Finite Group Databasebeta

← #11868264

Subgroups — #11868264

Order 1152.

1025 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594605C211yesmaximal, characteristic
2#10594374C211yesmaximal, characteristic, complemented
3C3⋊D3×#107C211yesmaximal, characteristic, complemented
4C3×#4890C212yesmaximal, complemented
5#10590940C211yesmaximal, characteristic
6#10590762C212yesmaximal, complemented
7#10590658C211yesmaximal, characteristic, complemented
8#10590593C211yesmaximal, characteristic
9#10590573C211yesmaximal, characteristic, complemented
10#10590555C212yesmaximal, complemented
11#10590463C212yesmaximal, complemented
12D3×#474—32nomaximal
13C2×#3802C2211yescharacteristic
14C2×C4×D32—21no—
15C2×#3797—21no—
16C2×C8×C3⋊D3C2211yescharacteristic
17C4⋊C4×C3⋊D3C2211yescharacteristic
18C4⋊C4×C3⋊D3C2211yescharacteristic
19C3×#893C2212yes—
20C3×#888C2212yescomplemented
21#63921—21no—
22#63918C2212yescomplemented
23#63900C2211yescharacteristic
24Dic3×D12C2212yes—
25#63883—21no—
26C4×#624C2211yescharacteristic
27#63879—22no—
28#63839—22no—
29C2×#3710C2211yescharacteristic
30C32×#107C2211yescharacteristic, complemented
31#63645C2211yescharacteristic, complemented
32#63634C2211yescharacteristic, complemented
33#63634C2211yescharacteristic, complemented
34C3×#821C2212yes—
35C3×Dic3⋊C8C2212yescomplemented
36C3×#809C2212yes—
37C3×#807C2212yescomplemented
38#63575C2212yescomplemented
39Dic3⋊(C3⋊C8)C2212yescomplemented
40#63563C2212yes—
41#63562C2212yes—
42D3×C4⋊Q8—32no—
43C4×D3×D4—32no—
44C3×#474—32no—
45#5087—32no—
46#5007—32no—
47#4890—32no—
48#4890D312yescomplemented
49D3×#107—32no—
50D3×#107—32no—
51D3×#107—61no—
52#4846—32no—
53D3×C4⋊C8—32no—
54D3×#102—32no—
55D3×#102—32no—
56#4759—32no—
57#4759—32no—
58C22×D32—21no—
59C2×C4×C3⋊D3—21no—
60C2×C4×C3⋊D3—21no—
61C2×C4×C3⋊D3C2311yescharacteristic
62C2×C3×D12C2312yes—
63C2×C3×C4×D3—22no—
64C2×C3×Dic6—22no—
65C2×#627—22no—
66C2×#625—21no—
67C2×#624—21no—
68C2×#624D411yescharacteristic
69C2×#624D411yescharacteristic
70C2×D3×Dic3—22no—
71#3802—22no—
72#3802Q814yescomplemented
73C4×D32—44no—
74#3797—44no—
75C2×C32×C8C2311yescharacteristic
76C32×C4⋊C4C2311yescharacteristic
77C32×C4⋊C4C2311yescharacteristic
78C4⋊(C3⋊Dic3)C2311yescharacteristic
79C4⋊(C3⋊Dic3)C2311yescharacteristic
80#3750—21no—
81#3750—21no—
82C2×C3⋊(C3⋊C8)C2311yescharacteristic
83C8×C3⋊D3—22no—
84C3×(C2×D3)⋊C4—22no—
85C3×C4⋊Dic3C2312yes—
86C3×Dic3⋊C4—22no—
87C3×C4×Dic3C2312yes—
88C2×C3×C3⋊C8C2312yes—
89#3724—21no—
90Dic3⋊Dic3—22no—
91(C2×D3)⋊Dic3—22no—
92Dic32D412yes—
93#3710—22no—
94C2×#474—91noSylow
95C2×D3×Q8—62no—
96C2×D3×D4—32no—
97C22×C4×D3—62no—
98C3×C4⋊Q8—32no—
99C3×C4×D4—32no—
100#944—62no—
101D4×Dic3—32no—
102C4×#67—62no—
103C2×D3×C8—32no—
