Finite Group Databasebeta

← #10729036

Subgroups — #10729036

Order 768.

2638 conjugacy classes of subgroups.

The subgroup lattice has 1356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#884C211yesmaximal, characteristic
2C2×#4956C211yesmaximal, characteristic, complemented
3C2×#4956C211yesmaximal, characteristic, complemented
4C2×#4665C211yesmaximal, characteristic, complemented
5C2×#4665C211yesmaximal, characteristic, complemented
6C2×D3×#95C211yesmaximal, characteristic, complemented
7C3×#1440C211yesmaximal, characteristic, complemented
8#71550C211yesmaximal, characteristic, complemented
9#71550C211yesmaximal, characteristic, complemented
10#71549C211yesmaximal, characteristic, complemented
11#69429C211yesmaximal, characteristic, complemented
12#69429C211yesmaximal, characteristic, complemented
13(C2×D3)⋊#95C211yesmaximal, characteristic, complemented
14#69414C211yesmaximal, characteristic, complemented
15#69413C211yesmaximal, characteristic, complemented
16#14913—31nomaximal, Sylow
17C23×#67C2211yescharacteristic
18C23×#67C2211yescharacteristic
19C23×D12C2211yescharacteristic
20C23×C4×D3C2211yescharacteristic
21C23×C4×D3C2211yescharacteristic
22C23×C4×D3C2211yescharacteristic
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×C3×C22⋊C4C2211yescharacteristic
25C22×C3×C22⋊C4C2211yescharacteristic
26C22×#217C2211yescharacteristic
27C22×#217C2211yescharacteristic
28C22×(C2×D3)⋊C4C2211yescharacteristic
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×Dic3⋊C4C2211yescharacteristic
36C2×#884—24no—
37C2×#884—24no—
38C2×#884—24no—
39C2×C3×#95C2211yescharacteristic
40C2×C3×#95C2211yescharacteristic
41C2×C3×#95C2211yescharacteristic
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
54C2×C3⋊#95C2211yescharacteristic
55#4956—24no—
56#4956—24no—
57#4665—24no—
58#4665—24no—
59D3×#95—24no—
60C22×#121—31no—
61C2×#386—31no—
62C2×#386—31no—
63C2×#386—31no—
64C2×#386—31no—
65C22×#95—31no—
66#1442—31no—
67#1442—31no—
68#1440—31no—
69#1440—31no—
70#1440—31no—
71#1440D311yescharacteristic, complemented
72#1438—31no—
73#1438—31no—
74C22⋊#95—31no—
75C25×C3C2311yescharacteristic
76C24×D3C2311yescharacteristic
77C24×D3C2311yescharacteristic
78C23×C3×C4C2311yescharacteristic
79C23×C3×C4C2311yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C22×#67—22no—
85C22×#67—22no—
86C22×#67—22no—
87C22×#67—22no—
88C22×#67—22no—
89C22×#67—22no—
90C22×#67—22no—
91C22×#67—22no—
92C22×#67—22no—
93C22×#67—22no—
94C22×#67—22no—
95C22×#67—41no—
96C22×#67—41no—
97C22×#67D414yes—
98C23×Dic3C2311yescharacteristic
99C23×Dic3C2311yescharacteristic
100C23×Dic3C2311yescharacteristic
101C23×Dic3C2311yescharacteristic
102C23×Dic3C2311yescharacteristic
103C23×Dic3C2311yescharacteristic
104C22×D12—22no—
105C22×D12—22no—
106C22×D12—22no—
107C22×D12—22no—
108C22×D12—22no—
109C22×D12—22no—
