Finite Group Databasebeta

← C3×#71698 #11788339

Subgroups — C3×#71698 #11788339

Order 1152.

837 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C22⋊Q8C211yesmaximal, characteristic
2C22×C3×#208C211yesmaximal, characteristic
3C2×C3×#836C212yesmaximal, complemented
4C3×#5207C211yesmaximal, characteristic
5C3×#4530C212yesmaximal, complemented
6C3×#1901—31nomaximal
7#71698C311yesmaximal, characteristic, direct product factor
8C22×C32×Q8C2211yescharacteristic
9C23×C32×C4C2211yescharacteristic
10C32×C22⋊Q8—21no—
11C32×C22⋊Q8—21no—
12C32×C22⋊Q8—21no—
13C32×C22⋊Q8—21no—
14C2×C32×C4⋊C4C412yes—
15C2×C32×C4⋊C4C2211yescharacteristic
16C2×C32×C22⋊C4C412yes—
17C2×C3×#208—21no—
18C2×C3×#208—24no—
19C2×C3×#208C2212yes—
20C2×C3×#208C2212yes—
21C22×C3×C3⋊C8—21no—
22C3×#836—24no—
23C3×#830—21no—
24C3×#830—21no—
25C22×C3×M16—31no—
26C2×C3×C22⋊Q8—21no—
27C2×C3×C22⋊Q8D311yescharacteristic
28C2×C3×C22⋊Q8C2×C311yescharacteristic
29C22×#208C2×C311yescharacteristic
30C2×C3×#101—32no—
31C3×#407—31no—
32C2×#836C2×C312yescomplemented
33#5207C2×C311yescharacteristic
34C3×#343—32no—
35#4530C2×C312yescomplemented
36C24×C32C2×C411yescharacteristic
37C2×C32×Q8—21no—
38C2×C32×Q8—21no—
39C2×C32×Q8—22no—
40C2×C32×Q8—22no—
41C22×C32×C4—22no—
42C22×C32×C4—22no—
43C22×C32×C4C2×C412yes—
44C22×C32×C4C2×C411yescharacteristic
45C22×C32×C4C2×C412yes—
46C22×C32×C4D411yescharacteristic
47C22×C32×C4D411yescharacteristic
48C22×C32×C4D411yescharacteristic
49C22×C32×C4D411yescharacteristic
50C22×C32×C4C2311yescharacteristic
51C32×C4⋊C4—22no—
52C32×C4⋊C4—22no—
53C32×C4⋊C4—21no—
54C32×C4⋊C4—21no—
55C32×C22⋊C4—22no—
56C32×C22⋊C4—22no—
57C3×#208—24no—
58C3×#208—22no—
59C3×#208—22no—
60C3×#208—22no—
61C3×#208D414yes—
62C2×C3×C3⋊C8—24no—
63C2×C3×C3⋊C8—22no—
64C2×C3×C3⋊C8—22no—
65#1901—31noSylow
66C22×C3×Q8—21no—
67C22×C3×Q8C2×D311yescharacteristic
68C22×C3×Q8C22×C311yescharacteristic
69C23×C3×C4—21no—
70C23×C3×C4C2×D311yescharacteristic
71C23×C3×C4C22×C311yescharacteristic
72C2×C3×M16—32no—
73C2×C3×M16—32no—
74C2×C3×M16—64no—
75C2×C3×M16—61no—
76C22×C3×C8—61no—
77C3×C22⋊Q8—22no—
78C3×C22⋊Q8—22no—
79C3×C22⋊Q8—22no—
80C3×C22⋊Q8—22no—
81C3×C22⋊Q8—21no—
82C3×C22⋊Q8—21no—
83C3×C22⋊Q8—21no—
84C3×C22⋊Q8—21no—
85C3×C22⋊Q8—21no—
86C3×C22⋊Q8—21no—
87C3×C22⋊Q8—21no—
88C3×C22⋊Q8—21no—
89C2×C3×C4⋊C4—22no—
90C2×C3×C4⋊C4—21no—
91C2×C3×C4⋊C4Dic312yes—
