Finite Group Databasebeta

← #11800863

Subgroups — #11800863

Order 1152.

1953 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×C22⋊C4C211yesmaximal, characteristic
2C2×D3×#217C211yesmaximal, characteristic
3C22×(C2×D3)⋊Dic3C211yesmaximal, characteristic
4C22⋊C4×C3⋊Dic3C211yesmaximal, characteristic, complemented
5C3×Dic3×C22⋊C4C211yesmaximal, characteristic, complemented
6#10591705C211yesmaximal, characteristic, complemented
7Dic3×#217C211yesmaximal, characteristic, complemented
8#10591368C212yesmaximal, complemented
9Dic3×(C2×D3)⋊C4C212yesmaximal, complemented
10C4×(C2×D3)⋊Dic3C212yesmaximal, complemented
11#10591237C212yesmaximal, complemented
12#82083—31nomaximal
13#73560—31nomaximal
14C24×C3×D3C2211yescharacteristic
15C23×C3⋊Dic3C2211yescharacteristic
16C23×C3×Dic3C2211yescharacteristic
17C22×C3×C4×D3C2212yes—
18C22×D3×Dic3C2212yes—
19C2×C32×C22⋊C4C2211yescharacteristic
20C2×#3757C2211yescharacteristic
21C2×C4×C3⋊Dic3C2212yescomplemented
22C2×C3×#217C2211yescharacteristic
23C2×C3×#217C2211yescharacteristic
24C2×C3×(C2×D3)⋊C4C2212yes—
25C2×C3×C4×Dic3C2212yescomplemented
26C3×D3×C22⋊C4C418yescomplemented
27D3×#217C418yescomplemented
28C2×(C2×D3)⋊Dic3C418yescomplemented
29C2×(C2×D3)⋊Dic3C2211yescharacteristic
30C2×(C2×D3)⋊Dic3C2212yes—
31C2×(C2×D3)⋊Dic3C2211yescharacteristic
32C2×(C2×D3)⋊Dic3C2211yescharacteristic
33C2×(C2×D3)⋊Dic3C2211yescharacteristic
34C2×Dic32C2212yescomplemented
35C2×Dic32C2212yescomplemented
36#63658C2212yescomplemented
37C3×C3⋊#95C2212yescomplemented
38#63579C2212yescomplemented
39#63579C2212yescomplemented
40C22×C3×C22⋊C4—31no—
41C22×#217—31no—
42C22×#217—31no—
43C22×(C2×D3)⋊C4—31no—
44C2×D3×C22⋊C4—31no—
45C2×D3×C22⋊C4D311yescharacteristic
46C3×C4×C22⋊C4—31no—
47C4×#217—31no—
48C4×#217—32no—
49C4×#217—32no—
50Dic3×C22⋊C4—31no—
51Dic3×C22⋊C4—31no—
52Dic3×C22⋊C4—31no—
53Dic3×C22⋊C4—31no—
54Dic3×C22⋊C4—31no—
55Dic3×C22⋊C4—32no—
56Dic3×C22⋊C4—32no—
57Dic3×C22⋊C4—61no—
58Dic3×C22⋊C4D311yescharacteristic, complemented
59C4×(C2×D3)⋊C4—32no—
60C4×(C2×D3)⋊C4—32no—
61#4666—32no—
62#4666—32no—
63C24×C32C2311yescharacteristic
64C23×C3×D3—42no—
65C23×C3×D3—42no—
66C23×C3×D3C2×C414yes—
67C23×C3×D3C2×C414yes—
68C23×C3×D3C2×C414yes—
69C23×C3×D3C2311yescharacteristic
70C23×C3×D3C2311yescharacteristic
71C22×C32×C4C2312yes—
72C22×C3⋊Dic3—42no—
73C22×C3⋊Dic3C2×C414yescomplemented
74C22×C3⋊Dic3C2312yes—
