Finite Group Databasebeta

← #10719452

Subgroups — #10719452

Order 768.

2046 conjugacy classes of subgroups.

The subgroup lattice has 1174 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×C22⋊C4C211yesmaximal, characteristic, complemented
2C2×#5213C211yesmaximal, characteristic
3C2×#5210C211yesmaximal, characteristic, complemented
4C2×#4957C211yesmaximal, characteristic
5C2×#4940C211yesmaximal, characteristic, complemented
6C2×#4940C211yesmaximal, characteristic, complemented
7C2×#4933C211yesmaximal, characteristic, complemented
8#71550C211yesmaximal, characteristic
9#71547C211yesmaximal, characteristic, complemented
10#71545C211yesmaximal, characteristic, complemented
11C4×C3⋊#95C211yesmaximal, characteristic, complemented
12#69428C211yesmaximal, characteristic, complemented
13#69421C211yesmaximal, characteristic, complemented
14#69408C211yesmaximal, characteristic, complemented
15Dic3⋊#95C211yesmaximal, characteristic, complemented
16#14084—31nomaximal, Sylow
17C24×C3×C4C2211yescharacteristic
18C23×#67C2211yescharacteristic
19C22×C3×C22⋊C4C2211yescharacteristic
20C22×C3×C22⋊C4C2211yescharacteristic
21C22×C3×C42C2211yescharacteristic
22C22×C3×C42C2211yescharacteristic
23C22×#217C2211yescharacteristic
24C22×#217C2211yescharacteristic
25C22×#217C2211yescharacteristic
26C22×(C2×D3)⋊C4C2211yescharacteristic
27C22×(C2×D3)⋊C4C2211yescharacteristic
28C22×(C2×D3)⋊C4C2211yescharacteristic
29C22×(C2×D3)⋊C4C2211yescharacteristic
30C22×(C2×D3)⋊C4C2211yescharacteristic
31C22×(C2×D3)⋊C4C2211yescharacteristic
32C22×Dic3⋊C4C2211yescharacteristic
33C22×Dic3⋊C4C2211yescharacteristic
34C22×Dic3⋊C4C2211yescharacteristic
35C22×Dic3⋊C4C2211yescharacteristic
36C22×C4×Dic3C2211yescharacteristic
37C22×C4×Dic3C2211yescharacteristic
38C3×C4×C22⋊C4—24no—
39C2×C3×#95C2211yescharacteristic
40C2×C3×#95C2211yescharacteristic
41#5213—24no—
42#5210—24no—
43C2×C3⋊#95C2211yescharacteristic
44C2×C3⋊#95C2211yescharacteristic
45C2×C3⋊#95C2211yescharacteristic
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
55#4957C418yescomplemented
56#4940—24no—
57#4940—24no—
58#4933—24no—
59C2×#390—31no—
60C2×#388—31no—
61C2×#388—31no—
62C2×#387—31no—
63C2×#386—31no—
64C2×#385—31no—
65C2×C4×C22⋊C4D311yescharacteristic, complemented
66#1445—31no—
67#1439—31no—
68#1439—31no—
69#1438—31no—
70#1437—31no—
71#1437—31no—
72C4⋊#95—31no—
73C4×#95—31no—
74C25×C3C2311yescharacteristic
75C24×D3C2311yescharacteristic
76C23×C3×C4—22no—
77C23×C3×C4—22no—
78C23×C3×C4—22no—
79C23×C3×C4—22no—
80C23×C3×C4—22no—
81C23×C3×C4—41no—
82C23×C3×C4—41no—
83C23×C3×C4C2311yescharacteristic
84C23×C3×C4C2311yescharacteristic
85C23×C3×C4C2311yescharacteristic
86C23×C3×C4C2311yescharacteristic
87C23×C3×C4C2311yescharacteristic
88C23×C3×C4C2311yescharacteristic
89C22×#67—22no—
90C22×#67—22no—
91C22×#67—22no—
92C22×#67—22no—
93C22×#67—41no—
94C22×#67—41no—
95C22×#67C2×C414yes—
96C23×Dic3C2311yescharacteristic
