Finite Group Databasebeta

← C17×#10426 #16868170

Subgroups — C17×#10426 #16868170

Order 4352.

444 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C17×#2820C211yesmaximal, characteristic
2C17×#1992C211yesmaximal, characteristic, complemented
3C17×#1959C211yesmaximal, characteristic
4C17×#1836C211yesmaximal, characteristic, complemented
5C2×C17×#330C211yesmaximal, characteristic, complemented
6C2×C17×#329C211yesmaximal, characteristic
7C17×#1295C211yesmaximal, characteristic, complemented
8C2×C17×#125C2211yescharacteristic
9C2×C17×#124C2211yescharacteristic
10C2×C17×#103—21no—
11C2×C17×#102—21no—
12C2×C17×#97C2211yescharacteristic
13C2×C17×#97C2211yescharacteristic
14C2×C17×#97C2211yescharacteristic
15C17×#399—21no—
16C17×#397—21no—
17C17×#396—21no—
18C17×#396—21no—
19C17×#395—21no—
20C17×#394—21no—
21C17×#384C2211yescharacteristic
22C17×#382C2211yescharacteristic
23C17×#340—21no—
24C17×#340—21no—
25C17×#340—21no—
26C17×#340—21no—
27C17×#330—22no—
28C17×#329—22no—
29C22×Q8×C17D411yescharacteristic
30C22×D4×C17D411yescharacteristic
31C22×C8×C17—21no—
32C22×C8×C17—21no—
33C22×C8×C17—21no—
34C17×#125—21no—
35C17×#125—21no—
36C17×#125—21no—
37C17×#125—21no—
38C17×#124—21no—
39C17×#124—21no—
40C17×#124—21no—
41C17×#124—21no—
42C2×C4⋊C4×C17—21no—
43C2×C4⋊C4×C17—21no—
44C2×C4⋊C4×C17—21no—
45C2×C4⋊C4×C17—21no—
46C2×C4⋊C4×C17—21no—
47C2×C4⋊C4×C17—21no—
48C2×C4⋊C4×C17—21no—
49C2×C4⋊C4×C17D411yescharacteristic
50C2×C4⋊C4×C17D411yescharacteristic
51C2×C4⋊C4×C17D411yescharacteristic
52C2×C4⋊C4×C17D411yescharacteristic
53C2×C22⋊C4×C17—21no—
54C2×C22⋊C4×C17—21no—
55C2×C22⋊C4×C17—21no—
56C2×C22⋊C4×C17—21no—
57C2×C22⋊C4×C17—21no—
58C2×C22⋊C4×C17—21no—
59C2×C42×C17C2311yescharacteristic
60C17×#103—42no—
61C17×#102—42no—
62C17×#97—21no—
63C17×#97—21no—
64C17×#97—21no—
65C17×#97—21no—
66C17×#97—21no—
67C17×#97D412yes—
68C17×#95—21no—
69C17×#95—21no—
70C17×#95—21no—
71C17×#95—21no—
72C24×C17—21no—
73C2×Q8×C17—21no—
74C2×Q8×C17—21no—
75C2×Q8×C17—41no—
76C2×Q8×C17—41no—
77C2×D4×C17—21no—
78C2×D4×C17—21no—
79C2×D4×C17—41no—
80C2×D4×C17—41no—
81C22×C4×C17—21no—
82C22×C4×C17—21no—
83C22×C4×C17—21no—
84C22×C4×C17—21no—
85C22×C4×C17—21no—
86C22×C4×C17—41no—
87C22×C4×C17C2×D411yescharacteristic
88C22×C4×C17C2×D411yescharacteristic
89C22×C4×C17C2×D411yescharacteristic
90C2×C8×C17—22no—
91C2×C8×C17—22no—
92C2×C8×C17—22no—
93C2×C8×C17—41no—
94C2×C8×C17—41no—
95C2×C8×C17—41no—
96C2×C8×C17—41no—
97C2×C8×C17—41no—
98C2×C8×C17—41no—
99C4⋊C4×C17—21no—
100C4⋊C4×C17—21no—
101C4⋊C4×C17—21no—
102C4⋊C4×C17—21no—
103C4⋊C4×C17—41no—
104C4⋊C4×C17—41no—
105C4⋊C4×C17—41no—
106C4⋊C4×C17—41no—
107C4⋊C4×C17—42no—
108C4⋊C4×C17—42no—
109C4⋊C4×C17—41no—
110C4⋊C4×C17—41no—
111C4⋊C4×C17—41no—
112C4⋊C4×C17—41no—
113C4⋊C4×C17—81no—
114C4⋊C4×C17—81no—
115C22⋊C4×C17—41no—
116C22⋊C4×C17—41no—
117C22⋊C4×C17—41no—
118C22⋊C4×C17—41no—
119C22⋊C4×C17—81no—
120C22⋊C4×C17—81no—
121C22⋊C4×C17—81no—
122C22⋊C4×C17—81no—
123C42×C17C2×D411yescharacteristic
124C42×C17#4111yescharacteristic
125C42×C17#4111yescharacteristic
126C42×C17#4111yescharacteristic
