Finite Group Databasebeta

← #11896285

Subgroups — #11896285

Order 1152.

516 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
1C9×#557C211yesmaximal, characteristic, complemented
2#10589687C211yesmaximal, characteristic
3#10588774C211yesmaximal, characteristic, complemented
4#10588769C211yesmaximal, characteristic, complemented
5#10588749C211yesmaximal, characteristic, complemented
6#10588748C211yesmaximal, characteristic
7#10588747C211yesmaximal, characteristic, complemented
8#10588745C211yesmaximal, characteristic, complemented
9#10588711C211yesmaximal, characteristic, complemented
10#10588711C211yesmaximal, characteristic, complemented
11#10588710C211yesmaximal, characteristic
12#10588709C211yesmaximal, characteristic, complemented
13C4×#3675C211yesmaximal, characteristic, complemented
14#10588706C211yesmaximal, characteristic, complemented
15#10588701C211yesmaximal, characteristic, complemented
16#83691—31nomaximal
17C9×C4⋊Q8—21no—
18C9×C4⋊Q8C2211yescharacteristic
19C9×#125—21no—
20C9×#125—21no—
21C9×#125C2211yescharacteristic
22C9×#125C2211yescharacteristic
23C4×Q8×C9—21no—
24C4×Q8×C9C2211yescharacteristic
25C4×Q8×C9C2211yescharacteristic
26C4×Q8×C9C2211yescharacteristic
27C4×Q8×C9C2211yescharacteristic
28#63509—21no—
29C2×#3675C2211yescharacteristic
30C2×#3675C2211yescharacteristic
31C2×#3674C2211yescharacteristic
32#63456—21no—
33#63456—21no—
34#63455—21no—
35#63437C2211yescharacteristic
36#63437C2211yescharacteristic
37#63436C2211yescharacteristic
38C4×D36C2211yescharacteristic
39C4×D36C2211yescharacteristic
40C4×Dic18C2211yescharacteristic
41#63395C2211yescharacteristic
42#63369C2211yescharacteristic
43#63369C2211yescharacteristic
44#63369C2211yescharacteristic
45#63369C2211yescharacteristic
46#63369C2211yescharacteristic
47#63369C2211yescharacteristic
48#63368C2211yescharacteristic
49#63368C2211yescharacteristic
50#63368C2211yescharacteristic
51#63367C2211yescharacteristic
52#63367C2211yescharacteristic
53#63366C2211yescharacteristic
54C4⋊(C9⋊C8)C2211yescharacteristic
55C4⋊(C9⋊C8)C2211yescharacteristic
56C4⋊(C9⋊C8)C2211yescharacteristic
57#63362C2211yescharacteristic
58#63362C2211yescharacteristic
59C4×C9⋊C8C2211yescharacteristic
60C3×#557D311yescharacteristic
61#5585—31no—
62#5089—31no—
63#5084—31no—
64#5068—31no—
65#5067—31no—
66#5066—31no—
67#5063—31no—
68#5030—31no—
69#5028—31no—
70#5028—31no—
71#5027—31no—
72#5026—31no—
73C4×#215—31no—
74#5024—31no—
75C2×Q8×C9—21no—
76C2×Q8×C9D411yescharacteristic
77C2×Q8×C9C2311yescharacteristic
78C2×D36—21no—
79C2×D36—21no—
80C2×D36C2311yescharacteristic
81C2×D36C2311yescharacteristic
82C2×C4×D9—21no—
83C2×C4×D9—21no—
84C2×Dic18C2311yescharacteristic
85C9×C4⋊C4—21no—
86C9×C4⋊C4—21no—
87C9×C4⋊C4—21no—
88C9×C4⋊C4—21no—
89C9×C4⋊C4—21no—
90C9×C4⋊C4—21no—
91C9×C4⋊C4—21no—
92C9×C4⋊C4—21no—
93C9×C4⋊C4D411yescharacteristic
94C9×C4⋊C4D411yescharacteristic
95C9×C4⋊C4D411yescharacteristic
