Finite Group Databasebeta

← D3×#5584 #11903380

Subgroups — D3×#5584 #11903380

Order 1152.

2330 conjugacy classes of subgroups.

The subgroup lattice has 949 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596055C211yesmaximal, characteristic, complemented
2C3×#5584C211yesmaximal, characteristic, complemented
3C3×C4×D3×Q8C211yesmaximal, characteristic, complemented
4D3×#946C212yesmaximal, complemented
5#10595411C212yesmaximal, complemented
6D3×#898C214yesmaximal, complemented
7D3×#892C212yesmaximal, complemented
8#10594565C212yesmaximal, complemented
9#10594421C214yesmaximal, complemented
10D3×#875C212yesmaximal
11C4×D3×D12C211yesmaximal, characteristic
12#10593932C212yesmaximal, complemented
13D3×#869C211yesmaximal, characteristic, complemented
14C4×D3×Dic6C212yesmaximal, complemented
15#10593879C211yesmaximal, characteristic, complemented
16#10593865C211yesmaximal, characteristic, complemented
17#10593850C212yesmaximal, complemented
18D3×#556—31nomaximal
19C2×#5584—31nomaximal
20C2×C3×D3×Q8C2211yescharacteristic
21C2×D3×D12C2211yescharacteristic
22C2×C4×D32C2212yes—
23C2×D3×Dic6C2212yes—
24C32×C4×Q8C2211yescharacteristic, complemented
25#64155C2212yescomplemented
26#64107C2214yescomplemented
27#64101C2212yescomplemented
28#64084C2212yes—
29C4×C4⋊(C3⋊D3)C2211yescharacteristic
30#64078C2211yescharacteristic, complemented
31C4×#634C2212yescomplemented
32C3×#946C2212yescomplemented
33C3×Q8×Dic3C2211yescharacteristic, complemented
34C3×#898C2214yescomplemented
35C3×#892C2212yescomplemented
36C3×D3×C4⋊C4C2211yescharacteristic
37C3×D3×C4⋊C4C2212yes—
38C3×#887C2211yescharacteristic, complemented
39C3×#887C2212yescomplemented
40C3×#875C2212yes—
41C3×C4×D12C2211yescharacteristic
42C3×C42×D3C2212yes—
43C3×C42×D3C2211yescharacteristic
44C3×#869C2211yescharacteristic, complemented
45C3×C4×Dic6C2212yescomplemented
46C3×C4×Dic6C2212yescomplemented
47C3×C4×Dic6C2211yescharacteristic, complemented
48D3×(C2×D3)⋊C4C2214yes—
49D3×(C2×D3)⋊C4C2212yes—
50D3×(C2×D3)⋊C4C2214yes—
51#63918C2212yescomplemented
52#63918C2212yescomplemented
53C4×#627C2214yescomplemented
54C4×#626C2212yes—
55#63894C2211yescharacteristic
56Dic3×D12C2211yescharacteristic
57D3×C4⋊Dic3C2212yes—
58D3×C4⋊Dic3C2212yes—
59D3×C4⋊Dic3C2211yescharacteristic
60#63888C2214yescomplemented
61#63887C2214yescomplemented
62#63880C2212yes—
63#63878C2214yescomplemented
64D3×Dic3⋊C4C2214yes—
65C4×D3×Dic3C2214yes—
66#63871C2212yescomplemented
67#63868C2214yescomplemented
68#63866C2212yescomplemented
69#63864C2212yes—
70#63862C2214yescomplemented
71#63861C2214yescomplemented
72#63860C2212yes—
73#63858C2214yescomplemented
74#63856C2212yescomplemented
75#63852C2214yes—
76#63852C2214yes—
77#63849C2212yescomplemented
