Finite Group Databasebeta

← #15759447

Subgroups — #15759447

Order 3328.

496 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125957C211yesmaximal, characteristic
2#13123579C211yesmaximal, characteristic
3#13115681C211yesmaximal, characteristic, complemented
4#13113511C211yesmaximal, characteristic
5#13112733C211yesmaximal, characteristic, complemented
6#13112686C211yesmaximal, characteristic, complemented
7C2×C13×#332C211yesmaximal, characteristic, complemented
8C2×C13×C4⋊Q8C2211yescharacteristic
9C2×#88155—21no—
10#11719182C2211yescharacteristic
11C2×C13×C4⋊C8C2211yescharacteristic
12C2×C13×C4⋊C8C2211yescharacteristic
13C2×#88076—21no—
14C2×#88076—21no—
15#11718771—21no—
16#11718749—21no—
17#11718748—22no—
18#11718739—21no—
19#11718628C414yes—
20#11718586C2211yescharacteristic
21#11718585C2211yescharacteristic
22C4×#6099C2211yescharacteristic
23#11718499—21no—
24#11718497—22no—
25#11718495—21no—
26C13×#332—21no—
27C13×#332—21no—
28#11718078—21no—
29#11718077—21no—
30C22×Q8×C13—21no—
31C2×#6127—21no—
32C22×C8×C13—21no—
33C22×C8×C13—21no—
34C13×C4⋊Q8—21no—
35C13×C4⋊Q8—21no—
36C13×C4⋊Q8—21no—
37C13×C4⋊Q8—21no—
38C2×C13×C4⋊C4—21no—
39C2×C13×C4⋊C4C2×C412yes—
40C2×C42×C13C2311yescharacteristic
41#88184—21no—
42#88184C2×C412yes—
43C2×#6099—21no—
44C2×#6099D411yescharacteristic
45C2×#6099D411yescharacteristic
46#88155—42no—
47#88155—42no—
48C2×#6094—22no—
49C2×C8×D13—22no—
50#88129—21no—
51#88128D411yescharacteristic
52C4×D52—21no—
53C4×D52D412yes—
54#88123D411yescharacteristic
55C13×C4⋊C8—21no—
56C13×C4⋊C8—21no—
57C13×C4⋊C8—21no—
58C13×C4⋊C8D411yescharacteristic
59C13×C4⋊C8D411yescharacteristic
60#88076—42no—
61#88076—42no—
62C22⋊#1055C2×C412yes—
63#88060—22no—
64#88060—22no—
65#88049—24no—
66#88047—24no—
67C4⋊#1055—21no—
68C4⋊#1055—21no—
69C4⋊#1055—21no—
70#88043—21no—
71C4×#1055—21no—
72C4×#1055—21no—
73#9271—131nomaximal, Sylow
74C2×Q8×C13—41no—
75C2×Q8×C13—41no—
76C2×Q8×C13—41no—
77C2×Q8×C13—41no—
78C2×Q8×C13—41no—
79C2×Q8×C13—41no—
80C22×C4×C13—22no—
81C22×C4×C13C22×C411yescharacteristic
82C22×C4×C13C2×D411yescharacteristic
83C22×C4×C13#4111yescharacteristic
84C2×C22⋊D13—22no—
85#6127—41no—
86#6127—41no—
87#6127—41no—
88#6127—41no—
89C2×D52—21no—
90C2×D52—21no—
91C2×D52C22⋊C412yes—
92C2×C4×D13—22no—
93C2×Dic26—21no—
94C2×C8×C13—21no—
95C2×C8×C13—21no—
96C2×C8×C13—41no—
97C2×C8×C13—41no—
98C2×C8×C13—41no—
99C2×C8×C13—81no—
100C13×C4⋊C4—22no—
101C13×C4⋊C4—22no—
102C13×C4⋊C4—41no—
103C13×C4⋊C4—41no—
104C42×C13C2×D411yescharacteristic
105C42×C13C2×D411yescharacteristic
106C42×C13C2×D411yescharacteristic
107C42×C13#4111yescharacteristic
108#6103—22no—
109#6103—22no—
110C4⋊Dic13—21no—
111C4⋊Dic13C22⋊C412yes—
112#6099—21no—
113#6099—21no—
114#6099—21no—
115#6099—41no—
116#6099—41no—
117#6099D812yes—
118C2×#1055—21no—
119C2×#1055—22no—
120C2×#1055—21no—
121C2×#1055—41no—
122#6094—44no—
123C8×D13—44no—
124#3226—131no—
