Finite Group Databasebeta

← #13176565

Subgroups — #13176565

Order 1728.

1728 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723939C211yesmaximal, characteristic, complemented
2C3×#64102C211yesmaximal, characteristic, complemented
3C32×#896C211yesmaximal, characteristic, complemented
4#11723541C211yesmaximal, characteristic
5C3⋊D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
6D3×#3752C211yesmaximal, characteristic, complemented
7C4×#6290C211yesmaximal, characteristic, complemented
8#11723488C211yesmaximal, characteristic, complemented
9#11723480C211yesmaximal, characteristic, complemented
10#11723466C211yesmaximal, characteristic, complemented
11#11723459C211yesmaximal, characteristic, complemented
12#11723446C211yesmaximal, characteristic, complemented
13#11723435C211yesmaximal, characteristic, complemented
14#11723417C211yesmaximal, characteristic, complemented
15#11723392C211yesmaximal, characteristic, complemented
16#10596108—31nomaximal
17#10594642—34nomaximal
18C22×D3×C3⋊D3C2211yescharacteristic
19C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
20C2×C3×C4×C3⋊D3C2211yescharacteristic
21C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
22C2×C32×C4×D3C2211yescharacteristic
23C2×C32×Dic6C2211yescharacteristic, complemented
24C2×#6292C2211yescharacteristic
25C2×#6290C2211yescharacteristic
26C2×Dic3×C3⋊D3C2211yescharacteristic
27C2×D3×C3⋊Dic3C2211yescharacteristic
28C33×C4⋊C4C2211yescharacteristic, complemented
29#88859C2211yescharacteristic
30#88859C2211yescharacteristic
31#88859C2211yescharacteristic
32C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic, complemented
33#88857C2211yescharacteristic, complemented
34C4×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
35C3×#3752C2211yescharacteristic
36C3×#3752C2211yescharacteristic, complemented
37C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
38C32×(C2×D3)⋊C4C2211yescharacteristic
39C32×(C2×D3)⋊C4C2211yescharacteristic
40C32×Dic3⋊C4C2211yescharacteristic, complemented
41C32×Dic3⋊C4C2211yescharacteristic, complemented
42#88806C2211yescharacteristic, complemented
43#88806C2211yescharacteristic, complemented
44Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
45#88804C2211yescharacteristic
46#88804C2211yescharacteristic
47#88803C2211yescharacteristic
48#88803C2211yescharacteristic
49#88803C2211yescharacteristic, complemented
50#88803C2211yescharacteristic, complemented
51(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
52Dic3×C3⋊Dic3C2211yescharacteristic, complemented
53C32×C22⋊Q8—31no—
54#64156—31no—
55#64155—31no—
56C4×#638—31no—
57C2×#3752—31no—
58#64107—31no—
59#64107—31no—
60#64107—34no—
61#64107—64no—
62#64103—31no—
63#64103—31no—
64#64102D311yescharacteristic, complemented
65#64101—31no—
66#64095—31no—
67#64091—31no—
68C22⋊C4×C3⋊D3—31no—
69#64086—31no—
