Finite Group Databasebeta

← C2×C3×#5641 #11903364

Subgroups — C2×C3×#5641 #11903364

Order 1152.

2385 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C22⋊Q8C211yesmaximal, characteristic, complemented
2C2×C3×#946C211yesmaximal, characteristic, complemented
3C2×C3×Q8×Dic3C211yesmaximal, characteristic, complemented
4C2×C3×C4×#67C211yesmaximal, characteristic
5C2×C3×#926C211yesmaximal, characteristic, complemented
6C3×#5641C2116yesmaximal, direct product factor
7C2×C3×#898C212yesmaximal, complemented
8C2×C3×#892C211yesmaximal, characteristic, complemented
9C2×C3×#888C211yesmaximal, characteristic, complemented
10C2×C3×#887C212yesmaximal, complemented
11C2×C3×#885C212yesmaximal
12C2×C3×#879C212yesmaximal, complemented
13C2×C3×#556—31nomaximal
14C2×#5641C311yesmaximal, characteristic, direct product factor
15C22×C32×Q8C2211yescharacteristic
16C23×C32×C4C2211yescharacteristic
17C22×C3×#67C2211yescharacteristic
18C22×C3×C4×D3C2211yescharacteristic
19C22×C3×Dic6C2212yes—
20C32×C22⋊Q8C2218yescomplemented
21C2×C32×C4⋊C4C2212yes—
22C2×C32×C4⋊C4C2211yescharacteristic
23C2×C32×C22⋊C4C2212yes—
24C2×C3×#217C2212yes—
25C2×C3×#217C2211yescharacteristic
26C3×#946C2218yescomplemented
27C3×Q8×Dic3C2218yescomplemented
28C3×C4×#67C2218yes—
29C2×C3×(C2×D3)⋊C4C2212yes—
30C2×C3×(C2×D3)⋊C4C2212yes—
31C2×C3×(C2×D3)⋊C4C2211yescharacteristic
32C3×#926C2218yescomplemented
33C2×C3×C4⋊Dic3C2211yescharacteristic
34C2×C3×C4⋊Dic3C2211yescharacteristic
35C2×C3×C4⋊Dic3C2212yes—
36C2×C3×Dic3⋊C4C2211yescharacteristic
37C2×C3×Dic3⋊C4C2212yes—
38C2×C3×Dic3⋊C4C2212yes—
39C2×C3×C4×Dic3C2212yes—
40C2×C3×C4×Dic3C2212yes—
41C2×C3×C4×Dic3C2212yes—
42C2×C3×C4×Dic3C2211yescharacteristic
43C3×#898C22116yescomplemented
44C3×#892C2218yescomplemented
45C3×#888C2218yescomplemented
46C3×#887C22116yescomplemented
47C3×#885C22116yes—
48C3×#879C22116yescomplemented
49C3×#556—316no—
50C2×C3×C4⋊Q8—31no—
51C2×C3×#126—32no—
52C2×C3×#126—32no—
53C2×C3×#124—32no—
54C2×C3×C22⋊Q8—21no—
55C2×C3×C22⋊Q8—31no—
56C2×C3×C22⋊Q8D311yescharacteristic, complemented
57C2×C3×C22⋊Q8C2×C311yescharacteristic, complemented
58C2×C3×C4×Q8—31no—
59C2×C3×C4×Q8—32no—
60C2×C3×C4×D4—31no—
61C2×C3×#117—31no—
62C2×C3×#117—31no—
63C2×#946C2×C311yescharacteristic, complemented
64C2×Q8×Dic3C2×C311yescharacteristic, complemented
65C2×C4×#67C2×C311yescharacteristic
