Finite Group Databasebeta

← C3×#80231 #11864577

Subgroups — C3×#80231 #11864577

Order 1152.

1604 conjugacy classes of subgroups.

The subgroup lattice has 1041 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1009C211yesmaximal, characteristic, complemented
2C2×C3×#919C211yesmaximal, characteristic, complemented
3C2×C3×#914C211yesmaximal, characteristic, complemented
4C3×#5629C211yesmaximal, characteristic, complemented
5C32×#452C211yesmaximal, characteristic, complemented
6C3×#5238C211yesmaximal, characteristic, complemented
7C3×#5187C211yesmaximal, characteristic, complemented
8C3×#5169C211yesmaximal, characteristic, complemented
9C3×#5046C211yesmaximal, characteristic, complemented
10C3×#4810C211yesmaximal, characteristic, complemented
11C3×#4803C211yesmaximal, characteristic, complemented
12C3×#4773C211yesmaximal, characteristic, complemented
13C3×D3×#102C211yesmaximal, characteristic, complemented
14C3×#4732C211yesmaximal, characteristic, complemented
15C3×#4727C211yesmaximal, characteristic, complemented
16C3×#3012—31nomaximal
17#80231C311yesmaximal, characteristic, direct product factor
18C2×C32×#41C2211yescharacteristic
19C3×#1009—24no—
20C3×#1009—24no—
21C2×C3×#239C2211yescharacteristic
22C2×C3×#239C2211yescharacteristic
23C2×C3×#239C2211yescharacteristic, complemented
24C2×C3×D3×D4—21no—
25C2×C3×D3×D4—21no—
26C2×C3×D3×D4C2211yescharacteristic
27C2×C3×D3×D4C2211yescharacteristic
28C2×C3×#235—21no—
29C2×C3×#235C2211yescharacteristic
30C22×C3×D12—21no—
31C22×C3×D12C2211yescharacteristic
32C2×C32×Q16C2211yescharacteristic, complemented
33C2×C32×SD16C2211yescharacteristic, complemented
34C32×C22⋊Q8C2211yescharacteristic, complemented
35C3×#946C2211yescharacteristic, complemented
36C2×C3×#215C2211yescharacteristic, complemented
37C2×C3×#215C2211yescharacteristic, complemented
38C2×C3×#215C2211yescharacteristic, complemented
39C2×C3×#213C2211yescharacteristic, complemented
40C3×#930C2211yescharacteristic, complemented
41C3×#919—24no—
42C3×#914—24no—
43C2×C3×D24C2211yescharacteristic, complemented
44C2×C3×D24C2211yescharacteristic, complemented
45C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
46C2×C3×D3×C8C2211yescharacteristic, complemented
47C3×#896—21no—
48C3×#895—21no—
49C3×#895C2211yescharacteristic, complemented
50C3×D3×C4⋊C4C2211yescharacteristic, complemented
51C3×#884—21no—
52C3×#884—21no—
53C32×#103C2211yescharacteristic, complemented
54C32×#102C2211yescharacteristic, complemented
55C32×C22⋊C8C2211yescharacteristic, complemented
56C3×#835C2211yescharacteristic, complemented
57C3×#832C2211yescharacteristic, complemented
58C3×#830C2211yescharacteristic, complemented
59C3×#821C2211yescharacteristic, complemented
60C3×#821C2211yescharacteristic, complemented
61C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
62C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
63C3×#809C2211yescharacteristic, complemented
64C3×#809C2211yescharacteristic, complemented
65C2×C3×H(5,𝔽2)—31no—
66C2×#1009C2×C311yescharacteristic, complemented
67C2×C3×AGL(1,ℤ/8)—31no—
68C2×C3×#135—31no—
69C3×#537—31no—
70C2×#919C2×C311yescharacteristic, complemented
71C2×#914C2×C311yescharacteristic, complemented
72#5629C2×C311yescharacteristic, complemented
73C3×#452—21no—
74C3×#452—31no—
75C3×#452D311yescharacteristic, complemented
