Finite Group Databasebeta

← #11805853

Subgroups — #11805853

Order 1152.

1429 conjugacy classes of subgroups.

The subgroup lattice has 707 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64135C211yesmaximal, characteristic, complemented
2C2×C3×C4×#67C211yesmaximal, characteristic
3C2×#63841C211yesmaximal, characteristic, complemented
4C3×#5212C211yesmaximal, characteristic, complemented
5#10591707C212yesmaximal
6#10591702C212yesmaximal, complemented
7#10591349C211yesmaximal, characteristic, complemented
8#10591313C211yesmaximal, characteristic, complemented
9#10591286C212yesmaximal, complemented
10Dic3×C4⋊Dic3C211yesmaximal, characteristic, complemented
11#10591241C212yesmaximal, complemented
12#82337—31nomaximal
13#73885—31nomaximal
14C23×C32×C4C2211yescharacteristic
15C22×C3×#67C2211yescharacteristic
16C22×C3×C4×D3C2211yescharacteristic
17C2×#3757C2212yes—
18#64135—24no—
19C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
20C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
21C2×C4×C3⋊Dic3C2212yes—
22C2×C3×#217C2212yes—
23C2×C3×#217C2211yescharacteristic
24C3×C4×#67C418yescomplemented
25C2×C3×(C2×D3)⋊C4C2211yescharacteristic
26C2×C3×C4⋊Dic3C2211yescharacteristic
27C2×C3×C4⋊Dic3C2211yescharacteristic
28C2×C3×Dic3⋊C4C2211yescharacteristic
29C2×C3×C4×Dic3C2211yescharacteristic
30C2×Dic3⋊Dic3C2212yes—
31C2×Dic3⋊Dic3C2212yes—
32C2×(C2×D3)⋊Dic3C2212yes—
33C2×(C2×D3)⋊Dic3C2212yes—
34C2×Dic32C2212yes—
35C2×Dic32C2212yes—
36#63841—24no—
37C3×C3⋊#95C2212yes—
38#63579C2212yes—
39#63579C2212yes—
40C2×C3×C4×D4—31no—
41C2×C4×#67D311yescharacteristic
42C2×#926—31no—
43C2×#926—31no—
44C2×#926—31no—
45C2×#926—61no—
46C2×#892—31no—
47C3×#380—31no—
48#5221—32no—
49#5212—31no—
50#5212D311yescharacteristic, complemented
51#4987—31no—
52#4975—31no—
53Dic3×C4⋊C4—31no—
54Dic3×C4⋊C4—32no—
55#4957—32no—
56#4951—32no—
57#4951—32no—
58#4945—32no—
59#4935—31no—
60C4×C4⋊Dic3—31no—
61#4669—32no—
62#4649—32no—
63C24×C32C2311yescharacteristic
64C23×C3×D3C2311yescharacteristic
65C22×C32×C4—22no—
66C22×C32×C4—22no—
67C22×C32×C4C2×C414yes—
68C22×C32×C4C2311yescharacteristic
69C22×C32×C4C2311yescharacteristic
70C22×C3⋊Dic3C2312yes—
71C22×C3⋊Dic3C2312yes—
72C2×C3×#67—22no—
73C2×C3×#67—22no—
74C2×C3×#67C2×C414yes—
75C22×C3×Dic3C2312yes—
76C22×C3×Dic3C2312yes—
77C22×C3×Dic3C2311yescharacteristic
78C22×C3×Dic3C2311yescharacteristic
79C22×C3×Dic3C2311yescharacteristic
80C2×C3×C4×D3—22no—
81C2×C3×C4×D3—22no—
82C2×C3×C4×D3C2×C414yes—
83#3757—24no—
84C4⋊(C3⋊Dic3)—22no—
85C4⋊(C3⋊Dic3)D414yescomplemented
86C4×C3⋊Dic3—24no—
87C3×#217—42no—
88C3×#217C2×C414yes—
89C3×(C2×D3)⋊C4C2×C414yes—
90C3×C4⋊Dic3—22no—
