Finite Group Databasebeta

← D3×#5542 #11903382

Subgroups — D3×#5542 #11903382

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#10596013C211yesmaximal, characteristic, complemented
2C3×C4×D3×D4C211yesmaximal, characteristic
3C3×#5542C211yesmaximal, characteristic, complemented
4#10595273C212yesmaximal, complemented
5D3×#936C212yesmaximal
6D3×#926C212yesmaximal, complemented
7D3×#924C212yesmaximal, complemented
8#10594841C212yesmaximal, complemented
9#10594840C212yesmaximal, complemented
10D3×#887C212yesmaximal, complemented
11#10594335C212yesmaximal, complemented
12#10594248C214yesmaximal, complemented
13D3×#879C214yesmaximal, complemented
14D3×#869C211yesmaximal, characteristic, complemented
15C4×D3×Dic6C211yesmaximal, characteristic, complemented
16#10593879C211yesmaximal, characteristic, complemented
17#10593863C211yesmaximal, characteristic, complemented
18D3×#556—31nomaximal
19C2×#5542—31nomaximal
20C2×C3×D3×D4C2211yescharacteristic
21C22×C3×C4×D3C2212yes—
22C2×D3×Dic6C2212yes—
23C2×D3×Dic6C2211yescharacteristic
24C32×C4×D4C2211yescharacteristic
25#64145C2212yes—
26#64135C2212yescomplemented
27#64133C2212yescomplemented
28#64096C2212yescomplemented
29#64088C2214yescomplemented
30#64078C2211yescharacteristic, complemented
31C4×#634C2211yescharacteristic, complemented
32C3×#936C2212yes—
33C3×D4×Dic3C2211yescharacteristic
34C3×C4×#67C2212yes—
35C3×#926C2212yescomplemented
36C3×#924C2212yescomplemented
37C3×#893C2211yescharacteristic
38C3×D3×C4⋊C4C2211yescharacteristic
39C3×#887C2212yescomplemented
40C3×#67⋊C4C2212yes—
41C3×D3×C22⋊C4C2212yes—
42C3×#879C2214yescomplemented
43C3×C4×D12C2211yescharacteristic
44C3×C42×D3C2211yescharacteristic
45C3×#869C2211yescharacteristic, complemented
46C3×C4×Dic6C2211yescharacteristic, complemented
47D3×#217C2214yes—
48D3×#217C2214yes—
49#63964C2214yescomplemented
50#63959C2214yes—
51#63959C2214yes—
52#63956C2214yescomplemented
53#63956C2214yescomplemented
54#63955C2214yescomplemented
55#63918C2212yescomplemented
56#63918C2212yescomplemented
57C4×#627C2212yescomplemented
58D3×C4⋊Dic3C2212yes—
59D3×C4⋊Dic3C2212yes—
60D3×C4⋊Dic3C2211yescharacteristic
61D3×Dic3⋊C4C2212yes—
62D3×Dic3⋊C4C2214yes—
63C4×D3×Dic3C2214yes—
64C4×D3×Dic3C2212yes—
65#63866C2212yescomplemented
66#63863C2212yes—
67#63862C2214yescomplemented
68#63861C2214yescomplemented
69#63860C2212yes—
70#63859C2214yescomplemented
71#63858C2214yescomplemented
72#63857C2212yescomplemented
73#63856C2212yescomplemented
74#63855C2214yescomplemented
75#63851C2214yescomplemented
76#63844C2211yescharacteristic, complemented
77#63844C2212yescomplemented
