Finite Group Databasebeta

← #10729193

Subgroups — #10729193

Order 768.

3030 conjugacy classes of subgroups.

The subgroup lattice has 1392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#894C211yesmaximal, characteristic, complemented
2C22×#883C211yesmaximal, characteristic, complemented
3C22×#884C211yesmaximal, characteristic
4C2×#4956C211yesmaximal, characteristic, complemented
5C2×#4665C211yesmaximal, characteristic, complemented
6C2×D3×#95C211yesmaximal, characteristic, complemented
7C3×#1439C211yesmaximal, characteristic, complemented
8#71568C211yesmaximal, characteristic, complemented
9#71550C211yesmaximal, characteristic, complemented
10#71550C211yesmaximal, characteristic, complemented
11#71547C211yesmaximal, characteristic, complemented
12#69428C211yesmaximal, characteristic, complemented
13#69427C211yesmaximal, characteristic, complemented
14(C2×D3)⋊#95C211yesmaximal, characteristic, complemented
15#69420C211yesmaximal, characteristic, complemented
16#14926—31nomaximal, Sylow
17C23×#67C2211yescharacteristic
18C23×#67C2211yescharacteristic
19C23×D12C2211yescharacteristic
20C23×C4×D3C2211yescharacteristic
21C23×C4×D3C2211yescharacteristic
22C23×C4×D3C2211yescharacteristic
23C22×C3×C4⋊C4C2211yescharacteristic
24C22×C3×C22⋊C4C2211yescharacteristic
25C22×C3×C22⋊C4C2211yescharacteristic
26C22×C3×C22⋊C4C2211yescharacteristic
27C22×#217C2211yescharacteristic
28C22×#217C2211yescharacteristic
29C22×(C2×D3)⋊C4C2211yescharacteristic
30C22×(C2×D3)⋊C4C2211yescharacteristic
31C22×(C2×D3)⋊C4C2211yescharacteristic
32C22×(C2×D3)⋊C4C2211yescharacteristic
33C22×(C2×D3)⋊C4C2211yescharacteristic
34C22×(C2×D3)⋊C4C2211yescharacteristic
35C22×(C2×D3)⋊C4C2211yescharacteristic
36C22×C4⋊Dic3C2211yescharacteristic
37C22×Dic3⋊C4C2211yescharacteristic
38C22×Dic3⋊C4C2211yescharacteristic
39C22×Dic3⋊C4C2211yescharacteristic
40C2×#894—24no—
41C2×#894—24no—
42C2×#894—24no—
43C2×#884—24no—
44C2×#884—24no—
45C2×#884—24no—
46C2×#883—24no—
47C2×#883—24no—
48C2×#883—24no—
49C2×C3×#95C2211yescharacteristic
50C2×C3×#95C2211yescharacteristic
51C2×C3×#95C2211yescharacteristic
52C2×C3⋊#95C2211yescharacteristic
53C2×C3⋊#95C2211yescharacteristic
54C2×C3⋊#95C2211yescharacteristic
55C2×C3⋊#95C2211yescharacteristic
56C2×C3⋊#95C2211yescharacteristic
57C2×C3⋊#95C2211yescharacteristic
58C2×C3⋊#95C2211yescharacteristic
59C2×C3⋊#95C2211yescharacteristic
60C2×C3⋊#95C2211yescharacteristic
61#4956—24no—
62#4665—24no—
63D3×#95—24no—
64C22×#123—31no—
65C22×#123—31no—
66C22×#121—31no—
67C2×#386—31no—
68C2×#386—31no—
69C22×#95—31no—
70#1444—31no—
71#1444—31no—
72#1439—31no—
73#1439—31no—
74#1439—31no—
75#1439D311yescharacteristic, complemented
76#1438—31no—
77#1438—31no—
78C22⋊#95—31no—
79C25×C3C2311yescharacteristic
80C24×D3C2311yescharacteristic
81C24×D3C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C23×C3×C4C2311yescharacteristic
85C23×C3×C4C2311yescharacteristic
86C23×C3×C4C2311yescharacteristic
87C23×C3×C4C2311yescharacteristic
88C22×#67—22no—
89C22×#67—22no—
90C22×#67—22no—
91C22×#67—22no—
92C22×#67—22no—
93C22×#67—22no—
94C22×#67—22no—
95C22×#67—22no—
96C22×#67—22no—
97C22×#67—22no—
98C22×#67—22no—
99C22×#67—41no—
100C22×#67—41no—
101C22×#67D414yes—
102C23×Dic3C2311yescharacteristic
103C23×Dic3C2311yescharacteristic
104C23×Dic3C2311yescharacteristic
105C23×Dic3C2311yescharacteristic
106C23×Dic3C2311yescharacteristic
