Finite Group Databasebeta

← #10733829

Subgroups — #10733829

Order 768.

1998 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×#399C211yesmaximal, characteristic, complemented
2C2×#4989C211yesmaximal, characteristic, complemented
3C2×#4989C211yesmaximal, characteristic, complemented
4C2×#4956C211yesmaximal, characteristic
5C2×#4958C211yesmaximal, characteristic
6C2×#4942C211yesmaximal, characteristic, complemented
7#71570C211yesmaximal, characteristic, complemented
8#71568C211yesmaximal, characteristic, complemented
9#71567C211yesmaximal, characteristic, complemented
10#71566C211yesmaximal, characteristic, complemented
11#71550C211yesmaximal, characteristic
12#71547C211yesmaximal, characteristic, complemented
13#71544C211yesmaximal, characteristic, complemented
14#69428C211yesmaximal, characteristic, complemented
15#69418C211yesmaximal, characteristic, complemented
16#15327—31nomaximal, Sylow
17C23×#67C2211yescharacteristic
18C24×Dic3C2211yescharacteristic
19C23×C4×D3C2211yescharacteristic
20C22×C3×C4⋊C4C2211yescharacteristic
21C22×C3×C4⋊C4C2211yescharacteristic
22C22×C3×C4⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×C3×C22⋊C4C2211yescharacteristic
25C22×C3×C22⋊C4C2211yescharacteristic
26C22×#217C2211yescharacteristic
27C22×#217C2211yescharacteristic
28C22×(C2×D3)⋊C4C2211yescharacteristic
29C22×(C2×D3)⋊C4C2211yescharacteristic
30C22×(C2×D3)⋊C4C2211yescharacteristic
31C22×(C2×D3)⋊C4C2211yescharacteristic
32C22×(C2×D3)⋊C4C2211yescharacteristic
33C22×Dic3⋊C4C2211yescharacteristic
34C22×Dic3⋊C4C2211yescharacteristic
35C22×Dic3⋊C4C2211yescharacteristic
36C3×#399—24no—
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#4989—24no—
54#4989—24no—
55#4958—24no—
56#4956—24no—
57#4942—24no—
58C2×#399D311yescharacteristic, complemented
59C2×#386—31no—
60C2×#386—31no—
61C2×#385—31no—
62C2×#385—31no—
63C2×#380—31no—
64#1444—31no—
65#1443—31no—
66#1442—31no—
67#1441—31no—
68#1439—31no—
69#1439—31no—
70#1439—31no—
71#1438—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×#67Q814yes—
88C23×Dic3—22no—
89C23×Dic3—22no—
90C23×Dic3—22no—
91C23×Dic3—22no—
92C23×Dic3—22no—
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—41no—
106C22×C4×D3—41no—
107C22×C4×D3—41no—
108C22×C4×D3—41no—
109C2×C3×C4⋊C4—22no—
110C2×C3×C4⋊C4—22no—
111C2×C3×C4⋊C4—22no—
112C2×C3×C4⋊C4—22no—
113C2×C3×C4⋊C4—22no—
114C2×C3×C4⋊C4—41no—
115C2×C3×C4⋊C4—41no—
116C2×C3×C4⋊C4—41no—
117C2×C3×C4⋊C4—41no—
118C2×C3×C22⋊C4—22no—
119C2×C3×C22⋊C4—22no—
120C2×C3×C22⋊C4—22no—
121C2×C3×C22⋊C4—22no—
122C2×C3×C22⋊C4—41no—
123C2×C3×C22⋊C4—41no—
124C2×C3×C22⋊C4—41no—
125C2×C3×C22⋊C4—41no—
126C2×C3×C22⋊C4D414yes—
127C2×#217—22no—
128C2×#217—22no—
129C2×#217—22no—
130C2×#217—22no—
131C2×#217—41no—
132C2×#217—41no—
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—22no—
141C2×(C2×D3)⋊C4—22no—
142C2×(C2×D3)⋊C4—22no—
143C2×(C2×D3)⋊C4—41no—
144C2×(C2×D3)⋊C4—41no—
145C2×(C2×D3)⋊C4—41no—
146C2×(C2×D3)⋊C4—41no—
147C2×(C2×D3)⋊C4D414yes—
148C2×Dic3⋊C4—22no—
149C2×Dic3⋊C4—22no—
