Finite Group Databasebeta

← #11786698

Subgroups — #11786698

Order 1152.

659 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594986C211yesmaximal, characteristic
2C3×#5133C211yesmaximal, characteristic
3#10591359C211yesmaximal, characteristic, complemented
4#10591130C211yesmaximal, characteristic, complemented
5C2×#63568C211yesmaximal, characteristic
6#10589421C211yesmaximal, characteristic, complemented
7C3×#4554C211yesmaximal, characteristic, complemented
8#70297—31nomaximal
9#69002—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12#64135C2211yescharacteristic
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17Dic3×#67—22no—
18C2×#3724—22no—
19#63898—21no—
20D3×C4⋊Dic3—21no—
21#63843—21no—
22#63841—21no—
23C3×#821—21no—
24C3×#816—21no—
25#63575—21no—
26#63573—21no—
27#63568C414yescomplemented
28#5827—31no—
29#5504—31no—
30C3×#417—31no—
31C2×#837—31no—
32C2×#825—31no—
33#5133D311yescharacteristic
34#5121—31no—
35#4975—31no—
36#4975—31no—
37#4964—31no—
38C3×#343—31no—
39#4555—31no—
40#4555—31no—
41#4555—61no—
42#4554D311yescharacteristic, complemented
43C22×C32×C4C2311yescharacteristic
44C22×C3⋊Dic3—21no—
45C2×C3×#67—21no—
46C22×C3×Dic3—21no—
47C22×C3×Dic3D412yes—
48C3×#235—21no—
49C3×#235—21no—
50C3×#235C2×C412yes—
51C3×#235Q812yes—
52C2×C3×D12D411yescharacteristic
53C2×C3×C4×D3—21no—
54C2×C3×Dic6D411yescharacteristic
55C2×D3×Dic3—22no—
56C32×M16—21no—
57C32×M16—21no—
58C2×C32×C8—21no—
59#3757—21no—
60C4⋊(C3⋊Dic3)D411yescharacteristic
61C4⋊(C3⋊Dic3)D411yescharacteristic
62C4×C3⋊Dic3—21no—
63C4×C3⋊Dic3—21no—
64C4×C3⋊Dic3C2×C412yescomplemented
65C3×C4⋊Dic3—21no—
66C3×C4⋊Dic3—21no—
67C3×C4⋊Dic3—21no—
68C3×C4⋊Dic3—21no—
69C3×#208—21no—
70C3×#208C2×C412yescomplemented
71C2×C3×C3⋊C8—21no—
72#3724—44no—
73Dic3⋊Dic3—22no—
74(C2×D3)⋊Dic3—22no—
75Dic32—22no—
76#1859—91noSylow
77C2×C3×#41—31no—
78C2×#235C2×D311yescharacteristic
79C2×C3×M16—21no—
80C2×C3×M16—31no—
81C2×C3×M16C2×D311yescharacteristic
82C2×C3×M16C2×D311yescharacteristic
83C2×C3×C4⋊C4—31no—
84C2×C3×C4⋊C4—31no—
85Q8×Dic3—61no—
86D4×Dic3—61no—
87D4×Dic3—62no—
88C4×#67—62no—
89#926—31no—
90#926—31no—
91#926—61no—
92#926—61no—
93C2×C4⋊Dic3—61no—
94C2×C4⋊Dic3C2×D311yescharacteristic
95C2×C4⋊Dic3C2×D311yescharacteristic
96C2×Dic3⋊C4—62no—
97C2×Dic3⋊C4—62no—
98C2×C4×Dic3—31no—
99C2×C4×Dic3—31no—
100C2×C4×Dic3—61no—
101C2×#208C2×D311yescharacteristic
102#893—61no—
103#892—61no—
104D3×C4⋊C4—61no—
105#887—61no—
106C3×#103—61no—
107C3×#102—61no—
108#837—34no—
109#825—34no—
110#821—21no—
111#818—61no—
112#817—61no—
113#816—21no—
114#808—61no—
115#807—61no—
116C23×C32C2×D411yescharacteristic
117C22×C3×D3—21no—
118C2×C32×C4C22×C411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4C2×Q811yescharacteristic
122C2×C32×C4#4111yescharacteristic