107C23×Dic3C2311yescharacteristic
108C22×D12—22no—
109C22×D12—22no—
110C22×D12—22no—
111C22×D12—22no—
112C22×D12—22no—
113C22×D12—22no—
114C22×D12D414yes—
115C22×C4×D3—22no—
116C22×C4×D3—22no—
117C22×C4×D3—22no—
118C22×C4×D3—22no—
119C22×C4×D3—22no—
120C22×C4×D3—22no—
121C22×C4×D3—22no—
122C22×C4×D3—22no—
123C22×C4×D3—22no—
124C22×C4×D3—22no—
125C22×C4×D3—22no—
126C22×C4×D3—22no—
127C22×C4×D3—22no—
128C22×C4×D3—22no—
129C22×C4×D3—22no—
130C22×C4×D3—41no—
131C22×C4×D3—41no—
132C22×C4×D3—41no—
133C22×C4×D3—41no—
134C22×C4×D3D414yes—
135C22×C4×D3D414yescomplemented
136C2×C3×C4⋊C4—22no—
137C2×C3×C4⋊C4—22no—
138C2×C3×C4⋊C4—22no—
139C2×C3×C22⋊C4—22no—
140C2×C3×C22⋊C4—22no—
141C2×C3×C22⋊C4—22no—
142C2×C3×C22⋊C4—22no—
143C2×C3×C22⋊C4—22no—
144C2×C3×C22⋊C4—22no—
145C2×C3×C22⋊C4—22no—
146C2×C3×C22⋊C4—22no—
147C2×C3×C22⋊C4—41no—
148C2×#217—22no—
149C2×#217—22no—
150C2×#217—22no—
151C2×#217—22no—
152C2×#217—22no—
153C2×#217—41no—
154C2×(C2×D3)⋊C4—22no—
155C2×(C2×D3)⋊C4—22no—
156C2×(C2×D3)⋊C4—22no—
157C2×(C2×D3)⋊C4—22no—
158C2×(C2×D3)⋊C4—22no—
159C2×(C2×D3)⋊C4—22no—
160C2×(C2×D3)⋊C4—22no—
161C2×(C2×D3)⋊C4—22no—
162C2×(C2×D3)⋊C4—22no—
163C2×(C2×D3)⋊C4—22no—
164C2×(C2×D3)⋊C4—22no—
165C2×(C2×D3)⋊C4—22no—
166C2×(C2×D3)⋊C4—22no—
167C2×(C2×D3)⋊C4—22no—
168C2×(C2×D3)⋊C4—22no—
169C2×(C2×D3)⋊C4—22no—
170C2×(C2×D3)⋊C4—22no—
171C2×(C2×D3)⋊C4—41no—
172C2×(C2×D3)⋊C4—41no—
173C2×(C2×D3)⋊C4D414yescomplemented
174C2×(C2×D3)⋊C4D414yescomplemented
175C2×C4⋊Dic3—22no—
176C2×C4⋊Dic3—22no—
177C2×C4⋊Dic3—22no—
178C2×Dic3⋊C4—22no—
179C2×Dic3⋊C4—22no—
180C2×Dic3⋊C4—22no—
181C2×Dic3⋊C4—22no—
182C2×Dic3⋊C4—22no—
183C2×Dic3⋊C4—22no—
184C2×Dic3⋊C4—22no—
185C2×Dic3⋊C4—22no—
186C2×Dic3⋊C4—22no—
187#894—232no—
188#884—232no—
189#883—232no—
190C3×#95—22no—
191C3×#95—22no—
192C3×#95—41no—
193C3⋊#95—22no—
194C3⋊#95—22no—
195C3⋊#95—22no—
196C3⋊#95—22no—
197C3⋊#95—22no—
198C3⋊#95—22no—
199C3⋊#95—22no—
200C3⋊#95—22no—
201C3⋊#95—41no—
202C23×D4—31no—
203C23×D4—31no—
204C23×D4—31no—
205C24×C4—31no—
206C24×C4—31no—
207C24×C4—31no—
208C2×#123—64no—
209C2×#123—64no—
210C2×#123—64no—
211C2×#123—64no—
212C2×#123—64no—
213C2×#123—64no—
214C2×#121—64no—
215C2×#121—64no—
216C2×#121—64no—
217C22×C4⋊C4—31no—
218C22×C4⋊C4—31no—
219C22×C4⋊C4—31no—
220C22×C4⋊C4—31no—
221C22×C4⋊C4C2×D311yescharacteristic
222C22×C22⋊C4—31no—
223C22×C22⋊C4—31no—
224C22×C22⋊C4—31no—
225C22×C22⋊C4—31no—
226C22×C22⋊C4—31no—
227C22×C22⋊C4—31no—
228C22×C22⋊C4—31no—
229C22×C22⋊C4—31no—
230C22×C22⋊C4—31no—
231C22×C22⋊C4C2×D311yescharacteristic
232C22×C22⋊C4C2×D311yescharacteristic
233C22×C22⋊C4C2×D311yescharacteristic
234#386—64no—
235#386—64no—
236C2×#95—31no—
237C2×#95—31no—
238C2×#95—31no—
239C2×#95—31no—
240C2×#95—31no—
241C2×#95—31no—
242C2×#95—31no—
243C2×#95—31no—
244C2×#95—31no—
245C2×#95—64no—
246C2×#95C2×D311yescharacteristic
247C2×#95C2×D311yescharacteristic
248C2×#95C2×D311yescharacteristic
249C24×C3—21no—
250C24×C3—21no—
251C24×C3—21no—
252C24×C3—21no—
253C24×C3—21no—
254C24×C3—21no—
255C24×C3—21no—
256C24×C3—21no—
257C24×C3—21no—
258C24×C3—21no—
259C24×C3—21no—
260C24×C3—21no—
261C24×C3—21no—
262C24×C3—21no—
263C24×C3C2×D412yes—
264C24×C3C2411yescharacteristic
265C23×D3—21no—
266C23×D3—21no—
267C23×D3—21no—
268C23×D3—21no—
269C23×D3—21no—
270C23×D3—21no—
271C23×D3—21no—
272C23×D3—21no—
273C23×D3—21no—
274C23×D3—21no—
275C23×D3—21no—
