Finite Group Databasebeta

← #11784144

Subgroups — #11784144

Order 1152.

669 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#948C211yesmaximal, characteristic
2C2×#63664C211yesmaximal, characteristic
3C3×#5233C211yesmaximal, characteristic
4C2×#63555C211yesmaximal, characteristic, complemented
5#10591055C211yesmaximal, characteristic, complemented
6#10589166C211yesmaximal, characteristic, complemented
7#10589160C211yesmaximal, characteristic, complemented
8#72009—31nomaximal
9#70290—31nomaximal
10C2×C32×#41C2211yescharacteristic
11C2×C4×C3⋊Dic3C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13C3×#948—22no—
14C3×#948C414yescomplemented
15C3×#926C2211yescharacteristic
16C2×C3×#208—21no—
17C2×C3×#208C2211yescharacteristic
18C22×C3×C3⋊C8—21no—
19C22×C3×C3⋊C8C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21#63664C414yescomplemented
22C3×#835C412yescomplemented
23C3×#832C412yescomplemented
24#63555—22no—
25#63554—21no—
26Dic3×C3⋊C8—21no—
27C2×C3×#131—31no—
28C2×#948D311yescharacteristic
29C3×#416—31no—
30C2×#837—31no—
31C2×#837—31no—
32C2×#837—61no—
33#5233D311yescharacteristic
34#5101—31no—
35C2×#815—31no—
36C2×#815—31no—
37#4997—31no—
38#4558—31no—
39#4555—31no—
40#4552—31no—
41#4532—31no—
42C32×#41—21no—
43C32×#41—21no—
44C32×#41C2×C412yes—
45C32×#41C2×C412yes—
46C2×C32×Q8C2×C411yescharacteristic
47C2×C32×D4—21no—
48C2×C32×D4C2×C411yescharacteristic
49C22×C32×C4—21no—
50C22×C32×C4C2311yescharacteristic
51C22×C3⋊Dic3—21no—
52C4×C3⋊Dic3—21no—
53C4×C3⋊Dic3C2×C412yes—
54#3748—21no—
55#3748C2×C412yes—
56C2×C3⋊(C3⋊C8)—21no—
57C3×#217—21no—
58C3×C4⋊Dic3C2×C412yes—
59C3×C4×Dic3—21no—
60C3×#208—21no—
61C3×#208—24no—
62C3×#208C2×C412yes—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8—24no—
67C2×C3×C3⋊C8C2×C412yes—
68C2×C3×C3⋊C8C2×C412yes—
69C2×C3×C3⋊C8D411yescharacteristic
70C2×C3×C3⋊C8D411yescharacteristic
71C2×C3×C3⋊C8D412yes—
72#1765—91noSylow
73C2×C3×#41—21no—
74C2×C3×#41C2×D311yescharacteristic
75C2×C3×#41C2×D311yescharacteristic
76C3×#131—34no—
77C3×#131—62no—
78C2×C3×M16—31no—
79C2×C3×M16—61no—
80C22×C3×C8—31no—
81C22×C3×C8—31no—
82C22×C3×C8—61no—
83C3×#117—31no—
84#948—22no—
85#948Dic314yescomplemented
86#926C2×D311yescharacteristic
87C2×C4×Dic3—31no—
88C2×C4×Dic3—31no—
89C2×C4×Dic3—61no—
90C2×#208—21no—
91C2×#208—31no—
92C2×#208—31no—
93C2×#208—61no—
94C2×#208C2×D311yescharacteristic
95C22×C3⋊C8—21no—
96C22×C3⋊C8C2×D311yescharacteristic
97C22×C3⋊C8C2×D311yescharacteristic
98C3×#103—32no—
99C3×#102—32no—
100#837—34no—
101#837—34no—
102#837—64no—
103#835Dic312yescomplemented
104#832Dic312yescomplemented
105#815—62no—
