Finite Group Databasebeta

← #13177959

Subgroups — #13177959

Order 1728.

1784 conjugacy classes of subgroups.

The subgroup lattice has 730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723987C211yesmaximal, characteristic, complemented
2C3×#64156C211yesmaximal, characteristic, complemented
3C32×#946C211yesmaximal, characteristic, complemented
4#11723541C211yesmaximal, characteristic
5#11723539C211yesmaximal, characteristic, complemented
6D3×#3752C211yesmaximal, characteristic, complemented
7#11723506C211yesmaximal, characteristic, complemented
8#11723504C211yesmaximal, characteristic, complemented
9#11723488C211yesmaximal, characteristic, complemented
10#11723480C211yesmaximal, characteristic, complemented
11#11723472C211yesmaximal, characteristic, complemented
12#11723469C211yesmaximal, characteristic, complemented
13#11723459C211yesmaximal, characteristic, complemented
14#11723408C211yesmaximal, characteristic, complemented
15#11723407C211yesmaximal, characteristic, complemented
16#10596108—31nomaximal
17#10595437—34nomaximal
18C22×D3×C3⋊D3C2211yescharacteristic
19C2×C33×Q8C2211yescharacteristic, complemented
20C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
21C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
22C2×C32×C4×D3C2211yescharacteristic
23C2×#6292C2211yescharacteristic
24C2×#6290C2211yescharacteristic
25C2×#6289C2211yescharacteristic
26C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
27C2×D3×C3⋊Dic3C2211yescharacteristic
28#88859C2211yescharacteristic
29#88859C2211yescharacteristic
30C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic, complemented
31#88857C2211yescharacteristic, complemented
32#88857C2211yescharacteristic, complemented
33C3×#3752C2211yescharacteristic
34C3×#3752C2211yescharacteristic
35C3×#3752C2211yescharacteristic, complemented
36C3×#3752C2211yescharacteristic, complemented
37C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
38C32×(C2×D3)⋊C4C2211yescharacteristic
39C32×(C2×D3)⋊C4C2211yescharacteristic
40C32×C4⋊Dic3C2211yescharacteristic, complemented
41C32×Dic3⋊C4C2211yescharacteristic, complemented
42C32×Dic3⋊C4C2211yescharacteristic, complemented
43#88806C2211yescharacteristic, complemented
44Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
45#88804C2211yescharacteristic
46#88803C2211yescharacteristic
47#88803C2211yescharacteristic
48#88803C2211yescharacteristic
49#88803C2211yescharacteristic, complemented
50(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
51Dic3×C3⋊Dic3C2211yescharacteristic, complemented
52Dic3×C3⋊Dic3C2211yescharacteristic, complemented
53C32×C22⋊Q8—31no—
54#64156D311yescharacteristic, complemented
