Finite Group Databasebeta

← C3×#24218 #10642825

Subgroups — C3×#24218 #10642825

Order 768.

1612 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#535C211yesmaximal, characteristic, complemented
2C2×C3×#463C211yesmaximal, characteristic, complemented
3C2×C3×#459C211yesmaximal, characteristic, complemented
4C2×C3×#449C211yesmaximal, characteristic, complemented
5C2×C3×#447C211yesmaximal, characteristic, complemented
6C3×#2324C211yesmaximal, characteristic, complemented
7C3×#2042C211yesmaximal, characteristic, complemented
8C3×#2041C211yesmaximal, characteristic, complemented
9C3×#2012C211yesmaximal, characteristic, complemented
10C3×#2011C211yesmaximal, characteristic, complemented
11C3×#1983C211yesmaximal, characteristic, complemented
12C3×#1982C211yesmaximal, characteristic, complemented
13C3×#1798C211yesmaximal, characteristic, complemented
14C3×#1788C211yesmaximal, characteristic, complemented
15C3×#1786C211yesmaximal, characteristic, complemented
16#24218C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×#41C2211yescharacteristic
18C23×C3×D4C2211yescharacteristic
19C22×C3×SD16C2211yescharacteristic, complemented
20C22×C3×D8C2211yescharacteristic
21C22×C3×D8C2211yescharacteristic
22C22×C3×D8C2211yescharacteristic, complemented
23C3×#535—24no—
24C3×#535—24no—
25C2×C3×#127C2211yescharacteristic
26C2×C3×#127C2211yescharacteristic
27C2×C3×#124C2211yescharacteristic
28C2×C3×#124C2211yescharacteristic
29C2×C3×#121—21no—
30C2×C3×#121—21no—
31C2×C3×#121C2211yescharacteristic
32C2×C3×#120—21no—
33C2×C3×#120—21no—
34C2×C3×C4×D4C2211yescharacteristic, complemented
35C2×C3×#117C2211yescharacteristic
36C3×#463—24no—
37C3×#459—24no—
38C3×#449—24no—
39C3×#447—24no—
40C2×C3×C4⋊C8C2211yescharacteristic, complemented
41C2×C3×C4⋊C8C2211yescharacteristic, complemented
42C2×C3×#103C2211yescharacteristic, complemented
43C2×C3×#103C2211yescharacteristic, complemented
44C2×C3×#103C2211yescharacteristic, complemented
45C2×C3×#102C2211yescharacteristic
46C2×C3×#102C2211yescharacteristic
47C2×C3×#102C2211yescharacteristic
48C2×C3×#102C2211yescharacteristic
49C2×C3×#102C2211yescharacteristic
50C2×C3×#102C2211yescharacteristic
51C2×C3×#102C2211yescharacteristic, complemented
52C2×C3×#102C2211yescharacteristic, complemented
53C2×C3×#102C2211yescharacteristic, complemented
54C2×C3×C22⋊C8C2211yescharacteristic
55C2×C3×C22⋊C8C2211yescharacteristic
56C3×#390—21no—
57C3×#390C2211yescharacteristic, complemented
58C3×#389C2211yescharacteristic, complemented
59C3×#388—21no—
60C3×#386—21no—
61C3×#385—21no—
62C3×#380C2211yescharacteristic
63C3×C4×C4⋊C4C2211yescharacteristic, complemented
64C3×#336C2211yescharacteristic, complemented
