Finite Group Databasebeta

← #10733113

Subgroups — #10733113

Order 768.

2466 conjugacy classes of subgroups.

The subgroup lattice has 1346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#939C211yesmaximal, characteristic
2C2×#5220C211yesmaximal, characteristic, complemented
3C2×#4953C211yesmaximal, characteristic, complemented
4C2×#4961C211yesmaximal, characteristic, complemented
5C2×#4958C211yesmaximal, characteristic, complemented
6C2×#4950C211yesmaximal, characteristic, complemented
7C3×#1438C211yesmaximal, characteristic, complemented
8#71550C211yesmaximal, characteristic, complemented
9#71550C211yesmaximal, characteristic, complemented
10#71544C211yesmaximal, characteristic, complemented
11#71544C211yesmaximal, characteristic, complemented
12#69429C211yesmaximal, characteristic, complemented
13#69427C211yesmaximal, characteristic, complemented
14#69413C211yesmaximal, characteristic, complemented
15#69411C211yesmaximal, characteristic, complemented
16#15277—31nomaximal, Sylow
17C23×C3×D4C2211yescharacteristic
18C23×#67C2211yescharacteristic
19C23×#67C2211yescharacteristic
20C24×Dic3C2211yescharacteristic
21C24×Dic3C2211yescharacteristic
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×C3×C22⋊C4C2211yescharacteristic
25C22×C3×C22⋊C4C2211yescharacteristic
26C22×#217C2211yescharacteristic
27C22×#217C2211yescharacteristic
28C22×#217C2211yescharacteristic
29C22×#217C2211yescharacteristic
30C2×#939—24no—
31C2×#939—24no—
32C2×#939—24no—
33C22×(C2×D3)⋊C4C2211yescharacteristic
34C22×(C2×D3)⋊C4C2211yescharacteristic
35C22×(C2×D3)⋊C4C2211yescharacteristic
36C22×(C2×D3)⋊C4C2211yescharacteristic
37C22×(C2×D3)⋊C4C2211yescharacteristic
38C22×C4⋊Dic3C2211yescharacteristic
39C22×C4⋊Dic3C2211yescharacteristic
40C22×Dic3⋊C4C2211yescharacteristic
41C2×C3×#95C2211yescharacteristic
42C2×C3×#95C2211yescharacteristic
43#5220—24no—
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
55C2×C3⋊#95C2211yescharacteristic
56#4961—24no—
57#4958—24no—
58#4953—24no—
59#4950—24no—
60C22×#121—31no—
61C2×#397—31no—
62C2×#394—31no—
63C2×#386—31no—
64C2×#386—31no—
65C2×#385—31no—
66#1442—31no—
67#1441—31no—
68#1440—31no—
69#1439—31no—
70#1438—31no—
71#1438—31no—
72#1438D311yescharacteristic, complemented
73C22⋊#95—31no—
74C22⋊#95—31no—
75C25×C3C2311yescharacteristic
76C25×C3C2311yescharacteristic
77C24×D3C2311yescharacteristic
78C22×C3×D4—22no—
79C22×C3×D4—22no—
80C22×C3×D4—22no—
81C22×C3×D4—22no—
82C22×C3×D4—41no—
83C22×C3×D4—41no—
84C22×C3×D4D414yes—
85C23×C3×C4C2311yescharacteristic
86C23×C3×C4C2311yescharacteristic
87C23×C3×C4C2311yescharacteristic
88C23×C3×C4C2311yescharacteristic
89C23×C3×C4C2311yescharacteristic
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×#67—41no—
102C22×#67—41no—
103C22×#67D414yes—
104C23×Dic3—22no—
105C23×Dic3—22no—
