Finite Group Databasebeta

← D3×#5579 #11903244

Subgroups — D3×#5579 #11903244

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#10596050C211yesmaximal, characteristic, complemented
2C3×#5579C211yesmaximal, characteristic, complemented
3C3×C4×D3×Q8C211yesmaximal, characteristic, complemented
4D3×#946C212yesmaximal, complemented
5#10595371C212yesmaximal, complemented
6D3×#896C214yesmaximal, complemented
7D32×C4⋊C4C212yesmaximal, complemented
8#10594536C212yesmaximal, complemented
9#10594392C214yesmaximal, complemented
10C4×D3×D12C211yesmaximal, characteristic
11C4×D3×D12C212yesmaximal
12#10593960C211yesmaximal, characteristic, complemented
13#10593958C211yesmaximal, characteristic, complemented
14#10593938C212yesmaximal, complemented
15#10593929C212yesmaximal, complemented
16D3×#870C212yesmaximal, complemented
17D3×#869C211yesmaximal, characteristic, complemented
18D3×#554—31nomaximal
19C2×#5579—31nomaximal
20C2×C3×D3×Q8C2211yescharacteristic
21C2×D3×D12C2211yescharacteristic
22C2×C4×D32C2212yes—
23C2×C4×D32C2214yes—
24C2×D3×Dic6C2212yes—
25C32×C4×Q8C2211yescharacteristic, complemented
26#64155C2212yescomplemented
27#64105C2214yescomplemented
28C4⋊C4×C3⋊D3C2212yescomplemented
29C4×C4⋊(C3⋊D3)C2212yes—
30C4×C4⋊(C3⋊D3)C2211yescharacteristic
31#64079C2212yescomplemented
32#64078C2211yescharacteristic, complemented
33C3×#946C2212yescomplemented
34C3×Q8×Dic3C2211yescharacteristic, complemented
35C3×#896C2214yescomplemented
36C3×D3×C4⋊C4C2211yescharacteristic
37C3×D3×C4⋊C4C2212yes—
38C3×D3×C4⋊C4C2212yescomplemented
39C3×#887C2212yescomplemented
40C3×#887C2211yescharacteristic, complemented
41C3×C4×D12C2212yes—
42C3×C4×D12C2211yescharacteristic
43C3×C42×D3C2211yescharacteristic
44C3×C42×D3C2212yes—
45C3×#870C2212yescomplemented
46C3×#869C2211yescharacteristic, complemented
47C3×C4×Dic6C2212yescomplemented
48C3×C4×Dic6C2211yescharacteristic, complemented
49D3×(C2×D3)⋊C4C2212yes—
50D3×(C2×D3)⋊C4C2214yes—
51#63918C2212yescomplemented
52#63918C2212yescomplemented
53C4×#626C2212yes—
54C4×#626C2214yes—
55#63900C2212yescomplemented
56#63899C2214yescomplemented
57#63896C2214yescomplemented
58#63895C2214yescomplemented
59#63894C2211yescharacteristic
60#63894C2212yes—
61Dic3×D12C2211yescharacteristic
62Dic3×D12C2212yes—
63D3×C4⋊Dic3C2212yes—
64D3×C4⋊Dic3C2212yes—
65D3×C4⋊Dic3C2211yescharacteristic
66D3×C4⋊Dic3C2212yescomplemented
67#63888C2214yescomplemented
68#63888C2214yescomplemented
69#63887C2214yescomplemented
70#63883C2214yescomplemented
71#63880C2214yes—
72#63880C2212yes—
73D3×Dic3⋊C4C2214yes—
74D3×Dic3⋊C4C2214yes—
75D3×Dic3⋊C4C2214yescomplemented
76#63871C2212yescomplemented
77#63869C2212yescomplemented
78#63869C2212yescomplemented
79#63867C2214yescomplemented
80#63867C2214yescomplemented
