Finite Group Databasebeta

← C3×#14140 #10632747

Subgroups — C3×#14140 #10632747

Order 768.

2278 conjugacy classes of subgroups.

The subgroup lattice has 1194 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#388C211yesmaximal, characteristic, complemented
2C2×C3×#386C211yesmaximal, characteristic
3C2×C3×#386C211yesmaximal, characteristic
4C2×C3×#386C211yesmaximal, characteristic
5C2×C3×#385C211yesmaximal, characteristic, complemented
6C2×C3×C4×C22⋊C4C211yesmaximal, characteristic, complemented
7C22×C3×#95C211yesmaximal, characteristic, complemented
8C3×#1443C211yesmaximal, characteristic, complemented
9C3×#1442C211yesmaximal, characteristic, complemented
10C3×#1440C211yesmaximal, characteristic, complemented
11C3×#1439C211yesmaximal, characteristic, complemented
12C3×#1437C211yesmaximal, characteristic, complemented
13C3×#1436C211yesmaximal, characteristic, complemented
14C3×#1434C211yesmaximal, characteristic, complemented
15C3×C22⋊#95C211yesmaximal, characteristic, complemented
16#14140C311yesmaximal, characteristic, direct product factor, Sylow
17C23×C3×D4C2211yescharacteristic
18C24×C3×C4C2211yescharacteristic
19C24×C3×C4C2211yescharacteristic
20C24×C3×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×C42C2211yescharacteristic
33C22×C3×C42C2211yescharacteristic
34C3×#388—24no—
35C3×#386—24no—
36C3×#386—24no—
37C3×#386C418yescomplemented
38C3×#385—24no—
39C3×C4×C22⋊C4—24no—
40C2×C3×#95—24no—
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×C3×#95C2211yescharacteristic
58C2×C3×#95C2211yescharacteristic
59C2×#388C2×C311yescharacteristic, complemented
60C2×#386C2×C311yescharacteristic
61C2×#386C2×C311yescharacteristic
62C2×#386C2×C311yescharacteristic
63C2×#385C2×C311yescharacteristic, complemented
64C2×C4×C22⋊C4C2×C311yescharacteristic, complemented
65C22×#95C2×C311yescharacteristic, complemented
66#1443C2×C311yescharacteristic, complemented
67#1442C2×C311yescharacteristic, complemented
68#1440C2×C311yescharacteristic, complemented
69#1439C2×C311yescharacteristic, complemented
70#1437C2×C311yescharacteristic, complemented
71#1436C2×C311yescharacteristic, complemented
72#1434C2×C311yescharacteristic, complemented
73C22⋊#95C2×C311yescharacteristic, complemented
74C25×C3C2311yescharacteristic
75C25×C3C2311yescharacteristic
76C22×C3×D4—22no—
77C22×C3×D4—22no—
78C22×C3×D4—22no—
79C22×C3×D4—22no—
80C22×C3×D4—22no—
81C22×C3×D4—22no—
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—22no—
89C23×C3×C4—22no—
90C23×C3×C4—22no—
91C23×C3×C4—22no—
92C23×C3×C4—22no—
93C23×C3×C4—22no—
94C23×C3×C4—22no—
95C23×C3×C4—22no—
96C23×C3×C4—22no—
97C23×C3×C4—41no—
98C23×C3×C4—41no—
99C23×C3×C4—41no—
100C23×C3×C4—41no—
101C23×C3×C4—41no—
102C23×C3×C4—41no—
103C23×C3×C4C2×C414yes—
104C23×C3×C4C2311yescharacteristic
105C23×C3×C4C2311yescharacteristic
106C23×C3×C4C2311yescharacteristic
107C23×C3×C4C2311yescharacteristic
108C23×C3×C4C2311yescharacteristic
109C23×C3×C4C2311yescharacteristic
110C23×C3×C4C2311yescharacteristic
