Finite Group Databasebeta

← #13178334

Subgroups — #13178334

Order 1728.

1114 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64101C211yesmaximal, characteristic
2C3×#64099C211yesmaximal, characteristic, complemented
3C3×#64097C211yesmaximal, characteristic, complemented
4C4⋊#6296C211yesmaximal, characteristic, complemented
5#11723692C212yesmaximal
6#11723688C212yesmaximal
7C4×#6294C211yesmaximal, characteristic
8#11723680C211yesmaximal, characteristic, complemented
9#11723668C212yesmaximal, complemented
10#11723667C211yesmaximal, characteristic
11#11723665C212yesmaximal, complemented
12#10594477—31nomaximal
13#10594448—31nomaximal
14#10594445—31nomaximal
15C2×C3×C4×C3⋊D3C2211yescharacteristic
16C2×C3×#634C2212yes—
17C2×#6296C2212yes—
18C2×#6294C2211yescharacteristic
19C2×#6294C2211yescharacteristic
20C33×C4⋊C4C2211yescharacteristic
21C3×#3752C2212yes—
22C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
23C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
24C3×C4⋊(C3⋊Dic3)C2212yes—
25C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
26C3×#3750C2212yes—
27C3×#3750C2212yes—
28C3×C4×C3⋊Dic3C2211yescharacteristic
29C3×C4×C3⋊Dic3C2211yescharacteristic
30C3×C4×C3⋊Dic3C2212yes—
31#88815C2212yes—
32#88815C2212yes—
33#88815C2212yes—
34#88814C2212yes—
35#88813C2211yescharacteristic
36#88813C2212yes—
37#88813C2211yescharacteristic
38#64101D311yescharacteristic
39#64099D311yescharacteristic, complemented
40#64097D311yescharacteristic, complemented
41C3×#892—31no—
42C3×#892—31no—
43C3×#892—61no—
44C3×#890—31no—
45C3×#890—31no—
46C3×#890—61no—
47C3×#888—31no—
48C3×#888—31no—
49C3×#888—61no—
50#63919—31no—
51#63918—31no—
52#63918—31no—
53#63899—32no—
54#63896—32no—
55#63895—32no—
56#63893—32no—
57#63888—32no—
58#63887—32no—
59C4×#624—31no—
60C4×D3×Dic3—31no—
61C4×D3×Dic3—31no—
62#63872—31no—
63#63869—31no—
64#63869—31no—
65#63849—31no—
66#63844—32no—
67#63843—32no—
68Dic3×Dic6—32no—
69#63841—31no—
70#63841—31no—
71#63838—32no—
72#63837—32no—
73#63837—32no—
74C22×C3×C3⋊D3C2311yescharacteristic
75C2×C33×C4C2312yes—
76C2×C33×C4C2311yescharacteristic
77C2×C3×C3⋊Dic3C2311yescharacteristic
78C2×C3×C3⋊Dic3C2311yescharacteristic
79C2×C3×C3⋊Dic3C2312yes—
80C2×C3×C3⋊Dic3C2312yes—
81C2×C3×C3⋊Dic3C2312yes—
82C2×C3×C3⋊Dic3C2311yescharacteristic
83C2×C3×C3⋊Dic3C2311yescharacteristic
84C2×C3×C3⋊Dic3C2311yescharacteristic
85C3×C4×C3⋊D3Q814yescomplemented
86C3×#634—24no—
87#6296—24no—
88#6294—22no—
89#6294—22no—
90#5728—91no—
91#5688—91no—
92#5517—91no—
93C2×C4×C3⋊D3C2×D311yescharacteristic
94C2×#634C2×D312yes—
