Finite Group Databasebeta

← #13178074

Subgroups — #13178074

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×#88864C211yesmaximal, characteristic, complemented
2C2×C3×#3757C211yesmaximal, characteristic, complemented
3C32×#953C211yesmaximal, characteristic
4#11723642C211yesmaximal, characteristic, complemented
5#11723641C211yesmaximal, characteristic, complemented
6#67⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
7#67×C3⋊Dic3C211yesmaximal, characteristic, complemented
8#11723614C211yesmaximal, characteristic, complemented
9#11723603C211yesmaximal, characteristic, complemented
10#11723602C211yesmaximal, characteristic, complemented
11#11723600C211yesmaximal, characteristic, complemented
12#11723598C211yesmaximal, characteristic, complemented
13#11723597C211yesmaximal, characteristic, complemented
14#11723596C211yesmaximal, characteristic, complemented
15#11723595C211yesmaximal, characteristic, complemented
16#10596058—31nomaximal
17#10595509—34nomaximal
18C24×C33C2211yescharacteristic
19C22×C3⋊(C3⋊Dic3)C2211yescharacteristic
20C22×C3⋊(C3⋊Dic3)C2211yescharacteristic
21C22×C3×C3⋊Dic3C2211yescharacteristic
22C22×C3×C3⋊Dic3C2211yescharacteristic
23C2×C32×#67C2211yescharacteristic
24C2×C32×#67C2211yescharacteristic
25C2×C32×#67C2211yescharacteristic
26C2×#6293C2211yescharacteristic, complemented
27C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
28#88864C2211yescharacteristic
29#88864C2211yescharacteristic
30#88864C2211yescharacteristic
31#88864C2211yescharacteristic
32C3×#3757C2211yescharacteristic
33C3×#3757C2211yescharacteristic
34C3×#3757C2211yescharacteristic
35C3×#3757C2211yescharacteristic
36C32×#217C2211yescharacteristic
37C32×#217C2211yescharacteristic
38C32×#217C2211yescharacteristic
39#88807C2211yescharacteristic, complemented
40#88807C2211yescharacteristic, complemented
41#88807C2211yescharacteristic, complemented
42#88806C2211yescharacteristic, complemented
43#88806C2211yescharacteristic, complemented
44#88806C2211yescharacteristic, complemented
45Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
46Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
47(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
48(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
49(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
50Dic3×C3⋊Dic3C2211yescharacteristic, complemented
51Dic3×C3⋊Dic3C2211yescharacteristic, complemented
52Dic3×C3⋊Dic3C2211yescharacteristic, complemented
53C32×#120—31no—
54C2×#3757—31no—
55C2×#3757—34no—
56C2×#3757—64no—
57C2×#3757D311yescharacteristic, complemented
58#64145—31no—
59#64144—31no—
60#64144—31no—
61#64144—31no—
62D4×C3⋊Dic3—31no—
63D4×C3⋊Dic3—31no—
64#64088—31no—
65#64088—31no—
66#64087—31no—
67#64087—31no—
68#64086—31no—
69#64086—31no—
70C3×#953D314yes—
71C2×C3×#217—34no—
72#63982—34no—
73#67⋊Dic3—34no—
