Finite Group Databasebeta

← #11860574

Subgroups — #11860574

Order 1152.

705 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63480C211yesmaximal, characteristic
2#10589676C211yesmaximal, characteristic
3#10589674C211yesmaximal, characteristic, complemented
4C9×#441C211yesmaximal, characteristic, complemented
5Q16×Dic9C211yesmaximal, characteristic, complemented
6C4×#3675C211yesmaximal, characteristic, complemented
7C4×#3674C211yesmaximal, characteristic, complemented
8#10588541C211yesmaximal, characteristic, complemented
9#10588532C211yesmaximal, characteristic, complemented
10#10588497C211yesmaximal, characteristic, complemented
11#10588484C211yesmaximal, characteristic
12D9×#103C211yesmaximal, characteristic, complemented
13#10588469C211yesmaximal, characteristic, complemented
14#10588391C211yesmaximal, characteristic, complemented
15#10588389C211yesmaximal, characteristic, complemented
16#79830—31nomaximal
17C2×#3701C2211yescharacteristic
18C2×Q8×D9C2211yescharacteristic
19C2×C9×Q16C2211yescharacteristic
20C4×Q8×C9C2211yescharacteristic
21C4×Q8×C9C2211yescharacteristic
22Q8×Dic9C2211yescharacteristic
23Q8×Dic9C2211yescharacteristic
24C2×#3675C2211yescharacteristic
25C2×#3674C2211yescharacteristic
26#63480C418yescomplemented
27C2×#3664C2211yescharacteristic
28C2×#3663C2211yescharacteristic
29C2×C8×D9C2211yescharacteristic
30#63455—21no—
31#63455C2211yescharacteristic
32#63454—21no—
33#63454C2211yescharacteristic
34C4⋊C4×D9—21no—
35C4⋊C4×D9C2211yescharacteristic
36#63449—21no—
37#63449C2211yescharacteristic
38C4×D36—21no—
39C4×D36C2211yescharacteristic
40#63434—21no—
41#63434—21no—
42#63434C2211yescharacteristic
43C4×Dic18—21no—
44C4×Dic18C2211yescharacteristic
45C9×#106C2211yescharacteristic
46C9×#103C2211yescharacteristic
47C9×#103C2211yescharacteristic
48C9×#97C2211yescharacteristic
49#63395C2211yescharacteristic
50#63395C2211yescharacteristic
51#63380C2211yescharacteristic
52#63378C2211yescharacteristic
53#63376C2211yescharacteristic
54#63375C2211yescharacteristic
55C8×Dic9C2211yescharacteristic
56#63369C2211yescharacteristic
57#63368C2211yescharacteristic
58#63367C2211yescharacteristic
59#63366C2211yescharacteristic
60C4×C9⋊C8C2211yescharacteristic
61C2×#918—31no—
62#5574—31no—
63#5572—31no—
64C3×#441D311yescharacteristic
65Dic3×Q16—31no—
66C4×#216—31no—
67C4×#215—31no—
68#4861—31no—
69#4852—31no—
70#4817—31no—
71#4804—31no—
72D3×#103—31no—
73#4789—31no—
74#4710—31no—
75#4708—31no—
76C2×Q8×C9C2311yescharacteristic
77C2×Q8×C9C2311yescharacteristic
78#3701—22no—
79#3701C2×C414yes—
80Q8×D9—22no—
81Q8×D9C2×C414yescomplemented
82C2×D36—21no—
83C2×D36C2311yescharacteristic
84C2×C4×D9—21no—
85C2×C4×D9—21no—
86C2×C4×D9—21no—
87C2×C4×D9—21no—
88C2×C4×D9—21no—
89C2×C4×D9C2311yescharacteristic
90C2×Dic18—21no—
91C2×Dic18C2311yescharacteristic
92C9×Q16C2×C414yescomplemented
93C2×C8×C9C2311yescharacteristic
94C2×C8×C9C2311yescharacteristic
95C9×C4⋊C4—21no—
96C9×C4⋊C4—21no—
97C9×C4⋊C4C2311yescharacteristic
98C9×C4⋊C4C2311yescharacteristic
99C42×C9—21no—
100C42×C9—21no—
101C42×C9C2311yescharacteristic