106#815—61no—
107#815—62no—
108C8×Dic3—61no—
109#803—61no—
110C4×C3⋊C8—61no—
111C23×C32—21no—
112C23×C32#4111yescharacteristic
113C32×Q8—21no—
114C32×Q8C4212yes—
115C32×D4—22no—
116C32×D4—22no—
117C32×D4—21no—
118C32×D4C4212yes—
119C2×C32×C4—21no—
120C2×C32×C4—22no—
121C2×C32×C4—22no—
122C2×C32×C4C22×C411yescharacteristic
123C2×C32×C4C22×C411yescharacteristic
124C2×C32×C4C22×C411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4#4111yescharacteristic
128C2×C3⋊Dic3—22no—
129C2×C3⋊Dic3—42no—
130C2×C3×Dic3—22no—
131C3⋊(C3⋊C8)—22no—
132C3×C3⋊C8—22no—
133C3×C3⋊C8—22no—
134C3×C3⋊C8C22⋊C412yes—
135C3×C3⋊C8C22⋊C412yes—
136C2×#131—31no—
137C2×#104—91no—
138#416—31no—
139#405—91no—
140C2×#97—91no—
141#341—91no—
142#339—91no—
143C3×#41—21no—
144C3×#41—21no—
145C3×#41—21no—
146C3×#41—21no—
147C3×#41—22no—
148C3×#41—22no—
149C3×#41—41no—
150C3×#41—41no—
151C3×#41C4×D312yes—
152C3×#41C4×D312yes—
153C3×#41C4×D312yes—
154C3×#41C2×Dic312yes—
155C2×C3×Q8—21no—
156C2×C3×Q8C4×D311yescharacteristic
157C2×C3×Q8C2×Dic311yescharacteristic
158C2×C3×D4—21no—
159C2×C3×D4—21no—
160C2×C3×D4—21no—
161C2×C3×D4—41no—
162C2×C3×D4C4×D311yescharacteristic
163C2×C3×D4C2×Dic311yescharacteristic
164C22×C3×C4—21no—
165C22×C3×C4—21no—
166C22×C3×C4—21no—
167C22×C3×C4—41no—
168C22×C3×C4C22×D311yescharacteristic
169C22×C3×C4C22×D311yescharacteristic
170C22×Dic3—61no—
171C22×Dic3—61no—
172C22×Dic3—121no—
173C3×M16—32no—
174C3×M16—64no—
175C3×M16—61no—
176C2×C3×C8—32no—
177C2×C3×C8—31no—
178C2×C3×C8—31no—
179C2×C3×C8—32no—
180C2×C3×C8—32no—
181C2×C3×C8—64no—
182C2×C3×C8—61no—
183C2×C3×C8—61no—
184C2×C3×C8—61no—
185C3×C4⋊C4—32no—
186C3×C22⋊C4—61no—
187C3×C42—61no—
188#217—21no—
189C4⋊Dic3C2×Dic312yes—
190C4×Dic3—21no—
191C4×Dic3—32no—
192C4×Dic3—32no—
193C4×Dic3—62no—
194C4×Dic3—61no—
195C4×Dic3—61no—
196C4×Dic3—121no—
197#208—21no—
198#208—24no—
199#208—32no—
200#208—32no—
201#208—62no—
202#208—61no—
203#208—61no—
204#208—121no—
205#208C2×Dic312yes—
206C2×C3⋊C8—21no—
207C2×C3⋊C8—21no—
208C2×C3⋊C8—21no—
209C2×C3⋊C8—24no—
210C2×C3⋊C8—61no—
211C2×C3⋊C8—61no—
212C2×C3⋊C8—121no—
213C2×C3⋊C8C2×Dic312yes—
214C2×C3⋊C8C2×Dic312yes—
215C2×C3⋊C8#6711yescharacteristic
216C2×C3⋊C8#6711yescharacteristic
217C2×C3⋊C8#6712yes—
218C22×C32—22no—
219C22×C32—22no—
220C22×C32—42no—
221C22×C32#11711yescharacteristic
222C22×C32C4×D411yescharacteristic
223C22×C32C4×D411yescharacteristic
224C32×C4—22no—
225C32×C4C2×C4211yescharacteristic
226C32×C4C2×C22⋊C411yescharacteristic
227C32×C4C4×D411yescharacteristic
228C32×C4C4×D411yescharacteristic
229C3⋊Dic3—42no—
230C3×Dic3—42no—
231C2×#41D3211yescharacteristic
232#131—34no—
