Finite Group Databasebeta

← C3×#15331 #10633938

Subgroups — C3×#15331 #10633938

Order 768.

1946 conjugacy classes of subgroups.

The subgroup lattice has 1182 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#393C211yesmaximal, characteristic, complemented
2C2×C3×#393C211yesmaximal, characteristic, complemented
3C2×C3×#391C211yesmaximal, characteristic, complemented
4C2×C3×#390C211yesmaximal, characteristic
5C2×C3×#386C211yesmaximal, characteristic
6C2×C3×#385C211yesmaximal, characteristic, complemented
7C3×#1442C211yesmaximal, characteristic, complemented
8C3×#1441C211yesmaximal, characteristic, complemented
9C3×#1439C211yesmaximal, characteristic, complemented
10C3×#1439C211yesmaximal, characteristic, complemented
11C3×#1439C211yesmaximal, characteristic, complemented
12C3×#1439C211yesmaximal, characteristic, complemented
13C3×#1438C211yesmaximal, characteristic
14C3×#1436C211yesmaximal, characteristic, complemented
15C3×C22⋊#95C211yesmaximal, characteristic, complemented
16#15331C311yesmaximal, characteristic, direct product factor, Sylow
17C23×C3×Q8C2211yescharacteristic
18C23×C3×D4C2211yescharacteristic
19C24×C3×C4C2211yescharacteristic
20C22×C3×C4⋊C4C2211yescharacteristic
21C22×C3×C4⋊C4C2211yescharacteristic
22C22×C3×C4⋊C4C2211yescharacteristic
23C22×C3×C4⋊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×C22⋊C4C2211yescharacteristic
34C22×C3×C22⋊C4C2211yescharacteristic
35C22×C3×C42C2211yescharacteristic
36C3×#393—24no—
37C3×#393—24no—
38C3×#391—24no—
39C3×#390—24no—
40C3×#386—24no—
41C3×#385—24no—
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×C3×#95C2211yescharacteristic
58C2×#393C2×C311yescharacteristic, complemented
59C2×#393C2×C311yescharacteristic, complemented
60C2×#391C2×C311yescharacteristic, complemented
61C2×#390C2×C311yescharacteristic
62C2×#386C2×C311yescharacteristic
63C2×#385C2×C311yescharacteristic, complemented
64#1442C2×C311yescharacteristic, complemented
65#1441C2×C311yescharacteristic, complemented
66#1439C2×C311yescharacteristic, complemented
67#1439C2×C311yescharacteristic, complemented
68#1439C2×C311yescharacteristic, complemented
69#1439C2×C311yescharacteristic, complemented
70#1438C2×C311yescharacteristic
71#1436C2×C311yescharacteristic, complemented
72C22⋊#95C2×C311yescharacteristic, complemented
73C25×C3C2311yescharacteristic
74C25×C3C2311yescharacteristic
75C22×C3×Q8—22no—
76C22×C3×Q8—22no—
77C22×C3×Q8—22no—
78C22×C3×Q8—22no—
79C22×C3×Q8—22no—
80C22×C3×Q8—41no—
81C22×C3×Q8—41no—
82C22×C3×D4—22no—
83C22×C3×D4—22no—
84C22×C3×D4—22no—
85C22×C3×D4—22no—
86C22×C3×D4—41no—
87C22×C3×D4—41no—
88C22×C3×D4Q814yescomplemented
89C23×C3×C4—22no—
90C23×C3×C4—22no—
91C23×C3×C4—22no—
92C23×C3×C4—41no—
93C23×C3×C4—41no—
94C23×C3×C4—41no—
95C23×C3×C4—41no—
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
108C23×C3×C4C2311yescharacteristic
109C2×C3×C4⋊C4—22no—
110C2×C3×C4⋊C4—22no—
111C2×C3×C4⋊C4—22no—
112C2×C3×C4⋊C4—22no—