106C23×Dic3—22no—
107C23×Dic3—22no—
108C23×Dic3—22no—
109C23×Dic3—22no—
110C23×Dic3—22no—
111C23×Dic3—22no—
112C23×Dic3—41no—
113C23×Dic3—41no—
114C23×Dic3—41no—
115C23×Dic3—41no—
116C23×Dic3—41no—
117C23×Dic3—41no—
118C23×Dic3C2311yescharacteristic
119C23×Dic3C2311yescharacteristic
120C23×Dic3C2311yescharacteristic
121C23×Dic3C2311yescharacteristic
122C23×Dic3C2311yescharacteristic
123C23×Dic3C2311yescharacteristic
124C23×Dic3C2311yescharacteristic
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—22no—
131C2×C3×C22⋊C4—22no—
132C2×C3×C22⋊C4—22no—
133C2×C3×C22⋊C4—41no—
134C2×C3×C22⋊C4—41no—
135C2×C3×C22⋊C4—41no—
136C2×C3×C22⋊C4—41no—
137C2×#217—22no—
138C2×#217—22no—
139C2×#217—22no—
140C2×#217—22no—
141C2×#217—22no—
142C2×#217—22no—
143C2×#217—22no—
144C2×#217—22no—
145C2×#217—22no—
146C2×#217—41no—
147C2×#217—41no—
148C2×#217D414yes—
149#939—232no—
150C2×(C2×D3)⋊C4—22no—
151C2×(C2×D3)⋊C4—22no—
152C2×(C2×D3)⋊C4—22no—
153C2×(C2×D3)⋊C4—22no—
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—41no—
160C2×(C2×D3)⋊C4—41no—
161C2×(C2×D3)⋊C4—41no—
162C2×(C2×D3)⋊C4—41no—
163C2×(C2×D3)⋊C4—41no—
164C2×(C2×D3)⋊C4—41no—
165C2×C4⋊Dic3—22no—
166C2×C4⋊Dic3—22no—
167C2×C4⋊Dic3—22no—
168C2×C4⋊Dic3—22no—
169C2×C4⋊Dic3—22no—
170C2×C4⋊Dic3—41no—
171C2×Dic3⋊C4—22no—
172C2×Dic3⋊C4—22no—
173C2×Dic3⋊C4—22no—
174C3×#95—41no—
175C3×#95—41no—
176C3⋊#95—22no—
177C3⋊#95—22no—
178C3⋊#95—22no—
179C3⋊#95—22no—
180C3⋊#95—22no—
181C3⋊#95—22no—
182C3⋊#95—22no—
183C3⋊#95—22no—
184C3⋊#95—41no—
185C3⋊#95—41no—
186C3⋊#95—41no—
187C3⋊#95D414yescomplemented
188C23×D4—31no—
189C23×D4—31no—
190C23×D4C2×D311yescharacteristic
191C24×C4—31no—
192C24×C4—31no—
193C2×#121—64no—
194C2×#121—64no—
195C2×#121—64no—
196C22×C4⋊C4—31no—
197C22×C4⋊C4—31no—
198C22×C4⋊C4—31no—
199C22×C22⋊C4—31no—
200C22×C22⋊C4—31no—
201C22×C22⋊C4—31no—
202C22×C22⋊C4—31no—
203C22×C22⋊C4—31no—
204C22×C22⋊C4—31no—
205C22×C22⋊C4—31no—
206C22×C22⋊C4—31no—
207C22×C22⋊C4—31no—
208C22×C22⋊C4C2×D311yescharacteristic
209C22×C22⋊C4C2×D311yescharacteristic
210C22×C22⋊C4C2×D311yescharacteristic
211C22×C22⋊C4C2×D311yescharacteristic
212#397—64no—
213#394—64no—
214#386—64no—
215#386—64no—
216#385—64no—
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×#95—31no—
227C2×#95—31no—
228C2×#95—31no—
229C2×#95C2×D311yescharacteristic
230C2×#95C2×D311yescharacteristic
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×C3—21no—
255C24×C3C2×D412yes—
256C24×C3C2×D412yes—
257C24×C3C2×D412yes—
258C24×C3C2×D412yes—
259C24×C3#4112yes—
260C24×C3#4112yes—
261C24×C3C2411yescharacteristic
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×D3—21no—
272C23×D3—21no—
273C23×D3—21no—
274C23×D3—21no—
275C23×D3—21no—
276C23×D3C2×D412yes—
277C2×C3×D4—28no—
278C2×C3×D4—28no—
279C2×C3×D4—44no—
280C2×C3×D4—44no—
281C2×C3×D4—44no—
282C2×C3×D4—44no—
