Finite Group Databasebeta

← #11778438

Subgroups — #11778438

Order 1152.

840 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 840 conjugacy classes of subgroups — too many to draw. Only its 119 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#10596076C211yesmaximal, characteristic
2#10592732C211yesmaximal, characteristic, complemented
3#10592435C211yesmaximal, characteristic, complemented
4#10592373C211yesmaximal, characteristic, complemented
5C32×#327C211yesmaximal, characteristic, complemented
6#10589334C211yesmaximal, characteristic, complemented
7#10589317C211yesmaximal, characteristic, complemented
8#68288—34nomaximal
9C2×D4×C3⋊D3—21no—
10C32×#121C2211yescharacteristic
11#64148—21no—
12#64146—21no—
13#64139C2211yescharacteristic
14C2×#3752—21no—
15C2×#3752C2211yescharacteristic
16C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
17#64103—21no—
18#64092—21no—
19#64091—21no—
20C32×C22⋊C8C2211yescharacteristic, complemented
21C32×#95C2211yescharacteristic, complemented
22#63659—21no—
23#63658—21no—
24#63657C2211yescharacteristic, complemented
25#63648—21no—
26#63645—21no—
27#63634—21no—
28#5605—34no—
29#5033—34no—
30#4736—34no—
31#4674—34no—
32C3×#327D314yescomplemented
33#4468—34no—
34#4451—34no—
35C23×C3⋊D3—21no—
36C23×C3⋊D3D411yescharacteristic
37C2×C32×D4—21no—
38C2×C32×D4D411yescharacteristic
39C22×C32×C4—21no—
40C22×C32×C4C2311yescharacteristic
41C2×#638—21no—
42C2×#638—21no—
43C2×#638—21no—
44C22×C3⋊Dic3—21no—
45C22×C3⋊Dic3D411yescharacteristic
46D4×C3⋊D3—42no—
47D4×C3⋊D3—42no—
48C2×C4⋊(C3⋊D3)—21no—
49C2×C4⋊(C3⋊D3)D411yescharacteristic
50C2×C4×C3⋊D3—21no—
51C2×C32×C8—21no—
52C32×C4⋊C4D411yescharacteristic
53C32×C22⋊C4—21no—
54#3757—21no—
55#3752—21no—
56#3752—21no—
57#3752—21no—
58#3752—21no—
59#3752—42no—
60C4⋊(C3⋊Dic3)—21no—
61C4⋊(C3⋊Dic3)—21no—
62C4⋊(C3⋊Dic3)D411yescharacteristic
63#3750—21no—
64C2×C3⋊(C3⋊C8)—21no—
65#1607—91noSylow
66C2×D3×D4—64no—
67C3×#121C2×D314yes—
68#939—64no—
69#937—64no—
70#930—34no—
71C2×(C2×D3)⋊C4—34no—
72C2×(C2×D3)⋊C4—64no—
73C2×C4⋊Dic3—34no—
74#894—64no—
75#883—64no—
76#882—64no—
77C3×C22⋊C8C2×D314yescomplemented
78C3×#95C2×D314yescomplemented
79#832—64no—
80C3⋊#95—64no—
81#830—34no—
82#821—64no—
83#818—64no—
84#807—64no—
85C23×C32—21no—
86C23×C32C2×D411yescharacteristic
87C22×C3⋊D3—21no—
88C22×C3⋊D3—21no—
89C22×C3⋊D3—21no—
90C22×C3⋊D3—42no—
91C22×C3⋊D3—41no—
92C22×C3⋊D3—41no—
93C22×C3⋊D3—81no—
94C22×C3⋊D3—81no—
95C22×C3⋊D3D812yes—
96C32×D4—41no—
97C32×D4—41no—
98C32×D4—41no—
99C2×C32×C4—21no—
100C2×C32×C4—41no—
101C2×C32×C4—41no—
102C2×C32×C4—41no—
103C2×C32×C4—41no—
104C2×C32×C4C2×D411yescharacteristic
105C2×C32×C4C2×D411yescharacteristic
106#638—42no—
107#638—41no—
108#638—41no—
109#638—81no—
110C2×C3⋊Dic3—21no—
111C2×C3⋊Dic3—21no—
112C2×C3⋊Dic3—41no—
113C2×C3⋊Dic3—41no—
