Finite Group Databasebeta

← #13177333

Subgroups — #13177333

Order 1728.

2660 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89076C211yesmaximal, characteristic, complemented
2C2×D3×#638C211yesmaximal, characteristic, complemented
3C3×#64138C211yesmaximal, characteristic, complemented
4C2×C32×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
5#11723632C211yesmaximal, characteristic, complemented
6#11723630C211yesmaximal, characteristic, complemented
7#11723618C211yesmaximal, characteristic, complemented
8#11723542C211yesmaximal, characteristic, complemented
9#11723539C211yesmaximal, characteristic, complemented
10#11723528C211yesmaximal, characteristic, complemented
11#11723527C211yesmaximal, characteristic, complemented
12#11723525C211yesmaximal, characteristic, complemented
13#11723496C211yesmaximal, characteristic, complemented
14#11723462C211yesmaximal, characteristic, complemented
15#11723420C211yesmaximal, characteristic, complemented
16#10595961—31nomaximal
17#10595077—34nomaximal
18C23×C32×D3C2211yescharacteristic
19C22×D3×C3⋊D3C2211yescharacteristic
20C22×C33×C4C2211yescharacteristic, complemented
21C2×#6312C2211yescharacteristic
22C2×#6312C2211yescharacteristic, complemented
23#89076—24no—
24C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic, complemented
25C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
26C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
27C2×#6308C2211yescharacteristic, complemented
28C2×C3×#638C2211yescharacteristic
29C22×C32×Dic3C2211yescharacteristic, complemented
30D3×#638—24no—
31C2×#6292C2211yescharacteristic, complemented
32C2×#6291C2211yescharacteristic
33C2×#6291C2211yescharacteristic
34C2×#6291C2211yescharacteristic, complemented
35C2×#6290C2211yescharacteristic
36C2×#6289C2211yescharacteristic, complemented
37C2×D3×C3⋊Dic3C2211yescharacteristic
38C3×#3757C2211yescharacteristic, complemented
39C3×#3752C2211yescharacteristic, complemented
40C3×#3752C2211yescharacteristic, complemented
41C3×#3750C2211yescharacteristic, complemented
42C3×#3750C2211yescharacteristic, complemented
43C32×(C2×D3)⋊C4C2211yescharacteristic
44C32×(C2×D3)⋊C4C2211yescharacteristic
45C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
46C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
47#88806C2211yescharacteristic, complemented
48Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
49#88804C2211yescharacteristic, complemented
50#88804C2211yescharacteristic, complemented
51#88803C2211yescharacteristic, complemented
