Finite Group Databasebeta

← #10718890

Subgroups — #10718890

Order 768.

2366 conjugacy classes of subgroups.

The subgroup lattice has 1088 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×C4⋊C4C211yesmaximal, characteristic
2C2×#4976C211yesmaximal, characteristic, complemented
3C2×#4928C211yesmaximal, characteristic, complemented
4C2×C4×(C2×D3)⋊C4C211yesmaximal, characteristic
5C2×#4668C211yesmaximal, characteristic
6C2×#4668C211yesmaximal, characteristic
7C2×#4668C211yesmaximal, characteristic
8C3×#1436C211yesmaximal, characteristic, complemented
9(C2×D3)⋊#95C211yesmaximal, characteristic
10(C2×D3)⋊#95C211yesmaximal, characteristic
11#69420C211yesmaximal, characteristic, complemented
12#69419C211yesmaximal, characteristic, complemented
13#69411C211yesmaximal, characteristic, complemented
14#69410C211yesmaximal, characteristic, complemented
15#69405C211yesmaximal, characteristic, complemented
16#14043—31nomaximal, Sylow
17C23×C4×D3C2211yescharacteristic
18C23×C4×D3C2211yescharacteristic
19C23×C4×D3C2211yescharacteristic
20C22×C3×C4⋊C4C2211yescharacteristic
21C22×C3×C42C2211yescharacteristic
22C22×(C2×D3)⋊C4C2211yescharacteristic
23C22×(C2×D3)⋊C4C2211yescharacteristic
24C22×(C2×D3)⋊C4C2211yescharacteristic
25C22×(C2×D3)⋊C4C2211yescharacteristic
26C22×C4⋊Dic3C2211yescharacteristic
27C22×C4⋊Dic3C2211yescharacteristic
28C22×C4⋊Dic3C2211yescharacteristic
29C22×C4⋊Dic3C2211yescharacteristic
30C22×Dic3⋊C4C2211yescharacteristic
31C22×Dic3⋊C4C2211yescharacteristic
32C22×Dic3⋊C4C2211yescharacteristic
33C22×Dic3⋊C4C2211yescharacteristic
34C22×Dic3⋊C4C2211yescharacteristic
35C22×C4×Dic3C2211yescharacteristic
36C2×D3×C4⋊C4—24no—
37C2×D3×C4⋊C4—24no—
38C2×D3×C4⋊C4—24no—
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
53C2×C3⋊#95C2211yescharacteristic
54C2×C3⋊#95C2211yescharacteristic
55#4976—24no—
56C4×(C2×D3)⋊C4—24no—
57#4928—24no—
58#4668—24no—
59#4668—24no—
60#4668C418yescomplemented
61C23×C4⋊C4—31no—
62C2×#389—31no—
63C2×#389—31no—
64C2×#385—31no—
65C2×#385—31no—
66C2×#385—31no—
67C2×C4×C22⋊C4—31no—
68#1444—31no—
69#1444—31no—
70#1441—31no—
71#1441—31no—
72#1436—31no—
73#1436D311yescharacteristic, complemented
74C22⋊#95—31no—
75C22⋊#95—31no—
76C24×D3C2311yescharacteristic
77C23×C3×C4C2311yescharacteristic
78C23×C3×C4C2311yescharacteristic
79C23×C3×C4C2311yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C23×Dic3C2311yescharacteristic
85C23×Dic3C2311yescharacteristic
86C23×Dic3C2311yescharacteristic
87C23×Dic3C2311yescharacteristic
