Finite Group Databasebeta

← C2×#10595083 #11902423

Subgroups — C2×#10595083 #11902423

Order 1152.

4013 conjugacy classes of subgroups.

The subgroup lattice has 1112 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×#67C211yesmaximal, characteristic, complemented
2C22×#3804C211yesmaximal, characteristic, complemented
3C2×C4×#638C211yesmaximal, characteristic, complemented
4C2×C3×#930C211yesmaximal, characteristic, complemented
5C22×C3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
6C2×#63976C211yesmaximal, characteristic, complemented
7C2×#63961C211yesmaximal, characteristic, complemented
8#10595083C2116yesmaximal, direct product factor
9C2×#63922C211yesmaximal, characteristic, complemented
10C2×#63921C211yesmaximal, characteristic, complemented
11C2×#63915C211yesmaximal, characteristic, complemented
12C2×#63912C211yesmaximal, characteristic, complemented
13C2×#63902C211yesmaximal, characteristic, complemented
14C2×#63899C211yesmaximal, characteristic, complemented
15C2×#63885C211yesmaximal, characteristic, complemented
16C2×#63854C211yesmaximal, characteristic, complemented
17C2×#5610—31nomaximal
18C2×#5490—31nomaximal
19C24×C3×D3C2211yescharacteristic
20C23×D32C2211yescharacteristic
21C23×C32×C4C2211yescharacteristic, complemented
22C22×#638C2211yescharacteristic
23C22×C4×C3⋊D3C2211yescharacteristic, complemented
24C22×C3×#67C2211yescharacteristic
25C22×C3×#67C2211yescharacteristic, complemented
26C23×C3×Dic3C2211yescharacteristic, complemented
27C22×C3×D12C2211yescharacteristic, complemented
28C2×D3×#67—28no—
29C2×D3×#67C2218yescomplemented
30C22×#627C2211yescharacteristic, complemented
31C22×#626C2211yescharacteristic
32C22×#626C2211yescharacteristic, complemented
33C22×#625C2211yescharacteristic
34C22×#625C2211yescharacteristic
35C22×#625C2211yescharacteristic, complemented
36C22×#624C2211yescharacteristic, complemented
37C2×#3804—28no—
38C2×#3804C2218yescomplemented
39C22×D3×Dic3C2211yescharacteristic
40C22×D3×Dic3C2211yescharacteristic, complemented
41C2×#3757C2211yescharacteristic, complemented
42C4×#638C2218yescomplemented
43C2×#3752C2211yescharacteristic, complemented
44C2×#3750C2211yescharacteristic, complemented
45C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
46C3×#930C2218yescomplemented
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
52C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
53C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
54C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
55#63976C2218yescomplemented
56C2×#3724C2211yescharacteristic, complemented
57C2×#3724C2211yescharacteristic, complemented
58#63961C2218yescomplemented
59C2×(C2×D3)⋊Dic3C2211yescharacteristic
60C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
61C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
62C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
63#63922C2218yescomplemented
64#63921C2218yescomplemented
65#63915C2218yescomplemented
66#63912C2218yescomplemented
67#63902C2218yescomplemented
68#63899C2218yescomplemented
69#63885C2218yescomplemented
70#63854C2218yescomplemented
71C23×#67—31no—
