Finite Group Databasebeta

← #10733897

Subgroups — #10733897

Order 768.

1946 conjugacy classes of subgroups.

The subgroup lattice has 1182 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#385C211yesmaximal, characteristic, complemented
2C2×#5213C211yesmaximal, characteristic
3C2×#4973C211yesmaximal, characteristic, complemented
4C2×#4947C211yesmaximal, characteristic, complemented
5C2×#4957C211yesmaximal, characteristic
6C2×#4673C211yesmaximal, characteristic, complemented
7#72127C211yesmaximal, characteristic, complemented
8#71570C211yesmaximal, characteristic, complemented
9#71570C211yesmaximal, characteristic, complemented
10#71566C211yesmaximal, characteristic, complemented
11#71550C211yesmaximal, characteristic
12#71546C211yesmaximal, characteristic, complemented
13#69427C211yesmaximal, characteristic, complemented
14#69413C211yesmaximal, characteristic, complemented
15#69407C211yesmaximal, characteristic, complemented
16#15331—31nomaximal, Sylow
17C24×C3×C4C2211yescharacteristic
18C23×#67C2211yescharacteristic
19C23×Dic6C2211yescharacteristic
20C22×C3×C4⋊C4C2211yescharacteristic
21C22×C3×C4⋊C4C2211yescharacteristic
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2211yescharacteristic
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×(C2×D3)⋊C4C2211yescharacteristic
33C22×C4⋊Dic3C2211yescharacteristic
34C22×Dic3⋊C4C2211yescharacteristic
35C22×C4×Dic3C2211yescharacteristic
36C3×#385—24no—
37C2×C3×#95C2211yescharacteristic
38C2×C3×#95C2211yescharacteristic
39#5213—24no—
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
54#4973—24no—
55#4957—24no—
56#4947—24no—
57#4673—24no—
58C2×#393—31no—
59C2×#393—31no—
60C2×#391—31no—
61C2×#390—31no—
62C2×#386—31no—
63C2×#385D311yescharacteristic, complemented
64#1442—31no—
65#1441—31no—
66#1439—31no—
67#1439—31no—
68#1439—31no—
69#1439—31no—
70#1438—31no—
71#1436—31no—
72C22⋊#95—31no—
73C25×C3C2311yescharacteristic
74C24×D3C2311yescharacteristic
75C23×C3×C4—22no—
76C23×C3×C4—22no—
77C23×C3×C4—22no—
78C23×C3×C4—41no—
79C23×C3×C4—41no—
80C23×C3×C4—41no—
81C23×C3×C4—41no—
82C23×C3×C4C2311yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C23×C3×C4C2311yescharacteristic
85C23×C3×C4C2311yescharacteristic
86C23×C3×C4C2311yescharacteristic
87C23×C3×C4C2311yescharacteristic
88C22×#67—22no—
89C22×#67—22no—
90C22×#67—22no—
91C22×#67—22no—
92C22×#67—41no—
93C22×#67—41no—
94C22×#67Q814yescomplemented
95C23×Dic3C2311yescharacteristic
96C23×Dic3C2311yescharacteristic
97C23×Dic3C2311yescharacteristic
98C23×Dic3C2311yescharacteristic
99C23×Dic3C2311yescharacteristic
100C23×Dic3C2311yescharacteristic
101C23×Dic3C2311yescharacteristic
102C22×Dic6—22no—
103C22×Dic6—22no—
104C22×Dic6—22no—
105C22×Dic6—22no—
106C22×Dic6—22no—
107C22×Dic6—41no—
108C22×Dic6—41no—
109C2×C3×C4⋊C4—22no—
110C2×C3×C4⋊C4—22no—
111C2×C3×C4⋊C4—22no—
112C2×C3×C4⋊C4—41no—
113C2×C3×C4⋊C4—41no—
114C2×C3×C4⋊C4—41no—
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—22no—
126C2×#217—22no—
127C2×#217—41no—
128C2×#217—41no—
129C2×#217—41no—
