Finite Group Databasebeta

← D3×#5543 #11903246

Subgroups — D3×#5543 #11903246

Order 1152.

2514 conjugacy classes of subgroups.

The subgroup lattice has 970 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596014C211yesmaximal, characteristic, complemented
2C3×C4×D3×D4C211yesmaximal, characteristic
3C3×#5543C211yesmaximal, characteristic, complemented
4#10595272C212yesmaximal, complemented
5D3×D4×Dic3C212yesmaximal
6#10594993C212yesmaximal, complemented
7#10594988C212yesmaximal, complemented
8C2×D3×C4⋊Dic3C212yesmaximal, complemented
9D3×#924C212yesmaximal, complemented
10#10594452C212yesmaximal, complemented
11D3×#890C212yesmaximal, complemented
12#10594146C214yesmaximal, complemented
13D3×#878C214yesmaximal, complemented
14#10593960C211yesmaximal, characteristic, complemented
15#10593956C211yesmaximal, characteristic, complemented
16D3×#869C211yesmaximal, characteristic, complemented
17C4×D3×Dic6C211yesmaximal, characteristic, complemented
18D3×#554—31nomaximal
19C2×#5543—31nomaximal
20C2×C3×D3×D4C2211yescharacteristic
21C22×C3×C4×D3C2212yes—
22C22×D3×Dic3C2214yes—
23C2×D3×Dic6C2211yescharacteristic
24C2×D3×Dic6C2212yes—
25C32×C4×D4C2211yescharacteristic
26D4×C3⋊Dic3C2212yes—
27C2×C4⋊(C3⋊Dic3)C2212yescomplemented
28#64133C2212yescomplemented
29#64099C2212yescomplemented
30#64087C2214yescomplemented
31#64078C2211yescharacteristic, complemented
32C4×#634C2211yescharacteristic, complemented
33C3×D4×Dic3C2212yes—
34C3×D4×Dic3C2211yescharacteristic
35C3×C4×#67C2212yes—
36C2×C3×C4⋊Dic3C2212yescomplemented
37C3×#924C2212yescomplemented
38C3×#893C2211yescharacteristic
39C3×D3×C4⋊C4C2211yescharacteristic
40C3×#890C2212yescomplemented
41C3×#67⋊C4C2212yes—
42C3×D3×C22⋊C4C2212yes—
43C3×#878C2214yescomplemented
44C3×C4×D12C2211yescharacteristic
45C3×C42×D3C2211yescharacteristic
46C3×#869C2211yescharacteristic, complemented
47C3×C4×Dic6C2211yescharacteristic, complemented
48#63982C2214yescomplemented
49#67⋊Dic3C2214yes—
50Dic3×#67C2214yes—
51D3×#217C2214yes—
52C2×Dic3⋊Dic3C2214yescomplemented
53#63964C2214yescomplemented
54#63964C2214yescomplemented
55#63918C2212yescomplemented
56#63918C2212yescomplemented
57C4×#627C2212yescomplemented
58#63899C2214yescomplemented
59#63898C2212yes—
60#63896C2214yescomplemented
61#63893C2214yescomplemented
62Dic3×D12C2212yes—
63D3×C4⋊Dic3C2214yes—
64D3×C4⋊Dic3C2212yes—
65D3×C4⋊Dic3C2212yes—
66D3×C4⋊Dic3C2211yescharacteristic
67D3×C4⋊Dic3C2214yescomplemented
68D3×C4⋊Dic3C2212yescomplemented
69D3×C4⋊Dic3C2212yescomplemented
70#63887C2214yescomplemented
71D3×Dic3⋊C4C2212yes—
72D3×Dic3⋊C4C2214yes—
73C4×D3×Dic3C2212yes—
74#63872C2212yescomplemented
75#63869C2212yescomplemented
76#63866C2212yescomplemented
77#63857C2212yescomplemented
78#63856C2212yescomplemented
79#63851C2214yescomplemented
80#63846C2214yescomplemented
