Finite Group Databasebeta

← #11805210

Subgroups — #11805210

Order 1152.

1644 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊C4×C3⋊D3C211yesmaximal, characteristic
2C32×C4×C4⋊C4C211yesmaximal, characteristic, complemented
3#10592686C211yesmaximal, characteristic
4C4⋊C4×C3⋊Dic3C211yesmaximal, characteristic, complemented
5#10592671C211yesmaximal, characteristic, complemented
6C4×#3752C211yesmaximal, characteristic
7C4×#3752C212yesmaximal
8#10592632C212yesmaximal, complemented
9#10592627C211yesmaximal, characteristic, complemented
10#10592366C212yesmaximal
11#10592351C212yesmaximal, complemented
12#73768—34nomaximal
13C22×C4×C3⋊D3C2211yescharacteristic
14C22×C4×C3⋊D3C2212yes—
15C2×C32×C4⋊C4C2211yescharacteristic
16C2×C32×C4⋊C4C2211yescharacteristic
17C2×C32×C42C2211yescharacteristic
18C2×C32×C42C2212yes—
19C2×#3752C2211yescharacteristic
20C2×#3752C2212yes—
21C2×#3752C2211yescharacteristic
22C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
23C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
24C2×#3750C2212yes—
25C2×#3750C2212yes—
26C2×#3750C2212yes—
27C2×C4×C3⋊Dic3C2211yescharacteristic
28C2×C4×C3⋊Dic3C2212yes—
29C4⋊C4×C3⋊D3C418yescomplemented
30C32×#95C2212yes—
31#63658C2211yescharacteristic
32#63658C2212yes—
33#63658C2212yes—
34#63658C2212yes—
35#63658C2212yes—
36#63658C2211yescharacteristic
37C2×D3×C4⋊C4—34no—
38C3×C4×C4⋊C4D314yescomplemented
39#4987—34no—
40Dic3×C4⋊C4—34no—
41#4972—34no—
42C4×(C2×D3)⋊C4—34no—
43C4×(C2×D3)⋊C4—38no—
44#4933—38no—
45#4928—34no—
46#4667—38no—
47#4652—38no—
48C23×C3⋊D3C2311yescharacteristic
49C22×C32×C4C2311yescharacteristic
50C22×C32×C4C2312yes—
51C22×C32×C4C2312yes—
52C22×C32×C4C2311yescharacteristic
53C22×C32×C4C2311yescharacteristic
54C22×C3⋊Dic3C2311yescharacteristic
55C22×C3⋊Dic3C2312yes—
56C22×C3⋊Dic3C2312yes—
57C22×C3⋊Dic3C2311yescharacteristic
58C22×C3⋊Dic3C2311yescharacteristic
59C2×C4×C3⋊D3—22no—
60C2×C4×C3⋊D3—22no—
61C2×C4×C3⋊D3—42no—
62C2×C4×C3⋊D3—42no—
63C2×C4×C3⋊D3C2×C414yes—
64C2×C4×C3⋊D3C2×C418yes—
65C32×C4⋊C4—22no—
66C32×C4⋊C4C2×C414yes—
67C32×C42—22no—
68C32×C42—42no—
69#3752—22no—
70#3752—24no—
71#3752Q814yes—
72C4⋊(C3⋊Dic3)—22no—
73C4⋊(C3⋊Dic3)C2×C414yes—
74#3750—42no—
75#3750—42no—
76#3750C2×C418yes—
77C4×C3⋊Dic3—22no—
78C4×C3⋊Dic3—42no—
79#2345—91noSylow
80C22×C4×D3—34no—
81C22×C4×D3—38no—
82C2×C3×C4⋊C4C2×D314yes—
83C2×C3×C4⋊C4C2×D314yes—
84C2×C3×C42C2×D314yes—
85C2×C3×C42C2×D318yes—
86C2×(C2×D3)⋊C4—34no—
87C2×(C2×D3)⋊C4—34no—
