Finite Group Databasebeta

← C3×D3×C3⋊#1020 #72220741

Subgroups — C3×D3×C3⋊#1020 #72220741

Order 5184.

3198 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 3198 conjugacy classes of subgroups — too many to draw. Only its 92 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C3⋊#1020C211yesmaximal, characteristic, complemented
2C3×C3⋊(C3⋊#1020)C211yesmaximal, characteristic, complemented
3C32×D3×C22⋊A4C211yesmaximal, characteristic, complemented
4C2×C3×C3⋊#1020—31nomaximal
5D3×C3⋊#1020C311yesmaximal, characteristic, direct product factor
6C3×D3×#1020—33nomaximal
7C3×D3×#953—31nomaximal
8C33×C22⋊A4C2211yescharacteristic, complemented
9C3×D3×C3⋊S4—43nomaximal
10C24×C32×D3D311yescharacteristic, complemented
11C2×C32×C22⋊A4—31no—
12C3×D3×C22⋊A4—21no—
13C3×D3×C22⋊A4—23no—
14C3×D3×C22⋊A4D313yescomplemented
15C3×D3×C22⋊A4C2×C311yescharacteristic, complemented
16C3⋊(C3⋊#1020)C2×C311yescharacteristic, complemented
17C3×C3⋊#1020—21no—
18C3×C3⋊#1020—31no—
19C3×C3⋊#1020—33no—
20C3×C3⋊#1020—61no—
21C3×C3⋊#1020—63no—
22C3×C3⋊#1020D311yescharacteristic, direct product factor
23C3×C3⋊#1020C2×C311yescharacteristic, complemented
24C32×#1020—33no—
25C2×C3×D3×#67—33no—
26C3×#64162—31no—
27C32×#953—31no—
28C3×#63977—33no—
29C3×#63976—33no—
30C3×D3×#217—33no—
31C32×D3×A4—43no—
32C32×D3×A4—81no—
33C3×C3⋊(C3⋊S4)—43no—
34C32×C3⋊S4—43no—
35C2×C3⋊#1020—31no—
36C2×C3×#1020—93no—
37D3×#1020—33no—
38C2×C3×#953—91no—
39C3×D3×#120—91no—
40D3×#953—31no—
41C24×C33C2×D311yescharacteristic, complemented
42C23×C32×D3—33no—
43C23×C32×D3—33no—
44C23×C32×D3—61no—
45C23×C32×D3—61no—
46C32×C22⋊A4—21no—
47C32×C22⋊A4—21no—
48C32×C22⋊A4—23no—
49C32×C22⋊A4—23no—
50C32×C22⋊A4—21no—
51C32×C22⋊A4—43no—
52C32×C22⋊A4—41no—
53C32×C22⋊A4C2×D311yescharacteristic, complemented
54C32×C22⋊A4C2×D313yescomplemented
55C32×C22⋊A4C22×C311yescharacteristic, complemented
56C22×C3×D32—31no—
57C2×C3×C3⋊S4—123no—
58D3×C3⋊S4—43no—
59C3×D3×S4—129no—
60C2×C3×#638—33no—
61C2×C32×#67—33no—
62C3×D3×#67—63no—
63C3×D3×#67—63no—
64C3×D3×#67—63no—
65C3×D3×#67—63no—
66C2×C3×#626—33no—
67C2×C3×#625—33no—
68C2×C3×D3×Dic3—33no—
69C3×#3757—33no—
70C32×#217—33no—
71C3×(C2×D3)⋊Dic3—36no—
72C33×A4—43no—
73C33×A4—81no—
74C3×D3×C3⋊D3—161no—
75C25×C32—31no—
76C24×C3×D3—21no—
77C24×C3×D3C3×D311yescharacteristic, complemented
78C24×C3×D3C3⋊D311yescharacteristic, complemented
79C2×C3×C22⋊A4—33no—
80C2×C3×C22⋊A4—31no—
81C2×C3×C22⋊A4—61no—
82C2×C3×C22⋊A4—63no—
83D3×C22⋊A4—23no—
84D3×C22⋊A4C3×D313yescomplemented
85C3⋊#1020—31no—
86C3⋊#1020—33no—
87C3⋊#1020—61no—
88C3⋊#1020—63no—
89C3⋊#1020C3×D311yescharacteristic, direct product factor
90C3×#1020—33no—
91C3×#1020—33no—
92C3×#1020—63no—
93C3×#1020—93no—
94C3×#1020—183no—
95C22×C3×#67—93no—
96C2×C3×D3×D4—93no—
97C2×D3×#67—33no—
98C32×#120—91no—
99#64162—31no—
100C3×#953—31no—
101C3×#953—31no—
102C3×#953—61no—
103C3×#953—93no—
104C3×#953—93no—
105C3×#953—91no—
106C3×#953—91no—
