Finite Group Databasebeta

← #15765367

Subgroups — #15765367

Order 3328.

524 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125977C211yesmaximal, characteristic
2#13119821C211yesmaximal, characteristic
3#13113509C211yesmaximal, characteristic
4#13113335C211yesmaximal, characteristic
5#13113231C211yesmaximal, characteristic
6#13112737C211yesmaximal, characteristic
7C13×#3078C211yesmaximal, characteristic
8C13×#533C2211yescharacteristic
9C2×C4×Q8×C13C2211yescharacteristic
10C2×#88198—21no—
11C2×#88123C2211yescharacteristic
12C13×#479—22no—
13C13×#477—21no—
14C13×#475—21no—
15C13×#428—21no—
16C13×#423C2211yescharacteristic
17C13×#419—21no—
18#11718742—21no—
19#11718740—21no—
20#11718704—22no—
21#11718681—22no—
22#11718644—22no—
23#11718635—21no—
24C4×C4⋊Dic13C2211yescharacteristic
25#11718589—22no—
26#11718586C2211yescharacteristic
27#11718586C2211yescharacteristic
28#11718130—22no—
29Q8⋊#1055—22no—
30#11718074—22no—
31C22×Q8×C13D411yescharacteristic
32C22×Dic26—21no—
33C2×C13×M16—21no—
34C13×C4⋊Q8D411yescharacteristic
35C13×C4⋊Q8D411yescharacteristic
36C13×#125—21no—
37C13×C22⋊Q8—21no—
38C13×C22⋊Q8—21no—
39C4×Q8×C13—21no—
40C4×Q8×C13—21no—
41C4×Q8×C13—21no—
42C4×Q8×C13—21no—
43C4×Q8×C13—21no—
44C4×Q8×C13—21no—
45C13×#117—21no—
46C2×C13×C4⋊C4—21no—
47C2×C13×C4⋊C4D411yescharacteristic
48C2×C42×C13—21no—
49C2×C42×C13C2311yescharacteristic
50#88198—42no—
51#88198—42no—
52C2×C4⋊Dic13—21no—
53C2×C4⋊Dic13—21no—
54C2×C4⋊Dic13D412yes—
55C2×#6101—24no—
56C2×C4×Dic13—21no—
57#88123—21no—
58#88123—21no—
59#88123—21no—
60#88123—21no—
61C13×#107—22no—
62C13×#106—22no—
63C13×C4⋊C8—21no—
64C13×C4⋊C8D412yes—
65C13×#103—22no—
66C13×#103—22no—
67#88075—24no—
68#88071—24no—
69#88071D412yes—
70C22⋊#1055—21no—
71C22⋊#1055—21no—
72#88048—24no—
73C4⋊#1055—21no—
74C4⋊#1055D412yes—
75C4×#1055—21no—
76C4×#1055—21no—
77#10251—131nomaximal, Sylow
78C2×Q8×C13—21no—
79C2×Q8×C13—21no—
80C2×Q8×C13—21no—
81C2×Q8×C13—21no—
82C2×Q8×C13—21no—
83C2×Q8×C13—21no—
84C2×Q8×C13—21no—
85C2×Q8×C13SD1612yes—
86C22×C4×C13—21no—
87C22×C4×C13—21no—
88C22×C4×C13C2×D411yescharacteristic
89C22×C4×C13C2×D411yescharacteristic
90C22×C4×C13C2×D411yescharacteristic
91C22×Dic13—22no—
92C22×Dic13—22no—
93C2×Dic26—41no—
94C2×Dic26—41no—
95C2×Dic26—41no—
96C2×Dic26—41no—
97C2×Dic26—41no—
98C2×Dic26—41no—
99C13×M16—41no—
100C13×M16—41no—
101C2×C8×C13—22no—
102C13×C4⋊C4—21no—
103C13×C4⋊C4—21no—
104C13×C4⋊C4—21no—
105C13×C4⋊C4—21no—
106C13×C4⋊C4—21no—
107C13×C4⋊C4—21no—
108C13×C4⋊C4—41no—
109C13×C4⋊C4—41no—
110C13×C4⋊C4—41no—
111C13×C4⋊C4—41no—
112C13×C22⋊C4—41no—
113C42×C13—41no—
114C42×C13—41no—
115C42×C13—41no—
116C42×C13C2×D411yescharacteristic
117C42×C13C2×D411yescharacteristic
118C42×C13C2×D411yescharacteristic
119C42×C13#4111yescharacteristic
120C4⋊Dic13—24no—
121C4⋊Dic13—22no—
122C4⋊Dic13—22no—
123C4⋊Dic13—41no—
