Finite Group Databasebeta

← #13176600

Subgroups — #13176600

Order 1728.

1876 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723934C211yesmaximal, characteristic, complemented
2C3×#64107C211yesmaximal, characteristic, complemented
3C32×#894C211yesmaximal, characteristic, complemented
4#11723542C211yesmaximal, characteristic, complemented
5#11723540C211yesmaximal, characteristic, complemented
6#11723539C211yesmaximal, characteristic, complemented
7#11723531C211yesmaximal, characteristic, complemented
8#11723530C211yesmaximal, characteristic, complemented
9#11723525C211yesmaximal, characteristic, complemented
10#11723514C211yesmaximal, characteristic, complemented
11C4×#6291C211yesmaximal, characteristic, complemented
12#11723485C211yesmaximal, characteristic, complemented
13#11723432C211yesmaximal, characteristic, complemented
14#11723421C211yesmaximal, characteristic, complemented
15#11723419C211yesmaximal, characteristic, complemented
16#10596128—31nomaximal
17#10594657—34nomaximal
18C22×D3×C3⋊D3C2211yescharacteristic
19C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic
20C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
21C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
22C2×C32×D12C2211yescharacteristic
23C2×C32×C4×D3C2211yescharacteristic, complemented
24C2×#6293C2211yescharacteristic, complemented
25C2×#6292C2211yescharacteristic
26C2×#6291C2211yescharacteristic
27C2×#6291C2211yescharacteristic
28C2×#6291C2211yescharacteristic, complemented
29C2×#6290C2211yescharacteristic
30C2×#6289C2211yescharacteristic
31C33×C4⋊C4C2211yescharacteristic, complemented
32#88859C2211yescharacteristic
33#88859C2211yescharacteristic, complemented
34C4×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
35C3×#3752C2211yescharacteristic
36C3×#3752C2211yescharacteristic
37C3×#3752C2211yescharacteristic
38C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
39C3×#3750C2211yescharacteristic, complemented
40C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
41C32×(C2×D3)⋊C4C2211yescharacteristic
42C32×(C2×D3)⋊C4C2211yescharacteristic
43C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
44C32×Dic3⋊C4C2211yescharacteristic, complemented
45#88807C2211yescharacteristic, complemented
46Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
47#88804C2211yescharacteristic
48#88804C2211yescharacteristic, complemented
49#88803C2211yescharacteristic
50(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
51(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
52(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
53C32×#123—31no—
54#64147—31no—
55#64146—31no—
56#64139—31no—
