Finite Group Databasebeta

← #11787808

Subgroups — #11787808

Order 1152.

795 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594982C211yesmaximal, characteristic
2C2×#63860C211yesmaximal, characteristic
3#10592819C211yesmaximal, characteristic, complemented
4C2×C3×#823C211yesmaximal, characteristic
5#10591107C211yesmaximal, characteristic, complemented
6C3×#4555C211yesmaximal, characteristic, complemented
7#10589162C211yesmaximal, characteristic, complemented
8#70069—31nomaximal
9#68759—31nomaximal
10C22×#634C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13#64135C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C2×C3×C4×Dic3C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17D3×#217—22no—
18C2×(C2×D3)⋊Dic3—22no—
19#63898—22no—
20Dic3×D12—22no—
21#63860—22no—
22#63860C414yescomplemented
23#63643—22no—
24C3×#823—22no—
25#63567—22no—
26#5798—31no—
27C2×#936—31no—
28#5521—31no—
29C2×#875—31no—
30C2×C3×#100—31no—
31C2×#823D311yescharacteristic
32#5120—31no—
33#5120—31no—
34#5120—31no—
35#5120—61no—
36#5004—31no—
37C3×#339—31no—
38#4555—31no—
39#4555D311yescharacteristic, complemented
40#4523—31no—
41C23×C3×D3D412yes—
42C22×C32×C4C2311yescharacteristic
43C22×C3⋊Dic3—21no—
44C2×#634—21no—
45C2×#634—21no—
46C2×#634—21no—
47C2×#634—21no—
48C2×#634—21no—
49C2×#634C2×C412yescomplemented
50C22×C3×Dic3—21no—
51C2×C3×D12—21no—
52C2×C3×D12—21no—
53C2×C3×D12—21no—
54C2×C3×D12—21no—
55C2×C3×D12C2×C412yes—
56C2×C3×D12D412yes—
57C2×D3×Dic3—24no—
58C32×M16—21no—
59C32×M16—21no—
60C2×C32×C8—21no—
61#3757—21no—
62C4⋊(C3⋊Dic3)D412yes—
63C4×C3⋊Dic3—21no—
64C3×#217—21no—
65C3×C4⋊Dic3D412yes—
66C3×C4×Dic3—21no—
67C3×C4×Dic3—21no—
68C3×C4×Dic3C2×C412yescomplemented
69C3×#208—21no—
70C3×#208—21no—
71C2×C3×C3⋊C8—21no—
72(C2×D3)⋊Dic3—24no—
73(C2×D3)⋊Dic3—28no—
74#1885—91noSylow
75C22×C3×D4—31no—
76C22×D12C2×D311yescharacteristic
77C22×Dic6—31no—
78C22×Dic6—31no—
79C22×Dic6—61no—
80C2×C3×M16—21no—
81C2×C3×M16—31no—
82C2×C3×M16C2×D311yescharacteristic
83C2×C3×M16C2×D311yescharacteristic
84C3×#117—31no—
85C2×C3×C42—31no—
86C2×#217—62no—
87C2×#217—62no—
88#936—34no—
89#936—62no—
90D4×Dic3—62no—
91D4×Dic3—62no—
92C2×(C2×D3)⋊C4—62no—
93#926—31no—
94#926—31no—
95#926—61no—
96#926C2×D311yescharacteristic
97C2×C4×Dic3C2×D311yescharacteristic
98C2×#208C2×D311yescharacteristic
99#893—62no—
100D3×C22⋊C4—62no—
101#875—34no—
102#875—62no—
103C4×D12—62no—
104C3×#100—62no—
105#823—22no—
106#816—62no—
107#816—62no—
108#816—64no—
109#816—62no—
110#810—62no—
111C23×C32C2×D411yescharacteristic
112C22×C3×D3—22no—
113C22×C3×D3—22no—
114C22×C3×D3—44no—
115C22×C3×D3C22⋊C414yes—
