Finite Group Databasebeta

← C2×C3×#5578 #11900815

Subgroups — C2×C3×#5578 #11900815

Order 1152.

2485 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C4×Q8C211yesmaximal, characteristic, complemented
2C2×C3×#946C211yesmaximal, characteristic
3C2×C3×#944C211yesmaximal, characteristic, complemented
4C3×#5578C2116yesmaximal, direct product factor
5C2×C3×#897C211yesmaximal, characteristic
6C2×C3×#896C212yesmaximal
7C2×C3×#889C212yesmaximal, complemented
8C2×C3×#888C211yesmaximal, characteristic, complemented
9C2×C3×#872C212yesmaximal
10C2×C3×C42×D3C211yesmaximal, characteristic
11C2×C3×C4×Dic6C212yesmaximal, complemented
12C2×C3×C4×Dic6C211yesmaximal, characteristic, complemented
13C2×C3×#533—31nomaximal
14C2×#5578C311yesmaximal, characteristic, direct product factor
15C22×C32×Q8C2211yescharacteristic
16C22×C3×C4×D3C2211yescharacteristic
17C22×C3×C4×D3C2211yescharacteristic
18C22×C3×C4×D3C2211yescharacteristic
19C22×C3×Dic6C2212yes—
20C22×C3×Dic6C2211yescharacteristic
21C32×C4×Q8C2218yescomplemented
22C2×C32×C4⋊C4C2211yescharacteristic
23C2×C32×C4⋊C4C2212yes—
24C2×C32×C42C2211yescharacteristic
25C2×C32×C42C2212yes—
26C3×#946C2218yes—
27C3×#944C2218yescomplemented
28C2×C3×(C2×D3)⋊C4C2212yes—
29C2×C3×(C2×D3)⋊C4C2212yes—
30C2×C3×C4⋊Dic3C2211yescharacteristic
31C2×C3×C4⋊Dic3C2212yes—
32C2×C3×Dic3⋊C4C2212yes—
33C2×C3×Dic3⋊C4C2212yes—
34C2×C3×Dic3⋊C4C2212yes—
35C2×C3×Dic3⋊C4C2212yes—
36C2×C3×Dic3⋊C4C2212yes—
37C2×C3×C4×Dic3C2211yescharacteristic
38C2×C3×C4×Dic3C2211yescharacteristic
39C2×C3×C4×Dic3C2211yescharacteristic
40C2×C3×C4×Dic3C2212yes—
41C3×#897C2218yes—
42C3×#896C22116yes—
43C3×#889C22116yescomplemented
44C3×#888C2218yescomplemented
45C3×#872C22116yes—
46C3×C42×D3C2218yes—
47C3×C4×Dic6C22116yescomplemented
48C3×C4×Dic6C2218yescomplemented
49C3×#533—316no—
50C2×C3×C4⋊Q8—31no—
51C2×C3×C4⋊Q8—31no—
52C2×C3×#125—32no—
53C2×C3×C22⋊Q8—31no—
54C2×C3×C22⋊Q8—32no—
55C2×C3×C22⋊Q8—31no—
56C2×C3×C4×Q8—21no—
57C2×C3×C4×Q8—32no—
58C2×C3×C4×Q8—31no—
59C2×C3×C4×Q8D311yescharacteristic, complemented
60C2×C3×C4×Q8C2×C311yescharacteristic, complemented
61C2×C3×#117—32no—
62C22×C3×C42—31no—
63C2×#946C2×C311yescharacteristic
64C2×#944C2×C311yescharacteristic, complemented
65#5578C2×C3116yesdirect product factor
66C2×#897C2×C311yescharacteristic
