C3×C4—34no—
431C22×C3×C4C22×D311yescharacteristic
432C22×C3×C4C22×D311yescharacteristic
433C2×#67—32no—
434C2×#67—32no—
435C2×#67—32no—
436C2×#67—32no—
437C2×#67—316no—
438C2×#67—32no—
439C2×#67—32no—
440C2×#67—62no—
441C2×#67C22×D312yes—
442C22×Dic3—32no—
443C22×Dic3—32no—
444C22×Dic3—32no—
445C22×Dic3—32no—
446C22×Dic3—34no—
447C22×Dic3—34no—
448C22×Dic3—34no—
449C22×Dic3—62no—
450C22×Dic3—124no—
451C22×Dic3C22×D312yes—
452C22×Dic3C22×D311yescharacteristic
453#239—38no—
454D3×Q8—38no—
455#237—316no—
456#237—38no—
457D3×D4—316no—
458D3×D4—38no—
459#235—38no—
460#235—38no—
461#235—316no—
462#235—38no—
463#235—316no—
464#235—316no—
465#235—38no—
466#235—68no—
467#235C4×D318yescomplemented
468C2×D12—32no—
469C2×D12—32no—
470C2×D12—31no—
471C2×D12—31no—
472C2×D12—38no—
473C2×D12—61no—
474C2×D12C22×D311yescharacteristic
475C2×C4×D3—32no—
476C2×C4×D3—32no—
477C2×C4×D3—32no—
478C2×C4×D3—32no—
479C2×C4×D3—32no—
480C2×C4×D3—32no—
481C2×C4×D3—316no—
482C2×C4×D3—316no—
483C2×C4×D3—34no—
484C2×C4×D3—34no—
485C2×C4×D3—34no—
486C2×C4×D3—34no—
487C2×C4×D3—34no—
488C2×C4×D3—34no—
489C2×C4×D3—34no—
490C2×C4×D3—62no—
491C2×C4×D3—64no—
492C2×C4×D3—128no—
493C2×C4×D3—128no—
494C2×C4×D3—124no—
495C2×C4×D3C4×D318yescomplemented
496C2×C4×D3C22×D312yes—
497C2×C4×D3C22×D312yes—
498C2×C4×D3C22×D314yes—
499C2×C4×D3C22×D311yescharacteristic
500C2×C4×D3C22×D311yescharacteristic
501C2×C4×D3C22×D311yescharacteristic
502C2×C4×D3C22×D311yescharacteristic
503C2×C4×D3C22×D312yes—
504C2×Dic6—31no—
505C2×Dic6—31no—
506C2×Dic6—32no—
507C2×Dic6—32no—
508C2×Dic6—38no—
509C2×Dic6—61no—
510C2×Dic6C22×D311yescharacteristic
511C3×C4⋊C4—21no—
512C3×C4⋊C4—21no—
513C3×C4⋊C4—34no—
514C3×C4⋊C4—32no—
515C3×C4⋊C4—32no—
516C3×C4⋊C4—31no—
517C3×C4⋊C4—32no—
518C3×C4⋊C4—32no—
519C3×C4⋊C4—31no—
520C3×C4⋊C4C22×D311yescharacteristic
521C3×C4⋊C4C22×D311yescharacteristic
522C3×C4⋊C4C22×D311yescharacteristic
523C3×C4⋊C4C22×D311yescharacteristic
524C3×C22⋊C4—22no—
525C3×C22⋊C4—32no—
526C3×C22⋊C4—34no—
527C3×C22⋊C4—32no—
528C3×C22⋊C4—32no—
529C3×C22⋊C4C22×D312yes—
530C3×C22⋊C4C22×D312yes—
531C3×C42—22no—
532C3×C42—32no—
533C3×C42—32no—
534C3×C42—32no—
535C3×C42—34no—
536C3×C42C22×D312yes—
537C3×C42C22×D312yes—
538#217—34no—
539#217C22×D312yes—
540(C2×D3)⋊C4—34no—
541(C2×D3)⋊C4—34no—
542(C2×D3)⋊C4—34no—
543(C2×D3)⋊C4—34no—
544(C2×D3)⋊C4—34no—
545(C2×D3)⋊C4—64no—
546(C2×D3)⋊C4C22×D312yes—
547(C2×D3)⋊C4C22×D312yes—
548(C2×D3)⋊C4C22×D314yes—
549C4⋊Dic3—32no—
550C4⋊Dic3—32no—
551C4⋊Dic3—32no—
552C4⋊Dic3—32no—
553C4⋊Dic3—34no—
554C4⋊Dic3—34no—
555C4⋊Dic3—34no—
556C4⋊Dic3—62no—
557C4⋊Dic3—62no—
558C4⋊Dic3C22×D312yes—
559C4⋊Dic3C22×D311yescharacteristic
