Finite Group Databasebeta

← C2×D3×#946 #11900327

Subgroups — C2×D3×#946 #11900327

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
1C22×C3×D3×Q8C211yesmaximal, characteristic, complemented
2C22×C4×D32C211yesmaximal, characteristic
3C2×#64155C211yesmaximal, characteristic, complemented
4C2×C3×#946C211yesmaximal, characteristic, complemented
5D3×#946C2116yesmaximal, direct product factor
6C2×D3×(C2×D3)⋊C4C212yesmaximal
7C2×D3×C4⋊Dic3C211yesmaximal, characteristic, complemented
8C2×#63888C212yesmaximal, complemented
9C2×#63887C212yesmaximal, complemented
10C2×D3×Dic3⋊C4C212yesmaximal, complemented
11C2×#63871C211yesmaximal, characteristic, complemented
12C2×#63856C211yesmaximal, characteristic, complemented
13C22×#946—31nomaximal
14C2×D3×C22⋊Q8—31nomaximal
15C23×D32C2211yescharacteristic
16C22×C32×Q8C2211yescharacteristic, complemented
17C22×C4×C3⋊D3C2211yescharacteristic
18C2×C3×D3×Q8—28no—
19C2×C3×D3×Q8C2218yescomplemented
20C22×C3×C4×D3C2211yescharacteristic
21C22×C3×C4×D3C2212yes—
22C22×C3×C4×D3C2211yescharacteristic
23C22×C3×Dic6C2211yescharacteristic, complemented
24C22×C3×Dic6C2212yescomplemented
25C22×#624C2211yescharacteristic
26C22×D3×Dic3C2211yescharacteristic
27C22×D3×Dic3C2212yes—
28C22×D3×Dic3C2211yescharacteristic
29C2×C4×D32—28no—
30C2×C4×D32C2218yes—
31#64155C2218yescomplemented
32C2×#3752C2212yes—
33C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
34C2×#3750C2212yescomplemented
35C3×#946C2218yescomplemented
36C2×C3×(C2×D3)⋊C4C2212yes—
37C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
38C2×C3×Dic3⋊C4C2212yescomplemented
39C2×#3724C2212yescomplemented
40C2×Dic3⋊Dic3C2212yescomplemented
41C2×Dic3⋊Dic3C2212yescomplemented
42C2×#3722C2212yes—
43C2×(C2×D3)⋊Dic3C2212yes—
44D3×(C2×D3)⋊C4C22116yes—
45D3×C4⋊Dic3C2218yescomplemented
46#63888C22116yescomplemented
47#63887C22116yescomplemented
48D3×Dic3⋊C4C22116yescomplemented
49#63871C2218yescomplemented
50#63856C2218yescomplemented
51C23×C3×Q8—31no—
52C22×D3×Q8D311yescharacteristic, complemented
53C23×C4×D3—31no—
54C23×C4×D3—31no—
55C2×C3×C22⋊Q8—31no—
56C2×#946—31no—
57C2×#946—31no—
58C2×#946—31no—
59C2×#946—316no—
60C2×#946—32no—
61C2×#946—31no—
62C2×#946—32no—
63C2×#946—61no—
64C2×#946D311yescharacteristic, direct product factor
65C22×(C2×D3)⋊C4—32no—
66C22×C4⋊Dic3—31no—
67C2×#924—31no—
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—
76C23×C3⋊D3C2311yescharacteristic
77C23×C3×D3C2311yescharacteristic
78C23×C3×D3C2311yescharacteristic
