Finite Group Databasebeta

← #10729170

Subgroups — #10729170

Order 768.

1802 conjugacy classes of subgroups.

The subgroup lattice has 1144 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#388C211yesmaximal, characteristic, complemented
2C2×#4956C211yesmaximal, characteristic
3C2×#4937C211yesmaximal, characteristic, complemented
4C2×C4×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
5#71570C211yesmaximal, characteristic, complemented
6#71567C211yesmaximal, characteristic, complemented
7#71550C211yesmaximal, characteristic
8#71550C211yesmaximal, characteristic
9#71549C211yesmaximal, characteristic, complemented
10#71547C211yesmaximal, characteristic, complemented
11#71545C211yesmaximal, characteristic, complemented
12#69428C211yesmaximal, characteristic, complemented
13(C2×D3)⋊#95C211yesmaximal, characteristic, complemented
14#69418C211yesmaximal, characteristic, complemented
15#69406C211yesmaximal, characteristic, complemented
16#14924—31nomaximal, Sylow
17C23×#67C2211yescharacteristic
18C23×C4×D3C2211yescharacteristic
19C22×C3×C4⋊C4C2211yescharacteristic
20C22×C3×C22⋊C4C2211yescharacteristic
21C22×C3×C22⋊C4C2211yescharacteristic
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×C3×C42C2211yescharacteristic
24C22×#217C2211yescharacteristic
25C22×#217C2211yescharacteristic
26C22×#217C2211yescharacteristic
27C22×(C2×D3)⋊C4C2211yescharacteristic
28C22×(C2×D3)⋊C4C2211yescharacteristic
29C22×(C2×D3)⋊C4C2211yescharacteristic
30C22×(C2×D3)⋊C4C2211yescharacteristic
31C22×(C2×D3)⋊C4C2211yescharacteristic
32C22×Dic3⋊C4C2211yescharacteristic
33C22×C4×Dic3C2211yescharacteristic
34C3×#388—24no—
35C2×C3×#95C2211yescharacteristic
36C2×C3×#95C2211yescharacteristic
37C2×C3⋊#95C2211yescharacteristic
38C2×C3⋊#95C2211yescharacteristic
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
53#4956—24no—
54C4×(C2×D3)⋊C4—24no—
55#4937—24no—
56C2×#388D311yescharacteristic, complemented
57C2×#386—31no—
58C2×#383—31no—
59C2×C4×C22⋊C4—31no—
60#1443—31no—
61#1442—31no—
62#1440—31no—
63#1439—31no—
64#1439—31no—
65#1439—31no—
66#1438—31no—
67#1438—31no—
68#1437—31no—
69#1436—31no—
70C22⋊#95—31no—
71C25×C3C2311yescharacteristic
72C24×D3C2311yescharacteristic
73C23×C3×C4C2311yescharacteristic
74C23×C3×C4C2311yescharacteristic
75C23×C3×C4C2311yescharacteristic
76C23×C3×C4C2311yescharacteristic
77C23×C3×C4C2311yescharacteristic
78C23×C3×C4C2311yescharacteristic
79C22×#67—22no—
80C22×#67—22no—
81C22×#67—22no—
82C22×#67—22no—
83C22×#67—22no—
84C22×#67—41no—
85C22×#67—41no—
86C23×Dic3C2311yescharacteristic
87C23×Dic3C2311yescharacteristic
88C23×Dic3C2311yescharacteristic
