Finite Group Databasebeta

← #10726597

Subgroups — #10726597

Order 768.

2982 conjugacy classes of subgroups.

The subgroup lattice has 1390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×C4⋊C4C211yesmaximal, characteristic, complemented
2C22×#884C211yesmaximal, characteristic
3C2×#4959C211yesmaximal, characteristic, complemented
4C2×#4956C211yesmaximal, characteristic, complemented
5C2×#4956C211yesmaximal, characteristic, complemented
6C2×#4961C211yesmaximal, characteristic, complemented
7C2×#4665C211yesmaximal, characteristic, complemented
8C2×#4665C211yesmaximal, characteristic, complemented
9C3×#1439C211yesmaximal, characteristic, complemented
10#71570C211yesmaximal, characteristic, complemented
11#71547C211yesmaximal, characteristic, complemented
12#69428C211yesmaximal, characteristic, complemented
13(C2×D3)⋊#95C211yesmaximal, characteristic, complemented
14#69411C211yesmaximal, characteristic, complemented
15#69409C211yesmaximal, characteristic, complemented
16#14719—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×D3×C4⋊C4—24no—
41C2×D3×C4⋊C4—24no—
42C2×D3×C4⋊C4—24no—
43C2×#884—24no—
44C2×#884—24no—
45C2×#884—24no—
46C2×C3×#95C2211yescharacteristic
47C2×C3×#95C2211yescharacteristic
48C2×C3×#95C2211yescharacteristic
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
58#4961—24no—
59#4959—24no—
60#4956—24no—
61#4956—24no—
62#4665—24no—
63#4665—24no—
64C22×#121—31no—
65C23×C4⋊C4—31no—
66C2×#394—31no—
67C2×#394—31no—
68C2×#386—31no—
69C2×#386—31no—
70C2×#386—31no—
71C2×#386—31no—
72#1441—31no—
73#1441—31no—
74#1439—31no—
75#1439—31no—
76#1439—31no—
77#1439D311yescharacteristic, complemented
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—22no—
172C2×(C2×D3)⋊C4—22no—
173C2×(C2×D3)⋊C4—41no—
174C2×(C2×D3)⋊C4—41no—
175C2×C4⋊Dic3—22no—
176C2×C4⋊Dic3—22no—
177C2×C4⋊Dic3D414yescomplemented
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⋊C4D414yescomplemented
187D3×C4⋊C4—232no—
188#884—232no—
189C3×#95—22no—
190C3×#95—22no—
191C3×#95—41no—
192C3⋊#95—22no—
193C3⋊#95—22no—
194C3⋊#95—22no—
195C3⋊#95—22no—
196C3⋊#95—22no—
197C3⋊#95—22no—
198C3⋊#95—22no—
199C3⋊#95—22no—
200C3⋊#95—41no—
201C23×D4—31no—
202C23×D4—31no—
203C23×D4—31no—
204C24×C4—31no—
205C24×C4—31no—
206C24×C4—31no—
207C2×#121—64no—
208C2×#121—64no—
209C2×#121—64no—
210C22×C4⋊C4—31no—
211C22×C4⋊C4—31no—
212C22×C4⋊C4—31no—
213C22×C4⋊C4—31no—
214C22×C4⋊C4—64no—
215C22×C4⋊C4—64no—
216C22×C4⋊C4—64no—
217C22×C4⋊C4C2×D311yescharacteristic
218C22×C22⋊C4—31no—
219C22×C22⋊C4—31no—
220C22×C22⋊C4—31no—
221C22×C22⋊C4—31no—
222C22×C22⋊C4—31no—
223C22×C22⋊C4—31no—
224C22×C22⋊C4—31no—
225C22×C22⋊C4—31no—
226C22×C22⋊C4—31no—
227C22×C22⋊C4C2×D311yescharacteristic
228C22×C22⋊C4C2×D311yescharacteristic
229C22×C22⋊C4C2×D311yescharacteristic
230#394—64no—
231#394—64no—
232#386—64no—
233#386—64no—
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×#95C2×D311yescharacteristic
246C2×#95C2×D311yescharacteristic
247C2×#95C2×D311yescharacteristic
248C24×C3—21no—
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×C3C2×D412yes—
263C24×C3C2411yescharacteristic
264C23×D3—21no—
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×D3C2×D412yes—
287C23×D3C2×D412yes—
288C23×D3C2×D412yes—
289C23×D3C2×D412yes—
