Finite Group Databasebeta

← C2×#10589940 #11918911

Subgroups — C2×#10589940 #11918911

Order 1152.

2112 conjugacy classes of subgroups.

The subgroup lattice has 357 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C9×2−1+4C211yesmaximal, characteristic, complemented
2C2×#63716C211yesmaximal, characteristic, complemented
3#10589940C2116yesmaximal, direct product factor
4C2×#63513C213yesmaximal, complemented
5C2×#63511C213yesmaximal, complemented
6C2×#63510C211yesmaximal, characteristic, complemented
7C2×#63505C213yesmaximal, complemented
8C22×#3674C213yesmaximal, complemented
9C2×#5838—31nomaximal
10C9×2−1+4—24no—
11C9×2−1+4C2218yescomplemented
12C2×C9×#41—23no—
13C2×C9×#41C2213yes—
14C2×C9×#41C2211yescharacteristic
15C22×Q8×C9—21no—
16C22×Q8×C9C2213yes—
17#63716—24no—
18#63716C2218yescomplemented
19C2×Q8×D9—21no—
20C2×#3699—23no—
21C2×#3697C2213yes—
22C22×Dic18C2213yes—
23#63513C22124yescomplemented
24#63511C22124yescomplemented
25#63510C2218yescomplemented
26#63505C22124yescomplemented
27C2×#3675C2213yes—
28C2×#3674C2213yes—
29C2×#3674C2216yes—
30C2×#3674C22124yescomplemented
31C2×#3673C2211yescharacteristic
32C2×#3672C2213yes—
33C2×#3667C2213yes—
34C22×C9⋊C8C2213yes—
35C2×C3×2−1+4D311yescharacteristic
36C2×#1010—31no—
37#5838—316no—
38C2×#951—33no—
39C2×#950—33no—
40C2×#948—31no—
41C22×#216—33no—
42C2×#942—33no—
43C9×#41—224no—
44C9×#41—26no—
45C9×#41D414yes—
46C9×#41C23112yes—
47C9×#41C2314yes—
48C2×Q8×C9—28no—
49C2×Q8×C9—23no—
50C2×Q8×C9—26no—
51C2×Q8×C9D411yescharacteristic
52C2×Q8×C9C2313yes—
53C2×Q8×C9C23112yes—
54C2×D4×C9—23no—
55C2×D4×C9D413yes—
56C2×D4×C9C2311yescharacteristic
57C22×C4×C9—23no—
58C22×C4×C9—23no—
59C22×C4×C9C2313yes—
60C2×#611—23no—
61C22×Dic9—23no—
62Q8×D9—28no—
63#3699—224no—
64#3697—26no—
65#3697C23112yes—
66C2×D36C2311yescharacteristic
67C2×C4×D9—23no—
68C2×Dic18—23no—
69C2×Dic18—26no—
70C2×Dic18C2313yes—
71C2×Dic18C23112yes—
72#3675C23112yes—
73#3674C23112yes—
74#3674C23124yes—
75#3673C2314yes—
76#3672C23112yes—
77#3667C23112yes—
78C2×C9⋊C8C2313yes—
79C2×C9⋊C8C2311yescharacteristic
80C2×C9⋊C8C23112yes—
81C2×#578—91noSylow
82C3×2−1+4—24no—
83C3×2−1+4C2×D318yes—
84C2×C3×#41—23no—
85C2×C3×#41C2×D313yes—
86C2×C3×#41C2×D311yescharacteristic
87C22×C3×Q8—21no—
88C22×C3×Q8C2×D313yes—
89#1010—38no—
90#1010—64no—
91C2×D3×Q8—61no—
92C2×#237—63no—
93C2×#235—33no—
94C22×Dic6—33no—
95#951—324no—
96#950—324no—
97#948—38no—
98C2×#216—36no—
99C2×#216—33no—
100C2×#216—324no—
101#942—324no—
102C2×#215—33no—
103C2×#214—33no—
104C2×#213—31no—
105C2×#208—33no—
106C22×C3⋊C8—33no—
107C23×C9—21no—
108C23×C9C2×D413yes—
109C22×D9—21no—
110Q8×C9—23no—
111Q8×C9—212no—
112Q8×C9C2×D414yes—
113Q8×C9C2416yes—
114D4×C9—212no—
115D4×C9—21no—
116D4×C9C2×D4112yes—