89C23×Dic3C2311yescharacteristic
90C23×Dic3C2311yescharacteristic
91C23×Dic3C2311yescharacteristic
92C23×Dic3C2311yescharacteristic
93C22×C4×D3—22no—
94C22×C4×D3—22no—
95C22×C4×D3—22no—
96C22×C4×D3—22no—
97C22×C4×D3—22no—
98C22×C4×D3—41no—
99C22×C4×D3—41no—
100C2×C3×C4⋊C4—22no—
101C2×C3×C4⋊C4—41no—
102C2×C3×C4⋊C4—41no—
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⋊C4—22no—
109C2×C3×C22⋊C4—22no—
110C2×C3×C22⋊C4—41no—
111C2×C3×C22⋊C4—41no—
112C2×C3×C42—22no—
113C2×C3×C42—22no—
114C2×C3×C42D414yescomplemented
115C2×#217—22no—
116C2×#217—22no—
117C2×#217—22no—
118C2×#217—22no—
119C2×#217—22no—
120C2×#217—41no—
121C2×#217—41no—
122C2×#217—41no—
123C2×#217—41no—
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—41no—
136C2×(C2×D3)⋊C4—41no—
137C2×(C2×D3)⋊C4—41no—
138C2×(C2×D3)⋊C4—41no—
139C2×Dic3⋊C4—22no—
140C2×Dic3⋊C4—41no—
141C2×Dic3⋊C4—41no—
142C2×C4×Dic3—22no—
143C2×C4×Dic3—41no—
144C2×C4×Dic3—41no—
145C3×#95—22no—
146C3×#95—22no—
147C3⋊#95—22no—
148C3⋊#95—22no—
149C3⋊#95—22no—
150C3⋊#95—22no—
151C3⋊#95—22no—
152C3⋊#95—22no—
153C3⋊#95—22no—
154C3⋊#95—22no—
155C3⋊#95—22no—
156C3⋊#95—22no—
157C3⋊#95—22no—
158C3⋊#95—41no—
159C3⋊#95—41no—
160C3⋊#95—41no—
161C3⋊#95—41no—
162C3⋊#95D414yes—
163C23×D4—31no—
164C24×C4—31no—
165C22×C4⋊C4—31no—
166C22×C4⋊C4C2×D311yescharacteristic
167C22×C22⋊C4—31no—
168C22×C22⋊C4—31no—
169C22×C22⋊C4—31no—
170C22×C22⋊C4—31no—
171C22×C22⋊C4—31no—
172C22×C22⋊C4—31no—
173C22×C22⋊C4—31no—
174C22×C22⋊C4—31no—
175C22×C22⋊C4C2×D311yescharacteristic
176C22×C22⋊C4C2×D311yescharacteristic
177C22×C22⋊C4C2×D311yescharacteristic
178C22×C42—31no—
179C22×C42C2×D311yescharacteristic
180#388—24no—
181#386—64no—
182#383—64no—
183C4×C22⋊C4—64no—
184C2×#95—31no—
185C2×#95—31no—
186C2×#95—31no—
187C2×#95—31no—
188C2×#95—31no—
189C2×#95—31no—
190C2×#95—31no—
191C2×#95—31no—
192C2×#95—31no—
193C2×#95—31no—
194C2×#95—31no—
195C2×#95—31no—
196C2×#95—31no—
197C2×#95—31no—
198C2×#95—31no—
199C2×#95—31no—
200C2×#95C2×D311yescharacteristic
201C2×#95C2×D311yescharacteristic
202C24×C3—21no—
203C24×C3—21no—
204C24×C3—21no—
205C24×C3—21no—
206C24×C3—21no—
207C24×C3—21no—
208C24×C3—21no—
209C24×C3—21no—
210C24×C3—21no—
211C24×C3—21no—
212C24×C3—21no—
213C24×C3—21no—
214C24×C3—21no—
215C24×C3—21no—
216C24×C3#4112yes—
217C24×C3C2411yescharacteristic
218C23×D3—21no—
219C23×D3—21no—
220C23×D3—21no—
221C23×D3—21no—
222C23×D3—21no—
223C23×D3—21no—
224C23×D3—21no—
225C23×D3—21no—
226C23×D3—21no—
227C23×D3—21no—
228C23×D3—21no—
229C23×D3—21no—
230C23×D3#4112yes—
231C23×D3#4112yes—
232C23×D3#4112yes—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