114C2×C3⋊Dic3—41no—
115C2×C3⋊Dic3—41no—
116C4⋊(C3⋊D3)—41no—
117C4⋊(C3⋊D3)—42no—
118C4×C3⋊D3—42no—
119C32×C8—41no—
120C3⋊(C3⋊C8)—41no—
121#534—91no—
122#480—91no—
123#480—91no—
124#397—91no—
125#327—91no—
126#327C3⋊D311yescharacteristic, complemented
127#323—91no—
128C23×D3—34no—
129C23×D3—64no—
130C2×C3×D4—24no—
131C2×C3×D4D1214yes—
132C22×C3×C4—24no—
133C22×C3×C4C22×D314yes—
134C2×#67—64no—
135C2×#67—64no—
136C2×#67—64no—
137C22×Dic3—34no—
138C22×Dic3—64no—
139D3×D4—128no—
140D3×D4—128no—
141C2×D12—34no—
142C2×D12—64no—
143C2×C4×D3—64no—
144C2×C3×C8—24no—
145C3×C4⋊C4D1214yes—
146C3×C22⋊C4—24no—
147#217—64no—
148(C2×D3)⋊C4—64no—
149(C2×D3)⋊C4—64no—
150(C2×D3)⋊C4—64no—
151(C2×D3)⋊C4—64no—
152(C2×D3)⋊C4—128no—
153C4⋊Dic3—34no—
154C4⋊Dic3—64no—
155C4⋊Dic3—64no—
156Dic3⋊C4—64no—
157C2×C3⋊C8—64no—
158C22×C32—21no—
159C22×C32—21no—
160C22×C32—41no—
161C22×C32—41no—
162C22×C32—41no—
163C22×C32#12011yescharacteristic
164C22×C32C2×D811yescharacteristic
165C22×C32AGL(1,ℤ/8)11yescharacteristic
166C2×C3⋊D3—22no—
167C2×C3⋊D3—41no—
168C2×C3⋊D3—41no—
169C2×C3⋊D3—42no—
170C2×C3⋊D3—41no—
171C2×C3⋊D3—41no—
172C2×C3⋊D3—41no—
173C2×C3⋊D3—81no—
174C2×C3⋊D3—84no—
175C32×C4—21no—
176C32×C4—21no—
177C32×C4—41no—
178C32×C4—81no—
179C3⋊Dic3—41no—
180C3⋊Dic3—41no—
181C3⋊Dic3—81no—
182C22×D4—181no—
183#123—181no—
184#123—181no—
185#121—91no—
186#121—181no—
187#121C2×C3⋊D311yescharacteristic
188#120—181no—
189#120—181no—
190C2×C4⋊C4—91no—
191C2×C22⋊C4—91no—
192C2×C22⋊C4—181no—
193#107—181no—
194#107—181no—
195#102—181no—
196#102—181no—
197C22⋊C8—91no—
198C22⋊C8C2×C3⋊D311yescharacteristic, complemented
199#95—181no—
200#95C2×C3⋊D311yescharacteristic, complemented
201C23×C3—24no—
202C23×C3D3×D414yes—
203C22×D3—38no—
204C22×D3—64no—
205C22×D3—64no—
206C22×D3—64no—
207C22×D3—128no—
208C22×D3—124no—
209C22×D3—124no—
210C22×D3—244no—
211C22×D3—244no—
212C3×D4—44no—
213C3×D4—44no—
214C3×D4—44no—
215C2×C3×C4—24no—
216C2×C3×C4—44no—
217C2×C3×C4—44no—
218C2×C3×C4—44no—
219C2×C3×C4—44no—
220C2×C3×C4C2×D1214yes—
221C2×C3×C4D3×D414yes—
222#67—128no—
223#67—124no—
224#67—124no—
225#67—244no—
226C2×Dic3—64no—
227C2×Dic3—64no—
228C2×Dic3—124no—
229C2×Dic3—124no—
230C2×Dic3—124no—
231C2×Dic3—124no—
232D12—124no—
233D12—128no—
234C4×D3—128no—
235C3×C8—44no—
236C3⋊C8—124no—
237C2×C32—21no—
238C2×C32—21no—
239C2×C32—81no—
240C2×C32#44711yescharacteristic
241C2×C32#45511yescharacteristic
242C2×C32#45811yescharacteristic
243C3⋊D3—42no—
244C3⋊D3—81no—
245C24—91no—
246C24—181no—
247C2×D4—21no—
248C2×D4—91no—
249C2×D4—181no—
250C2×D4—181no—
251C2×D4—181no—
252C2×D4—181no—
253C2×D4—362no—
254C2×D4—362no—
255C2×D4C4⋊(C3⋊D3)11yescharacteristic
256C22×C4—21no—
257C22×C4—91no—
258C22×C4—181no—
259C22×C4—181no—
260C22×C4C22×C3⋊D311yescharacteristic
261C2×C8—21no—
262C2×C8—181no—
263C4⋊C4—91no—
264C4⋊C4—181no—
