Finite Group Databasebeta

← #13177584

Subgroups — #13177584

Order 1728.

1876 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723979C211yesmaximal, characteristic, complemented
2C3×#64146C211yesmaximal, characteristic, complemented
3C32×#935C211yesmaximal, characteristic, complemented
4#11723636C211yesmaximal, characteristic, complemented
5#11723632C211yesmaximal, characteristic, complemented
6#11723624C211yesmaximal, characteristic, complemented
7C3⋊D3×#217C211yesmaximal, characteristic, complemented
8Dic3×#638C211yesmaximal, characteristic, complemented
9#11723597C211yesmaximal, characteristic, complemented
10#11723592C211yesmaximal, characteristic, complemented
11#11723591C211yesmaximal, characteristic, complemented
12#11723483C211yesmaximal, characteristic, complemented
13#11723472C211yesmaximal, characteristic, complemented
14#11723421C211yesmaximal, characteristic, complemented
15#11723408C211yesmaximal, characteristic, complemented
16#10596128—31nomaximal
17#10595185—34nomaximal
18C23×C3×C3⋊D3C2211yescharacteristic
19C2×C33×D4C2211yescharacteristic
20C2×#6312C2211yescharacteristic
21C2×#6312C2211yescharacteristic, complemented
22C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
23C2×C3×#638C2211yescharacteristic
24C2×C3×#638C2211yescharacteristic
25C22×C32×Dic3C2211yescharacteristic, complemented
26C2×#6293C2211yescharacteristic, complemented
27C2×#6292C2211yescharacteristic
28C2×#6292C2211yescharacteristic
29C2×Dic3×C3⋊D3C2211yescharacteristic
30C2×Dic3×C3⋊D3C2211yescharacteristic
31#88864C2211yescharacteristic
32#88864C2211yescharacteristic, complemented
33C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic, complemented
34C3×#3757C2211yescharacteristic
35C3×#3752C2211yescharacteristic
36C3×#3752C2211yescharacteristic
37C32×#217C2211yescharacteristic
38C32×#217C2211yescharacteristic
39C32×#217C2211yescharacteristic, complemented
40C32×Dic3⋊C4C2211yescharacteristic, complemented
41C32×Dic3⋊C4C2211yescharacteristic, complemented
42#88807C2211yescharacteristic, complemented
43#88806C2211yescharacteristic, complemented
44Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
45#88804C2211yescharacteristic, complemented
46#88804C2211yescharacteristic, complemented
47#88803C2211yescharacteristic
48#88803C2211yescharacteristic
49#88803C2211yescharacteristic
50#88803C2211yescharacteristic
51Dic3×C3⋊Dic3C2211yescharacteristic, complemented
52Dic3×C3⋊Dic3C2211yescharacteristic, complemented
53C32×#123—31no—
54#64147—31no—
55#64147—34no—
56#64147—64no—
