Finite Group Databasebeta

← #10724510

Subgroups — #10724510

Order 768.

1958 conjugacy classes of subgroups.

The subgroup lattice has 1174 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×#5210C211yesmaximal, characteristic, complemented
4C2×#4972C211yesmaximal, characteristic, complemented
5C2×#4961C211yesmaximal, characteristic
6C2×#4957C211yesmaximal, characteristic
7C2×#4669C211yesmaximal, characteristic, complemented
8#71570C211yesmaximal, characteristic, complemented
9#71570C211yesmaximal, characteristic, complemented
10#71568C211yesmaximal, characteristic, complemented
11#71549C211yesmaximal, characteristic, complemented
12#71545C211yesmaximal, characteristic, complemented
13#69428C211yesmaximal, characteristic, complemented
14#69407C211yesmaximal, characteristic, complemented
15#69403C211yesmaximal, characteristic, complemented
16#14518—31nomaximal, Sylow
17C24×C3×C4C2211yescharacteristic
18C23×#67C2211yescharacteristic
19C22×C3×C4⋊C4C2211yescharacteristic
20C22×C3×C4⋊C4C2211yescharacteristic
21C22×C3×C22⋊C4C2211yescharacteristic
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×#217C2211yescharacteristic
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×(C2×D3)⋊C4C2211yescharacteristic
32C22×C4⋊Dic3C2211yescharacteristic
33C22×Dic3⋊C4C2211yescharacteristic
34C22×Dic3⋊C4C2211yescharacteristic
35C22×Dic3⋊C4C2211yescharacteristic
36C22×C4×Dic3C2211yescharacteristic
37C22×C4×Dic3C2211yescharacteristic
38C3×#385—24no—
39C2×C3×#95C2211yescharacteristic
40C2×C3×#95C2211yescharacteristic
41#5213—24no—
42#5210—24no—
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
55#4972—24no—
56#4961C418yescomplemented
57#4957—24no—
58#4669—24no—
59C2×#394—31no—
60C2×#390—31no—
61C2×#389—31no—
62C2×#388—31no—
63C2×#386—31no—
64C2×#385—31no—
65C2×#385D311yescharacteristic, complemented
66#1444—31no—
67#1440—31no—
68#1439—31no—
69#1439—31no—
70#1439—31no—
71#1437—31no—
72#1436—31no—
73#1434—31no—
74C25×C3C2311yescharacteristic
75C24×D3C2311yescharacteristic
76C23×C3×C4—22no—
77C23×C3×C4—22no—
78C23×C3×C4—22no—
79C23×C3×C4—41no—
80C23×C3×C4—41no—
81C23×C3×C4—41no—
82C23×C3×C4—41no—
83C23×C3×C4C2311yescharacteristic
84C23×C3×C4C2311yescharacteristic
85C23×C3×C4C2311yescharacteristic
86C23×C3×C4C2311yescharacteristic
87C23×C3×C4C2311yescharacteristic
88C23×C3×C4C2311yescharacteristic
89C22×#67—22no—
90C22×#67—22no—
91C22×#67—22no—
92C22×#67—22no—
93C22×#67—41no—
94C22×#67—41no—
95C22×#67C2×C414yes—
96C23×Dic3C2311yescharacteristic
97C23×Dic3C2311yescharacteristic
98C23×Dic3C2311yescharacteristic
99C23×Dic3C2311yescharacteristic
100C23×Dic3C2311yescharacteristic
101C23×Dic3C2311yescharacteristic
102C23×Dic3C2311yescharacteristic
103C2×C3×C4⋊C4—22no—
104C2×C3×C4⋊C4—22no—
105C2×C3×C4⋊C4—22no—
106C2×C3×C4⋊C4—41no—
107C2×C3×C4⋊C4—41no—
108C2×C3×C4⋊C4—41no—
109C2×C3×C22⋊C4—22no—
