Finite Group Databasebeta

← #13175934

Subgroups — #13175934

Order 1728.

2316 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3⋊D3×#67C211yesmaximal, characteristic, complemented
2C2×#89029C211yesmaximal, characteristic, complemented
3#11723927C211yesmaximal, characteristic, complemented
4C3×#64091C211yesmaximal, characteristic, complemented
5C32×#67⋊C4C211yesmaximal, characteristic, complemented
6#11723632C211yesmaximal, characteristic, complemented
7C2×#88803C211yesmaximal, characteristic, complemented
8#11723541C211yesmaximal, characteristic, complemented
9D3×#3752C211yesmaximal, characteristic, complemented
10#11723515C211yesmaximal, characteristic, complemented
11#11723483C211yesmaximal, characteristic, complemented
12#11723482C211yesmaximal, characteristic, complemented
13Dic3×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
14#11723480C211yesmaximal, characteristic, complemented
15#11723416C211yesmaximal, characteristic, complemented
16#10596025—31nomaximal
17#10594292—34nomaximal
18C23×C3×C3⋊D3C2211yescharacteristic
19C22×D3×C3⋊D3C2211yescharacteristic
20C2×#6312C2211yescharacteristic
21C22×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
22C2×C3×#638C2211yescharacteristic, complemented
23C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
24C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
25C2×C32×#67C2211yescharacteristic
26C22×C32×Dic3C2211yescharacteristic, complemented
27C2×C32×C4×D3C2211yescharacteristic, complemented
28C3⋊D3×#67—24no—
29C2×#6293C2211yescharacteristic, complemented
30C2×#6292C2211yescharacteristic
31C2×#6292C2211yescharacteristic, complemented
32C2×#6290C2211yescharacteristic
33C2×#6290C2211yescharacteristic, complemented
34C2×Dic3×C3⋊D3C2211yescharacteristic
35C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
36#89029—24no—
37C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
38C33×C22⋊C4C2211yescharacteristic, complemented
39#88859C2211yescharacteristic, complemented
40#88859C2211yescharacteristic, complemented
41C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic, complemented
42C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic, complemented
43C3×#3752C2211yescharacteristic
44C3×#3752C2211yescharacteristic, complemented
45C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
46C32×Dic3⋊C4C2211yescharacteristic, complemented
47C32×C4×Dic3C2211yescharacteristic, complemented
48Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
49#88804C2211yescharacteristic, complemented
50#88803C2211yescharacteristic
51#88803C2211yescharacteristic
