Finite Group Databasebeta

← C3×#80149 #11864568

Subgroups — C3×#80149 #11864568

Order 1152.

1622 conjugacy classes of subgroups.

The subgroup lattice has 1047 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1004C211yesmaximal, characteristic, complemented
2C2×C3×#916C211yesmaximal, characteristic, complemented
3C2×C3×#914C211yesmaximal, characteristic, complemented
4C3×#5629C211yesmaximal, characteristic, complemented
5C32×#450C211yesmaximal, characteristic, complemented
6C3×#5217C211yesmaximal, characteristic, complemented
7C3×#5173C211yesmaximal, characteristic, complemented
8C3×#5169C211yesmaximal, characteristic, complemented
9C3×#5047C211yesmaximal, characteristic, complemented
10C3×#4781C211yesmaximal, characteristic, complemented
11C3×#4773C211yesmaximal, characteristic, complemented
12C3×#4771C211yesmaximal, characteristic, complemented
13C3×D3×#102C211yesmaximal, characteristic, complemented
14C3×#4734C211yesmaximal, characteristic, complemented
15C3×#4727C211yesmaximal, characteristic, complemented
16C3×#3012—31nomaximal
17#80149C311yesmaximal, characteristic, direct product factor
18C22×C32×D4C2211yescharacteristic
19C22×C3×#67—21no—
20C22×C3×#67—21no—
21C2×C3×#239C2211yescharacteristic, complemented
22C3×#1004—24no—
23C3×#1004—24no—
24C2×C3×#237—21no—
25C2×C3×#237C2211yescharacteristic
26C2×C3×#237C2211yescharacteristic
27C2×C3×D3×D4—21no—
28C2×C3×D3×D4C2211yescharacteristic
29C2×C3×D3×D4C2211yescharacteristic
30C2×C3×#235C2211yescharacteristic
31C2×C3×#235C2211yescharacteristic
32C2×C32×SD16C2211yescharacteristic, complemented
33C2×C32×SD16C2211yescharacteristic, complemented
34C32×C22⋊Q8C2211yescharacteristic, complemented
35C3×#946C2211yescharacteristic, complemented
36C2×C3×#216C2211yescharacteristic, complemented
37C2×C3×#215C2211yescharacteristic, complemented
38C2×C3×#213C2211yescharacteristic, complemented
39C2×C3×#213C2211yescharacteristic, complemented
40C3×#930C2211yescharacteristic, complemented
41C3×#916—24no—
42C3×#914—24no—
43C2×C3×D24C2211yescharacteristic, complemented
44C2×C3×#204C2211yescharacteristic, 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×#102C2211yescharacteristic, complemented
54C32×#102C2211yescharacteristic, complemented
55C32×C22⋊C8C2211yescharacteristic, complemented
56C3×#832C2211yescharacteristic, complemented
57C3×#832C2211yescharacteristic, complemented
58C3×#830C2211yescharacteristic, complemented
59C3×#821C2211yescharacteristic, complemented
60C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
61C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
62C3×#816C2211yescharacteristic, complemented
63C3×#810C2211yescharacteristic, complemented
64C3×#809C2211yescharacteristic, complemented
65C2×C3×H(5,𝔽2)—31no—
66C2×#1004C2×C311yescharacteristic, complemented
67C2×C3×AGL(1,ℤ/8)—31no—
68C2×C3×#135—31no—
69C3×#537—31no—
70C2×#916C2×C311yescharacteristic, complemented