110C2×C3×C22⋊C4—22no—
111C2×C3×C22⋊C4—22no—
112C2×C3×C22⋊C4—22no—
113C2×C3×C22⋊C4—41no—
114C2×C3×C22⋊C4C2×C414yes—
115C2×#217—22no—
116C2×#217—22no—
117C2×#217—22no—
118C2×#217—22no—
119C2×#217—41no—
120C2×#217—41no—
121C2×#217—41no—
122C2×#217C2×C414yes—
123C2×#217D414yes—
124C2×(C2×D3)⋊C4—22no—
125C2×(C2×D3)⋊C4—22no—
126C2×(C2×D3)⋊C4—22no—
127C2×(C2×D3)⋊C4—22no—
128C2×(C2×D3)⋊C4—22no—
129C2×(C2×D3)⋊C4—22no—
130C2×(C2×D3)⋊C4—22no—
131C2×(C2×D3)⋊C4—22no—
132C2×(C2×D3)⋊C4—41no—
133C2×(C2×D3)⋊C4—41no—
134C2×(C2×D3)⋊C4—41no—
135C2×(C2×D3)⋊C4—41no—
136C2×(C2×D3)⋊C4—41no—
137C2×(C2×D3)⋊C4—41no—
138C2×(C2×D3)⋊C4—41no—
139C2×(C2×D3)⋊C4—41no—
140C2×(C2×D3)⋊C4C2×C414yescomplemented
141C2×(C2×D3)⋊C4C2×C414yescomplemented
142C2×C4⋊Dic3—22no—
143C2×C4⋊Dic3—22no—
144C2×C4⋊Dic3C2×C414yescomplemented
145C2×Dic3⋊C4—22no—
146C2×Dic3⋊C4—22no—
147C2×Dic3⋊C4—22no—
148C2×Dic3⋊C4—22no—
149C2×Dic3⋊C4—22no—
150C2×Dic3⋊C4—22no—
151C2×Dic3⋊C4—41no—
152C2×Dic3⋊C4—41no—
153C2×Dic3⋊C4—41no—
154C2×C4×Dic3—22no—
155C2×C4×Dic3—22no—
156C2×C4×Dic3—22no—
157C2×C4×Dic3—22no—
158C2×C4×Dic3—41no—
159C2×C4×Dic3—41no—
160C3×#95—22no—
161C3×#95D414yescomplemented
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⋊#95C2×C414yescomplemented
173C3⋊#95D414yes—
174C23×D4—31no—
175C24×C4C2×D311yescharacteristic
176C22×C4⋊C4—31no—
177C22×C4⋊C4—31no—
178C22×C4⋊C4—31no—
179C22×C4⋊C4—31no—
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⋊C4—31no—
190C22×C22⋊C4—31no—
191C22×C22⋊C4C2×D311yescharacteristic
192C22×C22⋊C4C2×D311yescharacteristic
193C22×C42—31no—
194C22×C42—31no—
195#394—38no—
196#390—64no—
197#389—64no—
198#388—64no—
199#386—64no—
200#385—24no—
201#385—64no—
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×#95—31no—
214C2×#95C2×D311yescharacteristic
215C2×#95C2×D311yescharacteristic
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×C3—21no—
227C24×C3—21no—
228C24×C3C22×C412yes—
229C24×C3C2×D412yes—
230C24×C3#4112yes—
231C24×C3C2411yescharacteristic
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×D3—21no—
245C23×D3—21no—
246C23×D3C22×C412yes—
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—44no—
283C22×C3×C4—44no—
284C22×C3×C4—44no—
285C22×C3×C4—44no—
286C22×C3×C4—44no—
287C22×C3×C4—44no—
288C22×C3×C4—44no—
289C22×C3×C4C22×C412yes—
290C22×C3×C4C22×C412yes—
291C22×C3×C4C2×D412yes—
292C22×C3×C4C2×D412yes—
293C22×C3×C4C2×D412yes—
294C22×C3×C4C2×D412yes—
295C22×C3×C4#4112yes—
296C2×#67—28no—
297C2×#67—28no—
298C2×#67—44no—
299C2×#67—44no—
300C2×#67—44no—
301C2×#67—44no—
302C2×#67—44no—
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×Dic3C22×C412yes—
345C22×Dic3C22×C412yes—
346C22×Dic3C22×C412yes—
347C22×Dic3C2×D412yes—
348C22×Dic3C2×D412yes—
349C22×Dic3C2×D412yes—
350C22×Dic3C2×D412yes—
351C22×Dic3#4112yes—
352C3×C4⋊C4—44no—
353C3×C4⋊C4—44no—
354C3×C22⋊C4—28no—
355C3×C22⋊C4—44no—
