Finite Group Databasebeta

← #11783613

Subgroups — #11783613

Order 1152.

731 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63855C211yesmaximal, characteristic
2C2×C3×(C2×D3)⋊C8C211yesmaximal, characteristic
3C2×C3×C8×Dic3C211yesmaximal, characteristic, complemented
4C2×(C2×D3)⋊(C3⋊C8)C211yesmaximal, characteristic
5C2×#63554C211yesmaximal, characteristic, complemented
6#10589416C211yesmaximal, characteristic, complemented
7#10589156C211yesmaximal, characteristic, complemented
8#69907—31nomaximal
9#69753—31nomaximal
10C22×C3×C4×D3C2211yescharacteristic
11C22×C32×C8C2211yescharacteristic
12C2×C4×C3⋊Dic3C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C2×C3×C4×Dic3C2211yescharacteristic
15C22×C3×C3⋊C8C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C2×Dic3⋊Dic3C412yes—
18C2×(C2×D3)⋊Dic3C412yes—
19#63855—22no—
20#63855—22no—
21C3×(C2×D3)⋊C8C414yescomplemented
22C3×C8×Dic3—22no—
23(C2×D3)⋊(C3⋊C8)C414yescomplemented
24#63554—22no—
25C2×#926—31no—
26C2×#872—31no—
27C2×C3×C22⋊C8—31no—
28C2×C3×C4×C8—31no—
29C2×#830—31no—
30C2×(C2×D3)⋊C8—31no—
31C2×(C2×D3)⋊C8D311yescharacteristic
32C2×#815—31no—
33C2×C8×Dic3D311yescharacteristic, complemented
34C2×#803—31no—
35#4550—31no—
36#4550—31no—
37#4550—31no—
38#4550—31no—
39#4550—61no—
40C23×C3×D3C2×C411yescharacteristic
41C22×C32×C4C2311yescharacteristic
42C22×C3⋊Dic3C2×C412yes—
43C22×C3×Dic3C2×C411yescharacteristic
44C22×C3×Dic3C2×C412yes—
45C2×C3×C4×D3—21no—
46C2×C3×C4×D3—21no—
47C2×C3×C4×D3—21no—
48C2×C3×C4×D3—21no—
49C2×C3×C4×D3C2×C412yes—
50C2×C3×C4×D3C2×C412yes—
51C2×C32×C8—21no—
52C2×C32×C8—21no—
53C2×C32×C8C2×C412yes—
54C4×C3⋊Dic3—21no—
55C4×C3⋊Dic3—21no—
56C2×C3⋊(C3⋊C8)—21no—
57C2×C3⋊(C3⋊C8)—21no—
58C2×C3⋊(C3⋊C8)C2×C412yes—
59C3×C4×Dic3D412yes—
60C3×C4×Dic3D412yes—
61C2×C3×C3⋊C8—21no—
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65C2×C3×C3⋊C8C2×C412yes—
66C2×C3×C3⋊C8C2×C412yes—
67Dic3⋊Dic3—24no—
68(C2×D3)⋊Dic3—24no—
69#1750—91noSylow
70C23×C3×C4—31no—
71C22×C4×D3C2×D311yescharacteristic
72C22×C3×C8—21no—
73C22×C3×C8—31no—
74C22×C3×C8—31no—
75C22×C3×C8C2×D311yescharacteristic
76C22×C3×C8C2×D311yescharacteristic
77C2×C3×C42—31no—
78C2×#217—32no—
79C2×(C2×D3)⋊C4—32no—
80#926—62no—
81#926—62no—
82C2×C4⋊Dic3—32no—
83C2×Dic3⋊C4—32no—
84C2×C4×Dic3—31no—
85C2×C4×Dic3—31no—
86C2×C4×Dic3—61no—
87C2×C4×Dic3C2×D311yescharacteristic
88C22×C3⋊C8—31no—
89C22×C3⋊C8—31no—
90C22×C3⋊C8—61no—
91C22×C3⋊C8C2×D311yescharacteristic
92C22×C3⋊C8C2×D311yescharacteristic
93#872—62no—
94#872—62no—
95C3×C22⋊C8—34no—
96C3×C4×C8—62no—
97#830—34no—
98(C2×D3)⋊C8—34no—
99(C2×D3)⋊C8Dic314yescomplemented
100#815—62no—
101C8×Dic3—22no—
102#803—62no—
103C23×C32C22×C411yescharacteristic
104C22×C3×D3—21no—
105C22×C3×D3—21no—
106C22×C3×D3—22no—