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—21no—
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×C4C2×D412yes—
270C22×C3×C4C2×D412yes—
271C22×C3×C4C2×D412yes—
272C22×C3×C4C2×D412yes—
273C22×C3×C4#4112yes—
274C22×C3×C4#4112yes—
275C2×#67—28no—
276C2×#67—44no—
277C2×#67—44no—
278C2×#67—44no—
279C2×#67—44no—
280C2×#67—44no—
281C2×#67—44no—
282C22×Dic3—21no—
283C22×Dic3—21no—
284C22×Dic3—21no—
285C22×Dic3—21no—
286C22×Dic3—21no—
287C22×Dic3—21no—
288C22×Dic3—21no—
289C22×Dic3—21no—
290C22×Dic3—21no—
291C22×Dic3—21no—
292C22×Dic3—21no—
293C22×Dic3—21no—
294C22×Dic3—21no—
295C22×Dic3—21no—
296C22×Dic3—21no—
297C22×Dic3—21no—
298C22×Dic3—21no—
299C22×Dic3—21no—
300C22×Dic3—21no—
301C22×Dic3—21no—
302C22×Dic3—21no—
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×Dic3C2×D412yes—
327C22×Dic3C2×D412yes—
328C22×Dic3#4112yes—
329C22×Dic3#4112yes—
330C22×Dic3#4112yes—
331C2×C4×D3—28no—
332C2×C4×D3—44no—
333C2×C4×D3—44no—
334C2×C4×D3—44no—
335C2×C4×D3—44no—
336C2×C4×D3—44no—
337C2×C4×D3—44no—
338C3×C4⋊C4—44no—
339C3×C22⋊C4—28no—
340C3×C22⋊C4—44no—
341C3×C22⋊C4—44no—
342C3×C42—28no—
343#217—44no—
344#217—44no—
345#217—44no—
346(C2×D3)⋊C4—28no—
347(C2×D3)⋊C4—28no—
348(C2×D3)⋊C4—44no—
349(C2×D3)⋊C4—44no—
350(C2×D3)⋊C4—44no—
351Dic3⋊C4—44no—
352C4×Dic3—44no—
353C25—31no—
354C25C22×D311yescharacteristic
355C22×D4—62no—
356C22×D4—62no—
357C22×D4—62no—
358C22×D4—62no—
359C22×D4—62no—
360C22×D4—121no—
361C22×D4—121no—
362C23×C4—31no—
363C23×C4—31no—
364C23×C4—31no—
365C23×C4—31no—
366C23×C4—31no—
367C23×C4—31no—
368C23×C4—31no—
369C23×C4—62no—
370C23×C4—62no—
371C23×C4—62no—
372C23×C4—62no—
373C23×C4—62no—
374C23×C4—121no—
375C23×C4—121no—
376C23×C4C22×D311yescharacteristic
377C23×C4C22×D311yescharacteristic
378C23×C4C22×D311yescharacteristic
379C23×C4C22×D311yescharacteristic
380C23×C4C22×D311yescharacteristic
381C23×C4C22×D311yescharacteristic
382C2×C4⋊C4—22no—
383C2×C4⋊C4—41no—
384C2×C4⋊C4—41no—
385C2×C4⋊C4—62no—
386C2×C4⋊C4—121no—
387C2×C4⋊C4—121no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—22no—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—41no—
396C2×C22⋊C4—41no—
397C2×C22⋊C4—62no—
398C2×C22⋊C4—62no—
399C2×C22⋊C4—62no—
400C2×C22⋊C4—62no—
401C2×C22⋊C4—62no—
402C2×C22⋊C4—62no—
403C2×C22⋊C4—62no—
404C2×C22⋊C4—62no—
405C2×C22⋊C4—62no—
406C2×C22⋊C4—62no—
407C2×C22⋊C4—62no—
408C2×C22⋊C4—62no—
409C2×C22⋊C4—62no—
410C2×C22⋊C4—62no—
411C2×C22⋊C4—62no—
412C2×C22⋊C4—62no—
413C2×C22⋊C4—121no—
414C2×C22⋊C4—121no—
415C2×C22⋊C4—121no—
416C2×C22⋊C4—121no—
417C2×C22⋊C4—121no—
418C2×C22⋊C4—121no—
419C2×C22⋊C4—121no—
420C2×C22⋊C4—121no—
421C2×C42—22no—
