Finite Group Databasebeta

← #13175913

Subgroups — #13175913

Order 1728.

2556 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89039C211yesmaximal, characteristic
2C22⋊C4×C3⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
3C3×#64090C211yesmaximal, characteristic, complemented
4C32×#67⋊C4C211yesmaximal, characteristic, complemented
5#67×C3⋊Dic3C211yesmaximal, characteristic, complemented
6Dic3×#638C211yesmaximal, characteristic, complemented
7C2×#88804C211yesmaximal, characteristic, complemented
8C3⋊D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
9D3×#3752C211yesmaximal, characteristic, complemented
10C4×#6292C211yesmaximal, characteristic, complemented
11C4×#6291C211yesmaximal, characteristic, complemented
12#11723472C211yesmaximal, characteristic, complemented
13#11723469C211yesmaximal, characteristic, complemented
14#11723468C211yesmaximal, characteristic, complemented
15#11723462C211yesmaximal, characteristic, complemented
16#10596016—31nomaximal
17#10594256—34nomaximal
18C23×C3⋊(C3⋊D3)C2211yescharacteristic
19C22×D3×C3⋊D3C2211yescharacteristic
20C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
21C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
22C2×C3×#638C2211yescharacteristic
23C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
24C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
25C2×C32×#67C2211yescharacteristic
26C22×C32×Dic3C2211yescharacteristic, complemented
27C2×C32×C4×D3C2211yescharacteristic, complemented
28#89039C418yescomplemented
29C2×#6292C2211yescharacteristic
30C2×#6291C2211yescharacteristic
31C2×#6289C2211yescharacteristic
32C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
33C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
34C33×C22⋊C4C2211yescharacteristic, complemented
35#88864C2211yescharacteristic, complemented
36#88859C2211yescharacteristic
37#88859C2211yescharacteristic
38C3×#3752C2211yescharacteristic, complemented
39C3×#3750C2211yescharacteristic, complemented
40C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
41C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
42C32×Dic3⋊C4C2211yescharacteristic, complemented
43C32×C4×Dic3C2211yescharacteristic, complemented
44#88807C2211yescharacteristic, complemented
45Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
46#88804C2211yescharacteristic
47#88804C2211yescharacteristic
48#88804C2211yescharacteristic, complemented
49#88804C2211yescharacteristic, complemented
50#88803C2211yescharacteristic, complemented
51(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
52Dic3×C3⋊Dic3C2211yescharacteristic, complemented
