Finite Group Databasebeta

← #17979543

Subgroups — #17979543

Order 4352.

2738 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763888C212yesmaximal
2#14545430C214yesmaximal, complemented
3#14545429C2112yesmaximal, complemented
4#14545427C216yesmaximal, complemented
5C2×#11763813C213yesmaximal, complemented
6D17⋊#423C213yesmaximal, complemented
7C4×#41×D17C211yesmaximal, characteristic
8#11763888—216no—
9C2×#10587680C2214yes—
10C2×#10587678C22112yes—
11C22×#63243C2216yes—
12C2×D17⋊M16C2216yes—
13#11763816C22124yescomplemented
14#11763815C22124yescomplemented
15#11763814C2216yes—
16#11763813C2211yescharacteristic
17#11763813C2213yes—
18#11763813C2216yes—
19#11763813C22112yescomplemented
20#11763812C22112yescomplemented
21#11763810C22112yescomplemented
22C2×C4⋊#3624C22112yescomplemented
23C2×#41×D17C2211yescharacteristic
24#41×Dic17C411yescharacteristic
25C4×#63256C2212yes—
26C4×#63252C413yes—
27#11763277C413yes—
28C4×#63254C2216yes—
29C4×Q8×D17C412yes—
30C4×D4×D17C416yes—
31#117×D17C2213yes—
32C2×C42×D17C2213yes—
33C4×#41×C17C411yescharacteristic
34C2×#41×C17C2×C411yescharacteristic
35#41×D17D418yes—
36#41×D17Q818yes—
37C2×#63256C2311yescharacteristic
38C2×Q8×D17C2×C411yescharacteristic
39C2×#63254C2313yes—
40C2×D4×D17C2×C413yes—
41C2×#63252C2×C413yes—
42C22×C4×D17C2×C416yes—
43C22×C4×D17C2313yes—
44C2×#63247C23112yes—
45C22×#3624C23112yes—
46#10587680—216no—
47#10587678—248no—
48D17⋊M16—224no—
49C2×#63243—224no—
50C2×#63243C2316yes—
51C2×#63243C2312yes—
52C2×#63243C23112yes—
53C2×#63242C23112yes—
54C4×Q8×C17C2×C412yes—
55C4×D4×C17C2×C416yes—
56C17×#117C2×C413yes—
57C2×C42×C17C2×C413yes—
58Q8×Dic17C2×C412yes—
59D4×Dic17C2×C416yes—
60C4×C22⋊D17C2×C4112yes—
61#10587612C2×C413yes—
62C2×C4×Dic17C2×C413yes—
63C2×C4×Dic17C2316yes—
64#10587579C2×C416yes—
65#10587578C2316yes—
66C4⋊C4×D17C2×C416yes—
67#10587573C2×C416yes—
68#10587567C2×C4112yes—
69C22⋊C4×D17C2×C416yes—
70#10587563C2316yes—
71C4×D68C2×C416yes—
72#10587558C2×C416yes—
73C42×D17C2×C416yes—
74C42×D17C2×C413yes—
75C42×D17C2×C413yes—
76C42×D17C2311yescharacteristic
77C42×D17C2313yes—
78C42×D17C2316yes—
79C4×Dic34C2×C416yes—
80#10587544C23124yes—
81C4⋊#3624C23112yes—
82C4⋊#3624C23124yes—
83C4⋊#3624C2314yes—
84C23×D17C22×C413yes—
85#41×C17C4⋊C418yes—
86C2×Q8×C17C22×C411yescharacteristic
87C2×D4×C17C22×C413yes—
88C22×C4×C17C22×C416yes—
89C22×C4×C17C22×C413yes—
90C2×C22⋊D17C22×C416yes—
91C22×Dic17C22×C416yes—
92C22×Dic17C2413yes—
93#63256C2×D414yes—
94#63256C2×Q814yes—
95Q8×D17C4⋊C418yes—
96#63254C2×D4112yes—
97#63254C2×Q8112yes—
98D4×D17C4⋊C4124yes—
99#63252C4⋊C4124yes—
100C2×D68C22×C413yes—
101C2×C4×D17—412no—
102C2×C4×D17C22×C412yes—
103C2×C4×D17C22×C416yes—
104C2×C4×D17C22×C416yes—
105C2×C4×D17C22×C416yes—
106C2×C4×D17C22×C413yes—
107C2×C4×D17C22×C413yes—
108C2×C4×D17C2×D4112yes—
109C2×C4×D17C2×Q8112yes—
110C2×C4×D17C2413yes—
111C2×C4×D17C2411yescharacteristic
112C2×Dic34C22×C413yes—
113#63247—224no—
114C2×#3624—224no—
115C2×#3624C2414yes—
116C2×#3624C24112yes—
117#63243—212no—
118#63243—224no—
119#63243—24no—
120#63242—224no—
