Finite Group Databasebeta

← C2×C3×#5539 #11903231

Subgroups — C2×C3×#5539 #11903231

Order 1152.

2613 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×C4×D4C211yesmaximal, characteristic
2C2×C3×D4×Dic3C211yesmaximal, characteristic
3C2×C3×D4×Dic3C211yesmaximal, characteristic
4C2×C3×#924C212yesmaximal, complemented
5C22×C3×Dic3⋊C4C212yesmaximal, complemented
6C3×#5539C2116yesmaximal, direct product factor
7C2×C3×#890C211yesmaximal, characteristic, complemented
8C2×C3×#888C211yesmaximal, characteristic, complemented
9C2×C3×#878C212yesmaximal, complemented
10C2×C3×#878C212yesmaximal, complemented
11C2×C3×#870C211yesmaximal, characteristic, complemented
12C2×C3×C4×Dic6C211yesmaximal, characteristic, complemented
13C2×C3×#554—31nomaximal
14C2×#5539C311yesmaximal, characteristic, direct product factor
15C22×C32×D4C2211yescharacteristic
16C23×C32×C4C2212yes—
17C23×C3×Dic3C2212yes—
18C23×C3×Dic3C2212yes—
19C22×C3×Dic6C2211yescharacteristic
20C22×C3×Dic6C2212yes—
21C32×C4×D4C2218yes—
22C2×C32×C4⋊C4C2211yescharacteristic
23C2×C32×C22⋊C4C2212yes—
24C2×C32×C42C2211yescharacteristic
25C2×C3×#217C2212yes—
26C2×C3×#217C2212yes—
27C3×D4×Dic3C2218yes—
28C3×D4×Dic3C2218yes—
29C2×C3×C4⋊Dic3C2211yescharacteristic
30C2×C3×C4⋊Dic3C2212yes—
31C2×C3×C4⋊Dic3C2211yescharacteristic
32C2×C3×C4⋊Dic3C2211yescharacteristic
33C3×#924C22116yescomplemented
34C2×C3×Dic3⋊C4C2212yes—
35C2×C3×Dic3⋊C4C2212yes—
36C2×C3×Dic3⋊C4C2211yescharacteristic
37C2×C3×Dic3⋊C4C2212yes—
38C2×C3×Dic3⋊C4C2211yescharacteristic
39C2×C3×Dic3⋊C4C2212yes—
40C2×C3×Dic3⋊C4C22116yescomplemented
41C2×C3×C4×Dic3C2211yescharacteristic
42C2×C3×C4×Dic3C2211yescharacteristic
43C3×#890C2218yescomplemented
44C3×#888C2218yescomplemented
45C3×#878C22116yescomplemented
46C3×#878C22116yescomplemented
47C3×#870C2218yescomplemented
48C3×C4×Dic6C2218yescomplemented
49C3×#554—316no—
50C2×C3×C4⋊Q8—31no—
51C2×C3×#125—31no—
52C2×C3×#125—31no—
53C2×C3×C22⋊Q8—32no—
54C2×C3×C22⋊Q8—32no—
55C2×C3×C22⋊Q8—32no—
56C2×C3×C4×Q8—31no—
57C2×C3×C4×D4—21no—
58C2×C3×C4×D4—31no—
59C2×C3×C4×D4—31no—
60C2×C3×C4×D4D311yescharacteristic
61C2×C3×C4×D4C2×C311yescharacteristic
62C22×C3×C4⋊C4—32no—
63C2×D4×Dic3C2×C311yescharacteristic
64C2×D4×Dic3C2×C311yescharacteristic
65C2×#924C2×C312yescomplemented
66C22×Dic3⋊C4C2×C312yescomplemented
67#5539C2×C3116yesdirect product factor
