Finite Group Databasebeta

← D3×#63871 #13168220

Subgroups — D3×#63871 #13168220

Order 1728.

1726 conjugacy classes of subgroups.

The subgroup lattice has 934 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D3×C3⋊D3C211yesmaximal, characteristic
2C2×C3×D3×Dic6C211yesmaximal, characteristic, complemented
3#11723674C211yesmaximal, characteristic, complemented
4#11723456C211yesmaximal, characteristic, complemented
5#11723449C211yesmaximal, characteristic, complemented
6C3×D3×C4⋊Dic3C211yesmaximal, characteristic, complemented
7C3×#63871C211yesmaximal, characteristic, complemented
8#11722974C212yesmaximal, complemented
9#11722973C212yesmaximal, complemented
10D3×Dic3⋊Dic3C212yesmaximal, complemented
11D3×#3722C212yesmaximal
12D3×#946—31nomaximal
13C2×#63871—31nomaximal
14D3×#897—31nomaximal
15C22×D3×C3⋊D3C2211yescharacteristic
16C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
17C2×C3×C4×C3⋊D3C2211yescharacteristic
18C2×C3×#634C2211yescharacteristic, complemented
19C2×C32×C4×D3C2211yescharacteristic
20C2×C32×Dic6C2211yescharacteristic, complemented
21C2×#6289C2211yescharacteristic
22C2×Dic3×C3⋊D3C2211yescharacteristic
23C2×D3×C3⋊Dic3C2211yescharacteristic
24C4×D3×C3⋊D3—24no—
25C2×C3×#627C2212yescomplemented
26C2×C3×D3×Dic3C2212yes—
27C2×C3×D3×Dic3C2212yes—
28C3×D3×Dic6—24no—
29C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
30C32×C4⋊Dic3C2211yescharacteristic, complemented
31#88815C2212yescomplemented
32#88814C2212yes—
33#88807C2212yescomplemented
34Dic3⋊(C3⋊Dic3)C2212yescomplemented
35#88804C2212yes—
36#88804C2212yes—
37C3×Dic3⋊Dic3C2212yescomplemented
38C3×Dic3⋊Dic3C2212yescomplemented
39C3×#3722C2212yes—
40C22×C4×C3⋊D3—31no—
41C2×C3×D3×Q8—31no—
42C22×C3×Dic6—31no—
43C2×C4×D32—31no—
44C2×C4×D32—31no—
45C2×C4×D32—61no—
46C2×D3×Dic6D311yescharacteristic, complemented
47#64155—31no—
48#64106—31no—
49C3×#946—31no—
50C2×C3×C4⋊Dic3—31no—
51C3×#897—31no—
52C3×D3×C4⋊C4—31no—
53C2×Dic3⋊Dic3—32no—
54C2×#3722—32no—
55D3×(C2×D3)⋊C4—32no—
56D3×(C2×D3)⋊C4—32no—
57#63895—32no—
58#63893—32no—
59D3×C4⋊Dic3—32no—
60D3×C4⋊Dic3D311yescharacteristic, complemented
61#63888—32no—
62#63887—32no—
63D3×Dic3⋊C4—32no—
64#63871—31no—
65#63871—31no—
66#63871—31no—
67#63871—31no—
68#63871—31no—
69#63871—32no—
70#63871—32no—
71#63871—61no—
72#63871—61no—
73#63871D311yescharacteristic, direct product factor
74#63857—31no—
75#63856—31no—
76C22×C3⋊(C3⋊D3)C2311yescharacteristic
77C22×C3×C3⋊D3C2311yescharacteristic
78C22×C32×D3C2311yescharacteristic
79C2×D3×C3⋊D3—22no—
80C2×D3×C3⋊D3—22no—
81C2×D3×C3⋊D3Q814yescomplemented
82C2×C33×C4C2311yescharacteristic