125#2935—131no—
126#1966—131no—
127#1547—131no—
128C2×#332D1311yescharacteristic, complemented
129#1301—131no—
130#1283—131no—
131C23×C13C4×D411yescharacteristic
132C22×D13—22no—
133Q8×C13—81no—
134Q8×C13—81no—
135Q8×C13—81no—
136Q8×C13—81no—
137C2×C4×C13—21no—
138C2×C4×C13—21no—
139C2×C4×C13—41no—
140C2×C4×C13—42no—
141C2×C4×C13—42no—
142C2×C4×C13—42no—
143C2×C4×C13C2×C22⋊C411yescharacteristic
144C2×C4×C13C4×D411yescharacteristic
145C2×C4×C13#12011yescharacteristic
146C2×C4×C13#12111yescharacteristic
147C2×C4×C13#12111yescharacteristic
148C2×C4×C13#12311yescharacteristic
149C2×C4×C13C2×D811yescharacteristic
150C2×C4×C13#13511yescharacteristic
151C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
152C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
153C22⋊D13—42no—
154C22⋊D13—42no—
155C2×Dic13—22no—
156D52—42no—
157D52—41no—
158D52—41no—
159D52—41no—
160D52—41no—
161C4×D13—42no—
162C4×D13—42no—
163Dic26—41no—
164Dic26—41no—
165C8×C13—41no—
166C8×C13—41no—
167C8×C13—81no—
168#1055—22no—
169#1055—42no—
170#1055—41no—
171#1055—81no—
172C2×#131—261no—
173#532—131no—
174C2×C4⋊Q8C2×D1311yescharacteristic
175#500—261no—
176#486—261no—
177#480—134no—
178#474—262no—
179#436—261no—
180#435—262no—
181C8×D4—261no—
182#431—131no—
183#423—131no—
184C2×C4⋊C8C2×D1311yescharacteristic
185C2×C4⋊C8C2×D1311yescharacteristic
186C2×#101—261no—
187C2×#101—261no—
188#408—261no—
189C4×M16—131no—
190#332—21no—
191#332—21no—
192#332—261no—
193#331—261no—
194C22×C13—21no—
195C22×C13—21no—
196C22×C13#38611yescharacteristic
197C22×C13C4×D811yescharacteristic
198C22×C13#44211yescharacteristic
199C2×D13—42no—
200C2×D13—42no—
201C2×D13—42no—
202C4×C13—21no—
203C4×C13—21no—
204C4×C13—21no—
205C4×C13—82no—
206C4×C13#44711yescharacteristic
207C4×C13#44911yescharacteristic
208C4×C13#45911yescharacteristic
209C4×C13#46311yescharacteristic
210C4×C13#47111yescharacteristic
211C4×C13#47311yescharacteristic
212Dic13—42no—
213C2×#41—261no—
214C22×Q8—21no—
215#131—522no—
216#131—522no—
217C2×M16—131no—
218C2×M16—131no—
219C2×M16—262no—
220C2×M16—261no—
221C22×C8—21no—
222C22×C8—21no—
223C22×C8—262no—
224C4⋊Q8—21no—
225C4⋊Q8—21no—
226C4⋊Q8—21no—
227C4⋊Q8—21no—
228C4⋊Q8—131no—
229#127—131no—
230#124—261no—
231#121—132no—
232#121—261no—
233C4×D4—132no—
234C4×D4—261no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4C4×D1312yes—
237C2×C42C22×D1311yescharacteristic
238#107—264no—
239C4⋊C8—21no—
240C4⋊C8—21no—
241C4⋊C8—21no—
242C4⋊C8—261no—
243C4⋊C8—261no—
244C4⋊C8—261no—
245C4⋊C8C22⋊D1311yescharacteristic
246C4⋊C8C22⋊D1311yescharacteristic
247#102—264no—
248#101—522no—
249#101—522no—
250C22⋊C8—132no—
251C22⋊C8—262no—
252C22⋊C8—262no—
253#97—261no—
254C4×C8—261no—
255C4×C8—261no—
256C2×C13—21no—
257C2×C13—21no—
258C2×C13#187911yescharacteristic
259C2×C13#190811yescharacteristic
260C2×C13#191511yescharacteristic
261D13—82no—
262#41—521no—
263#41—521no—
264#41—521no—