52#88803C2211yescharacteristic, complemented
53#88803C2211yescharacteristic, complemented
54#88803C2211yescharacteristic, complemented
55C2×#3830—31no—
56C2×D4×C3⋊D3—31no—
57C2×D3×#67—34no—
58C2×#3805—34no—
59C32×C4×D4—31no—
60#64139—31no—
61#64139—31no—
62C2×#3752—31no—
63C2×#3752—31no—
64#64106—31no—
65#64104—31no—
66#64095—31no—
67#64095—31no—
68#64095—34no—
69#64095—64no—
70#64091—31no—
71#64091D311yescharacteristic, complemented
72#64084—31no—
73C4×C4⋊(C3⋊D3)—31no—
74C3×#882—34no—
75C3×#67⋊C4D314yescomplemented
76#63978—34no—
77C2×(C2×D3)⋊Dic3—34no—
78#63922—34no—
79D3×(C2×D3)⋊C4—34no—
80#63908—34no—
81#63893—34no—
82Dic3×D12—34no—
83#63891—34no—
84#63886—34no—
85#63852—34no—
86C23×C33C2311yescharacteristic
87C22×C3⋊(C3⋊D3)C2311yescharacteristic
88C22×C3×C3⋊D3—22no—
89C22×C3×C3⋊D3—22no—
90C22×C3×C3⋊D3—41no—
91C22×C3×C3⋊D3C2311yescharacteristic
92C22×C3×C3⋊D3C2311yescharacteristic
93C22×C3×C3⋊D3C2311yescharacteristic
94C22×C32×D3C2311yescharacteristic
95C2×D3×C3⋊D3—22no—
96C2×D3×C3⋊D3—22no—
97C2×D3×C3⋊D3—41no—
98C2×C33×C4C2311yescharacteristic
99C2×C33×C4C2311yescharacteristic
100#6312—22no—
101C2×C3⋊(C3⋊Dic3)—22no—
102C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
103C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
104C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
105C3×#638—22no—
106C2×C3×C3⋊Dic3C2311yescharacteristic
107C3×C4⋊(C3⋊D3)—22no—
108C3×C4⋊(C3⋊D3)—41no—
109C32×#67D414yescomplemented
110C2×C32×Dic3—41no—
111C2×C32×Dic3C2311yescharacteristic
112C2×C32×Dic3C2311yescharacteristic
113C2×C32×Dic3C2311yescharacteristic
114C32×C4×D3—41no—
115#6293—22no—
116#6292—22no—
117#6292—41no—
118#6290—22no—
119#6290—22no—
120Dic3×C3⋊D3—22no—
121Dic3×C3⋊D3—22no—
122D3×C3⋊Dic3—22no—
123#5591—91no—
124#5554—94no—
125C23×C3⋊D3—31no—
126C23×C3⋊D3C2×D311yescharacteristic
127C23×C3×D3—34no—
128C22×D32—34no—
129C2×C32×D4—31no—
130C22×C32×C4—31no—
131C22×C32×C4—31no—
132C2×#638—31no—
133C2×#638—34no—
134C2×#638—31no—
135C2×#638—31no—
136C2×#638—64no—
137C2×#638C2×D311yescharacteristic, complemented
138C22×C3⋊Dic3—31no—
139C22×C3⋊Dic3—34no—
140C22×C3⋊Dic3—31no—
141C22×C3⋊Dic3—64no—
142#3830—64no—
143D4×C3⋊D3—64no—
144C2×C4⋊(C3⋊D3)—31no—
145C2×C4⋊(C3⋊D3)—31no—
146C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
147C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
148C2×C4×C3⋊D3—31no—
149C2×C4×C3⋊D3—31no—
150C2×#634—31no—
151C2×C3×#67—34no—
152C2×C3×#67C2×D314yes—
153C22×C3×Dic3C2×D314yescomplemented
154C2×C3×D12—34no—
155C2×C3×D12—34no—
156C2×C3×C4×D3C2×D314yescomplemented
157D3×#67—616no—
158C2×#627—34no—
159C2×#626—34no—
