Finite Group Databasebeta

← #11870514

Subgroups — #11870514

Order 1152.

1109 conjugacy classes of subgroups.

The subgroup lattice has 523 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C4⋊(C3⋊D3)C211yesmaximal, characteristic
2C3×#5470C211yesmaximal, characteristic, complemented
3C3×#4925C211yesmaximal, characteristic, complemented
4#10591183C212yesmaximal
5#10591126C212yesmaximal, complemented
6#10590379C212yesmaximal, complemented
7C4×#3717C214yesmaximal, complemented
8#10590300C212yesmaximal, complemented
9#83351—31nomaximal
10#79298—31nomaximal
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C22×C4×C3⋊D3—21no—
13C2×C32×C42C2211yescharacteristic
14C2×#3752—21no—
15C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
16C4×C4⋊(C3⋊D3)—21no—
17C4×C4⋊(C3⋊D3)—21no—
18C4×C4⋊(C3⋊D3)C2212yes—
19C4×C4⋊(C3⋊D3)C2212yes—
20C3×#926—21no—
21C3×#924—21no—
22C3×#924C2212yes—
23C3×#870—21no—
24C3×#869C2211yescharacteristic, complemented
25C3×#869C2211yescharacteristic, complemented
26C3×C4×Dic6—21no—
27C3×C4×Dic6C2212yescomplemented
28C2×#3717C2214yes—
29C3×#830C2212yes—
30C3×C4⋊(C3⋊C8)C2212yescomplemented
31C3×C4×C3⋊C8C2212yescomplemented
32#63573C2214yescomplemented
33#63566C2214yescomplemented
34#63564C2214yes—
35C3×#533—31no—
36C2×C4×D12—31no—
37C2×C4×D12—31no—
38C2×C4×D12—61no—
39#5470D311yescharacteristic, complemented
40C3×#431—31no—
41#5084—32no—
42#5083—32no—
43#5046—32no—
44#5043—32no—
45C4×#215—34no—
46#4925D311yescharacteristic, complemented
47#4842—32no—
48#4841—32no—
49#4731—32no—
50#4721—32no—
51C4×#204—34no—
52C23×C3⋊D3—21no—
53C22×C32×C4D411yescharacteristic
54C22×C32×C4D411yescharacteristic
55C22×C32×C4C2311yescharacteristic
56C22×C3⋊Dic3—21no—
57C2×C4⋊(C3⋊D3)—21no—
58C2×C4⋊(C3⋊D3)—24no—
59C2×C4⋊(C3⋊D3)C2312yes—
60C2×C4×C3⋊D3—22no—
61C2×C4×C3⋊D3—22no—
62C2×C4×C3⋊D3—44no—
63C2×C3×Dic6—21no—
64C2×C3×Dic6C2312yes—
65C32×C42D411yescharacteristic
66C32×C42D411yescharacteristic
67C32×C42C2311yescharacteristic
68C32×C42C2311yescharacteristic
69#3752—22no—
70#3752—22no—
71C4⋊(C3⋊Dic3)—21no—
72C4⋊(C3⋊Dic3)C2312yes—
73C3×#217—22no—
74C3×C4⋊Dic3—21no—
75C3×C4⋊Dic3—21no—
76C3×C4⋊Dic3—21no—
77C3×C4⋊Dic3C2312yes—
78C3×Dic3⋊C4—22no—
79C3×Dic3⋊C4—22no—
80C3×C4×Dic3—22no—
81C2×C3×C3⋊C8C2314yes—
82#3717—28no—
83#3101—91noSylow
84C22×D12—31no—
85C22×D12—31no—
86C22×D12—61no—
87C22×C4×D3—62no—
88C22×C4×D3—61no—
89C22×C4×D3—61no—
90C3×C4⋊Q8—31no—
91C3×C4⋊Q8—31no—
92C3×#125—61no—