65C3×#336C2211yescharacteristic, complemented
66C2×#535C2×C311yescharacteristic, complemented
67C2×#463C2×C311yescharacteristic, complemented
68C2×#459C2×C311yescharacteristic, complemented
69C2×#449C2×C311yescharacteristic, complemented
70C2×#447C2×C311yescharacteristic, complemented
71#2324C2×C311yescharacteristic, complemented
72#2042C2×C311yescharacteristic, complemented
73#2041C2×C311yescharacteristic, complemented
74#2012C2×C311yescharacteristic, complemented
75#2011C2×C311yescharacteristic, complemented
76#1983C2×C311yescharacteristic, complemented
77#1982C2×C311yescharacteristic, complemented
78#1798C2×C311yescharacteristic, complemented
79#1788C2×C311yescharacteristic, complemented
80#1786C2×C311yescharacteristic, complemented
81C25×C3—21no—
82C2×C3×#41—22no—
83C2×C3×#41—22no—
84C2×C3×#41—22no—
85C2×C3×#41—22no—
86C2×C3×#41—41no—
87C2×C3×#41—41no—
88C22×C3×Q8C2311yescharacteristic
89C22×C3×D4—21no—
90C22×C3×D4—21no—
91C22×C3×D4—22no—
92C22×C3×D4—22no—
93C22×C3×D4—21no—
94C22×C3×D4—21no—
95C22×C3×D4—21no—
96C22×C3×D4—21no—
97C22×C3×D4—21no—
98C22×C3×D4—22no—
99C22×C3×D4—22no—
100C22×C3×D4—41no—
101C22×C3×D4—41no—
102C22×C3×D4C2311yescharacteristic
103C22×C3×D4C2311yescharacteristic
104C22×C3×D4C2311yescharacteristic
105C22×C3×D4C2311yescharacteristic
106C23×C3×C4—21no—
107C23×C3×C4—21no—
108C23×C3×C4C2311yescharacteristic
109C2×C3×SD16—22no—
110C2×C3×SD16—22no—
111C2×C3×SD16—41no—
112C2×C3×D8—22no—
113C2×C3×D8—22no—
114C2×C3×D8—22no—
115C2×C3×D8—22no—
116C2×C3×D8—22no—
117C2×C3×D8—22no—
118C2×C3×D8—41no—
119C2×C3×D8—41no—
120C2×C3×D8—41no—
121C22×C3×C8C2311yescharacteristic
122C22×C3×C8C2311yescharacteristic
123C22×C3×C8C2311yescharacteristic
124C22×C3×C8C2311yescharacteristic
125C3×#127—22no—
126C3×#127—22no—
127C3×#127—22no—
128C3×#127D414yescomplemented
129C3×#124—22no—
130C3×#124—22no—
131C3×#124—22no—
132C3×#124D414yescomplemented
133C3×#121—28no—
134C3×#121—28no—
135C3×#121—22no—
136C3×#121D414yescomplemented
137C3×#120—28no—
138C3×#120—28no—
139C3×C4×D4—22no—
140C3×C4×D4—22no—
141C3×#117—22no—
142C3×#117—22no—
143C2×C3×C4⋊C4—21no—
144C2×C3×C4⋊C4D411yescharacteristic
145C2×C3×C4⋊C4D411yescharacteristic
146C2×C3×C4⋊C4C2311yescharacteristic
147C2×C3×C4⋊C4C2311yescharacteristic
148C2×C3×C4⋊C4C2311yescharacteristic
149C2×C3×C22⋊C4—21no—
150C2×C3×C22⋊C4—21no—
151C2×C3×C22⋊C4—21no—
152C2×C3×C22⋊C4—21no—
153C2×C3×C22⋊C4—21no—
154C2×C3×C22⋊C4—21no—
155C2×C3×C22⋊C4—21no—
156C2×C3×C22⋊C4—21no—
157C2×C3×C22⋊C4—21no—
158C2×C3×C22⋊C4D411yescharacteristic
159C2×C3×C22⋊C4D411yescharacteristic
160C2×C3×C42—21no—
161C2×C3×C42C2311yescharacteristic
162C2×C3×C42C2311yescharacteristic
163C3×C4⋊C8—22no—
