Finite Group Databasebeta

← #16945091

Subgroups — #16945091

Order 4352.

582 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 582 conjugacy classes of subgroups — too many to draw. Only its 83 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#14532063C211yesmaximal, characteristic
2#14528772C211yesmaximal, characteristic, complemented
3#14526809C212yesmaximal, complemented
4#14526782C212yesmaximal, complemented
5C17×#1465C211yesmaximal, characteristic, complemented
6C2×C4×D68C411yescharacteristic, complemented
7C2×C4×C22⋊D17—21no—
8C2×C4×C22⋊D17—21no—
9C2×#10587505—21no—
10#11762745C411yescharacteristic, complemented
11#11762745C2211yescharacteristic
12#11762744—21no—
13#11762718C411yescharacteristic, complemented
14#11762718C2211yescharacteristic
15#11762717—21no—
16#11762669—21no—
17#11762655C411yescharacteristic, complemented
18#11762576C2212yes—
19C2×C4×D4×C17C2211yescharacteristic
20C17×#407—21no—
21C17×#324—21no—
22C17×#323C2212yes—
23C22×D4×C17D411yescharacteristic
24C23×C4×C17D411yescharacteristic
25C23×C4×C17D411yescharacteristic
26C22×C22⋊D17—21no—
27C22×C22⋊D17—21no—
28C22×D68C2×C411yescharacteristic
29C22×C4×D17—21no—
30C2×M16×C17—41no—
31C4×D4×C17—41no—
32C4×D4×C17—41no—
33C2×C4⋊C4×C17D411yescharacteristic
34C2×C22⋊C4×C17C2×C411yescharacteristic
35C2×C22⋊C4×C17C2311yescharacteristic
36C2×C42×C17C2×C411yescharacteristic
37C2×C22⋊Dic17—21no—
38C2×C22⋊Dic17—21no—
39C2×C22⋊Dic17—22no—
40C4×C22⋊D17—44no—
41C4×C22⋊D17—44no—
42C2×#63227—21no—
43C2×#63227—21no—
44C2×#63227—21no—
45C2×C4⋊Dic17—41no—
46C2×C4⋊Dic17C2×C411yescharacteristic
47C2×#63225—21no—
48C2×#63225—21no—
49C2×C4×Dic17—21no—
50C4×D68—41no—
51C4×D68—41no—
52C17×C22⋊C8—22no—
53C17×C22⋊C8—41no—
54#10587505—42no—
55#10587502—21no—
56#10587502—41no—
57#10587502C2×C411yescharacteristic
58#10587502C2×C411yescharacteristic
59C24×C17C22⋊C411yescharacteristic
60C24×C17C2×D411yescharacteristic
61C23×D17—21no—
62C2×D4×C17—21no—
63C2×D4×C17—21no—
64C2×D4×C17—41no—
65C2×D4×C17—41no—
66C22×C4×C17—21no—
67C22×C4×C17—21no—
68C22×C4×C17—21no—
69C22×C4×C17—21no—
70C22×C4×C17—42no—
71C22×C4×C17—42no—
72C22×C4×C17C22⋊C411yescharacteristic
73C22×C4×C17C22⋊C411yescharacteristic
74C22×C4×C17C22⋊C411yescharacteristic
75C22×C4×C17C22×C411yescharacteristic
76C22×C4×C17C2×D411yescharacteristic
77C2×C22⋊D17—42no—
78C2×C22⋊D17—42no—
79C2×C22⋊D17—42no—
80C2×C22⋊D17—42no—
81C2×C22⋊D17—42no—
82C2×C22⋊D17—41no—
83C2×C22⋊D17—41no—
84C22×Dic17—21no—
85C22×Dic17—21no—
86C22×Dic17—21no—
87C22×Dic17—42no—
88C2×D68—41no—
89C2×D68—42no—
90C2×C4×D17—42no—
91C2×C4×D17—42no—
92C2×C4×D17—41no—
93C2×C4×D17—41no—
94M16×C17—82no—
95C2×C8×C17—42no—
96C4⋊C4×C17—41no—
97C22⋊C4×C17—41no—
98C22⋊C4×C17—41no—
99C42×C17—21no—
100C42×C17—21no—
101C22⋊Dic17—42no—
102C22⋊Dic17—42no—
103C22⋊Dic17—42no—
104C22⋊Dic17—42no—
105#63227—42no—
106#63227—42no—
107#63227—42no—
108C4⋊Dic17—41no—
109C4⋊Dic17—82no—
110#63225—42no—
111#63225—42no—
112C4×Dic17—24no—
113#11821—171nomaximal, Sylow
114C23×C17—21no—
115C23×C17—21no—
116C23×C17—21no—
117C23×C17—21no—
118C23×C17—21no—
119C23×C17—41no—
120C23×C17—41no—
121C23×C17—41no—
122C23×C17—41no—