111C23×C3×C4C2311yescharacteristic
112C23×C3×C4C2311yescharacteristic
113C23×C3×C4C2311yescharacteristic
114C23×C3×C4C2311yescharacteristic
115C23×C3×C4C2311yescharacteristic
116C23×C3×C4C2311yescharacteristic
117C2×C3×C4⋊C4—22no—
118C2×C3×C4⋊C4—22no—
119C2×C3×C4⋊C4—22no—
120C2×C3×C4⋊C4—22no—
121C2×C3×C4⋊C4—41no—
122C2×C3×C4⋊C4—41no—
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—41no—
140C2×C3×C22⋊C4—41no—
141C2×C3×C22⋊C4—41no—
142C2×C3×C22⋊C4—41no—
143C2×C3×C22⋊C4—41no—
144C2×C3×C22⋊C4—41no—
145C2×C3×C22⋊C4C2×C414yes—
146C2×C3×C22⋊C4C2×C414yescomplemented
147C2×C3×C22⋊C4C2×C414yescomplemented
148C2×C3×C22⋊C4D414yes—
149C2×C3×C22⋊C4D414yes—
150C2×C3×C42—22no—
151C2×C3×C42—22no—
152C2×C3×C42—22no—
153C2×C3×C42—22no—
154C2×C3×C42—41no—
155C2×C3×C42—41no—
156C3×#95—22no—
157C3×#95—22no—
158C3×#95—22no—
159C3×#95—22no—
160C3×#95—22no—
161C3×#95—22no—
162C3×#95—22no—
163C3×#95—22no—
164C3×#95—22no—
165C3×#95—22no—
166C3×#95—22no—
167C3×#95—22no—
168C3×#95—22no—
169C3×#95—41no—
170C3×#95—41no—
171C3×#95C2×C414yescomplemented
172C3×#95C2×C414yescomplemented
173C3×#95D414yescomplemented
174C23×D4C22×C311yescharacteristic
175C24×C4C22×C311yescharacteristic
176C24×C4C22×C311yescharacteristic
177C24×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×C42C22×C311yescharacteristic
190C22×C42C22×C311yescharacteristic
191#388—24no—
192#386—24no—
193#386—24no—
194#386C3×C418yescomplemented
195#385—24no—
196C4×C22⋊C4—24no—
197C2×#95—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
214C2×#95C22×C311yescharacteristic
215C2×#95C22×C311yescharacteristic
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×C3C22×C412yes—
239C24×C3C22×C412yes—
240C24×C3C2×D412yes—
241C24×C3C2×D412yes—
242C24×C3#4112yes—
243C24×C3#4112yes—
244C24×C3#4112yes—
245C24×C3#4112yes—
246C24×C3C2411yescharacteristic
247C2×C3×D4—28no—
248C2×C3×D4—28no—
249C2×C3×D4—28no—
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—28no—
259C22×C3×C4—28no—
260C22×C3×C4—28no—
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—28no—
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×C4—44no—
341C22×C3×C4—44no—
342C22×C3×C4—44no—
343C22×C3×C4—44no—
344C22×C3×C4—44no—
345C22×C3×C4—44no—
346C22×C3×C4—44no—
347C22×C3×C4—44no—
348C22×C3×C4—44no—
349C22×C3×C4—44no—
350C22×C3×C4—44no—
351C22×C3×C4C22×C412yes—
352C22×C3×C4C22×C412yes—
353C22×C3×C4C22×C412yes—
354C22×C3×C4C22×C412yes—
355C22×C3×C4C22×C412yes—
356C22×C3×C4C2×D412yes—
357C22×C3×C4C2×D412yes—
358C22×C3×C4C2×D412yes—
359C22×C3×C4C2×D412yes—
360C22×C3×C4C2×D412yes—
361C22×C3×C4C2×D412yes—
362C22×C3×C4C2×D412yes—
363C22×C3×C4#4112yes—
364C22×C3×C4#4112yes—
365C22×C3×C4#4112yes—
366C3×C4⋊C4—44no—
367C3×C4⋊C4—44no—
368C3×C22⋊C4—28no—
369C3×C22⋊C4—28no—
370C3×C22⋊C4—28no—
371C3×C22⋊C4—28no—
372C3×C22⋊C4—44no—
373C3×C22⋊C4—44no—
374C3×C22⋊C4—44no—
375C3×C22⋊C4—44no—
376C3×C22⋊C4—44no—
377C3×C42—44no—
378C3×C42—44no—
379C25C23×C311yescharacteristic
380C25C23×C311yescharacteristic
381C22×D4—22no—
382C22×D4—22no—
