Finite Group Databasebeta

← C3×#82235 #11803455

Subgroups — C3×#82235 #11803455

Order 1152.

1277 conjugacy classes of subgroups.

The subgroup lattice has 657 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#117C211yesmaximal, characteristic
2C2×C3×#924C211yesmaximal, characteristic
3C2×C3×C4×Dic6C211yesmaximal, characteristic, complemented
4C3×#5212C211yesmaximal, characteristic
5C3×#4978C212yesmaximal, complemented
6C3×#4976C212yesmaximal, complemented
7C3×#4945C212yesmaximal
8C3×#4944C212yesmaximal
9C3×C4×C4⋊Dic3C211yesmaximal, characteristic, complemented
10C3×#4929C211yesmaximal, characteristic, complemented
11C3×#4928C211yesmaximal, characteristic, complemented
12C3×#2323—31nomaximal
13#82235C311yesmaximal, characteristic, direct product factor
14C23×C32×C4C2211yescharacteristic
15C22×C3×Dic6C2211yescharacteristic
16C32×#117—24no—
17C2×C32×C4⋊C4C2211yescharacteristic
18C2×C32×C4⋊C4C2211yescharacteristic
19C2×C32×C22⋊C4C2211yescharacteristic
20C2×C32×C22⋊C4C2211yescharacteristic
21C2×C32×C42C2211yescharacteristic
22C2×C32×C42C2211yescharacteristic
23C2×C3×#217C2212yes—
24C2×C3×#217C2212yes—
25C2×C3×C4⋊Dic3C2211yescharacteristic
26C2×C3×C4⋊Dic3C2211yescharacteristic
27C2×C3×C4⋊Dic3C2211yescharacteristic
28C3×#924C418yescomplemented
29C2×C3×Dic3⋊C4C2212yes—
30C2×C3×Dic3⋊C4C2212yes—
31C2×C3×Dic3⋊C4C2212yes—
32C2×C3×C4×Dic3C2212yes—
33C2×C3×C4×Dic3C2212yes—
34C3×C4×Dic6—24no—
35C3×C3⋊#95C2212yes—
36C3×C3⋊#95C2212yes—
37C3×C3⋊#95C2212yes—
38C3×C3⋊#95C2212yes—
39C3×C3⋊#95C2212yes—
40C2×C3×C22⋊Q8—31no—
41C2×C3×C4×Q8—31no—
42C2×C3×#117—21no—
43C2×C3×#117D311yescharacteristic
44C2×C3×#117C2×C311yescharacteristic
45C2×#924C2×C311yescharacteristic
46C2×C4×Dic6C2×C311yescharacteristic, complemented
47C3×#391—31no—
48C3×#389—32no—
49C3×#389—31no—
50C3×#388—32no—
51C3×#388—32no—
52C3×#387—32no—
53C3×#380—31no—
54C3×C4×C4⋊C4—31no—
55#5212C2×C311yescharacteristic
56#4978C2×C312yescomplemented
57#4976C2×C312yescomplemented
58#4945C2×C312yes—
59#4944C2×C312yes—
60C4×C4⋊Dic3C2×C311yescharacteristic, complemented
61#4929C2×C311yescharacteristic, complemented
62#4928C2×C311yescharacteristic, complemented
63C24×C32C2311yescharacteristic
64C22×C32×C4—22no—
65C22×C32×C4—22no—
66C22×C32×C4C2×C414yes—
67C22×C32×C4C2311yescharacteristic
68C22×C32×C4C2311yescharacteristic
69C22×C32×C4C2311yescharacteristic
70C22×C32×C4C2311yescharacteristic
71C22×C32×C4C2311yescharacteristic
72C22×C32×C4C2311yescharacteristic
73C22×C3×Dic3C2312yes—
74C22×C3×Dic3C2312yes—
75C22×C3×Dic3C2312yes—
76C22×C3×Dic3C2312yes—
77C2×C3×Dic6—22no—
78C2×C3×Dic6—22no—
79C2×C3×Dic6C2×C414yes—
80C32×C4⋊C4—22no—
