Finite Group Databasebeta

← C17×#13391 #16871135

Subgroups — C17×#13391 #16871135

Order 4352.

390 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C17×#3067C211yesmaximal, characteristic
2C17×#2161C211yesmaximal, characteristic, complemented
3C17×#2148C211yesmaximal, characteristic, complemented
4C2×C17×#360C211yesmaximal, characteristic, complemented
5C17×#2115C211yesmaximal, characteristic, complemented
6C17×#1815C211yesmaximal, characteristic, complemented
7C17×#1383C211yesmaximal, characteristic, complemented
8C17×#575—21no—
9C2×C17×#135C2211yescharacteristic
10C2×C17×#131C2211yescharacteristic
11C2×C17×M32C2211yescharacteristic
12C2×C17×M32C2211yescharacteristic
13C17×#473—21no—
14C17×#472—21no—
15C17×#471—22no—
16C2×C17×#108C2211yescharacteristic
17C2×C17×#108C2211yescharacteristic
18C2×C17×#106C2211yescharacteristic
19C17×#417—21no—
20C17×#413—21no—
21C17×#368—22no—
22C17×#362—21no—
23C17×#361—21no—
24C17×#360—22no—
25C17×#349—22no—
26C17×#343—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×C17D411yescharacteristic
49C22×C8×C17—21no—
50C22×C8×C17C2311yescharacteristic
51C2×C4⋊C4×C17—21no—
52C17×M32—21no—
53C17×M32—21no—
54C17×M32—21no—
55C17×M32D412yes—
56C2×C16×C17—21no—
57C2×C16×C17—21no—
58C17×#108—21no—
59C17×#108—21no—
60C17×#108—21no—
61C17×#108D412yes—
62C17×#106—21no—
63C17×#106—21no—
64C17×#103—41no—
65C17×#102—41no—
66C17×#101—22no—
67C17×#100—22no—
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×C17—41no—
85C22×C4×C17C2×D411yescharacteristic
86Q16×C17—21no—
87Q16×C17—21no—
88Q16×C17—42no—
89SD16×C17—42no—
90SD16×C17—42no—
91SD16×C17—41no—
92SD16×C17—41no—
93D8×C17—21no—
94D8×C17—21no—
95D8×C17—42no—
96M16×C17—22no—
97M16×C17—21no—
98M16×C17—21no—
99M16×C17—41no—
100M16×C17—41no—
101M16×C17—41no—
102M16×C17—41no—
103M16×C17—41no—
104C2×C8×C17—21no—
105C2×C8×C17—41no—
106C2×C8×C17—41no—
107C2×C8×C17—41no—
108C2×C8×C17—41no—
109C2×C8×C17C2×D411yescharacteristic
110C2×C8×C17C2×D411yescharacteristic
111C2×C8×C17C2×D411yescharacteristic
112C2×C8×C17#4111yescharacteristic
113C2×C8×C17#4111yescharacteristic
114C2×C8×C17#4111yescharacteristic
115C4⋊C4×C17—41no—
116C4⋊C4×C17—41no—
117C16×C17—22no—
118C16×C17—41no—
119#13391C1711yesmaximal, characteristic, direct product factor, Sylow
120C23×C17—21no—
121C23×C17—41no—
122C23×C17#13511yescharacteristic
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—81no—
142C2×C4×C17—161no—
143C2×C4×C17#12011yescharacteristic
144C2×C4×C17#12111yescharacteristic
145C2×C4×C17#12311yescharacteristic
146C2×C4×C17C2×D811yescharacteristic
147C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
148C2×C4×C17#13711yescharacteristic
149C8×C17—41no—
150C8×C17—42no—
151C8×C17—81no—
152C8×C17#12111yescharacteristic
153C8×C17#12111yescharacteristic
154C8×C17#12311yescharacteristic
155C8×C17#12411yescharacteristic
156#3067C2×C1711yescharacteristic
157#2161C2×C1711yescharacteristic, complemented
158#2148C2×C1711yescharacteristic, complemented
159C2×#360C2×C1711yescharacteristic, complemented
160#2115C2×C1711yescharacteristic, complemented
161#1815C2×C1711yescharacteristic, complemented
162#1383C2×C1711yescharacteristic, complemented
163C22×C17—41no—
164C22×C17—41no—
165C22×C17—81no—
166C22×C17—81no—
167C22×C17—161no—
168C22×C17#45211yescharacteristic
169C22×C17#46611yescharacteristic
170C22×C17#48211yescharacteristic
171C4×C17—41no—
172C4×C17—81no—
173C4×C17—161no—
174C4×C17#39411yescharacteristic
175C4×C17#44711yescharacteristic
176C4×C17#46811yescharacteristic
177C4×C17#48011yescharacteristic
178#575—21no—
179C2×#135C22×C1711yescharacteristic
180C2×#131C22×C1711yescharacteristic
181C2×M32C22×C1711yescharacteristic
182C2×M32C22×C1711yescharacteristic
183#473—21no—
184#472—21no—
185#471—22no—