75C22×C3⋊Dic3C2311yescharacteristic
76C22×C3⋊Dic3C2311yescharacteristic
77C22×C3×Dic3—42no—
78C22×C3×Dic3C2×C414yescomplemented
79C22×C3×Dic3C2311yescharacteristic
80C22×C3×Dic3C2312yes—
81C22×C3×Dic3C2312yes—
82C22×C3×Dic3C2311yescharacteristic
83C2×C3×C4×D3—42no—
84C2×C3×C4×D3—42no—
85C2×C3×C4×D3C2×C418yescomplemented
86C2×D3×Dic3—42no—
87C2×D3×Dic3—42no—
88C2×D3×Dic3C2×C418yescomplemented
89C32×C22⋊C4C2×C414yescomplemented
90#3757C2×C414yescomplemented
91C4×C3⋊Dic3—42no—
92C3×#217C2×C414yescomplemented
93C3×#217C2×C414yescomplemented
94C3×(C2×D3)⋊C4C2×C418yescomplemented
95C3×C4×Dic3—42no—
96(C2×D3)⋊Dic3C2×C414yescomplemented
97(C2×D3)⋊Dic3C2×C414yescomplemented
98(C2×D3)⋊Dic3C2×C414yescomplemented
99(C2×D3)⋊Dic3C2×C414yescomplemented
100(C2×D3)⋊Dic3C2×C418yescomplemented
101Dic32—42no—
102Dic32—42no—
103#2273—91noSylow
104C25×C3—31no—
105C24×D3C2×D311yescharacteristic
106C23×C3×C4—31no—
107C23×C3×C4—32no—
108C23×Dic3—31no—
109C23×Dic3—31no—
110C23×Dic3—32no—
111C23×Dic3—61no—
112C23×Dic3C2×D311yescharacteristic
113C22×C4×D3—32no—
114C22×C4×D3C2×D312yes—
115C2×C3×C22⋊C4—21no—
116C2×C3×C22⋊C4—31no—
117C2×C3×C22⋊C4—31no—
118C2×C3×C22⋊C4—32no—
119C2×C3×C22⋊C4—38no—
120C2×C3×C22⋊C4C2×D311yescharacteristic
121C2×C3×C22⋊C4C2×D311yescharacteristic
122C2×C3×C42—32no—
123C2×#217—31no—
124C2×#217—31no—
125C2×#217—38no—
126C2×#217—31no—
127C2×#217—31no—
128C2×#217—31no—
129C2×#217—32no—
130C2×#217—31no—
131C2×#217—38no—
132C2×#217—61no—
133C2×#217C2×D311yescharacteristic
134C2×#217C2×D311yescharacteristic
135C2×(C2×D3)⋊C4—38no—
136C2×(C2×D3)⋊C4—31no—
137C2×(C2×D3)⋊C4—31no—
138C2×(C2×D3)⋊C4—32no—
139C2×(C2×D3)⋊C4—31no—
140C2×(C2×D3)⋊C4—31no—
141C2×(C2×D3)⋊C4C2×D312yes—
142C2×C4×Dic3—32no—
143C2×C4×Dic3—32no—
144C2×C4×Dic3—32no—
145C2×C4×Dic3—32no—
146C2×C4×Dic3—32no—
147C2×C4×Dic3—32no—
148C2×C4×Dic3—62no—
149C2×C4×Dic3C2×D312yescomplemented
150D3×C22⋊C4—38no—
151D3×C22⋊C4Dic318yescomplemented
152C3×#95—32no—
153C3⋊#95—32no—
154C3⋊#95—32no—
155C3⋊#95—32no—
156C3⋊#95—32no—
157C3⋊#95—32no—
158C3⋊#95—32no—
159C3⋊#95—62no—
160C3⋊#95C2×D312yescomplemented
161C23×C32—22no—
162C23×C32—22no—
163C23×C32C22×C412yes—
164C23×C32C22×C412yes—
165C23×C32C22×C412yes—
166C23×C32C2411yescharacteristic
167C22×C3×D3—22no—
168C22×C3×D3—22no—
169C22×C3×D3—22no—
170C22×C3×D3—22no—
171C22×C3×D3—48no—
172C22×C3×D3—44no—
173C22×C3×D3—44no—
174C22×C3×D3—48no—
