Finite Group Databasebeta

← C17×#13393 #16871137

Subgroups — C17×#13393 #16871137

Order 4352.

412 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C17×#472C211yesmaximal, characteristic
2C2×C17×#368C211yesmaximal, characteristic, complemented
3C2×C17×#361C211yesmaximal, characteristic, complemented
4C2×C17×#357C211yesmaximal, characteristic, complemented
5C17×#2113C211yesmaximal, characteristic, complemented
6C17×#1816C211yesmaximal, characteristic, complemented
7C17×#1387C211yesmaximal, characteristic, complemented
8C2×C17×AGL(1,ℤ/8)—21no—
9C22×D8×C17C2211yescharacteristic
10C2×C17×#131C2211yescharacteristic
11C2×C17×M32C2211yescharacteristic
12C22×C16×C17C2211yescharacteristic
13C17×#472—22no—
14C17×#472—22no—
15C2×C17×#108C2211yescharacteristic
16C2×C17×#108C2211yescharacteristic
17C2×C17×#107C2211yescharacteristic
18C17×#417—21no—
19C2×C17×#100—21no—
20C17×#368—22no—
21C17×#361—22no—
22C17×#357—22no—
23C17×C22⋊C16—22no—
24C17×#343—21no—
25C2×#41×C17D411yescharacteristic
26C22×D4×C17—21no—
27C17×AGL(1,ℤ/8)—24no—
28C17×AGL(1,ℤ/8)—42no—
29C2×SD16×C17—41no—
30C2×D8×C17—21no—
31C2×D8×C17—21no—
32C2×D8×C17—21no—
33C2×D8×C17—21no—
34C2×D8×C17—21no—
35C2×D8×C17—41no—
36C2×D8×C17D412yes—
37C17×#131—21no—
38C17×#131—21no—
39C17×#131—21no—
40C17×#131—21no—
41C2×M16×C17—21no—
42C2×M16×C17—21no—
43C2×M16×C17—21no—
44C2×M16×C17D411yescharacteristic
45C22×C8×C17—21no—
46C22×C8×C17C2311yescharacteristic
47C2×C4⋊C4×C17—21no—
48C17×M32—21no—
49C17×M32—21no—
50C2×C16×C17—21no—
51C2×C16×C17—21no—
52C2×C16×C17—21no—
53C2×C16×C17D412yes—
54C17×#108—21no—
55C17×#108—21no—
56C17×#108—21no—
57C17×#108D412yes—
58C17×#107—21no—
59C17×#107—21no—
60C17×#103—41no—
61C17×#102—41no—
62C17×#100—24no—
63C24×C17—41no—
64#41×C17—21no—
65#41×C17—21no—
66#41×C17—21no—
67#41×C17—21no—
68C2×Q8×C17D811yescharacteristic
69C2×D4×C17—21no—
70C2×D4×C17—22no—
71C2×D4×C17—41no—
72C2×D4×C17—41no—
73C2×D4×C17—41no—
74C2×D4×C17—41no—
75C2×D4×C17—41no—
76C2×D4×C17D811yescharacteristic
77C22×C4×C17—21no—
78C22×C4×C17—41no—
79C22×C4×C17C2×D411yescharacteristic
80SD16×C17—44no—
81D8×C17—22no—
82D8×C17—22no—
83D8×C17—44no—
84D8×C17—41no—
85D8×C17—41no—
86M16×C17—22no—
87M16×C17—21no—
88M16×C17—21no—
89M16×C17—41no—
90M16×C17—41no—
91M16×C17—41no—
92M16×C17—41no—
93M16×C17—41no—
94C2×C8×C17—21no—
95C2×C8×C17—41no—
96C2×C8×C17—41no—
97C2×C8×C17—41no—
98C2×C8×C17—41no—
99C2×C8×C17C2×D411yescharacteristic
100C2×C8×C17C2×D411yescharacteristic
101C2×C8×C17C2×D411yescharacteristic
102C2×C8×C17#4111yescharacteristic
103C2×C8×C17#4111yescharacteristic
104C2×C8×C17#4111yescharacteristic
105C4⋊C4×C17—41no—
106C4⋊C4×C17—41no—
107C16×C17—22no—
108C16×C17—41no—
109#13393C1711yesmaximal, characteristic, direct product factor, Sylow
110C23×C17—21no—
111C23×C17—42no—
112C23×C17—81no—
113C23×C17—81no—
114C23×C17—161no—
