Finite Group Databasebeta

← #15780062

Subgroups — #15780062

Order 3328.

466 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718858C211yesmaximal, characteristic, complemented
2#13116585C211yesmaximal, characteristic, complemented
3#13116564C211yesmaximal, characteristic, complemented
4#13115730C211yesmaximal, characteristic, complemented
5#13112948C211yesmaximal, characteristic, complemented
6#13112919C211yesmaximal, characteristic, complemented
7C13×#3414C211yesmaximal, characteristic
8C2×C13×#135C2211yescharacteristic
9C2×C13×#135C2211yescharacteristic
10C2×#88202—21no—
11C13×#510—21no—
12C13×#510C412yescomplemented
13C13×#509—21no—
14C13×#509C412yescomplemented
15C13×#508—22no—
16C2×C13×M32C2211yescharacteristic
17C2×#88077—21no—
18C2×#88077—21no—
19#11718895—21no—
20#11718858—22no—
21#11718858—22no—
22C2×#88059C2211yescharacteristic
23C2×#88059C2211yescharacteristic
24C2×#88055C2211yescharacteristic
25C2×#88052C2211yescharacteristic
26#11718159—22no—
27#11718157—21no—
28#11718155—21no—
29C2×C13×#41—21no—
30C2×C13×#41—21no—
31C13×#135—21no—
32C13×#135—21no—
33C13×#135—21no—
34C13×#135—21no—
35C13×#135—21no—
36C13×#135—21no—
37C13×#135C2×C412yes—
38C13×#135D412yes—
39C2×C13×Q16C2×C411yescharacteristic
40C2×C13×Q16D411yescharacteristic
41C2×C13×SD16—21no—
42C2×C13×SD16—21no—
43C2×C13×D8C2×C411yescharacteristic
44C2×C13×D8D411yescharacteristic
45C22×C8×C13C2311yescharacteristic
46#88202—24no—
47#88202—42no—
48C2×C4×Dic13D411yescharacteristic
49C2×#6099—21no—
50C2×#6099—21no—
51C2×#6099—41no—
52C22×#1055—41no—
53C22×#1055D411yescharacteristic
54C13×Q32—22no—
55C13×SD32—22no—
56C13×SD32—22no—
57C13×D16—22no—
58C13×M32—21no—
59C13×M32C2×C412yes—
60C2×C13×C16—21no—
61#88077—24no—
62#88077—42no—
63C22⋊#1055—42no—
64#88059—21no—
65#88059—21no—
66#88059—21no—
67#88059D412yes—
68#88055—21no—
69#88055—21no—
70#88052—21no—
71#88052—21no—
72C2×#6090—21no—
73#13024—131nomaximal, Sylow
74C13×#41—22no—
75C13×#41—22no—
76C13×#41—41no—
77C13×#41—41no—
78C13×#41—41no—
79C13×#41—41no—
80C13×#41—41no—
81C13×#41—41no—
82C2×Q8×C13—21no—
83C2×Q8×C13—21no—
84C2×D4×C13—21no—
85C2×D4×C13—21no—
86C2×D4×C13—41no—
87C2×D4×C13—41no—
88C22×C4×C13—41no—
89C22×C4×C13—41no—
90C22×C4×C13C2×D411yescharacteristic
91C22×Dic13—21no—
92C13×Q16—21no—
93C13×Q16—21no—
94C13×Q16—21no—
95C13×Q16C22⋊C412yes—
96C13×SD16—22no—
97C13×SD16—22no—
98C13×SD16—41no—
99C13×SD16—41no—
100C13×D8—21no—
101C13×D8—21no—
102C13×D8—21no—
103C13×D8C22⋊C412yes—
104C2×C8×C13C22×C411yescharacteristic
105C2×C8×C13C2×D411yescharacteristic
106C2×C8×C13C2×D411yescharacteristic
107C2×C8×C13C2×D411yescharacteristic
108C2×C8×C13#4111yescharacteristic
109C2×C8×C13#4111yescharacteristic
110C4×Dic13—21no—
111C4×Dic13—21no—
112#6099—22no—
113#6099—44no—
114#6099—41no—
115#6099—41no—
116#6099—41no—
117C2×#1055—21no—
118C2×#1055—21no—
119C2×#1055—44no—
