Finite Group Databasebeta

← C4×D3×#625 #13170809

Subgroups — C4×D3×#625 #13170809

Order 1728.

2030 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×D32C212yesmaximal, complemented
2C2×D3×#625C211yesmaximal, characteristic
3C4×#6295C211yesmaximal, characteristic, complemented
4C4×#6290C212yesmaximal, complemented
5C4×D3×C3⋊Dic3C211yesmaximal, characteristic, complemented
6C3×C4×#625C211yesmaximal, characteristic, complemented
7#11722931C211yesmaximal, characteristic, complemented
8#11722930C212yesmaximal, complemented
9Dic3×#625C211yesmaximal, characteristic, complemented
10D3×#3724C211yesmaximal, characteristic, complemented
11D3×(C2×D3)⋊Dic3C212yesmaximal, complemented
12C4×D3×#67—32nomaximal
13C2×C4×#625—31nomaximal
14C22×C3×D32C2212yes—
15C2×C3×C4×C3⋊D3C2212yescomplemented
16C2×C32×C4×D3C2211yescharacteristic
17C2×C32×C4×D3C2212yescomplemented
18C2×#6295C2211yescharacteristic
19C2×#6290C2212yes—
20C2×D3×C3⋊Dic3C2211yescharacteristic
21C2×D3×C3⋊Dic3C2211yescharacteristic
22C2×C3×#625C2211yescharacteristic
23C2×C3×#624C2212yescomplemented
24C2×C3×D3×Dic3C2212yes—
25C2×C3×D3×Dic3C2212yescomplemented
26C3×C4×D32—28no—
27D3×#625C418yesdirect product factor
28C4×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
29C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
30#88815C2211yescharacteristic, complemented
31#88814C2212yescomplemented
32#88806C2212yescomplemented
33#88803C2212yescomplemented
34(C2×D3)⋊(C3⋊Dic3)C2212yescomplemented
35Dic3×C3⋊Dic3C2211yescharacteristic, complemented
36Dic3×C3⋊Dic3C2211yescharacteristic, complemented
37C3×#3724C2211yescharacteristic, complemented
38C3×(C2×D3)⋊Dic3C2212yescomplemented
39C22×C3×C4×D3—32no—
40C22×C3×C4×D3—32no—
41C2×D3×#67—32no—
42C22×#625—31no—
43C2×C4×D32D312yescomplemented
44C4×#638—32no—
45C2×C4×C3⋊Dic3—31no—
46C3×C4×#67—32no—
47Dic3×#67—32no—
48D3×#217—32no—
49C2×#3724—31no—
50C2×(C2×D3)⋊Dic3—32no—
51#63952—32no—
52D3×(C2×D3)⋊C4—32no—
53#63904—32no—
54C4×#626—32no—
55C4×#625—32no—
56C4×#625—32no—
57C4×#625—31no—
58C4×#625—31no—
59C4×#625—31no—
60C4×#625—32no—
61C4×#625—62no—
62C4×#625D311yescharacteristic, direct product factor
63#63879—32no—
64D3×Dic3⋊C4—32no—
65C4×D3×Dic3—32no—
66C4×D3×Dic3—61no—
67C22×C3×C3⋊D3C2312yes—
68C22×C32×D3C2312yes—
69C22×C32×D3C2311yescharacteristic
70C2×C3×D32—24no—