283C2×C3×D4—44no—
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×C4—21no—
314C22×C3×C4—21no—
315C22×C3×C4—21no—
316C22×C3×C4C2×D412yes—
317C22×C3×C4C2×D412yes—
318C22×C3×C4#4112yes—
319C2×#67—28no—
320C2×#67—28no—
321C2×#67—28no—
322C2×#67—44no—
323C2×#67—44no—
324C2×#67—44no—
325C2×#67—44no—
326C2×#67—44no—
327C2×#67—44no—
328C2×#67—44no—
329C2×#67—44no—
330C2×#67—44no—
331C2×#67—44no—
332C2×#67—44no—
333C22×Dic3—21no—
334C22×Dic3—21no—
335C22×Dic3—21no—
336C22×Dic3—21no—
337C22×Dic3—28no—
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—21no—
371C22×Dic3—21no—
372C22×Dic3—21no—
373C22×Dic3—21no—
374C22×Dic3—21no—
375C22×Dic3—21no—
376C22×Dic3—44no—
377C22×Dic3—44no—
378C22×Dic3—44no—
379C22×Dic3—44no—
380C22×Dic3—44no—
381C22×Dic3—44no—
382C22×Dic3—44no—
383C22×Dic3—44no—
384C22×Dic3—44no—
385C22×Dic3—44no—
386C22×Dic3—44no—
387C22×Dic3—44no—
388C22×Dic3—44no—
389C22×Dic3C2×D412yes—
390C22×Dic3C2×D412yes—
391C22×Dic3C2×D412yes—
392C22×Dic3C2×D412yes—
393C22×Dic3C2×D412yes—
394C22×Dic3#4112yes—
395C22×Dic3#4112yes—
396C3×C22⋊C4—28no—
397C3×C22⋊C4—44no—
398C3×C22⋊C4—44no—
399C3×C22⋊C4—44no—
400#217—28no—
401#217—44no—
402#217—44no—
403#217—44no—
404(C2×D3)⋊C4—28no—
405(C2×D3)⋊C4—44no—
406(C2×D3)⋊C4—44no—
407(C2×D3)⋊C4—44no—
408(C2×D3)⋊C4—44no—
409C4⋊Dic3—44no—
410C4⋊Dic3—44no—
411Dic3⋊C4—28no—
412C25—31no—
413C25C22×D311yescharacteristic
414C25C22×D311yescharacteristic
415C22×D4—22no—
416C22×D4—22no—
417C22×D4—22no—
418C22×D4—22no—
419C22×D4—34no—
420C22×D4—41no—
421C22×D4—41no—
422C22×D4—62no—
423C22×D4—62no—
424C22×D4—62no—
425C22×D4—62no—
426C22×D4—62no—
427C22×D4—62no—
428C22×D4—62no—
429C22×D4—62no—
430C22×D4—62no—
431C22×D4—121no—
432C22×D4—121no—
433C22×D4—121no—
434C22×D4—121no—
435C22×D4D1214yes—
436C23×C4—31no—
437C23×C4—31no—
438C23×C4—31no—
439C23×C4—31no—
440C23×C4—31no—
441C23×C4—31no—
442C23×C4—31no—
443C23×C4—62no—
444C23×C4—62no—
445C23×C4—62no—
446C23×C4—62no—
447C23×C4—62no—
448C23×C4—62no—
449C23×C4—62no—
450C23×C4—62no—
451C23×C4—121no—
452C23×C4—121no—
453C23×C4—121no—
454C23×C4—121no—
455C23×C4—121no—
456C23×C4—121no—
457C23×C4C22×D311yescharacteristic
458C23×C4C22×D311yescharacteristic
459C23×C4C22×D311yescharacteristic
460C23×C4C22×D311yescharacteristic
461C23×C4C22×D311yescharacteristic
462#121—632no—
463C2×C4⋊C4—62no—
464C2×C4⋊C4—62no—
465C2×C4⋊C4—62no—
466C2×C4⋊C4—62no—
467C2×C4⋊C4—62no—
468C2×C4⋊C4—62no—
469C2×C4⋊C4—62no—
470C2×C4⋊C4—62no—
471C2×C4⋊C4—121no—
472C2×C22⋊C4—22no—
473C2×C22⋊C4—22no—
474C2×C22⋊C4—22no—
475C2×C22⋊C4—22no—
476C2×C22⋊C4—22no—
477C2×C22⋊C4—22no—
478C2×C22⋊C4—22no—
479C2×C22⋊C4—22no—
480C2×C22⋊C4—34no—
481C2×C22⋊C4—41no—
482C2×C22⋊C4—41no—
483C2×C22⋊C4—41no—
484C2×C22⋊C4—41no—
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—62no—
493C2×C22⋊C4—62no—
