Finite Group Databasebeta

← C2×#10594272 #11902452

Subgroups — C2×#10594272 #11902452

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×#3798C211yesmaximal, characteristic, complemented
3C2×#64093C211yesmaximal, characteristic, complemented
4C2×C3×#883C211yesmaximal, characteristic, complemented
5C2×C3×D3×C22⋊C4C211yesmaximal, characteristic, complemented
6C2×#63977C211yesmaximal, characteristic, complemented
7C2×#63971C211yesmaximal, characteristic, complemented
8C2×#63953C211yesmaximal, characteristic, complemented
9C2×#63923C211yesmaximal, characteristic, complemented
10C2×D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
11C2×#63909C211yesmaximal, characteristic, complemented
12C2×#63899C211yesmaximal, characteristic, complemented
13C2×#63881C211yesmaximal, characteristic, complemented
14C2×#63879C211yesmaximal, characteristic, complemented
15C2×#63850C211yesmaximal, characteristic, complemented
16#10594272C2116yesmaximal, direct product factor
17C2×#5654—31nomaximal
18C2×#5490—31nomaximal
19C24×C3×D3C2211yescharacteristic
20C23×D32C2211yescharacteristic
21C22×#638C2211yescharacteristic
22C22×#638C2211yescharacteristic, complemented
23C22×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
24C22×C4×C3⋊D3C2211yescharacteristic, complemented
25C22×C3×#67C2211yescharacteristic
26C22×C3×C4×D3C2211yescharacteristic, complemented
27C22×C3×C4×D3C2211yescharacteristic, complemented
28C22×C3×C4×D3C2211yescharacteristic, complemented
29C2×D3×#67—28no—
30C2×D3×#67C2218yescomplemented
31C22×#627C2211yescharacteristic, complemented
32C22×#626C2211yescharacteristic
33C22×#626C2211yescharacteristic
34C22×#626C2211yescharacteristic, complemented
35C22×#626C2211yescharacteristic, complemented
36C22×#625C2211yescharacteristic
37C22×D3×Dic3C2211yescharacteristic
38C22×D3×Dic3C2211yescharacteristic, complemented
39C2×#3798—28no—
40C2×#3798C2218yescomplemented
41C2×C32×C22⋊C4C2211yescharacteristic, complemented
42C2×#3752C2211yescharacteristic, complemented
43C2×#3750C2211yescharacteristic, complemented
44#64093C2218yescomplemented
45C2×C3×#217C2211yescharacteristic, complemented
46C2×C3×#217C2211yescharacteristic, complemented
47C2×C3×(C2×D3)⋊C4C2211yescharacteristic
48C2×C3×(C2×D3)⋊C4C2211yescharacteristic
49C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
50C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
51C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
52C3×#883C2218yescomplemented
53C3×D3×C22⋊C4C2218yescomplemented
54#63977C2218yescomplemented
55#63971C2218yescomplemented
56C2×#3724C2211yescharacteristic, complemented
57C2×#3722C2211yescharacteristic, complemented
58C2×#3722C2211yescharacteristic, complemented
59C2×#3722C2211yescharacteristic, complemented
60C2×(C2×D3)⋊Dic3C2211yescharacteristic
61C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
62C2×Dic32C2211yescharacteristic, complemented
63#63953C2218yescomplemented
64#63923C2218yescomplemented