72C22×#237—31no—
73C22×D3×D4—31no—
74C22×#235—31no—
75C2×C3×#121—31no—
76C22×C3×C22⋊C4—31no—
77C2×#953—31no—
78C2×#939—31no—
79C2×#937—31no—
80C2×#937—31no—
81C2×#935—31no—
82C2×#930D311yescharacteristic, complemented
83C2×#929—31no—
84C2×C4×#67—31no—
85C2×C4×#67—31no—
86C2×C4×#67—61no—
87C22×(C2×D3)⋊C4D311yescharacteristic, complemented
88#5610—316no—
89C2×#896—31no—
90C2×#894—31no—
91C2×#885—31no—
92C2×#885—31no—
93#5490—316no—
94C2×#884—31no—
95C2×#884—31no—
96C2×#884—31no—
97C2×#883—31no—
98C2×#882—31no—
99C2×#67⋊C4—31no—
100C2×#67⋊C4—31no—
101C2×D3×C22⋊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×D3C2311yescharacteristic
112C23×C3×D3C2314yes—
113C23×C3×D3C2311yescharacteristic
114C22×D32—24no—
115C22×D32—24no—
116C22×D32—42no—
117C22×D32C2314yes—
118C22×C32×C4—42no—
119C22×C32×C4C2311yescharacteristic
120C22×C32×C4C2311yescharacteristic
121C22×C32×C4C2314yescomplemented
122C2×#638D418yescomplemented
123C2×#638C2314yes—
124C22×C3⋊Dic3C2311yescharacteristic
125C22×C3⋊Dic3C2311yescharacteristic
126C22×C3⋊Dic3C2311yescharacteristic
127C2×C4×C3⋊D3—42no—
128C2×C4×C3⋊D3C2314yescomplemented
129C2×C3×#67—24no—
130C2×C3×#67—24no—
131C2×C3×#67C2314yes—
132C2×C3×#67C2314yescomplemented
133C22×C3×Dic3—24no—
134C22×C3×Dic3C2311yescharacteristic
135C22×C3×Dic3C2311yescharacteristic
136C22×C3×Dic3C2311yescharacteristic
137C22×C3×Dic3C2311yescharacteristic
138C22×C3×Dic3C2314yescomplemented
139C2×C3×D12—42no—
140C2×C3×D12C2314yescomplemented
141D3×#67—232no—
142C2×#627—24no—
143C2×#627C2314yescomplemented
144C2×#626—24no—
145C2×#626—24no—
146C2×#626C2314yes—
147C2×#626C2314yescomplemented
148C2×#625—24no—
149C2×#625—24no—
150C2×#625—42no—
151C2×#625C2314yes—
152C2×#625C2314yes—
153C2×#625C2314yescomplemented
154C2×#624—24no—
155C2×#624C2314yescomplemented
156#3804—232no—
157C2×D3×Dic3—24no—
158C2×D3×Dic3—24no—
159C2×D3×Dic3C2314yes—
160C2×D3×Dic3C2314yescomplemented
161#3757C2314yescomplemented
162#3752C2314yescomplemented
163#3750C2314yescomplemented
164C4×C3⋊Dic3C2314yescomplemented
165C3×(C2×D3)⋊C4C2314yes—
166C3×(C2×D3)⋊C4C2314yes—
167C3×(C2×D3)⋊C4C2314yescomplemented
168C3×(C2×D3)⋊C4C2314yescomplemented
169C3×(C2×D3)⋊C4C2314yescomplemented
170C3×(C2×D3)⋊C4C2314yescomplemented
171C3×C4⋊Dic3C2314yescomplemented
172#3724C2314yescomplemented
173#3724C2314yescomplemented
174(C2×D3)⋊Dic3C2314yes—
175(C2×D3)⋊Dic3C2314yescomplemented
176(C2×D3)⋊Dic3C2314yescomplemented
177(C2×D3)⋊Dic3C2314yescomplemented
178C2×#546—91noSylow
179C25×C3—31no—
180C24×D3—31no—
181C24×D3—31no—
182C24×D3C2×D311yescharacteristic
183C22×C3×D4—31no—
184C22×C3×D4—31no—
185C22×C3×D4—31no—
186C23×C3×C4—21no—
187C23×C3×C4—31no—
188C23×C3×C4C2×D311yescharacteristic, complemented
189C23×C3×C4C2×D311yescharacteristic, complemented
190C22×#67—31no—
191C22×#67—31no—
192C22×#67—31no—
193C22×#67—31no—
194C22×#67—31no—
195C22×#67—31no—
196C22×#67—31no—
197C22×#67—31no—
198C22×#67—38no—
199C22×#67—31no—
200C22×#67—31no—
201C22×#67—61no—
202C22×#67—68no—
203C22×#67C2×D311yescharacteristic
204C22×#67C2×D311yescharacteristic, complemented
205C23×Dic3—31no—
206C23×Dic3—31no—
207C23×Dic3C2×D311yescharacteristic, complemented