422C2×C42—22no—
423C2×C42—62no—
424C2×C42—121no—
425C2×C42—121no—
426C2×C42#6714yescomplemented
427#95—22no—
428#95—22no—
429#95—34no—
430#95—62no—
431#95—62no—
432#95—62no—
433#95—62no—
434#95—62no—
435#95—62no—
436#95—62no—
437#95—62no—
438#95—62no—
439#95—62no—
440#95—62no—
441#95—121no—
442#95—121no—
443#95—121no—
444#95—121no—
445C23×C3—22no—
446C23×C3—22no—
447C23×C3—22no—
448C23×C3—22no—
449C23×C3—22no—
450C23×C3—22no—
451C23×C3—22no—
452C23×C3—41no—
453C23×C3—41no—
454C23×C3—41no—
455C23×C3—41no—
456C23×C3—41no—
457C23×C3—41no—
458C23×C3—41no—
459C23×C3—41no—
460C23×C3—41no—
461C23×C3—41no—
462C23×C3—41no—
463C23×C3—41no—
464C23×C3—41no—
465C23×C3—41no—
466C23×C3—41no—
467C23×C3—41no—
468C23×C3—41no—
469C23×C3—41no—
470C23×C3—41no—
471C23×C3—41no—
472C23×C3—41no—
473C23×C3—41no—
474C23×C3—41no—
475C23×C3—41no—
476C23×C3—41no—
477C23×C3—41no—
478C23×C3—41no—
479C23×C3—41no—
480C23×C3C22×D411yescharacteristic
481C23×C3C22×D411yescharacteristic
482C23×C3C2×#4111yescharacteristic
483C23×C3C2×#4111yescharacteristic
484C23×C3C2×#4111yescharacteristic
485C23×C3C2×#4111yescharacteristic
486C23×C3C2×#4111yescharacteristic
487C23×C3C2×#4111yescharacteristic
488C23×C3C2×#4111yescharacteristic
489C23×C3C2×#4111yescharacteristic
490C23×C3C2×#4111yescharacteristic
491C23×C3H(5,𝔽2)11yescharacteristic
492C23×C3H(5,𝔽2)11yescharacteristic
493C23×C3H(5,𝔽2)11yescharacteristic
494C23×C3H(5,𝔽2)11yescharacteristic
495C22×D3—22no—
496C22×D3—22no—
497C22×D3—22no—
498C22×D3—22no—
499C22×D3—22no—
500C22×D3—22no—
501C22×D3—22no—
502C22×D3—22no—
503C22×D3—22no—
504C22×D3—22no—
505C22×D3—22no—
506C22×D3—22no—
507C22×D3—22no—
508C22×D3—22no—
509C22×D3—22no—
510C22×D3—22no—
511C22×D3—22no—
512C22×D3—22no—
513C22×D3—41no—
514C22×D3—41no—
515C22×D3—41no—
516C22×D3—41no—
517C22×D3—41no—
518C22×D3—41no—
519C22×D3—41no—
520C22×D3—41no—
521C22×D3—41no—
522C22×D3—41no—
523C22×D3—41no—
524C22×D3—41no—
525C22×D3—41no—
526C22×D3—41no—
527C22×D3—41no—
528C22×D3—41no—
529C22×D3#12614yes—
530C2×C3×C4—22no—
531C2×C3×C4—22no—
532C2×C3×C4—22no—
533C2×C3×C4—22no—
534C2×C3×C4—22no—
535C2×C3×C4—22no—
536C2×C3×C4—22no—
537C2×C3×C4—22no—
538C2×C3×C4—22no—
539C2×C3×C4—22no—
540C2×C3×C4—22no—
541C2×C3×C4—22no—
542C2×C3×C4—22no—
543C2×C3×C4—22no—
544C2×C3×C4—22no—
545C2×C3×C4—41no—
546C2×C3×C4—41no—
547C2×C3×C4—41no—
548C2×C3×C4—41no—
549C2×C3×C4—41no—
550C2×C3×C4—41no—
551C2×C3×C4—41no—
552C2×C3×C4—41no—
553C2×C3×C4—41no—
554C2×C3×C4—41no—
555C2×C3×C4—41no—
556C2×C3×C4—41no—
557C2×C3×C4—41no—
558C2×C3×C4—41no—
559C2×C3×C4—41no—
560C2×C3×C4—41no—
561C2×C3×C4—41no—
562C2×C3×C4—41no—
563C2×C3×C4—41no—
