Finite Group Databasebeta

← #13177608

Subgroups — #13177608

Order 1728.

1804 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×C3⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
2C3×#64148C211yesmaximal, characteristic, complemented
3C32×#939C211yesmaximal, characteristic, complemented
4#11723637C211yesmaximal, characteristic, complemented
5#11723637C211yesmaximal, characteristic, complemented
6#11723621C211yesmaximal, characteristic, complemented
7#67×C3⋊Dic3C211yesmaximal, characteristic, complemented
8Dic3×#638C211yesmaximal, characteristic, complemented
9#11723614C211yesmaximal, characteristic, complemented
10C2×#88806C211yesmaximal, characteristic, complemented
11#11723598C211yesmaximal, characteristic, complemented
12#11723508C211yesmaximal, characteristic, complemented
13#11723448C211yesmaximal, characteristic, complemented
14#11723430C211yesmaximal, characteristic, complemented
15#11723408C211yesmaximal, characteristic, complemented
16#10596072—31nomaximal
17#10595206—34nomaximal
18C2×C33×D4C2211yescharacteristic
19C22×C3⋊(C3⋊Dic3)C2211yescharacteristic
20C22×C3⋊(C3⋊Dic3)C2211yescharacteristic
21C2×C3×#638C2211yescharacteristic
22C2×C3×#638C2211yescharacteristic
23C22×C3×C3⋊Dic3C2211yescharacteristic
24C2×C32×#67C2211yescharacteristic
25C2×C32×#67C2211yescharacteristic
26C22×C32×Dic3C2211yescharacteristic
27C2×#6290C2211yescharacteristic
28C2×Dic3×C3⋊D3C2211yescharacteristic
29C2×D3×C3⋊Dic3C2211yescharacteristic
30#88864C2211yescharacteristic
31#88864C2211yescharacteristic
32C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic
33C4×C3⋊(C3⋊Dic3)C2211yescharacteristic
34C3×#3757C2211yescharacteristic
35C3×#3752C2211yescharacteristic
36C3×#3750C2211yescharacteristic
37C32×#217C2211yescharacteristic
38C32×(C2×D3)⋊C4C2211yescharacteristic
39C32×Dic3⋊C4C2211yescharacteristic
40#88807C2211yescharacteristic
41#88806C2211yescharacteristic
42#88806C2211yescharacteristic
43#88806C2211yescharacteristic
44#88806C2211yescharacteristic
45#88806C2211yescharacteristic
46Dic3⋊(C3⋊Dic3)C2211yescharacteristic
47#88803C2211yescharacteristic
48#88803C2211yescharacteristic
49(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
50(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
51Dic3×C3⋊Dic3C2211yescharacteristic
52Dic3×C3⋊Dic3C2211yescharacteristic
53C32×#121—31no—
54#64148—31no—
55#64148—31no—
56#64148D311yescharacteristic, complemented
57#64144—31no—
58D4×C3⋊Dic3—31no—
59D4×C3⋊Dic3—31no—
60D4×C3⋊Dic3—34no—
61D4×C3⋊Dic3—64no—
62C4×#638—31no—
63C2×#3750—31no—
64#64107—31no—
65#64098—31no—
66#64092—31no—
67#64090—31no—
68#64088—31no—
69#64086—31no—
70C3×#939—34no—
71C3×#939D314yescomplemented
72#63980—34no—
73#63980—34no—
