Finite Group Databasebeta

← C3×#80334 #11866156

Subgroups — C3×#80334 #11866156

Order 1152.

1122 conjugacy classes of subgroups.

The subgroup lattice has 909 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#911C211yesmaximal, characteristic, complemented
2C2×C3×D3×D8C211yesmaximal, characteristic, complemented
3C3×#5715C211yesmaximal, characteristic, complemented
4C3×#5545C211yesmaximal, characteristic, complemented
5C32×#459C211yesmaximal, characteristic, complemented
6C3×#5153C211yesmaximal, characteristic, complemented
7C3×#5150C211yesmaximal, characteristic, complemented
8C3×#5072C211yesmaximal, characteristic, complemented
9C3×#5016C211yesmaximal, characteristic, complemented
10C3×#4844C211yesmaximal, characteristic, complemented
11C3×#4839C211yesmaximal, characteristic, complemented
12C3×#4787C211yesmaximal, characteristic, complemented
13C3×#4786C211yesmaximal, characteristic, complemented
14C3×#4772C211yesmaximal, characteristic, complemented
15C3×#4770C211yesmaximal, characteristic, complemented
16C3×#3041—31nomaximal
17#80334C311yesmaximal, characteristic, direct product factor
18C2×C3×#237C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C2×C3×D3×D4C2211yescharacteristic
21C2×C32×D8C2211yescharacteristic
22C2×C32×D8C2211yescharacteristic, complemented
23C32×#127C2211yescharacteristic, complemented
24C32×C4×D4C2211yescharacteristic, complemented
25C3×#940C2211yescharacteristic, complemented
26C3×#939—21no—
27C3×#939—21no—
28C3×#937—21no—
29C3×#937—21no—
30C3×#936C2211yescharacteristic, complemented
31C3×D4×Dic3C2211yescharacteristic, complemented
32C2×C3×#214C2211yescharacteristic, complemented
33C2×C3×#213C2211yescharacteristic
34C2×C3×#213C2211yescharacteristic
35C2×C3×#213C2211yescharacteristic, complemented
36C3×C4×#67—21no—
37C2×C3×(C2×D3)⋊C4—21no—
38C3×#911—24no—
39C3×D3×D8—24no—
40C2×C3×D24C2211yescharacteristic
41C2×C3×#204C2211yescharacteristic, complemented
42C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
43C2×C3×D3×C8C2211yescharacteristic
44C3×#893C2211yescharacteristic, complemented
45C3×#892C2211yescharacteristic
46C3×#67⋊C4—21no—
47C3×D3×C22⋊C4—21no—
48C3×#875C2211yescharacteristic, complemented
49C3×C4×D12C2211yescharacteristic, complemented
50C3×#872C2211yescharacteristic
51C32×C4⋊C8C2211yescharacteristic, complemented
52C32×#102C2211yescharacteristic, complemented
53C32×#102C2211yescharacteristic, complemented
54C3×#832C2211yescharacteristic, complemented
55C3×#832C2211yescharacteristic, complemented
56C3×#821C2211yescharacteristic, complemented
57C3×#816C2211yescharacteristic, complemented
58C3×Dic3⋊C8C2211yescharacteristic, complemented
59C3×Dic3⋊C8C2211yescharacteristic, complemented
60C3×#810C2211yescharacteristic, complemented
61C3×#809C2211yescharacteristic, complemented
62C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
63C2×C3×AGL(1,ℤ/8)—31no—
64C22×C3×D8—31no—
65C3×#535—31no—
66C3×#518—31no—
67C2×#911C2×C311yescharacteristic, complemented
