Finite Group Databasebeta

← #13176581

Subgroups — #13176581

Order 1728.

1800 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723935C211yesmaximal, characteristic, complemented
2C3×#64106C211yesmaximal, characteristic, complemented
3C32×#898C211yesmaximal, characteristic, complemented
4#11723542C211yesmaximal, characteristic
5#11723539C211yesmaximal, characteristic, complemented
6C3⋊D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
7#11723521C211yesmaximal, characteristic, complemented
8#11723512C211yesmaximal, characteristic, complemented
9#11723493C211yesmaximal, characteristic, complemented
10#11723489C211yesmaximal, characteristic, complemented
11#11723484C211yesmaximal, characteristic, complemented
12#11723464C211yesmaximal, characteristic, complemented
13#11723427C211yesmaximal, characteristic, complemented
14#11723422C211yesmaximal, characteristic, complemented
15#11723413C211yesmaximal, characteristic, complemented
16#10596176—31nomaximal
17#10594654—34nomaximal
18C22×D3×C3⋊D3C2211yescharacteristic
19C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic
20C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
21C2×C3×C4×C3⋊D3C2211yescharacteristic
22C2×C3×#634C2211yescharacteristic, complemented
23C2×#6292C2211yescharacteristic
24C2×#6291C2211yescharacteristic
25C2×#6289C2211yescharacteristic
26C2×#6289C2211yescharacteristic, complemented
27C2×Dic3×C3⋊D3C2211yescharacteristic
28C33×C4⋊C4C2211yescharacteristic, complemented
29#88859C2211yescharacteristic
30#88859C2211yescharacteristic, complemented
31#88859C2211yescharacteristic, complemented
32#88857C2211yescharacteristic, complemented
33C3×#3752C2211yescharacteristic
34C3×#3752C2211yescharacteristic
35C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
36C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
37C32×(C2×D3)⋊C4C2211yescharacteristic
38C32×(C2×D3)⋊C4C2211yescharacteristic
39C32×(C2×D3)⋊C4C2211yescharacteristic
40C32×C4⋊Dic3C2211yescharacteristic, complemented
41C32×Dic3⋊C4C2211yescharacteristic, complemented
42C32×C4×Dic3C2211yescharacteristic, complemented
43#88807C2211yescharacteristic, complemented
44#88806C2211yescharacteristic, complemented
45#88804C2211yescharacteristic
46#88804C2211yescharacteristic
47#88804C2211yescharacteristic, complemented
48#88803C2211yescharacteristic
49(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
50(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
51Dic3×C3⋊Dic3C2211yescharacteristic, complemented
52Dic3×C3⋊Dic3C2211yescharacteristic, complemented
