Finite Group Databasebeta

← #11802955

Subgroups — #11802955

Order 1152.

900 conjugacy classes of subgroups.

The subgroup lattice has 435 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63454C211yesmaximal, characteristic
2C2×C4⋊C4×D9C211yesmaximal, characteristic
3C2×#63434C211yesmaximal, characteristic
4C9×#389C211yesmaximal, characteristic, complemented
5#10588669C212yesmaximal
6#10588664C211yesmaximal, characteristic, complemented
7#10588655C212yesmaximal, complemented
8#10588652C211yesmaximal, characteristic, complemented
9#10588608C211yesmaximal, characteristic, complemented
10#10588348C212yesmaximal
11#10588330C212yesmaximal, complemented
12#75968—31nomaximal
13C22×C4×D9C2212yes—
14C22×C4×D9C2211yescharacteristic
15C2×C9×C4⋊C4C2211yescharacteristic
16C2×C9×C4⋊C4C2212yes—
17C2×C9×C4⋊C4C2211yescharacteristic
18C2×C42×C9C2211yescharacteristic
19C2×(C2×D9)⋊C4C2211yescharacteristic
20C2×(C2×D9)⋊C4C2211yescharacteristic
21C2×(C2×D9)⋊C4C2212yes—
22C2×C4⋊Dic9C2211yescharacteristic
23C2×C4⋊Dic9C2212yes—
24C2×C4⋊Dic9C2211yescharacteristic
25C2×Dic9⋊C4C2211yescharacteristic
26C2×Dic9⋊C4C2211yescharacteristic
27C2×Dic9⋊C4C2212yes—
28C2×Dic9⋊C4C2212yes—
29C2×Dic9⋊C4C2212yes—
30C2×C4×Dic9C2211yescharacteristic
31C2×C4×Dic9C2212yes—
32#63454C418yescomplemented
33C4⋊C4×D9—24no—
34#63434—24no—
35C9×#95C2212yes—
36C9⋊#95C2212yes—
37C9⋊#95C2212yes—
38C9⋊#95C2212yes—
39C2×#892—31no—
40C2×D3×C4⋊C4—31no—
41C2×#872—31no—
42C3×#389D311yescharacteristic
43#4989—32no—
44#4984—31no—
45#4975—32no—
46#4972—31no—
47#4928—31no—
48#4668—32no—
49#4650—32no—
50C23×D9C2311yescharacteristic
51C22×C4×C9C2311yescharacteristic
52C22×C4×C9C2311yescharacteristic
53C22×C4×C9C2312yes—
54C22×C4×C9C2312yes—
55C22×C4×C9C2311yescharacteristic
56C22×Dic9C2311yescharacteristic
57C22×Dic9C2311yescharacteristic
58C22×Dic9C2312yes—
59C22×Dic9C2312yes—
60C22×Dic9C2311yescharacteristic
61C2×C4×D9—24no—
62C2×C4×D9—42no—
63C2×C4×D9—42no—
64C2×C4×D9C2×C414yes—
65C2×C4×D9D414yes—
66C2×C4×D9Q814yes—
67C9×C4⋊C4—22no—
68C9×C4⋊C4—42no—
69C9×C4⋊C4C2×C414yescomplemented
70C42×C9—22no—
71(C2×D9)⋊C4—22no—
72(C2×D9)⋊C4—22no—
73(C2×D9)⋊C4C2×C418yes—
74C4⋊Dic9—22no—
75C4⋊Dic9—42no—
76C4⋊Dic9C2×C414yescomplemented
77Dic9⋊C4—22no—
78Dic9⋊C4—22no—
79Dic9⋊C4—24no—
80Dic9⋊C4—42no—
81Dic9⋊C4—42no—
82C4×Dic9—22no—
83C4×Dic9C2×C418yescomplemented
84#2317—91noSylow
85C22×C4×D3—31no—
86C22×C4×D3—32no—
87C2×C3×C4⋊C4C2×D311yescharacteristic
88C2×C3×C4⋊C4C2×D312yes—
89C2×C3×C4⋊C4C2×D311yescharacteristic
90C2×C3×C42C2×D311yescharacteristic
91C2×(C2×D3)⋊C4—32no—