175C22×C3×D3C42116yescomplemented
176C22×C3×D3C22×C412yes—
177C22×C3×D3C22×C412yes—
178C22×C3×D3C22×C412yes—
179C22×C3×D3C22×C412yes—
180C22×C3×D3C22×C412yes—
181C22×C3×D3C22×C412yes—
182C2×C32×C4—22no—
183C2×C32×C4—22no—
184C2×C32×C4C22×C414yes—
185C2×C3⋊Dic3—22no—
186C2×C3⋊Dic3—22no—
187C2×C3⋊Dic3—22no—
188C2×C3⋊Dic3—22no—
189C2×C3⋊Dic3—44no—
190C2×C3⋊Dic3C22×C412yes—
191C2×C3⋊Dic3C22×C412yes—
192C2×C3⋊Dic3C22×C414yes—
193C2×C3×Dic3—22no—
194C2×C3×Dic3—22no—
195C2×C3×Dic3—22no—
196C2×C3×Dic3—22no—
197C2×C3×Dic3—22no—
198C2×C3×Dic3—22no—
199C2×C3×Dic3—44no—
200C2×C3×Dic3C22×C412yes—
201C2×C3×Dic3C22×C412yes—
202C2×C3×Dic3C22×C414yes—
203C2×C3×Dic3C22×C414yes—
204C3×C4×D3—48no—
205D3×Dic3—48no—
206C22×C22⋊C4—31no—
207C22×C22⋊C4—91no—
208C22×C22⋊C4—91no—
209C4×C22⋊C4—31no—
210C4×C22⋊C4—92no—
211C4×C22⋊C4—92no—
212C4×C22⋊C4—92no—
213C4×C22⋊C4—92no—
214C4×C22⋊C4—91no—
215C4×C22⋊C4—91no—
216C4×C22⋊C4—91no—
217C24×C3—21no—
218C24×C3—31no—
219C24×C3—31no—
220C24×C3—34no—
221C24×C3—34no—
222C24×C3—34no—
223C24×C3—122no—
224C24×C3—122no—
225C24×C3C22×D311yescharacteristic
226C24×C3C22×D311yescharacteristic
227C23×D3—42no—
228C23×D3—42no—
229C23×D3C4×D314yes—
230C23×D3C4×D314yes—
231C23×D3C2×Dic314yes—
232C23×D3C22×D311yescharacteristic
233C23×D3C22×D311yescharacteristic
234C22×C3×C4—22no—
235C22×C3×C4—32no—
236C22×C3×C4—31no—
237C22×C3×C4—32no—
238C22×C3×C4—31no—
239C22×C3×C4—34no—
240C22×C3×C4—38no—
241C22×C3×C4—122no—
242C22×C3×C4—122no—
243C22×C3×C4—122no—
244C22×C3×C4C22×D312yes—
245C22×C3×C4C22×D312yes—
246C22×Dic3—31no—
247C22×Dic3—31no—
248C22×Dic3—32no—
249C22×Dic3—32no—
250C22×Dic3—31no—
251C22×Dic3—31no—
252C22×Dic3—34no—
253C22×Dic3—34no—
254C22×Dic3—38no—
255C22×Dic3—42no—
256C22×Dic3—61no—
257C22×Dic3—61no—
258C22×Dic3—62no—
259C22×Dic3—64no—
260C22×Dic3—122no—
261C22×Dic3—122no—
262C22×Dic3—122no—
263C22×Dic3—122no—
264C22×Dic3—124no—
265C22×Dic3C4×D314yescomplemented
266C22×Dic3C22×D311yescharacteristic
267C22×Dic3C22×D312yes—
268C22×Dic3C22×D311yescharacteristic
269C22×Dic3C22×D312yes—
270C2×C4×D3—38no—
271C2×C4×D3—42no—
272C2×C4×D3—42no—
273C2×C4×D3—122no—
274C2×C4×D3—122no—
275C2×C4×D3C2×Dic318yescomplemented
276C3×C22⋊C4—24no—
277C3×C22⋊C4—34no—
278C3×C22⋊C4—34no—
279C3×C22⋊C4—38no—
280C3×C22⋊C4C4×D314yescomplemented
281C3×C22⋊C4C2×Dic314yescomplemented
282C3×C42—122no—
283#217—34no—
284#217—34no—
285#217—34no—
