Finite Group Databasebeta

← #11805420

Subgroups — #11805420

Order 1152.

1164 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63455C211yesmaximal, characteristic
2C2×#63455C211yesmaximal, characteristic
3C2×C4⋊C4×D9C212yesmaximal, complemented
4C2×C4×D36C211yesmaximal, characteristic
5C9×#389C211yesmaximal, characteristic, complemented
6#10588669C212yesmaximal, complemented
7#10588664C211yesmaximal, characteristic, complemented
8#10588655C211yesmaximal, characteristic, complemented
9C4×Dic9⋊C4C211yesmaximal, characteristic, complemented
10#10588348C212yesmaximal, complemented
11#10588347C212yesmaximal, complemented
12#76202—31nomaximal
13C22×D36C2211yescharacteristic
14C22×C4×D9C2212yes—
15C22×C4×D9C2212yes—
16C22×C4×D9C2212yes—
17C2×C9×C4⋊C4C2212yes—
18C2×C9×C4⋊C4C2211yescharacteristic
19C2×C9×C4⋊C4C2211yescharacteristic
20C2×C42×C9C2211yescharacteristic
21C2×(C2×D9)⋊C4C2212yes—
22C2×(C2×D9)⋊C4C2212yes—
23C2×(C2×D9)⋊C4C2212yes—
24C2×C4⋊Dic9C2211yescharacteristic
25C2×C4⋊Dic9C2212yes—
26C2×Dic9⋊C4C2212yes—
27C2×Dic9⋊C4C2211yescharacteristic
28C2×Dic9⋊C4C2212yes—
29C2×Dic9⋊C4C2211yescharacteristic
30C2×C4×Dic9C2211yescharacteristic
31C2×C4×Dic9C2211yescharacteristic
32#63455—24no—
33#63455C418yescomplemented
34C4⋊C4×D9—28no—
35C4×D36—24no—
36C9×#95C2212yes—
37C9⋊#95C2212yes—
38C9⋊#95C2211yescharacteristic
39C9⋊#95C2211yescharacteristic
40C2×#893—31no—
41C2×#893—31no—
42C2×D3×C4⋊C4—32no—
43C2×C4×D12—31no—
44C3×#389D311yescharacteristic
45#4989—32no—
46#4984—31no—
47#4975—31no—
48C4×Dic3⋊C4—31no—
49#4668—32no—
50#4667—32no—
51C23×D9C2312yes—
52C22×C4×C9C2311yescharacteristic
53C22×C4×C9C2312yes—
54C22×C4×C9C2312yes—
55C22×C4×C9C2311yescharacteristic
56C22×C4×C9C2311yescharacteristic
57C22×Dic9C2311yescharacteristic
58C22×Dic9C2312yes—
59C22×Dic9C2311yescharacteristic
60C22×Dic9C2311yescharacteristic
61C22×Dic9C2311yescharacteristic
62C2×D36C2×C414yes—
63C2×D36D414yes—
64C2×D36Q814yes—
65C2×C4×D9—24no—
66C2×C4×D9—24no—
67C2×C4×D9—24no—
68C2×C4×D9—24no—
69C2×C4×D9—24no—
70C2×C4×D9—24no—
71C2×C4×D9—42no—
72C2×C4×D9—42no—
73C2×C4×D9C2×C418yescomplemented
74C9×C4⋊C4—24no—
75C9×C4⋊C4—22no—
76C9×C4⋊C4C2×C414yescomplemented
77C42×C9—22no—
78(C2×D9)⋊C4—24no—
79(C2×D9)⋊C4—24no—
80(C2×D9)⋊C4C2×C418yescomplemented
81C4⋊Dic9—22no—
82C4⋊Dic9—24no—
83Dic9⋊C4—24no—
84Dic9⋊C4—22no—
85Dic9⋊C4—42no—
86Dic9⋊C4D414yescomplemented
87C4×Dic9—22no—
88C4×Dic9C2×C414yescomplemented
89D4×C4⋊C4—91noSylow
90C22×D12—31no—
91C22×C4×D3—32no—
92C22×C4×D3—32no—
93C22×C4×D3—32no—
94C2×C3×C4⋊C4C2×D311yescharacteristic
95C2×C3×C4⋊C4C2×D312yes—
96C2×C3×C4⋊C4C2×D311yescharacteristic
97C2×C3×C42C2×D311yescharacteristic
98C2×(C2×D3)⋊C4—32no—
99C2×(C2×D3)⋊C4—32no—
100C2×(C2×D3)⋊C4—32no—