104C2×D3×C8—32no—
105C2×D3×C8—61no—
106#893C2×D312yes—
107D3×C4⋊C4—32no—
108D3×C4⋊C4—32no—
109D3×C4⋊C4—32no—
110D3×C4⋊C4—61no—
111D3×C4⋊C4—61no—
112D3×C4⋊C4—62no—
113#888—32no—
114#888—62no—
115#888C2×D312yescomplemented
116#67⋊C4—62no—
117D3×C22⋊C4—62no—
118C4×D12—32no—
119C42×D3—32no—
120#869—32no—
121C3×#107—21no—
122C3×#107—32no—
123C3×#107C2×D312yescomplemented
124C3×C4⋊C8—32no—
125C3×#102—32no—
126C3×#102—32no—
127#832—32no—
128#832—32no—
129#821—32no—
130#821C2×D312yes—
131#818—32no—
132#818—32no—
133#818—61no—
134Dic3⋊C8—32no—
135Dic3⋊C8C2×D312yescomplemented
136#809—32no—
137#809C2×D312yes—
138#807—32no—
139#807—32no—
140#807—32no—
141#807—61no—
142#807—61no—
143#807C2×D312yescomplemented
144C4⋊(C3⋊C8)—32no—
145C22×C3⋊D3C2×D411yescharacteristic
146C22×C3×D3—22no—
147C2×D32—24no—
148C2×D32—42no—
149C2×D32—42no—
150C2×C32×C4—21no—
151C2×C32×C4—21no—
152C2×C32×C4C2411yescharacteristic
153C2×C3⋊Dic3—21no—
154C2×C3⋊Dic3—21no—
155C2×C3⋊Dic3C2×D411yescharacteristic
156C4×C3⋊D3—42no—
157C4×C3⋊D3—42no—
158C4×C3⋊D3C2×Q812yes—
159C4×C3⋊D3#4112yes—
160C2×C3×Dic3—22no—
161C2×C3×Dic3C2×D412yes—
162C2×C3×Dic3C2×D412yes—
163C3×D12—22no—
164C3×D12C2×Q814yescomplemented
165C3×C4×D3—44no—
166C3×Dic6—44no—
167#627—44no—
168#625—24no—
169#624—22no—
170#624—42no—
171#624D814yes—
172D3×Dic3—44no—
173C32×C8—21no—
174C3⋊(C3⋊C8)—21no—
175C3×C3⋊C8—22no—
176C2×C4⋊Q8—91no—
177C2×C4×D4—91no—
178#474—32no—
179#474—92no—
180#474—92no—
181#474—92no—
182C2×#107—91no—
183C2×#107—91no—
184C2×C4⋊C8—91no—
185C2×#102—91no—
186C2×#102—91no—
187C23×D3—62no—
188C2×C3×Q8—62no—
189C2×C3×D4—32no—
190C22×C3×C4—62no—
191C2×#67—62no—
192C22×Dic3—62no—
193D3×Q8—128no—
194D3×D4—38no—
195D3×D4—64no—
196C2×D12C22×D312yes—
197C2×C4×D3—22no—
198C2×C4×D3—32no—
199C2×C4×D3—32no—
200C2×C4×D3—32no—
201C2×C4×D3—61no—
202C2×C4×D3—62no—
203C2×C4×D3—62no—
204C2×C4×D3—62no—
205C2×C4×D3—62no—
206C2×C4×D3—121no—
207C2×C4×D3—121no—
208C2×C4×D3—128no—
209C2×Dic6—22no—
210C2×Dic6—62no—
211C2×Dic6—62no—
212C2×C3×C8—21no—
213C2×C3×C8—32no—
214C2×C3×C8C22×D312yes—
215C3×C4⋊C4—21no—
216C3×C4⋊C4—21no—
217C3×C4⋊C4—32no—
218C3×C4⋊C4—62no—
219C3×C4⋊C4C22×D312yes—
220C3×C4⋊C4C22×D312yes—
221C3×C22⋊C4—62no—
222C3×C42—32no—
223#217—62no—
224(C2×D3)⋊C4—22no—
225(C2×D3)⋊C4—62no—
226C4⋊Dic3—32no—
227C4⋊Dic3—32no—
228C4⋊Dic3—61no—
229C4⋊Dic3—61no—
230C4⋊Dic3—62no—
231C4⋊Dic3C22×D312yes—
232Dic3⋊C4—22no—
233Dic3⋊C4—62no—
234Dic3⋊C4—62no—
235Dic3⋊C4—62no—
236Dic3⋊C4—62no—
237Dic3⋊C4—121no—
238Dic3⋊C4—121no—
239C4×Dic3—32no—
240C4×Dic3—32no—
241C4×Dic3C22×D312yes—
242C2×C3⋊C8—32no—
243C2×C3⋊C8—61no—
244C2×C3⋊C8C22×D312yes—
245D3×C8—64no—
246D3×C8—64no—
247D3×C8—64no—
248C22×C32C22×D411yescharacteristic