88C23×Dic3C2311yescharacteristic
89C23×Dic3C2311yescharacteristic
90C23×Dic3C2311yescharacteristic
91C22×C4×D3—22no—
92C22×C4×D3—22no—
93C22×C4×D3—22no—
94C22×C4×D3—22no—
95C22×C4×D3—22no—
96C22×C4×D3—22no—
97C22×C4×D3—22no—
98C22×C4×D3—22no—
99C22×C4×D3—22no—
100C22×C4×D3—22no—
101C22×C4×D3—22no—
102C22×C4×D3—22no—
103C22×C4×D3—22no—
104C22×C4×D3—22no—
105C22×C4×D3—22no—
106C22×C4×D3—41no—
107C22×C4×D3—41no—
108C22×C4×D3—41no—
109C22×C4×D3—41no—
110C22×C4×D3C2×C414yes—
111C22×C4×D3D414yes—
112C2×C3×C4⋊C4—22no—
113C2×C3×C4⋊C4—22no—
114C2×C3×C4⋊C4D414yes—
115C2×C3×C42—22no—
116C2×C3×C42—22no—
117C2×C3×C42—41no—
118C2×(C2×D3)⋊C4—22no—
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)⋊C4C2×C414yes—
126C2×(C2×D3)⋊C4C2×C414yes—
127C2×(C2×D3)⋊C4D414yes—
128C2×(C2×D3)⋊C4Q814yes—
129C2×(C2×D3)⋊C4Q814yes—
130C2×C4⋊Dic3—22no—
131C2×C4⋊Dic3—22no—
132C2×C4⋊Dic3—22no—
133C2×C4⋊Dic3—22no—
134C2×C4⋊Dic3—22no—
135C2×C4⋊Dic3—22no—
136C2×C4⋊Dic3—22no—
137C2×C4⋊Dic3—22no—
138C2×C4⋊Dic3—41no—
139C2×C4⋊Dic3—41no—
140C2×C4⋊Dic3—41no—
141C2×C4⋊Dic3C2×C414yescomplemented
142C2×Dic3⋊C4—22no—
143C2×Dic3⋊C4—22no—
144C2×Dic3⋊C4—22no—
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—22no—
152C2×Dic3⋊C4—22no—
153C2×Dic3⋊C4—22no—
154C2×Dic3⋊C4—41no—
155C2×Dic3⋊C4C2×C414yescomplemented
156C2×Dic3⋊C4D414yes—
157C2×C4×Dic3—22no—
158C2×C4×Dic3—22no—
159C2×C4×Dic3—41no—
160D3×C4⋊C4—232no—
161C3×#95—22no—
162C3×#95—22no—
163C3×#95—22no—
164C3×#95—41no—
165C3×#95C2×C414yescomplemented
166C3⋊#95—22no—
167C3⋊#95—22no—
168C3⋊#95—22no—
169C3⋊#95—22no—
170C3⋊#95—22no—
171C3⋊#95—22no—
172C3⋊#95—22no—
173C3⋊#95—22no—
174C3⋊#95—22no—
175C3⋊#95—41no—
176C3⋊#95C2×C414yescomplemented
177C24×C4—31no—
178C24×C4—31no—
179C24×C4—31no—
180C22×C4⋊C4—31no—
181C22×C4⋊C4—31no—
182C22×C4⋊C4—31no—
183C22×C4⋊C4—31no—
184C22×C4⋊C4—31no—
185C22×C4⋊C4—31no—
186C22×C4⋊C4—31no—
187C22×C4⋊C4—31no—
188C22×C4⋊C4—31no—
189C22×C4⋊C4—64no—
190C22×C4⋊C4—64no—
191C22×C4⋊C4—64no—
192C22×C4⋊C4C2×D311yescharacteristic
193C22×C22⋊C4—31no—
194C22×C22⋊C4—31no—
195C22×C22⋊C4—31no—
196C22×C22⋊C4—31no—
197C22×C42—31no—
198C22×C42C2×D311yescharacteristic
199#389—64no—
200#389—64no—
201#385—38no—
202#385—64no—
203#385—64no—
204C4×C22⋊C4—64no—
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×#95—31no—
215C2×#95—31no—
216C2×#95C2×D311yescharacteristic
217C2×#95C2×D311yescharacteristic
218C2×#95C2×D311yescharacteristic
219C2×#95C2×D311yescharacteristic
220C2×#95C2×D311yescharacteristic
