Finite Group Databasebeta

← #11796234

Subgroups — #11796234

Order 1152.

840 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 840 conjugacy classes of subgroups — too many to draw. Only its 157 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596275C211yesmaximal, characteristic
2C2×C32×#100C211yesmaximal, characteristic, complemented
3C2×#63661C211yesmaximal, characteristic, complemented
4#10589342C212yesmaximal, complemented
5#10589341C212yesmaximal, complemented
6#70094—34nomaximal
7C22×C32×D4C2211yescharacteristic
8C22×#638C411yescharacteristic, complemented
9C2×C32×M16—21no—
10#64162—21no—
11C2×#3757—21no—
12C2×#3757C411yescharacteristic, complemented
13#64148—21no—
14#64148—21no—
15#64146C411yescharacteristic, complemented
16#64146C2211yescharacteristic
17#64144C411yescharacteristic, complemented
18#64144C2211yescharacteristic
19#64138—21no—
20C32×#100—21no—
21C32×#100C2212yes—
22#63661—21no—
23#63661C2212yes—
24#5804—34no—
25C2×C3×#100D314yescomplemented
26C2×#834—34no—
27#4476—38no—
28#4475—38no—
29C24×C32C2×C411yescharacteristic
30C24×C32D411yescharacteristic
31C23×C3⋊D3C2×C411yescharacteristic, complemented
32C2×C32×D4—41no—
33C2×C32×D4—41no—
34C2×C32×D4C2×C411yescharacteristic
35C2×C32×D4D411yescharacteristic
36C2×C32×D4D411yescharacteristic
37C2×C32×D4C2311yescharacteristic
38C22×C32×C4D411yescharacteristic
39C2×#638—21no—
40C2×#638—21no—
41C2×#638—21no—
42C2×#638—21no—
43C2×#638—41no—
44C2×#638—41no—
45C22×C3⋊Dic3—21no—
46C22×C3⋊Dic3—41no—
47C22×C3⋊Dic3C2×C411yescharacteristic, complemented
48C32×M16—22no—
49C32×M16—41no—
50C2×C32×C8—41no—
51#3757—21no—
52#3757—21no—
53#3757—21no—
54#3757—22no—
55#3757—41no—
56#3757C2×C411yescharacteristic, complemented
57#3757C2×C411yescharacteristic, complemented
58#3752—21no—
59#3752—21no—
60#3750—21no—
61#3750—21no—
62#2121—91noSylow
63C22×C3×D4C2×D314yes—
64C22×#67—34no—
65C2×C3×M16—24no—
66#953—64no—
67C2×#217—34no—
68C2×#217—64no—
69#939—64no—
70#939—64no—
71#937—34no—
72#937—34no—
73#935—34no—
74#935—34no—
75#929—64no—
76C3×#100—24no—
77C3×#100C2×D318yes—
78#834—38no—
79#834—64no—
80C23×C32—21no—
81C23×C32—21no—
82C23×C32—21no—
83C23×C32—21no—
84C23×C32—81no—
85C23×C32—81no—
86C23×C32C22⋊C411yescharacteristic
87C23×C32C22⋊C411yescharacteristic
88C23×C32C22⋊C411yescharacteristic
89C23×C32C22×C411yescharacteristic
90C23×C32C2×D411yescharacteristic
91C22×C3⋊D3—21no—
92C22×C3⋊D3—41no—
93C22×C3⋊D3—81no—
94C32×D4—41no—
95C32×D4—41no—
96C32×D4—41no—
97C32×D4—41no—
98C2×C32×C4—21no—
99C2×C32×C4—21no—
100C2×C32×C4C22⋊C411yescharacteristic
101C2×C32×C4C2×D411yescharacteristic
102#638—42no—
103#638—41no—
104#638—41no—
105#638—81no—
106#638—81no—
107C2×C3⋊Dic3—21no—
108C2×C3⋊Dic3—21no—
109C2×C3⋊Dic3—21no—
110C2×C3⋊Dic3—41no—
111C2×C3⋊Dic3—42no—
112C2×C3⋊Dic3—81no—
113C2×C3⋊Dic3—82no—
114C32×C8—42no—