121C4⋊C4×C17C22×C416yes—
122C22⋊C4×C17C22×C416yes—
123C42×C17C22×C416yes—
124C42×C17C22×C411yescharacteristic
125C42×C17C22×C413yes—
126C22⋊Dic17C22×C416yes—
127#63227C22×C4112yes—
128C4⋊Dic17C22×C416yes—
129#63225C22×C4112yes—
130C4×Dic17C22×C416yes—
131C4×Dic17C22×C411yescharacteristic
132C4×Dic17C22×C416yes—
133C4×Dic17C22×C413yes—
134C4×Dic17C22×C416yes—
135C4×Dic17C2412yes—
136C4×Dic17C2416yes—
137#60099—171nomaximal, Sylow
138C23×C17C23×C413yes—
139C22×D17—46no—
140C22×D17C2×C4⋊C4112yes—
141C22×D17C23×C411yescharacteristic
142C22×D17C23×C413yes—
143Q8×C17C2×C4⋊C414yes—
144D4×C17C2×C4⋊C4112yes—
145C2×C4×C17—212no—
146C2×C4×C17C2×C4⋊C4112yes—
147C2×C4×C17C23×C416yes—
148C2×C4×C17C23×C411yescharacteristic
149C2×C4×C17C23×C413yes—
150C2×C4×C17C23×C412yes—
151C22⋊D17C2×C4⋊C4124yes—
152C2×Dic17—46no—
153C2×Dic17C23×C416yes—
154C2×Dic17C23×C412yes—
155C2×Dic17C23×C413yes—
156C2×Dic17C22×D416yes—
157C2×Dic17C22×Q816yes—
158C2×Dic17C2511yescharacteristic
159D68C2×C4⋊C4112yes—
160C4×D17—24no—
161C4×D17—212no—
162C4×D17—46no—
163C4×D17—46no—
164C4×D17C2×C4⋊C4112yes—
165C4×D17C2×C4⋊C4112yes—
166C4×D17C22×D416yes—
167C4×D17C22×D412yes—
168C4×D17C22×Q812yes—
169C4×D17C22×Q816yes—
170Dic34C2×C4⋊C4112yes—
171#3624—24no—
172#3624—212no—
173C2×#568—172no—
174C2×C4×#41—171no—
175#2906—1712no—
176#2906—174no—
177#2905—176no—
178C2×#423—173no—
179C2×#423—173no—
180C22×C17—26no—
181C22×C17C22×C4⋊C416yes—
182C22×C17C24×C411yescharacteristic
183C2×D17—22no—
184C2×D17—26no—
185C2×D17—412no—
186C2×D17C22×C4⋊C412yes—
187C2×D17C22×C4⋊C416yes—
188C4×C17—26no—
189C4×C17C22×C4⋊C416yes—
190C4×C17C22×C4⋊C412yes—
191C4×C17#56814yescomplemented
192Dic17—22no—
193Dic17—26no—
194Dic17C22×C4⋊C416yes—
195Dic17C23×D411yescharacteristic
196Dic17C23×Q811yescharacteristic
197C22×#41—171no—
198#568—3416no—
199C2×#131—1712no—
200C2×#131—174no—
201C22×M16—176no—
202C22×M16—176no—
203C4×#41—171no—
204C4×#41—172no—
205C4×#41—176no—
206C4×#41—173no—
207C4×#41—173no—
208C4×#41#59511yescharacteristic
209C2×C4×Q8—172no—
210C2×C4×D4—176no—
211C2×#117—173no—
212C22×C42—173no—
213#424—1724no—
214#424—1724no—
215#423—171no—
216#423—173no—
217#423—176no—
218#423—176no—
219#423—1712no—
220#423—1712no—
221C2×C4⋊C8—1712no—
222C2×C4⋊C8—1712no—
223C2×C17—26no—
224C2×C17C23×C4⋊C411yescharacteristic
225C2×C17C2×#56812yes—
226D17—22no—
227D17—26no—
228C2×#41—178no—
229C2×#41—178no—
230C2×#41—171no—
231C2×#41—173no—
232C2×#41—173no—
233C2×#41C2×#59511yescharacteristic
234C22×Q8—171no—
235C22×D4—173no—
236C23×C4—173no—
237C23×C4—176no—
238#131—3448no—
239#131—3416no—
240C2×M16—176no—
241C2×M16—172no—
242C2×M16—1712no—
243C2×M16—1712no—
244C2×M16—3424no—
245C2×M16—3424no—
246C22×C8—1712no—
247C22×C8—1712no—
248C4×Q8—172no—
249C4×Q8—176no—
250C4×Q8—176no—
251C4×Q8C2×#59512yes—
252C4×D4—176no—
253C4×D4—1712no—
254C4×D4—176no—
255C4×D4—1712no—
256C4×D4—176no—
257C4×D4C2×#59516yes—
258#117—173no—
259#117—176no—
260#117—176no—
261#117—176no—
262#117C2×#59513yes—
263C2×C4⋊C4—176no—
264C2×C22⋊C4—176no—
265C2×C42—176no—
266C2×C42—173no—
267C2×C42—173no—
