Finite Group Databasebeta

← #11786696

Subgroups — #11786696

Order 1152.

689 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594990C211yesmaximal, characteristic
2C2×#63652C211yesmaximal, characteristic
3C3×#5121C211yesmaximal, characteristic, complemented
4#10591359C211yesmaximal, characteristic, complemented
5#10591106C211yesmaximal, characteristic
6C3×#4554C211yesmaximal, characteristic, complemented
7#10589160C211yesmaximal, characteristic, complemented
8#70680—31nomaximal
9#69002—31nomaximal
10C2×#3828C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C2×C4×C3⋊Dic3C2211yescharacteristic
13C3×#926C2211yescharacteristic
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C2×#3724—22no—
18#63952—22no—
19#63900—21no—
20#63894—21no—
21#63849—21no—
22#63844—21no—
23#63652C414yescomplemented
24C3×#818—21no—
25C3×#817—21no—
26#63567—21no—
27#63564—21no—
28#5523—31no—
29#5504—31no—
30C3×#428—31no—
31C2×#825—31no—
32C2×#825—31no—
33C2×#825—61no—
34#5133—31no—
35#5121D311yescharacteristic, complemented
36#4975—31no—
37#4975—31no—
38#4966—31no—
39C3×#343—31no—
40#4555—31no—
41#4554D311yescharacteristic, complemented
42#4532—31no—
43C22×C32×C4C2311yescharacteristic
44C2×#638—21no—
45C22×C3⋊Dic3—21no—
46#3828—21no—
47#3828—21no—
48#3828C2×C412yes—
49#3828Q812yes—
50C2×C4⋊(C3⋊D3)D411yescharacteristic
51C2×C4×C3⋊D3—21no—
52C2×#634D411yescharacteristic
53C22×C3×Dic3—21no—
54C22×C3×Dic3D412yes—
55C2×#624—22no—
56C32×M16—21no—
57C32×M16C2×C412yescomplemented
58C2×C32×C8—21no—
59C4×C3⋊Dic3—21no—
60C4×C3⋊Dic3C2×C412yescomplemented
61C3×#217—21no—
62C3×C4⋊Dic3—21no—
63C3×C4⋊Dic3—21no—
64C3×C4⋊Dic3—21no—
65C3×C4⋊Dic3—21no—
66C3×C4⋊Dic3D411yescharacteristic
67C3×C4⋊Dic3D411yescharacteristic
68C3×C4×Dic3—21no—
69C3×#208—21no—
70C3×#208—21no—
71C2×C3×C3⋊C8—21no—
72#3724—22no—
73#3724—44no—
74#3722—22no—
75Dic32—22no—
76#1859—91noSylow
77C2×#235—31no—
78C2×#235—31no—
79C2×#235—61no—
80C2×C3×M16—21no—
81C2×C3×M16—31no—
82C2×C3×M16C2×D311yescharacteristic
83C2×C3×M16C2×D311yescharacteristic
84C3×#117—31no—
85C2×C3×C4⋊C4—31no—
86C2×C3×C4⋊C4—31no—
87C4×#67—62no—
88#926C2×D311yescharacteristic
89C2×C4⋊Dic3C2×D311yescharacteristic
90C2×C4⋊Dic3C2×D311yescharacteristic
91C2×Dic3⋊C4—62no—
92C2×Dic3⋊C4—62no—
93C2×C4×Dic3—31no—
94C2×C4×Dic3—31no—
95C2×C4×Dic3—61no—
96C2×#208C2×D311yescharacteristic
97#893—61no—
98#892—61no—
99#892—61no—
100D3×C4⋊C4—61no—
101D3×C4⋊C4—61no—
102#887—61no—
103#67⋊C4—62no—
104C4×D12—61no—
105C4×Dic6—61no—
106C3×#107—61no—
107C3×#106—61no—
108#825—34no—
109#825—34no—
110#825—64no—
111#821—61no—
112#818—21no—
113#817—21no—
114#816—61no—
115#810—61no—
116#809—61no—
117C23×C32C2×D411yescharacteristic
118C22×C3⋊D3—21no—
119C2×C32×C4C22×C411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4C2×Q811yescharacteristic