92C2×C3×C4⋊C4C3×C412yes—
93C2×C3×C4⋊C4C2×D311yescharacteristic
94C2×C3×C4⋊C4C22×C311yescharacteristic
95C2×C3×C22⋊C4—22no—
96C2×C3×C22⋊C4Dic312yes—
97C2×C3×C22⋊C4C3×C412yes—
98C2×#208—21no—
99C2×#208—24no—
100C2×#208C22×C312yes—
101C2×#208C22×C312yes—
102C22×C3⋊C8—21no—
103C3×#101—64no—
104C3×C22⋊C8—61no—
105C3×C22⋊C8—61no—
106#836—24no—
107#830—21no—
108#830—21no—
109C23×C32—22no—
110C23×C32—22no—
111C23×C32—41no—
112C23×C32C22⋊C411yescharacteristic
113C23×C32C22⋊C411yescharacteristic
114C23×C32C22×C411yescharacteristic
115C32×Q8—41no—
116C32×Q8—42no—
117C32×Q8—41no—
118C2×C32×C4—22no—
119C2×C32×C4—22no—
120C2×C32×C4—22no—
121C2×C32×C4—21no—
122C2×C32×C4—21no—
123C2×C32×C4—22no—
124C2×C32×C4—22no—
125C2×C32×C4—21no—
126C2×C32×C4—21no—
127C2×C32×C4—24no—
128C2×C32×C4—42no—
129C2×C32×C4C22⋊C411yescharacteristic
130C2×C32×C4C22⋊C411yescharacteristic
131C2×C32×C4C2×D412yes—
132C2×C32×C4C2×D411yescharacteristic
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4#4112yes—
135C3×C3⋊C8—24no—
136C3×C3⋊C8—42no—
137C22×M16—31no—
138C2×C22⋊Q8C3×D311yescharacteristic
139C2×#101—32no—
140#407—31no—
141#343—32no—
142C24×C3—21no—
143C24×C3C2×Dic311yescharacteristic
144C24×C3C2×C3×C411yescharacteristic
145C2×C3×Q8—22no—
146C2×C3×Q8—22no—
147C2×C3×Q8—22no—
148C2×C3×Q8—22no—
149C2×C3×Q8—21no—
150C2×C3×Q8—21no—
151C2×C3×Q8—22no—
152C2×C3×Q8—21no—
153C2×C3×Q8—21no—
154C2×C3×Q8—22no—
155C2×C3×Q8—42no—
156C2×C3×Q8—42no—
157C22×C3×C4—22no—
158C22×C3×C4—22no—
159C22×C3×C4—22no—
160C22×C3×C4—22no—
161C22×C3×C4—22no—
162C22×C3×C4—22no—
163C22×C3×C4—21no—
164C22×C3×C4—21no—
165C22×C3×C4—21no—
166C22×C3×C4—21no—
167C22×C3×C4—21no—
168C22×C3×C4—21no—
169C22×C3×C4—42no—
170C22×C3×C4—42no—
171C22×C3×C4C2×Dic312yes—
172C22×C3×C4C2×Dic311yescharacteristic
173C22×C3×C4C2×Dic312yes—
174C22×C3×C4#6711yescharacteristic
175C22×C3×C4#6711yescharacteristic
176C22×C3×C4#6711yescharacteristic
177C22×C3×C4#6711yescharacteristic
178C22×C3×C4C2×C3×C412yes—
179C22×C3×C4C2×C3×C411yescharacteristic
180C22×C3×C4C2×C3×C412yes—
181C22×C3×C4C3×D411yescharacteristic
182C22×C3×C4C3×D411yescharacteristic
183C22×C3×C4C3×D411yescharacteristic
184C22×C3×C4C3×D411yescharacteristic
185C22×C3×C4C22×D311yescharacteristic
186C22×C3×C4C23×C311yescharacteristic
187C3×M16—34no—
188C3×M16—64no—
189C3×M16—62no—
190C3×M16—62no—
191C3×M16—62no—
192C2×C3×C8—64no—
193C2×C3×C8—62no—
