Finite Group Databasebeta

← C2×D3×#924 #11900333

Subgroups — C2×D3×#924 #11900333

Order 1152.

3841 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×C4×D3C211yesmaximal, characteristic
2C22×D3×Dic6C211yesmaximal, characteristic, complemented
3C2×#64133C211yesmaximal, characteristic, complemented
4C2×C3×#924C211yesmaximal, characteristic, complemented
5C2×D3×#217C212yesmaximal
6C2×#63964C212yesmaximal, complemented
7C2×D3×C4⋊Dic3C211yesmaximal, characteristic, complemented
8D3×#924C2116yesmaximal, direct product factor
9C2×D3×Dic3⋊C4C212yesmaximal, complemented
10C2×#63857C211yesmaximal, characteristic, complemented
11C2×#63856C211yesmaximal, characteristic, complemented
12C2×#63851C212yesmaximal, complemented
13C22×#924—31nomaximal
14C2×D3×C22⋊Q8—31nomaximal
15C24×C3×D3C2211yescharacteristic
16C23×C32×C4C2211yescharacteristic
17C22×#634C2211yescharacteristic, complemented
18C23×C3×Dic3C2211yescharacteristic
19C22×C3×C4×D3—28no—
20C22×C3×C4×D3C2211yescharacteristic
21C22×C3×C4×D3C2211yescharacteristic
22C22×C3×C4×D3C2211yescharacteristic
23C22×C3×C4×D3C2218yes—
24C22×C3×C4×D3C2211yescharacteristic
25C22×C3×Dic6C2211yescharacteristic, complemented
26C22×#627C2212yescomplemented
27C22×D3×Dic3C2212yes—
28C22×D3×Dic3C2212yes—
29C2×D3×Dic6—28no—
30C2×D3×Dic6C2218yescomplemented
31C2×#3757C2212yes—
32C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
33#64133C2218yescomplemented
34C2×#3750C2212yescomplemented
35C2×C3×#217C2212yes—
36C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
37C3×#924C2218yescomplemented
38C2×C3×Dic3⋊C4C2212yescomplemented
39D3×#217C22116yes—
40C2×#3724C2212yescomplemented
41C2×Dic3⋊Dic3C2212yescomplemented
42C2×Dic3⋊Dic3C2212yescomplemented
43#63964C22116yescomplemented
44C2×(C2×D3)⋊Dic3C2212yes—
45C2×(C2×D3)⋊Dic3C2212yes—
46D3×C4⋊Dic3C2218yescomplemented
47D3×Dic3⋊C4C22116yescomplemented
48#63857C2218yescomplemented
49#63856C2218yescomplemented
50#63851C22116yescomplemented
51C24×C3×C4—31no—
52C22×D3×Q8—31no—
53C23×C4×D3D311yescharacteristic
54C23×Dic6—31no—
55C2×C3×C22⋊Q8—31no—
56C22×#217—32no—
57C2×#946—31no—
58C22×C4⋊Dic3—31no—
59C2×#924—31no—
60C2×#924—31no—
61C2×#924—31no—
62C2×#924—32no—
63C2×#924—31no—
64C2×#924—316no—
65C2×#924—32no—
66C2×#924—61no—
67C2×#924D311yescharacteristic, direct product factor
68C22×Dic3⋊C4—32no—
69D3×C22⋊Q8—316no—
