Finite Group Databasebeta

← #15752198

Subgroups — #15752198

Order 3328.

462 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 87 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#13121207C211yesmaximal, characteristic
2#13116398C211yesmaximal, characteristic, complemented
3#13116370C211yesmaximal, characteristic
4#13112660C211yesmaximal, characteristic, complemented
5#13112659C211yesmaximal, characteristic, complemented
6#13112656C211yesmaximal, characteristic
7C13×#2100C211yesmaximal, characteristic, complemented
8C2×#88151—21no—
9C2×#88150—21no—
10C13×#389C2211yescharacteristic
11C13×#384C2211yescharacteristic
12#11718655—21no—
13#11718655—21no—
14C2×#88049—21no—
15C2×#88048—21no—
16#11718600C2211yescharacteristic
17#11718589C2211yescharacteristic
18#11718326—21no—
19#11718317—21no—
20C13×#340—21no—
21C13×#340—21no—
22C13×#336C2211yescharacteristic
23#11718121—21no—
24#11718121—21no—
25#11718116C2211yescharacteristic
26#11718116C2211yescharacteristic
27C22×D52D411yescharacteristic
28C22×C4×D13—21no—
29C22×Dic26—21no—
30C22×C8×C13—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4—21no—
35C2×C13×C4⋊C4D411yescharacteristic
36C2×C13×C4⋊C4D411yescharacteristic
37C2×C42×C13C2311yescharacteristic
38C2×#6103—21no—
39C2×#6103—21no—
40C2×#6103—21no—
41C2×#6103—21no—
42C2×#6103—21no—
43C2×C4⋊Dic13—21no—
44C2×C4⋊Dic13D411yescharacteristic
45C2×C4⋊Dic13D411yescharacteristic
46C2×C4⋊Dic13D411yescharacteristic
47C2×#6101—21no—
48C2×#6101—21no—
49C22×#1055—21no—
50C22×#1055—21no—
51#88151—42no—
52#88151—42no—
53#88150—42no—
54#88150—42no—
55C13×#95—21no—
56#88071—21no—
57#88071—21no—
58#88049—42no—
59#88048—42no—
60#7826—131nomaximal, Sylow
61C23×D13—21no—
62C22×C4×C13—21no—
63C22×C4×C13—21no—
64C22×C4×C13—41no—
65C22×C4×C13C2×D411yescharacteristic
66C22×C4×C13C2×D411yescharacteristic
67C22×C4×C13C2×D411yescharacteristic
68C22×Dic13—21no—
69C22×Dic13—21no—
70C22×Dic13—21no—
71C2×D52—21no—
72C2×D52—41no—
73C2×D52—41no—
74C2×D52Q1612yes—
75C2×C4×D13—42no—
76C2×C4×D13—42no—
77C2×C4×D13—81no—
78C2×Dic26—42no—
79C2×Dic26—42no—
80C2×Dic26—81no—
81C2×C8×C13—41no—
82C2×C8×C13—41no—
83C2×C8×C13—41no—
84C13×C4⋊C4—21no—
85C13×C4⋊C4—41no—
86C13×C4⋊C4—42no—
87C13×C4⋊C4—42no—
88C13×C4⋊C4—41no—
89C13×C4⋊C4—41no—
90C13×C4⋊C4—41no—
91C13×C4⋊C4—41no—
92C13×C4⋊C4SD1612yes—
93C42×C13—41no—
94#6103—42no—
95#6103—42no—
96#6103—41no—
97#6103—41no—
98#6103—41no—
99#6103—41no—
100#6103—81no—
101C4⋊Dic13—21no—
102C4⋊Dic13—42no—
103C4⋊Dic13—41no—
104C4⋊Dic13—41no—
105C4⋊Dic13SD1612yes—
106#6101—42no—
107#6101—41no—
108#6101—41no—
109C2×#1055—22no—
110C2×#1055—41no—
111C2×#1055—41no—
112C2×#1055—41no—
113C2×#1055—41no—
114C2×#1055—41no—
115#2683—131no—
116#2100—131no—
117#2100D1311yescharacteristic, complemented
118#2094—131no—
119#1271—131no—
120#1271—131no—
121#1270—131no—
122C23×C13#12011yescharacteristic
123C22×D13—22no—
124C22×D13—41no—
125C22×D13—41no—