83C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
84C4×C3⋊(C3⋊D3)—22no—
85C2×C3×C3⋊Dic3C2312yes—
86C2×C3×C3⋊Dic3C2312yes—
87C2×C3×C3⋊Dic3C2311yescharacteristic
88C3×C4×C3⋊D3—22no—
89C3×#634—22no—
90C2×C32×Dic3C2312yes—
91C2×C32×Dic3C2312yes—
92C2×C32×Dic3C2311yescharacteristic
93C32×C4×D3D414yes—
94C32×Dic6—22no—
95#6289—22no—
96Dic3×C3⋊D3—22no—
97D3×C3⋊Dic3—22no—
98C3×#627—24no—
99C3×D3×Dic3—24no—
100C3×D3×Dic3—24no—
101C2×#946—91no—
102D3×C22⋊Q8—91no—
103C2×#897—91no—
104C23×C3⋊D3—31no—
105C22×D32—31no—
106C22×D32—31no—
107C22×D32—61no—
108C2×C32×Q8—31no—
109C22×C32×C4—31no—
110C22×C3⋊Dic3—31no—
111C2×C4×C3⋊D3—31no—
112C2×C4×C3⋊D3—31no—
113C2×C4×C3⋊D3—31no—
114C2×C4×C3⋊D3—31no—
115C2×C4×C3⋊D3—31no—
116C2×C4×C3⋊D3—64no—
117C2×C4×C3⋊D3—61no—
118C2×C4×C3⋊D3—61no—
119C2×C4×C3⋊D3—61no—
120C2×C4×C3⋊D3—121no—
121C2×C4×C3⋊D3C2×D311yescharacteristic
122C2×#634C2×D311yescharacteristic, complemented
123C22×C3×Dic3—32no—
124C22×C3×Dic3—32no—
125C3×D3×Q8—64no—
126C2×C3×C4×D3—21no—
127C2×C3×C4×D3—32no—
128C2×C3×C4×D3—32no—
129C2×C3×C4×D3—31no—
130C2×C3×C4×D3—31no—
131C2×C3×C4×D3—61no—
132C2×C3×C4×D3C2×D311yescharacteristic
133C2×C3×C4×D3C2×D311yescharacteristic
134C2×C3×Dic6—21no—
135C2×C3×Dic6—31no—
136C2×C3×Dic6—31no—
137C2×C3×Dic6—32no—
138C2×C3×Dic6—32no—
139C2×C3×Dic6—64no—
140C2×C3×Dic6—61no—
141C2×C3×Dic6C2×D311yescharacteristic, complemented
142C2×C3×Dic6C2×D311yescharacteristic, complemented
143C2×#627C2×D312yescomplemented
144C2×#624—31no—
145C2×#624—31no—
146C2×#624—61no—
147C2×D3×Dic3—31no—
148C2×D3×Dic3—31no—
149C2×D3×Dic3—31no—
150C2×D3×Dic3—31no—
151C2×D3×Dic3—61no—
152C2×D3×Dic3—61no—
153C2×D3×Dic3C2×D312yes—
154C2×D3×Dic3C2×D312yes—
155C4×D32—68no—
156C4×D32—64no—
157C4×D32—64no—
158D3×Dic6—24no—
159C32×C4⋊C4—31no—
160#3752—32no—
161#3752—32no—
162C4⋊(C3⋊Dic3)—32no—
163C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
164#3750—32no—
165C3×(C2×D3)⋊C4—32no—
166C3×(C2×D3)⋊C4—32no—
167C3×C4⋊Dic3—21no—
168C3×C4⋊Dic3—31no—
169C3×C4⋊Dic3—31no—
170C3×C4⋊Dic3—32no—
171C3×C4⋊Dic3—32no—
172C3×C4⋊Dic3—61no—
173C3×C4⋊Dic3C2×D311yescharacteristic, complemented
174C3×C4⋊Dic3C2×D311yescharacteristic, complemented
175C3×Dic3⋊C4—32no—
176C3×Dic3⋊C4—32no—
177#3724—32no—
178Dic3⋊Dic3—32no—
179Dic3⋊Dic3—32no—
180Dic3⋊Dic3—32no—
181Dic3⋊Dic3—32no—
182Dic3⋊Dic3—32no—
183Dic3⋊Dic3—32no—
184Dic3⋊Dic3—62no—
185Dic3⋊Dic3—62no—
186Dic3⋊Dic3C2×D312yescomplemented
187Dic3⋊Dic3C2×D312yescomplemented
188#3722—32no—
189#3722—32no—
190#3722—32no—
191#3722—32no—
192#3722—32no—
193#3722—62no—
194#3722—62no—
195#3722C2×D312yes—
196(C2×D3)⋊Dic3—32no—
197(C2×D3)⋊Dic3—32no—