97C23×Dic3C2311yescharacteristic
98C23×Dic3C2311yescharacteristic
99C23×Dic3C2311yescharacteristic
100C23×Dic3C2311yescharacteristic
101C23×Dic3C2311yescharacteristic
102C23×Dic3C2311yescharacteristic
103C2×C3×C22⋊C4—22no—
104C2×C3×C22⋊C4—22no—
105C2×C3×C22⋊C4—22no—
106C2×C3×C22⋊C4—22no—
107C2×C3×C22⋊C4—22no—
108C2×C3×C22⋊C4C2×C414yes—
109C2×C3×C42—22no—
110C2×C3×C42—22no—
111C2×C3×C42—22no—
112C2×C3×C42—41no—
113C2×C3×C42—41no—
114C2×C3×C42D414yescomplemented
115C2×#217—22no—
116C2×#217—22no—
117C2×#217—22no—
118C2×#217—22no—
119C2×#217—22no—
120C2×#217—22no—
121C2×#217—41no—
122C2×#217—41no—
123C2×#217C2×C414yes—
124C2×(C2×D3)⋊C4—22no—
125C2×(C2×D3)⋊C4—22no—
126C2×(C2×D3)⋊C4—22no—
127C2×(C2×D3)⋊C4—22no—
128C2×(C2×D3)⋊C4—22no—
129C2×(C2×D3)⋊C4—22no—
130C2×(C2×D3)⋊C4—22no—
131C2×(C2×D3)⋊C4—22no—
132C2×(C2×D3)⋊C4—22no—
133C2×(C2×D3)⋊C4—22no—
134C2×(C2×D3)⋊C4—22no—
135C2×(C2×D3)⋊C4—22no—
136C2×(C2×D3)⋊C4—41no—
137C2×(C2×D3)⋊C4—41no—
138C2×(C2×D3)⋊C4—41no—
139C2×(C2×D3)⋊C4—41no—
140C2×(C2×D3)⋊C4C2×C414yescomplemented
141C2×(C2×D3)⋊C4C2×C414yescomplemented
142C2×Dic3⋊C4—22no—
143C2×Dic3⋊C4—22no—
144C2×Dic3⋊C4—22no—
145C2×Dic3⋊C4—22no—
146C2×Dic3⋊C4—22no—
147C2×Dic3⋊C4—22no—
148C2×Dic3⋊C4—22no—
149C2×Dic3⋊C4—22no—
150C2×Dic3⋊C4—22no—
151C2×Dic3⋊C4—41no—
152C2×Dic3⋊C4—41no—
153C2×Dic3⋊C4C2×C414yescomplemented
154C2×C4×Dic3—22no—
155C2×C4×Dic3—41no—
156C2×C4×Dic3—41no—
157C2×C4×Dic3—41no—
158C2×C4×Dic3—41no—
159C2×C4×Dic3C2×C414yescomplemented
160C3×#95—22no—
161C3×#95—22no—
162C3⋊#95—22no—
163C3⋊#95—22no—
164C3⋊#95—22no—
165C3⋊#95—22no—
166C3⋊#95—22no—
167C3⋊#95—22no—
168C3⋊#95—22no—
169C3⋊#95—22no—
170C3⋊#95—22no—
171C3⋊#95—22no—
172C3⋊#95D414yes—
173C3⋊#95D414yescomplemented
174C23×D4—31no—
175C24×C4C2×D311yescharacteristic
176C22×C4⋊C4—31no—
177C22×C4⋊C4—31no—
178C22×C4⋊C4—31no—
179C22×C4⋊C4—31no—
180C22×C22⋊C4—31no—
181C22×C22⋊C4—31no—
182C22×C22⋊C4—31no—
183C22×C22⋊C4—31no—
184C22×C22⋊C4—31no—
185C22×C22⋊C4—31no—
186C22×C22⋊C4—31no—
187C22×C22⋊C4—31no—
188C22×C22⋊C4—31no—
189C22×C22⋊C4C2×D311yescharacteristic
190C22×C22⋊C4C2×D311yescharacteristic
191C22×C42—31no—
192C22×C42—31no—
193C22×C42C2×D311yescharacteristic
194C22×C42C2×D311yescharacteristic
195#390—38no—
196#388—64no—
197#388—64no—
198#387—64no—
199#386—64no—
200#385—64no—
201C4×C22⋊C4—24no—
202C2×#95—31no—
203C2×#95—31no—
204C2×#95—31no—
205C2×#95—31no—
206C2×#95—31no—
207C2×#95—31no—
208C2×#95—31no—
209C2×#95—31no—
210C2×#95—31no—
211C2×#95—31no—
212C2×#95—31no—
213C2×#95—31no—
214C2×#95C2×D311yescharacteristic
215C2×#95C2×D311yescharacteristic
216C24×C3—21no—
217C24×C3—21no—
218C24×C3—21no—
219C24×C3—21no—
220C24×C3—21no—
221C24×C3—21no—
222C24×C3—21no—
223C24×C3—21no—
224C24×C3—21no—
225C24×C3—21no—
226C24×C3—21no—
227C24×C3—21no—
228C24×C3C22×C412yes—
229C24×C3#4112yes—
230C24×C3#4112yes—
231C24×C3C2411yescharacteristic
232C23×D3—21no—
233C23×D3—21no—
234C23×D3—21no—
