Finite Group Databasebeta

← C2×#10595305 #11902413

Subgroups — C2×#10595305 #11902413

Order 1152.

4131 conjugacy classes of subgroups.

The subgroup lattice has 1132 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#237C211yesmaximal, characteristic, complemented
2C22×#3811C211yesmaximal, characteristic, complemented
3C2×#64146C211yesmaximal, characteristic, complemented
4C2×C3×#939C211yesmaximal, characteristic, complemented
5C2×#63983C211yesmaximal, characteristic, complemented
6C2×#63978C211yesmaximal, characteristic, complemented
7C2×Dic3×#67C211yesmaximal, characteristic, complemented
8C2×#63971C211yesmaximal, characteristic, complemented
9C22×#3722C211yesmaximal, characteristic, complemented
10C2×#63961C211yesmaximal, characteristic, complemented
11C2×#63952C211yesmaximal, characteristic, complemented
12#10595305C2116yesmaximal, direct product factor
13C2×D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
14C2×#63907C211yesmaximal, characteristic, complemented
15C2×#63888C211yesmaximal, characteristic, complemented
16C2×#63850C211yesmaximal, characteristic, complemented
17C2×#5829—31nomaximal
18C2×#5610—31nomaximal
19C24×C3⋊D3C2211yescharacteristic
20C23×D32C2211yescharacteristic
21C22×C32×D4C2211yescharacteristic, complemented
22C22×#638C2211yescharacteristic
23C22×#638C2211yescharacteristic, complemented
24C22×C3×#67C2211yescharacteristic
25C22×C3×#67C2211yescharacteristic
26C22×C3×#67C2211yescharacteristic, complemented
27C22×C3×#67C2211yescharacteristic, complemented
28C23×C3×Dic3C2211yescharacteristic, complemented
29C23×C3×Dic3C2211yescharacteristic, complemented
30C23×C3×Dic3C2211yescharacteristic, complemented
31C2×C3×#237—28no—
32C2×C3×#237C2218yescomplemented
33C22×C3×C4×D3C2211yescharacteristic, complemented
34C22×C3×Dic6C2211yescharacteristic, complemented
35C2×#3811—28no—
36C2×#3811C2218yescomplemented
37C22×#626C2211yescharacteristic
38C22×#626C2211yescharacteristic
39C22×#624C2211yescharacteristic
40C22×D3×Dic3C2211yescharacteristic, complemented
41C2×#3757C2211yescharacteristic, complemented
42#64146C2218yescomplemented
43C2×#3752C2211yescharacteristic
44C2×#3752C2211yescharacteristic, complemented
45C2×C3×#217C2211yescharacteristic, complemented
46C3×#939C2218yescomplemented
47C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
48C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
49#63983C2218yescomplemented
50#63978C2218yescomplemented
51Dic3×#67C2218yescomplemented
52#63971C2218yescomplemented
53C2×#3724C2211yescharacteristic, complemented
54C2×#3724C2211yescharacteristic, complemented
55C2×Dic3⋊Dic3C2211yescharacteristic, complemented
56C2×#3722C2211yescharacteristic
57C2×#3722C2211yescharacteristic
58C2×#3722C2218yescomplemented
59C2×#3722C2211yescharacteristic, complemented
60C2×#3722C2211yescharacteristic, complemented
61#63961C2218yescomplemented
62C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
63C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
64C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
65C2×Dic32C2211yescharacteristic, complemented
66#63952C2218yescomplemented
67D3×(C2×D3)⋊C4C2218yescomplemented
68#63907C2218yescomplemented
69#63888C2218yescomplemented
70#63850C2218yescomplemented
71C22×C3×#41—31no—
72C22×#237D311yescharacteristic, complemented
73C22×D3×D4—31no—
74C22×D3×D4—31no—
75C2×C3×#121—31no—
76#5829—316no—
77C2×#947—31no—
78C2×#946—31no—
