Finite Group Databasebeta

← C3×#14517 #10633124

Subgroups — C3×#14517 #10633124

Order 768.

1966 conjugacy classes of subgroups.

The subgroup lattice has 1168 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#394C211yesmaximal, characteristic
2C2×C3×#388C211yesmaximal, characteristic, complemented
3C2×C3×#386C211yesmaximal, characteristic
4C2×C3×#386C211yesmaximal, characteristic
5C2×C3×#385C211yesmaximal, characteristic, complemented
6C3×#1445C211yesmaximal, characteristic, complemented
7C3×#1443C211yesmaximal, characteristic, complemented
8C3×#1441C211yesmaximal, characteristic, complemented
9C3×#1440C211yesmaximal, characteristic, complemented
10C3×#1439C211yesmaximal, characteristic, complemented
11C3×#1437C211yesmaximal, characteristic, complemented
12C3×#1436C211yesmaximal, characteristic, complemented
13C3×C22⋊#95C211yesmaximal, characteristic, complemented
14C3×C22⋊#95C211yesmaximal, characteristic, complemented
15C3×C22⋊#95C211yesmaximal, characteristic, complemented
16#14517C311yesmaximal, characteristic, direct product factor, Sylow
17C23×C3×D4C2211yescharacteristic
18C24×C3×C4C2211yescharacteristic
19C24×C3×C4C2211yescharacteristic
20C22×C3×C4⋊C4C2211yescharacteristic
21C22×C3×C4⋊C4C2211yescharacteristic
22C22×C3×C4⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×C3×C22⋊C4C2211yescharacteristic
25C22×C3×C22⋊C4C2211yescharacteristic
26C22×C3×C22⋊C4C2211yescharacteristic
27C22×C3×C22⋊C4C2211yescharacteristic
28C22×C3×C22⋊C4C2211yescharacteristic
29C22×C3×C22⋊C4C2211yescharacteristic
30C22×C3×C22⋊C4C2211yescharacteristic
31C22×C3×C22⋊C4C2211yescharacteristic
32C22×C3×C22⋊C4C2211yescharacteristic
33C22×C3×C42C2211yescharacteristic
34C3×#394C418yescomplemented
35C3×#388—24no—
36C3×#386—24no—
37C3×#386—24no—
38C3×#385—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
55C2×C3×#95C2211yescharacteristic
56C2×C3×#95C2211yescharacteristic
57C2×#394C2×C311yescharacteristic
58C2×#388C2×C311yescharacteristic, complemented
59C2×#386C2×C311yescharacteristic
60C2×#386C2×C311yescharacteristic
61C2×#385C2×C311yescharacteristic, complemented
62#1445C2×C311yescharacteristic, complemented
63#1443C2×C311yescharacteristic, complemented
64#1441C2×C311yescharacteristic, complemented
65#1440C2×C311yescharacteristic, complemented
66#1439C2×C311yescharacteristic, complemented
67#1437C2×C311yescharacteristic, complemented
68#1436C2×C311yescharacteristic, complemented
69C22⋊#95C2×C311yescharacteristic, complemented
70C22⋊#95C2×C311yescharacteristic, complemented
71C22⋊#95C2×C311yescharacteristic, complemented
72C25×C3C2311yescharacteristic
73C25×C3C2311yescharacteristic
74C22×C3×D4—22no—
75C22×C3×D4—22no—
76C22×C3×D4—22no—
77C22×C3×D4—22no—
78C22×C3×D4—41no—
79C22×C3×D4—41no—
80C22×C3×D4C2×C414yes—
81C23×C3×C4—22no—
82C23×C3×C4—22no—
83C23×C3×C4—22no—
84C23×C3×C4—22no—
85C23×C3×C4—22no—
86C23×C3×C4—22no—
87C23×C3×C4—41no—
88C23×C3×C4—41no—
89C23×C3×C4—41no—
90C23×C3×C4—41no—