91C3×C4⋊Dic3—22no—
92C3×Dic3⋊C4C2×C414yes—
93C3×C4×Dic3C2×C414yes—
94Dic3⋊Dic3—24no—
95Dic3⋊Dic3—42no—
96(C2×D3)⋊Dic3—24no—
97(C2×D3)⋊Dic3—42no—
98Dic32—24no—
99Dic32—24no—
100#2354—91noSylow
101C22×C3×D4—31no—
102C23×C3×C4—21no—
103C23×C3×C4—31no—
104C23×C3×C4C2×D311yescharacteristic
105C23×C3×C4C2×D311yescharacteristic
106C22×#67C2×D311yescharacteristic
107C22×C4×D3C2×D311yescharacteristic
108C3×C4×D4—38no—
109C2×C3×C4⋊C4—31no—
110C2×C3×C4⋊C4—31no—
111C2×C3×C4⋊C4—31no—
112C2×C3×C22⋊C4—31no—
113C2×C3×C22⋊C4—31no—
114C2×C3×C22⋊C4—32no—
115C2×C3×C42—31no—
116C2×#217—32no—
117C2×#217—32no—
118C2×#217—32no—
119C2×#217—32no—
120C2×#217—62no—
121C2×#217C2×D312yes—
122C2×#217C2×D311yescharacteristic
123C4×#67Dic318yescomplemented
124C2×(C2×D3)⋊C4—32no—
125C2×(C2×D3)⋊C4—32no—
126C2×(C2×D3)⋊C4C2×D311yescharacteristic
127#926—64no—
128#926—64no—
129#926—64no—
130#926—68no—
131C2×C4⋊Dic3—31no—
132C2×C4⋊Dic3—31no—
133C2×C4⋊Dic3—31no—
134C2×C4⋊Dic3—31no—
135C2×C4⋊Dic3—32no—
136C2×C4⋊Dic3—32no—
137C2×C4⋊Dic3—61no—
138C2×C4⋊Dic3—61no—
139C2×C4⋊Dic3C2×D311yescharacteristic
140C2×C4⋊Dic3C2×D311yescharacteristic
141C2×Dic3⋊C4—32no—
142C2×Dic3⋊C4—32no—
143C2×Dic3⋊C4C2×D311yescharacteristic
144C2×C4×Dic3—32no—
145C2×C4×Dic3—32no—
146C2×C4×Dic3—32no—
147C2×C4×Dic3—32no—
148C2×C4×Dic3—32no—
149C2×C4×Dic3—32no—
150C2×C4×Dic3—62no—
151C2×C4×Dic3C2×D311yescharacteristic
152#892—64no—
153C3×#95—32no—
154C3⋊#95—32no—
155C3⋊#95—32no—
156C3⋊#95—32no—
157C3⋊#95—32no—
158C3⋊#95C2×D312yes—
159C23×C32—21no—
160C23×C32—21no—
161C23×C32—21no—
162C23×C32—21no—
163C23×C32—21no—
164C23×C32—21no—
165C23×C32C22×C412yes—
166C23×C32C2411yescharacteristic
167C22×C3×D3—21no—
168C22×C3×D3—21no—
169C22×C3×D3—21no—
170C22×C3×D3—21no—
171C22×C3×D3—21no—
172C22×C3×D3—21no—
173C22×C3×D3C22×C412yes—
174C2×C32×C4—21no—
175C2×C32×C4—21no—
176C2×C32×C4—28no—
177C2×C32×C4C22×C412yes—
178C2×C32×C4C22×C412yes—
179C2×C32×C4C2×D412yes—
180C2×C32×C4#4112yes—
181C2×C3⋊Dic3—22no—
182C2×C3⋊Dic3—22no—
183C2×C3⋊Dic3—22no—
184C2×C3⋊Dic3—22no—
185C2×C3⋊Dic3—22no—
186C2×C3⋊Dic3C2×D414yes—
187C3×#67—28no—
188C2×C3×Dic3—21no—
189C2×C3×Dic3—21no—
190C2×C3×Dic3—21no—
191C2×C3×Dic3—21no—
192C2×C3×Dic3—22no—
193C2×C3×Dic3—22no—
194C2×C3×Dic3—22no—
195C2×C3×Dic3—22no—
196C2×C3×Dic3—22no—
197C2×C3×Dic3—22no—
198C2×C3×Dic3C22×C412yes—
199C2×C3×Dic3C22×C412yes—
200C2×C3×Dic3C22×C412yes—
201C2×C3×Dic3#4112yes—
202C2×C3×Dic3#4112yes—
203C3×C4×D3—28no—
204C2×C4×D4—31no—
205C2×#117—91no—
206C2×#117—91no—
207#390—92no—
208#388—92no—
209#388—92no—
210#384—91no—
211#380—31no—
212#380—91no—
213C4×C4⋊C4—92no—
214C4×C4⋊C4—91no—
215C24×C3—21no—
