Finite Group Databasebeta

← #11788332

Subgroups — #11788332

Order 1152.

1014 conjugacy classes of subgroups.

The subgroup lattice has 405 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×M16×C3⋊D3C211yesmaximal, characteristic
2C2×#64106C211yesmaximal, characteristic
3C2×#63651C211yesmaximal, characteristic, complemented
4C2×#63651C211yesmaximal, characteristic, complemented
5#10592825C211yesmaximal, characteristic
6C32×#343C211yesmaximal, characteristic, complemented
7#10589396C211yesmaximal, characteristic, complemented
8#68993—34nomaximal
9C22×C4×C3⋊D3C2211yescharacteristic
10C22×#634C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13C2×C32×C4⋊C4C2211yescharacteristic
14C2×#3752C412yes—
15C2×C4⋊(C3⋊Dic3)C412yes—
16C2×#3748C2211yescharacteristic
17C2×#3748C2211yescharacteristic
18M16×C3⋊D3—22no—
19M16×C3⋊D3—22no—
20C2×#3743—21no—
21C2×C8×C3⋊D3—21no—
22#64106—21no—
23#64106—21no—
24#64106—21no—
25#64106—21no—
26#63651—22no—
27#63651—22no—
28#63647—21no—
29#63647—21no—
30C2×D3×M16—34no—
31C2×#897—34no—
32C2×#824—34no—
33C2×#824—34no—
34#5126—34no—
35C3×#343D314yescomplemented
36#4530—34no—
37C23×C3⋊D3C2×C411yescharacteristic
38C22×C32×C4C2×C412yes—
39C22×C32×C4C2311yescharacteristic
40C22×C3⋊Dic3C2×C412yes—
41C22×C3⋊Dic3C2×C411yescharacteristic
42C2×C4×C3⋊D3—21no—
43C2×C4×C3⋊D3—21no—
44C2×C4×C3⋊D3—21no—
45C2×C4×C3⋊D3—21no—
46C2×C4×C3⋊D3D411yescharacteristic
47C2×C4×C3⋊D3D411yescharacteristic
48C2×C4×C3⋊D3D411yescharacteristic
49C2×C4×C3⋊D3D411yescharacteristic
50C2×#634—21no—
51C2×#634—21no—
52C2×#634—21no—
53C2×#634—21no—
54C2×#634—21no—
55C2×#634—21no—
56C32×M16—21no—
57C32×M16—21no—
58C32×M16—21no—
59C32×M16D412yes—
60C2×C32×C8—21no—
61C2×C32×C8—21no—
62C32×C4⋊C4—21no—
63C32×C4⋊C4—21no—
64#3752—22no—
65#3752—22no—
66C4⋊(C3⋊Dic3)—22no—
67C4⋊(C3⋊Dic3)—22no—
68#3748—21no—
69#3748—21no—
70#3748—21no—
71#3748D412yes—
72C2×C3⋊(C3⋊C8)—21no—
73C2×C3⋊(C3⋊C8)—21no—
74#3743—24no—
75C8×C3⋊D3—24no—
76#1901—91noSylow
77C22×C4×D3—34no—
78C22×Dic6—34no—
79C2×C3×M16C2×D314yes—
80C2×C3×M16C2×D314yes—
81C2×C3×C4⋊C4C2×D314yes—
82C2×(C2×D3)⋊C4—38no—
83C2×C4⋊Dic3—38no—
84C2×#208—34no—
85C2×#208—34no—
86D3×M16—68no—
87D3×M16—68no—
88C2×ΓL(1,𝔽25)—64no—
89C2×D3×C8—64no—
90#897—64no—
91#897—64no—
92#897—64no—
93#897—64no—
94#824—68no—
95#824—68no—
96(C2×D3)⋊C8—64no—
97(C2×D3)⋊C8—64no—
98C23×C32C22×C411yescharacteristic
99C22×C3⋊D3—21no—
100C22×C3⋊D3—21no—
101C22×C3⋊D3—22no—
102C22×C3⋊D3—41no—
103C22×C3⋊D3C22⋊C411yescharacteristic
104C22×C3⋊D3C22⋊C411yescharacteristic
105C2×C32×C4—22no—
106C2×C32×C4—42no—
107C2×C32×C4C2×D411yescharacteristic
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4#4111yescharacteristic
112C2×C32×C4#4111yescharacteristic
113C2×C3⋊Dic3—21no—
114C2×C3⋊Dic3—21no—
115C2×C3⋊Dic3—22no—
116C2×C3⋊Dic3—22no—
117C2×C3⋊Dic3—22no—
118C2×C3⋊Dic3C22⋊C411yescharacteristic
119C2×C3⋊Dic3C22⋊C411yescharacteristic
120C4×C3⋊D3—21no—
121C4×C3⋊D3—21no—
122C4×C3⋊D3—21no—
123C4×C3⋊D3—21no—
124C4×C3⋊D3—21no—