92C2×(C2×D3)⋊C4—31no—
93C2×(C2×D3)⋊C4—31no—
94C2×C4⋊Dic3—31no—
95C2×C4⋊Dic3—31no—
96C2×C4⋊Dic3—32no—
97C2×Dic3⋊C4—31no—
98C2×Dic3⋊C4—32no—
99C2×Dic3⋊C4—31no—
100C2×Dic3⋊C4—32no—
101C2×Dic3⋊C4—32no—
102C2×C4×Dic3—32no—
103C2×C4×Dic3—31no—
104#892—38no—
105D3×C4⋊C4—64no—
106#872—64no—
107C3×#95C2×D312yes—
108C3⋊#95—32no—
109C3⋊#95—32no—
110C3⋊#95—32no—
111C23×C9C2411yescharacteristic
112C22×D9—21no—
113C22×D9—21no—
114C22×D9—21no—
115C22×D9—21no—
116C22×D9C22×C412yes—
117C22×D9C2×D412yes—
118C22×D9C2×Q812yes—
119C2×C4×C9—22no—
120C2×C4×C9—22no—
121C2×C4×C9—21no—
122C2×C4×C9—21no—
123C2×C4×C9—22no—
124C2×C4×C9—21no—
125C2×C4×C9—22no—
126C2×C4×C9—21no—
127C2×C4×C9—22no—
128C2×C4×C9—21no—
129C2×C4×C9—21no—
130C2×C4×C9C22×C414yes—
131C2×C4×C9C22×C412yes—
132C2×C4×C9C2×D412yes—
133C2×C4×C9C2×Q812yes—
134C2×Dic9—22no—
135C2×Dic9—22no—
136C2×Dic9—21no—
137C2×Dic9—21no—
138C2×Dic9—22no—
139C2×Dic9—21no—
140C2×Dic9—22no—
141C2×Dic9—21no—
142C2×Dic9—22no—
143C2×Dic9—21no—
144C2×Dic9—21no—
145C2×Dic9C22×C414yes—
146C2×Dic9C22×C412yes—
147C2×Dic9C2×D412yes—
148C2×Dic9C2×Q812yes—
149C4×D9—48no—
150C4×D9C4⋊C4116yescomplemented
151C2×#117—91no—
152C2×#117—91no—
153C22×C4⋊C4—91no—
154#389—91no—
155#389—91no—
156#389—91no—
157#389D911yescharacteristic, complemented
158#385—92no—
159#385—92no—
160#384—92no—
161#382—92no—
162C23×D3—31no—
163C22×C3×C4C22×D311yescharacteristic
164C22×C3×C4C22×D312yes—
165C22×C3×C4C22×D311yescharacteristic
166C22×C3×C4C22×D312yes—
167C22×C3×C4C22×D311yescharacteristic
168C22×Dic3—31no—
169C22×Dic3—32no—
170C22×Dic3—31no—
171C22×Dic3—32no—
172C22×Dic3—31no—
173C2×C4×D3—34no—
174C2×C4×D3—34no—
175C2×C4×D3—34no—
176C2×C4×D3—64no—
177C2×C4×D3—122no—
178C2×C4×D3—122no—
179C3×C4⋊C4—22no—
180C3×C4⋊C4—42no—
181C3×C4⋊C4C4×D314yes—
182C3×C42—22no—
183(C2×D3)⋊C4—38no—
184(C2×D3)⋊C4—62no—
185(C2×D3)⋊C4—62no—
186C4⋊Dic3—34no—
187C4⋊Dic3—62no—
188C4⋊Dic3—122no—
189Dic3⋊C4—62no—
190Dic3⋊C4—62no—
191Dic3⋊C4—64no—
192Dic3⋊C4—122no—
193Dic3⋊C4—122no—
194C4×Dic3—38no—
195C4×Dic3—62no—
196C22×C9C23×C411yescharacteristic
197C22×C9C22×D411yescharacteristic
198C22×C9C22×Q811yescharacteristic
199C22×C9H(5,𝔽2)11yescharacteristic
200C22×C9H(5,𝔽2)11yescharacteristic
201C22×C92−1+411yescharacteristic
202C22×C92−1+411yescharacteristic
203C2×D9—22no—
204C2×D9—22no—
205C2×D9—22no—
206C2×D9—22no—
207C2×D9—22no—
208C2×D9—22no—
209C2×D9C2×C4⋊C414yes—
210C4×C9—24no—
211C4×C9—42no—
212C4×C9—41no—
213C4×C9—41no—
214C4×C9C2×C4⋊C414yes—
215Dic9—24no—
216Dic9—42no—
217Dic9—41no—
218Dic9—41no—
219Dic9C2×C4⋊C414yes—
220C23×C4—91no—