249C2×C3⋊D3C22⋊Q812yes—
250C2×C3⋊D3C2×D812yes—
251C2×C3⋊D3#13712yes—
252C2×C3×D3—24no—
253C2×C3×D3—42no—
254C2×C3×D3—42no—
255D32—48no—
256C32×C4—41no—
257C32×C4—41no—
258C32×C4C22×Q811yescharacteristic
259C32×C4C2×#4111yescharacteristic
260C3⋊Dic3—41no—
261C3⋊Dic3—41no—
262C3⋊Dic3C22⋊Q812yes—
263C3×Dic3—22no—
264C3×Dic3—42no—
265C3×Dic3C2×D814yes—
266C22×Q8—181no—
267C22×D4—91no—
268C23×C4—181no—
269C22×C8—91no—
270C22×C8—91no—
271C4⋊Q8—32no—
272C4⋊Q8—92no—
273C4⋊Q8—182no—
274C4×D4—32no—
275C4×D4—92no—
276C4×D4—182no—
277C2×C4⋊C4—91no—
278C2×C4⋊C4—91no—
279C2×C4⋊C4—91no—
280C2×C4⋊C4—181no—
281C2×C22⋊C4—181no—
282C2×C42—91no—
283#107—32no—
284#107—92no—
285#107—91no—
286#107—91no—
287#107—91no—
288#107D3211yescharacteristic, complemented
289C4⋊C8—32no—
290C4⋊C8—92no—
291#102—32no—
292#102—32no—
293#102—92no—
294#102—92no—
295C23×C3—62no—
296C22×D3—22no—
297C22×D3—32no—
298C22×D3—61no—
299C22×D3—68no—
300C22×D3—124no—
301C22×D3—124no—
302C3×Q8—124no—
303C3×D4—34no—
304C3×D4—62no—
305C2×C3×C4—22no—
306C2×C3×C4—22no—
307C2×C3×C4—21no—
308C2×C3×C4—32no—
309C2×C3×C4—32no—
310C2×C3×C4—41no—
311C2×C3×C4—41no—
312C2×C3×C4—62no—
313C2×C3×C4—124no—
314C2×C3×C4C23×D312yes—
315#67—68no—
316C2×Dic3—22no—
317C2×Dic3—32no—
318C2×Dic3—61no—
319C2×Dic3—62no—
320C2×Dic3—62no—
321C2×Dic3—121no—
322C2×Dic3—121no—
323C2×Dic3—124no—
324C2×Dic3D3×D412yes—
325C2×Dic3D3×D412yes—
326D12—22no—
327D12D3×Q814yescomplemented
328C4×D3—34no—
329C4×D3—34no—
330C4×D3—38no—
331C4×D3—44no—
332C4×D3—62no—
333C4×D3—62no—
334C4×D3—64no—
335C4×D3—124no—
336C4×D3—124no—
337C4×D3—124no—
338C4×D3—124no—
339C4×D3—242no—
340C4×D3—242no—
341Dic6—44no—
342Dic6—124no—
343Dic6—124no—
344C3×C8—22no—
345C3×C8—22no—
346C3×C8—62no—
347C3⋊C8—22no—
348C3⋊C8—62no—
349C3⋊C8—62no—
350C2×C32C2×C22⋊Q811yescharacteristic
351C2×C32C22×D811yescharacteristic
352C2×C32C2×#13711yescharacteristic
353C3⋊D3#47414yescomplemented
354C3×D3—44no—
355C24—181no—
356C2×Q8—62no—
357C2×Q8—182no—
358C2×Q8—364no—
359C2×D4—32no—
360C2×D4—94no—
361C2×D4—182no—
362C2×D4—181no—
363C22×C4—62no—
364C22×C4—91no—
365C22×C4—91no—
366C22×C4—91no—
367C22×C4—181no—
368C22×C4—181no—
369C22×C4—182no—
370C22×C4—181no—
371C22×C4—364no—
372C2×C8—32no—
373C2×C8—91no—
374C2×C8—182no—
375C2×C8—182no—
376C2×C8C2×D3211yescharacteristic
377C4⋊C4—32no—
378C4⋊C4—62no—
379C4⋊C4—91no—
380C4⋊C4—91no—
381C4⋊C4—181no—
382C4⋊C4—181no—
383C4⋊C4—182no—
384C4⋊C4—181no—
385C4⋊C4C2×D3211yescharacteristic
386C4⋊C4C2×D3211yescharacteristic
387C22⋊C4—62no—
388C22⋊C4—182no—
389C42—32no—
390C42—92no—
391C22×C3—21no—
392C22×C3—64no—
393C22×C3—122no—
394C22×C3—122no—
395C22×C3C2×D3×D412yes—
396C2×D3—24no—
397C2×D3—34no—
398C2×D3—34no—
399C2×D3—34no—
400C2×D3—42no—
401C2×D3—42no—
