Finite Group Databasebeta

← C3×#80536 #11866165

Subgroups — C3×#80536 #11866165

Order 1152.

1114 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#914C211yesmaximal, characteristic, complemented
2C2×C3×D3×D8C211yesmaximal, characteristic, complemented
3C3×#5674C211yesmaximal, characteristic, complemented
4C3×#5545C211yesmaximal, characteristic, complemented
5C32×#463C211yesmaximal, characteristic, complemented
6C3×#5165C211yesmaximal, characteristic, complemented
7C3×#5150C211yesmaximal, characteristic, complemented
8C3×#5057C211yesmaximal, characteristic, complemented
9C3×#5015C211yesmaximal, characteristic, complemented
10C3×#4843C211yesmaximal, characteristic, complemented
11C3×#4839C211yesmaximal, characteristic, complemented
12C3×#4819C211yesmaximal, characteristic, complemented
13C3×#4804C211yesmaximal, characteristic, complemented
14C3×#4786C211yesmaximal, characteristic, complemented
15C3×#4770C211yesmaximal, characteristic, complemented
16C3×#3041—31nomaximal
17#80536C311yesmaximal, characteristic, direct product factor
18C2×C3×#239C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C2×C3×D3×D4C2211yescharacteristic
21C2×C32×SD16C2211yescharacteristic, complemented
22C2×C32×D8C2211yescharacteristic
23C32×#124C2211yescharacteristic, complemented
24C32×C4×D4C2211yescharacteristic, complemented
25C3×#947C2211yescharacteristic, complemented
26C2×C3×#215C2211yescharacteristic, complemented
27C3×#940C2211yescharacteristic, complemented
28C3×D4×Dic3C2211yescharacteristic, complemented
29C2×C3×#213C2211yescharacteristic
30C2×C3×#213C2211yescharacteristic
31C2×C3×#213C2211yescharacteristic, complemented
32C3×C4×#67—21no—
33C2×C3×(C2×D3)⋊C4—21no—
34C3×#914—24no—
35C3×D3×D8—24no—
36C2×C3×D24C2211yescharacteristic
37C2×C3×D24C2211yescharacteristic, complemented
38C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
39C2×C3×D3×C8C2211yescharacteristic
40C3×#893C2211yescharacteristic, complemented
41C3×#892C2211yescharacteristic
42C3×#884—21no—
43C3×#884—21no—
44C3×#882—21no—
45C3×#882—21no—
46C3×#67⋊C4—21no—
47C3×D3×C22⋊C4—21no—
48C3×#874C2211yescharacteristic, complemented
49C3×C4×D12C2211yescharacteristic, complemented
50C3×#872C2211yescharacteristic
51C32×C4⋊C8C2211yescharacteristic, complemented
52C32×#103C2211yescharacteristic, complemented
53C32×#102C2211yescharacteristic, complemented
54C3×#835C2211yescharacteristic, complemented
55C3×#832C2211yescharacteristic, complemented
56C3×#821C2211yescharacteristic, complemented
57C3×#821C2211yescharacteristic, complemented
58C3×Dic3⋊C8C2211yescharacteristic, complemented
59C3×Dic3⋊C8C2211yescharacteristic, complemented
60C3×#809C2211yescharacteristic, 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×#914C2×C311yescharacteristic, complemented
68C2×D3×D8C2×C311yescharacteristic, complemented
69#5674C2×C311yescharacteristic, complemented
70#5545C2×C311yescharacteristic, complemented
71C3×#463—21no—
72C3×#463—31no—
73C3×#463—31no—
74C3×#463—31no—