78#63848C2214yescomplemented
79#63848C2214yescomplemented
80#63844C2212yescomplemented
81Dic3×Dic6C2212yescomplemented
82#63841C2212yescomplemented
83#63837C2214yescomplemented
84#63836C2214yescomplemented
85C3×#556—31no—
86C2×C3×C4×Q8—31no—
87C2×#946—32no—
88#5732—31no—
89D3×C4⋊Q8—31no—
90D3×#126—34no—
91#5702—34no—
92D3×#124—32no—
93#5671—32no—
94#5641—32no—
95D3×C22⋊Q8—32no—
96#5584—31no—
97#5584—31no—
98#5584—32no—
99#5584—34no—
100#5584—32no—
101#5584—32no—
102#5584—31no—
103#5584—31no—
104#5584—32no—
105#5584—61no—
106#5584D311yescharacteristic, direct product factor
107C4×D3×Q8—32no—
108C4×D3×Q8D311yescharacteristic, complemented
109#5568—32no—
110C4×D3×D4—31no—
111#5542—31no—
112#5533—32no—
113D3×#117—32no—
114C2×#898—34no—
115C2×#892—32no—
116C2×#875—32no—
117C2×C4×D12—31no—
118C2×#869—31no—
119C2×C4×Dic6—32no—
120C22×D32C2312yes—
121C2×C32×Q8C2311yescharacteristic
122C2×C4⋊(C3⋊D3)C2311yescharacteristic
123C2×C4×C3⋊D3C2312yes—
124C2×#634C2312yes—
125C3×D3×Q8—24no—
126C2×C3×D12C2311yescharacteristic
127C2×C3×C4×D3C2312yes—
128C2×C3×C4×D3C2311yescharacteristic
129C2×C3×C4×D3C2312yes—
130C2×C3×C4×D3C2312yes—
131C2×C3×C4×D3C2311yescharacteristic
132C2×C3×C4×D3C2311yescharacteristic
133C2×C3×Dic6C2311yescharacteristic
134C2×C3×Dic6C2312yes—
135C2×C3×Dic6C2312yes—
136C2×#627C2314yes—
137C2×#626C2312yes—
138C2×#624C2312yes—
139C2×D3×Dic3C2314yes—
140C2×D3×Dic3C2312yes—
141C2×D3×Dic3C2312yes—
142D3×D12—24no—
143C4×D32—28no—
144D3×Dic6—28no—
145C32×C4⋊C4C2311yescharacteristic
146C32×C4⋊C4C2312yes—
147C32×C42C2312yes—
148C32×C42C2311yescharacteristic
149#3752C2312yes—
150#3752C2314yes—
151#3752C2314yes—
152C4⋊(C3⋊Dic3)C2311yescharacteristic
153C4⋊(C3⋊Dic3)C2312yes—
154C4⋊(C3⋊Dic3)C2312yes—
155#3750C2314yes—
156C4×C3⋊Dic3C2314yes—
157C3×(C2×D3)⋊C4C2314yes—
158C3×(C2×D3)⋊C4C2312yes—
159C3×(C2×D3)⋊C4C2314yes—
160C3×C4⋊Dic3C2311yescharacteristic
161C3×C4⋊Dic3C2312yes—
162C3×C4⋊Dic3C2312yes—
163C3×C4⋊Dic3C2312yes—
164C3×C4⋊Dic3C2311yescharacteristic
165C3×Dic3⋊C4C2312yes—
166C3×Dic3⋊C4C2312yes—
167C3×Dic3⋊C4C2312yes—
168C3×Dic3⋊C4C2314yes—
169C3×C4×Dic3C2312yes—
170C3×C4×Dic3C2311yescharacteristic
171C3×C4×Dic3C2312yes—
172C3×C4×Dic3C2311yescharacteristic
173C3×C4×Dic3C2314yes—
174C3×C4×Dic3C2312yes—
175C3×C4×Dic3C2311yescharacteristic
176#3724C2314yes—
177Dic3⋊Dic3C2314yes—
178Dic3⋊Dic3C2312yes—
179Dic3⋊Dic3C2314yes—
180Dic3⋊Dic3C2314yes—
181#3722C2314yes—
182#3722C2312yes—
183#3722C2314yes—
184(C2×D3)⋊Dic3C2314yes—
185(C2×D3)⋊Dic3C2314yes—
186(C2×D3)⋊Dic3C2312yes—
187Dic32C2314yes—
188Dic32C2314yes—
189C2×#556—91noSylow
190C22×C3×Q8—31no—
191C2×D3×Q8—32no—
192C2×D3×Q8C2×D311yescharacteristic
193C2×D3×D4—31no—
194C22×D12—31no—
195C22×C4×D3—32no—
196C22×C4×D3—32no—
