Finite Group Databasebeta

← C2×#10596309 #11918912

Subgroups — C2×#10596309 #11918912

Order 1152.

4224 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×C32×2−1+4C211yesmaximal, characteristic, complemented
2C2×#64367C211yesmaximal, characteristic, complemented
3#10596309C2116yesmaximal, direct product factor
4C2×#64160C213yesmaximal, complemented
5C2×#64159C213yesmaximal, complemented
6C2×#64157C211yesmaximal, characteristic, complemented
7C22×#3756C213yesmaximal, complemented
8C2×#64151C213yesmaximal, complemented
9C2×#5838—34nomaximal
10C32×2−1+4—24no—
11C32×2−1+4C2218yescomplemented
12C2×C32×#41—23no—
13C2×C32×#41C2213yes—
14C2×C32×#41C2211yescharacteristic
15C22×C32×Q8—21no—
16C22×C32×Q8C2213yes—
17#64367—24no—
18#64367C2218yescomplemented
19C2×Q8×C3⋊D3—21no—
20C2×#3830—23no—
21C2×#3828C2213yes—
22C22×#634C2213yes—
23#64160C22124yescomplemented
24#64159C22124yescomplemented
25#64157C2218yescomplemented
26C2×#3756C2216yes—
27C2×#3756C2213yes—
28C2×#3756C22124yescomplemented
29#64151C22124yescomplemented
30C2×#3755C2213yes—
31C2×#3754C2213yes—
32C2×#3753C2211yescharacteristic
33C2×#3748C2213yes—
34C22×C3⋊(C3⋊C8)C2213yes—
35C2×C3×2−1+4D314yescomplemented
36C2×#1010—34no—
37#5838—364no—
38C2×#951—312no—
39C2×#950—312no—
40C2×#948—34no—
41C22×#216—312no—
42C2×#942—312no—
43C32×#41—224no—
44C32×#41—26no—
45C32×#41D414yes—
46C32×#41C23112yes—
47C32×#41C2314yes—
48C2×C32×Q8—28no—
49C2×C32×Q8—23no—
50C2×C32×Q8—26no—
51C2×C32×Q8D411yescharacteristic
52C2×C32×Q8C2313yes—
53C2×C32×Q8C23112yes—
54C2×C32×D4—23no—
55C2×C32×D4D413yes—
56C2×C32×D4C2311yescharacteristic
57C22×C32×C4—23no—
58C22×C32×C4—23no—
59C22×C32×C4C2313yes—
60C2×#638—23no—
61C22×C3⋊Dic3—23no—
62Q8×C3⋊D3—28no—
63#3830—224no—
64#3828—26no—
65#3828C23112yes—
66C2×C4⋊(C3⋊D3)C2311yescharacteristic
67C2×C4×C3⋊D3—23no—
68C2×#634—23no—
69C2×#634—26no—
70C2×#634C2313yes—
71C2×#634C23112yes—
72#3756C23124yes—
73#3756C23112yes—
74#3755C23112yes—
75#3754C23112yes—
76#3753C2314yes—
77#3748C23112yes—
78C2×C3⋊(C3⋊C8)C2311yescharacteristic
79C2×C3⋊(C3⋊C8)C2313yes—
80C2×C3⋊(C3⋊C8)C23112yes—
81C2×#578—91noSylow
82C3×2−1+4—216no—
83C3×2−1+4C2×D3132yescomplemented
84C2×C3×#41—212no—
85C2×C3×#41C2×D3112yes—
86C2×C3×#41C2×D314yes—
87C22×C3×Q8—24no—
88C22×C3×Q8C2×D3112yes—
89#1010—332no—
90#1010—616no—
91C2×D3×Q8—64no—
92C2×#237—612no—
93C2×#235—312no—
94C22×Dic6—312no—
95#951—396no—
96#950—396no—
97#948—332no—
98C2×#216—324no—
99C2×#216—312no—
100C2×#216—396no—
101#942—396no—
102C2×#215—312no—
103C2×#214—312no—
104C2×#213—34no—
105C2×#208—312no—
106C22×C3⋊C8—312no—
107C23×C32—21no—
108C23×C32C2×D413yes—
109C22×C3⋊D3—21no—
110C32×Q8—23no—
111C32×Q8—212no—
112C32×Q8C2×D414yes—
113C32×Q8C2416yes—
114C32×D4—212no—
