Finite Group Databasebeta

← #13176604

Subgroups — #13176604

Order 1728.

1796 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723938C211yesmaximal, characteristic, complemented
2C3×#64103C211yesmaximal, characteristic, complemented
3C32×#894C211yesmaximal, characteristic, complemented
4#11723541C211yesmaximal, characteristic, complemented
5#11723540C211yesmaximal, characteristic, complemented
6#11723539C211yesmaximal, characteristic, complemented
7#11723528C211yesmaximal, characteristic, complemented
8#11723528C211yesmaximal, characteristic, complemented
9#11723527C211yesmaximal, characteristic, complemented
10#11723522C211yesmaximal, characteristic, complemented
11#11723515C211yesmaximal, characteristic, complemented
12#11723512C211yesmaximal, characteristic, complemented
13#11723510C211yesmaximal, characteristic, complemented
14#11723430C211yesmaximal, characteristic, complemented
15#11723408C211yesmaximal, characteristic, complemented
16#10596128—31nomaximal
17#10594659—34nomaximal
18C22×D3×C3⋊D3C2211yescharacteristic
19C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
20C2×#6308C2211yescharacteristic, complemented
21C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
22C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
23C2×C32×D12C2211yescharacteristic
24C2×C32×C4×D3C2211yescharacteristic, complemented
25C2×#6292C2211yescharacteristic
26C2×#6291C2211yescharacteristic
27C2×#6290C2211yescharacteristic
28C2×#6290C2211yescharacteristic
29C2×#6290C2211yescharacteristic, complemented
30C2×#6289C2211yescharacteristic
31C33×C4⋊C4C2211yescharacteristic, complemented
32#88859C2211yescharacteristic
33#88859C2211yescharacteristic
34C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic, complemented
35C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic, complemented
36C3×#3752C2211yescharacteristic
37C3×#3752C2211yescharacteristic
38C3×#3752C2211yescharacteristic, complemented
39C3×#3750C2211yescharacteristic, complemented
40C32×(C2×D3)⋊C4C2211yescharacteristic
41C32×(C2×D3)⋊C4C2211yescharacteristic
42C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
43C32×Dic3⋊C4C2211yescharacteristic, complemented
44#88806C2211yescharacteristic, complemented
45#88803C2211yescharacteristic
46#88803C2211yescharacteristic
47#88803C2211yescharacteristic, complemented
48(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
49(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
50(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