95C2×C3×C4×D3—31no—
96C2×C3×C4×D3—31no—
97C2×C3×C4×D3—61no—
98C2×C3×Dic6—32no—
99C2×C3×Dic6—32no—
100C2×C3×Dic6—62no—
101C2×#627—32no—
102C2×#627—32no—
103C2×#627—32no—
104C2×#624—31no—
105C2×#624—31no—
106C2×D3×Dic3—31no—
107C2×D3×Dic3—31no—
108C2×D3×Dic3—31no—
109C2×D3×Dic3—31no—
110C32×C4⋊C4—21no—
111C32×C4⋊C4—21no—
112C32×C4⋊C4—21no—
113C32×C4⋊C4—41no—
114C32×C4⋊C4C2×D311yescharacteristic
115C32×C4⋊C4C2×D311yescharacteristic
116C32×C4⋊C4C2×D311yescharacteristic
117#3752C2×D312yes—
118C4⋊(C3⋊Dic3)C2×D311yescharacteristic
119C4⋊(C3⋊Dic3)C2×D311yescharacteristic
120C4⋊(C3⋊Dic3)C2×D312yes—
121C4⋊(C3⋊Dic3)C2×D311yescharacteristic
122#3750C2×D312yes—
123#3750C2×D312yes—
124C4×C3⋊Dic3C2×D312yes—
125C4×C3⋊Dic3C2×D311yescharacteristic
126C4×C3⋊Dic3C2×D311yescharacteristic
127C3×(C2×D3)⋊C4—32no—
128C3×(C2×D3)⋊C4—32no—
129C3×(C2×D3)⋊C4—62no—
130C3×C4⋊Dic3—31no—
131C3×C4⋊Dic3—31no—
132C3×C4⋊Dic3—31no—
133C3×C4⋊Dic3—32no—
134C3×C4⋊Dic3—32no—
135C3×C4⋊Dic3—31no—
136C3×C4⋊Dic3—31no—
137C3×C4⋊Dic3—31no—
138C3×C4⋊Dic3—61no—
139C3×C4⋊Dic3—62no—
140C3×C4⋊Dic3—61no—
141C3×C4⋊Dic3—61no—
142C3×Dic3⋊C4—32no—
143C3×Dic3⋊C4—32no—
144C3×Dic3⋊C4—32no—
145C3×Dic3⋊C4—32no—
146C3×Dic3⋊C4—62no—
147C3×Dic3⋊C4—62no—
148C3×C4×Dic3—31no—
149C3×C4×Dic3—31no—
150C3×C4×Dic3—31no—
151C3×C4×Dic3—31no—
152C3×C4×Dic3—32no—
153C3×C4×Dic3—32no—
154C3×C4×Dic3—61no—
155C3×C4×Dic3—61no—
156C3×C4×Dic3—62no—
157#3724—32no—
158#3724—32no—
159#3724—32no—
160Dic3⋊Dic3—32no—
161Dic3⋊Dic3—32no—
162Dic3⋊Dic3—32no—
163Dic3⋊Dic3—32no—
164Dic3⋊Dic3—32no—
165Dic3⋊Dic3—32no—
166#3722—32no—
167(C2×D3)⋊Dic3—32no—
168(C2×D3)⋊Dic3—32no—
169Dic32—31no—
170Dic32—31no—
171Dic32—32no—
172Dic32—32no—
173Dic32—31no—
174Dic32—32no—
175Dic32—31no—
176Dic32—31no—
177Dic32—31no—
178C22×C33C2411yescharacteristic
179C2×C3×C3⋊D3—21no—
180C2×C3×C3⋊D3—21no—
181C2×C3×C3⋊D3C2×Q812yes—
182C33×C4—22no—
183C33×C4C2×Q812yes—
184C3×C3⋊Dic3—21no—
185C3×C3⋊Dic3—21no—
186C3×C3⋊Dic3—22no—
187C3×C3⋊Dic3—22no—
188C3×C3⋊Dic3—22no—
189C3×C3⋊Dic3C2×Q812yes—
190C3×C3⋊Dic3#4112yes—
191C3×C3⋊Dic3#4112yes—
192C3×C4⋊Q8—91no—
193C3×#125—91no—
194C3×#117—91no—
195#946—92no—
196Q8×Dic3—92no—
197#926—91no—
198C2×C4×Dic3—91no—
199#897—92no—
200#896—92no—
201#896—92no—
202#892—31no—
203#892—31no—
204#892—61no—
205#892—91no—
206#892—91no—
207#890—31no—
208#890—31no—
209#890—61no—
210#890—91no—
211#890—91no—
212#888—31no—
213#888—31no—
214#888—61no—
215#888—91no—
216#888—91no—
217#887—92no—
218#887—92no—
219#887—92no—
220#878—92no—
221#878—92no—
222C42×D3—91no—
223C42×D3—91no—
224#870—91no—
225#869—91no—
