Finite Group Databasebeta

← #15765492

Subgroups — #15765492

Order 3328.

594 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718745C211yesmaximal, characteristic
2C2×#11718744C211yesmaximal, characteristic
3#13115630C211yesmaximal, characteristic
4C2×#11718138C211yesmaximal, characteristic, complemented
5C2×#11718139C211yesmaximal, characteristic, complemented
6#13112671C211yesmaximal, characteristic, complemented
7C2×C13×#498C211yesmaximal, characteristic, complemented
8C2×C13×C4⋊Q8C2211yescharacteristic
9C2×C13×C4⋊Q8C2211yescharacteristic
10C22×#6106—21no—
11C2×C4×D52C2211yescharacteristic
12C13×#498—22no—
13C13×#498—22no—
14C2×C13×#106—22no—
15C2×C4×C8×C13C2211yescharacteristic
16C2×#88075—21no—
17C2×#88060—22no—
18#11718745—22no—
19#11718745—22no—
20#11718744—22no—
21#11718744—22no—
22C2×#88049—21no—
23C2×#88048—21no—
24C2×C4⋊#1055C2211yescharacteristic
25C2×C4⋊#1055C2211yescharacteristic
26C2×C4⋊#1055C2211yescharacteristic
27#11718139—22no—
28#11718138—22no—
29C22×Q8×C13—21no—
30C22×Q8×C13—21no—
31C22×D52D411yescharacteristic
32C22×C4×D13—21no—
33C22×C8×C13D412yes—
34C13×C4⋊Q8—21no—
35C13×C4⋊Q8—21no—
36C13×C4⋊Q8—21no—
37C13×C4⋊Q8—21no—
38C13×C4⋊Q8—21no—
39C13×C4⋊Q8—21no—
40C13×C4⋊Q8D412yes—
41C13×C4⋊Q8D412yes—
42C2×C13×C4⋊C4—21no—
43C2×C13×C4⋊C4—21no—
44C2×C13×C4⋊C4—21no—
45C2×C13×C4⋊C4—21no—
46C2×C42×C13C2311yescharacteristic
47C2×#6106—24no—
48C2×#6106—42no—
49C2×#6106—42no—
50C2×#6103—21no—
51C2×C4⋊Dic13D411yescharacteristic
52C22×#1055—21no—
53C22×#1055—21no—
54C22×#1055—21no—
55C4×D52—21no—
56C4×D52—21no—
57C4×D52—21no—
58C4×D52—21no—
59C13×#106—28no—
60C4×C8×C13—21no—
61C4×C8×C13—21no—
62#88075—24no—
63#88060—44no—
64#88049—24no—
65#88048—24no—
66C4⋊#1055—21no—
67C4⋊#1055—21no—
68C4⋊#1055—21no—
69C4⋊#1055—21no—
70C4⋊#1055D412yes—
71C4⋊#1055D412yes—
72#10271—131nomaximal, Sylow
73C23×D13—21no—
74C2×Q8×C13—22no—
75C2×Q8×C13—22no—
76C2×Q8×C13—41no—
77C2×Q8×C13—41no—
78C2×Q8×C13—41no—
79C2×Q8×C13—41no—
80C2×Q8×C13—41no—
81C2×Q8×C13—41no—
82C2×Q8×C13—82no—
83C22×C4×C13—41no—
84C22×C4×C13—41no—
85C22×C4×C13C2×D411yescharacteristic
86C22×C4×C13C2×D411yescharacteristic
87C22×C4×C13#4111yescharacteristic
88C22×Dic13—21no—
89C2×D52—21no—
90C2×D52—21no—
91C2×D52—21no—
92C2×D52—21no—
93C2×D52—21no—
94C2×D52SD1612yes—
95C2×C4×D13—41no—
96C2×C4×D13—41no—
97C2×C4×D13—42no—
98C2×C4×D13—42no—
99C2×C8×C13—22no—
100C2×C8×C13—22no—
101C2×C8×C13SD1614yescomplemented
102C13×C4⋊C4—22no—
103C13×C4⋊C4—22no—
104C13×C4⋊C4—22no—
105C13×C4⋊C4—22no—
106C13×C4⋊C4—41no—
107C13×C4⋊C4—41no—
108C13×C4⋊C4—41no—
109C13×C4⋊C4—41no—
110C42×C13C2×D411yescharacteristic
111C42×C13C2×D411yescharacteristic
112C42×C13C2×D411yescharacteristic
113C42×C13C2×D411yescharacteristic
114#6106—48no—
115#6103—41no—
116#6103—41no—
117C4⋊Dic13—21no—
118C4⋊Dic13—21no—
119C2×#1055—22no—
120C2×#1055—22no—
121C2×#1055—41no—
122C2×#1055—41no—
123C2×#1055—41no—
124C2×#1055—41no—
125C2×#1055—41no—
126C2×#1055—42no—
127C2×#498D1311yescharacteristic, complemented
128C2×#476—131no—
129C2×#461—131no—
130#1954—131no—
131C2×#333—131no—
