Finite Group Databasebeta

← #10724527

Subgroups — #10724527

Order 768.

2390 conjugacy classes of subgroups.

The subgroup lattice has 1342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5223C211yesmaximal, characteristic
2C2×#5220C211yesmaximal, characteristic, complemented
3C2×#4956C211yesmaximal, characteristic, complemented
4C2×#4956C211yesmaximal, characteristic, complemented
5C2×#4957C211yesmaximal, characteristic, complemented
6C2×#4958C211yesmaximal, characteristic, complemented
7C2×#4946C211yesmaximal, characteristic, complemented
8C3×#1438C211yesmaximal, characteristic, complemented
9#71549C211yesmaximal, characteristic, complemented
10#71547C211yesmaximal, characteristic, complemented
11#71545C211yesmaximal, characteristic, complemented
12#69428C211yesmaximal, characteristic, complemented
13(C2×D3)⋊#95C211yesmaximal, characteristic, complemented
14#69414C211yesmaximal, characteristic, complemented
15#69402C211yesmaximal, characteristic, complemented
16#14519—31nomaximal, Sylow
17C23×C3×D4C2211yescharacteristic
18C23×#67C2211yescharacteristic
19C23×#67C2211yescharacteristic
20C24×Dic3C2211yescharacteristic
21C23×C4×D3C2211yescharacteristic
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×C3×C22⋊C4C2211yescharacteristic
25C22×C3×C22⋊C4C2211yescharacteristic
26C22×#217C2211yescharacteristic
27C22×#217C2211yescharacteristic
28C22×#217C2211yescharacteristic
29C22×#217C2211yescharacteristic
30C22×#217C2211yescharacteristic
31C22×(C2×D3)⋊C4C2211yescharacteristic
32C22×(C2×D3)⋊C4C2211yescharacteristic
33C22×(C2×D3)⋊C4C2211yescharacteristic
34C22×(C2×D3)⋊C4C2211yescharacteristic
35C22×Dic3⋊C4C2211yescharacteristic
36C22×Dic3⋊C4C2211yescharacteristic
37C22×C4×Dic3C2211yescharacteristic
38C2×C3×#95C2211yescharacteristic
39C2×C3×#95C2211yescharacteristic
40#5223C418yescomplemented
41#5220—24no—
42C2×C3⋊#95C2211yescharacteristic
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
54#4958—24no—
55#4957—24no—
56#4956—24no—
57#4956—24no—
58#4946—24no—
59C2×#392—31no—
60C2×#390—31no—
61C2×#386—31no—
62C2×#386—31no—
63C2×#386—31no—
64C2×#386—31no—
65C2×#385—31no—
66#1442—31no—
67#1440—31no—
68#1439—31no—
69#1439—31no—
70#1438D311yescharacteristic, complemented
71#1437—31no—
72#1434—31no—
73C22⋊#95—31no—
74C25×C3C2311yescharacteristic
75C25×C3C2311yescharacteristic
76C24×D3C2311yescharacteristic
77C22×C3×D4—22no—
78C22×C3×D4—22no—
79C22×C3×D4—41no—
80C22×C3×D4—41no—
81C22×C3×D4—41no—
82C22×C3×D4—41no—
83C22×C3×D4C2×C414yescomplemented
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—22no—
94C22×#67—22no—
95C22×#67—22no—
96C22×#67—22no—
97C22×#67—41no—
98C22×#67—41no—
99C22×#67—41no—
100C22×#67—41no—
101C22×#67C2×C414yes—
102C22×#67C2×C414yescomplemented
103C23×Dic3—22no—
104C23×Dic3—22no—
105C23×Dic3—22no—
106C23×Dic3—41no—
107C23×Dic3—41no—
108C23×Dic3—41no—
109C23×Dic3—41no—
110C23×Dic3C2311yescharacteristic
111C23×Dic3C2311yescharacteristic
112C23×Dic3C2311yescharacteristic
113C23×Dic3C2311yescharacteristic
114C23×Dic3C2311yescharacteristic