107C22×C3×D3—22no—
108C22×C3×D3C4212yes—
109C2×C32×C4C22×C411yescharacteristic
110C2×C32×C4C22×C411yescharacteristic
111C2×C32×C4C2×D411yescharacteristic
112C2×C32×C4C2×D411yescharacteristic
113C2×C32×C4#4111yescharacteristic
114C2×C32×C4#4111yescharacteristic
115C2×C3⋊Dic3—22no—
116C2×C3⋊Dic3—22no—
117C2×C3⋊Dic3—22no—
118C2×C3×Dic3—21no—
119C2×C3×Dic3—21no—
120C2×C3×Dic3—22no—
121C2×C3×Dic3—22no—
122C2×C3×Dic3C4212yes—
123C2×C3×Dic3C22⋊C414yes—
124C3×C4×D3—22no—
125C3×C4×D3—22no—
126C3×C4×D3—22no—
127C3×C4×D3—22no—
128C32×C8—22no—
129C3⋊(C3⋊C8)—22no—
130C3×C3⋊C8—22no—
131C3×C3⋊C8—22no—
132C2×#117—91no—
133C2×C22⋊C8—31no—
134C2×C22⋊C8—91no—
135C2×#97—91no—
136C2×C4×C8—31no—
137#336—91no—
138#336—91no—
139C24×C3—31no—
140C23×D3C4×D311yescharacteristic
141C22×C3×C4—21no—
142C22×C3×C4—32no—
143C22×C3×C4—31no—
144C22×C3×C4—32no—
145C22×C3×C4—32no—
146C22×C3×C4—61no—
147C22×C3×C4—61no—
148C22×C3×C4—61no—
149C22×C3×C4—61no—
150C22×C3×C4C22×D311yescharacteristic
151C22×C3×C4C22×D311yescharacteristic
152C22×Dic3—32no—
153C22×Dic3—32no—
154C22×Dic3—62no—
155C22×Dic3C4×D311yescharacteristic
156C22×Dic3C4×D312yes—
157C2×C4×D3—21no—
158C2×C4×D3—21no—
159C2×C4×D3—21no—
160C2×C4×D3—21no—
161C2×C4×D3C4×D312yes—
162C2×C4×D3C2×Dic312yes—
163C2×C3×C8—21no—
164C2×C3×C8—21no—
165C2×C3×C8—21no—
166C2×C3×C8—21no—
167C2×C3×C8—22no—
168C2×C3×C8—32no—
169C2×C3×C8—32no—
170C2×C3×C8—41no—
171C2×C3×C8—41no—
172C2×C3×C8—61no—
173C2×C3×C8—61no—
174C2×C3×C8—61no—
175C2×C3×C8—61no—
176C2×C3×C8C4×D312yes—
177C2×C3×C8C2×Dic312yes—
178C3×C42—32no—
179C3×C42—32no—
180#217—64no—
181(C2×D3)⋊C4—64no—
182C4⋊Dic3—64no—
183Dic3⋊C4—64no—
184C4×Dic3—61no—
185C4×Dic3—61no—
186C4×Dic3—61no—
187C4×Dic3—61no—
188C4×Dic3—121no—
189C4×Dic3—121no—
190C4×Dic3D1212yes—
191C4×Dic3#6712yes—
192C2×C3⋊C8—21no—
193C2×C3⋊C8—21no—
194C2×C3⋊C8—21no—
195C2×C3⋊C8—21no—
196C2×C3⋊C8—32no—
197C2×C3⋊C8—32no—
198C2×C3⋊C8—62no—
199C2×C3⋊C8—61no—
200C2×C3⋊C8—61no—
201C2×C3⋊C8—61no—
202C2×C3⋊C8—61no—
203C2×C3⋊C8—121no—
204C2×C3⋊C8—121no—
205C2×C3⋊C8C4×D312yes—
206C2×C3⋊C8C2×Dic312yes—
207C22×C32C2×C4211yescharacteristic
208C22×C32C2×C22⋊C411yescharacteristic
209C22×C32#11711yescharacteristic
210C22×C32#13112yes—
211C22×C32#13112yes—
212C2×C3×D3—22no—
213C2×C3×D3—22no—
214C2×C3×D3—22no—
215C2×C3×D3—42no—
216C2×C3×D3—42no—
217C32×C4C4×D411yescharacteristic
218C32×C4C4×D411yescharacteristic
219C32×C4C4×D411yescharacteristic
220C32×C4C4×D411yescharacteristic
221C3⋊Dic3—42no—
222C3×Dic3—22no—
223C3×Dic3—24no—
224C23×C4—31no—
225C22×C8—31no—
226C22×C8—31no—
227C22×C8—91no—
228C22×C8D3211yescharacteristic
229#117—182no—
230#117—182no—
231C2×C4⋊C4—92no—
232C2×C22⋊C4—92no—
233C2×C42—31no—
234C2×C42—91no—
235C22⋊C8—34no—
236C22⋊C8—94no—