216C24×C3—31no—
217C24×C3C22×D311yescharacteristic
218C24×C3C22×D311yescharacteristic
219C23×D3C22×D311yescharacteristic
220C2×C3×D4—34no—
221C2×C3×D4—62no—
222C2×C3×D4—62no—
223C22×C3×C4—24no—
224C22×C3×C4—24no—
225C22×C3×C4—22no—
226C22×C3×C4—22no—
227C22×C3×C4—22no—
228C22×C3×C4—22no—
229C22×C3×C4—24no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—31no—
233C22×C3×C4—31no—
234C22×C3×C4—31no—
235C22×C3×C4—34no—
236C22×C3×C4—32no—
237C22×C3×C4—32no—
238C22×C3×C4—62no—
239C22×C3×C4—62no—
240C22×C3×C4C4×D314yes—
241C22×C3×C4C2×Dic314yes—
242C22×C3×C4C22×D311yescharacteristic
243C22×C3×C4C22×D311yescharacteristic
244C22×C3×C4C22×D311yescharacteristic
245C22×C3×C4C22×D311yescharacteristic
246C2×#67—22no—
247C2×#67—22no—
248C2×#67C2×Dic314yes—
249C22×Dic3—32no—
250C22×Dic3—32no—
251C22×Dic3—32no—
252C22×Dic3—32no—
253C22×Dic3—62no—
254C22×Dic3—62no—
255C22×Dic3C22×D312yes—
256C22×Dic3C22×D312yes—
257C22×Dic3C22×D311yescharacteristic
258C22×Dic3C22×D311yescharacteristic
259C22×Dic3C22×D311yescharacteristic
260C2×C4×D3—22no—
261C2×C4×D3—22no—
262C2×C4×D3C2×Dic314yes—
263C3×C4⋊C4—34no—
264C3×C4⋊C4—62no—
265C3×C4⋊C4—62no—
266C3×C22⋊C4—34no—
267C3×C22⋊C4—34no—
268C3×C22⋊C4—122no—
269C3×C42—34no—
270#217—42no—
271#217—64no—
272#217—64no—
273#217—64no—
274#217—68no—
275#217—122no—
276#217C2×Dic314yes—
277(C2×D3)⋊C4—64no—
278(C2×D3)⋊C4—122no—
279(C2×D3)⋊C4C2×Dic314yes—
280C4⋊Dic3—22no—
281C4⋊Dic3—22no—
282C4⋊Dic3—34no—
283C4⋊Dic3—34no—
284C4⋊Dic3—64no—
285C4⋊Dic3—64no—
286C4⋊Dic3—64no—
287C4⋊Dic3—62no—
288C4⋊Dic3—62no—
289C4⋊Dic3—122no—
290Dic3⋊C4—64no—
291Dic3⋊C4—122no—
292Dic3⋊C4C2×Dic314yes—
293C4×Dic3—64no—
294C4×Dic3—64no—
295C4×Dic3—64no—
296C4×Dic3—64no—
297C4×Dic3—64no—
298C4×Dic3—68no—
299C4×Dic3—64no—
300C4×Dic3C2×Dic314yes—
301C22×C32—22no—
302C22×C32—22no—
303C22×C32—22no—
304C22×C32—41no—
305C22×C32—41no—
306C22×C32—41no—
307C22×C32—41no—
308C22×C32C23×C411yescharacteristic
309C22×C32C22×D411yescharacteristic
310C22×C32C2×#4111yescharacteristic
311C22×C32C2×#4111yescharacteristic
312C22×C32C2×#4111yescharacteristic
313C22×C32H(5,𝔽2)11yescharacteristic
314C22×C322−1+411yescharacteristic
315C2×C3×D3—22no—
316C2×C3×D3—22no—
317C2×C3×D3—22no—
318C2×C3×D3—41no—
319C2×C3×D3—41no—
320C2×C3×D3—41no—
321C2×C3×D3—41no—
322C32×C4—22no—
323C32×C4C4×D414yes—
324C3⋊Dic3—24no—
325C3⋊Dic3—42no—
326C3×Dic3—22no—
327C3×Dic3—22no—
328C3×Dic3—42no—
329C3×Dic3—42no—
330C3×Dic3#11714yescomplemented
331C22×D4—31no—
332C23×C4—31no—
333C23×C4D3211yescharacteristic
334C4×D4—38no—
335#117—184no—
336#117—184no—
337C2×C4⋊C4—31no—
338C2×C4⋊C4—31no—
339C2×C4⋊C4—31no—
340C2×C4⋊C4—91no—
341C2×C4⋊C4—92no—
