Finite Group Databasebeta

← #11786592

Subgroups — #11786592

Order 1152.

703 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594982C211yesmaximal, characteristic
2C3×#4939C211yesmaximal, characteristic
3#10591139C211yesmaximal, characteristic, complemented
4#10591130C211yesmaximal, characteristic, complemented
5C2×#63558C211yesmaximal, characteristic
6#10589389C211yesmaximal, characteristic, complemented
7C3×#4523C211yesmaximal, characteristic, complemented
8#69642—31nomaximal
9#68758—31nomaximal
10C22×C3×D12C2211yescharacteristic
11C2×C32×C42C2211yescharacteristic
12#64135C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C2×C3×(C2×D3)⋊C4—22no—
15C3×#926C2211yescharacteristic
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C2×C3×#208C2211yescharacteristic
18D3×#217—22no—
19#63898—21no—
20#63898—21no—
21Dic3×D12—21no—
22Dic3×D12—21no—
23#63576—21no—
24#63575—21no—
25#63574—21no—
26#63573—21no—
27#63558C414yescomplemented
28#5798—31no—
29#5521—31no—
30C3×#390—31no—
31C2×#833—31no—
32C2×#823—31no—
33#5121—31no—
34#4995—31no—
35#4964—31no—
36#4964—31no—
37#4939D311yescharacteristic
38C3×#339—31no—
39#4523—31no—
40#4523—31no—
41#4523—61no—
42#4523D311yescharacteristic, complemented
43C23×C3×D3D412yes—
44C22×C32×C4—21no—
45C22×C32×C4C2311yescharacteristic
46C22×C3×Dic3—21no—
47C2×C3×D12—21no—
48C2×C3×D12—21no—
49C2×C3×D12—21no—
50C2×C3×D12—21no—
51C2×C3×D12C2×C412yes—
52C2×C3×D12Q812yes—
53C2×D3×Dic3—22no—
54C2×D3×Dic3—22no—
55C32×C42—21no—
56C32×C42—21no—
57#3757—21no—
58C4⋊(C3⋊Dic3)D411yescharacteristic
59C4⋊(C3⋊Dic3)D411yescharacteristic
60C4×C3⋊Dic3—21no—
61#3748—21no—
62#3748C2×C412yescomplemented
63C2×C3⋊(C3⋊C8)—21no—
64C3×#217—21no—
65C3×(C2×D3)⋊C4—44no—
66C3×C4⋊Dic3—21no—
67C3×C4⋊Dic3—21no—
68C3×C4⋊Dic3D411yescharacteristic
69C3×C4⋊Dic3D411yescharacteristic
70C3×C4×Dic3—21no—
71C3×#208—21no—
72C3×#208C2×C412yescomplemented
73C2×C3×C3⋊C8—21no—
74(C2×D3)⋊Dic3—22no—
75(C2×D3)⋊Dic3—22no—
76#1856—91noSylow
77C22×C3×D4—31no—
78C22×D12C2×D311yescharacteristic
79C2×C3×M16—31no—
80C3×#117—31no—
81C2×C3×C4⋊C4—31no—
82C2×C3×C22⋊C4—62no—
83C2×C3×C42—21no—
84C2×C3×C42C2×D311yescharacteristic
85C2×C3×C42C2×D311yescharacteristic
86C2×#217—62no—
87D4×Dic3—61no—
88D4×Dic3—61no—
89D4×Dic3—61no—
90D4×Dic3—61no—
91C2×(C2×D3)⋊C4—22no—
92#926—31no—
93#926—31no—
94#926—61no—
95#926C2×D311yescharacteristic
96C2×C4⋊Dic3C2×D311yescharacteristic
97C2×#208—31no—
98C2×#208—31no—
99C2×#208—61no—
100C2×#208C2×D311yescharacteristic
101#893—61no—
102#893—61no—
103D3×C22⋊C4—62no—
104C4×D12—61no—
105C4×D12—61no—
106#833—34no—
107#823—34no—
108#818—61no—
109#817—61no—
110#808—61no—
111#808—61no—
112#808—61no—
113#807—61no—
114#807—61no—
115#807—61no—
116C23×C32C2×D411yescharacteristic
117C22×C3×D3—22no—
118C22×C3×D3—22no—
