Finite Group Databasebeta

← C3×#82916 #11859319

Subgroups — C3×#82916 #11859319

Order 1152.

1205 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#525C211yesmaximal, characteristic
2C2×C3×#948C211yesmaximal, characteristic, complemented
3C23×C3×C3⋊C8C211yesmaximal, characteristic, complemented
4C3×#5234C211yesmaximal, characteristic, complemented
5C3×#5207C211yesmaximal, characteristic, complemented
6C3×#5011C214yesmaximal, complemented
7C3×D4×C3⋊C8C214yesmaximal, complemented
8C3×#4999C211yesmaximal, characteristic, complemented
9C3×#4997C211yesmaximal, characteristic, complemented
10C3×#2929—31nomaximal
11#82916C311yesmaximal, characteristic, direct product factor
12C2×C32×#41C2211yescharacteristic
13C23×C32×C4C2211yescharacteristic
14C32×#123C412yes—
15C32×C22⋊Q8C412yes—
16C32×#121C412yes—
17C32×#120C412yes—
18C32×C4×D4C2214yes—
19C32×#117C2211yescharacteristic
20C3×#948—24no—
21C2×C3×#208C2211yescharacteristic
22C2×C3×#208C2211yescharacteristic
23C2×C3×#208C2212yescomplemented
24C22×C3×C3⋊C8—24no—
25C22×C3×C3⋊C8C2211yescharacteristic
26C22×C3×C3⋊C8C2212yes—
27C22×C3×C3⋊C8C2212yes—
28C22×C3×C3⋊C8C2211yescharacteristic
29C22×C3×C3⋊C8C2212yescomplemented
30C3×#830C2214yes—
31C3×#830C2214yescomplemented
32C3×C4⋊(C3⋊C8)C2214yescomplemented
33C3×#803C2212yescomplemented
34C3×C4×C3⋊C8C2212yescomplemented
35C2×C3×#131—31no—
36C23×C3×C8—31no—
37C3×#525—21no—
38C3×#525D311yescharacteristic
39C3×#525C2×C311yescharacteristic
40C2×#948C2×C311yescharacteristic, complemented
41C23×C3⋊C8C2×C311yescharacteristic, complemented
42C3×#435—34no—
43C3×C8×D4—34no—
44C3×#424—31no—
45C3×#408—31no—
46C3×#407—31no—
47C3×#405—31no—
48#5234C2×C311yescharacteristic, complemented
49#5207C2×C311yescharacteristic, complemented
50#5011C2×C314yescomplemented
51D4×C3⋊C8C2×C314yescomplemented
52#4999C2×C311yescharacteristic, complemented
53#4997C2×C311yescharacteristic, complemented
54C24×C32C2×C411yescharacteristic
55C32×#41—22no—
56C32×#41—22no—
57C2×C32×Q8C2×C411yescharacteristic
58C2×C32×D4C2×C412yes—
59C2×C32×D4C2×C411yescharacteristic
60C2×C32×D4C2×C414yes—
61C22×C32×C4—22no—
62C22×C32×C4—22no—
63C22×C32×C4C2×C412yes—
64C22×C32×C4C2×C411yescharacteristic
65C22×C32×C4C2312yes—
66C22×C32×C4C2312yes—
67C22×C32×C4C2311yescharacteristic
68C32×C4⋊C4C2×C412yes—
69C32×C4⋊C4C2×C414yes—
70C32×C22⋊C4C2×C412yes—
71C32×C22⋊C4C2×C414yes—
72C32×C22⋊C4C2×C414yes—
73C32×C42C2312yes—
74C3×#208—22no—
75C3×#208—22no—
76C3×#208—24no—
77C2×C3×C3⋊C8—22no—
78C2×C3×C3⋊C8—24no—
79C2×C3×C3⋊C8—24no—
80C2×C3×C3⋊C8—24no—
81C2×C3×C3⋊C8D414yescomplemented
82C2×C3×C3⋊C8C2312yes—
83C2×C3×C3⋊C8C2312yes—
84C2×C3×C3⋊C8C2312yes—
85C2×C3×C3⋊C8C2311yescharacteristic
86C2×C3×C3⋊C8C2311yescharacteristic
87#2929—31noSylow
88C2×C3×#41—21no—
89C2×C3×#41C2×D311yescharacteristic
90C2×C3×#41C22×C311yescharacteristic
91C23×C3×C4—21no—
92C23×C3×C4C2×D311yescharacteristic
93C23×C3×C4C22×C311yescharacteristic
94C3×#131—64no—
95C2×C3×M16—31no—
96C2×C3×M16—32no—
97C2×C3×M16—31no—
98C22×C3×C8—31no—
99C22×C3×C8—31no—
100C22×C3×C8—32no—
101C22×C3×C8—32no—
102C22×C3×C8—32no—
103C22×C3×C8—64no—
104C3×#123—22no—