102#3675C2×C414yescomplemented
103#3674C2×C414yescomplemented
104(C2×D9)⋊C4—21no—
105(C2×D9)⋊C4—21no—
106(C2×D9)⋊C4—21no—
107(C2×D9)⋊C4D411yescharacteristic
108(C2×D9)⋊C4D411yescharacteristic
109C4⋊Dic9—21no—
110C4⋊Dic9—21no—
111C4⋊Dic9C2311yescharacteristic
112C4⋊Dic9C2311yescharacteristic
113Dic9⋊C4—21no—
114Dic9⋊C4—21no—
115Dic9⋊C4—21no—
116Dic9⋊C4D411yescharacteristic
117Dic9⋊C4D411yescharacteristic
118C4×Dic9—21no—
119C4×Dic9—21no—
120C4×Dic9—21no—
121C4×Dic9—21no—
122C4×Dic9—21no—
123C4×Dic9C2311yescharacteristic
124C2×C9⋊C8C2311yescharacteristic
125C2×C9⋊C8C2311yescharacteristic
126#3664C2×C414yescomplemented
127#3663C2×C414yescomplemented
128C8×D9—22no—
129#2947—91noSylow
130C2×#239—31no—
131C2×D3×Q8—31no—
132C2×C3×Q16C2×D311yescharacteristic
133C3×C4×Q8C2×D311yescharacteristic
134C3×C4×Q8C2×D311yescharacteristic
135Q8×Dic3—31no—
136Q8×Dic3—31no—
137C2×#216—31no—
138C2×#215—31no—
139#918—38no—
140C2×#204—31no—
141C2×ΓL(1,𝔽25)—31no—
142C2×D3×C8—31no—
143#893—31no—
144#893—61no—
145#892—31no—
146#892—61no—
147D3×C4⋊C4—31no—
148D3×C4⋊C4—61no—
149#887—31no—
150#887—61no—
151C4×D12—31no—
152C4×D12—61no—
153#872—31no—
154#872—61no—
155#872—61no—
156C4×Dic6—31no—
157C4×Dic6—61no—
158C3×#106C2×D311yescharacteristic
159C3×#103C2×D311yescharacteristic
160C3×#103C2×D311yescharacteristic
161C3×#97C2×D311yescharacteristic
162#835—31no—
163#835—31no—
164#821—31no—
165#818—31no—
166#816—31no—
167#815—31no—
168C8×Dic3—31no—
169#810—31no—
170#809—31no—
171#808—31no—
172#807—31no—
173C4×C3⋊C8—31no—
174C22×D9—21no—
175C22×D9C2×D411yescharacteristic
176Q8×C9—21no—
177Q8×C9—21no—
178Q8×C9C22×C412yes—
179Q8×C9C22×C412yes—
180C2×C4×C9—21no—
181C2×C4×C9—21no—
182C2×C4×C9—21no—
183C2×C4×C9—21no—
184C2×C4×C9C2×D411yescharacteristic
185C2×C4×C9C2×D411yescharacteristic
186C2×C4×C9C2411yescharacteristic
187C2×Dic9—21no—
188C2×Dic9—21no—
189C2×Dic9—21no—
190C2×Dic9C2×D411yescharacteristic
191C2×Dic9C2×D411yescharacteristic
192C2×Dic9C2×D411yescharacteristic
193D36—24no—
194D36—21no—
195D36C22×C412yes—
196C4×D9—24no—
197C4×D9—24no—
198C4×D9—81no—
199C4×D9—81no—
200C4×D9—81no—
201C4×D9C22×C412yes—
202C4×D9#4112yes—
203Dic18—21no—
204Dic18—24no—
205Dic18C22×C412yes—
206C8×C9—21no—
207C8×C9C22×C412yes—
208C9⋊C8—21no—
209C9⋊C8C22×C412yes—
210C2×#137—91no—
211#520—91no—
212#519—91no—
213#441—91no—
214#441D911yescharacteristic, complemented
215#440—91no—
216#440—91no—
217C4×Q16—91no—
218C4×Q16—91no—
219C4×SD16—91no—
220C4×SD16—91no—
221#428—91no—
222#416—91no—
223C2×#103—91no—
224#405—91no—
225C2×C3×Q8C22×D311yescharacteristic
226C2×C3×Q8C22×D311yescharacteristic
227#239—34no—
228#239—62no—
229D3×Q8—34no—
230D3×Q8—62no—
231C2×D12—31no—
232C2×D12—61no—
233C2×C4×D3—31no—
234C2×C4×D3—61no—
235C2×C4×D3—61no—
236C2×C4×D3—61no—
237C2×C4×D3—61no—
238C2×C4×D3—61no—
239C2×Dic6—31no—
240C2×Dic6—61no—
241C3×Q16C4×D314yes—
242C2×C3×C8C22×D311yescharacteristic
243C2×C3×C8C22×D311yescharacteristic
244C3×C4⋊C4—21no—
245C3×C4⋊C4—21no—
246C3×C4⋊C4C22×D311yescharacteristic
247C3×C4⋊C4C22×D311yescharacteristic
248C3×C42—21no—
249C3×C42—21no—
250C3×C42C22×D311yescharacteristic
