Finite Group Databasebeta

← #10728155

Subgroups — #10728155

Order 768.

1794 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×#4959C211yesmaximal, characteristic
2C2×#4958C211yesmaximal, characteristic
3C2×#4943C211yesmaximal, characteristic, complemented
4C2×Dic3×C22⋊C4C211yesmaximal, characteristic, complemented
5C3×#1440C211yesmaximal, characteristic, complemented
6#71550C211yesmaximal, characteristic
7#71547C211yesmaximal, characteristic, complemented
8#69429C211yesmaximal, characteristic, complemented
9#69428C211yesmaximal, characteristic, complemented
10#69416C211yesmaximal, characteristic, complemented
11#69414C211yesmaximal, characteristic, complemented
12#69408C211yesmaximal, characteristic, complemented
13#69408C211yesmaximal, characteristic, complemented
14Dic3⋊#95C211yesmaximal, characteristic, complemented
15#69401C211yesmaximal, characteristic, complemented
16#14838—31nomaximal, Sylow
17C23×#67C2211yescharacteristic
18C24×Dic3C2211yescharacteristic
19C22×C3×C22⋊C4C2211yescharacteristic
20C22×C3×C22⋊C4C2211yescharacteristic
21C22×C3×C22⋊C4C2211yescharacteristic
22C22×#217C2211yescharacteristic
23C22×#217C2211yescharacteristic
24C22×(C2×D3)⋊C4C2211yescharacteristic
25C22×(C2×D3)⋊C4C2211yescharacteristic
26C22×(C2×D3)⋊C4C2211yescharacteristic
27C22×(C2×D3)⋊C4C2211yescharacteristic
28C22×(C2×D3)⋊C4C2211yescharacteristic
29C22×(C2×D3)⋊C4C2211yescharacteristic
30C22×Dic3⋊C4C2211yescharacteristic
31C22×Dic3⋊C4C2211yescharacteristic
32C22×C4×Dic3C2211yescharacteristic
33C22×C4×Dic3C2211yescharacteristic
34C2×C3×#95C2211yescharacteristic
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
52#4959—24no—
53#4958—24no—
54#4943—24no—
55Dic3×C22⋊C4—24no—
56C2×#394—31no—
57C2×#386—31no—
58C2×#381—31no—
59C2×C4×C22⋊C4—31no—
60#1443—31no—
61#1442—31no—
62#1440—31no—
63#1440D311yescharacteristic, complemented
64#1439—31no—
65#1439—31no—
66#1438—31no—
67#1437—31no—
68#1437—31no—
69C4⋊#95—31no—
70#1434—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×Dic3—22no—
87C23×Dic3—22no—
88C23×Dic3—22no—
89C23×Dic3—22no—
90C23×Dic3—41no—
91C23×Dic3—41no—
92C23×Dic3D414yes—
93C23×Dic3C2311yescharacteristic
94C23×Dic3C2311yescharacteristic
95C23×Dic3C2311yescharacteristic
96C23×Dic3C2311yescharacteristic
97C23×Dic3C2311yescharacteristic
98C23×Dic3C2311yescharacteristic
99C23×Dic3C2311yescharacteristic
100C2×C3×C22⋊C4—22no—
101C2×C3×C22⋊C4—22no—
102C2×C3×C22⋊C4—22no—
103C2×C3×C22⋊C4—22no—
104C2×C3×C22⋊C4—22no—
105C2×C3×C22⋊C4—22no—
106C2×C3×C22⋊C4—22no—
107C2×C3×C22⋊C4—41no—
108C2×C3×C22⋊C4—41no—
109C2×#217—22no—
110C2×#217—22no—
111C2×#217—22no—
112C2×#217—41no—
113C2×#217—41no—
114C2×#217D414yes—
115C2×(C2×D3)⋊C4—22no—
116C2×(C2×D3)⋊C4—22no—
117C2×(C2×D3)⋊C4—22no—
118C2×(C2×D3)⋊C4—22no—
119C2×(C2×D3)⋊C4—22no—
120C2×(C2×D3)⋊C4—22no—
121C2×(C2×D3)⋊C4—22no—
122C2×(C2×D3)⋊C4—22no—
123C2×(C2×D3)⋊C4—22no—
124C2×(C2×D3)⋊C4—22no—
125C2×(C2×D3)⋊C4—22no—
126C2×(C2×D3)⋊C4—22no—
127C2×(C2×D3)⋊C4—41no—
128C2×(C2×D3)⋊C4—41no—
129C2×(C2×D3)⋊C4—41no—
130C2×(C2×D3)⋊C4—41no—
131C2×(C2×D3)⋊C4—41no—
132C2×(C2×D3)⋊C4—41no—
133C2×Dic3⋊C4—22no—
134C2×Dic3⋊C4—22no—
135C2×Dic3⋊C4—22no—
136C2×Dic3⋊C4—41no—
137C2×Dic3⋊C4—41no—
138C2×Dic3⋊C4—41no—
139C2×C4×Dic3—22no—
140C2×C4×Dic3—22no—
141C2×C4×Dic3—22no—
142C2×C4×Dic3—22no—
143C2×C4×Dic3—41no—
144C2×C4×Dic3—41no—
145C3×#95—22no—
146C3×#95—22no—
147C3×#95—41no—
148C3×#95—41no—
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—22no—
159C3⋊#95—22no—
160C3⋊#95—41no—
161C3⋊#95—41no—
162C3⋊#95—41no—
163C23×D4—31no—
164C24×C4—31no—
165C22×C4⋊C4—31no—
166C22×C4⋊C4—31no—
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×C42—31no—