74Dic3×#67—34no—
75Dic3×#67—34no—
76#63969—34no—
77#63969—34no—
78C2×#3724—34no—
79#63957—34no—
80#63902—34no—
81#63870—34no—
82#63861—34no—
83#63861—34no—
84C23×C33C2311yescharacteristic
85C23×C33C2311yescharacteristic
86C22×C3×C3⋊D3C2311yescharacteristic
87C22×C32×D3C2311yescharacteristic
88C33×D4—22no—
89C2×C33×C4C2311yescharacteristic
90C2×C3⋊(C3⋊Dic3)—22no—
91C2×C3⋊(C3⋊Dic3)—22no—
92C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
93C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
94C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
95C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
96C3×#638—22no—
97C3×#638—41no—
98C2×C3×C3⋊Dic3—41no—
99C2×C3×C3⋊Dic3C2311yescharacteristic
100C2×C3×C3⋊Dic3C2311yescharacteristic
101C2×C3×C3⋊Dic3C2311yescharacteristic
102C32×#67—22no—
103C32×#67—41no—
104C2×C32×Dic3—41no—
105C2×C32×Dic3C2311yescharacteristic
106C2×C32×Dic3C2311yescharacteristic
107C2×C32×Dic3C2311yescharacteristic
108#6290—22no—
109Dic3×C3⋊D3—41no—
110D3×C3⋊Dic3—41no—
111#5601—94no—
112#5601—91no—
113C2×C32×D4—24no—
114C2×C32×D4—31no—
115C2×C32×D4—31no—
116C2×C32×D4C2×D314yes—
117C2×C32×D4C2×D311yescharacteristic
118C22×C32×C4—31no—
119C2×#638—31no—
120C2×#638C2×D311yescharacteristic
121C2×#638C2×D311yescharacteristic
122C22×C3⋊Dic3—31no—
123C22×C3⋊Dic3—31no—
124C22×C3⋊Dic3—34no—
125C22×C3⋊Dic3—34no—
126C22×C3⋊Dic3—31no—
127C22×C3⋊Dic3—64no—
128C22×C3⋊Dic3—64no—
129C22×C3⋊Dic3C2×D311yescharacteristic
130C2×C4×C3⋊D3—31no—
131C2×C3×#67—34no—
132C2×C3×#67—34no—
133C2×C3×#67C2×D314yes—
134C2×C3×#67C2×D314yes—
135C22×C3×Dic3—34no—
136C22×C3×Dic3C2×D314yes—
137C2×#625—34no—
138C2×D3×Dic3—34no—
139C2×D3×Dic3—34no—
140C32×C4⋊C4—31no—
141C32×C22⋊C4—31no—
142C32×C22⋊C4—31no—
143#3757—31no—
144#3757—31no—
145#3757—34no—
146#3757—34no—
147#3757—31no—
148#3757—31no—
149#3757—64no—
150#3757—64no—
151#3757C2×D311yescharacteristic
152#3752—31no—
153#3752—31no—
154#3752C2×D311yescharacteristic
155C4⋊(C3⋊Dic3)—31no—
156C4⋊(C3⋊Dic3)—34no—
157C4⋊(C3⋊Dic3)—31no—
158C4⋊(C3⋊Dic3)—64no—
159#3750—31no—
160#3750—31no—
161#3750—31no—
162#3750—31no—
163#3750—31no—
164#3750—31no—
165#3750C2×D311yescharacteristic
166C4×C3⋊Dic3—31no—
167C4×C3⋊Dic3—34no—
168C4×C3⋊Dic3—31no—
169C4×C3⋊Dic3—31no—
170C4×C3⋊Dic3—64no—
171C3×#217—34no—
172C3×#217C2×D314yes—
173C3×(C2×D3)⋊C4—34no—
174C3×(C2×D3)⋊C4C2×D314yes—
175C3×Dic3⋊C4—34no—
176C3×Dic3⋊C4C2×D314yes—
177#3724—34no—
178#3724—34no—
179#3724—34no—
180#3724—34no—
181#3724—34no—
182Dic3⋊Dic3—34no—
183Dic3⋊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×C33—21no—
191C22×C33—21no—
192C22×C33—21no—
193C22×C33—21no—
194C22×C33—21no—
195C22×C33#4112yes—
196C22×C33C2411yescharacteristic