65D3×(C2×D3)⋊C4C2218yescomplemented
66#63909C2218yescomplemented
67#63899C2218yescomplemented
68#63881C2218yescomplemented
69#63879C2218yescomplemented
70#63850C2218yescomplemented
71C23×#67—31no—
72C22×D3×D4—31no—
73C22×#235—31no—
74C22×#235—31no—
75C2×C3×#123—31no—
76C22×C3×C22⋊C4—31no—
77C2×#953—31no—
78C2×#939—31no—
79C2×#930—31no—
80C2×#929—31no—
81C2×C4×#67—31no—
82C22×(C2×D3)⋊C4—31no—
83#5654—316no—
84C2×#896—31no—
85C2×#895—31no—
86C2×#894—31no—
87C2×#893—31no—
88C2×#885—31no—
89C2×#885—31no—
90#5490—316no—
91C2×#884—31no—
92C2×#884—31no—
93C2×#884—31no—
94C2×#884—61no—
95C2×#883D311yescharacteristic, complemented
96C2×#882—31no—
97C2×#882—31no—
98C2×#882—31no—
99C2×#67⋊C4—31no—
100C2×#67⋊C4—31no—
101C2×D3×C22⋊C4—31no—
102C2×D3×C22⋊C4D311yescharacteristic, complemented
103C2×#878—31no—
104C24×C32C2311yescharacteristic
105C23×C3⋊D3C2311yescharacteristic
106C23×C3⋊D3C2311yescharacteristic
107C23×C3×D3—24no—
108C23×C3×D3—24no—
109C23×C3×D3—42no—
110C23×C3×D3C2314yes—
111C23×C3×D3C2311yescharacteristic
112C23×C3×D3C2311yescharacteristic
113C23×C3×D3C2311yescharacteristic
114C22×D32—24no—
115C22×D32—24no—
116C22×D32—42no—
117C22×D32C2314yes—
118C22×C32×C4C2311yescharacteristic
119C22×C32×C4C2311yescharacteristic
120C2×#638—24no—
121C2×#638—42no—
122C2×#638C2314yes—
123C2×#638C2314yescomplemented
124C22×C3⋊Dic3C2311yescharacteristic
125C22×C3⋊Dic3C2311yescharacteristic
126C2×C4⋊(C3⋊D3)—42no—
127C2×C4⋊(C3⋊D3)C2314yescomplemented
128C2×C4×C3⋊D3—24no—
129C2×C4×C3⋊D3C2314yescomplemented
130C2×C3×#67—24no—
131C2×C3×#67C2314yes—
132C22×C3×Dic3C2311yescharacteristic
133C22×C3×Dic3C2311yescharacteristic
134C22×C3×Dic3C2311yescharacteristic
135C22×C3×Dic3C2311yescharacteristic
136C22×C3×Dic3C2311yescharacteristic
137C2×C3×C4×D3—24no—
138C2×C3×C4×D3—24no—
139C2×C3×C4×D3—42no—
140C2×C3×C4×D3C2314yescomplemented
141C2×C3×C4×D3C2314yescomplemented
142C2×C3×C4×D3C2314yescomplemented
143D3×#67—232no—
144C2×#627—24no—
145C2×#627C2314yescomplemented
146C2×#626—24no—
147C2×#626—24no—
148C2×#626—24no—
149C2×#626—24no—
150C2×#626C2314yes—
151C2×#626C2314yes—
152C2×#626C2314yescomplemented
153C2×#626C2314yescomplemented
154C2×#625D418yescomplemented
155C2×#625C2314yes—
156C2×D3×Dic3—24no—
157C2×D3×Dic3—42no—
158C2×D3×Dic3C2314yes—
159C2×D3×Dic3C2314yescomplemented
160#3798—232no—
161C32×C22⋊C4C2314yescomplemented
162#3752C2314yescomplemented
163#3750C2314yescomplemented
164C3×#217C2314yescomplemented
165C3×#217C2314yescomplemented
166C3×(C2×D3)⋊C4C2314yes—
167C3×(C2×D3)⋊C4C2314yes—
168C3×(C2×D3)⋊C4C2314yescomplemented
169C3×C4⋊Dic3C2314yescomplemented
170C3×Dic3⋊C4C2314yescomplemented
171#3724C2314yescomplemented
172#3722C2314yescomplemented
173#3722C2314yescomplemented
174#3722C2314yescomplemented
175(C2×D3)⋊Dic3C2314yes—
176(C2×D3)⋊Dic3C2314yescomplemented
177Dic32C2314yescomplemented
178C2×#546—91noSylow
179C25×C3—31no—
180C24×D3—31no—
181C24×D3—31no—
182C24×D3C2×D311yescharacteristic
