Finite Group Databasebeta

← #10719421

Subgroups — #10719421

Order 768.

1962 conjugacy classes of subgroups.

The subgroup lattice has 1158 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#4990C211yesmaximal, characteristic, complemented
2C2×#4957C211yesmaximal, characteristic
3C2×#4958C211yesmaximal, characteristic
4C2×Dic3×C22⋊C4C211yesmaximal, characteristic, complemented
5C2×#4648C211yesmaximal, characteristic, complemented
6C3×#1439C211yesmaximal, characteristic, complemented
7#71566C211yesmaximal, characteristic, complemented
8#71550C211yesmaximal, characteristic
9#71545C211yesmaximal, characteristic, complemented
10#71544C211yesmaximal, characteristic, complemented
11#69429C211yesmaximal, characteristic, complemented
12#69408C211yesmaximal, characteristic, complemented
13#69408C211yesmaximal, characteristic, complemented
14#69406C211yesmaximal, characteristic, complemented
15#69401C211yesmaximal, characteristic, complemented
16#14082—31nomaximal, Sylow
17C23×#67C2211yescharacteristic
18C24×Dic3C2211yescharacteristic
19C22×C3×C4⋊C4C2211yescharacteristic
20C22×C3×C22⋊C4C2211yescharacteristic
21C22×C3×C22⋊C4C2211yescharacteristic
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×#217C2211yescharacteristic
24C22×#217C2211yescharacteristic
25C22×(C2×D3)⋊C4C2211yescharacteristic
26C22×(C2×D3)⋊C4C2211yescharacteristic
27C22×(C2×D3)⋊C4C2211yescharacteristic
28C22×(C2×D3)⋊C4C2211yescharacteristic
29C22×(C2×D3)⋊C4C2211yescharacteristic
30C22×(C2×D3)⋊C4C2211yescharacteristic
31C22×Dic3⋊C4C2211yescharacteristic
32C22×C4×Dic3C2211yescharacteristic
33C22×C4×Dic3C2211yescharacteristic
34C22×C4×Dic3C2211yescharacteristic
35C22×C4×Dic3C2211yescharacteristic
36C2×C3×#95C2211yescharacteristic
37C2×C3×#95C2211yescharacteristic
38C2×C3×#95C2211yescharacteristic
39C2×C3⋊#95C2211yescharacteristic
40C2×C3⋊#95C2211yescharacteristic
41C2×C3⋊#95C2211yescharacteristic
42C2×C3⋊#95C2211yescharacteristic
43C2×C3⋊#95C2211yescharacteristic
44C2×C3⋊#95C2211yescharacteristic
45C2×C3⋊#95C2211yescharacteristic
46C2×C3⋊#95C2211yescharacteristic
47C2×C3⋊#95C2211yescharacteristic
48C2×C3⋊#95C2211yescharacteristic
49C2×C3⋊#95C2211yescharacteristic
50C2×C3⋊#95C2211yescharacteristic
51C2×C3⋊#95C2211yescharacteristic
52#4990—24no—
53#4958—24no—
54#4957C418yescomplemented
55Dic3×C22⋊C4—24no—
56#4648—24no—
57C2×#390—31no—
58C2×#388—31no—
59C2×#386—31no—
60C2×C4×C22⋊C4—31no—
61C2×#376—31no—
62#1441—31no—
63#1440—31no—
64#1439D311yescharacteristic, complemented
65#1438—31no—
66#1437—31no—
67#1437—31no—
68#1437—31no—
69#1436—31no—
70#1434—31no—
71C22⋊#95—31no—
72C25×C3C2311yescharacteristic
73C24×D3C2311yescharacteristic
74C23×C3×C4C2311yescharacteristic
75C23×C3×C4C2311yescharacteristic
76C23×C3×C4C2311yescharacteristic
77C23×C3×C4C2311yescharacteristic
78C23×C3×C4C2311yescharacteristic
79C23×C3×C4C2311yescharacteristic
80C22×#67—22no—
81C22×#67—22no—