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—21no—
203C33×C4—21no—
204C3⋊(C3⋊Dic3)—21no—
205C3⋊(C3⋊Dic3)—21no—
206C3⋊(C3⋊Dic3)—21no—
207C3⋊(C3⋊Dic3)#4112yes—
208C3×C3⋊Dic3—21no—
209C3×C3⋊Dic3—21no—
210C3×C3⋊Dic3—21no—
211C32×Dic3—21no—
212C32×Dic3—21no—
213C32×Dic3—21no—
214C3×#121—34no—
215C3×#121—91no—
216#939—34no—
217#939—94no—
218#939—94no—
219#939—91no—
220#939—91no—
221#939C3⋊D311yescharacteristic, complemented
222#935—94no—
223#935—91no—
224D4×Dic3—94no—
225D4×Dic3—94no—
226D4×Dic3—91no—
227D4×Dic3—91no—
228D4×Dic3—184no—
229C4×#67—94no—
230C4×#67—91no—
231C2×Dic3⋊C4—94no—
232C2×Dic3⋊C4—91no—
233#898—94no—
234#898—91no—
235#889—94no—
236#889—91no—
237#883—94no—
238#883—91no—
239#67⋊C4—94no—
240#67⋊C4—91no—
241#879—94no—
242#879—91no—
243#877—94no—
244#877—91no—
245C23×C32—24no—
246C23×C32—24no—
247C23×C32—31no—
248C23×C32C22×D314yes—
249C23×C32C22×D314yes—
250C23×C32C22×D311yescharacteristic
251C23×C32C22×D311yescharacteristic
252C22×C3⋊D3C22×D311yescharacteristic
253C22×C3×D3—34no—
254C22×C3×D3C22×D314yes—
255C32×D4—216no—
256C32×D4—28no—
257C32×D4—22no—
258C32×D4—62no—
259C32×D4—121no—
260C2×C32×C4—24no—
261C2×C32×C4—31no—
262C2×C32×C4—31no—
263C2×C32×C4—31no—
264C2×C32×C4—121no—
265C2×C32×C4C22×D314yes—
266C2×C32×C4C22×D311yescharacteristic
267#638—22no—
268#638—41no—
269#638—62no—
270C2×C3⋊Dic3—31no—
271C2×C3⋊Dic3—31no—
272C2×C3⋊Dic3—31no—
273C2×C3⋊Dic3—31no—
274C2×C3⋊Dic3—34no—
275C2×C3⋊Dic3—34no—
276C2×C3⋊Dic3—34no—
277C2×C3⋊Dic3—34no—
278C2×C3⋊Dic3—41no—
279C2×C3⋊Dic3—64no—
280C2×C3⋊Dic3—64no—
281C2×C3⋊Dic3—64no—
282C2×C3⋊Dic3—64no—
283C2×C3⋊Dic3—62no—
284C2×C3⋊Dic3—62no—
285C2×C3⋊Dic3—68no—
286C2×C3⋊Dic3—68no—
287C2×C3⋊Dic3—128no—
288C2×C3⋊Dic3—128no—
289C2×C3⋊Dic3—121no—
290C2×C3⋊Dic3C22×D311yescharacteristic
291C2×C3⋊Dic3C22×D311yescharacteristic
292C2×C3⋊Dic3C22×D311yescharacteristic
293C4×C3⋊D3—121no—
294C3×#67—28no—
295C3×#67—44no—
296C3×#67—68no—
297C3×#67—124no—
298C2×C3×Dic3—34no—
299C2×C3×Dic3—34no—
300C2×C3×Dic3—34no—
301C2×C3×Dic3—44no—
302C2×C3×Dic3—124no—
303C2×C3×Dic3C22×D314yes—
304C2×C3×Dic3C22×D314yes—
305C2×C3×Dic3C22×D314yes—
306#625—68no—
307D3×Dic3—124no—
308D3×Dic3—124no—
309#553—271noSylow
310C2×C33—22no—
311C2×C33—41no—
312C2×C33C2×#4111yescharacteristic
313C2×C33C2×#4111yescharacteristic
314C2×C33H(5,𝔽2)11yescharacteristic
315C3×C3⋊D3—41no—
316C32×D3—41no—
317C2×C3×D4—24no—
318C2×C3×D4—34no—
319C2×C3×D4—34no—
320C2×C3×D4—91no—
321C2×C3×D4—91no—
322C2×C3×D4D3214yes—
323C2×C3×D4C2×C3⋊D311yescharacteristic
324C22×C3×C4—34no—
325C22×C3×C4—91no—
326C2×#67—34no—
327C2×#67—34no—
328C2×#67—94no—
329C2×#67—91no—
330C2×#67C2×C3⋊D311yescharacteristic
331C2×#67C2×C3⋊D311yescharacteristic
332C22×Dic3—34no—
333C22×Dic3—94no—
