Finite Group Databasebeta

← #13177349

Subgroups — #13177349

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
1C4×#6312C211yesmaximal, characteristic, complemented
2C3×#64139C211yesmaximal, characteristic, complemented
3C32×#929C211yesmaximal, characteristic, complemented
4#11723643C211yesmaximal, characteristic, complemented
5#11723631C211yesmaximal, characteristic, complemented
6#11723623C211yesmaximal, characteristic, complemented
7#11723591C211yesmaximal, characteristic, complemented
8#11723541C211yesmaximal, characteristic, complemented
9#11723539C211yesmaximal, characteristic, complemented
10#11723530C211yesmaximal, characteristic, complemented
11#11723488C211yesmaximal, characteristic, complemented
12#11723485C211yesmaximal, characteristic, complemented
13#11723472C211yesmaximal, characteristic, complemented
14#11723433C211yesmaximal, characteristic, complemented
15#11723427C211yesmaximal, characteristic, complemented
16#10596128—31nomaximal
17#10595089—34nomaximal
18C22×D3×C3⋊D3C2211yescharacteristic
19C22×C33×C4C2211yescharacteristic, complemented
20C2×#6312C2211yescharacteristic
21C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
22C2×C3×#638C2211yescharacteristic
23C2×C3×#638C2211yescharacteristic, complemented
24C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
25C2×C32×#67C2211yescharacteristic
26C2×#6293C2211yescharacteristic, complemented
27C2×#6292C2211yescharacteristic
28C2×#6290C2211yescharacteristic
29C2×#6289C2211yescharacteristic
30C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
31#88864C2211yescharacteristic, complemented
32#88859C2211yescharacteristic
33#88857C2211yescharacteristic, complemented
34C4×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
35C3×#3752C2211yescharacteristic
36C3×#3752C2211yescharacteristic, complemented
37C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
38C32×#217C2211yescharacteristic, complemented
39C32×(C2×D3)⋊C4C2211yescharacteristic
40C32×(C2×D3)⋊C4C2211yescharacteristic
41C32×Dic3⋊C4C2211yescharacteristic, complemented
42C32×Dic3⋊C4C2211yescharacteristic, complemented
43#88807C2211yescharacteristic, complemented
44Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
45#88804C2211yescharacteristic
46#88803C2211yescharacteristic
47#88803C2211yescharacteristic
48#88803C2211yescharacteristic
49#88803C2211yescharacteristic, complemented
50(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
51(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
52Dic3×C3⋊Dic3C2211yescharacteristic, complemented
53C32×#123—31no—
54#64147—31no—
55#64146—31no—
56#64139D311yescharacteristic, complemented
57C4×#638—31no—
58C4×#638—34no—
59C4×#638—64no—
60#64107—31no—
61#64106—31no—
62#64103—31no—
63#64102—31no—
64#64094—31no—
65#64094—31no—
66#64093—31no—
67#64091—31no—
68C22⋊C4×C3⋊D3—31no—
69#64088—31no—
70C3×#930—34no—
71C3×#929D314yescomplemented
72#63983—34no—
73#63970—34no—
74#63959—34no—
75#63958—34no—
76#63922—34no—