113C2×C3×C4⋊C4—22no—
114C2×C3×C4⋊C4—22no—
115C2×C3×C4⋊C4—41no—
116C2×C3×C4⋊C4—41no—
117C2×C3×C4⋊C4—41no—
118C2×C3×C4⋊C4—41no—
119C2×C3×C4⋊C4—41no—
120C2×C3×C4⋊C4—41no—
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—22no—
130C2×C3×C22⋊C4—22no—
131C2×C3×C22⋊C4—22no—
132C2×C3×C22⋊C4—22no—
133C2×C3×C22⋊C4—22no—
134C2×C3×C22⋊C4—22no—
135C2×C3×C22⋊C4—22no—
136C2×C3×C22⋊C4—22no—
137C2×C3×C22⋊C4—22no—
138C2×C3×C22⋊C4—22no—
139C2×C3×C22⋊C4—22no—
140C2×C3×C22⋊C4—22no—
141C2×C3×C22⋊C4—41no—
142C2×C3×C22⋊C4—41no—
143C2×C3×C22⋊C4—41no—
144C2×C3×C22⋊C4—41no—
145C2×C3×C22⋊C4—41no—
146C2×C3×C22⋊C4—41no—
147C2×C3×C22⋊C4—41no—
148C2×C3×C22⋊C4—41no—
149C2×C3×C22⋊C4—41no—
150C2×C3×C22⋊C4—41no—
151C2×C3×C22⋊C4—41no—
152C2×C3×C22⋊C4—41no—
153C2×C3×C22⋊C4D414yes—
154C2×C3×C42—22no—
155C2×C3×C42—22no—
156C2×C3×C42—41no—
157C3×#95—22no—
158C3×#95—22no—
159C3×#95—22no—
160C3×#95—22no—
161C3×#95—22no—
162C3×#95—22no—
163C3×#95—22no—
164C3×#95—22no—
165C3×#95—22no—
166C3×#95—22no—
167C3×#95—22no—
168C3×#95—41no—
169C3×#95—41no—
170C3×#95—41no—
171C3×#95D414yes—
172C3×#95D414yescomplemented
173C23×Q8C22×C311yescharacteristic
174C23×D4C22×C311yescharacteristic
175C24×C4C22×C311yescharacteristic
176C22×C4⋊C4C22×C311yescharacteristic
177C22×C4⋊C4C22×C311yescharacteristic
178C22×C4⋊C4C22×C311yescharacteristic
179C22×C4⋊C4C22×C311yescharacteristic
180C22×C22⋊C4C22×C311yescharacteristic
181C22×C22⋊C4C22×C311yescharacteristic
182C22×C22⋊C4C22×C311yescharacteristic
183C22×C22⋊C4C22×C311yescharacteristic
184C22×C22⋊C4C22×C311yescharacteristic
185C22×C22⋊C4C22×C311yescharacteristic
186C22×C22⋊C4C22×C311yescharacteristic
187C22×C22⋊C4C22×C311yescharacteristic
188C22×C22⋊C4C22×C311yescharacteristic
189C22×C22⋊C4C22×C311yescharacteristic
190C22×C22⋊C4C22×C311yescharacteristic
191C22×C42C22×C311yescharacteristic
192#393—24no—
193#393—24no—
194#391—24no—
195#390—24no—
196#386—24no—
197#385—24no—
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
208C2×#95C22×C311yescharacteristic
209C2×#95C22×C311yescharacteristic
210C2×#95C22×C311yescharacteristic
211C2×#95C22×C311yescharacteristic
212C2×#95C22×C311yescharacteristic
213C2×#95C22×C311yescharacteristic
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×C3—21no—
233C24×C3—21no—
234C24×C3—21no—
235C24×C3—21no—
236C24×C3—21no—
237C24×C3—21no—
238C24×C3—21no—
239C24×C3—21no—
240C24×C3C2×D412yes—
241C24×C3C2×Q812yes—
242C24×C3C2×Q812yes—
243C24×C3#4112yes—
244C24×C3C2411yescharacteristic
245C2×C3×Q8—28no—
246C2×C3×Q8—44no—
247C2×C3×Q8—44no—
248C2×C3×Q8—44no—
249C2×C3×Q8—44no—
250C2×C3×Q8—44no—
251C2×C3×Q8—44no—
252C2×C3×D4—28no—
253C2×C3×D4—28no—
254C2×C3×D4—44no—
255C2×C3×D4—44no—
256C2×C3×D4—44no—
257C2×C3×D4—44no—
258C2×C3×D4—44no—
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—21no—
327C22×C3×C4—21no—
328C22×C3×C4—21no—
329C22×C3×C4—21no—
330C22×C3×C4—21no—
331C22×C3×C4—21no—
332C22×C3×C4—21no—
333C22×C3×C4—21no—