208C2×#237—38no—
209C2×#237—68no—
210C2×D3×D4—38no—
211C2×D3×D4—68no—
212C2×#235—38no—
213C2×#235—68no—
214C22×D12—31no—
215C22×D12—31no—
216C22×D12C2×D311yescharacteristic, complemented
217C22×C4×D3—31no—
218C22×C4×D3—31no—
219C22×C4×D3—31no—
220C22×C4×D3—31no—
221C22×C4×D3—31no—
222C22×C4×D3—31no—
223C22×C4×D3—61no—
224C22×Dic6—31no—
225C22×Dic6—31no—
226C3×#121—38no—
227C2×C3×C4⋊C4—31no—
228C2×C3×C22⋊C4—31no—
229C2×C3×C22⋊C4—31no—
230C2×C3×C22⋊C4—31no—
231C2×C3×C22⋊C4—31no—
232C2×C3×C22⋊C4—31no—
233C2×C3×C22⋊C4—31no—
234C2×C3×C22⋊C4—38no—
235#953—38no—
236C2×#217—31no—
237C2×#217—31no—
238C2×#217—31no—
239C2×#217—31no—
240C2×#217—31no—
241C2×#217—31no—
242C2×#217—61no—
243#939—38no—
244#937—38no—
245#937—38no—
246#935—38no—
247#930C2×D318yescomplemented
248#929—38no—
249C4×#67—38no—
250C4×#67—38no—
251C4×#67—68no—
252C2×(C2×D3)⋊C4—31no—
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—61no—
259C2×(C2×D3)⋊C4C2×D311yescharacteristic
260C2×(C2×D3)⋊C4C2×D311yescharacteristic
261C2×(C2×D3)⋊C4C2×D318yescomplemented
262C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
263C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
264C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
265C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
266C2×C4⋊Dic3C2×D311yescharacteristic, complemented
267C2×Dic3⋊C4—31no—
268C2×Dic3⋊C4—31no—
269C2×Dic3⋊C4—31no—
270C2×Dic3⋊C4—31no—
271C2×Dic3⋊C4—31no—
272C2×Dic3⋊C4—31no—
273C2×Dic3⋊C4—61no—
274C2×C4×Dic3—31no—
275C2×C4×Dic3—31no—
276C2×C4×Dic3—61no—
277#896—38no—
278#894—38no—
279#885—38no—
280#885—38no—
281#884—38no—
282#884—38no—
283#884—38no—
284#883—38no—
285#882—38no—
286#67⋊C4—38no—
287#67⋊C4—38no—
288D3×C22⋊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⋊D3C2×D414yes—
299C22×C3⋊D3C2412yes—
300C22×C3×D3—22no—
301C22×C3×D3—22no—
302C22×C3×D3—22no—
303C22×C3×D3—22no—
304C22×C3×D3—28no—
305C22×C3×D3—22no—
306C22×C3×D3—22no—
307C22×C3×D3—22no—
308C22×C3×D3—22no—
309C22×C3×D3—22no—
310C22×C3×D3—22no—
311C22×C3×D3—22no—
312C22×C3×D3—28no—
313C22×C3×D3—44no—
314C22×C3×D3—416no—
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—44no—
327C2×C32×C4C2412yes—
328C2×C32×C4C2412yes—
329#638C2×D4116yescomplemented
330C2×C3⋊Dic3—22no—
331C2×C3⋊Dic3—22no—
332C2×C3⋊Dic3C2×D414yes—
333C2×C3⋊Dic3C2412yes—
334C2×C3⋊Dic3C2412yes—
335C2×C3⋊Dic3C2412yes—
336C4×C3⋊D3—44no—
337C3×#67—28no—
338C3×#67—28no—
339C2×C3×Dic3—22no—
340C2×C3×Dic3—22no—
341C2×C3×Dic3—28no—
342C2×C3×Dic3—22no—
343C2×C3×Dic3—22no—
344C2×C3×Dic3C2412yes—
345C2×C3×Dic3C2412yes—
346C2×C3×Dic3C2412yes—
347C2×C3×Dic3C2412yes—
348C3×D12—44no—
349#627—28no—
350#626—28no—
351#626—28no—
352#625—28no—
353#625—28no—
354#625—44no—
355#624—28no—
356D3×Dic3—28no—
357D3×Dic3—28no—
358C22×#41—91no—
359C23×D4—91no—
360#546—916no—
361C2×#124—91no—
362C2×#123—91no—
363C2×#123—91no—
364C2×C22⋊Q8—91no—
365C2×#121—31no—
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×D311yescharacteristic
402C23×D3C22×D314yes—
403C23×D3C22×D311yescharacteristic
404C2×C3×D4—34no—
405C2×C3×D4—34no—
406C2×C3×D4—34no—
407C2×C3×D4—64no—
408C2×C3×D4—64no—
409C2×C3×D4—122no—
