Finite Group Databasebeta

← C17×#7633 #16865377

Subgroups — C17×#7633 #16865377

Order 4352.

640 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C17×#121C211yesmaximal, characteristic
2C17×#1749C211yesmaximal, characteristic, complemented
3C17×#1728C211yesmaximal, characteristic, complemented
4C17×#1271C212yesmaximal, complemented
5C17×#1270C212yesmaximal, complemented
6C22×M16×C17—21no—
7C2×C17×#121C411yescharacteristic
8C2×C4×D4×C17—21no—
9C2×C4×D4×C17C411yescharacteristic
10C22×C42×C17C2211yescharacteristic
11C2×C17×C22⋊C8—21no—
12C2×C17×#97—21no—
13C17×#390C2211yescharacteristic
14C17×#389C2211yescharacteristic
15C17×#388—21no—
16C17×#386—21no—
17C17×#380C411yescharacteristic
18C4×C4⋊C4×C17C411yescharacteristic
19C4×C22⋊C4×C17—21no—
20C17×#336—21no—
21C17×#336C2212yes—
22C17×#336C2212yes—
23C22×D4×C17—21no—
24C22×D4×C17C2×C411yescharacteristic
25C23×C4×C17—21no—
26C23×C4×C17C2×C411yescharacteristic
27C23×C4×C17D411yescharacteristic
28C23×C4×C17D411yescharacteristic
29C2×M16×C17—24no—
30C2×M16×C17—42no—
31C2×M16×C17—42no—
32C22×C8×C17—22no—
33C22×C8×C17—22no—
34C17×#121—22no—
35C17×#121—22no—
36C4×D4×C17—42no—
37C4×D4×C17—44no—
38C2×C4⋊C4×C17—21no—
39C2×C4⋊C4×C17C2×C411yescharacteristic
40C2×C4⋊C4×C17C2×C411yescharacteristic
41C2×C4⋊C4×C17C2×C411yescharacteristic
42C2×C22⋊C4×C17—21no—
43C2×C22⋊C4×C17—21no—
44C2×C22⋊C4×C17—21no—
45C2×C22⋊C4×C17—21no—
46C2×C22⋊C4×C17—21no—
47C2×C42×C17—21no—
48C2×C42×C17—42no—
49C2×C42×C17C2×C411yescharacteristic
50C2×C42×C17D411yescharacteristic
51C2×C42×C17D411yescharacteristic
52C2×C42×C17C2311yescharacteristic
53C17×C22⋊C8—24no—
54C17×#97—42no—
55C17×#95—21no—
56C17×#95—21no—
57C17×#95—21no—
58C24×C17—21no—
59C24×C17C22⋊C411yescharacteristic
60C2×D4×C17—24no—
61C2×D4×C17—21no—
62C2×D4×C17—41no—
63C2×D4×C17—41no—
64C2×D4×C17—42no—
65C2×D4×C17—42no—
66C2×D4×C17M1612yescomplemented
67C22×C4×C17—22no—
68C22×C4×C17—22no—
69C22×C4×C17—21no—
70C22×C4×C17—21no—
71C22×C4×C17—21no—
72C22×C4×C17—22no—
73C22×C4×C17—21no—
74C22×C4×C17—21no—
75C22×C4×C17—22no—
76C22×C4×C17—21no—
77C22×C4×C17—21no—
78C22×C4×C17—41no—
79C22×C4×C17—41no—
80C22×C4×C17—41no—
81C22×C4×C17—42no—
82C22×C4×C17—42no—
83C22×C4×C17—42no—
84C22×C4×C17C22⋊C411yescharacteristic
85C22×C4×C17C22⋊C411yescharacteristic
86C22×C4×C17C22⋊C411yescharacteristic
87C22×C4×C17C22×C411yescharacteristic
88C22×C4×C17C2×D411yescharacteristic
89C22×C4×C17C2×D411yescharacteristic
90M16×C17—48no—
91C2×C8×C17—24no—
92C2×C8×C17—24no—
93C2×C8×C17—42no—
94C2×C8×C17—42no—
95C2×C8×C17—42no—
96C2×C8×C17—42no—
97C4⋊C4×C17—21no—
98C4⋊C4×C17—41no—
99C4⋊C4×C17—41no—
100C4⋊C4×C17—42no—
101C4⋊C4×C17M1612yescomplemented
102C22⋊C4×C17—24no—
103C22⋊C4×C17—42no—
104C22⋊C4×C17—42no—
105C22⋊C4×C17—41no—
106C22⋊C4×C17—42no—
107C22⋊C4×C17—41no—
108C42×C17—22no—
109C42×C17—22no—
110C42×C17—41no—
111C42×C17—41no—
112C42×C17—42no—
113#7633C1711yesmaximal, characteristic, direct product factor, Sylow
114C23×C17—21no—
115C23×C17—21no—
116C23×C17—21no—
117C23×C17—21no—
118C23×C17—21no—
119C23×C17—21no—
120C23×C17—22no—
121C23×C17—41no—
122C23×C17—41no—
123C23×C17—41no—
124C23×C17—41no—
125C23×C17—41no—
126C23×C17—41no—
127C23×C17#10412yes—
128C23×C17C2×C22⋊C411yescharacteristic
129D4×C17—42no—
130D4×C17—42no—
131D4×C17—48no—
132C2×C4×C17—24no—
133C2×C4×C17—24no—
134C2×C4×C17—21no—