119C22×C3×D3—42no—
120C22×C3×D3—42no—
121C22×C3×D3C4⋊C414yes—
122C2×C32×C4—22no—
123C2×C32×C4—41no—
124C2×C32×C4—41no—
125C2×C32×C4C22×C411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4C2×Q811yescharacteristic
129C2×C32×C4#4111yescharacteristic
130C2×C32×C4#4111yescharacteristic
131C2×C3⋊Dic3—21no—
132C2×C3⋊Dic3—21no—
133C2×C3×Dic3—21no—
134C2×C3×Dic3—21no—
135C2×C3×Dic3—42no—
136C2×C3×Dic3—41no—
137C3×D12—22no—
138C3×D12—22no—
139C3×D12—22no—
140C3×D12—22no—
141D3×Dic3—82no—
142D3×Dic3—82no—
143C3⋊(C3⋊C8)—22no—
144C3×C3⋊C8—22no—
145#518—91no—
146#428—91no—
147#428—91no—
148C2×#100—91no—
149#390—31no—
150#339—31no—
151#339—91no—
152C24×C3—32no—
153C23×D3#6712yes—
154C2×C3×D4—32no—
155C2×C3×D4—32no—
156C2×C3×D4—61no—
157C2×C3×D4—61no—
158C2×C3×D4—61no—
159C2×C3×D4—61no—
160C22×C3×C4—21no—
161C22×C3×C4—21no—
162C22×C3×C4—21no—
163C22×C3×C4—41no—
164C22×C3×C4—61no—
165C22×C3×C4C22×D311yescharacteristic
166C22×C3×C4C22×D311yescharacteristic
167C22×Dic3—21no—
168C22×Dic3—62no—
169C22×Dic3—62no—
170C2×D12—21no—
171C2×D12—21no—
172C2×D12—21no—
173C2×D12—21no—
174C2×D12Dic612yes—
175C2×D12C4×D312yes—
176C2×C4×D3—62no—
177C2×C4×D3—62no—
178C3×M16—32no—
179C3×M16—61no—
180C2×C3×C8—61no—
181C3×C4⋊C4—31no—
182C3×C4⋊C4—31no—
183C3×C4⋊C4—61no—
184C3×C4⋊C4—61no—
185C3×C22⋊C4—61no—
186C3×C22⋊C4—124no—
187C3×C42—22no—
188C3×C42—21no—
189C3×C42—21no—
190C3×C42—21no—
191C3×C42—21no—
192C3×C42—41no—
193C3×C42—61no—
194#217—21no—
195#217—62no—
196#217—62no—
197#217—61no—
198#217—61no—
199#217—121no—
200(C2×D3)⋊C4—44no—
201(C2×D3)⋊C4—62no—
202(C2×D3)⋊C4—62no—
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⋊Dic3D1211yescharacteristic
212C4⋊Dic3D1211yescharacteristic
213C4×Dic3—21no—
214C4×Dic3—61no—
215C4×Dic3—61no—
216C4×Dic3—121no—
217#208—21no—
218#208—32no—
219#208—32no—
220#208—62no—
221#208—61no—
222#208—61no—
223#208—121no—
224#208C4×D312yescomplemented
225C2×C3⋊C8—21no—
226C2×C3⋊C8—61no—
227C2×C3⋊C8—61no—
228C2×C3⋊C8—121no—
229C22×C32—21no—
230C22×C32—21no—
231C22×C32C2×C4⋊C411yescharacteristic
232C22×C32#12011yescharacteristic
233C22×C32#12311yescharacteristic
234C2×C3×D3—24no—
235C2×C3×D3—42no—
236C2×C3×D3—42no—
237C2×C3×D3—44no—
238C2×C3×D3—82no—
239C32×C4—42no—
240C32×C4C4×D411yescharacteristic
241C32×C4C4×D411yescharacteristic
242C32×C4C22⋊Q811yescharacteristic
243C32×C4C22⋊Q811yescharacteristic
244C3⋊Dic3—41no—
245C3⋊Dic3—41no—
246C3×Dic3—41no—
247C3×Dic3—41no—
248C3×Dic3—81no—
249C22×D4—31no—
250C2×M16—31no—
251C2×M16—91no—
252C4×D4—181no—
253C4×D4—181no—
254C4×D4—181no—
255C4×D4—181no—
256#117—31no—
257#117—91no—
258C2×C4⋊C4—31no—
259C2×C22⋊C4—62no—
260C2×C22⋊C4—182no—
261C2×C42D3211yescharacteristic
262#107—181no—
263#107—181no—
264#106—181no—
265#106—181no—
266#100—94no—
267C23×C3—21no—
