Finite Group Databasebeta

← #15763030

Subgroups — #15763030

Order 3328.

440 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
1#13123212C211yesmaximal, characteristic
2#13114690C211yesmaximal, characteristic
3#13114584C211yesmaximal, characteristic
4#13112718C211yesmaximal, characteristic
5#13112718C211yesmaximal, characteristic
6#13112717C211yesmaximal, characteristic
7C13×#1295C211yesmaximal, characteristic
8C2×#88142C411yescharacteristic
9C2×#88142C411yescharacteristic
10C2×C13×#97C2211yescharacteristic
11C2×C13×#97C2211yescharacteristic
12C13×#382C2211yescharacteristic
13C2×#88054—21no—
14#11718638C411yescharacteristic
15#11718638C411yescharacteristic
16#11718597C2211yescharacteristic
17C42×Dic13C2211yescharacteristic
18C2×#88043C2211yescharacteristic
19C2×#88043C2211yescharacteristic
20#11718307—21no—
21#11718307—21no—
22#11718307—21no—
23#11718307—21no—
24#11718142—21no—
25#11718142—21no—
26#11718142—21no—
27C22×Dic26—21no—
28C22×Dic26—21no—
29C22×C8×C13—21no—
30C22×C8×C13—21no—
31C2×C13×C4⋊C4C2×C411yescharacteristic
32C2×C13×C4⋊C4C2×C411yescharacteristic
33C2×C42×C13C2311yescharacteristic
34C2×C4⋊Dic13C2×C411yescharacteristic
35C2×C4⋊Dic13C2×C411yescharacteristic
36C2×#6101—21no—
37C2×#6101—21no—
38C2×C4×Dic13C2×C411yescharacteristic
39C2×C4×Dic13C2×C411yescharacteristic
40C2×C4×Dic13D411yescharacteristic
41C2×C4×Dic13D411yescharacteristic
42C2×C4×Dic13D411yescharacteristic
43C2×C4×Dic13D411yescharacteristic
44C22×#1055—21no—
45C22×#1055—21no—
46#88142—42no—
47#88142—42no—
48C13×#97—21no—
49C13×#97—21no—
50C13×#97—21no—
51C13×#97Q812yescomplemented
52C13×#95—21no—
53C13×#95—21no—
54#88071—21no—
55#88071—21no—
56#88071—21no—
57#88071—21no—
58#88071—21no—
59#88071—21no—
60#88054—24no—
61#88043—21no—
62#88043—21no—
63#88043—21no—
64#88043Q812yescomplemented
65#9895—131nomaximal, Sylow
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13C22×C411yescharacteristic
69C22×C4×C13C2×D411yescharacteristic
70C22×C4×C13C2×D411yescharacteristic
71C22×Dic13—21no—
72C22×Dic13—21no—
73C22×Dic13C22⋊C411yescharacteristic
74C22×Dic13C22⋊C411yescharacteristic
75C22×Dic13C22⋊C411yescharacteristic
76C22×Dic13C22⋊C411yescharacteristic
77C2×Dic26—42no—
78C2×Dic26—42no—
79C2×Dic26—42no—
80C2×Dic26—42no—
81C2×Dic26—42no—
82C2×Dic26—42no—
83C2×C8×C13—22no—
84C2×C8×C13—22no—
85C2×C8×C13—41no—
86C2×C8×C13—41no—
87C2×C8×C13—41no—
88C2×C8×C13—41no—
89C13×C4⋊C4—41no—
90C13×C4⋊C4—41no—
91C42×C13C2×Q811yescharacteristic
92C42×C13C2×Q811yescharacteristic
93C42×C13#4111yescharacteristic
94C42×C13#4111yescharacteristic
95C4⋊Dic13—41no—
96C4⋊Dic13—41no—
97#6101—42no—
98#6101—42no—
99C4×Dic13—22no—
100C4×Dic13—22no—
101C4×Dic13—22no—
102C4×Dic13—41no—
103C4×Dic13—41no—
104C4×Dic13—41no—
105C2×#1055—22no—