334C22×Dic3—94no—
335C22×Dic3—94no—
336C22×Dic3—91no—
337C22×Dic3—91no—
338C22×Dic3—91no—
339C22×Dic3—184no—
340C22×Dic3—184no—
341C22×Dic3C2×C3⋊D311yescharacteristic
342C2×C4×D3—94no—
343C2×C4×D3—91no—
344C3×C4⋊C4—34no—
345C3×C4⋊C4—91no—
346C3×C22⋊C4—34no—
347C3×C22⋊C4—34no—
348C3×C22⋊C4—91no—
349C3×C22⋊C4—91no—
350#217—34no—
351#217—94no—
352#217—94no—
353#217—94no—
354#217—94no—
355#217—91no—
356#217—91no—
357#217—91no—
358#217—91no—
359#217—184no—
360#217—184no—
361#217C2×C3⋊D311yescharacteristic
362(C2×D3)⋊C4—34no—
363(C2×D3)⋊C4—94no—
364(C2×D3)⋊C4—94no—
365(C2×D3)⋊C4—91no—
366(C2×D3)⋊C4—91no—
367(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
368C4⋊Dic3—94no—
369C4⋊Dic3—94no—
370C4⋊Dic3—91no—
371C4⋊Dic3—91no—
372C4⋊Dic3—184no—
373Dic3⋊C4—34no—
374Dic3⋊C4—94no—
375Dic3⋊C4—94no—
376Dic3⋊C4—94no—
377Dic3⋊C4—94no—
378Dic3⋊C4—94no—
379Dic3⋊C4—94no—
380Dic3⋊C4—91no—
381Dic3⋊C4—91no—
382Dic3⋊C4—91no—
383Dic3⋊C4—91no—
384Dic3⋊C4—91no—
385Dic3⋊C4—91no—
386Dic3⋊C4C2×C3⋊D311yescharacteristic
387C4×Dic3—94no—
388C4×Dic3—94no—
389C4×Dic3—94no—
390C4×Dic3—91no—
391C4×Dic3—91no—
392C4×Dic3—91no—
393C4×Dic3—184no—
394C22×C32—21no—
395C22×C32—21no—
396C22×C32—28no—
397C22×C32—24no—
398C22×C32—21no—
399C22×C32—21no—
400C22×C32—21no—
401C22×C32—24no—
402C22×C32—28no—
403C22×C32—24no—
404C22×C32—24no—
405C22×C32—24no—
406C22×C32—24no—
407C22×C32—44no—
408C22×C32—44no—
409C22×C32—44no—
410C22×C32—44no—
411C22×C32—61no—
412C22×C32—61no—
413C22×C32—61no—
414C22×C32#23718yes—
415C22×C32#23712yes—
416C22×C32C23×D314yes—
417C22×C32C23×D311yescharacteristic
418C2×C3⋊D3—21no—
419C2×C3⋊D3—21no—
420C2×C3⋊D3—21no—
421C2×C3×D3—24no—
422C2×C3×D3—24no—
423C2×C3×D3—24no—
424C2×C3×D3—64no—
425C2×C3×D3—64no—
426C2×C3×D3—64no—
427C32×C4—28no—
428C32×C4—24no—
429C32×C4—21no—
430C32×C4—61no—
431C32×C4—61no—
432C32×C4—61no—
433C3⋊Dic3—21no—
434C3⋊Dic3—21no—
435C3⋊Dic3—21no—
436C3⋊Dic3—32no—
437C3⋊Dic3—38no—
438C3⋊Dic3—68no—
439C3⋊Dic3—61no—
440C3⋊Dic3—61no—
441C3⋊Dic3—61no—
442C3⋊Dic3—64no—
443C3⋊Dic3—64no—
444C3⋊Dic3—64no—
445C3⋊Dic3—124no—
446C3⋊Dic3—124no—
447C3⋊Dic3—124no—
448C3×Dic3—24no—
449C3×Dic3—24no—
450C3×Dic3—24no—
451C3×Dic3—64no—
452C3×Dic3—64no—
453C3×Dic3—64no—
454#126—271no—
455#126—271no—
456#125—271no—
457#123—271no—
458#123—271no—
459#121—31no—
460#121—91no—
461#121—271no—
462#121—271no—
463C4×D4—271no—
464C4×D4—271no—
465C4×D4—271no—
466C4×D4—271no—
467#117—271no—
468C2×C4⋊C4—271no—
469C33#55311yescharacteristic, complemented, Sylow
470C23×C3—24no—
471C23×C3—24no—
472C23×C3—34no—
473C23×C3—91no—
474C23×C3C2×D3214yes—
475C23×C3C2×D3214yes—
476C23×C3C22×C3⋊D311yescharacteristic
477C23×C3C22×C3⋊D311yescharacteristic
478C22×D3—34no—
479C22×D3C22×C3⋊D311yescharacteristic