81#63845C2214yescomplemented
82#63844C2211yescharacteristic, complemented
83Dic3×Dic6C2211yescharacteristic, complemented
84#63837C2212yescomplemented
85C3×#554—31no—
86C2×C3×C4×D4—31no—
87C2×D4×Dic3—32no—
88C22×C4⋊Dic3—32no—
89C2×#924—32no—
90#5730—31no—
91D3×C4⋊Q8—31no—
92#5690—32no—
93D3×#125—32no—
94#5636—34no—
95#5635—32no—
96D3×C22⋊Q8—32no—
97D3×C22⋊Q8—34no—
98#5579—31no—
99C4×D3×Q8—31no—
100C4×D3×D4—32no—
101C4×D3×D4D311yescharacteristic
102#5543—31no—
103#5543—31no—
104#5543—32no—
105#5543—32no—
106#5543—32no—
107#5543—32no—
108#5543—34no—
109#5543—31no—
110#5543—31no—
111#5543—61no—
112#5543D311yescharacteristic, direct product factor
113#5539—32no—
114#5511—32no—
115C2×D3×C4⋊C4—32no—
116C2×#890—32no—
117C2×#878—34no—
118C2×#869—31no—
119C2×C4×Dic6—31no—
120C23×C3×D3C2312yes—
121C2×C32×D4C2311yescharacteristic
122C22×C32×C4C2312yes—
123C22×C3⋊Dic3C2314yes—
124C2×#634C2311yescharacteristic
125C2×#634C2312yes—
126C2×C3×#67C2312yes—
127C22×C3×Dic3C2312yes—
128C22×C3×Dic3C2314yes—
129C3×D3×D4Q818yescomplemented
130C2×C3×D12C2311yescharacteristic
131C2×C3×C4×D3—28no—
132C2×C3×C4×D3C2311yescharacteristic
133C2×C3×C4×D3C2312yes—
134C2×C3×C4×D3C2312yes—
135C2×C3×C4×D3C2312yes—
136C2×C3×C4×D3C2311yescharacteristic
137C2×C3×C4×D3C2311yescharacteristic
138C2×C3×Dic6C2311yescharacteristic
139C2×C3×Dic6C2312yes—
140C2×#627C2312yes—
141C2×#627C2314yes—
142C2×D3×Dic3—48no—
143C2×D3×Dic3C2314yes—
144C2×D3×Dic3C2312yes—
145C2×D3×Dic3C2312yes—
146C2×D3×Dic3C2314yes—
147C2×D3×Dic3C2314yes—
148D3×Dic6—24no—
149D3×Dic6—44no—
150C32×C4⋊C4C2311yescharacteristic
151C32×C22⋊C4C2312yes—
152C32×C42C2311yescharacteristic
153#3757C2314yes—
154C4⋊(C3⋊Dic3)C2311yescharacteristic
155C4⋊(C3⋊Dic3)C2312yes—
156C4⋊(C3⋊Dic3)C2312yes—
157C4⋊(C3⋊Dic3)C2314yes—
158#3750C2312yes—
159#3750C2314yes—
160C4×C3⋊Dic3C2312yes—
161C3×#217C2314yes—
162C3×#217C2312yes—
163C3×(C2×D3)⋊C4C2312yes—
164C3×(C2×D3)⋊C4C2312yes—
165C3×C4⋊Dic3C2314yes—
166C3×C4⋊Dic3C2312yes—
167C3×C4⋊Dic3C2311yescharacteristic
168C3×C4⋊Dic3C2312yes—
169C3×C4⋊Dic3C2311yescharacteristic
170C3×Dic3⋊C4C2312yes—
171C3×Dic3⋊C4C2314yes—
172C3×Dic3⋊C4C2312yes—
173C3×C4×Dic3C2311yescharacteristic
174C3×C4×Dic3C2312yes—
175C3×C4×Dic3C2311yescharacteristic
176C3×C4×Dic3C2311yescharacteristic
177#3724C2312yes—
178#3724C2314yes—
179Dic3⋊Dic3C2312yes—
180Dic3⋊Dic3C2312yes—
181Dic3⋊Dic3C2314yes—
182Dic3⋊Dic3C2314yes—
183Dic3⋊Dic3C2314yes—
184Dic3⋊Dic3C2314yes—
185Dic3⋊Dic3C2314yes—
186(C2×D3)⋊Dic3C2314yes—
187(C2×D3)⋊Dic3C2314yes—
188Dic32C2312yes—
189Dic32C2312yes—
190C2×#554—91noSylow
191C22×C3×D4—31no—
192C23×C3×C4—32no—
193C23×Dic3—34no—
194C2×D3×Q8—31no—
195C2×D3×Q8—32no—
196C2×D3×D4C2×D311yescharacteristic
197C22×C4×D3—34no—
198C22×C4×D3C2×D312yes—
199C22×Dic6—31no—
200C22×Dic6—32no—
201C3×C4⋊Q8—31no—
202C3×#125—32no—
203C3×C22⋊Q8—32no—