57C4×#638—31no—
58#64107D311yescharacteristic, complemented
59#64106—31no—
60#64103—31no—
61#64102—31no—
62#64102—34no—
63#64102—64no—
64#64094—31no—
65#64094—31no—
66#64093—31no—
67#64091—31no—
68C22⋊C4×C3⋊D3—31no—
69#64088—31no—
70C3×#898—34no—
71C3×#894D314yescomplemented
72#63923—34no—
73#63922—34no—
74#63921—34no—
75#63916—34no—
76#63915—34no—
77#63910—34no—
78#63906—34no—
79C4×#626—34no—
80#63895—34no—
81#63862—34no—
82#63853—34no—
83#63852—34no—
84C22×C3⋊(C3⋊D3)C2311yescharacteristic
85C22×C3⋊(C3⋊D3)C2311yescharacteristic
86C22×C3×C3⋊D3C2311yescharacteristic
87C22×C32×D3C2311yescharacteristic
88C22×C32×D3C2311yescharacteristic
89C2×D3×C3⋊D3—22no—
90C2×D3×C3⋊D3—41no—
91C2×D3×C3⋊D3—41no—
92C2×C33×C4C2311yescharacteristic
93C2×C33×C4C2311yescharacteristic
94C2×C33×C4C2311yescharacteristic
95C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
96C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
97C4⋊(C3⋊(C3⋊D3))—22no—
98C4×C3⋊(C3⋊D3)—41no—
99C4×C3⋊(C3⋊D3)—41no—
100C2×C3×C3⋊Dic3C2311yescharacteristic
101C2×C3×C3⋊Dic3C2311yescharacteristic
102C2×C3×C3⋊Dic3C2311yescharacteristic
103C2×C32×Dic3C2311yescharacteristic
104C2×C32×Dic3C2311yescharacteristic
105C32×D12—41no—
106C32×C4×D3—41no—
107#6293—41no—
108#6292—41no—
109#6291—22no—
110#6291—41no—
111#6291—41no—
112#6290—41no—
113#6289—41no—
114#5704—91no—
115#5657—94no—
116C23×C3⋊D3—31no—
117C22×D32—34no—
118C2×C32×D4—31no—
119C22×C32×C4—31no—
120C2×#638—31no—
121C2×#638—31no—
122C2×#638—31no—
123C2×#638—31no—
124C2×C4⋊(C3⋊D3)—31no—
125C2×C4⋊(C3⋊D3)—34no—
126C2×C4⋊(C3⋊D3)—31no—
127C2×C4⋊(C3⋊D3)—64no—
128C2×C4×C3⋊D3—31no—
129C2×C4×C3⋊D3—31no—
130C2×C4×C3⋊D3—34no—
131C2×C4×C3⋊D3—34no—
132C2×C4×C3⋊D3—31no—
133C2×C4×C3⋊D3—64no—
134C2×C4×C3⋊D3—64no—
135C2×#634—31no—
136C2×C3×D12C2×D314yes—
137C2×C3×C4×D3C2×D314yescomplemented
138C2×#627—34no—
139C2×#626—34no—
140C2×#626—34no—
141C2×#626—34no—
142C2×#626—34no—
143C2×#625—34no—
144C2×#624—34no—
145C32×C4⋊C4—24no—
146C32×C4⋊C4—31no—
147C32×C4⋊C4C2×D314yescomplemented
148C32×C4⋊C4C2×D311yescharacteristic, complemented
149C32×C22⋊C4—31no—
150C32×C22⋊C4—31no—
151C32×C22⋊C4—31no—
152#3757—31no—
153#3757—31no—
154#3757—31no—
155#3752—31no—
156#3752—31no—
157#3752—31no—
158#3752—34no—
159#3752—34no—
160#3752—31no—
161#3752—31no—
162#3752—64no—
163#3752—64no—
164#3752C2×D311yescharacteristic
165#3752C2×D311yescharacteristic
166#3752C2×D311yescharacteristic
167C4⋊(C3⋊Dic3)—31no—
168C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
169#3750—31no—
170#3750C2×D311yescharacteristic, complemented
171C4×C3⋊Dic3—31no—
172C4×C3⋊Dic3—34no—
173C4×C3⋊Dic3—64no—