74Dic3×#67—34no—
75#63969—34no—
76#63964—34no—
77#63962—34no—
78#63961—34no—
79#63959—34no—
80#63957—34no—
81#63956—34no—
82#63956—34no—
83#63955—34no—
84C23×C33—22no—
85C23×C33—22no—
86C23×C33—41no—
87C23×C33C2311yescharacteristic
88C23×C33C2311yescharacteristic
89C23×C33C2311yescharacteristic
90C22×C32×D3C2311yescharacteristic
91C2×C3⋊(C3⋊Dic3)—22no—
92C2×C3⋊(C3⋊Dic3)—41no—
93C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
94C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
95C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
96C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
97C2×C3×C3⋊Dic3—22no—
98C2×C3×C3⋊Dic3—41no—
99C2×C3×C3⋊Dic3C2311yescharacteristic
100C2×C3×C3⋊Dic3C2311yescharacteristic
101C2×C3×C3⋊Dic3C2311yescharacteristic
102C2×C3×C3⋊Dic3C2311yescharacteristic
103C32×#67—22no—
104C32×#67—22no—
105C32×#67—41no—
106C2×C32×Dic3C2311yescharacteristic
107C2×C32×Dic3C2311yescharacteristic
108C2×C32×Dic3C2311yescharacteristic
109#6293—41no—
110D3×C3⋊Dic3—41no—
111#5587—94no—
112#5495—91no—
113C24×C32—24no—
114C24×C32C2×D314yes—
115C24×C32C2×D311yescharacteristic
116C2×C32×D4—31no—
117C2×C32×D4—31no—
118C2×C32×D4—31no—
119C22×C3⋊Dic3—31no—
120C22×C3⋊Dic3—34no—
121C22×C3⋊Dic3—31no—
122C22×C3⋊Dic3—34no—
123C22×C3⋊Dic3—31no—
124C22×C3⋊Dic3—64no—
125C22×C3⋊Dic3—64no—
126C22×C3⋊Dic3C2×D311yescharacteristic
127C22×C3⋊Dic3C2×D311yescharacteristic
128C2×#634—31no—
129C2×C3×#67C2×D314yes—
130C2×C3×#67C2×D314yes—
131C2×C3×#67C2×D314yes—
132C22×C3×Dic3—34no—
133C22×C3×Dic3—34no—
134C2×#627—34no—
135C2×D3×Dic3—34no—
136C32×C22⋊C4—31no—
137C32×C22⋊C4—31no—
138C32×C22⋊C4—31no—
139#3757—31no—
140#3757—31no—
141#3757—31no—
142#3757—31no—
143#3757—34no—
144#3757—34no—
145#3757—34no—
146#3757—34no—
147#3757—31no—
148#3757—31no—
149#3757—31no—
150#3757—64no—
151#3757—64no—
152#3757—64no—
153#3757—64no—
154#3757C2×D311yescharacteristic
155#3757C2×D311yescharacteristic
156#3757C2×D311yescharacteristic
157#3757C2×D311yescharacteristic
158C4⋊(C3⋊Dic3)—31no—
159C4⋊(C3⋊Dic3)—31no—
160#3750—31no—
161#3750—31no—
162#3750—31no—
163#3750—31no—
164#3750—31no—
165#3750—31no—
166C4×C3⋊Dic3—31no—
167C4×C3⋊Dic3—31no—
168C4×C3⋊Dic3—31no—
169C3×#217—34no—
170C3×#217—34no—
171C3×#217—34no—
172C3×#217—34no—
173C3×#217C2×D314yes—
174C3×#217C2×D314yes—
175C3×#217C2×D314yes—
176#3724—34no—
177#3724—34no—
178#3724—34no—
179Dic3⋊Dic3—34no—
180Dic3⋊Dic3—34no—
181Dic3⋊Dic3—34no—
182Dic3⋊Dic3—34no—
183Dic3⋊Dic3—34no—
184(C2×D3)⋊Dic3—34no—
185(C2×D3)⋊Dic3—34no—
186(C2×D3)⋊Dic3—34no—
187Dic32—34no—
188Dic32—34no—
189Dic32—34no—
190C22×C33—21no—
191C22×C33—21no—
192C22×C33—21no—
193C22×C33—21no—
194C22×C33—21no—
195C22×C33—21no—
196C22×C33—21no—
197C22×C33—44no—
198C22×C33#4112yes—
199C22×C33#4112yes—
200C22×C33C2411yescharacteristic
201C2×C32×D3—21no—
202C2×C32×D3—21no—
203C2×C32×D3—21no—
204C3⋊(C3⋊Dic3)—21no—