334C22×C3×C4—21no—
335C22×C3×C4—21no—
336C22×C3×C4—21no—
337C22×C3×C4—44no—
338C22×C3×C4—44no—
339C22×C3×C4—44no—
340C22×C3×C4—44no—
341C22×C3×C4—44no—
342C22×C3×C4—44no—
343C22×C3×C4—44no—
344C22×C3×C4C2×D412yes—
345C22×C3×C4C2×D412yes—
346C22×C3×C4C2×D412yes—
347C22×C3×C4C2×D412yes—
348C22×C3×C4C2×D412yes—
349C22×C3×C4C2×D412yes—
350C22×C3×C4C2×D412yes—
351C22×C3×C4C2×D412yes—
352C22×C3×C4C2×Q812yes—
353C22×C3×C4#4112yes—
354C22×C3×C4#4112yes—
355C22×C3×C4#4112yes—
356C22×C3×C4#4112yes—
357C3×C4⋊C4—44no—
358C3×C4⋊C4—44no—
359C3×C4⋊C4—44no—
360C3×C4⋊C4—44no—
361C3×C22⋊C4—28no—
362C3×C22⋊C4—44no—
363C3×C22⋊C4—44no—
364C3×C22⋊C4—44no—
365C3×C22⋊C4—44no—
366C3×C22⋊C4—44no—
367C3×C22⋊C4—44no—
368C3×C22⋊C4—44no—
369C3×C22⋊C4—44no—
370C3×C22⋊C4—44no—
371C3×C22⋊C4—44no—
372C3×C42—44no—
373C25C23×C311yescharacteristic
374C25C23×C311yescharacteristic
375C22×Q8—22no—
376C22×Q8—22no—
377C22×Q8—22no—
378C22×Q8—22no—
379C22×Q8—22no—
380C22×Q8—41no—
381C22×Q8—41no—
382C22×D4—22no—
383C22×D4—22no—
384C22×D4—22no—
385C22×D4—22no—
386C22×D4—41no—
387C22×D4—41no—
388C22×D4C3×Q814yescomplemented
389C23×C4—22no—
390C23×C4—22no—
391C23×C4—22no—
392C23×C4—41no—
393C23×C4—41no—
394C23×C4—41no—
395C23×C4—41no—
396C23×C4C23×C311yescharacteristic
397C23×C4C23×C311yescharacteristic
398C23×C4C23×C311yescharacteristic
399C23×C4C23×C311yescharacteristic
400C23×C4C23×C311yescharacteristic
401C23×C4C23×C311yescharacteristic
402C23×C4C23×C311yescharacteristic
403C23×C4C23×C311yescharacteristic
404C23×C4C23×C311yescharacteristic
405C23×C4C23×C311yescharacteristic
406C23×C4C23×C311yescharacteristic
407C23×C4C23×C311yescharacteristic
408C23×C4C23×C311yescharacteristic
409C2×C4⋊C4—22no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—41no—
416C2×C4⋊C4—41no—
417C2×C4⋊C4—41no—
418C2×C4⋊C4—41no—
419C2×C4⋊C4—41no—
420C2×C4⋊C4—41no—
421C2×C22⋊C4—22no—
422C2×C22⋊C4—22no—
423C2×C22⋊C4—22no—
424C2×C22⋊C4—22no—
425C2×C22⋊C4—22no—
426C2×C22⋊C4—22no—
427C2×C22⋊C4—22no—
428C2×C22⋊C4—22no—
429C2×C22⋊C4—22no—
430C2×C22⋊C4—22no—
431C2×C22⋊C4—22no—
432C2×C22⋊C4—22no—
433C2×C22⋊C4—22no—
434C2×C22⋊C4—22no—
435C2×C22⋊C4—22no—
436C2×C22⋊C4—22no—
437C2×C22⋊C4—22no—
438C2×C22⋊C4—22no—
439C2×C22⋊C4—22no—
440C2×C22⋊C4—22no—
441C2×C22⋊C4—41no—
442C2×C22⋊C4—41no—
443C2×C22⋊C4—41no—
444C2×C22⋊C4—41no—
445C2×C22⋊C4—41no—
446C2×C22⋊C4—41no—
447C2×C22⋊C4—41no—
448C2×C22⋊C4—41no—
449C2×C22⋊C4—41no—
450C2×C22⋊C4—41no—
451C2×C22⋊C4—41no—
452C2×C22⋊C4—41no—
453C2×C22⋊C4C3×D414yes—
454C2×C42—22no—
455C2×C42—22no—
456C2×C42—41no—
457#95—22no—
458#95—22no—
459#95—22no—
460#95—22no—
461#95—22no—
462#95—22no—
463#95—22no—
464#95—22no—
465#95—22no—
466#95—22no—
467#95—22no—
468#95—41no—
469#95—41no—
470#95—41no—
471#95C3×D414yes—
472#95C3×D414yescomplemented
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—22no—
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—41no—
541C23×C3—41no—
542C23×C3C22⋊Q814yes—
543C23×C3C22×D411yescharacteristic