174C4×C3⋊Dic3C2×D311yescharacteristic, complemented
175C3×(C2×D3)⋊C4—34no—
176C3×(C2×D3)⋊C4—34no—
177C3×(C2×D3)⋊C4—34no—
178C3×(C2×D3)⋊C4C2×D314yes—
179C3×(C2×D3)⋊C4C2×D314yes—
180C3×(C2×D3)⋊C4C2×D314yescomplemented
181C3×C4⋊Dic3—34no—
182C3×Dic3⋊C4—34no—
183C3×Dic3⋊C4C2×D314yescomplemented
184C3×C4×Dic3—34no—
185Dic3⋊Dic3—34no—
186Dic3⋊Dic3—34no—
187#3722—34no—
188#3722—34no—
189(C2×D3)⋊Dic3—34no—
190(C2×D3)⋊Dic3—34no—
191(C2×D3)⋊Dic3—34no—
192(C2×D3)⋊Dic3—34no—
193C22×C33C2411yescharacteristic
194C2×C3⋊(C3⋊D3)—21no—
195C2×C3⋊(C3⋊D3)—21no—
196C2×C3⋊(C3⋊D3)—21no—
197C2×C3⋊(C3⋊D3)—21no—
198C2×C3⋊(C3⋊D3)—21no—
199C2×C3⋊(C3⋊D3)#4112yes—
200C2×C3×C3⋊D3—21no—
201C2×C3×C3⋊D3—21no—
202C2×C3×C3⋊D3—21no—
203C2×C32×D3—21no—
204C2×C32×D3—21no—
205C2×C32×D3—21no—
206C2×C32×D3—21no—
207C2×C32×D3—21no—
208C2×C32×D3—21no—
209D3×C3⋊D3—44no—
210C33×C4—21no—
211C33×C4—21no—
212C33×C4—21no—
213C3⋊(C3⋊Dic3)—21no—
214C3⋊(C3⋊Dic3)—21no—
215C3×C3⋊Dic3—21no—
216C3×C3⋊Dic3—21no—
217C3×C3⋊Dic3—21no—
218C32×Dic3—21no—
219C32×Dic3—21no—
220C3×#126—91no—
221C3×#123—34no—
222#938—94no—
223#937—94no—
224#930—94no—
225C4×#67—94no—
226#898—34no—
227#898—91no—
228#897—94no—
229#896—91no—
230#895—91no—
231#895—91no—
232#894—94no—
233#894C3⋊D311yescharacteristic, complemented
234#893—94no—
235#893—91no—
236#893—184no—
237#885—94no—
238#885—94no—
239#885—91no—
240#884—94no—
241#884—91no—
242#883—91no—
243#882—94no—
244#882—91no—
245#882—91no—
246D3×C22⋊C4—94no—
247D3×C22⋊C4—91no—
248#879—94no—
249#875—91no—
250C4×D12—91no—
251C23×C32—31no—
252C23×C32—31no—
253C22×C3⋊D3—31no—
254C22×C3⋊D3—31no—
255C22×C3⋊D3—34no—
256C22×C3⋊D3—34no—
257C22×C3⋊D3—64no—
258C22×C3⋊D3—64no—
259C22×C3⋊D3—62no—
260C22×C3⋊D3—121no—
261C22×C3⋊D3—121no—
262C22×C3⋊D3C22×D311yescharacteristic
263C22×C3×D3—34no—
264C22×C3×D3C22×D314yes—
265C22×C3×D3C22×D314yes—
266C2×D32—68no—
267C2×D32—124no—
268C2×D32—124no—
269C32×D4—121no—
270C2×C32×C4—24no—
271C2×C32×C4—24no—
272C2×C32×C4—24no—
273C2×C32×C4—31no—
274C2×C32×C4—31no—
275C2×C32×C4—121no—
276C2×C32×C4C22×D314yes—
277C2×C32×C4C22×D314yes—
278C2×C32×C4C22×D314yes—
279C2×C32×C4C22×D311yescharacteristic
280C2×C32×C4C22×D311yescharacteristic
281C2×C32×C4C22×D311yescharacteristic
282#638—62no—
283#638—121no—
284#638—121no—
285#638—121no—
286C2×C3⋊Dic3—31no—
287C2×C3⋊Dic3—31no—
288C2×C3⋊Dic3—34no—
289C2×C3⋊Dic3—34no—
290C2×C3⋊Dic3—64no—
291C2×C3⋊Dic3—64no—
292C2×C3⋊Dic3C22×D311yescharacteristic
293C2×C3⋊Dic3C22×D311yescharacteristic
294C2×C3⋊Dic3C22×D311yescharacteristic
295C4⋊(C3⋊D3)—62no—
296C4⋊(C3⋊D3)—68no—
297C4⋊(C3⋊D3)—616no—
298C4⋊(C3⋊D3)—121no—
299C4×C3⋊D3—121no—
300C4×C3⋊D3—121no—
301C4×C3⋊D3—121no—
302C4×C3⋊D3—124no—
