Finite Group Databasebeta

← C2×#10595073 #11902424

Subgroups — C2×#10595073 #11902424

Order 1152.

4013 conjugacy classes of subgroups.

The subgroup lattice has 1120 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×#64139C211yesmaximal, characteristic, complemented
4C2×C3×C4×#67C211yesmaximal, characteristic, complemented
5C22×C3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
6C2×#63977C211yesmaximal, characteristic, complemented
7C2×#63966C211yesmaximal, characteristic, complemented
8#10595073C2116yesmaximal, direct product factor
9C2×#63923C211yesmaximal, characteristic, complemented
10C2×D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
11C2×#63910C211yesmaximal, characteristic, complemented
12C2×#63906C211yesmaximal, characteristic, complemented
13C2×#63893C211yesmaximal, characteristic, complemented
14C2×#63891C211yesmaximal, characteristic, complemented
15C2×#63880C211yesmaximal, characteristic, complemented
16C2×#63852C211yesmaximal, characteristic, complemented
17C2×#5554—31nomaximal
18C2×#5490—31nomaximal
19C24×C3×D3C2211yescharacteristic
20C23×D32C2211yescharacteristic
21C23×C32×C4C2211yescharacteristic, complemented
22C22×#638C2211yescharacteristic
23C22×#638C2211yescharacteristic, complemented
24C22×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
25C22×C3×#67C2211yescharacteristic
26C23×C3×Dic3C2211yescharacteristic, complemented
27C22×C3×C4×D3C2211yescharacteristic, complemented
28C2×D3×#67—28no—
29C2×D3×#67C2218yescomplemented
30C22×#627C2211yescharacteristic, complemented
31C22×#626C2211yescharacteristic
32C22×#626C2211yescharacteristic
33C22×#626C2211yescharacteristic, complemented
34C22×#626C2211yescharacteristic, complemented
35C22×#625C2211yescharacteristic
36C22×#624C2211yescharacteristic, complemented
37C2×#3804—28no—
38C2×#3804C2218yescomplemented
39C22×D3×Dic3C2211yescharacteristic
40C22×D3×Dic3C2211yescharacteristic, complemented
41#64139C2218yescomplemented
42C2×#3752C2211yescharacteristic, complemented
43C2×#3752C2211yescharacteristic, complemented
44C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
45C2×C3×#217C2211yescharacteristic, complemented
46C3×C4×#67C2218yescomplemented
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×Dic3⋊C4C2211yescharacteristic, complemented
54C2×C3×C4×Dic3C2211yescharacteristic, complemented
55#63977C2218yescomplemented
56#63966C2218yescomplemented
57C2×Dic3⋊Dic3C2211yescharacteristic, complemented
58C2×Dic3⋊Dic3C2211yescharacteristic, complemented
59C2×#3722C2211yescharacteristic, complemented
60C2×#3722C2211yescharacteristic, complemented
61C2×(C2×D3)⋊Dic3C2211yescharacteristic
62C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
63#63923C2218yescomplemented
64D3×(C2×D3)⋊C4C2218yescomplemented
65#63910C2218yescomplemented
66#63906C2218yescomplemented
67#63893C2218yescomplemented
68#63891C2218yescomplemented
69#63880C2218yescomplemented
70#63852C2218yescomplemented
71C23×#67—31no—
72C22×#237—31no—
73C22×D3×D4—31no—
74C22×#235—31no—
75C2×C3×C4×D4—31no—
76C22×C3×C22⋊C4—31no—
77C2×#953—31no—
78C2×#930—31no—
79C2×#930—31no—
80C2×#930—31no—
81C2×#930—61no—
82C2×#929—31no—
83C2×C4×#67D311yescharacteristic, complemented