71C2×#914C2×C311yescharacteristic, complemented
72#5629C2×C311yescharacteristic, complemented
73C3×#452—31no—
74C3×#452—31no—
75C3×#450—21no—
76C3×#450—31no—
77C3×#450D311yescharacteristic, complemented
78C3×#450C2×C311yescharacteristic, complemented
79C3×#449—31no—
80C3×#449—31no—
81C3×#447—31no—
82C3×#447—31no—
83C3×#417—31no—
84C2×C3×#102—31no—
85C3×#408—31no—
86#5217C2×C311yescharacteristic, complemented
87#5173C2×C311yescharacteristic, complemented
88#5169C2×C311yescharacteristic, complemented
89#5047C2×C311yescharacteristic, complemented
90#4781C2×C311yescharacteristic, complemented
91#4773C2×C311yescharacteristic, complemented
92#4771C2×C311yescharacteristic, complemented
93D3×#102C2×C311yescharacteristic, complemented
94#4734C2×C311yescharacteristic, complemented
95#4727C2×C311yescharacteristic, complemented
96C24×C32—21no—
97C23×C3×D3—21no—
98C23×C3×D3—21no—
99C2×C32×Q8C2311yescharacteristic
100C2×C32×D4—22no—
101C2×C32×D4—22no—
102C2×C32×D4—21no—
103C2×C32×D4C2311yescharacteristic
104C2×C32×D4C2311yescharacteristic
105C22×C32×C4C2311yescharacteristic
106C2×C3×#67—28no—
107C2×C3×#67—28no—
108C2×C3×#67—21no—
109C2×C3×#67—21no—
110C2×C3×#67—21no—
111C2×C3×#67—21no—
112C2×C3×#67—21no—
113C2×C3×#67—21no—
114C2×C3×#67D411yescharacteristic
115C2×C3×#67D411yescharacteristic
116C22×C3×Dic3—21no—
117C22×C3×Dic3—21no—
118C3×#239—22no—
119C3×#239—22no—
120C3×#237—28no—
121C3×#237—22no—
122C3×#237—22no—
123C3×#237—22no—
124C3×#237D414yescomplemented
125C3×D3×D4—28no—
126C3×D3×D4—22no—
127C3×D3×D4—22no—
128C3×D3×D4—22no—
129C3×D3×D4D414yescomplemented
130C3×#235—22no—
131C3×#235—22no—
132C3×#235—22no—
133C3×#235—22no—
134C2×C3×D12—21no—
135C2×C3×D12—21no—
136C2×C3×D12D411yescharacteristic
137C2×C3×D12C2311yescharacteristic
138C2×C3×D12C2311yescharacteristic
139C2×C3×C4×D3—21no—
140C2×C3×C4×D3—21no—
141C2×C3×C4×D3—21no—
142C2×C3×C4×D3C2311yescharacteristic
143C2×C3×C4×D3C2311yescharacteristic
144C2×C3×Dic6D411yescharacteristic
145C2×C3×Dic6C2311yescharacteristic
146C32×SD16—22no—
147C32×SD16—22no—
148C2×C32×C8C2311yescharacteristic
149C2×C32×C8C2311yescharacteristic
150C32×C4⋊C4—21no—
151C32×C4⋊C4C2311yescharacteristic
152C32×C22⋊C4—21no—
153C3×#216—22no—
154C3×#215—22no—
155C3×#213—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×#204—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—31no—
173C2×C3×#41—31no—
174C2×C3×#41—31no—
175C2×C3×#41—31no—
176C2×C3×#41—31no—
177C2×C3×#41—61no—
178C22×C3×D4—21no—
179C22×C3×D4—31no—
180C22×C3×D4—31no—
181C22×C3×D4—61no—
182C22×C3×D4—61no—
183C22×C3×D4—61no—
184C22×C3×D4C2×D311yescharacteristic
185C22×C3×D4C22×C311yescharacteristic
186C22×#67—21no—
187C22×#67—21no—
188C2×#239C22×C311yescharacteristic, complemented
189#1004—24no—
190#1004—24no—
191C2×#237—21no—
192C2×#237C22×C311yescharacteristic
193C2×#237C22×C311yescharacteristic
194C2×D3×D4—21no—
195C2×D3×D4C22×C311yescharacteristic