76C3×#452C2×C311yescharacteristic, complemented
77C3×#450—31no—
78C3×#450—31no—
79C3×#449—31no—
80C3×#449—31no—
81C3×#447—31no—
82C3×#447—31no—
83C3×#417—31no—
84C2×C3×#102—31no—
85C3×#408—31no—
86#5238C2×C311yescharacteristic, complemented
87#5187C2×C311yescharacteristic, complemented
88#5169C2×C311yescharacteristic, complemented
89#5046C2×C311yescharacteristic, complemented
90#4810C2×C311yescharacteristic, complemented
91#4803C2×C311yescharacteristic, complemented
92#4773C2×C311yescharacteristic, complemented
93D3×#102C2×C311yescharacteristic, complemented
94#4732C2×C311yescharacteristic, complemented
95#4727C2×C311yescharacteristic, complemented
96C23×C3×D3—21no—
97C23×C3×D3—21no—
98C23×C3×D3—21no—
99C32×#41—22no—
100C32×#41—22no—
101C2×C32×Q8C2311yescharacteristic
102C2×C32×Q8C2311yescharacteristic
103C2×C32×D4—21no—
104C2×C32×D4C2311yescharacteristic
105C22×C32×C4—21no—
106C22×C32×C4C2311yescharacteristic
107C2×C3×#67—21no—
108C2×C3×#67—21no—
109C2×C3×#67—21no—
110C2×C3×#67D411yescharacteristic
111C2×C3×#67D411yescharacteristic
112C3×#239—22no—
113C3×#239—22no—
114C3×#239—22no—
115C3×#239—22no—
116C3×#239—22no—
117C3×#239D414yescomplemented
118C3×D3×D4—28no—
119C3×D3×D4—28no—
120C3×D3×D4—22no—
121C3×D3×D4—22no—
122C3×D3×D4—22no—
123C3×D3×D4D414yescomplemented
124C3×#235—28no—
125C3×#235—22no—
126C3×#235—22no—
127C2×C3×D12—28no—
128C2×C3×D12—21no—
129C2×C3×D12—21no—
130C2×C3×D12—21no—
131C2×C3×D12—22no—
132C2×C3×D12—22no—
133C2×C3×D12—21no—
134C2×C3×D12—21no—
135C2×C3×D12D411yescharacteristic
136C2×C3×D12C2311yescharacteristic
137C2×C3×D12C2311yescharacteristic
138C2×C3×D12C2311yescharacteristic
139C2×C3×C4×D3—21no—
140C2×C3×C4×D3—21no—
141C2×C3×C4×D3—21no—
142C2×C3×C4×D3—21no—
143C2×C3×C4×D3C2311yescharacteristic
144C2×C3×C4×D3C2311yescharacteristic
145C2×C3×Dic6D411yescharacteristic
146C32×Q16—22no—
147C32×SD16—22no—
148C2×C32×C8C2311yescharacteristic
149C2×C32×C8C2311yescharacteristic
150C32×C4⋊C4—21no—
151C32×C4⋊C4C2311yescharacteristic
152C32×C22⋊C4—21no—
153C3×#215—22no—
154C3×#215—22no—
155C3×#215—22no—
156C3×#213—22no—
157C3×(C2×D3)⋊C4—21no—
158C3×(C2×D3)⋊C4—21no—
159C3×(C2×D3)⋊C4—21no—
160C3×C4⋊Dic3C2311yescharacteristic
161C3×Dic3⋊C4—21no—
162C3×Dic3⋊C4—21no—
163C2×C3×C3⋊C8C2311yescharacteristic
164C2×C3×C3⋊C8C2311yescharacteristic
165C3×D24—22no—
166C3×D24—22no—
167C3×ΓL(1,𝔽25)—22no—
168C3×D3×C8—22no—
169#3012—31noSylow
170C3×H(5,𝔽2)—64no—
171C3×H(5,𝔽2)—64no—
172C2×C3×#41—21no—
173C2×C3×#41—31no—
174C2×C3×#41—31no—
175C2×C3×#41—31no—
176C2×C3×#41—31no—
177C2×C3×#41—61no—
178C2×C3×#41C2×D311yescharacteristic
179C2×C3×#41C22×C311yescharacteristic
180C22×C3×D4—31no—
181C22×C3×D4—31no—
182C22×C3×D4—31no—
183C22×C3×D4—61no—
184C22×C3×D4—61no—
185C22×C3×D4—61no—
186#1009—24no—
187#1009—24no—
188C2×#239C22×C311yescharacteristic
189C2×#239C22×C311yescharacteristic
190C2×#239C22×C311yescharacteristic, complemented
191C2×D3×D4—21no—
192C2×D3×D4—21no—
193C2×D3×D4C22×C311yescharacteristic
194C2×D3×D4C22×C311yescharacteristic
195C2×#235—21no—
196C2×#235C22×C311yescharacteristic
197C22×D12—21no—
198C22×D12C22×C311yescharacteristic
199C3×AGL(1,ℤ/8)—64no—
200C3×#135—64no—
201C2×C3×Q16—21no—
202C2×C3×Q16C2×D311yescharacteristic, complemented
203C2×C3×Q16C22×C311yescharacteristic, complemented
204C2×C3×SD16—21no—