233#131—62no—
234C2×M16—31no—
235C2×M16—61no—
236C2×M16—91no—
237C22×C8—31no—
238C22×C8—31no—
239C22×C8—61no—
240#117—31no—
241C2×C42—91no—
242#104—94no—
243#103—32no—
244#102—32no—
245#97—181no—
246#97—182no—
247C4×C8—181no—
248C23×C3—21no—
249C23×C3—21no—
250C23×C3—21no—
251C23×C3—41no—
252C23×C3#23511yescharacteristic
253C23×C3#23711yescharacteristic
254C3×Q8—21no—
255C3×Q8—21no—
256C3×Q8—22no—
257C3×Q8—41no—
258C3×Q8C4×Dic312yes—
259C3×Q8C4×Dic312yes—
260C3×D4—22no—
261C3×D4—22no—
262C3×D4—22no—
263C3×D4—22no—
264C3×D4—21no—
265C3×D4—21no—
266C3×D4—22no—
267C3×D4—41no—
268C3×D4—42no—
269C3×D4—42no—
270C3×D4C4×Dic312yes—
271C3×D4C4×Dic312yes—
272C2×C3×C4—21no—
273C2×C3×C4—21no—
274C2×C3×C4—22no—
275C2×C3×C4—22no—
276C2×C3×C4—22no—
277C2×C3×C4—22no—
278C2×C3×C4—21no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—21no—
284C2×C3×C4—42no—
285C2×C3×C4—42no—
286C2×C3×C4—41no—
287C2×C3×C4—62no—
288C2×C3×C4C2×C4×D311yescharacteristic
289C2×C3×C4C2×C4×D311yescharacteristic
290C2×C3×C4C2×C4×D311yescharacteristic
291C2×C3×C4C2×C4×D311yescharacteristic
292C2×C3×C4#23511yescharacteristic
293C2×C3×C4D3×D411yescharacteristic
294C2×C3×C4D3×D411yescharacteristic
295C2×C3×C4#23711yescharacteristic
296C2×C3×C4C22×Dic311yescharacteristic
297C2×C3×C4C22×Dic311yescharacteristic
298C2×C3×C4C2×#6711yescharacteristic
299C2×C3×C4C2×#6711yescharacteristic
300C2×Dic3—22no—
301C2×Dic3—62no—
302C2×Dic3—62no—
303C2×Dic3—122no—
304C2×Dic3—122no—
305C2×Dic3—122no—
306C2×Dic3—124no—
307C3×C8—32no—
308C3×C8—32no—
309C3×C8—62no—
310C3×C8—62no—
311C3⋊C8—22no—
312C3⋊C8—22no—
313C3⋊C8—62no—
314C3⋊C8—62no—
315C3⋊C8—122no—
316C3⋊C8#21712yes—
317C3⋊C8#21712yes—
318C2×C32—21no—
319C2×C32—21no—
320C2×C32—42no—
321C2×C32C4×C22⋊C411yescharacteristic
322C2×C32#44412yes—
323#41—21no—
324#41—21no—
325#41D3×Dic312yes—
326#41#62412yes—
327C2×Q8D3×Dic311yescharacteristic
328C2×D4—21no—
329C2×D4D3×Dic311yescharacteristic
330C22×C4—21no—
331C22×C4—181no—
332C22×C4C2×D3211yescharacteristic
333M16—32no—
334M16—64no—
335M16—61no—
336M16—92no—
337M16—181no—
338C2×C8—32no—
339C2×C8—32no—
340C2×C8—31no—
341C2×C8—31no—
342C2×C8—32no—
343C2×C8—64no—
344C2×C8—61no—
345C2×C8—61no—
346C2×C8—61no—
347C2×C8—181no—
348C4⋊C4—32no—
349C22⋊C4—61no—
350C42—61no—
351C42—92no—
352C42—181no—
353C22×C3—22no—
354C22×C3—22no—
355C22×C3—22no—
356C22×C3—22no—
357C22×C3—21no—
358C22×C3—21no—
359C22×C3—21no—
360C22×C3—42no—
361C22×C3—42no—
362C22×C3—42no—
363C22×C3—42no—
364C22×C3—82no—
365C22×C3#87711yescharacteristic
366C22×C3#67⋊C411yescharacteristic
367C22×C3#92611yescharacteristic
368C22×C3C4×#6711yescharacteristic
