Finite Group Databasebeta

← #10719465

Subgroups — #10719465

Order 768.

2046 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×#386C211yesmaximal, characteristic
2C2×#5221C211yesmaximal, characteristic
3C2×#5210C211yesmaximal, characteristic, complemented
4C2×C4×#217C211yesmaximal, characteristic, complemented
5C2×#4945C211yesmaximal, characteristic, complemented
6C2×#4944C211yesmaximal, characteristic, complemented
7C2×#4653C211yesmaximal, characteristic, complemented
8#72131C211yesmaximal, characteristic
9#71547C211yesmaximal, characteristic, complemented
10#71547C211yesmaximal, characteristic, complemented
11#71545C211yesmaximal, characteristic, complemented
12#71545C211yesmaximal, characteristic, complemented
13#69423C211yesmaximal, characteristic, complemented
14Dic3⋊#95C211yesmaximal, characteristic, complemented
15Dic3×#95C211yesmaximal, characteristic, complemented
16#14084—31nomaximal, Sylow
17C23×C3×D4C2211yescharacteristic
18C24×C3×C4C2211yescharacteristic
19C22×C3×C22⋊C4C2211yescharacteristic
20C22×C3×C22⋊C4C2211yescharacteristic
21C22×C3×C22⋊C4C2211yescharacteristic
22C22×#217C2211yescharacteristic
23C22×#217C2211yescharacteristic
24C22×#217C2211yescharacteristic
25C22×#217C2211yescharacteristic
26C22×#217C2211yescharacteristic
27C22×#217C2211yescharacteristic
28C22×#217C2211yescharacteristic
29C22×#217C2211yescharacteristic
30C22×C4⋊Dic3C2211yescharacteristic
31C22×Dic3⋊C4C2211yescharacteristic
32C22×Dic3⋊C4C2211yescharacteristic
33C22×Dic3⋊C4C2211yescharacteristic
34C22×C4×Dic3C2211yescharacteristic
35C22×C4×Dic3C2211yescharacteristic
36C22×C4×Dic3C2211yescharacteristic
37C22×C4×Dic3C2211yescharacteristic
38C3×#386—24no—
39C2×C3×#95C2211yescharacteristic
40C2×C3×#95C2211yescharacteristic
41#5221C418yescomplemented
42#5210—24no—
43C4×#217—24no—
44C2×C3⋊#95C2211yescharacteristic
45C2×C3⋊#95C2211yescharacteristic
46C2×C3⋊#95C2211yescharacteristic
47C2×C3⋊#95C2211yescharacteristic
48C2×C3⋊#95C2211yescharacteristic
49C2×C3⋊#95C2211yescharacteristic
50C2×C3⋊#95C2211yescharacteristic
51C2×C3⋊#95C2211yescharacteristic
52C2×C3⋊#95C2211yescharacteristic
53C2×C3⋊#95C2211yescharacteristic
54C2×C3⋊#95C2211yescharacteristic
55C2×C3⋊#95C2211yescharacteristic
56#4945—24no—
57#4944—24no—
58#4653—24no—
59C2×#390—31no—
60C2×#388—31no—
61C2×#388—31no—
62C2×#387—31no—
63C2×#386D311yescharacteristic
64C2×#385—31no—
65C2×C4×C22⋊C4—31no—
66#1445—31no—
67#1439—31no—
68#1439—31no—
69#1438—31no—
70#1437—31no—
71#1437—31no—
72C4⋊#95—31no—
73C4×#95—31no—
74C25×C3C2311yescharacteristic
75C25×C3C2311yescharacteristic
76C22×C3×D4—22no—
77C22×C3×D4—22no—
78C22×C3×D4—22no—
79C22×C3×D4—22no—
80C22×C3×D4—41no—
81C22×C3×D4—41no—
82C22×C3×D4C2×C414yes—
83C23×C3×C4—22no—
84C23×C3×C4—22no—
85C23×C3×C4—22no—
