Finite Group Databasebeta

← C17×#13034 #16870778

Subgroups — C17×#13034 #16870778

Order 4352.

462 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×#510C211yesmaximal, characteristic
2C17×#2950C211yesmaximal, characteristic, complemented
3C17×#2145C211yesmaximal, characteristic
4C17×#2141C211yesmaximal, characteristic, complemented
5C17×#1976C211yesmaximal, characteristic
6C17×#1384C211yesmaximal, characteristic, complemented
7C17×#1378C211yesmaximal, characteristic, complemented
8C2×C17×#135C2211yescharacteristic
9C22×Q16×C17C2211yescharacteristic
10C17×#519—21no—
11C17×#510—22no—
12C17×#510—22no—
13C2×C17×Q32C412yescomplemented
14C2×C17×SD32C412yescomplemented
15C2×C17×M32C2211yescharacteristic
16C2×C17×M32C2211yescharacteristic
17C17×#441—22no—
18C4×Q16×C17—22no—
19C17×#427C2211yescharacteristic
20C17×#427C2211yescharacteristic
21C17×#421—21no—
22C17×#419—21no—
23C17×#410—21no—
24C17×#405C2211yescharacteristic
25C17×#360—22no—
26C17×#358—22no—
27C2×#41×C17—21no—
28C22×Q8×C17—21no—
29C17×#135—21no—
30C17×#135—21no—
31C17×#135—21no—
32C17×#135—21no—
33C2×Q16×C17—21no—
34C2×Q16×C17—21no—
35C2×Q16×C17—21no—
36C2×Q16×C17C2×C411yescharacteristic
37C2×Q16×C17C2×C412yes—
38C2×Q16×C17D412yes—
39C2×Q16×C17D412yes—
40C2×SD16×C17—21no—
41C2×D8×C17C2×C411yescharacteristic
42C2×M16×C17D411yescharacteristic
43C22×C8×C17C2311yescharacteristic
44C4×Q8×C17—24no—
45C4×Q8×C17—42no—
46C17×#117—21no—
47C17×#117—21no—
48C17×#117—42no—
49C17×#117D411yescharacteristic
50C17×Q32—24no—
51C17×SD32—24no—
52C17×M32—21no—
53C17×M32—21no—
54C17×M32—21no—
55C17×M32—21no—
56C2×C16×C17—21no—
57C2×C16×C17C2×C412yes—
58C17×#107—21no—
59C17×#107—21no—
60C17×#106—21no—
61C17×#106D412yes—
62C17×#104—42no—
63C17×#103—24no—
64C17×#99—42no—
65C17×#97—21no—
66C4×C8×C17—21no—
67#41×C17—41no—
68#41×C17—41no—
69#41×C17—41no—
70#41×C17—41no—
71C2×Q8×C17—22no—
72C2×Q8×C17—21no—
73C2×Q8×C17—22no—
74C2×Q8×C17—22no—
75C2×Q8×C17—41no—
76C2×Q8×C17—41no—
77C2×Q8×C17—41no—
78C2×D4×C17—21no—
79C2×D4×C17—41no—
80C22×C4×C17—41no—
81C22×C4×C17—41no—
82C22×C4×C17C2×D411yescharacteristic
83Q16×C17—21no—
84Q16×C17—22no—
85Q16×C17—21no—
86Q16×C17—22no—
87Q16×C17—22no—
88Q16×C17C22⋊C414yes—
89SD16×C17—41no—
90SD16×C17—41no—
91D8×C17—21no—
92D8×C17—21no—
93M16×C17—21no—
94M16×C17—21no—
95C2×C8×C17—21no—
96C2×C8×C17C22×C411yescharacteristic
97C2×C8×C17C2×D411yescharacteristic
98C2×C8×C17C2×D411yescharacteristic
99C2×C8×C17C2×D411yescharacteristic
100C2×C8×C17#4111yescharacteristic
101C2×C8×C17#4111yescharacteristic
102C4⋊C4×C17—21no—
103C4⋊C4×C17—22no—
104C4⋊C4×C17—44no—
105C4⋊C4×C17—41no—
106C22⋊C4×C17—41no—
107C22⋊C4×C17—41no—
108C22⋊C4×C17D812yes—
109C42×C17—21no—
110C42×C17—44no—
111C42×C17—41no—
112C42×C17—41no—
113C16×C17—22no—
114C16×C17—41no—
