Finite Group Databasebeta

← C2×#14530914 #17188893

Subgroups — C2×#14530914 #17188893

Order 4352.

658 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587471C211yesmaximal, characteristic, complemented
2C2×#11763084C211yesmaximal, characteristic, complemented
3C2×#11763079C211yesmaximal, characteristic
4#14530914C218yesmaximal, direct product factor
5C2×#11762639C211yesmaximal, characteristic, complemented
6C2×#11762626C211yesmaximal, characteristic, complemented
7C2×#11762623C211yesmaximal, characteristic, complemented
8C2×C17×#504C211yesmaximal, characteristic, complemented
9C2×#10587637—21no—
10C2×#10587635—21no—
11C22×Dic68C2211yescharacteristic
12C22×D136C2211yescharacteristic
13C2×#10587471—21no—
14C2×#10587471—21no—
15C2×#10587471—22no—
16C2×#10587471C2214yescomplemented
17#11763084—22no—
18#11763084C2214yescomplemented
19#11763079—22no—
20#11763079C2214yes—
21C2×#10587490C2211yescharacteristic
22C2×#10587490C2211yescharacteristic
23C2×#10587495—21no—
24C2×#10587494—21no—
25#11762639C2214yescomplemented
26#11762626C2214yescomplemented
27#11762623C2214yescomplemented
28C2×C17×#131C2211yescharacteristic
29C17×#504—22no—
30C17×#504C2214yescomplemented
31C2×C17×M32—21no—
32C2×C17×M32C2211yescharacteristic
33C22×C16×C17—21no—
34C22×C16×C17C2211yescharacteristic
35C2×#41×C17D411yescharacteristic
36C22×D68—21no—
37C22×Dic34—21no—
38C17×#131—21no—
39C17×#131—21no—
40C17×#131D412yes—
41C17×#131C2312yes—
42C2×M16×C17—21no—
43C2×M16×C17D411yescharacteristic
44C22×C8×C17—21no—
45C22×C8×C17C2311yescharacteristic
46#10587637—24no—
47#10587637—42no—
48#10587635—24no—
49#10587635—42no—
50C2×#63231—41no—
51C2×#63230—41no—
52C2×#63229—41no—
53C2×#63228—41no—
54C2×#63223—21no—
55C2×#63223—21no—
56C2×Dic68—21no—
57C2×Dic68—21no—
58C2×Dic68—21no—
59C2×Dic68—21no—
60C2×Dic68—21no—
61C2×Dic68C2312yes—
62C2×D136—21no—
63C2×D136—21no—
64C2×D136—21no—
65C2×D136—21no—
66C2×D136—21no—
67C2×D136C2312yes—
68C17×M32—24no—
69C17×M32—21no—
70C17×M32C2312yes—
71C2×C16×C17—24no—
72C2×C16×C17—21no—
73C2×C16×C17D411yescharacteristic
74C2×C16×C17D411yescharacteristic
75C2×C16×C17D412yes—
76C2×C16×C17C2312yes—
77#10587495—24no—
78#10587494—24no—
79#10587490—21no—
80#10587490—21no—
81#10587490C2312yes—
82#10587490C2312yes—
83#10587471—24no—
84#10587471—24no—
85C23×D17—41no—
86#41×C17—21no—
87#41×C17—21no—
88#41×C17D812yes—
89#41×C17C2×D412yes—
90C2×Q8×C17D811yescharacteristic
91C2×D4×C17—21no—
92C2×D4×C17D811yescharacteristic
93C22×C4×C17—21no—
94C22×C4×C17C2×D411yescharacteristic
95C22×Dic17—41no—
96C2×D68—22no—
97C2×D68—41no—
98C2×D68—41no—
99C2×D68—41no—
100C2×D68—41no—
101C2×D68—41no—
102C2×Dic34—22no—
103C2×Dic34—41no—
104C2×Dic34—41no—
105C2×Dic34—41no—
106C2×Dic34—41no—
107C2×Dic34—41no—
108M16×C17—21no—
109M16×C17—22no—
110M16×C17—22no—
111M16×C17C2×D412yes—
112C2×C8×C17—21no—
113C2×C8×C17—22no—
114C2×C8×C17—22no—
115C2×C8×C17C2×D411yescharacteristic
116C2×C8×C17C2×D411yescharacteristic
117C2×C8×C17C2×D411yescharacteristic
118C2×C8×C17#4111yescharacteristic
119C2×C8×C17#4111yescharacteristic
120C2×C8×C17C2411yescharacteristic
121#63231—44no—
122#63230—44no—
123#63229—44no—
124#63228—44no—
125#63223—22no—
126#63223—22no—
127#63223—41no—
128#63223—41no—
129C2×#3622—41no—
130C2×#3622—41no—
131Dic68—22no—
132Dic68—22no—
133Dic68—41no—