126C22×D13—41no—
127C22×D13—41no—
128C22×D13—41no—
129C22×D13—41no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—21no—
133C2×C4×C13—21no—
134C2×C4×C13—21no—
135C2×C4×C13—21no—
136C2×C4×C13—22no—
137C2×C4×C13—41no—
138C2×C4×C13—41no—
139C2×C4×C13—41no—
140C2×C4×C13—41no—
141C2×C4×C13—41no—
142C2×C4×C13—81no—
143C2×C4×C13—81no—
144C2×C4×C13—81no—
145C2×C4×C13C2×SD1611yescharacteristic
146C2×C4×C13C2×SD1611yescharacteristic
147C2×C4×C13C2×Q1611yescharacteristic
148C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
149C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
150C2×C4×C13#13711yescharacteristic
151C2×Dic13—22no—
152C2×Dic13—41no—
153C2×Dic13—41no—
154C2×Dic13—41no—
155C2×Dic13—41no—
156C2×Dic13—41no—
157C2×Dic13—41no—
158C2×Dic13—41no—
159C2×Dic13—41no—
160D52—42no—
161D52—81no—
162C4×D13—84no—
163Dic26—84no—
164C8×C13—81no—
165#1055—42no—
166#1055—81no—
167C2×C22⋊Q8—261no—
168C2×C22⋊Q8—261no—
169C2×#106—261no—
170C2×#102—261no—
171#396—261no—
172#396—261no—
173#395—261no—
174#390—131no—
175#389—131no—
176#389C2×D1311yescharacteristic
177#386—261no—
178#384C2×D1311yescharacteristic
179#340—21no—
180#340—21no—
181#340—261no—
182#340—261no—
183#336—131no—
184#336—131no—
185#336C2×D1311yescharacteristic
186C22×C13#45011yescharacteristic
187C22×C13#45011yescharacteristic
188C22×C13#45111yescharacteristic
189C22×C13#45311yescharacteristic
190C22×C13#45411yescharacteristic
191C22×C13#45411yescharacteristic
192C22×C13#45811yescharacteristic
193C2×D13—42no—
194C2×D13—42no—
195C2×D13—42no—
196C2×D13—81no—
197C2×D13—81no—
198C2×D13—81no—
199C2×D13—81no—
200C4×C13—21no—
201C4×C13—21no—
202C4×C13—21no—
203C4×C13—21no—
204C4×C13—21no—
205C4×C13—21no—
206C4×C13—42no—
207C4×C13—81no—
208C4×C13—161no—
209Dic13—42no—
210Dic13—81no—
211Dic13—81no—
212C22×Q8—261no—
213C22×D4—131no—
214C23×C4—261no—
215C22×C8—21no—
216C22×C8—261no—
217C22×C8—261no—
218C22⋊Q8—522no—
219C22⋊Q8—522no—
220C22⋊Q8—522no—
221C22⋊Q8—522no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—131no—
227C2×C4⋊C4—131no—
228C2×C4⋊C4—131no—
229C2×C4⋊C4—261no—
230C2×C4⋊C4—261no—
231C2×C4⋊C4—261no—
232C2×C4⋊C4C22⋊D1311yescharacteristic
233C2×C4⋊C4C22⋊D1311yescharacteristic
234C2×C22⋊C4—261no—
235C2×C22⋊C4—261no—
236C2×C22⋊C4—261no—
237C2×C22⋊C4—261no—
238C2×C22⋊C4—261no—
239C2×C42C22×D1311yescharacteristic
240#106—522no—
241#102—522no—
242#95—21no—
243#95—261no—
244#95—261no—
245C2×C13#161411yescharacteristic
246C2×C13#161611yescharacteristic
247C2×C13#161611yescharacteristic
248C2×C13#162911yescharacteristic
249C2×C13#163711yescharacteristic
250C2×C13#163711yescharacteristic
251C2×C13#165711yescharacteristic
252D13—82no—
253C24—261no—
254C2×Q8—522no—
255C2×Q8—522no—
256C2×Q8—1041no—
257C2×D4—132no—
258C2×D4—261no—
259C2×D4—521no—
260C2×D4—521no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—41no—
264C22×C4—261no—
265C22×C4—261no—
266C22×C4—261no—
267C22×C4—522no—