150C2×Dic3⋊C4—22no—
151C2×Dic3⋊C4—22no—
152C2×Dic3⋊C4—22no—
153C2×Dic3⋊C4—41no—
154C2×Dic3⋊C4—41no—
155C2×Dic3⋊C4—41no—
156C2×Dic3⋊C4—41no—
157C3×#95—22no—
158C3⋊#95—22no—
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—41no—
169C3⋊#95—41no—
170C3⋊#95—41no—
171C3⋊#95—41no—
172C3⋊#95D414yescomplemented
173C23×D4—31no—
174C24×C4—31no—
175C24×C4—31no—
176C22×C4⋊C4—31no—
177C22×C4⋊C4—31no—
178C22×C4⋊C4—31no—
179C22×C4⋊C4C2×D311yescharacteristic
180C22×C4⋊C4C2×D311yescharacteristic
181C22×C4⋊C4C2×D311yescharacteristic
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×C22⋊C4C2×D311yescharacteristic
192#399—24no—
193#386—64no—
194#386—64no—
195#385—64no—
196#385—64no—
197#380—64no—
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×#95—31no—
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×D3C2×D412yes—
243C23×D3C2×Q812yes—
244C23×D3#4112yes—
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×C4—21no—
282C22×C3×C4—21no—
283C22×C3×C4C2×D412yes—
284C22×C3×C4C2×D412yes—
285C22×C3×C4C2×D412yes—
286C22×C3×C4C2×D412yes—
287C2×#67—28no—
288C2×#67—28no—
289C2×#67—44no—
290C2×#67—44no—
291C2×#67—44no—
292C2×#67—44no—
293C2×#67—44no—
294C22×Dic3—21no—
295C22×Dic3—21no—
296C22×Dic3—21no—
297C22×Dic3—21no—
298C22×Dic3—28no—
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—21no—
335C22×Dic3—21no—
336C22×Dic3—21no—
337C22×Dic3—44no—
338C22×Dic3—44no—
339C22×Dic3—44no—
340C22×Dic3—44no—
341C22×Dic3—44no—
342C22×Dic3—44no—
343C22×Dic3C2×D412yes—
344C22×Dic3C2×D412yes—
345C22×Dic3C2×D412yes—
346C22×Dic3C2×Q812yes—
347C22×Dic3#4112yes—
348C22×Dic3#4112yes—
349C22×Dic3#4112yes—
350C2×C4×D3—44no—
351C2×C4×D3—44no—
352C2×C4×D3—44no—
353C2×C4×D3—44no—
354C2×C4×D3—44no—
355C2×C4×D3—44no—
356C2×C4×D3—44no—
357C3×C4⋊C4—44no—
358C3×C4⋊C4—44no—
359C3×C4⋊C4—44no—
360C3×C22⋊C4—44no—
361C3×C22⋊C4—44no—
362C3×C22⋊C4—44no—
363#217—44no—
364#217—44no—
365(C2×D3)⋊C4—28no—
366(C2×D3)⋊C4—28no—
367(C2×D3)⋊C4—44no—
368(C2×D3)⋊C4—44no—
369(C2×D3)⋊C4—44no—
370Dic3⋊C4—44no—
371Dic3⋊C4—44no—
372Dic3⋊C4—44no—
373C25—31no—
374C25C22×D311yescharacteristic
375C22×D4—34no—
376C22×D4—62no—
377C22×D4—62no—
378C22×D4—62no—
379C22×D4—62no—
380C22×D4—121no—
381C22×D4—121no—
382C23×C4—31no—
383C23×C4—31no—
384C23×C4—31no—
385C23×C4—31no—
386C23×C4—31no—
387C23×C4—31no—
388C23×C4—31no—
389C23×C4—62no—
390C23×C4—62no—
391C23×C4—62no—
392C23×C4—62no—
393C23×C4—62no—
394C23×C4—62no—
395C23×C4—62no—
396C23×C4—62no—
397C23×C4—121no—
398C23×C4—121no—
399C23×C4—121no—
400C23×C4—121no—
401C23×C4—121no—
402C23×C4—121no—
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—22no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—41no—
415C2×C4⋊C4—41no—
416C2×C4⋊C4—41no—
417C2×C4⋊C4—41no—
418C2×C4⋊C4—62no—
419C2×C4⋊C4—62no—
420C2×C4⋊C4—62no—
421C2×C4⋊C4—62no—
422C2×C4⋊C4—62no—
423C2×C4⋊C4—121no—
424C2×C4⋊C4—121no—
425C2×C4⋊C4—121no—
426C2×C4⋊C4—121no—
427C2×C22⋊C4—22no—
428C2×C22⋊C4—22no—
429C2×C22⋊C4—22no—
430C2×C22⋊C4—22no—
431C2×C22⋊C4—34no—
432C2×C22⋊C4—41no—