197C22×Dic6—32no—
198C3×C4⋊Q8—31no—
199C3×#126—34no—
200C3×#124—32no—
201C3×C22⋊Q8—32no—
202C3×C4×Q8—21no—
203C3×C4×Q8—31no—
204C3×C4×Q8—32no—
205C3×C4×Q8—31no—
206C3×C4×Q8—32no—
207C3×C4×Q8—31no—
208C3×C4×Q8—32no—
209C3×C4×Q8C2×D311yescharacteristic, complemented
210C3×C4×Q8C2×D311yescharacteristic, complemented
211C3×C4×D4—31no—
212C3×#117—32no—
213C2×C3×C4⋊C4—31no—
214C2×C3×C4⋊C4—32no—
215C2×C3×C42—32no—
216C2×C3×C42—31no—
217#947—32no—
218#946—32no—
219#946—32no—
220#946—32no—
221#946—34no—
222#946—32no—
223#946—34no—
224#946—62no—
225#946C2×D312yescomplemented
226Q8×Dic3—32no—
227Q8×Dic3C2×D311yescharacteristic, complemented
228#944—32no—
229#936—32no—
230D4×Dic3—31no—
231C4×#67—32no—
232C2×(C2×D3)⋊C4—32no—
233C2×(C2×D3)⋊C4—34no—
234C2×(C2×D3)⋊C4—34no—
235#926—32no—
236C2×C4⋊Dic3—31no—
237C2×C4⋊Dic3—32no—
238C2×C4⋊Dic3—32no—
239#924—32no—
240C2×Dic3⋊C4—34no—
241C2×C4×Dic3—34no—
242#898—34no—
243#898—34no—
244#898—34no—
245#898—34no—
246#898—34no—
247#898—34no—
248#898—34no—
249#898—34no—
250#898—34no—
251#898—34no—
252#898—64no—
253#898C2×D314yescomplemented
254#897—32no—
255#896—34no—
256#893—31no—
257#892—32no—
258#892—32no—
259#892—32no—
260#892—34no—
261#892—32no—
262#892—32no—
263#892—34no—
264#892—62no—
265#892C2×D312yescomplemented
266D3×C4⋊C4—32no—
267D3×C4⋊C4—34no—
268D3×C4⋊C4—32no—
269D3×C4⋊C4—31no—
270D3×C4⋊C4C2×D312yes—
271D3×C4⋊C4C2×D311yescharacteristic
272#888—32no—
273#888—32no—
274#887—34no—
275#887—32no—
276#887C2×D312yescomplemented
277#887C2×D311yescharacteristic, complemented
278#885—34no—
279#885—34no—
280#67⋊C4—32no—
281D3×C22⋊C4—34no—
282D3×C22⋊C4—34no—
283D3×C22⋊C4—32no—
284#879—34no—
285#879—34no—
286#879—34no—
287#878—34no—
288#877—34no—
289#876—34no—
290#875—32no—
291#875—32no—
292#875—32no—
293#875—32no—
294#875—34no—
295#875—34no—
296#875—62no—
297#875C2×D312yes—
298C4×D12—31no—
299C4×D12—32no—
300C4×D12—31no—
301C4×D12—31no—
302C4×D12—32no—
303C4×D12—31no—
304C4×D12—61no—
305C4×D12C2×D311yescharacteristic
306#872—34no—
307C42×D3—34no—
308C42×D3C2×D312yes—
309C42×D3C2×D311yescharacteristic
310#869—32no—
311#869—31no—
312#869—31no—
313#869—32no—
314#869—32no—
315#869—61no—
316#869C2×D311yescharacteristic, complemented
317C4×Dic6—32no—
318C4×Dic6—32no—
319C4×Dic6—32no—
320C4×Dic6—32no—
321C4×Dic6—34no—
322C4×Dic6—34no—
323C4×Dic6—34no—
324C4×Dic6—62no—
325C4×Dic6C2×D312yescomplemented
326C4×Dic6C2×D312yescomplemented
327C4×Dic6C2×D311yescharacteristic, complemented
328C22×C3⋊D3C2412yes—
329C22×C3×D3C2412yes—
330C22×C3×D3C2411yescharacteristic
331C2×D32—24no—
332C2×D32—24no—
333C2×D32—24no—
334C32×Q8—22no—
335C2×C32×C4C2412yes—
336C2×C32×C4C2411yescharacteristic
337C2×C32×C4C2412yes—
338C2×C32×C4C2411yescharacteristic