268C2×C42—176no—
269C2×C42—173no—
270C2×C42—173no—
271C2×C42—176no—
272C2×C42—171no—
273C2×C42C2×#59513yes—
274C4⋊C8—1712no—
275C4⋊C8—174no—
276C4⋊C8—1724no—
277C4⋊C8—1724no—
278C17#6009911yescharacteristic, complemented, Sylow
279C24—173no—
280#41—174no—
281#41—174no—
282#41—1712no—
283#41—1712no—
284#41—1724no—
285#41C4⋊#59518yes—
286C2×Q8—178no—
287C2×Q8—173no—
288C2×Q8C22×#59511yescharacteristic
289C2×D4—176no—
290C2×D4—1724no—
291C2×D4—173no—
292C2×D4C22×#59513yes—
293C22×C4—173no—
294C22×C4—1712no—
295C22×C4—1712no—
296C22×C4—173no—
297C22×C4—173no—
298C22×C4—171no—
299C22×C4—173no—
300C22×C4—176no—
301C22×C4—172no—
302C22×C4—176no—
303C22×C4—176no—
304C22×C4—176no—
305C22×C4—6812no—
306C22×C4C22×#59516yes—
307C22×C4C22×#59513yes—
308M16—3412no—
309M16—344no—
310M16—3424no—
311M16—3424no—
312C2×C8—174no—
313C2×C8—1712no—
314C2×C8—3424no—
315C2×C8—3424no—
316C4⋊C4—1712no—
317C4⋊C4—176no—
318C4⋊C4C22×#59516yes—
319C22⋊C4—176no—
320C22⋊C4—1712no—
321C22⋊C4C22×#59516yes—
322C42—172no—
323C42—176no—
324C42—171no—
325C42—173no—
326C42—176no—
327C42—176no—
328C42—176no—
329C42C22×#59511yescharacteristic
330C42C22×#59513yes—
331C42C22×#59516yes—
332C23—173no—
333C23—171no—
334C23—1712no—
335C23—686no—
336C23C23×#59513yes—
337Q8—1712no—
338Q8C2×C4⋊#59514yes—
339D4—1724no—
340D4—1712no—
341D4C2×C4⋊#595112yes—
342C2×C4—212no—
343C2×C4—176no—
344C2×C4—176no—
345C2×C4—171no—
346C2×C4—173no—
347C2×C4—176no—
348C2×C4—172no—
349C2×C4—172no—
350C2×C4—1712no—
351C2×C4—1712no—
352C2×C4—176no—
353C2×C4—172no—
354C2×C4—176no—
355C2×C4—344no—
356C2×C4—3412no—
357C2×C4—686no—
358C2×C4—686no—
359C2×C4—686no—
360C2×C4C2×C4⋊#595112yes—
361C2×C4C23×#59516yes—
362C2×C4C23×#59511yescharacteristic
363C2×C4C23×#59513yes—
364C2×C4C23×#59512yes—
365C8—344no—
366C8—3412no—
367C22—26no—
368C22—172no—
369C22—176no—
370C22—342no—
371C22—346no—
372C22—6812no—
373C22C22×C4⋊#59516yes—
374C22C24×#59511yescharacteristic
375C4—26no—
376C4—171no—
377C4—171no—
378C4—176no—
379C4—342no—
380C4—346no—
381C4C22×C4⋊#59512yes—
382C4C22×C4⋊#59516yes—
383C4#1176388814yescomplemented
384C2—26no—
385C2—342no—
386C2—346no—
387C2C23×C4⋊#59511yescharacteristic
388C2C2×#1176388812yes—
subgroupG/H
center, FrattiniC22C24×#595
commutator, socleC22×C17C24×C4
FittingC4×#41×C17C4
prime radicalC2×#41×D17C22
cosocleC2×Dic17C25
hypercenterC4×#41#595
hypocenterC17#60099
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C4×#41

Complements

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

NH ≅ G/Ntype
2. #14545430C2semidirect
3. #14545429C2semidirect
4. #14545427C2semidirect
5. C2×#11763813C2semidirect
6. D17⋊#423C2semidirect
13. #11763816C22semidirect
14. #11763815C22semidirect
19. #11763813C22semidirect
20. #11763812C22semidirect
21. #11763810C22semidirect
22. C2×C4⋊#3624C22semidirect
191. C4×C17#568semidirect
278. C17#60099semidirect
383. C4#11763888semidirect

Maximal subgroups

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

subgroupindex
C2×#117638882
#145454302
#145454292
#145454272
C2×#117638132
D17⋊#4232
C4×#41×D172
#6009917