Finite Group Databasebeta

← C2×C3×#5634 #11901861

Subgroups — C2×C3×#5634 #11901861

Order 1152.

2753 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C22⋊Q8C211yesmaximal, characteristic, complemented
2C2×C3×#946C212yesmaximal, complemented
3C22×C3×(C2×D3)⋊C4C211yesmaximal, characteristic
4C2×C3×#924C211yesmaximal, characteristic, complemented
5C3×#5634C2116yesmaximal, direct product factor
6C2×C3×#897C212yesmaximal, complemented
7C2×C3×#896C212yesmaximal, complemented
8C2×C3×#896C212yesmaximal, complemented
9C2×C3×D3×C22⋊C4C212yesmaximal
10C2×C3×#878C212yesmaximal, complemented
11C2×C3×#543—31nomaximal
12C2×#5634C311yesmaximal, characteristic, direct product factor
13C24×C3×D3C2211yescharacteristic
14C22×C32×Q8C2211yescharacteristic, complemented
15C23×C32×C4C2211yescharacteristic
16C23×C3×Dic3C2211yescharacteristic
17C22×C3×C4×D3C2212yes—
18C22×C3×C4×D3C2212yes—
19C22×C3×Dic6C2211yescharacteristic, complemented
20C22×C3×Dic6C2212yescomplemented
21C32×C22⋊Q8C2218yescomplemented
22C2×C32×C4⋊C4C2211yescharacteristic, complemented
23C2×C32×C4⋊C4C2212yescomplemented
24C2×C32×C22⋊C4C2212yes—
25C2×C3×#217C2212yes—
26C3×#946C22116yescomplemented
27C2×C3×(C2×D3)⋊C4C2212yes—
28C2×C3×(C2×D3)⋊C4C2212yes—
29C2×C3×(C2×D3)⋊C4C2212yes—
30C2×C3×(C2×D3)⋊C4C2212yes—
31C2×C3×(C2×D3)⋊C4C2218yes—
32C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
33C2×C3×C4⋊Dic3C2212yescomplemented
34C3×#924C2218yescomplemented
35C2×C3×Dic3⋊C4C2212yescomplemented
36C2×C3×Dic3⋊C4C2212yescomplemented
37C2×C3×Dic3⋊C4C2212yescomplemented
38C3×#897C22116yescomplemented
39C3×#896C22116yescomplemented
40C3×#896C22116yescomplemented
41C3×D3×C22⋊C4C22116yes—
42C3×#878C22116yescomplemented
43C3×#543—316no—
44C2×C3×C22⋊Q8—21no—
45C2×C3×C22⋊Q8—32no—
46C2×C3×C22⋊Q8—31no—
47C2×C3×C22⋊Q8—32no—
48C2×C3×C22⋊Q8—32no—
49C2×C3×C22⋊Q8—32no—
50C2×C3×C22⋊Q8—32no—
51C2×C3×C22⋊Q8D311yescharacteristic, complemented
52C2×C3×C22⋊Q8C2×C311yescharacteristic, complemented
53C22×C3×C22⋊C4—31no—
54C22×C3×C22⋊C4—32no—
55C2×#946C2×C312yescomplemented
56C22×(C2×D3)⋊C4C2×C311yescharacteristic
57C2×#924C2×C311yescharacteristic, complemented
58#5634C2×C3116yesdirect product factor
59C2×#897C2×C312yescomplemented
60C2×#896C2×C312yescomplemented
61C2×#896C2×C312yescomplemented
62C2×D3×C22⋊C4C2×C312yes—
63C2×#878C2×C312yescomplemented
64C24×C32C2311yescharacteristic
65C23×C3×D3—42no—
66C23×C3×D3—42no—
67C23×C3×D3Q818yescomplemented
68C23×C3×D3C2312yes—
69C23×C3×D3C2314yes—
70C2×C32×Q8—42no—
71C2×C32×Q8C2314yescomplemented
