Finite Group Databasebeta

← C2×C3×#5513 #11902979

Subgroups — C2×C3×#5513 #11902979

Order 1152.

2457 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
1C22×C32×C4⋊C4C211yesmaximal, characteristic, complemented
2C2×C3×#929C212yesmaximal
3C2×C3×C4×#67C211yesmaximal, characteristic
4C2×C3×#926C212yesmaximal, complemented
5C2×C3×#924C211yesmaximal, characteristic, complemented
6C3×#5513C2116yesmaximal, direct product factor
7C2×C3×#898C212yesmaximal, complemented
8C2×C3×#897C211yesmaximal, characteristic, complemented
9C2×C3×#892C211yesmaximal, characteristic, complemented
10C2×C3×#890C211yesmaximal, characteristic, complemented
11C2×C3×#889C212yesmaximal, complemented
12C2×C3×#887C211yesmaximal, characteristic, complemented
13C2×C3×#552—31nomaximal
14C2×#5513C311yesmaximal, characteristic, direct product factor
15C23×C32×C4C2211yescharacteristic
16C23×C32×C4C2212yes—
17C22×C3×#67C2211yescharacteristic
18C22×C3×C4×D3C2211yescharacteristic
19C22×C3×Dic6C2211yescharacteristic
20C2×C32×C4⋊C4C2211yescharacteristic
21C2×C32×C4⋊C4C2212yes—
22C2×C32×C4⋊C4C2211yescharacteristic
23C2×C32×C4⋊C4C2218yescomplemented
24C2×C3×#217C2212yes—
25C2×C3×#217C2211yescharacteristic
26C3×#929C22116yes—
27C3×C4×#67C2218yes—
28C2×C3×(C2×D3)⋊C4C2212yes—
29C2×C3×(C2×D3)⋊C4C2212yes—
30C2×C3×(C2×D3)⋊C4C2211yescharacteristic
31C3×#926C22116yescomplemented
32C2×C3×C4⋊Dic3C2212yes—
33C2×C3×C4⋊Dic3C2211yescharacteristic
34C2×C3×C4⋊Dic3C2212yes—
35C3×#924C2218yescomplemented
36C2×C3×Dic3⋊C4C2212yes—
37C2×C3×Dic3⋊C4C2211yescharacteristic
38C2×C3×Dic3⋊C4C2212yes—
39C2×C3×Dic3⋊C4C2212yes—
40C2×C3×C4×Dic3C2211yescharacteristic
41C2×C3×C4×Dic3C2212yes—
42C2×C3×C4×Dic3C2212yes—
43C3×#898C22116yescomplemented
44C3×#897C2218yescomplemented
45C3×#892C2218yescomplemented
46C3×#890C2218yescomplemented
47C3×#889C22116yescomplemented
48C3×#887C2218yescomplemented
49C3×#552—316no—
50C2×C3×#126—32no—
51C2×C3×#125—32no—
52C2×C3×#125—31no—
53C2×C3×#123—32no—
54C2×C3×C22⋊Q8—31no—
55C2×C3×C22⋊Q8—31no—
56C2×C3×C4×Q8—31no—
57C2×C3×C4×D4—31no—
58C2×C3×#117—32no—
59C2×C3×#117—31no—
60C22×C3×C4⋊C4—21no—
61C22×C3×C4⋊C4D311yescharacteristic, complemented
62C22×C3×C4⋊C4C2×C311yescharacteristic, complemented
63C2×#929C2×C312yes—
64C2×C4×#67C2×C311yescharacteristic
65C2×#926C2×C312yescomplemented
66C2×#924C2×C311yescharacteristic, complemented
67#5513C2×C3116yesdirect product factor
68C2×#898C2×C312yescomplemented
69C2×#897C2×C311yescharacteristic, complemented
70C2×#892C2×C311yescharacteristic, complemented
71C2×#890C2×C311yescharacteristic, complemented
72C2×#889C2×C312yescomplemented
73C2×#887C2×C311yescharacteristic, complemented
74C24×C32C2311yescharacteristic
