Finite Group Databasebeta

← #11896291

Subgroups — #11896291

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
1#10589687C211yesmaximal, characteristic
2#10589669C211yesmaximal, characteristic, complemented
3C9×#446C211yesmaximal, characteristic, complemented
4#10588531C211yesmaximal, characteristic, complemented
5#10588529C211yesmaximal, characteristic, complemented
6#10588529C211yesmaximal, characteristic, complemented
7#10588526C211yesmaximal, characteristic, complemented
8#10588512C211yesmaximal, characteristic
9#10588511C211yesmaximal, characteristic, complemented
10#10588395C211yesmaximal, characteristic, complemented
11#10588394C211yesmaximal, characteristic
12#10588391C211yesmaximal, characteristic, complemented
13#10588384C211yesmaximal, characteristic, complemented
14#10588379C211yesmaximal, characteristic, complemented
15C4×#3664C211yesmaximal, characteristic, complemented
16#79982—31nomaximal
17C4×Q8×C9C2211yescharacteristic
18#63509—21no—
19#63506—21no—
20C2×#3664C2211yescharacteristic
21C2×#3664C2211yescharacteristic
22C2×Dic36C2211yescharacteristic
23#63456—21no—
24#63456—21no—
25#63455—21no—
26#63451—21no—
27#63451—21no—
28#63449—21no—
29#63437C2211yescharacteristic
30#63437C2211yescharacteristic
31#63436C2211yescharacteristic
32C4×D36C2211yescharacteristic
33C4×D36C2211yescharacteristic
34#63432C2211yescharacteristic
35#63432C2211yescharacteristic
36#63431C2211yescharacteristic
37C4×Dic18C2211yescharacteristic
38C4×Dic18C2211yescharacteristic
39C4×Dic18C2211yescharacteristic
40C4×Dic18C2211yescharacteristic
41C9×C4⋊C8C2211yescharacteristic
42C9×C4⋊C8C2211yescharacteristic
43C9×C4⋊C8C2211yescharacteristic
44C9×#97C2211yescharacteristic
45C9×#97C2211yescharacteristic
46C4×C8×C9C2211yescharacteristic
47#63380C2211yescharacteristic
48#63380C2211yescharacteristic
49#63380C2211yescharacteristic
50#63380C2211yescharacteristic
51#63380C2211yescharacteristic
52#63380C2211yescharacteristic
53#63378C2211yescharacteristic
54#63377C2211yescharacteristic
55#63377C2211yescharacteristic
56#63376C2211yescharacteristic
57#63376C2211yescharacteristic
58#63376C2211yescharacteristic
59#63376C2211yescharacteristic
60#5585—31no—
61#5567—31no—
62C3×#446D311yescharacteristic
63#4848—31no—
64#4847—31no—
65#4845—31no—
66#4845—31no—
67#4842—31no—
68#4829—31no—
69#4716—31no—
70#4714—31no—
71#4713—31no—
72#4710—31no—
73#4697—31no—
74C4×#204—31no—
75C2×Q8×C9D411yescharacteristic
76C2×D36—21no—
77C2×D36—21no—
78C2×D36C2311yescharacteristic
79C2×D36C2311yescharacteristic
80C2×C4×D9—21no—
81C2×C4×D9—21no—
82C2×Dic18—21no—
83C2×Dic18C2311yescharacteristic
84C2×Dic18C2311yescharacteristic
85C2×C8×C9C2311yescharacteristic
86C2×C8×C9C2311yescharacteristic
87C2×C8×C9C2311yescharacteristic
88C2×C8×C9C2311yescharacteristic
89C9×C4⋊C4D411yescharacteristic