356#217—28no—
357#217—44no—
358#217—44no—
359(C2×D3)⋊C4—28no—
360(C2×D3)⋊C4—44no—
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—44no—
367Dic3⋊C4—44no—
368Dic3⋊C4—44no—
369C4×Dic3—44no—
370C4×Dic3—44no—
371C25—31no—
372C25C22×D311yescharacteristic
373C22×D4—34no—
374C22×D4—62no—
375C22×D4—62no—
376C22×D4—62no—
377C22×D4—62no—
378C22×D4—121no—
379C22×D4—121no—
380C23×C4—22no—
381C23×C4—22no—
382C23×C4—22no—
383C23×C4—31no—
384C23×C4—31no—
385C23×C4—31no—
386C23×C4—31no—
387C23×C4—31no—
388C23×C4—31no—
389C23×C4—31no—
390C23×C4—41no—
391C23×C4—41no—
392C23×C4—41no—
393C23×C4—41no—
394C23×C4C22×D311yescharacteristic
395C23×C4C22×D311yescharacteristic
396C23×C4C22×D311yescharacteristic
397C23×C4C22×D311yescharacteristic
398C23×C4C22×D311yescharacteristic
399C23×C4C22×D311yescharacteristic
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—34no—
404C2×C4⋊C4—41no—
405C2×C4⋊C4—41no—
406C2×C4⋊C4—41no—
407C2×C4⋊C4—62no—
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—121no—
416C2×C4⋊C4—121no—
417C2×C4⋊C4—121no—
418C2×C22⋊C4—22no—
419C2×C22⋊C4—22no—
420C2×C22⋊C4—22no—
421C2×C22⋊C4—22no—
422C2×C22⋊C4—34no—
423C2×C22⋊C4—34no—
424C2×C22⋊C4—34no—
425C2×C22⋊C4—34no—
426C2×C22⋊C4—41no—
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—121no—
440C2×C22⋊C4—121no—
441C2×C22⋊C4—121no—
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⋊C4C4×D314yes—
451C2×C42—62no—
452C2×C42—62no—
453C2×C42—62no—
454C2×C42—62no—
455C2×C42—121no—
456C2×C42—121no—
457#95—22no—
458#95—34no—
459#95—34no—
460#95—62no—
461#95—62no—
462#95—62no—
463#95—62no—
464#95—62no—
465#95—62no—
466#95—121no—
467#95—121no—
468#95—121no—
469#95—121no—
470#95#6714yescomplemented
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—22no—
484C23×C3—22no—
485C23×C3—22no—
486C23×C3—22no—
487C23×C3—22no—
488C23×C3—22no—
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—41no—
500C23×C3—41no—
501C23×C3—41no—
502C23×C3—41no—
503C23×C3—41no—
504C23×C3—41no—
505C23×C3C4×D414yes—
506C23×C3C23×C411yescharacteristic
507C23×C3C22×D411yescharacteristic
508C23×C3C22×D411yescharacteristic
509C23×C3C22×D411yescharacteristic
510C23×C3C2×#4111yescharacteristic
511C23×C3C2×#4111yescharacteristic
512C23×C3C2×#4111yescharacteristic
513C23×C3H(5,𝔽2)11yescharacteristic
514C23×C3H(5,𝔽2)11yescharacteristic
515C23×C3H(5,𝔽2)11yescharacteristic
516C23×C3H(5,𝔽2)11yescharacteristic
517C23×C3H(5,𝔽2)11yescharacteristic
518C23×C32−1+411yescharacteristic
519C23×C32−1+411yescharacteristic
520C23×C32−1+411yescharacteristic
521C22×D3—22no—
522C22×D3—22no—
523C22×D3—22no—
524C22×D3—22no—
525C22×D3—22no—
526C22×D3—22no—
527C22×D3—22no—
528C22×D3—41no—
529C22×D3—41no—
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—
556C2×C3×C4—22no—
557C2×C3×C4—22no—
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—416no—
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×C4C4×D414yes—