67C2×#896C2×C312yes—
68C2×#889C2×C312yescomplemented
69C2×#888C2×C311yescharacteristic, complemented
70C2×#872C2×C312yes—
71C2×C42×D3C2×C311yescharacteristic
72C2×C4×Dic6C2×C312yescomplemented
73C2×C4×Dic6C2×C311yescharacteristic, complemented
74C23×C3×D3C2311yescharacteristic
75C2×C32×Q8—24no—
76C2×C32×Q8C2314yes—
77C22×C32×C4C2311yescharacteristic
78C22×C32×C4C2312yes—
79C22×C32×C4C2312yes—
80C22×C32×C4C2311yescharacteristic
81C22×C32×C4C2311yescharacteristic
82C22×C3×Dic3C2311yescharacteristic
83C22×C3×Dic3C2312yes—
84C22×C3×Dic3C2312yes—
85C22×C3×Dic3C2311yescharacteristic
86C22×C3×Dic3C2311yescharacteristic
87C2×C3×C4×D3—24no—
88C2×C3×C4×D3—24no—
89C2×C3×C4×D3Q818yescomplemented
90C2×C3×C4×D3C2314yes—
91C2×C3×C4×D3C2314yes—
92C2×C3×C4×D3C2314yes—
93C2×C3×Dic6—24no—
94C2×C3×Dic6—28no—
95C2×C3×Dic6C2318yes—
96C2×C3×Dic6C2314yes—
97C32×C4⋊C4C2314yes—
98C32×C4⋊C4C2318yes—
99C32×C42C2314yes—
100C32×C42C2318yes—
101C3×(C2×D3)⋊C4C2318yes—
102C3×(C2×D3)⋊C4C2318yes—
103C3×C4⋊Dic3C2314yes—
104C3×C4⋊Dic3C2318yes—
105C3×Dic3⋊C4C2318yes—
106C3×Dic3⋊C4C2318yes—
107C3×Dic3⋊C4C2318yes—
108C3×Dic3⋊C4C2318yes—
109C3×Dic3⋊C4C2318yes—
110C3×C4×Dic3C2314yes—
111C3×C4×Dic3C2314yes—
112C3×C4×Dic3C2314yes—
113C3×C4×Dic3C2318yes—
114C2×#533—31noSylow
115C22×C3×Q8—21no—
116C22×C3×Q8—32no—
117C22×C3×Q8—31no—
118C22×C3×Q8C2×D311yescharacteristic
119C22×C3×Q8C22×C311yescharacteristic
120C23×C3×C4—31no—
121C23×C3×C4—31no—
122C23×C3×C4—31no—
123C22×C4×D3C22×C311yescharacteristic
124C22×C4×D3C22×C311yescharacteristic
125C22×C4×D3C22×C311yescharacteristic
126C22×Dic6C22×C312yes—
127C22×Dic6C22×C311yescharacteristic
128C3×C4⋊Q8—38no—
129C3×C4⋊Q8—38no—
130C3×#125—316no—
131C3×C22⋊Q8—38no—
132C3×C22⋊Q8—316no—
133C3×C22⋊Q8—38no—
134C3×C4×Q8—28no—
135C3×C4×Q8—316no—
136C3×C4×Q8—38no—
137C3×C4×Q8C2×D318yescomplemented
138C3×C4×Q8C22×C318yescomplemented
139C3×#117—316no—
140C2×C3×C4⋊C4—22no—
141C2×C3×C4⋊C4—21no—
142C2×C3×C4⋊C4—32no—
143C2×C3×C4⋊C4—32no—
144C2×C3×C4⋊C4—32no—
145C2×C3×C4⋊C4—32no—
146C2×C3×C4⋊C4—32no—
147C2×C3×C4⋊C4—32no—
148C2×C3×C4⋊C4—31no—
149C2×C3×C4⋊C4C2×D312yes—
150C2×C3×C4⋊C4C2×D311yescharacteristic
151C2×C3×C4⋊C4C22×C311yescharacteristic
152C2×C3×C4⋊C4C22×C312yes—
153C2×C3×C22⋊C4—32no—
154C2×C3×C22⋊C4—32no—
155C2×C3×C42—22no—