204C3×C22⋊Q8—34no—
205C3×C4×Q8—31no—
206C3×C4×D4—21no—
207C3×C4×D4—32no—
208C3×C4×D4—31no—
209C3×C4×D4—32no—
210C3×C4×D4—31no—
211C3×C4×D4—32no—
212C3×C4×D4—31no—
213C3×C4×D4C2×D311yescharacteristic
214C3×C4×D4C2×D311yescharacteristic
215C2×C3×C4⋊C4—32no—
216C2×C3×C4⋊C4—31no—
217C2×C3×C22⋊C4—32no—
218C2×C3×C42—31no—
219C2×#217—34no—
220#946—32no—
221#946—34no—
222Q8×Dic3—31no—
223#944—32no—
224D4×Dic3—32no—
225D4×Dic3—32no—
226D4×Dic3—34no—
227D4×Dic3—34no—
228D4×Dic3—32no—
229D4×Dic3—32no—
230D4×Dic3—62no—
231D4×Dic3C2×D311yescharacteristic
232D4×Dic3C2×D312yes—
233C4×#67—34no—
234C4×#67C2×D312yes—
235C2×C4⋊Dic3—32no—
236C2×C4⋊Dic3—32no—
237C2×C4⋊Dic3—34no—
238C2×C4⋊Dic3—31no—
239C2×C4⋊Dic3—32no—
240C2×C4⋊Dic3—32no—
241C2×C4⋊Dic3—34no—
242C2×C4⋊Dic3—32no—
243C2×C4⋊Dic3—32no—
244C2×C4⋊Dic3—34no—
245C2×C4⋊Dic3—62no—
246C2×C4⋊Dic3C2×D312yescomplemented
247#924—32no—
248#924—32no—
249#924—32no—
250#924—34no—
251#924—34no—
252#924—32no—
253#924—34no—
254#924—62no—
255#924C2×D312yescomplemented
256C2×Dic3⋊C4—34no—
257C2×Dic3⋊C4—32no—
258C2×Dic3⋊C4—34no—
259C2×C4×Dic3—32no—
260#897—32no—
261#897—34no—
262#896—34no—
263#896—34no—
264#896—34no—
265#893—32no—
266#893C2×D311yescharacteristic
267D3×C4⋊C4—32no—
268D3×C4⋊C4—34no—
269D3×C4⋊C4—32no—
270D3×C4⋊C4—34no—
271D3×C4⋊C4—34no—
272D3×C4⋊C4—32no—
273D3×C4⋊C4—31no—
274D3×C4⋊C4—32no—
275D3×C4⋊C4—32no—
276D3×C4⋊C4C2×D311yescharacteristic
277#890—32no—
278#890—32no—
279#890—32no—
280#890—34no—
281#890—32no—
282#890—34no—
283#890—32no—
284#890—62no—
285#890C2×D312yescomplemented
286#889—34no—
287#889—34no—
288#888—32no—
289#888—32no—
290#887—32no—
291#887—31no—
292#67⋊C4—34no—
293#67⋊C4C2×D312yes—
294D3×C22⋊C4—34no—
295D3×C22⋊C4C2×D312yes—
296#878—34no—
297#878—34no—
298#878—34no—
299#878—34no—
300#878—34no—
301#878—34no—
302#878—34no—
303#878—34no—
304#878—34no—
305#878—34no—
306#878—64no—
307#878C2×D314yescomplemented
308C4×D12—32no—
309C4×D12C2×D311yescharacteristic
310C42×D3—32no—
311C42×D3C2×D311yescharacteristic
312#870—32no—
313#869—32no—
314#869—31no—
315#869—31no—
316#869—32no—
317#869—32no—
318#869—61no—
319#869C2×D311yescharacteristic, complemented
320C4×Dic6—31no—
321C4×Dic6—31no—
322C4×Dic6—31no—
323C4×Dic6—31no—
324C4×Dic6—32no—
325C4×Dic6—32no—
326C4×Dic6—32no—
327C4×Dic6—61no—
328C4×Dic6C2×D311yescharacteristic, complemented
329C23×C32C2412yes—
330C22×C3×D3—24no—
331C22×C3×D3—24no—
332C22×C3×D3C2×Q818yes—
333C22×C3×D3C2412yes—
334C22×C3×D3C2411yescharacteristic
335C32×D4C2×Q814yescomplemented
336C2×C32×C4—24no—
337C2×C32×C4C2411yescharacteristic
338C2×C32×C4C2412yes—
339C2×C32×C4C2411yescharacteristic
340C2×C32×C4C2411yescharacteristic
341C2×C3⋊Dic3—44no—
342C2×C3⋊Dic3C2412yes—
343C2×C3⋊Dic3C2412yes—
344C2×C3⋊Dic3C2414yes—
345#634—22no—
346#634—42no—
347C3×#67C2×Q818yescomplemented
