Finite Group Databasebeta

← #13162052

Subgroups — #13162052

Order 1728.

1290 conjugacy classes of subgroups.

The subgroup lattice has 928 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3757C211yesmaximal, characteristic
2C2×C3×#3757C211yesmaximal, characteristic
3C2×C3×#3757C211yesmaximal, characteristic
4C2×#88815C211yesmaximal, characteristic, complemented
5C2×#88813C211yesmaximal, characteristic, complemented
6#11722082C211yesmaximal, characteristic, complemented
7#11722082C211yesmaximal, characteristic, complemented
8#10591703—31nomaximal
9#10591702—31nomaximal
10#10591701—31nomaximal
11C24×C33C2211yescharacteristic
12C22×C3×C3⋊Dic3C2211yescharacteristic
13C22×C3×C3⋊Dic3C2211yescharacteristic
14C22×C3×C3⋊Dic3C2211yescharacteristic
15C22×C3×C3⋊Dic3C2211yescharacteristic
16C22×C3×C3⋊Dic3C2211yescharacteristic
17C22×C3×C3⋊Dic3C2211yescharacteristic
18C3×#3757—22no—
19C3×#3757—22no—
20C3×#3757C414yescomplemented
21#88815—22no—
22#88813—22no—
23C2×#3757D311yescharacteristic
24C2×#3757D311yescharacteristic
25C2×#3757D311yescharacteristic
26C2×C3×#217—31no—
27C2×C3×#217—31no—
28C2×C3×#217—31no—
29C2×C3×#217—31no—
30C2×C3×#217—31no—
31C2×C3×#217—31no—
32C2×C3×#217—61no—
33C2×C3×#217—61no—
34C2×C3×#217—61no—
35C2×#3724—31no—
36C2×Dic3⋊Dic3—31no—
37C2×Dic3⋊Dic3—31no—
38C2×Dic32—31no—
39C2×Dic32—31no—
40C2×Dic32—31no—
41#63579—31no—
42#63579—31no—
43#63579—31no—
44#63579—31no—
45#63579—31no—
46#63579—31no—
47C23×C33—21no—
48C23×C33—21no—
49C23×C33—21no—
50C23×C33—21no—
51C23×C33—21no—
52C23×C33—21no—
53C23×C33C2×C412yes—
54C23×C33C2311yescharacteristic
55C2×C3×C3⋊Dic3—21no—
56C2×C3×C3⋊Dic3—21no—
57C2×C3×C3⋊Dic3—21no—
58C2×C3×C3⋊Dic3—21no—
59C2×C3×C3⋊Dic3—21no—
60C2×C3×C3⋊Dic3—21no—
61C2×C3×C3⋊Dic3—21no—
62C2×C3×C3⋊Dic3—21no—
63C2×C3×C3⋊Dic3—21no—
64C2×C3×C3⋊Dic3—21no—
65C2×C3×C3⋊Dic3—21no—
66C2×C3×C3⋊Dic3—21no—
67C2×C3×C3⋊Dic3—21no—
68C2×C3×C3⋊Dic3—21no—
69C2×C3×C3⋊Dic3C2×C412yes—
70C2×C3×C3⋊Dic3C2×C412yes—
71C2×C3×C3⋊Dic3D412yes—
72C2×C3×C3⋊Dic3D412yes—
73#4951—91no—
74#4945—91no—
75#4944—91no—
76C24×C32—21no—
77C24×C32—21no—
78C24×C32—21no—
79C24×C32—41no—
80C24×C32C2×D311yescharacteristic
81C24×C32C2×D311yescharacteristic
82C24×C32C2×D311yescharacteristic
83C22×C3⋊Dic3C2×D311yescharacteristic
84C22×C3⋊Dic3C2×D311yescharacteristic
85C22×C3⋊Dic3C2×D311yescharacteristic
86C22×C3⋊Dic3C2×D311yescharacteristic
87C22×C3⋊Dic3C2×D311yescharacteristic
88C22×C3⋊Dic3C2×D311yescharacteristic
89C22×C3×Dic3—31no—
90C22×C3×Dic3—31no—
