Finite Group Databasebeta

← C17×#33944 #16891688

Subgroups — C17×#33944 #16891688

Order 4352.

468 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C17×#3393C211yesmaximal, characteristic
2C17×#3383C211yesmaximal, characteristic, complemented
3C17×#2245C211yesmaximal, characteristic, complemented
4C17×#2243C211yesmaximal, characteristic
5C17×#2242C211yesmaximal, characteristic
6C17×#2229C211yesmaximal, characteristic, complemented
7C17×#2228C211yesmaximal, characteristic
8C17×#2227C211yesmaximal, characteristic, complemented
9C17×#2211C211yesmaximal, characteristic
10C17×#2211C211yesmaximal, characteristic
11C17×#2209C211yesmaximal, characteristic, complemented
12C17×#2183C211yesmaximal, characteristic, complemented
13C17×#2176C211yesmaximal, characteristic, complemented
14C17×#2175C211yesmaximal, characteristic
15C4×C17×Q32C211yesmaximal, characteristic, complemented
16C17×#557—21no—
17C17×#556—21no—
18C2×C17×Q32C2211yescharacteristic
19C2×C17×Q32C2211yescharacteristic
20C2×C17×SD32C2211yescharacteristic
21C17×#500C2211yescharacteristic
22C17×#499C2211yescharacteristic
23C17×#499C2211yescharacteristic
24C17×#495C2211yescharacteristic
25C17×#495C2211yescharacteristic
26C17×#494C2211yescharacteristic
27C17×#479—21no—
28C17×#479—21no—
29C17×#475—21no—
30C17×#464—21no—
31C17×#464—21no—
32C17×#461—21no—
33C8×Q8×C17C2211yescharacteristic
34C4×Q16×C17C2211yescharacteristic
35C4×Q16×C17C2211yescharacteristic
36C4×Q16×C17C2211yescharacteristic
37C4×Q16×C17C2211yescharacteristic
38C4×Q16×C17C2211yescharacteristic
39C4×D8×C17C2211yescharacteristic
40C17×#367C2211yescharacteristic
41C17×#366C2211yescharacteristic
42C17×#366C2211yescharacteristic
43C17×C4⋊C16C2211yescharacteristic
44C17×C4⋊C16C2211yescharacteristic
45C17×C4⋊C16C2211yescharacteristic
46C17×#358C2211yescharacteristic
47C17×#358C2211yescharacteristic
48C17×#358C2211yescharacteristic
49C17×#358C2211yescharacteristic
50C17×#358C2211yescharacteristic
51C17×#358C2211yescharacteristic
52C17×#358C2211yescharacteristic
53C17×#357C2211yescharacteristic
54C17×#357C2211yescharacteristic
55C17×#357C2211yescharacteristic
56C17×#346C2211yescharacteristic
57C17×#346C2211yescharacteristic
58C4×C16×C17C2211yescharacteristic
59C2×Q16×C17—21no—
60C2×Q16×C17C2311yescharacteristic
61C2×Q16×C17C2311yescharacteristic
62C2×Q16×C17C2311yescharacteristic
63C2×SD16×C17—21no—
64C2×SD16×C17—21no—
65C2×D8×C17C2311yescharacteristic
66C17×C4⋊Q8—21no—
67C17×C4⋊Q8—21no—
68C17×C4⋊Q8—41no—
69C17×#126—41no—
70C17×#126—41no—
71C17×#125—21no—
72C17×#125—21no—
73C17×#125—41no—
74C17×#125—41no—
75C17×#124—21no—
76C17×#124—21no—
77C17×C22⋊Q8—41no—
78C4×Q8×C17—21no—
79C4×Q8×C17—21no—
80C4×Q8×C17—21no—
81C4×Q8×C17—21no—
82C4×Q8×C17—21no—
83C4×Q8×C17—41no—
84C4×Q8×C17D411yescharacteristic
85C4×D4×C17—21no—
86C17×#117—41no—
87C17×Q32—22no—
88C17×Q32—22no—
89C17×SD32—22no—
90C2×C16×C17C2311yescharacteristic
91C2×C16×C17C2311yescharacteristic
92C2×C16×C17C2311yescharacteristic
93C2×C16×C17C2311yescharacteristic
94C17×#107—21no—
95C17×#107C2311yescharacteristic
96C17×#107C2311yescharacteristic
