Finite Group Databasebeta

← #11785744

Subgroups — #11785744

Order 1152.

593 conjugacy classes of subgroups.

The subgroup lattice has 445 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63841C211yesmaximal, characteristic
2C3×#5126C211yesmaximal, characteristic
3#10591069C211yesmaximal, characteristic
4#10589420C211yesmaximal, characteristic, complemented
5C3×#4554C211yesmaximal, characteristic, complemented
6#10589168C211yesmaximal, characteristic, complemented
7#10589167C211yesmaximal, characteristic, complemented
8#69974—31nomaximal
9#68991—31nomaximal
10C22×C3×C4×D3C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C2×(C2×D3)⋊Dic3C412yes—
18C2×Dic32C412yes—
19#63841—22no—
20#63841—22no—
21C3×(C2×D3)⋊C8—22no—
22(C2×D3)⋊(C3⋊C8)—22no—
23C2×#926—31no—
24C2×#892—31no—
25C3×#407—31no—
26#5207—31no—
27#5126—31no—
28#5126D311yescharacteristic
29C3×#343—31no—
30#4554—31no—
31#4554—31no—
32#4554—31no—
33#4554—31no—
34#4554—31no—
35#4554—61no—
36#4554D311yescharacteristic, complemented
37#4530—31no—
38C23×C3×D3C2×C411yescharacteristic
39C22×C32×C4C2311yescharacteristic
40C22×C3⋊Dic3C2×C412yes—
41C22×C3×Dic3C2×C411yescharacteristic
42C22×C3×Dic3C2×C412yes—
43C2×C3×C4×D3—21no—
44C2×C3×C4×D3—21no—
45C2×C3×C4×D3—21no—
46C2×C3×C4×D3—21no—
47C2×C3×C4×D3D412yes—
48C2×C3×C4×D3D412yes—
49C32×M16—21no—
50C32×M16—21no—
51C2×C32×C8—21no—
52C4⋊(C3⋊Dic3)—21no—
53C4⋊(C3⋊Dic3)—21no—
54#3748—21no—
55#3748—21no—
56C2×C3⋊(C3⋊C8)—21no—
57C3×C4⋊Dic3—21no—
58C3×C4⋊Dic3—21no—
59C3×#208—21no—
60C3×#208—21no—
61C3×#208—21no—
62C3×#208—21no—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65(C2×D3)⋊Dic3—24no—
66Dic32—24no—
67#1822—91noSylow
68C23×C3×C4—31no—
69C22×C4×D3C2×D311yescharacteristic
70C2×C3×M16—21no—
71C2×C3×M16—31no—
72C2×C3×M16—31no—
73C2×C3×M16C2×D311yescharacteristic
74C2×C3×M16C2×D311yescharacteristic
75C2×C3×C4⋊C4—31no—
76C2×#217—32no—
77C2×(C2×D3)⋊C4—32no—
78#926—62no—
79#926—62no—
80C2×C4⋊Dic3—31no—
81C2×C4⋊Dic3—31no—
82C2×C4⋊Dic3—61no—
83C2×C4⋊Dic3C2×D311yescharacteristic
84C2×C4×Dic3—32no—
85C2×C4×Dic3—32no—
86C2×#208—31no—
87C2×#208—31no—
88C2×#208—61no—
89C2×#208C2×D311yescharacteristic
90C2×#208C2×D311yescharacteristic
91#892—62no—
92#892—62no—
93C3×C22⋊C8—62no—
94#830—62no—
95(C2×D3)⋊C8—22no—
96(C2×D3)⋊C8—62no—
97C23×C32C22×C411yescharacteristic
98C22×C3×D3—21no—
99C22×C3×D3—21no—
100C22×C3×D3—41no—
101C22×C3×D3—41no—
102C22×C3×D3C22⋊C412yes—
103C2×C32×C4C2×D411yescharacteristic
104C2×C32×C4C2×D411yescharacteristic