51Dic3×C3⋊Dic3C2211yescharacteristic, complemented
52Dic3×C3⋊Dic3C2211yescharacteristic, complemented
53C32×#123—31no—
54#64147—31no—
55#64146—31no—
56#64139—31no—
57C4×#638—31no—
58#64107—31no—
59#64106—31no—
60#64106—34no—
61#64106—64no—
62#64103D311yescharacteristic, complemented
63#64102—31no—
64#64094—31no—
65#64094—31no—
66#64093—31no—
67#64091—31no—
68C22⋊C4×C3⋊D3—31no—
69#64088—31no—
70C3×#894—34no—
71C3×#894D314yescomplemented
72#63922—34no—
73#63922—34no—
74#63921—34no—
75#63913—34no—
76#63913—34no—
77#63912—34no—
78#63908—34no—
79#63908—34no—
80#63904—34no—
81#63904—34no—
82#63861—34no—
83#63861—34no—
84C22×C3⋊(C3⋊D3)C2311yescharacteristic
85C22×C3×C3⋊D3C2311yescharacteristic
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
97C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
98C4×C3⋊(C3⋊D3)—41no—
99#6308—41no—
100C2×C3×C3⋊Dic3C2311yescharacteristic
101C2×C3×C3⋊Dic3C2311yescharacteristic
102C3×C4⋊(C3⋊D3)—41no—
103C3×C4×C3⋊D3—41no—
104C2×C32×Dic3C2311yescharacteristic
105C2×C32×Dic3C2311yescharacteristic
106C32×D12—41no—
107C32×C4×D3—41no—
108#6292—22no—
109#6291—22no—
110#6290—41no—
111#6290—41no—
112#6290—41no—
113#6289—41no—
114#5657—94no—
115#5657—91no—
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)C2×D311yescharacteristic
126C2×C4×C3⋊D3—31no—
127C2×C4×C3⋊D3—34no—
128C2×C4×C3⋊D3—31no—
129C2×C4×C3⋊D3—64no—
130C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
131C2×#634—31no—
132C2×#634—34no—
133C2×#634—64no—
134C2×C3×D12—34no—
135C2×C3×D12C2×D314yes—
136C2×C3×C4×D3—34no—
137C2×C3×C4×D3C2×D314yescomplemented
138C2×#626—34no—
139C2×#626—34no—
140C2×#625—34no—
141C2×#625—34no—
142C2×#625—34no—
143C2×#624—34no—
144C32×C4⋊C4—24no—
145C32×C4⋊C4—31no—
146C32×C4⋊C4C2×D314yescomplemented
147C32×C4⋊C4C2×D311yescharacteristic, complemented
148C32×C22⋊C4—31no—
149C32×C22⋊C4—31no—
150C32×C22⋊C4—31no—
151#3757—31no—
152#3757—31no—
153#3757—31no—
154#3752—31no—
155#3752—31no—
156#3752—31no—
157#3752—31no—
158#3752—31no—
159#3752—34no—
160#3752—34no—
161#3752—64no—
162#3752—64no—
163#3752C2×D311yescharacteristic
164#3752C2×D311yescharacteristic
165#3752C2×D311yescharacteristic, complemented
166C4⋊(C3⋊Dic3)—31no—
167C4⋊(C3⋊Dic3)—31no—
168C4⋊(C3⋊Dic3)—34no—
169C4⋊(C3⋊Dic3)—34no—
170C4⋊(C3⋊Dic3)—64no—
171C4⋊(C3⋊Dic3)—64no—
172#3750—31no—
173#3750C2×D311yescharacteristic, complemented
174C4×C3⋊Dic3—31no—
175C4×C3⋊Dic3—31no—
176C3×(C2×D3)⋊C4—34no—
177C3×(C2×D3)⋊C4—34no—
178C3×(C2×D3)⋊C4—34no—
179C3×(C2×D3)⋊C4C2×D314yes—