110C22×D12D414yes—
111C22×C4×D3—22no—
112C22×C4×D3—22no—
113C22×C4×D3—22no—
114C22×C4×D3—22no—
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—41no—
123C22×C4×D3—41no—
124C22×C4×D3—41no—
125C22×C4×D3—41no—
126C22×C4×D3—41no—
127C22×C4×D3—41no—
128C22×C4×D3—41no—
129C22×C4×D3—41no—
130C22×C4×D3D414yes—
131C22×C4×D3D414yescomplemented
132C2×C3×C22⋊C4—22no—
133C2×C3×C22⋊C4—22no—
134C2×C3×C22⋊C4—22no—
135C2×C3×C22⋊C4—22no—
136C2×C3×C22⋊C4—22no—
137C2×C3×C22⋊C4—22no—
138C2×C3×C22⋊C4—41no—
139C2×C3×C22⋊C4—41no—
140C2×C3×C22⋊C4—41no—
141C2×#217—22no—
142C2×#217—22no—
143C2×#217—22no—
144C2×#217—41no—
145C2×#217—41no—
146C2×#217—41no—
147C2×(C2×D3)⋊C4—22no—
148C2×(C2×D3)⋊C4—22no—
149C2×(C2×D3)⋊C4—22no—
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—22no—
160C2×(C2×D3)⋊C4—22no—
161C2×(C2×D3)⋊C4—22no—
162C2×(C2×D3)⋊C4—41no—
163C2×(C2×D3)⋊C4—41no—
164C2×(C2×D3)⋊C4—41no—
165C2×(C2×D3)⋊C4—41no—
166C2×(C2×D3)⋊C4—41no—
167C2×(C2×D3)⋊C4—41no—
168C2×Dic3⋊C4—22no—
169C2×Dic3⋊C4—22no—
170C2×Dic3⋊C4—22no—
171#884—232no—
172C3×#95—22no—
173C3×#95—22no—
174C3×#95—22no—
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—22no—
185C3⋊#95—22no—
186C3⋊#95—22no—
187C3⋊#95—41no—
188C23×D4—31no—
189C23×D4—31no—
190C23×D4—31no—
191C24×C4—31no—
192C24×C4—31no—
193C24×C4—31no—
194C2×#121—64no—
195C2×#121—64no—
196C2×#121—64no—
197C22×C4⋊C4—31no—
198C22×C22⋊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⋊C4C2×D311yescharacteristic
208C22×C22⋊C4C2×D311yescharacteristic
209C22×C22⋊C4C2×D311yescharacteristic
210#386—64no—
211#386—64no—
212#386—64no—
213#386—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×#95—64no—
227C2×#95C2×D311yescharacteristic
228C2×#95C2×D311yescharacteristic
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×C3C2×D412yes—
246C24×C3C2411yescharacteristic
247C23×D3—21no—
248C23×D3—21no—
249C23×D3—21no—
250C23×D3—21no—
251C23×D3—21no—
252C23×D3—21no—
253C23×D3—21no—
254C23×D3—21no—
255C23×D3—21no—
256C23×D3—21no—
257C23×D3—21no—
258C23×D3—21no—
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×D3C2×D412yes—
270C23×D3C2×D412yes—
271C23×D3C2×D412yes—
272C23×D3C2×D412yes—
273C23×D3C2×D412yes—
274C23×D3#4112yes—
275C23×D3#4112yes—
276C23×D3#4112yes—
277C22×C3×C4—21no—
278C22×C3×C4—21no—
279C22×C3×C4—21no—
280C22×C3×C4—21no—
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×C4—21no—
314C22×C3×C4—21no—
315C22×C3×C4C2×D412yes—
316C22×C3×C4C2×D412yes—
317C22×C3×C4C2×D412yes—
318C22×C3×C4#4112yes—
319C2×#67—28no—
320C2×#67—28no—
321C2×#67—28no—
322C2×#67—28no—
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—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×Dic3C2×D412yes—
370C22×Dic3C2×D412yes—
371C22×Dic3C2×D412yes—
372C22×Dic3#4112yes—
373C22×Dic3#4112yes—
374C22×Dic3#4112yes—
375C2×D12—28no—
376C2×D12—28no—
377C2×D12—28no—
378C2×D12—44no—