72C22×C32×C4—42no—
73C22×C32×C4C2311yescharacteristic
74C22×C32×C4C2312yes—
75C22×C32×C4C2312yes—
76C22×C32×C4C2311yescharacteristic
77C22×C32×C4C2314yes—
78C22×C3×Dic3—42no—
79C22×C3×Dic3C2312yes—
80C22×C3×Dic3C2312yes—
81C22×C3×Dic3C2312yes—
82C22×C3×Dic3C2314yes—
83C2×C3×C4×D3—44no—
84C2×C3×C4×D3—44no—
85C2×C3×C4×D3C2318yes—
86C2×C3×C4×D3C2318yes—
87C2×C3×Dic6—42no—
88C2×C3×Dic6—44no—
89C2×C3×Dic6C2318yescomplemented
90C2×C3×Dic6C2314yescomplemented
91C32×C4⋊C4C2314yescomplemented
92C32×C4⋊C4C2318yescomplemented
93C32×C22⋊C4C2318yes—
94C3×#217C2318yes—
95C3×(C2×D3)⋊C4C2318yes—
96C3×(C2×D3)⋊C4C2318yes—
97C3×(C2×D3)⋊C4C2318yes—
98C3×(C2×D3)⋊C4C2318yes—
99C3×C4⋊Dic3C2318yescomplemented
100C3×C4⋊Dic3C2314yescomplemented
101C3×Dic3⋊C4C2318yescomplemented
102C3×Dic3⋊C4C2318yescomplemented
103C3×Dic3⋊C4C2318yescomplemented
104C2×#543—31noSylow
105C25×C3—31no—
106C24×D3C22×C311yescharacteristic
107C22×C3×Q8—21no—
108C22×C3×Q8—31no—
109C22×C3×Q8—32no—
110C22×C3×Q8C2×D311yescharacteristic, complemented
111C22×C3×Q8C22×C311yescharacteristic, complemented
112C23×C3×C4—21no—
113C23×C3×C4—31no—
114C23×C3×C4—32no—
115C23×C3×C4—32no—
116C23×C3×C4C2×D311yescharacteristic
117C23×C3×C4C22×C311yescharacteristic
118C23×Dic3C22×C311yescharacteristic
119C22×C4×D3C22×C312yes—
120C22×C4×D3C22×C312yes—
121C22×Dic6C22×C312yescomplemented
122C22×Dic6C22×C311yescharacteristic, complemented
123C3×C22⋊Q8—28no—
124C3×C22⋊Q8—316no—
125C3×C22⋊Q8—38no—
126C3×C22⋊Q8—316no—
127C3×C22⋊Q8—316no—
128C3×C22⋊Q8—316no—
129C3×C22⋊Q8—316no—
130C3×C22⋊Q8C2×D318yescomplemented
131C3×C22⋊Q8C22×C318yescomplemented
132C2×C3×C4⋊C4—21no—
133C2×C3×C4⋊C4—22no—
134C2×C3×C4⋊C4—32no—
135C2×C3×C4⋊C4—32no—
136C2×C3×C4⋊C4—32no—
137C2×C3×C4⋊C4—31no—
138C2×C3×C4⋊C4—32no—
139C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
140C2×C3×C4⋊C4C2×D312yescomplemented
141C2×C3×C4⋊C4C22×C311yescharacteristic, complemented
142C2×C3×C4⋊C4C22×C312yescomplemented
143C2×C3×C22⋊C4—22no—
144C2×C3×C22⋊C4—32no—
145C2×C3×C22⋊C4—32no—
146C2×C3×C22⋊C4—32no—
147C2×C3×C22⋊C4—32no—
148C2×C3×C22⋊C4—32no—
149C2×C3×C22⋊C4—38no—
150C2×C3×C22⋊C4—316no—
151C2×C3×C22⋊C4C2×D312yes—
152C2×C3×C22⋊C4C22×C312yes—
153C2×#217C22×C312yes—
154#946C22×C3116yescomplemented
155C2×(C2×D3)⋊C4C22×C318yes—
156C2×(C2×D3)⋊C4C22×C312yes—
157C2×(C2×D3)⋊C4C22×C312yes—
158C2×(C2×D3)⋊C4C22×C312yes—
159C2×(C2×D3)⋊C4C22×C312yes—
160C2×C4⋊Dic3C22×C312yescomplemented
161C2×C4⋊Dic3C22×C311yescharacteristic, complemented
162#924C22×C318yescomplemented
163C2×Dic3⋊C4C22×C312yescomplemented
