Finite Group Databasebeta

← #15759471

Subgroups — #15759471

Order 3328.

492 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125774C211yesmaximal, characteristic
2#13115676C211yesmaximal, characteristic
3#13113526C211yesmaximal, characteristic, complemented
4C2×#11718077C211yesmaximal, characteristic
5#13112733C211yesmaximal, characteristic, complemented
6#13112687C211yesmaximal, characteristic, complemented
7C13×#2962C211yesmaximal, characteristic, complemented
8C13×#533C2211yescharacteristic
9C2×#88128C2211yescharacteristic
10C13×#446—22no—
11C13×#446—21no—
12C8×Q8×C13—21no—
13C13×#424—21no—
14C2×C13×C4⋊C8C2211yescharacteristic
15C13×#405—21no—
16C4×C13×M16C2211yescharacteristic
17C2×#88063—21no—
18C2×#88063—21no—
19#11718749—21no—
20#11718746—21no—
21#11718707C414yes—
22#11718688—22no—
23#11718586C2211yescharacteristic
24#11718585C2211yescharacteristic
25C2×C4⋊#1055C2211yescharacteristic
26#11718139—21no—
27#11718138—21no—
28#11718077—21no—
29#11718077—21no—
30C22×D52—21no—
31C22×D52—21no—
32C22×D52C2×C412yes—
33C2×C13×M16D411yescharacteristic
34C2×C13×M16D411yescharacteristic
35C22×C8×C13—21no—
36C13×C4⋊Q8D411yescharacteristic
37C13×C4⋊Q8D411yescharacteristic
38C13×#125—21no—
39C13×C22⋊Q8—21no—
40C13×C22⋊Q8C2×C412yes—
41C4×Q8×C13—21no—
42C4×Q8×C13D412yes—
43C13×#117—21no—
44C2×C42×C13C2311yescharacteristic
45C2×#6106—24no—
46C2×#6099—21no—
47C22×#1055—21no—
48#88128—21no—
49#88128—21no—
50#88128—21no—
51#88128—21no—
52C13×C4⋊C8—22no—
53C13×C4⋊C8—22no—
54C13×C4⋊C8—21no—
55C13×C4⋊C8D411yescharacteristic
56C13×C4⋊C8D411yescharacteristic
57C13×#97—22no—
58C13×#97—21no—
59C4×C8×C13—22no—
60C4×C8×C13—21no—
61C22⋊#1055C2×C412yes—
62#88063—42no—
63#88063—42no—
64#88049—24no—
65C4⋊#1055—21no—
66C4⋊#1055—21no—
67C4⋊#1055—21no—
68C4⋊#1055—21no—
69C4⋊#1055—21no—
70C4×#1055—21no—
71#9274—131nomaximal, Sylow
72C23×D13—22no—
73C2×Q8×C13—21no—
74C2×Q8×C13C22⋊C412yes—
75C22×C4×C13C22×C411yescharacteristic
76C22×C4×C13C2×D411yescharacteristic
77C22×C4×C13#4111yescharacteristic
78C2×D52—22no—
79C2×D52—22no—
80C2×D52—41no—
81C2×D52—41no—
82C2×D52—41no—
83C2×D52—41no—
84C2×D52—41no—
85C2×D52—41no—
86C2×D52—41no—
87C2×D52—41no—
88C2×D52—82no—
89C2×D52—81no—
90C2×D52—81no—
91C13×M16—21no—
92C13×M16—21no—
93C13×M16—21no—
94C13×M16SD1612yescomplemented
95C2×C8×C13—21no—
96C2×C8×C13—21no—
97C2×C8×C13—21no—
98C2×C8×C13—21no—
99C2×C8×C13—41no—
100C2×C8×C13—41no—
101C13×C4⋊C4—22no—
102C13×C4⋊C4—21no—
103C13×C4⋊C4—21no—
104C13×C4⋊C4—21no—
105C13×C4⋊C4—22no—
106C13×C4⋊C4C22⋊C412yes—
107C13×C22⋊C4—22no—
108C42×C13—22no—
109C42×C13C2×D411yescharacteristic
110C42×C13C2×D411yescharacteristic
111C42×C13C2×D411yescharacteristic
112C42×C13#4111yescharacteristic
113#6106—84no—
114#6099—41no—
115#6099—41no—
116C2×#1055—22no—
117C2×#1055—41no—
118C2×#1055—41no—
119C2×#1055—81no—
120#3208—131no—
121#2962D1311yescharacteristic, complemented
122#1965—131no—
123#1550—131no—