564C2×C3×C4—41no—
565C2×C3×C4—41no—
566C2×C3×C4—41no—
567C2×C3×C4—41no—
568C2×C3×C4—41no—
569C2×C3×C4—41no—
570C2×C3×C4—41no—
571C2×C3×C4#12114yes—
572#67—416no—
573C2×Dic3—22no—
574C2×Dic3—22no—
575C2×Dic3—22no—
576C2×Dic3—22no—
577C2×Dic3—22no—
578C2×Dic3—22no—
579C2×Dic3—22no—
580C2×Dic3—22no—
581C2×Dic3—22no—
582C2×Dic3—22no—
583C2×Dic3—22no—
584C2×Dic3—22no—
585C2×Dic3—22no—
586C2×Dic3—22no—
587C2×Dic3—22no—
588C2×Dic3—41no—
589C2×Dic3—41no—
590C2×Dic3—41no—
591C2×Dic3—41no—
592C2×Dic3—41no—
593C2×Dic3—41no—
594C2×Dic3—41no—
595C2×Dic3—41no—
596C2×Dic3—41no—
597C2×Dic3—41no—
598C2×Dic3—41no—
599C2×Dic3—41no—
600C2×Dic3—41no—
601C2×Dic3—41no—
602C2×Dic3—41no—
603C2×Dic3—41no—
604C2×Dic3—41no—
605C2×Dic3—41no—
606C2×Dic3—41no—
607C2×Dic3—41no—
608C2×Dic3—41no—
609C2×Dic3—41no—
610C2×Dic3—41no—
611C2×Dic3—41no—
612C2×Dic3—41no—
613C2×Dic3—41no—
614C2×Dic3—41no—
615C2×Dic3—41no—
616C2×Dic3—41no—
617C2×Dic3—41no—
618C2×Dic3—41no—
619C2×Dic3—41no—
620C2×Dic3—41no—
621C2×Dic3—41no—
622C4×D3—416no—
623C24—21no—
624C24—21no—
625C24—21no—
626C24—21no—
627C24—21no—
628C24—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—32no—
638C24—32no—
639C24—32no—
640C24—61no—
641C24—61no—
642C24—61no—
643C24—61no—
644C24—61no—
645C24—61no—
646C24—61no—
647C24—61no—
648C24—61no—
649C24—61no—
650C24—61no—
651C24—61no—
652C24#23512yes—
653C24C23×D311yescharacteristic
654C2×D4—68no—
655C2×D4—124no—
656C2×D4—124no—
657C2×D4—124no—
658C2×D4—124no—
659C2×D4—124no—
660C2×D4—124no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
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—21no—
696C22×C4—21no—
697C22×C4—32no—
698C22×C4—32no—
699C22×C4—32no—
700C22×C4—32no—
701C22×C4—32no—
702C22×C4—68no—
703C22×C4—61no—
704C22×C4—61no—
705C22×C4—61no—
706C22×C4—61no—
707C22×C4—61no—
708C22×C4—61no—
709C22×C4—61no—
710C22×C4—61no—
711C22×C4—61no—
712C22×C4—61no—
713C22×C4—61no—
714C22×C4—61no—
715C22×C4—61no—
716C22×C4—61no—
717C22×C4—61no—
718C22×C4—61no—
719C22×C4—61no—
720C22×C4—61no—
721C22×C4—61no—
722C22×C4—61no—
723C22×C4—61no—
724C22×C4—61no—
725C22×C4—61no—
726C22×C4—61no—
727C22×C4—61no—
728C22×C4—61no—
729C22×C4—61no—
730C22×C4—61no—
731C22×C4—61no—
732C22×C4—61no—
733C22×C4—61no—
734C22×C4—61no—
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—124no—
748C22×C4—124no—
749C22×C4—124no—
750C22×C4—124no—
751C22×C4—124no—
752C22×C4—124no—
753C22×C4#23512yes—
754C22×C4D3×D412yes—
755C22×C4#23712yes—
756C22×C4C2×#6712yes—
757C22×C4C2×#6712yes—
758C22×C4C2×#6712yes—
759C4⋊C4—44no—
760C4⋊C4—124no—
761C22⋊C4—28no—
762C22⋊C4—44no—
763C22⋊C4—44no—
764C22⋊C4—68no—