84C22×(C2×D3)⋊C4—31no—
85C22×(C2×D3)⋊C4D311yescharacteristic, complemented
86#5554—316no—
87C2×#897—31no—
88C2×#895—31no—
89C2×#886—31no—
90C2×#886—31no—
91C2×#885—31no—
92#5490—316no—
93C2×#884—31no—
94C2×#884—31no—
95C2×#883—31no—
96C2×#882—31no—
97C2×#882—31no—
98C2×#882—31no—
99C2×#67⋊C4—31no—
100C2×D3×C22⋊C4—31no—
101C2×#878—31no—
102C2×#875—31no—
103C2×C4×D12—31no—
104C24×C32C2311yescharacteristic
105C23×C3⋊D3C2311yescharacteristic
106C23×C3⋊D3C2311yescharacteristic
107C23×C3×D3—24no—
108C23×C3×D3—24no—
109C23×C3×D3—42no—
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—42no—
119C22×C32×C4C2311yescharacteristic
120C22×C32×C4C2311yescharacteristic
121C22×C32×C4C2314yescomplemented
122C2×#638—24no—
123C2×#638—24no—
124C2×#638C2314yes—
125C2×#638C2314yescomplemented
126C22×C3⋊Dic3C2311yescharacteristic
127C22×C3⋊Dic3C2311yescharacteristic
128C2×C4⋊(C3⋊D3)—42no—
129C2×C4⋊(C3⋊D3)C2314yescomplemented
130C2×C3×#67D418yescomplemented
131C2×C3×#67C2314yes—
132C22×C3×Dic3—24no—
133C22×C3×Dic3C2311yescharacteristic
134C22×C3×Dic3C2311yescharacteristic
135C22×C3×Dic3C2311yescharacteristic
136C22×C3×Dic3C2311yescharacteristic
137C22×C3×Dic3C2311yescharacteristic
138C22×C3×Dic3C2314yescomplemented
139C2×C3×C4×D3—42no—
140C2×C3×C4×D3C2314yescomplemented
141D3×#67—232no—
142C2×#627—24no—
143C2×#627C2314yescomplemented
144C2×#626—24no—
145C2×#626—24no—
146C2×#626—24no—
147C2×#626—42no—
148C2×#626C2314yes—
149C2×#626C2314yes—
150C2×#626C2314yescomplemented
151C2×#626C2314yescomplemented
152C2×#625—24no—
153C2×#625C2314yes—
154C2×#624—24no—
155C2×#624C2314yescomplemented
156#3804—232no—
157C2×D3×Dic3—24no—
158C2×D3×Dic3—24no—
159C2×D3×Dic3C2314yes—
160C2×D3×Dic3C2314yescomplemented
161#3752C2314yescomplemented
162#3752C2314yescomplemented
163C4⋊(C3⋊Dic3)C2314yescomplemented
164C3×#217C2314yescomplemented
165C3×(C2×D3)⋊C4C2314yes—
166C3×(C2×D3)⋊C4C2314yes—
167C3×(C2×D3)⋊C4C2314yescomplemented
168C3×(C2×D3)⋊C4C2314yescomplemented
169C3×(C2×D3)⋊C4C2314yescomplemented
170C3×Dic3⋊C4C2314yescomplemented
171C3×C4×Dic3C2314yescomplemented
172Dic3⋊Dic3C2314yescomplemented
173Dic3⋊Dic3C2314yescomplemented
174#3722C2314yescomplemented
175#3722C2314yescomplemented
176(C2×D3)⋊Dic3C2314yes—
177(C2×D3)⋊Dic3C2314yescomplemented
178C2×#546—91noSylow
179C25×C3—31no—
180C24×D3—31no—
181C24×D3—31no—
182C24×D3C2×D311yescharacteristic
183C22×C3×D4—31no—
184C23×C3×C4—21no—
185C23×C3×C4—31no—
186C23×C3×C4—31no—
187C23×C3×C4C2×D311yescharacteristic, complemented
188C23×C3×C4C2×D311yescharacteristic, complemented
189C22×#67—31no—
190C22×#67—31no—
191C22×#67—31no—
192C22×#67—31no—
193C22×#67—31no—
194C22×#67—31no—
195C22×#67—38no—
196C22×#67—31no—
197C22×#67—31no—
198C22×#67—31no—
199C22×#67—31no—
200C22×#67—61no—
201C22×#67—61no—
202C22×#67—68no—
203C22×#67C2×D311yescharacteristic
204C23×Dic3—31no—
205C23×Dic3—31no—
206C23×Dic3C2×D311yescharacteristic, complemented
207C2×#237—38no—
208C2×#237—68no—
209C2×D3×D4—38no—
210C2×D3×D4—68no—
211C2×#235—38no—
212C2×#235—68no—
213C22×D12—31no—
214C22×D12—31no—
215C22×D12—31no—
216C22×D12—31no—
217C22×D12—31no—
218C22×D12—31no—
219C22×D12—61no—
220C22×C4×D3—31no—