560C4⋊Dic3C22×D312yes—
561C4⋊Dic3C22×D311yescharacteristic
562Dic3⋊C4—34no—
563Dic3⋊C4—34no—
564Dic3⋊C4—34no—
565Dic3⋊C4—34no—
566Dic3⋊C4—34no—
567Dic3⋊C4—34no—
568Dic3⋊C4—34no—
569Dic3⋊C4—64no—
570Dic3⋊C4C22×D314yes—
571Dic3⋊C4C22×D312yes—
572Dic3⋊C4C22×D312yes—
573C4×Dic3—34no—
574C4×Dic3—34no—
575C4×Dic3—34no—
576C4×Dic3—34no—
577C4×Dic3—34no—
578C4×Dic3—34no—
579C4×Dic3—64no—
580C4×Dic3C22×D312yes—
581C4×Dic3C22×D314yes—
582C4×Dic3C22×D312yes—
583C4×Dic3C22×D312yes—
584C22×C32—21no—
585C22×C32—21no—
586C22×C32C23×C412yes—
587C22×C32C2511yescharacteristic
588C2×C3⋊D3—22no—
589C2×C3⋊D3—22no—
590C2×C3⋊D3C23×C414yes—
591C2×C3×D3—21no—
592C2×C3×D3—22no—
593C2×C3×D3—22no—
594C2×C3×D3—21no—
595C2×C3×D3—28no—
596C2×C3×D3C23×C414yes—
597C2×C3×D3C23×C412yes—
598C2×C3×D3C23×C412yes—
599C2×C3×D3H(5,𝔽2)12yes—
600C2×C3×D32−1+412yes—
601D32—216no—
602C32×C4—22no—
603C32×C4—22no—
604C32×C4C23×C412yes—
605C32×C4C23×C412yes—
606C3⋊Dic3—24no—
607C3⋊Dic3C23×C414yes—
608C3×Dic3—24no—
609C3×Dic3—22no—
610C3×Dic3—22no—
611C3×Dic3C23×C414yes—
612C3×Dic3C23×C412yes—
613C3×Dic3C23×C412yes—
614C2×#41—31no—
615C2×#41—92no—
616C2×#41—92no—
617C2×#41—91no—
618C2×#41—91no—
619C2×#41—916no—
620C2×#41—91no—
621C22×Q8—91no—
622C22×D4—91no—
623C22×D4—92no—
624C23×C4—31no—
625C23×C4—92no—
626C23×C4—94no—
627C23×C4—92no—
628C4×Q8—32no—
629C4×Q8—94no—
630C4×Q8—94no—
631C4×Q8—92no—
632C4×Q8—92no—
633C4×Q8—92no—
634C4×D4—34no—
635C4×D4—32no—
636C4×D4—94no—
637C4×D4—94no—
638C4×D4—92no—
639C4×D4—94no—
640C4×D4—92no—
641C4×D4—94no—
642C4×D4—94no—
643C4×D4—94no—
644C4×D4—94no—
645C4×D4—94no—
646C4×D4—94no—
647C4×D4—92no—
648#117—31no—
649#117—31no—
650#117—31no—
651#117—32no—
652#117—32no—
653#117—32no—
654#117—94no—
655#117—94no—
656#117—92no—
657#117—92no—
658#117—92no—
659#117D3211yescharacteristic, complemented
660C2×C4⋊C4—31no—
661C2×C4⋊C4—31no—
662C2×C4⋊C4—32no—
663C2×C4⋊C4—31no—
664C2×C4⋊C4—92no—
665C2×C4⋊C4—94no—
666C2×C4⋊C4—92no—
667C2×C4⋊C4—94no—
668C2×C4⋊C4—92no—
669C2×C4⋊C4—94no—
670C2×C4⋊C4—92no—
671C2×C4⋊C4—92no—
672C2×C4⋊C4—92no—
673C2×C4⋊C4—92no—
674C2×C4⋊C4—91no—
675C2×C4⋊C4—92no—
676C2×C22⋊C4—32no—
677C2×C22⋊C4—94no—
678C2×C42—32no—
679C2×C42—94no—
680C23×C3—21no—
681C23×C3—31no—
682C23×C3—34no—
683C23×C3—32no—
684C23×C3—31no—
685C23×C3—62no—
686C23×C3—62no—
687C23×C3C23×D311yescharacteristic
688C23×C3C23×D311yescharacteristic
689C22×D3—22no—
690C22×D3—22no—
691C22×D3—32no—
692C22×D3—32no—
693C22×D3—38no—
694C22×D3—38no—
695C22×D3—62no—
696C22×D3—64no—
697C22×D3—64no—
698C22×D3—64no—
699C22×D3—64no—
700C22×D3C2×C4×D314yes—
701C22×D3C23×D312yes—
702C22×D3C23×D311yescharacteristic
703C22×D3C23×D311yescharacteristic