180C3×(C2×D3)⋊C4C2×D314yes—
181C3×(C2×D3)⋊C4C2×D314yescomplemented
182C3×Dic3⋊C4—34no—
183C3×Dic3⋊C4C2×D314yescomplemented
184#3724—34no—
185(C2×D3)⋊Dic3—34no—
186(C2×D3)⋊Dic3—34no—
187(C2×D3)⋊Dic3—34no—
188(C2×D3)⋊Dic3—34no—
189(C2×D3)⋊Dic3—34no—
190(C2×D3)⋊Dic3—34no—
191Dic32—34no—
192Dic32—34no—
193C22×C33C2411yescharacteristic
194C2×C3⋊(C3⋊D3)—21no—
195C2×C3⋊(C3⋊D3)—21no—
196C2×C3⋊(C3⋊D3)#4112yes—
197C2×C3×C3⋊D3—21no—
198C2×C3×C3⋊D3—21no—
199C2×C3×C3⋊D3—21no—
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×#123—34no—
221C3×#123—91no—
222#938—94no—
223#938—91no—
224#937—94no—
225#937—91no—
226#930—94no—
227#930—91no—
228C4×#67—94no—
229C4×#67—91no—
230#898—94no—
231#898—91no—
232#897—94no—
233#897—91no—
234#897—184no—
235#894—34no—
236#894C3⋊D311yescharacteristic, complemented
237#893—94no—
238#893—91no—
239#885—94no—
240#885—94no—
241#885—91no—
242#885—91no—
243#884—94no—
244#884—91no—
245#882—94no—
246#882—91no—
247D3×C22⋊C4—94no—
248D3×C22⋊C4—91no—
249#879—94no—
250#879—91no—
251C23×C32—31no—
252C23×C32—31no—
253C22×C3⋊D3—31no—
254C22×C3⋊D3—34no—
255C22×C3⋊D3—64no—
256C22×C3⋊D3—62no—
257C22×C3⋊D3—121no—
258C22×C3⋊D3—121no—
259C22×C3⋊D3C22×D311yescharacteristic
260C22×C3⋊D3C22×D311yescharacteristic
261C22×C3×D3—34no—
262C22×C3×D3—34no—
263C22×C3×D3C22×D314yes—
264C22×C3×D3C22×D314yes—
265C2×D32—68no—
266C2×D32—124no—
267C2×D32—124no—
268C32×D4—121no—
269C2×C32×C4—24no—
270C2×C32×C4—24no—
271C2×C32×C4—24no—
272C2×C32×C4—31no—
273C2×C32×C4—31no—
274C2×C32×C4—121no—
275C2×C32×C4C22×D314yes—
276C2×C32×C4C22×D314yes—
277C2×C32×C4C22×D314yes—
278C2×C32×C4C22×D311yescharacteristic
279C2×C32×C4C22×D311yescharacteristic
280C2×C32×C4C22×D311yescharacteristic
281#638—62no—
282#638—121no—
283#638—121no—
284#638—121no—
285C2×C3⋊Dic3—31no—
286C2×C3⋊Dic3—31no—
287C2×C3⋊Dic3—31no—
288C2×C3⋊Dic3—34no—
289C2×C3⋊Dic3—34no—
290C2×C3⋊Dic3—34no—
291C2×C3⋊Dic3—64no—
292C2×C3⋊Dic3—64no—
293C2×C3⋊Dic3—64no—
294C2×C3⋊Dic3C22×D311yescharacteristic
295C2×C3⋊Dic3C22×D311yescharacteristic
296C4⋊(C3⋊D3)—41no—
297C4⋊(C3⋊D3)—62no—
298C4×C3⋊D3—41no—
299C4×C3⋊D3—121no—
300C4×C3⋊D3—121no—
301C4×C3⋊D3—124no—
302C4×C3⋊D3—128no—
303#634—121no—
304#634—124no—
305#634—128no—
306C2×C3×Dic3—34no—
307C2×C3×Dic3—34no—
308C2×C3×Dic3C22×D314yes—
309C2×C3×Dic3C22×D314yes—
310C3×D12—44no—
311C3×D12—124no—
312C3×C4×D3—44no—
313C3×C4×D3—124no—
314#626—68no—
315#626—68no—
316#625—124no—
317#625—124no—
318#625—124no—
319#624—124no—
320#538—271noSylow