183C22×C3×D4—31no—
184C23×C3×C4—31no—
185C23×C3×C4—31no—
186C23×C3×C4—31no—
187C22×#67—31no—
188C22×#67—31no—
189C22×#67—31no—
190C22×#67—31no—
191C22×#67—31no—
192C22×#67—31no—
193C22×#67—38no—
194C22×#67—31no—
195C22×#67—31no—
196C22×#67—31no—
197C22×#67—31no—
198C22×#67—61no—
199C22×#67—61no—
200C22×#67—68no—
201C22×#67C2×D311yescharacteristic
202C23×Dic3—31no—
203C23×Dic3—31no—
204C2×D3×D4—38no—
205C2×D3×D4—68no—
206C2×#235—38no—
207C2×#235—38no—
208C2×#235—68no—
209C2×#235—68no—
210C22×D12—31no—
211C22×D12—31no—
212C22×D12—31no—
213C22×D12—31no—
214C22×D12—31no—
215C22×D12—31no—
216C22×D12—61no—
217C22×C4×D3—31no—
218C22×C4×D3—31no—
219C22×C4×D3—31no—
220C22×C4×D3—31no—
221C22×C4×D3—61no—
222C22×C4×D3C2×D311yescharacteristic, complemented
223C22×C4×D3C2×D311yescharacteristic, complemented
224C22×C4×D3C2×D311yescharacteristic, complemented
225C22×Dic6—31no—
226C22×Dic6—31no—
227C3×#123—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⋊C4—31no—
236C2×C3×C22⋊C4—38no—
237C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
238C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
239#953—38no—
240C2×#217—31no—
241C2×#217—31no—
242C2×#217C2×D311yescharacteristic, complemented
243C2×#217C2×D311yescharacteristic, complemented
244#939—38no—
245#930—38no—
246#929—38no—
247C4×#67—38no—
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—31no—
258C2×(C2×D3)⋊C4—38no—
259C2×(C2×D3)⋊C4—61no—
260C2×(C2×D3)⋊C4C2×D311yescharacteristic
261C2×(C2×D3)⋊C4C2×D311yescharacteristic
262C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
263C2×C4⋊Dic3C2×D311yescharacteristic, complemented
264C2×Dic3⋊C4—31no—
265C2×Dic3⋊C4—31no—
266C2×Dic3⋊C4—31no—
267C2×Dic3⋊C4—31no—
268C2×Dic3⋊C4—61no—
269C2×Dic3⋊C4C2×D311yescharacteristic, complemented
270C2×C4×Dic3—31no—
271C2×C4×Dic3—31no—
272#896—38no—
273#895—38no—
274#894—38no—
275#893—38no—
276#885—38no—
277#885—38no—
278#884—38no—
279#884—38no—
280#884—38no—
281#884—68no—
282#883C2×D318yescomplemented
283#882—38no—
284#882—38no—
285#882—38no—
286#67⋊C4—38no—
287#67⋊C4—38no—
288D3×C22⋊C4—38no—
289D3×C22⋊C4C2×D318yescomplemented
290#878—38no—
291C23×C32—22no—
292C23×C32—22no—
293C23×C32—22no—
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—22no—
310C22×C3×D3—28no—
311C22×C3×D3—28no—
312C22×C3×D3—44no—
313C22×C3×D3—416no—
314C22×C3×D3C2×D414yes—
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×C4C2412yes—
327C2×C32×C4C2412yes—
328#638—28no—
329#638—44no—
330C2×C3⋊Dic3—22no—
331C2×C3⋊Dic3C2×D414yes—
332C2×C3⋊Dic3C2412yes—
333C2×C3⋊Dic3C2412yes—
334C4⋊(C3⋊D3)—44no—
335C4×C3⋊D3—28no—
336C3×#67—28no—
337C2×C3×Dic3—22no—
338C2×C3×Dic3—22no—
339C2×C3×Dic3—22no—
340C2×C3×Dic3—22no—
341C2×C3×Dic3—22no—
342C2×C3×Dic3C2412yes—
343C2×C3×Dic3C2412yes—
344C2×C3×Dic3C2412yes—
345C2×C3×Dic3C2412yes—
346C2×C3×Dic3C2412yes—
347C3×C4×D3—28no—
348C3×C4×D3—28no—
349C3×C4×D3—44no—
350#627—28no—
351#626—28no—
352#626—28no—
353#626—28no—