70C2×#897—31no—
71C2×#896—32no—
72C2×D3×C4⋊C4—32no—
73C2×D3×C4⋊C4—31no—
74C2×D3×C22⋊C4—32no—
75C2×#878—32no—
76C24×C32C2311yescharacteristic
77C23×C3×D3—24no—
78C23×C3×D3—24no—
79C23×C3×D3Q818yescomplemented
80C23×C3×D3C2311yescharacteristic
81C23×C3×D3C2314yes—
82C23×C3×D3C2311yescharacteristic
83C22×C32×C4—24no—
84C22×C32×C4C2311yescharacteristic
85C22×C32×C4C2314yes—
86C22×C32×C4C2311yescharacteristic
87C22×C3⋊Dic3C2312yes—
88C22×C3⋊Dic3C2312yes—
89C2×#634—24no—
90C2×#634C2314yescomplemented
91C22×C3×Dic3—24no—
92C22×C3×Dic3C2312yes—
93C22×C3×Dic3C2312yes—
94C22×C3×Dic3C2314yes—
95C22×C3×Dic3C2311yescharacteristic
96C22×C3×Dic3C2311yescharacteristic
97C2×C3×C4×D3—24no—
98C2×C3×C4×D3—24no—
99C2×C3×C4×D3—24no—
100C2×C3×C4×D3—232no—
101C2×C3×C4×D3D418yes—
102C2×C3×C4×D3C2314yes—
103C2×C3×C4×D3C2314yes—
104C2×C3×C4×D3C2314yes—
105C2×C3×C4×D3C2314yes—
106C2×C3×Dic6—24no—
107C2×C3×Dic6C2314yescomplemented
108C2×#627—28no—
109C2×#627C2318yescomplemented
110C2×D3×Dic3—28no—
111C2×D3×Dic3—28no—
112C2×D3×Dic3C2318yes—
113C2×D3×Dic3C2318yes—
114D3×Dic6—232no—
115#3757C2318yes—
116C4⋊(C3⋊Dic3)C2314yescomplemented
117#3750C2318yescomplemented
118C3×#217C2318yes—
119C3×C4⋊Dic3C2314yescomplemented
120C3×Dic3⋊C4C2318yescomplemented
121#3724C2318yescomplemented
122Dic3⋊Dic3C2318yescomplemented
123Dic3⋊Dic3C2318yescomplemented
124(C2×D3)⋊Dic3C2318yes—
125(C2×D3)⋊Dic3C2318yes—
126C22×C22⋊Q8—91noSylow
127C25×C3—31no—
128C24×D3C2×D311yescharacteristic
129C22×C3×Q8—31no—
130C23×C3×C4—21no—
131C23×C3×C4—31no—
132C23×C3×C4—31no—
133C23×C3×C4—31no—
134C23×C3×C4—31no—
135C23×C3×C4—38no—
136C23×C3×C4—31no—
137C23×C3×C4—68no—
138C23×C3×C4C2×D311yescharacteristic
139C23×C3×C4C2×D311yescharacteristic
140C23×Dic3—32no—
141C23×Dic3—32no—
142C23×Dic3C2×D311yescharacteristic
143C2×D3×Q8—38no—
144C2×D3×Q8—68no—
145C22×C4×D3—28no—
146C22×C4×D3—32no—
147C22×C4×D3—32no—
148C22×C4×D3C2×D311yescharacteristic
149C22×C4×D3C2×D311yescharacteristic
150C22×C4×D3C2×D311yescharacteristic
151C22×C4×D3C2×D318yes—
152C22×C4×D3C2×D311yescharacteristic
153C22×Dic6—31no—
154C22×Dic6—31no—
155C22×Dic6—32no—
156C22×Dic6—32no—
157C22×Dic6—38no—
158C22×Dic6—61no—
159C22×Dic6—68no—
160C22×Dic6C2×D311yescharacteristic, complemented
161C3×C22⋊Q8—38no—
162C2×C3×C4⋊C4—32no—
163C2×C3×C4⋊C4—31no—
164C2×C3×C22⋊C4—32no—
165C2×#217—32no—
