Finite Group Databasebeta

← #11805741

Subgroups — #11805741

Order 1152.

1764 conjugacy classes of subgroups.

The subgroup lattice has 411 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C4×D4C211yesmaximal, characteristic
2#10592919C212yesmaximal
3#10592911C211yesmaximal, characteristic, complemented
4#10592910C211yesmaximal, characteristic, complemented
5C4×#3757C211yesmaximal, characteristic, complemented
6C2×#63658C211yesmaximal, characteristic, complemented
7#10592679C212yesmaximal, complemented
8#10592650C212yesmaximal, complemented
9C22⋊C4×C3⋊Dic3C212yesmaximal, complemented
10#10592636C211yesmaximal, characteristic, complemented
11#10592631C211yesmaximal, characteristic, complemented
12#82336—34nomaximal
13C22×C32×D4C2211yescharacteristic
14C23×C32×C4C2211yescharacteristic
15C23×C32×C4C2211yescharacteristic
16C23×C3⋊Dic3C2212yes—
17C32×C4×D4C418yescomplemented
18C2×C32×C4⋊C4C2211yescharacteristic
19C2×C32×C22⋊C4C2211yescharacteristic
20C2×C32×C22⋊C4C2211yescharacteristic
21C2×C32×C42C2211yescharacteristic
22C2×#3757C2212yes—
23C2×#3757C2212yes—
24C2×#3757C2212yes—
25C2×C4⋊(C3⋊Dic3)C2212yes—
26C2×C4×C3⋊Dic3C2212yes—
27C2×C4×C3⋊Dic3C2212yes—
28#63658C2211yescharacteristic
29#63658C2211yescharacteristic
30#63658C2212yes—
31#63658C2212yes—
32#63658C2211yescharacteristic
33#63658C2211yescharacteristic
34#63658C2212yes—
35#63658C2212yes—
36#63658C2212yes—
37C2×C3×C4×D4D314yes—
38#5220—38no—
39#5212—34no—
40#5211—34no—
41C4×#217—34no—
42C2×C3⋊#95—34no—
43#4980—38no—
44#4951—38no—
45Dic3×C22⋊C4—38no—
46#4937—34no—
47#4932—34no—
48C24×C32C2311yescharacteristic
49C24×C32C2311yescharacteristic
50C2×C32×D4—22no—
51C2×C32×D4—22no—
52C2×C32×D4C2×C414yes—
53C22×C32×C4—42no—
54C22×C32×C4—42no—
55C22×C32×C4C2×C414yes—
56C22×C32×C4C2×C414yescomplemented
57C22×C32×C4C2311yescharacteristic
58C22×C32×C4C2311yescharacteristic
59C22×C32×C4C2311yescharacteristic
60C22×C32×C4C2311yescharacteristic
61C22×C32×C4C2311yescharacteristic
62C22×C3⋊Dic3—24no—
63C22×C3⋊Dic3—24no—
64C22×C3⋊Dic3—42no—
65C22×C3⋊Dic3C2312yes—
66C22×C3⋊Dic3C2312yes—
67C22×C3⋊Dic3C2312yes—
68C22×C3⋊Dic3C2312yes—
69C32×C4⋊C4C2×C414yescomplemented
70C32×C22⋊C4C2×C414yes—
71C32×C22⋊C4C2×C414yescomplemented
72C32×C42C2×C414yescomplemented
73#3757—24no—
74#3757—24no—
75#3757—42no—
76C4⋊(C3⋊Dic3)—42no—
77C4×C3⋊Dic3—24no—
78C4×C3⋊Dic3—42no—
79#2353—91noSylow
80C22×C3×D4C2×D314yes—
81C23×C3×C4C2×D314yes—
82C23×C3×C4C2×D314yes—
83C23×Dic3—38no—
84C3×C4×D4Dic3132yescomplemented
85C2×C3×C4⋊C4C2×D314yes—
86C2×C3×C22⋊C4C2×D314yes—
87C2×C3×C22⋊C4C2×D314yes—
