Finite Group Databasebeta

← #13176597

Subgroups — #13176597

Order 1728.

1792 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723933C211yesmaximal, characteristic, complemented
2C3×#64103C211yesmaximal, characteristic, complemented
3C32×#896C211yesmaximal, characteristic, complemented
4#11723541C211yesmaximal, characteristic
5#11723539C211yesmaximal, characteristic, complemented
6D3×#3752C211yesmaximal, characteristic, complemented
7#11723512C211yesmaximal, characteristic, complemented
8C4×#6290C211yesmaximal, characteristic, complemented
9#11723480C211yesmaximal, characteristic, complemented
10#11723477C211yesmaximal, characteristic, complemented
11#11723460C211yesmaximal, characteristic, complemented
12#11723436C211yesmaximal, characteristic, complemented
13#11723433C211yesmaximal, characteristic, complemented
14#11723421C211yesmaximal, characteristic, complemented
15#11723408C211yesmaximal, characteristic, complemented
16#10596108—31nomaximal
17#10594653—34nomaximal
18C22×D3×C3⋊D3C2211yescharacteristic
19C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
20C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
21C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
22C2×C32×C4×D3C2211yescharacteristic
23C2×C32×Dic6C2211yescharacteristic, complemented
24C2×#6292C2211yescharacteristic
25C2×#6290C2211yescharacteristic
26C2×#6289C2211yescharacteristic
27C2×D3×C3⋊Dic3C2211yescharacteristic
28C33×C4⋊C4C2211yescharacteristic, complemented
29#88859C2211yescharacteristic
30#88859C2211yescharacteristic
31C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic, complemented
32C4×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
33C4×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
34C3×#3752C2211yescharacteristic
35C3×#3752C2211yescharacteristic
36C3×#3752C2211yescharacteristic, complemented
37C3×#3750C2211yescharacteristic, complemented
38C32×(C2×D3)⋊C4C2211yescharacteristic
39C32×(C2×D3)⋊C4C2211yescharacteristic
40C32×Dic3⋊C4C2211yescharacteristic, complemented
41C32×Dic3⋊C4C2211yescharacteristic, complemented
42#88807C2211yescharacteristic, complemented
43#88806C2211yescharacteristic, complemented
44Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
45#88804C2211yescharacteristic
46#88803C2211yescharacteristic
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#64103—31no—
61#64103D311yescharacteristic, complemented
62#64102—31no—
63#64101—31no—
64#64101—34no—
65#64101—64no—
66#64095—31no—
67#64091—31no—
68C22⋊C4×C3⋊D3—31no—
69#64086—31no—
70C3×#896D314yescomplemented
71C3×#894—34no—
72#63922—34no—
73#63921—34no—
74D3×(C2×D3)⋊C4—34no—
75#63904—34no—
76C4×#625—34no—
77#63891—34no—
78#63888—34no—
79#63878—34no—
80#63863—34no—
81#63862—34no—
82#63861—34no—
83#63853—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
97C4×C3⋊(C3⋊D3)—22no—
98C2×C3×C3⋊Dic3C2311yescharacteristic
99C2×C3×C3⋊Dic3C2311yescharacteristic
