Finite Group Databasebeta

← #13177224

Subgroups — #13177224

Order 1728.

2016 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88859C211yesmaximal, characteristic, complemented
2C3×C4×#638C211yesmaximal, characteristic, complemented
3C32×#924C211yesmaximal, characteristic, complemented
4#11723639C211yesmaximal, characteristic
5#11723627C211yesmaximal, characteristic, complemented
6#11723609C211yesmaximal, characteristic, complemented
7#11723598C211yesmaximal, characteristic, complemented
8#11723512C211yesmaximal, characteristic, complemented
9#11723504C211yesmaximal, characteristic, complemented
10#11723477C211yesmaximal, characteristic, complemented
11#11723469C211yesmaximal, characteristic, complemented
12#11723446C211yesmaximal, characteristic, complemented
13#11723417C211yesmaximal, characteristic, complemented
14#11723411C211yesmaximal, characteristic, complemented
15#11723392C211yesmaximal, characteristic, complemented
16#10596108—31nomaximal
17#10595035—34nomaximal
18C23×C3⋊(C3⋊D3)C2211yescharacteristic
19C22×C33×C4C2211yescharacteristic
20C22×C3⋊(C3⋊Dic3)C2211yescharacteristic
21C2×C3×#638C2211yescharacteristic
22C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
23C2×C32×Dic6C2211yescharacteristic, complemented
24C2×#6292C2211yescharacteristic
25C2×#6292C2211yescharacteristic
26C2×#6289C2211yescharacteristic
27C2×#6289C2211yescharacteristic
28#88859C2211yescharacteristic
29#88859C2211yescharacteristic
30#88859C2211yescharacteristic
31#88859C2211yescharacteristic
32C3×#3757C2211yescharacteristic
33C3×#3752C2211yescharacteristic, complemented
34C3×#3750C2211yescharacteristic, complemented
35C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
36C32×#217C2211yescharacteristic
37C32×#217C2211yescharacteristic
38C32×C4⋊Dic3C2211yescharacteristic, complemented
39C32×Dic3⋊C4C2211yescharacteristic, complemented
40C32×Dic3⋊C4C2211yescharacteristic, complemented
41#88806C2211yescharacteristic, complemented
42#88806C2211yescharacteristic, complemented
43Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
44Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
45#88804C2211yescharacteristic
46#88804C2211yescharacteristic
47#88804C2211yescharacteristic
48#88804C2211yescharacteristic
49#88803C2211yescharacteristic, complemented
50#88803C2211yescharacteristic, complemented
51Dic3×C3⋊Dic3C2211yescharacteristic, complemented
52Dic3×C3⋊Dic3C2211yescharacteristic, complemented
53C32×C22⋊Q8—31no—
54#64156—31no—
55#64155—31no—