68C2×D3×D8C2×C311yescharacteristic, complemented
69#5715C2×C311yescharacteristic, complemented
70#5545C2×C311yescharacteristic, complemented
71C3×#463—31no—
72C3×#463—31no—
73C3×#463—31no—
74C3×#463—31no—
75C3×#459—21no—
76C3×#459—31no—
77C3×#459—31no—
78C3×#459—31no—
79C3×#459D311yescharacteristic, complemented
80C3×#459C2×C311yescharacteristic, complemented
81C3×#424—31no—
82C3×#418—31no—
83C3×#416—31no—
84#5153C2×C311yescharacteristic, complemented
85#5150C2×C311yescharacteristic, complemented
86#5072C2×C311yescharacteristic, complemented
87#5016C2×C311yescharacteristic, complemented
88#4844C2×C311yescharacteristic, complemented
89#4839C2×C311yescharacteristic, complemented
90#4787C2×C311yescharacteristic, complemented
91#4786C2×C311yescharacteristic, complemented
92#4772C2×C311yescharacteristic, complemented
93#4770C2×C311yescharacteristic, complemented
94C23×C3×D3—21no—
95C23×C3×D3—21no—
96C2×C32×D4—21no—
97C2×C32×D4—21no—
98C2×C32×D4C2311yescharacteristic
99C2×C32×D4C2311yescharacteristic
100C2×C32×D4C2311yescharacteristic
101C22×C32×C4—21no—
102C2×C3×#67—21no—
103C2×C3×#67—21no—
104C2×C3×#67—21no—
105C2×C3×#67—21no—
106C2×C3×#67—21no—
107C22×C3×Dic3—21no—
108C22×C3×Dic3—21no—
109C3×#237—22no—
110C3×#237—22no—
111C3×D3×D4—22no—
112C3×D3×D4—22no—
113C3×D3×D4—22no—
114C3×D3×D4D414yescomplemented
115C2×C3×D12C2311yescharacteristic
116C2×C3×D12C2311yescharacteristic
117C2×C3×C4×D3—21no—
118C2×C3×C4×D3—21no—
119C2×C3×C4×D3C2311yescharacteristic
120C2×C3×Dic6C2311yescharacteristic
121C32×D8—22no—
122C32×D8—22no—
123C2×C32×C8C2311yescharacteristic
124C2×C32×C8C2311yescharacteristic
125C32×C4⋊C4C2311yescharacteristic
126C32×C22⋊C4—21no—
127C32×C42C2311yescharacteristic
128C3×#217—21no—
129C3×#217—21no—
130C3×#217—21no—
131C3×#214—22no—
132C3×#213—22no—
133C3×#213—22no—
134C3×#213—22no—
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4—21no—
137C3×(C2×D3)⋊C4—21no—
138C3×(C2×D3)⋊C4—21no—
139C3×(C2×D3)⋊C4—21no—
140C3×(C2×D3)⋊C4D411yescharacteristic
141C3×(C2×D3)⋊C4D411yescharacteristic
142C3×C4⋊Dic3C2311yescharacteristic
143C3×Dic3⋊C4D411yescharacteristic
144C3×Dic3⋊C4D411yescharacteristic
145C3×C4×Dic3—21no—
146C3×C4×Dic3C2311yescharacteristic
147C2×C3×C3⋊C8C2311yescharacteristic
148C2×C3×C3⋊C8C2311yescharacteristic
149C3×D24—22no—
150C3×#204—22no—
151C3×ΓL(1,𝔽25)—22no—
152C3×D3×C8—22no—
153#3041—31noSylow
154C2×C3×#41—31no—
155C22×C3×D4—31no—
156C22×C3×D4—31no—
157C2×#237C22×C311yescharacteristic
158C2×D3×D4C22×C311yescharacteristic
159C2×D3×D4C22×C311yescharacteristic
160C3×AGL(1,ℤ/8)—64no—
161C2×C3×SD16—31no—
162C2×C3×SD16—31no—
163C2×C3×D8—21no—
164C2×C3×D8—21no—
165C2×C3×D8—31no—
166C2×C3×D8—31no—
167C2×C3×D8—31no—
168C2×C3×D8—31no—
169C2×C3×D8—64no—
170C2×C3×D8C2×D311yescharacteristic
171C2×C3×D8C2×D311yescharacteristic, complemented
172C2×C3×D8C22×C311yescharacteristic
173C2×C3×D8C22×C311yescharacteristic, complemented
174C2×C3×M16—31no—
175C22×C3×C8—31no—