221C24×C3C2411yescharacteristic
222C23×D3—21no—
223C23×D3—21no—
224C23×D3—21no—
225C23×D3—21no—
226C23×D3—21no—
227C23×D3—21no—
228C23×D3—21no—
229C23×D3—21no—
230C23×D3C22×C412yes—
231C23×D3C2×D412yes—
232C23×D3C2×D412yes—
233C23×D3C2×Q812yes—
234C23×D3C2×Q812yes—
235C23×D3#4112yes—
236C23×D3#4112yes—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
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×C4C22×C412yes—
275C22×C3×C4C22×C412yes—
276C22×C3×C4C22×C412yes—
277C22×C3×C4C2×D412yes—
278C22×C3×C4C2×D412yes—
279C22×C3×C4C2×D412yes—
280C22×C3×C4C2×D412yes—
281C22×C3×C4C2×D412yes—
282C22×C3×C4C2×D412yes—
283C22×C3×C4C2×Q812yes—
284C22×C3×C4C2×Q812yes—
285C22×C3×C4#4112yes—
286C22×Dic3—21no—
287C22×Dic3—21no—
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—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×Dic3C22×C412yes—
326C22×Dic3C22×C412yes—
327C22×Dic3C22×C412yes—
328C22×Dic3C2×D412yes—
329C22×Dic3C2×D412yes—
330C22×Dic3C2×D412yes—
331C22×Dic3C2×D412yes—
332C22×Dic3C2×Q812yes—
333C22×Dic3C2×Q812yes—
334C22×Dic3#4112yes—
335C2×C4×D3—28no—
336C2×C4×D3—28no—
337C2×C4×D3—28no—
338C2×C4×D3—28no—
339C2×C4×D3—28no—
340C2×C4×D3—28no—
341C2×C4×D3—28no—
342C2×C4×D3—28no—
343C2×C4×D3—28no—
344C2×C4×D3—28no—
345C2×C4×D3—44no—
346C2×C4×D3—44no—
347C2×C4×D3—44no—
348C2×C4×D3—44no—
349C2×C4×D3—44no—
350C2×C4×D3—44no—
351C2×C4×D3—44no—
352C2×C4×D3—44no—
353C2×C4×D3—44no—
354C2×C4×D3—44no—
355C2×C4×D3—44no—
356C3×C4⋊C4—28no—
357C3×C42—44no—
358(C2×D3)⋊C4—28no—
359(C2×D3)⋊C4—28no—
360(C2×D3)⋊C4—44no—
361(C2×D3)⋊C4C4⋊C4116yescomplemented
362C4⋊Dic3—28no—
363C4⋊Dic3—28no—
364C4⋊Dic3—44no—
365C4⋊Dic3—44no—
366Dic3⋊C4—28no—
367Dic3⋊C4—28no—
368Dic3⋊C4—28no—
369Dic3⋊C4—44no—
370Dic3⋊C4—44no—
371C4×Dic3—44no—
372C25—31no—
373C23×C4—31no—
374C23×C4—31no—
375C23×C4—31no—
376C23×C4—31no—
377C23×C4—31no—
378C23×C4—31no—
379C23×C4—34no—
380C23×C4—34no—
381C23×C4—31no—
382C23×C4—62no—
383C23×C4—62no—
384C23×C4—62no—
385C23×C4—62no—
386C23×C4—62no—
387C23×C4—62no—
388C23×C4—62no—
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×C4C22×D311yescharacteristic
402C23×C4C22×D311yescharacteristic
403C23×C4C22×D311yescharacteristic
404C23×C4C22×D311yescharacteristic
405C23×C4C22×D311yescharacteristic
406C23×C4C22×D311yescharacteristic
407C23×C4C22×D311yescharacteristic
408C2×C4⋊C4—22no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—34no—
411C2×C4⋊C4—34no—
412C2×C4⋊C4—34no—
413C2×C4⋊C4—632no—
414C2×C4⋊C4—62no—
415C2×C4⋊C4—62no—
416C2×C4⋊C4—62no—
