Finite Group Databasebeta

← C22×#11718853 #16730303

Subgroups — C22×#11718853 #16730303

Order 3328.

2630 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88196C212yesmaximal
2C22×#88155C211yesmaximal, characteristic
3C2×#11718853C2124yesmaximal, direct product factor
4C22×#88059C211yesmaximal, characteristic, complemented
5C22×#88076C212yesmaximal, complemented
6C23×C13×Q16C211yesmaximal, characteristic, complemented
7C23×Q8×C13C2212yes—
8C22×#6127C2211yescharacteristic
9C22×C13×Q16—21no—
10C22×C13×Q16—21no—
11C22×C13×Q16—26no—
12C22×C13×Q16C22112yescomplemented
13C23×C8×C13C2211yescharacteristic
14C22×#6107—22no—
15C2×#88196—212no—
16C2×#88196C22124yes—
17C22×#6106—22no—
18C22×#6099C2211yescharacteristic
19C22×#6099C2212yes—
20C2×#88155—26no—
21C2×#88155C22112yes—
22C22×#6094—21no—
23C22×C8×D13—21no—
24C2×#88076C22124yescomplemented
25#11718853C22164yesdirect product factor
26C2×#88059C22112yescomplemented
27C22×Q8×C13—26no—
28C22×Q8×C13—22no—
29C22×Q8×C13—26no—
30C22×Q8×C13—22no—
31C22×Q8×C13—26no—
32C22×Q8×C13C23112yes—
33C23×C4×C13—22no—
34C23×C4×C13C2311yescharacteristic
35C22×C22⋊D13—21no—
36C2×#6127—23no—
37C2×#6127—23no—
38C2×#6127D416yes—
39C2×#6127C2316yes—
40C22×D52D411yescharacteristic
41C22×C4×D13—21no—
42C22×Dic26D411yescharacteristic
43C2×C13×Q16—212no—
44C2×C13×Q16—212no—
45C2×C13×Q16—224no—
46C2×C13×Q16C23116yescomplemented
47C22×C8×C13D411yescharacteristic
48C22×C8×C13D411yescharacteristic
49C22×C8×C13D416yes—
50C22×C8×C13C2316yes—
51C2×#6107—224no—
52#88196—248no—
53#88196C23132yes—
54C2×#6106—224no—
55C2×#6099—23no—
56C2×#6099—26no—
57C2×#6099C2316yes—
58C2×#6099C23112yes—
59C22×#1055—21no—
60C22×#1055—22no—
61#88155—224no—
62#88155C23116yes—
63C2×#6094—212no—
64C2×C8×D13—212no—
65#88076C23132yescomplemented
66#88059C23116yescomplemented
67C22×#473—131nomaximal, Sylow
68C24×C13#4111yescharacteristic
69C23×D13—21no—
70C2×Q8×C13—212no—
71C2×Q8×C13—212no—
72C2×Q8×C13—212no—
73C2×Q8×C13—212no—
74C2×Q8×C13—212no—
75C2×Q8×C13—46no—
76C2×Q8×C13—46no—
77C2×Q8×C13—412no—
78C2×Q8×C13C2418yes—
79C22×C4×C13—212no—
80C22×C4×C13—46no—
81C22×C4×C13—42no—
82C22×C4×C13C2×D411yescharacteristic
83C22×C4×C13C2×D413yes—
84C22×C4×C13C2×D411yescharacteristic
85C22×C4×C13C2×D413yes—
86C22×C4×C13#4113yes—
87C22×C4×C13C2413yes—
88C2×C22⋊D13—26no—
89C2×C22⋊D13—26no—
90C22×Dic13—21no—
91#6127—212no—
92#6127—26no—
93#6127—26no—
94#6127C2×D4112yes—
95#6127C2414yes—
96C2×D52—23no—
97C2×D52C2×D416yes—
98C2×C4×D13—26no—
99C2×C4×D13—26no—
100C2×Dic26—23no—
101C2×Dic26C2×D416yes—
102C13×Q16—216no—
103C13×Q16—216no—
104C2×C8×C13C2×D416yes—
105C2×C8×C13C2×D416yes—
106C2×C8×C13C2×D4112yes—
107C2×C8×C13C2414yes—
108#6107—232no—
109#6106—232no—
110#6099—26no—
111#6099—212no—
112#6099C2414yes—
113#6099C2418yes—
114C2×#1055—26no—