186C2×#108C22×C1711yescharacteristic
187C2×#108C22×C1711yescharacteristic
188C2×#106C22×C1711yescharacteristic
189#417—21no—
190#413—21no—
191#368—22no—
192#362—21no—
193#361—21no—
194#360—22no—
195#349—22no—
196#343—21no—
197C2×C17—21no—
198C2×C17—21no—
199C2×C17—21no—
200C2×C17—81no—
201C2×C17—161no—
202C2×C17#203311yescharacteristic
203C2×#41—21no—
204C2×#41D4×C1711yescharacteristic
205#137—22no—
206#137—41no—
207AGL(1,ℤ/8)—22no—
208AGL(1,ℤ/8)—41no—
209#135—21no—
210#135—21no—
211#135—21no—
212#135—21no—
213#135—42no—
214C2×Q16D4×C1711yescharacteristic
215C2×SD16—21no—
216C2×D8D4×C1711yescharacteristic
217#131—21no—
218#131—21no—
219#131—21no—
220#131—21no—
221C2×M16—21no—
222C2×M16—21no—
223C2×M16—21no—
224C2×M16D4×C1711yescharacteristic
225C22×C8—21no—
226C22×C8C23×C1711yescharacteristic
227C2×C4⋊C4—21no—
228M32—21no—
229M32—21no—
230M32—21no—
231M32D4×C1712yes—
232C2×C16—21no—
233C2×C16—21no—
234#108—21no—
235#108—21no—
236#108—21no—
237#108D4×C1712yes—
238#106—21no—
239#106—21no—
240#103—41no—
241#102—41no—
242#101—22no—
243#100—22no—
244C17#1339111yescharacteristic, direct product factor, Sylow
245#41—21no—
246#41—21no—
247#41—21no—
248#41—21no—
249#41—41no—
250#41—41no—
251#41—41no—
252#41—41no—
253C2×Q8—21no—
254C2×Q8D8×C1711yescharacteristic
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—41no—
258C2×D4D8×C1711yescharacteristic
259C22×C4—21no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4C2×D4×C1711yescharacteristic
263Q16—21no—
264Q16—21no—
265Q16—42no—
266SD16—42no—
267SD16—42no—
268SD16—41no—
269SD16—41no—
270D8—21no—
271D8—21no—
272D8—42no—
273M16—21no—
274M16—21no—
275M16—22no—
276M16—41no—
277M16—41no—
278M16—41no—
279M16—41no—
280M16—41no—
281C2×C8—21no—
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
292C4⋊C4—41no—
293C4⋊C4—41no—
294C16—22no—
295C16—41no—
296C23—21no—
297C23—41no—
298C23C17×#13511yescharacteristic
299Q8—21no—
300Q8—21no—
301Q8—41no—
302Q8—41no—
303D4—21no—
304D4—21no—
305D4—41no—
306D4—41no—
307D4—41no—
308D4—41no—
309D4—81no—
310D4—81no—
311C2×C4—21no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—161no—
319C2×C4C17×#12011yescharacteristic
320C2×C4C17×#12111yescharacteristic
321C2×C4C17×#12311yescharacteristic
322C2×C4C2×D8×C1711yescharacteristic
323C2×C4C17×AGL(1,ℤ/8)11yescharacteristic
324C2×C4C17×#13711yescharacteristic
325C8—41no—
326C8—42no—
327C8—81no—
328C8C17×#12111yescharacteristic
329C8C17×#12111yescharacteristic
330C8C17×#12311yescharacteristic
331C8C17×#12411yescharacteristic
332C22—41no—
333C22—41no—
334C22—81no—
335C22—81no—
336C22—161no—
337C22C17×#45211yescharacteristic
338C22C17×#46611yescharacteristic
339C22C17×#48211yescharacteristic
340C4—41no—
341C4—81no—
342C4—161no—
343C4C17×#39411yescharacteristic
344C4C17×#44711yescharacteristic
345C4C17×#46811yescharacteristic
346C4C17×#48011yescharacteristic
347C2—21no—
348C2—21no—
349C2—21no—
350C2—81no—
351C2—161no—
352C2C17×#203311yescharacteristic
subgroupG/H
center, socleC2×C17#2033
commutator, Frattini, cosocleC22×C8C23×C17
prime radicalC17×#3067C2
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C17 ◁ C22×C4×C17 ◁ C2×C17×#131 ◁ G

Complements

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

NH ≅ G/Ntype
2. C17×#2161C2semidirect
3. C17×#2148C2semidirect
4. C2×C17×#360C2semidirect
5. C17×#2115C2semidirect
6. C17×#1815C2semidirect
7. C17×#1383C2semidirect
119. #13391C17direct (N × H)
157. #2161C2×C17semidirect
158. #2148C2×C17semidirect
159. C2×#360C2×C17semidirect
160. #2115C2×C17semidirect
161. #1815C2×C17semidirect
162. #1383C2×C17semidirect
244. C17#13391direct (N × H)

Maximal subgroups

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

subgroupindex
C17×#30672
C17×#21612
C17×#21482
C2×C17×#3602
C17×#21152
C17×#18152
C17×#13832
#1339117