286#217—34no—
287#217—34no—
288#217—34no—
289#217—38no—
290#217—64no—
291#217C4×D314yescomplemented
292#217C2×Dic314yescomplemented
293(C2×D3)⋊C4—38no—
294(C2×D3)⋊C4—34no—
295(C2×D3)⋊C4—34no—
296(C2×D3)⋊C4—34no—
297(C2×D3)⋊C4—34no—
298(C2×D3)⋊C4C2×Dic318yescomplemented
299C4×Dic3—42no—
300C4×Dic3—122no—
301C4×Dic3—122no—
302C4×Dic3—122no—
303C4×Dic3—122no—
304C4×Dic3—122no—
305C4×Dic3—122no—
306C4×Dic3—124no—
307C22×C32—22no—
308C22×C32—22no—
309C22×C32—24no—
310C22×C32—24no—
311C22×C32C2×C4214yes—
312C22×C32C23×C411yescharacteristic
313C22×C32C23×C411yescharacteristic
314C22×C32C23×C411yescharacteristic
315C22×C32H(5,𝔽2)12yes—
316C22×C32H(5,𝔽2)12yes—
317C2×C3×D3—24no—
318C2×C3×D3—24no—
319C2×C3×D3—22no—
320C2×C3×D3—22no—
321C2×C3×D3—22no—
322C2×C3×D3—22no—
323C2×C3×D3—24no—
324C2×C3×D3—24no—
325C2×C3×D3—416no—
326C2×C3×D3C2×C4214yes—
327C2×C3×D3C2×C4214yes—
328C32×C4—24no—
329C3⋊Dic3—22no—
330C3⋊Dic3—24no—
331C3⋊Dic3—22no—
332C3×Dic3—24no—
333C3×Dic3—24no—
334C3×Dic3—22no—
335C3×Dic3—22no—
336C25—31no—
337C23×C4—31no—
338C23×C4—32no—
339C23×C4—92no—
340C23×C4—91no—
341C2×C22⋊C4—31no—
342C2×C22⋊C4—31no—
343C2×C22⋊C4—32no—
344C2×C22⋊C4—38no—
345C2×C22⋊C4—98no—
346C2×C22⋊C4—91no—
347C2×C22⋊C4—91no—
348C2×C22⋊C4—92no—
349C2×C22⋊C4—91no—
350C2×C22⋊C4—91no—
351C2×C22⋊C4—98no—
352C2×C22⋊C4—91no—
353C2×C22⋊C4D3211yescharacteristic
354C2×C42—32no—
355C2×C42—92no—
356C2×C42—92no—
357C2×C42—92no—
358#95—32no—
359#95—92no—
360#95—92no—
361#95—92no—
362C23×C3—22no—
363C23×C3—22no—
364C23×C3—22no—
365C23×C3—22no—
366C23×C3—21no—
367C23×C3—22no—
368C23×C3—22no—
369C23×C3—22no—
370C23×C3—32no—
371C23×C3—32no—
372C23×C3—32no—
373C23×C3—32no—
374C23×C3—32no—
375C23×C3—32no—
376C23×C3—316no—
377C23×C3—42no—
378C23×C3—42no—
379C23×C3—62no—
380C23×C3—62no—
381C23×C3—62no—
382C23×C3—62no—
383C23×C3—124no—
384C23×C3—124no—
385C23×C3—128no—
386C23×C3—128no—
387C23×C3C2×C4×D312yes—
388C23×C3C2×C4×D312yes—
389C23×C3C2×C4×D312yes—
390C23×C3C2×C4×D312yes—
391C23×C3C2×C4×D312yes—
392C23×C3C22×Dic312yes—
393C23×C3C23×D311yescharacteristic
394C23×C3C23×D311yescharacteristic
395C22×D3—22no—
396C22×D3—22no—
397C22×D3—22no—
398C22×D3—22no—
399C22×D3—48no—
400C22×D3—44no—
401C22×D3—44no—
402C22×D3—48no—
403C22×D3C4×Dic3116yescomplemented
404C22×D3C2×C4×D312yes—
405C22×D3C2×C4×D312yes—
406C22×D3C2×C4×D312yes—
407C22×D3C2×C4×D312yes—
408C22×D3C22×Dic312yes—