115C23×Dic3C2311yescharacteristic
116C23×Dic3C2311yescharacteristic
117C22×C4×D3—22no—
118C22×C4×D3—22no—
119C22×C4×D3—22no—
120C22×C4×D3—41no—
121C22×C4×D3—41no—
122C22×C4×D3—41no—
123C22×C4×D3—41no—
124C2×C3×C22⋊C4—22no—
125C2×C3×C22⋊C4—22no—
126C2×C3×C22⋊C4—22no—
127C2×C3×C22⋊C4—22no—
128C2×C3×C22⋊C4—22no—
129C2×C3×C22⋊C4—22no—
130C2×C3×C22⋊C4—41no—
131C2×C3×C22⋊C4—41no—
132C2×C3×C22⋊C4—41no—
133C2×C3×C22⋊C4—41no—
134C2×C3×C22⋊C4—41no—
135C2×C3×C22⋊C4—41no—
136C2×#217—22no—
137C2×#217—22no—
138C2×#217—22no—
139C2×#217—22no—
140C2×#217—22no—
141C2×#217—22no—
142C2×#217—41no—
143C2×#217—41no—
144C2×#217—41no—
145C2×#217—41no—
146C2×#217—41no—
147C2×#217—41no—
148C2×#217C2×C414yescomplemented
149C2×#217C2×C414yescomplemented
150C2×#217D414yescomplemented
151C2×(C2×D3)⋊C4—22no—
152C2×(C2×D3)⋊C4—22no—
153C2×(C2×D3)⋊C4—22no—
154C2×(C2×D3)⋊C4—22no—
155C2×(C2×D3)⋊C4—41no—
156C2×(C2×D3)⋊C4—41no—
157C2×(C2×D3)⋊C4—41no—
158C2×(C2×D3)⋊C4—41no—
159C2×(C2×D3)⋊C4—41no—
160C2×(C2×D3)⋊C4—41no—
161C2×(C2×D3)⋊C4C2×C414yescomplemented
162C2×(C2×D3)⋊C4D414yescomplemented
163C2×Dic3⋊C4—22no—
164C2×Dic3⋊C4—22no—
165C2×Dic3⋊C4—22no—
166C2×Dic3⋊C4—41no—
167C2×Dic3⋊C4—41no—
168C2×Dic3⋊C4—41no—
169C2×C4×Dic3—22no—
170C2×C4×Dic3—22no—
171C2×C4×Dic3—41no—
172C3×#95—41no—
173C3×#95—41no—
174C3⋊#95—22no—
175C3⋊#95—22no—
176C3⋊#95—22no—
177C3⋊#95—22no—
178C3⋊#95—22no—
179C3⋊#95—22no—
180C3⋊#95—22no—
181C3⋊#95—22no—
182C3⋊#95—41no—
183C3⋊#95—41no—
184C3⋊#95C2×C414yescomplemented
185C3⋊#95D414yescomplemented
186C23×D4—31no—
187C23×D4—31no—
188C23×D4C2×D311yescharacteristic
189C24×C4—31no—
190C24×C4—31no—
191C22×C4⋊C4—31no—
192C22×C4⋊C4—31no—
193C22×C22⋊C4—31no—
194C22×C22⋊C4—31no—
195C22×C22⋊C4—31no—
196C22×C22⋊C4—31no—
197C22×C22⋊C4—31no—
198C22×C22⋊C4—31no—
199C22×C22⋊C4—31no—
200C22×C22⋊C4—31no—
201C22×C22⋊C4—31no—
202C22×C22⋊C4C2×D311yescharacteristic
203C22×C22⋊C4C2×D311yescharacteristic
204C22×C22⋊C4C2×D311yescharacteristic
205C22×C22⋊C4C2×D311yescharacteristic
206C22×C42—31no—
207#392—38no—
208#390—64no—
209#386—64no—
210#386—64no—
211#386—64no—
212#386—64no—
213#385—64no—
214C2×#95—31no—
215C2×#95—31no—
216C2×#95—31no—
217C2×#95—31no—
218C2×#95—31no—
219C2×#95—31no—
220C2×#95—31no—
221C2×#95—31no—
222C2×#95—31no—
223C2×#95—31no—
224C2×#95—31no—
225C2×#95—31no—
226C2×#95C2×D311yescharacteristic
227C2×#95C2×D311yescharacteristic
228C24×C3—21no—
229C24×C3—21no—
230C24×C3—21no—
231C24×C3—21no—
232C24×C3—21no—
233C24×C3—21no—
234C24×C3—21no—
235C24×C3—21no—
236C24×C3—21no—
237C24×C3—21no—
238C24×C3—21no—
239C24×C3—21no—
240C24×C3—21no—
241C24×C3—21no—
242C24×C3—21no—
243C24×C3—21no—
244C24×C3—21no—
245C24×C3—21no—
246C24×C3—21no—
247C24×C3—21no—
248C24×C3—21no—
249C24×C3—21no—
250C24×C3—21no—
251C24×C3—21no—
252C24×C3—21no—
253C24×C3—21no—
254C24×C3C22×C412yes—
255C24×C3C22×C412yes—
256C24×C3C2×D412yes—
257C24×C3#4112yes—
258C24×C3C2411yescharacteristic
259C23×D3—21no—
260C23×D3—21no—
261C23×D3—21no—
262C23×D3—21no—
263C23×D3—21no—
264C23×D3—21no—
265C23×D3—21no—