544C23×C3C22×D411yescharacteristic
545C23×C3C22×D411yescharacteristic
546C23×C3C22×Q811yescharacteristic
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×C3H(5,𝔽2)11yescharacteristic
556C23×C3H(5,𝔽2)11yescharacteristic
557C23×C32−1+411yescharacteristic
558C3×Q8—416no—
559C3×D4—416no—
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—22no—
581C2×C3×C4—22no—
582C2×C3×C4—22no—
583C2×C3×C4—22no—
584C2×C3×C4—22no—
585C2×C3×C4—22no—
586C2×C3×C4—22no—
587C2×C3×C4—22no—
588C2×C3×C4—22no—
589C2×C3×C4—22no—
590C2×C3×C4—22no—
591C2×C3×C4—22no—
592C2×C3×C4—22no—
593C2×C3×C4—416no—
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—
640C2×C3×C4—41no—
641C2×C3×C4—41no—
642C2×C3×C4—41no—
643C2×C3×C4—41no—
644C2×C3×C4—41no—
645C2×C3×C4—41no—
646C2×C3×C4—41no—
647C2×C3×C4—41no—
648C2×C3×C4—41no—
649C2×C3×C4—41no—
650C2×C3×C4#12114yes—
651C2×C3×C4C22⋊Q814yes—
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—
675C24—21no—
676C24—21no—
677C24—21no—
678C24C2×C3×D412yes—
679C24C2×C3×Q812yes—
680C24C2×C3×Q812yes—
681C24C3×#4112yes—
682C24C24×C311yescharacteristic
683C2×Q8—28no—
684C2×Q8—44no—
685C2×Q8—44no—
686C2×Q8—44no—
687C2×Q8—44no—
688C2×Q8—44no—
689C2×Q8—44no—
690C2×D4—28no—
691C2×D4—28no—
692C2×D4—44no—
693C2×D4—44no—
694C2×D4—44no—
695C2×D4—44no—
696C2×D4—44no—
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—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—44no—
776C22×C4—44no—
777C22×C4—44no—
778C22×C4—44no—
779C22×C4—44no—
780C22×C4—44no—
781C22×C4—44no—
782C22×C4C2×C3×D412yes—
783C22×C4C2×C3×D412yes—
784C22×C4C2×C3×D412yes—
785C22×C4C2×C3×D412yes—
786C22×C4C2×C3×D412yes—
787C22×C4C2×C3×D412yes—
788C22×C4C2×C3×D412yes—
789C22×C4C2×C3×D412yes—
790C22×C4C2×C3×Q812yes—
791C22×C4C3×#4112yes—
792C22×C4C3×#4112yes—
793C22×C4C3×#4112yes—
794C22×C4C3×#4112yes—
795C4⋊C4—44no—
796C4⋊C4—44no—
797C4⋊C4—44no—
798C4⋊C4—44no—
799C22⋊C4—28no—
800C22⋊C4—44no—
801C22⋊C4—44no—
802C22⋊C4—44no—
803C22⋊C4—44no—
804C22⋊C4—44no—
805C22⋊C4—44no—
806C22⋊C4—44no—
807C22⋊C4—44no—
808C22⋊C4—44no—
809C22⋊C4—44no—
810C42—44no—
811C22×C3—24no—
812C22×C3—24no—
813C22×C3—24no—
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×C3—42no—
828C22×C3—42no—
829C22×C3—42no—
830C22×C3—42no—
831C22×C3—42no—
832C22×C3—42no—
833C22×C3—81no—
834C22×C3—81no—
835C22×C3—81no—
836C22×C3—81no—
837C22×C3—81no—
838C22×C3—81no—
839C22×C3—81no—
840C22×C3—81no—
841C22×C3C2×#12111yescharacteristic
842C22×C3C2×C22⋊Q811yescharacteristic
843C22×C3C2×C22⋊Q811yescharacteristic
844C22×C3#52511yescharacteristic
845C22×C3#52911yescharacteristic
846C22×C3#53211yescharacteristic
847C22×C3#53511yescharacteristic
848C22×C3#53511yescharacteristic
849C22×C3#53711yescharacteristic
850C22×C3#53811yescharacteristic
851C22×C3#53811yescharacteristic
852C22×C3#53811yescharacteristic
853C22×C3#54211yescharacteristic
854C22×C3#54211yescharacteristic
855C22×C3#54311yescharacteristic
