Finite Group Databasebeta

← #10735813

Subgroups — #10735813

Order 768.

2042 conjugacy classes of subgroups.

The subgroup lattice has 1172 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#883C211yesmaximal, characteristic
2C2×C3×#397C211yesmaximal, characteristic, complemented
3C2×#4952C211yesmaximal, characteristic, complemented
4C2×#4958C211yesmaximal, characteristic
5#71570C211yesmaximal, characteristic, complemented
6#71565C211yesmaximal, characteristic, complemented
7#71550C211yesmaximal, characteristic
8#71544C211yesmaximal, characteristic, complemented
9#71544C211yesmaximal, characteristic, complemented
10#69428C211yesmaximal, characteristic, complemented
11(C2×D3)⋊#95C211yesmaximal, characteristic, complemented
12(C2×D3)⋊#95C211yesmaximal, characteristic, complemented
13#69415C211yesmaximal, characteristic, complemented
14#69414C211yesmaximal, characteristic, complemented
15#69409C211yesmaximal, characteristic, complemented
16#15463—31nomaximal, Sylow
17C23×#67C2211yescharacteristic
18C24×Dic3C2211yescharacteristic
19C23×C4×D3C2211yescharacteristic
20C22×C3×C4⋊C4C2211yescharacteristic
21C22×C3×C22⋊C4C2211yescharacteristic
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×#217C2211yescharacteristic
25C22×#217C2211yescharacteristic
26C22×(C2×D3)⋊C4C2211yescharacteristic
27C22×(C2×D3)⋊C4C2211yescharacteristic
28C22×(C2×D3)⋊C4C2211yescharacteristic
29C22×(C2×D3)⋊C4C2211yescharacteristic
30C22×(C2×D3)⋊C4C2211yescharacteristic
31C22×C4⋊Dic3C2211yescharacteristic
32C22×Dic3⋊C4C2211yescharacteristic
33C22×Dic3⋊C4C2211yescharacteristic
34C2×#883—24no—
35C2×#883—24no—
36C2×#883—24no—
37C3×#397—24no—
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
53C2×C3⋊#95C2211yescharacteristic
54C2×C3⋊#95C2211yescharacteristic
55C2×C3⋊#95C2211yescharacteristic
56#4958—24no—
57#4952—24no—
58C22×#123—31no—
59C2×#397—31no—
60C2×#397D311yescharacteristic, complemented
61C2×#386—31no—
62#1442—31no—
63#1442—31no—
64#1441—31no—
65#1441—31no—
66#1439—31no—
67#1439—31no—
68#1438—31no—
69C22⋊#95—31no—
70C22⋊#95—31no—
71C22⋊#95—31no—
72C22⋊#95—31no—
73C25×C3C2311yescharacteristic
74C24×D3C2311yescharacteristic
75C23×C3×C4C2311yescharacteristic
76C23×C3×C4C2311yescharacteristic
77C23×C3×C4C2311yescharacteristic
78C23×C3×C4C2311yescharacteristic
79C23×C3×C4C2311yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C22×#67—22no—
82C22×#67—22no—
83C22×#67—22no—
84C22×#67—22no—
85C22×#67—41no—
86C22×#67—41no—
87C22×#67D414yes—
88C23×Dic3—22no—
89C23×Dic3—22no—
90C23×Dic3—22no—
91C23×Dic3—41no—
92C23×Dic3—41no—