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—22no—
108#6290—22no—
109#6289—41no—
110D3×C3⋊Dic3—22no—
111#5659—91no—
112#5637—94no—
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⋊D3—34no—
123C2×C4×C3⋊D3—31no—
124C2×C4×C3⋊D3—64no—
125C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
126C2×C3×D12—34no—
127C2×C3×C4×D3—34no—
128C2×C3×C4×D3C2×D314yes—
129C2×C3×Dic6C2×D314yescomplemented
130C2×#626—34no—
131C2×#625—34no—
132C2×#624—34no—
133C2×D3×Dic3—34no—
134C32×C4⋊C4—24no—
135C32×C4⋊C4—31no—
136C32×C4⋊C4—31no—
137C32×C4⋊C4C2×D314yescomplemented
138C32×C4⋊C4C2×D311yescharacteristic, complemented
139C32×C22⋊C4—31no—
140C32×C22⋊C4—31no—
141#3757—31no—
142#3752—31no—
143#3752—31no—
144#3752—31no—
145#3752—31no—
146#3752—31no—
147#3752—31no—
148#3752—31no—
149#3752—34no—
150#3752—34no—
151#3752—31no—
152#3752—64no—
153#3752—64no—
154#3752C2×D311yescharacteristic
155#3752C2×D311yescharacteristic
156#3752C2×D311yescharacteristic, complemented
157C4⋊(C3⋊Dic3)—31no—
158C4⋊(C3⋊Dic3)—34no—
159C4⋊(C3⋊Dic3)—31no—
160C4⋊(C3⋊Dic3)—64no—
161#3750—31no—
162#3750—31no—
163#3750C2×D311yescharacteristic, complemented
164C4×C3⋊Dic3—31no—
165C4×C3⋊Dic3—31no—
166C4×C3⋊Dic3—34no—
167C4×C3⋊Dic3—34no—
168C4×C3⋊Dic3—31no—
169C4×C3⋊Dic3—64no—
170C4×C3⋊Dic3—64no—
171C3×(C2×D3)⋊C4—34no—
172C3×(C2×D3)⋊C4—34no—
173C3×(C2×D3)⋊C4—34no—
174C3×(C2×D3)⋊C4C2×D314yes—
175C3×(C2×D3)⋊C4C2×D314yes—
176C3×Dic3⋊C4—34no—
177C3×Dic3⋊C4C2×D314yescomplemented
178C3×Dic3⋊C4C2×D314yescomplemented
179#3724—34no—
180Dic3⋊Dic3—34no—
181Dic3⋊Dic3—34no—
182#3722—34no—
183(C2×D3)⋊Dic3—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)#4112yes—
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—21no—
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×#123—91no—
216C3×C22⋊Q8—34no—
217#947—94no—
218#946—94no—
219#937—91no—
220#936—91no—
221C4×#67—94no—
222C4×#67—91no—
223C4×#67—91no—
224C2×(C2×D3)⋊C4—94no—
225#898—94no—
226#898—94no—
227#896—91no—
228#896C3⋊D311yescharacteristic, complemented
229#894—34no—
230#894—94no—
231#893—94no—
232#892—94no—
233#892—91no—
234#892—91no—
235#892—184no—
236#886—94no—
237#883—91no—
238#883—91no—
239#882—94no—
240D3×C22⋊C4—94no—
241D3×C22⋊C4—91no—
242D3×C22⋊C4—91no—
243#879—91no—
244#879—91no—
245#877—94no—
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)—41no—
289C4⋊(C3⋊D3)—62no—
290C4×C3⋊D3—41no—
291C4×C3⋊D3—62no—
292C4×C3⋊D3—68no—
293C4×C3⋊D3—616no—
294C4×C3⋊D3—121no—
295C2×C3×Dic3—34no—
296C2×C3×Dic3—34no—
297C2×C3×Dic3C22×D314yes—
298C2×C3×Dic3C22×D314yes—
299C2×C3×Dic3C22×D314yes—
300C3×D12—124no—
301C3×C4×D3—44no—
302C3×C4×D3—124no—
303C3×Dic6—44no—
304#626—68no—
305#625—68no—
306#624—124no—
307D3×Dic3—68no—
308#551—271noSylow
309C2×C33C2×#4111yescharacteristic
310C2×C33C2×#4111yescharacteristic
311C2×C33H(5,𝔽2)11yescharacteristic
312C3⋊(C3⋊D3)—22no—
313C3×C3⋊D3—41no—
314C3×C3⋊D3—41no—
315C32×D3—22no—
316C23×D3—94no—
317C23×D3—91no—
318C2×C3×Q8—34no—
319C2×C3×D4—91no—