237#97—182no—
238C4×C8—62no—
239C23×C3—21no—
240C23×C3—32no—
241C23×C3—61no—
242C23×C3—62no—
243C23×C3—62no—
244C23×C3—61no—
245C23×C3C2×C4×D311yescharacteristic
246C23×C3C2×C4×D311yescharacteristic
247C22×D3—21no—
248C22×D3—21no—
249C22×D3—22no—
250C22×D3—22no—
251C22×D3C4×Dic312yes—
252C2×C3×C4—21no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4—32no—
259C2×C3×C4—34no—
260C2×C3×C4—61no—
261C2×C3×C4—62no—
262C2×C3×C4—62no—
263C2×C3×C4—61no—
264C2×C3×C4—62no—
265C2×C3×C4—62no—
266C2×C3×C4—62no—
267C2×C3×C4—62no—
268C2×C3×C4C2×C4×D311yescharacteristic
269C2×C3×C4C2×C4×D311yescharacteristic
270C2×C3×C4C2×C4×D311yescharacteristic
271C2×C3×C4C2×D1211yescharacteristic
272C2×C3×C4#23511yescharacteristic
273C2×C3×C4#23511yescharacteristic
274C2×C3×C4D3×D411yescharacteristic
275C2×C3×C4D3×D411yescharacteristic
276C2×C3×C4#23711yescharacteristic
277C2×C3×C4#23711yescharacteristic
278C2×C3×C4C22×Dic311yescharacteristic
279C2×C3×C4C2×#6711yescharacteristic
280C2×Dic3—21no—
281C2×Dic3—21no—
282C2×Dic3—22no—
283C2×Dic3—22no—
284C2×Dic3—64no—
285C2×Dic3—62no—
286C2×Dic3—62no—
287C2×Dic3—62no—
288C2×Dic3—62no—
289C2×Dic3—62no—
290C2×Dic3—62no—
291C2×Dic3—122no—
292C2×Dic3—122no—
293C2×Dic3C4×Dic312yes—
294C2×Dic3(C2×D3)⋊C414yes—
295C4×D3—22no—
296C4×D3—22no—
297C4×D3—22no—
298C4×D3—22no—
299C3×C8—22no—
300C3×C8—22no—
301C3×C8—42no—
302C3×C8—62no—
303C3×C8—62no—
304C3⋊C8—22no—
305C3⋊C8—22no—
306C3⋊C8—62no—
307C3⋊C8—62no—
308C3⋊C8—122no—
309C2×C32C4×C22⋊C411yescharacteristic
310C2×C32#40511yescharacteristic
311C2×C32#40511yescharacteristic
312C2×C32#40812yes—
313C2×C32#43312yes—
314C3×D3—42no—
315C24—31no—
316C22×C4—32no—
317C22×C4—31no—
318C22×C4—32no—
319C22×C4—32no—
320C22×C4—61no—
321C22×C4—61no—
322C22×C4—61no—
323C22×C4—61no—
324C22×C4—92no—
325C22×C4C2×D3211yescharacteristic
326C2×C8—21no—
327C2×C8—21no—
328C2×C8—32no—
329C2×C8—32no—
330C2×C8—61no—
331C2×C8—61no—
332C2×C8—61no—
333C2×C8—61no—
334C2×C8—92no—
335C2×C8—181no—
336C2×C8—181no—
337C2×C8D3×Dic312yes—
338C4⋊C4—184no—
339C22⋊C4—184no—
340C42—32no—
341C42—32no—
342C42—181no—
343C42—181no—
344C22×C3—22no—
345C22×C3—22no—
346C22×C3—21no—
347C22×C3—21no—
348C22×C3—21no—
349C22×C3—62no—
350C22×C3—62no—
351C22×C3—62no—
352C22×C3—122no—
353C22×C3—122no—
354C22×C3C42×D311yescharacteristic
355C22×C3#87211yescharacteristic
356C22×C3#87711yescharacteristic
357C22×C3D3×C22⋊C411yescharacteristic
358C22×C3#90112yes—
359C22×C3#90112yes—
360C22×C3#90112yes—
361C22×C3#90712yes—
362C22×C3C2×C4×Dic311yescharacteristic
363C22×C3C2×(C2×D3)⋊C411yescharacteristic
364C2×D3—22no—
365C2×D3—22no—
366C2×D3—22no—
367C2×D3—42no—
368C2×D3—42no—
369C3×C4—21no—
370C3×C4—21no—
371C3×C4—21no—
372C3×C4—21no—
373C3×C4—62no—
374C3×C4—64no—
