Finite Group Databasebeta

← C2×C3×C4×#237 #11899947

Subgroups — C2×C3×C4×#237 #11899947

Order 1152.

3669 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#237C211yesmaximal, characteristic
2C2×C32×C4×D4C211yesmaximal, characteristic, complemented
3C2×C3×D4×Dic3C211yesmaximal, characteristic, complemented
4C2×C3×C4×#67C212yesmaximal, complemented
5C22×C3×C4×Dic3C212yesmaximal, complemented
6C3×C4×#237C2116yesmaximal, direct product factor
7C2×C3×#892C211yesmaximal, characteristic, complemented
8C2×C3×#887C211yesmaximal, characteristic, complemented
9C2×C3×#67⋊C4C212yesmaximal, complemented
10C2×C3×#877C212yesmaximal, complemented
11C2×C3×C42×D3C211yesmaximal, characteristic, complemented
12C2×C3×C4×Dic6C211yesmaximal, characteristic, complemented
13C2×C3×C4×#41—31nomaximal
14C2×C4×#237C311yesmaximal, characteristic, direct product factor
15C22×C32×D4C2211yescharacteristic
16C23×C32×C4C2212yes—
17C22×C3×#67C2212yes—
18C23×C3×Dic3C2212yes—
19C23×C3×Dic3C2212yes—
20C2×C3×#237C4116yesdirect product factor
21C2×C3×#237C2218yes—
22C22×C3×C4×D3C2211yescharacteristic
23C22×C3×C4×D3C2211yescharacteristic
24C22×C3×C4×D3C2211yescharacteristic
25C22×C3×Dic6C2211yescharacteristic
26C32×C4×D4C2218yescomplemented
27C2×C32×C4⋊C4C2211yescharacteristic
28C2×C32×C22⋊C4C2212yes—
29C2×C32×C42C2211yescharacteristic
30C2×C3×#217C2212yes—
31C3×D4×Dic3C2218yescomplemented
32C3×C4×#67C22116yescomplemented
33C2×C3×(C2×D3)⋊C4C2212yes—
34C2×C3×C4⋊Dic3C2211yescharacteristic
35C2×C3×Dic3⋊C4C2212yes—
36C2×C3×Dic3⋊C4C2212yes—
37C2×C3×C4×Dic3C2212yes—
38C2×C3×C4×Dic3C2211yescharacteristic
39C2×C3×C4×Dic3C2212yes—
40C2×C3×C4×Dic3C2211yescharacteristic
41C2×C3×C4×Dic3C2212yes—
42C2×C3×C4×Dic3C2211yescharacteristic
43C2×C3×C4×Dic3C22116yescomplemented
44C3×#892C2218yescomplemented
45C3×#887C2218yescomplemented
46C3×#67⋊C4C22116yescomplemented
47C3×#877C22116yescomplemented
48C3×C42×D3C2218yescomplemented
49C3×C4×Dic6C2218yescomplemented
50C22×C3×#41—31no—
51C22×#237C2×C311yescharacteristic
52C3×C4×#41—316no—
53C2×C3×C4×Q8—31no—
54C2×C3×C4×Q8—31no—
55C2×C3×C4×D4—21no—
56C2×C3×C4×D4—31no—
57C2×C3×C4×D4—32no—
58C2×C3×C4×D4—32no—
59C2×C3×C4×D4D311yescharacteristic, complemented
60C2×C3×C4×D4C2×C311yescharacteristic, complemented
61C2×C3×#117—31no—
62C2×C3×#117—32no—
63C22×C3×C42—32no—
64C22×C3×C42—31no—
65C2×D4×Dic3C2×C311yescharacteristic, complemented
66C2×C4×#67C2×C312yescomplemented
67C22×C4×Dic3C2×C312yescomplemented