221C22×C4×D3—31no—
222C22×C4×D3—31no—
223C22×C4×D3—31no—
224C22×C4×D3C2×D311yescharacteristic, complemented
225C22×Dic6—31no—
226C22×Dic6—31no—
227C3×C4×D4—38no—
228C2×C3×C4⋊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—31no—
235C2×C3×C22⋊C4—38no—
236C2×C3×C42—31no—
237#953—38no—
238C2×#217—31no—
239C2×#217—31no—
240C2×#217C2×D311yescharacteristic, complemented
241#930—38no—
242#930—38no—
243#930—38no—
244#930—68no—
245#929—38no—
246C4×#67C2×D318yescomplemented
247C2×(C2×D3)⋊C4—31no—
248C2×(C2×D3)⋊C4—31no—
249C2×(C2×D3)⋊C4—31no—
250C2×(C2×D3)⋊C4—31no—
251C2×(C2×D3)⋊C4—31no—
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—38no—
258C2×(C2×D3)⋊C4—61no—
259C2×(C2×D3)⋊C4—61no—
260C2×(C2×D3)⋊C4C2×D311yescharacteristic
261C2×(C2×D3)⋊C4C2×D311yescharacteristic
262C2×(C2×D3)⋊C4C2×D318yescomplemented
263C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
264C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
265C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
266C2×C4⋊Dic3—31no—
267C2×C4⋊Dic3—31no—
268C2×C4⋊Dic3—31no—
269C2×C4⋊Dic3—31no—
270C2×C4⋊Dic3—61no—
271C2×Dic3⋊C4—31no—
272C2×Dic3⋊C4—31no—
273C2×Dic3⋊C4C2×D311yescharacteristic, complemented
274C2×C4×Dic3C2×D311yescharacteristic, complemented
275#897—38no—
276#895—38no—
277#886—38no—
278#886—38no—
279#885—38no—
280#884—38no—
281#884—38no—
282#883—38no—
283#882—38no—
284#882—38no—
285#882—38no—
286#67⋊C4—38no—
287D3×C22⋊C4—38no—
288#878—38no—
289#875—38no—
290C4×D12—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⋊D3—22no—
300C22×C3⋊D3—22no—
301C22×C3⋊D3—22no—
302C22×C3⋊D3C2412yes—
303C22×C3⋊D3C2412yes—
304C22×C3×D3—22no—
305C22×C3×D3—22no—
306C22×C3×D3—22no—
307C22×C3×D3—22no—
308C22×C3×D3—22no—
309C22×C3×D3—28no—
310C22×C3×D3—22no—
311C22×C3×D3—22no—
312C22×C3×D3—28no—
313C22×C3×D3—44no—
314C22×C3×D3—416no—
315C22×C3×D3C2×D414yes—
316C22×C3×D3#4114yescomplemented
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#638—28no—
330#638—28no—
331C2×C3⋊Dic3—22no—
332C2×C3⋊Dic3—22no—
333C2×C3⋊Dic3C2412yes—
334C2×C3⋊Dic3C2412yes—
335C4⋊(C3⋊D3)—44no—
336C3×#67C2×D4116yescomplemented
337C2×C3×Dic3—22no—
338C2×C3×Dic3—28no—
339C2×C3×Dic3—22no—
340C2×C3×Dic3—22no—
341C2×C3×Dic3—22no—
342C2×C3×Dic3C2×D414yes—
343C2×C3×Dic3C2412yes—
344C2×C3×Dic3C2412yes—
345C2×C3×Dic3C2412yes—
346C2×C3×Dic3C2412yes—
347C2×C3×Dic3C2412yes—
348C3×C4×D3—44no—
349#627—28no—
350#626—28no—
351#626—28no—
352#626—28no—
353#626—44no—
354#625—28no—
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—91no—
366C2×#121—91no—
367C2×#121—91no—
368C2×#120—91no—
369C2×#120—91no—
370C2×C4×D4—31no—
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—34no—
379C24×C3—64no—
380C24×C3—64no—
381C24×C3—122no—
382C24×C3C22×D311yescharacteristic
383C24×C3C22×D311yescharacteristic
384C23×D3—24no—
385C23×D3—24no—
386C23×D3—31no—
387C23×D3—31no—
388C23×D3—31no—
389C23×D3—31no—
390C23×D3—34no—
391C23×D3—34no—
392C23×D3—42no—
393C23×D3—61no—
394C23×D3—61no—
395C23×D3—64no—
396C23×D3—64no—
397C23×D3—64no—
398C23×D3—64no—
399C23×D3—122no—
400C23×D3—122no—
401C23×D3C22×D311yescharacteristic
402C23×D3C22×D314yes—
403C23×D3C22×D311yescharacteristic
404C23×D3C22×D311yescharacteristic
