Finite Group Databasebeta

← #11783884

Subgroups — #11783884

Order 1152.

805 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594954C211yesmaximal, characteristic
2C2×#63652C211yesmaximal, characteristic
3C3×Dic3×M16C211yesmaximal, characteristic, complemented
4C4×Dic32C211yesmaximal, characteristic, complemented
5C2×#63570C211yesmaximal, characteristic
6C3×#4555C211yesmaximal, characteristic, complemented
7#10589160C211yesmaximal, characteristic, complemented
8C4×#825—31nomaximal
9#68728—31nomaximal
10C2×#3828C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C2×C4×C3⋊Dic3C2211yescharacteristic
13C3×#926C2211yescharacteristic
14C2×C3×C4×Dic3C2211yescharacteristic
15C2×C3×C4×Dic3C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C2×Dic32—22no—
18#63952—22no—
19#63894C412yescomplemented
20C4×#624—21no—
21#63874—21no—
22#63844C412yescomplemented
23#63652C414yescomplemented
24C3×#815—21no—
25C3×C8×Dic3—21no—
26#63570C414yescomplemented
27#5522—31no—
28C4×#235—31no—
29C3×C4×M16—31no—
30C2×#825—31no—
31C2×#825—31no—
32C2×#825—31no—
33C2×#825—61no—
34Dic3×M16D311yescharacteristic, complemented
35C42×Dic3—31no—
36C42×Dic3—31no—
37C2×#805—31no—
38C3×#339—31no—
39#4555—31no—
40#4555D311yescharacteristic, complemented
41#4532—31no—
42C22×C32×C4C2311yescharacteristic
43C2×#638—21no—
44C22×C3⋊Dic3—21no—
45#3828—21no—
46#3828—21no—
47#3828C2×C412yes—
48#3828C2×C412yes—
49C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
50C2×C4×C3⋊D3—21no—
51C2×#634C2×C411yescharacteristic
52C22×C3×Dic3—21no—
53C22×C3×Dic3D412yes—
54C2×#624—22no—
55C32×M16—21no—
56C32×M16C2×C412yescomplemented
57C2×C32×C8—21no—
58C4×C3⋊Dic3—21no—
59C4×C3⋊Dic3C2×C412yescomplemented
60C3×#217—21no—
61C3×C4⋊Dic3C2×C412yes—
62C3×C4×Dic3—21no—
63C3×C4×Dic3—21no—
64C3×C4×Dic3C2×C412yes—
65C3×C4×Dic3C2×C412yescomplemented
66C3×C4×Dic3D411yescharacteristic
67C3×C4×Dic3D411yescharacteristic
68C3×#208—21no—
69C3×#208C2×C412yescomplemented
70C2×C3×C3⋊C8—21no—
71#3724—22no—
72#3722—22no—
73Dic32—28no—
74Dic32—22no—
75C4×#104—91noSylow
76C2×#235—31no—
77C2×#235—31no—
78C2×#235—61no—
79C2×C3×M16—21no—
80C2×C3×M16—31no—
81C2×C3×M16C2×D311yescharacteristic
82C2×C3×M16C2×D311yescharacteristic
83C3×#117—31no—
84C2×C3×C42—31no—
85C2×C3×C42—31no—
86C4×#67—62no—
87#926C2×D311yescharacteristic
88C2×C4×Dic3—31no—
89C2×C4×Dic3—31no—
90C2×C4×Dic3—61no—
91C2×C4×Dic3—62no—
92C2×C4×Dic3—62no—
93C2×C4×Dic3C2×D311yescharacteristic
94C2×C4×Dic3C2×D311yescharacteristic
95C2×#208C2×D311yescharacteristic
96#893—32no—
97#887—32no—
98#67⋊C4—62no—
99C4×D12—32no—
100#872—61no—
101#872—61no—
102C42×D3—61no—
103C42×D3—61no—
104C4×Dic6—32no—
105C3×#97—61no—
106C3×C4×C8—61no—
107#825—34no—
108#825—34no—
109#825—34no—
110#825—64no—
111#815—21no—
112C8×Dic3—21no—
113#805—34no—
114C23×C32C2×D411yescharacteristic
115C22×C3⋊D3—21no—
116C2×C32×C4C22×C411yescharacteristic