68C4×#237C2×C3116yesdirect product factor
69C2×#892C2×C311yescharacteristic, complemented
70C2×#887C2×C311yescharacteristic, complemented
71C2×#67⋊C4C2×C312yescomplemented
72C2×#877C2×C312yescomplemented
73C2×C42×D3C2×C311yescharacteristic, complemented
74C2×C4×Dic6C2×C311yescharacteristic, complemented
75C24×C32C2312yes—
76C23×C3×D3C2311yescharacteristic
77C2×C32×D4C2×C418yescomplemented
78C2×C32×D4C2314yes—
79C22×C32×C4—28no—
80C22×C32×C4C2312yes—
81C22×C32×C4C2311yescharacteristic
82C22×C32×C4C2318yes—
83C22×C32×C4C2311yescharacteristic
84C22×C32×C4C2311yescharacteristic
85C2×C3×#67C2×C4116yescomplemented
86C2×C3×#67C2318yes—
87C22×C3×Dic3—28no—
88C22×C3×Dic3C2×C4116yescomplemented
89C22×C3×Dic3C2318yes—
90C22×C3×Dic3C2311yescharacteristic
91C22×C3×Dic3C2312yes—
92C22×C3×Dic3C2311yescharacteristic
93C22×C3×Dic3C2312yes—
94C22×C3×Dic3C2318yes—
95C22×C3×Dic3C2311yescharacteristic
96C3×#237C2×C4164yesdirect product factor
97C2×C3×C4×D3—24no—
98C2×C3×C4×D3—24no—
99C2×C3×C4×D3C2×C418yescomplemented
100C2×C3×C4×D3C2314yes—
101C2×C3×C4×D3C2314yes—
102C2×C3×C4×D3C2314yes—
103C2×C3×Dic6C2×C418yescomplemented
104C2×C3×Dic6C2314yes—
105C32×C4⋊C4C2314yes—
106C32×C22⋊C4C2318yes—
107C32×C42C2314yes—
108C3×#217C2318yes—
109C3×(C2×D3)⋊C4C2318yes—
110C3×C4⋊Dic3C2314yes—
111C3×Dic3⋊C4C2318yes—
112C3×Dic3⋊C4C2318yes—
113C3×C4×Dic3C2314yes—
114C3×C4×Dic3C2318yes—
115C3×C4×Dic3C2318yes—
116C3×C4×Dic3C2314yes—
117C3×C4×Dic3C2314yes—
118C3×C4×Dic3C2318yes—
119C2×C4×#41—31noSylow
120C2×C3×#41—316no—
121C2×C3×#41—38no—
122C22×C3×Q8—31no—
123C22×C3×D4—21no—
124C22×C3×D4—32no—
125C22×C3×D4C2×D311yescharacteristic
126C22×C3×D4C22×C311yescharacteristic
127C23×C3×C4—22no—
128C23×C3×C4—32no—
129C23×C3×C4—31no—
130C23×C3×C4—32no—
131C23×C3×C4—31no—
132C23×C3×C4—31no—
133C23×C3×C4C2×D312yes—
134C23×C3×C4C22×C312yes—
135C22×#67C22×C312yes—
136C23×Dic3C22×C312yes—
137C23×Dic3C22×C312yes—
138C2×#237C3×C4116yesdirect product factor
139C2×#237C22×C318yes—
140C22×C4×D3C22×C311yescharacteristic
141C22×C4×D3C22×C311yescharacteristic
142C22×C4×D3C22×C311yescharacteristic
143C22×Dic6C22×C311yescharacteristic
144C3×C4×Q8—38no—
145C3×C4×Q8—38no—
146C3×C4×D4—28no—
147C3×C4×D4—38no—
148C3×C4×D4—316no—
149C3×C4×D4—316no—
150C3×C4×D4C2×D318yescomplemented
151C3×C4×D4C22×C318yescomplemented
152C3×#117—38no—
153C3×#117—316no—
154C2×C3×C4⋊C4—21no—
155C2×C3×C4⋊C4—32no—
156C2×C3×C4⋊C4—32no—
157C2×C3×C4⋊C4—31no—
158C2×C3×C4⋊C4C2×D311yescharacteristic