52(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
53(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
54Dic3×C3⋊Dic3C2211yescharacteristic, complemented
55C22×#638—31no—
56C2×#3828—31no—
57C2×#3828—34no—
58C2×#3828—64no—
59C2×D3×#67—34no—
60C2×C32×C22⋊C4—31no—
61#64162—31no—
62#64139—31no—
63#64138D311yescharacteristic, complemented
64C4×#638—31no—
65#64094—31no—
66#64093—31no—
67#64093—31no—
68#64092—31no—
69#64091—31no—
70#64090—31no—
71C22⋊C4×C3⋊D3—31no—
72#64087—31no—
73C3×#929—34no—
74C2×C3×(C2×D3)⋊C4D314yescomplemented
75#63978—34no—
76#63977—34no—
77#63952—34no—
78#63923—34no—
79#63921—34no—
80#63913—34no—
81#63912—34no—
82#63910—34no—
83#63896—34no—
84#63881—34no—
85#63853—34no—
86C23×C33C2311yescharacteristic
87C22×C3⋊(C3⋊D3)C2311yescharacteristic
88C22×C3⋊(C3⋊D3)C2311yescharacteristic
89C22×C3×C3⋊D3C2311yescharacteristic
90C22×C32×D3—22no—
91C22×C32×D3—22no—
92C22×C32×D3—41no—
93C22×C32×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
101#6312—22no—
102#6312D414yescomplemented
103C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
104C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
105C4⋊(C3⋊(C3⋊D3))—22no—
106C4×C3⋊(C3⋊D3)—22no—
107C4×C3⋊(C3⋊D3)—22no—
108#6308—22no—
109C3×#638—22no—
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C2×C32×Dic3—41no—
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116#6292—41no—
117#6291—22no—
118#6291—22no—
119#6291—41no—
120#6290—22no—
121#6289—41no—
122D3×C3⋊Dic3—22no—
123#5654—91no—
124#5490—94no—
125C24×C32—31no—
126C23×C3⋊D3—31no—
127C23×C3×D3C2×D314yes—
128C22×D32—34no—
129C22×C32×C4—24no—
130C22×C32×C4—31no—
131C22×C32×C4C2×D314yescomplemented
132C22×C32×C4C2×D311yescharacteristic, complemented
133C2×#638—31no—
134C2×#638—34no—
135C2×#638—31no—
136C2×#638—34no—
137C2×#638—31no—
138C2×#638—31no—
139C2×#638—31no—
140C2×#638—31no—
141C2×#638—64no—
142C2×#638—64no—
143C2×#638—64no—
144C2×#638C2×D311yescharacteristic
145C22×C3⋊Dic3—31no—
146#3828—64no—
147#3828—616no—
148#3828—632no—
149C2×C4⋊(C3⋊D3)—31no—
150C2×C4⋊(C3⋊D3)—34no—
151C2×C4⋊(C3⋊D3)—31no—
152C2×C4⋊(C3⋊D3)—64no—
153C2×C4×C3⋊D3—31no—
154C2×C4×C3⋊D3—31no—
155C2×C4×C3⋊D3—34no—
156C2×C4×C3⋊D3—34no—
157C2×C4×C3⋊D3—31no—
158C2×C4×C3⋊D3—64no—
159C2×C4×C3⋊D3—64no—
160C2×#634—31no—
161C2×#634—34no—
162C2×#634—64no—
163C2×C3×#67—34no—
164C22×C3×Dic3C2×D314yescomplemented
165D3×#67—616no—
166C2×#626—34no—
167C2×#626—34no—
168C2×#626—34no—
169C2×#626—34no—
170C2×#625—34no—
171C2×#624—34no—
172C2×D3×Dic3—34no—
173C32×C22⋊C4—31no—
174C32×C22⋊C4—31no—