91C23×C3×C4—41no—
92C23×C3×C4—41no—
93C23×C3×C4—41no—
94C23×C3×C4—41no—
95C23×C3×C4C2311yescharacteristic
96C23×C3×C4C2311yescharacteristic
97C23×C3×C4C2311yescharacteristic
98C23×C3×C4C2311yescharacteristic
99C23×C3×C4C2311yescharacteristic
100C23×C3×C4C2311yescharacteristic
101C23×C3×C4C2311yescharacteristic
102C23×C3×C4C2311yescharacteristic
103C23×C3×C4C2311yescharacteristic
104C23×C3×C4C2311yescharacteristic
105C23×C3×C4C2311yescharacteristic
106C23×C3×C4C2311yescharacteristic
107C23×C3×C4C2311yescharacteristic
108C2×C3×C4⋊C4—22no—
109C2×C3×C4⋊C4—22no—
110C2×C3×C4⋊C4—22no—
111C2×C3×C4⋊C4—22no—
112C2×C3×C4⋊C4—41no—
113C2×C3×C4⋊C4—41no—
114C2×C3×C4⋊C4—41no—
115C2×C3×C4⋊C4—41no—
116C2×C3×C4⋊C4C2×C414yescomplemented
117C2×C3×C22⋊C4—22no—
118C2×C3×C22⋊C4—22no—
119C2×C3×C22⋊C4—22no—
120C2×C3×C22⋊C4—22no—
121C2×C3×C22⋊C4—22no—
122C2×C3×C22⋊C4—22no—
123C2×C3×C22⋊C4—22no—
124C2×C3×C22⋊C4—22no—
125C2×C3×C22⋊C4—22no—
126C2×C3×C22⋊C4—22no—
127C2×C3×C22⋊C4—22no—
128C2×C3×C22⋊C4—22no—
129C2×C3×C22⋊C4—41no—
130C2×C3×C22⋊C4—41no—
131C2×C3×C22⋊C4—41no—
132C2×C3×C22⋊C4—41no—
133C2×C3×C22⋊C4—41no—
134C2×C3×C22⋊C4—41no—
135C2×C3×C22⋊C4—41no—
136C2×C3×C22⋊C4—41no—
137C2×C3×C22⋊C4—41no—
138C2×C3×C22⋊C4—41no—
139C2×C3×C22⋊C4—41no—
140C2×C3×C22⋊C4—41no—
141C2×C3×C22⋊C4C2×C414yescomplemented
142C2×C3×C22⋊C4C2×C414yescomplemented
143C2×C3×C22⋊C4C2×C414yescomplemented
144C2×C3×C22⋊C4C2×C414yescomplemented
145C2×C3×C22⋊C4D414yes—
146C2×C3×C22⋊C4D414yes—
147C2×C3×C42—22no—
148C2×C3×C42—41no—
149C2×C3×C42—41no—
150C3×#95—22no—
151C3×#95—22no—
152C3×#95—22no—
153C3×#95—22no—
154C3×#95—22no—
155C3×#95—22no—
156C3×#95—22no—
157C3×#95—22no—
158C3×#95—22no—
159C3×#95—41no—
160C3×#95—41no—
161C3×#95—41no—
162C3×#95—41no—
163C3×#95—41no—
164C3×#95—41no—
165C3×#95—41no—
166C3×#95—41no—
167C3×#95C2×C414yescomplemented
168C23×D4C22×C311yescharacteristic
169C24×C4C22×C311yescharacteristic
170C24×C4C22×C311yescharacteristic
171C22×C4⋊C4C22×C311yescharacteristic
172C22×C4⋊C4C22×C311yescharacteristic
173C22×C4⋊C4C22×C311yescharacteristic
174C22×C22⋊C4C22×C311yescharacteristic
175C22×C22⋊C4C22×C311yescharacteristic
176C22×C22⋊C4C22×C311yescharacteristic
177C22×C22⋊C4C22×C311yescharacteristic
178C22×C22⋊C4C22×C311yescharacteristic
179C22×C22⋊C4C22×C311yescharacteristic
180C22×C22⋊C4C22×C311yescharacteristic
181C22×C22⋊C4C22×C311yescharacteristic
182C22×C22⋊C4C22×C311yescharacteristic
183C22×C22⋊C4C22×C311yescharacteristic
184C22×C42C22×C311yescharacteristic
185#394C3×C418yescomplemented
186#388—24no—
187#386—24no—
188#386—24no—
189#385—24no—
190C2×#95C22×C311yescharacteristic
191C2×#95C22×C311yescharacteristic
192C2×#95C22×C311yescharacteristic
193C2×#95C22×C311yescharacteristic
194C2×#95C22×C311yescharacteristic
195C2×#95C22×C311yescharacteristic
196C2×#95C22×C311yescharacteristic
197C2×#95C22×C311yescharacteristic
198C2×#95C22×C311yescharacteristic
199C2×#95C22×C311yescharacteristic
200C2×#95C22×C311yescharacteristic