276C23×D3—21no—
277C23×D3—21no—
278C23×D3—21no—
279C23×D3—21no—
280C23×D3—21no—
281C23×D3—21no—
282C23×D3—21no—
283C23×D3—21no—
284C23×D3—21no—
285C23×D3—21no—
286C23×D3—21no—
287C23×D3C2×D412yes—
288C23×D3C2×D412yes—
289C23×D3C2×D412yes—
290C23×D3C2×D412yes—
291C23×D3C2×D412yes—
292C23×D3C2×D412yes—
293C23×D3C2×D412yes—
294C23×D3#4112yes—
295C22×C3×C4—21no—
296C22×C3×C4—21no—
297C22×C3×C4—21no—
298C22×C3×C4—21no—
299C22×C3×C4—21no—
300C22×C3×C4—21no—
301C22×C3×C4—21no—
302C22×C3×C4—21no—
303C22×C3×C4—21no—
304C22×C3×C4—21no—
305C22×C3×C4—21no—
306C22×C3×C4—21no—
307C22×C3×C4—21no—
308C22×C3×C4—21no—
309C22×C3×C4—21no—
310C22×C3×C4—21no—
311C22×C3×C4—21no—
312C22×C3×C4—21no—
313C22×C3×C4—21no—
314C22×C3×C4—21no—
315C22×C3×C4—21no—
316C22×C3×C4—21no—
317C22×C3×C4—21no—
318C22×C3×C4—21no—
319C22×C3×C4—21no—
320C22×C3×C4—21no—
321C22×C3×C4—21no—
322C22×C3×C4—21no—
323C22×C3×C4—21no—
324C22×C3×C4—21no—
325C22×C3×C4—21no—
326C22×C3×C4—21no—
327C22×C3×C4—21no—
328C22×C3×C4—21no—
329C22×C3×C4—21no—
330C22×C3×C4—21no—
331C22×C3×C4C2×D412yes—
332C22×C3×C4C2×D412yes—
333C22×C3×C4C2×D412yes—
334C22×C3×C4C2×D412yes—
335C22×C3×C4C2×D412yes—
336C22×C3×C4#4112yes—
337C2×#67—28no—
338C2×#67—28no—
339C2×#67—28no—
340C2×#67—28no—
341C2×#67—44no—
342C2×#67—44no—
343C2×#67—44no—
344C2×#67—44no—
345C2×#67—44no—
346C2×#67—44no—
347C2×#67—44no—
348C2×#67—44no—
349C2×#67—44no—
350C2×#67—44no—
351C22×Dic3—21no—
352C22×Dic3—21no—
353C22×Dic3—21no—
354C22×Dic3—21no—
355C22×Dic3—21no—
356C22×Dic3—21no—
357C22×Dic3—21no—
358C22×Dic3—21no—
359C22×Dic3—21no—
360C22×Dic3—21no—
361C22×Dic3—21no—
362C22×Dic3—21no—
363C22×Dic3—21no—
364C22×Dic3—21no—
365C22×Dic3—21no—
366C22×Dic3—21no—
367C22×Dic3—21no—
368C22×Dic3—21no—
369C22×Dic3—21no—
370C22×Dic3—21no—
371C22×Dic3—21no—
372C22×Dic3—21no—
373C22×Dic3—21no—
374C22×Dic3—21no—
375C22×Dic3—21no—
376C22×Dic3—21no—
377C22×Dic3—21no—
378C22×Dic3—21no—
379C22×Dic3—21no—
380C22×Dic3—21no—
381C22×Dic3—21no—
382C22×Dic3—21no—
383C22×Dic3—21no—
384C22×Dic3—21no—
385C22×Dic3C2×D412yes—
386C22×Dic3C2×D412yes—
387C22×Dic3C2×D412yes—
388C22×Dic3C2×D412yes—
389C22×Dic3C2×D412yes—
390C22×Dic3#4112yes—
391C22×Dic3#4112yes—
392C22×Dic3#4112yes—
393C2×D12—28no—
394C2×D12—28no—
395C2×D12—28no—
396C2×D12—44no—
397C2×D12—44no—
398C2×D12—44no—
399C2×D12—44no—
400C2×C4×D3—28no—
401C2×C4×D3—28no—
402C2×C4×D3—28no—
403C2×C4×D3—28no—
404C2×C4×D3—28no—
405C2×C4×D3—28no—
406C2×C4×D3—44no—
407C2×C4×D3—44no—
408C2×C4×D3—44no—
409C2×C4×D3—44no—
410C2×C4×D3—44no—
411C2×C4×D3—44no—
412C2×C4×D3—44no—
413C2×C4×D3—44no—
414C2×C4×D3—44no—
415C2×C4×D3—44no—
416C2×C4×D3—44no—
417C2×C4×D3—44no—
418C2×C4×D3—44no—
419C2×C4×D3—44no—
420C2×C4×D3—44no—
421C3×C4⋊C4—28no—
422C3×C22⋊C4—28no—
423C3×C22⋊C4—28no—
424C3×C22⋊C4—44no—
425#217—28no—
426#217—44no—
427(C2×D3)⋊C4—28no—
428(C2×D3)⋊C4—28no—
429(C2×D3)⋊C4—28no—
430(C2×D3)⋊C4—28no—
431(C2×D3)⋊C4—28no—
432(C2×D3)⋊C4—44no—
433(C2×D3)⋊C4—44no—
434C4⋊Dic3—28no—
435Dic3⋊C4—28no—
436Dic3⋊C4—28no—
437Dic3⋊C4—28no—
438C25—31no—
439C25—31no—
440C25C22×D311yescharacteristic
441C22×D4—34no—
442C22×D4—34no—
443C22×D4—62no—
444C22×D4—62no—
445C22×D4—62no—
446C22×D4—62no—
447C22×D4—62no—
448C22×D4—62no—
449C22×D4—62no—
450C22×D4—62no—
451C22×D4—62no—
452C22×D4—62no—
453C22×D4—62no—
454C22×D4—62no—
455C22×D4—62no—
456C22×D4—62no—
457C22×D4—62no—
458C22×D4—62no—
459C22×D4—62no—