88C2×(C2×D3)⋊C4—38no—
89C2×C4⋊Dic3—34no—
90C2×C4⋊Dic3—34no—
91C2×Dic3⋊C4—38no—
92C2×Dic3⋊C4—38no—
93C2×Dic3⋊C4—38no—
94C2×C4×Dic3—34no—
95C2×C4×Dic3—38no—
96D3×C4⋊C4—332no—
97C3×#95C2×D318yes—
98C3⋊#95—34no—
99C3⋊#95—38no—
100C3⋊#95—38no—
101C3⋊#95—38no—
102C3⋊#95—38no—
103C3⋊#95—34no—
104C23×C32C2411yescharacteristic
105C22×C3⋊D3—21no—
106C22×C3⋊D3—21no—
107C22×C3⋊D3—21no—
108C22×C3⋊D3—21no—
109C22×C3⋊D3C22×C412yes—
110C22×C3⋊D3C2×Q812yes—
111C22×C3⋊D3#4112yes—
112C2×C32×C4—21no—
113C2×C32×C4—22no—
114C2×C32×C4—21no—
115C2×C32×C4—22no—
116C2×C32×C4—21no—
117C2×C32×C4—22no—
118C2×C32×C4—21no—
119C2×C32×C4—22no—
120C2×C32×C4—21no—
121C2×C32×C4—22no—
122C2×C32×C4C22×C414yes—
123C2×C32×C4C22×C412yes—
124C2×C32×C4C2×Q812yes—
125C2×C32×C4#4112yes—
126C2×C32×C4#4112yes—
127C2×C3⋊Dic3—21no—
128C2×C3⋊Dic3—21no—
129C2×C3⋊Dic3—21no—
130C2×C3⋊Dic3—21no—
131C2×C3⋊Dic3—22no—
132C2×C3⋊Dic3—22no—
133C2×C3⋊Dic3—21no—
134C2×C3⋊Dic3—22no—
135C2×C3⋊Dic3—21no—
136C2×C3⋊Dic3—22no—
137C2×C3⋊Dic3—22no—
138C2×C3⋊Dic3—21no—
139C2×C3⋊Dic3C22×C412yes—
140C2×C3⋊Dic3C22×C414yes—
141C2×C3⋊Dic3C2×Q812yes—
142C4×C3⋊D3—28no—
143C4×C3⋊D3—48no—
144C22×C4⋊C4—91no—
145#389—91no—
146#389—91no—
147#387—92no—
148#387—92no—
149#380—91no—
150#380—92no—
151C4×C4⋊C4—91no—
152C4×C4⋊C4C3⋊D311yescharacteristic, complemented
153C4×C22⋊C4—91no—
154C4×C22⋊C4—92no—
155C23×D3—34no—
156C22×C3×C4C22×D318yes—
157C22×C3×C4C22×D314yes—
158C22×C3×C4C22×D318yes—
159C22×C3×C4C22×D314yes—
160C22×C3×C4C22×D314yes—
161C22×Dic3—34no—
162C22×Dic3—34no—
163C22×Dic3—38no—
164C22×Dic3—34no—
165C22×Dic3—38no—
166C2×C4×D3—316no—
167C2×C4×D3—332no—
168C2×C4×D3—68no—
169C2×C4×D3—68no—
170C2×C4×D3—128no—
171C2×C4×D3—128no—
172C3×C4⋊C4—28no—
173C3×C4⋊C4C4×D3116yes—
174C3×C42—28no—
175C3×C42—48no—
176(C2×D3)⋊C4—316no—
177(C2×D3)⋊C4—68no—
178(C2×D3)⋊C4—616no—
179C4⋊Dic3—316no—
180C4⋊Dic3—68no—
181Dic3⋊C4—332no—
182Dic3⋊C4—128no—
183Dic3⋊C4—128no—
184C4×Dic3—68no—
185C4×Dic3—128no—
186C22×C32C23×C411yescharacteristic
187C22×C32C22×Q811yescharacteristic
188C22×C32C2×#4111yescharacteristic
189C22×C32C2×#4111yescharacteristic
190C22×C32C2×#4111yescharacteristic
191C22×C32H(5,𝔽2)11yescharacteristic
192C22×C32H(5,𝔽2)11yescharacteristic
193C2×C3⋊D3—22no—
194C2×C3⋊D3—22no—
195C2×C3⋊D3—22no—
196C2×C3⋊D3—22no—
197C2×C3⋊D3—22no—
198C2×C3⋊D3—22no—
199C2×C3⋊D3C4×Q814yes—
200C32×C4—24no—
201C32×C4—22no—
202C32×C4—41no—
203C32×C4—42no—
204C32×C4#11714yes—
205C3⋊Dic3—22no—