123C23×C17C2×C22⋊C411yescharacteristic
124C23×C17AGL(1,ℤ/8)11yescharacteristic
125C23×C17#13711yescharacteristic
126C22×D17—22no—
127C22×D17—41no—
128C22×D17—41no—
129C22×D17—41no—
130C22×D17—41no—
131C22×D17—41no—
132C22×D17—41no—
133D4×C17—42no—
134D4×C17—42no—
135C2×C4×C17—22no—
136C2×C4×C17—21no—
137C2×C4×C17—21no—
138C2×C4×C17—21no—
139C2×C4×C17—21no—
140C2×C4×C17—21no—
141C2×C4×C17—21no—
142C2×C4×C17—42no—
143C2×C4×C17—42no—
144C2×C4×C17—41no—
145C2×C4×C17—41no—
146C2×C4×C17—41no—
147C2×C4×C17—81no—
148C2×C4×C17—81no—
149C2×C4×C17#9911yescharacteristic
150C2×C4×C17#9911yescharacteristic
151C22⋊D17—44no—
152C22⋊D17—44no—
153C22⋊D17—48no—
154C2×Dic17—22no—
155C2×Dic17—22no—
156C2×Dic17—41no—
157C2×Dic17—41no—
158C2×Dic17—41no—
159C2×Dic17—41no—
160C2×Dic17—41no—
161C2×Dic17—41no—
162C2×Dic17—41no—
163C2×Dic17—82no—
164C2×Dic17—82no—
165C2×Dic17—82no—
166D68—42no—
167D68—42no—
168C4×D17—82no—
169C4×D17—82no—
170C8×C17—82no—
171#2397—171no—
172#1799—171no—
173#1465D1711yescharacteristic, complemented
174#1352—172no—
175#1343—172no—
176C22×C17—21no—
177C22×C17—21no—
178C22×C17—21no—
179C22×C17—21no—
180C22×C17—41no—
181C22×C17—41no—
182C22×C17—42no—
183C22×C17—41no—
184C22×C17—41no—
185C22×C17—41no—
186C22×C17—41no—
187C22×C17—41no—
188C22×C17—81no—
189C22×C17—81no—
190C22×C17C2×#9911yescharacteristic
191C22×C17#41711yescharacteristic
192C22×C17#42111yescharacteristic
193C2×D17—42no—
194C2×D17—42no—
195C2×D17—42no—
196C2×D17—81no—
197C2×D17—81no—
198C2×D17—81no—
199C2×D17—81no—
200C4×C17—21no—
201C4×C17—41no—
202C4×C17—41no—
203C4×C17—41no—
204C4×C17—41no—
205C4×C17#35312yes—
206Dic17—42no—
207Dic17—42no—
208Dic17—81no—
209Dic17—162no—
210C2×C4×D4—171no—
211C2×C4×D4—341no—
212C2×C4×D4—341no—
213C2×C4×D4C2×D1711yescharacteristic
214C2×#99—341no—
215#407—21no—
216#399—171no—
217#399—171no—
218#399—341no—
219#392—171no—
220#392—171no—
221#392—341no—
222#380—341no—
223#376—171no—
224#342—172no—
225#324—21no—
226#323C2×D1712yes—
227C2×C17—21no—
228C2×C17—21no—
229C2×C17—41no—
230C2×C17—41no—
231C2×C17—81no—
232C2×C17#151311yescharacteristic
233C2×C17#212011yescharacteristic
234C2×C17C2×#35311yescharacteristic
235D17—82no—
236C22×D4—171no—
237C22×D4—341no—
238C22×D4—341no—
239C22×D4D6811yescharacteristic
240C23×C4—341no—
241C23×C4D6811yescharacteristic
242C23×C4C22⋊D1711yescharacteristic
243C2×M16—41no—
244C4×D4—41no—
245C4×D4—41no—
246C4×D4—681no—
247C4×D4—681no—
248C4×D4—684no—
249C4×D4—684no—
250C2×C4⋊C4—171no—
251C2×C4⋊C4—341no—
252C2×C4⋊C4—341no—
253C2×C4⋊C4—681no—
254C2×C4⋊C4C22⋊D1711yescharacteristic
255C2×C22⋊C4—341no—
256C2×C22⋊C4—341no—
257C2×C22⋊C4—341no—
258C2×C22⋊C4—341no—
259C2×C22⋊C4—341no—
260C2×C22⋊C4—342no—
261C2×C22⋊C4C4×D1711yescharacteristic
262C2×C22⋊C4C22×D1711yescharacteristic
263C2×C42—341no—
264C2×C42C4×D1711yescharacteristic
265#99—682no—
266C22⋊C8—22no—
267C22⋊C8—41no—
268#95—171no—
269#95—171no—
270#95—341no—
271#95—681no—
272C17#1182111yescharacteristic, complemented, Sylow
273C24—341no—
274C24#6322711yescharacteristic
275C24C2×D6811yescharacteristic
276C2×D4—21no—
277C2×D4—21no—
278C2×D4—41no—
279C2×D4—41no—
280C2×D4—681no—
281C2×D4—682no—
282C2×D4—682no—