53Dic3×C3⋊Dic3C2211yescharacteristic, complemented
54C2×D4×C3⋊D3—31no—
55C2×#3811—34no—
56C32×C4×D4—31no—
57D4×C3⋊Dic3—31no—
58C4×#638—31no—
59C4×#638—31no—
60C2×#3752—31no—
61C2×#3752—31no—
62#64102—31no—
63#64101—31no—
64#64090—31no—
65#64090D311yescharacteristic, complemented
66C22⋊C4×C3⋊D3—31no—
67C22⋊C4×C3⋊D3—31no—
68C22⋊C4×C3⋊D3—34no—
69C22⋊C4×C3⋊D3—64no—
70C4×C4⋊(C3⋊D3)—31no—
71#64081—31no—
72C3×#67⋊C4—34no—
73C3×#67⋊C4D314yescomplemented
74Dic3×#67—34no—
75Dic3×#67—34no—
76C2×#3722—34no—
77D3×(C2×D3)⋊C4—34no—
78D3×(C2×D3)⋊C4—34no—
79C4×#626—34no—
80C4×#626—34no—
81#63881—34no—
82#63881—34no—
83#63836—34no—
84#63836—34no—
85C23×C33C2311yescharacteristic
86C22×C3⋊(C3⋊D3)—41no—
87C22×C3⋊(C3⋊D3)—41no—
88C22×C3⋊(C3⋊D3)C2×C414yescomplemented
89C22×C3⋊(C3⋊D3)C2311yescharacteristic
90C22×C3⋊(C3⋊D3)C2311yescharacteristic
91C22×C3×C3⋊D3C2311yescharacteristic
92C22×C32×D3C2311yescharacteristic
93C2×D3×C3⋊D3—41no—
94C2×D3×C3⋊D3—41no—
95C2×D3×C3⋊D3C2×C414yescomplemented
96C2×C33×C4C2311yescharacteristic
97C2×C33×C4C2311yescharacteristic
98C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
99C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
100C4×C3⋊(C3⋊D3)—41no—
101C4×C3⋊(C3⋊D3)—41no—
102C3×#638C2×C414yescomplemented
103C2×C3×C3⋊Dic3—41no—
104C2×C3×C3⋊Dic3C2311yescharacteristic
105C2×C3×C3⋊Dic3C2311yescharacteristic
106C2×C3×C3⋊Dic3C2311yescharacteristic
107C3×C4×C3⋊D3—41no—
108C32×#67C2×C414yescomplemented
109C2×C32×Dic3—41no—
110C2×C32×Dic3C2311yescharacteristic
111C2×C32×Dic3C2311yescharacteristic
112C2×C32×Dic3C2311yescharacteristic
113C32×C4×D3—41no—
114#6292C2×C414yescomplemented
115#6291C2×C414yescomplemented
116#6289C2×C414yescomplemented
117Dic3×C3⋊D3—41no—
118D3×C3⋊Dic3—41no—
119#5545—94no—
120#5545—91no—
121C23×C3⋊D3—31no—
122C23×C3⋊D3—34no—
123C23×C3⋊D3—31no—
124C23×C3⋊D3—64no—
125C22×D32—34no—
126C2×C32×D4—31no—
127C22×C32×C4—31no—
128C22×C32×C4—31no—
129C2×#638—31no—
130C2×#638C2×D311yescharacteristic
131C22×C3⋊Dic3—31no—
132C22×C3⋊Dic3C2×D311yescharacteristic, complemented
133D4×C3⋊D3—38no—
134C2×C4⋊(C3⋊D3)—31no—
135C2×C4×C3⋊D3—31no—
136C2×C4×C3⋊D3—31no—
137C2×C4×C3⋊D3—31no—
138C2×C4×C3⋊D3—31no—
139C2×C4×C3⋊D3—34no—
140C2×C4×C3⋊D3—34no—
141C2×C4×C3⋊D3—64no—
142C2×C4×C3⋊D3—64no—
143C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
144C2×C3×#67—34no—
145C2×C3×#67C2×D314yes—
146C22×C3×Dic3—34no—
147C22×C3×Dic3C2×D314yescomplemented
148C2×C3×C4×D3—34no—
149C2×C3×C4×D3C2×D314yescomplemented
150#3811—332no—
151C2×#626—34no—
152C2×#626—34no—
153C2×#624—34no—
154C2×D3×Dic3—34no—
155C2×D3×Dic3—34no—
156C32×C4⋊C4—31no—