75C23×C3×D3C2311yescharacteristic
76C22×C32×C4—28no—
77C22×C32×C4—24no—
78C22×C32×C4C2312yes—
79C22×C32×C4C2311yescharacteristic
80C22×C32×C4C2312yes—
81C22×C32×C4C2314yes—
82C22×C32×C4C2318yes—
83C22×C32×C4C2311yescharacteristic
84C2×C3×#67—24no—
85C2×C3×#67C2314yes—
86C22×C3×Dic3C2311yescharacteristic
87C22×C3×Dic3C2311yescharacteristic
88C22×C3×Dic3C2311yescharacteristic
89C22×C3×Dic3C2312yes—
90C22×C3×Dic3C2312yes—
91C2×C3×C4×D3—24no—
92C2×C3×C4×D3C2314yes—
93C2×C3×Dic6—24no—
94C2×C3×Dic6C2314yes—
95C32×C4⋊C4C2314yes—
96C32×C4⋊C4C2318yes—
97C32×C4⋊C4C2314yes—
98C3×#217C2318yes—
99C3×#217C2314yes—
100C3×(C2×D3)⋊C4C2318yes—
101C3×(C2×D3)⋊C4C2318yes—
102C3×(C2×D3)⋊C4C2314yes—
103C3×C4⋊Dic3C2318yes—
104C3×C4⋊Dic3C2314yes—
105C3×C4⋊Dic3C2318yes—
106C3×Dic3⋊C4C2318yes—
107C3×Dic3⋊C4C2314yes—
108C3×Dic3⋊C4C2318yes—
109C3×Dic3⋊C4C2318yes—
110C3×C4×Dic3C2314yes—
111C3×C4×Dic3C2318yes—
112C3×C4×Dic3C2318yes—
113C2×#552—31noSylow
114C22×C3×Q8—31no—
115C22×C3×D4—31no—
116C23×C3×C4—21no—
117C23×C3×C4—22no—
118C23×C3×C4—31no—
119C23×C3×C4C2×D312yes—
120C23×C3×C4C2×D311yescharacteristic
121C23×C3×C4C22×C311yescharacteristic
122C23×C3×C4C22×C312yes—
123C22×#67C22×C311yescharacteristic
124C22×C4×D3C22×C311yescharacteristic
125C22×Dic6C22×C311yescharacteristic
126C3×#126—316no—
127C3×#125—316no—
128C3×#125—38no—
129C3×#123—316no—
130C3×C22⋊Q8—38no—
131C3×C22⋊Q8—38no—
132C3×C4×Q8—38no—
133C3×C4×D4—38no—
134C3×#117—316no—
135C3×#117—38no—
136C2×C3×C4⋊C4—21no—
137C2×C3×C4⋊C4—21no—
138C2×C3×C4⋊C4—22no—
139C2×C3×C4⋊C4—28no—
140C2×C3×C4⋊C4—31no—
141C2×C3×C4⋊C4—32no—
142C2×C3×C4⋊C4—32no—
143C2×C3×C4⋊C4—32no—
144C2×C3×C4⋊C4—32no—
145C2×C3×C4⋊C4—31no—
146C2×C3×C4⋊C4—32no—
147C2×C3×C4⋊C4C2×D311yescharacteristic
148C2×C3×C4⋊C4C2×D311yescharacteristic
149C2×C3×C4⋊C4C2×D312yes—
150C2×C3×C4⋊C4C2×D318yescomplemented
151C2×C3×C4⋊C4C22×C311yescharacteristic
152C2×C3×C4⋊C4C22×C312yes—
153C2×C3×C4⋊C4C22×C311yescharacteristic
154C2×C3×C4⋊C4C22×C318yescomplemented
155C2×C3×C22⋊C4—31no—
156C2×C3×C22⋊C4—32no—
157C2×C3×C22⋊C4—32no—
158C2×C3×C22⋊C4—31no—
159C2×C3×C22⋊C4—32no—
160C2×C3×C42—32no—
161C2×C3×C42—32no—
162C2×C3×C42—31no—
163C2×#217C22×C312yes—
164C2×#217C22×C311yescharacteristic
165#929C22×C3116yes—
166C4×#67C22×C318yes—
167C2×(C2×D3)⋊C4C22×C312yes—
168C2×(C2×D3)⋊C4C22×C312yes—
169C2×(C2×D3)⋊C4C22×C311yescharacteristic
170#926C22×C3116yescomplemented
171C2×C4⋊Dic3C22×C312yes—
172C2×C4⋊Dic3C22×C311yescharacteristic
173C2×C4⋊Dic3C22×C312yes—
174#924C22×C318yescomplemented
175C2×Dic3⋊C4C22×C312yes—
176C2×Dic3⋊C4C22×C311yescharacteristic
177C2×Dic3⋊C4C22×C312yes—
178C2×Dic3⋊C4C22×C312yes—
179C2×C4×Dic3C22×C311yescharacteristic
