Finite Group Databasebeta

← C2×#26041448 #37543046

Subgroups — C2×#26041448 #37543046

Order 23168.

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

normal subgroups only

This group has 844 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×#19153862C211yesmaximal, characteristic, complemented
2C2×#19153844C211yesmaximal, characteristic, complemented
3C2×#19153841C211yesmaximal, characteristic, complemented
4C2×#19153813C211yesmaximal, characteristic, complemented
5#26041448C218yesmaximal, direct product factor
6C2×#19153744C211yesmaximal, characteristic, complemented
7C2×#19153732C211yesmaximal, characteristic, complemented
8C2×#104×C181C211yesmaximal, characteristic, complemented
9#19153862—22no—
10#19153862—22no—
11#19153862—22no—
12#19153862C2214yescomplemented
13C2×#15668450—21no—
14C2×#15668449—21no—
15C2×#15668449C2211yescharacteristic
16C22×D724—21no—
17C22×D724—22no—
18C22×D724C2211yescharacteristic
19C22×D724C2211yescharacteristic, complemented
20C2×D4×D181—22no—
21C2×D4×D181—21no—
22#19153844—22no—
23#19153844C2214yescomplemented
24#19153841—22no—
25#19153841C2214yescomplemented
26C2×#15668438—21no—
27C2×#15668436—21no—
28C2×D1448—21no—
29C2×#15668434—21no—
30C2×#15668433C2211yescharacteristic, complemented
31#19153813—22no—
32#19153813C2214yescomplemented
33#19153744C2214yescomplemented
34#19153732C2214yescomplemented
35C2×#41×C181C2211yescharacteristic
36C2×M16×C181C2211yescharacteristic, complemented
37C2×C42×C181C2211yescharacteristic, complemented
38#104×C181C2214yescomplemented
39C23×D181—22no—
40C23×D181—21no—
41C23×D181D412yes—
42#15668450—24no—
43#15668450—24no—
44#15668449—24no—
45#15668449—24no—
46#15668449—21no—
47#15668449—21no—
48#15668449D412yescomplemented
49#15668449C2312yes—
50C2×Dic362D411yescharacteristic, complemented
51C2×D724—22no—
52C2×D724—24no—
53C2×D724—24no—
54C2×D724—28no—
55C2×D724—21no—
56C2×D724—21no—
57C2×D724—21no—
58C2×D724—21no—
59C2×D724—21no—
60C2×D724—21no—
61C2×D724—21no—
62C2×D724—21no—
63C2×D724—21no—
64C2×D724—48no—
65C2×D724D412yes—
66C2×D724D411yescharacteristic, complemented
67C2×D724C2312yes—
68C2×D724C2312yescomplemented
69C2×C22⋊D181—22no—
70C2×C22⋊D181—21no—
71D4×D181—28no—
72D4×D181—24no—
73D4×D181—28no—
74D4×D181—24no—
75C2×C4×D181—22no—
76C2×C4×D181—21no—
77#15668438—24no—
78#15668436—24no—
79D1448—24no—
80#15668434—24no—
81#15668433—21no—
82#15668433C2312yescomplemented
83C2×#13089678—21no—
84#41×C181—21no—
85#41×C181—21no—
86#41×C181D412yescomplemented
87#41×C181C2312yes—
88C2×Q8×C181D411yescharacteristic, complemented
89C2×D4×C181—21no—
90C2×D4×C181D411yescharacteristic, complemented
91C22×C4×C181—21no—
92C22×C4×C181—21no—
93C22×C4×C181C2311yescharacteristic
94M16×C181—21no—
95M16×C181C2312yescomplemented
96C2×C8×C181—21no—
97C42×C181—21no—
98C42×C181C2312yescomplemented
99C22×D181—22no—
100C22×D181—21no—
101C22×D181—28no—
102C22×D181—22no—
103C22×D181—22no—
104C22×D181—44no—
105C22×D181—44no—
106C22×D181—41no—
107C22×D181—41no—
108C22×D181—84no—
109C22×D181C2×D414yes—
110Dic362—21no—
111Dic362C2×D412yescomplemented
112D724—28no—
113D724—22no—
114D724—22no—
115D724—21no—
116D724—22no—
117D724—22no—
118D724—22no—
119D724—22no—
120D724—416no—
121D724—41no—
122D724—41no—
123D724C2×D412yescomplemented
124C22⋊D181—28no—
125C22⋊D181—22no—
126C22⋊D181—22no—