123C2×C32×C4#4111yescharacteristic
124C2×C3⋊Dic3—22no—
125C2×C3⋊Dic3—22no—
126C2×C3⋊Dic3—22no—
127C2×C3⋊Dic3—21no—
128C2×C3⋊Dic3—21no—
129C3×#67—22no—
130C3×#67—22no—
131C2×C3×Dic3—21no—
132C2×C3×Dic3—22no—
133C2×C3×Dic3—42no—
134C2×C3×Dic3—42no—
135C2×C3×Dic3—41no—
136C3×D12—21no—
137C3×D12C4⋊C412yescomplemented
138C3×C4×D3—22no—
139C3×C4×D3—22no—
140C3×Dic6—21no—
141C3×Dic6C4⋊C412yescomplemented
142D3×Dic3—82no—
143C32×C8—41no—
144C3×C3⋊C8—22no—
145#520—91no—
146#428—91no—
147C2×#104—91no—
148#417—31no—
149#384—91no—
150#343—31no—
151#339—91no—
152C3×#41—32no—
153C3×#41—32no—
154C3×#41—61no—
155C3×#41—61no—
156C2×C3×Q8—31no—
157C2×C3×D4—31no—
158C2×C3×D4—61no—
159C22×C3×C4—21no—
160C22×C3×C4—32no—
161C22×C3×C4—61no—
162C22×C3×C4—61no—
163C22×C3×C4C22×D311yescharacteristic
164C22×C3×C4C22×D311yescharacteristic
165C2×#67—21no—
166C22×Dic3—21no—
167C22×Dic3—62no—
168C22×Dic3—61no—
169C22×Dic3—61no—
170C22×Dic3—121no—
171C22×Dic3D1212yes—
172#235—21no—
173#235—21no—
174#235Dic612yes—
175#235C4×D312yes—
176C2×D12#6711yescharacteristic
177C2×C4×D3—21no—
178C2×C4×D3—62no—
179C2×Dic6#6711yescharacteristic
180C3×M16—22no—
181C3×M16—21no—
182C3×M16—21no—
183C3×M16—21no—
184C3×M16—21no—
185C3×M16—32no—
186C3×M16—41no—
187C3×M16—61no—
188C2×C3×C8—21no—
189C2×C3×C8—21no—
190C2×C3×C8—41no—
191C2×C3×C8—61no—
192C3×C4⋊C4—61no—
193C3×C4⋊C4—61no—
194C3×C4⋊C4—61no—
195C3×C4⋊C4—61no—
196#217—62no—
197#217—61no—
198#217—61no—
199#217—121no—
200(C2×D3)⋊C4—62no—
201C4⋊Dic3—21no—
202C4⋊Dic3—21no—
203C4⋊Dic3—21no—
204C4⋊Dic3—21no—
205C4⋊Dic3—31no—
206C4⋊Dic3—31no—
207C4⋊Dic3—31no—
208C4⋊Dic3—31no—
209C4⋊Dic3—61no—
210C4⋊Dic3—61no—
211C4⋊Dic3—62no—
212Dic3⋊C4—62no—
213Dic3⋊C4—124no—
214Dic3⋊C4—124no—
215C4×Dic3—32no—
216C4×Dic3—32no—
217C4×Dic3—62no—
218C4×Dic3—62no—
219C4×Dic3—62no—
220C4×Dic3—61no—
221C4×Dic3—61no—
222C4×Dic3—61no—
223C4×Dic3—61no—
224C4×Dic3—121no—
225C4×Dic3—121no—
226#208—21no—
227#208C4×D312yescomplemented
228C2×C3⋊C8—21no—
229C22×C32—21no—
230C22×C32—21no—
231C22×C32C4×D411yescharacteristic
232C22×C32#12011yescharacteristic
233C22×C32C22⋊Q811yescharacteristic
234C2×C3×D3—22no—
235C2×C3×D3—41no—
236C2×C3×D3—41no—
237C32×C4C2×C4⋊C411yescharacteristic
238C32×C4C4×D411yescharacteristic
239C32×C4C22⋊Q811yescharacteristic
240C32×C4#12311yescharacteristic
241C3⋊Dic3—24no—
242C3⋊Dic3—41no—
243C3⋊Dic3—41no—
244C3×Dic3—22no—
245C3×Dic3—42no—
246C3×Dic3—81no—
247C2×#41—31no—
248C2×M16—31no—
249C2×M16D3211yescharacteristic
250C4×Q8—181no—
251C4×D4—181no—
252C4×D4—182no—
253#117—91no—
254#117—181no—
255C2×C4⋊C4—31no—
256C2×C4⋊C4—31no—
257C2×C4⋊C4—181no—
258C2×C4⋊C4—182no—
259C2×C42—91no—
260#107—181no—
261#106—181no—
262#104—94no—
263#103—61no—
264#102—61no—
265C23×C3—21no—
266C23×C3—61no—