68C2×#890C2×C311yescharacteristic, complemented
69C2×#888C2×C311yescharacteristic, complemented
70C2×#878C2×C312yescomplemented
71C2×#878C2×C312yescomplemented
72C2×#870C2×C311yescharacteristic, complemented
73C2×C4×Dic6C2×C311yescharacteristic, complemented
74C24×C32C2312yes—
75C2×C32×D4Q818yescomplemented
76C2×C32×D4C2314yes—
77C22×C32×C4—44no—
78C22×C32×C4C2311yescharacteristic
79C22×C32×C4C2312yes—
80C22×C32×C4C2311yescharacteristic
81C22×C32×C4C2318yes—
82C22×C32×C4C2311yescharacteristic
83C22×C3×Dic3—28no—
84C22×C3×Dic3—44no—
85C22×C3×Dic3C2318yes—
86C22×C3×Dic3C2311yescharacteristic
87C22×C3×Dic3C2311yescharacteristic
88C22×C3×Dic3C2311yescharacteristic
89C22×C3×Dic3C2312yes—
90C22×C3×Dic3C2312yes—
91C22×C3×Dic3C2318yes—
92C22×C3×Dic3C2311yescharacteristic
93C2×C3×Dic6—24no—
94C2×C3×Dic6—44no—
95C2×C3×Dic6C2314yes—
96C2×C3×Dic6C2318yes—
97C32×C4⋊C4C2314yes—
98C32×C22⋊C4C2318yes—
99C32×C42C2314yes—
100C3×#217C2318yes—
101C3×#217C2318yes—
102C3×C4⋊Dic3C2314yes—
103C3×C4⋊Dic3C2318yes—
104C3×C4⋊Dic3C2314yes—
105C3×C4⋊Dic3C2314yes—
106C3×Dic3⋊C4C2318yes—
107C3×Dic3⋊C4C2318yes—
108C3×Dic3⋊C4C2318yes—
109C3×Dic3⋊C4C2314yes—
110C3×Dic3⋊C4C2318yes—
111C3×Dic3⋊C4C2314yes—
112C3×C4×Dic3C2314yes—
113C3×C4×Dic3C2314yes—
114C2×#554—31noSylow
115C22×C3×Q8—31no—
116C22×C3×Q8—32no—
117C22×C3×D4—21no—
118C22×C3×D4C2×D311yescharacteristic
119C22×C3×D4C22×C311yescharacteristic
120C23×C3×C4—22no—
121C23×C3×C4—32no—
122C23×C3×C4—32no—
123C23×C3×C4C2×D312yes—
124C23×C3×C4C22×C312yes—
125C23×Dic3C22×C312yes—
126C23×Dic3C22×C312yes—
127C22×Dic6C22×C311yescharacteristic
128C22×Dic6C22×C312yes—
129C3×C4⋊Q8—38no—
130C3×#125—38no—
131C3×#125—38no—
132C3×C22⋊Q8—316no—
133C3×C22⋊Q8—316no—
134C3×C22⋊Q8—316no—
135C3×C4×Q8—38no—
136C3×C4×D4—28no—
137C3×C4×D4—38no—
138C3×C4×D4—38no—
139C3×C4×D4C2×D318yes—
140C3×C4×D4C22×C318yes—
141C2×C3×C4⋊C4—21no—
142C2×C3×C4⋊C4—31no—
143C2×C3×C4⋊C4—32no—
144C2×C3×C4⋊C4—32no—
145C2×C3×C4⋊C4—32no—
146C2×C3×C4⋊C4—31no—
147C2×C3×C4⋊C4—32no—
148C2×C3×C4⋊C4—316no—
149C2×C3×C4⋊C4—31no—
150C2×C3×C4⋊C4—31no—
151C2×C3×C4⋊C4—31no—
152C2×C3×C4⋊C4—32no—
153C2×C3×C4⋊C4C2×D311yescharacteristic
154C2×C3×C4⋊C4C22×C311yescharacteristic
155C2×C3×C22⋊C4—22no—
156C2×C3×C22⋊C4—32no—
157C2×C3×C22⋊C4—32no—
158C2×C3×C22⋊C4C2×D312yes—
159C2×C3×C22⋊C4C22×C312yes—
160C2×C3×C42—21no—