480C3×D4—216no—
481C3×D4—28no—
482C3×D4—22no—
483C3×D4—68no—
484C3×D4—124no—
485C3×D4—182no—
486C3×D4—361no—
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—91no—
494C2×C3×C4—124no—
495C2×C3×C4—361no—
496C2×C3×C4C2×D3214yes—
497C2×C3×C4C22×C3⋊D311yescharacteristic
498#67—22no—
499#67—41no—
500#67—68no—
501#67—124no—
502#67—182no—
503#67—188no—
504C2×Dic3—34no—
505C2×Dic3—34no—
506C2×Dic3—34no—
507C2×Dic3—41no—
508C2×Dic3—94no—
509C2×Dic3—91no—
510C2×Dic3—94no—
511C2×Dic3—94no—
512C2×Dic3—94no—
513C2×Dic3—91no—
514C2×Dic3—91no—
515C2×Dic3—91no—
516C2×Dic3—124no—
517C2×Dic3—184no—
518C2×Dic3—184no—
519C2×Dic3—184no—
520C2×Dic3—184no—
521C2×Dic3—182no—
522C2×Dic3—182no—
523C2×Dic3—188no—
524C2×Dic3—188no—
525C2×Dic3—368no—
526C2×Dic3—368no—
527C2×Dic3—361no—
528C2×Dic3—364no—
529C2×Dic3C22×C3⋊D311yescharacteristic
530C2×Dic3C22×C3⋊D311yescharacteristic
531C2×Dic3C22×C3⋊D311yescharacteristic
532C4×D3—364no—
533C4×D3—361no—
534C2×C32—22no—
535C2×C32—24no—
536C2×C32—24no—
537C2×C32—24no—
538C2×C32—28no—
539C2×C32—48no—
540C2×C32—48no—
541C2×C32—44no—
542C2×C32—41no—
543C2×C32—121no—
544C2×C32C2×#23714yes—
545C2×C32C2×#23711yescharacteristic
546C2×C32#100414yes—
547C2×C32#100411yescharacteristic
548C2×C32D3×#4114yes—
549C2×C32D3×#4111yescharacteristic
550C3⋊D3—41no—
551C3×D3—44no—
552C3×D3—124no—
553C2×D4—31no—
554C2×D4—31no—
555C2×D4—91no—
556C2×D4—91no—
557C2×D4—271no—
558C2×D4D3×C3⋊D311yescharacteristic
559C22×C4—31no—
560C22×C4—91no—
561C22×C4—271no—
562C22×C4—271no—
563C22×C4—271no—
564C22×C4—271no—
565C4⋊C4—31no—
566C4⋊C4—91no—
567C4⋊C4—271no—
568C4⋊C4—271no—
569C4⋊C4—271no—
570C4⋊C4—271no—
571C4⋊C4—271no—
572C4⋊C4—271no—
573C4⋊C4—271no—
574C4⋊C4—271no—
575C22⋊C4—31no—
576C22⋊C4—31no—
577C22⋊C4—91no—
578C22⋊C4—91no—
579C22⋊C4—271no—
580C22⋊C4—271no—
581C22⋊C4—271no—
582C22⋊C4—271no—
583C22⋊C4—271no—
584C22⋊C4—271no—
585C42—271no—
586C42—271no—
587C42—271no—
588C22×C3—24no—
589C22×C3—24no—
590C22×C3—21no—
591C22×C3—21no—
592C22×C3—28no—
593C22×C3—24no—
594C22×C3—24no—
595C22×C3—24no—
596C22×C3—21no—
597C22×C3—21no—
598C22×C3—21no—
599C22×C3—24no—
600C22×C3—28no—
601C22×C3—44no—
602C22×C3—44no—
603C22×C3—44no—
604C22×C3—44no—
605C22×C3—64no—
606C22×C3—64no—
607C22×C3—64no—
608C22×C3—181no—
609C22×C3—181no—
610C22×C3—181no—
611C22×C3#380518yes—
612C22×C3#383012yes—
613C22×C3C22×D3214yes—
614C22×C3C23×C3⋊D311yescharacteristic
615C2×D3—21no—
616C2×D3—21no—
617C2×D3—21no—
618C2×D3—64no—
619C2×D3—64no—
620C2×D3—64no—
621C3×C4—28no—
622C3×C4—24no—
623C3×C4—21no—
624C3×C4—64no—
625C3×C4—64no—
626C3×C4—64no—
627C3×C4—181no—
628C3×C4—181no—
629C3×C4—181no—
630Dic3—21no—
631Dic3—21no—
632Dic3—21no—
633Dic3—64no—
634Dic3—64no—