164C3×C4⋊C8—22no—
165C3×#103—22no—
166C3×#103—22no—
167C3×#103—41no—
168C3×#102—22no—
169C3×#102—22no—
170C3×#102—22no—
171C3×#102—22no—
172C3×#102—22no—
173C3×#102—22no—
174C3×#102—41no—
175C3×#102—41no—
176C3×#102—41no—
177C3×C22⋊C8—22no—
178C3×C22⋊C8—22no—
179C3×#95—21no—
180C3×#95—21no—
181C3×#95—21no—
182C22×#41C22×C311yescharacteristic
183C23×D4C22×C311yescharacteristic
184C22×SD16C22×C311yescharacteristic, complemented
185C22×D8C22×C311yescharacteristic
186C22×D8C22×C311yescharacteristic
187C22×D8C22×C311yescharacteristic, complemented
188#535—24no—
189#535—24no—
190C2×#127C22×C311yescharacteristic
191C2×#127C22×C311yescharacteristic
192C2×#124C22×C311yescharacteristic
193C2×#124C22×C311yescharacteristic
194C2×#121—21no—
195C2×#121—21no—
196C2×#121C22×C311yescharacteristic
197C2×#120—21no—
198C2×#120—21no—
199C2×C4×D4C22×C311yescharacteristic, complemented
200C2×#117C22×C311yescharacteristic
201#463—24no—
202#459—24no—
203#449—24no—
204#447—24no—
205C2×C4⋊C8C22×C311yescharacteristic, complemented
206C2×C4⋊C8C22×C311yescharacteristic, complemented
207C2×#103C22×C311yescharacteristic, complemented
208C2×#103C22×C311yescharacteristic, complemented
209C2×#103C22×C311yescharacteristic, complemented
210C2×#102C22×C311yescharacteristic
211C2×#102C22×C311yescharacteristic
212C2×#102C22×C311yescharacteristic
213C2×#102C22×C311yescharacteristic
214C2×#102C22×C311yescharacteristic
215C2×#102C22×C311yescharacteristic
216C2×#102C22×C311yescharacteristic, complemented
217C2×#102C22×C311yescharacteristic, complemented
218C2×#102C22×C311yescharacteristic, complemented
219C2×C22⋊C8C22×C311yescharacteristic
220C2×C22⋊C8C22×C311yescharacteristic
221#390—21no—
222#390C22×C311yescharacteristic, complemented
223#389C22×C311yescharacteristic, complemented
224#388—21no—
225#386—21no—
226#385—21no—
227#380C22×C311yescharacteristic
228C4×C4⋊C4C22×C311yescharacteristic, complemented
229#336C22×C311yescharacteristic, complemented
230#336C22×C311yescharacteristic, complemented
231C24×C3—24no—
232C24×C3—21no—
233C24×C3—21no—
234C24×C3—21no—
235C24×C3—21no—
236C24×C3—42no—
237C24×C3—42no—
238C24×C3—81no—
239C24×C3—81no—
240C24×C3—81no—
241C24×C3—81no—
242C24×C3C2×D411yescharacteristic
243C3×#41—44no—
244C3×#41—44no—
245C3×#41—44no—
246C3×#41—44no—
247C2×C3×Q8—21no—
248C2×C3×Q8—21no—
249C2×C3×Q8—21no—
250C2×C3×Q8—21no—
251C2×C3×Q8—21no—
252C2×C3×Q8C2×D412yes—
253C2×C3×D4—24no—
254C2×C3×D4—24no—
255C2×C3×D4—24no—
256C2×C3×D4—24no—
257C2×C3×D4—24no—
258C2×C3×D4—24no—
259C2×C3×D4—24no—
260C2×C3×D4—21no—
261C2×C3×D4—21no—
262C2×C3×D4—21no—
263C2×C3×D4—21no—
264C2×C3×D4—21no—
265C2×C3×D4—21no—
266C2×C3×D4—21no—
267C2×C3×D4—21no—
268C2×C3×D4—21no—