320C22×C3×C4—34no—
321C22×C3×C4—91no—
322C2×#67—94no—
323C2×#67—91no—
324C2×#67—91no—
325C22×Dic3—94no—
326C2×D12—34no—
327C2×D12—94no—
328C2×C4×D3—34no—
329C2×C4×D3—91no—
330C2×C4×D3—94no—
331C2×C4×D3—91no—
332C2×C4×D3—94no—
333C2×C4×D3—91no—
334C2×C4×D3—184no—
335C2×C4×D3C2×C3⋊D311yescharacteristic
336C2×Dic6C2×C3⋊D311yescharacteristic, complemented
337C3×C4⋊C4—24no—
338C3×C4⋊C4—34no—
339C3×C4⋊C4—34no—
340C3×C4⋊C4—91no—
341C3×C4⋊C4D3214yescomplemented
342C3×C4⋊C4C2×C3⋊D311yescharacteristic, complemented
343C3×C22⋊C4—34no—
344C3×C22⋊C4—34no—
345C3×C22⋊C4—91no—
346C3×C22⋊C4—91no—
347C3×C22⋊C4—91no—
348#217—94no—
349#217—91no—
350#217—91no—
351#217—91no—
352#217—91no—
353#217—91no—
354(C2×D3)⋊C4—34no—
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—94no—
362(C2×D3)⋊C4—94no—
363(C2×D3)⋊C4—91no—
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—184no—
370(C2×D3)⋊C4—184no—
371(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
372(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
373C4⋊Dic3—94no—
374C4⋊Dic3—94no—
375C4⋊Dic3—91no—
376C4⋊Dic3—91no—
377C4⋊Dic3—184no—
378Dic3⋊C4—34no—
379Dic3⋊C4—94no—
380Dic3⋊C4—94no—
381Dic3⋊C4—91no—
382Dic3⋊C4—91no—
383Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
384Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
385C4×Dic3—94no—
386C4×Dic3—94no—
387C4×Dic3—94no—
388C4×Dic3—91no—
389C4×Dic3—91no—
390C4×Dic3—91no—
391C4×Dic3—184no—
392C4×Dic3—184no—
393C22×C32—24no—
394C22×C32—32no—
395C22×C32—61no—
396C22×C32—61no—
397C22×C32C23×D314yes—
398C22×C32C23×D311yescharacteristic
399C2×C3⋊D3—21no—
400C2×C3⋊D3—21no—
401C2×C3⋊D3—21no—
402C2×C3⋊D3—21no—
403C2×C3⋊D3—21no—
404C2×C3⋊D3—21no—
405C2×C3⋊D3—32no—
406C2×C3⋊D3—38no—
407C2×C3⋊D3—68no—
408C2×C3⋊D3—61no—
409C2×C3⋊D3—61no—
410C2×C3⋊D3—64no—
411C2×C3⋊D3—64no—
412C2×C3⋊D3—124no—
413C2×C3⋊D3—124no—
414C2×C3⋊D3—124no—
415C2×C3×D3—24no—
416C2×C3×D3—24no—
417C2×C3×D3—64no—
418C2×C3×D3—64no—
419C2×C3×D3—64no—
420C2×C3×D3—64no—
421C2×C3×D3—64no—
422C2×C3×D3—64no—
423C2×C3×D3#23918yes—
424D32—1216no—
425C32×C4—28no—
426C32×C4—21no—
427C32×C4—21no—
428C32×C4—24no—
429C32×C4—21no—
430C32×C4—24no—
431C32×C4—24no—
432C32×C4—44no—
433C32×C4—44no—
434C32×C4—61no—
435C32×C4—61no—
436C32×C4—61no—
437C3⋊Dic3—21no—
438C3⋊Dic3—21no—
439C3⋊Dic3—68no—
440C3⋊Dic3—64no—
441C3⋊Dic3—61no—
442C3⋊Dic3—61no—
443C3⋊Dic3—61no—
444C3⋊Dic3—64no—
445C3⋊Dic3—64no—
446C3⋊Dic3—124no—
447C3⋊Dic3—124no—
448C3×Dic3—24no—
449C3×Dic3—24no—
450C3×Dic3—24no—
451C3×Dic3—64no—
452C3×Dic3—64no—
453#126—271no—
454#126—271no—
455#124—271no—
456#123—91no—
457#123—271no—
458#123—271no—
459C22⋊Q8—31no—
460C22⋊Q8—271no—
461#120—271no—
462C4×D4—271no—
463C4×D4—271no—
464#117—271no—
465#117—271no—
466C2×C22⋊C4—271no—
467C2×C22⋊C4—271no—
468C33#55111yescharacteristic, complemented, Sylow
469C23×C3—34no—
470C23×C3—91no—
471C23×C3—91no—
472C22×D3—34no—
473C22×D3—34no—
474C22×D3—94no—
475C22×D3—91no—
