Finite Group Databasebeta

← #15780349

Subgroups — #15780349

Order 3328.

456 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718801C211yesmaximal, characteristic, complemented
2#13116572C211yesmaximal, characteristic, complemented
3C2×#11718159C211yesmaximal, characteristic, complemented
4#13114890C211yesmaximal, characteristic, complemented
5#13112949C211yesmaximal, characteristic, complemented
6#13112933C211yesmaximal, characteristic, complemented
7C13×#3067C211yesmaximal, characteristic
8C13×#575—21no—
9C2×C13×#135C2211yescharacteristic
10C2×C13×#131C2211yescharacteristic
11C13×#473C412yescomplemented
12C13×#472C412yescomplemented
13C13×#471—22no—
14C2×C13×#108C2211yescharacteristic
15C13×#413—21no—
16#11718897—21no—
17#11718801—22no—
18#11718801—22no—
19C2×#88059C2211yescharacteristic
20#11718767C2211yescharacteristic
21C2×#88052—21no—
22C2×#88052C2211yescharacteristic
23C22×#6090—21no—
24C22×#6090C2211yescharacteristic
25#11718159—21no—
26#11718159—21no—
27#11718158—22no—
28#11718151—21no—
29C2×C13×#41—21no—
30C2×C13×#41D411yescharacteristic
31C13×#137—22no—
32C13×#137—41no—
33C13×AGL(1,ℤ/8)—22no—
34C13×AGL(1,ℤ/8)—41no—
35C13×#135—21no—
36C13×#135—21no—
37C13×#135—21no—
38C13×#135—21no—
39C13×#135—42no—
40C2×C13×Q16C2×C411yescharacteristic
41C2×C13×SD16—21no—
42C2×C13×D8C2×C411yescharacteristic
43C13×#131—21no—
44C13×#131—21no—
45C13×#131C2×C412yes—
46C13×#131D412yes—
47C2×C13×M16—21no—
48C2×C13×M16—21no—
49C2×C13×M16D411yescharacteristic
50C22×C8×C13—21no—
51C22×C8×C13C2311yescharacteristic
52#88180—21no—
53C2×#6099—21no—
54C13×#108—21no—
55C13×#108C2×C412yes—
56C13×#101—22no—
57C13×#100—22no—
58#88077—42no—
59#88059—21no—
60#88059—21no—
61#88058—21no—
62#88057—21no—
63#88052—24no—
64#88052—21no—
65#88052D412yes—
66C2×#6090—24no—
67C2×#6090—21no—
68C2×#6090—21no—
69C2×#6090—21no—
70C2×#6090D411yescharacteristic
71C2×#6090D411yescharacteristic
72#13071—131nomaximal, Sylow
73C13×#41—21no—
74C13×#41—21no—
75C13×#41—41no—
76C13×#41—41no—
77C13×#41—41no—
78C13×#41—41no—
79C13×#41C22⋊C412yes—
80C13×#41D812yes—
81C2×Q8×C13—21no—
82C2×Q8×C13SD1611yescharacteristic
83C2×D4×C13—21no—
84C2×D4×C13—21no—
85C2×D4×C13—41no—
86C2×D4×C13SD1611yescharacteristic
87C22×C4×C13—21no—
88C22×C4×C13—41no—
89C22×C4×C13C2×D411yescharacteristic
90C13×Q16—21no—
91C13×Q16—21no—
92C13×Q16—42no—
93C13×SD16—42no—
94C13×SD16—42no—
95C13×SD16—41no—
96C13×SD16—41no—
97C13×D8—21no—
98C13×D8—21no—
99C13×D8—42no—
100C13×M16—21no—
101C13×M16—22no—
102C13×M16—22no—
103C13×M16—22no—
104C13×M16—41no—
105C13×M16C22⋊C412yes—
106C2×C8×C13—21no—
107C2×C8×C13—22no—
108C2×C8×C13—22no—
109C2×C8×C13—41no—
110C2×C8×C13C22×C411yescharacteristic
111C2×C8×C13C2×D411yescharacteristic
112C2×C8×C13C2×D411yescharacteristic
113C2×C8×C13C2×D411yescharacteristic
114C2×C8×C13#4111yescharacteristic
115C2×C8×C13#4111yescharacteristic
116C22⋊Dic13—41no—