417C2×C4⋊C4—62no—
418C2×C4⋊C4—62no—
419C2×C4⋊C4—62no—
420C2×C4⋊C4—62no—
421C2×C4⋊C4—62no—
422C2×C4⋊C4—62no—
423C2×C4⋊C4—62no—
424C2×C4⋊C4—62no—
425C2×C4⋊C4—62no—
426C2×C4⋊C4—62no—
427C2×C4⋊C4—62no—
428C2×C4⋊C4—62no—
429C2×C4⋊C4—62no—
430C2×C4⋊C4—62no—
431C2×C4⋊C4—62no—
432C2×C4⋊C4—62no—
433C2×C4⋊C4—62no—
434C2×C4⋊C4—121no—
435C2×C4⋊C4—121no—
436C2×C4⋊C4—121no—
437C2×C4⋊C4—121no—
438C2×C4⋊C4D1214yes—
439C2×C22⋊C4—34no—
440C2×C22⋊C4—34no—
441C2×C22⋊C4—34no—
442C2×C22⋊C4—34no—
443C2×C22⋊C4—34no—
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—62no—
451C2×C42—22no—
452C2×C42—22no—
453C2×C42—41no—
454C2×C42—62no—
455C2×C42—62no—
456C2×C42—121no—
457#95—22no—
458#95—22no—
459#95—22no—
460#95—34no—
461#95—41no—
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—62no—
471#95—121no—
472#95C4×D314yescomplemented
473C23×C3C23×C411yescharacteristic
474C23×C3C22×D411yescharacteristic
475C23×C3C22×D411yescharacteristic
476C23×C3C22×D411yescharacteristic
477C23×C3C22×D411yescharacteristic
478C23×C3C22×Q811yescharacteristic
479C23×C3C22×Q811yescharacteristic
480C23×C3C2×#4111yescharacteristic
481C23×C3C2×#4111yescharacteristic
482C23×C3C2×#4111yescharacteristic
483C23×C3C2×#4111yescharacteristic
484C23×C3H(5,𝔽2)11yescharacteristic
485C23×C3H(5,𝔽2)11yescharacteristic
486C23×C32−1+411yescharacteristic
487C23×C32−1+411yescharacteristic
488C22×D3—22no—
489C22×D3—22no—
490C22×D3—22no—
491C22×D3—22no—
492C22×D3—22no—
493C22×D3—22no—
494C22×D3—22no—
495C22×D3—22no—
496C22×D3—22no—
497C22×D3—22no—
498C22×D3—22no—
499C22×D3—22no—
500C22×D3—22no—
501C22×D3—22no—
502C22×D3—22no—
503C22×D3—22no—
504C22×D3—22no—
505C22×D3—22no—
506C22×D3—22no—
507C22×D3—22no—
508C22×D3—22no—
509C22×D3—22no—
510C22×D3—22no—
511C22×D3—22no—
512C22×D3—22no—
513C22×D3—22no—
514C22×D3—22no—
515C22×D3—22no—
516C22×D3C2×C4⋊C414yes—
517C22×D3C4×D414yes—
518C22×D3C4×Q814yes—
519C22×D3#12114yes—
520C22×D3C22⋊Q814yes—
521C22×D3#12514yes—
522C22×D3C4⋊Q814yes—
523C2×C3×C4—22no—
524C2×C3×C4—22no—
525C2×C3×C4—22no—
526C2×C3×C4—22no—
527C2×C3×C4—22no—
528C2×C3×C4—22no—
529C2×C3×C4—22no—
530C2×C3×C4—22no—
531C2×C3×C4—22no—
532C2×C3×C4—22no—
533C2×C3×C4—22no—
534C2×C3×C4—22no—
535C2×C3×C4—22no—
536C2×C3×C4—22no—
537C2×C3×C4—22no—
538C2×C3×C4—22no—
539C2×C3×C4—22no—
540C2×C3×C4—22no—
541C2×C3×C4—22no—
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—41no—
551C2×C3×C4—41no—
552C2×C3×C4—41no—
553C2×C3×C4—41no—
554C2×C3×C4—41no—
555C2×C3×C4—41no—
556C2×C3×C4—41no—