125C4×C3⋊D3—21no—
126C4×C3⋊D3—21no—
127C4×C3⋊D3—21no—
128#634—41no—
129#634—41no—
130#634—41no—
131#634—41no—
132C32×C8—22no—
133C32×C8—41no—
134C3⋊(C3⋊C8)—22no—
135C3⋊(C3⋊C8)—41no—
136C22×M16—91no—
137C2×C22⋊Q8—91no—
138C2×#101—91no—
139C2×#101—91no—
140#407—91no—
141#343—91no—
142#343C3⋊D311yescharacteristic, complemented
143C23×D3—34no—
144C22×C3×C4C4×D318yes—
145C22×C3×C4C22×D314yes—
146C22×Dic3—34no—
147C22×Dic3—38no—
148C2×C4×D3—34no—
149C2×C4×D3—34no—
150C2×C4×D3—34no—
151C2×C4×D3—34no—
152C2×C4×D3—64no—
153C2×C4×D3—64no—
154C2×C4×D3—64no—
155C2×C4×D3—64no—
156C2×Dic6—64no—
157C2×Dic6—64no—
158C2×Dic6—64no—
159C2×Dic6—64no—
160C2×Dic6—64no—
161C2×Dic6—64no—
162C3×M16—24no—
163C3×M16—24no—
164C3×M16—24no—
165C3×M16D1218yes—
166C2×C3×C8—24no—
167C2×C3×C8—24no—
168C3×C4⋊C4—24no—
169C3×C4⋊C4—24no—
170(C2×D3)⋊C4—68no—
171(C2×D3)⋊C4—68no—
172C4⋊Dic3—68no—
173C4⋊Dic3—68no—
174#208—38no—
175#208—64no—
176#208—64no—
177#208—64no—
178C2×C3⋊C8—64no—
179C2×C3⋊C8—64no—
180ΓL(1,𝔽25)—616no—
181D3×C8—616no—
182C22×C32—21no—
183C22×C32—21no—
184C22×C32C2×C22⋊C411yescharacteristic
185C22×C32C4×D411yescharacteristic
186C22×C32C4×D411yescharacteristic
187C2×C3⋊D3—21no—
188C2×C3⋊D3—21no—
189C2×C3⋊D3—21no—
190C2×C3⋊D3—21no—
191C2×C3⋊D3—21no—
192C2×C3⋊D3—42no—
193C2×C3⋊D3—42no—
194C2×C3⋊D3#10112yescomplemented
195C32×C4—42no—
196C32×C4#12011yescharacteristic
197C32×C4#12111yescharacteristic
198C32×C4#12111yescharacteristic
199C32×C4#12311yescharacteristic
200C3⋊Dic3—21no—
201C3⋊Dic3—21no—
202C3⋊Dic3—42no—
203C22×Q8—91no—
204C23×C4—91no—
205C2×M16—91no—
206C2×M16—91no—
207C2×M16—181no—
208C2×M16—182no—
209C2×M16—182no—
210C2×M16C2×C3⋊D311yescharacteristic
211C2×M16C2×C3⋊D311yescharacteristic
212C22×C8—181no—
213C22⋊Q8—181no—
214C22⋊Q8—181no—
215C22⋊Q8—181no—
216C22⋊Q8—181no—
217C2×C4⋊C4—92no—
218C2×C4⋊C4C2×C3⋊D311yescharacteristic
219C2×C22⋊C4—92no—
220#101—182no—
221#101—182no—
222C22⋊C8—181no—
223C22⋊C8—181no—
224C23×C3C2×C4×D314yes—
225C22×D3—34no—
226C22×D3—34no—
227C22×D3—68no—
228C22×D3—64no—
229C22×D3—64no—
230C22×D3—124no—
231C2×C3×C4—28no—
232C2×C3×C4—48no—
233C2×C3×C4C2×D1214yes—
234C2×C3×C4#23514yes—
235C2×C3×C4D3×D414yes—
236C2×C3×C4D3×D414yes—
237C2×C3×C4D3×D414yes—
238C2×C3×C4#23914yes—
239C2×Dic3—34no—
240C2×Dic3—34no—
241C2×Dic3—64no—
242C2×Dic3—64no—
243C2×Dic3—68no—
244C2×Dic3—68no—
245C2×Dic3—68no—
246C4×D3—64no—
247C4×D3—64no—
248C4×D3—64no—
249C4×D3—64no—
250C4×D3—64no—
251C4×D3—64no—
252C4×D3—64no—
253C4×D3—64no—
254Dic6—124no—
255Dic6—124no—
256Dic6—124no—
257Dic6—124no—
258C3×C8—28no—
259C3×C8—44no—
260C3⋊C8—68no—
261C3⋊C8—124no—
262C2×C32—21no—
263C2×C32—21no—
264C2×C32#38611yescharacteristic
265C2×C32C2×#10111yescharacteristic
266C2×C32#41311yescharacteristic
267C3⋊D3—22no—
268C3⋊D3—41no—
269C24—91no—
270C2×Q8—181no—
271C2×Q8—181no—
272C2×Q8—181no—
273C2×Q8—181no—
274C2×Q8—181no—
275C2×Q8—181no—
276C22×C4—91no—
277C22×C4—91no—
278C22×C4—91no—
279C22×C4—91no—
280C22×C4—91no—
281C22×C4—92no—