123C2×C32×C4#4111yescharacteristic
124C2×C32×C4#4111yescharacteristic
125#638—22no—
126#638—22no—
127C2×C3⋊Dic3—22no—
128C2×C3⋊Dic3—22no—
129C2×C3⋊Dic3—22no—
130C2×C3⋊Dic3—21no—
131C4⋊(C3⋊D3)—21no—
132C4⋊(C3⋊D3)C4⋊C412yescomplemented
133C4×C3⋊D3—22no—
134C4×C3⋊D3—22no—
135#634—21no—
136#634C4⋊C412yescomplemented
137C2×C3×Dic3—21no—
138C2×C3×Dic3—22no—
139C2×C3×Dic3—21no—
140C2×C3×Dic3—42no—
141C2×C3×Dic3—42no—
142C2×C3×Dic3—41no—
143#624—82no—
144C32×C8—22no—
145C3×C3⋊C8—41no—
146#520—91no—
147#428—31no—
148C2×#104—91no—
149#417—91no—
150#384—91no—
151#343—31no—
152#339—91no—
153C22×C3×C4—21no—
154C22×C3×C4—32no—
155C22×C3×C4—61no—
156C22×C3×C4C22×D311yescharacteristic
157C22×C3×C4C22×D311yescharacteristic
158C2×#67—61no—
159C2×#67—61no—
160C2×#67—121no—
161C22×Dic3—21no—
162C22×Dic3—61no—
163C22×Dic3—61no—
164C22×Dic3—121no—
165C22×Dic3D1212yes—
166#235—32no—
167#235—32no—
168#235—32no—
169#235—32no—
170#235—62no—
171#235—62no—
172#235—61no—
173#235—61no—
174#235—61no—
175#235—61no—
176#235—121no—
177#235—121no—
178C2×D12—31no—
179C2×D12—31no—
180C2×D12—61no—
181C2×C4×D3—61no—
182C2×C4×D3—61no—
183C2×C4×D3—62no—
184C2×C4×D3—62no—
185C2×C4×D3—121no—
186C2×Dic6—31no—
187C2×Dic6—31no—
188C2×Dic6—61no—
189C3×M16—21no—
190C3×M16—21no—
191C3×M16—22no—
192C3×M16—41no—
193C3×M16—61no—
194C3×M16—61no—
195C3×M16C4×D312yescomplemented
196C3×M16C4×D312yescomplemented
197C2×C3×C8—21no—
198C2×C3×C8—21no—
199C2×C3×C8—41no—
200C2×C3×C8—61no—
201C3×C4⋊C4—31no—
202C3×C4⋊C4—31no—
203C3×C4⋊C4—61no—
204C3×C4⋊C4—61no—
205C3×C4⋊C4—61no—
206C3×C4⋊C4—61no—
207C3×C22⋊C4—61no—
208C3×C42—61no—
209#217—21no—
210(C2×D3)⋊C4—62no—
211(C2×D3)⋊C4—62no—
212C4⋊Dic3—21no—
213C4⋊Dic3—21no—
214C4⋊Dic3—21no—
215C4⋊Dic3—21no—
216C4⋊Dic3#6711yescharacteristic
217C4⋊Dic3#6711yescharacteristic
218Dic3⋊C4—62no—
219Dic3⋊C4—62no—
220Dic3⋊C4—124no—
221Dic3⋊C4—124no—
222C4×Dic3—21no—
223C4×Dic3—32no—
224C4×Dic3—32no—
225C4×Dic3—62no—
226C4×Dic3—62no—
227C4×Dic3—62no—
228C4×Dic3—61no—
229C4×Dic3—61no—
230C4×Dic3—121no—
231#208—21no—
232#208—21no—
233C2×C3⋊C8—21no—
234C22×C32—21no—
235C22×C32—21no—
236C22×C32C4×D411yescharacteristic
237C22×C32#12011yescharacteristic
238C22×C32C22⋊Q811yescharacteristic
239C2×C3⋊D3—22no—
240C2×C3⋊D3—41no—
241C2×C3⋊D3—41no—
242C32×C4C2×C4⋊C411yescharacteristic
243C32×C4C4×D411yescharacteristic
244C32×C4C22⋊Q811yescharacteristic
245C32×C4#12311yescharacteristic
246C3⋊Dic3—24no—
247C3⋊Dic3—22no—
248C3×Dic3—41no—
249C3×Dic3—42no—
250C3×Dic3—41no—
251C3×Dic3—81no—
252C2×#41—91no—
253C2×M16—31no—
254C2×M16D3211yescharacteristic
255C4×Q8—181no—
256C4×D4—181no—
257C4×D4—182no—
258#117—31no—
259#117—181no—
260C2×C4⋊C4—31no—
261C2×C4⋊C4—31no—
262C2×C4⋊C4—181no—
263C2×C4⋊C4—182no—
264C2×C42—91no—
265#107—61no—
266#106—61no—
267#104—94no—
