Finite Group Databasebeta

← C2×#10588884 #11867857

Subgroups — C2×#10588884 #11867857

Order 1152.

702 conjugacy classes of subgroups.

The subgroup lattice has 417 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C9×#137C211yesmaximal, characteristic, complemented
2C2×#63512C211yesmaximal, characteristic
3C2×#63510C211yesmaximal, characteristic, complemented
4C22×#3675C211yesmaximal, characteristic, complemented
5C2×#63394C211yesmaximal, characteristic, complemented
6#10588884C218yesmaximal, direct product factor
7C2×#63383C211yesmaximal, characteristic, complemented
8C2×#63381C211yesmaximal, characteristic, complemented
9C2×#5203—31nomaximal
10C2×C9×#41C2211yescharacteristic
11C22×Q8×C9C2211yescharacteristic
12C22×D36C2211yescharacteristic
13C9×#137—22no—
14C9×#137C2214yescomplemented
15C2×C9×Q16—21no—
16C2×C9×SD16—21no—
17C2×C9×M16C2211yescharacteristic
18#63512—22no—
19#63512C2214yes—
20#63510—22no—
21#63510C2214yescomplemented
22C2×#3675—21no—
23C2×#3675—22no—
24C2×#3675—21no—
25C2×#3675—21no—
26C2×#3675C2214yescomplemented
27C2×#3673—21no—
28C2×#3667—21no—
29C2×#3667C2211yescharacteristic
30C2×#3667C2211yescharacteristic
31C22×C9⋊C8—21no—
32C22×C9⋊C8C2211yescharacteristic
33#63394C2214yescomplemented
34#63383C2214yescomplemented
35#63381C2214yescomplemented
36C2×C3×#137D311yescharacteristic
37C2×#949—31no—
38C2×#948—31no—
39C22×#215—31no—
40C2×#836—31no—
41#5203—38no—
42C2×#823—31no—
43C2×#822—31no—
44C23×D9—21no—
45C9×#41—21no—
46C9×#41—21no—
47C9×#41D412yes—
48C9×#41C2312yes—
49C2×Q8×C9—21no—
50C2×Q8×C9—21no—
51C2×Q8×C9—21no—
52C2×Q8×C9—21no—
53C2×Q8×C9—21no—
54C2×Q8×C9D411yescharacteristic
55C2×Q8×C9C2312yes—
56C2×D4×C9—21no—
57C2×D4×C9D411yescharacteristic
58C22×C4×C9—21no—
59C22×C4×C9—21no—
60C22×C4×C9C2311yescharacteristic
61C2×D36—21no—
62C2×D36—21no—
63C2×D36—21no—
64C2×D36—21no—
65C2×D36—21no—
66C2×D36C2312yes—
67C9×Q16—24no—
68C9×SD16—24no—
69C9×M16—21no—
70C9×M16C2312yes—
71C2×C8×C9—21no—
72#3675—24no—
73#3675—24no—
74#3675—24no—
75#3673—24no—
76#3667—21no—
77#3667—21no—
78#3667—24no—
79#3667C2312yes—
80#3667C2312yes—
81C2×C9⋊C8—21no—
82C2×C9⋊C8—21no—
83C2×C9⋊C8—24no—
84C2×C9⋊C8D412yes—
85C2×C9⋊C8D411yescharacteristic
86C2×C9⋊C8D411yescharacteristic
87C2×C9⋊C8C2312yes—
88C2×#471—91noSylow
89C2×C3×#41C2×D311yescharacteristic
90C22×C3×Q8C2×D311yescharacteristic
91C22×D12—31no—
92C3×#137—22no—
93C3×#137C2×D314yes—
94C2×C3×Q16—21no—
95C2×C3×SD16—21no—
96C2×C3×M16C2×D311yescharacteristic
97#949—34no—
98#949—62no—
99#948—34no—
100#948—62no—
101C2×#215—34no—
102C2×#215—61no—
103C2×#215—61no—
104C2×#215—62no—
105C2×#215—61no—
106C2×#213—61no—
107C2×#208—31no—
108C2×#208—31no—
109C2×#208—61no—
110C22×C3⋊C8—31no—
111C22×C3⋊C8—61no—
112#836—34no—
113#823—34no—
114#822—34no—
115C23×C9—21no—
116C23×C9#4111yescharacteristic
117C22×D9—22no—
118C22×D9—41no—
119C22×D9—41no—
120C22×D9—82no—
121Q8×C9—21no—
122Q8×C9—22no—
123Q8×C9—22no—
124Q8×C9—41no—
125Q8×C9—41no—
126Q8×C9C2×D412yes—
127D4×C9—22no—
128D4×C9—22no—
129D4×C9—21no—
130D4×C9C2×D412yes—
131C2×C4×C9—21no—
132C2×C4×C9—22no—
133C2×C4×C9—22no—
134C2×C4×C9—22no—
135C2×C4×C9—41no—
136C2×C4×C9—41no—
