Finite Group Databasebeta

← C2×#26041463 #37543064

Subgroups — C2×#26041463 #37543064

Order 23168.

708 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 708 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19153863C211yesmaximal, characteristic
2C2×#19153849C211yesmaximal, characteristic, complemented
3C2×#19153846C211yesmaximal, characteristic, complemented
4C2×#19153816C211yesmaximal, characteristic, complemented
5#26041463C218yesmaximal, direct product factor
6C2×#19153744C211yesmaximal, characteristic, complemented
7C2×#19153734C211yesmaximal, characteristic, complemented
8C2×#104×C181C211yesmaximal, characteristic, complemented
9#19153863—22no—
10#19153863—22no—
11#19153863—22no—
12#19153863C2214yes—
13C2×#15668449—21no—
14C2×#15668449C2211yescharacteristic
15C2×#15668448—22no—
16C2×#15668448—21no—
17C22×Dic362—21no—
18C22×Dic362C2211yescharacteristic
19C22×Dic362C2211yescharacteristic
20C2×Q8×D181—21no—
21#19153849—22no—
22#19153849C2214yescomplemented
23#19153846—22no—
24#19153846C2214yescomplemented
25C2×Dic724—21no—
26C2×#15668439—21no—
27C2×#15668438—21no—
28C2×#15668437—21no—
29C2×#15668433C2211yescharacteristic
30#19153816—22no—
31#19153816C2214yescomplemented
32C2×C4⋊Dic181—22no—
33#19153744C2214yescomplemented
34#19153734C2214yescomplemented
35C2×#41×C181C2211yescharacteristic
36C2×M16×C181C2211yescharacteristic
37C2×C42×C181C2211yescharacteristic
38#104×C181C2214yescomplemented
39#15668449—24no—
40#15668449—24no—
41#15668449—21no—
42#15668449—21no—
43#15668449D412yes—
44#15668449C2312yes—
45#15668448—28no—
46#15668448—24no—
47#15668448—28no—
48#15668448—24no—
49C2×Dic362—22no—
50C2×Dic362—24no—
51C2×Dic362—24no—
52C2×Dic362—21no—
53C2×Dic362—21no—
54C2×Dic362—21no—
55C2×Dic362—21no—
56C2×Dic362—21no—
57C2×Dic362—21no—
58C2×Dic362—21no—
59C2×Dic362—21no—
60C2×Dic362—21no—
61C2×Dic362D411yescharacteristic
62C2×Dic362D412yes—
63C2×Dic362C2312yes—
64C2×Dic362C2312yes—
65Q8×D181—24no—
66Q8×D181—24no—
67C2×D724D411yescharacteristic
68C2×C22⋊D181—22no—
69C2×C22⋊D181—21no—
70C22×Dic181—22no—
71C22×Dic181—21no—
72C22×Dic181D412yes—
73C2×C4×D181—22no—
74C2×C4×D181—21no—
75Dic724—24no—
76#15668439—24no—
77#15668438—24no—
78#15668437—24no—
79#15668433—21no—
80#15668433C2312yes—
81C2×#13089678—21no—
82C4⋊Dic181—28no—
83#41×C181—21no—
84#41×C181—21no—
85#41×C181D412yes—
86#41×C181C2312yes—
87C2×Q8×C181D411yescharacteristic
88C2×D4×C181—21no—
89C2×D4×C181D411yescharacteristic
90C22×C4×C181—21no—
91C22×C4×C181—21no—
92C22×C4×C181C2311yescharacteristic
93M16×C181—21no—
94M16×C181C2312yes—
95C2×C8×C181—21no—
96C42×C181—21no—
97C42×C181C2312yes—
98C22×D181—21no—
99Dic362—28no—
100Dic362—22no—
101Dic362—21no—
102Dic362—22no—
103Dic362—22no—
104Dic362—22no—
105Dic362—22no—
106Dic362—22no—
107Dic362—41no—
108Dic362—41no—