160C2×#626—34no—
161C2×#625—34no—
162C2×#625—34no—
163#3805—616no—
164C2×D3×Dic3—34no—
165C2×D3×Dic3—34no—
166C2×D3×Dic3—34no—
167C32×C4⋊C4—31no—
168C32×C22⋊C4—24no—
169C32×C22⋊C4—31no—
170C32×C22⋊C4C2×D314yescomplemented
171C32×C22⋊C4C2×D311yescharacteristic, complemented
172C32×C42—31no—
173#3752—31no—
174#3752—31no—
175#3752—31no—
176#3752—31no—
177#3752—31no—
178#3752—31no—
179#3752—31no—
180#3752—34no—
181#3752—34no—
182#3752—31no—
183#3752—64no—
184#3752—64no—
185#3752C2×D311yescharacteristic
186#3752C2×D311yescharacteristic, complemented
187C4⋊(C3⋊Dic3)—31no—
188C4⋊(C3⋊Dic3)—31no—
189C4⋊(C3⋊Dic3)—34no—
190C4⋊(C3⋊Dic3)—34no—
191C4⋊(C3⋊Dic3)—31no—
192C4⋊(C3⋊Dic3)—64no—
193C4⋊(C3⋊Dic3)—64no—
194C3×(C2×D3)⋊C4—34no—
195C3×(C2×D3)⋊C4—34no—
196C3×(C2×D3)⋊C4C2×D314yescomplemented
197C3×Dic3⋊C4C2×D314yescomplemented
198C3×C4×Dic3C2×D314yescomplemented
199Dic3⋊Dic3—34no—
200#3722—34no—
201(C2×D3)⋊Dic3—34no—
202(C2×D3)⋊Dic3—34no—
203(C2×D3)⋊Dic3—34no—
204(C2×D3)⋊Dic3—34no—
205(C2×D3)⋊Dic3—34no—
206C22×C33—21no—
207C22×C33—21no—
208C22×C33C2×D412yes—
209C22×C33C2411yescharacteristic
210C2×C3⋊(C3⋊D3)—21no—
211C2×C3⋊(C3⋊D3)—21no—
212C2×C3⋊(C3⋊D3)—21no—
213C2×C3×C3⋊D3—21no—
214C2×C3×C3⋊D3—21no—
215C2×C3×C3⋊D3—21no—
216C2×C3×C3⋊D3—21no—
217C2×C3×C3⋊D3—21no—
218C2×C3×C3⋊D3—21no—
219C2×C3×C3⋊D3—21no—
220C2×C3×C3⋊D3—21no—
221C2×C3×C3⋊D3—44no—
222C2×C3×C3⋊D3#4112yescomplemented
223C2×C32×D3—21no—
224C2×C32×D3—21no—
225C2×C32×D3C2×D412yes—
226D3×C3⋊D3—44no—
227C33×C4—21no—
228C33×C4—21no—
229C3⋊(C3⋊Dic3)—21no—
230C3⋊(C3⋊Dic3)—21no—
231C3⋊(C3⋊Dic3)—21no—
232C3×C3⋊Dic3—21no—
233C32×Dic3—21no—
234C32×Dic3—21no—
235C32×Dic3C2×D412yes—
236C22×#67—91no—
237C2×#237—94no—
238C2×#237—91no—
239C2×D3×D4—94no—
240C3×#120—91no—
241C3×C4×D4—34no—
242C2×#217—91no—
243#939—91no—
244#939—91no—
245#938—91no—
246#937—91no—
247D4×Dic3—91no—
248#930—94no—
249#930—94no—
250C2×(C2×D3)⋊C4—94no—
251C2×(C2×D3)⋊C4—94no—
252#897—94no—
253#895—94no—
254#886—94no—
255#886—94no—
256#886—91no—
257#886—184no—
258#885—91no—
259#883—91no—
260#882—34no—
261#882—94no—
262#67⋊C4C3⋊D311yescharacteristic, complemented
263D3×C22⋊C4—91no—
264#878—91no—
265#875—94no—
266C4×D12—94no—
267C23×C32—24no—
268C23×C32—31no—
269C23×C32C22×D314yes—
270C23×C32C22×D311yescharacteristic
271C22×C3⋊D3—22no—
272C22×C3⋊D3—22no—
273C22×C3⋊D3—31no—
274C22×C3⋊D3—34no—
275C22×C3⋊D3—41no—
276C22×C3⋊D3—64no—
277C22×C3⋊D3—62no—
278C22×C3⋊D3—62no—
279C22×C3⋊D3—121no—
280C22×C3⋊D3C22×D311yescharacteristic
281C22×C3⋊D3C22×D311yescharacteristic
282C22×C3⋊D3C22×D311yescharacteristic
283C22×C3×D3—34no—
