Finite Group Databasebeta

← C2×#26011660 #36362888

Subgroups — C2×#26011660 #36362888

Order 22144.

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×#19149725C211yesmaximal, characteristic, complemented
2C2×#19149707C211yesmaximal, characteristic, complemented
3C2×#19149704C211yesmaximal, characteristic, complemented
4C2×#19149676C211yesmaximal, characteristic, complemented
5#26011660C218yesmaximal, direct product factor
6C2×#19149607C211yesmaximal, characteristic, complemented
7C2×#19149595C211yesmaximal, characteristic, complemented
8C2×#104×C173C211yesmaximal, characteristic, complemented
9#19149725—22no—
10#19149725—22no—
11#19149725—22no—
12#19149725C2214yescomplemented
13C2×#14583827—21no—
14C2×#14583826—21no—
15C2×#14583826C2211yescharacteristic
16C22×D692—21no—
17C22×D692—22no—
18C22×D692C2211yescharacteristic
19C22×D692C2211yescharacteristic, complemented
20C2×D4×D173—21no—
21C2×D4×D173—22no—
22#19149707—22no—
23#19149707C2214yescomplemented
24#19149704—22no—
25#19149704C2214yescomplemented
26C2×#14583815—21no—
27C2×#14583813—21no—
28C2×D1384—21no—
29C2×#14583811—21no—
30C2×#14583810C2211yescharacteristic, complemented
31#19149676—22no—
32#19149676C2214yescomplemented
33#19149607C2214yescomplemented
34#19149595C2214yescomplemented
35C2×#41×C173C2211yescharacteristic
36C2×M16×C173C2211yescharacteristic, complemented
37C2×C42×C173C2211yescharacteristic, complemented
38#104×C173C2214yescomplemented
39C23×D173—22no—
40C23×D173—21no—
41C23×D173D412yes—
42#14583827—24no—
43#14583827—24no—
44#14583826—24no—
45#14583826—24no—
46#14583826—21no—
47#14583826—21no—
48#14583826D412yescomplemented
49#14583826C2312yes—
50C2×Dic346D411yescharacteristic, complemented
51C2×D692—22no—
52C2×D692—24no—
53C2×D692—24no—
54C2×D692—28no—
55C2×D692—21no—
56C2×D692—21no—
57C2×D692—21no—
58C2×D692—21no—
59C2×D692—21no—
60C2×D692—21no—
61C2×D692—21no—
62C2×D692—21no—
63C2×D692—21no—
64C2×D692—48no—
65C2×D692D412yes—
66C2×D692D411yescharacteristic, complemented
67C2×D692C2312yes—
68C2×D692C2312yescomplemented
69C2×C22⋊D173—22no—
70C2×C22⋊D173—21no—
71D4×D173—28no—
72D4×D173—24no—
73D4×D173—28no—
74D4×D173—24no—
75C2×C4×D173—22no—
76C2×C4×D173—21no—
77#14583815—24no—
78#14583813—24no—
79D1384—24no—
80#14583811—24no—
81#14583810—21no—
82#14583810C2312yescomplemented
83C2×#13063436—21no—
84#41×C173—21no—
85#41×C173—21no—
86#41×C173D412yescomplemented
87#41×C173C2312yes—
88C2×Q8×C173D411yescharacteristic, complemented
89C2×D4×C173—21no—
90C2×D4×C173D411yescharacteristic, complemented
91C22×C4×C173—21no—
92C22×C4×C173—21no—
93C22×C4×C173C2311yescharacteristic
94M16×C173—21no—
95M16×C173C2312yescomplemented
96C2×C8×C173—21no—
97C42×C173—21no—
98C42×C173C2312yescomplemented
99C22×D173—22no—
100C22×D173—21no—
101C22×D173—28no—
102C22×D173—22no—
103C22×D173—22no—
104C22×D173—44no—
105C22×D173—44no—
106C22×D173—41no—
107C22×D173—41no—
108C22×D173—84no—
109C22×D173C2×D414yes—
110Dic346—21no—
111Dic346C2×D412yescomplemented
112D692—28no—
113D692—22no—
114D692—22no—
115D692—21no—
116D692—22no—
117D692—22no—
118D692—22no—
119D692—22no—
120D692—416no—
121D692—41no—
122D692—41no—
123D692C2×D412yescomplemented
124C22⋊D173—28no—
125C22⋊D173—22no—
126C22⋊D173—22no—
127C2×Dic173—21no—
128C4×D173—28no—
129C4×D173—22no—
130C4×D173—22no—
