Finite Group Databasebeta

← C2×#10595065 #11902421

Subgroups — C2×#10595065 #11902421

Order 1152.

3971 conjugacy classes of subgroups.

The subgroup lattice has 1110 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#235C211yesmaximal, characteristic, complemented
2C22×D3×#67C211yesmaximal, characteristic, complemented
3C2×#64138C211yesmaximal, characteristic, complemented
4C22×C3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
5C2×#63978C211yesmaximal, characteristic, complemented
6C2×#63976C211yesmaximal, characteristic, complemented
7C2×Dic3×#67C211yesmaximal, characteristic, complemented
8#10595065C2116yesmaximal, direct product factor
9C2×#63922C211yesmaximal, characteristic, complemented
10C2×D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
11C2×#63907C211yesmaximal, characteristic, complemented
12C2×#63906C211yesmaximal, characteristic, complemented
13C2×#63905C211yesmaximal, characteristic, complemented
14C2×#63887C211yesmaximal, characteristic, complemented
15C2×#63885C211yesmaximal, characteristic, complemented
16C2×#63879C211yesmaximal, characteristic, complemented
17C2×#5829—31nomaximal
18C2×#5490—31nomaximal
19C24×C3×D3C2211yescharacteristic
20C23×D32C2211yescharacteristic
21C23×C32×C4C2211yescharacteristic, complemented
22C22×#638C2211yescharacteristic
23C22×C3×#67C2211yescharacteristic
24C22×C3×#67C2211yescharacteristic, complemented
25C23×C3×Dic3C2211yescharacteristic, complemented
26C2×C3×#235—28no—
27C2×C3×#235C2218yescomplemented
28C22×C3×D12C2211yescharacteristic, complemented
29C22×C3×C4×D3C2211yescharacteristic, complemented
30C22×C3×C4×D3C2211yescharacteristic, complemented
31C22×C3×Dic6C2211yescharacteristic, complemented
32C2×D3×#67—28no—
33C2×D3×#67C2218yescomplemented
34C22×#626C2211yescharacteristic
35C22×#626C2211yescharacteristic, complemented
36C22×#625C2211yescharacteristic
37C22×#625C2211yescharacteristic
38C22×#625C2211yescharacteristic, complemented
39C22×D3×Dic3C2211yescharacteristic
40C22×D3×Dic3C2211yescharacteristic, complemented
41C2×#3757C2211yescharacteristic, complemented
42#64138C2218yescomplemented
43C2×#3752C2211yescharacteristic, complemented
44C2×#3752C2211yescharacteristic, complemented
45C2×#3750C2211yescharacteristic, complemented
46C2×#3750C2211yescharacteristic, complemented
47C2×C3×(C2×D3)⋊C4C2211yescharacteristic
48C2×C3×(C2×D3)⋊C4C2211yescharacteristic
49C2×C3×(C2×D3)⋊C4C2218yescomplemented
50C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
51C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
52#63978C2218yescomplemented
53#63976C2218yescomplemented
54Dic3×#67C2218yescomplemented
55C2×Dic3⋊Dic3C2211yescharacteristic, complemented
56C2×Dic3⋊Dic3C2211yescharacteristic, complemented
57C2×#3722C2211yescharacteristic, complemented
58C2×(C2×D3)⋊Dic3C2211yescharacteristic
59C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
60C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
61C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
62C2×Dic32C2211yescharacteristic, complemented
63#63922C2218yescomplemented
64D3×(C2×D3)⋊C4C2218yescomplemented
65#63907C2218yescomplemented
66#63906C2218yescomplemented
67#63905C2218yescomplemented
68#63887C2218yescomplemented
69#63885C2218yescomplemented
70#63879C2218yescomplemented
71C22×C3×#41—31no—
72C23×#67—31no—
73C22×D3×D4—31no—
74C22×#235D311yescharacteristic, complemented
75C22×C3×C22⋊C4—31no—