93C23×Dic3—41no—
94C23×Dic3—41no—
95C23×Dic3C2311yescharacteristic
96C23×Dic3C2311yescharacteristic
97C23×Dic3C2311yescharacteristic
98C23×Dic3C2311yescharacteristic
99C23×Dic3C2311yescharacteristic
100C23×Dic3C2311yescharacteristic
101C23×Dic3C2311yescharacteristic
102C22×C4×D3—22no—
103C22×C4×D3—22no—
104C22×C4×D3—22no—
105C22×C4×D3—22no—
106C22×C4×D3—22no—
107C22×C4×D3—41no—
108C22×C4×D3—41no—
109C2×C3×C4⋊C4—22no—
110C2×C3×C4⋊C4—22no—
111C2×C3×C4⋊C4—41no—
112C2×C3×C22⋊C4—22no—
113C2×C3×C22⋊C4—22no—
114C2×C3×C22⋊C4—22no—
115C2×C3×C22⋊C4—22no—
116C2×C3×C22⋊C4—22no—
117C2×C3×C22⋊C4—22no—
118C2×C3×C22⋊C4—22no—
119C2×C3×C22⋊C4—41no—
120C2×C3×C22⋊C4D414yes—
121C2×#217—22no—
122C2×#217—22no—
123C2×#217—22no—
124C2×#217—22no—
125C2×#217—41no—
126C2×#217D414yes—
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—22no—
136C2×(C2×D3)⋊C4—22no—
137C2×(C2×D3)⋊C4—22no—
138C2×(C2×D3)⋊C4—41no—
139C2×(C2×D3)⋊C4—41no—
140C2×(C2×D3)⋊C4—41no—
141C2×(C2×D3)⋊C4—41no—
142C2×C4⋊Dic3—22no—
143C2×C4⋊Dic3—22no—
144C2×C4⋊Dic3—22no—
145C2×Dic3⋊C4—22no—
146C2×Dic3⋊C4—22no—
147C2×Dic3⋊C4—22no—
148C2×Dic3⋊C4—22no—
149C2×Dic3⋊C4—22no—
150C2×Dic3⋊C4—41no—
151#883—232no—
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—22no—
161C3⋊#95—22no—
162C3⋊#95—41no—
163C3⋊#95—41no—
164C3⋊#95—41no—
165C3⋊#95—41no—
166C3⋊#95—41no—
167C3⋊#95—41no—
168C3⋊#95—41no—
169C3⋊#95—41no—
170C23×D4—31no—
171C24×C4—31no—
172C24×C4—31no—
173C2×#123—64no—
174C2×#123—64no—
175C2×#123—64no—
176C22×C4⋊C4—31no—
177C22×C4⋊C4—31no—
178C22×C4⋊C4—31no—
179C22×C4⋊C4C2×D311yescharacteristic
180C22×C22⋊C4—31no—
181C22×C22⋊C4—31no—
182C22×C22⋊C4—31no—
183C22×C22⋊C4—31no—
184C22×C22⋊C4—31no—
185C22×C22⋊C4—31no—
186C22×C22⋊C4—31no—
187C22×C22⋊C4C2×D311yescharacteristic
188C22×C22⋊C4C2×D311yescharacteristic
189C22×C22⋊C4C2×D311yescharacteristic
190#397—24no—
191#397—64no—
192#386—64no—
193C2×#95—31no—
194C2×#95—31no—
195C2×#95—31no—
196C2×#95—31no—
197C2×#95—31no—
198C2×#95—31no—
199C2×#95—31no—
200C2×#95—31no—
201C2×#95—31no—
202C2×#95—31no—
203C2×#95—31no—
204C2×#95—31no—
205C2×#95—31no—
206C2×#95—31no—
207C2×#95—31no—
208C2×#95C2×D311yescharacteristic
209C2×#95C2×D311yescharacteristic
210C2×#95C2×D311yescharacteristic
211C24×C3—21no—
212C24×C3—21no—
213C24×C3—21no—
214C24×C3—21no—
215C24×C3—21no—
216C24×C3—21no—
217C24×C3—21no—
218C24×C3—21no—
219C24×C3—21no—
220C24×C3—21no—
221C24×C3—21no—
222C24×C3—21no—
223C24×C3C2×D412yes—
224C24×C3C2×D412yes—
225C24×C3C2×D412yes—
226C24×C3C2411yescharacteristic
227C23×D3—21no—
228C23×D3—21no—
229C23×D3—21no—
230C23×D3—21no—