266C23×D3—21no—
267C23×D3—21no—
268C23×D3—21no—
269C23×D3—21no—
270C23×D3—21no—
271C23×D3C22×C412yes—
272C23×D3C2×D412yes—
273C23×D3#4112yes—
274C2×C3×D4—28no—
275C2×C3×D4—44no—
276C2×C3×D4—44no—
277C2×C3×D4—44no—
278C2×C3×D4—44no—
279C2×C3×D4—44no—
280C2×C3×D4—44no—
281C22×C3×C4—21no—
282C22×C3×C4—21no—
283C22×C3×C4—21no—
284C22×C3×C4—21no—
285C22×C3×C4—21no—
286C22×C3×C4—21no—
287C22×C3×C4—21no—
288C22×C3×C4—21no—
289C22×C3×C4—21no—
290C22×C3×C4—21no—
291C22×C3×C4—21no—
292C22×C3×C4—21no—
293C22×C3×C4—21no—
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×C4C22×C412yes—
314C22×C3×C4C2×D412yes—
315C22×C3×C4C2×D412yes—
316C2×#67—28no—
317C2×#67—28no—
318C2×#67—28no—
319C2×#67—28no—
320C2×#67—44no—
321C2×#67—44no—
322C2×#67—44no—
323C2×#67—44no—
324C2×#67—44no—
325C2×#67—44no—
326C2×#67—44no—
327C2×#67—44no—
328C2×#67—44no—
329C2×#67—44no—
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×Dic3—21no—
344C22×Dic3—21no—
345C22×Dic3—21no—
346C22×Dic3—21no—
347C22×Dic3—21no—
348C22×Dic3—21no—
349C22×Dic3—21no—
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—44no—
371C22×Dic3—44no—
372C22×Dic3—44no—
373C22×Dic3—44no—
374C22×Dic3—44no—
375C22×Dic3—44no—
376C22×Dic3—44no—
377C22×Dic3C22×C412yes—
378C22×Dic3C22×C412yes—
379C22×Dic3C22×C412yes—
380C22×Dic3C2×D412yes—
381C22×Dic3C2×D412yes—
382C22×Dic3C2×D412yes—
383C22×Dic3C2×D412yes—
384C22×Dic3C2×D412yes—
385C22×Dic3#4112yes—
386C2×C4×D3—44no—
387C2×C4×D3—44no—
388C2×C4×D3—44no—
389C2×C4×D3—44no—
390C2×C4×D3—44no—
391C2×C4×D3—44no—
392C2×C4×D3—44no—
393C3×C22⋊C4—44no—
394C3×C22⋊C4—44no—
395C3×C22⋊C4—44no—
396C3×C22⋊C4—44no—
397#217—28no—
398#217—44no—
399#217—44no—
400#217—44no—
401#217—44no—
402(C2×D3)⋊C4—44no—
403(C2×D3)⋊C4—44no—
404(C2×D3)⋊C4—44no—
405(C2×D3)⋊C4—44no—
406Dic3⋊C4—44no—
407Dic3⋊C4—44no—
408C4×Dic3—44no—
409C25—31no—
410C25C22×D311yescharacteristic
411C25C22×D311yescharacteristic
412C22×D4—22no—
413C22×D4—22no—
414C22×D4—34no—
415C22×D4—34no—
416C22×D4—41no—
417C22×D4—41no—
418C22×D4—41no—
419C22×D4—41no—
420C22×D4—62no—
421C22×D4—62no—
422C22×D4—62no—
423C22×D4—62no—
424C22×D4—62no—
425C22×D4—62no—
426C22×D4—62no—
427C22×D4—62no—
428C22×D4—121no—
429C22×D4—121no—
430C22×D4—121no—
431C22×D4—121no—
432C22×D4C4×D314yescomplemented
433C23×C4—31no—
434C23×C4—31no—
435C23×C4—31no—
436C23×C4—31no—
437C23×C4—31no—
438C23×C4—31no—
439C23×C4—31no—
440C23×C4—62no—
441C23×C4—62no—
442C23×C4—62no—
443C23×C4—62no—
444C23×C4—62no—
445C23×C4—62no—
446C23×C4—121no—
447C23×C4—121no—
448C23×C4—121no—
449C23×C4—121no—
450C23×C4—121no—
451C23×C4—121no—
452C23×C4—121no—
453C23×C4—121no—
454C23×C4C22×D311yescharacteristic
455C23×C4C22×D311yescharacteristic
456C23×C4C22×D311yescharacteristic
457C23×C4C22×D311yescharacteristic
458C23×C4C22×D311yescharacteristic
459C2×C4⋊C4—62no—
460C2×C4⋊C4—62no—
461C2×C4⋊C4—62no—
462C2×C4⋊C4—121no—
463C2×C4⋊C4—121no—
464C2×C4⋊C4—121no—
465C2×C22⋊C4—22no—
466C2×C22⋊C4—22no—
467C2×C22⋊C4—22no—
468C2×C22⋊C4—22no—
469C2×C22⋊C4—22no—
470C2×C22⋊C4—22no—
471C2×C22⋊C4—34no—