132C2×#332—131no—
133#1277—131no—
134C23×C13#12111yescharacteristic
135C22×D13—22no—
136C22×D13—41no—
137C22×D13—42no—
138C22×D13—41no—
139C22×D13—42no—
140Q8×C13—42no—
141Q8×C13—42no—
142Q8×C13—82no—
143Q8×C13—82no—
144Q8×C13—81no—
145Q8×C13—81no—
146C2×C4×C13—22no—
147C2×C4×C13—42no—
148C2×C4×C13—42no—
149C2×C4×C13—81no—
150C2×C4×C13—81no—
151C2×C4×C13—82no—
152C2×C4×C13#12011yescharacteristic
153C2×C4×C13#12011yescharacteristic
154C2×C4×C13#12011yescharacteristic
155C2×C4×C13#12111yescharacteristic
156C2×C4×C13#12111yescharacteristic
157C2×C4×C13#12711yescharacteristic
158C2×C4×C13C2×SD1611yescharacteristic
159C2×C4×C13C2×SD1612yes—
160C2×C4×C13#13511yescharacteristic
161C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
162C2×C4×C13#13711yescharacteristic
163C2×C4×C13#13712yes—
164C2×Dic13—41no—
165C2×Dic13—42no—
166D52—22no—
167D52—22no—
168D52—41no—
169D52—41no—
170C4×D13—82no—
171C4×D13—81no—
172C4×D13—81no—
173C8×C13—24no—
174#1055—42no—
175#1055—42no—
176#1055—81no—
177C22×SD16—261no—
178C2×C4⋊Q8C2×D1311yescharacteristic
179C2×C4⋊Q8C2×D1311yescharacteristic
180C2×C4×D4—131no—
181#498—22no—
182#498—22no—
183#476—262no—
184#476—262no—
185#461—262no—
186#461—262no—
187C2×#106—22no—
188C2×#106—261no—
189C2×C4⋊C8—131no—
190C2×C4⋊C8—131no—
191C2×C4⋊C8—131no—
192C2×#103—261no—
193C2×#102—261no—
194C2×C22⋊C8—262no—
195C2×C4×C8C2×D1311yescharacteristic
196#333—262no—
197#332—262no—
198C22×C13#39211yescharacteristic
199C22×C13#46112yes—
200C22×C13#46511yescharacteristic
201C22×C13#46811yescharacteristic
202C22×C13#47112yes—
203C2×D13—44no—
204C2×D13—42no—
205C2×D13—82no—
206C2×D13—81no—
207C2×D13—81no—
208C4×C13—21no—
209C4×C13—21no—
210C4×C13—82no—
211C4×C13—82no—
212C4×C13#44811yescharacteristic
213C4×C13#44812yes—
214C4×C13#44911yescharacteristic
215C4×C13#45011yescharacteristic
216C4×C13#45211yescharacteristic
217C4×C13#49211yescharacteristic
218C4×C13#49711yescharacteristic
219Dic13—81no—
220C22×Q8—21no—
221C22×Q8—21no—
222C22×D4—131no—
223C23×C4—261no—
224C2×SD16—264no—
225C2×SD16—522no—
226C2×SD16—522no—
227C22×C8—261no—
228C22×C8—261no—
229C22×C8—261no—
230C22×C8C22⋊D1312yes—
231C4⋊Q8—21no—
232C4⋊Q8—21no—
233C4⋊Q8—21no—
234C4⋊Q8—21no—
235C4⋊Q8—21no—
236C4⋊Q8—21no—
237C4⋊Q8C22⋊D1312yes—
238C4⋊Q8C22⋊D1312yes—
239C4×D4—261no—
240C4×D4—261no—
241C4×D4—261no—
242C4×D4—261no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—131no—
248C2×C22⋊C4—261no—
249C2×C42C22×D1311yescharacteristic
250#106—28no—
251#106—264no—
252C4⋊C8—132no—
253C4⋊C8—132no—
254C4⋊C8—261no—
255C4⋊C8—261no—
256C4⋊C8—261no—
257C4⋊C8—261no—
258#103—264no—
259#102—264no—
260C22⋊C8—524no—
261C4×C8—21no—
262C4×C8—21no—
263C2×C13#167112yes—
264C2×C13#169112yes—
265C2×C13#200011yescharacteristic
266C2×C13#201311yescharacteristic
267C2×C13#201911yescharacteristic
268D13—82no—
269C24—261no—
270C2×Q8—22no—
271C2×Q8—22no—
272C2×Q8—41no—
273C2×Q8—41no—
274C2×Q8—41no—
275C2×Q8—41no—
276C2×Q8—41no—
277C2×Q8—41no—
278C2×Q8—82no—
279C2×D4—132no—
280C2×D4—261no—
281C2×D4—261no—
282C2×D4—261no—
283C2×D4—261no—
284C2×D4—261no—
285C22×C4—41no—
