Finite Group Databasebeta

← C3×#82924 #11867132

Subgroups — C3×#82924 #11867132

Order 1152.

1261 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#525C211yesmaximal, characteristic, complemented
2C2×C3×#949C211yesmaximal, characteristic, complemented
3C2×C3×#930C211yesmaximal, characteristic, complemented
4C22×C3×#208C211yesmaximal, characteristic, complemented
5C3×#5232C211yesmaximal, characteristic, complemented
6C3×#5049C212yesmaximal, complemented
7C3×#5048C212yesmaximal, complemented
8C3×#5039C212yesmaximal, complemented
9C3×#5038C212yesmaximal, complemented
10C3×#5001C211yesmaximal, characteristic, complemented
11C3×#4995C211yesmaximal, characteristic, complemented
12C3×#3055—31nomaximal
13#82924C311yesmaximal, characteristic, direct product factor
14C2×C32×#41C2211yescharacteristic
15C23×C32×C4C2211yescharacteristic
16C22×C3×#67—21no—
17C22×C3×D12C2211yescharacteristic
18C32×#123—21no—
19C32×C22⋊Q8C2211yescharacteristic, complemented
20C32×C22⋊Q8C2211yescharacteristic, complemented
21C32×#121C2211yescharacteristic, complemented
22C32×#121C2211yescharacteristic, complemented
23C32×#120—21no—
24C32×C4×D4—21no—
25C32×C4×D4—21no—
26C32×#117C2211yescharacteristic
27C3×#949—24no—
28C2×C3×#215C2212yescomplemented
29C2×C3×#213C2212yescomplemented
30C3×#930—21no—
31C3×#930—21no—
32C3×#930C2212yes—
33C3×#930C2212yes—
34C2×C3×(C2×D3)⋊C4—21no—
35C2×C3×C4⋊Dic3C2211yescharacteristic
36C2×C3×#208—24no—
37C2×C3×#208C2211yescharacteristic
38C2×C3×#208C2211yescharacteristic
39C2×C3×#208C2212yescomplemented
40C22×C3×C3⋊C8C2212yescomplemented
41C3×#835C2212yescomplemented
42C3×#832C2212yescomplemented
43C3×#809C2212yescomplemented
44C3×#809C2212yescomplemented
45C3×#808C2212yescomplemented
46C3×#807C2212yescomplemented
47C2×C3×AGL(1,ℤ/8)—31no—
48C22×C3×M16—31no—
49C3×#525—21no—
50C3×#525D311yescharacteristic, complemented
51C3×#525C2×C311yescharacteristic, complemented
52C2×C3×#121—31no—
53C2×#949C2×C311yescharacteristic, complemented
54C2×#930C2×C311yescharacteristic, complemented
55C22×#208C2×C311yescharacteristic, complemented
56C3×#469—32no—
57C3×#468—32no—
58C3×#466—32no—
59C3×#465—32no—
60C3×#428—31no—
61C3×#418—31no—
62C3×#417—31no—
63#5232C2×C311yescharacteristic, complemented
64#5049C2×C312yescomplemented
65#5048C2×C312yescomplemented
66#5039C2×C312yescomplemented
67#5038C2×C312yescomplemented
68#5001C2×C311yescharacteristic, complemented
69#4995C2×C311yescharacteristic, complemented
70C24×C32D411yescharacteristic
71C23×C3×D3—21no—
72C32×#41—22no—
73C32×#41—22no—
74C2×C32×Q8C2311yescharacteristic
75C2×C32×D4—21no—
76C2×C32×D4—21no—
77C2×C32×D4—21no—
78C2×C32×D4C2311yescharacteristic
79C22×C32×C4—22no—
80C22×C32×C4—22no—
81C22×C32×C4—21no—
82C22×C32×C4D411yescharacteristic
83C22×C32×C4D411yescharacteristic