460C22×D4—121no—
461C22×D4—121no—
462C23×C4—31no—
463C23×C4—31no—
464C23×C4—31no—
465C23×C4—31no—
466C23×C4—31no—
467C23×C4—31no—
468C23×C4—34no—
469C23×C4—34no—
470C23×C4—62no—
471C23×C4—62no—
472C23×C4—62no—
473C23×C4—62no—
474C23×C4—62no—
475C23×C4—62no—
476C23×C4—62no—
477C23×C4—62no—
478C23×C4—62no—
479C23×C4—62no—
480C23×C4—62no—
481C23×C4—62no—
482C23×C4—62no—
483C23×C4—62no—
484C23×C4—62no—
485C23×C4—121no—
486C23×C4—121no—
487C23×C4—121no—
488C23×C4—121no—
489C23×C4C22×D311yescharacteristic
490C23×C4C22×D311yescharacteristic
491C23×C4C22×D311yescharacteristic
492C23×C4C22×D311yescharacteristic
493C23×C4C22×D311yescharacteristic
494C23×C4C22×D311yescharacteristic
495#123—632no—
496#123—632no—
497#121—632no—
498C2×C4⋊C4—22no—
499C2×C4⋊C4—22no—
500C2×C4⋊C4—22no—
501C2×C4⋊C4—62no—
502C2×C4⋊C4—62no—
503C2×C4⋊C4—62no—
504C2×C4⋊C4—62no—
505C2×C4⋊C4—62no—
506C2×C4⋊C4—62no—
507C2×C4⋊C4—62no—
508C2×C4⋊C4—62no—
509C2×C4⋊C4—62no—
510C2×C4⋊C4—62no—
511C2×C4⋊C4—62no—
512C2×C4⋊C4—62no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—22no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4—22no—
517C2×C22⋊C4—22no—
518C2×C22⋊C4—22no—
519C2×C22⋊C4—22no—
520C2×C22⋊C4—22no—
521C2×C22⋊C4—34no—
522C2×C22⋊C4—34no—
523C2×C22⋊C4—41no—
524C2×C22⋊C4—62no—
525C2×C22⋊C4—62no—
526C2×C22⋊C4—62no—
527C2×C22⋊C4—62no—
528C2×C22⋊C4—62no—
529C2×C22⋊C4—62no—
530C2×C22⋊C4—62no—
531C2×C22⋊C4—62no—
532C2×C22⋊C4—62no—
533C2×C22⋊C4—62no—
534C2×C22⋊C4—62no—
535C2×C22⋊C4—62no—
536C2×C22⋊C4—62no—
537C2×C22⋊C4—62no—
538C2×C22⋊C4—62no—
539C2×C22⋊C4—62no—
540C2×C22⋊C4—62no—
541C2×C22⋊C4—62no—
542C2×C22⋊C4—62no—
543C2×C22⋊C4—62no—
544C2×C22⋊C4—62no—
545C2×C22⋊C4—62no—
546C2×C22⋊C4—121no—
547C2×C22⋊C4—121no—
548C2×C22⋊C4—121no—
549#95—22no—
550#95—22no—
551#95—41no—
552#95—62no—
553#95—62no—
554#95—62no—
555#95—62no—
556#95—62no—
557#95—62no—
558#95—62no—
559#95—62no—
560#95—121no—
561C23×C3—22no—
562C23×C3—22no—
563C23×C3—22no—
564C23×C3—22no—
565C23×C3—22no—
566C23×C3—22no—
567C23×C3—22no—
568C23×C3—41no—
569C23×C3—41no—
570C23×C3—41no—
571C23×C3—41no—
572C23×C3—41no—
573C23×C3—41no—
574C23×C3—41no—
575C23×C3—41no—
576C23×C3—41no—
577C23×C3—41no—
578C23×C3—41no—
579C23×C3—41no—
580C23×C3—41no—
581C23×C3—41no—
582C23×C3—41no—
583C23×C3—41no—
584C23×C3—41no—
585C23×C3—41no—
586C23×C3—41no—
587C23×C3—41no—
588C23×C3—41no—
589C23×C3—41no—
590C23×C3—41no—
591C23×C3—41no—
592C23×C3—41no—
593C23×C3—41no—
594C23×C3—41no—
595C23×C3—41no—
596C23×C3C22×D411yescharacteristic
597C23×C3C22×D411yescharacteristic
598C23×C3C22×D411yescharacteristic
599C23×C3C22×D411yescharacteristic
600C23×C3C22×D411yescharacteristic
601C23×C3C22×D411yescharacteristic
602C23×C3C2×#4111yescharacteristic
603C23×C3C2×#4111yescharacteristic
604C23×C3C2×#4111yescharacteristic
605C23×C3C2×#4111yescharacteristic
606C23×C3C2×#4111yescharacteristic
607C23×C3H(5,𝔽2)11yescharacteristic
608C23×C3H(5,𝔽2)11yescharacteristic
609C23×C32−1+411yescharacteristic
610C23×C32−1+411yescharacteristic
611C22×D3—22no—
612C22×D3—22no—
613C22×D3—22no—
614C22×D3—22no—
615C22×D3—22no—
616C22×D3—22no—
617C22×D3—22no—
618C22×D3—22no—
619C22×D3—22no—
620C22×D3—22no—
621C22×D3—22no—
622C22×D3—22no—
623C22×D3—22no—
624C22×D3—22no—
625C22×D3—22no—
626C22×D3—22no—
627C22×D3—22no—
628C22×D3—22no—
629C22×D3—22no—
630C22×D3—22no—
631C22×D3—22no—
632C22×D3—22no—
633C22×D3—22no—