472C2×C22⋊C4—34no—
473C2×C22⋊C4—34no—
474C2×C22⋊C4—34no—
475C2×C22⋊C4—34no—
476C2×C22⋊C4—41no—
477C2×C22⋊C4—41no—
478C2×C22⋊C4—41no—
479C2×C22⋊C4—41no—
480C2×C22⋊C4—41no—
481C2×C22⋊C4—41no—
482C2×C22⋊C4—62no—
483C2×C22⋊C4—62no—
484C2×C22⋊C4—62no—
485C2×C22⋊C4—62no—
486C2×C22⋊C4—62no—
487C2×C22⋊C4—62no—
488C2×C22⋊C4—62no—
489C2×C22⋊C4—62no—
490C2×C22⋊C4—62no—
491C2×C22⋊C4—62no—
492C2×C22⋊C4—121no—
493C2×C22⋊C4—121no—
494C2×C22⋊C4—121no—
495C2×C22⋊C4—121no—
496C2×C22⋊C4—121no—
497C2×C22⋊C4—121no—
498C2×C22⋊C4—121no—
499C2×C22⋊C4—121no—
500C2×C22⋊C4—121no—
501C2×C22⋊C4—121no—
502C2×C22⋊C4—121no—
503C2×C22⋊C4—121no—
504C2×C42—62no—
505C2×C42—62no—
506C2×C42—121no—
507#95—34no—
508#95—34no—
509#95—41no—
510#95—41no—
511#95—62no—
512#95—62no—
513#95—62no—
514#95—62no—
515#95—62no—
516#95—62no—
517#95—62no—
518#95—62no—
519#95—121no—
520#95—121no—
521C23×C3—22no—
522C23×C3—22no—
523C23×C3—22no—
524C23×C3—22no—
525C23×C3—22no—
526C23×C3—22no—
527C23×C3—22no—
528C23×C3—22no—
529C23×C3—22no—
530C23×C3—22no—
531C23×C3—22no—
532C23×C3—22no—
533C23×C3—22no—
534C23×C3—22no—
535C23×C3—22no—
536C23×C3—22no—
537C23×C3—22no—
538C23×C3—22no—
539C23×C3—22no—
540C23×C3—22no—
541C23×C3—22no—
542C23×C3—22no—
543C23×C3—22no—
544C23×C3—22no—
545C23×C3—22no—
546C23×C3—41no—
547C23×C3—41no—
548C23×C3—41no—
549C23×C3—41no—
550C23×C3—41no—
551C23×C3—41no—
552C23×C3—41no—
553C23×C3—41no—
554C23×C3—41no—
555C23×C3—41no—
556C23×C3—41no—
557C23×C3—41no—
558C23×C3—41no—
559C23×C3—41no—
560C23×C3—41no—
561C23×C3—41no—
562C23×C3—41no—
563C23×C3—41no—
564C23×C3—41no—
565C23×C3—41no—
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×C3C4×D414yes—
591C23×C3C23×C411yescharacteristic
592C23×C3C22×D411yescharacteristic
593C23×C3C22×D411yescharacteristic
594C23×C3C22×D411yescharacteristic
595C23×C3C2×#4111yescharacteristic
596C23×C3C2×#4111yescharacteristic
597C23×C3C2×#4111yescharacteristic
598C23×C3H(5,𝔽2)11yescharacteristic
599C23×C3H(5,𝔽2)11yescharacteristic
600C23×C3H(5,𝔽2)11yescharacteristic
601C23×C3H(5,𝔽2)11yescharacteristic
602C23×C3H(5,𝔽2)11yescharacteristic
603C23×C3H(5,𝔽2)11yescharacteristic
604C23×C3H(5,𝔽2)11yescharacteristic
605C23×C32−1+411yescharacteristic
606C22×D3—22no—
607C22×D3—22no—
608C22×D3—22no—
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—41no—
625C22×D3—41no—
626C22×D3—41no—
627C22×D3—41no—
628C22×D3—41no—
629C22×D3—41no—
630C22×D3—41no—
631C22×D3—41no—
632C22×D3—41no—
633C22×D3—41no—
634C22×D3—41no—
635C22×D3—41no—
636C22×D3—41no—
637C22×D3—41no—
638C22×D3—41no—
639C22×D3—41no—
640C22×D3C4×D414yes—
641C3×D4—416no—
642C2×C3×C4—22no—
643C2×C3×C4—22no—
644C2×C3×C4—22no—
645C2×C3×C4—22no—
646C2×C3×C4—22no—
647C2×C3×C4—22no—
648C2×C3×C4—22no—
649C2×C3×C4—22no—
650C2×C3×C4—22no—
651C2×C3×C4—41no—
652C2×C3×C4—41no—
653C2×C3×C4—41no—
654C2×C3×C4—41no—
655C2×C3×C4—41no—
656C2×C3×C4—41no—
657C2×C3×C4—41no—
658C2×C3×C4—41no—
659C2×C3×C4—41no—
660C2×C3×C4—41no—
661C2×C3×C4—41no—
662C2×C3×C4—41no—
663C2×C3×C4—41no—
664C2×C3×C4—41no—
665C2×C3×C4—41no—
666C2×C3×C4—41no—