88C2×C3×C42C2×D314yes—
89C2×#217—38no—
90C2×#217—38no—
91C2×#217—38no—
92C2×C4⋊Dic3—38no—
93C2×C4×Dic3—38no—
94C2×C4×Dic3—38no—
95C3⋊#95—34no—
96C3⋊#95—34no—
97C3⋊#95—38no—
98C3⋊#95—38no—
99C3⋊#95—34no—
100C3⋊#95—34no—
101C3⋊#95—38no—
102C3⋊#95—38no—
103C3⋊#95—38no—
104C23×C32—22no—
105C23×C32—22no—
106C23×C32—22no—
107C23×C32—21no—
108C23×C32—21no—
109C23×C32—22no—
110C23×C32C22×C412yes—
111C23×C32C22×C412yes—
112C23×C32#4112yes—
113C23×C32#4112yes—
114C23×C32C2411yescharacteristic
115C32×D4—28no—
116C2×C32×C4—22no—
117C2×C32×C4—21no—
118C2×C32×C4—21no—
119C2×C32×C4—22no—
120C2×C32×C4—22no—
121C2×C32×C4—22no—
122C2×C32×C4—44no—
123C2×C32×C4—44no—
124C2×C32×C4C22×C412yes—
125C2×C32×C4C22×C412yes—
126C2×C32×C4C22×C412yes—
127C2×C32×C4C22×C412yes—
128C2×C32×C4C22×C412yes—
129C2×C3⋊Dic3—22no—
130C2×C3⋊Dic3—22no—
131C2×C3⋊Dic3—22no—
132C2×C3⋊Dic3—22no—
133C2×C3⋊Dic3—22no—
134C2×C3⋊Dic3—22no—
135C2×C3⋊Dic3—22no—
136C2×C3⋊Dic3—22no—
137C2×C3⋊Dic3—22no—
138C2×C3⋊Dic3—22no—
139C2×C3⋊Dic3—22no—
140C2×C3⋊Dic3—48no—
141C2×C3⋊Dic3#4114yes—
142C2×C4×D4C3⋊D311yescharacteristic
143#388—92no—
144#387—92no—
145#386—92no—
146#383—91no—
147#381—91no—
148#380—91no—
149C4×C22⋊C4—91no—
150C4×C22⋊C4—92no—
151#376—91no—
152C2×#95—91no—
153C24×C3C22×D314yes—
154C24×C3C22×D314yes—
155C2×C3×D4—28no—
156C2×C3×D4—28no—
157C2×C3×D4C2×Dic3116yes—
158C22×C3×C4—48no—
159C22×C3×C4—48no—
160C22×C3×C4C2×Dic3116yes—
161C22×C3×C4C2×Dic3116yescomplemented
162C22×C3×C4C22×D314yes—
163C22×C3×C4C22×D314yes—
164C22×C3×C4C22×D314yes—
165C22×C3×C4C22×D314yes—
166C22×C3×C4C22×D314yes—
167C22×Dic3—38no—
168C22×Dic3—38no—
169C22×Dic3—38no—
170C22×Dic3—38no—
171C22×Dic3—616no—
172C22×Dic3—616no—
173C22×Dic3—128no—
174C3×C4⋊C4C2×Dic3116yescomplemented
175C3×C22⋊C4C2×Dic3116yes—
176C3×C22⋊C4C2×Dic3116yescomplemented
177C3×C42C2×Dic3116yescomplemented
178#217—616no—
179#217—616no—
180#217—128no—
181C4⋊Dic3—128no—
182C4×Dic3—616no—
183C4×Dic3—128no—
184C22×C32—22no—
185C22×C32—22no—
186C22×C32—24no—
187C22×C32—24no—
188C22×C32—22no—
189C22×C32—22no—
190C22×C32—22no—
191C22×C32—42no—
192C22×C32—42no—
193C22×C32#11714yes—
194C22×C32C23×C411yescharacteristic
195C22×C32C2×#4111yescharacteristic
196C22×C32C2×#4111yescharacteristic
197C22×C32C2×#4112yes—
198C22×C32H(5,𝔽2)12yes—
199C32×C4—22no—
200C32×C4—22no—
201C32×C4—22no—
202C32×C4—22no—
203C32×C4—22no—
204C3⋊Dic3—24no—
205C3⋊Dic3—42no—
206C3⋊Dic3—42no—
207C3⋊Dic3—42no—
208C22×D4C2×C3⋊D311yescharacteristic
209C23×C4—92no—
210C23×C4C2×C3⋊D311yescharacteristic
211C23×C4C2×C3⋊D311yescharacteristic