82C22×#67—22no—
83C22×#67—22no—
84C22×#67—41no—
85C22×#67—41no—
86C22×#67C2×C414yes—
87C23×Dic3—22no—
88C23×Dic3—22no—
89C23×Dic3—22no—
90C23×Dic3—22no—
91C23×Dic3—22no—
92C23×Dic3—41no—
93C23×Dic3—41no—
94C23×Dic3C2311yescharacteristic
95C23×Dic3C2311yescharacteristic
96C23×Dic3C2311yescharacteristic
97C23×Dic3C2311yescharacteristic
98C23×Dic3C2311yescharacteristic
99C23×Dic3C2311yescharacteristic
100C23×Dic3C2311yescharacteristic
101C2×C3×C4⋊C4—22no—
102C2×C3×C4⋊C4—41no—
103C2×C3×C4⋊C4—41no—
104C2×C3×C22⋊C4—22no—
105C2×C3×C22⋊C4—22no—
106C2×C3×C22⋊C4—22no—
107C2×C3×C22⋊C4—22no—
108C2×C3×C22⋊C4—22no—
109C2×C3×C22⋊C4—41no—
110C2×C3×C22⋊C4—41no—
111C2×C3×C22⋊C4—41no—
112C2×C3×C22⋊C4C2×C414yes—
113C2×#217—22no—
114C2×#217—22no—
115C2×#217—22no—
116C2×#217—22no—
117C2×#217—41no—
118C2×#217C2×C414yes—
119C2×(C2×D3)⋊C4—22no—
120C2×(C2×D3)⋊C4—22no—
121C2×(C2×D3)⋊C4—22no—
122C2×(C2×D3)⋊C4—22no—
123C2×(C2×D3)⋊C4—22no—
124C2×(C2×D3)⋊C4—22no—
125C2×(C2×D3)⋊C4—22no—
126C2×(C2×D3)⋊C4—22no—
127C2×(C2×D3)⋊C4—22no—
128C2×(C2×D3)⋊C4—22no—
129C2×(C2×D3)⋊C4—41no—
130C2×(C2×D3)⋊C4—41no—
131C2×(C2×D3)⋊C4—41no—
132C2×(C2×D3)⋊C4—41no—
133C2×(C2×D3)⋊C4—41no—
134C2×(C2×D3)⋊C4—41no—
135C2×(C2×D3)⋊C4C2×C414yescomplemented
136C2×(C2×D3)⋊C4C2×C414yescomplemented
137C2×Dic3⋊C4—41no—
138C2×Dic3⋊C4—41no—
139C2×Dic3⋊C4C2×C414yescomplemented
140C2×C4×Dic3—22no—
141C2×C4×Dic3—22no—
142C2×C4×Dic3—22no—
143C2×C4×Dic3—22no—
144C2×C4×Dic3—22no—
145C2×C4×Dic3—22no—
146C2×C4×Dic3—22no—
147C2×C4×Dic3—22no—
148C2×C4×Dic3—41no—
149C2×C4×Dic3—41no—
150C2×C4×Dic3C2×C414yescomplemented
151C2×C4×Dic3D414yescomplemented
152C3×#95—22no—
153C3×#95—22no—
154C3×#95—41no—
155C3⋊#95—22no—
156C3⋊#95—22no—
157C3⋊#95—22no—
158C3⋊#95—22no—
159C3⋊#95—22no—
160C3⋊#95—22no—
161C3⋊#95—22no—
162C3⋊#95—22no—
163C3⋊#95—22no—
164C3⋊#95—41no—
165C3⋊#95—41no—
166C3⋊#95—41no—
167C3⋊#95D414yes—
168C23×D4—31no—
169C24×C4—31no—
170C22×C4⋊C4—31no—
171C22×C4⋊C4C2×D311yescharacteristic
172C22×C22⋊C4—31no—
173C22×C22⋊C4—31no—
174C22×C22⋊C4—31no—
175C22×C22⋊C4—31no—
176C22×C22⋊C4—31no—
177C22×C22⋊C4—31no—
178C22×C22⋊C4—31no—
179C22×C22⋊C4—31no—
180C22×C22⋊C4C2×D311yescharacteristic
181C22×C22⋊C4C2×D311yescharacteristic
182C22×C22⋊C4C2×D311yescharacteristic
183C22×C42—31no—
184C22×C42—31no—
185C22×C42—31no—
186C22×C42—31no—
187#390—38no—
188#388—64no—
189#386—64no—
190C4×C22⋊C4—64no—
191#376—64no—
192C2×#95—31no—
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×#95C2×D311yescharacteristic
206C2×#95C2×D311yescharacteristic
207C2×#95C2×D311yescharacteristic
208C24×C3—21no—
209C24×C3—21no—
210C24×C3—21no—
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×C3C22×C412yes—
221C24×C3#4112yes—
222C24×C3#4112yes—
223C24×C3C2411yescharacteristic
224C23×D3—21no—
225C23×D3—21no—
226C23×D3—21no—
227C23×D3—21no—
228C23×D3—21no—
229C23×D3—21no—
230C23×D3—21no—
231C23×D3—21no—
232C23×D3—21no—
233C23×D3—21no—