81C32×C4⋊C4—22no—
82C32×C22⋊C4—22no—
83C32×C22⋊C4—22no—
84C32×C42—22no—
85C32×C42D414yes—
86C3×#217—42no—
87C3×#217C2×C418yes—
88C3×C4⋊Dic3—22no—
89C3×C4⋊Dic3—22no—
90C3×C4⋊Dic3C2×C414yes—
91C3×Dic3⋊C4—24no—
92C3×Dic3⋊C4—42no—
93C3×Dic3⋊C4C2×C418yes—
94C3×C4×Dic3—24no—
95C3×C4×Dic3—42no—
96#2323—31noSylow
97C22×C3×Q8—31no—
98C23×C3×C4—21no—
99C23×C3×C4C2×D311yescharacteristic
100C23×C3×C4C22×C311yescharacteristic
101C22×Dic6C22×C311yescharacteristic
102C3×C22⋊Q8—38no—
103C3×C4×Q8—64no—
104C3×#117—28no—
105C3×#117—24no—
106C3×#117—24no—
107C2×C3×C4⋊C4—21no—
108C2×C3×C4⋊C4—21no—
109C2×C3×C4⋊C4—32no—
110C2×C3×C4⋊C4—31no—
111C2×C3×C4⋊C4—32no—
112C2×C3×C4⋊C4—31no—
113C2×C3×C4⋊C4—31no—
114C2×C3×C4⋊C4—32no—
115C2×C3×C4⋊C4C2×D311yescharacteristic
116C2×C3×C4⋊C4C2×D311yescharacteristic
117C2×C3×C4⋊C4C22×C311yescharacteristic
118C2×C3×C4⋊C4C22×C311yescharacteristic
119C2×C3×C22⋊C4—21no—
120C2×C3×C22⋊C4—21no—
121C2×C3×C22⋊C4—32no—
122C2×C3×C22⋊C4—32no—
123C2×C3×C22⋊C4C2×D311yescharacteristic
124C2×C3×C22⋊C4C2×D311yescharacteristic
125C2×C3×C22⋊C4C22×C311yescharacteristic
126C2×C3×C22⋊C4C22×C311yescharacteristic
127C2×C3×C42—21no—
128C2×C3×C42—21no—
129C2×C3×C42—32no—
130C2×C3×C42—32no—
131C2×C3×C42C2×D311yescharacteristic
132C2×C3×C42C2×D311yescharacteristic
133C2×C3×C42C22×C311yescharacteristic
134C2×C3×C42C22×C311yescharacteristic
135C2×#217C22×C312yes—
136C2×#217C22×C312yes—
137C2×C4⋊Dic3C22×C311yescharacteristic
138C2×C4⋊Dic3C22×C311yescharacteristic
139C2×C4⋊Dic3C22×C311yescharacteristic
140#924C3×C418yescomplemented
141C2×Dic3⋊C4C22×C312yes—
142C2×Dic3⋊C4C22×C312yes—
143C2×Dic3⋊C4C22×C312yes—
144C2×C4×Dic3C22×C312yes—
145C2×C4×Dic3C22×C312yes—
146C4×Dic6—24no—
147C3×#95—32no—
148C3×#95—32no—
149C3×#95—32no—
150C3×#95—32no—
151C3×#95—32no—
152C3⋊#95C22×C312yes—
153C3⋊#95C22×C312yes—
154C3⋊#95C22×C312yes—
155C3⋊#95C22×C312yes—
156C3⋊#95C22×C312yes—
157C23×C32—21no—
158C23×C32—21no—
159C23×C32—21no—
160C23×C32—21no—
161C23×C32—21no—
162C23×C32—21no—
163C23×C32C22×C412yes—
164C23×C32C2411yescharacteristic
165C2×C32×C4—21no—
166C2×C32×C4—21no—
167C2×C32×C4—28no—
168C2×C32×C4—21no—
169C2×C32×C4—21no—
170C2×C32×C4—21no—
171C2×C32×C4—21no—
172C2×C32×C4—21no—
173C2×C32×C4—21no—
174C2×C32×C4—21no—
175C2×C32×C4—21no—
176C2×C32×C4—21no—
177C2×C32×C4—21no—
178C2×C32×C4C22×C412yes—
179C2×C32×C4C22×C412yes—
180C2×C32×C4C2×D412yes—
181C2×C32×C4C2×D412yes—
182C2×C32×C4C2×D412yes—
183C2×C32×C4#4112yes—
184C2×C3×Dic3—22no—
185C2×C3×Dic3—22no—
186C2×C3×Dic3—22no—
187C2×C3×Dic3—22no—
188C2×C3×Dic3—22no—
189C2×C3×Dic3—22no—
190C2×C3×Dic3—22no—
191C2×C3×Dic3—22no—
192C2×C3×Dic3—22no—
