Finite Group Databasebeta

← #16932065

Subgroups — #16932065

Order 4352.

610 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 610 conjugacy classes of subgroups — too many to draw. Only its 93 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#14533256C211yesmaximal, characteristic
2#14531385C211yesmaximal, characteristic, complemented
3#14528862C211yesmaximal, characteristic, complemented
4#14527313C211yesmaximal, characteristic
5#14526638C211yesmaximal, characteristic, complemented
6#14526636C211yesmaximal, characteristic, complemented
7C17×#1510C211yesmaximal, characteristic
8C2×#10587621—21no—
9C2×#10587621—21no—
10C22×C4⋊Dic17C2211yescharacteristic
11#11762773C2211yescharacteristic
12#11762745—22no—
13#11762712C412yescomplemented
14#11762694—22no—
15#11762692—22no—
16#11762678C412yescomplemented
17#11762672C2211yescharacteristic
18#11762667—21no—
19C22⋊C4×Dic17—21no—
20C4×C22⋊Dic17C2211yescharacteristic
21#11762577—22no—
22#11762543—22no—
23C2×C17×#121C2211yescharacteristic
24C17×#407C2211yescharacteristic
25C17×#381C2211yescharacteristic
26C17×#327—22no—
27C22×D4×C17—21no—
28C22×D4×C17C2×C411yescharacteristic
29C23×C4×C17C2311yescharacteristic
30C23×Dic17D411yescharacteristic
31C23×Dic17D411yescharacteristic
32C2×M16×C17—21no—
33C17×#121—21no—
34C17×#121—21no—
35C17×#121—21no—
36C17×#121—21no—
37C2×C4⋊C4×C17C2×C411yescharacteristic
38C2×C22⋊C4×C17—21no—
39C2×C22⋊C4×C17—21no—
40C2×C22⋊Dic17—21no—
41C2×C22⋊Dic17—21no—
42C2×C22⋊Dic17—22no—
43C2×C22⋊Dic17—22no—
44#10587621—44no—
45#10587621—44no—
46C2×C4⋊Dic17—21no—
47C2×C4⋊Dic17—21no—
48C2×C4⋊Dic17—21no—
49C2×C4⋊Dic17—21no—
50C2×C4⋊Dic17C2×C412yes—
51C2×C4⋊Dic17D412yes—
52C2×#63225—22no—
53C2×#63225—22no—
54C2×#63225—22no—
55C2×C4×Dic17—22no—
56C2×C4×Dic17C2×C412yes—
57C2×#63223—21no—
58C17×C22⋊C8—21no—
59C17×C22⋊C8—21no—
60C17×#95—21no—
61C17×#95D412yes—
62#10587502—22no—
63#10587502—22no—
64#10587502—21no—
65#10587502—21no—
66#10587502D412yes—
67C22⋊#3622—21no—
68C22⋊#3622—21no—
69C24×C17—21no—
70C24×C17C2×D411yescharacteristic
71C2×D4×C17—21no—
72C2×D4×C17—21no—
73C2×D4×C17—42no—
74C2×D4×C17—42no—
75C2×D4×C17—42no—
76C2×D4×C17—41no—
77C2×D4×C17—41no—
78C22×C4×C17—21no—
79C22×C4×C17—22no—
80C22×C4×C17—42no—
81C22×C4×C17C22×C411yescharacteristic
82C22×C4×C17C2×D411yescharacteristic
83C22×C4×C17C2×D411yescharacteristic
84C22×C4×C17C2×D411yescharacteristic
85C22×C4×C17#4111yescharacteristic
86C22×C4×C17#4111yescharacteristic
87C22×Dic17—22no—
88C22×Dic17—21no—
89C22×Dic17—21no—
90C22×Dic17—21no—
91C22×Dic17—21no—
92C22×Dic17—22no—
93C22×Dic17—42no—
94C22×Dic17—42no—
95C22×Dic17C22⋊C412yes—
96C22×Dic17C22⋊C412yes—
97M16×C17—42no—
98C2×C8×C17—41no—
99C4⋊C4×C17—21no—
100C4⋊C4×C17—21no—
101C22⋊C4×C17—42no—
102C22⋊C4×C17—41no—
103C22⋊C4×C17—41no—
104C22⋊Dic17—24no—
105C22⋊Dic17—44no—
106C22⋊Dic17—44no—
107C22⋊Dic17—42no—
108C4⋊Dic17—22no—
109C4⋊Dic17—22no—
110C4⋊Dic17—22no—
111C4⋊Dic17—22no—
112#63225—44no—
113#63225—44no—
114#63225—82no—