84C22×C32×C4D411yescharacteristic
85C22×C32×C4C2311yescharacteristic
86C22×C32×C4C2311yescharacteristic
87C22×C32×C4C2311yescharacteristic
88C2×C3×#67—22no—
89C2×C3×#67—22no—
90C2×C3×#67—44no—
91C22×C3×Dic3—21no—
92C2×C3×D12—22no—
93C2×C3×D12—22no—
94C2×C3×D12—21no—
95C2×C3×D12C2312yes—
96C32×C4⋊C4—21no—
97C32×C4⋊C4—21no—
98C32×C4⋊C4C2311yescharacteristic
99C32×C4⋊C4C2311yescharacteristic
100C32×C22⋊C4—21no—
101C32×C22⋊C4—21no—
102C32×C22⋊C4—21no—
103C32×C22⋊C4—21no—
104C32×C22⋊C4—21no—
105C32×C42—21no—
106C3×#215—24no—
107C3×#213—24no—
108C3×(C2×D3)⋊C4—22no—
109C3×(C2×D3)⋊C4—22no—
110C3×C4⋊Dic3—21no—
111C3×C4⋊Dic3C2312yes—
112C3×#208—22no—
113C3×#208—24no—
114C3×#208D414yescomplemented
115C2×C3×C3⋊C8—24no—
116C2×C3×C3⋊C8C2312yes—
117C2×C3×C3⋊C8C2312yes—
118#3055—31noSylow
119C2×C3×#41—21no—
120C2×C3×#41C2×D311yescharacteristic
121C2×C3×#41C22×C311yescharacteristic
122C22×C3×D4—31no—
123C22×C3×D4—61no—
124C23×C3×C4—21no—
125C23×C3×C4C2×D311yescharacteristic
126C23×C3×C4C22×C311yescharacteristic
127C22×#67—21no—
128C22×D12C22×C311yescharacteristic
129C3×AGL(1,ℤ/8)—64no—
130C2×C3×SD16—32no—
131C2×C3×D8—32no—
132C2×C3×M16—31no—
133C2×C3×M16—31no—
134C2×C3×M16—32no—
135C2×C3×M16—64no—
136C22×C3×C8—32no—
137C3×#123—22no—
138C3×#123—21no—
139C3×#123—21no—
140C3×C22⋊Q8—21no—
141C3×C22⋊Q8—21no—
142C3×C22⋊Q8C2×D311yescharacteristic, complemented
143C3×C22⋊Q8C2×D311yescharacteristic, complemented
144C3×C22⋊Q8C22×C311yescharacteristic, complemented
145C3×C22⋊Q8C22×C311yescharacteristic, complemented
146C3×#121—21no—
147C3×#121—21no—
148C3×#121—32no—
149C3×#121—32no—
150C3×#121—61no—
151C3×#121—61no—
152C3×#121C2×D311yescharacteristic, complemented
153C3×#121C2×D311yescharacteristic, complemented
154C3×#121C22×C311yescharacteristic, complemented
155C3×#121C22×C311yescharacteristic, complemented
156C3×#120—22no—
157C3×#120—21no—
158C3×#120—21no—
159C3×C4×D4—22no—
160C3×C4×D4—22no—
161C3×C4×D4—21no—
162C3×C4×D4—21no—
163C3×C4×D4—21no—
164C3×C4×D4—21no—
165C3×#117—21no—
166C3×#117C2×D311yescharacteristic
167C3×#117C22×C311yescharacteristic
168C2×C3×C4⋊C4—31no—
169C2×C3×C22⋊C4—61no—
170#949—24no—
171C2×#215C22×C312yescomplemented
172C2×#213C22×C312yescomplemented
173#930—21no—
174#930—21no—
175#930C22×C312yes—
176#930C22×C312yes—
177C2×(C2×D3)⋊C4—21no—
178C2×C4⋊Dic3C22×C311yescharacteristic
179C2×#208—24no—
180C2×#208C22×C311yescharacteristic
181C2×#208C22×C311yescharacteristic
182C2×#208C22×C312yescomplemented
183C22×C3⋊C8C22×C312yescomplemented
184C3×#107—32no—
185C3×#106—32no—
186C3×#103—32no—
187C3×#102—32no—
188C3×#102—32no—
189C3×#102—32no—
190#835C22×C312yescomplemented
191#832C22×C312yescomplemented
192#809C22×C312yescomplemented
193#809C22×C312yescomplemented
194#808C22×C312yescomplemented
195#807C22×C312yescomplemented
196C23×C32—21no—