53C32×#126—31no—
54#64106D311yescharacteristic, complemented
55#64105—31no—
56#64103—31no—
57#64103—31no—
58#64103—34no—
59#64103—64no—
60#64102—31no—
61#64101—31no—
62#64094—31no—
63#64092—31no—
64#64091—31no—
65C22⋊C4×C3⋊D3—31no—
66C22⋊C4×C3⋊D3—31no—
67#64088—31no—
68C4×C4⋊(C3⋊D3)—31no—
69#64081—31no—
70C3×#898D314yescomplemented
71C3×#897—34no—
72#63923—34no—
73#63921—34no—
74D3×(C2×D3)⋊C4—34no—
75#63907—34no—
76#63904—34no—
77#63894—34no—
78#63890—34no—
79#63888—34no—
80#63877—34no—
81#63858—34no—
82#63854—34no—
83#63849—34no—
84C22×C3⋊(C3⋊D3)C2311yescharacteristic
85C22×C3⋊(C3⋊D3)C2311yescharacteristic
86C22×C3×C3⋊D3C2311yescharacteristic
87C22×C32×D3C2311yescharacteristic
88C2×D3×C3⋊D3—22no—
89C2×D3×C3⋊D3—22no—
90C2×D3×C3⋊D3—41no—
91C2×C33×C4C2311yescharacteristic
92C2×C33×C4C2311yescharacteristic
93C2×C33×C4C2311yescharacteristic
94C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
95C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
96C4⋊(C3⋊(C3⋊D3))—22no—
97C4×C3⋊(C3⋊D3)—22no—
98C2×C3×C3⋊Dic3C2311yescharacteristic
99C2×C3×C3⋊Dic3C2311yescharacteristic
100C2×C3×C3⋊Dic3C2311yescharacteristic
101C3×C4×C3⋊D3—41no—
102C3×#634—41no—
103C2×C32×Dic3C2311yescharacteristic
104C2×C32×Dic3C2311yescharacteristic
105C2×C32×Dic3C2311yescharacteristic
106#6292—22no—
107#6291—41no—
108#6289—41no—
109#6289—41no—
110Dic3×C3⋊D3—22no—
111#5705—94no—
112#5637—91no—
113C23×C3⋊D3—31no—
114C22×D32—34no—
115C2×#638—31no—
116C2×C4⋊(C3⋊D3)—31no—
117C2×C4⋊(C3⋊D3)—31no—
118C2×C4⋊(C3⋊D3)—34no—
119C2×C4⋊(C3⋊D3)—64no—
120C2×C4×C3⋊D3—31no—
121C2×C4×C3⋊D3—31no—
122C2×C4×C3⋊D3—34no—
123C2×C4×C3⋊D3—31no—
124C2×C4×C3⋊D3—31no—
125C2×C4×C3⋊D3—64no—
126C2×C4×C3⋊D3C2×D311yescharacteristic
127C2×#634C2×D311yescharacteristic, complemented
128C2×C3×C4×D3—34no—
129C2×C3×Dic6—34no—
130C2×#626—34no—
131C2×#626—34no—
132C2×#624—34no—
133C2×#624—34no—
134C2×D3×Dic3—34no—
135C32×C4⋊C4—24no—
136C32×C4⋊C4—31no—
137C32×C4⋊C4—31no—
138C32×C4⋊C4C2×D314yescomplemented
139C32×C4⋊C4C2×D311yescharacteristic, complemented
140C32×C22⋊C4—31no—
141C32×C22⋊C4—31no—
142C32×C22⋊C4—31no—
143C32×C42—31no—
144#3757—31no—
145#3757—31no—
146#3752—31no—
147#3752—31no—
148#3752—31no—
149#3752—31no—
150#3752—34no—
151#3752—34no—
152#3752—34no—
153#3752—31no—
154#3752—31no—
155#3752—31no—
156#3752—64no—
157#3752—64no—
158#3752—64no—
159#3752C2×D311yescharacteristic
160#3752C2×D311yescharacteristic
161C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
162C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
163#3750—31no—
164#3750—34no—