109Dic362C2×D412yes—
110D724—21no—
111D724C2×D412yes—
112C22⋊D181—28no—
113C22⋊D181—22no—
114C22⋊D181—22no—
115C2×Dic181—28no—
116C2×Dic181—21no—
117C2×Dic181—22no—
118C2×Dic181—22no—
119C2×Dic181—22no—
120C2×Dic181—41no—
121C2×Dic181—41no—
122C2×Dic181C2×D414yes—
123C4×D181—28no—
124C4×D181—22no—
125C4×D181—22no—
126#13089678—22no—
127C23×C181—21no—
128C23×C181C2×D411yescharacteristic
129Q8×C181—21no—
130Q8×C181C2×D412yes—
131D4×C181—22no—
132D4×C181—22no—
133D4×C181—21no—
134D4×C181C2×D412yes—
135C2×C4×C181—24no—
136C2×C4×C181—21no—
137C2×C4×C181—22no—
138C2×C4×C181—22no—
139C2×C4×C181—22no—
140C2×C4×C181C2×D411yescharacteristic
141C2×C4×C181C2×D411yescharacteristic
142C2×C4×C181C2×D411yescharacteristic
143C2×C4×C181C2×D411yescharacteristic
144C2×C4×C181C2×D411yescharacteristic
145C2×C4×C181C2411yescharacteristic
146C8×C181—22no—
147C22×C181—22no—
148C22×C181—22no—
149C22×C181—42no—
150C22×C181#12011yescharacteristic
151C22×C181#12011yescharacteristic
152C22×C181C22×D411yescharacteristic
153C2×D181—22no—
154C2×D181—42no—
155C4×C181—24no—
156C4×C181—22no—
157C4×C181#12011yescharacteristic
158C4×C181#12011yescharacteristic
159C4×C181C22×D411yescharacteristic
160C4×C181C22×D411yescharacteristic
161Dic181—22no—
162Dic181—24no—
163Dic181—42no—
164C2×C181—21no—
165C2×C181—21no—
166C2×C181—42no—
167C2×C181#45612yescomplemented
168C2×C181C2×#12011yescharacteristic
169D181—42no—
170C181C2×#45611yescharacteristic, complemented, Sylow
171C2×#456—1811nomaximal, Sylow
172C2×2−1+4—1811no—
173C2×#137—1811no—
174C2×#137—1811no—
175C2×C4⋊Q8—1811no—
176#456—1818no—
177C2×#104—1811no—
178C2×#104D18111yescharacteristic, complemented
179C2×#101—1811no—
1802−1+4—3622no—
1812−1+4—3622no—
1822−1+4—3622no—
1832−1+4—1814no—
184C2×#41—3621no—
185C2×#41—3621no—
186C2×#41—3622no—
187C2×#41—1811no—
188C2×#41C2×D18111yescharacteristic
189C22×Q8—3621no—
190C22×Q8—3621no—
191C22×Q8—1811no—
192C22×Q8—1811no—
193#137—3622no—
194#137—3622no—
195#137—1814no—
196#137—1814no—
197C2×Q16—3621no—
198C2×Q16—3621no—
199C2×SD16—3621no—
200C2×SD16—3621no—
201C2×M16—1811no—
202C2×M16C2×D18111yescharacteristic
203C4⋊Q8—3622no—
204C4⋊Q8—1814no—
205C2×C4⋊C4—3622no—
206C2×C42C2×D18111yescharacteristic
207#104—1814no—
208#104C2×D18114yescomplemented
209#101—1814no—
210#41—21no—
211#41—21no—
212#41—3624no—
213#41—3624no—
214#41—3628no—
215#41—3624no—
216#41—3624no—
217#41—3628no—
218#41—3621no—
219#41—3621no—
220#41—1812no—
221#41—1812no—
222#41D72412yes—
223#41C22×D18112yes—
224C2×Q8—3622no—
225C2×Q8—3624no—
226C2×Q8—3624no—
227C2×Q8—3624no—
228C2×Q8—3624no—
229C2×Q8—3621no—
230C2×Q8—3621no—
231C2×Q8—3621no—
232C2×Q8—3621no—
233C2×Q8—3621no—
234C2×Q8—3621no—
235C2×Q8—3621no—
236C2×Q8—3621no—
237C2×Q8—3621no—
238C2×Q8—1811no—
239C2×Q8—1812no—
240C2×Q8—1812no—
241C2×Q8—1812no—