96C9×C4⋊C4C2311yescharacteristic
97C9×C4⋊C4C2311yescharacteristic
98C9×C4⋊C4C2311yescharacteristic
99C42×C9—21no—
100C42×C9—21no—
101C42×C9—21no—
102C42×C9C2311yescharacteristic
103C42×C9C2311yescharacteristic
104C42×C9C2311yescharacteristic
105#3675—22no—
106#3675—22no—
107#3674—22no—
108(C2×D9)⋊C4—21no—
109(C2×D9)⋊C4—21no—
110(C2×D9)⋊C4—21no—
111(C2×D9)⋊C4—21no—
112(C2×D9)⋊C4—21no—
113(C2×D9)⋊C4—21no—
114C4⋊Dic9C2311yescharacteristic
115Dic9⋊C4—21no—
116C4×Dic9—21no—
117C2×C9⋊C8C2311yescharacteristic
118C2×C9⋊C8C2311yescharacteristic
119C2×C9⋊C8C2311yescharacteristic
120C2×C9⋊C8C2311yescharacteristic
121#3371—91noSylow
122C3×C4⋊Q8—21no—
123C3×C4⋊Q8C2×D311yescharacteristic
124C3×#125—21no—
125C3×#125—21no—
126C3×#125C2×D311yescharacteristic
127C3×#125C2×D311yescharacteristic
128C3×C4×Q8—21no—
129C3×C4×Q8C2×D311yescharacteristic
130C3×C4×Q8C2×D311yescharacteristic
131C3×C4×Q8C2×D311yescharacteristic
132C3×C4×Q8C2×D311yescharacteristic
133#947—61no—
134C2×#216—31no—
135C2×#215—31no—
136C2×#215—31no—
137#894—61no—
138#894—61no—
139#893—61no—
140#875—31no—
141#875—31no—
142#874—31no—
143C4×D12—31no—
144C4×D12—31no—
145C4×Dic6—31no—
146#835—31no—
147#810—31no—
148#810—31no—
149#810—31no—
150#809—31no—
151#809—31no—
152#809—31no—
153#809—31no—
154#809—31no—
155#809—31no—
156#808—31no—
157#808—31no—
158#807—31no—
159C4⋊(C3⋊C8)—31no—
160C4⋊(C3⋊C8)—31no—
161C4⋊(C3⋊C8)—31no—
162#803—31no—
163#803—31no—
164C4×C3⋊C8—31no—
165C22×D9—21no—
166C22×D9—21no—
167Q8×C9—21no—
168Q8×C9—41no—
169Q8×C9—42no—
170Q8×C9#4112yes—
171C2×C4×C9—21no—
172C2×C4×C9—21no—
173C2×C4×C9—21no—
174C2×C4×C9—21no—
175C2×C4×C9C2×D411yescharacteristic
176C2×C4×C9C2×D411yescharacteristic
177C2×C4×C9C2×D411yescharacteristic
178C2×C4×C9C2×D411yescharacteristic
179C2×C4×C9C2×D411yescharacteristic
180C2×C4×C9C2×D411yescharacteristic
181C2×C4×C9C2411yescharacteristic
182C2×Dic9—21no—
183C2×Dic9—21no—
184D36—21no—
185D36—21no—
186D36—21no—
187D36—21no—
188D36—42no—
189D36—81no—
190C4×D9—81no—
191C4×D9—81no—
192Dic18—21no—
193Dic18—21no—
194C9⋊C8—21no—
195C9⋊C8—21no—
196C9⋊C8—21no—
197C9⋊C8—21no—
198#559—91no—
199#557D911yescharacteristic, complemented
200#490—91no—
201#489—91no—
202#488—91no—
203#479—91no—
204#478—91no—
205#476—91no—
206#464—91no—
207#464—91no—
208#460—91no—
209#446—91no—
210#441—91no—
211#440—91no—
212C4×SD16—91no—
213C2×C3×Q8—21no—
214C2×C3×Q8#6711yescharacteristic
215C2×C3×Q8C22×D311yescharacteristic
216C2×D12—31no—
217C2×D12—31no—
218C2×D12—61no—
219C2×D12—61no—
220C2×C4×D3—61no—
221C2×C4×D3—61no—
222C2×Dic6—31no—
223C3×C4⋊C4—21no—
224C3×C4⋊C4—21no—
225C3×C4⋊C4—21no—
226C3×C4⋊C4—21no—
227C3×C4⋊C4—21no—
228C3×C4⋊C4—21no—
229C3×C4⋊C4—21no—
230C3×C4⋊C4—21no—
231C3×C4⋊C4#6711yescharacteristic
232C3×C4⋊C4#6711yescharacteristic
233C3×C4⋊C4#6711yescharacteristic
234C3×C4⋊C4C22×D311yescharacteristic
235C3×C4⋊C4C22×D311yescharacteristic
236C3×C4⋊C4C22×D311yescharacteristic