107C3×#953—181no—
108C2×C3×#217—93no—
109C3×#937—93no—
110C3×#882—93no—
111C3×D3×C22⋊C4—93no—
112#63977—33no—
113#63976—33no—
114D3×#217—33no—
115C23×C33—33no—
116C23×C33—61no—
117C22×C3×C3⋊D3—31no—
118C22×C32×D3—21no—
119C22×C32×D3—31no—
120C22×C32×D3—33no—
121C22×C32×D3—33no—
122C22×C32×D3—33no—
123C22×C32×D3—33no—
124C22×C32×D3—31no—
125C22×C32×D3—66no—
126C22×C32×D3—63no—
127C22×C32×D3—63no—
128C22×C32×D3—61no—
129C22×C32×D3—63no—
130C22×C32×D3S413yescomplemented
131C2×C32×A4—123no—
132C2×C32×A4—241no—
133C2×C3×D32—63no—
134C2×C3×D32—63no—
135C3×D3×A4—43no—
136C3×D3×A4—49no—
137C3×D3×A4—83no—
138C3×D3×A4—81no—
139C3×D3×A4—89no—
140C3×D3×A4—86no—
141C3×D3×A4—82no—
142C3×D3×A4—83no—
143C3⋊(C3⋊S4)—43no—
144C3×C3⋊S4—43no—
145C3×C3⋊S4—43no—
146C3×C3⋊S4—83no—
147C3×C3⋊S4—123no—
148C3×C3⋊S4—129no—
149C3×C3⋊S4—243no—
150C3×C3⋊S4—249no—
151C32×S4—129no—
152C3×#638—63no—
153C3×#638—63no—
154C2×C3×C3⋊Dic3—33no—
155C32×#67—63no—
156C32×#67—63no—
157C2×C32×Dic3—33no—
158C3×#626—63no—
159C3×#626—63no—
160C3×#625—63no—
161C3×#625—63no—
162C3×D3×Dic3—63no—
163C3×D3×Dic3—63no—
164C2×#1020—93no—
165C2×C3×#120—271no—
166C2×#953—91no—
167D3×#120—91no—
168C3×C3⋊(C3⋊D3)—161no—
169C32×C3⋊D3—161no—
170C33×D3—161no—
171C24×C32—21no—
172C24×C32—21no—
173C24×C32—21no—
174C24×C32—41no—
175C24×C32—93no—
176C24×C32—93no—
177C24×C32—181no—
178C24×C32—181no—
179C24×C32D3211yescharacteristic, complemented
180C24×C32C2×C3×D311yescharacteristic, complemented
181C24×C32C2×C3⋊D311yescharacteristic, complemented
182C23×C3×D3—33no—
183C23×C3×D3—33no—
184C23×C3×D3—33no—
185C23×C3×D3—33no—
186C23×C3×D3—61no—
187C23×C3×D3—61no—
188C23×C3×D3—63no—
189C23×C3×D3—62no—
190C23×C3×D3—61no—
191C23×C3×D3—61no—
192C23×C3×D3—63no—
193C23×C3×D3—62no—
194C23×C3×D3—91no—
195C23×C3×D3—91no—
196C3×C22⋊A4—21no—
197C3×C22⋊A4—23no—
198C3×C22⋊A4—23no—
199C3×C22⋊A4—21no—
200C3×C22⋊A4—23no—
201C3×C22⋊A4—23no—
202C3×C22⋊A4—23no—
203C3×C22⋊A4—43no—
204C3×C22⋊A4—46no—
205C3×C22⋊A4—43no—
206C3×C22⋊A4—43no—
207C3×C22⋊A4—41no—
208C3×C22⋊A4—43no—
209C3×C22⋊A4D3213yescomplemented
210C3×C22⋊A4C2×C3×D313yescomplemented
211C3×C22⋊A4C2×C3×D311yescharacteristic, complemented
212C22×D32—31no—
213C2×C3⋊S4—123no—
214C2×C3×S4—369no—
215D3×S4—129no—
216C2×C32×D4—93no—
217C2×#638—33no—
218C2×C3×#67—33no—
219C2×C3×#67—33no—
220C2×C3×#67—63no—
221C2×C3×#67—93no—
222C2×C3×#67—93no—
223C2×C3×#67—93no—
224C2×C3×#67—93no—
225C2×C3×#67—93no—
226C2×C3×#67—183no—
227C2×C3×#67—183no—
228C2×C3×#67—183no—
229C2×C3×#67—183no—
230C2×C3×#67—183no—
231C22×C3×Dic3—93no—
232C3×D3×D4—183no—
233C3×D3×D4—183no—
234C3×D3×D4—183no—
235C3×D3×D4—183no—
236C2×C3×D12—93no—
237C2×C3×C4×D3—93no—
238D3×#67—63no—
239D3×#67—63no—
240D3×#67—63no—
241D3×#67—63no—
242C2×#626—33no—
243C2×#625—33no—
244C2×D3×Dic3—33no—
245C32×C22⋊C4—93no—
246#3757—33no—
247C3×#217—33no—
248C3×#217—33no—
249C3×#217—63no—
250C3×#217—96no—
251C3×#217—93no—
252C3×#217—93no—