198C22×C33C2411yescharacteristic
199C2×C3⋊(C3⋊D3)—21no—
200C2×C3⋊(C3⋊D3)—21no—
201C2×C3⋊(C3⋊D3)C2×Q812yescomplemented
202C2×C3×C3⋊D3—21no—
203C2×C3×C3⋊D3—21no—
204C2×C3×C3⋊D3C2×Q812yescomplemented
205C2×C32×D3C2×D412yes—
206C2×C32×D3C2×Q812yes—
207C2×C32×D3#4112yes—
208D3×C3⋊D3—28no—
209C33×C4C2×D412yes—
210C3⋊(C3⋊Dic3)—21no—
211C3×C3⋊Dic3—21no—
212C3×C3⋊Dic3—22no—
213C3×C3⋊Dic3—22no—
214C32×Dic3—22no—
215C32×Dic3—22no—
216C32×Dic3C2×D412yes—
217C22×C3×Q8—91no—
218C2×D3×Q8—31no—
219C22×C4×D3—91no—
220C22×C4×D3—91no—
221C22×C4×D3—91no—
222C22×C4×D3—181no—
223C22×Dic6—31no—
224C3×C22⋊Q8—91no—
225C2×C3×C4⋊C4—91no—
226#946—31no—
227#946—92no—
228#946—92no—
229#946—91no—
230#946—91no—
231#946—91no—
232#946—91no—
233#946—181no—
234C2×(C2×D3)⋊C4—92no—
235C2×(C2×D3)⋊C4—92no—
236C2×C4⋊Dic3—31no—
237C2×C4⋊Dic3—92no—
238#924—91no—
239C2×Dic3⋊C4—92no—
240#897—31no—
241#897—92no—
242#897—92no—
243#897—91no—
244#897—91no—
245#897—91no—
246#897—91no—
247#897—181no—
248#896—92no—
249D3×C4⋊C4—31no—
250D3×C4⋊C4—92no—
251D3×C22⋊C4—92no—
252#878—92no—
253C23×C32—31no—
254C22×C3⋊D3—31no—
255C22×C3⋊D3—31no—
256C22×C3⋊D3—31no—
257C22×C3⋊D3—34no—
258C22×C3⋊D3—61no—
259C22×C3⋊D3—61no—
260C22×C3⋊D3—61no—
261C22×C3⋊D3—62no—
262C22×C3⋊D3—62no—
263C22×C3⋊D3—121no—
264C22×C3⋊D3C22×D311yescharacteristic
265C22×C3×D3—21no—
266C22×C3×D3—31no—
267C22×C3×D3—31no—
268C22×C3×D3—61no—
269C22×C3×D3C22×D311yescharacteristic
270C22×C3×D3C22×D311yescharacteristic
271C2×D32—34no—
272C2×D32—34no—
273C2×D32—64no—
274C2×D32—64no—
275C2×D32—64no—
276C2×D32—62no—
277C2×D32—62no—
278C2×D32—62no—
279C2×D32—62no—
280C32×Q8—62no—
281C2×C32×C4—21no—
282C2×C32×C4—21no—
283C2×C32×C4—21no—
284C2×C32×C4—31no—
285C2×C32×C4—34no—
286C2×C32×C4—32no—
287C2×C32×C4—32no—
288C2×C32×C4—41no—
289C2×C32×C4C22×D311yescharacteristic
290C2×C32×C4C22×D311yescharacteristic
291C2×C32×C4C22×D311yescharacteristic
292C2×C3⋊Dic3—31no—
293C2×C3⋊Dic3—31no—
294C2×C3⋊Dic3—31no—
295C2×C3⋊Dic3—61no—
296C2×C3⋊Dic3—61no—
297C2×C3⋊Dic3—61no—
298C2×C3⋊Dic3—62no—
299C2×C3⋊Dic3—121no—
300C2×C3⋊Dic3C22×D312yes—
301C2×C3⋊Dic3C22×D312yes—
302C2×C3⋊Dic3C22×D311yescharacteristic
303C4×C3⋊D3—22no—
304C4×C3⋊D3—62no—
305C4×C3⋊D3—62no—
306C4×C3⋊D3—62no—
307C4×C3⋊D3—64no—
308C4×C3⋊D3—62no—
309C4×C3⋊D3—62no—
310C4×C3⋊D3—122no—
311C4×C3⋊D3—122no—
312C4×C3⋊D3—124no—
313#634—22no—
314C2×C3×Dic3—21no—
315C2×C3×Dic3—22no—
316C2×C3×Dic3—22no—
317C2×C3×Dic3—32no—
318C2×C3×Dic3—32no—
319C2×C3×Dic3—32no—
320C2×C3×Dic3—32no—
321C2×C3×Dic3—31no—
322C2×C3×Dic3—31no—
323C2×C3×Dic3—61no—
324C2×C3×Dic3—62no—
325C2×C3×Dic3—62no—
326C2×C3×Dic3—64no—
