Finite Group Databasebeta

← #16945090

Subgroups — #16945090

Order 4352.

582 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 582 conjugacy classes of subgroups — too many to draw. Only its 91 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#14528772C211yesmaximal, characteristic, complemented
2#14527122C211yesmaximal, characteristic, complemented
3#14526808C212yesmaximal, complemented
4#14526781C212yesmaximal, complemented
5C17×#2397C211yesmaximal, characteristic
6C2×#10587505—21no—
7#11762773—21no—
8#11762669—21no—
9#11762576C2212yes—
10#11762535—21no—
11#11762533C2212yes—
12C2×C4×D4×C17—21no—
13C2×C4×D4×C17—21no—
14C2×C4×D4×C17C411yescharacteristic, complemented
15C2×C4×D4×C17C2211yescharacteristic
16C17×#399—21no—
17C17×#399C411yescharacteristic, complemented
18C17×#399C2211yescharacteristic
19C17×#392—21no—
20C17×#392C411yescharacteristic, complemented
21C17×#392C2211yescharacteristic
22C17×#376C411yescharacteristic, complemented
23C22×D4×C17—21no—
24C22×D4×C17—21no—
25C22×D4×C17C2×C411yescharacteristic
26C22×D4×C17D411yescharacteristic
27C23×C4×C17—21no—
28C23×C4×C17D411yescharacteristic
29C23×C4×C17D411yescharacteristic
30C4×D4×C17—41no—
31C4×D4×C17—41no—
32C4×D4×C17—44no—
33C4×D4×C17—44no—
34C4×D4×C17—41no—
35C4×D4×C17—41no—
36C2×C4⋊C4×C17—21no—
37C2×C4⋊C4×C17—21no—
38C2×C4⋊C4×C17C2×C411yescharacteristic
39C2×C4⋊C4×C17D411yescharacteristic
40C2×C22⋊C4×C17—21no—
41C2×C22⋊C4×C17—21no—
42C2×C22⋊C4×C17—21no—
43C2×C22⋊C4×C17—21no—
44C2×C22⋊C4×C17—21no—
45C2×C22⋊C4×C17C2×C411yescharacteristic
46C2×C22⋊C4×C17C2311yescharacteristic
47C2×C42×C17—21no—
48C2×C42×C17C2×C411yescharacteristic
49C2×C22⋊Dic17—22no—
50C2×C4⋊Dic17—41no—
51C2×#63223—41no—
52C17×#95—21no—
53C17×#95C2×C411yescharacteristic
54C17×#95C2×C411yescharacteristic
55#10587505—42no—
56#10587502—41no—
57C22⋊#3622—22no—
58C22⋊#3622—41no—
59C24×C17—21no—
60C24×C17C22⋊C411yescharacteristic
61C24×C17C2×D411yescharacteristic
62C2×D4×C17—21no—
63C2×D4×C17—21no—
64C2×D4×C17—41no—
65C2×D4×C17—41no—
66C2×D4×C17—41no—
67C2×D4×C17—42no—
68C2×D4×C17—42no—
69C2×D4×C17—42no—
70C2×D4×C17—42no—
71C2×D4×C17—42no—
72C2×D4×C17—41no—
73C2×D4×C17—41no—
74C2×D4×C17—42no—
75C22×C4×C17—21no—
76C22×C4×C17—21no—
77C22×C4×C17—21no—
78C22×C4×C17—21no—
79C22×C4×C17—21no—
80C22×C4×C17—21no—
81C22×C4×C17—21no—
82C22×C4×C17—42no—
83C22×C4×C17—42no—
84C22×C4×C17—42no—
85C22×C4×C17—42no—
86C22×C4×C17—41no—
87C22×C4×C17—41no—
88C22×C4×C17C22⋊C411yescharacteristic
89C22×C4×C17C22⋊C411yescharacteristic
90C22×C4×C17C22⋊C411yescharacteristic
91C22×C4×C17C22×C411yescharacteristic
92C22×C4×C17C2×D411yescharacteristic
93C22×Dic17—42no—
94C4⋊C4×C17—41no—
95C4⋊C4×C17—41no—
96C4⋊C4×C17—42no—
97C4⋊C4×C17—42no—
98C22⋊C4×C17—41no—
99C22⋊C4×C17—41no—
100C22⋊C4×C17—42no—
101C22⋊C4×C17—42no—
102C22⋊C4×C17—42no—
103C22⋊C4×C17—42no—
104C22⋊C4×C17—42no—
105C42×C17—24no—
106C42×C17—21no—
107C42×C17—21no—
108C22⋊Dic17—42no—
109C22⋊Dic17—42no—
110C4⋊Dic17—82no—
111#63223—82no—
112C2×#3622—42no—
113#11821—171nomaximal, Sylow
114C23×C17—21no—
115C23×C17—21no—
116C23×C17—22no—
117C23×C17—21no—
118C23×C17—21no—
119C23×C17—21no—
120C23×C17—41no—