157C32×C22⋊C4—24no—
158C32×C22⋊C4—31no—
159C32×C22⋊C4C2×D314yescomplemented
160C32×C22⋊C4C2×D311yescharacteristic, complemented
161C32×C42—31no—
162#3757—31no—
163#3757—34no—
164#3757—31no—
165#3757—64no—
166#3752—31no—
167#3752—31no—
168#3752—31no—
169#3752—34no—
170#3752—34no—
171#3752—31no—
172#3752—31no—
173#3752—31no—
174#3752—31no—
175#3752—64no—
176#3752—64no—
177#3752C2×D311yescharacteristic, complemented
178C4⋊(C3⋊Dic3)—31no—
179#3750—31no—
180#3750C2×D311yescharacteristic, complemented
181C4×C3⋊Dic3—31no—
182C4×C3⋊Dic3—31no—
183C4×C3⋊Dic3C2×D311yescharacteristic, complemented
184C3×(C2×D3)⋊C4—34no—
185C3×(C2×D3)⋊C4C2×D314yescomplemented
186C3×Dic3⋊C4—34no—
187C3×Dic3⋊C4C2×D314yescomplemented
188C3×C4×Dic3—34no—
189C3×C4×Dic3C2×D314yescomplemented
190Dic3⋊Dic3—34no—
191Dic3⋊Dic3—34no—
192#3722—34no—
193#3722—34no—
194#3722—34no—
195#3722—34no—
196(C2×D3)⋊Dic3—34no—
197(C2×D3)⋊Dic3—34no—
198Dic32—34no—
199Dic32—34no—
200C22×C33—21no—
201C22×C33—21no—
202C22×C33C22×C412yes—
203C22×C33C2411yescharacteristic
204C2×C3⋊(C3⋊D3)—21no—
205C2×C3⋊(C3⋊D3)—21no—
206C2×C3⋊(C3⋊D3)—21no—
207C2×C3⋊(C3⋊D3)—21no—
208C2×C3⋊(C3⋊D3)—44no—
209C2×C3⋊(C3⋊D3)C22×C412yes—
210C2×C3⋊(C3⋊D3)C22×C412yes—
211C2×C3×C3⋊D3—21no—
212C2×C3×C3⋊D3—21no—
213C2×C3×C3⋊D3C22×C412yes—
214C2×C32×D3—21no—
215C2×C32×D3—21no—
216C2×C32×D3C22×C412yes—
217D3×C3⋊D3—44no—
218C33×C4—21no—
219C33×C4—21no—
220C3⋊(C3⋊Dic3)—21no—
221C3⋊(C3⋊Dic3)—21no—
222C3×C3⋊Dic3—21no—
223C3×C3⋊Dic3—21no—
224C3×C3⋊Dic3C22×C412yes—
225C32×Dic3—21no—
226C32×Dic3—21no—
227C32×Dic3C22×C412yes—
228C2×D3×D4—94no—
229C2×D3×D4—91no—
230C3×C4×D4—34no—
231C3×C4×D4—91no—
232D4×Dic3—94no—
233D4×Dic3—91no—
234C4×#67—94no—
235C4×#67—94no—
236C4×#67—91no—
237C4×#67—91no—
238C2×(C2×D3)⋊C4—94no—
239C2×(C2×D3)⋊C4—94no—
240C2×(C2×D3)⋊C4—91no—
241C2×(C2×D3)⋊C4—91no—
242#893—94no—
243#893—91no—
244#892—94no—
245#892—91no—
246#67⋊C4—34no—
247#67⋊C4—94no—
248#67⋊C4—91no—
249#67⋊C4C3⋊D311yescharacteristic, complemented
250D3×C22⋊C4—94no—
251D3×C22⋊C4—91no—
252D3×C22⋊C4—94no—
253D3×C22⋊C4—91no—
254D3×C22⋊C4—184no—
255C4×D12—94no—
256C4×D12—91no—
257#872—94no—
258#872—91no—
259C23×C32—24no—
260C23×C32—31no—
261C23×C32C22×D314yes—
262C23×C32C22×D311yescharacteristic
263C22×C3⋊D3—31no—
264C22×C3⋊D3—31no—
265C22×C3⋊D3—34no—
266C22×C3⋊D3—34no—
267C22×C3⋊D3—34no—
268C22×C3⋊D3—34no—
269C22×C3⋊D3—316no—
270C22×C3⋊D3—64no—
271C22×C3⋊D3—64no—
272C22×C3⋊D3—616no—
273C22×C3⋊D3—121no—
274C22×C3⋊D3—121no—
275C22×C3⋊D3—121no—
276C22×C3⋊D3—121no—
277C22×C3⋊D3—124no—
278C22×C3⋊D3—124no—
279C22×C3⋊D3—128no—
280C22×C3⋊D3—128no—
