Finite Group Databasebeta

← #15752240

Subgroups — #15752240

Order 3328.

396 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 79 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#13122816C211yesmaximal, characteristic
2#13116398C211yesmaximal, characteristic, complemented
3#13116375C211yesmaximal, characteristic, complemented
4#13112661C211yesmaximal, characteristic, complemented
5#13112660C211yesmaximal, characteristic, complemented
6#13112657C211yesmaximal, characteristic
7C13×#2094C211yesmaximal, characteristic
8C2×C13×#106—21no—
9C2×C13×#102—21no—
10C13×#390C2211yescharacteristic
11C13×#384C2211yescharacteristic
12#11718883—21no—
13#11718639—21no—
14C2×#88050—21no—
15C2×#88047—21no—
16#11718614—21no—
17#11718612—21no—
18#11718612—21no—
19#11718608—21no—
20#11718590C2211yescharacteristic
21#11718589C2211yescharacteristic
22C13×#336C2211yescharacteristic
23#11718121—21no—
24#11718121—21no—
25#11718116C2211yescharacteristic
26#11718116C2211yescharacteristic
27C22×D4×C13D411yescharacteristic
28C22×Dic26D411yescharacteristic
29C22×C8×C13—21no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4D411yescharacteristic
34C2×C13×C22⋊C4—21no—
35C2×C13×C22⋊C4—21no—
36C2×C42×C13C2311yescharacteristic
37C2×C22⋊Dic13—21no—
38C2×C22⋊Dic13—21no—
39C2×C22⋊Dic13—21no—
40C2×C22⋊Dic13—21no—
41C2×C4⋊Dic13D411yescharacteristic
42C2×C4⋊Dic13D411yescharacteristic
43C2×C4⋊Dic13D411yescharacteristic
44C2×#6101—21no—
45C2×C4×Dic13—21no—
46C22×#1055—21no—
47C22×#1055—21no—
48C13×#106—42no—
49C13×#102—42no—
50#88071—21no—
51#88071—21no—
52#88071—21no—
53#88071—21no—
54#88071—21no—
55#88071—21no—
56#88050—42no—
57#88047—42no—
58#7834—131nomaximal, Sylow
59C24×C13—21no—
60C2×D4×C13—21no—
61C2×D4×C13—21no—
62C2×D4×C13—41no—
63C2×D4×C13—41no—
64C22×C4×C13—21no—
65C22×C4×C13—41no—
66C22×C4×C13C2×D411yescharacteristic
67C22×C4×C13C2×D411yescharacteristic
68C22×C4×C13C2×D411yescharacteristic
69C22×Dic13—21no—
70C22×Dic13—21no—
71C22×Dic13—21no—
72C22×Dic13—21no—
73C2×Dic26—21no—
74C2×Dic26—21no—
75C2×Dic26—41no—
76C2×Dic26—41no—
77C2×C8×C13—22no—
78C2×C8×C13—41no—
79C2×C8×C13—41no—
80C13×C4⋊C4—41no—
81C13×C4⋊C4—41no—
82C13×C4⋊C4—41no—
83C13×C4⋊C4—42no—
84C13×C4⋊C4—41no—
85C13×C4⋊C4—41no—
86C13×C22⋊C4—41no—
87C13×C22⋊C4—41no—
88C13×C22⋊C4—41no—
89C13×C22⋊C4—41no—
90C42×C13—41no—
91C22⋊Dic13—81no—
92C22⋊Dic13—81no—
93C22⋊Dic13—81no—
94C22⋊Dic13—81no—
95C4⋊Dic13—21no—
96C4⋊Dic13—21no—
97C4⋊Dic13—41no—
98C4⋊Dic13—41no—
99#6101—41no—
100#6101—41no—
101C4×Dic13—81no—
102C2×#1055—22no—
103C2×#1055—41no—
104C2×#1055—41no—
105C2×#1055—41no—
106C2×#1055—41no—
107C2×#1055—41no—
108#2808—131no—
109#2100—131no—
110#2095—131no—
111#2094D1311yescharacteristic
112#1272—131no—
113#1271—131no—
114#1270—131no—