166C2×#217—32no—
167C2×#217—32no—
168C2×#217—32no—
169C2×#217—316no—
170C2×#217—62no—
171C2×#217C2×D312yes—
172#946—38no—
173C2×(C2×D3)⋊C4—32no—
174C2×(C2×D3)⋊C4—32no—
175C2×C4⋊Dic3—31no—
176C2×C4⋊Dic3—31no—
177C2×C4⋊Dic3—32no—
178C2×C4⋊Dic3—32no—
179C2×C4⋊Dic3—38no—
180C2×C4⋊Dic3—61no—
181C2×C4⋊Dic3C2×D311yescharacteristic, complemented
182#924—38no—
183#924—38no—
184#924—38no—
185#924—316no—
186#924—38no—
187#924—316no—
188#924—68no—
189#924C2×D318yesdirect product factor
190C2×Dic3⋊C4—32no—
191C2×Dic3⋊C4—32no—
192C2×Dic3⋊C4—32no—
193C2×Dic3⋊C4—32no—
194C2×Dic3⋊C4—32no—
195C2×Dic3⋊C4—32no—
196C2×Dic3⋊C4—316no—
197C2×Dic3⋊C4—62no—
198C2×Dic3⋊C4C2×D312yescomplemented
199#897—38no—
200#896—316no—
201D3×C4⋊C4—316no—
202D3×C4⋊C4—38no—
203D3×C22⋊C4—316no—
204#878—316no—
205C23×C32—22no—
206C23×C32—22no—
207C23×C32C2×Q814yescomplemented
208C23×C32C2412yes—
209C23×C32C2411yescharacteristic
210C22×C3×D3—22no—
211C22×C3×D3—22no—
212C22×C3×D3—232no—
213C22×C3×D3—28no—
214C22×C3×D3—28no—
215C22×C3×D3C2×D414yes—
216C22×C3×D3C2×Q814yes—
217C22×C3×D3C2×Q8116yescomplemented
218C22×C3×D3C2×Q814yescomplemented
219C22×C3×D3#4114yes—
220C22×C3×D3C2412yes—
221C22×C3×D3C2412yes—
222C2×C32×C4—22no—
223C2×C32×C4—28no—
224C2×C32×C4C2×D414yes—
225C2×C32×C4C2412yes—
226C2×C32×C4C2412yes—
227C2×C3⋊Dic3—24no—
228C2×C3⋊Dic3—24no—
229C2×C3⋊Dic3C2414yes—
230C2×C3⋊Dic3C2414yes—
231#634—28no—
232C2×C3×Dic3—24no—
233C2×C3×Dic3—22no—
234C2×C3×Dic3—24no—
235C2×C3×Dic3—28no—
236C2×C3×Dic3C2×D414yes—
237C2×C3×Dic3C2414yes—
238C2×C3×Dic3C2414yes—
239C2×C3×Dic3C2412yes—
240C2×C3×Dic3C2412yes—
241C3×C4×D3—28no—
242C3×C4×D3—28no—
243C3×C4×D3—28no—
244C3×C4×D3C2×D4116yes—
245C3×Dic6—28no—
246#627—216no—
247D3×Dic3—216no—
248D3×Dic3—216no—
249C23×Q8—91no—
250C24×C4—31no—
251C2×C22⋊Q8—31no—
252C2×C22⋊Q8—92no—
253C2×C22⋊Q8—92no—
254C2×C22⋊Q8—91no—
255C2×C22⋊Q8—916no—
256C2×C22⋊Q8—91no—
257C2×C22⋊Q8—91no—
258C22×C4⋊C4—92no—
259C22×C4⋊C4—91no—
260C22×C22⋊C4—92no—
261C24×C3—21no—
262C24×C3—31no—
263C24×C3—38no—
264C24×C3—34no—
265C24×C3—31no—
266C24×C3—64no—
267C24×C3—64no—
268C24×C3C22×D311yescharacteristic
269C24×C3C22×D311yescharacteristic
270C23×D3—24no—
271C23×D3—24no—
272C23×D3Dic618yescomplemented
273C23×D3C22×D314yes—
274C23×D3C22×D311yescharacteristic
275C23×D3C22×D311yescharacteristic
276C2×C3×Q8—34no—
277C2×C3×Q8—64no—