78#63843C2212yescomplemented
79Dic3×Dic6C2211yescharacteristic, complemented
80#63841C2212yescomplemented
81#63841C2212yescomplemented
82#63838C2214yescomplemented
83#63837C2214yescomplemented
84#63837C2212yescomplemented
85C3×#556—31no—
86C2×C3×C4×D4—31no—
87C2×#936—32no—
88C2×#926—32no—
89C2×#924—32no—
90#5732—31no—
91D3×C4⋊Q8—31no—
92D3×#126—34no—
93#5702—34no—
94D3×#124—32no—
95#5671—32no—
96#5641—32no—
97D3×C22⋊Q8—32no—
98#5584—31no—
99C4×D3×Q8—32no—
100C4×D3×Q8—31no—
101#5568—32no—
102C4×D3×D4D311yescharacteristic
103#5542—31no—
104#5542—31no—
105#5542—32no—
106#5542—32no—
107#5542—32no—
108#5542—32no—
109#5542—34no—
110#5542—31no—
111#5542—31no—
112#5542—61no—
113#5542D311yescharacteristic, direct product factor
114#5533—32no—
115D3×#117—32no—
116C2×#887—32no—
117C2×#879—34no—
118C2×#869—31no—
119C2×C4×Dic6—31no—
120C23×C3×D3C2312yes—
121C2×C32×D4C2311yescharacteristic
122C22×C32×C4C2312yes—
123C2×#634C2311yescharacteristic
124C2×#634C2312yes—
125C2×C3×#67C2312yes—
126C22×C3×Dic3C2312yes—
127C3×D3×D4—24no—
128C2×C3×D12C2311yescharacteristic
129C2×C3×C4×D3—28no—
130C2×C3×C4×D3C2311yescharacteristic
131C2×C3×C4×D3C2312yes—
132C2×C3×C4×D3C2312yes—
133C2×C3×C4×D3C2312yes—
134C2×C3×C4×D3C2311yescharacteristic
135C2×C3×C4×D3C2311yescharacteristic
136C2×C3×Dic6C2312yes—
137C2×C3×Dic6C2311yescharacteristic
138C2×#627C2314yes—
139C2×#627C2312yes—
140C2×D3×Dic3C2312yes—
141C2×D3×Dic3C2314yes—
142C2×D3×Dic3C2312yes—
143D3×Dic6—28no—
144D3×Dic6—24no—
145C32×C4⋊C4C2311yescharacteristic
146C32×C22⋊C4C2312yes—
147C32×C42C2311yescharacteristic
148#3757C2314yes—
149#3757C2314yes—
150C4⋊(C3⋊Dic3)C2311yescharacteristic
151C4⋊(C3⋊Dic3)C2312yes—
152C4⋊(C3⋊Dic3)C2312yes—
153#3750C2312yes—
154#3750C2314yes—
155C4×C3⋊Dic3C2312yes—
156C4×C3⋊Dic3C2314yes—
157C3×#217C2314yes—
158C3×#217C2314yes—
159C3×#217C2312yes—
160C3×(C2×D3)⋊C4C2312yes—
161C3×(C2×D3)⋊C4C2312yes—
162C3×C4⋊Dic3C2312yes—
163C3×C4⋊Dic3C2311yescharacteristic
164C3×C4⋊Dic3C2312yes—
165C3×C4⋊Dic3C2311yescharacteristic
166C3×Dic3⋊C4C2312yes—
167C3×Dic3⋊C4C2314yes—
168C3×Dic3⋊C4C2312yes—
169C3×C4×Dic3C2314yes—
170C3×C4×Dic3C2311yescharacteristic
171C3×C4×Dic3C2312yes—
172C3×C4×Dic3C2311yescharacteristic
173C3×C4×Dic3C2311yescharacteristic
174#3724C2314yes—
175#3724C2312yes—
176Dic3⋊Dic3C2314yes—
177Dic3⋊Dic3C2312yes—
178Dic3⋊Dic3C2312yes—
179Dic3⋊Dic3C2314yes—
180Dic3⋊Dic3C2314yes—
181(C2×D3)⋊Dic3C2314yes—
182(C2×D3)⋊Dic3C2314yes—
183(C2×D3)⋊Dic3C2314yes—
184(C2×D3)⋊Dic3C2314yes—
185Dic32C2312yes—
186Dic32C2312yes—
187Dic32C2314yes—
188Dic32C2314yes—
189C2×#556—91noSylow