180#394—64no—
181#386—64no—
182#381—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×#95C2×D311yescharacteristic
199C2×#95C2×D311yescharacteristic
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×C3C2×D412yes—
215C24×C3C2×D412yes—
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—21no—
231C23×D3—21no—
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×C4—21no—
270C22×C3×C4—21no—
271C22×C3×C4—21no—
272C22×C3×C4—21no—
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—28no—
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—28no—
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—44no—
325C22×Dic3—44no—
326C22×Dic3—44no—
327C22×Dic3—44no—
328C22×Dic3—44no—
329C22×Dic3C2×D412yes—
330C22×Dic3C2×D412yes—
331C22×Dic3C2×D412yes—
332C22×Dic3C2×D412yes—
333C22×Dic3#4112yes—
334C22×Dic3#4112yes—
335C22×Dic3#4112yes—
336C22×Dic3#4112yes—
337C22×Dic3#4112yes—
338C3×C22⋊C4—28no—
339C3×C22⋊C4—44no—
340C3×C22⋊C4—44no—
341#217—28no—
342#217—44no—
343(C2×D3)⋊C4—44no—
344(C2×D3)⋊C4—44no—
345(C2×D3)⋊C4—44no—
346(C2×D3)⋊C4—44no—
347(C2×D3)⋊C4—44no—
348(C2×D3)⋊C4—44no—
349Dic3⋊C4—44no—
350Dic3⋊C4—44no—
351C4×Dic3—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—34no—
368C23×C4—31no—
369C23×C4—31no—
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—62no—
383C2×C4⋊C4—62no—
384C2×C4⋊C4—62no—
385C2×C4⋊C4—121no—
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—34no—
396C2×C22⋊C4—41no—
397C2×C22⋊C4—41no—
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—62no—
422C2×C42—62no—
423C2×C42—62no—
424C2×C42—62no—
425C2×C42—121no—
426C2×C42—121no—
427#95—22no—
428#95—22no—
429#95—41no—
430#95—41no—
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—62no—
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—22no—
453C23×C3—22no—
454C23×C3—22no—
455C23×C3—22no—
456C23×C3—22no—
457C23×C3—22no—
458C23×C3—22no—
459C23×C3—22no—
460C23×C3—22no—
461C23×C3—22no—
462C23×C3—22no—
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#12114yes—
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—41no—
503C22×D3—41no—
504C22×D3—41no—
505C22×D3—41no—
506C22×D3—41no—
507C22×D3—41no—
508C22×D3—41no—
509C22×D3—41no—
510C22×D3—41no—
511C22×D3—41no—
512C22×D3—41no—
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—41no—
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—41no—
537C2×C3×C4—41no—
538C2×C3×C4—41no—
539C2×C3×C4—41no—
540C2×C3×C4—41no—
541C2×C3×C4—41no—
542C2×C3×C4—41no—
543C2×C3×C4—41no—
544C2×C3×C4—41no—
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—41no—
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—22no—
589C2×Dic3—22no—
590C2×Dic3—22no—
591C2×Dic3—22no—
592C2×Dic3—22no—
593C2×Dic3—22no—
594C2×Dic3—416no—
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#12314yes—
622C2×Dic3#12314yes—
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—32no—
636C24—61no—
637C24—61no—
638C24—61no—
639C24—61no—
640C24—61no—
641C24—61no—
642C24—61no—
643C24—61no—
644C24—61no—
645C24—61no—
646C24—61no—
647C24—61no—
648C24—61no—
649C24—61no—
650C24#23512yes—
651C24D3×D412yes—
652C24D3×D412yes—
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—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—32no—
702C22×C4—32no—
703C22×C4—32no—
704C22×C4—32no—
705C22×C4—32no—
706C22×C4—32no—
707C22×C4—32no—
708C22×C4—32no—
709C22×C4—32no—
710C22×C4—68no—
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—68no—
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—61no—
748C22×C4—61no—
749C22×C4—61no—
750C22×C4—61no—
751C22×C4—61no—
752C22×C4—124no—
753C22×C4—124no—
754C22×C4—124no—
755C22×C4—124no—
756C22×C4—124no—