253C3×#217—183no—
254C3×(C2×D3)⋊C4—96no—
255(C2×D3)⋊Dic3—36no—
256C22×C33—21no—
257C22×C33—31no—
258C22×C33—33no—
259C22×C33—63no—
260C22×C33C2×S413yescomplemented
261C2×C3×C3⋊D3—63no—
262C2×C3×C3⋊D3—481no—
263C2×C32×D3—33no—
264C2×C32×D3—33no—
265C2×C32×D3—33no—
266C2×C32×D3—33no—
267C2×C32×D3—63no—
268C2×C32×D3—66no—
269C2×C32×D3—63no—
270C2×C32×D3—61no—
271C2×C32×D3—61no—
272C2×C32×D3—63no—
273C32×A4—43no—
274C32×A4—43no—
275C32×A4—49no—
276C32×A4—81no—
277C32×A4—83no—
278C32×A4—81no—
279C32×A4—83no—
280C32×A4—89no—
281C32×A4—89no—
282C32×A4—86no—
283C32×A4—82no—
284C32×A4—83no—
285C32×A4—83no—
286C32×A4—161no—
287C32×A4—163no—
288C32×A4—161no—
289C32×A4—169no—
290C32×A4—163no—
291C32×A4—162no—
292C32×A4—166no—
293D3×C3⋊D3—161no—
294C3×D32—123no—
295C3×D32—121no—
296C3×D32—483no—
297C3×C3⋊Dic3—63no—
298C32×Dic3—63no—
299C25×C3—31no—
300C25×C3—31no—
301C25×C3—61no—
302C24×D3C3×C3⋊D311yescharacteristic, complemented
303C2×C22⋊A4—33no—
304C2×C22⋊A4—63no—
305#1020—33no—
306#1020—93no—
307#1020—183no—
308C22×C3×D4—273no—
309C22×#67—93no—
310C2×D3×D4—93no—
311C3×#120—91no—
312C3×#120—91no—
313C3×#120—181no—
314C3×#120—273no—
315C3×#120—273no—
316C3×#120—271no—
317C2×C3×C22⋊C4—273no—
318#953—31no—
319#953—93no—
320#953—93no—
321#953—91no—
322#953—91no—
323#953—181no—
324C2×#217—93no—
325#937—93no—
326#882—93no—
327D3×C22⋊C4—93no—
328C34—161noSylow
329C23×C32—33no—
330C23×C32—33no—
331C23×C32—33no—
332C23×C32—33no—
333C23×C32—63no—
334C23×C32—63no—
335C23×C32—63no—
336C23×C32—61no—
337C23×C32—61no—
338C23×C32—61no—
339C23×C32—61no—
340C23×C32—62no—
341C23×C32—91no—
342C23×C32—93no—
343C23×C32—93no—
344C23×C32—93no—
345C23×C32—91no—
346C23×C32—93no—
347C23×C32—123no—
348C23×C32—121no—
349C23×C32—121no—
350C23×C32—122no—
351C23×C32—181no—
352C23×C32—183no—
353C23×C32—183no—
354C23×C32—186no—
355C23×C32—183no—
356C22×C3⋊D3—31no—
357C22×C3×D3—22no—
358C22×C3×D3—21no—
359C22×C3×D3—21no—
360C22×C3×D3—23no—
361C22×C3×D3—31no—
362C22×C3×D3—31no—
363C22×C3×D3—33no—
364C22×C3×D3—33no—
365C22×C3×D3—33no—
366C22×C3×D3—33no—
367C22×C3×D3—33no—
368C22×C3×D3—33no—
369C22×C3×D3—33no—
370C22×C3×D3—33no—
371C22×C3×D3—31no—
372C22×C3×D3—31no—
373C22×C3×D3—63no—
374C22×C3×D3—61no—
375C22×C3×D3—63no—
376C22×C3×D3—63no—
377C22×C3×D3—63no—
378C22×C3×D3—61no—
379C22×C3×D3—66no—
380C22×C3×D3—66no—
381C22×C3×D3—63no—
382C22×C3×D3—63no—
383C22×C3×D3—63no—
384C22×C3×D3—63no—
385C22×C3×D3—61no—
386C22×C3×D3—61no—
387C22×C3×D3—62no—
388C22×C3×D3—63no—
389C22×C3×D3—63no—
390C22×C3×D3—66no—
391C22×C3×D3—66no—
392C22×C3×D3—612no—
393C22×C3×D3—66no—
394C22×C3×D3—91no—
395C22×C3×D3—91no—
396C22×C3×D3—181no—
397C22×C3×D3—183no—
398C22×C3×D3—183no—
399C22×C3×D3—183no—
400C22×C3×D3—183no—
401C22×C3×D3C3×S413yescomplemented
402C22×C3×D3C3⋊S413yescomplemented
403C2×C3×A4—123no—
404C2×C3×A4—129no—
405C2×C3×A4—241no—
406C2×C3×A4—243no—
407C2×C3×A4—249no—
408C2×C3×A4—243no—
409C2×C3×A4—242no—