175C32×C22⋊C4—31no—
176C32×C22⋊C4—31no—
177#3757—31no—
178#3757—31no—
179#3757C2×D311yescharacteristic, complemented
180#3752—31no—
181#3752—31no—
182#3752—31no—
183#3752C2×D311yescharacteristic, complemented
184#3752C2×D311yescharacteristic, complemented
185C4⋊(C3⋊Dic3)—31no—
186#3750—31no—
187#3750C2×D311yescharacteristic, complemented
188#3750C2×D311yescharacteristic, complemented
189C4×C3⋊Dic3—31no—
190C3×#217—34no—
191C3×(C2×D3)⋊C4—34no—
192C3×(C2×D3)⋊C4—34no—
193C3×(C2×D3)⋊C4C2×D314yes—
194C3×(C2×D3)⋊C4C2×D314yes—
195C3×(C2×D3)⋊C4C2×D314yescomplemented
196C3×(C2×D3)⋊C4C2×D314yescomplemented
197C3×Dic3⋊C4—34no—
198C3×Dic3⋊C4—34no—
199#3724—34no—
200Dic3⋊Dic3—34no—
201#3722—34no—
202#3722—34no—
203(C2×D3)⋊Dic3—34no—
204(C2×D3)⋊Dic3—34no—
205(C2×D3)⋊Dic3—34no—
206Dic32—34no—
207C22×C33—21no—
208C22×C33—21no—
209C22×C33C2×D412yes—
210C22×C33C2411yescharacteristic
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)C2×D412yes—
217C2×C3×C3⋊D3—21no—
218C2×C3×C3⋊D3—21no—
219C2×C3×C3⋊D3—21no—
220C2×C32×D3—21no—
221C2×C32×D3—21no—
222C2×C32×D3—21no—
223C2×C32×D3—21no—
224C2×C32×D3—21no—
225C2×C32×D3—44no—
226C2×C32×D3#4112yescomplemented
227D3×C3⋊D3—44no—
228C33×C4—21no—
229C33×C4—21no—
230C3⋊(C3⋊Dic3)—21no—
231C3⋊(C3⋊Dic3)C2×D412yes—
232C3×C3⋊Dic3—21no—
233C3×C3⋊Dic3—21no—
234C3×C3⋊Dic3—21no—
235C32×Dic3—21no—
236C32×Dic3—21no—
237C22×#67—94no—
238C2×D3×D4—91no—
239C2×#235—94no—
240C2×#235—91no—
241C2×#235—184no—
242C3×#123—91no—
243C2×C3×C22⋊C4—34no—
244#953—94no—
245#939—91no—
246#930—94no—
247#929—34no—
248C4×#67—94no—
249C2×(C2×D3)⋊C4C3⋊D311yescharacteristic, complemented
250#896—91no—
251#895—91no—
252#894—91no—
253#893—91no—
254#885—94no—
255#885—91no—
256#884—94no—
257#884—94no—
258#884—91no—
259#883—94no—
260#882—94no—
261#882—91no—
262#882—91no—
263#67⋊C4—94no—
264#67⋊C4—91no—
265D3×C22⋊C4—94no—
266D3×C22⋊C4—91no—
267#878—94no—
268C23×C32—24no—
269C23×C32—31no—
270C23×C32—31no—
271C23×C32—62no—
272C23×C32—62no—
273C23×C32—121no—
274C23×C32C22×D314yes—
275C23×C32C22×D311yescharacteristic
276C22×C3⋊D3—31no—
277C22×C3⋊D3—31no—
278C22×C3⋊D3—34no—
279C22×C3⋊D3—34no—
280C22×C3⋊D3—64no—
281C22×C3⋊D3—64no—
282C22×C3⋊D3—62no—
283C22×C3⋊D3—62no—
284C22×C3⋊D3—121no—
285C22×C3⋊D3C22×D311yescharacteristic
286C22×C3×D3—28no—
287C22×C3×D3—28no—
288C22×C3×D3—34no—
289C22×C3×D3—44no—
290C22×C3×D3C22×D314yes—
291C22×C3×D3C22×D314yes—
292C2×D32—68no—
293C2×D32—68no—
294C2×D32—124no—
295C2×C32×C4—216no—
296C2×C32×C4—28no—
297C2×C32×C4—22no—
298C2×C32×C4—24no—
299C2×C32×C4—24no—
