Finite Group Databasebeta

← #11788326

Subgroups — #11788326

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×#64155C211yesmaximal, characteristic
2C2×M16×C3⋊D3C211yesmaximal, characteristic
3C2×C32×#101C211yesmaximal, characteristic, complemented
4C2×#63663C211yesmaximal, characteristic, complemented
5#10592825C211yesmaximal, characteristic
6#10589420C211yesmaximal, characteristic, complemented
7#10589420C211yesmaximal, characteristic, complemented
8#70115—34nomaximal
9C22×C32×Q8C2211yescharacteristic
10C22×C4×C3⋊D3C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13#64155—21no—
14#64155—21no—
15#64155—21no—
16#64155—21no—
17C2×#3752C412yes—
18C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
19C2×#3750C412yes—
20C2×#3748C2211yescharacteristic
21C2×#3748C2211yescharacteristic
22M16×C3⋊D3—22no—
23M16×C3⋊D3—22no—
24C2×#3743—21no—
25C2×C8×C3⋊D3—21no—
26C32×#101—22no—
27#63663—22no—
28#63647—21no—
29#63647—21no—
30C2×#946—34no—
31C2×D3×M16—34no—
32C2×C3×#101D314yescomplemented
33C2×#836—34no—
34#5126—34no—
35#4554—34no—
36#4554—34no—
37C23×C3⋊D3C2×C411yescharacteristic
38C2×C32×Q8—21no—
39C2×C32×Q8—21no—
40C2×C32×Q8—21no—
41C2×C32×Q8—21no—
42C2×C32×Q8—21no—
43C2×C32×Q8—21no—
44C22×C32×C4C2×C412yes—
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3C2×C411yescharacteristic
47C22×C3⋊Dic3C2×C412yes—
48C2×C4×C3⋊D3—21no—
49C2×C4×C3⋊D3—21no—
50C2×C4×C3⋊D3—21no—
51C2×C4×C3⋊D3—21no—
52C2×C4×C3⋊D3D411yescharacteristic
53C2×C4×C3⋊D3D411yescharacteristic
54C2×C4×C3⋊D3D411yescharacteristic
55C2×C4×C3⋊D3D411yescharacteristic
56C32×M16—21no—
57C32×M16—21no—
58C32×M16—21no—
59C32×M16D412yes—
60C2×C32×C8—21no—
61C2×C32×C8—21no—
62#3752—22no—
63#3752—22no—
64C4⋊(C3⋊Dic3)—21no—
65C4⋊(C3⋊Dic3)—21no—
66#3750—22no—
67#3750—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×C3×Q8C2×D314yes—
78C22×C4×D3—34no—
79C2×C3×M16C2×D314yes—
80C2×C3×M16C2×D314yes—
81#946—64no—
82#946—64no—
83#946—64no—
84#946—64no—
85C2×(C2×D3)⋊C4—38no—
86C2×C4⋊Dic3—34no—
87C2×Dic3⋊C4—38no—
88C2×#208—34no—
89C2×#208—34no—
90D3×M16—68no—
91D3×M16—68no—
92C2×ΓL(1,𝔽25)—64no—
93C2×D3×C8—64no—
94C3×#101—28no—
95#836—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
105C32×Q8—41no—
106C32×Q8—41no—
107C32×Q8—41no—
108C32×Q8—41no—
109C2×C32×C4—22no—
110C2×C32×C4—22no—
111C2×C32×C4—22no—
112C2×C32×C4C2×D411yescharacteristic
113C2×C32×C4C2×D411yescharacteristic
114C2×C32×C4C2×D411yescharacteristic
115C2×C32×C4C2×D411yescharacteristic
116C2×C32×C4#4111yescharacteristic
117C2×C32×C4#4111yescharacteristic
118C2×C3⋊Dic3—21no—
119C2×C3⋊Dic3—21no—
120C2×C3⋊Dic3—22no—
121C2×C3⋊Dic3—42no—
122C2×C3⋊Dic3C22⋊C411yescharacteristic
123C2×C3⋊Dic3C22⋊C411yescharacteristic
124C4×C3⋊D3—21no—
125C4×C3⋊D3—21no—
126C4×C3⋊D3—21no—
127C4×C3⋊D3—21no—
128C4×C3⋊D3—21no—
129C4×C3⋊D3—21no—
130C4×C3⋊D3—21no—
131C4×C3⋊D3—21no—
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×#101C3⋊D311yescharacteristic, complemented
140#407—91no—
141#343—91no—
142#343—91no—
143C23×D3—34no—
144C2×C3×Q8—24no—
145C2×C3×Q8—24no—
146C2×C3×Q8—24no—
147C2×C3×Q8—24no—
148C2×C3×Q8—24no—
149C2×C3×Q8—24no—
150C22×C3×C4C4×D318yes—
151C22×C3×C4C22×D314yes—
152C22×Dic3—34no—
153C22×Dic3—38no—
154C2×C4×D3—34no—
155C2×C4×D3—34no—
156C2×C4×D3—34no—
157C2×C4×D3—34no—
158C2×C4×D3—64no—
159C2×C4×D3—64no—
160C2×C4×D3—64no—
161C2×C4×D3—64no—
162C3×M16—24no—
163C3×M16—24no—
164C3×M16—24no—
165C3×M16#6718yes—