379C2×D12—44no—
380C2×D12—44no—
381C2×D12—44no—
382C2×C4×D3—28no—
383C2×C4×D3—28no—
384C2×C4×D3—28no—
385C2×C4×D3—28no—
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—
393C2×C4×D3—44no—
394C2×C4×D3—44no—
395C2×C4×D3—44no—
396C2×C4×D3—44no—
397C2×C4×D3—44no—
398C2×C4×D3—44no—
399C2×C4×D3—44no—
400C2×C4×D3—44no—
401C2×C4×D3—44no—
402C2×C4×D3—44no—
403C3×C22⋊C4—28no—
404C3×C22⋊C4—44no—
405C3×C22⋊C4—44no—
406#217—44no—
407#217—44no—
408(C2×D3)⋊C4—28no—
409(C2×D3)⋊C4—44no—
410(C2×D3)⋊C4—44no—
411(C2×D3)⋊C4—44no—
412(C2×D3)⋊C4—44no—
413(C2×D3)⋊C4—44no—
414(C2×D3)⋊C4—44no—
415Dic3⋊C4—28no—
416C25—31no—
417C25—31no—
418C25C22×D311yescharacteristic
419C22×D4—34no—
420C22×D4—34no—
421C22×D4—62no—
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—62no—
432C22×D4—62no—
433C22×D4—62no—
434C22×D4—62no—
435C22×D4—62no—
436C22×D4—62no—
437C22×D4—62no—
438C22×D4—121no—
439C22×D4—121no—
440C23×C4—31no—
441C23×C4—31no—
442C23×C4—31no—
443C23×C4—31no—
444C23×C4—34no—
445C23×C4—34no—
446C23×C4—31no—
447C23×C4—31no—
448C23×C4—62no—
449C23×C4—62no—
450C23×C4—62no—
451C23×C4—62no—
452C23×C4—62no—
453C23×C4—62no—
454C23×C4—62no—
455C23×C4—62no—
456C23×C4—62no—
457C23×C4—62no—
458C23×C4—62no—
459C23×C4—121no—
460C23×C4—121no—
461C23×C4—121no—
462C23×C4—121no—
463C23×C4—121no—
464C23×C4—121no—
465C23×C4—121no—
466C23×C4—121no—
467C23×C4C22×D311yescharacteristic
468C23×C4C22×D311yescharacteristic
469C23×C4C22×D311yescharacteristic
470C23×C4C22×D311yescharacteristic
471C23×C4C22×D311yescharacteristic
472C23×C4C22×D311yescharacteristic
473#121—632no—
474C2×C4⋊C4—62no—
475C2×C4⋊C4—62no—
476C2×C4⋊C4—62no—
477C2×C22⋊C4—22no—
478C2×C22⋊C4—22no—
479C2×C22⋊C4—22no—
480C2×C22⋊C4—22no—
481C2×C22⋊C4—22no—
482C2×C22⋊C4—22no—
483C2×C22⋊C4—41no—
484C2×C22⋊C4—41no—
485C2×C22⋊C4—41no—
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—62no—
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—
511C2×C22⋊C4—121no—
512C2×C22⋊C4—121no—
513#95—22no—
514#95—22no—
515#95—22no—
516#95—41no—
517#95—62no—
518#95—62no—
519#95—62no—
520#95—62no—
521#95—62no—
522#95—62no—
523#95—62no—
524#95—62no—
525#95—62no—
526#95—62no—
527#95—62no—
528#95—121no—
529C23×C3—22no—
530C23×C3—22no—
531C23×C3—22no—
532C23×C3—22no—
533C23×C3—22no—
534C23×C3—22no—
535C23×C3—22no—
536C23×C3—41no—
537C23×C3—41no—
538C23×C3—41no—
539C23×C3—41no—
540C23×C3—41no—
541C23×C3—41no—
542C23×C3—41no—
543C23×C3—41no—
544C23×C3—41no—
545C23×C3—41no—
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×C3C22×D411yescharacteristic
565C23×C3C22×D411yescharacteristic
566C23×C3C22×D411yescharacteristic
567C23×C3C22×D411yescharacteristic
568C23×C3C2×#4111yescharacteristic
569C23×C3C2×#4111yescharacteristic
570C23×C3C2×#4111yescharacteristic
571C23×C3C2×#4111yescharacteristic
572C23×C3C2×#4111yescharacteristic
573C23×C3C2×#4111yescharacteristic