278C22×C3×C4—24no—
279C22×C3×C4—24no—
280C22×C3×C4—21no—
281C22×C3×C4—21no—
282C22×C3×C4—24no—
283C22×C3×C4—31no—
284C22×C3×C4—38no—
285C22×C3×C4—34no—
286C22×C3×C4—31no—
287C22×C3×C4—32no—
288C22×C3×C4—32no—
289C22×C3×C4—34no—
290C22×C3×C4—34no—
291C22×C3×C4—34no—
292C22×C3×C4—34no—
293C22×C3×C4—44no—
294C22×C3×C4—64no—
295C22×C3×C4—632no—
296C22×C3×C4—64no—
297C22×C3×C4—64no—
298C22×C3×C4—64no—
299C22×C3×C4C22×D311yescharacteristic
300C22×C3×C4C22×D311yescharacteristic
301C22×C3×C4C22×D314yes—
302C22×C3×C4C22×D314yes—
303C22×C3×C4C22×D311yescharacteristic
304C22×C3×C4C22×D311yescharacteristic
305C22×Dic3—24no—
306C22×Dic3—32no—
307C22×Dic3—32no—
308C22×Dic3—32no—
309C22×Dic3—32no—
310C22×Dic3—38no—
311C22×Dic3—38no—
312C22×Dic3—62no—
313C22×Dic3—62no—
314C22×Dic3—68no—
315C22×Dic3—68no—
316C22×Dic3C22×D314yes—
317C22×Dic3C22×D311yescharacteristic
318C22×Dic3C22×D312yes—
319C22×Dic3C22×D312yes—
320C22×Dic3C22×D311yescharacteristic
321D3×Q8—632no—
322C2×C4×D3—24no—
323C2×C4×D3—24no—
324C2×C4×D3—24no—
325C2×C4×D3—232no—
326C2×C4×D3—38no—
327C2×C4×D3—38no—
328C2×C4×D3—68no—
329C2×C4×D3—68no—
330C2×C4×D3#6718yes—
331C2×C4×D3C22×D314yes—
332C2×C4×D3C22×D314yes—
333C2×C4×D3C22×D314yes—
334C2×C4×D3C22×D314yes—
335C2×Dic6—24no—
336C2×Dic6—34no—
337C2×Dic6—34no—
338C2×Dic6—38no—
339C2×Dic6—38no—
340C2×Dic6—64no—
341C2×Dic6—632no—
342C2×Dic6—68no—
343C2×Dic6—64no—
344C2×Dic6—64no—
345C2×Dic6—68no—
346C2×Dic6—124no—
347C2×Dic6C22×D314yescomplemented
348C3×C4⋊C4—38no—
349C3×C4⋊C4—34no—
350C3×C22⋊C4—38no—
351#217—38no—
352#217—38no—
353#217—38no—
354#217—38no—
355#217—68no—
356#217C22×D318yes—
357(C2×D3)⋊C4—38no—
358(C2×D3)⋊C4—38no—
359C4⋊Dic3—34no—
360C4⋊Dic3—34no—
361C4⋊Dic3—38no—
362C4⋊Dic3—38no—
363C4⋊Dic3—64no—
364C4⋊Dic3C22×D314yescomplemented
365Dic3⋊C4—38no—
366Dic3⋊C4—38no—
367Dic3⋊C4—38no—
368Dic3⋊C4—38no—
369Dic3⋊C4—38no—
370Dic3⋊C4—38no—
371Dic3⋊C4—68no—
372Dic3⋊C4C22×D318yescomplemented
373C22×C32—28no—
374C22×C32—22no—
375C22×C32—22no—
376C22×C32C22×D412yes—
377C22×C32C22×Q812yes—
378C22×C32C22×Q814yescomplemented
379C22×C32C2×#4112yes—
380C22×C32C2511yescharacteristic
381C2×C3×D3—28no—
382C2×C3×D3—22no—
383C2×C3×D3—22no—
384C2×C3×D3—232no—
385C2×C3×D3C22⋊Q8116yescomplemented
386C2×C3×D3C22×D414yes—
387C2×C3×D3C22×Q814yes—
388C2×C3×D3C22×Q814yescomplemented
389C2×C3×D3C2×#4114yes—
