Finite Group Databasebeta

← #13177306

Subgroups — #13177306

Order 1728.

2532 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3828C211yesmaximal, characteristic, complemented
2C2×#89039C211yesmaximal, characteristic, complemented
3C2×#88859C211yesmaximal, characteristic, complemented
4C32×#929C211yesmaximal, characteristic, complemented
5#11723639C211yesmaximal, characteristic, complemented
6#11723637C211yesmaximal, characteristic, complemented
7#11723626C211yesmaximal, characteristic, complemented
8#11723541C211yesmaximal, characteristic, complemented
9C3⋊D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
10#11723521C211yesmaximal, characteristic, complemented
11#11723520C211yesmaximal, characteristic, complemented
12#11723512C211yesmaximal, characteristic, complemented
13#11723489C211yesmaximal, characteristic, complemented
14#11723482C211yesmaximal, characteristic, complemented
15#11723417C211yesmaximal, characteristic, complemented
16#10596125—31nomaximal
17#10595068—34nomaximal
18C23×C3⋊(C3⋊D3)C2211yescharacteristic
19C22×D3×C3⋊D3C2211yescharacteristic
20C22×C33×C4C2211yescharacteristic, complemented
21C22×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
22C2×C3×#638C2211yescharacteristic
23C2×C3×#638C2211yescharacteristic, complemented
24C3×#3828—24no—
25C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
26C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
27C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
28C2×C3×#634C2211yescharacteristic, complemented
29C2×C32×#67C2211yescharacteristic
30#89039—24no—
31C2×#6292C2211yescharacteristic
32C2×#6292C2211yescharacteristic
33C2×#6292C2211yescharacteristic, complemented
34C2×#6291C2211yescharacteristic
35C2×#6290C2211yescharacteristic, complemented
36C2×#6289C2211yescharacteristic
37C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
38#88859C2211yescharacteristic
39#88859C2211yescharacteristic
40#88859C2211yescharacteristic, complemented
41#88859C2211yescharacteristic, complemented
42C32×#217C2211yescharacteristic, complemented
43C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
44C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
45C32×Dic3⋊C4C2211yescharacteristic, complemented
46C32×Dic3⋊C4C2211yescharacteristic, complemented
47#88807C2211yescharacteristic, complemented
48#88806C2211yescharacteristic, complemented
49#88804C2211yescharacteristic
50#88804C2211yescharacteristic, complemented
51#88803C2211yescharacteristic, complemented
52#88803C2211yescharacteristic, complemented