159C2×C3×C4⋊C4C22×C311yescharacteristic
160C2×C3×C22⋊C4—22no—
161C2×C3×C22⋊C4—32no—
162C2×C3×C22⋊C4—32no—
163C2×C3×C22⋊C4C2×D312yes—
164C2×C3×C22⋊C4C22×C312yes—
165C2×C3×C42—21no—
166C2×C3×C42—32no—
167C2×C3×C42—31no—
168C2×C3×C42—32no—
169C2×C3×C42—31no—
170C2×C3×C42—316no—
171C2×C3×C42—31no—
172C2×C3×C42—32no—
173C2×C3×C42—38no—
174C2×C3×C42C2×D311yescharacteristic
175C2×C3×C42C22×C311yescharacteristic
176C2×#217C22×C312yes—
177D4×Dic3C22×C318yescomplemented
178C4×#67C22×C3116yescomplemented
179C2×(C2×D3)⋊C4C22×C312yes—
180C2×C4⋊Dic3C22×C311yescharacteristic
181C2×Dic3⋊C4C22×C312yes—
182C2×Dic3⋊C4C22×C312yes—
183C2×C4×Dic3C22×C312yes—
184C2×C4×Dic3C22×C311yescharacteristic
185C2×C4×Dic3C22×C311yescharacteristic
186C2×C4×Dic3C22×C311yescharacteristic
187C2×C4×Dic3C22×C312yes—
188C2×C4×Dic3C22×C312yes—
189C2×C4×Dic3C22×C3116yescomplemented
190#892C22×C318yescomplemented
191#887C22×C318yescomplemented
192#67⋊C4C22×C3116yescomplemented
193#877C22×C3116yescomplemented
194C42×D3C22×C318yescomplemented
195C4×Dic6C22×C318yescomplemented
196C23×C32—24no—
197C23×C32—24no—
198C23×C32C22×C418yes—
199C23×C32C2414yes—
200C23×C32C2411yescharacteristic
201C22×C3×D3—22no—
202C22×C3×D3—22no—
203C22×C3×D3C22×C414yes—
204C22×C3×D3C2412yes—
205C32×D4C22×C4116yescomplemented
206C2×C32×C4—22no—
207C2×C32×C4—24no—
208C2×C32×C4—216no—
209C2×C32×C4C22×C414yes—
210C2×C32×C4#4114yescomplemented
211C2×C32×C4C2414yes—
212C2×C32×C4C2412yes—
213C2×C32×C4C2412yes—
214C2×C32×C4C2412yes—
215C3×#67C22×C4132yescomplemented
216C2×C3×Dic3—22no—
217C2×C3×Dic3—24no—
218C2×C3×Dic3—216no—
219C2×C3×Dic3C22×C418yes—
220C2×C3×Dic3C22×C414yes—
221C2×C3×Dic3C22×C4132yescomplemented
222C2×C3×Dic3#4114yescomplemented
223C2×C3×Dic3C2412yes—
224C2×C3×Dic3C2414yes—
225C2×C3×Dic3C2412yes—
226C2×C3×Dic3C2414yes—
227C2×C3×Dic3C2412yes—
228C3×C4×D3—28no—
229C3×C4×D3—28no—
230C3×C4×D3C22×C4116yescomplemented
231C3×Dic6C22×C4116yescomplemented
232C22×#41—31no—
233C4×#41—316no—
234C2×C4×Q8—31no—
235C2×C4×Q8—31no—
236C2×C4×D4—31no—
237C2×C4×D4—32no—
238C2×C4×D4—32no—
239C2×C4×D4C3×D311yescharacteristic, complemented
240C2×#117—31no—
241C2×#117—32no—
242C22×C42—32no—
243C22×C42—31no—
244C24×C3—22no—
245C24×C3—31no—
246C24×C3C22×D312yes—
247C24×C3C23×C312yes—
248C23×D3C23×C311yescharacteristic
249C3×#41—364no—
250C2×C3×Q8—38no—
251C2×C3×Q8—34no—
252C2×C3×D4—28no—
253C2×C3×D4—24no—
254C2×C3×D4—316no—
255C2×C3×D4—38no—
256C2×C3×D4C4×D318yescomplemented
257C2×C3×D4C2×C3×C418yescomplemented