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×C4C2×C4⋊C414yescomplemented
570C2×C3×C4C4×D414yes—
571C2×C3×C4#12014yes—
572C2×Dic3—22no—
573C2×Dic3—22no—
574C2×Dic3—22no—
575C2×Dic3—22no—
576C2×Dic3—22no—
577C2×Dic3—22no—
578C2×Dic3—22no—
579C2×Dic3—22no—
580C2×Dic3—22no—
581C2×Dic3—22no—
582C2×Dic3—22no—
583C2×Dic3—22no—
584C2×Dic3—22no—
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—41no—
597C2×Dic3—41no—
598C2×Dic3—41no—
599C2×Dic3—41no—
600C2×Dic3—41no—
601C2×Dic3—41no—
602C2×Dic3—41no—
603C2×Dic3—41no—
604C2×Dic3—41no—
605C2×Dic3—41no—
606C2×Dic3—41no—
607C2×Dic3—41no—
608C2×Dic3—41no—
609C2×Dic3—41no—
610C2×Dic3—41no—
611C2×Dic3—41no—
612C2×Dic3—41no—
613C2×Dic3—41no—
614C2×Dic3—41no—
615C2×Dic3—41no—
616C2×Dic3—41no—
617C2×Dic3—41no—
618C2×Dic3—41no—
619C2×Dic3C2×C4⋊C414yescomplemented
620C2×Dic3C4×D414yes—
621C4×D3—232no—
622C4×D3—416no—
623C4×D3—416no—
624C24—32no—
625C24—32no—
626C24—32no—
627C24—32no—
628C24—32no—
629C24—32no—
630C24—32no—
631C24—61no—
632C24—61no—
633C24—61no—
634C24—61no—
635C24—61no—
636C24—61no—
637C24—61no—
638C24—61no—
639C24C23×D311yescharacteristic
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—32no—
678C22×C4—32no—
679C22×C4—32no—
680C22×C4—32no—
681C22×C4—32no—
682C22×C4—32no—
683C22×C4—32no—
684C22×C4—32no—
685C22×C4—32no—
686C22×C4—32no—
687C22×C4—68no—
688C22×C4—68no—
689C22×C4—68no—
690C22×C4—68no—
691C22×C4—68no—
692C22×C4—68no—
693C22×C4—68no—
694C22×C4—68no—
695C22×C4—61no—
696C22×C4—61no—
697C22×C4—61no—
698C22×C4—61no—
699C22×C4—61no—
700C22×C4—61no—
701C22×C4—61no—
702C22×C4—61no—
703C22×C4—68no—
704C22×C4—61no—
705C22×C4—61no—
706C22×C4—61no—
707C22×C4—61no—
708C22×C4—61no—
709C22×C4—61no—
710C22×C4—61no—
711C22×C4—61no—
712C22×C4—61no—
713C22×C4—61no—
714C22×C4—61no—
715C22×C4—61no—
716C22×C4—61no—
717C22×C4—61no—
718C22×C4—61no—
719C22×C4—61no—
720C22×C4—61no—
721C22×C4—61no—
722C22×C4—61no—
723C22×C4—61no—
724C22×C4—61no—
725C22×C4—61no—
726C22×C4—61no—
727C22×C4—61no—
728C22×C4—68no—
729C22×C4—61no—
730C22×C4—61no—
731C22×C4—61no—
732C22×C4—61no—
733C22×C4—61no—
734C22×C4—61no—
735C22×C4—61no—
736C22×C4—124no—
737C22×C4—124no—
738C22×C4—124no—
739C22×C4—124no—
740C22×C4—124no—
741C22×C4—124no—
742C22×C4—124no—
743C22×C4—124no—
744C22×C4—124no—
745C22×C4—124no—
746C22×C4—124no—
747C22×C4C2×C4×D312yes—
748C22×C4C2×C4×D312yes—
749C22×C4C2×C4×D312yes—
750C22×C4C2×D1212yes—
751C22×C4C2×D1212yes—
752C22×C4C2×D1212yes—
753C22×C4#23512yes—
754C22×C4D3×D412yes—
755C22×C4D3×D412yes—
756C22×C4D3×D412yes—
