Finite Group Databasebeta

← C17×#13026 #16870770

Subgroups — C17×#13026 #16870770

Order 4352.

486 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
1C2×C17×#510C211yesmaximal, characteristic
2C17×#2943C211yesmaximal, characteristic
3C2×C17×#360C211yesmaximal, characteristic
4C17×#2141C211yesmaximal, characteristic, complemented
5C17×#1971C211yesmaximal, characteristic, complemented
6C17×#1386C211yesmaximal, characteristic, complemented
7C17×#1377C211yesmaximal, characteristic, complemented
8C2×C17×#135C2211yescharacteristic
9C22×Q16×C17C2211yescharacteristic
10C4×#41×C17—21no—
11C17×#510—22no—
12C17×#510C414yescomplemented
13C2×C17×Q32—21no—
14C2×C17×SD32—21no—
15C2×C17×M32C2211yescharacteristic
16C2×C17×M32C2211yescharacteristic
17C17×#442—21no—
18C17×#441—21no—
19C17×#440—22no—
20C17×#427C2211yescharacteristic
21C2×C17×#106C2211yescharacteristic
22C17×#416—21no—
23C2×C17×#103—21no—
24C2×C17×#97C2211yescharacteristic
25C17×#391—21no—
26C17×#360—22no—
27C17×#358—22no—
28C2×#41×C17—21no—
29C22×Q8×C17—21no—
30C17×#135—21no—
31C17×#135—21no—
32C17×#135C2×C412yes—
33C17×#135D412yes—
34C2×Q16×C17—21no—
35C2×Q16×C17—21no—
36C2×Q16×C17—21no—
37C2×Q16×C17—21no—
38C2×Q16×C17—21no—
39C2×Q16×C17C2×C412yescomplemented
40C2×Q16×C17D411yescharacteristic
41C2×SD16×C17—21no—
42C2×D8×C17D411yescharacteristic
43C22×C8×C17D411yescharacteristic
44C22×C8×C17C2311yescharacteristic
45C4×Q8×C17—22no—
46C4×D4×C17—22no—
47C4×D4×C17—42no—
48C17×#117—21no—
49C17×#117—41no—
50C2×C4⋊C4×C17—21no—
51C2×C42×C17—41no—
52C2×C42×C17D411yescharacteristic
53C17×Q32—24no—
54C17×SD32—24no—
55C17×M32—21no—
56C17×M32—21no—
57C17×M32—21no—
58C17×M32C2×C412yescomplemented
59C2×C16×C17—21no—
60C2×C16×C17—21no—
61C17×#107D412yes—
62C17×#106—21no—
63C17×#106—21no—
64C17×#106—21no—
65C17×#103—22no—
66C17×#103—42no—
67C17×#102—22no—
68C17×#97—21no—
69C17×#97—21no—
70C17×#95—42no—
71#41×C17—22no—
72#41×C17—22no—
73#41×C17—41no—
74#41×C17—41no—
75C2×Q8×C17—22no—
76C2×Q8×C17—21no—
77C2×Q8×C17—41no—
78C2×Q8×C17—41no—
79C2×Q8×C17—41no—
80C2×Q8×C17—41no—
81C2×Q8×C17—41no—
82C2×D4×C17—21no—
83C2×D4×C17—41no—
84C22×C4×C17—42no—
85C22×C4×C17—41no—
86C22×C4×C17—41no—
87C22×C4×C17—41no—
88C22×C4×C17D812yes—
89C22×C4×C17C2×D411yescharacteristic
90Q16×C17—22no—
91Q16×C17—22no—
92Q16×C17—21no—
93Q16×C17—41no—
94Q16×C17—41no—
95Q16×C17C22⋊C412yes—
96SD16×C17—22no—
97SD16×C17—22no—
98D8×C17—21no—
99D8×C17C22⋊C412yes—
100C2×C8×C17—21no—
101C2×C8×C17—21no—
102C2×C8×C17—21no—
103C2×C8×C17C22×C411yescharacteristic
104C2×C8×C17C2×D411yescharacteristic
105C2×C8×C17C2×D411yescharacteristic
106C2×C8×C17C2×D411yescharacteristic
107C2×C8×C17#4111yescharacteristic
108C2×C8×C17#4111yescharacteristic
109C4⋊C4×C17—22no—
110C4⋊C4×C17—42no—
111C4⋊C4×C17—41no—
112C4⋊C4×C17—41no—
113C22⋊C4×C17—42no—
114C22⋊C4×C17—41no—
115C42×C17—21no—
116C42×C17—21no—
117C42×C17—42no—
118C42×C17—41no—
119C16×C17—22no—
120C16×C17—41no—
