Finite Group Databasebeta

← C2×D3×#893 #11899899

Subgroups — C2×D3×#893 #11899899

Order 1152.

5269 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×D3×D12C211yesmaximal, characteristic
2C22×C4×D32C212yesmaximal, complemented
3C2×#64102C211yesmaximal, characteristic, complemented
4C2×C3×#893C211yesmaximal, characteristic, complemented
5C2×C3×D3×C4⋊C4C211yesmaximal, characteristic, complemented
6C2×D3×(C2×D3)⋊C4C212yesmaximal, complemented
7C2×#63904C212yesmaximal, complemented
8C2×#63898C211yesmaximal, characteristic, complemented
9C2×#63894C211yesmaximal, characteristic, complemented
10C2×#63881C212yesmaximal, complemented
11C2×C4×D3×Dic3C211yesmaximal, characteristic, complemented
12D3×#893C2116yesmaximal, direct product factor
13C2×C4×D3×D4—31nomaximal
14C22×#893—31nomaximal
15C23×D32C2212yes—
16C22×C4⋊(C3⋊D3)C2211yescharacteristic
17C22×C4×C3⋊D3C2212yescomplemented
18C22×C3×D12C2211yescharacteristic
19C22×C3×C4×D3C2212yes—
20C22×C3×C4×D3C2211yescharacteristic
21C22×C3×C4×D3C2212yescomplemented
22C22×#626C2212yes—
23C22×#624C2212yescomplemented
24C22×D3×Dic3C2211yescharacteristic
25C22×D3×Dic3C2211yescharacteristic
26C22×D3×Dic3C2212yescomplemented
27C2×D3×D12C4116yescomplemented
28C2×D3×D12C2218yes—
29C2×C4×D32—216no—
30C2×C4×D32C22116yescomplemented
31C2×C32×C4⋊C4C2211yescharacteristic, complemented
32C2×#3752C2212yescomplemented
33C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
34#64102C2218yescomplemented
35C2×C3×(C2×D3)⋊C4C2212yescomplemented
36C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
37C2×C3×Dic3⋊C4C2212yescomplemented
38C2×C3×C4×Dic3C2211yescharacteristic, complemented
39C3×#893C2218yescomplemented
40C3×D3×C4⋊C4C2218yescomplemented
41C2×#3722C2212yescomplemented
42C2×(C2×D3)⋊Dic3C2212yescomplemented
43C2×Dic32C2211yescharacteristic, complemented
44C2×Dic32C2211yescharacteristic, complemented
45D3×(C2×D3)⋊C4C22116yescomplemented
46#63904C22116yescomplemented
47#63898C2218yescomplemented
48#63894C2218yescomplemented
49#63881C22116yescomplemented
50C4×D3×Dic3C2218yescomplemented
51C22×D3×D4—31no—
52C23×D12—31no—
53C23×C4×D3—32no—
54C23×C4×D3—32no—
55C2×C3×C4×D4—31no—
56C22×C3×C4⋊C4—31no—
57C2×D4×Dic3—31no—
58C2×C4×#67—32no—
59C22×(C2×D3)⋊C4—32no—
60C22×C4×Dic3—31no—
61C4×D3×D4—316no—
62C2×#893—31no—
63C2×#893—32no—
64C2×#893—31no—
65C2×#893—31no—
66C2×#893—32no—
67C2×#893—31no—
68C2×#893—316no—
69C2×#893—61no—
70C2×#893D311yescharacteristic, direct product factor
71C2×D3×C4⋊C4D311yescharacteristic, complemented
72C2×#67⋊C4—32no—
73C2×D3×C22⋊C4—32no—
74C2×C4×D12—31no—
75C2×C42×D3—31no—