234C23×D3—21no—
235C23×D3—21no—
236C23×D3—21no—
237C23×D3—21no—
238C23×D3C22×C412yes—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4—21no—
259C22×C3×C4—21no—
260C22×C3×C4—21no—
261C22×C3×C4—21no—
262C22×C3×C4—21no—
263C22×C3×C4—21no—
264C22×C3×C4—21no—
265C22×C3×C4—21no—
266C22×C3×C4—21no—
267C22×C3×C4—21no—
268C22×C3×C4—21no—
269C22×C3×C4—21no—
270C22×C3×C4—21no—
271C22×C3×C4—21no—
272C22×C3×C4—21no—
273C22×C3×C4—21no—
274C22×C3×C4—21no—
275C22×C3×C4—21no—
276C22×C3×C4C22×C412yes—
277C22×C3×C4C22×C412yes—
278C22×C3×C4C2×D412yes—
279C22×C3×C4C2×D412yes—
280C22×C3×C4#4112yes—
281C2×#67—28no—
282C2×#67—28no—
283C2×#67—44no—
284C2×#67—44no—
285C2×#67—44no—
286C2×#67—44no—
287C2×#67—44no—
288C22×Dic3—21no—
289C22×Dic3—21no—
290C22×Dic3—21no—
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—28no—
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—44no—
327C22×Dic3—44no—
328C22×Dic3—44no—
329C22×Dic3—44no—
330C22×Dic3—44no—
331C22×Dic3—44no—
332C22×Dic3C22×C412yes—
333C22×Dic3C22×C412yes—
334C22×Dic3C22×C412yes—
335C22×Dic3C2×D412yes—
336C22×Dic3C2×D412yes—
337C22×Dic3C2×D412yes—
338C22×Dic3C2×D412yes—
339C22×Dic3#4112yes—
340C22×Dic3#4112yes—
341C22×Dic3#4112yes—
342C22×Dic3#4112yes—
343C22×Dic3#4112yes—
344C3×C4⋊C4—44no—
345C3×C22⋊C4—28no—
346C3×C22⋊C4—44no—
347C3×C22⋊C4—44no—
348#217—28no—
349#217—44no—
350(C2×D3)⋊C4—28no—
351(C2×D3)⋊C4—44no—
352(C2×D3)⋊C4—44no—
353(C2×D3)⋊C4—44no—
354(C2×D3)⋊C4—44no—
355(C2×D3)⋊C4—44no—
356Dic3⋊C4—44no—
357C4×Dic3—28no—
358C4×Dic3—28no—
359C4×Dic3—28no—
360C4×Dic3—44no—
361C25—31no—
362C25C22×D311yescharacteristic
363C22×D4—34no—
364C22×D4—62no—
365C22×D4—62no—
366C22×D4—62no—
367C22×D4—62no—
368C22×D4—121no—
369C22×D4—121no—
370C23×C4—31no—
371C23×C4—31no—
372C23×C4—31no—
373C23×C4—31no—
374C23×C4—31no—
375C23×C4—31no—
376C23×C4—31no—
377C23×C4—62no—
378C23×C4—62no—
379C23×C4—62no—
380C23×C4—62no—
381C23×C4—62no—
382C23×C4—121no—
383C23×C4—121no—
384C23×C4C22×D311yescharacteristic
385C23×C4C22×D311yescharacteristic
386C23×C4C22×D311yescharacteristic
387C23×C4C22×D311yescharacteristic
388C23×C4C22×D311yescharacteristic
389C23×C4C22×D311yescharacteristic
390C2×C4⋊C4—22no—
391C2×C4⋊C4—34no—
392C2×C4⋊C4—41no—
393C2×C4⋊C4—41no—
394C2×C4⋊C4—121no—
395C2×C4⋊C4—121no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—22no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—22no—
401C2×C22⋊C4—34no—
402C2×C22⋊C4—34no—
403C2×C22⋊C4—34no—
404C2×C22⋊C4—41no—
405C2×C22⋊C4—41no—
406C2×C22⋊C4—41no—
407C2×C22⋊C4—62no—
408C2×C22⋊C4—62no—
409C2×C22⋊C4—62no—
410C2×C22⋊C4—62no—
411C2×C22⋊C4—62no—
412C2×C22⋊C4—62no—
413C2×C22⋊C4—62no—
414C2×C22⋊C4—62no—
415C2×C22⋊C4—62no—
416C2×C22⋊C4—62no—
417C2×C22⋊C4—62no—
418C2×C22⋊C4—62no—
419C2×C22⋊C4—62no—
420C2×C22⋊C4—62no—
421C2×C22⋊C4—121no—
422C2×C22⋊C4—121no—
423C2×C22⋊C4—121no—
424C2×C22⋊C4—121no—
425C2×C22⋊C4—121no—
426C2×C22⋊C4—121no—