57#64146D311yescharacteristic, complemented
58#64139—31no—
59C4×#638—31no—
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×#937—34no—
71C3×#935D314yescomplemented
72#63978—34no—
73#63977—34no—
74Dic3×#67—34no—
75#63971—34no—
76D3×#217—34no—
77#63959—34no—
78#63956—34no—
79#63953—34no—
80#63893—34no—
81#63881—34no—
82#63861—34no—
83#63853—34no—
84C23×C33C2311yescharacteristic
85C23×C33C2311yescharacteristic
86C22×C3⋊(C3⋊D3)C2311yescharacteristic
87C22×C3×C3⋊D3—22no—
88C22×C3×C3⋊D3—41no—
89C22×C3×C3⋊D3—41no—
90C22×C3×C3⋊D3C2311yescharacteristic
91C22×C3×C3⋊D3C2311yescharacteristic
92C33×D4—41no—
93C2×C33×C4C2311yescharacteristic
94#6312—41no—
95#6312—41no—
96C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
97C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
98C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
99C4×C3⋊(C3⋊D3)—41no—
100C3×#638—22no—
101C3×#638—41no—
102C2×C3×C3⋊Dic3C2311yescharacteristic
103C2×C3×C3⋊Dic3C2311yescharacteristic
104C2×C32×Dic3—41no—
105C2×C32×Dic3C2311yescharacteristic
106C2×C32×Dic3C2311yescharacteristic
107C2×C32×Dic3C2311yescharacteristic
108C2×C32×Dic3C2311yescharacteristic
109#6293—41no—
110#6292—22no—
111#6292—41no—
112Dic3×C3⋊D3—41no—
113Dic3×C3⋊D3—41no—
114#5657—94no—
115#5593—91no—
116C23×C3⋊D3C2×D311yescharacteristic
117C23×C3×D3—34no—
118C2×C32×D4—24no—
119C2×C32×D4C2×D314yes—
120C2×C32×D4C2×D311yescharacteristic
121C22×C32×C4—31no—
122C2×#638—31no—
123C2×#638—31no—
124C2×#638—34no—
125C2×#638—34no—
126C2×#638—64no—
127C2×#638—64no—
128C2×#638C2×D311yescharacteristic
129C2×#638C2×D311yescharacteristic
130C2×C4⋊(C3⋊D3)—31no—
131C2×C4⋊(C3⋊D3)—31no—
132C2×C4×C3⋊D3—31no—
133C2×C4×C3⋊D3—31no—
134C2×C4×C3⋊D3—31no—
135C2×C4×C3⋊D3—34no—
136C2×C4×C3⋊D3—64no—
137C2×#634—31no—
138C2×C3×#67—34no—
139C2×C3×#67—34no—
140C22×C3×Dic3C2×D314yescomplemented
141C2×#627—34no—
142C2×#626—34no—
143C2×#626—34no—
144C2×D3×Dic3—34no—
145C2×D3×Dic3—34no—
146C32×C4⋊C4—31no—
147C32×C4⋊C4—31no—
148C32×C22⋊C4—31no—
149C32×C22⋊C4—31no—
150C32×C22⋊C4—31no—
151#3757—31no—
152#3757—31no—
153#3757—34no—
154#3757—34no—
155#3757—64no—
156#3757—64no—
157#3757C2×D311yescharacteristic
158#3752—31no—
159#3752—31no—
160#3752—31no—
161#3752—31no—
162#3752—31no—
163#3752—31no—
164#3752C2×D311yescharacteristic
165#3752C2×D311yescharacteristic
166C4⋊(C3⋊Dic3)—31no—
167C4⋊(C3⋊Dic3)—34no—
168C4⋊(C3⋊Dic3)—31no—
169C4⋊(C3⋊Dic3)—64no—
170#3750—31no—
171#3750—31no—
172C4×C3⋊Dic3—31no—
173C4×C3⋊Dic3—31no—
174C3×#217—34no—
175C3×#217C2×D314yes—
176C3×#217C2×D314yes—
177C3×#217C2×D314yescomplemented