76C23×C3⋊D3C2312yes—
77C23×C3×D3C2312yes—
78C23×C3×D3C2311yescharacteristic
79C22×D32—28no—
80C22×D32—28no—
81C22×D32C2×C4116yescomplemented
82C22×D32C2318yes—
83C22×C32×C4C2312yes—
84C22×C32×C4C2311yescharacteristic
85C22×C3⋊Dic3C2311yescharacteristic
86C22×C3⋊Dic3C2311yescharacteristic
87C2×C4⋊(C3⋊D3)C2×C418yescomplemented
88C2×C4⋊(C3⋊D3)C2314yes—
89C2×C4×C3⋊D3—28no—
90C2×C4×C3⋊D3C2318yescomplemented
91C22×C3×Dic3C2311yescharacteristic
92C22×C3×Dic3C2312yes—
93C22×C3×Dic3C2311yescharacteristic
94C22×C3×Dic3C2311yescharacteristic
95C2×C3×D12C2×C418yescomplemented
96C2×C3×D12C2314yes—
97C2×C3×C4×D3—28no—
98C2×C3×C4×D3—28no—
99C2×C3×C4×D3C2×C418yescomplemented
100C2×C3×C4×D3C2318yes—
101C2×C3×C4×D3C2314yes—
102C2×C3×C4×D3C2318yescomplemented
103C2×#626C2×C4116yescomplemented
104C2×#626C2318yes—
105C2×#624—28no—
106C2×#624C2318yescomplemented
107C2×D3×Dic3—24no—
108C2×D3×Dic3—28no—
109C2×D3×Dic3D418yescomplemented
110C2×D3×Dic3C2314yes—
111C2×D3×Dic3C2314yes—
112C2×D3×Dic3C2318yescomplemented
113D3×D12C2×C4164yescomplemented
114C4×D32—264no—
115C32×C4⋊C4C2314yescomplemented
116#3752C2318yescomplemented
117C4×C3⋊Dic3C2314yescomplemented
118C3×(C2×D3)⋊C4C2318yescomplemented
119C3×C4⋊Dic3C2314yescomplemented
120C3×Dic3⋊C4C2318yescomplemented
121C3×C4×Dic3C2314yescomplemented
122#3722C2318yescomplemented
123(C2×D3)⋊Dic3C2318yescomplemented
124Dic32C2314yescomplemented
125Dic32C2314yescomplemented
126C22×C4×D4—91noSylow
127C24×D3—32no—
128C24×D3—32no—
129C22×C3×D4—31no—
130C23×C3×C4—31no—
131C23×C3×C4—32no—
132C23×C3×C4—32no—
133C22×#67—32no—
134C23×Dic3—31no—
135C23×Dic3—32no—
136C23×Dic3—31no—
137C2×D3×D4—316no—
138C2×D3×D4—38no—
139C22×D12—32no—
140C22×D12—31no—
141C22×D12—31no—
142C22×D12—316no—
143C22×D12—38no—
144C22×D12—61no—
145C22×D12C2×D311yescharacteristic
146C22×C4×D3—31no—
147C22×C4×D3—32no—
148C22×C4×D3—31no—
149C22×C4×D3—32no—
150C22×C4×D3—32no—
151C22×C4×D3—32no—
152C22×C4×D3—32no—
153C22×C4×D3—316no—
154C22×C4×D3—316no—
155C22×C4×D3—62no—
156C22×C4×D3—616no—
157C22×C4×D3—616no—
158C22×C4×D3C2×D312yes—
159C22×C4×D3C2×D311yescharacteristic
160C22×C4×D3C2×D312yescomplemented
161C3×C4×D4—38no—
162C2×C3×C4⋊C4—21no—
163C2×C3×C4⋊C4—32no—
164C2×C3×C4⋊C4—31no—
165C2×C3×C4⋊C4—38no—
166C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
167C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
168C2×C3×C22⋊C4—32no—
169C2×C3×C42—31no—
170C2×#217—32no—
171D4×Dic3—38no—
172C4×#67—316no—
173C2×(C2×D3)⋊C4—32no—
174C2×(C2×D3)⋊C4—32no—
175C2×(C2×D3)⋊C4—32no—
176C2×(C2×D3)⋊C4—32no—
177C2×(C2×D3)⋊C4—32no—
178C2×(C2×D3)⋊C4—316no—