86C23×C3×C4—22no—
87C23×C3×C4—22no—
88C23×C3×C4—41no—
89C23×C3×C4—41no—
90C23×C3×C4C2311yescharacteristic
91C23×C3×C4C2311yescharacteristic
92C23×C3×C4C2311yescharacteristic
93C23×C3×C4C2311yescharacteristic
94C23×C3×C4C2311yescharacteristic
95C23×Dic3C2311yescharacteristic
96C23×Dic3C2311yescharacteristic
97C23×Dic3C2311yescharacteristic
98C23×Dic3C2311yescharacteristic
99C23×Dic3C2311yescharacteristic
100C23×Dic3C2311yescharacteristic
101C23×Dic3C2311yescharacteristic
102C23×Dic3C2311yescharacteristic
103C2×C3×C22⋊C4—22no—
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—22no—
110C2×C3×C22⋊C4—41no—
111C2×C3×C22⋊C4—41no—
112C2×#217—22no—
113C2×#217—22no—
114C2×#217—22no—
115C2×#217—22no—
116C2×#217—22no—
117C2×#217—22no—
118C2×#217—22no—
119C2×#217—22no—
120C2×#217—22no—
121C2×#217—22no—
122C2×#217—22no—
123C2×#217—22no—
124C2×#217—22no—
125C2×#217—22no—
126C2×#217—22no—
127C2×#217—22no—
128C2×#217—41no—
129C2×#217—41no—
130C2×#217—41no—
131C2×#217—41no—
132C2×#217C2×C414yes—
133C2×#217C2×C414yes—
134C2×#217C2×C414yescomplemented
135C2×#217C2×C414yescomplemented
136C2×C4⋊Dic3—22no—
137C2×C4⋊Dic3—22no—
138C2×C4⋊Dic3C2×C414yescomplemented
139C2×Dic3⋊C4—22no—
140C2×Dic3⋊C4—22no—
141C2×Dic3⋊C4—22no—
142C2×Dic3⋊C4—22no—
143C2×Dic3⋊C4—22no—
144C2×Dic3⋊C4—22no—
145C2×Dic3⋊C4—22no—
146C2×Dic3⋊C4—41no—
147C2×Dic3⋊C4—41no—
148C2×C4×Dic3—22no—
149C2×C4×Dic3—22no—
150C2×C4×Dic3—22no—
151C2×C4×Dic3—22no—
152C2×C4×Dic3—41no—
153C2×C4×Dic3—41no—
154C2×C4×Dic3—41no—
155C2×C4×Dic3—41no—
156C2×C4×Dic3—41no—
157C2×C4×Dic3—41no—
158C2×C4×Dic3C2×C414yescomplemented
159C2×C4×Dic3D414yescomplemented
160C3×#95—22no—
161C3×#95D414yes—
162C3⋊#95—22no—
163C3⋊#95—22no—
164C3⋊#95—22no—
165C3⋊#95—22no—
166C3⋊#95—22no—
167C3⋊#95—22no—
168C3⋊#95—22no—
169C3⋊#95—22no—
170C3⋊#95—22no—
171C3⋊#95—22no—
172C3⋊#95—22no—
173C3⋊#95D414yescomplemented
174C23×D4C2×D311yescharacteristic
175C24×C4C2×D311yescharacteristic
176C22×C4⋊C4—31no—
177C22×C4⋊C4—31no—
178C22×C4⋊C4—31no—
179C22×C4⋊C4—31no—
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⋊C4C2×D311yescharacteristic
189C22×C22⋊C4C2×D311yescharacteristic
190C22×C22⋊C4C2×D311yescharacteristic
191C22×C42—31no—
192C22×C42—31no—
193C22×C42—31no—
194C22×C42—31no—
195#390—38no—
196#388—64no—
197#388—64no—
198#387—64no—
199#386—24no—
200#385—64no—
201C4×C22⋊C4—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×C3—21no—
229C24×C3—21no—
230C24×C3—21no—
231C24×C3—21no—
232C24×C3—21no—
233C24×C3—21no—
234C24×C3—21no—
235C24×C3—21no—
236C24×C3—21no—
237C24×C3—21no—
238C24×C3—21no—
239C24×C3—21no—
240C24×C3—21no—
241C24×C3—21no—
242C24×C3C22×C412yes—
243C24×C3C22×C412yes—
244C24×C3#4112yes—
245C24×C3#4112yes—
246C24×C3C2411yescharacteristic
247C2×C3×D4—28no—
