Finite Group Databasebeta

← #11804291

Subgroups — #11804291

Order 1152.

714 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C9×#126C211yesmaximal, characteristic
2#10588664C211yesmaximal, characteristic, complemented
3#10588664C211yesmaximal, characteristic, complemented
4#10588660C211yesmaximal, characteristic, complemented
5#10588660C211yesmaximal, characteristic, complemented
6#10588660C211yesmaximal, characteristic, complemented
7C4⋊C4×Dic9C211yesmaximal, characteristic, complemented
8#10588631C211yesmaximal, characteristic
9#10588631C211yesmaximal, characteristic
10#10588631C211yesmaximal, characteristic
11#10588630C211yesmaximal, characteristic
12#10588630C211yesmaximal, characteristic
13C22⋊C4×Dic9C211yesmaximal, characteristic
14#10588616C211yesmaximal, characteristic, complemented
15C4×C4⋊Dic9C211yesmaximal, characteristic, complemented
16#83074—31nomaximal
17C23×Dic9C2211yescharacteristic
18C9×#126C418yescomplemented
19C2×C9×C4⋊C4C2211yescharacteristic
20C2×C9×C4⋊C4C2211yescharacteristic
21C2×C9×C4⋊C4C2211yescharacteristic
22C2×C9×C22⋊C4C2211yescharacteristic
23C2×C9×C22⋊C4C2211yescharacteristic
24C2×C9×C22⋊C4C2211yescharacteristic
25C2×C42×C9C2211yescharacteristic
26C2×#3676C2211yescharacteristic
27C2×#3676C2211yescharacteristic
28C2×#3676C2211yescharacteristic
29C2×C4⋊Dic9C2211yescharacteristic
30C2×C4⋊Dic9C2211yescharacteristic
31C2×C4⋊Dic9C2211yescharacteristic
32C2×C4⋊Dic9C2211yescharacteristic
33C2×C4⋊Dic9C2211yescharacteristic
34C2×C4⋊Dic9C2211yescharacteristic
35C2×C4⋊Dic9C2211yescharacteristic
36C2×C4×Dic9C2211yescharacteristic
37C2×C4×Dic9C2211yescharacteristic
38C2×C4×Dic9C2211yescharacteristic
39C2×C4×Dic9C2211yescharacteristic
40C2×C4×Dic9C2211yescharacteristic
41C9⋊#95C2211yescharacteristic
42C9⋊#95C2211yescharacteristic
43C9⋊#95C2211yescharacteristic
44C9⋊#95C2211yescharacteristic
45C9⋊#95C2211yescharacteristic
46C9⋊#95C2211yescharacteristic
47C9⋊#95C2211yescharacteristic
48C9⋊#95C2211yescharacteristic
49C9⋊#95C2211yescharacteristic
50C9⋊#95C2211yescharacteristic
51C9⋊#95C2211yescharacteristic
52C9⋊#95C2211yescharacteristic
53C2×C3×#126D311yescharacteristic
54#4984—31no—
55#4984—31no—
56#4980—31no—
57#4980—31no—
58#4980—31no—
59Dic3×C4⋊C4—31no—
60#4951—31no—
61#4951—31no—
62#4951—31no—
63#4950—31no—
64#4950—31no—
65Dic3×C22⋊C4—31no—
66#4936—31no—
67C4×C4⋊Dic3—31no—
68C24×C9C2311yescharacteristic
69C22×C4×C9C2311yescharacteristic
70C22×C4×C9C2311yescharacteristic
71C22×C4×C9C2311yescharacteristic
72C22×C4×C9C2311yescharacteristic
73C22×C4×C9C2311yescharacteristic
74C22×C4×C9C2311yescharacteristic