75C3×#463D311yescharacteristic, complemented
76C3×#463C2×C311yescharacteristic, complemented
77C3×#459—31no—
78C3×#459—31no—
79C3×#459—31no—
80C3×#459—31no—
81C3×#424—31no—
82C3×#418—31no—
83C3×#416—31no—
84#5165C2×C311yescharacteristic, complemented
85#5150C2×C311yescharacteristic, complemented
86#5057C2×C311yescharacteristic, complemented
87#5015C2×C311yescharacteristic, complemented
88#4843C2×C311yescharacteristic, complemented
89#4839C2×C311yescharacteristic, complemented
90#4819C2×C311yescharacteristic, complemented
91#4804C2×C311yescharacteristic, complemented
92#4786C2×C311yescharacteristic, complemented
93#4770C2×C311yescharacteristic, complemented
94C23×C3×D3—21no—
95C23×C3×D3—21no—
96C2×C32×Q8C2311yescharacteristic
97C2×C32×D4C2311yescharacteristic
98C2×C32×D4C2311yescharacteristic
99C22×C32×C4—21no—
100C2×C3×#67—21no—
101C2×C3×#67—21no—
102C2×C3×#67—21no—
103C2×C3×#67—21no—
104C22×C3×Dic3—21no—
105C3×#239—22no—
106C3×#239—22no—
107C3×D3×D4—22no—
108C3×D3×D4—22no—
109C3×D3×D4—22no—
110C3×D3×D4D414yescomplemented
111C2×C3×D12—21no—
112C2×C3×D12—21no—
113C2×C3×D12—21no—
114C2×C3×D12C2311yescharacteristic
115C2×C3×D12C2311yescharacteristic
116C2×C3×D12C2311yescharacteristic
117C2×C3×C4×D3—21no—
118C2×C3×C4×D3—21no—
119C2×C3×C4×D3—21no—
120C2×C3×C4×D3C2311yescharacteristic
121C32×SD16—22no—
122C32×D8—22no—
123C2×C32×C8C2311yescharacteristic
124C2×C32×C8C2311yescharacteristic
125C32×C4⋊C4C2311yescharacteristic
126C32×C22⋊C4—21no—
127C32×C22⋊C4—21no—
128C32×C22⋊C4—21no—
129C32×C42C2311yescharacteristic
130C3×#217—21no—
131C3×#215—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×D24—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×#239C22×C311yescharacteristic
158C2×D3×D4C22×C311yescharacteristic
159C2×D3×D4C22×C311yescharacteristic
160C3×AGL(1,ℤ/8)—64no—
161C2×C3×SD16—21no—
162C2×C3×SD16—31no—
163C2×C3×SD16C2×D311yescharacteristic, complemented
164C2×C3×SD16C22×C311yescharacteristic, complemented
165C2×C3×D8—21no—
166C2×C3×D8—31no—
167C2×C3×D8—31no—
168C2×C3×D8—31no—
169C2×C3×D8—31no—
170C2×C3×D8—31no—
171C2×C3×D8—64no—
172C2×C3×D8C2×D311yescharacteristic
173C2×C3×D8C22×C311yescharacteristic
174C2×C3×M16—31no—
175C22×C3×C8—31no—
176C3×#127—31no—
177C3×#127—31no—
178C3×#124—21no—
179C3×#124—31no—
180C3×#124C2×D311yescharacteristic, complemented
181C3×#124C22×C311yescharacteristic, complemented
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#947C22×C311yescharacteristic, complemented
199C2×#215C22×C311yescharacteristic, complemented
200#940C22×C311yescharacteristic, complemented
201D4×Dic3C22×C311yescharacteristic, complemented
202C2×#213C22×C311yescharacteristic
203C2×#213C22×C311yescharacteristic
204C2×#213C22×C311yescharacteristic, complemented
205C4×#67—21no—
206C2×(C2×D3)⋊C4—21no—
207#914—24no—
208D3×D8—24no—
209C2×D24C22×C311yescharacteristic
210C2×D24C22×C311yescharacteristic, complemented
211C2×ΓL(1,𝔽25)C22×C311yescharacteristic
212C2×D3×C8C22×C311yescharacteristic
213#893C22×C311yescharacteristic, complemented