856C22×C3D4211yescharacteristic
857C22×C3D4211yescharacteristic
858C22×C3#54611yescharacteristic
859C22×C3#54611yescharacteristic
860C22×C3#54611yescharacteristic
861C22×C3#54611yescharacteristic
862C22×C3#54611yescharacteristic
863C22×C3#54611yescharacteristic
864C22×C3#54811yescharacteristic
865C22×C3D4×Q811yescharacteristic
866C22×C3#55111yescharacteristic
867C22×C3#55211yescharacteristic
868C22×C3#55411yescharacteristic
869C22×C3#55411yescharacteristic
870C22×C3#55411yescharacteristic
871C22×C3#55911yescharacteristic
872C22×C3#55911yescharacteristic
873C22×C3#55911yescharacteristic
874C22×C3H(3,𝔽4)11yescharacteristic
875C22×C3#56211yescharacteristic
876C3×C4—24no—
877C3×C4—24no—
878C3×C4—42no—
879C3×C4—42no—
880C3×C4—42no—
881C3×C4—42no—
882C3×C4—42no—
883C3×C4—42no—
884C3×C4—42no—
885C3×C4—81no—
886C3×C4—81no—
887C3×C4—81no—
888C3×C4—81no—
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—22no—
912C23—22no—
913C23—22no—
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—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23C3×C22⋊Q814yes—
959C23C22×C3×D411yescharacteristic
960C23C22×C3×D411yescharacteristic
961C23C22×C3×D411yescharacteristic
962C23C22×C3×Q811yescharacteristic
963C23C2×C3×#4111yescharacteristic
964C23C2×C3×#4111yescharacteristic
965C23C2×C3×#4111yescharacteristic
966C23C2×C3×#4111yescharacteristic
967C23C2×C3×#4111yescharacteristic
968C23C3×H(5,𝔽2)11yescharacteristic
969C23C3×H(5,𝔽2)11yescharacteristic
970C23C3×H(5,𝔽2)11yescharacteristic
971C23C3×H(5,𝔽2)11yescharacteristic
972C23C3×H(5,𝔽2)11yescharacteristic
973C23C3×2−1+411yescharacteristic
974Q8—416no—
975D4—416no—
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—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—416no—
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×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4C3×#12114yes—
1067C2×C4C3×C22⋊Q814yes—
1068C2×C3—44no—
1069C2×C3—82no—
1070C2×C3#241711yescharacteristic
1071C2×C3#242411yescharacteristic
1072C2×C3#243711yescharacteristic
1073C2×C3#245011yescharacteristic
1074C2×C3#245211yescharacteristic
1075C2×C3#245811yescharacteristic
1076C2×C3#254411yescharacteristic
1077C2×C3#255711yescharacteristic
1078C2×C3#258011yescharacteristic
1079C2×C3#267011yescharacteristic
1080C2×C3#267611yescharacteristic
1081C2×C3#269211yescharacteristic
1082C2×C3#271211yescharacteristic
1083C2×C3#275111yescharacteristic
1084C2×C3#280411yescharacteristic
1085C22—24no—
1086C22—24no—
1087C22—24no—
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—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—42no—
1105C22—42no—
1106C22—42no—
1107C22—81no—
1108C22—81no—
1109C22—81no—
1110C22—81no—
1111C22—81no—
1112C22—81no—
1113C22—81no—
1114C22—81no—
1115C22C2×C3×#12111yescharacteristic
1116C22C2×C3×C22⋊Q811yescharacteristic
1117C22C2×C3×C22⋊Q811yescharacteristic
1118C22C3×#52511yescharacteristic
1119C22C3×#52911yescharacteristic