90C9×C4⋊C4D411yescharacteristic
91C9×C4⋊C4D411yescharacteristic
92C42×C9C2311yescharacteristic
93C42×C9C2311yescharacteristic
94C42×C9C2311yescharacteristic
95(C2×D9)⋊C4—21no—
96(C2×D9)⋊C4—21no—
97(C2×D9)⋊C4—21no—
98(C2×D9)⋊C4—21no—
99(C2×D9)⋊C4—21no—
100(C2×D9)⋊C4—21no—
101C4⋊Dic9—21no—
102C4⋊Dic9C2311yescharacteristic
103C4⋊Dic9C2311yescharacteristic
104C4⋊Dic9C2311yescharacteristic
105C4⋊Dic9C2311yescharacteristic
106Dic9⋊C4—21no—
107Dic9⋊C4—21no—
108Dic9⋊C4—21no—
109Dic9⋊C4—21no—
110Dic9⋊C4—21no—
111Dic9⋊C4—21no—
112Dic9⋊C4—21no—
113Dic9⋊C4—21no—
114C4×Dic9—21no—
115C4×Dic9—21no—
116C4×Dic9—21no—
117C4×Dic9—21no—
118#3664—22no—
119#3664—22no—
120Dic36—22no—
121#3371—91noSylow
122C3×C4×Q8C2×D311yescharacteristic
123#947—61no—
124#944—61no—
125C2×Dic12—31no—
126C2×#204—31no—
127C2×#204—31no—
128#894—61no—
129#894—61no—
130#893—61no—
131#889—61no—
132#889—61no—
133#887—61no—
134#875—31no—
135#875—31no—
136#874—31no—
137C4×D12—31no—
138C4×D12—31no—
139#870—31no—
140#870—31no—
141#869—31no—
142C4×Dic6—31no—
143C4×Dic6—31no—
144C4×Dic6—31no—
145C4×Dic6—31no—
146C3×C4⋊C8C2×D311yescharacteristic
147C3×C4⋊C8C2×D311yescharacteristic
148C3×C4⋊C8C2×D311yescharacteristic
149C3×#97C2×D311yescharacteristic
150C3×#97C2×D311yescharacteristic
151C3×C4×C8C2×D311yescharacteristic
152#821—31no—
153#821—31no—
154#821—31no—
155#821—31no—
156#821—31no—
157#821—31no—
158#818—31no—
159#817—31no—
160#817—31no—
161#816—31no—
162#816—31no—
163#816—31no—
164#816—31no—
165C22×D9—21no—
166C22×D9—21no—
167Q8×C9—41no—
168C2×C4×C9C2×D411yescharacteristic
169C2×C4×C9C2×D411yescharacteristic
170C2×C4×C9C2×D411yescharacteristic
171C2×C4×C9C2×D411yescharacteristic
172C2×C4×C9C2×D411yescharacteristic
173C2×C4×C9C2×D411yescharacteristic
174C2×C4×C9C2411yescharacteristic
175C2×Dic9—21no—
176C2×Dic9—21no—
177C2×Dic9—21no—
178C2×Dic9—21no—
179C2×Dic9—21no—
180C2×Dic9—21no—
181D36—21no—
182D36—21no—
183D36—21no—
184D36—21no—
185D36—42no—
186D36—81no—
187C4×D9—81no—
188C4×D9—81no—
189Dic18—21no—
190Dic18—21no—
191Dic18—21no—
192Dic18—42no—
193Dic18#4112yes—
194C8×C9—21no—
195C8×C9—21no—
196C8×C9—21no—
197C8×C9—21no—
198#559—91no—
199#557—91no—
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#446D911yescharacteristic, complemented
210#441—91no—
211#440—91no—
212C4×SD16—91no—
213C2×C3×Q8D1211yescharacteristic
214C2×D12—31no—
215C2×D12—31no—
216C2×D12—61no—
217C2×D12—61no—
218C2×C4×D3—61no—
219C2×C4×D3—61no—
220C2×Dic6—31no—
221C2×Dic6—31no—
222C2×Dic6—61no—
223C2×C3×C8C22×D311yescharacteristic
224C2×C3×C8C22×D311yescharacteristic
225C2×C3×C8C22×D311yescharacteristic
226C2×C3×C8C22×D311yescharacteristic
227C3×C4⋊C4D1211yescharacteristic
228C3×C4⋊C4D1211yescharacteristic
229C3×C4⋊C4D1211yescharacteristic
230C3×C42C22×D311yescharacteristic
231C3×C42C22×D311yescharacteristic
232C3×C42C22×D311yescharacteristic
