Finite Group Databasebeta

← C17×#10939 #16868683

Subgroups — C17×#10939 #16868683

Order 4352.

1058 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C17×#100C212yesmaximal
2C17×#2873C211yesmaximal, characteristic, complemented
3C17×#2309C211yesmaximal, characteristic
4C2×C17×#344C212yesmaximal, complemented
5C17×#1742C211yesmaximal, characteristic, complemented
6C23×D4×C17C2211yescharacteristic
7C22×M16×C17C2212yes—
8C22×M16×C17C2212yes—
9C2×C17×#117C2211yescharacteristic
10C2×C17×#117C2211yescharacteristic
11C2×C17×#100—24no—
12C2×C17×#100—24no—
13C2×C17×#100C418yescomplemented
14C17×#405—24no—
15C4×M16×C17—22no—
16C17×#390—22no—
17C17×#390—22no—
18C17×#379C414yes—
19C17×#344—24no—
20C17×#343—22no—
21C25×C17C2×C412yes—
22C22×D4×C17—21no—
23C22×D4×C17—21no—
24C22×D4×C17—22no—
25C22×D4×C17—22no—
26C22×D4×C17—22no—
27C22×D4×C17—22no—
28C22×D4×C17—22no—
29C22×D4×C17C2×C414yes—
30C23×C4×C17C2311yescharacteristic
31C2×M16×C17—22no—
32C2×M16×C17—22no—
33C2×M16×C17—22no—
34C2×M16×C17—22no—
35C2×M16×C17—22no—
36C2×M16×C17—22no—
37C2×M16×C17—22no—
38C2×M16×C17—22no—
39C2×M16×C17C2×C414yes—
40C2×M16×C17C2×C414yes—
41C2×M16×C17D414yes—
42C2×M16×C17D414yes—
43C22×C8×C17—22no—
44C22×C8×C17—22no—
45C17×#117—22no—
46C17×#117—22no—
47C17×#117—22no—
48C17×#117—22no—
49C2×C4⋊C4×C17—21no—
50C2×C4⋊C4×C17D412yes—
51C2×C22⋊C4×C17—28no—
52C2×C22⋊C4×C17C2×C412yes—
53C2×C22⋊C4×C17C2×C412yes—
54C2×C42×C17—21no—
55C2×C42×C17D412yes—
56C17×#100—216no—
57C17×#97—24no—
58C4×C8×C17—24no—
59C24×C17—22no—
60C24×C17—22no—
61C24×C17—24no—
62C24×C17—24no—
63C24×C17—84no—
64C24×C17C4214yes—
65C24×C17C22×C411yescharacteristic
66C2×D4×C17—24no—
67C2×D4×C17—24no—
68C2×D4×C17—24no—
69C2×D4×C17—24no—
70C2×D4×C17—24no—
71C2×D4×C17—24no—
72C2×D4×C17—41no—
73C2×D4×C17—42no—
74C2×D4×C17—42no—
75C2×D4×C17—42no—
76C2×D4×C17—42no—
77C2×D4×C17—41no—
78C2×D4×C17—41no—
79C2×D4×C17—42no—
80C2×D4×C17—42no—
81C2×D4×C17—41no—
82C22×C4×C17—22no—
83C22×C4×C17C22⋊C414yes—
84C22×C4×C17C22×C412yes—
85C22×C4×C17C2×D412yes—
86C22×C4×C17C2×D412yes—
87C22×C4×C17C2×D411yescharacteristic
88C22×C4×C17C2×D411yescharacteristic
89C22×C4×C17#4112yes—
90C22×C4×C17#4112yes—
91C22×C4×C17#4112yes—
92M16×C17—24no—
93M16×C17—24no—
94M16×C17—24no—
95M16×C17—24no—
96M16×C17—24no—
97M16×C17—42no—
98M16×C17—42no—
99M16×C17C22⋊C418yescomplemented
100C2×C8×C17—24no—
101C2×C8×C17—24no—
102C2×C8×C17—24no—
103C2×C8×C17—24no—
104C2×C8×C17—42no—
105C2×C8×C17—42no—
106C4⋊C4×C17—24no—
107C4⋊C4×C17—42no—
108C22⋊C4×C17—24no—
109C22⋊C4×C17—24no—
110C22⋊C4×C17—88no—
111C42×C17—22no—
112C42×C17—22no—
113C42×C17—41no—
114C42×C17—41no—
115#10939C1711yesmaximal, characteristic, direct product factor, Sylow
116C23×C17—24no—
117C23×C17—28no—
118C23×C17—42no—
119C23×C17—48no—
120C23×C17—42no—
121C23×C17—44no—
122C23×C17—42no—
123C23×C17—88no—
124C23×C17—84no—
125C23×C17—84no—
126C23×C17—88no—
