Finite Group Databasebeta

← #15759434

Subgroups — #15759434

Order 3328.

480 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125961C211yesmaximal, characteristic
2#13123580C211yesmaximal, characteristic
3#13115824C211yesmaximal, characteristic, complemented
4C2×#11718074C211yesmaximal, characteristic, complemented
5#13112731C211yesmaximal, characteristic, complemented
6#13112686C211yesmaximal, characteristic, complemented
7C13×#1547C211yesmaximal, characteristic
8C13×#532C2211yescharacteristic
9C2×#88202—21no—
10C2×#88123C2211yescharacteristic
11C13×#423C2211yescharacteristic
12C2×C13×C4⋊C8C2211yescharacteristic
13#11718895—21no—
14#11718740—21no—
15#11718731—21no—
16#11718695C414yes—
17#11718673—21no—
18#11718672—22no—
19D4×#1055—21no—
20#11718669—22no—
21#11718586C2211yescharacteristic
22C2×C4⋊#1055C2211yescharacteristic
23C4×#6099C2211yescharacteristic
24C13×#332—21no—
25C13×#331—21no—
26#11718146—21no—
27#11718146—21no—
28#11718074—21no—
29#11718074—21no—
30C2×C13×#41—21no—
31C22×Dic26—21no—
32C2×C13×M16—21no—
33C22×C8×C13—21no—
34C13×C4⋊Q8D411yescharacteristic
35C13×#127D411yescharacteristic
36C13×#124—21no—
37C13×#121—21no—
38C13×#121C2×C412yes—
39C4×D4×C13—21no—
40C4×D4×C13D412yes—
41C2×C42×C13C2311yescharacteristic
42#88202—42no—
43#88202—42no—
44C2×C4⋊Dic13—21no—
45C2×C4⋊Dic13C2×C412yes—
46C2×#6099—22no—
47C2×#6099D411yescharacteristic
48C2×#6099D411yescharacteristic
49C22×#1055—22no—
50C22×#1055—21no—
51#88123—21no—
52#88123—21no—
53#88123—21no—
54#88123—21no—
55C13×C4⋊C8—21no—
56C13×C4⋊C8—21no—
57C13×C4⋊C8—21no—
58C13×C4⋊C8—21no—
59#88072—24no—
60C22⋊#1055—22no—
61C22⋊#1055—22no—
62C22⋊#1055C2×C412yes—
63#88048—24no—
64C4⋊#1055—21no—
65C4⋊#1055—21no—
66C4⋊#1055D411yescharacteristic
67C4⋊#1055D411yescharacteristic
68#88043—21no—
69C4×#1055—21no—
70C4×#1055—21no—
71#9269—131nomaximal, Sylow
72C13×#41—41no—
73C13×#41—41no—
74C13×#41—41no—
75C13×#41—41no—
76C2×Q8×C13—21no—
77C2×D4×C13—22no—
78C2×D4×C13—21no—
79C2×D4×C13—21no—
80C2×D4×C13C22⋊C412yes—
81C22×C4×C13—22no—
82C22×C4×C13C22×C411yescharacteristic
83C22×C4×C13C2×D411yescharacteristic
84C22×C4×C13#4111yescharacteristic
85C22×Dic13—22no—
86C2×Dic26—41no—
87C2×Dic26—41no—
88C2×Dic26—81no—
89C2×Dic26—81no—
90C13×M16—41no—
91C13×M16—41no—
92C2×C8×C13—41no—
93C2×C8×C13—41no—
94C2×C8×C13—81no—
95C13×C4⋊C4—21no—
96C13×C4⋊C4C22⋊C412yes—
97C13×C22⋊C4—22no—
98C13×C22⋊C4—22no—
99C42×C13C2×D411yescharacteristic
100C42×C13C2×D411yescharacteristic
101C42×C13C2×D411yescharacteristic
102C42×C13#4111yescharacteristic
103C4⋊Dic13—22no—
104C4⋊Dic13—22no—
105C4⋊Dic13—41no—
106C4⋊Dic13—41no—
107#6099—21no—
108#6099—21no—
109#6099—21no—
110#6099—44no—
111#6099SD1612yes—
112C2×#1055—21no—
113C2×#1055—22no—
114C2×#1055—21no—
115C2×#1055—21no—
116C2×#1055—21no—
117C2×#1055—44no—
118C2×#1055—41no—
119C2×#1055—41no—
120#3227—131no—