237C3×C42—21no—
238C3×C42—21no—
239C3×C42—21no—
240C3×C42C22×D311yescharacteristic
241C3×C42C22×D311yescharacteristic
242C3×C42C22×D311yescharacteristic
243#216—62no—
244#215—62no—
245#215—62no—
246(C2×D3)⋊C4—61no—
247(C2×D3)⋊C4—61no—
248(C2×D3)⋊C4—61no—
249(C2×D3)⋊C4—61no—
250(C2×D3)⋊C4—61no—
251(C2×D3)⋊C4—61no—
252C4⋊Dic3—31no—
253Dic3⋊C4—61no—
254C4×Dic3—61no—
255C2×C3⋊C8—31no—
256C2×C3⋊C8—31no—
257C2×C3⋊C8—31no—
258C2×C3⋊C8—31no—
259C22×C9C22×D411yescharacteristic
260C2×D9—41no—
261C2×D9—41no—
262C2×D9—41no—
263C2×D9—41no—
264C2×D9—41no—
265C2×D9—41no—
266C4×C9—22no—
267C4×C9—21no—
268C4×C9—21no—
269C4×C9—21no—
270C4×C9—21no—
271C4×C9—21no—
272C4×C9—21no—
273C4×C9—41no—
274C4×C9—41no—
275C4×C9—41no—
276C4×C9C2×#4111yescharacteristic
277C4×C92−1+411yescharacteristic
278Dic9—41no—
279Dic9—41no—
280C2×Q16—91no—
281C2×SD16—91no—
282C2×SD16—91no—
283C4⋊Q8—21no—
284C4⋊Q8C2×D911yescharacteristic
285#127—91no—
286#125—21no—
287#125—21no—
288#125C2×D911yescharacteristic
289#125C2×D911yescharacteristic
290#124—91no—
291#124—91no—
292#124—181no—
293#123—181no—
294#123—181no—
295C4×Q8—21no—
296C4×Q8—91no—
297C4×Q8C2×D911yescharacteristic
298C4×Q8C2×D911yescharacteristic
299C4×Q8C2×D911yescharacteristic
300C4×Q8C2×D911yescharacteristic
301C4×D4—91no—
302C4×D4—91no—
303C4×D4—181no—
304#107—91no—
305#106—91no—
306#106—91no—
307C4⋊C8—91no—
308C4⋊C8—91no—
309C4⋊C8—91no—
310#103—91no—
311#103—91no—
312#103—91no—
313#103—91no—
314#102—91no—
315#102—91no—
316#102—91no—
317#102—91no—
318#102—91no—
319#102—91no—
320#97—91no—
321#97—91no—
322C4×C8—91no—
323C22×D3—61no—
324C22×D3—61no—
325C3×Q8—21no—
326C3×Q8—41no—
327C3×Q8—42no—
328C3×Q8#23912yes—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4C2×#6711yescharacteristic
334C2×C3×C4C2×#6711yescharacteristic
335C2×C3×C4C2×#6711yescharacteristic
336C2×C3×C4C2×#6711yescharacteristic
337C2×C3×C4C2×#6711yescharacteristic
338C2×C3×C4C2×#6711yescharacteristic
339C2×C3×C4C23×D311yescharacteristic
340C2×Dic3—61no—
341C2×Dic3—61no—
342D12—61no—
343D12—61no—
344D12—61no—
345D12—61no—
346D12—122no—
347D12—241no—
348C4×D3—241no—
349C4×D3—241no—
350Dic6—61no—
351Dic6—61no—
352C3⋊C8—61no—
353C3⋊C8—61no—
354C3⋊C8—61no—
355C3⋊C8—61no—
356C2×C9#54811yescharacteristic
357C2×C9#57511yescharacteristic
358C2×C9#57711yescharacteristic
359D9—81no—
360D9—81no—
361C2×Q8—21no—
362C2×Q8—91no—
363C2×Q8#61111yescharacteristic
364C2×Q8C22×D911yescharacteristic
365C2×D4—91no—
366C2×D4—91no—
367C2×D4—181no—
368C2×D4—181no—
369C22×C4—181no—
370C22×C4—181no—
371Q16—182no—
372SD16—182no—
373SD16—182no—
374C2×C8—91no—
375C2×C8—91no—
376C2×C8—91no—
377C2×C8—91no—
378C4⋊C4—21no—
379C4⋊C4—21no—
380C4⋊C4—21no—
381C4⋊C4—21no—
382C4⋊C4—21no—
383C4⋊C4—21no—
384C4⋊C4—21no—
385C4⋊C4—21no—
386C4⋊C4—91no—
387C4⋊C4—181no—
388C4⋊C4#61111yescharacteristic
389C4⋊C4#61111yescharacteristic
390C4⋊C4#61111yescharacteristic