105C2×C32×C4#4111yescharacteristic
106C2×C32×C4#4111yescharacteristic
107C2×C32×C4#4111yescharacteristic
108C2×C32×C4#4111yescharacteristic
109C2×C3⋊Dic3—22no—
110C2×C3⋊Dic3—42no—
111C2×C3×Dic3—21no—
112C2×C3×Dic3—21no—
113C2×C3×Dic3—22no—
114C2×C3×Dic3—42no—
115C2×C3×Dic3C22⋊C412yes—
116C3×C4×D3—22no—
117C3×C4×D3—22no—
118C3×C4×D3—22no—
119C3×C4×D3—22no—
120C32×C8—41no—
121C3⋊(C3⋊C8)—41no—
122C3×C3⋊C8—41no—
123C3×C3⋊C8—41no—
124C2×#117—91no—
125#407—31no—
126#407—91no—
127#343—31no—
128#343—91no—
129#343—91no—
130#343—91no—
131C24×C3—31no—
132C23×D3C4×D311yescharacteristic
133C22×C3×C4—21no—
134C22×C3×C4—31no—
135C22×C3×C4—32no—
136C22×C3×C4—32no—
137C22×C3×C4—32no—
138C22×C3×C4—61no—
139C22×C3×C4—61no—
140C22×C3×C4—61no—
141C22×C3×C4—61no—
142C22×C3×C4C22×D311yescharacteristic
143C22×C3×C4C22×D311yescharacteristic
144C22×Dic3—32no—
145C22×Dic3—32no—
146C22×Dic3—62no—
147C22×Dic3C4×D311yescharacteristic
148C22×Dic3C4×D312yes—
149C2×C4×D3—21no—
150C2×C4×D3—21no—
151C2×C4×D3—21no—
152C2×C4×D3—21no—
153C2×C4×D3D1212yes—
154C2×C4×D3#6712yes—
155C3×M16—22no—
156C3×M16—21no—
157C3×M16—21no—
158C3×M16—21no—
159C3×M16—21no—
160C3×M16—41no—
161C3×M16—61no—
162C3×M16—61no—
163C3×M16—61no—
164C3×M16—61no—
165C2×C3×C8—21no—
166C2×C3×C8—21no—
167C2×C3×C8—41no—
168C2×C3×C8—61no—
169C2×C3×C8—61no—
170C3×C4⋊C4—61no—
171C3×C4⋊C4—61no—
172#217—64no—
173(C2×D3)⋊C4—64no—
174C4⋊Dic3—21no—
175C4⋊Dic3—21no—
176C4⋊Dic3—61no—
177C4⋊Dic3—61no—
178C4⋊Dic3—61no—
179C4⋊Dic3—61no—
180C4⋊Dic3—121no—
181C4⋊Dic3—121no—
182C4×Dic3—64no—
183C4×Dic3—64no—
184#208—21no—
185#208—21no—
186#208—21no—
187#208—21no—
188#208—62no—
189#208—61no—
190#208—61no—
191#208—61no—
192#208—61no—
193#208—121no—
194C2×C3⋊C8—21no—
195C2×C3⋊C8—21no—
196C2×C3⋊C8—61no—
197C2×C3⋊C8—61no—
198C2×C3⋊C8—121no—
199C22×C32—21no—
200C22×C32—21no—
201C22×C32C2×C22⋊C411yescharacteristic
202C22×C32#11711yescharacteristic
203C22×C32#11711yescharacteristic
204C2×C3×D3—22no—
205C2×C3×D3—22no—
206C2×C3×D3—22no—
207C2×C3×D3—42no—
208C2×C3×D3—42no—
209C32×C4#12311yescharacteristic
210C32×C4#12311yescharacteristic
211C32×C4#12311yescharacteristic
212C32×C4#12311yescharacteristic
213C3⋊Dic3—42no—
214C3×Dic3—22no—
215C3×Dic3—42no—
216C23×C4—31no—
217C2×M16—31no—
218C2×M16—31no—
219C2×M16—91no—
220C2×M16D3211yescharacteristic
221#117—182no—
222#117—182no—
223C2×C4⋊C4—31no—
224C2×C4⋊C4—91no—
225C2×C22⋊C4—92no—
226C2×C42—92no—
227C22⋊C8—62no—
228C22⋊C8—182no—
229C23×C3—21no—
230C23×C3—32no—
231C23×C3—61no—
232C23×C3—61no—