115C4×Dic17—42no—
116C4×Dic17—82no—
117#63223—42no—
118C2×#3622—41no—
119#9464—171nomaximal, Sylow
120C23×C17—22no—
121C23×C17—22no—
122C23×C17—41no—
123C23×C17—41no—
124C23×C17—41no—
125C23×C17—42no—
126C23×C17—41no—
127C23×C17—42no—
128C23×C17C2×C22⋊C411yescharacteristic
129C23×C17#12011yescharacteristic
130C23×C17#12311yescharacteristic
131D4×C17—81no—
132D4×C17—81no—
133D4×C17—82no—
134D4×C17—82no—
135C2×C4×C17—22no—
136C2×C4×C17—22no—
137C2×C4×C17—41no—
138C2×C4×C17—41no—
139C2×C4×C17—41no—
140C2×C4×C17—41no—
141C2×C4×C17—42no—
142C2×C4×C17—42no—
143C2×C4×C17—41no—
144C2×C4×C17—41no—
145C2×C4×C17—41no—
146C2×C4×C17—42no—
147C2×C4×C17C4×D411yescharacteristic
148C2×C4×C17C4×D411yescharacteristic
149C2×C4×C17#12111yescharacteristic
150C2×C4×C17#12111yescharacteristic
151C2×Dic17—24no—
152C2×Dic17—22no—
153C2×Dic17—22no—
154C2×Dic17—42no—
155C2×Dic17—42no—
156C2×Dic17—42no—
157C2×Dic17—42no—
158C2×Dic17—42no—
159C2×Dic17—42no—
160C2×Dic17—42no—
161C2×Dic17—42no—
162C2×Dic17—42no—
163C2×Dic17—81no—
164C2×Dic17—81no—
165C8×C17—81no—
166#3622—81no—
167#2501—171no—
168#2313—171no—
169#1821—171no—
170#1510—171no—
171#1510D1711yescharacteristic
172#1284—171no—
173#1284—171no—
174C22×C17—21no—
175C22×C17—21no—
176C22×C17—21no—
177C22×C17—21no—
178C22×C17—21no—
179C22×C17—21no—
180C22×C17—21no—
181C22×C17—44no—
182C22×C17—82no—
183C22×C17—82no—
184C22×C17—81no—
185C22×C17—81no—
186C22×C17—81no—
187C22×C17#38611yescharacteristic
188C22×C17#41012yes—
189C22×C17#45312yes—
190C4×C17—21no—
191C4×C17—21no—
192C4×C17—21no—
193C4×C17—21no—
194C4×C17—82no—
195C4×C17—81no—
196Dic17—44no—
197Dic17—42no—
198Dic17—42no—
199Dic17—82no—
200C2×#123—341no—
201C2×#123—341no—
202C2×#121C2×D1711yescharacteristic
203C22×C4⋊C4—171no—
204#407—171no—
205#407C2×D1711yescharacteristic
206#399—342no—
207#390—172no—
208#387—342no—
209#387—342no—
210#384—172no—
211#381—171no—
212#381C2×D1711yescharacteristic
213#380—341no—
214C4×C22⋊C4—171no—
215C4×C22⋊C4—341no—
216#343—342no—
217#327—22no—
218#327—342no—
219C2×C17—22no—
220C2×C17—22no—
221C2×C17—41no—
222C2×C17—161no—
223C2×C17#188711yescharacteristic
224C2×C17#189911yescharacteristic
225C2×C17#191211yescharacteristic
226C22×D4—21no—
227C22×D4C4×D1711yescharacteristic
228C23×C4—171no—
229C23×C4—171no—
230C23×C4C22×D1711yescharacteristic
231C2×M16—21no—
232C2×M16—341no—
233#123—684no—
234#123—684no—
235#121—21no—
236#121—21no—
237#121—21no—
238#121—21no—
239C2×C4⋊C4—172no—
240C2×C4⋊C4—172no—
241C2×C4⋊C4—341no—
242C2×C4⋊C4—341no—
243C2×C4⋊C4—341no—
244C2×C4⋊C4—341no—
245C2×C4⋊C4—342no—
246C2×C4⋊C4—342no—
247C2×C4⋊C4—342no—
248C2×C4⋊C4C4×D1711yescharacteristic
249C2×C22⋊C4—21no—
250C2×C22⋊C4—21no—
251C2×C22⋊C4—341no—
252C2×C22⋊C4—342no—
253C2×C22⋊C4—342no—
254C2×C22⋊C4—341no—
255C2×C42—172no—
256C2×C42—342no—
257C22⋊C8—21no—
258C22⋊C8—21no—
259C22⋊C8—341no—
260C22⋊C8—341no—
261#95—21no—
262#95—172no—
263#95—342no—
264#95—342no—
265#95—341no—
266#95—341no—
267#95C22⋊D1712yes—