164C2×Dic3⋊C4C22×C312yescomplemented
165C2×Dic3⋊C4C22×C312yescomplemented
166#897C22×C3116yescomplemented
167#896C22×C3116yescomplemented
168#896C22×C3116yescomplemented
169D3×C22⋊C4C22×C3116yes—
170#878C22×C3116yescomplemented
171C23×C32—22no—
172C23×C32—22no—
173C23×C32C2×Q814yes—
174C23×C32C2412yes—
175C23×C32C2411yescharacteristic
176C22×C3×D3—24no—
177C22×C3×D3—24no—
178C22×C3×D3—416no—
179C22×C3×D3—44no—
180C22×C3×D3—44no—
181C22×C3×D3C2×Q818yes—
182C22×C3×D3C2×Q8116yescomplemented
183C22×C3×D3C2414yes—
184C32×Q8—44no—
185C2×C32×C4—22no—
186C2×C32×C4—24no—
187C2×C32×C4—22no—
188C2×C32×C4—24no—
189C2×C32×C4—44no—
190C2×C32×C4C2412yes—
191C2×C32×C4C2414yes—
192C2×C32×C4C2414yes—
193C2×C32×C4C2412yes—
194C2×C3×Dic3—24no—
195C2×C3×Dic3—24no—
196C2×C3×Dic3—24no—
197C2×C3×Dic3—44no—
198C2×C3×Dic3C2414yes—
199C2×C3×Dic3C2414yes—
200C2×C3×Dic3C2414yes—
201C3×C4×D3—48no—
202C3×C4×D3—48no—
203C3×Dic6—44no—
204C3×Dic6—48no—
205#543—316no—
206C2×C22⋊Q8—32no—
207C2×C22⋊Q8—31no—
208C2×C22⋊Q8—32no—
209C2×C22⋊Q8—32no—
210C2×C22⋊Q8—32no—
211C2×C22⋊Q8—32no—
212C2×C22⋊Q8C3×D311yescharacteristic, complemented
213C22×C22⋊C4—31no—
214C22×C22⋊C4—32no—
215C24×C3—21no—
216C24×C3—32no—
217C24×C3—38no—
218C24×C3—34no—
219C24×C3—122no—
220C24×C3—122no—
221C24×C3C22×D311yescharacteristic
222C24×C3C23×C311yescharacteristic
223C23×D3—42no—
224C23×D3—42no—
225C23×D3C3×Q818yescomplemented
226C23×D3C23×C312yes—
227C23×D3C23×C314yes—
228C2×C3×Q8—24no—
229C2×C3×Q8—34no—
230C2×C3×Q8—38no—
231C2×C3×Q8—42no—
232C2×C3×Q8—42no—
233C2×C3×Q8—44no—
234C2×C3×Q8—122no—
235C2×C3×Q8—124no—
236C2×C3×Q8C22×D314yescomplemented
237C2×C3×Q8C23×C314yescomplemented
238C22×C3×C4—21no—
239C22×C3×C4—22no—
240C22×C3×C4—22no—
241C22×C3×C4—21no—
242C22×C3×C4—24no—
243C22×C3×C4—32no—
244C22×C3×C4—32no—
245C22×C3×C4—32no—
246C22×C3×C4—34no—
247C22×C3×C4—38no—
248C22×C3×C4—38no—
249C22×C3×C4—42no—
250C22×C3×C4—42no—
251C22×C3×C4—44no—
252C22×C3×C4—124no—
253C22×C3×C4—124no—
254C22×C3×C4—122no—
255C22×C3×C4C22×D311yescharacteristic
256C22×C3×C4C22×D311yescharacteristic
257C22×C3×C4C22×D312yes—
258C22×C3×C4C22×D312yes—
259C22×C3×C4C22×D314yes—
260C22×C3×C4C23×C311yescharacteristic
261C22×C3×C4C23×C312yes—
262C22×C3×C4C23×C312yes—
263C22×C3×C4C23×C311yescharacteristic
264C22×C3×C4C23×C314yes—
265C22×Dic3—42no—
266C22×Dic3C23×C312yes—
267C22×Dic3C23×C312yes—
268C22×Dic3C23×C312yes—
269C22×Dic3C23×C314yes—
270C2×C4×D3—44no—
271C2×C4×D3—44no—
272C2×C4×D3C23×C318yes—
273C2×C4×D3C23×C318yes—
274C2×Dic6—42no—
275C2×Dic6—44no—