197C23×C32—22no—
198C23×C32—22no—
199C23×C32—41no—
200C23×C32C2×D411yescharacteristic
201C23×C32C2×D411yescharacteristic
202C23×C32C2×D411yescharacteristic
203C22×C3×D3—22no—
204C22×C3×D3—42no—
205C22×C3×D3—42no—
206C22×C3×D3—42no—
207C32×Q8—21no—
208C32×Q8—21no—
209C32×D4—21no—
210C32×D4—21no—
211C32×D4—42no—
212C32×D4—42no—
213C32×D4—42no—
214C2×C32×C4—21no—
215C2×C32×C4—21no—
216C2×C32×C4—21no—
217C2×C32×C4—22no—
218C2×C32×C4—22no—
219C2×C32×C4—22no—
220C2×C32×C4—21no—
221C2×C32×C4—21no—
222C2×C32×C4—21no—
223C2×C32×C4—21no—
224C2×C32×C4—42no—
225C2×C32×C4C2×D412yes—
226C2×C32×C4C2×D411yescharacteristic
227C2×C32×C4C2×D411yescharacteristic
228C2×C32×C4C2×D411yescharacteristic
229C2×C32×C4#4112yes—
230C2×C32×C4C2411yescharacteristic
231C3×#67—44no—
232C3×#67—44no—
233C2×C3×Dic3—22no—
234C2×C3×Dic3—42no—
235C3×D12—22no—
236C3×D12—22no—
237C3×D12—42no—
238C3×C3⋊C8—22no—
239C3×C3⋊C8C2×D414yescomplemented
240C2×AGL(1,ℤ/8)—31no—
241C22×M16—31no—
242#525C3×D311yescharacteristic, complemented
243C2×#121—31no—
244#469—32no—
245#468—32no—
246#466—32no—
247#465—32no—
248#428—31no—
249#418—31no—
250#417—31no—
251C24×C3—21no—
252C24×C3—61no—
253C24×C3#6711yescharacteristic
254C24×C3C3×D411yescharacteristic
255C23×D3—21no—
256C3×#41—22no—
257C3×#41—22no—
258C3×#41—22no—
259C3×#41—22no—
260C3×#41—42no—
261C3×#41—42no—
262C2×C3×Q8—21no—
263C2×C3×Q8C22×D311yescharacteristic
264C2×C3×Q8C23×C311yescharacteristic
265C2×C3×D4—22no—
266C2×C3×D4—22no—
267C2×C3×D4—22no—
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—32no—
276C2×C3×D4—62no—
277C2×C3×D4—62no—
278C2×C3×D4—62no—
279C2×C3×D4—62no—
280C2×C3×D4—61no—
281C2×C3×D4—124no—
282C2×C3×D4C22×D311yescharacteristic
283C2×C3×D4C23×C311yescharacteristic
284C22×C3×C4—22no—
285C22×C3×C4—22no—
286C22×C3×C4—22no—
287C22×C3×C4—22no—
288C22×C3×C4—22no—
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—42no—
298C22×C3×C4—42no—
299C22×C3×C4—61no—
300C22×C3×C4#6711yescharacteristic
301C22×C3×C4#6711yescharacteristic
302C22×C3×C4#6711yescharacteristic
303C22×C3×C4C3×D411yescharacteristic
304C22×C3×C4C3×D411yescharacteristic
305C22×C3×C4C3×D411yescharacteristic
306C22×C3×C4C22×D311yescharacteristic
307C22×C3×C4C22×D311yescharacteristic
308C22×C3×C4C22×D311yescharacteristic
309C22×C3×C4C23×C311yescharacteristic
310C22×C3×C4C23×C311yescharacteristic
311C22×C3×C4C23×C311yescharacteristic
312C2×#67—22no—
313C2×#67—22no—
314C2×#67—44no—
315C22×Dic3—21no—
316C2×D12—22no—
317C2×D12—22no—
318C2×D12—21no—
319C2×D12C23×C312yes—
320C3×SD16—64no—
321C3×D8—64no—
322C3×M16—34no—
323C3×M16—64no—
324C3×M16—62no—
325C2×C3×C8—32no—
326C2×C3×C8—32no—
327C2×C3×C8—64no—
328C3×C4⋊C4—22no—
329C3×C4⋊C4—22no—
330C3×C4⋊C4—21no—
331C3×C4⋊C4—21no—
332C3×C4⋊C4—21no—
333C3×C4⋊C4—21no—
334C3×C4⋊C4—21no—
335C3×C4⋊C4—21no—