56C4×#638D311yescharacteristic, complemented
57C2×#3752—31no—
58C2×#3752—34no—
59C2×#3752—64no—
60#64107—31no—
61#64107—31no—
62#64103—31no—
63#64103—31no—
64#64102—31no—
65#64101—31no—
66#64095—31no—
67#64091—31no—
68C22⋊C4×C3⋊D3—31no—
69#64086—31no—
70C3×C4×#67—34no—
71C3×#924D314yescomplemented
72#63981—34no—
73#63974—34no—
74#63962—34no—
75#63957—34no—
76#63907—34no—
77#63904—34no—
78#63888—34no—
79#63868—34no—
80#63854—34no—
81#63850—34no—
82#63848—34no—
83#63836—34no—
84C23×C33C2311yescharacteristic
85C22×C3⋊(C3⋊D3)—22no—
86C22×C3⋊(C3⋊D3)—22no—
87C22×C3⋊(C3⋊D3)—41no—
88C22×C3⋊(C3⋊D3)C2311yescharacteristic
89C22×C3⋊(C3⋊D3)C2311yescharacteristic
90C22×C3×C3⋊D3C2311yescharacteristic
91C2×C33×C4—41no—
92C2×C33×C4C2311yescharacteristic
93C2×C33×C4C2311yescharacteristic
94C2×C3⋊(C3⋊Dic3)—22no—
95C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
96C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
97C3×#638—22no—
98C2×C3×C3⋊Dic3C2311yescharacteristic
99C2×C3×C3⋊Dic3C2311yescharacteristic
100C2×C3×C3⋊Dic3C2311yescharacteristic
101C3×C4×C3⋊D3—41no—
102C2×C32×Dic3C2311yescharacteristic
103C2×C32×Dic3C2311yescharacteristic
104C2×C32×Dic3C2311yescharacteristic
105C2×C32×Dic3C2311yescharacteristic
106C32×Dic6—41no—
107#6292—22no—
108#6292—41no—
109#6289—22no—
110#6289—41no—
111#5637—94no—
112#5556—91no—
113C23×C3⋊D3—31no—
114C23×C3⋊D3—34no—
115C23×C3⋊D3—64no—
116C2×C32×Q8—31no—
117C22×C32×C4—24no—
118C22×C32×C4C2×D314yes—
119C22×C32×C4C2×D311yescharacteristic
120C2×#638C2×D311yescharacteristic
121C22×C3⋊Dic3—31no—
122C22×C3⋊Dic3—34no—
123C22×C3⋊Dic3—64no—
124C2×C4⋊(C3⋊D3)—31no—
125C2×C4⋊(C3⋊D3)—31no—
126C2×C4×C3⋊D3—31no—
127C2×C4×C3⋊D3—31no—
128C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
129C2×C3×#67—34no—
130C2×C3×C4×D3—34no—
131C2×C3×Dic6C2×D314yescomplemented
132C2×#626—34no—
133C2×#626—34no—
134C2×#624—34no—
135C2×#624—34no—
136C32×C4⋊C4—31no—
137C32×C4⋊C4—31no—
138C32×C4⋊C4—31no—
139C32×C22⋊C4—31no—
140C32×C22⋊C4—31no—
141#3757C2×D311yescharacteristic
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—34no—
152#3752—31no—
153#3752—31no—
154#3752—31no—
155#3752—31no—
156#3752—64no—
157#3752—64no—
158#3752—64no—
159#3752—64no—
160#3752C2×D311yescharacteristic, complemented
161C4⋊(C3⋊Dic3)—31no—
162C4⋊(C3⋊Dic3)—31no—
163#3750—31no—
164#3750—31no—
165#3750C2×D311yescharacteristic, complemented
166C4×C3⋊Dic3—31no—
167C4×C3⋊Dic3—31no—
168C4×C3⋊Dic3C2×D311yescharacteristic, complemented
169C3×#217—34no—
170C3×#217C2×D314yes—
171C3×#217C2×D314yes—