276C2×Dic6C23×C318yescomplemented
277C2×Dic6C23×C314yescomplemented
278C3×C4⋊C4—24no—
279C3×C4⋊C4—28no—
280C3×C4⋊C4—38no—
281C3×C4⋊C4—38no—
282C3×C4⋊C4—38no—
283C3×C4⋊C4—34no—
284C3×C4⋊C4—38no—
285C3×C4⋊C4C22×D314yescomplemented
286C3×C4⋊C4C22×D318yescomplemented
287C3×C4⋊C4C23×C314yescomplemented
288C3×C4⋊C4C23×C318yescomplemented
289C3×C22⋊C4—28no—
290C3×C22⋊C4—38no—
291C3×C22⋊C4—38no—
292C3×C22⋊C4—38no—
293C3×C22⋊C4—38no—
294C3×C22⋊C4—38no—
295C3×C22⋊C4C22×D318yes—
296C3×C22⋊C4C23×C318yes—
297#217C23×C318yes—
298(C2×D3)⋊C4C23×C318yes—
299(C2×D3)⋊C4C23×C318yes—
300(C2×D3)⋊C4C23×C318yes—
301(C2×D3)⋊C4C23×C318yes—
302C4⋊Dic3C23×C318yescomplemented
303C4⋊Dic3C23×C314yescomplemented
304Dic3⋊C4C23×C318yescomplemented
305Dic3⋊C4C23×C318yescomplemented
306Dic3⋊C4C23×C318yescomplemented
307C22×C32—28no—
308C22×C32—22no—
309C22×C32—22no—
310C22×C32C22×Q814yes—
311C22×C32C22×Q812yes—
312C22×C32H(5,𝔽2)12yes—
313C22×C32H(5,𝔽2)12yes—
314C22×C32C2511yescharacteristic
315C2×C3×D3—216no—
316C2×C3×D3—24no—
317C2×C3×D3—24no—
318C2×C3×D3—416no—
319C2×C3×D3C22×Q818yes—
320C32×C4—22no—
321C32×C4—24no—
322C32×C4—22no—
323C32×C4—24no—
324C3×Dic3—24no—
325C3×Dic3—24no—
326C3×Dic3—24no—
327C25—31no—
328C22×Q8—31no—
329C22×Q8—32no—
330C22×Q8C2×C3×D311yescharacteristic, complemented
331C23×C4—31no—
332C23×C4—32no—
333C23×C4—32no—
334C23×C4C2×C3×D311yescharacteristic
335C22⋊Q8—316no—
336C22⋊Q8—38no—
337C22⋊Q8—316no—
338C22⋊Q8—316no—
339C22⋊Q8—316no—
340C22⋊Q8—316no—
341C22⋊Q8C2×C3×D318yescomplemented
342C2×C4⋊C4—32no—
343C2×C4⋊C4—32no—
344C2×C4⋊C4—32no—
345C2×C4⋊C4—31no—
346C2×C4⋊C4—32no—
347C2×C4⋊C4C2×C3×D311yescharacteristic, complemented
348C2×C4⋊C4C2×C3×D312yescomplemented
349C2×C22⋊C4—32no—
350C2×C22⋊C4—32no—
351C2×C22⋊C4—32no—
352C2×C22⋊C4—32no—
353C2×C22⋊C4—32no—
354C2×C22⋊C4—38no—
355C2×C22⋊C4—316no—
356C2×C22⋊C4C2×C3×D312yes—
357C23×C3—22no—
358C23×C3—22no—
359C23×C3—22no—
360C23×C3—22no—
361C23×C3—21no—
362C23×C3—22no—
363C23×C3—24no—
364C23×C3—38no—
365C23×C3—34no—
366C23×C3—316no—
367C23×C3—42no—
368C23×C3—42no—
369C23×C3—64no—
370C23×C3—64no—
371C23×C3—1216no—
372C23×C3—124no—
373C23×C3—124no—
374C23×C3D3×Q814yes—
375C23×C3C2×C3×Q814yes—
376C23×C3C23×D312yes—
377C23×C3C23×D311yescharacteristic
378C23×C3C24×C312yes—
379C23×C3C24×C311yescharacteristic
380C22×D3—24no—
381C22×D3—24no—
382C22×D3—416no—
383C22×D3—44no—
384C22×D3—44no—
385C22×D3C2×C3×Q818yes—
386C22×D3C2×C3×Q8116yescomplemented
387C22×D3C24×C314yes—
388C3×Q8—44no—
389C3×Q8—44no—
390C3×Q8—48no—
391C3×Q8—124no—
392C3×Q8—128no—