427C2×C22⋊C4—121no—
428C2×C22⋊C4C4×D314yes—
429C2×C42—34no—
430C2×C42—34no—
431C2×C42—62no—
432C2×C42—62no—
433C2×C42—62no—
434C2×C42—62no—
435C2×C42—62no—
436C2×C42—62no—
437C2×C42—62no—
438C2×C42—62no—
439C2×C42—121no—
440C2×C42—121no—
441#95—22no—
442#95—22no—
443#95—34no—
444#95—41no—
445#95—62no—
446#95—62no—
447#95—62no—
448#95—62no—
449#95—62no—
450#95—62no—
451#95—62no—
452#95—62no—
453#95—62no—
454#95—121no—
455#95—121no—
456#95—121no—
457C23×C3—22no—
458C23×C3—22no—
459C23×C3—22no—
460C23×C3—22no—
461C23×C3—22no—
462C23×C3—22no—
463C23×C3—22no—
464C23×C3—22no—
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—41no—
476C23×C3—41no—
477C23×C3—41no—
478C23×C3—41no—
479C23×C3—41no—
480C23×C3—41no—
481C23×C3—41no—
482C23×C3—41no—
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#11714yes—
492C23×C3C23×C411yescharacteristic
493C23×C3C22×D411yescharacteristic
494C23×C3C22×D411yescharacteristic
495C23×C3C2×#4111yescharacteristic
496C23×C3C2×#4111yescharacteristic
497C23×C3C2×#4111yescharacteristic
498C23×C3C2×#4111yescharacteristic
499C23×C3C2×#4111yescharacteristic
500C23×C3C2×#4111yescharacteristic
501C23×C3C2×#4111yescharacteristic
502C23×C3C2×#4111yescharacteristic
503C23×C3H(5,𝔽2)11yescharacteristic
504C23×C3H(5,𝔽2)11yescharacteristic
505C23×C3H(5,𝔽2)11yescharacteristic
506C23×C3H(5,𝔽2)11yescharacteristic
507C22×D3—22no—
508C22×D3—22no—
509C22×D3—22no—
510C22×D3—22no—
511C22×D3—22no—
512C22×D3—22no—
513C22×D3—22no—
514C22×D3—41no—
515C22×D3—41no—
516C22×D3—41no—
517C22×D3—41no—
518C22×D3—41no—
519C22×D3—41no—
520C22×D3—41no—
521C22×D3—41no—
522C22×D3—41no—
523C22×D3—41no—
524C22×D3—41no—
525C22×D3—41no—
526C22×D3—41no—
527C22×D3—41no—
528C22×D3—41no—
529C22×D3—41no—
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—
542C2×C3×C4—22no—
543C2×C3×C4—22no—
544C2×C3×C4—22no—
545C2×C3×C4—22no—
546C2×C3×C4—22no—
547C2×C3×C4—22no—
548C2×C3×C4—22no—
549C2×C3×C4—22no—
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—41no—
558C2×C3×C4—41no—
559C2×C3×C4—41no—
560C2×C3×C4—41no—
561C2×C3×C4—41no—
562C2×C3×C4—41no—
563C2×C3×C4—41no—
564C2×C3×C4—41no—
565C2×C3×C4—41no—
566C2×C3×C4—41no—
567C2×C3×C4—41no—
568C2×C3×C4—41no—
569C2×C3×C4—41no—
570C2×C3×C4—41no—
571C2×C3×C4—41no—
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—
584#67—416no—
585C2×Dic3—22no—
586C2×Dic3—22no—
587C2×Dic3—22no—
588C2×Dic3—22no—
589C2×Dic3—22no—
590C2×Dic3—22no—
591C2×Dic3—22no—
592C2×Dic3—22no—
593C2×Dic3—22no—
594C2×Dic3—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—22no—
612C2×Dic3—416no—
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×Dic3C4×D414yes—
633C2×Dic3C4×D414yes—
634C2×Dic3#12114yes—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—32no—
648C24—61no—
649C24—61no—
650C24—61no—
651C24—61no—
652C24—61no—
653C24—61no—
654C24—61no—
655C24—61no—
656C24—61no—
657C24—61no—
658C24—61no—
659C24—61no—
660C24—61no—
