Finite Group Databasebeta

← #11872387

Subgroups — #11872387

Order 1152.

558 conjugacy classes of subgroups.

The subgroup lattice has 507 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10589929C211yesmaximal, characteristic
2#10589727C211yesmaximal, characteristic, complemented
3C9×#452C211yesmaximal, characteristic
4#10588918C211yesmaximal, characteristic
5#10588864C211yesmaximal, characteristic, complemented
6#10588862C211yesmaximal, characteristic, complemented
7#10588842C211yesmaximal, characteristic, complemented
8SD16×Dic9C211yesmaximal, characteristic, complemented
9#10588724C211yesmaximal, characteristic, complemented
10#10588479C211yesmaximal, characteristic, complemented
11#10588470C211yesmaximal, characteristic, complemented
12#10588443C211yesmaximal, characteristic, complemented
13#10588437C211yesmaximal, characteristic, complemented
14#10588401C211yesmaximal, characteristic, complemented
15#10588400C211yesmaximal, characteristic, complemented
16#80216—31nomaximal
17C2×C9×#41C2211yescharacteristic
18C2×C9×Q16C2211yescharacteristic
19C2×C9×SD16C2211yescharacteristic
20C9×C22⋊Q8C2211yescharacteristic
21Q8×Dic9C2211yescharacteristic
22Q8×Dic9C2211yescharacteristic
23Q8×Dic9C2211yescharacteristic
24#63506C2211yescharacteristic
25C2×#3674C2211yescharacteristic
26D4×Dic9—21no—
27D4×Dic9—21no—
28D4×Dic9C2211yescharacteristic
29D4×Dic9C2211yescharacteristic
30C2×#3672C2211yescharacteristic
31#63488—21no—
32#63488C2211yescharacteristic
33C2×C4⋊Dic9—21no—
34C2×C4⋊Dic9C2211yescharacteristic
35#63486C2211yescharacteristic
36#63452—21no—
37#63452C2211yescharacteristic
38#63451—21no—
39#63449C2211yescharacteristic
40#63441—21no—
41#63441—21no—
42C9×#103C2211yescharacteristic
43C9×#102C2211yescharacteristic
44C9×C22⋊C8C2211yescharacteristic
45#63395C2211yescharacteristic
46#63395C2211yescharacteristic
47#63395C2211yescharacteristic
48#63392C2211yescharacteristic
49#63389C2211yescharacteristic
50#63377C2211yescharacteristic
51#63377C2211yescharacteristic
52#63376C2211yescharacteristic
53#63376C2211yescharacteristic
54#63375C2211yescharacteristic
55Dic9⋊C8C2211yescharacteristic
56Dic9⋊C8C2211yescharacteristic
57C8×Dic9C2211yescharacteristic
58#63366C2211yescharacteristic
59#63366C2211yescharacteristic
60#5827—31no—
61#5625—31no—
62C3×#452D311yescharacteristic
63#5239—31no—
64#5184—31no—
65#5182—31no—
66#5162—31no—
67Dic3×SD16—31no—
68#5044—31no—
69#4799—31no—
70#4790—31no—
71#4763—31no—
72#4757—31no—
73#4721—31no—
74#4720—31no—
75C9×#41—22no—
76C9×#41—22no—
77C2×Q8×C9C2311yescharacteristic
78C2×Q8×C9C2311yescharacteristic
79C2×D4×C9—21no—
80C2×D4×C9C2311yescharacteristic
81C22×C4×C9—21no—
82C22×C4×C9C2311yescharacteristic
83C22×Dic9—21no—
84C22×Dic9—21no—
85C22×Dic9—21no—
86C2×Dic18C2311yescharacteristic
87C9×Q16—22no—
88C9×SD16—22no—
89C2×C8×C9C2311yescharacteristic
90C2×C8×C9C2311yescharacteristic