206C3⋊Dic3—24no—
207C3⋊Dic3—22no—
208C3⋊Dic3—42no—
209C3⋊Dic3—41no—
210C23×C4—91no—
211C23×C4—92no—
212C2×C4⋊C4—92no—
213C2×C4⋊C4—91no—
214C2×C4⋊C4—98no—
215C2×C4⋊C4—91no—
216C2×C4⋊C4—92no—
217C2×C4⋊C4—92no—
218C2×C4⋊C4C2×C3⋊D311yescharacteristic
219C2×C4⋊C4C2×C3⋊D311yescharacteristic
220C2×C22⋊C4—91no—
221C2×C22⋊C4—92no—
222C2×C22⋊C4—91no—
223C2×C42—91no—
224C2×C42—92no—
225C2×C42C2×C3⋊D311yescharacteristic
226C2×C42C2×C3⋊D312yes—
227#95—91no—
228#95—91no—
229#95—92no—
230#95—92no—
231#95—92no—
232#95—92no—
233#95C2×C3⋊D312yes—
234C23×C3C23×D314yes—
235C22×D3—38no—
236C22×D3—38no—
237C22×D3—38no—
238C22×D3—64no—
239C22×D3—64no—
240C22×D3—64no—
241C22×D3—64no—
242C2×C3×C4—24no—
243C2×C3×C4—24no—
244C2×C3×C4—28no—
245C2×C3×C4—28no—
246C2×C3×C4—24no—
247C2×C3×C4—28no—
248C2×C3×C4—28no—
249C2×C3×C4—24no—
250C2×C3×C4—28no—
251C2×C3×C4—24no—
252C2×C3×C4C2×C4×D3116yes—
253C2×C3×C4C2×C4×D318yes—
254C2×C3×C4#23518yes—
255C2×C3×C4#23518yes—
256C2×C3×C4D3×Q818yes—
257C2×Dic3—38no—
258C2×Dic3—316no—
259C2×Dic3—38no—
260C2×Dic3—64no—
261C2×Dic3—64no—
262C2×Dic3—64no—
263C2×Dic3—68no—
264C2×Dic3—64no—
265C2×Dic3—68no—
266C2×Dic3—64no—
267C2×Dic3—68no—
268C2×Dic3—64no—
269C2×Dic3—68no—
270C2×Dic3—64no—
271C2×Dic3—68no—
272C4×D3—632no—
273C4×D3—1232no—
274C2×C32C2×#11711yescharacteristic
275C2×C32C2×C4×Q811yescharacteristic
276C2×C32#51811yescharacteristic
277C2×C32#55311yescharacteristic
278C2×C32#55311yescharacteristic
279C2×C32#55411yescharacteristic
280C2×C32#55411yescharacteristic
281C3⋊D3—24no—
282C24—91no—
283C22×C4—91no—
284C22×C4—91no—
285C22×C4—92no—
286C22×C4—94no—
287C22×C4—98no—
288C22×C4—91no—
289C22×C4—92no—
290C22×C4—182no—
291C22×C4—182no—
292C22×C4—362no—
293C22×C4—362no—
294C22×C4C22×C3⋊D312yes—
295C22×C4C22×C3⋊D311yescharacteristic
296C22×C4C22×C3⋊D312yes—
297C22×C4C22×C3⋊D311yescharacteristic
298C22×C4C22×C3⋊D311yescharacteristic
299C4⋊C4—22no—
300C4⋊C4—98no—
301C4⋊C4—94no—
302C4⋊C4—182no—
303C4⋊C4—362no—
304C4⋊C4—362no—
305C4⋊C4C4×C3⋊D314yes—
306C22⋊C4—94no—
307C22⋊C4—182no—
308C22⋊C4—184no—
309C42—22no—
310C42—42no—
311C42—182no—
312C42—362no—
313C22×C3C22×C4×D314yes—
314C22×C3C2×#23514yes—
315C22×C3C2×#23514yes—
316C22×C3#100414yes—
317C22×C3C2×D3×Q814yes—
318C22×C3D3×#4114yes—
319C22×C3#100914yes—
320C2×D3—316no—
321C2×D3—68no—
322C2×D3—68no—
323C2×D3—68no—
324C2×D3—68no—
325C2×D3—68no—
326C2×D3—68no—
327C3×C4—28no—
328C3×C4—216no—
329C3×C4—44no—
330C3×C4—48no—
331C3×C4#872116yes—