115C23×C17—161no—
116C23×C17#13511yescharacteristic
117Q8×C17—21no—
118Q8×C17—21no—
119D4×C17—21no—
120D4×C17—21no—
121D4×C17—41no—
122D4×C17—41no—
123D4×C17—42no—
124D4×C17—42no—
125D4×C17—81no—
126D4×C17—81no—
127C2×C4×C17—21no—
128C2×C4×C17—41no—
129C2×C4×C17—41no—
130C2×C4×C17—81no—
131C2×C4×C17—161no—
132C2×C4×C17#12011yescharacteristic
133C2×C4×C17#12111yescharacteristic
134C2×C4×C17#12311yescharacteristic
135C2×C4×C17C2×D811yescharacteristic
136C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
137C2×C4×C17#13711yescharacteristic
138C8×C17—41no—
139C8×C17—42no—
140C8×C17—81no—
141C8×C17#12111yescharacteristic
142C8×C17#12111yescharacteristic
143C8×C17#12311yescharacteristic
144C8×C17#12411yescharacteristic
145C2×#472C2×C1711yescharacteristic
146C2×#368C2×C1711yescharacteristic, complemented
147C2×#361C2×C1711yescharacteristic, complemented
148C2×#357C2×C1711yescharacteristic, complemented
149#2113C2×C1711yescharacteristic, complemented
150#1816C2×C1711yescharacteristic, complemented
151#1387C2×C1711yescharacteristic, complemented
152C22×C17—21no—
153C22×C17—21no—
154C22×C17—41no—
155C22×C17—41no—
156C22×C17—41no—
157C22×C17—82no—
158C22×C17—162no—
159C22×C17—162no—
160C22×C17—161no—
161C22×C17—161no—
162C22×C17#45211yescharacteristic
163C22×C17#46611yescharacteristic
164C22×C17#48211yescharacteristic
165C4×C17—41no—
166C4×C17—161no—
167C4×C17#39411yescharacteristic
168C4×C17#44711yescharacteristic
169C4×C17#46811yescharacteristic
170C4×C17#48011yescharacteristic
171C2×AGL(1,ℤ/8)—21no—
172C22×D8C22×C1711yescharacteristic
173C2×#131C22×C1711yescharacteristic
174C2×M32C22×C1711yescharacteristic
175C22×C16C22×C1711yescharacteristic
176#472—22no—
177#472—22no—
178C2×#108C22×C1711yescharacteristic
179C2×#108C22×C1711yescharacteristic
180C2×#107C22×C1711yescharacteristic
181#417—21no—
182C2×#100—21no—
183#368—22no—
184#361—22no—
185#357—22no—
186C22⋊C16—22no—
187#343—21no—
188C2×C17—21no—
189C2×C17—21no—
190C2×C17—81no—
191C2×C17—162no—
192C2×C17#203311yescharacteristic
193C2×C17#222111yescharacteristic
194C2×C17#222311yescharacteristic
195C2×#41D4×C1711yescharacteristic
196C22×D4—21no—
197AGL(1,ℤ/8)—24no—
198AGL(1,ℤ/8)—42no—
199C2×SD16—41no—
200C2×D8—21no—
201C2×D8—21no—
202C2×D8—21no—
203C2×D8—21no—
204C2×D8—21no—
205C2×D8—41no—
206C2×D8D4×C1712yes—
207#131—21no—
208#131—21no—
209#131—21no—
210#131—21no—
211C2×M16—21no—
212C2×M16—21no—
213C2×M16—21no—
214C2×M16D4×C1711yescharacteristic
215C22×C8—21no—
216C22×C8C23×C1711yescharacteristic
217C2×C4⋊C4—21no—
218M32—21no—
219M32—21no—
220C2×C16—21no—
221C2×C16—21no—
222C2×C16—21no—
223C2×C16D4×C1712yes—
224#108—21no—
225#108—21no—
226#108—21no—
227#108D4×C1712yes—
228#107—21no—
229#107—21no—
230#103—41no—
231#102—41no—
232#100—24no—
233C17#1339311yescharacteristic, direct product factor, Sylow
234C24—41no—
235#41—21no—