231C23×D3—21no—
232C23×D3—21no—
233C23×D3—21no—
234C23×D3—21no—
235C23×D3—21no—
236C23×D3—21no—
237C23×D3—21no—
238C23×D3—21no—
239C23×D3C2×D412yes—
240C23×D3#4112yes—
241C23×D3#4112yes—
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—21no—
274C22×C3×C4—21no—
275C22×C3×C4—21no—
276C22×C3×C4—21no—
277C22×C3×C4—21no—
278C22×C3×C4—21no—
279C22×C3×C4—21no—
280C22×C3×C4—21no—
281C22×C3×C4C2×D412yes—
282C22×C3×C4C2×D412yes—
283C22×C3×C4#4112yes—
284C2×#67—28no—
285C2×#67—28no—
286C2×#67—44no—
287C2×#67—44no—
288C2×#67—44no—
289C2×#67—44no—
290C2×#67—44no—
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×Dic3—21no—
327C22×Dic3—21no—
328C22×Dic3—21no—
329C22×Dic3—21no—
330C22×Dic3—21no—
331C22×Dic3—21no—
332C22×Dic3—21no—
333C22×Dic3—21no—
334C22×Dic3—44no—
335C22×Dic3—44no—
336C22×Dic3—44no—
337C22×Dic3—44no—
338C22×Dic3—44no—
339C22×Dic3—44no—
340C22×Dic3—44no—
341C22×Dic3C2×D412yes—
342C22×Dic3C2×D412yes—
343C22×Dic3C2×D412yes—
344C22×Dic3#4112yes—
345C22×Dic3#4112yes—
346C22×Dic3#4112yes—
347C2×C4×D3—28no—
348C2×C4×D3—44no—
349C2×C4×D3—44no—
350C2×C4×D3—44no—
351C2×C4×D3—44no—
352C2×C4×D3—44no—
353C2×C4×D3—44no—
354C3×C4⋊C4—44no—
355C3×C22⋊C4—28no—
356C3×C22⋊C4—44no—
357C3×C22⋊C4—44no—
358#217—28no—
359#217—44no—
360(C2×D3)⋊C4—28no—
361(C2×D3)⋊C4—44no—
362(C2×D3)⋊C4—44no—
363(C2×D3)⋊C4—44no—
364(C2×D3)⋊C4—44no—
365C4⋊Dic3—28no—
366Dic3⋊C4—28no—
367Dic3⋊C4—44no—
368C25—31no—
369C25C22×D311yescharacteristic
370C22×D4—34no—
371C22×D4—62no—
372C22×D4—62no—
373C22×D4—62no—
374C22×D4—62no—
375C22×D4—121no—
376C22×D4—121no—
377C23×C4—31no—
378C23×C4—31no—
379C23×C4—31no—
380C23×C4—31no—
381C23×C4—31no—
382C23×C4—31no—
383C23×C4—31no—
384C23×C4—62no—
385C23×C4—62no—
386C23×C4—62no—
387C23×C4—62no—
388C23×C4—62no—
389C23×C4—62no—
390C23×C4—62no—
391C23×C4—62no—
392C23×C4—121no—
393C23×C4—121no—
394C23×C4—121no—
395C23×C4—121no—
396C23×C4—121no—
397C23×C4—121no—
398C23×C4C22×D311yescharacteristic
399C23×C4C22×D311yescharacteristic
400C23×C4C22×D311yescharacteristic
401C23×C4C22×D311yescharacteristic
402C23×C4C22×D311yescharacteristic
403C23×C4C22×D311yescharacteristic
404#123—632no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—41no—
408C2×C4⋊C4—62no—
409C2×C4⋊C4—62no—
410C2×C4⋊C4—62no—
411C2×C4⋊C4—62no—
412C2×C4⋊C4—62no—
413C2×C4⋊C4—62no—
414C2×C4⋊C4—62no—
415C2×C4⋊C4—62no—
416C2×C4⋊C4—121no—
417C2×C22⋊C4—22no—
418C2×C22⋊C4—22no—
419C2×C22⋊C4—22no—
420C2×C22⋊C4—22no—
421C2×C22⋊C4—22no—
422C2×C22⋊C4—22no—
423C2×C22⋊C4—22no—
424C2×C22⋊C4—34no—
425C2×C22⋊C4—41no—
426C2×C22⋊C4—62no—
427C2×C22⋊C4—62no—
