Finite Group Databasebeta

← C2×#10594294 #11902417

Subgroups — C2×#10594294 #11902417

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×#64090C211yesmaximal, characteristic, complemented
4C2×C3×#886C211yesmaximal, characteristic, complemented
5C2×C3×#882C211yesmaximal, characteristic, complemented
6C2×#63980C211yesmaximal, characteristic, complemented
7C22×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
8C2×#63922C211yesmaximal, characteristic, complemented
9C2×#63921C211yesmaximal, characteristic, complemented
10C2×#63916C211yesmaximal, characteristic, complemented
11C2×#63915C211yesmaximal, characteristic, complemented
12C2×#63899C211yesmaximal, characteristic, complemented
13C2×#63898C211yesmaximal, characteristic, complemented
14C2×#63885C211yesmaximal, characteristic, complemented
15C2×#63854C211yesmaximal, characteristic, complemented
16#10594294C2116yesmaximal, direct product factor
17C2×#5654—31nomaximal
18C2×#5591—31nomaximal
19C24×C3×D3C2211yescharacteristic
20C23×D32C2211yescharacteristic
21C22×#638C2211yescharacteristic
22C23×C3⋊Dic3C2211yescharacteristic, complemented
23C22×C4×C3⋊D3C2211yescharacteristic, complemented
24C22×C3×#67C2211yescharacteristic
25C22×C3×#67C2211yescharacteristic, complemented
26C23×C3×Dic3C2211yescharacteristic, complemented
27C22×C3×D12C2211yescharacteristic
28C22×C3×D12C2211yescharacteristic, complemented
29C2×D3×#67—28no—
30C2×D3×#67C2218yescomplemented
31C22×#627C2211yescharacteristic, complemented
32C22×#626C2211yescharacteristic
33C22×#626C2211yescharacteristic, complemented
34C22×#625C2211yescharacteristic
35C22×#625C2211yescharacteristic, complemented
36C22×#624C2211yescharacteristic, complemented
37C2×#3804—28no—
38C2×#3804C2218yescomplemented
39C22×D3×Dic3C2211yescharacteristic
40C22×D3×Dic3C2211yescharacteristic, complemented
41C2×C32×C22⋊C4C2211yescharacteristic, complemented
42C2×#3752C2211yescharacteristic, complemented
43C2×#3750C2211yescharacteristic, complemented
44C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
45#64090C2218yescomplemented
46C2×C3×(C2×D3)⋊C4C2211yescharacteristic
47C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
48C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
49C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
50C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
51C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
52C3×#886C2218yescomplemented
53C3×#882C2218yescomplemented
54#63980C2218yescomplemented
55C2×#3724C2211yescharacteristic, complemented
56C2×(C2×D3)⋊Dic3C2211yescharacteristic
57C2×(C2×D3)⋊Dic3C2211yescharacteristic
58C2×(C2×D3)⋊Dic3C2218yescomplemented
59C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
60C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
61C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
62C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
63#63922C2218yescomplemented
64#63921C2218yescomplemented
65#63916C2218yescomplemented
66#63915C2218yescomplemented
67#63899C2218yescomplemented
68#63898C2218yescomplemented
69#63885C2218yescomplemented