77#63921—34no—
78#63915—34no—
79#63895—34no—
80#63884—34no—
81#63881—34no—
82#63862—34no—
83#63858—34no—
84C23×C33C2311yescharacteristic
85C22×C3⋊(C3⋊D3)C2311yescharacteristic
86C22×C3×C3⋊D3C2311yescharacteristic
87C22×C3×C3⋊D3C2311yescharacteristic
88C22×C32×D3C2311yescharacteristic
89C2×D3×C3⋊D3—22no—
90C2×D3×C3⋊D3—41no—
91C2×D3×C3⋊D3—41no—
92C2×C33×C4—41no—
93C2×C33×C4C2311yescharacteristic
94C2×C33×C4C2311yescharacteristic
95#6312—22no—
96C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
97C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
98C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
99C4×C3⋊(C3⋊D3)—41no—
100C3×#638—41no—
101C3×#638—41no—
102C2×C3×C3⋊Dic3C2311yescharacteristic
103C2×C3×C3⋊Dic3C2311yescharacteristic
104C3×C4⋊(C3⋊D3)—41no—
105C32×#67—41no—
106C2×C32×Dic3C2311yescharacteristic
107C2×C32×Dic3C2311yescharacteristic
108C2×C32×Dic3C2311yescharacteristic
109#6293—41no—
110#6292—22no—
111#6290—41no—
112#6289—41no—
113Dic3×C3⋊D3—41no—
114#5657—94no—
115#5613—91no—
116C23×C3⋊D3—31no—
117C22×D32—34no—
118C2×C32×D4—31no—
119C22×C32×C4—24no—
120C22×C32×C4C2×D314yescomplemented
121C22×C32×C4C2×D311yescharacteristic, complemented
122C2×#638—31no—
123C2×#638—34no—
124C2×#638—31no—
125C2×#638—64no—
126C2×#638C2×D311yescharacteristic
127C2×#638C2×D311yescharacteristic, complemented
128C2×C4⋊(C3⋊D3)—31no—
129C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
130C2×C4×C3⋊D3—31no—
131C2×C4×C3⋊D3—31no—
132C2×C4×C3⋊D3—34no—
133C2×C4×C3⋊D3—31no—
134C2×C4×C3⋊D3—64no—
135C2×#634—31no—
136C2×C3×#67—34no—
137C2×C3×#67—34no—
138C2×C3×#67C2×D314yes—
139C2×C3×D12—34no—
140C2×#627—34no—
141C2×#626—34no—
142C2×#625—34no—
143C2×#624—34no—
144C2×D3×Dic3—34no—
145C32×C4⋊C4—31no—
146C32×C4⋊C4—31no—
147C32×C22⋊C4—31no—
148C32×C22⋊C4—31no—
149C32×C22⋊C4—31no—
150#3757—31no—
151#3757—34no—
152#3757—31no—
153#3757—31no—
154#3757—64no—
155#3752—31no—
156#3752—31no—
157#3752—31no—
158#3752—31no—
159#3752—31no—
160#3752—34no—
161#3752—31no—
162#3752—64no—
163#3752C2×D311yescharacteristic
164#3752C2×D311yescharacteristic, complemented
165C4⋊(C3⋊Dic3)—31no—
166C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
167#3750—31no—
168#3750—34no—
169#3750—31no—
170#3750—64no—
171C4×C3⋊Dic3—31no—
172C4×C3⋊Dic3—34no—
173C4×C3⋊Dic3—31no—
174C4×C3⋊Dic3—64no—
175C3×#217C2×D314yescomplemented
176C3×(C2×D3)⋊C4—34no—
177C3×(C2×D3)⋊C4—34no—
178C3×(C2×D3)⋊C4C2×D314yes—
179C3×(C2×D3)⋊C4C2×D314yes—
180C3×C4⋊Dic3—34no—
181C3×Dic3⋊C4C2×D314yescomplemented
182C3×Dic3⋊C4C2×D314yescomplemented
183Dic3⋊Dic3—34no—
184Dic3⋊Dic3—34no—
185#3722—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—
191(C2×D3)⋊Dic3—34no—
192Dic32—34no—
193C22×C33—21no—
194C22×C33—21no—
195C22×C33—21no—
196C22×C33C2411yescharacteristic
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×C3×C3⋊D3—21no—
204C2×C3×C3⋊D3—21no—
205C2×C3×C3⋊D3—21no—
206C2×C32×D3—21no—
207C2×C32×D3—21no—
208C2×C32×D3—21no—
209D3×C3⋊D3—44no—
