Finite Group Databasebeta

← C3×D4×#626 #13174777

Subgroups — C3×D4×#626 #13174777

Order 1728.

2332 conjugacy classes of subgroups.

The subgroup lattice has 1044 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D4×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×C32×D3×D4C211yesmaximal, characteristic, complemented
3C22×C3×#626C212yesmaximal, complemented
4C32×D4×Dic3C211yesmaximal, characteristic, complemented
5C3×#63981C212yesmaximal, complemented
6C3×#63978C212yesmaximal, complemented
7C3×#63977C212yesmaximal, complemented
8C3×#63916C211yesmaximal, characteristic, complemented
9C3×#63911C211yesmaximal, characteristic, complemented
10C3×#63909C211yesmaximal, characteristic, complemented
11C3×C4×#626C211yesmaximal, characteristic, complemented
12C3×D4×#67—31nomaximal
13C3×D4×D12—31nomaximal
14D4×#626C311yesmaximal, characteristic, direct product factor
15C23×C3×C3⋊D3C2212yescomplemented
16C23×C32×D3C2212yescomplemented
17C2×C33×D4C2211yescharacteristic
18C2×C3×#638C2212yescomplemented
19C3×D4×C3⋊D3—24no—
20C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
21C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
22C2×C32×#67C2212yescomplemented
23C22×C32×Dic3C2212yescomplemented
24C32×D3×D4—24no—
25C2×C32×D12C2211yescharacteristic, complemented
26C2×C32×C4×D3C2211yescharacteristic, complemented
27C2×C3×#626—28no—
28C2×C3×#626C2211yescharacteristic
29C2×C3×#626C2212yescomplemented
30C2×C3×#626C2212yescomplemented
31C2×C3×#626C2212yescomplemented
32C2×C3×#626C2212yescomplemented
33C32×#217C2212yescomplemented
34C32×C4⋊Dic3C2211yescharacteristic, complemented
35C32×C4×Dic3C2211yescharacteristic, complemented
36C3×Dic3⋊Dic3C2211yescharacteristic, complemented
37C3×#3722C2212yescomplemented
38C3×#3722C2211yescharacteristic, complemented
39C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
40C3×(C2×D3)⋊Dic3C2212yescomplemented
41C22×C32×D4—31no—
42C2×D4×C3⋊D3C2×C311yescharacteristic, complemented
43C22×C3×#67—32no—
44C2×C3×D3×D4—21no—
45C2×C3×D3×D4—31no—
46C2×C3×D3×D4—31no—
47C2×C3×D3×D4—61no—
48C2×C3×D3×D4D311yescharacteristic, complemented
49C2×C3×D3×D4C2×C311yescharacteristic, complemented
50C22×C3×D12—32no—
51C22×#626C2×C312yescomplemented
52C32×C4×D4—31no—
53C3×#953—32no—
54C3×#940—31no—
55C3×#939—32no—
56C3×#938—31no—
57C3×#937—32no—
58C3×D4×Dic3—21no—
59C3×D4×Dic3D311yescharacteristic, complemented
60C3×D4×Dic3C2×C311yescharacteristic, complemented
61C3×#930—32no—
62C3×#930—31no—
63C3×C4×#67—31no—
64C3×#895—31no—
65C3×#895—31no—
66C3×#882—32no—
67C3×#882—32no—
68C3×#874—31no—
69C3×C4×D12—31no—
70#63981C2×C312yescomplemented
71#63978C2×C312yescomplemented
72#63977C2×C312yescomplemented
73#63916C2×C311yescharacteristic, complemented
74#63911C2×C311yescharacteristic, complemented
75#63909C2×C311yescharacteristic, complemented
76C4×#626C2×C311yescharacteristic, complemented
77C23×C33C2312yes—
78C22×C3×C3⋊D3—24no—
79C22×C3×C3⋊D3—24no—
80C22×C3×C3⋊D3—42no—
81C22×C3×C3⋊D3C2312yes—
82C22×C3×C3⋊D3C2311yescharacteristic
83C22×C32×D3—24no—
84C22×C32×D3—24no—
85C22×C32×D3—42no—
86C22×C32×D3C2312yes—
87C22×C32×D3C2311yescharacteristic
88C33×D4D414yescomplemented
89C2×C33×C4C2311yescharacteristic
90C3×#638—24no—
91C2×C3×C3⋊Dic3C2311yescharacteristic
92C3×C4⋊(C3⋊D3)—22no—
93C3×C4×C3⋊D3—22no—
94C32×#67—24no—
95C2×C32×Dic3—24no—