410C2×C3×A4—246no—
411C2×D32—63no—
412C2×D32—63no—
413D3×A4—49no—
414D3×A4—83no—
415D3×A4—86no—
416D3×A4—89no—
417C3⋊S4—43no—
418C3⋊S4—123no—
419C3⋊S4—129no—
420C3⋊S4—243no—
421C3⋊S4—249no—
422C3×S4—129no—
423C3×S4—129no—
424C3×S4—249no—
425C3×S4—369no—
426C3×S4—729no—
427C32×D4—183no—
428C32×D4—183no—
429C2×C32×C4—93no—
430#638—63no—
431#638—63no—
432C2×C3⋊Dic3—33no—
433C3×#67—63no—
434C3×#67—63no—
435C3×#67—63no—
436C3×#67—63no—
437C3×#67—123no—
438C3×#67—123no—
439C3×#67—183no—
440C3×#67—183no—
441C3×#67—183no—
442C3×#67—183no—
443C3×#67—183no—
444C3×#67—183no—
445C3×#67—183no—
446C3×#67—183no—
447C3×#67—183no—
448C3×#67—183no—
449C3×#67—363no—
450C3×#67—363no—
451C2×C3×Dic3—33no—
452C2×C3×Dic3—33no—
453C2×C3×Dic3—63no—
454C2×C3×Dic3—93no—
455C2×C3×Dic3—93no—
456C2×C3×Dic3—183no—
457C2×C3×Dic3—183no—
458C2×C3×Dic3—183no—
459C3×D12—183no—
460C3×D12—183no—
461C3×C4×D3—183no—
462C3×C4×D3—183no—
463#626—63no—
464#626—63no—
465#625—63no—
466#625—63no—
467D3×Dic3—63no—
468D3×Dic3—63no—
469C2×#120—271noSylow
470C2×C33—33no—
471C2×C33—61no—
472C2×C33—481no—
473C3⋊(C3⋊D3)—161no—
474C3×C3⋊D3—121no—
475C3×C3⋊D3—161no—
476C3×C3⋊D3—161no—
477C3×C3⋊D3—321no—
478C3×C3⋊D3—483no—
479C3×C3⋊D3—481no—
480C3×C3⋊D3—961no—
481C3×C3⋊D3—963no—
482C32×D3—33no—
483C32×D3—61no—
484C32×D3—121no—
485C32×D3—161no—
486C32×D3—163no—
487C32×D3—323no—
488C32×D3—321no—
489C32×D3—483no—
490C32×D3#102011yescharacteristic, complemented
491C24×C3—21no—
492C24×C3—21no—
493C24×C3—21no—
494C24×C3—41no—
495C24×C3—93no—
496C24×C3—93no—
497C24×C3—93no—
498C24×C3—93no—
499C24×C3—183no—
500C24×C3—183no—
501C24×C3—181no—
502C24×C3—181no—
503C24×C3—182no—
504C24×C3—181no—
505C24×C3—181no—
506C24×C3—182no—
507C24×C3—271no—
508C24×C3C3×D3211yescharacteristic, complemented
509C24×C3D3×C3⋊D311yescharacteristic, complemented
510C24×C3C2×C3×C3⋊D311yescharacteristic, complemented
511C23×D3—33no—
512C23×D3—33no—
513C23×D3—61no—
514C23×D3—61no—
515C23×D3—91no—
516C23×D3—91no—
517C22⋊A4—23no—
518C22⋊A4—23no—
519C22⋊A4—43no—
520C22⋊A4C3×D3213yescomplemented
521C2×S4—369no—
522C2×C3×D4—93no—
523C2×C3×D4—93no—
524C2×C3×D4—183no—
525C2×C3×D4—273no—
526C2×C3×D4—273no—
527C2×C3×D4—273no—
528C2×C3×D4—543no—
529C2×C3×D4—543no—
530C2×C3×D4—543no—
531C2×C3×D4—543no—
532C22×C3×C4—273no—
533C2×#67—33no—
534C2×#67—93no—
535C2×#67—93no—
536C2×#67—93no—
537C2×#67—93no—
538C2×#67—93no—
539C2×#67—183no—
540C2×#67—183no—
541C2×#67—183no—
542C2×#67—183no—
543C2×#67—183no—
544C22×Dic3—93no—
545D3×D4—183no—
546D3×D4—183no—
547D3×D4—183no—
548D3×D4—183no—
549C2×D12—93no—
550C2×C4×D3—93no—
551C3×C22⋊C4—93no—
552C3×C22⋊C4—93no—
553C3×C22⋊C4—183no—
554C3×C22⋊C4—276no—
555C3×C22⋊C4—273no—
556#217—33no—
557#217—96no—
558#217—93no—
559#217—93no—
560#217—183no—
561(C2×D3)⋊C4—96no—
562C22×C32—21no—
563C22×C32—22no—
564C22×C32—21no—
565C22×C32—21no—
566C22×C32—23no—
567C22×C32—23no—
568C22×C32—23no—
569C22×C32—31no—
