Finite Group Databasebeta

← C17×#13442 #16871186

Subgroups — C17×#13442 #16871186

Order 4352.

398 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C17×#509C211yesmaximal, characteristic
2C17×#2153C211yesmaximal, characteristic, complemented
3C17×#2148C211yesmaximal, characteristic, complemented
4C17×#2140C211yesmaximal, characteristic, complemented
5C17×#1978C211yesmaximal, characteristic, complemented
6C17×#1976C211yesmaximal, characteristic, complemented
7C17×#1389C211yesmaximal, characteristic, complemented
8C2×C17×#135C2211yescharacteristic
9C22×D8×C17C2211yescharacteristic
10C17×#509—22no—
11C17×#509—22no—
12C2×C17×SD32—21no—
13C2×C17×D16—21no—
14C2×C17×M32C2211yescharacteristic
15C2×C17×M32C2211yescharacteristic
16C2×C17×#108C2211yescharacteristic
17C17×#427C2211yescharacteristic
18C17×#421—21no—
19C17×#418—21no—
20C2×C17×#100—21no—
21C17×#410—21no—
22C17×#405C2211yescharacteristic
23C17×#364—22no—
24C17×#362—21no—
25C17×#361—21no—
26C17×#357—22no—
27C2×#41×C17—21no—
28C22×D4×C17—21no—
29C17×#135—21no—
30C17×#135—21no—
31C17×#135—21no—
32C17×#135—21no—
33C2×Q16×C17D411yescharacteristic
34C2×SD16×C17—21no—
35C2×D8×C17—21no—
36C2×D8×C17—21no—
37C2×D8×C17—21no—
38C2×D8×C17—21no—
39C2×D8×C17—21no—
40C2×D8×C17D411yescharacteristic
41C2×D8×C17D412yes—
42C2×M16×C17—21no—
43C2×M16×C17D411yescharacteristic
44C22×C8×C17C2311yescharacteristic
45C17×#117—21no—
46C17×#117D411yescharacteristic
47C17×SD32—24no—
48C17×D16—24no—
49C17×M32—21no—
50C17×M32—21no—
51C17×M32—21no—
52C17×M32D412yes—
53C2×C16×C17—21no—
54C2×C16×C17—21no—
55C17×#108—21no—
56C17×#108—21no—
57C17×#107—21no—
58C17×#106—21no—
59C17×#104—42no—
60C17×#102—42no—
61C17×#100—42no—
62C17×#99—42no—
63C17×#97—21no—
64C4×C8×C17—21no—
65C24×C17—41no—
66#41×C17—41no—
67#41×C17—41no—
68#41×C17—41no—
69#41×C17—41no—
70C2×Q8×C17—21no—
71C2×D4×C17—22no—
72C2×D4×C17—21no—
73C2×D4×C17—41no—
74C2×D4×C17—41no—
75C2×D4×C17—41no—
76C2×D4×C17—41no—
77C2×D4×C17—41no—
78C2×D4×C17—41no—
79C22×C4×C17—41no—
80C22×C4×C17C2×D411yescharacteristic
81Q16×C17—21no—
82Q16×C17—21no—
83SD16×C17—41no—
84SD16×C17—41no—
85D8×C17—22no—
86D8×C17—21no—
87D8×C17—22no—
88D8×C17—21no—
89D8×C17—41no—
90D8×C17—41no—
91M16×C17—21no—
92M16×C17—41no—
93M16×C17—41no—
94M16×C17D812yes—
95C2×C8×C17—21no—
96C2×C8×C17—41no—
97C2×C8×C17C2×D411yescharacteristic
98C2×C8×C17C2×D411yescharacteristic
99C2×C8×C17C2×D411yescharacteristic
100C2×C8×C17#4111yescharacteristic
101C2×C8×C17#4111yescharacteristic
102C2×C8×C17#4111yescharacteristic
103C4⋊C4×C17—21no—
104C4⋊C4×C17—41no—
105C22⋊C4×C17—21no—
106C22⋊C4×C17—41no—
107C42×C17—21no—
108C42×C17—41no—
109C16×C17—22no—
110C16×C17—41no—
111#13442C1711yesmaximal, characteristic, direct product factor, Sylow
112C23×C17—42no—
113C23×C17—41no—