757C22×C4D3×Q812yes—
758C22×C4D3×Q812yes—
759C4⋊C4—28no—
760C4⋊C4—68no—
761C4⋊C4—68no—
762C4⋊C4—68no—
763C4⋊C4—68no—
764C4⋊C4—68no—
765C4⋊C4—124no—
766C4⋊C4—124no—
767C4⋊C4—124no—
768C4⋊C4—124no—
769C22⋊C4—316no—
770C22⋊C4—68no—
771C22⋊C4—68no—
772C22⋊C4—124no—
773C42—44no—
774C42—124no—
775C22×C3C22×C4⋊C411yescharacteristic
776C22×C3C2×C4×D411yescharacteristic
777C22×C3C2×C4×D411yescharacteristic
778C22×C3C2×C4×D411yescharacteristic
779C22×C3C2×C4×Q811yescharacteristic
780C22×C3#52011yescharacteristic
781C22×C3#52011yescharacteristic
782C22×C3C2×#12011yescharacteristic
783C22×C3C2×#12111yescharacteristic
784C22×C3C2×C22⋊Q811yescharacteristic
785C22×C3#52511yescharacteristic
786C22×C3#52511yescharacteristic
787C22×C3#52511yescharacteristic
788C22×C3C2×#12511yescharacteristic
789C22×C3C2×C4⋊Q811yescharacteristic
790C22×C3#53411yescharacteristic
791C22×C3#53611yescharacteristic
792C22×C3#53911yescharacteristic
793C22×C3#53911yescharacteristic
794C22×C3D4211yescharacteristic
795C22×C3D4211yescharacteristic
796C22×C3#54611yescharacteristic
797C22×C3#54611yescharacteristic
798C22×C3#54711yescharacteristic
799C22×C3#54711yescharacteristic
800C22×C3D4×Q811yescharacteristic
801C22×C3D4×Q811yescharacteristic
802C22×C3D4×Q811yescharacteristic
803C22×C3D4×Q811yescharacteristic
804C22×C3#55211yescharacteristic
805C22×C3#55211yescharacteristic
806C22×C3#55411yescharacteristic
807C22×C3#55411yescharacteristic
808C22×C3#55411yescharacteristic
809C22×C3#55411yescharacteristic
810C2×D3—24no—
811C2×D3—24no—
812C2×D3—24no—
813C2×D3—24no—
814C2×D3—24no—
815C2×D3—24no—
816C2×D3—24no—
817C2×D3—24no—
818C2×D3—24no—
819C2×D3—24no—
820C2×D3—24no—
821C2×D3—24no—
822C2×D3—24no—
823C2×D3—24no—
824C2×D3#38918yescomplemented
825C3×C4—24no—
826C3×C4—24no—
827C3×C4—24no—
828C3×C4—42no—
829C3×C4—42no—
830C3×C4—42no—
831C3×C4—81no—
832Dic3—24no—
833Dic3—24no—
834Dic3—42no—
835Dic3—42no—
836Dic3—42no—
837Dic3—42no—
838Dic3—81no—
839C23—34no—
840C23—34no—
841C23—34no—
842C23—34no—
843C23—34no—
844C23—34no—
845C23—34no—
846C23—62no—
847C23—62no—
848C23—62no—
849C23—62no—
850C23—62no—
851C23—62no—
852C23—62no—
853C23—62no—
854C23—62no—
855C23—62no—
856C23—62no—
857C23—62no—
858C23—62no—
859C23—62no—
860C23—62no—
861C23—62no—
862C23—62no—
863C23—62no—
864C23—62no—
865C23—62no—
866C23—62no—
867C23—62no—
868C23—62no—
869C23—62no—
870C23—62no—
871C23—62no—
872C23—62no—
873C23—62no—
874C23C22×C4×D311yescharacteristic
875C23C22×D1211yescharacteristic