321C2×C33C2×#4111yescharacteristic
322C2×C33H(5,𝔽2)11yescharacteristic
323C2×C33H(5,𝔽2)11yescharacteristic
324C3⋊(C3⋊D3)—22no—
325C3×C3⋊D3—41no—
326C3×C3⋊D3—41no—
327C32×D3—41no—
328C32×D3—41no—
329C23×D3—94no—
330C23×D3—91no—
331C2×C3×D4—34no—
332C2×C3×D4—91no—
333C22×C3×C4—34no—
334C22×C3×C4—91no—
335C2×#67—94no—
336C2×#67—94no—
337C2×#67—94no—
338C2×#67—94no—
339C2×#67—91no—
340C2×#67—91no—
341C2×#67—91no—
342C2×#67—91no—
343C2×D12—34no—
344C2×D12—94no—
345C2×D12—91no—
346C2×D12C2×C3⋊D311yescharacteristic
347C2×C4×D3—34no—
348C2×C4×D3—94no—
349C2×C4×D3—94no—
350C2×C4×D3—91no—
351C2×C4×D3—91no—
352C2×C4×D3—184no—
353C2×C4×D3C2×C3⋊D311yescharacteristic, complemented
354C2×Dic6—94no—
355C2×Dic6—91no—
356C2×Dic6—184no—
357C3×C4⋊C4—24no—
358C3×C4⋊C4—34no—
359C3×C4⋊C4—91no—
360C3×C4⋊C4D3214yescomplemented
361C3×C4⋊C4C2×C3⋊D311yescharacteristic, complemented
362C3×C22⋊C4—34no—
363C3×C22⋊C4—34no—
364C3×C22⋊C4—34no—
365C3×C22⋊C4—91no—
366C3×C22⋊C4—91no—
367C3×C22⋊C4—91no—
368#217—94no—
369#217—94no—
370#217—94no—
371#217—91no—
372#217—91no—
373#217—91no—
374(C2×D3)⋊C4—34no—
375(C2×D3)⋊C4—34no—
376(C2×D3)⋊C4—34no—
377(C2×D3)⋊C4—94no—
378(C2×D3)⋊C4—94no—
379(C2×D3)⋊C4—94no—
380(C2×D3)⋊C4—91no—
381(C2×D3)⋊C4—91no—
382(C2×D3)⋊C4—91no—
383(C2×D3)⋊C4—94no—
384(C2×D3)⋊C4—94no—
385(C2×D3)⋊C4—91no—
386(C2×D3)⋊C4—91no—
387(C2×D3)⋊C4—184no—
388(C2×D3)⋊C4—184no—
389(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
390(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
391(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
392C4⋊Dic3—94no—
393C4⋊Dic3—94no—
394C4⋊Dic3—91no—
395C4⋊Dic3—91no—
396C4⋊Dic3—184no—
397C4⋊Dic3—184no—
398Dic3⋊C4—34no—
399Dic3⋊C4—94no—
400Dic3⋊C4—91no—
401Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
402C4×Dic3—94no—
403C4×Dic3—94no—
404C4×Dic3—91no—
405C4×Dic3—91no—
406C22×C32—24no—
407C22×C32—61no—
408C22×C32—61no—
409C22×C32—61no—
410C22×C32—61no—
411C22×C32—61no—
412C22×C32—61no—
413C22×C32C23×D314yes—
414C22×C32C23×D311yescharacteristic
415C2×C3⋊D3—21no—
416C2×C3⋊D3—21no—
417C2×C3⋊D3—21no—
418C2×C3⋊D3—21no—
419C2×C3⋊D3—21no—
420C2×C3⋊D3—21no—
421C2×C3⋊D3—32no—
422C2×C3⋊D3—38no—
423C2×C3⋊D3—68no—
424C2×C3⋊D3—61no—
425C2×C3⋊D3—61no—
426C2×C3⋊D3—64no—
427C2×C3⋊D3—64no—
428C2×C3⋊D3—124no—
429C2×C3⋊D3—124no—
430C2×C3⋊D3—124no—
431C2×C3×D3—24no—
432C2×C3×D3—24no—
433C2×C3×D3—24no—
434C2×C3×D3—24no—
435C2×C3×D3—24no—
436C2×C3×D3—24no—
437C2×C3×D3—64no—
438C2×C3×D3—64no—
439C2×C3×D3—64no—
440C2×C3×D3—64no—
441C2×C3×D3—64no—