233(C2×D3)⋊C4—61no—
234(C2×D3)⋊C4—61no—
235(C2×D3)⋊C4—61no—
236(C2×D3)⋊C4—61no—
237(C2×D3)⋊C4—61no—
238(C2×D3)⋊C4—61no—
239C4⋊Dic3—31no—
240C4⋊Dic3—31no—
241C4⋊Dic3—31no—
242C4⋊Dic3—31no—
243C4⋊Dic3—61no—
244Dic3⋊C4—61no—
245Dic3⋊C4—61no—
246Dic3⋊C4—61no—
247Dic3⋊C4—61no—
248Dic3⋊C4—61no—
249Dic3⋊C4—61no—
250Dic3⋊C4—61no—
251Dic3⋊C4—61no—
252C4×Dic3—61no—
253C4×Dic3—61no—
254C4×Dic3—61no—
255C4×Dic3—61no—
256Dic12—62no—
257#204—62no—
258#204—62no—
259C22×C9C22×D411yescharacteristic
260C2×D9—41no—
261C2×D9—41no—
262C2×D9—41no—
263C2×D9—41no—
264C2×D9—41no—
265C2×D9—41no—
266C4×C9—21no—
267C4×C9—21no—
268C4×C9—21no—
269C4×C9—21no—
270C4×C9—21no—
271C4×C9—21no—
272C4×C9C2×#4111yescharacteristic
273C4×C92−1+411yescharacteristic
274Dic9—22no—
275Dic9—41no—
276Dic9—41no—
277Dic9—41no—
278Dic9—41no—
279Dic9—41no—
280C2×Q16—91no—
281C2×SD16—91no—
282C2×SD16—91no—
283C4⋊Q8—91no—
284C4⋊Q8—181no—
285#127—91no—
286#125—91no—
287#125—91no—
288#125—181no—
289#125—181no—
290#124—91no—
291#124—91no—
292#124—181no—
293#123—181no—
294#123—181no—
295C4×Q8—91no—
296C4×Q8—91no—
297C4×Q8—91no—
298C4×Q8—91no—
299C4×Q8—181no—
300C4×Q8C2×D911yescharacteristic
301C4×D4—91no—
302C4×D4—91no—
303C4×D4—181no—
304#107—91no—
305#106—91no—
306#106—91no—
307C4⋊C8C2×D911yescharacteristic
308C4⋊C8C2×D911yescharacteristic
309C4⋊C8C2×D911yescharacteristic
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#97C2×D911yescharacteristic
321#97C2×D911yescharacteristic
322C4×C8C2×D911yescharacteristic
323C22×D3—61no—
324C22×D3—61no—
325C3×Q8—41no—
326C2×C3×C4C2×D1211yescharacteristic
327C2×C3×C4C2×D1211yescharacteristic
328C2×C3×C4C2×D1211yescharacteristic
329C2×C3×C4C2×D1211yescharacteristic
330C2×C3×C4C2×D1211yescharacteristic
331C2×C3×C4C2×D1211yescharacteristic
332C2×C3×C4C23×D311yescharacteristic
333C2×Dic3—61no—
334C2×Dic3—61no—
335C2×Dic3—61no—
336C2×Dic3—61no—
337C2×Dic3—61no—
338C2×Dic3—61no—
339D12—61no—
340D12—61no—
341D12—61no—
342D12—61no—
343D12—122no—
344D12—241no—
345C4×D3—241no—
346C4×D3—241no—
347Dic6—32no—
348Dic6—61no—
349Dic6—61no—
350Dic6—61no—
351Dic6—122no—
352C3×C8—21no—
353C3×C8—21no—
354C3×C8—21no—
355C3×C8—21no—
356C2×C9#54811yescharacteristic
357C2×C9#57511yescharacteristic
358C2×C9#57711yescharacteristic
359D9—81no—
360D9—81no—
361C2×Q8—91no—
362C2×Q8—91no—
363C2×Q8—181no—
364C2×Q8D3611yescharacteristic
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×C8C22×D911yescharacteristic
375C2×C8C22×D911yescharacteristic
376C2×C8C22×D911yescharacteristic
377C2×C8C22×D911yescharacteristic
378C4⋊C4—91no—
379C4⋊C4—91no—
380C4⋊C4—91no—
381C4⋊C4—91no—
382C4⋊C4—181no—
383C4⋊C4—181no—
384C4⋊C4—181no—
385C4⋊C4—181no—
386C4⋊C4—181no—
387C4⋊C4—181no—
388C4⋊C4—181no—
389C4⋊C4—181no—
390C4⋊C4—181no—
391C4⋊C4D3611yescharacteristic
392C4⋊C4D3611yescharacteristic
393C4⋊C4D3611yescharacteristic
