Finite Group Databasebeta

← #15779989

Subgroups — #15779989

Order 3328.

554 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88040C211yesmaximal, characteristic
2C2×C4×D104C211yesmaximal, characteristic
3C2×#11718095C211yesmaximal, characteristic, complemented
4C2×#11718101C211yesmaximal, characteristic
5#13115697C211yesmaximal, characteristic, complemented
6#13112928C211yesmaximal, characteristic, complemented
7C13×#1374C211yesmaximal, characteristic, complemented
8C22×Dic52C2211yescharacteristic
9C22×D104C2211yescharacteristic
10C2×C4×D52—21no—
11C22×C13×C16C2211yescharacteristic
12C22×C13×C16C2211yescharacteristic
13C2×C4×C8×C13C2211yescharacteristic
14C2×#88061—21no—
15C2×#88058C2211yescharacteristic
16C2×#88058C2211yescharacteristic
17C2×#88056—21no—
18#11718590—21no—
19C2×#88040—22no—
20C2×#88040—22no—
21C2×#88040C414yescomplemented
22C4×D104—22no—
23C4×D104—22no—
24#11718101—22no—
25#11718095—22no—
26C22×D52—21no—
27C22×C4×D13—41no—
28C22×Dic26—21no—
29C22×C8×C13D411yescharacteristic
30C22×C8×C13C2311yescharacteristic
31C2×C42×C13D411yescharacteristic
32C2×#6103—41no—
33C2×C4⋊Dic13—21no—
34C2×C4⋊Dic13—21no—
35C2×Dic52—21no—
36C2×Dic52—21no—
37C2×Dic52—21no—
38C2×Dic52—21no—
39C2×Dic52—21no—
40C2×Dic52C2×C412yescomplemented
41C2×D104—21no—
42C2×D104—21no—
43C2×D104—21no—
44C2×D104C2×C412yes—
45C2×D104D412yes—
46C2×D104D412yes—
47C4×D52—24no—
48C4×D52—42no—
49C2×C13×C16—21no—
50C2×C13×C16—21no—
51C2×C13×C16—21no—
52C2×C13×C16—21no—
53C2×C13×C16—21no—
54C2×C13×C16C2×C412yescomplemented
55C4×C8×C13—21no—
56C4×C8×C13—21no—
57#88071—41no—
58#88071—41no—
59#88061—24no—
60#88058—21no—
61#88058—21no—
62#88058—21no—
63#88058D412yes—
64#88056—42no—
65#88040—28no—
66#13014—131nomaximal, Sylow
67C23×D13—41no—
68C22×C4×C13D811yescharacteristic
69C22×C4×C13D811yescharacteristic
70C22×C4×C13C2×D411yescharacteristic
71C22×Dic13—41no—
72C22×Dic13—41no—
73C22×Dic13—41no—
74C2×D52—22no—
75C2×D52—22no—
76C2×D52—22no—
77C2×D52—41no—
78C2×D52—41no—
79C2×D52—41no—
80C2×C4×D13—44no—
81C2×C4×D13—82no—
82C2×C4×D13—82no—
83C2×Dic26—22no—
84C2×Dic26—41no—
85C2×Dic26—41no—
86C2×Dic26—41no—
87C2×Dic26—41no—
88C2×Dic26—41no—
89C2×C8×C13—21no—
90C2×C8×C13—21no—
91C2×C8×C13—21no—
92C2×C8×C13C22×C411yescharacteristic
93C2×C8×C13C2×D411yescharacteristic
94C2×C8×C13C2×D411yescharacteristic
95C2×C8×C13C2×D411yescharacteristic
96C2×C8×C13#4111yescharacteristic
97C2×C8×C13#4111yescharacteristic
98C42×C13—21no—
99C42×C13—21no—
100#6103—44no—
101C4⋊Dic13—22no—
102C4⋊Dic13—41no—
103C4⋊Dic13—41no—
104C4⋊Dic13—41no—
105Dic52—22no—
106Dic52—22no—
107Dic52—41no—
108Dic52—41no—
109D104—22no—
110D104—22no—
111D104—22no—
112D104C22⋊C414yes—
113C13×C16—22no—
114C13×C16—41no—
115C22×SD32—131no—
116C2×C4×D8—131no—
117C2×#358—131no—
118C2×#357—131no—
119#1969—131no—
120#1380—131no—
121#1374D1311yescharacteristic, complemented
122C23×C13C2×D811yescharacteristic
123C22×D13—42no—
124C22×D13—42no—
125C22×D13—42no—
126C22×D13—81no—
127C22×D13—81no—
128C22×D13—81no—
129C22×D13—81no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—21no—