115C2×#1055—212no—
116#6094—216no—
117C8×D13—216no—
118C22×#137—132no—
119C23×Q16D1311yescharacteristic, complemented
120C22×#131—131no—
121C2×#473—1324no—
122C22×#108—131no—
123C22×#101—132no—
124C23×C13—24no—
125C23×C13#12113yes—
126C23×C13#12111yescharacteristic
127C23×C13C2×#4113yes—
128C22×D13—26no—
129C22×D13—44no—
130Q8×C13—28no—
131Q8×C13—28no—
132Q8×C13—412no—
133Q8×C13—412no—
134C2×C4×C13—28no—
135C2×C4×C13—412no—
136C2×C4×C13—412no—
137C2×C4×C13#12113yes—
138C2×C4×C13#12113yes—
139C2×C4×C13#12116yes—
140C2×C4×C13C22×D413yes—
141C2×C4×C13C22×D413yes—
142C2×C4×C13C22×D413yes—
143C2×C4×C13C22×D413yes—
144C2×C4×C13C2×#4113yes—
145C2×C4×C13C2511yescharacteristic
146C22⋊D13—212no—
147C22⋊D13—24no—
148C2×Dic13—26no—
149D52—26no—
150D52C22×D414yes—
151C4×D13—212no—
152C4×D13—24no—
153Dic26—26no—
154Dic26C22×D414yes—
155C8×C13C22×D414yes—
156C8×C13C22×D414yes—
157#1055—24no—
158#1055—28no—
159C22×#41—131no—
160C23×Q8C2×D1312yes—
161C2×#137—1324no—
162C2×#137—2612no—
163C22×Q16—21no—
164C22×Q16—21no—
165C22×Q16—26no—
166C22×Q16—262no—
167C22×Q16C2×D13112yescomplemented
168C22×SD16—262no—
169C2×#131—1312no—
170C2×#131—266no—
171C22×M16—131no—
172C22×M16—132no—
173C22×M16—261no—
174C23×C8—261no—
175C23×C8C2×D1311yescharacteristic
176#473—1364no—
177C2×#108—1312no—
178C2×#101—1324no—
179C22×C13—26no—
180C22×C13—26no—
181C22×C13#47314yescomplemented
182C22×C13C2×#12113yes—
183C22×C13C2×#12113yes—
184C22×C13C22×#4111yescharacteristic
185C2×D13—24no—
186C2×D13—412no—
187C4×C13—48no—
188C4×C13C2×#12113yes—
189C4×C13C2×#12113yes—
190C4×C13C23×D411yescharacteristic
191C4×C13C23×D411yescharacteristic
192Dic13—24no—
193C2×#41—136no—
194C2×#41—136no—
195C2×#41—263no—
196C2×#41—263no—
197C22×Q8—26no—
198C22×Q8—22no—
199C22×Q8—26no—
200C22×Q8—26no—
201C22×Q8—22no—
202C22×Q8—131no—
203C22×Q8C22×D13112yes—
204C22×D4—131no—
205C22×D4—261no—
206C23×C4—22no—
207C23×C4—261no—
208C23×C4C22×D1311yescharacteristic
209#137—1332no—
210#137—2648no—
211C2×Q16—212no—
212C2×Q16—212no—
213C2×Q16—224no—
214C2×Q16—2624no—
215C2×Q16C22×D13116yescomplemented
216C2×SD16—2624no—
217#131—1316no—
218#131—2624no—
219C2×M16—136no—
220C2×M16—1312no—
221C2×M16—266no—
222C2×M16—263no—
223C2×M16—2612no—
224C22×C8—262no—
225C22×C8—261no—
226C22×C8—2612no—
227C22×C8C22⋊D1311yescharacteristic
228C22×C8C22⋊D1311yescharacteristic
229C22×C8C22⋊D1316yes—
230C22×C8C22×D1316yes—
231#108—1316no—
232#101—1332no—
233C2×C13—23no—
234C2×C13—21no—
235C2×C13C2×#47316yescomplemented
236C2×C13C22×#12111yescharacteristic
237D13—44no—
238C24—261no—
239C24#612911yescharacteristic
240#41—1312no—
241#41—134no—
242#41—2612no—
243#41—266no—
244#41—266no—
245C2×Q8—212no—
246C2×Q8—212no—
247C2×Q8—212no—
248C2×Q8—212no—
249C2×Q8—212no—
250C2×Q8—46no—
251C2×Q8—46no—
252C2×Q8—412no—