494C2×C22⋊C4—62no—
495C2×C22⋊C4—62no—
496C2×C22⋊C4—62no—
497C2×C22⋊C4—62no—
498C2×C22⋊C4—62no—
499C2×C22⋊C4—62no—
500C2×C22⋊C4—62no—
501C2×C22⋊C4—62no—
502C2×C22⋊C4—62no—
503C2×C22⋊C4—121no—
504C2×C22⋊C4—121no—
505C2×C22⋊C4—121no—
506C2×C22⋊C4—121no—
507C2×C22⋊C4—121no—
508C2×C22⋊C4—121no—
509C2×C22⋊C4—121no—
510C2×C22⋊C4—121no—
511#95—34no—
512#95—41no—
513#95—41no—
514#95—62no—
515#95—62no—
516#95—62no—
517#95—62no—
518#95—62no—
519#95—62no—
520#95—62no—
521#95—62no—
522#95—121no—
523#95—121no—
524#95—121no—
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—22no—
547C23×C3—22no—
548C23×C3—22no—
549C23×C3—22no—
550C23×C3—22no—
551C23×C3—22no—
552C23×C3—22no—
553C23×C3—22no—
554C23×C3—22no—
555C23×C3—22no—
556C23×C3—22no—
557C23×C3—22no—
558C23×C3—22no—
559C23×C3—22no—
560C23×C3—22no—
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×C3—41no—
591C23×C3—41no—
592C23×C3—41no—
593C23×C3#12014yes—
594C23×C3#12314yes—
595C23×C3C22×D411yescharacteristic
596C23×C3C22×D411yescharacteristic
597C23×C3C22×D411yescharacteristic
598C23×C3C22×D411yescharacteristic
599C23×C3C2×#4111yescharacteristic
600C23×C3C2×#4111yescharacteristic
601C23×C3C2×#4111yescharacteristic
602C23×C3C2×#4111yescharacteristic
603C23×C3C2×#4111yescharacteristic
604C23×C3H(5,𝔽2)11yescharacteristic
605C23×C3H(5,𝔽2)11yescharacteristic
606C23×C3H(5,𝔽2)11yescharacteristic
607C23×C3H(5,𝔽2)11yescharacteristic
608C23×C3H(5,𝔽2)11yescharacteristic
609C23×C32−1+411yescharacteristic
610C22×D3—22no—
611C22×D3—22no—
612C22×D3—22no—
613C22×D3—22no—
614C22×D3—22no—
615C22×D3—22no—
616C22×D3—22no—
617C22×D3—41no—
618C22×D3—41no—
619C22×D3—41no—
620C22×D3—41no—
621C22×D3—41no—
622C22×D3—41no—
623C22×D3—41no—
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×D3—41no—
641C22×D3—41no—
642C22×D3—41no—
643C22×D3—41no—
644C22×D3—41no—
645C3×D4—416no—
646C2×C3×C4—22no—
647C2×C3×C4—22no—
648C2×C3×C4—22no—
649C2×C3×C4—22no—
650C2×C3×C4—22no—
651C2×C3×C4—22no—
652C2×C3×C4—22no—
653C2×C3×C4—22no—
654C2×C3×C4—22no—
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—
677C2×C3×C4—41no—
678C2×C3×C4—41no—
679C2×C3×C4—41no—
680C2×C3×C4—41no—
681#67—416no—
682#67—416no—
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—416no—
702C2×Dic3—416no—
703C2×Dic3—41no—
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×Dic3—41no—
729C2×Dic3—41no—
730C2×Dic3—41no—
731C2×Dic3—41no—
732C2×Dic3—41no—
733C2×Dic3#12114yes—
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—21no—
757C24—21no—
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—
771C24—61no—
772C24—61no—
773C24C2×D1212yes—
774C24C2×D1212yes—
775C24D3×D412yes—
776C24D3×D412yes—
777C24#23712yes—
778C24#23712yes—
779C24C23×D311yescharacteristic
780C2×D4—28no—
781C2×D4—28no—
782C2×D4—44no—
783C2×D4—44no—
784C2×D4—44no—
785C2×D4—44no—
786C2×D4—44no—
