Finite Group Databasebeta

← C17×#13382 #16871126

Subgroups — C17×#13382 #16871126

Order 4352.

446 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C17×#467C211yesmaximal, characteristic
2C2×C17×#367C211yesmaximal, characteristic, complemented
3C2×C17×#358C211yesmaximal, characteristic, complemented
4C2×C17×#358C211yesmaximal, characteristic, complemented
5C2×C17×C22⋊C16C211yesmaximal, characteristic
6C17×#1808C211yesmaximal, characteristic
7C17×#1380C211yesmaximal, characteristic, complemented
8C22×Q16×C17C2211yescharacteristic
9C23×C8×C17C2211yescharacteristic
10C2×C17×C22⋊Q8—21no—
11C22×C16×C17C2211yescharacteristic
12C22×C16×C17C2211yescharacteristic
13C17×#467—22no—
14C17×#467—22no—
15C2×C17×#107C2211yescharacteristic
16C2×C17×#107C2211yescharacteristic
17C2×C17×#107C2211yescharacteristic
18C2×C17×#103—21no—
19C17×#380—21no—
20C17×#367—22no—
21C17×#358—22no—
22C17×#358—22no—
23C17×C22⋊C16—22no—
24C17×#340—21no—
25C22×Q8×C17—21no—
26C23×C4×C17D411yescharacteristic
27C2×Q16×C17—21no—
28C2×Q16×C17—21no—
29C2×Q16×C17—21no—
30C2×Q16×C17—21no—
31C2×Q16×C17—21no—
32C2×Q16×C17D412yes—
33C22×C8×C17—21no—
34C22×C8×C17—21no—
35C22×C8×C17—21no—
36C22×C8×C17—21no—
37C22×C8×C17—21no—
38C22×C8×C17—21no—
39C22×C8×C17D411yescharacteristic
40C22×C8×C17C2311yescharacteristic
41C17×C22⋊Q8—24no—
42C17×C22⋊Q8—42no—
43C2×C4⋊C4×C17—21no—
44C2×C4⋊C4×C17—21no—
45C2×C4⋊C4×C17—21no—
46C2×C4⋊C4×C17—41no—
47C2×C22⋊C4×C17—41no—
48C2×C22⋊C4×C17—41no—
49C2×C16×C17—21no—
50C2×C16×C17—21no—
51C2×C16×C17—21no—
52C2×C16×C17—21no—
53C2×C16×C17—21no—
54C2×C16×C17D412yes—
55C17×#107—21no—
56C17×#107—21no—
57C17×#107—21no—
58C17×#107—21no—
59C17×#107—21no—
60C17×#107D412yes—
61C17×#103—24no—
62C17×#95—41no—
63C24×C17D811yescharacteristic
64C2×Q8×C17—22no—
65C2×Q8×C17—41no—
66C2×Q8×C17—41no—
67C2×Q8×C17—41no—
68C2×Q8×C17—41no—
69C2×Q8×C17—41no—
70C22×C4×C17—21no—
71C22×C4×C17—21no—
72C22×C4×C17—21no—
73C22×C4×C17—21no—
74C22×C4×C17—21no—
75C22×C4×C17—21no—
76C22×C4×C17—41no—
77C22×C4×C17—41no—
78C22×C4×C17—41no—
79C22×C4×C17—41no—
80C22×C4×C17D811yescharacteristic
81C22×C4×C17C2×D411yescharacteristic
82Q16×C17—22no—
83Q16×C17—22no—
84Q16×C17—41no—
85Q16×C17—41no—
86C2×C8×C17—21no—
87C2×C8×C17—21no—
88C2×C8×C17—21no—
89C2×C8×C17—41no—
90C2×C8×C17—41no—
91C2×C8×C17—41no—
92C2×C8×C17—41no—
93C2×C8×C17C2×D411yescharacteristic
94C2×C8×C17C2×D411yescharacteristic
95C2×C8×C17C2×D411yescharacteristic
96C2×C8×C17#4111yescharacteristic
97C2×C8×C17#4111yescharacteristic
98C2×C8×C17#4111yescharacteristic
99C4⋊C4×C17—22no—
100C4⋊C4×C17—44no—
101C4⋊C4×C17—41no—
102C4⋊C4×C17—41no—
103C4⋊C4×C17—41no—
104C4⋊C4×C17—41no—
105C4⋊C4×C17—41no—
106C22⋊C4×C17—44no—
107C22⋊C4×C17—82no—
108C16×C17—22no—
109C16×C17—41no—
110#13382C1711yesmaximal, characteristic, direct product factor, Sylow
111C23×C17—21no—
112C23×C17—21no—
113C23×C17—21no—
114C23×C17—21no—
115C23×C17—21no—
116C23×C17—21no—
117C23×C17SD3212yes—
118C23×C17C2×D811yescharacteristic