205C3⋊(C3⋊Dic3)—21no—
206C3⋊(C3⋊Dic3)—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×#120—34no—
216C2×C3×C22⋊C4—91no—
217#953C3⋊D311yescharacteristic
218C2×#217—34no—
219C2×#217—94no—
220C2×#217—91no—
221C2×#217—184no—
222#936—94no—
223#935—94no—
224#935—94no—
225#935—94no—
226D4×Dic3—94no—
227D4×Dic3—94no—
228#929—91no—
229C4×#67—91no—
230#926—91no—
231#924—91no—
232#886—91no—
233#885—91no—
234#883—91no—
235#67⋊C4—91no—
236#879—94no—
237#879—94no—
238#879—91no—
239#879—91no—
240#878—94no—
241#878—94no—
242#878—91no—
243#877—94no—
244#877—94no—
245#877—91no—
246C23×C32—216no—
247C23×C32—22no—
248C23×C32—28no—
249C23×C32—22no—
250C23×C32—24no—
251C23×C32—24no—
252C23×C32—24no—
253C23×C32—28no—
254C23×C32—31no—
255C23×C32—48no—
256C23×C32—41no—
257C23×C32—44no—
258C23×C32—48no—
259C23×C32C22×D314yes—
260C23×C32C22×D314yes—
261C23×C32C22×D314yes—
262C23×C32C22×D311yescharacteristic
263C23×C32C22×D311yescharacteristic
264C23×C32C22×D311yescharacteristic
265C22×C3×D3C22×D314yes—
266C32×D4—62no—
267C32×D4—62no—
268C32×D4—121no—
269C2×C32×C4—31no—
270C2×C32×C4—31no—
271C2×C32×C4—31no—
272C2×C3⋊Dic3—22no—
273C2×C3⋊Dic3—31no—
274C2×C3⋊Dic3—31no—
275C2×C3⋊Dic3—31no—
276C2×C3⋊Dic3—31no—
277C2×C3⋊Dic3—34no—
278C2×C3⋊Dic3—34no—
279C2×C3⋊Dic3—34no—
280C2×C3⋊Dic3—34no—
281C2×C3⋊Dic3—41no—
282C2×C3⋊Dic3—64no—
283C2×C3⋊Dic3—64no—
284C2×C3⋊Dic3—64no—
285C2×C3⋊Dic3—64no—
286C2×C3⋊Dic3—62no—
287C2×C3⋊Dic3—68no—
288C2×C3⋊Dic3—128no—
289C2×C3⋊Dic3—121no—
290C2×C3⋊Dic3—121no—
291C2×C3⋊Dic3—124no—
292C2×C3⋊Dic3—128no—
293C2×C3⋊Dic3C22×D311yescharacteristic
294C2×C3⋊Dic3C22×D311yescharacteristic
295C2×C3⋊Dic3C22×D311yescharacteristic
296C2×C3⋊Dic3C22×D311yescharacteristic
297#634—121no—
298C3×#67—28no—
299C3×#67—28no—
300C3×#67—44no—
301C2×C3×Dic3—34no—
302C2×C3×Dic3—34no—
303C2×C3×Dic3—34no—
304C2×C3×Dic3—34no—
305C2×C3×Dic3—68no—
306C2×C3×Dic3—124no—
307C2×C3×Dic3C22×D314yes—
308C2×C3×Dic3C22×D314yes—
309C2×C3×Dic3C22×D314yes—
310#627—124no—
311D3×Dic3—124no—
312#551—271noSylow
313C2×C33—22no—
314C2×C33—22no—
315C2×C33—41no—
316C2×C33C2×#4111yescharacteristic
317C2×C33C2×#4111yescharacteristic
318C2×C33H(5,𝔽2)11yescharacteristic
319C32×D3—41no—
320C24×C3—24no—
321C24×C3D3214yes—
322C24×C3C2×C3⋊D311yescharacteristic
323C2×C3×D4—34no—
324C2×C3×D4—34no—
325C2×C3×D4—34no—
326C22×C3×C4—91no—
327C22×C3×C4—91no—
328C2×#67C2×C3⋊D311yescharacteristic
329C2×#67C2×C3⋊D311yescharacteristic
330C2×#67C2×C3⋊D311yescharacteristic
331C22×Dic3—34no—
332C22×Dic3—34no—
333C22×Dic3—94no—
334C22×Dic3—94no—
335C22×Dic3—91no—
336C22×Dic3—94no—
337C22×Dic3—91no—
338C22×Dic3—184no—
339C22×Dic3—184no—
340C2×C4×D3—91no—
341C2×Dic6—94no—
342C2×Dic6—91no—
343C3×C22⋊C4—34no—
344C3×C22⋊C4—34no—
345C3×C22⋊C4—34no—
346C3×C22⋊C4—91no—
347C3×C22⋊C4—91no—
348C3×C22⋊C4—91no—
349C3×C22⋊C4—91no—
350#217—34no—
351#217—34no—