81#63866C2212yescomplemented
82#63865C2214yescomplemented
83#63856C2212yescomplemented
84#63851C2214yescomplemented
85C3×#554—31no—
86C2×C3×C4×Q8—31no—
87C2×#946—32no—
88#5730—31no—
89D3×C4⋊Q8—31no—
90#5690—32no—
91D3×#125—32no—
92#5636—34no—
93#5635—32no—
94D3×C22⋊Q8—32no—
95D3×C22⋊Q8—34no—
96#5579—31no—
97#5579—31no—
98#5579—32no—
99#5579—34no—
100#5579—32no—
101#5579—32no—
102#5579—31no—
103#5579—32no—
104#5579—31no—
105#5579—61no—
106#5579D311yescharacteristic, direct product factor
107C4×D3×Q8D311yescharacteristic, complemented
108C4×D3×D4—32no—
109C4×D3×D4—31no—
110#5543—31no—
111#5539—32no—
112#5511—32no—
113C2×#896—34no—
114C2×D3×C4⋊C4—32no—
115C2×D3×C4⋊C4—32no—
116C2×C4×D12—32no—
117C2×C4×D12—31no—
118C2×#870—32no—
119C2×#869—31no—
120C22×D32C2312yes—
121C2×C32×Q8C2311yescharacteristic
122C2×C4⋊(C3⋊D3)C2311yescharacteristic
123C2×C4×C3⋊D3C2312yes—
124C2×C4×C3⋊D3C2314yes—
125C2×#634C2312yes—
126C3×D3×Q8—24no—
127C2×C3×D12C2311yescharacteristic
128C2×C3×C4×D3C2311yescharacteristic
129C2×C3×C4×D3C2312yes—
130C2×C3×C4×D3C2312yes—
131C2×C3×C4×D3C2312yes—
132C2×C3×C4×D3C2314yes—
133C2×C3×C4×D3C2311yescharacteristic
134C2×C3×C4×D3C2311yescharacteristic
135C2×C3×Dic6C2311yescharacteristic
136C2×C3×Dic6C2312yes—
137C2×C3×Dic6C2312yes—
138C2×#627C2314yes—
139C2×#626C2312yes—
140C2×#624C2312yes—
141C2×#624C2314yes—
142C2×D3×Dic3C2314yes—
143C2×D3×Dic3C2312yes—
144C2×D3×Dic3C2312yes—
145C2×D3×Dic3C2314yes—
146D3×D12Q818yescomplemented
147C4×D32—28no—
148C4×D32—48no—
149D3×Dic6—44no—
150C32×C4⋊C4C2311yescharacteristic
151C32×C4⋊C4C2312yes—
152C32×C42C2311yescharacteristic
153C32×C42C2312yes—
154#3752C2312yes—
155#3752C2314yes—
156C4⋊(C3⋊Dic3)C2312yes—
157C4⋊(C3⋊Dic3)C2312yes—
158C4⋊(C3⋊Dic3)C2311yescharacteristic
159#3750C2314yes—
160#3750C2314yes—
161C3×(C2×D3)⋊C4C2312yes—
162C3×(C2×D3)⋊C4C2314yes—
163C3×C4⋊Dic3C2311yescharacteristic
164C3×C4⋊Dic3C2312yes—
165C3×C4⋊Dic3C2312yes—
166C3×C4⋊Dic3C2311yescharacteristic
167C3×C4⋊Dic3C2312yes—
168C3×Dic3⋊C4C2312yes—
169C3×Dic3⋊C4C2312yes—
170C3×Dic3⋊C4C2312yes—
171C3×Dic3⋊C4C2314yes—
172C3×Dic3⋊C4C2314yes—
173C3×C4×Dic3C2311yescharacteristic
174C3×C4×Dic3C2312yes—
175C3×C4×Dic3C2312yes—
176C3×C4×Dic3C2311yescharacteristic
177C3×C4×Dic3C2312yes—
178C3×C4×Dic3C2311yescharacteristic
179#3724C2314yes—
180#3724C2314yes—
181Dic3⋊Dic3C2314yes—
182Dic3⋊Dic3C2314yes—
183Dic3⋊Dic3C2314yes—
184Dic3⋊Dic3C2312yes—
185Dic3⋊Dic3C2314yes—
186#3722C2312yes—
187#3722C2314yes—
188(C2×D3)⋊Dic3C2312yes—
189(C2×D3)⋊Dic3C2314yes—
190C2×#554—91noSylow
191C22×C3×Q8—31no—
192C2×D3×Q8—32no—
193C2×D3×Q8C2×D311yescharacteristic
194C2×D3×D4—31no—
195C22×D12—31no—
196C22×C4×D3—32no—
197C22×C4×D3—32no—
198C22×C4×D3—34no—
199C22×C4×D3—34no—
200C22×Dic6—32no—
201C3×C4⋊Q8—31no—