339C2×C32×C4C2411yescharacteristic
340C2×C3⋊Dic3C2412yes—
341C2×C3⋊Dic3C2414yes—
342C4⋊(C3⋊D3)—22no—
343C4×C3⋊D3—24no—
344#634—24no—
345C2×C3×Dic3C2412yes—
346C2×C3×Dic3C2412yes—
347C2×C3×Dic3C2414yes—
348C2×C3×Dic3C2411yescharacteristic
349C2×C3×Dic3C2412yes—
350C2×C3×Dic3C2411yescharacteristic
351C2×C3×Dic3C2411yescharacteristic
352C3×D12—22no—
353C3×C4×D3—24no—
354C3×C4×D3—24no—
355C3×C4×D3—22no—
356C3×C4×D3—24no—
357C3×C4×D3#4114yes—
358C3×C4×D3#4114yes—
359C3×Dic6—24no—
360C3×Dic6—22no—
361C3×Dic6—24no—
362#627—28no—
363#626—24no—
364#624—24no—
365D3×Dic3—28no—
366D3×Dic3—24no—
367D3×Dic3—24no—
368#556—31no—
369#556—92no—
370#556—91no—
371#556—92no—
372#556—92no—
373#556—92no—
374#556—94no—
375#556—91no—
376#556—91no—
377C2×C4⋊Q8—91no—
378C2×#126—94no—
379C2×#124—92no—
380C2×C22⋊Q8—92no—
381C2×C4×Q8—31no—
382C2×C4×Q8—92no—
383C2×C4×D4—91no—
384C2×#117—92no—
385C23×D3—32no—
386C23×D3—32no—
387C2×C3×Q8—21no—
388C2×C3×Q8—32no—
389C2×C3×Q8—32no—
390C2×C3×Q8—31no—
391C2×C3×Q8—64no—
392C2×C3×Q8C22×D311yescharacteristic
393C2×C3×Q8C22×D311yescharacteristic
394C2×C3×D4—31no—
395C22×C3×C4—31no—
396C22×C3×C4—31no—
397C22×C3×C4—32no—
398C22×C3×C4—32no—
399C22×C3×C4—32no—
400C22×C3×C4—31no—
401C2×#67—32no—
402C22×Dic3—32no—
403C22×Dic3—32no—
404C22×Dic3—34no—
405D3×Q8—24no—
406D3×Q8—68no—
407D3×D4—64no—
408C2×D12—32no—
409C2×D12—31no—
410C2×D12—31no—
411C2×D12—61no—
412C2×D12—64no—
413C2×D12C22×D311yescharacteristic
414C2×C4×D3—32no—
415C2×C4×D3—34no—
416C2×C4×D3—32no—
417C2×C4×D3—32no—
418C2×C4×D3—32no—
419C2×C4×D3—32no—
420C2×C4×D3—32no—
421C2×C4×D3—62no—
422C2×C4×D3—68no—
423C2×C4×D3—68no—
424C2×C4×D3C22×D312yes—
425C2×C4×D3C22×D311yescharacteristic
426C2×C4×D3C22×D312yes—
427C2×C4×D3C22×D312yes—
428C2×C4×D3C22×D311yescharacteristic
429C2×C4×D3C22×D311yescharacteristic
430C2×Dic6—32no—
431C2×Dic6—32no—
432C2×Dic6—34no—
433C2×Dic6—34no—
434C2×Dic6—62no—
435C2×Dic6—68no—
436C2×Dic6C22×D312yes—
437C2×Dic6C22×D312yes—
438C2×Dic6C22×D311yescharacteristic
439C3×C4⋊C4—21no—
440C3×C4⋊C4—22no—
441C3×C4⋊C4—31no—
442C3×C4⋊C4—34no—
443C3×C4⋊C4—32no—
444C3×C4⋊C4—32no—
445C3×C4⋊C4—32no—
446C3×C4⋊C4—31no—
447C3×C4⋊C4—32no—
448C3×C4⋊C4—32no—
449C3×C4⋊C4—32no—
450C3×C4⋊C4C22×D311yescharacteristic
451C3×C4⋊C4C22×D312yes—
452C3×C4⋊C4C22×D311yescharacteristic
453C3×C4⋊C4C22×D312yes—
454C3×C22⋊C4—34no—
455C3×C22⋊C4—34no—
456C3×C22⋊C4—32no—
457C3×C42—22no—
458C3×C42—21no—
459C3×C42—32no—
460C3×C42—32no—
461C3×C42—32no—
462C3×C42—34no—
463C3×C42—31no—
464C3×C42—31no—
465C3×C42—31no—
466C3×C42C22×D312yes—
467C3×C42C22×D312yes—
468C3×C42C22×D311yescharacteristic
469C3×C42C22×D311yescharacteristic
470#217—34no—
471#217—34no—
472#217—32no—
473(C2×D3)⋊C4—32no—
474(C2×D3)⋊C4—34no—