176C3×#127—21no—
177C3×#127—31no—
178C3×#127C2×D311yescharacteristic, complemented
179C3×#127C22×C311yescharacteristic, complemented
180C3×#124—31no—
181C3×#124—31no—
182C3×#121—61no—
183C3×#121—61no—
184C3×#120—61no—
185C3×#120—61no—
186C3×C4×D4—21no—
187C3×C4×D4—31no—
188C3×C4×D4—31no—
189C3×C4×D4—31no—
190C3×C4×D4—61no—
191C3×C4×D4—61no—
192C3×C4×D4C2×D311yescharacteristic, complemented
193C3×C4×D4C22×C311yescharacteristic, complemented
194C3×#117—31no—
195C3×#117—31no—
196C2×C3×C22⋊C4—61no—
197C2×C3×C22⋊C4—61no—
198#940C22×C311yescharacteristic, complemented
199#939—21no—
200#939—21no—
201#937—21no—
202#937—21no—
203#936C22×C311yescharacteristic, complemented
204D4×Dic3C22×C311yescharacteristic, complemented
205C2×#214C22×C311yescharacteristic, complemented
206C2×#213C22×C311yescharacteristic
207C2×#213C22×C311yescharacteristic
208C2×#213C22×C311yescharacteristic, complemented
209C4×#67—21no—
210C2×(C2×D3)⋊C4—21no—
211#911—24no—
212D3×D8—24no—
213C2×D24C22×C311yescharacteristic
214C2×#204C22×C311yescharacteristic, complemented
215C2×ΓL(1,𝔽25)C22×C311yescharacteristic
216C2×D3×C8C22×C311yescharacteristic
217#893C22×C311yescharacteristic, complemented
218#892C22×C311yescharacteristic
219#67⋊C4—21no—
220D3×C22⋊C4—21no—
221#875C22×C311yescharacteristic, complemented
222C4×D12C22×C311yescharacteristic, complemented
223#872C22×C311yescharacteristic
224C3×C4⋊C8—21no—
225C3×C4⋊C8—31no—
226C3×C4⋊C8—31no—
227C3×C4⋊C8—31no—
228C3×C4⋊C8C2×D311yescharacteristic, complemented
229C3×C4⋊C8C22×C311yescharacteristic, complemented
230C3×#103—31no—
231C3×#103—31no—
232C3×#102—21no—
233C3×#102—21no—
234C3×#102—31no—
235C3×#102—31no—
236C3×#102—31no—
237C3×#102—31no—
238C3×#102C2×D311yescharacteristic, complemented
239C3×#102C2×D311yescharacteristic, complemented
240C3×#102C22×C311yescharacteristic, complemented
241C3×#102C22×C311yescharacteristic, complemented
242#832C22×C311yescharacteristic, complemented
243#832C22×C311yescharacteristic, complemented
244#821C22×C311yescharacteristic, complemented
245#816C22×C311yescharacteristic, complemented
246Dic3⋊C8C22×C311yescharacteristic, complemented
247Dic3⋊C8C22×C311yescharacteristic, complemented
248#810C22×C311yescharacteristic, complemented
249#809C22×C311yescharacteristic, complemented
250C4⋊(C3⋊C8)C22×C311yescharacteristic, complemented
251C23×C32—21no—
252C23×C32—21no—
253C23×C32—21no—
254C22×C3×D3—21no—
255C22×C3×D3—24no—
256C22×C3×D3—21no—
257C22×C3×D3—42no—
258C22×C3×D3—81no—
259C22×C3×D3—81no—
260C22×C3×D3—81no—
261C22×C3×D3—81no—
262C22×C3×D3C2×D411yescharacteristic
263C32×D4—21no—
264C32×D4—21no—
265C32×D4—21no—
266C32×D4—21no—
267C32×D4—21no—
268C32×D4—81no—
269C32×D4—81no—
270C32×D4C2×D412yes—
271C2×C32×C4—21no—
272C2×C32×C4—81no—
273C2×C32×C4C2×D411yescharacteristic
274C2×C32×C4C2×D411yescharacteristic
275C2×C32×C4C2411yescharacteristic
276C3×#67—24no—
277C3×#67—42no—
278C3×#67—42no—
279C3×#67—81no—