79C22×D32—24no—
80C22×D32—24no—
81C22×D32Q818yescomplemented
82C22×D32C2314yes—
83C2×C32×Q8—24no—
84C2×C32×Q8C2314yescomplemented
85C22×C32×C4C2312yes—
86C22×C32×C4C2311yescharacteristic
87C22×C3⋊Dic3C2311yescharacteristic
88C22×C3⋊Dic3C2312yes—
89C2×C4×C3⋊D3—24no—
90C2×C4×C3⋊D3C2314yes—
91C22×C3×Dic3C2311yescharacteristic
92C22×C3×Dic3C2312yes—
93C22×C3×Dic3C2312yes—
94C22×C3×Dic3C2311yescharacteristic
95C3×D3×Q8—232no—
96C2×C3×C4×D3—28no—
97C2×C3×C4×D3—24no—
98C2×C3×C4×D3D418yes—
99C2×C3×C4×D3C2314yes—
100C2×C3×C4×D3C2318yes—
101C2×C3×C4×D3C2314yes—
102C2×C3×Dic6—24no—
103C2×C3×Dic6—28no—
104C2×C3×Dic6C2314yescomplemented
105C2×C3×Dic6C2318yescomplemented
106C2×#624—24no—
107C2×#624C2314yes—
108C2×D3×Dic3—24no—
109C2×D3×Dic3—28no—
110C2×D3×Dic3—24no—
111C2×D3×Dic3C2314yes—
112C2×D3×Dic3C2314yes—
113C2×D3×Dic3C2318yes—
114C4×D32—232no—
115#3752C2318yes—
116C4⋊(C3⋊Dic3)C2314yescomplemented
117#3750C2318yescomplemented
118C3×(C2×D3)⋊C4C2318yes—
119C3×C4⋊Dic3C2314yescomplemented
120C3×Dic3⋊C4C2318yescomplemented
121#3724C2318yescomplemented
122Dic3⋊Dic3C2318yescomplemented
123Dic3⋊Dic3C2318yescomplemented
124#3722C2318yes—
125(C2×D3)⋊Dic3C2318yes—
126C22×C22⋊Q8—91noSylow
127C24×D3—31no—
128C24×D3—31no—
129C22×C3×Q8—21no—
130C22×C3×Q8—38no—
131C22×C3×Q8—32no—
132C22×C3×Q8—31no—
133C22×C3×Q8—68no—
134C22×C3×Q8C2×D311yescharacteristic, complemented
135C22×C3×Q8C2×D311yescharacteristic, complemented
136C23×C3×C4—31no—
137C23×C3×C4—31no—
138C23×C3×C4—32no—
139C23×Dic3—31no—
140C23×Dic3—31no—
141C23×Dic3—32no—
142C2×D3×Q8—28no—
143C2×D3×Q8C2×D318yescomplemented
144C22×C4×D3—31no—
145C22×C4×D3—31no—
146C22×C4×D3—32no—
147C22×C4×D3—31no—
148C22×C4×D3—31no—
149C22×C4×D3—31no—
150C22×C4×D3—31no—
151C22×C4×D3—38no—
152C22×C4×D3—38no—
153C22×C4×D3—61no—
154C22×C4×D3—68no—
155C22×C4×D3—68no—
156C22×C4×D3C2×D311yescharacteristic
157C22×C4×D3C2×D312yes—
158C22×C4×D3C2×D311yescharacteristic
159C22×Dic6C2×D312yescomplemented
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—
166#946—38no—
167#946—38no—
168#946—38no—
169#946—316no—
170#946—38no—
171#946—316no—
172#946—68no—
173#946C2×D318yesdirect product factor
174C2×(C2×D3)⋊C4—32no—
175C2×(C2×D3)⋊C4—32no—
176C2×(C2×D3)⋊C4—32no—
177C2×(C2×D3)⋊C4—32no—
178C2×(C2×D3)⋊C4—32no—
179C2×(C2×D3)⋊C4—316no—
180C2×(C2×D3)⋊C4—62no—
181C2×(C2×D3)⋊C4C2×D312yes—
182C2×C4⋊Dic3—31no—
183C2×C4⋊Dic3—31no—
184C2×C4⋊Dic3—32no—
185C2×C4⋊Dic3—32no—
186C2×C4⋊Dic3—38no—
187C2×C4⋊Dic3—61no—