704C3×Q8—34no—
705C3×D4—38no—
706C3×D4—34no—
707C2×C3×C4—21no—
708C2×C3×C4—21no—
709C2×C3×C4—22no—
710C2×C3×C4—22no—
711C2×C3×C4—24no—
712C2×C3×C4—34no—
713C2×C3×C4—32no—
714C2×C3×C4—31no—
715C2×C3×C4—31no—
716C2×C3×C4—34no—
717C2×C3×C4—34no—
718C2×C3×C4—38no—
719C2×C3×C4—34no—
720C2×C3×C4—34no—
721C2×C3×C4—32no—
722C2×C3×C4—34no—
723C2×C3×C4—32no—
724C2×C3×C4—64no—
725C2×C3×C4—64no—
726C2×C3×C4—124no—
727C2×C3×C4—122no—
728C2×C3×C4C2×C4×D314yescomplemented
729C2×C3×C4C2×C4×D314yescomplemented
730C2×C3×C4C23×D312yes—
731C2×C3×C4C23×D312yes—
732C2×C3×C4C23×D312yes—
733C2×C3×C4C23×D312yes—
734C2×C3×C4C23×D311yescharacteristic
735C2×C3×C4C23×D311yescharacteristic
736C2×C3×C4C23×D311yescharacteristic
737C2×C3×C4C23×D311yescharacteristic
738#67—38no—
739#67—38no—
740#67—38no—
741#67—38no—
742#67—38no—
743#67—38no—
744#67—68no—
745#67C2×C4×D318yescomplemented
746C2×Dic3—32no—
747C2×Dic3—32no—
748C2×Dic3—38no—
749C2×Dic3—38no—
750C2×Dic3—34no—
751C2×Dic3—34no—
752C2×Dic3—42no—
753C2×Dic3—62no—
754C2×Dic3—64no—
755C2×Dic3—68no—
756C2×Dic3—124no—
757C2×Dic3—124no—
758C2×Dic3—122no—
759C2×Dic3—122no—
760C2×Dic3—242no—
761C2×Dic3C2×C4×D314yescomplemented
762C2×Dic3C23×D312yes—
763C2×Dic3C23×D314yes—
764C2×Dic3C23×D312yes—
765C2×Dic3C23×D312yes—
766C2×Dic3C23×D311yescharacteristic
767C2×Dic3C23×D311yescharacteristic
768D12—38no—
769D12—38no—
770D12—34no—
771D12—34no—
772D12—64no—
773D12C2×C4×D314yescomplemented
774C4×D3—24no—
775C4×D3—24no—
776C4×D3—38no—
777C4×D3—38no—
778C4×D3—38no—
779C4×D3—38no—
780C4×D3—38no—
781C4×D3—38no—
782C4×D3—44no—
783C4×D3—68no—
784C4×D3—68no—
785C4×D3—124no—
786C4×D3—124no—
787C4×D3—124no—
788C4×D3—124no—
789C4×D3—124no—
790C4×D3—124no—
791C4×D3—244no—
792C4×D3C2×C4×D314yes—
793C4×D3C2×C4×D314yes—
794C4×D3C2×C4×D318yescomplemented
795C4×D3C2×C4×D314yescomplemented
796C4×D3C2×C4×D314yescomplemented
797Dic6—34no—
798Dic6—34no—
799Dic6—38no—
800Dic6—38no—
801Dic6—64no—
802Dic6C2×C4×D314yescomplemented
803C2×C32—22no—
804C2×C32C24×C411yescharacteristic
805C2×C32C2×H(5,𝔽2)11yescharacteristic
806C2×C32C2×2−1+411yescharacteristic
807C3⋊D3—24no—
808C3×D3—24no—
809C3×D3—22no—
810C3×D3#52014yescomplemented
811C24—31no—
812C24—92no—
813#41—38no—
814#41—916no—
815#41—916no—
816#41—98no—
817#41—98no—
818#41—98no—
819C2×Q8—31no—
820C2×Q8—92no—
821C2×Q8—98no—
822C2×Q8—91no—
823C2×D4—32no—
824C2×D4—31no—
825C2×D4—98no—
826C2×D4—92no—
827C2×D4—92no—
828C2×D4—916no—
829C2×D4—92no—
830C2×D4—92no—
831C2×D4—91no—
832C22×C4—31no—
833C22×C4—31no—
834C22×C4—31no—
835C22×C4—32no—
836C22×C4—31no—
837C22×C4—31no—
838C22×C4—38no—
839C22×C4—32no—
840C22×C4—32no—
841C22×C4—32no—
842C22×C4—34no—