194C2×C3×C8—62no—
195C3×C4⋊C4—24no—
196C3×C4⋊C4—24no—
197C3×C4⋊C4—22no—
198C3×C4⋊C4—22no—
199C3×C4⋊C4—22no—
200C3×C4⋊C4—22no—
201C3×C4⋊C4—22no—
202C3×C4⋊C4—22no—
203C3×C4⋊C4—21no—
204C3×C4⋊C4—21no—
205C3×C4⋊C4—21no—
206C3×C4⋊C4—21no—
207C3×C22⋊C4—24no—
208C3×C22⋊C4—24no—
209C3×C22⋊C4—22no—
210C3×C22⋊C4—22no—
211C3×C22⋊C4—22no—
212C3×C22⋊C4—22no—
213#208—24no—
214#208—22no—
215#208—22no—
216#208—22no—
217#208C3×D414yes—
218C2×C3⋊C8—24no—
219C2×C3⋊C8—22no—
220C2×C3⋊C8—22no—
221C22×C32—21no—
222C22×C32—21no—
223C22×C32—21no—
224C22×C32—21no—
225C22×C32—21no—
226C22×C32—21no—
227C22×C32—21no—
228C22×C32—44no—
229C22×C32#10112yescomplemented
230C22×C32C2×C22⋊C411yescharacteristic
231C22×C32C4×D412yes—
232C32×C4—21no—
233C32×C4—21no—
234C32×C4—42no—
235C32×C4—42no—
236C32×C4#12011yescharacteristic
237C32×C4#12112yes—
238C32×C4#12311yescharacteristic
239C22×Q8C2×C3×D311yescharacteristic
240C23×C4C2×C3×D311yescharacteristic
241C2×M16—32no—
242C2×M16—32no—
243C2×M16—64no—
244C2×M16—61no—
245C22×C8—61no—
246C22⋊Q8—21no—
247C22⋊Q8—21no—
248C22⋊Q8—21no—
249C22⋊Q8—21no—
250C2×C4⋊C4C3×Dic312yes—
251C2×C4⋊C4C2×C3×D311yescharacteristic
252C2×C22⋊C4C3×Dic312yes—
253#101—64no—
254C22⋊C8—61no—
255C22⋊C8—61no—
256C23×C3—24no—
257C23×C3—22no—
258C23×C3—22no—
259C23×C3—22no—
260C23×C3—22no—
261C23×C3—21no—
262C23×C3—21no—
263C23×C3—21no—
264C23×C3—42no—
265C23×C3—41no—
266C23×C3—41no—
267C23×C3—42no—
268C23×C3#21711yescharacteristic
269C23×C3#21711yescharacteristic
270C23×C3C3×C22⋊C411yescharacteristic
271C23×C3C3×C22⋊C411yescharacteristic
272C23×C3C22×Dic311yescharacteristic
273C23×C3C22×C3×C411yescharacteristic
274C3×Q8—42no—
275C3×Q8—42no—
276C3×Q8—44no—
277C3×Q8—41no—
278C3×Q8—41no—
279C3×Q8—42no—
280C3×Q8—41no—
281C3×Q8—42no—
282C3×Q8—41no—
283C2×C3×C4—22no—
284C2×C3×C4—22no—
285C2×C3×C4—21no—
286C2×C3×C4—21no—
287C2×C3×C4—21no—
288C2×C3×C4—21no—
289C2×C3×C4—22no—
290C2×C3×C4—22no—
291C2×C3×C4—21no—
292C2×C3×C4—21no—
293C2×C3×C4—22no—
294C2×C3×C4—22no—
295C2×C3×C4—21no—
296C2×C3×C4—21no—
297C2×C3×C4—24no—
298C2×C3×C4—24no—
299C2×C3×C4—24no—
300C2×C3×C4—22no—
301C2×C3×C4—22no—
302C2×C3×C4—22no—
303C2×C3×C4—22no—
304C2×C3×C4—24no—
305C2×C3×C4—21no—
306C2×C3×C4—21no—
307C2×C3×C4—22no—
308C2×C3×C4—22no—
309C2×C3×C4—21no—
310C2×C3×C4—21no—
311C2×C3×C4—41no—
312C2×C3×C4—41no—
313C2×C3×C4—41no—
314C2×C3×C4—41no—
315C2×C3×C4—42no—