269C2×C3×D4—21no—
270C2×C3×D4—21no—
271C2×C3×D4—21no—
272C2×C3×D4—21no—
273C2×C3×D4—21no—
274C2×C3×D4—21no—
275C2×C3×D4—21no—
276C2×C3×D4—21no—
277C2×C3×D4—21no—
278C2×C3×D4—21no—
279C2×C3×D4—21no—
280C2×C3×D4—44no—
281C2×C3×D4—44no—
282C2×C3×D4—44no—
283C2×C3×D4—44no—
284C2×C3×D4—42no—
285C2×C3×D4—42no—
286C2×C3×D4—42no—
287C2×C3×D4—42no—
288C2×C3×D4—81no—
289C2×C3×D4—81no—
290C2×C3×D4—81no—
291C2×C3×D4—81no—
292C2×C3×D4—81no—
293C2×C3×D4—81no—
294C2×C3×D4—81no—
295C2×C3×D4—81no—
296C2×C3×D4—81no—
297C2×C3×D4—81no—
298C2×C3×D4C2×D412yes—
299C2×C3×D4C2×D412yes—
300C2×C3×D4C2×D412yes—
301C2×C3×D4C2×D412yes—
302C22×C3×C4—21no—
303C22×C3×C4—21no—
304C22×C3×C4—21no—
305C22×C3×C4—21no—
306C22×C3×C4—24no—
307C22×C3×C4—21no—
308C22×C3×C4—21no—
309C22×C3×C4—21no—
310C22×C3×C4—21no—
311C22×C3×C4—42no—
312C22×C3×C4—42no—
313C22×C3×C4—42no—
314C22×C3×C4—81no—
315C22×C3×C4—81no—
316C22×C3×C4C2×D411yescharacteristic
317C22×C3×C4C2×D411yescharacteristic
318C22×C3×C4C2×D411yescharacteristic
319C22×C3×C4C2×D411yescharacteristic
320C22×C3×C4C2×D411yescharacteristic
321C22×C3×C4C2×D412yes—
322C22×C3×C4#4112yes—
323C22×C3×C4C2411yescharacteristic
324C3×SD16—44no—
325C3×D8—44no—
326C3×D8—44no—
327C3×D8—44no—
328C2×C3×C8—21no—
329C2×C3×C8—21no—
330C2×C3×C8—21no—
331C2×C3×C8—21no—
332C2×C3×C8—21no—
333C2×C3×C8—21no—
334C2×C3×C8—21no—
335C2×C3×C8—21no—
336C2×C3×C8—21no—
337C2×C3×C8—21no—
338C2×C3×C8—21no—
339C2×C3×C8—21no—
340C3×C4⋊C4—22no—
341C3×C4⋊C4—22no—
342C3×C4⋊C4—21no—
343C3×C4⋊C4—21no—
344C3×C4⋊C4—21no—
345C3×C4⋊C4—21no—
346C3×C4⋊C4—21no—
347C3×C4⋊C4—81no—
348C3×C4⋊C4C2×D412yes—
349C3×C22⋊C4—24no—
350C3×C22⋊C4—24no—
351C3×C22⋊C4—24no—
352C3×C22⋊C4—24no—
353C3×C22⋊C4—22no—
354C3×C22⋊C4—22no—
355C3×C22⋊C4—24no—
356C3×C22⋊C4—42no—
357C3×C22⋊C4—81no—
358C3×C22⋊C4—81no—
359C3×C22⋊C4—81no—
360C3×C42—21no—
361C3×C42—21no—
362C3×C42—81no—
363C3×C42C2×D412yes—
364C3×C42C2×D412yes—
365C25—21no—
366C2×#41—22no—
367C2×#41—22no—
368C2×#41—22no—
369C2×#41—22no—
370C2×#41—41no—
371C2×#41—41no—
372C22×Q8C23×C311yescharacteristic
373C22×D4—21no—
374C22×D4—21no—
375C22×D4—22no—
376C22×D4—22no—
377C22×D4—21no—
378C22×D4—21no—
379C22×D4—21no—
380C22×D4—21no—
381C22×D4—21no—
382C22×D4—22no—
383C22×D4—22no—
384C22×D4—41no—
385C22×D4—41no—
386C22×D4C23×C311yescharacteristic
387C22×D4C23×C311yescharacteristic
388C22×D4C23×C311yescharacteristic
389C22×D4C23×C311yescharacteristic
390C23×C4—21no—
391C23×C4—21no—
392C23×C4C23×C311yescharacteristic
393C2×SD16—22no—
394C2×SD16—22no—
395C2×SD16—41no—
396C2×D8—22no—
397C2×D8—22no—
398C2×D8—22no—
399C2×D8—22no—
400C2×D8—22no—
401C2×D8—22no—
402C2×D8—41no—
403C2×D8—41no—
404C2×D8—41no—
