Finite Group Databasebeta

← C4×#19149711 #36362383

Subgroups — C4×#19149711 #36362383

Order 22144.

484 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19149711C211yesmaximal, characteristic
2C4×#14583827C211yesmaximal, characteristic
3C4×Q8×D173C211yesmaximal, characteristic, complemented
4#26011598C211yesmaximal, characteristic, complemented
5#26011595C211yesmaximal, characteristic, complemented
6#26011594C211yesmaximal, characteristic, complemented
7#26011590C211yesmaximal, characteristic, complemented
8C4×#14583816C211yesmaximal, characteristic, complemented
9C4×#14583815C211yesmaximal, characteristic, complemented
10C4×#14583813C211yesmaximal, characteristic, complemented
11#26011532C211yesmaximal, characteristic, complemented
12#26011498C211yesmaximal, characteristic, complemented
13#26011491C211yesmaximal, characteristic
14C4×#14583809C211yesmaximal, characteristic, complemented
15C4×Q16×C173C211yesmaximal, characteristic, complemented
16C2×#14583827C2211yescharacteristic
17C2×Q8×D173C2211yescharacteristic
18#19149711C418yesdirect product factor
19C2×#14583816C2211yescharacteristic
20C2×#14583815C2211yescharacteristic
21C2×#14583813C2211yescharacteristic
22C2×#14583809C2211yescharacteristic
23C2×#14583809C2211yescharacteristic
24Q8×Dic173C2211yescharacteristic
25Q8×Dic173C2211yescharacteristic
26C4×Dic346—21no—
27C4×Dic346C2211yescharacteristic
28#19149644—21no—
29#19149644C2211yescharacteristic
30C4×D692—21no—
31C4×D692C2211yescharacteristic
32#19149641—21no—
33#19149641C2211yescharacteristic
34#19149637—21no—
35#19149637C2211yescharacteristic
36C4⋊C4×D173—21no—
37C4⋊C4×D173C2211yescharacteristic
38C42×D173—21no—
39C42×D173—21no—
40C42×D173C2211yescharacteristic
41#19149612C2211yescharacteristic
42#19149611C2211yescharacteristic
43#19149610C2211yescharacteristic
44#19149604C2211yescharacteristic
45#19149603C2211yescharacteristic
46#19149603C2211yescharacteristic
47#19149602C2211yescharacteristic
48#19149601C2211yescharacteristic
49#19149599C2211yescharacteristic
50#19149589C2211yescharacteristic
51#19149589C2211yescharacteristic
52C4×#13063436C2211yescharacteristic
53C2×Q16×C173C2211yescharacteristic
54C4×Q8×C173C2211yescharacteristic
55C4×Q8×C173C2211yescharacteristic
56#107×C173C2211yescharacteristic
57#103×C173C2211yescharacteristic
58#103×C173C2211yescharacteristic
59C4×C8×C173C2211yescharacteristic
60#14583827—22no—
61#14583827C2×C414yes—
62C2×Dic346—21no—
63C2×Dic346C2311yescharacteristic
64Q8×D173—22no—
65Q8×D173C2×C414yescomplemented
66C2×D692—21no—
67C2×D692C2311yescharacteristic
68C2×C4×D173—21no—
69C2×C4×D173—21no—
70C2×C4×D173—21no—
71C2×C4×D173—21no—
72C2×C4×D173—21no—
73C2×C4×D173D411yescharacteristic
74C2×C4×D173D411yescharacteristic
75C2×C4×D173C2311yescharacteristic
76#14583816C2×C414yescomplemented
77#14583815C2×C414yescomplemented
78#14583813C2×C414yescomplemented
79#14583809—22no—
80#14583809C2×C414yescomplemented
81C2×#13063436C2311yescharacteristic
82C2×#13063436C2311yescharacteristic
83C4⋊Dic173—21no—
84C4⋊Dic173—21no—
85C4⋊Dic173C2311yescharacteristic
86C4⋊Dic173C2311yescharacteristic
87#14583805—21no—
88#14583805—21no—
89#14583805—21no—
90#14583803—21no—
91#14583803—21no—
92#14583803—21no—
93C4×Dic173—21no—
94C4×Dic173—21no—
95C4×Dic173—21no—
96C4×Dic173—21no—