265#41—521no—
266C2×Q8—41no—
267C2×Q8—41no—
268C2×Q8—41no—
269C2×Q8—41no—
270C2×Q8—41no—
271C2×Q8—41no—
272C2×Q8—261no—
273C2×D4—132no—
274C2×D4—262no—
275C2×D4—261no—
276C2×D4—261no—
277C22×C4—22no—
278C22×C4—262no—
279C22×C4C2×C4×D1311yescharacteristic
280C22×C4D4×D1311yescharacteristic
281C22×C4#612911yescharacteristic
282M16—132no—
283M16—261no—
284M16—261no—
285M16—261no—
286M16—524no—
287M16—521no—
288M16—521no—
289C2×C8—21no—
290C2×C8—21no—
291C2×C8—41no—
292C2×C8—41no—
293C2×C8—41no—
294C2×C8—81no—
295C2×C8—261no—
296C2×C8—262no—
297C2×C8—261no—
298C2×C8—524no—
299C2×C8—521no—
300C4⋊C4—22no—
301C4⋊C4—22no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—132no—
305C4⋊C4—261no—
306C22⋊C4—262no—
307C22⋊C4—262no—
308C42#612711yescharacteristic
309C42D4×D1311yescharacteristic
310C42D4×D1311yescharacteristic
311C42C2×C22⋊D1311yescharacteristic
312C13#927111yescharacteristic, complemented, Sylow
313C23—262no—
314C23#8813511yescharacteristic
315Q8—81no—
316Q8—81no—
317Q8—81no—
318Q8—81no—
319Q8—521no—
320Q8—521no—
321D4—522no—
322D4—522no—
323D4—522no—
324D4—521no—
325D4—521no—
326D4—521no—
327D4—521no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—41no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—262no—
335C2×C4—522no—
336C2×C4—522no—
337C2×C4C22⋊C4×D1311yescharacteristic
338C2×C4#8813711yescharacteristic
339C2×C4#8813811yescharacteristic
340C2×C4D8×D1311yescharacteristic
341C2×C4#8816511yescharacteristic
342C2×C4#8816811yescharacteristic
343C2×C4#8817011yescharacteristic
344C2×C4C4×C22⋊D1311yescharacteristic
345C2×C4#8819111yescharacteristic
346C2×C4#8819211yescharacteristic
347C8—41no—
348C8—41no—
349C8—81no—
350C8—262no—
351C8—522no—
352C8—521no—
353C8—1041no—
354C22—21no—
355C22—21no—
356C22—522no—
357C22—522no—
358C22—522no—
359C22#1171841711yescharacteristic
360C22#1171844611yescharacteristic
361C22#1171861711yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—82no—
366C4—522no—
367C4#1171844711yescharacteristic
368C4#1171844811yescharacteristic
369C4#1171881711yescharacteristic
370C4#1171883311yescharacteristic
371C4#1171883811yescharacteristic
372C4#1171885311yescharacteristic
373C2—21no—
374C2—21no—
375C2—1042no—
376C2#1311518111yescharacteristic
377C2#1311535411yescharacteristic
378C2#1311538511yescharacteristic
subgroupG/H
centerC22#11718617
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC2×C13×#332C2
socleC22×C13#386
prime radical#11719182C22
cosocleC2×C42×C13C23
hypercenterC2×#332D13
hypocenterC13#9271
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
3. #13115681C2semidirect
5. #13112733C2semidirect
6. #13112686C2semidirect
7. C2×C13×#332C2semidirect
128. C2×#332D13semidirect
312. C13#9271semidirect

Maximal subgroups

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

subgroupindex
#131259572
#131235792
#131156812
#131135112
#131127332
#131126862
C2×C13×#3322
#927113