Finite Group Databasebeta

← C2×#10595304 #11902415

Subgroups — C2×#10595304 #11902415

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×C3×#237C211yesmaximal, characteristic, complemented
2C22×D3×#67C211yesmaximal, characteristic, complemented
3C2×#64148C211yesmaximal, characteristic, complemented
4C2×C3×#937C211yesmaximal, characteristic, complemented
5C2×#63983C211yesmaximal, characteristic, complemented
6C2×#63978C211yesmaximal, characteristic, complemented
7C2×#67⋊Dic3C211yesmaximal, characteristic, complemented
8C2×Dic3×#67C211yesmaximal, characteristic, complemented
9C2×#63970C211yesmaximal, characteristic, complemented
10C2×#63966C211yesmaximal, characteristic, complemented
11C22×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
12#10595304C2116yesmaximal, direct product factor
13C2×D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
14C2×#63907C211yesmaximal, characteristic, complemented
15C2×#63905C211yesmaximal, characteristic, complemented
16C2×#63887C211yesmaximal, characteristic, complemented
17C2×#5829—31nomaximal
18C2×#5591—31nomaximal
19C24×C3×D3C2211yescharacteristic
20C23×D32C2211yescharacteristic
21C22×C32×D4C2211yescharacteristic, complemented
22C22×#638C2211yescharacteristic
23C22×#638C2211yescharacteristic, complemented
24C23×C3⋊Dic3C2211yescharacteristic, complemented
25C22×C3×#67C2211yescharacteristic
26C22×C3×#67C2211yescharacteristic
27C22×C3×#67C2211yescharacteristic, complemented
28C22×C3×#67C2211yescharacteristic, 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×D3×#67—28no—
36C2×D3×#67C2218yescomplemented
37C22×#626C2211yescharacteristic
38C22×#625C2211yescharacteristic
39C22×D3×Dic3C2211yescharacteristic
40C22×D3×Dic3C2211yescharacteristic, complemented
41C2×#3757C2211yescharacteristic, complemented
42#64148C2218yescomplemented
43C2×#3752C2211yescharacteristic, complemented
44C2×#3750C2211yescharacteristic, complemented
45C2×C3×#217C2211yescharacteristic, complemented
46C3×#937C2218yescomplemented
47C2×C3×(C2×D3)⋊C4C2211yescharacteristic
48C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
49#63983C2218yescomplemented
50#63978C2218yescomplemented
51#67⋊Dic3C2218yescomplemented
52Dic3×#67C2218yescomplemented
53#63970C2218yescomplemented
54#63966C2218yescomplemented
55C2×Dic3⋊Dic3C2211yescharacteristic, complemented
56C2×Dic3⋊Dic3C2211yescharacteristic, complemented
57C2×Dic3⋊Dic3C2211yescharacteristic, complemented
58C2×#3722C2211yescharacteristic, complemented
59C2×#3722C2211yescharacteristic, complemented
60C2×(C2×D3)⋊Dic3C2211yescharacteristic
61C2×(C2×D3)⋊Dic3C2211yescharacteristic
62C2×(C2×D3)⋊Dic3C2218yescomplemented
63C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
64C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
65C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
66C2×Dic32C2211yescharacteristic, complemented
67D3×(C2×D3)⋊C4C2218yescomplemented
68#63907C2218yescomplemented
69#63905C2218yescomplemented