336C3×C4⋊C4—32no—
337C3×C4⋊C4—61no—
338C3×C4⋊C4C22×D311yescharacteristic
339C3×C4⋊C4C22×D311yescharacteristic
340C3×C4⋊C4C23×C311yescharacteristic
341C3×C4⋊C4C23×C311yescharacteristic
342C3×C22⋊C4—22no—
343C3×C22⋊C4—22no—
344C3×C22⋊C4—22no—
345C3×C22⋊C4—22no—
346C3×C22⋊C4—22no—
347C3×C22⋊C4—21no—
348C3×C22⋊C4—21no—
349C3×C22⋊C4—21no—
350C3×C22⋊C4—21no—
351C3×C22⋊C4—21no—
352C3×C22⋊C4—21no—
353C3×C22⋊C4—21no—
354C3×C22⋊C4—21no—
355C3×C22⋊C4—21no—
356C3×C22⋊C4—21no—
357C3×C22⋊C4—62no—
358C3×C22⋊C4—62no—
359C3×C42—22no—
360C3×C42—21no—
361C3×C42—21no—
362#215—24no—
363#213—24no—
364(C2×D3)⋊C4—22no—
365(C2×D3)⋊C4—22no—
366C4⋊Dic3—21no—
367C4⋊Dic3C23×C312yes—
368#208—22no—
369#208—24no—
370#208C3×D414yescomplemented
371C2×C3⋊C8—24no—
372C2×C3⋊C8C23×C312yes—
373C2×C3⋊C8C23×C312yes—
374C22×C32—21no—
375C22×C32—21no—
376C22×C32—21no—
377C22×C32—21no—
378C22×C32—21no—
379C22×C32—21no—
380C22×C32—21no—
381C22×C32—44no—
382C22×C32—41no—
383C22×C32—41no—
384C22×C32—41no—
385C22×C32#12112yes—
386C22×C32AGL(1,ℤ/8)12yescomplemented
387C22×C32C22×D411yescharacteristic
388C2×C3×D3—42no—
389C2×C3×D3—42no—
390C2×C3×D3—42no—
391C2×C3×D3—84no—
392C32×C4—21no—
393C32×C4—21no—
394C32×C4—41no—
395C32×C4—41no—
396C32×C4—41no—
397C32×C4#12112yes—
398C32×C4C22×D411yescharacteristic
399C32×C4C2×#4111yescharacteristic
400C3×Dic3—42no—
401C2×#41C2×C3×D311yescharacteristic
402C22×D4—31no—
403C22×D4—61no—
404C23×C4C2×C3×D311yescharacteristic
405AGL(1,ℤ/8)—64no—
406C2×SD16—32no—
407C2×D8—32no—
408C2×M16—31no—
409C2×M16—31no—
410C2×M16—32no—
411C2×M16—64no—
412C22×C8—32no—
413#123—21no—
414C22⋊Q8C2×C3×D311yescharacteristic, complemented
415C22⋊Q8C2×C3×D311yescharacteristic, complemented
416#121—32no—
417#121—32no—
418#121—61no—
419#121—61no—
420#121C2×C3×D311yescharacteristic, complemented
421#121C2×C3×D311yescharacteristic, complemented
422#120—21no—
423C4×D4—21no—
424C4×D4—21no—
425#117C2×C3×D311yescharacteristic
426C2×C4⋊C4—31no—
427C2×C22⋊C4—61no—
428#107—32no—
429#106—32no—
430#103—32no—
431#102—32no—
432#102—32no—
433#102—32no—
434C23×C3—22no—
435C23×C3—22no—
436C23×C3—22no—
437C23×C3—22no—
438C23×C3—22no—
439C23×C3—21no—
440C23×C3—21no—
441C23×C3—21no—
442C23×C3—21no—
443C23×C3—21no—
444C23×C3—42no—
445C23×C3—42no—
446C23×C3—41no—
447C23×C3—41no—
448C23×C3—42no—
449C23×C3—62no—
450C23×C3—122no—
451C23×C3—122no—
452C23×C3—122no—
453C23×C3C2×#6711yescharacteristic
454C23×C3C2×#6711yescharacteristic
455C23×C3C2×#6711yescharacteristic
456C23×C3C2×C3×D411yescharacteristic
457C23×C3C2×C3×D411yescharacteristic
458C23×C3C2×C3×D411yescharacteristic
459C22×D3—22no—
460C22×D3—42no—
461C22×D3—42no—
462C22×D3—42no—
463C3×Q8—21no—
464C3×Q8—21no—
465C3×Q8—21no—
466C3×Q8—21no—
467C3×Q8—41no—
468C3×Q8—41no—
469C3×D4—21no—
470C3×D4—21no—
471C3×D4—21no—
472C3×D4—21no—