282C22×C4—181no—
283C22×C4—181no—
284C22×C4—181no—
285C22×C4—181no—
286C22×C4C4×C3⋊D312yes—
287C22×C4C22×C3⋊D311yescharacteristic
288M16—21no—
289M16—21no—
290M16—21no—
291M16—92no—
292M16—184no—
293M16—181no—
294M16—181no—
295M16—181no—
296M16C4⋊(C3⋊D3)12yes—
297C2×C8—21no—
298C2×C8—21no—
299C2×C8—184no—
300C2×C8—181no—
301C2×C8—181no—
302C4⋊C4—21no—
303C4⋊C4—21no—
304C4⋊C4—182no—
305C4⋊C4—182no—
306C22⋊C4—182no—
307C22⋊C4—182no—
308C22×C3—24no—
309C22×C3—24no—
310C22×C3C4×D1214yes—
311C22×C3D3×C22⋊C414yes—
312C22×C3#89314yes—
313C2×D3—38no—
314C2×D3—64no—
315C2×D3—64no—
316C2×D3—64no—
317C2×D3—64no—
318C2×D3—64no—
319C2×D3—128no—
320C2×D3—128no—
321C3×C4—48no—
322C3×C4#88214yes—
323C3×C4#88414yes—
324C3×C4#89414yes—
325C3×C4#89514yes—
326Dic3—64no—
327Dic3—64no—
328Dic3—128no—
329C32#190111yescharacteristic, complemented, Sylow
330C23—91no—
331C23—91no—
332C23—182no—
333C23—181no—
334C23—181no—
335C23—361no—
336C23C2×C4×C3⋊D311yescharacteristic
337Q8—361no—
338Q8—361no—
339Q8—361no—
340Q8—361no—
341C2×C4—22no—
342C2×C4—42no—
343C2×C4—91no—
344C2×C4—91no—
345C2×C4—181no—
346C2×C4—181no—
347C2×C4—181no—
348C2×C4—181no—
349C2×C4—181no—
350C2×C4—181no—
351C2×C4—181no—
352C2×C4—181no—
353C2×C4—181no—
354C2×C4—181no—
355C2×C4—182no—
356C2×C4—182no—
357C2×C4—182no—
358C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
359C2×C4#382811yescharacteristic
360C2×C4D4×C3⋊D311yescharacteristic
361C2×C4D4×C3⋊D311yescharacteristic
362C2×C4D4×C3⋊D311yescharacteristic
363C2×C4#383211yescharacteristic
364C8—22no—
365C8—41no—
366C8—182no—
367C8—361no—
368C2×C3—24no—
369C2×C3—24no—
370C2×C3#466514yes—
371C2×C3#474514yes—
372C2×C3D3×#10114yes—
373D3—68no—
374D3—124no—
375C22—21no—
376C22—21no—
377C22—92no—
378C22—181no—
379C22—181no—
380C22—181no—
381C22—181no—
382C22—181no—
383C22—362no—
384C22—362no—
385C22C4×C4⋊(C3⋊D3)11yescharacteristic
386C22C22⋊C4×C3⋊D311yescharacteristic
387C22#6410211yescharacteristic
388C4—42no—
389C4—181no—
390C4—181no—
391C4—362no—
392C4#6409111yescharacteristic
393C4#6409311yescharacteristic
394C4#6410311yescharacteristic
395C4#6410411yescharacteristic
396C3#6899314yescomplemented
397C2—21no—
398C2—21no—
399C2—182no—
400C2—361no—
401C2#1059236411yescharacteristic
402C2#1059244411yescharacteristic
403C2C3⋊D3×#10111yescharacteristic
subgroupG/H
centerC22C22⋊C4×C3⋊D3
commutatorC23×C32C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC32×#343C2
socleC22×C32C2×C22⋊C4
prime radicalC23×C3⋊D3C2×C4
cosocleC22×C32×C4C23
hypercenter#343C3⋊D3
hypocenterC32#1901
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
3. C2×#63651C2semidirect
4. C2×#63651C2semidirect
6. C32×#343C2semidirect
7. #10589396C2semidirect
35. C3×#343D3semidirect
142. #343C3⋊D3semidirect
194. C2×C3⋊D3#101semidirect
329. C32#1901semidirect
396. C3#68993semidirect

Maximal subgroups

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

subgroupindex
C2×M16×C3⋊D32
C2×#641062
C2×#636512
#105928252
C32×#3432
#105893962
#689933