196C2×D3×D4C22×C311yescharacteristic
197C2×#235C22×C311yescharacteristic
198C2×#235C22×C311yescharacteristic
199C3×AGL(1,ℤ/8)—64no—
200C3×#135—64no—
201C2×C3×Q16—31no—
202C2×C3×SD16—21no—
203C2×C3×SD16—21no—
204C2×C3×SD16—31no—
205C2×C3×SD16—31no—
206C2×C3×SD16C2×D311yescharacteristic, complemented
207C2×C3×SD16C2×D311yescharacteristic, complemented
208C2×C3×SD16C22×C311yescharacteristic, 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×#216C22×C311yescharacteristic, complemented
228C2×#215C22×C311yescharacteristic, complemented
229C2×#213C22×C311yescharacteristic, complemented
230C2×#213C22×C311yescharacteristic, complemented
231#930C22×C311yescharacteristic, complemented
232#916—24no—
233#914—24no—
234C2×D24C22×C311yescharacteristic, complemented
235C2×#204C22×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—31no—
245C3×#103—31no—
246C3×#102—21no—
247C3×#102—21no—
248C3×#102—31no—
249C3×#102—31no—
250C3×#102—31no—
251C3×#102—31no—
252C3×#102C2×D311yescharacteristic, complemented
253C3×#102C2×D311yescharacteristic, complemented
254C3×#102C22×C311yescharacteristic, 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#832C22×C311yescharacteristic, complemented
263#832C22×C311yescharacteristic, complemented
264#830C22×C311yescharacteristic, complemented
265#821C22×C311yescharacteristic, complemented
266(C2×D3)⋊C8C22×C311yescharacteristic, complemented
267(C2×D3)⋊C8C22×C311yescharacteristic, complemented
268#816C22×C311yescharacteristic, complemented
269#810C22×C311yescharacteristic, complemented
270#809C22×C311yescharacteristic, complemented
271C23×C32—24no—
272C23×C32—21no—
273C23×C32—21no—
274C23×C32—81no—
275C23×C32—81no—
276C23×C32C2×D411yescharacteristic
277C22×C3×D3—21no—
278C22×C3×D3—24no—
279C22×C3×D3—24no—
280C22×C3×D3—21no—
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×D4—24no—
290C32×D4—21no—
291C32×D4—21no—
292C32×D4C2×D412yes—
293C32×D4C2×D412yes—
294C2×C32×C4—21no—
295C2×C32×C4—21no—
296C2×C32×C4—21no—
297C2×C32×C4—21no—
298C2×C32×C4C2×D411yescharacteristic
299C2×C32×C4C2411yescharacteristic
300C3×#67—24no—
301C3×#67—24no—
302C3×#67—24no—
303C3×#67—22no—
304C3×#67—24no—
305C3×#67—22no—
306C3×#67—24no—
307C3×#67—81no—
308C2×C3×Dic3—24no—
309C2×C3×Dic3—21no—
310C2×C3×Dic3—24no—
311C2×C3×Dic3—21no—
312C2×C3×Dic3C2×D411yescharacteristic
313C2×C3×Dic3C2×D411yescharacteristic
314C3×D12—22no—
315C3×D12—21no—
316C3×D12—21no—
317C3×D12—21no—
318C3×D12—42no—
319C3×D12—81no—
320C3×D12C2×D412yes—
321C3×C4×D3—24no—
322C3×C4×D3—21no—
323C3×C4×D3—21no—
324C3×C4×D3—42no—
325C3×C4×D3—81no—
326C3×C4×D3C2×D412yes—
327C3×C4×D3C2×D412yes—
328C3×Dic6—21no—
329C3×Dic6—22no—
330C3×Dic6C2×D412yes—
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#452—31no—
341#450—31no—
342#450C3×D311yescharacteristic, complemented
343#449—31no—
344#449—31no—
345#447—31no—
346#447—31no—
347#417—31no—
348C2×#102—31no—
349#408—31no—