202C3×#125—32no—
203C3×C22⋊Q8—32no—
204C3×C22⋊Q8—34no—
205C3×C4×Q8—21no—
206C3×C4×Q8—31no—
207C3×C4×Q8—32no—
208C3×C4×Q8—31no—
209C3×C4×Q8—32no—
210C3×C4×Q8—31no—
211C3×C4×Q8C2×D311yescharacteristic, complemented
212C3×C4×Q8C2×D311yescharacteristic, complemented
213C3×C4×D4—32no—
214C3×C4×D4—31no—
215C2×C3×C4⋊C4—31no—
216C2×C3×C4⋊C4—32no—
217C2×C3×C4⋊C4—32no—
218C2×C3×C42—31no—
219C2×C3×C42—32no—
220#946—32no—
221#946—32no—
222#946—32no—
223#946—34no—
224#946—32no—
225#946—34no—
226#946—34no—
227#946—62no—
228#946C2×D312yescomplemented
229Q8×Dic3C2×D311yescharacteristic, complemented
230#944—32no—
231D4×Dic3—31no—
232D4×Dic3—32no—
233C4×#67—32no—
234C4×#67—34no—
235C2×(C2×D3)⋊C4—32no—
236C2×(C2×D3)⋊C4—34no—
237C2×C4⋊Dic3—32no—
238C2×C4⋊Dic3—32no—
239C2×C4⋊Dic3—32no—
240C2×C4⋊Dic3—31no—
241#924—32no—
242#924—34no—
243C2×Dic3⋊C4—34no—
244C2×Dic3⋊C4—34no—
245C2×Dic3⋊C4—34no—
246#897—32no—
247#897—34no—
248#896—34no—
249#896—34no—
250#896—34no—
251#896—34no—
252#896—34no—
253#896—34no—
254#896—34no—
255#896—34no—
256#896—34no—
257#896—34no—
258#896—64no—
259#896C2×D314yescomplemented
260#893—31no—
261#893—32no—
262D3×C4⋊C4—31no—
263D3×C4⋊C4—32no—
264D3×C4⋊C4—34no—
265D3×C4⋊C4—34no—
266D3×C4⋊C4—32no—
267D3×C4⋊C4—34no—
268D3×C4⋊C4—32no—
269D3×C4⋊C4—32no—
270D3×C4⋊C4—32no—
271D3×C4⋊C4—32no—
272D3×C4⋊C4—32no—
273D3×C4⋊C4—34no—
274D3×C4⋊C4—34no—
275D3×C4⋊C4—62no—
276D3×C4⋊C4C2×D311yescharacteristic
277D3×C4⋊C4C2×D312yes—
278D3×C4⋊C4C2×D312yescomplemented
279#890—32no—
280#890—32no—
281#889—34no—
282#889—34no—
283#888—32no—
284#888—32no—
285#887C2×D312yescomplemented
286#887C2×D311yescharacteristic, complemented
287#67⋊C4—34no—
288#67⋊C4—32no—
289D3×C22⋊C4—34no—
290D3×C22⋊C4—32no—
291#878—34no—
292#878—34no—
293#878—34no—
294C4×D12—32no—
295C4×D12—31no—
296C4×D12—34no—
297C4×D12—32no—
298C4×D12—32no—
299C4×D12—32no—
300C4×D12—31no—
301C4×D12—31no—
302C4×D12—34no—
303C4×D12—32no—
304C4×D12—32no—
305C4×D12—31no—
306C4×D12—62no—
307C4×D12—61no—
308C4×D12C2×D312yes—
309C4×D12C2×D311yescharacteristic
310C42×D3C2×D312yes—
311C42×D3C2×D311yescharacteristic
312#870—32no—
313#870—32no—
314#870—32no—
315#870—32no—
316#870—34no—
317#870—34no—
318#870—62no—
319#870C2×D312yescomplemented
320#869—32no—
321#869—31no—
322#869—31no—
323#869—32no—
324#869—32no—
325#869—61no—
326#869C2×D311yescharacteristic, complemented
327C4×Dic6C2×D312yescomplemented
328C4×Dic6C2×D311yescharacteristic, complemented
329C22×C3⋊D3C2412yes—
330C22×C3×D3C2412yes—
331C22×C3×D3C2411yescharacteristic
332C2×D32—24no—
333C2×D32—24no—
334C2×D32C2×Q818yes—
335C32×Q8—22no—
336C2×C32×C4C2412yes—
337C2×C32×C4C2412yes—
338C2×C32×C4C2411yescharacteristic
339C2×C32×C4C2411yescharacteristic
340C2×C32×C4C2411yescharacteristic
341C2×C3⋊Dic3C2412yes—