76C2×#953—31no—
77#5829—316no—
78C2×#947—31no—
79C2×#946—31no—
80C2×#939—31no—
81C2×#939—31no—
82C2×#937—31no—
83C2×#937—31no—
84C2×D4×Dic3—31no—
85C2×#930—31no—
86C2×#930—31no—
87C2×#929—31no—
88C2×#929—31no—
89C2×#929—31no—
90C2×#929—61no—
91C2×C4×#67—31no—
92C2×C4×#67—31no—
93C22×(C2×D3)⋊C4—31no—
94C22×(C2×D3)⋊C4D311yescharacteristic, complemented
95C2×#885—31no—
96#5490—316no—
97C2×#884—31no—
98C2×#884—31no—
99C2×#883—31no—
100C2×#882—31no—
101C2×#67⋊C4—31no—
102C2×D3×C22⋊C4—31no—
103C2×#878—31no—
104C24×C32C2311yescharacteristic
105C23×C3⋊D3C2311yescharacteristic
106C23×C3×D3—24no—
107C23×C3×D3—24no—
108C23×C3×D3—42no—
109C23×C3×D3C2311yescharacteristic
110C23×C3×D3C2311yescharacteristic
111C23×C3×D3C2314yes—
112C23×C3×D3C2311yescharacteristic
113C23×C3×D3C2311yescharacteristic
114C22×D32—24no—
115C22×D32—24no—
116C22×D32—42no—
117C22×D32C2314yes—
118C22×C32×C4—24no—
119C22×C32×C4C2311yescharacteristic
120C22×C32×C4C2311yescharacteristic
121C22×C32×C4C2314yescomplemented
122C2×#638—24no—
123C2×#638C2314yes—
124C22×C3⋊Dic3C2311yescharacteristic
125C22×C3⋊Dic3C2311yescharacteristic
126C22×C3⋊Dic3C2311yescharacteristic
127C2×C3×#67—24no—
128C2×C3×#67D418yescomplemented
129C2×C3×#67C2314yes—
130C2×C3×#67C2314yescomplemented
131C22×C3×Dic3—42no—
132C22×C3×Dic3C2311yescharacteristic
133C22×C3×Dic3C2311yescharacteristic
134C22×C3×Dic3C2311yescharacteristic
135C22×C3×Dic3C2311yescharacteristic
136C22×C3×Dic3C2314yescomplemented
137C3×#235—232no—
138C2×C3×D12—24no—
139C2×C3×D12C2314yescomplemented
140C2×C3×C4×D3—24no—
141C2×C3×C4×D3—24no—
142C2×C3×C4×D3C2314yescomplemented
143C2×C3×C4×D3C2314yescomplemented
144C2×C3×Dic6—24no—
145C2×C3×Dic6C2314yescomplemented
146D3×#67—232no—
147C2×#626—24no—
148C2×#626—42no—
149C2×#626C2314yes—
150C2×#626C2314yescomplemented
151C2×#625—24no—
152C2×#625—24no—
153C2×#625—42no—
154C2×#625C2314yes—
155C2×#625C2314yes—
156C2×#625C2314yescomplemented
157C2×D3×Dic3—24no—
158C2×D3×Dic3—42no—
159C2×D3×Dic3C2314yes—
160C2×D3×Dic3C2314yescomplemented
161#3757C2314yescomplemented
162#3752C2314yescomplemented
163#3752C2314yescomplemented
164#3750C2314yescomplemented
165#3750C2314yescomplemented
166C3×(C2×D3)⋊C4C2314yes—
167C3×(C2×D3)⋊C4C2314yes—
168C3×(C2×D3)⋊C4C2314yescomplemented
169C3×(C2×D3)⋊C4C2314yescomplemented
170Dic3⋊Dic3C2314yescomplemented
171Dic3⋊Dic3C2314yescomplemented
172#3722C2314yescomplemented
173(C2×D3)⋊Dic3C2314yes—
174(C2×D3)⋊Dic3C2314yescomplemented
175(C2×D3)⋊Dic3C2314yescomplemented
176(C2×D3)⋊Dic3C2314yescomplemented
177Dic32C2314yescomplemented
178C2×#546—91noSylow
179C25×C3—31no—
180C24×D3—31no—
181C24×D3—31no—
182C24×D3C2×D311yescharacteristic
183C2×C3×#41—38no—
184C2×C3×#41—68no—
185C22×C3×Q8—31no—
186C22×C3×D4—31no—
187C22×C3×D4—31no—
188C22×C3×D4—31no—
189C23×C3×C4—21no—
190C23×C3×C4—31no—
191C23×C3×C4—31no—
192C23×C3×C4—31no—
193C23×C3×C4C2×D311yescharacteristic, complemented
194C23×C3×C4C2×D311yescharacteristic, complemented
195C22×#67—31no—
196C22×#67—31no—
197C22×#67—31no—
198C22×#67—31no—
199C22×#67—31no—
200C22×#67—31no—
201C22×#67—31no—
202C22×#67—31no—
203C22×#67—38no—
204C22×#67—31no—
205C22×#67—31no—
206C22×#67—61no—
207C22×#67—68no—
208C22×#67C2×D311yescharacteristic
209C22×#67C2×D311yescharacteristic, complemented
210C23×Dic3—31no—
211C23×Dic3—31no—
212C23×Dic3C2×D311yescharacteristic, complemented
213C2×D3×D4—38no—
214C2×D3×D4—68no—
215C2×#235—28no—