410C22×C3×C4—21no—
411C22×C3×C4—21no—
412C22×C3×C4—24no—
413C22×C3×C4—31no—
414C22×C3×C4—31no—
415C22×C3×C4—31no—
416C22×C3×C4—31no—
417C22×C3×C4—34no—
418C22×C3×C4—42no—
419C22×C3×C4—42no—
420C22×C3×C4—44no—
421C22×C3×C4—64no—
422C22×C3×C4C22×D311yescharacteristic
423C22×C3×C4C22×D311yescharacteristic
424C22×C3×C4C22×D311yescharacteristic
425C22×C3×C4C22×D311yescharacteristic
426C22×C3×C4C22×D314yescomplemented
427C22×C3×C4C22×D314yescomplemented
428C2×#67—24no—
429C2×#67—24no—
430C2×#67—38no—
431C2×#67—38no—
432C2×#67—34no—
433C2×#67—34no—
434C2×#67—34no—
435C2×#67—34no—
436C2×#67—34no—
437C2×#67—34no—
438C2×#67—34no—
439C2×#67—34no—
440C2×#67—34no—
441C2×#67—34no—
442C2×#67—64no—
443C2×#67—68no—
444C2×#67—64no—
445C2×#67—64no—
446C2×#67—64no—
447C2×#67—64no—
448C2×#67—632no—
449C2×#67—64no—
450C2×#67—64no—
451C2×#67—122no—
452C2×#67—122no—
453C2×#67C22×D314yes—
454C2×#67C22×D314yescomplemented
455C22×Dic3—24no—
456C22×Dic3—31no—
457C22×Dic3—31no—
458C22×Dic3—31no—
459C22×Dic3—31no—
460C22×Dic3—31no—
461C22×Dic3—31no—
462C22×Dic3—34no—
463C22×Dic3—34no—
464C22×Dic3—61no—
465C22×Dic3—61no—
466C22×Dic3—61no—
467C22×Dic3—64no—
468C22×Dic3—64no—
469C22×Dic3C22×D311yescharacteristic
470C22×Dic3C22×D311yescharacteristic
471C22×Dic3C22×D311yescharacteristic
472C22×Dic3C22×D311yescharacteristic
473C22×Dic3C22×D314yescomplemented
474#237—632no—
475D3×D4—632no—
476#235—632no—
477C2×D12—34no—
478C2×D12—34no—
479C2×D12—42no—
480C2×D12—64no—
481C2×D12—64no—
482C2×D12C22×D314yescomplemented
483C2×C4×D3—34no—
484C2×C4×D3—34no—
485C2×C4×D3—34no—
486C2×C4×D3—34no—
487C2×C4×D3—34no—
488C2×C4×D3—34no—
489C2×C4×D3—64no—
490C2×C4×D3—64no—
491C2×C4×D3—64no—
492C2×C4×D3—64no—
493C2×C4×D3—64no—
494C2×C4×D3—122no—
495C2×C4×D3—122no—
496C2×C4×D3—124no—
497C2×Dic6—34no—
498C2×Dic6—34no—
499C2×Dic6—64no—
500C2×Dic6—64no—
501C3×C4⋊C4—34no—
502C3×C22⋊C4—34no—
503C3×C22⋊C4—34no—
504C3×C22⋊C4—34no—
505C3×C22⋊C4—34no—
506C3×C22⋊C4—34no—
507C3×C22⋊C4—34no—
508#217—34no—
509#217—34no—
510#217—34no—
511#217—34no—
512#217—34no—
513#217—34no—
514#217—64no—
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—34no—
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
526(C2×D3)⋊C4C22×D314yescomplemented
527(C2×D3)⋊C4C22×D314yescomplemented
528C4⋊Dic3C22×D314yescomplemented
529Dic3⋊C4—34no—
530Dic3⋊C4—34no—
531Dic3⋊C4—34no—
532Dic3⋊C4—34no—
533Dic3⋊C4—34no—
534Dic3⋊C4—34no—
535Dic3⋊C4—64no—
536C4×Dic3—34no—
537C4×Dic3—34no—
538C4×Dic3—64no—
539C22×C32—28no—
540C22×C32—22no—
541C22×C32—22no—
542C22×C32C22×D414yes—
543C22×C32C22×D412yes—
544C22×C32C2×#4112yes—
545C22×C32H(5,𝔽2)12yes—
546C22×C32C2511yescharacteristic
547C2×C3⋊D3—28no—
548C2×C3⋊D3—22no—
549C2×C3⋊D3—22no—
550C2×C3⋊D3C22×D414yes—
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—22no—
563C2×C3×D3—416no—
564C2×C3×D3—44no—
565C2×C3×D3—44no—
566C2×C3×D3—44no—
567C2×C3×D3C2×#4114yescomplemented
568D32—416no—
569C32×C4—22no—
570C32×C4—22no—
571C3⋊Dic3—22no—
572C3⋊Dic3—22no—
573C3⋊Dic3C22×D414yes—
574C3×Dic3—22no—
575C3×Dic3—22no—
576C3×Dic3—22no—
577C3×Dic3—22no—
578C25—31no—
579C25—91no—
580C2×#41—98no—
581C2×#41—188no—