667C2×C3×C4—41no—
668C2×C3×C4—41no—
669C2×C3×C4—41no—
670C2×C3×C4—41no—
671C2×C3×C4—41no—
672C2×C3×C4—41no—
673C2×C3×C4—41no—
674C2×C3×C4—41no—
675C2×C3×C4—41no—
676C2×C3×C4—41no—
677#67—416no—
678#67—416no—
679C2×Dic3—22no—
680C2×Dic3—22no—
681C2×Dic3—22no—
682C2×Dic3—22no—
683C2×Dic3—22no—
684C2×Dic3—22no—
685C2×Dic3—22no—
686C2×Dic3—22no—
687C2×Dic3—22no—
688C2×Dic3—22no—
689C2×Dic3—22no—
690C2×Dic3—22no—
691C2×Dic3—22no—
692C2×Dic3—22no—
693C2×Dic3—22no—
694C2×Dic3—22no—
695C2×Dic3—22no—
696C2×Dic3—22no—
697C2×Dic3—22no—
698C2×Dic3—22no—
699C2×Dic3—22no—
700C2×Dic3—22no—
701C2×Dic3—22no—
702C2×Dic3—22no—
703C2×Dic3—416no—
704C2×Dic3—41no—
705C2×Dic3—41no—
706C2×Dic3—41no—
707C2×Dic3—41no—
708C2×Dic3—41no—
709C2×Dic3—41no—
710C2×Dic3—41no—
711C2×Dic3—41no—
712C2×Dic3—41no—
713C2×Dic3—41no—
714C2×Dic3—41no—
715C2×Dic3—41no—
716C2×Dic3—41no—
717C2×Dic3—41no—
718C2×Dic3—41no—
719C2×Dic3—41no—
720C2×Dic3—41no—
721C2×Dic3—41no—
722C2×Dic3—41no—
723C2×Dic3—41no—
724C2×Dic3—41no—
725C2×Dic3—41no—
726C2×Dic3—41no—
727C2×Dic3—41no—
728C2×Dic3C4×D414yes—
729C4×D3—416no—
730C24—21no—
731C24—21no—
732C24—21no—
733C24—21no—
734C24—21no—
735C24—21no—
736C24—21no—
737C24—21no—
738C24—21no—
739C24—21no—
740C24—21no—
741C24—21no—
742C24—21no—
743C24—21no—
744C24—21no—
745C24—21no—
746C24—21no—
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—32no—
757C24—32no—
758C24—32no—
759C24—61no—
760C24—61no—
761C24—61no—
762C24—61no—
763C24—61no—
764C24—61no—
765C24—61no—
766C24—61no—
767C24—61no—
768C24—61no—
769C24—61no—
770C24—61no—
771C24C2×C4×D312yes—
772C24C2×C4×D312yes—
773C24D3×D412yes—
774C24#23712yes—
775C24C23×D311yescharacteristic
776C2×D4—28no—
777C2×D4—44no—
778C2×D4—44no—
779C2×D4—44no—
780C2×D4—44no—
781C2×D4—44no—
782C2×D4—44no—
783C2×D4—68no—
784C2×D4—68no—
785C2×D4—68no—
786C2×D4—68no—
787C2×D4—124no—
788C2×D4—124no—
789C2×D4—124no—
790C2×D4—124no—
791C2×D4—124no—
792C2×D4—124no—
793C2×D4—124no—
794C2×D4—124no—
795C2×D4—124no—
796C2×D4—124no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—32no—
830C22×C4—32no—
831C22×C4—32no—
832C22×C4—32no—
833C22×C4—32no—
834C22×C4—32no—
835C22×C4—32no—
836C22×C4—32no—
837C22×C4—32no—
838C22×C4—61no—
839C22×C4—61no—
840C22×C4—61no—
841C22×C4—61no—
842C22×C4—61no—
843C22×C4—61no—
844C22×C4—61no—
845C22×C4—61no—
846C22×C4—61no—
847C22×C4—61no—
848C22×C4—61no—
849C22×C4—61no—
850C22×C4—61no—
851C22×C4—61no—
852C22×C4—61no—
853C22×C4—61no—
854C22×C4—61no—
855C22×C4—61no—
856C22×C4—61no—
857C22×C4—61no—
858C22×C4—61no—
859C22×C4—61no—
860C22×C4—61no—
861C22×C4—61no—
862C22×C4—61no—
863C22×C4—61no—
864C22×C4—61no—
865C22×C4—61no—
866C22×C4—61no—
867C22×C4—61no—
868C22×C4—61no—
869C22×C4—61no—
870C22×C4—61no—
871C22×C4—61no—
872C22×C4—61no—
873C22×C4—61no—
874C22×C4—61no—
875C22×C4—61no—
876C22×C4—61no—
877C22×C4—61no—
878C22×C4—124no—
879C22×C4—124no—
880C22×C4—124no—
881C22×C4—124no—
882C22×C4—124no—
883C22×C4—124no—
884C22×C4—124no—
885C22×C4—124no—
886C22×C4—124no—
887C22×C4—124no—
888C22×C4—124no—