216C2×#235C2×D318yescomplemented
217C22×D12—31no—
218C22×D12—31no—
219C22×D12C2×D311yescharacteristic, complemented
220C22×C4×D3—31no—
221C22×C4×D3—31no—
222C22×C4×D3C2×D311yescharacteristic, complemented
223C22×C4×D3C2×D311yescharacteristic, complemented
224C22×Dic6C2×D311yescharacteristic, complemented
225C2×C3×C22⋊C4—31no—
226C2×C3×C22⋊C4—31no—
227C2×C3×C22⋊C4—31no—
228C2×C3×C22⋊C4—31no—
229C2×C3×C22⋊C4—38no—
230#953—38no—
231C2×#217—31no—
232C2×#217—31no—
233C2×#217—31no—
234C2×#217—31no—
235C2×#217—31no—
236C2×#217—31no—
237C2×#217—61no—
238#947—38no—
239#946—38no—
240#939—38no—
241#939—38no—
242#937—38no—
243#937—38no—
244D4×Dic3—38no—
245#930—38no—
246#930—38no—
247#929—38no—
248#929—38no—
249#929—38no—
250#929—68no—
251C4×#67—38no—
252C4×#67—38no—
253C2×(C2×D3)⋊C4—31no—
254C2×(C2×D3)⋊C4—31no—
255C2×(C2×D3)⋊C4—31no—
256C2×(C2×D3)⋊C4—31no—
257C2×(C2×D3)⋊C4—31no—
258C2×(C2×D3)⋊C4—31no—
259C2×(C2×D3)⋊C4—31no—
260C2×(C2×D3)⋊C4—31no—
261C2×(C2×D3)⋊C4—31no—
262C2×(C2×D3)⋊C4—31no—
263C2×(C2×D3)⋊C4—38no—
264C2×(C2×D3)⋊C4—61no—
265C2×(C2×D3)⋊C4—61no—
266C2×(C2×D3)⋊C4C2×D311yescharacteristic
267C2×(C2×D3)⋊C4C2×D311yescharacteristic
268C2×(C2×D3)⋊C4C2×D318yescomplemented
269C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
270C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
271C2×C4⋊Dic3—31no—
272C2×C4⋊Dic3—31no—
273C2×Dic3⋊C4—31no—
274C2×Dic3⋊C4—31no—
275C2×Dic3⋊C4—31no—
276C2×Dic3⋊C4—31no—
277C2×Dic3⋊C4—31no—
278C2×Dic3⋊C4—31no—
279C2×Dic3⋊C4—61no—
280C2×Dic3⋊C4—61no—
281C2×C4×Dic3—31no—
282C2×C4×Dic3—31no—
283#885—38no—
284#884—38no—
285#884—38no—
286#883—38no—
287#882—38no—
288#67⋊C4—38no—
289D3×C22⋊C4—38no—
290#878—38no—
291C23×C32—22no—
292C23×C32—22no—
293C23×C32C2×D414yes—
294C23×C32C2412yes—
295C23×C32C2411yescharacteristic
296C22×C3⋊D3—22no—
297C22×C3⋊D3—22no—
298C22×C3⋊D3—22no—
299C22×C3⋊D3C2412yes—
300C22×C3×D3—22no—
301C22×C3×D3—22no—
302C22×C3×D3—22no—
303C22×C3×D3—22no—
304C22×C3×D3—22no—
305C22×C3×D3—28no—
306C22×C3×D3—22no—
307C22×C3×D3—22no—
308C22×C3×D3—22no—
309C22×C3×D3—22no—
310C22×C3×D3—22no—
311C22×C3×D3—28no—
312C22×C3×D3—44no—
313C22×C3×D3—416no—
314C22×C3×D3C2×D414yes—
315C22×C3×D3#4114yescomplemented
316C22×C3×D3C2412yes—
317C22×C3×D3C2412yes—
318C22×C3×D3C2412yes—
319C22×C3×D3C2412yes—
320C2×D32—28no—
321C2×D32—28no—
322C2×D32—44no—
323C2×D32—416no—
324C2×C32×C4—22no—
325C2×C32×C4—22no—
326C2×C32×C4—28no—
327C2×C32×C4C2412yes—
328C2×C32×C4C2412yes—
329#638—28no—
330C2×C3⋊Dic3—22no—
331C2×C3⋊Dic3—22no—
332C2×C3⋊Dic3—22no—
333C2×C3⋊Dic3C2412yes—
334C2×C3⋊Dic3C2412yes—
335C2×C3⋊Dic3C2412yes—
336C3×#67—28no—
337C3×#67C2×D4116yescomplemented
338C2×C3×Dic3—22no—
339C2×C3×Dic3—22no—
340C2×C3×Dic3—22no—
341C2×C3×Dic3—44no—
342C2×C3×Dic3C2×D414yes—
343C2×C3×Dic3C2412yes—
344C2×C3×Dic3C2412yes—
345C2×C3×Dic3C2412yes—
346C2×C3×Dic3C2412yes—
347C3×D12—28no—
348C3×C4×D3—28no—
349C3×C4×D3—28no—
350C3×Dic6—28no—
351#626—28no—
352#626—44no—
353#625—28no—
354#625—28no—
355#625—44no—
356D3×Dic3—28no—
357D3×Dic3—44no—
358C22×#41—31no—
359C23×D4—91no—
360#546—916no—
361C2×#124—91no—
362C2×#123—91no—
363C2×#123—91no—
364C2×C22⋊Q8—91no—
365C2×#121—91no—
366C2×#121—91no—
367C2×#121—91no—
368C2×#120—91no—
369C2×#120—91no—
370C2×C4×D4—91no—
371C2×C4×D4—91no—
372C22×C22⋊C4—31no—
373C22×C22⋊C4—91no—
374C24×C3—21no—
375C24×C3—31no—
376C24×C3—31no—
377C24×C3—31no—
378C24×C3—31no—
379C24×C3—34no—
380C24×C3—64no—
381C24×C3—64no—