253C2×Q8—136no—
254C2×Q8—263no—
255C2×Q8C23×D1318yes—
256C2×D4—136no—
257C2×D4—266no—
258C2×D4—266no—
259C2×D4—263no—
260C22×C4—212no—
261C22×C4—46no—
262C22×C4—42no—
263C22×C4—261no—
264C22×C4—266no—
265C22×C4—266no—
266C22×C4D4×D1313yes—
267C22×C4D4×D1311yescharacteristic
268C22×C4#612913yes—
269C22×C4C2×C22⋊D1313yes—
270C22×C4C2×C22⋊D1311yescharacteristic
271C22×C4C23×D1313yes—
272Q16—216no—
273Q16—216no—
274Q16—2632no—
275SD16—2632no—
276M16—134no—
277M16—138no—
278M16—2612no—
279M16—266no—
280M16—2616no—
281C2×C8—2612no—
282C2×C8—266no—
283C2×C8—2616no—
284C2×C8C2×C22⋊D1316yes—
285C2×C8C2×C22⋊D1316yes—
286C2×C8C2×C22⋊D13112yes—
287C2×C8C23×D1314yes—
288C13C22×#47311yescharacteristic, complemented, Sylow
289C23—24no—
290C23—266no—
291C23—524no—
292C23#8819213yes—
293C23#8819211yescharacteristic
294C23C2×#612913yes—
295Q8—28no—
296Q8—28no—
297Q8—412no—
298Q8—412no—
299Q8—134no—
300Q8—266no—
301D4—134no—
302D4—2612no—
303D4—264no—
304D4—266no—
305C2×C4—28no—
306C2×C4—412no—
307C2×C4—412no—
308C2×C4—266no—
309C2×C4—2612no—
310C2×C4—264no—
311C2×C4#8819213yes—
312C2×C4#8819213yes—
313C2×C4#8819216yes—
314C2×C4C2×D4×D1313yes—
315C2×C4C2×D4×D1313yes—
316C2×C4C2×#612913yes—
317C2×C4C22×C22⋊D1313yes—
318C2×C4C22×C22⋊D1313yes—
319C2×C4C24×D1311yescharacteristic
320C8—268no—
321C8—264no—
322C8C22×C22⋊D1314yes—
323C8C22×C22⋊D1314yes—
324C22—26no—
325C22—26no—
326C22—264no—
327C22—5212no—
328C22#1171885314yesdirect product factor
329C22C2×#8819213yes—
330C22C2×#8819213yes—
331C22C22×#612911yescharacteristic
332C4—48no—
333C4—264no—
334C4C2×#8819213yes—
335C4C2×#8819213yes—
336C4C22×D4×D1311yescharacteristic
337C4C23×C22⋊D1311yescharacteristic
338C2—23no—
339C2—21no—
340C2—524no—
341C2C2×#1171885316yesdirect product factor
342C2C22×#8819211yescharacteristic
subgroupG/H
centerC23#88192
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC23×C13×Q16C2
socleC23×C13#121
prime radicalC22×#6127C22
hypercenterC23×Q16D13
hypocenterC13C22×#473
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×Q16

Complements

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

NH ≅ G/Ntype
3. C2×#11718853C2direct (N × H)
4. C22×#88059C2semidirect
5. C22×#88076C2semidirect
6. C23×C13×Q16C2semidirect
12. C22×C13×Q16C22semidirect
24. C2×#88076C22semidirect
25. #11718853C22direct (N × H)
26. C2×#88059C22semidirect
46. C2×C13×Q16C23semidirect
65. #88076C23semidirect
66. #88059C23semidirect
119. C23×Q16D13semidirect
167. C22×Q16C2×D13semidirect
181. C22×C13#473semidirect
215. C2×Q16C22×D13semidirect
235. C2×C13C2×#473semidirect
288. C13C22×#473semidirect
328. C22#11718853direct (N × H)
341. C2C2×#11718853direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881962
C22×#881552
C2×#117188532
C22×#880592
C22×#880762
C23×C13×Q162
C22×#47313