Finite Group Databasebeta

← #17053146

Subgroups — #17053146

Order 4352.

732 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762938C212yesmaximal
2#14531261C211yesmaximal, characteristic
3#14529505C212yesmaximal
4#14529504C212yesmaximal
5#14529499C212yesmaximal
6#14528937C212yesmaximal
7#14528643C212yesmaximal
8#14528637C211yesmaximal, characteristic
9C17×#1842C211yesmaximal, characteristic
10C2×C4×Dic34C2211yescharacteristic
11#11762938—28no—
12C2×C4⋊#3622C2211yescharacteristic
13C2×C4⋊#3622C2211yescharacteristic
14C2×#10587485C2212yes—
15C2×#10587485C2212yes—
16C2×#10587485C2212yes—
17C2×#10587485C2212yes—
18C2×#10587474C2212yes—
19C2×#10587486C2212yes—
20C2×C8×Dic17C2212yes—
21#11762715C411yescharacteristic
22#11762715C411yescharacteristic
23#11762707C411yescharacteristic
24#11762707C411yescharacteristic
25#11762693C412yes—
26#11762693C412yes—
27C4×#63225C2212yes—
28C4×C4⋊Dic17C2211yescharacteristic
29#11762655C2212yes—
30#11762564C2212yes—
31#11762563C2212yes—
32#11762563C2212yes—
33C2×C17×C4⋊C8C2212yes—
34C2×C17×C4⋊C8C2212yes—
35C2×C17×C4⋊C8C2211yescharacteristic
36C2×C17×C4⋊C8C2211yescharacteristic
37C43×C17C2211yescharacteristic
38C22×Dic34C2×C411yescharacteristic
39C22×C8×C17C2312yes—
40C22×C8×C17C2312yes—
41C2×C42×C17C2×C411yescharacteristic
42C2×C42×C17C2×C411yescharacteristic
43C2×C42×C17C2×C411yescharacteristic
44C2×C42×C17C2×C411yescharacteristic
45C2×C42×C17C2311yescharacteristic
46C2×C42×C17C2311yescharacteristic
47C2×C42×C17C2311yescharacteristic
48C2×C4⋊Dic17C2×C411yescharacteristic
49C2×C4⋊Dic17C2×C411yescharacteristic
50C2×C4⋊Dic17C2×C411yescharacteristic
51C2×#63225C2×C412yes—
52C2×#63225C2×C412yes—
53C2×#63225C2×C412yes—
54C2×C4×Dic17C2312yes—
55C2×C4×Dic17C2312yes—
56C22×#3622C2312yes—
57C22×#3622C2312yes—
58C4×Dic34D414yes—
59C4×Dic34Q814yes—
60C17×C4⋊C8—24no—
61C17×C4⋊C8—24no—
62C17×C4⋊C8—41no—
63C17×C4⋊C8—41no—
64#10587502C2×C412yes—
65#10587502C2×C412yes—
66#10587502C2×C412yes—
67#10587502C2×C412yes—
68#10587502C2×C412yes—
69#10587502C2×C412yes—
70#10587502C2×C412yes—
71#10587486—24no—
72#10587485—24no—
73#10587485—24no—
74#10587485—42no—
75#10587485—42no—
76C8×Dic17—24no—
77C4⋊#3622—22no—
78C4⋊#3622Q814yescomplemented
79#10587474—24no—
80C22×C4×C17C22×C411yescharacteristic
81C22×C4×C17C22×C411yescharacteristic
82C22×C4×C17C22×C411yescharacteristic
83C22×C4×C17C22×C411yescharacteristic
84C22×C4×C17C22×C411yescharacteristic
85C22×C4×C17C22×C411yescharacteristic
86C22×C4×C17C2411yescharacteristic
87C22×Dic17C22×C412yes—
88C22×Dic17C22×C412yes—
89C22×Dic17C22×C412yes—
90C22×Dic17C22×C412yes—
91C2×Dic34—41no—
92C2×Dic34—41no—
93C2×Dic34C4⋊C414yes—
94C2×C8×C17—22no—
95C2×C8×C17—22no—
96C2×C8×C17—22no—
97C2×C8×C17—22no—
98C2×C8×C17—22no—
99C2×C8×C17—22no—
100C42×C17—22no—
101C42×C17—21no—
102C42×C17—21no—
103C42×C17—41no—
104C42×C17—41no—
105C42×C17—41no—
106C42×C17C2×D412yes—
107C42×C17C2×Q812yes—
108C42×C17C2×Q812yes—
109C42×C17#4112yes—
110C4⋊Dic17—41no—
111C4⋊Dic17—41no—
112C4⋊Dic17C4⋊C414yes—
113#63225—24no—
114#63225—42no—
115#63225C4⋊C418yes—
116C4×Dic17—22no—
117C4×Dic17—22no—
118C4×Dic17C2×D414yes—
119C4×Dic17C2×Q814yes—
120C2×#3622—22no—