787C2×D4—68no—
788C2×D4—68no—
789C2×D4—68no—
790C2×D4—124no—
791C2×D4—124no—
792C2×D4—124no—
793C2×D4—124no—
794C2×D4—124no—
795C2×D4—124no—
796C2×D4—124no—
797C2×D4—124no—
798C2×D4—124no—
799C2×D4—124no—
800C2×D4—124no—
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—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—32no—
834C22×C4—32no—
835C22×C4—32no—
836C22×C4—32no—
837C22×C4—32no—
838C22×C4—32no—
839C22×C4—32no—
840C22×C4—61no—
841C22×C4—61no—
842C22×C4—61no—
843C22×C4—61no—
844C22×C4—68no—
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—61no—
879C22×C4—61no—
880C22×C4—61no—
881C22×C4—61no—
882C22×C4—61no—
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×C4—124no—
893C22×C4—124no—
894C22×C4—124no—
895C22×C4—124no—
896C22×C4C2×D1212yes—
897C22×C4D3×D412yes—
898C22×C4#23712yes—
899C4⋊C4—68no—
900C4⋊C4—124no—
901C4⋊C4—124no—
902C22⋊C4—28no—
903C22⋊C4—44no—
904C22⋊C4—44no—
905C22⋊C4—44no—
906C22⋊C4—68no—
907C22⋊C4—68no—
908C22⋊C4—124no—
909C22⋊C4—124no—
910C22⋊C4—124no—
911C22⋊C4—124no—
912C22⋊C4—124no—
913C22⋊C4—124no—
914C22⋊C4—124no—
915C22×C3—24no—
916C22×C3—24no—
917C22×C3—24no—
918C22×C3—24no—
919C22×C3—24no—
920C22×C3—24no—
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—42no—
934C22×C3—42no—
935C22×C3—42no—
936C22×C3—42no—
937C22×C3—42no—
938C22×C3—42no—
939C22×C3—42no—
940C22×C3—42no—
941C22×C3—42no—
942C22×C3—42no—
943C22×C3—42no—
944C22×C3—42no—
945C22×C3C2×#12011yescharacteristic
946C22×C3C2×#12111yescharacteristic
947C22×C3C2×#12311yescharacteristic
948C22×C3#52511yescharacteristic
949C22×C3#52911yescharacteristic
950C22×C3#53211yescharacteristic
951C22×C3#53411yescharacteristic
952C22×C3#53411yescharacteristic
953C22×C3#53511yescharacteristic
954C22×C3#53711yescharacteristic
955C22×C3#53811yescharacteristic
956C22×C3#53811yescharacteristic
957C22×C3#53911yescharacteristic
958C22×C3#54011yescharacteristic
959C22×C3#54211yescharacteristic
960C22×C3D4211yescharacteristic
961C22×C3D4211yescharacteristic
962C22×C3#54611yescharacteristic
963C22×C3#54611yescharacteristic
964C22×C3#54611yescharacteristic
965C22×C3#54611yescharacteristic
966C22×C3#54611yescharacteristic
967C22×C3#54611yescharacteristic
968C22×C3#54611yescharacteristic
969C22×C3#54611yescharacteristic
970C22×C3#54611yescharacteristic
971C22×C3#54711yescharacteristic
972C22×C3#54711yescharacteristic
973C22×C3#54811yescharacteristic
974C22×C3#55311yescharacteristic
975C22×C3#55311yescharacteristic
976C22×C3#55311yescharacteristic
977C22×C3#55311yescharacteristic
978C22×C3#56011yescharacteristic
979C22×C3#56211yescharacteristic
980C2×D3—42no—
981C2×D3—42no—
982C2×D3—42no—
983C2×D3—42no—
984C2×D3—42no—
985C2×D3—42no—
986C2×D3—42no—
987C2×D3—81no—
988C2×D3—81no—
989C2×D3—81no—
990C2×D3—81no—
991C2×D3—81no—
992C2×D3—81no—
993C2×D3—81no—