280C3×#67—81no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3—42no—
284C2×C3×Dic3—81no—
285C2×C3×Dic3C2×D411yescharacteristic
286C2×C3×Dic3C2×D411yescharacteristic
287C2×C3×Dic3C2×D411yescharacteristic
288C3×D12—21no—
289C3×D12—21no—
290C3×D12—21no—
291C3×D12C2×D412yes—
292C3×C4×D3—81no—
293C3×C4×D3—81no—
294C3×C4×D3C2×D412yes—
295C3×C4×D3#4112yes—
296C3×Dic6—21no—
297C3×Dic6—21no—
298C32×C8—21no—
299C32×C8—21no—
300C3×C3⋊C8—21no—
301C3×C3⋊C8—21no—
302C2×AGL(1,ℤ/8)—31no—
303C22×D8—31no—
304#535—31no—
305#518—31no—
306#463—31no—
307#463—31no—
308#463—31no—
309#463—31no—
310#459—31no—
311#459—31no—
312#459—31no—
313#459C3×D311yescharacteristic, complemented
314#424—31no—
315#418—31no—
316#416—31no—
317C24×C3—61no—
318C24×C3—61no—
319C23×D3—21no—
320C23×D3—21no—
321C3×#41—62no—
322C3×#41—62no—
323C2×C3×Q8—31no—
324C2×C3×D4—21no—
325C2×C3×D4—21no—
326C2×C3×D4—21no—
327C2×C3×D4—21no—
328C2×C3×D4—21no—
329C2×C3×D4—21no—
330C2×C3×D4—21no—
331C2×C3×D4—34no—
332C2×C3×D4—31no—
333C2×C3×D4—31no—
334C2×C3×D4—41no—
335C2×C3×D4—41no—
336C2×C3×D4—62no—
337C2×C3×D4—62no—
338C2×C3×D4—62no—
339C2×C3×D4—61no—
340C2×C3×D4—61no—
341C2×C3×D4—61no—
342C2×C3×D4—61no—
343C2×C3×D4—61no—
344C2×C3×D4C22×D311yescharacteristic
345C2×C3×D4C22×D311yescharacteristic
346C2×C3×D4C22×D311yescharacteristic
347C2×C3×D4C23×C311yescharacteristic
348C2×C3×D4C23×C311yescharacteristic
349C2×C3×D4C23×C311yescharacteristic
350C22×C3×C4—21no—
351C22×C3×C4—21no—
352C22×C3×C4—31no—
353C22×C3×C4—41no—
354C22×C3×C4—61no—
355C22×C3×C4—61no—
356C22×C3×C4—61no—
357C22×C3×C4—61no—
358C2×#67—21no—
359C2×#67—21no—
360C2×#67—21no—
361C2×#67—21no—
362C2×#67—21no—
363C22×Dic3—21no—
364C22×Dic3—21no—
365#237—22no—
366#237—22no—
367D3×D4—22no—
368D3×D4—22no—
369D3×D4—22no—
370D3×D4C3×D414yescomplemented
371C2×D12C23×C311yescharacteristic
372C2×D12C23×C311yescharacteristic
373C2×C4×D3—21no—
374C2×C4×D3—21no—
375C2×C4×D3C23×C311yescharacteristic
376C2×Dic6C23×C311yescharacteristic
377C3×SD16—62no—
378C3×SD16—62no—
379C3×D8—22no—
380C3×D8—22no—
381C3×D8—22no—
382C3×D8—22no—
383C3×D8—42no—
384C3×D8—42no—
385C3×D8—62no—
386C3×D8—62no—
387C3×D8—62no—
388C3×D8—62no—
389C3×M16—62no—
390C2×C3×C8—21no—
391C2×C3×C8—21no—
392C2×C3×C8—31no—
393C2×C3×C8—31no—
394C2×C3×C8—62no—
395C2×C3×C8C22×D311yescharacteristic
396C2×C3×C8C22×D311yescharacteristic
397C2×C3×C8C23×C311yescharacteristic
398C2×C3×C8C23×C311yescharacteristic
399C3×C4⋊C4—21no—
400C3×C4⋊C4—31no—
401C3×C4⋊C4—31no—
402C3×C4⋊C4—31no—
403C3×C4⋊C4C22×D311yescharacteristic
404C3×C4⋊C4C23×C311yescharacteristic
405C3×C22⋊C4—21no—
406C3×C22⋊C4—21no—
407C3×C22⋊C4—31no—
408C3×C22⋊C4—31no—
409C3×C22⋊C4—41no—
410C3×C22⋊C4—61no—
411C3×C22⋊C4—61no—
412C3×C22⋊C4—61no—
413C3×C22⋊C4—61no—
414C3×C22⋊C4—61no—
415C3×C22⋊C4—61no—
416C3×C22⋊C4—61no—
417C3×C22⋊C4—61no—
418C3×C42—21no—
419C3×C42—31no—
420C3×C42—61no—
421C3×C42C22×D311yescharacteristic
422C3×C42C23×C311yescharacteristic
423#217—21no—
424#217—21no—
425#217—21no—
426#214—22no—