178C3×(C2×D3)⋊C4—34no—
179C3×(C2×D3)⋊C4—34no—
180C3×Dic3⋊C4C2×D314yescomplemented
181C3×Dic3⋊C4C2×D314yescomplemented
182#3724—34no—
183Dic3⋊Dic3—34no—
184Dic3⋊Dic3—34no—
185#3722—34no—
186#3722—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×C33—21no—
194C22×C33—21no—
195C22×C33—21no—
196C22×C33—21no—
197C22×C33—21no—
198C22×C33—21no—
199C22×C33C2411yescharacteristic
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×C3×C3⋊D3—21no—
207C2×C3×C3⋊D3—21no—
208C2×C3×C3⋊D3—44no—
209C2×C3×C3⋊D3#4112yes—
210C33×C4—21no—
211C3⋊(C3⋊Dic3)—21no—
212C3⋊(C3⋊Dic3)—21no—
213C3⋊(C3⋊Dic3)—21no—
214C3×C3⋊Dic3—21no—
215C3×C3⋊Dic3—21no—
216C32×Dic3—21no—
217C32×Dic3—21no—
218C32×Dic3—21no—
219C32×Dic3—21no—
220C3×#123—34no—
221C3×#120—91no—
222#953—91no—
223C2×#217—91no—
224#939—91no—
225#939—91no—
226#938—94no—
227#938—91no—
228#938—184no—
229#937—34no—
230#936—91no—
231#935C3⋊D311yescharacteristic, complemented
232D4×Dic3—91no—
233#930—94no—
234C4×#67—94no—
235#898—94no—
236#897—94no—
237#894—94no—
238#893—94no—
239#885—94no—
240#885—94no—
241#885—91no—
242#884—94no—
243#883—91no—
244#882—94no—
245#67⋊C4—91no—
246D3×C22⋊C4—94no—
247#879—94no—
248#879—91no—
249#879—91no—
250#878—91no—
251C23×C32—24no—
252C23×C32—24no—
253C23×C32C22×D314yes—
254C23×C32C22×D314yes—
255C23×C32C22×D311yescharacteristic
256C23×C32C22×D311yescharacteristic
257C22×C3⋊D3—22no—
258C22×C3⋊D3—31no—
259C22×C3⋊D3—34no—
260C22×C3⋊D3—41no—
261C22×C3⋊D3—41no—
262C22×C3⋊D3—64no—
263C22×C3⋊D3C22×D311yescharacteristic
264C22×C3⋊D3C22×D311yescharacteristic
265C22×C3×D3—34no—
266C22×C3×D3—34no—
267C22×C3×D3—68no—
268C22×C3×D3—124no—
269C22×C3×D3—124no—
270C32×D4—41no—
271C32×D4—44no—
272C32×D4—48no—
273C2×C32×C4—24no—
274C2×C32×C4—31no—
275C2×C32×C4—31no—
276C2×C32×C4—31no—
277C2×C32×C4—31no—
278C2×C32×C4—121no—
279C2×C32×C4C22×D314yes—
280C2×C32×C4C22×D311yescharacteristic
281#638—22no—
282#638—41no—
283#638—121no—
284#638—121no—
285#638—124no—
286#638—124no—
287#638—128no—
288#638—128no—
289C2×C3⋊Dic3—31no—
290C2×C3⋊Dic3—31no—
291C2×C3⋊Dic3—31no—
292C2×C3⋊Dic3—34no—
293C2×C3⋊Dic3—34no—
294C2×C3⋊Dic3—34no—
295C2×C3⋊Dic3—64no—
296C2×C3⋊Dic3—64no—
297C2×C3⋊Dic3—64no—
298C2×C3⋊Dic3C22×D311yescharacteristic
299C2×C3⋊Dic3C22×D311yescharacteristic
300C4⋊(C3⋊D3)—62no—
301C4⋊(C3⋊D3)—121no—
302C4×C3⋊D3—121no—
303C4×C3⋊D3—124no—
304C4×C3⋊D3—121no—
305C4×C3⋊D3—121no—
306C4×C3⋊D3—128no—
307#634—121no—
308C3×#67—68no—
309C3×#67—124no—
310C2×C3×Dic3—34no—
311C2×C3×Dic3—34no—
312C2×C3×Dic3—44no—
313C2×C3×Dic3C22×D314yes—
314C2×C3×Dic3C22×D314yes—
