Finite Group Databasebeta

← #11803456

Subgroups — #11803456

Order 1152.

834 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63459C211yesmaximal, characteristic
2C2×#63434C211yesmaximal, characteristic
3C2×C4×Dic18C211yesmaximal, characteristic, complemented
4C4×C9×C4⋊C4C211yesmaximal, characteristic, complemented
5#10588667C211yesmaximal, characteristic
6#10588664C211yesmaximal, characteristic, complemented
7#10588653C211yesmaximal, characteristic, complemented
8#10588620C212yesmaximal
9#10588608C212yesmaximal, complemented
10#10588350C212yesmaximal
11#10588333C212yesmaximal, complemented
12#73762—31nomaximal
13C22×C4×D9C2211yescharacteristic
14C22×Dic18C2211yescharacteristic
15C2×C9×C4⋊C4C2211yescharacteristic
16C2×C9×C4⋊C4C2211yescharacteristic
17C2×C42×C9C2212yes—
18C2×C42×C9C2211yescharacteristic
19C2×(C2×D9)⋊C4C2211yescharacteristic
20C2×(C2×D9)⋊C4C2211yescharacteristic
21C2×(C2×D9)⋊C4C2212yes—
22C2×(C2×D9)⋊C4C2212yes—
23C2×C4⋊Dic9C2211yescharacteristic
24C2×C4⋊Dic9C2212yes—
25C2×C4⋊Dic9C2212yes—
26C2×Dic9⋊C4C2212yes—
27C2×Dic9⋊C4C2211yescharacteristic
28C2×Dic9⋊C4C2211yescharacteristic
29C2×C4×Dic9C2212yes—
30C2×C4×Dic9C2211yescharacteristic
31#63459C418yescomplemented
32#63434—24no—
33C4×Dic18—24no—
34C9×#95C2212yes—
35C9⋊#95C2212yes—
36C9⋊#95C2212yes—
37C9⋊#95C2212yes—
38C9⋊#95C2212yes—
39C2×#897—31no—
40C2×#872—31no—
41C2×C4×Dic6—31no—
42C3×C4×C4⋊C4D311yescharacteristic
43#4987—31no—
44#4984—31no—
45#4973—31no—
46#4940—32no—
47#4928—32no—
48#4670—32no—
49#4653—32no—
50C23×D9C2311yescharacteristic
51C22×C4×C9C2312yes—
52C22×C4×C9C2312yes—
53C22×C4×C9C2311yescharacteristic
54C22×C4×C9C2311yescharacteristic
55C22×C4×C9C2311yescharacteristic
56C22×Dic9C2311yescharacteristic
57C22×Dic9C2312yes—
58C22×Dic9C2311yescharacteristic
59C22×Dic9C2312yes—
60C22×Dic9C2311yescharacteristic
61C2×C4×D9—22no—
62C2×C4×D9—22no—
63C2×C4×D9C2×C414yes—
64C2×Dic18—22no—
65C2×Dic18—22no—
66C2×Dic18C2×C414yes—
67C9×C4⋊C4—22no—
68C9×C4⋊C4C2×C414yes—
69C42×C9—42no—
70C42×C9D414yes—
71(C2×D9)⋊C4—22no—
72(C2×D9)⋊C4—22no—
73(C2×D9)⋊C4—42no—
74(C2×D9)⋊C4C2×C418yes—
75C4⋊Dic9—22no—
76C4⋊Dic9—42no—
77C4⋊Dic9C2×C418yes—
78Dic9⋊C4—24no—
79Dic9⋊C4—22no—
80Dic9⋊C4—22no—
81C4×Dic9—24no—
82C4×Dic9—22no—
83#2323—91noSylow
84C22×C4×D3—31no—
85C22×Dic6—31no—
86C2×C3×C4⋊C4C2×D311yescharacteristic
87C2×C3×C4⋊C4C2×D311yescharacteristic
88C2×C3×C42C2×D312yes—
89C2×C3×C42C2×D311yescharacteristic
90C2×(C2×D3)⋊C4—32no—
91C2×(C2×D3)⋊C4—31no—
92C2×(C2×D3)⋊C4—31no—
