Finite Group Databasebeta

← #11791388

Subgroups — #11791388

Order 1152.

504 conjugacy classes of subgroups.

The subgroup lattice has 447 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10589934C211yesmaximal, characteristic
2C2×C9×#104C211yesmaximal, characteristic, complemented
3C2×#63396C211yesmaximal, characteristic, complemented
4C2×#63384C211yesmaximal, characteristic, complemented
5M16×Dic9C211yesmaximal, characteristic, complemented
6C4×Dic9⋊C4C211yesmaximal, characteristic, complemented
7C2×#63364C211yesmaximal, characteristic, complemented
8#70358—31nomaximal
9C2×C9×#41C2211yescharacteristic
10C2×#3697C2211yescharacteristic
11C2×C9×M16C2211yescharacteristic
12C2×C42×C9C2211yescharacteristic
13#63509C411yescharacteristic, complemented
14#63506C411yescharacteristic, complemented
15#63502C411yescharacteristic, complemented
16#63501—21no—
17#63501—21no—
18#63498C411yescharacteristic, complemented
19C4×#611—21no—
20C4×#611—21no—
21C2×Dic9⋊C4—21no—
22C2×C4×Dic9C2211yescharacteristic
23C2×C4×Dic9C2211yescharacteristic
24C2×#3667C2211yescharacteristic
25C9×#104—22no—
26#63396—22no—
27C9⋊#95—21no—
28#63384—22no—
29#63375—21no—
30C8×Dic9—21no—
31#63364—22no—
32#5832—31no—
33C2×C3×#104D311yescharacteristic
34C2×#837—31no—
35C2×#825—31no—
36Dic3×M16—31no—
37C4×Dic3⋊C4—31no—
38C2×#805—31no—
39C9×#41—21no—
40C9×#41—21no—
41C9×#41—21no—
42C9×#41—21no—
43C2×Q8×C9C2×C411yescharacteristic
44C2×D4×C9—21no—
45C2×D4×C9C2×C411yescharacteristic
46C22×C4×C9—21no—
47C22×C4×C9—21no—
48C22×C4×C9C2311yescharacteristic
49C2×#611—21no—
50C2×#611—21no—
51C2×#611—21no—
52C22×Dic9—21no—
53C22×Dic9D411yescharacteristic
54C22×Dic9D411yescharacteristic
55#3697—21no—
56#3697—21no—
57#3697—21no—
58#3697—21no—
59C2×D36C2×C411yescharacteristic
60C2×C4×D9—21no—
61C2×Dic18C2×C411yescharacteristic
62C9×M16—21no—
63C9×M16D412yescomplemented
64C2×C8×C9—21no—
65C42×C9—21no—
66C42×C9—21no—
67#3676—21no—
68#3676—21no—
69(C2×D9)⋊C4—21no—
70(C2×D9)⋊C4—21no—
71Dic9⋊C4—24no—
72Dic9⋊C4—21no—
73Dic9⋊C4—21no—
74C4×Dic9—21no—
75C4×Dic9—21no—
76C4×Dic9C2×C411yescharacteristic
77C4×Dic9C2×C411yescharacteristic
78C4×Dic9D411yescharacteristic
79C4×Dic9D411yescharacteristic
80#3667—21no—
81#3667D412yescomplemented
82C2×C9⋊C8—21no—
83#1980—91noSylow
84C2×C3×#41C2×D311yescharacteristic
85C2×#235—31no—
86C2×C3×M16C2×D311yescharacteristic
87C2×C3×C42C2×D311yescharacteristic
88#947—31no—
89#944—31no—
90#940—31no—
91#939—61no—
92#939—61no—
93#936—31no—
94C4×#67—61no—
95C4×#67—61no—