352#217—34no—
353#217—34no—
354#217—94no—
355#217—94no—
356#217—94no—
357#217—94no—
358#217—94no—
359#217—94no—
360#217—94no—
361#217—91no—
362#217—91no—
363#217—91no—
364#217—91no—
365#217—184no—
366#217—184no—
367#217—184no—
368#217—184no—
369#217C2×C3⋊D311yescharacteristic
370#217C2×C3⋊D311yescharacteristic
371#217C2×C3⋊D311yescharacteristic
372(C2×D3)⋊C4—91no—
373(C2×D3)⋊C4—91no—
374(C2×D3)⋊C4—91no—
375C4⋊Dic3—94no—
376C4⋊Dic3—94no—
377C4⋊Dic3—91no—
378C4⋊Dic3—91no—
379C4⋊Dic3—91no—
380Dic3⋊C4—94no—
381Dic3⋊C4—94no—
382Dic3⋊C4—94no—
383Dic3⋊C4—94no—
384Dic3⋊C4—94no—
385Dic3⋊C4—94no—
386Dic3⋊C4—91no—
387Dic3⋊C4—91no—
388Dic3⋊C4—91no—
389Dic3⋊C4—91no—
390Dic3⋊C4—91no—
391C4×Dic3—94no—
392C4×Dic3—94no—
393C4×Dic3—94no—
394C4×Dic3—91no—
395C4×Dic3—91no—
396C4×Dic3—91no—
397C22×C32—28no—
398C22×C32—28no—
399C22×C32—21no—
400C22×C32—24no—
401C22×C32—21no—
402C22×C32—21no—
403C22×C32—24no—
404C22×C32—21no—
405C22×C32—28no—
406C22×C32—21no—
407C22×C32—24no—
408C22×C32—21no—
409C22×C32—21no—
410C22×C32—24no—
411C22×C32—28no—
412C22×C32—28no—
413C22×C32—24no—
414C22×C32—24no—
415C22×C32—24no—
416C22×C32—24no—
417C22×C32—44no—
418C22×C32—44no—
419C22×C32—44no—
420C22×C32—44no—
421C22×C32—44no—
422C22×C32—416no—
423C22×C32—432no—
424C22×C32—61no—
425C22×C32—61no—
426C22×C32—61no—
427C22×C32#23512yes—
428C22×C32#23718yes—
429C22×C32#23718yes—
430C22×C32#23712yes—
431C22×C32C23×D314yes—
432C22×C32C23×D311yescharacteristic
433C2×C3×D3—24no—
434C2×C3×D3—24no—
435C2×C3×D3—24no—
436C32×C4—61no—
437C32×C4—61no—
438C32×C4—61no—
439C3⋊Dic3—21no—
440C3⋊Dic3—21no—
441C3⋊Dic3—21no—
442C3⋊Dic3—21no—
443C3⋊Dic3—61no—
444C3⋊Dic3—61no—
445C3⋊Dic3—61no—
446C3⋊Dic3—61no—
447C3⋊Dic3—64no—
448C3⋊Dic3—64no—
449C3⋊Dic3—64no—
450C3⋊Dic3—64no—
451C3⋊Dic3—124no—
452C3⋊Dic3—124no—
453C3⋊Dic3—124no—
454C3⋊Dic3—124no—
455C3×Dic3—24no—
456C3×Dic3—24no—
457C3×Dic3—24no—
458C3×Dic3—64no—
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—271no—
469C22⋊Q8—271no—
470#120—31no—
471C4×D4—271no—
472C4×D4—271no—
473#117—271no—
474#117—271no—
475C2×C22⋊C4—91no—
476C2×C22⋊C4—271no—
477C33#55111yescharacteristic, complemented, Sylow
478C23×C3—216no—
479C23×C3—28no—
480C23×C3—28no—
481C23×C3—22no—
482C23×C3—22no—
483C23×C3—24no—
484C23×C3—24no—
485C23×C3—24no—
486C23×C3—34no—
487C23×C3—48no—
488C23×C3—44no—
489C23×C3—41no—
490C23×C3—48no—
491C23×C3C2×D3214yes—
492C23×C3C2×D3214yes—
493C23×C3C2×D3214yes—
494C23×C3C22×C3⋊D311yescharacteristic
495C23×C3C22×C3⋊D311yescharacteristic
496C23×C3C22×C3⋊D311yescharacteristic
497C22×D3C22×C3⋊D311yescharacteristic
498C3×D4—68no—
499C3×D4—68no—
500C3×D4—124no—
501C2×C3×C4—34no—
502C2×C3×C4—34no—
503C2×C3×C4—34no—
504C2×C3×C4—91no—
505C2×C3×C4—91no—
506C2×C3×C4—91no—
507C2×C3×C4—91no—
508C2×C3×C4—182no—
509C2×C3×C4—361no—
510#67—22no—
511#67—22no—
512#67—41no—
513C2×Dic3—34no—
514C2×Dic3—34no—