342C2×C4⋊C4—91no—
343C2×C4⋊C4—92no—
344C2×C22⋊C4—31no—
345C2×C22⋊C4—31no—
346C2×C22⋊C4—32no—
347C2×C22⋊C4—92no—
348C2×C22⋊C4—92no—
349C2×C22⋊C4—92no—
350C2×C42—31no—
351C2×C42—92no—
352C2×C42—92no—
353C2×C42—92no—
354#95—32no—
355#95—92no—
356#95—92no—
357C23×C3—22no—
358C23×C3—22no—
359C23×C3—21no—
360C23×C3—21no—
361C23×C3—21no—
362C23×C3—21no—
363C23×C3—21no—
364C23×C3—21no—
365C23×C3—21no—
366C23×C3—21no—
367C23×C3—21no—
368C23×C3—21no—
369C23×C3—21no—
370C23×C3—21no—
371C23×C3—21no—
372C23×C3—22no—
373C23×C3—32no—
374C23×C3—41no—
375C23×C3—41no—
376C23×C3—41no—
377C23×C3—41no—
378C23×C3—61no—
379C23×C3—61no—
380C23×C3—61no—
381C23×C3—61no—
382C23×C3—61no—
383C23×C3—61no—
384C23×C3C2×C4×D312yes—
385C23×C3C22×Dic312yes—
386C23×C3C23×D311yescharacteristic
387C23×C3C23×D311yescharacteristic
388C22×D3—21no—
389C22×D3—21no—
390C22×D3—21no—
391C22×D3—21no—
392C22×D3—21no—
393C22×D3—21no—
394C22×D3C22×Dic312yes—
395C3×D4—68no—
396C2×C3×C4—22no—
397C2×C3×C4—22no—
398C2×C3×C4—216no—
399C2×C3×C4—21no—
400C2×C3×C4—21no—
401C2×C3×C4—21no—
402C2×C3×C4—21no—
403C2×C3×C4—28no—
404C2×C3×C4—28no—
405C2×C3×C4—22no—
406C2×C3×C4—22no—
407C2×C3×C4—22no—
408C2×C3×C4—22no—
409C2×C3×C4—32no—
410C2×C3×C4—32no—
411C2×C3×C4—32no—
412C2×C3×C4—32no—
413C2×C3×C4—32no—
414C2×C3×C4—61no—
415C2×C3×C4—61no—
416C2×C3×C4—61no—
417C2×C3×C4—61no—
418C2×C3×C4—68no—
419C2×C3×C4—62no—
420C2×C3×C4—62no—
421C2×C3×C4—62no—
422C2×C3×C4—62no—
423C2×C3×C4—62no—
424C2×C3×C4—62no—
425C2×C3×C4C2×C4×D312yes—
426C2×C3×C4C2×C4×D312yes—
427C2×C3×C4D3×D412yes—
428C2×C3×C4D3×D412yes—
429C2×C3×C4#23712yes—
430C2×C3×C4#23712yes—
431C2×C3×C4C22×Dic312yes—
432C2×C3×C4C22×Dic312yes—
433#67—28no—
434C2×Dic3—21no—
435C2×Dic3—21no—
436C2×Dic3—21no—
437C2×Dic3—21no—
438C2×Dic3—22no—
439C2×Dic3—22no—
440C2×Dic3—22no—
441C2×Dic3—22no—
442C2×Dic3—22no—
443C2×Dic3—22no—
444C2×Dic3—34no—
445C2×Dic3—34no—
446C2×Dic3—64no—
447C2×Dic3—62no—
448C2×Dic3—62no—
449C2×Dic3—62no—
450C2×Dic3—62no—
451C2×Dic3—64no—
452C2×Dic3—62no—
453C2×Dic3—62no—
454C2×Dic3—62no—
455C2×Dic3—62no—
456C2×Dic3—62no—
457C2×Dic3—62no—
458C2×Dic3—122no—
459C2×Dic3—122no—
460C2×Dic3—122no—
461C2×Dic3—122no—
462C2×Dic3#23512yes—
463C2×Dic3#23512yes—
464C2×Dic3C22×Dic312yes—
465C2×Dic3C22×Dic312yes—
466C2×Dic3C22×Dic312yes—
467C4×D3—28no—
468C2×C32—42no—
469C2×C32C2×#11711yescharacteristic
470C2×C32C2×C4×D411yescharacteristic
471C2×C32#52011yescharacteristic
472C2×C32#54711yescharacteristic
473C2×C32#55011yescharacteristic
474C2×C32#55511yescharacteristic
475C2×C32#55611yescharacteristic
476C3×D3—42no—
477C24—31no—
478C24C2×D3211yescharacteristic
479C2×D4—34no—