409C22×D3C22×Dic312yes—
410C2×C3×C4—22no—
411C2×C3×C4—22no—
412C2×C3×C4—22no—
413C2×C3×C4—22no—
414C2×C3×C4—24no—
415C2×C3×C4—32no—
416C2×C3×C4—32no—
417C2×C3×C4—34no—
418C2×C3×C4—34no—
419C2×C3×C4—42no—
420C2×C3×C4—42no—
421C2×C3×C4—62no—
422C2×C3×C4—62no—
423C2×C3×C4—62no—
424C2×C3×C4—62no—
425C2×C3×C4—62no—
426C2×C3×C4—62no—
427C2×C3×C4—128no—
428C2×C3×C4—124no—
429C2×C3×C4C2×C4×D314yes—
430C2×C3×C4C22×Dic314yes—
431C2×Dic3—22no—
432C2×Dic3—22no—
433C2×Dic3—22no—
434C2×Dic3—22no—
435C2×Dic3—22no—
436C2×Dic3—22no—
437C2×Dic3—32no—
438C2×Dic3—32no—
439C2×Dic3—34no—
440C2×Dic3—32no—
441C2×Dic3—32no—
442C2×Dic3—34no—
443C2×Dic3—44no—
444C2×Dic3—62no—
445C2×Dic3—64no—
446C2×Dic3—62no—
447C2×Dic3—64no—
448C2×Dic3—62no—
449C2×Dic3—62no—
450C2×Dic3—62no—
451C2×Dic3—62no—
452C2×Dic3—62no—
453C2×Dic3—62no—
454C2×Dic3—62no—
455C2×Dic3—62no—
456C2×Dic3—122no—
457C2×Dic3—122no—
458C2×Dic3—122no—
459C2×Dic3—128no—
460C2×Dic3—124no—
461C2×Dic3—124no—
462C2×Dic3—128no—
463C2×Dic3C2×C4×D312yes—
464C2×Dic3C2×C4×D312yes—
465C2×Dic3C2×C4×D314yes—
466C2×Dic3C22×Dic314yes—
467C4×D3—48no—
468C4×D3—128no—
469C2×C32—24no—
470C2×C32C22×C4211yescharacteristic
471C2×C32#51811yescharacteristic
472C2×C32#51811yescharacteristic
473C2×C32#51812yes—
474C2×C32#51812yes—
475C3×D3—24no—
476C3×D3—24no—
477C24—31no—
478C24—31no—
479C24—34no—
480C24—34no—
481C24—34no—
482C24—122no—
483C24—122no—
484C24C2×D3211yescharacteristic
485C22×C4—31no—
486C22×C4—32no—
487C22×C4—31no—
488C22×C4—32no—
489C22×C4—34no—
490C22×C4—38no—
491C22×C4—98no—
492C22×C4—92no—
493C22×C4—91no—
494C22×C4—91no—
495C22×C4—94no—
496C22×C4—122no—
497C22×C4—122no—
498C22×C4—122no—
499C22×C4—362no—
500C22×C4—362no—
501C22×C4—362no—
502C22×C4C2×D3212yes—
503C22⋊C4—34no—
504C22⋊C4—34no—
505C22⋊C4—38no—
506C22⋊C4—98no—
507C22⋊C4—94no—
508C22⋊C4—94no—
509C22⋊C4—94no—
510C22⋊C4—94no—
511C22⋊C4—94no—
512C22⋊C4D3×Dic314yescomplemented
513C42—122no—
514C42—362no—
515C42—362no—
516C42—362no—
517C22×C3—22no—
518C22×C3—22no—
519C22×C3—22no—
520C22×C3—24no—
521C22×C3—22no—
522C22×C3—24no—
523C22×C3—24no—
524C22×C3—24no—
525C22×C3—21no—
526C22×C3—21no—
527C22×C3—22no—
528C22×C3—22no—
529C22×C3—21no—
530C22×C3—24no—
531C22×C3—34no—
532C22×C3—34no—
533C22×C3—42no—
534C22×C3—42no—
535C22×C3—44no—
536C22×C3—44no—
537C22×C3—62no—
538C22×C3—62no—
539C22×C3—62no—
540C22×C3—62no—
541C22×C3—64no—
542C22×C3—64no—