442C2×C3×D3—64no—
443D32—1216no—
444C32×C4—28no—
445C32×C4—21no—
446C32×C4—21no—
447C32×C4—24no—
448C32×C4—21no—
449C32×C4—24no—
450C32×C4—24no—
451C32×C4—44no—
452C32×C4—44no—
453C32×C4—61no—
454C32×C4—61no—
455C3⋊Dic3—21no—
456C3⋊Dic3—21no—
457C3⋊Dic3—61no—
458C3⋊Dic3—61no—
459C3⋊Dic3—61no—
460C3⋊Dic3—64no—
461C3⋊Dic3—64no—
462C3⋊Dic3—64no—
463C3⋊Dic3—124no—
464C3⋊Dic3—124no—
465C3⋊Dic3—124no—
466C3×Dic3—24no—
467C3×Dic3—24no—
468C3×Dic3—64no—
469C3×Dic3—64no—
470#126—271no—
471#126—271no—
472#124—271no—
473#124—271no—
474#123—31no—
475#123—91no—
476C22⋊Q8—271no—
477#121—271no—
478#121—271no—
479#121—271no—
480#120—271no—
481#120—271no—
482C4×D4—271no—
483C4×D4—271no—
484C2×C22⋊C4—271no—
485C33#53811yescharacteristic, complemented, Sylow
486C23×C3—34no—
487C23×C3—34no—
488C23×C3—91no—
489C23×C3—91no—
490C22×D3—34no—
491C22×D3—34no—
492C22×D3—94no—
493C22×D3—91no—
494C22×D3—184no—
495C22×D3—182no—
496C22×D3—188no—
497C22×D3—361no—
498C22×D3—361no—
499C22×D3—364no—
500C22×D3—364no—
501C22×D3C22×C3⋊D311yescharacteristic
502C22×D3C22×C3⋊D311yescharacteristic
503C3×D4—124no—
504C3×D4—361no—
505C2×C3×C4—24no—
506C2×C3×C4—24no—
507C2×C3×C4—24no—
508C2×C3×C4—34no—
509C2×C3×C4—34no—
510C2×C3×C4—91no—
511C2×C3×C4—91no—
512C2×C3×C4—124no—
513C2×C3×C4—361no—
514C2×C3×C4C2×D3214yes—
515C2×C3×C4C2×D3214yes—
516C2×C3×C4C2×D3214yes—
517C2×C3×C4C22×C3⋊D311yescharacteristic
518C2×C3×C4C22×C3⋊D311yescharacteristic
519C2×C3×C4C22×C3⋊D311yescharacteristic
520#67—182no—
521#67—188no—
522#67—361no—
523#67—361no—
524#67—361no—
525#67—364no—
526#67—364no—
527#67—364no—
528C2×Dic3—34no—
529C2×Dic3—34no—
530C2×Dic3—94no—
531C2×Dic3—94no—
532C2×Dic3—94no—
533C2×Dic3—91no—
534C2×Dic3—91no—
535C2×Dic3—91no—
536C2×Dic3—184no—
537C2×Dic3—184no—
538C2×Dic3—184no—
539C2×Dic3C22×C3⋊D311yescharacteristic
540C2×Dic3C22×C3⋊D311yescharacteristic
541D12—41no—
542D12—124no—
543D12—188no—
544D12—182no—
545C4×D3—41no—
546C4×D3—124no—
547C4×D3—361no—
548C4×D3—364no—
549C4×D3—364no—
550C4×D3—361no—
551C4×D3—368no—
552Dic6—364no—
553Dic6—361no—
554Dic6—368no—
555C2×C32—24no—
556C2×C32—24no—
557C2×C32—24no—
558C2×C32—121no—
559C2×C32—121no—
560C2×C32#100414yes—
561C2×C32#100411yescharacteristic
562C2×C32D3×#4114yes—
563C2×C32D3×#4111yescharacteristic
564C2×C32#100914yes—
565C2×C32#100911yescharacteristic
566C3⋊D3—41no—
567C3⋊D3—41no—
568C3⋊D3—62no—
569C3⋊D3—68no—
570C3⋊D3—128no—
571C3×D3—44no—
572C3×D3—44no—
573C3×D3—124no—
574C3×D3—124no—
575C24—271no—
576C2×Q8—271no—
577C2×D4—31no—