765C22⋊C4—68no—
766C22⋊C4—124no—
767C22⋊C4—124no—
768C22⋊C4—124no—
769C22⋊C4—124no—
770C22⋊C4—124no—
771C22⋊C4—124no—
772C42—28no—
773C42—124no—
774C22×C3—42no—
775C22×C3—42no—
776C22×C3—42no—
777C22×C3—42no—
778C22×C3—42no—
779C22×C3—42no—
780C22×C3—42no—
781C22×C3—81no—
782C22×C3—81no—
783C22×C3—81no—
784C22×C3—81no—
785C22×C3—81no—
786C22×C3—81no—
787C22×C3—81no—
788C22×C3—81no—
789C22×C3C2×#12111yescharacteristic
790C22×C3#52511yescharacteristic
791C22×C3#52511yescharacteristic
792C22×C3#52511yescharacteristic
793C22×C3#52511yescharacteristic
794C22×C3#52511yescharacteristic
795C22×C3C2×#12611yescharacteristic
796C22×C3#52911yescharacteristic
797C22×C3#52911yescharacteristic
798C22×C3#52911yescharacteristic
799C22×C3#52911yescharacteristic
800C22×C3#52911yescharacteristic
801C22×C3#53211yescharacteristic
802C22×C3#53511yescharacteristic
803C22×C3#53511yescharacteristic
804C22×C3#53811yescharacteristic
805C22×C3#53811yescharacteristic
806C22×C3#53811yescharacteristic
807C22×C3#53811yescharacteristic
808C22×C3#54611yescharacteristic
809C22×C3#54611yescharacteristic
810C22×C3#54611yescharacteristic
811C22×C3#55011yescharacteristic
812C22×C3#55111yescharacteristic
813C22×C3#55111yescharacteristic
814C22×C3#55111yescharacteristic
815C22×C3#55111yescharacteristic
816C22×C3#55111yescharacteristic
817C22×C3#55111yescharacteristic
818C22×C3#55311yescharacteristic
819C22×C3#55311yescharacteristic
820C22×C3#55311yescharacteristic
821C22×C3#55311yescharacteristic
822C22×C3#55311yescharacteristic
823C22×C3#55511yescharacteristic
824C2×D3—24no—
825C2×D3—24no—
826C2×D3—24no—
827C2×D3—42no—
828C2×D3—42no—
829C2×D3—42no—
830C2×D3—42no—
831C2×D3—42no—
832C2×D3—42no—
833C2×D3—42no—
834C2×D3—42no—
835C2×D3—42no—
836C2×D3—42no—
837C2×D3—42no—
838C2×D3—42no—
839C3×C4—24no—
840C3×C4—42no—
841C3×C4—42no—
842C3×C4—42no—
843C3×C4—81no—
844C3×C4—81no—
845Dic3—42no—
846Dic3—42no—
847Dic3—42no—
848Dic3—42no—
849Dic3—42no—
850Dic3—81no—
851Dic3—81no—
852C23—22no—
853C23—22no—
854C23—22no—
855C23—22no—
856C23—22no—
857C23—22no—
858C23—22no—
859C23—34no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23—41no—
868C23—41no—
869C23—41no—
870C23—41no—
871C23—41no—
872C23—41no—
873C23—41no—
874C23—41no—
875C23—41no—
876C23—41no—
877C23—41no—
878C23—41no—
879C23—41no—
880C23—41no—
881C23—41no—
882C23—41no—
883C23—41no—
884C23—41no—
885C23—41no—
886C23—41no—
887C23—41no—
888C23—62no—
889C23—62no—
890C23—62no—
891C23—62no—
892C23—62no—
893C23—62no—
894C23—62no—
895C23—62no—
896C23—62no—
897C23—62no—
898C23—62no—
899C23—62no—
900C23—62no—
901C23—62no—
902C23—62no—
903C23—62no—