91C9×C4⋊C4—21no—
92C9×C4⋊C4C2311yescharacteristic
93C9×C22⋊C4—21no—
94#3676—21no—
95#3676—21no—
96#3676—21no—
97#3676D411yescharacteristic
98#3676D411yescharacteristic
99#3674—22no—
100#3672—22no—
101C4⋊Dic9—21no—
102C4⋊Dic9—21no—
103C4⋊Dic9—21no—
104C4⋊Dic9—21no—
105C4⋊Dic9—21no—
106C4⋊Dic9D411yescharacteristic
107C4⋊Dic9D411yescharacteristic
108C4⋊Dic9C2311yescharacteristic
109C4⋊Dic9C2311yescharacteristic
110C4⋊Dic9C2311yescharacteristic
111Dic9⋊C4—21no—
112Dic9⋊C4—21no—
113Dic9⋊C4—21no—
114Dic9⋊C4—21no—
115Dic9⋊C4—21no—
116C4×Dic9—21no—
117C4×Dic9—21no—
118C4×Dic9—21no—
119C4×Dic9—21no—
120C4×Dic9C2311yescharacteristic
121C4×Dic9C2311yescharacteristic
122C2×C9⋊C8C2311yescharacteristic
123C2×C9⋊C8C2311yescharacteristic
124#3120—91noSylow
125C2×C3×#41C2×D311yescharacteristic
126C2×C3×Q16C2×D311yescharacteristic
127C2×C3×SD16C2×D311yescharacteristic
128C3×C22⋊Q8C2×D311yescharacteristic
129Q8×Dic3—31no—
130Q8×Dic3—31no—
131Q8×Dic3—31no—
132#944—31no—
133C2×#216—31no—
134D4×Dic3—31no—
135D4×Dic3—31no—
136D4×Dic3—61no—
137D4×Dic3—61no—
138C2×#214—31no—
139#926—31no—
140#926—61no—
141C2×C4⋊Dic3—31no—
142C2×C4⋊Dic3—61no—
143#924—31no—
144#890—31no—
145#890—61no—
146#889—61no—
147#887—31no—
148#879—61no—
149#879—61no—
150C3×#103C2×D311yescharacteristic
151C3×#102C2×D311yescharacteristic
152C3×C22⋊C8C2×D311yescharacteristic
153#835—31no—
154#835—31no—
155#835—31no—
156#832—31no—
157#830—31no—
158#817—31no—
159#817—31no—
160#816—31no—
161#816—31no—
162#815—31no—
163Dic3⋊C8—31no—
164Dic3⋊C8—31no—
165C8×Dic3—31no—
166#807—31no—
167#807—31no—
168C23×C9—21no—
169C23×C9C2×D411yescharacteristic
170Q8×C9—21no—
171Q8×C9—21no—
172Q8×C9—21no—
173Q8×C9#4112yes—
174D4×C9—24no—
175D4×C9—21no—
176D4×C9#4112yes—
177C2×C4×C9—24no—
178C2×C4×C9—21no—
179C2×C4×C9—21no—
180C2×C4×C9—21no—
181C2×C4×C9—21no—
182C2×C4×C9—21no—
183C2×C4×C9C2×D411yescharacteristic
184C2×C4×C9C2411yescharacteristic
185C2×Dic9—21no—
186C2×Dic9—21no—
187C2×Dic9—21no—
188C2×Dic9—21no—
189C2×Dic9—81no—
190C2×Dic9—81no—
191C2×Dic9—81no—
192C2×Dic9C2×D411yescharacteristic
193C2×Dic9C2×D411yescharacteristic
194C2×Dic9C2×D411yescharacteristic
195C2×Dic9C2×D411yescharacteristic
196Dic18—21no—
197Dic18—21no—
198C8×C9—21no—
199C8×C9—21no—
200C9⋊C8—21no—
201C9⋊C8—21no—
202#541—91no—
203#520—91no—
204#484—91no—
205#483—91no—
206#479—91no—
207#478—91no—
208#462—91no—
209#461—91no—
210#452—91no—
211#452D911yescharacteristic
212#441—91no—
213#440—91no—
214C4×Q16—91no—
215C4×SD16—91no—
216#433—91no—
217C3×#41—22no—
218C3×#41—22no—
219C2×C3×Q8C22×D311yescharacteristic
220C2×C3×Q8C22×D311yescharacteristic
221C2×C3×D4—21no—
222C2×C3×D4C22×D311yescharacteristic
223C22×C3×C4—21no—
224C22×C3×C4C22×D311yescharacteristic
225C22×Dic3—61no—
226C22×Dic3—61no—
227C22×Dic3—61no—
228C2×Dic6—31no—
229C3×Q16—22no—
230C3×SD16—22no—
231C2×C3×C8C22×D311yescharacteristic
232C2×C3×C8C22×D311yescharacteristic