300C2×C32×C4—31no—
301C2×C32×C4—31no—
302C2×C32×C4—121no—
303C2×C32×C4C22×D314yes—
304C2×C32×C4C22×D314yes—
305C2×C32×C4C22×D311yescharacteristic
306C2×C32×C4C22×D311yescharacteristic
307#638—22no—
308#638—34no—
309#638—316no—
310#638—616no—
311#638—62no—
312#638—62no—
313#638—62no—
314#638—616no—
315#638—68no—
316#638—62no—
317#638—121no—
318C2×C3⋊Dic3—31no—
319C2×C3⋊Dic3—31no—
320C2×C3⋊Dic3—34no—
321C2×C3⋊Dic3—34no—
322C2×C3⋊Dic3—64no—
323C2×C3⋊Dic3—64no—
324C2×C3⋊Dic3—62no—
325C2×C3⋊Dic3C22×D311yescharacteristic
326C2×C3⋊Dic3C22×D311yescharacteristic
327C2×C3⋊Dic3C22×D311yescharacteristic
328C4⋊(C3⋊D3)—62no—
329C4⋊(C3⋊D3)—68no—
330C4⋊(C3⋊D3)—616no—
331C4⋊(C3⋊D3)—121no—
332C4×C3⋊D3—62no—
333C4×C3⋊D3—68no—
334C4×C3⋊D3—62no—
335C4×C3⋊D3—68no—
336C4×C3⋊D3—616no—
337C4×C3⋊D3—616no—
338C4×C3⋊D3—121no—
339#634—62no—
340#634—68no—
341#634—616no—
342C3×#67—68no—
343C2×C3×Dic3—34no—
344C2×C3×Dic3—34no—
345C2×C3×Dic3—34no—
346C2×C3×Dic3—44no—
347C2×C3×Dic3C22×D314yes—
348C2×C3×Dic3C22×D314yes—
349#626—68no—
350#626—68no—
351#626—124no—
352#626—124no—
353#625—68no—
354#624—124no—
355D3×Dic3—68no—
356#546—271noSylow
357C2×C33—22no—
358C2×C33C22×D411yescharacteristic
359C2×C33C2×#4111yescharacteristic
360C2×C33H(5,𝔽2)11yescharacteristic
361C3⋊(C3⋊D3)—22no—
362C3⋊(C3⋊D3)—41no—
363C3×C3⋊D3—41no—
364C32×D3—22no—
365C32×D3—41no—
366C24×C3—34no—
367C23×D3—94no—
368C23×D3—91no—
369C23×D3C2×C3⋊D311yescharacteristic
370C2×C3×D4—91no—
371C22×C3×C4—24no—
372C22×C3×C4—34no—
373C22×C3×C4D3214yescomplemented
374C22×C3×C4C2×C3⋊D311yescharacteristic, complemented
375C2×#67—34no—
376C2×#67—94no—
377C2×#67—94no—
378C2×#67—94no—
379C2×#67—94no—
380C2×#67—91no—
381C2×#67—94no—
382C2×#67—94no—
383C2×#67—91no—
384C2×#67—91no—
385C2×#67—91no—
386C2×#67—184no—
387C2×#67—184no—
388C2×#67—1816no—
389C22×Dic3—94no—
390C22×Dic3C2×C3⋊D311yescharacteristic, complemented
391D3×D4—184no—
392#235—1816no—
393#235—184no—
394#235—1832no—
395C2×D12—91no—
396C2×D12—91no—
397C2×D12—94no—
398C2×D12—91no—
399C2×D12—94no—
400C2×D12—91no—
401C2×D12—184no—
402C2×C4×D3—91no—
403C2×C4×D3—94no—
404C2×C4×D3—94no—
405C2×C4×D3—91no—
406C2×C4×D3—91no—
407C2×C4×D3—94no—
408C2×C4×D3—91no—
409C2×C4×D3—184no—
410C2×C4×D3—184no—
411C2×Dic6—94no—
412C2×Dic6—91no—
413C2×Dic6—184no—
414C3×C4⋊C4—91no—
415C3×C4⋊C4—91no—
416C3×C22⋊C4—34no—
417C3×C22⋊C4—34no—
418C3×C22⋊C4—34no—
419C3×C22⋊C4—34no—
420C3×C22⋊C4—91no—
421C3×C22⋊C4—91no—
422C3×C22⋊C4—91no—
423#217—34no—
424#217—94no—
425#217—94no—
426#217—91no—
427(C2×D3)⋊C4—34no—
428(C2×D3)⋊C4—34no—