427#213—22no—
428#213—22no—
429#213—22no—
430(C2×D3)⋊C4—21no—
431(C2×D3)⋊C4—21no—
432(C2×D3)⋊C4—21no—
433(C2×D3)⋊C4—21no—
434(C2×D3)⋊C4—21no—
435(C2×D3)⋊C4C3×D411yescharacteristic
436(C2×D3)⋊C4C3×D411yescharacteristic
437C4⋊Dic3C23×C311yescharacteristic
438Dic3⋊C4C3×D411yescharacteristic
439Dic3⋊C4C3×D411yescharacteristic
440C4×Dic3—21no—
441C4×Dic3C23×C311yescharacteristic
442C2×C3⋊C8C23×C311yescharacteristic
443C2×C3⋊C8C23×C311yescharacteristic
444D24—22no—
445#204—22no—
446ΓL(1,𝔽25)—22no—
447D3×C8—22no—
448C22×C32—22no—
449C22×C32—41no—
450C22×C32—41no—
451C22×C32—41no—
452C22×C32—41no—
453C22×C32—41no—
454C22×C32—41no—
455C22×C32—41no—
456C22×C32—41no—
457C22×C32C22×D411yescharacteristic
458C2×C3×D3—21no—
459C2×C3×D3—21no—
460C2×C3×D3—22no—
461C2×C3×D3—41no—
462C2×C3×D3—41no—
463C2×C3×D3—41no—
464C2×C3×D3—41no—
465C2×C3×D3—41no—
466C2×C3×D3—84no—
467C2×C3×D3—84no—
468C2×C3×D3#12112yes—
469C32×C4—21no—
470C32×C4—21no—
471C32×C4—41no—
472C32×C4C22×D411yescharacteristic
473C32×C4C2×#4111yescharacteristic
474C3×Dic3—21no—
475C3×Dic3—21no—
476C3×Dic3—41no—
477C3×Dic3—41no—
478C3×Dic3#12112yes—
479C2×#41—31no—
480C22×D4—31no—
481C22×D4—31no—
482AGL(1,ℤ/8)—64no—
483C2×SD16—31no—
484C2×SD16—31no—
485C2×D8—31no—
486C2×D8—31no—
487C2×D8—31no—
488C2×D8—31no—
489C2×D8—64no—
490C2×D8C2×C3×D311yescharacteristic
491C2×D8C2×C3×D311yescharacteristic, complemented
492C2×M16—31no—
493C22×C8—31no—
494#127—31no—
495#127C2×C3×D311yescharacteristic, complemented
496#124—31no—
497#124—31no—
498#121—61no—
499#121—61no—
500#120—61no—
501#120—61no—
502C4×D4—31no—
503C4×D4—31no—
504C4×D4—31no—
505C4×D4—61no—
506C4×D4—61no—
507C4×D4C2×C3×D311yescharacteristic, complemented
508#117—31no—
509#117—31no—
510C2×C22⋊C4—61no—
511C2×C22⋊C4—61no—
512C4⋊C8—31no—
513C4⋊C8—31no—
514C4⋊C8—31no—
515C4⋊C8C2×C3×D311yescharacteristic, complemented
516#103—31no—
517#103—31no—
518#102—31no—
519#102—31no—
520#102—31no—
521#102—31no—
522#102C2×C3×D311yescharacteristic, complemented
523#102C2×C3×D311yescharacteristic, complemented
524C23×C3—21no—
525C23×C3—21no—
526C23×C3—21no—
527C23×C3—21no—
528C23×C3—21no—
529C23×C3—21no—
530C23×C3—31no—
531C23×C3—41no—
532C23×C3—41no—
533C23×C3—41no—
534C23×C3—64no—
535C23×C3—61no—
536C23×C3—61no—
537C23×C3—122no—
538C23×C3—241no—
539C23×C3—241no—
540C23×C3—241no—
541C23×C3—241no—
542C22×D3—21no—
543C22×D3—24no—
544C22×D3—21no—
545C22×D3—42no—
546C22×D3—81no—
547C22×D3—81no—
548C22×D3—81no—
549C22×D3—81no—
550C22×D3C2×C3×D411yescharacteristic
551C3×Q8—61no—
552C3×Q8—61no—
553C3×D4—21no—
554C3×D4—21no—
555C3×D4—21no—
556C3×D4—21no—
557C3×D4—21no—
558C3×D4—21no—
559C3×D4—21no—
560C3×D4—21no—
561C3×D4—21no—
562C3×D4—21no—
563C3×D4—22no—
564C3×D4—32no—
565C3×D4—41no—
566C3×D4—41no—
567C3×D4—41no—
568C3×D4—41no—
569C3×D4—41no—
570C3×D4—64no—
571C3×D4—61no—
572C3×D4—61no—
573C3×D4—61no—
574C3×D4—81no—
575C3×D4—81no—
576C3×D4—81no—
577C3×D4—81no—
578C3×D4—82no—
579C3×D4—82no—
580C3×D4—122no—
581C3×D4—122no—