96C2×C32×Dic3C2311yescharacteristic
97C2×C32×Dic3C2312yes—
98C2×C32×Dic3C2311yescharacteristic
99C2×C32×Dic3C2311yescharacteristic
100C32×D12—22no—
101C32×C4×D3—22no—
102C3×#626—24no—
103C3×#626—24no—
104C3×#626—24no—
105C3×#626—42no—
106C3×#626D414yesdirect product factor
107C3×D42—91no—
108D4×#67—31no—
109D4×D12—31no—
110C24×C32—32no—
111C23×C3⋊D3C22×C312yescomplemented
112C23×C3×D3—22no—
113C23×C3×D3—32no—
114C23×C3×D3—32no—
115C23×C3×D3—62no—
116C23×C3×D3C2×D312yescomplemented
117C23×C3×D3C22×C312yescomplemented
118C2×C32×D4—21no—
119C2×C32×D4—21no—
120C2×C32×D4—21no—
121C2×C32×D4—32no—
122C2×C32×D4—31no—
123C2×C32×D4—41no—
124C2×C32×D4—64no—
125C2×C32×D4C2×D311yescharacteristic
126C2×C32×D4C2×D311yescharacteristic
127C2×C32×D4C22×C311yescharacteristic
128C22×C32×C4—32no—
129C22×C32×C4—31no—
130C2×#638C22×C312yescomplemented
131D4×C3⋊D3—24no—
132C2×C4⋊(C3⋊D3)C22×C311yescharacteristic, complemented
133C2×C4×C3⋊D3C22×C311yescharacteristic, complemented
134C2×C3×#67—22no—
135C2×C3×#67—32no—
136C2×C3×#67—32no—
137C2×C3×#67—31no—
138C2×C3×#67—32no—
139C2×C3×#67—32no—
140C2×C3×#67—32no—
141C2×C3×#67—32no—
142C2×C3×#67—68no—
143C2×C3×#67—62no—
144C2×C3×#67C2×D312yescomplemented
145C2×C3×#67C22×C312yescomplemented
146C22×C3×Dic3—22no—
147C22×C3×Dic3C2×D312yescomplemented
148C22×C3×Dic3C22×C312yescomplemented
149C3×D3×D4—28no—
150C3×D3×D4—24no—
151C3×D3×D4—24no—
152C3×D3×D4—68no—
153C3×D3×D4—64no—
154C3×D3×D4—64no—
155C2×C3×D12—21no—
156C2×C3×D12—31no—
157C2×C3×D12—32no—
158C2×C3×D12—32no—
159C2×C3×D12—32no—
160C2×C3×D12—31no—
161C2×C3×D12—31no—
162C2×C3×D12—32no—
163C2×C3×D12—68no—
164C2×C3×D12—61no—
165C2×C3×D12C2×D311yescharacteristic, complemented
166C2×C3×D12C22×C311yescharacteristic, complemented
167C2×C3×C4×D3—21no—
168C2×C3×C4×D3—31no—
169C2×C3×C4×D3—31no—
170C2×C3×C4×D3—61no—
171C2×C3×C4×D3C2×D311yescharacteristic, complemented
172C2×C3×C4×D3C22×C311yescharacteristic, complemented
173C2×#626—28no—
174C2×#626C22×C311yescharacteristic
175C2×#626C22×C312yescomplemented
176C2×#626C22×C312yescomplemented
177C2×#626C22×C312yescomplemented
178C2×#626C22×C312yescomplemented
179C32×C4⋊C4—31no—
180C32×C22⋊C4—32no—
181C32×C42—31no—
182C3×#217—22no—
183C3×#217—31no—
184C3×#217—32no—
185C3×#217C2×D312yescomplemented
186C3×#217C22×C312yescomplemented
187C3×(C2×D3)⋊C4—31no—
188C3×(C2×D3)⋊C4—32no—
189C3×(C2×D3)⋊C4—31no—
190C3×(C2×D3)⋊C4—32no—
191C3×(C2×D3)⋊C4—31no—
192C3×(C2×D3)⋊C4—32no—
193C3×C4⋊Dic3—21no—
194C3×C4⋊Dic3—31no—
195C3×C4⋊Dic3C2×D311yescharacteristic, complemented
196C3×C4⋊Dic3C22×C311yescharacteristic, complemented
197C3×Dic3⋊C4—31no—
198C3×C4×Dic3—21no—
199C3×C4×Dic3C2×D311yescharacteristic, complemented
200C3×C4×Dic3C22×C311yescharacteristic, complemented
201Dic3⋊Dic3C22×C311yescharacteristic, complemented
202#3722C22×C311yescharacteristic, complemented
203#3722C22×C312yescomplemented
204(C2×D3)⋊Dic3C22×C311yescharacteristic, complemented
205(C2×D3)⋊Dic3C22×C312yescomplemented
206C22×C33—22no—
207C22×C33—22no—
208C22×C33C2×D414yescomplemented
209C22×C33C2411yescharacteristic
210C2×C3×C3⋊D3—21no—
211C2×C3×C3⋊D3—21no—
212C2×C3×C3⋊D3—22no—
213C2×C3×C3⋊D3—22no—
214C2×C3×C3⋊D3—22no—
215C2×C3×C3⋊D3—48no—
216C2×C3×C3⋊D3C2×D412yescomplemented
217C2×C32×D3—21no—
218C2×C32×D3—21no—
219C2×C32×D3—22no—
220C2×C32×D3—22no—
221C2×C32×D3—22no—
222C2×C32×D3—48no—