53(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
54Dic3×C3⋊Dic3C2211yescharacteristic, complemented
55C2×D4×C3⋊D3—31no—
56C2×#3828D311yescharacteristic, complemented
57C2×C3×#235—34no—
58C2×#3811—34no—
59C32×#123—31no—
60#64148—31no—
61C2×#3752—31no—
62C2×#3752—34no—
63C2×#3752—64no—
64#64105—31no—
65#64104—31no—
66#64103—31no—
67#64102—31no—
68#64094—31no—
69#64093—31no—
70#64091—31no—
71#64091—31no—
72#64090—31no—
73C22⋊C4×C3⋊D3—31no—
74C3×#929D314yescomplemented
75#63981—34no—
76#63980—34no—
77#67⋊Dic3—34no—
78#63922—34no—
79D3×(C2×D3)⋊C4—34no—
80#63907—34no—
81#63906—34no—
82#63904—34no—
83#63888—34no—
84#63886—34no—
85#63850—34no—
86C23×C33C2311yescharacteristic
87C22×C3⋊(C3⋊D3)—22no—
88C22×C3⋊(C3⋊D3)—22no—
89C22×C3⋊(C3⋊D3)—41no—
90C22×C3⋊(C3⋊D3)C2311yescharacteristic
91C22×C3⋊(C3⋊D3)C2311yescharacteristic
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×C4—22no—
99C2×C33×C4C2311yescharacteristic
100C2×C33×C4C2311yescharacteristic
101C2×C3⋊(C3⋊Dic3)—41no—
102C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
103C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
104C3×#638—22no—
105C3×#638D414yescomplemented
106C2×C3×C3⋊Dic3C2311yescharacteristic
107C2×C3×C3⋊Dic3C2311yescharacteristic
108C3×C4⋊(C3⋊D3)—22no—
109C3×C4×C3⋊D3—22no—
110C3×C4×C3⋊D3—22no—
111C3×#634—22no—
112C32×#67—22no—
113C2×C32×Dic3C2311yescharacteristic
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116#6292—22no—
117#6292—22no—
118#6292—41no—
119#6291—22no—
120#6290—41no—
121#6289—22no—
122Dic3×C3⋊D3—41no—
123#5829—91no—
124#5654—94no—
125C23×C3⋊D3—31no—
126C23×C3⋊D3—34no—
127C23×C3⋊D3—31no—
128C23×C3⋊D3—64no—
129C22×D32—34no—
130C2×C32×D4—31no—
131C22×C32×C4—24no—
132C22×C32×C4C2×D314yescomplemented
133C22×C32×C4C2×D311yescharacteristic, complemented
134C2×#638—31no—
135C2×#638—31no—
136C2×#638C2×D311yescharacteristic
137C2×#638C2×D311yescharacteristic, complemented
138C22×C3⋊Dic3—31no—
139C22×C3⋊Dic3—34no—
140C22×C3⋊Dic3—64no—
141D4×C3⋊D3—64no—
142#3828—24no—
143C2×C4⋊(C3⋊D3)—31no—
144C2×C4⋊(C3⋊D3)—31no—
145C2×C4⋊(C3⋊D3)—31no—
146C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
147C2×C4×C3⋊D3—31no—
148C2×C4×C3⋊D3—31no—
149C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
150C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
151C2×#634C2×D311yescharacteristic, complemented
152C2×C3×#67—34no—
153C2×C3×#67—34no—
154C2×C3×#67C2×D314yes—
155C3×#235—616no—
156C2×C3×D12—34no—
157C2×C3×C4×D3—34no—
158C2×C3×C4×D3—34no—
159C2×C3×Dic6—34no—
160#3811—616no—
161C2×#626—34no—