382C24×C3—122no—
383C24×C3C22×D311yescharacteristic
384C24×C3C22×D311yescharacteristic
385C23×D3—24no—
386C23×D3—24no—
387C23×D3—31no—
388C23×D3—31no—
389C23×D3—34no—
390C23×D3—34no—
391C23×D3—42no—
392C23×D3—61no—
393C23×D3—64no—
394C23×D3—64no—
395C23×D3—64no—
396C23×D3—64no—
397C23×D3—122no—
398C23×D3—122no—
399C23×D3C22×D311yescharacteristic
400C23×D3C22×D311yescharacteristic
401C23×D3C22×D314yes—
402C23×D3C22×D311yescharacteristic
403C23×D3C22×D311yescharacteristic
404C3×#41—632no—
405C2×C3×Q8—34no—
406C2×C3×Q8—64no—
407C2×C3×D4—38no—
408C2×C3×D4—34no—
409C2×C3×D4—34no—
410C2×C3×D4—34no—
411C2×C3×D4—64no—
412C2×C3×D4—64no—
413C22×C3×C4—24no—
414C22×C3×C4—24no—
415C22×C3×C4—21no—
416C22×C3×C4—21no—
417C22×C3×C4—24no—
418C22×C3×C4—31no—
419C22×C3×C4—31no—
420C22×C3×C4—31no—
421C22×C3×C4—31no—
422C22×C3×C4—34no—
423C22×C3×C4—34no—
424C22×C3×C4—34no—
425C22×C3×C4—44no—
426C22×C3×C4—64no—
427C22×C3×C4—64no—
428C22×C3×C4—122no—
429C22×C3×C4C22×D311yescharacteristic
430C22×C3×C4C22×D311yescharacteristic
431C22×C3×C4C22×D311yescharacteristic
432C22×C3×C4C22×D311yescharacteristic
433C22×C3×C4C22×D314yescomplemented
434C22×C3×C4C22×D314yescomplemented
435C2×#67—24no—
436C2×#67—34no—
437C2×#67—34no—
438C2×#67—34no—
439C2×#67—34no—
440C2×#67—34no—
441C2×#67—34no—
442C2×#67—34no—
443C2×#67—34no—
444C2×#67—34no—
445C2×#67—34no—
446C2×#67—64no—
447C2×#67—64no—
448C2×#67—64no—
449C2×#67—64no—
450C2×#67—64no—
451C2×#67—64no—
452C2×#67—64no—
453C2×#67—632no—
454C2×#67—64no—
455C2×#67—124no—
456C2×#67—122no—
457C2×#67—122no—
458C2×#67—122no—
459C2×#67#6718yescomplemented
460C2×#67C22×D314yes—
461C2×#67C22×D314yescomplemented
462C22×Dic3—31no—
463C22×Dic3—31no—
464C22×Dic3—31no—
465C22×Dic3—31no—
466C22×Dic3—31no—
467C22×Dic3—31no—
468C22×Dic3—34no—
469C22×Dic3—34no—
470C22×Dic3—42no—
471C22×Dic3—61no—
472C22×Dic3—61no—
473C22×Dic3—61no—
474C22×Dic3—64no—
475C22×Dic3—122no—
476C22×Dic3C22×D311yescharacteristic
477C22×Dic3C22×D311yescharacteristic
478C22×Dic3C22×D311yescharacteristic
479C22×Dic3C22×D311yescharacteristic
480C22×Dic3C22×D314yescomplemented
481D3×D4—632no—
482#235—232no—
483C2×D12—24no—
484C2×D12—34no—
485C2×D12—34no—
486C2×D12—64no—
487C2×D12—122no—
488C2×D12C22×D314yescomplemented
489C2×C4×D3—24no—
490C2×C4×D3—24no—
491C2×C4×D3—34no—
492C2×C4×D3—34no—
493C2×C4×D3—64no—
494C2×C4×D3—122no—
495C2×C4×D3C22×D314yescomplemented
496C2×C4×D3C22×D314yescomplemented
497C2×Dic6—24no—
498C2×Dic6C22×D314yescomplemented
499C3×C22⋊C4—34no—
500C3×C22⋊C4—34no—
501C3×C22⋊C4—34no—
502C3×C22⋊C4—34no—
503#217—34no—
504#217—34no—
505#217—34no—
506#217—34no—
507#217—34no—
508#217—34no—
509#217—64no—
510(C2×D3)⋊C4—34no—
511(C2×D3)⋊C4—34no—
512(C2×D3)⋊C4—34no—
513(C2×D3)⋊C4—34no—
514(C2×D3)⋊C4—34no—
515(C2×D3)⋊C4—34no—
516(C2×D3)⋊C4—34no—
517(C2×D3)⋊C4—34no—
518(C2×D3)⋊C4—34no—
519(C2×D3)⋊C4—34no—
520(C2×D3)⋊C4—64no—
521(C2×D3)⋊C4—64no—
522(C2×D3)⋊C4C22×D314yes—
523(C2×D3)⋊C4C22×D314yes—
524(C2×D3)⋊C4C22×D314yescomplemented
525(C2×D3)⋊C4C22×D314yescomplemented
526C4⋊Dic3—34no—
527C4⋊Dic3—34no—
528Dic3⋊C4—34no—
529Dic3⋊C4—34no—
530Dic3⋊C4—34no—
531Dic3⋊C4—34no—
532Dic3⋊C4—34no—
533Dic3⋊C4—34no—
534Dic3⋊C4—64no—
535Dic3⋊C4—64no—
536C4×Dic3—34no—
537C4×Dic3—34no—
538C22×C32—28no—
539C22×C32—22no—
540C22×C32—22no—
541C22×C32C22×D414yes—
542C22×C32C22×D412yes—
543C22×C32C2×#4112yes—
544C22×C32H(5,𝔽2)12yes—
545C22×C32C2511yescharacteristic