179C2×(C2×D3)⋊C4—62no—
180C2×(C2×D3)⋊C4C2×D312yescomplemented
181C2×C4⋊Dic3C2×D311yescharacteristic, complemented
182C2×Dic3⋊C4C2×D312yescomplemented
183C2×C4×Dic3—31no—
184C2×C4×Dic3—31no—
185C2×C4×Dic3—31no—
186C2×C4×Dic3—31no—
187C2×C4×Dic3—31no—
188C2×C4×Dic3—31no—
189C2×C4×Dic3—38no—
190C2×C4×Dic3—61no—
191C2×C4×Dic3C2×D311yescharacteristic, complemented
192#893—38no—
193#893—316no—
194#893—38no—
195#893—38no—
196#893—316no—
197#893—38no—
198#893—68no—
199#893C2×D318yesdirect product factor
200D3×C4⋊C4C2×D318yescomplemented
201#67⋊C4—316no—
202D3×C22⋊C4—316no—
203C4×D12—38no—
204C42×D3—38no—
205C23×C32C2411yescharacteristic
206C22×C3⋊D3—24no—
207C22×C3⋊D3—24no—
208C22×C3⋊D3C22×C418yescomplemented
209C22×C3⋊D3C2414yes—
210C22×C3×D3—24no—
211C22×C3×D3—24no—
212C22×C3×D3C22×C414yes—
213C22×C3×D3C22×C418yescomplemented
214C22×C3×D3C2×D414yes—
215C22×C3×D3#4114yes—
216C22×C3×D3C2414yes—
217C22×C3×D3C2412yes—
218C2×D32—264no—
219C2×D32—216no—
220C2×D32—216no—
221C2×D32C22×C4132yescomplemented
222C2×C32×C4—24no—
223C2×C32×C4C22×C414yescomplemented
224C2×C32×C4C2414yes—
225C2×C32×C4C2412yes—
226C2×C3⋊Dic3—22no—
227C2×C3⋊Dic3C2×D414yescomplemented
228C2×C3⋊Dic3C2412yes—
229C2×C3⋊Dic3C2412yes—
230C4⋊(C3⋊D3)C22×C4116yescomplemented
231C4×C3⋊D3—216no—
232C2×C3×Dic3—24no—
233C2×C3×Dic3—22no—
234C2×C3×Dic3C22×C414yescomplemented
235C2×C3×Dic3C2×D414yescomplemented
236C2×C3×Dic3C2412yes—
237C2×C3×Dic3C2414yes—
238C2×C3×Dic3C2412yes—
239C2×C3×Dic3C2412yes—
240C3×D12C22×C4116yescomplemented
241C3×C4×D3—216no—
242C3×C4×D3—216no—
243C3×C4×D3C22×C4116yescomplemented
244#626C22×C4132yescomplemented
245#624—216no—
246D3×Dic3—28no—
247D3×Dic3—216no—
248D3×Dic3C2×D4116yescomplemented
249C23×D4—91no—
250C24×C4—92no—
251C2×C4×D4—31no—
252C2×C4×D4—91no—
253C2×C4×D4—92no—
254C2×C4×D4—916no—
255C2×C4×D4—92no—
256C2×C4×D4—91no—
257C2×C4×D4—91no—
258C22×C4⋊C4—31no—
259C22×C22⋊C4—92no—
260C22×C42—91no—
261C24×C3—31no—
262C24×C3—32no—
263C23×D3—32no—
264C23×D3—32no—
265C23×D3—316no—
266C23×D3—316no—
267C23×D3—38no—
268C23×D3—38no—
269C23×D3—62no—
270C23×D3—68no—
271C23×D3—68no—
272C23×D3—68no—
273C23×D3—68no—
274C23×D3C22×D312yes—
275C23×D3C22×D311yescharacteristic
276C2×C3×D4—38no—
277C2×C3×D4—34no—
278C22×C3×C4—21no—
279C22×C3×C4—22no—
280C22×C3×C4—31no—
281C22×C3×C4—31no—
282C22×C3×C4—38no—
283C22×C3×C4—34no—
284C22×C3×C4—31no—
285C22×C3×C4—32no—
286C22×C3×C4—38no—
287C22×C3×C4—38no—
288C22×C3×C4—68no—
289C22×C3×C4—68no—
290C22×C3×C4C22×D312yes—
291C22×C3×C4C22×D312yes—
292C22×C3×C4C22×D311yescharacteristic
293C22×C3×C4C22×D311yescharacteristic