223C2×C32×D3C2×D412yescomplemented
224C33×C4C2×D412yescomplemented
225C3×C3⋊Dic3—21no—
226C32×Dic3—21no—
227C32×Dic3—22no—
228C32×Dic3—21no—
229C32×Dic3C2×D412yescomplemented
230C22×C3×D4—31no—
231C22×C3×D4—31no—
232C22×C3×D4—61no—
233C22×C3×D4—92no—
234C22×C3×D4—91no—
235C22×#67—32no—
236C2×D3×D4—31no—
237C2×D3×D4—31no—
238C2×D3×D4—61no—
239C2×D3×D4C3×D311yescharacteristic, complemented
240C22×D12—32no—
241C3×#127—91no—
242C3×#121—91no—
243C3×#121—91no—
244C3×#121—92no—
245C3×#120—92no—
246C3×#120—92no—
247C3×C4×D4—31no—
248C3×C4×D4—31no—
249C3×C4×D4—61no—
250C3×C4×D4—91no—
251#953—32no—
252#940—31no—
253#939—32no—
254#938—31no—
255#937—32no—
256D4×Dic3C3×D311yescharacteristic, complemented
257#930—32no—
258#930—31no—
259C4×#67—31no—
260#895—31no—
261#895—31no—
262#882—32no—
263#882—32no—
264#874—31no—
265C4×D12—31no—
266C23×C32—22no—
267C23×C32—22no—
268C23×C32—22no—
269C23×C32—31no—
270C23×C32—32no—
271C23×C32—42no—
272C23×C32—64no—
273C23×C32—64no—
274C23×C32—122no—
275C23×C32C22×D312yes—
276C23×C32C22×D312yes—
277C23×C32C23×C312yes—
278C22×C3⋊D3—24no—
279C22×C3⋊D3—24no—
280C22×C3⋊D3—42no—
281C22×C3⋊D3C23×C312yes—
282C22×C3⋊D3C23×C311yescharacteristic
283C22×C3×D3—28no—
284C22×C3×D3—24no—
285C22×C3×D3—24no—
286C22×C3×D3—24no—
287C22×C3×D3—24no—
288C22×C3×D3—21no—
289C22×C3×D3—22no—
290C22×C3×D3—31no—
291C22×C3×D3—31no—
292C22×C3×D3—32no—
293C22×C3×D3—32no—
294C22×C3×D3—44no—
295C22×C3×D3—42no—
296C22×C3×D3—42no—
297C22×C3×D3—44no—
298C22×C3×D3—61no—
299C22×C3×D3—62no—
300C22×C3×D3—64no—
301C22×C3×D3—64no—
302C22×C3×D3—68no—
303C22×C3×D3—64no—
304C22×C3×D3—64no—
305C22×C3×D3—124no—
306C22×C3×D3—122no—
307C22×C3×D3—122no—
308C22×C3×D3—124no—
309C22×C3×D3C22×D312yes—
310C22×C3×D3C22×D311yescharacteristic
311C22×C3×D3C23×C312yes—
312C22×C3×D3C23×C311yescharacteristic
313C32×D4—24no—
314C32×D4—24no—
315C32×D4—24no—
316C32×D4—44no—
317C32×D4—64no—
318C32×D4—62no—
319C32×D4D1214yescomplemented
320C32×D4#6714yescomplemented
321C32×D4C3×D414yescomplemented
322C2×C32×C4—21no—
323C2×C32×C4—21no—
324C2×C32×C4—21no—
325C2×C32×C4—31no—
326C2×C32×C4—31no—
327C2×C32×C4—31no—
328C2×C32×C4—32no—
329C2×C32×C4—41no—
330C2×C32×C4—62no—
331C2×C32×C4—64no—
332C2×C32×C4C22×D311yescharacteristic
333C2×C32×C4C22×D311yescharacteristic
334C2×C32×C4C23×C311yescharacteristic
335#638—24no—
336C2×C3⋊Dic3C23×C311yescharacteristic
337C4⋊(C3⋊D3)—22no—
338C4×C3⋊D3—22no—
339C3×#67—28no—
340C3×#67—24no—
341C3×#67—24no—
342C3×#67—34no—
343C3×#67—64no—
344C3×#67—64no—
345C3×#67—68no—
346C3×#67—64no—
347C3×#67—64no—
348C3×#67—64no—
349C3×#67—122no—
350C2×C3×Dic3—24no—
351C2×C3×Dic3—24no—
352C2×C3×Dic3—21no—
353C2×C3×Dic3—21no—
354C2×C3×Dic3—21no—
355C2×C3×Dic3—22no—
356C2×C3×Dic3—31no—
357C2×C3×Dic3—31no—
358C2×C3×Dic3—44no—
359C2×C3×Dic3—61no—
360C2×C3×Dic3C22×D311yescharacteristic
361C2×C3×Dic3C22×D311yescharacteristic
362C2×C3×Dic3C22×D312yes—
363C2×C3×Dic3C22×D311yescharacteristic
364C2×C3×Dic3C23×C311yescharacteristic
365C2×C3×Dic3C23×C312yes—
366C2×C3×Dic3C23×C311yescharacteristic
367C2×C3×Dic3C23×C311yescharacteristic
368C3×D12—24no—
369C3×D12—22no—
370C3×D12—22no—
371C3×D12—34no—
372C3×D12—64no—
373C3×D12—64no—
374C3×D12—64no—
375C3×D12—64no—
376C3×D12—62no—
377C3×D12—62no—
378C3×D12—122no—
379C3×C4×D3—24no—
380C3×C4×D3—22no—
381C3×C4×D3—22no—
382C3×C4×D3—64no—
383C3×C4×D3—62no—