190C22×C3×D4—31no—
191C23×C3×C4—32no—
192C2×D3×Q8—32no—
193C2×D3×Q8—31no—
194C2×D3×D4C2×D311yescharacteristic
195C22×C4×D3C2×D312yes—
196C22×Dic6—31no—
197C22×Dic6—32no—
198C3×C4⋊Q8—31no—
199C3×#126—34no—
200C3×#124—32no—
201C3×C22⋊Q8—32no—
202C3×C4×Q8—32no—
203C3×C4×Q8—31no—
204C3×C4×D4—21no—
205C3×C4×D4—31no—
206C3×C4×D4—32no—
207C3×C4×D4—31no—
208C3×C4×D4—32no—
209C3×C4×D4—31no—
210C3×C4×D4C2×D311yescharacteristic
211C3×C4×D4C2×D311yescharacteristic
212C3×#117—32no—
213C2×C3×C4⋊C4—31no—
214C2×C3×C22⋊C4—32no—
215C2×C3×C42—31no—
216C2×#217—34no—
217C2×#217—34no—
218#947—32no—
219#946—32no—
220Q8×Dic3—32no—
221Q8×Dic3—31no—
222#944—32no—
223#936—32no—
224#936—32no—
225#936—32no—
226#936—34no—
227#936—34no—
228#936—32no—
229#936—62no—
230#936C2×D312yes—
231D4×Dic3C2×D311yescharacteristic
232C4×#67C2×D312yes—
233#926—32no—
234#926—32no—
235#926—34no—
236#926—32no—
237#926—32no—
238#926—34no—
239#926—62no—
240#926C2×D312yescomplemented
241C2×C4⋊Dic3—31no—
242C2×C4⋊Dic3—32no—
243C2×C4⋊Dic3—32no—
244#924—32no—
245#924—32no—
246#924—32no—
247#924—34no—
248#924—32no—
249#924—34no—
250#924—62no—
251#924C2×D312yescomplemented
252C2×Dic3⋊C4—32no—
253C2×Dic3⋊C4—34no—
254C2×C4×Dic3—32no—
255C2×C4×Dic3—34no—
256#898—34no—
257#898—34no—
258#898—34no—
259#897—32no—
260#896—34no—
261#893C2×D311yescharacteristic
262#892—32no—
263#892—32no—
264D3×C4⋊C4—32no—
265D3×C4⋊C4—32no—
266D3×C4⋊C4—34no—
267D3×C4⋊C4—32no—
268D3×C4⋊C4—31no—
269D3×C4⋊C4C2×D311yescharacteristic
270#888—32no—
271#888—32no—
272#887—32no—
273#887—32no—
274#887—32no—
275#887—34no—
276#887—34no—
277#887—32no—
278#887—34no—
279#887—32no—
280#887—31no—
281#887—62no—
282#887C2×D312yescomplemented
283#885—34no—
284#885—34no—
285#67⋊C4C2×D312yes—
286D3×C22⋊C4—34no—
287D3×C22⋊C4—34no—
288D3×C22⋊C4C2×D312yes—
289#879—34no—
290#879—34no—
291#879—34no—
292#879—34no—
293#879—34no—
294#879—34no—
295#879—34no—
296#879—34no—
297#879—34no—
298#879—34no—
299#879—64no—
300#879C2×D314yescomplemented
301#878—34no—
302#877—34no—
303#876—34no—
304#875—32no—
305C4×D12C2×D311yescharacteristic
306#872—34no—
307C42×D3—32no—
308C42×D3—34no—
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—31no—
318C4×Dic6—31no—
319C4×Dic6—31no—
320C4×Dic6—32no—
321C4×Dic6—31no—
322C4×Dic6—34no—
323C4×Dic6—32no—
324C4×Dic6—32no—
325C4×Dic6—32no—
326C4×Dic6—61no—
327C4×Dic6C2×D311yescharacteristic, complemented
328C23×C32C2412yes—
329C22×C3×D3—24no—
330C22×C3×D3—24no—
331C22×C3×D3—24no—
332C22×C3×D3C2412yes—
333C22×C3×D3C2411yescharacteristic
334C32×D4—22no—
335C2×C32×C4—24no—
336C2×C32×C4C2412yes—
337C2×C32×C4C2411yescharacteristic