235C23×D3—21no—
236C23×D3—21no—
237C23×D3—21no—
238C23×D3—21no—
239C23×D3—21no—
240C23×D3—21no—
241C23×D3—21no—
242C23×D3—21no—
243C23×D3—21no—
244C23×D3—21no—
245C23×D3—21no—
246C23×D3C22×C412yes—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4—21no—
255C22×C3×C4—28no—
256C22×C3×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4—21no—
259C22×C3×C4—21no—
260C22×C3×C4—21no—
261C22×C3×C4—21no—
262C22×C3×C4—21no—
263C22×C3×C4—21no—
264C22×C3×C4—21no—
265C22×C3×C4—21no—
266C22×C3×C4—21no—
267C22×C3×C4—21no—
268C22×C3×C4—21no—
269C22×C3×C4—21no—
270C22×C3×C4—21no—
271C22×C3×C4—21no—
272C22×C3×C4—21no—
273C22×C3×C4—21no—
274C22×C3×C4—21no—
275C22×C3×C4—21no—
276C22×C3×C4—21no—
277C22×C3×C4—21no—
278C22×C3×C4—21no—
279C22×C3×C4—21no—
280C22×C3×C4—44no—
281C22×C3×C4—44no—
282C22×C3×C4—44no—
283C22×C3×C4—44no—
284C22×C3×C4—44no—
285C22×C3×C4—44no—
286C22×C3×C4C22×C412yes—
287C22×C3×C4C22×C412yes—
288C22×C3×C4C2×D412yes—
289C22×C3×C4C2×D412yes—
290C22×C3×C4C2×D412yes—
291C22×C3×C4C2×D412yes—
292C22×C3×C4C2×D412yes—
293C22×C3×C4#4112yes—
294C22×C3×C4#4112yes—
295C22×C3×C4#4112yes—
296C2×#67—28no—
297C2×#67—28no—
298C2×#67—44no—
299C2×#67—44no—
300C2×#67—44no—
301C2×#67—44no—
302C2×#67—44no—
303C22×Dic3—21no—
304C22×Dic3—21no—
305C22×Dic3—21no—
306C22×Dic3—21no—
307C22×Dic3—21no—
308C22×Dic3—21no—
309C22×Dic3—21no—
310C22×Dic3—21no—
311C22×Dic3—21no—
312C22×Dic3—21no—
313C22×Dic3—21no—
314C22×Dic3—21no—
315C22×Dic3—21no—
316C22×Dic3—21no—
317C22×Dic3—21no—
318C22×Dic3—21no—
319C22×Dic3—21no—
320C22×Dic3—21no—
321C22×Dic3—21no—
322C22×Dic3—21no—
323C22×Dic3—21no—
324C22×Dic3—21no—
325C22×Dic3—21no—
326C22×Dic3—21no—
327C22×Dic3—21no—
328C22×Dic3—21no—
329C22×Dic3—21no—
330C22×Dic3—21no—
331C22×Dic3—21no—
332C22×Dic3—21no—
333C22×Dic3—21no—
334C22×Dic3—21no—
335C22×Dic3—21no—
336C22×Dic3—21no—
337C22×Dic3—21no—
338C22×Dic3—21no—
339C22×Dic3—21no—
340C22×Dic3—21no—
341C22×Dic3—21no—
342C22×Dic3—21no—
343C22×Dic3C22×C412yes—
344C22×Dic3C22×C412yes—
345C22×Dic3C22×C412yes—
346C22×Dic3C2×D412yes—
347C22×Dic3C2×D412yes—
348C22×Dic3C2×D412yes—
349C22×Dic3C2×D412yes—
350C22×Dic3#4112yes—
351C22×Dic3#4112yes—
352C3×C22⋊C4—28no—
353C3×C22⋊C4—28no—
354C3×C42—44no—
355C3×C42—44no—
356#217—28no—
357#217—44no—
358#217—44no—
359(C2×D3)⋊C4—28no—
360(C2×D3)⋊C4—28no—
361(C2×D3)⋊C4—44no—
362(C2×D3)⋊C4—44no—
363(C2×D3)⋊C4—44no—
364(C2×D3)⋊C4—44no—
365Dic3⋊C4—28no—
366Dic3⋊C4—44no—
367Dic3⋊C4—44no—
368Dic3⋊C4—44no—
369C4×Dic3—44no—
370C4×Dic3—44no—
371C25—31no—
372C25C22×D311yescharacteristic
373C22×D4—34no—
374C22×D4—62no—
375C22×D4—62no—
376C22×D4—62no—
377C22×D4—62no—
378C22×D4—121no—
379C22×D4—121no—
380C23×C4—22no—
381C23×C4—22no—
382C23×C4—22no—
383C23×C4—22no—
384C23×C4—22no—
385C23×C4—31no—
386C23×C4—31no—
387C23×C4—31no—
388C23×C4—31no—
389C23×C4—31no—
390C23×C4—31no—
391C23×C4—31no—
392C23×C4—41no—
393C23×C4—41no—
394C23×C4C22×D311yescharacteristic