294C2×#67—316no—
295C2×#67—38no—
296C22×Dic3—31no—
297C22×Dic3—31no—
298C22×Dic3—38no—
299C22×Dic3—34no—
300C22×Dic3—31no—
301C22×Dic3—31no—
302C22×Dic3—38no—
303C22×Dic3—34no—
304C22×Dic3—61no—
305C22×Dic3—61no—
306C22×Dic3—68no—
307C22×Dic3—64no—
308C22×Dic3C22×D311yescharacteristic
309C22×Dic3C22×D312yes—
310C22×Dic3C22×D311yescharacteristic
311C22×Dic3C22×D311yescharacteristic
312D3×D4—364no—
313C2×D12—316no—
314C2×D12—38no—
315C2×D12—38no—
316C2×D12—38no—
317C2×D12—34no—
318C2×D12—34no—
319C2×D12—364no—
320C2×D12—64no—
321C2×D12—68no—
322C2×D12C4×D318yescomplemented
323C2×D12C22×D314yes—
324C2×C4×D3—28no—
325C2×C4×D3—28no—
326C2×C4×D3—38no—
327C2×C4×D3—34no—
328C2×C4×D3—34no—
329C2×C4×D3—38no—
330C2×C4×D3—38no—
331C2×C4×D3—38no—
332C2×C4×D3—38no—
333C2×C4×D3—38no—
334C2×C4×D3—68no—
335C2×C4×D3—664no—
336C2×C4×D3—664no—
337C2×C4×D3—68no—
338C2×C4×D3—68no—
339C2×C4×D3—68no—
340C2×C4×D3—68no—
341C2×C4×D3—64no—
342C2×C4×D3—68no—
343C2×C4×D3—128no—
344C2×C4×D3C4×D318yescomplemented
345C2×C4×D3C22×D318yes—
346C2×C4×D3C22×D314yes—
347C2×C4×D3C22×D318yescomplemented
348C3×C4⋊C4—24no—
349C3×C4⋊C4—38no—
350C3×C4⋊C4—34no—
351C3×C4⋊C4C22×D314yescomplemented
352C3×C4⋊C4C22×D314yescomplemented
353C3×C22⋊C4—38no—
354C3×C42—34no—
355#217—38no—
356(C2×D3)⋊C4—38no—
357(C2×D3)⋊C4—38no—
358(C2×D3)⋊C4—38no—
359(C2×D3)⋊C4—38no—
360(C2×D3)⋊C4—38no—
361(C2×D3)⋊C4—68no—
362(C2×D3)⋊C4C22×D318yescomplemented
363C4⋊Dic3C22×D314yescomplemented
364Dic3⋊C4C22×D318yescomplemented
365C4×Dic3—34no—
366C4×Dic3—34no—
367C4×Dic3—34no—
368C4×Dic3—34no—
369C4×Dic3—34no—
370C4×Dic3—34no—
371C4×Dic3—64no—
372C4×Dic3C22×D314yescomplemented
373C22×C32C23×C412yes—
374C22×C32C22×D412yes—
375C22×C32C2×#4112yes—
376C22×C32C2511yescharacteristic
377C2×C3⋊D3—216no—
378C2×C3⋊D3—24no—
379C2×C3⋊D3—24no—
380C2×C3⋊D3C23×C418yescomplemented
381C2×C3×D3—216no—
382C2×C3×D3—24no—
383C2×C3×D3—24no—
384C2×C3×D3C4×D4116yescomplemented
385C2×C3×D3C23×C414yes—
386C2×C3×D3C23×C418yescomplemented
387C2×C3×D3C22×D414yes—
388C2×C3×D3C2×#4114yes—
389D32—264no—
390C32×C4—24no—
391C32×C4C23×C414yescomplemented
392C3⋊Dic3—22no—
393C3⋊Dic3C22×D414yescomplemented
394C3×Dic3—24no—
395C3×Dic3—22no—
396C3×Dic3C23×C414yescomplemented
397C3×Dic3C22×D414yescomplemented
398C25—92no—
399C22×D4—31no—
400C22×D4—98no—
401C22×D4—916no—
402C22×D4—92no—
403C22×D4—91no—
404C23×C4—31no—
405C23×C4—32no—
406C23×C4—32no—
407C23×C4—92no—
408C23×C4—916no—
409C23×C4—91no—
410C23×C4—91no—
411C23×C4—92no—
412C23×C4—92no—
413C23×C4—1816no—
414C4×D4—38no—
415C4×D4—98no—
416C4×D4—916no—
417C4×D4—916no—
418C4×D4—98no—