75C22×Dic9—22no—
76C22×Dic9—41no—
77C22×Dic9—41no—
78C22×Dic9C2311yescharacteristic
79C22×Dic9C2311yescharacteristic
80C22×Dic9C2311yescharacteristic
81C22×Dic9C2311yescharacteristic
82C22×Dic9C2311yescharacteristic
83C22×Dic9C2311yescharacteristic
84C22×Dic9C2311yescharacteristic
85C22×Dic9C2311yescharacteristic
86C9×C4⋊C4C2×C414yescomplemented
87C9×C4⋊C4C2×C414yescomplemented
88C9×C4⋊C4C2×C414yescomplemented
89C9×C22⋊C4C2×C414yes—
90C9×C22⋊C4C2×C414yes—
91C9×C22⋊C4C2×C414yes—
92C42×C9C2×C414yescomplemented
93#3676—22no—
94#3676—41no—
95#3676—41no—
96C4⋊Dic9—22no—
97C4⋊Dic9—22no—
98C4⋊Dic9—22no—
99C4⋊Dic9—41no—
100C4⋊Dic9—41no—
101C4⋊Dic9—41no—
102C4⋊Dic9—41no—
103C4×Dic9—22no—
104C4×Dic9—41no—
105C4×Dic9—41no—
106C4×Dic9—41no—
107C4×Dic9—41no—
108#2334—91noSylow
109C23×Dic3—31no—
110C3×#126Dic318yes—
111C2×C3×C4⋊C4C2×D311yescharacteristic
112C2×C3×C4⋊C4C2×D311yescharacteristic
113C2×C3×C4⋊C4C2×D311yescharacteristic
114C2×C3×C22⋊C4C2×D311yescharacteristic
115C2×C3×C22⋊C4C2×D311yescharacteristic
116C2×C3×C22⋊C4C2×D311yescharacteristic
117C2×C3×C42C2×D311yescharacteristic
118C2×#217—31no—
119C2×#217—31no—
120C2×#217—31no—
121C2×C4⋊Dic3—31no—
122C2×C4⋊Dic3—31no—
123C2×C4⋊Dic3—31no—
124C2×C4⋊Dic3—31no—
125C2×C4⋊Dic3—31no—
126C2×C4⋊Dic3—31no—
127C2×C4⋊Dic3—31no—
128C2×C4×Dic3—31no—
129C2×C4×Dic3—31no—
130C2×C4×Dic3—31no—
131C2×C4×Dic3—31no—
132C2×C4×Dic3—31no—
133C3⋊#95—31no—
134C3⋊#95—31no—
135C3⋊#95—31no—
136C3⋊#95—31no—
137C3⋊#95—31no—
138C3⋊#95—31no—
139C3⋊#95—31no—
140C3⋊#95—31no—
141C3⋊#95—31no—
142C3⋊#95—31no—
143C3⋊#95—31no—
144C3⋊#95—31no—
145C23×C9—21no—
146C23×C9—21no—
147C23×C9—21no—
148C23×C9—21no—
149C23×C9—21no—
150C23×C9—21no—
151C23×C9C22×C412yes—
152C23×C9C2411yescharacteristic
153C2×C4×C9—21no—
154C2×C4×C9—21no—
155C2×C4×C9—21no—
156C2×C4×C9—21no—
157C2×C4×C9—21no—
158C2×C4×C9—21no—
159C2×C4×C9—21no—
160C2×C4×C9—21no—
161C2×C4×C9—21no—
162C2×C4×C9—21no—
163C2×C4×C9—21no—
164C2×C4×C9—21no—
165C2×C4×C9C22×C412yes—
166C2×C4×C9C22×C412yes—
167C2×C4×C9C22×C412yes—
168C2×C4×C9C22×C412yes—
169C2×C4×C9C22×C412yes—
170C2×C4×C9C22×C412yes—
171C2×Dic9—21no—
172C2×Dic9—21no—
173C2×Dic9—21no—
174C2×Dic9—21no—
175C2×Dic9—21no—
176C2×Dic9—21no—
177C2×Dic9—21no—
178C2×Dic9—21no—
179C2×Dic9—21no—
180C2×Dic9—21no—
181C2×Dic9—21no—
182C2×Dic9—21no—
183C2×Dic9—21no—
184C2×Dic9—21no—
185C2×Dic9—21no—
186C2×Dic9—21no—
187C2×Dic9—21no—
188C2×Dic9—21no—
189C2×Dic9—21no—
190C2×Dic9—21no—
191C2×Dic9—21no—
192C2×Dic9—21no—
193C2×Dic9—44no—
194C2×Dic9#4112yes—
195C2×Dic9#4112yes—
196C2×#126D911yescharacteristic
197#389—91no—