332Dic3—68no—
333Dic3—616no—
334Dic3—68no—
335Dic3—128no—
336Dic3—124no—
337C32#234511yescharacteristic, complemented, Sylow
338C23—92no—
339C23—92no—
340C23—92no—
341C23—181no—
342C23—181no—
343C23—181no—
344C23—181no—
345C23C23×C3⋊D311yescharacteristic
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—22no—
349C2×C4—22no—
350C2×C4—21no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—21no—
354C2×C4—22no—
355C2×C4—21no—
356C2×C4—92no—
357C2×C4—94no—
358C2×C4—92no—
359C2×C4—181no—
360C2×C4—181no—
361C2×C4—181no—
362C2×C4—182no—
363C2×C4—181no—
364C2×C4—182no—
365C2×C4—188no—
366C2×C4—181no—
367C2×C4—182no—
368C2×C4—181no—
369C2×C4—182no—
370C2×C4—181no—
371C2×C4—182no—
372C2×C4—368no—
373C2×C4C2×C4×C3⋊D314yes—
374C2×C4C2×C4×C3⋊D312yes—
375C2×C4#382812yes—
376C2×C4#382812yes—
377C2×C4Q8×C3⋊D312yes—
378C2×C3C2×#87214yes—
379C2×C3#551114yes—
380C2×C3#553014yes—
381C2×C3#554514yes—
382C2×C3#555814yes—
383C2×C3C4×D3×Q814yes—
384C2×C3#557914yes—
385D3—616no—
386C22—94no—
387C22—182no—
388C22—182no—
389C22—182no—
390C22—182no—
391C22—182no—
392C22—182no—
393C22C22×C4×C3⋊D311yescharacteristic
394C22C2×#382811yescharacteristic
395C22C2×#382811yescharacteristic
396C22#6436111yescharacteristic
397C22C2×Q8×C3⋊D311yescharacteristic
398C22#41×C3⋊D311yescharacteristic
399C22#6436611yescharacteristic
400C4—22no—
401C4—24no—
402C4—41no—
403C4—42no—
404C4—182no—
405C4—184no—
406C4—182no—
407C4—362no—
408C4—361no—
409C4#6408114yes—
410C3#7376814yescomplemented
411C2—184no—
412C2C2×#6408111yescharacteristic
413C2#1059598211yescharacteristic
414C2#1059600111yescharacteristic
415C2#1059601611yescharacteristic
416C2#1059602911yescharacteristic
417C2C4×Q8×C3⋊D311yescharacteristic
418C2#1059605011yescharacteristic
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutatorC22×C32C23×C4
FittingC32×C4×C4⋊C4C2
socle, cosocleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenterC4×C4⋊C4C3⋊D3
hypocenterC32#2345
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C32×C4×C4⋊C4C2semidirect
4. C4⋊C4×C3⋊Dic3C2semidirect
5. #10592671C2semidirect
8. #10592632C2semidirect
9. #10592627C2semidirect
11. #10592351C2semidirect
29. C4⋊C4×C3⋊D3C4semidirect
38. C3×C4×C4⋊C4D3semidirect
152. C4×C4⋊C4C3⋊D3semidirect
337. C32#2345semidirect
410. C3#73768semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×C3⋊D32
C32×C4×C4⋊C42
#105926862
C4⋊C4×C3⋊Dic32
#105926712
C4×#37522
#105926322
#105926272
#105923662
#105923512
#737683