Finite Group Databasebeta

← #11802694

Subgroups — #11802694

Order 1152.

1320 conjugacy classes of subgroups.

The subgroup lattice has 519 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3699C211yesmaximal, characteristic
2C22×Dic9⋊C4C211yesmaximal, characteristic, complemented
3C2×#63439C211yesmaximal, characteristic, complemented
4C9×#386C211yesmaximal, characteristic, complemented
5#10588900C211yesmaximal, characteristic, complemented
6#10588893C211yesmaximal, characteristic, complemented
7#10588638C211yesmaximal, characteristic, complemented
8#10588637C212yesmaximal, complemented
9#10588622C212yesmaximal, complemented
10#10588347C212yesmaximal, complemented
11#10588326C212yesmaximal, complemented
12#74662—31nomaximal
13C22×D4×C9C2211yescharacteristic
14C23×C4×C9C2211yescharacteristic
15C22×#611C2211yescharacteristic
16C22×#611C2211yescharacteristic
17C23×Dic9C2211yescharacteristic
18C23×Dic9C2211yescharacteristic
19C23×Dic9C2211yescharacteristic
20C2×#3699—24no—
21C2×#3699—24no—
22C2×#3699C418yescomplemented
23C22×C4×D9C2211yescharacteristic
24C22×Dic18C2211yescharacteristic
25C2×C9×C22⋊C4C2211yescharacteristic
26C2×C9×C22⋊C4C2212yes—
27C2×#3676C2211yescharacteristic
28C2×#3676C2212yes—
29C2×(C2×D9)⋊C4C2212yes—
30C2×(C2×D9)⋊C4C2212yes—
31C2×Dic9⋊C4—24no—
32C2×Dic9⋊C4C2212yes—
33C2×Dic9⋊C4C2212yes—
34C2×Dic9⋊C4C2212yes—
35C2×C4×Dic9C2212yes—
36#63439—24no—
37C9×#95C2212yes—
38C9⋊#95C2212yes—
39C9⋊#95C2212yes—
40C9⋊#95C2212yes—
41C22×#237—31no—
42C22×Dic3⋊C4—31no—
43C2×#877—31no—
44C3×#386D311yescharacteristic
45#5220—31no—
46#5213—31no—
47#4958—31no—
48#4957—32no—
49#4942—32no—
50#4667—32no—
51#4646—32no—
52C24×C9C2311yescharacteristic
53C24×C9C2311yescharacteristic
54C23×D9C2311yescharacteristic
55C2×D4×C9—22no—
56C2×D4×C9—22no—
57C2×D4×C9C2×C414yes—
58C22×C4×C9—22no—
59C22×C4×C9—42no—
60C22×C4×C9C2312yes—
61C22×C4×C9C2312yes—
62C22×C4×C9C2311yescharacteristic
63C2×#611—22no—
64C2×#611—22no—
65C2×#611—22no—
66C2×#611—22no—
67C2×#611C2×C414yes—
68C2×#611C2×C414yescomplemented
69C22×Dic9—22no—
70C22×Dic9—22no—
71C22×Dic9—22no—
72C22×Dic9—42no—
73C22×Dic9C2×C414yes—
74C22×Dic9C2×C414yescomplemented
75C22×Dic9D414yes—
76C22×Dic9D414yes—
77C22×Dic9C2312yes—
78C22×Dic9C2312yes—
79C22×Dic9C2311yescharacteristic
80C22×Dic9C2311yescharacteristic
81C22×Dic9C2311yescharacteristic
82#3699—232no—
83C2×C4×D9—22no—
84C2×C4×D9—22no—
85C2×C4×D9C2×C414yescomplemented
86C2×Dic18—22no—
87C2×Dic18—22no—
88C2×Dic18C2×C414yescomplemented
89C9×C22⋊C4—22no—
90C9×C22⋊C4—42no—
91#3676—22no—
92#3676—42no—
93(C2×D9)⋊C4—42no—
94(C2×D9)⋊C4—42no—
95Dic9⋊C4—24no—
96Dic9⋊C4—24no—
97Dic9⋊C4—24no—
98C4×Dic9—24no—
99#2311—91noSylow
100C22×C3×D4C2×D311yescharacteristic
101C23×C3×C4C2×D311yescharacteristic
102C22×#67—31no—
103C22×#67—31no—
104C23×Dic3—31no—
105C23×Dic3—31no—