71C2×C3×D32—24no—
72C2×C3×D32C2×C418yescomplemented
73C2×C33×C4C2311yescharacteristic
74C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
75C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
76C2×C3×C3⋊Dic3C2311yescharacteristic
77C2×C3×C3⋊Dic3C2312yes—
78C2×C3×C3⋊Dic3C2311yescharacteristic
79C3×C4×C3⋊D3—24no—
80C2×C32×Dic3C2312yes—
81C2×C32×Dic3C2311yescharacteristic
82C32×C4×D3—24no—
83C32×C4×D3D414yescomplemented
84#6295C2×C414yescomplemented
85#6290C2×C418yescomplemented
86D3×C3⋊Dic3—22no—
87D3×C3⋊Dic3C2×C414yescomplemented
88C3×#625C2×C414yescomplemented
89C3×#624—24no—
90C3×D3×Dic3—24no—
91C3×D3×Dic3—24no—
92C2×C4×#67—92no—
93C4×D3×D4—91no—
94C23×C3×D3—32no—
95C23×C3×D3—32no—
96C22×D32C2×D312yes—
97C22×C32×C4—31no—
98C22×C32×C4—32no—
99C2×#638—32no—
100C22×C3⋊Dic3—31no—
101C22×C3⋊Dic3—31no—
102C2×C4×C3⋊D3C2×D312yescomplemented
103C2×C3×#67—32no—
104C22×C3×Dic3—32no—
105C22×C3×Dic3—32no—
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3—22no—
108C2×C3×C4×D3—32no—
109C2×C3×C4×D3—32no—
110C2×C3×C4×D3—32no—
111C2×C3×C4×D3—32no—
112C2×C3×C4×D3—32no—
113C2×C3×C4×D3—32no—
114C2×C3×C4×D3—68no—
115C2×C3×C4×D3—68no—
116C2×C3×C4×D3—62no—
117C2×C3×C4×D3C2×D312yes—
118C2×C3×C4×D3C2×D312yescomplemented
119C2×C3×C4×D3C2×D312yescomplemented
120D3×#67—316no—
121C2×#626—32no—
122C2×#625—32no—
123C2×#625—32no—
124C2×#625—31no—
125C2×#625—38no—
126C2×#625—62no—
127C2×#625C2×D311yescharacteristic
128C2×#624C2×D312yescomplemented
129C2×D3×Dic3—32no—
130C2×D3×Dic3—32no—
131C2×D3×Dic3—61no—
132C2×D3×Dic3—61no—
133C2×D3×Dic3C2×D312yes—
134C2×D3×Dic3C2×D312yescomplemented
135C4×D32—28no—
136#3757—32no—
137#3752—32no—
138#3750—32no—
139C4×C3⋊Dic3—32no—
140C4×C3⋊Dic3—31no—
141C4×C3⋊Dic3—31no—
142C4×C3⋊Dic3—31no—
143C4×C3⋊Dic3—61no—
144C4×C3⋊Dic3—62no—
145C4×C3⋊Dic3—121no—
146C4×C3⋊Dic3C2×D311yescharacteristic, complemented
147C3×#217—32no—
148C3×(C2×D3)⋊C4—32no—
149C3×Dic3⋊C4—32no—
150C3×C4×Dic3—32no—
151C3×C4×Dic3—61no—
152#3724—31no—
153#3724—32no—
154#3724—32no—
155#3724—62no—
156#3724C2×D311yescharacteristic, complemented
157Dic3⋊Dic3—32no—
158#3722—32no—
159(C2×D3)⋊Dic3—32no—
160(C2×D3)⋊Dic3—32no—
161(C2×D3)⋊Dic3—32no—
162(C2×D3)⋊Dic3—32no—
163(C2×D3)⋊Dic3—32no—
164(C2×D3)⋊Dic3—32no—
165(C2×D3)⋊Dic3—62no—
166(C2×D3)⋊Dic3—62no—
167(C2×D3)⋊Dic3C2×D312yescomplemented