201C2×#95C22×C311yescharacteristic
202C2×#95C22×C311yescharacteristic
203C2×#95C22×C311yescharacteristic
204C2×#95C22×C311yescharacteristic
205C2×#95C22×C311yescharacteristic
206C2×#95C22×C311yescharacteristic
207C2×#95C22×C311yescharacteristic
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×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×C3C22×C412yes—
233C24×C3C22×C412yes—
234C24×C3C2×D412yes—
235C24×C3C2×D412yes—
236C24×C3#4112yes—
237C24×C3#4112yes—
238C24×C3C2411yescharacteristic
239C2×C3×D4—28no—
240C2×C3×D4—28no—
241C2×C3×D4—44no—
242C2×C3×D4—44no—
243C2×C3×D4—44no—
244C2×C3×D4—44no—
245C2×C3×D4—44no—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4—21no—
259C22×C3×C4—21no—
260C22×C3×C4—21no—
261C22×C3×C4—21no—
262C22×C3×C4—21no—
263C22×C3×C4—21no—
264C22×C3×C4—21no—
265C22×C3×C4—21no—
266C22×C3×C4—21no—
267C22×C3×C4—21no—
268C22×C3×C4—21no—
269C22×C3×C4—21no—
270C22×C3×C4—21no—
271C22×C3×C4—21no—
272C22×C3×C4—21no—
273C22×C3×C4—21no—
274C22×C3×C4—21no—
275C22×C3×C4—21no—
276C22×C3×C4—21no—
277C22×C3×C4—21no—
278C22×C3×C4—21no—
279C22×C3×C4—21no—
280C22×C3×C4—21no—
281C22×C3×C4—21no—
282C22×C3×C4—21no—
283C22×C3×C4—21no—
284C22×C3×C4—21no—
285C22×C3×C4—21no—
286C22×C3×C4—21no—
287C22×C3×C4—21no—
288C22×C3×C4—21no—
289C22×C3×C4—21no—
290C22×C3×C4—21no—
291C22×C3×C4—21no—
292C22×C3×C4—21no—
293C22×C3×C4—21no—
294C22×C3×C4—21no—
295C22×C3×C4—21no—
296C22×C3×C4—21no—
297C22×C3×C4—21no—
298C22×C3×C4—21no—
299C22×C3×C4—21no—
300C22×C3×C4—21no—
301C22×C3×C4—21no—
302C22×C3×C4—21no—
303C22×C3×C4—21no—
304C22×C3×C4—21no—
305C22×C3×C4—21no—
306C22×C3×C4—21no—
307C22×C3×C4—21no—
308C22×C3×C4—21no—
309C22×C3×C4—21no—
310C22×C3×C4—21no—
311C22×C3×C4—21no—
312C22×C3×C4—21no—
313C22×C3×C4—21no—
314C22×C3×C4—21no—
315C22×C3×C4—21no—
316C22×C3×C4—21no—
317C22×C3×C4—21no—
318C22×C3×C4—21no—
319C22×C3×C4—21no—
320C22×C3×C4—21no—
321C22×C3×C4—21no—
322C22×C3×C4—21no—
323C22×C3×C4—21no—
324C22×C3×C4—21no—
325C22×C3×C4—21no—
326C22×C3×C4—44no—
327C22×C3×C4—44no—
328C22×C3×C4—44no—
329C22×C3×C4—44no—
330C22×C3×C4—44no—
331C22×C3×C4—44no—
332C22×C3×C4—44no—
333C22×C3×C4—44no—
334C22×C3×C4—44no—
335C22×C3×C4—44no—
336C22×C3×C4—44no—
337C22×C3×C4—44no—
338C22×C3×C4—44no—
339C22×C3×C4—44no—
340C22×C3×C4C22×C412yes—
341C22×C3×C4C22×C412yes—
342C22×C3×C4C22×C412yes—
343C22×C3×C4C22×C412yes—
344C22×C3×C4C22×C412yes—
345C22×C3×C4C2×D412yes—
346C22×C3×C4C2×D412yes—
347C22×C3×C4C2×D412yes—
348C22×C3×C4C2×D412yes—
349C22×C3×C4#4112yes—
350C22×C3×C4#4112yes—
351C3×C4⋊C4—44no—
352C3×C4⋊C4—44no—
353C3×C4⋊C4—44no—
354C3×C22⋊C4—28no—
355C3×C22⋊C4—28no—
356C3×C22⋊C4—44no—
357C3×C22⋊C4—44no—
358C3×C22⋊C4—44no—
359C3×C22⋊C4—44no—
360C3×C22⋊C4—44no—
361C3×C22⋊C4—44no—
362C3×C22⋊C4—44no—
363C3×C22⋊C4—44no—
364C3×C42—44no—
365C25C23×C311yescharacteristic
366C25C23×C311yescharacteristic
367C22×D4—22no—
368C22×D4—22no—
369C22×D4—22no—
370C22×D4—22no—
371C22×D4—41no—
372C22×D4—41no—
373C22×D4C2×C3×C414yes—