127C2×Dic181—21no—
128C4×D181—28no—
129C4×D181—22no—
130C4×D181—22no—
131#13089678—22no—
132C23×C181—21no—
133C23×C181C2×D411yescharacteristic
134Q8×C181—21no—
135Q8×C181C2×D412yescomplemented
136D4×C181—22no—
137D4×C181—22no—
138D4×C181—21no—
139D4×C181C2×D412yescomplemented
140C2×C4×C181—24no—
141C2×C4×C181—21no—
142C2×C4×C181—22no—
143C2×C4×C181—22no—
144C2×C4×C181—22no—
145C2×C4×C181C2×D411yescharacteristic
146C2×C4×C181C2×D411yescharacteristic
147C2×C4×C181C2×D411yescharacteristic
148C2×C4×C181C2×D411yescharacteristic
149C2×C4×C181C2×D411yescharacteristic
150C2×C4×C181C2411yescharacteristic
151C8×C181—22no—
152C22×C181—22no—
153C22×C181—22no—
154C22×C181—42no—
155C22×C181#12011yescharacteristic
156C22×C181#12011yescharacteristic
157C22×C181C22×D411yescharacteristic
158C2×D181—24no—
159C2×D181—22no—
160C2×D181—44no—
161C2×D181—42no—
162C2×D181—44no—
163C2×D181—44no—
164C2×D181—42no—
165C2×D181—82no—
166C2×D181—88no—
167C2×D181—82no—
168C2×D181—82no—
169C4×C181—24no—
170C4×C181—22no—
171C4×C181#12011yescharacteristic
172C4×C181#12011yescharacteristic
173C4×C181C22×D411yescharacteristic
174C4×C181C22×D411yescharacteristic
175Dic181—22no—
176C2×C181—21no—
177C2×C181—21no—
178C2×C181—42no—
179C2×C181#45312yescomplemented
180C2×C181C2×#12011yescharacteristic
181D181—44no—
182D181—42no—
183D181—82no—
184C181C2×#45311yescharacteristic, complemented, Sylow
185C2×#453—1811nomaximal, Sylow
186C2×H(5,𝔽2)—1811no—
187C2×AGL(1,ℤ/8)—1811no—
188C2×AGL(1,ℤ/8)—1811no—
189C2×#127—1811no—
190#453—1818no—
191C2×#104—1811no—
192C2×#104D18111yescharacteristic, complemented
193C2×#100—1811no—
194H(5,𝔽2)—3622no—
195H(5,𝔽2)—3622no—
196H(5,𝔽2)—3622no—
197H(5,𝔽2)—1814no—
198C2×#41—3621no—
199C2×#41—3621no—
200C2×#41—1811no—
201C2×#41C2×D18111yescharacteristic
202C22×D4—3621no—
203C22×D4—3622no—
204C22×D4—3622no—
205C22×D4—3621no—
206C22×D4—1811no—
207C22×D4—1811no—
208AGL(1,ℤ/8)—3622no—
209AGL(1,ℤ/8)—3622no—
210AGL(1,ℤ/8)—1814no—
211AGL(1,ℤ/8)—1814no—
212C2×SD16—3621no—
213C2×SD16—3621no—
214C2×D8—3621no—
215C2×D8—3621no—
216C2×M16—1811no—
217C2×M16C2×D18111yescharacteristic, complemented
218#127—3622no—
219#127—1814no—
220C2×C42C2×D18111yescharacteristic, complemented
221#104—1814no—
222#104C2×D18114yescomplemented
223#100—1814no—
224C24—3622no—
225C24—3621no—
226C24—1812no—
227#41—21no—
228#41—21no—
229#41—3624no—
230#41—3624no—
231#41—3624no—
232#41—3624no—
233#41—3621no—
234#41—3621no—
235#41—1812no—
236#41—1812no—
237#41D72412yescomplemented
238#41C22×D18112yes—
239C2×Q8—1811no—
240C2×Q8D72411yescharacteristic, complemented
241C2×D4—21no—
242C2×D4—3622no—
243C2×D4—3624no—
244C2×D4—3624no—
245C2×D4—3628no—
246C2×D4—3628no—
247C2×D4—3624no—
248C2×D4—3628no—
249C2×D4—3622no—
250C2×D4—3621no—
251C2×D4—3624no—
252C2×D4—3621no—
253C2×D4—3621no—
254C2×D4—3621no—
255C2×D4—3621no—
256C2×D4—3621no—
257C2×D4—3621no—
258C2×D4—3621no—
259C2×D4—3621no—
260C2×D4—3621no—
261C2×D4—1812no—
262C2×D4—1811no—
263C2×D4—1812no—
264C2×D4—1812no—
265C2×D4—7248no—
266C2×D4D72411yescharacteristic, complemented
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—3622no—
270C22×C4—3621no—
271C22×C4C22×D18111yescharacteristic
272SD16—3624no—
273SD16—3624no—
274D8—3624no—
275D8—3624no—
276M16—21no—
277M16—3621no—
278M16—1812no—
279M16C22×D18112yescomplemented
280C2×C8—21no—