284C22×C3×D3—34no—
285C22×C3×D3—34no—
286C22×C3×D3—68no—
287C22×C3×D3—68no—
288C22×C3×D3—124no—
289C22×C3×D3C22×D314yes—
290C2×D32—68no—
291C2×D32—68no—
292C2×D32—124no—
293C32×D4—34no—
294C2×C32×C4—24no—
295C2×C32×C4—24no—
296C2×C32×C4—31no—
297C2×C32×C4—31no—
298C2×C32×C4—31no—
299C2×C32×C4—121no—
300C2×C32×C4—121no—
301C2×C32×C4C22×D314yes—
302C2×C32×C4C22×D314yes—
303C2×C32×C4C22×D311yescharacteristic
304C2×C32×C4C22×D311yescharacteristic
305#638—22no—
306#638—62no—
307#638—62no—
308#638—62no—
309#638—68no—
310#638—128no—
311C2×C3⋊Dic3—31no—
312C2×C3⋊Dic3—31no—
313C2×C3⋊Dic3—31no—
314C2×C3⋊Dic3—34no—
315C2×C3⋊Dic3—34no—
316C2×C3⋊Dic3—34no—
317C2×C3⋊Dic3—64no—
318C2×C3⋊Dic3—64no—
319C2×C3⋊Dic3—64no—
320C2×C3⋊Dic3—62no—
321C2×C3⋊Dic3—62no—
322C2×C3⋊Dic3—68no—
323C2×C3⋊Dic3—128no—
324C2×C3⋊Dic3C22×D311yescharacteristic
325C4⋊(C3⋊D3)—22no—
326C4⋊(C3⋊D3)—41no—
327C4⋊(C3⋊D3)—62no—
328C4⋊(C3⋊D3)—121no—
329C4×C3⋊D3—62no—
330C4×C3⋊D3—62no—
331#634—62no—
332C3×#67—68no—
333C3×#67D12116yescomplemented
334C2×C3×Dic3—34no—
335C2×C3×Dic3—44no—
336C2×C3×Dic3C22×D314yes—
337C2×C3×Dic3C22×D314yes—
338C2×C3×Dic3C22×D314yes—
339C3×D12—68no—
340C3×D12—124no—
341C3×C4×D3—44no—
342#627—68no—
343#626—68no—
344#626—124no—
345#625—68no—
346#625—68no—
347D3×Dic3—68no—
348D3×Dic3—68no—
349D3×Dic3—68no—
350#546—271noSylow
351C2×C33—22no—
352C2×C33C22×D411yescharacteristic
353C2×C33C2×#4111yescharacteristic
354C2×C33H(5,𝔽2)11yescharacteristic
355C3⋊(C3⋊D3)—41no—
356C3×C3⋊D3—22no—
357C3×C3⋊D3—41no—
358C3×C3⋊D3—41no—
359C32×D3—22no—
360C24×C3—91no—
361C23×D3—34no—
362C23×D3—94no—
363C23×D3—91no—
364C2×C3×D4—34no—
365C2×C3×D4—91no—
366C2×C3×D4—91no—
367C2×C3×D4—91no—
368C22×C3×C4—34no—
369C22×C3×C4—34no—
370C2×#67—34no—
371C2×#67—94no—
372C2×#67—94no—
373C2×#67—94no—
374C2×#67—91no—
375C2×#67—91no—
376C2×#67—91no—
377C2×#67—91no—
378C2×#67—91no—
379C2×#67—184no—
380C2×#67—184no—
381C2×#67C2×C3⋊D311yescharacteristic
382C22×Dic3—94no—
383C22×Dic3—94no—
384C22×Dic3—91no—
385C22×Dic3—91no—
386C22×Dic3—91no—
387C22×Dic3—184no—
388C22×Dic3C2×C3⋊D311yescharacteristic, complemented
389#237—1816no—
390#237—184no—
391D3×D4—1816no—
392C2×D12—34no—
393C2×D12—34no—
394C2×D12—94no—
395C2×D12—94no—
396C2×C4×D3—94no—
397C2×C4×D3—94no—
398C2×C4×D3—91no—
399C2×C4×D3C2×C3⋊D311yescharacteristic, complemented
400C2×Dic6—94no—
401C2×Dic6—91no—
402C3×C4⋊C4—34no—
403C3×C22⋊C4—24no—
404C3×C22⋊C4—34no—
405C3×C22⋊C4—91no—
406C3×C22⋊C4—91no—
407C3×C22⋊C4D3214yescomplemented
408C3×C22⋊C4C2×C3⋊D311yescharacteristic, complemented
409C3×C42—34no—
410#217—91no—
411#217—91no—
412#217—91no—