268C23×C3—34no—
269C23×C3—62no—
270C23×C3—62no—
271C23×C3—122no—
272C23×C3—122no—
273C23×C3D3×D411yescharacteristic
274C23×C3C2×#6711yescharacteristic
275C22×D3—22no—
276C22×D3—22no—
277C22×D3—42no—
278C22×D3—42no—
279C22×D3Dic3⋊C414yes—
280C3×D4—62no—
281C3×D4—62no—
282C3×D4—62no—
283C3×D4—62no—
284C2×C3×C4—22no—
285C2×C3×C4—22no—
286C2×C3×C4—21no—
287C2×C3×C4—21no—
288C2×C3×C4—21no—
289C2×C3×C4—21no—
290C2×C3×C4—21no—
291C2×C3×C4—21no—
292C2×C3×C4—42no—
293C2×C3×C4—42no—
294C2×C3×C4—41no—
295C2×C3×C4—41no—
296C2×C3×C4—42no—
297C2×C3×C4—41no—
298C2×C3×C4—41no—
299C2×C3×C4—61no—
300C2×C3×C4—61no—
301C2×C3×C4—122no—
302C2×C3×C4—121no—
303C2×C3×C4C2×Dic611yescharacteristic
304C2×C3×C4C2×C4×D311yescharacteristic
305C2×C3×C4C2×C4×D311yescharacteristic
306C2×C3×C4C2×D1211yescharacteristic
307C2×C3×C4#23511yescharacteristic
308C2×C3×C4D3×D411yescharacteristic
309C2×C3×C4D3×D411yescharacteristic
310C2×C3×C4D3×D411yescharacteristic
311C2×C3×C4#23711yescharacteristic
312C2×C3×C4#23711yescharacteristic
313C2×C3×C4#23711yescharacteristic
314C2×C3×C4D3×Q811yescharacteristic
315C2×Dic3—21no—
316C2×Dic3—21no—
317C2×Dic3—42no—
318C2×Dic3—41no—
319C2×Dic3—61no—
320C2×Dic3—61no—
321C2×Dic3—61no—
322C2×Dic3—61no—
323C2×Dic3—121no—
324C2×Dic3—121no—
325C2×Dic3—242no—
326C2×Dic3—242no—
327D12—22no—
328D12—22no—
329D12—22no—
330D12—22no—
331C4×D3—242no—
332C4×D3—242no—
333C3×C8—62no—
334C3⋊C8—22no—
335C3⋊C8—62no—
336C3⋊C8—62no—
337C3⋊C8—122no—
338C2×C32—21no—
339C2×C32—21no—
340C2×C32#38511yescharacteristic
341C2×C32#45311yescharacteristic
342C2×C32#45511yescharacteristic
343C3×D3—44no—
344C24—32no—
345C2×D4—32no—
346C2×D4—32no—
347C2×D4—61no—
348C2×D4—61no—
349C2×D4—61no—
350C2×D4—61no—
351C22×C4—21no—
352C22×C4—61no—
353C22×C4—182no—
354C22×C4—182no—
355C22×C4C2×D3211yescharacteristic
356M16—32no—
357M16—61no—
358M16—92no—
359M16—181no—
360C2×C8—61no—
361C2×C8—181no—
362C4⋊C4—31no—
363C4⋊C4—31no—
364C4⋊C4—61no—
365C4⋊C4—61no—
366C4⋊C4—91no—
367C4⋊C4—91no—
368C22⋊C4—61no—
369C22⋊C4—124no—
370C22⋊C4—182no—
371C22⋊C4—182no—
372C22⋊C4—181no—
373C42—21no—
374C42—21no—
375C42—61no—
376C42—181no—
377C22×C3—21no—
378C22×C3—21no—
379C22×C3—21no—
380C22×C3—21no—
381C22×C3—21no—
382C22×C3—21no—
383C22×C3—21no—
384C22×C3—41no—
385C22×C3—41no—
386C22×C3—64no—
387C22×C3—124no—
388C22×C3—122no—
389C22×C3—122no—
390C22×C3—242no—
391C22×C3#88211yescharacteristic
392C22×C3#88311yescharacteristic
393C22×C3D3×C4⋊C411yescharacteristic
394C22×C3C2×Dic3⋊C411yescharacteristic
395C22×C3#93511yescharacteristic
396C22×C3#93711yescharacteristic
397C2×D3—24no—
398C2×D3—42no—
399C2×D3—42no—
400C2×D3—44no—
401C2×D3—82no—
402C3×C4—21no—
403C3×C4—21no—
404C3×C4—21no—
405C3×C4—21no—
406C3×C4—42no—
407C3×C4—42no—
408C3×C4—44no—
409C3×C4—121no—