843C22×C4—92no—
844C22×C4—916no—
845C22×C4—94no—
846C22×C4—92no—
847C22×C4—92no—
848C22×C4—94no—
849C22×C4—94no—
850C22×C4—94no—
851C22×C4—92no—
852C22×C4—92no—
853C22×C4—94no—
854C22×C4—368no—
855C22×C4—364no—
856C22×C4C2×D3211yescharacteristic
857C4⋊C4—32no—
858C4⋊C4—32no—
859C4⋊C4—31no—
860C4⋊C4—34no—
861C4⋊C4—32no—
862C4⋊C4—32no—
863C4⋊C4—31no—
864C4⋊C4—94no—
865C4⋊C4—94no—
866C4⋊C4—94no—
867C4⋊C4—94no—
868C4⋊C4—92no—
869C4⋊C4—94no—
870C4⋊C4—92no—
871C4⋊C4C2×D3211yescharacteristic
872C4⋊C4C2×D3211yescharacteristic
873C22⋊C4—32no—
874C22⋊C4—32no—
875C22⋊C4—32no—
876C22⋊C4—34no—
877C22⋊C4—94no—
878C22⋊C4—94no—
879C22⋊C4—94no—
880C22⋊C4C2×D3212yes—
881C42—32no—
882C42—32no—
883C42—32no—
884C42—34no—
885C42—94no—
886C42—94no—
887C42—94no—
888C42C2×D3212yes—
889C22×C3—21no—
890C22×C3—21no—
891C22×C3—21no—
892C22×C3—21no—
893C22×C3—22no—
894C22×C3—21no—
895C22×C3—32no—
896C22×C3—32no—
897C22×C3—32no—
898C22×C3—34no—
899C22×C3—32no—
900C22×C3—41no—
901C22×C3—41no—
902C22×C3—68no—
903C22×C3—62no—
904C22×C3—62no—
905C22×C3—61no—
906C22×C3—61no—
907C22×C3C22×C4×D312yes—
908C22×C3C22×C4×D312yes—
909C22×C3C24×D311yescharacteristic
910C22×C3C24×D311yescharacteristic
911C2×D3—21no—
912C2×D3—21no—
913C2×D3—22no—
914C2×D3—22no—
915C2×D3—28no—
916C2×D3—34no—
917C2×D3—34no—
918C2×D3—64no—
919C2×D3—616no—
920C2×D3—62no—
921C2×D3—62no—
922C2×D3—62no—
923C2×D3—62no—
924C2×D3—616no—
925C2×D3—122no—
926C2×D3—122no—
927C2×D3C22×C4×D314yes—
928C2×D3C22×C4×D312yes—
929C2×D3C22×C4×D312yes—
930C2×D3#100912yes—
931C2×D3#101012yes—
932C3×C4—22no—
933C3×C4—22no—
934C3×C4—22no—
935C3×C4—22no—
936C3×C4—22no—
937C3×C4—22no—
938C3×C4—32no—
939C3×C4—34no—
940C3×C4—32no—
941C3×C4—42no—
942C3×C4—42no—
943C3×C4—64no—
944C3×C4—62no—
945C3×C4—62no—
946C3×C4C22×C4×D312yes—
947C3×C4C22×C4×D312yes—
948C3×C4C22×C4×D312yes—
949C3×C4C22×C4×D312yes—
950Dic3—22no—
951Dic3—22no—
952Dic3—24no—
953Dic3—34no—
954Dic3—34no—
955Dic3—64no—
956Dic3—64no—
957Dic3—64no—
958Dic3—124no—
959Dic3C22×C4×D312yes—
960Dic3C22×C4×D314yes—
961Dic3C22×C4×D312yes—
962C32C2×#52011yescharacteristic, complemented, Sylow
963C23—31no—
964C23—34no—
965C23—31no—
966C23—32no—
967C23—62no—
968C23—62no—
969C23—98no—
970C23—92no—
971C23—184no—
972C23—184no—
973C23C22×D3211yescharacteristic
974Q8—34no—
975Q8—98no—
976Q8—94no—
977D4—38no—
978D4—34no—
979D4—98no—
980D4—98no—
981D4—98no—
982D4—98no—
983D4—94no—
984C2×C4—34no—
985C2×C4—31no—
986C2×C4—32no—
987C2×C4—31no—
988C2×C4—34no—
989C2×C4—34no—
990C2×C4—34no—
991C2×C4—34no—
992C2×C4—38no—
993C2×C4—32no—
994C2×C4—32no—
995C2×C4—34no—
996C2×C4—64no—
997C2×C4—64no—
998C2×C4—98no—
999C2×C4—98no—
1000C2×C4—98no—