172C3×(C2×D3)⋊C4—34no—
173C3×C4⋊Dic3C2×D314yescomplemented
174C3×Dic3⋊C4—34no—
175C3×Dic3⋊C4C2×D314yescomplemented
176C3×Dic3⋊C4C2×D314yescomplemented
177C3×C4×Dic3—34no—
178#3724—34no—
179#3724—34no—
180Dic3⋊Dic3—34no—
181Dic3⋊Dic3—34no—
182#3722—34no—
183#3722—34no—
184#3722—34no—
185#3722—34no—
186(C2×D3)⋊Dic3—34no—
187(C2×D3)⋊Dic3—34no—
188Dic32—34no—
189Dic32—34no—
190C22×C33—21no—
191C22×C33—21no—
192C22×C33#4112yes—
193C22×C33C2411yescharacteristic
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)—44no—
200C2×C3⋊(C3⋊D3)#4112yes—
201C2×C3×C3⋊D3—21no—
202C2×C3×C3⋊D3—21no—
203C2×C3×C3⋊D3—21no—
204C33×C4—21no—
205C33×C4—21no—
206C3⋊(C3⋊Dic3)—21no—
207C3⋊(C3⋊Dic3)—21no—
208C3×C3⋊Dic3—21no—
209C3×C3⋊Dic3—21no—
210C3×C3⋊Dic3—21no—
211C32×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—34no—
223C4×#67—91no—
224C2×(C2×D3)⋊C4—94no—
225C2×(C2×D3)⋊C4—91no—
226C2×(C2×D3)⋊C4—184no—
227#924C3⋊D311yescharacteristic, complemented
228#898—94no—
229#898—94no—
230#898—91no—
231#896—91no—
232#894—94no—
233#894—94no—
234#893—94no—
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—24no—
247C23×C32C22×D314yes—
248C23×C32C22×D311yescharacteristic
249C22×C3⋊D3—31no—
250C22×C3⋊D3—31no—
251C22×C3⋊D3—34no—
252C22×C3⋊D3—34no—
253C22×C3⋊D3—64no—
254C22×C3⋊D3—64no—
255C22×C3⋊D3—62no—
256C22×C3⋊D3—68no—
257C22×C3⋊D3—616no—
258C22×C3⋊D3—62no—
259C22×C3⋊D3—68no—
260C22×C3⋊D3—128no—
261C22×C3⋊D3—121no—
262C22×C3⋊D3—124no—
263C22×C3⋊D3—128no—
264C22×C3⋊D3C22×D311yescharacteristic
265C22×C3×D3—34no—
266C32×Q8—121no—
267C2×C32×C4—24no—
268C2×C32×C4—24no—
269C2×C32×C4—31no—
270C2×C32×C4—31no—
271C2×C32×C4—31no—
272C2×C32×C4—31no—
273C2×C32×C4—41no—
274C2×C32×C4—44no—
275C2×C32×C4—48no—
276C2×C32×C4C22×D314yes—
277C2×C32×C4C22×D314yes—
278C2×C32×C4C22×D311yescharacteristic
279C2×C32×C4C22×D311yescharacteristic
280#638—22no—
281C2×C3⋊Dic3—31no—
282C2×C3⋊Dic3—31no—
283C2×C3⋊Dic3—34no—
284C2×C3⋊Dic3—34no—
285C2×C3⋊Dic3—64no—
286C2×C3⋊Dic3—64no—
287C2×C3⋊Dic3—62no—
288C2×C3⋊Dic3—68no—
289C2×C3⋊Dic3—128no—
290C2×C3⋊Dic3C22×D311yescharacteristic
291C2×C3⋊Dic3C22×D311yescharacteristic
292C2×C3⋊Dic3C22×D311yescharacteristic
293C4⋊(C3⋊D3)—62no—
294C4⋊(C3⋊D3)—121no—
295C4×C3⋊D3—41no—
296C4×C3⋊D3—62no—
297C4×C3⋊D3—121no—
298C3×#67—68no—
299C2×C3×Dic3—34no—
300C2×C3×Dic3—34no—
301C2×C3×Dic3—34no—
302C2×C3×Dic3C22×D314yes—
303C2×C3×Dic3C22×D314yes—
304C2×C3×Dic3C22×D314yes—
305C2×C3×Dic3C22×D314yes—
306C3×C4×D3—124no—
307C3×Dic6—44no—
308#626—68no—
309#626—124no—