994C2×D3—81no—
995C3×C4—42no—
996C3×C4—42no—
997C3×C4—42no—
998C3×C4—81no—
999C3×C4—81no—
1000Dic3—24no—
1001Dic3—42no—
1002Dic3—42no—
1003Dic3—42no—
1004Dic3—42no—
1005Dic3—81no—
1006Dic3—81no—
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—22no—
1029C23—22no—
1030C23—22no—
1031C23—22no—
1032C23—22no—
1033C23—22no—
1034C23—22no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—22no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
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—41no—
1074C23—41no—
1075C23—62no—
1076C23—62no—
1077C23—62no—
1078C23—62no—
1079C23—62no—
1080C23—62no—
1081C23—62no—
1082C23—121no—
1083C23—121no—
1084C23—121no—
1085C23—121no—
1086C23—121no—
1087C23—121no—
1088C23—121no—
1089C23—121no—
1090C23—121no—
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—121no—
1108C23—121no—
1109C23—121no—
1110C23#88214yes—
1111C23#88614yes—
1112C23C22×D1211yescharacteristic
1113C23C2×D3×D411yescharacteristic
1114C23C2×D3×D411yescharacteristic
1115C23C2×D3×D411yescharacteristic
1116C23C2×#23711yescharacteristic
1117C23C2×#23711yescharacteristic
1118C23C2×#23711yescharacteristic
1119C23#100411yescharacteristic
1120C23#100411yescharacteristic
1121C23#100411yescharacteristic
1122C23#100411yescharacteristic
1123C23D3×#4111yescharacteristic
1124C23D3×#4111yescharacteristic
1125C23#100911yescharacteristic
1126C23#101011yescharacteristic
1127D4—416no—
1128D4—1216no—
1129D4—1216no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—34no—
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—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
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—1216no—
1185C2×C4—1216no—
1186C2×C4—121no—
1187C2×C4—121no—
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×C4—121no—
1213C2×C4—121no—
1214C2×C4—121no—
1215C2×C4—121no—
1216C2×C3—44no—
1217C2×C3—44no—
1218C2×C3#240511yescharacteristic
1219C2×C3#241011yescharacteristic
1220C2×C3#242711yescharacteristic
1221C2×C3#243011yescharacteristic
1222C2×C3#244311yescharacteristic
1223C2×C3#244411yescharacteristic
1224C2×C3#246411yescharacteristic
1225C2×C3#253511yescharacteristic
1226C2×C3#255911yescharacteristic
1227C2×C3#267611yescharacteristic
1228C2×C3#267811yescharacteristic
1229C2×C3#268811yescharacteristic
1230C2×C3#269111yescharacteristic
1231C2×C3#270111yescharacteristic
1232C2×C3#270811yescharacteristic
1233D3—82no—
1234C22—24no—
1235C22—24no—
1236C22—24no—
1237C22—24no—
1238C22—24no—
1239C22—24no—
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—42no—
1253C22—42no—
1254C22—42no—
1255C22—42no—
1256C22—42no—
1257C22—42no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—122no—
1265C22—122no—
1266C22—122no—
1267C22—122no—
1268C22—122no—
1269C22—122no—
1270C22—122no—
1271C22—241no—
1272C22—241no—
1273C22—241no—