419C4×D4—98no—
420C2×C4⋊C4—32no—
421C2×C4⋊C4—31no—
422C2×C4⋊C4—38no—
423C2×C4⋊C4D3211yescharacteristic, complemented
424C2×C22⋊C4—32no—
425C2×C22⋊C4—916no—
426C2×C22⋊C4—92no—
427C2×C22⋊C4—92no—
428C2×C22⋊C4—92no—
429C2×C42—31no—
430C2×C42—98no—
431C2×C42—91no—
432C2×C42—91no—
433C2×C42—91no—
434C23×C3—21no—
435C23×C3—34no—
436C23×C3—34no—
437C23×C3—34no—
438C23×C3—32no—
439C23×C3—38no—
440C23×C3—34no—
441C23×C3—64no—
442C23×C3—64no—
443C23×C3C23×D311yescharacteristic
444C23×C3C23×D311yescharacteristic
445C22×D3—24no—
446C22×D3—24no—
447C22×D3—38no—
448C22×D3—38no—
449C22×D3—34no—
450C22×D3—34no—
451C22×D3—332no—
452C22×D3—332no—
453C22×D3—68no—
454C22×D3—64no—
455C22×D3—616no—
456C22×D3—616no—
457C22×D3—664no—
458C22×D3—64no—
459C22×D3—64no—
460C22×D3—64no—
461C22×D3—64no—
462C22×D3—664no—
463C22×D3—616no—
464C22×D3—616no—
465C22×D3—124no—
466C22×D3—124no—
467C22×D3C2×C4×D314yes—
468C22×D3C2×C4×D318yescomplemented
469C22×D3D3×D414yes—
470C22×D3#23914yes—
471C22×D3C23×D314yes—
472C22×D3C23×D312yes—
473C3×D4—316no—
474C2×C3×C4—24no—
475C2×C3×C4—24no—
476C2×C3×C4—22no—
477C2×C3×C4—24no—
478C2×C3×C4—24no—
479C2×C3×C4—34no—
480C2×C3×C4—34no—
481C2×C3×C4—32no—
482C2×C3×C4—32no—
483C2×C3×C4—316no—
484C2×C3×C4—32no—
485C2×C3×C4—34no—
486C2×C3×C4—44no—
487C2×C3×C4—616no—
488C2×C3×C4—616no—
489C2×C3×C4—64no—
490C2×C3×C4—62no—
491C2×C3×C4C2×C4×D314yescomplemented
492C2×C3×C4C2×C4×D314yescomplemented
493C2×C3×C4C23×D314yes—
494C2×C3×C4C23×D314yes—
495C2×C3×C4C23×D312yes—
496C2×C3×C4C23×D312yes—
497#67—332no—
498C2×Dic3—24no—
499C2×Dic3—22no—
500C2×Dic3—34no—
501C2×Dic3—34no—
502C2×Dic3—32no—
503C2×Dic3—32no—
504C2×Dic3—316no—
505C2×Dic3—32no—
506C2×Dic3—32no—
507C2×Dic3—64no—
508C2×Dic3—62no—
509C2×Dic3—62no—
510C2×Dic3—616no—
511C2×Dic3—68no—
512C2×Dic3—62no—
513C2×Dic3—62no—
514C2×Dic3—122no—
515C2×Dic3C2×C4×D314yescomplemented
516C2×Dic3D3×D414yescomplemented
517C2×Dic3C23×D312yes—
518C2×Dic3C23×D314yes—
519C2×Dic3C23×D312yes—
520C2×Dic3C23×D312yes—
521D12—332no—
522D12—316no—
523D12—316no—
524D12—616no—
525D12C2×C4×D3116yescomplemented
526C4×D3—216no—
527C4×D3—216no—
528C4×D3—316no—
529C4×D3—616no—
530C4×D3—616no—
531C4×D3—616no—
532C4×D3—616no—
533C4×D3—68no—
534C4×D3—616no—
535C4×D3—1216no—
536C4×D3C2×C4×D3116yescomplemented
537C2×C32C2×C4×D414yescomplemented
538C2×C32C24×C411yescharacteristic
539C2×C32C23×D411yescharacteristic
540C2×C32C22×#4111yescharacteristic
541C3⋊D3—28no—
542C3×D3—28no—
543C3×D3C2×C4×D418yescomplemented
544C24—31no—
545C24—32no—
546C24—98no—
547C24—916no—
548C24—92no—
549C24—188no—
550C24—188no—
551C2×D4—34no—