226C4×Dic6—92no—
227C4×Dic6—92no—
228C22×C3⋊D3C22×D311yescharacteristic
229C22×C3×D3—31no—
230C22×C3×D3—31no—
231C22×C3×D3—61no—
232C2×C32×C4—21no—
233C2×C32×C4—21no—
234C2×C32×C4—21no—
235C2×C32×C4—22no—
236C2×C32×C4—22no—
237C2×C32×C4—22no—
238C2×C32×C4—41no—
239C2×C32×C4—42no—
240C2×C32×C4C22×D312yes—
241C2×C32×C4C22×D312yes—
242C2×C32×C4C22×D312yes—
243C2×C32×C4C22×D311yescharacteristic
244C2×C32×C4C22×D311yescharacteristic
245C2×C32×C4C22×D311yescharacteristic
246C2×C3⋊Dic3C22×D312yes—
247C2×C3⋊Dic3C22×D312yes—
248C2×C3⋊Dic3C22×D311yescharacteristic
249C2×C3⋊Dic3C22×D311yescharacteristic
250C2×C3⋊Dic3C22×D312yes—
251C2×C3⋊Dic3C22×D311yescharacteristic
252C2×C3⋊Dic3C22×D311yescharacteristic
253C2×C3⋊Dic3C22×D311yescharacteristic
254C4×C3⋊D3Dic614yescomplemented
255#634—24no—
256C2×C3×Dic3—31no—
257C2×C3×Dic3—31no—
258C2×C3×Dic3—31no—
259C2×C3×Dic3—31no—
260C2×C3×Dic3—31no—
261C2×C3×Dic3—31no—
262C2×C3×Dic3—32no—
263C2×C3×Dic3—32no—
264C2×C3×Dic3—32no—
265C2×C3×Dic3—32no—
266C2×C3×Dic3—31no—
267C2×C3×Dic3—31no—
268C2×C3×Dic3—31no—
269C2×C3×Dic3—31no—
270C2×C3×Dic3—32no—
271C2×C3×Dic3—32no—
272C2×C3×Dic3—61no—
273C2×C3×Dic3—61no—
274C2×C3×Dic3—61no—
275C2×C3×Dic3—61no—
276C2×C3×Dic3—61no—
277C2×C3×Dic3—62no—
278C2×C3×Dic3—62no—
279C2×C3×Dic3—62no—
280C3×C4×D3—34no—
281C3×C4×D3—34no—
282C3×C4×D3—64no—
283C3×Dic6—64no—
284C3×Dic6—64no—
285C3×Dic6—124no—
286#627—64no—
287#627—64no—
288#627—64no—
289#624—62no—
290#624—62no—
291D3×Dic3—62no—
292D3×Dic3—62no—
293D3×Dic3—62no—
294D3×Dic3—62no—
295#533—271noSylow
296C2×C33C22×Q811yescharacteristic
297C2×C33C2×#4111yescharacteristic
298C2×C33C2×#4111yescharacteristic
299C3×C3⋊D3—22no—
300C2×C3×Q8—92no—
301C22×C3×C4—91no—
302C22×Dic3—91no—
303C22×Dic3—91no—
304C2×C4×D3—31no—
305C2×C4×D3—31no—
306C2×C4×D3—61no—
307C2×C4×D3—91no—
308C2×C4×D3—91no—
309C2×C4×D3—91no—
310C2×C4×D3—91no—
311C2×Dic6—32no—
312C2×Dic6—32no—
313C2×Dic6—62no—
314C2×Dic6—92no—
315C2×Dic6—92no—
316C2×Dic6—92no—
317C3×C4⋊C4—21no—
318C3×C4⋊C4—21no—
319C3×C4⋊C4—21no—
320C3×C4⋊C4—41no—
321C3×C4⋊C4—92no—
322C3×C4⋊C4—92no—
323C3×C4⋊C4—92no—
324C3×C4⋊C4—91no—
325C3×C4⋊C4—91no—
326C3×C4⋊C4—91no—
327C3×C4⋊C4D3211yescharacteristic
328C3×C4⋊C4D3211yescharacteristic
329C3×C4⋊C4D3211yescharacteristic
330C3×C22⋊C4—92no—
331C3×C42—92no—
332C3×C42—91no—
333C3×C42—91no—
334#217—92no—
335(C2×D3)⋊C4—32no—
336(C2×D3)⋊C4—32no—
337(C2×D3)⋊C4—62no—
338(C2×D3)⋊C4—92no—
339(C2×D3)⋊C4—92no—
340C4⋊Dic3—32no—
341C4⋊Dic3—31no—
342C4⋊Dic3—31no—
343C4⋊Dic3—31no—
344C4⋊Dic3—31no—
345C4⋊Dic3—31no—
346C4⋊Dic3—31no—