354#626—28no—
355#625C2×D4116yescomplemented
356D3×Dic3—28no—
357D3×Dic3—44no—
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—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—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×D314yes—
402C23×D3C22×D311yescharacteristic
403C23×D3C22×D311yescharacteristic
404C23×D3C22×D311yescharacteristic
405C2×C3×D4—34no—
406C2×C3×D4—64no—
407C22×C3×C4—21no—
408C22×C3×C4—21no—
409C22×C3×C4—31no—
410C22×C3×C4—31no—
411C22×C3×C4—31no—
412C22×C3×C4—31no—
413C22×C3×C4—31no—
414C22×C3×C4—34no—
415C22×C3×C4—34no—
416C22×C3×C4—34no—
417C22×C3×C4—64no—
418C22×C3×C4—64no—
419C22×C3×C4—122no—
420C22×C3×C4C22×D311yescharacteristic
421C22×C3×C4C22×D311yescharacteristic
422C22×C3×C4C22×D311yescharacteristic
423C22×C3×C4C22×D311yescharacteristic
424C2×#67—24no—
425C2×#67—38no—
426C2×#67—38no—
427C2×#67—34no—
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—64no—
438C2×#67—64no—
439C2×#67—64no—
440C2×#67—64no—
441C2×#67—64no—
442C2×#67—64no—
443C2×#67—64no—
444C2×#67—64no—
445C2×#67—632no—
446C2×#67—124no—
447C2×#67—122no—
448C2×#67—122no—
449C2×#67—124no—
450C2×#67C22×D314yes—
451C22×Dic3—31no—
452C22×Dic3—31no—
453C22×Dic3—31no—
454C22×Dic3—31no—
455C22×Dic3—34no—
456C22×Dic3—34no—
457C22×Dic3—61no—
458C22×Dic3—61no—
459C22×Dic3—64no—
460C22×Dic3—122no—
461C22×Dic3C22×D311yescharacteristic
462C22×Dic3C22×D311yescharacteristic
463C22×Dic3C22×D311yescharacteristic
464C22×Dic3C22×D311yescharacteristic
465C22×Dic3C22×D311yescharacteristic
466D3×D4—632no—
467#235—632no—
468#235—632no—
469C2×D12—34no—
470C2×D12—34no—
471C2×D12—34no—
472C2×D12—34no—
473C2×D12—34no—
474C2×D12—34no—
475C2×D12—64no—
476C2×D12—64no—
477C2×D12—64no—
478C2×D12—64no—
479C2×D12—64no—
480C2×D12—122no—
481C2×D12—122no—
482C2×D12—124no—
483C2×C4×D3—24no—
484C2×C4×D3—24no—
485C2×C4×D3—34no—
486C2×C4×D3—34no—
487C2×C4×D3—34no—
488C2×C4×D3—34no—
489C2×C4×D3—42no—
490C2×C4×D3—64no—
491C2×C4×D3—64no—
492C2×C4×D3—64no—
493C2×C4×D3—64no—
494C2×C4×D3—124no—
495C2×C4×D3—122no—
496C2×C4×D3C22×D314yescomplemented
497C2×C4×D3C22×D314yescomplemented
498C2×C4×D3C22×D314yescomplemented
499C2×Dic6—34no—
500C2×Dic6—34no—
501C2×Dic6—64no—
502C2×Dic6—64no—
503C3×C4⋊C4—34no—
504C3×C4⋊C4—34no—
505C3×C22⋊C4—24no—
506C3×C22⋊C4—34no—
507C3×C22⋊C4—34no—
508C3×C22⋊C4—34no—
509C3×C22⋊C4—34no—
510C3×C22⋊C4—34no—
511C3×C22⋊C4C22×D314yescomplemented
512C3×C22⋊C4C22×D314yescomplemented
513#217—34no—
514#217—34no—
515#217C22×D314yescomplemented
516#217C22×D314yescomplemented
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—34no—
525(C2×D3)⋊C4—34no—
526(C2×D3)⋊C4—34no—
527(C2×D3)⋊C4—64no—
528(C2×D3)⋊C4C22×D314yes—
529(C2×D3)⋊C4C22×D314yes—
530(C2×D3)⋊C4C22×D314yescomplemented
531C4⋊Dic3C22×D314yescomplemented
532Dic3⋊C4—34no—
533Dic3⋊C4—34no—
534Dic3⋊C4—34no—
535Dic3⋊C4—34no—
536Dic3⋊C4—64no—
537Dic3⋊C4C22×D314yescomplemented
538C4×Dic3—34no—
539C4×Dic3—34no—
540C22×C32—22no—
541C22×C32—22no—