413#217—91no—
414#217—91no—
415(C2×D3)⋊C4—34no—
416(C2×D3)⋊C4—34no—
417(C2×D3)⋊C4—94no—
418(C2×D3)⋊C4—94no—
419(C2×D3)⋊C4—94no—
420(C2×D3)⋊C4—94no—
421(C2×D3)⋊C4—94no—
422(C2×D3)⋊C4—94no—
423(C2×D3)⋊C4—94no—
424(C2×D3)⋊C4—94no—
425(C2×D3)⋊C4—91no—
426(C2×D3)⋊C4—91no—
427(C2×D3)⋊C4—91no—
428(C2×D3)⋊C4—184no—
429(C2×D3)⋊C4—184no—
430(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
431C4⋊Dic3—94no—
432C4⋊Dic3—94no—
433C4⋊Dic3—94no—
434C4⋊Dic3—91no—
435C4⋊Dic3—91no—
436C4⋊Dic3—184no—
437C4⋊Dic3—184no—
438Dic3⋊C4—91no—
439Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
440C4×Dic3C2×C3⋊D311yescharacteristic, complemented
441C22×C32—21no—
442C22×C32—21no—
443C22×C32—24no—
444C22×C32—28no—
445C22×C32—24no—
446C22×C32—24no—
447C22×C32—32no—
448C22×C32—44no—
449C22×C32—44no—
450C22×C32—61no—
451C22×C32—61no—
452C22×C32C2×D1218yes—
453C22×C32D3×D412yes—
454C22×C32C23×D314yes—
455C22×C32C23×D311yescharacteristic
456C2×C3⋊D3—21no—
457C2×C3⋊D3—21no—
458C2×C3⋊D3—21no—
459C2×C3⋊D3—21no—
460C2×C3⋊D3—21no—
461C2×C3⋊D3—21no—
462C2×C3⋊D3—21no—
463C2×C3⋊D3—21no—
464C2×C3⋊D3—44no—
465C2×C3⋊D3—61no—
466C2×C3⋊D3—61no—
467C2×C3⋊D3—61no—
468C2×C3⋊D3—64no—
469C2×C3⋊D3—64no—
470C2×C3⋊D3—64no—
471C2×C3⋊D3—124no—
472C2×C3⋊D3—124no—
473C2×C3⋊D3—124no—
474C2×C3⋊D3—124no—
475C2×C3⋊D3#23712yescomplemented
476C2×C3×D3—24no—
477C2×C3×D3—24no—
478C2×C3×D3—38no—
479C2×C3×D3—64no—
480C2×C3×D3—64no—
481C2×C3×D3—64no—
482C2×C3×D3—64no—
483C2×C3×D3—64no—
484C2×C3×D3—64no—
485C2×C3×D3—64no—
486C2×C3×D3—64no—
487C2×C3×D3—1216no—
488C2×C3×D3C2×D1218yes—
489D32—1216no—
490C32×C4—21no—
491C32×C4—21no—
492C32×C4—24no—
493C32×C4—24no—
494C32×C4—32no—
495C32×C4—44no—
496C32×C4—44no—
497C32×C4—61no—
498C32×C4—61no—
499C3⋊Dic3—21no—
500C3⋊Dic3—61no—
501C3⋊Dic3—61no—
502C3⋊Dic3—61no—
503C3⋊Dic3—64no—
504C3⋊Dic3—64no—
505C3⋊Dic3—64no—
506C3⋊Dic3—124no—
507C3⋊Dic3—124no—
508C3⋊Dic3—124no—
509C3×Dic3—24no—
510C3×Dic3—24no—
511C3×Dic3—64no—
512C3×Dic3C2×D1218yes—
513C2×#41—271no—
514C22×D4—271no—
515#124—271no—
516#123—271no—
517#123—271no—
518C22⋊Q8—271no—
519#121—271no—
520#121—271no—
521#121—271no—
522#120—91no—
523#120—271no—
524C4×D4—31no—
525C4×D4—271no—
526C2×C22⋊C4—271no—
527C2×C22⋊C4—271no—
528C33#54611yescharacteristic, complemented, Sylow
529C23×C3—24no—
530C23×C3—34no—
531C23×C3—91no—
532C23×C3—91no—
533C23×C3—91no—
534C23×C3—182no—
535C23×C3—182no—
536C23×C3—361no—
537C23×C3C2×D3214yes—
538C23×C3C22×C3⋊D311yescharacteristic
539C22×D3—34no—
540C22×D3—34no—
541C22×D3—34no—
542C22×D3—68no—
543C22×D3—68no—
544C22×D3—94no—
545C22×D3—91no—
546C22×D3—124no—