168Dic32—32no—
169Dic32—32no—
170Dic32—61no—
171Dic32—61no—
172C22×C33C2411yescharacteristic
173C2×C3×C3⋊D3—22no—
174C2×C3×C3⋊D3—22no—
175C2×C3×C3⋊D3C22×C414yescomplemented
176C2×C32×D3—22no—
177C2×C32×D3—22no—
178C2×C32×D3C22×C412yes—
179C2×C32×D3C22×C414yescomplemented
180C2×C32×D3C2×D412yes—
181C2×C32×D3#4112yes—
182C3×D32—216no—
183C33×C4C2×D412yescomplemented
184C3⋊(C3⋊Dic3)—21no—
185C3⋊(C3⋊Dic3)C22×C412yescomplemented
186C3×C3⋊Dic3—22no—
187C3×C3⋊Dic3—21no—
188C3×C3⋊Dic3C22×C412yescomplemented
189C32×Dic3—22no—
190C32×Dic3C2×D412yescomplemented
191C23×C3×C4—92no—
192C22×#67—92no—
193C2×D3×D4—91no—
194C22×C4×D3—32no—
195C22×C4×D3—32no—
196C3×C4×D4—91no—
197C2×#217—92no—
198D4×Dic3—91no—
199C4×#67—32no—
200C4×#67—92no—
201C4×#67—92no—
202C4×#67—92no—
203C4×#67—92no—
204C4×#67—92no—
205C4×#67—92no—
206C4×#67—92no—
207C4×#67—92no—
208C4×#67—182no—
209C2×(C2×D3)⋊C4—92no—
210C2×Dic3⋊C4—92no—
211C2×C4×Dic3—92no—
212C2×C4×Dic3—181no—
213#893—91no—
214D3×C4⋊C4—91no—
215#67⋊C4—92no—
216D3×C22⋊C4—92no—
217C4×D12—91no—
218C42×D3—91no—
219C23×C32—31no—
220C23×C32—32no—
221C22×C3⋊D3C22×D312yes—
222C22×C3×D3—21no—
223C22×C3×D3—22no—
224C22×C3×D3—32no—
225C22×C3×D3—32no—
226C22×C3×D3—38no—
227C22×C3×D3—38no—
228C22×C3×D3—62no—
229C22×C3×D3—64no—
230C22×C3×D3—64no—
231C22×C3×D3—64no—
232C22×C3×D3—64no—
233C22×C3×D3C22×D312yes—
234C22×C3×D3C22×D312yes—
235C22×C3×D3C22×D312yes—
236C2×D32—24no—
237C2×D32—24no—
238C2×D32C4×D318yescomplemented
239C2×C32×C4—21no—
240C2×C32×C4—22no—
241C2×C32×C4—31no—
242C2×C32×C4—34no—
243C2×C32×C4—32no—
244C2×C32×C4—41no—
245C2×C32×C4—64no—
246C2×C32×C4C22×D311yescharacteristic
247C2×C32×C4C22×D312yes—
248#638—38no—
249C2×C3⋊Dic3—32no—
250C2×C3⋊Dic3—31no—
251C2×C3⋊Dic3—34no—
252C2×C3⋊Dic3—32no—
253C2×C3⋊Dic3—31no—
254C2×C3⋊Dic3—61no—
255C2×C3⋊Dic3—61no—
256C2×C3⋊Dic3—62no—
257C2×C3⋊Dic3—62no—
258C2×C3⋊Dic3—62no—
259C2×C3⋊Dic3—121no—
260C2×C3⋊Dic3—121no—
261C2×C3⋊Dic3C22×D311yescharacteristic
262C2×C3⋊Dic3C22×D312yes—
263C2×C3⋊Dic3C22×D311yescharacteristic
264C4×C3⋊D3—24no—
265C3×#67—38no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—22no—
268C2×C3×Dic3—32no—
269C2×C3×Dic3—32no—
270C2×C3×Dic3—32no—
271C2×C3×Dic3—32no—
272C2×C3×Dic3—61no—
273C2×C3×Dic3—61no—
274C2×C3×Dic3—62no—
275C2×C3×Dic3—64no—
276C2×C3×Dic3—64no—
277C2×C3×Dic3C22×D312yes—