198#389—91no—
199#388—91no—
200#388—91no—
201#388—91no—
202#387—91no—
203#387—91no—
204#387—91no—
205#385—91no—
206#385—91no—
207#382—91no—
208C4×C4⋊C4—91no—
209C4×C4⋊C4—91no—
210C4×C22⋊C4—91no—
211C24×C3C22×D311yescharacteristic
212C22×C3×C4C22×D311yescharacteristic
213C22×C3×C4C22×D311yescharacteristic
214C22×C3×C4C22×D311yescharacteristic
215C22×C3×C4C22×D311yescharacteristic
216C22×C3×C4C22×D311yescharacteristic
217C22×C3×C4C22×D311yescharacteristic
218C22×Dic3—31no—
219C22×Dic3—31no—
220C22×Dic3—31no—
221C22×Dic3—31no—
222C22×Dic3—31no—
223C22×Dic3—31no—
224C22×Dic3—31no—
225C22×Dic3—31no—
226C22×Dic3—62no—
227C22×Dic3—121no—
228C22×Dic3—121no—
229C3×C4⋊C4C2×Dic314yes—
230C3×C4⋊C4C2×Dic314yes—
231C3×C4⋊C4C2×Dic314yes—
232C3×C22⋊C4C2×Dic314yes—
233C3×C22⋊C4C2×Dic314yes—
234C3×C22⋊C4C2×Dic314yes—
235C3×C42C2×Dic314yes—
236#217—62no—
237#217—121no—
238#217—121no—
239C4⋊Dic3—62no—
240C4⋊Dic3—62no—
241C4⋊Dic3—62no—
242C4⋊Dic3—121no—
243C4⋊Dic3—121no—
244C4⋊Dic3—121no—
245C4⋊Dic3—121no—
246C4×Dic3—62no—
247C4×Dic3—121no—
248C4×Dic3—121no—
249C4×Dic3—121no—
250C4×Dic3—121no—
251C22×C9—22no—
252C22×C9—22no—
253C22×C9—22no—
254C22×C9—41no—
255C22×C9—41no—
256C22×C9—41no—
257C22×C9—41no—
258C22×C9C23×C411yescharacteristic
259C22×C9C2×#4111yescharacteristic
260C22×C9C2×#4111yescharacteristic
261C22×C9H(5,𝔽2)11yescharacteristic
262C22×C9H(5,𝔽2)11yescharacteristic
263C22×C92−1+411yescharacteristic
264C22×C92−1+411yescharacteristic
265C4×C9—22no—
266C4×C9—22no—
267C4×C9—22no—
268C4×C9—22no—
269C4×C9—22no—
270C4×C9—22no—
271Dic9—22no—
272Dic9—22no—
273Dic9—41no—
274Dic9—41no—
275Dic9—41no—
276Dic9—41no—
277Dic9—41no—
278Dic9—41no—
279C23×C4—91no—
280#126Dic918yescomplemented
281C2×C4⋊C4—91no—
282C2×C4⋊C4—91no—
283C2×C4⋊C4—91no—
284C2×C4⋊C4—91no—
285C2×C4⋊C4—91no—
286C2×C4⋊C4—91no—
287C2×C4⋊C4—91no—
288C2×C4⋊C4C2×D911yescharacteristic
289C2×C4⋊C4C2×D911yescharacteristic
290C2×C4⋊C4C2×D911yescharacteristic
291C2×C22⋊C4—91no—
292C2×C22⋊C4—91no—
293C2×C22⋊C4—91no—
294C2×C22⋊C4C2×D911yescharacteristic
295C2×C22⋊C4C2×D911yescharacteristic
296C2×C22⋊C4C2×D911yescharacteristic
297C2×C42—91no—
298C2×C42—91no—
299C2×C42—91no—
300C2×C42—91no—
301C2×C42—91no—
302C2×C42C2×D911yescharacteristic
303#95—91no—
304#95—91no—
305#95—91no—
306#95—91no—
307#95—91no—
308#95—91no—
309#95—91no—
310#95—91no—
311#95—91no—
312#95—91no—
313#95—91no—
314#95—91no—
315C23×C3—21no—
316C23×C3—21no—
317C23×C3—21no—
318C23×C3—21no—
319C23×C3—21no—
320C23×C3—21no—
321C23×C3C22×Dic312yes—
322C23×C3C23×D311yescharacteristic
323C2×C3×C4—21no—
324C2×C3×C4—21no—
325C2×C3×C4—21no—