93C3×C22⋊Q8—32no—
94C3×C22⋊Q8—61no—
95C3×C4×Q8—32no—
96C3×C4×Q8—61no—
97C3×#117—61no—
98C2×C3×C42—21no—
99C2×C3×C42C2×D311yescharacteristic
100C2×C3×C42C2×D311yescharacteristic
101C2×#215—34no—
102C2×(C2×D3)⋊C4—62no—
103C2×(C2×D3)⋊C4—61no—
104C2×(C2×D3)⋊C4—61no—
105#926—21no—
106C2×C4⋊Dic3—31no—
107C2×C4⋊Dic3—31no—
108C2×C4⋊Dic3—61no—
109#924—21no—
110#924C2×D312yes—
111C2×#204—34no—
112C4×D12—32no—
113C4×D12—32no—
114C4×D12—32no—
115C4×D12—32no—
116C4×D12—62no—
117C4×D12—62no—
118C4×D12—62no—
119C4×D12—62no—
120C4×D12—61no—
121C4×D12—61no—
122C4×D12—61no—
123C4×D12—61no—
124#870—21no—
125#869C2×D311yescharacteristic, complemented
126#869C2×D311yescharacteristic, complemented
127C4×Dic6—21no—
128C4×Dic6C2×D312yescomplemented
129C3×C4⋊C8—32no—
130C3×C22⋊C8—32no—
131C3×C4×C8—32no—
132#835—34no—
133#830C2×D312yes—
134#821—34no—
135#817—34no—
136#816—34no—
137#809—34no—
138#808—34no—
139C4⋊(C3⋊C8)C2×D312yescomplemented
140C4×C3⋊C8C2×D312yescomplemented
141C23×C32C2×D411yescharacteristic
142C22×C3⋊D3—24no—
143C22×C3⋊D3—22no—
144C22×C3⋊D3—42no—
145C22×C3⋊D3—42no—
146C2×C32×C4—22no—
147C2×C32×C4—41no—
148C2×C32×C4SD1614yescomplemented
149C2×C32×C4C2×D411yescharacteristic
150C2×C32×C4C2×D411yescharacteristic
151C2×C32×C4C2×D411yescharacteristic
152C2×C32×C4C2×D411yescharacteristic
153C2×C32×C4C2×D411yescharacteristic
154C2×C32×C4C2411yescharacteristic
155C2×C3⋊Dic3—22no—
156C2×C3⋊Dic3—42no—
157C4⋊(C3⋊D3)—24no—
158C4⋊(C3⋊D3)—22no—
159C4⋊(C3⋊D3)#4114yes—
160C4×C3⋊D3—44no—
161C4×C3⋊D3—44no—
162C2×C3×Dic3—22no—
163C2×C3×Dic3—22no—
164C3×Dic6—24no—
165C3×Dic6—42no—
166C3×C3⋊C8—24no—
167#533—31no—
168C2×C4×D4—91no—
169#483—92no—
170#476—92no—
171#461—92no—
172#450—92no—
173C4×SD16—94no—
174#431—31no—
175C23×D3—62no—
176C23×D3—61no—
177C23×D3—61no—
178C2×C3×Q8—32no—
179C2×C3×Q8—61no—
180C22×C3×C4—21no—
181C22×C3×C4—21no—
182C22×C3×C4—21no—
183C22×C3×C4D1211yescharacteristic
184C22×C3×C4D1211yescharacteristic
185C22×C3×C4#6711yescharacteristic
186C22×C3×C4#6711yescharacteristic
187C22×C3×C4C22×D311yescharacteristic
188C22×C3×C4C22×D311yescharacteristic
189C22×Dic3—62no—
190C22×Dic3—61no—
191C22×Dic3—61no—
192C2×D12—32no—
193C2×D12—32no—
194C2×D12—62no—
195C2×D12—64no—
196C2×D12—64no—
197C2×D12—62no—
198C2×D12—68no—
199C2×D12—61no—
200C2×D12—61no—
201C2×C4×D3—64no—
202C2×C4×D3—64no—
203C2×C4×D3—62no—
204C2×C4×D3—62no—
205C2×C4×D3—62no—
206C2×C4×D3—62no—
207C2×C4×D3—128no—
208C2×C4×D3—124no—