405C22×C8C23×C311yescharacteristic
406C22×C8C23×C311yescharacteristic
407C22×C8C23×C311yescharacteristic
408C22×C8C23×C311yescharacteristic
409#127—22no—
410#127—22no—
411#127—22no—
412#127C3×D414yescomplemented
413#124—22no—
414#124—22no—
415#124—22no—
416#124C3×D414yescomplemented
417#121—28no—
418#121—28no—
419#121—22no—
420#121C3×D414yescomplemented
421#120—28no—
422#120—28no—
423C4×D4—22no—
424C4×D4—22no—
425#117—22no—
426#117—22no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4C3×D411yescharacteristic
429C2×C4⋊C4C3×D411yescharacteristic
430C2×C4⋊C4C23×C311yescharacteristic
431C2×C4⋊C4C23×C311yescharacteristic
432C2×C4⋊C4C23×C311yescharacteristic
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4C3×D411yescharacteristic
443C2×C22⋊C4C3×D411yescharacteristic
444C2×C42—21no—
445C2×C42C23×C311yescharacteristic
446C2×C42C23×C311yescharacteristic
447C4⋊C8—22no—
448C4⋊C8—22no—
449#103—22no—
450#103—22no—
451#103—41no—
452#102—22no—
453#102—22no—
454#102—22no—
455#102—22no—
456#102—22no—
457#102—22no—
458#102—41no—
459#102—41no—
460#102—41no—
461C22⋊C8—22no—
462C22⋊C8—22no—
463#95—21no—
464#95—21no—
465#95—21no—
466C23×C3—21no—
467C23×C3—21no—
468C23×C3—21no—
469C23×C3—21no—
470C23×C3—21no—
471C23×C3—21no—
472C23×C3—22no—
473C23×C3—22no—
474C23×C3—22no—
475C23×C3—22no—
476C23×C3—48no—
477C23×C3—41no—
478C23×C3—41no—
479C23×C3—41no—
480C23×C3—41no—
481C23×C3—41no—
482C23×C3—41no—
483C23×C3—41no—
484C23×C3—41no—
485C23×C3—41no—
486C23×C3—41no—
487C23×C3—41no—
488C23×C3—41no—
489C23×C3—41no—
490C23×C3—41no—
491C23×C3—41no—
492C23×C3—41no—
493C23×C3—41no—
494C23×C3—41no—
495C23×C3—41no—
496C23×C3—41no—
497C23×C3—41no—
498C23×C3—41no—
499C23×C3—41no—
500C23×C3—41no—
501C23×C3—84no—
502C23×C3—84no—
503C23×C3—84no—
504C23×C3—84no—
505C23×C3—84no—
506C23×C3—84no—
507C23×C3#12112yes—
508C23×C3C22×D411yescharacteristic
509C3×Q8—22no—
510C3×Q8—22no—
511C3×Q8—41no—
512C3×Q8—41no—
513C3×D4—22no—
514C3×D4—22no—
515C3×D4—22no—
516C3×D4—22no—
517C3×D4—22no—
518C3×D4—22no—
519C3×D4—22no—
520C3×D4—22no—
521C3×D4—48no—
522C3×D4—48no—
523C3×D4—41no—
524C3×D4—41no—
525C3×D4—41no—
526C3×D4—41no—
527C3×D4—41no—
528C3×D4—41no—
529C3×D4—41no—
530C3×D4—41no—
531C3×D4—84no—
532C3×D4—84no—
533C3×D4—84no—
534C3×D4—84no—
535C3×D4—84no—
536C2×C3×C4—21no—
537C2×C3×C4—21no—
538C2×C3×C4—21no—
539C2×C3×C4—21no—
540C2×C3×C4—21no—
541C2×C3×C4—21no—
542C2×C3×C4—22no—
543C2×C3×C4—22no—
544C2×C3×C4—22no—
545C2×C3×C4—22no—
546C2×C3×C4—21no—
547C2×C3×C4—21no—
548C2×C3×C4—22no—
549C2×C3×C4—22no—
550C2×C3×C4—21no—
551C2×C3×C4—21no—
552C2×C3×C4—21no—
553C2×C3×C4—21no—
554C2×C3×C4—48no—
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—84no—
566C2×C3×C4#12012yes—