79C2×#939—31no—
80C2×#939—31no—
81C2×#939D311yescharacteristic, complemented
82C2×#937—31no—
83C2×#937—31no—
84C2×#937—31no—
85C2×#937—31no—
86C2×#937—61no—
87C2×#935—31no—
88C2×D4×Dic3—31no—
89C2×#930—31no—
90C2×#929—31no—
91C2×#929—31no—
92C2×C4×#67—31no—
93C2×C4×#67—31no—
94C22×(C2×D3)⋊C4—31no—
95C22×(C2×D3)⋊C4—31no—
96C22×(C2×D3)⋊C4—31no—
97#5610—316no—
98C2×#896—31no—
99C2×#894—31no—
100C2×#885—31no—
101C2×#884—31no—
102C2×#67⋊C4—31no—
103C2×D3×C22⋊C4—31no—
104C24×C32C2311yescharacteristic
105C24×C32C2311yescharacteristic
106C23×C3⋊D3—24no—
107C23×C3⋊D3—24no—
108C23×C3⋊D3—42no—
109C23×C3⋊D3C2311yescharacteristic
110C23×C3⋊D3C2314yes—
111C23×C3⋊D3C2311yescharacteristic
112C23×C3×D3C2311yescharacteristic
113C23×C3×D3C2311yescharacteristic
114C22×D32—24no—
115C22×D32—24no—
116C22×D32—42no—
117C22×D32C2314yes—
118C2×C32×D4—24no—
119C2×C32×D4C2314yescomplemented
120C22×C32×C4C2311yescharacteristic
121C2×#638—24no—
122C2×#638—42no—
123C2×#638C2314yes—
124C2×#638C2314yescomplemented
125C22×C3⋊Dic3C2311yescharacteristic
126C22×C3⋊Dic3C2311yescharacteristic
127C2×C3×#67—24no—
128C2×C3×#67—24no—
129C2×C3×#67—42no—
130C2×C3×#67D418yescomplemented
131C2×C3×#67C2314yes—
132C2×C3×#67C2314yes—
133C2×C3×#67C2314yescomplemented
134C2×C3×#67C2314yescomplemented
135C22×C3×Dic3—24no—
136C22×C3×Dic3—24no—
137C22×C3×Dic3—42no—
138C22×C3×Dic3C2311yescharacteristic
139C22×C3×Dic3C2311yescharacteristic
140C22×C3×Dic3C2311yescharacteristic
141C22×C3×Dic3C2311yescharacteristic
142C22×C3×Dic3C2311yescharacteristic
143C22×C3×Dic3C2311yescharacteristic
144C22×C3×Dic3C2314yescomplemented
145C22×C3×Dic3C2314yescomplemented
146C22×C3×Dic3C2314yescomplemented
147C3×#237—232no—
148C2×C3×C4×D3—24no—
149C2×C3×C4×D3C2314yescomplemented
150C2×C3×Dic6—24no—
151C2×C3×Dic6C2314yescomplemented
152#3811—232no—
153C2×#626—24no—
154C2×#626—24no—
155C2×#626C2314yes—
156C2×#626C2314yes—
157C2×#624—24no—
158C2×#624C2314yes—
159C2×D3×Dic3—42no—
160C2×D3×Dic3C2314yescomplemented
161#3757C2314yescomplemented
162#3752C2314yes—
163#3752C2314yescomplemented
164C3×#217C2314yescomplemented
165C3×(C2×D3)⋊C4C2314yescomplemented
166C3×Dic3⋊C4C2314yescomplemented
167#3724C2314yescomplemented
168#3724C2314yescomplemented
169Dic3⋊Dic3C2314yescomplemented
170#3722C2314yes—
171#3722C2314yes—
172#3722C2314yescomplemented
173#3722C2314yescomplemented
174(C2×D3)⋊Dic3C2314yescomplemented
175(C2×D3)⋊Dic3C2314yescomplemented
176(C2×D3)⋊Dic3C2314yescomplemented
177Dic32C2314yescomplemented
178C2×#546—91noSylow
179C24×D3—31no—
180C24×D3—31no—
181C24×D3—31no—
182C24×D3—31no—
183C24×D3—61no—
184C2×C3×#41—38no—
185C2×C3×#41—68no—
186C22×C3×Q8—31no—
187C22×C3×D4—21no—
188C22×C3×D4—31no—
189C22×C3×D4—31no—
190C22×C3×D4—31no—
191C22×C3×D4—31no—
192C22×C3×D4C2×D311yescharacteristic, complemented
193C22×C3×D4C2×D311yescharacteristic, complemented
194C23×C3×C4—31no—
195C23×C3×C4—31no—
196C23×C3×C4—31no—
197C23×C3×C4—31no—
198C22×#67—31no—
199C22×#67—31no—
200C22×#67—31no—
201C22×#67—31no—
202C22×#67—31no—
203C22×#67—31no—
204C22×#67—61no—
205C22×#67—61no—
206C22×#67C2×D311yescharacteristic
207C22×#67C2×D311yescharacteristic
208C22×#67C2×D311yescharacteristic, complemented
209C22×#67C2×D311yescharacteristic, complemented
210C23×Dic3—31no—
211C23×Dic3C2×D311yescharacteristic, complemented
212C23×Dic3C2×D311yescharacteristic, complemented
213C23×Dic3C2×D311yescharacteristic, complemented
