Finite Group Databasebeta

← #11868714

Subgroups — #11868714

Order 1152.

564 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10589790C211yesmaximal, characteristic
2C4×Q8×D9C211yesmaximal, characteristic
3C9×#479C211yesmaximal, characteristic, complemented
4#10588745C211yesmaximal, characteristic, complemented
5#10588704C211yesmaximal, characteristic, complemented
6#10588561C211yesmaximal, characteristic
7#10588555C211yesmaximal, characteristic, complemented
8#10588541C211yesmaximal, characteristic
9#10588534C211yesmaximal, characteristic, complemented
10#10588521C211yesmaximal, characteristic
11#10588511C211yesmaximal, characteristic, complemented
12#10588482C211yesmaximal, characteristic
13#10588482C211yesmaximal, characteristic
14#10588473C211yesmaximal, characteristic, complemented
15#10588471C211yesmaximal, characteristic, complemented
16#81230—31nomaximal
17C2×Q8×D9C2211yescharacteristic
18C9×#125C2211yescharacteristic
19C4×Q8×C9C2211yescharacteristic
20Q8×Dic9C2211yescharacteristic
21C2×#3663C2211yescharacteristic
22C2×#3663C2211yescharacteristic
23#63458—21no—
24#63458—21no—
25#63454C2211yescharacteristic
26#63454C2211yescharacteristic
27C4⋊C4×D9—21no—
28C4⋊C4×D9C2211yescharacteristic
29#63450C2211yescharacteristic
30#63450C2211yescharacteristic
31#63449—21no—
32#63449—21no—
33#63449—21no—
34#63449C2211yescharacteristic
35C42×D9—21no—
36C42×D9C2211yescharacteristic
37#63432C2211yescharacteristic
38C4×Dic18—21no—
39C4×Dic18C2211yescharacteristic
40C9×#107C2211yescharacteristic
41C9×#106C2211yescharacteristic
42C9×C4⋊C8C2211yescharacteristic
43C9×#103C2211yescharacteristic
44C9×#103C2211yescharacteristic
45#63395C2211yescharacteristic
46#63395C2211yescharacteristic
47#63378C2211yescharacteristic
48#63377C2211yescharacteristic
49#63376C2211yescharacteristic
50#63376C2211yescharacteristic
51Dic9⋊C8C2211yescharacteristic
52Dic9⋊C8C2211yescharacteristic
53#63368C2211yescharacteristic
54#63368C2211yescharacteristic
55#63367C2211yescharacteristic
56#63367C2211yescharacteristic
57#63366C2211yescharacteristic
58#63366C2211yescharacteristic
59C4⋊(C9⋊C8)C2211yescharacteristic
60#5688—31no—
61C4×D3×Q8—31no—
62C3×#479D311yescharacteristic
63#5063—31no—
64#5022—31no—
65#4881—31no—
66#4875—31no—
67#4861—31no—
68#4854—31no—
69#4837—31no—
70#4829—31no—
71#4802—31no—
72#4802—31no—
73#4793—31no—
74#4791—31no—
75C2×Q8×C9C2311yescharacteristic
76Q8×D9—22no—
77Q8×D9Q814yescomplemented
78C2×C4×D9—21no—
79C2×C4×D9—21no—
80C2×C4×D9D411yescharacteristic
81C2×C4×D9D411yescharacteristic
82C2×C4×D9C2311yescharacteristic
83C2×Dic18—21no—
84C2×Dic18—21no—
85C2×Dic18—21no—
86C2×Dic18C2311yescharacteristic
87C2×C8×C9C2311yescharacteristic
88C2×C8×C9C2311yescharacteristic
89C9×C4⋊C4—21no—