248C2×C3×D4—28no—
249C2×C3×D4—44no—
250C2×C3×D4—44no—
251C2×C3×D4—44no—
252C2×C3×D4—44no—
253C2×C3×D4—44no—
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—28no—
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×C4C22×C412yes—
289C22×C3×C4C2×D412yes—
290C22×C3×C4C2×D412yes—
291C22×C3×C4C2×D412yes—
292C22×C3×C4C2×D412yes—
293C22×C3×C4C2×D412yes—
294C22×C3×C4#4112yes—
295C22×C3×C4#4112yes—
296C22×Dic3—21no—
297C22×Dic3—21no—
298C22×Dic3—21no—
299C22×Dic3—21no—
300C22×Dic3—21no—
301C22×Dic3—21no—
302C22×Dic3—21no—
303C22×Dic3—21no—
304C22×Dic3—21no—
305C22×Dic3—21no—
306C22×Dic3—21no—
307C22×Dic3—21no—
308C22×Dic3—21no—
309C22×Dic3—21no—
310C22×Dic3—21no—
311C22×Dic3—21no—
312C22×Dic3—21no—
313C22×Dic3—21no—
314C22×Dic3—21no—
315C22×Dic3—21no—
316C22×Dic3—21no—
317C22×Dic3—21no—
318C22×Dic3—21no—
319C22×Dic3—21no—
320C22×Dic3—21no—
321C22×Dic3—21no—
322C22×Dic3—21no—
323C22×Dic3—21no—
324C22×Dic3—21no—
325C22×Dic3—21no—
326C22×Dic3—21no—
327C22×Dic3—21no—
328C22×Dic3—21no—
329C22×Dic3—21no—
330C22×Dic3—21no—
331C22×Dic3—21no—
332C22×Dic3—21no—
333C22×Dic3—21no—
334C22×Dic3—21no—
335C22×Dic3—21no—
336C22×Dic3—21no—
337C22×Dic3—21no—
338C22×Dic3—21no—
339C22×Dic3—21no—
340C22×Dic3—21no—
341C22×Dic3C22×C412yes—
342C22×Dic3C22×C412yes—
343C22×Dic3C22×C412yes—
344C22×Dic3C22×C412yes—
345C22×Dic3C2×D412yes—
346C22×Dic3C2×D412yes—
347C22×Dic3C2×D412yes—
348C22×Dic3C2×D412yes—
349C22×Dic3#4112yes—
350C22×Dic3#4112yes—
351C22×Dic3#4112yes—
352C3×C22⋊C4—44no—
353C3×C22⋊C4—44no—
354C3×C22⋊C4—44no—
355#217—28no—
356#217—28no—
357#217—28no—
358#217—28no—
359#217—28no—
360#217—44no—
361#217—44no—
362#217—44no—
363C4⋊Dic3—28no—
364Dic3⋊C4—44no—
365Dic3⋊C4—44no—
366Dic3⋊C4—44no—
367C4×Dic3—44no—
368C4×Dic3—44no—
369C4×Dic3—44no—
370C4×Dic3—44no—
371C25C22×D311yescharacteristic
372C25C22×D311yescharacteristic
373C22×D4—22no—
374C22×D4—22no—
375C22×D4—22no—
376C22×D4—22no—
377C22×D4—41no—
378C22×D4—41no—
379C22×D4C4×D314yes—
380C23×C4—22no—
381C23×C4—22no—
382C23×C4—22no—
383C23×C4—22no—
384C23×C4—22no—
385C23×C4—31no—
386C23×C4—31no—
387C23×C4—31no—
388C23×C4—31no—
389C23×C4—31no—
390C23×C4—31no—
391C23×C4—31no—
392C23×C4—31no—
393C23×C4—41no—
394C23×C4—41no—
395C23×C4C22×D311yescharacteristic
396C23×C4C22×D311yescharacteristic
397C23×C4C22×D311yescharacteristic
398C23×C4C22×D311yescharacteristic
399C23×C4C22×D311yescharacteristic
400C2×C4⋊C4—34no—
401C2×C4⋊C4—62no—
402C2×C4⋊C4—62no—
403C2×C4⋊C4—62no—
404C2×C4⋊C4—62no—
405C2×C4⋊C4—62no—
406C2×C4⋊C4—62no—
407C2×C4⋊C4—62no—
408C2×C4⋊C4—62no—
409C2×C4⋊C4—62no—
410C2×C4⋊C4—121no—
411C2×C4⋊C4—121no—
412C2×C22⋊C4—22no—
413C2×C22⋊C4—22no—
414C2×C22⋊C4—22no—
415C2×C22⋊C4—22no—
416C2×C22⋊C4—22no—
417C2×C22⋊C4—22no—
418C2×C22⋊C4—22no—
419C2×C22⋊C4—34no—
