Finite Group Databasebeta

← C17×#13405 #16871149

Subgroups — C17×#13405 #16871149

Order 4352.

386 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C17×#473C211yesmaximal, characteristic
2C17×#2155C211yesmaximal, characteristic, complemented
3C17×#2141C211yesmaximal, characteristic, complemented
4C17×#2141C211yesmaximal, characteristic, complemented
5C17×#2117C211yesmaximal, characteristic
6C17×#1812C211yesmaximal, characteristic
7C17×#1389C211yesmaximal, characteristic, complemented
8C2×C17×#137—21no—
9C22×Q16×C17C2211yescharacteristic
10C2×C17×#131C2211yescharacteristic
11C2×C17×M32C2211yescharacteristic
12C2×C17×M32C2211yescharacteristic
13C17×#473—22no—
14C17×#473—22no—
15C2×C17×#108C2211yescharacteristic
16C17×#427C2211yescharacteristic
17C17×#427C2211yescharacteristic
18C2×C17×#101—21no—
19C17×#410—21no—
20C17×#365—22no—
21C17×#358—22no—
22C17×#358—22no—
23C17×#350—22no—
24C17×H(3,ℤ/4)—21no—
25C2×#41×C17D411yescharacteristic
26C22×Q8×C17—21no—
27C17×#137—24no—
28C17×#137—42no—
29C2×Q16×C17—21no—
30C2×Q16×C17—21no—
31C2×Q16×C17—21no—
32C2×Q16×C17—21no—
33C2×Q16×C17—21no—
34C2×Q16×C17—41no—
35C2×Q16×C17D412yes—
36C2×SD16×C17—41no—
37C17×#131—21no—
38C17×#131—21no—
39C17×#131—21no—
40C17×#131—21no—
41C2×M16×C17—21no—
42C2×M16×C17—21no—
43C2×M16×C17D411yescharacteristic
44C22×C8×C17—21no—
45C22×C8×C17C2311yescharacteristic
46C17×#117—21no—
47C17×#117—21no—
48C17×M32—21no—
49C17×M32—21no—
50C17×M32—21no—
51C17×M32—21no—
52C2×C16×C17—21no—
53C2×C16×C17D412yes—
54C17×#108—21no—
55C17×#108D412yes—
56C17×#107—21no—
57C17×#107—21no—
58C17×#106—21no—
59C17×#106—21no—
60C17×#101—24no—
61C17×#99—42no—
62#41×C17—21no—
63#41×C17—21no—
64#41×C17—21no—
65#41×C17—21no—
66C2×Q8×C17—22no—
67C2×Q8×C17—41no—
68C2×Q8×C17—41no—
69C2×Q8×C17—41no—
70C2×Q8×C17—41no—
71C2×Q8×C17—41no—
72C2×Q8×C17SD1611yescharacteristic
73C2×D4×C17—21no—
74C2×D4×C17SD1611yescharacteristic
75C22×C4×C17—21no—
76C22×C4×C17—41no—
77C22×C4×C17C2×D411yescharacteristic
78Q16×C17—22no—
79Q16×C17—22no—
80Q16×C17—44no—
81Q16×C17—41no—
82Q16×C17—41no—
83SD16×C17—44no—
84M16×C17—22no—
85M16×C17—21no—
86M16×C17—21no—
87M16×C17—41no—
88M16×C17—41no—
89M16×C17—41no—
90C2×C8×C17—21no—
91C2×C8×C17—41no—
92C2×C8×C17—41no—
93C2×C8×C17—41no—
94C2×C8×C17C2×D411yescharacteristic
95C2×C8×C17C2×D411yescharacteristic
96C2×C8×C17C2×D411yescharacteristic
97C2×C8×C17#4111yescharacteristic
98C2×C8×C17#4111yescharacteristic
99C2×C8×C17#4111yescharacteristic
100C4⋊C4×C17—41no—
101C4⋊C4×C17—41no—
102C22⋊C4×C17—41no—
103C22⋊C4×C17—41no—
104C42×C17—41no—
105C42×C17—41no—
106C16×C17—22no—
107C16×C17—41no—