116C2×C32×C4C22×C411yescharacteristic
117C2×C32×C4C2×D411yescharacteristic
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4#4111yescharacteristic
121C2×C32×C4#4111yescharacteristic
122C2×C3⋊Dic3—22no—
123C2×C3⋊Dic3—22no—
124C2×C3⋊Dic3—41no—
125C2×C3⋊Dic3—41no—
126#634—22no—
127#634—22no—
128#634—41no—
129#634—41no—
130C2×C3×Dic3—22no—
131C2×C3×Dic3—22no—
132C2×C3×Dic3—42no—
133C3×D12—22no—
134C3×D12—22no—
135C3×D12—22no—
136C3×D12—22no—
137D3×Dic3—84no—
138C32×C8—41no—
139C3×C3⋊C8—41no—
140C2×#124—91no—
141#518—91no—
142#419—91no—
143#419—91no—
144C2×#100—31no—
145#339—31no—
146#339—91no—
147C24×C3—32no—
148C23×D3D1212yes—
149C2×C3×D4—32no—
150C2×C3×D4—32no—
151C2×C3×D4—61no—
152C2×C3×D4—61no—
153C2×C3×D4—61no—
154C2×C3×D4—61no—
155C22×C3×C4—21no—
156C22×C3×C4—61no—
157C22×C3×C4C22×D311yescharacteristic
158C22×C3×C4C22×D311yescharacteristic
159C22×Dic3—21no—
160C22×Dic3—64no—
161C22×Dic3—61no—
162C22×Dic3—61no—
163C22×Dic3—121no—
164C2×D12—21no—
165C2×D12—21no—
166C2×D12—21no—
167C2×D12—21no—
168C2×D12C4×D312yes—
169C2×D12#6712yes—
170C2×C4×D3—64no—
171C2×Dic6—32no—
172C2×Dic6—32no—
173C2×Dic6—62no—
174C2×Dic6—62no—
175C2×Dic6—62no—
176C2×Dic6—61no—
177C2×Dic6—61no—
178C2×Dic6—61no—
179C2×Dic6—61no—
180C2×Dic6—61no—
181C2×Dic6—61no—
182C2×Dic6—61no—
183C2×Dic6—61no—
184C2×Dic6—61no—
185C2×Dic6—61no—
186C2×Dic6—121no—
187C2×Dic6—121no—
188C2×Dic6—121no—
189C3×M16—21no—
190C3×M16—21no—
191C3×M16—21no—
192C3×M16—21no—
193C3×M16—41no—
194C3×M16—41no—
195C3×M16—61no—
196C3×M16—61no—
197C2×C3×C8—22no—
198C2×C3×C8—21no—
199C2×C3×C8—21no—
200C2×C3×C8—61no—
201C3×C4⋊C4—32no—
202C3×C22⋊C4—61no—
203C3×C42—32no—
204C3×C42—61no—
205C3×C42—61no—
206#217—21no—
207#217—68no—
208#217—64no—
209#217—61no—
210#217—61no—
211#217—121no—
212(C2×D3)⋊C4—64no—
213(C2×D3)⋊C4—68no—
214C4⋊Dic3—32no—
215C4⋊Dic3—32no—
216C4⋊Dic3—62no—
217C4⋊Dic3D1212yes—
218C4×Dic3—21no—
219C4×Dic3—21no—
220C4×Dic3—61no—
221C4×Dic3—61no—
222C4×Dic3—121no—
223C4×Dic3C4×D312yescomplemented
224#208—21no—
225#208—21no—
226C2×C3⋊C8—21no—
227C22×C32—22no—
228C22×C32C2×C22⋊C411yescharacteristic
229C22×C32#12011yescharacteristic
230C22×C32#12311yescharacteristic
231C2×C3×D3—24no—
232C2×C3×D3—44no—
233C2×C3×D3—44no—
234C2×C3×D3—82no—
235C32×C4C4×D411yescharacteristic
236C32×C4C4×D411yescharacteristic
237C32×C4#12111yescharacteristic
238C32×C4#12111yescharacteristic
239C3⋊Dic3—42no—
240C3⋊Dic3—42no—
241C3×Dic3—42no—
242C3×Dic3—42no—
243C22×Q8—91no—
244C22×D4—31no—
245C2×M16—31no—
246C2×M16D3211yescharacteristic
247#124—94no—
248#124—182no—
249C4×D4—182no—
250C4×D4—182no—
251#117—31no—
252#117—91no—