278C2×C3×Dic3C22×D312yes—
279C2×C3×Dic3C22×D312yes—
280C3×C4×D3—24no—
281C3×C4×D3—24no—
282C3×C4×D3—24no—
283C3×C4×D3—44no—
284C3×C4×D3—64no—
285C3×C4×D3—64no—
286C3×C4×D3—64no—
287C3×C4×D3—64no—
288C3×C4×D3—64no—
289C3×C4×D3—64no—
290C3×C4×D3—124no—
291C3×C4×D3#6718yescomplemented
292#626—38no—
293#625—38no—
294#625—38no—
295#625—34no—
296#625—68no—
297#625C4×D314yesdirect product factor
298#624—24no—
299D3×Dic3—24no—
300D3×Dic3—24no—
301D3×Dic3—38no—
302D3×Dic3—64no—
303D3×Dic3—64no—
304D3×Dic3—64no—
305C2×C4×D4—271noSylow
306C2×C33C23×C411yescharacteristic
307C2×C33C22×D411yescharacteristic
308C2×C33C2×#4111yescharacteristic
309C3×C3⋊D3—24no—
310C32×D3—24no—
311C32×D3C4×D414yescomplemented
312C24×C3—92no—
313C23×D3—32no—
314C23×D3—32no—
315C2×C3×D4—91no—
316C22×C3×C4—32no—
317C22×C3×C4—32no—
318C22×C3×C4—32no—
319C22×C3×C4—61no—
320C22×C3×C4—62no—
321C22×C3×C4—92no—
322C22×C3×C4—92no—
323C22×C3×C4—92no—
324C22×C3×C4—92no—
325C22×C3×C4—188no—
326C2×#67—32no—
327C2×#67—92no—
328C2×#67—916no—
329C2×#67—92no—
330C2×#67—92no—
331C2×#67—92no—
332C2×#67—182no—
333C22×Dic3—32no—
334C22×Dic3—32no—
335C22×Dic3—92no—
336C22×Dic3—92no—
337C22×Dic3—181no—
338C22×Dic3—181no—
339D3×D4—98no—
340C2×D12—91no—
341C2×C4×D3—32no—
342C2×C4×D3—32no—
343C2×C4×D3—32no—
344C2×C4×D3—32no—
345C2×C4×D3—32no—
346C2×C4×D3—32no—
347C2×C4×D3—62no—
348C2×C4×D3—68no—
349C2×C4×D3—68no—
350C2×C4×D3—91no—
351C2×C4×D3—91no—
352C2×C4×D3D3211yescharacteristic
353C2×C4×D3D3212yescomplemented
354C3×C4⋊C4—91no—
355C3×C22⋊C4—92no—
356C3×C42—91no—
357#217—32no—
358#217—92no—
359#217—92no—
360#217—92no—
361#217—92no—
362#217—182no—
363(C2×D3)⋊C4—32no—
364(C2×D3)⋊C4—92no—
365(C2×D3)⋊C4—92no—
366(C2×D3)⋊C4—92no—
367(C2×D3)⋊C4—92no—
368(C2×D3)⋊C4—92no—
369(C2×D3)⋊C4—182no—
370C4⋊Dic3—91no—
371Dic3⋊C4—32no—
372Dic3⋊C4—92no—
373Dic3⋊C4—92no—
374Dic3⋊C4—92no—
375Dic3⋊C4—92no—
376Dic3⋊C4—182no—
377C4×Dic3—32no—
378C4×Dic3—61no—
379C4×Dic3—92no—
380C4×Dic3—92no—
381C4×Dic3—91no—
382C4×Dic3—92no—
383C4×Dic3—91no—
384C4×Dic3—91no—
385C4×Dic3—181no—
386C4×Dic3—181no—
387C4×Dic3—181no—
388C4×Dic3—182no—
389C4×Dic3—361no—
390C22×C32—21no—
391C22×C32—22no—
392C22×C32—32no—
393C22×C32—32no—
394C22×C32—32no—
395C22×C32—34no—
396C22×C32—41no—
397C22×C32—62no—
398C22×C32—62no—
399C22×C32C23×D312yes—