428C2×C22⋊C4—62no—
429C2×C22⋊C4—62no—
430C2×C22⋊C4—62no—
431C2×C22⋊C4—62no—
432C2×C22⋊C4—62no—
433C2×C22⋊C4—62no—
434C2×C22⋊C4—62no—
435C2×C22⋊C4—62no—
436C2×C22⋊C4—62no—
437C2×C22⋊C4—62no—
438C2×C22⋊C4—62no—
439C2×C22⋊C4—62no—
440C2×C22⋊C4—62no—
441C2×C22⋊C4—121no—
442C2×C22⋊C4—121no—
443C2×C22⋊C4—121no—
444C2×C22⋊C4—121no—
445C2×C22⋊C4—121no—
446C2×C22⋊C4#6714yes—
447#95—22no—
448#95—22no—
449#95—22no—
450#95—62no—
451#95—62no—
452#95—62no—
453#95—62no—
454#95—62no—
455#95—62no—
456#95—62no—
457#95—121no—
458#95—121no—
459#95—121no—
460#95—121no—
461#95—121no—
462#95—121no—
463#95—121no—
464#95—121no—
465C23×C3—22no—
466C23×C3—22no—
467C23×C3—22no—
468C23×C3—22no—
469C23×C3—22no—
470C23×C3—22no—
471C23×C3—22no—
472C23×C3—22no—
473C23×C3—22no—
474C23×C3—22no—
475C23×C3—22no—
476C23×C3—22no—
477C23×C3—22no—
478C23×C3—22no—
479C23×C3—22no—
480C23×C3—22no—
481C23×C3—22no—
482C23×C3—22no—
483C23×C3—41no—
484C23×C3—41no—
485C23×C3—41no—
486C23×C3—41no—
487C23×C3—41no—
488C23×C3—41no—
489C23×C3—41no—
490C23×C3—41no—
491C23×C3—41no—
492C23×C3—41no—
493C23×C3—41no—
494C23×C3—41no—
495C23×C3—41no—
496C23×C3—41no—
497C23×C3—41no—
498C23×C3—41no—
499C23×C3#12014yes—
500C23×C3C22×D411yescharacteristic
501C23×C3C22×D411yescharacteristic
502C23×C3C22×D411yescharacteristic
503C23×C3C2×#4111yescharacteristic
504C23×C3C2×#4111yescharacteristic
505C23×C3C2×#4111yescharacteristic
506C23×C3C2×#4111yescharacteristic
507C23×C3C2×#4111yescharacteristic
508C23×C3C2×#4111yescharacteristic
509C23×C3H(5,𝔽2)11yescharacteristic
510C23×C3H(5,𝔽2)11yescharacteristic
511C23×C3H(5,𝔽2)11yescharacteristic
512C23×C3H(5,𝔽2)11yescharacteristic
513C23×C32−1+411yescharacteristic
514C23×C32−1+411yescharacteristic
515C22×D3—22no—
516C22×D3—22no—
517C22×D3—22no—
518C22×D3—22no—
519C22×D3—22no—
520C22×D3—22no—
521C22×D3—22no—
522C22×D3—22no—
523C22×D3—22no—
524C22×D3—22no—
525C22×D3—22no—
526C22×D3—22no—
527C22×D3—22no—
528C22×D3—22no—
529C22×D3—22no—
530C22×D3—22no—
531C22×D3—22no—
532C22×D3—22no—
533C22×D3—41no—
534C22×D3—41no—
535C22×D3—41no—
536C22×D3—41no—
537C22×D3—41no—
538C22×D3—41no—
539C22×D3—41no—
540C22×D3—41no—
541C22×D3—41no—
542C22×D3—41no—
543C22×D3—41no—
544C22×D3—41no—
545C22×D3—41no—
546C22×D3—41no—
547C22×D3—41no—
548C22×D3—41no—
549C22×D3#12314yes—
550C2×C3×C4—22no—
551C2×C3×C4—22no—
552C2×C3×C4—22no—
553C2×C3×C4—22no—
554C2×C3×C4—22no—
555C2×C3×C4—22no—
556C2×C3×C4—22no—
557C2×C3×C4—22no—
558C2×C3×C4—22no—
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—
572C2×C3×C4—41no—
573C2×C3×C4—41no—
574C2×C3×C4—41no—