193C2×C3×Dic3—22no—
194C2×C3×Dic3C22×C414yes—
195C2×C3×Dic3C22×C414yes—
196C3×Dic6—28no—
197C2×C22⋊Q8—31no—
198C2×C4×Q8—31no—
199C2×#117C3×D311yescharacteristic
200#391—31no—
201#389—32no—
202#389—31no—
203#388—32no—
204#388—32no—
205#387—32no—
206#380—31no—
207C4×C4⋊C4—31no—
208C24×C3—21no—
209C24×C3C22×D311yescharacteristic
210C24×C3C23×C311yescharacteristic
211C2×C3×Q8—34no—
212C2×C3×Q8—62no—
213C2×C3×Q8—62no—
214C22×C3×C4—24no—
215C22×C3×C4—24no—
216C22×C3×C4—22no—
217C22×C3×C4—22no—
218C22×C3×C4—22no—
219C22×C3×C4—22no—
220C22×C3×C4—24no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—32no—
228C22×C3×C4—32no—
229C22×C3×C4—32no—
230C22×C3×C4—32no—
231C22×C3×C4C4×D314yes—
232C22×C3×C4C2×C3×C414yes—
233C22×C3×C4C22×D311yescharacteristic
234C22×C3×C4C22×D311yescharacteristic
235C22×C3×C4C22×D311yescharacteristic
236C22×C3×C4C22×D311yescharacteristic
237C22×C3×C4C22×D311yescharacteristic
238C22×C3×C4C22×D311yescharacteristic
239C22×C3×C4C23×C311yescharacteristic
240C22×C3×C4C23×C311yescharacteristic
241C22×C3×C4C23×C311yescharacteristic
242C22×C3×C4C23×C311yescharacteristic
243C22×C3×C4C23×C311yescharacteristic
244C22×C3×C4C23×C311yescharacteristic
245C22×Dic3C23×C312yes—
246C22×Dic3C23×C312yes—
247C22×Dic3C23×C312yes—
248C22×Dic3C23×C312yes—
249C2×Dic6—22no—
250C2×Dic6—22no—
251C2×Dic6C2×C3×C414yes—
252C3×C4⋊C4—24no—
253C3×C4⋊C4—24no—
254C3×C4⋊C4—22no—
255C3×C4⋊C4—22no—
256C3×C4⋊C4—22no—
257C3×C4⋊C4—22no—
258C3×C4⋊C4—38no—
259C3×C4⋊C4—34no—
260C3×C4⋊C4—62no—
261C3×C4⋊C4—64no—
262C3×C4⋊C4—62no—
263C3×C4⋊C4—122no—
264C3×C22⋊C4—24no—
265C3×C22⋊C4—24no—
266C3×C22⋊C4—22no—
267C3×C22⋊C4—22no—
268C3×C22⋊C4—22no—
269C3×C22⋊C4—22no—
270C3×C22⋊C4—38no—
271C3×C22⋊C4—122no—
272C3×C42—24no—
273C3×C42—22no—
274C3×C42—22no—
275C3×C42—24no—
276C3×C42—64no—
277C3×C42—122no—
278C3×C42#6714yes—
279C3×C42C3×D414yes—
280#217—42no—
281#217C2×C3×C418yes—
282C4⋊Dic3—22no—
283C4⋊Dic3—22no—
284C4⋊Dic3C2×C3×C414yes—
285Dic3⋊C4—24no—
286Dic3⋊C4—42no—
287Dic3⋊C4C2×C3×C418yes—
288C4×Dic3—24no—
289C4×Dic3—42no—
290C22×C32—22no—
291C22×C32—22no—
292C22×C32—22no—
293C22×C32—41no—
294C22×C32—41no—
295C22×C32—41no—
296C22×C32—41no—
297C22×C32C23×C411yescharacteristic
298C22×C32C22×D411yescharacteristic
299C22×C32C2×#4111yescharacteristic
300C22×C32H(5,𝔽2)11yescharacteristic
301C22×C322−1+411yescharacteristic
302C22×C322−1+411yescharacteristic
303C22×C322−1+411yescharacteristic
304C32×C4—22no—
305C32×C4—22no—
306C32×C4—22no—
307C32×C4—41no—
308C32×C4—41no—
309C32×C4C4×D414yes—
310C3×Dic3—24no—
311C3×Dic3—24no—
312C3×Dic3—42no—
313C3×Dic3—42no—
314C22×Q8—31no—
315C23×C4C2×C3×D311yescharacteristic