131#13063436—22no—
132C23×C173—21no—
133C23×C173C2×D411yescharacteristic
134Q8×C173—21no—
135Q8×C173C2×D412yescomplemented
136D4×C173—22no—
137D4×C173—22no—
138D4×C173—21no—
139D4×C173C2×D412yescomplemented
140C2×C4×C173—24no—
141C2×C4×C173—21no—
142C2×C4×C173—22no—
143C2×C4×C173—22no—
144C2×C4×C173—22no—
145C2×C4×C173C2×D411yescharacteristic
146C2×C4×C173C2×D411yescharacteristic
147C2×C4×C173C2×D411yescharacteristic
148C2×C4×C173C2×D411yescharacteristic
149C2×C4×C173C2×D411yescharacteristic
150C2×C4×C173C2411yescharacteristic
151C8×C173—22no—
152C22×C173—22no—
153C22×C173—22no—
154C22×C173—42no—
155C22×C173#12011yescharacteristic
156C22×C173#12011yescharacteristic
157C22×C173C22×D411yescharacteristic
158C2×D173—24no—
159C2×D173—22no—
160C2×D173—44no—
161C2×D173—42no—
162C2×D173—44no—
163C2×D173—44no—
164C2×D173—42no—
165C2×D173—82no—
166C2×D173—88no—
167C2×D173—82no—
168C2×D173—82no—
169C4×C173—24no—
170C4×C173—22no—
171C4×C173#12011yescharacteristic
172C4×C173#12011yescharacteristic
173C4×C173C22×D411yescharacteristic
174C4×C173C22×D411yescharacteristic
175Dic173—22no—
176C2×C173—21no—
177C2×C173—21no—
178C2×C173—42no—
179C2×C173#45312yescomplemented
180C2×C173C2×#12011yescharacteristic
181D173—44no—
182D173—42no—
183D173—82no—
184C173C2×#45311yescharacteristic, complemented, Sylow
185C2×#453—1731nomaximal, Sylow
186C2×H(5,𝔽2)—1731no—
187C2×AGL(1,ℤ/8)—1731no—
188C2×AGL(1,ℤ/8)—1731no—
189C2×#127—1731no—
190#453—1738no—
191C2×#104—1731no—
192C2×#104D17311yescharacteristic, complemented
193C2×#100—1731no—
194H(5,𝔽2)—3462no—
195H(5,𝔽2)—3462no—
196H(5,𝔽2)—3462no—
197H(5,𝔽2)—1734no—
198C2×#41—3461no—
199C2×#41—3461no—
200C2×#41—1731no—
201C2×#41C2×D17311yescharacteristic
202C22×D4—3461no—
203C22×D4—3462no—
204C22×D4—3462no—
205C22×D4—3461no—
206C22×D4—1731no—
207C22×D4—1731no—
208AGL(1,ℤ/8)—3462no—
209AGL(1,ℤ/8)—3462no—
210AGL(1,ℤ/8)—1734no—
211AGL(1,ℤ/8)—1734no—
212C2×SD16—3461no—
213C2×SD16—3461no—
214C2×D8—3461no—
215C2×D8—3461no—
216C2×M16—1731no—
217C2×M16C2×D17311yescharacteristic, complemented
218#127—3462no—
219#127—1734no—
220C2×C42C2×D17311yescharacteristic, complemented
221#104—1734no—
222#104C2×D17314yescomplemented
223#100—1734no—
224C24—3462no—
225C24—3461no—
226C24—1732no—
227#41—21no—
228#41—21no—
229#41—3464no—
230#41—3464no—
231#41—3464no—
232#41—3464no—
233#41—3461no—
234#41—3461no—
235#41—1732no—
236#41—1732no—
237#41D69212yescomplemented
238#41C22×D17312yes—
239C2×Q8—1731no—
240C2×Q8D69211yescharacteristic, complemented
241C2×D4—21no—
242C2×D4—3462no—
243C2×D4—3464no—
244C2×D4—3464no—
245C2×D4—3468no—
246C2×D4—3468no—
247C2×D4—3464no—
248C2×D4—3468no—
249C2×D4—3462no—
250C2×D4—3461no—
251C2×D4—3464no—
252C2×D4—3461no—
253C2×D4—3461no—
254C2×D4—3461no—
255C2×D4—3461no—
256C2×D4—3461no—
257C2×D4—3461no—
258C2×D4—3461no—
259C2×D4—3461no—
260C2×D4—3461no—
261C2×D4—1732no—
262C2×D4—1731no—
263C2×D4—1732no—
264C2×D4—1732no—
265C2×D4—6928no—
266C2×D4D69211yescharacteristic, complemented
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—3462no—
270C22×C4—3461no—
271C22×C4C22×D17311yescharacteristic
272SD16—3464no—
273SD16—3464no—
274D8—3464no—
275D8—3464no—
276M16—21no—
277M16—3461no—
278M16—1732no—
279M16C22×D17312yescomplemented
280C2×C8—21no—
281C2×C8—3461no—
282C42—21no—
283C42C22×D17312yescomplemented