290C23×D3C2×D412yes—
291C23×D3#4112yes—
292C23×D3#4112yes—
293C23×D3#4112yes—
294C22×C3×C4—21no—
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×C4C2×D412yes—
331C22×C3×C4C2×D412yes—
332C22×C3×C4C2×D412yes—
333C22×C3×C4C2×D412yes—
334C22×C3×C4C2×D412yes—
335C22×C3×C4#4112yes—
336C2×#67—28no—
337C2×#67—28no—
338C2×#67—28no—
339C2×#67—28no—
340C2×#67—44no—
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—
350C22×Dic3—21no—
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×Dic3C2×D412yes—
385C22×Dic3C2×D412yes—
386C22×Dic3C2×D412yes—
387C22×Dic3C2×D412yes—
388C22×Dic3C2×D412yes—
389C22×Dic3C2×D412yes—
390C22×Dic3C2×D412yes—
391C22×Dic3#4112yes—
392C2×D12—28no—
393C2×D12—28no—
394C2×D12—28no—
395C2×D12—44no—
396C2×D12—44no—
397C2×D12—44no—
398C2×D12—44no—
399C2×C4×D3—28no—
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—28no—
407C2×C4×D3—28no—
408C2×C4×D3—28no—
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—
420C3×C4⋊C4—28no—
421C3×C22⋊C4—28no—
422C3×C22⋊C4—44no—
423C3×C22⋊C4—44no—
424#217—44no—
425#217—44no—
426(C2×D3)⋊C4—28no—
427(C2×D3)⋊C4—44no—
428(C2×D3)⋊C4—44no—
429(C2×D3)⋊C4—44no—
430(C2×D3)⋊C4—44no—
431(C2×D3)⋊C4—44no—
432(C2×D3)⋊C4—44no—
433C4⋊Dic3—28no—
434Dic3⋊C4—28no—
435Dic3⋊C4—28no—
436Dic3⋊C4—28no—
437C25—31no—
438C25—31no—
439C25C22×D311yescharacteristic
440C22×D4—34no—
441C22×D4—34no—
442C22×D4—62no—
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—121no—
460C22×D4—121no—
461C23×C4—31no—
462C23×C4—31no—
463C23×C4—31no—
464C23×C4—31no—
465C23×C4—34no—
466C23×C4—34no—
467C23×C4—31no—
468C23×C4—31no—
469C23×C4—62no—
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—121no—
485C23×C4—121no—
486C23×C4—121no—
487C23×C4—121no—
488C23×C4C22×D311yescharacteristic
489C23×C4C22×D311yescharacteristic
490C23×C4C22×D311yescharacteristic
491C23×C4C22×D311yescharacteristic
492C23×C4C22×D311yescharacteristic
493C23×C4C22×D311yescharacteristic
494#121—632no—
495C2×C4⋊C4—22no—
496C2×C4⋊C4—22no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—34no—
499C2×C4⋊C4—34no—
500C2×C4⋊C4—632no—
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×C22⋊C4—22no—
512C2×C22⋊C4—22no—
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—41no—
520C2×C22⋊C4—62no—
521C2×C22⋊C4—62no—
522C2×C22⋊C4—62no—
523C2×C22⋊C4—62no—
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—121no—
545C2×C22⋊C4—121no—
546C2×C22⋊C4—121no—
547#95—22no—
548#95—22no—
549#95—41no—
550#95—62no—
551#95—62no—
552#95—62no—
553#95—62no—
554#95—62no—
555#95—62no—
556#95—62no—
557#95—62no—
558#95—121no—
559C23×C3—22no—
560C23×C3—22no—
561C23×C3—22no—
562C23×C3—22no—
563C23×C3—22no—
564C23×C3—22no—
565C23×C3—22no—
566C23×C3—41no—
567C23×C3—41no—
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×C3C22×D411yescharacteristic
595C23×C3C22×D411yescharacteristic
596C23×C3C22×D411yescharacteristic
597C23×C3C22×D411yescharacteristic
598C23×C3C22×D411yescharacteristic
599C23×C3C22×D411yescharacteristic
600C23×C3C2×#4111yescharacteristic
601C23×C3C2×#4111yescharacteristic
602C23×C3C2×#4111yescharacteristic
603C23×C3C2×#4111yescharacteristic
604C23×C3C2×#4111yescharacteristic
605C23×C3H(5,𝔽2)11yescharacteristic
606C23×C3H(5,𝔽2)11yescharacteristic
607C23×C32−1+411yescharacteristic