315C2×C3×Dic3C22×D314yes—
316C2×C3×Dic3C22×D314yes—
317#627—124no—
318#626—68no—
319#626—124no—
320D3×Dic3—124no—
321D3×Dic3—124no—
322#538—271noSylow
323C2×C33—41no—
324C2×C33—41no—
325C2×C33C2×#4111yescharacteristic
326C2×C33H(5,𝔽2)11yescharacteristic
327C2×C33H(5,𝔽2)11yescharacteristic
328C3⋊(C3⋊D3)—41no—
329C3×C3⋊D3—22no—
330C3×C3⋊D3—41no—
331C24×C3—91no—
332C23×D3—34no—
333C2×C3×D4—24no—
334C2×C3×D4—91no—
335C2×C3×D4—91no—
336C2×C3×D4D3214yes—
337C2×C3×D4C2×C3⋊D311yescharacteristic
338C22×C3×C4—34no—
339C2×#67—34no—
340C2×#67—34no—
341C2×#67—94no—
342C2×#67—94no—
343C2×#67—91no—
344C2×#67—91no—
345C2×#67—91no—
346C2×#67—91no—
347C2×#67—184no—
348C2×#67—184no—
349C22×Dic3—91no—
350C22×Dic3—91no—
351C22×Dic3C2×C3⋊D311yescharacteristic, complemented
352C2×D12—94no—
353C2×D12—94no—
354C2×C4×D3—94no—
355C2×C4×D3—94no—
356C2×C4×D3—94no—
357C2×C4×D3—91no—
358C2×C4×D3—184no—
359C2×Dic6—94no—
360C2×Dic6—91no—
361C3×C4⋊C4—34no—
362C3×C4⋊C4—34no—
363C3×C22⋊C4—34no—
364C3×C22⋊C4—34no—
365C3×C22⋊C4—34no—
366C3×C22⋊C4—91no—
367C3×C22⋊C4—91no—
368C3×C22⋊C4—91no—
369#217—34no—
370#217—94no—
371#217—94no—
372#217—91no—
373#217—91no—
374#217—91no—
375#217—91no—
376#217—91no—
377#217—91no—
378#217—184no—
379#217—184no—
380#217C2×C3⋊D311yescharacteristic
381#217C2×C3⋊D311yescharacteristic
382#217C2×C3⋊D311yescharacteristic, complemented
383(C2×D3)⋊C4—34no—
384(C2×D3)⋊C4—34no—
385(C2×D3)⋊C4—94no—
386(C2×D3)⋊C4—94no—
387(C2×D3)⋊C4—94no—
388(C2×D3)⋊C4—94no—
389(C2×D3)⋊C4—94no—
390(C2×D3)⋊C4—94no—
391(C2×D3)⋊C4—91no—
392(C2×D3)⋊C4—91no—
393C4⋊Dic3—94no—
394C4⋊Dic3—94no—
395C4⋊Dic3—91no—
396C4⋊Dic3—91no—
397C4⋊Dic3—184no—
398Dic3⋊C4—94no—
399Dic3⋊C4—94no—
400Dic3⋊C4—91no—
401Dic3⋊C4—91no—
402Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
403Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
404C4×Dic3—94no—
405C4×Dic3—94no—
406C4×Dic3—91no—
407C4×Dic3—91no—
408C22×C32—21no—
409C22×C32—21no—
410C22×C32—21no—
411C22×C32—21no—
412C22×C32—21no—
413C22×C32—21no—
414C22×C32—24no—
415C22×C32—24no—
416C22×C32—24no—
417C22×C32—24no—
418C22×C32—24no—
419C22×C32—24no—
420C22×C32—24no—
421C22×C32—44no—
422C22×C32—44no—
423C22×C32—44no—
424C22×C32—44no—
425C22×C32—44no—
426C22×C32—44no—
427C22×C32C23×D314yes—
428C22×C32C23×D311yescharacteristic
429C2×C3⋊D3—21no—
430C2×C3⋊D3—21no—
431C2×C3⋊D3—21no—
432C2×C3⋊D3—21no—
433C2×C3⋊D3—21no—
434C2×C3⋊D3—44no—
435C2×C3⋊D3—68no—
436C2×C3⋊D3—61no—
437C2×C3⋊D3—61no—
438C2×C3⋊D3—61no—
439C2×C3⋊D3—64no—
440C2×C3⋊D3—64no—
441C2×C3⋊D3—64no—
442C2×C3⋊D3—124no—
443C2×C3⋊D3—124no—