570C22×C32—31no—
571C22×C32—31no—
572C22×C32—33no—
573C22×C32—33no—
574C22×C32—33no—
575C22×C32—43no—
576C22×C32—41no—
577C22×C32—41no—
578C22×C32—42no—
579C22×C32—61no—
580C22×C32—61no—
581C22×C32—61no—
582C22×C32—63no—
583C22×C32—63no—
584C22×C32—63no—
585C22×C32—63no—
586C22×C32—63no—
587C22×C32—63no—
588C22×C32—66no—
589C22×C32—93no—
590C22×C32—93no—
591C22×C32—93no—
592C22×C32—93no—
593C22×C32—121no—
594C22×C32—123no—
595C22×C32—123no—
596C22×C32—123no—
597C22×C32—126no—
598C22×C32—181no—
599C22×C32—186no—
600C22×C32—183no—
601C22×C32—183no—
602C22×C32—181no—
603C22×C32—183no—
604C22×C32D3×S413yescomplemented
605C22×C32C2×C3×S413yescomplemented
606C22×C32C2×C3⋊S413yescomplemented
607C2×C3⋊D3—63no—
608C2×C3⋊D3—481no—
609C2×C3×D3—33no—
610C2×C3×D3—33no—
611C2×C3×D3—33no—
612C2×C3×D3—33no—
613C2×C3×D3—33no—
614C2×C3×D3—33no—
615C2×C3×D3—33no—
616C2×C3×D3—33no—
617C2×C3×D3—63no—
618C2×C3×D3—63no—
619C2×C3×D3—63no—
620C2×C3×D3—63no—
621C2×C3×D3—62no—
622C2×C3×D3—63no—
623C2×C3×D3—63no—
624C2×C3×D3—66no—
625C2×C3×D3—66no—
626C2×C3×D3—63no—
627C2×C3×D3—63no—
628C2×C3×D3—66no—
629C2×C3×D3—612no—
630C2×C3×D3—66no—
631C2×C3×D3—61no—
632C2×C3×D3—61no—
633C2×C3×D3—62no—
634C2×C3×D3—61no—
635C2×C3×D3—61no—
636C2×C3×D3—63no—
637C2×C3×D3—63no—
638C2×C3×D3—123no—
639C2×C3×D3—183no—
640C2×C3×D3—183no—
641C2×C3×D3—363no—
642C2×C3×D3—363no—
643C2×C3×D3—361no—
644C2×C3×D3—363no—
645C2×C3×D3—361no—
646C2×C3×D3—1443no—
647C3×A4—43no—
648C3×A4—49no—
649C3×A4—49no—
650C3×A4—83no—
651C3×A4—81no—
652C3×A4—83no—
653C3×A4—89no—
654C3×A4—89no—
655C3×A4—89no—
656C3×A4—86no—
657C3×A4—82no—
658C3×A4—83no—
659C3×A4—83no—
660C3×A4—86no—
661C3×A4—89no—
662C3×A4—89no—
663C3×A4—163no—
664C3×A4—163no—
665C3×A4—161no—
666C3×A4—163no—
667C3×A4—169no—
668C3×A4—169no—
669C3×A4—1618no—
670C3×A4—169no—
671C3×A4—169no—
672C3×A4—166no—
673C3×A4—166no—
674C3×A4—166no—
675C3×A4—1612no—
676C3×A4—166no—
677C3×A4—162no—
678C3×A4—163no—
679D32—123no—
680D32—121no—
681D32—483no—
682C32×C4—183no—
683C3⋊Dic3—63no—
684C3×Dic3—63no—
685C3×Dic3—63no—
686C3×Dic3—123no—
687C3×Dic3—183no—
688C3×Dic3—183no—
689C3×Dic3—363no—
690C25—31no—
691C22×D4—273no—
692#120—91no—
693#120—273no—
694#120—273no—
695#120—271no—
696C2×C22⋊C4—273no—
697C33—161no—
698C33—161no—
699C33—163no—
700C33—323no—
701C33—321no—
702C33—323no—
703C33—321no—
704C33—321no—
705C33—641no—
706C33—643no—
707C33C2×#102011yescharacteristic, complemented
708C23×C3—33no—
709C23×C3—33no—
710C23×C3—33no—
711C23×C3—33no—
712C23×C3—33no—
713C23×C3—63no—
714C23×C3—63no—
715C23×C3—63no—
716C23×C3—63no—
717C23×C3—61no—
718C23×C3—61no—
719C23×C3—61no—
720C23×C3—62no—
721C23×C3—61no—
722C23×C3—61no—
723C23×C3—62no—
724C23×C3—91no—
725C23×C3—91no—
726C23×C3—93no—
727C23×C3—93no—
728C23×C3—93no—
729C23×C3—93no—
730C23×C3—93no—
731C23×C3—93no—
732C23×C3—91no—
733C23×C3—91no—
734C23×C3—93no—
735C23×C3—93no—
736C23×C3—123no—
737C23×C3—121no—
738C23×C3—121no—