578C2×D4—91no—
579C2×D4—271no—
580C2×D4—271no—
581C2×D4—271no—
582C2×D4—271no—
583C2×D4—271no—
584C22×C4—31no—
585C22×C4—91no—
586C22×C4—271no—
587C22×C4—271no—
588C4⋊C4—31no—
589C4⋊C4—91no—
590C4⋊C4—271no—
591C4⋊C4—271no—
592C4⋊C4—271no—
593C4⋊C4D3×C3⋊D311yescharacteristic, complemented
594C22⋊C4—31no—
595C22⋊C4—31no—
596C22⋊C4—31no—
597C22⋊C4—91no—
598C22⋊C4—91no—
599C22⋊C4—91no—
600C22⋊C4—271no—
601C22⋊C4—271no—
602C22⋊C4—271no—
603C22⋊C4—271no—
604C22⋊C4—271no—
605C22⋊C4—271no—
606C22⋊C4—271no—
607C22⋊C4—271no—
608C42—271no—
609C42—271no—
610C22×C3—24no—
611C22×C3—64no—
612C22×C3—64no—
613C22×C3—64no—
614C22×C3—64no—
615C22×C3—64no—
616C22×C3—64no—
617C22×C3—181no—
618C22×C3—181no—
619C22×C3—181no—
620C22×C3—181no—
621C22×C3—181no—
622C22×C3—181no—
623C22×C3C22×D3214yes—
624C22×C3C23×C3⋊D311yescharacteristic
625C2×D3—21no—
626C2×D3—21no—
627C2×D3—21no—
628C2×D3—21no—
629C2×D3—21no—
630C2×D3—21no—
631C2×D3—64no—
632C2×D3—64no—
633C2×D3—64no—
634C2×D3—64no—
635C2×D3—64no—
636C2×D3—64no—
637C2×D3—98no—
638C2×D3—92no—
639C2×D3—188no—
640C2×D3—184no—
641C2×D3—184no—
642C2×D3—181no—
643C2×D3—181no—
644C2×D3—364no—
645C2×D3—364no—
646C2×D3—364no—
647C2×D3—3616no—
648C3×C4—28no—
649C3×C4—24no—
650C3×C4—24no—
651C3×C4—24no—
652C3×C4—21no—
653C3×C4—21no—
654C3×C4—21no—
655C3×C4—44no—
656C3×C4—44no—
657C3×C4—64no—
658C3×C4—64no—
659C3×C4—181no—
660C3×C4—181no—
661Dic3—21no—
662Dic3—21no—
663Dic3—64no—
664Dic3—64no—
665Dic3—184no—
666Dic3—184no—
667Dic3—184no—
668Dic3—181no—
669Dic3—181no—
670Dic3—181no—
671Dic3—364no—
672Dic3—364no—
673Dic3—364no—
674C32—24no—
675C32#565714yescomplemented
676C32#565711yescharacteristic, complemented
677C23—31no—
678C23—31no—
679C23—91no—
680C23—91no—
681C23—271no—
682C23—542no—
683C23—1081no—
684C23—1081no—
685Q8—1081no—
686D4—121no—
687D4—361no—
688D4—542no—
689D4—542no—
690D4—1081no—
691D4—1081no—
692D4—1081no—
693C2×C4—31no—
694C2×C4—31no—
695C2×C4—91no—
696C2×C4—91no—
697C2×C4—121no—
698C2×C4—271no—
699C2×C4—271no—
700C2×C4—271no—
701C2×C4—361no—
702C2×C4—1081no—
703C2×C4—1081no—
704C2×C4C2×D3×C3⋊D311yescharacteristic
705C2×C4C2×D3×C3⋊D311yescharacteristic
706C2×C4C2×D3×C3⋊D311yescharacteristic
707C2×C3—24no—
708C2×C3—24no—
709C2×C3—24no—
710C2×C3—124no—
711C2×C3—124no—
712C2×C3—361no—
713C2×C3—361no—
714C2×C3#6430814yes—
715C2×C3#6431314yes—
716C2×C3#6431914yes—
717C2×C3#6436111yescharacteristic
718C2×C3#41×C3⋊D311yescharacteristic
719C2×C3#6436611yescharacteristic
720D3—41no—
721D3—41no—
722D3—124no—