108#13405C1711yesmaximal, characteristic, direct product factor, Sylow
109C23×C17—21no—
110C23×C17AGL(1,ℤ/8)11yescharacteristic
111Q8×C17—21no—
112Q8×C17—21no—
113Q8×C17—42no—
114Q8×C17—42no—
115Q8×C17—81no—
116Q8×C17—81no—
117D4×C17—21no—
118D4×C17—21no—
119D4×C17—41no—
120D4×C17—41no—
121C2×C4×C17—21no—
122C2×C4×C17—41no—
123C2×C4×C17—41no—
124C2×C4×C17—42no—
125C2×C4×C17—81no—
126C2×C4×C17—81no—
127C2×C4×C17—81no—
128C2×C4×C17—81no—
129C2×C4×C17#12011yescharacteristic
130C2×C4×C17#12111yescharacteristic
131C2×C4×C17#12311yescharacteristic
132C2×C4×C17C2×SD1611yescharacteristic
133C2×C4×C17#13511yescharacteristic
134C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
135C8×C17—41no—
136C8×C17—42no—
137C8×C17#12111yescharacteristic
138C8×C17#12111yescharacteristic
139C8×C17#12311yescharacteristic
140C8×C17#12411yescharacteristic
141C2×#473C2×C1711yescharacteristic
142#2155C2×C1711yescharacteristic, complemented
143#2141C2×C1711yescharacteristic, complemented
144#2141C2×C1711yescharacteristic, complemented
145#2117C2×C1711yescharacteristic
146#1812C2×C1711yescharacteristic
147#1389C2×C1711yescharacteristic, complemented
148C22×C17—41no—
149C22×C17—41no—
150C22×C17—81no—
151C22×C17#44911yescharacteristic
152C22×C17#46911yescharacteristic
153C22×C17#48111yescharacteristic
154C4×C17—41no—
155C4×C17—82no—
156C4×C17—161no—
157C4×C17—161no—
158C4×C17#39411yescharacteristic
159C4×C17#45011yescharacteristic
160C4×C17#46511yescharacteristic
161C4×C17#48211yescharacteristic
162C2×#137—21no—
163C22×Q16C22×C1711yescharacteristic
164C2×#131C22×C1711yescharacteristic
165C2×M32C22×C1711yescharacteristic
166C2×M32C22×C1711yescharacteristic
167#473—22no—
168#473—22no—
169C2×#108C22×C1711yescharacteristic
170#427C22×C1711yescharacteristic
171#427C22×C1711yescharacteristic
172C2×#101—21no—
173#410—21no—
174#365—22no—
175#358—22no—
176#358—22no—
177#350—22no—
178H(3,ℤ/4)—21no—
179C2×C17—21no—
180C2×C17—21no—
181C2×C17—21no—
182C2×C17—81no—
183C2×C17#203411yescharacteristic
184C2×#41D4×C1711yescharacteristic
185C22×Q8—21no—
186#137—24no—
187#137—42no—
188C2×Q16—21no—
189C2×Q16—21no—
190C2×Q16—21no—
191C2×Q16—21no—
192C2×Q16—21no—
193C2×Q16—41no—
194C2×Q16D4×C1712yes—
195C2×SD16—41no—
196#131—21no—
197#131—21no—
198#131—21no—
199#131—21no—
200C2×M16—21no—
201C2×M16—21no—
202C2×M16D4×C1711yescharacteristic
203C22×C8—21no—
204C22×C8C23×C1711yescharacteristic
205#117—21no—
206#117—21no—
207M32—21no—
208M32—21no—
209M32—21no—
210M32—21no—
211C2×C16—21no—
212C2×C16D4×C1712yes—
213#108—21no—
214#108D4×C1712yes—
215#107—21no—
216#107—21no—
217#106—21no—
218#106—21no—
219#101—24no—
220#99—42no—
221C17#1340511yescharacteristic, direct product factor, Sylow