316C22⋊Q8—38no—
317C4×Q8—64no—
318#117—24no—
319C2×C4⋊C4—31no—
320C2×C4⋊C4—32no—
321C2×C4⋊C4—31no—
322C2×C4⋊C4—32no—
323C2×C4⋊C4—31no—
324C2×C4⋊C4—32no—
325C2×C4⋊C4C2×C3×D311yescharacteristic
326C2×C4⋊C4C2×C3×D311yescharacteristic
327C2×C22⋊C4—32no—
328C2×C22⋊C4—32no—
329C2×C22⋊C4C2×C3×D311yescharacteristic
330C2×C22⋊C4C2×C3×D311yescharacteristic
331C2×C42—32no—
332C2×C42—32no—
333C2×C42C2×C3×D311yescharacteristic
334C2×C42C2×C3×D311yescharacteristic
335#95—32no—
336#95—32no—
337#95—32no—
338#95—32no—
339#95—32no—
340C23×C3—22no—
341C23×C3—22no—
342C23×C3—21no—
343C23×C3—21no—
344C23×C3—21no—
345C23×C3—21no—
346C23×C3—21no—
347C23×C3—21no—
348C23×C3—21no—
349C23×C3—21no—
350C23×C3—21no—
351C23×C3—21no—
352C23×C3—21no—
353C23×C3—21no—
354C23×C3—21no—
355C23×C3—22no—
356C23×C3—41no—
357C23×C3—41no—
358C23×C3—41no—
359C23×C3—41no—
360C23×C3C2×C4×D312yes—
361C23×C3C22×C3×C412yes—
362C23×C3C23×D311yescharacteristic
363C23×C3C24×C311yescharacteristic
364C3×Q8—68no—
365C2×C3×C4—22no—
366C2×C3×C4—22no—
367C2×C3×C4—216no—
368C2×C3×C4—21no—
369C2×C3×C4—21no—
370C2×C3×C4—21no—
371C2×C3×C4—21no—
372C2×C3×C4—21no—
373C2×C3×C4—21no—
374C2×C3×C4—21no—
375C2×C3×C4—21no—
376C2×C3×C4—21no—
377C2×C3×C4—21no—
378C2×C3×C4—21no—
379C2×C3×C4—21no—
380C2×C3×C4—28no—
381C2×C3×C4—28no—
382C2×C3×C4—22no—
383C2×C3×C4—22no—
384C2×C3×C4—21no—
385C2×C3×C4—21no—
386C2×C3×C4—21no—
387C2×C3×C4—21no—
388C2×C3×C4—21no—
389C2×C3×C4—21no—
390C2×C3×C4—21no—
391C2×C3×C4—21no—
392C2×C3×C4—21no—
393C2×C3×C4—21no—
394C2×C3×C4—21no—
395C2×C3×C4—21no—
396C2×C3×C4—22no—
397C2×C3×C4—22no—
398C2×C3×C4—22no—
399C2×C3×C4—22no—
400C2×C3×C4—22no—
401C2×C3×C4—22no—
402C2×C3×C4—34no—
403C2×C3×C4—34no—
404C2×C3×C4—41no—
405C2×C3×C4—41no—
406C2×C3×C4—41no—
407C2×C3×C4—41no—
408C2×C3×C4—41no—
409C2×C3×C4—41no—
410C2×C3×C4—41no—
411C2×C3×C4—41no—
412C2×C3×C4—62no—
413C2×C3×C4—62no—
414C2×C3×C4—62no—
415C2×C3×C4—62no—
416C2×C3×C4—62no—
417C2×C3×C4—62no—
418C2×C3×C4—62no—
419C2×C3×C4—62no—
420C2×C3×C4—62no—
421C2×C3×C4—62no—
422C2×C3×C4C2×C4×D312yes—
423C2×C3×C4C2×C4×D312yes—
424C2×C3×C4#23512yes—
425C2×C3×C4C2×#6712yes—
426C2×C3×C4C2×#6712yes—
427C2×C3×C4C2×#6712yes—
428C2×C3×C4C22×C3×C412yes—
429C2×C3×C4C22×C3×C412yes—
430C2×C3×C4C2×C3×D412yes—
431C2×C3×C4C2×C3×D412yes—
432C2×C3×C4C2×C3×D412yes—
433C2×C3×C4C3×#4112yes—
434C2×Dic3—22no—
435C2×Dic3—22no—
436C2×Dic3—22no—
437C2×Dic3—22no—
438C2×Dic3—22no—
439C2×Dic3—22no—
440C2×Dic3—22no—
441C2×Dic3—22no—
442C2×Dic3—22no—
443C2×Dic3—22no—
444C2×Dic3C22×C3×C414yes—
445C2×Dic3C22×C3×C414yes—
446Dic6—28no—
447C2×C32—42no—
448C2×C32C2×C4×D411yescharacteristic
449C2×C32#51911yescharacteristic