106C23×Dic3—31no—
107C2×#237—38no—
108C2×#237—64no—
109C2×#237—64no—
110C22×C4×D3—31no—
111C22×Dic6—31no—
112C2×C3×C22⋊C4C2×D311yescharacteristic
113C2×C3×C22⋊C4C2×D312yes—
114C2×#217—31no—
115C2×#217—32no—
116C2×(C2×D3)⋊C4—32no—
117C2×(C2×D3)⋊C4—32no—
118C2×Dic3⋊C4—32no—
119C2×Dic3⋊C4—32no—
120C2×Dic3⋊C4—32no—
121C2×Dic3⋊C4—64no—
122C2×C4×Dic3—32no—
123#877—64no—
124C3×#95C2×D312yes—
125C3⋊#95—32no—
126C3⋊#95—32no—
127C3⋊#95—32no—
128C23×C9—22no—
129C23×C9—22no—
130C23×C9—21no—
131C23×C9—21no—
132C23×C9—22no—
133C23×C9—22no—
134C23×C9C22×C412yes—
135C23×C9C22×C412yes—
136C23×C9C2×D412yes—
137C23×C9C2×D412yes—
138C23×C9C2411yescharacteristic
139C22×D9—21no—
140C22×D9—21no—
141C22×D9—22no—
142C22×D9—22no—
143C22×D9C22×C412yes—
144D4×C9—28no—
145C2×C4×C9—21no—
146C2×C4×C9—21no—
147C2×C4×C9—22no—
148C2×C4×C9—22no—
149C2×C4×C9—22no—
150C2×C4×C9—22no—
151C2×C4×C9—22no—
152C2×C4×C9—22no—
153C2×C4×C9—44no—
154C2×C4×C9C22×C412yes—
155#611—28no—
156#611—28no—
157C2×Dic9—21no—
158C2×Dic9—21no—
159C2×Dic9—28no—
160C2×Dic9—22no—
161C2×Dic9—22no—
162C2×Dic9—22no—
163C2×Dic9—22no—
164C2×Dic9—22no—
165C2×Dic9—22no—
166C2×Dic9—44no—
167C2×Dic9C22⋊C4116yescomplemented
168C2×Dic9C22×C412yes—
169C2×Dic9C22×C412yes—
170C2×Dic9C22×C412yes—
171C2×Dic9C2×D412yes—
172C2×Dic9C2×D412yes—
173C2×Dic9C2×D412yes—
174C2×Dic9C2×D412yes—
175C4×D9—28no—
176Dic18—28no—
177C22×#41—91no—
178C2×#117—91no—
179C22×C4⋊C4—91no—
180#391—92no—
181#390—92no—
182#386—91no—
183#386—91no—
184#386—91no—
185#386D911yescharacteristic, complemented
186#380—92no—
187#380—92no—
188C24×C3C22×D311yescharacteristic
189C24×C3C22×D311yescharacteristic
190C23×D3—31no—
191C2×C3×D4—22no—
192C2×C3×D4—22no—
193C2×C3×D4C4×D314yes—
194C22×C3×C4—22no—
195C22×C3×C4—42no—
196C22×C3×C4C22×D312yes—
197C22×C3×C4C22×D312yes—
198C22×C3×C4C22×D311yescharacteristic
199C2×#67—34no—
200C2×#67—34no—
201C2×#67—62no—
202C2×#67—62no—
203C2×#67—62no—
204C2×#67—62no—
205C22×Dic3—34no—
206C22×Dic3—34no—
207C22×Dic3—34no—
208C22×Dic3—31no—
209C22×Dic3—31no—
210C22×Dic3—34no—
211C22×Dic3—31no—
212C22×Dic3—32no—
213C22×Dic3—32no—
214C22×Dic3—62no—
215C22×Dic3—62no—
216C22×Dic3—62no—
217C22×Dic3—122no—
218#237—632no—
219C2×C4×D3—34no—
220C2×C4×D3—62no—
221C2×C4×D3—62no—
222C2×Dic6—34no—
223C2×Dic6—62no—
224C2×Dic6—62no—
225C3×C22⋊C4—22no—
226C3×C22⋊C4—42no—
227#217—62no—
228#217—122no—
229(C2×D3)⋊C4—122no—
230(C2×D3)⋊C4—122no—
231Dic3⋊C4—64no—
232Dic3⋊C4—64no—
233Dic3⋊C4—64no—
234C4×Dic3—64no—
235C22×C9—24no—
236C22×C9—22no—
237C22×C9—22no—
238C22×C9—24no—
239C22×C9—22no—
240C22×C9—24no—
241C22×C9—41no—
242C22×C9—41no—
243C22×C9—42no—
244C22×C9C2×C22⋊C414yes—
245C22×C9C23×C411yescharacteristic
246C22×C9C22×D411yescharacteristic
247C22×C9C22×D411yescharacteristic
248C22×C9H(5,𝔽2)12yes—
249C22×C92−1+412yes—
250C2×D9—22no—
251C2×D9—24no—