400C22×C32C23×D311yescharacteristic
401C2×C3⋊D3—22no—
402C2×C3⋊D3—22no—
403C2×C3⋊D3C2×C4×D314yescomplemented
404C2×C3×D3—22no—
405C2×C3×D3—22no—
406C2×C3×D3—22no—
407C2×C3×D3—22no—
408C2×C3×D3—22no—
409C2×C3×D3—22no—
410C2×C3×D3—24no—
411C2×C3×D3—22no—
412C2×C3×D3—34no—
413C2×C3×D3—34no—
414C2×C3×D3—42no—
415C2×C3×D3—42no—
416C2×C3×D3—64no—
417C2×C3×D3—616no—
418C2×C3×D3—62no—
419C2×C3×D3—62no—
420C2×C3×D3—62no—
421C2×C3×D3—62no—
422C2×C3×D3—616no—
423C2×C3×D3—122no—
424C2×C3×D3—122no—
425C2×C3×D3C2×C4×D314yes—
426C2×C3×D3C2×C4×D314yescomplemented
427C2×C3×D3C2×C4×D314yescomplemented
428C2×C3×D3#23514yes—
429C2×C3×D3C2×#6714yes—
430D32—216no—
431C32×C4—22no—
432C32×C4—24no—
433C32×C4—32no—
434C32×C4—42no—
435C32×C4—62no—
436C32×C4D3×D412yescomplemented
437C32×C4C2×#6714yescomplemented
438C3⋊Dic3—21no—
439C3⋊Dic3—22no—
440C3⋊Dic3—34no—
441C3⋊Dic3—32no—
442C3⋊Dic3—62no—
443C3⋊Dic3—64no—
444C3⋊Dic3—61no—
445C3⋊Dic3—62no—
446C3⋊Dic3—62no—
447C3⋊Dic3—122no—
448C3⋊Dic3—122no—
449C3⋊Dic3—122no—
450C3⋊Dic3C2×C4×D312yescomplemented
451C3×Dic3—22no—
452C3×Dic3—22no—
453C3×Dic3—22no—
454C3×Dic3—34no—
455C3×Dic3—42no—
456C3×Dic3—62no—
457C3×Dic3—62no—
458C3×Dic3—62no—
459C3×Dic3—62no—
460C3×Dic3—62no—
461C3×Dic3—122no—
462C3×Dic3C2×#6714yescomplemented
463C22×D4—271no—
464C23×C4—92no—
465C4×D4—91no—
466C4×D4—271no—
467C4×D4—272no—
468C4×D4—271no—
469C4×D4—272no—
470C4×D4—271no—
471C2×C4⋊C4—271no—
472C2×C22⋊C4—272no—
473C2×C42—271no—
474C33C2×C4×D411yescharacteristic, complemented, Sylow
475C23×C3—32no—
476C23×C3—32no—
477C23×C3—32no—
478C23×C3—61no—
479C23×C3—62no—
480C23×C3—98no—
481C23×C3—92no—
482C23×C3—184no—
483C23×C3—184no—
484C22×D3—32no—
485C22×D3—32no—
486C22×D3—38no—
487C22×D3—38no—
488C22×D3—62no—
489C22×D3—64no—
490C22×D3—64no—
491C22×D3—64no—
492C22×D3—64no—
493C22×D3C2×D3212yes—
494C22×D3C2×D3211yescharacteristic
495C3×D4—94no—
496C2×C3×C4—21no—
497C2×C3×C4—22no—
498C2×C3×C4—32no—
499C2×C3×C4—38no—
500C2×C3×C4—32no—
501C2×C3×C4—32no—
502C2×C3×C4—41no—
503C2×C3×C4—64no—
504C2×C3×C4—61no—
505C2×C3×C4—62no—
506C2×C3×C4—64no—
507C2×C3×C4—64no—
508C2×C3×C4—91no—
509C2×C3×C4—91no—
510C2×C3×C4—92no—
511C2×C3×C4—124no—
512C2×C3×C4—184no—
513C2×C3×C4—184no—
514C2×C3×C4—184no—
515C2×C3×C4—184no—
516C2×C3×C4C2×D3211yescharacteristic
517C2×C3×C4C2×D3212yes—
518#67—38no—