91C22×C3×Dic3—31no—
92C22×C3×Dic3—31no—
93C22×C3×Dic3—31no—
94C22×C3×Dic3—31no—
95C22×C3×Dic3—31no—
96C22×C3×Dic3—31no—
97C22×C3×Dic3—31no—
98C22×C3×Dic3—31no—
99C22×C3×Dic3—31no—
100C22×C3×Dic3—31no—
101C22×C3×Dic3—61no—
102C22×C3×Dic3—61no—
103C22×C3×Dic3—61no—
104C22×C3×Dic3—61no—
105C22×C3×Dic3—61no—
106C22×C3×Dic3—61no—
107#3757—22no—
108#3757—22no—
109#3757Dic314yescomplemented
110C3×#217—34no—
111C3×#217—34no—
112C3×#217—62no—
113C3×#217—62no—
114C3×#217—62no—
115C3×#217—62no—
116C3×#217—64no—
117C3×#217—64no—
118C3×#217—64no—
119#3724—62no—
120Dic3⋊Dic3—62no—
121Dic3⋊Dic3—62no—
122Dic32—62no—
123Dic32—62no—
124Dic32—62no—
125C22×C33—22no—
126C22×C33—22no—
127C22×C33—22no—
128C22×C33—41no—
129C22×C33—41no—
130C22×C33—41no—
131C22×C33—41no—
132C22×C33C22×C411yescharacteristic
133C22×C33C2×D411yescharacteristic
134C22×C33C2×D411yescharacteristic
135C22×C33#4111yescharacteristic
136C22×C33#4111yescharacteristic
137C22×C33#4111yescharacteristic
138C22×C33#4111yescharacteristic
139C3×C3⋊Dic3—22no—
140C3×C3⋊Dic3—22no—
141C3×C3⋊Dic3—22no—
142C3×C3⋊Dic3—22no—
143C3×C3⋊Dic3—41no—
144C3×C3⋊Dic3—41no—
145C2×C3×C22⋊C4—91no—
146C2×C3×C22⋊C4—91no—
147C2×C3×C22⋊C4—91no—
148C2×#217—31no—
149C2×#217—31no—
150C2×#217—31no—
151C2×#217—31no—
152C2×#217—31no—
153C2×#217—31no—
154C2×#217—61no—
155C2×#217—61no—
156C2×#217—61no—
157C2×C4⋊Dic3—91no—
158C2×Dic3⋊C4—91no—
159C2×Dic3⋊C4—91no—
160C2×C4×Dic3—91no—
161C2×C4×Dic3—91no—
162C2×C4×Dic3—91no—
163C3⋊#95—91no—
164C3⋊#95—91no—
165C3⋊#95—91no—
166C3⋊#95—91no—
167C3⋊#95—91no—
168C3⋊#95—91no—
169C23×C32—21no—
170C23×C32—21no—
171C23×C32—21no—
172C23×C32—21no—
173C23×C32—21no—
174C23×C32—21no—
175C23×C32—22no—
176C23×C32—22no—
177C23×C32—22no—
178C23×C32—22no—
179C23×C32—22no—
180C23×C32—22no—
181C23×C32—21no—
182C23×C32—21no—
183C23×C32—21no—
184C23×C32—21no—
185C23×C32—21no—
186C23×C32—21no—
187C23×C32—21no—
188C23×C32—21no—
189C23×C32—21no—
190C23×C32—21no—
191C23×C32—21no—
192C23×C32—21no—
193C23×C32—22no—
194C23×C32—22no—
195C23×C32—22no—
196C23×C32—21no—
197C23×C32—21no—
198C23×C32—21no—
199C23×C32—42no—
200C23×C32—41no—
201C23×C32—41no—
202C23×C32—41no—
203C23×C32—41no—
204C23×C32—41no—
205C23×C32—41no—
206C23×C32—41no—
207C23×C32—41no—
208C23×C32—41no—
209C23×C32—41no—
210C23×C32—41no—
211C23×C32—41no—
212C23×C32—41no—
213C23×C32—42no—
214C23×C32—42no—
215C23×C32—42no—
216C23×C32—42no—
217C23×C32—42no—
218C23×C32—42no—
219C23×C32C4×D312yes—
220C23×C32C4×D312yes—
221C23×C32C2×Dic312yes—