214#892C22×C311yescharacteristic
215#884—21no—
216#884—21no—
217#882—21no—
218#882—21no—
219#67⋊C4—21no—
220D3×C22⋊C4—21no—
221#874C22×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—21no—
231C3×#103—31no—
232C3×#103C2×D311yescharacteristic, complemented
233C3×#103C22×C311yescharacteristic, complemented
234C3×#102—21no—
235C3×#102—31no—
236C3×#102—31no—
237C3×#102—31no—
238C3×#102—31no—
239C3×#102—31no—
240C3×#102C2×D311yescharacteristic, complemented
241C3×#102C22×C311yescharacteristic, complemented
242#835C22×C311yescharacteristic, complemented
243#832C22×C311yescharacteristic, complemented
244#821C22×C311yescharacteristic, complemented
245#821C22×C311yescharacteristic, complemented
246Dic3⋊C8C22×C311yescharacteristic, complemented
247Dic3⋊C8C22×C311yescharacteristic, complemented
248#809C22×C311yescharacteristic, complemented
249#809C22×C311yescharacteristic, complemented
250C4⋊(C3⋊C8)C22×C311yescharacteristic, complemented
251C23×C32—21no—
252C23×C32—21no—
253C22×C3×D3—21no—
254C22×C3×D3—24no—
255C22×C3×D3—21no—
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×Q8—21no—
264C32×Q8—21no—
265C32×D4—21no—
266C32×D4—21no—
267C32×D4—21no—
268C32×D4C2×D412yes—
269C2×C32×C4—21no—
270C2×C32×C4—21no—
271C2×C32×C4—81no—
272C2×C32×C4C2×D411yescharacteristic
273C2×C32×C4C2×D411yescharacteristic
274C2×C32×C4C2411yescharacteristic
275C3×#67—24no—
276C3×#67—42no—
277C3×#67—81no—
278C3×#67—81no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—81no—
281C2×C3×Dic3C2×D411yescharacteristic
282C2×C3×Dic3C2×D411yescharacteristic
283C2×C3×Dic3C2×D411yescharacteristic
284C3×D12—21no—
285C3×D12—21no—
286C3×D12—21no—
287C3×D12—21no—
288C3×D12—21no—
289C3×D12—42no—
290C3×D12—81no—
291C3×D12—81no—
292C3×D12C2×D412yes—
293C3×C4×D3—42no—
294C3×C4×D3—81no—
295C3×C4×D3—81no—
296C3×C4×D3C2×D412yes—
297C3×C4×D3#4112yes—
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#463C3×D311yescharacteristic, complemented
310#459—31no—
311#459—31no—
312#459—31no—
313#459—31no—
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—21no—
324C2×C3×Q8C22×D311yescharacteristic
325C2×C3×Q8C23×C311yescharacteristic
326C2×C3×D4—21no—
327C2×C3×D4—21no—
328C2×C3×D4—34no—
329C2×C3×D4—31no—
330C2×C3×D4—31no—
331C2×C3×D4—31no—
332C2×C3×D4—61no—
333C2×C3×D4—62no—
334C2×C3×D4—62no—
335C2×C3×D4—62no—
336C2×C3×D4—61no—
337C2×C3×D4—61no—
338C2×C3×D4—61no—
339C2×C3×D4—61no—
340C2×C3×D4—61no—
341C2×C3×D4—61no—
342C2×C3×D4C22×D311yescharacteristic
343C2×C3×D4C22×D311yescharacteristic
344C2×C3×D4C23×C311yescharacteristic
345C2×C3×D4C23×C311yescharacteristic
346C22×C3×C4—21no—
347C22×C3×C4—21no—
348C22×C3×C4—31no—
349C22×C3×C4—41no—
350C22×C3×C4—61no—
351C22×C3×C4—61no—
352C22×C3×C4—61no—
353C22×C3×C4—61no—
354C2×#67—21no—
355C2×#67—21no—
356C2×#67—21no—
357C2×#67—21no—
358C22×Dic3—21no—
359#239—22no—
360#239—22no—
361D3×D4—22no—
362D3×D4—22no—
363D3×D4—22no—
364D3×D4C3×D414yescomplemented
365C2×D12—21no—
366C2×D12—21no—
367C2×D12—21no—
