Finite Group Databasebeta

← C2×D3×#930 #11900289

Subgroups — C2×D3×#930 #11900289

Order 1152.

5269 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×C4×D3C211yesmaximal, characteristic, complemented
2C22×D3×#67C212yesmaximal, complemented
3C22×D3×D12C211yesmaximal, characteristic, complemented
4C2×#64139C211yesmaximal, characteristic, complemented
5C2×C3×#930C211yesmaximal, characteristic, complemented
6C2×#63978C212yesmaximal, complemented
7D3×#930C2116yesmaximal, direct product factor
8C2×D3×(C2×D3)⋊C4C212yesmaximal, complemented
9C2×#63909C211yesmaximal, characteristic, complemented
10C2×#63908C211yesmaximal, characteristic, complemented
11C2×#63906C212yesmaximal, complemented
12C2×D3×C4⋊Dic3C211yesmaximal, characteristic, complemented
13C22×#930—31nomaximal
14C2×D3×#121—31nomaximal
15C24×C3×D3C2211yescharacteristic
16C23×D32C2212yes—
17C23×C32×C4C2211yescharacteristic, complemented
18C22×#638C2212yescomplemented
19C22×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
20C22×C3×#67C2212yescomplemented
21C23×C3×Dic3C2211yescharacteristic, complemented
22C22×C3×D12C2211yescharacteristic, complemented
23C22×C3×C4×D3—28no—
24C22×C3×C4×D3C2211yescharacteristic
25C22×C3×C4×D3C2211yescharacteristic
26C22×C3×C4×D3C2218yescomplemented
27C22×C3×C4×D3C2211yescharacteristic, complemented
28C22×C3×C4×D3C2211yescharacteristic, complemented
29C2×D3×#67—216no—
30C2×D3×#67C22116yescomplemented
31C22×#626C2212yescomplemented
32C22×#626C2212yescomplemented
33C22×#625C2212yescomplemented
34C22×D3×Dic3C2212yes—
35C2×D3×D12—28no—
36C2×D3×D12C2218yescomplemented
37#64139C2218yescomplemented
38C2×#3752C2212yescomplemented
39C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
40C3×#930C2218yescomplemented
41C2×C3×(C2×D3)⋊C4C2212yescomplemented
42C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
43#63978C22116yescomplemented
44C2×Dic3⋊Dic3C2212yescomplemented
45C2×#3722C2212yescomplemented
46C2×(C2×D3)⋊Dic3C2212yescomplemented
47D3×(C2×D3)⋊C4C22116yescomplemented
48#63909C2218yescomplemented
49#63908C2218yescomplemented
50#63906C22116yescomplemented
51D3×C4⋊Dic3C2218yescomplemented
52C24×C3×C4—31no—
53C23×#67—32no—
54C22×D3×D4—32no—
55C22×D3×D4—31no—
56C23×D12—31no—
57C23×C4×D3D311yescharacteristic, complemented
58C2×C3×#121—31no—
59C2×#939—32no—
60C2×#938—31no—
61C2×#930—31no—
62C2×#930—31no—
63C2×#930—32no—
64C2×#930—31no—
65C2×#930—316no—
66C2×#930—32no—
67C2×#930—31no—
68C2×#930—61no—
69C2×#930D311yescharacteristic, direct product factor
70C22×(C2×D3)⋊C4—32no—
71C22×C4⋊Dic3—31no—
72D3×#121—316no—
73C2×#895—31no—
74C2×D3×C4⋊C4—31no—
75C2×#884—32no—
76C2×D3×C22⋊C4—32no—
77C24×C32C2311yescharacteristic
78C23×C3⋊D3C2312yes—
79C23×C3×D3—24no—
80C23×C3×D3—24no—
81C23×C3×D3D418yescomplemented
82C23×C3×D3C2312yes—
83C23×C3×D3C2311yescharacteristic
84C23×C3×D3C2314yes—