326C2×C3×C4—21no—
327C2×C3×C4—21no—
328C2×C3×C4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4C22×Dic312yes—
336C2×C3×C4C22×Dic312yes—
337C2×C3×C4C22×Dic312yes—
338C2×C3×C4C22×Dic312yes—
339C2×C3×C4C22×Dic312yes—
340C2×C3×C4C22×Dic312yes—
341C2×Dic3—32no—
342C2×Dic3—32no—
343C2×Dic3—61no—
344C2×Dic3—61no—
345C2×Dic3—61no—
346C2×Dic3—61no—
347C2×Dic3—61no—
348C2×Dic3—61no—
349C2×Dic3—61no—
350C2×Dic3—61no—
351C2×Dic3—61no—
352C2×Dic3—61no—
353C2×Dic3—61no—
354C2×Dic3—61no—
355C2×Dic3—61no—
356C2×Dic3—61no—
357C2×Dic3—61no—
358C2×Dic3—61no—
359C2×Dic3—61no—
360C2×Dic3—61no—
361C2×Dic3—61no—
362C2×Dic3—61no—
363C2×Dic3—61no—
364C2×Dic3—61no—
365C2×Dic3—124no—
366C2×C9—42no—
367C2×C9C4×#4111yescharacteristic
368C2×C9#52011yescharacteristic
369C2×C9#52011yescharacteristic
370C2×C9#53811yescharacteristic
371C2×C9#53911yescharacteristic
372C2×C9#54111yescharacteristic
373C2×C9#54211yescharacteristic
374C24C22×D911yescharacteristic
375C22×C4—91no—
376C22×C4—91no—
377C22×C4—91no—
378C22×C4—91no—
379C22×C4—91no—
380C22×C4—91no—
381C22×C4—91no—
382C22×C4—91no—
383C22×C4—182no—
384C22×C4—361no—
385C22×C4—361no—
386C22×C4C22×D911yescharacteristic
387C22×C4C22×D911yescharacteristic
388C22×C4C22×D911yescharacteristic
389C22×C4C22×D911yescharacteristic
390C22×C4C22×D911yescharacteristic
391C22×C4C22×D911yescharacteristic
392C4⋊C4—182no—
393C4⋊C4—182no—
394C4⋊C4—182no—
395C4⋊C4—361no—
396C4⋊C4—361no—
397C4⋊C4—361no—
398C4⋊C4—361no—
399C4⋊C4C2×Dic914yescomplemented
400C4⋊C4C2×Dic914yescomplemented
401C4⋊C4C2×Dic914yescomplemented
402C22⋊C4—182no—
403C22⋊C4—361no—
404C22⋊C4—361no—
405C22⋊C4C2×Dic914yes—
406C22⋊C4C2×Dic914yes—
407C22⋊C4C2×Dic914yes—
408C42—182no—
409C42—361no—
410C42—361no—
411C42—361no—
412C42—361no—
413C42C2×Dic914yescomplemented
414C22×C3—22no—
415C22×C3—22no—
416C22×C3—22no—
417C22×C3—41no—
418C22×C3—41no—
419C22×C3—41no—
420C22×C3—41no—
421C22×C3D3×#4111yescharacteristic
422C22×C3D3×#4111yescharacteristic
423C22×C3#100911yescharacteristic
424C22×C3#100911yescharacteristic
425C22×C3#101011yescharacteristic
426C22×C3#101011yescharacteristic
427C22×C3C23×Dic311yescharacteristic
428C3×C4—22no—
429C3×C4—22no—
430C3×C4—22no—
431C3×C4—22no—
432C3×C4—22no—
433C3×C4—22no—
434Dic3—62no—
435Dic3—62no—
436Dic3—121no—
437Dic3—121no—
438Dic3—121no—
439Dic3—121no—
440Dic3—121no—
441Dic3—121no—
442C9#233411yescharacteristic, complemented, Sylow
443C23—21no—
444C23—21no—
445C23—21no—
446C23—21no—
447C23—21no—
448C23—21no—
449C23C22×Dic912yes—
450C23C23×D911yescharacteristic
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—92no—