383C22×D4—22no—
384C22×D4—22no—
385C22×D4—22no—
386C22×D4—22no—
387C22×D4C2×C3×C414yes—
388C23×C4—22no—
389C23×C4—22no—
390C23×C4—22no—
391C23×C4—22no—
392C23×C4—22no—
393C23×C4—22no—
394C23×C4—22no—
395C23×C4—22no—
396C23×C4—22no—
397C23×C4—22no—
398C23×C4—22no—
399C23×C4—22no—
400C23×C4—22no—
401C23×C4—22no—
402C23×C4—41no—
403C23×C4—41no—
404C23×C4—41no—
405C23×C4—41no—
406C23×C4—41no—
407C23×C4—41no—
408C23×C4C2×C3×C414yes—
409C23×C4C23×C311yescharacteristic
410C23×C4C23×C311yescharacteristic
411C23×C4C23×C311yescharacteristic
412C23×C4C23×C311yescharacteristic
413C23×C4C23×C311yescharacteristic
414C23×C4C23×C311yescharacteristic
415C23×C4C23×C311yescharacteristic
416C23×C4C23×C311yescharacteristic
417C23×C4C23×C311yescharacteristic
418C23×C4C23×C311yescharacteristic
419C23×C4C23×C311yescharacteristic
420C23×C4C23×C311yescharacteristic
421C23×C4C23×C311yescharacteristic
422C2×C4⋊C4—22no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—41no—
427C2×C4⋊C4—41no—
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—22no—
442C2×C22⋊C4—22no—
443C2×C22⋊C4—22no—
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⋊C4C2×C3×C414yes—
451C2×C22⋊C4C2×C3×C414yescomplemented
452C2×C22⋊C4C2×C3×C414yescomplemented
453C2×C22⋊C4C3×D414yes—
454C2×C22⋊C4C3×D414yes—
455C2×C42—22no—
456C2×C42—22no—
457C2×C42—22no—
458C2×C42—22no—
459C2×C42—41no—
460C2×C42—41no—
461#95—22no—
462#95—22no—
463#95—22no—
464#95—22no—
465#95—22no—
466#95—22no—
467#95—22no—
468#95—22no—
469#95—22no—
470#95—22no—
471#95—22no—
472#95—22no—
473#95—22no—
474#95—41no—
475#95—41no—
476#95C2×C3×C414yescomplemented
477#95C2×C3×C414yescomplemented
478#95C3×D414yescomplemented
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—22no—
499C23×C3—22no—
500C23×C3—22no—
501C23×C3—22no—
502C23×C3—22no—
503C23×C3—22no—
504C23×C3—22no—
505C23×C3—22no—
506C23×C3—22no—
507C23×C3—22no—
508C23×C3—22no—
509C23×C3—22no—
510C23×C3—22no—
511C23×C3—22no—
512C23×C3—22no—
513C23×C3—22no—
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×C3#11714yes—
543C23×C3C4×D414yes—
544C23×C3C4×D414yes—
545C23×C3#12114yes—
546C23×C3#12314yes—
547C23×C3#12414yes—
548C23×C3#12614yes—
549C23×C3C23×C411yescharacteristic
550C23×C3C22×D411yescharacteristic
551C23×C3C22×D411yescharacteristic
552C23×C3C22×D411yescharacteristic
553C23×C3C2×#4111yescharacteristic
554C23×C3C2×#4111yescharacteristic
555C23×C3C2×#4111yescharacteristic
556C23×C3C2×#4111yescharacteristic
557C23×C3C2×#4111yescharacteristic
558C23×C3C2×#4111yescharacteristic
559C23×C3C2×#4111yescharacteristic
560C23×C3H(5,𝔽2)11yescharacteristic
561C23×C3H(5,𝔽2)11yescharacteristic
562C23×C3H(5,𝔽2)11yescharacteristic
563C23×C32−1+411yescharacteristic
564C3×D4—416no—
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—22no—
594C2×C3×C4—22no—
595C2×C3×C4—22no—
596C2×C3×C4—22no—
597C2×C3×C4—22no—
598C2×C3×C4—22no—
599C2×C3×C4—22no—
600C2×C3×C4—22no—
601C2×C3×C4—22no—
602C2×C3×C4—22no—
603C2×C3×C4—22no—
604C2×C3×C4—22no—
605C2×C3×C4—22no—
606C2×C3×C4—22no—