105C3×#123Dic312yes—
106C3×#123C3×C412yes—
107C3×C22⋊Q8—22no—
108C3×C22⋊Q8Dic312yes—
109C3×C22⋊Q8C3×C412yes—
110C3×#121—22no—
111C3×#121Dic312yes—
112C3×#121C3×C412yes—
113C3×#120—22no—
114C3×#120Dic312yes—
115C3×#120C3×C412yes—
116C3×C4×D4—24no—
117C3×C4×D4C2×D314yes—
118C3×C4×D4C22×C314yes—
119C3×#117—21no—
120C3×#117C2×D311yescharacteristic
121C3×#117C22×C311yescharacteristic
122#948—24no—
123C2×#208C22×C311yescharacteristic
124C2×#208C22×C311yescharacteristic
125C2×#208C22×C312yescomplemented
126C22×C3⋊C8—24no—
127C22×C3⋊C8C22×C311yescharacteristic
128C22×C3⋊C8C22×C312yes—
129C22×C3⋊C8C22×C312yes—
130C22×C3⋊C8C22×C311yescharacteristic
131C22×C3⋊C8C22×C312yescomplemented
132C3×C4⋊C8—34no—
133C3×C22⋊C8—34no—
134C3×C22⋊C8—34no—
135C3×#97—32no—
136C3×C4×C8—32no—
137#830C22×C314yes—
138#830C22×C314yescomplemented
139C4⋊(C3⋊C8)C22×C314yescomplemented
140#803C22×C312yescomplemented
141C4×C3⋊C8C22×C312yescomplemented
142C23×C32—22no—
143C23×C32—24no—
144C23×C32C22×C412yes—
145C23×C32C22×C411yescharacteristic
146C23×C32C22×C412yes—
147C32×Q8—22no—
148C32×D4—24no—
149C32×D4—28no—
150C32×D4—22no—
151C2×C32×C4—22no—
152C2×C32×C4—24no—
153C2×C32×C4—22no—
154C2×C32×C4—22no—
155C2×C32×C4—22no—
156C2×C32×C4—22no—
157C2×C32×C4C22×C414yes—
158C2×C32×C4C22×C412yes—
159C2×C32×C4C22×C412yes—
160C2×C32×C4C22×C411yescharacteristic
161C2×C32×C4C2×D412yes—
162C2×C32×C4#4112yes—
163C2×C32×C4C2411yescharacteristic
164C3×C3⋊C8—22no—
165C3×C3⋊C8—22no—
166C3×C3⋊C8—22no—
167C3×C3⋊C8C2×D412yes—
168C3×C3⋊C8C2×D412yes—
169C2×#131—31no—
170C23×C8—31no—
171#525C3×D311yescharacteristic
172#435—34no—
173C8×D4—34no—
174#424—31no—
175#408—31no—
176#407—31no—
177#405—31no—
178C24×C3—21no—
179C24×C3C2×Dic311yescharacteristic
180C24×C3C2×C3×C411yescharacteristic
181C3×#41—22no—
182C3×#41—22no—
183C3×#41—22no—
184C3×#41—22no—
185C3×#41—42no—
186C3×#41—42no—
187C2×C3×Q8—21no—
188C2×C3×Q8C2×Dic311yescharacteristic
189C2×C3×Q8C2×C3×C411yescharacteristic
190C2×C3×D4—24no—
191C2×C3×D4—22no—
192C2×C3×D4—21no—
193C2×C3×D4C2×Dic314yes—
194C2×C3×D4C2×Dic312yes—
195C2×C3×D4C2×Dic311yescharacteristic
196C2×C3×D4C2×C3×C414yes—
197C2×C3×D4C2×C3×C412yes—
198C2×C3×D4C2×C3×C411yescharacteristic
199C22×C3×C4—22no—
200C22×C3×C4—22no—
201C22×C3×C4—22no—
202C22×C3×C4—22no—
203C22×C3×C4—22no—
204C22×C3×C4—21no—
205C22×C3×C4—21no—
206C22×C3×C4—22no—
207C22×C3×C4—22no—
208C22×C3×C4—42no—
209C22×C3×C4—42no—
210C22×C3×C4C2×Dic312yes—
211C22×C3×C4C2×Dic311yescharacteristic
212C22×C3×C4C2×C3×C412yes—
213C22×C3×C4C2×C3×C411yescharacteristic
214C22×C3×C4C22×D312yes—
215C22×C3×C4C22×D312yes—
216C22×C3×C4C22×D311yescharacteristic
217C22×C3×C4C23×C312yes—
218C22×C3×C4C23×C312yes—
219C22×C3×C4C23×C311yescharacteristic
220C3×M16—64no—
221C3×M16—62no—
222C3×M16—62no—
223C2×C3×C8—34no—
224C2×C3×C8—31no—
225C2×C3×C8—31no—
226C2×C3×C8—32no—
227C2×C3×C8—32no—
228C2×C3×C8—32no—
229C2×C3×C8—64no—
230C2×C3×C8—64no—
231C2×C3×C8—64no—
232C2×C3×C8—62no—
233C3×C4⋊C4—22no—
234C3×C4⋊C4—24no—
235C3×C4⋊C4C2×Dic312yes—
236C3×C4⋊C4C2×Dic314yes—
237C3×C4⋊C4C2×C3×C412yes—
238C3×C4⋊C4C2×C3×C414yes—
239C3×C22⋊C4—22no—