133C2×C4×C13—21no—
134C2×C4×C13—21no—
135C2×C4×C13SD3212yescomplemented
136C2×C4×C13C4×D411yescharacteristic
137C2×C4×C13#12011yescharacteristic
138C2×C4×C13#12111yescharacteristic
139C2×C4×C13#13511yescharacteristic
140C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
142C2×Dic13—42no—
143C2×Dic13—42no—
144C2×Dic13—81no—
145C2×Dic13—81no—
146C2×Dic13—81no—
147C2×Dic13—81no—
148C2×Dic13—81no—
149C2×Dic13—81no—
150C2×Dic13—81no—
151D52—24no—
152D52—42no—
153D52—42no—
154D52—42no—
155C4×D13—88no—
156Dic26—42no—
157Dic26—42no—
158Dic26—81no—
159Dic26—81no—
160C8×C13—41no—
161C8×C13C2×C22⋊C411yescharacteristic
162C8×C13C4×D411yescharacteristic
163C8×C13#12111yescharacteristic
164C8×C13#12311yescharacteristic
165C22×Q16—131no—
166C22×D8—131no—
167C2×C4×D4—261no—
168C2×SD32—134no—
169C2×SD32—262no—
170C2×SD32—262no—
171C22×C16C2×D1311yescharacteristic
172C22×C16C2×D1311yescharacteristic
173C4×D8—262no—
174C4×D8—262no—
175C2×#107—131no—
176C2×#107—131no—
177C2×#103—261no—
178C2×#102—261no—
179C2×C4×C8C2×D1311yescharacteristic
180#391—261no—
181#358—262no—
182#357—262no—
183C22×C13C4×D811yescharacteristic
184C22×C13#44711yescharacteristic
185C22×C13#45911yescharacteristic
186C22×C13C2×SD3211yescharacteristic
187C22×C13#50811yescharacteristic
188C22×C13#50911yescharacteristic
189C22×C13#51011yescharacteristic
190C2×D13—44no—
191C2×D13—82no—
192C2×D13—82no—
193C2×D13—82no—
194C2×D13—82no—
195C2×D13—82no—
196C2×D13—82no—
197C4×C13—22no—
198C4×C13—41no—
199C4×C13#38611yescharacteristic
200C4×C13#44211yescharacteristic
201C4×C13#44911yescharacteristic
202C4×C13#46311yescharacteristic
203Dic13—82no—
204Dic13—82no—
205Dic13—161no—
206C22×Q8—261no—
207C22×D4—261no—
208C23×C4—521no—
209C2×Q16—132no—
210C2×Q16—261no—
211C2×Q16—261no—
212C2×Q16—261no—
213C2×Q16—261no—
214C2×Q16—261no—
215C2×D8—132no—
216C2×D8—132no—
217C2×D8—132no—
218C2×D8—261no—
219C2×D8—261no—
220C2×D8—261no—
221C22×C8D5211yescharacteristic
222C22×C8C22×D1311yescharacteristic
223C4×D4—264no—
224C4×D4—522no—
225C2×C4⋊C4—261no—
226C2×C4⋊C4—261no—
227C2×C22⋊C4—521no—
228C2×C42D5211yescharacteristic
229SD32—268no—
230C2×C16—21no—
231C2×C16—21no—
232C2×C16—21no—
233C2×C16—21no—
234C2×C16—21no—
235C2×C16C4×D1312yescomplemented
236#107—132no—
237#107—261no—
238#107—261no—
239#107—261no—
240#103—522no—
241#102—264no—
242C4×C8—21no—
243C4×C8—21no—
244#95—521no—
245#95—521no—
246C2×C13#187911yescharacteristic
247C2×C13C4×SD3211yescharacteristic
248C2×C13#217511yescharacteristic
249C2×C13#218711yescharacteristic
250C2×C13#218911yescharacteristic
251C2×C13#220811yescharacteristic
252C2×C13#221011yescharacteristic
253D13—84no—
254C24—521no—
255C2×Q8—262no—
256C2×Q8—521no—
257C2×Q8—521no—
258C2×Q8—521no—
259C2×Q8—521no—
260C2×Q8—521no—
261C2×D4—262no—
262C2×D4—262no—
263C2×D4—262no—
264C2×D4—521no—
265C2×D4—521no—
266C2×D4—521no—
267C22×C4—524no—
268C22×C4—521no—
269C22×C4—521no—
270C22×C4—521no—
271C22×C4—1042no—
272C22×C4—1042no—
273C22×C4D10411yescharacteristic
274C22×C4D10411yescharacteristic
275C22×C4C2×D5211yescharacteristic