162C2×#626—34no—
163C2×#626—34no—
164C2×#626—34no—
165C2×#625—34no—
166C2×#624—34no—
167C2×D3×Dic3—34no—
168C32×C4⋊C4—31no—
169C32×C4⋊C4—31no—
170C32×C22⋊C4—31no—
171C32×C22⋊C4—31no—
172C32×C22⋊C4—31no—
173#3757—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—34no—
183#3752—34no—
184#3752—31no—
185#3752—31no—
186#3752—64no—
187#3752—64no—
188#3752—64no—
189#3752—64no—
190#3750—31no—
191#3750—31no—
192C4×C3⋊Dic3—31no—
193C3×#217C2×D314yescomplemented
194C3×(C2×D3)⋊C4C2×D314yescomplemented
195C3×(C2×D3)⋊C4C2×D314yescomplemented
196C3×Dic3⋊C4C2×D314yescomplemented
197C3×Dic3⋊C4C2×D314yescomplemented
198#3724—34no—
199Dic3⋊Dic3—34no—
200#3722—34no—
201#3722—34no—
202(C2×D3)⋊Dic3—34no—
203(C2×D3)⋊Dic3—34no—
204(C2×D3)⋊Dic3—34no—
205Dic32—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)—44no—
216C2×C3⋊(C3⋊D3)#4112yescomplemented
217C2×C3×C3⋊D3—21no—
218C2×C3×C3⋊D3—21no—
219C2×C3×C3⋊D3—21no—
220C2×C3×C3⋊D3—21no—
221C2×C3×C3⋊D3—21no—
222C2×C3×C3⋊D3C2×D412yes—
223C2×C32×D3—21no—
224C2×C32×D3—21no—
225C2×C32×D3—21no—
226D3×C3⋊D3—44no—
227C33×C4—21no—
228C33×C4—21no—
229C3⋊(C3⋊Dic3)—21no—
230C3⋊(C3⋊Dic3)—21no—
231C3×C3⋊Dic3—21no—
232C3×C3⋊Dic3C2×D412yes—
233C32×Dic3—21no—
234C32×Dic3—21no—
235C32×Dic3—21no—
236C2×C3×#41—91no—
237C2×D3×D4—94no—
238C2×D3×D4—91no—
239C2×#235—34no—
240C3×#123—34no—
241#947—91no—
242#946—91no—
243#939—94no—
244#939—91no—
245#939—91no—
246#937—91no—
247#937—91no—
248D4×Dic3—91no—
249#930—91no—
250#929—91no—
251#929C3⋊D311yescharacteristic, complemented
252C4×#67—91no—
253C2×(C2×D3)⋊C4—94no—
254C2×(C2×D3)⋊C4—91no—
255C2×(C2×D3)⋊C4—91no—
256C2×(C2×D3)⋊C4—184no—
257#896—94no—
258#895—94no—
259#894—94no—
260#893—94no—
261#885—94no—
262#884—94no—
263#882—94no—
264#882—94no—
265#67⋊C4—94no—
266D3×C22⋊C4—94no—
267C23×C32—24no—
268C23×C32—31no—
269C23×C32C22×D314yes—
270C23×C32C22×D311yescharacteristic
271C22×C3⋊D3—31no—
272C22×C3⋊D3—31no—
273C22×C3⋊D3—34no—
274C22×C3⋊D3—34no—
275C22×C3⋊D3—64no—
276C22×C3⋊D3—64no—
277C22×C3⋊D3—62no—
278C22×C3⋊D3—62no—
279C22×C3⋊D3—68no—
280C22×C3⋊D3—616no—
281C22×C3⋊D3—62no—
282C22×C3⋊D3—62no—
283C22×C3⋊D3—68no—
284C22×C3⋊D3—128no—
285C22×C3⋊D3—121no—
286C22×C3⋊D3—121no—
287C22×C3⋊D3—124no—
288C22×C3⋊D3—128no—
289C22×C3⋊D3C22×D311yescharacteristic
290C22×C3⋊D3C22×D311yescharacteristic
291C22×C3×D3—34no—
292C22×C3×D3—34no—
293C22×C3×D3C22×D314yes—
294C2×D32—68no—
295C2×D32—68no—
296C2×D32—124no—
297C32×D4—62no—
298C2×C32×C4—22no—
299C2×C32×C4—24no—
300C2×C32×C4—24no—
301C2×C32×C4—28no—
302C2×C32×C4—31no—
303C2×C32×C4—31no—