115#534—91no—
116C2×#100C3⋊D311yescharacteristic, complemented
117C2×#99—91no—
118#352—92no—
119AΣL(1,𝔽16)—92no—
120C24×C3C4×D314yes—
121C24×C3D1214yes—
122C23×D3—34no—
123C2×C3×D4—44no—
124C2×C3×D4—44no—
125C2×C3×D4C4×D314yes—
126C2×C3×D4D1214yes—
127C2×C3×D4#6714yes—
128C2×C3×D4C22×D314yes—
129C22×C3×C4#6714yes—
130C2×#67—64no—
131C2×#67—64no—
132C2×#67—64no—
133C2×#67—64no—
134C2×#67—124no—
135C2×#67—124no—
136C22×Dic3—34no—
137C22×Dic3—64no—
138C22×Dic3—124no—
139C3×M16—28no—
140C3×M16—44no—
141C2×C3×C8—44no—
142#217—34no—
143#217—34no—
144#217—64no—
145#217—64no—
146#217—64no—
147#217—68no—
148#217—124no—
149(C2×D3)⋊C4—64no—
150(C2×D3)⋊C4—64no—
151Dic3⋊C4—64no—
152Dic3⋊C4—64no—
153C22×C32—21no—
154C22×C32—21no—
155C22×C32—21no—
156C22×C32—21no—
157C22×C32—41no—
158C22×C32—41no—
159C22×C32—41no—
160C22×C32—41no—
161C22×C32—41no—
162C22×C32—42no—
163C22×C32—81no—
164C22×C32—81no—
165C22×C32—81no—
166C22×C32#9911yescharacteristic
167C22×C32#9911yescharacteristic
168C22×C32C2×C22⋊C411yescharacteristic
169C2×C3⋊D3—41no—
170C2×C3⋊D3—41no—
171C2×C3⋊D3—41no—
172C2×C3⋊D3—82no—
173C32×C4—21no—
174C32×C4—21no—
175C3⋊Dic3—41no—
176C3⋊Dic3—41no—
177C3⋊Dic3—41no—
178C3⋊Dic3—82no—
179C22×D4—91no—
180C22×D4C2×C3⋊D311yescharacteristic
181C2×M16—21no—
182#123—91no—
183#123—91no—
184#123—181no—
185#121—181no—
186#121—181no—
187#120—91no—
188#120—91no—
189#120—181no—
190C2×C22⋊C4—91no—
191C2×C22⋊C4—181no—
192#100—21no—
193#100C2×C3⋊D312yes—
194#99—92no—
195#99—181no—
196C23×C3—24no—
197C23×C3—24no—
198C23×C3—24no—
199C23×C3—24no—
200C23×C3—84no—
201C23×C3—84no—
202C23×C3(C2×D3)⋊C414yes—
203C23×C3(C2×D3)⋊C414yes—
204C23×C3(C2×D3)⋊C414yes—
205C23×C3C2×C4×D314yes—
206C23×C3C2×D1214yes—
207C22×D3—64no—
208C22×D3—124no—
209C22×D3—244no—
210C3×D4—44no—
211C3×D4—44no—
212C3×D4—44no—
213C3×D4—44no—
214C2×C3×C4—24no—
215C2×C3×C4—24no—
216C2×C3×C4(C2×D3)⋊C414yes—
217C2×C3×C4C2×#6714yes—
218#67—128no—
219#67—124no—
220#67—124no—
221#67—244no—
222#67—244no—
223C2×Dic3—64no—
224C2×Dic3—64no—
225C2×Dic3—64no—
226C2×Dic3—124no—
227C2×Dic3—128no—
228C2×Dic3—244no—
229C2×Dic3—248no—
230C3×C8—48no—
231C2×C32—21no—
232C2×C32—21no—
233C2×C32—21no—
234C2×C32—41no—
235C2×C32—41no—
236C2×C32—41no—
237C2×C32—41no—
238C2×C32C2×#9911yescharacteristic
239C3⋊D3—81no—
240C24—91no—
241C24C4×C3⋊D311yescharacteristic
242C24C4⋊(C3⋊D3)11yescharacteristic
243C2×D4—41no—
244C2×D4—41no—
245C2×D4—181no—
246C2×D4—181no—
247C2×D4—181no—
248C2×D4—181no—
249C2×D4—361no—
250C2×D4—361no—
251C2×D4C4×C3⋊D311yescharacteristic
252C2×D4C4⋊(C3⋊D3)11yescharacteristic
253C2×D4#63811yescharacteristic
254C2×D4C22×C3⋊D311yescharacteristic
255C22×C4—91no—
256C22×C4—181no—
257C22×C4—361no—
258C22×C4#63811yescharacteristic
259M16—22no—
260M16—41no—
261C2×C8—41no—
262C4⋊C4—181no—
263C4⋊C4—181no—
264C22⋊C4—91no—
265C22⋊C4—91no—