70#63854C2218yescomplemented
71C23×#67—31no—
72C22×#237—31no—
73C22×D3×D4—31no—
74C22×#235—31no—
75C2×C3×#123—31no—
76C2×C3×#120—31no—
77C22×#217—31no—
78C2×#939—31no—
79C2×#939—31no—
80C2×#939—31no—
81C2×#938—31no—
82C2×#937—31no—
83C2×D4×Dic3—31no—
84C22×(C2×D3)⋊C4—31no—
85#5654—316no—
86#5591—316no—
87C2×#896—31no—
88C2×#895—31no—
89C2×#894—31no—
90C2×#893—31no—
91C2×#886D311yescharacteristic, complemented
92C2×#885—31no—
93C2×#885—31no—
94C2×#884—31no—
95C2×#883—31no—
96C2×#882—31no—
97C2×#882D311yescharacteristic, complemented
98C2×#67⋊C4—31no—
99C2×#67⋊C4—31no—
100C2×#67⋊C4—61no—
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×C4C2311yescharacteristic
119C22×C32×C4C2311yescharacteristic
120C2×#638D418yescomplemented
121C2×#638C2314yes—
122C22×C3⋊Dic3—42no—
123C22×C3⋊Dic3C2311yescharacteristic
124C22×C3⋊Dic3C2311yescharacteristic
125C22×C3⋊Dic3C2311yescharacteristic
126C22×C3⋊Dic3C2314yescomplemented
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—24no—
140C2×C3×D12—42no—
141C2×C3×D12C2314yes—
142C2×C3×D12C2314yescomplemented
143D3×#67—232no—
144C2×#627—24no—
145C2×#627C2314yescomplemented
146C2×#626—24no—
147C2×#626—24no—
148C2×#626C2314yes—
149C2×#626C2314yescomplemented
150C2×#625—24no—
151C2×#625—42no—
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
161C32×C22⋊C4C2314yescomplemented
162#3752C2314yescomplemented
163#3750C2314yescomplemented
164C4×C3⋊Dic3C2314yescomplemented
165C3×(C2×D3)⋊C4C2314yes—
166C3×(C2×D3)⋊C4C2314yescomplemented
167C3×(C2×D3)⋊C4C2314yescomplemented
168C3×(C2×D3)⋊C4C2314yescomplemented
169C3×C4⋊Dic3C2314yescomplemented
170C3×C4⋊Dic3C2314yescomplemented
171#3724C2314yescomplemented
172(C2×D3)⋊Dic3C2314yes—
173(C2×D3)⋊Dic3C2314yes—
174(C2×D3)⋊Dic3C2314yescomplemented
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—
186C22×C3×D4—31no—
187C23×C3×C4—31no—
188C22×#67—31no—
189C22×#67—31no—
190C22×#67—31no—
191C22×#67—31no—
192C22×#67—31no—
193C22×#67—31no—
194C22×#67—38no—
195C22×#67—31no—
196C22×#67—31no—
197C22×#67—61no—
198C22×#67—68no—
199C22×#67C2×D311yescharacteristic
200C22×#67C2×D311yescharacteristic, complemented
201C23×Dic3—31no—
202C23×Dic3—31no—
203C23×Dic3—31no—
204C23×Dic3—31no—
205C23×Dic3—61no—
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×D12C2×D311yescharacteristic
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×#123—38no—
227C3×#120—38no—
228C2×C3×C4⋊C4—31no—
229C2×C3×C4⋊C4—31no—
230C2×C3×C22⋊C4—21no—
231C2×C3×C22⋊C4—31no—
232C2×C3×C22⋊C4—31no—
233C2×C3×C22⋊C4—31no—
234C2×C3×C22⋊C4—31no—
235C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
236C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
237C2×#217—31no—
238C2×#217—31no—
239C2×#217—31no—
240C2×#217—31no—
241C2×#217—31no—
242C2×#217—31no—
243C2×#217—38no—
244#939—38no—
245#939—38no—
246#939—38no—
247#938—38no—
248#937—38no—
249D4×Dic3—38no—
250C2×(C2×D3)⋊C4—38no—
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—31no—
258C2×(C2×D3)⋊C4—31no—
259C2×(C2×D3)⋊C4—61no—
260C2×(C2×D3)⋊C4C2×D311yescharacteristic
261C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
