Finite Group Databasebeta

← #15759453

Subgroups — #15759453

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#13123582C211yesmaximal, characteristic
3#13113514C211yesmaximal, characteristic
4C2×#11718139C211yesmaximal, characteristic, complemented
5#13112731C211yesmaximal, characteristic, complemented
6#13112687C211yesmaximal, characteristic, complemented
7C13×#1966C211yesmaximal, characteristic, complemented
8C2×C13×C4⋊Q8C2211yescharacteristic
9C2×#88161—21no—
10#11719182C2211yescharacteristic
11C13×#423C2211yescharacteristic
12C2×C13×#101—21no—
13C2×C13×#101—21no—
14C4×C13×M16C2211yescharacteristic
15#11718790—21no—
16#11718749—21no—
17#11718748—22no—
18#11718739—21no—
19#11718628C414yes—
20#11718586C2211yescharacteristic
21C2×C4⋊#1055C2211yescharacteristic
22C2×C4⋊#1055C2211yescharacteristic
23#11718367—22no—
24#11718349—21no—
25C8×D52—21no—
26#11718139—21no—
27#11718139—21no—
28#11718077—21no—
29#11718074—21no—
30C22×Q8×C13—21no—
31C2×#6127—21no—
32C2×C13×M16—21no—
33C2×C13×M16D411yescharacteristic
34C2×C13×M16D411yescharacteristic
35C13×C4⋊Q8—21no—
36C13×C4⋊Q8—21no—
37C13×C4⋊Q8—21no—
38C13×C4⋊Q8—21no—
39C2×C13×C4⋊C4—21no—
40C2×C13×C4⋊C4C2×C412yes—
41C2×C42×C13C2311yescharacteristic
42#88184—21no—
43#88184C2×C412yes—
44C22×#1055—21no—
45C22×#1055—21no—
46#88161—42no—
47#88161—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×#101—42no—
58C13×#101—42no—
59C13×#97—21no—
60C4×C8×C13—21no—
61C22⋊#1055C2×C412yes—
62#88060—22no—
63#88060—22no—
64#88049—24no—
65#88047—24no—
66C4⋊#1055—21no—
67C4⋊#1055—21no—
68C4⋊#1055—21no—
69C4⋊#1055—21no—
70C4⋊#1055D411yescharacteristic
71C4⋊#1055D411yescharacteristic
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—
94C13×M16—21no—
95C13×M16—21no—
96C13×M16—21no—
97C13×M16—41no—
98C13×M16—41no—
99C13×M16D812yes—
100C2×C8×C13—21no—
101C2×C8×C13—21no—
102C2×C8×C13—41no—
103C13×C4⋊C4—22no—
104C13×C4⋊C4—22no—
105C13×C4⋊C4—41no—
106C13×C4⋊C4—41no—
107C42×C13C2×D411yescharacteristic
108C42×C13C2×D411yescharacteristic
109C42×C13C2×D411yescharacteristic
110C42×C13#4111yescharacteristic
111#6103—22no—
112#6103—22no—
113C4⋊Dic13—21no—
114C4⋊Dic13C22⋊C412yes—
115C2×#1055—22no—
116C2×#1055—21no—
117C2×#1055—21no—
118C2×#1055—41no—
119C2×#1055—41no—
120C2×#1055—41no—
121C2×#1055—81no—
122#6094—44no—
123C8×D13—44no—
124#3226—131no—
125#2935—131no—
126#1966D1311yescharacteristic, complemented
127#1547—131no—
128C2×#332—131no—
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—22no—
166C8×C13—41no—
167C8×C13—81no—
168#1055—42no—
169#1055—41no—
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#423C2×D1311yescharacteristic
184C2×C4⋊C8—131no—
185C2×C4⋊C8—131no—
186C2×#101—21no—
187C2×#101—21no—
188#408—261no—
189C4×M16C2×D1311yescharacteristic
190#332—261no—
191#332—261no—
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—21no—
218C2×M16—262no—
219C2×M16C22⋊D1311yescharacteristic
220C2×M16C22⋊D1311yescharacteristic
221C22×C8—262no—
222C22×C8—261no—
223C22×C8—261no—
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—131no—
242C4⋊C8—131no—
243C4⋊C8—261no—
244C4⋊C8—261no—
245C4⋊C8—261no—
246C4⋊C8—261no—
247#102—264no—
248#101—42no—
249#101—42no—
250C22⋊C8—132no—
251C22⋊C8—262no—
252C22⋊C8—262no—
253#97—21no—
254C4×C8—21no—
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×C4#612711yescharacteristic
281C22×C4C2×C22⋊D1311yescharacteristic
282M16—21no—
283M16—21no—
284M16—21no—
285M16—41no—
286M16—41no—
287M16—524no—
288M16#610412yes—
289C2×C8—21no—
290C2×C8—21no—
291C2×C8—41no—
292C2×C8—262no—
293C2×C8—261no—
294C2×C8—261no—
295C2×C8—524no—
296C2×C8—521no—
297C2×C8—521no—
298C2×C8—521no—
299C2×C8—1041no—
300C4⋊C4—22no—
301C4⋊C4—22no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—132no—
305C4⋊C4—261no—
306C22⋊C4—262no—
307C22⋊C4—262no—
308C42D4×D1311yescharacteristic
309C42D4×D1311yescharacteristic
310C42D4×D1311yescharacteristic
311C42#612911yescharacteristic
312C13#927111yescharacteristic, complemented, Sylow
313C23—262no—
314C23C4×C22⋊D1311yescharacteristic
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#8813511yescharacteristic
339C2×C4#8813711yescharacteristic
340C2×C4#8813811yescharacteristic
341C2×C4C2×#610411yescharacteristic
342C2×C4#8818611yescharacteristic
343C2×C4#8819111yescharacteristic
344C2×C4#8819211yescharacteristic
345C2×C4#8820311yescharacteristic
346C2×C4#8820411yescharacteristic
347C8—22no—
348C8—41no—
349C8—81no—
350C8—522no—
351C8—521no—
352C8—521no—
353C8—1041no—
354C22—21no—
355C22—21no—
356C22—522no—
357C22—522no—
358C22—522no—
359C22#1171861711yescharacteristic
360C22C4×#610411yescharacteristic
361C22#1171867511yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—82no—
366C4—522no—
367C4#1171841511yescharacteristic
368C4#1171841611yescharacteristic
369C4#1171869711yescharacteristic
370C4#1171869811yescharacteristic
371C4#1171871811yescharacteristic
372C4#1171873311yescharacteristic
373C2—21no—
374C2—21no—
375C2—1042no—
376C2#1311518711yescharacteristic
377C2#1311534811yescharacteristic
378C2#1311538511yescharacteristic
subgroupG/H
centerC22#11718617
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1966C2
socleC22×C13#386
prime radical#11719182C22
cosocleC2×C42×C13C23
hypercenter#1966D13
hypocenterC13#9271
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1966

Complements

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

NH ≅ G/Ntype
4. C2×#11718139C2semidirect
5. #13112731C2semidirect
6. #13112687C2semidirect
7. C13×#1966C2semidirect
126. #1966D13semidirect
312. C13#9271semidirect

Maximal subgroups

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

subgroupindex
#131259572
#131235822
#131135142
C2×#117181392
#131127312
#131126872
C13×#19662
#927113