327C2×C3×Dic3—64no—
328C2×C3×Dic3C22×D312yes—
329C2×C3×Dic3C22×D312yes—
330C2×C3×Dic3C22×D312yes—
331C2×C3×Dic3C22×D312yes—
332C2×C3×Dic3C22×D311yescharacteristic
333C2×C3×Dic3C22×D311yescharacteristic
334C3×C4×D3—24no—
335C3×C4×D3—64no—
336C3×C4×D3—64no—
337C3×C4×D3—64no—
338C3×C4×D3—62no—
339C3×C4×D3—62no—
340C3×C4×D3D1214yes—
341C3×C4×D3#6714yes—
342C3×Dic6—22no—
343C3×Dic6—22no—
344C3×Dic6—42no—
345C3×Dic6—64no—
346C3×Dic6—62no—
347C3×Dic6—62no—
348C3×Dic6—64no—
349C3×Dic6—122no—
350#627—24no—
351#624—64no—
352#624—62no—
353#624—62no—
354D3×Dic3—24no—
355D3×Dic3—24no—
356D3×Dic3—64no—
357D3×Dic3—64no—
358D3×Dic3—62no—
359D3×Dic3—62no—
360D3×Dic3—62no—
361D3×Dic3—62no—
362C2×C22⋊Q8—271noSylow
363C2×C33C22×D411yescharacteristic
364C2×C33C22×Q811yescharacteristic
365C2×C33C2×#4111yescharacteristic
366C3⋊(C3⋊D3)—22no—
367C3×C3⋊D3—22no—
368C32×D3C22⋊Q814yescomplemented
369C23×D3—91no—
370C23×D3—91no—
371C23×D3—91no—
372C23×D3—181no—
373C2×C3×Q8—31no—
374C2×C3×Q8—31no—
375C2×C3×Q8—61no—
376C2×C3×Q8—92no—
377C2×C3×Q8—91no—
378C2×C3×Q8—184no—
379C22×C3×C4—31no—
380C22×C3×C4—31no—
381C22×C3×C4—61no—
382C22×C3×C4—92no—
383C22×C3×C4—92no—
384C22×C3×C4—91no—
385C22×Dic3—32no—
386C22×Dic3—32no—
387C22×Dic3—91no—
388C22×Dic3—91no—
389C22×Dic3—91no—
390C22×Dic3—181no—
391D3×Q8—64no—
392C2×C4×D3—32no—
393C2×C4×D3—32no—
394C2×C4×D3—31no—
395C2×C4×D3—31no—
396C2×C4×D3—61no—
397C2×C4×D3—91no—
398C2×C4×D3—91no—
399C2×C4×D3—91no—
400C2×C4×D3—91no—
401C2×C4×D3—91no—
402C2×C4×D3—91no—
403C2×C4×D3—91no—
404C2×C4×D3—91no—
405C2×C4×D3—91no—
406C2×C4×D3—181no—
407C2×C4×D3—181no—
408C2×C4×D3—181no—
409C2×C4×D3—181no—
410C2×C4×D3—181no—
411C2×C4×D3—184no—
412C2×C4×D3—184no—
413C2×C4×D3—188no—
414C2×C4×D3—184no—
415C2×C4×D3—361no—
416C2×C4×D3D3211yescharacteristic
417C2×Dic6—31no—
418C2×Dic6—31no—
419C2×Dic6—32no—
420C2×Dic6—32no—
421C2×Dic6—61no—
422C2×Dic6—64no—
423C2×Dic6D3211yescharacteristic, complemented
424C3×C4⋊C4—31no—
425C3×C4⋊C4—31no—
426C3×C4⋊C4—61no—
427C3×C4⋊C4—92no—
428C3×C4⋊C4—92no—
429C3×C4⋊C4—91no—
430C3×C22⋊C4—92no—
431#217—92no—
432(C2×D3)⋊C4—32no—
433(C2×D3)⋊C4—32no—
434(C2×D3)⋊C4—92no—
435(C2×D3)⋊C4—92no—
436(C2×D3)⋊C4—92no—
437(C2×D3)⋊C4—92no—
438(C2×D3)⋊C4—92no—
439(C2×D3)⋊C4—92no—
440(C2×D3)⋊C4—92no—
441(C2×D3)⋊C4—92no—
442(C2×D3)⋊C4—182no—
443(C2×D3)⋊C4—182no—
444C4⋊Dic3—31no—
445C4⋊Dic3—31no—
446C4⋊Dic3—32no—
447C4⋊Dic3—32no—
448C4⋊Dic3—61no—
449C4⋊Dic3—92no—
450C4⋊Dic3—92no—
451C4⋊Dic3—92no—
452C4⋊Dic3—92no—
453C4⋊Dic3—182no—
454C4⋊Dic3D3211yescharacteristic, complemented
455Dic3⋊C4—32no—
456Dic3⋊C4—32no—
457Dic3⋊C4—92no—
458Dic3⋊C4—92no—