444C2×C3⋊D3#23712yes—
445C2×C3×D3—38no—
446C2×C3×D3—64no—
447C2×C3×D3—64no—
448C2×C3×D3—64no—
449C2×C3×D3—64no—
450C2×C3×D3—64no—
451C2×C3×D3—1216no—
452C32×C4—28no—
453C32×C4—24no—
454C32×C4—21no—
455C32×C4—61no—
456C32×C4—61no—
457C32×C4—61no—
458C32×C4—61no—
459C3⋊Dic3—21no—
460C3⋊Dic3—21no—
461C3⋊Dic3—61no—
462C3⋊Dic3—61no—
463C3⋊Dic3—61no—
464C3⋊Dic3—64no—
465C3⋊Dic3—64no—
466C3⋊Dic3—64no—
467C3⋊Dic3—124no—
468C3⋊Dic3—124no—
469C3⋊Dic3—124no—
470C3×Dic3—24no—
471C3×Dic3—24no—
472C3×Dic3—24no—
473C3×Dic3—24no—
474C3×Dic3—64no—
475C3×Dic3—64no—
476#126—271no—
477#126—271no—
478#124—271no—
479#124—271no—
480#123—31no—
481#123—271no—
482C22⋊Q8—271no—
483#121—271no—
484#121—271no—
485#121—271no—
486#120—91no—
487#120—271no—
488C4×D4—271no—
489C4×D4—271no—
490C2×C22⋊C4—271no—
491C33#53811yescharacteristic, complemented, Sylow
492C23×C3—24no—
493C23×C3—24no—
494C23×C3—91no—
495C23×C3—91no—
496C23×C3—182no—
497C23×C3—361no—
498C23×C3—361no—
499C23×C3C2×D3214yes—
500C23×C3C2×D3214yes—
501C23×C3C22×C3⋊D311yescharacteristic
502C23×C3C22×C3⋊D311yescharacteristic
503C22×D3—34no—
504C22×D3—34no—
505C22×D3—68no—
506C22×D3—94no—
507C22×D3—91no—
508C22×D3—124no—
509C22×D3—124no—
510C22×D3—184no—
511C3×D4—44no—
512C3×D4—41no—
513C3×D4—48no—
514C3×D4—182no—
515C3×D4—361no—
516C2×C3×C4—24no—
517C2×C3×C4—34no—
518C2×C3×C4—34no—
519C2×C3×C4—34no—
520C2×C3×C4—34no—
521C2×C3×C4—91no—
522C2×C3×C4—91no—
523C2×C3×C4—124no—
524C2×C3×C4C2×D3214yes—
525C2×C3×C4C22×C3⋊D311yescharacteristic
526#67—68no—
527#67—124no—
528#67—182no—
529#67—361no—
530#67—364no—
531#67—364no—
532#67—361no—
533#67—361no—
534#67—368no—
535#67—368no—
536C2×Dic3—34no—
537C2×Dic3—34no—
538C2×Dic3—41no—
539C2×Dic3—94no—
540C2×Dic3—94no—
541C2×Dic3—94no—
542C2×Dic3—91no—
543C2×Dic3—91no—
544C2×Dic3—91no—
545C2×Dic3—184no—
546C2×Dic3—184no—
547C2×Dic3—184no—
548C2×Dic3—361no—
549C2×Dic3—361no—
550C2×Dic3C22×C3⋊D311yescharacteristic
551C2×Dic3C22×C3⋊D311yescharacteristic
552C2×Dic3C22×C3⋊D311yescharacteristic
553C2×Dic3C22×C3⋊D311yescharacteristic
554D12—188no—
555D12—364no—
556C4×D3—364no—
557C4×D3—361no—
558C4×D3—364no—
559C4×D3—364no—
560C4×D3—368no—
561Dic6—361no—
562Dic6—364no—
563C2×C32—24no—
564C2×C32—24no—
565C2×C32—24no—
566C2×C32—41no—
567C2×C32—41no—
568C2×C32—44no—
569C2×C32—44no—
570C2×C32—84no—
571C2×C32—84no—
572C2×C32C2×#23711yescharacteristic
573C2×C32#100414yes—
574C2×C32#100411yescharacteristic
575C2×C32#100411yescharacteristic
576C2×C32D3×#4114yes—
577C2×C32#100914yes—
578C3⋊D3—22no—
579C3⋊D3—41no—
580C3⋊D3—128no—