135C2×C4×C17—21no—
136C2×C4×C17—21no—
137C2×C4×C17—21no—
138C2×C4×C17—21no—
139C2×C4×C17—21no—
140C2×C4×C17—21no—
141C2×C4×C17—21no—
142C2×C4×C17—21no—
143C2×C4×C17—21no—
144C2×C4×C17—21no—
145C2×C4×C17—22no—
146C2×C4×C17—21no—
147C2×C4×C17—21no—
148C2×C4×C17—44no—
149C2×C4×C17—42no—
150C2×C4×C17—42no—
151C2×C4×C17—41no—
152C2×C4×C17—41no—
153C2×C4×C17—41no—
154C2×C4×C17—41no—
155C2×C4×C17—41no—
156C2×C4×C17—41no—
157C2×C4×C17—41no—
158C2×C4×C17—41no—
159C2×C4×C17—84no—
160C2×C4×C17#9912yes—
161C2×C4×C17#10412yes—
162C2×C4×C17C2×M1611yescharacteristic
163C2×C4×C17C2×M1611yescharacteristic
164C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
165C2×C4×C17AGL(1,ℤ/8)12yes—
166C2×C4×C17#13711yescharacteristic
167C8×C17—44no—
168C8×C17—44no—
169C4×#121C2×C1711yescharacteristic
170#1749C2×C1711yescharacteristic, complemented
171#1728C2×C1711yescharacteristic, complemented
172#1271C2×C1712yescomplemented
173#1270C2×C1712yescomplemented
174C22×C17—22no—
175C22×C17—22no—
176C22×C17—22no—
177C22×C17—41no—
178C22×C17—41no—
179C22×C17—41no—
180C22×C17—41no—
181C22×C17—42no—
182C22×C17—42no—
183C22×C17—42no—
184C22×C17—81no—
185C22×C17—81no—
186C22×C17—81no—
187C22×C17—81no—
188C22×C17#40711yescharacteristic
189C22×C17C2×#9911yescharacteristic
190C22×C17#41311yescharacteristic
191C22×C17#41711yescharacteristic
192C22×C17#41811yescharacteristic
193C22×C17C2×#10411yescharacteristic
194C22×C17C2×#10411yescharacteristic
195C4×C17—21no—
196C4×C17—21no—
197C4×C17—21no—
198C4×C17—22no—
199C4×C17—21no—
200C4×C17—22no—
201C4×C17—22no—
202C4×C17—41no—
203C4×C17—42no—
204C4×C17—81no—
205C4×C17—81no—
206C22×M16—21no—
207C2×#121C4×C1711yescharacteristic
208C2×C4×D4—21no—
209C2×C4×D4C4×C1711yescharacteristic
210C22×C42C22×C1711yescharacteristic
211C2×C22⋊C8—21no—
212C2×#97—21no—
213#390C22×C1711yescharacteristic
214#389C22×C1711yescharacteristic
215#388—21no—
216#386—21no—
217#380C4×C1711yescharacteristic
218C4×C4⋊C4C4×C1711yescharacteristic
219C4×C22⋊C4—21no—
220#336—21no—
221#336C22×C1712yes—
222#336C22×C1712yes—
223C2×C17—42no—
224C2×C17—82no—
225C2×C17#146511yescharacteristic
226C2×C17#148911yescharacteristic
227C2×C17#149011yescharacteristic
228C2×C17#150411yescharacteristic
229C2×C17#150711yescharacteristic
230C2×C17#152411yescharacteristic
231C2×C17#155711yescharacteristic
232C22×D4—21no—
233C22×D4C2×C4×C1711yescharacteristic
234C23×C4—21no—
235C23×C4C2×C4×C1711yescharacteristic
236C23×C4D4×C1711yescharacteristic
237C23×C4D4×C1711yescharacteristic
238C2×M16—24no—
239C2×M16—42no—
240C2×M16—42no—
241C22×C8—22no—
242C22×C8—22no—
243#121—22no—
244#121—22no—
245C4×D4—42no—
246C4×D4—44no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4C2×C4×C1711yescharacteristic
249C2×C4⋊C4C2×C4×C1711yescharacteristic
250C2×C4⋊C4C2×C4×C1711yescharacteristic
251C2×C22⋊C4—21no—
252C2×C22⋊C4—21no—
253C2×C22⋊C4—21no—
254C2×C22⋊C4—21no—
255C2×C22⋊C4—21no—
256C2×C42—21no—
257C2×C42—42no—
258C2×C42C2×C4×C1711yescharacteristic
259C2×C42D4×C1711yescharacteristic
260C2×C42D4×C1711yescharacteristic
261C2×C42C23×C1711yescharacteristic
262C22⋊C8—24no—
263#97—42no—
264#95—21no—
265#95—21no—
266#95—21no—
267C17#763311yescharacteristic, direct product factor, Sylow
268C24—21no—
269C24C22⋊C4×C1711yescharacteristic
270C2×D4—24no—
271C2×D4—21no—
272C2×D4—41no—
273C2×D4—41no—
274C2×D4—42no—