240C3×C22⋊C4—24no—
241C3×C22⋊C4—24no—
242C3×C22⋊C4C2×Dic312yes—
243C3×C22⋊C4C2×Dic314yes—
244C3×C22⋊C4C2×Dic314yes—
245C3×C22⋊C4C2×C3×C412yes—
246C3×C22⋊C4C2×C3×C414yes—
247C3×C22⋊C4C2×C3×C414yes—
248C3×C42—22no—
249C3×C42C22×D312yes—
250C3×C42C23×C312yes—
251#208—22no—
252#208—22no—
253#208—24no—
254C2×C3⋊C8—22no—
255C2×C3⋊C8—24no—
256C2×C3⋊C8—24no—
257C2×C3⋊C8—24no—
258C2×C3⋊C8C3×D414yescomplemented
259C2×C3⋊C8C23×C312yes—
260C2×C3⋊C8C23×C312yes—
261C2×C3⋊C8C23×C312yes—
262C2×C3⋊C8C23×C311yescharacteristic
263C2×C3⋊C8C23×C311yescharacteristic
264C22×C32—28no—
265C22×C32—22no—
266C22×C32—22no—
267C22×C32—22no—
268C22×C32—22no—
269C22×C32—24no—
270C22×C32C4×D412yes—
271C22×C32#13114yescomplemented
272C22×C32C23×C411yescharacteristic
273C32×C4—22no—
274C32×C4—22no—
275C32×C4—24no—
276C32×C4C4×D412yes—
277C32×C4C22×D411yescharacteristic
278C32×C4C2×#4111yescharacteristic
279C2×#41C2×C3×D311yescharacteristic
280C23×C4C2×C3×D311yescharacteristic
281#131—64no—
282C2×M16—31no—
283C2×M16—32no—
284C2×M16—31no—
285C22×C8—31no—
286C22×C8—31no—
287C22×C8—32no—
288C22×C8—32no—
289C22×C8—32no—
290C22×C8—64no—
291#123C3×Dic312yes—
292C22⋊Q8C3×Dic312yes—
293#121C3×Dic312yes—
294#120C3×Dic312yes—
295C4×D4C2×C3×D314yes—
296#117C2×C3×D311yescharacteristic
297C4⋊C8—34no—
298C22⋊C8—34no—
299C22⋊C8—34no—
300#97—32no—
301C4×C8—32no—
302C23×C3—22no—
303C23×C3—24no—
304C23×C3—22no—
305C23×C3—24no—
306C23×C3—21no—
307C23×C3—22no—
308C23×C3—22no—
309C23×C3—42no—
310C23×C3—44no—
311C23×C3C22×Dic312yes—
312C23×C3C22×Dic311yescharacteristic
313C23×C3C22×Dic312yes—
314C23×C3C22×C3×C412yes—
315C23×C3C22×C3×C411yescharacteristic
316C23×C3C22×C3×C412yes—
317C3×Q8—22no—
318C3×Q8—22no—
319C3×Q8—42no—
320C3×D4—24no—
321C3×D4—28no—
322C3×D4—24no—
323C3×D4—28no—
324C3×D4—22no—
325C3×D4—22no—
326C3×D4—42no—
327C3×D4—48no—
328C3×D4—44no—
329C2×C3×C4—22no—
330C2×C3×C4—22no—
331C2×C3×C4—24no—
332C2×C3×C4—24no—
333C2×C3×C4—22no—
334C2×C3×C4—22no—
335C2×C3×C4—22no—
336C2×C3×C4—22no—
337C2×C3×C4—22no—
338C2×C3×C4—22no—
339C2×C3×C4—22no—
340C2×C3×C4—22no—
341C2×C3×C4—21no—
342C2×C3×C4—22no—
343C2×C3×C4—22no—
344C2×C3×C4—21no—
345C2×C3×C4—24no—
346C2×C3×C4—22no—
347C2×C3×C4—22no—
348C2×C3×C4—44no—
349C2×C3×C4—42no—
350C2×C3×C4—42no—
351C2×C3×C4—42no—
352C2×C3×C4—42no—
353C2×C3×C4—42no—
354C2×C3×C4D3×D412yes—
355C2×C3×C4#23712yes—
356C2×C3×C4C22×Dic314yes—
357C2×C3×C4C22×Dic312yes—
358C2×C3×C4C22×Dic312yes—
359C2×C3×C4C22×Dic311yescharacteristic
360C2×C3×C4C22×C3×C414yes—
361C2×C3×C4C22×C3×C412yes—
362C2×C3×C4C22×C3×C412yes—
363C2×C3×C4C22×C3×C411yescharacteristic
364C2×C3×C4C2×C3×D412yes—
365C2×C3×C4C3×#4112yes—
366C2×C3×C4C23×D311yescharacteristic
367C2×C3×C4C24×C311yescharacteristic
368C3×C8—32no—
369C3×C8—32no—
370C3×C8—62no—
371C3×C8—62no—
372C3×C8—62no—
373C3⋊C8—22no—
374C3⋊C8—22no—
375C3⋊C8—22no—
376C3⋊C8C2×C3×D412yes—
377C3⋊C8C2×C3×D412yes—
378C2×C32—22no—
379C2×C32—24no—
380C2×C32—42no—
381C2×C32C2×C4×D411yescharacteristic
382C2×C32C2×#13112yes—
383C24C2×C3×Dic311yescharacteristic
384#41—22no—
385#41—22no—
386C2×Q8C2×C3×Dic311yescharacteristic
387C2×D4C2×C3×Dic314yes—