473C3×D4—41no—
474C3×D4—41no—
475C3×D4—44no—
476C3×D4—42no—
477C3×D4—42no—
478C3×D4—44no—
479C3×D4—44no—
480C3×D4—42no—
481C3×D4—42no—
482C3×D4—42no—
483C3×D4—42no—
484C3×D4—62no—
485C3×D4—62no—
486C3×D4—124no—
487C3×D4—124no—
488C3×D4—122no—
489C2×C3×C4—22no—
490C2×C3×C4—22no—
491C2×C3×C4—22no—
492C2×C3×C4—22no—
493C2×C3×C4—22no—
494C2×C3×C4—22no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—22no—
504C2×C3×C4—22no—
505C2×C3×C4—22no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—22no—
514C2×C3×C4—22no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—42no—
519C2×C3×C4—42no—
520C2×C3×C4—41no—
521C2×C3×C4—41no—
522C2×C3×C4—41no—
523C2×C3×C4—41no—
524C2×C3×C4—42no—
525C2×C3×C4—44no—
526C2×C3×C4—42no—
527C2×C3×C4—42no—
528C2×C3×C4—62no—
529C2×C3×C4—122no—
530C2×C3×C4D3×D412yes—
531C2×C3×C4#23712yes—
532C2×C3×C4C2×#6711yescharacteristic
533C2×C3×C4C2×#6711yescharacteristic
534C2×C3×C4C2×#6711yescharacteristic
535C2×C3×C4C2×C3×D412yes—
536C2×C3×C4C2×C3×D411yescharacteristic
537C2×C3×C4C2×C3×D411yescharacteristic
538C2×C3×C4C2×C3×D411yescharacteristic
539C2×C3×C4C3×#4112yes—
540C2×C3×C4C23×D311yescharacteristic
541C2×C3×C4C24×C311yescharacteristic
542#67—44no—
543#67—44no—
544C2×Dic3—22no—
545C2×Dic3—42no—
546D12—22no—
547D12—22no—
548D12—42no—
549C3×C8—34no—
550C3×C8—62no—
551C3⋊C8—22no—
552C3⋊C8C2×C3×D414yescomplemented
553C2×C32—22no—
554C2×C32—22no—
555C2×C32—41no—
556C2×C32—81no—
557C2×C32C2×#12111yescharacteristic
558C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
559C2×C32#57511yescharacteristic
560C3×D3—82no—
561C24—61no—
562C24C3×#6711yescharacteristic
563#41—22no—
564#41—22no—
565C2×Q8C22×C3×D311yescharacteristic
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—32no—
570C2×D4—62no—
571C2×D4—62no—
572C2×D4—62no—
573C2×D4—62no—
574C2×D4—61no—
575C2×D4—124no—
576C2×D4C22×C3×D311yescharacteristic
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—21no—
580C22×C4—61no—
581C22×C4C3×#6711yescharacteristic
582C22×C4C3×#6711yescharacteristic
583C22×C4C3×#6711yescharacteristic
584C22×C4C22×C3×D311yescharacteristic
585C22×C4C22×C3×D311yescharacteristic
586C22×C4C22×C3×D311yescharacteristic
587SD16—64no—
588D8—64no—
589M16—34no—
590M16—64no—
591M16—62no—
592C2×C8—32no—
593C2×C8—32no—
594C2×C8—64no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—32no—
598C4⋊C4—61no—
599C4⋊C4C22×C3×D311yescharacteristic
600C4⋊C4C22×C3×D311yescharacteristic
601C22⋊C4—21no—
602C22⋊C4—21no—
603C22⋊C4—21no—
604C22⋊C4—21no—
605C22⋊C4—21no—
606C22⋊C4—62no—
607C22⋊C4—62no—
608C42—21no—
609C22×C3—21no—
610C22×C3—21no—
611C22×C3—21no—
612C22×C3—21no—
613C22×C3—21no—
614C22×C3—21no—
615C22×C3—21no—
616C22×C3—21no—
617C22×C3—22no—
618C22×C3—21no—
619C22×C3—21no—
620C22×C3—21no—
621C22×C3—21no—
622C22×C3—21no—
623C22×C3—21no—