1001C2×C4—92no—
1002C2×C4—98no—
1003C2×C4—94no—
1004C2×C4—124no—
1005C2×C4—122no—
1006C2×C4—188no—
1007C2×C4—364no—
1008C2×C4—364no—
1009C2×C4—364no—
1010C2×C4—364no—
1011C2×C4—362no—
1012C2×C4C4×D3214yescomplemented
1013C2×C4C22×D3212yes—
1014C2×C4C22×D3212yes—
1015C2×C4C22×D3211yescharacteristic
1016C2×C4C22×D3211yescharacteristic
1017C2×C3—22no—
1018C2×C3—22no—
1019C2×C3—21no—
1020C2×C3—21no—
1021C2×C3—21no—
1022C2×C3—34no—
1023C2×C3—42no—
1024C2×C3—62no—
1025C2×C3—64no—
1026C2×C3C23×C4×D311yescharacteristic
1027C2×C3C23×C4×D311yescharacteristic
1028C2×C3C2×#100911yescharacteristic
1029C2×C3C2×#101011yescharacteristic
1030C2×C3D3×H(5,𝔽2)11yescharacteristic
1031C2×C3D3×2−1+411yescharacteristic
1032D3—24no—
1033D3—22no—
1034D3—64no—
1035D3—64no—
1036D3—124no—
1037D3#552314yesdirect product factor
1038C22—21no—
1039C22—21no—
1040C22—32no—
1041C22—32no—
1042C22—32no—
1043C22—32no—
1044C22—34no—
1045C22—68no—
1046C22—62no—
1047C22—61no—
1048C22—61no—
1049C22—62no—
1050C22—94no—
1051C22—1816no—
1052C22—182no—
1053C22—182no—
1054C22C2×C4×D3212yes—
1055C22C23×D3211yescharacteristic
1056C4—22no—
1057C4—22no—
1058C4—32no—
1059C4—32no—
1060C4—34no—
1061C4—62no—
1062C4—64no—
1063C4—62no—
1064C4—94no—
1065C4—184no—
1066C4C2×C4×D3212yes—
1067C4C2×C4×D3212yes—
1068C3—21no—
1069C3C2×#552311yescharacteristic, complemented
1070C3D3×#52011yescharacteristic, complemented
1071C2—22no—
1072C2—34no—
1073C2—62no—
1074C2—64no—
1075C2—184no—
1076C2C22×C4×D3211yescharacteristic
1077C2D3×#100911yescharacteristic
1078C2D3×#101011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutatorC2×C32C24×C4
FittingC32×#117C22
socle, cosocleC22×C32C25
prime radicalC2×D3×#235C2
hypercenter#117D32
hypocenterC32C2×#520
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
2. #10595994C2semidirect
3. C3×#5523C2semidirect
4. C3×D3×#117C2semidirect
5. #10594992C2semidirect
6. #10594990C2semidirect
7. C2×D3×C4⋊Dic3C2semidirect
8. D3×#892C2semidirect
9. D32×C4⋊C4C2semidirect
10. #10594511C2semidirect
11. #10594510C2semidirect
12. D3×#67⋊C4C2semidirect
13. #10594049C2semidirect
14. C4×D3×D12C2semidirect
15. #10593890C2semidirect
16. #10593887C2semidirect
17. C4×D3×Dic6C2semidirect
26. D3×#235C4semidirect
34. C32×#117C22semidirect
35. C2×C4⋊(C3⋊Dic3)C22semidirect
36. #64101C22semidirect
37. C4⋊C4×C3⋊D3C22semidirect
38. #64090C22semidirect
39. C4×C4⋊(C3⋊D3)C22semidirect
40. C4×#634C22semidirect
41. C3×#926C22semidirect
42. C2×C3×C4⋊Dic3C22semidirect
43. C3×#892C22semidirect
44. C3×#892C22semidirect
45. C3×#892C22semidirect
48. C3×D3×C4⋊C4C22semidirect
49. C3×#67⋊C4C22semidirect
51. C3×#877C22semidirect
52. C3×C4×D12C22semidirect