574C23×C3C2×#4111yescharacteristic
575C23×C3H(5,𝔽2)11yescharacteristic
576C23×C3H(5,𝔽2)11yescharacteristic
577C23×C3H(5,𝔽2)11yescharacteristic
578C23×C3H(5,𝔽2)11yescharacteristic
579C22×D3—22no—
580C22×D3—22no—
581C22×D3—22no—
582C22×D3—22no—
583C22×D3—22no—
584C22×D3—22no—
585C22×D3—22no—
586C22×D3—22no—
587C22×D3—22no—
588C22×D3—22no—
589C22×D3—22no—
590C22×D3—22no—
591C22×D3—22no—
592C22×D3—22no—
593C22×D3—22no—
594C22×D3—22no—
595C22×D3—22no—
596C22×D3—22no—
597C22×D3—22no—
598C22×D3—22no—
599C22×D3—22no—
600C22×D3—22no—
601C22×D3—22no—
602C22×D3—22no—
603C22×D3—22no—
604C22×D3—22no—
605C22×D3—22no—
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—41no—
615C22×D3—41no—
616C22×D3—41no—
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#12014yes—
643C22×D3#12114yes—
644C22×D3#12114yes—
645C22×D3#12114yes—
646C22×D3#12314yes—
647C22×D3#12314yes—
648C22×D3#12414yes—
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—22no—
656C2×C3×C4—22no—
657C2×C3×C4—22no—
658C2×C3×C4—22no—
659C2×C3×C4—22no—
660C2×C3×C4—22no—
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—
681C2×C3×C4—41no—
682C2×C3×C4—41no—
683C2×C3×C4—41no—
684C2×C3×C4—41no—
685C2×C3×C4—41no—
686C2×C3×C4—41no—
687C2×C3×C4—41no—
688C2×C3×C4—41no—
689C2×C3×C4—41no—
690C2×C3×C4—41no—
691#67—416no—
692#67—416no—
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—22no—
704C2×Dic3—22no—
705C2×Dic3—22no—
706C2×Dic3—22no—
707C2×Dic3—22no—
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—41no—
734C2×Dic3#12314yes—
735D12—416no—
736C4×D3—416no—
737C4×D3—416no—
738C4×D3—416no—
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—32no—
754C24—32no—
755C24—32no—
756C24—32no—
757C24—32no—
758C24—32no—
759C24—32no—
760C24—32no—
761C24—61no—
762C24—61no—
763C24—61no—
764C24—61no—
765C24—61no—
766C24—61no—
767C24—61no—
768C24—61no—
769C24—61no—
770C24—61no—
771C24—61no—
772C24—61no—
773C24—61no—
774C24—61no—
775C24—61no—
776C24—61no—
777C24—61no—
778C24—61no—
779C24—61no—
780C24—61no—
781C24—61no—
782C24—61no—
783C24D3×D412yes—
784C24C23×D311yescharacteristic
785C2×D4—68no—
786C2×D4—68no—
787C2×D4—68no—
788C2×D4—68no—
789C2×D4—68no—
790C2×D4—68no—
791C2×D4—68no—
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—
801C2×D4—124no—
802C2×D4—124no—
803C2×D4—124no—
804C2×D4—124no—
805C2×D4—124no—
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—21no—
834C22×C4—21no—
835C22×C4—21no—
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—32no—
845C22×C4—32no—
846C22×C4—32no—
847C22×C4—32no—
848C22×C4—32no—
849C22×C4—32no—
850C22×C4—68no—
851C22×C4—68no—
852C22×C4—68no—
853C22×C4—68no—
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—61no—
884C22×C4—61no—
885C22×C4—61no—
886C22×C4—61no—
887C22×C4—61no—
888C22×C4—61no—
889C22×C4—61no—
890C22×C4—124no—
891C22×C4—124no—
892C22×C4—124no—
893C22×C4—124no—