904C23—62no—
905C23—62no—
906C23—121no—
907C23—121no—
908C23—121no—
909C23—121no—
910C23—121no—
911C23—121no—
912C23—121no—
913C23—121no—
914C23—121no—
915C23—121no—
916C23—121no—
917C23—121no—
918C23—121no—
919C23—121no—
920C23—121no—
921C23—121no—
922C23C2×#23511yescharacteristic
923C23C2×#23511yescharacteristic
924C23C2×D3×D411yescharacteristic
925C23C2×#23711yescharacteristic
926C23#100411yescharacteristic
927C23#100411yescharacteristic
928C23D3×#4111yescharacteristic
929C23D3×#4111yescharacteristic
930C23D3×#4111yescharacteristic
931C23D3×#4111yescharacteristic
932C23D3×#4111yescharacteristic
933C23D3×#4111yescharacteristic
934C23#100911yescharacteristic
935C23#100911yescharacteristic
936C23C22×#6711yescharacteristic
937D4—1216no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—62no—
980C2×C4—62no—
981C2×C4—62no—
982C2×C4—62no—
983C2×C4—62no—
984C2×C4—62no—
985C2×C4—62no—
986C2×C4—62no—
987C2×C4—62no—
988C2×C4—62no—
989C2×C4—62no—
990C2×C4—62no—
991C2×C4—62no—
992C2×C4—62no—
993C2×C4—62no—
994C2×C4—1216no—
995C2×C4—121no—
996C2×C4—121no—
997C2×C4—121no—
998C2×C4—121no—
999C2×C4—121no—
1000C2×C4—121no—
1001C2×C4—121no—
1002C2×C4—121no—
1003C2×C4—121no—
1004C2×C4—121no—
1005C2×C4—121no—
1006C2×C4—121no—
1007C2×C4—121no—
1008C2×C4—121no—
1009C2×C4—121no—
1010C2×C4—121no—
1011C2×C4—121no—
1012C2×C4—121no—
1013C2×C4—121no—
1014C2×C4—121no—
1015C2×C4—121no—
1016C2×C4—121no—
1017C2×C4—121no—
1018C2×C4—121no—
1019C2×C4—121no—
1020C2×C4—121no—
1021C2×C4—121no—
1022C2×C4—121no—
1023C2×C4—121no—
1024C2×C4—121no—
1025C2×C4—121no—
1026C2×C4—121no—
1027C2×C4—121no—
1028C2×C4—121no—
1029C2×C4#93914yes—
1030C2×C3—82no—
1031C2×C3#239211yescharacteristic
1032C2×C3#241111yescharacteristic
1033C2×C3#241411yescharacteristic
1034C2×C3#246711yescharacteristic
1035C2×C3#248011yescharacteristic
1036C2×C3#251011yescharacteristic
1037C2×C3#251811yescharacteristic
1038C2×C3#255411yescharacteristic
1039C2×C3#255911yescharacteristic
1040C2×C3#257211yescharacteristic
1041C2×C3#257811yescharacteristic
1042C2×C3#259811yescharacteristic
1043C2×C3#259811yescharacteristic
1044C2×C3#263111yescharacteristic
1045C2×C3#285211yescharacteristic
1046D3—44no—
1047C22—42no—
1048C22—42no—
1049C22—42no—
1050C22—42no—
1051C22—42no—
1052C22—42no—
1053C22—42no—
1054C22—64no—
1055C22—64no—
1056C22—64no—
1057C22—81no—
1058C22—81no—
1059C22—81no—
1060C22—81no—
1061C22—81no—
1062C22—81no—
1063C22—81no—
1064C22—81no—
1065C22—122no—
1066C22—122no—
1067C22—122no—
1068C22—122no—
1069C22—122no—
1070C22—122no—
1071C22—122no—
1072C22—122no—
1073C22—122no—
1074C22—122no—
1075C22—122no—
1076C22—122no—