121#2935—131no—
122#1997—131no—
123#1547D1311yescharacteristic
124C2×#332—131no—
125#1301—131no—
126#1283—131no—
127C23×C13—22no—
128C23×C13C4×D411yescharacteristic
129Q8×C13—41no—
130Q8×C13—41no—
131D4×C13—42no—
132D4×C13—42no—
133D4×C13—42no—
134D4×C13—41no—
135D4×C13—41no—
136D4×C13—41no—
137D4×C13—41no—
138C2×C4×C13—21no—
139C2×C4×C13—21no—
140C2×C4×C13—22no—
141C2×C4×C13—41no—
142C2×C4×C13—42no—
143C2×C4×C13—42no—
144C2×C4×C13C2×C22⋊C411yescharacteristic
145C2×C4×C13C4×D411yescharacteristic
146C2×C4×C13#12011yescharacteristic
147C2×C4×C13#12111yescharacteristic
148C2×C4×C13#12111yescharacteristic
149C2×C4×C13#12311yescharacteristic
150C2×C4×C13C2×SD1611yescharacteristic
151C2×C4×C13#13511yescharacteristic
152C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
153C2×C4×C13#13711yescharacteristic
154C2×Dic13—42no—
155C2×Dic13—82no—
156Dic26—82no—
157Dic26—81no—
158Dic26—81no—
159C8×C13—81no—
160C8×C13—81no—
161#1055—22no—
162#1055—42no—
163#1055—41no—
164#1055—41no—
165#1055—41no—
166C2×#131—261no—
167#532C2×D1311yescharacteristic
168C2×C4⋊Q8—131no—
169#498—261no—
170#486—261no—
171#481—134no—
172#476—262no—
173#436—261no—
174#435—262no—
175C8×D4—261no—
176#431—131no—
177#423C2×D1311yescharacteristic
178C2×C4⋊C8—131no—
179C2×C4⋊C8C2×D1311yescharacteristic
180#408—261no—
181C4×M16—131no—
182#343—261no—
183#343—261no—
184#332—21no—
185#332—261no—
186#332—261no—
187#331—21no—
188C22×C13—21no—
189C22×C13—21no—
190C22×C13—42no—
191C22×C13—42no—
192C22×C13—42no—
193C22×C13#38611yescharacteristic
194C22×C13C4×SD1611yescharacteristic
195C22×C13#44011yescharacteristic
196C4×C13—21no—
197C4×C13—21no—
198C4×C13—21no—
199C4×C13—42no—
200C4×C13#45011yescharacteristic
201C4×C13#45211yescharacteristic
202C4×C13#46111yescharacteristic
203C4×C13#46311yescharacteristic
204C4×C13#47111yescharacteristic
205C4×C13#47211yescharacteristic
206Dic13—82no—
207C2×#41—21no—
208C22×Q8—261no—
209#131—522no—
210#131—522no—
211C2×M16—21no—
212C2×M16—131no—
213C2×M16—131no—
214C2×M16—262no—
215C22×C8—21no—
216C22×C8—262no—
217C22×C8—261no—
218C4⋊Q8—261no—
219C4⋊Q8—261no—
220C4⋊Q8—261no—
221C4⋊Q8—261no—
222C4⋊Q8C22⋊D1311yescharacteristic
223#127C22⋊D1311yescharacteristic
224#124—21no—
225#121—21no—
226#121C4×D1312yes—
227C4×D4—21no—
228C4×D4D5212yes—
229C2×C4⋊C4—132no—
230C2×C4⋊C4—261no—
231C2×C42C22×D1311yescharacteristic
232#106—264no—
233C4⋊C8—21no—
234C4⋊C8—21no—
235C4⋊C8—21no—
236C4⋊C8—21no—
237C4⋊C8—131no—
238C4⋊C8—131no—
239C4⋊C8—261no—
240C4⋊C8—261no—
241#102—264no—
242C22⋊C8—132no—
243C22⋊C8—262no—
244C22⋊C8—262no—
245#97—261no—
246C4×C8—261no—
247C4×C8—261no—
248C2×C13—21no—
249C2×C13—21no—
250C2×C13—82no—
251C2×C13#187711yescharacteristic
252C2×C13#190711yescharacteristic
253C2×C13#191511yescharacteristic
254#41—41no—
255#41—41no—
256#41—41no—
257#41—41no—
258C2×Q8—21no—
259C2×Q8—521no—