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—22no—
139C2×(C2×D3)⋊C4—22no—
140C2×(C2×D3)⋊C4—41no—
141C2×(C2×D3)⋊C4—41no—
142C2×(C2×D3)⋊C4—41no—
143C2×(C2×D3)⋊C4—41no—
144C2×(C2×D3)⋊C4—41no—
145C2×(C2×D3)⋊C4—41no—
146C2×(C2×D3)⋊C4—41no—
147C2×(C2×D3)⋊C4—41no—
148C2×C4⋊Dic3—22no—
149C2×C4⋊Dic3—41no—
150C2×C4⋊Dic3—41no—
151C2×Dic3⋊C4—22no—
152C2×Dic3⋊C4—22no—
153C2×Dic3⋊C4—41no—
154C2×C4×Dic3—22no—
155C2×C4×Dic3—22no—
156C2×C4×Dic3—41no—
157C3×#95—22no—
158C3×#95D414yescomplemented
159C3⋊#95—22no—
160C3⋊#95—22no—
161C3⋊#95—22no—
162C3⋊#95—22no—
163C3⋊#95—22no—
164C3⋊#95—22no—
165C3⋊#95—22no—
166C3⋊#95—22no—
167C3⋊#95—22no—
168C3⋊#95—22no—
169C3⋊#95—41no—
170C3⋊#95—41no—
171C3⋊#95—41no—
172C3⋊#95D414yes—
173C23×Q8—31no—
174C23×D4—31no—
175C24×C4C2×D311yescharacteristic
176C22×C4⋊C4—31no—
177C22×C4⋊C4—31no—
178C22×C4⋊C4C2×D311yescharacteristic
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⋊C4—31no—
188C22×C22⋊C4—31no—
189C22×C22⋊C4C2×D311yescharacteristic
190C22×C22⋊C4C2×D311yescharacteristic
191C22×C42—31no—
192#393—64no—
193#393—64no—
194#391—64no—
195#390—64no—
196#386—64no—
197#385—24no—
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×#95—31no—
209C2×#95—31no—
210C2×#95—31no—
211C2×#95—31no—
212C2×#95C2×D311yescharacteristic
213C2×#95C2×D311yescharacteristic
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×C3—21no—
224C24×C3—21no—
225C24×C3—21no—
226C24×C3C2×D412yes—
227C24×C3C2×Q812yes—
228C24×C3#4112yes—
229C24×C3C2411yescharacteristic
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×D3—21no—
240C23×D3—21no—
241C23×D3—21no—
242C23×D3—21no—
243C23×D3—21no—
244C23×D3C2×Q812yes—
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—44no—
281C22×C3×C4—44no—
282C22×C3×C4—44no—
283C22×C3×C4—44no—
284C22×C3×C4—44no—
285C22×C3×C4—44no—
286C22×C3×C4—44no—
287C22×C3×C4C2×D412yes—
288C22×C3×C4C2×D412yes—
289C22×C3×C4C2×D412yes—
290C22×C3×C4C2×D412yes—
291C22×C3×C4C2×D412yes—
292C22×C3×C4C2×D412yes—
293C22×C3×C4#4112yes—
294C2×#67—28no—
295C2×#67—28no—
296C2×#67—44no—
297C2×#67—44no—
298C2×#67—44no—
299C2×#67—44no—
300C2×#67—44no—
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—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×Dic3C2×D412yes—
345C22×Dic3C2×D412yes—
346C22×Dic3C2×Q812yes—
347C22×Dic3#4112yes—
348C22×Dic3#4112yes—
349C22×Dic3#4112yes—
350C2×Dic6—28no—
351C2×Dic6—44no—
352C2×Dic6—44no—
353C2×Dic6—44no—
354C2×Dic6—44no—
355C2×Dic6—44no—
356C2×Dic6—44no—
357C3×C4⋊C4—44no—
358C3×C4⋊C4—44no—
359C3×C22⋊C4—28no—
360C3×C22⋊C4—44no—
361#217—44no—
362#217—44no—
363#217—44no—
364(C2×D3)⋊C4—44no—
365(C2×D3)⋊C4—44no—
366(C2×D3)⋊C4—44no—
367(C2×D3)⋊C4—44no—
368(C2×D3)⋊C4—44no—
369(C2×D3)⋊C4—44no—
370C4⋊Dic3—44no—
371Dic3⋊C4—44no—
372C4×Dic3—44no—
373C25—31no—
374C25C22×D311yescharacteristic
375C22×Q8—62no—
376C22×Q8—62no—
377C22×Q8—62no—
378C22×Q8—62no—
379C22×Q8—62no—
380C22×Q8—121no—
381C22×Q8—121no—
382C22×D4—34no—
383C22×D4—62no—
384C22×D4—62no—
385C22×D4—62no—
386C22×D4—62no—
387C22×D4—121no—
388C22×D4—121no—