739C23×C3—122no—
740C23×C3—183no—
741C23×C3—181no—
742C23×C3—183no—
743C23×C3—183no—
744C23×C3—183no—
745C23×C3—181no—
746C23×C3—181no—
747C23×C3—181no—
748C23×C3—182no—
749C23×C3—183no—
750C23×C3—183no—
751C23×C3—183no—
752C23×C3—183no—
753C23×C3—186no—
754C23×C3—186no—
755C23×C3—183no—
756C23×C3—183no—
757C23×C3—186no—
758C23×C3—186no—
759C23×C3—1812no—
760C23×C3—186no—
761C23×C3—271no—
762C23×C3—543no—
763C23×C3—543no—
764C22×D3—21no—
765C22×D3—31no—
766C22×D3—33no—
767C22×D3—33no—
768C22×D3—33no—
769C22×D3—33no—
770C22×D3—31no—
771C22×D3—66no—
772C22×D3—63no—
773C22×D3—63no—
774C22×D3—61no—
775C22×D3—63no—
776C22×D3—91no—
777C22×D3—91no—
778C22×D3—181no—
779C22×D3—183no—
780C22×D3—183no—
781C22×D3—183no—
782C22×D3—183no—
783C22×D3C3×C3⋊S413yescomplemented
784C2×A4—129no—
785C2×A4—243no—
786C2×A4—249no—
787C2×A4—246no—
788S4—129no—
789S4—369no—
790S4—729no—
791C3×D4—183no—
792C3×D4—183no—
793C3×D4—183no—
794C3×D4—183no—
795C3×D4—363no—
796C3×D4—363no—
797C3×D4—543no—
798C3×D4—543no—
799C3×D4—543no—
800C3×D4—543no—
801C3×D4—543no—
802C3×D4—543no—
803C2×C3×C4—93no—
804C2×C3×C4—93no—
805C2×C3×C4—183no—
806C2×C3×C4—273no—
807C2×C3×C4—543no—
808C2×C3×C4—543no—
809#67—63no—
810#67—63no—
811#67—183no—
812#67—183no—
813#67—183no—
814#67—183no—
815#67—183no—
816#67—183no—
817#67—183no—
818#67—183no—
819#67—183no—
820#67—183no—
821#67—363no—
822#67—363no—
823C2×Dic3—33no—
824C2×Dic3—93no—
825C2×Dic3—93no—
826C2×Dic3—183no—
827C2×Dic3—183no—
828C2×Dic3—183no—
829D12—183no—
830D12—183no—
831C4×D3—183no—
832C4×D3—183no—
833C2×C32—31no—
834C2×C32—33no—
835C2×C32—33no—
836C2×C32—33no—
837C2×C32—63no—
838C2×C32—63no—
839C2×C32—63no—
840C2×C32—61no—
841C2×C32—62no—
842C2×C32—61no—
843C2×C32—61no—
844C2×C32—93no—
845C2×C32—123no—
846C2×C32—121no—
847C2×C32—121no—
848C2×C32—122no—
849C2×C32—181no—
850C2×C32—361no—
851C2×C32—481no—
852C2×C32—483no—
853C2×C32—961no—
854C2×C32—963no—
855C3⋊D3—121no—
856C3⋊D3—161no—
857C3⋊D3—483no—
858C3⋊D3—481no—
859C3⋊D3—961no—
860C3⋊D3—963no—
861C3×D3—21no—
862C3×D3—33no—
863C3×D3—33no—
864C3×D3—63no—
865C3×D3—62no—
866C3×D3—61no—
867C3×D3—61no—
868C3×D3—121no—
869C3×D3—121no—
870C3×D3—163no—
871C3×D3—241no—
872C3×D3—323no—
873C3×D3—2883no—
874C3×D3—361no—
875C3×D3—361no—
876C3×D3—483no—
877C3×D3—483no—
878C3×D3—721no—
879C3×D3—963no—
880C3×D3—1443no—
881C3×D3C3×#102011yescharacteristic, complemented
882C3×D3C3⋊#102011yescharacteristic, direct product factor
883C24—93no—
884C24—93no—
885C24—181no—
886C24—181no—
887C24—271no—
888C24C3×D3×C3⋊D311yescharacteristic, complemented
889C2×D4—93no—
890C2×D4—273no—
891C2×D4—273no—
892C2×D4—273no—
893C2×D4—543no—
894C2×D4—543no—
895C2×D4—543no—
896C2×D4—543no—
897C22×C4—273no—
898C22⋊C4—93no—
899C22⋊C4—276no—
900C22⋊C4—273no—
901C22×C3—21no—
902C22×C3—22no—
903C22×C3—21no—
904C22×C3—21no—
905C22×C3—23no—
906C22×C3—23no—
907C22×C3—23no—
908C22×C3—31no—
909C22×C3—31no—
910C22×C3—31no—
