Finite Group Databasebeta

← #11775313

Subgroups — #11775313

Order 1152.

822 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 822 conjugacy classes of subgroups — too many to draw. Only its 131 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
1C3⋊D3×C22⋊Q8C211yesmaximal, characteristic
2#10592425C211yesmaximal, characteristic
3#10592363C211yesmaximal, characteristic
4C32×#328C211yesmaximal, characteristic, complemented
5#10589404C211yesmaximal, characteristic, complemented
6#10589333C211yesmaximal, characteristic, complemented
7#10589318C211yesmaximal, characteristic, complemented
8#68336—34nomaximal
9C2×Q8×C3⋊D3C411yescharacteristic, complemented
10C22×C4×C3⋊D3C2211yescharacteristic
11C32×C22⋊Q8C2211yescharacteristic
12#64155C411yescharacteristic, complemented
13C2×#3752—21no—
14#64133C2211yescharacteristic
15C2×#3743—21no—
16#64106C411yescharacteristic, complemented
17#64105—21no—
18C4⋊C4×C3⋊D3—21no—
19C4⋊C4×C3⋊D3C411yescharacteristic, complemented
20C22⋊C4×C3⋊D3—21no—
21#64087—21no—
22C32×C22⋊C8C2211yescharacteristic
23C32×#95C2211yescharacteristic
24#63658—21no—
25#63658C2211yescharacteristic
26#63657C2211yescharacteristic
27#63647—21no—
28D3×C22⋊Q8—34no—
29#4726—34no—
30#4664—34no—
31C3×#328D314yescomplemented
32#4538—34no—
33#4467—34no—
34#4452—34no—
35C23×C3⋊D3D411yescharacteristic
36C2×C32×Q8C2×C411yescharacteristic
37C22×C32×C4—21no—
38C22×C32×C4C2311yescharacteristic
39C22×C3⋊Dic3—21no—
40C22×C3⋊Dic3D411yescharacteristic
41Q8×C3⋊D3—42no—
42C2×C4×C3⋊D3—21no—
43C2×C4×C3⋊D3—21no—
44C2×C4×C3⋊D3—42no—
45C2×C4×C3⋊D3C2×C411yescharacteristic
46C2×C4×C3⋊D3C2×C411yescharacteristic
47C2×C4×C3⋊D3D411yescharacteristic
48C2×C4×C3⋊D3D411yescharacteristic
49C2×#634—21no—
50C2×#634C2×C411yescharacteristic
51C2×C32×C8—21no—
52C32×C4⋊C4—21no—
53C32×C4⋊C4C2×C411yescharacteristic
54C32×C22⋊C4—21no—
55#3757—21no—
56#3752—21no—
57#3752—21no—
58#3752—42no—
59C4⋊(C3⋊Dic3)—21no—
60C4⋊(C3⋊Dic3)C2×C411yescharacteristic
61#3750—21no—
62#3750—21no—
63#3750—21no—
64C2×C3⋊(C3⋊C8)—21no—
65#3743—42no—
66#1511—91noSylow
67C2×D3×Q8—34no—
68C22×C4×D3—34no—
69C3×C22⋊Q8C2×D314yes—
70#946—34no—
71C2×(C2×D3)⋊C4—64no—
72#924—34no—
73C2×ΓL(1,𝔽25)—64no—
74#897—34no—
75#896—64no—
76D3×C4⋊C4—34no—
77D3×C4⋊C4—64no—
78D3×C22⋊C4—64no—
79#878—64no—
80C3×C22⋊C8C2×D314yes—
81C3×#95C2×D314yes—
82C3⋊#95—34no—
83C3⋊#95—64no—
84#830—34no—
85(C2×D3)⋊C8—64no—
86C23×C32C2×D411yescharacteristic
87C22×C3⋊D3—21no—
88C22×C3⋊D3—21no—
89C22×C3⋊D3—22no—
90C22×C3⋊D3—41no—
91C22×C3⋊D3C22⋊C411yescharacteristic
92C22×C3⋊D3C22⋊C411yescharacteristic
93C32×Q8—41no—
94C2×C32×C4—21no—
95C2×C32×C4—21no—
96C2×C32×C4—41no—
97C2×C32×C4—41no—
98C2×C32×C4—41no—
99C2×C32×C4—41no—
100C2×C32×C4C22×C411yescharacteristic
101C2×C32×C4C2×D411yescharacteristic