599#67—416no—
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—22no—
612C2×Dic3—22no—
613C2×Dic3—22no—
614C2×Dic3—22no—
615C2×Dic3—22no—
616C2×Dic3—22no—
617C2×Dic3—22no—
618C2×Dic3—22no—
619C2×Dic3—22no—
620C2×Dic3—22no—
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×Dic3C4×D414yes—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24—21no—
654C24—21no—
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—32no—
662C24—61no—
663C24—61no—
664C24—61no—
665C24—61no—
666C24—61no—
667C24—61no—
668C24—61no—
669C24—61no—
670C24—61no—
671C24—61no—
672C24—61no—
673C24—61no—
674C24—61no—
675C24—61no—
676C24C2×C4×D312yes—
677C24D3×D412yes—
678C24#23912yes—
679C24C23×D311yescharacteristic
680C2×D4—68no—
681C2×D4—68no—
682C2×D4—124no—
683C2×D4—124no—
684C2×D4—124no—
685C2×D4—124no—
686C2×D4—124no—
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—21no—
722C22×C4—32no—
723C22×C4—32no—
724C22×C4—32no—
725C22×C4—32no—
726C22×C4—32no—
727C22×C4—32no—
728C22×C4—32no—
729C22×C4—32no—
730C22×C4—44no—
731C22×C4—44no—
732C22×C4—44no—
733C22×C4—44no—
734C22×C4—44no—
735C22×C4—44no—
736C22×C4—44no—
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—61no—
772C22×C4—61no—
773C22×C4—61no—
774C22×C4—61no—
775C22×C4—61no—
776C22×C4—61no—
777C22×C4—61no—
778C22×C4C2×C4×D312yes—
779C22×C4C2×C4×D312yes—
780C22×C4#23512yes—
781C22×C4D3×D412yes—
782C22×C4C2×#6712yes—
783C22×C4C2×#6712yes—
784C22×C4C2×#6712yes—
785C4⋊C4—44no—
786C4⋊C4—44no—
787C4⋊C4—68no—
788C4⋊C4—124no—
789C4⋊C4—124no—
790C4⋊C4—124no—
791C22⋊C4—28no—
792C22⋊C4—44no—
793C22⋊C4—68no—
794C22⋊C4—68no—
795C22⋊C4—124no—
796C22⋊C4—124no—
797C22⋊C4—124no—
798C22⋊C4—124no—
799C22⋊C4—124no—
800C22⋊C4—124no—
801C22⋊C4—124no—
802C42—124no—
803C42—124no—
804C22×C3—24no—
805C22×C3—24no—
806C22×C3—24no—
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×C3—42no—
817C22×C3—42no—
818C22×C3—42no—
819C22×C3C2×C4×D411yescharacteristic
820C22×C3C2×C4×D411yescharacteristic
821C22×C3C2×C4×D411yescharacteristic
822C22×C3#51811yescharacteristic
823C22×C3#52011yescharacteristic
824C22×C3#52011yescharacteristic
825C22×C3#52011yescharacteristic
826C22×C3#53411yescharacteristic
827C22×C3#53511yescharacteristic
828C22×C3#53511yescharacteristic
829C22×C3#53611yescharacteristic
830C22×C3#53611yescharacteristic
831C22×C3#53711yescharacteristic
832C22×C3#53911yescharacteristic
833C22×C3#53911yescharacteristic
834C22×C3#54011yescharacteristic
835C22×C3#54211yescharacteristic
836C22×C3#54211yescharacteristic
837C22×C3#54211yescharacteristic
838C22×C3D4211yescharacteristic
839C22×C3D4211yescharacteristic
840C22×C3D4211yescharacteristic
841C22×C3#54611yescharacteristic
842C22×C3#54611yescharacteristic
843C22×C3#54711yescharacteristic
844C22×C3#54711yescharacteristic
845C22×C3#54811yescharacteristic
846C22×C3#54811yescharacteristic