547C22×D3—184no—
548C22×D3—182no—
549C22×D3—188no—
550C22×D3—188no—
551C22×D3—182no—
552C22×D3—361no—
553C22×D3—364no—
554C22×D3C22×C3⋊D311yescharacteristic
555C3×D4—316no—
556C3×D4—182no—
557C3×D4—182no—
558C3×D4—361no—
559C2×C3×C4—24no—
560C2×C3×C4—24no—
561C2×C3×C4—34no—
562C2×C3×C4—34no—
563C2×C3×C4—34no—
564C2×C3×C4—91no—
565C2×C3×C4—124no—
566C2×C3×C4—124no—
567C2×C3×C4C2×D3214yes—
568C2×C3×C4C2×D3214yes—
569C2×C3×C4C22×C3⋊D311yescharacteristic
570C2×C3×C4C22×C3⋊D311yescharacteristic
571#67—68no—
572#67—188no—
573#67—188no—
574#67—188no—
575#67—182no—
576#67—182no—
577#67—182no—
578#67—182no—
579#67—368no—
580#67—361no—
581#67C4⋊(C3⋊D3)14yescomplemented
582C2×Dic3—34no—
583C2×Dic3—41no—
584C2×Dic3—94no—
585C2×Dic3—94no—
586C2×Dic3—94no—
587C2×Dic3—91no—
588C2×Dic3—91no—
589C2×Dic3—91no—
590C2×Dic3—184no—
591C2×Dic3—184no—
592C2×Dic3—184no—
593C2×Dic3—188no—
594C2×Dic3—188no—
595C2×Dic3—182no—
596C2×Dic3—182no—
597C2×Dic3—182no—
598C2×Dic3—368no—
599C2×Dic3C22×C3⋊D311yescharacteristic
600C2×Dic3C22×C3⋊D311yescharacteristic
601C2×Dic3C22×C3⋊D311yescharacteristic
602D12—68no—
603D12—124no—
604D12—188no—
605D12—364no—
606C4×D3—41no—
607C4×D3—188no—
608C4×D3—188no—
609C4×D3—182no—
610Dic6—188no—
611Dic6—182no—
612C2×C32—22no—
613C2×C32—24no—
614C2×C32—24no—
615C2×C32—24no—
616C2×C32—28no—
617C2×C32—48no—
618C2×C32—62no—
619C2×C32C22×D1214yes—
620C2×C32C2×D3×D411yescharacteristic
621C2×C32C2×#23711yescharacteristic
622C2×C32#100414yes—
623C2×C32#100411yescharacteristic
624C2×C32D3×#4114yes—
625C3⋊D3—22no—
626C3⋊D3—41no—
627C3⋊D3—41no—
628C3⋊D3—121no—
629C3⋊D3—124no—
630C3⋊D3—244no—
631C3×D3—28no—
632C3×D3—68no—
633C3×D3—124no—
634C3×D3—124no—
635C24—91no—
636C24—271no—
637#41—544no—
638C2×Q8—271no—
639C2×D4—31no—
640C2×D4—91no—
641C2×D4—91no—
642C2×D4—91no—
643C2×D4—271no—
644C2×D4—271no—
645C2×D4—271no—
646C2×D4—271no—
647C2×D4—271no—
648C2×D4—544no—
649C22×C4—31no—
650C22×C4—31no—
651C22×C4—271no—
652C22×C4—271no—
653C22×C4—271no—
654C22×C4—271no—
655C4⋊C4—31no—
656C4⋊C4—271no—
657C4⋊C4—271no—
658C4⋊C4—271no—
659C22⋊C4—31no—
660C22⋊C4—91no—
661C22⋊C4—91no—
662C22⋊C4—271no—
663C22⋊C4—271no—
664C22⋊C4—271no—
665C22⋊C4—271no—
666C22⋊C4—271no—
667C22⋊C4—271no—
668C22⋊C4—271no—
669C22⋊C4—271no—
670C22⋊C4D3×C3⋊D311yescharacteristic, complemented
671C42—31no—
672C22×C3—24no—
673C22×C3—24no—
674C22×C3—21no—
675C22×C3—21no—
676C22×C3—24no—
677C22×C3—28no—
678C22×C3—38no—
679C22×C3—44no—
680C22×C3—44no—
681C22×C3—64no—
682C22×C3—64no—
683C22×C3—92no—
684C22×C3—181no—
685C22×C3—181no—
686C22×C3—181no—
687C22×C3—181no—
688C22×C3—181no—