66C2×#926C2×C311yescharacteristic, complemented
67#5641C2×C3116yesdirect product factor
68C2×#898C2×C312yescomplemented
69C2×#892C2×C311yescharacteristic, complemented
70C2×#888C2×C311yescharacteristic, complemented
71C2×#887C2×C312yescomplemented
72C2×#885C2×C312yes—
73C2×#879C2×C312yescomplemented
74C24×C32C2311yescharacteristic
75C23×C3×D3C2311yescharacteristic
76C2×C32×Q8—24no—
77C2×C32×Q8C2314yes—
78C22×C32×C4—24no—
79C22×C32×C4C2311yescharacteristic
80C22×C32×C4C2312yes—
81C22×C32×C4C2312yes—
82C22×C32×C4C2314yes—
83C22×C32×C4C2311yescharacteristic
84C2×C3×#67—24no—
85C2×C3×#67C2314yes—
86C22×C3×Dic3C2312yes—
87C22×C3×Dic3C2311yescharacteristic
88C22×C3×Dic3C2311yescharacteristic
89C22×C3×Dic3C2312yes—
90C22×C3×Dic3C2311yescharacteristic
91C2×C3×C4×D3—24no—
92C2×C3×C4×D3C2314yes—
93C2×C3×Dic6—28no—
94C2×C3×Dic6C2318yes—
95C32×C4⋊C4C2318yes—
96C32×C4⋊C4C2314yes—
97C32×C22⋊C4C2318yes—
98C3×#217C2314yes—
99C3×#217C2318yes—
100C3×(C2×D3)⋊C4C2318yes—
101C3×(C2×D3)⋊C4C2318yes—
102C3×(C2×D3)⋊C4C2314yes—
103C3×C4⋊Dic3C2318yes—
104C3×C4⋊Dic3C2314yes—
105C3×C4⋊Dic3C2314yes—
106C3×Dic3⋊C4C2318yes—
107C3×Dic3⋊C4C2318yes—
108C3×Dic3⋊C4C2314yes—
109C3×C4×Dic3C2318yes—
110C3×C4×Dic3C2318yes—
111C3×C4×Dic3C2318yes—
112C3×C4×Dic3C2314yes—
113C2×#556—31noSylow
114C22×C3×Q8—21no—
115C22×C3×Q8—32no—
116C22×C3×Q8C2×D311yescharacteristic
117C22×C3×Q8C22×C311yescharacteristic
118C22×C3×D4—31no—
119C23×C3×C4—21no—
120C23×C3×C4—31no—
121C23×C3×C4C2×D311yescharacteristic
122C23×C3×C4C22×C311yescharacteristic
123C22×#67C22×C311yescharacteristic
124C22×C4×D3C22×C311yescharacteristic
125C22×Dic6C22×C312yes—
126C3×C4⋊Q8—38no—
127C3×#126—316no—
128C3×#126—316no—
129C3×#124—316no—
130C3×C22⋊Q8—28no—
131C3×C22⋊Q8—38no—
132C3×C22⋊Q8C2×D318yescomplemented
133C3×C22⋊Q8C22×C318yescomplemented
134C3×C4×Q8—38no—
135C3×C4×Q8—316no—
136C3×C4×D4—38no—
137C3×#117—38no—
138C3×#117—38no—
139C2×C3×C4⋊C4—21no—
140C2×C3×C4⋊C4—22no—
141C2×C3×C4⋊C4—31no—
142C2×C3×C4⋊C4—32no—
143C2×C3×C4⋊C4—32no—
144C2×C3×C4⋊C4—31no—
145C2×C3×C4⋊C4—31no—
146C2×C3×C4⋊C4—32no—
147C2×C3×C4⋊C4C2×D311yescharacteristic
148C2×C3×C4⋊C4C2×D312yes—
149C2×C3×C4⋊C4C22×C312yes—
150C2×C3×C4⋊C4C22×C311yescharacteristic
151C2×C3×C22⋊C4—22no—
152C2×C3×C22⋊C4—32no—
153C2×C3×C22⋊C4—31no—
154C2×C3×C22⋊C4—32no—
155C2×C3×C22⋊C4—31no—
156C2×C3×C22⋊C4—32no—