233C3×C4⋊C4—21no—
234C3×C4⋊C4C22×D311yescharacteristic
235C3×C22⋊C4—21no—
236#217—31no—
237#217—31no—
238#217—61no—
239#217—61no—
240#217—61no—
241#216—62no—
242#214—62no—
243C4⋊Dic3—31no—
244C4⋊Dic3—31no—
245C4⋊Dic3—31no—
246C4⋊Dic3—31no—
247C4⋊Dic3—31no—
248C4⋊Dic3—61no—
249C4⋊Dic3—61no—
250C4⋊Dic3—61no—
251C4⋊Dic3—61no—
252C4⋊Dic3—61no—
253Dic3⋊C4—61no—
254Dic3⋊C4—61no—
255Dic3⋊C4—61no—
256Dic3⋊C4—61no—
257Dic3⋊C4—61no—
258C4×Dic3—31no—
259C4×Dic3—31no—
260C4×Dic3—61no—
261C4×Dic3—61no—
262C4×Dic3—61no—
263C4×Dic3—61no—
264C2×C3⋊C8—31no—
265C2×C3⋊C8—31no—
266C22×C9—21no—
267C22×C9—22no—
268C22×C9—21no—
269C22×C9—21no—
270C22×C9—41no—
271C22×C9—41no—
272C22×C9C22×D411yescharacteristic
273C4×C9—21no—
274C4×C9—22no—
275C4×C9—41no—
276C4×C9—41no—
277C4×C9C2×#4111yescharacteristic
278C4×C9C2×#4111yescharacteristic
279Dic9—21no—
280Dic9—21no—
281Dic9—21no—
282Dic9—21no—
283Dic9—41no—
284Dic9—41no—
285Dic9—41no—
286Dic9—41no—
287C2×#41C2×D911yescharacteristic
288C2×Q16—91no—
289C2×Q16C2×D911yescharacteristic
290C2×SD16—91no—
291C2×SD16C2×D911yescharacteristic
292C4⋊Q8—91no—
293#126—181no—
294#126—181no—
295#125—91no—
296#125—181no—
297#125—181no—
298C22⋊Q8—91no—
299C22⋊Q8C2×D911yescharacteristic
300C4×Q8—91no—
301C4×Q8—91no—
302C4×Q8—91no—
303C4×Q8—91no—
304C4×D4—91no—
305C4×D4—91no—
306C4×D4—181no—
307C4×D4—181no—
308#117—91no—
309#117—181no—
310C2×C4⋊C4—91no—
311C2×C4⋊C4—181no—
312#107—91no—
313#107—91no—
314#106—91no—
315#106—91no—
316C4⋊C8—91no—
317C4⋊C8—91no—
318#103—91no—
319#103—91no—
320#103—91no—
321#103—91no—
322#103—91no—
323#103C2×D911yescharacteristic
324#102—91no—
325#102C2×D911yescharacteristic
326C22⋊C8—91no—
327C22⋊C8C2×D911yescharacteristic
328#97—91no—
329C4×C8—91no—
330C23×C3—21no—
331C23×C3D3×D411yescharacteristic
332C3×Q8—21no—
333C3×Q8—21no—
334C3×Q8—21no—
335C3×Q8#23712yes—
336C3×D4—24no—
337C3×D4—21no—
338C3×D4#23712yes—
339C2×C3×C4—24no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—21no—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4D3×D411yescharacteristic
346C2×C3×C4C23×D311yescharacteristic
347C2×Dic3—31no—
348C2×Dic3—31no—
349C2×Dic3—31no—
350C2×Dic3—31no—
351C2×Dic3—61no—
352C2×Dic3—61no—
353C2×Dic3—61no—
354C2×Dic3—61no—
355C2×Dic3—241no—
356C2×Dic3—241no—
357C2×Dic3—241no—
358Dic6—61no—
359Dic6—61no—
360C3×C8—21no—
361C3×C8—21no—
362C3⋊C8—61no—
363C3⋊C8—61no—
364C2×C9—41no—
365C2×C9—42no—
366C2×C9#52511yescharacteristic
367C2×C9#57711yescharacteristic
368C2×C9#57811yescharacteristic
369#41—22no—
370#41—22no—
371C2×Q8—91no—
372C2×Q8C22×D911yescharacteristic
373C2×Q8C22×D911yescharacteristic
374C2×D4—21no—
375C2×D4C22×D911yescharacteristic
376C22×C4—21no—
377C22×C4—181no—
378C22×C4—181no—
379C22×C4—181no—
380C22×C4C22×D911yescharacteristic
381Q16—22no—
382Q16—182no—
383SD16—22no—
384SD16—182no—
385C2×C8—91no—
386C2×C8—91no—
387C2×C8C22×D911yescharacteristic