251#216—34no—
252#215—34no—
253(C2×D3)⋊C4—31no—
254(C2×D3)⋊C4—31no—
255(C2×D3)⋊C4—61no—
256(C2×D3)⋊C4—61no—
257(C2×D3)⋊C4—61no—
258C4⋊Dic3—31no—
259C4⋊Dic3—31no—
260C4⋊Dic3—61no—
261C4⋊Dic3—61no—
262Dic3⋊C4—31no—
263Dic3⋊C4—31no—
264Dic3⋊C4—61no—
265Dic3⋊C4—61no—
266Dic3⋊C4—61no—
267C4×Dic3—31no—
268C4×Dic3—61no—
269C4×Dic3—61no—
270C4×Dic3—61no—
271C4×Dic3—61no—
272C4×Dic3—61no—
273C2×C3⋊C8—31no—
274C2×C3⋊C8—31no—
275#204—34no—
276ΓL(1,𝔽25)—34no—
277D3×C8—62no—
278C22×C9C22×D411yescharacteristic
279C2×D9—21no—
280C2×D9—21no—
281C2×D9—22no—
282C2×D9—41no—
283C2×D9—41no—
284C2×D9C4×D412yes—
285C4×C9—22no—
286C4×C9—22no—
287C4×C9—21no—
288C4×C9—21no—
289C4×C9—41no—
290C4×C9—41no—
291C4×C9C23×C411yescharacteristic
292C4×C9C2×#4111yescharacteristic
293Dic9—22no—
294Dic9—21no—
295Dic9—21no—
296Dic9—41no—
297Dic9—41no—
298Dic9C4×D412yes—
299C2×#41—91no—
300C22×Q8—91no—
301#137—98no—
302C2×Q16—91no—
303C2×Q16C2×D911yescharacteristic
304C2×SD16—91no—
305C2×SD16—91no—
306C2×M16—91no—
307C22×C8—91no—
308C4×Q8—91no—
309C4×Q8—91no—
310C4×Q8—91no—
311C4×Q8—91no—
312C4×Q8—181no—
313C4×Q8—181no—
314C4×Q8C2×D911yescharacteristic
315C4×Q8C2×D911yescharacteristic
316C4×D4—91no—
317C4×D4—91no—
318C4×D4—181no—
319C4×D4—181no—
320#117—91no—
321#117—91no—
322#117—181no—
323#117—181no—
324#117—181no—
325C2×C4⋊C4—91no—
326C2×C4⋊C4—181no—
327#107—91no—
328#107—91no—
329#106—91no—
330#106C2×D911yescharacteristic
331#103—91no—
332#103—91no—
333#103—91no—
334#103—91no—
335#103C2×D911yescharacteristic
336#103C2×D911yescharacteristic
337#102—91no—
338#102—91no—
339#97—91no—
340#97C2×D911yescharacteristic
341C4×C8—91no—
342C4×C8—91no—
343C22×D3—31no—
344C22×D3—61no—
345C3×Q8—21no—
346C3×Q8—21no—
347C3×Q8C2×C4×D312yes—
348C3×Q8C2×C4×D312yes—
349C2×C3×C4—21no—
350C2×C3×C4—21no—
351C2×C3×C4—21no—
352C2×C3×C4—21no—
353C2×C3×C4D3×D411yescharacteristic
354C2×C3×C4D3×D411yescharacteristic
355C2×C3×C4C23×D311yescharacteristic
356C2×Dic3—31no—
357C2×Dic3—31no—
358C2×Dic3—31no—
359C2×Dic3—61no—
360C2×Dic3—61no—
361C2×Dic3—61no—
362D12—32no—
363D12—64no—
364D12—61no—
365C4×D3—32no—
366C4×D3—32no—
367C4×D3—64no—
368C4×D3—64no—
369C4×D3—241no—
370C4×D3—241no—
371C4×D3—241no—
372Dic6—32no—
373Dic6—64no—
374Dic6—61no—
375C3×C8—21no—
376C3×C8C2×C4×D312yes—
377C3⋊C8—32no—
378C3⋊C8—61no—
379C2×C9C2×C4×D411yescharacteristic
380C2×C9#57711yescharacteristic
381C2×C9#57811yescharacteristic
382D9—22no—
383D9—42no—
384#41—94no—
385#41—182no—
386C2×Q8—94no—
387C2×Q8—91no—
388C2×Q8—181no—
389C2×Q8—182no—
390C2×Q8C22×D911yescharacteristic
391C2×Q8C22×D911yescharacteristic
392C2×D4—91no—
393C2×D4—181no—
394C22×C4—91no—
395C22×C4—181no—
396C22×C4—181no—
397C22×C4—181no—
398C22×C4—181no—
399C22×C4—181no—
400Q16—94no—
401Q16C4×D914yescomplemented
402SD16—94no—
403SD16—94no—
404M16—94no—
405C2×C8—91no—
406C2×C8—91no—
407C2×C8—182no—
408C2×C8C22×D911yescharacteristic
409C2×C8C22×D911yescharacteristic
410C4⋊C4—21no—
411C4⋊C4—21no—
412C4⋊C4—91no—
413C4⋊C4—91no—
414C4⋊C4—91no—
415C4⋊C4—91no—
416C4⋊C4—181no—
417C4⋊C4—181no—
418C4⋊C4—181no—
419C4⋊C4—181no—