389C23×C4—22no—
390C23×C4—22no—
391C23×C4—22no—
392C23×C4—31no—
393C23×C4—31no—
394C23×C4—31no—
395C23×C4—31no—
396C23×C4—31no—
397C23×C4—31no—
398C23×C4—31no—
399C23×C4—41no—
400C23×C4—41no—
401C23×C4—41no—
402C23×C4—41no—
403C23×C4C22×D311yescharacteristic
404C23×C4C22×D311yescharacteristic
405C23×C4C22×D311yescharacteristic
406C23×C4C22×D311yescharacteristic
407C23×C4C22×D311yescharacteristic
408C23×C4C22×D311yescharacteristic
409C2×C4⋊C4—22no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—41no—
413C2×C4⋊C4—41no—
414C2×C4⋊C4—41no—
415C2×C4⋊C4—62no—
416C2×C4⋊C4—62no—
417C2×C4⋊C4—62no—
418C2×C4⋊C4—121no—
419C2×C4⋊C4—121no—
420C2×C4⋊C4—121no—
421C2×C22⋊C4—22no—
422C2×C22⋊C4—22no—
423C2×C22⋊C4—22no—
424C2×C22⋊C4—22no—
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—62no—
442C2×C22⋊C4—121no—
443C2×C22⋊C4—121no—
444C2×C22⋊C4—121no—
445C2×C22⋊C4—121no—
446C2×C22⋊C4—121no—
447C2×C22⋊C4—121no—
448C2×C22⋊C4—121no—
449C2×C22⋊C4—121no—
450C2×C22⋊C4—121no—
451C2×C22⋊C4—121no—
452C2×C22⋊C4—121no—
453C2×C22⋊C4D1214yes—
454C2×C42—62no—
455C2×C42—62no—
456C2×C42—121no—
457#95—22no—
458#95—34no—
459#95—62no—
460#95—62no—
461#95—62no—
462#95—62no—
463#95—62no—
464#95—62no—
465#95—62no—
466#95—62no—
467#95—62no—
468#95—62no—
469#95—121no—
470#95—121no—
471#95—121no—
472#95#6714yescomplemented
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—22no—
484C23×C3—22no—
485C23×C3—22no—
486C23×C3—22no—
487C23×C3—22no—
488C23×C3—22no—
489C23×C3—22no—
490C23×C3—22no—
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—41no—
500C23×C3—41no—
501C23×C3—41no—
502C23×C3—41no—
503C23×C3—41no—
504C23×C3—41no—
505C23×C3—41no—
506C23×C3—41no—
507C23×C3C22⋊Q814yes—
508C23×C3C22×D411yescharacteristic
509C23×C3C22×D411yescharacteristic
510C23×C3C22×D411yescharacteristic
511C23×C3C22×Q811yescharacteristic
512C23×C3C2×#4111yescharacteristic
513C23×C3C2×#4111yescharacteristic
514C23×C3C2×#4111yescharacteristic
515C23×C3C2×#4111yescharacteristic
516C23×C3C2×#4111yescharacteristic
517C23×C3H(5,𝔽2)11yescharacteristic
518C23×C3H(5,𝔽2)11yescharacteristic
519C23×C3H(5,𝔽2)11yescharacteristic
520C23×C3H(5,𝔽2)11yescharacteristic
521C23×C3H(5,𝔽2)11yescharacteristic
522C23×C32−1+411yescharacteristic
523C22×D3—22no—
524C22×D3—22no—
525C22×D3—22no—
526C22×D3—22no—
527C22×D3—22no—
528C22×D3—22no—
529C22×D3—22no—
530C22×D3—41no—
531C22×D3—41no—
532C22×D3—41no—
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—41no—
550C22×D3—41no—
551C22×D3—41no—
552C22×D3—41no—
553C22×D3—41no—
554C22×D3—41no—
555C22×D3—41no—
556C22×D3—41no—
557C22×D3—41no—
558C2×C3×C4—22no—
559C2×C3×C4—22no—
560C2×C3×C4—22no—
561C2×C3×C4—22no—
562C2×C3×C4—22no—
563C2×C3×C4—22no—
564C2×C3×C4—22no—
565C2×C3×C4—22no—
566C2×C3×C4—22no—
567C2×C3×C4—22no—
568C2×C3×C4—22no—
569C2×C3×C4—22no—
570C2×C3×C4—22no—
571C2×C3×C4—22no—
572C2×C3×C4—22no—
573C2×C3×C4—22no—
574C2×C3×C4—22no—
575C2×C3×C4—22no—
576C2×C3×C4—416no—
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—
592C2×C3×C4—41no—
593C2×C3×C4—41no—
594C2×C3×C4—41no—