262C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
263C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
264C2×C4⋊Dic3C2×D311yescharacteristic, complemented
265C2×C4⋊Dic3C2×D311yescharacteristic, complemented
266C2×Dic3⋊C4—31no—
267C2×Dic3⋊C4—31no—
268C2×Dic3⋊C4—31no—
269C2×Dic3⋊C4—31no—
270C2×Dic3⋊C4—61no—
271C2×C4×Dic3—31no—
272C2×C4×Dic3—31no—
273C2×C4×Dic3—61no—
274#896—38no—
275#895—38no—
276#894—38no—
277#893—38no—
278#886C2×D318yescomplemented
279#885—38no—
280#885—38no—
281#884—38no—
282#883—38no—
283#882—38no—
284#882C2×D318yescomplemented
285#67⋊C4—38no—
286#67⋊C4—38no—
287#67⋊C4—68no—
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×C4C2412yes—
327C2×C32×C4C2412yes—
328#638C2×D4116yescomplemented
329C2×C3⋊Dic3—22no—
330C2×C3⋊Dic3—22no—
331C2×C3⋊Dic3—44no—
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—28no—
349C3×D12—44no—
350#627—28no—
351#626—28no—
352#626—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—31no—
363C2×#123—91no—
364C2×C22⋊Q8—91no—
365C2×#121—91no—
366C2×#121—91no—
367C2×#121—91no—
368C2×#120—31no—
369C2×#120—91no—
370C2×C4×D4—91no—
371C2×C4×D4—91no—
372C22×C22⋊C4—91no—
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—34no—
408C2×C3×D4—64no—
409C2×C3×D4—64no—
410C2×C3×D4—64no—
411C2×C3×D4—122no—
412C22×C3×C4—21no—
413C22×C3×C4—21no—
414C22×C3×C4—31no—
415C22×C3×C4—31no—
416C22×C3×C4—31no—
417C22×C3×C4—31no—
418C22×C3×C4—34no—
419C22×C3×C4—64no—
420C22×C3×C4C22×D311yescharacteristic
421C22×C3×C4C22×D311yescharacteristic
422C22×C3×C4C22×D311yescharacteristic
423C22×C3×C4C22×D311yescharacteristic
424C2×#67—24no—
425C2×#67—24no—
426C2×#67—38no—
427C2×#67—38no—
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—64no—
437C2×#67—68no—
438C2×#67—64no—
439C2×#67—64no—
440C2×#67—64no—
441C2×#67—64no—
442C2×#67—632no—
443C2×#67—122no—
444C2×#67—122no—
445C2×#67C22×D314yes—
446C2×#67C22×D314yescomplemented
447C22×Dic3—24no—
448C22×Dic3—31no—
449C22×Dic3—31no—
450C22×Dic3—31no—
451C22×Dic3—31no—
452C22×Dic3—31no—
453C22×Dic3—31no—
454C22×Dic3—34no—
455C22×Dic3—34no—
456C22×Dic3—34no—
457C22×Dic3—34no—
458C22×Dic3—61no—
459C22×Dic3—61no—
460C22×Dic3—64no—
461C22×Dic3—61no—
462C22×Dic3—64no—
463C22×Dic3—64no—
464C22×Dic3—122no—
465C22×Dic3—122no—
466C22×Dic3—124no—
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—24no—
476C2×D12—34no—
477C2×D12—34no—
478C2×D12—42no—
479C2×D12—64no—
480C2×D12—64no—
481C2×D12C22×D314yes—
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×C4⋊C4—34no—
503C3×C22⋊C4—24no—
504C3×C22⋊C4—34no—
505C3×C22⋊C4—34no—
506C3×C22⋊C4—34no—
507C3×C22⋊C4—34no—
508C3×C22⋊C4C22×D314yescomplemented
509C3×C22⋊C4C22×D314yescomplemented
510#217—34no—
511#217—34no—
512#217—34no—
513#217—34no—
514#217—34no—
515#217—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)⋊C4C22×D314yes—
526(C2×D3)⋊C4C22×D314yescomplemented
527(C2×D3)⋊C4C22×D314yescomplemented
528(C2×D3)⋊C4C22×D314yescomplemented
529C4⋊Dic3C22×D314yescomplemented
530C4⋊Dic3C22×D314yescomplemented
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—31no—
587C22×D4—91no—
588C22×D4—91no—
589C22×D4—98no—