214C2×#237—28no—
215C2×#237C2×D318yescomplemented
216C2×D3×D4—38no—
217C2×D3×D4—38no—
218C2×D3×D4—68no—
219C2×D3×D4—68no—
220C22×D12—31no—
221C22×D12—31no—
222C22×C4×D3—31no—
223C22×C4×D3—31no—
224C22×C4×D3—31no—
225C22×C4×D3C2×D311yescharacteristic, complemented
226C22×Dic6C2×D311yescharacteristic, complemented
227C3×#121—38no—
228C2×C3×C4⋊C4—31no—
229C2×C3×C22⋊C4—31no—
230C2×C3×C22⋊C4—31no—
231C2×#217—31no—
232C2×#217—31no—
233C2×#217—31no—
234C2×#217—31no—
235C2×#217—31no—
236C2×#217—61no—
237C2×#217C2×D311yescharacteristic, complemented
238#947—38no—
239#946—38no—
240#939—38no—
241#939—38no—
242#939C2×D318yescomplemented
243#937—38no—
244#937—38no—
245#937—38no—
246#937—38no—
247#937—68no—
248#935—38no—
249D4×Dic3—38no—
250#930—38no—
251#929—38no—
252#929—38no—
253C4×#67—38no—
254C4×#67—38no—
255C2×(C2×D3)⋊C4—31no—
256C2×(C2×D3)⋊C4—31no—
257C2×(C2×D3)⋊C4—31no—
258C2×(C2×D3)⋊C4—31no—
259C2×(C2×D3)⋊C4—31no—
260C2×(C2×D3)⋊C4—31no—
261C2×(C2×D3)⋊C4—31no—
262C2×(C2×D3)⋊C4—31no—
263C2×(C2×D3)⋊C4—31no—
264C2×(C2×D3)⋊C4—31no—
265C2×(C2×D3)⋊C4—31no—
266C2×(C2×D3)⋊C4—31no—
267C2×(C2×D3)⋊C4—31no—
268C2×(C2×D3)⋊C4—31no—
269C2×(C2×D3)⋊C4—31no—
270C2×(C2×D3)⋊C4—38no—
271C2×(C2×D3)⋊C4—38no—
272C2×(C2×D3)⋊C4—38no—
273C2×(C2×D3)⋊C4—61no—
274C2×(C2×D3)⋊C4—61no—
275C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
276C2×C4⋊Dic3—31no—
277C2×Dic3⋊C4—31no—
278C2×Dic3⋊C4—31no—
279C2×Dic3⋊C4—31no—
280C2×Dic3⋊C4—31no—
281C2×Dic3⋊C4—31no—
282C2×Dic3⋊C4C2×D311yescharacteristic, complemented
283C2×C4×Dic3—31no—
284C2×C4×Dic3—31no—
285#896—38no—
286#894—38no—
287#885—38no—
288#884—38no—
289#67⋊C4—38no—
290D3×C22⋊C4—38no—
291C23×C32—22no—
292C23×C32—22no—
293C23×C32—22no—
294C23×C32—22no—
295C23×C32—22no—
296C23×C32C2×D414yes—
297C23×C32C2412yes—
298C23×C32C2412yes—
299C23×C32C2411yescharacteristic
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—28no—
307C22×C3⋊D3—44no—
308C22×C3⋊D3—416no—
309C22×C3⋊D3#4114yescomplemented
310C22×C3⋊D3C2412yes—
311C22×C3⋊D3C2412yes—
312C22×C3×D3—22no—
313C22×C3×D3—22no—
314C22×C3×D3—22no—
315C22×C3×D3—22no—
316C22×C3×D3—22no—
317C22×C3×D3C2×D414yes—
318C22×C3×D3C2412yes—
319C22×C3×D3C2412yes—
320C2×D32—28no—
321C2×D32—28no—
322C2×D32—44no—
323C2×D32—416no—
324C32×D4—28no—
325C2×C32×C4—22no—
326C2×C32×C4C2412yes—
327#638—28no—
328#638—44no—
329C2×C3⋊Dic3—22no—
330C2×C3⋊Dic3—22no—
331C2×C3⋊Dic3C2412yes—
332C2×C3⋊Dic3C2412yes—
333C3×#67—28no—
334C3×#67—28no—
335C3×#67—44no—
336C3×#67C2×D4116yescomplemented
337C2×C3×Dic3—22no—
338C2×C3×Dic3—22no—
339C2×C3×Dic3—22no—
340C2×C3×Dic3—28no—
341C2×C3×Dic3—22no—
342C2×C3×Dic3—22no—
343C2×C3×Dic3—28no—
344C2×C3×Dic3—44no—
345C2×C3×Dic3C2×D414yes—
346C2×C3×Dic3C2412yes—
347C2×C3×Dic3C2412yes—
348C2×C3×Dic3C2412yes—
349C2×C3×Dic3C2412yes—
350C2×C3×Dic3C2412yes—
351C2×C3×Dic3C2412yes—
352C3×C4×D3—28no—
353C3×Dic6—28no—
354#626—28no—
355#626—28no—
356#624—28no—
357D3×Dic3—44no—
358C22×#41—31no—
359C23×D4—91no—
360#546—916no—
361C2×#124—91no—
362C2×#123—91no—
363C2×#123—91no—
364C2×C22⋊Q8—91no—
365C2×#121—31no—
366C2×#121—91no—
367C2×#121—91no—
368C2×#120—91no—
369C2×#120—91no—
370C2×C4×D4—91no—
371C2×C4×D4—91no—
372C22×C22⋊C4—91no—
373C22×C22⋊C4—91no—
374C24×C3—21no—
375C24×C3—21no—
376C24×C3—31no—
377C24×C3—31no—
378C24×C3C22×D311yescharacteristic
379C24×C3C22×D311yescharacteristic
380C24×C3C22×D311yescharacteristic
381C24×C3C22×D311yescharacteristic