188C2×C4⋊Dic3C2×D311yescharacteristic, complemented
189#924—38no—
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×C32C2411yescharacteristic
206C22×C3⋊D3—22no—
207C22×C3⋊D3—22no—
208C22×C3⋊D3C2×Q814yescomplemented
209C22×C3⋊D3C2412yes—
210C22×C3×D3—22no—
211C22×C3×D3—22no—
212C22×C3×D3C2×D414yes—
213C22×C3×D3C2×Q814yes—
214C22×C3×D3C2×Q814yescomplemented
215C22×C3×D3#4114yes—
216C22×C3×D3C2412yes—
217C22×C3×D3C2412yes—
218C2×D32—232no—
219C2×D32—28no—
220C2×D32—28no—
221C2×D32C2×Q8116yescomplemented
222C32×Q8—28no—
223C2×C32×C4—24no—
224C2×C32×C4C2×D414yes—
225C2×C32×C4C2414yes—
226C2×C32×C4C2412yes—
227C2×C3⋊Dic3—22no—
228C2×C3⋊Dic3—24no—
229C2×C3⋊Dic3C2414yes—
230C2×C3⋊Dic3C2412yes—
231C4×C3⋊D3—28no—
232C2×C3×Dic3—22no—
233C2×C3×Dic3—24no—
234C2×C3×Dic3—24no—
235C2×C3×Dic3C2×D414yes—
236C2×C3×Dic3C2414yes—
237C2×C3×Dic3C2414yes—
238C2×C3×Dic3C2412yes—
239C2×C3×Dic3C2412yes—
240C3×C4×D3—216no—
241C3×C4×D3—28no—
242C3×C4×D3C2×D4116yes—
243C3×Dic6—28no—
244C3×Dic6—216no—
245#624—28no—
246D3×Dic3—28no—
247D3×Dic3—216no—
248D3×Dic3—28no—
249C23×Q8—31no—
250C24×C4—91no—
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—31no—
262C24×C3—31no—
263C23×D3—31no—
264C23×D3—31no—
265C23×D3—38no—
266C23×D3—38no—
267C23×D3—34no—
268C23×D3—34no—
269C23×D3—61no—
270C23×D3—64no—
271C23×D3—64no—
272C23×D3—64no—
273C23×D3—64no—
274C23×D3C22×D311yescharacteristic
275C23×D3C22×D311yescharacteristic
276C2×C3×Q8—24no—
277C2×C3×Q8—24no—
278C2×C3×Q8—24no—
279C2×C3×Q8—38no—
280C2×C3×Q8—34no—
281C2×C3×Q8—44no—
282C2×C3×Q8—68no—
283C2×C3×Q8—632no—
284C2×C3×Q8—64no—
285C2×C3×Q8C22×D314yescomplemented
286C2×C3×Q8C22×D314yescomplemented
287C22×C3×C4—21no—
288C22×C3×C4—22no—
289C22×C3×C4—31no—
290C22×C3×C4—38no—
291C22×C3×C4—34no—
292C22×C3×C4—32no—
293C22×C3×C4—31no—
294C22×C3×C4—32no—
295C22×C3×C4—38no—
296C22×C3×C4—34no—
297C22×C3×C4—68no—
298C22×C3×C4—64no—
299C22×C3×C4C22×D312yes—
300C22×C3×C4C22×D312yes—
301C22×C3×C4C22×D311yescharacteristic
302C22×C3×C4C22×D311yescharacteristic
303C22×Dic3—31no—
304C22×Dic3—32no—
305C22×Dic3—32no—
306C22×Dic3—31no—
307C22×Dic3—34no—
308C22×Dic3—34no—
309C22×Dic3—38no—
310C22×Dic3—61no—
311C22×Dic3—62no—
312C22×Dic3—64no—
313C22×Dic3—68no—
314C22×Dic3—64no—
315C22×Dic3C22×D311yescharacteristic
316C22×Dic3C22×D312yes—
317C22×Dic3C22×D312yes—
318C22×Dic3C22×D311yescharacteristic
319D3×Q8—232no—
320C2×C4×D3—28no—
321C2×C4×D3—24no—
322C2×C4×D3—38no—
323C2×C4×D3—34no—
324C2×C4×D3—34no—