543C22×C3—64no—
544C22×C3—64no—
545C22×C3—1216no—
546C22×C3C42×D314yes—
547C22×C3C2×C4×Dic314yes—
548C22×C3C22×C4×D311yescharacteristic
549C22×C3C22×C4×D311yescharacteristic
550C22×C3C22×C4×D311yescharacteristic
551C22×C3C22×C4×D311yescharacteristic
552C22×C3C22×C4×D311yescharacteristic
553C22×C3#100412yes—
554C22×C3#100412yes—
555C22×C3#100412yes—
556C22×C3#100912yes—
557C22×C3C23×Dic311yescharacteristic
558C2×D3—24no—
559C2×D3—22no—
560C2×D3—22no—
561C2×D3—22no—
562C2×D3—22no—
563C2×D3—24no—
564C2×D3—24no—
565C2×D3—24no—
566C2×D3—416no—
567C2×D3C2×C4×Dic314yes—
568C2×D3C2×C4×Dic314yes—
569C3×C4—24no—
570C3×C4—24no—
571C3×C4—44no—
572C3×C4—64no—
573C3×C4—62no—
574C3×C4—62no—
575C3×C4—64no—
576Dic3—22no—
577Dic3—22no—
578Dic3—24no—
579Dic3—24no—
580Dic3—64no—
581Dic3—64no—
582Dic3—62no—
583Dic3—62no—
584Dic3—62no—
585Dic3—62no—
586Dic3—64no—
587Dic3—122no—
588Dic3—124no—
589C32#227311yescharacteristic, complemented, Sylow
590C23—22no—
591C23—22no—
592C23—32no—
593C23—32no—
594C23—32no—
595C23—32no—
596C23—32no—
597C23—32no—
598C23—316no—
599C23—62no—
600C23—62no—
601C23—62no—
602C23—62no—
603C23—124no—
604C23—124no—
605C23—128no—
606C23—128no—
607C23C4×D3212yes—
608C23C4×D3212yes—
609C23C2×D3×Dic312yes—
610C23C22×D3211yescharacteristic
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—34no—
614C2×C4—32no—
615C2×C4—32no—
616C2×C4—34no—
617C2×C4—62no—
618C2×C4—62no—
619C2×C4—62no—
620C2×C4—62no—
621C2×C4—62no—
622C2×C4—62no—
623C2×C4—92no—
624C2×C4—92no—
625C2×C4—94no—
626C2×C4—128no—
627C2×C4—124no—
628C2×C4—182no—
629C2×C4—182no—
630C2×C4—182no—
631C2×C4—182no—
632C2×C4—368no—
633C2×C4—364no—
634C2×C4C2×D3×Dic314yes—
635C2×C3—24no—
636C2×C3—24no—
637C2×C3—21no—
638C2×C3—21no—
639C2×C3—21no—
640C2×C3—22no—
641C2×C3—22no—
642C2×C3—44no—
643C2×C3—64no—
644C2×C3—64no—
645C2×C3C2×C42×D311yescharacteristic
646C2×C3#548611yescharacteristic
647C2×C3#548611yescharacteristic
648C2×C3#548611yescharacteristic
649C2×C3#548612yes—
650C2×C3#552111yescharacteristic
651C2×C3#554512yes—
652C2×C3#554512yes—
653C2×C3C22×C4×Dic311yescharacteristic
654C2×C3#579812yes—
655D3—24no—
656D3—24no—
657C22—22no—
658C22—22no—
659C22—24no—
660C22—24no—
661C22—34no—
662C22—34no—
663C22—62no—
664C22—62no—
665C22—62no—
666C22—62no—
667C22—64no—
668C22—64no—
669C22—64no—
670C22—64no—
671C22—1216no—
672C22C4×D3×Dic314yes—
673C22C2×C4×D3211yescharacteristic
