Finite Group Databasebeta

← #16936774

Subgroups — #16936774

Order 4352.

524 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 101 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#14539925C211yesmaximal, characteristic
2#14538585C211yesmaximal, characteristic
3#14533772C211yesmaximal, characteristic
4#14527455C211yesmaximal, characteristic
5#14527180C211yesmaximal, characteristic
6#14526687C211yesmaximal, characteristic
7C17×#1503C211yesmaximal, characteristic
8C2×#10587555—21no—
9C2×#10587555C2211yescharacteristic
10C2×C4×Dic34C2211yescharacteristic
11#11763205—21no—
12#11763159—21no—
13#11763137—22no—
14#11763113—22no—
15#11763101—21no—
16#11763094—22no—
17#11763091—21no—
18#11762862C2211yescharacteristic
19#11762852—21no—
20#11762833C2211yescharacteristic
21#11762817—21no—
22#11762741—22no—
23#11762715—21no—
24#11762708—22no—
25#11762554—22no—
26#11762541—22no—
27C17×#533C2211yescharacteristic
28C17×#431C2211yescharacteristic
29C4×C4⋊C4×C17C2211yescharacteristic
30C17×#328—22no—
31C22×Dic34—21no—
32C22×Dic34D411yescharacteristic
33C17×C4⋊Q8D411yescharacteristic
34C17×C4⋊Q8D411yescharacteristic
35C17×#125—21no—
36C17×C22⋊Q8—21no—
37C17×C22⋊Q8—21no—
38C4×Q8×C17—21no—
39C4×Q8×C17—21no—
40C17×#117—21no—
41C2×C4⋊C4×C17—21no—
42C2×C42×C17—21no—
43C2×C42×C17C2311yescharacteristic
44C2×C4⋊Dic17—24no—
45C2×C4⋊Dic17—21no—
46C2×C4⋊Dic17D412yes—
47C2×C4⋊Dic17D411yescharacteristic
48C2×#63225—21no—
49C2×C4×Dic17—21no—
50C2×#63223—21no—
51#10587555—21no—
52#10587555—21no—
53#10587555—21no—
54#10587555—21no—
55#10587555—42no—
56#10587555—42no—
57C4×Dic34—21no—
58C4×Dic34—21no—
59C4×Dic34—21no—
60C4×Dic34—21no—
61C17×C4⋊C8—21no—
62C17×C22⋊C8—21no—
63C4×C8×C17—21no—
64C17×#95D412yes—
65#10587506—24no—
66#10587502—24no—
67C22⋊#3622—21no—
68#10587481—22no—
69#10587481—22no—
70#10587479—24no—
71#10587479—22no—
72#10587478—22no—
73C4⋊#3622—21no—
74C4⋊#3622D412yes—
75C4⋊#3622D412yes—
76C4×#3622—21no—
77C2×Q8×C17—21no—
78C2×Q8×C17—21no—
79C22×C4×C17—22no—
80C22×C4×C17C2×D411yescharacteristic
81C22×C4×C17C2×D411yescharacteristic
82C22×C4×C17C2×D411yescharacteristic
83C22×Dic17—21no—
84C22×Dic17—22no—
85C22×Dic17—21no—
86C2×Dic34—21no—
87C2×Dic34—21no—
88C2×Dic34—21no—
89C2×Dic34—21no—
90C2×Dic34—21no—
91C2×Dic34—41no—
92C2×Dic34—41no—
93C2×Dic34—41no—
94C2×Dic34—41no—
95C2×Dic34—41no—
96C2×Dic34—41no—
97C2×Dic34SD1612yes—
98C2×C8×C17—41no—
99C4⋊C4×C17—24no—
100C4⋊C4×C17—21no—
101C4⋊C4×C17—21no—
102C4⋊C4×C17—21no—
103C4⋊C4×C17—21no—
104C4⋊C4×C17—41no—
105C4⋊C4×C17—41no—
106C22⋊C4×C17—41no—
107C42×C17—41no—
108C42×C17—41no—
109C42×C17—41no—
110C42×C17C2×D411yescharacteristic
111C42×C17C2×D411yescharacteristic
112C42×C17C2×D411yescharacteristic
113C42×C17#4111yescharacteristic
114C4⋊Dic17—21no—