325C2×C4×D3—34no—
326C2×C4×D3—34no—
327C2×C4×D3—34no—
328C2×C4×D3—34no—
329C2×C4×D3—64no—
330C2×C4×D3—632no—
331C2×C4×D3—64no—
332C2×C4×D3—64no—
333C2×C4×D3—68no—
334C2×C4×D3—64no—
335C2×C4×D3—64no—
336C2×C4×D3—64no—
337C2×C4×D3—64no—
338C2×C4×D3—632no—
339C2×C4×D3—124no—
340C2×C4×D3#6718yes—
341C2×C4×D3C22×D318yes—
342C2×C4×D3C22×D314yes—
343C2×C4×D3C22×D314yes—
344C2×Dic6—24no—
345C2×Dic6—28no—
346C2×Dic6C22×D318yescomplemented
347C2×Dic6C22×D314yescomplemented
348C3×C4⋊C4—38no—
349C3×C4⋊C4—34no—
350C3×C22⋊C4—38no—
351#217—38no—
352(C2×D3)⋊C4—38no—
353(C2×D3)⋊C4—38no—
354(C2×D3)⋊C4—38no—
355(C2×D3)⋊C4—38no—
356(C2×D3)⋊C4—38no—
357(C2×D3)⋊C4—68no—
358(C2×D3)⋊C4C22×D318yes—
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×C32C22×D412yes—
374C22×C32C22×Q812yes—
375C22×C32C2×#4112yes—
376C22×C32C2511yescharacteristic
377C2×C3⋊D3—28no—
378C2×C3⋊D3—22no—
379C2×C3⋊D3—22no—
380C2×C3⋊D3C22×Q814yescomplemented
381C2×C3×D3—28no—
382C2×C3×D3—22no—
383C2×C3×D3—22no—
384C2×C3×D3C22⋊Q8116yescomplemented
385C2×C3×D3C22×D414yes—
386C2×C3×D3C22×Q814yes—
387C2×C3×D3C22×Q814yescomplemented
388C2×C3×D3C2×#4114yes—
389D32—232no—
390C32×C4—24no—
391C32×C4C22×D414yes—
392C3⋊Dic3—22no—
393C3⋊Dic3—24no—
394C3×Dic3—22no—
395C3×Dic3—24no—
396C3×Dic3—24no—
397C3×Dic3C22×D414yes—
398C25—91no—
399C22×Q8—38no—
400C22×Q8—32no—
401C22×Q8—31no—
402C22×Q8—68no—
403C22×Q8D3211yescharacteristic, complemented
404C23×C4—31no—
405C23×C4—32no—
406C23×C4—31no—
407C23×C4—91no—
408C23×C4—98no—
409C23×C4—92no—
410C23×C4—91no—
411C23×C4—91no—
412C23×C4—91no—
413C23×C4—188no—
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—21no—
435C23×C3—34no—
436C23×C3—34no—
437C23×C3—34no—
438C23×C3—32no—
439C23×C3—34no—
440C23×C3—32no—
441C23×C3—62no—
442C23×C3—62no—
443C23×C3C23×D311yescharacteristic
444C23×C3C23×D311yescharacteristic
445C22×D3—22no—
446C22×D3—22no—
447C22×D3—34no—
448C22×D3—34no—
449C22×D3—32no—
450C22×D3—32no—
451C22×D3—316no—
452C22×D3—316no—
453C22×D3—64no—
454C22×D3—62no—
455C22×D3—68no—
456C22×D3—68no—
457C22×D3—632no—
458C22×D3—62no—
459C22×D3—62no—
460C22×D3—62no—
461C22×D3—62no—
462C22×D3—632no—
463C22×D3—68no—
464C22×D3—68no—
465C22×D3—122no—
466C22×D3—122no—
467C22×D3D3×Q814yes—
468C22×D3D3×Q814yescomplemented
469C22×D3#23914yes—
470C22×D3C2×#6714yes—
471C22×D3C23×D312yes—
472C22×D3C23×D312yes—
473C3×Q8—28no—
474C3×Q8—28no—
475C3×Q8—48no—
476C3×Q8—616no—
477C3×Q8—68no—
478C2×C3×C4—24no—
479C2×C3×C4—24no—
480C2×C3×C4—22no—