519#67—98no—
520#67—98no—
521#67—98no—
522#67—98no—
523#67—188no—
524C2×Dic3—32no—
525C2×Dic3—32no—
526C2×Dic3—32no—
527C2×Dic3—32no—
528C2×Dic3—61no—
529C2×Dic3—61no—
530C2×Dic3—62no—
531C2×Dic3—64no—
532C2×Dic3—64no—
533C2×Dic3—98no—
534C2×Dic3—91no—
535C2×Dic3—92no—
536C2×Dic3—91no—
537C2×Dic3—92no—
538C2×Dic3—184no—
539C2×Dic3—181no—
540C2×Dic3—181no—
541C2×Dic3—182no—
542C2×Dic3—182no—
543C2×Dic3—184no—
544C2×Dic3—184no—
545C2×Dic3—361no—
546C2×Dic3—361no—
547C2×Dic3C2×D3212yes—
548C2×Dic3C2×D3211yescharacteristic
549D12—94no—
550C4×D3—24no—
551C4×D3—64no—
552C4×D3—64no—
553C4×D3—64no—
554C4×D3—64no—
555C4×D3—64no—
556C4×D3—64no—
557C4×D3—94no—
558C4×D3—124no—
559C4×D3—182no—
560C4×D3#62514yesdirect product factor
561C2×C32—21no—
562C2×C32—21no—
563C2×C32—22no—
564C2×C32—22no—
565C2×C32—21no—
566C2×C32—22no—
567C2×C32—34no—
568C2×C32—41no—
569C2×C32—41no—
570C2×C32—41no—
571C2×C32—64no—
572C2×C32C22×C4×D312yes—
573C2×C32C22×C4×D311yescharacteristic
574C2×C32C2×#23512yes—
575C2×C32C2×D3×D411yescharacteristic
576C2×C32D3×#4111yescharacteristic
577C2×C32C22×#6712yes—
578C3⋊D3—24no—
579C3×D3—24no—
580C3×D3—24no—
581C3×D3—24no—
582C3×D3—44no—
583C3×D3—64no—
584C3×D3—64no—
585C3×D3—124no—
586C3×D3C4×#6718yescomplemented
587C24—92no—
588C2×D4—91no—
589C2×D4—271no—
590C2×D4—278no—
591C2×D4—272no—
592C22×C4—31no—
593C22×C4—32no—
594C22×C4—92no—
595C22×C4—92no—
596C22×C4—92no—
597C22×C4—92no—
598C22×C4—188no—
599C22×C4—271no—
600C22×C4—271no—
601C4⋊C4—91no—
602C4⋊C4—272no—
603C4⋊C4—271no—
604C22⋊C4—92no—
605C22⋊C4—272no—
606C22⋊C4—272no—
607C22⋊C4—272no—
608C42—91no—
609C42—271no—
610C42—271no—
611C42—271no—
612C22×C3—21no—
613C22×C3—22no—
614C22×C3—34no—
615C22×C3—34no—
616C22×C3—34no—
617C22×C3—34no—
618C22×C3—34no—
619C22×C3—41no—
620C22×C3—62no—
621C22×C3—62no—
622C22×C3—62no—
623C22×C3—64no—
624C22×C3—62no—
625C22×C3—62no—
626C22×C3—62no—
627C22×C3—62no—
628C22×C3—94no—
629C22×C3—122no—
630C22×C3—122no—
631C22×C3—1816no—
632C22×C3—182no—
633C22×C3—182no—
634C22×C3C22×D3211yescharacteristic
635C22×C3C22×D3212yes—
636C2×D3—22no—
637C2×D3—22no—
638C2×D3—34no—
639C2×D3—34no—
640C2×D3—64no—
641C2×D3—616no—
642C2×D3—62no—
643C2×D3—62no—
644C2×D3—62no—
645C2×D3—62no—
646C2×D3—616no—
647C2×D3—122no—
648C2×D3—122no—
649C2×D3#379812yes—
650C2×D3C4×D3212yes—
651C2×D3C4×D3214yescomplemented