402C2×D3—62no—
403C2×D3—62no—
404C2×D3—62no—
405C2×D3—1216no—
406C3×C4—21no—
407C3×C4—21no—
408C3×C4—34no—
409C3×C4—42no—
410C3×C4—42no—
411C3×C4—62no—
412C3×C4—81no—
413C3×C4—81no—
414C3×C4—122no—
415C3×C4C2×D3×Q812yes—
416C3×C4D3×#4112yes—
417Dic3—22no—
418Dic3—34no—
419Dic3—42no—
420Dic3—62no—
421Dic3—122no—
422Dic3—122no—
423Dic3—241no—
424Dic3—241no—
425Dic3D3×D814yes—
426C32C2×#47411yescharacteristic, complemented, Sylow
427C23—62no—
428C23—91no—
429C23—184no—
430C23—362no—
431C23—362no—
432Q8—124no—
433Q8—364no—
434D4—34no—
435D4—62no—
436D4—184no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—32no—
440C2×C4—32no—
441C2×C4—62no—
442C2×C4—94no—
443C2×C4—91no—
444C2×C4—92no—
445C2×C4—92no—
446C2×C4—124no—
447C2×C4—182no—
448C2×C4—181no—
449C2×C4—181no—
450C2×C4—364no—
451C2×C4—362no—
452C2×C4—362no—
453C2×C4—362no—
454C2×C4C22×D3211yescharacteristic
455C8—21no—
456C8—62no—
457C8—181no—
458C2×C3—21no—
459C2×C3—21no—
460C2×C3—21no—
461C2×C3—124no—
462C2×C3D3×C22⋊Q812yes—
463C2×C3C2×D3×D812yes—
464C2×C3D3×#13712yes—
465D3—38no—
466D3—44no—
467D3—64no—
468C22—64no—
469C22—92no—
470C22—92no—
471C22—92no—
472C22—122no—
473C22—122no—
474C22—368no—
475C22D32×D411yescharacteristic
476C4—34no—
477C4—41no—
478C4—41no—
479C4—62no—
480C4—92no—
481C4—122no—
482C4—361no—
483C4—361no—
484C4#6430611yescharacteristic
485C4D32×Q811yescharacteristic
486C3—21no—
487C3D3×#47412yescomplemented
488C2—94no—
489C2—124no—
490C2#1059462411yescharacteristic
491C2D32×D811yescharacteristic
492C2#1059476011yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#107C22
socleC22×C32C22×D4
prime radicalC2×#3802C22
hypercenter#107D32
hypocenterC32C2×#474
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
2. #10594374C2semidirect
3. C3⋊D3×#107C2semidirect
4. C3×#4890C2semidirect
6. #10590762C2semidirect
7. #10590658C2semidirect
9. #10590573C2semidirect
10. #10590555C2semidirect
11. #10590463C2semidirect
20. C3×#888C22semidirect
22. #63918C22semidirect
30. C32×#107C22semidirect
31. #63645C22semidirect
32. #63634C22semidirect
33. #63634C22semidirect
35. C3×Dic3⋊C8C22semidirect
37. C3×#807C22semidirect
38. #63575C22semidirect
39. Dic3⋊(C3⋊C8)C22semidirect
48. #4890D3semidirect
72. #3802Q8semidirect
115. #888C2×D3semidirect
123. C3×#107C2×D3semidirect
135. Dic3⋊C8C2×D3semidirect
143. #807C2×D3semidirect
164. C3×D12C2×Q8semidirect
288. #107D32semidirect
327. D12D3×Q8semidirect
353. C3⋊D3#474semidirect
426. C32C2×#474semidirect
487. C3D3×#474semidirect

Maximal subgroups

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

subgroupindex
#105946052
#105943742
C3⋊D3×#1072
C3×#48902
#105909402
#105907622
#105906582
#105905932
#105905732
#105905552
#105904632
D3×#4743