137C2×C4×C9C2×D411yescharacteristic
138C2×C4×C9C2×D411yescharacteristic
139C2×C4×C9C2×D411yescharacteristic
140C2×C4×C9C2×D411yescharacteristic
141C2×C4×C9#4111yescharacteristic
142C2×C4×C9C2411yescharacteristic
143D36—22no—
144D36—22no—
145D36—41no—
146D36—41no—
147C8×C9—22no—
148C9⋊C8—22no—
149C9⋊C8—22no—
150C9⋊C8C2×D412yes—
151C9⋊C8C2×D412yes—
152C2×#137D911yescharacteristic, complemented
153C2×AGL(1,ℤ/8)—91no—
154C22×SD16—91no—
155C2×#131—91no—
156#471—98no—
157C2×#108—91no—
158C2×#101—91no—
159C2×#100—91no—
160C23×D3—61no—
161C3×#41—21no—
162C3×#41—21no—
163C3×#41#6712yes—
164C3×#41C22×D312yes—
165C2×C3×Q8—21no—
166C2×C3×Q8—21no—
167C2×C3×Q8—21no—
168C2×C3×Q8—21no—
169C2×C3×Q8—21no—
170C2×C3×Q8#6711yescharacteristic
171C2×C3×Q8C22×D312yes—
172C2×C3×D4—21no—
173C2×C3×D4#6711yescharacteristic
174C22×C3×C4—21no—
175C22×C3×C4—21no—
176C22×C3×C4C22×D311yescharacteristic
177C2×D12—32no—
178C2×D12—61no—
179C2×D12—61no—
180C2×D12—61no—
181C2×D12—61no—
182C2×D12—61no—
183C3×Q16—24no—
184C3×SD16—24no—
185C3×M16—21no—
186C3×M16C22×D312yes—
187C2×C3×C8—21no—
188#215—64no—
189#215—64no—
190#215—64no—
191#213—64no—
192#208—32no—
193#208—32no—
194#208—64no—
195#208—61no—
196#208—61no—
197C2×C3⋊C8—31no—
198C2×C3⋊C8—31no—
199C2×C3⋊C8—32no—
200C2×C3⋊C8—32no—
201C2×C3⋊C8—64no—
202C2×C3⋊C8—61no—
203C2×C3⋊C8—61no—
204C22×C9—22no—
205C22×C9—22no—
206C22×C9—42no—
207C22×C9#12111yescharacteristic
208C22×C9#12111yescharacteristic
209C22×C9C2×#4111yescharacteristic
210C2×D9—42no—
211C2×D9—82no—
212C2×D9—82no—
213C2×D9—82no—
214C4×C9—22no—
215C4×C9—42no—
216C4×C9#12111yescharacteristic
217C4×C9#12111yescharacteristic
218C4×C9C22×D411yescharacteristic
219C4×C9C22×D411yescharacteristic
220C2×#41C2×D911yescharacteristic
221C22×Q8C2×D911yescharacteristic
222C22×D4—91no—
223#137—22no—
224#137C2×D914yescomplemented
225AGL(1,ℤ/8)—94no—
226AGL(1,ℤ/8)—182no—
227C2×Q16—21no—
228C2×SD16—21no—
229C2×SD16—94no—
230C2×SD16—181no—
231C2×SD16—181no—
232C2×SD16—182no—
233C2×SD16—181no—
234C2×D8—181no—
235#131—94no—
236#131—182no—
237C2×M16—91no—
238C2×M16—91no—
239C2×M16—181no—
240C2×M16C2×D911yescharacteristic
241C22×C8—91no—
242C22×C8—181no—
243#108—94no—
244#101—94no—
245#100—94no—
246C23×C3—21no—
247C23×C3#23711yescharacteristic
248C22×D3—62no—
249C22×D3—121no—
250C22×D3—121no—
251C22×D3—242no—
252C3×Q8—21no—
253C3×Q8—22no—
254C3×Q8—22no—
255C3×Q8—41no—
256C3×Q8—41no—
257C3×Q8C2×#6712yes—
258C3×D4—22no—
259C3×D4—22no—
260C3×D4—21no—
261C3×D4C2×#6712yes—
262C2×C3×C4—21no—
263C2×C3×C4—22no—
264C2×C3×C4—22no—
265C2×C3×C4—22no—
266C2×C3×C4—41no—
267C2×C3×C4—41no—
268C2×C3×C4D3×D411yescharacteristic
269C2×C3×C4D3×D411yescharacteristic
270C2×C3×C4#23711yescharacteristic
271C2×C3×C4C2×#6711yescharacteristic
272C2×C3×C4C2×#6711yescharacteristic
273C2×C3×C4C23×D311yescharacteristic
274D12—62no—
275D12—62no—
276D12—121no—
277D12—121no—
278C3×C8—22no—
279C3⋊C8—32no—
280C3⋊C8—32no—
281C3⋊C8—62no—
282C3⋊C8—62no—
283C2×C9—21no—
284C2×C9—21no—
285C2×C9—42no—
286C2×C9#47112yescomplemented
287C2×C9C2×#12111yescharacteristic
288D9—82no—
289C24—181no—
290#41—21no—
291#41—21no—
292#41#61112yes—
293#41C22×D912yes—
294C2×Q8—21no—
295C2×Q8—21no—