166C2×C3×C8—24no—
167C2×C3×C8—24no—
168(C2×D3)⋊C4—68no—
169(C2×D3)⋊C4—68no—
170C4⋊Dic3—64no—
171C4⋊Dic3—64no—
172Dic3⋊C4—68no—
173Dic3⋊C4—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×Q8C2×C3⋊D311yescharacteristic
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⋊C4—91no—
219C2×C22⋊C4—92no—
220#101—22no—
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—
231C3×Q8—44no—
232C3×Q8—44no—
233C3×Q8—44no—
234C3×Q8—44no—
235C2×C3×C4—28no—
236C2×C3×C4—28no—
237C2×C3×C4—28no—
238C2×C3×C4#23514yes—
239C2×C3×C4D3×D414yes—
240C2×C3×C4D3×D414yes—
241C2×C3×C4D3×D414yes—
242C2×C3×C4#23714yes—
243C2×C3×C4C2×#6714yes—
244C2×Dic3—34no—
245C2×Dic3—34no—
246C2×Dic3—64no—
247C2×Dic3—64no—
248C2×Dic3—68no—
249C2×Dic3—128no—
250C4×D3—64no—
251C4×D3—64no—
252C4×D3—64no—
253C4×D3—64no—
254C4×D3—64no—
255C4×D3—64no—
256C4×D3—64no—
257C4×D3—64no—
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—21no—
271C2×Q8—21no—
272C2×Q8—21no—
273C2×Q8—21no—
274C2×Q8—21no—
275C2×Q8—21no—
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—
296M16#63812yes—
297C2×C8—21no—
298C2×C8—21no—
299C2×C8—184no—
300C2×C8—181no—
301C2×C8—181no—
302C4⋊C4—182no—
303C4⋊C4—182no—
304C4⋊C4—181no—
305C4⋊C4—181no—
306C22⋊C4—182no—
307C22⋊C4—182no—
308C22×C3—24no—
309C22×C3—24no—
310C22×C3D3×C22⋊C414yes—
311C22×C3#67⋊C414yes—
312C22×C3C4×#6714yes—
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#88314yes—
323C3×C4#88414yes—
324C3×C4#93714yes—
325C3×C4#93814yes—
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—41no—
338Q8—41no—
339Q8—41no—
340Q8—41no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—22no—
344C2×C4—91no—
345C2×C4—91no—
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—181no—
356C2×C4—182no—
357C2×C4—362no—
358C2×C4#382811yescharacteristic
359C2×C4D4×C3⋊D311yescharacteristic
360C2×C4D4×C3⋊D311yescharacteristic
361C2×C4D4×C3⋊D311yescharacteristic
362C2×C4#383011yescharacteristic
363C2×C4C2×#63811yescharacteristic
364C8—22no—
365C8—41no—
366C8—182no—
367C8—361no—
368C2×C3—24no—
369C2×C3—24no—
370C2×C3D3×#10114yes—
371C2×C3#475114yes—
372C2×C3#495614yes—
373D3—68no—
374D3—124no—
375C22—21no—
376C22—21no—
377C22—92no—
378C22—181no—
379C22—181no—
380C22—181no—
381C22—181no—
382C22—181no—
383C22—362no—
384C22—362no—
385C22C22⋊C4×C3⋊D311yescharacteristic
386C22#6409011yescharacteristic
387C22C4×#63811yescharacteristic
388C4—42no—
389C4—181no—
390C4—181no—
391C4—362no—
392C4#6409211yescharacteristic
393C4#6409311yescharacteristic
394C4#6414611yescharacteristic
395C4#6414711yescharacteristic
396C3#7011514yescomplemented
397C2—21no—
398C2—21no—
399C2—182no—
400C2—361no—
401C2C3⋊D3×#10111yescharacteristic
402C2#1059245011yescharacteristic
403C2#1059265511yescharacteristic
subgroupG/H
centerC22C22⋊C4×C3⋊D3
commutatorC23×C32C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC2×C32×#101C2
socleC22×C32C2×C22⋊C4
prime radicalC23×C3⋊D3C2×C4
cosocleC22×C32×C4C23
hypercenterC2×#101C3⋊D3
hypocenterC32#1901
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
3. C2×C32×#101C2semidirect
4. C2×#63663C2semidirect
6. #10589420C2semidirect
7. #10589420C2semidirect
32. C2×C3×#101D3semidirect
139. C2×#101C3⋊D3semidirect
194. C2×C3⋊D3#101semidirect
329. C32#1901semidirect
396. C3#70115semidirect

Maximal subgroups

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

subgroupindex
C2×#641552
C2×M16×C3⋊D32
C2×C32×#1012
C2×#636632
#105928252
#105894202
#701153