542C22×C32—22no—
543C22×C32—44no—
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—28no—
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×D3C22×D414yes—
567C2×C3×D3C22×D414yes—
568C2×C3×D3C2×#4114yescomplemented
569D32—416no—
570C32×C4—22no—
571C32×C4—22no—
572C3⋊Dic3—22no—
573C3⋊Dic3C22×D414yes—
574C3×Dic3—22no—
575C3×Dic3—22no—
576C3×Dic3—22no—
577C3×Dic3—22no—
578C3×Dic3—22no—
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—31no—
598C23×C4—91no—
599C23×C4—91no—
600C23×C4—91no—
601#124—98no—
602#123—38no—
603#123—98no—
604C22⋊Q8—98no—
605#121—98no—
606#121—98no—
607#121—98no—
608#120—98no—
609#120—98no—
610C4×D4—98no—
611C4×D4—98no—
612C2×C4⋊C4—31no—
613C2×C4⋊C4—31no—
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—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×C22⋊C4D3211yescharacteristic, complemented
630C2×C42—91no—
631C23×C3—22no—
632C23×C3—22no—
633C23×C3—22no—
634C23×C3—22no—
635C23×C3—22no—
636C23×C3—22no—
637C23×C3—22no—
638C23×C3—21no—
639C23×C3—34no—
640C23×C3—34no—
641C23×C3—34no—
642C23×C3—32no—
643C23×C3—32no—
644C23×C3—32no—
645C23×C3—42no—
646C23×C3—42no—
647C23×C3—42no—
648C23×C3—68no—
649C23×C3—68no—
650C23×C3—62no—
651C23×C3—62no—
652C23×C3—62no—
653C23×C3—62no—
654C23×C3—62no—
655C23×C3—62no—
656C23×C3—124no—
657C23×C3—1216no—
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—28no—
670C22×D3—32no—
671C22×D3—32no—
672C22×D3—32no—
673C22×D3—32no—
674C22×D3—44no—
675C22×D3—416no—
676C22×D3—62no—
677C22×D3—62no—
678C22×D3—68no—
679C22×D3—68no—
680C22×D3—64no—
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—124no—
701C22×D3—124no—
702C22×D3—1216no—
703C22×D3—1216no—
704C22×D3#23514yescomplemented
705C22×D3D3×D414yes—
706C22×D3D3×D414yes—
707C22×D3C23×D312yes—
708C22×D3C23×D312yes—
709C22×D3C23×D312yes—
710C3×D4—68no—
711C2×C3×C4—22no—
712C2×C3×C4—22no—
713C2×C3×C4—22no—
714C2×C3×C4—22no—
715C2×C3×C4—22no—
716C2×C3×C4—22no—
717C2×C3×C4—32no—
718C2×C3×C4—32no—
719C2×C3×C4—32no—
720C2×C3×C4—32no—
721C2×C3×C4—32no—
722C2×C3×C4—42no—
723C2×C3×C4—42no—
724C2×C3×C4—68no—
725C2×C3×C4—68no—
726C2×C3×C4—62no—
727C2×C3×C4—62no—
728C2×C3×C4—62no—
729C2×C3×C4—62no—
730C2×C3×C4—62no—
731C2×C3×C4—124no—
732C2×C3×C4C23×D312yes—
733C2×C3×C4C23×D312yes—
734C2×C3×C4C23×D312yes—
735C2×C3×C4C23×D312yes—
736#67—28no—
737#67—316no—
738#67—316no—
739#67—68no—
740#67—68no—
741#67—68no—
742#67—68no—
743#67—68no—
744#67—68no—
745#67—128no—
746#67—124no—
747#67—124no—
748#67—128no—
749C2×Dic3—22no—
750C2×Dic3—22no—
751C2×Dic3—22no—
752C2×Dic3—22no—
753C2×Dic3—22no—
754C2×Dic3—34no—
755C2×Dic3—34no—
756C2×Dic3—32no—
757C2×Dic3—32no—
758C2×Dic3—32no—
759C2×Dic3—32no—
760C2×Dic3—64no—
761C2×Dic3—62no—
762C2×Dic3—62no—
763C2×Dic3—68no—
764C2×Dic3—62no—
765C2×Dic3—62no—
766C2×Dic3—122no—
767C2×Dic3—124no—
768C2×Dic3C23×D312yes—
769C2×Dic3C23×D312yes—
770C2×Dic3C23×D312yes—
771C2×Dic3C23×D312yes—
772C2×Dic3C23×D312yes—
773D12—68no—
774D12—68no—