97C4×Dic173—21no—
98C4×Dic173D411yescharacteristic
99C4×Dic173D411yescharacteristic
100C4×Dic173C2311yescharacteristic
101C2×Q8×C173C2311yescharacteristic
102C2×Q8×C173C2311yescharacteristic
103Q16×C173C2×C414yescomplemented
104C2×C8×C173C2311yescharacteristic
105C2×C8×C173C2311yescharacteristic
106C4⋊C4×C173—21no—
107C4⋊C4×C173—21no—
108C4⋊C4×C173C2311yescharacteristic
109C4⋊C4×C173C2311yescharacteristic
110C42×C173—21no—
111C42×C173—21no—
112C42×C173C2311yescharacteristic
113C22×D173—21no—
114C22×D173C2×D411yescharacteristic
115Dic346—21no—
116Dic346—24no—
117Dic346C22×C412yes—
118D692—24no—
119D692—21no—
120D692C22×C412yes—
121C2×Dic173—21no—
122C2×Dic173—21no—
123C2×Dic173—21no—
124C2×Dic173C2×D411yescharacteristic
125C2×Dic173C2×D411yescharacteristic
126C2×Dic173C2×D411yescharacteristic
127C4×D173—24no—
128C4×D173—22no—
129C4×D173—24no—
130C4×D173—41no—
131C4×D173—42no—
132C4×D173—42no—
133C4×D173—42no—
134C4×D173C22×C412yes—
135C4×D173#4112yes—
136#13063436—21no—
137#13063436C22×C412yes—
138Q8×C173—21no—
139Q8×C173—21no—
140Q8×C173C22×C412yes—
141Q8×C173C22×C412yes—
142C2×C4×C173—21no—
143C2×C4×C173—21no—
144C2×C4×C173—21no—
145C2×C4×C173—21no—
146C2×C4×C173C2×D411yescharacteristic
147C2×C4×C173C2×D411yescharacteristic
148C2×C4×C173C2411yescharacteristic
149C8×C173—21no—
150C8×C173C22×C412yes—
151C22×C173C22×D411yescharacteristic
152C2×D173—21no—
153C2×D173—21no—
154C2×D173—22no—
155C2×D173—41no—
156C2×D173—41no—
157C2×D173C4×D412yes—
158C4×C173—22no—
159C4×C173—22no—
160C4×C173—21no—
161C4×C173—41no—
162C4×C173—41no—
163C4×C173#13712yescomplemented
164C4×C173C23×C411yescharacteristic
165C4×C173C2×#4111yescharacteristic
166Dic173—22no—
167Dic173—21no—
168Dic173—21no—
169Dic173—41no—
170Dic173—41no—
171Dic173C4×D412yes—
172C2×C173C2×C4×D411yescharacteristic
173C2×C173C2×#13711yescharacteristic
174C2×C173#57511yescharacteristic
175D173—22no—
176D173—42no—
177C173C4×#13711yescharacteristic, complemented, Sylow
178C4×#137—1731nomaximal, Sylow
179C2×#137—1731no—
180C4×#41—1731no—
181C2×C4×Q8—1731no—
182#441—1731no—
183#441—1731no—
184#440—1731no—
185#440—1731no—
186C4×Q16—1731no—
187C4×Q16D17311yescharacteristic, complemented
188C4×SD16—1731no—
189C4×SD16—1731no—
190#428—1731no—
191#419—1731no—
192#417—1731no—
193C4×M16—1731no—
194C2×#41—1731no—
195C22×Q8—1731no—
196#137—1738no—
197C2×Q16—1731no—
198C2×Q16C2×D17311yescharacteristic
199C2×SD16—1731no—
200C2×SD16—1731no—
201C2×M16—1731no—
202C2×M16—1731no—
203C4×Q8—3461no—
204C4×Q8—3461no—
205C4×Q8—1731no—
206C4×Q8—1731no—
207C4×Q8—1731no—
208C4×Q8—1731no—
209C4×Q8C2×D17311yescharacteristic
210C4×Q8C2×D17311yescharacteristic
211C4×D4—3461no—
212C4×D4—3461no—
213C4×D4—1731no—
214C4×D4—1731no—
215#117—3461no—
216#117—1731no—
217C2×C4⋊C4—3461no—
218C2×C4⋊C4—1731no—
219C2×C42—3461no—
220C2×C42—3461no—
221C2×C42—1731no—
222#107—1731no—
223#107C2×D17311yescharacteristic
224#106—1731no—
225#106—1731no—
226#103—1731no—
227#103—1731no—
228#103—1731no—
229#103—1731no—
230#103C2×D17311yescharacteristic
231#103C2×D17311yescharacteristic
232#102—1731no—
233#102—1731no—
234#97—1731no—
235#97—1731no—
236C4×C8—1731no—
237C4×C8C2×D17311yescharacteristic
238#41—3462no—
239#41—1734no—
240C2×Q8—3461no—
241C2×Q8—3462no—
242C2×Q8—1734no—
243C2×Q8—1731no—
244C2×Q8C22×D17311yescharacteristic