268#103—181no—
269#102—181no—
270C23×C3—21no—
271C23×C3C2×D1211yescharacteristic
272C23×C3D3×D411yescharacteristic
273C22×D3—61no—
274C22×D3—61no—
275C22×D3—121no—
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—61no—
284C2×C3×C4—62no—
285C2×C3×C4—122no—
286C2×C3×C4—122no—
287C2×C3×C4—121no—
288C2×C3×C4C2×C4×D311yescharacteristic
289C2×C3×C4C2×C4×D311yescharacteristic
290C2×C3×C4#23511yescharacteristic
291C2×C3×C4#23511yescharacteristic
292C2×C3×C4D3×D411yescharacteristic
293C2×C3×C4D3×D411yescharacteristic
294C2×C3×C4D3×D411yescharacteristic
295C2×C3×C4#23711yescharacteristic
296C2×C3×C4D3×Q811yescharacteristic
297C2×C3×C4D3×Q811yescharacteristic
298C2×C3×C4#23911yescharacteristic
299C2×C3×C4C2×#6711yescharacteristic
300#67—62no—
301#67—62no—
302#67—62no—
303#67—62no—
304#67—122no—
305#67—122no—
306C2×Dic3—22no—
307C2×Dic3—21no—
308C2×Dic3—21no—
309C2×Dic3—42no—
310C2×Dic3—42no—
311C2×Dic3—41no—
312C2×Dic3—62no—
313C2×Dic3—62no—
314C2×Dic3—62no—
315C2×Dic3—62no—
316C2×Dic3—62no—
317C2×Dic3—61no—
318C2×Dic3—62no—
319C2×Dic3—61no—
320C2×Dic3—122no—
321C2×Dic3—121no—
322C2×Dic3—122no—
323C2×Dic3—122no—
324D12—32no—
325D12—32no—
326D12—62no—
327D12—61no—
328D12—61no—
329D12—121no—
330C4×D3—62no—
331C4×D3—62no—
332C4×D3—62no—
333C4×D3—62no—
334C4×D3—122no—
335C4×D3—122no—
336C4×D3—242no—
337C4×D3—242no—
338Dic6—32no—
339Dic6—32no—
340Dic6—62no—
341Dic6—61no—
342Dic6—61no—
343Dic6—121no—
344C3×C8—22no—
345C3×C8—22no—
346C3×C8—42no—
347C3×C8—121no—
348C3⋊C8—41no—
349C2×C32—21no—
350C2×C32—21no—
351C2×C32#38511yescharacteristic
352C2×C32#45311yescharacteristic
353C2×C32#45611yescharacteristic
354C3⋊D3—42no—
355#41—92no—
356#41—92no—
357#41—181no—
358#41—181no—
359C2×Q8—91no—
360C2×D4—91no—
361C2×D4—181no—
362C22×C4—32no—
363C22×C4—61no—
364C22×C4—182no—
365C22×C4—181no—
366C22×C4—181no—
367C22×C4C2×D3211yescharacteristic
368M16—21no—
369M16—61no—
370M16—61no—
371M16#62412yescomplemented
372C2×C8—21no—
373C2×C8—61no—
374C4⋊C4—31no—
375C4⋊C4—31no—
376C4⋊C4—61no—
377C4⋊C4—61no—
378C4⋊C4—61no—
379C4⋊C4—61no—
380C4⋊C4—182no—
381C4⋊C4—364no—
382C22⋊C4—61no—
383C22⋊C4—182no—
384C42—61no—
385C42—92no—
386C42—182no—
387C42—181no—
388C22×C3—21no—
389C22×C3—21no—
390C22×C3—21no—
391C22×C3—21no—
392C22×C3—21no—
393C22×C3—21no—
394C22×C3—21no—
395C22×C3—41no—
396C22×C3—41no—
397C22×C3C4×D1211yescharacteristic
398C22×C3#88211yescharacteristic
399C22×C3#89311yescharacteristic
400C22×C3#89611yescharacteristic
401C22×C3#89711yescharacteristic
402C22×C3#93711yescharacteristic
403C2×D3—62no—
404C2×D3—62no—
405C2×D3—122no—
406C2×D3—121no—
407C2×D3—121no—
408C2×D3—121no—
409C2×D3—121no—
410C2×D3—241no—
411C2×D3—241no—
412C3×C4—21no—
413C3×C4—21no—
414C3×C4—21no—
415C3×C4—21no—
416C3×C4—122no—
417C3×C4—121no—
418C3×C4—121no—
419C3×C4—241no—