395C23×C4C22×D311yescharacteristic
396C23×C4C22×D311yescharacteristic
397C23×C4C22×D311yescharacteristic
398C23×C4C22×D311yescharacteristic
399C23×C4C22×D311yescharacteristic
400C2×C4⋊C4—34no—
401C2×C4⋊C4—62no—
402C2×C4⋊C4—62no—
403C2×C4⋊C4—62no—
404C2×C4⋊C4—62no—
405C2×C4⋊C4—62no—
406C2×C4⋊C4—62no—
407C2×C4⋊C4—62no—
408C2×C4⋊C4—62no—
409C2×C4⋊C4—62no—
410C2×C4⋊C4—121no—
411C2×C4⋊C4—121no—
412C2×C22⋊C4—22no—
413C2×C22⋊C4—22no—
414C2×C22⋊C4—22no—
415C2×C22⋊C4—22no—
416C2×C22⋊C4—22no—
417C2×C22⋊C4—34no—
418C2×C22⋊C4—34no—
419C2×C22⋊C4—34no—
420C2×C22⋊C4—62no—
421C2×C22⋊C4—62no—
422C2×C22⋊C4—62no—
423C2×C22⋊C4—62no—
424C2×C22⋊C4—62no—
425C2×C22⋊C4—62no—
426C2×C22⋊C4—62no—
427C2×C22⋊C4—62no—
428C2×C22⋊C4—62no—
429C2×C22⋊C4—62no—
430C2×C22⋊C4—62no—
431C2×C22⋊C4—62no—
432C2×C22⋊C4—62no—
433C2×C22⋊C4—62no—
434C2×C22⋊C4—62no—
435C2×C22⋊C4—62no—
436C2×C22⋊C4—62no—
437C2×C22⋊C4—62no—
438C2×C22⋊C4—121no—
439C2×C22⋊C4—121no—
440C2×C22⋊C4—121no—
441C2×C22⋊C4—121no—
442C2×C22⋊C4—121no—
443C2×C22⋊C4—121no—
444C2×C22⋊C4C4×D314yes—
445C2×C42—22no—
446C2×C42—22no—
447C2×C42—22no—
448C2×C42—34no—
449C2×C42—41no—
450C2×C42—41no—
451C2×C42—62no—
452C2×C42—121no—
453C2×C42—121no—
454C2×C42—121no—
455C2×C42—121no—
456C2×C42#6714yescomplemented
457#95—22no—
458#95—22no—
459#95—34no—
460#95—34no—
461#95—62no—
462#95—62no—
463#95—62no—
464#95—62no—
465#95—62no—
466#95—62no—
467#95—62no—
468#95—62no—
469#95—62no—
470#95—62no—
471C23×C3—22no—
472C23×C3—22no—
473C23×C3—22no—
474C23×C3—22no—
475C23×C3—22no—
476C23×C3—22no—
477C23×C3—22no—
478C23×C3—22no—
479C23×C3—22no—
480C23×C3—22no—
481C23×C3—22no—
482C23×C3—22no—
483C23×C3—22no—
484C23×C3—22no—
485C23×C3—22no—
486C23×C3—22no—
487C23×C3—22no—
488C23×C3—22no—
489C23×C3—41no—
490C23×C3—41no—
491C23×C3—41no—
492C23×C3—41no—
493C23×C3—41no—
494C23×C3—41no—
495C23×C3—41no—
496C23×C3—41no—
497C23×C3—41no—
498C23×C3—41no—
499C23×C3—41no—
500C23×C3—41no—
501C23×C3—41no—
502C23×C3—41no—
503C23×C3—41no—
504C23×C3—41no—
505C23×C3#11714yes—
506C23×C3C23×C411yescharacteristic
507C23×C3C22×D411yescharacteristic
508C23×C3C22×D411yescharacteristic
509C23×C3C22×D411yescharacteristic
510C23×C3C2×#4111yescharacteristic
511C23×C3C2×#4111yescharacteristic
512C23×C3C2×#4111yescharacteristic
513C23×C3C2×#4111yescharacteristic
514C23×C3C2×#4111yescharacteristic
515C23×C3C2×#4111yescharacteristic
516C23×C3C2×#4111yescharacteristic
517C23×C3H(5,𝔽2)11yescharacteristic
518C23×C3H(5,𝔽2)11yescharacteristic
519C23×C3H(5,𝔽2)11yescharacteristic
520C23×C32−1+411yescharacteristic
521C22×D3—22no—
522C22×D3—22no—
523C22×D3—22no—
524C22×D3—22no—
525C22×D3—22no—
526C22×D3—22no—
527C22×D3—22no—
528C22×D3—41no—
529C22×D3—41no—
530C22×D3—41no—
531C22×D3—41no—
532C22×D3—41no—
533C22×D3—41no—
534C22×D3—41no—
535C22×D3—41no—
536C22×D3—41no—
537C22×D3—41no—
538C22×D3—41no—
539C22×D3—41no—
540C22×D3—41no—
541C22×D3—41no—
542C22×D3—41no—
543C22×D3—41no—