310#624—68no—
311#624—124no—
312#551—271noSylow
313C2×C33—22no—
314C2×C33C2×#4111yescharacteristic
315C2×C33C2×#4111yescharacteristic
316C2×C33H(5,𝔽2)11yescharacteristic
317C3⋊(C3⋊D3)—22no—
318C3⋊(C3⋊D3)—41no—
319C3×C3⋊D3—41no—
320C23×D3—94no—
321C23×D3—91no—
322C23×D3—184no—
323C2×C3×Q8—34no—
324C2×C3×D4—91no—
325C22×C3×C4—24no—
326C22×C3×C4—91no—
327C22×C3×C4D3214yes—
328C22×C3×C4C2×C3⋊D311yescharacteristic
329C2×#67—34no—
330C2×#67—91no—
331C2×#67—91no—
332C22×Dic3—94no—
333C22×Dic3—91no—
334C22×Dic3—184no—
335C2×D12—94no—
336C2×D12—94no—
337C2×C4×D3—34no—
338C2×C4×D3—94no—
339C2×C4×D3—91no—
340C2×C4×D3—94no—
341C2×C4×D3—91no—
342C2×Dic6C2×C3⋊D311yescharacteristic, complemented
343C3×C4⋊C4—34no—
344C3×C4⋊C4—34no—
345C3×C4⋊C4—34no—
346C3×C4⋊C4—91no—
347C3×C22⋊C4—34no—
348C3×C22⋊C4—34no—
349C3×C22⋊C4—91no—
350C3×C22⋊C4—91no—
351C3×C42—91no—
352#217—34no—
353#217—91no—
354#217—91no—
355#217C2×C3⋊D311yescharacteristic
356#217C2×C3⋊D311yescharacteristic
357(C2×D3)⋊C4—34no—
358(C2×D3)⋊C4—94no—
359(C2×D3)⋊C4—94no—
360(C2×D3)⋊C4—94no—
361(C2×D3)⋊C4—94no—
362(C2×D3)⋊C4—94no—
363(C2×D3)⋊C4—94no—
364(C2×D3)⋊C4—94no—
365(C2×D3)⋊C4—94no—
366(C2×D3)⋊C4—94no—
367(C2×D3)⋊C4—94no—
368(C2×D3)⋊C4—91no—
369(C2×D3)⋊C4—91no—
370(C2×D3)⋊C4—91no—
371(C2×D3)⋊C4—91no—
372(C2×D3)⋊C4—91no—
373(C2×D3)⋊C4—91no—
374(C2×D3)⋊C4—91no—
375(C2×D3)⋊C4—91no—
376(C2×D3)⋊C4—184no—
377(C2×D3)⋊C4—184no—
378(C2×D3)⋊C4—184no—
379(C2×D3)⋊C4—184no—
380C4⋊Dic3—94no—
381C4⋊Dic3—94no—
382C4⋊Dic3C2×C3⋊D311yescharacteristic, complemented
383Dic3⋊C4—34no—
384Dic3⋊C4—94no—
385Dic3⋊C4—94no—
386Dic3⋊C4—91no—
387Dic3⋊C4—91no—
388Dic3⋊C4—91no—
389Dic3⋊C4—91no—
390Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
391Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
392C4×Dic3—34no—
393C4×Dic3—94no—
394C4×Dic3—94no—
395C4×Dic3—91no—
396C4×Dic3—91no—
397C22×C32—28no—
398C22×C32—28no—
399C22×C32—24no—
400C22×C32—21no—
401C22×C32—24no—
402C22×C32—21no—
403C22×C32—24no—
404C22×C32—28no—
405C22×C32#23512yes—
406C22×C32#23918yes—
407C22×C32C23×D314yes—
408C22×C32C23×D311yescharacteristic
409C2×C3⋊D3—21no—
410C2×C3⋊D3—21no—
411C2×C3⋊D3—21no—
412C2×C3⋊D3—32no—
413C2×C3⋊D3—38no—
414C2×C3⋊D3—68no—
415C2×C3⋊D3—61no—
416C2×C3⋊D3—61no—
417C2×C3⋊D3—68no—
418C2×C3⋊D3—61no—
419C2×C3⋊D3—61no—
420C2×C3⋊D3—64no—
421C2×C3⋊D3—61no—
422C2×C3⋊D3—64no—
423C2×C3⋊D3—64no—
424C2×C3⋊D3—64no—
425C2×C3⋊D3—64no—
426C2×C3⋊D3—124no—
427C2×C3⋊D3—124no—
428C2×C3⋊D3—124no—
429C2×C3⋊D3—124no—
430C2×C3⋊D3—124no—
431C2×C3⋊D3—1216no—