388C2×D4C2×C3×Dic312yes—
389C2×D4C2×C3×Dic311yescharacteristic
390C22×C4—22no—
391C22×C4—22no—
392C22×C4C2×C3×Dic312yes—
393C22×C4C2×C3×Dic311yescharacteristic
394C22×C4C22×C3×D312yes—
395C22×C4C22×C3×D312yes—
396C22×C4C22×C3×D311yescharacteristic
397M16—64no—
398M16—62no—
399M16—62no—
400C2×C8—31no—
401C2×C8—31no—
402C2×C8—34no—
403C2×C8—32no—
404C2×C8—32no—
405C2×C8—32no—
406C2×C8—64no—
407C2×C8—64no—
408C2×C8—64no—
409C2×C8—62no—
410C4⋊C4C2×C3×Dic312yes—
411C4⋊C4C2×C3×Dic314yes—
412C22⋊C4C2×C3×Dic312yes—
413C22⋊C4C2×C3×Dic314yes—
414C22⋊C4C2×C3×Dic314yes—
415C42C22×C3×D312yes—
416C22×C3—28no—
417C22×C3—28no—
418C22×C3—22no—
419C22×C3—22no—
420C22×C3—22no—
421C22×C3—22no—
422C22×C3—22no—
423C22×C3—22no—
424C22×C3—24no—
425C22×C3—22no—
426C22×C3—24no—
427C22×C3—22no—
428C22×C3—22no—
429C22×C3—24no—
430C22×C3—21no—
431C22×C3—42no—
432C22×C3—42no—
433C22×C3—42no—
434C22×C3—42no—
435C22×C3—44no—
436C22×C3—48no—
437C22×C3D4×Dic312yes—
438C22×C3#94814yescomplemented
439C22×C3C3×C4×D412yes—
440C22×C3C3×#13114yescomplemented
441C22×C3C23×Dic311yescharacteristic
442C22×C3C23×C3×C411yescharacteristic
443C3×C4—24no—
444C3×C4—22no—
445C3×C4—22no—
446C3×C4—24no—
447C3×C4—22no—
448C3×C4—22no—
449C3×C4—22no—
450C3×C4—21no—
451C3×C4—21no—
452C3×C4—42no—
453C3×C4—42no—
454C3×C4—44no—
455C3×C4D4×Dic312yes—
456C3×C4C3×C4×D412yes—
457C3×C4C2×D3×D411yescharacteristic
458C3×C4C2×#23711yescharacteristic
459C3×C4C22×C3×D411yescharacteristic
460C3×C4C2×C3×#4111yescharacteristic
461C32#292911yescharacteristic, complemented, Sylow
462C23—22no—
463C23—24no—
464C23C22×C3×Dic312yes—
465C23C22×C3×Dic311yescharacteristic
466C23C22×C3×Dic312yes—
467Q8—22no—
468D4—24no—
469D4—28no—
470D4—22no—
471C2×C4—22no—
472C2×C4—24no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4C3×D3×D412yes—
478C2×C4C3×#23712yes—
479C2×C4C22×C3×Dic314yes—
480C2×C4C22×C3×Dic312yes—
481C2×C4C22×C3×Dic312yes—
482C2×C4C22×C3×Dic311yescharacteristic
483C2×C4C23×C3×D311yescharacteristic
484C8—32no—
485C8—32no—
486C8—62no—
487C8—62no—
488C8—62no—
489C2×C3—22no—
490C2×C3—24no—
491C2×C3—22no—
492C2×C3—24no—
493C2×C3—21no—
494C2×C3—22no—
495C2×C3—42no—
496C2×C3—44no—
497C2×C3—42no—
498C2×C3—42no—
499C2×C3—82no—
500C2×C3C2×D4×Dic311yescharacteristic
501C2×C3C2×#94812yes—
502C2×C3C2×C3×C4×D411yescharacteristic
503C2×C3C2×C3×#13112yes—
504C22—28no—
505C22—22no—
506C22—22no—
507C22—22no—
508C22—22no—
509C22—24no—
510C22C3×D4×Dic312yes—
511C22C3×#94814yescomplemented
512C22C23×C3×Dic311yescharacteristic
513C4—22no—
514C4—22no—
515C4—24no—
516C4C3×D4×Dic312yes—
517C4C2×C3×D3×D411yescharacteristic
518C4C2×C3×#23711yescharacteristic
519C3—21no—
520C3#8291611yescharacteristic, direct product factor
521C3C3×#292911yescharacteristic, complemented
522C2—22no—
523C2—24no—
524C2—42no—
525C2C2×C3×D4×Dic311yescharacteristic
526C2C2×C3×#94812yes—
subgroupG/H
centerC2×C3×C4C23×D3
commutatorC22×C3C23×C3×C4
FrattiniC2×C4C23×C3×D3
Fitting, prime radicalC32×#525C2
socleC22×C32C23×C4
cosocleC2×C3×C4C24×C3
hypercenterC3×#525D3
hypocenterC3C3×#2929
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C3×#525