97C17×#107C2311yescharacteristic
98C17×#107C2311yescharacteristic
99C17×#106—21no—
100C17×#106—21no—
101C17×C4⋊C8D411yescharacteristic
102C17×C4⋊C8D411yescharacteristic
103C17×C4⋊C8D411yescharacteristic
104C17×#103—21no—
105C17×#103—21no—
106C17×#103—21no—
107C17×#103—21no—
108C17×#103—21no—
109C17×#102—21no—
110C4×C8×C17C2311yescharacteristic
111C4×C8×C17C2311yescharacteristic
112C4×C8×C17C2311yescharacteristic
113C2×Q8×C17—21no—
114C2×Q8×C17—21no—
115C2×Q8×C17—21no—
116C2×Q8×C17—41no—
117C2×Q8×C17D811yescharacteristic
118C2×D4×C17—21no—
119C22×C4×C17—41no—
120Q16×C17—21no—
121Q16×C17—21no—
122Q16×C17—21no—
123Q16×C17—21no—
124Q16×C17—21no—
125Q16×C17—81no—
126Q16×C17#4112yes—
127SD16×C17—81no—
128SD16×C17—81no—
129D8×C17—21no—
130D8×C17—21no—
131C2×C8×C17C2×D411yescharacteristic
132C2×C8×C17C2×D411yescharacteristic
133C2×C8×C17C2×D411yescharacteristic
134C2×C8×C17C2411yescharacteristic
135C4⋊C4×C17—21no—
136C4⋊C4×C17—21no—
137C4⋊C4×C17—21no—
138C4⋊C4×C17—21no—
139C4⋊C4×C17—41no—
140C4⋊C4×C17—41no—
141C4⋊C4×C17—41no—
142C4⋊C4×C17—41no—
143C4⋊C4×C17—41no—
144C4⋊C4×C17—41no—
145C4⋊C4×C17—41no—
146C4⋊C4×C17—41no—
147C4⋊C4×C17—41no—
148C4⋊C4×C17—41no—
149C4⋊C4×C17—41no—
150C4⋊C4×C17—41no—
151C4⋊C4×C17D811yescharacteristic
152C4⋊C4×C17D811yescharacteristic
153C4⋊C4×C17D811yescharacteristic
154C22⋊C4×C17—41no—
155C22⋊C4×C17—41no—
156C22⋊C4×C17—41no—
157C22⋊C4×C17—41no—
158C22⋊C4×C17—41no—
159C42×C17—41no—
160C42×C17—41no—
161C42×C17—41no—
162C42×C17—41no—
163C42×C17—41no—
164C42×C17C2×D411yescharacteristic
165C42×C17C2×D411yescharacteristic
166C42×C17C2×D411yescharacteristic
167C16×C17—21no—
168C16×C17—21no—
169C16×C17—21no—
170C16×C17—21no—
171#33944C1711yesmaximal, characteristic, direct product factor, Sylow
172C23×C17—41no—
173Q8×C17—22no—
174Q8×C17—41no—
175Q8×C17—41no—
176Q8×C17—41no—
177Q8×C17—41no—
178Q8×C17—41no—
179Q8×C17—41no—
180Q8×C17—82no—
181D4×C17—41no—
182D4×C17—41no—
183C2×C4×C17—41no—
184C2×C4×C17—41no—
185C2×C4×C17—41no—
186C2×C4×C17—41no—
187C2×C4×C17—41no—
188C2×C4×C17—41no—
189C2×C4×C17—41no—
190C2×C4×C17—82no—
191C2×C4×C17C2×D811yescharacteristic
192C2×C4×C17C2×D811yescharacteristic
193C2×C4×C17C2×D811yescharacteristic
194C2×C4×C17C2×D811yescharacteristic
195C2×C4×C17C2×D811yescharacteristic
196C2×C4×C17C2×D811yescharacteristic
197C2×C4×C17C22×D411yescharacteristic
198C8×C17—21no—
199C8×C17—21no—
200C8×C17—21no—
201C8×C17C2×#4111yescharacteristic
202C8×C172−1+411yescharacteristic
203#3393C2×C1711yescharacteristic
204#3383C2×C1711yescharacteristic, complemented
205#2245C2×C1711yescharacteristic, complemented
206#2243C2×C1711yescharacteristic
207#2242C2×C1711yescharacteristic
208#2229C2×C1711yescharacteristic, complemented
209#2228C2×C1711yescharacteristic
210#2227C2×C1711yescharacteristic, complemented
211#2211C2×C1711yescharacteristic
212#2211C2×C1711yescharacteristic
213#2209C2×C1711yescharacteristic, complemented
214#2183C2×C1711yescharacteristic, complemented
215#2176C2×C1711yescharacteristic, complemented
216#2175C2×C1711yescharacteristic