303C4×C3⋊D3—124no—
304C4×C3⋊D3—128no—
305C4×C3⋊D3—128no—
306#634—121no—
307C2×C3×Dic3—34no—
308C2×C3×Dic3—34no—
309C2×C3×Dic3—34no—
310C2×C3×Dic3C22×D314yes—
311C2×C3×Dic3C22×D314yes—
312C3×D12—44no—
313C3×C4×D3—44no—
314#627—124no—
315#626—68no—
316#626—124no—
317#626—124no—
318#626—124no—
319#625—124no—
320#624—124no—
321#538—271noSylow
322C2×C33C2×#4111yescharacteristic
323C2×C33H(5,𝔽2)11yescharacteristic
324C2×C33H(5,𝔽2)11yescharacteristic
325C3⋊(C3⋊D3)—22no—
326C3⋊(C3⋊D3)—41no—
327C3×C3⋊D3—41no—
328C32×D3—41no—
329C32×D3—41no—
330C23×D3—94no—
331C23×D3—91no—
332C2×C3×D4—34no—
333C22×C3×C4—34no—
334C2×#67—94no—
335C2×#67—94no—
336C2×#67—94no—
337C2×#67—94no—
338C2×#67—91no—
339C2×#67—91no—
340C2×D12—91no—
341C2×D12—94no—
342C2×D12—91no—
343C2×D12—94no—
344C2×D12—91no—
345C2×D12—91no—
346C2×D12—184no—
347C2×D12C2×C3⋊D311yescharacteristic
348C2×C4×D3—94no—
349C2×C4×D3—94no—
350C2×C4×D3—94no—
351C2×C4×D3—91no—
352C2×C4×D3—91no—
353C2×C4×D3—91no—
354C2×C4×D3—184no—
355C2×C4×D3—184no—
356C2×C4×D3C2×C3⋊D311yescharacteristic, complemented
357C2×Dic6—94no—
358C2×Dic6—91no—
359C3×C4⋊C4—24no—
360C3×C4⋊C4—34no—
361C3×C4⋊C4—91no—
362C3×C4⋊C4—91no—
363C3×C4⋊C4D3214yescomplemented
364C3×C4⋊C4C2×C3⋊D311yescharacteristic, complemented
365C3×C22⋊C4—34no—
366C3×C22⋊C4—34no—
367C3×C22⋊C4—34no—
368C3×C22⋊C4—91no—
369C3×C22⋊C4—91no—
370C3×C22⋊C4—91no—
371C3×C42—91no—
372#217—94no—
373#217—94no—
374#217—94no—
375#217—91no—
376(C2×D3)⋊C4—34no—
377(C2×D3)⋊C4—34no—
378(C2×D3)⋊C4—34no—
379(C2×D3)⋊C4—94no—
380(C2×D3)⋊C4—94no—
381(C2×D3)⋊C4—94no—
382(C2×D3)⋊C4—91no—
383(C2×D3)⋊C4—91no—
384(C2×D3)⋊C4—91no—
385(C2×D3)⋊C4—94no—
386(C2×D3)⋊C4—94no—
387(C2×D3)⋊C4—91no—
388(C2×D3)⋊C4—91no—
389(C2×D3)⋊C4—91no—
390(C2×D3)⋊C4—91no—
391(C2×D3)⋊C4—184no—
392(C2×D3)⋊C4—184no—
393(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
394(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
395(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
396C4⋊Dic3—34no—
397C4⋊Dic3—94no—
398C4⋊Dic3—91no—
399Dic3⋊C4—34no—
400Dic3⋊C4—94no—
401Dic3⋊C4—91no—
402Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
403C4×Dic3—34no—
404C4×Dic3—94no—
405C4×Dic3—91no—
406C4×Dic3—184no—
407C22×C32—24no—
408C22×C32—61no—
409C22×C32—61no—
410C22×C32—61no—
411C22×C32—61no—
412C22×C32—61no—
413C22×C32—61no—
414C22×C32C23×D314yes—
415C22×C32C23×D311yescharacteristic
416C2×C3⋊D3—21no—
417C2×C3⋊D3—21no—
418C2×C3⋊D3—21no—
419C2×C3⋊D3—32no—
420C2×C3⋊D3—38no—
421C2×C3⋊D3—68no—
422C2×C3⋊D3—61no—
423C2×C3⋊D3—61no—
424C2×C3⋊D3—68no—
425C2×C3⋊D3—64no—
426C2×C3⋊D3—61no—
427C2×C3⋊D3—61no—
428C2×C3⋊D3—61no—
429C2×C3⋊D3—64no—
430C2×C3⋊D3—64no—