157C2×C3×C22⋊C4C2×D312yes—
158C2×C3×C22⋊C4C22×C312yes—
159C2×C3×C42—32no—
160C2×C3×C42—32no—
161C2×C3×C42—31no—
162C2×C3×C42—32no—
163C2×#217C22×C311yescharacteristic
164C2×#217C22×C312yes—
165#946C22×C318yescomplemented
166Q8×Dic3C22×C318yescomplemented
167C4×#67C22×C318yes—
168C2×(C2×D3)⋊C4C22×C312yes—
169C2×(C2×D3)⋊C4C22×C312yes—
170C2×(C2×D3)⋊C4C22×C311yescharacteristic
171#926C22×C318yescomplemented
172C2×C4⋊Dic3C22×C312yes—
173C2×C4⋊Dic3C22×C311yescharacteristic
174C2×C4⋊Dic3C22×C311yescharacteristic
175C2×Dic3⋊C4C22×C312yes—
176C2×Dic3⋊C4C22×C312yes—
177C2×Dic3⋊C4C22×C311yescharacteristic
178C2×C4×Dic3C22×C312yes—
179C2×C4×Dic3C22×C312yes—
180C2×C4×Dic3C22×C312yes—
181C2×C4×Dic3C22×C311yescharacteristic
182#898C22×C3116yescomplemented
183#892C22×C318yescomplemented
184#888C22×C318yescomplemented
185#887C22×C3116yescomplemented
186#885C22×C3116yes—
187#879C22×C3116yescomplemented
188C23×C32—22no—
189C23×C32—22no—
190C23×C32—22no—
191C23×C32C2412yes—
192C23×C32C2411yescharacteristic
193C22×C3×D3—22no—
194C22×C3×D3—22no—
195C22×C3×D3—22no—
196C22×C3×D3C2412yes—
197C32×Q8—28no—
198C2×C32×C4—24no—
199C2×C32×C4—22no—
200C2×C32×C4—24no—
201C2×C32×C4—28no—
202C2×C32×C4#4114yes—
203C2×C32×C4C2412yes—
204C2×C32×C4C2414yes—
205C2×C32×C4C2414yes—
206C2×C32×C4C2412yes—
207C3×#67—28no—
208C2×C3×Dic3—24no—
209C2×C3×Dic3—22no—
210C2×C3×Dic3—24no—
211C2×C3×Dic3—22no—
212C2×C3×Dic3#4114yes—
213C2×C3×Dic3C2414yes—
214C2×C3×Dic3C2412yes—
215C2×C3×Dic3C2412yes—
216C2×C3×Dic3C2414yes—
217C2×C3×Dic3C2412yes—
218C3×C4×D3—28no—
219C3×Dic6—216no—
220#556—316no—
221C2×C4⋊Q8—31no—
222C2×#126—32no—
223C2×#126—32no—
224C2×#124—32no—
225C2×C22⋊Q8—31no—
226C2×C22⋊Q8C3×D311yescharacteristic, complemented
227C2×C4×Q8—31no—
228C2×C4×Q8—32no—
229C2×C4×D4—31no—
230C2×#117—31no—
231C2×#117—31no—
232C24×C3—21no—
233C24×C3—31no—
234C24×C3C22×D311yescharacteristic
235C24×C3C23×C311yescharacteristic
236C23×D3C23×C311yescharacteristic
237C2×C3×Q8—24no—
238C2×C3×Q8—24no—
239C2×C3×Q8—24no—
240C2×C3×Q8—38no—
241C2×C3×Q8—44no—
242C2×C3×Q8—68no—
243C2×C3×Q8C22×D314yes—
244C2×C3×Q8C23×C314yes—
245C2×C3×D4—34no—
246C2×C3×D4—64no—
247C22×C3×C4—24no—
248C22×C3×C4—24no—
249C22×C3×C4—21no—
250C22×C3×C4—22no—
251C22×C3×C4—22no—
252C22×C3×C4—21no—
253C22×C3×C4—24no—
254C22×C3×C4—31no—
255C22×C3×C4—32no—
256C22×C3×C4—31no—
