Finite Group Databasebeta

← #11803435

Subgroups — #11803435

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×C4×Q8×C9C211yesmaximal, characteristic, complemented
2C2×#63508C211yesmaximal, characteristic
3C2×#63434C211yesmaximal, characteristic
4#10588909C211yesmaximal, characteristic, complemented
5#10588670C212yesmaximal
6#10588667C211yesmaximal, characteristic
7#10588656C212yesmaximal, complemented
8#10588652C211yesmaximal, characteristic, complemented
9#10588620C212yesmaximal
10C4×C4⋊Dic9C211yesmaximal, characteristic, complemented
11#10588613C212yesmaximal, complemented
12#82488—31nomaximal
13C22×Q8×C9C2211yescharacteristic
14C22×C4×D9C2211yescharacteristic
15C4×Q8×C9—24no—
16C2×C9×C4⋊C4C2211yescharacteristic
17C2×C9×C4⋊C4C2212yes—
18C2×C42×C9C2212yes—
19C2×C42×C9C2211yescharacteristic
20#63508C418yescomplemented
21C2×(C2×D9)⋊C4C2211yescharacteristic
22C2×(C2×D9)⋊C4C2211yescharacteristic
23C2×(C2×D9)⋊C4C2212yes—
24C2×(C2×D9)⋊C4C2212yes—
25C2×C4⋊Dic9C2211yescharacteristic
26C2×C4⋊Dic9C2211yescharacteristic
27C2×Dic9⋊C4C2211yescharacteristic
28C2×Dic9⋊C4C2211yescharacteristic
29C2×Dic9⋊C4C2212yes—
30C2×Dic9⋊C4C2212yes—
31C2×C4×Dic9C2211yescharacteristic
32C2×C4×Dic9C2212yes—
33#63434—24no—
34C9⋊#95C2212yes—
35C9⋊#95C2212yes—
36C9⋊#95C2212yes—
37C9⋊#95C2212yes—
38C9⋊#95C2212yes—
39C2×C3×C4×Q8D311yescharacteristic
40C2×#946—31no—
41C2×#872—31no—
42#5229—31no—
43#4990—32no—
44#4987—31no—
45#4976—32no—
46#4972—31no—
47#4940—32no—
48C4×C4⋊Dic3—31no—
49#4933—32no—
50C23×D9C2311yescharacteristic
51C2×Q8×C9—22no—
52C2×Q8×C9—22no—
53C2×Q8×C9C2×C414yes—
54C22×C4×C9C2312yes—
55C22×C4×C9C2312yes—
56C22×C4×C9C2311yescharacteristic
57C22×C4×C9C2311yescharacteristic
58C22×C4×C9C2311yescharacteristic
59C22×Dic9C2311yescharacteristic
60C22×Dic9C2312yes—
61C22×Dic9C2311yescharacteristic
62C22×Dic9C2312yes—
63C22×Dic9C2311yescharacteristic
64C2×C4×D9—22no—
65C2×C4×D9—22no—
66C2×C4×D9C2×C414yes—
67C9×C4⋊C4—24no—
68C9×C4⋊C4—22no—
69C42×C9—24no—
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⋊Dic9C2×C414yes—
77Dic9⋊C4—22no—
78Dic9⋊C4—22no—
79Dic9⋊C4—42no—
80Dic9⋊C4C2×C418yes—
81C4×Dic9—22no—
82C4×Dic9—42no—
83#2323—91noSylow
84C22×C3×Q8C2×D311yescharacteristic
85C22×C4×D3—31no—
86C3×C4×Q8—24no—
87C2×C3×C4⋊C4C2×D311yescharacteristic
88C2×C3×C4⋊C4C2×D312yes—
89C2×C3×C42C2×D312yes—
90C2×C3×C42C2×D311yescharacteristic
91#946—38no—
92C2×(C2×D3)⋊C4—32no—
93C2×(C2×D3)⋊C4—31no—
94C2×(C2×D3)⋊C4—31no—
95C2×(C2×D3)⋊C4—32no—
96C2×C4⋊Dic3—31no—
97C2×C4⋊Dic3—31no—
98C2×Dic3⋊C4—32no—
99C2×Dic3⋊C4—31no—
100C2×Dic3⋊C4—31no—
101C2×Dic3⋊C4—32no—
102C2×C4×Dic3—31no—
103C2×C4×Dic3—32no—
104#872—64no—
105C3⋊#95—32no—
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—
118Q8×C9—28no—
119C2×C4×C9—22no—
120C2×C4×C9—22no—
121C2×C4×C9—21no—
122C2×C4×C9—21no—
123C2×C4×C9—21no—
124C2×C4×C9—21no—
125C2×C4×C9—22no—
126C2×C4×C9—22no—
127C2×C4×C9—22no—
128C2×C4×C9C22×C414yes—