210C33×C4—21no—
211C33×C4—21no—
212C3⋊(C3⋊Dic3)—21no—
213C3⋊(C3⋊Dic3)—21no—
214C3⋊(C3⋊Dic3)—21no—
215C3×C3⋊Dic3—21no—
216C3×C3⋊Dic3—21no—
217C32×Dic3—21no—
218C32×Dic3—21no—
219C32×Dic3—21no—
220C3×#123—34no—
221C3×#121—91no—
222#939—91no—
223#938—94no—
224#938—91no—
225#937—94no—
226#937—91no—
227#937—91no—
228#936—91no—
229#935—91no—
230#930—34no—
231#929C3⋊D311yescharacteristic, complemented
232C4×#67—94no—
233C4×#67—91no—
234C4×#67—184no—
235#898—94no—
236#898—91no—
237#897—94no—
238#896—91no—
239#894—94no—
240#893—94no—
241#885—94no—
242#885—94no—
243#885—91no—
244#884—94no—
245#882—94no—
246#67⋊C4—91no—
247D3×C22⋊C4—94no—
248D3×C22⋊C4—91no—
249#879—94no—
250#879—91no—
251C23×C32—24no—
252C23×C32—31no—
253C23×C32C22×D314yes—
254C23×C32C22×D311yescharacteristic
255C22×C3⋊D3—31no—
256C22×C3⋊D3—34no—
257C22×C3⋊D3—64no—
258C22×C3⋊D3—62no—
259C22×C3⋊D3—121no—
260C22×C3⋊D3—121no—
261C22×C3⋊D3C22×D311yescharacteristic
262C22×C3⋊D3C22×D311yescharacteristic
263C22×C3×D3—34no—
264C22×C3×D3—34no—
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—31no—
273C2×C32×C4—31no—
274C2×C32×C4—31no—
275C2×C32×C4—41no—
276C2×C32×C4—44no—
277C2×C32×C4—48no—
278C2×C32×C4C22×D314yes—
279C2×C32×C4C22×D314yes—
280C2×C32×C4C22×D311yescharacteristic
281C2×C32×C4C22×D311yescharacteristic
282#638—41no—
283#638—41no—
284#638—62no—
285#638—68no—
286#638—616no—
287#638—121no—
288C2×C3⋊Dic3—31no—
289C2×C3⋊Dic3—31no—
290C2×C3⋊Dic3—31no—
291C2×C3⋊Dic3—34no—
292C2×C3⋊Dic3—34no—
293C2×C3⋊Dic3—34no—
294C2×C3⋊Dic3—64no—
295C2×C3⋊Dic3—64no—
296C2×C3⋊Dic3—64no—
297C2×C3⋊Dic3C22×D311yescharacteristic
298C2×C3⋊Dic3C22×D311yescharacteristic
299C4⋊(C3⋊D3)—41no—
300C4⋊(C3⋊D3)—62no—
301C4×C3⋊D3—121no—
302C4×C3⋊D3—121no—
303C4×C3⋊D3—124no—
304C4×C3⋊D3—121no—
305C4×C3⋊D3—128no—
306#634—121no—
307C3×#67—44no—
308C3×#67—124no—
309C3×#67—124no—
310C2×C3×Dic3—34no—
311C2×C3×Dic3—34no—
312C2×C3×Dic3C22×D314yes—
313C2×C3×Dic3C22×D314yes—
314C2×C3×Dic3C22×D314yes—
315C3×D12—124no—
316#627—124no—
317#626—68no—
318#625—124no—
319#624—124no—
320D3×Dic3—124no—
321#538—271noSylow
322C2×C33—41no—
323C2×C33C2×#4111yescharacteristic
324C2×C33H(5,𝔽2)11yescharacteristic
325C2×C33H(5,𝔽2)11yescharacteristic
326C3⋊(C3⋊D3)—22no—
327C3×C3⋊D3—41no—
328C3×C3⋊D3—41no—
329C32×D3—41no—
330C23×D3—94no—
331C23×D3—91no—
332C2×C3×D4—34no—
333C2×C3×D4—91no—
334C2×C3×D4—91no—
335C2×C3×D4—91no—
336C22×C3×C4—24no—
337C22×C3×C4D3214yescomplemented
338C22×C3×C4C2×C3⋊D311yescharacteristic, complemented
339C2×#67—34no—
340C2×#67—34no—
341C2×#67—94no—
342C2×#67—91no—
343C2×#67—94no—
344C2×#67—91no—
345C2×#67—91no—
346C2×#67—184no—
347C2×#67C2×C3⋊D311yescharacteristic
348C22×Dic3—91no—
349C2×D12—34no—
350C2×D12—94no—
351C2×C4×D3—94no—
352C2×C4×D3—94no—
353C2×C4×D3—94no—
354C2×C4×D3—91no—
355C2×C4×D3—91no—
356C2×C4×D3—184no—
357C2×Dic6—94no—
358C2×Dic6—91no—
359C3×C4⋊C4—34no—
360C3×C4⋊C4—34no—
361C3×C4⋊C4—91no—
362C3×C22⋊C4—34no—
363C3×C22⋊C4—34no—
364C3×C22⋊C4—34no—