117D4×C9C2412yes—
118C2×C4×C9—23no—
119C2×C4×C9—212no—
120C2×C4×C9—212no—
121C2×C4×C9C2×D413yes—
122C2×C4×C9C2×D416yes—
123C2×C4×C9C2411yescharacteristic
124C2×C4×C9C2416yes—
125#611—212no—
126C2×Dic9—23no—
127C2×Dic9—212no—
128D36—21no—
129D36C2412yes—
130C4×D9—212no—
131Dic18—23no—
132Dic18—212no—
133Dic18C2416yes—
134C9⋊C8C2412yes—
135C9⋊C8C2416yes—
136C2×2−1+4—91no—
137C2×2−1+4D911yescharacteristic, complemented
138#578—916no—
139C2×#137—93no—
140C2×#137—93no—
141C2×#135—93no—
142C22×Q16—93no—
143C2×#131—91no—
144C3×#41—224no—
145C3×#41—26no—
146C3×#41#6714yes—
147C3×#41C22×D3112yes—
148C3×#41C22×D314yes—
149C2×C3×Q8—28no—
150C2×C3×Q8—23no—
151C2×C3×Q8—26no—
152C2×C3×Q8#6711yescharacteristic
153C2×C3×Q8C22×D313yes—
154C2×C3×Q8C22×D3112yes—
155C2×C3×D4—23no—
156C2×C3×D4#6713yes—
157C2×C3×D4C22×D311yescharacteristic
158C22×C3×C4—23no—
159C22×C3×C4—23no—
160C22×C3×C4C22×D313yes—
161C2×#67—63no—
162C22×Dic3—63no—
163D3×Q8—68no—
164#237—624no—
165#235—312no—
166#235—66no—
167C2×D12—31no—
168C2×C4×D3—63no—
169C2×Dic6—33no—
170C2×Dic6—312no—
171C2×Dic6—63no—
172C2×Dic6—66no—
173#216—324no—
174#216—312no—
175#215—312no—
176#214—312no—
177#213—34no—
178#208—312no—
179C2×C3⋊C8—31no—
180C2×C3⋊C8—33no—
181C2×C3⋊C8—312no—
182C22×C9—26no—
183C22×C9—22no—
184C22×C9—42no—
185C22×C9C22×D416yes—
186C22×C9C22×D411yescharacteristic
187C2×D9—22no—
188C2×D9—42no—
189C4×C9—26no—
190C4×C9C22×D411yescharacteristic
191C4×C9C22×D416yes—
192C4×C9C2511yescharacteristic
193Dic9—26no—
1942−1+4—24no—
1952−1+4—98no—
1962−1+4—184no—
1972−1+4C2×D918yescomplemented
198C2×#41—23no—
199C2×#41—93no—
200C2×#41—183no—
201C2×#41C2×D913yes—
202C2×#41C2×D911yescharacteristic
203C22×Q8—21no—
204C22×Q8—93no—
205C22×Q8—181no—
206C22×Q8C2×D913yes—
207#137—924no—
208#137—924no—
209#135—924no—
210C2×Q16—93no—
211C2×Q16—96no—
212C2×Q16—924no—
213C2×SD16—93no—
214C2×SD16—93no—
215C2×D8—91no—
216#131—98no—
217C2×M16—93no—
218C22×C8—93no—
219C23×C3—21no—
220C23×C3C2×#6713yes—
221C22×D3—61no—
222C3×Q8—23no—
223C3×Q8—212no—
224C3×Q8C2×#6714yes—
225C3×Q8C23×D316yes—
226C3×D4—212no—
227C3×D4—21no—
228C3×D4C2×#67112yes—
229C3×D4C23×D312yes—
230C2×C3×C4—23no—
231C2×C3×C4—212no—
232C2×C3×C4—212no—
233C2×C3×C4C2×#6713yes—
234C2×C3×C4C2×#6716yes—
235C2×C3×C4C23×D311yescharacteristic
236C2×C3×C4C23×D316yes—
237#67—612no—
238C2×Dic3—63no—
239C2×Dic3—612no—
240D12—32no—
241D12—61no—
242C4×D3—612no—
243Dic6—36no—
244Dic6—63no—
245Dic6—612no—
246C3⋊C8—32no—
247C3⋊C8—36no—
248C2×C9—26no—
249C2×C9—42no—
250C2×C9#57812yescomplemented
251C2×C9C23×D411yescharacteristic
252D9—42no—
253#41—224no—
254#41—26no—
255#41—912no—
256#41—1824no—
257#41—186no—
258#41#61114yes—
259#41C22×D9112yes—
260#41C22×D914yes—
261C2×Q8—28no—