70#63887C2218yescomplemented
71C22×C3×#41—31no—
72C23×#67—31no—
73C22×#237D311yescharacteristic, complemented
74C22×D3×D4—31no—
75C2×C3×#120—31no—
76C22×#217—31no—
77#5829—316no—
78C2×#947—31no—
79C2×#946—31no—
80C2×#939—31no—
81C2×#939—31no—
82C2×#939—31no—
83C2×#939—31no—
84C2×#939—61no—
85C2×#938—31no—
86C2×#937—31no—
87C2×#937—31no—
88C2×#937D311yescharacteristic, complemented
89C2×D4×Dic3—31no—
90C2×D4×Dic3—31no—
91C2×#930—31no—
92C2×#929—31no—
93C2×#929—31no—
94C2×C4×#67—31no—
95C22×(C2×D3)⋊C4—31no—
96C22×(C2×D3)⋊C4—31no—
97#5591—316no—
98C2×#886—31no—
99C2×#885—31no—
100C2×#883—31no—
101C2×#67⋊C4—31no—
102C2×D3×C22⋊C4—31no—
103C2×#878—31no—
104C24×C32C2311yescharacteristic
105C24×C32C2311yescharacteristic
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—
118C2×C32×D4—24no—
119C2×C32×D4C2314yescomplemented
120C22×C32×C4C2311yescharacteristic
121C2×#638—24no—
122C2×#638—42no—
123C2×#638C2314yes—
124C2×#638C2314yescomplemented
125C22×C3⋊Dic3—42no—
126C22×C3⋊Dic3C2311yescharacteristic
127C22×C3⋊Dic3C2311yescharacteristic
128C22×C3⋊Dic3C2311yescharacteristic
129C22×C3⋊Dic3C2314yescomplemented
130C2×C3×#67—24no—
131C2×C3×#67—24no—
132C2×C3×#67—42no—
133C2×C3×#67D418yescomplemented
134C2×C3×#67C2314yes—
135C2×C3×#67C2314yes—
136C2×C3×#67C2314yescomplemented
137C2×C3×#67C2314yescomplemented
138C22×C3×Dic3—24no—
139C22×C3×Dic3—24no—
140C22×C3×Dic3C2311yescharacteristic
141C22×C3×Dic3C2311yescharacteristic
142C22×C3×Dic3C2311yescharacteristic
143C22×C3×Dic3C2311yescharacteristic
144C22×C3×Dic3C2311yescharacteristic
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
152D3×#67—232no—
153C2×#626—24no—
154C2×#626C2314yes—
155C2×#625—24no—
156C2×#625C2314yes—
157C2×D3×Dic3—24no—
158C2×D3×Dic3—42no—
159C2×D3×Dic3C2314yes—
160C2×D3×Dic3C2314yescomplemented
161#3757C2314yescomplemented
162#3752C2314yescomplemented
163#3750C2314yescomplemented
164C3×#217C2314yescomplemented
165C3×(C2×D3)⋊C4C2314yes—
166C3×(C2×D3)⋊C4C2314yescomplemented
167Dic3⋊Dic3C2314yescomplemented
168Dic3⋊Dic3C2314yescomplemented
169Dic3⋊Dic3C2314yescomplemented
170#3722C2314yescomplemented
171#3722C2314yescomplemented
172(C2×D3)⋊Dic3C2314yes—
173(C2×D3)⋊Dic3C2314yes—
174(C2×D3)⋊Dic3C2314yescomplemented
175(C2×D3)⋊Dic3C2314yescomplemented
176(C2×D3)⋊Dic3C2314yescomplemented
177Dic32C2314yescomplemented
178C2×#546—91noSylow
179C25×C3—31no—
180C24×D3—31no—
181C24×D3—31no—
182C24×D3C2×D311yescharacteristic
183C2×C3×#41—38no—
184C2×C3×#41—68no—
185C22×C3×Q8—31no—
186C22×C3×D4—21no—
187C22×C3×D4—31no—
188C22×C3×D4—31no—
189C22×C3×D4—31no—
190C22×C3×D4—31no—
191C22×C3×D4C2×D311yescharacteristic, complemented
192C22×C3×D4C2×D311yescharacteristic, complemented
193C23×C3×C4—31no—
194C23×C3×C4—31no—
195C23×C3×C4—31no—
196C22×#67—31no—
197C22×#67—31no—
198C22×#67—31no—
199C22×#67—31no—
200C22×#67—31no—
201C22×#67—31no—
202C22×#67—38no—
203C22×#67—31no—
204C22×#67—61no—
205C22×#67—61no—
206C22×#67—68no—
207C22×#67C2×D311yescharacteristic