134Dic68—41no—
135D136—22no—
136D136—22no—
137D136—41no—
138D136—41no—
139C16×C17—22no—
140C16×C17C2×D412yes—
141C16×C17C2×D412yes—
142C2×#2223—171nomaximal, Sylow
143C23×C17—21no—
144C23×C17#13511yescharacteristic
145C22×D17—42no—
146C22×D17—81no—
147C22×D17—81no—
148C22×D17—162no—
149Q8×C17—21no—
150Q8×C17C2×D812yes—
151D4×C17—22no—
152D4×C17—22no—
153D4×C17—21no—
154D4×C17C2×D812yes—
155C2×C4×C17—21no—
156C2×C4×C17—22no—
157C2×C4×C17—22no—
158C2×C4×C17#12111yescharacteristic
159C2×C4×C17#12111yescharacteristic
160C2×C4×C17C2×D811yescharacteristic
161C2×C4×C17C2×D811yescharacteristic
162C2×C4×C17#13511yescharacteristic
163C2×C4×C17C22×D411yescharacteristic
164C2×Dic17—42no—
165C2×Dic17—81no—
166C2×Dic17—81no—
167D68—42no—
168D68—42no—
169D68—81no—
170D68—81no—
171Dic34—42no—
172Dic34—42no—
173Dic34—81no—
174Dic34—81no—
175C8×C17—22no—
176C8×C17#12111yescharacteristic
177C8×C17#12111yescharacteristic
178C8×C17C22×D411yescharacteristic
179C8×C17C2×#4111yescharacteristic
180#3622—42no—
181#3622—42no—
182C22×SD32—171no—
183C2×#504D1711yescharacteristic, complemented
184C2×#473—171no—
185C2×#472—171no—
186#2223—178no—
187C2×#368—171no—
188C2×#362—171no—
189C2×#361—171no—
190C22×C17—22no—
191C22×C17—22no—
192C22×C17—42no—
193C22×C17#46611yescharacteristic
194C22×C17#46611yescharacteristic
195C22×C17C2×#13511yescharacteristic
196C2×D17—82no—
197C2×D17—162no—
198C2×D17—162no—
199C2×D17—162no—
200C4×C17—22no—
201C4×C17#46611yescharacteristic
202C4×C17#46611yescharacteristic
203C4×C17C2×#12111yescharacteristic
204C4×C17C22×D811yescharacteristic
205Dic17—82no—
206C2×#137—341no—
207C2×AGL(1,ℤ/8)—341no—
208C22×Q16—171no—
209C22×D8—171no—
210C2×#131C2×D1711yescharacteristic
211C2×SD32—174no—
212C2×SD32—341no—
213C2×SD32—341no—
214C2×SD32—342no—
215#504—22no—
216#504C2×D1714yescomplemented
217C2×M32—21no—
218C2×M32C2×D1711yescharacteristic
219C22×C16—21no—
220C22×C16C2×D1711yescharacteristic
221#473—174no—
222#473—342no—
223#472—174no—
224#472—342no—
225C2×#108—171no—
226C2×#108—171no—
227C2×#101—341no—
228C2×#100—341no—
229#368—174no—
230#362—174no—
231#361—174no—
232C2×C17—21no—
233C2×C17—21no—
234C2×C17—42no—
235C2×C17#222312yescomplemented
236C2×C17C2×#46611yescharacteristic
237D17—162no—
238C2×#41D6811yescharacteristic
239C22×Q8—341no—
240C22×D4—341no—
241#137—344no—
242#137—682no—
243AGL(1,ℤ/8)—344no—
244AGL(1,ℤ/8)—682no—
245C2×Q16—172no—
246C2×Q16—341no—
247C2×Q16—341no—
248C2×Q16—341no—
249C2×Q16—341no—
250C2×Q16—341no—
251C2×Q16—681no—
252C2×SD16—681no—
253C2×SD16—681no—
254C2×D8—172no—
255C2×D8—341no—
256C2×D8—341no—
257C2×D8—341no—
258C2×D8—341no—
259C2×D8—341no—
260C2×D8—681no—
261#131—21no—
262#131—21no—
263#131D6812yes—
264#131C22×D1712yes—
265C2×M16—21no—
266C2×M16—341no—
267C2×M16—341no—
268C2×M16D6811yescharacteristic
269C22×C8—21no—
270C22×C8C22×D1711yescharacteristic
271SD32—344no—
272SD32—344no—
273M32—21no—
274M32—24no—
275M32C22×D1712yes—
276C2×C16—21no—
277C2×C16—24no—
278C2×C16C22⋊D1711yescharacteristic
279C2×C16C22⋊D1711yescharacteristic
280C2×C16C22⋊D1712yes—
281C2×C16C22×D1712yes—
282#108—172no—
283#108—172no—
284#108—341no—
285#108—341no—
286#101—344no—
287#100—344no—
288C17C2×#222311yescharacteristic, complemented, Sylow
289C24—681no—
290#41—21no—
291#41—21no—
292#41D13612yes—
293#41C2×D6812yes—