552C2×D4—38no—
553C2×D4—964no—
554C2×D4—98no—
555C2×D4—916no—
556C2×D4—94no—
557C2×D4—98no—
558C22×C4—31no—
559C22×C4—31no—
560C22×C4—34no—
561C22×C4—38no—
562C22×C4—31no—
563C22×C4—32no—
564C22×C4—38no—
565C22×C4—38no—
566C22×C4—68no—
567C22×C4—68no—
568C22×C4—98no—
569C22×C4—94no—
570C22×C4—98no—
571C22×C4—94no—
572C22×C4—98no—
573C22×C4—91no—
574C22×C4—91no—
575C22×C4—98no—
576C22×C4—188no—
577C22×C4—188no—
578C22×C4—1864no—
579C22×C4—188no—
580C22×C4—184no—
581C22×C4C2×D3212yes—
582C22×C4C2×D3211yescharacteristic
583C4⋊C4—38no—
584C4⋊C4—34no—
585C4⋊C4C2×D3214yescomplemented
586C22⋊C4—38no—
587C22⋊C4—98no—
588C22⋊C4—98no—
589C22⋊C4—98no—
590C42—34no—
591C42—94no—
592C42—94no—
593C42—94no—
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—38no—
603C22×C3—64no—
604C22×C3—64no—
605C22×C3—616no—
606C22×C3C22×C4×D312yes—
607C22×C3C22×C4×D312yes—
608C22×C3C2×D3×D412yes—
609C22×C3C2×D3×D412yes—
610C22×C3C2×#23912yes—
611C22×C3D3×#4112yes—
612C22×C3C24×D311yescharacteristic
613C22×C3C24×D311yescharacteristic
614C2×D3—24no—
615C2×D3—24no—
616C2×D3—216no—
617C2×D3—38no—
618C2×D3—38no—
619C2×D3—68no—
620C2×D3—664no—
621C2×D3—64no—
622C2×D3—64no—
623C2×D3—64no—
624C2×D3—64no—
625C2×D3—616no—
626C2×D3—616no—
627C2×D3—664no—
628C2×D3—124no—
629C2×D3—1216no—
630C2×D3—124no—
631C2×D3#893116yesdirect product factor
632C2×D3C22×C4×D314yes—
633C2×D3C22×C4×D318yescomplemented
634C2×D3C2×D3×D414yes—
635C2×D3C2×#23914yes—
636C3×C4—24no—
637C3×C4—24no—
638C3×C4—24no—
639C3×C4—34no—
640C3×C4—34no—
641C3×C4—44no—
642C3×C4—64no—
643C3×C4—62no—
644C3×C4C22×C4×D314yescomplemented
645C3×C4C22×C4×D314yescomplemented
646Dic3—24no—
647Dic3—22no—
648Dic3—34no—
649Dic3—34no—
650Dic3—64no—
651Dic3—62no—
652Dic3—62no—
653Dic3—122no—
654Dic3C22×C4×D314yescomplemented
655Dic3C2×D3×D414yescomplemented
656C32C22×C4×D411yescharacteristic, complemented, Sylow
657C23—34no—
658C23—34no—
659C23—34no—
660C23—32no—
661C23—38no—
662C23—34no—
663C23—64no—
664C23—64no—
665C23—932no—
666C23—98no—
667C23—94no—
668C23—1816no—
669C23—1864no—
670C23—1816no—
671C23—184no—
672C23—184no—
673C23C22×D3211yescharacteristic
674D4—316no—
675D4—932no—
676D4—916no—
677C2×C4—24no—
678C2×C4—34no—
679C2×C4—34no—
680C2×C4—32no—
681C2×C4—32no—
682C2×C4—316no—
683C2×C4—32no—
684C2×C4—34no—
685C2×C4—616no—
686C2×C4—616no—
687C2×C4—64no—
688C2×C4—62no—
689C2×C4—916no—
690C2×C4—94no—
691C2×C4—92no—
692C2×C4—92no—
693C2×C4—1816no—
694C2×C4—1816no—
695C2×C4—1816no—
696C2×C4—188no—
697C2×C4—182no—
698C2×C4C4×D3214yescomplemented
699C2×C4C22×D3214yes—
700C2×C4C22×D3212yes—
701C2×C3—24no—