382C23×D3—31no—
383C23×D3—31no—
384C23×D3—31no—
385C23×D3—31no—
386C23×D3—34no—
387C23×D3—34no—
388C23×D3—34no—
389C23×D3—34no—
390C23×D3—61no—
391C23×D3—61no—
392C23×D3—64no—
393C23×D3—64no—
394C23×D3—64no—
395C23×D3—64no—
396C23×D3—64no—
397C23×D3—64no—
398C23×D3—64no—
399C23×D3—64no—
400C23×D3—64no—
401C23×D3—124no—
402C23×D3—124no—
403C23×D3—122no—
404C23×D3—122no—
405C23×D3—122no—
406C23×D3—122no—
407C23×D3—124no—
408C23×D3C22×D311yescharacteristic
409C23×D3C22×D311yescharacteristic
410C3×#41—632no—
411C2×C3×Q8—34no—
412C2×C3×Q8—64no—
413C2×C3×D4—24no—
414C2×C3×D4—24no—
415C2×C3×D4—24no—
416C2×C3×D4—38no—
417C2×C3×D4—34no—
418C2×C3×D4—34no—
419C2×C3×D4—34no—
420C2×C3×D4—34no—
421C2×C3×D4—44no—
422C2×C3×D4—64no—
423C2×C3×D4—64no—
424C2×C3×D4—122no—
425C2×C3×D4C22×D314yescomplemented
426C2×C3×D4C22×D314yescomplemented
427C22×C3×C4—21no—
428C22×C3×C4—31no—
429C22×C3×C4—31no—
430C22×C3×C4—31no—
431C22×C3×C4—31no—
432C22×C3×C4—31no—
433C22×C3×C4—31no—
434C22×C3×C4—34no—
435C22×C3×C4—34no—
436C22×C3×C4—34no—
437C22×C3×C4—34no—
438C22×C3×C4—64no—
439C22×C3×C4—64no—
440C22×C3×C4—64no—
441C22×C3×C4—122no—
442C22×C3×C4C22×D311yescharacteristic
443C22×C3×C4C22×D311yescharacteristic
444C2×#67—24no—
445C2×#67—24no—
446C2×#67—34no—
447C2×#67—34no—
448C2×#67—34no—
449C2×#67—34no—
450C2×#67—34no—
451C2×#67—34no—
452C2×#67—42no—
453C2×#67—64no—
454C2×#67—64no—
455C2×#67—64no—
456C2×#67—64no—
457C2×#67—64no—
458C2×#67—64no—
459C2×#67—124no—
460C2×#67—122no—
461C2×#67—122no—
462C2×#67—124no—
463C2×#67#6718yescomplemented
464C2×#67C22×D314yes—
465C2×#67C22×D314yes—
466C2×#67C22×D314yescomplemented
467C2×#67C22×D314yescomplemented
468C22×Dic3—24no—
469C22×Dic3—24no—
470C22×Dic3—31no—
471C22×Dic3—31no—
472C22×Dic3—31no—
473C22×Dic3—31no—
474C22×Dic3—34no—
475C22×Dic3—42no—
476C22×Dic3—61no—
477C22×Dic3—61no—
478C22×Dic3—122no—
479C22×Dic3C22×D311yescharacteristic
480C22×Dic3C22×D311yescharacteristic
481C22×Dic3C22×D311yescharacteristic
482C22×Dic3C22×D311yescharacteristic
483C22×Dic3C22×D311yescharacteristic
484C22×Dic3C22×D311yescharacteristic
485C22×Dic3C22×D314yescomplemented
486C22×Dic3C22×D314yescomplemented
487C22×Dic3C22×D314yescomplemented
488#237—232no—
489D3×D4—632no—
490D3×D4—632no—
491C2×D12—34no—
492C2×D12—34no—
493C2×D12—64no—
494C2×D12—64no—
495C2×C4×D3—24no—
496C2×C4×D3—34no—
497C2×C4×D3—34no—
498C2×C4×D3—34no—
499C2×C4×D3—64no—
500C2×C4×D3—64no—
501C2×C4×D3—122no—
502C2×C4×D3C22×D314yescomplemented
503C2×Dic6—24no—
504C2×Dic6C22×D314yescomplemented
505C3×C4⋊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—64no—
514#217C22×D314yescomplemented
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—34no—
525(C2×D3)⋊C4—34no—
526(C2×D3)⋊C4—34no—
527(C2×D3)⋊C4—34no—
528(C2×D3)⋊C4—34no—
529(C2×D3)⋊C4—34no—
530(C2×D3)⋊C4—64no—
531(C2×D3)⋊C4—64no—
532(C2×D3)⋊C4C22×D314yescomplemented
533C4⋊Dic3—34no—
534Dic3⋊C4—34no—
535Dic3⋊C4—34no—
536Dic3⋊C4—34no—
537Dic3⋊C4—34no—
538Dic3⋊C4—34no—
539Dic3⋊C4C22×D314yescomplemented
540C4×Dic3—34no—
541C4×Dic3—34no—
542C22×C32—28no—
543C22×C32—22no—
544C22×C32—22no—
545C22×C32—22no—
546C22×C32—22no—
547C22×C32—22no—
548C22×C32—44no—
549C22×C32C22×D414yes—
550C22×C32C22×D412yes—
551C22×C32C2×#4112yes—
552C22×C32H(5,𝔽2)12yes—
553C22×C32C2511yescharacteristic
554C2×C3⋊D3—22no—
555C2×C3⋊D3—28no—
556C2×C3⋊D3—22no—
557C2×C3⋊D3—22no—
558C2×C3⋊D3—22no—
559C2×C3⋊D3—22no—
560C2×C3⋊D3—416no—
561C2×C3⋊D3—44no—