316C2×C3×C4—42no—
317C2×C3×C4—42no—
318C2×C3×C4—44no—
319C2×C3×C4—44no—
320C2×C3×C4—42no—
321C2×C3×C4—42no—
322C2×C3×C4#21711yescharacteristic
323C2×C3×C4#21711yescharacteristic
324C2×C3×C4C3×C22⋊C411yescharacteristic
325C2×C3×C4C3×C22⋊C411yescharacteristic
326C2×C3×C4D3×D412yes—
327C2×C3×C4#23712yes—
328C2×C3×C4C2×#6711yescharacteristic
329C2×C3×C4C2×#6711yescharacteristic
330C2×C3×C4C2×C3×D412yes—
331C2×C3×C4C2×C3×D411yescharacteristic
332C2×C3×C4C2×C3×D411yescharacteristic
333C2×C3×C4C3×#4112yes—
334C3×C8—64no—
335C3×C8—122no—
336C3⋊C8—24no—
337C3⋊C8—42no—
338C2×C32—22no—
339C2×C32—22no—
340C2×C32—41no—
341C2×C32#38611yescharacteristic
342C2×C32C2×#10111yescharacteristic
343C2×C32#41311yescharacteristic
344C24C2×C3×Dic311yescharacteristic
345C2×Q8—22no—
346C2×Q8—22no—
347C2×Q8—21no—
348C2×Q8—21no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4C2×C3×Dic312yes—
352C22×C4C2×C3×Dic311yescharacteristic
353C22×C4C2×C3×Dic312yes—
354C22×C4C3×#6711yescharacteristic
355C22×C4C3×#6711yescharacteristic
356C22×C4C3×#6711yescharacteristic
357C22×C4C3×#6711yescharacteristic
358C22×C4C22×C3×D311yescharacteristic
359M16—34no—
360M16—64no—
361M16—62no—
362M16—62no—
363M16—62no—
364C2×C8—64no—
365C2×C8—62no—
366C2×C8—62no—
367C4⋊C4—22no—
368C4⋊C4—22no—
369C4⋊C4—21no—
370C4⋊C4—21no—
371C22⋊C4—22no—
372C22⋊C4—22no—
373C22×C3—22no—
374C22×C3—22no—
375C22×C3—21no—
376C22×C3—21no—
377C22×C3—21no—
378C22×C3—21no—
379C22×C3—21no—
380C22×C3—21no—
381C22×C3—21no—
382C22×C3—21no—
383C22×C3—22no—
384C22×C3—21no—
385C22×C3—21no—
386C22×C3—21no—
387C22×C3—21no—
388C22×C3—21no—
389C22×C3—21no—
390C22×C3—22no—
391C22×C3—21no—
392C22×C3—22no—
393C22×C3—41no—
394C22×C3—41no—
395C22×C3—41no—
396C22×C3—41no—
397C22×C3—44no—
398C22×C3—44no—
399C22×C3—48no—
400C22×C3#83612yescomplemented
401C22×C3C3×#10112yescomplemented
402C22×C3D4×Dic312yes—
403C22×C3C2×#21711yescharacteristic
404C22×C3C2×C3×C22⋊C411yescharacteristic
405C22×C3C3×C4×D412yes—
406C3×C4—21no—
407C3×C4—21no—
408C3×C4—21no—
409C3×C4—21no—
410C3×C4—21no—
411C3×C4—21no—
412C3×C4—22no—
413C3×C4—41no—
414C3×C4—41no—
415C3×C4—44no—
416C3×C4—44no—
417C3×C4—42no—
418C3×C4—42no—
419C3×C4—42no—
420C3×C4—42no—
421C3×C4#93511yescharacteristic
422C3×C4#93711yescharacteristic
423C3×C4#93912yes—
424C3×C4C3×#12011yescharacteristic
425C3×C4C3×#12112yes—
426C3×C4C3×#12311yescharacteristic