93C2×(C2×D3)⋊C4—32no—
94C2×C4⋊Dic3—32no—
95C2×C4⋊Dic3—31no—
96C2×C4⋊Dic3—32no—
97C2×Dic3⋊C4—31no—
98C2×Dic3⋊C4—31no—
99C2×Dic3⋊C4—32no—
100C2×C4×Dic3—32no—
101C2×C4×Dic3—31no—
102#897—38no—
103#872—64no—
104C4×Dic6—64no—
105C3×#95C2×D312yes—
106C3⋊#95—32no—
107C3⋊#95—32no—
108C3⋊#95—32no—
109C3⋊#95—32no—
110C23×C9C2411yescharacteristic
111C22×D9—21no—
112C22×D9—21no—
113C22×D9—21no—
114C22×D9—21no—
115C22×D9—21no—
116C22×D9—21no—
117C22×D9C22×C412yes—
118C2×C4×C9—22no—
119C2×C4×C9—21no—
120C2×C4×C9—21no—
121C2×C4×C9—22no—
122C2×C4×C9—21no—
123C2×C4×C9—21no—
124C2×C4×C9—22no—
125C2×C4×C9—22no—
126C2×C4×C9—22no—
127C2×C4×C9C22×C414yes—
128C2×C4×C9C22×C412yes—
129C2×C4×C9C2×D412yes—
130C2×C4×C9C2×D412yes—
131C2×C4×C9C2×D412yes—
132C2×C4×C9#4112yes—
133C2×Dic9—22no—
134C2×Dic9—21no—
135C2×Dic9—22no—
136C2×Dic9—21no—
137C2×Dic9—22no—
138C2×Dic9—21no—
139C2×Dic9—21no—
140C2×Dic9—21no—
141C2×Dic9—22no—
142C2×Dic9—22no—
143C2×Dic9—21no—
144C2×Dic9—21no—
145C2×Dic9—21no—
146C2×Dic9C22×C412yes—
147C2×Dic9C22×C414yes—
148C4×D9—28no—
149Dic18—28no—
150C2×C22⋊Q8—91no—
151C2×C4×Q8—91no—
152C2×#117—91no—
153#391—91no—
154#389—91no—
155#389—92no—
156#388—92no—
157#388—92no—
158#387—92no—
159#380—91no—
160C4×C4⋊C4D911yescharacteristic, complemented
161C23×D3—31no—
162C22×C3×C4C22×D312yes—
163C22×C3×C4C22×D312yes—
164C22×C3×C4C22×D311yescharacteristic
165C22×C3×C4C22×D311yescharacteristic
166C22×C3×C4C22×D311yescharacteristic
167C22×Dic3—32no—
168C22×Dic3—31no—
169C22×Dic3—31no—
170C22×Dic3—32no—
171C22×Dic3—31no—
172C2×C4×D3—34no—
173C2×C4×D3—62no—
174C2×C4×D3—62no—
175C2×Dic6—34no—
176C2×Dic6—62no—
177C2×Dic6—62no—
178C3×C4⋊C4—22no—
179C3×C4⋊C4C4×D314yes—
180C3×C42—42no—
181C3×C42D1214yes—
182(C2×D3)⋊C4—38no—
183(C2×D3)⋊C4—62no—
184(C2×D3)⋊C4—62no—
185(C2×D3)⋊C4—122no—
186C4⋊Dic3—38no—
187C4⋊Dic3—62no—
188C4⋊Dic3—122no—
189Dic3⋊C4—64no—
190Dic3⋊C4—62no—
191Dic3⋊C4—62no—
192C4×Dic3—64no—
193C4×Dic3—62no—
194C22×C9C23×C411yescharacteristic
195C22×C9C22×D411yescharacteristic
196C22×C9C2×#4111yescharacteristic
197C22×C9H(5,𝔽2)11yescharacteristic
198C22×C92−1+411yescharacteristic
199C22×C92−1+411yescharacteristic
200C22×C92−1+411yescharacteristic
201C2×D9—22no—
202C2×D9—22no—
203C2×D9—22no—
204C2×D9—41no—
205C2×D9—41no—
206C2×D9—41no—
207C2×D9—41no—
208C4×C9—24no—
209C4×C9—22no—
210C4×C9—22no—
211C4×C9—42no—
212C4×C9C4×D414yes—
213Dic9—24no—
214Dic9—22no—
215Dic9—41no—
216Dic9—42no—
217Dic9—41no—
218C22×Q8—91no—
219C23×C4—91no—
220C22⋊Q8—98no—