567C2×C3×C4#12012yes—
568C2×C3×C4#12112yes—
569C2×C3×C4C22×D411yescharacteristic
570C2×C3×C4C22×D411yescharacteristic
571C2×C3×C4C22×D411yescharacteristic
572C2×C3×C4C2×#4111yescharacteristic
573C2×C3×C4H(5,𝔽2)11yescharacteristic
574C2×C3×C4H(5,𝔽2)11yescharacteristic
575C3×C8—41no—
576C3×C8—41no—
577C3×C8—41no—
578C3×C8—41no—
579C24—24no—
580C24—21no—
581C24—21no—
582C24—21no—
583C24—21no—
584C24—42no—
585C24—42no—
586C24—81no—
587C24—81no—
588C24—81no—
589C24—81no—
590C24C2×C3×D411yescharacteristic
591#41—44no—
592#41—44no—
593#41—44no—
594#41—44no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×Q8—21no—
598C2×Q8—21no—
599C2×Q8—21no—
600C2×Q8C2×C3×D412yes—
601C2×D4—24no—
602C2×D4—24no—
603C2×D4—24no—
604C2×D4—24no—
605C2×D4—24no—
606C2×D4—24no—
607C2×D4—24no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—44no—
629C2×D4—44no—
630C2×D4—44no—
631C2×D4—44no—
632C2×D4—42no—
633C2×D4—42no—
634C2×D4—42no—
635C2×D4—42no—
636C2×D4—81no—
637C2×D4—81no—
638C2×D4—81no—
639C2×D4—81no—
640C2×D4—81no—
641C2×D4—81no—
642C2×D4—81no—
643C2×D4—81no—
644C2×D4—81no—
645C2×D4—81no—
646C2×D4C2×C3×D412yes—
647C2×D4C2×C3×D412yes—
648C2×D4C2×C3×D412yes—
649C2×D4C2×C3×D412yes—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—24no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—42no—
660C22×C4—42no—
661C22×C4—42no—
662C22×C4—81no—
663C22×C4—81no—
664C22×C4C2×C3×D411yescharacteristic
665C22×C4C2×C3×D411yescharacteristic
666C22×C4C2×C3×D411yescharacteristic
667C22×C4C2×C3×D411yescharacteristic
668C22×C4C2×C3×D411yescharacteristic
669C22×C4C2×C3×D412yes—
670C22×C4C3×#4112yes—
671C22×C4C24×C311yescharacteristic
672SD16—44no—
673D8—44no—
674D8—44no—
675D8—44no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C4⋊C4—22no—
689C4⋊C4—22no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—81no—
696C4⋊C4C2×C3×D412yes—
697C22⋊C4—24no—
698C22⋊C4—24no—
699C22⋊C4—24no—
700C22⋊C4—24no—
701C22⋊C4—22no—
702C22⋊C4—22no—
703C22⋊C4—24no—
704C22⋊C4—42no—
705C22⋊C4—81no—
706C22⋊C4—81no—
707C22⋊C4—81no—
708C42—21no—
709C42—21no—
710C42—81no—
711C42C2×C3×D412yes—
712C42C2×C3×D412yes—
713C22×C3—22no—
714C22×C3—22no—
715C22×C3—22no—
716C22×C3—41no—
717C22×C3—41no—
718C22×C3—41no—
719C22×C3—41no—
720C22×C3—42no—
721C22×C3—42no—
722C22×C3—42no—
723C22×C3—42no—
724C22×C3—42no—
725C22×C3—42no—
726C22×C3—42no—
727C22×C3—42no—
728C22×C3—42no—
729C22×C3—42no—
730C22×C3—42no—
731C22×C3—42no—
732C22×C3—816no—
733C22×C3—81no—
734C22×C3—81no—
735C22×C3—81no—
736C22×C3—81no—
737C22×C3—81no—
738C22×C3—81no—
739C22×C3—81no—
740C22×C3—81no—
741C22×C3—81no—
742C22×C3—81no—
743C22×C3—81no—
744C22×C3—81no—
745C22×C3—81no—
746C22×C3—81no—