338C2×C32×C4C2411yescharacteristic
339C2×C32×C4C2411yescharacteristic
340C2×C3⋊Dic3C2412yes—
341C2×C3⋊Dic3C2412yes—
342C2×C3⋊Dic3C2414yes—
343#634—24no—
344#634—22no—
345C3×#67—24no—
346C2×C3×Dic3—24no—
347C2×C3×Dic3C2412yes—
348C2×C3×Dic3C2412yes—
349C2×C3×Dic3C2414yes—
350C2×C3×Dic3C2412yes—
351C2×C3×Dic3C2411yescharacteristic
352C2×C3×Dic3C2411yescharacteristic
353C2×C3×Dic3C2411yescharacteristic
354C3×D12—22no—
355C3×C4×D3—24no—
356C3×C4×D3—22no—
357C3×C4×D3—24no—
358C3×C4×D3—24no—
359C3×C4×D3#4114yes—
360C3×C4×D3#4114yes—
361C3×Dic6—24no—
362C3×Dic6—22no—
363#627—28no—
364#627—24no—
365D3×Dic3—28no—
366D3×Dic3—24no—
367D3×Dic3—24no—
368#556—31no—
369#556—92no—
370#556—92no—
371#556—91no—
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—91no—
382C2×C4×Q8—92no—
383C2×C4×D4—31no—
384C2×#117—92no—
385C24×C3—32no—
386C23×D3C22×D312yes—
387C2×C3×Q8—32no—
388C2×C3×Q8—31no—
389C2×C3×D4—21no—
390C2×C3×D4—32no—
391C2×C3×D4—31no—
392C2×C3×D4—64no—
393C2×C3×D4C22×D311yescharacteristic
394C2×C3×D4C22×D311yescharacteristic
395C22×C3×C4—22no—
396C22×C3×C4—31no—
397C22×C3×C4—31no—
398C22×C3×C4—32no—
399C22×C3×C4—32no—
400C22×C3×C4—31no—
401C22×C3×C4—32no—
402C22×C3×C4—32no—
403C22×C3×C4—68no—
404C22×C3×C4C22×D312yes—
405C22×C3×C4C22×D312yes—
406C2×#67C22×D312yes—
407C22×Dic3—32no—
408C22×Dic3—32no—
409C22×Dic3—34no—
410C22×Dic3C22×D312yes—
411D3×Q8—68no—
412D3×Q8—64no—
413D3×D4—24no—
414C2×D12C22×D311yescharacteristic
415C2×C4×D3—28no—
416C2×C4×D3—32no—
417C2×C4×D3—34no—
418C2×C4×D3—32no—
419C2×C4×D3C22×D312yes—
420C2×C4×D3C22×D311yescharacteristic
421C2×C4×D3C22×D312yes—
422C2×C4×D3C22×D312yes—
423C2×C4×D3C22×D311yescharacteristic
424C2×C4×D3C22×D311yescharacteristic
425C2×Dic6—31no—
426C2×Dic6—32no—
427C2×Dic6—31no—
428C2×Dic6—32no—
429C2×Dic6—32no—
430C2×Dic6—32no—
431C2×Dic6—34no—
432C2×Dic6—34no—
433C2×Dic6—61no—
434C2×Dic6—62no—
435C2×Dic6—68no—
436C2×Dic6—64no—
437C2×Dic6C22×D311yescharacteristic
438C2×Dic6C22×D312yes—
439C3×C4⋊C4—21no—
440C3×C4⋊C4—32no—
441C3×C4⋊C4—31no—
442C3×C4⋊C4—31no—
443C3×C4⋊C4—34no—
444C3×C4⋊C4—32no—
445C3×C4⋊C4—32no—
446C3×C4⋊C4—32no—
447C3×C4⋊C4C22×D311yescharacteristic
448C3×C4⋊C4C22×D311yescharacteristic
449C3×C22⋊C4—22no—
450C3×C22⋊C4—34no—
451C3×C22⋊C4—34no—
452C3×C22⋊C4—32no—
453C3×C22⋊C4—32no—
454C3×C22⋊C4—32no—
455C3×C22⋊C4C22×D312yes—
456C3×C22⋊C4C22×D312yes—
457C3×C42—21no—
458C3×C42—31no—
459C3×C42—31no—
460C3×C42—31no—
461C3×C42—32no—
462C3×C42—34no—
463C3×C42C22×D311yescharacteristic
464C3×C42C22×D311yescharacteristic
465#217—34no—
466#217—34no—
467#217—34no—
468#217—34no—
469#217—34no—