222C23×C32C22×D311yescharacteristic
223C23×C32C22×D311yescharacteristic
224C23×C32C22×D311yescharacteristic
225C2×C3⋊Dic3—21no—
226C2×C3⋊Dic3—21no—
227C2×C3⋊Dic3—21no—
228C2×C3⋊Dic3—21no—
229C2×C3⋊Dic3—21no—
230C2×C3⋊Dic3—21no—
231C2×C3⋊Dic3—21no—
232C2×C3⋊Dic3—21no—
233C2×C3⋊Dic3—21no—
234C2×C3⋊Dic3—21no—
235C2×C3⋊Dic3—21no—
236C2×C3⋊Dic3—21no—
237C2×C3⋊Dic3—21no—
238C2×C3⋊Dic3—21no—
239C2×C3⋊Dic3C2×Dic312yes—
240C2×C3⋊Dic3C2×Dic312yes—
241C2×C3⋊Dic3#6712yes—
242C2×C3⋊Dic3#6712yes—
243C2×C3×Dic3—32no—
244C2×C3×Dic3—32no—
245C2×C3×Dic3—32no—
246C2×C3×Dic3—32no—
247C2×C3×Dic3—32no—
248C2×C3×Dic3—32no—
249C2×C3×Dic3—32no—
250C2×C3×Dic3—32no—
251C2×C3×Dic3—62no—
252C2×C3×Dic3—62no—
253C2×C3×Dic3—62no—
254C2×C3×Dic3—62no—
255C2×C3×Dic3—61no—
256C2×C3×Dic3—61no—
257C2×C3×Dic3—61no—
258C2×C3×Dic3—61no—
259C2×C3×Dic3—61no—
260C2×C3×Dic3—61no—
261C2×C3×Dic3—61no—
262C2×C3×Dic3—61no—
263C2×C3×Dic3—61no—
264C2×C3×Dic3—61no—
265C2×C3×Dic3—61no—
266C2×C3×Dic3—61no—
267C2×C3×Dic3—61no—
268C2×C3×Dic3—61no—
269C2×C3×Dic3—61no—
270C2×C3×Dic3—61no—
271C2×C3×Dic3—62no—
272C2×C3×Dic3—62no—
273C2×C3×Dic3—61no—
274C2×C3×Dic3—61no—
275C2×C3×Dic3—61no—
276C2×C3×Dic3—61no—
277C2×C3×Dic3—61no—
278C2×C3×Dic3—61no—
279C2×C3×Dic3—61no—
280C2×C3×Dic3—61no—
281C2×C3×Dic3—61no—
282C2×C3×Dic3—61no—
283C2×C3×Dic3—61no—
284C2×C3×Dic3—61no—
285C2×C3×Dic3—121no—
286C2×C3×Dic3—121no—
287C2×C3×Dic3—121no—
288C2×C3×Dic3—121no—
289C2×C3×Dic3—121no—
290C2×C3×Dic3—121no—
291C2×C3×Dic3—121no—
292C2×C3×Dic3—121no—
293C2×C3×Dic3—121no—
294C2×C3×Dic3—121no—
295C2×C3×Dic3—121no—
296C2×C3×Dic3—121no—
297#388—271noSylow
298C2×C33—42no—
299C2×C33#11711yescharacteristic
300C2×C33C4×D411yescharacteristic
301C2×C33C4×D411yescharacteristic
302C2×C33#12111yescharacteristic
303C2×C33#12311yescharacteristic
304C2×C33#12411yescharacteristic
305C2×C33#12611yescharacteristic
306C24×C3—21no—
307C24×C3—21no—
308C24×C3—21no—
309C24×C3—41no—
310C24×C3D3211yescharacteristic
311C24×C3D3211yescharacteristic
312C24×C3D3211yescharacteristic
313C22×C3×C4—91no—
314C22×C3×C4—91no—
315C22×C3×C4—91no—
316C22×C3×C4—91no—
317C22×C3×C4—91no—
318C22×C3×C4—91no—
319C22×Dic3—31no—
320C22×Dic3—31no—
321C22×Dic3—31no—
322C22×Dic3—31no—
323C22×Dic3—31no—
324C22×Dic3—31no—
325C22×Dic3—31no—
326C22×Dic3—31no—
327C22×Dic3—31no—
328C22×Dic3—31no—
329C22×Dic3—31no—
330C22×Dic3—31no—
331C22×Dic3—61no—
332C22×Dic3—61no—
333C22×Dic3—61no—
334C22×Dic3—61no—
335C22×Dic3—61no—
336C22×Dic3—61no—
337C3×C22⋊C4—94no—
338C3×C22⋊C4—182no—