180C2×C4×Dic3C22×C312yes—
181C2×C4×Dic3C22×C312yes—
182#898C22×C3116yescomplemented
183#897C22×C318yescomplemented
184#892C22×C318yescomplemented
185#890C22×C318yescomplemented
186#889C22×C3116yescomplemented
187#887C22×C318yescomplemented
188C23×C32—22no—
189C23×C32—22no—
190C23×C32#4114yes—
191C23×C32C2412yes—
192C23×C32C2411yescharacteristic
193C22×C3×D3—22no—
194C22×C3×D3—22no—
195C22×C3×D3—22no—
196C22×C3×D3C2412yes—
197C2×C32×C4—22no—
198C2×C32×C4—28no—
199C2×C32×C4—216no—
200C2×C32×C4—24no—
201C2×C32×C4—24no—
202C2×C32×C4#4114yes—
203C2×C32×C4C2414yes—
204C2×C32×C4C2412yes—
205C2×C32×C4C2414yes—
206C2×C32×C4C2412yes—
207C3×#67—28no—
208C2×C3×Dic3—24no—
209C2×C3×Dic3—22no—
210C2×C3×Dic3—22no—
211C2×C3×Dic3—22no—
212C2×C3×Dic3—24no—
213C2×C3×Dic3C2412yes—
214C2×C3×Dic3C2412yes—
215C2×C3×Dic3C2412yes—
216C2×C3×Dic3C2414yes—
217C2×C3×Dic3C2414yes—
218C3×C4×D3—28no—
219C3×Dic6—28no—
220#552—316no—
221C2×#126—32no—
222C2×#125—32no—
223C2×#125—31no—
224C2×#123—32no—
225C2×C22⋊Q8—31no—
226C2×C22⋊Q8—31no—
227C2×C4×Q8—31no—
228C2×C4×D4—31no—
229C2×#117—32no—
230C2×#117—31no—
231C22×C4⋊C4C3×D311yescharacteristic, complemented
232C24×C3—21no—
233C24×C3—31no—
234C24×C3C22×D311yescharacteristic
235C24×C3C23×C311yescharacteristic
236C23×D3C23×C311yescharacteristic
237C2×C3×Q8—34no—
238C2×C3×Q8—64no—
239C2×C3×D4—34no—
240C2×C3×D4—64no—
241C22×C3×C4—28no—
242C22×C3×C4—28no—
243C22×C3×C4—28no—
244C22×C3×C4—24no—
245C22×C3×C4—24no—
246C22×C3×C4—21no—
247C22×C3×C4—24no—
248C22×C3×C4—21no—
249C22×C3×C4—22no—
250C22×C3×C4—22no—
251C22×C3×C4—28no—
252C22×C3×C4—31no—
253C22×C3×C4—31no—
254C22×C3×C4—32no—
255C22×C3×C4—32no—
256C22×C3×C4—31no—
257C22×C3×C4—34no—
258C22×C3×C4—48no—
259C22×C3×C4—64no—
260C22×C3×C4C22×D318yes—
261C22×C3×C4C22×D314yes—
262C22×C3×C4C22×D312yes—
263C22×C3×C4C22×D311yescharacteristic
264C22×C3×C4C22×D312yes—
265C22×C3×C4C22×D311yescharacteristic
266C22×C3×C4C23×C312yes—
267C22×C3×C4C23×C311yescharacteristic
268C22×C3×C4C23×C312yes—
269C22×C3×C4C23×C314yes—
270C22×C3×C4C23×C318yes—
271C22×C3×C4C23×C311yescharacteristic
272C2×#67—24no—
273C2×#67C23×C314yes—
274C22×Dic3C23×C311yescharacteristic
275C22×Dic3C23×C311yescharacteristic
276C22×Dic3C23×C311yescharacteristic
277C22×Dic3C23×C312yes—
278C22×Dic3C23×C312yes—
279C2×C4×D3—24no—
280C2×C4×D3C23×C314yes—
281C2×Dic6—24no—
282C2×Dic6C23×C314yes—
283C3×C4⋊C4—24no—
284C3×C4⋊C4—24no—
285C3×C4⋊C4—28no—
286C3×C4⋊C4—34no—
287C3×C4⋊C4—38no—
288C3×C4⋊C4—38no—
289C3×C4⋊C4—38no—
290C3×C4⋊C4—38no—
291C3×C4⋊C4—34no—
292C3×C4⋊C4—38no—
293C3×C4⋊C4C22×D314yes—
294C3×C4⋊C4C22×D314yes—
295C3×C4⋊C4C22×D318yes—
296C3×C4⋊C4C23×C314yes—
297C3×C4⋊C4C23×C318yes—