129C2×C4×C9C22×C412yes—
130C2×C4×C9C2×D412yes—
131C2×C4×C9C2×D412yes—
132C2×C4×C9C2×D412yes—
133C2×C4×C9#4112yes—
134C2×Dic9—21no—
135C2×Dic9—21no—
136C2×Dic9—22no—
137C2×Dic9—22no—
138C2×Dic9—21no—
139C2×Dic9—21no—
140C2×Dic9—22no—
141C2×Dic9—22no—
142C2×Dic9—21no—
143C2×Dic9—21no—
144C2×Dic9—21no—
145C2×Dic9—22no—
146C2×Dic9—21no—
147C2×Dic9C22×C412yes—
148C2×Dic9C22×C414yes—
149C4×D9—28no—
150C2×C22⋊Q8—91no—
151C2×C4×Q8D911yescharacteristic, complemented
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⋊C4—91no—
161C23×D3—31no—
162C2×C3×Q8—22no—
163C2×C3×Q8—22no—
164C2×C3×Q8C4×D314yes—
165C22×C3×C4C22×D312yes—
166C22×C3×C4C22×D312yes—
167C22×C3×C4C22×D311yescharacteristic
168C22×C3×C4C22×D311yescharacteristic
169C22×C3×C4C22×D311yescharacteristic
170C22×Dic3—32no—
171C22×Dic3—31no—
172C22×Dic3—31no—
173C22×Dic3—32no—
174C22×Dic3—31no—
175C2×C4×D3—34no—
176C2×C4×D3—62no—
177C2×C4×D3—62no—
178C3×C4⋊C4—24no—
179C3×C4⋊C4—22no—
180C3×C42—24no—
181C3×C42#6714yes—
182(C2×D3)⋊C4—38no—
183(C2×D3)⋊C4—62no—
184(C2×D3)⋊C4—62no—
185(C2×D3)⋊C4—122no—
186C4⋊Dic3—34no—
187C4⋊Dic3—62no—
188Dic3⋊C4—38no—
189Dic3⋊C4—62no—
190Dic3⋊C4—62no—
191Dic3⋊C4—122no—
192C4×Dic3—62no—
193C4×Dic3—122no—
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—22no—
214Dic9—24no—
215Dic9—41no—
216Dic9—41no—
217Dic9—42no—
218C22×Q8C2×D911yescharacteristic
219C23×C4—91no—
220C22⋊Q8—98no—
221C4×Q8—24no—
222#117—184no—
223C2×C4⋊C4—91no—
224C2×C4⋊C4—92no—
225C2×C4⋊C4—91no—
226C2×C4⋊C4—91no—
227C2×C4⋊C4—91no—
228C2×C4⋊C4—92no—
229C2×C4⋊C4C2×D911yescharacteristic
230C2×C4⋊C4C2×D912yes—
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#95—92no—
244C23×C3C23×D311yescharacteristic
245C22×D3—32no—
246C22×D3—61no—
247C22×D3—61no—
248C22×D3—61no—
249C22×D3—61no—
250C22×D3—61no—
251C22×D3—61no—
252C3×Q8—28no—
253C2×C3×C4—22no—
254C2×C3×C4—21no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4—22no—
259C2×C3×C4—22no—
260C2×C3×C4—22no—
261C2×C3×C4—22no—
262C2×C3×C4C2×C4×D314yes—
263C2×C3×C4C2×C4×D312yes—
264C2×C3×C4#23512yes—
265C2×C3×C4C2×#6712yes—
266C2×C3×C4C2×#6712yes—
267C2×C3×C4C2×#6712yes—
268C2×Dic3—32no—
269C2×Dic3—34no—
270C2×Dic3—61no—
271C2×Dic3—62no—
272C2×Dic3—62no—
273C2×Dic3—61no—
274C2×Dic3—62no—
275C2×Dic3—61no—
276C2×Dic3—61no—
277C2×Dic3—62no—
278C2×Dic3—62no—
279C2×Dic3—61no—
280C2×Dic3—61no—
281C2×Dic3—61no—
282C2×Dic3—61no—
283C4×D3—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—22no—
294C2×Q8—22no—
295C2×Q8C4×D914yes—
296C22×C4—92no—
297C22×C4—91no—
298C22×C4—94no—
299C22×C4—92no—
300C22×C4—91no—
301C22×C4—91no—
302C22×C4—182no—
303C22×C4—182no—
304C22×C4C22×D912yes—
305C22×C4C22×D912yes—
306C22×C4C22×D911yescharacteristic
307C22×C4C22×D911yescharacteristic
308C22×C4C22×D911yescharacteristic
309C4⋊C4—24no—
310C4⋊C4—22no—
311C4⋊C4—98no—
312C4⋊C4—94no—
313C4⋊C4—182no—
314C4⋊C4—182no—
315C4⋊C4—182no—
316C4⋊C4—362no—
317C22⋊C4—98no—
318C22⋊C4—182no—