575C2×C3×C4—41no—
576C2×C3×C4—41no—
577C2×C3×C4—41no—
578C2×C3×C4—41no—
579C2×C3×C4—41no—
580C2×C3×C4—41no—
581C2×C3×C4—41no—
582C2×C3×C4—41no—
583C2×C3×C4—41no—
584C2×C3×C4—41no—
585C2×C3×C4—41no—
586C2×C3×C4—41no—
587C2×C3×C4—41no—
588C2×C3×C4—41no—
589C2×C3×C4—41no—
590C2×C3×C4—41no—
591C2×C3×C4—41no—
592#67—416no—
593C2×Dic3—22no—
594C2×Dic3—22no—
595C2×Dic3—22no—
596C2×Dic3—22no—
597C2×Dic3—22no—
598C2×Dic3—22no—
599C2×Dic3—22no—
600C2×Dic3—22no—
601C2×Dic3—22no—
602C2×Dic3—22no—
603C2×Dic3—22no—
604C2×Dic3—22no—
605C2×Dic3—22no—
606C2×Dic3—22no—
607C2×Dic3—22no—
608C2×Dic3—22no—
609C2×Dic3—22no—
610C2×Dic3—22no—
611C2×Dic3—416no—
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—
622C2×Dic3—41no—
623C2×Dic3—41no—
624C2×Dic3—41no—
625C2×Dic3—41no—
626C2×Dic3—41no—
627C2×Dic3—41no—
628C2×Dic3—41no—
629C2×Dic3—41no—
630C2×Dic3—41no—
631C2×Dic3—41no—
632C2×Dic3—41no—
633C2×Dic3—41no—
634C2×Dic3—41no—
635C2×Dic3—41no—
636C2×Dic3—41no—
637C2×Dic3—41no—
638C2×Dic3—41no—
639C2×Dic3—41no—
640C2×Dic3—41no—
641C2×Dic3—41no—
642C2×Dic3—41no—
643C4×D3—416no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24—21no—
654C24—21no—
655C24—21no—
656C24—32no—
657C24—32no—
658C24—32no—
659C24—61no—
660C24—61no—
661C24—61no—
662C24—61no—
663C24—61no—
664C24—61no—
665C24—61no—
666C24—61no—
667C24—61no—
668C24—61no—
669C24—61no—
670C24—61no—
671C24D3×D412yes—
672C24D3×D412yes—
673C24C2×#6712yes—
674C24C23×D311yescharacteristic
675C2×D4—68no—
676C2×D4—68no—
677C2×D4—124no—
678C2×D4—124no—
679C2×D4—124no—
680C2×D4—124no—
681C2×D4—124no—
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—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—32no—
722C22×C4—32no—
723C22×C4—32no—
724C22×C4—32no—
725C22×C4—32no—
726C22×C4—32no—
727C22×C4—68no—
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—61no—
753C22×C4—61no—
754C22×C4—61no—
755C22×C4—61no—
756C22×C4—61no—
757C22×C4—61no—
758C22×C4—61no—
759C22×C4—61no—
760C22×C4—61no—
761C22×C4—61no—
762C22×C4—61no—
763C22×C4—61no—
764C22×C4—61no—
765C22×C4—61no—
766C22×C4—61no—
767C22×C4—61no—
768C22×C4—61no—
769C22×C4—61no—
770C22×C4—61no—
771C22×C4—124no—
772C22×C4—124no—
773C22×C4—124no—
774C22×C4—124no—
775C22×C4—124no—
776C22×C4—124no—
777C22×C4—124no—
778C22×C4—124no—
779C22×C4—124no—
780C22×C4—124no—
781C22×C4—124no—
782C22×C4—124no—
783C22×C4—124no—
784C22×C4#23712yes—
785C22×C4C2×#6712yes—
786C22×C4C2×#6712yes—
787C4⋊C4—44no—
788C4⋊C4—68no—
789C4⋊C4—68no—
790C4⋊C4—124no—
791C22⋊C4—28no—
792C22⋊C4—44no—
793C22⋊C4—44no—
794C22⋊C4—68no—
795C22⋊C4—68no—
796C22⋊C4—124no—