420C2×C22⋊C4—34no—
421C2×C22⋊C4—34no—
422C2×C22⋊C4—34no—
423C2×C22⋊C4—41no—
424C2×C22⋊C4—41no—
425C2×C22⋊C4—62no—
426C2×C22⋊C4—62no—
427C2×C22⋊C4—62no—
428C2×C22⋊C4—62no—
429C2×C22⋊C4—62no—
430C2×C22⋊C4—62no—
431C2×C22⋊C4—62no—
432C2×C22⋊C4—62no—
433C2×C22⋊C4—62no—
434C2×C22⋊C4—62no—
435C2×C22⋊C4—62no—
436C2×C22⋊C4—62no—
437C2×C22⋊C4—62no—
438C2×C22⋊C4—62no—
439C2×C22⋊C4—62no—
440C2×C22⋊C4—62no—
441C2×C22⋊C4—121no—
442C2×C22⋊C4—121no—
443C2×C22⋊C4—121no—
444C2×C22⋊C4—121no—
445C2×C42—34no—
446C2×C42—34no—
447C2×C42—62no—
448C2×C42—62no—
449C2×C42—62no—
450C2×C42—62no—
451C2×C42—121no—
452C2×C42—121no—
453C2×C42—121no—
454C2×C42—121no—
455C2×C42—121no—
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—62no—
470#95#6714yes—
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—22no—
490C23×C3—22no—
491C23×C3—22no—
492C23×C3—22no—
493C23×C3—22no—
494C23×C3—22no—
495C23×C3—22no—
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×C3—41no—
508C23×C3—41no—
509C23×C3—41no—
510C23×C3—41no—
511C23×C3—41no—
512C23×C3—41no—
513C23×C3—41no—
514C23×C3—41no—
515C23×C3—41no—
516C23×C3—41no—
517C23×C3—41no—
518C23×C3—41no—
519C23×C3—41no—
520C23×C3—41no—
521C23×C3—41no—
522C23×C3—41no—
523C23×C3—41no—
524C23×C3—41no—
525C23×C3—41no—
526C23×C3—41no—
527C23×C3—41no—
528C23×C3—41no—
529C23×C3—41no—
530C23×C3—41no—
531C23×C3—41no—
532C23×C3—41no—
533C23×C3—41no—
534C23×C3—41no—
535C23×C3—41no—
536C23×C3—41no—
537C23×C3—41no—
538C23×C3—41no—
539C23×C3—41no—
540C23×C3#11714yes—
541C23×C3C23×C411yescharacteristic
542C23×C3C22×D411yescharacteristic
543C23×C3C22×D411yescharacteristic
544C23×C3C22×D411yescharacteristic
545C23×C3C2×#4111yescharacteristic
546C23×C3C2×#4111yescharacteristic
547C23×C3C2×#4111yescharacteristic
548C23×C3C2×#4111yescharacteristic
549C23×C3C2×#4111yescharacteristic
550C23×C3C2×#4111yescharacteristic
551C23×C3C2×#4111yescharacteristic
552C23×C3H(5,𝔽2)11yescharacteristic
553C23×C3H(5,𝔽2)11yescharacteristic
554C23×C3H(5,𝔽2)11yescharacteristic
555C23×C32−1+411yescharacteristic
556C3×D4—416no—
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—22no—
575C2×C3×C4—416no—
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×C4C4×D414yes—
592C2×C3×C4#12714yes—
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—22no—
613C2×Dic3—22no—
614C2×Dic3—22no—
615C2×Dic3—22no—
616C2×Dic3—22no—
617C2×Dic3—22no—
618C2×Dic3—22no—
619C2×Dic3—22no—
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×Dic3C4×D414yes—
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—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24—21no—
668C24—21no—
669C24—21no—
670C24—21no—
671C24—21no—
672C24—21no—
673C24—21no—
674C24—21no—
675C24C2×C4×D312yes—
676C24C2×C4×D312yes—
677C24#23712yes—
678C24#23712yes—