390C32×C4—22no—
391C32×C4C22×D414yes—
392C3⋊Dic3—24no—
393C3⋊Dic3—24no—
394C3×Dic3—24no—
395C3×Dic3—22no—
396C3×Dic3—24no—
397C3×Dic3C22×D414yes—
398C25—31no—
399C22×Q8—31no—
400C22×Q8—92no—
401C22×Q8—98no—
402C22×Q8—91no—
403C22×Q8—188no—
404C23×C4—31no—
405C23×C4—31no—
406C23×C4—31no—
407C23×C4—31no—
408C23×C4—38no—
409C23×C4—31no—
410C23×C4—68no—
411C23×C4—92no—
412C23×C4—92no—
413C23×C4D3211yescharacteristic
414C22⋊Q8—38no—
415C22⋊Q8—916no—
416C22⋊Q8—916no—
417C22⋊Q8—98no—
418C22⋊Q8—98no—
419C22⋊Q8—98no—
420C2×C4⋊C4—32no—
421C2×C4⋊C4—31no—
422C2×C4⋊C4—916no—
423C2×C4⋊C4—98no—
424C2×C4⋊C4—92no—
425C2×C4⋊C4—92no—
426C2×C4⋊C4—92no—
427C2×C4⋊C4—92no—
428C2×C4⋊C4—91no—
429C2×C22⋊C4—32no—
430C2×C22⋊C4—916no—
431C2×C22⋊C4—92no—
432C2×C22⋊C4—92no—
433C2×C22⋊C4—92no—
434C23×C3—22no—
435C23×C3—22no—
436C23×C3—22no—
437C23×C3—22no—
438C23×C3—22no—
439C23×C3—21no—
440C23×C3—24no—
441C23×C3—34no—
442C23×C3—34no—
443C23×C3—34no—
444C23×C3—32no—
445C23×C3—34no—
446C23×C3—316no—
447C23×C3—32no—
448C23×C3—42no—
449C23×C3—42no—
450C23×C3—68no—
451C23×C3—68no—
452C23×C3—632no—
453C23×C3—62no—
454C23×C3—62no—
455C23×C3C2×Dic614yescomplemented
456C23×C3D3×Q814yescomplemented
457C23×C3C23×D312yes—
458C23×C3C23×D312yes—
459C23×C3C23×D311yescharacteristic
460C23×C3C23×D311yescharacteristic
461C22×D3—22no—
462C22×D3—22no—
463C22×D3—232no—
464C22×D3—28no—
465C22×D3—28no—
466C22×D3C2×Dic614yes—
467C22×D3C2×Dic6116yescomplemented
468C22×D3C2×Dic614yescomplemented
469C22×D3#23514yes—
470C22×D3C2×#6714yes—
471C22×D3C23×D312yes—
472C22×D3C23×D312yes—
473C3×Q8—68no—
474C2×C3×C4—22no—
475C2×C3×C4—22no—
476C2×C3×C4—28no—
477C2×C3×C4—28no—
478C2×C3×C4—22no—
479C2×C3×C4—22no—
480C2×C3×C4—24no—
481C2×C3×C4—34no—
482C2×C3×C4—32no—
483C2×C3×C4—316no—
484C2×C3×C4—32no—
485C2×C3×C4—34no—
486C2×C3×C4—34no—
487C2×C3×C4—48no—
488C2×C3×C4—42no—
489C2×C3×C4—68no—
490C2×C3×C4—68no—
491C2×C3×C4—68no—
492C2×C3×C4—64no—
493C2×C3×C4—62no—
494C2×C3×C4—64no—
495C2×C3×C4—68no—
496C2×C3×C4D3×D414yes—
497C2×C3×C4C2×#6714yes—
498C2×C3×C4C23×D312yes—
499C2×C3×C4C23×D312yes—
500C2×C3×C4C23×D312yes—
501C2×C3×C4C23×D312yes—
502C2×Dic3—24no—
503C2×Dic3—24no—
504C2×Dic3—22no—
505C2×Dic3—28no—
506C2×Dic3—34no—
507C2×Dic3—34no—
508C2×Dic3—34no—
509C2×Dic3—34no—
510C2×Dic3—64no—
511C2×Dic3—64no—
512C2×Dic3—616no—
513C2×Dic3—616no—
514C2×Dic3—64no—