209C2×C4×D3—124no—
210C2×Dic6—21no—
211C2×Dic6C22×D312yes—
212C2×C3×C8—34no—
213C3×C4⋊C4—32no—
214C3×C4⋊C4—62no—
215C3×C4⋊C4—62no—
216C3×C4⋊C4—61no—
217C3×C4⋊C4—61no—
218C3×C4⋊C4—61no—
219C3×C22⋊C4—62no—
220C3×C42—21no—
221C3×C42—21no—
222C3×C42—21no—
223C3×C42—21no—
224C3×C42—62no—
225C3×C42D1211yescharacteristic
226C3×C42D1211yescharacteristic
227C3×C42#6711yescharacteristic
228C3×C42#6711yescharacteristic
229C3×C42C22×D311yescharacteristic
230C3×C42C22×D311yescharacteristic
231C3×C42C22×D311yescharacteristic
232C3×C42C22×D311yescharacteristic
233#217—22no—
234#215—68no—
235(C2×D3)⋊C4—64no—
236(C2×D3)⋊C4—64no—
237(C2×D3)⋊C4—62no—
238(C2×D3)⋊C4—62no—
239(C2×D3)⋊C4—62no—
240(C2×D3)⋊C4—62no—
241C4⋊Dic3—21no—
242C4⋊Dic3—21no—
243C4⋊Dic3—21no—
244C4⋊Dic3—32no—
245C4⋊Dic3—32no—
246C4⋊Dic3—62no—
247C4⋊Dic3—62no—
248C4⋊Dic3—61no—
249C4⋊Dic3—61no—
250C4⋊Dic3C22×D312yes—
251Dic3⋊C4—22no—
252Dic3⋊C4—22no—
253C4×Dic3—22no—
254C2×C3⋊C8C22×D314yes—
255#204—68no—
256C22×C32—21no—
257C22×C32—21no—
258C22×C32C2×SD1612yes—
259C22×C32C22×D411yescharacteristic
260C2×C3⋊D3—24no—
261C2×C3⋊D3—48no—
262C2×C3⋊D3—42no—
263C2×C3⋊D3—42no—
264C32×C4—21no—
265C32×C4—21no—
266C32×C4—21no—
267C32×C4C2×SD1612yes—
268C32×C4C2×SD1612yes—
269C32×C4C2×#4112yes—
270C3⋊Dic3—42no—
271C3×Dic3—42no—
272C3×Dic3—42no—
273C22×D4—91no—
274C23×C4—181no—
275C2×SD16—94no—
276C4⋊Q8—31no—
277C4⋊Q8—31no—
278#125—61no—
279C22⋊Q8—32no—
280C22⋊Q8—61no—
281C4×Q8—32no—
282C4×Q8—61no—
283C4×D4—92no—
284C4×D4—92no—
285C4×D4—181no—
286C4×D4—181no—
287#117—61no—
288C2×C4⋊C4—91no—
289C2×C22⋊C4—181no—
290C2×C42D3211yescharacteristic
291#106—94no—
292C4⋊C8—32no—
293#103—94no—
294#102—94no—
295C22⋊C8—32no—
296C4×C8—32no—
297C23×C3—21no—
298C23×C3C2×D1211yescharacteristic
299C23×C3C2×#6711yescharacteristic
300C22×D3—64no—
301C22×D3—68no—
302C22×D3—64no—
303C22×D3—64no—
304C22×D3—62no—
305C22×D3—62no—
306C22×D3—124no—
307C22×D3—124no—
308C22×D3—122no—
309C22×D3—122no—
310C22×D3—122no—
311C22×D3—122no—
312C3×Q8—64no—
313C3×Q8—122no—
314C2×C3×C4—24no—
315C2×C3×C4—22no—
316C2×C3×C4—22no—
317C2×C3×C4—21no—
318C2×C3×C4—24no—
319C2×C3×C4—21no—
320C2×C3×C4—21no—
321C2×C3×C4—21no—
322C2×C3×C4—21no—
323C2×C3×C4—21no—
324C2×C3×C4—41no—
325C2×C3×C4—41no—
326C2×C3×C4—42no—
327C2×C3×C4—62no—
328C2×C3×C4—62no—
329C2×C3×C4#20414yescomplemented
330C2×C3×C4#21514yescomplemented
331C2×C3×C4C2×D1211yescharacteristic
332C2×C3×C4C2×D1211yescharacteristic