661C24—61no—
662C24C2×C4×D312yes—
663C24#23712yes—
664C24#23912yes—
665C24C23×D311yescharacteristic
666C2×D4—68no—
667C2×D4—68no—
668C2×D4—124no—
669C2×D4—124no—
670C2×D4—124no—
671C2×D4—124no—
672C2×D4—124no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—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—32no—
711C22×C4—32no—
712C22×C4—32no—
713C22×C4—32no—
714C22×C4—32no—
715C22×C4—32no—
716C22×C4—32no—
717C22×C4—32no—
718C22×C4—32no—
719C22×C4—32no—
720C22×C4—32no—
721C22×C4—32no—
722C22×C4—61no—
723C22×C4—61no—
724C22×C4—61no—
725C22×C4—61no—
726C22×C4—61no—
727C22×C4—61no—
728C22×C4—61no—
729C22×C4—61no—
730C22×C4—61no—
731C22×C4—61no—
732C22×C4—61no—
733C22×C4—61no—
734C22×C4—68no—
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—124no—
761C22×C4—124no—
762C22×C4—124no—
763C22×C4—124no—
764C22×C4—124no—
765C22×C4—124no—
766C22×C4C2×C4×D312yes—
767C22×C4C2×C4×D312yes—
768C22×C4D3×D412yes—
769C22×C4D3×D412yes—
770C22×C4#23712yes—
771C4⋊C4—44no—
772C4⋊C4—124no—
773C22⋊C4—28no—
774C22⋊C4—44no—
775C22⋊C4—44no—
776C22⋊C4—68no—
777C22⋊C4—68no—
778C22⋊C4—124no—
779C22⋊C4—124no—
780C22⋊C4—124no—
781C22⋊C4—124no—
782C22⋊C4—124no—
783C22⋊C4—124no—
784C42—68no—
785C42—68no—
786C42—68no—
787C42—124no—
788C22×C3—24no—
789C22×C3—24no—
790C22×C3—24no—
791C22×C3—42no—
792C22×C3—42no—
793C22×C3—42no—
794C22×C3—42no—
795C22×C3—42no—
796C22×C3—42no—
797C22×C3—42no—
798C22×C3—42no—
799C22×C3—42no—
800C22×C3—42no—
801C22×C3—42no—
802C22×C3—42no—
803C22×C3C2×#11711yescharacteristic
804C22×C3C2×C4×D411yescharacteristic
805C22×C3C2×C4×D411yescharacteristic
806C22×C3C4×#4111yescharacteristic
807C22×C3C4×#4111yescharacteristic
808C22×C3#51811yescharacteristic
809C22×C3#51811yescharacteristic
810C22×C3C2×#12111yescharacteristic
811C22×C3#52511yescharacteristic
812C22×C3#52511yescharacteristic
813C22×C3#52511yescharacteristic
814C22×C3#52911yescharacteristic
815C22×C3#52911yescharacteristic
816C22×C3#52911yescharacteristic
817C22×C3#53211yescharacteristic
818C22×C3#53511yescharacteristic
819C22×C3#53511yescharacteristic
820C22×C3#54011yescharacteristic
821C22×C3#54011yescharacteristic
822C22×C3#54611yescharacteristic
823C22×C3#54611yescharacteristic
824C22×C3#54611yescharacteristic
825C22×C3#55011yescharacteristic
826C22×C3#55111yescharacteristic
827C22×C3#55111yescharacteristic
828C22×C3#55111yescharacteristic
829C22×C3#55111yescharacteristic
830C22×C3#55111yescharacteristic
831C22×C3#55111yescharacteristic
832C22×C3#55311yescharacteristic
833C22×C3#55311yescharacteristic
834C22×C3#55311yescharacteristic
835C22×C3#55511yescharacteristic
836C22×C3#55511yescharacteristic
837C22×C3#55511yescharacteristic
838C2×D3—42no—
839C2×D3—42no—
840C2×D3—42no—
841C2×D3—42no—
842C2×D3—42no—
843C2×D3—42no—
844C2×D3—42no—
845C2×D3—81no—
846C2×D3—81no—
847C2×D3—81no—
848C2×D3—81no—
849C2×D3—81no—
850C2×D3—81no—
851C2×D3—81no—
852C2×D3—81no—
853C3×C4—42no—