319C22⋊C4—182no—
320C22⋊C4—362no—
321C42—24no—
322C42—182no—
323C42—362no—
324C42#61114yes—
325C22×C3C22×C4×D311yescharacteristic
326C22×C3C2×#23511yescharacteristic
327C22×C3#100711yescharacteristic
328C22×C3#100711yescharacteristic
329C22×C3#100911yescharacteristic
330C22×C3#101011yescharacteristic
331C22×C3C22×#6711yescharacteristic
332C2×D3—62no—
333C2×D3—62no—
334C2×D3—62no—
335C2×D3—121no—
336C2×D3—121no—
337C2×D3—121no—
338C2×D3—121no—
339C3×C4—24no—
340C3×C4—22no—
341C3×C4—22no—
342C3×C4—42no—
343C3×C4C4×#6714yes—
344Dic3—62no—
345Dic3—64no—
346Dic3—121no—
347Dic3—121no—
348Dic3—122no—
349C9#232311yescharacteristic, complemented, Sylow
350C23—92no—
351C23—181no—
352C23—181no—
353C23—181no—
354C23—181no—
355C23—181no—
356C23—181no—
357C23C23×D911yescharacteristic
358Q8—28no—
359C2×C4—22no—
360C2×C4—21no—
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—181no—
371C2×C4—182no—
372C2×C4—182no—
373C2×C4—181no—
374C2×C4—188no—
375C2×C4—182no—
376C2×C4—181no—
377C2×C4—181no—
378C2×C4—182no—
379C2×C4—182no—
380C2×C4—181no—
381C2×C4—181no—
382C2×C4—181no—
383C2×C4—181no—
384C2×C4C2×C4×D914yes—
385C2×C4C2×C4×D912yes—
386C2×C4#369712yes—
387C2×C4C2×#61112yes—
388C2×C4C2×#61112yes—
389C2×C4C2×#61112yes—
390C2×C3#557211yescharacteristic
391C2×C3#557411yescharacteristic
392C2×C3#558211yescharacteristic
393C2×C3#558311yescharacteristic
394C2×C3C2×C4×#6711yescharacteristic
395C2×C3#581611yescharacteristic
396C2×C3#583311yescharacteristic
397D3—122no—
398C22—182no—
399C22—182no—
400C22—182no—
401C22—361no—
402C22—361no—
403C22—361no—
404C22—361no—
405C22C22×C4×D911yescharacteristic
406C22C2×#369711yescharacteristic
407C22#6371311yescharacteristic
408C22#6371311yescharacteristic
409C22#6371511yescharacteristic
410C22#6371611yescharacteristic
411C22C22×#61111yescharacteristic
412C4—24no—
413C4—22no—
414C4—22no—
415C4—42no—
416C4—182no—
417C4—184no—
418C4—361no—
419C4—361no—
420C4—362no—
421C4C4×#61114yes—
422C3#8248811yescharacteristic
423C2—362no—
424C2#1058967411yescharacteristic
425C2#1058967611yescharacteristic
426C2#1058968411yescharacteristic
427C2#1058968511yescharacteristic
428C2C2×C4×#61111yescharacteristic
429C2#1058991811yescharacteristic
430C2#1058993511yescharacteristic
subgroupG/H
centerC23C23×D9
commutatorC22×C9C23×C4
Frattini, socleC23×C3C23×D3
FittingC2×C4×Q8×C9C2
prime radicalC23×D9C23
cosocleC23×C9C24
hypercenterC2×C4×Q8D9
hypocenterC9#2323
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C23 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C4×Q8×C9C2semidirect
4. #10588909C2semidirect
7. #10588656C2semidirect
8. #10588652C2semidirect
10. C4×C4⋊Dic9C2semidirect
11. #10588613C2semidirect
20. #63508C4semidirect
151. C2×C4×Q8D9semidirect
349. C9#2323semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Q8×C92
C2×#635082
C2×#634342
#105889092
#105886702
#105886672
#105886562
#105886522
#105886202
C4×C4⋊Dic92
#105886132
#824883