208C22×#67C2×D311yescharacteristic
209C22×#67C2×D311yescharacteristic, complemented
210C22×#67C2×D311yescharacteristic, complemented
211C23×Dic3—31no—
212C23×Dic3—31no—
213C23×Dic3—31no—
214C23×Dic3—31no—
215C23×Dic3—61no—
216C23×Dic3C2×D311yescharacteristic, complemented
217C23×Dic3C2×D311yescharacteristic, complemented
218C2×#237—28no—
219C2×#237C2×D318yescomplemented
220C2×D3×D4—38no—
221C2×D3×D4—68no—
222C22×D12—31no—
223C22×C4×D3—31no—
224C22×C4×D3—31no—
225C22×C4×D3C2×D311yescharacteristic, complemented
226C22×Dic6C2×D311yescharacteristic, complemented
227C3×#120—38no—
228C2×C3×C22⋊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—31no—
237C2×#217—31no—
238C2×#217—38no—
239C2×#217—61no—
240C2×#217C2×D311yescharacteristic, complemented
241#947—38no—
242#946—38no—
243#939—38no—
244#939—38no—
245#939—38no—
246#939—38no—
247#939—68no—
248#938—38no—
249#937—38no—
250#937—38no—
251#937C2×D318yescomplemented
252D4×Dic3—38no—
253D4×Dic3—38no—
254#930—38no—
255#929—38no—
256#929—38no—
257C4×#67—38no—
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—38no—
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—61no—
272C2×(C2×D3)⋊C4C2×D311yescharacteristic
273C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
274C2×C4⋊Dic3—31no—
275C2×C4⋊Dic3—31no—
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⋊C4—61no—
283C2×C4×Dic3—31no—
284C2×C4×Dic3—31no—
285#886—38no—
286#885—38no—
287#883—38no—
288#67⋊C4—38no—
289D3×C22⋊C4—38no—
290#878—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⋊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—
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⋊Dic3—22no—
332C2×C3⋊Dic3—44no—
333C2×C3⋊Dic3C2412yes—
334C2×C3⋊Dic3C2412yes—
335C2×C3⋊Dic3C2412yes—
336C3×#67—28no—
337C3×#67—28no—
338C3×#67—44no—
339C3×#67C2×D4116yescomplemented
340C2×C3×Dic3—22no—
341C2×C3×Dic3—22no—
342C2×C3×Dic3—28no—
343C2×C3×Dic3—22no—
344C2×C3×Dic3—22no—
345C2×C3×Dic3—28no—
346C2×C3×Dic3C2×D414yes—
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#625—28no—
356D3×Dic3—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—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—21no—
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
385C24×C3C22×D311yescharacteristic
386C24×C3C22×D311yescharacteristic
387C23×D3—24no—
388C23×D3—24no—
389C23×D3—31no—
390C23×D3—31no—
391C23×D3—34no—
392C23×D3—34no—
393C23×D3—42no—
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
405C3×#41—632no—
406C2×C3×Q8—34no—
407C2×C3×Q8—64no—
408C2×C3×D4—24no—
409C2×C3×D4—24no—
410C2×C3×D4—24no—
411C2×C3×D4—38no—
412C2×C3×D4—34no—
413C2×C3×D4—34no—
414C2×C3×D4—34no—
415C2×C3×D4—34no—
416C2×C3×D4—44no—
417C2×C3×D4—64no—
418C2×C3×D4—64no—
419C2×C3×D4—122no—
420C2×C3×D4C22×D314yescomplemented
421C2×C3×D4C22×D314yescomplemented
422C22×C3×C4—21no—
423C22×C3×C4—31no—
424C22×C3×C4—31no—
425C22×C3×C4—31no—
426C22×C3×C4—31no—
427C22×C3×C4—31no—
428C22×C3×C4—34no—
429C22×C3×C4—34no—
430C22×C3×C4—34no—