581C3⋊D3—124no—
582C3⋊D3—121no—
583C3×D3—68no—
584C3×D3—124no—
585C24—91no—
586C2×Q8—271no—
587C2×D4—91no—
588C2×D4—91no—
589C2×D4—271no—
590C2×D4—271no—
591C2×D4—271no—
592C2×D4—271no—
593C2×D4D3×C3⋊D311yescharacteristic
594C22×C4—31no—
595C22×C4—271no—
596C22×C4—271no—
597C22×C4—271no—
598C4⋊C4—31no—
599C4⋊C4—31no—
600C4⋊C4—271no—
601C4⋊C4—271no—
602C4⋊C4—271no—
603C4⋊C4—271no—
604C22⋊C4—31no—
605C22⋊C4—31no—
606C22⋊C4—31no—
607C22⋊C4—91no—
608C22⋊C4—91no—
609C22⋊C4—91no—
610C22⋊C4—271no—
611C22⋊C4—271no—
612C22⋊C4—271no—
613C22⋊C4—271no—
614C22⋊C4—271no—
615C22⋊C4—271no—
616C22⋊C4—271no—
617C22⋊C4—271no—
618C42—271no—
619C42—271no—
620C22×C3—24no—
621C22×C3—24no—
622C22×C3—24no—
623C22×C3—24no—
624C22×C3—24no—
625C22×C3—24no—
626C22×C3—21no—
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—21no—
630C22×C3—21no—
631C22×C3—21no—
632C22×C3—24no—
633C22×C3—44no—
634C22×C3—44no—
635C22×C3—44no—
636C22×C3—44no—
637C22×C3—44no—
638C22×C3—44no—
639C22×C3—92no—
640C22×C3—181no—
641C22×C3—181no—
642C22×C3—181no—
643C22×C3—181no—
644C22×C3—181no—
645C22×C3—364no—
646C22×C3C22×D3214yes—
647C22×C3C23×C3⋊D311yescharacteristic
648C2×D3—38no—
649C2×D3—64no—
650C2×D3—64no—
651C2×D3—64no—
652C2×D3—64no—
653C2×D3—64no—
654C2×D3—1216no—
655C2×D3—188no—
656C2×D3—184no—
657C2×D3—184no—
658C2×D3—184no—
659C2×D3—181no—
660C2×D3—181no—
661C2×D3—181no—
662C2×D3—364no—
663C2×D3—364no—
664C3×C4—28no—
665C3×C4—24no—
666C3×C4—21no—
667C3×C4—64no—
668C3×C4—64no—
669C3×C4—64no—
670C3×C4—64no—
671C3×C4—181no—
672C3×C4—181no—
673Dic3—21no—
674Dic3—21no—
675Dic3—21no—
676Dic3—21no—
677Dic3—64no—
678Dic3—64no—
679Dic3—184no—
680Dic3—184no—
681Dic3—184no—
682Dic3—181no—
683Dic3—181no—
684Dic3—181no—
685Dic3—364no—
686Dic3—364no—
687Dic3—364no—
688C32—24no—
689C32#559311yescharacteristic, complemented
690C32#565714yescomplemented
691C23—91no—
692C23—91no—
693C23—182no—
694C23—271no—
695C23—361no—
696C23—361no—
697C23C2×D3×C3⋊D311yescharacteristic
698C23C2×D3×C3⋊D311yescharacteristic
699Q8—1081no—
700D4—41no—
701D4—182no—
702D4—361no—
703D4—542no—
704D4—1081no—
705D4—1081no—
706D4—1081no—
707C2×C4—31no—
708C2×C4—31no—
709C2×C4—31no—
710C2×C4—31no—
711C2×C4—91no—
712C2×C4—91no—
713C2×C4—121no—
714C2×C4—271no—
715C2×C4—271no—
716C2×C4—271no—
717C2×C4—1081no—
718C2×C4—1081no—
719C2×C4—1081no—
720C2×C4C2×D3×C3⋊D311yescharacteristic
721C2×C3—24no—
722C2×C3—24no—
723C2×C3—24no—
724C2×C3—41no—
725C2×C3—41no—
726C2×C3—44no—
727C2×C3—44no—
728C2×C3—84no—
729C2×C3—84no—
730C2×C3—182no—
731C2×C3—361no—
732C2×C3D3×#23714yes—