281C22×C3⋊D3C22×D311yescharacteristic
282C22×C3×D3—34no—
283C22×C3×D3C22×D314yes—
284C2×D32—316no—
285C2×D32—124no—
286C2×D32—124no—
287C32×D4—34no—
288C2×C32×C4—24no—
289C2×C32×C4—24no—
290C2×C32×C4—31no—
291C2×C32×C4—31no—
292C2×C32×C4—31no—
293C2×C32×C4—121no—
294C2×C32×C4—121no—
295C2×C32×C4C22×D314yes—
296C2×C32×C4C22×D314yes—
297C2×C32×C4C22×D311yescharacteristic
298C2×C32×C4C22×D311yescharacteristic
299#638—34no—
300#638C4×D314yescomplemented
301C2×C3⋊Dic3—31no—
302C2×C3⋊Dic3—31no—
303C2×C3⋊Dic3—34no—
304C2×C3⋊Dic3—34no—
305C2×C3⋊Dic3—41no—
306C2×C3⋊Dic3—64no—
307C2×C3⋊Dic3—64no—
308C2×C3⋊Dic3—121no—
309C2×C3⋊Dic3C22×D311yescharacteristic
310C2×C3⋊Dic3C22×D311yescharacteristic
311C2×C3⋊Dic3C22×D311yescharacteristic
312C4⋊(C3⋊D3)—34no—
313C4×C3⋊D3—34no—
314C4×C3⋊D3—41no—
315C4×C3⋊D3—121no—
316C4×C3⋊D3—121no—
317C4×C3⋊D3—124no—
318C4×C3⋊D3—124no—
319C4×C3⋊D3—121no—
320C4×C3⋊D3—128no—
321C4×C3⋊D3—128no—
322C3×#67—316no—
323C3×#67C4×D3116yescomplemented
324C2×C3×Dic3—34no—
325C2×C3×Dic3—34no—
326C2×C3×Dic3—34no—
327C2×C3×Dic3—44no—
328C2×C3×Dic3—124no—
329C2×C3×Dic3C22×D314yes—
330C2×C3×Dic3C22×D314yes—
331C2×C3×Dic3C22×D314yes—
332C3×C4×D3—44no—
333C3×C4×D3—124no—
334#626—316no—
335#626—316no—
336#624—316no—
337D3×Dic3—124no—
338D3×Dic3—124no—
339#518—271noSylow
340C2×C33—22no—
341C2×C33C23×C411yescharacteristic
342C2×C33H(5,𝔽2)11yescharacteristic
343C2×C33H(5,𝔽2)11yescharacteristic
344C3⋊(C3⋊D3)—22no—
345C3⋊(C3⋊D3)—22no—
346C3×C3⋊D3—22no—
347C32×D3—22no—
348C23×D3—94no—
349C23×D3—94no—
350C23×D3—91no—
351C23×D3—91no—
352C23×D3—184no—
353C2×C3×D4—34no—
354C2×C3×D4—91no—
355C22×C3×C4—34no—
356C22×C3×C4—34no—
357C22×C3×C4—91no—
358C22×C3×C4—91no—
359C2×#67—34no—
360C2×#67—94no—
361C2×#67—91no—
362C2×#67C2×C3⋊D311yescharacteristic
363C22×Dic3—34no—
364C22×Dic3—94no—
365C22×Dic3—91no—
366C22×Dic3C2×C3⋊D311yescharacteristic, complemented
367D3×D4—932no—
368D3×D4—98no—
369C2×D12—94no—
370C2×D12—91no—
371C2×C4×D3—34no—
372C2×C4×D3—94no—
373C2×C4×D3—91no—
374C2×C4×D3—94no—
375C2×C4×D3—91no—
376C2×C4×D3—94no—
377C2×C4×D3—94no—
378C2×C4×D3—91no—
379C2×C4×D3—91no—
380C2×C4×D3—184no—
381C2×C4×D3—184no—
382C2×C4×D3C2×C3⋊D311yescharacteristic, complemented
383C3×C4⋊C4—34no—
384C3×C4⋊C4—91no—
385C3×C22⋊C4—24no—
386C3×C22⋊C4—34no—
387C3×C22⋊C4—91no—
388C3×C22⋊C4D3214yescomplemented
389C3×C22⋊C4C2×C3⋊D311yescharacteristic, complemented
390C3×C42—34no—
391C3×C42—91no—
392#217—94no—
393#217—94no—
394#217—91no—
395#217—91no—
396#217—184no—
397(C2×D3)⋊C4—34no—
398(C2×D3)⋊C4—94no—
399(C2×D3)⋊C4—94no—
400(C2×D3)⋊C4—94no—
401(C2×D3)⋊C4—94no—
402(C2×D3)⋊C4—94no—