723D3—124no—
724D3—182no—
725D3—188no—
726D3—368no—
727C22—61no—
728C22—61no—
729C22—61no—
730C22—61no—
731C22—61no—
732C22—61no—
733C22—181no—
734C22—181no—
735C22—181no—
736C22—181no—
737C22—181no—
738C22—181no—
739C22—272no—
740C22—541no—
741C22—541no—
742C22—1084no—
743C22C22×D3×C3⋊D311yescharacteristic
744C4—21no—
745C4—21no—
746C4—21no—
747C4—61no—
748C4—61no—
749C4—181no—
750C4—181no—
751C4—541no—
752C4—541no—
753C4—541no—
754C3—24no—
755C3#1059465914yescomplemented
756C3#1059612811yescharacteristic, complemented
757C2—121no—
758C2—121no—
759C2—361no—
760C2—361no—
761C2—542no—
762C2#1172458111yescharacteristic
763C2#1172458711yescharacteristic
764C2#1172459611yescharacteristic
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. #11723938C2semidirect
2. C3×#64103C2semidirect
3. C32×#894C2semidirect
4. #11723541C2semidirect
5. #11723540C2semidirect
6. #11723539C2semidirect
7. #11723528C2semidirect
8. #11723528C2semidirect
9. #11723527C2semidirect
10. #11723522C2semidirect
11. #11723515C2semidirect
12. #11723512C2semidirect
13. #11723510C2semidirect
14. #11723430C2semidirect
15. #11723408C2semidirect
20. C2×#6308C22semidirect
22. C2×C3×C4×C3⋊D3C22semidirect
24. C2×C32×C4×D3C22semidirect
29. C2×#6290C22semidirect
31. C33×C4⋊C4C22semidirect
34. C4⋊(C3⋊(C3⋊Dic3))C22semidirect
35. C4⋊(C3⋊(C3⋊Dic3))C22semidirect
38. C3×#3752C22semidirect
39. C3×#3750C22semidirect
42. C32×(C2×D3)⋊C4C22semidirect
43. C32×Dic3⋊C4C22semidirect
44. #88806C22semidirect
47. #88803C22semidirect
50. (C2×D3)⋊(C3⋊Dic3)C22semidirect
51. Dic3×C3⋊Dic3C22semidirect
52. Dic3×C3⋊Dic3C22semidirect
62. #64103D3semidirect
71. C3×#894D3semidirect
130. C2×C4×C3⋊D3C2×D3semidirect
137. C2×C3×C4×D3C2×D3semidirect
146. C32×C4⋊C4C2×D3semidirect
147. C32×C4⋊C4C2×D3semidirect
165. #3752C2×D3semidirect
173. #3750C2×D3semidirect
181. C3×(C2×D3)⋊C4C2×D3semidirect
183. C3×Dic3⋊C4C2×D3semidirect
236. #894C3⋊D3semidirect
353. C2×C4×D3C2×C3⋊D3semidirect
360. C3×C4⋊C4D32semidirect
361. C3×C4⋊C4C2×C3⋊D3semidirect
391. (C2×D3)⋊C4C2×C3⋊D3semidirect
401. Dic3⋊C4C2×C3⋊D3semidirect
485. C33#538semidirect
593. C4⋊C4D3×C3⋊D3semidirect
675. C32#5657semidirect
676. C32#5657semidirect
755. C3#10594659semidirect
756. C3#10596128semidirect

Maximal subgroups

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

subgroupindex
#117239382
C3×#641032
C32×#8942
#117235412
#117235402
#117235392
#117235282
#117235272
#117235222
#117235152
#117235122
#117235102
#117234302
#117234082
#105961283
#105946593