Finite Group Databasebeta

← C17×#13394 #16871138

Subgroups — C17×#13394 #16871138

Order 4352.

392 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C17×#473C211yesmaximal, characteristic
2C2×C17×#368C211yesmaximal, characteristic, complemented
3C2×C17×#362C211yesmaximal, characteristic, complemented
4C2×C17×#358C211yesmaximal, characteristic, complemented
5C17×#2113C211yesmaximal, characteristic
6C17×#1816C211yesmaximal, characteristic
7C17×#1387C211yesmaximal, characteristic, complemented
8C2×C17×#137—21no—
9C22×Q16×C17C2211yescharacteristic
10C2×C17×#131C2211yescharacteristic
11C2×C17×M32C2211yescharacteristic
12C22×C16×C17C2211yescharacteristic
13C17×#473—22no—
14C17×#473—22no—
15C2×C17×#108C2211yescharacteristic
16C2×C17×#108C2211yescharacteristic
17C2×C17×#107C2211yescharacteristic
18C17×#417—21no—
19C2×C17×#101—21no—
20C17×#368—22no—
21C17×#362—22no—
22C17×#358—22no—
23C17×C22⋊C16—22no—
24C17×#343—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×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×#101—24no—
63#41×C17—21no—
64#41×C17—21no—
65#41×C17—21no—
66#41×C17—21no—
67C2×Q8×C17—22no—
68C2×Q8×C17—41no—
69C2×Q8×C17—41no—
70C2×Q8×C17—41no—
71C2×Q8×C17—41no—
72C2×Q8×C17—41no—
73C2×Q8×C17D811yescharacteristic
74C2×D4×C17—21no—
75C2×D4×C17D811yescharacteristic
76C22×C4×C17—21no—
77C22×C4×C17—41no—
78C22×C4×C17—41no—
79C22×C4×C17C2×D411yescharacteristic
80Q16×C17—22no—
81Q16×C17—22no—
82Q16×C17—44no—
83Q16×C17—41no—
84Q16×C17—41no—
85SD16×C17—44no—
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#13394C1711yesmaximal, characteristic, direct product factor, Sylow
110C23×C17—21no—
111C23×C17#13511yescharacteristic
112Q8×C17—21no—
113Q8×C17—21no—
114Q8×C17—42no—
115Q8×C17—42no—
116Q8×C17—81no—
117Q8×C17—81no—
118D4×C17—21no—
119D4×C17—21no—
120D4×C17—41no—
121D4×C17—41no—
122C2×C4×C17—21no—
123C2×C4×C17—41no—
124C2×C4×C17—41no—
125C2×C4×C17—42no—
126C2×C4×C17—81no—
127C2×C4×C17—81no—
128C2×C4×C17—81no—
129C2×C4×C17—161no—
130C2×C4×C17#12011yescharacteristic
131C2×C4×C17#12111yescharacteristic
132C2×C4×C17#12311yescharacteristic
133C2×C4×C17C2×D811yescharacteristic
134C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
135C2×C4×C17#13711yescharacteristic
136C8×C17—41no—
137C8×C17—42no—
138C8×C17—81no—
139C8×C17#12111yescharacteristic
140C8×C17#12111yescharacteristic
141C8×C17#12311yescharacteristic
142C8×C17#12411yescharacteristic
143C2×#473C2×C1711yescharacteristic
144C2×#368C2×C1711yescharacteristic, complemented
145C2×#362C2×C1711yescharacteristic, complemented
146C2×#358C2×C1711yescharacteristic, complemented
147#2113C2×C1711yescharacteristic
148#1816C2×C1711yescharacteristic
149#1387C2×C1711yescharacteristic, complemented
150C22×C17—21no—
151C22×C17—21no—
152C22×C17—41no—
153C22×C17—41no—
154C22×C17—41no—
155C22×C17#45211yescharacteristic
156C22×C17#46611yescharacteristic
157C22×C17#48211yescharacteristic
158C4×C17—41no—
159C4×C17—82no—
160C4×C17—161no—
161C4×C17#39411yescharacteristic
162C4×C17#44711yescharacteristic
163C4×C17#46811yescharacteristic
164C4×C17#48011yescharacteristic
165C2×#137—21no—
166C22×Q16C22×C1711yescharacteristic
167C2×#131C22×C1711yescharacteristic
168C2×M32C22×C1711yescharacteristic
169C22×C16C22×C1711yescharacteristic
170#473—22no—
171#473—22no—
172C2×#108C22×C1711yescharacteristic
173C2×#108C22×C1711yescharacteristic
174C2×#107C22×C1711yescharacteristic
175#417—21no—
176C2×#101—21no—
177#368—22no—
178#362—22no—
179#358—22no—