90C9×C4⋊C4—21no—
91C9×C4⋊C4—21no—
92C9×C4⋊C4C2311yescharacteristic
93C9×C4⋊C4C2311yescharacteristic
94C9×C4⋊C4C2311yescharacteristic
95C42×C9—21no—
96C42×C9C2311yescharacteristic
97(C2×D9)⋊C4—21no—
98(C2×D9)⋊C4—21no—
99C4⋊Dic9—21no—
100C4⋊Dic9C2311yescharacteristic
101C4⋊Dic9C2311yescharacteristic
102C4⋊Dic9C2311yescharacteristic
103Dic9⋊C4—21no—
104Dic9⋊C4—21no—
105Dic9⋊C4—21no—
106Dic9⋊C4—21no—
107Dic9⋊C4—21no—
108Dic9⋊C4—21no—
109Dic9⋊C4—21no—
110C4×Dic9—21no—
111C4×Dic9—21no—
112C4×Dic9—21no—
113C4×Dic9—21no—
114C4×Dic9—21no—
115C4×Dic9D411yescharacteristic
116C4×Dic9D411yescharacteristic
117C4×Dic9C2311yescharacteristic
118C2×C9⋊C8C2311yescharacteristic
119C2×C9⋊C8C2311yescharacteristic
120#3663—22no—
121#3663—22no—
122#3078—91noSylow
123C2×D3×Q8—31no—
124C3×#125C2×D311yescharacteristic
125C3×C4×Q8C2×D311yescharacteristic
126Q8×Dic3—31no—
127C2×ΓL(1,𝔽25)—31no—
128C2×ΓL(1,𝔽25)—31no—
129#896—61no—
130#896—61no—
131#892—31no—
132#892—31no—
133D3×C4⋊C4—31no—
134D3×C4⋊C4—61no—
135#888—31no—
136#888—31no—
137#887—31no—
138#887—61no—
139#887—61no—
140#887—61no—
141C42×D3—31no—
142C42×D3—61no—
143#870—31no—
144C4×Dic6—31no—
145C4×Dic6—61no—
146C3×#107C2×D311yescharacteristic
147C3×#106C2×D311yescharacteristic
148C3×C4⋊C8C2×D311yescharacteristic
149C3×#103C2×D311yescharacteristic
150C3×#103C2×D311yescharacteristic
151#835—31no—
152#835—31no—
153#818—31no—
154#817—31no—
155#816—31no—
156#816—31no—
157Dic3⋊C8—31no—
158Dic3⋊C8—31no—
159#810—31no—
160#810—31no—
161#808—31no—
162#808—31no—
163#807—31no—
164#807—31no—
165C4⋊(C3⋊C8)—31no—
166C22×D9C2×D411yescharacteristic
167Q8×C9—21no—
168Q8×C9C2×Q812yes—
169C2×C4×C9—21no—
170C2×C4×C9—21no—
171C2×C4×C9—21no—
172C2×C4×C9—21no—
173C2×C4×C9C2×D411yescharacteristic
174C2×C4×C9C2×D411yescharacteristic
175C2×C4×C9C2411yescharacteristic
176C2×Dic9—21no—
177C2×Dic9—21no—
178C2×Dic9—21no—
179C2×Dic9—21no—
180C2×Dic9C2×D411yescharacteristic
181C2×Dic9C2×D411yescharacteristic
182C2×Dic9C2×D411yescharacteristic
183C4×D9—24no—
184C4×D9—22no—
185C4×D9—41no—
186C4×D9—42no—
187C4×D9C2×Q812yes—
188C4×D9#4112yes—
189Dic18—21no—
190Dic18—24no—
191Dic18—42no—
192Dic18—42no—
193Dic18C2×Q812yes—
194C8×C9—21no—
195C8×C9—21no—
196C9⋊C8—21no—
197C9⋊C8—21no—
198#533—91no—
199C2×C4×Q8—91no—
200#479—91no—
201#479—91no—
202#479—91no—
203#479D911yescharacteristic, complemented
204#477—91no—
205#477—91no—
206#475—91no—
207#475—91no—
208#428—91no—
209#428—91no—
210#423—91no—
211#419—91no—
212#419—91no—
213C2×C3×Q8C22×D311yescharacteristic
214D3×Q8—34no—
215D3×Q8—62no—
216C2×C4×D3—31no—
217C2×C4×D3—31no—
218C2×C4×D3—31no—
219C2×C4×D3—61no—
220C2×C4×D3—61no—
221C2×Dic6—31no—
222C2×Dic6—61no—
223C2×Dic6—61no—
224C2×Dic6—61no—
225C2×C3×C8C22×D311yescharacteristic