475(C2×D3)⋊C4—34no—
476(C2×D3)⋊C4—34no—
477(C2×D3)⋊C4—32no—
478(C2×D3)⋊C4—32no—
479(C2×D3)⋊C4—34no—
480(C2×D3)⋊C4—34no—
481(C2×D3)⋊C4—34no—
482(C2×D3)⋊C4—34no—
483(C2×D3)⋊C4—32no—
484(C2×D3)⋊C4—34no—
485(C2×D3)⋊C4—34no—
486(C2×D3)⋊C4—32no—
487(C2×D3)⋊C4—34no—
488(C2×D3)⋊C4—62no—
489(C2×D3)⋊C4—64no—
490(C2×D3)⋊C4—64no—
491(C2×D3)⋊C4C22×D312yes—
492(C2×D3)⋊C4C22×D314yes—
493(C2×D3)⋊C4C22×D314yes—
494C4⋊Dic3—31no—
495C4⋊Dic3—31no—
496C4⋊Dic3—32no—
497C4⋊Dic3—32no—
498C4⋊Dic3—32no—
499C4⋊Dic3—32no—
500C4⋊Dic3—32no—
501C4⋊Dic3—34no—
502C4⋊Dic3—34no—
503C4⋊Dic3—34no—
504C4⋊Dic3—61no—
505C4⋊Dic3—62no—
506C4⋊Dic3—62no—
507C4⋊Dic3C22×D311yescharacteristic
508C4⋊Dic3C22×D312yes—
509C4⋊Dic3C22×D311yescharacteristic
510C4⋊Dic3C22×D312yes—
511C4⋊Dic3C22×D312yes—
512Dic3⋊C4—34no—
513Dic3⋊C4—34no—
514Dic3⋊C4—32no—
515Dic3⋊C4—34no—
516Dic3⋊C4—34no—
517Dic3⋊C4—34no—
518Dic3⋊C4—34no—
519Dic3⋊C4—34no—
520Dic3⋊C4—64no—
521Dic3⋊C4C22×D314yes—
522Dic3⋊C4C22×D312yes—
523Dic3⋊C4C22×D312yes—
524Dic3⋊C4C22×D312yes—
525C4×Dic3—34no—
526C4×Dic3—34no—
527C4×Dic3—34no—
528C4×Dic3—34no—
529C4×Dic3—34no—
530C4×Dic3—34no—
531C4×Dic3—64no—
532C4×Dic3C22×D312yes—
533C4×Dic3C22×D314yes—
534C4×Dic3C22×D312yes—
535C4×Dic3C22×D311yescharacteristic
536C4×Dic3C22×D311yescharacteristic
537C4×Dic3C22×D312yes—
538C4×Dic3C22×D311yescharacteristic
539C22×C32C2511yescharacteristic
540C2×C3⋊D3—22no—
541C2×C3⋊D3—22no—
542C2×C3⋊D3—22no—
543C2×C3×D3—22no—
544C2×C3×D3—22no—
545C2×C3×D3—22no—
546C2×C3×D3C2×#4112yes—
547C2×C3×D3C2×#4112yes—
548C2×C3×D32−1+412yes—
549D32—48no—
550C32×C4—22no—
551C32×C4—22no—
552C32×C4—21no—
553C32×C4C2×#4112yes—
554C32×C4C2×#4112yes—
555C3⋊Dic3—22no—
556C3⋊Dic3—24no—
557C3×Dic3—22no—
558C3×Dic3—24no—
559C3×Dic3—22no—
560C3×Dic3—22no—
561C3×Dic3—21no—
562C3×Dic3C2×#4112yes—
563C3×Dic3C2×#4112yes—
564C22×Q8—31no—
565C22×Q8—92no—
566C22×D4—91no—
567C23×C4—92no—
568C4⋊Q8—31no—
569C4⋊Q8—92no—
570C4⋊Q8—92no—
571C4⋊Q8—92no—
572C4⋊Q8—91no—
573#126—34no—
574#126—94no—
575#126—94no—
576#126—94no—
577#126—94no—
578#126—94no—
579#126—94no—
580#126—94no—
581#124—32no—
582#124—94no—
583#124—94no—
584#124—92no—
585#124—92no—
586#124—92no—
587C22⋊Q8—32no—
588C22⋊Q8—94no—
589C22⋊Q8—94no—
590C22⋊Q8—92no—
591C22⋊Q8—92no—
592C22⋊Q8—92no—
593C4×Q8—31no—
594C4×Q8—32no—
595C4×Q8—31no—
596C4×Q8—32no—
597C4×Q8—31no—
598C4×Q8—32no—
599C4×Q8—94no—
600C4×Q8—92no—
601C4×Q8—94no—
602C4×Q8—92no—
603C4×Q8—92no—
604C4×Q8D3211yescharacteristic, complemented
605C4×D4—31no—
606C4×D4—92no—
607C4×D4—91no—
608C4×D4—92no—
609C4×D4—91no—
610C4×D4—91no—
611#117—32no—
612#117—94no—
613#117—94no—
614#117—92no—
615#117—92no—
616#117—92no—
617C2×C4⋊C4—31no—
618C2×C4⋊C4—32no—
619C2×C4⋊C4—92no—
620C2×C4⋊C4—91no—
621C2×C4⋊C4—94no—