221C23×C4—92no—
222#117—98no—
223#117—184no—
224C2×C4⋊C4—91no—
225C2×C4⋊C4—92no—
226C2×C4⋊C4—91no—
227C2×C4⋊C4—91no—
228C2×C4⋊C4—91no—
229C2×C4⋊C4—92no—
230C2×C4⋊C4—92no—
231C2×C4⋊C4—92no—
232C2×C4⋊C4—184no—
233C2×C4⋊C4C2×D911yescharacteristic
234C2×C4⋊C4C2×D912yes—
235C2×C4⋊C4C2×D911yescharacteristic
236C2×C22⋊C4—92no—
237C2×C22⋊C4—91no—
238C2×C22⋊C4—91no—
239C2×C42—92no—
240C2×C42—91no—
241C2×C42C2×D911yescharacteristic
242#95—92no—
243#95—92no—
244#95—92no—
245#95C2×D912yes—
246C23×C3C23×D311yescharacteristic
247C22×D3—32no—
248C22×D3—32no—
249C22×D3—32no—
250C22×D3—61no—
251C22×D3—61no—
252C22×D3—61no—
253C22×D3—61no—
254C2×C3×C4—22no—
255C2×C3×C4—22no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4—22no—
259C2×C3×C4—21no—
260C2×C3×C4—22no—
261C2×C3×C4—21no—
262C2×C3×C4—21no—
263C2×C3×C4—22no—
264C2×C3×C4—21no—
265C2×C3×C4C2×C4×D314yes—
266C2×C3×C4C2×C4×D312yes—
267C2×C3×C4D3×D412yes—
268C2×C3×C4D3×Q812yes—
269C2×Dic3—32no—
270C2×Dic3—32no—
271C2×Dic3—32no—
272C2×Dic3—34no—
273C2×Dic3—62no—
274C2×Dic3—62no—
275C2×Dic3—61no—
276C2×Dic3—61no—
277C2×Dic3—62no—
278C2×Dic3—61no—
279C2×Dic3—62no—
280C2×Dic3—61no—
281C2×Dic3—61no—
282C2×Dic3—62no—
283C2×Dic3—61no—
284C4×D3—316no—
285C4×D3—128no—
286C2×C9C22×C4⋊C411yescharacteristic
287C2×C9#52011yescharacteristic
288C2×C9#52011yescharacteristic
289C2×C9#53511yescharacteristic
290C2×C9#53611yescharacteristic
291C2×C9#54411yescharacteristic
292C2×C9#54411yescharacteristic
293D9—24no—
294C24—91no—
295C22×C4—91no—
296C22×C4—94no—
297C22×C4—94no—
298C22×C4—94no—
299C22×C4—92no—
300C22×C4—91no—
301C22×C4—92no—
302C22×C4—91no—
303C22×C4—184no—
304C22×C4—362no—
305C22×C4—362no—
306C22×C4C22×D911yescharacteristic
307C22×C4C22×D912yes—
308C22×C4C22×D911yescharacteristic
309C22×C4C22×D912yes—
310C22×C4C22×D911yescharacteristic
311C4⋊C4—22no—
312C4⋊C4—42no—
313C4⋊C4—94no—
314C4⋊C4—184no—
315C4⋊C4—182no—
316C4⋊C4—182no—
317C4⋊C4—182no—
318C4⋊C4—362no—
319C4⋊C4—362no—
320C4⋊C4—362no—
321C4⋊C4C4×D914yescomplemented
322C22⋊C4—98no—
323C22⋊C4—182no—
324C22⋊C4—182no—
325C42—22no—
326C42—98no—
327C42—182no—
328C22×C3C22×C4×D311yescharacteristic
329C22×C3C2×D3×D411yescharacteristic
330C22×C3#100411yescharacteristic
331C22×C3C2×D3×Q811yescharacteristic
332C22×C3#100711yescharacteristic
333C22×C3#100911yescharacteristic
334C22×C3#101011yescharacteristic
335C2×D3—34no—
336C2×D3—62no—
337C2×D3—62no—
338C2×D3—62no—
339C2×D3—62no—
340C2×D3—62no—
341C2×D3—62no—
342C3×C4—24no—
343C3×C4—42no—
344C3×C4—41no—
345C3×C4—41no—
346C3×C4D3×C4⋊C414yes—
347Dic3—34no—
348Dic3—64no—
349Dic3—122no—