267C23×C3C2×D1211yescharacteristic
268C23×C3D3×D411yescharacteristic
269C22×D3—21no—
270C3×Q8—32no—
271C3×Q8—61no—
272C3×D4—32no—
273C3×D4—62no—
274C3×D4—62no—
275C3×D4—61no—
276C2×C3×C4—21no—
277C2×C3×C4—21no—
278C2×C3×C4—21no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—61no—
283C2×C3×C4—62no—
284C2×C3×C4—62no—
285C2×C3×C4—62no—
286C2×C3×C4—122no—
287C2×C3×C4—122no—
288C2×C3×C4—121no—
289C2×C3×C4C2×Dic611yescharacteristic
290C2×C3×C4C2×C4×D311yescharacteristic
291C2×C3×C4C2×C4×D311yescharacteristic
292C2×C3×C4#23511yescharacteristic
293C2×C3×C4D3×D411yescharacteristic
294C2×C3×C4D3×D411yescharacteristic
295C2×C3×C4D3×D411yescharacteristic
296C2×C3×C4#23711yescharacteristic
297C2×C3×C4#23711yescharacteristic
298C2×C3×C4#23711yescharacteristic
299C2×C3×C4D3×Q811yescharacteristic
300C2×C3×C4C2×#6711yescharacteristic
301#67—22no—
302#67—22no—
303C2×Dic3—21no—
304C2×Dic3—22no—
305C2×Dic3—42no—
306C2×Dic3—42no—
307C2×Dic3—41no—
308C2×Dic3—62no—
309C2×Dic3—62no—
310C2×Dic3—62no—
311C2×Dic3—62no—
312C2×Dic3—62no—
313C2×Dic3—62no—
314C2×Dic3—61no—
315C2×Dic3—61no—
316C2×Dic3—61no—
317C2×Dic3—61no—
318C2×Dic3—122no—
319C2×Dic3—122no—
320C2×Dic3—122no—
321C2×Dic3—121no—
322C2×Dic3—121no—
323C2×Dic3—242no—
324D12—21no—
325D12Dic3⋊C412yescomplemented
326C4×D3—22no—
327C4×D3—22no—
328C4×D3—242no—
329Dic6—21no—
330Dic6Dic3⋊C412yescomplemented
331C3×C8—42no—
332C3×C8—41no—
333C3×C8—41no—
334C3×C8—62no—
335C3⋊C8—22no—
336C2×C32—21no—
337C2×C32—21no—
338C2×C32#38511yescharacteristic
339C2×C32#45311yescharacteristic
340C2×C32#45611yescharacteristic
341C3×D3—42no—
342#41—32no—
343#41—32no—
344#41—61no—
345#41—61no—
346C2×Q8—31no—
347C2×D4—31no—
348C2×D4—61no—
349C22×C4—32no—
350C22×C4—61no—
351C22×C4—61no—
352C22×C4—182no—
353C22×C4—181no—
354C22×C4C2×D3211yescharacteristic
355M16—21no—
356M16—21no—
357M16—32no—
358M16—61no—
359C2×C8—21no—
360C2×C8—61no—
361C4⋊C4—61no—
362C4⋊C4—61no—
363C4⋊C4—61no—
364C4⋊C4—61no—
365C4⋊C4—91no—
366C4⋊C4—91no—
367C4⋊C4—182no—
368C4⋊C4—364no—
369C22⋊C4—182no—
370C22⋊C4—181no—
371C42—92no—
372C42—182no—
373C42—181no—
374C42—181no—
375C22×C3—21no—
376C22×C3—21no—
377C22×C3—21no—
378C22×C3—21no—
379C22×C3—21no—
380C22×C3—21no—
381C22×C3—21no—
382C22×C3—41no—
383C22×C3—41no—
384C22×C3—62no—
385C22×C3—121no—
386C22×C3—121no—
387C22×C3C4×D1211yescharacteristic
388C22×C3#87811yescharacteristic
389C22×C3#67⋊C411yescharacteristic
390C22×C3#88211yescharacteristic
391C22×C3#89711yescharacteristic
392C22×C3#93711yescharacteristic
393C2×D3—22no—
394C2×D3—41no—
395C2×D3—41no—
396C3×C4—21no—
397C3×C4—21no—
398C3×C4—21no—
399C3×C4—21no—
400C3×C4—62no—
401C3×C4—122no—
402C3×C4—241no—
403C3×C4#87811yescharacteristic
404C3×C4#67⋊C411yescharacteristic
405C3×C4#67⋊C411yescharacteristic