470#217—34no—
471#217—34no—
472#217—34no—
473#217—64no—
474#217—64no—
475#217C22×D312yes—
476#217C22×D314yes—
477#217C22×D314yes—
478(C2×D3)⋊C4—34no—
479(C2×D3)⋊C4—34no—
480(C2×D3)⋊C4—34no—
481(C2×D3)⋊C4—34no—
482(C2×D3)⋊C4C22×D312yes—
483(C2×D3)⋊C4C22×D312yes—
484C4⋊Dic3—31no—
485C4⋊Dic3—31no—
486C4⋊Dic3—32no—
487C4⋊Dic3—32no—
488C4⋊Dic3—32no—
489C4⋊Dic3—32no—
490C4⋊Dic3—32no—
491C4⋊Dic3—34no—
492C4⋊Dic3—32no—
493C4⋊Dic3—34no—
494C4⋊Dic3—34no—
495C4⋊Dic3—61no—
496C4⋊Dic3—62no—
497C4⋊Dic3—62no—
498C4⋊Dic3C22×D311yescharacteristic
499C4⋊Dic3C22×D311yescharacteristic
500C4⋊Dic3C22×D312yes—
501C4⋊Dic3C22×D312yes—
502Dic3⋊C4—32no—
503Dic3⋊C4—34no—
504Dic3⋊C4—32no—
505Dic3⋊C4—34no—
506Dic3⋊C4—32no—
507Dic3⋊C4—32no—
508Dic3⋊C4—32no—
509Dic3⋊C4—32no—
510Dic3⋊C4—34no—
511Dic3⋊C4—34no—
512Dic3⋊C4—34no—
513Dic3⋊C4—34no—
514Dic3⋊C4—34no—
515Dic3⋊C4—62no—
516Dic3⋊C4—64no—
517Dic3⋊C4C22×D312yes—
518Dic3⋊C4C22×D312yes—
519Dic3⋊C4C22×D314yes—
520C4×Dic3—32no—
521C4×Dic3—32no—
522C4×Dic3—34no—
523C4×Dic3—34no—
524C4×Dic3—34no—
525C4×Dic3—32no—
526C4×Dic3—32no—
527C4×Dic3—32no—
528C4×Dic3—34no—
529C4×Dic3—32no—
530C4×Dic3—34no—
531C4×Dic3—34no—
532C4×Dic3—62no—
533C4×Dic3—64no—
534C4×Dic3C22×D311yescharacteristic
535C4×Dic3C22×D312yes—
536C4×Dic3C22×D311yescharacteristic
537C4×Dic3C22×D311yescharacteristic
538C4×Dic3C22×D314yes—
539C22×C32—22no—
540C22×C32—22no—
541C22×C32—22no—
542C22×C32C2511yescharacteristic
543C2×C3×D3—22no—
544C2×C3×D3—22no—
545C2×C3×D3—22no—
546C2×C3×D3—48no—
547C2×C3×D3C2×#4112yes—
548C2×C3×D3C2×#4112yes—
549C2×C3×D32−1+412yes—
550C32×C4—22no—
551C32×C4—21no—
552C32×C4C2×#4112yes—
553C32×C4C2×#4112yes—
554C3⋊Dic3—24no—
555C3⋊Dic3—22no—
556C3⋊Dic3—22no—
557C3×Dic3—24no—
558C3×Dic3—22no—
559C3×Dic3—22no—
560C3×Dic3—22no—
561C3×Dic3—21no—
562C3×Dic3C2×#4112yes—
563C3×Dic3C2×#4112yes—
564C22×Q8—91no—
565C22×Q8—92no—
566C22×D4—31no—
567C23×C4—32no—
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—92no—
583#124—94no—
584#124—94no—
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—32no—
594C4×Q8—31no—
595C4×Q8—92no—
596C4×Q8—91no—
597C4×Q8—92no—
598C4×Q8—94no—
599C4×Q8—92no—
600C4×Q8—91no—
601C4×Q8—94no—
602C4×Q8—92no—
603C4×Q8—92no—
604C4×Q8—91no—
605C4×D4—31no—
606C4×D4—32no—
607C4×D4—31no—
608C4×D4—32no—
609C4×D4—31no—
610C4×D4D3211yescharacteristic
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—91no—
619C2×C4⋊C4—92no—
620C2×C4⋊C4—94no—
621C2×C4⋊C4—92no—
622C2×C4⋊C4—92no—
623C2×C22⋊C4—32no—
624C2×C22⋊C4—94no—
625C2×C22⋊C4—94no—
626C2×C42—31no—
627C2×C42—94no—
628C2×C42—92no—
629C23×C3—22no—
630C23×C3—31no—