115C32×D4—21no—
116C32×D4C2×D4112yes—
117C32×D4C2412yes—
118C2×C32×C4—23no—
119C2×C32×C4—212no—
120C2×C32×C4—212no—
121C2×C32×C4C2×D413yes—
122C2×C32×C4C2×D416yes—
123C2×C32×C4C2411yescharacteristic
124C2×C32×C4C2416yes—
125#638—212no—
126C2×C3⋊Dic3—23no—
127C2×C3⋊Dic3—212no—
128C4⋊(C3⋊D3)—21no—
129C4⋊(C3⋊D3)C2412yes—
130C4×C3⋊D3—212no—
131#634—23no—
132#634—212no—
133#634C2416yes—
134C3⋊(C3⋊C8)C2412yes—
135C3⋊(C3⋊C8)C2416yes—
136C2×2−1+4—91no—
137C2×2−1+4C3⋊D311yescharacteristic, complemented
138#578—916no—
139C2×#137—93no—
140C2×#137—93no—
141C2×#135—93no—
142C22×Q16—93no—
143C2×#131—91no—
144C3×#41—296no—
145C3×#41—224no—
146C3×#41#67116yes—
147C3×#41C22×D3148yes—
148C3×#41C22×D3116yes—
149C2×C3×Q8—232no—
150C2×C3×Q8—212no—
151C2×C3×Q8—224no—
152C2×C3×Q8#6714yes—
153C2×C3×Q8C22×D3112yes—
154C2×C3×Q8C22×D3148yes—
155C2×C3×D4—212no—
156C2×C3×D4#67112yes—
157C2×C3×D4C22×D314yes—
158C22×C3×C4—212no—
159C22×C3×C4—212no—
160C22×C3×C4C22×D3112yes—
161C2×#67—612no—
162C22×Dic3—612no—
163D3×Q8—632no—
164#237—696no—
165#235—348no—
166#235—624no—
167C2×D12—34no—
168C2×C4×D3—612no—
169C2×Dic6—312no—
170C2×Dic6—348no—
171C2×Dic6—612no—
172C2×Dic6—624no—
173#216—396no—
174#216—348no—
175#215—348no—
176#214—348no—
177#213—316no—
178#208—348no—
179C2×C3⋊C8—34no—
180C2×C3⋊C8—312no—
181C2×C3⋊C8—348no—
182C22×C32—26no—
183C22×C32—22no—
184C22×C32—42no—
185C22×C32C22×D416yes—
186C22×C32C22×D411yescharacteristic
187C2×C3⋊D3—22no—
188C2×C3⋊D3—42no—
189C32×C4—26no—
190C32×C4C22×D411yescharacteristic
191C32×C4C22×D416yes—
192C32×C4C2511yescharacteristic
193C3⋊Dic3—26no—
1942−1+4—24no—
1952−1+4—98no—
1962−1+4—184no—
1972−1+4C2×C3⋊D318yescomplemented
198C2×#41—23no—
199C2×#41—93no—
200C2×#41—183no—
201C2×#41C2×C3⋊D313yes—
202C2×#41C2×C3⋊D311yescharacteristic
203C22×Q8—21no—
204C22×Q8—93no—
205C22×Q8—181no—
206C22×Q8C2×C3⋊D313yes—
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—24no—
220C23×C3C2×#67112yes—
221C22×D3—64no—
222C3×Q8—212no—
223C3×Q8—248no—
224C3×Q8C2×#67116yes—
225C3×Q8C23×D3124yes—
226C3×D4—248no—
227C3×D4—24no—
228C3×D4C2×#67148yes—
229C3×D4C23×D318yes—
230C2×C3×C4—212no—
231C2×C3×C4—248no—
232C2×C3×C4—248no—
233C2×C3×C4C2×#67112yes—
234C2×C3×C4C2×#67124yes—
235C2×C3×C4C23×D314yes—
236C2×C3×C4C23×D3124yes—
237#67—648no—
238C2×Dic3—612no—
239C2×Dic3—648no—
240D12—38no—
241D12—64no—
242C4×D3—648no—
243Dic6—324no—
244Dic6—612no—
245Dic6—648no—
246C3⋊C8—38no—
247C3⋊C8—324no—
248C2×C32—26no—
249C2×C32—42no—
250C2×C32#57812yescomplemented
251C2×C32C23×D411yescharacteristic
252C3⋊D3—42no—
253#41—224no—
254#41—26no—
255#41—912no—
256#41—1824no—
257#41—186no—
258#41#63814yes—
259#41C22×C3⋊D3112yes—
260#41C22×C3⋊D314yes—
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#63811yescharacteristic