115C23×C13—41no—
116C23×C13—41no—
117C23×C13—41no—
118C23×C13—41no—
119C23×C13—41no—
120C23×C13—41no—
121C23×C13—41no—
122C23×C13#12011yescharacteristic
123D4×C13—42no—
124D4×C13—81no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—41no—
132C2×C4×C13—41no—
133C2×C4×C13—41no—
134C2×C4×C13—81no—
135C2×C4×C13—81no—
136C2×C4×C13—81no—
137C2×C4×C13#13511yescharacteristic
138C2×C4×C13#13511yescharacteristic
139C2×C4×C13#13511yescharacteristic
140C2×C4×C13#13711yescharacteristic
141C2×C4×C13#13711yescharacteristic
142C2×C4×C13#13711yescharacteristic
143C2×Dic13—41no—
144C2×Dic13—41no—
145C2×Dic13—41no—
146C2×Dic13—41no—
147C2×Dic13—41no—
148C2×Dic13—41no—
149C2×Dic13—41no—
150C2×Dic13—41no—
151C2×Dic13—41no—
152C2×Dic13—41no—
153C2×Dic13—41no—
154C2×Dic13—41no—
155Dic26—42no—
156Dic26—81no—
157C8×C13—42no—
158#1055—42no—
159#1055—81no—
160C2×#107—261no—
161C2×#106—21no—
162C2×#103—261no—
163C2×#102—21no—
164#397—261no—
165#394—261no—
166#393—261no—
167#391—131no—
168#390C2×D1311yescharacteristic
169#389—131no—
170#388—261no—
171#388—261no—
172#387—261no—
173#384C2×D1311yescharacteristic
174#340—261no—
175#340—261no—
176#336—131no—
177#336—131no—
178#336C2×D1311yescharacteristic
179C22×C13—81no—
180C22×C13—81no—
181C22×C13—81no—
182C22×C13—81no—
183C22×C13—81no—
184C22×C13—81no—
185C22×C13—81no—
186C22×C13#45211yescharacteristic
187C22×C13#45211yescharacteristic
188C22×C13#45211yescharacteristic
189C22×C13#45311yescharacteristic
190C22×C13#45311yescharacteristic
191C22×C13#45411yescharacteristic
192C22×C13#45811yescharacteristic
193C4×C13—21no—
194C4×C13—21no—
195C4×C13—21no—
196C4×C13—21no—
197C4×C13—21no—
198C4×C13—21no—
199C4×C13—81no—
200C4×C13—161no—
201Dic13—81no—
202Dic13—81no—
203Dic13—81no—
204Dic13—81no—
205C22×Q8—131no—
206C22×D4C22⋊D1311yescharacteristic
207C22×C8—21no—
208C22×C8—261no—
209C22×C8—261no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—131no—
214C2×C4⋊C4—131no—
215C2×C4⋊C4—131no—
216C2×C4⋊C4—261no—
217C2×C4⋊C4C22⋊D1311yescharacteristic
218C2×C22⋊C4—21no—
219C2×C22⋊C4—21no—
220C2×C22⋊C4—261no—
221C2×C22⋊C4—261no—
222C2×C22⋊C4—261no—
223C2×C22⋊C4—261no—
224C2×C42—261no—
225C2×C42C22×D1311yescharacteristic
226#107—522no—
227#106—42no—
228#103—522no—
229#102—42no—
230#95—261no—
231#95—261no—
232#95—261no—
233#95—261no—
234#95—261no—
235#95—261no—
236C2×C13—161no—
237C2×C13#161511yescharacteristic
238C2×C13#161811yescharacteristic
239C2×C13#161811yescharacteristic
240C2×C13#163011yescharacteristic
241C2×C13#163411yescharacteristic
242C2×C13#163811yescharacteristic
243C2×C13#165611yescharacteristic
244C24—21no—
245C2×Q8—261no—
246C2×Q8—261no—
247C2×Q8—521no—
248C2×Q8—521no—
249C2×D4—21no—
250C2×D4—21no—
251C2×D4—41no—
252C2×D4—41no—
253C22×C4—21no—