275C2×D4—42no—
276C2×D4M16×C1712yescomplemented
277C22×C4—22no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—22no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—22no—
285C22×C4—22no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—41no—
289C22×C4—41no—
290C22×C4—41no—
291C22×C4—42no—
292C22×C4—42no—
293C22×C4—42no—
294C22×C4C22⋊C4×C1711yescharacteristic
295C22×C4C22⋊C4×C1711yescharacteristic
296C22×C4C22⋊C4×C1711yescharacteristic
297C22×C4C22×C4×C1711yescharacteristic
298C22×C4C2×D4×C1711yescharacteristic
299C22×C4C2×D4×C1711yescharacteristic
300M16—48no—
301C2×C8—24no—
302C2×C8—24no—
303C2×C8—42no—
304C2×C8—42no—
305C2×C8—42no—
306C2×C8—42no—
307C4⋊C4—21no—
308C4⋊C4—41no—
309C4⋊C4—41no—
310C4⋊C4—42no—
311C4⋊C4M16×C1712yescomplemented
312C22⋊C4—24no—
313C22⋊C4—42no—
314C22⋊C4—41no—
315C22⋊C4—42no—
316C22⋊C4—41no—
317C22⋊C4—42no—
318C42—22no—
319C42—22no—
320C42—41no—
321C42—41no—
322C42—42no—
323C23—21no—
324C23—21no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23—21no—
329C23—22no—
330C23—41no—
331C23—41no—
332C23—41no—
333C23—41no—
334C23—41no—
335C23—41no—
336C23C17×#10412yes—
337C23C2×C22⋊C4×C1711yescharacteristic
338D4—42no—
339D4—42no—
340D4—48no—
341C2×C4—24no—
342C2×C4—24no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—22no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—44no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—84no—
369C2×C4C17×#9912yes—
370C2×C4C17×#10412yes—
371C2×C4C2×M16×C1711yescharacteristic
372C2×C4C2×M16×C1711yescharacteristic
373C2×C4C17×AGL(1,ℤ/8)11yescharacteristic
374C2×C4C17×AGL(1,ℤ/8)12yes—
375C2×C4C17×#13711yescharacteristic
376C8—44no—
377C8—44no—
378C22—22no—
379C22—22no—
380C22—22no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—41no—
385C22—42no—
386C22—42no—
387C22—42no—
388C22—81no—
389C22—81no—
390C22—81no—
391C22—81no—
392C22C17×#40711yescharacteristic
393C22C2×C17×#9911yescharacteristic
394C22C17×#41311yescharacteristic
395C22C17×#41711yescharacteristic
396C22C17×#41811yescharacteristic
397C22C2×C17×#10411yescharacteristic
398C22C2×C17×#10411yescharacteristic
399C4—21no—
400C4—21no—
401C4—21no—
402C4—21no—
403C4—22no—
404C4—22no—
405C4—22no—
406C4—41no—
407C4—42no—
408C4—81no—
409C4—81no—
410C2—42no—
411C2—82no—
412C2C17×#146511yescharacteristic
413C2C17×#148911yescharacteristic
414C2C17×#149011yescharacteristic
415C2C17×#150411yescharacteristic
416C2C17×#150711yescharacteristic
417C2C17×#152411yescharacteristic
418C2C17×#155711yescharacteristic
subgroupG/H
center, socleC23×C17C2×C22⋊C4
commutatorC22×C4C22×C4×C17
Frattini, cosocleC2×C42C23×C17
prime radicalC2×C17×#121C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C17 ◁ C22×C42×C17 ◁ G

Complements

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

NH ≅ G/Ntype
2. C17×#1749C2semidirect
3. C17×#1728C2semidirect
4. C17×#1271C2semidirect
5. C17×#1270C2semidirect
66. C2×D4×C17M16semidirect
101. C4⋊C4×C17M16semidirect
113. #7633C17direct (N × H)
170. #1749C2×C17semidirect
171. #1728C2×C17semidirect
172. #1271C2×C17semidirect
173. #1270C2×C17semidirect
267. C17#7633direct (N × H)
276. C2×D4M16×C17semidirect
311. C4⋊C4M16×C17semidirect

Maximal subgroups

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

subgroupindex
C4×C17×#1212
C17×#17492
C17×#17282
C17×#12712
C17×#12702
#763317