622C2×C4⋊C4—92no—
623C2×C22⋊C4—94no—
624C2×C22⋊C4—92no—
625C2×C22⋊C4—94no—
626C2×C42—31no—
627C2×C42—32no—
628C2×C42—94no—
629C23×C3—31no—
630C23×C3—32no—
631C22×D3—32no—
632C22×D3—32no—
633C22×D3—62no—
634C22×D3—64no—
635C22×D3—64no—
636C22×D3—64no—
637C22×D3—64no—
638C22×D3—64no—
639C22×D3—64no—
640C22×D3C23×D312yes—
641C22×D3C23×D311yescharacteristic
642C3×Q8—22no—
643C3×Q8—22no—
644C3×Q8—42no—
645C3×Q8—64no—
646C3×Q8—64no—
647C3×Q8—62no—
648C3×D4—62no—
649C2×C3×C4—21no—
650C2×C3×C4—21no—
651C2×C3×C4—22no—
652C2×C3×C4—22no—
653C2×C3×C4—21no—
654C2×C3×C4—31no—
655C2×C3×C4—31no—
656C2×C3×C4—34no—
657C2×C3×C4—34no—
658C2×C3×C4—32no—
659C2×C3×C4—32no—
660C2×C3×C4—34no—
661C2×C3×C4—32no—
662C2×C3×C4—31no—
663C2×C3×C4—64no—
664C2×C3×C4—62no—
665C2×C3×C4—64no—
666C2×C3×C4—64no—
667C2×C3×C4C23×D312yes—
668C2×C3×C4C23×D312yes—
669C2×C3×C4C23×D312yes—
670C2×C3×C4C23×D311yescharacteristic
671C2×C3×C4C23×D312yes—
672C2×C3×C4C23×D311yescharacteristic
673C2×C3×C4C23×D311yescharacteristic
674C2×C3×C4C23×D311yescharacteristic
675C2×C3×C4C23×D311yescharacteristic
676C2×C3×C4C23×D311yescharacteristic
677#67—64no—
678C2×Dic3—32no—
679C2×Dic3—32no—
680C2×Dic3—34no—
681C2×Dic3—34no—
682C2×Dic3—62no—
683C2×Dic3—64no—
684C2×Dic3—68no—
685C2×Dic3—64no—
686C2×Dic3—64no—
687C2×Dic3C23×D312yes—
688C2×Dic3C23×D312yes—
689C2×Dic3C23×D314yes—
690C2×Dic3C23×D311yescharacteristic
691C2×Dic3C23×D312yes—
692C2×Dic3C23×D311yescharacteristic
693C2×Dic3C23×D311yescharacteristic
694D12—22no—
695D12—64no—
696D12—62no—
697D12—62no—
698D12—122no—
699C4×D3—24no—
700C4×D3—24no—
701C4×D3—22no—
702C4×D3—24no—
703C4×D3—64no—
704C4×D3—64no—
705C4×D3—64no—
706C4×D3—68no—
707C4×D3—64no—
708C4×D3—64no—
709C4×D3—64no—
710C4×D3—124no—
711C4×D3#23514yes—
712C4×D3#23914yes—
713Dic6—22no—
714Dic6—24no—
715Dic6—24no—
716Dic6—68no—
717Dic6—64no—
718Dic6—64no—
719Dic6—68no—
720Dic6—124no—
721C2×C32C22×#4111yescharacteristic
722C2×C32C22×#4111yescharacteristic
723C2×C32C2×2−1+411yescharacteristic
724C3⋊D3—42no—
725C3×D3—42no—
726C3×D3#55614yescomplemented
727C24—92no—
728C2×Q8—32no—
729C2×Q8—31no—
730C2×Q8—32no—
731C2×Q8—64no—
732C2×Q8—94no—
733C2×Q8—92no—
734C2×Q8—188no—
735C2×Q8C2×D3211yescharacteristic
736C2×D4—31no—
737C2×D4—92no—
738C2×D4—91no—
739C2×D4—184no—
740C22×C4—31no—
741C22×C4—31no—
742C22×C4—32no—
743C22×C4—31no—
744C22×C4—32no—
745C22×C4—32no—
746C22×C4—92no—
747C22×C4—92no—
748C22×C4—94no—
749C22×C4—92no—
750C22×C4—92no—
751C22×C4—188no—
752C4⋊C4—32no—
753C4⋊C4—31no—
754C4⋊C4—32no—
755C4⋊C4—32no—
756C4⋊C4—32no—
757C4⋊C4—32no—
758C4⋊C4—31no—
759C4⋊C4—34no—
760C4⋊C4—32no—
761C4⋊C4—94no—
762C4⋊C4—92no—
763C4⋊C4—94no—
764C4⋊C4—94no—
765C4⋊C4—94no—
766C4⋊C4—92no—
767C4⋊C4—91no—
768C4⋊C4—94no—