156C2×C3×C42—21no—
157C2×C3×C42—31no—
158C2×C3×C42—31no—
159C2×C3×C42—31no—
160C2×C3×C42—32no—
161C2×C3×C42—38no—
162C2×C3×C42C2×D311yescharacteristic
163C2×C3×C42C2×D312yes—
164C2×C3×C42C22×C311yescharacteristic
165C2×C3×C42C22×C312yes—
166#946C22×C318yes—
167#944C22×C318yescomplemented
168C2×(C2×D3)⋊C4C22×C312yes—
169C2×(C2×D3)⋊C4C22×C312yes—
170C2×C4⋊Dic3C22×C311yescharacteristic
171C2×C4⋊Dic3C22×C312yes—
172C2×Dic3⋊C4C22×C312yes—
173C2×Dic3⋊C4C22×C312yes—
174C2×Dic3⋊C4C22×C312yes—
175C2×Dic3⋊C4C22×C312yes—
176C2×Dic3⋊C4C22×C312yes—
177C2×C4×Dic3C22×C311yescharacteristic
178C2×C4×Dic3C22×C312yes—
179C2×C4×Dic3C22×C311yescharacteristic
180C2×C4×Dic3C22×C311yescharacteristic
181#897C22×C318yes—
182#896C22×C3116yes—
183#889C22×C3116yescomplemented
184#888C22×C318yescomplemented
185#872C22×C3116yes—
186C42×D3C22×C318yes—
187C4×Dic6C22×C3116yescomplemented
188C4×Dic6C22×C318yescomplemented
189C23×C32C2411yescharacteristic
190C22×C3×D3—22no—
191C22×C3×D3—22no—
192C22×C3×D3C2×Q814yes—
193C22×C3×D3C2412yes—
194C32×Q8—28no—
195C2×C32×C4—24no—
196C2×C32×C4—24no—
197C2×C32×C4—22no—
198C2×C32×C4C2×Q814yes—
199C2×C32×C4#4114yes—
200C2×C32×C4C2412yes—
201C2×C32×C4C2414yes—
202C2×C32×C4C2414yes—
203C2×C32×C4C2412yes—
204C2×C32×C4C2412yes—
205C2×C3×Dic3—24no—
206C2×C3×Dic3—24no—
207C2×C3×Dic3—22no—
208C2×C3×Dic3C2×Q814yes—
209C2×C3×Dic3#4114yes—
210C2×C3×Dic3C2412yes—
211C2×C3×Dic3C2414yes—
212C2×C3×Dic3C2414yes—
213C2×C3×Dic3C2412yes—
214C2×C3×Dic3C2412yes—
215C3×C4×D3—28no—
216C3×C4×D3—28no—
217C3×C4×D3C2×Q8116yescomplemented
218C3×Dic6—28no—
219C3×Dic6—216no—
220#533—316no—
221C2×C4⋊Q8—31no—
222C2×C4⋊Q8—31no—
223C2×#125—32no—
224C2×C22⋊Q8—31no—
225C2×C22⋊Q8—32no—
226C2×C22⋊Q8—31no—
227C2×C4×Q8—31no—
228C2×C4×Q8—32no—
229C2×C4×Q8C3×D311yescharacteristic, complemented
230C2×#117—32no—
231C22×C42—31no—
232C24×C3—31no—
233C23×D3C23×C311yescharacteristic
234C2×C3×Q8—28no—
235C2×C3×Q8—24no—
236C2×C3×Q8—24no—
237C2×C3×Q8—24no—
238C2×C3×Q8—38no—
239C2×C3×Q8—34no—
240C2×C3×Q8—68no—
241C2×C3×Q8—64no—
242C2×C3×Q8C22×D314yes—
243C2×C3×Q8C23×C314yes—
244C22×C3×C4—21no—
245C22×C3×C4—22no—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4—22no—
249C22×C3×C4—31no—
250C22×C3×C4—31no—
251C22×C3×C4—38no—
252C22×C3×C4—34no—
253C22×C3×C4—31no—