429(C2×D3)⋊C4—94no—
430(C2×D3)⋊C4—94no—
431(C2×D3)⋊C4—94no—
432(C2×D3)⋊C4—91no—
433(C2×D3)⋊C4—91no—
434(C2×D3)⋊C4—91no—
435(C2×D3)⋊C4—91no—
436(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
437(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
438(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
439(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
440C4⋊Dic3—94no—
441Dic3⋊C4—34no—
442Dic3⋊C4—34no—
443Dic3⋊C4—94no—
444Dic3⋊C4—91no—
445Dic3⋊C4—91no—
446C4×Dic3—94no—
447C4×Dic3—91no—
448C22×C32—21no—
449C22×C32—21no—
450C22×C32—24no—
451C22×C32—28no—
452C22×C32—24no—
453C22×C32—24no—
454C22×C32—32no—
455C22×C32—44no—
456C22×C32—44no—
457C22×C32—61no—
458C22×C32—61no—
459C22×C32—61no—
460C22×C32—61no—
461C22×C32—61no—
462C22×C32—124no—
463C22×C32D3×D418yes—
464C22×C32D3×D412yes—
465C22×C32C23×D314yes—
466C22×C32C23×D311yescharacteristic
467C2×C3⋊D3—21no—
468C2×C3⋊D3—21no—
469C2×C3⋊D3—21no—
470C2×C3⋊D3—32no—
471C2×C3⋊D3—38no—
472C2×C3⋊D3—68no—
473C2×C3⋊D3—61no—
474C2×C3⋊D3—61no—
475C2×C3⋊D3—68no—
476C2×C3⋊D3—64no—
477C2×C3⋊D3—61no—
478C2×C3⋊D3—61no—
479C2×C3⋊D3—61no—
480C2×C3⋊D3—64no—
481C2×C3⋊D3—64no—
482C2×C3⋊D3—64no—
483C2×C3⋊D3—64no—
484C2×C3⋊D3—124no—
485C2×C3⋊D3—124no—
486C2×C3⋊D3—124no—
487C2×C3⋊D3—124no—
488C2×C3⋊D3—124no—
489C2×C3×D3—24no—
490C2×C3×D3—24no—
491C2×C3×D3—24no—
492C2×C3×D3—24no—
493C2×C3×D3—24no—
494C2×C3×D3—416no—
495C2×C3×D3—64no—
496C2×C3×D3—64no—
497C2×C3×D3—64no—
498C2×C3×D3#23518yescomplemented
499D32—1216no—
500C32×C4—28no—
501C32×C4—28no—
502C32×C4—24no—
503C32×C4—21no—
504C32×C4—24no—
505C32×C4—21no—
506C32×C4—61no—
507C32×C4—61no—
508C3⋊Dic3—21no—
509C3⋊Dic3—21no—
510C3⋊Dic3—21no—
511C3⋊Dic3—32no—
512C3⋊Dic3—38no—
513C3⋊Dic3—68no—
514C3⋊Dic3—68no—
515C3⋊Dic3—64no—
516C3⋊Dic3—61no—
517C3×Dic3—24no—
518C3×Dic3—24no—
519C3×Dic3—64no—
520C3×Dic3—64no—
521C3×Dic3—64no—
522C2×#41—271no—
523C22×D4—271no—
524#124—271no—
525#123—91no—
526#123—271no—
527C22⋊Q8—271no—
528#121—271no—
529#121—271no—
530#121—271no—
531#120—271no—
532#120—271no—
533C4×D4—271no—
534C4×D4—271no—
535C2×C22⋊C4—31no—
536C2×C22⋊C4—271no—
537C33#54611yescharacteristic, complemented, Sylow
538C23×C3—24no—
539C23×C3—34no—
540C23×C3—34no—
541C23×C3—68no—
542C23×C3—68no—
543C23×C3—91no—
544C23×C3—124no—
545C23×C3C2×D3214yes—
546C23×C3C22×C3⋊D311yescharacteristic
547C22×D3—22no—
548C22×D3—22no—
549C22×D3—34no—
550C22×D3—41no—
551C22×D3—94no—
552C22×D3—91no—
553C22×D3—94no—
554C22×D3—91no—
555C22×D3—184no—
556C22×D3—184no—
557C22×D3—182no—
558C22×D3—188no—