459Dic3⋊C4—92no—
460Dic3⋊C4—92no—
461Dic3⋊C4—92no—
462Dic3⋊C4—182no—
463C22×C32—21no—
464C22×C32—21no—
465C22×C32—21no—
466C22×C32—32no—
467C22×C32—32no—
468C22×C32—32no—
469C22×C32—41no—
470C22×C32C23×D311yescharacteristic
471C22×C32C23×D311yescharacteristic
472C22×C32C23×D311yescharacteristic
473C2×C3⋊D3—21no—
474C2×C3⋊D3—21no—
475C2×C3⋊D3—32no—
476C2×C3⋊D3—32no—
477C2×C3⋊D3—32no—
478C2×C3⋊D3—62no—
479C2×C3⋊D3—62no—
480C2×C3⋊D3—62no—
481C2×C3⋊D3—68no—
482C2×C3⋊D3—61no—
483C2×C3⋊D3—61no—
484C2×C3⋊D3—62no—
485C2×C3⋊D3—62no—
486C2×C3⋊D3—61no—
487C2×C3⋊D3—61no—
488C2×C3⋊D3—61no—
489C2×C3⋊D3—61no—
490C2×C3⋊D3—122no—
491C2×C3⋊D3—121no—
492C2×C3⋊D3—121no—
493C2×C3⋊D3—121no—
494C2×C3⋊D3—121no—
495C2×C3⋊D3—122no—
496C2×C3⋊D3—122no—
497C2×C3⋊D3D3×Q812yescomplemented
498C2×C3×D3—22no—
499C2×C3×D3—22no—
500C2×C3×D3—22no—
501C2×C3×D3—32no—
502C2×C3×D3—32no—
503C2×C3×D3—62no—
504C2×C3×D3—62no—
505C2×C3×D3—62no—
506C2×C3×D3—61no—
507C2×C3×D3—61no—
508C2×C3×D3—61no—
509C2×C3×D3—61no—
510C2×C3×D3C2×D1212yes—
511C2×C3×D3#23712yes—
512C2×C3×D3D3×Q812yes—
513C2×C3×D3D3×Q812yes—
514C2×C3×D3#23912yes—
515C2×C3×D3C2×#6712yes—
516D32—616no—
517D32—68no—
518D32—68no—
519C32×C4—22no—
520C32×C4—22no—
521C32×C4—22no—
522C32×C4—32no—
523C32×C4—42no—
524C32×C4—62no—
525C32×C4—62no—
526C32×C4C2×D1212yes—
527C32×C4D3×D412yes—
528C32×C4C2×#6712yes—
529C3⋊Dic3—21no—
530C3⋊Dic3—22no—
531C3⋊Dic3—22no—
532C3⋊Dic3—61no—
533C3⋊Dic3—62no—
534C3⋊Dic3—61no—
535C3⋊Dic3—61no—
536C3⋊Dic3—121no—
537C3⋊Dic3—121no—
538C3⋊Dic3—122no—
539C3×Dic3—22no—
540C3×Dic3—22no—
541C3×Dic3—22no—
542C3×Dic3—22no—
543C3×Dic3—22no—
544C3×Dic3—42no—
545C3×Dic3—42no—
546C3×Dic3—62no—
547C3×Dic3—61no—
548C3×Dic3—62no—
549C3×Dic3—62no—
550C3×Dic3—62no—
551C3×Dic3—62no—
552C3×Dic3—61no—
553C3×Dic3—122no—
554C3×Dic3—122no—
555C3×Dic3C2×D1212yes—
556C3×Dic3C2×#6712yes—
557C22×Q8—91no—
558C23×C4—271no—
559C22⋊Q8—91no—
560C22⋊Q8—272no—
561C22⋊Q8—271no—
562C22⋊Q8—272no—
563C22⋊Q8—271no—
564C22⋊Q8—271no—
565C2×C4⋊C4—91no—
566C2×C4⋊C4—272no—
567C2×C22⋊C4—272no—
568C33C2×C22⋊Q811yescharacteristic, complemented, Sylow
569C23×C3—31no—
570C23×C3—31no—
571C23×C3—61no—
572C23×C3—91no—
573C22×D3—31no—
574C22×D3—31no—
575C22×D3—61no—
576C22×D3—94no—
577C22×D3—94no—
578C22×D3—91no—
579C22×D3—91no—
580C22×D3—91no—
581C22×D3—94no—
582C22×D3—184no—
583C22×D3—181no—
584C22×D3—181no—
585C22×D3—181no—
586C22×D3—182no—
587C22×D3—182no—
588C22×D3—182no—
589C22×D3—182no—
590C22×D3—184no—
591C22×D3—184no—
592C22×D3—182no—
593C22×D3—182no—
594C22×D3—361no—
595C22×D3C2×D3211yescharacteristic
596C3×Q8—62no—
597C3×Q8—62no—
598C3×Q8—122no—