333C2×C3×C4C2×D1211yescharacteristic
334C2×C3×C4C2×D1211yescharacteristic
335C2×C3×C4C2×D1211yescharacteristic
336C2×C3×C4C2×#6711yescharacteristic
337C2×C3×C4C2×#6711yescharacteristic
338C2×C3×C4C2×#6711yescharacteristic
339C2×C3×C4C2×#6711yescharacteristic
340C2×C3×C4C2×#6711yescharacteristic
341C2×C3×C4C23×D311yescharacteristic
342C2×C3×C4C23×D311yescharacteristic
343C2×Dic3—22no—
344C2×Dic3—22no—
345C2×Dic3—64no—
346C2×Dic3—62no—
347C2×Dic3—62no—
348C2×Dic3—124no—
349C2×Dic3—122no—
350C2×Dic3—122no—
351D12—34no—
352D12—34no—
353D12—64no—
354D12—68no—
355D12—64no—
356D12—64no—
357D12—64no—
358D12—62no—
359D12—62no—
360C4×D3—128no—
361C4×D3—128no—
362C4×D3—124no—
363C4×D3—124no—
364C4×D3—124no—
365C4×D3—124no—
366Dic6—24no—
367Dic6—42no—
368C3×C8—64no—
369C3⋊C8—24no—
370C2×C32—22no—
371C2×C32#52511yescharacteristic
372C2×C32C22×SD1611yescharacteristic
373C2×C32#57511yescharacteristic
374C3⋊D3—44no—
375C24—181no—
376C2×Q8—32no—
377C2×Q8—61no—
378C2×D4—92no—
379C2×D4—184no—
380C2×D4—181no—
381C22×C4—181no—
382C22×C4—182no—
383C22×C4—182no—
384C22×C4—364no—
385C22×C4#62611yescharacteristic
386C22×C4#62611yescharacteristic
387C22×C4C2×D3211yescharacteristic
388SD16—188no—
389C2×C8—34no—
390C4⋊C4—32no—
391C4⋊C4—61no—
392C4⋊C4—61no—
393C4⋊C4—62no—
394C4⋊C4—62no—
395C4⋊C4—61no—
396C4⋊C4—92no—
397C4⋊C4—181no—
398C22⋊C4—62no—
399C22⋊C4—182no—
400C22⋊C4—182no—
401C42—62no—
402C42#62611yescharacteristic
403C42#62611yescharacteristic
404C42C2×D3211yescharacteristic
405C42C2×D3211yescharacteristic
406C22×C3—22no—
407C22×C3—22no—
408C22×C3—21no—
409C22×C3—21no—
410C22×C3—21no—
411C22×C3—21no—
412C22×C3—21no—
413C22×C3—22no—
414C22×C3C2×#20412yes—
415C22×C3C2×#21512yes—
416C22×C3C22×D1211yescharacteristic
417C22×C3C22×#6711yescharacteristic
418C2×D3—68no—
419C2×D3—64no—
420C2×D3—64no—
421C2×D3—124no—
422C2×D3—1216no—
423C2×D3—128no—
424C2×D3—128no—
425C2×D3—124no—
426C2×D3—122no—
427C2×D3—122no—
428C2×D3—122no—
429C2×D3—122no—
430C3×C4—22no—
431C3×C4—21no—
432C3×C4—21no—
433C3×C4—21no—
434C3×C4—21no—
435C3×C4—21no—
436C3×C4—21no—
437C3×C4—22no—
438C3×C4—22no—
439C3×C4—22no—
440C3×C4—41no—
441C3×C4—41no—
442C3×C4—122no—
443C3×C4—122no—
444C3×C4C2×#20412yes—
445C3×C4C2×#20412yes—
446C3×C4C2×#21512yes—
447C3×C4C2×#21512yes—
448C3×C4D3×#4112yes—
449C3×C4D3×#4112yes—
450Dic3—42no—
451Dic3—42no—
452Dic3—124no—
453Dic3—122no—
454Dic3—122no—
455C32#310111yescharacteristic, complemented, Sylow
456C23—184no—
457C23—182no—