258C2×C3×D4C22×D314yes—
259C2×C3×D4C23×C314yes—
260C22×C3×C4—28no—
261C22×C3×C4—28no—
262C22×C3×C4—21no—
263C22×C3×C4—21no—
264C22×C3×C4—21no—
265C22×C3×C4—22no—
266C22×C3×C4—28no—
267C22×C3×C4—316no—
268C22×C3×C4—31no—
269C22×C3×C4—31no—
270C22×C3×C4—32no—
271C22×C3×C4—38no—
272C22×C3×C4—38no—
273C22×C3×C4—34no—
274C22×C3×C4—31no—
275C22×C3×C4—32no—
276C22×C3×C4—38no—
277C22×C3×C4—34no—
278C22×C3×C4—34no—
279C22×C3×C4—48no—
280C22×C3×C4—64no—
281C22×C3×C4—68no—
282C22×C3×C4—64no—
283C22×C3×C4C22×D312yes—
284C22×C3×C4C22×D318yes—
285C22×C3×C4C22×D311yescharacteristic
286C22×C3×C4C22×D311yescharacteristic
287C22×C3×C4C22×D311yescharacteristic
288C22×C3×C4C23×C312yes—
289C22×C3×C4C23×C311yescharacteristic
290C22×C3×C4C23×C318yes—
291C22×C3×C4C23×C311yescharacteristic
292C22×C3×C4C23×C311yescharacteristic
293C2×#67C2×C3×C4116yescomplemented
294C2×#67C23×C318yes—
295C22×Dic3—28no—
296C22×Dic3C2×C3×C4116yescomplemented
297C22×Dic3C23×C318yes—
298C22×Dic3C23×C311yescharacteristic
299C22×Dic3C23×C312yes—
300C22×Dic3C23×C311yescharacteristic
301C22×Dic3C23×C312yes—
302C22×Dic3C23×C318yes—
303C22×Dic3C23×C311yescharacteristic
304#237C2×C3×C4164yesdirect product factor
305C2×C4×D3—24no—
306C2×C4×D3—24no—
307C2×C4×D3C2×C3×C418yescomplemented
308C2×C4×D3C23×C314yes—
309C2×C4×D3C23×C314yes—
310C2×C4×D3C23×C314yes—
311C2×Dic6C2×C3×C418yescomplemented
312C2×Dic6C23×C314yes—
313C3×C4⋊C4—24no—
314C3×C4⋊C4—38no—
315C3×C4⋊C4—38no—
316C3×C4⋊C4—34no—
317C3×C4⋊C4C22×D314yes—
318C3×C4⋊C4C23×C314yes—
319C3×C22⋊C4—28no—
320C3×C22⋊C4—38no—
321C3×C22⋊C4—38no—
322C3×C22⋊C4C22×D318yes—
323C3×C22⋊C4C23×C318yes—
324C3×C42—24no—
325C3×C42—34no—
326C3×C42—38no—
327C3×C42—34no—
328C3×C42—38no—
329C3×C42—34no—
330C3×C42—38no—
331C3×C42C22×D314yes—
332C3×C42C23×C314yes—
333#217C23×C318yes—
334(C2×D3)⋊C4C23×C318yes—
335C4⋊Dic3C23×C314yes—
336Dic3⋊C4C23×C318yes—
337Dic3⋊C4C23×C318yes—
338C4×Dic3C23×C318yes—
339C4×Dic3C23×C314yes—
340C4×Dic3C23×C314yes—
341C4×Dic3C23×C314yes—
342C4×Dic3C23×C318yes—
343C4×Dic3C23×C318yes—
344C22×C32—216no—
345C22×C32—24no—
346C22×C32—24no—
347C22×C32C23×C418yes—
348C22×C32C23×C412yes—
349C22×C32C2×#4112yes—
350C22×C32C2×#4112yes—
351C22×C32C2511yescharacteristic
352C2×C3×D3—28no—
353C2×C3×D3—22no—
354C2×C3×D3—22no—
355C2×C3×D3C23×C414yes—
356C32×C4—22no—
357C32×C4—24no—
358C32×C4C23×C414yes—
359C32×C4C2×#4114yescomplemented
360C3×Dic3—22no—
361C3×Dic3—24no—
362C3×Dic3C23×C418yes—