254C22×C3×C4—32no—
255C22×C3×C4—32no—
256C22×C3×C4—34no—
257C22×C3×C4—34no—
258C22×C3×C4—64no—
259C22×C3×C4—64no—
260C22×C3×C4C22×D311yescharacteristic
261C22×C3×C4C22×D312yes—
262C22×C3×C4C22×D312yes—
263C22×C3×C4C22×D311yescharacteristic
264C22×C3×C4C22×D311yescharacteristic
265C22×C3×C4C23×C311yescharacteristic
266C22×C3×C4C23×C312yes—
267C22×C3×C4C23×C312yes—
268C22×C3×C4C23×C311yescharacteristic
269C22×C3×C4C23×C311yescharacteristic
270C22×Dic3C23×C311yescharacteristic
271C22×Dic3C23×C312yes—
272C22×Dic3C23×C312yes—
273C22×Dic3C23×C311yescharacteristic
274C22×Dic3C23×C311yescharacteristic
275C2×C4×D3—24no—
276C2×C4×D3—24no—
277C2×C4×D3C3×Q818yescomplemented
278C2×C4×D3C23×C314yes—
279C2×C4×D3C23×C314yes—
280C2×C4×D3C23×C314yes—
281C2×Dic6—24no—
282C2×Dic6—28no—
283C2×Dic6C23×C318yes—
284C2×Dic6C23×C314yes—
285C3×C4⋊C4—28no—
286C3×C4⋊C4—24no—
287C3×C4⋊C4—38no—
288C3×C4⋊C4—38no—
289C3×C4⋊C4—38no—
290C3×C4⋊C4—38no—
291C3×C4⋊C4—38no—
292C3×C4⋊C4—38no—
293C3×C4⋊C4—34no—
294C3×C4⋊C4C22×D318yes—
295C3×C4⋊C4C22×D314yes—
296C3×C4⋊C4C23×C314yes—
297C3×C4⋊C4C23×C318yes—
298C3×C22⋊C4—38no—
299C3×C22⋊C4—38no—
300C3×C42—24no—
301C3×C42—28no—
302C3×C42—34no—
303C3×C42—34no—
304C3×C42—34no—
305C3×C42—38no—
306C3×C42C22×D314yes—
307C3×C42C22×D318yes—
308C3×C42C23×C314yes—
309C3×C42C23×C318yes—
310(C2×D3)⋊C4C23×C318yes—
311(C2×D3)⋊C4C23×C318yes—
312C4⋊Dic3C23×C314yes—
313C4⋊Dic3C23×C318yes—
314Dic3⋊C4C23×C318yes—
315Dic3⋊C4C23×C318yes—
316Dic3⋊C4C23×C318yes—
317Dic3⋊C4C23×C318yes—
318Dic3⋊C4C23×C318yes—
319C4×Dic3C23×C314yes—
320C4×Dic3C23×C318yes—
321C4×Dic3C23×C314yes—
322C4×Dic3C23×C314yes—
323C22×C32C22×Q812yes—
324C22×C32C2×#4112yes—
325C22×C32C2×#4112yes—
326C22×C32C2511yescharacteristic
327C2×C3×D3—28no—
328C2×C3×D3—22no—
329C2×C3×D3—22no—
330C2×C3×D3C22×Q814yes—
331C32×C4—24no—
332C32×C4—24no—
333C32×C4—22no—
334C32×C4C22×Q814yes—
335C32×C4C2×#4114yes—
336C3×Dic3—24no—
337C3×Dic3—24no—
338C3×Dic3—22no—
339C3×Dic3C22×Q814yes—
340C3×Dic3C2×#4114yes—
341C22×Q8—32no—
342C22×Q8—31no—
343C22×Q8C2×C3×D311yescharacteristic
344C23×C4—31no—
345C23×C4—31no—
346C23×C4—31no—
347C4⋊Q8—38no—
348C4⋊Q8—38no—
349#125—316no—
350C22⋊Q8—38no—
351C22⋊Q8—316no—
352C22⋊Q8—38no—
353C4×Q8—316no—
354C4×Q8—38no—
355C4×Q8C2×C3×D318yescomplemented
356#117—316no—