450C2×C32#52011yescharacteristic
451C2×C32#53611yescharacteristic
452C2×C32#53711yescharacteristic
453C2×C32#54111yescharacteristic
454C2×C32#54211yescharacteristic
455C24C22×C3×D311yescharacteristic
456C2×Q8—34no—
457C2×Q8—62no—
458C2×Q8—62no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—32no—
462C22×C4—32no—
463C22×C4—32no—
464C22×C4—32no—
465C22×C4C3×C4×D314yes—
466C22×C4C22×C3×D311yescharacteristic
467C22×C4C22×C3×D311yescharacteristic
468C22×C4C22×C3×D311yescharacteristic
469C22×C4C22×C3×D311yescharacteristic
470C22×C4C22×C3×D311yescharacteristic
471C22×C4C22×C3×D311yescharacteristic
472C4⋊C4—22no—
473C4⋊C4—22no—
474C4⋊C4—38no—
475C4⋊C4—34no—
476C4⋊C4—62no—
477C4⋊C4—64no—
478C4⋊C4—62no—
479C4⋊C4—122no—
480C22⋊C4—22no—
481C22⋊C4—22no—
482C22⋊C4—38no—
483C22⋊C4—122no—
484C42—22no—
485C42—64no—
486C42—122no—
487C42C3×#6714yes—
488C22×C3—24no—
489C22×C3—22no—
490C22×C3—22no—
491C22×C3—22no—
492C22×C3—22no—
493C22×C3—22no—
494C22×C3—22no—
495C22×C3—21no—
496C22×C3—21no—
497C22×C3—21no—
498C22×C3—21no—
499C22×C3—21no—
500C22×C3—21no—
501C22×C3—21no—
502C22×C3—42no—
503C22×C3—42no—
504C22×C3—42no—
505C22×C3—42no—
506C22×C3—42no—
507C22×C3—42no—
508C22×C3—41no—
509C22×C3—41no—
510C22×C3—41no—
511C22×C3—41no—
512C22×C3—41no—
513C22×C3—41no—
514C22×C3—41no—
515C22×C3—41no—
516C22×C3C22×C4×D311yescharacteristic
517C22×C3C2×#23511yescharacteristic
518C22×C3#100911yescharacteristic
519C22×C3#101011yescharacteristic
520C22×C3#101011yescharacteristic
521C22×C3#101011yescharacteristic
522C22×C3C22×#6711yescharacteristic
523C22×C3C23×C3×C411yescharacteristic
524C22×C3C22×C3×D411yescharacteristic
525C22×C3C2×C3×#4111yescharacteristic
526C22×C3C3×H(5,𝔽2)11yescharacteristic
527C22×C3C3×2−1+411yescharacteristic
528C22×C3C3×2−1+411yescharacteristic
529C22×C3C3×2−1+411yescharacteristic
530C3×C4—24no—
531C3×C4—22no—
532C3×C4—22no—
533C3×C4—22no—
534C3×C4—22no—
535C3×C4—22no—
536C3×C4—22no—
537C3×C4—24no—
538C3×C4—42no—
539C3×C4—42no—
540C3×C4—42no—
541C3×C4—42no—
542C3×C4—41no—
543C3×C4—41no—
544C3×C4—41no—
545C3×C4—41no—
546C3×C4—64no—
547C3×C4—64no—
548C3×C4—122no—
549C3×C4—122no—
550C3×C4C4×#6714yes—
551C3×C4C3×C4×D414yes—
552Dic3—24no—
553Dic3—24no—
554Dic3—42no—
555Dic3—42no—
556C32#232311yescharacteristic, complemented, Sylow
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23C2×C3×C4×D312yes—
564C23C23×C3×D311yescharacteristic
565Q8—68no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—28no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—34no—
580C2×C4—34no—
581C2×C4—62no—
582C2×C4—62no—
583C2×C4—62no—
584C2×C4—62no—
585C2×C4—62no—
586C2×C4—62no—