747C22×C3—81no—
748C22×C3—81no—
749C22×C3C2×#12011yescharacteristic
750C22×C3C2×#12111yescharacteristic
751C22×C3#53511yescharacteristic
752C22×C3#57611yescharacteristic
753C22×C3#57611yescharacteristic
754C22×C3#57611yescharacteristic
755C22×C3#57711yescharacteristic
756C3×C4—22no—
757C3×C4—22no—
758C3×C4—22no—
759C3×C4—42no—
760C3×C4—41no—
761C3×C4—41no—
762C3×C4—42no—
763C3×C4—81no—
764C3×C4—81no—
765C3×C4D4211yescharacteristic
766C3×C4D4211yescharacteristic
767C3×C4#54611yescharacteristic
768C3×C4#54611yescharacteristic
769C23—21no—
770C23—21no—
771C23—21no—
772C23—21no—
773C23—21no—
774C23—21no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—48no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—84no—
805C23—84no—
806C23—84no—
807C23—84no—
808C23—84no—
809C23—84no—
810C23C3×#12112yes—
811C23C22×C3×D411yescharacteristic
812Q8—22no—
813Q8—22no—
814Q8—41no—
815Q8—41no—
816D4—22no—
817D4—22no—
818D4—22no—
819D4—22no—
820D4—22no—
821D4—22no—
822D4—22no—
823D4—22no—
824D4—48no—
825D4—48no—
826D4—41no—
827D4—41no—
828D4—41no—
829D4—41no—
830D4—41no—
831D4—41no—
832D4—41no—
833D4—41no—
834D4—84no—
835D4—84no—
836D4—84no—
837D4—84no—
838D4—84no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—48no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—84no—
869C2×C4C3×#12012yes—
870C2×C4C3×#12012yes—
871C2×C4C3×#12112yes—
872C2×C4C22×C3×D411yescharacteristic
873C2×C4C22×C3×D411yescharacteristic
874C2×C4C22×C3×D411yescharacteristic
875C2×C4C2×C3×#4111yescharacteristic
876C2×C4C3×H(5,𝔽2)11yescharacteristic
877C2×C4C3×H(5,𝔽2)11yescharacteristic
878C8—41no—
879C8—41no—
880C8—41no—
881C8—41no—
882C2×C3—42no—
883C2×C3—82no—
884C2×C3—82no—
885C2×C3—82no—
886C2×C3—82no—
887C2×C3#240811yescharacteristic
888C2×C3#300811yescharacteristic
889C2×C3#301211yescharacteristic
890C2×C3#304111yescharacteristic
891C2×C3#304511yescharacteristic
892C2×C3#322011yescharacteristic
893C2×C3#322411yescharacteristic
894C22—22no—
895C22—22no—
896C22—22no—
897C22—41no—
898C22—41no—
899C22—41no—
900C22—41no—
901C22—42no—
902C22—42no—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—42no—
907C22—42no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—42no—
913C22—816no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22—81no—
920C22—81no—
921C22—81no—
922C22—81no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22C2×C3×#12011yescharacteristic
931C22C2×C3×#12111yescharacteristic
932C22C3×#53511yescharacteristic
933C22C3×#57611yescharacteristic
934C22C3×#57611yescharacteristic
935C22C3×#57611yescharacteristic
936C22C3×#57711yescharacteristic
937C4—22no—
938C4—22no—
939C4—22no—
940C4—42no—
941C4—41no—
942C4—41no—
943C4—42no—