431C2×C3⋊D3—64no—
432C2×C3⋊D3—64no—
433C2×C3⋊D3—124no—
434C2×C3⋊D3—124no—
435C2×C3⋊D3—124no—
436C2×C3⋊D3—124no—
437C2×C3⋊D3—124no—
438C2×C3×D3—24no—
439C2×C3×D3—24no—
440C2×C3×D3—24no—
441C2×C3×D3—24no—
442C2×C3×D3—24no—
443C2×C3×D3—24no—
444C2×C3×D3—64no—
445C2×C3×D3—64no—
446C2×C3×D3—64no—
447D32—1216no—
448C32×C4—28no—
449C32×C4—24no—
450C32×C4—21no—
451C32×C4—21no—
452C32×C4—21no—
453C32×C4—24no—
454C32×C4—24no—
455C32×C4—44no—
456C32×C4—44no—
457C32×C4—61no—
458C32×C4—61no—
459C3⋊Dic3—21no—
460C3⋊Dic3—21no—
461C3⋊Dic3—21no—
462C3⋊Dic3—68no—
463C3⋊Dic3—64no—
464C3⋊Dic3—61no—
465C3⋊Dic3—61no—
466C3⋊Dic3—64no—
467C3⋊Dic3—124no—
468C3×Dic3—24no—
469C3×Dic3—24no—
470C3×Dic3—64no—
471C3×Dic3—64no—
472C3×Dic3—64no—
473#126—91no—
474#126—271no—
475#124—271no—
476#124—271no—
477#123—31no—
478#123—271no—
479C22⋊Q8—271no—
480#121—271no—
481#121—271no—
482#121—271no—
483#120—271no—
484#120—271no—
485C4×D4—271no—
486C4×D4—271no—
487C2×C22⋊C4—271no—
488C33#53811yescharacteristic, complemented, Sylow
489C23×C3—34no—
490C23×C3—34no—
491C23×C3—91no—
492C22×D3—34no—
493C22×D3—94no—
494C22×D3—91no—
495C22×D3—94no—
496C22×D3—91no—
497C22×D3—184no—
498C22×D3—184no—
499C22×D3—182no—
500C22×D3—188no—
501C22×D3—361no—
502C22×D3—361no—
503C22×D3—364no—
504C22×D3—364no—
505C22×D3C22×C3⋊D311yescharacteristic
506C22×D3C22×C3⋊D311yescharacteristic
507C3×D4—124no—
508C2×C3×C4—24no—
509C2×C3×C4—24no—
510C2×C3×C4—24no—
511C2×C3×C4—34no—
512C2×C3×C4—34no—
513C2×C3×C4—91no—
514C2×C3×C4—91no—
515C2×C3×C4—91no—
516C2×C3×C4—124no—
517C2×C3×C4C2×D3214yes—
518C2×C3×C4C2×D3214yes—
519C2×C3×C4C2×D3214yes—
520C2×C3×C4C22×C3⋊D311yescharacteristic
521C2×C3×C4C22×C3⋊D311yescharacteristic
522C2×C3×C4C22×C3⋊D311yescharacteristic
523#67—188no—
524#67—361no—
525#67—364no—
526#67—364no—
527#67—361no—
528#67—364no—
529C2×Dic3—34no—
530C2×Dic3—34no—
531C2×Dic3—34no—
532C2×Dic3—94no—
533C2×Dic3—94no—
534C2×Dic3—91no—
535C2×Dic3—91no—
536C2×Dic3—184no—
537C2×Dic3—184no—
538C2×Dic3C22×C3⋊D311yescharacteristic
539C2×Dic3C22×C3⋊D311yescharacteristic
540D12—41no—
541D12—188no—
542D12—182no—
543D12—1816no—
544D12—182no—
545D12—364no—
546D12—361no—
547D12—361no—
548C4×D3—41no—
549C4×D3—361no—
550C4×D3—364no—
551C4×D3—364no—
552C4×D3—364no—
553C4×D3—361no—
554C4×D3—361no—
555C4×D3—368no—
556C4×D3—368no—
557Dic6—361no—
558Dic6—364no—
559C2×C32—24no—
560C2×C32—24no—
561C2×C32—24no—
562C2×C32—121no—
563C2×C32—121no—
564C2×C32#100414yes—
565C2×C32D3×#4114yes—
566C2×C32D3×#4111yescharacteristic
567C2×C32#100914yes—
568C2×C32#100911yescharacteristic
569C2×C32#100911yescharacteristic
570C3⋊D3—41no—
571C3⋊D3—62no—
572C3⋊D3—68no—
573C3⋊D3—128no—