350C24×C3—21no—
351C24×C3—21no—
352C24×C3—41no—
353C24×C3—61no—
354C24×C3—61no—
355C23×D3—21no—
356C23×D3—21no—
357C3×#41—34no—
358C3×#41—62no—
359C3×#41—62no—
360C3×#41—62no—
361C3×#41—62no—
362C3×#41—62no—
363C3×#41—62no—
364C3×#41—62no—
365C3×#41—62no—
366C3×#41—68no—
367C3×#41—62no—
368C2×C3×Q8—21no—
369C2×C3×Q8—31no—
370C2×C3×Q8—31no—
371C2×C3×Q8C22×D311yescharacteristic
372C2×C3×Q8C23×C311yescharacteristic
373C2×C3×D4—22no—
374C2×C3×D4—22no—
375C2×C3×D4—22no—
376C2×C3×D4—22no—
377C2×C3×D4—21no—
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—41no—
388C2×C3×D4—42no—
389C2×C3×D4—42no—
390C2×C3×D4—61no—
391C2×C3×D4—61no—
392C2×C3×D4—62no—
393C2×C3×D4—61no—
394C2×C3×D4—61no—
395C2×C3×D4—62no—
396C2×C3×D4—68no—
397C2×C3×D4—61no—
398C2×C3×D4—61no—
399C2×C3×D4—68no—
400C2×C3×D4—68no—
401C2×C3×D4—61no—
402C2×C3×D4—62no—
403C2×C3×D4—61no—
404C2×C3×D4C22×D311yescharacteristic
405C2×C3×D4C22×D311yescharacteristic
406C2×C3×D4C23×C311yescharacteristic
407C2×C3×D4C23×C311yescharacteristic
408C22×C3×C4—21no—
409C22×C3×C4—31no—
410C22×C3×C4—31no—
411C22×C3×C4—61no—
412C22×C3×C4—61no—
413C22×C3×C4—61no—
414C22×C3×C4—61no—
415C22×C3×C4—61no—
416C22×C3×C4C22×D311yescharacteristic
417C22×C3×C4C23×C311yescharacteristic
418C2×#67—28no—
419C2×#67—28no—
420C2×#67—21no—
421C2×#67—21no—
422C2×#67—21no—
423C2×#67—21no—
424C2×#67—21no—
425C2×#67—21no—
426C2×#67C3×D411yescharacteristic
427C2×#67C3×D411yescharacteristic
428C22×Dic3—21no—
429C22×Dic3—21no—
430#239—22no—
431#239—22no—
432#237—28no—
433#237—22no—
434#237—22no—
435#237—22no—
436#237C3×D414yescomplemented
437D3×D4—28no—
438D3×D4—22no—
439D3×D4—22no—
440D3×D4—22no—
441D3×D4C3×D414yescomplemented
442#235—22no—
443#235—22no—
444#235—22no—
445#235—22no—
446C2×D12—21no—
447C2×D12—21no—
448C2×D12C3×D411yescharacteristic
449C2×D12C23×C311yescharacteristic
450C2×D12C23×C311yescharacteristic
451C2×C4×D3—21no—
452C2×C4×D3—21no—
453C2×C4×D3—21no—
454C2×C4×D3C23×C311yescharacteristic
455C2×C4×D3C23×C311yescharacteristic
456C2×Dic6C3×D411yescharacteristic
457C2×Dic6C23×C311yescharacteristic
458C3×Q16—62no—
459C3×SD16—22no—
460C3×SD16—22no—
461C3×SD16—22no—
462C3×SD16—22no—
463C3×SD16—42no—
464C3×SD16—42no—
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#216—22no—
496#215—22no—
497#213—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—
508#204—22no—
509ΓL(1,𝔽25)—22no—
510D3×C8—22no—
511C22×C32—21no—
512C22×C32—22no—
513C22×C32—22no—
514C22×C32—21no—
515C22×C32—21no—
516C22×C32—41no—
517C22×C32—41no—
518C22×C32—41no—
519C22×C32—41no—
520C22×C32—84no—
521C22×C32C22×D411yescharacteristic
522C2×C3×D3—21no—
523C2×C3×D3—21no—
524C2×C3×D3—21no—
525C2×C3×D3—22no—
526C2×C3×D3—21no—
527C2×C3×D3—21no—
528C2×C3×D3—41no—
529C2×C3×D3—41no—
530C2×C3×D3—41no—
531C2×C3×D3—41no—
532C2×C3×D3—41no—
533C2×C3×D3—84no—
534C2×C3×D3—84no—
535C2×C3×D3#12012yes—
536C32×C4—21no—
537C32×C4—41no—
538C32×C4—41no—