Complements

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

NH ≅ G/Ntype
2. C2×C3×#948C2semidirect
3. C23×C3×C3⋊C8C2semidirect
4. C3×#5234C2semidirect
5. C3×#5207C2semidirect
6. C3×#5011C2semidirect
7. C3×D4×C3⋊C8C2semidirect
8. C3×#4999C2semidirect
9. C3×#4997C2semidirect
11. #82916C3direct (N × H)
23. C2×C3×#208C22semidirect
29. C22×C3×C3⋊C8C22semidirect
31. C3×#830C22semidirect
32. C3×C4⋊(C3⋊C8)C22semidirect
33. C3×#803C22semidirect
34. C3×C4×C3⋊C8C22semidirect
40. C2×#948C2×C3semidirect
41. C23×C3⋊C8C2×C3semidirect
48. #5234C2×C3semidirect
49. #5207C2×C3semidirect
50. #5011C2×C3semidirect
51. D4×C3⋊C8C2×C3semidirect
52. #4999C2×C3semidirect
53. #4997C2×C3semidirect
81. C2×C3×C3⋊C8D4semidirect
125. C2×#208C22×C3semidirect
131. C22×C3⋊C8C22×C3semidirect
138. #830C22×C3semidirect
139. C4⋊(C3⋊C8)C22×C3semidirect
140. #803C22×C3semidirect
141. C4×C3⋊C8C22×C3semidirect
258. C2×C3⋊C8C3×D4semidirect
271. C22×C32#131semidirect
438. C22×C3#948semidirect
440. C22×C3C3×#131semidirect
461. C32#2929semidirect
511. C22C3×#948semidirect
520. C3#82916direct (N × H)
521. C3C3×#2929semidirect

Maximal subgroups

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

subgroupindex
C32×#5252
C2×C3×#9482
C23×C3×C3⋊C82
C3×#52342
C3×#52072
C3×#50112
C3×D4×C3⋊C82
C3×#49992
C3×#49972
C3×#29293
#829163