253C2×C22⋊C4—182no—
254C2×C22⋊C4—182no—
255C2×C42—31no—
256#103—182no—
257#103—182no—
258#100—62no—
259C23×C3—21no—
260C23×C3—34no—
261C23×C3—62no—
262C23×C3—62no—
263C23×C3—124no—
264C23×C3C2×D1211yescharacteristic
265C23×C3D3×D411yescharacteristic
266C22×D3—22no—
267C22×D3—22no—
268C22×D3—44no—
269C22×D3(C2×D3)⋊C414yes—
270C3×D4—62no—
271C3×D4—62no—
272C3×D4—62no—
273C3×D4—62no—
274C2×C3×C4—21no—
275C2×C3×C4—21no—
276C2×C3×C4—21no—
277C2×C3×C4—21no—
278C2×C3×C4—21no—
279C2×C3×C4—21no—
280C2×C3×C4—62no—
281C2×C3×C4—62no—
282C2×C3×C4—122no—
283C2×C3×C4C2×C4×D311yescharacteristic
284C2×C3×C4C2×C4×D311yescharacteristic
285C2×C3×C4C2×D1211yescharacteristic
286C2×C3×C4#23511yescharacteristic
287C2×C3×C4D3×D411yescharacteristic
288C2×C3×C4D3×D411yescharacteristic
289C2×C3×C4D3×D411yescharacteristic
290C2×C3×C4D3×D411yescharacteristic
291C2×C3×C4#23711yescharacteristic
292C2×C3×C4#23711yescharacteristic
293C2×C3×C4#23911yescharacteristic
294C2×C3×C4C2×#6711yescharacteristic
295C2×Dic3—22no—
296C2×Dic3—22no—
297C2×Dic3—42no—
298C2×Dic3—62no—
299C2×Dic3—62no—
300C2×Dic3—62no—
301C2×Dic3—62no—
302C2×Dic3—122no—
303C2×Dic3—122no—
304C2×Dic3—122no—
305C2×Dic3—122no—
306C2×Dic3—121no—
307C2×Dic3—121no—
308C2×Dic3—121no—
309C2×Dic3—121no—
310C2×Dic3—244no—
311D12—22no—
312D12—22no—
313D12—22no—
314D12—22no—
315C4×D3—244no—
316Dic6—64no—
317Dic6—62no—
318Dic6—62no—
319Dic6—62no—
320Dic6—62no—
321Dic6—122no—
322Dic6—122no—
323Dic6—122no—
324Dic6—121no—
325Dic6—121no—
326Dic6—121no—
327Dic6—121no—
328C3×C8—42no—
329C3×C8—41no—
330C3×C8—41no—
331C3×C8—121no—
332C3⋊C8—41no—
333C2×C32—21no—
334C2×C32—21no—
335C2×C32#38611yescharacteristic
336C2×C32#45512yes—
337C3×D3—44no—
338C24—32no—
339C2×Q8—92no—
340C2×Q8—181no—
341C2×Q8—181no—
342C2×Q8—181no—
343C2×Q8—181no—
344C2×Q8—181no—
345C2×D4—32no—
346C2×D4—32no—
347C2×D4—61no—
348C2×D4—61no—
349C2×D4—61no—
350C2×D4—61no—
351C22×C4—61no—
352C22×C4—184no—
353C22×C4—181no—
354C22×C4C2×D3211yescharacteristic
355M16—21no—
356M16—21no—
357M16—61no—
358M16—61no—
359C2×C8—21no—
360C2×C8—61no—
361C4⋊C4—32no—
362C4⋊C4—92no—
363C22⋊C4—61no—
364C22⋊C4—188no—
365C22⋊C4—184no—
366C22⋊C4—181no—
367C42—32no—
368C42—61no—
369C42—61no—
370C42—181no—
371C22×C3—22no—
372C22×C3—22no—
373C22×C3—21no—
374C22×C3—21no—
375C22×C3—21no—
376C22×C3—42no—
377C22×C3—64no—
378C22×C3—124no—
379C22×C3—124no—
380C22×C3—242no—
381C22×C3D3×C22⋊C411yescharacteristic
382C22×C3#88211yescharacteristic
383C22×C3#88211yescharacteristic
384C22×C3#88611yescharacteristic
385C22×C3#89411yescharacteristic
386C22×C3C2×(C2×D3)⋊C411yescharacteristic
387C2×D3—24no—
388C2×D3—44no—