539C32×C4C22×D411yescharacteristic
540C32×C4C22×D411yescharacteristic
541C3×Dic3—21no—
542C3×Dic3—22no—
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—31no—
552C2×#41—61no—
553C22×D4—31no—
554C22×D4—31no—
555C22×D4—61no—
556C22×D4—61no—
557C22×D4—61no—
558C22×D4C2×C3×D311yescharacteristic
559AGL(1,ℤ/8)—64no—
560#135—64no—
561C2×Q16—31no—
562C2×SD16—31no—
563C2×SD16—31no—
564C2×SD16C2×C3×D311yescharacteristic, complemented
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#103—31no—
582#102—31no—
583#102—31no—
584#102—31no—
585#102—31no—
586#102C2×C3×D311yescharacteristic, complemented
587#102C2×C3×D311yescharacteristic, complemented
588C22⋊C8—31no—
589C22⋊C8—31no—
590C22⋊C8—31no—
591C22⋊C8C2×C3×D311yescharacteristic, complemented
592C23×C3—24no—
593C23×C3—24no—
594C23×C3—21no—
595C23×C3—21no—
596C23×C3—21no—
597C23×C3—21no—
598C23×C3—21no—
599C23×C3—31no—
600C23×C3—31no—
601C23×C3—41no—
602C23×C3—41no—
603C23×C3—44no—
604C23×C3—64no—
605C23×C3—64no—
606C23×C3—61no—
607C23×C3—61no—
608C23×C3—81no—
609C23×C3—81no—
610C23×C3—81no—
611C23×C3—81no—
612C23×C3—82no—
613C23×C3—82no—
614C23×C3—241no—
615C23×C3—241no—
616C23×C3—241no—
617C23×C3—241no—
618C23×C3D3×D411yescharacteristic
619C23×C3C2×C3×D411yescharacteristic
620C22×D3—21no—
621C22×D3—24no—
622C22×D3—24no—
623C22×D3—21no—
624C22×D3—81no—
625C22×D3—81no—
626C22×D3—81no—
627C22×D3—81no—
628C22×D3C2×C3×D411yescharacteristic
629C22×D3C2×C3×D411yescharacteristic
630C3×Q8—21no—
631C3×Q8—21no—
632C3×Q8—21no—
633C3×Q8—21no—
634C3×Q8—32no—
635C3×Q8—41no—
636C3×Q8—41no—
637C3×Q8—62no—
638C3×Q8—61no—
639C3×D4—24no—
640C3×D4—24no—
641C3×D4—21no—
642C3×D4—21no—
643C3×D4—21no—
644C3×D4—21no—
645C3×D4—22no—
646C3×D4—22no—
647C3×D4—32no—
648C3×D4—41no—
649C3×D4—41no—
650C3×D4—44no—
651C3×D4—62no—
652C3×D4—62no—
653C3×D4—64no—
654C3×D4—62no—
655C3×D4—64no—
656C3×D4—64no—
657C3×D4—64no—
658C3×D4—64no—
659C3×D4—61no—
660C3×D4—61no—
661C3×D4—61no—
662C3×D4—122no—
663C3×D4—241no—
664C3×D4—241no—
665C3×D4D3×D412yes—
666C3×D4D3×D412yes—
667C3×D4C2×C3×D412yes—
668C3×D4C2×C3×D412yes—
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—41no—
687C2×C3×C4—64no—
688C2×C3×C4—64no—
689C2×C3×C4—64no—
690C2×C3×C4—61no—
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—24no—
702#67—24no—
703#67—22no—
704#67—24no—
705#67—22no—
706#67—24no—
707#67—81no—
708C2×Dic3—24no—
709C2×Dic3—21no—
710C2×Dic3—24no—
711C2×Dic3—21no—
712C2×Dic3C2×C3×D411yescharacteristic
713C2×Dic3C2×C3×D411yescharacteristic
714D12—22no—
715D12—21no—
716D12—21no—
717D12—21no—
718D12—42no—
719D12—81no—
720D12C2×C3×D412yes—
721C4×D3—24no—
722C4×D3—21no—
723C4×D3—21no—
724C4×D3—42no—
725C4×D3—81no—
726C4×D3C2×C3×D412yes—
727C4×D3C2×C3×D412yes—
728Dic6—21no—
729Dic6—22no—
730Dic6C2×C3×D412yes—
731C3×C8—21no—
732C3×C8—21no—
733C3×C8—21no—
734C3×C8—21no—
735C3×C8—41no—
736C3×C8—41no—
737C3×C8—61no—
738C3×C8—61no—
739C3⋊C8—21no—