127#10426C1711yesmaximal, characteristic, direct product factor, Sylow
128C23×C17—41no—
129C23×C17—41no—
130C23×C17—41no—
131C23×C17—41no—
132C23×C17—41no—
133C23×C17—41no—
134C23×C17—41no—
135C23×C17#12011yescharacteristic
136Q8×C17—42no—
137Q8×C17—81no—
138D4×C17—42no—
139D4×C17—81no—
140C2×C4×C17—21no—
141C2×C4×C17—21no—
142C2×C4×C17—21no—
143C2×C4×C17—21no—
144C2×C4×C17—21no—
145C2×C4×C17—21no—
146C2×C4×C17—41no—
147C2×C4×C17—41no—
148C2×C4×C17—41no—
149C2×C4×C17—41no—
150C2×C4×C17—41no—
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—41no—
160C2×C4×C17—41no—
161C2×C4×C17—81no—
162C2×C4×C17—81no—
163C2×C4×C17—81no—
164C2×C4×C17#12111yescharacteristic
165C2×C4×C17#12111yescharacteristic
166C2×C4×C17#12111yescharacteristic
167C2×C4×C17#12311yescharacteristic
168C2×C4×C17#12311yescharacteristic
169C2×C4×C17#12411yescharacteristic
170C8×C17—42no—
171C8×C17—42no—
172C8×C17—42no—
173#2820C2×C1711yescharacteristic
174#1992C2×C1711yescharacteristic, complemented
175#1959C2×C1711yescharacteristic
176#1836C2×C1711yescharacteristic, complemented
177C2×#330C2×C1711yescharacteristic, complemented
178C2×#329C2×C1711yescharacteristic
179#1295C2×C1711yescharacteristic, complemented
180C22×C17—81no—
181C22×C17—81no—
182C22×C17—81no—
183C22×C17—81no—
184C22×C17—81no—
185C22×C17—81no—
186C22×C17—81no—
187C22×C17#39411yescharacteristic
188C22×C17#45311yescharacteristic
189C22×C17#45411yescharacteristic
190C22×C17#45411yescharacteristic
191C22×C17#45511yescharacteristic
192C22×C17#45511yescharacteristic
193C22×C17#45611yescharacteristic
194C4×C17—21no—
195C4×C17—21no—
196C4×C17—21no—
197C4×C17—21no—
198C4×C17—21no—
199C4×C17—21no—
200C4×C17—81no—
201C4×C17—81no—
202C4×C17—81no—
203C4×C17—81no—
204C4×C17—81no—
205C4×C17—161no—
206C2×#125C22×C1711yescharacteristic
207C2×#124C22×C1711yescharacteristic
208C2×#103—21no—
209C2×#102—21no—
210C2×#97C22×C1711yescharacteristic
211C2×#97C22×C1711yescharacteristic
212C2×#97C22×C1711yescharacteristic
213#399—21no—
214#397—21no—
215#396—21no—
216#396—21no—
217#395—21no—
218#394—21no—
219#384C22×C1711yescharacteristic
220#382C22×C1711yescharacteristic
221#340—21no—
222#340—21no—
223#340—21no—
224#340—21no—
225#330—22no—
226#329—22no—
227C2×C17—161no—
228C2×C17#165711yescharacteristic
229C2×C17#166111yescharacteristic
230C2×C17#166211yescharacteristic
231C2×C17#166411yescharacteristic
232C2×C17#203711yescharacteristic
233C2×C17#203811yescharacteristic
234C2×C17#204011yescharacteristic
235C22×Q8D4×C1711yescharacteristic
236C22×D4D4×C1711yescharacteristic
237C22×C8—21no—
238C22×C8—21no—
239C22×C8—21no—
240#125—21no—
241#125—21no—
242#125—21no—
243#125—21no—
244#124—21no—
245#124—21no—
246#124—21no—
247#124—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4D4×C1711yescharacteristic
256C2×C4⋊C4D4×C1711yescharacteristic
257C2×C4⋊C4D4×C1711yescharacteristic
258C2×C4⋊C4D4×C1711yescharacteristic
259C2×C22⋊C4—21no—
260C2×C22⋊C4—21no—
261C2×C22⋊C4—21no—
262C2×C22⋊C4—21no—
263C2×C22⋊C4—21no—
264C2×C22⋊C4—21no—
265C2×C42C23×C1711yescharacteristic
266#103—42no—
267#102—42no—
268#97—21no—
269#97—21no—