797C22⋊C4—124no—
798C22⋊C4—124no—
799C22⋊C4—124no—
800C22⋊C4—124no—
801C22×C3—24no—
802C22×C3—24no—
803C22×C3—24no—
804C22×C3—42no—
805C22×C3—42no—
806C22×C3—42no—
807C22×C3—42no—
808C22×C3—42no—
809C22×C3—42no—
810C22×C3—42no—
811C22×C3—42no—
812C22×C3—42no—
813C22×C3—42no—
814C22×C3—42no—
815C22×C3—42no—
816C22×C3C2×#12011yescharacteristic
817C22×C3C2×#12311yescharacteristic
818C22×C3#52911yescharacteristic
819C22×C3#52911yescharacteristic
820C22×C3#53211yescharacteristic
821C22×C3#53211yescharacteristic
822C22×C3#53411yescharacteristic
823C22×C3#53711yescharacteristic
824C22×C3#53711yescharacteristic
825C22×C3#53811yescharacteristic
826C22×C3#53811yescharacteristic
827C22×C3#53911yescharacteristic
828C22×C3#53911yescharacteristic
829C22×C3#53911yescharacteristic
830C22×C3#53911yescharacteristic
831C22×C3#54611yescharacteristic
832C22×C3#54611yescharacteristic
833C22×C3#54611yescharacteristic
834C22×C3#54611yescharacteristic
835C22×C3#54611yescharacteristic
836C22×C3#54611yescharacteristic
837C22×C3#54611yescharacteristic
838C22×C3#54611yescharacteristic
839C22×C3#54711yescharacteristic
840C22×C3#54711yescharacteristic
841C22×C3#54711yescharacteristic
842C22×C3#54711yescharacteristic
843C22×C3#55111yescharacteristic
844C22×C3#55111yescharacteristic
845C22×C3#55111yescharacteristic
846C22×C3#55211yescharacteristic
847C22×C3#55211yescharacteristic
848C22×C3#55911yescharacteristic
849C22×C3#56011yescharacteristic
850C22×C3#56311yescharacteristic
851C2×D3—24no—
852C2×D3—24no—
853C2×D3—24no—
854C2×D3—42no—
855C2×D3—42no—
856C2×D3—42no—
857C2×D3—42no—
858C2×D3—42no—
859C2×D3—42no—
860C2×D3—42no—
861C2×D3—42no—
862C2×D3—42no—
863C2×D3—42no—
864C2×D3—42no—
865C2×D3—42no—
866C3×C4—42no—
867C3×C4—42no—
868C3×C4—42no—
869C3×C4—81no—
870C3×C4—81no—
871C3×C4—81no—
872Dic3—42no—
873Dic3—42no—
874Dic3—42no—
875Dic3—42no—
876Dic3—42no—
877Dic3—42no—
878Dic3—81no—
879C23—22no—
880C23—22no—
881C23—22no—
882C23—22no—
883C23—22no—
884C23—22no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—34no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—62no—
915C23—62no—
916C23—62no—
917C23—62no—
918C23—62no—
919C23—62no—
920C23—62no—
921C23—62no—
922C23—62no—
923C23—62no—
924C23—62no—
925C23—62no—
926C23—62no—
927C23—62no—
928C23—62no—
929C23—62no—
930C23—62no—
931C23—62no—
932C23—121no—
933C23—121no—
934C23—121no—
935C23—121no—
936C23—121no—
937C23—121no—
938C23—121no—
939C23—121no—
940C23—121no—
941C23—121no—
942C23—121no—
943C23—121no—
944C23—121no—
945C23—121no—
946C23—121no—
947C23—121no—
948C23#93714yes—
