Finite Group Databasebeta

← #16936350

Subgroups — #16936350

Order 4352.

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

normal subgroups only

This group has 528 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, complemented
2#14538581C211yesmaximal, characteristic
3#14527456C211yesmaximal, characteristic, complemented
4#14527186C211yesmaximal, characteristic, complemented
5#14527105C211yesmaximal, characteristic
6#14526681C211yesmaximal, characteristic, complemented
7C2×C17×#461C211yesmaximal, characteristic
8#11763366C2211yescharacteristic
9#11763205—21no—
10#11763161—21no—
11#11763139—22no—
12#11763109—22no—
13#11763099—21no—
14#11763091—22no—
15#11763089—21no—
16#11762862C2211yescharacteristic
17#11762862C2211yescharacteristic
18#11762849—21no—
19#11762833C2211yescharacteristic
20#11762814—21no—
21#11762555—22no—
22#11762539—22no—
23#11762533—22no—
24C22×SD16×C17—21no—
25C2×C17×C4⋊Q8C2211yescharacteristic
26C2×C4×D4×C17C2211yescharacteristic
27C17×#461—22no—
28C17×#461—22no—
29C2×C17×C4⋊C8C2211yescharacteristic
30C2×C17×#103—21no—
31C22×Q8×C17—21no—
32C22×D4×C17D411yescharacteristic
33C23×C4×C17—21no—
34C2×SD16×C17—24no—
35C2×SD16×C17—42no—
36C2×SD16×C17—42no—
37C22×C8×C17—21no—
38C17×C4⋊Q8—21no—
39C17×C4⋊Q8—21no—
40C17×C4⋊Q8—21no—
41C17×C4⋊Q8D412yes—
42C4×D4×C17—21no—
43C4×D4×C17—21no—
44C4×D4×C17—21no—
45C4×D4×C17—21no—
46C2×C4⋊C4×C17—21no—
47C2×C4⋊C4×C17—21no—
48C2×C4⋊C4×C17D411yescharacteristic
49C2×C22⋊C4×C17—21no—
50C2×C42×C17C2311yescharacteristic
51#10587612—21no—
52#10587610—21no—
53#10587610—21no—
54C2×#63223—21no—
55#10587556—21no—
56#10587555D411yescharacteristic
57#10587555D411yescharacteristic
58C4×Dic34—21no—
59C4×Dic34—21no—
60C17×C4⋊C8—21no—
61C17×C4⋊C8D412yes—
62C17×#103—24no—
63#10587503—22no—
64#10587503—22no—
65C22⋊#3622—21no—
66C22⋊#3622D412yes—
67#10587481—24no—
68#10587479—24no—
69#10587479—22no—
70#10587478—22no—
71C4⋊#3622—21no—
72C4⋊#3622—21no—
73C4⋊#3622—21no—
74C4⋊#3622D412yes—
75C4×#3622—21no—
76C4×#3622—21no—
77C24×C17—21no—
78C2×Q8×C17—22no—
79C2×Q8×C17—41no—
80C2×Q8×C17—41no—
81C2×Q8×C17—41no—
82C2×Q8×C17—41no—
83C2×Q8×C17—41no—
84C2×D4×C17—21no—
85C2×D4×C17—21no—
86C2×D4×C17—21no—
87C2×D4×C17—21no—
88C2×D4×C17—21no—
89C2×D4×C17SD1612yes—
90C22×C4×C17—21no—
91C22×C4×C17—41no—
92C22×C4×C17—41no—
93C22×C4×C17—41no—
94C22×C4×C17—82no—
95C22×C4×C17C2×D411yescharacteristic
96C22×C4×C17C2×D411yescharacteristic
97C22×C4×C17#4111yescharacteristic
98C2×Dic34—21no—
99C2×Dic34—21no—
100SD16×C17—48no—
101C2×C8×C17—22no—
102C2×C8×C17—41no—
103C2×C8×C17—41no—
104C4⋊C4×C17—22no—
105C4⋊C4×C17—21no—
106C4⋊C4×C17—21no—
107C4⋊C4×C17—22no—
108C4⋊C4×C17—41no—
109C4⋊C4×C17—41no—
110C22⋊C4×C17—41no—
111C22⋊C4×C17—41no—
112C42×C17C2×D411yescharacteristic
113C42×C17C2×D411yescharacteristic
114C42×C17C2×D411yescharacteristic
115C42×C17C2×D411yescharacteristic
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#10186—171nomaximal, Sylow
130C23×C17—22no—
131C23×C17—41no—