262C2×Q8—23no—
263C2×Q8—26no—
264C2×Q8—93no—
265C2×Q8—912no—
266C2×Q8—188no—
267C2×Q8—183no—
268C2×Q8—186no—
269C2×Q8#61111yescharacteristic
270C2×Q8C22×D913yes—
271C2×Q8C22×D9112yes—
272C2×D4—23no—
273C2×D4—91no—
274C2×D4—183no—
275C2×D4#61113yes—
276C2×D4C22×D911yescharacteristic
277C22×C4—23no—
278C22×C4—23no—
279C22×C4—183no—
280C22×C4—183no—
281C22×C4C22×D913yes—
282Q16—912no—
283Q16—924no—
284SD16—912no—
285SD16—912no—
286D8—94no—
287M16—912no—
288C2×C8—91no—
289C2×C8—93no—
290C2×C8—912no—
291C22×C3—26no—
292C22×C3—22no—
293C22×C3—42no—
294C22×C3C22×#6716yes—
295C22×C3C22×#6711yescharacteristic
296C2×D3—62no—
297C2×D3—122no—
298C3×C4—26no—
299C3×C4C22×#6711yescharacteristic
300C3×C4C22×#6716yes—
301C3×C4C24×D311yescharacteristic
302Dic3—66no—
303C9C2×#57811yescharacteristic, complemented, Sylow
304C23—21no—
305C23—181no—
306C23C2×#61113yes—
307Q8—212no—
308Q8—23no—
309Q8—96no—
310Q8—1812no—
311Q8—183no—
312Q8C2×#61114yes—
313Q8C23×D916yes—
314D4—212no—
315D4—21no—
316D4—92no—
317D4—1812no—
318D4—181no—
319D4C2×#611112yes—
320D4C23×D912yes—
321C2×C4—212no—
322C2×C4—23no—
323C2×C4—212no—
324C2×C4—1812no—
325C2×C4—183no—
326C2×C4—1812no—
327C2×C4C2×#61116yes—
328C2×C4C2×#61113yes—
329C2×C4C23×D916yes—
330C2×C4C23×D911yescharacteristic
331C8—92no—
332C8—96no—
333C2×C3—26no—
334C2×C3—42no—
335C2×C3#583812yes—
336C2×C3C23×#6711yescharacteristic
337D3—122no—
338C22—26no—
339C22—22no—
340C22—42no—
341C22—182no—
342C22—362no—
343C22C22×#61116yes—
344C22C22×#61111yescharacteristic
345C4—26no—
346C4—186no—
347C4C22×#61116yes—
348C4C22×#61111yescharacteristic
349C4C24×D911yescharacteristic
350C3C2×#583811yescharacteristic
351C2—26no—
352C2—42no—
353C2—362no—
354C2#1058994012yesdirect product factor
355C2C23×#61111yescharacteristic
subgroupG/H
centerC22C22×#611
commutator, cosocleC4×C9C25
FrattiniC3×C4C24×D3
FittingC2×C9×2−1+4C2
socleC22×C3C22×#67
hypercenterC2×2−1+4D9
hypocenterC9C2×#578
LCSG ▷ C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×2−1+4

Complements

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

NH ≅ G/Ntype
1. C2×C9×2−1+4C2semidirect
2. C2×#63716C2semidirect
3. #10589940C2direct (N × H)
4. C2×#63513C2semidirect
5. C2×#63511C2semidirect
6. C2×#63510C2semidirect
7. C2×#63505C2semidirect
8. C22×#3674C2semidirect
11. C9×2−1+4C22semidirect
18. #63716C22semidirect
23. #63513C22semidirect
24. #63511C22semidirect
25. #63510C22semidirect
26. #63505C22semidirect
30. C2×#3674C22semidirect
137. C2×2−1+4D9semidirect
197. 2−1+4C2×D9semidirect
250. C2×C9#578semidirect
303. C9C2×#578semidirect
354. C2#10589940direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C9×2−1+42
C2×#637162
#105899402
C2×#635132
C2×#635112
C2×#635102
C2×#635052
C22×#36742
C2×#58383