481C2×C3×C4—24no—
482C2×C3×C4—24no—
483C2×C3×C4—34no—
484C2×C3×C4—32no—
485C2×C3×C4—316no—
486C2×C3×C4—34no—
487C2×C3×C4—32no—
488C2×C3×C4—34no—
489C2×C3×C4—44no—
490C2×C3×C4—616no—
491C2×C3×C4—64no—
492C2×C3×C4—64no—
493C2×C3×C4—62no—
494C2×C3×C4—68no—
495C2×C3×C4D3×D414yes—
496C2×C3×C4C2×#6714yes—
497C2×C3×C4C23×D314yes—
498C2×C3×C4C23×D314yes—
499C2×C3×C4C23×D312yes—
500C2×C3×C4C23×D312yes—
501C2×Dic3—22no—
502C2×Dic3—24no—
503C2×Dic3—24no—
504C2×Dic3—32no—
505C2×Dic3—34no—
506C2×Dic3—34no—
507C2×Dic3—32no—
508C2×Dic3—62no—
509C2×Dic3—64no—
510C2×Dic3—68no—
511C2×Dic3—616no—
512C2×Dic3—62no—
513C2×Dic3—64no—
514C2×Dic3—64no—
515C2×Dic3—62no—
516C2×Dic3—68no—
517C2×Dic3—122no—
518C2×Dic3—124no—
519C2×Dic3C2×#6714yes—
520C2×Dic3C23×D312yes—
521C2×Dic3C23×D314yes—
522C2×Dic3C23×D314yes—
523C2×Dic3C23×D312yes—
524C4×D3—216no—
525C4×D3—28no—
526C4×D3—68no—
527C4×D3—68no—
528C4×D3—616no—
529C4×D3—68no—
530C4×D3—68no—
531C4×D3—68no—
532C4×D3—68no—
533C4×D3—128no—
534C4×D3C2×#67116yes—
535Dic6—28no—
536Dic6—216no—
537C2×C32C2×C22⋊Q814yescomplemented
538C2×C32C23×D411yescharacteristic
539C2×C32C23×Q811yescharacteristic
540C2×C32C22×#4111yescharacteristic
541C3⋊D3—24no—
542C3×D3—24no—
543C3×D3C2×C22⋊Q818yescomplemented
544C24—31no—
545C24—31no—
546C24—94no—
547C24—98no—
548C24—91no—
549C24—184no—
550C24—184no—
551C2×Q8—24no—
552C2×Q8—38no—
553C2×Q8—34no—
554C2×Q8—68no—
555C2×Q8—632no—
556C2×Q8—64no—
557C2×Q8C2×D3214yescomplemented
558C22×C4—31no—
559C22×C4—34no—
560C22×C4—38no—
561C22×C4—32no—
562C22×C4—32no—
563C22×C4—31no—
564C22×C4—38no—
565C22×C4—34no—
566C22×C4—68no—
567C22×C4—64no—
568C22×C4—94no—
569C22×C4—98no—
570C22×C4—94no—
571C22×C4—94no—
572C22×C4—92no—
573C22×C4—91no—
574C22×C4—94no—
575C22×C4—184no—
576C22×C4—1832no—
577C22×C4—184no—
578C22×C4—184no—
579C22×C4—188no—
580C22×C4—184no—
581C22×C4C2×D3212yes—
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—21no—
598C22×C3—34no—
599C22×C3—34no—
600C22×C3—34no—
601C22×C3—316no—
602C22×C3—34no—
603C22×C3—62no—
604C22×C3—62no—
605C22×C3—68no—
606C22×C3C2×D3×D412yes—
607C22×C3C2×D3×Q812yes—
608C22×C3C2×D3×Q812yes—
609C22×C3C2×#23912yes—
610C22×C3D3×#4112yes—
611C22×C3C22×#6712yes—
612C22×C3C24×D311yescharacteristic
613C22×C3C24×D311yescharacteristic
614C2×D3—22no—
615C2×D3—22no—
616C2×D3—28no—
617C2×D3—34no—
618C2×D3—34no—
619C2×D3—64no—
620C2×D3—632no—
621C2×D3—62no—
622C2×D3—62no—
623C2×D3—62no—
624C2×D3—62no—
625C2×D3—68no—
626C2×D3—68no—
627C2×D3—632no—