114C23×C17—81no—
115C23×C17—81no—
116C23×C17—162no—
117C23×C17AGL(1,ℤ/8)11yescharacteristic
118Q8×C17—41no—
119Q8×C17—41no—
120D4×C17—42no—
121D4×C17—41no—
122D4×C17—41no—
123D4×C17—42no—
124D4×C17—81no—
125D4×C17—81no—
126D4×C17—81no—
127D4×C17—81no—
128C2×C4×C17—41no—
129C2×C4×C17—41no—
130C2×C4×C17—81no—
131C2×C4×C17—81no—
132C2×C4×C17—81no—
133C2×C4×C17#12111yescharacteristic
134C2×C4×C17#12111yescharacteristic
135C2×C4×C17#12111yescharacteristic
136C2×C4×C17C2×D811yescharacteristic
137C2×C4×C17#13511yescharacteristic
138C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
139C8×C17—22no—
140C8×C17—81no—
141C8×C17#12011yescharacteristic
142C8×C17#12311yescharacteristic
143C8×C17#12311yescharacteristic
144C8×C17#12411yescharacteristic
145C2×#509C2×C1711yescharacteristic
146#2153C2×C1711yescharacteristic, complemented
147#2148C2×C1711yescharacteristic, complemented
148#2140C2×C1711yescharacteristic, complemented
149#1978C2×C1711yescharacteristic, complemented
150#1976C2×C1711yescharacteristic, complemented
151#1389C2×C1711yescharacteristic, complemented
152C22×C17—41no—
153C22×C17—81no—
154C22×C17—82no—
155C22×C17—161no—
156C22×C17—162no—
157C22×C17—162no—
158C22×C17—162no—
159C22×C17#45911yescharacteristic
160C22×C17#46311yescharacteristic
161C22×C17#46911yescharacteristic
162C4×C17—81no—
163C4×C17—81no—
164C4×C17—161no—
165C4×C17#39411yescharacteristic
166C4×C17#45911yescharacteristic
167C4×C17#46311yescharacteristic
168C4×C17#46611yescharacteristic
169C2×#135C22×C1711yescharacteristic
170C22×D8C22×C1711yescharacteristic
171#509—22no—
172#509—22no—
173C2×SD32—21no—
174C2×D16—21no—
175C2×M32C22×C1711yescharacteristic
176C2×M32C22×C1711yescharacteristic
177C2×#108C22×C1711yescharacteristic
178#427C22×C1711yescharacteristic
179#421—21no—
180#418—21no—
181C2×#100—21no—
182#410—21no—
183#405C22×C1711yescharacteristic
184#364—22no—
185#362—21no—
186#361—21no—
187#357—22no—
188C2×C17—21no—
189C2×C17—21no—
190C2×C17—21no—
191C2×C17—161no—
192C2×C17—162no—
193C2×C17#205411yescharacteristic
194C2×#41—21no—
195C22×D4—21no—
196#135—21no—
197#135—21no—
198#135—21no—
199#135—21no—
200C2×Q16D4×C1711yescharacteristic
201C2×SD16—21no—
202C2×D8—21no—
203C2×D8—21no—
204C2×D8—21no—
205C2×D8—21no—
206C2×D8—21no—
207C2×D8D4×C1712yes—
208C2×D8D4×C1711yescharacteristic
209C2×M16—21no—
210C2×M16D4×C1711yescharacteristic
211C22×C8C23×C1711yescharacteristic
212#117—21no—
213#117D4×C1711yescharacteristic
214SD32—24no—
215D16—24no—
216M32—21no—
217M32—21no—
218M32—21no—
219M32D4×C1712yes—
220C2×C16—21no—
221C2×C16—21no—
222#108—21no—
223#108—21no—
224#107—21no—
225#106—21no—
226#104—42no—
227#102—42no—
228#100—42no—
229#99—42no—
230#97—21no—
231C4×C8—21no—
232C17#1344211yescharacteristic, direct product factor, Sylow