740C3⋊C8—21no—
741C2×C32—41no—
742C2×C32—42no—
743C2×C32—42no—
744C2×C32C2×#12011yescharacteristic
745C2×C32#57611yescharacteristic
746C2×C32#57711yescharacteristic
747C3×D3—22no—
748C3×D3—41no—
749C3×D3—42no—
750C3×D3—81no—
751C24—21no—
752C24—61no—
753C24—61no—
754#41—34no—
755#41—62no—
756#41—62no—
757#41—62no—
758#41—62no—
759#41—62no—
760#41—62no—
761#41—62no—
762#41—62no—
763#41—68no—
764#41—62no—
765C2×Q8—31no—
766C2×Q8—31no—
767C2×Q8C22×C3×D311yescharacteristic
768C2×D4—22no—
769C2×D4—22no—
770C2×D4—21no—
771C2×D4—34no—
772C2×D4—31no—
773C2×D4—31no—
774C2×D4—31no—
775C2×D4—31no—
776C2×D4—31no—
777C2×D4—61no—
778C2×D4—61no—
779C2×D4—62no—
780C2×D4—61no—
781C2×D4—61no—
782C2×D4—62no—
783C2×D4—68no—
784C2×D4—61no—
785C2×D4—61no—
786C2×D4—68no—
787C2×D4—68no—
788C2×D4—61no—
789C2×D4—62no—
790C2×D4—61no—
791C2×D4C22×C3×D311yescharacteristic
792C2×D4C22×C3×D311yescharacteristic
793C22×C4—31no—
794C22×C4—31no—
795C22×C4—61no—
796C22×C4—61no—
797C22×C4—61no—
798C22×C4—61no—
799C22×C4—61no—
800C22×C4C22×C3×D311yescharacteristic
801Q16—62no—
802SD16—22no—
803SD16—22no—
804SD16—62no—
805SD16—62no—
806D8—62no—
807D8—62no—
808D8—62no—
809M16—62no—
810C2×C8—31no—
811C2×C8—31no—
812C2×C8—62no—
813C2×C8C22×C3×D311yescharacteristic
814C2×C8C22×C3×D311yescharacteristic
815C4⋊C4—21no—
816C4⋊C4—31no—
817C4⋊C4—61no—
818C4⋊C4—61no—
819C4⋊C4C22×C3×D311yescharacteristic
820C22⋊C4—21no—
821C22⋊C4—61no—
822C22⋊C4—61no—
823C22⋊C4—61no—
824C22×C3—22no—
825C22×C3—21no—
826C22×C3—21no—
827C22×C3—21no—
828C22×C3—21no—
829C22×C3—21no—
830C22×C3—22no—
831C22×C3—22no—
832C22×C3—22no—
833C22×C3—22no—
834C22×C3—21no—
835C22×C3—21no—
836C22×C3—32no—
837C22×C3—41no—
838C22×C3—41no—
839C22×C3—42no—
840C22×C3—42no—
841C22×C3—41no—
842C22×C3—41no—
843C22×C3—41no—
844C22×C3—41no—
845C22×C3—41no—
846C22×C3—41no—
847C22×C3—41no—
848C22×C3—41no—
849C22×C3—61no—
850C22×C3—61no—
851C22×C3—61no—
852C22×C3—61no—
853C22×C3—62no—
854C22×C3—61no—
855C22×C3—81no—
856C22×C3—81no—
857C22×C3—81no—
858C22×C3—81no—
859C22×C3—84no—
860C22×C3—84no—
861C22×C3—88no—
862C22×C3—121no—
863C22×C3—121no—
864C22×C3—121no—
865C22×C3—121no—
866C22×C3—121no—
867C22×C3—244no—
868C22×C3—244no—
869C22×C3C2×D3×D411yescharacteristic
870C22×C3C22×C3×D411yescharacteristic
871C2×D3—21no—
872C2×D3—21no—
873C2×D3—21no—
874C2×D3—21no—
875C2×D3—21no—
876C2×D3—22no—
877C2×D3—41no—
878C2×D3—41no—
879C2×D3—41no—
880C2×D3—41no—
881C2×D3—41no—
882C2×D3—84no—
883C2×D3—84no—
884C2×D3C3×#12012yes—
885C3×C4—21no—
886C3×C4—21no—
887C3×C4—21no—
888C3×C4—21no—
889C3×C4—32no—
890C3×C4—41no—
891C3×C4—41no—
892C3×C4—41no—
893C3×C4—41no—
894C3×C4—41no—
895C3×C4—61no—
896C3×C4—62no—
897C3×C4—81no—
898C3×C4—81no—
899C3×C4—121no—
900C3×C4C2×D3×D411yescharacteristic
901C3×C4C2×D3×D411yescharacteristic
902C3×C4C22×C3×D411yescharacteristic
903C3×C4C22×C3×D411yescharacteristic
904Dic3—21no—
905Dic3—22no—
906Dic3—41no—