70C3×#896D314yescomplemented
71C3×#893—34no—
72#63922—34no—
73D3×(C2×D3)⋊C4—34no—
74D3×(C2×D3)⋊C4—34no—
75#63907—34no—
76C4×#625—34no—
77#63891—34no—
78#63884—34no—
79#63878—34no—
80#63877—34no—
81#63868—34no—
82#63856—34no—
83#63850—34no—
84C22×C3⋊(C3⋊D3)C2311yescharacteristic
85C22×C3×C3⋊D3C2311yescharacteristic
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
96C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
97C2×C3×C3⋊Dic3C2311yescharacteristic
98C2×C3×C3⋊Dic3C2311yescharacteristic
99C3×C4⋊(C3⋊D3)—22no—
100C3×C4×C3⋊D3—41no—
101C3×C4×C3⋊D3—41no—
102C2×C32×Dic3C2311yescharacteristic
103C2×C32×Dic3C2311yescharacteristic
104C2×C32×Dic3C2311yescharacteristic
105C32×C4×D3—41no—
106C32×Dic6—41no—
107#6292—41no—
108#6290—22no—
109Dic3×C3⋊D3—22no—
110D3×C3⋊Dic3—22no—
111#5637—94no—
112#5556—91no—
113C23×C3⋊D3—31no—
114C22×D32—34no—
115C2×C32×Q8—31no—
116C22×C32×C4—31no—
117C2×#638—31no—
118C22×C3⋊Dic3—31no—
119C2×C4⋊(C3⋊D3)—31no—
120C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
121C2×C4×C3⋊D3—31no—
122C2×C4×C3⋊D3C2×D311yescharacteristic
123C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
124C2×C3×D12—34no—
125C2×C3×C4×D3—34no—
126C2×C3×C4×D3—34no—
127C2×C3×C4×D3C2×D314yes—
128C2×C3×Dic6C2×D314yescomplemented
129C2×#626—34no—
130C2×#625—34no—
131C2×D3×Dic3—34no—
132C2×D3×Dic3—34no—
133C32×C4⋊C4—24no—
134C32×C4⋊C4—31no—
135C32×C4⋊C4—31no—
136C32×C4⋊C4C2×D314yescomplemented
137C32×C4⋊C4C2×D311yescharacteristic, complemented
138C32×C22⋊C4—31no—
139C32×C22⋊C4—31no—
140#3757—31no—
141#3752—31no—
142#3752—31no—
143#3752—31no—
144#3752—31no—
145#3752—31no—
146#3752—31no—
147#3752—31no—
148#3752—34no—
149#3752—34no—
150#3752—34no—
151#3752—31no—
152#3752—31no—
153#3752—64no—
154#3752—64no—
155#3752—64no—
156#3752C2×D311yescharacteristic
157#3752C2×D311yescharacteristic, complemented
158C4⋊(C3⋊Dic3)—31no—
159C4⋊(C3⋊Dic3)—34no—
160C4⋊(C3⋊Dic3)—31no—
161C4⋊(C3⋊Dic3)—64no—
162#3750—31no—
163#3750—34no—
164#3750—31no—
165#3750—31no—
166#3750—64no—
167C4×C3⋊Dic3—31no—
168C4×C3⋊Dic3—34no—
169C4×C3⋊Dic3—31no—
170C4×C3⋊Dic3—64no—
171C4×C3⋊Dic3C2×D311yescharacteristic, complemented
172C3×(C2×D3)⋊C4—34no—
173C3×(C2×D3)⋊C4—34no—
174C3×(C2×D3)⋊C4C2×D314yes—
175C3×(C2×D3)⋊C4C2×D314yes—
176C3×Dic3⋊C4C2×D314yescomplemented
177C3×Dic3⋊C4C2×D314yescomplemented
178C3×C4×Dic3—34no—
179#3724—34no—
180#3724—34no—
181Dic3⋊Dic3—34no—
182#3722—34no—
183#3722—34no—
184(C2×D3)⋊Dic3—34no—
185(C2×D3)⋊Dic3—34no—
186(C2×D3)⋊Dic3—34no—
187(C2×D3)⋊Dic3—34no—
188(C2×D3)⋊Dic3—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—21no—
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#4112yes—
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×C22⋊Q8—34no—
216C3×C4×D4—91no—
217#947—94no—
218#946—94no—
219#937—91no—
220#935—91no—
221#929—91no—
222C4×#67—94no—
223C4×#67—91no—