679C24C23×D311yescharacteristic
680C2×D4—28no—
681C2×D4—28no—
682C2×D4—44no—
683C2×D4—44no—
684C2×D4—44no—
685C2×D4—44no—
686C2×D4—44no—
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—28no—
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—32no—
716C22×C4—32no—
717C22×C4—32no—
718C22×C4—32no—
719C22×C4—32no—
720C22×C4—32no—
721C22×C4—32no—
722C22×C4—32no—
723C22×C4—32no—
724C22×C4—32no—
725C22×C4—32no—
726C22×C4—44no—
727C22×C4—44no—
728C22×C4—44no—
729C22×C4—44no—
730C22×C4—44no—
731C22×C4—44no—
732C22×C4—61no—
733C22×C4—61no—
734C22×C4—61no—
735C22×C4—61no—
736C22×C4—61no—
737C22×C4—61no—
738C22×C4—61no—
739C22×C4—61no—
740C22×C4—61no—
741C22×C4—61no—
742C22×C4—61no—
743C22×C4—61no—
744C22×C4—61no—
745C22×C4—61no—
746C22×C4—61no—
747C22×C4—61no—
748C22×C4—61no—
749C22×C4—61no—
750C22×C4—61no—
751C22×C4—61no—
752C22×C4—61no—
753C22×C4—61no—
754C22×C4—61no—
755C22×C4—61no—
756C22×C4—61no—
757C22×C4—61no—
758C22×C4—61no—
759C22×C4—61no—
760C22×C4—61no—
761C22×C4—61no—
762C22×C4—61no—
763C22×C4—61no—
764C22×C4—61no—
765C22×C4—61no—
766C22×C4—61no—
767C22×C4—61no—
768C22×C4—61no—
769C22×C4—61no—
770C22×C4—61no—
771C22×C4—61no—
772C22×C4—61no—
773C22×C4—61no—
774C22×C4—61no—
775C22×C4—61no—
776C22×C4—61no—
777C22×C4C2×C4×D312yes—
778C22×C4#23512yes—
779C22×C4D3×D412yes—
780C22×C4D3×D412yes—
781C22×C4#23712yes—
782C22×C4C2×#6712yes—
783C22×C4C2×#6712yes—
784C22×C4C2×#6712yes—
785C4⋊C4—68no—
786C4⋊C4—124no—
787C4⋊C4—124no—
788C4⋊C4—124no—
789C22⋊C4—44no—
790C22⋊C4—44no—
791C22⋊C4—44no—
792C22⋊C4—68no—
793C22⋊C4—68no—
794C22⋊C4—68no—
795C22⋊C4—68no—
796C22⋊C4—68no—
797C22⋊C4—124no—
798C22⋊C4—124no—
799C22⋊C4—124no—
800C42—124no—
801C42—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×C3—42no—
820C22×C3—42no—
821C22×C3—42no—
822C22×C3—42no—
823C22×C3—42no—
824C22×C3—42no—
825C22×C3—42no—
826C22×C3—81no—
827C22×C3—81no—
828C22×C3—81no—
829C22×C3—81no—
830C22×C3—81no—
831C22×C3—81no—
832C22×C3—81no—
833C22×C3—81no—
834C22×C3C2×#11711yescharacteristic
835C22×C3C2×C4×D411yescharacteristic
836C22×C3C2×C4×D411yescharacteristic
837C22×C3C2×C4×D411yescharacteristic
838C22×C3C4×#4111yescharacteristic
839C22×C3#51811yescharacteristic
840C22×C3#52011yescharacteristic
841C22×C3#52511yescharacteristic
842C22×C3#52511yescharacteristic
843C22×C3#52911yescharacteristic
844C22×C3#52911yescharacteristic
845C22×C3C2×#12711yescharacteristic
846C22×C3#53211yescharacteristic
847C22×C3#53211yescharacteristic
848C22×C3#53211yescharacteristic
849C22×C3#53411yescharacteristic
850C22×C3#53711yescharacteristic
851C22×C3#53811yescharacteristic
852C22×C3#53911yescharacteristic
853C22×C3#54611yescharacteristic
854C22×C3#54611yescharacteristic
855C22×C3#54611yescharacteristic
856C22×C3#54611yescharacteristic