702C2×C3—21no—
703C2×C3—21no—
704C2×C3—21no—
705C2×C3—38no—
706C2×C3—68no—
707C2×C3C2×#89314yescomplemented
708C2×C3C4×D3×D414yescomplemented
709C2×C3C23×C4×D311yescharacteristic
710C2×C3C23×C4×D311yescharacteristic
711C2×C3C22×D3×D411yescharacteristic
712C2×C3C22×D3×D411yescharacteristic
713C2×C3C22×#23911yescharacteristic
714C2×C3C2×D3×#4111yescharacteristic
715D3—28no—
716D3—68no—
717D3—68no—
718D3—128no—
719D3C2×#89318yesdirect product factor
720C22—316no—
721C22—34no—
722C22—34no—
723C22—34no—
724C22—38no—
725C22—616no—
726C22—64no—
727C22—64no—
728C22—98no—
729C22—1864no—
730C22—1816no—
731C22—184no—
732C22—184no—
733C22C2×C4×D3212yes—
734C22D32×D412yes—
735C22D3×#23912yes—
736C22C23×D3211yescharacteristic
737C4—24no—
738C4—34no—
739C4—34no—
740C4—64no—
741C4—62no—
742C4—94no—
743C4—182no—
744C4C2×C4×D3214yescomplemented
745C3—21no—
746C3C22×#89311yescharacteristic, complemented
747C3C2×C4×D3×D411yescharacteristic, complemented
748C2—38no—
749C2—68no—
750C2—188no—
751C2D3×#89314yesdirect product factor
752C2C22×C4×D3211yescharacteristic
753C2C2×D32×D411yescharacteristic
754C2C2×D3×#23911yescharacteristic
subgroupG/H
centerC23C22×D32
commutatorC2×C32C24×C4
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C24
prime radicalC22×D3×D12C2
cosocleC22×C32C25
hypercenterC2×C4⋊C4D32
hypocenterC32C22×C4×D4
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×C4×D32C2semidirect
3. C2×#64102C2semidirect
4. C2×C3×#893C2semidirect
5. C2×C3×D3×C4⋊C4C2semidirect
6. C2×D3×(C2×D3)⋊C4C2semidirect
7. C2×#63904C2semidirect
8. C2×#63898C2semidirect
9. C2×#63894C2semidirect
10. C2×#63881C2semidirect
11. C2×C4×D3×Dic3C2semidirect
12. D3×#893C2direct (N × H)
17. C22×C4×C3⋊D3C22semidirect
21. C22×C3×C4×D3C22semidirect
23. C22×#624C22semidirect
26. C22×D3×Dic3C22semidirect
27. C2×D3×D12C4semidirect
30. C2×C4×D32C22semidirect
31. C2×C32×C4⋊C4C22semidirect
32. C2×#3752C22semidirect
33. C2×C4×C3⋊Dic3C22semidirect
34. #64102C22semidirect
35. C2×C3×(C2×D3)⋊C4C22semidirect
36. C2×C3×C4⋊Dic3C22semidirect
37. C2×C3×Dic3⋊C4C22semidirect
38. C2×C3×C4×Dic3C22semidirect
39. C3×#893C22semidirect
40. C3×D3×C4⋊C4C22semidirect
41. C2×#3722C22semidirect
42. C2×(C2×D3)⋊Dic3C22semidirect
43. C2×Dic32C22semidirect
44. C2×Dic32C22semidirect
45. D3×(C2×D3)⋊C4C22semidirect
46. #63904C22semidirect
47. #63898C22semidirect
48. #63894C22semidirect
49. #63881C22semidirect
50. C4×D3×Dic3C22semidirect
70. C2×#893D3direct (N × H)
71. C2×D3×C4⋊C4D3semidirect
81. C22×D32C2×C4semidirect
87. C2×C4⋊(C3⋊D3)C2×C4semidirect
90. C2×C4×C3⋊D3C23semidirect
95. C2×C3×D12C2×C4semidirect