431C22×C3×C4—64no—
432C22×C3×C4—64no—
433C22×C3×C4—64no—
434C22×C3×C4C22×D311yescharacteristic
435C22×C3×C4C22×D311yescharacteristic
436C2×#67—24no—
437C2×#67—24no—
438C2×#67—34no—
439C2×#67—34no—
440C2×#67—34no—
441C2×#67—34no—
442C2×#67—34no—
443C2×#67—34no—
444C2×#67—34no—
445C2×#67—42no—
446C2×#67—64no—
447C2×#67—64no—
448C2×#67—64no—
449C2×#67—64no—
450C2×#67—64no—
451C2×#67—64no—
452C2×#67—632no—
453C2×#67—64no—
454C2×#67—124no—
455C2×#67—122no—
456C2×#67—122no—
457C2×#67—124no—
458C2×#67#6718yescomplemented
459C2×#67C22×D314yes—
460C2×#67C22×D314yes—
461C2×#67C22×D314yescomplemented
462C2×#67C22×D314yescomplemented
463C22×Dic3—24no—
464C22×Dic3—24no—
465C22×Dic3—31no—
466C22×Dic3—31no—
467C22×Dic3—31no—
468C22×Dic3—31no—
469C22×Dic3—31no—
470C22×Dic3—31no—
471C22×Dic3—34no—
472C22×Dic3—34no—
473C22×Dic3—34no—
474C22×Dic3—34no—
475C22×Dic3—61no—
476C22×Dic3—61no—
477C22×Dic3—61no—
478C22×Dic3—64no—
479C22×Dic3—64no—
480C22×Dic3—122no—
481C22×Dic3—122no—
482C22×Dic3—122no—
483C22×Dic3—124no—
484C22×Dic3C22×D311yescharacteristic
485C22×Dic3C22×D311yescharacteristic
486C22×Dic3C22×D311yescharacteristic
487C22×Dic3C22×D311yescharacteristic
488C22×Dic3C22×D311yescharacteristic
489C22×Dic3C22×D314yescomplemented
490C22×Dic3C22×D314yescomplemented
491#237—232no—
492D3×D4—632no—
493C2×D12—34no—
494C2×D12—64no—
495C2×C4×D3—24no—
496C2×C4×D3—34no—
497C2×C4×D3—34no—
498C2×C4×D3—64no—
499C2×C4×D3—122no—
500C2×C4×D3C22×D314yescomplemented
501C2×Dic6—24no—
502C2×Dic6C22×D314yescomplemented
503C3×C22⋊C4—34no—
504C3×C22⋊C4—34no—
505C3×C22⋊C4—34no—
506#217—34no—
507#217—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—64no—
527(C2×D3)⋊C4C22×D314yes—
528(C2×D3)⋊C4C22×D314yescomplemented
529C4⋊Dic3—34no—
530C4⋊Dic3—34no—
531C4⋊Dic3—34no—
532Dic3⋊C4—34no—
533Dic3⋊C4—34no—
534Dic3⋊C4—34no—
535Dic3⋊C4—34no—
536Dic3⋊C4—34no—
537Dic3⋊C4—64no—
538C4×Dic3—34no—
539C4×Dic3—34no—
540C22×C32—28no—
541C22×C32—22no—
542C22×C32—22no—
543C22×C32—22no—
544C22×C32—22no—
545C22×C32—22no—
546C22×C32—44no—
547C22×C32C22×D414yes—
548C22×C32C22×D412yes—
549C22×C32C2×#4112yes—
550C22×C32H(5,𝔽2)12yes—
551C22×C32C2511yescharacteristic
552C2×C3⋊D3—22no—
553C2×C3⋊D3—22no—
554C2×C3⋊D3—22no—
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—
571C3⋊Dic3—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—38no—
582C2×#41—68no—
583C22×Q8—31no—
584C22×D4—31no—
585C22×D4—31no—
586C22×D4—31no—
587C22×D4—31no—
588C22×D4—91no—
589C22×D4—98no—
590C22×D4—91no—
591C22×D4—91no—
592C22×D4—91no—
593C22×D4—188no—
594C22×D4D3211yescharacteristic, complemented
595C23×C4—31no—
596C23×C4—31no—
597C23×C4—31no—
598C23×C4—91no—
599C23×C4—91no—
600C23×C4—91no—
601#124—98no—
602#123—98no—
603#123—98no—
604C22⋊Q8—98no—
605#121—98no—
606#121—98no—
607#121—98no—
608#120—38no—
609#120—98no—
610C4×D4—98no—
611C4×D4—98no—
612C2×C4⋊C4—91no—
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—98no—
620C2×C22⋊C4—91no—
621C2×C22⋊C4—91no—