515C2×Dic3—64no—
516C2×Dic3—64no—
517C2×Dic3—64no—
518C2×Dic3—124no—
519C2×Dic3—124no—
520C2×Dic3C2×#6714yes—
521C2×Dic3C23×D312yes—
522C2×Dic3C23×D314yes—
523C2×Dic3C23×D314yes—
524C2×Dic3C23×D312yes—
525C4×D3—28no—
526C4×D3—28no—
527C4×D3—28no—
528C4×D3—616no—
529C4×D3—616no—
530C4×D3C2×#67116yes—
531Dic6—28no—
532Dic6—616no—
533Dic6—68no—
534Dic6—68no—
535Dic6—616no—
536Dic6—128no—
537C2×C32—24no—
538C2×C32C2×C22⋊Q814yescomplemented
539C2×C32C23×D411yescharacteristic
540C2×C32C23×Q811yescharacteristic
541C2×C32C22×#4111yescharacteristic
542C3×D3—24no—
543C3×D3C2×C22⋊Q818yescomplemented
544C24—31no—
545C24—34no—
546C24—31no—
547C24—38no—
548C24—64no—
549C24—64no—
550C24C2×D3211yescharacteristic
551C2×Q8—34no—
552C2×Q8—64no—
553C2×Q8—98no—
554C2×Q8—94no—
555C2×Q8—188no—
556C2×Q8—1832no—
557C2×Q8—184no—
558C22×C4—24no—
559C22×C4—31no—
560C22×C4—34no—
561C22×C4—38no—
562C22×C4—34no—
563C22×C4—32no—
564C22×C4—32no—
565C22×C4—31no—
566C22×C4—34no—
567C22×C4—34no—
568C22×C4—34no—
569C22×C4—64no—
570C22×C4—632no—
571C22×C4—64no—
572C22×C4—64no—
573C22×C4—64no—
574C22×C4—98no—
575C22×C4—98no—
576C22×C4—92no—
577C22×C4—92no—
578C22×C4—188no—
579C22×C4—188no—
580C22×C4C2×D3214yes—
581C22×C4C2×D3211yescharacteristic
582C22×C4C2×D3211yescharacteristic
583C4⋊C4—38no—
584C4⋊C4—34no—
585C4⋊C4—98no—
586C4⋊C4—98no—
587C4⋊C4—98no—
588C4⋊C4—98no—
589C4⋊C4—94no—
590C22⋊C4—38no—
591C22⋊C4—98no—
592C22⋊C4—98no—
593C22⋊C4—98no—
594C22×C3—22no—
595C22×C3—22no—
596C22×C3—22no—
597C22×C3—22no—
598C22×C3—28no—
599C22×C3—28no—
600C22×C3—22no—
601C22×C3—24no—
602C22×C3—22no—
603C22×C3—22no—
604C22×C3—21no—
605C22×C3—34no—
606C22×C3—34no—
607C22×C3—34no—
608C22×C3—316no—
609C22×C3—34no—
610C22×C3—42no—
611C22×C3—42no—
612C22×C3—48no—
613C22×C3—632no—
614C22×C3—62no—
615C22×C3—62no—
616C22×C3—68no—
617C22×C3C22×Dic612yes—
618C22×C3C22×Dic614yescomplemented
619C22×C3C2×#23512yes—
620C22×C3C2×D3×D412yes—
621C22×C3C2×D3×Q812yes—
622C22×C3C2×D3×Q814yescomplemented
623C22×C3D3×#4112yes—
624C22×C3C22×#6712yes—
625C22×C3C24×D311yescharacteristic
626C22×C3C24×D311yescharacteristic
627C2×D3—22no—
628C2×D3—22no—
629C2×D3—28no—
630C2×D3—232no—
631C2×D3#924116yesdirect product factor
632C2×D3C22×Dic614yes—
633C2×D3C22×Dic614yescomplemented
634C2×D3C2×#23514yes—
635C2×D3C22×#6714yes—
636C3×C4—22no—
637C3×C4—22no—
638C3×C4—24no—