562C2×C3⋊D3C2×#4114yescomplemented
563C2×C3×D3—28no—
564C2×C3×D3—22no—
565C2×C3×D3—22no—
566C2×C3×D3—22no—
567C2×C3×D3—22no—
568C2×C3×D3—22no—
569C2×C3×D3—44no—
570C2×C3×D3C22×D414yes—
571D32—416no—
572C32×C4—22no—
573C3⋊Dic3—22no—
574C3⋊Dic3—22no—
575C3×Dic3—22no—
576C3×Dic3—22no—
577C3×Dic3—22no—
578C3×Dic3—22no—
579C3×Dic3—22no—
580C3×Dic3C22×D414yes—
581C25—91no—
582C25—91no—
583C2×#41—38no—
584C2×#41—68no—
585C22×Q8—31no—
586C22×D4—31no—
587C22×D4—31no—
588C22×D4—31no—
589C22×D4—31no—
590C22×D4—91no—
591C22×D4—91no—
592C22×D4—98no—
593C22×D4—91no—
594C22×D4—91no—
595C22×D4—188no—
596C22×D4D3211yescharacteristic, complemented
597C23×C4—31no—
598C23×C4—31no—
599C23×C4—31no—
600C23×C4—31no—
601C23×C4—91no—
602C23×C4—91no—
603#124—98no—
604#123—98no—
605#123—98no—
606C22⋊Q8—98no—
607#121—38no—
608#121—98no—
609#121—98no—
610#120—98no—
611#120—98no—
612C4×D4—98no—
613C4×D4—98no—
614C2×C4⋊C4—31no—
615C2×C4⋊C4—91no—
616C2×C4⋊C4—91no—
617C2×C4⋊C4—91no—
618C2×C22⋊C4—31no—
619C2×C22⋊C4—31no—
620C2×C22⋊C4—98no—
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⋊C4—91no—
629C2×C22⋊C4—91no—
630C2×C22⋊C4—91no—
631C2×C22⋊C4—91no—
632C2×C42—91no—
633C23×C3—22no—
634C23×C3—22no—
635C23×C3—22no—
636C23×C3—22no—
637C23×C3—22no—
638C23×C3—22no—
639C23×C3—22no—
640C23×C3—22no—
641C23×C3—22no—
642C23×C3—22no—
643C23×C3—22no—
644C23×C3—22no—
645C23×C3—21no—
646C23×C3—24no—
647C23×C3—34no—
648C23×C3—32no—
649C23×C3—32no—
650C23×C3—42no—
651C23×C3—42no—
652C23×C3—42no—
653C23×C3—42no—
654C23×C3—42no—
655C23×C3—62no—
656C23×C3—62no—
657C23×C3—62no—
658C23×C3—62no—
659C23×C3—62no—
660C23×C3D3×D414yes—
661C23×C3C2×#6714yes—
662C23×C3C23×D312yes—
663C23×C3C23×D312yes—
664C23×C3C23×D312yes—
665C23×C3C23×D312yes—
666C23×C3C23×D311yescharacteristic
667C23×C3C23×D311yescharacteristic
668C22×D3—22no—
669C22×D3—22no—
670C22×D3—22no—
671C22×D3—22no—
672C22×D3—22no—
673C22×D3—34no—
674C22×D3—34no—
675C22×D3—32no—
676C22×D3—32no—
677C22×D3—32no—
678C22×D3—32no—
679C22×D3—64no—
680C22×D3—62no—
681C22×D3—62no—
682C22×D3—68no—
683C22×D3—68no—
684C22×D3—68no—
685C22×D3—68no—
686C22×D3—68no—
687C22×D3—62no—
688C22×D3—62no—
689C22×D3—62no—
690C22×D3—62no—
691C22×D3—64no—
692C22×D3—62no—
693C22×D3—68no—
694C22×D3—62no—
695C22×D3—62no—
696C22×D3—62no—
697C22×D3—62no—
698C22×D3—62no—
699C22×D3—68no—
700C22×D3—68no—
701C22×D3—128no—
702C22×D3—122no—
703C22×D3—122no—
704C22×D3—122no—
705C22×D3—122no—
706C22×D3—128no—
707C22×D3—124no—
708C22×D3—124no—
709C22×D3—1216no—
710C22×D3—1216no—
711C22×D3—124no—
712C22×D3—124no—
713C22×D3—1216no—
714C22×D3—1216no—
715C22×D3—128no—
716C22×D3—1232no—
717C22×D3C2×#6714yes—
718C22×D3C23×D312yes—
719C22×D3C23×D312yes—
720C3×Q8—68no—
721C3×D4—28no—
722C3×D4—28no—
723C3×D4—316no—
724C3×D4—48no—
725C3×D4—68no—
726C3×D4—68no—
727C3×D4—124no—
728C2×C3×C4—22no—
729C2×C3×C4—22no—
730C2×C3×C4—22no—
731C2×C3×C4—34no—
732C2×C3×C4—32no—
733C2×C3×C4—32no—
734C2×C3×C4—32no—
735C2×C3×C4—32no—
736C2×C3×C4—32no—
737C2×C3×C4—32no—
738C2×C3×C4—42no—
739C2×C3×C4—68no—
740C2×C3×C4—68no—
741C2×C3×C4—62no—
742C2×C3×C4—62no—
743C2×C3×C4—68no—
744C2×C3×C4—62no—
745C2×C3×C4—62no—
746C2×C3×C4—62no—
747C2×C3×C4—124no—
748C2×C3×C4C23×D312yes—
749C2×C3×C4C23×D312yes—
750#67—28no—
751#67—28no—
752#67—44no—
753#67—68no—
754#67—68no—
755#67—68no—
756#67—68no—
757#67—128no—
758#67—124no—
759#67—124no—
760#67—128no—
761#67C2×#67116yescomplemented