347C4⋊Dic3—32no—
348C4⋊Dic3—61no—
349C4⋊Dic3—61no—
350C4⋊Dic3—62no—
351C4⋊Dic3—61no—
352C4⋊Dic3—92no—
353C4⋊Dic3—92no—
354C4⋊Dic3—92no—
355Dic3⋊C4—32no—
356Dic3⋊C4—32no—
357Dic3⋊C4—32no—
358Dic3⋊C4—32no—
359Dic3⋊C4—62no—
360Dic3⋊C4—62no—
361Dic3⋊C4—92no—
362Dic3⋊C4—92no—
363Dic3⋊C4—92no—
364Dic3⋊C4—92no—
365Dic3⋊C4—92no—
366Dic3⋊C4—92no—
367C4×Dic3—31no—
368C4×Dic3—31no—
369C4×Dic3—32no—
370C4×Dic3—32no—
371C4×Dic3—31no—
372C4×Dic3—31no—
373C4×Dic3—61no—
374C4×Dic3—61no—
375C4×Dic3—62no—
376C4×Dic3—91no—
377C4×Dic3—91no—
378C4×Dic3—92no—
379C4×Dic3—91no—
380C4×Dic3—91no—
381C4×Dic3—91no—
382C4×Dic3—91no—
383C4×Dic3—92no—
384C4×Dic3—92no—
385C22×C32—21no—
386C22×C32—21no—
387C22×C32—21no—
388C22×C32—41no—
389C22×C32C23×D311yescharacteristic
390C22×C32C23×D311yescharacteristic
391C22×C32C23×D311yescharacteristic
392C2×C3⋊D3—21no—
393C2×C3⋊D3—21no—
394C2×C3⋊D3C2×Dic612yes—
395C2×C3×D3—32no—
396C2×C3×D3—32no—
397C2×C3×D3—62no—
398C2×C3×D3—61no—
399C2×C3×D3—61no—
400C2×C3×D3—61no—
401C2×C3×D3—61no—
402C2×C3×D3—121no—
403C2×C3×D3—121no—
404C32×C4—22no—
405C32×C4—22no—
406C32×C4—22no—
407C32×C4—22no—
408C32×C4—22no—
409C32×C4—22no—
410C32×C4—42no—
411C32×C4—42no—
412C32×C4—42no—
413C32×C4—42no—
414C32×C4—82no—
415C32×C4C2×Dic612yes—
416C32×C4D3×Q812yes—
417C32×C4D3×Q812yes—
418C3⋊Dic3—22no—
419C3⋊Dic3—21no—
420C3⋊Dic3—21no—
421C3⋊Dic3—22no—
422C3⋊Dic3—22no—
423C3⋊Dic3C2×Dic612yes—
424C3⋊Dic3#23712yes—
425C3⋊Dic3#23912yes—
426C3×Dic3—32no—
427C3×Dic3—32no—
428C3×Dic3—32no—
429C3×Dic3—32no—
430C3×Dic3—32no—
431C3×Dic3—32no—
432C3×Dic3—62no—
433C3×Dic3—62no—
434C3×Dic3—62no—
435C3×Dic3—61no—
436C3×Dic3—61no—
437C3×Dic3—62no—
438C3×Dic3—62no—
439C3×Dic3—61no—
440C3×Dic3—61no—
441C3×Dic3—62no—
442C3×Dic3—62no—
443C3×Dic3—62no—
444C3×Dic3—62no—
445C3×Dic3—122no—
446C3×Dic3—121no—
447C3×Dic3—122no—
448C3×Dic3—122no—
449C3×Dic3—121no—
450C4⋊Q8—91no—
451C4⋊Q8—271no—
452#125—91no—
453#125—271no—
454C22⋊Q8—272no—
455C22⋊Q8—272no—
456C4×Q8—272no—
457C4×Q8—272no—
458#117—91no—
459#117—271no—
460C2×C42—271no—
461C33#53311yescharacteristic, complemented, Sylow
462C23×C3—91no—
463C22×D3—31no—
464C22×D3—31no—
465C22×D3—61no—
466C3×Q8—184no—
467C2×C3×C4—21no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—22no—
471C2×C3×C4—22no—
472C2×C3×C4—22no—
473C2×C3×C4—41no—
474C2×C3×C4—42no—
475C2×C3×C4—91no—
476C2×C3×C4—91no—
477C2×C3×C4—91no—
478C2×C3×C4—94no—
479C2×C3×C4—91no—
480C2×C3×C4—91no—
481C2×C3×C4—92no—
482C2×C3×C4—92no—
483C2×C3×C4—92no—
484C2×C3×C4C2×D3212yes—
485C2×C3×C4C2×D3212yes—
486C2×C3×C4C2×D3212yes—