405C2×C3×D4—38no—
406C2×C3×D4—34no—
407C22×C3×C4—21no—
408C22×C3×C4—21no—
409C22×C3×C4—24no—
410C22×C3×C4—31no—
411C22×C3×C4—31no—
412C22×C3×C4—31no—
413C22×C3×C4—31no—
414C22×C3×C4—31no—
415C22×C3×C4—34no—
416C22×C3×C4—34no—
417C22×C3×C4—42no—
418C22×C3×C4—42no—
419C22×C3×C4—44no—
420C22×C3×C4—64no—
421C22×C3×C4—122no—
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—34no—
429C2×#67—34no—
430C2×#67—34no—
431C2×#67—34no—
432C2×#67—34no—
433C2×#67—34no—
434C2×#67—34no—
435C2×#67—34no—
436C2×#67—34no—
437C2×#67—34no—
438C2×#67—64no—
439C2×#67—64no—
440C2×#67—64no—
441C2×#67—64no—
442C2×#67—64no—
443C2×#67—64no—
444C2×#67—64no—
445C2×#67—64no—
446C2×#67—64no—
447C2×#67—64no—
448C2×#67—632no—
449C2×#67—64no—
450C2×#67—124no—
451C2×#67—124no—
452C2×#67—122no—
453C2×#67D1218yescomplemented
454C2×#67C22×D314yes—
455C22×Dic3—24no—
456C22×Dic3—31no—
457C22×Dic3—31no—
458C22×Dic3—31no—
459C22×Dic3—31no—
460C22×Dic3—34no—
461C22×Dic3—34no—
462C22×Dic3—61no—
463C22×Dic3—61no—
464C22×Dic3—64no—
465C22×Dic3—64no—
466C22×Dic3C22×D311yescharacteristic
467C22×Dic3C22×D311yescharacteristic
468C22×Dic3C22×D311yescharacteristic
469C22×Dic3C22×D311yescharacteristic
470C22×Dic3C22×D311yescharacteristic
471C22×Dic3C22×D314yescomplemented
472#237—632no—
473D3×D4—632no—
474#235—632no—
475C2×D12—34no—
476C2×D12—34no—
477C2×D12—34no—
478C2×D12—34no—
479C2×D12—34no—
480C2×D12—34no—
481C2×D12—64no—
482C2×D12—64no—
483C2×D12—64no—
484C2×D12—64no—
485C2×D12—122no—
486C2×D12—122no—
487C2×D12—124no—
488C2×D12—122no—
489C2×C4×D3—34no—
490C2×C4×D3—34no—
491C2×C4×D3—34no—
492C2×C4×D3—34no—
493C2×C4×D3—42no—
494C2×C4×D3—64no—
495C2×C4×D3—64no—
496C2×C4×D3—64no—
497C2×C4×D3—64no—
498C2×C4×D3C22×D314yescomplemented
499C2×Dic6—34no—
500C2×Dic6—34no—
501C2×Dic6—64no—
502C2×Dic6—64no—
503C3×C4⋊C4—34no—
504C3×C22⋊C4—34no—
505C3×C22⋊C4—34no—
506C3×C22⋊C4—34no—
507C3×C22⋊C4—34no—
508C3×C22⋊C4—34no—
509C3×C22⋊C4—34no—
510C3×C42—34no—
511#217—34no—
512#217—34no—
513#217C22×D314yescomplemented
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—34no—
521(C2×D3)⋊C4—34no—
522(C2×D3)⋊C4—34no—
523(C2×D3)⋊C4—34no—
524(C2×D3)⋊C4—64no—
525(C2×D3)⋊C4—64no—
526(C2×D3)⋊C4C22×D314yes—
527(C2×D3)⋊C4C22×D314yes—
528(C2×D3)⋊C4C22×D314yescomplemented
529(C2×D3)⋊C4C22×D314yescomplemented
530(C2×D3)⋊C4C22×D314yescomplemented
531C4⋊Dic3—34no—
532C4⋊Dic3—34no—
533C4⋊Dic3—34no—
534C4⋊Dic3—34no—
535C4⋊Dic3—64no—
536Dic3⋊C4—34no—
537Dic3⋊C4—34no—
538Dic3⋊C4C22×D314yescomplemented
539C4×Dic3C22×D314yescomplemented
540C22×C32—28no—
541C22×C32—22no—
542C22×C32—22no—
543C22×C32C22×D414yes—
544C22×C32C22×D412yes—
545C22×C32C2×#4112yes—
546C22×C32H(5,𝔽2)12yes—
547C22×C32C2511yescharacteristic
548C2×C3⋊D3—22no—
549C2×C3⋊D3—22no—
550C2×C3⋊D3—22no—
551C2×C3⋊D3—22no—
552C2×C3⋊D3—22no—
553C2×C3⋊D3—22no—
554C2×C3⋊D3—44no—
555C2×C3⋊D3—44no—
556C2×C3×D3—28no—
557C2×C3×D3—28no—
558C2×C3×D3—22no—
559C2×C3×D3—22no—
560C2×C3×D3—22no—
561C2×C3×D3—22no—
562C2×C3×D3—22no—
563C2×C3×D3—22no—
564C2×C3×D3—22no—
565C2×C3×D3—416no—
566C2×C3×D3—44no—
567C2×C3×D3C22×D414yes—
568C2×C3×D3C2×#4114yescomplemented
569D32—416no—
570C32×C4—22no—
571C32×C4—22no—
572C3⋊Dic3—22no—
573C3⋊Dic3—22no—