559C22×D3—188no—
560C22×D3—182no—
561C22×D3—361no—
562C22×D3—364no—
563C22×D3C22×C3⋊D311yescharacteristic
564C22×D3C22×C3⋊D311yescharacteristic
565C3×D4—182no—
566C2×C3×C4—216no—
567C2×C3×C4—28no—
568C2×C3×C4—22no—
569C2×C3×C4—24no—
570C2×C3×C4—24no—
571C2×C3×C4—34no—
572C2×C3×C4—34no—
573C2×C3×C4—91no—
574C2×C3×C4—91no—
575C2×C3×C4—91no—
576C2×C3×C4—124no—
577C2×C3×C4C2×D3214yes—
578C2×C3×C4C2×D3214yes—
579C2×C3×C4C22×C3⋊D311yescharacteristic
580C2×C3×C4C22×C3⋊D311yescharacteristic
581#67—68no—
582#67—916no—
583#67—94no—
584#67—1816no—
585#67—188no—
586#67—188no—
587#67—182no—
588#67—188no—
589#67—1816no—
590#67—188no—
591#67—182no—
592#67—361no—
593#67—364no—
594C2×Dic3—34no—
595C2×Dic3—34no—
596C2×Dic3—34no—
597C2×Dic3—41no—
598C2×Dic3—94no—
599C2×Dic3—91no—
600C2×Dic3—94no—
601C2×Dic3—91no—
602C2×Dic3—184no—
603C2×Dic3—184no—
604C2×Dic3—188no—
605C2×Dic3C22×C3⋊D311yescharacteristic
606C2×Dic3C22×C3⋊D311yescharacteristic
607D12—188no—
608D12—182no—
609D12—1816no—
610D12—182no—
611D12—182no—
612D12—364no—
613D12—361no—
614C4×D3—188no—
615C4×D3—182no—
616C4×D3—182no—
617C4×D3—188no—
618C4×D3—182no—
619C4×D3—1816no—
620C4×D3—1816no—
621C4×D3—361no—
622C4×D3—364no—
623Dic6—188no—
624Dic6—182no—
625Dic6—1816no—
626C2×C32—22no—
627C2×C32—24no—
628C2×C32—24no—
629C2×C32—24no—
630C2×C32—28no—
631C2×C32—48no—
632C2×C32—62no—
633C2×C32—121no—
634C2×C32C2×#23514yes—
635C2×C32C2×D3×D414yes—
636C2×C32C2×D3×D411yescharacteristic
637C2×C32#100414yes—
638C2×C32D3×#4111yescharacteristic
639C2×C32#100911yescharacteristic
640C3⋊D3—41no—
641C3⋊D3—62no—
642C3⋊D3—68no—
643C3⋊D3—128no—
644C3⋊D3—128no—
645C3⋊D3—121no—
646C3⋊D3—124no—
647C3×D3—28no—
648C3×D3—44no—
649C3×D3—124no—
650C24—31no—
651C24—271no—
652#41—544no—
653C2×Q8—271no—
654C2×D4—91no—
655C2×D4—271no—
656C2×D4—271no—
657C2×D4—271no—
658C2×D4—271no—
659C2×D4—271no—
660C2×D4—271no—
661C2×D4—271no—
662C2×D4—271no—
663C2×D4—544no—
664C22×C4—31no—
665C22×C4—271no—
666C22×C4—271no—
667C22×C4—271no—
668C22×C4—271no—
669C22×C4D3×C3⋊D311yescharacteristic, complemented
670C4⋊C4—91no—
671C4⋊C4—91no—
672C4⋊C4—271no—
673C4⋊C4—271no—
674C22⋊C4—31no—
675C22⋊C4—31no—
676C22⋊C4—31no—
677C22⋊C4—31no—
678C22⋊C4—91no—
679C22⋊C4—91no—
680C22⋊C4—91no—
681C22⋊C4—271no—
682C22⋊C4—271no—
683C22⋊C4—271no—
684C22⋊C4—271no—
685C22⋊C4—271no—
686C42—271no—
687C22×C3—24no—
688C22×C3—24no—
689C22×C3—21no—
690C22×C3—21no—
691C22×C3—24no—
692C22×C3—28no—
693C22×C3—38no—
694C22×C3—44no—
695C22×C3—44no—
696C22×C3—64no—
697C22×C3—64no—
698C22×C3—64no—
699C22×C3—64no—