631C23×C3—32no—
632C23×C3—64no—
633C23×C3—64no—
634C23×C3—64no—
635C23×C3C23×D312yes—
636C23×C3C23×D312yes—
637C22×D3—24no—
638C22×D3—24no—
639C22×D3—24no—
640C22×D3C23×D312yes—
641C22×D3C23×D311yescharacteristic
642C3×Q8—64no—
643C3×Q8—62no—
644C3×D4—22no—
645C3×D4—22no—
646C3×D4—42no—
647C3×D4—64no—
648C3×D4—62no—
649C2×C3×C4—24no—
650C2×C3×C4—24no—
651C2×C3×C4—21no—
652C2×C3×C4—21no—
653C2×C3×C4—22no—
654C2×C3×C4—21no—
655C2×C3×C4—31no—
656C2×C3×C4—31no—
657C2×C3×C4—34no—
658C2×C3×C4—34no—
659C2×C3×C4—32no—
660C2×C3×C4—32no—
661C2×C3×C4—34no—
662C2×C3×C4—32no—
663C2×C3×C4—31no—
664C2×C3×C4—44no—
665C2×C3×C4—64no—
666C2×C3×C4—62no—
667C2×C3×C4—64no—
668C2×C3×C4—64no—
669C2×C3×C4—64no—
670C2×C3×C4C23×D312yes—
671C2×C3×C4C23×D312yes—
672C2×C3×C4C23×D311yescharacteristic
673C2×C3×C4C23×D311yescharacteristic
674C2×C3×C4C23×D311yescharacteristic
675C2×C3×C4C23×D311yescharacteristic
676C2×C3×C4C23×D311yescharacteristic
677C2×C3×C4C23×D311yescharacteristic
678#67—24no—
679C2×Dic3—24no—
680C2×Dic3—32no—
681C2×Dic3—32no—
682C2×Dic3—32no—
683C2×Dic3—34no—
684C2×Dic3—32no—
685C2×Dic3—34no—
686C2×Dic3—62no—
687C2×Dic3—62no—
688C2×Dic3—64no—
689C2×Dic3—68no—
690C2×Dic3—64no—
691C2×Dic3—64no—
692C2×Dic3C23×D312yes—
693C2×Dic3C23×D312yes—
694C2×Dic3C23×D312yes—
695C2×Dic3C23×D314yes—
696C2×Dic3C23×D311yescharacteristic
697C2×Dic3C23×D311yescharacteristic
698C2×Dic3C23×D311yescharacteristic
699D12—22no—
700C4×D3—24no—
701C4×D3—22no—
702C4×D3—24no—
703C4×D3—24no—
704C4×D3—68no—
705C4×D3—64no—
706C4×D3—64no—
707C4×D3#23514yes—
708C4×D3#23714yes—
709Dic6—24no—
710Dic6—22no—
711Dic6—68no—
712Dic6—64no—
713Dic6—64no—
714Dic6—62no—
715Dic6—64no—
716Dic6—62no—
717Dic6—68no—
718Dic6—64no—
719Dic6—124no—
720Dic6—122no—
721C2×C32—42no—
722C2×C32C22×#4111yescharacteristic
723C2×C32C22×#4111yescharacteristic
724C2×C32C2×2−1+411yescharacteristic
725C3×D3—42no—
726C3×D3#55614yescomplemented
727C24—32no—
728C2×Q8—31no—
729C2×Q8—32no—
730C2×Q8—92no—
731C2×Q8—94no—
732C2×Q8—91no—
733C2×Q8—92no—
734C2×Q8—188no—
735C2×Q8—184no—
736C2×D4—32no—
737C2×D4—31no—
738C2×D4—64no—
739C2×D4C2×D3211yescharacteristic
740C22×C4—31no—
741C22×C4—31no—
742C22×C4—32no—
743C22×C4—31no—
744C22×C4—32no—
745C22×C4—32no—
746C22×C4—32no—
747C22×C4—68no—
748C22×C4—92no—
749C22×C4—94no—
750C22×C4—92no—
751C22×C4C2×D3212yes—
752C4⋊C4—32no—
753C4⋊C4—31no—
754C4⋊C4—31no—
755C4⋊C4—32no—
756C4⋊C4—34no—
757C4⋊C4—32no—
758C4⋊C4—32no—
759C4⋊C4—92no—
760C4⋊C4—94no—
761C4⋊C4—94no—
762C4⋊C4—94no—
763C4⋊C4—92no—
764C4⋊C4—92no—
765C4⋊C4—94no—
766C4⋊C4—91no—
767C4⋊C4—92no—
768C4⋊C4—94no—
769C4⋊C4—92no—