608C23×C32−1+411yescharacteristic
609C22×D3—22no—
610C22×D3—22no—
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—41no—
645C22×D3—41no—
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#12014yes—
673C22×D3#12114yes—
674C22×D3#12114yes—
675C22×D3#12114yes—
676C22×D3#12314yes—
677C22×D3#12314yes—
678C22×D3#12414yes—
679C2×C3×C4—22no—
680C2×C3×C4—22no—
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—41no—
695C2×C3×C4—41no—
696C2×C3×C4—41no—
697C2×C3×C4—41no—
698C2×C3×C4—41no—
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#12114yescomplemented
721#67—416no—
722#67—416no—
723C2×Dic3—22no—
724C2×Dic3—22no—
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—41no—
742C2×Dic3—41no—
743C2×Dic3—41no—
744C2×Dic3—41no—
745C2×Dic3—41no—
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#12014yes—
764C2×Dic3#12114yescomplemented
765D12—416no—
766C4×D3—232no—
767C4×D3—416no—
768C4×D3—416no—
769C24—21no—
770C24—21no—
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—32no—
784C24—32no—
785C24—32no—
786C24—32no—
787C24—32no—
788C24—32no—
789C24—32no—
790C24—32no—
791C24—61no—
792C24—61no—
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—
813C24D3×D412yes—
814C24C23×D311yescharacteristic
815C2×D4—68no—
816C2×D4—68no—
817C2×D4—68no—
818C2×D4—68no—
819C2×D4—68no—
820C2×D4—68no—
821C2×D4—68no—
822C2×D4—124no—
823C2×D4—124no—
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—
836C22×C4—21no—
837C22×C4—21no—
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—32no—
873C22×C4—32no—
874C22×C4—32no—
875C22×C4—32no—
876C22×C4—32no—
877C22×C4—32no—
878C22×C4—32no—
879C22×C4—32no—
880C22×C4—68no—
881C22×C4—68no—
882C22×C4—68no—
883C22×C4—68no—
884C22×C4—68no—
885C22×C4—68no—
886C22×C4—68no—
887C22×C4—68no—
888C22×C4—68no—
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—68no—
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—61no—
923C22×C4—61no—
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#23512yes—
936C22×C4D3×D412yes—
937C22×C4D3×D412yes—
938C22×C4D3×D412yes—
939C22×C4D3×D412yes—
940C22×C4D3×D412yes—
941C4⋊C4—28no—
942C4⋊C4—68no—
943C4⋊C4—68no—
944C4⋊C4—68no—
945C4⋊C4—68no—
946C22⋊C4—28no—
947C22⋊C4—44no—
948C22⋊C4—44no—
949C22⋊C4—68no—
950C22⋊C4—124no—
951C22⋊C4—124no—
952C22⋊C4—124no—
953C22⋊C4—124no—
954C22⋊C4—124no—
955C22⋊C4—124no—
956C22⋊C4—124no—
957C22⋊C4—124no—
958C22×C3—42no—
959C22×C3—42no—
960C22×C3—42no—
961C22×C3—42no—
962C22×C3—42no—
963C22×C3—42no—
964C22×C3—42no—
965C22×C3—81no—
966C22×C3—81no—
967C22×C3—81no—
968C22×C3—81no—
969C22×C3—81no—
970C22×C3—81no—
971C22×C3—81no—
972C22×C3—81no—
973C22×C3C2×#12011yescharacteristic
974C22×C3C2×#12011yescharacteristic
975C22×C3C2×#12111yescharacteristic
976C22×C3C2×#12111yescharacteristic
977C22×C3C2×#12111yescharacteristic
978C22×C3C2×#12111yescharacteristic
979C22×C3C2×#12111yescharacteristic
980C22×C3C2×#12311yescharacteristic
981C22×C3C2×#12311yescharacteristic
982C22×C3#52511yescharacteristic
983C22×C3#52511yescharacteristic
984C22×C3#52511yescharacteristic
985C22×C3C2×#12411yescharacteristic
986C22×C3#53411yescharacteristic
987C22×C3#53611yescharacteristic
988C22×C3#53711yescharacteristic
989C22×C3#53711yescharacteristic
990C22×C3#53911yescharacteristic
991C22×C3#53911yescharacteristic