304C2×C32×C4—31no—
305C2×C32×C4—48no—
306C2×C32×C4C22×D314yes—
307C2×C32×C4C22×D314yes—
308C2×C32×C4C22×D311yescharacteristic
309C2×C32×C4C22×D311yescharacteristic
310#638—22no—
311#638—62no—
312#638—121no—
313#638#6714yescomplemented
314C2×C3⋊Dic3—31no—
315C2×C3⋊Dic3—31no—
316C2×C3⋊Dic3—34no—
317C2×C3⋊Dic3—34no—
318C2×C3⋊Dic3—64no—
319C2×C3⋊Dic3—64no—
320C2×C3⋊Dic3—121no—
321C2×C3⋊Dic3—124no—
322C2×C3⋊Dic3—128no—
323C2×C3⋊Dic3C22×D311yescharacteristic
324C2×C3⋊Dic3C22×D311yescharacteristic
325C4⋊(C3⋊D3)—22no—
326C4⋊(C3⋊D3)—62no—
327C4⋊(C3⋊D3)—62no—
328C4⋊(C3⋊D3)—121no—
329C4×C3⋊D3—22no—
330C4×C3⋊D3—22no—
331C4×C3⋊D3—62no—
332C4×C3⋊D3—121no—
333#634—22no—
334C3×#67—28no—
335C3×#67—316no—
336C3×#67—68no—
337C2×C3×Dic3—34no—
338C2×C3×Dic3—34no—
339C2×C3×Dic3C22×D314yes—
340C2×C3×Dic3C22×D314yes—
341C2×C3×Dic3C22×D314yes—
342C3×D12—68no—
343C3×C4×D3—68no—
344C3×C4×D3—68no—
345C3×Dic6—68no—
346#626—68no—
347#626—68no—
348#626—68no—
349#626—124no—
350#625—124no—
351#624—68no—
352D3×Dic3—124no—
353#546—271noSylow
354C2×C33—22no—
355C2×C33C22×D411yescharacteristic
356C2×C33C2×#4111yescharacteristic
357C2×C33H(5,𝔽2)11yescharacteristic
358C3⋊(C3⋊D3)—22no—
359C3⋊(C3⋊D3)—41no—
360C3×C3⋊D3—22no—
361C3×C3⋊D3—41no—
362C32×D3—41no—
363C23×D3—94no—
364C23×D3—94no—
365C23×D3—91no—
366C23×D3—91no—
367C23×D3—184no—
368C3×#41—184no—
369C2×C3×Q8—91no—
370C2×C3×D4—34no—
371C2×C3×D4—91no—
372C2×C3×D4—91no—
373C2×C3×D4—91no—
374C22×C3×C4—24no—
375C22×C3×C4—91no—
376C22×C3×C4—91no—
377C22×C3×C4D3214yescomplemented
378C22×C3×C4C2×C3⋊D311yescharacteristic, complemented
379C2×#67—34no—
380C2×#67—34no—
381C2×#67—94no—
382C2×#67—94no—
383C2×#67—91no—
384C2×#67—91no—
385C2×#67—91no—
386C2×#67—91no—
387C2×#67C2×C3⋊D311yescharacteristic
388C22×Dic3—94no—
389C22×Dic3—91no—
390C22×Dic3—91no—
391C22×Dic3—184no—
392D3×D4—184no—
393D3×D4—1816no—
394#235—616no—
395C2×D12—34no—
396C2×D12—94no—
397C2×D12—94no—
398C2×D12—91no—
399C2×D12—94no—
400C2×C4×D3—34no—
401C2×C4×D3—34no—
402C2×C4×D3—94no—
403C2×C4×D3—91no—
404C2×C4×D3—94no—
405C2×Dic6—34no—
406C3×C4⋊C4—34no—
407C3×C4⋊C4—34no—
408C3×C22⋊C4—34no—
409C3×C22⋊C4—34no—
410C3×C22⋊C4—34no—
411#217—94no—
412#217—91no—
413#217—91no—
414#217C2×C3⋊D311yescharacteristic, complemented
415(C2×D3)⋊C4—94no—
416(C2×D3)⋊C4—94no—
417(C2×D3)⋊C4—94no—
418(C2×D3)⋊C4—94no—
419(C2×D3)⋊C4—91no—
420(C2×D3)⋊C4—94no—
421(C2×D3)⋊C4—94no—
422(C2×D3)⋊C4—94no—
423(C2×D3)⋊C4—94no—
424(C2×D3)⋊C4—91no—
425(C2×D3)⋊C4—91no—
426(C2×D3)⋊C4—91no—
427(C2×D3)⋊C4—91no—
428(C2×D3)⋊C4—91no—