770C4⋊C4—92no—
771C4⋊C4C2×D3211yescharacteristic
772C22⋊C4—32no—
773C22⋊C4—34no—
774C22⋊C4—34no—
775C22⋊C4—32no—
776C22⋊C4—32no—
777C22⋊C4—94no—
778C22⋊C4—94no—
779C22⋊C4—94no—
780C22⋊C4—94no—
781C22⋊C4—94no—
782C22⋊C4—94no—
783C22⋊C4C2×D3212yes—
784C42—31no—
785C42—31no—
786C42—31no—
787C42—34no—
788C42—32no—
789C42—94no—
790C42—94no—
791C42—92no—
792C42—92no—
793C42—94no—
794C42—92no—
795C42C2×D3211yescharacteristic
796C22×C3—22no—
797C22×C3—22no—
798C22×C3—22no—
799C22×C3—22no—
800C22×C3—22no—
801C22×C3—22no—
802C22×C3—21no—
803C22×C3—32no—
804C22×C3—32no—
805C22×C3—32no—
806C22×C3—42no—
807C22×C3—42no—
808C22×C3—42no—
809C22×C3—62no—
810C22×C3—62no—
811C22×C3—62no—
812C22×C3—128no—
813C22×C3C24×D311yescharacteristic
814C22×C3C24×D311yescharacteristic
815C2×D3—22no—
816C2×D3—22no—
817C2×D3—22no—
818C2×D3—48no—
819C2×D3C2×#23512yes—
820C2×D3C2×#23712yes—
821C2×D3#101012yes—
822C3×C4—22no—
823C3×C4—22no—
824C3×C4—21no—
825C3×C4—21no—
826C3×C4—22no—
827C3×C4—22no—
828C3×C4—32no—
829C3×C4—32no—
830C3×C4—42no—
831C3×C4—41no—
832C3×C4—64no—
833C3×C4—62no—
834C3×C4—62no—
835C3×C4—62no—
836C3×C4—61no—
837C3×C4C2×#23512yes—
838C3×C4C2×#23712yes—
839C3×C4D3×#4112yes—
840C3×C4D3×#4112yes—
841Dic3—22no—
842Dic3—24no—
843Dic3—22no—
844Dic3—21no—
845Dic3—22no—
846Dic3—64no—
847Dic3—62no—
848Dic3—64no—
849Dic3—62no—
850Dic3—62no—
851Dic3—62no—
852Dic3—124no—
853Dic3—122no—
854Dic3—122no—
855Dic3C2×#23512yes—
856Dic3C2×#23712yes—
857C32C2×#55611yescharacteristic, complemented, Sylow
858C23—31no—
859C23—32no—
860C23—64no—
861C23—64no—
862C23—64no—
863C23C22×D3212yes—
864Q8—64no—
865Q8—62no—
866Q8—188no—
867Q8—184no—
868Q8—184no—
869Q8—182no—
870D4—22no—
871D4—64no—
872D4—62no—
873C2×C4—24no—
874C2×C4—31no—
875C2×C4—31no—
876C2×C4—34no—
877C2×C4—34no—
878C2×C4—32no—
879C2×C4—31no—
880C2×C4—34no—
881C2×C4—32no—
882C2×C4—32no—
883C2×C4—64no—
884C2×C4—64no—
885C2×C4—62no—
886C2×C4—64no—
887C2×C4—64no—
888C2×C4—92no—
889C2×C4—94no—
890C2×C4—92no—
891C2×C4—188no—
892C2×C4—184no—
893C2×C4—184no—
894C2×C4C22×D3212yes—
895C2×C4C22×D3211yescharacteristic
896C2×C4C22×D3211yescharacteristic
897C2×C4C22×D3211yescharacteristic
898C2×C3—21no—
899C2×C3—21no—
900C2×C3—21no—
901C2×C3—34no—
902C2×C3—42no—
903C2×C3—42no—
904C2×C3—82no—
905C2×C3—122no—
906C2×C3C22×#23511yescharacteristic
907C2×C3C22×#23711yescharacteristic
908C2×C3C2×D3×#4111yescharacteristic
909C2×C3C2×D3×#4111yescharacteristic
910C2×C3C2×#101011yescharacteristic
911C2×C3D3×2−1+411yescharacteristic
912D3—42no—
913D3#554214yesdirect product factor
914C22—22no—
915C22—22no—
916C22—22no—
917C22—32no—