165#3750—31no—
166#3750—31no—
167#3750—64no—
168C4×C3⋊Dic3—31no—
169C4×C3⋊Dic3—31no—
170C3×(C2×D3)⋊C4—34no—
171C3×(C2×D3)⋊C4—34no—
172C3×(C2×D3)⋊C4C2×D314yes—
173C3×(C2×D3)⋊C4C2×D314yes—
174C3×(C2×D3)⋊C4C2×D314yes—
175C3×C4⋊Dic3—34no—
176C3×C4⋊Dic3—34no—
177C3×C4⋊Dic3C2×D314yescomplemented
178C3×Dic3⋊C4C2×D314yescomplemented
179C3×C4×Dic3C2×D314yescomplemented
180#3724—34no—
181Dic3⋊Dic3—34no—
182#3722—34no—
183#3722—34no—
184#3722—34no—
185(C2×D3)⋊Dic3—34no—
186(C2×D3)⋊Dic3—34no—
187(C2×D3)⋊Dic3—34no—
188Dic32—34no—
189Dic32—34no—
190C22×C33C2411yescharacteristic
191C2×C3⋊(C3⋊D3)—21no—
192C2×C3⋊(C3⋊D3)—21no—
193C2×C3⋊(C3⋊D3)—21no—
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#4112yes—
200C2×C32×D3—21no—
201C2×C32×D3—21no—
202C2×C32×D3—21no—
203D3×C3⋊D3—44no—
204C33×C4—21no—
205C33×C4—21no—
206C33×C4—21no—
207C3⋊(C3⋊Dic3)—21no—
208C3⋊(C3⋊Dic3)—21no—
209C3×C3⋊Dic3—21no—
210C3×C3⋊Dic3—21no—
211C3×C3⋊Dic3—21no—
212C32×Dic3—21no—
213C32×Dic3—21no—
214C32×Dic3—21no—
215C3×#126—34no—
216C3×C22⋊Q8—91no—
217#947—91no—
218#946—91no—
219C4×#67—91no—
220C2×(C2×D3)⋊C4—91no—
221#898—91no—
222#898C3⋊D311yescharacteristic, complemented
223#897—34no—
224#896—94no—
225#894—94no—
226#894—94no—
227#894—91no—
228#894—91no—
229#894—184no—
230#893—94no—
231#893—91no—
232#892—94no—
233#892—91no—
234#886—91no—
235#885—94no—
236#883—94no—
237#882—94no—
238#882—91no—
239D3×C22⋊C4—94no—
240D3×C22⋊C4—94no—
241D3×C22⋊C4—91no—
242#879—94no—
243#877—91no—
244C4×D12—94no—
245#872—94no—
246C23×C32—31no—
247C22×C3⋊D3—31no—
248C22×C3⋊D3—31no—
249C22×C3⋊D3—34no—
250C22×C3⋊D3—34no—
251C22×C3⋊D3—64no—
252C22×C3⋊D3—64no—
253C22×C3⋊D3—62no—
254C22×C3⋊D3—62no—
255C22×C3⋊D3—121no—
256C22×C3⋊D3C22×D311yescharacteristic
257C22×C3×D3—34no—
258C22×C3×D3C22×D314yes—
259C2×D32—68no—
260C2×D32—68no—
261C2×D32—124no—
262C2×C32×C4—24no—
263C2×C32×C4—24no—
264C2×C32×C4—24no—
265C2×C32×C4—31no—
266C2×C32×C4—31no—
267C2×C32×C4—31no—
268C2×C32×C4C22×D314yes—
269C2×C32×C4C22×D314yes—
270C2×C32×C4C22×D314yes—
271C2×C32×C4C22×D311yescharacteristic
272C2×C32×C4C22×D311yescharacteristic
273C2×C32×C4C22×D311yescharacteristic
274#638—121no—
275C2×C3⋊Dic3—31no—
276C2×C3⋊Dic3—31no—
277C2×C3⋊Dic3—34no—
278C2×C3⋊Dic3—34no—
279C2×C3⋊Dic3—64no—
280C2×C3⋊Dic3—64no—
281C2×C3⋊Dic3C22×D311yescharacteristic
282C2×C3⋊Dic3C22×D311yescharacteristic
283C2×C3⋊Dic3C22×D311yescharacteristic
284C4⋊(C3⋊D3)—62no—
285C4⋊(C3⋊D3)—62no—
286C4⋊(C3⋊D3)—68no—
287C4⋊(C3⋊D3)—128no—
288C4×C3⋊D3—41no—
289C4×C3⋊D3—62no—
290C4×C3⋊D3—62no—
291C4×C3⋊D3—68no—
292C4×C3⋊D3—128no—