634C22×D3—22no—
635C22×D3—22no—
636C22×D3—22no—
637C22×D3—22no—
638C22×D3—22no—
639C22×D3—22no—
640C22×D3—22no—
641C22×D3—22no—
642C22×D3—22no—
643C22×D3—22no—
644C22×D3—22no—
645C22×D3—22no—
646C22×D3—41no—
647C22×D3—41no—
648C22×D3—41no—
649C22×D3—41no—
650C22×D3—41no—
651C22×D3—41no—
652C22×D3—41no—
653C22×D3—41no—
654C22×D3—41no—
655C22×D3—41no—
656C22×D3—41no—
657C22×D3—41no—
658C22×D3—41no—
659C22×D3—41no—
660C22×D3—41no—
661C22×D3—41no—
662C22×D3—41no—
663C22×D3—41no—
664C22×D3—41no—
665C22×D3—41no—
666C22×D3—41no—
667C22×D3—41no—
668C22×D3—41no—
669C22×D3—41no—
670C22×D3—41no—
671C22×D3—41no—
672C22×D3—41no—
673C22×D3—41no—
674C22×D3#12014yes—
675C22×D3#12014yes—
676C22×D3#12014yes—
677C22×D3#12114yes—
678C22×D3#12114yes—
679C22×D3#12114yes—
680C22×D3#12714yes—
681C2×C3×C4—22no—
682C2×C3×C4—22no—
683C2×C3×C4—22no—
684C2×C3×C4—22no—
685C2×C3×C4—22no—
686C2×C3×C4—22no—
687C2×C3×C4—22no—
688C2×C3×C4—22no—
689C2×C3×C4—22no—
690C2×C3×C4—22no—
691C2×C3×C4—22no—
692C2×C3×C4—22no—
693C2×C3×C4—22no—
694C2×C3×C4—22no—
695C2×C3×C4—22no—
696C2×C3×C4—22no—
697C2×C3×C4—22no—
698C2×C3×C4—22no—
699C2×C3×C4—41no—
700C2×C3×C4—41no—
701C2×C3×C4—41no—
702C2×C3×C4—41no—
703C2×C3×C4—41no—
704C2×C3×C4—41no—
705C2×C3×C4—41no—
706C2×C3×C4—41no—
707C2×C3×C4—41no—
708C2×C3×C4—41no—
709C2×C3×C4—41no—
710C2×C3×C4—41no—
711C2×C3×C4—41no—
712C2×C3×C4—41no—
713C2×C3×C4—41no—
714C2×C3×C4—41no—
715C2×C3×C4—41no—
716C2×C3×C4—41no—
717C2×C3×C4—41no—
718C2×C3×C4—41no—
719C2×C3×C4—41no—
720C2×C3×C4—41no—
721C2×C3×C4—41no—
722C2×C3×C4—41no—
723#67—416no—
724#67—416no—
725C2×Dic3—22no—
726C2×Dic3—22no—
727C2×Dic3—22no—
728C2×Dic3—22no—
729C2×Dic3—22no—
730C2×Dic3—22no—
731C2×Dic3—22no—
732C2×Dic3—22no—
733C2×Dic3—22no—
734C2×Dic3—22no—
735C2×Dic3—22no—
736C2×Dic3—22no—
737C2×Dic3—22no—
738C2×Dic3—22no—
739C2×Dic3—22no—
740C2×Dic3—22no—
741C2×Dic3—22no—
742C2×Dic3—22no—
743C2×Dic3—22no—
744C2×Dic3—22no—
745C2×Dic3—22no—
746C2×Dic3—41no—
747C2×Dic3—41no—
748C2×Dic3—41no—
749C2×Dic3—41no—
750C2×Dic3—41no—
751C2×Dic3—41no—
752C2×Dic3—41no—
753C2×Dic3—41no—
754C2×Dic3—41no—
755C2×Dic3—41no—
756C2×Dic3—41no—
757C2×Dic3—41no—
758C2×Dic3—41no—
759C2×Dic3—41no—
760C2×Dic3—41no—
761C2×Dic3—41no—
762C2×Dic3—41no—
763C2×Dic3—41no—
764C2×Dic3—41no—
765C2×Dic3—41no—
766C2×Dic3#12314yescomplemented
767D12—416no—
768C4×D3—416no—
769C4×D3—416no—
770C4×D3—416no—
771C24—21no—
772C24—21no—
773C24—21no—
774C24—21no—
775C24—21no—
776C24—21no—
777C24—21no—
778C24—21no—
779C24—21no—
780C24—21no—
781C24—21no—
782C24—21no—
783C24—21no—
784C24—21no—
785C24—32no—
786C24—32no—
787C24—32no—
788C24—32no—
789C24—32no—
790C24—32no—
791C24—32no—
792C24—32no—
793C24—61no—
794C24—61no—
795C24—61no—
796C24—61no—
797C24—61no—
798C24—61no—
799C24—61no—
800C24—61no—
801C24—61no—
802C24—61no—
803C24—61no—
804C24—61no—
805C24—61no—
806C24—61no—
807C24—61no—
808C24—61no—
809C24—61no—
810C24—61no—
811C24—61no—
812C24—61no—
813C24—61no—
814C24—61no—
815C24D3×D412yes—
816C24C23×D311yescharacteristic
817C2×D4—68no—
818C2×D4—68no—
819C2×D4—68no—
820C2×D4—68no—
821C2×D4—68no—
822C2×D4—68no—
823C2×D4—68no—
824C2×D4—124no—
825C2×D4—124no—
826C2×D4—124no—
827C2×D4—124no—
828C2×D4—124no—
829C2×D4—124no—
830C2×D4—124no—
831C2×D4—124no—
832C2×D4—124no—
833C2×D4—124no—
834C2×D4—124no—
835C2×D4—124no—
836C2×D4—124no—
837C2×D4—124no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—32no—