599C3×Q8—184no—
600C3×Q8—182no—
601C2×C3×C4—21no—
602C2×C3×C4—21no—
603C2×C3×C4—21no—
604C2×C3×C4—31no—
605C2×C3×C4—31no—
606C2×C3×C4—34no—
607C2×C3×C4—34no—
608C2×C3×C4—32no—
609C2×C3×C4—32no—
610C2×C3×C4—32no—
611C2×C3×C4—32no—
612C2×C3×C4—41no—
613C2×C3×C4—64no—
614C2×C3×C4—61no—
615C2×C3×C4—62no—
616C2×C3×C4—62no—
617C2×C3×C4—92no—
618C2×C3×C4—91no—
619C2×C3×C4—92no—
620C2×C3×C4—184no—
621C2×C3×C4—184no—
622C2×C3×C4—182no—
623C2×C3×C4C2×D3211yescharacteristic
624C2×C3×C4C2×D3211yescharacteristic
625C2×C3×C4C2×D3211yescharacteristic
626C2×Dic3—31no—
627C2×Dic3—32no—
628C2×Dic3—32no—
629C2×Dic3—32no—
630C2×Dic3—31no—
631C2×Dic3—32no—
632C2×Dic3—61no—
633C2×Dic3—62no—
634C2×Dic3—62no—
635C2×Dic3—64no—
636C2×Dic3—64no—
637C2×Dic3—91no—
638C2×Dic3—91no—
639C2×Dic3—91no—
640C2×Dic3—181no—
641C2×Dic3—181no—
642C2×Dic3—181no—
643C2×Dic3—182no—
644C2×Dic3—182no—
645C2×Dic3—184no—
646C2×Dic3—182no—
647C2×Dic3—361no—
648C2×Dic3C2×D3212yes—
649C2×Dic3C2×D3212yes—
650C2×Dic3C2×D3211yescharacteristic
651C4×D3—64no—
652C4×D3—64no—
653C4×D3—64no—
654C4×D3—62no—
655C4×D3—62no—
656C4×D3—182no—
657C4×D3—182no—
658C4×D3—184no—
659C4×D3—184no—
660C4×D3—182no—
661C4×D3—182no—
662C4×D3—184no—
663C4×D3—182no—
664C4×D3—182no—
665C4×D3—182no—
666C4×D3—182no—
667C4×D3—182no—
668C4×D3—362no—
669C4×D3—362no—
670C4×D3—364no—
671C4×D3#62614yes—
672Dic6—22no—
673Dic6—64no—
674Dic6—62no—
675Dic6—62no—
676Dic6—64no—
677Dic6—122no—
678C2×C32—21no—
679C2×C32—21no—
680C2×C32—21no—
681C2×C32—21no—
682C2×C32—21no—
683C2×C32—21no—
684C2×C32—21no—
685C2×C32—21no—
686C2×C32—21no—
687C2×C32—34no—
688C2×C32—41no—
689C2×C32—41no—
690C2×C32—41no—
691C2×C32C22×D1211yescharacteristic
692C2×C32C2×D3×D411yescharacteristic
693C2×C32C2×#23711yescharacteristic
694C2×C32C2×D3×Q811yescharacteristic
695C2×C32C2×D3×Q811yescharacteristic
696C2×C32C2×D3×Q811yescharacteristic
697C2×C32C2×#23911yescharacteristic
698C2×C32D3×#4111yescharacteristic
699C2×C32C22×#6711yescharacteristic
700C3⋊D3—22no—
701C3⋊D3—62no—
702C3⋊D3—64no—
703C3⋊D3—62no—
704C3⋊D3—62no—
705C3⋊D3—122no—
706C3⋊D3—122no—
707C3⋊D3—124no—
708C3×D3—24no—
709C3×D3—64no—
710C3×D3—62no—
711C3×D3—62no—
712C3×D3#89714yescomplemented
713C3×D3#94614yescomplemented
714C24—271no—
715C2×Q8—31no—
716C2×Q8—92no—
717C2×Q8—91no—
718C2×Q8—184no—
719C22×C4—31no—
720C22×C4—92no—
721C22×C4—92no—
722C22×C4—91no—
723C22×C4—271no—
724C22×C4—271no—
725C22×C4—271no—
726C22×C4—271no—
727C22×C4—544no—
728C4⋊C4—31no—
729C4⋊C4—92no—
730C4⋊C4—92no—
731C4⋊C4—91no—
732C4⋊C4—272no—
733C4⋊C4—272no—
734C4⋊C4—272no—
735C22⋊C4—92no—
736C22⋊C4—272no—
737C22⋊C4—272no—