384C3×C4×D3—62no—
385#626—24no—
386#626—24no—
387#626—24no—
388#626—42no—
389#626C3×D414yesdirect product factor
390D42—91noSylow
391C2×C33—24no—
392C2×C33C22×D411yescharacteristic
393C2×C33C22×D411yescharacteristic
394C2×C33H(5,𝔽2)11yescharacteristic
395C3×C3⋊D3—22no—
396C3×C3⋊D3—42no—
397C32×D3—22no—
398C32×D3—42no—
399C24×C3—32no—
400C24×C3—32no—
401C24×C3—62no—
402C24×C3—92no—
403C23×D3—32no—
404C23×D3—32no—
405C23×D3—62no—
406C23×D3C2×C3×D312yescomplemented
407C2×C3×D4—21no—
408C2×C3×D4—21no—
409C2×C3×D4—21no—
410C2×C3×D4—32no—
411C2×C3×D4—32no—
412C2×C3×D4—31no—
413C2×C3×D4—31no—
414C2×C3×D4—41no—
415C2×C3×D4—61no—
416C2×C3×D4—62no—
417C2×C3×D4—68no—
418C2×C3×D4—64no—
419C2×C3×D4—64no—
420C2×C3×D4—91no—
421C2×C3×D4—92no—
422C2×C3×D4—92no—
423C2×C3×D4—92no—
424C2×C3×D4—92no—
425C2×C3×D4—92no—
426C2×C3×D4—91no—
427C2×C3×D4—188no—
428C2×C3×D4—184no—
429C2×C3×D4D3211yescharacteristic
430C2×C3×D4C2×C3×D311yescharacteristic
431C2×C3×D4C2×C3×D311yescharacteristic
432C22×C3×C4—32no—
433C22×C3×C4—32no—
434C22×C3×C4—31no—
435C22×C3×C4—31no—
436C22×C3×C4—61no—
437C22×C3×C4—62no—
438C22×C3×C4—91no—
439C2×#67—32no—
440C2×#67—32no—
441C2×#67—31no—
442C2×#67—32no—
443C2×#67—32no—
444C2×#67—32no—
445C2×#67—32no—
446C2×#67—62no—
447C2×#67—68no—
448C2×#67C2×C3×D312yescomplemented
449C22×Dic3C2×C3×D312yescomplemented
450D3×D4—24no—
451D3×D4—68no—
452D3×D4—64no—
453D3×D4—64no—
454C2×D12—31no—
455C2×D12—32no—
456C2×D12—32no—
457C2×D12—32no—
458C2×D12—31no—
459C2×D12—31no—
460C2×D12—32no—
461C2×D12—61no—
462C2×D12—68no—
463C2×D12C2×C3×D311yescharacteristic, complemented
464C2×C4×D3—31no—
465C2×C4×D3—31no—
466C2×C4×D3—61no—
467C2×C4×D3C2×C3×D311yescharacteristic, complemented
468C3×C4⋊C4—31no—
469C3×C4⋊C4—31no—
470C3×C4⋊C4—61no—
471C3×C4⋊C4—91no—
472C3×C22⋊C4—32no—
473C3×C22⋊C4—32no—
474C3×C22⋊C4—62no—
475C3×C22⋊C4—91no—
476C3×C22⋊C4—92no—
477C3×C22⋊C4—91no—
478C3×C22⋊C4—92no—
479C3×C42—31no—
480C3×C42—31no—
481C3×C42—61no—
482#217—31no—
483#217—32no—
484#217C2×C3×D312yescomplemented
485(C2×D3)⋊C4—31no—
486(C2×D3)⋊C4—32no—
487(C2×D3)⋊C4—31no—
488(C2×D3)⋊C4—32no—
489(C2×D3)⋊C4—31no—
490(C2×D3)⋊C4—32no—
491C4⋊Dic3—31no—
492C4⋊Dic3C2×C3×D311yescharacteristic, complemented
493Dic3⋊C4—31no—
494C4×Dic3C2×C3×D311yescharacteristic, complemented
495C22×C32—22no—
496C22×C32—22no—
497C22×C32—22no—
498C22×C32—22no—
499C22×C32—22no—
500C22×C32—22no—
501C22×C32—21no—
502C22×C32—21no—
503C22×C32—21no—
504C22×C32—24no—
505C22×C32—24no—
506C22×C32—24no—
507C22×C32—32no—
508C22×C32—41no—
509C22×C32—44no—
510C22×C32—42no—
511C22×C32—42no—
512C22×C32—42no—
513C22×C32—42no—
514C22×C32—42no—
515C22×C32—42no—
516C22×C32—61no—
517C22×C32—61no—
518C22×C32—62no—
519C22×C32—62no—
520C22×C32—62no—
521C22×C32—82no—
522C22×C32—82no—
523C22×C32—128no—
524C22×C32C2×D1214yescomplemented
525C22×C32C2×#6714yescomplemented
526C22×C32C2×C3×D414yescomplemented
527C22×C32C23×D311yescharacteristic
528C22×C32C23×D311yescharacteristic
529C22×C32C24×C311yescharacteristic
530C2×C3⋊D3—21no—
531C2×C3⋊D3—21no—
532C2×C3⋊D3—22no—
533C2×C3⋊D3—22no—
534C2×C3⋊D3—22no—
535C2×C3⋊D3—48no—
536C2×C3⋊D3C2×C3×D412yescomplemented
537C2×C3×D3—22no—
538C2×C3×D3—22no—
539C2×C3×D3—21no—
540C2×C3×D3—21no—
541C2×C3×D3—21no—
542C2×C3×D3—21no—
543C2×C3×D3—24no—
544C2×C3×D3—22no—
545C2×C3×D3—22no—
546C2×C3×D3—22no—
547C2×C3×D3—22no—