252C2×D9—41no—
253C2×D9—41no—
254C2×D9—42no—
255C4×C9—22no—
256C4×C9—42no—
257C4×C9—42no—
258Dic9—22no—
259Dic9—42no—
260Dic9—42no—
261Dic9C2×C22⋊C414yes—
262Dic9C2×C22⋊C414yes—
263C2×#41—98no—
264C2×#41—184no—
265C2×#41—184no—
266C22×Q8—91no—
267C22×D4—91no—
268C22×D4—91no—
269C22×D4C2×D911yescharacteristic
270C23×C4—91no—
271C23×C4—91no—
272C23×C4—91no—
273C23×C4—91no—
274C23×C4C2×D911yescharacteristic
275#117—184no—
276C2×C4⋊C4—92no—
277C2×C4⋊C4—92no—
278C2×C4⋊C4—92no—
279C2×C4⋊C4—184no—
280C2×C22⋊C4—91no—
281C2×C22⋊C4—92no—
282C2×C22⋊C4—92no—
283C2×C22⋊C4—92no—
284C2×C22⋊C4C2×D911yescharacteristic
285C2×C22⋊C4C2×D912yes—
286C2×C42—92no—
287#95—92no—
288#95—92no—
289#95—92no—
290#95C2×D912yes—
291C23×C3—22no—
292C23×C3—22no—
293C23×C3—21no—
294C23×C3—21no—
295C23×C3—22no—
296C23×C3—22no—
297C23×C3C2×C4×D312yes—
298C23×C3C2×C4×D312yes—
299C23×C3D3×D412yes—
300C23×C3D3×D412yes—
301C23×C3C23×D311yescharacteristic
302C22×D3—32no—
303C22×D3—61no—
304C22×D3—61no—
305C22×D3—62no—
306C22×D3—62no—
307C3×D4—28no—
308C2×C3×C4—21no—
309C2×C3×C4—21no—
310C2×C3×C4—22no—
311C2×C3×C4—22no—
312C2×C3×C4—22no—
313C2×C3×C4—22no—
314C2×C3×C4—22no—
315C2×C3×C4—22no—
316C2×C3×C4—44no—
317C2×C3×C4C2×C4×D312yes—
318#67—68no—
319#67—68no—
320C2×Dic3—316no—
321C2×Dic3—32no—
322C2×Dic3—32no—
323C2×Dic3—32no—
324C2×Dic3—32no—
325C2×Dic3—32no—
326C2×Dic3—32no—
327C2×Dic3—32no—
328C2×Dic3—68no—
329C2×Dic3—61no—
330C2×Dic3—61no—
331C2×Dic3—62no—
332C2×Dic3—62no—
333C2×Dic3—62no—
334C2×Dic3—62no—
335C2×Dic3—62no—
336C2×Dic3—62no—
337C2×Dic3—124no—
338C4×D3—68no—
339Dic6—68no—
340C2×C9—24no—
341C2×C9—42no—
342C2×C9C22×C22⋊C411yescharacteristic
343C2×C9#52012yes—
344C2×C9#53511yescharacteristic
345C2×C9#53611yescharacteristic
346C2×C9#53712yes—
347D9—42no—
348C24—91no—
349C24C22×D911yescharacteristic
350C24C22×D911yescharacteristic
351#41—1832no—
352C2×Q8—94no—
353C2×Q8—182no—
354C2×Q8—182no—
355C2×D4—22no—
356C2×D4—22no—
357C2×D4—94no—
358C2×D4—94no—
359C2×D4—182no—
360C2×D4—182no—
361C2×D4—182no—
362C2×D4—182no—
363C2×D4C4×D914yes—
364C22×C4—22no—
365C22×C4—42no—
366C22×C4—94no—
367C22×C4—94no—
368C22×C4—94no—
369C22×C4—91no—
370C22×C4—91no—
371C22×C4—94no—
372C22×C4—91no—
373C22×C4—94no—
374C22×C4—92no—
375C22×C4—92no—
376C22×C4—182no—
377C22×C4—182no—
378C22×C4—182no—
379C22×C4—182no—
380C22×C4—182no—
381C22×C4—362no—
382C22×C4C22×D912yes—
383C22×C4C22×D912yes—
384C22×C4C22×D911yescharacteristic
385C4⋊C4—184no—
386C4⋊C4—184no—
387C4⋊C4—184no—
388C22⋊C4—22no—
389C22⋊C4—42no—
390C22⋊C4—182no—
391C22⋊C4—362no—
392C22⋊C4—362no—
393C22⋊C4—362no—
394C42—184no—
395C22×C3—22no—
396C22×C3—24no—
397C22×C3—22no—
398C22×C3—24no—
399C22×C3—22no—
400C22×C3—24no—
401C22×C3—41no—
402C22×C3—41no—
403C22×C3—42no—
404C22×C3D3×C22⋊C414yes—
405C22×C3C22×C4×D311yescharacteristic