944C4—81no—
945C4—81no—
946C4C3×D4211yescharacteristic
947C4C3×D4211yescharacteristic
948C4C3×#54611yescharacteristic
949C4C3×#54611yescharacteristic
950C3#2421811yescharacteristic, direct product factor, Sylow
951C2—42no—
952C2—82no—
953C2—82no—
954C2—82no—
955C2—82no—
956C2C3×#240811yescharacteristic
957C2C3×#300811yescharacteristic
958C2C3×#301211yescharacteristic
959C2C3×#304111yescharacteristic
960C2C3×#304511yescharacteristic
961C2C3×#322011yescharacteristic
962C2C3×#322411yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C2×C3×#117 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×#535C2semidirect
2. C2×C3×#463C2semidirect
3. C2×C3×#459C2semidirect
4. C2×C3×#449C2semidirect
5. C2×C3×#447C2semidirect
6. C3×#2324C2semidirect
7. C3×#2042C2semidirect
8. C3×#2041C2semidirect
9. C3×#2012C2semidirect
10. C3×#2011C2semidirect
11. C3×#1983C2semidirect
12. C3×#1982C2semidirect
13. C3×#1798C2semidirect
14. C3×#1788C2semidirect
15. C3×#1786C2semidirect
16. #24218C3direct (N × H)
19. C22×C3×SD16C22semidirect
22. C22×C3×D8C22semidirect
34. C2×C3×C4×D4C22semidirect
40. C2×C3×C4⋊C8C22semidirect
41. C2×C3×C4⋊C8C22semidirect
42. C2×C3×#103C22semidirect
43. C2×C3×#103C22semidirect
44. C2×C3×#103C22semidirect
51. C2×C3×#102C22semidirect
52. C2×C3×#102C22semidirect
53. C2×C3×#102C22semidirect
57. C3×#390C22semidirect
58. C3×#389C22semidirect
63. C3×C4×C4⋊C4C22semidirect
64. C3×#336C22semidirect
65. C3×#336C22semidirect
66. C2×#535C2×C3semidirect
67. C2×#463C2×C3semidirect
68. C2×#459C2×C3semidirect
69. C2×#449C2×C3semidirect
70. C2×#447C2×C3semidirect
71. #2324C2×C3semidirect
72. #2042C2×C3semidirect
73. #2041C2×C3semidirect
74. #2012C2×C3semidirect
75. #2011C2×C3semidirect
76. #1983C2×C3semidirect
77. #1982C2×C3semidirect
78. #1798C2×C3semidirect
79. #1788C2×C3semidirect
80. #1786C2×C3semidirect
128. C3×#127D4semidirect
132. C3×#124D4semidirect
136. C3×#121D4semidirect
184. C22×SD16C22×C3semidirect
187. C22×D8C22×C3semidirect
199. C2×C4×D4C22×C3semidirect
205. C2×C4⋊C8C22×C3semidirect
206. C2×C4⋊C8C22×C3semidirect
207. C2×#103C22×C3semidirect
208. C2×#103C22×C3semidirect
209. C2×#103C22×C3semidirect
216. C2×#102C22×C3semidirect
217. C2×#102C22×C3semidirect
218. C2×#102C22×C3semidirect
222. #390C22×C3semidirect
223. #389C22×C3semidirect
228. C4×C4⋊C4C22×C3semidirect
229. #336C22×C3semidirect
230. #336C22×C3semidirect
412. #127C3×D4semidirect
416. #124C3×D4semidirect
420. #121C3×D4semidirect
950. C3#24218direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5352
C2×C3×#4632
C2×C3×#4592
C2×C3×#4492
C2×C3×#4472
C3×#23242
C3×#20422
C3×#20412
C3×#20122
C3×#20112
C3×#19832
C3×#19822
C3×#17982
C3×#17882
C3×#17862
#242183