121C2×#3622—22no—
122C2×#3622—22no—
123C2×#3622—22no—
124C2×#3622—22no—
125C2×#3622C2×Q814yes—
126#22723—171nomaximal, Sylow
127C23×C17C23×C411yescharacteristic
128C2×C4×C17—21no—
129C2×C4×C17—21no—
130C2×C4×C17—21no—
131C2×C4×C17—21no—
132C2×C4×C17—21no—
133C2×C4×C17—21no—
134C2×C4×C17—21no—
135C2×C4×C17—21no—
136C2×C4×C17—21no—
137C2×C4×C17—21no—
138C2×C4×C17—21no—
139C2×C4×C17—21no—
140C2×C4×C17—21no—
141C2×C4×C17C2×C4⋊C412yes—
142C2×C4×C17C2×C4⋊C412yes—
143C2×C4×C17C4×Q812yes—
144C2×C4×C17C4×Q812yes—
145C2×C4×C17#13112yes—
146C2×C4×C17C22×D411yescharacteristic
147C2×C4×C17C22×Q811yescharacteristic
148C2×C4×C17C22×Q811yescharacteristic
149C2×C4×C17C2×#4111yescharacteristic
150C2×C4×C17H(5,𝔽2)11yescharacteristic
151C2×C4×C172−1+411yescharacteristic
152C2×Dic17—22no—
153C2×Dic17—22no—
154C2×Dic17—22no—
155C2×Dic17—22no—
156C2×Dic17—22no—
157C2×Dic17—22no—
158C2×Dic17—22no—
159C2×Dic17—22no—
160C2×Dic17—22no—
161C2×Dic17—22no—
162C2×Dic17C2×C4⋊C414yes—
163C2×Dic17C2×C4⋊C414yes—
164Dic34—44no—
165C8×C17—42no—
166C8×C17—42no—
167#3622—24no—
168#3622—42no—
169C2×#446—172no—
170#2295—171no—
171#1940—172no—
172#1940—172no—
173#1939—172no—
174#1843—172no—
175#1842D1711yescharacteristic
176#1768—172no—
177#1767—171no—
178C22×C17C22×C4⋊C411yescharacteristic
179C22×C17C2×C4×Q811yescharacteristic
180C22×C17#52011yescharacteristic
181C22×C17C2×#13111yescharacteristic
182C22×C17#56811yescharacteristic
183C22×C17#56811yescharacteristic
184C22×C17#56811yescharacteristic
185C4×C17—22no—
186C4×C17—22no—
187C4×C17—22no—
188C4×C17—22no—
189C4×C17—22no—
190C4×C17—41no—
191C4×C17D4×Q811yescharacteristic
192C4×C17#55011yescharacteristic
193C4×C17#55711yescharacteristic
194C4×C17Q8211yescharacteristic
195Dic17—24no—
196Dic17—24no—
197Dic17—42no—
198Dic17—42no—
199C2×C4×Q8—171no—
200#446—348no—
201C2×C4⋊C8—171no—
202C2×C4⋊C8—172no—
203C2×C4⋊C8—172no—
204C2×C4⋊C8—171no—
205C2×C4⋊C8—172no—
206C2×C4⋊C8—172no—
207C2×C4⋊C8C2×D1712yes—
208C2×C4⋊C8C2×D1712yes—
209C2×C4⋊C8C2×D1711yescharacteristic
210C2×C4⋊C8C2×D1711yescharacteristic
211C2×#97—172no—
212C2×#97—172no—
213C2×C4×C8—172no—
214#391—171no—
215#391—171no—
216#389—171no—
217#389—171no—
218#387—172no—
219#387—172no—
220C4×C4⋊C4—172no—
221C4×C4⋊C4—171no—
222#376—172no—
223C43C2×D1711yescharacteristic
224#336—172no—
225#336—172no—
226#336—172no—
227C2×C17Q8×C4⋊C411yescharacteristic
228C2×C17#290511yescharacteristic
229C2×C17#290611yescharacteristic
230C2×C17#296111yescharacteristic
231C2×C17#296211yescharacteristic
232C2×C17#299211yescharacteristic
233C2×C17#299511yescharacteristic
234C22×Q8—171no—
235C22×C8—172no—
236C22×C8—172no—
237C22×C8C22×D1712yes—
238C22×C8C22×D1712yes—
239C4×Q8—174no—
240C4×Q8—174no—
241C2×C4⋊C4—172no—
242C2×C4⋊C4—171no—
243C2×C4⋊C4—172no—
244C2×C4⋊C4—172no—
245C2×C4⋊C4—171no—
246C2×C4⋊C4—171no—
247C2×C42—172no—
248C2×C42—172no—
249C2×C42C4×D1711yescharacteristic
250C2×C42C4×D1711yescharacteristic
251C2×C42C4×D1711yescharacteristic
252C2×C42C4×D1711yescharacteristic
253C2×C42C22×D1711yescharacteristic
254C2×C42C22×D1711yescharacteristic
255C2×C42C22×D1711yescharacteristic
256C4⋊C8—24no—
257C4⋊C8—24no—
258C4⋊C8—41no—
259C4⋊C8—41no—
260C4⋊C8—174no—