406C22×C3C2×D3×D411yescharacteristic
407C22×C3C2×D3×D411yescharacteristic
408C22×C3#100412yes—
409C22×C3#101012yes—
410C2×D3—62no—
411C2×D3—64no—
412C2×D3—121no—
413C2×D3—121no—
414C2×D3—122no—
415C3×C4—22no—
416C3×C4—42no—
417C3×C4—42no—
418Dic3—34no—
419Dic3—34no—
420Dic3—62no—
421Dic3—122no—
422Dic3—122no—
423C9#231111yescharacteristic, complemented, Sylow
424C23—22no—
425C23—22no—
426C23—21no—
427C23—21no—
428C23—22no—
429C23—22no—
430C23—92no—
431C23—181no—
432C23—181no—
433C23—182no—
434C23—182no—
435C23C2×C4×D912yes—
436C23C2×C4×D912yes—
437C23D4×D912yes—
438C23D4×D912yes—
439C23C23×D911yescharacteristic
440Q8—188no—
441D4—28no—
442D4—188no—
443D4—188no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—44no—
453C2×C4—916no—
454C2×C4—92no—
455C2×C4—92no—
456C2×C4—92no—
457C2×C4—92no—
458C2×C4—92no—
459C2×C4—92no—
460C2×C4—92no—
461C2×C4—188no—
462C2×C4—188no—
463C2×C4—181no—
464C2×C4—181no—
465C2×C4—182no—
466C2×C4—182no—
467C2×C4—182no—
468C2×C4—182no—
469C2×C4—182no—
470C2×C4—182no—
471C2×C4—364no—
472C2×C4C2×C4×D912yes—
473C2×C3—24no—
474C2×C3—42no—
475C2×C3C2×D3×C22⋊C411yescharacteristic
476C2×C3#554612yes—
477C2×C3#559211yescharacteristic
478C2×C3#559712yes—
479C2×C3#564811yescharacteristic
480D3—122no—
481C22—24no—
482C22—22no—
483C22—24no—
484C22—22no—
485C22—22no—
486C22—24no—
487C22—42no—
488C22—41no—
489C22—41no—
490C22—182no—
491C22—184no—
492C22—362no—
493C22—361no—
494C22—361no—
495C22C22⋊C4×D914yes—
496C22C22×C4×D911yescharacteristic
497C22C2×D4×D911yescharacteristic
498C22C2×D4×D911yescharacteristic
499C22#6371012yes—
500C22#6371612yes—
501C4—22no—
502C4—42no—
503C4—42no—
504C4—94no—
505C4—94no—
506C4—182no—
507C4—362no—
508C4—362no—
509C3#7466211yescharacteristic
510C2—24no—
511C2—42no—
512C2—362no—
513C2C2×C22⋊C4×D911yescharacteristic
514C2#1058964812yes—
515C2#1058969411yescharacteristic
516C2#1058969912yes—
517C2#1058975011yescharacteristic
subgroupG/H
centerC23C23×D9
commutatorC22×C9C23×C4
Frattini, socleC23×C3C23×D3
FittingC9×#386C2
prime radicalC22×#3699C2
cosocleC23×C9C24
hypercenter#386D9
hypocenterC9#2311
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C22×Dic9⋊C4C2semidirect
3. C2×#63439C2semidirect
4. C9×#386C2semidirect
5. #10588900C2semidirect
6. #10588893C2semidirect
7. #10588638C2semidirect
8. #10588637C2semidirect
9. #10588622C2semidirect
10. #10588347C2semidirect
11. #10588326C2semidirect
22. C2×#3699C4semidirect
68. C2×#611C2×C4semidirect
74. C22×Dic9C2×C4semidirect
85. C2×C4×D9C2×C4semidirect
88. C2×Dic18C2×C4semidirect
167. C2×Dic9C22⋊C4semidirect
185. #386D9semidirect
423. C9#2311semidirect

Maximal subgroups

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

subgroupindex
C22×#36992
C22×Dic9⋊C42
C2×#634392
C9×#3862
#105889002
#105888932
#105886382
#105886372
#105886222
#105883472
#105883262
#746623