574C3⋊D3—128no—
575C3⋊D3—124no—
576C3⋊D3—121no—
577C3×D3—44no—
578C3×D3—44no—
579C3×D3—124no—
580C24—271no—
581C2×Q8—271no—
582C2×D4—31no—
583C2×D4—271no—
584C2×D4—271no—
585C2×D4—271no—
586C2×D4—271no—
587C2×D4—271no—
588C2×D4—271no—
589C22×C4—31no—
590C22×C4—271no—
591C22×C4—271no—
592C22×C4—271no—
593C4⋊C4—31no—
594C4⋊C4—91no—
595C4⋊C4—91no—
596C4⋊C4—271no—
597C4⋊C4—271no—
598C4⋊C4D3×C3⋊D311yescharacteristic, complemented
599C22⋊C4—31no—
600C22⋊C4—31no—
601C22⋊C4—31no—
602C22⋊C4—91no—
603C22⋊C4—91no—
604C22⋊C4—91no—
605C22⋊C4—271no—
606C22⋊C4—271no—
607C22⋊C4—271no—
608C22⋊C4—271no—
609C22⋊C4—271no—
610C22⋊C4—271no—
611C22⋊C4—271no—
612C22⋊C4—271no—
613C42—91no—
614C42—271no—
615C22×C3—24no—
616C22×C3—64no—
617C22×C3—64no—
618C22×C3—64no—
619C22×C3—64no—
620C22×C3—64no—
621C22×C3—64no—
622C22×C3—181no—
623C22×C3—181no—
624C22×C3—181no—
625C22×C3C22×D3214yes—
626C22×C3C23×C3⋊D311yescharacteristic
627C2×D3—21no—
628C2×D3—21no—
629C2×D3—21no—
630C2×D3—21no—
631C2×D3—21no—
632C2×D3—21no—
633C2×D3—64no—
634C2×D3—64no—
635C2×D3—64no—
636C2×D3—98no—
637C2×D3—92no—
638C2×D3—188no—
639C2×D3—184no—
640C2×D3—184no—
641C2×D3—181no—
642C2×D3—181no—
643C2×D3—188no—
644C2×D3—184no—
645C2×D3—184no—
646C2×D3—184no—
647C2×D3—181no—
648C2×D3—181no—
649C2×D3—181no—
650C2×D3—364no—
651C2×D3—364no—
652C2×D3—364no—
653C2×D3—364no—
654C2×D3—364no—
655C2×D3—3616no—
656C3×C4—28no—
657C3×C4—24no—
658C3×C4—24no—
659C3×C4—24no—
660C3×C4—21no—
661C3×C4—21no—
662C3×C4—21no—
663C3×C4—44no—
664C3×C4—44no—
665C3×C4—64no—
666C3×C4—64no—
667C3×C4—181no—
668C3×C4—181no—
669C3×C4—181no—
670Dic3—21no—
671Dic3—21no—
672Dic3—64no—
673Dic3—64no—
674Dic3—64no—
675Dic3—188no—
676Dic3—184no—
677Dic3—184no—
678Dic3—181no—
679Dic3—181no—
680Dic3—364no—
681C32—24no—
682C32#565714yescomplemented
683C32#570411yescharacteristic, complemented
684C23—31no—
685C23—31no—
686C23—91no—
687C23—271no—
688C23—271no—
689C23—542no—
690C23—1081no—
691C23—1081no—
692Q8—1081no—
693D4—121no—
694D4—542no—
695D4—542no—
696D4—1081no—
697D4—1081no—
698D4—1081no—
699D4—1081no—
700C2×C4—31no—
701C2×C4—31no—
702C2×C4—91no—
703C2×C4—91no—
704C2×C4—91no—
705C2×C4—121no—
706C2×C4—271no—
707C2×C4—271no—
708C2×C4—1081no—
709C2×C4—1081no—
710C2×C4—1081no—
711C2×C4C2×D3×C3⋊D311yescharacteristic
712C2×C4C2×D3×C3⋊D311yescharacteristic
713C2×C4C2×D3×C3⋊D311yescharacteristic
714C2×C3—24no—
715C2×C3—24no—
716C2×C3—24no—
717C2×C3—124no—
718C2×C3—124no—
719C2×C3—361no—
720C2×C3#6430614yes—
721C2×C3#6431414yes—
722C2×C3#6432014yes—
723C2×C3#6436111yescharacteristic
724C2×C3#41×C3⋊D311yescharacteristic
725C2×C3#6436611yescharacteristic
726D3—41no—
727D3—41no—