476C22×D3—184no—
477C22×D3—182no—
478C22×D3—188no—
479C22×D3—188no—
480C22×D3—182no—
481C22×D3—361no—
482C22×D3—364no—
483C22×D3C22×C3⋊D311yescharacteristic
484C3×Q8—124no—
485C3×D4—361no—
486C2×C3×C4—24no—
487C2×C3×C4—24no—
488C2×C3×C4—24no—
489C2×C3×C4—34no—
490C2×C3×C4—34no—
491C2×C3×C4—34no—
492C2×C3×C4—91no—
493C2×C3×C4—91no—
494C2×C3×C4—124no—
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—182no—
503#67—188no—
504#67—182no—
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—188no—
517C2×Dic3C22×C3⋊D311yescharacteristic
518C2×Dic3C22×C3⋊D311yescharacteristic
519C2×Dic3C22×C3⋊D311yescharacteristic
520D12—124no—
521D12—188no—
522C4×D3—41no—
523C4×D3—124no—
524C4×D3—188no—
525C4×D3—182no—
526C4×D3—1816no—
527C4×D3—182no—
528C4×D3—361no—
529C4×D3—364no—
530Dic6—41no—
531C2×C32—24no—
532C2×C32—24no—
533C2×C32—24no—
534C2×C32—62no—
535C2×C32#100414yes—
536C2×C32#100411yescharacteristic
537C2×C32C2×#23914yes—
538C2×C32D3×#4114yes—
539C2×C32D3×#4111yescharacteristic
540C2×C32D3×#4111yescharacteristic
541C3⋊D3—41no—
542C3⋊D3—41no—
543C3⋊D3—62no—
544C3⋊D3—68no—
545C3⋊D3—128no—
546C3×D3—28no—
547C3×D3—124no—
548C3×D3—124no—
549C24—271no—
550C2×Q8—31no—
551C2×D4—91no—
552C2×D4—271no—
553C2×D4—271no—
554C22×C4—31no—
555C22×C4—91no—
556C22×C4—271no—
557C22×C4—271no—
558C22×C4—271no—
559C4⋊C4—31no—
560C4⋊C4—31no—
561C4⋊C4—91no—
562C4⋊C4—271no—
563C4⋊C4—271no—
564C4⋊C4—271no—
565C4⋊C4—271no—
566C4⋊C4D3×C3⋊D311yescharacteristic, complemented
567C22⋊C4—31no—
568C22⋊C4—31no—
569C22⋊C4—91no—
570C22⋊C4—91no—
571C22⋊C4—91no—
572C22⋊C4—271no—
573C22⋊C4—271no—
574C22⋊C4—271no—
575C22⋊C4—271no—
576C22⋊C4—271no—
577C22⋊C4—271no—
578C22⋊C4—271no—
579C22⋊C4—271no—
580C22⋊C4—271no—
581C42—271no—
582C42—271no—
583C42—271no—
584C22×C3—24no—
585C22×C3—38no—
586C22×C3—64no—
587C22×C3—64no—
588C22×C3—181no—
589C22×C3—181no—
590C22×C3—181no—
591C22×C3—181no—
592C22×C3—181no—
593C22×C3—181no—
594C22×C3C22×D3214yes—
595C22×C3C23×C3⋊D311yescharacteristic
596C2×D3—21no—
597C2×D3—21no—
598C2×D3—64no—
599C2×D3—64no—
600C2×D3—64no—
601C2×D3—64no—
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—364no—
612C2×D3—364no—
613C2×D3—364no—
614C2×D3—3616no—
615C2×D3#383212yes—
616C3×C4—28no—
617C3×C4—24no—
618C3×C4—24no—
619C3×C4—24no—
620C3×C4—21no—
621C3×C4—21no—
622C3×C4—21no—
623C3×C4—44no—
624C3×C4—44no—
625C3×C4—64no—
626C3×C4—64no—
627C3×C4—64no—
628C3×C4—181no—
629C3×C4—181no—
630Dic3—21no—
631Dic3—21no—
632Dic3—21no—
633Dic3—64no—
634Dic3—64no—
635Dic3—188no—
636Dic3—184no—
637Dic3—184no—
638Dic3—184no—
639Dic3—181no—
640Dic3—181no—
641Dic3—181no—
642Dic3—364no—
643Dic3—364no—
644C32—24no—
645C32#563714yescomplemented
646C32#565911yescharacteristic, complemented
647C23—31no—
648C23—91no—
649C23—91no—
650C23—271no—
651C23—542no—
652C23—542no—
653C23—1081no—
654Q8—121no—
655D4—361no—
656D4—542no—
657D4—542no—
658C2×C4—31no—
659C2×C4—31no—
660C2×C4—31no—
661C2×C4—91no—
662C2×C4—91no—