205C2×C3×SD16—31no—
206C2×C3×SD16—31no—
207C2×C3×SD16—31no—
208C2×C3×SD16C2×D311yescharacteristic, complemented
209C2×C3×SD16C22×C311yescharacteristic, complemented
210C2×C3×D8—31no—
211C2×C3×D8—31no—
212C2×C3×D8—31no—
213C2×C3×M16—31no—
214C22×C3×C8—31no—
215C3×C22⋊Q8—21no—
216C3×C22⋊Q8—31no—
217C3×C22⋊Q8—61no—
218C3×C22⋊Q8C2×D311yescharacteristic, complemented
219C3×C22⋊Q8C22×C311yescharacteristic, complemented
220C3×#121—31no—
221C3×#121—31no—
222C3×#121—61no—
223C3×#121—61no—
224C3×#121—61no—
225C2×C3×C4⋊C4—31no—
226#946C22×C311yescharacteristic, complemented
227C2×#215C22×C311yescharacteristic, complemented
228C2×#215C22×C311yescharacteristic, complemented
229C2×#215C22×C311yescharacteristic, complemented
230C2×#213C22×C311yescharacteristic, complemented
231#930C22×C311yescharacteristic, complemented
232#919—24no—
233#914—24no—
234C2×D24C22×C311yescharacteristic, complemented
235C2×D24C22×C311yescharacteristic, complemented
236C2×ΓL(1,𝔽25)C22×C311yescharacteristic, complemented
237C2×D3×C8C22×C311yescharacteristic, complemented
238#896—21no—
239#895—21no—
240#895C22×C311yescharacteristic, complemented
241D3×C4⋊C4C22×C311yescharacteristic, complemented
242#884—21no—
243#884—21no—
244C3×#103—21no—
245C3×#103—31no—
246C3×#103C2×D311yescharacteristic, complemented
247C3×#103C22×C311yescharacteristic, complemented
248C3×#102—21no—
249C3×#102—31no—
250C3×#102—31no—
251C3×#102—31no—
252C3×#102—31no—
253C3×#102—31no—
254C3×#102C2×D311yescharacteristic, complemented
255C3×#102C22×C311yescharacteristic, complemented
256C3×C22⋊C8—21no—
257C3×C22⋊C8—31no—
258C3×C22⋊C8—31no—
259C3×C22⋊C8—31no—
260C3×C22⋊C8C2×D311yescharacteristic, complemented
261C3×C22⋊C8C22×C311yescharacteristic, complemented
262#835C22×C311yescharacteristic, complemented
263#832C22×C311yescharacteristic, complemented
264#830C22×C311yescharacteristic, complemented
265#821C22×C311yescharacteristic, complemented
266#821C22×C311yescharacteristic, complemented
267(C2×D3)⋊C8C22×C311yescharacteristic, complemented
268(C2×D3)⋊C8C22×C311yescharacteristic, complemented
269#809C22×C311yescharacteristic, complemented
270#809C22×C311yescharacteristic, complemented
271C23×C32—21no—
272C23×C32C2×D411yescharacteristic
273C22×C3×D3—21no—
274C22×C3×D3—21no—
275C22×C3×D3—24no—
276C22×C3×D3—24no—
277C22×C3×D3—24no—
278C22×C3×D3—21no—
279C22×C3×D3—81no—
280C22×C3×D3—81no—
281C22×C3×D3—81no—
282C22×C3×D3—81no—
283C22×C3×D3—81no—
284C22×C3×D3—81no—
285C22×C3×D3C2×D411yescharacteristic
286C22×C3×D3C2×D411yescharacteristic
287C32×Q8—21no—
288C32×Q8—21no—
289C32×Q8—21no—
290C32×Q8C2×D412yes—
291C32×D4—24no—
292C32×D4—21no—
293C32×D4C2×D412yes—
294C2×C32×C4—24no—
295C2×C32×C4—21no—
296C2×C32×C4—21no—
297C2×C32×C4—21no—
298C2×C32×C4—21no—
299C2×C32×C4—21no—
300C2×C32×C4C2×D411yescharacteristic
301C2×C32×C4C2411yescharacteristic
302C3×#67—24no—
303C3×#67—22no—
304C3×#67—22no—
305C3×#67—24no—
306C3×#67—81no—
307C2×C3×Dic3—21no—
308C2×C3×Dic3C2×D411yescharacteristic
309C2×C3×Dic3C2×D411yescharacteristic
310C3×D12—24no—
311C3×D12—24no—
312C3×D12—22no—
313C3×D12—24no—
314C3×D12—21no—
315C3×D12—21no—
316C3×D12—21no—
317C3×D12—21no—
318C3×D12—42no—
319C3×D12—81no—
320C3×D12C2×D412yes—
321C3×D12C2×D412yes—
322C3×C4×D3—24no—
323C3×C4×D3—21no—
324C3×C4×D3—21no—
325C3×C4×D3—24no—
326C3×C4×D3—42no—