348C2×C3×Dic3—24no—
349C2×C3×Dic3—44no—
350C2×C3×Dic3C2412yes—
351C2×C3×Dic3C2412yes—
352C2×C3×Dic3C2414yes—
353C2×C3×Dic3C2412yes—
354C2×C3×Dic3C2411yescharacteristic
355C2×C3×Dic3C2411yescharacteristic
356C2×C3×Dic3C2411yescharacteristic
357C3×D12C2×Q814yescomplemented
358C3×C4×D3—24no—
359C3×C4×D3—22no—
360C3×C4×D3—24no—
361C3×C4×D3—24no—
362C3×C4×D3C2×Q814yes—
363C3×C4×D3#4114yes—
364C3×Dic6—22no—
365C3×Dic6—42no—
366#627—24no—
367#627—44no—
368D3×Dic3—24no—
369D3×Dic3—28no—
370D3×Dic3—24no—
371D3×Dic3—44no—
372D3×Dic3—44no—
373#554—31no—
374#554—92no—
375#554—92no—
376#554—91no—
377#554—92no—
378#554—94no—
379#554—92no—
380#554—91no—
381#554—91no—
382C2×C4⋊Q8—91no—
383C2×#125—92no—
384C2×C22⋊Q8—94no—
385C2×C22⋊Q8—92no—
386C2×C4×Q8—91no—
387C2×C4×D4—31no—
388C2×C4×D4—92no—
389C22×C4⋊C4—92no—
390C24×C3—32no—
391C23×D3C22×D312yes—
392C2×C3×Q8—31no—
393C2×C3×Q8—32no—
394C2×C3×D4—21no—
395C2×C3×D4—32no—
396C2×C3×D4—38no—
397C2×C3×D4—31no—
398C2×C3×D4C22×D311yescharacteristic
399C2×C3×D4C22×D311yescharacteristic
400C22×C3×C4—22no—
401C22×C3×C4—31no—
402C22×C3×C4—31no—
403C22×C3×C4—32no—
404C22×C3×C4—34no—
405C22×C3×C4—32no—
406C22×C3×C4—31no—
407C22×C3×C4—32no—
408C22×C3×C4—32no—
409C22×C3×C4—68no—
410C22×C3×C4C22×D312yes—
411C22×C3×C4C22×D312yes—
412C2×#67C22×D312yes—
413C22×Dic3—34no—
414C22×Dic3—34no—
415C22×Dic3—32no—
416C22×Dic3—32no—
417C22×Dic3—34no—
418C22×Dic3—34no—
419C22×Dic3—34no—
420C22×Dic3—64no—
421C22×Dic3—128no—
422C22×Dic3C22×D312yes—
423C22×Dic3C22×D314yes—
424D3×Q8—64no—
425D3×Q8—124no—
426D3×D4Dic618yescomplemented
427C2×D12C22×D311yescharacteristic
428C2×C4×D3—28no—
429C2×C4×D3—32no—
430C2×C4×D3—32no—
431C2×C4×D3—34no—
432C2×C4×D3—34no—
433C2×C4×D3—34no—
434C2×C4×D3—128no—
435C2×C4×D3C22×D311yescharacteristic
436C2×C4×D3C22×D312yes—
437C2×C4×D3C22×D312yes—
438C2×C4×D3C22×D312yes—
439C2×C4×D3C22×D311yescharacteristic
440C2×C4×D3C22×D311yescharacteristic
441C2×Dic6—31no—
442C2×Dic6—31no—
443C2×Dic6—32no—
444C2×Dic6—32no—
445C2×Dic6—32no—
446C2×Dic6—32no—
447C2×Dic6—34no—
448C2×Dic6—34no—
449C2×Dic6—61no—
450C2×Dic6—62no—
451C2×Dic6—64no—
452C2×Dic6—124no—
453C2×Dic6C22×D311yescharacteristic
454C2×Dic6C22×D312yes—
455C3×C4⋊C4—21no—
456C3×C4⋊C4—31no—
457C3×C4⋊C4—32no—
458C3×C4⋊C4—32no—
459C3×C4⋊C4—32no—
460C3×C4⋊C4—34no—
461C3×C4⋊C4—34no—
462C3×C4⋊C4—32no—
463C3×C4⋊C4—31no—
464C3×C4⋊C4C22×D311yescharacteristic
465C3×C4⋊C4C22×D311yescharacteristic
466C3×C22⋊C4—22no—
467C3×C22⋊C4—32no—
468C3×C22⋊C4—34no—
469C3×C22⋊C4—32no—
470C3×C22⋊C4—32no—
471C3×C22⋊C4C22×D312yes—
472C3×C22⋊C4C22×D312yes—
473C3×C42—21no—
474C3×C42—31no—
475C3×C42—31no—
476C3×C42—31no—
477C3×C42—32no—
478C3×C42C22×D311yescharacteristic
479C3×C42C22×D311yescharacteristic
480#217—34no—
481#217—34no—
482#217—34no—
483#217—34no—
484#217—64no—
485#217C22×D312yes—
486#217C22×D314yes—