546C2×C3⋊D3—22no—
547C2×C3⋊D3—22no—
548C2×C3⋊D3—22no—
549C2×C3⋊D3—44no—
550C2×C3×D3—28no—
551C2×C3×D3—28no—
552C2×C3×D3—22no—
553C2×C3×D3—22no—
554C2×C3×D3—22no—
555C2×C3×D3—22no—
556C2×C3×D3—22no—
557C2×C3×D3—22no—
558C2×C3×D3—22no—
559C2×C3×D3—22no—
560C2×C3×D3—22no—
561C2×C3×D3—22no—
562C2×C3×D3—416no—
563C2×C3×D3—44no—
564C2×C3×D3—44no—
565C2×C3×D3C22×D414yes—
566C2×C3×D3C2×#4114yescomplemented
567D32—416no—
568C32×C4—22no—
569C32×C4—22no—
570C3⋊Dic3—22no—
571C3⋊Dic3—22no—
572C3⋊Dic3—22no—
573C3×Dic3—22no—
574C3×Dic3—22no—
575C3×Dic3—22no—
576C3×Dic3C22×D414yes—
577C25—31no—
578C25—91no—
579C2×#41—38no—
580C2×#41—68no—
581C22×Q8—31no—
582C22×D4—31no—
583C22×D4—31no—
584C22×D4—31no—
585C22×D4—91no—
586C22×D4—91no—
587C22×D4—98no—
588C22×D4—91no—
589C22×D4—91no—
590C22×D4—91no—
591C22×D4—91no—
592C22×D4—188no—
593C23×C4—31no—
594C23×C4—31no—
595C23×C4—31no—
596C23×C4—91no—
597C23×C4—91no—
598C23×C4D3211yescharacteristic, complemented
599#124—98no—
600#123—98no—
601#123—98no—
602C22⋊Q8—98no—
603#121—98no—
604#121—98no—
605#121—98no—
606#120—98no—
607#120—98no—
608C4×D4—98no—
609C4×D4—98no—
610C2×C4⋊C4—91no—
611C2×C4⋊C4—91no—
612C2×C4⋊C4—91no—
613C2×C4⋊C4—91no—
614C2×C22⋊C4—31no—
615C2×C22⋊C4—31no—
616C2×C22⋊C4—31no—
617C2×C22⋊C4—31no—
618C2×C22⋊C4—38no—
619C2×C22⋊C4—98no—
620C2×C22⋊C4—91no—
621C2×C22⋊C4—91no—
622C2×C22⋊C4—91no—
623C2×C22⋊C4—91no—
624C2×C22⋊C4—91no—
625C2×C22⋊C4—91no—
626C2×C22⋊C4—91no—
627C2×C22⋊C4—91no—
628C2×C42—91no—
629C23×C3—22no—
630C23×C3—22no—
631C23×C3—22no—
632C23×C3—22no—
633C23×C3—22no—
634C23×C3—21no—
635C23×C3—24no—
636C23×C3—34no—
637C23×C3—34no—
638C23×C3—32no—
639C23×C3—32no—
640C23×C3—32no—
641C23×C3—32no—
642C23×C3—42no—
643C23×C3—42no—
644C23×C3—68no—
645C23×C3—62no—
646C23×C3—62no—
647C23×C3—62no—
648C23×C3—62no—
649C23×C3—62no—
650C23×C3—62no—
651C23×C3—62no—
652C23×C3—62no—
653C23×C3—62no—
654C23×C3—68no—
655C23×C3—62no—
656C23×C3—124no—
657C23×C3—1216no—
658C23×C3D3×D414yes—
659C23×C3C2×#6714yes—
660C23×C3C23×D312yes—
661C23×C3C23×D312yes—
662C23×C3C23×D311yescharacteristic
663C23×C3C23×D311yescharacteristic
664C22×D3—22no—
665C22×D3—22no—
666C22×D3—22no—
667C22×D3—22no—
668C22×D3—22no—
669C22×D3—22no—
670C22×D3—28no—
671C22×D3—22no—
672C22×D3—22no—
673C22×D3—22no—
674C22×D3—22no—
675C22×D3—28no—
676C22×D3—32no—
677C22×D3—32no—
678C22×D3—44no—
679C22×D3—416no—
680C22×D3—62no—
681C22×D3—68no—
682C22×D3—68no—
683C22×D3—62no—
684C22×D3—62no—
685C22×D3—62no—
686C22×D3—62no—
687C22×D3—62no—
688C22×D3—62no—
689C22×D3—68no—
690C22×D3—68no—
691C22×D3—122no—
692C22×D3—122no—
693C22×D3—122no—
694C22×D3—124no—
695C22×D3—124no—
696C22×D3—1216no—
697C22×D3—1216no—
698C22×D3#23514yescomplemented
699C22×D3C2×#6714yes—
700C22×D3C23×D312yes—
701C22×D3C23×D312yes—
702C22×D3C23×D312yes—
703C22×D3C23×D312yes—
704C3×Q8—68no—
705C3×D4—316no—
706C3×D4—68no—
707C3×D4—68no—
708C2×C3×C4—22no—
709C2×C3×C4—22no—
710C2×C3×C4—28no—
711C2×C3×C4—22no—
712C2×C3×C4—22no—
713C2×C3×C4—28no—
714C2×C3×C4—22no—
715C2×C3×C4—22no—
716C2×C3×C4—34no—
717C2×C3×C4—32no—
718C2×C3×C4—32no—
719C2×C3×C4—32no—
720C2×C3×C4—32no—
721C2×C3×C4—42no—
722C2×C3×C4—42no—
723C2×C3×C4—48no—
724C2×C3×C4—68no—
725C2×C3×C4—68no—
726C2×C3×C4—62no—
727C2×C3×C4—62no—
728C2×C3×C4—62no—
729C2×C3×C4—124no—
730C2×C3×C4C23×D312yes—
731C2×C3×C4C23×D312yes—
732C2×C3×C4C23×D312yes—
733C2×C3×C4C23×D312yes—
734#67—28no—
735#67—68no—
736#67—68no—
737#67—68no—