85C23×C3×D3C2311yescharacteristic
86C22×D32—28no—
87C22×D32—28no—
88C22×D32—28no—
89C22×D32C2318yes—
90C22×C32×C4—24no—
91C22×C32×C4C2311yescharacteristic
92C22×C32×C4C2311yescharacteristic
93C22×C32×C4C2314yescomplemented
94C2×#638—28no—
95C2×#638C2318yescomplemented
96C22×C3⋊Dic3C2312yes—
97C2×C4⋊(C3⋊D3)—24no—
98C2×C4⋊(C3⋊D3)C2314yescomplemented
99C2×C3×#67—28no—
100C2×C3×#67C2318yescomplemented
101C22×C3×Dic3—24no—
102C22×C3×Dic3C2312yes—
103C22×C3×Dic3C2311yescharacteristic
104C22×C3×Dic3C2311yescharacteristic
105C22×C3×Dic3C2314yescomplemented
106C2×C3×D12—24no—
107C2×C3×D12C2314yescomplemented
108C2×C3×C4×D3—24no—
109C2×C3×C4×D3—24no—
110C2×C3×C4×D3—24no—
111C2×C3×C4×D3—232no—
112C2×C3×C4×D3D418yescomplemented
113C2×C3×C4×D3C2314yes—
114C2×C3×C4×D3C2314yes—
115C2×C3×C4×D3C2314yescomplemented
116C2×C3×C4×D3C2314yescomplemented
117D3×#67—264no—
118C2×#626—28no—
119C2×#626—28no—
120C2×#626C2318yescomplemented
121C2×#626C2318yescomplemented
122C2×#625—28no—
123C2×#625C2318yescomplemented
124C2×D3×Dic3—28no—
125C2×D3×Dic3C2318yes—
126D3×D12—232no—
127#3752C2318yescomplemented
128C4⋊(C3⋊Dic3)C2314yescomplemented
129C3×(C2×D3)⋊C4C2318yescomplemented
130C3×C4⋊Dic3C2314yescomplemented
131Dic3⋊Dic3C2318yescomplemented
132#3722C2318yescomplemented
133(C2×D3)⋊Dic3C2318yescomplemented
134C22×#121—91noSylow
135C25×C3—31no—
136C24×D3—32no—
137C24×D3—32no—
138C24×D3C2×D311yescharacteristic
139C22×C3×D4—32no—
140C22×C3×D4—31no—
141C23×C3×C4—21no—
142C23×C3×C4—31no—
143C23×C3×C4—31no—
144C23×C3×C4—31no—
145C23×C3×C4—31no—
146C23×C3×C4—31no—
147C23×C3×C4—38no—
148C23×C3×C4—68no—
149C23×C3×C4C2×D311yescharacteristic, complemented
150C23×C3×C4C2×D311yescharacteristic, complemented
151C22×#67—32no—
152C22×#67—32no—
153C22×#67—32no—
154C22×#67—32no—
155C22×#67—316no—
156C22×#67—32no—
157C22×#67—32no—
158C22×#67—62no—
159C22×#67—616no—
160C22×#67C2×D312yescomplemented
161C23×Dic3—32no—
162C23×Dic3C2×D311yescharacteristic, complemented
163C2×D3×D4—316no—
164C2×D3×D4—38no—
165C2×D3×D4—616no—
166C2×D3×D4—68no—
167C22×D12—32no—
168C22×D12—32no—
169C22×D12—31no—
170C22×D12—31no—
171C22×D12—38no—
172C22×D12—61no—
173C22×D12—68no—
174C22×D12C2×D311yescharacteristic, complemented
175C22×C4×D3—28no—
176C22×C4×D3—32no—
177C22×C4×D3C2×D311yescharacteristic
178C22×C4×D3C2×D311yescharacteristic
179C22×C4×D3C2×D318yescomplemented
180C22×C4×D3C2×D311yescharacteristic, complemented
181C22×C4×D3C2×D311yescharacteristic, complemented
182C3×#121—38no—
183C2×C3×C4⋊C4—31no—
184C2×C3×C22⋊C4—32no—
185C2×#217—32no—
186#939—316no—
187#938—38no—
188#930—38no—
189#930—38no—
190#930—316no—
191#930—38no—
192#930—316no—
193#930—38no—
194#930—68no—
195#930C2×D318yesdirect product factor
196C2×(C2×D3)⋊C4—32no—
197C2×(C2×D3)⋊C4—32no—
198C2×(C2×D3)⋊C4—32no—
199C2×(C2×D3)⋊C4—32no—
200C2×(C2×D3)⋊C4—32no—