374C23×C4—22no—
375C23×C4—22no—
376C23×C4—22no—
377C23×C4—22no—
378C23×C4—22no—
379C23×C4—22no—
380C23×C4—41no—
381C23×C4—41no—
382C23×C4—41no—
383C23×C4—41no—
384C23×C4—41no—
385C23×C4—41no—
386C23×C4—41no—
387C23×C4—41no—
388C23×C4C23×C311yescharacteristic
389C23×C4C23×C311yescharacteristic
390C23×C4C23×C311yescharacteristic
391C23×C4C23×C311yescharacteristic
392C23×C4C23×C311yescharacteristic
393C23×C4C23×C311yescharacteristic
394C23×C4C23×C311yescharacteristic
395C23×C4C23×C311yescharacteristic
396C23×C4C23×C311yescharacteristic
397C23×C4C23×C311yescharacteristic
398C23×C4C23×C311yescharacteristic
399C23×C4C23×C311yescharacteristic
400C23×C4C23×C311yescharacteristic
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—41no—
406C2×C4⋊C4—41no—
407C2×C4⋊C4—41no—
408C2×C4⋊C4—41no—
409C2×C4⋊C4C2×C3×C414yescomplemented
410C2×C22⋊C4—22no—
411C2×C22⋊C4—22no—
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—22no—
420C2×C22⋊C4—22no—
421C2×C22⋊C4—22no—
422C2×C22⋊C4—41no—
423C2×C22⋊C4—41no—
424C2×C22⋊C4—41no—
425C2×C22⋊C4—41no—
426C2×C22⋊C4—41no—
427C2×C22⋊C4—41no—
428C2×C22⋊C4—41no—
429C2×C22⋊C4—41no—
430C2×C22⋊C4—41no—
431C2×C22⋊C4—41no—
432C2×C22⋊C4—41no—
433C2×C22⋊C4—41no—
434C2×C22⋊C4C2×C3×C414yescomplemented
435C2×C22⋊C4C2×C3×C414yescomplemented
436C2×C22⋊C4C2×C3×C414yescomplemented
437C2×C22⋊C4C2×C3×C414yescomplemented
438C2×C22⋊C4C3×D414yes—
439C2×C22⋊C4C3×D414yes—
440C2×C42—22no—
441C2×C42—41no—
442C2×C42—41no—
443#95—22no—
444#95—22no—
445#95—22no—
446#95—22no—
447#95—22no—
448#95—22no—
449#95—22no—
450#95—22no—
451#95—22no—
452#95—41no—
453#95—41no—
454#95—41no—
455#95—41no—
456#95—41no—
457#95—41no—
458#95—41no—
459#95—41no—
460#95C2×C3×C414yescomplemented
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—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—22no—
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×C3C4×D414yes—
530C23×C3C4×D414yes—
531C23×C3C23×C411yescharacteristic
532C23×C3C22×D411yescharacteristic
533C23×C3C22×D411yescharacteristic
534C23×C3C2×#4111yescharacteristic
535C23×C3C2×#4111yescharacteristic
536C23×C3C2×#4111yescharacteristic
537C23×C3C2×#4111yescharacteristic
538C23×C3H(5,𝔽2)11yescharacteristic
539C23×C3H(5,𝔽2)11yescharacteristic
540C23×C3H(5,𝔽2)11yescharacteristic
541C23×C3H(5,𝔽2)11yescharacteristic
542C23×C3H(5,𝔽2)11yescharacteristic
543C23×C3H(5,𝔽2)11yescharacteristic
544C23×C32−1+411yescharacteristic
545C23×C32−1+411yescharacteristic
546C3×D4—416no—
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—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—22no—
576C2×C3×C4—22no—
577C2×C3×C4—22no—
578C2×C3×C4—22no—
579C2×C3×C4—22no—
580C2×C3×C4—416no—
581C2×C3×C4—416no—
582C2×C3×C4—41no—
583C2×C3×C4—41no—
584C2×C3×C4—41no—
585C2×C3×C4—41no—
586C2×C3×C4—41no—
587C2×C3×C4—41no—
588C2×C3×C4—41no—
589C2×C3×C4—41no—
590C2×C3×C4—41no—
591C2×C3×C4—41no—
592C2×C3×C4—41no—
593C2×C3×C4—41no—
594C2×C3×C4—41no—
595C2×C3×C4—41no—
596C2×C3×C4—41no—