357C2×C4⋊C4—32no—
358C2×C4⋊C4—32no—
359C2×C4⋊C4—32no—
360C2×C4⋊C4—32no—
361C2×C4⋊C4—32no—
362C2×C4⋊C4—32no—
363C2×C4⋊C4—31no—
364C2×C4⋊C4C2×C3×D312yes—
365C2×C4⋊C4C2×C3×D311yescharacteristic
366C2×C22⋊C4—32no—
367C2×C22⋊C4—32no—
368C2×C42—32no—
369C2×C42—31no—
370C2×C42—31no—
371C2×C42—31no—
372C2×C42—38no—
373C2×C42C2×C3×D312yes—
374C2×C42C2×C3×D311yescharacteristic
375C23×C3—21no—
376C23×C3—34no—
377C23×C3—32no—
378C23×C3—62no—
379C23×C3—62no—
380C23×C3C23×D311yescharacteristic
381C23×C3C24×C311yescharacteristic
382C22×D3—22no—
383C22×D3—22no—
384C22×D3C2×C3×Q814yes—
385C22×D3C24×C312yes—
386C3×Q8—216no—
387C3×Q8—28no—
388C3×Q8—28no—
389C3×Q8—616no—
390C3×Q8—68no—
391C2×C3×C4—28no—
392C2×C3×C4—24no—
393C2×C3×C4—22no—
394C2×C3×C4—24no—
395C2×C3×C4—24no—
396C2×C3×C4—22no—
397C2×C3×C4—24no—
398C2×C3×C4—22no—
399C2×C3×C4—24no—
400C2×C3×C4—22no—
401C2×C3×C4—22no—
402C2×C3×C4—24no—
403C2×C3×C4—24no—
404C2×C3×C4—24no—
405C2×C3×C4—34no—
406C2×C3×C4—34no—
407C2×C3×C4—32no—
408C2×C3×C4—32no—
409C2×C3×C4—316no—
410C2×C3×C4—32no—
411C2×C3×C4—34no—
412C2×C3×C4—34no—
413C2×C3×C4—42no—
414C2×C3×C4—44no—
415C2×C3×C4—68no—
416C2×C3×C4—62no—
417C2×C3×C4—64no—
418C2×C3×C4—64no—
419C2×C3×C4—68no—
420C2×C3×C4#23514yes—
421C2×C3×C4D3×Q814yes—
422C2×C3×C4C2×C3×Q814yes—
423C2×C3×C4C3×#4114yes—
424C2×C3×C4C23×D312yes—
425C2×C3×C4C23×D314yes—
426C2×C3×C4C23×D314yes—
427C2×C3×C4C23×D312yes—
428C2×C3×C4C23×D312yes—
429C2×C3×C4C24×C312yes—
430C2×C3×C4C24×C314yes—
431C2×C3×C4C24×C314yes—
432C2×C3×C4C24×C312yes—
433C2×C3×C4C24×C312yes—
434C2×Dic3—24no—
435C2×Dic3—24no—
436C2×Dic3—22no—
437C2×Dic3C2×C3×Q814yes—
438C2×Dic3C3×#4114yes—
439C2×Dic3C24×C312yes—
440C2×Dic3C24×C314yes—
441C2×Dic3C24×C314yes—
442C2×Dic3C24×C312yes—
443C2×Dic3C24×C312yes—
444C4×D3—28no—
445C4×D3—28no—
446C4×D3C2×C3×Q8116yescomplemented
447Dic6—28no—
448Dic6—216no—
449C2×C32#53314yescomplemented
450C2×C32C23×Q811yescharacteristic
451C2×C32C22×#4111yescharacteristic
452C2×C32C22×#4111yescharacteristic
453C3×D3—24no—
454C24—31no—
455C2×Q8—24no—
456C2×Q8—38no—
457C2×Q8—34no—
458C2×Q8—68no—
459C2×Q8—64no—
460C2×Q8C22×C3×D314yes—
461C22×C4—31no—
462C22×C4—31no—
463C22×C4—34no—
464C22×C4—38no—
465C22×C4—31no—
466C22×C4—32no—
467C22×C4—32no—
468C22×C4—34no—
469C22×C4—34no—