889C22×C4—124no—
890C22×C4—124no—
891C22×C4—124no—
892C22×C4C2×C4×D312yes—
893C22×C4D3×D412yes—
894C22×C4D3×D412yes—
895C4⋊C4—124no—
896C4⋊C4—124no—
897C22⋊C4—44no—
898C22⋊C4—44no—
899C22⋊C4—44no—
900C22⋊C4—44no—
901C22⋊C4—68no—
902C22⋊C4—124no—
903C22⋊C4—124no—
904C22⋊C4—124no—
905C22⋊C4—124no—
906C22⋊C4—124no—
907C22⋊C4—124no—
908C22⋊C4—124no—
909C22⋊C4—124no—
910C42—124no—
911C22×C3—24no—
912C22×C3—24no—
913C22×C3—24no—
914C22×C3—42no—
915C22×C3—42no—
916C22×C3—42no—
917C22×C3—42no—
918C22×C3—42no—
919C22×C3—42no—
920C22×C3—42no—
921C22×C3—42no—
922C22×C3—42no—
923C22×C3—42no—
924C22×C3—42no—
925C22×C3—42no—
926C22×C3—42no—
927C22×C3—42no—
928C22×C3—42no—
929C22×C3—42no—
930C22×C3—42no—
931C22×C3—42no—
932C22×C3—42no—
933C22×C3—81no—
934C22×C3—81no—
935C22×C3—81no—
936C22×C3—81no—
937C22×C3—81no—
938C22×C3—81no—
939C22×C3—81no—
940C22×C3—81no—
941C22×C3C2×C4×D411yescharacteristic
942C22×C3C2×C4×D411yescharacteristic
943C22×C3C2×C4×D411yescharacteristic
944C22×C3#51811yescharacteristic
945C22×C3#51811yescharacteristic
946C22×C3#51811yescharacteristic
947C22×C3#52011yescharacteristic
948C22×C3#53411yescharacteristic
949C22×C3#53411yescharacteristic
950C22×C3#53511yescharacteristic
951C22×C3#53511yescharacteristic
952C22×C3#53511yescharacteristic
953C22×C3#53711yescharacteristic
954C22×C3#53811yescharacteristic
955C22×C3#53811yescharacteristic
956C22×C3#53811yescharacteristic
957C22×C3#53911yescharacteristic
958C22×C3#54011yescharacteristic
959C22×C3#54011yescharacteristic
960C22×C3D4211yescharacteristic
961C22×C3D4211yescharacteristic
962C22×C3D4211yescharacteristic
963C22×C3#54611yescharacteristic
964C22×C3#54611yescharacteristic
965C22×C3#54611yescharacteristic
966C22×C3#54611yescharacteristic
967C22×C3#54711yescharacteristic
968C22×C3#54811yescharacteristic
969C22×C3#55111yescharacteristic
970C22×C3#55111yescharacteristic
971C22×C3#55311yescharacteristic
972C22×C3#56011yescharacteristic
973C22×C3#56011yescharacteristic
974C22×C3#56211yescharacteristic
975C22×C3#56211yescharacteristic
976C2×D3—24no—
977C2×D3—24no—
978C2×D3—24no—
979C2×D3—42no—
980C2×D3—42no—
981C2×D3—42no—
982C2×D3—42no—
983C2×D3—42no—
984C2×D3—42no—
985C2×D3—42no—
986C2×D3—42no—
987C2×D3—42no—
988C2×D3—42no—
989C2×D3—42no—
990C2×D3—42no—
991C3×C4—42no—
992C3×C4—42no—
993C3×C4—42no—
994C3×C4—81no—
995C3×C4—81no—
996Dic3—24no—
997Dic3—42no—
998Dic3—42no—
999Dic3—42no—
1000Dic3—42no—
1001Dic3—42no—
1002Dic3—42no—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—22no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—22no—
1012C23—22no—
1013C23—22no—
1014C23—22no—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—22no—
1021C23—22no—
1022C23—22no—
1023C23—22no—
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—34no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—62no—
1074C23—62no—
1075C23—62no—
1076C23—62no—
1077C23—62no—
1078C23—62no—
1079C23—62no—
1080C23—62no—
1081C23—62no—
1082C23—62no—
1083C23—62no—
1084C23—62no—
1085C23—62no—
1086C23—62no—
1087C23—62no—
1088C23—62no—