403(C2×D3)⋊C4—91no—
404(C2×D3)⋊C4—94no—
405(C2×D3)⋊C4—94no—
406(C2×D3)⋊C4—91no—
407(C2×D3)⋊C4—91no—
408(C2×D3)⋊C4—91no—
409(C2×D3)⋊C4—91no—
410(C2×D3)⋊C4—91no—
411(C2×D3)⋊C4—91no—
412(C2×D3)⋊C4—184no—
413(C2×D3)⋊C4—184no—
414(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
415C4⋊Dic3—94no—
416C4⋊Dic3—91no—
417Dic3⋊C4—34no—
418Dic3⋊C4—94no—
419Dic3⋊C4—91no—
420Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
421C4×Dic3—34no—
422C4×Dic3—94no—
423C4×Dic3—94no—
424C4×Dic3—91no—
425C4×Dic3—91no—
426C4×Dic3C2×C3⋊D311yescharacteristic, complemented
427C22×C32—21no—
428C22×C32—21no—
429C22×C32—24no—
430C22×C32—28no—
431C22×C32—24no—
432C22×C32—24no—
433C22×C32—32no—
434C22×C32—44no—
435C22×C32—44no—
436C22×C32—61no—
437C22×C32—61no—
438C22×C32C2×C4×D318yes—
439C22×C32C2×C4×D312yes—
440C22×C32C23×D314yes—
441C22×C32C23×D311yescharacteristic
442C2×C3⋊D3—21no—
443C2×C3⋊D3—21no—
444C2×C3⋊D3—32no—
445C2×C3⋊D3—32no—
446C2×C3⋊D3—38no—
447C2×C3⋊D3—38no—
448C2×C3⋊D3—68no—
449C2×C3⋊D3—68no—
450C2×C3⋊D3—68no—
451C2×C3⋊D3—68no—
452C2×C3⋊D3—64no—
453C2×C3⋊D3—61no—
454C2×C3⋊D3—61no—
455C2×C3⋊D3—64no—
456C2×C3⋊D3—61no—
457C2×C3⋊D3—61no—
458C2×C3⋊D3—64no—
459C2×C3⋊D3—64no—
460C2×C3⋊D3—124no—
461C2×C3⋊D3—124no—
462C2×C3⋊D3—124no—
463C2×C3⋊D3—124no—
464C2×C3⋊D3—1216no—
465C2×C3⋊D3—1232no—
466C2×C3⋊D3C2×C4×D312yes—
467C2×C3×D3—24no—
468C2×C3×D3—24no—
469C2×C3×D3—38no—
470C2×C3×D3—64no—
471C2×C3×D3—64no—
472C2×C3×D3C2×C4×D318yes—
473D32—1216no—
474C32×C4—21no—
475C32×C4—21no—
476C32×C4—24no—
477C32×C4—24no—
478C32×C4—32no—
479C32×C4—44no—
480C32×C4—44no—
481C32×C4—61no—
482C32×C4—61no—
483C3⋊Dic3—21no—
484C3⋊Dic3—21no—
485C3⋊Dic3—61no—
486C3⋊Dic3—61no—
487C3⋊Dic3—64no—
488C3⋊Dic3—64no—
489C3⋊Dic3—124no—
490C3⋊Dic3—124no—
491C3⋊Dic3C2×C4×D312yes—
492C3×Dic3—24no—
493C3×Dic3—24no—
494C3×Dic3—38no—
495C3×Dic3—64no—
496C3×Dic3—64no—
497C3×Dic3C2×C4×D318yes—
498C22×D4—271no—
499C4×D4—31no—
500C4×D4—91no—
501C4×D4—271no—
502C4×D4—271no—
503C4×D4—271no—
504C4×D4—271no—
505C4×D4—271no—
506C4×D4—271no—
507#117—271no—
508#117—271no—
509C2×C22⋊C4—271no—
510C2×C22⋊C4—271no—
511C2×C22⋊C4—271no—
512C2×C22⋊C4—271no—
513C33#51811yescharacteristic, complemented, Sylow
514C23×C3—24no—
515C23×C3—34no—
516C23×C3—91no—
517C23×C3C2×D3214yes—
518C23×C3C22×C3⋊D311yescharacteristic
519C22×D3—34no—
520C22×D3—916no—
521C22×D3—94no—
522C22×D3—94no—
523C22×D3—91no—
524C22×D3—91no—
525C22×D3—916no—
526C22×D3—94no—
527C22×D3—94no—
528C22×D3—184no—
529C22×D3—184no—
530C22×D3—1816no—
531C22×D3—361no—
532C22×D3—361no—
533C22×D3—364no—
534C22×D3—364no—
535C22×D3—364no—
536C22×D3—364no—