432C2×C3⋊D3—1232no—
433C2×C3×D3—64no—
434C2×C3×D3—64no—
435C2×C3×D3—64no—
436C32×C4—21no—
437C32×C4—21no—
438C32×C4—24no—
439C32×C4—24no—
440C32×C4—44no—
441C32×C4—44no—
442C32×C4—61no—
443C32×C4—61no—
444C32×C4—61no—
445C32×C4—61no—
446C3⋊Dic3—21no—
447C3⋊Dic3—21no—
448C3⋊Dic3—21no—
449C3⋊Dic3—61no—
450C3⋊Dic3—61no—
451C3⋊Dic3—64no—
452C3⋊Dic3—64no—
453C3⋊Dic3—124no—
454C3⋊Dic3—124no—
455C3×Dic3—24no—
456C3×Dic3—24no—
457C3×Dic3—24no—
458C3×Dic3—24no—
459C3×Dic3—64no—
460C3×Dic3—64no—
461C3×Dic3—64no—
462#126—271no—
463#126—271no—
464#124—271no—
465#123—271no—
466#123—271no—
467#123—271no—
468C22⋊Q8—31no—
469C22⋊Q8—271no—
470#120—271no—
471C4×D4—91no—
472C4×D4—271no—
473#117—271no—
474#117—271no—
475C2×C22⋊C4—271no—
476C2×C22⋊C4—271no—
477C33#55111yescharacteristic, complemented, Sylow
478C23×C3—24no—
479C23×C3—91no—
480C23×C3C2×D3214yes—
481C23×C3C22×C3⋊D311yescharacteristic
482C22×D3—34no—
483C22×D3—94no—
484C22×D3—91no—
485C22×D3—94no—
486C22×D3—91no—
487C22×D3—184no—
488C22×D3—184no—
489C22×D3—188no—
490C22×D3—182no—
491C22×D3—1816no—
492C22×D3—188no—
493C22×D3—182no—
494C22×D3—368no—
495C22×D3—364no—
496C22×D3—361no—
497C22×D3—368no—
498C3×Q8—124no—
499C3×D4—182no—
500C2×C3×C4—24no—
501C2×C3×C4—24no—
502C2×C3×C4—34no—
503C2×C3×C4—34no—
504C2×C3×C4—34no—
505C2×C3×C4—34no—
506C2×C3×C4—44no—
507C2×C3×C4—41no—
508C2×C3×C4—48no—
509C2×C3×C4—91no—
510C2×C3×C4—91no—
511C2×C3×C4—91no—
512C2×C3×C4—361no—
513C2×C3×C4C2×D3214yes—
514C2×C3×C4C2×D3214yes—
515C2×C3×C4C22×C3⋊D311yescharacteristic
516C2×C3×C4C22×C3⋊D311yescharacteristic
517#67—68no—
518#67—182no—
519#67—361no—
520C2×Dic3—34no—
521C2×Dic3—34no—
522C2×Dic3—34no—
523C2×Dic3—94no—
524C2×Dic3—94no—
525C2×Dic3—91no—
526C2×Dic3—91no—
527C2×Dic3—184no—
528C2×Dic3—184no—
529C2×Dic3—188no—
530C2×Dic3—182no—
531C2×Dic3—368no—
532C2×Dic3C22×C3⋊D311yescharacteristic
533C2×Dic3C22×C3⋊D311yescharacteristic
534C2×Dic3C22×C3⋊D311yescharacteristic
535C2×Dic3C22×C3⋊D311yescharacteristic
536D12—188no—
537D12—364no—
538C4×D3—124no—
539C4×D3—182no—
540C4×D3—188no—
541C4×D3—361no—
542C4×D3—364no—
543Dic6—41no—
544C2×C32—216no—
545C2×C32—28no—
546C2×C32—22no—
547C2×C32—24no—
548C2×C32—24no—
549C2×C32—24no—
550C2×C32C2×#23511yescharacteristic
551C2×C32#100414yes—
552C2×C32#100411yescharacteristic
553C2×C32C2×#23914yes—
554C2×C32D3×#4114yes—
555C2×C32D3×#4111yescharacteristic
556C3⋊D3—41no—
557C3⋊D3—62no—
558C3⋊D3—68no—
559C3⋊D3—128no—
560C3⋊D3—128no—
561C3⋊D3—124no—
562C3⋊D3—121no—
563C3×D3—124no—