327C3×C4×D3—81no—
328C3×C4×D3C2×D412yes—
329C3×C4×D3C2×D412yes—
330C3×Dic6—22no—
331C32×C8—21no—
332C32×C8—21no—
333C3×C3⋊C8—21no—
334C3×C3⋊C8—21no—
335C2×H(5,𝔽2)—31no—
336C2×AGL(1,ℤ/8)—31no—
337C2×#135—31no—
338#537—31no—
339#452—31no—
340#452C3×D311yescharacteristic, complemented
341#450—31no—
342#450—31no—
343#449—31no—
344#449—31no—
345#447—31no—
346#447—31no—
347#417—31no—
348C2×#102—31no—
349#408—31no—
350C24×C3—61no—
351C24×C3—61no—
352C24×C3—61no—
353C23×D3—21no—
354C23×D3—21no—
355C23×D3—21no—
356C3×#41—22no—
357C3×#41—22no—
358C3×#41—22no—
359C3×#41—22no—
360C3×#41—34no—
361C3×#41—42no—
362C3×#41—42no—
363C3×#41—62no—
364C3×#41—62no—
365C3×#41—68no—
366C3×#41—62no—
367C3×#41—62no—
368C3×#41—62no—
369C3×#41—62no—
370C3×#41—62no—
371C2×C3×Q8—21no—
372C2×C3×Q8—21no—
373C2×C3×Q8—31no—
374C2×C3×Q8C22×D311yescharacteristic
375C2×C3×Q8C22×D311yescharacteristic
376C2×C3×Q8C23×C311yescharacteristic
377C2×C3×Q8C23×C311yescharacteristic
378C2×C3×D4—21no—
379C2×C3×D4—21no—
380C2×C3×D4—21no—
381C2×C3×D4—34no—
382C2×C3×D4—31no—
383C2×C3×D4—31no—
384C2×C3×D4—31no—
385C2×C3×D4—31no—
386C2×C3×D4—31no—
387C2×C3×D4—31no—
388C2×C3×D4—41no—
389C2×C3×D4—62no—
390C2×C3×D4—62no—
391C2×C3×D4—61no—
392C2×C3×D4—61no—
393C2×C3×D4—68no—
394C2×C3×D4—61no—
395C2×C3×D4—61no—
396C2×C3×D4—62no—
397C2×C3×D4—61no—
398C2×C3×D4—61no—
399C2×C3×D4—62no—
400C2×C3×D4—68no—
401C2×C3×D4—68no—
402C2×C3×D4—62no—
403C2×C3×D4—61no—
404C2×C3×D4—61no—
405C2×C3×D4C22×D311yescharacteristic
406C2×C3×D4C23×C311yescharacteristic
407C22×C3×C4—21no—
408C22×C3×C4—21no—
409C22×C3×C4—21no—
410C22×C3×C4—31no—
411C22×C3×C4—31no—
412C22×C3×C4—41no—
413C22×C3×C4—61no—
414C22×C3×C4—61no—
415C22×C3×C4—61no—
416C22×C3×C4—61no—
417C22×C3×C4C22×D311yescharacteristic
418C22×C3×C4C23×C311yescharacteristic
419C2×#67—21no—
420C2×#67—21no—
421C2×#67—21no—
422C2×#67C3×D411yescharacteristic
423C2×#67C3×D411yescharacteristic
424#239—22no—
425#239—22no—
426#239—22no—
427#239—22no—
428#239—22no—
429#239C3×D414yescomplemented
430D3×D4—28no—
431D3×D4—28no—
432D3×D4—22no—
433D3×D4—22no—
434D3×D4—22no—
435D3×D4C3×D414yescomplemented
436#235—28no—
437#235—22no—
438#235—22no—
439C2×D12—28no—
440C2×D12—21no—
441C2×D12—21no—
442C2×D12—21no—
443C2×D12—22no—
444C2×D12—22no—
445C2×D12—21no—
446C2×D12—21no—
447C2×D12C3×D411yescharacteristic
448C2×D12C23×C311yescharacteristic
449C2×D12C23×C311yescharacteristic
450C2×D12C23×C311yescharacteristic
451C2×C4×D3—21no—
452C2×C4×D3—21no—
453C2×C4×D3—21no—
454C2×C4×D3—21no—
455C2×C4×D3C23×C311yescharacteristic
456C2×C4×D3C23×C311yescharacteristic
457C2×Dic6C3×D411yescharacteristic
458C3×Q16—22no—
459C3×Q16—22no—
460C3×Q16—42no—
461C3×SD16—22no—
462C3×SD16—22no—
463C3×SD16—42no—
464C3×SD16—62no—
465C3×SD16—62no—
466C3×SD16—62no—
467C3×D8—62no—
468C3×D8—62no—
469C3×D8—62no—
470C3×M16—62no—
471C2×C3×C8—21no—
472C2×C3×C8—21no—
473C2×C3×C8—31no—
474C2×C3×C8—31no—
475C2×C3×C8—62no—
476C2×C3×C8C22×D311yescharacteristic
477C2×C3×C8C22×D311yescharacteristic
478C2×C3×C8C23×C311yescharacteristic
479C2×C3×C8C23×C311yescharacteristic
480C3×C4⋊C4—21no—
481C3×C4⋊C4—21no—
482C3×C4⋊C4—21no—
483C3×C4⋊C4—31no—
484C3×C4⋊C4—41no—
485C3×C4⋊C4—61no—
486C3×C4⋊C4—61no—
487C3×C4⋊C4C22×D311yescharacteristic
488C3×C4⋊C4C23×C311yescharacteristic
489C3×C22⋊C4—21no—
490C3×C22⋊C4—21no—