487(C2×D3)⋊C4—34no—
488(C2×D3)⋊C4—34no—
489(C2×D3)⋊C4C22×D312yes—
490(C2×D3)⋊C4C22×D312yes—
491C4⋊Dic3—31no—
492C4⋊Dic3—31no—
493C4⋊Dic3—32no—
494C4⋊Dic3—32no—
495C4⋊Dic3—32no—
496C4⋊Dic3—32no—
497C4⋊Dic3—34no—
498C4⋊Dic3—34no—
499C4⋊Dic3—32no—
500C4⋊Dic3—32no—
501C4⋊Dic3—34no—
502C4⋊Dic3—34no—
503C4⋊Dic3—34no—
504C4⋊Dic3—34no—
505C4⋊Dic3—34no—
506C4⋊Dic3—61no—
507C4⋊Dic3—62no—
508C4⋊Dic3—62no—
509C4⋊Dic3—64no—
510C4⋊Dic3C22×D311yescharacteristic
511C4⋊Dic3C22×D312yes—
512C4⋊Dic3C22×D312yes—
513C4⋊Dic3C22×D311yescharacteristic
514C4⋊Dic3C22×D314yes—
515Dic3⋊C4—32no—
516Dic3⋊C4—32no—
517Dic3⋊C4—34no—
518Dic3⋊C4—34no—
519Dic3⋊C4—32no—
520Dic3⋊C4—32no—
521Dic3⋊C4—32no—
522Dic3⋊C4—32no—
523Dic3⋊C4—34no—
524Dic3⋊C4—34no—
525Dic3⋊C4—34no—
526Dic3⋊C4—34no—
527Dic3⋊C4—34no—
528Dic3⋊C4—34no—
529Dic3⋊C4—34no—
530Dic3⋊C4—62no—
531Dic3⋊C4—64no—
532Dic3⋊C4C22×D312yes—
533Dic3⋊C4C22×D314yes—
534Dic3⋊C4C22×D312yes—
535C4×Dic3—32no—
536C4×Dic3—32no—
537C4×Dic3—32no—
538C4×Dic3—32no—
539C4×Dic3—32no—
540C4×Dic3—32no—
541C4×Dic3—62no—
542C4×Dic3C22×D311yescharacteristic
543C4×Dic3C22×D312yes—
544C4×Dic3C22×D311yescharacteristic
545C4×Dic3C22×D311yescharacteristic
546C22×C32—22no—
547C22×C32—22no—
548C22×C32C22×Q814yes—
549C22×C32C2511yescharacteristic
550C2×C3×D3—22no—
551C2×C3×D3—22no—
552C2×C3×D3—216no—
553C2×C3×D3C22×Q814yes—
554C2×C3×D3C22×Q812yes—
555C2×C3×D3C2×#4112yes—
556C2×C3×D3H(5,𝔽2)12yes—
557C32×C4—22no—
558C32×C4—21no—
559C32×C4C22×Q812yes—
560C32×C4C2×#4112yes—
561C3⋊Dic3—22no—
562C3⋊Dic3—22no—
563C3⋊Dic3—24no—
564C3×Dic3—22no—
565C3×Dic3—22no—
566C3×Dic3—22no—
567C3×Dic3—24no—
568C3×Dic3—21no—
569C3×Dic3C22×Q812yes—
570C3×Dic3C2×#4112yes—
571C22×Q8—91no—
572C22×Q8—92no—
573C22×D4—31no—
574C23×C4—32no—
575C23×C4—94no—
576C4⋊Q8—31no—
577C4⋊Q8—92no—
578C4⋊Q8—92no—
579C4⋊Q8—92no—
580C4⋊Q8—91no—
581#125—32no—
582#125—92no—
583#125—94no—
584#125—94no—
585#125—92no—
586#125—92no—
587C22⋊Q8—32no—
588C22⋊Q8—34no—
589C22⋊Q8—94no—
590C22⋊Q8—94no—
591C22⋊Q8—94no—
592C22⋊Q8—94no—
593C22⋊Q8—94no—
594C22⋊Q8—94no—
595C22⋊Q8—94no—
596C22⋊Q8—94no—
597C22⋊Q8—92no—
598C22⋊Q8—92no—
599C22⋊Q8—92no—
600C22⋊Q8—94no—
601C4×Q8—31no—
602C4×Q8—92no—
603C4×Q8—91no—
604C4×Q8—92no—
605C4×Q8—91no—
606C4×Q8—91no—
607C4×D4—31no—
608C4×D4—32no—
609C4×D4—32no—
610C4×D4—31no—
611C4×D4—32no—
612C4×D4—31no—
613C4×D4—92no—
614C4×D4—94no—
615C4×D4—92no—
616C4×D4—94no—
617C4×D4—92no—
618C4×D4D3211yescharacteristic
619C2×C4⋊C4—32no—
620C2×C4⋊C4—31no—
621C2×C4⋊C4—91no—
622C2×C4⋊C4—94no—
623C2×C4⋊C4—92no—
624C2×C4⋊C4—92no—
625C2×C4⋊C4—94no—
626C2×C4⋊C4—92no—
627C2×C4⋊C4—92no—
628C2×C4⋊C4—92no—
629C2×C4⋊C4—94no—
630C2×C4⋊C4—94no—
631C2×C4⋊C4—92no—
632C2×C22⋊C4—32no—
633C2×C22⋊C4—94no—
634C2×C42—31no—
635C2×C42—92no—
636C23×C3—22no—
637C23×C3—31no—
638C23×C3—38no—
639C23×C3—32no—
640C23×C3—64no—