161C2×C3×C42—31no—
162C2×C3×C42—31no—
163C2×C3×C42C2×D311yescharacteristic
164C2×C3×C42C22×C311yescharacteristic
165C2×#217C22×C312yes—
166C2×#217C22×C312yes—
167D4×Dic3C22×C318yes—
168D4×Dic3C22×C318yes—
169C2×C4⋊Dic3C22×C311yescharacteristic
170C2×C4⋊Dic3C22×C311yescharacteristic
171C2×C4⋊Dic3C22×C311yescharacteristic
172C2×C4⋊Dic3C22×C312yes—
173#924C22×C3116yescomplemented
174C2×Dic3⋊C4C22×C311yescharacteristic
175C2×Dic3⋊C4C22×C311yescharacteristic
176C2×Dic3⋊C4C22×C312yes—
177C2×Dic3⋊C4C22×C312yes—
178C2×Dic3⋊C4C22×C312yes—
179C2×Dic3⋊C4C22×C312yes—
180C2×Dic3⋊C4C22×C3116yescomplemented
181C2×C4×Dic3C22×C311yescharacteristic
182C2×C4×Dic3C22×C311yescharacteristic
183#890C22×C318yescomplemented
184#888C22×C318yescomplemented
185#878C22×C3116yescomplemented
186#878C22×C3116yescomplemented
187#870C22×C318yescomplemented
188C4×Dic6C22×C318yescomplemented
189C23×C32—24no—
190C23×C32—24no—
191C23×C32C2×Q818yes—
192C23×C32C2414yes—
193C23×C32C2411yescharacteristic
194C32×D4C2×Q8116yescomplemented
195C2×C32×C4—22no—
196C2×C32×C4—22no—
197C2×C32×C4—24no—
198C2×C32×C4—48no—
199C2×C32×C4C2×Q814yes—
200C2×C32×C4C2412yes—
201C2×C32×C4C2412yes—
202C2×C32×C4C2414yes—
203C2×C32×C4C2412yes—
204C2×C3×Dic3—22no—
205C2×C3×Dic3—24no—
206C2×C3×Dic3—22no—
207C2×C3×Dic3—24no—
208C2×C3×Dic3—22no—
209C2×C3×Dic3—216no—
210C2×C3×Dic3—48no—
211C2×C3×Dic3#4114yes—
212C2×C3×Dic3C2412yes—
213C2×C3×Dic3C2412yes—
214C2×C3×Dic3C2412yes—
215C2×C3×Dic3C2414yes—
216C2×C3×Dic3C2414yes—
217C2×C3×Dic3C2412yes—
218C3×Dic6—28no—
219C3×Dic6—48no—
220#554—316no—
221C2×C4⋊Q8—31no—
222C2×#125—31no—
223C2×#125—31no—
224C2×C22⋊Q8—32no—
225C2×C22⋊Q8—32no—
226C2×C22⋊Q8—32no—
227C2×C4×Q8—31no—
228C2×C4×D4—31no—
229C2×C4×D4—31no—
230C2×C4×D4C3×D311yescharacteristic
231C22×C4⋊C4—32no—
232C24×C3—22no—
233C24×C3C22×D312yes—
234C24×C3C23×C312yes—
235C2×C3×Q8—34no—
236C2×C3×Q8—38no—
237C2×C3×Q8—64no—
238C2×C3×Q8—124no—
239C2×C3×D4—28no—
240C2×C3×D4—24no—
241C2×C3×D4Dic618yescomplemented
242C2×C3×D4C3×Q818yescomplemented
243C2×C3×D4C22×D314yes—
244C2×C3×D4C23×C314yes—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4—22no—
249C22×C3×C4—28no—
250C22×C3×C4—31no—
251C22×C3×C4—38no—
252C22×C3×C4—31no—
253C22×C3×C4—31no—
254C22×C3×C4—31no—
255C22×C3×C4—32no—
256C22×C3×C4—32no—
257C22×C3×C4—38no—
258C22×C3×C4—44no—
259C22×C3×C4—44no—
