Finite Group Databasebeta

← #16936775

Subgroups — #16936775

Order 4352.

524 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14539928C211yesmaximal, characteristic
2#14538589C211yesmaximal, characteristic
3#14527456C211yesmaximal, characteristic
4#14527282C211yesmaximal, characteristic
5#14527179C211yesmaximal, characteristic
6#14526687C211yesmaximal, characteristic
7C17×#2546C211yesmaximal, characteristic
8#11763366C2211yescharacteristic
9#11763205—21no—
10#11763161—21no—
11#11763139—22no—
12#11763116—22no—
13#11763104—21no—
14#11763094—21no—
15#11763091—22no—
16#11762862C2211yescharacteristic
17#11762862C2211yescharacteristic
18#11762849—21no—
19#11762833C2211yescharacteristic
20#11762818—21no—
21#11762555—22no—
22#11762545—22no—
23Q8⋊#3622—22no—
24C2×C17×C4⋊Q8—21no—
25C2×C17×C4⋊Q8C2211yescharacteristic
26C2×C4×Q8×C17C2211yescharacteristic
27C17×#398—22no—
28C17×#391—21no—
29C17×#389—22no—
30C4×C4⋊C4×C17C2211yescharacteristic
31C22×Q8×C17—21no—
32C22×Q8×C17D411yescharacteristic
33C17×C4⋊Q8—21no—
34C17×C4⋊Q8—21no—
35C17×C4⋊Q8—21no—
36C17×C4⋊Q8—21no—
37C17×C4⋊Q8—42no—
38C17×C4⋊Q8—42no—
39C4×Q8×C17—21no—
40C4×Q8×C17—21no—
41C4×Q8×C17—21no—
42C4×Q8×C17—21no—
43C2×C4⋊C4×C17—21no—
44C2×C4⋊C4×C17—24no—
45C2×C4⋊C4×C17—21no—
46C2×C4⋊C4×C17—21no—
47C2×C4⋊C4×C17D411yescharacteristic
48C2×C4⋊C4×C17D412yes—
49C2×C42×C17—21no—
50C2×C42×C17—21no—
51C2×C42×C17C2311yescharacteristic
52#10587612—21no—
53#10587610—21no—
54#10587610—21no—
55C2×#63223—21no—
56#10587556—21no—
57#10587555D411yescharacteristic
58#10587555D411yescharacteristic
59C4×Dic34—21no—
60C4×Dic34—21no—
61C17×#95—24no—
62C17×#95D412yes—
63#10587506—22no—
64#10587506—22no—
65C22⋊#3622—21no—
66C22⋊#3622—21no—
67#10587481—24no—
68#10587479—24no—
69#10587479—22no—
70#10587478—22no—
71C4⋊#3622—21no—
72C4⋊#3622—21no—
73C4⋊#3622D412yes—
74C4⋊#3622D412yes—
75C4×#3622—21no—
76C4×#3622—21no—
77C2×Q8×C17—21no—
78C2×Q8×C17—21no—
79C2×Q8×C17—21no—
80C2×Q8×C17—21no—
81C2×Q8×C17—21no—
82C2×Q8×C17—41no—
83C2×Q8×C17—41no—
84C2×Q8×C17—41no—
85C2×Q8×C17—41no—
86C2×Q8×C17—41no—
87C2×Q8×C17—41no—
88C2×Q8×C17SD1612yes—
89C22×C4×C17—21no—
90C22×C4×C17—22no—
91C22×C4×C17—22no—
92C22×C4×C17—21no—
93C22×C4×C17C2×D411yescharacteristic
94C22×C4×C17C2×D411yescharacteristic
95C22×C4×C17C2×D411yescharacteristic
96C2×Dic34—21no—
97C2×Dic34—21no—
98C4⋊C4×C17—24no—
99C4⋊C4×C17—22no—
100C4⋊C4×C17—21no—
101C4⋊C4×C17—22no—
102C4⋊C4×C17—21no—
103C4⋊C4×C17—48no—
104C4⋊C4×C17—41no—
105C4⋊C4×C17—41no—
106C4⋊C4×C17—41no—
107C4⋊C4×C17—41no—
108C42×C17—41no—
109C42×C17—41no—
110C42×C17—41no—
111C42×C17—41no—
112C42×C17C2×D411yescharacteristic
113C42×C17C2×D411yescharacteristic
114C42×C17C2×D411yescharacteristic
115C42×C17#4111yescharacteristic
116C22⋊Dic17—41no—
117C4⋊Dic17—21no—
118C4⋊Dic17—21no—
119C4⋊Dic17—21no—
120C4⋊Dic17—21no—
121#63225—41no—
122#63225—41no—
123C4×Dic17—41no—
