Finite Group Databasebeta

← #13178076

Subgroups — #13178076

Order 1728.

2008 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723994C211yesmaximal, characteristic
2C2×C3×#3757C211yesmaximal, characteristic, complemented
3C2×C32×#217C211yesmaximal, characteristic, complemented
4#11723641C211yesmaximal, characteristic, complemented
5#11723640C211yesmaximal, characteristic, complemented
6#11723628C211yesmaximal, characteristic, complemented
7#11723622C211yesmaximal, characteristic, complemented
8#11723618C211yesmaximal, characteristic, complemented
9#11723612C211yesmaximal, characteristic, complemented
10#11723608C211yesmaximal, characteristic, complemented
11#11723597C211yesmaximal, characteristic, complemented
12#11723596C211yesmaximal, characteristic, complemented
13#11723595C211yesmaximal, characteristic, complemented
14#11723594C211yesmaximal, characteristic, complemented
15#11723592C211yesmaximal, characteristic, complemented
16#10595966—31nomaximal
17#10595476—34nomaximal
18C24×C33C2211yescharacteristic
19C2×#6312C2211yescharacteristic
20C2×#6312C2211yescharacteristic
21C2×#6312C2211yescharacteristic
22C22×C3×C3⋊Dic3C2211yescharacteristic
23C22×C3×C3⋊Dic3C2211yescharacteristic
24C22×C32×Dic3C2211yescharacteristic
25C22×C32×Dic3C2211yescharacteristic
26C2×#6293C2211yescharacteristic, complemented
27C2×#6289C2211yescharacteristic, complemented
28#88864C2211yescharacteristic
29#88864C2211yescharacteristic
30#88864C2211yescharacteristic
31C3×#3757C2211yescharacteristic
32C3×#3757C2211yescharacteristic
33C3×#3757C2211yescharacteristic
34C3×#3757C2211yescharacteristic
35C32×#217C2211yescharacteristic
36C32×#217C2211yescharacteristic
37C32×#217C2211yescharacteristic
38C32×#217C2211yescharacteristic
39#88807C2211yescharacteristic, complemented
40#88807C2211yescharacteristic, complemented
41#88807C2211yescharacteristic, complemented
42#88806C2211yescharacteristic, complemented
43#88806C2211yescharacteristic, complemented
44Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
45Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
46Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
47#88804C2211yescharacteristic, complemented
48#88804C2211yescharacteristic, complemented
49#88804C2211yescharacteristic, complemented
50Dic3×C3⋊Dic3C2211yescharacteristic, complemented
51Dic3×C3⋊Dic3C2211yescharacteristic, complemented
52Dic3×C3⋊Dic3C2211yescharacteristic, complemented
53C2×C32×C22⋊C4—31no—
54#64162—31no—
55#64162—34no—
56#64162—64no—
57C2×#3757D311yescharacteristic, complemented
58#64138—31no—
59C4×#638—31no—
60#64135—31no—
61#64133—31no—
62#64095—31no—
63#64094—31no—
64#64092—31no—
65#64090—31no—
66#64088—31no—
67#64088—31no—
68#64087—31no—
69#64086—31no—
70C2×C3×#217—34no—
71C2×C3×#217D314yescomplemented