96C2×Dic3⋊C4—61no—
97C2×C4×Dic3—31no—
98C2×C4×Dic3—31no—
99C2×#208—31no—
100C3×#104—22no—
101#837—62no—
102C3⋊#95—61no—
103#825—62no—
104#815—61no—
105C8×Dic3—61no—
106#805—62no—
107C23×C9—21no—
108C23×C9C2×D411yescharacteristic
109C22×D9—21no—
110Q8×C9—21no—
111Q8×C9—21no—
112D4×C9—21no—
113D4×C9—21no—
114D4×C9—41no—
115D4×C9—41no—
116C2×C4×C9—22no—
117C2×C4×C9—21no—
118C2×C4×C9—41no—
119C2×C4×C9—41no—
120C2×C4×C9—41no—
121C2×C4×C9—41no—
122C2×C4×C9C22×C411yescharacteristic
123C2×C4×C9C2×D411yescharacteristic
124C2×C4×C9C2×D411yescharacteristic
125C2×C4×C9C2×D411yescharacteristic
126C2×C4×C9#4111yescharacteristic
127C2×C4×C9#4111yescharacteristic
128#611—42no—
129#611—41no—
130#611—41no—
131#611—42no—
132C2×Dic9—22no—
133C2×Dic9—22no—
134C2×Dic9—21no—
135C2×Dic9—41no—
136C2×Dic9—41no—
137C2×Dic9—41no—
138C2×Dic9C22⋊C411yescharacteristic
139C2×Dic9C22⋊C411yescharacteristic
140C2×Dic9C22⋊C411yescharacteristic
141C2×Dic9C22⋊C411yescharacteristic
142D36—21no—
143D36—21no—
144C4×D9—41no—
145C4×D9—41no—
146Dic18—21no—
147Dic18—21no—
148C8×C9—22no—
149C9⋊C8—22no—
150#532—91no—
151C2×#104—91no—
152C2×#104—91no—
153C2×#104—91no—
154C2×#104D911yescharacteristic, complemented
155C4×M16—91no—
156C4×C4⋊C4—91no—
157C3×#41—21no—
158C3×#41—21no—
159C3×#41—21no—
160C3×#41—21no—
161C2×C3×Q8C4×D311yescharacteristic
162C2×C3×D4—21no—
163C2×C3×D4C4×D311yescharacteristic
164C22×C3×C4—21no—
165C22×C3×C4—21no—
166C22×C3×C4C22×D311yescharacteristic
167C2×#67—61no—
168C2×#67—61no—
169C2×#67—61no—
170C22×Dic3—31no—
171C22×Dic3—31no—
172C22×Dic3—61no—
173#235—61no—
174#235—61no—
175#235—61no—
176#235—61no—
177C2×D12—31no—
178C2×C4×D3—61no—
179C2×Dic6—31no—
180C3×M16—21no—
181C3×M16#6712yes—
182C2×C3×C8—21no—
183C3×C42—21no—
184C3×C42—21no—
185#217—61no—
186#217—61no—
187(C2×D3)⋊C4—61no—
188(C2×D3)⋊C4—61no—
189Dic3⋊C4—61no—
190Dic3⋊C4—61no—
191Dic3⋊C4—64no—
192C4×Dic3—31no—
193C4×Dic3—31no—
194C4×Dic3—31no—
195C4×Dic3—31no—
196C4×Dic3—61no—
197C4×Dic3—61no—
198#208—32no—
199#208—61no—
200C2×C3⋊C8—61no—
201C22×C9—21no—
202C22×C9—21no—
203C22×C9—41no—
204C22×C9—41no—
205C22×C9—41no—
206C22×C9C2×C22⋊C411yescharacteristic
207C22×C9#12411yescharacteristic
208C22×C9#12711yescharacteristic
209C2×D9—41no—
210C2×D9—41no—
211C2×D9—41no—
212C4×C9—42no—
213C4×C9—41no—
214C4×C9C4×D411yescharacteristic
215C4×C9C4×D411yescharacteristic
216C4×C9#12111yescharacteristic
217C4×C9#12111yescharacteristic
218Dic9—21no—
219Dic9—21no—
220Dic9—21no—
221Dic9—42no—
222Dic9—41no—
223Dic9#10412yescomplemented