595C2×C3×C4—41no—
596C2×C3×C4—41no—
597C2×C3×C4—41no—
598C2×C3×C4—41no—
599C2×C3×C4—41no—
600C2×C3×C4#12114yes—
601#67—416no—
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—22no—
612C2×Dic3—22no—
613C2×Dic3—22no—
614C2×Dic3—22no—
615C2×Dic3—22no—
616C2×Dic3—22no—
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—
643C2×Dic3—41no—
644C2×Dic3—41no—
645C2×Dic3—41no—
646C2×Dic3—41no—
647C2×Dic3—41no—
648C2×Dic3—41no—
649C2×Dic3—41no—
650C2×Dic3C22⋊Q814yes—
651Dic6—416no—
652C24—21no—
653C24—21no—
654C24—21no—
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—32no—
665C24—61no—
666C24—61no—
667C24—61no—
668C24—61no—
669C24—61no—
670C24—61no—
671C24—61no—
672C24—61no—
673C24—61no—
674C24—61no—
675C24—61no—
676C24—61no—
677C24—61no—
678C24—61no—
679C24C2×D1212yes—
680C24#23712yes—
681C24D3×Q812yes—
682C24C23×D311yescharacteristic
683C2×Q8—68no—
684C2×Q8—124no—
685C2×Q8—124no—
686C2×Q8—124no—
687C2×Q8—124no—
688C2×Q8—124no—
689C2×Q8—124no—
690C2×D4—68no—
691C2×D4—68no—
692C2×D4—124no—
693C2×D4—124no—
694C2×D4—124no—
695C2×D4—124no—
696C2×D4—124no—
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—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—32no—
733C22×C4—32no—
734C22×C4—32no—
735C22×C4—32no—
736C22×C4—32no—
737C22×C4—32no—
738C22×C4—44no—
739C22×C4—44no—
740C22×C4—44no—
741C22×C4—44no—
742C22×C4—44no—
743C22×C4—44no—
744C22×C4—44no—
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—61no—
772C22×C4—61no—
773C22×C4—61no—
774C22×C4—61no—
775C22×C4—61no—
776C22×C4—61no—
777C22×C4—61no—
778C22×C4—61no—
779C22×C4—61no—
780C22×C4—61no—
781C22×C4—61no—
782C22×C4—61no—
783C22×C4—61no—
784C22×C4—61no—
785C22×C4—61no—
786C22×C4—61no—
787C22×C4—61no—
788C22×C4C2×D1212yes—
789C22×C4C2×D1212yes—
790C22×C4#23512yes—
791C22×C4D3×D412yes—
792C22×C4C2×#6712yes—
793C22×C4C2×#6712yes—
794C22×C4C2×#6712yes—
795C4⋊C4—44no—
796C4⋊C4—44no—
797C4⋊C4—124no—
798C4⋊C4—124no—
799C22⋊C4—28no—
800C22⋊C4—44no—
801C22⋊C4—124no—
802C22⋊C4—124no—
803C22⋊C4—124no—
804C22⋊C4—124no—
805C22⋊C4—124no—
806C22⋊C4—124no—
807C22⋊C4—124no—
808C22⋊C4—124no—
809C22⋊C4—124no—
810C42—124no—
811C22×C3—24no—
812C22×C3—24no—
813C22×C3—24no—
814C22×C3—42no—
815C22×C3—42no—
816C22×C3—42no—
817C22×C3—42no—
818C22×C3—42no—
819C22×C3—42no—
820C22×C3—42no—
821C22×C3—42no—
822C22×C3—42no—
823C22×C3—42no—
824C22×C3—42no—
825C22×C3—42no—
826C22×C3C2×#12111yescharacteristic
827C22×C3C2×C22⋊Q811yescharacteristic
828C22×C3C2×C22⋊Q811yescharacteristic
829C22×C3#52511yescharacteristic
830C22×C3#52911yescharacteristic
831C22×C3#53211yescharacteristic
832C22×C3#53511yescharacteristic
833C22×C3#53511yescharacteristic
834C22×C3#53711yescharacteristic
835C22×C3#53811yescharacteristic
836C22×C3#53811yescharacteristic
837C22×C3#53811yescharacteristic
838C22×C3#54211yescharacteristic
839C22×C3#54211yescharacteristic
840C22×C3#54311yescharacteristic
841C22×C3D4211yescharacteristic
842C22×C3D4211yescharacteristic
843C22×C3#54611yescharacteristic
844C22×C3#54611yescharacteristic