597C2×C3×C4—41no—
598C2×C3×C4—41no—
599C2×C3×C4—41no—
600C2×C3×C4—41no—
601C2×C3×C4—41no—
602C2×C3×C4—41no—
603C2×C3×C4—41no—
604C2×C3×C4—41no—
605C2×C3×C4—41no—
606C2×C3×C4—41no—
607C2×C3×C4—41no—
608C2×C3×C4—41no—
609C2×C3×C4—41no—
610C2×C3×C4—41no—
611C2×C3×C4—41no—
612C2×C3×C4—41no—
613C2×C3×C4—41no—
614C2×C3×C4—41no—
615C2×C3×C4—41no—
616C2×C3×C4—41no—
617C2×C3×C4—41no—
618C2×C3×C4—41no—
619C2×C3×C4—41no—
620C2×C3×C4—41no—
621C2×C3×C4—41no—
622C2×C3×C4—41no—
623C2×C3×C4—41no—
624C2×C3×C4—41no—
625C2×C3×C4—41no—
626C2×C3×C4—41no—
627C2×C3×C4—41no—
628C2×C3×C4—41no—
629C2×C3×C4—41no—
630C2×C3×C4—41no—
631C2×C3×C4—41no—
632C2×C3×C4—41no—
633C2×C3×C4—41no—
634C2×C3×C4—41no—
635C2×C3×C4—41no—
636C2×C3×C4—41no—
637C2×C3×C4—41no—
638C2×C3×C4—41no—
639C2×C3×C4—41no—
640C24—21no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
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—
664C24C22×C3×C412yes—
665C24C22×C3×C412yes—
666C24C2×C3×D412yes—
667C24C2×C3×D412yes—
668C24C3×#4112yes—
669C24C3×#4112yes—
670C24C24×C311yescharacteristic
671C2×D4—28no—
672C2×D4—28no—
673C2×D4—44no—
674C2×D4—44no—
675C2×D4—44no—
676C2×D4—44no—
677C2×D4—44no—
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—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—44no—
759C22×C4—44no—
760C22×C4—44no—
761C22×C4—44no—
762C22×C4—44no—
763C22×C4—44no—
764C22×C4—44no—
765C22×C4—44no—
766C22×C4—44no—
767C22×C4—44no—
768C22×C4—44no—
769C22×C4—44no—
770C22×C4—44no—
771C22×C4—44no—
772C22×C4C22×C3×C412yes—
773C22×C4C22×C3×C412yes—
774C22×C4C22×C3×C412yes—
775C22×C4C22×C3×C412yes—
776C22×C4C22×C3×C412yes—
777C22×C4C2×C3×D412yes—
778C22×C4C2×C3×D412yes—
779C22×C4C2×C3×D412yes—
780C22×C4C2×C3×D412yes—
781C22×C4C3×#4112yes—
782C22×C4C3×#4112yes—
783C4⋊C4—44no—
784C4⋊C4—44no—
785C4⋊C4—44no—
786C22⋊C4—28no—
787C22⋊C4—28no—
788C22⋊C4—44no—
789C22⋊C4—44no—
790C22⋊C4—44no—
791C22⋊C4—44no—
792C22⋊C4—44no—
793C22⋊C4—44no—
794C22⋊C4—44no—
795C22⋊C4—44no—
796C42—44no—
797C22×C3—24no—
798C22×C3—24no—
799C22×C3—24no—
800C22×C3—24no—
801C22×C3—24no—
802C22×C3—24no—
803C22×C3—42no—
804C22×C3—42no—
805C22×C3—42no—
806C22×C3—42no—
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—42no—
827C22×C3C2×C4×D411yescharacteristic
828C22×C3C2×C4×D411yescharacteristic
829C22×C3C4×#4111yescharacteristic
830C22×C3#51811yescharacteristic
831C22×C3#51811yescharacteristic
832C22×C3#52011yescharacteristic
833C22×C3#52011yescharacteristic
834C22×C3#53411yescharacteristic
835C22×C3#53411yescharacteristic
836C22×C3#53611yescharacteristic
837C22×C3#53711yescharacteristic
838C22×C3#53811yescharacteristic
839C22×C3#53811yescharacteristic
840C22×C3#53811yescharacteristic
841C22×C3#53911yescharacteristic
842C22×C3#53911yescharacteristic
843C22×C3#53911yescharacteristic
844C22×C3#54211yescharacteristic
845C22×C3#54211yescharacteristic
846C22×C3D4211yescharacteristic
847C22×C3#54611yescharacteristic
848C22×C3#54611yescharacteristic