1089C23—62no—
1090C23—62no—
1091C23—121no—
1092C23—121no—
1093C23—121no—
1094C23—121no—
1095C23—121no—
1096C23—121no—
1097C23—121no—
1098C23—121no—
1099C23—121no—
1100C23—121no—
1101C23—121no—
1102C23—121no—
1103C23—121no—
1104C23—121no—
1105C23—121no—
1106C23—121no—
1107C23#67⋊C414yes—
1108C23C22×C4×D311yescharacteristic
1109C23C2×D3×D411yescharacteristic
1110C23C2×D3×D411yescharacteristic
1111C23C2×D3×D411yescharacteristic
1112C23C2×#23711yescharacteristic
1113C23#100411yescharacteristic
1114C23#100411yescharacteristic
1115C23#100411yescharacteristic
1116C23#100411yescharacteristic
1117C23#100411yescharacteristic
1118C23#100411yescharacteristic
1119C23D3×#4111yescharacteristic
1120C23D3×#4111yescharacteristic
1121C23#100911yescharacteristic
1122C23#101011yescharacteristic
1123D4—416no—
1124D4—1216no—
1125D4—1216no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—34no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—62no—
1163C2×C4—62no—
1164C2×C4—62no—
1165C2×C4—62no—
1166C2×C4—62no—
1167C2×C4—62no—
1168C2×C4—62no—
1169C2×C4—62no—
1170C2×C4—62no—
1171C2×C4—62no—
1172C2×C4—62no—
1173C2×C4—62no—
1174C2×C4—62no—
1175C2×C4—62no—
1176C2×C4—62no—
1177C2×C4—62no—
1178C2×C4—62no—
1179C2×C4—62no—
1180C2×C4—62no—
1181C2×C4—62no—
1182C2×C4—62no—
1183C2×C4—62no—
1184C2×C4—62no—
1185C2×C4—62no—
1186C2×C4—1216no—
1187C2×C4—1216no—
1188C2×C4—121no—
1189C2×C4—121no—
1190C2×C4—121no—
1191C2×C4—121no—
1192C2×C4—121no—
1193C2×C4—121no—
1194C2×C4—121no—
1195C2×C4—121no—
1196C2×C4—121no—
1197C2×C4—121no—
1198C2×C4—121no—
1199C2×C4—121no—
1200C2×C4—121no—
1201C2×C4—121no—
1202C2×C4—121no—
1203C2×C4—121no—
1204C2×C4—121no—
1205C2×C4—121no—
1206C2×C4—121no—
1207C2×C4—121no—
1208C2×C4—121no—
1209C2×C4—121no—
1210C2×C4—121no—
1211C2×C4—121no—
1212C2×C3—44no—
1213C2×C3—82no—
1214C2×C3#232111yescharacteristic
1215C2×C3#232511yescharacteristic
1216C2×C3#232811yescharacteristic
1217C2×C3#235811yescharacteristic
1218C2×C3#235811yescharacteristic
1219C2×C3#236111yescharacteristic
1220C2×C3#237711yescharacteristic
1221C2×C3#266911yescharacteristic
1222C2×C3#267111yescharacteristic
1223C2×C3#267611yescharacteristic
1224C2×C3#267811yescharacteristic
1225C2×C3#268811yescharacteristic
1226C2×C3#269611yescharacteristic
1227C2×C3#270611yescharacteristic
1228C2×C3#274911yescharacteristic
1229D3—44no—
1230C22—24no—
1231C22—24no—
1232C22—24no—
1233C22—42no—
1234C22—42no—
1235C22—42no—
1236C22—42no—
1237C22—42no—
1238C22—42no—
1239C22—42no—
1240C22—42no—
1241C22—42no—
1242C22—42no—
1243C22—42no—
1244C22—42no—
1245C22—42no—
1246C22—42no—
1247C22—42no—
1248C22—42no—
1249C22—42no—
1250C22—42no—
1251C22—42no—
1252C22—64no—
1253C22—64no—
1254C22—64no—
1255C22—81no—
1256C22—81no—
1257C22—81no—
1258C22—81no—
1259C22—81no—
1260C22—81no—
1261C22—81no—
1262C22—81no—
1263C22—122no—
1264C22—122no—
1265C22—122no—
1266C22—122no—
1267C22—122no—
1268C22—122no—
1269C22—122no—
1270C22—122no—
1271C22—122no—
1272C22—122no—
1273C22—122no—
1274C22—122no—
1275C22C2×#67⋊C411yescharacteristic