72#63975—34no—
73#63966—34no—
74#63966—34no—
75#63964—34no—
76#63964—34no—
77#63956—34no—
78#63956—34no—
79#63955—34no—
80#63955—34no—
81#63953—34no—
82#63952—34no—
83#63952—34no—
84C23×C33—22no—
85C23×C33—22no—
86C23×C33—41no—
87C23×C33C2311yescharacteristic
88C23×C33C2311yescharacteristic
89C23×C33C2311yescharacteristic
90C22×C3⋊(C3⋊D3)C2311yescharacteristic
91#6312—22no—
92#6312—22no—
93#6312—41no—
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
103C2×C32×Dic3—22no—
104C2×C32×Dic3—41no—
105C2×C32×Dic3C2311yescharacteristic
106C2×C32×Dic3C2311yescharacteristic
107C2×C32×Dic3C2311yescharacteristic
108C2×C32×Dic3C2311yescharacteristic
109#6293—41no—
110#6289—41no—
111#5495—94no—
112#5495—91no—
113C24×C32—24no—
114C24×C32C2×D314yes—
115C24×C32C2×D311yescharacteristic
116C22×C32×C4—31no—
117C22×C32×C4—31no—
118C2×#638—31no—
119C2×#638—31no—
120C2×#638—34no—
121C2×#638—34no—
122C2×#638—31no—
123C2×#638—34no—
124C2×#638—64no—
125C2×#638—64no—
126C2×#638—64no—
127C22×C3⋊Dic3C2×D311yescharacteristic
128C22×C3⋊Dic3C2×D311yescharacteristic
129C2×C4×C3⋊D3—31no—
130C2×#634—31no—
131C22×C3×Dic3—34no—
132C22×C3×Dic3—34no—
133C22×C3×Dic3C2×D314yes—
134C22×C3×Dic3C2×D314yes—
135C2×#627—34no—
136C2×#624—34no—
137C32×C22⋊C4—31no—
138C32×C22⋊C4—31no—
139C32×C22⋊C4—31no—
140C32×C22⋊C4—31no—
141#3757—31no—
142#3757—31no—
143#3757—31no—
144#3757—34no—
145#3757—34no—
146#3757—34no—
147#3757—64no—
148#3757—64no—
149#3757—64no—
150#3757C2×D311yescharacteristic
151#3757C2×D311yescharacteristic
152#3757C2×D311yescharacteristic
153#3757C2×D311yescharacteristic
154#3752—31no—
155#3752—31no—
156#3752—31no—
157C4⋊(C3⋊Dic3)—31no—
158C4⋊(C3⋊Dic3)—31no—
159C4⋊(C3⋊Dic3)—31no—
160#3750—31no—
161#3750—31no—
162#3750—31no—
163#3750—31no—
164#3750—31no—
165C4×C3⋊Dic3—31no—
166C4×C3⋊Dic3—31no—
167C4×C3⋊Dic3—31no—
168C3×#217—34no—
169C3×#217—34no—
170C3×#217—34no—
171C3×#217—34no—
172C3×#217C2×D314yes—
173C3×#217C2×D314yes—
174C3×#217C2×D314yes—
175C3×#217C2×D314yes—
176#3724—34no—
177#3724—34no—
178Dic3⋊Dic3—34no—
179Dic3⋊Dic3—34no—
180Dic3⋊Dic3—34no—
181Dic3⋊Dic3—34no—
182Dic3⋊Dic3—34no—
183Dic3⋊Dic3—34no—
184#3722—34no—
185#3722—34no—
186#3722—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×C3⋊(C3⋊D3)—21no—
202C2×C3⋊(C3⋊D3)—21no—
203C2×C3⋊(C3⋊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—
211C32×Dic3—21no—
212C32×Dic3—21no—
213C32×Dic3—21no—
214C32×Dic3—21no—
215C2×C3×C22⋊C4—34no—
216C2×C3×C22⋊C4—91no—
217#953—94no—
218#953—91no—
219#953—184no—
220C2×#217—34no—
221C2×#217C3⋊D311yescharacteristic, complemented
222#929—94no—
223#929—91no—
224C4×#67—94no—
225C4×#67—91no—
226#926—94no—
227#926—91no—
228#924—94no—
229#924—91no—
230#886—94no—
231#886—91no—
232#885—94no—
233#885—91no—
234#883—94no—