641C23×C3—64no—
642C23×C3C23×D312yes—
643C23×C3C23×D312yes—
644C22×D3—24no—
645C22×D3—24no—
646C22×D3C2×Dic618yes—
647C22×D3C23×D312yes—
648C22×D3C23×D311yescharacteristic
649C3×Q8—62no—
650C3×Q8—122no—
651C3×D4—24no—
652C3×D4—38no—
653C3×D4—34no—
654C3×D4C2×Dic614yescomplemented
655C3×D4D3×Q814yescomplemented
656C2×C3×C4—24no—
657C2×C3×C4—24no—
658C2×C3×C4—21no—
659C2×C3×C4—21no—
660C2×C3×C4—22no—
661C2×C3×C4—21no—
662C2×C3×C4—31no—
663C2×C3×C4—31no—
664C2×C3×C4—34no—
665C2×C3×C4—34no—
666C2×C3×C4—32no—
667C2×C3×C4—32no—
668C2×C3×C4—32no—
669C2×C3×C4—31no—
670C2×C3×C4—34no—
671C2×C3×C4—44no—
672C2×C3×C4—64no—
673C2×C3×C4—62no—
674C2×C3×C4—64no—
675C2×C3×C4—64no—
676C2×C3×C4—64no—
677C2×C3×C4—124no—
678C2×C3×C4C23×D311yescharacteristic
679C2×C3×C4C23×D312yes—
680C2×C3×C4C23×D311yescharacteristic
681C2×C3×C4C23×D312yes—
682C2×C3×C4C23×D311yescharacteristic
683C2×C3×C4C23×D311yescharacteristic
684C2×C3×C4C23×D311yescharacteristic
685C2×C3×C4C23×D311yescharacteristic
686#67C2×Dic618yescomplemented
687C2×Dic3—24no—
688C2×Dic3—32no—
689C2×Dic3—32no—
690C2×Dic3—32no—
691C2×Dic3—32no—
692C2×Dic3—34no—
693C2×Dic3—34no—
694C2×Dic3—44no—
695C2×Dic3—62no—
696C2×Dic3—62no—
697C2×Dic3—64no—
698C2×Dic3—64no—
699C2×Dic3—68no—
700C2×Dic3—64no—
701C2×Dic3—124no—
702C2×Dic3—124no—
703C2×Dic3—124no—
704C2×Dic3—124no—
705C2×Dic3—244no—
706C2×Dic3C23×D312yes—
707C2×Dic3C23×D312yes—
708C2×Dic3C23×D311yescharacteristic
709C2×Dic3C23×D312yes—
710C2×Dic3C23×D314yes—
711C2×Dic3C23×D311yescharacteristic
712C2×Dic3C23×D311yescharacteristic
713D12C2×Dic614yescomplemented
714C4×D3—24no—
715C4×D3—22no—
716C4×D3—24no—
717C4×D3—24no—
718C4×D3—64no—
719C4×D3—64no—
720C4×D3—68no—
721C4×D3—124no—
722C4×D3—124no—
723C4×D3C2×Dic614yes—
724C4×D3#23714yes—
725Dic6—22no—
726Dic6—42no—
727Dic6—64no—
728Dic6—62no—
729Dic6—62no—
730Dic6—64no—
731Dic6—122no—
732Dic6—124no—
733Dic6—124no—
734Dic6—122no—
735Dic6—122no—
736Dic6—242no—
737C2×C32—24no—
738C2×C32C23×Q811yescharacteristic
739C2×C32C22×#4111yescharacteristic
740C2×C32C2×H(5,𝔽2)11yescharacteristic
741C3×D3—24no—
742C3×D3#55414yescomplemented
743C24—32no—
744C2×Q8—31no—
745C2×Q8—32no—
746C2×Q8—92no—
747C2×Q8—94no—
748C2×Q8—91no—
749C2×Q8—92no—
750C2×Q8—184no—
751C2×Q8—364no—
752C2×D4—32no—
753C2×D4—38no—
754C2×D4—31no—
755C2×D4C2×D3211yescharacteristic
756C22×C4—31no—
757C22×C4—31no—
758C22×C4—32no—
759C22×C4—34no—
760C22×C4—31no—
761C22×C4—32no—
762C22×C4—32no—
763C22×C4—32no—
764C22×C4—68no—
765C22×C4—92no—
766C22×C4—92no—
767C22×C4—94no—
768C22×C4—94no—
769C22×C4—94no—
770C22×C4—94no—
771C22×C4—368no—
772C22×C4C2×D3212yes—
773C4⋊C4—31no—
774C4⋊C4—34no—
775C4⋊C4—32no—
776C4⋊C4—32no—
777C4⋊C4—31no—
778C4⋊C4—32no—
779C4⋊C4—32no—
780C4⋊C4—34no—
781C4⋊C4—92no—
782C4⋊C4—94no—
783C4⋊C4—94no—
784C4⋊C4—94no—
785C4⋊C4—94no—
786C4⋊C4—92no—