544C22×D3—41no—
545C22×D3—41no—
546C22×D3—41no—
547C22×D3—41no—
548C22×D3—41no—
549C22×D3—41no—
550C22×D3—41no—
551C22×D3—41no—
552C22×D3—41no—
553C22×D3—41no—
554C22×D3—41no—
555C22×D3—41no—
556C2×C3×C4—22no—
557C2×C3×C4—22no—
558C2×C3×C4—22no—
559C2×C3×C4—22no—
560C2×C3×C4—22no—
561C2×C3×C4—22no—
562C2×C3×C4—22no—
563C2×C3×C4—22no—
564C2×C3×C4—22no—
565C2×C3×C4—22no—
566C2×C3×C4—22no—
567C2×C3×C4—22no—
568C2×C3×C4—22no—
569C2×C3×C4—22no—
570C2×C3×C4—22no—
571C2×C3×C4—22no—
572C2×C3×C4—22no—
573C2×C3×C4—22no—
574C2×C3×C4—22no—
575C2×C3×C4—22no—
576C2×C3×C4—22no—
577C2×C3×C4—22no—
578C2×C3×C4—22no—
579C2×C3×C4—22no—
580C2×C3×C4—416no—
581C2×C3×C4—41no—
582C2×C3×C4—41no—
583C2×C3×C4—41no—
584C2×C3×C4—41no—
585C2×C3×C4—41no—
586C2×C3×C4—41no—
587C2×C3×C4—41no—
588C2×C3×C4—41no—
589C2×C3×C4—41no—
590C2×C3×C4—41no—
591C2×C3×C4—41no—
592C2×C3×C4—41no—
593C2×C3×C4—41no—
594C2×C3×C4—41no—
595C2×C3×C4—41no—
596C2×C3×C4—41no—
597C2×C3×C4C4×D414yes—
598C2×C3×C4#12714yes—
599#67—416no—
600C2×Dic3—22no—
601C2×Dic3—22no—
602C2×Dic3—22no—
603C2×Dic3—22no—
604C2×Dic3—22no—
605C2×Dic3—22no—
606C2×Dic3—22no—
607C2×Dic3—22no—
608C2×Dic3—22no—
609C2×Dic3—22no—
610C2×Dic3—22no—
611C2×Dic3—22no—
612C2×Dic3—22no—
613C2×Dic3—22no—
614C2×Dic3—22no—
615C2×Dic3—22no—
616C2×Dic3—22no—
617C2×Dic3—22no—
618C2×Dic3—22no—
619C2×Dic3—22no—
620C2×Dic3—22no—
621C2×Dic3—41no—
622C2×Dic3—41no—
623C2×Dic3—41no—
624C2×Dic3—41no—
625C2×Dic3—41no—
626C2×Dic3—41no—
627C2×Dic3—41no—
628C2×Dic3—41no—
629C2×Dic3—41no—
630C2×Dic3—41no—
631C2×Dic3—41no—
632C2×Dic3—41no—
633C2×Dic3—41no—
634C2×Dic3—41no—
635C2×Dic3—41no—
636C2×Dic3—41no—
637C2×Dic3—41no—
638C2×Dic3—41no—
639C2×Dic3—41no—
640C2×Dic3—41no—
641C2×Dic3—41no—
642C2×Dic3—41no—
643C2×Dic3—41no—
644C2×Dic3—41no—
645C2×Dic3—41no—
646C2×Dic3—41no—
647C2×Dic3C4×D414yes—
648C2×Dic3C4×D414yes—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24—21no—
654C24—21no—
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—32no—
662C24—61no—
663C24—61no—
664C24—61no—
665C24—61no—
666C24—61no—
667C24—61no—
668C24—61no—
669C24—61no—
670C24—61no—
671C24—61no—
672C24—61no—
673C24—61no—
674C24—61no—
675C24—61no—
676C24C2×C4×D312yes—
677C24#23512yes—
678C24#23512yes—
679C24C23×D311yescharacteristic
680C2×D4—68no—
681C2×D4—68no—
682C2×D4—124no—
683C2×D4—124no—
684C2×D4—124no—
685C2×D4—124no—
686C2×D4—124no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—28no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—32no—
721C22×C4—32no—
722C22×C4—32no—
723C22×C4—32no—
724C22×C4—32no—
725C22×C4—32no—
726C22×C4—32no—
727C22×C4—32no—
728C22×C4—32no—
729C22×C4—44no—
730C22×C4—44no—
731C22×C4—44no—
732C22×C4—44no—
733C22×C4—44no—
734C22×C4—44no—
735C22×C4—61no—
736C22×C4—61no—
737C22×C4—61no—
738C22×C4—61no—
739C22×C4—61no—
740C22×C4—61no—
741C22×C4—61no—
742C22×C4—61no—
743C22×C4—61no—
744C22×C4—61no—
745C22×C4—61no—
746C22×C4—61no—