293C4×C3⋊D3—121no—
294C4×C3⋊D3—121no—
295#634—41no—
296C2×C3×Dic3—34no—
297C2×C3×Dic3—34no—
298C2×C3×Dic3—34no—
299C2×C3×Dic3C22×D314yes—
300C2×C3×Dic3C22×D314yes—
301C2×C3×Dic3C22×D314yes—
302C3×C4×D3—124no—
303C3×Dic6—124no—
304#626—68no—
305#626—124no—
306#624—124no—
307#624—124no—
308D3×Dic3—68no—
309#551—271noSylow
310C2×C33C2×#4111yescharacteristic
311C2×C33C2×#4111yescharacteristic
312C2×C33H(5,𝔽2)11yescharacteristic
313C3⋊(C3⋊D3)—22no—
314C3⋊(C3⋊D3)—41no—
315C3×C3⋊D3—22no—
316C32×D3—41no—
317C23×D3—94no—
318C23×D3—91no—
319C2×C3×Q8—91no—
320C22×C3×C4—91no—
321C2×#67—94no—
322C2×#67—91no—
323C22×Dic3—91no—
324C2×D12—94no—
325C2×D12—94no—
326C2×D12—91no—
327C2×D12—91no—
328C2×D12—184no—
329C2×C4×D3—34no—
330C2×C4×D3—94no—
331C2×C4×D3—94no—
332C2×C4×D3—91no—
333C2×C4×D3—94no—
334C2×C4×D3—94no—
335C2×C4×D3—91no—
336C2×C4×D3—91no—
337C2×C4×D3—184no—
338C2×Dic6—34no—
339C3×C4⋊C4—24no—
340C3×C4⋊C4—34no—
341C3×C4⋊C4—34no—
342C3×C4⋊C4—91no—
343C3×C4⋊C4—91no—
344C3×C4⋊C4D3214yescomplemented
345C3×C4⋊C4C2×C3⋊D311yescharacteristic, complemented
346C3×C22⋊C4—34no—
347C3×C22⋊C4—34no—
348C3×C22⋊C4—34no—
349C3×C22⋊C4—91no—
350C3×C22⋊C4—91no—
351C3×C42—34no—
352#217—94no—
353#217—94no—
354#217—91no—
355(C2×D3)⋊C4—34no—
356(C2×D3)⋊C4—34no—
357(C2×D3)⋊C4—94no—
358(C2×D3)⋊C4—94no—
359(C2×D3)⋊C4—94no—
360(C2×D3)⋊C4—94no—
361(C2×D3)⋊C4—91no—
362(C2×D3)⋊C4—91no—
363(C2×D3)⋊C4—94no—
364(C2×D3)⋊C4—94no—
365(C2×D3)⋊C4—94no—
366(C2×D3)⋊C4—91no—
367(C2×D3)⋊C4—91no—
368(C2×D3)⋊C4—91no—
369(C2×D3)⋊C4—91no—
370(C2×D3)⋊C4—91no—
371(C2×D3)⋊C4—91no—
372(C2×D3)⋊C4—184no—
373(C2×D3)⋊C4—184no—
374(C2×D3)⋊C4—184no—
375(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
376(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
377(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
378C4⋊Dic3—34no—
379C4⋊Dic3—34no—
380C4⋊Dic3—91no—
381C4⋊Dic3C2×C3⋊D311yescharacteristic, complemented
382Dic3⋊C4—94no—
383Dic3⋊C4—94no—
384Dic3⋊C4—94no—
385Dic3⋊C4—91no—
386Dic3⋊C4—91no—
387Dic3⋊C4—184no—
388Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
389C4×Dic3—94no—
390C4×Dic3—94no—
391C4×Dic3—91no—
392C4×Dic3—91no—
393C4×Dic3C2×C3⋊D311yescharacteristic, complemented
394C22×C32—24no—
395C22×C32—61no—
396C22×C32—61no—
397C22×C32—61no—
398C22×C32C23×D314yes—
399C22×C32C23×D311yescharacteristic
400C2×C3⋊D3—21no—
401C2×C3⋊D3—21no—
402C2×C3⋊D3—32no—
403C2×C3⋊D3—38no—
404C2×C3⋊D3—68no—
405C2×C3⋊D3—61no—
406C2×C3⋊D3—61no—
407C2×C3⋊D3—61no—
408C2×C3⋊D3—61no—
409C2×C3⋊D3—61no—
410C2×C3⋊D3—64no—
411C2×C3⋊D3—64no—
412C2×C3⋊D3—64no—