201C2×(C2×D3)⋊C4—316no—
202C2×(C2×D3)⋊C4—62no—
203C2×(C2×D3)⋊C4C2×D312yescomplemented
204C2×C4⋊Dic3—31no—
205C2×C4⋊Dic3—31no—
206C2×C4⋊Dic3—32no—
207C2×C4⋊Dic3—38no—
208C2×C4⋊Dic3—61no—
209C2×C4⋊Dic3C2×D311yescharacteristic, complemented
210C2×Dic3⋊C4—32no—
211#895—38no—
212D3×C4⋊C4—38no—
213#884—316no—
214D3×C22⋊C4—316no—
215C23×C32—22no—
216C23×C32—22no—
217C23×C32C2×D414yescomplemented
218C23×C32C2412yes—
219C23×C32C2411yescharacteristic
220C22×C3⋊D3—24no—
221C22×C3⋊D3—24no—
222C22×C3⋊D3—24no—
223C22×C3⋊D3C2414yes—
224C22×C3×D3—22no—
225C22×C3×D3—22no—
226C22×C3×D3—232no—
227C22×C3×D3—28no—
228C22×C3×D3—28no—
229C22×C3×D3—24no—
230C22×C3×D3—24no—
231C22×C3×D3—24no—
232C22×C3×D3C2×D414yes—
233C22×C3×D3C2×D414yes—
234C22×C3×D3C2×D4116yescomplemented
235C22×C3×D3C2×D414yescomplemented
236C22×C3×D3#4114yes—
237C22×C3×D3C2414yes—
238C22×C3×D3C2412yes—
239C22×C3×D3C2412yes—
240C2×D32—216no—
241C2×D32—216no—
242C2×D32—216no—
243C2×D32—432no—
244C2×C32×C4—22no—
245C2×C32×C4—28no—
246C2×C32×C4C2×D414yescomplemented
247C2×C32×C4C2412yes—
248C2×C32×C4C2412yes—
249#638—216no—
250C2×C3⋊Dic3—24no—
251C2×C3⋊Dic3C2414yes—
252C4⋊(C3⋊D3)—28no—
253C3×#67—216no—
254C2×C3×Dic3—24no—
255C2×C3×Dic3—22no—
256C2×C3×Dic3—28no—
257C2×C3×Dic3C2×D414yescomplemented
258C2×C3×Dic3C2412yes—
259C2×C3×Dic3C2414yes—
260C2×C3×Dic3C2412yes—
261C3×D12—28no—
262C3×C4×D3—28no—
263C3×C4×D3—28no—
264C3×C4×D3—28no—
265C3×C4×D3C2×D4116yescomplemented
266#626—216no—
267#626—216no—
268#625—216no—
269D3×Dic3—216no—
270C23×D4—91no—
271C23×D4—92no—
272C24×C4—31no—
273C2×#121—31no—
274C2×#121—92no—
275C2×#121—91no—
276C2×#121—916no—
277C2×#121—91no—
278C2×#121—92no—
279C2×#121—91no—
280C22×C4⋊C4—91no—
281C22×C22⋊C4—92no—
282C24×C3—21no—
283C24×C3—31no—
284C24×C3—38no—
285C24×C3—34no—
286C24×C3—31no—
287C24×C3—32no—
288C24×C3—64no—
289C24×C3—64no—
290C24×C3C22×D311yescharacteristic
291C24×C3C22×D311yescharacteristic
292C23×D3—24no—
293C23×D3—24no—
294C23×D3—32no—
295C23×D3—32no—
296C23×D3—38no—
297C23×D3—38no—
298C23×D3—62no—
299C23×D3—68no—
300C23×D3—68no—
301C23×D3—68no—
302C23×D3—68no—
303C23×D3—68no—
304C23×D3—68no—
305C23×D3D1218yescomplemented
306C23×D3C22×D312yes—
307C23×D3C22×D311yescharacteristic
308C23×D3C22×D314yes—
309C23×D3C22×D311yescharacteristic
310C2×C3×D4—38no—
311C2×C3×D4—34no—
312C2×C3×D4—68no—
313C2×C3×D4—64no—
314C22×C3×C4—24no—
315C22×C3×C4—24no—
316C22×C3×C4—21no—
317C22×C3×C4—21no—
318C22×C3×C4—24no—
319C22×C3×C4—31no—
320C22×C3×C4—38no—
321C22×C3×C4—34no—
322C22×C3×C4—32no—
323C22×C3×C4—31no—
324C22×C3×C4—34no—
325C22×C3×C4—34no—
326C22×C3×C4—34no—
327C22×C3×C4—34no—
328C22×C3×C4—44no—
329C22×C3×C4—64no—
330C22×C3×C4—632no—
331C22×C3×C4—64no—
332C22×C3×C4—64no—
333C22×C3×C4—64no—
334C22×C3×C4C22×D311yescharacteristic
335C22×C3×C4C22×D311yescharacteristic