787C4⋊C4—92no—
788C4⋊C4—94no—
789C4⋊C4—94no—
790C4⋊C4—91no—
791C4⋊C4—94no—
792C4⋊C4—92no—
793C4⋊C4—92no—
794C4⋊C4—92no—
795C4⋊C4—94no—
796C4⋊C4C2×D3211yescharacteristic
797C22⋊C4—32no—
798C22⋊C4—34no—
799C22⋊C4—32no—
800C22⋊C4—32no—
801C22⋊C4—94no—
802C22⋊C4—94no—
803C22⋊C4—94no—
804C22⋊C4C2×D3212yes—
805C42—31no—
806C42—31no—
807C42—31no—
808C42—32no—
809C42—92no—
810C42—92no—
811C42—92no—
812C42C2×D3211yescharacteristic
813C22×C3—22no—
814C22×C3—22no—
815C22×C3—22no—
816C22×C3—22no—
817C22×C3—24no—
818C22×C3—21no—
819C22×C3—32no—
820C22×C3—32no—
821C22×C3—32no—
822C22×C3—34no—
823C22×C3—42no—
824C22×C3—42no—
825C22×C3—616no—
826C22×C3—62no—
827C22×C3—62no—
828C22×C3C22×Dic614yes—
829C22×C3C2×D3×Q814yes—
830C22×C3C24×D311yescharacteristic
831C22×C3C24×D311yescharacteristic
832C2×D3—22no—
833C2×D3—22no—
834C2×D3—216no—
835C2×D3C22×Dic614yes—
836C2×D3C22×Dic612yes—
837C2×D3C2×#23712yes—
838C2×D3#100912yes—
839C3×C4—22no—
840C3×C4—22no—
841C3×C4—21no—
842C3×C4—21no—
843C3×C4—22no—
844C3×C4—22no—
845C3×C4—32no—
846C3×C4—32no—
847C3×C4—41no—
848C3×C4—42no—
849C3×C4—62no—
850C3×C4—62no—
851C3×C4—64no—
852C3×C4—62no—
853C3×C4—61no—
854C3×C4C22×Dic612yes—
855C3×C4C2×#23712yes—
856C3×C4C2×D3×Q812yes—
857C3×C4D3×#4112yes—
858Dic3—22no—
859Dic3—22no—
860Dic3—21no—
861Dic3—24no—
862Dic3—22no—
863Dic3—62no—
864Dic3—62no—
865Dic3—64no—
866Dic3—62no—
867Dic3—64no—
868Dic3—62no—
869Dic3—122no—
870Dic3—124no—
871Dic3—122no—
872Dic3C22×Dic612yes—
873Dic3C2×#23712yes—
874C32C2×#55411yescharacteristic, complemented, Sylow
875C23—31no—
876C23—38no—
877C23—32no—
878C23—64no—
879C23—64no—
880C23C22×D3212yes—
881Q8—62no—
882Q8—122no—
883Q8—184no—
884Q8—182no—
885Q8—362no—
886Q8—364no—
887D4—38no—
888D4—34no—
889D4D3×Dic614yescomplemented
890C2×C4—24no—
891C2×C4—31no—
892C2×C4—31no—
893C2×C4—34no—
894C2×C4—34no—
895C2×C4—31no—
896C2×C4—32no—
897C2×C4—32no—
898C2×C4—32no—
899C2×C4—34no—
900C2×C4—64no—
901C2×C4—64no—
902C2×C4—62no—
903C2×C4—64no—
904C2×C4—64no—
905C2×C4—92no—
906C2×C4—92no—
907C2×C4—94no—
908C2×C4—124no—
909C2×C4—184no—
910C2×C4—188no—
911C2×C4—184no—
912C2×C4—364no—
913C2×C4—364no—
914C2×C4—364no—
915C2×C4C22×D3211yescharacteristic
916C2×C4C22×D3212yes—
917C2×C4C22×D3211yescharacteristic
918C2×C4C22×D3211yescharacteristic
919C2×C3—24no—
920C2×C3—24no—
921C2×C3—21no—
922C2×C3—21no—
923C2×C3—21no—
924C2×C3—34no—
925C2×C3—44no—
926C2×C3—64no—
927C2×C3C23×Dic611yescharacteristic
928C2×C3C22×#23711yescharacteristic
929C2×C3C22×D3×Q811yescharacteristic
930C2×C3C2×D3×#4111yescharacteristic
931C2×C3C2×#100911yescharacteristic
932C2×C3D3×H(5,𝔽2)11yescharacteristic
933D3—24no—
934D3#554314yesdirect product factor
935C22—22no—
936C22—22no—
937C22—32no—
938C22—32no—
939C22—32no—
940C22—34no—
941C22—616no—
942C22—62no—
943C22—62no—
944C22C2×D3×Dic614yes—