99. C2×C3×C4×D3C2×C4semidirect
102. C2×C3×C4×D3C23semidirect
103. C2×#626C2×C4semidirect
106. C2×#624C23semidirect
109. C2×D3×Dic3D4semidirect
112. C2×D3×Dic3C23semidirect
113. D3×D12C2×C4semidirect
115. C32×C4⋊C4C23semidirect
116. #3752C23semidirect
117. C4×C3⋊Dic3C23semidirect
118. C3×(C2×D3)⋊C4C23semidirect
119. C3×C4⋊Dic3C23semidirect
120. C3×Dic3⋊C4C23semidirect
121. C3×C4×Dic3C23semidirect
122. #3722C23semidirect
123. (C2×D3)⋊Dic3C23semidirect
124. Dic32C23semidirect
125. Dic32C23semidirect
160. C22×C4×D3C2×D3semidirect
166. C2×C3×C4⋊C4C2×D3semidirect
167. C2×C3×C4⋊C4C2×D3semidirect
180. C2×(C2×D3)⋊C4C2×D3semidirect
181. C2×C4⋊Dic3C2×D3semidirect
182. C2×Dic3⋊C4C2×D3semidirect
191. C2×C4×Dic3C2×D3semidirect
199. #893C2×D3direct (N × H)
200. D3×C4⋊C4C2×D3semidirect
208. C22×C3⋊D3C22×C4semidirect
213. C22×C3×D3C22×C4semidirect
221. C2×D32C22×C4semidirect
223. C2×C32×C4C22×C4semidirect
227. C2×C3⋊Dic3C2×D4semidirect
230. C4⋊(C3⋊D3)C22×C4semidirect
234. C2×C3×Dic3C22×C4semidirect
235. C2×C3×Dic3C2×D4semidirect
240. C3×D12C22×C4semidirect
243. C3×C4×D3C22×C4semidirect
244. #626C22×C4semidirect
248. D3×Dic3C2×D4semidirect
322. C2×D12C4×D3semidirect
344. C2×C4×D3C4×D3semidirect
347. C2×C4×D3C22×D3semidirect
351. C3×C4⋊C4C22×D3semidirect
352. C3×C4⋊C4C22×D3semidirect
362. (C2×D3)⋊C4C22×D3semidirect
363. C4⋊Dic3C22×D3semidirect
364. Dic3⋊C4C22×D3semidirect
372. C4×Dic3C22×D3semidirect
380. C2×C3⋊D3C23×C4semidirect
384. C2×C3×D3C4×D4semidirect
386. C2×C3×D3C23×C4semidirect
391. C32×C4C23×C4semidirect
393. C3⋊Dic3C22×D4semidirect
396. C3×Dic3C23×C4semidirect
397. C3×Dic3C22×D4semidirect
423. C2×C4⋊C4D32semidirect
468. C22×D3C2×C4×D3semidirect
491. C2×C3×C4C2×C4×D3semidirect
492. C2×C3×C4C2×C4×D3semidirect
515. C2×Dic3C2×C4×D3semidirect
516. C2×Dic3D3×D4semidirect
525. D12C2×C4×D3semidirect
536. C4×D3C2×C4×D3semidirect
537. C2×C32C2×C4×D4semidirect
543. C3×D3C2×C4×D4semidirect
585. C4⋊C4C2×D32semidirect
631. C2×D3#893direct (N × H)
633. C2×D3C22×C4×D3semidirect
644. C3×C4C22×C4×D3semidirect
645. C3×C4C22×C4×D3semidirect
654. Dic3C22×C4×D3semidirect
655. Dic3C2×D3×D4semidirect
656. C32C22×C4×D4semidirect
698. C2×C4C4×D32semidirect
707. C2×C3C2×#893semidirect
708. C2×C3C4×D3×D4semidirect
719. D3C2×#893direct (N × H)
744. C4C2×C4×D32semidirect
746. C3C22×#893semidirect
747. C3C2×C4×D3×D4semidirect
751. C2D3×#893direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D3×D122
C22×C4×D322
C2×#641022
C2×C3×#8932
C2×C3×D3×C4⋊C42
C2×D3×(C2×D3)⋊C42
C2×#639042
C2×#638982
C2×#638942
C2×#638812
C2×C4×D3×Dic32
D3×#8932
C2×C4×D3×D43
C22×#8933