336C22×C3×C4C22×D311yescharacteristic
337C22×C3×C4C22×D311yescharacteristic
338C22×C3×C4C22×D314yescomplemented
339C22×C3×C4C22×D314yescomplemented
340C2×#67—28no—
341C2×#67—38no—
342C2×#67—38no—
343C2×#67—38no—
344C2×#67—38no—
345C2×#67—38no—
346C2×#67—38no—
347C2×#67—68no—
348C2×#67—68no—
349C2×#67—664no—
350C2×#67—68no—
351C2×#67—68no—
352C2×#67—68no—
353C2×#67—68no—
354C2×#67—68no—
355C2×#67—128no—
356C2×#67C22×D318yescomplemented
357C22×Dic3—24no—
358C22×Dic3—32no—
359C22×Dic3—32no—
360C22×Dic3—38no—
361C22×Dic3—62no—
362C22×Dic3—68no—
363C22×Dic3C22×D312yes—
364C22×Dic3C22×D311yescharacteristic
365C22×Dic3C22×D311yescharacteristic
366C22×Dic3C22×D314yescomplemented
367D3×D4—664no—
368D3×D4—632no—
369C2×D12—24no—
370C2×D12—38no—
371C2×D12—38no—
372C2×D12—34no—
373C2×D12—34no—
374C2×D12—64no—
375C2×D12—632no—
376C2×D12—68no—
377C2×D12—68no—
378C2×D12—64no—
379C2×D12—64no—
380C2×D12—124no—
381C2×D12C22×D314yescomplemented
382C2×C4×D3—24no—
383C2×C4×D3—24no—
384C2×C4×D3—24no—
385C2×C4×D3—232no—
386C2×C4×D3—38no—
387C2×C4×D3—68no—
388C2×C4×D3#6718yescomplemented
389C2×C4×D3C22×D314yes—
390C2×C4×D3C22×D314yes—
391C2×C4×D3C22×D314yescomplemented
392C2×C4×D3C22×D314yescomplemented
393C3×C4⋊C4—34no—
394C3×C22⋊C4—38no—
395#217—38no—
396(C2×D3)⋊C4—38no—
397(C2×D3)⋊C4—38no—
398(C2×D3)⋊C4—38no—
399(C2×D3)⋊C4—38no—
400(C2×D3)⋊C4—38no—
401(C2×D3)⋊C4—68no—
402(C2×D3)⋊C4C22×D318yescomplemented
403C4⋊Dic3—34no—
404C4⋊Dic3—34no—
405C4⋊Dic3—38no—
406C4⋊Dic3—64no—
407C4⋊Dic3C22×D314yescomplemented
408Dic3⋊C4—38no—
409C22×C32—28no—
410C22×C32—22no—
411C22×C32—22no—
412C22×C32C22×D412yes—
413C22×C32C22×D412yes—
414C22×C32C22×D414yescomplemented
415C22×C32C2×#4112yes—
416C22×C32C2511yescharacteristic
417C2×C3⋊D3—24no—
418C2×C3⋊D3—24no—
419C2×C3⋊D3—24no—
420C2×C3⋊D3—48no—
421C2×C3×D3—28no—
422C2×C3×D3—22no—
423C2×C3×D3—22no—
424C2×C3×D3—232no—
425C2×C3×D3—24no—
426C2×C3×D3—24no—
427C2×C3×D3—24no—
428C2×C3×D3—48no—
429C2×C3×D3#121116yescomplemented
430C2×C3×D3C22×D414yes—
431C2×C3×D3C22×D414yes—
432C2×C3×D3C22×D414yescomplemented
433C2×C3×D3C2×#4114yes—
434D32—432no—
435C32×C4—22no—
436C32×C4C22×D414yescomplemented
437C3⋊Dic3—24no—
438C3×Dic3—24no—
439C3×Dic3—22no—
440C3×Dic3C22×D414yescomplemented
441C25—31no—
442C25—92no—
443C22×D4—32no—
444C22×D4—31no—
445C22×D4—98no—
446C22×D4—92no—
447C22×D4—92no—
448C22×D4—916no—
449C22×D4—92no—
450C22×D4—92no—
451C22×D4—91no—
452C22×D4—188no—
453C22×D4—1816no—
454C23×C4—31no—
455C23×C4—31no—
456C23×C4—31no—
457C23×C4—31no—
458C23×C4—31no—
459C23×C4—38no—
460C23×C4—68no—
461C23×C4—92no—
462C23×C4D3211yescharacteristic, complemented
463#121—38no—
464#121—916no—
465#121—98no—
466#121—98no—
467#121—916no—
468#121—98no—
469C2×C4⋊C4—31no—
470C2×C4⋊C4—98no—
471C2×C4⋊C4—92no—
472C2×C4⋊C4—91no—
473C2×C22⋊C4—32no—
474C2×C22⋊C4—916no—
475C2×C22⋊C4—92no—