298C3×C4⋊C4C23×C314yes—
299C3×C22⋊C4—34no—
300C3×C22⋊C4—38no—
301C3×C22⋊C4—38no—
302C3×C22⋊C4—34no—
303C3×C22⋊C4—38no—
304C3×C42—38no—
305C3×C42—38no—
306C3×C42—34no—
307#217C23×C318yes—
308#217C23×C314yes—
309(C2×D3)⋊C4C23×C318yes—
310(C2×D3)⋊C4C23×C318yes—
311(C2×D3)⋊C4C23×C314yes—
312C4⋊Dic3C23×C318yes—
313C4⋊Dic3C23×C314yes—
314C4⋊Dic3C23×C318yes—
315Dic3⋊C4C23×C318yes—
316Dic3⋊C4C23×C314yes—
317Dic3⋊C4C23×C318yes—
318Dic3⋊C4C23×C318yes—
319C4×Dic3C23×C314yes—
320C4×Dic3C23×C318yes—
321C4×Dic3C23×C318yes—
322C22×C32—28no—
323C22×C32—22no—
324C22×C32—22no—
325C22×C32C2×#4112yes—
326C22×C32C2×#4114yes—
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—22no—
335C32×C4—24no—
336C32×C4—24no—
337C32×C4C2×#4114yes—
338C3×Dic3—24no—
339C3×Dic3—22no—
340C3×Dic3—22no—
341C3×Dic3—22no—
342C3×Dic3—24no—
343C22×Q8—31no—
344C22×D4—31no—
345C23×C4—31no—
346C23×C4C2×C3×D312yes—
347C23×C4C2×C3×D311yescharacteristic
348#126—316no—
349#125—316no—
350#125—38no—
351#123—316no—
352C22⋊Q8—38no—
353C22⋊Q8—38no—
354C4×Q8—38no—
355C4×D4—38no—
356#117—316no—
357#117—38no—
358C2×C4⋊C4—32no—
359C2×C4⋊C4—31no—
360C2×C4⋊C4—32no—
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×D311yescharacteristic
367C2×C4⋊C4C2×C3×D312yes—
368C2×C4⋊C4C2×C3×D318yescomplemented
369C2×C22⋊C4—31no—
370C2×C22⋊C4—32no—
371C2×C22⋊C4—32no—
372C2×C22⋊C4—31no—
373C2×C22⋊C4—32no—
374C2×C42—32no—
375C2×C42—32no—
376C2×C42—31no—
377C23×C3—24no—
378C23×C3—24no—
379C23×C3—22no—
380C23×C3—22no—
381C23×C3—22no—
382C23×C3—22no—
383C23×C3—22no—
384C23×C3—21no—
385C23×C3—24no—
386C23×C3—32no—
387C23×C3—62no—
388C23×C3—62no—
389C23×C3—62no—
390C23×C3#23714yes—
391C23×C3C3×#4114yes—
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—68no—
401C3×D4—68no—
402C2×C3×C4—24no—
403C2×C3×C4—216no—
404C2×C3×C4—22no—
405C2×C3×C4—216no—
406C2×C3×C4—24no—
407C2×C3×C4—24no—
408C2×C3×C4—22no—
409C2×C3×C4—216no—
410C2×C3×C4—24no—
411C2×C3×C4—24no—
412C2×C3×C4—28no—
413C2×C3×C4—28no—
414C2×C3×C4—22no—
415C2×C3×C4—22no—
416C2×C3×C4—24no—
417C2×C3×C4—24no—
418C2×C3×C4—24no—
419C2×C3×C4—32no—
420C2×C3×C4—32no—
421C2×C3×C4—34no—
422C2×C3×C4—34no—
423C2×C3×C4—32no—
424C2×C3×C4—416no—
425C2×C3×C4—44no—
426C2×C3×C4—44no—
427C2×C3×C4—62no—
428C2×C3×C4—64no—
429C2×C3×C4—62no—
430C2×C3×C4—62no—
431C2×C3×C4—64no—
432C2×C3×C4—68no—
433C2×C3×C4#23514yes—
434C2×C3×C4C3×#4114yes—
435C2×C3×C4C23×D314yes—
436C2×C3×C4C23×D312yes—
437C2×C3×C4C23×D314yes—
438C2×C3×C4C23×D312yes—
439C2×C3×C4C24×C314yes—
440C2×C3×C4C24×C312yes—
441C2×C3×C4C24×C314yes—
442C2×C3×C4C24×C312yes—
443#67—28no—
444C2×Dic3—24no—
445C2×Dic3—22no—
446C2×Dic3—22no—
447C2×Dic3—22no—
448C2×Dic3—24no—
449C2×Dic3C24×C312yes—