342C2×C3⋊Dic3C2414yes—
343C4⋊(C3⋊D3)C2×Q814yescomplemented
344C4×C3⋊D3—24no—
345C4×C3⋊D3—44no—
346#634—42no—
347C2×C3×Dic3C2412yes—
348C2×C3×Dic3C2411yescharacteristic
349C2×C3×Dic3C2412yes—
350C2×C3×Dic3C2414yes—
351C2×C3×Dic3C2412yes—
352C2×C3×Dic3C2411yescharacteristic
353C2×C3×Dic3C2411yescharacteristic
354C3×D12C2×Q814yescomplemented
355C3×C4×D3—24no—
356C3×C4×D3—22no—
357C3×C4×D3—24no—
358C3×C4×D3—24no—
359C3×C4×D3—44no—
360C3×C4×D3C2×Q814yes—
361C3×C4×D3#4114yes—
362C3×Dic6—22no—
363C3×Dic6—24no—
364C3×Dic6—42no—
365#627—44no—
366#626C2×Q818yescomplemented
367#624—24no—
368#624—44no—
369D3×Dic3—24no—
370D3×Dic3—28no—
371D3×Dic3—24no—
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—31no—
387C2×C4×D4—92no—
388C2×C4×D4—91no—
389C22×C4⋊C4—92no—
390C23×D3—32no—
391C23×D3—32no—
392C2×C3×Q8—21no—
393C2×C3×Q8—32no—
394C2×C3×Q8—31no—
395C2×C3×Q8—32no—
396C2×C3×Q8—64no—
397C2×C3×Q8C22×D311yescharacteristic
398C2×C3×Q8C22×D311yescharacteristic
399C2×C3×D4—31no—
400C22×C3×C4—31no—
401C22×C3×C4—31no—
402C22×C3×C4—32no—
403C22×C3×C4—32no—
404C22×C3×C4—32no—
405C22×C3×C4—31no—
406C22×C3×C4—34no—
407C2×#67—32no—
408C22×Dic3—32no—
409C22×Dic3—32no—
410C22×Dic3—34no—
411C22×Dic3—34no—
412D3×Q8—24no—
413D3×Q8—124no—
414D3×D4—38no—
415C2×D12—32no—
416C2×D12—31no—
417C2×D12—31no—
418C2×D12—38no—
419C2×D12—61no—
420C2×D12C22×D311yescharacteristic
421C2×C4×D3—32no—
422C2×C4×D3—32no—
423C2×C4×D3—34no—
424C2×C4×D3—32no—
425C2×C4×D3—32no—
426C2×C4×D3—32no—
427C2×C4×D3—32no—
428C2×C4×D3—34no—
429C2×C4×D3—34no—
430C2×C4×D3—34no—
431C2×C4×D3—34no—
432C2×C4×D3—34no—
433C2×C4×D3—62no—
434C2×C4×D3—64no—
435C2×C4×D3—68no—
436C2×C4×D3—68no—
437C2×C4×D3—128no—
438C2×C4×D3—128no—
439C2×C4×D3C22×D312yes—
440C2×C4×D3C22×D311yescharacteristic
441C2×C4×D3C22×D312yes—
442C2×C4×D3C22×D312yes—
443C2×C4×D3C22×D314yes—
444C2×C4×D3C22×D311yescharacteristic
445C2×C4×D3C22×D311yescharacteristic
446C2×Dic6—32no—
447C2×Dic6—32no—
448C2×Dic6—34no—
449C2×Dic6—34no—
450C2×Dic6—62no—
451C2×Dic6—124no—
452C2×Dic6C22×D312yes—
453C2×Dic6C22×D311yescharacteristic
454C2×Dic6C22×D312yes—
455C3×C4⋊C4—21no—
456C3×C4⋊C4—22no—
457C3×C4⋊C4—32no—
458C3×C4⋊C4—32no—
459C3×C4⋊C4—34no—
460C3×C4⋊C4—34no—
461C3×C4⋊C4—31no—
462C3×C4⋊C4—32no—
463C3×C4⋊C4—31no—
464C3×C4⋊C4—32no—
465C3×C4⋊C4—32no—
466C3×C4⋊C4—32no—
467C3×C4⋊C4C22×D311yescharacteristic
468C3×C4⋊C4C22×D312yes—
469C3×C4⋊C4C22×D311yescharacteristic
470C3×C4⋊C4C22×D312yes—
471C3×C22⋊C4—32no—
472C3×C22⋊C4—34no—
473C3×C42—21no—
474C3×C42—22no—
475C3×C42—31no—
476C3×C42—31no—
477C3×C42—31no—
478C3×C42—32no—
479C3×C42—32no—
480C3×C42—32no—
481C3×C42C22×D311yescharacteristic
482C3×C42C22×D312yes—
483C3×C42C22×D311yescharacteristic
484C3×C42C22×D312yes—
485#217—32no—
486#217—34no—