350Dic3—121no—
351Dic3—121no—
352C9#231711yescharacteristic, complemented, Sylow
353C23—92no—
354C23—92no—
355C23—92no—
356C23—181no—
357C23—181no—
358C23—181no—
359C23—181no—
360C23C23×D911yescharacteristic
361C2×C4—22no—
362C2×C4—22no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—22no—
366C2×C4—21no—
367C2×C4—22no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—22no—
371C2×C4—21no—
372C2×C4—92no—
373C2×C4—92no—
374C2×C4—92no—
375C2×C4—916no—
376C2×C4—94no—
377C2×C4—182no—
378C2×C4—182no—
379C2×C4—181no—
380C2×C4—181no—
381C2×C4—182no—
382C2×C4—181no—
383C2×C4—182no—
384C2×C4—181no—
385C2×C4—181no—
386C2×C4—182no—
387C2×C4—181no—
388C2×C4—368no—
389C2×C4C2×C4×D914yes—
390C2×C4C2×C4×D912yes—
391C2×C4D4×D912yes—
392C2×C4Q8×D912yes—
393C2×C3C2×D3×C4⋊C411yescharacteristic
394C2×C3#554611yescharacteristic
395C2×C3#557411yescharacteristic
396C2×C3#560711yescharacteristic
397C2×C3#562811yescharacteristic
398C2×C3#568911yescharacteristic
399C2×C3#572911yescharacteristic
400D3—64no—
401C22—94no—
402C22—182no—
403C22—182no—
404C22—182no—
405C22—182no—
406C22—182no—
407C22—182no—
408C22C22×C4×D911yescharacteristic
409C22C2×D4×D911yescharacteristic
410C22#6371011yescharacteristic
411C22C2×Q8×D911yescharacteristic
412C22#6371311yescharacteristic
413C22#6371511yescharacteristic
414C22#6371611yescharacteristic
415C4—24no—
416C4—42no—
417C4—41no—
418C4—41no—
419C4—94no—
420C4—184no—
421C4—362no—
422C4—361no—
423C4—361no—
424C4C4⋊C4×D914yes—
425C3#7596811yescharacteristic
426C2—184no—
427C2C2×C4⋊C4×D911yescharacteristic
428C2#1058964811yescharacteristic
429C2#1058967611yescharacteristic
430C2#1058970911yescharacteristic
431C2#1058973011yescharacteristic
432C2#1058979111yescharacteristic
433C2#1058983111yescharacteristic
subgroupG/H
centerC23C23×D9
commutatorC22×C9C23×C4
Frattini, socleC23×C3C23×D3
FittingC9×#389C2
prime radicalC23×D9C23
cosocleC23×C9C24
hypercenter#389D9
hypocenterC9#2317
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
4. C9×#389C2semidirect
6. #10588664C2semidirect
7. #10588655C2semidirect
8. #10588652C2semidirect
9. #10588608C2semidirect
11. #10588330C2semidirect
32. #63454C4semidirect
69. C9×C4⋊C4C2×C4semidirect
76. C4⋊Dic9C2×C4semidirect
83. C4×Dic9C2×C4semidirect
150. C4×D9C4⋊C4semidirect
157. #389D9semidirect
321. C4⋊C4C4×D9semidirect
352. C9#2317semidirect

Maximal subgroups

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

subgroupindex
C2×#634542
C2×C4⋊C4×D92
C2×#634342
C9×#3892
#105886692
#105886642
#105886552
#105886522
#105886082
#105883482
#105883302
#759683