476C2×C22⋊C4—92no—
477C2×C22⋊C4—92no—
478C23×C3—22no—
479C23×C3—22no—
480C23×C3—22no—
481C23×C3—22no—
482C23×C3—22no—
483C23×C3—21no—
484C23×C3—24no—
485C23×C3—34no—
486C23×C3—34no—
487C23×C3—34no—
488C23×C3—32no—
489C23×C3—34no—
490C23×C3—316no—
491C23×C3—32no—
492C23×C3—34no—
493C23×C3—42no—
494C23×C3—42no—
495C23×C3—68no—
496C23×C3—68no—
497C23×C3—632no—
498C23×C3—62no—
499C23×C3—62no—
500C23×C3—64no—
501C23×C3—64no—
502C23×C3—64no—
503C23×C3C2×D1214yescomplemented
504C23×C3D3×D414yescomplemented
505C23×C3C23×D312yes—
506C23×C3C23×D312yes—
507C23×C3C23×D311yescharacteristic
508C23×C3C23×D311yescharacteristic
509C22×D3—22no—
510C22×D3—22no—
511C22×D3—232no—
512C22×D3—28no—
513C22×D3—28no—
514C22×D3—24no—
515C22×D3—24no—
516C22×D3—24no—
517C22×D3—34no—
518C22×D3—34no—
519C22×D3—64no—
520C22×D3—616no—
521C22×D3—616no—
522C22×D3—616no—
523C22×D3—64no—
524C22×D3—64no—
525C22×D3—64no—
526C22×D3—64no—
527C22×D3—64no—
528C22×D3—64no—
529C22×D3—616no—
530C22×D3—616no—
531C22×D3—616no—
532C22×D3—124no—
533C22×D3—124no—
534C22×D3—124no—
535C22×D3—1232no—
536C22×D3—1232no—
537C22×D3C2×D1214yes—
538C22×D3C2×D12116yescomplemented
539C22×D3C2×D1214yescomplemented
540C22×D3#23514yes—
541C22×D3C2×#6714yes—
542C22×D3C23×D314yes—
543C22×D3C23×D312yes—
544C22×D3C23×D312yes—
545C3×D4—616no—
546C3×D4—68no—
547C2×C3×C4—22no—
548C2×C3×C4—22no—
549C2×C3×C4—28no—
550C2×C3×C4—28no—
551C2×C3×C4—22no—
552C2×C3×C4—22no—
553C2×C3×C4—24no—
554C2×C3×C4—34no—
555C2×C3×C4—32no—
556C2×C3×C4—316no—
557C2×C3×C4—34no—
558C2×C3×C4—32no—
559C2×C3×C4—48no—
560C2×C3×C4—42no—
561C2×C3×C4—68no—
562C2×C3×C4—68no—
563C2×C3×C4—68no—
564C2×C3×C4—64no—
565C2×C3×C4—62no—
566C2×C3×C4—68no—
567C2×C3×C4D3×D414yescomplemented
568C2×C3×C4C2×#6714yescomplemented
569C2×C3×C4C23×D312yes—
570C2×C3×C4C23×D312yes—
571C2×C3×C4C23×D312yes—
572C2×C3×C4C23×D312yes—
573#67—216no—
574#67—616no—
575#67—616no—
576#67—616no—
577#67—616no—
578#67—616no—
579#67—616no—
580#67—1216no—
581C2×Dic3—24no—
582C2×Dic3—22no—
583C2×Dic3—28no—
584C2×Dic3—34no—
585C2×Dic3—34no—
586C2×Dic3—64no—
587C2×Dic3—616no—
588C2×Dic3—64no—
589C2×Dic3—64no—
590C2×Dic3—124no—
591C2×Dic3C2×#6714yescomplemented
592C2×Dic3C23×D314yes—
593C2×Dic3C23×D312yes—
594C2×Dic3C23×D312yes—
595D12—28no—
596D12—616no—
597D12—616no—
598D12—68no—
599D12—68no—
600D12—128no—
601C4×D3—28no—
602C4×D3—28no—
603C4×D3—28no—
604C4×D3—616no—
605C4×D3C2×#67116yescomplemented
606C2×C32—24no—
607C2×C32C2×#12114yescomplemented
608C2×C32C23×D411yescharacteristic
609C2×C32C23×D411yescharacteristic
610C2×C32C22×#4111yescharacteristic
611C3⋊D3—44no—
612C3×D3—24no—
613C3×D3—44no—
614C3×D3C2×#12118yescomplemented
615C24—31no—
616C24—34no—
617C24—31no—
618C24—38no—
619C24—32no—
620C24—64no—
621C24—64no—
622C24—98no—
623C24—92no—
624C24—188no—
625C24—188no—
626C24—188no—