106C2×#1055—22no—
107C2×#1055—41no—
108C2×#1055—41no—
109C2×#1055—41no—
110C2×#1055—41no—
111#2862—131no—
112#1767—131no—
113#1745—131no—
114#1295—131no—
115#1295—131no—
116#1295—131no—
117#1295D1311yescharacteristic
118C23×C13C2×C22⋊C411yescharacteristic
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—41no—
126C2×C4×C13—41no—
127C2×C4×C13—41no—
128C2×C4×C13—41no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13C4×Q811yescharacteristic
132C2×C4×C13C4×Q811yescharacteristic
133C2×C4×C13C22⋊Q811yescharacteristic
134C2×C4×C13C22⋊Q811yescharacteristic
135C2×C4×C13#12411yescharacteristic
136C2×C4×C13C4⋊Q811yescharacteristic
137C2×Dic13—21no—
138C2×Dic13—21no—
139C2×Dic13—21no—
140C2×Dic13—21no—
141C2×Dic13—21no—
142C2×Dic13—21no—
143C2×Dic13—21no—
144C2×Dic13—21no—
145C2×Dic13—21no—
146C2×Dic13—41no—
147C2×Dic13—41no—
148C2×Dic13—41no—
149C2×Dic13—41no—
150C2×Dic13—41no—
151C2×Dic13—41no—
152C2×Dic13#10012yes—
153C2×Dic13#10112yes—
154C2×Dic13#10412yes—
155Dic26—84no—
156Dic26—84no—
157C8×C13—42no—
158C8×C13—42no—
159#1055—42no—
160#1055—42no—
161C2×C4⋊Q8—131no—
162C2×C4⋊Q8—131no—
163C2×C4⋊C8—261no—
164C2×#97—131no—
165C2×#97—131no—
166C2×#97C2×D1311yescharacteristic
167C2×#97C2×D1311yescharacteristic
168#391—261no—
169#391—261no—
170#391—261no—
171#391—261no—
172#382—131no—
173#382—131no—
174#382—131no—
175#382C2×D1311yescharacteristic
176C43—131no—
177#336—261no—
178#336—261no—
179#336—261no—
180C22×C13#39111yescharacteristic
181C22×C13C2×#10011yescharacteristic
182C22×C13C2×#10111yescharacteristic
183C22×C13C2×#10411yescharacteristic
184C22×C13#42111yescharacteristic
185C22×C13#42111yescharacteristic
186C22×C13#42111yescharacteristic
187C4×C13—21no—
188C4×C13—21no—
189C4×C13—21no—
190C4×C13—21no—
191C4×C13—21no—
192C4×C13—21no—
193C4×C13—81no—
194C4×C13—81no—
195Dic13—22no—
196Dic13—22no—
197Dic13—22no—
198Dic13—41no—
199Dic13—81no—
200Dic13—81no—
201C22×Q8—261no—
202C22×Q8—261no—
203C22×C8—21no—
204C22×C8—21no—
205C22×C8—261no—
206C22×C8—261no—
207C4⋊Q8—522no—
208C4⋊Q8—522no—
209C2×C4⋊C4—131no—
210C2×C4⋊C4—131no—
211C2×C4⋊C4—261no—
212C2×C4⋊C4—261no—
213C2×C4⋊C4C4×D1311yescharacteristic
214C2×C4⋊C4C4×D1311yescharacteristic
215C2×C42—131no—
216C2×C42—131no—
217C2×C42—131no—
218C2×C42—131no—
219C2×C42—131no—
220C2×C42—131no—
221C2×C42C22×D1311yescharacteristic
222C4⋊C8—264no—
223#97—21no—
224#97—21no—
225#97—21no—
226#97—132no—
227#97—261no—
228#97—261no—
229#97—261no—
230#97Dic2612yescomplemented
231#95—21no—
232#95—21no—
233#95—261no—
234#95—261no—
235#95—261no—
236#95—261no—
237#95—261no—
238#95—261no—
239C2×C13#152711yescharacteristic
240C2×C13#153111yescharacteristic
241C2×C13#153311yescharacteristic
242C2×C13#153711yescharacteristic
243C2×C13#198611yescharacteristic