413C2×C3⋊D3—64no—
414C2×C3⋊D3—64no—
415C2×C3⋊D3—124no—
416C2×C3⋊D3—124no—
417C2×C3⋊D3—124no—
418C2×C3⋊D3—124no—
419C2×C3⋊D3—124no—
420C2×C3⋊D3—124no—
421C2×C3⋊D3#23912yes—
422C2×C3×D3—24no—
423C2×C3×D3—24no—
424C2×C3×D3—24no—
425C2×C3×D3—38no—
426C2×C3×D3—64no—
427C2×C3×D3—64no—
428D32—1216no—
429C32×C4—21no—
430C32×C4—21no—
431C32×C4—21no—
432C32×C4—24no—
433C32×C4—24no—
434C32×C4—24no—
435C32×C4—44no—
436C32×C4—44no—
437C32×C4—44no—
438C32×C4—61no—
439C32×C4—61no—
440C32×C4—61no—
441C3⋊Dic3—21no—
442C3⋊Dic3—21no—
443C3⋊Dic3—21no—
444C3⋊Dic3—61no—
445C3⋊Dic3—61no—
446C3⋊Dic3—64no—
447C3⋊Dic3—64no—
448C3⋊Dic3—124no—
449C3⋊Dic3—124no—
450C3×Dic3—24no—
451C3×Dic3—24no—
452C3×Dic3—24no—
453C3×Dic3—64no—
454C3×Dic3—64no—
455C3×Dic3—64no—
456#126—31no—
457#126—271no—
458#124—271no—
459#123—271no—
460#123—271no—
461#123—271no—
462C22⋊Q8—91no—
463C22⋊Q8—271no—
464#120—271no—
465C4×D4—271no—
466C4×D4—271no—
467#117—271no—
468#117—271no—
469C2×C22⋊C4—271no—
470C2×C22⋊C4—271no—
471C33#55111yescharacteristic, complemented, Sylow
472C23×C3—34no—
473C23×C3—91no—
474C22×D3—34no—
475C22×D3—94no—
476C22×D3—91no—
477C22×D3—94no—
478C22×D3—91no—
479C22×D3—184no—
480C22×D3—184no—
481C22×D3—182no—
482C22×D3—182no—
483C22×D3—188no—
484C22×D3—188no—
485C22×D3—361no—
486C22×D3—364no—
487C22×D3C22×C3⋊D311yescharacteristic
488C3×Q8—361no—
489C2×C3×C4—24no—
490C2×C3×C4—24no—
491C2×C3×C4—24no—
492C2×C3×C4—34no—
493C2×C3×C4—34no—
494C2×C3×C4—34no—
495C2×C3×C4—91no—
496C2×C3×C4—91no—
497C2×C3×C4—91no—
498C2×C3×C4—361no—
499C2×C3×C4C2×D3214yes—
500C2×C3×C4C2×D3214yes—
501C2×C3×C4C2×D3214yes—
502C2×C3×C4C22×C3⋊D311yescharacteristic
503C2×C3×C4C22×C3⋊D311yescharacteristic
504C2×C3×C4C22×C3⋊D311yescharacteristic
505#67—182no—
506#67—364no—
507C2×Dic3—34no—
508C2×Dic3—34no—
509C2×Dic3—34no—
510C2×Dic3—94no—
511C2×Dic3—94no—
512C2×Dic3—91no—
513C2×Dic3—91no—
514C2×Dic3—184no—
515C2×Dic3—184no—
516C2×Dic3—182no—
517C2×Dic3C22×C3⋊D311yescharacteristic
518C2×Dic3C22×C3⋊D311yescharacteristic
519C2×Dic3C22×C3⋊D311yescharacteristic
520D12—182no—
521D12—188no—
522D12—188no—
523D12—368no—
524D12—361no—
525C4×D3—124no—
526C4×D3—182no—
527C4×D3—188no—
528C4×D3—188no—
529C4×D3—368no—
530C4×D3—361no—
531C4×D3—361no—
532C4×D3—364no—
533C4×D3—364no—
534Dic6—124no—
535C2×C32—24no—
536C2×C32—24no—
537C2×C32—24no—
538C2×C32—121no—
539C2×C32#100411yescharacteristic
540C2×C32C2×#23911yescharacteristic
541C2×C32D3×#4114yes—
542C2×C32D3×#4114yes—
543C2×C32D3×#4111yescharacteristic
544C2×C32#100914yes—
545C3⋊D3—22no—
546C3⋊D3—62no—
547C3⋊D3—68no—