487(C2×D3)⋊C4—32no—
488(C2×D3)⋊C4—34no—
489(C2×D3)⋊C4—32no—
490(C2×D3)⋊C4—34no—
491(C2×D3)⋊C4—34no—
492(C2×D3)⋊C4—32no—
493(C2×D3)⋊C4—32no—
494(C2×D3)⋊C4—34no—
495(C2×D3)⋊C4—32no—
496(C2×D3)⋊C4—34no—
497(C2×D3)⋊C4—62no—
498(C2×D3)⋊C4—64no—
499(C2×D3)⋊C4C22×D312yes—
500(C2×D3)⋊C4C22×D314yes—
501C4⋊Dic3—32no—
502C4⋊Dic3—32no—
503C4⋊Dic3—32no—
504C4⋊Dic3—32no—
505C4⋊Dic3—31no—
506C4⋊Dic3—31no—
507C4⋊Dic3—34no—
508C4⋊Dic3—34no—
509C4⋊Dic3—32no—
510C4⋊Dic3—34no—
511C4⋊Dic3—34no—
512C4⋊Dic3—62no—
513C4⋊Dic3—62no—
514C4⋊Dic3—61no—
515C4⋊Dic3C22×D312yes—
516C4⋊Dic3C22×D311yescharacteristic
517C4⋊Dic3C22×D312yes—
518C4⋊Dic3C22×D312yes—
519C4⋊Dic3C22×D311yescharacteristic
520Dic3⋊C4—34no—
521Dic3⋊C4—34no—
522Dic3⋊C4—34no—
523Dic3⋊C4—34no—
524Dic3⋊C4—34no—
525Dic3⋊C4—34no—
526Dic3⋊C4—34no—
527Dic3⋊C4—34no—
528Dic3⋊C4—34no—
529Dic3⋊C4—34no—
530Dic3⋊C4—34no—
531Dic3⋊C4—34no—
532Dic3⋊C4—32no—
533Dic3⋊C4—64no—
534Dic3⋊C4—64no—
535Dic3⋊C4C22×D312yes—
536Dic3⋊C4C22×D312yes—
537Dic3⋊C4C22×D312yes—
538Dic3⋊C4C22×D314yes—
539Dic3⋊C4C22×D314yes—
540C4×Dic3C22×D311yescharacteristic
541C4×Dic3C22×D312yes—
542C4×Dic3C22×D311yescharacteristic
543C4×Dic3C22×D312yes—
544C4×Dic3C22×D312yes—
545C4×Dic3C22×D311yescharacteristic
546C22×C32C2511yescharacteristic
547C2×C3⋊D3—22no—
548C2×C3⋊D3—22no—
549C2×C3⋊D3C22×Q814yes—
550C2×C3×D3—22no—
551C2×C3×D3—22no—
552C2×C3×D3C22×Q814yes—
553C2×C3×D3C22×Q812yes—
554C2×C3×D3C2×#4112yes—
555C2×C3×D3H(5,𝔽2)12yes—
556D32—216no—
557C32×C4—22no—
558C32×C4—21no—
559C32×C4—22no—
560C32×C4C22×Q812yes—
561C32×C4C2×#4112yes—
562C3⋊Dic3—22no—
563C3⋊Dic3—24no—
564C3×Dic3—22no—
565C3×Dic3—22no—
566C3×Dic3—24no—
567C3×Dic3—22no—
568C3×Dic3—21no—
569C3×Dic3C22×Q812yes—
570C3×Dic3C2×#4112yes—
571C22×Q8—31no—
572C22×Q8—92no—
573C22×D4—91no—
574C23×C4—92no—
575C23×C4—94no—
576C4⋊Q8—31no—
577C4⋊Q8—92no—
578C4⋊Q8—92no—
579C4⋊Q8—92no—
580C4⋊Q8—91no—
581#125—32no—
582#125—94no—
583#125—94no—
584#125—92no—
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—32no—
603C4×Q8—31no—
604C4×Q8—31no—
605C4×Q8—32no—
606C4×Q8D3211yescharacteristic, complemented
607C4×D4—32no—
608C4×D4—31no—
609C4×D4—94no—
610C4×D4—92no—
611C4×D4—92no—
612C4×D4—91no—
613C4×D4—94no—
614C4×D4—92no—
615C4×D4—92no—
616C4×D4—91no—
617C4×D4—92no—
618C4×D4—91no—
619C2×C4⋊C4—31no—
620C2×C4⋊C4—32no—
621C2×C4⋊C4—32no—
622C2×C4⋊C4—94no—
623C2×C4⋊C4—92no—
624C2×C4⋊C4—94no—
625C2×C4⋊C4—92no—
626C2×C4⋊C4—94no—
627C2×C4⋊C4—92no—
628C2×C4⋊C4—91no—
629C2×C4⋊C4—92no—
630C2×C4⋊C4—94no—
631C2×C4⋊C4—92no—
632C2×C22⋊C4—92no—
633C2×C22⋊C4—94no—
634C2×C42—32no—
635C2×C42—31no—
636C23×C3—31no—
637C23×C3—32no—
638C22×D3—32no—
639C22×D3—32no—
640C22×D3—38no—
641C22×D3—38no—
642C22×D3—62no—
643C22×D3—64no—
644C22×D3—64no—
645C22×D3—64no—
646C22×D3—64no—