574C3×Dic3—22no—
575C3×Dic3—22no—
576C3×Dic3—22no—
577C3×Dic3—22no—
578C3×Dic3C22×D414yes—
579C25—31no—
580C25—91no—
581C2×#41—98no—
582C2×#41—188no—
583C22×Q8—91no—
584C22×D4—31no—
585C22×D4—91no—
586C22×D4—91no—
587C22×D4—91no—
588C22×D4—91no—
589C22×D4—98no—
590C22×D4—91no—
591C22×D4—91no—
592C22×D4—91no—
593C22×D4—91no—
594C22×D4—188no—
595C23×C4—31no—
596C23×C4—31no—
597C23×C4—91no—
598C23×C4—91no—
599C23×C4—91no—
600C23×C4D3211yescharacteristic, complemented
601#124—98no—
602#123—98no—
603#123—98no—
604C22⋊Q8—98no—
605#121—98no—
606#121—98no—
607#121—98no—
608#120—98no—
609#120—98no—
610C4×D4—38no—
611C4×D4—98no—
612C2×C4⋊C4—31no—
613C2×C4⋊C4—91no—
614C2×C4⋊C4—91no—
615C2×C4⋊C4—91no—
616C2×C22⋊C4—31no—
617C2×C22⋊C4—31no—
618C2×C22⋊C4—31no—
619C2×C22⋊C4—31no—
620C2×C22⋊C4—31no—
621C2×C22⋊C4—31no—
622C2×C22⋊C4—38no—
623C2×C22⋊C4—98no—
624C2×C22⋊C4—91no—
625C2×C22⋊C4—91no—
626C2×C22⋊C4—91no—
627C2×C22⋊C4—91no—
628C2×C22⋊C4—91no—
629C2×C22⋊C4—91no—
630C2×C42—31no—
631C23×C3—22no—
632C23×C3—22no—
633C23×C3—22no—
634C23×C3—22no—
635C23×C3—22no—
636C23×C3—21no—
637C23×C3—24no—
638C23×C3—34no—
639C23×C3—34no—
640C23×C3—32no—
641C23×C3—32no—
642C23×C3—32no—
643C23×C3—42no—
644C23×C3—42no—
645C23×C3—68no—
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—124no—
655C23×C3—1216no—
656C23×C3C2×D1214yes—
657C23×C3D3×D414yes—
658C23×C3C23×D312yes—
659C23×C3C23×D312yes—
660C23×C3C23×D311yescharacteristic
661C23×C3C23×D311yescharacteristic
662C22×D3—22no—
663C22×D3—22no—
664C22×D3—22no—
665C22×D3—22no—
666C22×D3—22no—
667C22×D3—22no—
668C22×D3—28no—
669C22×D3—22no—
670C22×D3—28no—
671C22×D3—32no—
672C22×D3—32no—
673C22×D3—32no—
674C22×D3—32no—
675C22×D3—44no—
676C22×D3—416no—
677C22×D3—62no—
678C22×D3—62no—
679C22×D3—68no—
680C22×D3—68no—
681C22×D3—62no—
682C22×D3—62no—
683C22×D3—62no—
684C22×D3—62no—
685C22×D3—62no—
686C22×D3—62no—
687C22×D3—62no—
688C22×D3—62no—
689C22×D3—62no—
690C22×D3—62no—
691C22×D3—62no—
692C22×D3—62no—
693C22×D3—68no—
694C22×D3—68no—
695C22×D3—122no—
696C22×D3—122no—
697C22×D3—122no—
698C22×D3—122no—
699C22×D3—122no—
700C22×D3—122no—
701C22×D3—124no—
702C22×D3—124no—
703C22×D3—1216no—
704C22×D3—1216no—
705C22×D3C2×D1214yes—
706C22×D3#23514yescomplemented
707C22×D3C23×D312yes—
708C22×D3C23×D312yes—
709C22×D3C23×D312yes—
710C3×D4—316no—
711C2×C3×C4—24no—
712C2×C3×C4—22no—
713C2×C3×C4—22no—
714C2×C3×C4—22no—
715C2×C3×C4—22no—
716C2×C3×C4—22no—
717C2×C3×C4—22no—
718C2×C3×C4—34no—
719C2×C3×C4—32no—
720C2×C3×C4—32no—
721C2×C3×C4—32no—
722C2×C3×C4—32no—
723C2×C3×C4—32no—
724C2×C3×C4—42no—
725C2×C3×C4—44no—
726C2×C3×C4—44no—
727C2×C3×C4—48no—
728C2×C3×C4—62no—
729C2×C3×C4—62no—
730C2×C3×C4—68no—
731C2×C3×C4—62no—
732C2×C3×C4—62no—
733C2×C3×C4—124no—
734C2×C3×C4C23×D312yes—
735C2×C3×C4C23×D312yes—
736C2×C3×C4C23×D312yes—
737C2×C3×C4C23×D312yes—
738#67—68no—
739#67—68no—
740#67—68no—
741#67—68no—
742#67—68no—
743#67—68no—
744#67—68no—
745#67—68no—
746#67—68no—
747#67—128no—
748#67—128no—
749#67—124no—
750#67C2×D12116yescomplemented
751C2×Dic3—22no—
752C2×Dic3—22no—
753C2×Dic3—28no—
754C2×Dic3—22no—
755C2×Dic3—22no—
756C2×Dic3—32no—
757C2×Dic3—32no—
758C2×Dic3—32no—
759C2×Dic3—32no—