548C2×C3×D3—22no—
549C2×C3×D3—22no—
550C2×C3×D3—22no—
551C2×C3×D3—32no—
552C2×C3×D3—32no—
553C2×C3×D3—42no—
554C2×C3×D3—42no—
555C2×C3×D3—48no—
556C2×C3×D3—48no—
557C2×C3×D3—416no—
558C2×C3×D3—62no—
559C2×C3×D3—62no—
560C2×C3×D3—62no—
561C2×C3×D3—61no—
562C2×C3×D3—61no—
563C2×C3×D3—61no—
564C2×C3×D3—61no—
565C2×C3×D3—64no—
566C2×C3×D3—62no—
567C2×C3×D3—62no—
568C2×C3×D3—62no—
569C2×C3×D3—62no—
570C2×C3×D3—62no—
571C2×C3×D3—62no—
572C2×C3×D3—122no—
573C2×C3×D3—122no—
574C2×C3×D3—128no—
575C2×C3×D3—128no—
576C2×C3×D3—1216no—
577C2×C3×D3D3×D412yescomplemented
578C2×C3×D3C2×C3×D412yescomplemented
579C32×C4—22no—
580C32×C4—22no—
581C32×C4—22no—
582C32×C4—32no—
583C32×C4—42no—
584C32×C4—61no—
585C32×C4—62no—
586C32×C4—61no—
587C32×C4C2×D1212yescomplemented
588C32×C4C2×#6712yescomplemented
589C32×C4C2×C3×D412yescomplemented
590C3⋊Dic3—21no—
591C3×Dic3—22no—
592C3×Dic3—22no—
593C3×Dic3—21no—
594C3×Dic3—21no—
595C3×Dic3—22no—
596C3×Dic3—21no—
597C3×Dic3—21no—
598C3×Dic3—22no—
599C3×Dic3—41no—
600C3×Dic3—42no—
601C3×Dic3—62no—
602C3×Dic3—61no—
603C3×Dic3—61no—
604C3×Dic3D3×D412yescomplemented
605C3×Dic3C2×C3×D412yescomplemented
606C22×D4—31no—
607C22×D4—92no—
608C22×D4—91no—
609#127—91no—
610#121—91no—
611#121—91no—
612#121—92no—
613#120—92no—
614#120—92no—
615C4×D4—31no—
616C4×D4—91no—
617C33D4211yescharacteristic, complemented, Sylow
618C23×C3—22no—
619C23×C3—22no—
620C23×C3—22no—
621C23×C3—31no—
622C23×C3—31no—
623C23×C3—32no—
624C23×C3—32no—
625C23×C3—42no—
626C23×C3—61no—
627C23×C3—62no—
628C23×C3—64no—
629C23×C3—64no—
630C23×C3—68no—
631C23×C3—64no—
632C23×C3—64no—
633C23×C3—91no—
634C23×C3—92no—
635C23×C3—124no—
636C23×C3—122no—
637C23×C3—122no—
638C23×C3—124no—
639C23×C3—184no—
640C23×C3—184no—
641C23×C3—362no—
642C23×C3C2×D3212yes—
643C23×C3C22×C3×D312yes—
644C23×C3C22×C3×D312yes—
645C22×D3—24no—
646C22×D3—24no—
647C22×D3—31no—
648C22×D3—31no—
649C22×D3—32no—
650C22×D3—32no—
651C22×D3—42no—
652C22×D3—61no—
653C22×D3—62no—
654C22×D3—64no—
655C22×D3—64no—
656C22×D3—68no—
657C22×D3—64no—
658C22×D3—64no—
659C22×D3—124no—
660C22×D3—122no—
661C22×D3—122no—
662C22×D3—124no—
663C22×D3C22×C3×D312yes—
664C22×D3C22×C3×D311yescharacteristic
665C3×D4—24no—
666C3×D4—24no—
667C3×D4—24no—
668C3×D4—44no—
669C3×D4—64no—
670C3×D4—68no—
671C3×D4—64no—
672C3×D4—64no—
673C3×D4—62no—
674C3×D4—62no—
675C3×D4—94no—
676C3×D4—184no—
677C3×D4—184no—
678C3×D4—184no—
679C3×D4—184no—
680C3×D4—182no—
681C3×D4—362no—
682C3×D4#62614yesdirect product factor
683C3×D4C3×D1214yescomplemented
684C3×D4C3×#6714yescomplemented
685C2×C3×C4—21no—
686C2×C3×C4—21no—
687C2×C3×C4—21no—
688C2×C3×C4—31no—
689C2×C3×C4—31no—
690C2×C3×C4—31no—
691C2×C3×C4—32no—
692C2×C3×C4—31no—
693C2×C3×C4—31no—
694C2×C3×C4—31no—
695C2×C3×C4—32no—
696C2×C3×C4—41no—
697C2×C3×C4—61no—
698C2×C3×C4—61no—
699C2×C3×C4—61no—
700C2×C3×C4—62no—
701C2×C3×C4—64no—
702C2×C3×C4—64no—
703C2×C3×C4—64no—
704C2×C3×C4—62no—
705C2×C3×C4—62no—
706C2×C3×C4—91no—
707C2×C3×C4—124no—
708C2×C3×C4—182no—
709C2×C3×C4C2×D3211yescharacteristic
710C2×C3×C4C22×C3×D311yescharacteristic
711C2×C3×C4C22×C3×D311yescharacteristic
712#67—24no—
713#67—34no—
714#67—64no—
715#67—64no—
716#67—68no—
717#67—64no—
718#67—64no—
719#67—64no—
720#67—122no—
721C2×Dic3—24no—
722C2×Dic3—31no—
723C2×Dic3—31no—
724C2×Dic3—61no—
725C2×Dic3C22×C3×D311yescharacteristic