582C3×D4—241no—
583C3×D4—241no—
584C3×D4D3×D412yes—
585C3×D4C2×C3×D412yes—
586C2×C3×C4—21no—
587C2×C3×C4—21no—
588C2×C3×C4—21no—
589C2×C3×C4—21no—
590C2×C3×C4—21no—
591C2×C3×C4—31no—
592C2×C3×C4—32no—
593C2×C3×C4—32no—
594C2×C3×C4—31no—
595C2×C3×C4—31no—
596C2×C3×C4—41no—
597C2×C3×C4—61no—
598C2×C3×C4—61no—
599C2×C3×C4—81no—
600C2×C3×C4—81no—
601C2×C3×C4—82no—
602C2×C3×C4—122no—
603C2×C3×C4—241no—
604C2×C3×C4—241no—
605C2×C3×C4—241no—
606C2×C3×C4D3×D411yescharacteristic
607C2×C3×C4D3×D411yescharacteristic
608C2×C3×C4C2×C3×D411yescharacteristic
609C2×C3×C4C2×C3×D411yescharacteristic
610C2×C3×C4C23×D311yescharacteristic
611C2×C3×C4C24×C311yescharacteristic
612#67—24no—
613#67—42no—
614#67—42no—
615#67—81no—
616#67—81no—
617C2×Dic3—21no—
618C2×Dic3—21no—
619C2×Dic3—42no—
620C2×Dic3—81no—
621C2×Dic3C2×C3×D411yescharacteristic
622C2×Dic3C2×C3×D411yescharacteristic
623C2×Dic3C2×C3×D411yescharacteristic
624D12—21no—
625D12—21no—
626D12—21no—
627D12C2×C3×D412yes—
628C4×D3—81no—
629C4×D3—81no—
630C4×D3C2×C3×D412yes—
631C4×D3C3×#4112yes—
632Dic6—21no—
633Dic6—21no—
634C3×C8—21no—
635C3×C8—21no—
636C3×C8—21no—
637C3×C8—21no—
638C3×C8—41no—
639C3×C8—41no—
640C3×C8—61no—
641C3×C8—61no—
642C3⋊C8—21no—
643C3⋊C8—21no—
644C2×C32—42no—
645C2×C32—81no—
646C2×C32—81no—
647C2×C32C2×#12111yescharacteristic
648C2×C32#57611yescharacteristic
649C2×C32#57611yescharacteristic
650C3×D3—22no—
651C3×D3—42no—
652C3×D3—81no—
653C24—61no—
654C24—61no—
655#41—62no—
656#41—62no—
657C2×Q8—31no—
658C2×D4—21no—
659C2×D4—21no—
660C2×D4—34no—
661C2×D4—31no—
662C2×D4—31no—
663C2×D4—62no—
664C2×D4—62no—
665C2×D4—62no—
666C2×D4—61no—
667C2×D4—61no—
668C2×D4—61no—
669C2×D4—61no—
670C2×D4—61no—
671C2×D4C22×C3×D311yescharacteristic
672C2×D4C22×C3×D311yescharacteristic
673C2×D4C22×C3×D311yescharacteristic
674C22×C4—21no—
675C22×C4—31no—
676C22×C4—61no—
677C22×C4—61no—
678C22×C4—61no—
679C22×C4—61no—
680SD16—62no—
681SD16—62no—
682D8—22no—
683D8—22no—
684D8—62no—
685D8—62no—
686D8—62no—
687D8—62no—
688M16—62no—
689C2×C8—31no—
690C2×C8—31no—
691C2×C8—62no—
692C2×C8C22×C3×D311yescharacteristic
693C2×C8C22×C3×D311yescharacteristic
694C4⋊C4—31no—
695C4⋊C4—31no—
696C4⋊C4—31no—
697C4⋊C4C22×C3×D311yescharacteristic
698C22⋊C4—21no—
699C22⋊C4—31no—
700C22⋊C4—31no—
701C22⋊C4—61no—
702C22⋊C4—61no—
703C22⋊C4—61no—
704C22⋊C4—61no—
705C22⋊C4—61no—
706C22⋊C4—61no—
707C22⋊C4—61no—
708C22⋊C4—61no—
709C42—31no—
710C42—61no—
711C42C22×C3×D311yescharacteristic
712C22×C3—22no—
713C22×C3—22no—
714C22×C3—21no—
715C22×C3—32no—
716C22×C3—42no—
717C22×C3—41no—
718C22×C3—41no—
719C22×C3—41no—
720C22×C3—41no—
721C22×C3—41no—
722C22×C3—41no—
723C22×C3—41no—
724C22×C3—41no—
725C22×C3—41no—
726C22×C3—41no—
727C22×C3—41no—
728C22×C3—41no—
729C22×C3—41no—
730C22×C3—41no—
731C22×C3—41no—
732C22×C3—41no—
733C22×C3—61no—
734C22×C3—61no—
735C22×C3—62no—
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—121no—
745C22×C3—121no—
746C22×C3—121no—
747C22×C3—121no—