564C24—271no—
565C2×Q8—31no—
566C2×D4—91no—
567C2×D4—271no—
568C2×D4—271no—
569C22×C4—91no—
570C22×C4—271no—
571C22×C4—271no—
572C22×C4—271no—
573C22×C4D3×C3⋊D311yescharacteristic
574C4⋊C4—31no—
575C4⋊C4—31no—
576C4⋊C4—31no—
577C4⋊C4—91no—
578C4⋊C4—271no—
579C4⋊C4—271no—
580C4⋊C4—271no—
581C4⋊C4—271no—
582C22⋊C4—31no—
583C22⋊C4—31no—
584C22⋊C4—91no—
585C22⋊C4—91no—
586C22⋊C4—271no—
587C22⋊C4—271no—
588C22⋊C4—271no—
589C22⋊C4—271no—
590C22⋊C4—271no—
591C22⋊C4—271no—
592C22⋊C4—271no—
593C22⋊C4—271no—
594C22⋊C4—271no—
595C22⋊C4—271no—
596C42—91no—
597C42—271no—
598C42—271no—
599C22×C3—28no—
600C22×C3—28no—
601C22×C3—24no—
602C22×C3—24no—
603C22×C3—21no—
604C22×C3—21no—
605C22×C3—24no—
606C22×C3—28no—
607C22×C3—181no—
608C22×C3—181no—
609C22×C3—181no—
610C22×C3#379918yes—
611C22×C3#383212yes—
612C22×C3C22×D3214yes—
613C22×C3C23×C3⋊D311yescharacteristic
614C2×D3—64no—
615C2×D3—64no—
616C2×D3—64no—
617C2×D3—98no—
618C2×D3—92no—
619C2×D3—188no—
620C2×D3—184no—
621C2×D3—184no—
622C2×D3—181no—
623C2×D3—181no—
624C2×D3—188no—
625C2×D3—184no—
626C2×D3—184no—
627C2×D3—184no—
628C2×D3—181no—
629C2×D3—181no—
630C2×D3—181no—
631C2×D3—364no—
632C2×D3—364no—
633C2×D3—364no—
634C2×D3—364no—
635C2×D3—364no—
636C2×D3—3616no—
637C2×D3—3632no—
638C3×C4—24no—
639C3×C4—24no—
640C3×C4—21no—
641C3×C4—21no—
642C3×C4—44no—
643C3×C4—44no—
644C3×C4—64no—
645C3×C4—64no—
646C3×C4—64no—
647C3×C4—64no—
648C3×C4—181no—
649C3×C4—181no—
650C3×C4—181no—
651Dic3—21no—
652Dic3—21no—
653Dic3—21no—
654Dic3—21no—
655Dic3—64no—
656Dic3—64no—
657Dic3—64no—
658Dic3—184no—
659Dic3—184no—
660Dic3—181no—
661Dic3—181no—
662Dic3—364no—
663Dic3—364no—
664C32—24no—
665C32#555611yescharacteristic, complemented
666C32#563714yescomplemented
667C23—91no—
668C23—271no—
669C23—271no—
670C23—542no—
671C23—542no—
672C23—1081no—
673C23C2×D3×C3⋊D311yescharacteristic
674Q8—121no—
675D4—182no—
676D4—542no—
677D4—1081no—
678C2×C4—31no—
679C2×C4—31no—
680C2×C4—31no—
681C2×C4—31no—
682C2×C4—41no—
683C2×C4—91no—
684C2×C4—91no—
685C2×C4—91no—
686C2×C4—271no—
687C2×C4—271no—
688C2×C4—361no—
689C2×C4—542no—
690C2×C4—542no—
691C2×C4—1081no—
692C2×C4C2×D3×C3⋊D311yescharacteristic
693C2×C4C2×D3×C3⋊D311yescharacteristic
694C2×C3—216no—
695C2×C3—22no—
696C2×C3—28no—
697C2×C3—24no—
698C2×C3—24no—
699C2×C3—24no—
700C2×C3—361no—
701C2×C3C2×#379914yes—
702C2×C3#6430614yes—
703C2×C3#6433014yes—
704C2×C3#6436111yescharacteristic
705C2×C3C2×#383211yescharacteristic
706C2×C3#41×C3⋊D311yescharacteristic
707D3—124no—
708D3—182no—