257C22×C3×C4—31no—
258C22×C3×C4—32no—
259C22×C3×C4—34no—
260C22×C3×C4—44no—
261C22×C3×C4—64no—
262C22×C3×C4C22×D314yes—
263C22×C3×C4C22×D311yescharacteristic
264C22×C3×C4C22×D312yes—
265C22×C3×C4C22×D312yes—
266C22×C3×C4C22×D311yescharacteristic
267C22×C3×C4C23×C311yescharacteristic
268C22×C3×C4C23×C312yes—
269C22×C3×C4C23×C312yes—
270C22×C3×C4C23×C314yes—
271C22×C3×C4C23×C311yescharacteristic
272C2×#67—24no—
273C2×#67C23×C314yes—
274C22×Dic3C23×C312yes—
275C22×Dic3C23×C311yescharacteristic
276C22×Dic3C23×C311yescharacteristic
277C22×Dic3C23×C312yes—
278C22×Dic3C23×C311yescharacteristic
279C2×C4×D3—24no—
280C2×C4×D3C23×C314yes—
281C2×Dic6—28no—
282C2×Dic6C23×C318yes—
283C3×C4⋊C4—24no—
284C3×C4⋊C4—28no—
285C3×C4⋊C4—34no—
286C3×C4⋊C4—38no—
287C3×C4⋊C4—38no—
288C3×C4⋊C4—34no—
289C3×C4⋊C4—34no—
290C3×C4⋊C4—38no—
291C3×C4⋊C4C22×D314yes—
292C3×C4⋊C4C22×D318yes—
293C3×C4⋊C4C23×C318yes—
294C3×C4⋊C4C23×C314yes—
295C3×C22⋊C4—28no—
296C3×C22⋊C4—38no—
297C3×C22⋊C4—34no—
298C3×C22⋊C4—38no—
299C3×C22⋊C4—34no—
300C3×C22⋊C4—38no—
301C3×C22⋊C4C22×D318yes—
302C3×C22⋊C4C23×C318yes—
303C3×C42—38no—
304C3×C42—38no—
305C3×C42—34no—
306C3×C42—38no—
307#217C23×C314yes—
308#217C23×C318yes—
309(C2×D3)⋊C4C23×C318yes—
310(C2×D3)⋊C4C23×C318yes—
311(C2×D3)⋊C4C23×C314yes—
312C4⋊Dic3C23×C318yes—
313C4⋊Dic3C23×C314yes—
314C4⋊Dic3C23×C314yes—
315Dic3⋊C4C23×C318yes—
316Dic3⋊C4C23×C318yes—
317Dic3⋊C4C23×C314yes—
318C4×Dic3C23×C318yes—
319C4×Dic3C23×C318yes—
320C4×Dic3C23×C318yes—
321C4×Dic3C23×C314yes—
322C22×C32—22no—
323C22×C32—22no—
324C22×C32—22no—
325C22×C32—44no—
326C22×C32C2×#4112yes—
327C22×C32C2×#4112yes—
328C22×C322−1+412yes—
329C22×C32C2511yescharacteristic
330C2×C3×D3—22no—
331C2×C3×D3—22no—
332C2×C3×D3—22no—
333C2×C3×D3—44no—
334C32×C4—24no—
335C32×C4—22no—
336C32×C4—24no—
337C32×C4C2×#4114yes—
338C3×Dic3—24no—
339C3×Dic3—22no—
340C3×Dic3—24no—
341C3×Dic3—22no—
342C3×Dic3C2×#4114yes—
343C22×Q8—32no—
344C22×Q8C2×C3×D311yescharacteristic
345C22×D4—31no—
346C23×C4—31no—
347C23×C4C2×C3×D311yescharacteristic
348C4⋊Q8—38no—
349#126—316no—
350#126—316no—
351#124—316no—
352C22⋊Q8—38no—
353C22⋊Q8C2×C3×D318yescomplemented
354C4×Q8—38no—
355C4×Q8—316no—
356C4×D4—38no—
357#117—38no—
358#117—38no—
359C2×C4⋊C4—31no—
360C2×C4⋊C4—31no—
361C2×C4⋊C4—31no—
362C2×C4⋊C4—32no—
363C2×C4⋊C4—32no—
364C2×C4⋊C4—32no—