261C4⋊C8—344no—
262C4⋊C8—344no—
263C4⋊C8—342no—
264C4⋊C8—682no—
265C4⋊C8—682no—
266#97—344no—
267#97—344no—
268C4×C8—344no—
269#95—172no—
270#95—172no—
271#95—172no—
272#95—172no—
273#95—172no—
274#95—172no—
275#95—172no—
276C17#2272311yescharacteristic, complemented, Sylow
277C2×Q8—174no—
278C2×Q8—681no—
279C2×Q8—681no—
280C22×C4—172no—
281C22×C4—172no—
282C22×C4—172no—
283C22×C4—172no—
284C22×C4C2×C4×D1711yescharacteristic
285C22×C4C2×C4×D1711yescharacteristic
286C22×C4C2×C4×D1711yescharacteristic
287C22×C4C2×C4×D1711yescharacteristic
288C22×C4C2×C4×D1711yescharacteristic
289C22×C4C2×C4×D1711yescharacteristic
290C22×C4C23×D1711yescharacteristic
291C2×C8—22no—
292C2×C8—22no—
293C2×C8—22no—
294C2×C8—22no—
295C2×C8—22no—
296C2×C8—22no—
297C2×C8—174no—
298C2×C8—342no—
299C2×C8—342no—
300C2×C8—342no—
301C2×C8—342no—
302C2×C8—342no—
303C4⋊C4—178no—
304C4⋊C4—174no—
305C4⋊C4—344no—
306C4⋊C4—682no—
307C4⋊C4—681no—
308C4⋊C4—681no—
309C42—21no—
310C42—21no—
311C42—22no—
312C42—41no—
313C42—41no—
314C42—41no—
315C42—174no—
316C42—174no—
317C42—342no—
318C42—342no—
319C42D4×D1712yes—
320C42#6325412yes—
321C42Q8×D1712yes—
322C42Q8×D1712yes—
323C23C22×C4×D1711yescharacteristic
324Q8—684no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—174no—
339C2×C4—174no—
340C2×C4—342no—
341C2×C4—342no—
342C2×C4—342no—
343C2×C4—342no—
344C2×C4—342no—
345C2×C4—342no—
346C2×C4—342no—
347C2×C4—342no—
348C2×C4—342no—
349C2×C4—342no—
350C2×C4#1058757312yes—
351C2×C4#1058757312yes—
352C2×C4C4⋊C4×D1712yes—
353C2×C4C4⋊C4×D1712yes—
354C2×C4#1058758712yes—
355C2×C4C2×D4×D1711yescharacteristic
356C2×C4C2×#6325411yescharacteristic
357C2×C4#1058769111yescharacteristic
358C2×C4C2×Q8×D1711yescharacteristic
359C2×C4C2×Q8×D1711yescharacteristic
360C2×C4#1058769411yescharacteristic
361C8—42no—
362C8—42no—
363C8—344no—
364C8—682no—
365C22C2×C4⋊C4×D1711yescharacteristic
366C22C2×#1058757311yescharacteristic
367C22#1176329011yescharacteristic
368C22C2×#1058758711yescharacteristic
369C22#1176357511yescharacteristic
370C22#1176357511yescharacteristic
371C22#1176357511yescharacteristic
372C4—22no—
373C4—22no—
374C4—22no—
375C4—22no—
376C4—22no—
377C4—41no—
378C4—344no—
379C4—344no—
380C4—682no—
381C4—682no—
382C4#1176347411yescharacteristic
383C4#1176347911yescharacteristic
384C4#1176353411yescharacteristic
385C4#1176353911yescharacteristic
386C2#1453169611yescharacteristic
387C2#1453734611yescharacteristic
388C2#1453734911yescharacteristic
389C2#1453772111yescharacteristic
390C2#1453772711yescharacteristic
391C2#1453792011yescharacteristic
392C2#1453795111yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D17
commutator, socle, prime radicalC23×C17C23×C4
FittingC17×#1842C2
cosocleC22×C4×C17C24
hypercenter#1842D17
hypocenterC17#22723
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ #1842

Complements

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

NH ≅ G/Ntype
78. C4⋊#3622Q8semidirect
276. C17#22723semidirect

Maximal subgroups

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

subgroupindex
C2×#117629382
#145312612
#145295052
#145295042
#145294992
#145289372
#145286432
#145286372
C17×#18422
#2272317