949C23C2×D3×D411yescharacteristic
950C23C2×D3×D411yescharacteristic
951C23C2×#23711yescharacteristic
952C23#100411yescharacteristic
953C23D3×#4111yescharacteristic
954C23D3×#4111yescharacteristic
955C23D3×#4111yescharacteristic
956C23D3×#4111yescharacteristic
957C23D3×#4111yescharacteristic
958C23#100911yescharacteristic
959C23#100911yescharacteristic
960C23#100911yescharacteristic
961C23#101011yescharacteristic
962C23#101011yescharacteristic
963C23C22×#6711yescharacteristic
964D4—1216no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
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—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—62no—
1008C2×C4—62no—
1009C2×C4—62no—
1010C2×C4—62no—
1011C2×C4—62no—
1012C2×C4—62no—
1013C2×C4—62no—
1014C2×C4—62no—
1015C2×C4—62no—
1016C2×C4—62no—
1017C2×C4—62no—
1018C2×C4—62no—
1019C2×C4—62no—
1020C2×C4—62no—
1021C2×C4—62no—
1022C2×C4—62no—
1023C2×C4—62no—
1024C2×C4—62no—
1025C2×C4—1216no—
1026C2×C4—1216no—
1027C2×C4—121no—
1028C2×C4—121no—
1029C2×C4—121no—
1030C2×C4—121no—
1031C2×C4—121no—
1032C2×C4—121no—
1033C2×C4—121no—
1034C2×C4—121no—
1035C2×C4—121no—
1036C2×C4—121no—
1037C2×C4—121no—
1038C2×C4—121no—
1039C2×C4—121no—
1040C2×C4—121no—
1041C2×C4—121no—
1042C2×C4—121no—
1043C2×C4—121no—
1044C2×C4—121no—
1045C2×C4—121no—
1046C2×C4—121no—
1047C2×C4—121no—
1048C2×C4—121no—
1049C2×C4—121no—
1050C2×C4—121no—
1051C2×C4—121no—
1052C2×C4—121no—
1053C2×C4—121no—
1054C2×C4—121no—
1055C2×C4—121no—
1056C2×C4—121no—
1057C2×C4—121no—
1058C2×C3—44no—
1059C2×C3#240511yescharacteristic
1060C2×C3#241911yescharacteristic
1061C2×C3#241911yescharacteristic
1062C2×C3#243011yescharacteristic
1063C2×C3#243011yescharacteristic
1064C2×C3#255311yescharacteristic
1065C2×C3#255311yescharacteristic
1066C2×C3#255711yescharacteristic
1067C2×C3#255711yescharacteristic
1068C2×C3#269311yescharacteristic
1069C2×C3#269311yescharacteristic
1070C2×C3#269511yescharacteristic
1071C2×C3#269511yescharacteristic
1072C2×C3#269711yescharacteristic
1073C2×C3#272411yescharacteristic
1074D3—44no—
1075C22—24no—
1076C22—24no—
1077C22—24no—
1078C22—42no—
1079C22—42no—
1080C22—42no—
1081C22—42no—
1082C22—42no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—42no—
1089C22—42no—
1090C22—64no—
1091C22—64no—
1092C22—64no—
1093C22—122no—
1094C22—122no—
1095C22—122no—
1096C22—122no—
1097C22—122no—
1098C22—122no—
1099C22—122no—
1100C22—122no—
1101C22—122no—
1102C22—122no—
1103C22—122no—
1104C22—122no—
1105C22#559611yescharacteristic
1106C22#559711yescharacteristic
1107C22#561011yescharacteristic
1108C22#561111yescharacteristic