101C2×C4⋊Dic3—32no—
102C2×C4⋊Dic3—31no—
103C2×Dic3⋊C4—31no—
104C2×Dic3⋊C4—31no—
105C2×Dic3⋊C4—32no—
106C2×Dic3⋊C4—32no—
107C2×C4×Dic3—31no—
108C2×C4×Dic3—31no—
109#893—38no—
110#893—64no—
111D3×C4⋊C4—68no—
112C4×D12—64no—
113C3×#95C2×D312yes—
114C3⋊#95—32no—
115C3⋊#95—31no—
116C3⋊#95—31no—
117C23×C9C2411yescharacteristic
118C22×D9—22no—
119C22×D9—22no—
120C22×D9—22no—
121C22×D9—22no—
122C22×D9C22×C414yes—
123C22×D9C2×D414yes—
124C22×D9C2×Q814yes—
125C2×C4×C9—22no—
126C2×C4×C9—21no—
127C2×C4×C9—22no—
128C2×C4×C9—21no—
129C2×C4×C9—22no—
130C2×C4×C9—21no—
131C2×C4×C9—22no—
132C2×C4×C9—21no—
133C2×C4×C9—22no—
134C2×C4×C9—21no—
135C2×C4×C9C22×C414yes—
136C2×C4×C9C22×C412yes—
137C2×C4×C9C2×D412yes—
138C2×C4×C9C2×D412yes—
139C2×C4×C9C2×Q812yes—
140C2×Dic9—21no—
141C2×Dic9—21no—
142C2×Dic9—21no—
143C2×Dic9—21no—
144C2×Dic9—21no—
145C2×Dic9—22no—
146C2×Dic9—22no—
147C2×Dic9—21no—
148C2×Dic9—22no—
149C2×Dic9—21no—
150C2×Dic9C22×C412yes—
151C2×Dic9C22×C412yes—
152C2×Dic9C2×D412yes—
153C2×Dic9C2×D412yes—
154C2×Dic9#4112yes—
155D36C4⋊C4116yescomplemented
156C4×D9—216no—
157C4×D9—48no—
158C4×D9—48no—
159C2×C4×D4—91no—
160C2×C4×D4—91no—
161C2×C4×D4—91no—
162C22×C4⋊C4—92no—
163#389—91no—
164#389D911yescharacteristic, complemented
165#385—92no—
166#385—92no—
167#384—91no—
168#380—92no—
169C4×C4⋊C4—91no—
170C23×D3—32no—
171C22×C3×C4C22×D311yescharacteristic
172C22×C3×C4C22×D312yes—
173C22×C3×C4C22×D312yes—
174C22×C3×C4C22×D311yescharacteristic
175C22×C3×C4C22×D311yescharacteristic
176C22×Dic3—31no—
177C22×Dic3—31no—
178C22×Dic3—31no—
179C22×Dic3—31no—
180C22×Dic3—32no—
181C2×D12—34no—
182C2×D12—34no—
183C2×D12—34no—
184C2×C4×D3—38no—
185C2×C4×D3—64no—
186C2×C4×D3—64no—
187C2×C4×D3—64no—
188C2×C4×D3—64no—
189C2×C4×D3—64no—
190C2×C4×D3—64no—
191C2×C4×D3—122no—
192C2×C4×D3—122no—
193C3×C4⋊C4—24no—
194C3×C4⋊C4—22no—
195C3×C4⋊C4C4×D314yes—
196C3×C42—22no—
197(C2×D3)⋊C4—38no—
198(C2×D3)⋊C4—64no—
199(C2×D3)⋊C4—64no—
200C4⋊Dic3—64no—
201C4⋊Dic3—62no—
202Dic3⋊C4—34no—
203Dic3⋊C4—64no—
204Dic3⋊C4—62no—
205Dic3⋊C4—122no—
206C4×Dic3—34no—
207C4×Dic3—62no—
208C22×C9C23×C411yescharacteristic
209C22×C9C22×D411yescharacteristic
210C22×C9C22×D411yescharacteristic
211C22×C9C22×Q811yescharacteristic
212C22×C9C2×#4111yescharacteristic
213C22×C9H(5,𝔽2)11yescharacteristic
214C22×C92−1+411yescharacteristic
215C2×D9—24no—
216C2×D9—24no—
217C2×D9—24no—
218C2×D9—24no—
219C2×D9—24no—
220C2×D9—24no—
221C2×D9C2×C4⋊C418yescomplemented
222C4×C9—24no—
223C4×C9—22no—
224C4×C9—42no—
225C4×C9—41no—
226C4×C9C2×C4⋊C414yescomplemented
227Dic9—22no—
228Dic9—22no—
229Dic9—42no—
230Dic9—41no—
231Dic9C4×D414yescomplemented
232C22×D4—91no—
233C23×C4—92no—
234C23×C4—92no—
235C23×C4—92no—
236C4×D4—98no—
237C4×D4—184no—