115C4⋊Dic17—22no—
116C4⋊Dic17—21no—
117C4⋊Dic17—22no—
118C4⋊Dic17—48no—
119C4⋊Dic17—41no—
120C4⋊Dic17—41no—
121#63225—41no—
122#63225—41no—
123C4×Dic17—41no—
124C4×Dic17—41no—
125#63223—41no—
126#63223—41no—
127C2×#3622—22no—
128C2×#3622—22no—
129#10251—171nomaximal, Sylow
130C23×C17#12011yescharacteristic
131Q8×C17—42no—
132Q8×C17—81no—
133C2×C4×C17—22no—
134C2×C4×C17—24no—
135C2×C4×C17—41no—
136C2×C4×C17—42no—
137C2×C4×C17—42no—
138C2×C4×C17—41no—
139C2×C4×C17—41no—
140C2×C4×C17#12011yescharacteristic
141C2×C4×C17#12011yescharacteristic
142C2×C4×C17#12111yescharacteristic
143C2×C4×C17#12111yescharacteristic
144C2×C4×C17#12111yescharacteristic
145C2×C4×C17#12711yescharacteristic
146C2×C4×C17C2×SD1611yescharacteristic
147C2×C4×C17#13511yescharacteristic
148C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
149C2×C4×C17#13711yescharacteristic
150C2×Dic17—22no—
151C2×Dic17—41no—
152C2×Dic17—41no—
153C2×Dic17—42no—
154C2×Dic17—42no—
155C2×Dic17—41no—
156C2×Dic17—42no—
157C2×Dic17—42no—
158Dic34—22no—
159Dic34—22no—
160Dic34—41no—
161Dic34—41no—
162Dic34—81no—
163Dic34—81no—
164Dic34—81no—
165Dic34—81no—
166C8×C17—81no—
167#3622—42no—
168#3622—42no—
169#3229—171no—
170#3078—171no—
171#2546—171no—
172#1546—171no—
173#1503D1711yescharacteristic
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—81no—
186C4×C17—81no—
187C4×C17#44811yescharacteristic
188C4×C17#44911yescharacteristic
189C4×C17#45612yes—
190C4×C17#46511yescharacteristic
191C4×C17#46811yescharacteristic
192Dic17—42no—
193Dic17—82no—
194Dic17—81no—
195#533C2×D1711yescharacteristic
196C2×C4⋊Q8—171no—
197C2×C4⋊Q8—341no—
198C2×C4×Q8—171no—
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#431C2×D1711yescharacteristic
208#428—341no—
209#423—171no—
210#419—341no—
211#398—342no—
212#391—341no—
213#389—342no—
214C4×C4⋊C4C2×D1711yescharacteristic
215#332—342no—
216#328—22no—
217Q8⋊C8—342no—
218C2×C17—21no—
219C2×C17—21no—
220C2×C17#200011yescharacteristic
221C2×C17#200511yescharacteristic
222C2×C17#200911yescharacteristic
223C22×Q8—171no—
224C22×Q8—341no—
225C2×M16—341no—
226C4⋊Q8—341no—
227C4⋊Q8—341no—
228C4⋊Q8—341no—
229C4⋊Q8—341no—
230C4⋊Q8—682no—
231C4⋊Q8—682no—
232C4⋊Q8D6811yescharacteristic
233C4⋊Q8D6811yescharacteristic
234#125—21no—
235C22⋊Q8—21no—
236C22⋊Q8—21no—
237C4×Q8—21no—
238C4×Q8—21no—
239C4×Q8—341no—
240C4×Q8—341no—
241C4×Q8—341no—
242C4×Q8—341no—
243#117—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—171no—
246C2×C4⋊C4—172no—
247C2×C4⋊C4—344no—
248C2×C4⋊C4—341no—
249C2×C4⋊C4—341no—
250C2×C42—21no—
251C2×C42—341no—
252C2×C42C22×D1711yescharacteristic
253#107—342no—
254#106—342no—
255#106—344no—
256C4⋊C8—21no—
257C4⋊C8—172no—
258C4⋊C8—172no—
259C4⋊C8—341no—
260#103—342no—
261#103—342no—
262#103—344no—