622C2×C22⋊C4—91no—
623C2×C22⋊C4—91no—
624C2×C22⋊C4—91no—
625C2×C22⋊C4—91no—
626C2×C22⋊C4—98no—
627C2×C22⋊C4—91no—
628C2×C22⋊C4—91no—
629C2×C22⋊C4—91no—
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—22no—
639C23×C3—22no—
640C23×C3—22no—
641C23×C3—22no—
642C23×C3—22no—
643C23×C3—21no—
644C23×C3—24no—
645C23×C3—34no—
646C23×C3—34no—
647C23×C3—32no—
648C23×C3—32no—
649C23×C3—32no—
650C23×C3—42no—
651C23×C3—42no—
652C23×C3—42no—
653C23×C3—42no—
654C23×C3—42no—
655C23×C3—68no—
656C23×C3—62no—
657C23×C3—62no—
658C23×C3—62no—
659C23×C3—62no—
660C23×C3—62no—
661C23×C3—62no—
662C23×C3—68no—
663C23×C3—62no—
664C23×C3—124no—
665C23×C3—1216no—
666C23×C3D3×D414yes—
667C23×C3C2×#6714yes—
668C23×C3C23×D312yes—
669C23×C3C23×D312yes—
670C23×C3C23×D312yes—
671C23×C3C23×D312yes—
672C23×C3C23×D311yescharacteristic
673C23×C3C23×D311yescharacteristic
674C22×D3—22no—
675C22×D3—22no—
676C22×D3—22no—
677C22×D3—22no—
678C22×D3—22no—
679C22×D3—28no—
680C22×D3—22no—
681C22×D3—22no—
682C22×D3—28no—
683C22×D3—32no—
684C22×D3—32no—
685C22×D3—44no—
686C22×D3—416no—
687C22×D3—62no—
688C22×D3—68no—
689C22×D3—68no—
690C22×D3—62no—
691C22×D3—62no—
692C22×D3—62no—
693C22×D3—62no—
694C22×D3—62no—
695C22×D3—62no—
696C22×D3—68no—
697C22×D3—68no—
698C22×D3—122no—
699C22×D3—122no—
700C22×D3—122no—
701C22×D3—124no—
702C22×D3—124no—
703C22×D3—1216no—
704C22×D3—1216no—
705C22×D3#23714yescomplemented
706C22×D3C2×#6714yes—
707C22×D3C23×D312yes—
708C22×D3C23×D312yes—
709C22×D3C23×D312yes—
710C3×Q8—68no—
711C3×D4—28no—
712C3×D4—28no—
713C3×D4—316no—
714C3×D4—48no—
715C3×D4—68no—
716C3×D4—68no—
717C3×D4—124no—
718C2×C3×C4—22no—
719C2×C3×C4—22no—
720C2×C3×C4—22no—
721C2×C3×C4—34no—
722C2×C3×C4—32no—
723C2×C3×C4—32no—
724C2×C3×C4—32no—
725C2×C3×C4—32no—
726C2×C3×C4—32no—
727C2×C3×C4—42no—
728C2×C3×C4—68no—
729C2×C3×C4—68no—
730C2×C3×C4—62no—
731C2×C3×C4—62no—
732C2×C3×C4—68no—
733C2×C3×C4—62no—
734C2×C3×C4—62no—
735C2×C3×C4C23×D312yes—
736C2×C3×C4C23×D312yes—
737#67—28no—
738#67—28no—
739#67—44no—
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—
749#67C2×#67116yescomplemented
750C2×Dic3—22no—
751C2×Dic3—22no—
752C2×Dic3—22no—
753C2×Dic3—22no—
754C2×Dic3—28no—
755C2×Dic3—28no—
756C2×Dic3—32no—
757C2×Dic3—32no—
758C2×Dic3—32no—
759C2×Dic3—32no—
760C2×Dic3—32no—
761C2×Dic3—32no—
762C2×Dic3—62no—
763C2×Dic3—62no—
764C2×Dic3—62no—
765C2×Dic3—64no—
766C2×Dic3—62no—
767C2×Dic3—62no—
768C2×Dic3—62no—
769C2×Dic3—62no—
770C2×Dic3—62no—
771C2×Dic3—62no—
772C2×Dic3—68no—
773C2×Dic3—122no—
774C2×Dic3—122no—
775C2×Dic3—124no—
776C2×Dic3—124no—
777C2×Dic3—124no—
778C2×Dic3—128no—
779C2×Dic3C2×#6714yes—
780C2×Dic3C23×D312yes—
781C2×Dic3C23×D312yes—
782C2×Dic3C23×D312yes—
783C2×Dic3C23×D312yes—
784C2×Dic3C23×D312yes—
785D12—68no—
786C4×D3—28no—
787C4×D3—68no—
788C4×D3—124no—
789Dic6—28no—
790C2×C32—24no—
791C2×C32—42no—
792C2×C32#54614yescomplemented
793C2×C32C23×D411yescharacteristic
794C2×C32C22×#4111yescharacteristic
795C2×C32C2×H(5,𝔽2)11yescharacteristic