627C24C2×D3211yescharacteristic
628C2×D4—38no—
629C2×D4—34no—
630C2×D4—68no—
631C2×D4—64no—
632C2×D4—98no—
633C2×D4—98no—
634C2×D4—98no—
635C2×D4—98no—
636C2×D4—94no—
637C2×D4—1832no—
638C2×D4—188no—
639C2×D4—188no—
640C2×D4—1864no—
641C2×D4—188no—
642C2×D4—188no—
643C2×D4—184no—
644C22×C4—24no—
645C22×C4—31no—
646C22×C4—34no—
647C22×C4—38no—
648C22×C4—34no—
649C22×C4—32no—
650C22×C4—31no—
651C22×C4—34no—
652C22×C4—34no—
653C22×C4—34no—
654C22×C4—64no—
655C22×C4—632no—
656C22×C4—64no—
657C22×C4—64no—
658C22×C4—64no—
659C22×C4—98no—
660C22×C4—92no—
661C22×C4—188no—
662C22×C4C2×D3211yescharacteristic
663C22×C4C2×D3211yescharacteristic
664C22×C4C2×D3214yescomplemented
665C4⋊C4—34no—
666C4⋊C4—98no—
667C4⋊C4—94no—
668C22⋊C4—38no—
669C22⋊C4—98no—
670C22⋊C4—98no—
671C22⋊C4—98no—
672C22×C3—22no—
673C22×C3—22no—
674C22×C3—22no—
675C22×C3—22no—
676C22×C3—28no—
677C22×C3—28no—
678C22×C3—22no—
679C22×C3—24no—
680C22×C3—22no—
681C22×C3—22no—
682C22×C3—21no—
683C22×C3—34no—
684C22×C3—34no—
685C22×C3—34no—
686C22×C3—316no—
687C22×C3—34no—
688C22×C3—42no—
689C22×C3—42no—
690C22×C3—48no—
691C22×C3—632no—
692C22×C3—62no—
693C22×C3—62no—
694C22×C3—68no—
695C22×C3—64no—
696C22×C3—64no—
697C22×C3—64no—
698C22×C3—128no—
699C22×C3C22×D1212yes—
700C22×C3C22×D1214yescomplemented
701C22×C3C2×#23512yes—
702C22×C3C2×D3×D412yes—
703C22×C3C2×D3×D412yes—
704C22×C3C2×D3×D414yescomplemented
705C22×C3D3×#4112yes—
706C22×C3C22×#6712yes—
707C22×C3C24×D311yescharacteristic
708C22×C3C24×D311yescharacteristic
709C2×D3—22no—
710C2×D3—22no—
711C2×D3—28no—
712C2×D3—232no—
713C2×D3—24no—
714C2×D3—24no—
715C2×D3—24no—
716C2×D3—48no—
717C2×D3—64no—
718C2×D3—64no—
719C2×D3—64no—
720C2×D3—64no—
721C2×D3—64no—
722C2×D3—64no—
723C2×D3—124no—
724C2×D3—124no—
725C2×D3—124no—
726C2×D3—1232no—
727C2×D3—128no—
728C2×D3—128no—
729C2×D3—1232no—
730C2×D3—248no—
731C2×D3#930116yesdirect product factor
732C2×D3C22×D1214yes—
733C2×D3C22×D1214yescomplemented
734C2×D3C2×#23514yes—
735C2×D3C22×#6714yes—
736C3×C4—22no—
737C3×C4—22no—
738C3×C4—24no—
739C3×C4—34no—
740C3×C4—42no—
741C3×C4—64no—
742C3×C4—62no—
743C3×C4C2×D3×D414yescomplemented
744C3×C4C22×#6714yescomplemented
745Dic3—24no—
746Dic3—22no—
747Dic3—64no—
748Dic3—64no—
749Dic3—124no—
750Dic3C22×#6714yescomplemented
751C32C22×#12111yescharacteristic, complemented, Sylow
752C23—22no—
753C23—22no—
754C23—34no—
755C23—34no—
756C23—34no—
757C23—32no—
758C23—34no—
759C23—316no—
760C23—32no—
761C23—34no—
762C23—68no—
763C23—68no—
764C23—632no—
765C23—62no—
766C23—62no—
767C23—64no—
768C23—64no—
769C23—64no—
770C23—94no—
771C23—1816no—
772C23—1816no—
773C23—1816no—
774C23—184no—
775C23—184no—
776C23—184no—
777C23—3632no—
778C23D3×D1214yescomplemented
779C23C22×D3212yes—
780C23C22×D3211yescharacteristic
781D4—616no—
782D4—68no—
783D4—1816no—
784D4—1816no—
785D4—1816no—
786D4—1816no—