224C2×(C2×D3)⋊C4—94no—
225C2×(C2×D3)⋊C4—91no—
226#924—91no—
227#898—94no—
228#898—94no—
229#898—91no—
230#898—184no—
231#896C3⋊D311yescharacteristic, complemented
232#894—94no—
233#894—94no—
234#893—34no—
235#892—94no—
236#886—94no—
237#885—91no—
238#883—91no—
239#882—94no—
240D3×C22⋊C4—94no—
241D3×C22⋊C4—91no—
242#877—94no—
243#877—91no—
244#876—91no—
245#872—91no—
246C23×C32—31no—
247C22×C3⋊D3—31no—
248C22×C3⋊D3—34no—
249C22×C3⋊D3—64no—
250C22×C3⋊D3—62no—
251C22×C3⋊D3—62no—
252C22×C3⋊D3—121no—
253C22×C3⋊D3C22×D311yescharacteristic
254C22×C3⋊D3C22×D311yescharacteristic
255C22×C3×D3—34no—
256C22×C3×D3—34no—
257C22×C3×D3C22×D314yes—
258C2×D32—68no—
259C2×D32—68no—
260C2×D32—124no—
261C32×Q8—121no—
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×C4—121no—
269C2×C32×C4C22×D314yes—
270C2×C32×C4C22×D314yes—
271C2×C32×C4C22×D314yes—
272C2×C32×C4C22×D311yescharacteristic
273C2×C32×C4C22×D311yescharacteristic
274C2×C32×C4C22×D311yescharacteristic
275#638—62no—
276C2×C3⋊Dic3—31no—
277C2×C3⋊Dic3—31no—
278C2×C3⋊Dic3—31no—
279C2×C3⋊Dic3—34no—
280C2×C3⋊Dic3—34no—
281C2×C3⋊Dic3—34no—
282C2×C3⋊Dic3—64no—
283C2×C3⋊Dic3—64no—
284C2×C3⋊Dic3—64no—
285C2×C3⋊Dic3—62no—
286C2×C3⋊Dic3C22×D311yescharacteristic
287C2×C3⋊Dic3C22×D311yescharacteristic
288C4⋊(C3⋊D3)—22no—
289C4⋊(C3⋊D3)—121no—
290C4×C3⋊D3—41no—
291C4×C3⋊D3—41no—
292C4×C3⋊D3—62no—
293C2×C3×Dic3—34no—
294C2×C3×Dic3—34no—
295C2×C3×Dic3C22×D314yes—
296C2×C3×Dic3C22×D314yes—
297C2×C3×Dic3C22×D314yes—
298C3×D12—68no—
299C3×C4×D3—44no—
300C3×C4×D3—124no—
301C3×C4×D3—124no—
302C3×Dic6—44no—
303#626—124no—
304#625—68no—
305D3×Dic3—68no—
306D3×Dic3—68no—
307#551—271noSylow
308C2×C33C2×#4111yescharacteristic
309C2×C33C2×#4111yescharacteristic
310C2×C33H(5,𝔽2)11yescharacteristic
311C3⋊(C3⋊D3)—41no—
312C3×C3⋊D3—22no—
313C3×C3⋊D3—41no—
314C32×D3—22no—
315C23×D3—94no—
316C23×D3—91no—
317C2×C3×Q8—34no—
318C2×C3×D4—91no—
319C22×C3×C4—34no—
320C22×C3×C4—91no—
321C22×C3×C4—91no—
322C2×#67—94no—
323C2×#67—91no—
324C2×#67—91no—
325C22×Dic3—94no—
326C22×Dic3—91no—
327C2×D12—34no—
328C2×D12—94no—
329C2×C4×D3—34no—
330C2×C4×D3—34no—
331C2×C4×D3—94no—
332C2×C4×D3—91no—
333C2×C4×D3C2×C3⋊D311yescharacteristic
334C2×Dic6C2×C3⋊D311yescharacteristic, complemented
335C3×C4⋊C4—24no—
336C3×C4⋊C4—34no—
337C3×C4⋊C4—34no—
338C3×C4⋊C4D3214yescomplemented
339C3×C4⋊C4C2×C3⋊D311yescharacteristic, complemented
340C3×C22⋊C4—34no—
341C3×C22⋊C4—34no—
342C3×C22⋊C4—91no—
343C3×C22⋊C4—91no—
344C3×C42—91no—
345#217—94no—
346#217—91no—
347#217—91no—
348#217—91no—
349#217—91no—
350(C2×D3)⋊C4—34no—
351(C2×D3)⋊C4—34no—
352(C2×D3)⋊C4—94no—
353(C2×D3)⋊C4—94no—
354(C2×D3)⋊C4—94no—
355(C2×D3)⋊C4—94no—
356(C2×D3)⋊C4—94no—
357(C2×D3)⋊C4—94no—
358(C2×D3)⋊C4—91no—
359(C2×D3)⋊C4—94no—
360(C2×D3)⋊C4—94no—
361(C2×D3)⋊C4—94no—
362(C2×D3)⋊C4—91no—
363(C2×D3)⋊C4—91no—
364(C2×D3)⋊C4—91no—