121#13026C1711yesmaximal, characteristic, direct product factor, Sylow
122C23×C17—41no—
123C23×C17C2×D811yescharacteristic
124Q8×C17—22no—
125Q8×C17—41no—
126Q8×C17—42no—
127Q8×C17—42no—
128Q8×C17—81no—
129Q8×C17—81no—
130D4×C17—22no—
131D4×C17—42no—
132D4×C17—42no—
133D4×C17—41no—
134C2×C4×C17—22no—
135C2×C4×C17—41no—
136C2×C4×C17—42no—
137C2×C4×C17—42no—
138C2×C4×C17—42no—
139C2×C4×C17—42no—
140C2×C4×C17—42no—
141C2×C4×C17—84no—
142C2×C4×C17—81no—
143C2×C4×C17—81no—
144C2×C4×C17—82no—
145C2×C4×C17—81no—
146C2×C4×C17C4×D411yescharacteristic
147C2×C4×C17#12011yescharacteristic
148C2×C4×C17#12111yescharacteristic
149C2×C4×C17#13511yescharacteristic
150C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
151C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
152C8×C17—41no—
153C8×C17C2×C22⋊C411yescharacteristic
154C8×C17C4×D411yescharacteristic
155C8×C17#12111yescharacteristic
156C8×C17#12311yescharacteristic
157C2×#510C2×C1711yescharacteristic
158#2943C2×C1711yescharacteristic
159C2×#360C2×C1711yescharacteristic
160#2141C2×C1711yescharacteristic, complemented
161#1971C2×C1711yescharacteristic, complemented
162#1386C2×C1711yescharacteristic, complemented
163#1377C2×C1711yescharacteristic, complemented
164C22×C17—22no—
165C22×C17—42no—
166C22×C17—82no—
167C22×C17C4×D811yescharacteristic
168C22×C17#44711yescharacteristic
169C22×C17#45911yescharacteristic
170C4×C17—42no—
171C4×C17—42no—
172C4×C17—82no—
173C4×C17—82no—
174C4×C17—161no—
175C4×C17#38611yescharacteristic
176C4×C17#44211yescharacteristic
177C4×C17#44911yescharacteristic
178C4×C17#46311yescharacteristic
179C2×#135C22×C1711yescharacteristic
180C22×Q16C22×C1711yescharacteristic
181C4×#41—21no—
182#510—22no—
183#510C4×C1714yescomplemented
184C2×Q32—21no—
185C2×SD32—21no—
186C2×M32C22×C1711yescharacteristic
187C2×M32C22×C1711yescharacteristic
188#442—21no—
189#441—21no—
190#440—22no—
191#427C22×C1711yescharacteristic
192C2×#106C22×C1711yescharacteristic
193#416—21no—
194C2×#103—21no—
195C2×#97C22×C1711yescharacteristic
196#391—21no—
197#360—22no—
198#358—22no—
199C2×C17—21no—
200C2×C17—21no—
201C2×C17—82no—
202C2×C17#187911yescharacteristic
203C2×C17#219112yes—
204C2×#41—21no—
205C22×Q8—21no—
206#135—21no—
207#135—21no—
208#135C2×C4×C1712yes—
209#135D4×C1712yes—
210C2×Q16—21no—
211C2×Q16—21no—
212C2×Q16—21no—
213C2×Q16—21no—
214C2×Q16—21no—
215C2×Q16C2×C4×C1712yescomplemented
216C2×Q16D4×C1711yescharacteristic
217C2×SD16—21no—
218C2×D8D4×C1711yescharacteristic
219C22×C8D4×C1711yescharacteristic
220C22×C8C23×C1711yescharacteristic
221C4×Q8—22no—
222C4×D4—22no—
223C4×D4—42no—
224#117—21no—
225#117—41no—
226C2×C4⋊C4—21no—
227C2×C42—41no—
228C2×C42D4×C1711yescharacteristic
229Q32—24no—
230SD32—24no—
231M32—21no—
232M32—21no—
233M32—21no—
234M32C2×C4×C1712yescomplemented
235C2×C16—21no—
236C2×C16—21no—
237#107D4×C1712yes—
238#106—21no—
239#106—21no—
240#106—21no—
241#103—22no—
242#103—42no—
243#102—22no—
244#97—21no—
245#97—21no—
246#95—42no—