491C3×C22⋊C4—41no—
492C3×C22⋊C4—61no—
493C3×C22⋊C4—61no—
494C3×C22⋊C4—61no—
495#215—22no—
496#215—22no—
497#215—22no—
498#213—22no—
499(C2×D3)⋊C4—21no—
500(C2×D3)⋊C4—21no—
501(C2×D3)⋊C4—21no—
502C4⋊Dic3C23×C311yescharacteristic
503Dic3⋊C4—21no—
504Dic3⋊C4—21no—
505C2×C3⋊C8C23×C311yescharacteristic
506C2×C3⋊C8C23×C311yescharacteristic
507D24—22no—
508D24—22no—
509ΓL(1,𝔽25)—22no—
510D3×C8—22no—
511C22×C32—21no—
512C22×C32—22no—
513C22×C32—21no—
514C22×C32—21no—
515C22×C32—41no—
516C22×C32—41no—
517C22×C32C22×D411yescharacteristic
518C2×C3×D3—21no—
519C2×C3×D3—21no—
520C2×C3×D3—21no—
521C2×C3×D3—22no—
522C2×C3×D3—22no—
523C2×C3×D3—21no—
524C2×C3×D3—21no—
525C2×C3×D3—41no—
526C2×C3×D3—41no—
527C2×C3×D3—41no—
528C2×C3×D3—41no—
529C2×C3×D3—41no—
530C2×C3×D3—41no—
531C2×C3×D3—41no—
532C2×C3×D3—84no—
533C2×C3×D3—84no—
534C2×C3×D3—84no—
535C2×C3×D3#12012yes—
536C32×C4—21no—
537C32×C4—22no—
538C32×C4—41no—
539C32×C4—41no—
540C32×C4C22×D411yescharacteristic
541C32×C4C22×D411yescharacteristic
542C3×Dic3—21no—
543C3×Dic3—41no—
544C3×Dic3#12012yes—
545H(5,𝔽2)—64no—
546H(5,𝔽2)—64no—
547C2×#41—31no—
548C2×#41—31no—
549C2×#41—31no—
550C2×#41—31no—
551C2×#41—61no—
552C2×#41C2×C3×D311yescharacteristic
553C22×D4—31no—
554C22×D4—31no—
555C22×D4—31no—
556C22×D4—61no—
557C22×D4—61no—
558C22×D4—61no—
559AGL(1,ℤ/8)—64no—
560#135—64no—
561C2×Q16C2×C3×D311yescharacteristic, complemented
562C2×SD16—31no—
563C2×SD16—31no—
564C2×SD16—31no—
565C2×SD16C2×C3×D311yescharacteristic, complemented
566C2×D8—31no—
567C2×D8—31no—
568C2×D8—31no—
569C2×M16—31no—
570C22×C8—31no—
571C22⋊Q8—31no—
572C22⋊Q8—61no—
573C22⋊Q8C2×C3×D311yescharacteristic, complemented
574#121—31no—
575#121—31no—
576#121—61no—
577#121—61no—
578#121—61no—
579C2×C4⋊C4—31no—
580#103—31no—
581#103C2×C3×D311yescharacteristic, complemented
582#102—31no—
583#102—31no—
584#102—31no—
585#102—31no—
586#102—31no—
587#102C2×C3×D311yescharacteristic, complemented
588C22⋊C8—31no—
589C22⋊C8—31no—
590C22⋊C8—31no—
591C22⋊C8C2×C3×D311yescharacteristic, complemented
592C23×C3—21no—
593C23×C3—21no—
594C23×C3—21no—
595C23×C3—31no—
596C23×C3—31no—
597C23×C3—41no—
598C23×C3—64no—
599C23×C3—64no—
600C23×C3—64no—
601C23×C3—61no—
602C23×C3—61no—
603C23×C3—61no—
604C23×C3—241no—
605C23×C3—241no—
606C23×C3—241no—
607C23×C3—241no—
608C23×C3—241no—
609C23×C3—241no—
610C23×C3D3×D411yescharacteristic
611C23×C3C2×C3×D411yescharacteristic
612C22×D3—21no—
613C22×D3—21no—
614C22×D3—24no—
615C22×D3—24no—
616C22×D3—24no—
617C22×D3—21no—
618C22×D3—81no—
619C22×D3—81no—
620C22×D3—81no—
621C22×D3—81no—
622C22×D3—81no—
623C22×D3—81no—
624C22×D3C2×C3×D411yescharacteristic
625C22×D3C2×C3×D411yescharacteristic
626C3×Q8—21no—
627C3×Q8—21no—
628C3×Q8—21no—
629C3×Q8—21no—
630C3×Q8—21no—
631C3×Q8—21no—
632C3×Q8—22no—
633C3×Q8—41no—
634C3×Q8—41no—
635C3×Q8—41no—
636C3×Q8—62no—
637C3×Q8D3×D412yes—
638C3×Q8C2×C3×D412yes—
639C3×D4—24no—
640C3×D4—24no—
641C3×D4—21no—
642C3×D4—21no—
643C3×D4—22no—
644C3×D4—32no—
645C3×D4—32no—
646C3×D4—41no—
647C3×D4—44no—
648C3×D4—62no—
649C3×D4—64no—
650C3×D4—64no—
651C3×D4—64no—
652C3×D4—62no—
653C3×D4—64no—
654C3×D4—62no—
655C3×D4—64no—
656C3×D4—61no—
657C3×D4—61no—
658C3×D4—61no—
659C3×D4—61no—
660C3×D4—122no—
661C3×D4—241no—
662C3×D4—241no—
663C3×D4D3×D412yes—
664C3×D4C2×C3×D412yes—
665C2×C3×C4—24no—