121C23×C17—41no—
122C23×C17—41no—
123C23×C17—41no—
124C23×C17—41no—
125C23×C17—41no—
126C23×C17—41no—
127C23×C17—41no—
128C23×C17—41no—
129C23×C17—41no—
130C23×C17C2×C22⋊C411yescharacteristic
131C23×C17AGL(1,ℤ/8)11yescharacteristic
132C23×C17#13711yescharacteristic
133D4×C17—42no—
134D4×C17—42no—
135D4×C17—42no—
136D4×C17—44no—
137D4×C17—44no—
138D4×C17—48no—
139D4×C17—42no—
140C2×C4×C17—22no—
141C2×C4×C17—22no—
142C2×C4×C17—22no—
143C2×C4×C17—21no—
144C2×C4×C17—21no—
145C2×C4×C17—21no—
146C2×C4×C17—21no—
147C2×C4×C17—21no—
148C2×C4×C17—21no—
149C2×C4×C17—41no—
150C2×C4×C17—41no—
151C2×C4×C17—41no—
152C2×C4×C17—41no—
153C2×C4×C17—42no—
154C2×C4×C17—42no—
155C2×C4×C17—41no—
156C2×C4×C17—41no—
157C2×C4×C17—41no—
158C2×C4×C17—41no—
159C2×C4×C17—41no—
160C2×C4×C17—41no—
161C2×C4×C17—81no—
162C2×C4×C17—81no—
163C2×C4×C17—82no—
164C2×C4×C17—82no—
165C2×C4×C17#9911yescharacteristic
166C2×C4×C17#9911yescharacteristic
167C2×Dic17—82no—
168C2×Dic17—82no—
169C2×Dic17—82no—
170#3622—82no—
171#2397D1711yescharacteristic
172#1799—171no—
173#1465—171no—
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—42no—
184C22×C17—42no—
185C22×C17—41no—
186C22×C17—41no—
187C22×C17—42no—
188C22×C17—41no—
189C22×C17—41no—
190C22×C17—41no—
191C22×C17—81no—
192C22×C17—81no—
193C22×C17—81no—
194C22×C17—81no—
195C22×C17—81no—
196C22×C17—81no—
197C22×C17C2×#9911yescharacteristic
198C22×C17#41711yescharacteristic
199C22×C17#42111yescharacteristic
200C4×C17—21no—
201C4×C17—42no—
202C4×C17—42no—
203C4×C17—41no—
204C4×C17—41no—
205C4×C17—41no—
206C4×C17—41no—
207C4×C17—81no—
208C4×C17#35312yes—
209Dic17—162no—
210C2×C4×D4—21no—
211C2×C4×D4—21no—
212C2×C4×D4Dic1711yescharacteristic, complemented
213C2×C4×D4C2×D1711yescharacteristic
214C2×#99—341no—
215#407—341no—
216#399—21no—
217#399Dic1711yescharacteristic, complemented
218#399C2×D1711yescharacteristic
219#392—21no—
220#392Dic1711yescharacteristic, complemented
221#392C2×D1711yescharacteristic
222#380—341no—
223#376Dic1711yescharacteristic, complemented
224#342—172no—
225#324—341no—
226#323—172no—
227C2×C17—21no—
228C2×C17—21no—
229C2×C17—41no—
230C2×C17—41no—
231C2×C17—81no—
232C2×C17—82no—
233C2×C17#151311yescharacteristic
234C2×C17#212011yescharacteristic
235C2×C17C2×#35311yescharacteristic
236C22×D4—21no—
237C22×D4—21no—
238C22×D4C2×Dic1711yescharacteristic
239C22×D4C22⋊D1711yescharacteristic
240C23×C4—21no—
241C23×C4C22⋊D1711yescharacteristic
242C23×C4C22⋊D1711yescharacteristic
243C2×M16—681no—
244C4×D4—41no—
245C4×D4—41no—
246C4×D4—44no—
247C4×D4—44no—
248C4×D4—41no—
249C4×D4—41no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—681no—
253C2×C4⋊C4C2×Dic1711yescharacteristic
254C2×C4⋊C4C22⋊D1711yescharacteristic
255C2×C22⋊C4—21no—
256C2×C22⋊C4—21no—
257C2×C22⋊C4—21no—
258C2×C22⋊C4—21no—
259C2×C22⋊C4—21no—
260C2×C22⋊C4—342no—
261C2×C22⋊C4C2×Dic1711yescharacteristic
262C2×C22⋊C4C22×D1711yescharacteristic
263C2×C42—21no—
264C2×C42C2×Dic1711yescharacteristic
265#99—682no—
266C22⋊C8—342no—
267C22⋊C8—681no—
268#95—21no—
269#95—681no—
270#95C2×Dic1711yescharacteristic
271#95C2×Dic1711yescharacteristic
272C17#1182111yescharacteristic, complemented, Sylow