339C3×C22⋊C4—182no—
340#217—34no—
341#217—34no—
342#217—64no—
343#217—62no—
344#217—62no—
345#217—62no—
346#217—62no—
347#217—64no—
348#217—64no—
349C4⋊Dic3—182no—
350Dic3⋊C4—182no—
351Dic3⋊C4—182no—
352C4×Dic3—182no—
353C4×Dic3—182no—
354C4×Dic3—182no—
355C22×C32—22no—
356C22×C32—22no—
357C22×C32—22no—
358C22×C32—24no—
359C22×C32—24no—
360C22×C32—24no—
361C22×C32—22no—
362C22×C32—22no—
363C22×C32—22no—
364C22×C32—22no—
365C22×C32—22no—
366C22×C32—22no—
367C22×C32—21no—
368C22×C32—21no—
369C22×C32—21no—
370C22×C32—21no—
371C22×C32—21no—
372C22×C32—21no—
373C22×C32—21no—
374C22×C32—21no—
375C22×C32—21no—
376C22×C32—21no—
377C22×C32—21no—
378C22×C32—21no—
379C22×C32—21no—
380C22×C32—21no—
381C22×C32—21no—
382C22×C32—21no—
383C22×C32—21no—
384C22×C32—21no—
385C22×C32—21no—
386C22×C32—21no—
387C22×C32—21no—
388C22×C32—41no—
389C22×C32—41no—
390C22×C32—41no—
391C22×C32—41no—
392C22×C32—41no—
393C22×C32—41no—
394C22×C32—41no—
395C22×C32—42no—
396C22×C32—42no—
397C22×C32—42no—
398C22×C32—42no—
399C22×C32—42no—
400C22×C32—42no—
401C22×C32—44no—
402C22×C32—44no—
403C22×C32—44no—
404C22×C32—42no—
405C22×C32—42no—
406C22×C32—42no—
407C22×C32—42no—
408C22×C32—42no—
409C22×C32—42no—
410C22×C32—42no—
411C22×C32—42no—
412C22×C32—42no—
413C22×C32—42no—
414C22×C32—42no—
415C22×C32—42no—
416C22×C32—44no—
417C22×C32—44no—
418C22×C32—44no—
419C22×C32—44no—
420C22×C32—41no—
421C22×C32—41no—
422C22×C32—41no—
423C22×C32—41no—
424C22×C32—41no—
425C22×C32—41no—
426C22×C32—41no—
427C22×C32—41no—
428C22×C32—41no—
429C22×C32—41no—
430C22×C32—41no—
431C22×C32—41no—
432C22×C32C2×C4×D311yescharacteristic
433C22×C32C2×C4×D311yescharacteristic
434C22×C32#23511yescharacteristic
435C22×C32#23511yescharacteristic
436C22×C32#23511yescharacteristic
437C22×C32#23511yescharacteristic
438C22×C32D3×D411yescharacteristic
439C22×C32D3×D411yescharacteristic
440C22×C32D3×D411yescharacteristic
441C22×C32D3×D411yescharacteristic
442C22×C32#23711yescharacteristic
443C22×C32#23711yescharacteristic
444C22×C32#23711yescharacteristic
445C22×C32#23711yescharacteristic
446C22×C32#23711yescharacteristic
447C22×C32#23711yescharacteristic
448C22×C32#23711yescharacteristic
449C22×C32#23711yescharacteristic
450C22×C32C22×Dic311yescharacteristic
451C22×C32C2×#6711yescharacteristic
452C22×C32C2×#6711yescharacteristic
453C3⋊Dic3—22no—
454C3⋊Dic3—22no—
455C3⋊Dic3—22no—
456C3⋊Dic3—22no—
457C3⋊Dic3—41no—
458C3⋊Dic3—41no—
459C3×Dic3—62no—
460C3×Dic3—62no—
461C3×Dic3—62no—
462C3×Dic3—62no—