433C2×C22⋊C4—41no—
434C2×C22⋊C4—41no—
435C2×C22⋊C4—41no—
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—62no—
443C2×C22⋊C4—62no—
444C2×C22⋊C4—62no—
445C2×C22⋊C4—62no—
446C2×C22⋊C4—62no—
447C2×C22⋊C4—62no—
448C2×C22⋊C4—62no—
449C2×C22⋊C4—62no—
450C2×C22⋊C4—121no—
451C2×C22⋊C4—121no—
452C2×C22⋊C4—121no—
453C2×C22⋊C4—121no—
454C2×C22⋊C4—121no—
455C2×C22⋊C4—121no—
456C2×C22⋊C4#6714yes—
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—121no—
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—22no—
531C22×D3—22no—
532C22×D3—22no—
533C22×D3—22no—
534C22×D3—22no—
535C22×D3—22no—
536C22×D3—22no—
537C22×D3—22no—
538C22×D3—22no—
539C22×D3—22no—
540C22×D3—22no—
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×D3C22⋊Q814yes—
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—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—
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—
600#67—416no—
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—22no—
612C2×Dic3—22no—
613C2×Dic3—22no—
614C2×Dic3—22no—
615C2×Dic3—22no—
616C2×Dic3—22no—
617C2×Dic3—22no—
618C2×Dic3—22no—
619C2×Dic3—416no—
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×Dic3#12314yes—
651C4×D3—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—32no—
666C24—32no—
667C24—61no—
668C24—61no—
669C24—61no—
670C24—61no—
671C24—61no—
672C24—61no—
673C24—61no—
674C24—61no—
675C24—61no—
676C24—61no—
677C24—61no—
678C24—61no—
679C24D3×Q812yes—
680C24#23912yes—
681C24C2×#6712yes—
682C24C23×D311yescharacteristic
683C2×D4—68no—
684C2×D4—68no—
685C2×D4—124no—
686C2×D4—124no—
687C2×D4—124no—
688C2×D4—124no—
689C2×D4—124no—
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—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—32no—
729C22×C4—32no—
730C22×C4—32no—
731C22×C4—32no—
732C22×C4—32no—
733C22×C4—32no—
734C22×C4—32no—
735C22×C4—61no—
736C22×C4—61no—
737C22×C4—61no—
738C22×C4—61no—
739C22×C4—68no—
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—61no—
772C22×C4—61no—
773C22×C4—61no—
774C22×C4—61no—
775C22×C4—61no—
776C22×C4—61no—
777C22×C4—61no—
778C22×C4—124no—
779C22×C4—124no—
780C22×C4—124no—
781C22×C4—124no—
782C22×C4—124no—
783C22×C4—124no—
784C22×C4—124no—
785C22×C4—124no—
786C22×C4—124no—
787C22×C4—124no—
788C22×C4—124no—
789C22×C4—124no—
790C22×C4—124no—
791C22×C4D3×D412yes—
792C22×C4D3×D412yes—
793C22×C4C2×#6712yes—
794C22×C4C2×#6712yes—
795C4⋊C4—44no—
796C4⋊C4—44no—
797C4⋊C4—44no—
798C4⋊C4—124no—
799C4⋊C4—124no—
800C4⋊C4—124no—
801C22⋊C4—44no—
802C22⋊C4—44no—
803C22⋊C4—44no—
804C22⋊C4—68no—
805C22⋊C4—68no—
806C22⋊C4—124no—
807C22⋊C4—124no—
808C22⋊C4—124no—
809C22⋊C4—124no—
810C22⋊C4—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×C22⋊Q811yescharacteristic
827C22×C3C2×C22⋊Q811yescharacteristic
828C22×C3C2×#12311yescharacteristic
829C22×C3#52511yescharacteristic
830C22×C3#52511yescharacteristic
831C22×C3#53211yescharacteristic
832C22×C3#53411yescharacteristic
833C22×C3#53511yescharacteristic
834C22×C3#53511yescharacteristic