757C22×C4#23712yes—
758C22×C4#23712yes—
759C4⋊C4—124no—
760C4⋊C4—124no—
761C22⋊C4—28no—
762C22⋊C4—44no—
763C22⋊C4—44no—
764C22⋊C4—68no—
765C22⋊C4—124no—
766C22⋊C4—124no—
767C22⋊C4—124no—
768C22⋊C4—124no—
769C22⋊C4—124no—
770C22⋊C4—124no—
771C22⋊C4—124no—
772C42—124no—
773C42—124no—
774C22×C3—24no—
775C22×C3—24no—
776C22×C3—24no—
777C22×C3—42no—
778C22×C3—42no—
779C22×C3—42no—
780C22×C3—42no—
781C22×C3—42no—
782C22×C3—42no—
783C22×C3—42no—
784C22×C3—42no—
785C22×C3—42no—
786C22×C3—42no—
787C22×C3—42no—
788C22×C3—42no—
789C22×C3C2×#12111yescharacteristic
790C22×C3C2×#12311yescharacteristic
791C22×C3C2×#12311yescharacteristic
792C22×C3#52511yescharacteristic
793C22×C3#52511yescharacteristic
794C22×C3#52911yescharacteristic
795C22×C3#52911yescharacteristic
796C22×C3#52911yescharacteristic
797C22×C3#52911yescharacteristic
798C22×C3#52911yescharacteristic
799C22×C3#52911yescharacteristic
800C22×C3#53211yescharacteristic
801C22×C3#53211yescharacteristic
802C22×C3#53411yescharacteristic
803C22×C3#53511yescharacteristic
804C22×C3#53811yescharacteristic
805C22×C3#53811yescharacteristic
806C22×C3#54011yescharacteristic
807C22×C3#54011yescharacteristic
808C22×C3#54611yescharacteristic
809C22×C3#54611yescharacteristic
810C22×C3#54611yescharacteristic
811C22×C3#54611yescharacteristic
812C22×C3#55111yescharacteristic
813C22×C3#55111yescharacteristic
814C22×C3#55111yescharacteristic
815C22×C3#55111yescharacteristic
816C22×C3#55111yescharacteristic
817C22×C3#55311yescharacteristic
818C22×C3#55311yescharacteristic
819C22×C3#55311yescharacteristic
820C22×C3#55311yescharacteristic
821C22×C3#55511yescharacteristic
822C22×C3#55511yescharacteristic
823C22×C3#55911yescharacteristic
824C2×D3—42no—
825C2×D3—42no—
826C2×D3—42no—
827C2×D3—42no—
828C2×D3—42no—
829C2×D3—42no—
830C2×D3—42no—
831C2×D3—81no—
832C2×D3—81no—
833C2×D3—81no—
834C2×D3—81no—
835C2×D3—81no—
836C2×D3—81no—
837C2×D3—81no—
838C2×D3—81no—
839C3×C4—42no—
840C3×C4—42no—
841C3×C4—81no—
842C3×C4—81no—
843C3×C4—81no—
844C3×C4—81no—
845Dic3—24no—
846Dic3—24no—
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—22no—
860C23—22no—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—22no—
865C23—22no—
866C23—22no—
867C23—22no—
868C23—22no—
869C23—22no—
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—62no—
887C23—62no—
888C23—62no—
889C23—62no—
890C23—62no—
891C23—62no—
892C23—62no—
893C23—121no—
894C23—121no—
895C23—121no—
896C23—121no—
897C23—121no—
898C23—121no—
899C23—121no—
900C23—121no—
901C23—121no—
902C23—121no—
903C23—121no—
904C23—121no—
905C23—121no—
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#88414yes—
922C23C2×#23511yescharacteristic
923C23C2×D3×D411yescharacteristic
924C23C2×D3×D411yescharacteristic
925C23C2×#23711yescharacteristic
926C23C2×#23711yescharacteristic
927C23#100411yescharacteristic
928C23#100411yescharacteristic
929C23D3×#4111yescharacteristic
930C23D3×#4111yescharacteristic
931C23D3×#4111yescharacteristic
932C23D3×#4111yescharacteristic
933C23D3×#4111yescharacteristic
934C23D3×#4111yescharacteristic
935C23#100911yescharacteristic
936C23#100911yescharacteristic
937D4—1216no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—34no—
945C2×C4—34no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—41no—
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—41no—
980C2×C4—41no—
981C2×C4—41no—
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—62no—
995C2×C4—62no—
996C2×C4—62no—
997C2×C4—62no—
998C2×C4—62no—
999C2×C4—62no—
1000C2×C4—62no—
1001C2×C4—62no—
1002C2×C4—62no—
1003C2×C4—1216no—
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—121no—
1030C2×C3—44no—