127C23×C17C2×C4211yescharacteristic
128C23×C17C2×C22⋊C411yescharacteristic
129C23×C17#11711yescharacteristic
130C23×C17C4×D412yes—
131C23×C17C4×D412yes—
132D4×C17—44no—
133D4×C17—44no—
134D4×C17—44no—
135D4×C17—44no—
136C2×C4×C17—24no—
137C2×C4×C17—44no—
138C2×C4×C17—44no—
139C2×C4×C17—42no—
140C2×C4×C17C2×C22⋊C412yes—
141C2×C4×C17#11712yes—
142C2×C4×C17C4×D412yes—
143C2×C4×C17C4×D412yes—
144C2×C4×C17C4×D412yes—
145C2×C4×C17C4×D412yes—
146C2×C4×C17#12011yescharacteristic
147C2×C4×C17#12112yes—
148C2×C4×C17#12112yes—
149C2×C4×C17#12112yes—
150C2×C4×C17#12312yes—
151C2×C4×C17#12311yescharacteristic
152C2×C4×C17#12411yescharacteristic
153C2×C4×C17#12412yes—
154C2×C4×C17#12612yes—
155C2×C4×C17#12711yescharacteristic
156C8×C17—28no—
157C8×C17—44no—
158C22×#100C2×C1712yes—
159#2873C2×C1711yescharacteristic, complemented
160#2309C2×C1711yescharacteristic
161C2×#344C2×C1712yescomplemented
162#1742C2×C1711yescharacteristic, complemented
163C22×C17—22no—
164C22×C17—24no—
165C22×C17—41no—
166C22×C17—41no—
167C22×C17—42no—
168C22×C17—48no—
169C22×C17—44no—
170C22×C17—88no—
171C22×C17—84no—
172C22×C17—88no—
173C22×C17—84no—
174C22×C17C4×C22⋊C412yes—
175C22×C17C4×C22⋊C411yescharacteristic
176C22×C17#38611yescharacteristic
177C22×C17#38812yes—
178C22×C17#39011yescharacteristic
179C4×C17—44no—
180C4×C17—82no—
181C4×C17#38612yes—
182C4×C17#38812yes—
183C4×C17#38812yes—
184C4×C17#39012yes—
185C23×D4C22×C1711yescharacteristic
186C22×M16C22×C1712yes—
187C22×M16C22×C1712yes—
188C2×#117C22×C1711yescharacteristic
189C2×#117C22×C1711yescharacteristic
190C2×#100—24no—
191C2×#100—24no—
192C2×#100C4×C1718yescomplemented
193#405—24no—
194C4×M16—22no—
195#390—22no—
196#390—22no—
197#379C4×C1714yes—
198#344—24no—
199#343—22no—
200C2×C17—21no—
201C2×C17—21no—
202C2×C17—22no—
203C2×C17—22no—
204C2×C17—84no—
205C2×C17#143711yescharacteristic
206C2×C17#191412yes—
207C25C2×C4×C1712yes—
208C22×D4—21no—
209C22×D4—21no—
210C22×D4—22no—
211C22×D4—22no—
212C22×D4—22no—
213C22×D4—22no—
214C22×D4—22no—
215C22×D4C2×C4×C1714yes—
216C23×C4C23×C1711yescharacteristic
217C2×M16—22no—
218C2×M16—22no—
219C2×M16—22no—
220C2×M16—22no—
221C2×M16—22no—
222C2×M16—22no—
223C2×M16—22no—
224C2×M16—22no—
225C2×M16C2×C4×C1714yes—
226C2×M16C2×C4×C1714yes—
227C2×M16D4×C1714yes—
228C2×M16D4×C1714yes—
229C22×C8—22no—
230C22×C8—22no—
231#117—22no—
232#117—22no—
233#117—22no—
234#117—22no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4D4×C1712yes—
237C2×C22⋊C4—28no—
238C2×C22⋊C4C2×C4×C1712yes—
239C2×C22⋊C4C2×C4×C1712yes—
240C2×C42—21no—
241C2×C42D4×C1712yes—
242#100—216no—
243#97—24no—
244C4×C8—24no—
245C17#1093911yescharacteristic, direct product factor, Sylow
246C24—22no—
247C24—22no—
248C24—24no—
249C24—24no—
250C24—84no—
251C24C42×C1714yes—
252C24C22×C4×C1711yescharacteristic
253C2×D4—24no—
254C2×D4—24no—
255C2×D4—24no—
256C2×D4—24no—
257C2×D4—24no—
258C2×D4—24no—
259C2×D4—42no—
260C2×D4—41no—