700C22×C3—64no—
701C22×C3—1216no—
702C22×C3—181no—
703C22×C3—181no—
704C22×C3—181no—
705C22×C3#381118yes—
706C22×C3D4×C3⋊D312yes—
707C22×C3C22×D3214yes—
708C22×C3C23×C3⋊D311yescharacteristic
709C2×D3—21no—
710C2×D3—21no—
711C2×D3—21no—
712C2×D3—21no—
713C2×D3—21no—
714C2×D3—44no—
715C2×D3—64no—
716C2×D3—64no—
717C2×D3—64no—
718C2×D3—98no—
719C2×D3—92no—
720C2×D3—188no—
721C2×D3—184no—
722C2×D3—184no—
723C2×D3—181no—
724C2×D3—181no—
725C2×D3—188no—
726C2×D3—184no—
727C2×D3—184no—
728C2×D3—184no—
729C2×D3—181no—
730C2×D3—181no—
731C2×D3—181no—
732C2×D3—364no—
733C2×D3—364no—
734C2×D3—364no—
735C2×D3—364no—
736C2×D3—364no—
737C2×D3—3616no—
738C2×D3#382812yescomplemented
739C3×C4—28no—
740C3×C4—28no—
741C3×C4—24no—
742C3×C4—24no—
743C3×C4—21no—
744C3×C4—21no—
745C3×C4—64no—
746C3×C4—64no—
747C3×C4—181no—
748C3×C4—181no—
749C3×C4—181no—
750Dic3—21no—
751Dic3—21no—
752Dic3—64no—
753Dic3—64no—
754Dic3—64no—
755Dic3—98no—
756Dic3—92no—
757Dic3—188no—
758Dic3—188no—
759Dic3—184no—
760Dic3—181no—
761C32—24no—
762C32#549014yescomplemented
763C32#565411yescharacteristic, complemented
764C23—31no—
765C23—31no—
766C23—62no—
767C23—62no—
768C23—91no—
769C23—121no—
770C23—271no—
771C23—271no—
772C23—542no—
773C23—542no—
774C23—1081no—
775C23C2×D3×C3⋊D311yescharacteristic
776Q8—542no—
777D4—182no—
778D4—274no—
779D4—542no—
780D4—542no—
781D4—542no—
782D4—542no—
783D4—542no—
784D4—1081no—
785D4—1081no—
786C2×C4—22no—
787C2×C4—31no—
788C2×C4—31no—
789C2×C4—91no—
790C2×C4—91no—
791C2×C4—91no—
792C2×C4—121no—
793C2×C4—271no—
794C2×C4—271no—
795C2×C4—542no—
796C2×C4—542no—
797C2×C4—542no—
798C2×C4—1081no—
799C2×C4C2×D3×C3⋊D311yescharacteristic
800C2×C4C2×D3×C3⋊D311yescharacteristic
801C2×C3—28no—
802C2×C3—22no—
803C2×C3—24no—
804C2×C3—24no—
805C2×C3—24no—
806C2×C3—48no—
807C2×C3—68no—
808C2×C3—124no—
809C2×C3—361no—
810C2×C3D3×#23514yes—
811C2×C3#6430714yes—
812C2×C3C2×#381114yes—
813C2×C3C2×#382811yescharacteristic
814C2×C3C2×D4×C3⋊D311yescharacteristic
815C2×C3#6436111yescharacteristic
816D3—22no—
817D3—41no—
818D3—124no—
819D3—188no—
820D3—182no—
821D3—368no—
822D3—368no—
823D3—364no—
824D3—361no—
825C22—21no—
826C22—21no—
827C22—32no—
828C22—61no—
829C22—61no—
830C22—61no—
831C22—61no—
832C22—61no—
833C22—124no—
834C22—181no—
835C22—181no—
836C22—181no—
837C22—272no—
838C22—541no—
839C22—541no—
840C22—541no—
841C22—541no—
842C22—541no—
843C22—1084no—
844C22#8903912yes—
845C22C22×D3×C3⋊D311yescharacteristic
846C4—21no—
847C4—21no—
848C4—61no—
849C4—61no—
850C4—181no—
851C4—181no—