582C22×Q8—91no—
583C22×D4—31no—
584C22×D4—31no—
585C22×D4—31no—
586C22×D4—91no—
587C22×D4—91no—
588C22×D4—98no—
589C22×D4—91no—
590C22×D4—91no—
591C22×D4—91no—
592C22×D4—91no—
593C22×D4—188no—
594C23×C4—31no—
595C23×C4—91no—
596C23×C4—91no—
597C23×C4—91no—
598C23×C4—91no—
599C23×C4D3211yescharacteristic, complemented
600#124—98no—
601#123—98no—
602#123—98no—
603C22⋊Q8—98no—
604#121—38no—
605#121—98no—
606#121—98no—
607#120—98no—
608#120—98no—
609C4×D4—98no—
610C4×D4—98no—
611C2×C4⋊C4—31no—
612C2×C4⋊C4—91no—
613C2×C4⋊C4—91no—
614C2×C4⋊C4—91no—
615C2×C22⋊C4—31no—
616C2×C22⋊C4—31no—
617C2×C22⋊C4—31no—
618C2×C22⋊C4—31no—
619C2×C22⋊C4—31no—
620C2×C22⋊C4—31no—
621C2×C22⋊C4—38no—
622C2×C22⋊C4—98no—
623C2×C22⋊C4—91no—
624C2×C22⋊C4—91no—
625C2×C22⋊C4—91no—
626C2×C22⋊C4—91no—
627C2×C22⋊C4—91no—
628C2×C22⋊C4—91no—
629C2×C42—91no—
630C23×C3—22no—
631C23×C3—22no—
632C23×C3—22no—
633C23×C3—22no—
634C23×C3—22no—
635C23×C3—21no—
636C23×C3—24no—
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—68no—
651C23×C3—62no—
652C23×C3—62no—
653C23×C3—62no—
654C23×C3—62no—
655C23×C3—62no—
656C23×C3—62no—
657C23×C3—124no—
658C23×C3—1216no—
659C23×C3D3×D414yes—
660C23×C3D3×D414yes—
661C23×C3C23×D312yes—
662C23×C3C23×D312yes—
663C23×C3C23×D311yescharacteristic
664C23×C3C23×D311yescharacteristic
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—22no—
676C22×D3—22no—
677C22×D3—28no—
678C22×D3—34no—
679C22×D3—34no—
680C22×D3—32no—
681C22×D3—32no—
682C22×D3—44no—
683C22×D3—416no—
684C22×D3—64no—
685C22×D3—62no—
686C22×D3—68no—
687C22×D3—68no—
688C22×D3—68no—
689C22×D3—62no—
690C22×D3—62no—
691C22×D3—62no—
692C22×D3—62no—
693C22×D3—68no—
694C22×D3—122no—
695C22×D3—122no—
696C22×D3—124no—
697C22×D3—124no—
698C22×D3—1216no—
699C22×D3—1216no—
700C22×D3#23514yescomplemented
701C22×D3C23×D312yes—
702C22×D3C23×D312yes—
703C22×D3C23×D312yes—
704C22×D3C23×D312yes—
705C3×D4—68no—
706C3×D4—68no—
707C3×D4—124no—
708C2×C3×C4—24no—
709C2×C3×C4—22no—
710C2×C3×C4—22no—
711C2×C3×C4—22no—
712C2×C3×C4—22no—
713C2×C3×C4—22no—
714C2×C3×C4—22no—
715C2×C3×C4—32no—
716C2×C3×C4—32no—
717C2×C3×C4—32no—
718C2×C3×C4—32no—
719C2×C3×C4—42no—
720C2×C3×C4—44no—
721C2×C3×C4—44no—
722C2×C3×C4—48no—
723C2×C3×C4—62no—
724C2×C3×C4—62no—
725C2×C3×C4—62no—
726C2×C3×C4—62no—
727C2×C3×C4—68no—
728C2×C3×C4C23×D312yes—
729C2×C3×C4C23×D312yes—
730C2×C3×C4C23×D312yes—
731C2×C3×C4C23×D312yes—
732#67—28no—
733#67—28no—
734#67—316no—
735#67—316no—
736#67—616no—
737#67—68no—
738#67—68no—
739#67—68no—
740#67—68no—
741#67—68no—
742#67—68no—
743#67—124no—
744#67—124no—
745C2×Dic3—22no—
746C2×Dic3—22no—
747C2×Dic3—22no—
748C2×Dic3—28no—
749C2×Dic3—22no—
750C2×Dic3—34no—
751C2×Dic3—34no—
752C2×Dic3—32no—
753C2×Dic3—32no—
754C2×Dic3—32no—
755C2×Dic3—32no—
756C2×Dic3—32no—
757C2×Dic3—32no—
758C2×Dic3—64no—
759C2×Dic3—62no—
760C2×Dic3—62no—
761C2×Dic3—62no—
762C2×Dic3—68no—
763C2×Dic3—68no—
764C2×Dic3—62no—
765C2×Dic3—62no—
766C2×Dic3—62no—
767C2×Dic3—62no—
768C2×Dic3—122no—
769C2×Dic3—122no—
770C2×Dic3C23×D312yes—
771C2×Dic3C23×D312yes—
772C2×Dic3C23×D312yes—
773C2×Dic3C23×D312yes—
774D12—44no—
775D12—68no—
776D12—68no—
777C4×D3—68no—