760C2×Dic3—62no—
761C2×Dic3—62no—
762C2×Dic3—68no—
763C2×Dic3—62no—
764C2×Dic3—62no—
765C2×Dic3—62no—
766C2×Dic3—62no—
767C2×Dic3—68no—
768C2×Dic3—122no—
769C2×Dic3—122no—
770C2×Dic3C2×D1214yes—
771C2×Dic3C23×D312yes—
772C2×Dic3C23×D312yes—
773C2×Dic3C23×D312yes—
774C2×Dic3C23×D312yes—
775C2×Dic3C23×D312yes—
776D12—68no—
777D12—68no—
778D12—68no—
779D12—124no—
780D12—124no—
781D12—128no—
782D12—124no—
783C4×D3—44no—
784C4×D3—68no—
785C4×D3—68no—
786C4×D3—68no—
787C4×D3—68no—
788Dic6—68no—
789Dic6—68no—
790C2×C32—24no—
791C2×C32#54614yescomplemented
792C2×C32C23×D411yescharacteristic
793C2×C32C22×#4111yescharacteristic
794C2×C32C2×H(5,𝔽2)11yescharacteristic
795C3⋊D3—42no—
796C3⋊D3—42no—
797C3×D3—24no—
798C3×D3—24no—
799C3×D3—42no—
800C24—31no—
801C24—31no—
802C24—31no—
803C24—34no—
804C24—64no—
805C24—64no—
806C24—94no—
807C24—91no—
808C24—91no—
809C24—122no—
810C24—184no—
811C24—184no—
812C24—362no—
813C24C2×D3211yescharacteristic
814#41—1832no—
815C2×Q8—94no—
816C2×Q8—184no—
817C2×D4—34no—
818C2×D4—38no—
819C2×D4—94no—
820C2×D4—94no—
821C2×D4—94no—
822C2×D4—94no—
823C2×D4—94no—
824C2×D4—94no—
825C2×D4—94no—
826C2×D4—94no—
827C2×D4—184no—
828C2×D4—184no—
829C2×D4—184no—
830C2×D4—1832no—
831C2×D4—184no—
832C2×D4—184no—
833C2×D4—184no—
834C2×D4—362no—
835C2×D4—362no—
836C22×C4—31no—
837C22×C4—34no—
838C22×C4—31no—
839C22×C4—31no—
840C22×C4—31no—
841C22×C4—31no—
842C22×C4—34no—
843C22×C4—42no—
844C22×C4—64no—
845C22×C4—94no—
846C22×C4—94no—
847C22×C4—94no—
848C22×C4—91no—
849C22×C4—91no—
850C22×C4—122no—
851C22×C4—184no—
852C22×C4—184no—
853C22×C4—184no—
854C22×C4C2×D3211yescharacteristic
855C22×C4C2×D3211yescharacteristic
856C22×C4C2×D3214yescomplemented
857C4⋊C4—34no—
858C4⋊C4—94no—
859C4⋊C4—94no—
860C4⋊C4—94no—
861C22⋊C4—34no—
862C22⋊C4—34no—
863C22⋊C4—34no—
864C22⋊C4—34no—
865C22⋊C4—34no—
866C22⋊C4—34no—
867C22⋊C4—94no—
868C22⋊C4—94no—
869C22⋊C4—94no—
870C22⋊C4—94no—
871C22⋊C4—94no—
872C22⋊C4—94no—
873C42—34no—
874C22×C3—22no—
875C22×C3—22no—
876C22×C3—22no—
877C22×C3—22no—
878C22×C3—28no—
879C22×C3—28no—
880C22×C3—22no—
881C22×C3—24no—
882C22×C3—22no—
883C22×C3—22no—
884C22×C3—21no—
885C22×C3—34no—
886C22×C3—34no—
887C22×C3—42no—
888C22×C3—48no—
889C22×C3—42no—
890C22×C3—62no—
891C22×C3—62no—
892C22×C3—62no—
893C22×C3—62no—
894C22×C3—68no—
895C22×C3—68no—
896C22×C3—62no—
897C22×C3—62no—
898C22×C3—62no—
899C22×C3—1216no—
900C22×C3—124no—
901C22×C3C22×D1214yes—
902C22×C3C22×D1212yes—
903C22×C3C2×#23512yes—
904C22×C3C2×D3×D414yes—
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—22no—
914C2×D3—22no—
915C2×D3—28no—
916C2×D3—28no—
917C2×D3—22no—
918C2×D3—22no—
919C2×D3—22no—
920C2×D3—416no—
921C2×D3—44no—
922C2×D3—62no—
923C2×D3—62no—
924C2×D3—62no—
925C2×D3—62no—
926C2×D3—62no—
927C2×D3—62no—
928C2×D3—62no—
929C2×D3—62no—
930C2×D3—62no—
931C2×D3—62no—
932C2×D3—62no—
933C2×D3—62no—
934C2×D3—122no—
935C2×D3—122no—
936C2×D3—122no—
937C2×D3—122no—
938C2×D3—122no—
939C2×D3—122no—
940C2×D3—1216no—
941C2×D3—1216no—
942C2×D3—124no—
943C2×D3—124no—
944C2×D3—124no—
945C2×D3—124no—
946C2×D3—244no—
947C2×D3—244no—
948C2×D3C22×D1214yes—
949C2×D3C2×#23514yescomplemented
950C3×C4—24no—
951C3×C4—22no—