537C22×D3—361no—
538C22×D3—361no—
539C22×D3—368no—
540C22×D3—368no—
541C22×D3C22×C3⋊D311yescharacteristic
542C3×D4—316no—
543C3×D4—94no—
544C2×C3×C4—24no—
545C2×C3×C4—24no—
546C2×C3×C4—34no—
547C2×C3×C4—34no—
548C2×C3×C4—34no—
549C2×C3×C4—91no—
550C2×C3×C4—91no—
551C2×C3×C4—91no—
552C2×C3×C4—124no—
553C2×C3×C4—124no—
554C2×C3×C4—361no—
555C2×C3×C4—361no—
556C2×C3×C4C2×D3214yes—
557C2×C3×C4C2×D3214yes—
558C2×C3×C4C22×C3⋊D311yescharacteristic
559C2×C3×C4C22×C3⋊D311yescharacteristic
560#67—316no—
561#67—916no—
562#67—94no—
563#67C4×C3⋊D314yescomplemented
564C2×Dic3—34no—
565C2×Dic3—34no—
566C2×Dic3—34no—
567C2×Dic3—41no—
568C2×Dic3—94no—
569C2×Dic3—94no—
570C2×Dic3—91no—
571C2×Dic3—91no—
572C2×Dic3—124no—
573C2×Dic3—184no—
574C2×Dic3—184no—
575C2×Dic3—361no—
576C2×Dic3—364no—
577C2×Dic3C22×C3⋊D311yescharacteristic
578C2×Dic3C22×C3⋊D311yescharacteristic
579C2×Dic3C22×C3⋊D311yescharacteristic
580D12—916no—
581D12—94no—
582C4×D3—41no—
583C4×D3—916no—
584C4×D3—94no—
585C4×D3—124no—
586C4×D3—364no—
587C4×D3—364no—
588C4×D3—361no—
589C4×D3—361no—
590C4×D3—364no—
591C4×D3—361no—
592C4×D3—368no—
593C4×D3—368no—
594C2×C32—22no—
595C2×C32—24no—
596C2×C32—24no—
597C2×C32—24no—
598C2×C32—28no—
599C2×C32—48no—
600C2×C32—62no—
601C2×C32C22×C4×D314yes—
602C2×C32C22×C4×D311yescharacteristic
603C2×C32#100414yes—
604C2×C32#100411yescharacteristic
605C2×C32#100914yes—
606C2×C32#100911yescharacteristic
607C3⋊D3—22no—
608C3⋊D3—616no—
609C3⋊D3—68no—
610C3⋊D3—62no—
611C3⋊D3—62no—
612C3⋊D3—68no—
613C3⋊D3—128no—
614C3×D3—28no—
615C3×D3—68no—
616C24—271no—
617C24—271no—
618C2×D4—31no—
619C2×D4—91no—
620C2×D4—271no—
621C2×D4—271no—
622C2×D4—278no—
623C22×C4—31no—
624C22×C4—31no—
625C22×C4—91no—
626C22×C4—91no—
627C22×C4—271no—
628C22×C4—271no—
629C22×C4—271no—
630C22×C4—271no—
631C22×C4—271no—
632C4⋊C4—31no—
633C4⋊C4—91no—
634C4⋊C4—271no—
635C4⋊C4—271no—
636C22⋊C4—31no—
637C22⋊C4—91no—
638C22⋊C4—271no—
639C22⋊C4—271no—
640C22⋊C4—271no—
641C22⋊C4—271no—
642C22⋊C4—271no—
643C22⋊C4—271no—
644C22⋊C4—271no—
645C22⋊C4—271no—
646C22⋊C4—271no—
647C22⋊C4D3×C3⋊D311yescharacteristic, complemented
648C42—31no—
649C42—91no—
650C42—271no—
651C42—271no—
652C22×C3—24no—
653C22×C3—24no—
654C22×C3—21no—
655C22×C3—21no—
656C22×C3—24no—
657C22×C3—28no—
658C22×C3—38no—
659C22×C3—44no—
660C22×C3—44no—
661C22×C3—64no—
662C22×C3—64no—
663C22×C3—92no—
664C22×C3—181no—
665C22×C3—181no—
666C22×C3C4×D3218yes—
667C22×C3C2×C4×C3⋊D312yes—
668C22×C3C22×D3214yes—
669C22×C3C23×C3⋊D311yescharacteristic
670C2×D3—21no—
671C2×D3—21no—
672C2×D3—38no—
673C2×D3—64no—
674C2×D3—64no—
675C2×D3—98no—
676C2×D3—98no—