363C3×Dic3C23×C414yes—
364C3×Dic3C2×#4114yescomplemented
365C2×#41—316no—
366C2×#41—38no—
367C22×Q8—31no—
368C22×D4—32no—
369C22×D4C2×C3×D311yescharacteristic
370C23×C4—32no—
371C23×C4—31no—
372C23×C4—32no—
373C23×C4—31no—
374C23×C4—31no—
375C23×C4C2×C3×D312yes—
376C4×Q8—38no—
377C4×Q8—38no—
378C4×D4—38no—
379C4×D4—316no—
380C4×D4—316no—
381C4×D4C2×C3×D318yescomplemented
382#117—38no—
383#117—316no—
384C2×C4⋊C4—32no—
385C2×C4⋊C4—32no—
386C2×C4⋊C4—31no—
387C2×C4⋊C4C2×C3×D311yescharacteristic
388C2×C22⋊C4—32no—
389C2×C22⋊C4—32no—
390C2×C22⋊C4C2×C3×D312yes—
391C2×C42—32no—
392C2×C42—31no—
393C2×C42—32no—
394C2×C42—31no—
395C2×C42—32no—
396C2×C42—316no—
397C2×C42—31no—
398C2×C42—38no—
399C2×C42C2×C3×D311yescharacteristic
400C23×C3—24no—
401C23×C3—24no—
402C23×C3—24no—
403C23×C3—24no—
404C23×C3—21no—
405C23×C3—24no—
406C23×C3—28no—
407C23×C3—34no—
408C23×C3—32no—
409C23×C3—44no—
410C23×C3—44no—
411C23×C3—62no—
412C23×C3—62no—
413C23×C3C2×C4×D318yes—
414C23×C3C22×C3×C418yes—
415C23×C3C23×D314yes—
416C23×C3C23×D311yescharacteristic
417C23×C3C24×C314yes—
418C23×C3C24×C311yescharacteristic
419C22×D3—22no—
420C22×D3—22no—
421C22×D3C22×C3×C414yes—
422C22×D3C24×C312yes—
423C3×Q8—316no—
424C3×D4—216no—
425C3×D4—332no—
426C3×D4C2×C4×D3116yescomplemented
427C3×D4C22×C3×C4116yescomplemented
428C2×C3×C4—24no—
429C2×C3×C4—22no—
430C2×C3×C4—22no—
431C2×C3×C4—24no—
432C2×C3×C4—216no—
433C2×C3×C4—216no—
434C2×C3×C4—22no—
435C2×C3×C4—22no—
436C2×C3×C4—22no—
437C2×C3×C4—24no—
438C2×C3×C4—24no—
439C2×C3×C4—24no—
440C2×C3×C4—34no—
441C2×C3×C4—38no—
442C2×C3×C4—332no—
443C2×C3×C4—34no—
444C2×C3×C4—32no—
445C2×C3×C4—32no—
446C2×C3×C4—34no—
447C2×C3×C4—316no—
448C2×C3×C4—32no—
449C2×C3×C4—34no—
450C2×C3×C4—416no—
451C2×C3×C4—42no—
452C2×C3×C4—44no—
453C2×C3×C4—68no—
454C2×C3×C4—616no—
455C2×C3×C4—62no—
456C2×C3×C4—64no—
457C2×C3×C4—68no—
458C2×C3×C4C2×C4×D314yes—
459C2×C3×C4#23714yesdirect product factor
460C2×C3×C4C22×C3×C414yes—
461C2×C3×C4C3×#4114yescomplemented
462C2×C3×C4C23×D314yes—
463C2×C3×C4C23×D312yes—
464C2×C3×C4C23×D312yes—
465C2×C3×C4C23×D312yes—
466C2×C3×C4C24×C314yes—
467C2×C3×C4C24×C312yes—
468C2×C3×C4C24×C312yes—
469C2×C3×C4C24×C312yes—
470#67C22×C3×C4132yescomplemented
471C2×Dic3—22no—
472C2×Dic3—24no—
473C2×Dic3—216no—
474C2×Dic3C22×C3×C418yes—
475C2×Dic3C22×C3×C414yes—
476C2×Dic3C22×C3×C4132yescomplemented
477C2×Dic3C3×#4114yescomplemented
478C2×Dic3C24×C312yes—
479C2×Dic3C24×C314yes—
480C2×Dic3C24×C312yes—