845C22×C3#54611yescharacteristic
846C22×C3#54611yescharacteristic
847C22×C3#54611yescharacteristic
848C22×C3#54611yescharacteristic
849C22×C3#54811yescharacteristic
850C22×C3D4×Q811yescharacteristic
851C22×C3#55111yescharacteristic
852C22×C3#55211yescharacteristic
853C22×C3#55411yescharacteristic
854C22×C3#55411yescharacteristic
855C22×C3#55411yescharacteristic
856C22×C3#55911yescharacteristic
857C22×C3#55911yescharacteristic
858C22×C3#55911yescharacteristic
859C22×C3H(3,𝔽4)11yescharacteristic
860C22×C3#56211yescharacteristic
861C2×D3—42no—
862C2×D3—42no—
863C2×D3—42no—
864C2×D3—42no—
865C2×D3—42no—
866C2×D3—42no—
867C2×D3—42no—
868C2×D3—81no—
869C2×D3—81no—
870C2×D3—81no—
871C2×D3—81no—
872C2×D3—81no—
873C2×D3—81no—
874C2×D3—81no—
875C2×D3—81no—
876C3×C4—24no—
877C3×C4—42no—
878C3×C4—42no—
879C3×C4—42no—
880C3×C4—42no—
881C3×C4—81no—
882Dic3—24no—
883Dic3—42no—
884Dic3—42no—
885Dic3—42no—
886Dic3—81no—
887Dic3—81no—
888Dic3—81no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—22no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—62no—
924C23—62no—
925C23—62no—
926C23—62no—
927C23—62no—
928C23—62no—
929C23—62no—
930C23—121no—
931C23—121no—
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—121no—
949C23—121no—
950C23—121no—
951C23—121no—
952C23—121no—
953C23—121no—
954C23—121no—
955C23—121no—
956C23—121no—
957C23—121no—
958C23#89714yes—
959C23C22×D1211yescharacteristic
960C23C2×#23511yescharacteristic
961C23C2×D3×D411yescharacteristic
962C23C2×#23711yescharacteristic
963C23#100411yescharacteristic
964C23#100411yescharacteristic
965C23#100411yescharacteristic
966C23#100411yescharacteristic
967C23C2×D3×Q811yescharacteristic
968C23#100711yescharacteristic
969C23D3×#4111yescharacteristic
970C23D3×#4111yescharacteristic
971C23D3×#4111yescharacteristic
972C23#100911yescharacteristic
973C23C22×#6711yescharacteristic
974Q8—1216no—
975D4—1216no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—34no—
995C2×C4—416no—
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—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—62no—
1020C2×C4—62no—
1021C2×C4—62no—
1022C2×C4—62no—
1023C2×C4—62no—
1024C2×C4—62no—
1025C2×C4—62no—
1026C2×C4—62no—
1027C2×C4—62no—
1028C2×C4—62no—
1029C2×C4—62no—
1030C2×C4—62no—
1031C2×C4—62no—
1032C2×C4—62no—
1033C2×C4—62no—
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×C4—121no—
1059C2×C4—121no—
1060C2×C4—121no—
1061C2×C4—121no—
1062C2×C4—121no—
1063C2×C4—121no—
1064C2×C4—121no—
1065C2×C4—121no—
1066C2×C4—121no—
1067C2×C4#93014yes—
1068C2×C3—44no—
1069C2×C3#241711yescharacteristic
1070C2×C3#242411yescharacteristic
1071C2×C3#243711yescharacteristic
1072C2×C3#245011yescharacteristic
1073C2×C3#245211yescharacteristic
1074C2×C3#245811yescharacteristic
1075C2×C3#254411yescharacteristic
1076C2×C3#255711yescharacteristic
1077C2×C3#258011yescharacteristic
1078C2×C3#267011yescharacteristic
1079C2×C3#267611yescharacteristic
1080C2×C3#269211yescharacteristic
1081C2×C3#271211yescharacteristic
1082C2×C3#275111yescharacteristic