1077C22#552711yescharacteristic
1078C22#552711yescharacteristic
1079C22#553011yescharacteristic
1080C22#553011yescharacteristic
1081C22#553811yescharacteristic
1082C22#554011yescharacteristic
1083C22#554011yescharacteristic
1084C22#554711yescharacteristic
1085C22#554811yescharacteristic
1086C22#555611yescharacteristic
1087C22#555611yescharacteristic
1088C22#555711yescharacteristic
1089C22#559911yescharacteristic
1090C22#561211yescharacteristic
1091C22#561411yescharacteristic
1092C22#561611yescharacteristic
1093C22#565411yescharacteristic
1094C22#565411yescharacteristic
1095C22#565811yescharacteristic
1096C22#565811yescharacteristic
1097C22#567811yescharacteristic
1098C22#567811yescharacteristic
1099C22#567811yescharacteristic
1100C22#567811yescharacteristic
1101C22D3×#12611yescharacteristic
1102C22#570611yescharacteristic
1103C22#570611yescharacteristic
1104C22#570611yescharacteristic
1105C22#579111yescharacteristic
1106C22C2×#93911yescharacteristic
1107C22#580511yescharacteristic
1108C22#582811yescharacteristic
1109C22#582811yescharacteristic
1110C22#582811yescharacteristic
1111C22#583011yescharacteristic
1112C4—24no—
1113C4—42no—
1114C4—42no—
1115C4—42no—
1116C4—81no—
1117C4—81no—
1118C4—122no—
1119C4—122no—
1120C4—122no—
1121C4—122no—
1122C4—122no—
1123C4—241no—
1124C4—241no—
1125C3#1492411yescharacteristic, complemented, Sylow
1126C2—82no—
1127C2—124no—
1128C2#7553911yescharacteristic
1129C2#7556111yescharacteristic
1130C2#7585911yescharacteristic
1131C2#7587011yescharacteristic
1132C2#7588311yescharacteristic
1133C2#7588811yescharacteristic
1134C2#7589111yescharacteristic
1135C2#7589311yescharacteristic
1136C2#8228411yescharacteristic
1137C2#8234511yescharacteristic
1138C2#8241811yescharacteristic
1139C2#8270411yescharacteristic
1140C2#8289411yescharacteristic
1141C2#8300211yescharacteristic
1142C2#8312011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC2×C3×#388C2
prime radicalC23×#67C22
hypercenterC2×#388D3
hypocenterC3#14924
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. C2×C3×#388C2semidirect
3. C2×#4937C2semidirect
4. C2×C4×(C2×D3)⋊C4C2semidirect
5. #71570C2semidirect
6. #71567C2semidirect
9. #71549C2semidirect
10. #71547C2semidirect
11. #71545C2semidirect
12. #69428C2semidirect
13. (C2×D3)⋊#95C2semidirect
14. #69418C2semidirect
15. #69406C2semidirect
56. C2×#388D3semidirect
114. C2×C3×C42D4semidirect
426. C2×C42#67semidirect
1125. C3#14924semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#3882
C2×#49562
C2×#49372
C2×C4×(C2×D3)⋊C42
#715702
#715672
#715502
#715492
#715472
#715452
#694282
(C2×D3)⋊#952
#694182
#694062
#149243