124#63223—41no—
125#63223—41no—
126C2×#3622—22no—
127C2×#3622—22no—
128C2×#3622—41no—
129#10251—171nomaximal, Sylow
130C23×C17#12011yescharacteristic
131Q8×C17—22no—
132Q8×C17—22no—
133Q8×C17—41no—
134Q8×C17—41no—
135Q8×C17—81no—
136Q8×C17—81no—
137Q8×C17—81no—
138Q8×C17—81no—
139C2×C4×C17—22no—
140C2×C4×C17—24no—
141C2×C4×C17—22no—
142C2×C4×C17—41no—
143C2×C4×C17—42no—
144C2×C4×C17—41no—
145C2×C4×C17—42no—
146C2×C4×C17—41no—
147C2×C4×C17—42no—
148C2×C4×C17—41no—
149C2×C4×C17—42no—
150C2×C4×C17—42no—
151C2×C4×C17—42no—
152C2×C4×C17#12011yescharacteristic
153C2×C4×C17#12011yescharacteristic
154C2×C4×C17#12111yescharacteristic
155C2×C4×C17#12111yescharacteristic
156C2×C4×C17#12111yescharacteristic
157C2×C4×C17#12711yescharacteristic
158C2×C4×C17C2×SD1611yescharacteristic
159C2×C4×C17#13511yescharacteristic
160C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
161C2×C4×C17#13711yescharacteristic
162C2×Dic17—41no—
163C2×Dic17—41no—
164Dic34—42no—
165Dic34—81no—
166#3622—42no—
167#3622—42no—
168#3622—81no—
169#3229—171no—
170#3078—171no—
171#2546D1711yescharacteristic
172#1546—171no—
173#1503—171no—
174#1479—171no—
175#1303—171no—
176C22×C17—21no—
177C22×C17—21no—
178C22×C17#39211yescharacteristic
179C22×C17#45011yescharacteristic
180C22×C17#45211yescharacteristic
181C4×C17—21no—
182C4×C17—21no—
183C4×C17—21no—
184C4×C17—44no—
185C4×C17—42no—
186C4×C17—82no—
187C4×C17—81no—
188C4×C17#44811yescharacteristic
189C4×C17#44911yescharacteristic
190C4×C17#45612yes—
191C4×C17#46511yescharacteristic
192C4×C17#46811yescharacteristic
193Dic17—81no—
194Dic17—81no—
195#533—171no—
196C2×C4⋊Q8—21no—
197C2×C4⋊Q8C2×D1711yescharacteristic
198C2×C4×Q8C2×D1711yescharacteristic
199#498—341no—
200#487—341no—
201#483—342no—
202#479—342no—
203#477—341no—
204#475—342no—
205#475—341no—
206#431—171no—
207#431—171no—
208#428—341no—
209#423—171no—
210#419—341no—
211#398—22no—
212#391—21no—
213#389—22no—
214C4×C4⋊C4C2×D1711yescharacteristic
215#332—342no—
216#328—342no—
217Q8⋊C8—342no—
218C2×C17—21no—
219C2×C17—21no—
220C2×C17#200011yescharacteristic
221C2×C17#200511yescharacteristic
222C2×C17#200911yescharacteristic
223C22×Q8—21no—
224C22×Q8C22⋊D1711yescharacteristic
225C2×M16—341no—
226C4⋊Q8—21no—
227C4⋊Q8—21no—
228C4⋊Q8—21no—
229C4⋊Q8—21no—
230C4⋊Q8—42no—
231C4⋊Q8—42no—
232C4⋊Q8—171no—
233C4⋊Q8—171no—
234#125—341no—
235C22⋊Q8—341no—
236C22⋊Q8—341no—
237C4×Q8—21no—
238C4×Q8—21no—
239C4×Q8—21no—
240C4×Q8—21no—
241C4×Q8—341no—
242C4×Q8—341no—
243#117—341no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—24no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4C22⋊D1711yescharacteristic
249C2×C4⋊C4C22⋊D1712yes—
250C2×C42—21no—
251C2×C42—21no—
252C2×C42C22×D1711yescharacteristic
253#107—342no—
254#106—342no—
255#106—344no—
256C4⋊C8—172no—
257C4⋊C8—172no—
258C4⋊C8—341no—
259C4⋊C8—341no—
260#103—344no—
261#103—342no—
262#103—342no—