132C23×C17—41no—
133C23×C17—81no—
134C23×C17—81no—
135C23×C17#12111yescharacteristic
136Q8×C17—42no—
137Q8×C17—42no—
138Q8×C17—81no—
139Q8×C17—81no—
140D4×C17—22no—
141D4×C17—22no—
142D4×C17—41no—
143D4×C17—41no—
144C2×C4×C17—22no—
145C2×C4×C17—41no—
146C2×C4×C17—41no—
147C2×C4×C17—42no—
148C2×C4×C17—82no—
149C2×C4×C17—81no—
150C2×C4×C17—81no—
151C2×C4×C17—82no—
152C2×C4×C17—81no—
153C2×C4×C17#12011yescharacteristic
154C2×C4×C17#12011yescharacteristic
155C2×C4×C17#12011yescharacteristic
156C2×C4×C17#12111yescharacteristic
157C2×C4×C17#12111yescharacteristic
158C2×C4×C17#12711yescharacteristic
159C2×C4×C17C2×SD1611yescharacteristic
160C2×C4×C17#13511yescharacteristic
161C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
162C2×C4×C17#13711yescharacteristic
163C2×Dic17—41no—
164C2×Dic17—41no—
165Dic34—42no—
166Dic34—42no—
167C8×C17—42no—
168#3622—42no—
169#3622—42no—
170#3622—81no—
171#3229—171no—
172#3077—171no—
173C2×#461D1711yescharacteristic
174#1546—171no—
175#1481—171no—
176#1460—171no—
177#1301—171no—
178C22×C17—21no—
179C22×C17—21no—
180C22×C17—42no—
181C22×C17—82no—
182C22×C17—82no—
183C22×C17—81no—
184C22×C17—81no—
185C22×C17#39211yescharacteristic
186C22×C17#46511yescharacteristic
187C22×C17#46811yescharacteristic
188C4×C17—21no—
189C4×C17—21no—
190C4×C17—21no—
191C4×C17—82no—
192C4×C17—81no—
193C4×C17#44811yescharacteristic
194C4×C17#44911yescharacteristic
195C4×C17#45011yescharacteristic
196C4×C17#45211yescharacteristic
197C4×C17#47112yes—
198Dic17—81no—
199Dic17—81no—
200C22×SD16—21no—
201#533—171no—
202C2×C4⋊Q8C2×D1711yescharacteristic
203C2×C4×D4C2×D1711yescharacteristic
204#498—341no—
205#487—341no—
206#483—342no—
207#478—342no—
208#476—341no—
209#475—342no—
210#474—341no—
211#461—22no—
212#461—22no—
213#431—171no—
214#431—171no—
215#428—341no—
216#423—171no—
217C2×C4⋊C8C2×D1711yescharacteristic
218#418—341no—
219C2×#103—21no—
220#332—342no—
221Q8⋊C8—342no—
222#323—342no—
223C2×C17—21no—
224C2×C17—21no—
225C2×C17—82no—
226C2×C17#200011yescharacteristic
227C2×C17#200911yescharacteristic
228C2×C17#201911yescharacteristic
229C22×Q8—21no—
230C22×D4C22⋊D1711yescharacteristic
231C23×C4—21no—
232C2×SD16—24no—
233C2×SD16—42no—
234C2×SD16—42no—
235C2×M16—341no—
236C22×C8—21no—
237C4⋊Q8—21no—
238C4⋊Q8—21no—
239C4⋊Q8—21no—
240C4⋊Q8—171no—
241C4⋊Q8—171no—
242C4⋊Q8C22⋊D1712yes—
243#125—341no—
244C22⋊Q8—341no—
245C22⋊Q8—341no—
246C4×Q8—341no—
247C4×Q8—341no—
248C4×D4—21no—
249C4×D4—21no—
250C4×D4—21no—
251C4×D4—21no—
252#117—341no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4C22⋊D1711yescharacteristic
256C2×C22⋊C4—21no—
257C2×C42C22×D1711yescharacteristic
258#107—342no—
259#106—342no—
260#106—344no—
261C4⋊C8—21no—
262C4⋊C8—172no—
263C4⋊C8—341no—
264C4⋊C8—341no—
265C4⋊C8—341no—
266C4⋊C8C22⋊D1712yes—
267#103—24no—
268#103—344no—
269#102—342no—
270#102—342no—
271C22⋊C8—172no—
272C22⋊C8—341no—
273C4×C8—341no—
274C4×C8—341no—
275C17#1018611yescharacteristic, complemented, Sylow
276C24—21no—