876C23C2×#23511yescharacteristic
877C23C2×D3×D411yescharacteristic
878C23C2×D3×D411yescharacteristic
879C23C2×D3×D411yescharacteristic
880C23#100411yescharacteristic
881C23C2×D3×Q811yescharacteristic
882C23C2×D3×Q811yescharacteristic
883C23D3×#4111yescharacteristic
884C23D3×#4111yescharacteristic
885C23D3×#4111yescharacteristic
886C23#100911yescharacteristic
887C23#101011yescharacteristic
888C23#101011yescharacteristic
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—34no—
917C2×C4—34no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—632no—
938C2×C4—62no—
939C2×C4—62no—
940C2×C4—62no—
941C2×C4—62no—
942C2×C4—62no—
943C2×C4—62no—
944C2×C4—62no—
945C2×C4—62no—
946C2×C4—62no—
947C2×C4—62no—
948C2×C4—62no—
949C2×C4—62no—
950C2×C4—62no—
951C2×C4—62no—
952C2×C4—62no—
953C2×C4—62no—
954C2×C4—62no—
955C2×C4—62no—
956C2×C4—62no—
957C2×C4—62no—
958C2×C4—62no—
959C2×C4—62no—
960C2×C4—62no—
961C2×C4—62no—
962C2×C4—1216no—
963C2×C4—1216no—
964C2×C4—121no—
965C2×C4—121no—
966C2×C4—121no—
967C2×C4—121no—
968C2×C4—121no—
969C2×C4—121no—
970C2×C4—121no—
971C2×C4—121no—
972C2×C4—121no—
973C2×C4—121no—
974C2×C4—121no—
975C2×C4—121no—
976C2×C4—121no—
977C2×C4—121no—
978C2×C4—121no—
979C2×C4—121no—
980C2×C4—121no—
981C2×C4—121no—
982C2×C4—121no—
983C2×C4—121no—
984C2×C4—121no—
985C2×C4—121no—
986C2×C4—121no—
987C2×C4C4×D1214yes—
988C2×C4#88214yes—
989C2×C4D3×C4⋊C414yescomplemented
990C2×C3C2×#38911yescharacteristic
991C2×C3C4×#12011yescharacteristic
992C2×C3#232211yescharacteristic
993C2×C3D4×C4⋊C411yescharacteristic
994C2×C3D4×C4⋊C411yescharacteristic
995C2×C3#236011yescharacteristic
996C2×C3#236011yescharacteristic
997C2×C3#241011yescharacteristic
998C2×C3#241311yescharacteristic
999C2×C3#243411yescharacteristic
1000C2×C3#244911yescharacteristic
1001C2×C3#244911yescharacteristic
1002C2×C3#247311yescharacteristic
1003C2×C3#247311yescharacteristic
1004C2×C3#258311yescharacteristic
1005D3—28no—
1006C22—38no—
1007C22—64no—
1008C22—64no—
1009C22—64no—
1010C22—64no—
1011C22—64no—
1012C22—64no—
1013C22—64no—
1014C22—64no—
1015C22—64no—
1016C22—64no—
1017C22—64no—
1018C22—64no—
1019C22—64no—
1020C22—64no—
1021C22C2×C4×D1211yescharacteristic
1022C22C2×#88211yescharacteristic
1023C22C2×D3×C4⋊C411yescharacteristic
1024C22#551111yescharacteristic
1025C22#552311yescharacteristic
1026C22#552411yescharacteristic
1027C22#552911yescharacteristic
1028C22C4×D3×D411yescharacteristic
1029C22C4×D3×D411yescharacteristic
1030C22#554611yescharacteristic
1031C22#554711yescharacteristic
