Finite Group Databasebeta

← C17×#13392 #16871136

Subgroups — C17×#13392 #16871136

Order 4352.

386 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C17×#3067C211yesmaximal, characteristic
2C2×C17×#368C211yesmaximal, characteristic, complemented
3C17×#2148C211yesmaximal, characteristic, complemented
4C2×C17×#359C211yesmaximal, characteristic, complemented
5C2×C17×#350C211yesmaximal, characteristic, complemented
6C17×#1813C211yesmaximal, characteristic, complemented
7C17×#1385C211yesmaximal, characteristic, complemented
8C17×#575—21no—
9C2×C17×#135C2211yescharacteristic
10C2×C17×#131C2211yescharacteristic
11C2×C17×M32C2211yescharacteristic
12C22×C16×C17C2211yescharacteristic
13C17×#473—21no—
14C17×#472—21no—
15C17×#471—22no—
16C2×C17×#108C2211yescharacteristic
17C2×C17×#108C2211yescharacteristic
18C2×C17×#108C2211yescharacteristic
19C17×#413—21no—
20C17×#413—21no—
21C17×#368—22no—
22C17×#362—21no—
23C17×#361—21no—
24C17×#359—22no—
25C17×#350—22no—
26C17×#338—21no—
27C2×#41×C17—21no—
28C2×#41×C17D411yescharacteristic
29C17×#137—22no—
30C17×#137—41no—
31C17×AGL(1,ℤ/8)—22no—
32C17×AGL(1,ℤ/8)—41no—
33C17×#135—21no—
34C17×#135—21no—
35C17×#135—21no—
36C17×#135—21no—
37C17×#135—42no—
38C2×Q16×C17D411yescharacteristic
39C2×SD16×C17—21no—
40C2×D8×C17D411yescharacteristic
41C17×#131—21no—
42C17×#131—21no—
43C17×#131—21no—
44C17×#131—21no—
45C2×M16×C17—21no—
46C2×M16×C17—21no—
47C2×M16×C17—21no—
48C2×M16×C17—21no—
49C2×M16×C17D411yescharacteristic
50C22×C8×C17—21no—
51C22×C8×C17C2311yescharacteristic
52C17×M32—21no—
53C17×M32—21no—
54C2×C16×C17—21no—
55C2×C16×C17—21no—
56C2×C16×C17—21no—
57C2×C16×C17D412yes—
58C17×#108—21no—
59C17×#108—21no—
60C17×#108—21no—
61C17×#108—21no—
62C17×#108—21no—
63C17×#108D412yes—
64C17×#101—22no—
65C17×#101—41no—
66C17×#100—22no—
67C17×#100—41no—
68#41×C17—21no—
69#41×C17—21no—
70#41×C17—21no—
71#41×C17—21no—
72#41×C17—41no—
73#41×C17—41no—
74#41×C17—41no—
75#41×C17—41no—
76C2×Q8×C17—21no—
77C2×Q8×C17D811yescharacteristic
78C2×D4×C17—21no—
79C2×D4×C17—21no—
80C2×D4×C17—41no—
81C2×D4×C17D811yescharacteristic
82C22×C4×C17—21no—
83C22×C4×C17—41no—
84C22×C4×C17C2×D411yescharacteristic
85Q16×C17—21no—
86Q16×C17—21no—
87Q16×C17—42no—
88SD16×C17—42no—
89SD16×C17—42no—
90SD16×C17—41no—
91SD16×C17—41no—
92D8×C17—21no—
93D8×C17—21no—
94D8×C17—42no—
95M16×C17—22no—
96M16×C17—21no—
97M16×C17—21no—
98M16×C17—41no—
99M16×C17—41no—
100M16×C17—41no—
101M16×C17—41no—
102M16×C17—41no—
103M16×C17—41no—
104M16×C17—41no—
105C2×C8×C17—21no—
106C2×C8×C17—41no—
107C2×C8×C17—41no—
108C2×C8×C17—41no—
109C2×C8×C17—41no—
110C2×C8×C17—41no—
111C2×C8×C17C2×D411yescharacteristic
112C2×C8×C17C2×D411yescharacteristic
113C2×C8×C17C2×D411yescharacteristic
114C2×C8×C17#4111yescharacteristic
115C2×C8×C17#4111yescharacteristic
116C2×C8×C17#4111yescharacteristic
117C16×C17—22no—