224C2×#41—91no—
225C2×#41C2×D911yescharacteristic
226C2×M16—91no—
227C2×M16C2×D911yescharacteristic
228C4⋊Q8—91no—
229#127—91no—
230#124—91no—
231#124—91no—
232#121—181no—
233#121—181no—
234C4×D4—181no—
235C4×D4—181no—
236C2×C4⋊C4—181no—
237C2×C42—91no—
238C2×C42—91no—
239C2×C42C2×D911yescharacteristic
240#104—22no—
241#104—182no—
242#104—182no—
243#104—182no—
244#97—181no—
245C4×C8—181no—
246#95—181no—
247C23×C3—21no—
248C23×C3D3×D411yescharacteristic
249C22×D3—61no—
250C3×Q8—21no—
251C3×Q8—21no—
252C3×D4—21no—
253C3×D4—21no—
254C3×D4—41no—
255C3×D4—41no—
256C2×C3×C4—22no—
257C2×C3×C4—21no—
258C2×C3×C4—41no—
259C2×C3×C4—41no—
260C2×C3×C4—41no—
261C2×C3×C4—41no—
262C2×C3×C4C2×C4×D311yescharacteristic
263C2×C3×C4#23511yescharacteristic
264C2×C3×C4D3×D411yescharacteristic
265C2×C3×C4D3×D411yescharacteristic
266C2×C3×C4#23711yescharacteristic
267C2×C3×C4C2×#6711yescharacteristic
268#67—122no—
269#67—122no—
270#67—121no—
271#67—121no—
272C2×Dic3—31no—
273C2×Dic3—31no—
274C2×Dic3—31no—
275C2×Dic3—31no—
276C2×Dic3—62no—
277C2×Dic3—62no—
278C2×Dic3—61no—
279C2×Dic3—121no—
280C2×Dic3—121no—
281C2×Dic3—121no—
282D12—61no—
283D12—61no—
284C4×D3—121no—
285C4×D3—121no—
286Dic6—61no—
287Dic6—61no—
288C3×C8—22no—
289C3⋊C8—62no—
290C2×C9—21no—
291C2×C9—21no—
292C2×C9—81no—
293C2×C9#39011yescharacteristic
294C2×C9C2×#10411yescharacteristic
295C2×C9#42111yescharacteristic
296D9—81no—
297#41—21no—
298#41—21no—
299#41—21no—
300#41—21no—
301#41—181no—
302#41—181no—
303#41—181no—
304#41—181no—
305C2×Q8—91no—
306C2×Q8C4×D911yescharacteristic
307C2×D4—21no—
308C2×D4—91no—
309C2×D4—181no—
310C2×D4—181no—
311C2×D4—181no—
312C2×D4C4×D911yescharacteristic
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—91no—
316C22×C4—91no—
317C22×C4—181no—
318C22×C4—181no—
319C22×C4C22×D911yescharacteristic
320M16—21no—
321M16—92no—
322M16—181no—
323M16#61112yescomplemented
324C2×C8—21no—
325C2×C8—181no—
326C4⋊C4—181no—
327C4⋊C4—181no—
328C4⋊C4—184no—
329C22⋊C4—181no—
330C22⋊C4—181no—
331C22⋊C4—181no—
332C22⋊C4—181no—
333C42—21no—
334C42—21no—
335C42—91no—
336C42—91no—
337C42—91no—
338C42—91no—
339C42—181no—
340C42—181no—
341C22×C3—21no—
342C22×C3—21no—
343C22×C3—41no—
344C22×C3—41no—
345C22×C3—41no—
346C22×C3D3×C22⋊C411yescharacteristic
347C22×C3#88511yescharacteristic
348C22×C3#94011yescharacteristic
349C2×D3—121no—
350C2×D3—121no—
351C2×D3—121no—
352C3×C4—42no—
353C3×C4—41no—
354C3×C4#67⋊C411yescharacteristic
355C3×C4#88411yescharacteristic
356C3×C4C4×#6711yescharacteristic