481C2×Dic3C24×C314yes—
482C2×Dic3C24×C312yes—
483C4×D3—28no—
484C4×D3—28no—
485C4×D3C22×C3×C4116yescomplemented
486Dic6C22×C3×C4116yescomplemented
487C2×C32—28no—
488C2×C32C4×#4114yescomplemented
489C2×C32C24×C411yescharacteristic
490C2×C32C22×#4111yescharacteristic
491C2×C32C22×#4111yescharacteristic
492C3×D3—24no—
493C24—31no—
494C24C22×C3×D312yes—
495#41—364no—
496C2×Q8—34no—
497C2×Q8—38no—
498C2×D4—38no—
499C2×D4—316no—
500C2×D4C3×C4×D318yescomplemented
501C2×D4C22×C3×D314yes—
502C22×C4—28no—
503C22×C4—31no—
504C22×C4—31no—
505C22×C4—32no—
506C22×C4—38no—
507C22×C4—316no—
508C22×C4—34no—
509C22×C4—38no—
510C22×C4—31no—
511C22×C4—32no—
512C22×C4—38no—
513C22×C4—34no—
514C22×C4—34no—
515C22×C4—64no—
516C22×C4—68no—
517C22×C4—64no—
518C22×C4C22×C3×D312yes—
519C22×C4C22×C3×D318yes—
520C22×C4C22×C3×D311yescharacteristic
521C22×C4C22×C3×D311yescharacteristic
522C22×C4C22×C3×D311yescharacteristic
523C4⋊C4—38no—
524C4⋊C4—38no—
525C4⋊C4—34no—
526C4⋊C4C22×C3×D314yes—
527C22⋊C4—38no—
528C22⋊C4—38no—
529C22⋊C4C22×C3×D318yes—
530C42—34no—
531C42—38no—
532C42—34no—
533C42—38no—
534C42—34no—
535C42—38no—
536C42C22×C3×D314yes—
537C22×C3—24no—
538C22×C3—24no—
539C22×C3—24no—
540C22×C3—24no—
541C22×C3—216no—
542C22×C3—216no—
543C22×C3—22no—
544C22×C3—28no—
545C22×C3—22no—
546C22×C3—22no—
547C22×C3—21no—
548C22×C3—34no—
549C22×C3—44no—
550C22×C3—416no—
551C22×C3—44no—
552C22×C3—62no—
553C22×C3—62no—
554C22×C3—68no—
555C22×C3C22×C4×D318yes—
556C22×C3C22×C4×D312yes—
557C22×C3C2×#23712yes—
558C22×C3D3×#4112yes—
559C22×C3C23×C3×C418yes—
560C22×C3C23×C3×C412yes—
561C22×C3C2×C3×#4112yes—
562C22×C3C2×C3×#4112yes—
563C22×C3C24×D311yescharacteristic
564C22×C3C25×C311yescharacteristic
565C2×D3—22no—
566C2×D3—22no—
567C2×D3—28no—
568C2×D3C23×C3×C414yes—
569C3×C4—24no—
570C3×C4—22no—
571C3×C4—22no—
572C3×C4—24no—
573C3×C4—24no—
574C3×C4—24no—
575C3×C4—34no—
576C3×C4—38no—
577C3×C4—34no—
578C3×C4—44no—
579C3×C4—42no—
580C3×C4—62no—
581C3×C4—64no—
582C3×C4C22×C4×D314yes—
583C3×C4C2×#23714yesdirect product factor
584C3×C4C23×C3×C414yes—
585C3×C4C2×C3×#4114yescomplemented
586Dic3—22no—
587Dic3—24no—
588Dic3C23×C3×C418yes—
589Dic3C23×C3×C414yes—
590Dic3C2×C3×#4114yescomplemented
591C32C2×C4×#4111yescharacteristic, complemented, Sylow
592C23—24no—
593C23—24no—
594C23—34no—
595C23—32no—
596C23—62no—
597C23—62no—
598C23C2×C3×C4×D318yes—
599C23C23×C3×D314yes—
600C23C23×C3×D311yescharacteristic
601Q8—316no—
602D4—332no—
603D4C2×C3×C4×D3116yescomplemented