296C2×Q8—21no—
297C2×Q8—21no—
298C2×Q8—21no—
299C2×Q8#61111yescharacteristic
300C2×Q8C22×D912yes—
301C2×D4—21no—
302C2×D4—92no—
303C2×D4—181no—
304C2×D4—181no—
305C2×D4—181no—
306C2×D4—181no—
307C2×D4—181no—
308C2×D4#61111yescharacteristic
309C22×C4—21no—
310C22×C4—21no—
311C22×C4C22×D911yescharacteristic
312Q16—24no—
313SD16—24no—
314SD16—184no—
315SD16—184no—
316SD16—184no—
317D8—184no—
318M16—21no—
319M16—92no—
320M16—92no—
321M16—184no—
322M16—181no—
323M16—181no—
324M16C22×D912yes—
325C2×C8—21no—
326C2×C8—91no—
327C2×C8—91no—
328C2×C8—92no—
329C2×C8—92no—
330C2×C8—184no—
331C2×C8—181no—
332C2×C8—181no—
333C22×C3—22no—
334C22×C3—22no—
335C22×C3—42no—
336C22×C3#93911yescharacteristic
337C22×C3#93911yescharacteristic
338C22×C3C2×#23711yescharacteristic
339C2×D3—122no—
340C2×D3—242no—
341C2×D3—242no—
342C2×D3—242no—
343C3×C4—22no—
344C3×C4—42no—
345C3×C4#93911yescharacteristic
346C3×C4#93911yescharacteristic
347C3×C4C2×D3×D411yescharacteristic
348C3×C4C22×#6711yescharacteristic
349C9C2×#47111yescharacteristic, complemented, Sylow
350C23—21no—
351C23—182no—
352C23—361no—
353C23—361no—
354C23—722no—
355C23#369911yescharacteristic
356Q8—21no—
357Q8—22no—
358Q8—22no—
359Q8—41no—
360Q8—41no—
361Q8C2×#61112yes—
362D4—22no—
363D4—22no—
364D4—21no—
365D4—182no—
366D4—182no—
367D4—361no—
368D4—361no—
369D4C2×#61112yes—
370C2×C4—21no—
371C2×C4—22no—
372C2×C4—22no—
373C2×C4—22no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4D4×D911yescharacteristic
377C2×C4D4×D911yescharacteristic
378C2×C4#369911yescharacteristic
379C2×C4C2×#61111yescharacteristic
380C2×C4C2×#61111yescharacteristic
381C2×C4C23×D911yescharacteristic
382C8—22no—
383C8—92no—
384C8—92no—
385C8—182no—
386C8—182no—
387C2×C3—21no—
388C2×C3—21no—
389C2×C3—42no—
390C2×C3#520312yes—
391C2×C3C2×#93911yescharacteristic
392D3—242no—
393C22—22no—
394C22—22no—
395C22—42no—
396C22—362no—
397C22—722no—
398C22—722no—
399C22—722no—
400C22#6350111yescharacteristic
401C22#6350111yescharacteristic
402C22C2×#369911yescharacteristic
403C4—22no—
404C4—42no—
405C4#6350111yescharacteristic
406C4#6350111yescharacteristic
407C4C2×D4×D911yescharacteristic
408C4C22×#61111yescharacteristic
409C3C2×#520311yescharacteristic
410C2—21no—
411C2—21no—
412C2—42no—
413C2—722no—
414C2#1058888412yesdirect product factor
415C2C2×#6350111yescharacteristic
subgroupG/H
centerC22#63501
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC2×C9×#137C2
socleC22×C3#939
prime radicalC2×#63512C2
hypercenterC2×#137D9
hypocenterC9C2×#471
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C2×C9×#137C2semidirect
3. C2×#63510C2semidirect
4. C22×#3675C2semidirect
5. C2×#63394C2semidirect
6. #10588884C2direct (N × H)
7. C2×#63383C2semidirect
8. C2×#63381C2semidirect
14. C9×#137C22semidirect
21. #63510C22semidirect
26. C2×#3675C22semidirect
33. #63394C22semidirect
34. #63383C22semidirect
35. #63381C22semidirect
152. C2×#137D9semidirect
224. #137C2×D9semidirect
286. C2×C9#471semidirect
349. C9C2×#471semidirect
414. C2#10588884direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C9×#1372
C2×#635122
C2×#635102
C22×#36752
C2×#633942
#105888842
C2×#633832
C2×#633812
C2×#52033