857C22×C3#54611yescharacteristic
858C22×C3#54611yescharacteristic
859C22×C3#54811yescharacteristic
860C22×C3#54811yescharacteristic
861C22×C3#55111yescharacteristic
862C22×C3#55111yescharacteristic
863C22×C3#55211yescharacteristic
864C22×C3#55311yescharacteristic
865C22×C3#55311yescharacteristic
866C22×C3#55311yescharacteristic
867C22×C3#55611yescharacteristic
868C22×C3#55911yescharacteristic
869C3×C4—24no—
870C3×C4—24no—
871C3×C4—42no—
872C3×C4—42no—
873C3×C4—81no—
874Dic3—24no—
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—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—41no—
924C23—41no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23#87714yes—
952C23C22×C4×D311yescharacteristic
953C23C2×#23511yescharacteristic
954C23C2×D3×D411yescharacteristic
955C23C2×D3×D411yescharacteristic
956C23C2×#23711yescharacteristic
957C23C2×#23711yescharacteristic
958C23C2×#23711yescharacteristic
959C23#100411yescharacteristic
960C23#100411yescharacteristic
961C23#100411yescharacteristic
962C23D3×#4111yescharacteristic
963C23D3×#4111yescharacteristic
964C23D3×#4111yescharacteristic
965C23#101011yescharacteristic
966C23C22×#6711yescharacteristic
967D4—416no—
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—34no—
988C2×C4—416no—
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—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—62no—
1025C2×C4—62no—
1026C2×C4—62no—
1027C2×C4—62no—
1028C2×C4—62no—
1029C2×C4—62no—
1030C2×C4—62no—
1031C2×C4—121no—
1032C2×C4—121no—
1033C2×C4—121no—
1034C2×C4—121no—
1035C2×C4—121no—
1036C2×C4—121no—
1037C2×C4—121no—
1038C2×C4—121no—
1039C2×C4—121no—
1040C2×C4—121no—
1041C2×C4—121no—
1042C2×C4—121no—
1043C2×C4—121no—
1044C2×C4—121no—
1045C2×C4—121no—
1046C2×C4—121no—
1047C2×C4—121no—
1048C2×C4—121no—
1049C2×C4—121no—
1050C2×C4—121no—
1051C2×C4—121no—
1052C2×C4—121no—
1053C2×C4—121no—
1054C2×C4—121no—
1055C2×C4—121no—
1056C2×C4—121no—
1057C2×C4—121no—
1058C2×C4C4×#6714yes—
1059C2×C4#94014yes—
1060C2×C3—44no—
1061C2×C3—82no—
1062C2×C3#229011yescharacteristic
1063C2×C3C4×#12711yescharacteristic
1064C2×C3#232511yescharacteristic
1065C2×C3#234211yescharacteristic
1066C2×C3#235211yescharacteristic
1067C2×C3#236411yescharacteristic
1068C2×C3#236711yescharacteristic
1069C2×C3#253911yescharacteristic
1070C2×C3#254011yescharacteristic
1071C2×C3#255711yescharacteristic
1072C2×C3#255811yescharacteristic
1073C2×C3#255911yescharacteristic
1074C2×C3#256011yescharacteristic
1075C2×C3#260111yescharacteristic
1076C2×C3#260211yescharacteristic
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—42no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—81no—
1100C22—81no—
1101C22—81no—
1102C22—81no—
1103C22—81no—
1104C22—81no—
1105C22—81no—
1106C22—81no—