875C22×C4—32no—
876C22×C4—32no—
877C22×C4—32no—
878C22×C4—32no—
879C22×C4—32no—
880C22×C4—32no—
881C22×C4—32no—
882C22×C4—68no—
883C22×C4—68no—
884C22×C4—68no—
885C22×C4—68no—
886C22×C4—68no—
887C22×C4—68no—
888C22×C4—61no—
889C22×C4—61no—
890C22×C4—61no—
891C22×C4—61no—
892C22×C4—61no—
893C22×C4—61no—
894C22×C4—61no—
895C22×C4—61no—
896C22×C4—61no—
897C22×C4—61no—
898C22×C4—61no—
899C22×C4—61no—
900C22×C4—61no—
901C22×C4—61no—
902C22×C4—61no—
903C22×C4—61no—
904C22×C4—61no—
905C22×C4—61no—
906C22×C4—61no—
907C22×C4—61no—
908C22×C4—61no—
909C22×C4—61no—
910C22×C4—61no—
911C22×C4—61no—
912C22×C4—61no—
913C22×C4—61no—
914C22×C4—61no—
915C22×C4—61no—
916C22×C4—61no—
917C22×C4—61no—
918C22×C4—61no—
919C22×C4—61no—
920C22×C4—61no—
921C22×C4—61no—
922C22×C4—124no—
923C22×C4—124no—
924C22×C4—124no—
925C22×C4—124no—
926C22×C4—124no—
927C22×C4—124no—
928C22×C4—124no—
929C22×C4—124no—
930C22×C4—124no—
931C22×C4—124no—
932C22×C4—124no—
933C22×C4—124no—
934C22×C4—124no—
935C22×C4—124no—
936C22×C4—124no—
937C22×C4#23512yes—
938C22×C4D3×D412yes—
939C22×C4D3×D412yes—
940C22×C4D3×D412yes—
941C22×C4D3×D412yes—
942C22×C4D3×D412yes—
943C4⋊C4—28no—
944C4⋊C4—68no—
945C4⋊C4—68no—
946C4⋊C4—68no—
947C4⋊C4—68no—
948C22⋊C4—28no—
949C22⋊C4—28no—
950C22⋊C4—44no—
951C22⋊C4—68no—
952C22⋊C4—68no—
953C22⋊C4—68no—
954C22⋊C4—68no—
955C22⋊C4—68no—
956C22⋊C4—68no—
957C22⋊C4—124no—
958C22⋊C4—124no—
959C22⋊C4—124no—
960C22×C3—42no—
961C22×C3—42no—
962C22×C3—42no—
963C22×C3—42no—
964C22×C3—42no—
965C22×C3—42no—
966C22×C3—42no—
967C22×C3—81no—
968C22×C3—81no—
969C22×C3—81no—
970C22×C3—81no—
971C22×C3—81no—
972C22×C3—81no—
973C22×C3—81no—
974C22×C3—81no—
975C22×C3C2×#12011yescharacteristic
976C22×C3C2×#12011yescharacteristic
977C22×C3C2×#12011yescharacteristic
978C22×C3C2×#12111yescharacteristic
979C22×C3C2×#12111yescharacteristic
980C22×C3C2×#12111yescharacteristic
981C22×C3C2×#12311yescharacteristic
982C22×C3#52511yescharacteristic
983C22×C3#52911yescharacteristic
984C22×C3#52911yescharacteristic
985C22×C3C2×#12711yescharacteristic
986C22×C3#53211yescharacteristic
987C22×C3#53211yescharacteristic
988C22×C3#53411yescharacteristic
989C22×C3#53611yescharacteristic
990C22×C3#53711yescharacteristic
991C22×C3#53711yescharacteristic
992C22×C3#53911yescharacteristic
993C22×C3#53911yescharacteristic
994C22×C3#54611yescharacteristic
995C22×C3#54611yescharacteristic
996C22×C3#54611yescharacteristic
997C22×C3#54611yescharacteristic
998C22×C3#54611yescharacteristic
999C22×C3#54611yescharacteristic
1000C22×C3#54611yescharacteristic
1001C22×C3#54611yescharacteristic
1002C22×C3#54711yescharacteristic
1003C22×C3#54711yescharacteristic
1004C22×C3#54711yescharacteristic
1005C22×C3#54711yescharacteristic
1006C22×C3#54711yescharacteristic
1007C22×C3#54711yescharacteristic
1008C22×C3#54711yescharacteristic
1009C22×C3#54711yescharacteristic
1010C2×D3—24no—
1011C2×D3—24no—
1012C2×D3—24no—
1013C2×D3—24no—
1014C2×D3—24no—
1015C2×D3—24no—
1016C2×D3—24no—
1017C2×D3—24no—
1018C2×D3—24no—
1019C2×D3—24no—
1020C2×D3—24no—
1021C2×D3—24no—
1022C2×D3—24no—
1023C2×D3—24no—
1024C2×D3—42no—
1025C2×D3—42no—
1026C2×D3—42no—
1027C2×D3—42no—
1028C2×D3—42no—
1029C2×D3—42no—
1030C2×D3—42no—
1031C2×D3—81no—
1032C2×D3—81no—
1033C2×D3—81no—
1034C2×D3—81no—
1035C2×D3—81no—
1036C2×D3—81no—
1037C2×D3—81no—
1038C2×D3—81no—
1039C2×D3#39218yes—