604C2×C4—24no—
605C2×C4—22no—
606C2×C4—216no—
607C2×C4—34no—
608C2×C4—38no—
609C2×C4—332no—
610C2×C4—34no—
611C2×C4—32no—
612C2×C4—32no—
613C2×C4—34no—
614C2×C4—316no—
615C2×C4—32no—
616C2×C4—34no—
617C2×C4—68no—
618C2×C4—616no—
619C2×C4—62no—
620C2×C4—64no—
621C2×C4—68no—
622C2×C4C2×C3×C4×D314yes—
623C2×C4C3×#23714yesdirect product factor
624C2×C4C23×C3×D314yes—
625C2×C4C23×C3×D312yes—
626C2×C4C23×C3×D312yes—
627C2×C4C23×C3×D312yes—
628C2×C3—28no—
629C2×C3—28no—
630C2×C3—24no—
631C2×C3—21no—
632C2×C3—21no—
633C2×C3—21no—
634C2×C3—48no—
635C2×C3—64no—
636C2×C3C4×#23714yesdirect product factor
637C2×C3C3×C4×#4114yescomplemented
638C2×C3C23×C4×D311yescharacteristic
639C2×C3C22×#23711yescharacteristic
640C2×C3C2×D3×#4111yescharacteristic
641C2×C3C24×C3×C411yescharacteristic
642C2×C3C22×C3×#4111yescharacteristic
643C2×C3C22×C3×#4111yescharacteristic
644D3—24no—
645C22—216no—
646C22—24no—
647C22—24no—
648C22—34no—
649C22—68no—
650C22—62no—
651C22—62no—
652C22C22×C3×C4×D318yes—
653C22C22×C3×C4×D312yes—
654C22C2×C3×#23712yes—
655C22C3×D3×#4112yes—
656C22C24×C3×D311yescharacteristic
657C4—24no—
658C4—22no—
659C4—34no—
660C4—38no—
661C4—34no—
662C4—62no—
663C4—64no—
664C4C22×C3×C4×D314yes—
665C4C2×C3×#23714yesdirect product factor
666C3—21no—
667C3C2×C4×#23711yescharacteristic, direct product factor
668C3C2×C3×C4×#4111yescharacteristic, complemented
669C2—28no—
670C2—64no—
671C2C3×C4×#23714yesdirect product factor
672C2C23×C3×C4×D311yescharacteristic
673C2C22×C3×#23711yescharacteristic
674C2C2×C3×D3×#4111yescharacteristic
subgroupG/H
centerC22×C3×C4C22×D3
commutatorC2×C3C24×C3×C4
FrattiniC22C24×C3×D3
FittingC2×C32×C4×D4C2
socleC23×C32C24
prime radicalC22×C3×#237C2
cosocleC22×C3C25×C3
hypercenterC2×C3×C4×D4D3
hypocenterC3C2×C3×C4×#41
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3×C4 ◁ C2×C3×C4×D4

Complements

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

NH ≅ G/Ntype
2. C2×C32×C4×D4C2semidirect
3. C2×C3×D4×Dic3C2semidirect
4. C2×C3×C4×#67C2semidirect
5. C22×C3×C4×Dic3C2semidirect
6. C3×C4×#237C2direct (N × H)
7. C2×C3×#892C2semidirect
8. C2×C3×#887C2semidirect
9. C2×C3×#67⋊C4C2semidirect
10. C2×C3×#877C2semidirect
11. C2×C3×C42×D3C2semidirect
12. C2×C3×C4×Dic6C2semidirect
14. C2×C4×#237C3direct (N × H)
20. C2×C3×#237C4direct (N × H)
26. C32×C4×D4C22semidirect
31. C3×D4×Dic3C22semidirect
32. C3×C4×#67C22semidirect
43. C2×C3×C4×Dic3C22semidirect
44. C3×#892C22semidirect
45. C3×#887C22semidirect