709D3—188no—
710D3—368no—
711D3—368no—
712D3—361no—
713D3—364no—
714C22—21no—
715C22—21no—
716C22—181no—
717C22—181no—
718C22—181no—
719C22—272no—
720C22—541no—
721C22—541no—
722C22—541no—
723C22—541no—
724C22—541no—
725C22—1084no—
726C22#8901812yes—
727C22C22×D3×C3⋊D311yescharacteristic
728C4—21no—
729C4—21no—
730C4—61no—
731C4—61no—
732C4—61no—
733C4—61no—
734C4—181no—
735C4—181no—
736C4—181no—
737C4—541no—
738C4—541no—
739C3—24no—
740C3#1059503514yescomplemented
741C3#1059610811yescharacteristic, complemented
742C2—22no—
743C2—361no—
744C2—542no—
745C2—1081no—
746C2C2×#8901811yescharacteristic
747C2#1172457811yescharacteristic
748C2#1172461111yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC22×C33×C4C22
prime radical#11723639C2
hypercenterC22×C4D3×C3⋊D3
hypocenterC33#551
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C2×#88859C2semidirect
2. C3×C4×#638C2semidirect
3. C32×#924C2semidirect
5. #11723627C2semidirect
6. #11723609C2semidirect
7. #11723598C2semidirect
8. #11723512C2semidirect
9. #11723504C2semidirect
10. #11723477C2semidirect
11. #11723469C2semidirect
12. #11723446C2semidirect
13. #11723417C2semidirect
14. #11723411C2semidirect
15. #11723392C2semidirect
22. C2×C3×C4×C3⋊D3C22semidirect
23. C2×C32×Dic6C22semidirect
33. C3×#3752C22semidirect
34. C3×#3750C22semidirect
35. C3×C4×C3⋊Dic3C22semidirect
38. C32×C4⋊Dic3C22semidirect
39. C32×Dic3⋊C4C22semidirect
40. C32×Dic3⋊C4C22semidirect
41. #88806C22semidirect
42. #88806C22semidirect
43. Dic3⋊(C3⋊Dic3)C22semidirect
44. Dic3⋊(C3⋊Dic3)C22semidirect
49. #88803C22semidirect
50. #88803C22semidirect
51. Dic3×C3⋊Dic3C22semidirect
52. Dic3×C3⋊Dic3C22semidirect
56. C4×#638D3semidirect
71. C3×#924D3semidirect
128. C2×C4×C3⋊D3C2×D3semidirect
131. C2×C3×Dic6C2×D3semidirect
160. #3752C2×D3semidirect
165. #3750C2×D3semidirect
168. C4×C3⋊Dic3C2×D3semidirect
173. C3×C4⋊Dic3C2×D3semidirect
175. C3×Dic3⋊C4C2×D3semidirect
176. C3×Dic3⋊C4C2×D3semidirect
227. #924C3⋊D3semidirect
342. C2×Dic6C2×C3⋊D3semidirect
382. C4⋊Dic3C2×C3⋊D3semidirect
390. Dic3⋊C4C2×C3⋊D3semidirect
391. Dic3⋊C4C2×C3⋊D3semidirect
477. C33#551semidirect
665. C32#5556semidirect
666. C32#5637semidirect
740. C3#10595035semidirect
741. C3#10596108semidirect

Maximal subgroups

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

subgroupindex
C2×#888592
C3×C4×#6382
C32×#9242
#117236392
#117236272
#117236092
#117235982
#117235122
#117235042
#117234772
#117234692
#117234462
#117234172
#117234112
#117233922
#105961083
#105950353