180C22⋊C16—22no—
181#343—21no—
182C2×C17—21no—
183C2×C17—21no—
184C2×C17—81no—
185C2×C17#203311yescharacteristic
186C2×C17#222211yescharacteristic
187C2×C17#222311yescharacteristic
188C2×#41D4×C1711yescharacteristic
189C22×Q8—21no—
190#137—24no—
191#137—42no—
192C2×Q16—21no—
193C2×Q16—21no—
194C2×Q16—21no—
195C2×Q16—21no—
196C2×Q16—21no—
197C2×Q16—41no—
198C2×Q16D4×C1712yes—
199C2×SD16—41no—
200#131—21no—
201#131—21no—
202#131—21no—
203#131—21no—
204C2×M16—21no—
205C2×M16—21no—
206C2×M16—21no—
207C2×M16D4×C1711yescharacteristic
208C22×C8—21no—
209C22×C8C23×C1711yescharacteristic
210C2×C4⋊C4—21no—
211M32—21no—
212M32—21no—
213C2×C16—21no—
214C2×C16—21no—
215C2×C16—21no—
216C2×C16D4×C1712yes—
217#108—21no—
218#108—21no—
219#108—21no—
220#108D4×C1712yes—
221#107—21no—
222#107—21no—
223#103—41no—
224#102—41no—
225#101—24no—
226C17#1339411yescharacteristic, direct product factor, Sylow
227#41—21no—
228#41—21no—
229#41—21no—
230#41—21no—
231C2×Q8—22no—
232C2×Q8—41no—
233C2×Q8—41no—
234C2×Q8—41no—
235C2×Q8—41no—
236C2×Q8—41no—
237C2×Q8D8×C1711yescharacteristic
238C2×D4—21no—
239C2×D4D8×C1711yescharacteristic
240C22×C4—21no—
241C22×C4—41no—
242C22×C4—41no—
243C22×C4C2×D4×C1711yescharacteristic
244Q16—22no—
245Q16—22no—
246Q16—44no—
247Q16—41no—
248Q16—41no—
249SD16—44no—
250M16—21no—
251M16—21no—
252M16—22no—
253M16—41no—
254M16—41no—
255M16—41no—
256M16—41no—
257M16—41no—
258C2×C8—21no—
259C2×C8—41no—
260C2×C8—41no—
261C2×C8—41no—
262C2×C8—41no—
263C2×C8C2×D4×C1711yescharacteristic
264C2×C8C2×D4×C1711yescharacteristic
265C2×C8C2×D4×C1711yescharacteristic
266C2×C8#41×C1711yescharacteristic
267C2×C8#41×C1711yescharacteristic
268C2×C8#41×C1711yescharacteristic
269C4⋊C4—41no—
270C4⋊C4—41no—
271C16—22no—
272C16—41no—
273C23—21no—
274C23C17×#13511yescharacteristic
275Q8—21no—
276Q8—21no—
277Q8—42no—
278Q8—42no—
279Q8—81no—
280Q8—81no—
281D4—21no—
282D4—21no—
283D4—41no—
284D4—41no—
285C2×C4—21no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—42no—
289C2×C4—81no—
290C2×C4—81no—
291C2×C4—81no—
292C2×C4—161no—
293C2×C4C17×#12011yescharacteristic
294C2×C4C17×#12111yescharacteristic
295C2×C4C17×#12311yescharacteristic
296C2×C4C2×D8×C1711yescharacteristic
297C2×C4C17×AGL(1,ℤ/8)11yescharacteristic
298C2×C4C17×#13711yescharacteristic
299C8—41no—
300C8—42no—
301C8—81no—
302C8C17×#12111yescharacteristic
303C8C17×#12111yescharacteristic
304C8C17×#12311yescharacteristic
305C8C17×#12411yescharacteristic
306C22—21no—
307C22—21no—
308C22—41no—
309C22—41no—
310C22—41no—
311C22C17×#45211yescharacteristic
312C22C17×#46611yescharacteristic
313C22C17×#48211yescharacteristic
314C4—41no—
315C4—82no—
316C4—161no—
317C4C17×#39411yescharacteristic
318C4C17×#44711yescharacteristic
319C4C17×#46811yescharacteristic
320C4C17×#48011yescharacteristic
321C2—21no—
322C2—21no—
323C2—81no—
324C2C17×#203311yescharacteristic
325C2C17×#222211yescharacteristic
326C2C17×#222311yescharacteristic
subgroupG/H
center, socleC22×C17#466
commutator, Frattini, cosocleC22×C8C23×C17
prime radicalC2×#41×C17D4
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×#362C2semidirect
4. C2×C17×#358C2semidirect
7. C17×#1387C2semidirect
109. #13394C17direct (N × H)
144. C2×#368C2×C17semidirect
145. C2×#362C2×C17semidirect
146. C2×#358C2×C17semidirect
149. #1387C2×C17semidirect
226. C17#13394direct (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
C2×C17×#3682
C2×C17×#3622
C2×C17×#3582
C17×#21132
C17×#18162
C17×#13872
#1339417