1276C22#548611yescharacteristic
1277C22#548611yescharacteristic
1278C22C4×D3×D411yescharacteristic
1279C22C4×D3×D411yescharacteristic
1280C22#554511yescharacteristic
1281C22#554611yescharacteristic
1282C22#558911yescharacteristic
1283C22#558911yescharacteristic
1284C22#559011yescharacteristic
1285C22#559111yescharacteristic
1286C22#559211yescharacteristic
1287C22#559211yescharacteristic
1288C22#559311yescharacteristic
1289C22#559311yescharacteristic
1290C22#559811yescharacteristic
1291C22#560111yescharacteristic
1292C22#560711yescharacteristic
1293C22#560811yescharacteristic
1294C22#560911yescharacteristic
1295C22#561011yescharacteristic
1296C22#561011yescharacteristic
1297C22#561011yescharacteristic
1298C22#561311yescharacteristic
1299C22#561511yescharacteristic
1300C22#562011yescharacteristic
1301C22#562111yescharacteristic
1302C22#565511yescharacteristic
1303C22#565811yescharacteristic
1304C22#566011yescharacteristic
1305C22#566311yescharacteristic
1306C22#567911yescharacteristic
1307C22#568411yescharacteristic
1308C22#571711yescharacteristic
1309C22#572011yescharacteristic
1310C4—42no—
1311C4—42no—
1312C4—42no—
1313C4—64no—
1314C4—81no—
1315C4—81no—
1316C4—122no—
1317C4—122no—
1318C4—122no—
1319C4—122no—
1320C4—122no—
1321C4—122no—
1322C3#1451911yescharacteristic, complemented, Sylow
1323C2—44no—
1324C2—82no—
1325C2—124no—
1326C2#7382111yescharacteristic
1327C2#7466711yescharacteristic
1328C2#7467611yescharacteristic
1329C2#7487711yescharacteristic
1330C2#7487911yescharacteristic
1331C2#7631011yescharacteristic
1332C2#7643211yescharacteristic
1333C2#7671511yescharacteristic
1334C2#7671711yescharacteristic
1335C2#7676511yescharacteristic
1336C2#7677111yescharacteristic
1337C2#7699911yescharacteristic
1338C2#7701711yescharacteristic
1339C2#7702611yescharacteristic
1340C2#7715411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC3×#1438C2
socle, cosocleC24×C3C24
prime radicalC2×#5223C2
hypercenter#1438D3
hypocenterC3#14519
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1438

Complements

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

NH ≅ G/Ntype
2. C2×#5220C2semidirect
3. C2×#4956C2semidirect
4. C2×#4956C2semidirect
5. C2×#4957C2semidirect
6. C2×#4958C2semidirect
7. C2×#4946C2semidirect
8. C3×#1438C2semidirect
9. #71549C2semidirect
10. #71547C2semidirect
11. #71545C2semidirect
12. #69428C2semidirect
13. (C2×D3)⋊#95C2semidirect
14. #69414C2semidirect
15. #69402C2semidirect
40. #5223C4semidirect
70. #1438D3semidirect
83. C22×C3×D4C2×C4semidirect
102. C22×#67C2×C4semidirect
148. C2×#217C2×C4semidirect
149. C2×#217C2×C4semidirect
150. C2×#217D4semidirect
161. C2×(C2×D3)⋊C4C2×C4semidirect
162. C2×(C2×D3)⋊C4D4semidirect
184. C3⋊#95C2×C4semidirect
185. C3⋊#95D4semidirect
432. C22×D4C4×D3semidirect
1322. C3#14519semidirect

Maximal subgroups

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

subgroupindex
C2×#52232
C2×#52202
C2×#49562
C2×#49572
C2×#49582
C2×#49462
C3×#14382
#715492
#715472
#715452
#694282
(C2×D3)⋊#952
#694142
#694022
#145193