365(C2×D3)⋊C4—91no—
366(C2×D3)⋊C4—91no—
367(C2×D3)⋊C4—184no—
368(C2×D3)⋊C4—184no—
369(C2×D3)⋊C4—184no—
370(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
371(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
372C4⋊Dic3—94no—
373C4⋊Dic3—94no—
374C4⋊Dic3—91no—
375C4⋊Dic3—184no—
376Dic3⋊C4—94no—
377Dic3⋊C4—94no—
378Dic3⋊C4—94no—
379Dic3⋊C4—91no—
380Dic3⋊C4—91no—
381Dic3⋊C4—91no—
382Dic3⋊C4—91no—
383Dic3⋊C4—184no—
384Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
385Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
386C4×Dic3—34no—
387C4×Dic3—94no—
388C4×Dic3—94no—
389C4×Dic3—91no—
390C4×Dic3—91no—
391C4×Dic3—184no—
392C22×C32—24no—
393C22×C32—32no—
394C22×C32—61no—
395C22×C32—61no—
396C22×C32C23×D314yes—
397C22×C32C23×D311yescharacteristic
398C2×C3⋊D3—21no—
399C2×C3⋊D3—21no—
400C2×C3⋊D3—21no—
401C2×C3⋊D3—21no—
402C2×C3⋊D3—21no—
403C2×C3⋊D3—61no—
404C2×C3⋊D3—61no—
405C2×C3⋊D3—61no—
406C2×C3⋊D3—64no—
407C2×C3⋊D3—64no—
408C2×C3⋊D3—64no—
409C2×C3⋊D3—124no—
410C2×C3⋊D3—124no—
411C2×C3⋊D3—124no—
412C2×C3⋊D3—124no—
413C2×C3⋊D3#23512yes—
414C2×C3×D3—24no—
415C2×C3×D3—24no—
416C2×C3×D3—38no—
417C2×C3×D3—64no—
418C2×C3×D3—64no—
419C2×C3×D3—64no—
420C2×C3×D3—64no—
421C2×C3×D3—64no—
422C2×C3×D3#23918yes—
423D32—1216no—
424C32×C4—21no—
425C32×C4—21no—
426C32×C4—21no—
427C32×C4—24no—
428C32×C4—24no—
429C32×C4—24no—
430C32×C4—44no—
431C32×C4—44no—
432C32×C4—44no—
433C32×C4—61no—
434C32×C4—61no—
435C32×C4—61no—
436C3⋊Dic3—21no—
437C3⋊Dic3—21no—
438C3⋊Dic3—61no—
439C3⋊Dic3—61no—
440C3⋊Dic3—61no—
441C3⋊Dic3—64no—
442C3⋊Dic3—64no—
443C3⋊Dic3—64no—
444C3⋊Dic3—124no—
445C3⋊Dic3—124no—
446C3⋊Dic3—124no—
447C3×Dic3—24no—
448C3×Dic3—24no—
449C3×Dic3—24no—
450C3×Dic3—64no—
451C3×Dic3—64no—
452#126—271no—
453#126—271no—
454#124—271no—
455#123—271no—
456#123—271no—
457#123—271no—
458C22⋊Q8—31no—
459C22⋊Q8—271no—
460#120—271no—
461C4×D4—91no—
462C4×D4—271no—
463#117—271no—
464#117—271no—
465C2×C22⋊C4—271no—
466C2×C22⋊C4—271no—
467C33#55111yescharacteristic, complemented, Sylow
468C23×C3—34no—
469C23×C3—91no—
470C23×C3—91no—
471C22×D3—34no—
472C22×D3—34no—
473C22×D3—94no—
474C22×D3—91no—
475C22×D3—184no—
476C22×D3—182no—
477C22×D3—188no—
478C22×D3—188no—
479C22×D3—182no—
480C22×D3—361no—
481C22×D3—364no—
482C22×D3C22×C3⋊D311yescharacteristic
483C3×Q8—124no—
484C3×D4—182no—
485C2×C3×C4—24no—
486C2×C3×C4—24no—
487C2×C3×C4—24no—
488C2×C3×C4—34no—
489C2×C3×C4—34no—
490C2×C3×C4—34no—
491C2×C3×C4—91no—
492C2×C3×C4—91no—
493C2×C3×C4—124no—
494C2×C3×C4—361no—
495C2×C3×C4—361no—
496C2×C3×C4C2×D3214yes—
497C2×C3×C4C2×D3214yes—
498C2×C3×C4C2×D3214yes—
499C2×C3×C4C22×C3⋊D311yescharacteristic
500C2×C3×C4C22×C3⋊D311yescharacteristic
501C2×C3×C4C22×C3⋊D311yescharacteristic
502#67—188no—
503#67—182no—
504#67—361no—
505C2×Dic3—34no—
506C2×Dic3—34no—
507C2×Dic3—94no—
508C2×Dic3—94no—
509C2×Dic3—94no—