55#64155—31no—
56#64155—34no—
57#64155—64no—
58C4×#638—31no—
59C2×#3752—31no—
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×#947—34no—
71C3×#946D314yescomplemented
72#63922—34no—
73#63921—34no—
74D3×(C2×D3)⋊C4—34no—
75#63891—34no—
76#63884—34no—
77#63881—34no—
78#63879—34no—
79#63877—34no—
80#63861—34no—
81#63858—34no—
82#63854—34no—
83#63836—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—
91C33×Q8—41no—
92C2×C33×C4C2311yescharacteristic
93C2×C33×C4C2311yescharacteristic
94C2×C33×C4C2311yescharacteristic
95C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
96C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
97C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
98C4×C3⋊(C3⋊D3)—41no—
99C2×C3×C3⋊Dic3C2311yescharacteristic
100C2×C3×C3⋊Dic3C2311yescharacteristic
101C3×C4⋊(C3⋊D3)—41no—
102C2×C32×Dic3C2311yescharacteristic
103C2×C32×Dic3C2311yescharacteristic
104C2×C32×Dic3C2311yescharacteristic
105C32×C4×D3—41no—
106#6292—22no—
107#6290—22no—
108#6289—22no—
109Dic3×C3⋊D3—41no—
110D3×C3⋊Dic3—22no—
111#5679—91no—
112#5637—94no—
113C23×C3⋊D3—31no—
114C22×D32—34no—
115C2×C32×Q8—24no—
116C2×C32×Q8C2×D314yescomplemented
117C2×C32×Q8C2×D311yescharacteristic, complemented
118C22×C32×C4—31no—
119C2×#638—31no—
120C22×C3⋊Dic3—31no—
121C2×C4⋊(C3⋊D3)—31no—
122C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
123C2×C4×C3⋊D3—31no—
124C2×C4×C3⋊D3—31no—
125C2×C4×C3⋊D3—31no—
126C2×C4×C3⋊D3—34no—
127C2×C4×C3⋊D3—64no—
128C2×C3×D12—34no—
129C2×C3×C4×D3C2×D314yes—
130C2×#626—34no—
131C2×#625—34no—
132C2×#624—34no—
133C2×D3×Dic3—34no—
134C2×D3×Dic3—34no—
135C32×C4⋊C4—31no—
136C32×C4⋊C4—31no—
137C32×C4⋊C4—31no—
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—34no—
148#3752—34no—
149#3752—31no—
150#3752—64no—
151#3752—64no—
152#3752C2×D311yescharacteristic
153#3752C2×D311yescharacteristic
154#3752C2×D311yescharacteristic, complemented
155#3752C2×D311yescharacteristic, complemented
156C4⋊(C3⋊Dic3)—31no—
157C4⋊(C3⋊Dic3)—34no—
158C4⋊(C3⋊Dic3)—31no—
159C4⋊(C3⋊Dic3)—64no—
160#3750—31no—
161#3750—31no—
162#3750—34no—
163#3750—34no—
164#3750—31no—
165#3750—64no—
166#3750—64no—
167C4×C3⋊Dic3—31no—
168C4×C3⋊Dic3—31no—
169C4×C3⋊Dic3C2×D311yescharacteristic, complemented
170C3×(C2×D3)⋊C4—34no—
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×C4⋊Dic3C2×D314yescomplemented
177C3×Dic3⋊C4C2×D314yescomplemented
178C3×Dic3⋊C4C2×D314yescomplemented
179C3×C4×Dic3—34no—
180#3724—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—
188Dic32—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×#124—91no—
216C3×C22⋊Q8—34no—
217#947—34no—
218#946—94no—
219#946—91no—