748C22×C3—121no—
749C22×C3—244no—
750C22×C3—244no—
751C22×C3C2×D3×D411yescharacteristic
752C22×C3C22×C3×D411yescharacteristic
753C2×D3—21no—
754C2×D3—21no—
755C2×D3—22no—
756C2×D3—41no—
757C2×D3—41no—
758C2×D3—41no—
759C2×D3—41no—
760C2×D3—41no—
761C2×D3—84no—
762C2×D3—84no—
763C2×D3C3×#12112yes—
764C3×C4—22no—
765C3×C4—21no—
766C3×C4—21no—
767C3×C4—21no—
768C3×C4—21no—
769C3×C4—21no—
770C3×C4—21no—
771C3×C4—32no—
772C3×C4—41no—
773C3×C4—41no—
774C3×C4—41no—
775C3×C4—61no—
776C3×C4—61no—
777C3×C4—81no—
778C3×C4—121no—
779C3×C4—121no—
780C3×C4C2×D3×D411yescharacteristic
781C3×C4D3×#4111yescharacteristic
782C3×C4C22×C3×D411yescharacteristic
783C3×C4C2×C3×#4111yescharacteristic
784Dic3—21no—
785Dic3—21no—
786Dic3—41no—
787Dic3—41no—
788Dic3C3×#12112yes—
789C32#304111yescharacteristic, complemented, Sylow
790C23—21no—
791C23—21no—
792C23—21no—
793C23—31no—
794C23—64no—
795C23—61no—
796C23—61no—
797C23—122no—
798C23—241no—
799C23—241no—
800C23—241no—
801C23—241no—
802Q8—61no—
803Q8—61no—
804D4—21no—
805D4—21no—
806D4—21no—
807D4—21no—
808D4—21no—
809D4—32no—
810D4—64no—
811D4—61no—
812D4—61no—
813D4—61no—
814D4—81no—
815D4—81no—
816D4—122no—
817D4—122no—
818D4—241no—
819D4—241no—
820D4C3×D3×D412yes—
821C2×C4—21no—
822C2×C4—31no—
823C2×C4—32no—
824C2×C4—32no—
825C2×C4—31no—
826C2×C4—31no—
827C2×C4—61no—
828C2×C4—61no—
829C2×C4—81no—
830C2×C4—122no—
831C2×C4—241no—
832C2×C4—241no—
833C2×C4—241no—
834C2×C4C3×D3×D411yescharacteristic
835C2×C4C3×D3×D411yescharacteristic
836C2×C4C23×C3×D311yescharacteristic
837C8—21no—
838C8—21no—
839C8—61no—
840C8—61no—
841C2×C3—21no—
842C2×C3—21no—
843C2×C3—21no—
844C2×C3—42no—
845C2×C3—42no—
846C2×C3—62no—
847C2×C3—82no—
848C2×C3—81no—
849C2×C3—81no—
850C2×C3—81no—
851C2×C3—81no—
852C2×C3—122no—
853C2×C3—161no—
854C2×C3—161no—
855C2×C3—241no—
856C2×C3D3×#12111yescharacteristic
857C2×C3#575711yescharacteristic
858C2×C3#577411yescharacteristic
859C2×C3C2×C3×#12111yescharacteristic
860C2×C3C3×#57611yescharacteristic
861C2×C3C3×#57611yescharacteristic
862D3—22no—
863D3—42no—
864D3—81no—
865C22—22no—
866C22—32no—
867C22—41no—
868C22—41no—
869C22—41no—
870C22—41no—
871C22—41no—
872C22—41no—
873C22—41no—
874C22—41no—
875C22—61no—
876C22—61no—
877C22—62no—
878C22—121no—
879C22—121no—
880C22—121no—
881C22—121no—
882C22—121no—
883C22—244no—
884C22—244no—
885C22C2×C3×D3×D411yescharacteristic
886C4—21no—
887C4—21no—
888C4—32no—
889C4—41no—
890C4—61no—
891C4—61no—
892C4—121no—
893C4—121no—
894C4C2×C3×D3×D411yescharacteristic
895C4C3×D3×#4111yescharacteristic
896C3—21no—
897C3#8033411yescharacteristic, direct product factor
898C3C3×#304111yescharacteristic, complemented
899C2—42no—
900C2—62no—
901C2—81no—
902C2—81no—
903C2—122no—
904C2—241no—
905C2C3×D3×#12111yescharacteristic
906C2C3×#575711yescharacteristic
907C2C3×#577411yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#459C2
socleC22×C32C22×D4
hypercenterC3×#459D3
hypocenterC3C3×#3041