235#883—91no—
236#67⋊C4—94no—
237#67⋊C4—91no—
238#879—94no—
239#879—94no—
240#879—91no—
241#879—91no—
242#878—94no—
243#878—91no—
244#877—94no—
245#877—91no—
246C23×C32—22no—
247C23×C32—22no—
248C23×C32—24no—
249C23×C32—24no—
250C23×C32—24no—
251C23×C32—28no—
252C23×C32—28no—
253C23×C32—48no—
254C23×C32—48no—
255C23×C32—41no—
256C23×C32—44no—
257C23×C32—48no—
258C23×C32C22×D314yes—
259C23×C32C22×D314yes—
260C23×C32C22×D314yes—
261C23×C32C22×D311yescharacteristic
262C23×C32C22×D311yescharacteristic
263C23×C32C22×D311yescharacteristic
264C22×C3⋊D3—31no—
265C22×C3⋊D3—34no—
266C22×C3⋊D3—64no—
267C2×C32×C4—31no—
268C2×C32×C4—31no—
269C2×C32×C4—31no—
270C2×C32×C4—31no—
271C2×C32×C4—62no—
272C2×C32×C4—121no—
273#638—62no—
274#638—62no—
275#638—68no—
276#638—68no—
277#638—128no—
278#638—128no—
279#638—121no—
280#638—124no—
281#638—128no—
282C2×C3⋊Dic3—22no—
283C2×C3⋊Dic3—31no—
284C2×C3⋊Dic3—31no—
285C2×C3⋊Dic3—31no—
286C2×C3⋊Dic3—34no—
287C2×C3⋊Dic3—34no—
288C2×C3⋊Dic3—34no—
289C2×C3⋊Dic3—41no—
290C2×C3⋊Dic3—64no—
291C2×C3⋊Dic3—64no—
292C2×C3⋊Dic3—64no—
293C2×C3⋊Dic3C22×D311yescharacteristic
294C2×C3⋊Dic3C22×D311yescharacteristic
295C2×C3⋊Dic3C22×D311yescharacteristic
296C2×C3⋊Dic3C22×D311yescharacteristic
297C4×C3⋊D3—121no—
298#634—121no—
299C2×C3×Dic3—28no—
300C2×C3×Dic3—34no—
301C2×C3×Dic3—34no—
302C2×C3×Dic3—34no—
303C2×C3×Dic3—34no—
304C2×C3×Dic3—44no—
305C2×C3×Dic3—68no—
306C2×C3×Dic3—124no—
307C2×C3×Dic3C22×D314yes—
308C2×C3×Dic3C22×D314yes—
309C2×C3×Dic3C22×D314yes—
310C2×C3×Dic3C22×D314yes—
311#627—124no—
312#624—124no—
313#551—271noSylow
314C2×C33—22no—
315C2×C33—22no—
316C2×C33—41no—
317C2×C33C2×#4111yescharacteristic
318C2×C33C2×#4111yescharacteristic
319C2×C33H(5,𝔽2)11yescharacteristic
320C3⋊(C3⋊D3)—41no—
321C24×C3—24no—
322C24×C3D3214yes—
323C24×C3C2×C3⋊D311yescharacteristic
324C22×C3×C4—34no—
325C22×C3×C4—34no—
326C22×C3×C4—91no—
327C22×C3×C4—91no—
328C2×#67—94no—
329C2×#67—94no—
330C2×#67—91no—
331C2×#67—91no—
332C2×#67—94no—
333C2×#67—91no—
334C2×#67—184no—
335C2×#67—184no—
336C2×#67—184no—
337C22×Dic3—34no—
338C22×Dic3—34no—
339C22×Dic3C2×C3⋊D311yescharacteristic
340C22×Dic3C2×C3⋊D311yescharacteristic
341C2×C4×D3—94no—
342C2×C4×D3—91no—
343C2×Dic6—94no—
344C2×Dic6—91no—
345C3×C22⋊C4—34no—
346C3×C22⋊C4—34no—
347C3×C22⋊C4—34no—
348C3×C22⋊C4—34no—
349C3×C22⋊C4—91no—
350C3×C22⋊C4—91no—
351C3×C22⋊C4—91no—
352C3×C22⋊C4—91no—
353#217—34no—
354#217—34no—
355#217—34no—
356#217—34no—
357#217—94no—
358#217—94no—
359#217—94no—
360#217—91no—
361#217—91no—
362#217—91no—
363#217—184no—
364#217—184no—
365#217—184no—
366#217C2×C3⋊D311yescharacteristic
367#217C2×C3⋊D311yescharacteristic
368#217C2×C3⋊D311yescharacteristic
369#217C2×C3⋊D311yescharacteristic
370(C2×D3)⋊C4—94no—
371(C2×D3)⋊C4—94no—
372(C2×D3)⋊C4—94no—