115#13034C1711yesmaximal, characteristic, direct product factor, Sylow
116C23×C17—41no—
117C23×C17C2×D811yescharacteristic
118Q8×C17—24no—
119Q8×C17—42no—
120Q8×C17—42no—
121Q8×C17—42no—
122Q8×C17—41no—
123Q8×C17—41no—
124D4×C17—41no—
125D4×C17—41no—
126D4×C17—81no—
127D4×C17—81no—
128C2×C4×C17—22no—
129C2×C4×C17—42no—
130C2×C4×C17—42no—
131C2×C4×C17—42no—
132C2×C4×C17—41no—
133C2×C4×C17—42no—
134C2×C4×C17—81no—
135C2×C4×C17—81no—
136C2×C4×C17—81no—
137C2×C4×C17C4×D411yescharacteristic
138C2×C4×C17#12011yescharacteristic
139C2×C4×C17#12111yescharacteristic
140C2×C4×C17#13511yescharacteristic
141C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
142C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
143C8×C17—41no—
144C8×C17C2×C22⋊C411yescharacteristic
145C8×C17C4×D411yescharacteristic
146C8×C17#12111yescharacteristic
147C8×C17#12311yescharacteristic
148C2×#510C2×C1711yescharacteristic
149#2950C2×C1711yescharacteristic, complemented
150#2145C2×C1711yescharacteristic
151#2141C2×C1711yescharacteristic, complemented
152#1976C2×C1711yescharacteristic
153#1384C2×C1711yescharacteristic, complemented
154#1378C2×C1711yescharacteristic, complemented
155C22×C17—41no—
156C22×C17—81no—
157C22×C17—161no—
158C22×C17C4×D811yescharacteristic
159C22×C17#44711yescharacteristic
160C22×C17#45911yescharacteristic
161C4×C17—42no—
162C4×C17—44no—
163C4×C17—82no—
164C4×C17—81no—
165C4×C17—161no—
166C4×C17#38611yescharacteristic
167C4×C17#44211yescharacteristic
168C4×C17#44911yescharacteristic
169C4×C17#46311yescharacteristic
170C2×#135C22×C1711yescharacteristic
171C22×Q16C22×C1711yescharacteristic
172#519—21no—
173#510—22no—
174#510—22no—
175C2×Q32C4×C1712yescomplemented
176C2×SD32C4×C1712yescomplemented
177C2×M32C22×C1711yescharacteristic
178C2×M32C22×C1711yescharacteristic
179#441—22no—
180C4×Q16—22no—
181#427C22×C1711yescharacteristic
182#427C22×C1711yescharacteristic
183#421—21no—
184#419—21no—
185#410—21no—
186#405C22×C1711yescharacteristic
187#360—22no—
188#358—22no—
189C2×C17—21no—
190C2×C17—21no—
191C2×C17—21no—
192C2×C17—161no—
193C2×C17#187911yescharacteristic
194C2×#41—21no—
195C22×Q8—21no—
196#135—21no—
197#135—21no—
198#135—21no—
199#135—21no—
200C2×Q16—21no—
201C2×Q16—21no—
202C2×Q16—21no—
203C2×Q16C2×C4×C1711yescharacteristic
204C2×Q16C2×C4×C1712yes—
205C2×Q16D4×C1712yes—
206C2×Q16D4×C1712yes—
207C2×SD16—21no—
208C2×D8C2×C4×C1711yescharacteristic
209C2×M16D4×C1711yescharacteristic
210C22×C8C23×C1711yescharacteristic
211C4×Q8—24no—
212C4×Q8—42no—
213#117—21no—
214#117—21no—
215#117—42no—
216#117D4×C1711yescharacteristic
217Q32—24no—
218SD32—24no—
219M32—21no—
220M32—21no—
221M32—21no—
222M32—21no—
223C2×C16—21no—
224C2×C16C2×C4×C1712yes—
225#107—21no—
226#107—21no—
227#106—21no—
228#106D4×C1712yes—
229#104—42no—
230#103—24no—