647C22×D3C23×D312yes—
648C22×D3C23×D311yescharacteristic
649C3×Q8—22no—
650C3×Q8—22no—
651C3×Q8—42no—
652C3×Q8—64no—
653C3×Q8—62no—
654C3×Q8—122no—
655C3×D4—34no—
656C2×C3×C4—21no—
657C2×C3×C4—21no—
658C2×C3×C4—22no—
659C2×C3×C4—22no—
660C2×C3×C4—21no—
661C2×C3×C4—31no—
662C2×C3×C4—31no—
663C2×C3×C4—34no—
664C2×C3×C4—34no—
665C2×C3×C4—32no—
666C2×C3×C4—32no—
667C2×C3×C4—32no—
668C2×C3×C4—34no—
669C2×C3×C4—31no—
670C2×C3×C4—62no—
671C2×C3×C4—64no—
672C2×C3×C4—64no—
673C2×C3×C4—64no—
674C2×C3×C4—124no—
675C2×C3×C4C23×D312yes—
676C2×C3×C4C23×D312yes—
677C2×C3×C4C23×D311yescharacteristic
678C2×C3×C4C23×D312yes—
679C2×C3×C4C23×D312yes—
680C2×C3×C4C23×D311yescharacteristic
681C2×C3×C4C23×D311yescharacteristic
682C2×C3×C4C23×D311yescharacteristic
683C2×C3×C4C23×D311yescharacteristic
684C2×C3×C4C23×D311yescharacteristic
685#67—38no—
686C2×Dic3—32no—
687C2×Dic3—32no—
688C2×Dic3—34no—
689C2×Dic3—34no—
690C2×Dic3—62no—
691C2×Dic3—64no—
692C2×Dic3—68no—
693C2×Dic3—64no—
694C2×Dic3—64no—
695C2×Dic3—124no—
696C2×Dic3C23×D312yes—
697C2×Dic3C23×D312yes—
698C2×Dic3C23×D311yescharacteristic
699C2×Dic3C23×D312yes—
700C2×Dic3C23×D314yes—
701C2×Dic3C23×D311yescharacteristic
702C2×Dic3C23×D311yescharacteristic
703D12—38no—
704D12—34no—
705D12—34no—
706D12—64no—
707D12D3×Q814yescomplemented
708C4×D3—24no—
709C4×D3—24no—
710C4×D3—22no—
711C4×D3—24no—
712C4×D3—44no—
713C4×D3—64no—
714C4×D3—64no—
715C4×D3—64no—
716C4×D3—68no—
717C4×D3—64no—
718C4×D3—64no—
719C4×D3—64no—
720C4×D3—124no—
721C4×D3—124no—
722C4×D3—124no—
723C4×D3—124no—
724C4×D3—124no—
725C4×D3—124no—
726C4×D3—244no—
727C4×D3#23514yes—
728C4×D3D3×Q814yes—
729Dic6—22no—
730Dic6—24no—
731Dic6—42no—
732Dic6—124no—
733Dic6—124no—
734Dic6—122no—
735Dic6—122no—
736Dic6—242no—
737C2×C32C23×Q811yescharacteristic
738C2×C32C22×#4111yescharacteristic
739C2×C32C2×H(5,𝔽2)11yescharacteristic
740C3⋊D3—24no—
741C3×D3—24no—
742C3×D3#55414yescomplemented
743C24—92no—
744C2×Q8—32no—
745C2×Q8—31no—
746C2×Q8—32no—
747C2×Q8—64no—
748C2×Q8—94no—
749C2×Q8—92no—
750C2×Q8—364no—
751C2×Q8C2×D3211yescharacteristic
752C2×D4—31no—
753C2×D4—98no—
754C2×D4—92no—
755C2×D4—91no—
756C22×C4—31no—
757C22×C4—31no—
758C22×C4—31no—
759C22×C4—32no—
760C22×C4—32no—
761C22×C4—32no—
762C22×C4—34no—
763C22×C4—92no—
764C22×C4—94no—
765C22×C4—92no—
766C22×C4—94no—
767C22×C4—92no—
768C22×C4—94no—
769C22×C4—92no—
770C22×C4—94no—
771C22×C4—188no—
772C22×C4—368no—
773C4⋊C4—32no—
774C4⋊C4—31no—
775C4⋊C4—34no—
776C4⋊C4—32no—
777C4⋊C4—32no—
778C4⋊C4—32no—
779C4⋊C4—32no—
780C4⋊C4—31no—
781C4⋊C4—32no—
782C4⋊C4—34no—
783C4⋊C4—94no—
784C4⋊C4—94no—
785C4⋊C4—94no—
786C4⋊C4—92no—
787C4⋊C4—94no—
788C4⋊C4—94no—
789C4⋊C4—94no—
790C4⋊C4—94no—
791C4⋊C4—92no—
792C4⋊C4—91no—
793C4⋊C4—92no—
794C4⋊C4—94no—