283C2×D4—682no—
284C2×D4—682no—
285C2×D4—682no—
286C2×D4—682no—
287C2×D4—681no—
288C2×D4—681no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—42no—
294C22×C4—42no—
295C22×C4—341no—
296C22×C4—341no—
297C22×C4—341no—
298C22×C4—682no—
299C22×C4—682no—
300C22×C4—681no—
301C22×C4—681no—
302C22×C4—682no—
303C22×C4#6322711yescharacteristic
304C22×C4#6322711yescharacteristic
305C22×C4#6322711yescharacteristic
306C22×C4C2×C4×D1711yescharacteristic
307C22×C4C2×C22⋊D1711yescharacteristic
308M16—82no—
309C2×C8—42no—
310C4⋊C4—41no—
311C4⋊C4—681no—
312C4⋊C4—682no—
313C4⋊C4—682no—
314C4⋊C4—1362no—
315C22⋊C4—41no—
316C22⋊C4—41no—
317C22⋊C4—682no—
318C22⋊C4—682no—
319C22⋊C4—682no—
320C22⋊C4—682no—
321C22⋊C4—682no—
322C22⋊C4—682no—
323C22⋊C4—682no—
324C42—21no—
325C42—21no—
326C42—344no—
327C23—21no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23—41no—
333C23—41no—
334C23—41no—
335C23—41no—
336C23—342no—
337C23—681no—
338C23—681no—
339C23—681no—
340C23—681no—
341C23—681no—
342C23—681no—
343C23#1058759411yescharacteristic
344C23#1058759511yescharacteristic
345C23C2×#6322711yescharacteristic
346D4—42no—
347D4—42no—
348D4—682no—
349D4—682no—
350D4—684no—
351D4—684no—
352D4—688no—
353C2×C4—22no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—42no—
361C2×C4—42no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—81no—
366C2×C4—81no—
367C2×C4—342no—
368C2×C4—342no—
369C2×C4—681no—
370C2×C4—681no—
371C2×C4—681no—
372C2×C4—681no—
373C2×C4—681no—
374C2×C4—681no—
375C2×C4—681no—
376C2×C4—1362no—
377C2×C4—1362no—
378C2×C4—1362no—
379C2×C4—1362no—
380C2×C4—1362no—
381C2×C4#1058747711yescharacteristic
382C2×C4#1058747711yescharacteristic
383C8—82no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—41no—
389C22—41no—
390C22—42no—
391C22—41no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—81no—
397C22—81no—
398C22—682no—
399C22—682no—
400C22—682no—
401C22—1361no—
402C22—1361no—
403C22—1361no—
404C22—1361no—
405C22C2×#1058747711yescharacteristic
406C22#1176281111yescharacteristic
407C22#1176282511yescharacteristic
408C4—21no—
409C4—41no—
410C4—41no—
411C4—41no—
412C4—41no—
413C4—2722no—
414C4—682no—
415C4—682no—
416C4—1361no—
417C4#1176260112yes—
418C2—21no—
419C2—21no—
420C2—41no—
421C2—41no—
422C2—81no—
423C2—1362no—
424C2#1452732811yescharacteristic
425C2#1453042611yescharacteristic
426C2C2×#1176260111yescharacteristic
subgroupG/H
centerC22C2×#10587477
commutatorC22×C4×C17C22×C4
FrattiniC2×C22⋊C4C22×D17
FittingC17×#1465C2
socleC22×C17C2×#99
prime radical#14532063C2
cosocleC2×C22⋊C4×C17C23
hypercenter#1465D17
hypocenterC17#11821
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1465

Complements

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

NH ≅ G/Ntype
2. #14528772C2semidirect
3. #14526809C2semidirect
4. #14526782C2semidirect
5. C17×#1465C2semidirect
6. C2×C4×D68C4semidirect
10. #11762745C4semidirect
13. #11762718C4semidirect
17. #11762655C4semidirect
173. #1465D17semidirect
272. C17#11821semidirect

Maximal subgroups

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

subgroupindex
#145320632
#145287722
#145268092
#145267822
C17×#14652
#1182117