286C22×C4—41no—
287C22×C4—261no—
288C22×C4—521no—
289C22×C4—522no—
290C22×C4—522no—
291C22×C4—521no—
292C22×C4D4×D1311yescharacteristic
293C22×C4#612911yescharacteristic
294C22×C4C2×C22⋊D1311yescharacteristic
295SD16—528no—
296C2×C8—22no—
297C2×C8—22no—
298C2×C8—262no—
299C2×C8—262no—
300C2×C8—521no—
301C2×C8—521no—
302C2×C8—521no—
303C2×C8—521no—
304C2×C8—521no—
305C2×C8—522no—
306C2×C8#610614yescomplemented
307C4⋊C4—22no—
308C4⋊C4—22no—
309C4⋊C4—22no—
310C4⋊C4—22no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4—41no—
314C4⋊C4—41no—
315C4⋊C4—261no—
316C4⋊C4—261no—
317C22⋊C4—521no—
318C22⋊C4—521no—
319C42D4×D1311yescharacteristic
320C42D4×D1311yescharacteristic
321C42C2×C22⋊D1311yescharacteristic
322C42C2×C22⋊D1311yescharacteristic
323C13#1027111yescharacteristic, complemented, Sylow
324C23—262no—
325C23—522no—
326C23—521no—
327C23—522no—
328C23—521no—
329C23#8819211yescharacteristic
330Q8—42no—
331Q8—42no—
332Q8—82no—
333Q8—82no—
334Q8—81no—
335Q8—81no—
336D4—262no—
337D4—262no—
338D4—521no—
339D4—521no—
340C2×C4—22no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—81no—
344C2×C4—81no—
345C2×C4—82no—
346C2×C4—522no—
347C2×C4—521no—
348C2×C4—1041no—
349C2×C4—1041no—
350C2×C4—1042no—
351C2×C4SD16×D1311yescharacteristic
352C2×C4#8816811yescharacteristic
353C2×C4#8816911yescharacteristic
354C2×C4#8817011yescharacteristic
355C2×C4#8819111yescharacteristic
356C2×C4#8819111yescharacteristic
357C2×C4#8819311yescharacteristic
358C2×C4#8819311yescharacteristic
359C2×C4#8819411yescharacteristic
360C2×C4C2×#610612yes—
361C2×C4#8819612yes—
362C2×C4#8820711yescharacteristic
363C8—24no—
364C8—522no—
365C8—522no—
366C8—1041no—
367C22—524no—
368C22—522no—
369C22—1041no—
370C22—1041no—
371C22—1042no—
372C22#1171874412yes—
373C22#1171883211yescharacteristic
374C22#1171883511yescharacteristic
375C22#1171883812yes—
376C22#1171888411yescharacteristic
377C4—21no—
378C4—21no—
379C4—82no—
380C4—82no—
381C4—1041no—
382C4#1171874611yescharacteristic
383C4#1171874711yescharacteristic
384C4#1171883011yescharacteristic
385C4#1171883111yescharacteristic
386C4#1171883311yescharacteristic
387C4#1171883411yescharacteristic
388C4#1171888812yes—
389C2—1042no—
390C2#1311420812yes—
391C2#1311433212yes—
392C2#1311583611yescharacteristic
393C2#1311591911yescharacteristic
394C2#1311594811yescharacteristic
subgroupG/H
centerC23#88192
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC2×C13×#498C2
socleC23×C13#121
prime radicalC22×D52D4
hypercenterC2×#498D13
hypocenterC13#10271
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#498

Complements

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

NH ≅ G/Ntype
4. C2×#11718138C2semidirect
5. C2×#11718139C2semidirect
6. #13112671C2semidirect
7. C2×C13×#498C2semidirect
101. C2×C8×C13SD16semidirect
127. C2×#498D13semidirect
306. C2×C8#6106semidirect
323. C13#10271semidirect

Maximal subgroups

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

subgroupindex
C2×#117187452
C2×#117187442
#131156302
C2×#117181382
C2×#117181392
#131126712
C2×C13×#4982
#1027113