726C2×Dic3C22×C3×D311yescharacteristic
727C2×Dic3C22×C3×D312yes—
728C2×Dic3C22×C3×D311yescharacteristic
729D12—22no—
730D12—34no—
731D12—64no—
732D12—64no—
733D12—64no—
734D12—64no—
735D12—62no—
736D12—62no—
737D12—122no—
738C4×D3—22no—
739C4×D3—64no—
740C4×D3—62no—
741C4×D3—62no—
742C2×C32—24no—
743C2×C32—24no—
744C2×C32—24no—
745C2×C32—21no—
746C2×C32—21no—
747C2×C32—21no—
748C2×C32—21no—
749C2×C32—21no—
750C2×C32—21no—
751C2×C32—21no—
752C2×C32—21no—
753C2×C32—21no—
754C2×C32—41no—
755C2×C32—41no—
756C2×C32—41no—
757C2×C32—44no—
758C2×C32—44no—
759C2×C32—44no—
760C2×C32—62no—
761C2×C32—84no—
762C2×C32—122no—
763C2×C32C22×D1211yescharacteristic
764C2×C32C2×D3×D411yescharacteristic
765C2×C32C2×D3×D411yescharacteristic
766C2×C32#100411yescharacteristic
767C2×C32#100911yescharacteristic
768C2×C32C22×#6711yescharacteristic
769C2×C32C22×C3×D411yescharacteristic
770C2×C32C22×C3×D411yescharacteristic
771C2×C32C3×H(5,𝔽2)11yescharacteristic
772C3⋊D3—22no—
773C3⋊D3—42no—
774C3×D3—24no—
775C3×D3—22no—
776C3×D3—22no—
777C3×D3—44no—
778C3×D3—42no—
779C3×D3—42no—
780C3×D3—64no—
781C3×D3—62no—
782C3×D3—62no—
783C3×D3—124no—
784C3×D3—122no—
785C3×D3—122no—
786C24—32no—
787C24—92no—
788C2×D4—32no—
789C2×D4—31no—
790C2×D4—64no—
791C2×D4—91no—
792C2×D4—92no—
793C2×D4—92no—
794C2×D4—92no—
795C2×D4—92no—
796C2×D4—92no—
797C2×D4—91no—
798C2×D4—188no—
799C2×D4—184no—
800C2×D4C3×D3211yescharacteristic
801C22×C4—32no—
802C22×C4—31no—
803C22×C4—91no—
804C4⋊C4—31no—
805C4⋊C4—91no—
806C22⋊C4—32no—
807C22⋊C4—91no—
808C22⋊C4—92no—
809C22⋊C4—91no—
810C22⋊C4—92no—
811C42—31no—
812C22×C3—22no—
813C22×C3—22no—
814C22×C3—22no—
815C22×C3—22no—
816C22×C3—22no—
817C22×C3—22no—
818C22×C3—21no—
819C22×C3—21no—
820C22×C3—21no—
821C22×C3—24no—
822C22×C3—24no—
823C22×C3—24no—
824C22×C3—32no—
825C22×C3—32no—
826C22×C3—42no—
827C22×C3—42no—
828C22×C3—42no—
829C22×C3—42no—
830C22×C3—42no—
831C22×C3—42no—
832C22×C3—41no—
833C22×C3—44no—
834C22×C3—62no—
835C22×C3—62no—
836C22×C3—62no—
837C22×C3—64no—
838C22×C3—61no—
839C22×C3—61no—
840C22×C3—61no—
841C22×C3—61no—
842C22×C3—62no—
843C22×C3—62no—
844C22×C3—62no—
845C22×C3—62no—
846C22×C3—62no—
847C22×C3—62no—
848C22×C3—82no—
849C22×C3—82no—
850C22×C3—92no—
851C22×C3—122no—
852C22×C3—122no—
853C22×C3—128no—
854C22×C3—128no—
855C22×C3—1216no—
856C22×C3—181no—
857C22×C3—181no—
858C22×C3—182no—
859C22×C3—182no—
860C22×C3—182no—
861C22×C3—368no—
862C22×C3C2×#62614yescomplemented
863C22×C3C2×C3×D1214yescomplemented
864C22×C3C2×C3×#6714yescomplemented
865C22×C3C22×D3211yescharacteristic
866C22×C3C23×C3×D311yescharacteristic
867C22×C3C23×C3×D311yescharacteristic
868C2×D3—21no—
869C2×D3—21no—
870C2×D3—22no—
871C2×D3—22no—
872C2×D3—22no—
873C2×D3—32no—
874C2×D3—32no—
875C2×D3—48no—
876C2×D3—62no—
877C2×D3—62no—
878C2×D3—62no—
879C2×D3—61no—
880C2×D3—61no—
881C2×D3—61no—
882C2×D3—61no—
883C2×D3—64no—
884C2×D3—62no—
885C2×D3—62no—
886C2×D3—62no—
887C2×D3—62no—
888C2×D3—62no—
889C2×D3—62no—
890C2×D3—122no—
891C2×D3—122no—
892C2×D3—128no—
893C2×D3—128no—
894C2×D3—1216no—
895C2×D3C3×D3×D412yescomplemented
896C3×C4—22no—
897C3×C4—22no—
898C3×C4—22no—
899C3×C4—32no—
900C3×C4—32no—
901C3×C4—42no—
902C3×C4—62no—
903C3×C4—62no—
904C3×C4—62no—
905C3×C4—61no—
906C3×C4—61no—
907C3×C4—61no—
908C3×C4—62no—
909C3×C4—61no—
910C3×C4—122no—
911C3×C4—121no—
912C3×C4—181no—