212C4×D4C3⋊Dic318yescomplemented
213C2×C4⋊C4—92no—
214C2×C4⋊C4C2×C3⋊D311yescharacteristic
215C2×C22⋊C4—92no—
216C2×C22⋊C4—92no—
217C2×C22⋊C4—92no—
218C2×C22⋊C4C2×C3⋊D311yescharacteristic
219C2×C22⋊C4C2×C3⋊D311yescharacteristic
220C2×C42—92no—
221C2×C42—92no—
222C2×C42C2×C3⋊D311yescharacteristic
223#95—91no—
224#95—91no—
225#95—92no—
226#95—91no—
227#95—92no—
228#95—91no—
229#95—92no—
230#95—92no—
231#95—92no—
232C23×C3—28no—
233C23×C3—28no—
234C23×C3—24no—
235C23×C3—24no—
236C23×C3—28no—
237C23×C3—28no—
238C23×C3#23518yes—
239C23×C3#23518yes—
240C23×C3C22×Dic318yes—
241C23×C3C22×Dic318yes—
242C23×C3C23×D314yes—
243C3×D4—232no—
244C2×C3×C4—24no—
245C2×C3×C4—24no—
246C2×C3×C4—28no—
247C2×C3×C4—28no—
248C2×C3×C4—28no—
249C2×C3×C4—28no—
250C2×C3×C4—416no—
251C2×C3×C4—416no—
252C2×C3×C4C22×Dic318yes—
253C2×C3×C4C22×Dic318yes—
254C2×C3×C4C22×Dic318yes—
255C2×C3×C4C22×Dic318yes—
256C2×C3×C4C22×Dic318yes—
257C2×Dic3—316no—
258C2×Dic3—68no—
259C2×Dic3—68no—
260C2×Dic3—68no—
261C2×Dic3—68no—
262C2×Dic3—68no—
263C2×Dic3—68no—
264C2×Dic3—68no—
265C2×Dic3—68no—
266C2×Dic3—68no—
267C2×Dic3—68no—
268C2×Dic3—68no—
269C2×Dic3—1232no—
270C2×C32—24no—
271C2×C32—42no—
272C2×C32C2×#11711yescharacteristic
273C2×C32C4×#4111yescharacteristic
274C2×C32#51811yescharacteristic
275C2×C32#55112yes—
276C2×C32#55312yes—
277C24C22×C3⋊D311yescharacteristic
278C24C22×C3⋊D311yescharacteristic
279C2×D4—22no—
280C2×D4—22no—
281C2×D4C2×C3⋊Dic314yes—
282C22×C4—42no—
283C22×C4—42no—
284C22×C4—92no—
285C22×C4—92no—
286C22×C4—92no—
287C22×C4—92no—
288C22×C4—184no—
289C22×C4—184no—
290C22×C4—362no—
291C22×C4C2×C3⋊Dic314yes—
292C22×C4C2×C3⋊Dic314yescomplemented
293C22×C4C22×C3⋊D311yescharacteristic
294C22×C4C22×C3⋊D311yescharacteristic
295C22×C4C22×C3⋊D311yescharacteristic
296C22×C4C22×C3⋊D311yescharacteristic
297C22×C4C22×C3⋊D311yescharacteristic
298C4⋊C4—362no—
299C4⋊C4C2×C3⋊Dic314yescomplemented
300C22⋊C4—184no—
301C22⋊C4—184no—
302C22⋊C4—362no—
303C22⋊C4C2×C3⋊Dic314yes—
304C22⋊C4C2×C3⋊Dic314yescomplemented
305C42—184no—
306C42—362no—
307C42C2×C3⋊Dic314yescomplemented
308C22×C3—216no—
309C22×C3—28no—
310C22×C3—216no—
311C22×C3—28no—
312C22×C3—28no—
313C22×C3—28no—
314C22×C3—28no—
315C22×C3—48no—
316C22×C3—48no—
317C22×C3#926116yes—
318C22×C3C2×#23514yes—
319C22×C3C2×#23514yes—
320C22×C3#100418yes—
321C22×C3D3×#4118yes—
322C22×C3C23×Dic314yes—
323C3×C4—28no—
324C3×C4—28no—
325C3×C4—28no—
326C3×C4—28no—
327C3×C4—28no—
328Dic3—616no—
329Dic3—128no—
330Dic3—128no—
331Dic3—128no—
332C32#235311yescharacteristic, complemented, Sylow
333C23—22no—