420C3×C4#67⋊C411yescharacteristic
421C3×C4#88311yescharacteristic
422C3×C4D3×C4⋊C411yescharacteristic
423C3×C4D3×C4⋊C411yescharacteristic
424C3×C4#89411yescharacteristic
425C3×C4#89611yescharacteristic
426C3×C4C4×#6711yescharacteristic
427C3×C4#94611yescharacteristic
428Dic3—41no—
429Dic3—41no—
430Dic3—42no—
431Dic3—64no—
432Dic3—64no—
433Dic3—62no—
434Dic3—62no—
435Dic3—81no—
436Dic3—122no—
437Dic3—124no—
438C32#185911yescharacteristic, complemented, Sylow
439C23—181no—
440C23D3×D1211yescharacteristic
441Q8—92no—
442Q8—181no—
443D4—92no—
444D4—182no—
445D4—182no—
446D4—181no—
447C2×C4—61no—
448C2×C4—61no—
449C2×C4—62no—
450C2×C4—122no—
451C2×C4—122no—
452C2×C4—121no—
453C2×C4—182no—
454C2×C4—182no—
455C2×C4—182no—
456C2×C4—181no—
457C2×C4—182no—
458C2×C4—182no—
459C2×C4—722no—
460C2×C4#379711yescharacteristic
461C2×C4#379911yescharacteristic
462C2×C4#380211yescharacteristic
463C2×C4#380411yescharacteristic
464C2×C4C2×#62411yescharacteristic
465C2×C4D3×#6711yescharacteristic
466C8—22no—
467C8—121no—
468C2×C3—21no—
469C2×C3—21no—
470C2×C3—21no—
471C2×C3—21no—
472C2×C3—21no—
473C2×C3—21no—
474C2×C3—21no—
475C2×C3—41no—
476C2×C3—41no—
477C2×C3#466811yescharacteristic
478C2×C3#474711yescharacteristic
479C2×C3#475211yescharacteristic
480C2×C3#498911yescharacteristic
481C2×C3#519811yescharacteristic
482C2×C3#520511yescharacteristic
483D3—122no—
484D3—122no—
485D3—242no—
486C22—21no—
487C22—21no—
488C22—182no—
489C22—361no—
490C22—361no—
491C22#6389411yescharacteristic
492C22#6389511yescharacteristic
493C22#6392211yescharacteristic
494C4—122no—
495C4—121no—
496C4—121no—
497C4—184no—
498C4—182no—
499C4—241no—
500C4#6385411yescharacteristic
501C4#6388811yescharacteristic
502C4#6390011yescharacteristic
503C4#6395211yescharacteristic
504C3—21no—
505C3#6900211yescharacteristic, complemented
506C3#7068011yescharacteristic, complemented
507C2—21no—
508C2—21no—
509C2—362no—
510C2#1059101411yescharacteristic
511C2#1059101811yescharacteristic
512C2#1059137811yescharacteristic
subgroupG/H
centerC22#63922
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32#120
prime radicalC2×#3828C22
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. C3×#5121C2semidirect
4. #10591359C2semidirect
6. C3×#4554C2semidirect
7. #10589160C2semidirect
23. #63652C4semidirect
35. #5121D3semidirect
41. #4554D3semidirect
57. C32×M16C2×C4semidirect
60. C4×C3⋊Dic3C2×C4semidirect
132. C4⋊(C3⋊D3)C4⋊C4semidirect
136. #634C4⋊C4semidirect
195. C3×M16C4×D3semidirect
196. C3×M16C4×D3semidirect
371. M16#624semidirect
438. C32#1859semidirect
505. C3#69002semidirect
506. C3#70680semidirect

Maximal subgroups

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

subgroupindex
#105949902
C2×#636522
C3×#51212
#105913592
#105911062
C3×#45542
#105891602
#706803
#690023