373(C2×D3)⋊C4—91no—
374(C2×D3)⋊C4—91no—
375(C2×D3)⋊C4—91no—
376C4⋊Dic3—94no—
377C4⋊Dic3—94no—
378C4⋊Dic3—94no—
379C4⋊Dic3—91no—
380C4⋊Dic3—91no—
381C4⋊Dic3—91no—
382Dic3⋊C4—94no—
383Dic3⋊C4—94no—
384Dic3⋊C4—94no—
385Dic3⋊C4—94no—
386Dic3⋊C4—94no—
387Dic3⋊C4—91no—
388Dic3⋊C4—91no—
389Dic3⋊C4—91no—
390Dic3⋊C4—91no—
391Dic3⋊C4—91no—
392C4×Dic3—94no—
393C4×Dic3—94no—
394C4×Dic3—94no—
395C4×Dic3—91no—
396C4×Dic3—91no—
397C4×Dic3—91no—
398C22×C32—21no—
399C22×C32—21no—
400C22×C32—21no—
401C22×C32—21no—
402C22×C32—28no—
403C22×C32—21no—
404C22×C32—21no—
405C22×C32—24no—
406C22×C32—21no—
407C22×C32—24no—
408C22×C32—28no—
409C22×C32—28no—
410C22×C32—24no—
411C22×C32—24no—
412C22×C32—24no—
413C22×C32—24no—
414C22×C32—24no—
415C22×C32—24no—
416C22×C32—44no—
417C22×C32—44no—
418C22×C32—44no—
419C22×C32—44no—
420C22×C32—44no—
421C22×C32—44no—
422C22×C32—44no—
423C22×C32—416no—
424C22×C32—432no—
425C22×C32#23518yes—
426C22×C32#23512yes—
427C22×C32#23718yes—
428C22×C32#23712yes—
429C22×C32C23×D314yes—
430C22×C32C23×D311yescharacteristic
431C2×C3⋊D3—61no—
432C2×C3⋊D3—61no—
433C2×C3⋊D3—61no—
434C2×C3⋊D3—64no—
435C2×C3⋊D3—64no—
436C2×C3⋊D3—64no—
437C2×C3⋊D3—124no—
438C2×C3⋊D3—124no—
439C2×C3⋊D3—124no—
440C32×C4—61no—
441C32×C4—61no—
442C32×C4—61no—
443C32×C4—61no—
444C3⋊Dic3—21no—
445C3⋊Dic3—21no—
446C3⋊Dic3—21no—
447C3⋊Dic3—21no—
448C3⋊Dic3—61no—
449C3⋊Dic3—61no—
450C3⋊Dic3—61no—
451C3⋊Dic3—64no—
452C3⋊Dic3—64no—
453C3⋊Dic3—64no—
454C3⋊Dic3—124no—
455C3⋊Dic3—124no—
456C3⋊Dic3—124no—
457C3×Dic3—24no—
458C3×Dic3—24no—
459C3×Dic3—24no—
460C3×Dic3—24no—
461C3×Dic3—64no—
462C3×Dic3—64no—
463C3×Dic3—64no—
464C3×Dic3—64no—
465#126—271no—
466#126—271no—
467#124—271no—
468#123—271no—
469#123—271no—
470#123—271no—
471C22⋊Q8—271no—
472C22⋊Q8—271no—
473#120—271no—
474C4×D4—271no—
475C4×D4—271no—
476#117—271no—
477#117—271no—
478C2×C22⋊C4—31no—
479C2×C22⋊C4—91no—
480C33#55111yescharacteristic, complemented, Sylow
481C23×C3—28no—
482C23×C3—28no—
483C23×C3—22no—
484C23×C3—22no—
485C23×C3—24no—
486C23×C3—24no—
487C23×C3—24no—
488C23×C3—48no—
489C23×C3—48no—
490C23×C3—44no—
491C23×C3—41no—
492C23×C3—48no—
493C23×C3C2×D3214yes—
494C23×C3C2×D3214yes—
495C23×C3C2×D3214yes—
496C23×C3C22×C3⋊D311yescharacteristic
497C23×C3C22×C3⋊D311yescharacteristic
498C23×C3C22×C3⋊D311yescharacteristic
499C22×D3—94no—
500C22×D3—91no—
501C22×D3—184no—
502C2×C3×C4—34no—
503C2×C3×C4—34no—
504C2×C3×C4—34no—
505C2×C3×C4—34no—
506C2×C3×C4—68no—
507C2×C3×C4—91no—
508C2×C3×C4—91no—
509C2×C3×C4—91no—
510C2×C3×C4—91no—
511C2×C3×C4—124no—
512C2×C3×C4—182no—
513C2×C3×C4—361no—
514#67—188no—
515#67—188no—
516#67—182no—
517#67—182no—
518#67—368no—
519#67—368no—
520#67—364no—
521#67—361no—
522#67—368no—
523C2×Dic3—22no—
524C2×Dic3—34no—
525C2×Dic3—34no—