847C22×C3#55111yescharacteristic
848C22×C3#55311yescharacteristic
849C22×C3#55311yescharacteristic
850C22×C3#56011yescharacteristic
851C22×C3#56211yescharacteristic
852C22×C3#56211yescharacteristic
853C22×C3#56311yescharacteristic
854C2×D3—42no—
855C2×D3—42no—
856C2×D3—42no—
857C2×D3—42no—
858C2×D3—42no—
859C2×D3—42no—
860C2×D3—42no—
861C2×D3—81no—
862C2×D3—81no—
863C2×D3—81no—
864C2×D3—81no—
865C2×D3—81no—
866C2×D3—81no—
867C2×D3—81no—
868C2×D3—81no—
869C3×C4—24no—
870C3×C4—42no—
871C3×C4—42no—
872C3×C4—42no—
873C3×C4—42no—
874C3×C4—81no—
875Dic3—24no—
876Dic3—42no—
877Dic3—42no—
878Dic3—42no—
879Dic3—42no—
880Dic3—42no—
881Dic3—81no—
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—22no—
898C23—22no—
899C23—22no—
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—41no—
915C23—41no—
916C23—62no—
917C23—62no—
918C23—62no—
919C23—62no—
920C23—62no—
921C23—62no—
922C23—62no—
923C23—121no—
924C23—121no—
925C23—121no—
926C23—121no—
927C23—121no—
928C23—121no—
929C23—121no—
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#89314yes—
952C23C22×C4×D311yescharacteristic
953C23C2×#23511yescharacteristic
954C23C2×D3×D411yescharacteristic
955C23C2×D3×D411yescharacteristic
956C23#100411yescharacteristic
957C23#100411yescharacteristic
958C23#100411yescharacteristic
959C23#100411yescharacteristic
960C23C2×#23911yescharacteristic
961C23#100711yescharacteristic
962C23D3×#4111yescharacteristic
963C23#100911yescharacteristic
964C23#101011yescharacteristic
965C23#101011yescharacteristic
966C23C22×#6711yescharacteristic
967D4—1216no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
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—34no—
987C2×C4—416no—
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—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—62no—
1026C2×C4—62no—
1027C2×C4—62no—
1028C2×C4—62no—
1029C2×C4—62no—
1030C2×C4—62no—
1031C2×C4—62no—
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×C4—121no—
1059C2×C4C4×#6714yes—
1060C2×C3—44no—
1061C2×C3#232211yescharacteristic
1062C2×C3#232411yescharacteristic
1063C2×C3#232611yescharacteristic
1064C2×C3#235811yescharacteristic
1065C2×C3#236111yescharacteristic
1066C2×C3#236111yescharacteristic
1067C2×C3#237611yescharacteristic
1068C2×C3#266911yescharacteristic
1069C2×C3#267211yescharacteristic
1070C2×C3#267411yescharacteristic
1071C2×C3#268111yescharacteristic
1072C2×C3#270111yescharacteristic
1073C2×C3#271111yescharacteristic
1074C2×C3#272311yescharacteristic
1075C2×C3#275711yescharacteristic
1076D3—82no—
1077C22—24no—
1078C22—24no—
1079C22—24no—
1080C22—42no—
1081C22—42no—
1082C22—42no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—42no—
1089C22—42no—
1090C22—42no—
1091C22—42no—
1092C22—122no—
1093C22—122no—
1094C22—122no—
1095C22—122no—
1096C22—122no—
1097C22—122no—
1098C22—122no—
1099C22—241no—