470C22×C4—64no—
471C22×C4—64no—
472C22×C4C22×C3×D311yescharacteristic
473C22×C4C22×C3×D312yes—
474C22×C4C22×C3×D312yes—
475C22×C4C22×C3×D311yescharacteristic
476C22×C4C22×C3×D311yescharacteristic
477C4⋊C4—38no—
478C4⋊C4—38no—
479C4⋊C4—38no—
480C4⋊C4—38no—
481C4⋊C4—38no—
482C4⋊C4—38no—
483C4⋊C4—34no—
484C4⋊C4C22×C3×D318yes—
485C4⋊C4C22×C3×D314yes—
486C22⋊C4—38no—
487C22⋊C4—38no—
488C42—34no—
489C42—34no—
490C42—34no—
491C42—38no—
492C42C22×C3×D314yes—
493C42C22×C3×D318yes—
494C22×C3—22no—
495C22×C3—22no—
496C22×C3—22no—
497C22×C3—21no—
498C22×C3—34no—
499C22×C3—62no—
500C22×C3—62no—
501C22×C3—68no—
502C22×C3C2×#23512yes—
503C22×C3C2×D3×Q812yes—
504C22×C3D3×#4112yes—
505C22×C3C22×C3×Q812yes—
506C22×C3C2×C3×#4112yes—
507C22×C3C2×C3×#4112yes—
508C22×C3C24×D311yescharacteristic
509C22×C3C25×C311yescharacteristic
510C2×D3—22no—
511C2×D3—22no—
512C2×D3—28no—
513C2×D3C22×C3×Q814yes—
514C3×C4—28no—
515C3×C4—24no—
516C3×C4—22no—
517C3×C4—24no—
518C3×C4—24no—
519C3×C4—22no—
520C3×C4—24no—
521C3×C4—24no—
522C3×C4—24no—
523C3×C4—34no—
524C3×C4—34no—
525C3×C4—42no—
526C3×C4—44no—
527C3×C4—62no—
528C3×C4—64no—
529C3×C4—64no—
530C3×C4C2×#23514yes—
531C3×C4C2×D3×Q814yes—
532C3×C4C22×C3×Q814yes—
533C3×C4C2×C3×#4114yes—
534Dic3—24no—
535Dic3—24no—
536Dic3—22no—
537Dic3C22×C3×Q814yes—
538Dic3C2×C3×#4114yes—
539C32C2×#53311yescharacteristic, complemented, Sylow
540C23—34no—
541C23—32no—
542C23—62no—
543C23—62no—
544C23C23×C3×D311yescharacteristic
545Q8—28no—
546Q8—616no—
547Q8—68no—
548C2×C4—24no—
549C2×C4—22no—
550C2×C4—24no—
551C2×C4—34no—
552C2×C4—34no—
553C2×C4—32no—
554C2×C4—32no—
555C2×C4—316no—
556C2×C4—32no—
557C2×C4—34no—
558C2×C4—34no—
559C2×C4—68no—
560C2×C4—62no—
561C2×C4—64no—
562C2×C4—64no—
563C2×C4—68no—
564C2×C4C3×#23514yes—
565C2×C4C3×D3×Q814yes—
566C2×C4C23×C3×D312yes—
567C2×C4C23×C3×D314yes—
568C2×C4C23×C3×D314yes—
569C2×C4C23×C3×D312yes—
570C2×C4C23×C3×D312yes—
571C2×C3—24no—
572C2×C3—21no—
573C2×C3—21no—
574C2×C3—21no—
575C2×C3—64no—
576C2×C3#557814yesdirect product factor
577C2×C3C3×#53314yescomplemented
578C2×C3C22×#23511yescharacteristic
579C2×C3C22×D3×Q811yescharacteristic
580C2×C3C2×D3×#4111yescharacteristic
581C2×C3C23×C3×Q811yescharacteristic
582C2×C3C22×C3×#4111yescharacteristic
583C2×C3C22×C3×#4111yescharacteristic