281C2×C8—3621no—
282C42—21no—
283C42C22×D18112yescomplemented
284C23—21no—
285C23—3628no—
286C23—3622no—
287C23—3622no—
288C23—3621no—
289C23—3622no—
290C23—14484no—
291C23—1814no—
292C23—7244no—
293C23—7244no—
294C23—7241no—
295C23—7241no—
296C23D4×D18111yescharacteristic
297Q8—21no—
298Q8—3621no—
299Q8—1812no—
300Q8C2×D72412yescomplemented
301D4—22no—
302D4—22no—
303D4—21no—
304D4—3628no—
305D4—3628no—
306D4—3622no—
307D4—3622no—
308D4—3622no—
309D4—3621no—
310D4—3622no—
311D4—3622no—
312D4—3622no—
313D4—3622no—
314D4—3622no—
315D4—1812no—
316D4—72416no—
317D4—7241no—
318D4—7241no—
319D4C2×D72412yescomplemented
320C2×C4—24no—
321C2×C4—21no—
322C2×C4—22no—
323C2×C4—22no—
324C2×C4—22no—
325C2×C4—3628no—
326C2×C4—3621no—
327C2×C4—3622no—
328C2×C4—3622no—
329C2×C4D4×D18111yescharacteristic
330C2×C4D4×D18111yescharacteristic
331C2×C4D4×D18111yescharacteristic
332C2×C4C2×D72411yescharacteristic
333C2×C4C2×D72411yescharacteristic
334C2×C4C23×D18111yescharacteristic
335C8—22no—
336C8—3622no—
337C22—22no—
338C22—22no—
339C22—42no—
340C22—3624no—
341C22—3622no—
342C22—14482no—
343C22—14482no—
344C22—14488no—
345C22—14482no—
346C22—7244no—
347C22—7244no—
348C22—7242no—
349C22—7242no—
350C22—7244no—
351C22#1915378611yescharacteristic
352C22#1915378611yescharacteristic
353C22C2×D4×D18111yescharacteristic
354C4—24no—
355C4—22no—
356C4—3622no—
357C4#1915378611yescharacteristic
358C4#1915378611yescharacteristic
359C4C2×D4×D18111yescharacteristic
360C4C22×D72411yescharacteristic
361C2—21no—
362C2—21no—
363C2—42no—
364C2—14482no—
365C2—7242no—
366C2—7244no—
367C2#2604144812yesdirect product factor
368C2C2×#1915378611yescharacteristic
subgroupG/H
centerC22#19153786
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
FittingC2×#104×C181C2
socleC22×C181#120
hypercenterC2×#104D181
hypocenterC181C2×#453
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
1. C2×#19153862C2semidirect
2. C2×#19153844C2semidirect
3. C2×#19153841C2semidirect
4. C2×#19153813C2semidirect
5. #26041448C2direct (N × H)
6. C2×#19153744C2semidirect
7. C2×#19153732C2semidirect
8. C2×#104×C181C2semidirect
12. #19153862C22semidirect
19. C22×D724C22semidirect
23. #19153844C22semidirect
25. #19153841C22semidirect
30. C2×#15668433C22semidirect
32. #19153813C22semidirect
33. #19153744C22semidirect
34. #19153732C22semidirect
36. C2×M16×C181C22semidirect
37. C2×C42×C181C22semidirect
38. #104×C181C22semidirect
48. #15668449D4semidirect
50. C2×Dic362D4semidirect
66. C2×D724D4semidirect
68. C2×D724C23semidirect
82. #15668433C23semidirect
86. #41×C181D4semidirect
88. C2×Q8×C181D4semidirect
90. C2×D4×C181D4semidirect
95. M16×C181C23semidirect
98. C42×C181C23semidirect
111. Dic362C2×D4semidirect
123. D724C2×D4semidirect
135. Q8×C181C2×D4semidirect
139. D4×C181C2×D4semidirect
179. C2×C181#453semidirect
184. C181C2×#453semidirect
192. C2×#104D181semidirect
217. C2×M16C2×D181semidirect
220. C2×C42C2×D181semidirect
222. #104C2×D181semidirect
237. #41D724semidirect
240. C2×Q8D724semidirect
266. C2×D4D724semidirect
279. M16C22×D181semidirect
283. C42C22×D181semidirect
300. Q8C2×D724semidirect
319. D4C2×D724semidirect
367. C2#26041448direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191538622
C2×#191538442
C2×#191538412
C2×#191538132
#260414482
C2×#191537442
C2×#191537322
C2×#104×C1812
C2×#453181