221C4×Q8—184no—
222#117—184no—
223C2×C4⋊C4—92no—
224C2×C4⋊C4—91no—
225C2×C4⋊C4—91no—
226C2×C4⋊C4—91no—
227C2×C4⋊C4—92no—
228C2×C4⋊C4—92no—
229C2×C4⋊C4C2×D911yescharacteristic
230C2×C4⋊C4C2×D911yescharacteristic
231C2×C22⋊C4—92no—
232C2×C22⋊C4—91no—
233C2×C22⋊C4—91no—
234C2×C22⋊C4—92no—
235C2×C42—91no—
236C2×C42—92no—
237C2×C42C2×D912yes—
238C2×C42C2×D911yescharacteristic
239#95—92no—
240#95—92no—
241#95—92no—
242#95—92no—
243#95C2×D912yes—
244C23×C3C23×D311yescharacteristic
245C22×D3—32no—
246C22×D3—61no—
247C22×D3—61no—
248C22×D3—61no—
249C22×D3—61no—
250C22×D3—61no—
251C22×D3—61no—
252C2×C3×C4—22no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—22no—
258C2×C3×C4—22no—
259C2×C3×C4—22no—
260C2×C3×C4—22no—
261C2×C3×C4C2×C4×D314yes—
262C2×C3×C4C2×C4×D312yes—
263C2×C3×C4C2×D1212yes—
264C2×C3×C4C2×D1212yes—
265C2×C3×C4C2×D1212yes—
266C2×C3×C4#23512yes—
267C2×Dic3—32no—
268C2×Dic3—34no—
269C2×Dic3—62no—
270C2×Dic3—61no—
271C2×Dic3—62no—
272C2×Dic3—61no—
273C2×Dic3—62no—
274C2×Dic3—61no—
275C2×Dic3—61no—
276C2×Dic3—61no—
277C2×Dic3—62no—
278C2×Dic3—62no—
279C2×Dic3—61no—
280C2×Dic3—61no—
281C2×Dic3—61no—
282C4×D3—68no—
283Dic6—68no—
284C2×C9C2×C4×D411yescharacteristic
285C2×C9#51911yescharacteristic
286C2×C9#52011yescharacteristic
287C2×C9#53611yescharacteristic
288C2×C9#53711yescharacteristic
289C2×C9#54111yescharacteristic
290C2×C9#54211yescharacteristic
291D9—42no—
292C24—91no—
293C2×Q8—94no—
294C2×Q8—182no—
295C2×Q8—182no—
296C22×C4—92no—
297C22×C4—91no—
298C22×C4—94no—
299C22×C4—91no—
300C22×C4—91no—
301C22×C4—92no—
302C22×C4—182no—
303C22×C4—182no—
304C22×C4C22×D912yes—
305C22×C4C22×D912yes—
306C22×C4C22×D911yescharacteristic
307C22×C4C22×D911yescharacteristic
308C22×C4C22×D911yescharacteristic
309C4⋊C4—22no—
310C4⋊C4—98no—
311C4⋊C4—182no—
312C4⋊C4—182no—
313C4⋊C4—184no—
314C4⋊C4—182no—
315C4⋊C4—362no—
316C4⋊C4C4×D914yes—
317C22⋊C4—98no—
318C22⋊C4—182no—
319C22⋊C4—182no—
320C22⋊C4—362no—
321C42—42no—
322C42—182no—
323C42—184no—
324C42D3614yes—
325C22×C3C22×C4×D311yescharacteristic
326C22×C3C22×D1211yescharacteristic
327C22×C3C2×#23511yescharacteristic
328C22×C3#100411yescharacteristic
329C22×C3#100711yescharacteristic
330C22×C3#101011yescharacteristic
331C22×C3#101011yescharacteristic
332C2×D3—62no—
333C2×D3—62no—
334C2×D3—62no—
335C2×D3—121no—
336C2×D3—121no—
337C2×D3—121no—
338C2×D3—121no—
339C3×C4—22no—
340C3×C4—22no—
341C3×C4—24no—
342C3×C4—42no—
343C3×C4C4×D1214yes—
344Dic3—64no—
345Dic3—62no—
346Dic3—122no—