463C3×Dic3—62no—
464C3×Dic3—62no—
465C3×Dic3—62no—
466C3×Dic3—62no—
467C3×Dic3—122no—
468C3×Dic3—122no—
469C3×Dic3—122no—
470C3×Dic3—122no—
471C3×Dic3—122no—
472C3×Dic3—122no—
473C3×Dic3—121no—
474C3×Dic3—121no—
475C3×Dic3—121no—
476C3×Dic3—121no—
477C2×C4⋊C4—271no—
478C2×C22⋊C4—91no—
479C2×C22⋊C4—91no—
480C2×C22⋊C4—91no—
481C2×C42—271no—
482#95—271no—
483#95—271no—
484C33#38811yescharacteristic, complemented, Sylow
485C23×C3—22no—
486C23×C3—22no—
487C23×C3—22no—
488C23×C3—22no—
489C23×C3—22no—
490C23×C3—22no—
491C23×C3—21no—
492C23×C3—21no—
493C23×C3—21no—
494C23×C3—21no—
495C23×C3—21no—
496C23×C3—21no—
497C23×C3—21no—
498C23×C3—21no—
499C23×C3—21no—
500C23×C3—21no—
501C23×C3—21no—
502C23×C3—21no—
503C23×C3—21no—
504C23×C3—21no—
505C23×C3—21no—
506C23×C3—21no—
507C23×C3—21no—
508C23×C3—21no—
509C23×C3—22no—
510C23×C3—22no—
511C23×C3—22no—
512C23×C3—21no—
513C23×C3—21no—
514C23×C3—21no—
515C23×C3—41no—
516C23×C3—41no—
517C23×C3—41no—
518C23×C3—41no—
519C23×C3—41no—
520C23×C3—41no—
521C23×C3—41no—
522C23×C3—41no—
523C23×C3—41no—
524C23×C3—41no—
525C23×C3—41no—
526C23×C3—41no—
527C23×C3—42no—
528C23×C3—42no—
529C23×C3—42no—
530C23×C3—42no—
531C23×C3—42no—
532C23×C3—42no—
533C23×C3—42no—
534C23×C3—41no—
535C23×C3D3×Dic312yes—
536C23×C3D3×Dic312yes—
537C23×C3#62412yes—
538C23×C3C2×D3211yescharacteristic
539C23×C3C2×D3211yescharacteristic
540C23×C3C2×D3211yescharacteristic
541C2×C3×C4—92no—
542C2×C3×C4—92no—
543C2×C3×C4—92no—
544C2×C3×C4—92no—
545C2×C3×C4—181no—
546C2×C3×C4—181no—
547C2×C3×C4—181no—
548C2×C3×C4—181no—
549C2×C3×C4—181no—
550C2×C3×C4—181no—
551C2×C3×C4—181no—
552C2×C3×C4—181no—
553C2×C3×C4—181no—
554C2×C3×C4—181no—
555C2×C3×C4—181no—
556C2×C3×C4—181no—
557C2×C3×C4—181no—
558C2×C3×C4—181no—
559C2×Dic3—32no—
560C2×Dic3—32no—
561C2×Dic3—32no—
562C2×Dic3—32no—
563C2×Dic3—32no—
564C2×Dic3—32no—
565C2×Dic3—32no—
566C2×Dic3—32no—
567C2×Dic3—62no—
568C2×Dic3—62no—
569C2×Dic3—62no—
570C2×Dic3—62no—
571C2×Dic3—61no—
572C2×Dic3—61no—
573C2×Dic3—61no—
574C2×Dic3—61no—
575C2×Dic3—61no—
576C2×Dic3—61no—
577C2×Dic3—61no—
578C2×Dic3—61no—
579C2×Dic3—61no—
580C2×Dic3—61no—
581C2×Dic3—61no—
582C2×Dic3—61no—
583C2×Dic3—61no—
584C2×Dic3—61no—
585C2×Dic3—61no—
586C2×Dic3—61no—
587C2×Dic3—62no—
588C2×Dic3—62no—
589C2×Dic3—61no—
590C2×Dic3—61no—
591C2×Dic3—61no—
592C2×Dic3—61no—
593C2×Dic3—61no—
594C2×Dic3—61no—
595C2×Dic3—61no—
596C2×Dic3—61no—
597C2×Dic3—61no—
598C2×Dic3—61no—
599C2×Dic3—61no—
600C2×Dic3—61no—
601C2×Dic3—121no—