231#99—42no—
232#97—21no—
233C4×C8—21no—
234C17#1303411yescharacteristic, direct product factor, Sylow
235#41—41no—
236#41—41no—
237#41—41no—
238#41—41no—
239C2×Q8—22no—
240C2×Q8—21no—
241C2×Q8—22no—
242C2×Q8—22no—
243C2×Q8—41no—
244C2×Q8—41no—
245C2×Q8—41no—
246C2×D4—21no—
247C2×D4—41no—
248C22×C4—41no—
249C22×C4—41no—
250C22×C4C2×D4×C1711yescharacteristic
251Q16—22no—
252Q16—21no—
253Q16—22no—
254Q16—21no—
255Q16—22no—
256Q16C22⋊C4×C1714yes—
257SD16—41no—
258SD16—41no—
259D8—21no—
260D8—21no—
261M16—21no—
262M16—21no—
263C2×C8—21no—
264C2×C8C22×C4×C1711yescharacteristic
265C2×C8C2×D4×C1711yescharacteristic
266C2×C8C2×D4×C1711yescharacteristic
267C2×C8C2×D4×C1711yescharacteristic
268C2×C8#41×C1711yescharacteristic
269C2×C8#41×C1711yescharacteristic
270C4⋊C4—21no—
271C4⋊C4—22no—
272C4⋊C4—44no—
273C4⋊C4—41no—
274C22⋊C4—41no—
275C22⋊C4—41no—
276C22⋊C4D8×C1712yes—
277C42—21no—
278C42—44no—
279C42—41no—
280C42—41no—
281C16—22no—
282C16—41no—
283C23—41no—
284C23C2×D8×C1711yescharacteristic
285Q8—24no—
286Q8—42no—
287Q8—42no—
288Q8—42no—
289Q8—41no—
290Q8—41no—
291D4—41no—
292D4—41no—
293D4—81no—
294D4—81no—
295C2×C4—22no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4—42no—
299C2×C4—41no—
300C2×C4—42no—
301C2×C4—81no—
302C2×C4—81no—
303C2×C4—81no—
304C2×C4C4×D4×C1711yescharacteristic
305C2×C4C17×#12011yescharacteristic
306C2×C4C17×#12111yescharacteristic
307C2×C4C17×#13511yescharacteristic
308C2×C4C17×AGL(1,ℤ/8)11yescharacteristic
309C2×C4C17×AGL(1,ℤ/8)11yescharacteristic
310C8—41no—
311C8C2×C22⋊C4×C1711yescharacteristic
312C8C4×D4×C1711yescharacteristic
313C8C17×#12111yescharacteristic
314C8C17×#12311yescharacteristic
315C22—41no—
316C22—81no—
317C22—161no—
318C22C4×D8×C1711yescharacteristic
319C22C17×#44711yescharacteristic
320C22C17×#45911yescharacteristic
321C4—42no—
322C4—44no—
323C4—82no—
324C4—81no—
325C4—161no—
326C4C17×#38611yescharacteristic
327C4C17×#44211yescharacteristic
328C4C17×#44911yescharacteristic
329C4C17×#46311yescharacteristic
330C2—21no—
331C2—21no—
332C2—21no—
333C2—161no—
334C2C17×#187911yescharacteristic
subgroupG/H
center, socleC2×C17#1879
commutatorC2×C8C22×C4×C17
Frattini, cosocleC22×C8C23×C17
prime radicalC2×C17×#135C22
LCSG ▷ C2×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×#2950C2semidirect
4. C17×#2141C2semidirect
6. C17×#1384C2semidirect
7. C17×#1378C2semidirect
13. C2×C17×Q32C4semidirect
14. C2×C17×SD32C4semidirect
115. #13034C17direct (N × H)
149. #2950C2×C17semidirect
151. #2141C2×C17semidirect
153. #1384C2×C17semidirect
154. #1378C2×C17semidirect
175. C2×Q32C4×C17semidirect
176. C2×SD32C4×C17semidirect
234. C17#13034direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C17×#5102
C17×#29502
C17×#21452
C17×#21412
C17×#19762
C17×#13842
C17×#13782
#1303417