992C22×C3D4211yescharacteristic
993C22×C3D4211yescharacteristic
994C22×C3D4211yescharacteristic
995C22×C3D4211yescharacteristic
996C22×C3#54711yescharacteristic
997C22×C3#54711yescharacteristic
998C22×C3#54711yescharacteristic
999C22×C3#54711yescharacteristic
1000C22×C3#54811yescharacteristic
1001C22×C3#54811yescharacteristic
1002C22×C3#54811yescharacteristic
1003C22×C3#54811yescharacteristic
1004C22×C3#55311yescharacteristic
1005C22×C3#55311yescharacteristic
1006C22×C3#55311yescharacteristic
1007C22×C3#55311yescharacteristic
1008C2×D3—24no—
1009C2×D3—24no—
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—42no—
1023C2×D3—42no—
1024C2×D3—42no—
1025C2×D3—42no—
1026C2×D3—42no—
1027C2×D3—42no—
1028C2×D3—42no—
1029C2×D3—81no—
1030C2×D3—81no—
1031C2×D3—81no—
1032C2×D3—81no—
1033C2×D3—81no—
1034C2×D3—81no—
1035C2×D3—81no—
1036C2×D3—81no—
1037C2×D3#39418yescomplemented
1038C3×C4—24no—
1039C3×C4—42no—
1040C3×C4—42no—
1041C3×C4—42no—
1042C3×C4—81no—
1043C3×C4—81no—
1044Dic3—24no—
1045Dic3—24no—
1046Dic3—42no—
1047Dic3—42no—
1048Dic3—81no—
1049Dic3—81no—
1050C23—22no—
1051C23—22no—
1052C23—22no—
1053C23—22no—
1054C23—22no—
1055C23—22no—
1056C23—22no—
1057C23—34no—
1058C23—34no—
1059C23—34no—
1060C23—34no—
1061C23—34no—
1062C23—34no—
1063C23—34no—
1064C23—41no—
1065C23—41no—
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—62no—
1093C23—62no—
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—121no—
1128C23—121no—
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—
1155C23C2×#23511yescharacteristic
1156C23C2×D3×D411yescharacteristic
1157C23C2×D3×D411yescharacteristic
1158C23C2×D3×D411yescharacteristic
1159C23C2×D3×D411yescharacteristic
1160C23C2×D3×D411yescharacteristic
1161C23C2×D3×D411yescharacteristic
1162C23#100411yescharacteristic
1163C23#100711yescharacteristic
1164C23D3×#4111yescharacteristic
1165C23D3×#4111yescharacteristic
1166C23D3×#4111yescharacteristic
1167C23D3×#4111yescharacteristic
1168C23#100911yescharacteristic
1169C23#101011yescharacteristic
1170D4—1216no—
1171D4—1216no—
1172D4—1216no—
1173C2×C4—22no—
1174C2×C4—22no—
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—34no—
1189C2×C4—34no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
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—632no—
1217C2×C4—62no—
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—1216no—
1236C2×C4—1216no—
1237C2×C4—121no—
1238C2×C4—121no—
1239C2×C4—121no—
1240C2×C4—121no—
1241C2×C4—121no—
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#88414yescomplemented
1260C2×C3—82no—
1261C2×C3C2×#39411yescharacteristic
1262C2×C3#240311yescharacteristic
1263C2×C3#240611yescharacteristic
1264C2×C3#241611yescharacteristic
1265C2×C3#241611yescharacteristic
1266C2×C3#241611yescharacteristic
1267C2×C3#241611yescharacteristic
1268C2×C3#243611yescharacteristic
1269C2×C3#244311yescharacteristic
1270C2×C3#244311yescharacteristic
1271C2×C3#244311yescharacteristic
1272C2×C3#244311yescharacteristic
1273C2×C3#259111yescharacteristic
1274C2×C3#261811yescharacteristic
1275C2×C3#284711yescharacteristic
1276D3—28no—
1277D3—82no—
1278C22—38no—
1279C22—42no—
1280C22—42no—
1281C22—42no—
1282C22—42no—
1283C22—42no—
1284C22—42no—
1285C22—42no—
1286C22—64no—