217C4×Q32C2×C1711yescharacteristic, complemented
218C22×C17—81no—
219C22×C17—81no—
220C22×C17—81no—
221C22×C17C22×D811yescharacteristic
222C4×C17—21no—
223C4×C17—21no—
224C4×C17—21no—
225C4×C17—21no—
226C4×C17—21no—
227C4×C17—21no—
228C4×C17—42no—
229C4×C17—81no—
230C4×C17—81no—
231C4×C17—81no—
232C4×C17—81no—
233C4×C17—81no—
234C4×C17—81no—
235C4×C17#54811yescharacteristic
236C4×C17#57711yescharacteristic
237#557—21no—
238#556—21no—
239C2×Q32C22×C1711yescharacteristic
240C2×Q32C22×C1711yescharacteristic
241C2×SD32C22×C1711yescharacteristic
242#500C22×C1711yescharacteristic
243#499C22×C1711yescharacteristic
244#499C22×C1711yescharacteristic
245#495C22×C1711yescharacteristic
246#495C22×C1711yescharacteristic
247#494C22×C1711yescharacteristic
248#479—21no—
249#479—21no—
250#475—21no—
251#464—21no—
252#464—21no—
253#461—21no—
254C8×Q8C22×C1711yescharacteristic
255C4×Q16C22×C1711yescharacteristic
256C4×Q16C22×C1711yescharacteristic
257C4×Q16C22×C1711yescharacteristic
258C4×Q16C22×C1711yescharacteristic
259C4×Q16C22×C1711yescharacteristic
260C4×D8C22×C1711yescharacteristic
261#367C22×C1711yescharacteristic
262#366C22×C1711yescharacteristic
263#366C22×C1711yescharacteristic
264C4⋊C16C22×C1711yescharacteristic
265C4⋊C16C22×C1711yescharacteristic
266C4⋊C16C22×C1711yescharacteristic
267#358C22×C1711yescharacteristic
268#358C22×C1711yescharacteristic
269#358C22×C1711yescharacteristic
270#358C22×C1711yescharacteristic
271#358C22×C1711yescharacteristic
272#358C22×C1711yescharacteristic
273#358C22×C1711yescharacteristic
274#357C22×C1711yescharacteristic
275#357C22×C1711yescharacteristic
276#357C22×C1711yescharacteristic
277#346C22×C1711yescharacteristic
278#346C22×C1711yescharacteristic
279C4×C16C22×C1711yescharacteristic
280C2×C17—161no—
281C2×C17#335811yescharacteristic
282C2×C17#341411yescharacteristic
283C2×C17#341711yescharacteristic
284C2×Q16—21no—
285C2×Q16C23×C1711yescharacteristic
286C2×Q16C23×C1711yescharacteristic
287C2×Q16C23×C1711yescharacteristic
288C2×SD16—21no—
289C2×SD16—21no—
290C2×D8C23×C1711yescharacteristic
291C4⋊Q8—21no—
292C4⋊Q8—21no—
293C4⋊Q8—41no—
294#126—41no—
295#126—41no—
296#125—21no—
297#125—21no—
298#125—41no—
299#125—41no—
300#124—21no—
301#124—21no—
302C22⋊Q8—41no—
303C4×Q8—21no—
304C4×Q8—21no—
305C4×Q8—21no—
306C4×Q8—21no—
307C4×Q8—21no—
308C4×Q8—41no—
309C4×Q8D4×C1711yescharacteristic
310C4×D4—21no—
311#117—41no—
312Q32—22no—
313Q32—22no—
314SD32—22no—
315C2×C16C23×C1711yescharacteristic
316C2×C16C23×C1711yescharacteristic
317C2×C16C23×C1711yescharacteristic
318C2×C16C23×C1711yescharacteristic
319#107—21no—
320#107C23×C1711yescharacteristic
321#107C23×C1711yescharacteristic
322#107C23×C1711yescharacteristic
323#107C23×C1711yescharacteristic
324#106—21no—
325#106—21no—
326C4⋊C8D4×C1711yescharacteristic
327C4⋊C8D4×C1711yescharacteristic
328C4⋊C8D4×C1711yescharacteristic
329#103—21no—
330#103—21no—
331#103—21no—
332#103—21no—
333#103—21no—
334#102—21no—
335C4×C8C23×C1711yescharacteristic
336C4×C8C23×C1711yescharacteristic
337C4×C8C23×C1711yescharacteristic
338C17#3394411yescharacteristic, direct product factor, Sylow