284C23—21no—
285C23—3468no—
286C23—3462no—
287C23—3462no—
288C23—3461no—
289C23—3462no—
290C23—13844no—
291C23—1734no—
292C23—6924no—
293C23—6924no—
294C23—6921no—
295C23—6921no—
296C23D4×D17311yescharacteristic
297Q8—21no—
298Q8—3461no—
299Q8—1732no—
300Q8C2×D69212yescomplemented
301D4—22no—
302D4—22no—
303D4—21no—
304D4—3468no—
305D4—3468no—
306D4—3462no—
307D4—3462no—
308D4—3462no—
309D4—3461no—
310D4—3462no—
311D4—3462no—
312D4—3462no—
313D4—3462no—
314D4—3462no—
315D4—1732no—
316D4—69216no—
317D4—6921no—
318D4—6921no—
319D4C2×D69212yescomplemented
320C2×C4—24no—
321C2×C4—21no—
322C2×C4—22no—
323C2×C4—22no—
324C2×C4—22no—
325C2×C4—3468no—
326C2×C4—3461no—
327C2×C4—3462no—
328C2×C4—3462no—
329C2×C4D4×D17311yescharacteristic
330C2×C4D4×D17311yescharacteristic
331C2×C4D4×D17311yescharacteristic
332C2×C4C2×D69211yescharacteristic
333C2×C4C2×D69211yescharacteristic
334C2×C4C23×D17311yescharacteristic
335C8—22no—
336C8—3462no—
337C22—22no—
338C22—22no—
339C22—42no—
340C22—3464no—
341C22—3462no—
342C22—13842no—
343C22—13842no—
344C22—13848no—
345C22—13842no—
346C22—6924no—
347C22—6924no—
348C22—6922no—
349C22—6922no—
350C22—6924no—
351C22#1914964911yescharacteristic
352C22#1914964911yescharacteristic
353C22C2×D4×D17311yescharacteristic
354C4—24no—
355C4—22no—
356C4—3462no—
357C4#1914964911yescharacteristic
358C4#1914964911yescharacteristic
359C4C2×D4×D17311yescharacteristic
360C4C22×D69211yescharacteristic
361C2—21no—
362C2—21no—
363C2—42no—
364C2—13842no—
365C2—6922no—
366C2—6924no—
367C2#2601166012yesdirect product factor
368C2C2×#1914964911yescharacteristic
subgroupG/H
centerC22#19149649
commutator, cosocleC2×C4×C173C24
FrattiniC2×C4C23×D173
FittingC2×#104×C173C2
socleC22×C173#120
hypercenterC2×#104D173
hypocenterC173C2×#453
LCSG ▷ C2×C4×C173 ▷ C2×C173 ▷ C173
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
1. C2×#19149725C2semidirect
2. C2×#19149707C2semidirect
3. C2×#19149704C2semidirect
4. C2×#19149676C2semidirect
5. #26011660C2direct (N × H)
6. C2×#19149607C2semidirect
7. C2×#19149595C2semidirect
8. C2×#104×C173C2semidirect
12. #19149725C22semidirect
19. C22×D692C22semidirect
23. #19149707C22semidirect
25. #19149704C22semidirect
30. C2×#14583810C22semidirect
32. #19149676C22semidirect
33. #19149607C22semidirect
34. #19149595C22semidirect
36. C2×M16×C173C22semidirect
37. C2×C42×C173C22semidirect
38. #104×C173C22semidirect
48. #14583826D4semidirect
50. C2×Dic346D4semidirect
66. C2×D692D4semidirect
68. C2×D692C23semidirect
82. #14583810C23semidirect
86. #41×C173D4semidirect
88. C2×Q8×C173D4semidirect
90. C2×D4×C173D4semidirect
95. M16×C173C23semidirect
98. C42×C173C23semidirect
111. Dic346C2×D4semidirect
123. D692C2×D4semidirect
135. Q8×C173C2×D4semidirect
139. D4×C173C2×D4semidirect
179. C2×C173#453semidirect
184. C173C2×#453semidirect
192. C2×#104D173semidirect
217. C2×M16C2×D173semidirect
220. C2×C42C2×D173semidirect
222. #104C2×D173semidirect
237. #41D692semidirect
240. C2×Q8D692semidirect
266. C2×D4D692semidirect
279. M16C22×D173semidirect
283. C42C22×D173semidirect
300. Q8C2×D692semidirect
319. D4C2×D692semidirect
367. C2#26011660direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191497252
C2×#191497072
C2×#191497042
C2×#191496762
#260116602
C2×#191496072
C2×#191495952
C2×#104×C1732
C2×#453173