220#946—184no—
221#946C3⋊D311yescharacteristic, complemented
222#937—91no—
223#935—91no—
224C4×#67—94no—
225C2×(C2×D3)⋊C4—94no—
226#898—94no—
227#898—94no—
228#894—94no—
229#894—94no—
230#893—94no—
231#892—94no—
232#886—94no—
233#883—91no—
234#883—91no—
235#882—94no—
236#67⋊C4—91no—
237#67⋊C4—91no—
238D3×C22⋊C4—94no—
239D3×C22⋊C4—91no—
240D3×C22⋊C4—91no—
241#879—91no—
242#879—91no—
243#877—94no—
244#872—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—41no—
262C32×Q8—44no—
263C32×Q8—48no—
264C2×C32×C4—24no—
265C2×C32×C4—24no—
266C2×C32×C4—24no—
267C2×C32×C4—31no—
268C2×C32×C4—31no—
269C2×C32×C4—31no—
270C2×C32×C4—121no—
271C2×C32×C4C22×D314yes—
272C2×C32×C4C22×D314yes—
273C2×C32×C4C22×D314yes—
274C2×C32×C4C22×D311yescharacteristic
275C2×C32×C4C22×D311yescharacteristic
276C2×C32×C4C22×D311yescharacteristic
277#638—62no—
278C2×C3⋊Dic3—31no—
279C2×C3⋊Dic3—31no—
280C2×C3⋊Dic3—31no—
281C2×C3⋊Dic3—34no—
282C2×C3⋊Dic3—34no—
283C2×C3⋊Dic3—34no—
284C2×C3⋊Dic3—64no—
285C2×C3⋊Dic3—64no—
286C2×C3⋊Dic3—64no—
287C2×C3⋊Dic3—62no—
288C2×C3⋊Dic3C22×D311yescharacteristic
289C2×C3⋊Dic3C22×D311yescharacteristic
290C4⋊(C3⋊D3)—41no—
291C4⋊(C3⋊D3)—62no—
292C4×C3⋊D3—62no—
293C4×C3⋊D3—121no—
294C4×C3⋊D3—124no—
295C4×C3⋊D3—121no—
296C4×C3⋊D3—128no—
297C2×C3×Dic3—34no—
298C2×C3×Dic3—34no—
299C2×C3×Dic3C22×D314yes—
300C2×C3×Dic3C22×D314yes—
301C2×C3×Dic3C22×D314yes—
302C3×D12—124no—
303C3×C4×D3—44no—
304#626—68no—
305#625—68no—
306#624—68no—
307D3×Dic3—68no—
308D3×Dic3—124no—
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—41no—
316C32×D3—22no—
317C23×D3—94no—
318C23×D3—91no—
319C2×C3×Q8—24no—
320C2×C3×Q8D3214yescomplemented
321C2×C3×Q8C2×C3⋊D311yescharacteristic, complemented
322C2×C3×D4—91no—
323C22×C3×C4—34no—
324C2×#67—94no—
325C2×#67—91no—
326C2×#67—91no—
327C22×Dic3—94no—
328C22×Dic3—91no—
329C2×D12—34no—
330C2×D12—94no—
331C2×C4×D3—94no—
332C2×C4×D3—91no—
333C2×C4×D3—91no—
334C2×C4×D3—94no—
335C2×C4×D3—94no—
336C2×C4×D3—91no—
337C2×C4×D3—184no—
338C2×C4×D3C2×C3⋊D311yescharacteristic
339C3×C4⋊C4—34no—
340C3×C4⋊C4—34no—
341C3×C4⋊C4—34no—
342C3×C22⋊C4—34no—
343C3×C22⋊C4—34no—
344C3×C22⋊C4—91no—
345C3×C22⋊C4—91no—
346C3×C22⋊C4—91no—
347C3×C22⋊C4—91no—
348C3×C42—91no—
349#217—94no—
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—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—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—184no—
377C4⋊Dic3C2×C3⋊D311yescharacteristic, complemented
378Dic3⋊C4—94no—
379Dic3⋊C4—94no—
380Dic3⋊C4—94no—
381Dic3⋊C4—91no—
382Dic3⋊C4—91no—
383Dic3⋊C4—91no—
384Dic3⋊C4—91no—
385Dic3⋊C4—184no—
386Dic3⋊C4—184no—
387Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
388Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
389C4×Dic3—34no—
390C4×Dic3—94no—
391C4×Dic3—94no—
392C4×Dic3—91no—
393C4×Dic3—91no—
394C22×C32—24no—
395C22×C32—32no—
396C22×C32—61no—
397C22×C32—61no—
398C22×C32C23×D314yes—
399C22×C32C23×D311yescharacteristic
400C2×C3⋊D3—21no—
401C2×C3⋊D3—21no—
402C2×C3⋊D3—21no—
403C2×C3⋊D3—21no—
404C2×C3⋊D3—21no—
405C2×C3⋊D3—21no—
406C2×C3⋊D3—32no—
407C2×C3⋊D3—38no—
408C2×C3⋊D3—68no—
409C2×C3⋊D3—61no—
410C2×C3⋊D3—61no—
411C2×C3⋊D3—64no—
412C2×C3⋊D3—64no—
413C2×C3⋊D3—124no—
414C2×C3⋊D3—124no—
415C2×C3⋊D3—124no—
416C2×C3×D3—24no—
417C2×C3×D3—24no—
418C2×C3×D3—64no—
419C2×C3×D3—64no—
420C2×C3×D3—64no—
421C2×C3×D3—64no—
422C2×C3×D3—64no—
423C2×C3×D3—64no—
424C2×C3×D3#23918yes—
425D32—1216no—
426C32×C4—28no—
427C32×C4—24no—
428C32×C4—21no—
429C32×C4—21no—
430C32×C4—21no—
431C32×C4—24no—
432C32×C4—24no—
433C32×C4—44no—
434C32×C4—44no—
435C32×C4—61no—
436C32×C4—61no—
437C32×C4—61no—
438C3⋊Dic3—21no—
439C3⋊Dic3—21no—
440C3⋊Dic3—61no—
441C3⋊Dic3—61no—
442C3⋊Dic3—61no—
443C3⋊Dic3—64no—
444C3⋊Dic3—64no—
445C3⋊Dic3—64no—
446C3⋊Dic3—124no—
447C3⋊Dic3—124no—
448C3⋊Dic3—124no—
449C3×Dic3—24no—
450C3×Dic3—24no—
451C3×Dic3—24no—
452C3×Dic3—64no—
453C3×Dic3—64no—
454#126—271no—
455#126—271no—
456#124—91no—
457#123—271no—
458#123—271no—
459#123—271no—
460C22⋊Q8—31no—
461C22⋊Q8—271no—
462#120—271no—
463C4×D4—271no—
464C4×D4—271no—
465#117—271no—
466#117—271no—
467C2×C22⋊C4—271no—
468C2×C22⋊C4—271no—
469C33#55111yescharacteristic, complemented, Sylow
470C23×C3—34no—
471C23×C3—91no—
472C23×C3—91no—
473C22×D3—34no—
474C22×D3—34no—
475C22×D3—94no—
476C22×D3—91no—
477C22×D3—184no—
478C22×D3—182no—
479C22×D3—188no—
480C22×D3—188no—
481C22×D3—182no—
482C22×D3—361no—
483C22×D3—364no—
484C22×D3C22×C3⋊D311yescharacteristic
485C3×Q8—44no—
486C3×Q8—41no—
487C3×Q8—48no—
488C3×D4—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—124no—
498C2×C3×C4C2×D3214yes—
499C2×C3×C4C2×D3214yes—
500C2×C3×C4C2×D3214yes—
501C2×C3×C4C22×C3⋊D311yescharacteristic
502C2×C3×C4C22×C3⋊D311yescharacteristic
503C2×C3×C4C22×C3⋊D311yescharacteristic
504#67—182no—
505#67—188no—
506#67—182no—
507C2×Dic3—34no—
508C2×Dic3—34no—
509C2×Dic3—94no—
510C2×Dic3—94no—
511C2×Dic3—94no—
512C2×Dic3—91no—
513C2×Dic3—91no—
514C2×Dic3—91no—
515C2×Dic3—184no—
516C2×Dic3—184no—
517C2×Dic3—184no—
518C2×Dic3—188no—
519C2×Dic3—361no—
520C2×Dic3C22×C3⋊D311yescharacteristic
521C2×Dic3C22×C3⋊D311yescharacteristic
522C2×Dic3C22×C3⋊D311yescharacteristic
523D12—124no—
524D12—188no—
525C4×D3—41no—
526C4×D3—182no—
527C4×D3—188no—
528C4×D3—182no—
529C4×D3—364no—
530C4×D3—361no—
531C4×D3—364no—
532C4×D3—368no—
533C2×C32—24no—