778C4×D3—68no—
779C4×D3—68no—
780C4×D3—68no—
781C4×D3—124no—
782C4×D3—124no—
783C4×D3—128no—
784Dic6—68no—
785Dic6—68no—
786C2×C32—24no—
787C2×C32#54614yescomplemented
788C2×C32C23×D411yescharacteristic
789C2×C32C22×#4111yescharacteristic
790C2×C32C2×H(5,𝔽2)11yescharacteristic
791C3⋊D3—24no—
792C3×D3—24no—
793C3×D3—42no—
794C3×D3—42no—
795C3×D3—42no—
796C24—31no—
797C24—31no—
798C24—31no—
799C24—31no—
800C24—34no—
801C24—64no—
802C24—64no—
803C24—94no—
804C24—91no—
805C24—122no—
806C24—184no—
807C24—184no—
808C24—362no—
809C24C2×D3211yescharacteristic
810#41—1832no—
811C2×Q8—94no—
812C2×Q8—184no—
813C2×D4—34no—
814C2×D4—34no—
815C2×D4—34no—
816C2×D4—64no—
817C2×D4—64no—
818C2×D4—94no—
819C2×D4—94no—
820C2×D4—94no—
821C2×D4—98no—
822C2×D4—94no—
823C2×D4—94no—
824C2×D4—94no—
825C2×D4—122no—
826C2×D4—184no—
827C2×D4—184no—
828C2×D4—184no—
829C2×D4—1832no—
830C2×D4—184no—
831C2×D4—362no—
832C22×C4—34no—
833C22×C4—31no—
834C22×C4—31no—
835C22×C4—31no—
836C22×C4—31no—
837C22×C4—42no—
838C22×C4—64no—
839C22×C4—94no—
840C22×C4—94no—
841C22×C4—94no—
842C22×C4—91no—
843C22×C4—91no—
844C22×C4—91no—
845C22×C4—94no—
846C22×C4—184no—
847C22×C4—184no—
848C22×C4—184no—
849C22×C4—362no—
850C22×C4C2×D3211yescharacteristic
851C22×C4C2×D3211yescharacteristic
852C22×C4C2×D3214yescomplemented
853C4⋊C4—34no—
854C4⋊C4—94no—
855C4⋊C4—94no—
856C4⋊C4—94no—
857C22⋊C4—34no—
858C22⋊C4—34no—
859C22⋊C4—34no—
860C22⋊C4—34no—
861C22⋊C4—34no—
862C22⋊C4—34no—
863C22⋊C4—94no—
864C22⋊C4—94no—
865C22⋊C4—94no—
866C22⋊C4—94no—
867C22⋊C4—94no—
868C22⋊C4—94no—
869C42—94no—
870C22×C3—22no—
871C22×C3—22no—
872C22×C3—22no—
873C22×C3—22no—
874C22×C3—28no—
875C22×C3—28no—
876C22×C3—22no—
877C22×C3—24no—
878C22×C3—22no—
879C22×C3—22no—
880C22×C3—21no—
881C22×C3—34no—
882C22×C3—42no—
883C22×C3—48no—
884C22×C3—42no—
885C22×C3—62no—
886C22×C3—62no—
887C22×C3—68no—
888C22×C3—62no—
889C22×C3—62no—
890C22×C3—62no—
891C22×C3—62no—
892C22×C3—62no—
893C22×C3—62no—
894C22×C3—62no—
895C22×C3—62no—
896C22×C3—62no—
897C22×C3—1216no—
898C22×C3—124no—
899C22×C3—124no—
900C22×C3—124no—
901C22×C3C2×#23512yes—
902C22×C3C2×D3×D414yes—
903C22×C3C2×D3×D414yes—
904C22×C3C2×D3×D412yes—
905C22×C3C2×D3×D412yes—
906C22×C3#100412yes—
907C22×C3#100412yes—
908C22×C3D3×#4112yes—
909C22×C3C24×D311yescharacteristic
910C22×C3C24×D311yescharacteristic
911C2×D3—22no—
912C2×D3—22no—
913C2×D3—28no—
914C2×D3—22no—
915C2×D3—22no—
916C2×D3—22no—
917C2×D3—22no—
918C2×D3—22no—
919C2×D3—22no—
920C2×D3—22no—
921C2×D3—22no—
922C2×D3—22no—
923C2×D3—34no—
924C2×D3—34no—
925C2×D3—416no—
926C2×D3—44no—
927C2×D3—44no—
928C2×D3—44no—
929C2×D3—64no—
930C2×D3—62no—
931C2×D3—62no—
932C2×D3—62no—
933C2×D3—62no—
934C2×D3—68no—
935C2×D3—68no—
936C2×D3—122no—
937C2×D3—128no—
938C2×D3—122no—
939C2×D3—1216no—
940C2×D3—1216no—
941C2×D3C2×#23514yescomplemented
942C3×C4—24no—
943C3×C4—22no—
944C3×C4—22no—
945C3×C4—22no—
946C3×C4—22no—
947C3×C4—42no—
948C3×C4—62no—
949C3×C4—62no—
950C3×C4—62no—
951C3×C4—62no—
952Dic3—22no—
953Dic3—22no—
954Dic3—22no—
955Dic3—22no—
956Dic3—34no—
957Dic3—34no—
958Dic3—64no—
959Dic3—62no—
960Dic3—62no—
961Dic3—62no—
962Dic3—62no—