268C17#946411yescharacteristic, complemented, Sylow
269C24—21no—
270C24D4×D1711yescharacteristic
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—42no—
274C2×D4—42no—
275C2×D4—42no—
276C2×D4—41no—
277C2×D4—41no—
278C22×C4—21no—
279C22×C4—22no—
280C22×C4—42no—
281C22×C4—172no—
282C22×C4—172no—
283C22×C4—342no—
284C22×C4—341no—
285C22×C4—341no—
286C22×C4—341no—
287C22×C4—341no—
288C22×C4—342no—
289C22×C4—682no—
290C22×C4—682no—
291C22×C4C2×C4×D1711yescharacteristic
292C22×C4#6325211yescharacteristic
293C22×C4D4×D1711yescharacteristic
294C22×C4D4×D1711yescharacteristic
295C22×C4#6325411yescharacteristic
296C22×C4C2×C22⋊D1711yescharacteristic
297M16—42no—
298M16—682no—
299C2×C8—41no—
300C2×C8—681no—
301C4⋊C4—21no—
302C4⋊C4—21no—
303C4⋊C4—342no—
304C4⋊C4—342no—
305C4⋊C4—342no—
306C4⋊C4—342no—
307C4⋊C4—684no—
308C4⋊C4—684no—
309C4⋊C4—1362no—
310C22⋊C4—42no—
311C22⋊C4—41no—
312C22⋊C4—41no—
313C22⋊C4—344no—
314C22⋊C4—684no—
315C22⋊C4—684no—
316C22⋊C4—682no—
317C42—682no—
318C42—1362no—
319C23—22no—
320C23—22no—
321C23—41no—
322C23—41no—
323C23—41no—
324C23—42no—
325C23—42no—
326C23—41no—
327C23C22⋊C4×D1711yescharacteristic
328C23#1058756911yescharacteristic
329C23#1058762311yescharacteristic
330D4—81no—
331D4—81no—
332D4—82no—
333D4—82no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—42no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—41no—
346C2×C4—344no—
347C2×C4—342no—
348C2×C4—342no—
349C2×C4—682no—
350C2×C4—682no—
351C2×C4—682no—
352C2×C4—682no—
353C2×C4—682no—
354C2×C4—682no—
355C2×C4—682no—
356C2×C4—682no—
357C2×C4—682no—
358C2×C4—1361no—
359C2×C4—1361no—
360C2×C4#1058756711yescharacteristic
361C2×C4#1058757011yescharacteristic
362C2×C4C4×C22⋊D1711yescharacteristic
363C2×C4#1058762411yescharacteristic
364C8—81no—
365C8—1361no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—44no—
374C22—82no—
375C22—82no—
376C22—81no—
377C22—81no—
378C22—81no—
379C22#1176268511yescharacteristic
380C22#1176278112yes—
381C22#1176297512yes—
382C4—21no—
383C4—21no—
384C4—21no—
385C4—21no—
386C4—82no—
387C4—81no—
388C4—684no—
389C4—682no—
390C4—682no—
391C4—1362no—
392C2—22no—
393C2—22no—
394C2—41no—
395C2—161no—
396C2#1452917911yescharacteristic
397C2#1452923911yescharacteristic
398C2#1452931811yescharacteristic
subgroupG/H
centerC22#11762685
commutatorC22×C4×C17C22×C4
FrattiniC23×C4C22×D17
FittingC17×#1510C2
socleC22×C17#386
prime radicalC2×C17×#121C22
cosocleC23×C4×C17C23
hypercenter#1510D17
hypocenterC17#9464
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1510

Complements

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

NH ≅ G/Ntype
2. #14531385C2semidirect
3. #14528862C2semidirect
5. #14526638C2semidirect
6. #14526636C2semidirect
13. #11762712C4semidirect
16. #11762678C4semidirect
268. C17#9464semidirect

Maximal subgroups

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

subgroupindex
#145332562
#145313852
#145288622
#145273132
#145266382
#145266362
C17×#15102
#946417