102C2×C3⋊Dic3—21no—
103C2×C3⋊Dic3—21no—
104C2×C3⋊Dic3—41no—
105C2×C3⋊Dic3—41no—
106C2×C3⋊Dic3—41no—
107C2×C3⋊Dic3—41no—
108C2×C3⋊Dic3C22⋊C411yescharacteristic
109C2×C3⋊Dic3C22⋊C411yescharacteristic
110C4×C3⋊D3—22no—
111C4×C3⋊D3—22no—
112C4×C3⋊D3—41no—
113C4×C3⋊D3—41no—
114C4×C3⋊D3—42no—
115C4×C3⋊D3—42no—
116#634—42no—
117#634—41no—
118C32×C8—41no—
119C3⋊(C3⋊C8)—41no—
120C2×C22⋊Q8—91no—
121#407—91no—
122#381—91no—
123#328—91no—
124#328—91no—
125#328—91no—
126#328C3⋊D311yescharacteristic, complemented
127C23×D3—34no—
128C2×C3×Q8C4×D314yes—
129C22×C3×C4—24no—
130C22×C3×C4C22×D314yes—
131C22×Dic3—34no—
132C22×Dic3—64no—
133D3×Q8—128no—
134C2×C4×D3—34no—
135C2×C4×D3—34no—
136C2×C4×D3—34no—
137C2×C4×D3—34no—
138C2×C4×D3—64no—
139C2×C4×D3—64no—
140C2×C4×D3—128no—
141C2×Dic6—34no—
142C2×Dic6—64no—
143C2×C3×C8—24no—
144C3×C4⋊C4—24no—
145C3×C4⋊C4C4×D314yes—
146C3×C22⋊C4—24no—
147#217—64no—
148(C2×D3)⋊C4—64no—
149(C2×D3)⋊C4—64no—
150(C2×D3)⋊C4—128no—
151C4⋊Dic3—34no—
152C4⋊Dic3—64no—
153Dic3⋊C4—64no—
154Dic3⋊C4—64no—
155Dic3⋊C4—64no—
156C2×C3⋊C8—64no—
157ΓL(1,𝔽25)—128no—
158C22×C32—21no—
159C22×C32—21no—
160C22×C32C2×C22⋊C411yescharacteristic
161C22×C32#13711yescharacteristic
162C22×C32#13711yescharacteristic
163C2×C3⋊D3—21no—
164C2×C3⋊D3—21no—
165C2×C3⋊D3—21no—
166C2×C3⋊D3—21no—
167C2×C3⋊D3—21no—
168C2×C3⋊D3—42no—
169C2×C3⋊D3—42no—
170C2×C3⋊D3#9912yes—
171C32×C4—21no—
172C32×C4—21no—
173C32×C4—41no—
174C32×C4—41no—
175C32×C4—81no—
176C3⋊Dic3—21no—
177C3⋊Dic3—21no—
178C3⋊Dic3—41no—
179C3⋊Dic3—41no—
180C3⋊Dic3—81no—
181C22×Q8—91no—
182C23×C4—91no—
183C2×M16—181no—
184C22⋊Q8—91no—
185C22⋊Q8—91no—
186C22⋊Q8—91no—
187C22⋊Q8—181no—
188C22⋊Q8—181no—
189C22⋊Q8C2×C3⋊D311yescharacteristic
190C2×C4⋊C4—91no—
191C2×C4⋊C4—181no—
192C2×C22⋊C4—181no—
193C2×C22⋊C4—181no—
194C22⋊C8—91no—
195C22⋊C8—181no—
196C22⋊C8C2×C3⋊D311yescharacteristic
197#95—91no—
198#95—181no—
199#95C2×C3⋊D311yescharacteristic
200C23×C3D3×D414yes—
201C22×D3—34no—
202C22×D3—34no—
203C22×D3—68no—
204C22×D3—64no—
205C22×D3—64no—
206C22×D3—124no—
207C3×Q8—44no—
208C2×C3×C4—24no—
209C2×C3×C4—24no—
210C2×C3×C4—44no—
211C2×C3×C4—44no—
212C2×C3×C4—44no—
213C2×C3×C4—44no—
214C2×C3×C4C2×C4×D314yes—
215C2×C3×C4D3×D414yes—
216C2×Dic3—34no—
217C2×Dic3—34no—
218C2×Dic3—64no—
219C2×Dic3—64no—
220C2×Dic3—124no—
221C2×Dic3—124no—
222C2×Dic3—124no—
223C2×Dic3—124no—
224C4×D3—68no—
225C4×D3—68no—
226C4×D3—124no—
227C4×D3—124no—
228C4×D3—128no—
229C4×D3—128no—
230Dic6—128no—
231Dic6—124no—
232C3×C8—44no—
233C3⋊C8—124no—
234C2×C32—21no—
235C2×C32—21no—
236C2×C32C2×#9911yescharacteristic
237C2×C32#41911yescharacteristic
238C2×C32#42111yescharacteristic
239C3⋊D3—22no—
240C3⋊D3—41no—
241C24—91no—
242C2×Q8—91no—
243C2×Q8—181no—
244C2×Q8—362no—
245C2×Q8C4×C3⋊D311yescharacteristic