268C22×C4—522no—
269C22×C4—1041no—
270C22×C4D4×D1311yescharacteristic
271C22×C4D4×D1311yescharacteristic
272C22×C4C2×C22⋊D1311yescharacteristic
273C2×C8—41no—
274C2×C8—41no—
275C2×C8—41no—
276C2×C8—262no—
277C2×C8—521no—
278C2×C8—521no—
279C2×C8—521no—
280C2×C8—521no—
281C2×C8—521no—
282C4⋊C4—21no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—42no—
287C4⋊C4—42no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C4⋊C4—132no—
291C4⋊C4—261no—
292C4⋊C4—521no—
293C4⋊C4—521no—
294C4⋊C4—522no—
295C4⋊C4—522no—
296C4⋊C4—521no—
297C4⋊C4—521no—
298C4⋊C4#610612yes—
299C22⋊C4—522no—
300C22⋊C4—522no—
301C22⋊C4—521no—
302C22⋊C4—521no—
303C22⋊C4—521no—
304C22⋊C4—521no—
305C22⋊C4—1041no—
306C42—41no—
307C13#782611yescharacteristic, complemented, Sylow
308C23—262no—
309C23—521no—
310C23—521no—
311C23—521no—
312C23—521no—
313C23—521no—
314C23—521no—
315C23#8819111yescharacteristic
316Q8—1044no—
317D4—522no—
318D4—1041no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—22no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—81no—
332C2×C4—81no—
333C2×C4—81no—
334C2×C4—262no—
335C2×C4—521no—
336C2×C4—521no—
337C2×C4—521no—
338C2×C4—521no—
339C2×C4—521no—
340C2×C4—521no—
341C2×C4—521no—
342C2×C4—521no—
343C2×C4—1044no—
344C2×C4SD16×D1311yescharacteristic
345C2×C4#8816811yescharacteristic
346C2×C4Q16×D1311yescharacteristic
347C2×C4#8817211yescharacteristic
348C2×C4C2×#610611yescharacteristic
349C2×C4#8820311yescharacteristic
350C8—81no—
351C8—522no—
352C8—1041no—
353C22—522no—
354C22—522no—
355C22—522no—
356C22—1041no—
357C22—1041no—
358C22—1041no—
359C22—1041no—
360C22#1171870711yescharacteristic
361C22#1171871411yescharacteristic
362C22#1171872311yescharacteristic
363C22#1171883011yescharacteristic
364C22#1171884711yescharacteristic
365C22#1171885911yescharacteristic
366C22#1171886211yescharacteristic
367C4—21no—
368C4—21no—
369C4—21no—
370C4—21no—
371C4—21no—
372C4—21no—
373C4—42no—
374C4—81no—
375C4—161no—
376C4—522no—
377C4—1041no—
378C4—1041no—
379C2—1042no—
380C2#1311385911yescharacteristic
381C2#1311387111yescharacteristic
382C2#1311387211yescharacteristic
383C2#1311395111yescharacteristic
384C2#1311399811yescharacteristic
385C2#1311399911yescharacteristic
386C2#1311413311yescharacteristic
subgroupG/H
centerC23#88191
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#2100C2
socleC23×C13#120
prime radicalC22×D52D4
hypercenter#2100D13
hypocenterC13#7826
LCSG ▷ C2×C42×C13 ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2100

Complements

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

NH ≅ G/Ntype
2. #13116398C2semidirect
4. #13112660C2semidirect
5. #13112659C2semidirect
7. C13×#2100C2semidirect
117. #2100D13semidirect
307. C13#7826semidirect

Maximal subgroups

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

subgroupindex
#131212072
#131163982
#131163702
#131126602
#131126592
#131126562
C13×#21002
#782613