368C2×D12C23×C311yescharacteristic
369C2×D12C23×C311yescharacteristic
370C2×D12C23×C311yescharacteristic
371C2×C4×D3—21no—
372C2×C4×D3—21no—
373C2×C4×D3—21no—
374C2×C4×D3C23×C311yescharacteristic
375C3×SD16—22no—
376C3×SD16—22no—
377C3×SD16—42no—
378C3×SD16—62no—
379C3×D8—22no—
380C3×D8—22no—
381C3×D8—42no—
382C3×D8—62no—
383C3×D8—62no—
384C3×D8—62no—
385C3×D8—62no—
386C3×D8—62no—
387C3×M16—62no—
388C2×C3×C8—21no—
389C2×C3×C8—21no—
390C2×C3×C8—31no—
391C2×C3×C8—31no—
392C2×C3×C8—62no—
393C2×C3×C8C22×D311yescharacteristic
394C2×C3×C8C22×D311yescharacteristic
395C2×C3×C8C23×C311yescharacteristic
396C2×C3×C8C23×C311yescharacteristic
397C3×C4⋊C4—21no—
398C3×C4⋊C4—31no—
399C3×C4⋊C4—31no—
400C3×C4⋊C4—31no—
401C3×C4⋊C4C22×D311yescharacteristic
402C3×C4⋊C4C23×C311yescharacteristic
403C3×C22⋊C4—21no—
404C3×C22⋊C4—21no—
405C3×C22⋊C4—21no—
406C3×C22⋊C4—21no—
407C3×C22⋊C4—21no—
408C3×C22⋊C4—21no—
409C3×C22⋊C4—31no—
410C3×C22⋊C4—31no—
411C3×C22⋊C4—41no—
412C3×C22⋊C4—41no—
413C3×C22⋊C4—41no—
414C3×C22⋊C4—61no—
415C3×C22⋊C4—61no—
416C3×C22⋊C4—61no—
417C3×C22⋊C4—61no—
418C3×C22⋊C4—61no—
419C3×C22⋊C4—61no—
420C3×C42—21no—
421C3×C42—31no—
422C3×C42—61no—
423C3×C42C22×D311yescharacteristic
424C3×C42C23×C311yescharacteristic
425#217—21no—
426#215—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—
445D24—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×C32C22×D411yescharacteristic
455C2×C3×D3—21no—
456C2×C3×D3—21no—
457C2×C3×D3—22no—
458C2×C3×D3—41no—
459C2×C3×D3—41no—
460C2×C3×D3—41no—
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×C4—41no—
473C32×C4C22×D411yescharacteristic
474C32×C4C2×#4111yescharacteristic
475C3×Dic3—21no—
476C3×Dic3—21no—
477C3×Dic3—41no—
478C3×Dic3#12112yes—
479C2×#41—31no—
480C22×D4—31no—
481C22×D4—31no—
482AGL(1,ℤ/8)—64no—
483C2×SD16—31no—
484C2×SD16C2×C3×D311yescharacteristic, complemented
485C2×D8—31no—
486C2×D8—31no—
487C2×D8—31no—
488C2×D8—31no—
489C2×D8—31no—
490C2×D8—64no—
491C2×D8C2×C3×D311yescharacteristic
492C2×M16—31no—
493C22×C8—31no—
494#127—31no—
495#127—31no—
496#124—31no—
497#124C2×C3×D311yescharacteristic, complemented
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#103C2×C3×D311yescharacteristic, complemented
518#102—31no—
519#102—31no—
520#102—31no—
521#102—31no—
522#102—31no—
523#102C2×C3×D311yescharacteristic, complemented
524C23×C3—21no—
525C23×C3—21no—
526C23×C3—21no—
527C23×C3—21no—
528C23×C3—31no—
529C23×C3—41no—
530C23×C3—41no—
531C23×C3—64no—
532C23×C3—61no—
533C23×C3—61no—
534C23×C3—61no—
535C23×C3—122no—
536C23×C3—241no—
537C23×C3—241no—
538C23×C3—241no—
539C23×C3—241no—
540C22×D3—21no—
541C22×D3—24no—
542C22×D3—21no—
543C22×D3—21no—
544C22×D3—42no—
545C22×D3—81no—
546C22×D3—81no—
547C22×D3—81no—
548C22×D3—81no—
549C22×D3C2×C3×D411yescharacteristic
550C3×Q8—21no—
551C3×Q8—21no—
552C3×Q8—21no—
553C3×Q8—21no—
554C3×Q8—41no—
555C3×Q8—41no—
556C3×D4—21no—
557C3×D4—21no—
558C3×D4—21no—
559C3×D4—21no—
560C3×D4—21no—
561C3×D4—21no—
562C3×D4—22no—
563C3×D4—32no—
564C3×D4—41no—
565C3×D4—41no—