607C2×C3×C4—416no—
608C2×C3×C4—416no—
609C2×C3×C4—416no—
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—41no—
651C2×C3×C4—41no—
652C2×C3×C4—41no—
653C2×C3×C4—41no—
654C2×C3×C4—41no—
655C2×C3×C4—41no—
656C2×C3×C4—41no—
657C2×C3×C4—41no—
658C2×C3×C4C4×D414yes—
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—
678C24—21no—
679C24—21no—
680C24—21no—
681C24C22×C3×C412yes—
682C24C22×C3×C412yes—
683C24C2×C3×D412yes—
684C24C2×C3×D412yes—
685C24C3×#4112yes—
686C24C3×#4112yes—
687C24C3×#4112yes—
688C24C3×#4112yes—
689C24C24×C311yescharacteristic
690C2×D4—28no—
691C2×D4—28no—
692C2×D4—28no—
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—28no—
702C22×C4—28no—
703C22×C4—28no—
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—21no—
776C22×C4—28no—
777C22×C4—44no—
778C22×C4—44no—
779C22×C4—44no—
780C22×C4—44no—
781C22×C4—44no—
782C22×C4—44no—
783C22×C4—44no—
784C22×C4—44no—
785C22×C4—44no—
786C22×C4—44no—
787C22×C4—44no—
788C22×C4—44no—
789C22×C4—44no—
790C22×C4—44no—
791C22×C4—44no—
792C22×C4—44no—
793C22×C4—44no—
794C22×C4C22×C3×C412yes—
795C22×C4C22×C3×C412yes—
796C22×C4C22×C3×C412yes—
797C22×C4C22×C3×C412yes—
798C22×C4C22×C3×C412yes—
799C22×C4C2×C3×D412yes—
800C22×C4C2×C3×D412yes—
801C22×C4C2×C3×D412yes—
802C22×C4C2×C3×D412yes—
803C22×C4C2×C3×D412yes—
804C22×C4C2×C3×D412yes—
805C22×C4C2×C3×D412yes—
806C22×C4C3×#4112yes—
807C22×C4C3×#4112yes—
808C22×C4C3×#4112yes—
809C4⋊C4—44no—
810C4⋊C4—44no—
811C22⋊C4—28no—
812C22⋊C4—28no—
813C22⋊C4—28no—
814C22⋊C4—28no—
815C22⋊C4—44no—
816C22⋊C4—44no—
817C22⋊C4—44no—
818C22⋊C4—44no—
819C22⋊C4—44no—
820C42—44no—
821C42—44no—
822C22×C3—24no—
823C22×C3—24no—
824C22×C3—24no—
825C22×C3—24no—
826C22×C3—24no—
827C22×C3—24no—
828C22×C3—24no—
829C22×C3—24no—
830C22×C3—24no—
831C22×C3—24no—
832C22×C3—24no—
833C22×C3—24no—
834C22×C3—24no—
835C22×C3—24no—
836C22×C3—42no—
837C22×C3—42no—
838C22×C3—42no—
839C22×C3—42no—
840C22×C3—42no—
841C22×C3—42no—
842C22×C3—42no—
843C22×C3—81no—
844C22×C3—81no—
845C22×C3—81no—
846C22×C3—81no—
847C22×C3—81no—
848C22×C3—81no—
849C22×C3—81no—
850C22×C3—81no—
851C22×C3#38818yescomplemented
852C22×C3C2×#11711yescharacteristic
853C22×C3C2×C4×D411yescharacteristic
854C22×C3C2×C4×D411yescharacteristic
855C22×C3C2×C4×D411yescharacteristic
856C22×C3C4×#4111yescharacteristic
857C22×C3#51811yescharacteristic
858C22×C3#52011yescharacteristic
859C22×C3C2×#12111yescharacteristic
860C22×C3C2×#12311yescharacteristic
861C22×C3#52511yescharacteristic
862C22×C3#52511yescharacteristic
863C22×C3C2×#12411yescharacteristic
864C22×C3C2×#12611yescharacteristic
865C22×C3#52911yescharacteristic
866C22×C3#52911yescharacteristic
867C22×C3#53811yescharacteristic
868C22×C3#53811yescharacteristic
869C22×C3#53911yescharacteristic
870C22×C3#53911yescharacteristic
871C22×C3D4211yescharacteristic
872C22×C3D4211yescharacteristic
873C22×C3#54611yescharacteristic
874C22×C3#54611yescharacteristic
875C22×C3#54611yescharacteristic
876C22×C3#54611yescharacteristic
877C22×C3#54611yescharacteristic