429(C2×D3)⋊C4—91no—
430(C2×D3)⋊C4—184no—
431(C2×D3)⋊C4—184no—
432(C2×D3)⋊C4—184no—
433(C2×D3)⋊C4—184no—
434(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
435(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
436C4⋊Dic3—91no—
437Dic3⋊C4—94no—
438Dic3⋊C4—94no—
439Dic3⋊C4—91no—
440Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
441Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
442C4×Dic3—94no—
443C4×Dic3—91no—
444C22×C32—28no—
445C22×C32—28no—
446C22×C32—24no—
447C22×C32—21no—
448C22×C32—24no—
449C22×C32—21no—
450C22×C32—24no—
451C22×C32—28no—
452C22×C32—61no—
453C22×C32—61no—
454C22×C32—61no—
455C22×C32D3×D418yes—
456C22×C32C2×#6712yes—
457C22×C32C23×D314yes—
458C22×C32C23×D311yescharacteristic
459C2×C3⋊D3—21no—
460C2×C3⋊D3—21no—
461C2×C3⋊D3—21no—
462C2×C3⋊D3—21no—
463C2×C3⋊D3—21no—
464C2×C3⋊D3—32no—
465C2×C3⋊D3—38no—
466C2×C3⋊D3—68no—
467C2×C3⋊D3—61no—
468C2×C3⋊D3—61no—
469C2×C3⋊D3—68no—
470C2×C3⋊D3—64no—
471C2×C3⋊D3—61no—
472C2×C3⋊D3—61no—
473C2×C3⋊D3—61no—
474C2×C3⋊D3—64no—
475C2×C3⋊D3—64no—
476C2×C3⋊D3—64no—
477C2×C3⋊D3—64no—
478C2×C3⋊D3—124no—
479C2×C3⋊D3—124no—
480C2×C3⋊D3—124no—
481C2×C3⋊D3—124no—
482C2×C3⋊D3—124no—
483C2×C3⋊D3—124no—
484C2×C3⋊D3—1216no—
485C2×C3⋊D3—1232no—
486C2×C3⋊D3C2×#6712yes—
487C2×C3×D3—24no—
488C2×C3×D3—24no—
489C2×C3×D3—24no—
490C2×C3×D3—38no—
491C2×C3×D3—64no—
492C2×C3×D3—64no—
493C2×C3×D3—64no—
494C2×C3×D3—64no—
495C2×C3×D3—64no—
496D32—1216no—
497C32×C4—21no—
498C32×C4—21no—
499C32×C4—24no—
500C32×C4—24no—
501C32×C4—44no—
502C32×C4—44no—
503C32×C4—61no—
504C32×C4—61no—
505C32×C4—61no—
506C3⋊Dic3—21no—
507C3⋊Dic3—61no—
508C3⋊Dic3—61no—
509C3⋊Dic3—64no—
510C3⋊Dic3—64no—
511C3⋊Dic3—124no—
512C3⋊Dic3—124no—
513C3⋊Dic3C2×#6712yes—
514C3×Dic3—24no—
515C3×Dic3—24no—
516C3×Dic3—24no—
517C3×Dic3—38no—
518C3×Dic3—64no—
519C2×#41—91no—
520C22×D4—271no—
521#124—271no—
522#123—31no—
523#123—271no—
524C22⋊Q8—271no—
525#121—271no—
526#121—271no—
527#121—271no—
528#120—271no—
529#120—271no—
530C4×D4—271no—
531C4×D4—271no—
532C2×C22⋊C4—271no—
533C2×C22⋊C4—271no—
534C33#54611yescharacteristic, complemented, Sylow
535C23×C3—24no—
536C23×C3—34no—
537C23×C3—91no—
538C23×C3—91no—
539C23×C3C2×D3214yes—
540C23×C3C22×C3⋊D311yescharacteristic
541C22×D3—34no—
542C22×D3—34no—
543C22×D3—94no—
544C22×D3—91no—
545C22×D3—94no—
546C22×D3—91no—
547C22×D3—184no—
548C22×D3—184no—
549C22×D3—182no—
550C22×D3—182no—
551C22×D3—188no—
552C22×D3—188no—
553C22×D3—188no—
554C22×D3—182no—
555C22×D3—1816no—
556C22×D3—188no—
557C22×D3—182no—
558C22×D3—368no—
559C22×D3—361no—