365C2×C4⋊C4C2×C3×D311yescharacteristic
366C2×C4⋊C4C2×C3×D312yes—
367C2×C22⋊C4—32no—
368C2×C22⋊C4—31no—
369C2×C22⋊C4—32no—
370C2×C22⋊C4—31no—
371C2×C22⋊C4—32no—
372C2×C22⋊C4C2×C3×D312yes—
373C2×C42—32no—
374C2×C42—32no—
375C2×C42—31no—
376C2×C42—32no—
377C23×C3—24no—
378C23×C3—22no—
379C23×C3—22no—
380C23×C3—22no—
381C23×C3—22no—
382C23×C3—22no—
383C23×C3—22no—
384C23×C3—21no—
385C23×C3—22no—
386C23×C3—32no—
387C23×C3—42no—
388C23×C3—42no—
389C23×C3—62no—
390C23×C3—62no—
391C23×C3—62no—
392C23×C3C23×D312yes—
393C23×C3C23×D311yescharacteristic
394C23×C3C24×C312yes—
395C23×C3C24×C311yescharacteristic
396C22×D3—22no—
397C22×D3—22no—
398C22×D3—22no—
399C22×D3C24×C312yes—
400C3×Q8—28no—
401C3×Q8—28no—
402C3×Q8—48no—
403C3×Q8—616no—
404C3×D4—68no—
405C2×C3×C4—22no—
406C2×C3×C4—24no—
407C2×C3×C4—24no—
408C2×C3×C4—24no—
409C2×C3×C4—22no—
410C2×C3×C4—24no—
411C2×C3×C4—28no—
412C2×C3×C4—28no—
413C2×C3×C4—22no—
414C2×C3×C4—24no—
415C2×C3×C4—24no—
416C2×C3×C4—22no—
417C2×C3×C4—24no—
418C2×C3×C4—34no—
419C2×C3×C4—32no—
420C2×C3×C4—34no—
421C2×C3×C4—32no—
422C2×C3×C4—32no—
423C2×C3×C4—34no—
424C2×C3×C4—48no—
425C2×C3×C4—44no—
426C2×C3×C4—42no—
427C2×C3×C4—44no—
428C2×C3×C4—62no—
429C2×C3×C4—64no—
430C2×C3×C4—62no—
431C2×C3×C4—64no—
432C2×C3×C4—68no—
433C2×C3×C4#23714yes—
434C2×C3×C4C3×#4114yes—
435C2×C3×C4C23×D312yes—
436C2×C3×C4C23×D314yes—
437C2×C3×C4C23×D314yes—
438C2×C3×C4C23×D312yes—
439C2×C3×C4C24×C312yes—
440C2×C3×C4C24×C314yes—
441C2×C3×C4C24×C314yes—
442C2×C3×C4C24×C312yes—
443#67—28no—
444C2×Dic3—24no—
445C2×Dic3—22no—
446C2×Dic3—24no—
447C2×Dic3—22no—
448C2×Dic3C3×#4114yes—
449C2×Dic3C24×C314yes—
450C2×Dic3C24×C312yes—
451C2×Dic3C24×C312yes—
452C2×Dic3C24×C314yes—
453C2×Dic3C24×C312yes—
454C4×D3—28no—
455Dic6—216no—
456C2×C32—42no—
457C2×C32#55614yescomplemented
458C2×C32C22×#4111yescharacteristic
459C2×C32C22×#4111yescharacteristic
460C2×C32C2×2−1+411yescharacteristic
461C3×D3—42no—
462C24—31no—
463C24C22×C3×D311yescharacteristic
464C2×Q8—24no—
465C2×Q8—38no—
466C2×Q8—68no—
467C2×Q8C22×C3×D314yes—
468C2×D4—34no—
469C2×D4—64no—
470C22×C4—24no—
471C22×C4—31no—
472C22×C4—32no—
473C22×C4—31no—
474C22×C4—31no—
475C22×C4—32no—
476C22×C4—34no—
477C22×C4—64no—
478C22×C4C22×C3×D311yescharacteristic
479C22×C4C22×C3×D312yes—
480C22×C4C22×C3×D312yes—
481C22×C4C22×C3×D314yes—
482C22×C4C22×C3×D311yescharacteristic