738#67—68no—
739#67—68no—
740#67—68no—
741#67—68no—
742#67—128no—
743#67—124no—
744#67—124no—
745#67—124no—
746#67C2×#67116yescomplemented
747C2×Dic3—22no—
748C2×Dic3—22no—
749C2×Dic3—22no—
750C2×Dic3—32no—
751C2×Dic3—32no—
752C2×Dic3—32no—
753C2×Dic3—32no—
754C2×Dic3—32no—
755C2×Dic3—32no—
756C2×Dic3—44no—
757C2×Dic3—62no—
758C2×Dic3—62no—
759C2×Dic3—62no—
760C2×Dic3—62no—
761C2×Dic3—62no—
762C2×Dic3—62no—
763C2×Dic3—62no—
764C2×Dic3—62no—
765C2×Dic3—62no—
766C2×Dic3—68no—
767C2×Dic3—122no—
768C2×Dic3—122no—
769C2×Dic3—122no—
770C2×Dic3—124no—
771C2×Dic3C2×#6714yes—
772C2×Dic3C23×D312yes—
773C2×Dic3C23×D312yes—
774C2×Dic3C23×D312yes—
775C2×Dic3C23×D312yes—
776D12—28no—
777D12—68no—
778D12—124no—
779C4×D3—28no—
780C4×D3—28no—
781C4×D3—68no—
782C4×D3—124no—
783Dic6—28no—
784C2×C32—24no—
785C2×C32#54614yescomplemented
786C2×C32C23×D411yescharacteristic
787C2×C32C22×#4111yescharacteristic
788C2×C32C2×H(5,𝔽2)11yescharacteristic
789C3⋊D3—42no—
790C3×D3—24no—
791C3×D3—24no—
792C3×D3—42no—
793C3×D3—42no—
794C24—31no—
795C24—31no—
796C24—31no—
797C24—31no—
798C24—34no—
799C24—64no—
800C24—64no—
801C24—94no—
802C24—91no—
803C24—122no—
804C24—184no—
805C24—184no—
806C24—362no—
807C24C2×D3211yescharacteristic
808#41—632no—
809C2×Q8—34no—
810C2×Q8—64no—
811C2×D4—34no—
812C2×D4—38no—
813C2×D4—34no—
814C2×D4—34no—
815C2×D4—64no—
816C2×D4—64no—
817C2×D4—94no—
818C2×D4—94no—
819C2×D4—94no—
820C2×D4—94no—
821C2×D4—94no—
822C2×D4—94no—
823C2×D4—184no—
824C2×D4—1832no—
825C2×D4—184no—
826C2×D4—184no—
827C2×D4—184no—
828C2×D4—362no—
829C2×D4—362no—
830C22×C4—24no—
831C22×C4—31no—
832C22×C4—31no—
833C22×C4—31no—
834C22×C4—31no—
835C22×C4—34no—
836C22×C4—34no—
837C22×C4—34no—
838C22×C4—64no—
839C22×C4—64no—
840C22×C4—94no—
841C22×C4—94no—
842C22×C4—91no—
843C22×C4—91no—
844C22×C4—91no—
845C22×C4—122no—
846C22×C4—184no—
847C22×C4—362no—
848C22×C4C2×D3211yescharacteristic
849C22×C4C2×D3211yescharacteristic
850C22×C4C2×D3214yescomplemented
851C4⋊C4—94no—
852C4⋊C4—94no—
853C4⋊C4—94no—
854C4⋊C4—94no—
855C22⋊C4—34no—
856C22⋊C4—34no—
857C22⋊C4—34no—
858C22⋊C4—34no—
859C22⋊C4—94no—
860C22⋊C4—94no—
861C22⋊C4—94no—
862C22⋊C4—94no—
863C22⋊C4—94no—
864C22⋊C4—94no—
865C22⋊C4—94no—
866C22⋊C4—94no—
867C42—94no—
868C22×C3—22no—
869C22×C3—22no—
870C22×C3—22no—
871C22×C3—22no—
872C22×C3—28no—
873C22×C3—28no—
874C22×C3—22no—
875C22×C3—22no—
876C22×C3—22no—
877C22×C3—24no—
878C22×C3—21no—
879C22×C3—34no—
880C22×C3—34no—
881C22×C3—42no—
882C22×C3—42no—
883C22×C3—48no—
884C22×C3—62no—
885C22×C3—62no—
886C22×C3—62no—
887C22×C3—62no—
888C22×C3—68no—
889C22×C3—68no—
890C22×C3—62no—
891C22×C3—62no—
892C22×C3—62no—
893C22×C3—62no—
894C22×C3—62no—
895C22×C3—62no—
896C22×C3—1216no—
897C22×C3—124no—
898C22×C3—124no—
899C22×C3C2×#23512yes—
900C22×C3C2×D3×D414yes—
901C22×C3C2×D3×D412yes—
902C22×C3#100412yes—
903C22×C3D3×#4112yes—
904C22×C3#100912yes—
905C22×C3C22×#6714yes—
906C22×C3C22×#6712yes—
907C22×C3C24×D311yescharacteristic
908C22×C3C24×D311yescharacteristic
909C2×D3—22no—
910C2×D3—22no—
911C2×D3—22no—
912C2×D3—22no—
913C2×D3—28no—
914C2×D3—28no—
915C2×D3—22no—
916C2×D3—22no—
917C2×D3—22no—
918C2×D3—22no—
919C2×D3—22no—
920C2×D3—22no—
921C2×D3—416no—
922C2×D3—44no—
923C2×D3—44no—
924C2×D3—62no—
925C2×D3—62no—
926C2×D3—62no—
927C2×D3—62no—
928C2×D3—62no—
929C2×D3—62no—
930C2×D3—122no—
931C2×D3—122no—
932C2×D3—122no—
933C2×D3—1216no—
934C2×D3—1216no—
935C2×D3—124no—