124C2×#331—131no—
125#1301—131no—
126#1283—131no—
127C23×C13C4×D411yescharacteristic
128C22×D13—42no—
129C22×D13—42no—
130C22×D13—42no—
131C22×D13—82no—
132C22×D13—82no—
133Q8×C13—42no—
134Q8×C13—41no—
135Q8×C13—41no—
136C2×C4×C13—21no—
137C2×C4×C13—21no—
138C2×C4×C13—22no—
139C2×C4×C13—22no—
140C2×C4×C13—41no—
141C2×C4×C13C2×C22⋊C411yescharacteristic
142C2×C4×C13C4×D411yescharacteristic
143C2×C4×C13#12011yescharacteristic
144C2×C4×C13#12111yescharacteristic
145C2×C4×C13#12111yescharacteristic
146C2×C4×C13#12311yescharacteristic
147C2×C4×C13C2×SD1611yescharacteristic
148C2×C4×C13#13511yescharacteristic
149C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
150C2×C4×C13#13711yescharacteristic
151D52—44no—
152D52—82no—
153D52—82no—
154D52—81no—
155D52—81no—
156D52—81no—
157D52—81no—
158D52—81no—
159D52—81no—
160C8×C13—22no—
161C8×C13—41no—
162C8×C13—41no—
163C8×C13—41no—
164#1055—42no—
165#1055—81no—
166#1055—81no—
167#533C2×D1311yescharacteristic
168C2×#127—131no—
169#492—261no—
170#486—261no—
171#460—262no—
172#450—134no—
173#446—22no—
174#446—21no—
175C8×Q8—21no—
176#431—131no—
177#424—21no—
178#423—131no—
179C2×C4⋊C8—131no—
180C2×C4⋊C8C2×D1311yescharacteristic
181C2×#100—261no—
182C2×#100—261no—
183#405—21no—
184C4×M16C2×D1311yescharacteristic
185#333—261no—
186#332—261no—
187#331—261no—
188#331—261no—
189C22×C13—21no—
190C22×C13—21no—
191C22×C13#38611yescharacteristic
192C22×C13C4×SD1611yescharacteristic
193C22×C13#44011yescharacteristic
194C2×D13—82no—
195C2×D13—82no—
196C2×D13—82no—
197C2×D13—162no—
198C2×D13—162no—
199C4×C13—21no—
200C4×C13—21no—
201C4×C13—21no—
202C4×C13—42no—
203C4×C13—42no—
204C4×C13#44811yescharacteristic
205C4×C13#44911yescharacteristic
206C4×C13#46011yescharacteristic
207C4×C13#46411yescharacteristic
208C4×C13#47111yescharacteristic
209C4×C13#47211yescharacteristic
210C22×D4—132no—
211C22×D4—261no—
212C22×D4—261no—
213C2×SD16—264no—
214C2×M16—261no—
215C2×M16C22⋊D1311yescharacteristic
216C2×M16C22⋊D1311yescharacteristic
217C22×C8—21no—
218C22×C8—261no—
219C4⋊Q8D5211yescharacteristic
220C4⋊Q8D5211yescharacteristic
221#127—261no—
222#127—261no—
223#127—261no—
224#127—261no—
225#125—21no—
226C22⋊Q8—21no—
227C22⋊Q8C4×D1312yes—
228C4×Q8—21no—
229C4×Q8C22⋊D1312yes—
230#117—21no—
231C2×C42C22×D1311yescharacteristic
232C4⋊C8—22no—
233C4⋊C8—22no—
234C4⋊C8—21no—
235C4⋊C8—261no—
236C4⋊C8—261no—
237C4⋊C8—261no—
238C4⋊C8—261no—
239C4⋊C8—261no—
240C4⋊C8C22⋊D1311yescharacteristic
241C4⋊C8C22⋊D1311yescharacteristic
242#102—264no—
243#100—522no—
244#100—522no—
245C22⋊C8—132no—
246#97—22no—
247#97—21no—
248C4×C8—22no—
249C4×C8—21no—
250C4×C8—261no—
251C2×C13—21no—
252C2×C13—21no—
253C2×C13#188011yescharacteristic
254C2×C13#190711yescharacteristic
255C2×C13#191411yescharacteristic
256D13—162no—
257C24—262no—
258C2×Q8—21no—
259C2×Q8#610312yes—
260C2×D4—262no—
261C2×D4—262no—
262C2×D4—521no—
263C2×D4—521no—
264C2×D4—521no—