483C4⋊C4—34no—
484C4⋊C4—34no—
485C4⋊C4—34no—
486C4⋊C4—38no—
487C4⋊C4—38no—
488C4⋊C4—38no—
489C4⋊C4C22×C3×D314yes—
490C4⋊C4C22×C3×D318yes—
491C22⋊C4—38no—
492C22⋊C4—34no—
493C22⋊C4—38no—
494C22⋊C4—34no—
495C22⋊C4—38no—
496C22⋊C4C22×C3×D318yes—
497C42—38no—
498C42—38no—
499C42—34no—
500C42—38no—
501C22×C3—24no—
502C22×C3—22no—
503C22×C3—22no—
504C22×C3—22no—
505C22×C3—22no—
506C22×C3—22no—
507C22×C3—22no—
508C22×C3—22no—
509C22×C3—22no—
510C22×C3—22no—
511C22×C3—21no—
512C22×C3—42no—
513C22×C3—42no—
514C22×C3—48no—
515C22×C3—44no—
516C22×C3—44no—
517C22×C3—62no—
518C22×C3—62no—
519C22×C3—62no—
520C22×C3—124no—
521C22×C3C2×#23712yes—
522C22×C3#100712yes—
523C22×C3D3×#4112yes—
524C22×C3C2×C3×#4112yes—
525C22×C3C2×C3×#4112yes—
526C22×C3C3×2−1+412yes—
527C22×C3C24×D311yescharacteristic
528C22×C3C25×C311yescharacteristic
529C2×D3—22no—
530C2×D3—22no—
531C2×D3—22no—
532C2×D3—44no—
533C3×C4—22no—
534C3×C4—24no—
535C3×C4—24no—
536C3×C4—24no—
537C3×C4—22no—
538C3×C4—24no—
539C3×C4—24no—
540C3×C4—34no—
541C3×C4—42no—
542C3×C4—44no—
543C3×C4—44no—
544C3×C4—62no—
545C3×C4—64no—
546C3×C4—62no—
547C3×C4—64no—
548C3×C4C2×#23714yes—
549C3×C4C2×C3×#4114yes—
550Dic3—24no—
551Dic3—22no—
552Dic3—24no—
553Dic3—22no—
554Dic3C2×C3×#4114yes—
555C32C2×#55611yescharacteristic, complemented, Sylow
556C23—22no—
557C23—22no—
558C23—22no—
559C23—32no—
560C23—62no—
561C23—62no—
562C23—62no—
563C23C23×C3×D312yes—
564C23C23×C3×D311yescharacteristic
565Q8—28no—
566Q8—616no—
567D4—68no—
568C2×C4—22no—
569C2×C4—24no—
570C2×C4—24no—
571C2×C4—28no—
572C2×C4—34no—
573C2×C4—32no—
574C2×C4—34no—
575C2×C4—32no—
576C2×C4—32no—
577C2×C4—34no—
578C2×C4—62no—
579C2×C4—64no—
580C2×C4—62no—
581C2×C4—64no—
582C2×C4—68no—
583C2×C4C3×#23714yes—
584C2×C4C23×C3×D312yes—
585C2×C4C23×C3×D314yes—
586C2×C4C23×C3×D314yes—
587C2×C4C23×C3×D312yes—
588C2×C3—21no—
589C2×C3—21no—
590C2×C3—21no—
591C2×C3—24no—
592C2×C3—44no—
593C2×C3—42no—
594C2×C3—42no—
595C2×C3—122no—
596C2×C3#564114yesdirect product factor
597C2×C3C3×#55614yescomplemented
598C2×C3C22×#23711yescharacteristic
599C2×C3C2×#100711yescharacteristic
600C2×C3C2×D3×#4111yescharacteristic
601C2×C3C22×C3×#4111yescharacteristic
602C2×C3C22×C3×#4111yescharacteristic
603C2×C3C2×C3×2−1+411yescharacteristic
604D3—42no—
605C22—22no—
606C22—22no—
607C22—22no—
608C22—44no—
609C22—62no—