233C24—41no—
234#41—41no—
235#41—41no—
236#41—41no—
237#41—41no—
238C2×Q8—21no—
239C2×D4—22no—
240C2×D4—21no—
241C2×D4—41no—
242C2×D4—41no—
243C2×D4—41no—
244C2×D4—41no—
245C2×D4—41no—
246C2×D4—41no—
247C22×C4—41no—
248C22×C4C2×D4×C1711yescharacteristic
249Q16—21no—
250Q16—21no—
251SD16—41no—
252SD16—41no—
253D8—22no—
254D8—21no—
255D8—21no—
256D8—22no—
257D8—41no—
258D8—41no—
259M16—21no—
260M16—41no—
261M16—41no—
262M16D8×C1712yes—
263C2×C8—21no—
264C2×C8—41no—
265C2×C8C2×D4×C1711yescharacteristic
266C2×C8C2×D4×C1711yescharacteristic
267C2×C8C2×D4×C1711yescharacteristic
268C2×C8#41×C1711yescharacteristic
269C2×C8#41×C1711yescharacteristic
270C2×C8#41×C1711yescharacteristic
271C4⋊C4—21no—
272C4⋊C4—41no—
273C22⋊C4—21no—
274C22⋊C4—41no—
275C42—21no—
276C42—41no—
277C16—22no—
278C16—41no—
279C23—42no—
280C23—41no—
281C23—81no—
282C23—81no—
283C23—162no—
284C23C17×AGL(1,ℤ/8)11yescharacteristic
285Q8—41no—
286Q8—41no—
287D4—42no—
288D4—41no—
289D4—41no—
290D4—42no—
291D4—81no—
292D4—81no—
293D4—81no—
294D4—81no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—81no—
298C2×C4—81no—
299C2×C4—81no—
300C2×C4C17×#12111yescharacteristic
301C2×C4C17×#12111yescharacteristic
302C2×C4C17×#12111yescharacteristic
303C2×C4C2×D8×C1711yescharacteristic
304C2×C4C17×#13511yescharacteristic
305C2×C4C17×AGL(1,ℤ/8)11yescharacteristic
306C8—22no—
307C8—81no—
308C8C17×#12011yescharacteristic
309C8C17×#12311yescharacteristic
310C8C17×#12311yescharacteristic
311C8C17×#12411yescharacteristic
312C22—41no—
313C22—81no—
314C22—82no—
315C22—162no—
316C22—161no—
317C22—162no—
318C22—162no—
319C22C17×#45911yescharacteristic
320C22C17×#46311yescharacteristic
321C22C17×#46911yescharacteristic
322C4—81no—
323C4—81no—
324C4—161no—
325C4C17×#39411yescharacteristic
326C4C17×#45911yescharacteristic
327C4C17×#46311yescharacteristic
328C4C17×#46611yescharacteristic
329C2—21no—
330C2—21no—
331C2—21no—
332C2—162no—
333C2—161no—
334C2C17×#205411yescharacteristic
subgroupG/H
center, socleC2×C17#2054
commutator, Frattini, cosocleC22×C8C23×C17
prime radicalC2×C17×#509C2
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C17 ◁ C22×C4×C17 ◁ C17×#405 ◁ G

Complements

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

NH ≅ G/Ntype
2. C17×#2153C2semidirect
3. C17×#2148C2semidirect
4. C17×#2140C2semidirect
5. C17×#1978C2semidirect
6. C17×#1976C2semidirect
7. C17×#1389C2semidirect
111. #13442C17direct (N × H)
146. #2153C2×C17semidirect
147. #2148C2×C17semidirect
148. #2140C2×C17semidirect
149. #1978C2×C17semidirect
150. #1976C2×C17semidirect
151. #1389C2×C17semidirect
232. C17#13442direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C17×#5092
C17×#21532
C17×#21482
C17×#21402
C17×#19782
C17×#19762
C17×#13892
#1344217