1274C22—241no—
1275C22—241no—
1276C22—241no—
1277C22—241no—
1278C22—241no—
1279C22C2×#88211yescharacteristic
1280C22C2×#88611yescharacteristic
1281C22#549311yescharacteristic
1282C22D4×D1211yescharacteristic
1283C22#555411yescharacteristic
1284C22#555411yescharacteristic
1285C22#555511yescharacteristic
1286C22#558611yescharacteristic
1287C22#559011yescharacteristic
1288C22#559111yescharacteristic
1289C22#559111yescharacteristic
1290C22#559111yescharacteristic
1291C22#559111yescharacteristic
1292C22#559111yescharacteristic
1293C22#559311yescharacteristic
1294C22#559611yescharacteristic
1295C22#559711yescharacteristic
1296C22#559811yescharacteristic
1297C22#560111yescharacteristic
1298C22#560111yescharacteristic
1299C22#560111yescharacteristic
1300C22D3×#12111yescharacteristic
1301C22#560511yescharacteristic
1302C22#561011yescharacteristic
1303C22#561811yescharacteristic
1304C22#562011yescharacteristic
1305C22#562111yescharacteristic
1306C22#564911yescharacteristic
1307C22#565411yescharacteristic
1308C22#565511yescharacteristic
1309C22#566511yescharacteristic
1310C22#566911yescharacteristic
1311C22#567811yescharacteristic
1312C22#571511yescharacteristic
1313C22#571911yescharacteristic
1314C4—42no—
1315C4—42no—
1316C4—42no—
1317C4—64no—
1318C4—81no—
1319C4—81no—
1320C4—122no—
1321C4—122no—
1322C4—122no—
1323C4—122no—
1324C4—241no—
1325C4—241no—
1326C3#1527711yescharacteristic, complemented, Sylow
1327C2—44no—
1328C2—44no—
1329C2—242no—
1330C2#7382311yescharacteristic
1331C2#7469911yescharacteristic
1332C2#7470311yescharacteristic
1333C2#7470611yescharacteristic
1334C2#7488811yescharacteristic
1335C2#7638611yescharacteristic
1336C2#7646311yescharacteristic
1337C2#7668211yescharacteristic
1338C2#7668611yescharacteristic
1339C2#7671411yescharacteristic
1340C2#7677311yescharacteristic
1341C2#7690211yescharacteristic
1342C2#7695111yescharacteristic
1343C2#7701211yescharacteristic
1344C2#7715011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1438C2
prime radicalC22×#939C2
hypercenter#1438D3
hypocenterC3#15277
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1438

Complements

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

NH ≅ G/Ntype
2. C2×#5220C2semidirect
3. C2×#4953C2semidirect
4. C2×#4961C2semidirect
5. C2×#4958C2semidirect
6. C2×#4950C2semidirect
7. C3×#1438C2semidirect
8. #71550C2semidirect
9. #71550C2semidirect
10. #71544C2semidirect
11. #71544C2semidirect
12. #69429C2semidirect
13. #69427C2semidirect
14. #69413C2semidirect
15. #69411C2semidirect
72. #1438D3semidirect
187. C3⋊#95D4semidirect
1326. C3#15277semidirect

Maximal subgroups

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

subgroupindex
C22×#9392
C2×#52202
C2×#49532
C2×#49612
C2×#49582
C2×#49502
C3×#14382
#715502
#715442
#694292
#694272
#694132
#694112
#152773