852C4—181no—
853C4—272no—
854C4—541no—
855C3—24no—
856C3#1059507714yescomplemented
857C3#1059596111yescharacteristic, complemented
858C2—22no—
859C2—62no—
860C2—121no—
861C2—361no—
862C2—542no—
863C2—1081no—
864C2D3×#382811yescharacteristic
865C2#1172457911yescharacteristic
866C2C2×#8903911yescharacteristic
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×#89076C2semidirect
2. C2×D3×#638C2semidirect
3. C3×#64138C2semidirect
4. C2×C32×(C2×D3)⋊C4C2semidirect
5. #11723632C2semidirect
6. #11723630C2semidirect
7. #11723618C2semidirect
8. #11723542C2semidirect
9. #11723539C2semidirect
10. #11723528C2semidirect
11. #11723527C2semidirect
12. #11723525C2semidirect
13. #11723496C2semidirect
14. #11723462C2semidirect
15. #11723420C2semidirect
20. C22×C33×C4C22semidirect
22. C2×#6312C22semidirect
24. C2×C4⋊(C3⋊(C3⋊D3))C22semidirect
25. C2×C4×C3⋊(C3⋊D3)C22semidirect
26. C2×C4×C3⋊(C3⋊D3)C22semidirect
27. C2×#6308C22semidirect
29. C22×C32×Dic3C22semidirect
31. C2×#6292C22semidirect
34. C2×#6291C22semidirect
36. C2×#6289C22semidirect
38. C3×#3757C22semidirect
39. C3×#3752C22semidirect
40. C3×#3752C22semidirect
41. C3×#3750C22semidirect
42. C3×#3750C22semidirect
45. C32×(C2×D3)⋊C4C22semidirect
46. C32×(C2×D3)⋊C4C22semidirect
47. #88806C22semidirect
48. Dic3⋊(C3⋊Dic3)C22semidirect
49. #88804C22semidirect
50. #88804C22semidirect
51. #88803C22semidirect
53. (C2×D3)⋊(C3⋊Dic3)C22semidirect
54. Dic3×C3⋊Dic3C22semidirect
63. #64138D3semidirect
74. C2×C3×(C2×D3)⋊C4D3semidirect
102. #6312D4semidirect
131. C22×C32×C4C2×D3semidirect
132. C22×C32×C4C2×D3semidirect
164. C22×C3×Dic3C2×D3semidirect
179. #3757C2×D3semidirect
183. #3752C2×D3semidirect
184. #3752C2×D3semidirect
187. #3750C2×D3semidirect
188. #3750C2×D3semidirect
195. C3×(C2×D3)⋊C4C2×D3semidirect
196. C3×(C2×D3)⋊C4C2×D3semidirect
226. C2×C32×D3#41semidirect
249. C2×(C2×D3)⋊C4C3⋊D3semidirect
373. C22×C3×C4D32semidirect
374. C22×C3×C4C2×C3⋊D3semidirect
390. C22×Dic3C2×C3⋊D3semidirect
438. (C2×D3)⋊C4C2×C3⋊D3semidirect
439. (C2×D3)⋊C4C2×C3⋊D3semidirect
498. C2×C3×D3#235semidirect
537. C33#546semidirect
669. C22×C4D3×C3⋊D3semidirect
738. C2×D3#3828semidirect
762. C32#5490semidirect
763. C32#5654semidirect
856. C3#10595077semidirect
857. C3#10595961semidirect

Maximal subgroups

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

subgroupindex
C2×#890762
C2×D3×#6382
C3×#641382
C2×C32×(C2×D3)⋊C42
#117236322
#117236302
#117236182
#117235422
#117235392
#117235282
#117235272
#117235252
#117234962
#117234622
#117234202
#105959613
#105950773