261C2×D4—41no—
262C2×D4—42no—
263C2×D4—42no—
264C2×D4—41no—
265C2×D4—41no—
266C2×D4—42no—
267C2×D4—42no—
268C2×D4—42no—
269C22×C4—22no—
270C22×C4C22⋊C4×C1714yes—
271C22×C4C22×C4×C1712yes—
272C22×C4C2×D4×C1712yes—
273C22×C4C2×D4×C1711yescharacteristic
274C22×C4C2×D4×C1712yes—
275C22×C4C2×D4×C1711yescharacteristic
276C22×C4#41×C1712yes—
277C22×C4#41×C1712yes—
278C22×C4#41×C1712yes—
279M16—24no—
280M16—24no—
281M16—24no—
282M16—24no—
283M16—24no—
284M16—42no—
285M16—42no—
286M16C22⋊C4×C1718yescomplemented
287C2×C8—24no—
288C2×C8—24no—
289C2×C8—24no—
290C2×C8—24no—
291C2×C8—42no—
292C2×C8—42no—
293C4⋊C4—24no—
294C4⋊C4—42no—
295C22⋊C4—24no—
296C22⋊C4—24no—
297C22⋊C4—88no—
298C42—22no—
299C42—22no—
300C42—41no—
301C42—41no—
302C23—24no—
303C23—28no—
304C23—42no—
305C23—48no—
306C23—42no—
307C23—44no—
308C23—42no—
309C23—88no—
310C23—84no—
311C23—84no—
312C23—88no—
313C23C2×C42×C1711yescharacteristic
314C23C2×C22⋊C4×C1711yescharacteristic
315C23C17×#11711yescharacteristic
316C23C4×D4×C1712yes—
317C23C4×D4×C1712yes—
318D4—44no—
319D4—44no—
320D4—44no—
321D4—44no—
322C2×C4—24no—
323C2×C4—44no—
324C2×C4—44no—
325C2×C4—42no—
326C2×C4C2×C22⋊C4×C1712yes—
327C2×C4C17×#11712yes—
328C2×C4C4×D4×C1712yes—
329C2×C4C4×D4×C1712yes—
330C2×C4C4×D4×C1712yes—
331C2×C4C4×D4×C1712yes—
332C2×C4C17×#12011yescharacteristic
333C2×C4C17×#12112yes—
334C2×C4C17×#12112yes—
335C2×C4C17×#12112yes—
336C2×C4C17×#12312yes—
337C2×C4C17×#12311yescharacteristic
338C2×C4C17×#12411yescharacteristic
339C2×C4C17×#12412yes—
340C2×C4C17×#12612yes—
341C2×C4C17×#12711yescharacteristic
342C8—28no—
343C8—44no—
344C22—22no—
345C22—24no—
346C22—41no—
347C22—41no—
348C22—42no—
349C22—48no—
350C22—44no—
351C22—88no—
352C22—84no—
353C22—88no—
354C22—84no—
355C22C4×C22⋊C4×C1712yes—
356C22C4×C22⋊C4×C1711yescharacteristic
357C22C17×#38611yescharacteristic
358C22C17×#38812yes—
359C22C17×#39011yescharacteristic
360C4—44no—
361C4—82no—
362C4C17×#38612yes—
363C4C17×#38812yes—
364C4C17×#38812yes—
365C4C17×#39012yes—
366C2—21no—
367C2—21no—
368C2—22no—
369C2—22no—
370C2—84no—
371C2C17×#143711yescharacteristic
372C2C17×#191412yes—
subgroupG/H
center, socleC22×C17#386
commutatorC23C2×C42×C17
Frattini, cosocleC23×C4C23×C17
prime radicalC23×D4×C17C22
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C17 ◁ C23×C4×C17 ◁ G

Complements

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

NH ≅ G/Ntype
2. C17×#2873C2semidirect
4. C2×C17×#344C2semidirect
5. C17×#1742C2semidirect
13. C2×C17×#100C4semidirect
99. M16×C17C22⋊C4semidirect
115. #10939C17direct (N × H)
159. #2873C2×C17semidirect
161. C2×#344C2×C17semidirect
162. #1742C2×C17semidirect
192. C2×#100C4×C17semidirect
245. C17#10939direct (N × H)
286. M16C22⋊C4×C17semidirect

Maximal subgroups

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

subgroupindex
C22×C17×#1002
C17×#28732
C17×#23092
C2×C17×#3442
C17×#17422
#1093917