487C2×C3×C4C2×D3211yescharacteristic
488C2×C3×C4C2×D3211yescharacteristic
489C2×C3×C4C2×D3211yescharacteristic
490C2×Dic3—31no—
491C2×Dic3—31no—
492C2×Dic3—31no—
493C2×Dic3—31no—
494C2×Dic3—31no—
495C2×Dic3—31no—
496C2×Dic3—31no—
497C2×Dic3—31no—
498C2×Dic3—31no—
499C2×Dic3—31no—
500C2×Dic3—32no—
501C2×Dic3—32no—
502C2×Dic3—32no—
503C2×Dic3—32no—
504C2×Dic3—32no—
505C2×Dic3—32no—
506C2×Dic3—61no—
507C2×Dic3—61no—
508C2×Dic3—61no—
509C2×Dic3—61no—
510C2×Dic3—61no—
511C2×Dic3—62no—
512C2×Dic3—62no—
513C2×Dic3—62no—
514C2×Dic3—182no—
515C2×Dic3—182no—
516C4×D3—34no—
517C4×D3—34no—
518C4×D3—64no—
519C4×D3—182no—
520C4×D3—182no—
521C4×D3—182no—
522C4×D3—182no—
523Dic6—64no—
524Dic6—64no—
525Dic6—124no—
526Dic6—184no—
527Dic6—184no—
528Dic6—184no—
529C2×C32—21no—
530C2×C32—21no—
531C2×C32—21no—
532C2×C32—21no—
533C2×C32—21no—
534C2×C32—21no—
535C2×C32—21no—
536C2×C32—21no—
537C2×C32—21no—
538C2×C32—41no—
539C2×C32—41no—
540C2×C32—41no—
541C2×C32C22×Dic611yescharacteristic
542C2×C32C2×#23711yescharacteristic
543C2×C32C2×D3×Q811yescharacteristic
544C2×C32C2×D3×Q811yescharacteristic
545C2×C32C2×#23911yescharacteristic
546C2×C32D3×#4111yescharacteristic
547C2×C32D3×#4111yescharacteristic
548C2×C32D3×#4111yescharacteristic
549C2×C32D3×#4111yescharacteristic
550C3⋊D3—22no—
551C3×D3—62no—
552C3×D3—62no—
553C3×D3—122no—
554C2×Q8—92no—
555C2×Q8—272no—
556C22×C4—91no—
557C22×C4—271no—
558C22×C4—271no—
559C4⋊C4—91no—
560C4⋊C4—91no—
561C4⋊C4—91no—
562C4⋊C4—92no—
563C4⋊C4—92no—
564C4⋊C4—92no—
565C4⋊C4—272no—
566C4⋊C4—272no—
567C4⋊C4—272no—
568C4⋊C4#111311yescharacteristic
569C22⋊C4—92no—
570C22⋊C4—272no—
571C42—91no—
572C42—91no—
573C42—92no—
574C42—271no—
575C42—271no—
576C42—272no—
577C22×C3—21no—
578C22×C3—21no—
579C22×C3—21no—
580C22×C3—41no—
581C22×C3—92no—
582C22×C3—181no—
583C22×C3—181no—
584C22×C3C22×D3211yescharacteristic
585C22×C3C22×D3211yescharacteristic
586C22×C3C22×D3211yescharacteristic
587C2×D3—32no—
588C2×D3—32no—
589C2×D3—62no—
590C2×D3—61no—
591C2×D3—61no—
592C2×D3—61no—
593C2×D3—61no—
594C2×D3—121no—
595C2×D3—121no—
596C3×C4—22no—
597C3×C4—22no—
598C3×C4—22no—
599C3×C4—22no—
600C3×C4—22no—
601C3×C4—22no—
602C3×C4—42no—
603C3×C4—42no—
604C3×C4—42no—
605C3×C4—42no—
606C3×C4—82no—
607C3×C4—92no—
608C3×C4—92no—
609C3×C4—92no—
610C3×C4—181no—
611C3×C4—182no—
612C3×C4—182no—
613C3×C4—182no—
614C3×C4—181no—
615C3×C4D3×Dic612yes—
616C3×C4D3×Dic612yes—
617C3×C4#379712yes—
618Dic3—32no—
619Dic3—32no—
620Dic3—32no—
621Dic3—32no—
622Dic3—32no—
623Dic3—32no—
624Dic3—62no—
625Dic3—62no—
626Dic3—62no—
627Dic3—62no—
628Dic3—62no—