652C2×D3C2×#62512yes—
653C3×C4—24no—
654C3×C4—22no—
655C3×C4—34no—
656C3×C4—42no—
657C3×C4—62no—
658C3×C4—62no—
659C3×C4—62no—
660C3×C4—92no—
661C3×C4—122no—
662C3×C4—181no—
663C3×C4—182no—
664C3×C4C2×#62512yescomplemented
665C3×C4D3×#6714yescomplemented
666Dic3—22no—
667Dic3—34no—
668Dic3—62no—
669Dic3—62no—
670Dic3—62no—
671Dic3—62no—
672Dic3—62no—
673Dic3—92no—
674Dic3—94no—
675Dic3—122no—
676Dic3—182no—
677Dic3—184no—
678Dic3—182no—
679Dic3—181no—
680Dic3—182no—
681Dic3—362no—
682Dic3—362no—
683Dic3—362no—
684Dic3C2×#62512yescomplemented
685C32—21no—
686C32—22no—
687C32—41no—
688C32C4×D3×D411yescharacteristic, complemented
689C32C2×C4×#6712yescomplemented
690C23—31no—
691C23—32no—
692C23—98no—
693C23—92no—
694C23—184no—
695C23—184no—
696D4—94no—
697D4—274no—
698D4—278no—
699C2×C4—31no—
700C2×C4—34no—
701C2×C4—32no—
702C2×C4—64no—
703C2×C4—91no—
704C2×C4—91no—
705C2×C4—92no—
706C2×C4—184no—
707C2×C4—184no—
708C2×C4—184no—
709C2×C4—184no—
710C2×C4—274no—
711C2×C4—271no—
712C2×C4—271no—
713C2×C4—542no—
714C2×C4D3311yescharacteristic
715C2×C3—21no—
716C2×C3—22no—
717C2×C3—21no—
718C2×C3—22no—
719C2×C3—22no—
720C2×C3—21no—
721C2×C3—38no—
722C2×C3—41no—
723C2×C3—41no—
724C2×C3—41no—
725C2×C3—64no—
726C2×C3—64no—
727C2×C3—64no—
728C2×C3—124no—
729C2×C3—184no—
730C2×C3C2×#379811yescharacteristic
731C2×C3C2×C4×D3211yescharacteristic
732C2×C3C2×C4×D3212yes—
733C2×C3D3×#23512yes—
734C2×C3C22×#62511yescharacteristic
735C2×C3C2×D3×#6712yes—
736D3—24no—
737D3—64no—
738D3—64no—
739D3—124no—
740D3C4×#62514yesdirect product factor
741C22—32no—
742C22—32no—
743C22—32no—
744C22—34no—
745C22—62no—
746C22—62no—
747C22—94no—
748C22—1816no—
749C22—182no—
750C22—182no—
751C22C2×D3311yescharacteristic
752C4—32no—
753C4—62no—
754C4—92no—
755C4—181no—
756C4—182no—
757C4—272no—
758C4—541no—
759C4D3×#62512yesdirect product factor
760C3—22no—
761C3—21no—
762C3—41no—
763C3C2×C4×#62511yescharacteristic, complemented
764C3C4×D3×#6712yescomplemented
765C2—34no—
766C2—64no—
767C2—184no—
768C2D3×#379811yescharacteristic
769C2C4×D3311yescharacteristic
770C2C2×D3×#62511yescharacteristic
subgroupG/H
center, hypercenterC2×C4D33
commutatorC2×C33C23×C4
FrattiniC22C2×D33
FittingC2×C33×C4C23
socle, cosocleC22×C33C24
prime radicalC2×D3×#625C2
hypocenterC33C2×C4×D4