1031C2×C3#239511yescharacteristic
1032C2×C3#241111yescharacteristic
1033C2×C3#241211yescharacteristic
1034C2×C3#242011yescharacteristic
1035C2×C3#244411yescharacteristic
1036C2×C3#245711yescharacteristic
1037C2×C3#245911yescharacteristic
1038C2×C3#250011yescharacteristic
1039C2×C3#251611yescharacteristic
1040C2×C3#252611yescharacteristic
1041C2×C3#257211yescharacteristic
1042C2×C3#257611yescharacteristic
1043C2×C3#260211yescharacteristic
1044C2×C3#266111yescharacteristic
1045C2×C3#285411yescharacteristic
1046D3—82no—
1047C22—24no—
1048C22—24no—
1049C22—24no—
1050C22—42no—
1051C22—42no—
1052C22—42no—
1053C22—42no—
1054C22—42no—
1055C22—42no—
1056C22—42no—
1057C22—42no—
1058C22—42no—
1059C22—42no—
1060C22—42no—
1061C22—42no—
1062C22—122no—
1063C22—122no—
1064C22—122no—
1065C22—122no—
1066C22—122no—
1067C22—122no—
1068C22—122no—
1069C22—241no—
1070C22—241no—
1071C22—241no—
1072C22—241no—
1073C22—241no—
1074C22—241no—
1075C22—241no—
1076C22—241no—
1077C22C2×#88411yescharacteristic
1078C22#552711yescharacteristic
1079C22#552711yescharacteristic
1080C22#553811yescharacteristic
1081C22#553811yescharacteristic
1082C22#555611yescharacteristic
1083C22#555611yescharacteristic
1084C22#558611yescharacteristic
1085C22#559211yescharacteristic
1086C22#559611yescharacteristic
1087C22#559611yescharacteristic
1088C22#560111yescharacteristic
1089C22#561011yescharacteristic
1090C22#561011yescharacteristic
1091C22#561611yescharacteristic
1092C22#561711yescharacteristic
1093C22#561911yescharacteristic
1094C22#564911yescharacteristic
1095C22D3×#12311yescharacteristic
1096C22D3×#12311yescharacteristic
1097C22#565311yescharacteristic
1098C22#565411yescharacteristic
1099C22#565411yescharacteristic
1100C22#565611yescharacteristic
1101C22#565811yescharacteristic
1102C22#566111yescharacteristic
1103C22#566311yescharacteristic
1104C22#567011yescharacteristic
1105C22#567811yescharacteristic
1106C22#568011yescharacteristic
1107C22#568111yescharacteristic
1108C22#570611yescharacteristic
1109C22#570611yescharacteristic
1110C22#570911yescharacteristic
1111C22#570911yescharacteristic
1112C4—42no—
1113C4—42no—
1114C4—64no—
1115C4—64no—
1116C4—81no—
1117C4—81no—
1118C4—81no—
1119C4—81no—
1120C4—122no—
1121C4—122no—
1122C4—122no—
1123C4—241no—
1124C4—241no—
1125C3#1483811yescharacteristic, complemented, Sylow
1126C2—44no—
1127C2—242no—
1128C2#7412611yescharacteristic
1129C2#7487211yescharacteristic
1130C2#7488911yescharacteristic
1131C2#7555711yescharacteristic
1132C2#7557411yescharacteristic
1133C2#7561111yescharacteristic
1134C2#7589111yescharacteristic
1135C2#7690911yescharacteristic
1136C2#7691111yescharacteristic
1137C2#7693611yescharacteristic
1138C2#7699411yescharacteristic
1139C2#7745911yescharacteristic
1140C2#7746311yescharacteristic
1141C2#7753511yescharacteristic
1142C2#7767411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1440C2
prime radicalC23×#67C22
hypercenter#1440D3
hypocenterC3#14838
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1440

Complements

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

NH ≅ G/Ntype
3. C2×#4943C2semidirect
4. C2×Dic3×C22⋊C4C2semidirect
5. C3×#1440C2semidirect
7. #71547C2semidirect
8. #69429C2semidirect
9. #69428C2semidirect
10. #69416C2semidirect
11. #69414C2semidirect
12. #69408C2semidirect
13. #69408C2semidirect
14. Dic3⋊#95C2semidirect
15. #69401C2semidirect
63. #1440D3semidirect
1125. C3#14838semidirect

Maximal subgroups

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

subgroupindex
C2×#49592
C2×#49582
C2×#49432
C2×Dic3×C22⋊C42
C3×#14402
#715502
#715472
#694292
#694282
#694162
#694142
#694082
Dic3⋊#952
#694012
#148383