629Dic3—61no—
630Dic3—61no—
631Dic3—62no—
632Dic3—62no—
633Dic3—61no—
634Dic3—62no—
635Dic3—62no—
636Dic3—61no—
637Dic3—122no—
638Dic3—121no—
639Dic3—121no—
640Dic3—122no—
641Dic3—122no—
642C32—21no—
643C32—21no—
644C32—21no—
645C32—41no—
646C32#551711yescharacteristic, complemented
647C32#568811yescharacteristic, complemented
648C32#572811yescharacteristic, complemented
649C23—91no—
650Q8—184no—
651Q8—544no—
652C2×C4—91no—
653C2×C4—91no—
654C2×C4—91no—
655C2×C4—94no—
656C2×C4—91no—
657C2×C4—91no—
658C2×C4—92no—
659C2×C4—92no—
660C2×C4—92no—
661C2×C4—542no—
662C2×C4—542no—
663C2×C4C2×#111312yes—
664C2×C4C2×#111311yescharacteristic
665C2×C3—21no—
666C2×C3—21no—
667C2×C3—21no—
668C2×C3—21no—
669C2×C3—21no—
670C2×C3—21no—
671C2×C3—21no—
672C2×C3—21no—
673C2×C3—21no—
674C2×C3—41no—
675C2×C3—41no—
676C2×C3—41no—
677C2×C3—182no—
678C2×C3C2×D3×Dic611yescharacteristic
679C2×C3C2×D3×Dic611yescharacteristic
680C2×C3C2×#379711yescharacteristic
681C2×C3D3×#23711yescharacteristic
682C2×C3D3×#23711yescharacteristic
683C2×C3#6431211yescharacteristic
684C2×C3D3×#23911yescharacteristic
685C2×C3D3×#23911yescharacteristic
686C2×C3#6431911yescharacteristic
687D3—62no—
688D3—62no—
689D3—122no—
690C22—92no—
691C22—181no—
692C22—181no—
693C22C22×#111311yescharacteristic
694C4—22no—
695C4—92no—
696C4—92no—
697C4—92no—
698C4—181no—
699C4—182no—
700C4—181no—
701C4—182no—
702C4—182no—
703C4#8904012yes—
704C3—21no—
705C3—21no—
706C3—21no—
707C3—41no—
708C3#1059444511yescharacteristic, complemented
709C3#1059444811yescharacteristic, complemented
710C3#1059447711yescharacteristic, complemented
711C2—182no—
712C2C2×#8904011yescharacteristic
713C2#1172462211yescharacteristic
714C2#1172462611yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC33×C4⋊C4C22
prime radicalC22×C3×C3⋊D3C23
hypercenterC4⋊C4#1113
hypocenterC33#533
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C3×#64099C2semidirect
3. C3×#64097C2semidirect
4. C4⋊#6296C2semidirect
8. #11723680C2semidirect
9. #11723668C2semidirect
11. #11723665C2semidirect
39. #64099D3semidirect
40. #64097D3semidirect
85. C3×C4×C3⋊D3Q8semidirect
254. C4×C3⋊D3Dic6semidirect
461. C33#533semidirect
646. C32#5517semidirect
647. C32#5688semidirect
648. C32#5728semidirect
708. C3#10594445semidirect
709. C3#10594448semidirect
710. C3#10594477semidirect

Maximal subgroups

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

subgroupindex
C3×#641012
C3×#640992
C3×#640972
C4⋊#62962
#117236922
#117236882
C4×#62942
#117236802
#117236682
#117236672
#117236652
#105944773
#105944483
#105944453