795C4⋊C4C2×D3211yescharacteristic
796C4⋊C4C2×D3212yes—
797C22⋊C4—32no—
798C22⋊C4—34no—
799C22⋊C4—92no—
800C22⋊C4—94no—
801C22⋊C4—92no—
802C22⋊C4—94no—
803C22⋊C4—92no—
804C22⋊C4—94no—
805C42—32no—
806C42—32no—
807C42—32no—
808C42—31no—
809C42—31no—
810C42—31no—
811C42C2×D3212yes—
812C42C2×D3211yescharacteristic
813C22×C3—21no—
814C22×C3—32no—
815C22×C3—32no—
816C22×C3—32no—
817C22×C3—34no—
818C22×C3—62no—
819C22×C3—62no—
820C22×C3C24×D311yescharacteristic
821C22×C3C24×D311yescharacteristic
822C2×D3—22no—
823C2×D3—22no—
824C2×D3—34no—
825C2×D3—34no—
826C2×D3—64no—
827C2×D3—616no—
828C2×D3—62no—
829C2×D3—62no—
830C2×D3—62no—
831C2×D3—62no—
832C2×D3—616no—
833C2×D3—122no—
834C2×D3—122no—
835C2×D3C2×#23512yes—
836C2×D3C2×D3×Q814yes—
837C2×D3C2×D3×Q812yes—
838C2×D3#100912yes—
839C3×C4—22no—
840C3×C4—22no—
841C3×C4—21no—
842C3×C4—22no—
843C3×C4—21no—
844C3×C4—22no—
845C3×C4—22no—
846C3×C4—22no—
847C3×C4—32no—
848C3×C4—32no—
849C3×C4—41no—
850C3×C4—42no—
851C3×C4—42no—
852C3×C4—62no—
853C3×C4—62no—
854C3×C4—64no—
855C3×C4—61no—
856C3×C4—62no—
857C3×C4C2×#23512yes—
858C3×C4C2×D3×Q812yes—
859C3×C4C2×D3×Q812yes—
860C3×C4D3×#4112yes—
861Dic3—22no—
862Dic3—22no—
863Dic3—21no—
864Dic3—22no—
865Dic3—24no—
866Dic3—62no—
867Dic3—62no—
868Dic3—64no—
869Dic3—64no—
870Dic3—124no—
871Dic3—122no—
872Dic3C2×#23512yes—
873Dic3C2×D3×Q812yes—
874C32C2×#55411yescharacteristic, complemented, Sylow
875C23—31no—
876C23—32no—
877C23—98no—
878C23—92no—
879C23—184no—
880C23—184no—
881Q8—22no—
882Q8—64no—
883Q8—62no—
884Q8—122no—
885Q8—362no—
886Q8—364no—
887D4—34no—
888D4—98no—
889D4—94no—
890C2×C4—31no—
891C2×C4—31no—
892C2×C4—34no—
893C2×C4—34no—
894C2×C4—31no—
895C2×C4—32no—
896C2×C4—32no—
897C2×C4—32no—
898C2×C4—34no—
899C2×C4—64no—
900C2×C4—64no—
901C2×C4—62no—
902C2×C4—64no—
903C2×C4—92no—
904C2×C4—94no—
905C2×C4—124no—
906C2×C4—184no—
907C2×C4—184no—
908C2×C4—184no—
909C2×C4—188no—
910C2×C4—184no—
911C2×C4—364no—
912C2×C4—364no—
913C2×C4—364no—
914C2×C4C22×D3212yes—
915C2×C4C22×D3211yescharacteristic
916C2×C4C22×D3212yes—
917C2×C4C22×D3211yescharacteristic
918C2×C4C22×D3211yescharacteristic
919C2×C3—21no—
920C2×C3—21no—
921C2×C3—21no—
922C2×C3—34no—
923C2×C3—64no—
924C2×C3C22×#23511yescharacteristic
925C2×C3C22×D3×Q811yescharacteristic
926C2×C3C22×D3×Q811yescharacteristic
927C2×C3C2×D3×#4111yescharacteristic
928C2×C3C2×#100911yescharacteristic
929C2×C3D3×H(5,𝔽2)11yescharacteristic
930D3—24no—
931D3—64no—
932D3—64no—
933D3—124no—
934D3#557914yesdirect product factor
935C22—32no—
936C22—32no—
937C22—32no—
938C22—34no—
939C22—62no—
940C22—62no—
941C22—94no—
942C22—1816no—
943C22—182no—
944C22—182no—
945C22C23×D3211yescharacteristic
946C4—22no—
947C4—22no—
948C4—21no—
949C4—32no—
950C4—32no—
951C4—62no—
952C4—62no—
953C4—62no—