849C22×C3#54611yescharacteristic
850C22×C3#54611yescharacteristic
851C22×C3#54611yescharacteristic
852C22×C3#54711yescharacteristic
853C22×C3#55111yescharacteristic
854C22×C3#55111yescharacteristic
855C22×C3#55211yescharacteristic
856C22×C3#55311yescharacteristic
857C22×C3#55311yescharacteristic
858C22×C3#56011yescharacteristic
859C22×C3#56011yescharacteristic
860C22×C3#56211yescharacteristic
861C22×C3#56211yescharacteristic
862C3×C4—42no—
863C3×C4—42no—
864C3×C4—42no—
865C3×C4—42no—
866C3×C4—42no—
867C3×C4—42no—
868C3×C4—42no—
869C3×C4—42no—
870C3×C4—42no—
871C3×C4—42no—
872C3×C4—42no—
873C3×C4—81no—
874C3×C4—81no—
875C23—22no—
876C23—22no—
877C23—22no—
878C23—22no—
879C23—22no—
880C23—22no—
881C23—22no—
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—22no—
908C23—22no—
909C23—22no—
910C23—22no—
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—
943C23C3×C4×D414yes—
944C23C3×C4×D414yes—
945C23C23×C3×C411yescharacteristic
946C23C22×C3×D411yescharacteristic
947C23C22×C3×D411yescharacteristic
948C23C2×C3×#4111yescharacteristic
949C23C2×C3×#4111yescharacteristic
950C23C2×C3×#4111yescharacteristic
951C23C2×C3×#4111yescharacteristic
952C23C3×H(5,𝔽2)11yescharacteristic
953C23C3×H(5,𝔽2)11yescharacteristic
954C23C3×H(5,𝔽2)11yescharacteristic
955C23C3×H(5,𝔽2)11yescharacteristic
956C23C3×H(5,𝔽2)11yescharacteristic
957C23C3×H(5,𝔽2)11yescharacteristic
958C23C3×2−1+411yescharacteristic
959C23C3×2−1+411yescharacteristic
960D4—416no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
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—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—416no—
995C2×C4—416no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C3—44no—
1055C2×C3—44no—
1056C2×C3#232211yescharacteristic
1057C2×C3#232511yescharacteristic
1058C2×C3#233711yescharacteristic
1059C2×C3#235811yescharacteristic
1060C2×C3#235911yescharacteristic
1061C2×C3#236411yescharacteristic
1062C2×C3#237711yescharacteristic
1063C2×C3#266811yescharacteristic
1064C2×C3#267211yescharacteristic
1065C2×C3#268711yescharacteristic
1066C2×C3#269111yescharacteristic
1067C2×C3#269711yescharacteristic
1068C2×C3#270811yescharacteristic
1069C2×C3#274611yescharacteristic
1070C2×C3#275011yescharacteristic
1071C22—24no—
1072C22—24no—
1073C22—24no—
1074C22—24no—
1075C22—24no—
1076C22—24no—
1077C22—42no—
1078C22—42no—
1079C22—42no—
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—42no—
1100C22—42no—
1101C22C2×C3×C4×D411yescharacteristic
1102C22C2×C3×C4×D411yescharacteristic
1103C22C3×C4×#4111yescharacteristic
1104C22C3×#51811yescharacteristic
1105C22C3×#51811yescharacteristic
1106C22C3×#52011yescharacteristic
1107C22C3×#52011yescharacteristic
1108C22C3×#53411yescharacteristic
1109C22C3×#53411yescharacteristic
1110C22C3×#53611yescharacteristic
1111C22C3×#53711yescharacteristic
1112C22C3×#53811yescharacteristic
1113C22C3×#53811yescharacteristic
1114C22C3×#53811yescharacteristic
1115C22C3×#53911yescharacteristic