1040C3×C4—42no—
1041C3×C4—42no—
1042C3×C4—42no—
1043C3×C4—42no—
1044C3×C4—42no—
1045C3×C4—42no—
1046Dic3—24no—
1047Dic3—42no—
1048Dic3—42no—
1049Dic3—42no—
1050Dic3—42no—
1051Dic3—42no—
1052C23—22no—
1053C23—22no—
1054C23—22no—
1055C23—22no—
1056C23—22no—
1057C23—22no—
1058C23—22no—
1059C23—34no—
1060C23—34no—
1061C23—34no—
1062C23—34no—
1063C23—34no—
1064C23—34no—
1065C23—34no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—62no—
1095C23—62no—
1096C23—62no—
1097C23—62no—
1098C23—62no—
1099C23—62no—
1100C23—62no—
1101C23—62no—
1102C23—62no—
1103C23—62no—
1104C23—62no—
1105C23—62no—
1106C23—62no—
1107C23—62no—
1108C23—62no—
1109C23—62no—
1110C23—62no—
1111C23—62no—
1112C23—62no—
1113C23—62no—
1114C23—62no—
1115C23—62no—
1116C23—62no—
1117C23—62no—
1118C23—62no—
1119C23—62no—
1120C23—62no—
1121C23—62no—
1122C23—62no—
1123C23—62no—
1124C23—62no—
1125C23—62no—
1126C23—62no—
1127C23—62no—
1128C23—62no—
1129C23—121no—
1130C23—121no—
1131C23—121no—
1132C23—121no—
1133C23—121no—
1134C23—121no—
1135C23—121no—
1136C23—121no—
1137C23—121no—
1138C23—121no—
1139C23—121no—
1140C23—121no—
1141C23—121no—
1142C23—121no—
1143C23—121no—
1144C23—121no—
1145C23—121no—
1146C23—121no—
1147C23—121no—
1148C23—121no—
1149C23—121no—
1150C23—121no—
1151C23—121no—
1152C23—121no—
1153C23—121no—
1154C23—121no—
1155C23—121no—
1156C23—121no—
1157C23C2×#23511yescharacteristic
1158C23C2×D3×D411yescharacteristic
1159C23C2×D3×D411yescharacteristic
1160C23C2×D3×D411yescharacteristic
1161C23C2×D3×D411yescharacteristic
1162C23C2×D3×D411yescharacteristic
1163C23C2×D3×D411yescharacteristic
1164C23#100411yescharacteristic
1165C23#100711yescharacteristic
1166C23D3×#4111yescharacteristic
1167C23D3×#4111yescharacteristic
1168C23D3×#4111yescharacteristic
1169C23D3×#4111yescharacteristic
1170C23#100911yescharacteristic
1171C23#101011yescharacteristic
1172D4—1216no—
1173D4—1216no—
1174D4—1216no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—34no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—62no—
1219C2×C4—62no—
1220C2×C4—62no—
1221C2×C4—62no—
1222C2×C4—62no—
1223C2×C4—62no—
1224C2×C4—62no—
1225C2×C4—62no—
1226C2×C4—62no—
1227C2×C4—62no—
1228C2×C4—62no—
1229C2×C4—62no—
1230C2×C4—62no—
1231C2×C4—62no—
1232C2×C4—62no—
1233C2×C4—62no—
1234C2×C4—62no—
1235C2×C4—62no—
1236C2×C4—62no—
1237C2×C4—62no—
1238C2×C4—62no—
1239C2×C4—1216no—
1240C2×C4—1216no—
1241C2×C4—1216no—
1242C2×C4—121no—
1243C2×C4—121no—
1244C2×C4—121no—
1245C2×C4—121no—
1246C2×C4—121no—
1247C2×C4—121no—
1248C2×C4—121no—
1249C2×C4—121no—
1250C2×C4—121no—
1251C2×C4—121no—
1252C2×C4—121no—
1253C2×C4—121no—
1254C2×C4—121no—
1255C2×C4—121no—
1256C2×C4—121no—
1257C2×C4—121no—
1258C2×C4—121no—
1259C2×C4—121no—
1260C2×C4—121no—
1261C2×C4—121no—
1262C2×C3—82no—
1263C2×C3C2×#39211yescharacteristic
1264C2×C3#240511yescharacteristic
1265C2×C3#240611yescharacteristic
1266C2×C3#242511yescharacteristic
1267C2×C3#242511yescharacteristic
1268C2×C3#242511yescharacteristic
1269C2×C3#242511yescharacteristic
1270C2×C3#243011yescharacteristic
1271C2×C3#243011yescharacteristic
1272C2×C3#243011yescharacteristic
1273C2×C3#243011yescharacteristic
1274C2×C3#250111yescharacteristic
1275C2×C3#253911yescharacteristic
1276C2×C3#261811yescharacteristic
1277C2×C3#285411yescharacteristic
1278D3—28no—
1279D3—82no—
1280C22—38no—
1281C22—42no—
1282C22—42no—
1283C22—42no—