624C22×C3—22no—
625C22×C3—22no—
626C22×C3—21no—
627C22×C3—41no—
628C22×C3—41no—
629C22×C3—41no—
630C22×C3—41no—
631C22×C3—41no—
632C22×C3—41no—
633C22×C3—44no—
634C22×C3—44no—
635C22×C3—42no—
636C22×C3—42no—
637C22×C3—42no—
638C22×C3—48no—
639C22×C3—41no—
640C22×C3—41no—
641C22×C3—41no—
642C22×C3—41no—
643C22×C3—41no—
644C22×C3—41no—
645C22×C3—122no—
646C22×C3—122no—
647C22×C3—122no—
648C22×C3—244no—
649C22×C3#93912yes—
650C22×C3#94912yescomplemented
651C22×C3C3×#12112yes—
652C22×C3C3×AGL(1,ℤ/8)12yescomplemented
653C22×C3C22×#6711yescharacteristic
654C22×C3C22×C3×D411yescharacteristic
655C2×D3—42no—
656C2×D3—42no—
657C2×D3—42no—
658C2×D3—84no—
659C3×C4—21no—
660C3×C4—21no—
661C3×C4—21no—
662C3×C4—21no—
663C3×C4—22no—
664C3×C4—21no—
665C3×C4—21no—
666C3×C4—41no—
667C3×C4—41no—
668C3×C4—42no—
669C3×C4—42no—
670C3×C4—42no—
671C3×C4—41no—
672C3×C4—41no—
673C3×C4—41no—
674C3×C4—41no—
675C3×C4—41no—
676C3×C4—41no—
677C3×C4—122no—
678C3×C4#93912yes—
679C3×C4C3×#12112yes—
680C3×C4C2×D3×D411yescharacteristic
681C3×C4C2×#23711yescharacteristic
682C3×C4C22×C3×D411yescharacteristic
683C3×C4C2×C3×#4111yescharacteristic
684Dic3—42no—
685C32#305511yescharacteristic, complemented, Sylow
686C23—22no—
687C23—22no—
688C23—21no—
689C23—41no—
690C23—62no—
691C23—122no—
692C23—122no—
693C23—122no—
694C23C2×C3×#6711yescharacteristic
695C23C2×C3×#6711yescharacteristic
696C23C2×C3×#6711yescharacteristic
697Q8—21no—
698Q8—21no—
699D4—21no—
700D4—21no—
701D4—42no—
702D4—42no—
703D4—42no—
704D4—62no—
705D4—62no—
706D4—124no—
707D4—124no—
708D4—122no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—42no—
720C2×C4—62no—
721C2×C4—122no—
722C2×C4C3×D3×D412yes—
723C2×C4C3×#23712yes—
724C2×C4C2×C3×#6711yescharacteristic
725C2×C4C2×C3×#6711yescharacteristic
726C2×C4C2×C3×#6711yescharacteristic
727C2×C4C23×C3×D311yescharacteristic
728C8—34no—
729C8—62no—
730C2×C3—22no—
731C2×C3—22no—
732C2×C3—22no—
733C2×C3—22no—
734C2×C3—21no—
735C2×C3—21no—
736C2×C3—21no—
737C2×C3—42no—
738C2×C3—42no—
739C2×C3—42no—
740C2×C3—41no—
741C2×C3—41no—
742C2×C3—82no—
743C2×C3—81no—
744C2×C3—81no—
745C2×C3—242no—
746C2×C3C2×#93911yescharacteristic
747C2×C3C2×#94911yescharacteristic
748C2×C3#582211yescharacteristic
749C2×C3C2×C3×#12111yescharacteristic
750C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
751C2×C3C3×#57511yescharacteristic
752D3—82no—
753C22—21no—
754C22—21no—
755C22—21no—
756C22—21no—
757C22—21no—
758C22—21no—
759C22—21no—
760C22—44no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—122no—
765C22—122no—
766C22—122no—
767C22—244no—
768C22C3×#93912yes—
769C22C3×#94912yescomplemented
770C22C22×C3×#6711yescharacteristic
771C4—21no—
772C4—21no—
773C4—41no—
774C4—41no—
775C4—41no—
776C4—122no—
777C4C3×#93912yes—
778C4C2×C3×D3×D411yescharacteristic