894C22×C4—124no—
895C22×C4—124no—
896C22×C4—124no—
897C22×C4—124no—
898C22×C4—124no—
899C22×C4—124no—
900C22×C4—124no—
901C22×C4—124no—
902C22×C4—124no—
903C22×C4—124no—
904C22×C4—124no—
905C22×C4—124no—
906C22×C4—124no—
907C22×C4#23512yes—
908C22×C4D3×D412yes—
909C22×C4D3×D412yes—
910C22×C4D3×D412yes—
911C4⋊C4—68no—
912C22⋊C4—28no—
913C22⋊C4—44no—
914C22⋊C4—44no—
915C22⋊C4—68no—
916C22⋊C4—124no—
917C22⋊C4—124no—
918C22⋊C4—124no—
919C22⋊C4—124no—
920C22⋊C4—124no—
921C22⋊C4—124no—
922C22⋊C4—124no—
923C22⋊C4—124no—
924C22×C3—42no—
925C22×C3—42no—
926C22×C3—42no—
927C22×C3—42no—
928C22×C3—42no—
929C22×C3—42no—
930C22×C3—42no—
931C22×C3—81no—
932C22×C3—81no—
933C22×C3—81no—
934C22×C3—81no—
935C22×C3—81no—
936C22×C3—81no—
937C22×C3—81no—
938C22×C3—81no—
939C22×C3C2×#12011yescharacteristic
940C22×C3C2×#12111yescharacteristic
941C22×C3C2×#12111yescharacteristic
942C22×C3C2×#12111yescharacteristic
943C22×C3C2×#12311yescharacteristic
944C22×C3C2×#12311yescharacteristic
945C22×C3C2×#12311yescharacteristic
946C22×C3#52511yescharacteristic
947C22×C3C2×#12411yescharacteristic
948C22×C3#52911yescharacteristic
949C22×C3#52911yescharacteristic
950C22×C3#53211yescharacteristic
951C22×C3#53211yescharacteristic
952C22×C3#53411yescharacteristic
953C22×C3#53411yescharacteristic
954C22×C3#53411yescharacteristic
955C22×C3#53511yescharacteristic
956C22×C3#53811yescharacteristic
957C22×C3#53811yescharacteristic
958C22×C3#54611yescharacteristic
959C22×C3#54611yescharacteristic
960C22×C3#54611yescharacteristic
961C22×C3#54611yescharacteristic
962C22×C3#54611yescharacteristic
963C22×C3#54611yescharacteristic
964C22×C3#54611yescharacteristic
965C22×C3#54611yescharacteristic
966C22×C3#55311yescharacteristic
967C22×C3#55311yescharacteristic
968C22×C3#55311yescharacteristic
969C22×C3#55311yescharacteristic
970C22×C3#55311yescharacteristic
971C22×C3#55311yescharacteristic
972C22×C3#55311yescharacteristic
973C22×C3#55311yescharacteristic
974C2×D3—24no—
975C2×D3—24no—
976C2×D3—24no—
977C2×D3—24no—
978C2×D3—24no—
979C2×D3—24no—
980C2×D3—24no—
981C2×D3—24no—
982C2×D3—24no—
983C2×D3—24no—
984C2×D3—24no—
985C2×D3—24no—
986C2×D3—24no—
987C2×D3—24no—
988C2×D3—42no—
989C2×D3—42no—
990C2×D3—42no—
991C2×D3—42no—
992C2×D3—42no—
993C2×D3—42no—
994C2×D3—42no—
995C2×D3—81no—
996C2×D3—81no—
997C2×D3—81no—
998C2×D3—81no—
999C2×D3—81no—
1000C2×D3—81no—
1001C2×D3—81no—
1002C2×D3—81no—
1003C2×D3#39418yes—
1004C3×C4—42no—
1005C3×C4—42no—
1006C3×C4—42no—
1007C3×C4—42no—
1008C3×C4—81no—
1009C3×C4—81no—
1010Dic3—24no—
1011Dic3—42no—
1012Dic3—42no—
1013Dic3—42no—
1014Dic3—81no—
1015Dic3—81no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—22no—
1021C23—22no—
1022C23—22no—
1023C23—34no—
1024C23—34no—
1025C23—34no—
1026C23—34no—
1027C23—34no—
1028C23—34no—
1029C23—34no—
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—62no—