118C16×C17—41no—
119#13392C1711yesmaximal, characteristic, direct product factor, Sylow
120C23×C17—21no—
121C23×C17—41no—
122C23×C17#13711yescharacteristic
123Q8×C17—21no—
124Q8×C17—21no—
125Q8×C17—41no—
126Q8×C17—41no—
127D4×C17—21no—
128D4×C17—21no—
129D4×C17—41no—
130D4×C17—41no—
131D4×C17—41no—
132D4×C17—41no—
133D4×C17—81no—
134D4×C17—81no—
135C2×C4×C17—21no—
136C2×C4×C17—41no—
137C2×C4×C17—41no—
138C2×C4×C17—41no—
139C2×C4×C17—81no—
140C2×C4×C17—81no—
141C2×C4×C17#12011yescharacteristic
142C2×C4×C17#12111yescharacteristic
143C2×C4×C17#12311yescharacteristic
144C2×C4×C17C2×D811yescharacteristic
145C2×C4×C17#13511yescharacteristic
146C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
147C8×C17—41no—
148C8×C17—42no—
149C8×C17—81no—
150C8×C17—81no—
151C8×C17#12111yescharacteristic
152C8×C17#12111yescharacteristic
153C8×C17#12311yescharacteristic
154C8×C17#12411yescharacteristic
155#3067C2×C1711yescharacteristic
156C2×#368C2×C1711yescharacteristic, complemented
157#2148C2×C1711yescharacteristic, complemented
158C2×#359C2×C1711yescharacteristic, complemented
159C2×#350C2×C1711yescharacteristic, complemented
160#1813C2×C1711yescharacteristic, complemented
161#1385C2×C1711yescharacteristic, complemented
162C22×C17—41no—
163C22×C17—41no—
164C22×C17—81no—
165C22×C17—81no—
166C22×C17—161no—
167C22×C17#45211yescharacteristic
168C22×C17#46811yescharacteristic
169C22×C17#48011yescharacteristic
170C4×C17—41no—
171C4×C17—81no—
172C4×C17#39411yescharacteristic
173C4×C17#44711yescharacteristic
174C4×C17#46611yescharacteristic
175C4×C17#48211yescharacteristic
176#575—21no—
177C2×#135C22×C1711yescharacteristic
178C2×#131C22×C1711yescharacteristic
179C2×M32C22×C1711yescharacteristic
180C22×C16C22×C1711yescharacteristic
181#473—21no—
182#472—21no—
183#471—22no—
184C2×#108C22×C1711yescharacteristic
185C2×#108C22×C1711yescharacteristic
186C2×#108C22×C1711yescharacteristic
187#413—21no—
188#413—21no—
189#368—22no—
190#362—21no—
191#361—21no—
192#359—22no—
193#350—22no—
194#338—21no—
195C2×C17—21no—
196C2×C17—21no—
197C2×C17—21no—
198C2×C17—81no—
199C2×C17—161no—
200C2×C17#203311yescharacteristic
201C2×#41—21no—
202C2×#41D4×C1711yescharacteristic
203#137—22no—
204#137—41no—
205AGL(1,ℤ/8)—22no—
206AGL(1,ℤ/8)—41no—
207#135—21no—
208#135—21no—
209#135—21no—
210#135—21no—
211#135—42no—
212C2×Q16D4×C1711yescharacteristic
213C2×SD16—21no—
214C2×D8D4×C1711yescharacteristic
215#131—21no—
216#131—21no—
217#131—21no—
218#131—21no—
219C2×M16—21no—
220C2×M16—21no—
221C2×M16—21no—
222C2×M16—21no—
223C2×M16D4×C1711yescharacteristic
224C22×C8—21no—
225C22×C8C23×C1711yescharacteristic
226M32—21no—
227M32—21no—
228C2×C16—21no—
229C2×C16—21no—
230C2×C16—21no—
231C2×C16D4×C1712yes—
232#108—21no—
233#108—21no—
234#108—21no—
235#108—21no—
236#108—21no—
237#108D4×C1712yes—
238#101—22no—
239#101—41no—