602C2×Dic3—121no—
603C2×Dic3—121no—
604C2×Dic3—121no—
605C2×Dic3—121no—
606C2×Dic3—121no—
607C2×Dic3—121no—
608C2×Dic3—121no—
609C2×Dic3—121no—
610C2×Dic3—121no—
611C2×Dic3—121no—
612C2×Dic3—121no—
613C2×C32—21no—
614C2×C32—21no—
615C2×C32—21no—
616C2×C32—21no—
617C2×C32—21no—
618C2×C32—21no—
619C2×C32—21no—
620C2×C32—21no—
621C2×C32—21no—
622C2×C32—21no—
623C2×C32—21no—
624C2×C32—21no—
625C2×C32—21no—
626C2×C32—21no—
627C2×C32—21no—
628C2×C32—21no—
629C2×C32—21no—
630C2×C32—21no—
631C2×C32—21no—
632C2×C32—21no—
633C2×C32—21no—
634C2×C32—41no—
635C2×C32—41no—
636C2×C32—41no—
637C2×C32—41no—
638C2×C32—41no—
639C2×C32—41no—
640C2×C32—41no—
641C2×C32—44no—
642C2×C32—44no—
643C2×C32—44no—
644C2×C32—48no—
645C2×C32—42no—
646C2×C32—42no—
647C2×C32—42no—
648C2×C32#87711yescharacteristic
649C2×C32#87711yescharacteristic
650C2×C32#87911yescharacteristic
651C2×C32#87911yescharacteristic
652C2×C32#87911yescharacteristic
653C2×C32#67⋊C411yescharacteristic
654C2×C32#67⋊C411yescharacteristic
655C2×C32#88311yescharacteristic
656C2×C32#88311yescharacteristic
657C2×C32#88411yescharacteristic
658C2×C32#88511yescharacteristic
659C2×C32#88511yescharacteristic
660C2×C32#92611yescharacteristic
661C2×C32C4×#6711yescharacteristic
662C2×C32C4×#6711yescharacteristic
663C2×C32D4×Dic311yescharacteristic
664C2×C32D4×Dic311yescharacteristic
665C2×C32#93511yescharacteristic
666C2×C32#93611yescharacteristic
667C2×C32#93811yescharacteristic
668C2×C32#93911yescharacteristic
669C24#111311yescharacteristic
670C22×C4—91no—
671C22×C4—91no—
672C22×C4—91no—
673C22×C4—91no—
674C22×C4—91no—
675C22×C4—91no—
676C4⋊C4—542no—
677C22⋊C4—94no—
678C22⋊C4—182no—
679C22⋊C4—182no—
680C42—542no—
681C22×C3—24no—
682C22×C3—24no—
683C22×C3—24no—
684C22×C3—22no—
685C22×C3—22no—
686C22×C3—22no—
687C22×C3—22no—
688C22×C3—22no—
689C22×C3—22no—
690C22×C3—22no—
691C22×C3—22no—
692C22×C3—22no—
693C22×C3—21no—
694C22×C3—21no—
695C22×C3—21no—
696C22×C3—21no—
697C22×C3—21no—
698C22×C3—21no—
699C22×C3—21no—
700C22×C3—21no—
701C22×C3—21no—
702C22×C3—21no—
703C22×C3—21no—
704C22×C3—21no—
705C22×C3—21no—
706C22×C3—21no—
707C22×C3—21no—
708C22×C3—21no—
709C22×C3—21no—
710C22×C3—21no—
711C22×C3—21no—
712C22×C3—21no—
713C22×C3—21no—
714C22×C3—42no—
715C22×C3—42no—
716C22×C3—42no—
717C22×C3—42no—
718C22×C3—42no—
719C22×C3—42no—
720C22×C3—44no—
721C22×C3—44no—
722C22×C3—44no—
723C22×C3—42no—
724C22×C3—42no—
725C22×C3—42no—
726C22×C3—42no—
727C22×C3—42no—
728C22×C3—42no—
729C22×C3—42no—
730C22×C3—42no—