728D3—124no—
729D3—182no—
730D3—188no—
731D3—368no—
732D3—368no—
733D3—361no—
734D3—364no—
735C22—61no—
736C22—61no—
737C22—61no—
738C22—61no—
739C22—61no—
740C22—61no—
741C22—181no—
742C22—181no—
743C22—181no—
744C22—272no—
745C22—541no—
746C22—541no—
747C22—541no—
748C22—541no—
749C22—541no—
750C22—1084no—
751C22C22×D3×C3⋊D311yescharacteristic
752C4—21no—
753C4—21no—
754C4—21no—
755C4—61no—
756C4—61no—
757C4—181no—
758C4—181no—
759C4—181no—
760C4—541no—
761C4—541no—
762C3—24no—
763C3#1059465714yescomplemented
764C3#1059612811yescharacteristic, complemented
765C2—121no—
766C2—121no—
767C2—361no—
768C2—542no—
769C2—1081no—
770C2#1172457811yescharacteristic
771C2#1172458811yescharacteristic
772C2#1172459711yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC33×C4⋊C4C22
hypercenterC4⋊C4D3×C3⋊D3
hypocenterC33#538
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #11723934C2semidirect
2. C3×#64107C2semidirect
3. C32×#894C2semidirect
4. #11723542C2semidirect
5. #11723540C2semidirect
6. #11723539C2semidirect
7. #11723531C2semidirect
8. #11723530C2semidirect
9. #11723525C2semidirect
10. #11723514C2semidirect
11. C4×#6291C2semidirect
12. #11723485C2semidirect
13. #11723432C2semidirect
14. #11723421C2semidirect
15. #11723419C2semidirect
21. C2×C4×C3⋊(C3⋊D3)C22semidirect
23. C2×C32×C4×D3C22semidirect
24. C2×#6293C22semidirect
28. C2×#6291C22semidirect
31. C33×C4⋊C4C22semidirect
33. #88859C22semidirect
34. C4×C3⋊(C3⋊Dic3)C22semidirect
38. C3×C4⋊(C3⋊Dic3)C22semidirect
39. C3×#3750C22semidirect
40. C3×C4×C3⋊Dic3C22semidirect
43. C32×(C2×D3)⋊C4C22semidirect
44. C32×Dic3⋊C4C22semidirect
45. #88807C22semidirect
46. Dic3⋊(C3⋊Dic3)C22semidirect
48. #88804C22semidirect
52. (C2×D3)⋊(C3⋊Dic3)C22semidirect
58. #64107D3semidirect
71. C3×#894D3semidirect
137. C2×C3×C4×D3C2×D3semidirect
147. C32×C4⋊C4C2×D3semidirect
148. C32×C4⋊C4C2×D3semidirect
168. C4⋊(C3⋊Dic3)C2×D3semidirect
170. #3750C2×D3semidirect
174. C4×C3⋊Dic3C2×D3semidirect
180. C3×(C2×D3)⋊C4C2×D3semidirect
183. C3×Dic3⋊C4C2×D3semidirect
233. #894C3⋊D3semidirect
356. C2×C4×D3C2×C3⋊D3semidirect
363. C3×C4⋊C4D32semidirect
364. C3×C4⋊C4C2×C3⋊D3semidirect
395. (C2×D3)⋊C4C2×C3⋊D3semidirect
402. Dic3⋊C4C2×C3⋊D3semidirect
488. C33#538semidirect
598. C4⋊C4D3×C3⋊D3semidirect
682. C32#5657semidirect
683. C32#5704semidirect
763. C3#10594657semidirect
764. C3#10596128semidirect

Maximal subgroups

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

subgroupindex
#117239342
C3×#641072
C32×#8942
#117235422
#117235402
#117235392
#117235312
#117235302
#117235252
#117235142
C4×#62912
#117234852
#117234322
#117234212
#117234192
#105961283
#105946573