775D12—68no—
776D12—68no—
777D12—124no—
778D12—124no—
779D12—128no—
780C4×D3—28no—
781C4×D3—28no—
782C4×D3—44no—
783C4×D3—68no—
784C4×D3—68no—
785C4×D3—68no—
786C4×D3—128no—
787C4×D3—124no—
788Dic6—68no—
789Dic6—68no—
790C2×C32—42no—
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—24no—
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—64no—
819C2×D4—94no—
820C2×D4—94no—
821C2×D4—94no—
822C2×D4—94no—
823C2×D4—94no—
824C2×D4—98no—
825C2×D4—94no—
826C2×D4—94no—
827C2×D4—94no—
828C2×D4—184no—
829C2×D4—184no—
830C2×D4—184no—
831C2×D4—184no—
832C2×D4—184no—
833C2×D4—1832no—
834C2×D4—362no—
835C2×D4—362no—
836C22×C4—31no—
837C22×C4—31no—
838C22×C4—31no—
839C22×C4—31no—
840C22×C4—31no—
841C22×C4—34no—
842C22×C4—34no—
843C22×C4—34no—
844C22×C4—64no—
845C22×C4—64no—
846C22×C4—94no—
847C22×C4—94no—
848C22×C4—91no—
849C22×C4—91no—
850C22×C4—94no—
851C22×C4—122no—
852C22×C4—184no—
853C22×C4—184no—
854C22×C4—362no—
855C22×C4C2×D3211yescharacteristic
856C22×C4C2×D3211yescharacteristic
857C4⋊C4—34no—
858C4⋊C4—34no—
859C4⋊C4—94no—
860C4⋊C4—94no—
861C22⋊C4—34no—
862C22⋊C4—34no—
863C22⋊C4—34no—
864C22⋊C4—34no—
865C22⋊C4—34no—
866C22⋊C4—94no—
867C22⋊C4—94no—
868C22⋊C4—94no—
869C22⋊C4—94no—
870C22⋊C4—94no—
871C22⋊C4—94no—
872C22⋊C4C2×D3214yescomplemented
873C42—94no—
874C22×C3—22no—
875C22×C3—22no—
876C22×C3—22no—
877C22×C3—22no—
878C22×C3—22no—
879C22×C3—22no—
880C22×C3—22no—
881C22×C3—22no—
882C22×C3—22no—
883C22×C3—21no—
884C22×C3—34no—
885C22×C3—34no—
886C22×C3—34no—
887C22×C3—42no—
888C22×C3—42no—
889C22×C3—42no—
890C22×C3—44no—
891C22×C3—44no—
892C22×C3—68no—
893C22×C3—68no—
894C22×C3—62no—
895C22×C3—62no—
896C22×C3—62no—
897C22×C3—62no—
898C22×C3—62no—
899C22×C3—62no—
900C22×C3—68no—
901C22×C3—84no—
902C22×C3—1216no—
903C22×C3C2×#23512yes—
904C22×C3C2×D3×D412yes—
905C22×C3C2×D3×D412yes—
906C22×C3#100412yes—
907C22×C3D3×#4112yes—
908C22×C3#100912yes—
909C22×C3C24×D311yescharacteristic
910C22×C3C24×D311yescharacteristic
911C2×D3—28no—
912C2×D3—22no—
913C2×D3—22no—
914C2×D3—22no—
915C2×D3—22no—
916C2×D3—22no—
917C2×D3—22no—
918C2×D3—28no—
919C2×D3—28no—
920C2×D3—416no—
921C2×D3—64no—
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—1216no—
940C2×D3—1216no—
941C2×D3—128no—
942C2×D3—124no—
943C2×D3—124no—
944C2×D3—124no—
945C2×D3—124no—
946C2×D3—244no—
947C2×D3C2×#23514yescomplemented
948C2×D3C2×D3×D414yes—
949C2×D3C2×D3×D414yes—
950C3×C4—22no—
951C3×C4—22no—
952C3×C4—22no—
953C3×C4—22no—
954C3×C4—42no—
955C3×C4—42no—
956C3×C4—62no—
957C3×C4—62no—
958C3×C4—62no—
959C3×C4—62no—
960C3×C4—62no—
961Dic3—22no—
962Dic3—22no—
963Dic3—22no—
964Dic3—22no—
965Dic3—22no—
966Dic3—34no—
967Dic3—34no—
968Dic3—64no—
969Dic3—62no—
970Dic3—62no—
971Dic3—122no—
972C32C2×#54611yescharacteristic, complemented, Sylow
973C23—22no—
974C23—22no—
975C23—22no—
976C23—34no—
977C23—34no—
978C23—34no—
979C23—32no—
980C23—32no—
981C23—32no—
982C23—68no—
983C23—68no—
984C23—62no—
985C23—62no—
986C23—62no—