674C22C2×C4×D3211yescharacteristic
675C22#6431312yes—
676C22#6431412yes—
677C22C22×D3×Dic311yescharacteristic
678C4—24no—
679C4—62no—
680C4—62no—
681C4—64no—
682C4—64no—
683C4—182no—
684C4—182no—
685C4—184no—
686C3—21no—
687C3#7356011yescharacteristic, complemented
688C3#8208311yescharacteristic, complemented
689C2—24no—
690C2—64no—
691C2—64no—
692C2#1059418111yescharacteristic
693C2#1059418211yescharacteristic
694C2#1059425412yes—
695C2C2×C4×D3×Dic311yescharacteristic
696C2#1059521512yes—
subgroupG/H
center, FrattiniC23C22×D32
commutatorC2×C32C22×C42
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC24×C3×D3C22
hypercenterC2×C22⋊C4D32
hypocenterC32#2273
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
4. C22⋊C4×C3⋊Dic3C2semidirect
5. C3×Dic3×C22⋊C4C2semidirect
6. #10591705C2semidirect
7. Dic3×#217C2semidirect
8. #10591368C2semidirect
9. Dic3×(C2×D3)⋊C4C2semidirect
10. C4×(C2×D3)⋊Dic3C2semidirect
11. #10591237C2semidirect
21. C2×C4×C3⋊Dic3C22semidirect
25. C2×C3×C4×Dic3C22semidirect
26. C3×D3×C22⋊C4C4semidirect
27. D3×#217C4semidirect
28. C2×(C2×D3)⋊Dic3C4semidirect
34. C2×Dic32C22semidirect
35. C2×Dic32C22semidirect
36. #63658C22semidirect
37. C3×C3⋊#95C22semidirect
38. #63579C22semidirect
39. #63579C22semidirect
58. Dic3×C22⋊C4D3semidirect
73. C22×C3⋊Dic3C2×C4semidirect
78. C22×C3×Dic3C2×C4semidirect
85. C2×C3×C4×D3C2×C4semidirect
88. C2×D3×Dic3C2×C4semidirect
89. C32×C22⋊C4C2×C4semidirect
90. #3757C2×C4semidirect
92. C3×#217C2×C4semidirect
93. C3×#217C2×C4semidirect
94. C3×(C2×D3)⋊C4C2×C4semidirect
96. (C2×D3)⋊Dic3C2×C4semidirect
97. (C2×D3)⋊Dic3C2×C4semidirect
98. (C2×D3)⋊Dic3C2×C4semidirect
99. (C2×D3)⋊Dic3C2×C4semidirect
100. (C2×D3)⋊Dic3C2×C4semidirect
149. C2×C4×Dic3C2×D3semidirect
151. D3×C22⋊C4Dic3semidirect
160. C3⋊#95C2×D3semidirect
175. C22×C3×D3C42semidirect
265. C22×Dic3C4×D3semidirect
275. C2×C4×D3C2×Dic3semidirect
280. C3×C22⋊C4C4×D3semidirect
281. C3×C22⋊C4C2×Dic3semidirect
291. #217C4×D3semidirect
292. #217C2×Dic3semidirect
298. (C2×D3)⋊C4C2×Dic3semidirect
403. C22×D3C4×Dic3semidirect
512. C22⋊C4D3×Dic3semidirect
589. C32#2273semidirect
687. C3#73560semidirect
688. C3#82083semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×C22⋊C42
C2×D3×#2172
C22×(C2×D3)⋊Dic32
C22⋊C4×C3⋊Dic32
C3×Dic3×C22⋊C42
#105917052
Dic3×#2172
#105913682
Dic3×(C2×D3)⋊C42
C4×(C2×D3)⋊Dic32
#105912372
#820833
#735603