266C22⋊C4—181no—
267C22⋊C4—181no—
268C22⋊C4—181no—
269C22⋊C4—181no—
270C22⋊C4—181no—
271C22⋊C4—182no—
272C22⋊C4—361no—
273C22×C3—24no—
274C22×C3—24no—
275C22×C3—24no—
276C22×C3—24no—
277C22×C3—44no—
278C22×C3—44no—
279C22×C3—44no—
280C22×C3—44no—
281C22×C3—44no—
282C22×C3—48no—
283C22×C3—84no—
284C22×C3—84no—
285C22×C3—84no—
286C22×C3#80614yes—
287C22×C3#80614yes—
288C22×C3C2×(C2×D3)⋊C414yes—
289C2×D3—124no—
290C2×D3—124no—
291C2×D3—124no—
292C2×D3—248no—
293C3×C4—24no—
294C3×C4—24no—
295Dic3—124no—
296Dic3—124no—
297Dic3—124no—
298Dic3—248no—
299C32#212111yescharacteristic, complemented, Sylow
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—81no—
305C23—81no—
306C23—181no—
307C23—361no—
308C23—721no—
309C23#375211yescharacteristic
310C23#375211yescharacteristic
311C23#375211yescharacteristic
312C23C2×C4×C3⋊D311yescharacteristic
313C23C2×C4⋊(C3⋊D3)11yescharacteristic
314D4—41no—
315D4—41no—
316D4—41no—
317D4—41no—
318D4—362no—
319D4—361no—
320D4—361no—
321D4—721no—
322D4—721no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—181no—
326C2×C4—181no—
327C2×C4—181no—
328C2×C4—361no—
329C2×C4—362no—
330C2×C4—721no—
331C2×C4—722no—
332C2×C4#375211yescharacteristic
333C2×C4C2×#63811yescharacteristic
334C8—42no—
335C2×C3—24no—
336C2×C3—24no—
337C2×C3—24no—
338C2×C3—44no—
339C2×C3—44no—
340C2×C3—44no—
341C2×C3—44no—
342C2×C3C2×#80614yes—
343D3—244no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—42no—
354C22—81no—
355C22—81no—
356C22—81no—
357C22—361no—
358C22—361no—
359C22—361no—
360C22—722no—
361C22#6363311yescharacteristic
362C22#6363311yescharacteristic
363C22C2×#375211yescharacteristic
364C4—21no—
365C4—21no—
366C4—361no—
367C4—361no—
368C4—361no—
369C4—722no—
370C3#7009414yescomplemented
371C2—21no—
372C2—21no—
373C2—21no—
374C2—41no—
375C2—41no—
376C2—41no—
377C2—41no—
378C2—721no—
379C2C2×#6363311yescharacteristic
subgroupG/H
centerC2C2×#63633
commutatorC23×C32C22×C4
FrattiniC2×D4C22×C3⋊D3
FittingC2×C32×#100C2
socleC2×C32C2×#99
prime radical#10596275C2
cosocleC2×C32×D4C23
hypercenterC2×#100C3⋊D3
hypocenterC32#2121
LCSG ▷ C23×C32 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C23 ◁ C22×D4 ◁ C2×#100

Complements

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

NH ≅ G/Ntype
2. C2×C32×#100C2semidirect
3. C2×#63661C2semidirect
4. #10589342C2semidirect
5. #10589341C2semidirect
8. C22×#638C4semidirect
12. C2×#3757C4semidirect
15. #64146C4semidirect
17. #64144C4semidirect
25. C2×C3×#100D3semidirect
31. C23×C3⋊D3C2×C4semidirect
47. C22×C3⋊Dic3C2×C4semidirect
56. #3757C2×C4semidirect
57. #3757C2×C4semidirect
116. C2×#100C3⋊D3semidirect
299. C32#2121semidirect
370. C3#70094semidirect

Maximal subgroups

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

subgroupindex
#105962752
C2×C32×#1002
C2×#636612
#105893422
#105893412
#700943