226C2×C3×C8C22×D311yescharacteristic
227C3×C4⋊C4—21no—
228C3×C4⋊C4—21no—
229C3×C4⋊C4—21no—
230C3×C4⋊C4C22×D311yescharacteristic
231C3×C4⋊C4C22×D311yescharacteristic
232C3×C4⋊C4C22×D311yescharacteristic
233C3×C42—21no—
234C3×C42C22×D311yescharacteristic
235(C2×D3)⋊C4—61no—
236(C2×D3)⋊C4—61no—
237C4⋊Dic3—31no—
238C4⋊Dic3—31no—
239C4⋊Dic3—31no—
240C4⋊Dic3—61no—
241Dic3⋊C4—61no—
242Dic3⋊C4—61no—
243Dic3⋊C4—61no—
244Dic3⋊C4—61no—
245Dic3⋊C4—61no—
246Dic3⋊C4—61no—
247Dic3⋊C4—61no—
248C4×Dic3—31no—
249C4×Dic3—31no—
250C4×Dic3—31no—
251C4×Dic3—61no—
252C4×Dic3—61no—
253C4×Dic3—61no—
254C4×Dic3—61no—
255C4×Dic3—61no—
256C2×C3⋊C8—31no—
257C2×C3⋊C8—31no—
258ΓL(1,𝔽25)—62no—
259ΓL(1,𝔽25)—62no—
260C22×C9C22×D411yescharacteristic
261C2×D9—21no—
262C2×D9—21no—
263C2×D9C22⋊Q812yes—
264C4×C9—22no—
265C4×C9—21no—
266C4×C9—21no—
267C4×C9—41no—
268C4×C9—41no—
269C4×C9—41no—
270C4×C9C22×Q811yescharacteristic
271C4×C9C2×#4111yescharacteristic
272Dic9—22no—
273Dic9—21no—
274Dic9—41no—
275Dic9—41no—
276Dic9—41no—
277Dic9C22⋊Q812yes—
278Dic9#13712yes—
279C22×Q8—91no—
280C2×M16—91no—
281C2×M16—91no—
282C4⋊Q8—91no—
283C4⋊Q8—91no—
284#125—91no—
285#125C2×D911yescharacteristic
286C22⋊Q8—181no—
287C22⋊Q8—181no—
288C4×Q8—91no—
289C4×Q8—91no—
290C4×Q8—91no—
291C4×Q8—181no—
292C4×Q8—181no—
293C4×Q8—181no—
294C4×Q8—181no—
295C4×Q8C2×D911yescharacteristic
296#117—91no—
297#117—91no—
298C2×C4⋊C4—91no—
299C2×C4⋊C4—181no—
300C2×C42—91no—
301C2×C42—181no—
302#107—91no—
303#107—91no—
304#107—91no—
305#107C2×D911yescharacteristic
306#106—91no—
307#106—91no—
308#106—91no—
309#106C2×D911yescharacteristic
310C4⋊C8—91no—
311C4⋊C8—91no—
312C4⋊C8—91no—
313C4⋊C8C2×D911yescharacteristic
314#103—91no—
315#103—91no—
316#103—91no—
317#103—91no—
318#103—91no—
319#103—91no—
320#103C2×D911yescharacteristic
321#103C2×D911yescharacteristic
322C22×D3—31no—
323C3×Q8—21no—
324C3×Q8D3×Q812yes—
325C2×C3×C4—21no—
326C2×C3×C4—21no—
327C2×C3×C4—21no—
328C2×C3×C4—21no—
329C2×C3×C4D3×D411yescharacteristic
330C2×C3×C4D3×D411yescharacteristic
331C2×C3×C4C23×D311yescharacteristic
332C2×Dic3—31no—
333C2×Dic3—31no—
334C2×Dic3—31no—
335C2×Dic3—61no—
336C2×Dic3—61no—
337C2×Dic3—61no—
338C2×Dic3—61no—
339C4×D3—32no—
340C4×D3—32no—
341C4×D3—62no—
342C4×D3—64no—
343C4×D3—121no—
344C4×D3—122no—
345Dic6—32no—
346Dic6—64no—
347Dic6—61no—
348Dic6—122no—
349Dic6—122no—
350C3×C8—21no—
351C3×C8—21no—
352C3⋊C8—61no—
353C3⋊C8—61no—
354C2×C9C2×C22⋊Q811yescharacteristic
355C2×C9C2×#13711yescharacteristic
356C2×C9#57511yescharacteristic
357D9—22no—
358C2×Q8—94no—
359C2×Q8—91no—
360C2×Q8—181no—
361C2×Q8—181no—
362C2×Q8—181no—
363C2×Q8—182no—
364C2×Q8C22×D911yescharacteristic
365C22×C4—91no—
366C22×C4—91no—
367C22×C4—91no—
368C22×C4—181no—
369C22×C4—181no—