628C2×D3—122no—
629C2×D3—122no—
630C2×D3—128no—
631C2×D3#946116yesdirect product factor
632C2×D3C2×D3×Q814yes—
633C2×D3C2×D3×Q814yescomplemented
634C2×D3C2×#23914yes—
635C2×D3C22×#6714yes—
636C3×C4—24no—
637C3×C4—24no—
638C3×C4—24no—
639C3×C4—34no—
640C3×C4—44no—
641C3×C4—64no—
642C3×C4—64no—
643C3×C4—62no—
644C3×C4C2×D3×D414yes—
645C3×C4C22×#6714yes—
646Dic3—22no—
647Dic3—24no—
648Dic3—24no—
649Dic3—62no—
650Dic3—64no—
651Dic3—64no—
652Dic3—62no—
653Dic3—122no—
654Dic3—124no—
655Dic3C22×#6714yes—
656C32C22×C22⋊Q811yescharacteristic, complemented, Sylow
657C23—34no—
658C23—34no—
659C23—34no—
660C23—32no—
661C23—34no—
662C23—32no—
663C23—62no—
664C23—62no—
665C23—916no—
666C23—94no—
667C23—92no—
668C23—188no—
669C23—188no—
670C23—1832no—
671C23—182no—
672C23—182no—
673C23C22×D3211yescharacteristic
674Q8—28no—
675Q8—616no—
676Q8—68no—
677C2×C4—24no—
678C2×C4—34no—
679C2×C4—32no—
680C2×C4—316no—
681C2×C4—34no—
682C2×C4—34no—
683C2×C4—32no—
684C2×C4—616no—
685C2×C4—64no—
686C2×C4—62no—
687C2×C4—64no—
688C2×C4—68no—
689C2×C4—94no—
690C2×C4—92no—
691C2×C4—188no—
692C2×C4—188no—
693C2×C4—188no—
694C2×C4—1816no—
695C2×C4—184no—
696C2×C4—182no—
697C2×C4—188no—
698C2×C4D3×#6714yes—
699C2×C4C22×D3214yes—
700C2×C4C22×D3212yes—
701C2×C3—21no—
702C2×C3—21no—
703C2×C3—24no—
704C2×C3—21no—
705C2×C3—38no—
706C2×C3—64no—
707C2×C3D3×C22⋊Q814yescomplemented
708C2×C3C2×#94614yescomplemented
709C2×C3C22×D3×D411yescharacteristic
710C2×C3C22×D3×Q811yescharacteristic
711C2×C3C22×D3×Q811yescharacteristic
712C2×C3C22×#23911yescharacteristic
713C2×C3C2×D3×#4111yescharacteristic
714C2×C3C23×#6711yescharacteristic
715D3—24no—
716D3—64no—
717D3—64no—
718D3—124no—
719D3C2×#94618yesdirect product factor
720C22—34no—
721C22—34no—
722C22—316no—
723C22—34no—
724C22—34no—
725C22—62no—
726C22—68no—
727C22—62no—
728C22—94no—
729C22—1832no—
730C22—182no—
731C22—188no—
732C22—182no—
733C22D32×Q812yes—
734C22D3×#23912yes—
735C22C2×D3×#6712yes—
736C22C23×D3211yescharacteristic
737C4—24no—
738C4—34no—
739C4—64no—
740C4—62no—
741C4—64no—
742C4—184no—
743C4—182no—
744C4C2×D3×#6714yes—
745C3—21no—
746C3C2×D3×C22⋊Q811yescharacteristic, complemented
747C3C22×#94611yescharacteristic, complemented
748C2—38no—
749C2—64no—
750C2—184no—
751C2D3×#94614yesdirect product factor
752C2C2×D32×Q811yescharacteristic
753C2C2×D3×#23911yescharacteristic
754C2C22×D3×#6711yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×Q8C22
socleC23×C32C24
prime radicalC23×D32C22