233C23×C3—121no—
234C23×C3—121no—
235C23×C3C2×C4×D311yescharacteristic
236C23×C3C2×C4×D311yescharacteristic
237C22×D3—21no—
238C22×D3—21no—
239C22×D3—41no—
240C22×D3—41no—
241C22×D3(C2×D3)⋊C412yes—
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—21no—
248C2×C3×C4—32no—
249C2×C3×C4—61no—
250C2×C3×C4—61no—
251C2×C3×C4—62no—
252C2×C3×C4—62no—
253C2×C3×C4—62no—
254C2×C3×C4—62no—
255C2×C3×C4—62no—
256C2×C3×C4—122no—
257C2×C3×C4C2×D1211yescharacteristic
258C2×C3×C4#23511yescharacteristic
259C2×C3×C4#23511yescharacteristic
260C2×C3×C4D3×D411yescharacteristic
261C2×C3×C4D3×D411yescharacteristic
262C2×C3×C4#23711yescharacteristic
263C2×C3×C4#23711yescharacteristic
264C2×C3×C4#23711yescharacteristic
265C2×C3×C4#23711yescharacteristic
266C2×C3×C4#23711yescharacteristic
267C2×C3×C4#23911yescharacteristic
268C2×C3×C4C2×#6711yescharacteristic
269C2×Dic3—21no—
270C2×Dic3—21no—
271C2×Dic3—22no—
272C2×Dic3—42no—
273C2×Dic3—62no—
274C2×Dic3—62no—
275C2×Dic3—122no—
276C2×Dic3—122no—
277C2×Dic3—122no—
278C2×Dic3—242no—
279C2×Dic3(C2×D3)⋊C412yes—
280C4×D3—22no—
281C4×D3—22no—
282C4×D3—22no—
283C4×D3—22no—
284C3×C8—42no—
285C3×C8—41no—
286C3×C8—41no—
287C3×C8—121no—
288C3×C8—121no—
289C3⋊C8—41no—
290C3⋊C8—41no—
291C3⋊C8—122no—
292C3⋊C8—121no—
293C3⋊C8—121no—
294C2×C32—21no—
295C2×C32—21no—
296C2×C32#38111yescharacteristic
297C2×C32#41311yescharacteristic
298C2×C32#41311yescharacteristic
299C3×D3—42no—
300C24—31no—
301C22×C4—31no—
302C22×C4—32no—
303C22×C4—32no—
304C22×C4—32no—
305C22×C4—61no—
306C22×C4—61no—
307C22×C4—61no—
308C22×C4—61no—
309C22×C4—92no—
310C22×C4C2×D3211yescharacteristic
311M16—21no—
312M16—21no—
313M16—61no—
314M16—61no—
315M16—61no—
316M16—61no—
317M16—181no—
318M16—181no—
319C2×C8—21no—
320C2×C8—61no—
321C2×C8—61no—
322C2×C8—181no—
323C4⋊C4—61no—
324C4⋊C4—61no—
325C4⋊C4—181no—
326C4⋊C4—181no—
327C22⋊C4—184no—
328C42—184no—
329C22×C3—21no—
330C22×C3—21no—
331C22×C3—21no—
332C22×C3—21no—
333C22×C3—21no—
334C22×C3—21no—
335C22×C3—21no—
336C22×C3—41no—
337C22×C3—41no—
338C22×C3—62no—
339C22×C3—62no—
340C22×C3—62no—
341C22×C3—122no—
342C22×C3—122no—
343C22×C3#87211yescharacteristic
344C22×C3#87711yescharacteristic
345C22×C3#87711yescharacteristic
346C22×C3D3×C22⋊C411yescharacteristic
347C22×C3#89211yescharacteristic
348C22×C3C2×(C2×D3)⋊C411yescharacteristic
349C2×D3—22no—
350C2×D3—22no—
351C2×D3—22no—
352C2×D3—42no—
353C2×D3—42no—
354C3×C4—21no—
355C3×C4—21no—
356C3×C4—21no—
357C3×C4—21no—
358C3×C4—62no—
359C3×C4—122no—