260C2×Q8—521no—
261C2×Q8—1041no—
262C2×Q8—1041no—
263C2×D4—22no—
264C2×D4—21no—
265C2×D4—21no—
266C2×D4#610312yes—
267C22×C4—22no—
268C22×C4—262no—
269C22×C4C2×C4×D1311yescharacteristic
270C22×C4D4×D1311yescharacteristic
271C22×C4#612911yescharacteristic
272M16—41no—
273M16—41no—
274M16—132no—
275M16—261no—
276M16—261no—
277M16—261no—
278M16—524no—
279C2×C8—41no—
280C2×C8—41no—
281C2×C8—81no—
282C2×C8—261no—
283C2×C8—261no—
284C2×C8—261no—
285C2×C8—261no—
286C2×C8—262no—
287C2×C8—524no—
288C2×C8—521no—
289C2×C8—521no—
290C4⋊C4—21no—
291C4⋊C4—262no—
292C4⋊C4—262no—
293C4⋊C4—521no—
294C4⋊C4—521no—
295C4⋊C4#610312yes—
296C22⋊C4—22no—
297C22⋊C4—22no—
298C42C2×D5211yescharacteristic
299C42D4×D1311yescharacteristic
300C42#612911yescharacteristic
301C42C2×C22⋊D1311yescharacteristic
302C13#926911yescharacteristic, complemented, Sylow
303C23—22no—
304C23#8813511yescharacteristic
305Q8—41no—
306Q8—41no—
307Q8—1042no—
308Q8—1041no—
309Q8—1041no—
310D4—42no—
311D4—42no—
312D4—42no—
313D4—41no—
314D4—41no—
315D4—41no—
316D4—41no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—22no—
320C2×C4—41no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—522no—
324C2×C4—1042no—
325C2×C4#8813511yescharacteristic
326C2×C4#8813611yescharacteristic
327C2×C4#8814011yescharacteristic
328C2×C4#8816511yescharacteristic
329C2×C4#8816611yescharacteristic
330C2×C4SD16×D1311yescharacteristic
331C2×C4#8816911yescharacteristic
332C2×C4C2×#610311yescharacteristic
333C2×C4#8819311yescharacteristic
334C2×C4#8819311yescharacteristic
335C8—81no—
336C8—81no—
337C8—262no—
338C8—522no—
339C8—521no—
340C8—521no—
341C8—521no—
342C22—21no—
343C22—21no—
344C22—42no—
345C22—42no—
346C22—42no—
347C22#1171841811yescharacteristic
348C22#1171841911yescharacteristic
349C22#1171861911yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—42no—
354C4—1042no—
355C4#1171843711yescharacteristic
356C4#1171844411yescharacteristic
357C4#1171881411yescharacteristic
358C4#1171882311yescharacteristic
359C4#1171886011yescharacteristic
360C4#1171886411yescharacteristic
361C2—21no—
362C2—21no—
363C2—82no—
364C2#1311516811yescharacteristic
365C2#1311534211yescharacteristic
366C2#1311538611yescharacteristic
subgroupG/H
centerC22#11718619
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1547C2
socleC22×C13#386
prime radicalC13×#532C22
cosocleC2×C42×C13C23
hypercenter#1547D13
hypocenterC13#9269
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1547

Complements

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

NH ≅ G/Ntype
3. #13115824C2semidirect
4. C2×#11718074C2semidirect
5. #13112731C2semidirect
6. #13112686C2semidirect
302. C13#9269semidirect

Maximal subgroups

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

subgroupindex
#131259612
#131235802
#131158242
C2×#117180742
#131127312
#131126862
C13×#15472
#926913