260C22×C3×C4—48no—
261C22×C3×C4—68no—
262C22×C3×C4—124no—
263C22×C3×C4C22×D311yescharacteristic
264C22×C3×C4C22×D311yescharacteristic
265C22×C3×C4C22×D312yes—
266C22×C3×C4C22×D318yes—
267C22×C3×C4C22×D311yescharacteristic
268C22×C3×C4C23×C311yescharacteristic
269C22×C3×C4C23×C311yescharacteristic
270C22×C3×C4C23×C312yes—
271C22×C3×C4C23×C318yes—
272C22×C3×C4C23×C311yescharacteristic
273C22×Dic3—28no—
274C22×Dic3—44no—
275C22×Dic3C23×C318yes—
276C22×Dic3C23×C311yescharacteristic
277C22×Dic3C23×C311yescharacteristic
278C22×Dic3C23×C311yescharacteristic
279C22×Dic3C23×C312yes—
280C22×Dic3C23×C312yes—
281C22×Dic3C23×C318yes—
282C22×Dic3C23×C311yescharacteristic
283C2×Dic6—24no—
284C2×Dic6—44no—
285C2×Dic6C23×C314yes—
286C2×Dic6C23×C318yes—
287C3×C4⋊C4—24no—
288C3×C4⋊C4—34no—
289C3×C4⋊C4—38no—
290C3×C4⋊C4—38no—
291C3×C4⋊C4—38no—
292C3×C4⋊C4—34no—
293C3×C4⋊C4—38no—
294C3×C4⋊C4—34no—
295C3×C4⋊C4—34no—
296C3×C4⋊C4—34no—
297C3×C4⋊C4—38no—
298C3×C4⋊C4C22×D314yes—
299C3×C4⋊C4C23×C314yes—
300C3×C22⋊C4—28no—
301C3×C22⋊C4—38no—
302C3×C22⋊C4—38no—
303C3×C22⋊C4C22×D318yes—
304C3×C22⋊C4C23×C318yes—
305C3×C42—24no—
306C3×C42—34no—
307C3×C42—34no—
308C3×C42C22×D314yes—
309C3×C42C23×C314yes—
310#217C23×C318yes—
311#217C23×C318yes—
312C4⋊Dic3C23×C314yes—
313C4⋊Dic3C23×C314yes—
314C4⋊Dic3C23×C314yes—
315C4⋊Dic3C23×C318yes—
316Dic3⋊C4C23×C314yes—
317Dic3⋊C4C23×C314yes—
318Dic3⋊C4C23×C318yes—
319Dic3⋊C4C23×C318yes—
320Dic3⋊C4C23×C318yes—
321Dic3⋊C4C23×C318yes—
322C4×Dic3C23×C314yes—
323C4×Dic3C23×C314yes—
324C22×C32—216no—
325C22×C32—24no—
326C22×C32—24no—
327C22×C32C22×Q818yes—
328C22×C32C22×Q812yes—
329C22×C32C2×#4112yes—
330C22×C32H(5,𝔽2)12yes—
331C22×C32C2511yescharacteristic
332C32×C4—22no—
333C32×C4—22no—
334C32×C4—24no—
335C32×C4C22×Q814yes—
336C3×Dic3—22no—
337C3×Dic3—24no—
338C3×Dic3—22no—
339C3×Dic3—24no—
340C3×Dic3—22no—
341C3×Dic3C2×#4114yes—
342C22×Q8—31no—
343C22×Q8—32no—
344C22×D4C2×C3×D311yescharacteristic
345C23×C4—32no—
346C23×C4—32no—
347C23×C4C2×C3×D312yes—
348C4⋊Q8—38no—
349#125—38no—
350#125—38no—
351C22⋊Q8—316no—
352C22⋊Q8—316no—
353C22⋊Q8—316no—
354C4×Q8—38no—
355C4×D4—38no—
356C4×D4—38no—
357C4×D4C2×C3×D318yes—
358C2×C4⋊C4—31no—
359C2×C4⋊C4—32no—
360C2×C4⋊C4—32no—
361C2×C4⋊C4—32no—
362C2×C4⋊C4—316no—
363C2×C4⋊C4—31no—
364C2×C4⋊C4—31no—
365C2×C4⋊C4—31no—
366C2×C4⋊C4—31no—
367C2×C4⋊C4—32no—