560C22×D3—364no—
561C22×D3—364no—
562C22×D3—361no—
563C22×D3—368no—
564C22×D3C22×C3⋊D311yescharacteristic
565C3×Q8—182no—
566C3×D4—68no—
567C3×D4—94no—
568C3×D4—182no—
569C3×D4—182no—
570C2×C3×C4—28no—
571C2×C3×C4—22no—
572C2×C3×C4—24no—
573C2×C3×C4—24no—
574C2×C3×C4—34no—
575C2×C3×C4—34no—
576C2×C3×C4—34no—
577C2×C3×C4—48no—
578C2×C3×C4—91no—
579C2×C3×C4—91no—
580C2×C3×C4—182no—
581C2×C3×C4—182no—
582C2×C3×C4C2×D3214yes—
583C2×C3×C4C2×D3214yes—
584C2×C3×C4C22×C3⋊D311yescharacteristic
585C2×C3×C4C22×C3⋊D311yescharacteristic
586#67—22no—
587#67—316no—
588#67—68no—
589#67—182no—
590#67—182no—
591#67—188no—
592#67—361no—
593#67—361no—
594#67—364no—
595C2×Dic3—34no—
596C2×Dic3—34no—
597C2×Dic3—94no—
598C2×Dic3—94no—
599C2×Dic3—91no—
600C2×Dic3—91no—
601C2×Dic3—184no—
602C2×Dic3—184no—
603C2×Dic3—361no—
604C2×Dic3—364no—
605C2×Dic3—361no—
606C2×Dic3—368no—
607C2×Dic3C22×C3⋊D311yescharacteristic
608C2×Dic3C22×C3⋊D311yescharacteristic
609C2×Dic3C22×C3⋊D311yescharacteristic
610D12—68no—
611D12—188no—
612D12—188no—
613D12—182no—
614D12—364no—
615C4×D3—68no—
616C4×D3—68no—
617C4×D3—182no—
618C4×D3—188no—
619C4×D3—364no—
620Dic6—68no—
621C2×C32—216no—
622C2×C32—28no—
623C2×C32—22no—
624C2×C32—24no—
625C2×C32—24no—
626C2×C32—24no—
627C2×C32—121no—
628C2×C32C2×D3×D414yes—
629C2×C32D3×#4114yes—
630C2×C32D3×#4111yescharacteristic
631C2×C32#100914yes—
632C2×C32#100911yescharacteristic
633C2×C32C22×#6711yescharacteristic
634C3⋊D3—22no—
635C3⋊D3—41no—
636C3⋊D3—62no—
637C3⋊D3—68no—
638C3⋊D3—128no—
639C3⋊D3—128no—
640C3⋊D3—124no—
641C3⋊D3—121no—
642C3×D3—44no—
643C3×D3—68no—
644C3×D3—124no—
645C24—271no—
646C24—271no—
647#41—184no—
648C2×Q8—91no—
649C2×D4—31no—
650C2×D4—91no—
651C2×D4—91no—
652C2×D4—91no—
653C2×D4—271no—
654C2×D4—271no—
655C2×D4—271no—
656C2×D4—271no—
657C2×D4—271no—
658C2×D4—544no—
659C22×C4—91no—
660C22×C4—91no—
661C22×C4—271no—
662C22×C4—271no—
663C22×C4—271no—
664C22×C4D3×C3⋊D311yescharacteristic, complemented
665C4⋊C4—31no—
666C4⋊C4—31no—
667C4⋊C4—271no—
668C4⋊C4—271no—
669C22⋊C4—31no—
670C22⋊C4—31no—
671C22⋊C4—31no—
672C22⋊C4—271no—
673C22⋊C4—271no—
674C22⋊C4—271no—
675C22⋊C4—271no—
676C22⋊C4—271no—
677C22⋊C4—271no—
678C22⋊C4—271no—
679C22⋊C4—271no—
680C22⋊C4—271no—
681C42—271no—
682C22×C3—28no—
683C22×C3—28no—
684C22×C3—24no—
685C22×C3—24no—
686C22×C3—21no—
687C22×C3—21no—
688C22×C3—24no—
689C22×C3—28no—
690C22×C3—64no—
691C22×C3—64no—
692C22×C3—64no—
693C22×C3—92no—
694C22×C3—181no—
695C22×C3—181no—
696C22×C3—181no—
697C22×C3—181no—
698C22×C3—181no—
699C22×C3D3×#6718yes—