510C2×Dic3—91no—
511C2×Dic3—91no—
512C2×Dic3—91no—
513C2×Dic3—184no—
514C2×Dic3—184no—
515C2×Dic3—184no—
516C2×Dic3—182no—
517C2×Dic3—188no—
518C2×Dic3C22×C3⋊D311yescharacteristic
519C2×Dic3C22×C3⋊D311yescharacteristic
520C2×Dic3C22×C3⋊D311yescharacteristic
521D12—68no—
522D12—364no—
523C4×D3—41no—
524C4×D3—124no—
525C4×D3—124no—
526C4×D3—188no—
527C4×D3—182no—
528Dic6—41no—
529C2×C32—24no—
530C2×C32—24no—
531C2×C32—24no—
532C2×C32—62no—
533C2×C32C2×#23511yescharacteristic
534C2×C32#100414yes—
535C2×C32#100411yescharacteristic
536C2×C32C2×#23914yes—
537C2×C32D3×#4114yes—
538C2×C32D3×#4111yescharacteristic
539C3⋊D3—22no—
540C3⋊D3—41no—
541C3⋊D3—121no—
542C3⋊D3—124no—
543C3⋊D3—244no—
544C3×D3—28no—
545C3×D3—68no—
546C3×D3—124no—
547C24—271no—
548C2×Q8—31no—
549C2×D4—91no—
550C2×D4—271no—
551C2×D4—271no—
552C22×C4—31no—
553C22×C4—91no—
554C22×C4—91no—
555C22×C4—271no—
556C22×C4—271no—
557C4⋊C4—31no—
558C4⋊C4—31no—
559C4⋊C4—271no—
560C4⋊C4—271no—
561C4⋊C4—271no—
562C4⋊C4—271no—
563C4⋊C4—271no—
564C4⋊C4D3×C3⋊D311yescharacteristic, complemented
565C22⋊C4—31no—
566C22⋊C4—31no—
567C22⋊C4—91no—
568C22⋊C4—91no—
569C22⋊C4—271no—
570C22⋊C4—271no—
571C22⋊C4—271no—
572C22⋊C4—271no—
573C22⋊C4—271no—
574C22⋊C4—271no—
575C22⋊C4—271no—
576C22⋊C4—271no—
577C22⋊C4—271no—
578C22⋊C4—271no—
579C42—91no—
580C42—271no—
581C42—271no—
582C22×C3—24no—
583C22×C3—38no—
584C22×C3—64no—
585C22×C3—64no—
586C22×C3—92no—
587C22×C3—181no—
588C22×C3—181no—
589C22×C3—181no—
590C22×C3—181no—
591C22×C3—181no—
592C22×C3C22×D3214yes—
593C22×C3C23×C3⋊D311yescharacteristic
594C2×D3—21no—
595C2×D3—21no—
596C2×D3—38no—
597C2×D3—64no—
598C2×D3—64no—
599C2×D3—64no—
600C2×D3—64no—
601C2×D3—64no—
602C2×D3—184no—
603C2×D3—184no—
604C2×D3—184no—
605C2×D3—181no—
606C2×D3—181no—
607C2×D3—181no—
608C2×D3—364no—
609C2×D3—364no—
610C2×D3—364no—
611C2×D3—364no—
612C2×D3—3616no—
613C2×D3#383212yes—
614C3×C4—24no—
615C3×C4—24no—
616C3×C4—24no—
617C3×C4—21no—
618C3×C4—21no—
619C3×C4—21no—
620C3×C4—44no—
621C3×C4—44no—
622C3×C4—44no—
623C3×C4—64no—
624C3×C4—64no—
625C3×C4—64no—
626C3×C4—181no—
627C3×C4—181no—
628Dic3—21no—
629Dic3—21no—
630Dic3—21no—
631Dic3—64no—
632Dic3—64no—
633Dic3—184no—
634Dic3—184no—
635Dic3—184no—
636Dic3—181no—
637Dic3—181no—
638Dic3—181no—
639Dic3—364no—
640Dic3—364no—
641Dic3—364no—
642C32—24no—
643C32#555611yescharacteristic, complemented
644C32#563714yescomplemented
645C23—31no—
646C23—91no—
647C23—91no—
648C23—271no—
649C23—542no—
650C23—542no—
651C23—1081no—
652Q8—121no—
653D4—182no—
654D4—542no—
655D4—1081no—
656C2×C4—31no—
657C2×C4—31no—
658C2×C4—31no—
659C2×C4—91no—
660C2×C4—91no—
661C2×C4—121no—
662C2×C4—271no—
663C2×C4—271no—
664C2×C4—271no—
665C2×C4—361no—
666C2×C4—361no—
667C2×C4—542no—
668C2×C4—542no—
669C2×C4C2×D3×C3⋊D311yescharacteristic
670C2×C4C2×D3×C3⋊D311yescharacteristic
