Finite Group Databasebeta

← #11897520

Subgroups — #11897520

Order 1152.

561 conjugacy classes of subgroups.

The subgroup lattice has 495 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10589641C211yesmaximal, characteristic, complemented
2D4×Dic18C211yesmaximal, characteristic, complemented
3C9×#442C211yesmaximal, characteristic
4#10588832C211yesmaximal, characteristic
5D8×Dic9C211yesmaximal, characteristic
6#10588692C211yesmaximal, characteristic, complemented
7#10588691C211yesmaximal, characteristic, complemented
8#10588536C211yesmaximal, characteristic, complemented
9#10588535C211yesmaximal, characteristic, complemented
10#10588446C211yesmaximal, characteristic, complemented
11#10588441C211yesmaximal, characteristic, complemented
12#10588441C211yesmaximal, characteristic, complemented
13#10588439C211yesmaximal, characteristic, complemented
14#10588382C211yesmaximal, characteristic, complemented
15#10588381C211yesmaximal, characteristic, complemented
16#79855—31nomaximal
17C22×Dic18—21no—
18C2×C9×D8C2211yescharacteristic
19C4×D4×C9C2211yescharacteristic
20C4×D4×C9C2211yescharacteristic
21D4×Dic9C2211yescharacteristic
22D4×Dic9C2211yescharacteristic
23D4×Dic9C2211yescharacteristic
24D4×Dic9C2211yescharacteristic
25#63486—21no—
26#63486—21no—
27C2×Dic9⋊C4—21no—
28#63452C2211yescharacteristic
29#63450C2211yescharacteristic
30#63450C2211yescharacteristic
31#63450C2211yescharacteristic
32#63440—21no—
33#63440—21no—
34#63440—21no—
35#63440—21no—
36#63432C2211yescharacteristic
37#63431C2211yescharacteristic
38C4×Dic18C2211yescharacteristic
39C9×#106C2211yescharacteristic
40C9×#102C2211yescharacteristic
41C9×#102C2211yescharacteristic
42C9×#97C2211yescharacteristic
43#63392C2211yescharacteristic
44#63392C2211yescharacteristic
45#63392C2211yescharacteristic
46#63392C2211yescharacteristic
47#63378C2211yescharacteristic
48#63378C2211yescharacteristic
49#63377C2211yescharacteristic
50#63377C2211yescharacteristic
51#63375C2211yescharacteristic
52Dic9⋊C8C2211yescharacteristic
53Dic9⋊C8C2211yescharacteristic
54C8×Dic9C2211yescharacteristic
55#63367C2211yescharacteristic
56#63367C2211yescharacteristic
57#63367C2211yescharacteristic
58#63366C2211yescharacteristic
59C4⋊(C9⋊C8)C2211yescharacteristic
60#5539—31no—
61D4×Dic6—31no—
62C3×#442D311yescharacteristic
63#5152—31no—
64Dic3×D8—31no—
65#5009—31no—
66#5008—31no—
67#4856—31no—
68#4855—31no—
69#4766—31no—
70#4761—31no—
71#4761—31no—
72#4759—31no—
73#4702—31no—
74#4701—31no—
75C2×D4×C9C2311yescharacteristic
76C2×D4×C9C2311yescharacteristic
77C22×C4×C9—21no—
78C22×C4×C9—21no—
79C22×Dic9—21no—
80C22×Dic9—21no—
81C22×Dic9—21no—
82C22×Dic9—21no—
83C2×Dic18—21no—
84C2×Dic18—21no—
85C2×Dic18—21no—
86C2×Dic18—21no—
87C2×Dic18—44no—
88C2×Dic18D411yescharacteristic
89C9×D8Q814yescomplemented
90C2×C8×C9C2311yescharacteristic
91C2×C8×C9C2311yescharacteristic
92C9×C4⋊C4C2311yescharacteristic
93C9×C4⋊C4C2311yescharacteristic