666C2×C3×C4—24no—
667C2×C3×C4—21no—
668C2×C3×C4—21no—
669C2×C3×C4—21no—
670C2×C3×C4—21no—
671C2×C3×C4—21no—
672C2×C3×C4—21no—
673C2×C3×C4—21no—
674C2×C3×C4—21no—
675C2×C3×C4—21no—
676C2×C3×C4—21no—
677C2×C3×C4—21no—
678C2×C3×C4—21no—
679C2×C3×C4—31no—
680C2×C3×C4—32no—
681C2×C3×C4—32no—
682C2×C3×C4—31no—
683C2×C3×C4—41no—
684C2×C3×C4—41no—
685C2×C3×C4—41no—
686C2×C3×C4—44no—
687C2×C3×C4—41no—
688C2×C3×C4—41no—
689C2×C3×C4—64no—
690C2×C3×C4—64no—
691C2×C3×C4—61no—
692C2×C3×C4—61no—
693C2×C3×C4—61no—
694C2×C3×C4—122no—
695C2×C3×C4—241no—
696C2×C3×C4D3×D411yescharacteristic
697C2×C3×C4C2×C3×D411yescharacteristic
698C2×C3×C4C23×D311yescharacteristic
699C2×C3×C4C24×C311yescharacteristic
700#67—24no—
701#67—22no—
702#67—22no—
703#67—24no—
704#67—81no—
705C2×Dic3—21no—
706C2×Dic3C2×C3×D411yescharacteristic
707C2×Dic3C2×C3×D411yescharacteristic
708D12—24no—
709D12—24no—
710D12—22no—
711D12—24no—
712D12—21no—
713D12—21no—
714D12—21no—
715D12—21no—
716D12—42no—
717D12—81no—
718D12C2×C3×D412yes—
719D12C2×C3×D412yes—
720C4×D3—24no—
721C4×D3—21no—
722C4×D3—21no—
723C4×D3—24no—
724C4×D3—42no—
725C4×D3—81no—
726C4×D3C2×C3×D412yes—
727C4×D3C2×C3×D412yes—
728Dic6—22no—
729C3×C8—21no—
730C3×C8—21no—
731C3×C8—21no—
732C3×C8—21no—
733C3×C8—41no—
734C3×C8—41no—
735C3×C8—61no—
736C3×C8—61no—
737C3⋊C8—21no—
738C3⋊C8—21no—
739C2×C32—41no—
740C2×C32—42no—
741C2×C32C2×#12011yescharacteristic
742C2×C32#57611yescharacteristic
743C2×C32#57711yescharacteristic
744C3×D3—22no—
745C3×D3—41no—
746C3×D3—42no—
747C3×D3—42no—
748C3×D3—81no—
749C24—61no—
750C24—61no—
751C24—61no—
752#41—22no—
753#41—22no—
754#41—34no—
755#41—62no—
756#41—62no—
757#41—68no—
758#41—62no—
759#41—62no—
760#41—62no—
761#41—62no—
762#41—62no—
763C2×Q8—31no—
764C2×Q8C22×C3×D311yescharacteristic
765C2×Q8C22×C3×D311yescharacteristic
766C2×D4—21no—
767C2×D4—34no—
768C2×D4—31no—
769C2×D4—31no—
770C2×D4—31no—
771C2×D4—31no—
772C2×D4—31no—
773C2×D4—31no—
774C2×D4—62no—
775C2×D4—62no—
776C2×D4—61no—
777C2×D4—61no—
778C2×D4—68no—
779C2×D4—61no—
780C2×D4—61no—
781C2×D4—62no—
782C2×D4—61no—
783C2×D4—61no—
784C2×D4—62no—
785C2×D4—68no—
786C2×D4—68no—
787C2×D4—62no—
788C2×D4—61no—
789C2×D4—61no—
790C2×D4C22×C3×D311yescharacteristic
791C22×C4—21no—
792C22×C4—31no—
793C22×C4—31no—
794C22×C4—61no—
795C22×C4—61no—
796C22×C4—61no—
797C22×C4—61no—
798C22×C4C22×C3×D311yescharacteristic
799Q16—22no—
800SD16—22no—
801SD16—62no—
802SD16—62no—
803SD16—62no—
804D8—62no—
805D8—62no—
806D8—62no—
807M16—62no—
808C2×C8—31no—
809C2×C8—31no—
810C2×C8—62no—
811C2×C8C22×C3×D311yescharacteristic
812C2×C8C22×C3×D311yescharacteristic
813C4⋊C4—21no—
814C4⋊C4—31no—
815C4⋊C4—61no—
816C4⋊C4—61no—
817C4⋊C4C22×C3×D311yescharacteristic
818C22⋊C4—21no—
819C22⋊C4—61no—
820C22⋊C4—61no—
821C22⋊C4—61no—
822C22×C3—21no—
823C22×C3—21no—
824C22×C3—21no—
825C22×C3—21no—
826C22×C3—21no—
827C22×C3—22no—
828C22×C3—21no—
829C22×C3—22no—
830C22×C3—21no—
831C22×C3—32no—
832C22×C3—42no—
833C22×C3—41no—
834C22×C3—41no—
835C22×C3—41no—
836C22×C3—41no—
837C22×C3—41no—
838C22×C3—41no—
839C22×C3—41no—
840C22×C3—61no—
841C22×C3—61no—
842C22×C3—61no—
843C22×C3—61no—
844C22×C3—62no—
845C22×C3—62no—
846C22×C3—61no—
847C22×C3—81no—
848C22×C3—81no—
849C22×C3—121no—
850C22×C3—121no—
851C22×C3—121no—
852C22×C3—121no—
853C22×C3—121no—
854C22×C3—121no—