273C24—21no—
274C24C22⋊Dic1711yescharacteristic
275C24C2×C22⋊D1711yescharacteristic
276C2×D4—21no—
277C2×D4—21no—
278C2×D4—41no—
279C2×D4—41no—
280C2×D4—41no—
281C2×D4—42no—
282C2×D4—42no—
283C2×D4—42no—
284C2×D4—42no—
285C2×D4—42no—
286C2×D4—41no—
287C2×D4—41no—
288C2×D4—42no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—42no—
297C22×C4—42no—
298C22×C4—42no—
299C22×C4—42no—
300C22×C4—41no—
301C22×C4—41no—
302C22×C4—682no—
303C22×C4C22⋊Dic1711yescharacteristic
304C22×C4C22⋊Dic1711yescharacteristic
305C22×C4C22⋊Dic1711yescharacteristic
306C22×C4C22×Dic1711yescharacteristic
307C22×C4C2×C22⋊D1711yescharacteristic
308M16—1362no—
309C2×C8—682no—
310C4⋊C4—41no—
311C4⋊C4—41no—
312C4⋊C4—42no—
313C4⋊C4—42no—
314C4⋊C4—1362no—
315C22⋊C4—41no—
316C22⋊C4—41no—
317C22⋊C4—42no—
318C22⋊C4—42no—
319C22⋊C4—42no—
320C22⋊C4—42no—
321C22⋊C4—42no—
322C22⋊C4—682no—
323C22⋊C4—682no—
324C42—24no—
325C42—21no—
326C42—21no—
327C23—21no—
328C23—21no—
329C23—22no—
330C23—21no—
331C23—21no—
332C23—21no—
333C23—41no—
334C23—41no—
335C23—41no—
336C23—41no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23—41no—
341C23—41no—
342C23—41no—
343C23#1058763511yescharacteristic
344C23#1058763711yescharacteristic
345C23C2×C22⋊Dic1711yescharacteristic
346D4—42no—
347D4—42no—
348D4—42no—
349D4—44no—
350D4—44no—
351D4—48no—
352D4—42no—
353C2×C4—22no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—81no—
375C2×C4—81no—
376C2×C4—82no—
377C2×C4—82no—
378C2×C4—1362no—
379C2×C4—1362no—
380C2×C4—1362no—
381C2×C4#1058750511yescharacteristic
382C2×C4#1058750511yescharacteristic
383C8—1362no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—41no—
389C22—41no—
390C22—42no—
391C22—42no—
392C22—42no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—42no—
397C22—41no—
398C22—41no—
399C22—81no—
400C22—81no—
401C22—81no—
402C22—81no—
403C22—81no—
404C22—81no—
405C22C2×#1058750511yescharacteristic
406C22#1176281011yescharacteristic
407C22#1176282611yescharacteristic
408C4—21no—
409C4—42no—
410C4—42no—
411C4—41no—
412C4—41no—
413C4—41no—
414C4—41no—
415C4—81no—
416C4—2722no—
417C4#1176260212yes—
418C2—21no—
419C2—21no—
420C2—41no—
421C2—41no—
422C2—81no—
423C2—82no—
424C2#1452732711yescharacteristic
425C2#1453042511yescharacteristic
426C2C2×#1176260211yescharacteristic
subgroupG/H
centerC22C2×#10587505
commutatorC22×C4×C17C22×C4
FrattiniC2×C22⋊C4C22×D17
Fitting, prime radicalC17×#2397C2
socleC22×C17C2×#99
cosocleC2×C22⋊C4×C17C23
hypercenter#2397D17
hypocenterC17#11821
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2397

Complements

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

NH ≅ G/Ntype
1. #14528772C2semidirect
2. #14527122C2semidirect
3. #14526808C2semidirect
4. #14526781C2semidirect
14. C2×C4×D4×C17C4semidirect
17. C17×#399C4semidirect
20. C17×#392C4semidirect
22. C17×#376C4semidirect
212. C2×C4×D4Dic17semidirect
217. #399Dic17semidirect
220. #392Dic17semidirect
223. #376Dic17semidirect
272. C17#11821semidirect

Maximal subgroups

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

subgroupindex
#145287722
#145271222
#145268082
#145267812
C17×#23972
#1182117