878C22×C3#54711yescharacteristic
879C22×C3#54711yescharacteristic
880C22×C3#54811yescharacteristic
881C22×C3#55111yescharacteristic
882C22×C3#55111yescharacteristic
883C22×C3#55211yescharacteristic
884C22×C3#55311yescharacteristic
885C22×C3#55311yescharacteristic
886C22×C3#55311yescharacteristic
887C3×C4—24no—
888C3×C4—42no—
889C3×C4—42no—
890C3×C4—42no—
891C3×C4—42no—
892C3×C4—42no—
893C3×C4—42no—
894C3×C4—42no—
895C3×C4—42no—
896C3×C4—42no—
897C3×C4—42no—
898C3×C4—42no—
899C3×C4—42no—
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—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
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—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23C3×#11714yes—
964C23C3×C4×D414yes—
965C23C3×C4×D414yes—
966C23C3×#12114yes—
967C23C3×#12314yes—
968C23C3×#12414yes—
969C23C3×#12614yes—
970C23C23×C3×C411yescharacteristic
971C23C22×C3×D411yescharacteristic
972C23C22×C3×D411yescharacteristic
973C23C22×C3×D411yescharacteristic
974C23C2×C3×#4111yescharacteristic
975C23C2×C3×#4111yescharacteristic
976C23C2×C3×#4111yescharacteristic
977C23C2×C3×#4111yescharacteristic
978C23C2×C3×#4111yescharacteristic
979C23C2×C3×#4111yescharacteristic
980C23C2×C3×#4111yescharacteristic
981C23C3×H(5,𝔽2)11yescharacteristic
982C23C3×H(5,𝔽2)11yescharacteristic
983C23C3×H(5,𝔽2)11yescharacteristic
984C23C3×2−1+411yescharacteristic
985D4—416no—
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—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—416no—
1029C2×C4—416no—
1030C2×C4—416no—
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×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4C3×C4×D414yes—
1080C2×C3—28no—
1081C2×C3—82no—
1082C2×C3C2×#38811yescharacteristic
1083C2×C3#229011yescharacteristic
1084C2×C3#231811yescharacteristic
1085C2×C3#235811yescharacteristic
1086C2×C3#235911yescharacteristic
1087C2×C3#236111yescharacteristic
1088C2×C3#236411yescharacteristic
1089C2×C3#242411yescharacteristic
1090C2×C3#242511yescharacteristic
1091C2×C3#244311yescharacteristic
1092C2×C3#244411yescharacteristic
1093C2×C3#247211yescharacteristic
1094C2×C3#248111yescharacteristic
1095C2×C3#248811yescharacteristic
1096C2×C3#251011yescharacteristic
1097C22—24no—
1098C22—24no—
1099C22—24no—
1100C22—24no—
1101C22—24no—
1102C22—24no—
1103C22—24no—
1104C22—24no—
1105C22—24no—
1106C22—24no—
1107C22—24no—
1108C22—24no—
1109C22—24no—
1110C22—24no—
1111C22—42no—
1112C22—42no—
1113C22—42no—
1114C22—42no—
1115C22—42no—
1116C22—42no—
1117C22—42no—
1118C22—81no—
1119C22—81no—
1120C22—81no—
1121C22—81no—
1122C22—81no—
1123C22—81no—
1124C22—81no—
1125C22—81no—
1126C22C3×#38818yescomplemented
1127C22C2×C3×#11711yescharacteristic
1128C22C2×C3×C4×D411yescharacteristic
1129C22C2×C3×C4×D411yescharacteristic
1130C22C2×C3×C4×D411yescharacteristic
1131C22C3×C4×#4111yescharacteristic
1132C22C3×#51811yescharacteristic
1133C22C3×#52011yescharacteristic
1134C22C2×C3×#12111yescharacteristic
1135C22C2×C3×#12311yescharacteristic