410C3×C4—121no—
411C3×C4—241no—
412C3×C4C4×D1211yescharacteristic
413C3×C4#87811yescharacteristic
414C3×C4#87811yescharacteristic
415C3×C4#67⋊C411yescharacteristic
416C3×C4#67⋊C411yescharacteristic
417C3×C4#67⋊C411yescharacteristic
418C3×C4#89611yescharacteristic
419C3×C4#89711yescharacteristic
420Dic3—41no—
421Dic3—41no—
422Dic3—81no—
423Dic3—121no—
424Dic3—121no—
425Dic3—121no—
426Dic3—121no—
427Dic3—241no—
428Dic3—241no—
429C32#185611yescharacteristic, complemented, Sylow
430C23—34no—
431C23—62no—
432C23—62no—
433C23—122no—
434C23—122no—
435C23D3×#6711yescharacteristic
436D4—62no—
437D4—62no—
438D4—62no—
439D4—62no—
440C2×C4—22no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—61no—
444C2×C4—61no—
445C2×C4—122no—
446C2×C4—121no—
447C2×C4—181no—
448C2×C4—181no—
449C2×C4—722no—
450C2×C4—722no—
451C2×C4D3×Dic611yescharacteristic
452C2×C4C4×D3211yescharacteristic
453C2×C4D3×D1211yescharacteristic
454C2×C4#380211yescharacteristic
455C2×C4#380411yescharacteristic
456C2×C4#380511yescharacteristic
457C8—62no—
458C8—182no—
459C2×C3—21no—
460C2×C3—21no—
461C2×C3—21no—
462C2×C3—21no—
463C2×C3—21no—
464C2×C3—21no—
465C2×C3—21no—
466C2×C3—41no—
467C2×C3—41no—
468C2×C3—124no—
469C2×C3#466811yescharacteristic
470C2×C3#482211yescharacteristic
471C2×C3#482511yescharacteristic
472C2×C3#494611yescharacteristic
473C2×C3#506111yescharacteristic
474C2×C3#507711yescharacteristic
475D3—44no—
476C22—21no—
477C22—21no—
478C22—64no—
479C22—124no—
480C22—122no—
481C22—122no—
482C22—242no—
483C22D3×Dic3⋊C411yescharacteristic
484C22#6392211yescharacteristic
485C22#6396911yescharacteristic
486C4—42no—
487C4—121no—
488C4—121no—
489C4—241no—
490C4—361no—
491C4—361no—
492C4#6388011yescharacteristic
493C4#6389311yescharacteristic
494C4#6389911yescharacteristic
495C4#6390211yescharacteristic
496C3—21no—
497C3#6875811yescharacteristic, complemented
498C3#6964211yescharacteristic, complemented
499C2—21no—
500C2—21no—
501C2—124no—
502C2#1059039511yescharacteristic
503C2#1059039611yescharacteristic
504C2#1059137311yescharacteristic
subgroupG/H
centerC22#63922
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socleC22×C32#120
prime radicalC22×C3×D12C22
cosocleC22×C32×C4C23
hypercenterC2×C42D32
hypocenterC32#1856
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
3. #10591139C2semidirect
4. #10591130C2semidirect
6. #10589389C2semidirect
7. C3×#4523C2semidirect
27. #63558C4semidirect
42. #4523D3semidirect
62. #3748C2×C4semidirect
72. C3×#208C2×C4semidirect
224. #208C4×D3semidirect
429. C32#1856semidirect
497. C3#68758semidirect
498. C3#69642semidirect

Maximal subgroups

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

subgroupindex
#105949822
C3×#49392
#105911392
#105911302
C2×#635582
#105893892
C3×#45232
#696423
#687583