420C4⋊C4—181no—
421C4⋊C4C22×D911yescharacteristic
422C4⋊C4C22×D911yescharacteristic
423C22⋊C4—91no—
424C22⋊C4—91no—
425C22⋊C4—181no—
426C22⋊C4—181no—
427C22⋊C4—181no—
428C42—21no—
429C42—21no—
430C42—91no—
431C42—181no—
432C42—181no—
433C42—181no—
434C42—181no—
435C42—181no—
436C42C22×D911yescharacteristic
437C22×C3C2×D3×D411yescharacteristic
438C2×D3—32no—
439C2×D3—61no—
440C2×D3—61no—
441C2×D3—62no—
442C2×D3—121no—
443C2×D3—121no—
444C3×C4—21no—
445C3×C4—21no—
446C3×C4—22no—
447C3×C4—22no—
448C3×C4—41no—
449C3×C4—41no—
450C3×C4C22×C4×D311yescharacteristic
451C3×C4D3×#4111yescharacteristic
452Dic3—32no—
453Dic3—61no—
454Dic3—61no—
455Dic3—62no—
456Dic3—121no—
457Dic3—121no—
458C9#294711yescharacteristic, complemented, Sylow
459C23—91no—
460C23—181no—
461Q8—21no—
462Q8—21no—
463Q8—92no—
464Q8—184no—
465Q8—181no—
466Q8C2×C4×D912yes—
467Q8C2×C4×D912yes—
468D4—92no—
469D4—184no—
470D4—181no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—91no—
476C2×C4—92no—
477C2×C4—92no—
478C2×C4—91no—
479C2×C4—91no—
480C2×C4—184no—
481C2×C4—184no—
482C2×C4—181no—
483C2×C4—181no—
484C2×C4—181no—
485C2×C4—721no—
486C2×C4—721no—
487C2×C4—721no—
488C2×C4D4×D911yescharacteristic
489C2×C4D4×D911yescharacteristic
490C2×C4C23×D911yescharacteristic
491C8—21no—
492C8—92no—
493C8—181no—
494C8C2×C4×D912yes—
495C2×C3C4×D3×D411yescharacteristic
496C2×C3#577811yescharacteristic
497C2×C3#577911yescharacteristic
498D3—62no—
499D3—122no—
500C22—92no—
501C22—181no—
502C22—181no—
503C22—182no—
504C22—361no—
505C22—361no—
506C22C2×D4×D911yescharacteristic
507C4—21no—
508C4—21no—
509C4—22no—
510C4—22no—
511C4—41no—
512C4—41no—
513C4—92no—
514C4—181no—
515C4—181no—
516C4—182no—
517C4—361no—
518C4—361no—
519C4C22×C4×D911yescharacteristic
520C4#41×D911yescharacteristic
521C3#7983011yescharacteristic
522C2—182no—
523C2—362no—
524C2C4×D4×D911yescharacteristic
525C2#1058988011yescharacteristic
526C2#1058988111yescharacteristic
subgroupG/H
centerC22C2×D4×D9
commutatorC4×C9C23×C4
FrattiniC2×C3×C4C23×D3
FittingC9×#441C2
socleC22×C3C2×D3×D4
prime radicalC2×#3701C22
cosocleC2×C4×C9C24
hypercenter#441D9
hypocenterC9#2947
LCSG ▷ C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C42 ◁ #441

Complements

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

NH ≅ G/Ntype
3. #10589674C2semidirect
4. C9×#441C2semidirect
5. Q16×Dic9C2semidirect
6. C4×#3675C2semidirect
7. C4×#3674C2semidirect
8. #10588541C2semidirect
9. #10588532C2semidirect
10. #10588497C2semidirect
12. D9×#103C2semidirect
13. #10588469C2semidirect
14. #10588391C2semidirect
15. #10588389C2semidirect
26. #63480C4semidirect
81. Q8×D9C2×C4semidirect
92. C9×Q16C2×C4semidirect
102. #3675C2×C4semidirect
103. #3674C2×C4semidirect
126. #3664C2×C4semidirect
127. #3663C2×C4semidirect
214. #441D9semidirect
401. Q16C4×D9semidirect
458. C9#2947semidirect

Maximal subgroups

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

subgroupindex
C2×#634802
#105896762
#105896742
C9×#4412
Q16×Dic92
C4×#36752
C4×#36742
#105885412
#105885322
#105884972
#105884842
D9×#1032
#105884692
#105883912
#105883892
#798303