368C2×C4⋊C4—32no—
369C2×C4⋊C4C2×C3×D311yescharacteristic
370C2×C22⋊C4—32no—
371C2×C22⋊C4—32no—
372C2×C22⋊C4C2×C3×D312yes—
373C2×C42—31no—
374C2×C42—31no—
375C2×C42C2×C3×D311yescharacteristic
376C23×C3—24no—
377C23×C3—24no—
378C23×C3—24no—
379C23×C3—24no—
380C23×C3—21no—
381C23×C3—24no—
382C23×C3—28no—
383C23×C3—44no—
384C23×C3—44no—
385C23×C3C2×Dic618yes—
386C23×C3C2×C3×Q818yes—
387C23×C3C23×D314yes—
388C23×C3C23×D311yescharacteristic
389C23×C3C24×C314yes—
390C23×C3C24×C311yescharacteristic
391C3×Q8—68no—
392C3×Q8—128no—
393C3×D4—216no—
394C3×D4C2×Dic6116yescomplemented
395C3×D4C2×C3×Q8116yescomplemented
396C2×C3×C4—24no—
397C2×C3×C4—22no—
398C2×C3×C4—24no—
399C2×C3×C4—22no—
400C2×C3×C4—22no—
401C2×C3×C4—24no—
402C2×C3×C4—22no—
403C2×C3×C4—22no—
404C2×C3×C4—22no—
405C2×C3×C4—22no—
406C2×C3×C4—24no—
407C2×C3×C4—24no—
408C2×C3×C4—34no—
409C2×C3×C4—32no—
410C2×C3×C4—32no—
411C2×C3×C4—32no—
412C2×C3×C4—32no—
413C2×C3×C4—34no—
414C2×C3×C4—34no—
415C2×C3×C4—42no—
416C2×C3×C4—44no—
417C2×C3×C4—48no—
418C2×C3×C4—48no—
419C2×C3×C4—416no—
420C2×C3×C4—616no—
421C2×C3×C4—62no—
422C2×C3×C4—64no—
423C2×C3×C4—62no—
424C2×C3×C4—64no—
425C2×C3×C4—62no—
426C2×C3×C4—128no—
427C2×C3×C4C2×Dic614yes—
428C2×C3×C4C2×C3×Q814yes—
429C2×C3×C4C23×D312yes—
430C2×C3×C4C23×D312yes—
431C2×C3×C4C23×D314yes—
432C2×C3×C4C23×D312yes—
433C2×C3×C4C24×C312yes—
434C2×C3×C4C24×C312yes—
435C2×C3×C4C24×C314yes—
436C2×C3×C4C24×C312yes—
437C2×Dic3—22no—
438C2×Dic3—24no—
439C2×Dic3—22no—
440C2×Dic3—24no—
441C2×Dic3—22no—
442C2×Dic3—216no—
443C2×Dic3—48no—
444C2×Dic3C3×#4114yes—
445C2×Dic3C24×C312yes—
446C2×Dic3C24×C312yes—
447C2×Dic3C24×C312yes—
448C2×Dic3C24×C314yes—
449C2×Dic3C24×C314yes—
450C2×Dic3C24×C312yes—
451Dic6—28no—
452Dic6—48no—
453C2×C32—28no—
454C2×C32#55414yescomplemented
455C2×C32C23×Q811yescharacteristic
456C2×C32C22×#4111yescharacteristic
457C2×C32C2×H(5,𝔽2)11yescharacteristic
458C24C22×C3×D312yes—
459C2×Q8—34no—
460C2×Q8—38no—
461C2×Q8—64no—
462C2×Q8—124no—
463C2×D4C3×Dic618yescomplemented
464C2×D4C22×C3×D314yes—
465C22×C4—31no—
466C22×C4—31no—
467C22×C4—31no—
468C22×C4—31no—
469C22×C4—32no—
470C22×C4—32no—
471C22×C4—38no—
472C22×C4—38no—
473C22×C4—44no—
474C22×C4—68no—
475C22×C4—124no—
476C22×C4C22×C3×D311yescharacteristic
477C22×C4C22×C3×D311yescharacteristic
478C22×C4C22×C3×D312yes—