1100C22—241no—
1101C22—241no—
1102C22—241no—
1103C22—241no—
1104C22—241no—
1105C22—241no—
1106C22—241no—
1107C22C2×#89311yescharacteristic
1108C22#550411yescharacteristic
1109C22#550711yescharacteristic
1110C22#551411yescharacteristic
1111C22#554011yescharacteristic
1112C22C4×D3×D411yescharacteristic
1113C22#554511yescharacteristic
1114C22#554611yescharacteristic
1115C22#554611yescharacteristic
1116C22#555211yescharacteristic
1117C22#556111yescharacteristic
1118C22#556211yescharacteristic
1119C22#558911yescharacteristic
1120C22#559011yescharacteristic
1121C22#559211yescharacteristic
1122C22#559511yescharacteristic
1123C22#562811yescharacteristic
1124C22#563011yescharacteristic
1125C22#563711yescharacteristic
1126C22#564011yescharacteristic
1127C22#564511yescharacteristic
1128C22#564511yescharacteristic
1129C22#564611yescharacteristic
1130C22#564711yescharacteristic
1131C22#564811yescharacteristic
1132C22#565411yescharacteristic
1133C22#566211yescharacteristic
1134C22#566711yescharacteristic
1135C22C2×C4×#6711yescharacteristic
1136C22D4×#6711yescharacteristic
1137C22D4×#6711yescharacteristic
1138C22#580511yescharacteristic
1139C22#581711yescharacteristic
1140C22#582411yescharacteristic
1141C22#583311yescharacteristic
1142C4—24no—
1143C4—42no—
1144C4—42no—
1145C4—42no—
1146C4—42no—
1147C4—64no—
1148C4—81no—
1149C4—122no—
1150C4—122no—
1151C4—122no—
1152C4—122no—
1153C4—122no—
1154C4—241no—
1155C3#1451811yescharacteristic, complemented, Sylow
1156C2—44no—
1157C2—242no—
1158C2#7438411yescharacteristic
1159C2#7438611yescharacteristic
1160C2#7450811yescharacteristic
1161C2#7452711yescharacteristic
1162C2#7455011yescharacteristic
1163C2#7459611yescharacteristic
1164C2#7459811yescharacteristic
1165C2#7463611yescharacteristic
1166C2#8216311yescharacteristic
1167C2#8234011yescharacteristic
1168C2#8239611yescharacteristic
1169C2#8260911yescharacteristic
1170C2#8280411yescharacteristic
1171C2#8282911yescharacteristic
1172C2#8286911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC2×C3×#385C2
socle, cosocleC24×C3C24
prime radicalC23×#67C22
hypercenterC2×#385D3
hypocenterC3#14518
LCSG ▷ C23×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×#5210C2semidirect
4. C2×#4972C2semidirect
7. C2×#4669C2semidirect
8. #71570C2semidirect
9. #71570C2semidirect
10. #71568C2semidirect
11. #71549C2semidirect
12. #71545C2semidirect
13. #69428C2semidirect
14. #69407C2semidirect
15. #69403C2semidirect
56. #4961C4semidirect
65. C2×#385D3semidirect
140. C2×(C2×D3)⋊C4C2×C4semidirect
141. C2×(C2×D3)⋊C4C2×C4semidirect
144. C2×C4⋊Dic3C2×C4semidirect
161. C3×#95D4semidirect
172. C3⋊#95C2×C4semidirect
470. #95#67semidirect
1155. C3#14518semidirect

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×#52102
C2×#49722
C2×#49612
C2×#49572
C2×#46692
#715702
#715682
#715492
#715452
#694282
#694072
#694032
#145183