1109C22D3×#12311yescharacteristic
1110C22#565311yescharacteristic
1111C22#565411yescharacteristic
1112C22#565411yescharacteristic
1113C22#565411yescharacteristic
1114C22#565411yescharacteristic
1115C22#565511yescharacteristic
1116C22#565511yescharacteristic
1117C22#565811yescharacteristic
1118C22#566011yescharacteristic
1119C22#566511yescharacteristic
1120C22#566611yescharacteristic
1121C22#567811yescharacteristic
1122C22#567911yescharacteristic
1123C22#568011yescharacteristic
1124C22#568111yescharacteristic
1125C22#570411yescharacteristic
1126C22#570511yescharacteristic
1127C22#570611yescharacteristic
1128C22#570711yescharacteristic
1129C22#570711yescharacteristic
1130C22#570811yescharacteristic
1131C22#570811yescharacteristic
1132C22#571211yescharacteristic
1133C22C2×#93711yescharacteristic
1134C22#580611yescharacteristic
1135C22#582411yescharacteristic
1136C22#582911yescharacteristic
1137C22#582911yescharacteristic
1138C22#583211yescharacteristic
1139C22#583311yescharacteristic
1140C4—42no—
1141C4—42no—
1142C4—42no—
1143C4—81no—
1144C4—81no—
1145C4—81no—
1146C4—122no—
1147C4—122no—
1148C4—122no—
1149C4—122no—
1150C4—122no—
1151C4—122no—
1152C4—241no—
1153C3#1546311yescharacteristic, complemented, Sylow
1154C2—44no—
1155C2—124no—
1156C2#7751511yescharacteristic
1157C2#7751611yescharacteristic
1158C2#7757411yescharacteristic
1159C2#7757611yescharacteristic
1160C2#7759511yescharacteristic
1161C2#7767011yescharacteristic
1162C2#7767111yescharacteristic
1163C2#7769611yescharacteristic
1164C2#8265111yescharacteristic
1165C2#8284811yescharacteristic
1166C2#8287511yescharacteristic
1167C2#8289311yescharacteristic
1168C2#8299911yescharacteristic
1169C2#8309211yescharacteristic
1170C2#8310711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC2×C3×#397C2
prime radicalC23×#67C22
hypercenterC2×#397D3
hypocenterC3#15463
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#397

Complements

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

NH ≅ G/Ntype
2. C2×C3×#397C2semidirect
3. C2×#4952C2semidirect
5. #71570C2semidirect
6. #71565C2semidirect
8. #71544C2semidirect
9. #71544C2semidirect
10. #69428C2semidirect
11. (C2×D3)⋊#95C2semidirect
12. (C2×D3)⋊#95C2semidirect
13. #69415C2semidirect
14. #69414C2semidirect
15. #69409C2semidirect
60. C2×#397D3semidirect
1153. C3#15463semidirect

Maximal subgroups

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

subgroupindex
C22×#8832
C2×C3×#3972
C2×#49522
C2×#49582
#715702
#715652
#715502
#715442
#694282
(C2×D3)⋊#952
#694152
#694142
#694092
#154633