548C3⋊D3—128no—
549C3⋊D3—121no—
550C3⋊D3—124no—
551C3⋊D3—244no—
552C3×D3—44no—
553C3×D3—68no—
554C24—271no—
555C2×Q8—91no—
556C2×D4—271no—
557C2×D4—271no—
558C2×D4—271no—
559C22×C4—91no—
560C22×C4—271no—
561C22×C4—271no—
562C22×C4—271no—
563C22×C4—271no—
564C4⋊C4—31no—
565C4⋊C4—31no—
566C4⋊C4—91no—
567C4⋊C4—91no—
568C4⋊C4—271no—
569C4⋊C4—271no—
570C4⋊C4—271no—
571C4⋊C4D3×C3⋊D311yescharacteristic, complemented
572C22⋊C4—31no—
573C22⋊C4—31no—
574C22⋊C4—31no—
575C22⋊C4—91no—
576C22⋊C4—91no—
577C22⋊C4—271no—
578C22⋊C4—271no—
579C22⋊C4—271no—
580C22⋊C4—271no—
581C22⋊C4—271no—
582C22⋊C4—271no—
583C22⋊C4—271no—
584C22⋊C4—271no—
585C22⋊C4—271no—
586C42—31no—
587C42—271no—
588C42—271no—
589C22×C3—24no—
590C22×C3—64no—
591C22×C3—64no—
592C22×C3—64no—
593C22×C3—92no—
594C22×C3—181no—
595C22×C3—181no—
596C22×C3C22×D3214yes—
597C22×C3C23×C3⋊D311yescharacteristic
598C2×D3—21no—
599C2×D3—21no—
600C2×D3—21no—
601C2×D3—38no—
602C2×D3—64no—
603C2×D3—64no—
604C2×D3—98no—
605C2×D3—92no—
606C2×D3—188no—
607C2×D3—184no—
608C2×D3—184no—
609C2×D3—181no—
610C2×D3—181no—
611C2×D3—184no—
612C2×D3—184no—
613C2×D3—184no—
614C2×D3—181no—
615C2×D3—181no—
616C2×D3—181no—
617C2×D3—364no—
618C2×D3—364no—
619C2×D3—364no—
620C2×D3—364no—
621C2×D3—364no—
622C2×D3—364no—
623C2×D3—3616no—
624C3×C4—24no—
625C3×C4—24no—
626C3×C4—24no—
627C3×C4—21no—
628C3×C4—21no—
629C3×C4—21no—
630C3×C4—44no—
631C3×C4—44no—
632C3×C4—44no—
633C3×C4—64no—
634C3×C4—64no—
635C3×C4—64no—
636C3×C4—181no—
637C3×C4—181no—
638C3×C4—181no—
639Dic3—21no—
640Dic3—21no—
641Dic3—21no—
642Dic3—64no—
643Dic3—64no—
644Dic3—64no—
645Dic3—184no—
646Dic3—184no—
647Dic3—181no—
648Dic3—181no—
649Dic3—364no—
650Dic3—364no—
651C32—24no—
652C32#563711yescharacteristic, complemented
653C32#570514yescomplemented
654C23—31no—
655C23—91no—
656C23—271no—
657C23—271no—
658C23—542no—
659C23—542no—
660C23—1081no—
661Q8—361no—
662D4—542no—
663D4—542no—
664D4—1081no—
665C2×C4—31no—
666C2×C4—31no—
667C2×C4—31no—
668C2×C4—91no—
669C2×C4—91no—
670C2×C4—91no—
671C2×C4—271no—
672C2×C4—271no—
673C2×C4—361no—
674C2×C4—542no—
675C2×C4—542no—
676C2×C4—1081no—
677C2×C4—1081no—
678C2×C4C2×D3×C3⋊D311yescharacteristic
679C2×C4C2×D3×C3⋊D311yescharacteristic
680C2×C4C2×D3×C3⋊D311yescharacteristic
681C2×C3—24no—
682C2×C3—24no—
683C2×C3—24no—
684C2×C3—124no—
685C2×C3—182no—
686C2×C3#6430714yes—
687C2×C3#6431214yes—
688C2×C3D3×#23914yes—
689C2×C3#41×C3⋊D311yescharacteristic
690C2×C3#41×C3⋊D311yescharacteristic
691C2×C3#6436611yescharacteristic
692D3—41no—
693D3—68no—
694D3—182no—
695D3—188no—