731C22×C3—42no—
732C22×C3—42no—
733C22×C3—42no—
734C22×C3—42no—
735C22×C3—44no—
736C22×C3—44no—
737C22×C3—44no—
738C22×C3—44no—
739C22×C3—41no—
740C22×C3—41no—
741C22×C3—41no—
742C22×C3—41no—
743C22×C3—41no—
744C22×C3—41no—
745C22×C3—41no—
746C22×C3—41no—
747C22×C3—41no—
748C22×C3—41no—
749C22×C3—41no—
750C22×C3—41no—
751C22×C3—41no—
752C22×C3—41no—
753C22×C3—41no—
754C22×C3—41no—
755C22×C3—41no—
756C22×C3—41no—
757C22×C3—41no—
758C22×C3C2×D3×Dic311yescharacteristic
759C22×C3C2×D3×Dic311yescharacteristic
760C22×C3#380411yescharacteristic
761C22×C3#380411yescharacteristic
762C22×C3#380411yescharacteristic
763C22×C3#380411yescharacteristic
764C22×C3#380411yescharacteristic
765C22×C3#380411yescharacteristic
766C22×C3#380411yescharacteristic
767C22×C3#380411yescharacteristic
768C22×C3#380511yescharacteristic
769C22×C3#380511yescharacteristic
770C22×C3#380511yescharacteristic
771C22×C3#380511yescharacteristic
772C22×C3C2×#62411yescharacteristic
773C22×C3D3×#6711yescharacteristic
774C22×C3D3×#6711yescharacteristic
775C22×C3D3×#6711yescharacteristic
776C22×C3D3×#6711yescharacteristic
777C22×C3#381111yescharacteristic
778C22×C3#381111yescharacteristic
779C3×C4—182no—
780C3×C4—182no—
781C3×C4—182no—
782C3×C4—182no—
783C3×C4—361no—
784C3×C4—361no—
785Dic3—62no—
786Dic3—62no—
787Dic3—62no—
788Dic3—62no—
789Dic3—62no—
790Dic3—62no—
791Dic3—62no—
792Dic3—62no—
793Dic3—122no—
794Dic3—122no—
795Dic3—122no—
796Dic3—122no—
797Dic3—122no—
798Dic3—122no—
799Dic3—121no—
800Dic3—121no—
801Dic3—121no—
802Dic3—121no—
803C32—21no—
804C32—21no—
805C32—21no—
806C32—41no—
807C32#494411yescharacteristic, complemented
808C32#494511yescharacteristic, complemented
809C32#495111yescharacteristic, complemented
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—21no—
815C23—21no—
816C23#629412yes—
817C23C2×#111311yescharacteristic
818C2×C4—92no—
819C2×C4—92no—
820C2×C4—92no—
821C2×C4—92no—
822C2×C4—181no—
823C2×C4—181no—
824C2×C4—181no—
825C2×C4—181no—
826C2×C4—181no—
827C2×C4—181no—
828C2×C4—181no—
829C2×C4—181no—
830C2×C4—181no—
831C2×C4—181no—
832C2×C4—181no—
833C2×C4—181no—
834C2×C4—181no—
835C2×C4—181no—
836C2×C3—21no—
837C2×C3—21no—
838C2×C3—21no—
839C2×C3—21no—
840C2×C3—21no—
841C2×C3—21no—
842C2×C3—21no—
843C2×C3—21no—
844C2×C3—21no—
845C2×C3—21no—
846C2×C3—21no—
847C2×C3—21no—
848C2×C3—21no—
849C2×C3—21no—
850C2×C3—21no—
851C2×C3—21no—
852C2×C3—21no—
853C2×C3—21no—
854C2×C3—21no—
855C2×C3—21no—
856C2×C3—21no—
857C2×C3—44no—
858C2×C3—44no—
859C2×C3—44no—