276Q16—262no—
277Q16—262no—
278Q16—521no—
279Q16—521no—
280D8—134no—
281D8—262no—
282D8—262no—
283D8—262no—
284C2×C8—21no—
285C2×C8—21no—
286C2×C8—21no—
287C2×C8C2×C4×D1311yescharacteristic
288C2×C8#612711yescharacteristic
289C2×C8D4×D1311yescharacteristic
290C2×C8D4×D1311yescharacteristic
291C2×C8D4×D1311yescharacteristic
292C2×C8#613111yescharacteristic
293C4⋊C4—262no—
294C4⋊C4—521no—
295C4⋊C4—521no—
296C4⋊C4—521no—
297C22⋊C4—524no—
298C42—21no—
299C42—21no—
300C16—22no—
301C16—41no—
302C13#1301411yescharacteristic, complemented, Sylow
303C23—522no—
304C23—522no—
305C23—522no—
306C23—1041no—
307C23—1041no—
308C23—1041no—
309C23—1041no—
310C23C2×D10411yescharacteristic
311Q8—522no—
312Q8—522no—
313Q8—1041no—
314Q8—1041no—
315D4—264no—
316D4—522no—
317D4—522no—
318D4—522no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—522no—
325C2×C4—522no—
326C2×C4—1048no—
327C2×C4—1041no—
328C2×C4—1041no—
329C2×C4—1041no—
330C2×C4—1041no—
331C2×C4—1041no—
332C2×C4—1041no—
333C2×C4—1041no—
334C2×C4#8804012yescomplemented
335C2×C4C4×D5211yescharacteristic
336C2×C4#8813611yescharacteristic
337C2×C4#8814911yescharacteristic
338C2×C4#8815811yescharacteristic
339C2×C4#8816211yescharacteristic
340C2×C4#8816211yescharacteristic
341C8—41no—
342C8C22⋊C4×D1311yescharacteristic
343C8#8813811yescharacteristic
344C8#8814711yescharacteristic
345C8#8814811yescharacteristic
346C22—524no—
347C22—1042no—
348C22—1042no—
349C22—1042no—
350C22—1042no—
351C22—1042no—
352C22—1042no—
353C22C4×D10411yescharacteristic
354C22#1171839311yescharacteristic
355C22#1171850411yescharacteristic
356C22C2×#8804011yescharacteristic
357C22#1171856511yescharacteristic
358C22#1171856911yescharacteristic
359C22#1171857011yescharacteristic
360C4—22no—
361C4—41no—
362C4—1042no—
363C4—1042no—
364C4—2081no—
365C4#1171832611yescharacteristic
366C4#1171837211yescharacteristic
367C4#1171839511yescharacteristic
368C4#1171850511yescharacteristic
369C2—1044no—
370C2#1311518311yescharacteristic
371C2C4×#8804011yescharacteristic
372C2#1311670211yescharacteristic
373C2#1311676711yescharacteristic
374C2#1311677811yescharacteristic
375C2#1311688211yescharacteristic
376C2#1311689211yescharacteristic
subgroupG/H
centerC23C2×D104
commutatorC2×C8×C13C22×C4
FrattiniC22×C8C22×D13
FittingC13×#1374C2
socleC23×C13C2×D8
prime radicalC22×D104C22
cosocleC22×C8×C13C23
hypercenter#1374D13
hypocenterC13#13014
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8 ◁ #1374

Complements

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

NH ≅ G/Ntype
3. C2×#11718095C2semidirect
5. #13115697C2semidirect
6. #13112928C2semidirect
7. C13×#1374C2semidirect
21. C2×#88040C4semidirect
40. C2×Dic52C2×C4semidirect
54. C2×C13×C16C2×C4semidirect
121. #1374D13semidirect
135. C2×C4×C13SD32semidirect
235. C2×C16C4×D13semidirect
302. C13#13014semidirect
334. C2×C4#88040semidirect

Maximal subgroups

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

subgroupindex
C22×#880402
C2×C4×D1042
C2×#117180952
C2×#117181012
#131156972
#131129282
C13×#13742
#1301413