747C22×C4—61no—
748C22×C4—61no—
749C22×C4—61no—
750C22×C4—61no—
751C22×C4—61no—
752C22×C4—61no—
753C22×C4—61no—
754C22×C4—61no—
755C22×C4—61no—
756C22×C4—61no—
757C22×C4—61no—
758C22×C4—61no—
759C22×C4—61no—
760C22×C4—61no—
761C22×C4—61no—
762C22×C4—61no—
763C22×C4—61no—
764C22×C4—61no—
765C22×C4—61no—
766C22×C4—61no—
767C22×C4—61no—
768C22×C4—61no—
769C22×C4—61no—
770C22×C4—61no—
771C22×C4—61no—
772C22×C4—61no—
773C22×C4—61no—
774C22×C4—61no—
775C22×C4C2×C4×D312yes—
776C22×C4C2×C4×D312yes—
777C22×C4#23512yes—
778C22×C4#23512yes—
779C22×C4#23512yes—
780C22×C4D3×D412yes—
781C22×C4D3×D412yes—
782C22×C4C2×#6712yes—
783C22×C4C2×#6712yes—
784C22×C4C2×#6712yes—
785C4⋊C4—68no—
786C4⋊C4—124no—
787C4⋊C4—124no—
788C4⋊C4—124no—
789C22⋊C4—28no—
790C22⋊C4—28no—
791C22⋊C4—68no—
792C22⋊C4—68no—
793C22⋊C4—68no—
794C22⋊C4—124no—
795C22⋊C4—124no—
796C22⋊C4—124no—
797C22⋊C4—124no—
798C22⋊C4—124no—
799C22⋊C4—124no—
800C42—44no—
801C42—44no—
802C42—124no—
803C42—124no—
804C22×C3—24no—
805C22×C3—24no—
806C22×C3—24no—
807C22×C3—42no—
808C22×C3—42no—
809C22×C3—42no—
810C22×C3—42no—
811C22×C3—42no—
812C22×C3—42no—
813C22×C3—42no—
814C22×C3—42no—
815C22×C3—42no—
816C22×C3—42no—
817C22×C3—42no—
818C22×C3—42no—
819C22×C3C2×#11711yescharacteristic
820C22×C3C2×C4×D411yescharacteristic
821C22×C3C2×C4×D411yescharacteristic
822C22×C3C2×C4×D411yescharacteristic
823C22×C3C4×#4111yescharacteristic
824C22×C3#51811yescharacteristic
825C22×C3#52011yescharacteristic
826C22×C3#52511yescharacteristic
827C22×C3#52511yescharacteristic
828C22×C3#52911yescharacteristic
829C22×C3#52911yescharacteristic
830C22×C3C2×#12711yescharacteristic
831C22×C3#53211yescharacteristic
832C22×C3#53211yescharacteristic
833C22×C3#53211yescharacteristic
834C22×C3#53411yescharacteristic
835C22×C3#53711yescharacteristic
836C22×C3#53811yescharacteristic
837C22×C3#53911yescharacteristic
838C22×C3#54611yescharacteristic
839C22×C3#54611yescharacteristic
840C22×C3#54611yescharacteristic
841C22×C3#54611yescharacteristic
842C22×C3#54611yescharacteristic
843C22×C3#54611yescharacteristic
844C22×C3#54811yescharacteristic
845C22×C3#54811yescharacteristic
846C22×C3#55111yescharacteristic
847C22×C3#55111yescharacteristic
848C22×C3#55211yescharacteristic
849C22×C3#55311yescharacteristic
850C22×C3#55311yescharacteristic
851C22×C3#55311yescharacteristic
852C22×C3#55611yescharacteristic
853C22×C3#55911yescharacteristic
854C2×D3—42no—
855C2×D3—42no—
856C2×D3—42no—
857C2×D3—42no—
858C2×D3—42no—
859C2×D3—42no—
860C2×D3—42no—
861C2×D3—81no—
862C2×D3—81no—
863C2×D3—81no—
864C2×D3—81no—
865C2×D3—81no—
866C2×D3—81no—
867C2×D3—81no—
868C2×D3—81no—
869C3×C4—24no—
870C3×C4—24no—
871C3×C4—42no—
872C3×C4—42no—
873C3×C4—42no—
874C3×C4—42no—
875Dic3—24no—
876Dic3—24no—
877Dic3—42no—
878Dic3—42no—
879Dic3—42no—
880Dic3—81no—
881Dic3—81no—
882C23—22no—
883C23—22no—
884C23—22no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—22no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—62no—