936C2×D3—124no—
937C2×D3—244no—
938C2×D3C2×#23514yescomplemented
939C2×D3C22×#6714yes—
940C3×C4—22no—
941C3×C4—22no—
942C3×C4—22no—
943C3×C4—22no—
944C3×C4—34no—
945C3×C4—42no—
946C3×C4—42no—
947C3×C4—62no—
948C3×C4—62no—
949C3×C4—62no—
950Dic3—22no—
951Dic3—22no—
952Dic3—22no—
953Dic3—62no—
954Dic3—62no—
955Dic3—62no—
956Dic3—62no—
957Dic3—62no—
958Dic3—62no—
959Dic3—122no—
960Dic3—122no—
961Dic3—122no—
962Dic3C22×#6714yes—
963C32C2×#54611yescharacteristic, complemented, Sylow
964C23—22no—
965C23—22no—
966C23—34no—
967C23—34no—
968C23—32no—
969C23—32no—
970C23—32no—
971C23—32no—
972C23—68no—
973C23—62no—
974C23—62no—
975C23—62no—
976C23—62no—
977C23—62no—
978C23—62no—
979C23—62no—
980C23—62no—
981C23—62no—
982C23—68no—
983C23—62no—
984C23—92no—
985C23—124no—
986C23—1216no—
987C23—188no—
988C23—188no—
989C23—182no—
990C23—182no—
991C23—182no—
992C23—364no—
993C23—3616no—
994C23D3×#6714yes—
995C23C22×D3212yes—
996C23C22×D3211yescharacteristic
997Q8—68no—
998D4—316no—
999D4—68no—
1000D4—68no—
1001D4—188no—
1002D4—188no—
1003D4—188no—
1004D4—188no—
1005D4—364no—
1006D4—364no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—28no—
1010C2×C4—34no—
1011C2×C4—32no—
1012C2×C4—32no—
1013C2×C4—32no—
1014C2×C4—32no—
1015C2×C4—68no—
1016C2×C4—68no—
1017C2×C4—62no—
1018C2×C4—62no—
1019C2×C4—62no—
1020C2×C4—92no—
1021C2×C4—92no—
1022C2×C4—92no—
1023C2×C4—124no—
1024C2×C4—188no—
1025C2×C4—182no—
1026C2×C4—182no—
1027C2×C4—182no—
1028C2×C4—364no—
1029C2×C4C22×D3212yes—
1030C2×C4C22×D3212yes—
1031C2×C3—24no—
1032C2×C3—24no—
1033C2×C3—21no—
1034C2×C3—21no—
1035C2×C3—21no—
1036C2×C3—24no—
1037C2×C3—44no—
1038C2×C3—64no—
1039C2×C3—64no—
1040C2×C3—122no—
1041C2×C3—122no—
1042C2×C3#549014yescomplemented
1043C2×C3#582914yescomplemented
1044C2×C3C22×#23511yescharacteristic
1045C2×C3C22×D3×D411yescharacteristic
1046C2×C3C2×#100411yescharacteristic
1047C2×C3C2×D3×#4111yescharacteristic
1048C2×C3C2×#100911yescharacteristic
1049C2×C3C23×#6711yescharacteristic
1050D3—24no—
1051D3—24no—
1052D3—42no—
1053D3—42no—
1054D3—122no—
1055D3—122no—
1056D3—242no—
1057C22—22no—
1058C22—22no—
1059C22—28no—
1060C22—34no—
1061C22—34no—
1062C22—62no—
1063C22—62no—
1064C22—62no—
1065C22—62no—
1066C22—68no—
1067C22—68no—
1068C22—62no—
1069C22—62no—
1070C22—62no—
1071C22—62no—
1072C22—62no—
1073C22—62no—
1074C22—1216no—
1075C22—124no—
1076C22—124no—
1077C22—182no—
1078C22—182no—
1079C22—182no—
1080C22—3616no—
1081C22—364no—
1082C22D3×#23512yes—
1083C22#6430712yes—
1084C22C2×D3×#6714yes—
1085C22C2×D3×#6712yes—
1086C22C23×D3211yescharacteristic
1087C4—22no—
1088C4—22no—
1089C4—34no—
1090C4—62no—
1091C4—62no—
1092C4—62no—
1093C4—182no—
1094C4—182no—
1095C4—182no—
1096C3—21no—
1097C3C2×#549011yescharacteristic, complemented
1098C3C2×#582911yescharacteristic, complemented
1099C2—24no—
1100C2—64no—
1101C2—64no—
1102C2—122no—
1103C2—122no—
1104C2—362no—
1105C2#1059506514yesdirect product factor
1106C2C2×D3×#23511yescharacteristic
1107C2C2×#6430711yescharacteristic
1108C2C22×D3×#6711yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC23×C32×C4C22
socleC23×C32C24
hypercenterC23×C4D32
hypocenterC32C2×#546
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C22×C3×#235C2semidirect
2. C22×D3×#67C2semidirect
3. C2×#64138C2semidirect
4. C22×C3×(C2×D3)⋊C4C2semidirect
5. C2×#63978C2semidirect
6. C2×#63976C2semidirect
7. C2×Dic3×#67C2semidirect
8. #10595065C2direct (N × H)