365C3×C22⋊C4—91no—
366C3×C22⋊C4—91no—
367#217—94no—
368#217—94no—
369#217—94no—
370#217—91no—
371#217—91no—
372#217—91no—
373#217—91no—
374#217—91no—
375#217—184no—
376#217C2×C3⋊D311yescharacteristic, complemented
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—94no—
383(C2×D3)⋊C4—94no—
384(C2×D3)⋊C4—91no—
385(C2×D3)⋊C4—91no—
386(C2×D3)⋊C4—94no—
387(C2×D3)⋊C4—91no—
388(C2×D3)⋊C4—91no—
389(C2×D3)⋊C4—184no—
390(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
391(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
392C4⋊Dic3—34no—
393C4⋊Dic3—94no—
394C4⋊Dic3—91no—
395Dic3⋊C4—94no—
396Dic3⋊C4—94no—
397Dic3⋊C4—91no—
398Dic3⋊C4—91no—
399Dic3⋊C4—184no—
400Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
401Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
402C4×Dic3—94no—
403C4×Dic3—94no—
404C4×Dic3—91no—
405C4×Dic3—91no—
406C4×Dic3—184no—
407C22×C32—28no—
408C22×C32—21no—
409C22×C32—21no—
410C22×C32—24no—
411C22×C32—21no—
412C22×C32—24no—
413C22×C32—24no—
414C22×C32—24no—
415C22×C32—44no—
416C22×C32—44no—
417C22×C32—61no—
418C22×C32—61no—
419C22×C32—61no—
420C22×C32C23×D314yes—
421C22×C32C23×D311yescharacteristic
422C2×C3⋊D3—21no—
423C2×C3⋊D3—21no—
424C2×C3⋊D3—21no—
425C2×C3⋊D3—21no—
426C2×C3⋊D3—21no—
427C2×C3⋊D3—21no—
428C2×C3⋊D3—32no—
429C2×C3⋊D3—38no—
430C2×C3⋊D3—68no—
431C2×C3⋊D3—61no—
432C2×C3⋊D3—61no—
433C2×C3⋊D3—64no—
434C2×C3⋊D3—64no—
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—64no—
442C2×C3×D3—64no—
443C2×C3×D3—64no—
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—24no—
453C32×C4—44no—
454C32×C4—61no—
455C32×C4—61no—
456C32×C4—61no—
457C3⋊Dic3—21no—
458C3⋊Dic3—21no—
459C3⋊Dic3—68no—
460C3⋊Dic3—61no—
461C3⋊Dic3—61no—
462C3⋊Dic3—64no—
463C3⋊Dic3—61no—
464C3⋊Dic3—64no—
465C3⋊Dic3—64no—
466C3⋊Dic3—124no—
467C3⋊Dic3—124no—
468C3×Dic3—24no—
469C3×Dic3—24no—
470C3×Dic3—24no—
471C3×Dic3—64no—
472C3×Dic3—64no—
473#126—271no—
474#126—271no—
475#124—271no—
476#124—271no—
477#123—31no—
478#123—271no—
479C22⋊Q8—271no—
480#121—91no—
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—24no—
490C23×C3—34no—
491C23×C3—91no—
492C23×C3—91no—
493C23×C3C2×D3214yes—
494C23×C3C22×C3⋊D311yescharacteristic
495C22×D3—34no—
496C22×D3—34no—
497C22×D3—94no—
498C22×D3—91no—
499C22×D3—184no—
500C22×D3—182no—
501C22×D3—188no—
502C22×D3—361no—
503C22×D3—361no—
504C22×D3—364no—
505C22×D3—364no—
506C22×D3C22×C3⋊D311yescharacteristic
507C3×D4—124no—
508C3×D4—361no—
509C3×D4—361no—
510C3×D4—361no—
511C2×C3×C4—24no—
512C2×C3×C4—24no—
513C2×C3×C4—34no—
514C2×C3×C4—34no—
515C2×C3×C4—34no—
516C2×C3×C4—44no—
517C2×C3×C4—41no—
518C2×C3×C4—48no—
519C2×C3×C4—91no—
520C2×C3×C4—91no—
521C2×C3×C4C2×D3214yes—
522C2×C3×C4C2×D3214yes—
523C2×C3×C4C22×C3⋊D311yescharacteristic
524C2×C3×C4C22×C3⋊D311yescharacteristic
525#67—41no—
526#67—124no—
527#67—124no—
528#67—182no—
529#67—188no—
530#67—182no—
531#67—1816no—
532#67—361no—
533#67—364no—
534C2×Dic3—34no—
535C2×Dic3—34no—
536C2×Dic3—94no—