1083C2×C3#280411yescharacteristic
1084D3—82no—
1085C22—24no—
1086C22—24no—
1087C22—24no—
1088C22—42no—
1089C22—42no—
1090C22—42no—
1091C22—42no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—122no—
1101C22—122no—
1102C22—122no—
1103C22—122no—
1104C22—122no—
1105C22—122no—
1106C22—122no—
1107C22—241no—
1108C22—241no—
1109C22—241no—
1110C22—241no—
1111C22—241no—
1112C22—241no—
1113C22—241no—
1114C22—241no—
1115C22C2×#89711yescharacteristic
1116C22#551011yescharacteristic
1117C22#551111yescharacteristic
1118C22#551311yescharacteristic
1119C22#554711yescharacteristic
1120C22D4×D1211yescharacteristic
1121C22#555411yescharacteristic
1122C22#555411yescharacteristic
1123C22#555411yescharacteristic
1124C22#555911yescharacteristic
1125C22#555911yescharacteristic
1126C22#556011yescharacteristic
1127C22#559111yescharacteristic
1128C22#559211yescharacteristic
1129C22#559311yescharacteristic
1130C22#559411yescharacteristic
1131C22D3×C22⋊Q811yescharacteristic
1132C22#563311yescharacteristic
1133C22#563411yescharacteristic
1134C22#563611yescharacteristic
1135C22#563611yescharacteristic
1136C22#564011yescharacteristic
1137C22#564011yescharacteristic
1138C22#564711yescharacteristic
1139C22#564911yescharacteristic
1140C22#565711yescharacteristic
1141C22#565811yescharacteristic
1142C22#566411yescharacteristic
1143C22C2×#93011yescharacteristic
1144C22D4×#6711yescharacteristic
1145C22#580511yescharacteristic
1146C22#580611yescharacteristic
1147C22Q8×#6711yescharacteristic
1148C22#582911yescharacteristic
1149C22#583211yescharacteristic
1150C4—24no—
1151C4—42no—
1152C4—42no—
1153C4—42no—
1154C4—42no—
1155C4—64no—
1156C4—81no—
1157C4—122no—
1158C4—122no—
1159C4—122no—
1160C4—241no—
1161C4—241no—
1162C4—241no—
1163C3#1533111yescharacteristic, complemented, Sylow
1164C2—44no—
1165C2—242no—
1166C2#7441311yescharacteristic
1167C2#7442411yescharacteristic
1168C2#7442811yescharacteristic
1169C2#7448711yescharacteristic
1170C2#7450911yescharacteristic
1171C2#7452911yescharacteristic
1172C2#7454811yescharacteristic
1173C2#7458111yescharacteristic
1174C2#8219411yescharacteristic
1175C2#8238111yescharacteristic
1176C2#8240711yescharacteristic
1177C2#8259511yescharacteristic
1178C2#8276611yescharacteristic
1179C2#8283011yescharacteristic
1180C2#8286211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC2×C3×#385C2
prime radicalC23×#67C22
hypercenterC2×#385D3
hypocenterC3#15331
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. C2×C3×#385C2semidirect
3. C2×#4973C2semidirect
4. C2×#4947C2semidirect
6. C2×#4673C2semidirect
7. #72127C2semidirect
8. #71570C2semidirect
9. #71570C2semidirect
10. #71566C2semidirect
12. #71546C2semidirect
13. #69427C2semidirect
14. #69413C2semidirect
15. #69407C2semidirect
63. C2×#385D3semidirect
94. C22×#67Q8semidirect
158. C3×#95D4semidirect
472. #95#67semidirect
1163. C3#15331semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#3852
C2×#52132
C2×#49732
C2×#49472
C2×#49572
C2×#46732
#721272
#715702
#715662
#715502
#715462
#694272
#694132
#694072
#153313