222#41—21no—
223#41—21no—
224#41—21no—
225#41—21no—
226C2×Q8—22no—
227C2×Q8—41no—
228C2×Q8—41no—
229C2×Q8—41no—
230C2×Q8—41no—
231C2×Q8—41no—
232C2×Q8SD16×C1711yescharacteristic
233C2×D4—21no—
234C2×D4SD16×C1711yescharacteristic
235C22×C4—21no—
236C22×C4—41no—
237C22×C4C2×D4×C1711yescharacteristic
238Q16—22no—
239Q16—22no—
240Q16—44no—
241Q16—41no—
242Q16—41no—
243SD16—44no—
244M16—21no—
245M16—22no—
246M16—21no—
247M16—41no—
248M16—41no—
249M16—41no—
250C2×C8—21no—
251C2×C8—41no—
252C2×C8—41no—
253C2×C8—41no—
254C2×C8C2×D4×C1711yescharacteristic
255C2×C8C2×D4×C1711yescharacteristic
256C2×C8C2×D4×C1711yescharacteristic
257C2×C8#41×C1711yescharacteristic
258C2×C8#41×C1711yescharacteristic
259C2×C8#41×C1711yescharacteristic
260C4⋊C4—41no—
261C4⋊C4—41no—
262C22⋊C4—41no—
263C22⋊C4—41no—
264C42—41no—
265C42—41no—
266C16—22no—
267C16—41no—
268C23—21no—
269C23C17×AGL(1,ℤ/8)11yescharacteristic
270Q8—21no—
271Q8—21no—
272Q8—42no—
273Q8—42no—
274Q8—81no—
275Q8—81no—
276D4—21no—
277D4—21no—
278D4—41no—
279D4—41no—
280C2×C4—21no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—42no—
284C2×C4—81no—
285C2×C4—81no—
286C2×C4—81no—
287C2×C4—81no—
288C2×C4C17×#12011yescharacteristic
289C2×C4C17×#12111yescharacteristic
290C2×C4C17×#12311yescharacteristic
291C2×C4C2×SD16×C1711yescharacteristic
292C2×C4C17×#13511yescharacteristic
293C2×C4C17×AGL(1,ℤ/8)11yescharacteristic
294C8—41no—
295C8—42no—
296C8C17×#12111yescharacteristic
297C8C17×#12111yescharacteristic
298C8C17×#12311yescharacteristic
299C8C17×#12411yescharacteristic
300C22—41no—
301C22—41no—
302C22—81no—
303C22C17×#44911yescharacteristic
304C22C17×#46911yescharacteristic
305C22C17×#48111yescharacteristic
306C4—41no—
307C4—82no—
308C4—161no—
309C4—161no—
310C4C17×#39411yescharacteristic
311C4C17×#45011yescharacteristic
312C4C17×#46511yescharacteristic
313C4C17×#48211yescharacteristic
314C2—21no—
315C2—21no—
316C2—21no—
317C2—81no—
318C2C17×#203411yescharacteristic
subgroupG/H
center, socleC2×C17#2034
commutator, Frattini, cosocleC22×C8C23×C17
prime radicalC2×#41×C17D4
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C17 ◁ C22×C4×C17 ◁ C2×C17×#131 ◁ G

Complements

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

NH ≅ G/Ntype
2. C17×#2155C2semidirect
3. C17×#2141C2semidirect
4. C17×#2141C2semidirect
7. C17×#1389C2semidirect
108. #13405C17direct (N × H)
142. #2155C2×C17semidirect
143. #2141C2×C17semidirect
144. #2141C2×C17semidirect
147. #1389C2×C17semidirect
221. C17#13405direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C17×#4732
C17×#21552
C17×#21412
C17×#21172
C17×#18122
C17×#13892
#1340517