610C22—62no—
611C22—62no—
612C22—124no—
613C22C2×C3×#23712yes—
614C22C3×#100712yes—
615C22C3×D3×#4112yes—
616C22C24×C3×D311yescharacteristic
617C4—22no—
618C4—24no—
619C4—24no—
620C4—34no—
621C4—62no—
622C4—64no—
623C4—62no—
624C4—64no—
625C4C2×C3×#23714yes—
626C3—21no—
627C3C2×#564111yescharacteristic, direct product factor
628C3C2×C3×#55611yescharacteristic, complemented
629C2—42no—
630C2—122no—
631C2C3×#564114yesdirect product factor
632C2C22×C3×#23711yescharacteristic
633C2C2×C3×#100711yescharacteristic
634C2C2×C3×D3×#4111yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC2×C32×C22⋊Q8C2
socleC23×C32C24
prime radicalC22×C3×#67C22
hypercenterC2×C3×C22⋊Q8D3
hypocenterC3C2×C3×#556
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×C32×C22⋊Q8C2semidirect
2. C2×C3×#946C2semidirect
3. C2×C3×Q8×Dic3C2semidirect
5. C2×C3×#926C2semidirect
6. C3×#5641C2direct (N × H)
7. C2×C3×#898C2semidirect
8. C2×C3×#892C2semidirect
9. C2×C3×#888C2semidirect
10. C2×C3×#887C2semidirect
12. C2×C3×#879C2semidirect
14. C2×#5641C3direct (N × H)
20. C32×C22⋊Q8C22semidirect
26. C3×#946C22semidirect
27. C3×Q8×Dic3C22semidirect
32. C3×#926C22semidirect
43. C3×#898C22semidirect
44. C3×#892C22semidirect
45. C3×#888C22semidirect
46. C3×#887C22semidirect
48. C3×#879C22semidirect
56. C2×C3×C22⋊Q8D3semidirect
57. C2×C3×C22⋊Q8C2×C3semidirect
63. C2×#946C2×C3semidirect
64. C2×Q8×Dic3C2×C3semidirect
66. C2×#926C2×C3semidirect
67. #5641C2×C3direct (N × H)
68. C2×#898C2×C3semidirect
69. C2×#892C2×C3semidirect
70. C2×#888C2×C3semidirect
71. C2×#887C2×C3semidirect
73. C2×#879C2×C3semidirect
132. C3×C22⋊Q8C2×D3semidirect
133. C3×C22⋊Q8C22×C3semidirect
165. #946C22×C3semidirect
166. Q8×Dic3C22×C3semidirect
171. #926C22×C3semidirect
182. #898C22×C3semidirect
183. #892C22×C3semidirect
184. #888C22×C3semidirect
185. #887C22×C3semidirect
187. #879C22×C3semidirect
226. C2×C22⋊Q8C3×D3semidirect
353. C22⋊Q8C2×C3×D3semidirect
457. C2×C32#556semidirect
555. C32C2×#556semidirect
596. C2×C3#5641direct (N × H)
597. C2×C3C3×#556semidirect
627. C3C2×#5641direct (N × H)
628. C3C2×C3×#556semidirect
631. C2C3×#5641direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×C22⋊Q82
C2×C3×#9462
C2×C3×Q8×Dic32
C2×C3×C4×#672
C2×C3×#9262
C3×#56412
C2×C3×#8982
C2×C3×#8922
C2×C3×#8882
C2×C3×#8872
C2×C3×#8852
C2×C3×#8792
C2×C3×#5563
C2×#56413