236#41—21no—
237#41—21no—
238#41—21no—
239C2×Q8D8×C1711yescharacteristic
240C2×D4—21no—
241C2×D4—22no—
242C2×D4—41no—
243C2×D4—41no—
244C2×D4—41no—
245C2×D4—41no—
246C2×D4—41no—
247C2×D4D8×C1711yescharacteristic
248C22×C4—21no—
249C22×C4—41no—
250C22×C4C2×D4×C1711yescharacteristic
251SD16—44no—
252D8—22no—
253D8—22no—
254D8—44no—
255D8—41no—
256D8—41no—
257M16—21no—
258M16—21no—
259M16—22no—
260M16—41no—
261M16—41no—
262M16—41no—
263M16—41no—
264M16—41no—
265C2×C8—21no—
266C2×C8—41no—
267C2×C8—41no—
268C2×C8—41no—
269C2×C8—41no—
270C2×C8C2×D4×C1711yescharacteristic
271C2×C8C2×D4×C1711yescharacteristic
272C2×C8C2×D4×C1711yescharacteristic
273C2×C8#41×C1711yescharacteristic
274C2×C8#41×C1711yescharacteristic
275C2×C8#41×C1711yescharacteristic
276C4⋊C4—41no—
277C4⋊C4—41no—
278C16—22no—
279C16—41no—
280C23—21no—
281C23—42no—
282C23—81no—
283C23—81no—
284C23—161no—
285C23—161no—
286C23C17×#13511yescharacteristic
287Q8—21no—
288Q8—21no—
289D4—21no—
290D4—21no—
291D4—41no—
292D4—41no—
293D4—42no—
294D4—42no—
295D4—81no—
296D4—81no—
297C2×C4—21no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—81no—
301C2×C4—161no—
302C2×C4C17×#12011yescharacteristic
303C2×C4C17×#12111yescharacteristic
304C2×C4C17×#12311yescharacteristic
305C2×C4C2×D8×C1711yescharacteristic
306C2×C4C17×AGL(1,ℤ/8)11yescharacteristic
307C2×C4C17×#13711yescharacteristic
308C8—41no—
309C8—42no—
310C8—81no—
311C8C17×#12111yescharacteristic
312C8C17×#12111yescharacteristic
313C8C17×#12311yescharacteristic
314C8C17×#12411yescharacteristic
315C22—21no—
316C22—21no—
317C22—41no—
318C22—41no—
319C22—41no—
320C22—82no—
321C22—162no—
322C22—162no—
323C22—161no—
324C22—161no—
325C22C17×#45211yescharacteristic
326C22C17×#46611yescharacteristic
327C22C17×#48211yescharacteristic
328C4—41no—
329C4—161no—
330C4C17×#39411yescharacteristic
331C4C17×#44711yescharacteristic
332C4C17×#46811yescharacteristic
333C4C17×#48011yescharacteristic
334C2—21no—
335C2—21no—
336C2—81no—
337C2—162no—
338C2C17×#203311yescharacteristic
339C2C17×#222111yescharacteristic
340C2C17×#222311yescharacteristic
subgroupG/H
center, socleC22×C17#466
commutator, Frattini, cosocleC22×C8C23×C17
prime radicalC2×C17×#472C2
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C17 ◁ C22×C4×C17 ◁ C2×C17×#131 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C17×#368C2semidirect
3. C2×C17×#361C2semidirect
4. C2×C17×#357C2semidirect
5. C17×#2113C2semidirect
6. C17×#1816C2semidirect
7. C17×#1387C2semidirect
109. #13393C17direct (N × H)
146. C2×#368C2×C17semidirect
147. C2×#361C2×C17semidirect
148. C2×#357C2×C17semidirect
149. #2113C2×C17semidirect
150. #1816C2×C17semidirect
151. #1387C2×C17semidirect
233. C17#13393direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C17×#4722
C2×C17×#3682
C2×C17×#3612
C2×C17×#3572
C17×#21132
C17×#18162
C17×#13872
#1339317