911C22×C3—33no—
912C22×C3—33no—
913C22×C3—33no—
914C22×C3—41no—
915C22×C3—41no—
916C22×C3—42no—
917C22×C3—43no—
918C22×C3—61no—
919C22×C3—61no—
920C22×C3—61no—
921C22×C3—63no—
922C22×C3—63no—
923C22×C3—63no—
924C22×C3—63no—
925C22×C3—63no—
926C22×C3—63no—
927C22×C3—66no—
928C22×C3—93no—
929C22×C3—93no—
930C22×C3—93no—
931C22×C3—93no—
932C22×C3—93no—
933C22×C3—93no—
934C22×C3—93no—
935C22×C3—93no—
936C22×C3—121no—
937C22×C3—123no—
938C22×C3—123no—
939C22×C3—123no—
940C22×C3—126no—
941C22×C3—183no—
942C22×C3—183no—
943C22×C3—183no—
944C22×C3—183no—
945C22×C3—181no—
946C22×C3—181no—
947C22×C3—186no—
948C22×C3—186no—
949C22×C3—183no—
950C22×C3—183no—
951C22×C3—182no—
952C22×C3—183no—
953C22×C3—183no—
954C22×C3—183no—
955C22×C3—183no—
956C22×C3—182no—
957C22×C3—181no—
958C22×C3—181no—
959C22×C3—1812no—
960C22×C3—186no—
961C22×C3—186no—
962C22×C3—363no—
963C22×C3—543no—
964C22×C3—1081no—
965C22×C3—1083no—
966C22×C3C3×D3×S413yescomplemented
967C22×C3D3×C3⋊S413yescomplemented
968C22×C3C2×C3×C3⋊S413yescomplemented
969C2×D3—33no—
970C2×D3—33no—
971C2×D3—33no—
972C2×D3—33no—
973C2×D3—63no—
974C2×D3—66no—
975C2×D3—63no—
976C2×D3—61no—
977C2×D3—61no—
978C2×D3—63no—
979C2×D3—183no—
980C2×D3—183no—
981C2×D3—363no—
982C2×D3—363no—
983C2×D3—361no—
984C2×D3—363no—
985C2×D3—361no—
986C2×D3—1443no—
987A4—49no—
988A4—83no—
989A4—86no—
990A4—89no—
991A4—89no—
992A4—163no—
993A4—166no—
994A4—169no—
995C3×C4—183no—
996C3×C4—183no—
997C3×C4—363no—
998C3×C4—543no—
999Dic3—63no—
1000Dic3—183no—
1001Dic3—183no—
1002Dic3—363no—
1003C32—21no—
1004C32—21no—
1005C32—21no—
1006C32—41no—
1007C32—161no—
1008C32—163no—
1009C32—163no—
1010C32—323no—
1011C32—323no—
1012C32—323no—
1013C32—321no—
1014C32—321no—
1015C32—323no—
1016C32—323no—
1017C32—643no—
1018C32—643no—
1019C32—643no—
1020C32—643no—
1021C32—646no—
1022C32—641no—
1023C32D3×#102011yescharacteristic, complemented
1024C32C2×C3×#102011yescharacteristic, complemented
1025C32C2×C3⋊#102011yescharacteristic, complemented
1026C23—33no—
1027C23—33no—
1028C23—61no—
1029C23—61no—
1030C23—91no—
1031C23—93no—
1032C23—93no—
1033C23—93no—
1034C23—91no—
1035C23—93no—
1036C23—181no—
1037C23—183no—
1038C23—183no—
1039C23—186no—
1040C23—183no—
1041C23—271no—
1042C23—543no—
1043C23—543no—
1044D4—183no—
1045D4—183no—
1046D4—543no—
1047D4—543no—
1048D4—543no—
1049D4—543no—
1050D4—543no—
1051D4—543no—
1052C2×C4—93no—
1053C2×C4—273no—
1054C2×C4—543no—
1055C2×C4—543no—
1056C2×C3—33no—
1057C2×C3—31no—
1058C2×C3—33no—
1059C2×C3—31no—
1060C2×C3—33no—
1061C2×C3—63no—
1062C2×C3—63no—
1063C2×C3—63no—
1064C2×C3—61no—
1065C2×C3—62no—
1066C2×C3—61no—
1067C2×C3—61no—
1068C2×C3—61no—
1069C2×C3—93no—
1070C2×C3—93no—
1071C2×C3—123no—
1072C2×C3—121no—
1073C2×C3—121no—
1074C2×C3—122no—
1075C2×C3—183no—
1076C2×C3—182no—
1077C2×C3—181no—
1078C2×C3—181no—
1079C2×C3—361no—
1080C2×C3—361no—
1081C2×C3—483no—
1082C2×C3—721no—
1083C2×C3—963no—
1084C2×C3—1081no—