987C23—62no—
988C23—62no—
989C23—62no—
990C23—92no—
991C23—92no—
992C23—124no—
993C23—1216no—
994C23—188no—
995C23—188no—
996C23—182no—
997C23—182no—
998C23—182no—
999C23—182no—
1000C23—182no—
1001C23—182no—
1002C23—364no—
1003C23—3616no—
1004C23C22×D3212yes—
1005C23C22×D3211yescharacteristic
1006Q8—188no—
1007D4—68no—
1008D4—916no—
1009D4—188no—
1010D4—188no—
1011D4—188no—
1012D4—188no—
1013D4—188no—
1014D4—364no—
1015D4—364no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—32no—
1019C2×C4—32no—
1020C2×C4—32no—
1021C2×C4—32no—
1022C2×C4—32no—
1023C2×C4—68no—
1024C2×C4—68no—
1025C2×C4—62no—
1026C2×C4—62no—
1027C2×C4—62no—
1028C2×C4—62no—
1029C2×C4—62no—
1030C2×C4—94no—
1031C2×C4—92no—
1032C2×C4—92no—
1033C2×C4—124no—
1034C2×C4—188no—
1035C2×C4—188no—
1036C2×C4—182no—
1037C2×C4—364no—
1038C2×C4C22×D3212yes—
1039C2×C4C22×D3212yes—
1040C2×C3—21no—
1041C2×C3—21no—
1042C2×C3—21no—
1043C2×C3—24no—
1044C2×C3—42no—
1045C2×C3—42no—
1046C2×C3—64no—
1047C2×C3—64no—
1048C2×C3—64no—
1049C2×C3—82no—
1050C2×C3#549014yescomplemented
1051C2×C3#565414yescomplemented
1052C2×C3C22×#23511yescharacteristic
1053C2×C3C22×D3×D411yescharacteristic
1054C2×C3C22×D3×D411yescharacteristic
1055C2×C3C2×#100411yescharacteristic
1056C2×C3C2×D3×#4111yescharacteristic
1057C2×C3C2×#100911yescharacteristic
1058D3—24no—
1059D3—24no—
1060D3—24no—
1061D3—124no—
1062D3—122no—
1063D3—122no—
1064D3—122no—
1065D3—122no—
1066D3—242no—
1067C22—22no—
1068C22—22no—
1069C22—22no—
1070C22—34no—
1071C22—34no—
1072C22—34no—
1073C22—44no—
1074C22—62no—
1075C22—62no—
1076C22—62no—
1077C22—62no—
1078C22—62no—
1079C22—62no—
1080C22—68no—
1081C22—68no—
1082C22—68no—
1083C22—1216no—
1084C22—182no—
1085C22—182no—
1086C22—182no—
1087C22—182no—
1088C22—182no—
1089C22—182no—
1090C22—3616no—
1091C22—364no—
1092C22—364no—
1093C22D3×#23512yes—
1094C22D32×D412yes—
1095C22#6431412yes—
1096C22C23×D3211yescharacteristic
1097C4—22no—
1098C4—22no—
1099C4—62no—
1100C4—62no—
1101C4—62no—
1102C4—62no—
1103C4—62no—
1104C4—94no—
1105C4—182no—
1106C3—21no—
1107C3C2×#549011yescharacteristic, complemented
1108C3C2×#565411yescharacteristic, complemented
1109C2—42no—
1110C2—64no—
1111C2—64no—
1112C2—64no—
1113C2—362no—
1114C2—362no—
1115C2#1059427214yesdirect product factor
1116C2C2×D3×#23511yescharacteristic
1117C2C2×D32×D411yescharacteristic
1118C2C2×#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×#3798C2semidirect
3. C2×#64093C2semidirect
4. C2×C3×#883C2semidirect
5. C2×C3×D3×C22⋊C4C2semidirect
6. C2×#63977C2semidirect
7. C2×#63971C2semidirect
8. C2×#63953C2semidirect
9. C2×#63923C2semidirect
10. C2×D3×(C2×D3)⋊C4C2semidirect
11. C2×#63909C2semidirect
12. C2×#63899C2semidirect
13. C2×#63881C2semidirect
14. C2×#63879C2semidirect
15. C2×#63850C2semidirect
16. #10594272C2direct (N × H)
22. C22×#638C22semidirect
23. C22×C4⋊(C3⋊D3)C22semidirect
24. C22×C4×C3⋊D3C22semidirect
26. C22×C3×C4×D3C22semidirect
27. C22×C3×C4×D3C22semidirect