918C22—32no—
919C22—32no—
920C22—62no—
921C22—62no—
922C22—62no—
923C22—128no—
924C22C23×D3211yescharacteristic
925C4—22no—
926C4—21no—
927C4—32no—
928C4—32no—
929C4—64no—
930C4—62no—
931C4—62no—
932C4—61no—
933C4—62no—
934C4—184no—
935C4—182no—
936C4—182no—
937C4D3×#23512yes—
938C4D3×#23712yes—
939C3—21no—
940C3C2×#554211yescharacteristic, complemented
941C3D3×#55611yescharacteristic, complemented
942C2—34no—
943C2—42no—
944C2—122no—
945C2C2×D3×#23511yescharacteristic
946C2C2×D3×#23711yescharacteristic
947C2D3×#101011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×D4C22
prime radicalC2×C3×D3×D4C22
hypercenterC4×D4D32
hypocenterC32C2×#556
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #10596013C2semidirect
3. C3×#5542C2semidirect
4. #10595273C2semidirect
6. D3×#926C2semidirect
7. D3×#924C2semidirect
8. #10594841C2semidirect
9. #10594840C2semidirect
10. D3×#887C2semidirect
11. #10594335C2semidirect
12. #10594248C2semidirect
13. D3×#879C2semidirect
14. D3×#869C2semidirect
15. C4×D3×Dic6C2semidirect
16. #10593879C2semidirect
17. #10593863C2semidirect
26. #64135C22semidirect
27. #64133C22semidirect
28. #64096C22semidirect
29. #64088C22semidirect
30. #64078C22semidirect
31. C4×#634C22semidirect
35. C3×#926C22semidirect
36. C3×#924C22semidirect
39. C3×#887C22semidirect
42. C3×#879C22semidirect
45. C3×#869C22semidirect
46. C3×C4×Dic6C22semidirect
49. #63964C22semidirect
52. #63956C22semidirect
53. #63956C22semidirect
54. #63955C22semidirect
55. #63918C22semidirect
56. #63918C22semidirect
57. C4×#627C22semidirect
65. #63866C22semidirect
67. #63862C22semidirect
68. #63861C22semidirect
70. #63859C22semidirect
71. #63858C22semidirect
72. #63857C22semidirect
73. #63856C22semidirect
74. #63855C22semidirect
75. #63851C22semidirect
76. #63844C22semidirect
77. #63844C22semidirect
78. #63843C22semidirect
79. Dic3×Dic6C22semidirect
80. #63841C22semidirect
81. #63841C22semidirect
82. #63838C22semidirect
83. #63837C22semidirect
84. #63837C22semidirect
113. #5542D3direct (N × H)
240. #926C2×D3semidirect
251. #924C2×D3semidirect
282. #887C2×D3semidirect
300. #879C2×D3semidirect
316. #869C2×D3semidirect
327. C4×Dic6C2×D3semidirect
726. C3×D3#556semidirect
857. C32C2×#556semidirect
913. D3#5542direct (N × H)
940. C3C2×#5542semidirect
941. C3D3×#556semidirect

Maximal subgroups

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

subgroupindex
#105960132
C3×C4×D3×D42
C3×#55422
#105952732
D3×#9362
D3×#9262
D3×#9242
#105948412
#105948402
D3×#8872
#105943352
#105942482
D3×#8792
D3×#8692
C4×D3×Dic62
#105938792
#105938632
D3×#5563
C2×#55423