427C32#190111yescharacteristic, complemented, Sylow
428C23—22no—
429C23—22no—
430C23—41no—
431C23C3×#21711yescharacteristic
432C23C3×#21711yescharacteristic
433C23C22×C3×Dic311yescharacteristic
434Q8—41no—
435Q8—41no—
436Q8—42no—
437C2×C4—22no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—24no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—42no—
448C2×C4C3×#21711yescharacteristic
449C2×C4C3×#21711yescharacteristic
450C2×C4C3×D3×D412yes—
451C2×C4C3×#23712yes—
452C2×C4C2×C3×#6711yescharacteristic
453C2×C4C2×C3×#6711yescharacteristic
454C8—64no—
455C8—122no—
456C2×C3—24no—
457C2×C3—22no—
458C2×C3—22no—
459C2×C3—22no—
460C2×C3—22no—
461C2×C3—21no—
462C2×C3—21no—
463C2×C3—21no—
464C2×C3—42no—
465C2×C3—42no—
466C2×C3—41no—
467C2×C3—41no—
468C2×C3#522011yescharacteristic
469C2×C3C2×#83611yescharacteristic
470C2×C3#523711yescharacteristic
471C2×C3C3×#38611yescharacteristic
472C2×C3C2×C3×#10111yescharacteristic
473C2×C3C3×#41311yescharacteristic
474C22—21no—
475C22—21no—
476C22—21no—
477C22—21no—
478C22—21no—
479C22—21no—
480C22—21no—
481C22—44no—
482C22C3×#83612yescomplemented
483C22C3×D4×Dic312yes—
484C22C2×C3×#21711yescharacteristic
485C4—21no—
486C4—21no—
487C4—42no—
488C4—42no—
489C4C3×#93511yescharacteristic
490C4C3×#93711yescharacteristic
491C4C3×#93912yes—
492C3—21no—
493C3#7169811yescharacteristic, direct product factor
494C3C3×#190111yescharacteristic, complemented
495C2—22no—
496C2—22no—
497C2—41no—
498C2C3×#522011yescharacteristic
499C2C2×C3×#83611yescharacteristic
500C2C3×#523711yescharacteristic
subgroupG/H
centerC22×C3C2×#217
commutatorC23×C3C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC2×C32×C22⋊Q8C2
socleC22×C32C2×C22⋊C4
prime radicalC24×C32C2×C4
cosocleC22×C3×C4C23×C3
hypercenterC2×C3×C22⋊Q8D3
hypocenterC3C3×#1901
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C23×C3×C4 ◁ C2×C3×C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. C2×C3×#836C2semidirect
5. C3×#4530C2semidirect
7. #71698C3direct (N × H)
32. C2×#836C2×C3semidirect
35. #4530C2×C3semidirect
229. C22×C32#101semidirect
400. C22×C3#836semidirect
401. C22×C3C3×#101semidirect
427. C32#1901semidirect
482. C22C3×#836semidirect
493. C3#71698direct (N × H)
494. C3C3×#1901semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C22⋊Q82
C22×C3×#2082
C2×C3×#8362
C3×#52072
C3×#45302
C3×#19013
#716983