53. C3×#872C22semidirect
55. C3×C4×Dic6C22semidirect
56. #67⋊Dic3C22semidirect
57. C2×Dic3⋊Dic3C22semidirect
58. #63952C22semidirect
60. C4×#627C22semidirect
61. C4×#626C22semidirect
62. #63902C22semidirect
63. #63900C22semidirect
64. #63894C22semidirect
65. Dic3×D12C22semidirect
68. D3×C4⋊Dic3C22semidirect
69. D3×C4⋊Dic3C22semidirect
70. D3×C4⋊Dic3C22semidirect
71. #63883C22semidirect
72. #63881C22semidirect
73. #63880C22semidirect
74. #63880C22semidirect
75. #63879C22semidirect
76. #63878C22semidirect
78. D3×Dic3⋊C4C22semidirect
80. #63849C22semidirect
81. #63844C22semidirect
82. Dic3×Dic6C22semidirect
83. #63841C22semidirect
84. #63837C22semidirect
85. #63836C22semidirect
109. #5523D3direct (N × H)
111. D3×#117D3semidirect
126. #3828C2×C4semidirect
134. C3×#235C2×C4semidirect
136. C2×C3×C4×D3C2×C4semidirect
146. D3×#67C2×C4semidirect
153. #3804C2×C4semidirect
160. D3×D12C2×C4semidirect
162. C4×D32C2×C4semidirect
163. #3799C2×C4semidirect
164. #3798C2×C4semidirect
165. #3795C2×C4semidirect
166. D3×Dic6C2×C4semidirect
239. C3×#117C2×D3semidirect
240. C3×#117C2×D3semidirect
255. #926C2×D3semidirect
265. C2×C4⋊Dic3C2×D3semidirect
280. #892C2×D3semidirect
281. #892C2×D3semidirect
282. #892C2×D3semidirect
299. D3×C4⋊C4C2×D3semidirect
313. #67⋊C4C2×D3semidirect
317. #877C2×D3semidirect
326. C4×D12C2×D3semidirect
328. #872C2×D3semidirect
339. C4×Dic6C2×D3semidirect
351. C2×C32×C4C22×C4semidirect
356. #638C22×C4semidirect
360. C4⋊(C3⋊D3)C22×C4semidirect
362. C4×C3⋊D3C22×C4semidirect
363. #634C22×C4semidirect
364. C3×#67C22×C4semidirect
366. C2×C3×Dic3C22×C4semidirect
373. C3×D12C22×C4semidirect
379. C3×C4×D3C22×C4semidirect
380. C3×C4×D3C22×C4semidirect
381. C3×C4×D3C22×C4semidirect
382. C3×Dic6C22×C4semidirect
383. #627C22×C4semidirect
384. #626C22×C4semidirect
385. #626C22×C4semidirect
386. #625C22×C4semidirect
388. #624C22×C4semidirect
393. D3×Dic3C22×C4semidirect
467. #235C4×D3semidirect
495. C2×C4×D3C4×D3semidirect
659. #117D32semidirect
728. C2×C3×C4C2×C4×D3semidirect
729. C2×C3×C4C2×C4×D3semidirect
745. #67C2×C4×D3semidirect
761. C2×Dic3C2×C4×D3semidirect
773. D12C2×C4×D3semidirect
794. C4×D3C2×C4×D3semidirect
795. C4×D3C2×C4×D3semidirect
796. C4×D3C2×C4×D3semidirect
802. Dic6C2×C4×D3semidirect
810. C3×D3#520semidirect
962. C32C2×#520semidirect
1012. C2×C4C4×D32semidirect
1037. D3#5523direct (N × H)
1069. C3C2×#5523semidirect
1070. C3D3×#520semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#2352
#105959942
C3×#55232
C3×D3×#1172
#105949922
#105949902
C2×D3×C4⋊Dic32
D3×#8922
D32×C4⋊C42
#105945112
#105945102
D3×#67⋊C42
#105940492
C4×D3×D122
#105938902
#105938872
C4×D3×Dic62
D3×#5203
C2×#55233