907Dic3C3×#12012yes—
908C32#301211yescharacteristic, complemented, Sylow
909C23—24no—
910C23—21no—
911C23—21no—
912C23—31no—
913C23—31no—
914C23—64no—
915C23—64no—
916C23—61no—
917C23—61no—
918C23—81no—
919C23—81no—
920C23—241no—
921C23—241no—
922C23—241no—
923C23—241no—
924C23C3×D3×D411yescharacteristic
925Q8—21no—
926Q8—21no—
927Q8—32no—
928Q8—62no—
929Q8—61no—
930D4—24no—
931D4—21no—
932D4—21no—
933D4—32no—
934D4—62no—
935D4—62no—
936D4—64no—
937D4—62no—
938D4—64no—
939D4—64no—
940D4—64no—
941D4—64no—
942D4—61no—
943D4—61no—
944D4—61no—
945D4—122no—
946D4—241no—
947D4—241no—
948D4C3×D3×D412yes—
949D4C3×D3×D412yes—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—21no—
954C2×C4—31no—
955C2×C4—32no—
956C2×C4—32no—
957C2×C4—31no—
958C2×C4—64no—
959C2×C4—64no—
960C2×C4—64no—
961C2×C4—61no—
962C2×C4—61no—
963C2×C4—61no—
964C2×C4—61no—
965C2×C4—122no—
966C2×C4—241no—
967C2×C4C3×D3×D411yescharacteristic
968C2×C4C23×C3×D311yescharacteristic
969C8—21no—
970C8—21no—
971C8—61no—
972C8—61no—
973C2×C3—21no—
974C2×C3—21no—
975C2×C3—21no—
976C2×C3—42no—
977C2×C3—41no—
978C2×C3—42no—
979C2×C3—42no—
980C2×C3—42no—
981C2×C3—42no—
982C2×C3—41no—
983C2×C3—62no—
984C2×C3—82no—
985C2×C3—82no—
986C2×C3—121no—
987C2×C3—122no—
988C2×C3—241no—
989C2×C3D3×#12011yescharacteristic
990C2×C3#576211yescharacteristic
991C2×C3#577411yescharacteristic
992C2×C3C2×C3×#12011yescharacteristic
993C2×C3C3×#57611yescharacteristic
994C2×C3C3×#57711yescharacteristic
995D3—22no—
996D3—41no—
997D3—42no—
998D3—81no—
999C22—21no—
1000C22—21no—
1001C22—21no—
1002C22—22no—
1003C22—22no—
1004C22—32no—
1005C22—41no—
1006C22—41no—
1007C22—41no—
1008C22—41no—
1009C22—61no—
1010C22—61no—
1011C22—61no—
1012C22—61no—
1013C22—62no—
1014C22—61no—
1015C22—84no—
1016C22—121no—
1017C22—121no—
1018C22—121no—
1019C22—121no—
1020C22—121no—
1021C22—244no—
1022C22—244no—
1023C22C2×C3×D3×D411yescharacteristic
1024C4—21no—
1025C4—32no—
1026C4—41no—
1027C4—41no—
1028C4—61no—
1029C4—62no—
1030C4—121no—
1031C4C2×C3×D3×D411yescharacteristic
1032C4C2×C3×D3×D411yescharacteristic
1033C3—21no—
1034C3#8014911yescharacteristic, direct product factor
1035C3C3×#301211yescharacteristic, complemented
1036C2—41no—
1037C2—42no—
1038C2—42no—
1039C2—62no—
1040C2—121no—
1041C2—122no—
1042C2—241no—
1043C2C3×D3×#12011yescharacteristic
1044C2C3×#576211yescharacteristic
1045C2C3×#577411yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#450C2
socleC22×C32C22×D4
hypercenterC3×#450D3
hypocenterC3C3×#3012
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#450

Complements

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

NH ≅ G/Ntype
1. C2×C3×#1004C2semidirect
2. C2×C3×#916C2semidirect
3. C2×C3×#914C2semidirect
4. C3×#5629C2semidirect
5. C32×#450C2semidirect
6. C3×#5217C2semidirect
7. C3×#5173C2semidirect
8. C3×#5169C2semidirect
9. C3×#5047C2semidirect
10. C3×#4781C2semidirect
11. C3×#4773C2semidirect