406C3×C4#88311yescharacteristic
407C3×C4D3×C4⋊C411yescharacteristic
408C3×C4#89611yescharacteristic
409C3×C4C2×Dic3⋊C411yescharacteristic
410C3×C4#93511yescharacteristic
411Dic3—22no—
412Dic3—42no—
413Dic3—64no—
414Dic3—64no—
415Dic3—81no—
416Dic3—124no—
417Dic3—121no—
418Dic3—121no—
419Dic3—121no—
420Dic3—121no—
421Dic3—241no—
422Dic3—241no—
423C32#185911yescharacteristic, complemented, Sylow
424C23—61no—
425C23D3×D1211yescharacteristic
426Q8—32no—
427Q8—61no—
428D4—32no—
429D4—62no—
430D4—62no—
431D4—61no—
432C2×C4—61no—
433C2×C4—62no—
434C2×C4—62no—
435C2×C4—62no—
436C2×C4—122no—
437C2×C4—122no—
438C2×C4—121no—
439C2×C4—182no—
440C2×C4—182no—
441C2×C4—182no—
442C2×C4—181no—
443C2×C4—181no—
444C2×C4—722no—
445C2×C4D3×Dic611yescharacteristic
446C2×C4C4×D3211yescharacteristic
447C2×C4#380211yescharacteristic
448C2×C4#380411yescharacteristic
449C2×C4#380511yescharacteristic
450C2×C4D3×#6711yescharacteristic
451C8—41no—
452C8—62no—
453C2×C3—21no—
454C2×C3—21no—
455C2×C3—21no—
456C2×C3—21no—
457C2×C3—21no—
458C2×C3—21no—
459C2×C3—21no—
460C2×C3—41no—
461C2×C3—41no—
462C2×C3—122no—
463C2×C3#466811yescharacteristic
464C2×C3#474711yescharacteristic
465C2×C3#475211yescharacteristic
466C2×C3#494611yescharacteristic
467C2×C3#519811yescharacteristic
468C2×C3#520511yescharacteristic
469D3—42no—
470C22—21no—
471C22—21no—
472C22—62no—
473C22—121no—
474C22—121no—
475C22#6388011yescharacteristic
476C22#6389311yescharacteristic
477C22#6392211yescharacteristic
478C4—62no—
479C4—122no—
480C4—184no—
481C4—241no—
482C4—361no—
483C4—361no—
484C4D3×Dic3⋊C411yescharacteristic
485C4#6389911yescharacteristic
486C4#6390211yescharacteristic
487C4#6396911yescharacteristic
488C3—21no—
489C3#6900211yescharacteristic, complemented
490C3#7029711yescharacteristic, complemented
491C2—21no—
492C2—21no—
493C2—122no—
494C2#1059101411yescharacteristic
495C2#1059101811yescharacteristic
496C2#1059137311yescharacteristic
subgroupG/H
centerC22#63922
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32#120
prime radicalC2×C3×#235C22
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1859
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
3. #10591359C2semidirect
4. #10591130C2semidirect
6. #10589421C2semidirect
7. C3×#4554C2semidirect
27. #63568C4semidirect
42. #4554D3semidirect
64. C4×C3⋊Dic3C2×C4semidirect
70. C3×#208C2×C4semidirect
137. C3×D12C4⋊C4semidirect
141. C3×Dic6C4⋊C4semidirect
227. #208C4×D3semidirect
325. D12Dic3⋊C4semidirect
330. Dic6Dic3⋊C4semidirect
423. C32#1859semidirect
489. C3#69002semidirect
490. C3#70297semidirect

Maximal subgroups

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

subgroupindex
#105949862
C3×#51332
#105913592
#105911302
C2×#635682
#105894212
C3×#45542
#702973
#690023