464C2×C4—92no—
465C2×C4—181no—
466C2×C4—181no—
467C2×C4—181no—
468C2×C4—181no—
469C2×C4—181no—
470C2×C4—181no—
471C2×C4—181no—
472C2×C4—181no—
473C2×C4—181no—
474C2×C4—181no—
475C2×C4—181no—
476C2×C4—181no—
477C2×C4—181no—
478C2×C4—181no—
479C2×C4—181no—
480C2×C4—181no—
481C2×C4—181no—
482C2×C4—181no—
483C2×C4—181no—
484C2×C4—181no—
485C2×C4—181no—
486C2×C4—181no—
487C2×C4—364no—
488C2×C4C22×Dic912yes—
489C2×C4C22×Dic912yes—
490C2×C4C22×Dic912yes—
491C2×C4C22×Dic912yes—
492C2×C4C22×Dic912yes—
493C2×C4C22×Dic912yes—
494C2×C3—42no—
495C2×C3#570111yescharacteristic
496C2×C3#570411yescharacteristic
497C2×C3#570711yescharacteristic
498C2×C3#571011yescharacteristic
499C2×C3Dic3×#4111yescharacteristic
500C2×C3#582711yescharacteristic
501C2×C3#582711yescharacteristic
502C22—22no—
503C22—22no—
504C22—22no—
505C22—41no—
506C22—41no—
507C22—41no—
508C22—41no—
509C22#41×D911yescharacteristic
510C22#41×D911yescharacteristic
511C22#6371511yescharacteristic
512C22#6371511yescharacteristic
513C22#6371611yescharacteristic
514C22#6371611yescharacteristic
515C22C23×Dic911yescharacteristic
516C4—22no—
517C4—22no—
518C4—22no—
519C4—22no—
520C4—22no—
521C4—22no—
522C4—182no—
523C4—182no—
524C4—361no—
525C4—361no—
526C4—361no—
527C4—361no—
528C4—361no—
529C4—361no—
530C3#8307411yescharacteristic
531C2—42no—
532C2#1058980311yescharacteristic
533C2#1058980611yescharacteristic
534C2#1058980911yescharacteristic
535C2#1058981211yescharacteristic
536C2#41×Dic911yescharacteristic
537C2#1058992911yescharacteristic
538C2#1058992911yescharacteristic
subgroupG/H
centerC23C23×D9
commutatorC22×C9C23×C4
Frattini, socleC23×C3C23×D3
FittingC2×C9×#126C2
prime radicalC24×C3C22×D3
cosocleC23×C9C24
hypercenterC2×#126D9
hypocenterC9#2334
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C23 ◁ C2×#126

Complements

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

NH ≅ G/Ntype
2. #10588664C2semidirect
3. #10588664C2semidirect
4. #10588660C2semidirect
5. #10588660C2semidirect
6. #10588660C2semidirect
7. C4⋊C4×Dic9C2semidirect
14. #10588616C2semidirect
15. C4×C4⋊Dic9C2semidirect
18. C9×#126C4semidirect
86. C9×C4⋊C4C2×C4semidirect
87. C9×C4⋊C4C2×C4semidirect
88. C9×C4⋊C4C2×C4semidirect
92. C42×C9C2×C4semidirect
280. #126Dic9semidirect
399. C4⋊C4C2×Dic9semidirect
400. C4⋊C4C2×Dic9semidirect
401. C4⋊C4C2×Dic9semidirect
413. C42C2×Dic9semidirect
442. C9#2334semidirect

Maximal subgroups

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

subgroupindex
C2×C9×#1262
#105886642
#105886602
C4⋊C4×Dic92
#105886312
#105886302
C22⋊C4×Dic92
#105886162
C4×C4⋊Dic92
#830743