294C2×Q8—342no—
295C2×Q8—681no—
296C2×Q8—681no—
297C2×Q8—681no—
298C2×Q8—681no—
299C2×Q8—681no—
300C2×Q8D13611yescharacteristic
301C2×D4—21no—
302C2×D4—342no—
303C2×D4—681no—
304C2×D4—681no—
305C2×D4—681no—
306C2×D4—681no—
307C2×D4—681no—
308C2×D4D13611yescharacteristic
309C22×C4—21no—
310C22×C4—681no—
311C22×C4C2×D6811yescharacteristic
312Q16—342no—
313Q16—342no—
314Q16—684no—
315Q16—681no—
316Q16—681no—
317SD16—684no—
318SD16—684no—
319D8—342no—
320D8—342no—
321D8—684no—
322D8—681no—
323D8—681no—
324M16—21no—
325M16—22no—
326M16—22no—
327M16—342no—
328M16—342no—
329M16—681no—
330M16—681no—
331M16C2×D6812yes—
332C2×C8—21no—
333C2×C8—22no—
334C2×C8—22no—
335C2×C8—681no—
336C2×C8—681no—
337C2×C8C2×D6811yescharacteristic
338C2×C8#6325211yescharacteristic
339C2×C8#6325211yescharacteristic
340C2×C8C2×C22⋊D1711yescharacteristic
341C2×C8C2×C22⋊D1711yescharacteristic
342C2×C8C23×D1711yescharacteristic
343C16—22no—
344C16C2×C22⋊D1712yes—
345C16C2×C22⋊D1712yes—
346C23—21no—
347C23—2722no—
348C23—682no—
349C23—1361no—
350C23—1361no—
351C23#1058759011yescharacteristic
352Q8—21no—
353Q8—682no—
354Q8—682no—
355Q8—1361no—
356Q8—1361no—
357Q8C2×D13612yes—
358D4—22no—
359D4—22no—
360D4—21no—
361D4—682no—
362D4—682no—
363D4—1361no—
364D4—1361no—
365D4C2×D13612yes—
366C2×C4—21no—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—682no—
370C2×C4—1361no—
371C2×C4—1361no—
372C2×C4C2×D13611yescharacteristic
373C2×C4C2×D13611yescharacteristic
374C2×C4#1058759011yescharacteristic
375C2×C4#1058761611yescharacteristic
376C2×C4#1058761611yescharacteristic
377C2×C4C22×D6811yescharacteristic
378C8—22no—
379C8—682no—
380C8—682no—
381C8#1058761611yescharacteristic
382C8#1058761611yescharacteristic
383C8C2×#6325211yescharacteristic
384C8C22×C22⋊D1711yescharacteristic
385C22—22no—
386C22—22no—
387C22—42no—
388C22—2722no—
389C22—2722no—
390C22—2722no—
391C22—1362no—
392C22#1176304511yescharacteristic
393C22#1176304511yescharacteristic
394C22C2×#1058759011yescharacteristic
395C4—22no—
396C4—1362no—
397C4#1176304511yescharacteristic
398C4#1176304511yescharacteristic
399C4C2×#1058761611yescharacteristic
400C4C22×D13611yescharacteristic
401C2—21no—
402C2—21no—
403C2—42no—
404C2—2722no—
405C2#1453091412yesdirect product factor
406C2C2×#1176304511yescharacteristic
subgroupG/H
centerC22#11763045
commutator, cosocleC2×C8×C17C24
FrattiniC2×C8C23×D17
FittingC2×C17×#504C2
socleC22×C17#466
prime radicalC2×#11763079C2
hypercenterC2×#504D17
hypocenterC17C2×#2223
LCSG ▷ C2×C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#131 ◁ C2×#504

Complements

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

NH ≅ G/Ntype
1. C22×#10587471C2semidirect
2. C2×#11763084C2semidirect
4. #14530914C2direct (N × H)
5. C2×#11762639C2semidirect
6. C2×#11762626C2semidirect
7. C2×#11762623C2semidirect
8. C2×C17×#504C2semidirect
16. C2×#10587471C22semidirect
18. #11763084C22semidirect
25. #11762639C22semidirect
26. #11762626C22semidirect
27. #11762623C22semidirect
30. C17×#504C22semidirect
183. C2×#504D17semidirect
216. #504C2×D17semidirect
235. C2×C17#2223semidirect
288. C17C2×#2223semidirect
405. C2#14530914direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#105874712
C2×#117630842
C2×#117630792
#145309142
C2×#117626392
C2×#117626262
C2×#117626232
C2×C17×#5042
C2×#222317