1284C22—42no—
1285C22—42no—
1286C22—42no—
1287C22—42no—
1288C22—64no—
1289C22—64no—
1290C22—64no—
1291C22—64no—
1292C22—64no—
1293C22—64no—
1294C22—64no—
1295C22—64no—
1296C22—64no—
1297C22—64no—
1298C22—64no—
1299C22—64no—
1300C22—64no—
1301C22—64no—
1302C22—81no—
1303C22—81no—
1304C22—81no—
1305C22—81no—
1306C22—81no—
1307C22—81no—
1308C22—81no—
1309C22—81no—
1310C22—122no—
1311C22—122no—
1312C22—122no—
1313C22—122no—
1314C22—122no—
1315C22—122no—
1316C22—122no—
1317C22—241no—
1318C22—241no—
1319C22—241no—
1320C22—241no—
1321C22—241no—
1322C22—241no—
1323C22—241no—
1324C22—241no—
1325C22#549011yescharacteristic
1326C22#550711yescharacteristic
1327C22#552811yescharacteristic
1328C22#554711yescharacteristic
1329C22#554811yescharacteristic
1330C22#555011yescharacteristic
1331C22#555111yescharacteristic
1332C22D3×#12011yescharacteristic
1333C22D3×#12011yescharacteristic
1334C22D3×#12011yescharacteristic
1335C22D3×#12111yescharacteristic
1336C22D3×#12111yescharacteristic
1337C22D3×#12111yescharacteristic
1338C22#560511yescharacteristic
1339C22#560811yescharacteristic
1340C22#561011yescharacteristic
1341C22#561011yescharacteristic
1342C22#561211yescharacteristic
1343C22#562811yescharacteristic
1344C22#562911yescharacteristic
1345C22#563111yescharacteristic
1346C22#563111yescharacteristic
1347C22#563111yescharacteristic
1348C22#563811yescharacteristic
1349C22D3×#12311yescharacteristic
1350C22#565411yescharacteristic
1351C22#565511yescharacteristic
1352C22#565511yescharacteristic
1353C22#565511yescharacteristic
1354C22#566811yescharacteristic
1355C22#567611yescharacteristic
1356C22#567611yescharacteristic
1357C22#570611yescharacteristic
1358C22#570711yescharacteristic
1359C22D3×#12711yescharacteristic
1360C4—42no—
1361C4—42no—
1362C4—42no—
1363C4—42no—
1364C4—42no—
1365C4—42no—
1366C4—64no—
1367C4—122no—
1368C4—122no—
1369C4—122no—
1370C4—122no—
1371C4—122no—
1372C3#1492611yescharacteristic, complemented, Sylow
1373C2—68no—
1374C2—82no—
1375C2—242no—
1376C2#7402211yescharacteristic
1377C2#7460011yescharacteristic
1378C2#7460611yescharacteristic
1379C2#7489611yescharacteristic
1380C2#7584711yescharacteristic
1381C2#7596011yescharacteristic
1382C2#7645411yescharacteristic
1383C2D3×#39211yescharacteristic
1384C2#7686411yescharacteristic
1385C2#7710611yescharacteristic
1386C2#7711611yescharacteristic
1387C2#7741711yescharacteristic
1388C2#7742311yescharacteristic
1389C2#7767211yescharacteristic
1390C2#7803011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1439C2
prime radicalC22×#884C2
hypercenter#1439D3
hypocenterC3#14926
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
1. C22×#894C2semidirect
2. C22×#883C2semidirect
4. C2×#4956C2semidirect
5. C2×#4665C2semidirect
6. C2×D3×#95C2semidirect
7. C3×#1439C2semidirect
8. #71568C2semidirect
9. #71550C2semidirect
10. #71550C2semidirect
11. #71547C2semidirect
12. #69428C2semidirect
13. #69427C2semidirect
14. (C2×D3)⋊#95C2semidirect
15. #69420C2semidirect
75. #1439D3semidirect
135. C22×C4×D3D4semidirect
173. C2×(C2×D3)⋊C4D4semidirect
174. C2×(C2×D3)⋊C4D4semidirect
766. C2×Dic3#123semidirect
1372. C3#14926semidirect

Maximal subgroups

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

subgroupindex
C22×#8942
C22×#8832
C22×#8842
C2×#49562
C2×#46652
C2×D3×#952
C3×#14392
#715682
#715502
#715472
#694282
#694272
(C2×D3)⋊#952
#694202
#149263