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#459

Complements

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

NH ≅ G/Ntype
1. C2×C3×#911C2semidirect
2. C2×C3×D3×D8C2semidirect
3. C3×#5715C2semidirect
4. C3×#5545C2semidirect
5. C32×#459C2semidirect
6. C3×#5153C2semidirect
7. C3×#5150C2semidirect
8. C3×#5072C2semidirect
9. C3×#5016C2semidirect
10. C3×#4844C2semidirect
11. C3×#4839C2semidirect
12. C3×#4787C2semidirect
13. C3×#4786C2semidirect
14. C3×#4772C2semidirect
15. C3×#4770C2semidirect
17. #80334C3direct (N × H)
22. C2×C32×D8C22semidirect
23. C32×#127C22semidirect
24. C32×C4×D4C22semidirect
25. C3×#940C22semidirect
30. C3×#936C22semidirect
31. C3×D4×Dic3C22semidirect
32. C2×C3×#214C22semidirect
35. C2×C3×#213C22semidirect
41. C2×C3×#204C22semidirect
44. C3×#893C22semidirect
48. C3×#875C22semidirect
49. C3×C4×D12C22semidirect
51. C32×C4⋊C8C22semidirect
52. C32×#102C22semidirect
53. C32×#102C22semidirect
54. C3×#832C22semidirect
55. C3×#832C22semidirect
56. C3×#821C22semidirect
57. C3×#816C22semidirect
58. C3×Dic3⋊C8C22semidirect
59. C3×Dic3⋊C8C22semidirect
60. C3×#810C22semidirect
61. C3×#809C22semidirect
62. C3×C4⋊(C3⋊C8)C22semidirect
67. C2×#911C2×C3semidirect
68. C2×D3×D8C2×C3semidirect
69. #5715C2×C3semidirect
70. #5545C2×C3semidirect
79. C3×#459D3semidirect
80. C3×#459C2×C3semidirect
84. #5153C2×C3semidirect
85. #5150C2×C3semidirect
86. #5072C2×C3semidirect
87. #5016C2×C3semidirect
88. #4844C2×C3semidirect
89. #4839C2×C3semidirect
90. #4787C2×C3semidirect
91. #4786C2×C3semidirect
92. #4772C2×C3semidirect
93. #4770C2×C3semidirect
114. C3×D3×D4D4semidirect
171. C2×C3×D8C2×D3semidirect
173. C2×C3×D8C22×C3semidirect
178. C3×#127C2×D3semidirect
179. C3×#127C22×C3semidirect
192. C3×C4×D4C2×D3semidirect
193. C3×C4×D4C22×C3semidirect
198. #940C22×C3semidirect
203. #936C22×C3semidirect
204. D4×Dic3C22×C3semidirect
205. C2×#214C22×C3semidirect
208. C2×#213C22×C3semidirect
214. C2×#204C22×C3semidirect
217. #893C22×C3semidirect
221. #875C22×C3semidirect
222. C4×D12C22×C3semidirect
228. C3×C4⋊C8C2×D3semidirect
229. C3×C4⋊C8C22×C3semidirect
238. C3×#102C2×D3semidirect
239. C3×#102C2×D3semidirect
240. C3×#102C22×C3semidirect
241. C3×#102C22×C3semidirect
242. #832C22×C3semidirect
243. #832C22×C3semidirect
244. #821C22×C3semidirect
245. #816C22×C3semidirect
246. Dic3⋊C8C22×C3semidirect
247. Dic3⋊C8C22×C3semidirect
248. #810C22×C3semidirect
249. #809C22×C3semidirect
250. C4⋊(C3⋊C8)C22×C3semidirect
313. #459C3×D3semidirect
370. D3×D4C3×D4semidirect
491. C2×D8C2×C3×D3semidirect
495. #127C2×C3×D3semidirect
507. C4×D4C2×C3×D3semidirect
515. C4⋊C8C2×C3×D3semidirect
522. #102C2×C3×D3semidirect
523. #102C2×C3×D3semidirect
789. C32#3041semidirect
897. C3#80334direct (N × H)
898. C3C3×#3041semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9112
C2×C3×D3×D82
C3×#57152
C3×#55452
C32×#4592
C3×#51532
C3×#51502
C3×#50722
C3×#50162
C3×#48442
C3×#48392
C3×#47872
C3×#47862
C3×#47722
C3×#47702
C3×#30413
#803343