120C2×#1055—41no—
121C2×#1055—41no—
122C2×#1055D812yes—
123C13×C16—22no—
124#6090—41no—
125#3414D1311yescharacteristic
126C2×#444—131no—
127#2148—131no—
128#2143—131no—
129#1975—131no—
130#1388—131no—
131#1377—131no—
132C23×C13—41no—
133C23×C13—41no—
134C23×C13#13511yescharacteristic
135Q8×C13—22no—
136Q8×C13—41no—
137Q8×C13—41no—
138Q8×C13—41no—
139D4×C13—22no—
140D4×C13—42no—
141D4×C13—42no—
142D4×C13—41no—
143D4×C13—41no—
144D4×C13—41no—
145D4×C13—81no—
146D4×C13—81no—
147C2×C4×C13—41no—
148C2×C4×C13—42no—
149C2×C4×C13—42no—
150C2×C4×C13—41no—
151C2×C4×C13—81no—
152C2×C4×C13—81no—
153C2×C4×C13C4×D411yescharacteristic
154C2×C4×C13#12011yescharacteristic
155C2×C4×C13#12111yescharacteristic
156C2×C4×C13C2×D811yescharacteristic
157C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
158C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
159C2×Dic13—41no—
160C2×Dic13—81no—
161C8×C13C2×C22⋊C411yescharacteristic
162C8×C13C4×D411yescharacteristic
163C8×C13#12111yescharacteristic
164C8×C13#12311yescharacteristic
165#1055—22no—
166#1055—42no—
167#1055—81no—
168C2×#135C2×D1311yescharacteristic
169C2×#135C2×D1311yescharacteristic
170C2×#131—261no—
171#510—21no—
172#510Dic1312yescomplemented
173#509—21no—
174#509Dic1312yescomplemented
175#508—22no—
176C2×M32—131no—
177C2×M32C2×D1311yescharacteristic
178#444—262no—
179#444—262no—
180C2×#108—131no—
181C2×#108—131no—
182C2×#104—261no—
183C2×#104—261no—
184#408—261no—
185C2×#97—131no—
186#362—261no—
187#361—261no—
188#359—262no—
189C22×C13—41no—
190C22×C13—42no—
191C22×C13—82no—
192C22×C13—82no—
193C22×C13—81no—
194C22×C13C4×D811yescharacteristic
195C22×C13#44911yescharacteristic
196C22×C13#46311yescharacteristic
197C4×C13—42no—
198C4×C13—81no—
199C4×C13#38611yescharacteristic
200C4×C13#44211yescharacteristic
201C4×C13#44711yescharacteristic
202C4×C13#45911yescharacteristic
203Dic13—81no—
204C2×#41—21no—
205C2×#41—21no—
206#135—21no—
207#135—21no—
208#135—21no—
209#135—21no—
210#135—21no—
211#135—21no—
212#135C2×Dic1312yes—
213#135C22⋊D1312yes—
214C2×Q16C2×Dic1311yescharacteristic
215C2×Q16C22⋊D1311yescharacteristic
216C2×SD16—21no—
217C2×SD16—21no—
218C2×D8C2×Dic1311yescharacteristic
219C2×D8C22⋊D1311yescharacteristic
220#131—264no—
221#131—522no—
222C2×M16—261no—
223C2×M16—261no—
224C2×M16—521no—
225C22×C8—131no—
226C22×C8—521no—
227C22×C8C22×D1311yescharacteristic
228C2×C42—131no—
229Q32—22no—
230SD32—22no—
231SD32—22no—
232D16—22no—
233M32—21no—
234M32—261no—
235M32—261no—
236M32C2×Dic1312yes—
237C2×C16—21no—
238C2×C16—261no—
239#108—132no—
240#108—261no—
241#108—261no—
242#108—261no—
243#104—264no—
244#104—522no—
245C22⋊C8—522no—
246#97—261no—
247#97—261no—
248C2×C13—21no—
249C2×C13—21no—
250C2×C13—21no—
251C2×C13—82no—
252C2×C13—161no—
253C2×C13#187911yescharacteristic
254#41—22no—
255#41—22no—
256#41—41no—
257#41—41no—
258#41—41no—