917C23—62no—
918C23—62no—
919C23—62no—
920C23—62no—
921C23—62no—
922C23—62no—
923C23—121no—
924C23—121no—
925C23—121no—
926C23—121no—
927C23—121no—
928C23—121no—
929C23—121no—
930C23—121no—
931C23—121no—
932C23—121no—
933C23—121no—
934C23—121no—
935C23—121no—
936C23—121no—
937C23—121no—
938C23—121no—
939C23—121no—
940C23—121no—
941C23—121no—
942C23—121no—
943C23—121no—
944C23—121no—
945C23—121no—
946C23—121no—
947C23—121no—
948C23—121no—
949C23—121no—
950C23—121no—
951C23#87214yes—
952C23C22×C4×D311yescharacteristic
953C23C2×#23511yescharacteristic
954C23C2×#23511yescharacteristic
955C23C2×#23511yescharacteristic
956C23C2×#23511yescharacteristic
957C23C2×#23511yescharacteristic
958C23C2×D3×D411yescharacteristic
959C23C2×D3×D411yescharacteristic
960C23#100411yescharacteristic
961C23#100411yescharacteristic
962C23D3×#4111yescharacteristic
963C23D3×#4111yescharacteristic
964C23#100911yescharacteristic
965C23#101011yescharacteristic
966C23C22×#6711yescharacteristic
967D4—1216no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—34no—
993C2×C4—34no—
994C2×C4—416no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—62no—
1012C2×C4—62no—
1013C2×C4—62no—
1014C2×C4—62no—
1015C2×C4—62no—
1016C2×C4—62no—
1017C2×C4—62no—
1018C2×C4—62no—
1019C2×C4—62no—
1020C2×C4—62no—
1021C2×C4—62no—
1022C2×C4—62no—
1023C2×C4—62no—
1024C2×C4—62no—
1025C2×C4—62no—
1026C2×C4—62no—
1027C2×C4—62no—
1028C2×C4—62no—
1029C2×C4—62no—
1030C2×C4—62no—
1031C2×C4—62no—
1032C2×C4—121no—
1033C2×C4—121no—
1034C2×C4—121no—
1035C2×C4—121no—
1036C2×C4—121no—
1037C2×C4—121no—
1038C2×C4—121no—
1039C2×C4—121no—
1040C2×C4—121no—
1041C2×C4—121no—
1042C2×C4—121no—
1043C2×C4—121no—
1044C2×C4—121no—
1045C2×C4—121no—
1046C2×C4—121no—
1047C2×C4—121no—
1048C2×C4—121no—
1049C2×C4—121no—
1050C2×C4—121no—
1051C2×C4—121no—
1052C2×C4—121no—
1053C2×C4—121no—
1054C2×C4—121no—
1055C2×C4—121no—
1056C2×C4—121no—
1057C2×C4—121no—
1058C2×C4C4×#6714yes—
1059C2×C4#94014yes—
1060C2×C3—44no—
1061C2×C3#229011yescharacteristic
1062C2×C3C4×#12711yescharacteristic
1063C2×C3#232511yescharacteristic
1064C2×C3#234211yescharacteristic
1065C2×C3#235211yescharacteristic
1066C2×C3#236411yescharacteristic
1067C2×C3#236711yescharacteristic
1068C2×C3#253911yescharacteristic
1069C2×C3#254011yescharacteristic
1070C2×C3#255711yescharacteristic
1071C2×C3#255811yescharacteristic
1072C2×C3#255911yescharacteristic
1073C2×C3#256011yescharacteristic
1074C2×C3#260111yescharacteristic
1075C2×C3#260211yescharacteristic
1076D3—82no—
1077C22—24no—
1078C22—24no—
1079C22—24no—
1080C22—42no—
1081C22—42no—
1082C22—42no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—42no—
1089C22—42no—
1090C22—42no—
1091C22—42no—
1092C22—122no—
1093C22—122no—
1094C22—122no—
1095C22—122no—
1096C22—122no—
1097C22—122no—
1098C22—122no—
1099C22—241no—
1100C22—241no—
1101C22—241no—