700C22×C3D4×C3⋊D312yes—
701C22×C3C22×D3214yes—
702C22×C3C23×C3⋊D311yescharacteristic
703C2×D3—21no—
704C2×D3—21no—
705C2×D3—21no—
706C2×D3—38no—
707C2×D3—64no—
708C2×D3—64no—
709C2×D3—64no—
710C2×D3—64no—
711C2×D3—64no—
712C2×D3—98no—
713C2×D3—92no—
714C2×D3—188no—
715C2×D3—184no—
716C2×D3—184no—
717C2×D3—181no—
718C2×D3—181no—
719C2×D3—188no—
720C2×D3—184no—
721C2×D3—184no—
722C2×D3—184no—
723C2×D3—181no—
724C2×D3—181no—
725C2×D3—181no—
726C2×D3—364no—
727C2×D3—364no—
728C2×D3—364no—
729C2×D3—364no—
730C2×D3—364no—
731C2×D3—3616no—
732C2×D3—364no—
733C2×D3—3616no—
734C2×D3—3632no—
735C3×C4—24no—
736C3×C4—24no—
737C3×C4—21no—
738C3×C4—21no—
739C3×C4—44no—
740C3×C4—44no—
741C3×C4—64no—
742C3×C4—64no—
743C3×C4—64no—
744C3×C4—92no—
745C3×C4—181no—
746Dic3—21no—
747Dic3—21no—
748Dic3—21no—
749Dic3—38no—
750Dic3—64no—
751Dic3—184no—
752Dic3—184no—
753Dic3—181no—
754Dic3—181no—
755Dic3—364no—
756Dic3—364no—
757C32—24no—
758C32#565414yescomplemented
759C32#582911yescharacteristic, complemented
760C23—31no—
761C23—91no—
762C23—91no—
763C23—271no—
764C23—271no—
765C23—542no—
766C23—542no—
767C23—542no—
768C23—542no—
769C23—1081no—
770C23—1081no—
771C23C2×D3×C3⋊D311yescharacteristic
772Q8—182no—
773D4—62no—
774D4—94no—
775D4—182no—
776D4—182no—
777D4—542no—
778D4—542no—
779D4—542no—
780D4—1081no—
781D4—1081no—
782C2×C4—22no—
783C2×C4—31no—
784C2×C4—31no—
785C2×C4—31no—
786C2×C4—91no—
787C2×C4—91no—
788C2×C4—182no—
789C2×C4—182no—
790C2×C4—271no—
791C2×C4—271no—
792C2×C4—542no—
793C2×C4—1081no—
794C2×C4—1081no—
795C2×C4C2×D3×C3⋊D311yescharacteristic
796C2×C4C2×D3×C3⋊D311yescharacteristic
797C2×C3—216no—
798C2×C3—22no—
799C2×C3—28no—
800C2×C3—24no—
801C2×C3—24no—
802C2×C3—24no—
803C2×C3—124no—
804C2×C3—182no—
805C2×C3—361no—
806C2×C3#6430614yes—
807C2×C3#6430814yes—
808C2×C3C2×D3×#6714yes—
809C2×C3C2×D4×C3⋊D311yescharacteristic
810C2×C3#41×C3⋊D311yescharacteristic
811C2×C3#6436611yescharacteristic
812D3—41no—
813D3—68no—
814D3—124no—
815D3—182no—
816D3—188no—
817D3—368no—
818D3—368no—
819D3—361no—
820D3—364no—
821C22—21no—
822C22—21no—
823C22—61no—
824C22—61no—
825C22—61no—
826C22—92no—
827C22—181no—
828C22—181no—
829C22—181no—
830C22—181no—
831C22—181no—
832C22—272no—
833C22—541no—
834C22—541no—
835C22—541no—
836C22—541no—
837C22—541no—
838C22—1084no—
839C22—1084no—
840C22C3⋊D3×#6712yes—
841C22C22×D3×C3⋊D311yescharacteristic
842C4—21no—
843C4—21no—
844C4—61no—
845C4—61no—
846C4—61no—
847C4—92no—
848C4—181no—
849C4—541no—
850C4—541no—
851C3—24no—
852C3#1059506814yescomplemented