639C3×C4—34no—
640C3×C4—42no—
641C3×C4—64no—
642C3×C4—62no—
643C3×C4—64no—
644C3×C4C2×D3×D414yes—
645C3×C4C22×#6714yes—
646Dic3—24no—
647Dic3—24no—
648Dic3—22no—
649Dic3—64no—
650Dic3—64no—
651Dic3—64no—
652Dic3—64no—
653Dic3—124no—
654Dic3—124no—
655Dic3C22×#6714yes—
656C32C22×C22⋊Q811yescharacteristic, complemented, Sylow
657C23—22no—
658C23—22no—
659C23—34no—
660C23—34no—
661C23—34no—
662C23—32no—
663C23—34no—
664C23—316no—
665C23—32no—
666C23—68no—
667C23—68no—
668C23—632no—
669C23—62no—
670C23—62no—
671C23D3×Dic614yescomplemented
672C23C22×D3212yes—
673C23C22×D3211yescharacteristic
674Q8—68no—
675Q8—1816no—
676Q8—188no—
677C2×C4—22no—
678C2×C4—28no—
679C2×C4—34no—
680C2×C4—32no—
681C2×C4—316no—
682C2×C4—34no—
683C2×C4—34no—
684C2×C4—32no—
685C2×C4—68no—
686C2×C4—68no—
687C2×C4—68no—
688C2×C4—64no—
689C2×C4—62no—
690C2×C4—64no—
691C2×C4—68no—
692C2×C4—94no—
693C2×C4—94no—
694C2×C4—1816no—
695C2×C4—1816no—
696C2×C4—184no—
697C2×C4—184no—
698C2×C4D3×#6714yes—
699C2×C4C22×D3212yes—
700C2×C4C22×D3212yes—
701C2×C3—24no—
702C2×C3—24no—
703C2×C3—21no—
704C2×C3—21no—
705C2×C3—24no—
706C2×C3—21no—
707C2×C3—38no—
708C2×C3—44no—
709C2×C3—64no—
710C2×C3D3×C22⋊Q814yescomplemented
711C2×C3C2×#92414yescomplemented
712C2×C3C23×Dic611yescharacteristic
713C2×C3C22×#23511yescharacteristic
714C2×C3C22×D3×D411yescharacteristic
715C2×C3C22×D3×Q811yescharacteristic
716C2×C3C2×D3×#4111yescharacteristic
717C2×C3C23×#6711yescharacteristic
718D3—24no—
719D3C2×#92418yesdirect product factor
720C22—22no—
721C22—28no—
722C22—22no—
723C22—34no—
724C22—34no—
725C22—316no—
726C22—34no—
727C22—34no—
728C22—632no—
729C22—62no—
730C22—68no—
731C22—62no—
732C22C2×D3×Dic612yes—
733C22C2×D3×Dic614yescomplemented
734C22D3×#23512yes—
735C22C2×D3×#6712yes—
736C22C23×D3211yescharacteristic
737C4—22no—
738C4—34no—
739C4—64no—
740C4—62no—
741C4—64no—
742C4—184no—
743C4—184no—
744C4C2×D3×#6714yes—
745C3—21no—
746C3C2×D3×C22⋊Q811yescharacteristic, complemented
747C3C22×#92411yescharacteristic, complemented
748C2—24no—
749C2—38no—
750C2—64no—
751C2D3×#92414yesdirect product factor
752C2C22×D3×Dic611yescharacteristic
753C2C2×D3×#23511yescharacteristic
754C2C22×D3×#6711yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC23×C32×C4C22
socleC23×C32C24
prime radicalC24×C3×D3C22
hypercenterC23×C4D32
hypocenterC32C22×C22⋊Q8