334C23—22no—
335C23—21no—
336C23—21no—
337C23—22no—
338C23—22no—
339C23#382812yes—
340C23#382812yes—
341C23C22×C3⋊Dic312yes—
342C23C22×C3⋊Dic312yes—
343C23C23×C3⋊D311yescharacteristic
344D4—28no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—22no—
348C2×C4—22no—
349C2×C4—22no—
350C2×C4—22no—
351C2×C4—44no—
352C2×C4—44no—
353C2×C4—94no—
354C2×C4—182no—
355C2×C4—182no—
356C2×C4—182no—
357C2×C4—182no—
358C2×C4—182no—
359C2×C4—182no—
360C2×C4—182no—
361C2×C4—182no—
362C2×C4—182no—
363C2×C4—182no—
364C2×C4—182no—
365C2×C4—368no—
366C2×C4C22×C3⋊Dic312yes—
367C2×C4C22×C3⋊Dic312yes—
368C2×C4C22×C3⋊Dic312yes—
369C2×C4C22×C3⋊Dic312yes—
370C2×C4C22×C3⋊Dic312yes—
371C2×C3—216no—
372C2×C3—48no—
373C2×C3#554018yes—
374C2×C3#555618yes—
375C2×C3C2×#92614yes—
376C2×C3#579814yes—
377C2×C3Dic3×#4114yes—
378C22—24no—
379C22—22no—
380C22—24no—
381C22—22no—
382C22—22no—
383C22—22no—
384C22—22no—
385C22—42no—
386C22—42no—
387C22#6413514yes—
388C22C2×#382811yescharacteristic
389C22C2×#382811yescharacteristic
390C22#6436112yes—
391C22#41×C3⋊D312yes—
392C22C23×C3⋊Dic311yescharacteristic
393C4—22no—
394C4—22no—
395C4—22no—
396C4—22no—
397C4—22no—
398C4—184no—
399C4—362no—
400C4—362no—
401C4—362no—
402C3#8233614yescomplemented
403C2—24no—
404C2—42no—
405C2#1059601112yes—
406C2#1059602712yes—
407C2C2×#6413511yescharacteristic
408C2#1059626911yescharacteristic
409C2#41×C3⋊Dic311yescharacteristic
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutatorC22×C32C23×C4
FittingC2×C32×C4×D4C2
socle, cosocleC23×C32C24
prime radicalC22×C32×D4C22
hypercenterC2×C4×D4C3⋊D3
hypocenterC32#2353
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
3. #10592911C2semidirect
4. #10592910C2semidirect
5. C4×#3757C2semidirect
6. C2×#63658C2semidirect
7. #10592679C2semidirect
8. #10592650C2semidirect
9. C22⋊C4×C3⋊Dic3C2semidirect
10. #10592636C2semidirect
11. #10592631C2semidirect
17. C32×C4×D4C4semidirect
56. C22×C32×C4C2×C4semidirect
69. C32×C4⋊C4C2×C4semidirect
71. C32×C22⋊C4C2×C4semidirect
72. C32×C42C2×C4semidirect
84. C3×C4×D4Dic3semidirect
161. C22×C3×C4C2×Dic3semidirect
174. C3×C4⋊C4C2×Dic3semidirect
176. C3×C22⋊C4C2×Dic3semidirect
177. C3×C42C2×Dic3semidirect
212. C4×D4C3⋊Dic3semidirect
292. C22×C4C2×C3⋊Dic3semidirect
299. C4⋊C4C2×C3⋊Dic3semidirect
304. C22⋊C4C2×C3⋊Dic3semidirect
307. C42C2×C3⋊Dic3semidirect
332. C32#2353semidirect
402. C3#82336semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C4×D42
#105929192
#105929112
#105929102
C4×#37572
C2×#636582
#105926792
#105926502
C22⋊C4×C3⋊Dic32
#105926362
#105926312
#823363