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—122no—
809C24—184no—
810C24—184no—
811C24—362no—
812C24C2×D3211yescharacteristic
813C24C2×D3211yescharacteristic
814#41—632no—
815C2×Q8—34no—
816C2×Q8—64no—
817C2×D4—24no—
818C2×D4—34no—
819C2×D4—38no—
820C2×D4—34no—
821C2×D4—34no—
822C2×D4—34no—
823C2×D4—64no—
824C2×D4—64no—
825C2×D4—94no—
826C2×D4—94no—
827C2×D4—94no—
828C2×D4—94no—
829C2×D4—122no—
830C2×D4—184no—
831C2×D4—1832no—
832C2×D4—184no—
833C2×D4—184no—
834C2×D4—362no—
835C2×D4C2×D3214yescomplemented
836C22×C4—31no—
837C22×C4—34no—
838C22×C4—34no—
839C22×C4—31no—
840C22×C4—31no—
841C22×C4—31no—
842C22×C4—31no—
843C22×C4—34no—
844C22×C4—64no—
845C22×C4—64no—
846C22×C4—64no—
847C22×C4—94no—
848C22×C4—94no—
849C22×C4—91no—
850C22×C4—91no—
851C22×C4—91no—
852C22×C4—94no—
853C22×C4—184no—
854C22×C4—362no—
855C22×C4—362no—
856C22×C4C2×D3211yescharacteristic
857C4⋊C4—94no—
858C4⋊C4—94no—
859C4⋊C4—94no—
860C4⋊C4—94no—
861C22⋊C4—34no—
862C22⋊C4—34no—
863C22⋊C4—34no—
864C22⋊C4—94no—
865C22⋊C4—94no—
866C22⋊C4—94no—
867C22⋊C4—94no—
868C22⋊C4—94no—
869C22⋊C4—94no—
870C22⋊C4—94no—
871C22⋊C4—94no—
872C22⋊C4—94no—
873C42—94no—
874C22×C3—22no—
875C22×C3—22no—
876C22×C3—22no—
877C22×C3—22no—
878C22×C3—28no—
879C22×C3—28no—
880C22×C3—22no—
881C22×C3—22no—
882C22×C3—22no—
883C22×C3—22no—
884C22×C3—22no—
885C22×C3—22no—
886C22×C3—22no—
887C22×C3—22no—
888C22×C3—22no—
889C22×C3—24no—
890C22×C3—21no—
891C22×C3—34no—
892C22×C3—34no—
893C22×C3—42no—
894C22×C3—42no—
895C22×C3—48no—
896C22×C3—42no—
897C22×C3—42no—
898C22×C3—42no—
899C22×C3—44no—
900C22×C3—44no—
901C22×C3—62no—
902C22×C3—62no—
903C22×C3—62no—
904C22×C3—62no—
905C22×C3—68no—
906C22×C3—68no—
907C22×C3—62no—
908C22×C3—62no—
909C22×C3—62no—
910C22×C3—84no—
911C22×C3—1216no—
912C22×C3—124no—
913C22×C3C2×D3×D414yes—
914C22×C3C2×D3×D412yes—
915C22×C3C2×#23712yes—
916C22×C3#100412yes—
917C22×C3D3×#4112yes—
918C22×C3#100912yes—
919C22×C3C22×#6714yes—
920C22×C3C22×#6712yes—
921C22×C3C24×D311yescharacteristic
922C22×C3C24×D311yescharacteristic
923C2×D3—22no—
924C2×D3—22no—
925C2×D3—22no—
926C2×D3—22no—
927C2×D3—28no—
928C2×D3—28no—
929C2×D3—22no—
930C2×D3—22no—
931C2×D3—22no—
932C2×D3—416no—
933C2×D3—44no—
934C2×D3—62no—
935C2×D3—62no—
936C2×D3—62no—
937C2×D3—62no—
938C2×D3—62no—
939C2×D3—62no—
940C2×D3—122no—
941C2×D3—122no—
942C2×D3—122no—
943C2×D3—1216no—
944C2×D3—1216no—
945C2×D3—124no—
946C2×D3—124no—
947C2×D3—244no—
948C2×D3C2×#23714yescomplemented
949C2×D3C22×#6714yes—
950C3×C4—22no—
951C3×C4—22no—
952C3×C4—34no—
953C3×C4—42no—
954C3×C4—62no—
955C3×C4—62no—
956C3×C4—62no—
957C3×C4—62no—
958Dic3—22no—
959Dic3—22no—
960Dic3—22no—
961Dic3—22no—
962Dic3—64no—
963Dic3—62no—
964Dic3—62no—
965Dic3—62no—
966Dic3—62no—
967Dic3—62no—
968Dic3—62no—
969Dic3—122no—
970Dic3—122no—
971Dic3C22×#6714yes—
972C32C2×#54611yescharacteristic, complemented, Sylow
973C23—22no—
974C23—22no—
975C23—22no—
976C23—22no—
977C23—22no—
978C23—34no—
979C23—34no—