733C2×C3#6431414yes—
734C2×C3#6433014yes—
735C2×C3#6436111yescharacteristic
736C2×C3#41×C3⋊D311yescharacteristic
737C2×C3#6436611yescharacteristic
738D3—68no—
739D3—124no—
740D3—368no—
741D3—361no—
742D3—364no—
743C22—21no—
744C22—21no—
745C22—21no—
746C22—21no—
747C22—21no—
748C22—21no—
749C22—92no—
750C22—181no—
751C22—181no—
752C22—181no—
753C22—181no—
754C22—181no—
755C22—364no—
756C22—541no—
757C22—541no—
758C22—541no—
759C22C22×D3×C3⋊D311yescharacteristic
760C4—21no—
761C4—61no—
762C4—61no—
763C4—61no—
764C4—61no—
765C4—181no—
766C4—181no—
767C4—541no—
768C4—541no—
769C4—541no—
770C3—24no—
771C3#1059518514yescomplemented
772C3#1059612811yescharacteristic, complemented
773C2—41no—
774C2—41no—
775C2—182no—
776C2—361no—
777C2—1081no—
778C2C3⋊D3×#23711yescharacteristic
779C2#1172458911yescharacteristic
780C2#1172461111yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC2×C33×D4C22
hypercenterC2×D4D3×C3⋊D3
hypocenterC33#538
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. #11723979C2semidirect
2. C3×#64146C2semidirect
3. C32×#935C2semidirect
4. #11723636C2semidirect
5. #11723632C2semidirect
6. #11723624C2semidirect
7. C3⋊D3×#217C2semidirect
8. Dic3×#638C2semidirect
9. #11723597C2semidirect
10. #11723592C2semidirect
11. #11723591C2semidirect
12. #11723483C2semidirect
13. #11723472C2semidirect
14. #11723421C2semidirect
15. #11723408C2semidirect
21. C2×#6312C22semidirect
22. C2×C4×C3⋊(C3⋊D3)C22semidirect
25. C22×C32×Dic3C22semidirect
26. C2×#6293C22semidirect
32. #88864C22semidirect
33. C4⋊(C3⋊(C3⋊Dic3))C22semidirect
39. C32×#217C22semidirect
40. C32×Dic3⋊C4C22semidirect
41. C32×Dic3⋊C4C22semidirect
42. #88807C22semidirect
43. #88806C22semidirect
44. Dic3⋊(C3⋊Dic3)C22semidirect
45. #88804C22semidirect
46. #88804C22semidirect
51. Dic3×C3⋊Dic3C22semidirect
52. Dic3×C3⋊Dic3C22semidirect
57. #64146D3semidirect
71. C3×#935D3semidirect
140. C22×C3×Dic3C2×D3semidirect
177. C3×#217C2×D3semidirect
180. C3×Dic3⋊C4C2×D3semidirect
181. C3×Dic3⋊C4C2×D3semidirect
231. #935C3⋊D3semidirect
351. C22×Dic3C2×C3⋊D3semidirect
382. #217C2×C3⋊D3semidirect
402. Dic3⋊C4C2×C3⋊D3semidirect
403. Dic3⋊C4C2×C3⋊D3semidirect
491. C33#538semidirect
689. C32#5593semidirect
690. C32#5657semidirect
771. C3#10595185semidirect
772. C3#10596128semidirect

Maximal subgroups

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

subgroupindex
#117239792
C3×#641462
C32×#9352
#117236362
#117236322
#117236242
C3⋊D3×#2172
Dic3×#6382
#117235972
#117235922
#117235912
#117234832
#117234722
#117234212
#117234082
#105961283
#105951853