450C2×Dic3C24×C312yes—
451C2×Dic3C24×C312yes—
452C2×Dic3C24×C314yes—
453C2×Dic3C24×C314yes—
454C4×D3—28no—
455Dic6—28no—
456C2×C32—24no—
457C2×C32#55214yescomplemented
458C2×C32C22×#4111yescharacteristic
459C2×C32C22×#4111yescharacteristic
460C2×C32C2×2−1+411yescharacteristic
461C3×D3—42no—
462C24—31no—
463C24C22×C3×D311yescharacteristic
464C2×Q8—34no—
465C2×Q8—64no—
466C2×D4—34no—
467C2×D4—64no—
468C22×C4—28no—
469C22×C4—24no—
470C22×C4—31no—
471C22×C4—31no—
472C22×C4—32no—
473C22×C4—32no—
474C22×C4—31no—
475C22×C4—34no—
476C22×C4—64no—
477C22×C4C22×C3×D312yes—
478C22×C4C22×C3×D311yescharacteristic
479C22×C4C22×C3×D312yes—
480C22×C4C22×C3×D318yes—
481C22×C4C22×C3×D314yes—
482C22×C4C22×C3×D311yescharacteristic
483C4⋊C4—38no—
484C4⋊C4—34no—
485C4⋊C4—38no—
486C4⋊C4—34no—
487C4⋊C4—38no—
488C4⋊C4—38no—
489C4⋊C4—38no—
490C4⋊C4C22×C3×D314yes—
491C4⋊C4C22×C3×D314yes—
492C4⋊C4C22×C3×D318yes—
493C22⋊C4—34no—
494C22⋊C4—38no—
495C22⋊C4—38no—
496C22⋊C4—34no—
497C22⋊C4—38no—
498C42—38no—
499C42—38no—
500C42—34no—
501C22×C3—24no—
502C22×C3—216no—
503C22×C3—24no—
504C22×C3—22no—
505C22×C3—22no—
506C22×C3—22no—
507C22×C3—22no—
508C22×C3—28no—
509C22×C3—28no—
510C22×C3—22no—
511C22×C3—24no—
512C22×C3—22no—
513C22×C3—22no—
514C22×C3—21no—
515C22×C3—62no—
516C22×C3—62no—
517C22×C3—62no—
518C22×C3—124no—
519C22×C3C2×#23512yes—
520C22×C3C2×#23714yes—
521C22×C3C2×#23712yes—
522C22×C3#100712yes—
523C22×C3C2×C3×#4112yes—
524C22×C3C2×C3×#4114yes—
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—24no—
534C3×C4—22no—
535C3×C4—24no—
536C3×C4—24no—
537C3×C4—22no—
538C3×C4—24no—
539C3×C4—24no—
540C3×C4—24no—
541C3×C4—44no—
542C3×C4—44no—
543C3×C4—62no—
544C3×C4—64no—
545C3×C4—62no—
546C3×C4—62no—
547C3×C4—64no—
548C3×C4C2×#23514yes—
549C3×C4C2×C3×#4114yes—
550Dic3—24no—
551Dic3—22no—
552Dic3—22no—
553Dic3—22no—
554Dic3—24no—
555C32C2×#55211yescharacteristic, complemented, Sylow
556C23—22no—
557C23—22no—
558C23—32no—
559C23—62no—
560C23—62no—
561C23—62no—
562C23C3×#23714yes—
563C23C23×C3×D312yes—
564C23C23×C3×D311yescharacteristic
565Q8—68no—
566D4—68no—
567C2×C4—22no—
568C2×C4—216no—
569C2×C4—24no—
570C2×C4—24no—
571C2×C4—28no—
572C2×C4—32no—
573C2×C4—32no—
574C2×C4—34no—
575C2×C4—34no—
576C2×C4—32no—
577C2×C4—62no—
578C2×C4—64no—
579C2×C4—62no—
580C2×C4—62no—
581C2×C4—64no—
582C2×C4—68no—
583C2×C4C3×#23514yes—
584C2×C4C23×C3×D314yes—
585C2×C4C23×C3×D312yes—
586C2×C4C23×C3×D314yes—
587C2×C4C23×C3×D312yes—
588C2×C3—28no—
589C2×C3—24no—
590C2×C3—24no—
591C2×C3—24no—
592C2×C3—21no—
593C2×C3—21no—
594C2×C3—21no—
595C2×C3—122no—
596C2×C3#551314yesdirect product factor
597C2×C3C3×#55214yescomplemented
598C2×C3C22×#23511yescharacteristic