389C2×D3—44no—
390C2×D3—82no—
391C3×C4—21no—
392C3×C4—21no—
393C3×C4—21no—
394C3×C4—21no—
395C3×C4—122no—
396C3×C4—122no—
397C3×C4C4×D1211yescharacteristic
398C3×C4#67⋊C411yescharacteristic
399C3×C4#67⋊C411yescharacteristic
400C3×C4#88411yescharacteristic
401C3×C4#89311yescharacteristic
402C3×C4#89511yescharacteristic
403C3×C4#93911yescharacteristic
404C3×C4#93911yescharacteristic
405Dic3—42no—
406Dic3—42no—
407Dic3—124no—
408Dic3—122no—
409Dic3—122no—
410Dic3—122no—
411Dic3—122no—
412Dic3—242no—
413C32#188511yescharacteristic, complemented, Sylow
414C23—34no—
415C23—62no—
416C23—62no—
417C23—124no—
418C23D3×D1211yescharacteristic
419Q8—182no—
420Q8—182no—
421Q8—361no—
422Q8—361no—
423D4—62no—
424D4—62no—
425D4—62no—
426D4—62no—
427C2×C4—62no—
428C2×C4—62no—
429C2×C4—122no—
430C2×C4—182no—
431C2×C4—182no—
432C2×C4—361no—
433C2×C4—361no—
434C2×C4—724no—
435C2×C4#379611yescharacteristic
436C2×C4C4×D3211yescharacteristic
437C2×C4D3×D1211yescharacteristic
438C2×C4#380411yescharacteristic
439C2×C4D3×#6711yescharacteristic
440C2×C4#381111yescharacteristic
441C8—41no—
442C8—121no—
443C2×C3—21no—
444C2×C3—21no—
445C2×C3—21no—
446C2×C3—21no—
447C2×C3—22no—
448C2×C3—21no—
449C2×C3—41no—
450C2×C3—41no—
451C2×C3—124no—
452C2×C3#466511yescharacteristic
453C2×C3#474612yes—
454C2×C3#482512yes—
455C2×C3#495811yescharacteristic
456D3—44no—
457C22—22no—
458C22—64no—
459C22—124no—
460C22—124no—
461C22—242no—
462C22#6389011yescharacteristic
463C22D3×(C2×D3)⋊C411yescharacteristic
464C22#6392311yescharacteristic
465C4—122no—
466C4—122no—
467C4—362no—
468C4—362no—
469C4#6388011yescharacteristic
470C4#6388111yescharacteristic
471C4#6388611yescharacteristic
472C4#6397111yescharacteristic
473C3—21no—
474C3#6875911yescharacteristic, complemented
475C3#7006911yescharacteristic, complemented
476C2—21no—
477C2—21no—
478C2—124no—
479C2#1059101612yes—
480C2#1059136411yescharacteristic
subgroupG/H
centerC22#63923
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32#120
prime radicalC22×C3×D12C22
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1885
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. #10592819C2semidirect
5. #10591107C2semidirect
6. C3×#4555C2semidirect
7. #10589162C2semidirect
22. #63860C4semidirect
39. #4555D3semidirect
49. C2×#634C2×C4semidirect
68. C3×C4×Dic3C2×C4semidirect
223. C4×Dic3C4×D3semidirect
413. C32#1885semidirect
474. C3#68759semidirect
475. C3#70069semidirect

Maximal subgroups

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

subgroupindex
#105949822
C2×#638602
#105928192
C2×C3×#8232
#105911072
C3×#45552
#105891622
#700693
#687593