270C2×Q8C22×C3⋊D313yes—
271C2×Q8C22×C3⋊D3112yes—
272C2×D4—23no—
273C2×D4—91no—
274C2×D4—183no—
275C2×D4#63813yes—
276C2×D4C22×C3⋊D311yescharacteristic
277C22×C4—23no—
278C22×C4—23no—
279C22×C4—183no—
280C22×C4—183no—
281C22×C4C22×C3⋊D313yes—
282Q16—912no—
283Q16—924no—
284SD16—912no—
285SD16—912no—
286D8—94no—
287M16—912no—
288C2×C8—91no—
289C2×C8—93no—
290C2×C8—912no—
291C22×C3—224no—
292C22×C3—28no—
293C22×C3—48no—
294C22×C3C22×#67124yes—
295C22×C3C22×#6714yes—
296C2×D3—68no—
297C2×D3—128no—
298C3×C4—224no—
299C3×C4C22×#6714yes—
300C3×C4C22×#67124yes—
301C3×C4C24×D314yes—
302Dic3—624no—
303C32C2×#57811yescharacteristic, complemented, Sylow
304C23—21no—
305C23—181no—
306C23C2×#63813yes—
307Q8—212no—
308Q8—23no—
309Q8—96no—
310Q8—1812no—
311Q8—183no—
312Q8C2×#63814yes—
313Q8C23×C3⋊D316yes—
314D4—212no—
315D4—21no—
316D4—92no—
317D4—1812no—
318D4—181no—
319D4C2×#638112yes—
320D4C23×C3⋊D312yes—
321C2×C4—212no—
322C2×C4—23no—
323C2×C4—212no—
324C2×C4—1812no—
325C2×C4—183no—
326C2×C4—1812no—
327C2×C4C2×#63816yes—
328C2×C4C2×#63813yes—
329C2×C4C23×C3⋊D316yes—
330C2×C4C23×C3⋊D311yescharacteristic
331C8—92no—
332C8—96no—
333C2×C3—224no—
334C2×C3—48no—
335C2×C3#583818yescomplemented
336C2×C3C23×#6714yes—
337D3—128no—
338C22—26no—
339C22—22no—
340C22—42no—
341C22—182no—
342C22—362no—
343C22C22×#63816yes—
344C22C22×#63811yescharacteristic
345C4—26no—
346C4—186no—
347C4C22×#63816yes—
348C4C22×#63811yescharacteristic
349C4C24×C3⋊D311yescharacteristic
350C3C2×#583814yescomplemented
351C2—26no—
352C2—42no—
353C2—362no—
354C2#1059630912yesdirect product factor
355C2C23×#63811yescharacteristic
subgroupG/H
centerC22C22×#638
commutator, cosocleC32×C4C25
FrattiniC4C24×C3⋊D3
FittingC2×C32×2−1+4C2
socleC22×C32C22×D4
hypercenterC2×2−1+4C3⋊D3
hypocenterC32C2×#578
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×2−1+4

Complements

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

NH ≅ G/Ntype
1. C2×C32×2−1+4C2semidirect
2. C2×#64367C2semidirect
3. #10596309C2direct (N × H)
4. C2×#64160C2semidirect
5. C2×#64159C2semidirect
6. C2×#64157C2semidirect
7. C22×#3756C2semidirect
8. C2×#64151C2semidirect
11. C32×2−1+4C22semidirect
18. #64367C22semidirect
23. #64160C22semidirect
24. #64159C22semidirect
25. #64157C22semidirect
28. C2×#3756C22semidirect
29. #64151C22semidirect
35. C2×C3×2−1+4D3semidirect
83. C3×2−1+4C2×D3semidirect
137. C2×2−1+4C3⋊D3semidirect
197. 2−1+4C2×C3⋊D3semidirect
250. C2×C32#578semidirect
303. C32C2×#578semidirect
335. C2×C3#5838semidirect
350. C3C2×#5838semidirect
354. C2#10596309direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×2−1+42
C2×#643672
#105963092
C2×#641602
C2×#641592
C2×#641572
C22×#37562
C2×#641512
C2×#58383