738C22⋊C4—272no—
739C22×C3—21no—
740C22×C3—21no—
741C22×C3—21no—
742C22×C3—32no—
743C22×C3—32no—
744C22×C3—32no—
745C22×C3—32no—
746C22×C3—32no—
747C22×C3—32no—
748C22×C3—41no—
749C22×C3—62no—
750C22×C3—62no—
751C22×C3—62no—
752C22×C3—92no—
753C22×C3—181no—
754C22×C3—181no—
755C22×C3C22×D3211yescharacteristic
756C22×C3C22×D3211yescharacteristic
757C22×C3C22×D3211yescharacteristic
758C2×D3—32no—
759C2×D3—32no—
760C2×D3—62no—
761C2×D3—62no—
762C2×D3—62no—
763C2×D3—61no—
764C2×D3—61no—
765C2×D3—61no—
766C2×D3—61no—
767C2×D3—92no—
768C2×D3—92no—
769C2×D3—92no—
770C2×D3—182no—
771C2×D3—182no—
772C2×D3—182no—
773C2×D3—188no—
774C2×D3—188no—
775C2×D3—1816no—
776C2×D3—182no—
777C2×D3—182no—
778C2×D3—181no—
779C2×D3—181no—
780C2×D3—181no—
781C2×D3—181no—
782C2×D3—181no—
783C2×D3—181no—
784C2×D3—188no—
785C2×D3—362no—
786C2×D3—361no—
787C2×D3—361no—
788C2×D3—361no—
789C2×D3—361no—
790C2×D3—362no—
791C2×D3—362no—
792C2×D3#379612yes—
793C2×D3#379712yes—
794C2×D3C2×#62612yes—
795C3×C4—22no—
796C3×C4—22no—
797C3×C4—22no—
798C3×C4—32no—
799C3×C4—32no—
800C3×C4—42no—
801C3×C4—62no—
802C3×C4—62no—
803C3×C4—62no—
804C3×C4—62no—
805C3×C4—62no—
806C3×C4—122no—
807C3×C4—122no—
808C3×C4—182no—
809C3×C4—182no—
810C3×C4—181no—
811C3×C4D3×D1212yes—
812C3×C4C2×#62612yes—
813C3×C4D3×#6712yes—
814Dic3—22no—
815Dic3—22no—
816Dic3—62no—
817Dic3—62no—
818Dic3—61no—
819Dic3—62no—
820Dic3—62no—
821Dic3—62no—
822Dic3—61no—
823Dic3—122no—
824Dic3—122no—
825Dic3—182no—
826Dic3—181no—
827Dic3—181no—
828Dic3—181no—
829Dic3—361no—
830Dic3—361no—
831Dic3—362no—
832Dic3C2×#62612yes—
833C32—21no—
834C32—21no—
835C32—21no—
836C32—41no—
837C32C2×#89711yescharacteristic, complemented
838C32D3×C22⋊Q811yescharacteristic, complemented
839C32C2×#94611yescharacteristic, complemented
840C23—31no—
841C23—91no—
842C23—274no—
843C23—271no—
844C23—542no—
845C23—542no—
846Q8—62no—
847Q8—184no—
848Q8—182no—
849C2×C4—31no—
850C2×C4—34no—
851C2×C4—32no—
852C2×C4—32no—
853C2×C4—92no—
854C2×C4—92no—
855C2×C4—91no—
856C2×C4—184no—
857C2×C4—184no—
858C2×C4—182no—
859C2×C4—271no—
860C2×C4—542no—
861C2×C4—542no—
862C2×C4—542no—
863C2×C4—542no—
864C2×C4D3311yescharacteristic
865C2×C3—21no—
866C2×C3—21no—
867C2×C3—21no—
868C2×C3—21no—
869C2×C3—21no—
870C2×C3—21no—
871C2×C3—21no—
872C2×C3—21no—
873C2×C3—21no—
874C2×C3—34no—
875C2×C3—34no—
876C2×C3—41no—
877C2×C3—41no—
878C2×C3—41no—
879C2×C3—64no—
880C2×C3—182no—
881C2×C3C2×#379611yescharacteristic
882C2×C3C2×#379711yescharacteristic
883C2×C3C2×D3×D1211yescharacteristic
884C2×C3D3×#23711yescharacteristic
885C2×C3D32×Q811yescharacteristic