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×C4—91no—
600#124—98no—
601#123—38no—
602#123—98no—
603C22⋊Q8—98no—
604#121—98no—
605#121—98no—
606#121—98no—
607#120—38no—
608#120—98no—
609C4×D4—98no—
610C4×D4—98no—
611C2×C4⋊C4—31no—
612C2×C4⋊C4—31no—
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—98no—
620C2×C22⋊C4—91no—
621C2×C22⋊C4—91no—
622C2×C22⋊C4—91no—
623C2×C22⋊C4—91no—
624C2×C22⋊C4—91no—
625C2×C22⋊C4—98no—
626C2×C22⋊C4—91no—
627C2×C22⋊C4—91no—
628C2×C22⋊C4D3211yescharacteristic, complemented
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—68no—
649C23×C3—62no—
650C23×C3—62no—
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—28no—
670C22×D3—22no—
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#23714yescomplemented
701C22×D3C23×D312yes—
702C22×D3C23×D312yes—
703C22×D3C23×D312yes—
704C22×D3C23×D312yes—
705C3×D4—68no—
706C3×D4—68no—
707C3×D4—68no—
708C3×D4—124no—
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—42no—
721C2×C3×C4—62no—
722C2×C3×C4—62no—
723C2×C3×C4—62no—
724C2×C3×C4—62no—
725C2×C3×C4—68no—
726C2×C3×C4C23×D312yes—
727C2×C3×C4C23×D312yes—
728C2×C3×C4C23×D312yes—
729C2×C3×C4C23×D312yes—
730#67—28no—
731#67—28no—
732#67—316no—
733#67—316no—
734#67—616no—
735#67—68no—
736#67—68no—
737#67—68no—
738#67—68no—
739#67—124no—
740#67—124no—
741C2×Dic3—22no—
742C2×Dic3—22no—
743C2×Dic3—22no—
744C2×Dic3—28no—
745C2×Dic3—22no—
746C2×Dic3—34no—
747C2×Dic3—34no—
748C2×Dic3—32no—
749C2×Dic3—32no—
750C2×Dic3—32no—
751C2×Dic3—32no—
752C2×Dic3—32no—
753C2×Dic3—32no—
754C2×Dic3—64no—
755C2×Dic3—62no—
756C2×Dic3—62no—
757C2×Dic3—62no—
758C2×Dic3—68no—
759C2×Dic3—68no—
760C2×Dic3—64no—
761C2×Dic3—62no—
762C2×Dic3—62no—
763C2×Dic3—62no—
764C2×Dic3—62no—
765C2×Dic3—122no—
766C2×Dic3—124no—
767C2×Dic3—124no—
768C2×Dic3—128no—
769C2×Dic3C23×D312yes—
770C2×Dic3C23×D312yes—
771C2×Dic3C23×D312yes—
772C2×Dic3C23×D312yes—
773D12—28no—
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—34no—
817C2×D4—64no—
818C2×D4—64no—
819C2×D4—64no—
820C2×D4—94no—
821C2×D4—94no—
822C2×D4—94no—
823C2×D4—98no—
824C2×D4—94no—
825C2×D4—94no—
826C2×D4—122no—
827C2×D4—184no—
828C2×D4—184no—
829C2×D4—184no—
830C2×D4—1832no—
831C2×D4—362no—
832C22×C4—34no—
833C22×C4—31no—
834C22×C4—31no—
835C22×C4—31no—
836C22×C4—31no—
837C22×C4—64no—
838C22×C4—94no—
839C22×C4—94no—
840C22×C4—94no—
841C22×C4—91no—
842C22×C4—91no—
843C22×C4—91no—
844C22×C4—94no—
845C22×C4—94no—
846C22×C4—184no—
847C22×C4—184no—
848C22×C4—184no—
849C22×C4—362no—
850C22×C4—362no—
851C22×C4C2×D3211yescharacteristic
852C22×C4C2×D3211yescharacteristic
853C4⋊C4—34no—
854C4⋊C4—34no—
855C4⋊C4—94no—
856C4⋊C4—94no—
857C22⋊C4—34no—
858C22⋊C4—34no—
859C22⋊C4—34no—
860C22⋊C4—34no—
861C22⋊C4—94no—
862C22⋊C4—94no—
863C22⋊C4—94no—
864C22⋊C4—94no—
865C22⋊C4—94no—
866C22⋊C4—94no—
867C22⋊C4—94no—
868C22⋊C4C2×D3214yescomplemented
869C42—94no—
870C22×C3—28no—
871C22×C3—22no—
872C22×C3—22no—
873C22×C3—22no—
874C22×C3—22no—
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—42no—
884C22×C3—48no—
885C22×C3—68no—
886C22×C3—62no—
887C22×C3—62no—