254C22×C4—41no—
255C22×C4—261no—
256C22×C4—261no—
257C22×C4—261no—
258C22×C4—261no—
259C22×C4D4×D1311yescharacteristic
260C22×C4D4×D1311yescharacteristic
261C22×C4C2×C22⋊D1311yescharacteristic
262C2×C8—22no—
263C2×C8—41no—
264C2×C8—41no—
265C2×C8—262no—
266C2×C8—521no—
267C2×C8—521no—
268C2×C8—521no—
269C2×C8—521no—
270C2×C8—521no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—42no—
277C4⋊C4—261no—
278C4⋊C4—261no—
279C4⋊C4—521no—
280C4⋊C4—521no—
281C4⋊C4—521no—
282C4⋊C4—521no—
283C22⋊C4—41no—
284C22⋊C4—41no—
285C22⋊C4—41no—
286C22⋊C4—41no—
287C22⋊C4—1041no—
288C22⋊C4—1041no—
289C22⋊C4—1041no—
290C22⋊C4—1041no—
291C42—41no—
292C42—1041no—
293C13#783411yescharacteristic, complemented, Sylow
294C23—41no—
295C23—41no—
296C23—41no—
297C23—41no—
298C23—41no—
299C23—41no—
300C23—41no—
301C23#8819111yescharacteristic
302Q8—522no—
303Q8—1041no—
304D4—42no—
305D4—81no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—521no—
319C2×C4—521no—
320C2×C4—521no—
321C2×C4—521no—
322C2×C4—521no—
323C2×C4—521no—
324C2×C4—521no—
325C2×C4—521no—
326C2×C4—521no—
327C2×C4—521no—
328C2×C4—521no—
329C2×C4—521no—
330C2×C4#8816911yescharacteristic
331C2×C4#8816911yescharacteristic
332C2×C4#8817011yescharacteristic
333C2×C4#8817011yescharacteristic
334C2×C4#8819611yescharacteristic
335C2×C4#8820411yescharacteristic
336C8—42no—
337C8—522no—
338C8—1041no—
339C22—81no—
340C22—81no—
341C22—81no—
342C22—81no—
343C22—81no—
344C22—81no—
345C22—81no—
346C22#1171870811yescharacteristic
347C22#1171871411yescharacteristic
348C22#1171873811yescharacteristic
349C22#1171883411yescharacteristic
350C22#1171883411yescharacteristic
351C22#1171885911yescharacteristic
352C22#1171886211yescharacteristic
353C4—21no—
354C4—21no—
355C4—21no—
356C4—21no—
357C4—21no—
358C4—21no—
359C4—81no—
360C4—161no—
361C4—1041no—
362C4—1041no—
363C4—1041no—
364C4—1041no—
365C2—161no—
366C2#1311386411yescharacteristic
367C2#1311388111yescharacteristic
368C2#1311388211yescharacteristic
369C2#1311395511yescharacteristic
370C2#1311398011yescharacteristic
371C2#1311400611yescharacteristic
372C2#1311412711yescharacteristic
subgroupG/H
centerC23#88191
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#2094C2
socleC23×C13#120
prime radicalC22×D4×C13D4
hypercenter#2094D13
hypocenterC13#7834
LCSG ▷ C2×C42×C13 ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2094

Complements

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

NH ≅ G/Ntype
2. #13116398C2semidirect
3. #13116375C2semidirect
4. #13112661C2semidirect
5. #13112660C2semidirect
293. C13#7834semidirect

Maximal subgroups

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

subgroupindex
#131228162
#131163982
#131163752
#131126612
#131126602
#131126572
C13×#20942
#783413