117C4⋊Dic13—41no—
118C4×Dic13—41no—
119#6099—41no—
120#6099—41no—
121C2×#1055—41no—
122#6090—21no—
123#6090—22no—
124#6090—21no—
125C2×#504—131no—
126#3067D1311yescharacteristic
127#2145—131no—
128C2×#359—131no—
129#1814—131no—
130#1388—131no—
131#1382—131no—
132C23×C13—21no—
133C23×C13—41no—
134C23×C13#13511yescharacteristic
135Q8×C13—21no—
136Q8×C13—41no—
137Q8×C13—41no—
138Q8×C13#10212yes—
139D4×C13—22no—
140D4×C13—22no—
141D4×C13—21no—
142D4×C13—41no—
143D4×C13—41no—
144D4×C13—81no—
145D4×C13—81no—
146D4×C13#10212yes—
147C2×C4×C13—21no—
148C2×C4×C13—22no—
149C2×C4×C13—22no—
150C2×C4×C13—41no—
151C2×C4×C13—81no—
152C2×C4×C13—81no—
153C2×C4×C13C2×C22⋊C411yescharacteristic
154C2×C4×C13#12111yescharacteristic
155C2×C4×C13#12111yescharacteristic
156C2×C4×C13C2×D811yescharacteristic
157C2×C4×C13C2×SD1611yescharacteristic
158C2×C4×C13#13511yescharacteristic
159C2×Dic13—81no—
160C8×C13—22no—
161C8×C13—42no—
162C8×C13C4×D411yescharacteristic
163C8×C13C4×D411yescharacteristic
164C8×C13#12011yescharacteristic
165C8×C13#12311yescharacteristic
166#1055—81no—
167#575—21no—
168C2×#135C2×D1311yescharacteristic
169C2×#131C2×D1311yescharacteristic
170#504—262no—
171#504—262no—
172C2×M32—131no—
173C2×M32—261no—
174C22×C16—131no—
175C22×C16—261no—
176#473Dic1312yescomplemented
177#472Dic1312yescomplemented
178#471—22no—
179C2×#108—131no—
180C2×#108C2×D1311yescharacteristic
181#427—131no—
182#421—261no—
183#413—21no—
184#360—262no—
185#359—261no—
186#359—261no—
187#344—261no—
188C22×C13—22no—
189C22×C13—41no—
190C22×C13—42no—
191C22×C13—81no—
192C22×C13—161no—
193C22×C13#41611yescharacteristic
194C22×C13#46511yescharacteristic
195C22×C13#46611yescharacteristic
196C4×C13—22no—
197C4×C13—81no—
198C4×C13#38611yescharacteristic
199C4×C13C2×#10211yescharacteristic
200C4×C13#46511yescharacteristic
201C4×C13#46611yescharacteristic
202Dic13—161no—
203C2×#41—21no—
204C2×#41C22⋊D1311yescharacteristic
205#137—22no—
206#137—41no—
207AGL(1,ℤ/8)—22no—
208AGL(1,ℤ/8)—41no—
209#135—21no—
210#135—21no—
211#135—21no—
212#135—21no—
213#135—42no—
214C2×Q16C2×Dic1311yescharacteristic
215C2×SD16—21no—
216C2×D8C2×Dic1311yescharacteristic
217#131—21no—
218#131—21no—
219#131C2×Dic1312yes—
220#131C22⋊D1312yes—
221C2×M16—21no—
222C2×M16—21no—
223C2×M16—261no—
224C2×M16C22⋊D1311yescharacteristic
225C22×C8—21no—
226C22×C8C22×D1311yescharacteristic
227#117—261no—
228M32—132no—
229M32—264no—
230M32—261no—
231C2×C16—131no—
232C2×C16—131no—
233C2×C16—264no—
234C2×C16—261no—
235C2×C16—261no—
236C2×C16—261no—
237#108—21no—
238#108—261no—
239#108—261no—
240#108C2×Dic1312yes—
241#107—261no—
242#106—261no—
243#104—522no—
244#101—22no—
245#100—22no—
246C2×C13—21no—
247C2×C13—21no—
248C2×C13—21no—
249C2×C13—42no—
250C2×C13—161no—
251C2×C13#189311yescharacteristic
252#41—21no—
253#41—21no—
254#41—41no—
255#41—41no—
256#41—41no—
257#41—41no—
258#41#610412yes—