124C4⋊Dic13—41no—
125#6101—48no—
126C4×Dic13—41no—
127C4×Dic13—41no—
128C2×#1055—22no—
129C2×#1055—41no—
130#3229—131no—
131#3078D1311yescharacteristic
132#2546—131no—
133#1546—131no—
134#1503—131no—
135#1479—131no—
136#1303—131no—
137C23×C13#12011yescharacteristic
138Q8×C13—22no—
139Q8×C13—22no—
140Q8×C13—41no—
141Q8×C13—41no—
142Q8×C13—42no—
143Q8×C13—81no—
144C2×C4×C13—22no—
145C2×C4×C13—22no—
146C2×C4×C13—41no—
147C2×C4×C13—41no—
148C2×C4×C13—41no—
149C2×C4×C13—42no—
150C2×C4×C13—41no—
151C2×C4×C13—41no—
152C2×C4×C13—41no—
153C2×C4×C13#12011yescharacteristic
154C2×C4×C13#12011yescharacteristic
155C2×C4×C13#12111yescharacteristic
156C2×C4×C13#12111yescharacteristic
157C2×C4×C13#12111yescharacteristic
158C2×C4×C13#12711yescharacteristic
159C2×C4×C13C2×SD1611yescharacteristic
160C2×C4×C13#13511yescharacteristic
161C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
162C2×C4×C13#13711yescharacteristic
163C2×Dic13—24no—
164C2×Dic13—42no—
165C2×Dic13—42no—
166C2×Dic13—42no—
167C2×Dic13—42no—
168C2×Dic13—42no—
169Dic26—81no—
170Dic26—81no—
171Dic26—81no—
172Dic26—81no—
173C8×C13—42no—
174#1055—42no—
175#1055—81no—
176#533C2×D1311yescharacteristic
177C2×C4⋊Q8—131no—
178C2×C4⋊Q8—261no—
179C2×C4×Q8C2×D1311yescharacteristic
180#498—261no—
181#487—261no—
182#483—262no—
183#479—22no—
184#477—21no—
185#475—21no—
186#475—262no—
187#431—131no—
188#431—131no—
189#428—21no—
190#423C2×D1311yescharacteristic
191#419—21no—
192#398—262no—
193#391—261no—
194#389—262no—
195C4×C4⋊C4—131no—
196#332—262no—
197#328—262no—
198Q8⋊C8—262no—
199C22×C13—21no—
200C22×C13—21no—
201C22×C13#39211yescharacteristic
202C22×C13#45011yescharacteristic
203C22×C13#45211yescharacteristic
204C4×C13—21no—
205C4×C13—21no—
206C4×C13—21no—
207C4×C13—42no—
208C4×C13—81no—
209C4×C13—81no—
210C4×C13—81no—
211C4×C13#44811yescharacteristic
212C4×C13#44911yescharacteristic
213C4×C13#45612yes—
214C4×C13#46511yescharacteristic
215C4×C13#46811yescharacteristic
216Dic13—44no—
217Dic13—82no—
218C22×Q8—261no—
219C22×Q8C22⋊D1311yescharacteristic
220C2×M16—21no—
221C4⋊Q8—261no—
222C4⋊Q8—261no—
223C4⋊Q8—261no—
224C4⋊Q8—261no—
225C4⋊Q8—522no—
226C4⋊Q8—522no—
227C4⋊Q8C22⋊D1311yescharacteristic
228C4⋊Q8C22⋊D1311yescharacteristic
229#125—21no—
230C22⋊Q8—21no—
231C22⋊Q8—21no—
232C4×Q8—21no—
233C4×Q8—21no—
234C4×Q8—21no—
235C4×Q8—21no—
236C4×Q8—21no—
237C4×Q8—21no—
238#117—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—132no—
241C2×C4⋊C4—261no—
242C2×C4⋊C4—264no—
243C2×C4⋊C4—261no—
244C2×C4⋊C4C22⋊D1311yescharacteristic
245C2×C42—21no—
246C2×C42—261no—
247C2×C42C22×D1311yescharacteristic
248#107—22no—
249#106—22no—
250#106—264no—
251C4⋊C8—21no—
252C4⋊C8—132no—
253C4⋊C8—261no—
254C4⋊C8C22⋊D1312yes—
255#103—22no—
256#103—22no—
257#103—264no—
258C22⋊C8—261no—
259C22⋊C8—261no—
260C4×C8—261no—
261C4×C8—261no—
262#95—132no—