370M16—182no—
371M16—182no—
372C2×C8—91no—
373C2×C8—91no—
374C2×C8C22×D911yescharacteristic
375C2×C8C22×D911yescharacteristic
376C4⋊C4—21no—
377C4⋊C4—21no—
378C4⋊C4—21no—
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⋊C4C22×D911yescharacteristic
391C4⋊C4C22×D911yescharacteristic
392C4⋊C4C22×D911yescharacteristic
393C22⋊C4—181no—
394C22⋊C4—181no—
395C42—21no—
396C42—91no—
397C42—91no—
398C42—91no—
399C42—181no—
400C42—181no—
401C42—181no—
402C42—181no—
403C42—181no—
404C42C22×D911yescharacteristic
405C22×C3C2×D3×D411yescharacteristic
406C2×D3—32no—
407C2×D3—61no—
408C2×D3—61no—
409C3×C4—21no—
410C3×C4—21no—
411C3×C4—22no—
412C3×C4—41no—
413C3×C4—41no—
414C3×C4—41no—
415C3×C4C2×D3×Q811yescharacteristic
416C3×C4D3×#4111yescharacteristic
417Dic3—32no—
418Dic3—32no—
419Dic3—61no—
420Dic3—62no—
421Dic3—121no—
422Dic3—121no—
423Dic3—121no—
424C9#307811yescharacteristic, complemented, Sylow
425C23—91no—
426Q8—21no—
427Q8—92no—
428Q8—184no—
429Q8—181no—
430Q8—362no—
431Q8—362no—
432Q8Q8×D912yes—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—91no—
438C2×C4—91no—
439C2×C4—92no—
440C2×C4—92no—
441C2×C4—91no—
442C2×C4—182no—
443C2×C4—184no—
444C2×C4—181no—
445C2×C4—181no—
446C2×C4—181no—
447C2×C4—181no—
448C2×C4—361no—
449C2×C4—362no—
450C2×C4D4×D911yescharacteristic
451C2×C4D4×D911yescharacteristic
452C2×C4C23×D911yescharacteristic
453C8—21no—
454C8—21no—
455C8—181no—
456C8—181no—
457C2×C3D3×C22⋊Q811yescharacteristic
458C2×C3#576811yescharacteristic
459C2×C3D3×#13711yescharacteristic
460D3—62no—
461C22—92no—
462C22—181no—
463C22—181no—
464C22C2×D4×D911yescharacteristic
465C4—22no—
466C4—21no—
467C4—21no—
468C4—41no—
469C4—41no—
470C4—41no—
471C4—92no—
472C4—92no—
473C4—182no—
474C4—181no—
475C4—361no—
476C4—361no—
477C4—361no—
478C4C2×Q8×D911yescharacteristic
479C4#41×D911yescharacteristic
480C3#8123011yescharacteristic
481C2—182no—
482C2D9×C22⋊Q811yescharacteristic
483C2#1058987011yescharacteristic
484C2D9×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D9
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#479C2
socleC22×C3C2×D3×D4
prime radicalC22×D9C2×D4
hypercenter#479D9
hypocenterC9#3078
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
3. C9×#479C2semidirect
4. #10588745C2semidirect
5. #10588704C2semidirect
7. #10588555C2semidirect
9. #10588534C2semidirect
11. #10588511C2semidirect
14. #10588473C2semidirect
15. #10588471C2semidirect
77. Q8×D9Q8semidirect
203. #479D9semidirect
424. C9#3078semidirect

Maximal subgroups

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

subgroupindex
#105897902
C4×Q8×D92
C9×#4792
#105887452
#105887042
#105885612
#105885552
#105885412
#105885342
#105885212
#105885112
#105884822
#105884732
#105884712
#812303