945C22C23×D3211yescharacteristic
946C4—22no—
947C4—21no—
948C4—32no—
949C4—32no—
950C4—62no—
951C4—62no—
952C4—61no—
953C4—62no—
954C4—64no—
955C4—182no—
956C4—182no—
957C4—184no—
958C4C2×D3×Dic612yes—
959C4D3×#23712yes—
960C3—21no—
961C3C2×#554311yescharacteristic, complemented
962C3D3×#55411yescharacteristic, complemented
963C2—24no—
964C2—34no—
965C2—64no—
966C2C22×D3×Dic611yescharacteristic
967C2C2×D3×#23711yescharacteristic
968C2D3×#100911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×D4C22
prime radicalC2×C3×D3×D4C22
hypercenterC4×D4D32
hypocenterC32C2×#554
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #10596014C2semidirect
3. C3×#5543C2semidirect
4. #10595272C2semidirect
6. #10594993C2semidirect
7. #10594988C2semidirect
8. C2×D3×C4⋊Dic3C2semidirect
9. D3×#924C2semidirect
10. #10594452C2semidirect
11. D3×#890C2semidirect
12. #10594146C2semidirect
13. D3×#878C2semidirect
14. #10593960C2semidirect
15. #10593956C2semidirect
16. D3×#869C2semidirect
17. C4×D3×Dic6C2semidirect
27. C2×C4⋊(C3⋊Dic3)C22semidirect
28. #64133C22semidirect
29. #64099C22semidirect
30. #64087C22semidirect
31. #64078C22semidirect
32. C4×#634C22semidirect
36. C2×C3×C4⋊Dic3C22semidirect
37. C3×#924C22semidirect
40. C3×#890C22semidirect
43. C3×#878C22semidirect
46. C3×#869C22semidirect
47. C3×C4×Dic6C22semidirect
48. #63982C22semidirect
52. C2×Dic3⋊Dic3C22semidirect
53. #63964C22semidirect
54. #63964C22semidirect
55. #63918C22semidirect
56. #63918C22semidirect
57. C4×#627C22semidirect
58. #63899C22semidirect
60. #63896C22semidirect
61. #63893C22semidirect
67. D3×C4⋊Dic3C22semidirect
68. D3×C4⋊Dic3C22semidirect
69. D3×C4⋊Dic3C22semidirect
70. #63887C22semidirect
74. #63872C22semidirect
75. #63869C22semidirect
76. #63866C22semidirect
77. #63857C22semidirect
78. #63856C22semidirect
79. #63851C22semidirect
80. #63846C22semidirect
81. #63845C22semidirect
82. #63844C22semidirect
83. Dic3×Dic6C22semidirect
84. #63837C22semidirect
112. #5543D3direct (N × H)
129. C3×D3×D4Q8semidirect
246. C2×C4⋊Dic3C2×D3semidirect
255. #924C2×D3semidirect
285. #890C2×D3semidirect
307. #878C2×D3semidirect
319. #869C2×D3semidirect
328. C4×Dic6C2×D3semidirect
335. C32×D4C2×Q8semidirect
347. C3×#67C2×Q8semidirect
357. C3×D12C2×Q8semidirect
426. D3×D4Dic6semidirect
654. C3×D4C2×Dic6semidirect
655. C3×D4D3×Q8semidirect
686. #67C2×Dic6semidirect
713. D12C2×Dic6semidirect
742. C3×D3#554semidirect
874. C32C2×#554semidirect
889. D4D3×Dic6semidirect
934. D3#5543direct (N × H)
961. C3C2×#5543semidirect
962. C3D3×#554semidirect

Maximal subgroups

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

subgroupindex
#105960142
C3×C4×D3×D42
C3×#55432
#105952722
D3×D4×Dic32
#105949932
#105949882
C2×D3×C4⋊Dic32
D3×#9242
#105944522
D3×#8902
#105941462
D3×#8782
#105939602
#105939562
D3×#8692
C4×D3×Dic62
D3×#5543
C2×#55433