117C2×C32×C4C22×C411yescharacteristic
118C2×C32×C4C22×C411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4#4111yescharacteristic
121C2×C32×C4#4111yescharacteristic
122#638—22no—
123#638—22no—
124C2×C3⋊Dic3—24no—
125C2×C3⋊Dic3—21no—
126C2×C3⋊Dic3—22no—
127C4⋊(C3⋊D3)—21no—
128C4⋊(C3⋊D3)C4212yescomplemented
129C4×C3⋊D3—22no—
130C4×C3⋊D3—22no—
131#634—21no—
132#634C4212yescomplemented
133C2×C3×Dic3—24no—
134C2×C3×Dic3—22no—
135C2×C3×Dic3—24no—
136C2×C3×Dic3—22no—
137C2×C3×Dic3C22⋊C412yes—
138C2×C3×Dic3C22⋊C412yes—
139#624—44no—
140C32×C8—22no—
141C3×C3⋊C8—22no—
142C4×#41—91no—
143C2×#104—91no—
144C2×#104—91no—
145C4×M16—31no—
146C43—91no—
147#339—31no—
148#339—91no—
149C22×C3×C4—21no—
150C22×C3×C4—32no—
151C22×C3×C4—61no—
152C22×C3×C4C22×D311yescharacteristic
153C22×C3×C4C22×D311yescharacteristic
154C2×#67—61no—
155C2×#67—61no—
156C2×#67—121no—
157C22×Dic3—21no—
158C22×Dic3—61no—
159C22×Dic3—61no—
160C22×Dic3—121no—
161C22×Dic3D1212yes—
162#235—32no—
163#235—32no—
164#235—32no—
165#235—32no—
166#235—62no—
167#235—62no—
168#235—61no—
169#235—61no—
170#235—61no—
171#235—61no—
172#235—121no—
173#235—121no—
174C2×D12—31no—
175C2×D12—31no—
176C2×D12—61no—
177C2×C4×D3—61no—
178C2×C4×D3—61no—
179C2×C4×D3—62no—
180C2×C4×D3—62no—
181C2×C4×D3—121no—
182C2×Dic6—31no—
183C2×Dic6—31no—
184C2×Dic6—61no—
185C3×M16—21no—
186C3×M16—21no—
187C3×M16—22no—
188C3×M16—32no—
189C3×M16—41no—
190C3×M16—61no—
191C3×M16C4×D312yescomplemented
192C3×M16C4×D312yescomplemented
193C2×C3×C8—21no—
194C2×C3×C8—21no—
195C2×C3×C8—41no—
196C2×C3×C8—61no—
197C3×C4⋊C4—32no—
198C3×C22⋊C4—61no—
199C3×C42—32no—
200C3×C42—31no—
201C3×C42—31no—
202C3×C42—32no—
203C3×C42—61no—
204C3×C42—61no—
205#217—21no—
206(C2×D3)⋊C4—62no—
207(C2×D3)⋊C4—62no—
208C4⋊Dic3C4×D312yes—
209Dic3⋊C4—62no—
210Dic3⋊C4—62no—
211C4×Dic3—21no—
212C4×Dic3—21no—
213C4×Dic3—32no—
214C4×Dic3—32no—
215C4×Dic3—62no—
216C4×Dic3—62no—
217C4×Dic3—68no—
218C4×Dic3—68no—
219C4×Dic3—61no—
220C4×Dic3—61no—
221C4×Dic3—62no—
222C4×Dic3—121no—
223C4×Dic3C4×D312yes—
224C4×Dic3C4×D312yescomplemented
225C4×Dic3#6711yescharacteristic
226C4×Dic3#6711yescharacteristic
227#208—21no—
228#208C4×D312yescomplemented
229C2×C3⋊C8—21no—
230C22×C32—22no—
231C22×C32C2×C22⋊C411yescharacteristic
232C22×C32C4×D411yescharacteristic
233C22×C32C4×D411yescharacteristic
234C2×C3⋊D3—22no—
235C2×C3⋊D3—42no—
236C32×C4C2×C4211yescharacteristic
237C32×C4#11711yescharacteristic
238C32×C4C4×D411yescharacteristic
239C32×C4C4×D411yescharacteristic
240C3⋊Dic3—24no—
241C3⋊Dic3—22no—
242C3×Dic3—24no—
243C3×Dic3—22no—
244C3×Dic3—42no—
245C3×Dic3#10414yescomplemented
246C2×#41—91no—
247C2×M16—31no—
248C2×M16D3211yescharacteristic
249C4×Q8—92no—
250C4×D4—92no—
251C4×D4—182no—
252#117—31no—
253#117—181no—
254C2×C42—31no—
255C2×C42—31no—
256C2×C42—91no—
257C2×C42—181no—
258C2×C42—182no—