854C3×C4—42no—
855C3×C4—42no—
856C3×C4—42no—
857C3×C4—42no—
858C3×C4—81no—
859Dic3—24no—
860Dic3—24no—
861Dic3—24no—
862Dic3—42no—
863Dic3—42no—
864Dic3—42no—
865Dic3—81no—
866C23—22no—
867C23—22no—
868C23—22no—
869C23—22no—
870C23—22no—
871C23—22no—
872C23—22no—
873C23—22no—
874C23—22no—
875C23—22no—
876C23—22no—
877C23—22no—
878C23—22no—
879C23—22no—
880C23—22no—
881C23—22no—
882C23—22no—
883C23—22no—
884C23—41no—
885C23—41no—
886C23—41no—
887C23—41no—
888C23—41no—
889C23—41no—
890C23—41no—
891C23—41no—
892C23—41no—
893C23—41no—
894C23—41no—
895C23—41no—
896C23—41no—
897C23—41no—
898C23—41no—
899C23—41no—
900C23—62no—
901C23—62no—
902C23—62no—
903C23—62no—
904C23—62no—
905C23—62no—
906C23—62no—
907C23—121no—
908C23—121no—
909C23—121no—
910C23—121no—
911C23—121no—
912C23—121no—
913C23—121no—
914C23—121no—
915C23—121no—
916C23—121no—
917C23—121no—
918C23—121no—
919C23—121no—
920C23—121no—
921C23—121no—
922C23—121no—
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#89214yes—
936C23C22×C4×D311yescharacteristic
937C23C2×D3×D411yescharacteristic
938C23C2×D3×D411yescharacteristic
939C23C2×#23711yescharacteristic
940C23C2×#23711yescharacteristic
941C23#100411yescharacteristic
942C23#100411yescharacteristic
943C23#100411yescharacteristic
944C23C2×#23911yescharacteristic
945C23D3×#4111yescharacteristic
946C23D3×#4111yescharacteristic
947C23D3×#4111yescharacteristic
948C23D3×#4111yescharacteristic
949C23D3×#4111yescharacteristic
950C23#100911yescharacteristic
951D4—1216no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—34no—
968C2×C4—34no—
969C2×C4—34no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—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—62no—
998C2×C4—62no—
999C2×C4—62no—
1000C2×C4—62no—
1001C2×C4—62no—
1002C2×C4—62no—
1003C2×C4—62no—
1004C2×C4—62no—
1005C2×C4—62no—
1006C2×C4—62no—
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—1216no—
1025C2×C4—121no—
1026C2×C4—121no—
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×C3—44no—
1045C2×C3#229011yescharacteristic
1046C2×C3C4×#12111yescharacteristic
1047C2×C3#232811yescharacteristic
1048C2×C3#234211yescharacteristic
1049C2×C3#235311yescharacteristic
1050C2×C3#236311yescharacteristic
1051C2×C3#237211yescharacteristic
1052C2×C3#241111yescharacteristic
1053C2×C3#241411yescharacteristic
1054C2×C3#247111yescharacteristic
1055C2×C3#247611yescharacteristic
1056C2×C3#252611yescharacteristic
1057C2×C3#253111yescharacteristic
1058C2×C3#260311yescharacteristic
1059C2×C3#261011yescharacteristic
1060D3—82no—
1061C22—24no—
1062C22—24no—
1063C22—24no—
1064C22—42no—
1065C22—42no—
1066C22—42no—
1067C22—42no—
1068C22—42no—
1069C22—42no—
1070C22—42no—
1071C22—42no—
1072C22—42no—
1073C22—42no—
1074C22—42no—
1075C22—42no—
1076C22—122no—
1077C22—122no—
1078C22—122no—
1079C22—122no—
1080C22—122no—
1081C22—122no—
1082C22—122no—
1083C22—241no—
1084C22—241no—