1059C23—62no—
1060C23—62no—
1061C23—62no—
1062C23—62no—
1063C23—62no—
1064C23—62no—
1065C23—62no—
1066C23—62no—
1067C23—62no—
1068C23—62no—
1069C23—62no—
1070C23—62no—
1071C23—62no—
1072C23—62no—
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—62no—
1092C23—62no—
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—121no—
1111C23—121no—
1112C23—121no—
1113C23—121no—
1114C23—121no—
1115C23—121no—
1116C23—121no—
1117C23—121no—
1118C23—121no—
1119C23—121no—
1120C23—121no—
1121C23C2×#23511yescharacteristic
1122C23C2×D3×D411yescharacteristic
1123C23C2×D3×D411yescharacteristic
1124C23C2×D3×D411yescharacteristic
1125C23C2×D3×D411yescharacteristic
1126C23#100411yescharacteristic
1127C23#100411yescharacteristic
1128C23D3×#4111yescharacteristic
1129C23D3×#4111yescharacteristic
1130C23D3×#4111yescharacteristic
1131C23D3×#4111yescharacteristic
1132C23D3×#4111yescharacteristic
1133C23D3×#4111yescharacteristic
1134C23#100911yescharacteristic
1135C23#100911yescharacteristic
1136D4—1216no—
1137D4—1216no—
1138D4—1216no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—34no—
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—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—62no—
1183C2×C4—62no—
1184C2×C4—62no—
1185C2×C4—62no—
1186C2×C4—62no—
1187C2×C4—62no—
1188C2×C4—62no—
1189C2×C4—62no—
1190C2×C4—62no—
1191C2×C4—62no—
1192C2×C4—62no—
1193C2×C4—62no—
1194C2×C4—62no—
1195C2×C4—62no—
1196C2×C4—62no—
1197C2×C4—1216no—
1198C2×C4—1216no—
1199C2×C4—1216no—
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×C4—121no—
1217C2×C4—121no—
1218C2×C4—121no—
1219C2×C4—121no—
1220C2×C4—121no—
1221C2×C4—121no—
1222C2×C4—121no—
1223C2×C4—121no—
1224C2×C4—121no—
1225C2×C4—121no—
1226C2×C3—82no—
1227C2×C3C2×#39411yescharacteristic
1228C2×C3#240411yescharacteristic
1229C2×C3#240511yescharacteristic
1230C2×C3#244411yescharacteristic
1231C2×C3#244411yescharacteristic
1232C2×C3#244411yescharacteristic
1233C2×C3#244411yescharacteristic
1234C2×C3#250411yescharacteristic
1235C2×C3#254311yescharacteristic
1236C2×C3#254311yescharacteristic
1237C2×C3#254311yescharacteristic
1238C2×C3#254311yescharacteristic
1239C2×C3#259111yescharacteristic
1240C2×C3#261711yescharacteristic
1241C2×C3#285411yescharacteristic
1242D3—28no—
1243D3—82no—
1244C22—38no—
1245C22—42no—
1246C22—42no—
1247C22—42no—
1248C22—42no—
1249C22—42no—
1250C22—42no—
1251C22—42no—
1252C22—64no—
1253C22—64no—
1254C22—64no—
1255C22—64no—
1256C22—64no—
1257C22—64no—
1258C22—64no—
1259C22—64no—
1260C22—64no—
1261C22—64no—
1262C22—64no—
1263C22—64no—
1264C22—64no—
1265C22—64no—
1266C22—81no—
1267C22—81no—
1268C22—81no—
1269C22—81no—
1270C22—81no—
1271C22—81no—
1272C22—81no—
1273C22—81no—
1274C22—122no—
1275C22—122no—
1276C22—122no—
1277C22—122no—
1278C22—122no—
1279C22—122no—
1280C22—122no—
1281C22—241no—
1282C22—241no—