853C3#1059612511yescharacteristic, complemented
854C2—22no—
855C2—121no—
856C2—182no—
857C2—361no—
858C2—542no—
859C2—1081no—
860C2#1172457811yescharacteristic
861C2#1172458111yescharacteristic
862C2C2×C3⋊D3×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC22×C33×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×#3828C2semidirect
2. C2×#89039C2semidirect
3. C2×#88859C2semidirect
4. C32×#929C2semidirect
5. #11723639C2semidirect
6. #11723637C2semidirect
7. #11723626C2semidirect
8. #11723541C2semidirect
9. C3⋊D3×(C2×D3)⋊C4C2semidirect
10. #11723521C2semidirect
11. #11723520C2semidirect
12. #11723512C2semidirect
13. #11723489C2semidirect
14. #11723482C2semidirect
15. #11723417C2semidirect
20. C22×C33×C4C22semidirect
21. C22×C3⋊(C3⋊Dic3)C22semidirect
23. C2×C3×#638C22semidirect
25. C2×C3×C4⋊(C3⋊D3)C22semidirect
26. C2×C3×C4×C3⋊D3C22semidirect
27. C2×C3×C4×C3⋊D3C22semidirect
28. C2×C3×#634C22semidirect
33. C2×#6292C22semidirect
35. C2×#6290C22semidirect
37. C2×Dic3×C3⋊D3C22semidirect
40. #88859C22semidirect
41. #88859C22semidirect
42. C32×#217C22semidirect
43. C32×(C2×D3)⋊C4C22semidirect
44. C32×(C2×D3)⋊C4C22semidirect
45. C32×Dic3⋊C4C22semidirect
46. C32×Dic3⋊C4C22semidirect
47. #88807C22semidirect
48. #88806C22semidirect
50. #88804C22semidirect
51. #88803C22semidirect
52. #88803C22semidirect
53. (C2×D3)⋊(C3⋊Dic3)C22semidirect
54. Dic3×C3⋊Dic3C22semidirect
56. C2×#3828D3semidirect
74. C3×#929D3semidirect
105. C3×#638D4semidirect
132. C22×C32×C4C2×D3semidirect
133. C22×C32×C4C2×D3semidirect
137. C2×#638C2×D3semidirect
146. C2×C4⋊(C3⋊D3)C2×D3semidirect
149. C2×C4×C3⋊D3C2×D3semidirect
150. C2×C4×C3⋊D3C2×D3semidirect
151. C2×#634C2×D3semidirect
193. C3×#217C2×D3semidirect
194. C3×(C2×D3)⋊C4C2×D3semidirect
195. C3×(C2×D3)⋊C4C2×D3semidirect
196. C3×Dic3⋊C4C2×D3semidirect
197. C3×Dic3⋊C4C2×D3semidirect
216. C2×C3⋊(C3⋊D3)#41semidirect
251. #929C3⋊D3semidirect
313. #638#67semidirect
377. C22×C3×C4D32semidirect
378. C22×C3×C4C2×C3⋊D3semidirect
414. #217C2×C3⋊D3semidirect
434. (C2×D3)⋊C4C2×C3⋊D3semidirect
435. (C2×D3)⋊C4C2×C3⋊D3semidirect
440. Dic3⋊C4C2×C3⋊D3semidirect
441. Dic3⋊C4C2×C3⋊D3semidirect
534. C33#546semidirect
664. C22×C4D3×C3⋊D3semidirect
758. C32#5654semidirect
759. C32#5829semidirect
852. C3#10595068semidirect
853. C3#10596125semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#38282
C2×#890392
C2×#888592
C32×#9292
#117236392
#117236372
#117236262
#117235412
C3⋊D3×(C2×D3)⋊C42
#117235212
#117235202
#117235122
#117234892
#117234822
#117234172
#105961253
#105950683