246C22×C4—21no—
247C22×C4—91no—
248C22×C4—91no—
249C22×C4—91no—
250C22×C4—91no—
251C22×C4—91no—
252C22×C4—181no—
253C22×C4—181no—
254C22×C4—181no—
255C22×C4—362no—
256C22×C4C22×C3⋊D311yescharacteristic
257M16—362no—
258C2×C8—21no—
259C2×C8—181no—
260C4⋊C4—21no—
261C4⋊C4—91no—
262C4⋊C4—181no—
263C4⋊C4—181no—
264C4⋊C4—181no—
265C4⋊C4—181no—
266C4⋊C4C4×C3⋊D311yescharacteristic
267C22⋊C4—21no—
268C22⋊C4—181no—
269C22⋊C4—181no—
270C22⋊C4—181no—
271C22⋊C4—362no—
272C22×C3—24no—
273C22×C3—24no—
274C22×C3D3×C22⋊C414yes—
275C22×C3#91514yes—
276C22×C3#91814yes—
277C2×D3—38no—
278C2×D3—64no—
279C2×D3—64no—
280C2×D3—64no—
281C2×D3—64no—
282C2×D3—64no—
283C2×D3—128no—
284C2×D3—128no—
285C3×C4—24no—
286C3×C4—24no—
287C3×C4—44no—
288C3×C4—44no—
289C3×C4—84no—
290Dic3—64no—
291Dic3—64no—
292Dic3—124no—
293Dic3—124no—
294Dic3—244no—
295C32#151111yescharacteristic, complemented, Sylow
296C23—91no—
297C23—91no—
298C23—182no—
299C23—181no—
300C23—181no—
301C23—361no—
302C23D4×C3⋊D311yescharacteristic
303Q8—41no—
304Q8—361no—
305Q8—362no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—91no—
313C2×C4—91no—
314C2×C4—182no—
315C2×C4—182no—
316C2×C4—181no—
317C2×C4—181no—
318C2×C4—361no—
319C2×C4—361no—
320C2×C4—362no—
321C2×C4—362no—
322C2×C4—361no—
323C2×C4—361no—
324C2×C4—361no—
325C2×C4—361no—
326C2×C4C2×C4×C3⋊D311yescharacteristic
327C2×C4D4×C3⋊D311yescharacteristic
328C8—41no—
329C8—361no—
330C2×C3—24no—
331C2×C3—24no—
332C2×C3D3×#9914yes—
333C2×C3#480214yes—
334C2×C3#482114yes—
335D3—68no—
336D3—124no—
337C22—21no—
338C22—21no—
339C22—92no—
340C22—181no—
341C22—181no—
342C22—181no—
343C22—181no—
344C22—181no—
345C22—362no—
346C22—362no—
347C22C22⋊C4×C3⋊D311yescharacteristic
348C22#6412411yescharacteristic
349C22#6412711yescharacteristic
350C4—21no—
351C4—21no—
352C4—41no—
353C4—41no—
354C4—81no—
355C4—181no—
356C4—181no—
357C4—361no—
358C4—361no—
359C4—721no—
360C3#6833614yescomplemented
361C2—21no—
362C2—21no—
363C2—182no—
364C2—361no—
365C2C3⋊D3×#9911yescharacteristic
366C2#1059250111yescharacteristic
367C2#1059252011yescharacteristic
subgroupG/H
centerC22C22⋊C4×C3⋊D3
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC32×#328C2
socleC22×C32C2×C22⋊C4
prime radicalC23×C3⋊D3D4
cosocleC22×C32×C4C23
hypercenter#328C3⋊D3
hypocenterC32#1511
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
4. C32×#328C2semidirect
5. #10589404C2semidirect
6. #10589333C2semidirect
7. #10589318C2semidirect
9. C2×Q8×C3⋊D3C4semidirect
12. #64155C4semidirect
16. #64106C4semidirect
19. C4⋊C4×C3⋊D3C4semidirect
31. C3×#328D3semidirect
126. #328C3⋊D3semidirect
295. C32#1511semidirect
360. C3#68336semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×C22⋊Q82
#105924252
#105923632
C32×#3282
#105894042
#105893332
#105893182
#683363