394C22⋊C4—181no—
395C22⋊C4—181no—
396C22⋊C4—181no—
397C22⋊C4—181no—
398C22⋊C4—181no—
399C22⋊C4—181no—
400C42—181no—
401C42—181no—
402C42—181no—
403C42—181no—
404C42C22×D911yescharacteristic
405C42C22×D911yescharacteristic
406C42C22×D911yescharacteristic
407C22×C3C22×D1211yescharacteristic
408C2×D3—121no—
409C2×D3—121no—
410C2×D3—121no—
411C2×D3—121no—
412C2×D3—121no—
413C2×D3—121no—
414C3×C4—21no—
415C3×C4—21no—
416C3×C4—21no—
417C3×C4—21no—
418C3×C4—21no—
419C3×C4—21no—
420C3×C4#100711yescharacteristic
421C3×C4D3×#4111yescharacteristic
422Dic3—62no—
423Dic3—121no—
424Dic3—121no—
425Dic3—121no—
426Dic3—121no—
427Dic3—121no—
428C9#337111yescharacteristic, complemented, Sylow
429C23—181no—
430C23—181no—
431Q8—41no—
432Q8—92no—
433Q8—181no—
434Q8—181no—
435Q8—181no—
436Q8—362no—
437D4—181no—
438D4—181no—
439D4—181no—
440D4—181no—
441D4—362no—
442D4—721no—
443C2×C4—181no—
444C2×C4—181no—
445C2×C4—181no—
446C2×C4—181no—
447C2×C4—181no—
448C2×C4—181no—
449C2×C4—721no—
450C2×C4—721no—
451C2×C4C2×D3611yescharacteristic
452C2×C4C2×D3611yescharacteristic
453C2×C4C2×D3611yescharacteristic
454C2×C4C2×D3611yescharacteristic
455C2×C4C2×D3611yescharacteristic
456C2×C4C2×D3611yescharacteristic
457C2×C4C23×D911yescharacteristic
458C8—21no—
459C8—21no—
460C8—21no—
461C8—21no—
462C2×C3#557611yescharacteristic
463C2×C3#574811yescharacteristic
464C2×C3#575111yescharacteristic
465D3—241no—
466D3—241no—
467C22—361no—
468C22—361no—
469C22—361no—
470C22—361no—
471C22—361no—
472C22—361no—
473C22C22×D3611yescharacteristic
474C4—21no—
475C4—21no—
476C4—21no—
477C4—21no—
478C4—21no—
479C4—21no—
480C4—182no—
481C4—361no—
482C4—361no—
483C4—361no—
484C4—361no—
485C4—361no—
486C4#6371311yescharacteristic
487C4#41×D911yescharacteristic
488C3#7998211yescharacteristic
489C2—721no—
490C2—721no—
491C2#1058967811yescharacteristic
492C2#1058985011yescharacteristic
493C2#1058985311yescharacteristic
subgroupG/H
centerC22C22×D36
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#446C2
socleC22×C3C22×D12
prime radical#63436C22
hypercenter#446D9
hypocenterC9#3371
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #446

Complements

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

NH ≅ G/Ntype
2. #10589669C2semidirect
3. C9×#446C2semidirect
4. #10588531C2semidirect
5. #10588529C2semidirect
6. #10588529C2semidirect
7. #10588526C2semidirect
9. #10588511C2semidirect
10. #10588395C2semidirect
12. #10588391C2semidirect
13. #10588384C2semidirect
14. #10588379C2semidirect
15. C4×#3664C2semidirect
209. #446D9semidirect
428. C9#3371semidirect

Maximal subgroups

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

subgroupindex
#105896872
#105896692
C9×#4462
#105885312
#105885292
#105885262
#105885122
#105885112
#105883952
#105883942
#105883912
#105883842
#105883792
C4×#36642
#799823