587C2×C4—62no—
588C2×C4—62no—
589C2×C4—62no—
590C2×C4—62no—
591C2×C4C2×C3×C4×D312yes—
592C2×C4C2×C3×C4×D312yes—
593C2×C4C3×#23512yes—
594C2×C4C2×C3×#6712yes—
595C2×C4C2×C3×#6712yes—
596C2×C4C2×C3×#6712yes—
597C2×C3—21no—
598C2×C3—21no—
599C2×C3—21no—
600C2×C3—21no—
601C2×C3—21no—
602C2×C3—21no—
603C2×C3—21no—
604C2×C3—44no—
605C2×C3—42no—
606C2×C3—42no—
607C2×C3#551611yescharacteristic
608C2×C3#551811yescharacteristic
609C2×C3#552311yescharacteristic
610C2×C3#553411yescharacteristic
611C2×C3C2×C4×#6711yescharacteristic
612C2×C3#582511yescharacteristic
613C2×C3#583311yescharacteristic
614C2×C3C2×C3×C4×D411yescharacteristic
615C2×C3C3×#51911yescharacteristic
616C2×C3C3×#52011yescharacteristic
617C2×C3C3×#53611yescharacteristic
618C2×C3C3×#53711yescharacteristic
619C2×C3C3×#54111yescharacteristic
620C2×C3C3×#54211yescharacteristic
621C22—22no—
622C22—22no—
623C22—22no—
624C22—41no—
625C22—41no—
626C22—41no—
627C22—41no—
628C22C22×C3×C4×D311yescharacteristic
629C22C2×C3×#23511yescharacteristic
630C22C3×#100911yescharacteristic
631C22C3×#101011yescharacteristic
632C22C3×#101011yescharacteristic
633C22C3×#101011yescharacteristic
634C22C22×C3×#6711yescharacteristic
635C4—22no—
636C4—22no—
637C4—22no—
638C4—41no—
639C4—41no—
640C4—64no—
641C4—64no—
642C4—122no—
643C4—122no—
644C4C3×C4×#6714yes—
645C3—21no—
646C3#8223511yescharacteristic, direct product factor
647C3C3×#232311yescharacteristic, complemented
648C2—42no—
649C2C3×#551611yescharacteristic
650C2C3×#551811yescharacteristic
651C2C3×#552311yescharacteristic
652C2C3×#553411yescharacteristic
653C2C2×C3×C4×#6711yescharacteristic
654C2C3×#582511yescharacteristic
655C2C3×#583311yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC2×C32×#117C2
socleC23×C32C24
prime radicalC24×C32C23
cosocleC23×C3C24×C3
hypercenterC2×C3×#117D3
hypocenterC3C3×#2323
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×#117

Complements

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

NH ≅ G/Ntype
3. C2×C3×C4×Dic6C2semidirect
5. C3×#4978C2semidirect
6. C3×#4976C2semidirect
9. C3×C4×C4⋊Dic3C2semidirect
10. C3×#4929C2semidirect
11. C3×#4928C2semidirect
13. #82235C3direct (N × H)
28. C3×#924C4semidirect
46. C2×C4×Dic6C2×C3semidirect
56. #4978C2×C3semidirect
57. #4976C2×C3semidirect
60. C4×C4⋊Dic3C2×C3semidirect
61. #4929C2×C3semidirect
62. #4928C2×C3semidirect
140. #924C3×C4semidirect
556. C32#2323semidirect
646. C3#82235direct (N × H)
647. C3C3×#2323semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1172
C2×C3×#9242
C2×C3×C4×Dic62
C3×#52122
C3×#49782
C3×#49762
C3×#49452
C3×#49442
C3×C4×C4⋊Dic32
C3×#49292
C3×#49282
C3×#23233
#822353