537C2×Dic3—94no—
538C2×Dic3—94no—
539C2×Dic3—91no—
540C2×Dic3—91no—
541C2×Dic3—91no—
542C2×Dic3—184no—
543C2×Dic3—184no—
544C2×Dic3—184no—
545C2×Dic3—361no—
546C2×Dic3C22×C3⋊D311yescharacteristic
547C2×Dic3C22×C3⋊D311yescharacteristic
548C2×Dic3C22×C3⋊D311yescharacteristic
549D12—124no—
550D12—188no—
551C4×D3—361no—
552C4×D3—364no—
553C4×D3—364no—
554C4×D3—361no—
555C4×D3—364no—
556C4×D3—368no—
557Dic6—361no—
558Dic6—364no—
559C2×C32—24no—
560C2×C32—24no—
561C2×C32—24no—
562C2×C32—48no—
563C2×C32—44no—
564C2×C32—41no—
565C2×C32—121no—
566C2×C32#100414yes—
567C2×C32#100411yescharacteristic
568C2×C32#100411yescharacteristic
569C2×C32D3×#4114yes—
570C2×C32D3×#4111yescharacteristic
571C2×C32#100914yes—
572C3⋊D3—41no—
573C3⋊D3—41no—
574C3⋊D3—62no—
575C3⋊D3—68no—
576C3⋊D3—128no—
577C3×D3—44no—
578C3×D3—124no—
579C3×D3—124no—
580C24—271no—
581C2×Q8—271no—
582C2×D4—31no—
583C2×D4—91no—
584C2×D4—91no—
585C2×D4—91no—
586C2×D4—271no—
587C2×D4—271no—
588C2×D4—271no—
589C22×C4—271no—
590C22×C4—271no—
591C22×C4—271no—
592C22×C4D3×C3⋊D311yescharacteristic, complemented
593C4⋊C4—31no—
594C4⋊C4—31no—
595C4⋊C4—91no—
596C4⋊C4—271no—
597C4⋊C4—271no—
598C4⋊C4—271no—
599C22⋊C4—31no—
600C22⋊C4—31no—
601C22⋊C4—31no—
602C22⋊C4—91no—
603C22⋊C4—91no—
604C22⋊C4—271no—
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—271no—
614C42—271no—
615C22×C3—28no—
616C22×C3—24no—
617C22×C3—24no—
618C22×C3—24no—
619C22×C3—21no—
620C22×C3—21no—
621C22×C3—21no—
622C22×C3—24no—
623C22×C3—44no—
624C22×C3—44no—
625C22×C3—64no—
626C22×C3—64no—
627C22×C3—64no—
628C22×C3—181no—
629C22×C3—181no—
630C22×C3—181no—
631C22×C3—181no—
632C22×C3—181no—
633C22×C3—181no—
634C22×C3C22×D3214yes—
635C22×C3C23×C3⋊D311yescharacteristic
636C2×D3—21no—
637C2×D3—21no—
638C2×D3—21no—
639C2×D3—64no—
640C2×D3—64no—
641C2×D3—64no—
642C2×D3—64no—
643C2×D3—64no—
644C2×D3—64no—
645C2×D3—98no—
646C2×D3—92no—
647C2×D3—188no—
648C2×D3—184no—
649C2×D3—184no—
650C2×D3—181no—
651C2×D3—181no—
652C2×D3—364no—
653C2×D3—364no—
654C2×D3—364no—
655C2×D3—3616no—
656C3×C4—28no—
657C3×C4—24no—
658C3×C4—24no—
659C3×C4—21no—
660C3×C4—21no—
661C3×C4—44no—
662C3×C4—64no—
663C3×C4—64no—
664C3×C4—64no—
665C3×C4—181no—
666C3×C4—181no—
667Dic3—21no—
668Dic3—21no—
669Dic3—21no—
670Dic3—64no—
671Dic3—64no—
672Dic3—188no—
673Dic3—184no—
674Dic3—184no—
675Dic3—184no—
676Dic3—181no—
677Dic3—181no—
678Dic3—181no—
679Dic3—364no—
680Dic3—364no—
681C32—24no—
682C32#561311yescharacteristic, complemented
683C32#565714yescomplemented
684C23—31no—
685C23—91no—
686C23—91no—
687C23—271no—
688C23—542no—
689C23—1081no—
690C23—1081no—
691C23C2×D3×C3⋊D311yescharacteristic
692Q8—1081no—
693D4—121no—
694D4—361no—
695D4—361no—
696D4—361no—
697D4—542no—
698D4—542no—
699D4—1081no—
700C2×C4—31no—
701C2×C4—31no—
702C2×C4—31no—
703C2×C4—41no—
704C2×C4—91no—
705C2×C4—91no—
706C2×C4—271no—
707C2×C4—271no—
708C2×C4—271no—
709C2×C4—1081no—
710C2×C4—1081no—
711C2×C4—1081no—
712C2×C4C2×D3×C3⋊D311yescharacteristic