1032C22#554711yescharacteristic
1033C22D4×D1211yescharacteristic
1034C22#555111yescharacteristic
1035C22#555411yescharacteristic
1036C22C4×D3×Q811yescharacteristic
1037C22Q8×D1211yescharacteristic
1038C22Q8×D1211yescharacteristic
1039C22#557911yescharacteristic
1040C22#559011yescharacteristic
1041C22D3×#12111yescharacteristic
1042C22#560511yescharacteristic
1043C22D3×C22⋊Q811yescharacteristic
1044C22#563211yescharacteristic
1045C22#563211yescharacteristic
1046C22#563611yescharacteristic
1047C22#565411yescharacteristic
1048C22#565511yescharacteristic
1049C22#566011yescharacteristic
1050C22#567511yescharacteristic
1051C22D3×#12511yescharacteristic
1052C22#569011yescharacteristic
1053C22#570711yescharacteristic
1054C22#570811yescharacteristic
1055C22D3×C4⋊Q811yescharacteristic
1056C4—24no—
1057C4—24no—
1058C4—24no—
1059C4—42no—
1060C4—42no—
1061C4—42no—
1062C4—64no—
1063C4—64no—
1064C4—81no—
1065C4—122no—
1066C4—122no—
1067C4—122no—
1068C4—122no—
1069C4—241no—
1070C3#1404311yescharacteristic, complemented, Sylow
1071C2—68no—
1072C2C4×#88211yescharacteristic
1073C2C4⋊C4×D1211yescharacteristic
1074C2#7377311yescharacteristic
1075C2#7439311yescharacteristic
1076C2#7460911yescharacteristic
1077C2#7488811yescharacteristic
1078C2#7496511yescharacteristic
1079C2#7500811yescharacteristic
1080C2#7500911yescharacteristic
1081C2#7532111yescharacteristic
1082C2#7582811yescharacteristic
1083C2#7584311yescharacteristic
1084C2D3×#38911yescharacteristic
1085C2#7624711yescharacteristic
1086C2#7649911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC3×#1436C2
socle, cosocleC24×C3C24
prime radicalC24×D3C23
hypercenter#1436D3
hypocenterC3#14043
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
2. C2×#4976C2semidirect
3. C2×#4928C2semidirect
8. C3×#1436C2semidirect
11. #69420C2semidirect
12. #69419C2semidirect
13. #69411C2semidirect
14. #69410C2semidirect
15. #69405C2semidirect
60. #4668C4semidirect
73. #1436D3semidirect
141. C2×C4⋊Dic3C2×C4semidirect
155. C2×Dic3⋊C4C2×C4semidirect
165. C3×#95C2×C4semidirect
176. C3⋊#95C2×C4semidirect
361. (C2×D3)⋊C4C4⋊C4semidirect
472. #95C4×D3semidirect
569. C2×C3×C4C2×C4⋊C4semidirect
619. C2×Dic3C2×C4⋊C4semidirect
824. C2×D3#389semidirect
989. C2×C4D3×C4⋊C4semidirect
1070. C3#14043semidirect

Maximal subgroups

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

subgroupindex
C22×D3×C4⋊C42
C2×#49762
C2×#49282
C2×C4×(C2×D3)⋊C42
C2×#46682
C3×#14362
(C2×D3)⋊#952
#694202
#694192
#694112
#694102
#694052
#140433