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×D3×D414yes—
902C22×C3C2×D3×D414yes—
903C22×C3C2×D3×D412yes—
904C22×C3C2×D3×D412yes—
905C22×C3C2×#23712yes—
906C22×C3#100412yes—
907C22×C3D3×#4112yes—
908C22×C3#100912yes—
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—68no—
931C2×D3—62no—
932C2×D3—62no—
933C2×D3—62no—
934C2×D3—62no—
935C2×D3—68no—
936C2×D3—122no—
937C2×D3—122no—
938C2×D3—128no—
939C2×D3—1216no—
940C2×D3—1216no—
941C2×D3C2×#23714yescomplemented
942C3×C4—22no—
943C3×C4—22no—
944C3×C4—22no—
945C3×C4—22no—
946C3×C4—42no—
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—64no—
960Dic3—62no—
961Dic3—62no—
962Dic3—62no—
963Dic3—62no—
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—68no—
1003D4—916no—
1004D4—124no—
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—62no—
1016C2×C4—62no—
1017C2×C4—68no—
1018C2×C4—62no—
1019C2×C4—62no—
1020C2×C4—94no—
1021C2×C4—92no—
1022C2×C4—92no—
1023C2×C4—92no—
1024C2×C4—188no—
1025C2×C4—188no—
1026C2×C4—188no—
1027C2×C4—182no—
1028C2×C4—182no—
1029C2×C4—364no—
1030C2×C4—364no—
1031C2×C4C22×D3212yes—
1032C2×C4C22×D3212yes—
1033C2×C3—24no—
1034C2×C3—24no—
1035C2×C3—21no—
1036C2×C3—21no—
1037C2×C3—21no—
1038C2×C3—24no—
1039C2×C3—44no—
1040C2×C3—64no—
1041C2×C3—122no—
1042C2×C3—122no—
1043C2×C3—122no—
1044C2×C3#559114yescomplemented
1045C2×C3#565414yescomplemented
1046C2×C3C22×D3×D411yescharacteristic
1047C2×C3C22×D3×D411yescharacteristic
1048C2×C3C22×#23711yescharacteristic
1049C2×C3C2×#100411yescharacteristic
1050C2×C3C2×D3×#4111yescharacteristic
1051C2×C3C2×#100911yescharacteristic
1052D3—24no—
1053D3—42no—
1054D3—42no—
1055D3—42no—
1056D3—64no—
1057D3—64no—
1058D3—124no—
1059C22—22no—
1060C22—22no—
1061C22—28no—
1062C22—34no—
1063C22—62no—
1064C22—62no—
1065C22—68no—
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—182no—
1081C22—182no—
1082C22—188no—
1083C22—3616no—
1084C22C2×#380214yes—
1085C22C2×#380212yes—
1086C22D3×#23712yes—
1087C22#6431412yes—
1088C22C23×D3211yescharacteristic
1089C4—22no—
1090C4—22no—
1091C4—62no—
1092C4—62no—
1093C4—62no—
1094C4—62no—
1095C4—94no—
1096C4—182no—
1097C4—182no—
1098C3—21no—
1099C3C2×#559111yescharacteristic, complemented
1100C3C2×#565411yescharacteristic, complemented
1101C2—24no—
1102C2—64no—
1103C2—122no—
1104C2—122no—
1105C2—122no—
1106C2—184no—
1107C2#1059429414yesdirect product factor
1108C2C22×#380211yescharacteristic
1109C2C2×D3×#23711yescharacteristic
1110C2C2×#6431411yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C22⋊C4C22
socleC23×C32C24
hypercenterC2×C22⋊C4D32
hypocenterC32C2×#546
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×D3×#67C2semidirect
2. C22×#3804C2semidirect
3. C2×#64090C2semidirect
4. C2×C3×#886C2semidirect
5. C2×C3×#882C2semidirect
6. C2×#63980C2semidirect
7. C22×(C2×D3)⋊Dic3C2semidirect
8. C2×#63922C2semidirect
9. C2×#63921C2semidirect
10. C2×#63916C2semidirect
11. C2×#63915C2semidirect
12. C2×#63899C2semidirect
13. C2×#63898C2semidirect
14. C2×#63885C2semidirect
15. C2×#63854C2semidirect
16. #10594294C2direct (N × H)
22. C23×C3⋊Dic3C22semidirect
23. C22×C4×C3⋊D3C22semidirect