265C2×D4—521no—
266C2×D4—521no—
267C2×D4—521no—
268C2×D4—521no—
269C2×D4—521no—
270C2×D4—1041no—
271C2×D4—1041no—
272C2×D4—1042no—
273C22×C4C2×C4×D1311yescharacteristic
274C22×C4#612711yescharacteristic
275C22×C4C2×C22⋊D1311yescharacteristic
276SD16—1044no—
277M16—21no—
278M16—21no—
279M16—21no—
280M16—521no—
281M16—521no—
282M16#610612yescomplemented
283C2×C8—21no—
284C2×C8—21no—
285C2×C8—21no—
286C2×C8—21no—
287C2×C8—41no—
288C2×C8—41no—
289C2×C8—262no—
290C2×C8—521no—
291C2×C8—521no—
292C2×C8—1041no—
293C4⋊C4—22no—
294C4⋊C4—22no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4#610312yes—
299C22⋊C4—22no—
300C42—22no—
301C42C2×D5211yescharacteristic
302C42#612711yescharacteristic
303C42C2×C22⋊D1311yescharacteristic
304C42C2×C22⋊D1311yescharacteristic
305C13#927411yescharacteristic, complemented, Sylow
306C23—522no—
307C23—522no—
308C23—522no—
309C23—1042no—
310C23—1042no—
311C23C4×C22⋊D1311yescharacteristic
312Q8—42no—
313Q8—41no—
314Q8—41no—
315D4—524no—
316D4—1042no—
317D4—1042no—
318D4—1041no—
319D4—1041no—
320D4—1041no—
321D4—1041no—
322D4—1041no—
323D4—1041no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—41no—
329C2×C4C2×#610311yescharacteristic
330C2×C4C4×C22⋊D1311yescharacteristic
331C2×C4#8818311yescharacteristic
332C2×C4#8818411yescharacteristic
333C2×C4#8818411yescharacteristic
334C2×C4C2×#610611yescharacteristic
335C2×C4#8819611yescharacteristic
336C2×C4#8820311yescharacteristic
337C2×C4#8820411yescharacteristic
338C2×C4#8820711yescharacteristic
339C8—22no—
340C8—41no—
341C8—41no—
342C8—41no—
343C8—522no—
344C8—1041no—
345C8—1041no—
346C22—21no—
347C22—21no—
348C22—1042no—
349C22—1042no—
350C22—1042no—
351C22—2082no—
352C22—2082no—
353C22C4×#610611yescharacteristic
354C22#1171868711yescharacteristic
355C22#1171887411yescharacteristic
356C4—21no—
357C4—21no—
358C4—21no—
359C4—42no—
360C4—42no—
361C4#1171868811yescharacteristic
362C4#1171868911yescharacteristic
363C4#1171880211yescharacteristic
364C4#1171880311yescharacteristic
365C4#1171888811yescharacteristic
366C4#1171889911yescharacteristic
367C2—21no—
368C2—21no—
369C2—2082no—
370C2#1311519111yescharacteristic
371C2#1311534411yescharacteristic
372C2#1311538311yescharacteristic
subgroupG/H
centerC22#11718874
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2962C2
socleC22×C13#386
prime radicalC2×#88128C22
cosocleC2×C42×C13C23
hypercenter#2962D13
hypocenterC13#9274
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2962

Complements

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

NH ≅ G/Ntype
3. #13113526C2semidirect
5. #13112733C2semidirect
6. #13112687C2semidirect
7. C13×#2962C2semidirect
94. C13×M16SD16semidirect
121. #2962D13semidirect
282. M16#6106semidirect
305. C13#9274semidirect

Maximal subgroups

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

subgroupindex
#131257742
#131156762
#131135262
C2×#117180772
#131127332
#131126872
C13×#29622
#927413