584D3—24no—
585C22—34no—
586C22—68no—
587C22—62no—
588C22—62no—
589C22C2×C3×#23512yes—
590C22C2×C3×D3×Q812yes—
591C22C3×D3×#4112yes—
592C22C24×C3×D311yescharacteristic
593C4—24no—
594C4—22no—
595C4—24no—
596C4—34no—
597C4—34no—
598C4—62no—
599C4—64no—
600C4—64no—
601C4C2×C3×#23514yes—
602C4C2×C3×D3×Q814yes—
603C3—21no—
604C3C2×#557811yescharacteristic, direct product factor
605C3C2×C3×#53311yescharacteristic, complemented
606C2—64no—
607C2C3×#557814yesdirect product factor
608C2C22×C3×#23511yescharacteristic
609C2C22×C3×D3×Q811yescharacteristic
610C2C2×C3×D3×#4111yescharacteristic
subgroupG/H
centerC22×C3×C4C22×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC2×C32×C4×Q8C2
socleC23×C32C24
prime radicalC23×C3×D3C23
hypercenterC2×C3×C4×Q8D3
hypocenterC3C2×C3×#533
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3×C4 ◁ C2×C3×C4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C32×C4×Q8C2semidirect
3. C2×C3×#944C2semidirect
4. C3×#5578C2direct (N × H)
7. C2×C3×#889C2semidirect
8. C2×C3×#888C2semidirect
11. C2×C3×C4×Dic6C2semidirect
12. C2×C3×C4×Dic6C2semidirect
14. C2×#5578C3direct (N × H)
21. C32×C4×Q8C22semidirect
27. C3×#944C22semidirect
43. C3×#889C22semidirect
44. C3×#888C22semidirect
47. C3×C4×Dic6C22semidirect
48. C3×C4×Dic6C22semidirect
59. C2×C3×C4×Q8D3semidirect
60. C2×C3×C4×Q8C2×C3semidirect
64. C2×#944C2×C3semidirect
65. #5578C2×C3direct (N × H)
68. C2×#889C2×C3semidirect
69. C2×#888C2×C3semidirect
72. C2×C4×Dic6C2×C3semidirect
73. C2×C4×Dic6C2×C3semidirect
89. C2×C3×C4×D3Q8semidirect
137. C3×C4×Q8C2×D3semidirect
138. C3×C4×Q8C22×C3semidirect
167. #944C22×C3semidirect
183. #889C22×C3semidirect
184. #888C22×C3semidirect
187. C4×Dic6C22×C3semidirect
188. C4×Dic6C22×C3semidirect
217. C3×C4×D3C2×Q8semidirect
229. C2×C4×Q8C3×D3semidirect
277. C2×C4×D3C3×Q8semidirect
355. C4×Q8C2×C3×D3semidirect
446. C4×D3C2×C3×Q8semidirect
449. C2×C32#533semidirect
539. C32C2×#533semidirect
576. C2×C3#5578direct (N × H)
577. C2×C3C3×#533semidirect
604. C3C2×#5578direct (N × H)
605. C3C2×C3×#533semidirect
607. C2C3×#5578direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×C4×Q82
C2×C3×#9462
C2×C3×#9442
C3×#55782
C2×C3×#8972
C2×C3×#8962
C2×C3×#8892
C2×C3×#8882
C2×C3×#8722
C2×C3×C42×D32
C2×C3×C4×Dic62
C2×C3×#5333
C2×#55783