393C2×C3×C4—24no—
394C2×C3×C4—22no—
395C2×C3×C4—22no—
396C2×C3×C4—24no—
397C2×C3×C4—24no—
398C2×C3×C4—24no—
399C2×C3×C4—22no—
400C2×C3×C4—24no—
401C2×C3×C4—22no—
402C2×C3×C4—22no—
403C2×C3×C4—24no—
404C2×C3×C4—24no—
405C2×C3×C4—22no—
406C2×C3×C4—34no—
407C2×C3×C4—34no—
408C2×C3×C4—34no—
409C2×C3×C4—44no—
410C2×C3×C4—42no—
411C2×C3×C4—44no—
412C2×C3×C4—44no—
413C2×C3×C4—44no—
414C2×C3×C4—48no—
415C2×C3×C4—64no—
416C2×C3×C4—64no—
417C2×C3×C4—64no—
418C2×C3×C4—128no—
419C2×C3×C4—128no—
420C2×C3×C4—124no—
421C2×C3×C4C23×D312yes—
422C2×C3×C4C23×D312yes—
423C2×C3×C4C23×D314yes—
424C2×C3×C4C23×D314yes—
425C2×C3×C4C24×C312yes—
426C2×C3×C4C24×C314yes—
427C2×C3×C4C24×C314yes—
428C2×C3×C4C24×C312yes—
429C2×Dic3—24no—
430C2×Dic3—24no—
431C2×Dic3—24no—
432C2×Dic3—44no—
433C2×Dic3C24×C314yes—
434C2×Dic3C24×C314yes—
435C2×Dic3C24×C314yes—
436C4×D3—48no—
437C4×D3—48no—
438Dic6—44no—
439Dic6—48no—
440C2×C32—24no—
441C2×C32#54314yescomplemented
442C2×C32C23×Q811yescharacteristic
443C2×C32C2×H(5,𝔽2)11yescharacteristic
444C2×C32C2×H(5,𝔽2)11yescharacteristic
445C3×D3—28no—
446C24—32no—
447C24—34no—
448C24—38no—
449C24—122no—
450C24—122no—
451C24C22×C3×D311yescharacteristic
452C2×Q8—34no—
453C2×Q8—38no—
454C2×Q8—42no—
455C2×Q8—122no—
456C2×Q8—124no—
457C2×Q8C22×C3×D314yescomplemented
458C22×C4—32no—
459C22×C4—32no—
460C22×C4—32no—
461C22×C4—34no—
462C22×C4—38no—
463C22×C4—38no—
464C22×C4—42no—
465C22×C4—124no—
466C22×C4—124no—
467C22×C4—122no—
468C22×C4C22×C3×D311yescharacteristic
469C22×C4C22×C3×D311yescharacteristic
470C22×C4C22×C3×D312yes—
471C22×C4C22×C3×D312yes—
472C22×C4C22×C3×D314yes—
473C4⋊C4—38no—
474C4⋊C4—38no—
475C4⋊C4—38no—
476C4⋊C4—34no—
477C4⋊C4—38no—
478C4⋊C4C22×C3×D314yescomplemented
479C4⋊C4C22×C3×D318yescomplemented
480C22⋊C4—38no—
481C22⋊C4—38no—
482C22⋊C4—38no—
483C22⋊C4—38no—
484C22⋊C4—38no—
485C22⋊C4C22×C3×D318yes—
486C22×C3—28no—
487C22×C3—22no—
488C22×C3—22no—
489C22×C3—22no—
490C22×C3—22no—
491C22×C3—28no—
492C22×C3—22no—
493C22×C3—22no—
494C22×C3—24no—
495C22×C3—22no—
496C22×C3—21no—
497C22×C3—38no—
498C22×C3—42no—
499C22×C3—42no—
500C22×C3—48no—
501C22×C3—616no—
502C22×C3—64no—
503C22×C3—64no—
504C22×C3—1216no—
505C22×C3#100412yes—
506C22×C3C2×D3×Q814yes—
507C22×C3C2×D3×Q812yes—
508C22×C3#100912yes—
509C22×C3C22×C3×Q814yes—
510C22×C3C22×C3×Q812yes—
511C22×C3C3×H(5,𝔽2)12yes—
512C22×C3C3×H(5,𝔽2)12yes—
513C22×C3C24×D311yescharacteristic
514C22×C3C25×C311yescharacteristic
515C2×D3—24no—
516C2×D3—24no—
517C2×D3—216no—
518C2×D3—416no—
519C2×D3C22×C3×Q818yes—