952C3×C4—22no—
953C3×C4—22no—
954C3×C4—22no—
955C3×C4—34no—
956C3×C4—42no—
957C3×C4—62no—
958C3×C4—62no—
959C3×C4—62no—
960C3×C4—62no—
961Dic3—22no—
962Dic3—22no—
963Dic3—22no—
964Dic3—22no—
965Dic3—62no—
966Dic3—62no—
967Dic3—62no—
968Dic3—62no—
969Dic3—122no—
970Dic3—122no—
971Dic3C22×D1214yes—
972C32C2×#54611yescharacteristic, complemented, Sylow
973C23—22no—
974C23—22no—
975C23—34no—
976C23—34no—
977C23—32no—
978C23—32no—
979C23—32no—
980C23—68no—
981C23—62no—
982C23—62no—
983C23—62no—
984C23—62no—
985C23—68no—
986C23—62no—
987C23—62no—
988C23—62no—
989C23—92no—
990C23—92no—
991C23—124no—
992C23—1216no—
993C23—188no—
994C23—188no—
995C23—182no—
996C23—182no—
997C23—182no—
998C23—182no—
999C23—182no—
1000C23—182no—
1001C23—364no—
1002C23—3616no—
1003C23D3×D1214yes—
1004C23C22×D3212yes—
1005C23C22×D3211yescharacteristic
1006Q8—188no—
1007D4—316no—
1008D4—188no—
1009D4—188no—
1010D4—188no—
1011D4—188no—
1012D4—188no—
1013D4—188no—
1014D4—364no—
1015D4—364no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—34no—
1019C2×C4—32no—
1020C2×C4—32no—
1021C2×C4—32no—
1022C2×C4—32no—
1023C2×C4—32no—
1024C2×C4—44no—
1025C2×C4—62no—
1026C2×C4—62no—
1027C2×C4—68no—
1028C2×C4—62no—
1029C2×C4—62no—
1030C2×C4—92no—
1031C2×C4—92no—
1032C2×C4—124no—
1033C2×C4—188no—
1034C2×C4—188no—
1035C2×C4—188no—
1036C2×C4—182no—
1037C2×C4—182no—
1038C2×C4C22×D3212yes—
1039C2×C4C22×D3212yes—
1040C2×C3—24no—
1041C2×C3—24no—
1042C2×C3—24no—
1043C2×C3—21no—
1044C2×C3—21no—
1045C2×C3—21no—
1046C2×C3—44no—
1047C2×C3—64no—
1048C2×C3—64no—
1049C2×C3—122no—
1050C2×C3#549014yescomplemented
1051C2×C3#555414yescomplemented
1052C2×C3C23×D1211yescharacteristic
1053C2×C3C22×#23511yescharacteristic
1054C2×C3C22×D3×D411yescharacteristic
1055C2×C3C2×#100411yescharacteristic
1056C2×C3C2×#100411yescharacteristic
1057C2×C3C2×D3×#4111yescharacteristic
1058D3—24no—
1059D3—24no—
1060D3—42no—
1061D3—122no—
1062D3—122no—
1063D3—122no—
1064D3—122no—
1065D3—242no—
1066D3—242no—
1067C22—28no—
1068C22—22no—
1069C22—22no—
1070C22—34no—
1071C22—34no—
1072C22—68no—
1073C22—68no—
1074C22—62no—
1075C22—62no—
1076C22—62no—
1077C22—62no—
1078C22—62no—
1079C22—62no—
1080C22—62no—
1081C22—1216no—
1082C22—124no—
1083C22—182no—
1084C22—182no—
1085C22—182no—
1086C22—182no—
1087C22—182no—
1088C22—182no—
1089C22—3616no—
1090C22—364no—
1091C22—364no—
1092C22C2×D3×D1214yes—
1093C22C2×D3×D1212yes—
1094C22D3×#23512yes—
1095C22#6433012yes—
1096C22C23×D3211yescharacteristic
1097C4—22no—
1098C4—22no—
1099C4—34no—
1100C4—62no—
1101C4—62no—
1102C4—62no—
1103C4—62no—
1104C4—182no—
1105C4—182no—
1106C3—21no—
1107C3C2×#549011yescharacteristic, complemented
1108C3C2×#555411yescharacteristic, complemented
1109C2—24no—
1110C2—64no—
1111C2—64no—
1112C2—122no—
1113C2—362no—
1114C2—362no—
1115C2#1059507314yesdirect product factor
1116C2C22×D3×D1211yescharacteristic
1117C2C2×D3×#23511yescharacteristic
1118C2C2×#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×#64139C2semidirect
4. C2×C3×C4×#67C2semidirect
5. C22×C3×(C2×D3)⋊C4C2semidirect
6. C2×#63977C2semidirect
7. C2×#63966C2semidirect
8. #10595073C2direct (N × H)
9. C2×#63923C2semidirect
10. C2×D3×(C2×D3)⋊C4C2semidirect