787D4—188no—
788C2×C4—22no—
789C2×C4—28no—
790C2×C4—34no—
791C2×C4—32no—
792C2×C4—316no—
793C2×C4—34no—
794C2×C4—32no—
795C2×C4—68no—
796C2×C4—68no—
797C2×C4—68no—
798C2×C4—64no—
799C2×C4—62no—
800C2×C4—68no—
801C2×C4—94no—
802C2×C4—1816no—
803C2×C4—184no—
804C2×C4D3×#6714yescomplemented
805C2×C4C22×D3212yes—
806C2×C4C22×D3212yes—
807C2×C3—24no—
808C2×C3—24no—
809C2×C3—21no—
810C2×C3—21no—
811C2×C3—21no—
812C2×C3—24no—
813C2×C3—38no—
814C2×C3—44no—
815C2×C3—64no—
816C2×C3—124no—
817C2×C3D3×#12114yescomplemented
818C2×C3C2×#93014yescomplemented
819C2×C3C23×D1211yescharacteristic
820C2×C3C22×#23511yescharacteristic
821C2×C3C22×D3×D411yescharacteristic
822C2×C3C22×D3×D411yescharacteristic
823C2×C3C2×D3×#4111yescharacteristic
824C2×C3C23×#6711yescharacteristic
825D3—24no—
826D3—44no—
827D3—124no—
828D3—124no—
829D3—244no—
830D3C2×#93018yesdirect product factor
831C22—22no—
832C22—22no—
833C22—28no—
834C22—34no—
835C22—34no—
836C22—34no—
837C22—316no—
838C22—34no—
839C22—632no—
840C22—62no—
841C22—62no—
842C22—68no—
843C22—64no—
844C22—64no—
845C22—64no—
846C22—128no—
847C22—184no—
848C22—184no—
849C22—184no—
850C22—3632no—
851C22—368no—
852C22C2×D3×D1212yes—
853C22C2×D3×D1214yescomplemented
854C22D3×#23512yes—
855C22C2×D3×#6712yes—
856C22C23×D3211yescharacteristic
857C4—22no—
858C4—34no—
859C4—64no—
860C4—62no—
861C4—184no—
862C4C2×D3×#6714yescomplemented
863C3—21no—
864C3C2×D3×#12111yescharacteristic, complemented
865C3C22×#93011yescharacteristic, complemented
866C2—24no—
867C2—38no—
868C2—64no—
869C2—124no—
870C2—364no—
871C2D3×#93014yesdirect product factor
872C2C22×D3×D1211yescharacteristic
873C2C2×D3×#23511yescharacteristic
874C2C22×D3×#6711yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC23×C32×C4C22
socleC23×C32C24
hypercenterC23×C4D32
hypocenterC32C22×#121
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C23×C3×C4×D3C2semidirect
2. C22×D3×#67C2semidirect
3. C22×D3×D12C2semidirect
4. C2×#64139C2semidirect
5. C2×C3×#930C2semidirect
6. C2×#63978C2semidirect
7. D3×#930C2direct (N × H)
8. C2×D3×(C2×D3)⋊C4C2semidirect
9. C2×#63909C2semidirect
10. C2×#63908C2semidirect
11. C2×#63906C2semidirect
12. C2×D3×C4⋊Dic3C2semidirect
17. C23×C32×C4C22semidirect
18. C22×#638C22semidirect
19. C22×C4⋊(C3⋊D3)C22semidirect
20. C22×C3×#67C22semidirect
21. C23×C3×Dic3C22semidirect
22. C22×C3×D12C22semidirect
26. C22×C3×C4×D3C22semidirect
27. C22×C3×C4×D3C22semidirect
28. C22×C3×C4×D3C22semidirect
30. C2×D3×#67C22semidirect
31. C22×#626C22semidirect
32. C22×#626C22semidirect
33. C22×#625C22semidirect
36. C2×D3×D12C22semidirect
37. #64139C22semidirect
38. C2×#3752C22semidirect
39. C2×C4⋊(C3⋊Dic3)C22semidirect
40. C3×#930C22semidirect
41. C2×C3×(C2×D3)⋊C4C22semidirect
42. C2×C3×C4⋊Dic3C22semidirect
43. #63978C22semidirect
44. C2×Dic3⋊Dic3C22semidirect