238C4×D4—184no—
239C2×C4⋊C4—91no—
240C2×C4⋊C4—92no—
241C2×C4⋊C4—92no—
242C2×C4⋊C4—91no—
243C2×C4⋊C4—91no—
244C2×C4⋊C4—92no—
245C2×C4⋊C4—188no—
246C2×C4⋊C4C2×D912yes—
247C2×C4⋊C4C2×D911yescharacteristic
248C2×C4⋊C4C2×D911yescharacteristic
249C2×C22⋊C4—92no—
250C2×C22⋊C4—92no—
251C2×C22⋊C4—92no—
252C2×C42—91no—
253C2×C42—91no—
254C2×C42C2×D911yescharacteristic
255#95—91no—
256#95—91no—
257#95—92no—
258#95C2×D912yes—
259C23×C3C23×D311yescharacteristic
260C22×D3—34no—
261C22×D3—34no—
262C22×D3—34no—
263C22×D3—62no—
264C22×D3—62no—
265C22×D3—62no—
266C22×D3—62no—
267C2×C3×C4—22no—
268C2×C3×C4—21no—
269C2×C3×C4—22no—
270C2×C3×C4—21no—
271C2×C3×C4—22no—
272C2×C3×C4—21no—
273C2×C3×C4—22no—
274C2×C3×C4—21no—
275C2×C3×C4—21no—
276C2×C3×C4—22no—
277C2×C3×C4C2×C4×D314yes—
278C2×C3×C4C2×C4×D312yes—
279C2×C3×C4D3×D412yes—
280C2×C3×C4D3×D412yes—
281C2×C3×C4D3×Q812yes—
282C2×Dic3—32no—
283C2×Dic3—32no—
284C2×Dic3—32no—
285C2×Dic3—32no—
286C2×Dic3—32no—
287C2×Dic3—61no—
288C2×Dic3—61no—
289C2×Dic3—61no—
290C2×Dic3—61no—
291C2×Dic3—61no—
292C2×Dic3—62no—
293C2×Dic3—62no—
294C2×Dic3—61no—
295C2×Dic3—61no—
296C2×Dic3—62no—
297D12—316no—
298C4×D3—616no—
299C4×D3—128no—
300C4×D3—128no—
301C2×C9C22×C4⋊C411yescharacteristic
302C2×C9C2×C4×D411yescharacteristic
303C2×C9#52011yescharacteristic
304C2×C9D4211yescharacteristic
305C2×C9#54711yescharacteristic
306C2×C9D4×Q811yescharacteristic
307C2×C9#55411yescharacteristic
308D9—28no—
309C24—92no—
310C2×D4—94no—
311C2×D4—94no—
312C2×D4—94no—
313C22×C4—91no—
314C22×C4—91no—
315C22×C4—91no—
316C22×C4—98no—
317C22×C4—91no—
318C22×C4—92no—
319C22×C4—184no—
320C22×C4—184no—
321C22×C4—184no—
322C22×C4—184no—
323C22×C4—184no—
324C22×C4—184no—
325C22×C4—362no—
326C22×C4—362no—
327C22×C4C22×D911yescharacteristic
328C22×C4C22×D912yes—
329C22×C4C22×D912yes—
330C22×C4C22×D911yescharacteristic
331C22×C4C22×D911yescharacteristic
332C4⋊C4—24no—
333C4⋊C4—22no—
334C4⋊C4—94no—
335C4⋊C4—184no—
336C4⋊C4—184no—
337C4⋊C4—182no—
338C4⋊C4—182no—
339C4⋊C4—362no—
340C4⋊C4C4×D914yescomplemented
341C22⋊C4—98no—
342C22⋊C4—184no—
343C22⋊C4—184no—
344C42—22no—
345C42—94no—
346C42—182no—
347C22×C3C22×C4×D311yescharacteristic
348C22×C3C2×D3×D411yescharacteristic
349C22×C3C2×D3×D411yescharacteristic
350C22×C3C2×D3×Q811yescharacteristic
351C22×C3#100711yescharacteristic
352C22×C3D3×#4111yescharacteristic
353C22×C3#100911yescharacteristic
354C2×D3—38no—
355C2×D3—64no—
356C2×D3—64no—
357C2×D3—64no—
358C2×D3—64no—
359C2×D3—64no—
360C2×D3—64no—
361C3×C4—24no—
362C3×C4—22no—
363C3×C4—42no—
364C3×C4—41no—
365C3×C4D3×C4⋊C414yes—
366Dic3—34no—
367Dic3—62no—
368Dic3—62no—
369Dic3—122no—
370Dic3—121no—
371C9D4×C4⋊C411yescharacteristic, complemented, Sylow
372C23—94no—
373C23—94no—