270#97—21no—
271#97—21no—
272#97—21no—
273#97D4×C1712yes—
274#95—21no—
275#95—21no—
276#95—21no—
277#95—21no—
278C17#1042611yescharacteristic, direct product factor, Sylow
279C24—21no—
280C2×Q8—21no—
281C2×Q8—21no—
282C2×Q8—41no—
283C2×Q8—41no—
284C2×D4—21no—
285C2×D4—21no—
286C2×D4—41no—
287C2×D4—41no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—41no—
294C22×C4C2×D4×C1711yescharacteristic
295C22×C4C2×D4×C1711yescharacteristic
296C22×C4C2×D4×C1711yescharacteristic
297C2×C8—22no—
298C2×C8—22no—
299C2×C8—22no—
300C2×C8—41no—
301C2×C8—41no—
302C2×C8—41no—
303C2×C8—41no—
304C2×C8—41no—
305C2×C8—41no—
306C4⋊C4—21no—
307C4⋊C4—21no—
308C4⋊C4—21no—
309C4⋊C4—21no—
310C4⋊C4—41no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4—41no—
314C4⋊C4—42no—
315C4⋊C4—42no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—81no—
321C4⋊C4—81no—
322C22⋊C4—41no—
323C22⋊C4—41no—
324C22⋊C4—41no—
325C22⋊C4—41no—
326C22⋊C4—81no—
327C22⋊C4—81no—
328C22⋊C4—81no—
329C22⋊C4—81no—
330C42C2×D4×C1711yescharacteristic
331C42#41×C1711yescharacteristic
332C42#41×C1711yescharacteristic
333C42#41×C1711yescharacteristic
334C23—41no—
335C23—41no—
336C23—41no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23—41no—
341C23C17×#12011yescharacteristic
342Q8—42no—
343Q8—81no—
344D4—42no—
345D4—81no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—81no—
368C2×C4—81no—
369C2×C4—81no—
370C2×C4C17×#12111yescharacteristic
371C2×C4C17×#12111yescharacteristic
372C2×C4C17×#12111yescharacteristic
373C2×C4C17×#12311yescharacteristic
374C2×C4C17×#12311yescharacteristic
375C2×C4C17×#12411yescharacteristic
376C8—42no—
377C8—42no—
378C8—42no—
379C22—81no—
380C22—81no—
381C22—81no—
382C22—81no—
383C22—81no—
384C22—81no—
385C22—81no—
386C22C17×#39411yescharacteristic
387C22C17×#45311yescharacteristic
388C22C17×#45411yescharacteristic
389C22C17×#45411yescharacteristic
390C22C17×#45511yescharacteristic
391C22C17×#45511yescharacteristic
392C22C17×#45611yescharacteristic
393C4—21no—
394C4—21no—
395C4—21no—
396C4—21no—
397C4—21no—
398C4—21no—
399C4—81no—
400C4—81no—
401C4—81no—
402C4—81no—
403C4—81no—
404C4—161no—
405C2—161no—
406C2C17×#165711yescharacteristic
407C2C17×#166111yescharacteristic
408C2C17×#166211yescharacteristic
409C2C17×#166411yescharacteristic
410C2C17×#203711yescharacteristic
411C2C17×#203811yescharacteristic
412C2C17×#204011yescharacteristic
subgroupG/H
center, socleC23×C17#120
commutator, Frattini, cosocleC2×C42C23×C17
prime radicalC22×D4×C17D4
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C17 ◁ C2×C42×C17 ◁ G

Complements

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

NH ≅ G/Ntype
2. C17×#1992C2semidirect
4. C17×#1836C2semidirect
5. C2×C17×#330C2semidirect
7. C17×#1295C2semidirect
127. #10426C17direct (N × H)
174. #1992C2×C17semidirect
176. #1836C2×C17semidirect
177. C2×#330C2×C17semidirect
179. #1295C2×C17semidirect
278. C17#10426direct (N × H)

Maximal subgroups

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

subgroupindex
C17×#28202
C17×#19922
C17×#19592
C17×#18362
C2×C17×#3302
C2×C17×#3292
C17×#12952
#1042617