259#104—94no—
260#104—94no—
261#97—61no—
262C4×C8—61no—
263C23×C3—21no—
264C23×C3C2×D1211yescharacteristic
265C23×C3D3×D411yescharacteristic
266C22×D3—61no—
267C22×D3—61no—
268C22×D3—121no—
269C2×C3×C4—21no—
270C2×C3×C4—21no—
271C2×C3×C4—21no—
272C2×C3×C4—21no—
273C2×C3×C4—21no—
274C2×C3×C4—21no—
275C2×C3×C4—32no—
276C2×C3×C4—32no—
277C2×C3×C4—64no—
278C2×C3×C4—64no—
279C2×C3×C4—62no—
280C2×C3×C4—62no—
281C2×C3×C4C2×C4×D311yescharacteristic
282C2×C3×C4C2×C4×D311yescharacteristic
283C2×C3×C4C2×C4×D311yescharacteristic
284C2×C3×C4C2×C4×D311yescharacteristic
285C2×C3×C4C2×C4×D311yescharacteristic
286C2×C3×C4C2×C4×D311yescharacteristic
287C2×C3×C4#23511yescharacteristic
288C2×C3×C4#23511yescharacteristic
289C2×C3×C4D3×D411yescharacteristic
290C2×C3×C4#23711yescharacteristic
291C2×C3×C4#23911yescharacteristic
292C2×C3×C4C2×#6711yescharacteristic
293#67—62no—
294#67—62no—
295#67—62no—
296#67—62no—
297#67—122no—
298#67—122no—
299C2×Dic3—24no—
300C2×Dic3—22no—
301C2×Dic3—24no—
302C2×Dic3—22no—
303C2×Dic3—64no—
304C2×Dic3—64no—
305C2×Dic3—62no—
306C2×Dic3—61no—
307C2×Dic3—62no—
308C2×Dic3—61no—
309C2×Dic3—122no—
310C2×Dic3—121no—
311C2×Dic3—124no—
312C2×Dic3(C2×D3)⋊C412yes—
313C2×Dic3(C2×D3)⋊C412yes—
314D12—32no—
315D12—32no—
316D12—62no—
317D12—61no—
318D12—61no—
319D12—121no—
320C4×D3—62no—
321C4×D3—62no—
322C4×D3—62no—
323C4×D3—62no—
324C4×D3—122no—
325C4×D3—122no—
326C4×D3—124no—
327C4×D3—124no—
328Dic6—32no—
329Dic6—32no—
330Dic6—62no—
331Dic6—61no—
332Dic6—61no—
333Dic6—121no—
334C3×C8—22no—
335C3×C8—22no—
336C3×C8—42no—
337C3×C8—62no—
338C3⋊C8—22no—
339C2×C32—21no—
340C2×C32—21no—
341C2×C32C4×C22⋊C411yescharacteristic
342C2×C32C2×#10412yes—
343C3⋊D3—42no—
344#41—92no—
345#41—92no—
346#41—181no—
347#41—181no—
348C2×Q8—91no—
349C2×D4—91no—
350C2×D4—181no—
351C22×C4—32no—
352C22×C4—61no—
353C22×C4—182no—
354C22×C4—181no—
355C22×C4—181no—
356C22×C4C2×D3211yescharacteristic
357M16—21no—
358M16—32no—
359M16—61no—
360M16#62412yescomplemented
361C2×C8—21no—
362C2×C8—61no—
363C4⋊C4—32no—
364C4⋊C4—182no—
365C22⋊C4—61no—
366C22⋊C4—182no—
367C42—32no—
368C42—31no—
369C42—31no—
370C42—32no—
371C42—61no—
372C42—61no—
373C42—92no—
374C42—182no—
375C42—188no—
376C42—181no—
377C22×C3—22no—
378C22×C3—22no—
379C22×C3—21no—
380C22×C3—21no—
381C22×C3—21no—
382C22×C3—42no—
383C22×C3C4×D1211yescharacteristic
384C22×C3C4×D1211yescharacteristic
385C22×C3D3×C22⋊C411yescharacteristic
386C22×C3#67⋊C411yescharacteristic
387C22×C3#89311yescharacteristic
388C22×C3C2×(C2×D3)⋊C411yescharacteristic
389C2×D3—62no—
390C2×D3—62no—
391C2×D3—122no—
392C2×D3—122no—
393C2×D3—122no—
394C2×D3—242no—
395C3×C4—21no—
396C3×C4—21no—
397C3×C4—21no—
398C3×C4—21no—
399C3×C4—34no—
400C3×C4—64no—
401C3×C4—62no—
402C3×C4—122no—
403C3×C4C42×D311yescharacteristic
404C3×C4C42×D311yescharacteristic
405C3×C4#87211yescharacteristic