696D3—368no—
697D3—361no—
698D3—364no—
699D3—724no—
700C22—61no—
701C22—61no—
702C22—61no—
703C22—92no—
704C22—181no—
705C22—181no—
706C22—272no—
707C22—541no—
708C22—541no—
709C22—541no—
710C22—541no—
711C22—541no—
712C22—1084no—
713C22C22×D3×C3⋊D311yescharacteristic
714C4—21no—
715C4—21no—
716C4—21no—
717C4—61no—
718C4—61no—
719C4—61no—
720C4—181no—
721C4—181no—
722C4—181no—
723C4—541no—
724C4—541no—
725C3—24no—
726C3#1059465414yescomplemented
727C3#1059617611yescharacteristic, complemented
728C2—121no—
729C2—182no—
730C2—542no—
731C2—1081no—
732C2#1172458011yescharacteristic
733C2#1172458611yescharacteristic
734C2C3⋊D3×#23911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC33×C4⋊C4C22
prime radical#11723542C2
hypercenterC4⋊C4D3×C3⋊D3
hypocenterC33#551
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #11723935C2semidirect
2. C3×#64106C2semidirect
3. C32×#898C2semidirect
5. #11723539C2semidirect
6. C3⋊D3×(C2×D3)⋊C4C2semidirect
7. #11723521C2semidirect
8. #11723512C2semidirect
9. #11723493C2semidirect
10. #11723489C2semidirect
11. #11723484C2semidirect
12. #11723464C2semidirect
13. #11723427C2semidirect
14. #11723422C2semidirect
15. #11723413C2semidirect
22. C2×C3×#634C22semidirect
26. C2×#6289C22semidirect
28. C33×C4⋊C4C22semidirect
30. #88859C22semidirect
31. #88859C22semidirect
32. #88857C22semidirect
35. C3×C4⋊(C3⋊Dic3)C22semidirect
36. C3×C4⋊(C3⋊Dic3)C22semidirect
40. C32×C4⋊Dic3C22semidirect
41. C32×Dic3⋊C4C22semidirect
42. C32×C4×Dic3C22semidirect
43. #88807C22semidirect
44. #88806C22semidirect
47. #88804C22semidirect
51. Dic3×C3⋊Dic3C22semidirect
52. Dic3×C3⋊Dic3C22semidirect
54. #64106D3semidirect
70. C3×#898D3semidirect
127. C2×#634C2×D3semidirect
138. C32×C4⋊C4C2×D3semidirect
139. C32×C4⋊C4C2×D3semidirect
161. C4⋊(C3⋊Dic3)C2×D3semidirect
162. C4⋊(C3⋊Dic3)C2×D3semidirect
177. C3×C4⋊Dic3C2×D3semidirect
178. C3×Dic3⋊C4C2×D3semidirect
179. C3×C4×Dic3C2×D3semidirect
222. #898C3⋊D3semidirect
344. C3×C4⋊C4D32semidirect
345. C3×C4⋊C4C2×C3⋊D3semidirect
381. C4⋊Dic3C2×C3⋊D3semidirect
388. Dic3⋊C4C2×C3⋊D3semidirect
393. C4×Dic3C2×C3⋊D3semidirect
471. C33#551semidirect
571. C4⋊C4D3×C3⋊D3semidirect
652. C32#5637semidirect
653. C32#5705semidirect
726. C3#10594654semidirect
727. C3#10596176semidirect

Maximal subgroups

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

subgroupindex
#117239352
C3×#641062
C32×#8982
#117235422
#117235392
C3⋊D3×(C2×D3)⋊C42
#117235212
#117235122
#117234932
#117234892
#117234842
#117234642
#117234272
#117234222
#117234132
#105961763
#105946543