244C2×C13#199511yescharacteristic
245C2×C13#199711yescharacteristic
246C2×Q8—522no—
247C2×Q8—522no—
248C2×Q8—522no—
249C2×Q8—522no—
250C2×Q8—522no—
251C2×Q8—522no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—131no—
255C22×C4—131no—
256C22×C4—131no—
257C22×C4—131no—
258C22×C4—261no—
259C22×C4—261no—
260C22×C4C2×C4×D1311yescharacteristic
261C22×C4D4×D1311yescharacteristic
262C22×C4D4×D1311yescharacteristic
263C2×C8—22no—
264C2×C8—22no—
265C2×C8—41no—
266C2×C8—41no—
267C2×C8—41no—
268C2×C8—41no—
269C2×C8—262no—
270C2×C8—262no—
271C2×C8—521no—
272C2×C8—521no—
273C2×C8—521no—
274C2×C8—521no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—521no—
278C4⋊C4—521no—
279C4⋊C4—522no—
280C4⋊C4—522no—
281C42—262no—
282C42—262no—
283C42—262no—
284C42—521no—
285C42—521no—
286C42—521no—
287C42C2×Dic2611yescharacteristic
288C42#612711yescharacteristic
289C42#612911yescharacteristic
290C42Q8×D1311yescharacteristic
291C13#989511yescharacteristic, complemented, Sylow
292C23C22⋊C4×D1311yescharacteristic
293Q8—1044no—
294Q8—1044no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—132no—
308C2×C4—132no—
309C2×C4—132no—
310C2×C4—261no—
311C2×C4—261no—
312C2×C4—261no—
313C2×C4—261no—
314C2×C4—261no—
315C2×C4—261no—
316C2×C4—261no—
317C2×C4—261no—
318C2×C4—261no—
319C2×C4—521no—
320C2×C4—521no—
321C2×C4—521no—
322C2×C4—521no—
323C2×C4—521no—
324C2×C4—521no—
325C2×C4C4×Dic2611yescharacteristic
326C2×C4#8813211yescharacteristic
327C2×C4#8813911yescharacteristic
328C2×C4#8814111yescharacteristic
329C2×C4#8814211yescharacteristic
330C2×C4#8815011yescharacteristic
331C8—42no—
332C8—42no—
333C8—522no—
334C8—522no—
335C22#1171830711yescharacteristic
336C22D13×#10011yescharacteristic
337C22D13×#10111yescharacteristic
338C22D13×#10411yescharacteristic
339C22#1171848211yescharacteristic
340C22#1171848211yescharacteristic
341C22#1171848211yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—81no—
349C4—81no—
350C4—262no—
351C4—262no—
352C4—262no—
353C4—521no—
354C4—1041no—
355C4—1041no—
356C2#1311343211yescharacteristic
357C2#1311344911yescharacteristic
358C2#1311345811yescharacteristic
359C2#1311347211yescharacteristic
360C2#1311577811yescharacteristic
361C2#1311581511yescharacteristic
362C2#1311582311yescharacteristic
subgroupG/H
centerC23C22⋊C4×D13
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1295C2
socle, prime radicalC23×C13C2×C22⋊C4
cosocleC2×C42×C13C23
hypercenter#1295D13
hypocenterC13#9895
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
51. C13×#97Q8semidirect
64. #88043Q8semidirect
230. #97Dic26semidirect
291. C13#9895semidirect

Maximal subgroups

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

subgroupindex
#131232122
#131146902
#131145842
#131127182
#131127172
C13×#12952
#989513