1136C22C3×#52511yescharacteristic
1137C22C3×#52511yescharacteristic
1138C22C2×C3×#12411yescharacteristic
1139C22C2×C3×#12611yescharacteristic
1140C22C3×#52911yescharacteristic
1141C22C3×#52911yescharacteristic
1142C22C3×#53811yescharacteristic
1143C22C3×#53811yescharacteristic
1144C22C3×#53911yescharacteristic
1145C22C3×#53911yescharacteristic
1146C22C3×D4211yescharacteristic
1147C22C3×D4211yescharacteristic
1148C22C3×#54611yescharacteristic
1149C22C3×#54611yescharacteristic
1150C22C3×#54611yescharacteristic
1151C22C3×#54611yescharacteristic
1152C22C3×#54611yescharacteristic
1153C22C3×#54711yescharacteristic
1154C22C3×#54711yescharacteristic
1155C22C3×#54811yescharacteristic
1156C22C3×#55111yescharacteristic
1157C22C3×#55111yescharacteristic
1158C22C3×#55211yescharacteristic
1159C22C3×#55311yescharacteristic
1160C22C3×#55311yescharacteristic
1161C22C3×#55311yescharacteristic
1162C4—24no—
1163C4—42no—
1164C4—42no—
1165C4—42no—
1166C4—42no—
1167C4—42no—
1168C4—42no—
1169C4—42no—
1170C4—42no—
1171C4—42no—
1172C4—42no—
1173C4—42no—
1174C4—42no—
1175C3#1414011yescharacteristic, direct product factor, Sylow
1176C2—28no—
1177C2—82no—
1178C2C2×C3×#38811yescharacteristic
1179C2C3×#229011yescharacteristic
1180C2C3×#231811yescharacteristic
1181C2C3×#235811yescharacteristic
1182C2C3×#235911yescharacteristic
1183C2C3×#236111yescharacteristic
1184C2C3×#236411yescharacteristic
1185C2C3×#242411yescharacteristic
1186C2C3×#242511yescharacteristic
1187C2C3×#244311yescharacteristic
1188C2C3×#244411yescharacteristic
1189C2C3×#247211yescharacteristic
1190C2C3×#248111yescharacteristic
1191C2C3×#248811yescharacteristic
1192C2C3×#251011yescharacteristic
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
1. C2×C3×#388C2semidirect
5. C2×C3×#385C2semidirect
6. C2×C3×C4×C22⋊C4C2semidirect
7. C22×C3×#95C2semidirect
8. C3×#1443C2semidirect
9. C3×#1442C2semidirect
10. C3×#1440C2semidirect
11. C3×#1439C2semidirect
12. C3×#1437C2semidirect
13. C3×#1436C2semidirect
14. C3×#1434C2semidirect
15. C3×C22⋊#95C2semidirect
16. #14140C3direct (N × H)
37. C3×#386C4semidirect
59. C2×#388C2×C3semidirect
63. C2×#385C2×C3semidirect
64. C2×C4×C22⋊C4C2×C3semidirect
65. C22×#95C2×C3semidirect
66. #1443C2×C3semidirect
67. #1442C2×C3semidirect
68. #1440C2×C3semidirect
69. #1439C2×C3semidirect
70. #1437C2×C3semidirect
71. #1436C2×C3semidirect
72. #1434C2×C3semidirect
73. C22⋊#95C2×C3semidirect
146. C2×C3×C22⋊C4C2×C4semidirect
147. C2×C3×C22⋊C4C2×C4semidirect
171. C3×#95C2×C4semidirect
172. C3×#95C2×C4semidirect
173. C3×#95D4semidirect
194. #386C3×C4semidirect
451. C2×C22⋊C4C2×C3×C4semidirect
452. C2×C22⋊C4C2×C3×C4semidirect
476. #95C2×C3×C4semidirect
477. #95C2×C3×C4semidirect
478. #95C3×D4semidirect
851. C22×C3#388semidirect
1126. C22C3×#388semidirect
1175. C3#14140direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#3882
C2×C3×#3862
C2×C3×#3852
C2×C3×C4×C22⋊C42
C22×C3×#952
C3×#14432
C3×#14422
C3×#14402
C3×#14392
C3×#14372
C3×#14362
C3×#14342
C3×C22⋊#952
#141403