1085D3—33no—
1086D3—61no—
1087D3—121no—
1088D3—2883no—
1089D3—361no—
1090D3—361no—
1091D3—483no—
1092D3—721no—
1093D3—1443no—
1094D3C3×C3⋊#102011yescharacteristic, direct product factor
1095C22—21no—
1096C22—31no—
1097C22—33no—
1098C22—63no—
1099C22—93no—
1100C22—93no—
1101C22—93no—
1102C22—93no—
1103C22—181no—
1104C22—186no—
1105C22—183no—
1106C22—183no—
1107C22—183no—
1108C22—181no—
1109C22—543no—
1110C22—1081no—
1111C22—1083no—
1112C22C3×D3×C3⋊S413yescomplemented
1113C4—183no—
1114C4—543no—
1115C3—21no—
1116C3—21no—
1117C3—21no—
1118C3—41no—
1119C3—163no—
1120C3—323no—
1121C3—323no—
1122C3—643no—
1123C3C3×D3×#102011yescharacteristic, complemented
1124C3D3×C3⋊#102011yescharacteristic, direct product factor
1125C3C2×C3×C3⋊#102011yescharacteristic, complemented
1126C2—33no—
1127C2—31no—
1128C2—61no—
1129C2—93no—
1130C2—181no—
1131C2—361no—
1132C2—1081no—
subgroupG/H
center, hypercenterC3D3×C3⋊#1020
commutator, cosocle, hypocenterC32×C22⋊A4C22×C3
FrattiniC1G
Fitting, socleC24×C33C2×D3
LCSG ▷ C32×C22⋊A4
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C32×C3⋊#1020C2semidirect
2. C3×C3⋊(C3⋊#1020)C2semidirect
3. C32×D3×C22⋊A4C2semidirect
5. D3×C3⋊#1020C3direct (N × H)
8. C33×C22⋊A4C22semidirect
10. C24×C32×D3D3semidirect
14. C3×D3×C22⋊A4D3semidirect
15. C3×D3×C22⋊A4C2×C3semidirect
16. C3⋊(C3⋊#1020)C2×C3semidirect
22. C3×C3⋊#1020D3direct (N × H)
23. C3×C3⋊#1020C2×C3semidirect
41. C24×C33C2×D3semidirect
53. C32×C22⋊A4C2×D3semidirect
54. C32×C22⋊A4C2×D3semidirect
55. C32×C22⋊A4C22×C3semidirect
77. C24×C3×D3C3×D3semidirect
78. C24×C3×D3C3⋊D3semidirect
84. D3×C22⋊A4C3×D3semidirect
89. C3⋊#1020C3×D3direct (N × H)
130. C22×C32×D3S4semidirect
179. C24×C32D32semidirect
180. C24×C32C2×C3×D3semidirect
181. C24×C32C2×C3⋊D3semidirect
209. C3×C22⋊A4D32semidirect
210. C3×C22⋊A4C2×C3×D3semidirect
211. C3×C22⋊A4C2×C3×D3semidirect
260. C22×C33C2×S4semidirect
302. C24×D3C3×C3⋊D3semidirect
401. C22×C3×D3C3×S4semidirect
402. C22×C3×D3C3⋊S4semidirect
490. C32×D3#1020semidirect
508. C24×C3C3×D32semidirect
509. C24×C3D3×C3⋊D3semidirect
510. C24×C3C2×C3×C3⋊D3semidirect
520. C22⋊A4C3×D32semidirect
604. C22×C32D3×S4semidirect
605. C22×C32C2×C3×S4semidirect
606. C22×C32C2×C3⋊S4semidirect
707. C33C2×#1020semidirect
783. C22×D3C3×C3⋊S4semidirect
881. C3×D3C3×#1020semidirect
882. C3×D3C3⋊#1020direct (N × H)
888. C24C3×D3×C3⋊D3semidirect
966. C22×C3C3×D3×S4semidirect
967. C22×C3D3×C3⋊S4semidirect
968. C22×C3C2×C3×C3⋊S4semidirect
1023. C32D3×#1020semidirect
1024. C32C2×C3×#1020semidirect
1025. C32C2×C3⋊#1020semidirect
1094. D3C3×C3⋊#1020direct (N × H)
1112. C22C3×D3×C3⋊S4semidirect
1123. C3C3×D3×#1020semidirect
1124. C3D3×C3⋊#1020direct (N × H)
1125. C3C2×C3×C3⋊#1020semidirect

Maximal subgroups

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

subgroupindex
C32×C3⋊#10202
C3×C3⋊(C3⋊#1020)2
C32×D3×C22⋊A42
C2×C3×C3⋊#10203
D3×C3⋊#10203
C3×D3×#10203
C3×D3×#9533
C3×D3×C3⋊S44