119Q8×C17—42no—
120Q8×C17—42no—
121Q8×C17—81no—
122Q8×C17—81no—
123C2×C4×C17—21no—
124C2×C4×C17—21no—
125C2×C4×C17—21no—
126C2×C4×C17—41no—
127C2×C4×C17—41no—
128C2×C4×C17—41no—
129C2×C4×C17—41no—
130C2×C4×C17—42no—
131C2×C4×C17—42no—
132C2×C4×C17—81no—
133C2×C4×C17—81no—
134C2×C4×C17—81no—
135C2×C4×C17—81no—
136C2×C4×C17—81no—
137C2×C4×C17—81no—
138C2×C4×C17—81no—
139C2×C4×C17—81no—
140C2×C4×C17—81no—
141C2×C4×C17—81no—
142C2×C4×C17#12011yescharacteristic
143C2×C4×C17#12111yescharacteristic
144C2×C4×C17#12311yescharacteristic
145C2×C4×C17#13511yescharacteristic
146C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
147C2×C4×C17#13711yescharacteristic
148C8×C17—41no—
149C8×C17#12111yescharacteristic
150C8×C17#12111yescharacteristic
151C8×C17#12311yescharacteristic
152C8×C17#12411yescharacteristic
153C2×#467C2×C1711yescharacteristic
154C2×#367C2×C1711yescharacteristic, complemented
155C2×#358C2×C1711yescharacteristic, complemented
156C2×#358C2×C1711yescharacteristic, complemented
157C2×C22⋊C16C2×C1711yescharacteristic
158#1808C2×C1711yescharacteristic
159#1380C2×C1711yescharacteristic, complemented
160C22×C17—22no—
161C22×C17—22no—
162C22×C17—22no—
163C22×C17—41no—
164C22×C17—41no—
165C22×C17—41no—
166C22×C17—41no—
167C22×C17#44711yescharacteristic
168C22×C17#46611yescharacteristic
169C22×C17#48011yescharacteristic
170C22×C17C2×SD3211yescharacteristic
171C22×C17#50811yescharacteristic
172C22×C17#51011yescharacteristic
173C22×C17#51011yescharacteristic
174C4×C17—41no—
175C4×C17—82no—
176C4×C17—82no—
177C4×C17—161no—
178C4×C17—161no—
179C4×C17#39411yescharacteristic
180C4×C17#45211yescharacteristic
181C4×C17#46811yescharacteristic
182C4×C17#48211yescharacteristic
183C22×Q16C22×C1711yescharacteristic
184C23×C8C22×C1711yescharacteristic
185C2×C22⋊Q8—21no—
186C22×C16C22×C1711yescharacteristic
187C22×C16C22×C1711yescharacteristic
188#467—22no—
189#467—22no—
190C2×#107C22×C1711yescharacteristic
191C2×#107C22×C1711yescharacteristic
192C2×#107C22×C1711yescharacteristic
193C2×#103—21no—
194#380—21no—
195#367—22no—
196#358—22no—
197#358—22no—
198C22⋊C16—22no—
199#340—21no—
200C2×C17—42no—
201C2×C17#203311yescharacteristic
202C2×C17#218511yescharacteristic
203C2×C17#218911yescharacteristic
204C2×C17#221711yescharacteristic
205C2×C17#221911yescharacteristic
206C2×C17#223511yescharacteristic
207C2×C17#223711yescharacteristic
208C22×Q8—21no—
209C23×C4D4×C1711yescharacteristic
210C2×Q16—21no—
211C2×Q16—21no—
212C2×Q16—21no—
213C2×Q16—21no—
214C2×Q16—21no—
215C2×Q16D4×C1712yes—
216C22×C8—21no—
217C22×C8—21no—
218C22×C8—21no—
219C22×C8—21no—
220C22×C8—21no—
221C22×C8—21no—
222C22×C8D4×C1711yescharacteristic
223C22×C8C23×C1711yescharacteristic
224C22⋊Q8—24no—
225C22⋊Q8—42no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—41no—
230C2×C22⋊C4—41no—
231C2×C22⋊C4—41no—
232C2×C16—21no—
233C2×C16—21no—
234C2×C16—21no—
235C2×C16—21no—
236C2×C16—21no—
237C2×C16D4×C1712yes—
238#107—21no—
239#107—21no—