242C2×Q8D72411yescharacteristic
243C2×D4—21no—
244C2×D4—3622no—
245C2×D4—3621no—
246C2×D4—1811no—
247C2×D4D72411yescharacteristic
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—3622no—
251C22×C4—3622no—
252C22×C4—3621no—
253C22×C4—3621no—
254C22×C4—1812no—
255C22×C4C22×D18111yescharacteristic
256Q16—3624no—
257Q16—3624no—
258SD16—3624no—
259SD16—3624no—
260M16—21no—
261M16—3621no—
262M16—1812no—
263M16C22×D18112yes—
264C2×C8—21no—
265C2×C8—3621no—
266C4⋊C4—3628no—
267C42—21no—
268C42C22×D18112yes—
269C23—21no—
270C23—3621no—
271C23D4×D18111yescharacteristic
272Q8—21no—
273Q8—3628no—
274Q8—3621no—
275Q8—3622no—
276Q8—3622no—
277Q8—3622no—
278Q8—3622no—
279Q8—3622no—
280Q8—3622no—
281Q8—1812no—
282Q8—7241no—
283Q8—7241no—
284Q8C2×D72412yes—
285D4—22no—
286D4—22no—
287D4—21no—
288D4—3628no—
289D4—3622no—
290D4—3622no—
291D4—3621no—
292D4—1812no—
293D4C2×D72412yes—
294C2×C4—24no—
295C2×C4—21no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—3628no—
300C2×C4—3628no—
301C2×C4—3622no—
302C2×C4—3621no—
303C2×C4—3622no—
304C2×C4—3622no—
305C2×C4—3622no—
306C2×C4—3622no—
307C2×C4—1814no—
308C2×C4—7241no—
309C2×C4—7241no—
310C2×C4D4×D18111yescharacteristic
311C2×C4D4×D18111yescharacteristic
312C2×C4D4×D18111yescharacteristic
313C2×C4C2×D72411yescharacteristic
314C2×C4C2×D72411yescharacteristic
315C2×C4C23×D18111yescharacteristic
316C8—22no—
317C8—3622no—
318C22—22no—
319C22—22no—
320C22—42no—
321C22—3622no—
322C22—7242no—
323C22#1915378611yescharacteristic
324C22#1915378611yescharacteristic
325C22C2×D4×D18111yescharacteristic
326C4—24no—
327C4—22no—
328C4—3622no—
329C4—3624no—
330C4—7242no—
331C4#1915378611yescharacteristic
332C4#1915378611yescharacteristic
333C4C2×D4×D18111yescharacteristic
334C4C22×D72411yescharacteristic
335C2—21no—
336C2—21no—
337C2—42no—
338C2—7242no—
339C2#2604146312yesdirect product factor
340C2C2×#1915378611yescharacteristic
subgroupG/H
centerC22#19153786
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
FittingC2×#104×C181C2
socleC22×C181#120
prime radicalC2×#19153863C2
hypercenterC2×#104D181
hypocenterC181C2×#456
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
2. C2×#19153849C2semidirect
3. C2×#19153846C2semidirect
4. C2×#19153816C2semidirect
5. #26041463C2direct (N × H)
6. C2×#19153744C2semidirect
7. C2×#19153734C2semidirect
8. C2×#104×C181C2semidirect
22. #19153849C22semidirect
24. #19153846C22semidirect
31. #19153816C22semidirect
33. #19153744C22semidirect
34. #19153734C22semidirect
38. #104×C181C22semidirect
167. C2×C181#456semidirect
170. C181C2×#456semidirect
178. C2×#104D181semidirect
208. #104C2×D181semidirect
339. C2#26041463direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191538632
C2×#191538492
C2×#191538462
C2×#191538162
#260414632
C2×#191537442
C2×#191537342
C2×#104×C1812
C2×#456181