963Dic3—122no—
964Dic3—122no—
965C32C2×#54611yescharacteristic, complemented, Sylow
966C23—22no—
967C23—22no—
968C23—34no—
969C23—32no—
970C23—32no—
971C23—32no—
972C23—32no—
973C23—68no—
974C23—62no—
975C23—62no—
976C23—62no—
977C23—62no—
978C23—68no—
979C23—62no—
980C23—62no—
981C23—62no—
982C23—62no—
983C23—62no—
984C23—62no—
985C23—62no—
986C23—94no—
987C23—92no—
988C23—124no—
989C23—1216no—
990C23—188no—
991C23—188no—
992C23—182no—
993C23—182no—
994C23—364no—
995C23—3616no—
996C23#380214yes—
997C23C22×D3212yes—
998C23C22×D3211yescharacteristic
999Q8—188no—
1000D4—68no—
1001D4—68no—
1002D4—916no—
1003D4—124no—
1004D4—188no—
1005D4—188no—
1006D4—188no—
1007D4—188no—
1008D4—364no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—32no—
1012C2×C4—32no—
1013C2×C4—32no—
1014C2×C4—32no—
1015C2×C4—44no—
1016C2×C4—62no—
1017C2×C4—62no—
1018C2×C4—68no—
1019C2×C4—62no—
1020C2×C4—62no—
1021C2×C4—94no—
1022C2×C4—92no—
1023C2×C4—92no—
1024C2×C4—92no—
1025C2×C4—188no—
1026C2×C4—188no—
1027C2×C4—188no—
1028C2×C4—182no—
1029C2×C4—182no—
1030C2×C4—364no—
1031C2×C4C22×D3212yes—
1032C2×C4C22×D3212yes—
1033C2×C3—24no—
1034C2×C3—24no—
1035C2×C3—24no—
1036C2×C3—21no—
1037C2×C3—21no—
1038C2×C3—21no—
1039C2×C3—44no—
1040C2×C3—64no—
1041C2×C3—122no—
1042C2×C3—122no—
1043C2×C3—122no—
1044C2×C3#549014yescomplemented
1045C2×C3#561014yescomplemented
1046C2×C3C22×#23511yescharacteristic
1047C2×C3C22×D3×D411yescharacteristic
1048C2×C3C22×D3×D411yescharacteristic
1049C2×C3C2×#100411yescharacteristic
1050C2×C3C2×#100411yescharacteristic
1051C2×C3C2×D3×#4111yescharacteristic
1052D3—24no—
1053D3—42no—
1054D3—42no—
1055D3—42no—
1056D3—64no—
1057D3—64no—
1058D3—124no—
1059C22—28no—
1060C22—22no—
1061C22—22no—
1062C22—34no—
1063C22—68no—
1064C22—62no—
1065C22—62no—
1066C22—62no—
1067C22—62no—
1068C22—62no—
1069C22—62no—
1070C22—62no—
1071C22—62no—
1072C22—62no—
1073C22—62no—
1074C22—62no—
1075C22—94no—
1076C22—1216no—
1077C22—124no—
1078C22—124no—
1079C22—124no—
1080C22—188no—
1081C22—182no—
1082C22—182no—
1083C22—3616no—
1084C22C2×#380214yes—
1085C22C2×#380212yes—
1086C22D3×#23512yes—
1087C22#6433012yes—
1088C22C23×D3211yescharacteristic
1089C4—22no—
1090C4—22no—
1091C4—62no—
1092C4—62no—
1093C4—62no—
1094C4—62no—
1095C4—94no—
1096C4—182no—
1097C4—182no—
1098C3—21no—
1099C3C2×#549011yescharacteristic, complemented
1100C3C2×#561011yescharacteristic, complemented
1101C2—24no—
1102C2—64no—
1103C2—122no—
1104C2—122no—
1105C2—122no—
1106C2—184no—
1107C2#1059508314yesdirect product factor
1108C2C22×#380211yescharacteristic
1109C2C2×D3×#23511yescharacteristic
1110C2C2×#6433011yescharacteristic
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×D3×#67C2semidirect
2. C22×#3804C2semidirect
3. C2×C4×#638C2semidirect
4. C2×C3×#930C2semidirect
5. C22×C3×(C2×D3)⋊C4C2semidirect
6. C2×#63976C2semidirect
7. C2×#63961C2semidirect
8. #10595083C2direct (N × H)
9. C2×#63922C2semidirect
10. C2×#63921C2semidirect
11. C2×#63915C2semidirect
12. C2×#63912C2semidirect
13. C2×#63902C2semidirect
14. C2×#63899C2semidirect
15. C2×#63885C2semidirect
16. C2×#63854C2semidirect
21. C23×C32×C4C22semidirect