769C4⋊C4—92no—
770C4⋊C4C2×D3211yescharacteristic
771C4⋊C4C2×D3212yes—
772C22⋊C4—34no—
773C22⋊C4—32no—
774C22⋊C4—34no—
775C22⋊C4—94no—
776C22⋊C4—92no—
777C22⋊C4—94no—
778C22⋊C4—94no—
779C22⋊C4—92no—
780C22⋊C4—94no—
781C22⋊C4—94no—
782C22⋊C4—92no—
783C22⋊C4—94no—
784C42—31no—
785C42—31no—
786C42—31no—
787C42—32no—
788C42—32no—
789C42—32no—
790C42—34no—
791C42—94no—
792C42—94no—
793C42—94no—
794C42C2×D3211yescharacteristic
795C42C2×D3212yes—
796C22×C3—21no—
797C22×C3—32no—
798C22×C3—32no—
799C22×C3—32no—
800C22×C3—62no—
801C22×C3—62no—
802C22×C3—62no—
803C22×C3C24×D311yescharacteristic
804C22×C3C24×D311yescharacteristic
805C2×D3—22no—
806C2×D3—22no—
807C2×D3—22no—
808C2×D3—62no—
809C2×D3—62no—
810C2×D3—62no—
811C2×D3—62no—
812C2×D3—62no—
813C2×D3—62no—
814C2×D3—122no—
815C2×D3—122no—
816C2×D3—122no—
817C2×D3—128no—
818C2×D3—128no—
819C2×D3C2×#23512yes—
820C2×D3C2×#23912yes—
821C2×D3#101012yes—
822C3×C4—22no—
823C3×C4—22no—
824C3×C4—22no—
825C3×C4—21no—
826C3×C4—22no—
827C3×C4—21no—
828C3×C4—22no—
829C3×C4—22no—
830C3×C4—32no—
831C3×C4—32no—
832C3×C4—42no—
833C3×C4—42no—
834C3×C4—41no—
835C3×C4—62no—
836C3×C4—64no—
837C3×C4—62no—
838C3×C4—62no—
839C3×C4—61no—
840C3×C4C2×#23512yes—
841C3×C4C2×#23912yes—
842C3×C4D3×#4112yes—
843C3×C4D3×#4112yes—
844Dic3—22no—
845Dic3—24no—
846Dic3—22no—
847Dic3—22no—
848Dic3—21no—
849Dic3—62no—
850Dic3—64no—
851Dic3—64no—
852Dic3—62no—
853Dic3—124no—
854Dic3—122no—
855Dic3C2×#23512yes—
856Dic3C2×#23912yes—
857C32C2×#55611yescharacteristic, complemented, Sylow
858C23—31no—
859C23—32no—
860C23—92no—
861C23—184no—
862C23—184no—
863C23—184no—
864Q8—22no—
865Q8—64no—
866Q8—62no—
867Q8—64no—
868Q8—188no—
869Q8—184no—
870D4—62no—
871D4—184no—
872D4—182no—
873C2×C4—31no—
874C2×C4—31no—
875C2×C4—34no—
876C2×C4—34no—
877C2×C4—32no—
878C2×C4—32no—
879C2×C4—31no—
880C2×C4—32no—
881C2×C4—34no—
882C2×C4—64no—
883C2×C4—64no—
884C2×C4—62no—
885C2×C4—64no—
886C2×C4—92no—
887C2×C4—94no—
888C2×C4—184no—
889C2×C4—184no—
890C2×C4—184no—
891C2×C4—188no—
892C2×C4—184no—
893C2×C4C22×D3212yes—
894C2×C4C22×D3211yescharacteristic
895C2×C4C22×D3212yes—
896C2×C4C22×D3211yescharacteristic
897C2×C4C22×D3211yescharacteristic
898C2×C3—21no—
899C2×C3—21no—
900C2×C3—21no—
901C2×C3—34no—
902C2×C3—122no—
903C2×C3C22×#23511yescharacteristic
904C2×C3C22×#23911yescharacteristic
905C2×C3C2×D3×#4111yescharacteristic
906C2×C3C2×D3×#4111yescharacteristic
907C2×C3C2×#101011yescharacteristic
908C2×C3D3×2−1+411yescharacteristic
909D3—42no—
910D3—122no—
911D3—122no—
912D3—242no—
913D3#558414yesdirect product factor
914C22—32no—
915C22—32no—
916C22—32no—
917C22—62no—
918C22—62no—
919C22—62no—
920C22—182no—
921C22—182no—
922C22—182no—
923C22—368no—
924C22C23×D3211yescharacteristic