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×C4×D32C2semidirect
3. C4×#6295C2semidirect
4. C4×#6290C2semidirect
5. C4×D3×C3⋊Dic3C2semidirect
6. C3×C4×#625C2semidirect
7. #11722931C2semidirect
8. #11722930C2semidirect
9. Dic3×#625C2semidirect
10. D3×#3724C2semidirect
11. D3×(C2×D3)⋊Dic3C2semidirect
15. C2×C3×C4×C3⋊D3C22semidirect
17. C2×C32×C4×D3C22semidirect
23. C2×C3×#624C22semidirect
25. C2×C3×D3×Dic3C22semidirect
27. D3×#625C4direct (N × H)
28. C4×C3⋊(C3⋊Dic3)C22semidirect
29. C3×C4×C3⋊Dic3C22semidirect
30. #88815C22semidirect
31. #88814C22semidirect
32. #88806C22semidirect
33. #88803C22semidirect
34. (C2×D3)⋊(C3⋊Dic3)C22semidirect
35. Dic3×C3⋊Dic3C22semidirect
36. Dic3×C3⋊Dic3C22semidirect
37. C3×#3724C22semidirect
38. C3×(C2×D3)⋊Dic3C22semidirect
43. C2×C4×D32D3semidirect
62. C4×#625D3direct (N × H)
72. C2×C3×D32C2×C4semidirect
83. C32×C4×D3D4semidirect
84. #6295C2×C4semidirect
85. #6290C2×C4semidirect
87. D3×C3⋊Dic3C2×C4semidirect
88. C3×#625C2×C4semidirect
102. C2×C4×C3⋊D3C2×D3semidirect
118. C2×C3×C4×D3C2×D3semidirect
119. C2×C3×C4×D3C2×D3semidirect
128. C2×#624C2×D3semidirect
134. C2×D3×Dic3C2×D3semidirect
146. C4×C3⋊Dic3C2×D3semidirect
156. #3724C2×D3semidirect
167. (C2×D3)⋊Dic3C2×D3semidirect
175. C2×C3×C3⋊D3C22×C4semidirect
179. C2×C32×D3C22×C4semidirect
183. C33×C4C2×D4semidirect
185. C3⋊(C3⋊Dic3)C22×C4semidirect
188. C3×C3⋊Dic3C22×C4semidirect
190. C32×Dic3C2×D4semidirect
238. C2×D32C4×D3semidirect
291. C3×C4×D3#67semidirect
297. #625C4×D3direct (N × H)
311. C32×D3C4×D4semidirect
353. C2×C4×D3D32semidirect
403. C2×C3⋊D3C2×C4×D3semidirect
426. C2×C3×D3C2×C4×D3semidirect
427. C2×C3×D3C2×C4×D3semidirect
436. C32×C4D3×D4semidirect
437. C32×C4C2×#67semidirect
450. C3⋊Dic3C2×C4×D3semidirect
462. C3×Dic3C2×#67semidirect
474. C33C2×C4×D4semidirect
560. C4×D3#625direct (N × H)
586. C3×D3C4×#67semidirect
651. C2×D3C4×D32semidirect
664. C3×C4C2×#625semidirect
665. C3×C4D3×#67semidirect
684. Dic3C2×#625semidirect
688. C32C4×D3×D4semidirect
689. C32C2×C4×#67semidirect
740. D3C4×#625direct (N × H)
759. C4D3×#625direct (N × H)
763. C3C2×C4×#625semidirect
764. C3C4×D3×#67semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×D322
C2×D3×#6252
C4×#62952
C4×#62902
C4×D3×C3⋊Dic32
C3×C4×#6252
#117229312
#117229302
Dic3×#6252
D3×#37242
D3×(C2×D3)⋊Dic32
C4×D3×#673
C2×C4×#6253