9. C2×#63922C2semidirect
10. C2×D3×(C2×D3)⋊C4C2semidirect
11. C2×#63907C2semidirect
12. C2×#63906C2semidirect
13. C2×#63905C2semidirect
14. C2×#63887C2semidirect
15. C2×#63885C2semidirect
16. C2×#63879C2semidirect
21. C23×C32×C4C22semidirect
24. C22×C3×#67C22semidirect
25. C23×C3×Dic3C22semidirect
27. C2×C3×#235C22semidirect
28. C22×C3×D12C22semidirect
29. C22×C3×C4×D3C22semidirect
30. C22×C3×C4×D3C22semidirect
31. C22×C3×Dic6C22semidirect
33. C2×D3×#67C22semidirect
35. C22×#626C22semidirect
38. C22×#625C22semidirect
40. C22×D3×Dic3C22semidirect
41. C2×#3757C22semidirect
42. #64138C22semidirect
43. C2×#3752C22semidirect
44. C2×#3752C22semidirect
45. C2×#3750C22semidirect
46. C2×#3750C22semidirect
49. C2×C3×(C2×D3)⋊C4C22semidirect
50. C2×C3×(C2×D3)⋊C4C22semidirect
51. C2×C3×(C2×D3)⋊C4C22semidirect
52. #63978C22semidirect
53. #63976C22semidirect
54. Dic3×#67C22semidirect
55. C2×Dic3⋊Dic3C22semidirect
56. C2×Dic3⋊Dic3C22semidirect
57. C2×#3722C22semidirect
59. C2×(C2×D3)⋊Dic3C22semidirect
60. C2×(C2×D3)⋊Dic3C22semidirect
61. C2×(C2×D3)⋊Dic3C22semidirect
62. C2×Dic32C22semidirect
63. #63922C22semidirect
64. D3×(C2×D3)⋊C4C22semidirect
65. #63907C22semidirect
66. #63906C22semidirect
67. #63905C22semidirect
68. #63887C22semidirect
69. #63885C22semidirect
70. #63879C22semidirect
74. C22×#235D3semidirect
94. C22×(C2×D3)⋊C4D3semidirect
121. C22×C32×C4C23semidirect
128. C2×C3×#67D4semidirect
130. C2×C3×#67C23semidirect
136. C22×C3×Dic3C23semidirect
139. C2×C3×D12C23semidirect
142. C2×C3×C4×D3C23semidirect
143. C2×C3×C4×D3C23semidirect
145. C2×C3×Dic6C23semidirect
150. C2×#626C23semidirect
156. C2×#625C23semidirect
160. C2×D3×Dic3C23semidirect
161. #3757C23semidirect
162. #3752C23semidirect
163. #3752C23semidirect
164. #3750C23semidirect
165. #3750C23semidirect
168. C3×(C2×D3)⋊C4C23semidirect
169. C3×(C2×D3)⋊C4C23semidirect
170. Dic3⋊Dic3C23semidirect
171. Dic3⋊Dic3C23semidirect
172. #3722C23semidirect
174. (C2×D3)⋊Dic3C23semidirect
175. (C2×D3)⋊Dic3C23semidirect
176. (C2×D3)⋊Dic3C23semidirect
177. Dic32C23semidirect
193. C23×C3×C4C2×D3semidirect
194. C23×C3×C4C2×D3semidirect
209. C22×#67C2×D3semidirect
212. C23×Dic3C2×D3semidirect
216. C2×#235C2×D3semidirect
219. C22×D12C2×D3semidirect
222. C22×C4×D3C2×D3semidirect
223. C22×C4×D3C2×D3semidirect
224. C22×Dic6C2×D3semidirect
268. C2×(C2×D3)⋊C4C2×D3semidirect
269. C2×(C2×D3)⋊C4C2×D3semidirect
270. C2×(C2×D3)⋊C4C2×D3semidirect
315. C22×C3×D3#41semidirect
337. C3×#67C2×D4semidirect
433. C22×C3×C4C22×D3semidirect
434. C22×C3×C4C22×D3semidirect
459. C2×#67#67semidirect
461. C2×#67C22×D3semidirect
480. C22×Dic3C22×D3semidirect
488. C2×D12C22×D3semidirect
495. C2×C4×D3C22×D3semidirect
496. C2×C4×D3C22×D3semidirect
498. C2×Dic6C22×D3semidirect
524. (C2×D3)⋊C4C22×D3semidirect
525. (C2×D3)⋊C4C22×D3semidirect
566. C2×C3×D3C2×#41semidirect
598. C23×C4D32semidirect
698. C22×D3#235semidirect
746. #67C2×#67semidirect
785. C2×C32#546semidirect
850. C22×C4C2×D32semidirect
938. C2×D3C2×#235semidirect
963. C32C2×#546semidirect
1042. C2×C3#5490semidirect
1043. C2×C3#5829semidirect
1097. C3C2×#5490semidirect
1098. C3C2×#5829semidirect
1105. C2#10595065direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#2352
C22×D3×#672
C2×#641382
C22×C3×(C2×D3)⋊C42
C2×#639782
C2×#639762
C2×Dic3×#672
#105950652
C2×#639222
C2×D3×(C2×D3)⋊C42
C2×#639072
C2×#639062
C2×#639052
C2×#638872
C2×#638852
C2×#638792
C2×#58293
C2×#54903