245C2×Q8C22×D17311yescharacteristic
246C2×D4—3461no—
247C2×D4—1731no—
248C22×C4—3461no—
249C22×C4—3461no—
250C22×C4—3461no—
251C22×C4—3461no—
252C22×C4—3461no—
253C22×C4—1731no—
254C22×C4—1731no—
255C22×C4—1731no—
256Q16—1734no—
257Q16C4×D17314yescomplemented
258SD16—1734no—
259SD16—1734no—
260M16—3462no—
261M16—1734no—
262C2×C8—1731no—
263C2×C8—1731no—
264C2×C8C22×D17311yescharacteristic
265C2×C8C22×D17311yescharacteristic
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—3461no—
269C4⋊C4—3461no—
270C4⋊C4—3461no—
271C4⋊C4—3461no—
272C4⋊C4—3461no—
273C4⋊C4—1731no—
274C4⋊C4—1731no—
275C4⋊C4C22×D17311yescharacteristic
276C4⋊C4C22×D17311yescharacteristic
277C22⋊C4—3461no—
278C22⋊C4—3461no—
279C22⋊C4—3461no—
280C42—21no—
281C42—21no—
282C42—3461no—
283C42—3461no—
284C42—3461no—
285C42—3461no—
286C42—3461no—
287C42—1731no—
288C42—1731no—
289C42—1731no—
290C42C22×D17311yescharacteristic
291C23—3461no—
292C23—1731no—
293Q8—21no—
294Q8—21no—
295Q8—3464no—
296Q8—3461no—
297Q8—1732no—
298Q8C2×C4×D17312yes—
299Q8C2×C4×D17312yes—
300D4—3464no—
301D4—3461no—
302D4—1732no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—3464no—
308C2×C4—3464no—
309C2×C4—3461no—
310C2×C4—3462no—
311C2×C4—3461no—
312C2×C4—3461no—
313C2×C4—1731no—
314C2×C4—1731no—
315C2×C4—1731no—
316C2×C4—1732no—
317C2×C4—1732no—
318C2×C4—6921no—
319C2×C4—6922no—
320C2×C4—6922no—
321C2×C4—6922no—
322C2×C4D4×D17311yescharacteristic
323C2×C4D4×D17311yescharacteristic
324C2×C4C23×D17311yescharacteristic
325C8—21no—
326C8—3461no—
327C8—1732no—
328C8C2×C4×D17312yes—
329C22—3461no—
330C22—3461no—
331C22—3462no—
332C22—1732no—
333C22—6921no—
334C22—6921no—
335C22C2×D4×D17311yescharacteristic
336C4—22no—
337C4—22no—
338C4—21no—
339C4—41no—
340C4—41no—
341C4—3462no—
342C4—3461no—
343C4—3461no—
344C4—1732no—
345C4—6921no—
346C4—6921no—
347C4#1914971112yesdirect product factor
348C4C22×C4×D17311yescharacteristic
349C4#41×D17311yescharacteristic
350C2—3462no—
351C2—6922no—
352C2C4×D4×D17311yescharacteristic
353C2C2×#1914971111yescharacteristic
354C2#2601228811yescharacteristic
subgroupG/H
centerC2×C4D4×D173
commutatorC4×C173C23×C4
FrattiniC2×C4C23×D173
FittingC4×Q16×C173C2
socleC22×C173C22×D4
prime radicalC2×#14583827C22
cosocleC2×C4×C173C24
hypercenterC4×Q16D173
hypocenterC173C4×#137
LCSG ▷ C4×C173 ▷ C2×C173 ▷ C173
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
3. C4×Q8×D173C2semidirect
4. #26011598C2semidirect
5. #26011595C2semidirect
6. #26011594C2semidirect
7. #26011590C2semidirect
8. C4×#14583816C2semidirect
9. C4×#14583815C2semidirect
10. C4×#14583813C2semidirect
11. #26011532C2semidirect
12. #26011498C2semidirect
14. C4×#14583809C2semidirect
15. C4×Q16×C173C2semidirect
18. #19149711C4direct (N × H)
65. Q8×D173C2×C4semidirect
76. #14583816C2×C4semidirect
77. #14583815C2×C4semidirect
78. #14583813C2×C4semidirect
80. #14583809C2×C4semidirect
103. Q16×C173C2×C4semidirect
163. C4×C173#137semidirect
177. C173C4×#137semidirect
187. C4×Q16D173semidirect
257. Q16C4×D173semidirect
347. C4#19149711direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191497112
C4×#145838272
C4×Q8×D1732
#260115982
#260115952
#260115942
#260115902
C4×#145838162
C4×#145838152
C4×#145838132
#260115322
#260114982
#260114912
C4×#145838092
C4×Q16×C1732
C4×#137173