1287C22—64no—
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—81no—
1301C22—81no—
1302C22—81no—
1303C22—81no—
1304C22—81no—
1305C22—81no—
1306C22—81no—
1307C22—81no—
1308C22—122no—
1309C22—122no—
1310C22—122no—
1311C22—122no—
1312C22—122no—
1313C22—122no—
1314C22—122no—
1315C22—241no—
1316C22—241no—
1317C22—241no—
1318C22—241no—
1319C22—241no—
1320C22—241no—
1321C22—241no—
1322C22—241no—
1323C22C2×#88411yescharacteristic
1324C22#550711yescharacteristic
1325C22#553011yescharacteristic
1326C22#554711yescharacteristic
1327C22#554711yescharacteristic
1328C22#555111yescharacteristic
1329C22#555811yescharacteristic
1330C22D3×#12011yescharacteristic
1331C22D3×#12011yescharacteristic
1332C22#559011yescharacteristic
1333C22D3×#12111yescharacteristic
1334C22D3×#12111yescharacteristic
1335C22D3×#12111yescharacteristic
1336C22D3×#12111yescharacteristic
1337C22#560511yescharacteristic
1338C22#560811yescharacteristic
1339C22#560911yescharacteristic
1340C22#560911yescharacteristic
1341C22#562811yescharacteristic
1342C22#562911yescharacteristic
1343C22#563111yescharacteristic
1344C22#563311yescharacteristic
1345C22#563311yescharacteristic
1346C22#563811yescharacteristic
1347C22D3×#12311yescharacteristic
1348C22D3×#12311yescharacteristic
1349C22#565511yescharacteristic
1350C22#565611yescharacteristic
1351C22#566111yescharacteristic
1352C22D3×#12411yescharacteristic
1353C22#567711yescharacteristic
1354C22#567711yescharacteristic
1355C22#570711yescharacteristic
1356C22#570911yescharacteristic
1357C22#571711yescharacteristic
1358C4—24no—
1359C4—42no—
1360C4—42no—
1361C4—42no—
1362C4—64no—
1363C4—64no—
1364C4—81no—
1365C4—81no—
1366C4—122no—
1367C4—122no—
1368C4—241no—
1369C4—241no—
1370C3#1471911yescharacteristic, complemented, Sylow
1371C2—68no—
1372C2—82no—
1373C2—242no—
1374C2#7388711yescharacteristic
1375C2#7460011yescharacteristic
1376C2#7460811yescharacteristic
1377C2#7493511yescharacteristic
1378C2#7584811yescharacteristic
1379C2#7589411yescharacteristic
1380C2#7643911yescharacteristic
1381C2#7675311yescharacteristic
1382C2#7678111yescharacteristic
1383C2#7689811yescharacteristic
1384C2D3×#39411yescharacteristic
1385C2#7728411yescharacteristic
1386C2#7742311yescharacteristic
1387C2#7767311yescharacteristic
1388C2#7810311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1439C2
prime radicalC22×#884C2
hypercenter#1439D3
hypocenterC3#14719
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
1. C22×D3×C4⋊C4C2semidirect
3. C2×#4959C2semidirect
4. C2×#4956C2semidirect
5. C2×#4956C2semidirect
6. C2×#4961C2semidirect
7. C2×#4665C2semidirect
8. C2×#4665C2semidirect
9. C3×#1439C2semidirect
10. #71570C2semidirect
11. #71547C2semidirect
12. #69428C2semidirect
13. (C2×D3)⋊#95C2semidirect
14. #69411C2semidirect
15. #69409C2semidirect
77. #1439D3semidirect
135. C22×C4×D3D4semidirect
177. C2×C4⋊Dic3D4semidirect
186. C2×Dic3⋊C4D4semidirect
720. C2×C3×C4#121semidirect
764. C2×Dic3#121semidirect
1037. C2×D3#394semidirect
1259. C2×C4#884semidirect
1370. C3#14719semidirect

Maximal subgroups

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

subgroupindex
C22×D3×C4⋊C42
C22×#8842
C2×#49592
C2×#49562
C2×#49612
C2×#46652
C3×#14392
#715702
#715472
#694282
(C2×D3)⋊#952
#694112
#694092
#147193