980C23—32no—
981C23—32no—
982C23—32no—
983C23—68no—
984C23—62no—
985C23—62no—
986C23—62no—
987C23—62no—
988C23—62no—
989C23—62no—
990C23—68no—
991C23—62no—
992C23—92no—
993C23—124no—
994C23—1216no—
995C23—188no—
996C23—188no—
997C23—182no—
998C23—182no—
999C23—182no—
1000C23—364no—
1001C23—3616no—
1002C23D3×#6714yes—
1003C23C22×D3212yes—
1004C23C22×D3212yes—
1005C23C22×D3211yescharacteristic
1006Q8—68no—
1007D4—28no—
1008D4—316no—
1009D4—68no—
1010D4—68no—
1011D4—124no—
1012D4—188no—
1013D4—188no—
1014D4—188no—
1015D4—364no—
1016C2×C4—22no—
1017C2×C4—34no—
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—68no—
1030C2×C4—92no—
1031C2×C4—92no—
1032C2×C4—92no—
1033C2×C4—188no—
1034C2×C4—182no—
1035C2×C4—182no—
1036C2×C4—182no—
1037C2×C4—364no—
1038C2×C4—364no—
1039C2×C4C22×D3212yes—
1040C2×C3—24no—
1041C2×C3—24no—
1042C2×C3—21no—
1043C2×C3—21no—
1044C2×C3—21no—
1045C2×C3—24no—
1046C2×C3—44no—
1047C2×C3—42no—
1048C2×C3—42no—
1049C2×C3—64no—
1050C2×C3—64no—
1051C2×C3—82no—
1052C2×C3—122no—
1053C2×C3#559114yescomplemented
1054C2×C3#582914yescomplemented
1055C2×C3C22×D3×D411yescharacteristic
1056C2×C3C22×#23711yescharacteristic
1057C2×C3C2×#100411yescharacteristic
1058C2×C3C2×D3×#4111yescharacteristic
1059C2×C3C2×#100911yescharacteristic
1060C2×C3C23×#6711yescharacteristic
1061D3—24no—
1062D3—24no—
1063D3—42no—
1064D3—122no—
1065D3—122no—
1066D3—242no—
1067C22—22no—
1068C22—22no—
1069C22—28no—
1070C22—22no—
1071C22—22no—
1072C22—22no—
1073C22—34no—
1074C22—34no—
1075C22—44no—
1076C22—62no—
1077C22—62no—
1078C22—62no—
1079C22—62no—
1080C22—68no—
1081C22—68no—
1082C22—62no—
1083C22—62no—
1084C22—62no—
1085C22—1216no—
1086C22—124no—
1087C22—182no—
1088C22—182no—
1089C22—182no—
1090C22—3616no—
1091C22—364no—
1092C22D3×#23712yes—
1093C22#6431412yes—
1094C22C2×D3×#6714yes—
1095C22C2×D3×#6712yes—
1096C22C23×D3211yescharacteristic
1097C4—22no—
1098C4—34no—
1099C4—62no—
1100C4—62no—
1101C4—62no—
1102C4—62no—
1103C4—182no—
1104C4—182no—
1105C4—182no—
1106C3—21no—
1107C3C2×#559111yescharacteristic, complemented
1108C3C2×#582911yescharacteristic, complemented
1109C2—24no—
1110C2—42no—
1111C2—64no—
1112C2—64no—
1113C2—122no—
1114C2—362no—
1115C2#1059530414yesdirect product factor
1116C2C2×D3×#23711yescharacteristic
1117C2C2×#6431411yescharacteristic
1118C2C22×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×D3×#67C2semidirect
3. C2×#64148C2semidirect
4. C2×C3×#937C2semidirect
5. C2×#63983C2semidirect
6. C2×#63978C2semidirect
7. C2×#67⋊Dic3C2semidirect
8. C2×Dic3×#67C2semidirect
9. C2×#63970C2semidirect
10. C2×#63966C2semidirect
11. C22×(C2×D3)⋊Dic3C2semidirect
12. #10595304C2direct (N × H)
13. C2×D3×(C2×D3)⋊C4C2semidirect
14. C2×#63907C2semidirect
15. C2×#63905C2semidirect
16. C2×#63887C2semidirect
21. C22×C32×D4C22semidirect
23. C22×#638C22semidirect
24. C23×C3⋊Dic3C22semidirect
27. C22×C3×#67C22semidirect
28. C22×C3×#67C22semidirect
29. C23×C3×Dic3C22semidirect
30. C23×C3×Dic3C22semidirect