1283C22—241no—
1284C22—241no—
1285C22—241no—
1286C22—241no—
1287C22—241no—
1288C22—241no—
1289C22#549011yescharacteristic
1290C22#552811yescharacteristic
1291C22#553011yescharacteristic
1292C22#554711yescharacteristic
1293C22#554811yescharacteristic
1294C22#555011yescharacteristic
1295C22#555811yescharacteristic
1296C22D3×#12011yescharacteristic
1297C22#558911yescharacteristic
1298C22D3×#12111yescharacteristic
1299C22D3×#12111yescharacteristic
1300C22D3×#12111yescharacteristic
1301C22#560511yescharacteristic
1302C22#560711yescharacteristic
1303C22#561011yescharacteristic
1304C22#561211yescharacteristic
1305C22#561211yescharacteristic
1306C22D3×#12311yescharacteristic
1307C22D3×#12311yescharacteristic
1308C22D3×#12311yescharacteristic
1309C22#565311yescharacteristic
1310C22#565411yescharacteristic
1311C22#565411yescharacteristic
1312C22#565711yescharacteristic
1313C22#566111yescharacteristic
1314C22#566111yescharacteristic
1315C22#566111yescharacteristic
1316C22#566811yescharacteristic
1317C22D3×#12411yescharacteristic
1318C22#567611yescharacteristic
1319C22#567811yescharacteristic
1320C22#570611yescharacteristic
1321C22#570911yescharacteristic
1322C22#570911yescharacteristic
1323C22#570911yescharacteristic
1324C4—42no—
1325C4—42no—
1326C4—42no—
1327C4—42no—
1328C4—64no—
1329C4—81no—
1330C4—81no—
1331C4—122no—
1332C4—122no—
1333C4—122no—
1334C4—241no—
1335C4—241no—
1336C3#1491311yescharacteristic, complemented, Sylow
1337C2—68no—
1338C2—82no—
1339C2—242no—
1340C2#7412811yescharacteristic
1341C2#7488611yescharacteristic
1342C2#7490211yescharacteristic
1343C2#7584911yescharacteristic
1344C2#7588211yescharacteristic
1345C2#7589411yescharacteristic
1346C2#7596011yescharacteristic
1347C2D3×#39411yescharacteristic
1348C2#7710611yescharacteristic
1349C2#7712011yescharacteristic
1350C2#7712311yescharacteristic
1351C2#7749211yescharacteristic
1352C2#7767411yescharacteristic
1353C2#7767511yescharacteristic
1354C2#7768211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1440C2
prime radicalC22×#884C2
hypercenter#1440D3
hypocenterC3#14913
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1440

Complements

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

NH ≅ G/Ntype
2. C2×#4956C2semidirect
3. C2×#4956C2semidirect
4. C2×#4665C2semidirect
5. C2×#4665C2semidirect
6. C2×D3×#95C2semidirect
7. C3×#1440C2semidirect
8. #71550C2semidirect
9. #71550C2semidirect
10. #71549C2semidirect
11. #69429C2semidirect
12. #69429C2semidirect
13. (C2×D3)⋊#95C2semidirect
14. #69414C2semidirect
15. #69413C2semidirect
71. #1440D3semidirect
131. C22×C4×D3D4semidirect
1336. C3#14913semidirect

Maximal subgroups

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

subgroupindex
C22×#8842
C2×#49562
C2×#46652
C2×D3×#952
C3×#14402
#715502
#715492
#694292
(C2×D3)⋊#952
#694142
#694132
#149133