954C4—61no—
955C4—64no—
956C4—182no—
957C4—184no—
958C4D3×#23512yes—
959C4D32×Q812yes—
960C3—21no—
961C3C2×#557911yescharacteristic, complemented
962C3D3×#55411yescharacteristic, complemented
963C2—34no—
964C2—64no—
965C2—184no—
966C2C2×D3×#23511yescharacteristic
967C2C2×D32×Q811yescharacteristic
968C2D3×#100911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×Q8C22
prime radicalC2×D3×D12C22
hypercenterC4×Q8D32
hypocenterC32C2×#554
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. #10596050C2semidirect
2. C3×#5579C2semidirect
3. C3×C4×D3×Q8C2semidirect
4. D3×#946C2semidirect
5. #10595371C2semidirect
6. D3×#896C2semidirect
7. D32×C4⋊C4C2semidirect
8. #10594536C2semidirect
9. #10594392C2semidirect
12. #10593960C2semidirect
13. #10593958C2semidirect
14. #10593938C2semidirect
15. #10593929C2semidirect
16. D3×#870C2semidirect
17. D3×#869C2semidirect
25. C32×C4×Q8C22semidirect
26. #64155C22semidirect
27. #64105C22semidirect
28. C4⋊C4×C3⋊D3C22semidirect
31. #64079C22semidirect
32. #64078C22semidirect
33. C3×#946C22semidirect
34. C3×Q8×Dic3C22semidirect
35. C3×#896C22semidirect
38. C3×D3×C4⋊C4C22semidirect
39. C3×#887C22semidirect
40. C3×#887C22semidirect
45. C3×#870C22semidirect
46. C3×#869C22semidirect
47. C3×C4×Dic6C22semidirect
48. C3×C4×Dic6C22semidirect
51. #63918C22semidirect
52. #63918C22semidirect
55. #63900C22semidirect
56. #63899C22semidirect
57. #63896C22semidirect
58. #63895C22semidirect
66. D3×C4⋊Dic3C22semidirect
67. #63888C22semidirect
68. #63888C22semidirect
69. #63887C22semidirect
70. #63883C22semidirect
75. D3×Dic3⋊C4C22semidirect
76. #63871C22semidirect
77. #63869C22semidirect
78. #63869C22semidirect
79. #63867C22semidirect
80. #63867C22semidirect
81. #63866C22semidirect
82. #63865C22semidirect
83. #63856C22semidirect
84. #63851C22semidirect
106. #5579D3direct (N × H)
107. C4×D3×Q8D3semidirect
146. D3×D12Q8semidirect
211. C3×C4×Q8C2×D3semidirect
212. C3×C4×Q8C2×D3semidirect
228. #946C2×D3semidirect
229. Q8×Dic3C2×D3semidirect
259. #896C2×D3semidirect
278. D3×C4⋊C4C2×D3semidirect
285. #887C2×D3semidirect
286. #887C2×D3semidirect
319. #870C2×D3semidirect
326. #869C2×D3semidirect
327. C4×Dic6C2×D3semidirect
328. C4×Dic6C2×D3semidirect
343. C4⋊(C3⋊D3)C2×Q8semidirect
354. C3×D12C2×Q8semidirect
366. #626C2×Q8semidirect
606. C4×Q8D32semidirect
707. D12D3×Q8semidirect
742. C3×D3#554semidirect
874. C32C2×#554semidirect
934. D3#5579direct (N × H)
961. C3C2×#5579semidirect
962. C3D3×#554semidirect

Maximal subgroups

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

subgroupindex
#105960502
C3×#55792
C3×C4×D3×Q82
D3×#9462
#105953712
D3×#8962
D32×C4⋊C42
#105945362
#105943922
C4×D3×D122
#105939602
#105939582
#105939382
#105939292
D3×#8702
D3×#8692
D3×#5543
C2×#55793