534C2×C32—24no—
535C2×C32—24no—
536C2×C32—62no—
537C2×C32#100414yes—
538C2×C32#100411yescharacteristic
539C2×C32C2×#23914yes—
540C2×C32D3×#4114yes—
541C2×C32D3×#4111yescharacteristic
542C2×C32D3×#4111yescharacteristic
543C3⋊D3—41no—
544C3⋊D3—41no—
545C3⋊D3—62no—
546C3⋊D3—68no—
547C3⋊D3—128no—
548C3×D3—28no—
549C3×D3—124no—
550C3×D3—124no—
551C24—271no—
552C2×Q8D3×C3⋊D311yescharacteristic, complemented
553C2×D4—91no—
554C2×D4—271no—
555C2×D4—271no—
556C22×C4—31no—
557C22×C4—271no—
558C22×C4—271no—
559C22×C4—271no—
560C22×C4—271no—
561C4⋊C4—31no—
562C4⋊C4—31no—
563C4⋊C4—31no—
564C4⋊C4—271no—
565C4⋊C4—271no—
566C4⋊C4—271no—
567C4⋊C4—271no—
568C4⋊C4—271no—
569C22⋊C4—31no—
570C22⋊C4—31no—
571C22⋊C4—91no—
572C22⋊C4—91no—
573C22⋊C4—91no—
574C22⋊C4—91no—
575C22⋊C4—271no—
576C22⋊C4—271no—
577C22⋊C4—271no—
578C22⋊C4—271no—
579C22⋊C4—271no—
580C22⋊C4—271no—
581C22⋊C4—271no—
582C22⋊C4—271no—
583C42—91no—
584C42—271no—
585C42—271no—
586C22×C3—24no—
587C22×C3—38no—
588C22×C3—64no—
589C22×C3—64no—
590C22×C3—181no—
591C22×C3—181no—
592C22×C3—181no—
593C22×C3—181no—
594C22×C3—181no—
595C22×C3—181no—
596C22×C3C22×D3214yes—
597C22×C3C23×C3⋊D311yescharacteristic
598C2×D3—21no—
599C2×D3—21no—
600C2×D3—64no—
601C2×D3—64no—
602C2×D3—64no—
603C2×D3—64no—
604C2×D3—64no—
605C2×D3—64no—
606C2×D3—98no—
607C2×D3—92no—
608C2×D3—188no—
609C2×D3—184no—
610C2×D3—184no—
611C2×D3—181no—
612C2×D3—181no—
613C2×D3—364no—
614C2×D3—364no—
615C2×D3—364no—
616C2×D3—3616no—
617C2×D3#383212yes—
618C3×C4—28no—
619C3×C4—24no—
620C3×C4—24no—
621C3×C4—24no—
622C3×C4—21no—
623C3×C4—21no—
624C3×C4—21no—
625C3×C4—44no—
626C3×C4—44no—
627C3×C4—64no—
628C3×C4—64no—
629C3×C4—64no—
630C3×C4—181no—
631C3×C4—181no—
632Dic3—21no—
633Dic3—21no—
634Dic3—21no—
635Dic3—64no—
636Dic3—64no—
637Dic3—184no—
638Dic3—184no—
639Dic3—184no—
640Dic3—181no—
641Dic3—181no—
642Dic3—181no—
643Dic3—364no—
644Dic3—364no—
645Dic3—364no—
646C32—24no—
647C32#563714yescomplemented
648C32#567911yescharacteristic, complemented
649C23—31no—
650C23—91no—
651C23—91no—
652C23—271no—
653C23—542no—
654C23—542no—
655C23—1081no—
656Q8—41no—
657D4—361no—
658D4—542no—
659D4—542no—
660C2×C4—31no—
661C2×C4—31no—
662C2×C4—31no—
663C2×C4—91no—
664C2×C4—91no—
665C2×C4—121no—
666C2×C4—271no—
667C2×C4—271no—
668C2×C4—271no—
669C2×C4—542no—
670C2×C4—542no—
671C2×C4—1081no—
672C2×C4—1081no—
673C2×C4C2×D3×C3⋊D311yescharacteristic
674C2×C4C2×D3×C3⋊D311yescharacteristic
675C2×C4C2×D3×C3⋊D311yescharacteristic
676C2×C3—24no—
677C2×C3—24no—
678C2×C3—24no—
679C2×C3—68no—
680C2×C3—361no—
681C2×C3—361no—
682C2×C3D3×#23914yes—
683C2×C3#6431914yes—
684C2×C3#6433014yes—
685C2×C3#6436111yescharacteristic