1085C22—241no—
1086C22—241no—
1087C22—241no—
1088C22—241no—
1089C22—241no—
1090C22—241no—
1091C22#548611yescharacteristic
1092C22C2×#89211yescharacteristic
1093C22#552211yescharacteristic
1094C22C4×#23711yescharacteristic
1095C22C4×D3×D411yescharacteristic
1096C22C4×D3×D411yescharacteristic
1097C22#554511yescharacteristic
1098C22#558611yescharacteristic
1099C22#559111yescharacteristic
1100C22#559211yescharacteristic
1101C22#560111yescharacteristic
1102C22#560111yescharacteristic
1103C22#560111yescharacteristic
1104C22D3×#12111yescharacteristic
1105C22#560711yescharacteristic
1106C22#561011yescharacteristic
1107C22#561511yescharacteristic
1108C22#561611yescharacteristic
1109C22#562411yescharacteristic
1110C22#562711yescharacteristic
1111C22#563011yescharacteristic
1112C22#563711yescharacteristic
1113C22#563711yescharacteristic
1114C22#563711yescharacteristic
1115C22#564911yescharacteristic
1116C22#565611yescharacteristic
1117C22#565811yescharacteristic
1118C22#565811yescharacteristic
1119C22#566311yescharacteristic
1120C22#566811yescharacteristic
1121C22#567011yescharacteristic
1122C22#567011yescharacteristic
1123C22#570511yescharacteristic
1124C22#570611yescharacteristic
1125C22#571811yescharacteristic
1126C4—42no—
1127C4—42no—
1128C4—42no—
1129C4—42no—
1130C4—42no—
1131C4—64no—
1132C4—64no—
1133C4—64no—
1134C4—81no—
1135C4—122no—
1136C4—122no—
1137C4—122no—
1138C4—241no—
1139C3#1408211yescharacteristic, complemented, Sylow
1140C2—44no—
1141C2—242no—
1142C2#7388411yescharacteristic
1143C2#7437711yescharacteristic
1144C2#7459511yescharacteristic
1145C2#7466711yescharacteristic
1146C2#7545211yescharacteristic
1147C2#7548311yescharacteristic
1148C2#7630511yescharacteristic
1149C2#7667011yescharacteristic
1150C2#7680811yescharacteristic
1151C2#7692811yescharacteristic
1152C2#7696711yescharacteristic
1153C2#7731211yescharacteristic
1154C2#7741411yescharacteristic
1155C2#7751011yescharacteristic
1156C2#7802611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC3×#1439C2
socle, cosocleC24×C3C24
prime radicalC23×#67C22
hypercenter#1439D3
hypocenterC3#14082
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
1. C2×#4990C2semidirect
4. C2×Dic3×C22⋊C4C2semidirect
5. C2×#4648C2semidirect
6. C3×#1439C2semidirect
7. #71566C2semidirect
9. #71545C2semidirect
10. #71544C2semidirect
11. #69429C2semidirect
12. #69408C2semidirect
13. #69408C2semidirect
14. #69406C2semidirect
15. #69401C2semidirect
54. #4957C4semidirect
64. #1439D3semidirect
135. C2×(C2×D3)⋊C4C2×C4semidirect
136. C2×(C2×D3)⋊C4C2×C4semidirect
139. C2×Dic3⋊C4C2×C4semidirect
150. C2×C4×Dic3C2×C4semidirect
151. C2×C4×Dic3D4semidirect
1139. C3#14082semidirect

Maximal subgroups

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

subgroupindex
C2×#49902
C2×#49572
C2×#49582
C2×Dic3×C22⋊C42
C2×#46482
C3×#14392
#715662
#715502
#715452
#715442
#694292
#694082
#694062
#694012
#140823