689C22×C3—181no—
690C22×C3—181no—
691C22×C3—181no—
692C22×C3—364no—
693C22×C3D3×D1218yes—
694C22×C3C2×C4⋊(C3⋊D3)12yes—
695C22×C3C22×D3214yes—
696C22×C3C23×C3⋊D311yescharacteristic
697C2×D3—21no—
698C2×D3—21no—
699C2×D3—38no—
700C2×D3—64no—
701C2×D3—64no—
702C2×D3—64no—
703C2×D3—64no—
704C2×D3—64no—
705C2×D3—64no—
706C2×D3—64no—
707C2×D3—64no—
708C2×D3—1216no—
709C2×D3—184no—
710C2×D3—184no—
711C2×D3—184no—
712C2×D3—181no—
713C2×D3—181no—
714C2×D3—181no—
715C2×D3—364no—
716C2×D3—364no—
717C2×D3—364no—
718C2×D3—364no—
719C2×D3—3616no—
720C2×D3C2×C4⋊(C3⋊D3)12yes—
721C3×C4—24no—
722C3×C4—24no—
723C3×C4—21no—
724C3×C4—21no—
725C3×C4—38no—
726C3×C4—44no—
727C3×C4—44no—
728C3×C4—64no—
729C3×C4—64no—
730C3×C4—181no—
731Dic3—21no—
732Dic3—21no—
733Dic3—64no—
734Dic3—184no—
735Dic3—184no—
736Dic3—184no—
737Dic3—181no—
738Dic3—181no—
739Dic3—181no—
740Dic3—364no—
741Dic3—364no—
742Dic3—364no—
743Dic3C2×C4⋊(C3⋊D3)12yes—
744C32—24no—
745C32#555414yescomplemented
746C32#559111yescharacteristic, complemented
747C23—31no—
748C23—91no—
749C23—91no—
750C23—91no—
751C23—182no—
752C23—182no—
753C23—271no—
754C23—361no—
755C23—542no—
756C23—542no—
757C23—1081no—
758C23C2×D3×C3⋊D311yescharacteristic
759Q8—542no—
760D4—34no—
761D4—182no—
762D4—182no—
763D4—361no—
764D4—542no—
765D4—542no—
766D4—542no—
767D4—542no—
768D4—1081no—
769C2×C4—31no—
770C2×C4—31no—
771C2×C4—31no—
772C2×C4—91no—
773C2×C4—121no—
774C2×C4—121no—
775C2×C4—271no—
776C2×C4—271no—
777C2×C4—271no—
778C2×C4—542no—
779C2×C4—542no—
780C2×C4—542no—
781C2×C4—542no—
782C2×C4C2×D3×C3⋊D311yescharacteristic
783C2×C4C2×D3×C3⋊D311yescharacteristic
784C2×C3—22no—
785C2×C3—28no—
786C2×C3—24no—
787C2×C3—24no—
788C2×C3—24no—
789C2×C3—48no—
790C2×C3—68no—
791C2×C3—182no—
792C2×C3—361no—
793C2×C3—361no—
794C2×C3C2×D3×D1214yes—
795C2×C3D3×#23714yes—
796C2×C3#6431314yes—
797C2×C3C22×C4⋊(C3⋊D3)11yescharacteristic
798C2×C3#6436111yescharacteristic
799C2×C3#41×C3⋊D311yescharacteristic
800D3—22no—
801D3—68no—
802D3—124no—
803D3—124no—
804D3—361no—
805D3—364no—
806D3—724no—
807C22—21no—
808C22—21no—
809C22—32no—
810C22—61no—
811C22—61no—
812C22—92no—
813C22—181no—
814C22—181no—
815C22—181no—
816C22—181no—
817C22—181no—
818C22—181no—
819C22—181no—
820C22—181no—
821C22—364no—
822C22—541no—
823C22—541no—
824C22—541no—
825C22—1084no—
826C22D3×C4⋊(C3⋊D3)12yes—
827C22C22×D3×C3⋊D311yescharacteristic
828C4—21no—
829C4—21no—
830C4—32no—
831C4—61no—
832C4—61no—
833C4—181no—
834C4—541no—
835C4—541no—
836C4—541no—
837C3—24no—
838C3#1059429214yescomplemented
839C3#1059602511yescharacteristic, complemented
840C2—22no—