566C3×D4—41no—
567C3×D4—64no—
568C3×D4—61no—
569C3×D4—61no—
570C3×D4—61no—
571C3×D4—61no—
572C3×D4—61no—
573C3×D4—122no—
574C3×D4—122no—
575C3×D4—241no—
576C3×D4—241no—
577C3×D4—241no—
578C3×D4—241no—
579C3×D4D3×D412yes—
580C3×D4C2×C3×D412yes—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—21no—
584C2×C3×C4—21no—
585C2×C3×C4—21no—
586C2×C3×C4—21no—
587C2×C3×C4—21no—
588C2×C3×C4—31no—
589C2×C3×C4—32no—
590C2×C3×C4—32no—
591C2×C3×C4—31no—
592C2×C3×C4—31no—
593C2×C3×C4—41no—
594C2×C3×C4—41no—
595C2×C3×C4—61no—
596C2×C3×C4—81no—
597C2×C3×C4—81no—
598C2×C3×C4—82no—
599C2×C3×C4—122no—
600C2×C3×C4—241no—
601C2×C3×C4—241no—
602C2×C3×C4—241no—
603C2×C3×C4D3×D411yescharacteristic
604C2×C3×C4D3×D411yescharacteristic
605C2×C3×C4C2×C3×D411yescharacteristic
606C2×C3×C4C2×C3×D411yescharacteristic
607C2×C3×C4C23×D311yescharacteristic
608C2×C3×C4C24×C311yescharacteristic
609#67—24no—
610#67—42no—
611#67—81no—
612#67—81no—
613C2×Dic3—21no—
614C2×Dic3—81no—
615C2×Dic3C2×C3×D411yescharacteristic
616C2×Dic3C2×C3×D411yescharacteristic
617C2×Dic3C2×C3×D411yescharacteristic
618D12—21no—
619D12—21no—
620D12—21no—
621D12—21no—
622D12—21no—
623D12—42no—
624D12—81no—
625D12—81no—
626D12C2×C3×D412yes—
627C4×D3—42no—
628C4×D3—81no—
629C4×D3—81no—
630C4×D3C2×C3×D412yes—
631C4×D3C3×#4112yes—
632C3×C8—21no—
633C3×C8—21no—
634C3×C8—21no—
635C3×C8—21no—
636C3×C8—41no—
637C3×C8—41no—
638C3×C8—61no—
639C3×C8—61no—
640C3⋊C8—21no—
641C3⋊C8—21no—
642C2×C32—42no—
643C2×C32—81no—
644C2×C32C2×#12111yescharacteristic
645C2×C32#57611yescharacteristic
646C2×C32#57611yescharacteristic
647C3×D3—22no—
648C3×D3—42no—
649C3×D3—81no—
650C3×D3—81no—
651C24—61no—
652C24—61no—
653#41—62no—
654#41—62no—
655C2×Q8C22×C3×D311yescharacteristic
656C2×D4—34no—
657C2×D4—31no—
658C2×D4—31no—
659C2×D4—31no—
660C2×D4—61no—
661C2×D4—62no—
662C2×D4—62no—
663C2×D4—62no—
664C2×D4—61no—
665C2×D4—61no—
666C2×D4—61no—
667C2×D4—61no—
668C2×D4—61no—
669C2×D4—61no—
670C2×D4C22×C3×D311yescharacteristic
671C2×D4C22×C3×D311yescharacteristic
672C22×C4—21no—
673C22×C4—31no—
674C22×C4—61no—
675C22×C4—61no—
676C22×C4—61no—
677C22×C4—61no—
678SD16—22no—
679SD16—62no—
680D8—22no—
681D8—62no—
682D8—62no—
683D8—62no—
684D8—62no—
685D8—62no—
686M16—62no—
687C2×C8—31no—
688C2×C8—31no—
689C2×C8—62no—
690C2×C8C22×C3×D311yescharacteristic
691C2×C8C22×C3×D311yescharacteristic
692C4⋊C4—31no—
693C4⋊C4—31no—
694C4⋊C4—31no—
695C4⋊C4C22×C3×D311yescharacteristic
696C22⋊C4—21no—
697C22⋊C4—21no—
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—
707C42—31no—
708C42—61no—
709C42C22×C3×D311yescharacteristic
710C22×C3—22no—
711C22×C3—22no—
712C22×C3—21no—
713C22×C3—32no—
714C22×C3—42no—
715C22×C3—41no—
716C22×C3—41no—
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—61no—
726C22×C3—61no—
727C22×C3—62no—
728C22×C3—81no—
729C22×C3—81no—
730C22×C3—81no—
731C22×C3—81no—
732C22×C3—81no—
733C22×C3—121no—
734C22×C3—121no—
735C22×C3—121no—
736C22×C3—121no—
737C22×C3—121no—
738C22×C3—121no—
739C22×C3—121no—