480C2×D4—62no—
481C2×D4—62no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—31no—
485C22×C4—31no—
486C22×C4—31no—
487C22×C4—34no—
488C22×C4—32no—
489C22×C4—32no—
490C22×C4—62no—
491C22×C4—62no—
492C22×C4—92no—
493C22×C4—92no—
494C22×C4D3×Dic314yes—
495C22×C4C2×D3211yescharacteristic
496C22×C4C2×D3211yescharacteristic
497C4⋊C4—34no—
498C4⋊C4—62no—
499C4⋊C4—62no—
500C4⋊C4—94no—
501C4⋊C4—184no—
502C4⋊C4—182no—
503C4⋊C4—362no—
504C22⋊C4—34no—
505C22⋊C4—34no—
506C22⋊C4—122no—
507C22⋊C4—184no—
508C22⋊C4—184no—
509C22⋊C4—362no—
510C42—34no—
511C42—184no—
512C42—184no—
513C42—184no—
514C22×C3—24no—
515C22×C3—22no—
516C22×C3—22no—
517C22×C3—22no—
518C22×C3—22no—
519C22×C3—22no—
520C22×C3—22no—
521C22×C3—21no—
522C22×C3—21no—
523C22×C3—21no—
524C22×C3—21no—
525C22×C3—21no—
526C22×C3—21no—
527C22×C3—21no—
528C22×C3—42no—
529C22×C3—42no—
530C22×C3—42no—
531C22×C3—42no—
532C22×C3—42no—
533C22×C3—42no—
534C22×C3—41no—
535C22×C3—41no—
536C22×C3—41no—
537C22×C3—41no—
538C22×C3—41no—
539C22×C3—41no—
540C22×C3—41no—
541C22×C3—41no—
542C22×C3—62no—
543C22×C3—62no—
544C22×C3—62no—
545C22×C3—121no—
546C22×C3—121no—
547C22×C3—121no—
548C22×C3—121no—
549C22×C3C22×C4×D311yescharacteristic
550C22×C3C2×#23511yescharacteristic
551C22×C3C2×#23511yescharacteristic
552C22×C3C2×D3×D411yescharacteristic
553C22×C3C2×D3×D411yescharacteristic
554C22×C3C2×#23711yescharacteristic
555C22×C3C2×#23711yescharacteristic
556C22×C3#100411yescharacteristic
557C22×C3#100711yescharacteristic
558C22×C3D3×#4111yescharacteristic
559C22×C3D3×#4111yescharacteristic
560C22×C3#100911yescharacteristic
561C22×C3#101011yescharacteristic
562C22×C3C23×Dic311yescharacteristic
563C2×D3—22no—
564C2×D3—22no—
565C2×D3—22no—
566C2×D3—41no—
567C2×D3—41no—
568C2×D3—41no—
569C2×D3—41no—
570C3×C4—24no—
571C3×C4—22no—
572C3×C4—22no—
573C3×C4—24no—
574C3×C4—34no—
575C3×C4—62no—
576C3×C4—62no—
577C3×C4—122no—
578C3×C4—122no—
579C3×C4#67⋊C414yes—
580C3×C4D4×Dic314yes—
581Dic3—22no—
582Dic3—22no—
583Dic3—42no—
584Dic3—42no—
585Dic3—64no—
586Dic3—64no—
587Dic3—124no—
588Dic3—124no—
589Dic3—122no—
590Dic3—122no—
591Dic3#92614yescomplemented
592C32#235411yescharacteristic, complemented, Sylow
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—32no—
600C23—61no—
601C23—61no—
602C23—61no—
603C23—61no—
604C23—61no—
605C23—61no—
606C23C2×D3×Dic312yes—
607C23C22×D3211yescharacteristic
608D4—68no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—28no—
612C2×C4—32no—
613C2×C4—32no—
614C2×C4—32no—
615C2×C4—32no—
616C2×C4—32no—
617C2×C4—61no—
618C2×C4—61no—
619C2×C4—61no—
620C2×C4—61no—
621C2×C4—68no—
622C2×C4—62no—
623C2×C4—62no—
624C2×C4—62no—