479C22×C4C22×C3×D318yes—
480C22×C4C22×C3×D311yescharacteristic
481C4⋊C4—34no—
482C4⋊C4—38no—
483C4⋊C4—38no—
484C4⋊C4—38no—
485C4⋊C4—34no—
486C4⋊C4—34no—
487C4⋊C4—34no—
488C4⋊C4—34no—
489C4⋊C4—38no—
490C4⋊C4—38no—
491C4⋊C4C22×C3×D314yes—
492C22⋊C4—38no—
493C22⋊C4—38no—
494C22⋊C4C22×C3×D318yes—
495C42—34no—
496C42—34no—
497C42C22×C3×D314yes—
498C22×C3—24no—
499C22×C3—24no—
500C22×C3—24no—
501C22×C3—24no—
502C22×C3—216no—
503C22×C3—216no—
504C22×C3—22no—
505C22×C3—28no—
506C22×C3—22no—
507C22×C3—22no—
508C22×C3—21no—
509C22×C3—44no—
510C22×C3—416no—
511C22×C3—44no—
512C22×C3C22×Dic618yes—
513C22×C3C22×Dic612yes—
514C22×C3#100412yes—
515C22×C3D3×#4112yes—
516C22×C3C22×C3×Q818yes—
517C22×C3C22×C3×Q812yes—
518C22×C3C2×C3×#4112yes—
519C22×C3C3×H(5,𝔽2)12yes—
520C22×C3C24×D311yescharacteristic
521C22×C3C25×C311yescharacteristic
522C3×C4—24no—
523C3×C4—22no—
524C3×C4—24no—
525C3×C4—22no—
526C3×C4—22no—
527C3×C4—24no—
528C3×C4—22no—
529C3×C4—24no—
530C3×C4—34no—
531C3×C4—44no—
532C3×C4—42no—
533C3×C4—62no—
534C3×C4—64no—
535C3×C4—62no—
536C3×C4—64no—
537C3×C4—62no—
538C3×C4C22×Dic614yes—
539C3×C4C22×C3×Q814yes—
540Dic3—22no—
541Dic3—24no—
542Dic3—22no—
543Dic3—24no—
544Dic3—22no—
545Dic3C2×C3×#4114yes—
546C32C2×#55411yescharacteristic, complemented, Sylow
547C23—24no—
548C23—24no—
549C23C2×C3×Dic618yes—
550C23C23×C3×D314yes—
551C23C23×C3×D311yescharacteristic
552Q8—68no—
553Q8—128no—
554D4C2×C3×Dic6116yescomplemented
555C2×C4—22no—
556C2×C4—24no—
557C2×C4—22no—
558C2×C4—34no—
559C2×C4—32no—
560C2×C4—32no—
561C2×C4—32no—
562C2×C4—32no—
563C2×C4—34no—
564C2×C4—34no—
565C2×C4—48no—
566C2×C4—616no—
567C2×C4—62no—
568C2×C4—64no—
569C2×C4—62no—
570C2×C4—64no—
571C2×C4—62no—
572C2×C4—128no—
573C2×C4C2×C3×Dic614yes—
574C2×C4C23×C3×D312yes—
575C2×C4C23×C3×D312yes—
576C2×C4C23×C3×D314yes—
577C2×C4C23×C3×D312yes—
578C2×C3—28no—
579C2×C3—28no—
580C2×C3—24no—
581C2×C3—21no—
582C2×C3—21no—
583C2×C3—21no—
584C2×C3—48no—
585C2×C3#553914yesdirect product factor
586C2×C3C3×#55414yescomplemented
587C2×C3C23×Dic611yescharacteristic
588C2×C3C2×#100411yescharacteristic
589C2×C3C2×D3×#4111yescharacteristic
590C2×C3C23×C3×Q811yescharacteristic
591C2×C3C22×C3×#4111yescharacteristic
592C2×C3C2×C3×H(5,𝔽2)11yescharacteristic
593C22—216no—
594C22—24no—
595C22—24no—
596C22C22×C3×Dic618yes—
597C22C22×C3×Dic612yes—
598C22C3×#100412yes—