635Dic3—64no—
636Dic3—98no—
637Dic3—92no—
638Dic3—188no—
639Dic3—184no—
640Dic3—184no—
641Dic3—184no—
642Dic3—181no—
643Dic3—181no—
644Dic3—181no—
645Dic3—364no—
646Dic3—364no—
647Dic3—364no—
648C32—24no—
649C32#560114yescomplemented
650C32#560111yescharacteristic, complemented
651C23—31no—
652C23—91no—
653C23C2×D3×C3⋊D311yescharacteristic
654C23C2×D3×C3⋊D311yescharacteristic
655D4—22no—
656D4—62no—
657D4—121no—
658D4—182no—
659D4—361no—
660D4—542no—
661C2×C4—31no—
662C2×C4—31no—
663C2×C4—31no—
664C2×C4—91no—
665C2×C4—91no—
666C2×C4—91no—
667C2×C4—121no—
668C2×C4—271no—
669C2×C4—271no—
670C2×C4—271no—
671C2×C4—271no—
672C2×C4—361no—
673C2×C4—542no—
674C2×C4—542no—
675C2×C4—1081no—
676C2×C4—1081no—
677C2×C4C2×D3×C3⋊D311yescharacteristic
678C2×C3—28no—
679C2×C3—22no—
680C2×C3—24no—
681C2×C3—24no—
682C2×C3—24no—
683C2×C3—48no—
684C2×C3—48no—
685C2×C3—44no—
686C2×C3—41no—
687C2×C3—124no—
688C2×C3—361no—
689C2×C3#6431214yes—
690C2×C3#6431314yes—
691C2×C3C2×#380514yes—
692C2×C3C2×#383011yescharacteristic
693C2×C3#6436111yescharacteristic
694C2×C3#41×C3⋊D311yescharacteristic
695D3—41no—
696D3—124no—
697C22—21no—
698C22—21no—
699C22—21no—
700C22—21no—
701C22—21no—
702C22—61no—
703C22—61no—
704C22—61no—
705C22—181no—
706C22—181no—
707C22—181no—
708C22#8902912yes—
709C22C22×D3×C3⋊D311yescharacteristic
710C4—21no—
711C4—61no—
712C4—61no—
713C4—61no—
714C4—181no—
715C4—181no—
716C4—181no—
717C4—272no—
718C4—541no—
719C4—541no—
720C4—541no—
721C3—24no—
722C3#1059520614yescomplemented
723C3#1059607211yescharacteristic, complemented
724C2—22no—
725C2—41no—
726C2—121no—
727C2—361no—
728C2#1172458611yescharacteristic
729C2#1172458711yescharacteristic
730C2C2×#8902911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC2×C33×D4C22
hypercenterC2×D4D3×C3⋊D3
hypocenterC33#553
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. D4×C3⋊(C3⋊Dic3)C2semidirect
2. C3×#64148C2semidirect
3. C32×#939C2semidirect
4. #11723637C2semidirect
5. #11723637C2semidirect
6. #11723621C2semidirect
7. #67×C3⋊Dic3C2semidirect
8. Dic3×#638C2semidirect
9. #11723614C2semidirect
10. C2×#88806C2semidirect
11. #11723598C2semidirect
12. #11723508C2semidirect
13. #11723448C2semidirect
14. #11723430C2semidirect
15. #11723408C2semidirect
56. #64148D3semidirect
71. C3×#939D3semidirect
221. #939C3⋊D3semidirect
469. C33#553semidirect
649. C32#5601semidirect
650. C32#5601semidirect
722. C3#10595206semidirect
723. C3#10596072semidirect

Maximal subgroups

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

subgroupindex
D4×C3⋊(C3⋊Dic3)2
C3×#641482
C32×#9392
#117236372
#117236212
#67×C3⋊Dic32
Dic3×#6382
#117236142
C2×#888062
#117235982
#117235082
#117234482
#117234302
#117234082
#105960723
#105952063