265C4⋊C4—181no—
266C4⋊C4—181no—
267C4⋊C4C4⋊(C3⋊D3)11yescharacteristic
268C22⋊C4—21no—
269C22⋊C4—181no—
270C22⋊C4—181no—
271C22⋊C4—181no—
272C22⋊C4—181no—
273C22⋊C4—181no—
274C22⋊C4—362no—
275C22×C3—24no—
276C22×C3—24no—
277C22×C3—44no—
278C22×C3—44no—
279C22×C3—44no—
280C22×C3#88214yes—
281C22×C3D3×D814yes—
282C22×C3#91414yes—
283C2×D3—68no—
284C2×D3—124no—
285C2×D3—124no—
286C2×D3—128no—
287C2×D3—124no—
288C2×D3—124no—
289C2×D3—124no—
290C2×D3—244no—
291C2×D3—2416no—
292C3×C4—24no—
293C3×C4—24no—
294C3×C4—44no—
295C3×C4—84no—
296Dic3—124no—
297Dic3—124no—
298Dic3—244no—
299C32#160711yescharacteristic, complemented, Sylow
300C23—21no—
301C23—92no—
302C23—181no—
303C23—181no—
304C23—181no—
305C23—361no—
306C23—361no—
307C23—362no—
308C23—721no—
309C23—721no—
310C23D4×C3⋊D311yescharacteristic
311D4—41no—
312D4—41no—
313D4—41no—
314D4—361no—
315D4—362no—
316D4—362no—
317D4—361no—
318D4—361no—
319D4—721no—
320C2×C4—21no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—181no—
326C2×C4—181no—
327C2×C4—362no—
328C2×C4—361no—
329C2×C4—361no—
330C2×C4—361no—
331C2×C4—361no—
332C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
333C2×C4D4×C3⋊D311yescharacteristic
334C8—41no—
335C8—361no—
336C2×C3—24no—
337C2×C3—24no—
338C2×C3—84no—
339C2×C3#474214yes—
340C2×C3#477314yes—
341C2×C3#482514yes—
342D3—128no—
343D3—244no—
344C22—21no—
345C22—21no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—182no—
350C22—362no—
351C22—361no—
352C22—361no—
353C22—361no—
354C22—361no—
355C22—361no—
356C22—721no—
357C22—724no—
358C22#6409111yescharacteristic
359C22D8×C3⋊D311yescharacteristic
360C22#6412311yescharacteristic
361C4—21no—
362C4—21no—
363C4—41no—
364C4—81no—
365C4—361no—
366C4—361no—
367C4—721no—
368C3#6828814yescomplemented
369C2—21no—
370C2—21no—
371C2—81no—
372C2—362no—
373C2—721no—
374C2#1059244111yescharacteristic
375C2#1059247211yescharacteristic
376C2#1059252411yescharacteristic
subgroupG/H
centerC22#64091
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C22×C3⋊D3
FittingC32×#327C2
socleC22×C32#120
prime radical#10596076C2
hypercenter#327C3⋊D3
hypocenterC32#1607
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #10592732C2semidirect
3. #10592435C2semidirect
4. #10592373C2semidirect
5. C32×#327C2semidirect
6. #10589334C2semidirect
7. #10589317C2semidirect
16. C2×C4⋊(C3⋊Dic3)C22semidirect
20. C32×C22⋊C8C22semidirect
21. C32×#95C22semidirect
24. #63657C22semidirect
32. C3×#327D3semidirect
77. C3×C22⋊C8C2×D3semidirect
78. C3×#95C2×D3semidirect
126. #327C3⋊D3semidirect
198. C22⋊C8C2×C3⋊D3semidirect
200. #95C2×C3⋊D3semidirect
299. C32#1607semidirect
368. C3#68288semidirect

Maximal subgroups

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

subgroupindex
#105960762
#105927322
#105924352
#105923732
C32×#3272
#105893342
#105893172
#682883