23. C22×C4×C3⋊D3C22semidirect
25. C22×C3×#67C22semidirect
26. C23×C3×Dic3C22semidirect
27. C22×C3×D12C22semidirect
29. C2×D3×#67C22semidirect
30. C22×#627C22semidirect
32. C22×#626C22semidirect
35. C22×#625C22semidirect
36. C22×#624C22semidirect
38. C2×#3804C22semidirect
40. C22×D3×Dic3C22semidirect
41. C2×#3757C22semidirect
42. C4×#638C22semidirect
43. C2×#3752C22semidirect
44. C2×#3750C22semidirect
45. C2×C4×C3⋊Dic3C22semidirect
46. C3×#930C22semidirect
49. C2×C3×(C2×D3)⋊C4C22semidirect
50. C2×C3×(C2×D3)⋊C4C22semidirect
51. C2×C3×(C2×D3)⋊C4C22semidirect
52. C2×C3×(C2×D3)⋊C4C22semidirect
53. C2×C3×(C2×D3)⋊C4C22semidirect
54. C2×C3×C4⋊Dic3C22semidirect
55. #63976C22semidirect
56. C2×#3724C22semidirect
57. C2×#3724C22semidirect
58. #63961C22semidirect
60. C2×(C2×D3)⋊Dic3C22semidirect
61. C2×(C2×D3)⋊Dic3C22semidirect
62. C2×(C2×D3)⋊Dic3C22semidirect
63. #63922C22semidirect
64. #63921C22semidirect
65. #63915C22semidirect
66. #63912C22semidirect
67. #63902C22semidirect
68. #63899C22semidirect
69. #63885C22semidirect
70. #63854C22semidirect
82. C2×#930D3semidirect
87. C22×(C2×D3)⋊C4D3semidirect
121. C22×C32×C4C23semidirect
122. C2×#638D4semidirect
128. C2×C4×C3⋊D3C23semidirect
132. C2×C3×#67C23semidirect
138. C22×C3×Dic3C23semidirect
140. C2×C3×D12C23semidirect
143. C2×#627C23semidirect
147. C2×#626C23semidirect
153. C2×#625C23semidirect
155. C2×#624C23semidirect
160. C2×D3×Dic3C23semidirect
161. #3757C23semidirect
162. #3752C23semidirect
163. #3750C23semidirect
164. C4×C3⋊Dic3C23semidirect
167. C3×(C2×D3)⋊C4C23semidirect
168. C3×(C2×D3)⋊C4C23semidirect
169. C3×(C2×D3)⋊C4C23semidirect
170. C3×(C2×D3)⋊C4C23semidirect
171. C3×C4⋊Dic3C23semidirect
172. #3724C23semidirect
173. #3724C23semidirect
175. (C2×D3)⋊Dic3C23semidirect
176. (C2×D3)⋊Dic3C23semidirect
177. (C2×D3)⋊Dic3C23semidirect
188. C23×C3×C4C2×D3semidirect
189. C23×C3×C4C2×D3semidirect
204. C22×#67C2×D3semidirect
207. C23×Dic3C2×D3semidirect
216. C22×D12C2×D3semidirect
247. #930C2×D3semidirect
261. C2×(C2×D3)⋊C4C2×D3semidirect
262. C2×(C2×D3)⋊C4C2×D3semidirect
263. C2×(C2×D3)⋊C4C2×D3semidirect
264. C2×(C2×D3)⋊C4C2×D3semidirect
265. C2×(C2×D3)⋊C4C2×D3semidirect
266. C2×C4⋊Dic3C2×D3semidirect
315. C22×C3×D3#41semidirect
329. #638C2×D4semidirect
426. C22×C3×C4C22×D3semidirect
427. C22×C3×C4C22×D3semidirect
454. C2×#67C22×D3semidirect
473. C22×Dic3C22×D3semidirect
482. C2×D12C22×D3semidirect
524. (C2×D3)⋊C4C22×D3semidirect
525. (C2×D3)⋊C4C22×D3semidirect
526. (C2×D3)⋊C4C22×D3semidirect
527. (C2×D3)⋊C4C22×D3semidirect
528. C4⋊Dic3C22×D3semidirect
567. C2×C3×D3C2×#41semidirect
599. C23×C4D32semidirect
700. C22×D3#235semidirect
787. C2×C32#546semidirect
852. C22×C4C2×D32semidirect
941. C2×D3C2×#235semidirect
965. C32C2×#546semidirect
1044. C2×C3#5490semidirect
1045. C2×C3#5610semidirect
1099. C3C2×#5490semidirect
1100. C3C2×#5610semidirect
1107. C2#10595083direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D3×#672
C22×#38042
C2×C4×#6382
C2×C3×#9302
C22×C3×(C2×D3)⋊C42
C2×#639762
C2×#639612
#105950832
C2×#639222
C2×#639212
C2×#639152
C2×#639122
C2×#639022
C2×#638992
C2×#638852
C2×#638542
C2×#56103
C2×#54903