347Dic3—121no—
348Dic3—121no—
349C9#232311yescharacteristic, complemented, Sylow
350C23—92no—
351C23—181no—
352C23—181no—
353C23—181no—
354C23—181no—
355C23—181no—
356C23—181no—
357C23C23×D911yescharacteristic
358Q8—188no—
359C2×C4—21no—
360C2×C4—22no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—22no—
365C2×C4—22no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—94no—
369C2×C4—92no—
370C2×C4—182no—
371C2×C4—181no—
372C2×C4—181no—
373C2×C4—182no—
374C2×C4—188no—
375C2×C4—181no—
376C2×C4—181no—
377C2×C4—182no—
378C2×C4—182no—
379C2×C4—181no—
380C2×C4—181no—
381C2×C4—182no—
382C2×C4—181no—
383C2×C4—181no—
384C2×C4C2×C4×D914yes—
385C2×C4C2×C4×D912yes—
386C2×C4C2×D3612yes—
387C2×C4C2×D3612yes—
388C2×C4C2×D3612yes—
389C2×C4#369712yes—
390C2×C3C2×C4×D1211yescharacteristic
391C2×C3#551011yescharacteristic
392C2×C3#552611yescharacteristic
393C2×C3#554611yescharacteristic
394C2×C3#556111yescharacteristic
395C2×C3#557211yescharacteristic
396C2×C3#558311yescharacteristic
397D3—122no—
398C22—182no—
399C22—182no—
400C22—182no—
401C22—361no—
402C22—361no—
403C22—361no—
404C22—361no—
405C22C22×C4×D911yescharacteristic
406C22C22×D3611yescharacteristic
407C22C2×#369711yescharacteristic
408C22#6371011yescharacteristic
409C22#6371311yescharacteristic
410C22#6371611yescharacteristic
411C22#6371611yescharacteristic
412C4—22no—
413C4—22no—
414C4—24no—
415C4—42no—
416C4—182no—
417C4—184no—
418C4—361no—
419C4—362no—
420C4—361no—
421C4C4×D3614yes—
422C3#7376211yescharacteristic
423C2—362no—
424C2C2×C4×D3611yescharacteristic
425C2#1058961211yescharacteristic
426C2#1058962811yescharacteristic
427C2#1058964811yescharacteristic
428C2#1058966311yescharacteristic
429C2#1058967411yescharacteristic
430C2#1058968511yescharacteristic
subgroupG/H
centerC23C23×D9
commutatorC22×C9C23×C4
Frattini, socleC23×C3C23×D3
FittingC4×C9×C4⋊C4C2
prime radicalC23×D9C23
cosocleC23×C9C24
hypercenterC4×C4⋊C4D9
hypocenterC9#2323
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C23 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×C4×Dic18C2semidirect
4. C4×C9×C4⋊C4C2semidirect
6. #10588664C2semidirect
7. #10588653C2semidirect
9. #10588608C2semidirect
11. #10588333C2semidirect
31. #63459C4semidirect
160. C4×C4⋊C4D9semidirect
349. C9#2323semidirect

Maximal subgroups

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

subgroupindex
C2×#634592
C2×#634342
C2×C4×Dic182
C4×C9×C4⋊C42
#105886672
#105886642
#105886532
#105886202
#105886082
#105883502
#105883332
#737623