263C22⋊C8—21no—
264C22⋊C8—341no—
265C4×C8—21no—
266C4×C8—341no—
267#95—344no—
268#95C22⋊D1712yes—
269C17#1025111yescharacteristic, complemented, Sylow
270C2×Q8—21no—
271C2×Q8—21no—
272C2×Q8—172no—
273C2×Q8—341no—
274C2×Q8—341no—
275C2×Q8—341no—
276C2×Q8—341no—
277C2×Q8—341no—
278C2×Q8—681no—
279C2×Q8—681no—
280C2×Q8—681no—
281C2×Q8—681no—
282C2×Q8—681no—
283C2×Q8—681no—
284C22×C4—22no—
285C22×C4—341no—
286C22×C4—341no—
287C22×C4—342no—
288C22×C4D4×D1711yescharacteristic
289C22×C4D4×D1711yescharacteristic
290C22×C4C2×C22⋊D1711yescharacteristic
291M16—681no—
292M16—681no—
293C2×C8—41no—
294C2×C8—342no—
295C2×C8—342no—
296C4⋊C4—24no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—342no—
304C4⋊C4—341no—
305C4⋊C4—341no—
306C4⋊C4—342no—
307C4⋊C4—688no—
308C4⋊C4—681no—
309C4⋊C4—681no—
310C4⋊C4—681no—
311C4⋊C4—681no—
312C22⋊C4—41no—
313C42—41no—
314C42—41no—
315C42—41no—
316C42—681no—
317C42—681no—
318C42C2×D6811yescharacteristic
319C42#6325211yescharacteristic
320C42D4×D1711yescharacteristic
321C42D4×D1711yescharacteristic
322C23#1058762311yescharacteristic
323Q8—42no—
324Q8—81no—
325Q8—342no—
326Q8—342no—
327Q8—681no—
328Q8—681no—
329Q8—1361no—
330Q8—1361no—
331Q8—1361no—
332Q8—1361no—
333C2×C4—22no—
334C2×C4—24no—
335C2×C4—41no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—342no—
341C2×C4—681no—
342C2×C4—681no—
343C2×C4—682no—
344C2×C4—682no—
345C2×C4—682no—
346C2×C4—681no—
347C2×C4—682no—
348C2×C4#1058756811yescharacteristic
349C2×C4#1058756811yescharacteristic
350C2×C4#1058757011yescharacteristic
351C2×C4#1058757011yescharacteristic
352C2×C4SD16×D1711yescharacteristic
353C2×C4#1058760011yescharacteristic
354C2×C4#1058760411yescharacteristic
355C2×C4#1058760511yescharacteristic
356C2×C4#1058761611yescharacteristic
357C2×C4#1058762611yescharacteristic
358C8—81no—
359C8—682no—
360C8—682no—
361C22—21no—
362C22—21no—
363C22#1176271811yescharacteristic
364C22#1176295811yescharacteristic
365C22#1176297011yescharacteristic
366C4—21no—
367C4—21no—
368C4—21no—
369C4—44no—
370C4—81no—
371C4—81no—
372C4—682no—
373C4—1361no—
374C4—1362no—
375C4#1176294911yescharacteristic
376C4#1176295711yescharacteristic
377C4#1176299312yes—
378C4#1176304111yescharacteristic
379C4#1176305811yescharacteristic
380C2—21no—
381C2—21no—
382C2#1452978611yescharacteristic
383C2#1452981911yescharacteristic
384C2#1452984311yescharacteristic
subgroupG/H
centerC22#11762718
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#1503C2
socleC22×C17#392
prime radicalC23×C17#120
hypercenter#1503D17
hypocenterC17#10251
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1503

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
#145399252
#145385852
#145337722
#145274552
#145271802
#145266872
C17×#15032
#1025117