1107C22C2×#87711yescharacteristic
1108C22#548611yescharacteristic
1109C22#549511yescharacteristic
1110C22#549511yescharacteristic
1111C22C4×#23711yescharacteristic
1112C22#554211yescharacteristic
1113C22C4×D3×D411yescharacteristic
1114C22C4×D3×D411yescharacteristic
1115C22#554611yescharacteristic
1116C22#554811yescharacteristic
1117C22#554811yescharacteristic
1118C22#555911yescharacteristic
1119C22#558611yescharacteristic
1120C22#558911yescharacteristic
1121C22#559111yescharacteristic
1122C22#559111yescharacteristic
1123C22#559811yescharacteristic
1124C22#560011yescharacteristic
1125C22#560111yescharacteristic
1126C22#560611yescharacteristic
1127C22#560811yescharacteristic
1128C22#561211yescharacteristic
1129C22#561311yescharacteristic
1130C22#561411yescharacteristic
1131C22#564911yescharacteristic
1132C22#565011yescharacteristic
1133C22#566011yescharacteristic
1134C22#566111yescharacteristic
1135C22C2×C4×#6711yescharacteristic
1136C22C2×#94011yescharacteristic
1137C22#580611yescharacteristic
1138C22#580611yescharacteristic
1139C22#580611yescharacteristic
1140C22#583111yescharacteristic
1141C22#583211yescharacteristic
1142C4—24no—
1143C4—24no—
1144C4—42no—
1145C4—42no—
1146C4—64no—
1147C4—64no—
1148C4—81no—
1149C4—122no—
1150C4—122no—
1151C4—122no—
1152C4—122no—
1153C4—122no—
1154C4—241no—
1155C3#1408411yescharacteristic, complemented, Sylow
1156C2—44no—
1157C2—82no—
1158C2#7465711yescharacteristic
1159C2#7467311yescharacteristic
1160C2#7475711yescharacteristic
1161C2#7476211yescharacteristic
1162C2#7477711yescharacteristic
1163C2#7487711yescharacteristic
1164C2#7488111yescharacteristic
1165C2#7490411yescharacteristic
1166C2#8209811yescharacteristic
1167C2C4×#94011yescharacteristic
1168C2#8234411yescharacteristic
1169C2#8259111yescharacteristic
1170C2#8266811yescharacteristic
1171C2#8267311yescharacteristic
1172C2#8286311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC2×C3×#386C2
socle, cosocleC24×C3C24
prime radicalC23×C3×D4C22
hypercenterC2×#386D3
hypocenterC3#14084
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
3. C2×#5210C2semidirect
4. C2×C4×#217C2semidirect
5. C2×#4945C2semidirect
6. C2×#4944C2semidirect
7. C2×#4653C2semidirect
9. #71547C2semidirect
10. #71547C2semidirect
11. #71545C2semidirect
12. #71545C2semidirect
13. #69423C2semidirect
14. Dic3⋊#95C2semidirect
15. Dic3×#95C2semidirect
41. #5221C4semidirect
134. C2×#217C2×C4semidirect
135. C2×#217C2×C4semidirect
138. C2×C4⋊Dic3C2×C4semidirect
158. C2×C4×Dic3C2×C4semidirect
159. C2×C4×Dic3D4semidirect
173. C3⋊#95D4semidirect
1155. C3#14084semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#3862
C2×#52212
C2×#52102
C2×C4×#2172
C2×#49452
C2×#49442
C2×#46532
#721312
#715472
#715452
#694232
Dic3⋊#952
Dic3×#952
#140843