247C17#1302611yescharacteristic, direct product factor, Sylow
248#41—22no—
249#41—22no—
250#41—41no—
251#41—41no—
252C2×Q8—22no—
253C2×Q8—21no—
254C2×Q8—41no—
255C2×Q8—41no—
256C2×Q8—41no—
257C2×Q8—41no—
258C2×Q8—41no—
259C2×D4—21no—
260C2×D4—41no—
261C22×C4—42no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4D8×C1712yes—
266C22×C4C2×D4×C1711yescharacteristic
267Q16—21no—
268Q16—22no—
269Q16—22no—
270Q16—41no—
271Q16—41no—
272Q16C22⋊C4×C1712yes—
273SD16—22no—
274SD16—22no—
275D8—21no—
276D8C22⋊C4×C1712yes—
277C2×C8—21no—
278C2×C8—21no—
279C2×C8—21no—
280C2×C8C22×C4×C1711yescharacteristic
281C2×C8C2×D4×C1711yescharacteristic
282C2×C8C2×D4×C1711yescharacteristic
283C2×C8C2×D4×C1711yescharacteristic
284C2×C8#41×C1711yescharacteristic
285C2×C8#41×C1711yescharacteristic
286C4⋊C4—22no—
287C4⋊C4—42no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C22⋊C4—42no—
291C22⋊C4—41no—
292C42—21no—
293C42—21no—
294C42—42no—
295C42—41no—
296C16—22no—
297C16—41no—
298C23—41no—
299C23C2×D8×C1711yescharacteristic
300Q8—22no—
301Q8—41no—
302Q8—42no—
303Q8—42no—
304Q8—81no—
305Q8—81no—
306D4—22no—
307D4—42no—
308D4—42no—
309D4—41no—
310C2×C4—22no—
311C2×C4—41no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—84no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—82no—
321C2×C4—81no—
322C2×C4C4×D4×C1711yescharacteristic
323C2×C4C17×#12011yescharacteristic
324C2×C4C17×#12111yescharacteristic
325C2×C4C17×#13511yescharacteristic
326C2×C4C17×AGL(1,ℤ/8)11yescharacteristic
327C2×C4C17×AGL(1,ℤ/8)11yescharacteristic
328C8—41no—
329C8C2×C22⋊C4×C1711yescharacteristic
330C8C4×D4×C1711yescharacteristic
331C8C17×#12111yescharacteristic
332C8C17×#12311yescharacteristic
333C22—22no—
334C22—42no—
335C22—82no—
336C22C4×D8×C1711yescharacteristic
337C22C17×#44711yescharacteristic
338C22C17×#45911yescharacteristic
339C4—42no—
340C4—42no—
341C4—82no—
342C4—82no—
343C4—161no—
344C4C17×#38611yescharacteristic
345C4C17×#44211yescharacteristic
346C4C17×#44911yescharacteristic
347C4C17×#46311yescharacteristic
348C2—21no—
349C2—21no—
350C2—82no—
351C2C17×#187911yescharacteristic
352C2C17×#219112yes—
subgroupG/H
center, socleC22×C17#447
commutatorC2×C8C22×C4×C17
Frattini, cosocleC22×C8C23×C17
prime radicalC2×C17×#135C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C17 ◁ C22×C4×C17 ◁ C2×C17×#97 ◁ G

Complements

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

NH ≅ G/Ntype
4. C17×#2141C2semidirect
5. C17×#1971C2semidirect
6. C17×#1386C2semidirect
7. C17×#1377C2semidirect
12. C17×#510C4semidirect
39. C2×Q16×C17C2×C4semidirect
58. C17×M32C2×C4semidirect
121. #13026C17direct (N × H)
160. #2141C2×C17semidirect
161. #1971C2×C17semidirect
162. #1386C2×C17semidirect
163. #1377C2×C17semidirect
183. #510C4×C17semidirect
215. C2×Q16C2×C4×C17semidirect
234. M32C2×C4×C17semidirect
247. C17#13026direct (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×#29432
C2×C17×#3602
C17×#21412
C17×#19712
C17×#13862
C17×#13772
#1302617