913C3×C4C2×#62612yescomplemented
914C3×C4C2×C3×D1212yescomplemented
915C3×C4C2×C3×#6712yescomplemented
916Dic3—22no—
917Dic3—21no—
918Dic3—21no—
919Dic3—62no—
920Dic3—61no—
921Dic3—61no—
922Dic3C3×D3×D412yescomplemented
923C32—21no—
924C32—21no—
925C32—21no—
926C32—41no—
927C32D4×D1211yescharacteristic, complemented
928C32D4×#6711yescharacteristic, complemented
929C32C3×D4211yescharacteristic, complemented
930C23—31no—
931C23—32no—
932C23—64no—
933C23—64no—
934C23—91no—
935C23—92no—
936C23—122no—
937C23—184no—
938C23—184no—
939C23—362no—
940C23C2×C3×D3212yes—
941D4—64no—
942D4—62no—
943D4—94no—
944D4—184no—
945D4—184no—
946D4—184no—
947D4—184no—
948D4—182no—
949D4—362no—
950D4C3×#62614yesdirect product factor
951C2×C4—31no—
952C2×C4—31no—
953C2×C4—32no—
954C2×C4—31no—
955C2×C4—64no—
956C2×C4—62no—
957C2×C4—91no—
958C2×C4—182no—
959C2×C4C2×C3×D3211yescharacteristic
960C2×C3—24no—
961C2×C3—24no—
962C2×C3—24no—
963C2×C3—21no—
964C2×C3—21no—
965C2×C3—21no—
966C2×C3—21no—
967C2×C3—21no—
968C2×C3—21no—
969C2×C3—21no—
970C2×C3—21no—
971C2×C3—21no—
972C2×C3—44no—
973C2×C3—44no—
974C2×C3—44no—
975C2×C3—41no—
976C2×C3—41no—
977C2×C3—41no—
978C2×C3—64no—
979C2×C3—62no—
980C2×C3—62no—
981C2×C3—84no—
982C2×C3—124no—
983C2×C3—122no—
984C2×C3—122no—
985C2×C3—182no—
986C2×C3—362no—
987C2×C3D32×D411yescharacteristic
988C2×C3#6431411yescharacteristic
989C2×C3C22×#62611yescharacteristic
990C2×C3C22×C3×D1211yescharacteristic
991C2×C3C2×C3×D3×D411yescharacteristic
992C2×C3C2×C3×D3×D411yescharacteristic
993C2×C3C3×#100411yescharacteristic
994C2×C3C3×#100911yescharacteristic
995C2×C3C22×C3×#6711yescharacteristic
996D3—22no—
997D3—42no—
998D3—64no—
999D3—62no—
1000D3—62no—
1001D3—124no—
1002D3—122no—
1003D3—122no—
1004C22—22no—
1005C22—22no—
1006C22—32no—
1007C22—61no—
1008C22—61no—
1009C22—62no—
1010C22—62no—
1011C22—62no—
1012C22—92no—
1013C22—128no—
1014C22—181no—
1015C22—181no—
1016C22—182no—
1017C22—182no—
1018C22—182no—
1019C22—368no—
1020C22C2×C3×#62614yescomplemented
1021C22C22×C3×D3211yescharacteristic
1022C4—32no—
1023C4—61no—
1024C4—62no—
1025C4—61no—
1026C4—181no—
1027C4C2×C3×#62612yescomplemented
1028C3—21no—
1029C3—21no—
1030C3—21no—
1031C3—41no—
1032C3D4×#62611yescharacteristic, direct product factor
1033C3C3×D4×D1211yescharacteristic, complemented
1034C3C3×D4×#6711yescharacteristic, complemented
1035C2—24no—
1036C2—62no—
1037C2—122no—
1038C2—182no—
1039C2—362no—
1040C2C3×D32×D411yescharacteristic
1041C2C3×#6431411yescharacteristic
1042C2C22×C3×#62611yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC2×C33×D4C22
socleC22×C33C24
hypercenterC2×C3×D4D32
hypocenterC32C3×D42
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C2×C3×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3×D4×C3⋊D3C2semidirect
2. C2×C32×D3×D4C2semidirect
3. C22×C3×#626C2semidirect
4. C32×D4×Dic3C2semidirect
5. C3×#63981C2semidirect
6. C3×#63978C2semidirect
7. C3×#63977C2semidirect
8. C3×#63916C2semidirect
9. C3×#63911C2semidirect
10. C3×#63909C2semidirect
11. C3×C4×#626C2semidirect
14. D4×#626C3direct (N × H)
15. C23×C3×C3⋊D3C22semidirect
16. C23×C32×D3C22semidirect
18. C2×C3×#638C22semidirect
20. C2×C3×C4⋊(C3⋊D3)C22semidirect
21. C2×C3×C4×C3⋊D3C22semidirect
22. C2×C32×#67C22semidirect
23. C22×C32×Dic3C22semidirect
25. C2×C32×D12C22semidirect
26. C2×C32×C4×D3C22semidirect