671C2×C4C2×D3×C3⋊D311yescharacteristic
672C2×C3—24no—
673C2×C3—24no—
674C2×C3—24no—
675C2×C3—68no—
676C2×C3—182no—
677C2×C3—361no—
678C2×C3D3×#23514yes—
679C2×C3#6431314yes—
680C2×C3D3×#23914yes—
681C2×C3#6436111yescharacteristic
682C2×C3C2×#383211yescharacteristic
683C2×C3#41×C3⋊D311yescharacteristic
684D3—22no—
685D3—68no—
686D3—124no—
687D3—361no—
688D3—364no—
689D3—724no—
690C22—32no—
691C22—61no—
692C22—61no—
693C22—92no—
694C22—181no—
695C22—181no—
696C22—181no—
697C22—181no—
698C22—181no—
699C22—541no—
700C22—541no—
701C22—541no—
702C22—1084no—
703C22C22×D3×C3⋊D311yescharacteristic
704C4—21no—
705C4—21no—
706C4—21no—
707C4—61no—
708C4—61no—
709C4—61no—
710C4—181no—
711C4—181no—
712C4—541no—
713C4—541no—
714C4—541no—
715C3—24no—
716C3#1059464214yescomplemented
717C3#1059610811yescharacteristic, complemented
718C2—62no—
719C2—182no—
720C2—361no—
721C2—1081no—
722C2C3⋊D3×#23511yescharacteristic
723C2#1172458711yescharacteristic
724C2D3×#383211yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC33×C4⋊C4C22
prime radical#11723541C2
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. #11723939C2semidirect
2. C3×#64102C2semidirect
3. C32×#896C2semidirect
5. C3⋊D3×(C2×D3)⋊C4C2semidirect
6. D3×#3752C2semidirect
7. C4×#6290C2semidirect
8. #11723488C2semidirect
9. #11723480C2semidirect
10. #11723466C2semidirect
11. #11723459C2semidirect
12. #11723446C2semidirect
13. #11723435C2semidirect
14. #11723417C2semidirect
15. #11723392C2semidirect
21. C2×C3×C4×C3⋊D3C22semidirect
23. C2×C32×Dic6C22semidirect
28. C33×C4⋊C4C22semidirect
32. C4⋊(C3⋊(C3⋊Dic3))C22semidirect
33. #88857C22semidirect
34. C4×C3⋊(C3⋊Dic3)C22semidirect
36. C3×#3752C22semidirect
37. C3×C4×C3⋊Dic3C22semidirect
40. C32×Dic3⋊C4C22semidirect
41. C32×Dic3⋊C4C22semidirect
42. #88806C22semidirect
43. #88806C22semidirect
44. Dic3⋊(C3⋊Dic3)C22semidirect
49. #88803C22semidirect
50. #88803C22semidirect
52. Dic3×C3⋊Dic3C22semidirect
64. #64102D3semidirect
70. C3×#896D3semidirect
123. C2×C4×C3⋊D3C2×D3semidirect
128. C2×C3×Dic6C2×D3semidirect
136. C32×C4⋊C4C2×D3semidirect
137. C32×C4⋊C4C2×D3semidirect
157. #3752C2×D3semidirect
171. C4×C3⋊Dic3C2×D3semidirect
176. C3×Dic3⋊C4C2×D3semidirect
177. C3×Dic3⋊C4C2×D3semidirect
231. #896C3⋊D3semidirect
334. C2×Dic6C2×C3⋊D3semidirect
338. C3×C4⋊C4D32semidirect
339. C3×C4⋊C4C2×C3⋊D3semidirect
384. Dic3⋊C4C2×C3⋊D3semidirect
385. Dic3⋊C4C2×C3⋊D3semidirect
467. C33#551semidirect
564. C4⋊C4D3×C3⋊D3semidirect
643. C32#5556semidirect
644. C32#5637semidirect
716. C3#10594642semidirect
717. C3#10596108semidirect

Maximal subgroups

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

subgroupindex
#117239392
C3×#641022
C32×#8962
#117235412
C3⋊D3×(C2×D3)⋊C42
D3×#37522
C4×#62902
#117234882
#117234802
#117234662
#117234592
#117234462
#117234352
#117234172
#117233922
#105961083
#105946423