263#95—264no—
264C2×C13—21no—
265C2×C13—21no—
266C2×C13#200011yescharacteristic
267C2×C13#200511yescharacteristic
268C2×C13#200911yescharacteristic
269C2×Q8—21no—
270C2×Q8—21no—
271C2×Q8—21no—
272C2×Q8—21no—
273C2×Q8—21no—
274C2×Q8—21no—
275C2×Q8—21no—
276C2×Q8—521no—
277C2×Q8—521no—
278C2×Q8—521no—
279C2×Q8—521no—
280C2×Q8—521no—
281C2×Q8—521no—
282C2×Q8#610612yes—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—262no—
286C22×C4—262no—
287C22×C4D4×D1311yescharacteristic
288C22×C4D4×D1311yescharacteristic
289C22×C4C2×C22⋊D1311yescharacteristic
290M16—41no—
291M16—41no—
292C2×C8—22no—
293C2×C8—262no—
294C2×C8—521no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—264no—
306C4⋊C4—262no—
307C4⋊C4—262no—
308C4⋊C4—528no—
309C4⋊C4—521no—
310C4⋊C4—521no—
311C22⋊C4—41no—
312C42—41no—
313C42—41no—
314C42—41no—
315C42—521no—
316C42—521no—
317C42D4×D1311yescharacteristic
318C42#612911yescharacteristic
319C42C2×C22⋊D1311yescharacteristic
320C42C2×C22⋊D1311yescharacteristic
321C13#1025111yescharacteristic, complemented, Sylow
322C23#8819111yescharacteristic
323Q8—22no—
324Q8—22no—
325Q8—41no—
326Q8—41no—
327Q8—42no—
328Q8—81no—
329Q8—1041no—
330Q8—1041no—
331Q8—1041no—
332Q8—1041no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—42no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—264no—
343C2×C4—522no—
344C2×C4—522no—
345C2×C4—522no—
346C2×C4—522no—
347C2×C4—522no—
348C2×C4#8819111yescharacteristic
349C2×C4#8819211yescharacteristic
350C2×C4#8819311yescharacteristic
351C2×C4#8819311yescharacteristic
352C2×C4#8819411yescharacteristic
353C2×C4C2×#610611yescharacteristic
354C2×C4#8819611yescharacteristic
355C2×C4#8820311yescharacteristic
356C2×C4#8820411yescharacteristic
357C2×C4#8820711yescharacteristic
358C8—42no—
359C8—522no—
360C8—1041no—
361C22—21no—
362C22—21no—
363C22#1171870711yescharacteristic
364C22#1171870811yescharacteristic
365C22#1171888411yescharacteristic
366C4—21no—
367C4—21no—
368C4—21no—
369C4—42no—
370C4—81no—
371C4—81no—
372C4—81no—
373C4—524no—
374C4—1042no—
375C4#1171870911yescharacteristic
376C4#1171871011yescharacteristic
377C4#1171886612yes—
378C4#1171888811yescharacteristic
379C4#1171889911yescharacteristic
380C2—21no—
381C2—21no—
382C2#1311583711yescharacteristic
383C2#1311586911yescharacteristic
384C2#1311589311yescharacteristic
subgroupG/H
centerC22#11718884
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#3078C2
socleC22×C13#392
prime radicalC23×C13#120
hypercenter#3078D13
hypocenterC13#10251
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3078

Complements

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

NH ≅ G/Ntype
321. C13#10251semidirect

Maximal subgroups

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

subgroupindex
#131259772
#131198212
#131135092
#131133352
#131132312
#131127372
C13×#30782
#1025113