835C22×C3#53811yescharacteristic
836C22×C3#53911yescharacteristic
837C22×C3#53911yescharacteristic
838C22×C3#54011yescharacteristic
839C22×C3#54211yescharacteristic
840C22×C3#54311yescharacteristic
841C22×C3D4211yescharacteristic
842C22×C3D4211yescharacteristic
843C22×C3D4211yescharacteristic
844C22×C3#54611yescharacteristic
845C22×C3#54611yescharacteristic
846C22×C3#54611yescharacteristic
847C22×C3#54711yescharacteristic
848C22×C3#54711yescharacteristic
849C22×C3D4×Q811yescharacteristic
850C22×C3#55111yescharacteristic
851C22×C3#55111yescharacteristic
852C22×C3#55111yescharacteristic
853C22×C3#55311yescharacteristic
854C22×C3#55311yescharacteristic
855C22×C3#55311yescharacteristic
856C22×C3#55411yescharacteristic
857C22×C3#55411yescharacteristic
858C22×C3#55411yescharacteristic
859C22×C3#56011yescharacteristic
860C22×C3#56211yescharacteristic
861C2×D3—24no—
862C2×D3—24no—
863C2×D3—24no—
864C2×D3—42no—
865C2×D3—42no—
866C2×D3—42no—
867C2×D3—42no—
868C2×D3—42no—
869C2×D3—42no—
870C2×D3—42no—
871C2×D3—42no—
872C2×D3—42no—
873C2×D3—42no—
874C2×D3—42no—
875C2×D3—42no—
876C3×C4—42no—
877C3×C4—42no—
878C3×C4—42no—
879C3×C4—42no—
880C3×C4—81no—
881C3×C4—81no—
882Dic3—24no—
883Dic3—42no—
884Dic3—42no—
885Dic3—42no—
886Dic3—42no—
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—34no—
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—41no—
924C23—62no—
925C23—62no—
926C23—62no—
927C23—62no—
928C23—62no—
929C23—62no—
930C23—62no—
931C23—62no—
932C23—62no—
933C23—62no—
934C23—62no—
935C23—62no—
936C23—62no—
937C23—62no—
938C23—62no—
939C23—62no—
940C23—62no—
941C23—62no—
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#94614yes—
959C23C2×D3×D411yescharacteristic
960C23C2×D3×D411yescharacteristic
961C23#100411yescharacteristic
962C23#100411yescharacteristic
963C23#100411yescharacteristic
964C23#100411yescharacteristic
965C23C2×D3×Q811yescharacteristic
966C23C2×#23911yescharacteristic
967C23D3×#4111yescharacteristic
968C23D3×#4111yescharacteristic
969C23D3×#4111yescharacteristic
970C23D3×#4111yescharacteristic
971C23#100911yescharacteristic
972C23#101011yescharacteristic
973C23C22×#6711yescharacteristic
974D4—1216no—
975C2×C4—22no—
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—34no—
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—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—62no—
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—62no—
1035C2×C4—62no—
1036C2×C4—1216no—
1037C2×C4—1216no—
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—121no—
1068C2×C3—44no—
1069C2×C3#241811yescharacteristic
1070C2×C3#242211yescharacteristic
1071C2×C3#243711yescharacteristic
1072C2×C3#244911yescharacteristic
1073C2×C3#244911yescharacteristic
1074C2×C3#246411yescharacteristic
1075C2×C3#248711yescharacteristic
1076C2×C3#256411yescharacteristic
1077C2×C3#259811yescharacteristic
1078C2×C3#266911yescharacteristic
1079C2×C3#269211yescharacteristic
1080C2×C3#270611yescharacteristic
1081C2×C3#270811yescharacteristic