762C2×Dic3—22no—
763C2×Dic3—22no—
764C2×Dic3—22no—
765C2×Dic3—22no—
766C2×Dic3—22no—
767C2×Dic3—28no—
768C2×Dic3—28no—
769C2×Dic3—32no—
770C2×Dic3—32no—
771C2×Dic3—32no—
772C2×Dic3—32no—
773C2×Dic3—44no—
774C2×Dic3—62no—
775C2×Dic3—62no—
776C2×Dic3—62no—
777C2×Dic3—62no—
778C2×Dic3—62no—
779C2×Dic3—62no—
780C2×Dic3—122no—
781C2×Dic3—122no—
782C2×Dic3—124no—
783C2×Dic3C2×#6714yes—
784C2×Dic3C23×D312yes—
785C2×Dic3C23×D312yes—
786C2×Dic3C23×D312yes—
787C2×Dic3C23×D312yes—
788C2×Dic3C23×D312yes—
789C2×Dic3C23×D312yes—
790D12—68no—
791D12—68no—
792C4×D3—28no—
793C4×D3—68no—
794C4×D3—68no—
795C4×D3—124no—
796Dic6—28no—
797C2×C32—24no—
798C2×C32—42no—
799C2×C32#54614yescomplemented
800C2×C32C23×D411yescharacteristic
801C2×C32C22×#4111yescharacteristic
802C2×C32C2×H(5,𝔽2)11yescharacteristic
803C3⋊D3—24no—
804C3⋊D3—42no—
805C3×D3—24no—
806C3×D3—42no—
807C24—31no—
808C24—31no—
809C24—94no—
810C24—91no—
811C24—91no—
812C24—94no—
813C24—184no—
814C24—184no—
815C24—184no—
816C24—184no—
817C24—362no—
818C24—362no—
819C24C2×D3211yescharacteristic
820C24C2×D3211yescharacteristic
821#41—632no—
822C2×Q8—34no—
823C2×Q8—64no—
824C2×D4—24no—
825C2×D4—34no—
826C2×D4—38no—
827C2×D4—34no—
828C2×D4—34no—
829C2×D4—34no—
830C2×D4—64no—
831C2×D4—64no—
832C2×D4—94no—
833C2×D4—94no—
834C2×D4—94no—
835C2×D4—94no—
836C2×D4—122no—
837C2×D4—184no—
838C2×D4—184no—
839C2×D4—1832no—
840C2×D4—184no—
841C2×D4—362no—
842C2×D4C2×D3214yescomplemented
843C22×C4—31no—
844C22×C4—34no—
845C22×C4—34no—
846C22×C4—31no—
847C22×C4—31no—
848C22×C4—31no—
849C22×C4—31no—
850C22×C4—31no—
851C22×C4—34no—
852C22×C4—34no—
853C22×C4—64no—
854C22×C4—64no—
855C22×C4—64no—
856C22×C4—94no—
857C22×C4—94no—
858C22×C4—91no—
859C22×C4—91no—
860C22×C4—122no—
861C22×C4—184no—
862C22×C4—362no—
863C22×C4C2×D3211yescharacteristic
864C4⋊C4—34no—
865C4⋊C4—94no—
866C4⋊C4—94no—
867C4⋊C4—94no—
868C22⋊C4—34no—
869C22⋊C4—34no—
870C22⋊C4—94no—
871C22⋊C4—94no—
872C22⋊C4—94no—
873C22⋊C4—94no—
874C22⋊C4—94no—
875C22⋊C4—94no—
876C22⋊C4—94no—
877C22⋊C4—94no—
878C22⋊C4—94no—
879C22⋊C4—94no—
880C42—94no—
881C22×C3—22no—
882C22×C3—22no—
883C22×C3—22no—
884C22×C3—22no—
885C22×C3—28no—
886C22×C3—28no—
887C22×C3—22no—
888C22×C3—22no—
889C22×C3—22no—
890C22×C3—22no—
891C22×C3—22no—
892C22×C3—22no—
893C22×C3—22no—
894C22×C3—22no—
895C22×C3—22no—
896C22×C3—24no—
897C22×C3—21no—
898C22×C3—34no—
899C22×C3—42no—
900C22×C3—42no—
901C22×C3—48no—
902C22×C3—42no—
903C22×C3—42no—
904C22×C3—42no—
905C22×C3—44no—
906C22×C3—44no—
907C22×C3—62no—
908C22×C3—62no—
909C22×C3—68no—
910C22×C3—62no—
911C22×C3—62no—
912C22×C3—62no—
913C22×C3—84no—
914C22×C3—124no—
915C22×C3C2×D3×D414yes—
916C22×C3C2×D3×D412yes—
917C22×C3#100412yes—
918C22×C3D3×#4112yes—
919C22×C3D3×#4112yes—
920C22×C3#100912yes—
921C22×C3C22×#6714yes—
922C22×C3C22×#6712yes—
923C22×C3C24×D311yescharacteristic
924C22×C3C24×D311yescharacteristic
925C2×D3—22no—
926C2×D3—22no—
927C2×D3—28no—
928C2×D3—22no—
929C2×D3—22no—
930C2×D3—22no—
931C2×D3—34no—
932C2×D3—34no—
933C2×D3—44no—
934C2×D3—64no—
935C2×D3—62no—
936C2×D3—62no—
937C2×D3—62no—
938C2×D3—62no—
939C2×D3—68no—
940C2×D3—68no—
941C2×D3—64no—
942C2×D3—62no—
943C2×D3—62no—
944C2×D3—62no—
945C2×D3—62no—
946C2×D3—62no—
947C2×D3—62no—
948C2×D3—122no—
949C2×D3—122no—
950C2×D3—128no—
951C2×D3—122no—
952C2×D3—122no—
953C2×D3—1216no—
954C2×D3—1216no—
955C2×D3—1216no—
956C2×D3—1216no—
957C2×D3—128no—
958C2×D3—1232no—