677C2×D3—92no—
678C2×D3—92no—
679C2×D3—188no—
680C2×D3—188no—
681C2×D3—188no—
682C2×D3—188no—
683C2×D3—184no—
684C2×D3—184no—
685C2×D3—184no—
686C2×D3—184no—
687C2×D3—181no—
688C2×D3—181no—
689C2×D3—181no—
690C2×D3—181no—
691C2×D3—364no—
692C2×D3—364no—
693C2×D3—364no—
694C2×D3—3616no—
695C2×D3—364no—
696C2×D3—3616no—
697C2×D3—3632no—
698C2×D3C2×C4×C3⋊D312yes—
699C3×C4—24no—
700C3×C4—24no—
701C3×C4—21no—
702C3×C4—21no—
703C3×C4—38no—
704C3×C4—44no—
705C3×C4—44no—
706C3×C4—64no—
707C3×C4—64no—
708C3×C4—92no—
709C3×C4—181no—
710C3×C4—181no—
711Dic3—21no—
712Dic3—21no—
713Dic3—38no—
714Dic3—64no—
715Dic3—64no—
716Dic3—184no—
717Dic3—184no—
718Dic3—181no—
719Dic3—181no—
720Dic3—364no—
721Dic3—364no—
722Dic3C2×C4×C3⋊D312yes—
723C32—24no—
724C32#554514yescomplemented
725C32#554511yescharacteristic, complemented
726C23—31no—
727C23—91no—
728C23—274no—
729C23—271no—
730C23—271no—
731C23—274no—
732C23—1081no—
733C23—1081no—
734C23—1081no—
735C23—1081no—
736C23C2×D3×C3⋊D311yescharacteristic
737D4—34no—
738D4—94no—
739D4—274no—
740D4—274no—
741C2×C4—31no—
742C2×C4—31no—
743C2×C4—31no—
744C2×C4—91no—
745C2×C4—91no—
746C2×C4—91no—
747C2×C4—121no—
748C2×C4—121no—
749C2×C4—274no—
750C2×C4—271no—
751C2×C4—271no—
752C2×C4—361no—
753C2×C4—361no—
754C2×C4—1081no—
755C2×C4—1081no—
756C2×C4—1081no—
757C2×C4—1081no—
758C2×C4C2×D3×C3⋊D311yescharacteristic
759C2×C4C2×D3×C3⋊D311yescharacteristic
760C2×C3—22no—
761C2×C3—28no—
762C2×C3—24no—
763C2×C3—24no—
764C2×C3—24no—
765C2×C3—48no—
766C2×C3—68no—
767C2×C3—182no—
768C2×C3C2×C4×D3214yes—
769C2×C3#6431414yes—
770C2×C3#6431414yes—
771C2×C3C22×C4×C3⋊D311yescharacteristic
772C2×C3#6436111yescharacteristic
773C2×C3#6436611yescharacteristic
774D3—22no—
775D3—68no—
776D3—1816no—
777D3—182no—
778D3—182no—
779D3—188no—
780D3—188no—
781D3—368no—
782C22—21no—
783C22—21no—
784C22—32no—
785C22—61no—
786C22—61no—
787C22—92no—
788C22—181no—
789C22—181no—
790C22—272no—
791C22—272no—
792C22—541no—
793C22—541no—
794C22—541no—
795C22—541no—
796C22—1084no—
797C22—1084no—
798C22C4×D3×C3⋊D312yes—
799C22C22×D3×C3⋊D311yescharacteristic
800C4—21no—
801C4—21no—
802C4—32no—
803C4—61no—
804C4—61no—
805C4—92no—
806C4—181no—
807C4—181no—
808C4—541no—
809C4—541no—
810C3—24no—
811C3#1059425614yescomplemented
812C3#1059601611yescharacteristic, complemented
813C2—22no—
814C2—62no—
815C2—182no—
816C2—542no—
817C2—542no—
818C2C2×C4×D3×C3⋊D311yescharacteristic
819C2#1172458811yescharacteristic
820C2#1172458911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutatorC2×C33C23×C4
FittingC33×C22⋊C4C22
socle, cosocleC22×C33C24
prime radicalC2×#89039C2