374C23—94no—
375C23—182no—
376C23—182no—
377C23—182no—
378C23—182no—
379C23C23×D911yescharacteristic
380D4—916no—
381C2×C4—21no—
382C2×C4—22no—
383C2×C4—22no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—22no—
387C2×C4—22no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—22no—
391C2×C4—92no—
392C2×C4—92no—
393C2×C4—92no—
394C2×C4—92no—
395C2×C4—92no—
396C2×C4—1816no—
397C2×C4—181no—
398C2×C4—181no—
399C2×C4—181no—
400C2×C4—181no—
401C2×C4—181no—
402C2×C4—182no—
403C2×C4—182no—
404C2×C4—181no—
405C2×C4—181no—
406C2×C4—182no—
407C2×C4—368no—
408C2×C4—368no—
409C2×C4C2×C4×D914yes—
410C2×C4C2×C4×D912yes—
411C2×C4D4×D912yes—
412C2×C4D4×D912yes—
413C2×C4Q8×D912yes—
414C2×C3C2×D3×C4⋊C411yescharacteristic
415C2×C3C4×D3×D411yescharacteristic
416C2×C3#557411yescharacteristic
417C2×C3#560911yescharacteristic
418C2×C3#563111yescharacteristic
419C2×C3#569011yescharacteristic
420C2×C3#572711yescharacteristic
421D3—68no—
422C22—98no—
423C22—184no—
424C22—184no—
425C22—184no—
426C22—184no—
427C22—184no—
428C22—184no—
429C22C22×C4×D911yescharacteristic
430C22C2×D4×D911yescharacteristic
431C22C2×D4×D911yescharacteristic
432C22C2×Q8×D911yescharacteristic
433C22#6371311yescharacteristic
434C22#41×D911yescharacteristic
435C22#6371511yescharacteristic
436C4—22no—
437C4—24no—
438C4—42no—
439C4—41no—
440C4—94no—
441C4—182no—
442C4—182no—
443C4—362no—
444C4—361no—
445C4C4⋊C4×D914yescomplemented
446C3#7620211yescharacteristic
447C2—188no—
448C2C2×C4⋊C4×D911yescharacteristic
449C2C4×D4×D911yescharacteristic
450C2#1058967611yescharacteristic
451C2#1058971111yescharacteristic
452C2#1058973311yescharacteristic
453C2#1058979211yescharacteristic
454C2#1058982911yescharacteristic
subgroupG/H
centerC23C23×D9
commutatorC22×C9C23×C4
Frattini, socleC23×C3C23×D3
FittingC9×#389C2
prime radicalC22×D36C22
cosocleC23×C9C24
hypercenter#389D9
hypocenterC9D4×C4⋊C4
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
3. C2×C4⋊C4×D9C2semidirect
5. C9×#389C2semidirect
6. #10588669C2semidirect
7. #10588664C2semidirect
8. #10588655C2semidirect
9. C4×Dic9⋊C4C2semidirect
10. #10588348C2semidirect
11. #10588347C2semidirect
33. #63455C4semidirect
73. C2×C4×D9C2×C4semidirect
76. C9×C4⋊C4C2×C4semidirect
80. (C2×D9)⋊C4C2×C4semidirect
86. Dic9⋊C4D4semidirect
88. C4×Dic9C2×C4semidirect
155. D36C4⋊C4semidirect
164. #389D9semidirect
221. C2×D9C2×C4⋊C4semidirect
226. C4×C9C2×C4⋊C4semidirect
231. Dic9C4×D4semidirect
340. C4⋊C4C4×D9semidirect
371. C9D4×C4⋊C4semidirect
445. C4C4⋊C4×D9semidirect

Maximal subgroups

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

subgroupindex
C2×#634552
C2×C4⋊C4×D92
C2×C4×D362
C9×#3892
#105886692
#105886642
#105886552
C4×Dic9⋊C42
#105883482
#105883472
#762023