515C2×Dic3—34no—
516C2×Dic3—34no—
517C2×Dic3—68no—
518C2×Dic3—94no—
519C2×Dic3—94no—
520C2×Dic3—94no—
521C2×Dic3—94no—
522C2×Dic3—91no—
523C2×Dic3—91no—
524C2×Dic3—91no—
525C2×Dic3—91no—
526C2×Dic3—124no—
527C2×Dic3—184no—
528C2×Dic3—184no—
529C2×Dic3—184no—
530C2×Dic3—184no—
531C2×Dic3—188no—
532C2×Dic3—182no—
533C2×Dic3—368no—
534C2×Dic3—364no—
535C2×Dic3—364no—
536C2×Dic3—361no—
537C2×Dic3—368no—
538C2×Dic3C22×C3⋊D311yescharacteristic
539C2×Dic3C22×C3⋊D311yescharacteristic
540C2×Dic3C22×C3⋊D311yescharacteristic
541C4×D3—361no—
542Dic6—361no—
543Dic6—364no—
544C2×C32—216no—
545C2×C32—22no—
546C2×C32—22no—
547C2×C32—28no—
548C2×C32—24no—
549C2×C32—24no—
550C2×C32—24no—
551C2×C32—28no—
552C2×C32—48no—
553C2×C32—48no—
554C2×C32—41no—
555C2×C32—44no—
556C2×C32—121no—
557C2×C32C2×#23511yescharacteristic
558C2×C32C2×#23714yes—
559C2×C32C2×#23714yes—
560C2×C32C2×#23711yescharacteristic
561C2×C32#100414yes—
562C2×C32#100411yescharacteristic
563C3×D3—44no—
564C24D3×C3⋊D311yescharacteristic
565C2×Q8—271no—
566C2×D4—31no—
567C2×D4—31no—
568C2×D4—31no—
569C22×C4—91no—
570C22×C4—91no—
571C22×C4—271no—
572C22×C4—271no—
573C22×C4—271no—
574C4⋊C4—271no—
575C4⋊C4—271no—
576C4⋊C4—271no—
577C4⋊C4—271no—
578C4⋊C4—271no—
579C4⋊C4—271no—
580C4⋊C4—271no—
581C4⋊C4—271no—
582C22⋊C4—31no—
583C22⋊C4—31no—
584C22⋊C4—31no—
585C22⋊C4—91no—
586C22⋊C4—91no—
587C22⋊C4—91no—
588C22⋊C4—91no—
589C22⋊C4—271no—
590C22⋊C4—271no—
591C22⋊C4—271no—
592C22⋊C4—271no—
593C22⋊C4—271no—
594C22⋊C4—271no—
595C22⋊C4—271no—
596C42—271no—
597C42—271no—
598C42—271no—
599C22×C3—28no—
600C22×C3—28no—
601C22×C3—24no—
602C22×C3—24no—
603C22×C3—24no—
604C22×C3—24no—
605C22×C3—21no—
606C22×C3—21no—
607C22×C3—21no—
608C22×C3—21no—
609C22×C3—28no—
610C22×C3—24no—
611C22×C3—24no—
612C22×C3—24no—
613C22×C3—21no—
614C22×C3—21no—
615C22×C3—21no—
616C22×C3—24no—
617C22×C3—28no—
618C22×C3—28no—
619C22×C3—44no—
620C22×C3—44no—
621C22×C3—44no—
622C22×C3—44no—
623C22×C3—416no—
624C22×C3—44no—
625C22×C3—432no—
626C22×C3—64no—
627C22×C3—64no—
628C22×C3—64no—
629C22×C3#380418yes—
630C22×C3#380518yes—
631C22×C3#383012yes—
632C22×C3#383012yes—
633C22×C3C22×D3214yes—
634C22×C3C23×C3⋊D311yescharacteristic
635C2×D3—21no—
636C2×D3—21no—
637C2×D3—21no—
638C3×C4—64no—
639C3×C4—64no—
640C3×C4—64no—
641C3×C4—181no—
642C3×C4—181no—
643C3×C4—181no—
644C3×C4—181no—
645Dic3—21no—
646Dic3—21no—
647Dic3—21no—
648Dic3—64no—
649Dic3—64no—
650Dic3—64no—
651Dic3—64no—
652Dic3—184no—
653Dic3—184no—
654Dic3—184no—
655Dic3—184no—
656Dic3—181no—
657Dic3—181no—
658Dic3—181no—
659Dic3—181no—
660Dic3—364no—
661Dic3—364no—
662Dic3—364no—
663Dic3—364no—
664C32—24no—
665C32#549511yescharacteristic, complemented
666C32#558714yescomplemented
667C23—22no—
668C23—22no—
669C23—31no—
670C23—41no—
671C23C2×D3×C3⋊D311yescharacteristic
672C23C2×D3×C3⋊D311yescharacteristic