32. C2×C3×#237C22semidirect
33. C22×C3×C4×D3C22semidirect
34. C22×C3×Dic6C22semidirect
36. C2×D3×#67C22semidirect
40. C22×D3×Dic3C22semidirect
41. C2×#3757C22semidirect
42. #64148C22semidirect
43. C2×#3752C22semidirect
44. C2×#3750C22semidirect
45. C2×C3×#217C22semidirect
46. C3×#937C22semidirect
48. C2×C3×(C2×D3)⋊C4C22semidirect
49. #63983C22semidirect
50. #63978C22semidirect
51. #67⋊Dic3C22semidirect
52. Dic3×#67C22semidirect
53. #63970C22semidirect
54. #63966C22semidirect
55. C2×Dic3⋊Dic3C22semidirect
56. C2×Dic3⋊Dic3C22semidirect
57. C2×Dic3⋊Dic3C22semidirect
58. C2×#3722C22semidirect
59. C2×#3722C22semidirect
62. C2×(C2×D3)⋊Dic3C22semidirect
63. C2×(C2×D3)⋊Dic3C22semidirect
64. C2×(C2×D3)⋊Dic3C22semidirect
65. C2×(C2×D3)⋊Dic3C22semidirect
66. C2×Dic32C22semidirect
67. D3×(C2×D3)⋊C4C22semidirect
68. #63907C22semidirect
69. #63905C22semidirect
70. #63887C22semidirect
73. C22×#237D3semidirect
88. C2×#937D3semidirect
119. C2×C32×D4C23semidirect
124. C2×#638C23semidirect
129. C22×C3⋊Dic3C23semidirect
133. C2×C3×#67D4semidirect
136. C2×C3×#67C23semidirect
137. C2×C3×#67C23semidirect
145. C22×C3×Dic3C23semidirect
146. C22×C3×Dic3C23semidirect
149. C2×C3×C4×D3C23semidirect
151. C2×C3×Dic6C23semidirect
160. C2×D3×Dic3C23semidirect
161. #3757C23semidirect
162. #3752C23semidirect
163. #3750C23semidirect
164. C3×#217C23semidirect
166. C3×(C2×D3)⋊C4C23semidirect
167. Dic3⋊Dic3C23semidirect
168. Dic3⋊Dic3C23semidirect
169. Dic3⋊Dic3C23semidirect
170. #3722C23semidirect
171. #3722C23semidirect
174. (C2×D3)⋊Dic3C23semidirect
175. (C2×D3)⋊Dic3C23semidirect
176. (C2×D3)⋊Dic3C23semidirect
177. Dic32C23semidirect
191. C22×C3×D4C2×D3semidirect
192. C22×C3×D4C2×D3semidirect
209. C22×#67C2×D3semidirect
210. C22×#67C2×D3semidirect
216. C23×Dic3C2×D3semidirect
217. C23×Dic3C2×D3semidirect
219. C2×#237C2×D3semidirect
225. C22×C4×D3C2×D3semidirect
226. C22×Dic6C2×D3semidirect
240. C2×#217C2×D3semidirect
251. #937C2×D3semidirect
273. C2×(C2×D3)⋊C4C2×D3semidirect
316. C22×C3×D3#41semidirect
339. C3×#67C2×D4semidirect
420. C2×C3×D4C22×D3semidirect
421. C2×C3×D4C22×D3semidirect
458. C2×#67#67semidirect
461. C2×#67C22×D3semidirect
462. C2×#67C22×D3semidirect
489. C22×Dic3C22×D3semidirect
490. C22×Dic3C22×D3semidirect
500. C2×C4×D3C22×D3semidirect
502. C2×Dic6C22×D3semidirect
514. #217C22×D3semidirect
528. (C2×D3)⋊C4C22×D3semidirect
568. C2×C3×D3C2×#41semidirect
594. C22×D4D32semidirect
705. C22×D3#237semidirect
749. #67C2×#67semidirect
792. C2×C32#546semidirect
835. C2×D4C2×D32semidirect
948. C2×D3C2×#237semidirect
972. C32C2×#546semidirect
1053. C2×C3#5591semidirect
1054. C2×C3#5829semidirect
1107. C3C2×#5591semidirect
1108. C3C2×#5829semidirect
1115. C2#10595304direct (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×D3×#672
C2×#641482
C2×C3×#9372
C2×#639832
C2×#639782
C2×#67⋊Dic32
C2×Dic3×#672
C2×#639702
C2×#639662
C22×(C2×D3)⋊Dic32
#105953042
C2×D3×(C2×D3)⋊C42
C2×#639072
C2×#639052
C2×#638872
C2×#58293
C2×#55913