713C2×C4C2×D3×C3⋊D311yescharacteristic
714C2×C3—24no—
715C2×C3—24no—
716C2×C3—24no—
717C2×C3—48no—
718C2×C3—44no—
719C2×C3—41no—
720C2×C3—124no—
721C2×C3—361no—
722C2×C3—361no—
723C2×C3#6430614yes—
724C2×C3#6430714yes—
725C2×C3#6433014yes—
726C2×C3#6436111yescharacteristic
727C2×C3#41×C3⋊D311yescharacteristic
728C2×C3#6436611yescharacteristic
729D3—41no—
730D3—124no—
731D3—124no—
732D3—188no—
733D3—182no—
734D3—368no—
735C22—21no—
736C22—21no—
737C22—21no—
738C22—61no—
739C22—61no—
740C22—61no—
741C22—181no—
742C22—181no—
743C22—181no—
744C22—181no—
745C22—181no—
746C22—181no—
747C22—272no—
748C22—541no—
749C22—541no—
750C22—1084no—
751C22C22×D3×C3⋊D311yescharacteristic
752C4—21no—
753C4—21no—
754C4—61no—
755C4—61no—
756C4—61no—
757C4—181no—
758C4—181no—
759C4—541no—
760C4—541no—
761C4—541no—
762C3—24no—
763C3#1059508914yescomplemented
764C3#1059612811yescharacteristic, complemented
765C2—41no—
766C2—121no—
767C2—361no—
768C2—361no—
769C2—542no—
770C2#1172457811yescharacteristic
771C2#1172458011yescharacteristic
772C2#1172461111yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC22×C33×C4C22
hypercenterC22×C4D3×C3⋊D3
hypocenterC33#538
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C4×#6312C2semidirect
2. C3×#64139C2semidirect
3. C32×#929C2semidirect
4. #11723643C2semidirect
5. #11723631C2semidirect
6. #11723623C2semidirect
7. #11723591C2semidirect
8. #11723541C2semidirect
9. #11723539C2semidirect
10. #11723530C2semidirect
11. #11723488C2semidirect
12. #11723485C2semidirect
13. #11723472C2semidirect
14. #11723433C2semidirect
15. #11723427C2semidirect
19. C22×C33×C4C22semidirect
23. C2×C3×#638C22semidirect
26. C2×#6293C22semidirect
30. C2×Dic3×C3⋊D3C22semidirect
31. #88864C22semidirect
33. #88857C22semidirect
34. C4×C3⋊(C3⋊Dic3)C22semidirect
36. C3×#3752C22semidirect
37. C3×C4⋊(C3⋊Dic3)C22semidirect
38. C32×#217C22semidirect
41. C32×Dic3⋊C4C22semidirect
42. C32×Dic3⋊C4C22semidirect
43. #88807C22semidirect
44. Dic3⋊(C3⋊Dic3)C22semidirect
49. #88803C22semidirect
52. Dic3×C3⋊Dic3C22semidirect
56. #64139D3semidirect
71. C3×#929D3semidirect
120. C22×C32×C4C2×D3semidirect
121. C22×C32×C4C2×D3semidirect
127. C2×#638C2×D3semidirect
164. #3752C2×D3semidirect
166. C4⋊(C3⋊Dic3)C2×D3semidirect
175. C3×#217C2×D3semidirect
181. C3×Dic3⋊C4C2×D3semidirect
182. C3×Dic3⋊C4C2×D3semidirect
231. #929C3⋊D3semidirect
337. C22×C3×C4D32semidirect
338. C22×C3×C4C2×C3⋊D3semidirect
376. #217C2×C3⋊D3semidirect
400. Dic3⋊C4C2×C3⋊D3semidirect
401. Dic3⋊C4C2×C3⋊D3semidirect
488. C33#538semidirect
592. C22×C4D3×C3⋊D3semidirect
682. C32#5613semidirect
683. C32#5657semidirect
763. C3#10595089semidirect
764. C3#10596128semidirect

Maximal subgroups

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

subgroupindex
C4×#63122
C3×#641392
C32×#9292
#117236432
#117236312
#117236232
#117235912
#117235412
#117235392
#117235302
#117234882
#117234852
#117234722
#117234332
#117234272
#105961283
#105950893