779C4C2×C3×#23711yescharacteristic
780C3—21no—
781C3#8292411yescharacteristic, direct product factor
782C3C3×#305511yescharacteristic, complemented
783C2—22no—
784C2—22no—
785C2—41no—
786C2—81no—
787C2—242no—
788C2C2×C3×#93911yescharacteristic
789C2C2×C3×#94911yescharacteristic
790C2C3×#582211yescharacteristic
subgroupG/H
centerC22×C3C22×#67
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#525C2
socleC22×C32C22×D4
hypercenterC3×#525D3
hypocenterC3C3×#3055
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C23×C3×C4 ◁ C3×#525

Complements

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

NH ≅ G/Ntype
1. C32×#525C2semidirect
2. C2×C3×#949C2semidirect
3. C2×C3×#930C2semidirect
4. C22×C3×#208C2semidirect
5. C3×#5232C2semidirect
6. C3×#5049C2semidirect
7. C3×#5048C2semidirect
8. C3×#5039C2semidirect
9. C3×#5038C2semidirect
10. C3×#5001C2semidirect
11. C3×#4995C2semidirect
13. #82924C3direct (N × H)
19. C32×C22⋊Q8C22semidirect
20. C32×C22⋊Q8C22semidirect
21. C32×#121C22semidirect
22. C32×#121C22semidirect
28. C2×C3×#215C22semidirect
29. C2×C3×#213C22semidirect
39. C2×C3×#208C22semidirect
40. C22×C3×C3⋊C8C22semidirect
41. C3×#835C22semidirect
42. C3×#832C22semidirect
43. C3×#809C22semidirect
44. C3×#809C22semidirect
45. C3×#808C22semidirect
46. C3×#807C22semidirect
50. C3×#525D3semidirect
51. C3×#525C2×C3semidirect
53. C2×#949C2×C3semidirect
54. C2×#930C2×C3semidirect
55. C22×#208C2×C3semidirect
63. #5232C2×C3semidirect
64. #5049C2×C3semidirect
65. #5048C2×C3semidirect
66. #5039C2×C3semidirect
67. #5038C2×C3semidirect
68. #5001C2×C3semidirect
69. #4995C2×C3semidirect
114. C3×#208D4semidirect
142. C3×C22⋊Q8C2×D3semidirect
143. C3×C22⋊Q8C2×D3semidirect
144. C3×C22⋊Q8C22×C3semidirect
145. C3×C22⋊Q8C22×C3semidirect
152. C3×#121C2×D3semidirect
153. C3×#121C2×D3semidirect
154. C3×#121C22×C3semidirect
155. C3×#121C22×C3semidirect
171. C2×#215C22×C3semidirect
172. C2×#213C22×C3semidirect
182. C2×#208C22×C3semidirect
183. C22×C3⋊C8C22×C3semidirect
190. #835C22×C3semidirect
191. #832C22×C3semidirect
192. #809C22×C3semidirect
193. #809C22×C3semidirect
194. #808C22×C3semidirect
195. #807C22×C3semidirect
239. C3×C3⋊C8C2×D4semidirect
242. #525C3×D3semidirect
370. #208C3×D4semidirect
386. C22×C32AGL(1,ℤ/8)semidirect
414. C22⋊Q8C2×C3×D3semidirect
415. C22⋊Q8C2×C3×D3semidirect
420. #121C2×C3×D3semidirect
421. #121C2×C3×D3semidirect
552. C3⋊C8C2×C3×D4semidirect
650. C22×C3#949semidirect
652. C22×C3C3×AGL(1,ℤ/8)semidirect
685. C32#3055semidirect
769. C22C3×#949semidirect
781. C3#82924direct (N × H)
782. C3C3×#3055semidirect

Maximal subgroups

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

subgroupindex
C32×#5252
C2×C3×#9492
C2×C3×#9302
C22×C3×#2082
C3×#52322
C3×#50492
C3×#50482
C3×#50392
C3×#50382
C3×#50012
C3×#49952
C3×#30553
#829243