240#100—22no—
241#100—41no—
242C17#1339211yescharacteristic, direct product factor, Sylow
243#41—21no—
244#41—21no—
245#41—21no—
246#41—21no—
247#41—41no—
248#41—41no—
249#41—41no—
250#41—41no—
251C2×Q8—21no—
252C2×Q8D8×C1711yescharacteristic
253C2×D4—21no—
254C2×D4—21no—
255C2×D4—41no—
256C2×D4D8×C1711yescharacteristic
257C22×C4—21no—
258C22×C4—41no—
259C22×C4C2×D4×C1711yescharacteristic
260Q16—21no—
261Q16—21no—
262Q16—42no—
263SD16—42no—
264SD16—42no—
265SD16—41no—
266SD16—41no—
267D8—21no—
268D8—21no—
269D8—42no—
270M16—21no—
271M16—22no—
272M16—21no—
273M16—41no—
274M16—41no—
275M16—41no—
276M16—41no—
277M16—41no—
278M16—41no—
279M16—41no—
280C2×C8—21no—
281C2×C8—41no—
282C2×C8—41no—
283C2×C8—41no—
284C2×C8—41no—
285C2×C8—41no—
286C2×C8C2×D4×C1711yescharacteristic
287C2×C8C2×D4×C1711yescharacteristic
288C2×C8C2×D4×C1711yescharacteristic
289C2×C8#41×C1711yescharacteristic
290C2×C8#41×C1711yescharacteristic
291C2×C8#41×C1711yescharacteristic
292C16—22no—
293C16—41no—
294C23—21no—
295C23—41no—
296C23C17×#13711yescharacteristic
297Q8—21no—
298Q8—21no—
299Q8—41no—
300Q8—41no—
301D4—21no—
302D4—21no—
303D4—41no—
304D4—41no—
305D4—41no—
306D4—41no—
307D4—81no—
308D4—81no—
309C2×C4—21no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4C17×#12011yescharacteristic
316C2×C4C17×#12111yescharacteristic
317C2×C4C17×#12311yescharacteristic
318C2×C4C2×D8×C1711yescharacteristic
319C2×C4C17×#13511yescharacteristic
320C2×C4C17×AGL(1,ℤ/8)11yescharacteristic
321C8—41no—
322C8—42no—
323C8—81no—
324C8—81no—
325C8C17×#12111yescharacteristic
326C8C17×#12111yescharacteristic
327C8C17×#12311yescharacteristic
328C8C17×#12411yescharacteristic
329C22—41no—
330C22—41no—
331C22—81no—
332C22—81no—
333C22—161no—
334C22C17×#45211yescharacteristic
335C22C17×#46811yescharacteristic
336C22C17×#48011yescharacteristic
337C4—41no—
338C4—81no—
339C4C17×#39411yescharacteristic
340C4C17×#44711yescharacteristic
341C4C17×#46611yescharacteristic
342C4C17×#48211yescharacteristic
343C2—21no—
344C2—21no—
345C2—21no—
346C2—81no—
347C2—161no—
348C2C17×#203311yescharacteristic
subgroupG/H
centerC4×C17#482
commutator, Frattini, cosocleC22×C8C23×C17
socleC2×C17#2033
prime radicalC17×#3067C2
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×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. C17×#2148C2semidirect
4. C2×C17×#359C2semidirect
5. C2×C17×#350C2semidirect
6. C17×#1813C2semidirect
7. C17×#1385C2semidirect
119. #13392C17direct (N × H)
156. C2×#368C2×C17semidirect
157. #2148C2×C17semidirect
158. C2×#359C2×C17semidirect
159. C2×#350C2×C17semidirect
160. #1813C2×C17semidirect
161. #1385C2×C17semidirect
242. C17#13392direct (N × H)

Maximal subgroups

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

subgroupindex
C17×#30672
C2×C17×#3682
C17×#21482
C2×C17×#3592
C2×C17×#3502
C17×#18132
C17×#13852
#1339217