406C3×C4#67⋊C411yescharacteristic
407C3×C4#89211yescharacteristic
408C3×C4#89311yescharacteristic
409C3×C4C4×#6711yescharacteristic
410C3×C4C4×#6711yescharacteristic
411Dic3—24no—
412Dic3—22no—
413Dic3—42no—
414Dic3—64no—
415Dic3—64no—
416Dic3—62no—
417Dic3—62no—
418Dic3—122no—
419Dic3—124no—
420Dic3#82514yescomplemented
421C32C4×#10411yescharacteristic, complemented, Sylow
422C23—181no—
423C23D3×D1211yescharacteristic
424Q8—92no—
425Q8—181no—
426D4—92no—
427D4—182no—
428D4—182no—
429D4—181no—
430C2×C4—32no—
431C2×C4—32no—
432C2×C4—64no—
433C2×C4—64no—
434C2×C4—62no—
435C2×C4—62no—
436C2×C4—184no—
437C2×C4—182no—
438C2×C4—181no—
439C2×C4—182no—
440C2×C4—182no—
441C2×C4—364no—
442C2×C4#379911yescharacteristic
443C2×C4C4×D3211yescharacteristic
444C2×C4C4×D3211yescharacteristic
445C2×C4#380411yescharacteristic
446C2×C4C2×#62411yescharacteristic
447C2×C4D3×#6711yescharacteristic
448C8—22no—
449C8—62no—
450C2×C3—21no—
451C2×C3—21no—
452C2×C3—21no—
453C2×C3—21no—
454C2×C3—21no—
455C2×C3—22no—
456C2×C3—41no—
457C2×C3—41no—
458C2×C3#466611yescharacteristic
459C2×C3D3×#10412yes—
460C2×C3C4×(C2×D3)⋊C411yescharacteristic
461C2×C3C2×#82512yes—
462D3—122no—
463D3—122no—
464D3—242no—
465C22—22no—
466C22—182no—
467C22—362no—
468C22#6388011yescharacteristic
469C22#6389411yescharacteristic
470C22D3×(C2×D3)⋊C411yescharacteristic
471C4—34no—
472C4—64no—
473C4—62no—
474C4—122no—
475C4—184no—
476C4—182no—
477C4#6383611yescharacteristic
478C4C4×#62411yescharacteristic
479C4#6390411yescharacteristic
480C4#6395211yescharacteristic
481C3—21no—
482C3#6872811yescharacteristic, complemented
483C3C4×#82511yescharacteristic, complemented
484C2—21no—
485C2—21no—
486C2—362no—
487C2D3×#82512yes—
488C2#1059123311yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutatorC32×C4C2×C42
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32C2×C22⋊C4
prime radicalC2×#3828C22
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32C4×#104
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
3. C3×Dic3×M16C2semidirect
4. C4×Dic32C2semidirect
6. C3×#4555C2semidirect
7. #10589160C2semidirect
19. #63894C4semidirect
22. #63844C4semidirect
23. #63652C4semidirect
26. #63570C4semidirect
34. Dic3×M16D3semidirect
40. #4555D3semidirect
56. C32×M16C2×C4semidirect
59. C4×C3⋊Dic3C2×C4semidirect
65. C3×C4×Dic3C2×C4semidirect
69. C3×#208C2×C4semidirect
128. C4⋊(C3⋊D3)C42semidirect
132. #634C42semidirect
191. C3×M16C4×D3semidirect
192. C3×M16C4×D3semidirect
224. C4×Dic3C4×D3semidirect
228. #208C4×D3semidirect
245. C3×Dic3#104semidirect
360. M16#624semidirect
420. Dic3#825semidirect
421. C32C4×#104semidirect
482. C3#68728semidirect
483. C3C4×#825semidirect

Maximal subgroups

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

subgroupindex
#105949542
C2×#636522
C3×Dic3×M162
C4×Dic322
C2×#635702
C3×#45552
#105891602
C4×#8253
#687283