11. C2×#63910C2semidirect
12. C2×#63906C2semidirect
13. C2×#63893C2semidirect
14. C2×#63891C2semidirect
15. C2×#63880C2semidirect
16. C2×#63852C2semidirect
21. C23×C32×C4C22semidirect
23. C22×#638C22semidirect
24. C22×C4⋊(C3⋊D3)C22semidirect
26. C23×C3×Dic3C22semidirect
27. C22×C3×C4×D3C22semidirect
29. C2×D3×#67C22semidirect
30. C22×#627C22semidirect
33. C22×#626C22semidirect
34. C22×#626C22semidirect
36. C22×#624C22semidirect
38. C2×#3804C22semidirect
40. C22×D3×Dic3C22semidirect
41. #64139C22semidirect
42. C2×#3752C22semidirect
43. C2×#3752C22semidirect
44. C2×C4⋊(C3⋊Dic3)C22semidirect
45. C2×C3×#217C22semidirect
46. C3×C4×#67C22semidirect
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×Dic3⋊C4C22semidirect
54. C2×C3×C4×Dic3C22semidirect
55. #63977C22semidirect
56. #63966C22semidirect
57. C2×Dic3⋊Dic3C22semidirect
58. C2×Dic3⋊Dic3C22semidirect
59. C2×#3722C22semidirect
60. C2×#3722C22semidirect
62. C2×(C2×D3)⋊Dic3C22semidirect
63. #63923C22semidirect
64. D3×(C2×D3)⋊C4C22semidirect
65. #63910C22semidirect
66. #63906C22semidirect
67. #63893C22semidirect
68. #63891C22semidirect
69. #63880C22semidirect
70. #63852C22semidirect
83. C2×C4×#67D3semidirect
85. C22×(C2×D3)⋊C4D3semidirect
121. C22×C32×C4C23semidirect
125. C2×#638C23semidirect
129. C2×C4⋊(C3⋊D3)C23semidirect
130. C2×C3×#67D4semidirect
138. C22×C3×Dic3C23semidirect
140. C2×C3×C4×D3C23semidirect
143. C2×#627C23semidirect
150. C2×#626C23semidirect
151. C2×#626C23semidirect
155. C2×#624C23semidirect
160. C2×D3×Dic3C23semidirect
161. #3752C23semidirect
162. #3752C23semidirect
163. C4⋊(C3⋊Dic3)C23semidirect
164. C3×#217C23semidirect
167. C3×(C2×D3)⋊C4C23semidirect
168. C3×(C2×D3)⋊C4C23semidirect
169. C3×(C2×D3)⋊C4C23semidirect
170. C3×Dic3⋊C4C23semidirect
171. C3×C4×Dic3C23semidirect
172. Dic3⋊Dic3C23semidirect
173. Dic3⋊Dic3C23semidirect
174. #3722C23semidirect
175. #3722C23semidirect
177. (C2×D3)⋊Dic3C23semidirect
187. C23×C3×C4C2×D3semidirect
188. C23×C3×C4C2×D3semidirect
206. C23×Dic3C2×D3semidirect
224. C22×C4×D3C2×D3semidirect
240. C2×#217C2×D3semidirect
246. C4×#67C2×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
273. C2×Dic3⋊C4C2×D3semidirect
274. C2×C4×Dic3C2×D3semidirect
316. C22×C3×D3#41semidirect
336. C3×#67C2×D4semidirect
426. C22×C3×C4C22×D3semidirect
427. C22×C3×C4C22×D3semidirect
453. C2×#67D12semidirect
471. C22×Dic3C22×D3semidirect
498. C2×C4×D3C22×D3semidirect
513. #217C22×D3semidirect
528. (C2×D3)⋊C4C22×D3semidirect
529. (C2×D3)⋊C4C22×D3semidirect
530. (C2×D3)⋊C4C22×D3semidirect
538. Dic3⋊C4C22×D3semidirect
539. C4×Dic3C22×D3semidirect
568. C2×C3×D3C2×#41semidirect
600. C23×C4D32semidirect
706. C22×D3#235semidirect
750. #67C2×D12semidirect
791. C2×C32#546semidirect
856. C22×C4C2×D32semidirect
949. C2×D3C2×#235semidirect
972. C32C2×#546semidirect
1050. C2×C3#5490semidirect
1051. C2×C3#5554semidirect
1107. C3C2×#5490semidirect
1108. C3C2×#5554semidirect
1115. C2#10595073direct (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×#641392
C2×C3×C4×#672
C22×C3×(C2×D3)⋊C42
C2×#639772
C2×#639662
#105950732
C2×#639232
C2×D3×(C2×D3)⋊C42
C2×#639102
C2×#639062
C2×#638932
C2×#638912
C2×#638802
C2×#638522
C2×#55543
C2×#54903