686C2×C3C2×#383211yescharacteristic
687C2×C3#41×C3⋊D311yescharacteristic
688D3—22no—
689D3—124no—
690D3—124no—
691D3—182no—
692D3—188no—
693D3—368no—
694C22—32no—
695C22—61no—
696C22—61no—
697C22—181no—
698C22—181no—
699C22—181no—
700C22—181no—
701C22—181no—
702C22—181no—
703C22—272no—
704C22—541no—
705C22—541no—
706C22—1084no—
707C22C22×D3×C3⋊D311yescharacteristic
708C4—21no—
709C4—21no—
710C4—21no—
711C4—61no—
712C4—61no—
713C4—61no—
714C4—181no—
715C4—181no—
716C4—541no—
717C4—541no—
718C4—541no—
719C3—24no—
720C3#1059543714yescomplemented
721C3#1059610811yescharacteristic, complemented
722C2—62no—
723C2—361no—
724C2—361no—
725C2—542no—
726C2D3×#383211yescharacteristic
727C2#1172459611yescharacteristic
728C2#1172461111yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC2×C33×Q8C22
prime radical#11723541C2
hypercenterC2×Q8D3×C3⋊D3
hypocenterC33#551
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
1. #11723987C2semidirect
2. C3×#64156C2semidirect
3. C32×#946C2semidirect
5. #11723539C2semidirect
6. D3×#3752C2semidirect
7. #11723506C2semidirect
8. #11723504C2semidirect
9. #11723488C2semidirect
10. #11723480C2semidirect
11. #11723472C2semidirect
12. #11723469C2semidirect
13. #11723459C2semidirect
14. #11723408C2semidirect
15. #11723407C2semidirect
19. C2×C33×Q8C22semidirect
26. C2×Dic3×C3⋊D3C22semidirect
30. C4⋊(C3⋊(C3⋊Dic3))C22semidirect
31. #88857C22semidirect
32. #88857C22semidirect
35. C3×#3752C22semidirect
36. C3×#3752C22semidirect
37. C3×C4×C3⋊Dic3C22semidirect
40. C32×C4⋊Dic3C22semidirect
41. C32×Dic3⋊C4C22semidirect
42. C32×Dic3⋊C4C22semidirect
43. #88806C22semidirect
44. Dic3⋊(C3⋊Dic3)C22semidirect
49. #88803C22semidirect
51. Dic3×C3⋊Dic3C22semidirect
52. Dic3×C3⋊Dic3C22semidirect
54. #64156D3semidirect
71. C3×#946D3semidirect
116. C2×C32×Q8C2×D3semidirect
117. C2×C32×Q8C2×D3semidirect
154. #3752C2×D3semidirect
155. #3752C2×D3semidirect
169. C4×C3⋊Dic3C2×D3semidirect
176. C3×C4⋊Dic3C2×D3semidirect
177. C3×Dic3⋊C4C2×D3semidirect
178. C3×Dic3⋊C4C2×D3semidirect
221. #946C3⋊D3semidirect
320. C2×C3×Q8D32semidirect
321. C2×C3×Q8C2×C3⋊D3semidirect
377. C4⋊Dic3C2×C3⋊D3semidirect
387. Dic3⋊C4C2×C3⋊D3semidirect
388. Dic3⋊C4C2×C3⋊D3semidirect
469. C33#551semidirect
552. C2×Q8D3×C3⋊D3semidirect
647. C32#5637semidirect
648. C32#5679semidirect
720. C3#10595437semidirect
721. C3#10596108semidirect

Maximal subgroups

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

subgroupindex
#117239872
C3×#641562
C32×#9462
#117235412
#117235392
D3×#37522
#117235062
#117235042
#117234882
#117234802
#117234722
#117234692
#117234592
#117234082
#117234072
#105961083
#105954373