855C22×C3—121no—
856C22×C3—244no—
857C22×C3—244no—
858C22×C3—244no—
859C22×C3C2×D3×D411yescharacteristic
860C22×C3C22×C3×D411yescharacteristic
861C2×D3—21no—
862C2×D3—21no—
863C2×D3—21no—
864C2×D3—21no—
865C2×D3—21no—
866C2×D3—22no—
867C2×D3—22no—
868C2×D3—41no—
869C2×D3—41no—
870C2×D3—41no—
871C2×D3—41no—
872C2×D3—41no—
873C2×D3—41no—
874C2×D3—41no—
875C2×D3—84no—
876C2×D3—84no—
877C2×D3—84no—
878C2×D3C3×#12012yes—
879C3×C4—21no—
880C3×C4—22no—
881C3×C4—21no—
882C3×C4—22no—
883C3×C4—21no—
884C3×C4—21no—
885C3×C4—32no—
886C3×C4—41no—
887C3×C4—42no—
888C3×C4—41no—
889C3×C4—41no—
890C3×C4—41no—
891C3×C4—41no—
892C3×C4—61no—
893C3×C4—81no—
894C3×C4—81no—
895C3×C4—121no—
896C3×C4C2×D3×D411yescharacteristic
897C3×C4C2×D3×D411yescharacteristic
898C3×C4C22×C3×D411yescharacteristic
899C3×C4C22×C3×D411yescharacteristic
900Dic3—21no—
901Dic3—41no—
902Dic3C3×#12012yes—
903C32#301211yescharacteristic, complemented, Sylow
904C23—21no—
905C23—31no—
906C23—31no—
907C23—64no—
908C23—64no—
909C23—64no—
910C23—61no—
911C23—61no—
912C23—61no—
913C23—241no—
914C23—241no—
915C23—241no—
916C23—241no—
917C23—241no—
918C23—241no—
919C23C3×D3×D411yescharacteristic
920Q8—21no—
921Q8—21no—
922Q8—21no—
923Q8—62no—
924Q8C3×D3×D412yes—
925D4—24no—
926D4—21no—
927D4—32no—
928D4—32no—
929D4—62no—
930D4—64no—
931D4—64no—
932D4—64no—
933D4—62no—
934D4—64no—
935D4—62no—
936D4—64no—
937D4—61no—
938D4—61no—
939D4—61no—
940D4—61no—
941D4—122no—
942D4—241no—
943D4—241no—
944D4C3×D3×D412yes—
945C2×C4—24no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—31no—
952C2×C4—32no—
953C2×C4—32no—
954C2×C4—31no—
955C2×C4—64no—
956C2×C4—64no—
957C2×C4—61no—
958C2×C4—61no—
959C2×C4—61no—
960C2×C4—122no—
961C2×C4—241no—
962C2×C4C3×D3×D411yescharacteristic
963C2×C4C23×C3×D311yescharacteristic
964C8—21no—
965C8—21no—
966C8—61no—
967C8—61no—
968C2×C3—21no—
969C2×C3—21no—
970C2×C3—21no—
971C2×C3—41no—
972C2×C3—42no—
973C2×C3—41no—
974C2×C3—42no—
975C2×C3—62no—
976C2×C3—81no—
977C2×C3—82no—
978C2×C3—121no—
979C2×C3—122no—
980C2×C3—122no—
981C2×C3—241no—
982C2×C3D3×#12011yescharacteristic
983C2×C3#576911yescharacteristic
984C2×C3#577811yescharacteristic
985C2×C3C2×C3×#12011yescharacteristic
986C2×C3C3×#57611yescharacteristic
987C2×C3C3×#57711yescharacteristic
988D3—22no—
989D3—41no—
990D3—42no—
991D3—42no—
992D3—81no—
993C22—21no—
994C22—21no—
995C22—21no—
996C22—22no—
997C22—32no—
998C22—41no—
999C22—41no—
1000C22—61no—
1001C22—61no—
1002C22—61no—
1003C22—61no—
1004C22—62no—
1005C22—62no—
1006C22—61no—
1007C22—121no—
1008C22—121no—
1009C22—121no—
1010C22—121no—
1011C22—121no—
1012C22—121no—
1013C22—121no—
1014C22—244no—
1015C22—244no—
1016C22—244no—
1017C22C2×C3×D3×D411yescharacteristic
1018C4—21no—
1019C4—22no—
1020C4—32no—
1021C4—41no—
1022C4—41no—
1023C4—61no—
1024C4—121no—
1025C4C2×C3×D3×D411yescharacteristic
1026C4C2×C3×D3×D411yescharacteristic
1027C3—21no—
1028C3#8023111yescharacteristic, direct product factor
1029C3C3×#301211yescharacteristic, complemented
1030C2—41no—
1031C2—42no—
1032C2—62no—
1033C2—121no—
1034C2—122no—
1035C2—122no—
1036C2—241no—
1037C2C3×D3×#12011yescharacteristic
1038C2C3×#576911yescharacteristic
1039C2C3×#577811yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#452C2
socleC22×C32C22×D4
hypercenterC3×#452D3
hypocenterC3C3×#3012