391C4⋊C4C22×D911yescharacteristic
392C4⋊C4C22×D911yescharacteristic
393C4⋊C4C22×D911yescharacteristic
394C22⋊C4—181no—
395C22⋊C4—181no—
396C22⋊C4—181no—
397C22⋊C4—181no—
398C22⋊C4—181no—
399C22⋊C4—181no—
400C42—21no—
401C42—21no—
402C42—21no—
403C42—181no—
404C42C22×D911yescharacteristic
405C42C22×D911yescharacteristic
406C42C22×D911yescharacteristic
407C22×C3C22×#6711yescharacteristic
408C2×D3—121no—
409C2×D3—121no—
410C2×D3—121no—
411C2×D3—121no—
412C2×D3—121no—
413C2×D3—121no—
414C3×C4—22no—
415C3×C4—21no—
416C3×C4—21no—
417C3×C4—21no—
418C3×C4—21no—
419C3×C4—21no—
420C3×C4—21no—
421C3×C4—41no—
422C3×C4—41no—
423C3×C4—41no—
424C3×C4C2×#23911yescharacteristic
425C3×C4#100711yescharacteristic
426Dic3—121no—
427Dic3—121no—
428C9#337111yescharacteristic, complemented, Sylow
429C23—181no—
430C23—181no—
431Q8—21no—
432Q8—41no—
433Q8—42no—
434Q8—181no—
435Q8—181no—
436Q8#370112yes—
437D4—181no—
438D4—181no—
439D4—181no—
440D4—181no—
441D4—362no—
442D4—721no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—181no—
448C2×C4—181no—
449C2×C4—721no—
450C2×C4—721no—
451C2×C4C2×#61111yescharacteristic
452C2×C4C2×#61111yescharacteristic
453C2×C4C2×#61111yescharacteristic
454C2×C4C2×#61111yescharacteristic
455C2×C4C2×#61111yescharacteristic
456C2×C4C2×#61111yescharacteristic
457C2×C4C23×D911yescharacteristic
458C8—181no—
459C8—181no—
460C8—181no—
461C8—181no—
462C2×C3#581711yescharacteristic
463C2×C3#582211yescharacteristic
464C2×C3#583711yescharacteristic
465D3—241no—
466D3—241no—
467C22—361no—
468C22—361no—
469C22—361no—
470C22—361no—
471C22—361no—
472C22—361no—
473C22C22×#61111yescharacteristic
474C4—22no—
475C4—21no—
476C4—21no—
477C4—21no—
478C4—21no—
479C4—21no—
480C4—21no—
481C4—41no—
482C4—41no—
483C4—41no—
484C4—361no—
485C4—361no—
486C4C2×#370111yescharacteristic
487C4#6371311yescharacteristic
488C3#8369111yescharacteristic
489C2—721no—
490C2—721no—
491C2#1058991911yescharacteristic
492C2#1058992511yescharacteristic
493C2#1058993911yescharacteristic
subgroupG/H
centerC22C22×#611
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#557C2
socleC22×C3C22×#67
prime radical#63436C22
hypercenter#557D9
hypocenterC9#3371
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #557

Complements

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

NH ≅ G/Ntype
1. C9×#557C2semidirect
3. #10588774C2semidirect
4. #10588769C2semidirect
5. #10588749C2semidirect
7. #10588747C2semidirect
8. #10588745C2semidirect
9. #10588711C2semidirect
10. #10588711C2semidirect
12. #10588709C2semidirect
13. C4×#3675C2semidirect
14. #10588706C2semidirect
15. #10588701C2semidirect
199. #557D9semidirect
428. C9#3371semidirect

Maximal subgroups

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

subgroupindex
C9×#5572
#105896872
#105887742
#105887692
#105887492
#105887482
#105887472
#105887452
#105887112
#105887102
#105887092
C4×#36752
#105887062
#105887012
#836913