25. C22×C3×#67C22semidirect
26. C23×C3×Dic3C22semidirect
28. C22×C3×D12C22semidirect
30. C2×D3×#67C22semidirect
31. C22×#627C22semidirect
33. C22×#626C22semidirect
35. C22×#625C22semidirect
36. C22×#624C22semidirect
38. C2×#3804C22semidirect
40. C22×D3×Dic3C22semidirect
41. C2×C32×C22⋊C4C22semidirect
42. C2×#3752C22semidirect
43. C2×#3750C22semidirect
44. C2×C4×C3⋊Dic3C22semidirect
45. #64090C22semidirect
47. C2×C3×(C2×D3)⋊C4C22semidirect
48. C2×C3×(C2×D3)⋊C4C22semidirect
49. C2×C3×(C2×D3)⋊C4C22semidirect
50. C2×C3×C4⋊Dic3C22semidirect
51. C2×C3×C4⋊Dic3C22semidirect
52. C3×#886C22semidirect
53. C3×#882C22semidirect
54. #63980C22semidirect
55. C2×#3724C22semidirect
58. C2×(C2×D3)⋊Dic3C22semidirect
59. C2×(C2×D3)⋊Dic3C22semidirect
60. C2×(C2×D3)⋊Dic3C22semidirect
61. C2×(C2×D3)⋊Dic3C22semidirect
62. C2×(C2×D3)⋊Dic3C22semidirect
63. #63922C22semidirect
64. #63921C22semidirect
65. #63916C22semidirect
66. #63915C22semidirect
67. #63899C22semidirect
68. #63898C22semidirect
69. #63885C22semidirect
70. #63854C22semidirect
91. C2×#886D3semidirect
97. C2×#882D3semidirect
120. C2×#638D4semidirect
126. C22×C3⋊Dic3C23semidirect
128. C2×C4×C3⋊D3C23semidirect
132. C2×C3×#67C23semidirect
138. C22×C3×Dic3C23semidirect
142. C2×C3×D12C23semidirect
145. C2×#627C23semidirect
149. C2×#626C23semidirect
153. C2×#625C23semidirect
155. C2×#624C23semidirect
160. C2×D3×Dic3C23semidirect
161. C32×C22⋊C4C23semidirect
162. #3752C23semidirect
163. #3750C23semidirect
164. C4×C3⋊Dic3C23semidirect
166. C3×(C2×D3)⋊C4C23semidirect
167. C3×(C2×D3)⋊C4C23semidirect
168. C3×(C2×D3)⋊C4C23semidirect
169. C3×C4⋊Dic3C23semidirect
170. C3×C4⋊Dic3C23semidirect
171. #3724C23semidirect
174. (C2×D3)⋊Dic3C23semidirect
175. (C2×D3)⋊Dic3C23semidirect
176. (C2×D3)⋊Dic3C23semidirect
177. (C2×D3)⋊Dic3C23semidirect
200. C22×#67C2×D3semidirect
206. C23×Dic3C2×D3semidirect
216. C22×D12C2×D3semidirect
235. C2×C3×C22⋊C4C2×D3semidirect
236. C2×C3×C22⋊C4C2×D3semidirect
261. C2×(C2×D3)⋊C4C2×D3semidirect
262. C2×(C2×D3)⋊C4C2×D3semidirect
263. C2×(C2×D3)⋊C4C2×D3semidirect
264. C2×C4⋊Dic3C2×D3semidirect
265. C2×C4⋊Dic3C2×D3semidirect
278. #886C2×D3semidirect
284. #882C2×D3semidirect
315. C22×C3×D3#41semidirect
328. #638C2×D4semidirect
446. C2×#67C22×D3semidirect
471. C22×Dic3C22×D3semidirect
482. C2×D12C22×D3semidirect
508. C3×C22⋊C4C22×D3semidirect
509. C3×C22⋊C4C22×D3semidirect
526. (C2×D3)⋊C4C22×D3semidirect
527. (C2×D3)⋊C4C22×D3semidirect
528. (C2×D3)⋊C4C22×D3semidirect
529. C4⋊Dic3C22×D3semidirect
530. C4⋊Dic3C22×D3semidirect
567. C2×C3×D3C2×#41semidirect
628. C2×C22⋊C4D32semidirect
700. C22×D3#237semidirect
787. C2×C32#546semidirect
868. C22⋊C4C2×D32semidirect
941. C2×D3C2×#237semidirect
965. C32C2×#546semidirect
1044. C2×C3#5591semidirect
1045. C2×C3#5654semidirect
1099. C3C2×#5591semidirect
1100. C3C2×#5654semidirect
1107. C2#10594294direct (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×#640902
C2×C3×#8862
C2×C3×#8822
C2×#639802
C22×(C2×D3)⋊Dic32
C2×#639222
C2×#639212
C2×#639162
C2×#639152
C2×#638992
C2×#638982
C2×#638852
C2×#638542
#105942942
C2×#56543
C2×#55913