520C3×C4—24no—
521C3×C4—22no—
522C3×C4—22no—
523C3×C4—24no—
524C3×C4—24no—
525C3×C4—24no—
526C3×C4—22no—
527C3×C4—24no—
528C3×C4—22no—
529C3×C4—42no—
530C3×C4—44no—
531C3×C4—44no—
532C3×C4—64no—
533C3×C4—64no—
534C3×C4—64no—
535Dic3—24no—
536Dic3—24no—
537Dic3—24no—
538C32C2×#54311yescharacteristic, complemented, Sylow
539C23—22no—
540C23—22no—
541C23—38no—
542C23—34no—
543C23—316no—
544C23—64no—
545C23—64no—
546C23—124no—
547C23—124no—
548C23—1216no—
549C23C3×D3×Q814yes—
550C23C23×C3×D312yes—
551C23C23×C3×D311yescharacteristic
552Q8—44no—
553Q8—124no—
554Q8—128no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—34no—
560C2×C4—34no—
561C2×C4—34no—
562C2×C4—44no—
563C2×C4—64no—
564C2×C4—64no—
565C2×C4—64no—
566C2×C4—128no—
567C2×C4—128no—
568C2×C4—124no—
569C2×C4C23×C3×D312yes—
570C2×C4C23×C3×D312yes—
571C2×C4C23×C3×D314yes—
572C2×C4C23×C3×D314yes—
573C2×C3—24no—
574C2×C3—24no—
575C2×C3—21no—
576C2×C3—21no—
577C2×C3—21no—
578C2×C3—24no—
579C2×C3—44no—
580C2×C3—68no—
581C2×C3#563414yesdirect product factor
582C2×C3C3×#54314yescomplemented
583C2×C3C2×#100411yescharacteristic
584C2×C3C22×D3×Q811yescharacteristic
585C2×C3C2×#100911yescharacteristic
586C2×C3C23×C3×Q811yescharacteristic
587C2×C3C2×C3×H(5,𝔽2)11yescharacteristic
588C2×C3C2×C3×H(5,𝔽2)11yescharacteristic
589D3—28no—
590C22—22no—
591C22—22no—
592C22—28no—
593C22—38no—
594C22—64no—
595C22—64no—
596C22—616no—
597C22—1216no—
598C22C3×#100412yes—
599C22C2×C3×D3×Q814yes—
600C22C2×C3×D3×Q812yes—
601C22C3×#100912yes—
602C22C24×C3×D311yescharacteristic
603C4—22no—
604C4—22no—
605C4—24no—
606C4—24no—
607C4—64no—
608C4—64no—
609C4—64no—
610C3—21no—
611C3C2×#563411yescharacteristic, direct product factor
612C3C2×C3×#54311yescharacteristic, complemented
613C2—24no—
614C2—68no—
615C2C3×#563414yesdirect product factor
616C2C2×C3×#100411yescharacteristic
617C2C22×C3×D3×Q811yescharacteristic
618C2C2×C3×#100911yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC2×C32×C22⋊Q8C2
socleC23×C32C24
prime radicalC24×C3×D3C22
hypercenterC2×C3×C22⋊Q8D3
hypocenterC3C2×C3×#543
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
4. C2×C3×#924C2semidirect
5. C3×#5634C2direct (N × H)
6. C2×C3×#897C2semidirect
7. C2×C3×#896C2semidirect
8. C2×C3×#896C2semidirect
10. C2×C3×#878C2semidirect
12. C2×#5634C3direct (N × H)
14. C22×C32×Q8C22semidirect
19. C22×C3×Dic6C22semidirect
20. C22×C3×Dic6C22semidirect
21. C32×C22⋊Q8C22semidirect
22. C2×C32×C4⋊C4C22semidirect
23. C2×C32×C4⋊C4C22semidirect
26. C3×#946C22semidirect
32. C2×C3×C4⋊Dic3C22semidirect