357C3×C4#93911yescharacteristic
358Dic3—32no—
359Dic3—61no—
360Dic3—61no—
361Dic3—61no—
362Dic3—122no—
363Dic3—121no—
364C9#198011yescharacteristic, complemented, Sylow
365C23—21no—
366C23—181no—
367C23D4×D911yescharacteristic
368Q8—21no—
369Q8—21no—
370Q8—181no—
371Q8—181no—
372D4—21no—
373D4—21no—
374D4—41no—
375D4—41no—
376D4—181no—
377D4—181no—
378D4—362no—
379D4—362no—
380D4—361no—
381D4—361no—
382C2×C4—22no—
383C2×C4—21no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—91no—
389C2×C4—91no—
390C2×C4—91no—
391C2×C4—91no—
392C2×C4—182no—
393C2×C4—182no—
394C2×C4—181no—
395C2×C4—361no—
396C2×C4—361no—
397C2×C4—361no—
398C2×C4—361no—
399C2×C4—361no—
400C2×C4C2×C4×D911yescharacteristic
401C2×C4#369711yescharacteristic
402C2×C4D4×D911yescharacteristic
403C2×C4D4×D911yescharacteristic
404C2×C4#369911yescharacteristic
405C2×C4C2×#61111yescharacteristic
406C8—22no—
407C8—182no—
408C2×C3—21no—
409C2×C3—21no—
410C2×C3—81no—
411C2×C3D3×#10411yescharacteristic
412C2×C3#482111yescharacteristic
413C2×C3#495711yescharacteristic
414D3—241no—
415C22—21no—
416C22—21no—
417C22—41no—
418C22—41no—
419C22—41no—
420C22—361no—
421C22—361no—
422C22—361no—
423C22C22⋊C4×D911yescharacteristic
424C22#6344711yescharacteristic
425C22#6350211yescharacteristic
426C4—42no—
427C4—41no—
428C4—92no—
429C4—181no—
430C4—181no—
431C4—181no—
432C4—362no—
433C4—361no—
434C4#611⋊C411yescharacteristic
435C4#6344611yescharacteristic
436C4C4×#61111yescharacteristic
437C4#6350111yescharacteristic
438C3#7035811yescharacteristic
439C2—21no—
440C2—21no—
441C2—81no—
442C2—721no—
443C2D9×#10411yescharacteristic
444C2#1058850111yescharacteristic
445C2#1058863711yescharacteristic
subgroupG/H
centerC2×C4D4×D9
commutatorC2×C4×C9C22×C4
FrattiniC22×C3×C4C22×D3
FittingC2×C9×#104C2
socleC22×C3D3×C22⋊C4
prime radical#10589934C2
cosocleC22×C4×C9C23
hypercenterC2×#104D9
hypocenterC9#1980
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
2. C2×C9×#104C2semidirect
3. C2×#63396C2semidirect
4. C2×#63384C2semidirect
5. M16×Dic9C2semidirect
6. C4×Dic9⋊C4C2semidirect
7. C2×#63364C2semidirect
13. #63509C4semidirect
14. #63506C4semidirect
15. #63502C4semidirect
18. #63498C4semidirect
63. C9×M16D4semidirect
81. #3667D4semidirect
154. C2×#104D9semidirect
223. Dic9#104semidirect
323. M16#611semidirect
364. C9#1980semidirect

Maximal subgroups

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

subgroupindex
#105899342
C2×C9×#1042
C2×#633962
C2×#633842
M16×Dic92
C4×Dic9⋊C42
C2×#633642
#703583