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C22×D3×Dic6C2semidirect
3. C2×#64133C2semidirect
4. C2×C3×#924C2semidirect
6. C2×#63964C2semidirect
7. C2×D3×C4⋊Dic3C2semidirect
8. D3×#924C2direct (N × H)
9. C2×D3×Dic3⋊C4C2semidirect
10. C2×#63857C2semidirect
11. C2×#63856C2semidirect
12. C2×#63851C2semidirect
17. C22×#634C22semidirect
25. C22×C3×Dic6C22semidirect
26. C22×#627C22semidirect
30. C2×D3×Dic6C22semidirect
32. C2×C4⋊(C3⋊Dic3)C22semidirect
33. #64133C22semidirect
34. C2×#3750C22semidirect
36. C2×C3×C4⋊Dic3C22semidirect
37. C3×#924C22semidirect
38. C2×C3×Dic3⋊C4C22semidirect
40. C2×#3724C22semidirect
41. C2×Dic3⋊Dic3C22semidirect
42. C2×Dic3⋊Dic3C22semidirect
43. #63964C22semidirect
46. D3×C4⋊Dic3C22semidirect
47. D3×Dic3⋊C4C22semidirect
48. #63857C22semidirect
49. #63856C22semidirect
50. #63851C22semidirect
67. C2×#924D3direct (N × H)
79. C23×C3×D3Q8semidirect
90. C2×#634C23semidirect
107. C2×C3×Dic6C23semidirect
109. C2×#627C23semidirect
116. C4⋊(C3⋊Dic3)C23semidirect
117. #3750C23semidirect
119. C3×C4⋊Dic3C23semidirect
120. C3×Dic3⋊C4C23semidirect
121. #3724C23semidirect
122. Dic3⋊Dic3C23semidirect
123. Dic3⋊Dic3C23semidirect
160. C22×Dic6C2×D3semidirect
181. C2×C4⋊Dic3C2×D3semidirect
189. #924C2×D3direct (N × H)
198. C2×Dic3⋊C4C2×D3semidirect
207. C23×C32C2×Q8semidirect
217. C22×C3×D3C2×Q8semidirect
218. C22×C3×D3C2×Q8semidirect
272. C23×D3Dic6semidirect
347. C2×Dic6C22×D3semidirect
364. C4⋊Dic3C22×D3semidirect
372. Dic3⋊C4C22×D3semidirect
378. C22×C32C22×Q8semidirect
385. C2×C3×D3C22⋊Q8semidirect
388. C2×C3×D3C22×Q8semidirect
455. C23×C3C2×Dic6semidirect
456. C23×C3D3×Q8semidirect
467. C22×D3C2×Dic6semidirect
468. C22×D3C2×Dic6semidirect
538. C2×C32C2×C22⋊Q8semidirect
543. C3×D3C2×C22⋊Q8semidirect
618. C22×C3C22×Dic6semidirect
622. C22×C3C2×D3×Q8semidirect
631. C2×D3#924direct (N × H)
633. C2×D3C22×Dic6semidirect
656. C32C22×C22⋊Q8semidirect
671. C23D3×Dic6semidirect
710. C2×C3D3×C22⋊Q8semidirect
711. C2×C3C2×#924semidirect
719. D3C2×#924direct (N × H)
733. C22C2×D3×Dic6semidirect
746. C3C2×D3×C22⋊Q8semidirect
747. C3C22×#924semidirect
751. C2D3×#924direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×C4×D32
C22×D3×Dic62
C2×#641332
C2×C3×#9242
C2×D3×#2172
C2×#639642
C2×D3×C4⋊Dic32
D3×#9242
C2×D3×Dic3⋊C42
C2×#638572
C2×#638562
C2×#638512
C22×#9243
C2×D3×C22⋊Q83