375C3×C4C4×D1211yescharacteristic
376C3×C4C4×D1211yescharacteristic
377C3×C4#67⋊C411yescharacteristic
378C3×C4#67⋊C411yescharacteristic
379C3×C4C4×#6711yescharacteristic
380C3×C4C4×#6711yescharacteristic
381C3×C4D4×Dic311yescharacteristic
382C3×C4D4×Dic311yescharacteristic
383Dic3—22no—
384Dic3—24no—
385Dic3—124no—
386Dic3—122no—
387Dic3—122no—
388C32#175011yescharacteristic, complemented, Sylow
389C23—32no—
390C23—62no—
391C23—62no—
392C23—61no—
393C23—61no—
394C23C4×D3211yescharacteristic
395C2×C4—32no—
396C2×C4—34no—
397C2×C4—62no—
398C2×C4—62no—
399C2×C4—61no—
400C2×C4—61no—
401C2×C4—62no—
402C2×C4—62no—
403C2×C4—62no—
404C2×C4—62no—
405C2×C4—182no—
406C2×C4—182no—
407C2×C4—182no—
408C2×C4#379511yescharacteristic
409C2×C4C4×D3211yescharacteristic
410C2×C4D3×D1211yescharacteristic
411C2×C4C2×D3×Dic311yescharacteristic
412C2×C4#380411yescharacteristic
413C2×C4D3×#6711yescharacteristic
414C8—22no—
415C8—62no—
416C8—62no—
417C8—182no—
418C2×C3—21no—
419C2×C3—21no—
420C2×C3—21no—
421C2×C3—22no—
422C2×C3—22no—
423C2×C3—122no—
424C2×C3#468911yescharacteristic
425C2×C3#468911yescharacteristic
426C2×C3#469012yes—
427C2×C3#472012yes—
428C2×C3#472712yes—
429C2×C3C4×(C2×D3)⋊C411yescharacteristic
430C2×C3Dic3×C22⋊C411yescharacteristic
431C2×C3#510111yescharacteristic
432C2×C3#511012yes—
433C2×C3#512211yescharacteristic
434D3—42no—
435C22—62no—
436C22—62no—
437C22—62no—
438C22—122no—
439C22—122no—
440C22#6380312yes—
441C22#6380412yes—
442C22C4×D3×Dic311yescharacteristic
443C22#6387711yescharacteristic
444C22D3×(C2×D3)⋊C411yescharacteristic
445C4—62no—
446C4—64no—
447C4—362no—
448C4#6387911yescharacteristic
449C4#6388011yescharacteristic
450C4Dic3×D1211yescharacteristic
451C4Dic3×#6711yescharacteristic
452C3—21no—
453C3#6975311yescharacteristic, complemented
454C3#6990711yescharacteristic, complemented
455C2—122no—
456C2#1059069211yescharacteristic
457C2#1059069612yes—
458C2#1059090811yescharacteristic
459C2#1059095312yes—
460C2Dic3×(C2×D3)⋊C411yescharacteristic
subgroupG/H
center, FrattiniC22×C4C2×D32
commutatorC22×C32C2×C42
FittingC22×C32×C8C22
socleC23×C32C22×C4
prime radicalC23×C3×D3C2×C4
cosocleC22×C32×C4C23
hypercenterC22×C8D32
hypocenterC32#1750
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
3. C2×C3×C8×Dic3C2semidirect
5. C2×#63554C2semidirect
6. #10589416C2semidirect
7. #10589156C2semidirect
21. C3×(C2×D3)⋊C8C4semidirect
23. (C2×D3)⋊(C3⋊C8)C4semidirect
33. C2×C8×Dic3D3semidirect
99. (C2×D3)⋊C8Dic3semidirect
388. C32#1750semidirect
453. C3#69753semidirect
454. C3#69907semidirect

Maximal subgroups

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

subgroupindex
C2×#638552
C2×C3×(C2×D3)⋊C82
C2×C3×C8×Dic32
C2×(C2×D3)⋊(C3⋊C8)2
C2×#635542
#105894162
#105891562
#699073
#697533