45. C2×#3722C22semidirect
46. C2×(C2×D3)⋊Dic3C22semidirect
47. D3×(C2×D3)⋊C4C22semidirect
48. #63909C22semidirect
49. #63908C22semidirect
50. #63906C22semidirect
51. D3×C4⋊Dic3C22semidirect
57. C23×C4×D3D3semidirect
69. C2×#930D3direct (N × H)
81. C23×C3×D3D4semidirect
93. C22×C32×C4C23semidirect
95. C2×#638C23semidirect
98. C2×C4⋊(C3⋊D3)C23semidirect
100. C2×C3×#67C23semidirect
105. C22×C3×Dic3C23semidirect
107. C2×C3×D12C23semidirect
112. C2×C3×C4×D3D4semidirect
115. C2×C3×C4×D3C23semidirect
116. C2×C3×C4×D3C23semidirect
120. C2×#626C23semidirect
121. C2×#626C23semidirect
123. C2×#625C23semidirect
127. #3752C23semidirect
128. C4⋊(C3⋊Dic3)C23semidirect
129. C3×(C2×D3)⋊C4C23semidirect
130. C3×C4⋊Dic3C23semidirect
131. Dic3⋊Dic3C23semidirect
132. #3722C23semidirect
133. (C2×D3)⋊Dic3C23semidirect
149. C23×C3×C4C2×D3semidirect
150. C23×C3×C4C2×D3semidirect
160. C22×#67C2×D3semidirect
162. C23×Dic3C2×D3semidirect
174. C22×D12C2×D3semidirect
179. C22×C4×D3C2×D3semidirect
180. C22×C4×D3C2×D3semidirect
181. C22×C4×D3C2×D3semidirect
195. #930C2×D3direct (N × H)
203. C2×(C2×D3)⋊C4C2×D3semidirect
209. C2×C4⋊Dic3C2×D3semidirect
217. C23×C32C2×D4semidirect
234. C22×C3×D3C2×D4semidirect
235. C22×C3×D3C2×D4semidirect
246. C2×C32×C4C2×D4semidirect
257. C2×C3×Dic3C2×D4semidirect
265. C3×C4×D3C2×D4semidirect
305. C23×D3D12semidirect
338. C22×C3×C4C22×D3semidirect
339. C22×C3×C4C22×D3semidirect
356. C2×#67C22×D3semidirect
366. C22×Dic3C22×D3semidirect
381. C2×D12C22×D3semidirect
388. C2×C4×D3#67semidirect
391. C2×C4×D3C22×D3semidirect
392. C2×C4×D3C22×D3semidirect
402. (C2×D3)⋊C4C22×D3semidirect
407. C4⋊Dic3C22×D3semidirect
414. C22×C32C22×D4semidirect
429. C2×C3×D3#121semidirect
432. C2×C3×D3C22×D4semidirect
436. C32×C4C22×D4semidirect
440. C3×Dic3C22×D4semidirect
462. C23×C4D32semidirect
503. C23×C3C2×D12semidirect
504. C23×C3D3×D4semidirect
538. C22×D3C2×D12semidirect
539. C22×D3C2×D12semidirect
567. C2×C3×C4D3×D4semidirect
568. C2×C3×C4C2×#67semidirect
591. C2×Dic3C2×#67semidirect
605. C4×D3C2×#67semidirect
607. C2×C32C2×#121semidirect
614. C3×D3C2×#121semidirect
664. C22×C4C2×D32semidirect
700. C22×C3C22×D12semidirect
704. C22×C3C2×D3×D4semidirect
731. C2×D3#930direct (N × H)
733. C2×D3C22×D12semidirect
743. C3×C4C2×D3×D4semidirect
744. C3×C4C22×#67semidirect
750. Dic3C22×#67semidirect
751. C32C22×#121semidirect
778. C23D3×D12semidirect
804. C2×C4D3×#67semidirect
817. C2×C3D3×#121semidirect
818. C2×C3C2×#930semidirect
830. D3C2×#930direct (N × H)
853. C22C2×D3×D12semidirect
862. C4C2×D3×#67semidirect
864. C3C2×D3×#121semidirect
865. C3C22×#930semidirect
871. C2D3×#930direct (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×#672
C22×D3×D122
C2×#641392
C2×C3×#9302
C2×#639782
D3×#9302
C2×D3×(C2×D3)⋊C42
C2×#639092
C2×#639082
C2×#639062
C2×D3×C4⋊Dic32
C22×#9303
C2×D3×#1213