263C22⋊C8—341no—
264C22⋊C8—341no—
265C4×C8—341no—
266C4×C8—341no—
267#95—24no—
268#95C22⋊D1712yes—
269C17#1025111yescharacteristic, complemented, Sylow
270C2×Q8—21no—
271C2×Q8—21no—
272C2×Q8—21no—
273C2×Q8—21no—
274C2×Q8—21no—
275C2×Q8—41no—
276C2×Q8—41no—
277C2×Q8—41no—
278C2×Q8—41no—
279C2×Q8—41no—
280C2×Q8—41no—
281C2×Q8—341no—
282C2×Q8—341no—
283C2×Q8#6322912yes—
284C22×C4—22no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—22no—
288C22×C4C2×C22⋊D1711yescharacteristic
289C22×C4C2×C22⋊D1711yescharacteristic
290C22×C4C2×C22⋊D1711yescharacteristic
291M16—681no—
292M16—681no—
293C2×C8—342no—
294C2×C8—342no—
295C2×C8—681no—
296C4⋊C4—24no—
297C4⋊C4—22no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—22no—
301C4⋊C4—48no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4—341no—
307C4⋊C4—341no—
308C4⋊C4—341no—
309C4⋊C4—341no—
310C4⋊C4—681no—
311C4⋊C4—681no—
312C22⋊C4—681no—
313C42—41no—
314C42—41no—
315C42—41no—
316C42—41no—
317C42—681no—
318C42D4×D1711yescharacteristic
319C42D4×D1711yescharacteristic
320C42D4×D1711yescharacteristic
321C42#6325411yescharacteristic
322C23#1058763911yescharacteristic
323Q8—22no—
324Q8—22no—
325Q8—41no—
326Q8—41no—
327Q8—81no—
328Q8—81no—
329Q8—81no—
330Q8—81no—
331Q8—682no—
332Q8—1361no—
333C2×C4—22no—
334C2×C4—24no—
335C2×C4—22no—
336C2×C4—41no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—41no—
345C2×C4—42no—
346C2×C4—681no—
347C2×C4—681no—
348C2×C4#1058761811yescharacteristic
349C2×C4C2×#6322911yescharacteristic
350C2×C4#1058762311yescharacteristic
351C2×C4#1058762311yescharacteristic
352C2×C4#1058762411yescharacteristic
353C2×C4#1058762511yescharacteristic
354C2×C4#1058762511yescharacteristic
355C2×C4#1058762611yescharacteristic
356C2×C4#1058763611yescharacteristic
357C2×C4#1058763711yescharacteristic
358C8—682no—
359C8—682no—
360C8—1361no—
361C22—21no—
362C22—21no—
363C22#1176271711yescharacteristic
364C22#1176296011yescharacteristic
365C22#1176297111yescharacteristic
366C4—21no—
367C4—21no—
368C4—21no—
369C4—44no—
370C4—42no—
371C4—81no—
372C4—82no—
373C4—1361no—
374C4—1361no—
375C4#1176294711yescharacteristic
376C4#1176295211yescharacteristic
377C4#1176299112yes—
378C4#1176303611yescharacteristic
379C4#1176305311yescharacteristic
380C2—21no—
381C2—21no—
382C2#1452978711yescharacteristic
383C2#1452982011yescharacteristic
384C2#1452984411yescharacteristic
subgroupG/H
centerC22#11762717
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#2546C2
socleC22×C17#392
prime radicalC23×C17#120
hypercenter#2546D17
hypocenterC17#10251
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2546

Complements

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

NH ≅ G/Ntype
269. C17#10251semidirect

Maximal subgroups

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

subgroupindex
#145399282
#145385892
#145274562
#145272822
#145271792
#145266872
C17×#25462
#1025117