33. C2×C3×C4⋊Dic3C22semidirect
34. C3×#924C22semidirect
35. C2×C3×Dic3⋊C4C22semidirect
36. C2×C3×Dic3⋊C4C22semidirect
37. C2×C3×Dic3⋊C4C22semidirect
38. C3×#897C22semidirect
39. C3×#896C22semidirect
40. C3×#896C22semidirect
42. C3×#878C22semidirect
51. C2×C3×C22⋊Q8D3semidirect
52. C2×C3×C22⋊Q8C2×C3semidirect
55. C2×#946C2×C3semidirect
57. C2×#924C2×C3semidirect
58. #5634C2×C3direct (N × H)
59. C2×#897C2×C3semidirect
60. C2×#896C2×C3semidirect
61. C2×#896C2×C3semidirect
63. C2×#878C2×C3semidirect
67. C23×C3×D3Q8semidirect
71. C2×C32×Q8C23semidirect
89. C2×C3×Dic6C23semidirect
90. C2×C3×Dic6C23semidirect
91. C32×C4⋊C4C23semidirect
92. C32×C4⋊C4C23semidirect
99. C3×C4⋊Dic3C23semidirect
100. C3×C4⋊Dic3C23semidirect
101. C3×Dic3⋊C4C23semidirect
102. C3×Dic3⋊C4C23semidirect
103. C3×Dic3⋊C4C23semidirect
110. C22×C3×Q8C2×D3semidirect
111. C22×C3×Q8C22×C3semidirect
121. C22×Dic6C22×C3semidirect
122. C22×Dic6C22×C3semidirect
130. C3×C22⋊Q8C2×D3semidirect
131. C3×C22⋊Q8C22×C3semidirect
139. C2×C3×C4⋊C4C2×D3semidirect
140. C2×C3×C4⋊C4C2×D3semidirect
141. C2×C3×C4⋊C4C22×C3semidirect
142. C2×C3×C4⋊C4C22×C3semidirect
154. #946C22×C3semidirect
160. C2×C4⋊Dic3C22×C3semidirect
161. C2×C4⋊Dic3C22×C3semidirect
162. #924C22×C3semidirect
163. C2×Dic3⋊C4C22×C3semidirect
164. C2×Dic3⋊C4C22×C3semidirect
165. C2×Dic3⋊C4C22×C3semidirect
166. #897C22×C3semidirect
167. #896C22×C3semidirect
168. #896C22×C3semidirect
170. #878C22×C3semidirect
182. C22×C3×D3C2×Q8semidirect
212. C2×C22⋊Q8C3×D3semidirect
225. C23×D3C3×Q8semidirect
236. C2×C3×Q8C22×D3semidirect
237. C2×C3×Q8C23×C3semidirect
276. C2×Dic6C23×C3semidirect
277. C2×Dic6C23×C3semidirect
285. C3×C4⋊C4C22×D3semidirect
286. C3×C4⋊C4C22×D3semidirect
287. C3×C4⋊C4C23×C3semidirect
288. C3×C4⋊C4C23×C3semidirect
302. C4⋊Dic3C23×C3semidirect
303. C4⋊Dic3C23×C3semidirect
304. Dic3⋊C4C23×C3semidirect
305. Dic3⋊C4C23×C3semidirect
306. Dic3⋊C4C23×C3semidirect
330. C22×Q8C2×C3×D3semidirect
341. C22⋊Q8C2×C3×D3semidirect
347. C2×C4⋊C4C2×C3×D3semidirect
348. C2×C4⋊C4C2×C3×D3semidirect
386. C22×D3C2×C3×Q8semidirect
441. C2×C32#543semidirect
457. C2×Q8C22×C3×D3semidirect
478. C4⋊C4C22×C3×D3semidirect
479. C4⋊C4C22×C3×D3semidirect
538. C32C2×#543semidirect
581. C2×C3#5634direct (N × H)
582. C2×C3C3×#543semidirect
611. C3C2×#5634direct (N × H)
612. C3C2×C3×#543semidirect
615. C2C3×#5634direct (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
C22×C3×(C2×D3)⋊C42
C2×C3×#9242
C3×#56342
C2×C3×#8972
C2×C3×#8962
C2×C3×D3×C22⋊C42
C2×C3×#8782
C2×C3×#5433
C2×#56343