458C23—362no—
459C23—362no—
460C23C2×#62611yescharacteristic
461Q8—64no—
462Q8—122no—
463D4—94no—
464D4—184no—
465D4—182no—
466C2×C4—22no—
467C2×C4—41no—
468C2×C4—62no—
469C2×C4—62no—
470C2×C4—182no—
471C2×C4—362no—
472C2×C4—364no—
473C2×C4—364no—
474C2×C4#371714yescomplemented
475C2×C4C2×#62611yescharacteristic
476C2×C4C2×#62611yescharacteristic
477C2×C4C2×#62611yescharacteristic
478C2×C4C2×#62611yescharacteristic
479C2×C4C2×#62611yescharacteristic
480C2×C4C22×D3211yescharacteristic
481C8—64no—
482C2×C3—24no—
483C2×C3—22no—
484C2×C3—22no—
485C2×C3—21no—
486C2×C3—21no—
487C2×C3—21no—
488C2×C3#552411yescharacteristic
489C2×C3C22×#20411yescharacteristic
490C2×C3#574811yescharacteristic
491C2×C3C22×#21511yescharacteristic
492C2×C3#582211yescharacteristic
493C2×C3#582811yescharacteristic
494D3—128no—
495D3—124no—
496D3—124no—
497C22—21no—
498C22—21no—
499C22—184no—
500C22—368no—
501C22—362no—
502C22—362no—
503C22C2×#371712yes—
504C22C22×#62611yescharacteristic
505C4—21no—
506C4—21no—
507C4—21no—
508C4—122no—
509C4—122no—
510C4—362no—
511C4C2×#371712yes—
512C4C2×#371712yes—
513C4#6430612yes—
514C3—21no—
515C3#7929811yescharacteristic, complemented
516C3#8335111yescharacteristic, complemented
517C2—22no—
518C2—364no—
519C2#1059479511yescharacteristic
520C2C22×#371711yescharacteristic
521C2#1059503411yescharacteristic
subgroupG/H
centerC2×C4C2×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C42C22
socleC22×C32C22×D4
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenterC2×C42D32
hypocenterC32#3101
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C3×#5470C2semidirect
3. C3×#4925C2semidirect
5. #10591126C2semidirect
6. #10590379C2semidirect
7. C4×#3717C2semidirect
8. #10590300C2semidirect
24. C3×#869C22semidirect
25. C3×#869C22semidirect
27. C3×C4×Dic6C22semidirect
30. C3×C4⋊(C3⋊C8)C22semidirect
31. C3×C4×C3⋊C8C22semidirect
32. #63573C22semidirect
33. #63566C22semidirect
39. #5470D3semidirect
46. #4925D3semidirect
125. #869C2×D3semidirect
126. #869C2×D3semidirect
128. C4×Dic6C2×D3semidirect
139. C4⋊(C3⋊C8)C2×D3semidirect
140. C4×C3⋊C8C2×D3semidirect
148. C2×C32×C4SD16semidirect
329. C2×C3×C4#204semidirect
330. C2×C3×C4#215semidirect
455. C32#3101semidirect
474. C2×C4#3717semidirect
515. C3#79298semidirect
516. C3#83351semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C4⋊(C3⋊D3)2
C3×#54702
C3×#49252
#105911832
#105911262
#105903792
C4×#37172
#105903002
#833513
#792983