959C2×D3—124no—
960C2×D3—124no—
961C2×D3C22×#6714yes—
962C3×C4—22no—
963C3×C4—22no—
964C3×C4—34no—
965C3×C4—42no—
966C3×C4—62no—
967C3×C4—62no—
968C3×C4—62no—
969C3×C4—62no—
970C3×C4—62no—
971Dic3—22no—
972Dic3—22no—
973Dic3—22no—
974Dic3—22no—
975Dic3—22no—
976Dic3—62no—
977Dic3—62no—
978Dic3—62no—
979Dic3—62no—
980Dic3—122no—
981Dic3—122no—
982Dic3C22×#6714yes—
983C32C2×#54611yescharacteristic, complemented, Sylow
984C23—22no—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—22no—
989C23—34no—
990C23—32no—
991C23—32no—
992C23—62no—
993C23—62no—
994C23—62no—
995C23—62no—
996C23—62no—
997C23—94no—
998C23—92no—
999C23—92no—
1000C23—188no—
1001C23—188no—
1002C23—188no—
1003C23—182no—
1004C23—182no—
1005C23—182no—
1006C23—182no—
1007C23—188no—
1008C23—182no—
1009C23—364no—
1010C23—3616no—
1011C23—364no—
1012C23—3616no—
1013C23D3×#6714yes—
1014C23C22×D3212yes—
1015C23C22×D3212yes—
1016C23C22×D3211yescharacteristic
1017Q8—68no—
1018D4—28no—
1019D4—316no—
1020D4—68no—
1021D4—68no—
1022D4—124no—
1023D4—188no—
1024D4—188no—
1025D4—188no—
1026D4—364no—
1027C2×C4—22no—
1028C2×C4—34no—
1029C2×C4—32no—
1030C2×C4—32no—
1031C2×C4—32no—
1032C2×C4—32no—
1033C2×C4—32no—
1034C2×C4—32no—
1035C2×C4—68no—
1036C2×C4—68no—
1037C2×C4—62no—
1038C2×C4—62no—
1039C2×C4—62no—
1040C2×C4—62no—
1041C2×C4—68no—
1042C2×C4—62no—
1043C2×C4—92no—
1044C2×C4—92no—
1045C2×C4—124no—
1046C2×C4—188no—
1047C2×C4—182no—
1048C2×C4—182no—
1049C2×C4—364no—
1050C2×C4C22×D3212yes—
1051C2×C3—24no—
1052C2×C3—24no—
1053C2×C3—21no—
1054C2×C3—21no—
1055C2×C3—21no—
1056C2×C3—24no—
1057C2×C3—44no—
1058C2×C3—42no—
1059C2×C3—42no—
1060C2×C3—64no—
1061C2×C3—82no—
1062C2×C3—122no—
1063C2×C3#561014yescomplemented
1064C2×C3#582914yescomplemented
1065C2×C3C22×D3×D411yescharacteristic
1066C2×C3C2×#100411yescharacteristic
1067C2×C3C2×D3×#4111yescharacteristic
1068C2×C3C2×D3×#4111yescharacteristic
1069C2×C3C2×#100911yescharacteristic
1070C2×C3C23×#6711yescharacteristic
1071D3—24no—
1072D3—42no—
1073D3—64no—
1074D3—64no—
1075D3—124no—
1076D3—124no—
1077D3—122no—
1078D3—122no—
1079C22—22no—
1080C22—22no—
1081C22—28no—
1082C22—22no—
1083C22—22no—
1084C22—22no—
1085C22—34no—
1086C22—44no—
1087C22—62no—
1088C22—62no—
1089C22—68no—
1090C22—62no—
1091C22—62no—
1092C22—62no—
1093C22—94no—
1094C22—124no—
1095C22—182no—
1096C22—182no—
1097C22—188no—
1098C22—182no—
1099C22—182no—
1100C22—182no—
1101C22—3616no—
1102C22—3616no—
1103C22—364no—
1104C22#6431212yes—
1105C22#6431412yes—
1106C22C2×D3×#6714yes—
1107C22C2×D3×#6712yes—
1108C22C23×D3211yescharacteristic
1109C4—22no—
1110C4—34no—
1111C4—62no—
1112C4—62no—
1113C4—62no—
1114C4—62no—
1115C4—62no—
1116C4—182no—
1117C4—182no—
1118C3—21no—
1119C3C2×#561011yescharacteristic, complemented
1120C3C2×#582911yescharacteristic, complemented
1121C2—24no—
1122C2—42no—
1123C2—64no—
1124C2—122no—
1125C2—184no—
1126C2—362no—
1127C2#1059530514yesdirect product factor
1128C2C2×#6431211yescharacteristic
1129C2C2×#6431411yescharacteristic
1130C2C22×D3×#6711yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×D4C22
socleC23×C32C24
hypercenterC22×D4D32
hypocenterC32C2×#546
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×C3×#237C2semidirect
2. C22×#3811C2semidirect
3. C2×#64146C2semidirect
4. C2×C3×#939C2semidirect
5. C2×#63983C2semidirect
6. C2×#63978C2semidirect
7. C2×Dic3×#67C2semidirect
8. C2×#63971C2semidirect
9. C22×#3722C2semidirect