369C22×C3C4×#6711yescharacteristic
370C22×C3D4×Dic311yescharacteristic
371C3×C4—22no—
372C3×C4—22no—
373C3×C4—21no—
374C3×C4—21no—
375C3×C4—21no—
376C3×C4—21no—
377C3×C4—42no—
378C3×C4—122no—
379C3×C4D3×C22⋊C411yescharacteristic
380C3×C4#67⋊C411yescharacteristic
381C3×C4C2×C4×Dic311yescharacteristic
382C3×C4C2×C4×Dic311yescharacteristic
383C3×C4C4×#6711yescharacteristic
384C3×C4C4×#6711yescharacteristic
385C3×C4D4×Dic311yescharacteristic
386C3×C4C2×#21711yescharacteristic
387Dic3—42no—
388Dic3—122no—
389Dic3—122no—
390Dic3—124no—
391C32#176511yescharacteristic, complemented, Sylow
392C23—21no—
393C23#380411yescharacteristic
394Q8—21no—
395Q8Dic3212yes—
396D4—22no—
397D4—22no—
398D4—21no—
399D4Dic3212yes—
400C2×C4—21no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—62no—
404C2×C4—182no—
405C2×C4—362no—
406C2×C4C2×D3×Dic311yescharacteristic
407C2×C4C2×D3×Dic311yescharacteristic
408C2×C4#380411yescharacteristic
409C2×C4C2×#62411yescharacteristic
410C2×C4D3×#6711yescharacteristic
411C2×C4D3×#6711yescharacteristic
412C8—32no—
413C8—32no—
414C8—62no—
415C8—62no—
416C8—182no—
417C2×C3—21no—
418C2×C3—21no—
419C2×C3—21no—
420C2×C3—21no—
421C2×C3—22no—
422C2×C3—21no—
423C2×C3—41no—
424C2×C3—41no—
425C2×C3—42no—
426C2×C3—42no—
427C2×C3—82no—
428C2×C3Dic3×C22⋊C411yescharacteristic
429C2×C3#514512yes—
430C2×C3#519712yes—
431C2×C3C4×#21711yescharacteristic
432C22—22no—
433C22—22no—
434C22—42no—
435C22#6395211yescharacteristic
436C22#6395511yescharacteristic
437C22Dic3×#6711yescharacteristic
438C4—22no—
439C4—122no—
440C4—362no—
441C4#6395211yescharacteristic
442C4C2×Dic3211yescharacteristic
443C4D3×#21711yescharacteristic
444C4Dic3×#6711yescharacteristic
445C3—21no—
446C3#7029011yescharacteristic, complemented
447C3#7200911yescharacteristic, complemented
448C2—21no—
449C2—21no—
450C2—42no—
451C2#1059167412yes—
452C2Dic3×#21711yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutatorC32×C4C2×C42
FrattiniC22×C4C2×D32
Fitting, prime radicalC2×C32×#41C22
socleC22×C32C4×D4
cosocleC22×C32×C4C23
hypercenterC2×#41D32
hypocenterC32#1765
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
4. C2×#63555C2semidirect
5. #10591055C2semidirect
6. #10589166C2semidirect
7. #10589160C2semidirect
14. C3×#948C4semidirect
21. #63664C4semidirect
22. C3×#835C4semidirect
23. C3×#832C4semidirect
85. #948Dic3semidirect
103. #835Dic3semidirect
104. #832Dic3semidirect
391. C32#1765semidirect
446. C3#70290semidirect
447. C3#72009semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9482
C2×#636642
C3×#52332
C2×#635552
#105910552
#105891662
#105891602
#720093
#702903