841C2—62no—
842C2—182no—
843C2—361no—
844C2—361no—
845C2—1081no—
846C2C2×D3×C4⋊(C3⋊D3)11yescharacteristic
847C2C3⋊D3×#23711yescharacteristic
848C2#1172458711yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC33×C22⋊C4C22
hypercenterC22⋊C4D3×C3⋊D3
hypocenterC33#546
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3⋊D3×#67C2semidirect
2. C2×#89029C2semidirect
3. #11723927C2semidirect
4. C3×#64091C2semidirect
5. C32×#67⋊C4C2semidirect
6. #11723632C2semidirect
7. C2×#88803C2semidirect
8. #11723541C2semidirect
9. D3×#3752C2semidirect
10. #11723515C2semidirect
11. #11723483C2semidirect
12. #11723482C2semidirect
13. Dic3×C4⋊(C3⋊D3)C2semidirect
14. #11723480C2semidirect
15. #11723416C2semidirect
21. C22×C3⋊(C3⋊Dic3)C22semidirect
22. C2×C3×#638C22semidirect
24. C2×C3×C4⋊(C3⋊D3)C22semidirect
26. C22×C32×Dic3C22semidirect
27. C2×C32×C4×D3C22semidirect
29. C2×#6293C22semidirect
31. C2×#6292C22semidirect
33. C2×#6290C22semidirect
35. C2×Dic3×C3⋊D3C22semidirect
37. C2×D3×C3⋊Dic3C22semidirect
38. C33×C22⋊C4C22semidirect
39. #88859C22semidirect
40. #88859C22semidirect
41. C4⋊(C3⋊(C3⋊Dic3))C22semidirect
42. C4⋊(C3⋊(C3⋊Dic3))C22semidirect
44. C3×#3752C22semidirect
45. C32×(C2×D3)⋊C4C22semidirect
46. C32×Dic3⋊C4C22semidirect
47. C32×C4×Dic3C22semidirect
48. Dic3⋊(C3⋊Dic3)C22semidirect
49. #88804C22semidirect
52. #88803C22semidirect
53. #88803C22semidirect
54. #88803C22semidirect
71. #64091D3semidirect
75. C3×#67⋊C4D3semidirect
109. C32×#67D4semidirect
137. C2×#638C2×D3semidirect
147. C2×C4⋊(C3⋊D3)C2×D3semidirect
153. C22×C3×Dic3C2×D3semidirect
156. C2×C3×C4×D3C2×D3semidirect
170. C32×C22⋊C4C2×D3semidirect
171. C32×C22⋊C4C2×D3semidirect
186. #3752C2×D3semidirect
196. C3×(C2×D3)⋊C4C2×D3semidirect
197. C3×Dic3⋊C4C2×D3semidirect
198. C3×C4×Dic3C2×D3semidirect
222. C2×C3×C3⋊D3#41semidirect
262. #67⋊C4C3⋊D3semidirect
333. C3×#67D12semidirect
388. C22×Dic3C2×C3⋊D3semidirect
399. C2×C4×D3C2×C3⋊D3semidirect
407. C3×C22⋊C4D32semidirect
408. C3×C22⋊C4C2×C3⋊D3semidirect
430. (C2×D3)⋊C4C2×C3⋊D3semidirect
439. Dic3⋊C4C2×C3⋊D3semidirect
440. C4×Dic3C2×C3⋊D3semidirect
475. C2×C3⋊D3#237semidirect
528. C33#546semidirect
581. #67C4⋊(C3⋊D3)semidirect
670. C22⋊C4D3×C3⋊D3semidirect
745. C32#5554semidirect
746. C32#5591semidirect
838. C3#10594292semidirect
839. C3#10596025semidirect

Maximal subgroups

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

subgroupindex
C2×C3⋊D3×#672
C2×#890292
#117239272
C3×#640912
C32×#67⋊C42
#117236322
C2×#888032
#117235412
D3×#37522
#117235152
#117234832
#117234822
Dic3×C4⋊(C3⋊D3)2
#117234802
#117234162
#105960253
#105942923