94C9×C22⋊C4—21no—
95C9×C22⋊C4—21no—
96C42×C9C2311yescharacteristic
97#3676—21no—
98#3676—21no—
99#3676—21no—
100#3676—21no—
101C4⋊Dic9—21no—
102C4⋊Dic9—21no—
103C4⋊Dic9D411yescharacteristic
104C4⋊Dic9C2311yescharacteristic
105C4⋊Dic9C2311yescharacteristic
106C4⋊Dic9C2311yescharacteristic
107C4⋊Dic9C2311yescharacteristic
108Dic9⋊C4—21no—
109Dic9⋊C4—21no—
110Dic9⋊C4—21no—
111Dic9⋊C4—21no—
112Dic9⋊C4—21no—
113Dic9⋊C4—21no—
114Dic9⋊C4D411yescharacteristic
115Dic9⋊C4D411yescharacteristic
116C4×Dic9C2311yescharacteristic
117C4×Dic9C2311yescharacteristic
118C2×C9⋊C8C2311yescharacteristic
119C2×C9⋊C8C2311yescharacteristic
120#3384—91noSylow
121C22×Dic6—61no—
122C2×C3×D8C2×D311yescharacteristic
123C3×C4×D4C2×D311yescharacteristic
124C3×C4×D4C2×D311yescharacteristic
125D4×Dic3—31no—
126D4×Dic3—31no—
127D4×Dic3—31no—
128D4×Dic3—31no—
129#924—61no—
130#924—61no—
131C2×Dic3⋊C4—61no—
132#890—31no—
133#888—31no—
134#888—31no—
135#888—31no—
136#878—61no—
137#878—61no—
138#878—61no—
139#878—61no—
140#870—31no—
141#869—31no—
142C4×Dic6—31no—
143C3×#106C2×D311yescharacteristic
144C3×#102C2×D311yescharacteristic
145C3×#102C2×D311yescharacteristic
146C3×#97C2×D311yescharacteristic
147#832—31no—
148#832—31no—
149#832—31no—
150#832—31no—
151#818—31no—
152#818—31no—
153#817—31no—
154#817—31no—
155#815—31no—
156Dic3⋊C8—31no—
157Dic3⋊C8—31no—
158C8×Dic3—31no—
159#808—31no—
160#808—31no—
161#808—31no—
162#807—31no—
163C4⋊(C3⋊C8)—31no—
164C23×C9—21no—
165C23×C9—21no—
166D4×C9—21no—
167D4×C9—21no—
168D4×C9C2×Q812yes—
169D4×C9C2×Q812yescomplemented
170C2×C4×C9—21no—
171C2×C4×C9—21no—
172C2×C4×C9—42no—
173C2×C4×C9—81no—
174C2×C4×C9C2×D411yescharacteristic
175C2×C4×C9C2×D411yescharacteristic
176C2×C4×C9C2411yescharacteristic
177C2×Dic9—21no—
178C2×Dic9—21no—
179C2×Dic9—21no—
180C2×Dic9—21no—
181C2×Dic9—42no—
182C2×Dic9—42no—
183C2×Dic9—42no—
184C2×Dic9—81no—
185C2×Dic9C2×D411yescharacteristic
186C2×Dic9C2×D411yescharacteristic
187C2×Dic9C2×D411yescharacteristic
188C2×Dic9C2×D411yescharacteristic
189Dic18—22no—
190Dic18—42no—
191Dic18—42no—
192Dic18—42no—
193Dic18—81no—
194C8×C9—21no—
195C8×C9C2×Q812yescomplemented
196C9⋊C8—21no—
197C9⋊C8—21no—
198#554—91no—
199D4×Q8—91no—
200#501—91no—
201#501—91no—
202#498—91no—
203#478—91no—
204#478—91no—
205#476—91no—
206#476—91no—
207#476—91no—
208#474—91no—
209#446—91no—
210#442—91no—
211#442D911yescharacteristic
212C4×D8—91no—
213C2×C3×D4C22×D311yescharacteristic
214C2×C3×D4C22×D311yescharacteristic
215C22×C3×C4—21no—
216C22×C3×C4—21no—
217C22×Dic3—61no—
218C22×Dic3—61no—
219C22×Dic3—61no—
220C22×Dic3—61no—
221C2×Dic6—31no—
222C2×Dic6—61no—
223C2×Dic6—61no—
224C2×Dic6—61no—
225C2×Dic6—61no—
226C2×Dic6—124no—
227C3×D8Dic614yes—
228C2×C3×C8C22×D311yescharacteristic
229C2×C3×C8C22×D311yescharacteristic
230C3×C4⋊C4C22×D311yescharacteristic
231C3×C4⋊C4C22×D311yescharacteristic
232C3×C22⋊C4—21no—
233C3×C22⋊C4—21no—
234C3×C42C22×D311yescharacteristic