28. C22×C3×C4×D3C22semidirect
30. C2×D3×#67C22semidirect
31. C22×#627C22semidirect
34. C22×#626C22semidirect
35. C22×#626C22semidirect
38. C22×D3×Dic3C22semidirect
40. C2×#3798C22semidirect
41. C2×C32×C22⋊C4C22semidirect
42. C2×#3752C22semidirect
43. C2×#3750C22semidirect
44. #64093C22semidirect
45. C2×C3×#217C22semidirect
46. C2×C3×#217C22semidirect
49. C2×C3×(C2×D3)⋊C4C22semidirect
50. C2×C3×C4⋊Dic3C22semidirect
51. C2×C3×Dic3⋊C4C22semidirect
52. C3×#883C22semidirect
53. C3×D3×C22⋊C4C22semidirect
54. #63977C22semidirect
55. #63971C22semidirect
56. C2×#3724C22semidirect
57. C2×#3722C22semidirect
58. C2×#3722C22semidirect
59. C2×#3722C22semidirect
61. C2×(C2×D3)⋊Dic3C22semidirect
62. C2×Dic32C22semidirect
63. #63953C22semidirect
64. #63923C22semidirect
65. D3×(C2×D3)⋊C4C22semidirect
66. #63909C22semidirect
67. #63899C22semidirect
68. #63881C22semidirect
69. #63879C22semidirect
70. #63850C22semidirect
95. C2×#883D3semidirect
102. C2×D3×C22⋊C4D3semidirect
123. C2×#638C23semidirect
127. C2×C4⋊(C3⋊D3)C23semidirect
129. C2×C4×C3⋊D3C23semidirect
140. C2×C3×C4×D3C23semidirect
141. C2×C3×C4×D3C23semidirect
142. C2×C3×C4×D3C23semidirect
145. C2×#627C23semidirect
152. C2×#626C23semidirect
153. C2×#626C23semidirect
154. C2×#625D4semidirect
159. C2×D3×Dic3C23semidirect
161. C32×C22⋊C4C23semidirect
162. #3752C23semidirect
163. #3750C23semidirect
164. C3×#217C23semidirect
165. C3×#217C23semidirect
168. C3×(C2×D3)⋊C4C23semidirect
169. C3×C4⋊Dic3C23semidirect
170. C3×Dic3⋊C4C23semidirect
171. #3724C23semidirect
172. #3722C23semidirect
173. #3722C23semidirect
174. #3722C23semidirect
176. (C2×D3)⋊Dic3C23semidirect
177. Dic32C23semidirect
222. C22×C4×D3C2×D3semidirect
223. C22×C4×D3C2×D3semidirect
224. C22×C4×D3C2×D3semidirect
237. C2×C3×C22⋊C4C2×D3semidirect
238. C2×C3×C22⋊C4C2×D3semidirect
242. C2×#217C2×D3semidirect
243. C2×#217C2×D3semidirect
262. C2×(C2×D3)⋊C4C2×D3semidirect
263. C2×C4⋊Dic3C2×D3semidirect
269. C2×Dic3⋊C4C2×D3semidirect
282. #883C2×D3semidirect
289. D3×C22⋊C4C2×D3semidirect
316. C22×C3×D3#41semidirect
355. #625C2×D4semidirect
496. C2×C4×D3C22×D3semidirect
497. C2×C4×D3C22×D3semidirect
498. C2×C4×D3C22×D3semidirect
511. C3×C22⋊C4C22×D3semidirect
512. C3×C22⋊C4C22×D3semidirect
515. #217C22×D3semidirect
516. #217C22×D3semidirect
530. (C2×D3)⋊C4C22×D3semidirect
531. C4⋊Dic3C22×D3semidirect
537. Dic3⋊C4C22×D3semidirect
568. C2×C3×D3C2×#41semidirect
629. C2×C22⋊C4D32semidirect
704. C22×D3#235semidirect
791. C2×C32#546semidirect
872. C22⋊C4C2×D32semidirect
947. C2×D3C2×#235semidirect
972. C32C2×#546semidirect
1050. C2×C3#5490semidirect
1051. C2×C3#5654semidirect
1107. C3C2×#5490semidirect
1108. C3C2×#5654semidirect
1115. C2#10594272direct (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×#37982
C2×#640932
C2×C3×#8832
C2×C3×D3×C22⋊C42
C2×#639772
C2×#639712
C2×#639532
C2×#639232
C2×D3×(C2×D3)⋊C42
C2×#639092
C2×#638992
C2×#638812
C2×#638792
C2×#638502
#105942722
C2×#56543
C2×#54903