hypercenterC22⋊C4D3×C3⋊D3
hypocenterC33#518
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22⋊C4×C3⋊(C3⋊D3)C2semidirect
3. C3×#64090C2semidirect
4. C32×#67⋊C4C2semidirect
5. #67×C3⋊Dic3C2semidirect
6. Dic3×#638C2semidirect
7. C2×#88804C2semidirect
8. C3⋊D3×(C2×D3)⋊C4C2semidirect
9. D3×#3752C2semidirect
10. C4×#6292C2semidirect
11. C4×#6291C2semidirect
12. #11723472C2semidirect
13. #11723469C2semidirect
14. #11723468C2semidirect
15. #11723462C2semidirect
20. C2×C4×C3⋊(C3⋊D3)C22semidirect
21. C2×C4×C3⋊(C3⋊D3)C22semidirect
23. C22×C3×C3⋊Dic3C22semidirect
24. C2×C3×C4×C3⋊D3C22semidirect
26. C22×C32×Dic3C22semidirect
27. C2×C32×C4×D3C22semidirect
28. #89039C4semidirect
32. C2×Dic3×C3⋊D3C22semidirect
33. C2×D3×C3⋊Dic3C22semidirect
34. C33×C22⋊C4C22semidirect
35. #88864C22semidirect
38. C3×#3752C22semidirect
39. C3×#3750C22semidirect
40. C3×C4×C3⋊Dic3C22semidirect
41. C32×(C2×D3)⋊C4C22semidirect
42. C32×Dic3⋊C4C22semidirect
43. C32×C4×Dic3C22semidirect
44. #88807C22semidirect
45. Dic3⋊(C3⋊Dic3)C22semidirect
48. #88804C22semidirect
49. #88804C22semidirect
50. #88803C22semidirect
51. (C2×D3)⋊(C3⋊Dic3)C22semidirect
52. Dic3×C3⋊Dic3C22semidirect
53. Dic3×C3⋊Dic3C22semidirect
65. #64090D3semidirect
73. C3×#67⋊C4D3semidirect
88. C22×C3⋊(C3⋊D3)C2×C4semidirect
95. C2×D3×C3⋊D3C2×C4semidirect
102. C3×#638C2×C4semidirect
108. C32×#67C2×C4semidirect
114. #6292C2×C4semidirect
115. #6291C2×C4semidirect
116. #6289C2×C4semidirect
132. C22×C3⋊Dic3C2×D3semidirect
143. C2×C4×C3⋊D3C2×D3semidirect
147. C22×C3×Dic3C2×D3semidirect
149. C2×C3×C4×D3C2×D3semidirect
159. C32×C22⋊C4C2×D3semidirect
160. C32×C22⋊C4C2×D3semidirect
177. #3752C2×D3semidirect
180. #3750C2×D3semidirect
183. C4×C3⋊Dic3C2×D3semidirect
185. C3×(C2×D3)⋊C4C2×D3semidirect
187. C3×Dic3⋊C4C2×D3semidirect
189. C3×C4×Dic3C2×D3semidirect
249. #67⋊C4C3⋊D3semidirect
300. #638C4×D3semidirect
323. C3×#67C4×D3semidirect
366. C22×Dic3C2×C3⋊D3semidirect
382. C2×C4×D3C2×C3⋊D3semidirect
388. C3×C22⋊C4D32semidirect
389. C3×C22⋊C4C2×C3⋊D3semidirect
414. (C2×D3)⋊C4C2×C3⋊D3semidirect
420. Dic3⋊C4C2×C3⋊D3semidirect
426. C4×Dic3C2×C3⋊D3semidirect
513. C33#518semidirect
563. #67C4×C3⋊D3semidirect
647. C22⋊C4D3×C3⋊D3semidirect
724. C32#5545semidirect
725. C32#5545semidirect
811. C3#10594256semidirect
812. C3#10596016semidirect

Maximal subgroups

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

subgroupindex
C2×#890392
C22⋊C4×C3⋊(C3⋊D3)2
C3×#640902
C32×#67⋊C42
#67×C3⋊Dic32
Dic3×#6382
C2×#888042
C3⋊D3×(C2×D3)⋊C42
D3×#37522
C4×#62922
C4×#62912
#117234722
#117234692
#117234682
#117234622
#105960163
#105942563