259#41C22⋊Dic1312yes—
260C2×Q8—21no—
261C2×Q8#610511yescharacteristic
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—41no—
265C2×D4#610511yescharacteristic
266C22×C4—21no—
267C22×C4—41no—
268C22×C4C2×C22⋊D1311yescharacteristic
269Q16—21no—
270Q16—21no—
271Q16—42no—
272SD16—42no—
273SD16—42no—
274SD16—41no—
275SD16—41no—
276D8—21no—
277D8—21no—
278D8—42no—
279M16—21no—
280M16—22no—
281M16—22no—
282M16—22no—
283M16—41no—
284M16—521no—
285M16—521no—
286M16C22⋊Dic1312yes—
287C2×C8—21no—
288C2×C8—22no—
289C2×C8—22no—
290C2×C8—41no—
291C2×C8—521no—
292C2×C8D4×D1311yescharacteristic
293C2×C8D4×D1311yescharacteristic
294C2×C8#612911yescharacteristic
295C2×C8#612911yescharacteristic
296C2×C8C22×Dic1311yescharacteristic
297C2×C8C2×C22⋊D1311yescharacteristic
298C4⋊C4—521no—
299C22⋊C4—521no—
300C42—521no—
301C16—261no—
302C16—261no—
303C16—262no—
304C13#1307111yescharacteristic, complemented, Sylow
305C23—21no—
306C23—41no—
307C23#8820411yescharacteristic
308Q8—21no—
309Q8—41no—
310Q8—41no—
311Q8#8807212yes—
312D4—22no—
313D4—22no—
314D4—21no—
315D4—41no—
316D4—41no—
317D4—81no—
318D4—81no—
319D4#8807212yes—
320C2×C4—21no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—41no—
324C2×C4—81no—
325C2×C4—81no—
326C2×C4—1041no—
327C2×C4C2×#610411yescharacteristic
328C2×C4C2×#610511yescharacteristic
329C2×C4#8819311yescharacteristic
330C2×C4#8819311yescharacteristic
331C2×C4#8820411yescharacteristic
332C2×C4C2×C22⋊Dic1311yescharacteristic
333C8—22no—
334C8—42no—
335C8—1041no—
336C8D4×Dic1311yescharacteristic
337C8D4×Dic1311yescharacteristic
338C8#8818911yescharacteristic
339C8#8819111yescharacteristic
340C22—22no—
341C22—41no—
342C22—42no—
343C22—81no—
344C22—161no—
345C22#1171869911yescharacteristic
346C22#1171870211yescharacteristic
347C22#1171889411yescharacteristic
348C4—22no—
349C4—81no—
350C4—2081no—
351C4#1171869911yescharacteristic
352C4#1171870211yescharacteristic
353C4C2×#8807211yescharacteristic
354C4#1171888111yescharacteristic
355C2—21no—
356C2—21no—
357C2—21no—
358C2—42no—
359C2—161no—
360C2#1311526511yescharacteristic
subgroupG/H
centerC4#11718699
commutatorC2×C8×C13C22×C4
FrattiniC22×C8C22×D13
Fitting, prime radicalC13×#3067C2
socleC2×C13#1893
cosocleC22×C8×C13C23
hypercenter#3067D13
hypocenterC13#13071
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#131 ◁ #3067

Complements

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

NH ≅ G/Ntype
1. C2×#11718801C2semidirect
2. #13116572C2semidirect
3. C2×#11718159C2semidirect
4. #13114890C2semidirect
5. #13112949C2semidirect
6. #13112933C2semidirect
11. C13×#473C4semidirect
12. C13×#472C4semidirect
176. #473Dic13semidirect
177. #472Dic13semidirect
304. C13#13071semidirect

Maximal subgroups

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

subgroupindex
C2×#117188012
#131165722
C2×#117181592
#131148902
#131129492
#131129332
C13×#30672
#1307113