740C22×C3—121no—
741C22×C3—244no—
742C22×C3—244no—
743C22×C3C2×D3×D411yescharacteristic
744C22×C3C22×C3×D411yescharacteristic
745C2×D3—21no—
746C2×D3—21no—
747C2×D3—22no—
748C2×D3—41no—
749C2×D3—41no—
750C2×D3—41no—
751C2×D3—41no—
752C2×D3—41no—
753C2×D3—41no—
754C2×D3—41no—
755C2×D3—41no—
756C2×D3—84no—
757C2×D3—84no—
758C2×D3C3×#12112yes—
759C3×C4—21no—
760C3×C4—21no—
761C3×C4—21no—
762C3×C4—21no—
763C3×C4—21no—
764C3×C4—21no—
765C3×C4—32no—
766C3×C4—41no—
767C3×C4—41no—
768C3×C4—41no—
769C3×C4—41no—
770C3×C4—41no—
771C3×C4—41no—
772C3×C4—61no—
773C3×C4—61no—
774C3×C4—81no—
775C3×C4—81no—
776C3×C4—121no—
777C3×C4C2×D3×D411yescharacteristic
778C3×C4D3×#4111yescharacteristic
779C3×C4C22×C3×D411yescharacteristic
780C3×C4C2×C3×#4111yescharacteristic
781Dic3—21no—
782Dic3—21no—
783Dic3—41no—
784Dic3C3×#12112yes—
785C32#304111yescharacteristic, complemented, Sylow
786C23—21no—
787C23—21no—
788C23—31no—
789C23—64no—
790C23—61no—
791C23—61no—
792C23—61no—
793C23—122no—
794C23—241no—
795C23—241no—
796C23—241no—
797C23—241no—
798Q8—21no—
799Q8—21no—
800D4—21no—
801D4—21no—
802D4—21no—
803D4—32no—
804D4—64no—
805D4—61no—
806D4—61no—
807D4—61no—
808D4—61no—
809D4—61no—
810D4—122no—
811D4—122no—
812D4—241no—
813D4—241no—
814D4—241no—
815D4—241no—
816D4C3×D3×D412yes—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—31no—
820C2×C4—32no—
821C2×C4—32no—
822C2×C4—31no—
823C2×C4—31no—
824C2×C4—61no—
825C2×C4—81no—
826C2×C4—122no—
827C2×C4—241no—
828C2×C4—241no—
829C2×C4—241no—
830C2×C4C3×D3×D411yescharacteristic
831C2×C4C3×D3×D411yescharacteristic
832C2×C4C23×C3×D311yescharacteristic
833C8—21no—
834C8—21no—
835C8—61no—
836C8—61no—
837C2×C3—21no—
838C2×C3—21no—
839C2×C3—21no—
840C2×C3—42no—
841C2×C3—42no—
842C2×C3—62no—
843C2×C3—82no—
844C2×C3—81no—
845C2×C3—81no—
846C2×C3—122no—
847C2×C3—161no—
848C2×C3—241no—
849C2×C3—241no—
850C2×C3D3×#12111yescharacteristic
851C2×C3#576911yescharacteristic
852C2×C3#577411yescharacteristic
853C2×C3C2×C3×#12111yescharacteristic
854C2×C3C3×#57611yescharacteristic
855C2×C3C3×#57611yescharacteristic
856D3—22no—
857D3—42no—
858D3—81no—
859D3—81no—
860C22—22no—
861C22—32no—
862C22—41no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22—41no—
867C22—61no—
868C22—61no—
869C22—62no—
870C22—121no—
871C22—121no—
872C22—121no—
873C22—121no—
874C22—121no—
875C22—121no—
876C22—121no—
877C22—121no—
878C22—244no—
879C22—244no—
880C22C2×C3×D3×D411yescharacteristic
881C4—21no—
882C4—21no—
883C4—32no—
884C4—41no—
885C4—41no—
886C4—61no—
887C4—61no—
888C4—121no—
889C4C2×C3×D3×D411yescharacteristic
890C4C3×D3×#4111yescharacteristic
891C3—21no—
892C3#8053611yescharacteristic, direct product factor
893C3C3×#304111yescharacteristic, complemented
894C2—42no—
895C2—62no—
896C2—81no—
897C2—122no—
898C2—241no—
899C2—241no—
900C2C3×D3×#12111yescharacteristic
901C2C3×#576911yescharacteristic
902C2C3×#577411yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#463C2
socleC22×C32C22×D4
hypercenterC3×#463D3
hypocenterC3C3×#3041