240#107—21no—
241#107—21no—
242#107—21no—
243#107D4×C1712yes—
244#103—24no—
245#95—41no—
246C17#1338211yescharacteristic, direct product factor, Sylow
247C24D8×C1711yescharacteristic
248C2×Q8—22no—
249C2×Q8—41no—
250C2×Q8—41no—
251C2×Q8—41no—
252C2×Q8—41no—
253C2×Q8—41no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4D8×C1711yescharacteristic
265C22×C4C2×D4×C1711yescharacteristic
266Q16—22no—
267Q16—22no—
268Q16—41no—
269Q16—41no—
270C2×C8—21no—
271C2×C8—21no—
272C2×C8—21no—
273C2×C8—41no—
274C2×C8—41no—
275C2×C8—41no—
276C2×C8—41no—
277C2×C8C2×D4×C1711yescharacteristic
278C2×C8C2×D4×C1711yescharacteristic
279C2×C8C2×D4×C1711yescharacteristic
280C2×C8#41×C1711yescharacteristic
281C2×C8#41×C1711yescharacteristic
282C2×C8#41×C1711yescharacteristic
283C4⋊C4—22no—
284C4⋊C4—44no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C22⋊C4—44no—
291C22⋊C4—82no—
292C16—22no—
293C16—41no—
294C23—21no—
295C23—21no—
296C23—21no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23C17×SD3212yes—
301C23C2×D8×C1711yescharacteristic
302Q8—42no—
303Q8—42no—
304Q8—81no—
305Q8—81no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4—81no—
324C2×C4—81no—
325C2×C4C17×#12011yescharacteristic
326C2×C4C17×#12111yescharacteristic
327C2×C4C17×#12311yescharacteristic
328C2×C4C17×#13511yescharacteristic
329C2×C4C17×AGL(1,ℤ/8)11yescharacteristic
330C2×C4C17×#13711yescharacteristic
331C8—41no—
332C8C17×#12111yescharacteristic
333C8C17×#12111yescharacteristic
334C8C17×#12311yescharacteristic
335C8C17×#12411yescharacteristic
336C22—22no—
337C22—22no—
338C22—22no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22C17×#44711yescharacteristic
344C22C17×#46611yescharacteristic
345C22C17×#48011yescharacteristic
346C22C2×C17×SD3211yescharacteristic
347C22C17×#50811yescharacteristic
348C22C17×#51011yescharacteristic
349C22C17×#51011yescharacteristic
350C4—41no—
351C4—82no—
352C4—82no—
353C4—161no—
354C4—161no—
355C4C17×#39411yescharacteristic
356C4C17×#45211yescharacteristic
357C4C17×#46811yescharacteristic
358C4C17×#48211yescharacteristic
359C2—42no—
360C2C17×#203311yescharacteristic
361C2C17×#218511yescharacteristic
362C2C17×#218911yescharacteristic
363C2C17×#221711yescharacteristic
364C2C17×#221911yescharacteristic
365C2C17×#223511yescharacteristic
366C2C17×#223711yescharacteristic
subgroupG/H
center, socleC23×C17C2×D8
commutator, Frattini, cosocleC22×C8C23×C17
prime radicalC24×C17D8
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C17 ◁ C23×C4×C17 ◁ C23×C8×C17 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C17×#367C2semidirect
3. C2×C17×#358C2semidirect
4. C2×C17×#358C2semidirect
7. C17×#1380C2semidirect
110. #13382C17direct (N × H)
154. C2×#367C2×C17semidirect
155. C2×#358C2×C17semidirect
156. C2×#358C2×C17semidirect
159. #1380C2×C17semidirect
246. C17#13382direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C17×#4672
C2×C17×#3672
C2×C17×#3582
C2×C17×C22⋊C162
C17×#18082
C17×#13802
#1338217