360C3×C4#88311yescharacteristic
361C3×C4#88311yescharacteristic
362C3×C4#88611yescharacteristic
363C3×C4#88611yescharacteristic
364C3×C4#89411yescharacteristic
365C3×C4#89411yescharacteristic
366C3×C4#93511yescharacteristic
367C3×C4#93511yescharacteristic
368Dic3—22no—
369Dic3—42no—
370Dic3—122no—
371Dic3—122no—
372Dic3—242no—
373C32#182211yescharacteristic, complemented, Sylow
374C23—32no—
375C23—61no—
376C23—61no—
377C23—121no—
378C23—121no—
379C23C4×D3211yescharacteristic
380C2×C4—32no—
381C2×C4—61no—
382C2×C4—61no—
383C2×C4—62no—
384C2×C4—62no—
385C2×C4—62no—
386C2×C4—62no—
387C2×C4—62no—
388C2×C4—122no—
389C2×C4—182no—
390C2×C4—362no—
391C2×C4#379511yescharacteristic
392C2×C4#379611yescharacteristic
393C2×C4D3×D1211yescharacteristic
394C2×C4#380411yescharacteristic
395C2×C4#380511yescharacteristic
396C2×C4D3×#6711yescharacteristic
397C8—41no—
398C8—121no—
399C8—121no—
400C8—361no—
401C2×C3—21no—
402C2×C3—21no—
403C2×C3—21no—
404C2×C3—21no—
405C2×C3—21no—
406C2×C3—21no—
407C2×C3—21no—
408C2×C3—41no—
409C2×C3—41no—
410C2×C3—122no—
411C2×C3#466411yescharacteristic
412C2×C3#474511yescharacteristic
413C2×C3#475111yescharacteristic
414C2×C3#494311yescharacteristic
415C2×C3#513211yescharacteristic
416C2×C3#513211yescharacteristic
417D3—42no—
418C22—21no—
419C22—21no—
420C22—62no—
421C22—62no—
422C22—62no—
423C22—122no—
424C22—122no—
425C22#6387711yescharacteristic
426C22#6387811yescharacteristic
427C22D3×(C2×D3)⋊C411yescharacteristic
428C4—62no—
429C4—122no—
430C4—362no—
431C4#6388411yescharacteristic
432C4#6389011yescharacteristic
433C4#6389111yescharacteristic
434C4#6396911yescharacteristic
435C3—21no—
436C3#6899111yescharacteristic, complemented
437C3#6997411yescharacteristic, complemented
438C2—21no—
439C2—21no—
440C2—122no—
441C2#1059100611yescharacteristic
442C2#1059100711yescharacteristic
443C2#1059136211yescharacteristic
subgroupG/H
centerC22D3×(C2×D3)⋊C4
commutatorC23×C32C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32C2×C22⋊C4
prime radicalC23×C3×D3C2×C4
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1822
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
4. #10589420C2semidirect
5. C3×#4554C2semidirect
6. #10589168C2semidirect
7. #10589167C2semidirect
36. #4554D3semidirect
373. C32#1822semidirect
436. C3#68991semidirect
437. C3#69974semidirect

Maximal subgroups

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

subgroupindex
C2×#638412
C3×#51262
#105910692
#105894202
C3×#45542
#105891682
#105891672
#699743
#689913