277C2×Q8—22no—
278C2×Q8—41no—
279C2×Q8—41no—
280C2×Q8—41no—
281C2×Q8—41no—
282C2×Q8—41no—
283C2×Q8—341no—
284C2×Q8—341no—
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—21no—
289C2×D4—21no—
290C2×D4#6322912yes—
291C22×C4—21no—
292C22×C4—41no—
293C22×C4—41no—
294C22×C4—41no—
295C22×C4—82no—
296C22×C4D4×D1711yescharacteristic
297C22×C4#6325411yescharacteristic
298C22×C4C2×C22⋊D1711yescharacteristic
299SD16—48no—
300M16—681no—
301M16—681no—
302C2×C8—22no—
303C2×C8—41no—
304C2×C8—41no—
305C2×C8—342no—
306C2×C8—342no—
307C2×C8—681no—
308C4⋊C4—22no—
309C4⋊C4—21no—
310C4⋊C4—22no—
311C4⋊C4—21no—
312C4⋊C4—41no—
313C4⋊C4—41no—
314C4⋊C4—341no—
315C4⋊C4—341no—
316C4⋊C4—341no—
317C4⋊C4—341no—
318C4⋊C4—681no—
319C4⋊C4—681no—
320C22⋊C4—41no—
321C22⋊C4—41no—
322C22⋊C4—681no—
323C42—681no—
324C42D4×D1711yescharacteristic
325C42D4×D1711yescharacteristic
326C42C2×C22⋊D1711yescharacteristic
327C42C2×C22⋊D1711yescharacteristic
328C23—22no—
329C23—41no—
330C23—41no—
331C23—81no—
332C23—81no—
333C23#1058762511yescharacteristic
334Q8—42no—
335Q8—42no—
336Q8—81no—
337Q8—81no—
338Q8—682no—
339Q8—682no—
340D4—22no—
341D4—22no—
342D4—41no—
343D4—41no—
344C2×C4—22no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—42no—
348C2×C4—82no—
349C2×C4—81no—
350C2×C4—81no—
351C2×C4—82no—
352C2×C4—81no—
353C2×C4—681no—
354C2×C4—681no—
355C2×C4#1058761811yescharacteristic
356C2×C4C2×#6322911yescharacteristic
357C2×C4#1058762311yescharacteristic
358C2×C4#1058762311yescharacteristic
359C2×C4#1058762411yescharacteristic
360C2×C4#1058762511yescharacteristic
361C2×C4#1058762611yescharacteristic
362C2×C4#1058763611yescharacteristic
363C2×C4#1058763711yescharacteristic
364C2×C4#1058763911yescharacteristic
365C8—42no—
366C8—682no—
367C8—682no—
368C8—1361no—
369C22—21no—
370C22—21no—
371C22—42no—
372C22—82no—
373C22—82no—
374C22—81no—
375C22—81no—
376C22#1176271711yescharacteristic
377C22#1176303611yescharacteristic
378C22#1176305311yescharacteristic
379C4—21no—
380C4—21no—
381C4—21no—
382C4—81no—
383C4—82no—
384C4—1361no—
385C4—1361no—
386C4#1176294711yescharacteristic
387C4#1176295211yescharacteristic
388C4#1176296011yescharacteristic
389C4#1176297111yescharacteristic
390C4#1176306912yes—
391C2—21no—
392C2—21no—
393C2—82no—
394C2#1452978711yescharacteristic
395C2#1452984211yescharacteristic
396C2#1452989611yescharacteristic
subgroupG/H
centerC22#11762717
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC2×C17×#461C2
socleC22×C17#392
prime radicalC22×D4×C17D4
hypercenterC2×#461D17
hypocenterC17#10186
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#461

Complements

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

NH ≅ G/Ntype
1. #14539928C2semidirect
3. #14527456C2semidirect
4. #14527186C2semidirect
6. #14526681C2semidirect
275. C17#10186semidirect

Maximal subgroups

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

subgroupindex
#145399282
#145385812
#145274562
#145271862
#145271052
#145266812
C2×C17×#4612
#1018617