599C22C3×D3×#4112yes—
600C22C24×C3×D311yescharacteristic
601C4—22no—
602C4—24no—
603C4—22no—
604C4—34no—
605C4—62no—
606C4—64no—
607C4—62no—
608C4—64no—
609C4—62no—
610C4C22×C3×Dic614yes—
611C3—21no—
612C3C2×#553911yescharacteristic, direct product factor
613C3C2×C3×#55411yescharacteristic, complemented
614C2—28no—
615C2C3×#553914yesdirect product factor
616C2C23×C3×Dic611yescharacteristic
617C2C2×C3×#100411yescharacteristic
618C2C2×C3×D3×#4111yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC2×C32×C4×D4C2
socleC23×C32C24
prime radicalC22×C32×D4C22
hypercenterC2×C3×C4×D4D3
hypocenterC3C2×C3×#554
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×C4×D4

Complements

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

NH ≅ G/Ntype
4. C2×C3×#924C2semidirect
5. C22×C3×Dic3⋊C4C2semidirect
6. C3×#5539C2direct (N × H)
7. C2×C3×#890C2semidirect
8. C2×C3×#888C2semidirect
9. C2×C3×#878C2semidirect
10. C2×C3×#878C2semidirect
11. C2×C3×#870C2semidirect
12. C2×C3×C4×Dic6C2semidirect
14. C2×#5539C3direct (N × H)
33. C3×#924C22semidirect
40. C2×C3×Dic3⋊C4C22semidirect
43. C3×#890C22semidirect
44. C3×#888C22semidirect
45. C3×#878C22semidirect
46. C3×#878C22semidirect
47. C3×#870C22semidirect
48. C3×C4×Dic6C22semidirect
65. C2×#924C2×C3semidirect
66. C22×Dic3⋊C4C2×C3semidirect
67. #5539C2×C3direct (N × H)
68. C2×#890C2×C3semidirect
69. C2×#888C2×C3semidirect
70. C2×#878C2×C3semidirect
71. C2×#878C2×C3semidirect
72. C2×#870C2×C3semidirect
73. C2×C4×Dic6C2×C3semidirect
75. C2×C32×D4Q8semidirect
173. #924C22×C3semidirect
180. C2×Dic3⋊C4C22×C3semidirect
183. #890C22×C3semidirect
184. #888C22×C3semidirect
185. #878C22×C3semidirect
186. #878C22×C3semidirect
187. #870C22×C3semidirect
188. C4×Dic6C22×C3semidirect
194. C32×D4C2×Q8semidirect
241. C2×C3×D4Dic6semidirect
242. C2×C3×D4C3×Q8semidirect
394. C3×D4C2×Dic6semidirect
395. C3×D4C2×C3×Q8semidirect
454. C2×C32#554semidirect
463. C2×D4C3×Dic6semidirect
546. C32C2×#554semidirect
554. D4C2×C3×Dic6semidirect
585. C2×C3#5539direct (N × H)
586. C2×C3C3×#554semidirect
612. C3C2×#5539direct (N × H)
613. C3C2×C3×#554semidirect
615. C2C3×#5539direct (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×D42
C2×C3×D4×Dic32
C2×C3×#9242
C22×C3×Dic3⋊C42
C3×#55392
C2×C3×#8902
C2×C3×#8882
C2×C3×#8782
C2×C3×#8702
C2×C3×C4×Dic62
C2×C3×#5543
C2×#55393