526C2×Dic3—34no—
527C2×Dic3—34no—
528C2×Dic3—41no—
529C2×Dic3—68no—
530C2×Dic3—94no—
531C2×Dic3—94no—
532C2×Dic3—94no—
533C2×Dic3—91no—
534C2×Dic3—91no—
535C2×Dic3—91no—
536C2×Dic3—124no—
537C2×Dic3—184no—
538C2×Dic3—184no—
539C2×Dic3—184no—
540C2×Dic3C22×C3⋊D311yescharacteristic
541C2×Dic3C22×C3⋊D311yescharacteristic
542C2×Dic3C22×C3⋊D311yescharacteristic
543C2×Dic3C22×C3⋊D311yescharacteristic
544C4×D3—361no—
545C4×D3—364no—
546Dic6—361no—
547Dic6—364no—
548C2×C32—22no—
549C2×C32—22no—
550C2×C32—24no—
551C2×C32—24no—
552C2×C32—24no—
553C2×C32—28no—
554C2×C32—28no—
555C2×C32—48no—
556C2×C32—48no—
557C2×C32—48no—
558C2×C32—44no—
559C2×C32—41no—
560C2×C32C2×#23514yes—
561C2×C32C2×#23511yescharacteristic
562C2×C32C2×#23714yes—
563C2×C32C2×#23711yescharacteristic
564C2×C32#100414yes—
565C2×C32#100411yescharacteristic
566C3⋊D3—121no—
567C3⋊D3—124no—
568C3⋊D3—244no—
569C24D3×C3⋊D311yescharacteristic
570C2×Q8—271no—
571C2×D4—271no—
572C2×D4—271no—
573C2×D4—271no—
574C22×C4—31no—
575C22×C4—31no—
576C22×C4—91no—
577C22×C4—91no—
578C22×C4—271no—
579C4⋊C4—271no—
580C4⋊C4—271no—
581C4⋊C4—271no—
582C4⋊C4—271no—
583C4⋊C4—271no—
584C4⋊C4—271no—
585C4⋊C4—271no—
586C4⋊C4—271no—
587C22⋊C4—31no—
588C22⋊C4—31no—
589C22⋊C4—31no—
590C22⋊C4—31no—
591C22⋊C4—91no—
592C22⋊C4—91no—
593C22⋊C4—91no—
594C22⋊C4—91no—
595C22⋊C4—271no—
596C22⋊C4—271no—
597C22⋊C4—271no—
598C22⋊C4—271no—
599C22⋊C4—271no—
600C22⋊C4—271no—
601C42—271no—
602C42—271no—
603C42—271no—
604C22×C3—24no—
605C22×C3—24no—
606C22×C3—24no—
607C22×C3—24no—
608C22×C3—21no—
609C22×C3—21no—
610C22×C3—21no—
611C22×C3—21no—
612C22×C3—28no—
613C22×C3—24no—
614C22×C3—24no—
615C22×C3—24no—
616C22×C3—21no—
617C22×C3—21no—
618C22×C3—21no—
619C22×C3—24no—
620C22×C3—28no—
621C22×C3—28no—
622C22×C3—44no—
623C22×C3—44no—
624C22×C3—44no—
625C22×C3—44no—
626C22×C3—44no—
627C22×C3—44no—
628C22×C3—44no—
629C22×C3—416no—
630C22×C3—432no—
631C22×C3#380418yes—
632C22×C3#380418yes—
633C22×C3#382812yes—
634C22×C3#383012yes—
635C22×C3C22×D3214yes—
636C22×C3C23×C3⋊D311yescharacteristic
637C2×D3—184no—
638C2×D3—184no—
639C2×D3—184no—
640C2×D3—181no—
641C2×D3—181no—
642C2×D3—181no—
643C2×D3—364no—
644C2×D3—364no—
645C2×D3—364no—
646C3×C4—64no—
647C3×C4—64no—
648C3×C4—64no—
649C3×C4—64no—
650C3×C4—181no—
651C3×C4—181no—
652C3×C4—181no—
653C3×C4—181no—
654Dic3—21no—
655Dic3—21no—
656Dic3—21no—
657Dic3—21no—
658Dic3—64no—
659Dic3—64no—
660Dic3—64no—
661Dic3—64no—
662Dic3—184no—
663Dic3—184no—
664Dic3—184no—
665Dic3—181no—
666Dic3—181no—
667Dic3—181no—
668Dic3—364no—
669Dic3—364no—
670Dic3—364no—
671C32—24no—
672C32#549514yescomplemented
673C32#549511yescharacteristic, complemented
674C23—22no—
675C23—22no—
676C23—41no—
677C23—271no—
678C23C2×D3×C3⋊D311yescharacteristic
679C23C2×D3×C3⋊D311yescharacteristic