1120C22C3×#53211yescharacteristic
1121C22C3×#53511yescharacteristic
1122C22C3×#53511yescharacteristic
1123C22C3×#53711yescharacteristic
1124C22C3×#53811yescharacteristic
1125C22C3×#53811yescharacteristic
1126C22C3×#53811yescharacteristic
1127C22C3×#54211yescharacteristic
1128C22C3×#54211yescharacteristic
1129C22C3×#54311yescharacteristic
1130C22C3×D4211yescharacteristic
1131C22C3×D4211yescharacteristic
1132C22C3×#54611yescharacteristic
1133C22C3×#54611yescharacteristic
1134C22C3×#54611yescharacteristic
1135C22C3×#54611yescharacteristic
1136C22C3×#54611yescharacteristic
1137C22C3×#54611yescharacteristic
1138C22C3×#54811yescharacteristic
1139C22C3×D4×Q811yescharacteristic
1140C22C3×#55111yescharacteristic
1141C22C3×#55211yescharacteristic
1142C22C3×#55411yescharacteristic
1143C22C3×#55411yescharacteristic
1144C22C3×#55411yescharacteristic
1145C22C3×#55911yescharacteristic
1146C22C3×#55911yescharacteristic
1147C22C3×#55911yescharacteristic
1148C22C3×H(3,𝔽4)11yescharacteristic
1149C22C3×#56211yescharacteristic
1150C4—24no—
1151C4—24no—
1152C4—42no—
1153C4—42no—
1154C4—42no—
1155C4—42no—
1156C4—42no—
1157C4—42no—
1158C4—42no—
1159C4—81no—
1160C4—81no—
1161C4—81no—
1162C4—81no—
1163C3#1533111yescharacteristic, direct product factor, Sylow
1164C2—44no—
1165C2—82no—
1166C2C3×#241711yescharacteristic
1167C2C3×#242411yescharacteristic
1168C2C3×#243711yescharacteristic
1169C2C3×#245011yescharacteristic
1170C2C3×#245211yescharacteristic
1171C2C3×#245811yescharacteristic
1172C2C3×#254411yescharacteristic
1173C2C3×#255711yescharacteristic
1174C2C3×#258011yescharacteristic
1175C2C3×#267011yescharacteristic
1176C2C3×#267611yescharacteristic
1177C2C3×#269211yescharacteristic
1178C2C3×#271211yescharacteristic
1179C2C3×#275111yescharacteristic
1180C2C3×#280411yescharacteristic
subgroupG/H
center, socleC24×C3C24
commutator, Frattini, cosocleC24C24×C3
prime radicalC23×C3×D4C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C3 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×#393C2semidirect
2. C2×C3×#393C2semidirect
3. C2×C3×#391C2semidirect
6. C2×C3×#385C2semidirect
7. C3×#1442C2semidirect
8. C3×#1441C2semidirect
9. C3×#1439C2semidirect
10. C3×#1439C2semidirect
11. C3×#1439C2semidirect
12. C3×#1439C2semidirect
14. C3×#1436C2semidirect
15. C3×C22⋊#95C2semidirect
16. #15331C3direct (N × H)
58. C2×#393C2×C3semidirect
59. C2×#393C2×C3semidirect
60. C2×#391C2×C3semidirect
63. C2×#385C2×C3semidirect
64. #1442C2×C3semidirect
65. #1441C2×C3semidirect
66. #1439C2×C3semidirect
67. #1439C2×C3semidirect
68. #1439C2×C3semidirect
69. #1439C2×C3semidirect
71. #1436C2×C3semidirect
72. C22⋊#95C2×C3semidirect
88. C22×C3×D4Q8semidirect
172. C3×#95D4semidirect
388. C22×D4C3×Q8semidirect
472. #95C3×D4semidirect
1163. C3#15331direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#3932
C2×C3×#3912
C2×C3×#3902
C2×C3×#3862
C2×C3×#3852
C3×#14422
C3×#14412
C3×#14392
C3×#14382
C3×#14362
C3×C22⋊#952
#153313