388C2×C8C22×D911yescharacteristic
389C4⋊C4—21no—
390C4⋊C4—91no—
391C4⋊C4—91no—
392C4⋊C4—91no—
393C4⋊C4—91no—
394C4⋊C4—91no—
395C4⋊C4—181no—
396C4⋊C4—181no—
397C4⋊C4—181no—
398C4⋊C4—181no—
399C4⋊C4—181no—
400C4⋊C4—181no—
401C4⋊C4—181no—
402C4⋊C4—181no—
403C4⋊C4—181no—
404C4⋊C4—181no—
405C4⋊C4C22×D911yescharacteristic
406C22⋊C4—21no—
407C22⋊C4—91no—
408C22⋊C4—91no—
409C22⋊C4—181no—
410C22⋊C4—181no—
411C22⋊C4—181no—
412C42—91no—
413C42—91no—
414C42—181no—
415C42—181no—
416C42—181no—
417C42—181no—
418C22×C3—21no—
419C22×C3—21no—
420C22×C3—21no—
421C22×C3—22no—
422C22×C3—41no—
423C22×C3—41no—
424C22×C3C2×D3×D411yescharacteristic
425C3×C4—21no—
426C3×C4—22no—
427C3×C4—41no—
428C3×C4—41no—
429C3×C4C2×#23711yescharacteristic
430C3×C4C2×#23711yescharacteristic
431Dic3—61no—
432Dic3—61no—
433Dic3—61no—
434Dic3—61no—
435Dic3—121no—
436Dic3—121no—
437Dic3—121no—
438Dic3—121no—
439C9#312011yescharacteristic, complemented, Sylow
440C23—21no—
441C23D4×D911yescharacteristic
442Q8—21no—
443Q8—21no—
444Q8—21no—
445Q8—181no—
446Q8—181no—
447Q8#369912yes—
448D4—24no—
449D4—21no—
450D4#369912yes—
451C2×C4—24no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—91no—
458C2×C4—91no—
459C2×C4—91no—
460C2×C4—91no—
461C2×C4—181no—
462C2×C4—181no—
463C2×C4—181no—
464C2×C4—181no—
465C2×C4—721no—
466C2×C4—721no—
467C2×C4—721no—
468C2×C4D4×D911yescharacteristic
469C2×C4C23×D911yescharacteristic
470C8—21no—
471C8—21no—
472C8—181no—
473C8—181no—
474C2×C3—41no—
475C2×C3—42no—
476C2×C3#558611yescharacteristic
477C2×C3#577011yescharacteristic
478C2×C3#577911yescharacteristic
479C22—21no—
480C22—21no—
481C22—21no—
482C22—22no—
483C22—41no—
484C22—41no—
485C22C2×D4×D911yescharacteristic
486C4—21no—
487C4—22no—
488C4—41no—
489C4—41no—
490C4—181no—
491C4—181no—
492C4—181no—
493C4—181no—
494C4—361no—
495C4—361no—
496C4—361no—
497C4—361no—
498C4C2×#369911yescharacteristic
499C4C2×#369911yescharacteristic
500C3#8021611yescharacteristic
501C2—41no—
502C2—42no—
503C2#1058968811yescharacteristic
504C2#1058987211yescharacteristic
505C2#1058988111yescharacteristic
subgroupG/H
centerC22C2×D4×D9
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#452C2
socleC22×C3C2×D3×D4
prime radicalC2×C3×#41C2×D3
hypercenter#452D9
hypocenterC9#3120
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
2. #10589727C2semidirect
5. #10588864C2semidirect
6. #10588862C2semidirect
7. #10588842C2semidirect
8. SD16×Dic9C2semidirect
9. #10588724C2semidirect
10. #10588479C2semidirect
11. #10588470C2semidirect
12. #10588443C2semidirect
13. #10588437C2semidirect
14. #10588401C2semidirect
15. #10588400C2semidirect
439. C9#3120semidirect

Maximal subgroups

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

subgroupindex
#105899292
#105897272
C9×#4522
#105889182
#105888642
#105888622
#105888422
SD16×Dic92
#105887242
#105884792
#105884702
#105884432
#105884372
#105884012
#105884002
#802163