680C23C2×D3×C3⋊D311yescharacteristic
681Q8—1081no—
682D4—542no—
683D4—542no—
684D4—1081no—
685C2×C4—31no—
686C2×C4—31no—
687C2×C4—31no—
688C2×C4—31no—
689C2×C4—62no—
690C2×C4—91no—
691C2×C4—91no—
692C2×C4—91no—
693C2×C4—91no—
694C2×C4—121no—
695C2×C4—182no—
696C2×C4—271no—
697C2×C4—271no—
698C2×C4—271no—
699C2×C4—361no—
700C2×C4—1081no—
701C2×C3—22no—
702C2×C3—22no—
703C2×C3—28no—
704C2×C3—28no—
705C2×C3—24no—
706C2×C3—24no—
707C2×C3—24no—
708C2×C3—48no—
709C2×C3—48no—
710C2×C3—48no—
711C2×C3—41no—
712C2×C3—44no—
713C2×C3C2×#380414yes—
714C2×C3C2×#380414yes—
715C2×C3#6433014yes—
716C2×C3C2×#382811yescharacteristic
717C2×C3C2×#383011yescharacteristic
718C2×C3#6436111yescharacteristic
719D3—361no—
720D3—364no—
721D3—724no—
722C22—21no—
723C22—21no—
724C22—21no—
725C22—21no—
726C22—21no—
727C22—21no—
728C22—21no—
729C22—44no—
730C22—541no—
731C22—541no—
732C22—541no—
733C22#8902812yes—
734C22#8903112yes—
735C22C22×D3×C3⋊D311yescharacteristic
736C4—61no—
737C4—61no—
738C4—61no—
739C4—61no—
740C4—181no—
741C4—181no—
742C4—181no—
743C4—181no—
744C4—541no—
745C4—541no—
746C4—541no—
747C3—24no—
748C3#1059547614yescomplemented
749C3#1059596611yescharacteristic, complemented
750C2—22no—
751C2—22no—
752C2—41no—
753C2—1081no—
754C2C2×#8902811yescharacteristic
755C2C2×#8903111yescharacteristic
756C2#1172461111yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC24×C33C22
prime radical#11723994C2
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
2. C2×C3×#3757C2semidirect
3. C2×C32×#217C2semidirect
4. #11723641C2semidirect
5. #11723640C2semidirect
6. #11723628C2semidirect
7. #11723622C2semidirect
8. #11723618C2semidirect
9. #11723612C2semidirect
10. #11723608C2semidirect
11. #11723597C2semidirect
12. #11723596C2semidirect
13. #11723595C2semidirect
14. #11723594C2semidirect
15. #11723592C2semidirect
26. C2×#6293C22semidirect
27. C2×#6289C22semidirect
39. #88807C22semidirect
40. #88807C22semidirect
41. #88807C22semidirect
42. #88806C22semidirect
43. #88806C22semidirect
44. Dic3⋊(C3⋊Dic3)C22semidirect
45. Dic3⋊(C3⋊Dic3)C22semidirect
46. Dic3⋊(C3⋊Dic3)C22semidirect
47. #88804C22semidirect
48. #88804C22semidirect
49. #88804C22semidirect
50. Dic3×C3⋊Dic3C22semidirect
51. Dic3×C3⋊Dic3C22semidirect
52. Dic3×C3⋊Dic3C22semidirect
57. C2×#3757D3semidirect
71. C2×C3×#217D3semidirect
221. C2×#217C3⋊D3semidirect
480. C33#551semidirect
672. C32#5495semidirect
673. C32#5495semidirect
748. C3#10595476semidirect
749. C3#10595966semidirect

Maximal subgroups

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

subgroupindex
#117239942
C2×C3×#37572
C2×C32×#2172
#117236412
#117236402
#117236282
#117236222
#117236182
#117236122
#117236082
#117235972
#117235962
#117235952
#117235942
#117235922
#105959663
#105954763