886C2×C3D32×Q811yescharacteristic
887C2×C3D3×#23911yescharacteristic
888C2×C3C22×#62611yescharacteristic
889C2×C3C2×D3×#6711yescharacteristic
890D3—64no—
891D3—62no—
892D3—62no—
893D3—184no—
894D3—182no—
895D3—182no—
896D3—182no—
897D3—362no—
898D3—362no—
899D3—364no—
900D3#6387114yesdirect product factor
901C22—32no—
902C22—32no—
903C22—32no—
904C22—92no—
905C22—181no—
906C22—181no—
907C22—272no—
908C22—548no—
909C22—541no—
910C22—541no—
911C22C2×D3311yescharacteristic
912C4—32no—
913C4—62no—
914C4—62no—
915C4—182no—
916C4—181no—
917C4—182no—
918C4—541no—
919C4D3×#62612yes—
920C3—21no—
921C3—21no—
922C3—21no—
923C3—41no—
924C3D3×#89711yescharacteristic, complemented
925C3C2×#6387111yescharacteristic, complemented
926C3D3×#94611yescharacteristic, complemented
927C2—34no—
928C2—182no—
929C2—542no—
930C2D3×#379611yescharacteristic
931C2D3×#379711yescharacteristic
932C2C2×D3×#62611yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radicalC22×D3×C3⋊D3C22
hypercenterC2×C4D33
hypocenterC33C2×C22⋊Q8
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×D3×Dic6C2semidirect
3. #11723674C2semidirect
4. #11723456C2semidirect
5. #11723449C2semidirect
6. C3×D3×C4⋊Dic3C2semidirect
7. C3×#63871C2semidirect
8. #11722974C2semidirect
9. #11722973C2semidirect
10. D3×Dic3⋊Dic3C2semidirect
18. C2×C3×#634C22semidirect
20. C2×C32×Dic6C22semidirect
25. C2×C3×#627C22semidirect
29. C3×C4⋊(C3⋊Dic3)C22semidirect
30. C32×C4⋊Dic3C22semidirect
31. #88815C22semidirect
33. #88807C22semidirect
34. Dic3⋊(C3⋊Dic3)C22semidirect
37. C3×Dic3⋊Dic3C22semidirect
38. C3×Dic3⋊Dic3C22semidirect
46. C2×D3×Dic6D3semidirect
60. D3×C4⋊Dic3D3semidirect
73. #63871D3direct (N × H)
81. C2×D3×C3⋊D3Q8semidirect
122. C2×#634C2×D3semidirect
141. C2×C3×Dic6C2×D3semidirect
142. C2×C3×Dic6C2×D3semidirect
143. C2×#627C2×D3semidirect
163. C4⋊(C3⋊Dic3)C2×D3semidirect
173. C3×C4⋊Dic3C2×D3semidirect
174. C3×C4⋊Dic3C2×D3semidirect
186. Dic3⋊Dic3C2×D3semidirect
187. Dic3⋊Dic3C2×D3semidirect
201. C2×C3⋊(C3⋊D3)C2×Q8semidirect
204. C2×C3×C3⋊D3C2×Q8semidirect
368. C32×D3C22⋊Q8semidirect
423. C2×Dic6D32semidirect
454. C4⋊Dic3D32semidirect
497. C2×C3⋊D3D3×Q8semidirect
568. C33C2×C22⋊Q8semidirect
712. C3×D3#897semidirect
713. C3×D3#946semidirect
837. C32C2×#897semidirect
838. C32D3×C22⋊Q8semidirect
839. C32C2×#946semidirect
900. D3#63871direct (N × H)
924. C3D3×#897semidirect
925. C3C2×#63871semidirect
926. C3D3×#946semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D3×C3⋊D32
C2×C3×D3×Dic62
#117236742
#117234562
#117234492
C3×D3×C4⋊Dic32
C3×#638712
#117229742
#117229732
D3×Dic3⋊Dic32
D3×#37222
D3×#9463
C2×#638713
D3×#8973