235#217—61no—
236#217—61no—
237#217—61no—
238#217—61no—
239C4⋊Dic3—31no—
240C4⋊Dic3—31no—
241C4⋊Dic3—31no—
242C4⋊Dic3—31no—
243C4⋊Dic3—31no—
244C4⋊Dic3—61no—
245C4⋊Dic3—61no—
246Dic3⋊C4—31no—
247Dic3⋊C4—31no—
248Dic3⋊C4—61no—
249Dic3⋊C4—61no—
250Dic3⋊C4—61no—
251Dic3⋊C4—61no—
252Dic3⋊C4—61no—
253Dic3⋊C4—61no—
254C4×Dic3—31no—
255C4×Dic3—31no—
256C2×C3⋊C8—31no—
257C2×C3⋊C8—31no—
258C22×C9—22no—
259C22×C9—22no—
260C22×C9—41no—
261C22×C9—41no—
262C22×C9—41no—
263C22×C9—41no—
264C22×C9C22×D411yescharacteristic
265C4×C9—21no—
266C4×C9—21no—
267C4×C9—41no—
268C4×C9—41no—
269C4×C9C22×Q811yescharacteristic
270C4×C92−1+411yescharacteristic
271Dic9—21no—
272Dic9—21no—
273Dic9—21no—
274Dic9—41no—
275Dic9—41no—
276Dic9—41no—
277Dic9—41no—
278Dic9AGL(1,ℤ/8)12yes—
279C22×Q8—181no—
280C2×D8C2×D911yescharacteristic
281C4⋊Q8—91no—
282C4⋊Q8—91no—
283C4⋊Q8—91no—
284C4⋊Q8—91no—
285#125—91no—
286#125—91no—
287C22⋊Q8—181no—
288C22⋊Q8—181no—
289C22⋊Q8—181no—
290C22⋊Q8—181no—
291C22⋊Q8—181no—
292C22⋊Q8—181no—
293C4×Q8—91no—
294C4×D4—91no—
295C4×D4—91no—
296C4×D4—91no—
297C4×D4—91no—
298C4×D4C2×D911yescharacteristic
299C4×D4C2×D911yescharacteristic
300C2×C4⋊C4—181no—
301#107—91no—
302#107—91no—
303#107—91no—
304#106—91no—
305#106—91no—
306#106—91no—
307#106—91no—
308#106—91no—
309#106C2×D911yescharacteristic
310C4⋊C8—91no—
311C4⋊C8—91no—
312C4⋊C8—91no—
313#102—91no—
314#102—91no—
315#102—91no—
316#102—91no—
317#102C2×D911yescharacteristic
318#102C2×D911yescharacteristic
319#97—91no—
320#97C2×D911yescharacteristic
321C4×C8—91no—
322C23×C3—21no—
323C23×C3—21no—
324C3×D4—21no—
325C3×D4—21no—
326C3×D4C2×Dic612yes—
327C3×D4C2×Dic612yes—
328C2×C3×C4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—42no—
331C2×C3×C4—81no—
332C2×C3×C4D3×D411yescharacteristic
333C2×C3×C4D3×D411yescharacteristic
334C2×C3×C4C23×D311yescharacteristic
335C2×Dic3—31no—
336C2×Dic3—31no—
337C2×Dic3—31no—
338C2×Dic3—31no—
339C2×Dic3—61no—
340C2×Dic3—61no—
341C2×Dic3—61no—
342C2×Dic3—61no—
343C2×Dic3—122no—
344C2×Dic3—122no—
345C2×Dic3—122no—
346C2×Dic3—241no—
347Dic6—62no—
348Dic6—122no—
349Dic6—122no—
350Dic6—122no—
351Dic6—241no—
352C3×C8—21no—
353C3×C8C2×Dic612yes—
354C3⋊C8—61no—
355C3⋊C8—61no—
356C2×C9—42no—
357C2×C9—42no—
358C2×C9D4×Q811yescharacteristic
359C2×C9C2×AGL(1,ℤ/8)11yescharacteristic
360C2×C9#57711yescharacteristic
361C2×Q8—91no—
362C2×Q8—181no—
363C2×Q8—181no—
364C2×Q8—181no—
365C2×Q8—181no—
366C2×Q8—364no—
367C2×D4C22×D911yescharacteristic
368C2×D4C22×D911yescharacteristic
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—181no—
372C22×C4—181no—
373C22×C4—181no—
374C22×C4—181no—
375D8Dic1814yescomplemented
376C2×C8—91no—
377C2×C8—91no—
378C2×C8C22×D911yescharacteristic
379C2×C8C22×D911yescharacteristic
380C4⋊C4—91no—
381C4⋊C4—91no—
382C4⋊C4—91no—
383C4⋊C4—91no—
384C4⋊C4—91no—
385C4⋊C4—91no—
386C4⋊C4—91no—
387C4⋊C4—181no—
388C4⋊C4—181no—
389C4⋊C4—181no—
390C4⋊C4—181no—