12. C3×#4771C2semidirect
13. C3×D3×#102C2semidirect
14. C3×#4734C2semidirect
15. C3×#4727C2semidirect
17. #80149C3direct (N × H)
21. C2×C3×#239C22semidirect
32. C2×C32×SD16C22semidirect
33. C2×C32×SD16C22semidirect
34. C32×C22⋊Q8C22semidirect
35. C3×#946C22semidirect
36. C2×C3×#216C22semidirect
37. C2×C3×#215C22semidirect
38. C2×C3×#213C22semidirect
39. C2×C3×#213C22semidirect
40. C3×#930C22semidirect
43. C2×C3×D24C22semidirect
44. C2×C3×#204C22semidirect
45. C2×C3×ΓL(1,𝔽25)C22semidirect
46. C2×C3×D3×C8C22semidirect
49. C3×#895C22semidirect
50. C3×D3×C4⋊C4C22semidirect
53. C32×#102C22semidirect
54. C32×#102C22semidirect
55. C32×C22⋊C8C22semidirect
56. C3×#832C22semidirect
57. C3×#832C22semidirect
58. C3×#830C22semidirect
59. C3×#821C22semidirect
60. C3×(C2×D3)⋊C8C22semidirect
61. C3×(C2×D3)⋊C8C22semidirect
62. C3×#816C22semidirect
63. C3×#810C22semidirect
64. C3×#809C22semidirect
66. C2×#1004C2×C3semidirect
70. C2×#916C2×C3semidirect
71. C2×#914C2×C3semidirect
72. #5629C2×C3semidirect
77. C3×#450D3semidirect
78. C3×#450C2×C3semidirect
86. #5217C2×C3semidirect
87. #5173C2×C3semidirect
88. #5169C2×C3semidirect
89. #5047C2×C3semidirect
90. #4781C2×C3semidirect
91. #4773C2×C3semidirect
92. #4771C2×C3semidirect
93. D3×#102C2×C3semidirect
94. #4734C2×C3semidirect
95. #4727C2×C3semidirect
124. C3×#237D4semidirect
129. C3×D3×D4D4semidirect
188. C2×#239C22×C3semidirect
206. C2×C3×SD16C2×D3semidirect
207. C2×C3×SD16C2×D3semidirect
208. C2×C3×SD16C22×C3semidirect
209. C2×C3×SD16C22×C3semidirect
218. C3×C22⋊Q8C2×D3semidirect
219. C3×C22⋊Q8C22×C3semidirect
226. #946C22×C3semidirect
227. C2×#216C22×C3semidirect
228. C2×#215C22×C3semidirect
229. C2×#213C22×C3semidirect
230. C2×#213C22×C3semidirect
231. #930C22×C3semidirect
234. C2×D24C22×C3semidirect
235. C2×#204C22×C3semidirect
236. C2×ΓL(1,𝔽25)C22×C3semidirect
237. C2×D3×C8C22×C3semidirect
240. #895C22×C3semidirect
241. D3×C4⋊C4C22×C3semidirect
252. C3×#102C2×D3semidirect
253. C3×#102C2×D3semidirect
254. C3×#102C22×C3semidirect
255. C3×#102C22×C3semidirect
260. C3×C22⋊C8C2×D3semidirect
261. C3×C22⋊C8C22×C3semidirect
262. #832C22×C3semidirect
263. #832C22×C3semidirect
264. #830C22×C3semidirect
265. #821C22×C3semidirect
266. (C2×D3)⋊C8C22×C3semidirect
267. (C2×D3)⋊C8C22×C3semidirect
268. #816C22×C3semidirect
269. #810C22×C3semidirect
270. #809C22×C3semidirect
342. #450C3×D3semidirect
436. #237C3×D4semidirect
441. D3×D4C3×D4semidirect
564. C2×SD16C2×C3×D3semidirect
565. C2×SD16C2×C3×D3semidirect
573. C22⋊Q8C2×C3×D3semidirect
586. #102C2×C3×D3semidirect
587. #102C2×C3×D3semidirect
591. C22⋊C8C2×C3×D3semidirect
908. C32#3012semidirect
1034. C3#80149direct (N × H)
1035. C3C3×#3012semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10042
C2×C3×#9162
C2×C3×#9142
C3×#56292
C32×#4502
C3×#52172
C3×#51732
C3×#51692
C3×#50472
C3×#47812
C3×#47732
C3×#47712
C3×D3×#1022
C3×#47342
C3×#47272
C3×#30123
#801493