1116C22C3×#53911yescharacteristic
1117C22C3×#53911yescharacteristic
1118C22C3×#54211yescharacteristic
1119C22C3×#54211yescharacteristic
1120C22C3×D4211yescharacteristic
1121C22C3×#54611yescharacteristic
1122C22C3×#54611yescharacteristic
1123C22C3×#54611yescharacteristic
1124C22C3×#54611yescharacteristic
1125C22C3×#54611yescharacteristic
1126C22C3×#54711yescharacteristic
1127C22C3×#55111yescharacteristic
1128C22C3×#55111yescharacteristic
1129C22C3×#55211yescharacteristic
1130C22C3×#55311yescharacteristic
1131C22C3×#55311yescharacteristic
1132C22C3×#56011yescharacteristic
1133C22C3×#56011yescharacteristic
1134C22C3×#56211yescharacteristic
1135C22C3×#56211yescharacteristic
1136C4—42no—
1137C4—42no—
1138C4—42no—
1139C4—42no—
1140C4—42no—
1141C4—42no—
1142C4—42no—
1143C4—42no—
1144C4—42no—
1145C4—42no—
1146C4—42no—
1147C4—81no—
1148C4—81no—
1149C3#1451711yescharacteristic, direct product factor, Sylow
1150C2—44no—
1151C2—44no—
1152C2C3×#232211yescharacteristic
1153C2C3×#232511yescharacteristic
1154C2C3×#233711yescharacteristic
1155C2C3×#235811yescharacteristic
1156C2C3×#235911yescharacteristic
1157C2C3×#236411yescharacteristic
1158C2C3×#237711yescharacteristic
1159C2C3×#266811yescharacteristic
1160C2C3×#267211yescharacteristic
1161C2C3×#268711yescharacteristic
1162C2C3×#269111yescharacteristic
1163C2C3×#269711yescharacteristic
1164C2C3×#270811yescharacteristic
1165C2C3×#274611yescharacteristic
1166C2C3×#275011yescharacteristic
subgroupG/H
center, socleC24×C3C24
commutatorC23C23×C3×C4
Frattini, cosocleC24C24×C3
prime radicalC23×C3×D4C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C3 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C3×#388C2semidirect
5. C2×C3×#385C2semidirect
6. C3×#1445C2semidirect
7. C3×#1443C2semidirect
8. C3×#1441C2semidirect
9. C3×#1440C2semidirect
10. C3×#1439C2semidirect
11. C3×#1437C2semidirect
12. C3×#1436C2semidirect
13. C3×C22⋊#95C2semidirect
14. C3×C22⋊#95C2semidirect
15. C3×C22⋊#95C2semidirect
16. #14517C3direct (N × H)
34. C3×#394C4semidirect
58. C2×#388C2×C3semidirect
61. C2×#385C2×C3semidirect
62. #1445C2×C3semidirect
63. #1443C2×C3semidirect
64. #1441C2×C3semidirect
65. #1440C2×C3semidirect
66. #1439C2×C3semidirect
67. #1437C2×C3semidirect
68. #1436C2×C3semidirect
69. C22⋊#95C2×C3semidirect
70. C22⋊#95C2×C3semidirect
71. C22⋊#95C2×C3semidirect
116. C2×C3×C4⋊C4C2×C4semidirect
141. C2×C3×C22⋊C4C2×C4semidirect
142. C2×C3×C22⋊C4C2×C4semidirect
143. C2×C3×C22⋊C4C2×C4semidirect
144. C2×C3×C22⋊C4C2×C4semidirect
167. C3×#95C2×C4semidirect
185. #394C3×C4semidirect
409. C2×C4⋊C4C2×C3×C4semidirect
434. C2×C22⋊C4C2×C3×C4semidirect
435. C2×C22⋊C4C2×C3×C4semidirect
436. C2×C22⋊C4C2×C3×C4semidirect
437. C2×C22⋊C4C2×C3×C4semidirect
460. #95C2×C3×C4semidirect
1149. C3#14517direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#3942
C2×C3×#3882
C2×C3×#3862
C2×C3×#3852
C3×#14452
C3×#14432
C3×#14412
C3×#14402
C3×#14392
C3×#14372
C3×#14362
C3×C22⋊#952
#145173