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#452

Complements

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

NH ≅ G/Ntype
1. C2×C3×#1009C2semidirect
2. C2×C3×#919C2semidirect
3. C2×C3×#914C2semidirect
4. C3×#5629C2semidirect
5. C32×#452C2semidirect
6. C3×#5238C2semidirect
7. C3×#5187C2semidirect
8. C3×#5169C2semidirect
9. C3×#5046C2semidirect
10. C3×#4810C2semidirect
11. C3×#4803C2semidirect
12. C3×#4773C2semidirect
13. C3×D3×#102C2semidirect
14. C3×#4732C2semidirect
15. C3×#4727C2semidirect
17. #80231C3direct (N × H)
23. C2×C3×#239C22semidirect
32. C2×C32×Q16C22semidirect
33. C2×C32×SD16C22semidirect
34. C32×C22⋊Q8C22semidirect
35. C3×#946C22semidirect
36. C2×C3×#215C22semidirect
37. C2×C3×#215C22semidirect
38. C2×C3×#215C22semidirect
39. C2×C3×#213C22semidirect
40. C3×#930C22semidirect
43. C2×C3×D24C22semidirect
44. C2×C3×D24C22semidirect
45. C2×C3×ΓL(1,𝔽25)C22semidirect
46. C2×C3×D3×C8C22semidirect
49. C3×#895C22semidirect
50. C3×D3×C4⋊C4C22semidirect
53. C32×#103C22semidirect
54. C32×#102C22semidirect
55. C32×C22⋊C8C22semidirect
56. C3×#835C22semidirect
57. C3×#832C22semidirect
58. C3×#830C22semidirect
59. C3×#821C22semidirect
60. C3×#821C22semidirect
61. C3×(C2×D3)⋊C8C22semidirect
62. C3×(C2×D3)⋊C8C22semidirect
63. C3×#809C22semidirect
64. C3×#809C22semidirect
66. C2×#1009C2×C3semidirect
70. C2×#919C2×C3semidirect
71. C2×#914C2×C3semidirect
72. #5629C2×C3semidirect
75. C3×#452D3semidirect
76. C3×#452C2×C3semidirect
86. #5238C2×C3semidirect
87. #5187C2×C3semidirect
88. #5169C2×C3semidirect
89. #5046C2×C3semidirect
90. #4810C2×C3semidirect
91. #4803C2×C3semidirect
92. #4773C2×C3semidirect
93. D3×#102C2×C3semidirect
94. #4732C2×C3semidirect
95. #4727C2×C3semidirect
117. C3×#239D4semidirect
123. C3×D3×D4D4semidirect
190. C2×#239C22×C3semidirect
202. C2×C3×Q16C2×D3semidirect
203. C2×C3×Q16C22×C3semidirect
208. C2×C3×SD16C2×D3semidirect
209. C2×C3×SD16C22×C3semidirect
218. C3×C22⋊Q8C2×D3semidirect
219. C3×C22⋊Q8C22×C3semidirect
226. #946C22×C3semidirect
227. C2×#215C22×C3semidirect
228. C2×#215C22×C3semidirect
229. C2×#215C22×C3semidirect
230. C2×#213C22×C3semidirect
231. #930C22×C3semidirect
234. C2×D24C22×C3semidirect
235. C2×D24C22×C3semidirect
236. C2×ΓL(1,𝔽25)C22×C3semidirect
237. C2×D3×C8C22×C3semidirect
240. #895C22×C3semidirect
241. D3×C4⋊C4C22×C3semidirect
246. C3×#103C2×D3semidirect
247. C3×#103C22×C3semidirect
254. C3×#102C2×D3semidirect
255. C3×#102C22×C3semidirect
260. C3×C22⋊C8C2×D3semidirect
261. C3×C22⋊C8C22×C3semidirect
262. #835C22×C3semidirect
263. #832C22×C3semidirect
264. #830C22×C3semidirect
265. #821C22×C3semidirect
266. #821C22×C3semidirect
267. (C2×D3)⋊C8C22×C3semidirect
268. (C2×D3)⋊C8C22×C3semidirect
269. #809C22×C3semidirect
270. #809C22×C3semidirect
340. #452C3×D3semidirect
429. #239C3×D4semidirect
435. D3×D4C3×D4semidirect
561. C2×Q16C2×C3×D3semidirect
565. C2×SD16C2×C3×D3semidirect
573. C22⋊Q8C2×C3×D3semidirect
581. #103C2×C3×D3semidirect
587. #102C2×C3×D3semidirect
591. C22⋊C8C2×C3×D3semidirect
903. C32#3012semidirect
1028. C3#80231direct (N × H)
1029. C3C3×#3012semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10092
C2×C3×#9192
C2×C3×#9142
C3×#56292
C32×#4522
C3×#52382
C3×#51872
C3×#51692
C3×#50462
C3×#48102
C3×#48032
C3×#47732
C3×D3×#1022
C3×#47322
C3×#47272
C3×#30123
#802313