663C2×C4—121no—
664C2×C4—271no—
665C2×C4—271no—
666C2×C4—271no—
667C2×C4—361no—
668C2×C4—542no—
669C2×C4—542no—
670C2×C4—1081no—
671C2×C4C2×D3×C3⋊D311yescharacteristic
672C2×C4C2×D3×C3⋊D311yescharacteristic
673C2×C4C2×D3×C3⋊D311yescharacteristic
674C2×C3—24no—
675C2×C3—24no—
676C2×C3—24no—
677C2×C3—68no—
678C2×C3—361no—
679C2×C3—361no—
680C2×C3#6430614yes—
681C2×C3#6431314yes—
682C2×C3D3×#23914yes—
683C2×C3#6436111yescharacteristic
684C2×C3C2×#383211yescharacteristic
685C2×C3#41×C3⋊D311yescharacteristic
686D3—22no—
687D3—124no—
688D3—124no—
689D3—182no—
690D3—188no—
691D3—368no—
692C22—32no—
693C22—61no—
694C22—61no—
695C22—181no—
696C22—181no—
697C22—181no—
698C22—181no—
699C22—181no—
700C22—181no—
701C22—272no—
702C22—541no—
703C22—541no—
704C22—1084no—
705C22C22×D3×C3⋊D311yescharacteristic
706C4—21no—
707C4—21no—
708C4—21no—
709C4—61no—
710C4—61no—
711C4—61no—
712C4—181no—
713C4—181no—
714C4—541no—
715C4—541no—
716C4—541no—
717C3—24no—
718C3#1059465314yescomplemented
719C3#1059610811yescharacteristic, complemented
720C2—62no—
721C2—361no—
722C2—361no—
723C2—542no—
724C2#1172457811yescharacteristic
725C2#1172458711yescharacteristic
726C2D3×#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. #11723933C2semidirect
2. C3×#64103C2semidirect
3. C32×#896C2semidirect
5. #11723539C2semidirect
6. D3×#3752C2semidirect
7. #11723512C2semidirect
8. C4×#6290C2semidirect
9. #11723480C2semidirect
10. #11723477C2semidirect
11. #11723460C2semidirect
12. #11723436C2semidirect
13. #11723433C2semidirect
14. #11723421C2semidirect
15. #11723408C2semidirect
21. C2×C3×C4×C3⋊D3C22semidirect
23. C2×C32×Dic6C22semidirect
28. C33×C4⋊C4C22semidirect
31. C4⋊(C3⋊(C3⋊Dic3))C22semidirect
32. C4×C3⋊(C3⋊Dic3)C22semidirect
33. C4×C3⋊(C3⋊Dic3)C22semidirect
36. C3×#3752C22semidirect
37. C3×#3750C22semidirect
40. C32×Dic3⋊C4C22semidirect
41. C32×Dic3⋊C4C22semidirect
42. #88807C22semidirect
43. #88806C22semidirect
44. Dic3⋊(C3⋊Dic3)C22semidirect
49. #88803C22semidirect
50. #88803C22semidirect
52. Dic3×C3⋊Dic3C22semidirect
61. #64103D3semidirect
70. C3×#896D3semidirect
125. C2×C4×C3⋊D3C2×D3semidirect
129. C2×C3×Dic6C2×D3semidirect
137. C32×C4⋊C4C2×D3semidirect
138. C32×C4⋊C4C2×D3semidirect
156. #3752C2×D3semidirect
163. #3750C2×D3semidirect
177. C3×Dic3⋊C4C2×D3semidirect
178. C3×Dic3⋊C4C2×D3semidirect
228. #896C3⋊D3semidirect
336. C2×Dic6C2×C3⋊D3semidirect
341. C3×C4⋊C4D32semidirect
342. C3×C4⋊C4C2×C3⋊D3semidirect
383. Dic3⋊C4C2×C3⋊D3semidirect
384. Dic3⋊C4C2×C3⋊D3semidirect
468. C33#551semidirect
566. C4⋊C4D3×C3⋊D3semidirect
645. C32#5637semidirect
646. C32#5659semidirect
718. C3#10594653semidirect
719. C3#10596108semidirect

Maximal subgroups

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

subgroupindex
#117239332
C3×#641032
C32×#8962
#117235412
#117235392
D3×#37522
#117235122
C4×#62902
#117234802
#117234772
#117234602
#117234362
#117234332
#117234212
#117234082
#105961083
#105946533