29. C2×C3×#626C22semidirect
30. C2×C3×#626C22semidirect
31. C2×C3×#626C22semidirect
32. C2×C3×#626C22semidirect
33. C32×#217C22semidirect
34. C32×C4⋊Dic3C22semidirect
35. C32×C4×Dic3C22semidirect
36. C3×Dic3⋊Dic3C22semidirect
37. C3×#3722C22semidirect
38. C3×#3722C22semidirect
39. C3×(C2×D3)⋊Dic3C22semidirect
40. C3×(C2×D3)⋊Dic3C22semidirect
42. C2×D4×C3⋊D3C2×C3semidirect
48. C2×C3×D3×D4D3semidirect
49. C2×C3×D3×D4C2×C3semidirect
51. C22×#626C2×C3semidirect
59. C3×D4×Dic3D3semidirect
60. C3×D4×Dic3C2×C3semidirect
70. #63981C2×C3semidirect
71. #63978C2×C3semidirect
72. #63977C2×C3semidirect
73. #63916C2×C3semidirect
74. #63911C2×C3semidirect
75. #63909C2×C3semidirect
76. C4×#626C2×C3semidirect
88. C33×D4D4semidirect
106. C3×#626D4direct (N × H)
111. C23×C3⋊D3C22×C3semidirect
116. C23×C3×D3C2×D3semidirect
117. C23×C3×D3C22×C3semidirect
130. C2×#638C22×C3semidirect
132. C2×C4⋊(C3⋊D3)C22×C3semidirect
133. C2×C4×C3⋊D3C22×C3semidirect
144. C2×C3×#67C2×D3semidirect
145. C2×C3×#67C22×C3semidirect
147. C22×C3×Dic3C2×D3semidirect
148. C22×C3×Dic3C22×C3semidirect
165. C2×C3×D12C2×D3semidirect
166. C2×C3×D12C22×C3semidirect
171. C2×C3×C4×D3C2×D3semidirect
172. C2×C3×C4×D3C22×C3semidirect
175. C2×#626C22×C3semidirect
176. C2×#626C22×C3semidirect
177. C2×#626C22×C3semidirect
178. C2×#626C22×C3semidirect
185. C3×#217C2×D3semidirect
186. C3×#217C22×C3semidirect
195. C3×C4⋊Dic3C2×D3semidirect
196. C3×C4⋊Dic3C22×C3semidirect
199. C3×C4×Dic3C2×D3semidirect
200. C3×C4×Dic3C22×C3semidirect
201. Dic3⋊Dic3C22×C3semidirect
202. #3722C22×C3semidirect
203. #3722C22×C3semidirect
204. (C2×D3)⋊Dic3C22×C3semidirect
205. (C2×D3)⋊Dic3C22×C3semidirect
208. C22×C33C2×D4semidirect
216. C2×C3×C3⋊D3C2×D4semidirect
223. C2×C32×D3C2×D4semidirect
224. C33×C4C2×D4semidirect
229. C32×Dic3C2×D4semidirect
239. C2×D3×D4C3×D3semidirect
256. D4×Dic3C3×D3semidirect
319. C32×D4D12semidirect
320. C32×D4#67semidirect
321. C32×D4C3×D4semidirect
389. #626C3×D4direct (N × H)
406. C23×D3C2×C3×D3semidirect
448. C2×#67C2×C3×D3semidirect
449. C22×Dic3C2×C3×D3semidirect
463. C2×D12C2×C3×D3semidirect
467. C2×C4×D3C2×C3×D3semidirect
484. #217C2×C3×D3semidirect
492. C4⋊Dic3C2×C3×D3semidirect
494. C4×Dic3C2×C3×D3semidirect
524. C22×C32C2×D12semidirect
525. C22×C32C2×#67semidirect
526. C22×C32C2×C3×D4semidirect
536. C2×C3⋊D3C2×C3×D4semidirect
577. C2×C3×D3D3×D4semidirect
578. C2×C3×D3C2×C3×D4semidirect
587. C32×C4C2×D12semidirect
588. C32×C4C2×#67semidirect
589. C32×C4C2×C3×D4semidirect
604. C3×Dic3D3×D4semidirect
605. C3×Dic3C2×C3×D4semidirect
617. C33D42semidirect
682. C3×D4#626direct (N × H)
683. C3×D4C3×D12semidirect
684. C3×D4C3×#67semidirect
862. C22×C3C2×#626semidirect
863. C22×C3C2×C3×D12semidirect
864. C22×C3C2×C3×#67semidirect
895. C2×D3C3×D3×D4semidirect
913. C3×C4C2×#626semidirect
914. C3×C4C2×C3×D12semidirect
915. C3×C4C2×C3×#67semidirect
922. Dic3C3×D3×D4semidirect
927. C32D4×D12semidirect
928. C32D4×#67semidirect
929. C32C3×D42semidirect
950. D4C3×#626direct (N × H)
1020. C22C2×C3×#626semidirect
1027. C4C2×C3×#626semidirect
1032. C3D4×#626direct (N × H)
1033. C3C3×D4×D12semidirect
1034. C3C3×D4×#67semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D4×C3⋊D32
C2×C32×D3×D42
C22×C3×#6262
C32×D4×Dic32
C3×#639812
C3×#639782
C3×#639772
C3×#639162
C3×#639112
C3×#639092
C3×C4×#6262
C3×D4×#673
C3×D4×D123
D4×#6263