925C4—22no—
926C4—22no—
927C4—21no—
928C4—32no—
929C4—32no—
930C4—62no—
931C4—62no—
932C4—64no—
933C4—62no—
934C4—61no—
935C4—182no—
936C4—184no—
937C4D3×#23512yes—
938C4D3×#23912yes—
939C3—21no—
940C3C2×#558411yescharacteristic, complemented
941C3D3×#55611yescharacteristic, complemented
942C2—34no—
943C2—122no—
944C2—362no—
945C2C2×D3×#23511yescharacteristic
946C2C2×D3×#23911yescharacteristic
947C2D3×#101011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×Q8C22
prime radicalC2×D3×D12C22
hypercenterC4×Q8D32
hypocenterC32C2×#556
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. #10596055C2semidirect
2. C3×#5584C2semidirect
3. C3×C4×D3×Q8C2semidirect
4. D3×#946C2semidirect
5. #10595411C2semidirect
6. D3×#898C2semidirect
7. D3×#892C2semidirect
8. #10594565C2semidirect
9. #10594421C2semidirect
12. #10593932C2semidirect
13. D3×#869C2semidirect
14. C4×D3×Dic6C2semidirect
15. #10593879C2semidirect
16. #10593865C2semidirect
17. #10593850C2semidirect
24. C32×C4×Q8C22semidirect
25. #64155C22semidirect
26. #64107C22semidirect
27. #64101C22semidirect
30. #64078C22semidirect
31. C4×#634C22semidirect
32. C3×#946C22semidirect
33. C3×Q8×Dic3C22semidirect
34. C3×#898C22semidirect
35. C3×#892C22semidirect
38. C3×#887C22semidirect
39. C3×#887C22semidirect
44. C3×#869C22semidirect
45. C3×C4×Dic6C22semidirect
46. C3×C4×Dic6C22semidirect
47. C3×C4×Dic6C22semidirect
51. #63918C22semidirect
52. #63918C22semidirect
53. C4×#627C22semidirect
60. #63888C22semidirect
61. #63887C22semidirect
63. #63878C22semidirect
66. #63871C22semidirect
67. #63868C22semidirect
68. #63866C22semidirect
70. #63862C22semidirect
71. #63861C22semidirect
73. #63858C22semidirect
74. #63856C22semidirect
77. #63849C22semidirect
78. #63848C22semidirect
79. #63848C22semidirect
80. #63844C22semidirect
81. Dic3×Dic6C22semidirect
82. #63841C22semidirect
83. #63837C22semidirect
84. #63836C22semidirect
106. #5584D3direct (N × H)
108. C4×D3×Q8D3semidirect
209. C3×C4×Q8C2×D3semidirect
210. C3×C4×Q8C2×D3semidirect
225. #946C2×D3semidirect
227. Q8×Dic3C2×D3semidirect
253. #898C2×D3semidirect
265. #892C2×D3semidirect
276. #887C2×D3semidirect
277. #887C2×D3semidirect
316. #869C2×D3semidirect
325. C4×Dic6C2×D3semidirect
326. C4×Dic6C2×D3semidirect
327. C4×Dic6C2×D3semidirect
604. C4×Q8D32semidirect
726. C3×D3#556semidirect
857. C32C2×#556semidirect
913. D3#5584direct (N × H)
940. C3C2×#5584semidirect
941. C3D3×#556semidirect

Maximal subgroups

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

subgroupindex
#105960552
C3×#55842
C3×C4×D3×Q82
D3×#9462
#105954112
D3×#8982
D3×#8922
#105945652
#105944212
D3×#8752
C4×D3×D122
#105939322
D3×#8692
C4×D3×Dic62
#105938792
#105938652
#105938502
D3×#5563
C2×#55843