259#41—41no—
260#41—41no—
261#41—41no—
262C2×Q8—21no—
263C2×Q8—21no—
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—41no—
267C2×D4—41no—
268C22×C4—41no—
269C22×C4—41no—
270C22×C4—261no—
271C22×C4D4×D1311yescharacteristic
272Q16—21no—
273Q16—21no—
274Q16—21no—
275Q16C22⋊Dic1312yes—
276SD16—22no—
277SD16—22no—
278SD16—41no—
279SD16—41no—
280D8—21no—
281D8—21no—
282D8—21no—
283D8C22⋊Dic1312yes—
284M16—262no—
285M16—524no—
286M16—521no—
287M16—521no—
288M16—521no—
289C2×C8—132no—
290C2×C8—261no—
291C2×C8—261no—
292C2×C8—524no—
293C2×C8—521no—
294C2×C8—521no—
295C2×C8D4×D1311yescharacteristic
296C2×C8#612911yescharacteristic
297C2×C8#612911yescharacteristic
298C2×C8C22×Dic1311yescharacteristic
299C2×C8C2×C22⋊D1311yescharacteristic
300C2×C8C2×C22⋊D1311yescharacteristic
301C42—261no—
302C42—261no—
303C16—22no—
304C16—521no—
305C13#1302411yescharacteristic, complemented, Sylow
306C23—41no—
307C23—41no—
308C23#8816611yescharacteristic
309Q8—22no—
310Q8—41no—
311Q8—41no—
312Q8—41no—
313D4—22no—
314D4—42no—
315D4—42no—
316D4—41no—
317D4—41no—
318D4—41no—
319D4—81no—
320D4—81no—
321C2×C4—41no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—41no—
325C2×C4—81no—
326C2×C4—81no—
327C2×C4—521no—
328C2×C4—1041no—
329C2×C4D8×D1311yescharacteristic
330C2×C4#8816511yescharacteristic
331C2×C4#8816511yescharacteristic
332C2×C4D4×Dic1311yescharacteristic
333C2×C4#8819111yescharacteristic
334C2×C4#8819311yescharacteristic
335C8—262no—
336C8—522no—
337C8—1041no—
338C8D4×Dic1311yescharacteristic
339C8#8818911yescharacteristic
340C8#8819311yescharacteristic
341C8C2×C22⋊Dic1311yescharacteristic
342C22—41no—
343C22—42no—
344C22—82no—
345C22—82no—
346C22—81no—
347C22D8×Dic1311yescharacteristic
348C22#1171881411yescharacteristic
349C22#1171881911yescharacteristic
350C4—42no—
351C4—81no—
352C4—1041no—
353C4#1171881111yescharacteristic
354C4#1171881311yescharacteristic
355C4#1171881711yescharacteristic
356C4#1171888111yescharacteristic
357C2—21no—
358C2—21no—
359C2—21no—
360C2—82no—
361C2—161no—
362C2#1311518611yescharacteristic
subgroupG/H
centerC4#11718817
commutatorC2×C8×C13C22×C4
FrattiniC22×C8C22×D13
Fitting, prime radicalC13×#3414C2
socleC2×C13#1879
cosocleC22×C8×C13C23
hypercenter#3414D13
hypocenterC13#13024
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×C8 ◁ #3414

Complements

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

NH ≅ G/Ntype
1. C2×#11718858C2semidirect
2. #13116585C2semidirect
3. #13116564C2semidirect
4. #13115730C2semidirect
5. #13112948C2semidirect
6. #13112919C2semidirect
12. C13×#510C4semidirect
14. C13×#509C4semidirect
172. #510Dic13semidirect
174. #509Dic13semidirect
305. C13#13024semidirect

Maximal subgroups

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

subgroupindex
C2×#117188582
#131165852
#131165642
#131157302
#131129482
#131129192
C13×#34142
#1302413