391C4⋊C4—181no—
392C4⋊C4—181no—
393C4⋊C4—181no—
394C4⋊C4—181no—
395C4⋊C4C22×D911yescharacteristic
396C4⋊C4C22×D911yescharacteristic
397C22⋊C4—21no—
398C22⋊C4—21no—
399C22⋊C4—181no—
400C22⋊C4—181no—
401C22⋊C4—181no—
402C22⋊C4—181no—
403C42—91no—
404C42—91no—
405C42C22×D911yescharacteristic
406C22×C3—22no—
407C22×C3—22no—
408C22×C3—41no—
409C22×C3—41no—
410C22×C3—41no—
411C22×C3—41no—
412C22×C3C2×D3×D411yescharacteristic
413C3×C4—21no—
414C3×C4—21no—
415C3×C4—41no—
416C3×C4—41no—
417C3×C4C22×Dic611yescharacteristic
418C3×C4#101011yescharacteristic
419Dic3—32no—
420Dic3—61no—
421Dic3—61no—
422Dic3—61no—
423Dic3—121no—
424Dic3—121no—
425Dic3—121no—
426Dic3—121no—
427C9#338411yescharacteristic, complemented, Sylow
428C23—21no—
429C23—21no—
430Q8—182no—
431Q8—362no—
432Q8—362no—
433Q8—362no—
434Q8—721no—
435D4—21no—
436D4—21no—
437D4C2×Dic1812yes—
438D4C2×Dic1812yescomplemented
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—42no—
442C2×C4—81no—
443C2×C4—91no—
444C2×C4—91no—
445C2×C4—91no—
446C2×C4—91no—
447C2×C4—181no—
448C2×C4—181no—
449C2×C4—181no—
450C2×C4—181no—
451C2×C4—362no—
452C2×C4—362no—
453C2×C4—362no—
454C2×C4—721no—
455C2×C4D4×D911yescharacteristic
456C2×C4D4×D911yescharacteristic
457C2×C4C23×D911yescharacteristic
458C8—21no—
459C8—181no—
460C8—181no—
461C8C2×Dic1812yescomplemented
462C2×C3—42no—
463C2×C3—42no—
464C2×C3D4×Dic611yescharacteristic
465C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
466C2×C3#577511yescharacteristic
467C22—22no—
468C22—22no—
469C22—41no—
470C22—41no—
471C22—41no—
472C22—41no—
473C22C2×D4×D911yescharacteristic
474C4—21no—
475C4—21no—
476C4—41no—
477C4—41no—
478C4—92no—
479C4—181no—
480C4—181no—
481C4—181no—
482C4—361no—
483C4—361no—
484C4—361no—
485C4—361no—
486C4C22×Dic1811yescharacteristic
487C4#6371611yescharacteristic
488C3#7985511yescharacteristic
489C2—42no—
490C2—42no—
491C2D4×Dic1811yescharacteristic
492C2D9×AGL(1,ℤ/8)11yescharacteristic
493C2#1058987711yescharacteristic
subgroupG/H
centerC22C2×D4×D9
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#442C2
socleC22×C3C2×D3×D4
prime radicalC2×C3×D8C2×D3
hypercenter#442D9
hypocenterC9#3384
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #10589641C2semidirect
2. D4×Dic18C2semidirect
6. #10588692C2semidirect
7. #10588691C2semidirect
8. #10588536C2semidirect
9. #10588535C2semidirect
10. #10588446C2semidirect
11. #10588441C2semidirect
12. #10588441C2semidirect
13. #10588439C2semidirect
14. #10588382C2semidirect
15. #10588381C2semidirect
89. C9×D8Q8semidirect
169. D4×C9C2×Q8semidirect
195. C8×C9C2×Q8semidirect
375. D8Dic18semidirect
427. C9#3384semidirect
438. D4C2×Dic18semidirect
461. C8C2×Dic18semidirect

Maximal subgroups

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

subgroupindex
#105896412
D4×Dic182
C9×#4422
#105888322
D8×Dic92
#105886922
#105886912
#105885362
#105885352
#105884462
#105884412
#105884392
#105883822
#105883812
#798553