46. C3×#67⋊C4C22semidirect
47. C3×#877C22semidirect
48. C3×C42×D3C22semidirect
49. C3×C4×Dic6C22semidirect
59. C2×C3×C4×D4D3semidirect
60. C2×C3×C4×D4C2×C3semidirect
65. C2×D4×Dic3C2×C3semidirect
66. C2×C4×#67C2×C3semidirect
67. C22×C4×Dic3C2×C3semidirect
68. C4×#237C2×C3direct (N × H)
69. C2×#892C2×C3semidirect
70. C2×#887C2×C3semidirect
71. C2×#67⋊C4C2×C3semidirect
72. C2×#877C2×C3semidirect
73. C2×C42×D3C2×C3semidirect
74. C2×C4×Dic6C2×C3semidirect
77. C2×C32×D4C2×C4semidirect
85. C2×C3×#67C2×C4semidirect
88. C22×C3×Dic3C2×C4semidirect
96. C3×#237C2×C4direct (N × H)
99. C2×C3×C4×D3C2×C4semidirect
103. C2×C3×Dic6C2×C4semidirect
138. C2×#237C3×C4direct (N × H)
150. C3×C4×D4C2×D3semidirect
151. C3×C4×D4C22×C3semidirect
177. D4×Dic3C22×C3semidirect
178. C4×#67C22×C3semidirect
189. C2×C4×Dic3C22×C3semidirect
190. #892C22×C3semidirect
191. #887C22×C3semidirect
192. #67⋊C4C22×C3semidirect
193. #877C22×C3semidirect
194. C42×D3C22×C3semidirect
195. C4×Dic6C22×C3semidirect
205. C32×D4C22×C4semidirect
210. C2×C32×C4#41semidirect
215. C3×#67C22×C4semidirect
221. C2×C3×Dic3C22×C4semidirect
222. C2×C3×Dic3#41semidirect
230. C3×C4×D3C22×C4semidirect
231. C3×Dic6C22×C4semidirect
239. C2×C4×D4C3×D3semidirect
256. C2×C3×D4C4×D3semidirect
257. C2×C3×D4C2×C3×C4semidirect
293. C2×#67C2×C3×C4semidirect
296. C22×Dic3C2×C3×C4semidirect
304. #237C2×C3×C4direct (N × H)
307. C2×C4×D3C2×C3×C4semidirect
311. C2×Dic6C2×C3×C4semidirect
359. C32×C4C2×#41semidirect
364. C3×Dic3C2×#41semidirect
381. C4×D4C2×C3×D3semidirect
426. C3×D4C2×C4×D3semidirect
427. C3×D4C22×C3×C4semidirect
459. C2×C3×C4#237direct (N × H)
461. C2×C3×C4C3×#41semidirect
470. #67C22×C3×C4semidirect
476. C2×Dic3C22×C3×C4semidirect
477. C2×Dic3C3×#41semidirect
485. C4×D3C22×C3×C4semidirect
486. Dic6C22×C3×C4semidirect
488. C2×C32C4×#41semidirect
500. C2×D4C3×C4×D3semidirect
583. C3×C4C2×#237direct (N × H)
585. C3×C4C2×C3×#41semidirect
590. Dic3C2×C3×#41semidirect
591. C32C2×C4×#41semidirect
603. D4C2×C3×C4×D3semidirect
623. C2×C4C3×#237direct (N × H)
636. C2×C3C4×#237direct (N × H)
637. C2×C3C3×C4×#41semidirect
665. C4C2×C3×#237direct (N × H)
667. C3C2×C4×#237direct (N × H)
668. C3C2×C3×C4×#41semidirect
671. C2C3×C4×#237direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#2372
C2×C32×C4×D42
C2×C3×D4×Dic32
C2×C3×C4×#672
C22×C3×C4×Dic32
C3×C4×#2372
C2×C3×#8922
C2×C3×#8872
C2×C3×#67⋊C42
C2×C3×#8772
C2×C3×C42×D32
C2×C3×C4×Dic62
C2×C3×C4×#413
C2×C4×#2373