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#463

Complements

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

NH ≅ G/Ntype
1. C2×C3×#914C2semidirect
2. C2×C3×D3×D8C2semidirect
3. C3×#5674C2semidirect
4. C3×#5545C2semidirect
5. C32×#463C2semidirect
6. C3×#5165C2semidirect
7. C3×#5150C2semidirect
8. C3×#5057C2semidirect
9. C3×#5015C2semidirect
10. C3×#4843C2semidirect
11. C3×#4839C2semidirect
12. C3×#4819C2semidirect
13. C3×#4804C2semidirect
14. C3×#4786C2semidirect
15. C3×#4770C2semidirect
17. #80536C3direct (N × H)
21. C2×C32×SD16C22semidirect
23. C32×#124C22semidirect
24. C32×C4×D4C22semidirect
25. C3×#947C22semidirect
26. C2×C3×#215C22semidirect
27. C3×#940C22semidirect
28. C3×D4×Dic3C22semidirect
31. C2×C3×#213C22semidirect
37. C2×C3×D24C22semidirect
40. C3×#893C22semidirect
48. C3×#874C22semidirect
49. C3×C4×D12C22semidirect
51. C32×C4⋊C8C22semidirect
52. C32×#103C22semidirect
53. C32×#102C22semidirect
54. C3×#835C22semidirect
55. C3×#832C22semidirect
56. C3×#821C22semidirect
57. C3×#821C22semidirect
58. C3×Dic3⋊C8C22semidirect
59. C3×Dic3⋊C8C22semidirect
60. C3×#809C22semidirect
61. C3×#809C22semidirect
62. C3×C4⋊(C3⋊C8)C22semidirect
67. C2×#914C2×C3semidirect
68. C2×D3×D8C2×C3semidirect
69. #5674C2×C3semidirect
70. #5545C2×C3semidirect
75. C3×#463D3semidirect
76. C3×#463C2×C3semidirect
84. #5165C2×C3semidirect
85. #5150C2×C3semidirect
86. #5057C2×C3semidirect
87. #5015C2×C3semidirect
88. #4843C2×C3semidirect
89. #4839C2×C3semidirect
90. #4819C2×C3semidirect
91. #4804C2×C3semidirect
92. #4786C2×C3semidirect
93. #4770C2×C3semidirect
110. C3×D3×D4D4semidirect
163. C2×C3×SD16C2×D3semidirect
164. C2×C3×SD16C22×C3semidirect
180. C3×#124C2×D3semidirect
181. C3×#124C22×C3semidirect
192. C3×C4×D4C2×D3semidirect
193. C3×C4×D4C22×C3semidirect
198. #947C22×C3semidirect
199. C2×#215C22×C3semidirect
200. #940C22×C3semidirect
201. D4×Dic3C22×C3semidirect
204. C2×#213C22×C3semidirect
210. C2×D24C22×C3semidirect
213. #893C22×C3semidirect
221. #874C22×C3semidirect
222. C4×D12C22×C3semidirect
228. C3×C4⋊C8C2×D3semidirect
229. C3×C4⋊C8C22×C3semidirect
232. C3×#103C2×D3semidirect
233. C3×#103C22×C3semidirect
240. C3×#102C2×D3semidirect
241. C3×#102C22×C3semidirect
242. #835C22×C3semidirect
243. #832C22×C3semidirect
244. #821C22×C3semidirect
245. #821C22×C3semidirect
246. Dic3⋊C8C22×C3semidirect
247. Dic3⋊C8C22×C3semidirect
248. #809C22×C3semidirect
249. #809C22×C3semidirect
250. C4⋊(C3⋊C8)C22×C3semidirect
309. #463C3×D3semidirect
364. D3×D4C3×D4semidirect
484. C2×SD16C2×C3×D3semidirect
497. #124C2×C3×D3semidirect
507. C4×D4C2×C3×D3semidirect
515. C4⋊C8C2×C3×D3semidirect
517. #103C2×C3×D3semidirect
523. #102C2×C3×D3semidirect
785. C32#3041semidirect
892. C3#80536direct (N × H)
893. C3C3×#3041semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9142
C2×C3×D3×D82
C3×#56742
C3×#55452
C32×#4632
C3×#51652
C3×#51502
C3×#50572
C3×#50152
C3×#48432
C3×#48392
C3×#48192
C3×#48042
C3×#47862
C3×#47702
C3×#30413
#805363