10. C2×#63961C2semidirect
11. C2×#63952C2semidirect
12. #10595305C2direct (N × H)
13. C2×D3×(C2×D3)⋊C4C2semidirect
14. C2×#63907C2semidirect
15. C2×#63888C2semidirect
16. C2×#63850C2semidirect
21. C22×C32×D4C22semidirect
23. C22×#638C22semidirect
26. C22×C3×#67C22semidirect
27. C22×C3×#67C22semidirect
28. C23×C3×Dic3C22semidirect
29. C23×C3×Dic3C22semidirect
30. C23×C3×Dic3C22semidirect
32. C2×C3×#237C22semidirect
33. C22×C3×C4×D3C22semidirect
34. C22×C3×Dic6C22semidirect
36. C2×#3811C22semidirect
40. C22×D3×Dic3C22semidirect
41. C2×#3757C22semidirect
42. #64146C22semidirect
44. C2×#3752C22semidirect
45. C2×C3×#217C22semidirect
46. C3×#939C22semidirect
47. C2×C3×(C2×D3)⋊C4C22semidirect
48. C2×C3×Dic3⋊C4C22semidirect
49. #63983C22semidirect
50. #63978C22semidirect
51. Dic3×#67C22semidirect
52. #63971C22semidirect
53. C2×#3724C22semidirect
54. C2×#3724C22semidirect
55. C2×Dic3⋊Dic3C22semidirect
58. C2×#3722C22semidirect
59. C2×#3722C22semidirect
60. C2×#3722C22semidirect
61. #63961C22semidirect
62. C2×(C2×D3)⋊Dic3C22semidirect
63. C2×(C2×D3)⋊Dic3C22semidirect
64. C2×(C2×D3)⋊Dic3C22semidirect
65. C2×Dic32C22semidirect
66. #63952C22semidirect
67. D3×(C2×D3)⋊C4C22semidirect
68. #63907C22semidirect
69. #63888C22semidirect
70. #63850C22semidirect
72. C22×#237D3semidirect
81. C2×#939D3semidirect
119. C2×C32×D4C23semidirect
124. C2×#638C23semidirect
130. C2×C3×#67D4semidirect
133. C2×C3×#67C23semidirect
134. C2×C3×#67C23semidirect
144. C22×C3×Dic3C23semidirect
145. C22×C3×Dic3C23semidirect
146. C22×C3×Dic3C23semidirect
149. C2×C3×C4×D3C23semidirect
151. C2×C3×Dic6C23semidirect
160. C2×D3×Dic3C23semidirect
161. #3757C23semidirect
163. #3752C23semidirect
164. C3×#217C23semidirect
165. C3×(C2×D3)⋊C4C23semidirect
166. C3×Dic3⋊C4C23semidirect
167. #3724C23semidirect
168. #3724C23semidirect
169. Dic3⋊Dic3C23semidirect
172. #3722C23semidirect
173. #3722C23semidirect
174. (C2×D3)⋊Dic3C23semidirect
175. (C2×D3)⋊Dic3C23semidirect
176. (C2×D3)⋊Dic3C23semidirect
177. Dic32C23semidirect
192. C22×C3×D4C2×D3semidirect
193. C22×C3×D4C2×D3semidirect
208. C22×#67C2×D3semidirect
209. C22×#67C2×D3semidirect
211. C23×Dic3C2×D3semidirect
212. C23×Dic3C2×D3semidirect
213. C23×Dic3C2×D3semidirect
215. C2×#237C2×D3semidirect
225. C22×C4×D3C2×D3semidirect
226. C22×Dic6C2×D3semidirect
237. C2×#217C2×D3semidirect
242. #939C2×D3semidirect
275. C2×(C2×D3)⋊C4C2×D3semidirect
282. C2×Dic3⋊C4C2×D3semidirect
309. C22×C3⋊D3#41semidirect
336. C3×#67C2×D4semidirect
425. C2×C3×D4C22×D3semidirect
426. C2×C3×D4C22×D3semidirect
463. C2×#67#67semidirect
466. C2×#67C22×D3semidirect
467. C2×#67C22×D3semidirect
485. C22×Dic3C22×D3semidirect
486. C22×Dic3C22×D3semidirect
487. C22×Dic3C22×D3semidirect
502. C2×C4×D3C22×D3semidirect
504. C2×Dic6C22×D3semidirect
514. #217C22×D3semidirect
532. (C2×D3)⋊C4C22×D3semidirect
539. Dic3⋊C4C22×D3semidirect
562. C2×C3⋊D3C2×#41semidirect
596. C22×D4D32semidirect
761. #67C2×#67semidirect
799. C2×C32#546semidirect
842. C2×D4C2×D32semidirect
983. C32C2×#546semidirect
1063. C2×C3#5610semidirect
1064. C2×C3#5829semidirect
1119. C3C2×#5610semidirect
1120. C3C2×#5829semidirect
1127. C2#10595305direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#2372
C22×#38112
C2×#641462
C2×C3×#9392
C2×#639832
C2×#639782
C2×Dic3×#672
C2×#639712
C22×#37222
C2×#639612
C2×#639522
#105953052
C2×D3×(C2×D3)⋊C42
C2×#639072
C2×#638882
C2×#638502
C2×#58293
C2×#56103