339C2×Q8—21no—
340C2×Q8—21no—
341C2×Q8—21no—
342C2×Q8—41no—
343C2×Q8D8×C1711yescharacteristic
344C2×D4—21no—
345C22×C4—41no—
346Q16—21no—
347Q16—21no—
348Q16—21no—
349Q16—21no—
350Q16—21no—
351Q16—81no—
352Q16#41×C1712yes—
353SD16—81no—
354SD16—81no—
355D8—21no—
356D8—21no—
357C2×C8C2×D4×C1711yescharacteristic
358C2×C8C2×D4×C1711yescharacteristic
359C2×C8C2×D4×C1711yescharacteristic
360C2×C8C24×C1711yescharacteristic
361C4⋊C4—21no—
362C4⋊C4—21no—
363C4⋊C4—21no—
364C4⋊C4—21no—
365C4⋊C4—41no—
366C4⋊C4—41no—
367C4⋊C4—41no—
368C4⋊C4—41no—
369C4⋊C4—41no—
370C4⋊C4—41no—
371C4⋊C4—41no—
372C4⋊C4—41no—
373C4⋊C4—41no—
374C4⋊C4—41no—
375C4⋊C4—41no—
376C4⋊C4—41no—
377C4⋊C4D8×C1711yescharacteristic
378C4⋊C4D8×C1711yescharacteristic
379C4⋊C4D8×C1711yescharacteristic
380C22⋊C4—41no—
381C22⋊C4—41no—
382C22⋊C4—41no—
383C22⋊C4—41no—
384C22⋊C4—41no—
385C42—41no—
386C42—41no—
387C42—41no—
388C42—41no—
389C42—41no—
390C42C2×D4×C1711yescharacteristic
391C42C2×D4×C1711yescharacteristic
392C42C2×D4×C1711yescharacteristic
393C16—21no—
394C16—21no—
395C16—21no—
396C16—21no—
397C23—41no—
398Q8—22no—
399Q8—41no—
400Q8—41no—
401Q8—41no—
402Q8—41no—
403Q8—41no—
404Q8—41no—
405Q8—82no—
406D4—41no—
407D4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—82no—
416C2×C4C2×D8×C1711yescharacteristic
417C2×C4C2×D8×C1711yescharacteristic
418C2×C4C2×D8×C1711yescharacteristic
419C2×C4C2×D8×C1711yescharacteristic
420C2×C4C2×D8×C1711yescharacteristic
421C2×C4C2×D8×C1711yescharacteristic
422C2×C4C22×D4×C1711yescharacteristic
423C8—21no—
424C8—21no—
425C8—21no—
426C8C2×#41×C1711yescharacteristic
427C8C17×2−1+411yescharacteristic
428C22—81no—
429C22—81no—
430C22—81no—
431C22C22×D8×C1711yescharacteristic
432C4—21no—
433C4—21no—
434C4—21no—
435C4—21no—
436C4—21no—
437C4—21no—
438C4—42no—
439C4—81no—
440C4—81no—
441C4—81no—
442C4—81no—
443C4—81no—
444C4—81no—
445C4C17×#54811yescharacteristic
446C4C17×#57711yescharacteristic
447C2—161no—
448C2C17×#335811yescharacteristic
449C2C17×#341411yescharacteristic
450C2C17×#341711yescharacteristic
subgroupG/H
center, socleC22×C17C22×D8
commutator, Frattini, cosocleC2×C8C24×C17
prime radicalC2×D8×C17C23
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C17 ◁ C4×Q8×C17 ◁ C8×Q8×C17 ◁ G

Complements

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

NH ≅ G/Ntype
2. C17×#3383C2semidirect
3. C17×#2245C2semidirect
6. C17×#2229C2semidirect
8. C17×#2227C2semidirect
11. C17×#2209C2semidirect
12. C17×#2183C2semidirect
13. C17×#2176C2semidirect
15. C4×C17×Q32C2semidirect
171. #33944C17direct (N × H)
204. #3383C2×C17semidirect
205. #2245C2×C17semidirect
208. #2229C2×C17semidirect
210. #2227C2×C17semidirect
213. #2209C2×C17semidirect
214. #2183C2×C17semidirect
215. #2176C2×C17semidirect
217. C4×Q32C2×C17semidirect
338. C17#33944direct (N × H)

Maximal subgroups

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

subgroupindex
C17×#33932
C17×#33832
C17×#22452
C17×#22432
C17×#22422
C17×#22292
C17×#22282
C17×#22272
C17×#22112
C17×#22092
C17×#21832
C17×#21762
C17×#21752
C4×C17×Q322
#3394417