673C23C2×D3×C3⋊D311yescharacteristic
674Q8—1081no—
675D4—62no—
676D4—62no—
677D4—121no—
678C2×C4—31no—
679C2×C4—31no—
680C2×C4—31no—
681C2×C4—91no—
682C2×C4—91no—
683C2×C4—91no—
684C2×C4—91no—
685C2×C4—182no—
686C2×C4—271no—
687C2×C4—271no—
688C2×C4—271no—
689C2×C4—271no—
690C2×C4—361no—
691C2×C4—542no—
692C2×C4—1081no—
693C2×C4—1081no—
694C2×C3—216no—
695C2×C3—28no—
696C2×C3—28no—
697C2×C3—22no—
698C2×C3—22no—
699C2×C3—24no—
700C2×C3—24no—
701C2×C3—24no—
702C2×C3—48no—
703C2×C3—48no—
704C2×C3—44no—
705C2×C3—41no—
706C2×C3—124no—
707C2×C3C2×#380414yes—
708C2×C3C2×#380514yes—
709C2×C3#6433014yes—
710C2×C3C2×#383011yescharacteristic
711C2×C3C2×#383011yescharacteristic
712C2×C3#6436111yescharacteristic
713D3—41no—
714C22—21no—
715C22—21no—
716C22—21no—
717C22—21no—
718C22—21no—
719C22—21no—
720C22—21no—
721C22—44no—
722C22—61no—
723C22—61no—
724C22—61no—
725C22#8902812yes—
726C22#8902912yes—
727C22C22×D3×C3⋊D311yescharacteristic
728C4—61no—
729C4—61no—
730C4—61no—
731C4—181no—
732C4—181no—
733C4—181no—
734C4—181no—
735C4—541no—
736C4—541no—
737C4—541no—
738C4—541no—
739C3—24no—
740C3#1059550914yescomplemented
741C3#1059605811yescharacteristic, complemented
742C2—22no—
743C2—22no—
744C2—41no—
745C2—121no—
746C2C2×#8902811yescharacteristic
747C2C2×#8902911yescharacteristic
748C2#1172461111yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC24×C33C22
prime radicalC32×#953C2
hypercenterC24D3×C3⋊D3
hypocenterC33#551
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C24

Complements

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

NH ≅ G/Ntype
1. C2×#88864C2semidirect
2. C2×C3×#3757C2semidirect
4. #11723642C2semidirect
5. #11723641C2semidirect
6. #67⋊(C3⋊Dic3)C2semidirect
7. #67×C3⋊Dic3C2semidirect
8. #11723614C2semidirect
9. #11723603C2semidirect
10. #11723602C2semidirect
11. #11723600C2semidirect
12. #11723598C2semidirect
13. #11723597C2semidirect
14. #11723596C2semidirect
15. #11723595C2semidirect
26. C2×#6293C22semidirect
27. C2×D3×C3⋊Dic3C22semidirect
39. #88807C22semidirect
40. #88807C22semidirect
41. #88807C22semidirect
42. #88806C22semidirect
43. #88806C22semidirect
44. #88806C22semidirect
45. Dic3⋊(C3⋊Dic3)C22semidirect
46. Dic3⋊(C3⋊Dic3)C22semidirect
47. (C2×D3)⋊(C3⋊Dic3)C22semidirect
48. (C2×D3)⋊(C3⋊Dic3)C22semidirect
49. (C2×D3)⋊(C3⋊Dic3)C22semidirect
50. Dic3×C3⋊Dic3C22semidirect
51. Dic3×C3⋊Dic3C22semidirect
52. Dic3×C3⋊Dic3C22semidirect
57. C2×#3757D3semidirect
477. C33#551semidirect
665. C32#5495semidirect
666. C32#5587semidirect
740. C3#10595509semidirect
741. C3#10596058semidirect

Maximal subgroups

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

subgroupindex
C2×#888642
C2×C3×#37572
C32×#9532
#117236422
#117236412
#67⋊(C3⋊Dic3)2
#67×C3⋊Dic32
#117236142
#117236032
#117236022
#117236002
#117235982
#117235972
#117235962
#117235952
#105960583
#105955093