1082C2×C3#274611yescharacteristic
1083C2×C3#278011yescharacteristic
1084D3—44no—
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—64no—
1101C22—64no—
1102C22—64no—
1103C22—122no—
1104C22—122no—
1105C22—122no—
1106C22—122no—
1107C22—122no—
1108C22—122no—
1109C22—122no—
1110C22—122no—
1111C22—122no—
1112C22—122no—
1113C22—122no—
1114C22—122no—
1115C22D3×C22⋊Q811yescharacteristic
1116C22#562711yescharacteristic
1117C22#563011yescharacteristic
1118C22#563211yescharacteristic
1119C22#563411yescharacteristic
1120C22#563611yescharacteristic
1121C22#563611yescharacteristic
1122C22#563611yescharacteristic
1123C22#563711yescharacteristic
1124C22#563711yescharacteristic
1125C22#563711yescharacteristic
1126C22#564511yescharacteristic
1127C22D3×#12311yescharacteristic
1128C22#565411yescharacteristic
1129C22#565511yescharacteristic
1130C22#565611yescharacteristic
1131C22#565711yescharacteristic
1132C22#566011yescharacteristic
1133C22#566111yescharacteristic
1134C22#566111yescharacteristic
1135C22#566111yescharacteristic
1136C22#566211yescharacteristic
1137C22#566311yescharacteristic
1138C22#566711yescharacteristic
1139C22#571511yescharacteristic
1140C22#571511yescharacteristic
1141C22#571711yescharacteristic
1142C22#572011yescharacteristic
1143C22D4×#6711yescharacteristic
1144C22D4×#6711yescharacteristic
1145C22#580411yescharacteristic
1146C22C2×#94611yescharacteristic
1147C22#582411yescharacteristic
1148C22#582911yescharacteristic
1149C22#583211yescharacteristic
1150C4—42no—
1151C4—42no—
1152C4—42no—
1153C4—42no—
1154C4—64no—
1155C4—81no—
1156C4—81no—
1157C4—122no—
1158C4—122no—
1159C4—122no—
1160C4—122no—
1161C4—241no—
1162C4—241no—
1163C3#1532711yescharacteristic, complemented, Sylow
1164C2—44no—
1165C2—124no—
1166C2#7802911yescharacteristic
1167C2#7804411yescharacteristic
1168C2#7806211yescharacteristic
1169C2#7806611yescharacteristic
1170C2#7807711yescharacteristic
1171C2#7808511yescharacteristic
1172C2#7810111yescharacteristic
1173C2#7810411yescharacteristic
1174C2#8276411yescharacteristic
1175C2#8278411yescharacteristic
1176C2#8281611yescharacteristic
1177C2#8284511yescharacteristic
1178C2#8285311yescharacteristic
1179C2#8291011yescharacteristic
1180C2#8319011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC2×C3×#399C2
prime radicalC23×#67C22
hypercenterC2×#399D3
hypocenterC3#15327
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#399

Complements

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

NH ≅ G/Ntype
1. C2×C3×#399C2semidirect
2. C2×#4989C2semidirect
3. C2×#4989C2semidirect
6. C2×#4942C2semidirect
7. #71570C2semidirect
8. #71568C2semidirect
9. #71567C2semidirect
10. #71566C2semidirect
12. #71547C2semidirect
13. #71544C2semidirect
14. #69428C2semidirect
15. #69418C2semidirect
58. C2×#399D3semidirect
172. C3⋊#95D4semidirect
1163. C3#15327semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#3992
C2×#49892
C2×#49562
C2×#49582
C2×#49422
#715702
#715682
#715672
#715662
#715502
#715472
#715442
#694282
#694182
#153273