599C2×C3C22×#23711yescharacteristic
600C2×C3C2×#100711yescharacteristic
601C2×C3C22×C3×#4111yescharacteristic
602C2×C3C22×C3×#4111yescharacteristic
603C2×C3C2×C3×2−1+411yescharacteristic
604D3—42no—
605C22—28no—
606C22—22no—
607C22—22no—
608C22—62no—
609C22—62no—
610C22—62no—
611C22—124no—
612C22C2×C3×#23512yes—
613C22C2×C3×#23714yes—
614C22C2×C3×#23712yes—
615C22C3×#100712yes—
616C22C24×C3×D311yescharacteristic
617C4—22no—
618C4—24no—
619C4—24no—
620C4—62no—
621C4—64no—
622C4—62no—
623C4—62no—
624C4—64no—
625C4C2×C3×#23514yes—
626C3—21no—
627C3C2×#551311yescharacteristic, direct product factor
628C3C2×C3×#55211yescharacteristic, complemented
629C2—24no—
630C2—122no—
631C2C3×#551314yesdirect product factor
632C2C22×C3×#23511yescharacteristic
633C2C22×C3×#23711yescharacteristic
634C2C2×C3×#100711yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC22×C32×C4⋊C4C2
socleC23×C32C24
prime radicalC22×C3×#67C22
hypercenterC22×C3×C4⋊C4D3
hypocenterC3C2×C3×#552
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C22×C3×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×C32×C4⋊C4C2semidirect
4. C2×C3×#926C2semidirect
5. C2×C3×#924C2semidirect
6. C3×#5513C2direct (N × H)
7. C2×C3×#898C2semidirect
8. C2×C3×#897C2semidirect
9. C2×C3×#892C2semidirect
10. C2×C3×#890C2semidirect
11. C2×C3×#889C2semidirect
12. C2×C3×#887C2semidirect
14. C2×#5513C3direct (N × H)
23. C2×C32×C4⋊C4C22semidirect
31. C3×#926C22semidirect
35. C3×#924C22semidirect
43. C3×#898C22semidirect
44. C3×#897C22semidirect
45. C3×#892C22semidirect
46. C3×#890C22semidirect
47. C3×#889C22semidirect
48. C3×#887C22semidirect
61. C22×C3×C4⋊C4D3semidirect
62. C22×C3×C4⋊C4C2×C3semidirect
65. C2×#926C2×C3semidirect
66. C2×#924C2×C3semidirect
67. #5513C2×C3direct (N × H)
68. C2×#898C2×C3semidirect
69. C2×#897C2×C3semidirect
70. C2×#892C2×C3semidirect
71. C2×#890C2×C3semidirect
72. C2×#889C2×C3semidirect
73. C2×#887C2×C3semidirect
150. C2×C3×C4⋊C4C2×D3semidirect
154. C2×C3×C4⋊C4C22×C3semidirect
170. #926C22×C3semidirect
174. #924C22×C3semidirect
182. #898C22×C3semidirect
183. #897C22×C3semidirect
184. #892C22×C3semidirect
185. #890C22×C3semidirect
186. #889C22×C3semidirect
187. #887C22×C3semidirect
231. C22×C4⋊C4C3×D3semidirect
368. C2×C4⋊C4C2×C3×D3semidirect
457. C2×C32#552semidirect
555. C32C2×#552semidirect
596. C2×C3#5513direct (N × H)
597. C2×C3C3×#552semidirect
627. C3C2×#5513direct (N × H)
628. C3C2×C3×#552semidirect
631. C2C3×#5513direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C32×C4⋊C42
C2×C3×#9292
C2×C3×C4×#672
C2×C3×#9262
C2×C3×#9242
C3×#55132
C2×C3×#8982
C2×C3×#8972
C2×C3×#8922
C2×C3×#8902
C2×C3×#8892
C2×C3×#8872
C2×C3×#5523
C2×#55133