860C2×C3—48no—
861C2×C3—42no—
862C2×C3—42no—
863C2×C3—42no—
864C2×C3—41no—
865C2×C3—41no—
866C2×C3—41no—
867C2×C3—41no—
868C2×C3—41no—
869C2×C3—41no—
870C2×C3—41no—
871C2×C3#6395211yescharacteristic
872C2×C3#6395211yescharacteristic
873C2×C3#6395311yescharacteristic
874C2×C3#6395511yescharacteristic
875C2×C3#6395511yescharacteristic
876C2×C3#6395611yescharacteristic
877C2×C3#6395611yescharacteristic
878C2×C3#6395611yescharacteristic
879C2×C3#6395711yescharacteristic
880C2×C3#6395811yescharacteristic
881C2×C3#6395911yescharacteristic
882C2×C3#6395911yescharacteristic
883C2×C3#6396911yescharacteristic
884C2×C3#6396911yescharacteristic
885C2×C3#6397011yescharacteristic
886C2×C3#6397111yescharacteristic
887C2×C3Dic3×#6711yescharacteristic
888C2×C3Dic3×#6711yescharacteristic
889C2×C3#67⋊Dic311yescharacteristic
890C2×C3#67⋊Dic311yescharacteristic
891C2×C3#6397511yescharacteristic
892C22—22no—
893C22—22no—
894C22—22no—
895C22—41no—
896C22—41no—
897C22—41no—
898C22—41no—
899C22C2×#629411yescharacteristic
900C22#8904611yescharacteristic
901C22#8904611yescharacteristic
902C22#8904611yescharacteristic
903C22#8904611yescharacteristic
904C22#8904911yescharacteristic
905C22#8904911yescharacteristic
906C4—182no—
907C4—182no—
908C4—182no—
909C4—182no—
910C4—361no—
911C4—361no—
912C3—21no—
913C3—21no—
914C3—21no—
915C3—41no—
916C3#1059170111yescharacteristic, complemented
917C3#1059170211yescharacteristic, complemented
918C3#1059170311yescharacteristic, complemented
919C2—42no—
920C2#1172371511yescharacteristic
921C2#1172371611yescharacteristic
922C2#1172371811yescharacteristic
923C2#1172372411yescharacteristic
924C2#1172372511yescharacteristic
925C2#1172372611yescharacteristic
926C2#1172372611yescharacteristic
subgroupG/H
center, FrattiniC23C2×#1113
commutatorC22×C33C22×C4
Fitting, prime radicalC24×C33C22
socle, cosocleC23×C33C23
hypercenterC24#1113
hypocenterC33#388
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C23 ◁ C24

Complements

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

NH ≅ G/Ntype
4. C2×#88815C2semidirect
5. C2×#88813C2semidirect
6. #11722082C2semidirect
7. #11722082C2semidirect
20. C3×#3757C4semidirect
109. #3757Dic3semidirect
484. C33#388semidirect
807. C32#4944semidirect
808. C32#4945semidirect
809. C32#4951semidirect
916. C3#10591701semidirect
917. C3#10591702semidirect
918. C3#10591703semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#37572
C2×#888152
C2×#888132
#117220822
#105917033
#105917023
#105917013