625C2×C4—62no—
626C2×C4—62no—
627C2×C4—62no—
628C2×C4—94no—
629C2×C4—182no—
630C2×C4—182no—
631C2×C4—182no—
632C2×C4—182no—
633C2×C4—182no—
634C2×C4C2×D3×Dic312yes—
635C2×C4C2×D3×Dic312yes—
636C2×C4#380512yes—
637C2×C4#381112yes—
638C2×C3—21no—
639C2×C3—21no—
640C2×C3—21no—
641C2×C3—21no—
642C2×C3—21no—
643C2×C3—21no—
644C2×C3—21no—
645C2×C3—44no—
646C2×C3—42no—
647C2×C3—42no—
648C2×C3—122no—
649C2×C3C2×#67⋊C411yescharacteristic
650C2×C3#550411yescharacteristic
651C2×C3D3×#11711yescharacteristic
652C2×C3#554211yescharacteristic
653C2×C3#555111yescharacteristic
654C2×C3#555311yescharacteristic
655C2×C3#556311yescharacteristic
656C2×C3#559911yescharacteristic
657C2×C3#561611yescharacteristic
658C2×C3#563111yescharacteristic
659C2×C3#564111yescharacteristic
660C2×C3C2×#92611yescharacteristic
661C2×C3C2×D4×Dic311yescharacteristic
662C2×C3#582711yescharacteristic
663D3—42no—
664C22—22no—
665C22—22no—
666C22—22no—
667C22—41no—
668C22—41no—
669C22—41no—
670C22—41no—
671C22—62no—
672C22—62no—
673C22—62no—
674C22—121no—
675C22—121no—
676C22—121no—
677C22—121no—
678C22#6429711yescharacteristic
679C22D3×#23511yescharacteristic
680C22D3×#23511yescharacteristic
681C22#6430711yescharacteristic
682C22C22×D3×Dic311yescharacteristic
683C22C2×#380511yescharacteristic
684C22C2×#381111yescharacteristic
685C4—22no—
686C4—34no—
687C4—62no—
688C4—62no—
689C4—122no—
690C4—122no—
691C4—184no—
692C4—362no—
693C4#67⋊Dic314yes—
694C3—21no—
695C3#7388511yescharacteristic, complemented
696C3#8233711yescharacteristic, complemented
697C2—42no—
698C2—122no—
699C2#1059483411yescharacteristic
700C2#1059484111yescharacteristic
701C2#1059491911yescharacteristic
702C2D3×#92611yescharacteristic
703C2#1059498611yescharacteristic
704C2#1059502611yescharacteristic
705C2C2×#67⋊Dic311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC22×C3×#67C22
hypercenterC23×C4D32
hypocenterC32#2354
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C2×#64135C2semidirect
3. C2×#63841C2semidirect
4. C3×#5212C2semidirect
6. #10591702C2semidirect
7. #10591349C2semidirect
8. #10591313C2semidirect
9. #10591286C2semidirect
10. Dic3×C4⋊Dic3C2semidirect
11. #10591241C2semidirect
24. C3×C4×#67C4semidirect
50. #5212D3semidirect
85. C4⋊(C3⋊Dic3)D4semidirect
123. C4×#67Dic3semidirect
330. C3×Dic3#117semidirect
591. Dic3#926semidirect
592. C32#2354semidirect
695. C3#73885semidirect
696. C3#82337semidirect

Maximal subgroups

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

subgroupindex
C2×#641352
C2×C3×C4×#672
C2×#638412
C3×#52122
#105917072
#105917022
#105913492
#105913132
#105912862
Dic3×C4⋊Dic32
#105912412
#823373
#738853