hypercenterC22×Q8D32
hypocenterC32C22×C22⋊Q8
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C22×C3×D3×Q8C2semidirect
3. C2×#64155C2semidirect
4. C2×C3×#946C2semidirect
5. D3×#946C2direct (N × H)
7. C2×D3×C4⋊Dic3C2semidirect
8. C2×#63888C2semidirect
9. C2×#63887C2semidirect
10. C2×D3×Dic3⋊C4C2semidirect
11. C2×#63871C2semidirect
12. C2×#63856C2semidirect
16. C22×C32×Q8C22semidirect
19. C2×C3×D3×Q8C22semidirect
23. C22×C3×Dic6C22semidirect
24. C22×C3×Dic6C22semidirect
31. #64155C22semidirect
33. C2×C4⋊(C3⋊Dic3)C22semidirect
34. C2×#3750C22semidirect
35. C3×#946C22semidirect
37. C2×C3×C4⋊Dic3C22semidirect
38. C2×C3×Dic3⋊C4C22semidirect
39. C2×#3724C22semidirect
40. C2×Dic3⋊Dic3C22semidirect
41. C2×Dic3⋊Dic3C22semidirect
45. D3×C4⋊Dic3C22semidirect
46. #63888C22semidirect
47. #63887C22semidirect
48. D3×Dic3⋊C4C22semidirect
49. #63871C22semidirect
50. #63856C22semidirect
52. C22×D3×Q8D3semidirect
64. C2×#946D3direct (N × H)
81. C22×D32Q8semidirect
84. C2×C32×Q8C23semidirect
104. C2×C3×Dic6C23semidirect
105. C2×C3×Dic6C23semidirect
116. C4⋊(C3⋊Dic3)C23semidirect
117. #3750C23semidirect
119. C3×C4⋊Dic3C23semidirect
120. C3×Dic3⋊C4C23semidirect
121. #3724C23semidirect
122. Dic3⋊Dic3C23semidirect
123. Dic3⋊Dic3C23semidirect
134. C22×C3×Q8C2×D3semidirect
135. C22×C3×Q8C2×D3semidirect
143. C2×D3×Q8C2×D3semidirect
159. C22×Dic6C2×D3semidirect
160. C22×Dic6C2×D3semidirect
173. #946C2×D3direct (N × H)
188. C2×C4⋊Dic3C2×D3semidirect
198. C2×Dic3⋊C4C2×D3semidirect
208. C22×C3⋊D3C2×Q8semidirect
214. C22×C3×D3C2×Q8semidirect
221. C2×D32C2×Q8semidirect
285. C2×C3×Q8C22×D3semidirect
286. C2×C3×Q8C22×D3semidirect
346. C2×Dic6C22×D3semidirect
347. C2×Dic6C22×D3semidirect
364. C4⋊Dic3C22×D3semidirect
372. Dic3⋊C4C22×D3semidirect
380. C2×C3⋊D3C22×Q8semidirect
384. C2×C3×D3C22⋊Q8semidirect
387. C2×C3×D3C22×Q8semidirect
403. C22×Q8D32semidirect
468. C22×D3D3×Q8semidirect
537. C2×C32C2×C22⋊Q8semidirect
543. C3×D3C2×C22⋊Q8semidirect
557. C2×Q8C2×D32semidirect
631. C2×D3#946direct (N × H)
633. C2×D3C2×D3×Q8semidirect
656. C32C22×C22⋊Q8semidirect
707. C2×C3D3×C22⋊Q8semidirect
708. C2×C3C2×#946semidirect
719. D3C2×#946direct (N × H)
746. C3C2×D3×C22⋊Q8semidirect
747. C3C22×#946semidirect
751. C2D3×#946direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×D3×Q82
C22×C4×D322
C2×#641552
C2×C3×#9462
D3×#9462
C2×D3×(C2×D3)⋊C42
C2×D3×C4⋊Dic32
C2×#638882
C2×#638872
C2×D3×Dic3⋊C42
C2×#638712
C2×#638562
C22×#9463
C2×D3×C22⋊Q83