1102C22—241no—
1103C22—241no—
1104C22—241no—
1105C22—241no—
1106C22—241no—
1107C22C2×#87211yescharacteristic
1108C22C4×#23511yescharacteristic
1109C22#547911yescharacteristic
1110C22#547911yescharacteristic
1111C22#549011yescharacteristic
1112C22#549011yescharacteristic
1113C22#549011yescharacteristic
1114C22#549011yescharacteristic
1115C22#552711yescharacteristic
1116C22#553011yescharacteristic
1117C22#553111yescharacteristic
1118C22#553311yescharacteristic
1119C22#554011yescharacteristic
1120C22C4×D3×D411yescharacteristic
1121C22C4×D3×D411yescharacteristic
1122C22#554511yescharacteristic
1123C22#554611yescharacteristic
1124C22#554811yescharacteristic
1125C22#554811yescharacteristic
1126C22#555011yescharacteristic
1127C22#555011yescharacteristic
1128C22#555211yescharacteristic
1129C22#555211yescharacteristic
1130C22#555611yescharacteristic
1131C22#555811yescharacteristic
1132C22#555911yescharacteristic
1133C22#556011yescharacteristic
1134C22#556411yescharacteristic
1135C22C2×C4×#6711yescharacteristic
1136C22#579111yescharacteristic
1137C22#579111yescharacteristic
1138C22C2×#94011yescharacteristic
1139C22#580411yescharacteristic
1140C22#583211yescharacteristic
1141C22#583311yescharacteristic
1142C4—24no—
1143C4—24no—
1144C4—42no—
1145C4—42no—
1146C4—42no—
1147C4—42no—
1148C4—64no—
1149C4—64no—
1150C4—122no—
1151C4—122no—
1152C4—122no—
1153C4—241no—
1154C4—241no—
1155C3#1408411yescharacteristic, complemented, Sylow
1156C2—44no—
1157C2—242no—
1158C2#7346111yescharacteristic
1159C2#7347211yescharacteristic
1160C2#7353711yescharacteristic
1161C2#7353811yescharacteristic
1162C2#7357411yescharacteristic
1163C2#7357911yescharacteristic
1164C2#7360111yescharacteristic
1165C2#7360311yescharacteristic
1166C2#8206511yescharacteristic
1167C2#8211511yescharacteristic
1168C2#8225911yescharacteristic
1169C2C4×#94011yescharacteristic
1170C2#8232711yescharacteristic
1171C2#8237711yescharacteristic
1172C2#8238911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC2×C3×C4×C22⋊C4C2
socle, cosocleC24×C3C24
prime radicalC23×#67C22
hypercenterC2×C4×C22⋊C4D3
hypocenterC3#14084
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×C4×C22⋊C4C2semidirect
3. C2×#5210C2semidirect
5. C2×#4940C2semidirect
6. C2×#4940C2semidirect
7. C2×#4933C2semidirect
9. #71547C2semidirect
10. #71545C2semidirect
11. C4×C3⋊#95C2semidirect
12. #69428C2semidirect
13. #69421C2semidirect
14. #69408C2semidirect
15. Dic3⋊#95C2semidirect
55. #4957C4semidirect
65. C2×C4×C22⋊C4D3semidirect
114. C2×C3×C42D4semidirect
140. C2×(C2×D3)⋊C4C2×C4semidirect
141. C2×(C2×D3)⋊C4C2×C4semidirect
153. C2×Dic3⋊C4C2×C4semidirect
159. C2×C4×Dic3C2×C4semidirect
173. C3⋊#95D4semidirect
456. C2×C42#67semidirect
1155. C3#14084semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×C22⋊C42
C2×#52132
C2×#52102
C2×#49572
C2×#49402
C2×#49332
#715502
#715472
#715452
C4×C3⋊#952
#694282
#694212
#694082
Dic3⋊#952
#140843