Finite Group Databasebeta

← #15772027

Subgroups — #15772027

Order 3328.

594 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 594 conjugacy classes of subgroups — too many to draw. Only its 115 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#13117429C211yesmaximal, characteristic
2C2×#11718120C211yesmaximal, characteristic, complemented
3#13112769C212yesmaximal, complemented
4#13112767C212yesmaximal, complemented
5C2×C13×#324C211yesmaximal, characteristic, complemented
6C22×#6127C411yescharacteristic
7C22×C13×C4⋊C4C2211yescharacteristic
8C2×#88180C411yescharacteristic
9C2×C13×C22⋊C8—21no—
10#11718874—21no—
11#11718874—21no—
12C2×C22⋊#1055—21no—
13#11718649C411yescharacteristic
14#11718649C2211yescharacteristic
15#11718648—21no—
16#11718648—21no—
17#11718635C411yescharacteristic
18#11718635C2211yescharacteristic
19C13×#324—21no—
20C13×#324C2212yes—
21#11718120—21no—
22#11718120C2212yes—
23C23×C4×C13C2×C411yescharacteristic
24C23×C4×C13D411yescharacteristic
25C23×C4×C13D411yescharacteristic
26C22×C22⋊D13—21no—
27C2×#6127—22no—
28C2×#6127—41no—
29C2×#6127—41no—
30C2×#6127—42no—
31C2×#6127C814yescomplemented
32C22×D52C2×C411yescharacteristic
33C22×C4×D13—21no—
34C22×Dic26C2×C411yescharacteristic
35C22×C8×C13—41no—
36C2×C13×C4⋊C4—41no—
37C2×C13×C4⋊C4—41no—
38C2×C13×C4⋊C4C2×C411yescharacteristic
39C2×C13×C4⋊C4D411yescharacteristic
40C2×C13×C4⋊C4D411yescharacteristic
41C2×C13×C4⋊C4C2311yescharacteristic
42C2×C22⋊Dic13—21no—
43C2×#6103—21no—
44C2×#6103—21no—
45C2×#6103—21no—
46C2×#6103—21no—
47#88180—42no—
48C2×C4⋊Dic13—21no—
49C2×C4×Dic13C2×C411yescharacteristic
50C2×C4×Dic13C2×C411yescharacteristic
51C22×#1055—41no—
52C13×C22⋊C8—22no—
53C13×C22⋊C8—41no—
54#88071—21no—
55#88071—21no—
56#88071—21no—
57#88071—21no—
58C22⋊#1055—22no—
59C22⋊#1055—41no—
60#11432—131nomaximal, Sylow
61C24×C13C22⋊C411yescharacteristic
62C23×D13—21no—
63C22×C4×C13—21no—
64C22×C4×C13—21no—
65C22×C4×C13—22no—
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13—21no—
69C22×C4×C13—21no—
70C22×C4×C13—81no—
71C22×C4×C13—81no—
72C22×C4×C13C22⋊C411yescharacteristic
73C22×C4×C13C22⋊C411yescharacteristic
74C22×C4×C13C22⋊C411yescharacteristic
75C22×C4×C13C2×C812yes—
76C22×C4×C13M1612yes—
77C22×C4×C13C22×C411yescharacteristic
78C22×C4×C13C2×D411yescharacteristic
79C22×C4×C13C2×D411yescharacteristic
80C2×C22⋊D13—24no—
81C2×C22⋊D13—41no—
82C2×C22⋊D13—41no—
83C2×C22⋊D13—42no—
84C22×Dic13—21no—
85C22×Dic13—21no—
86C22×Dic13—21no—
87#6127—44no—
88#6127—44no—
89#6127—44no—
90#6127—44no—
91C2×D52—21no—
92C2×D52—41no—
93C2×D52—41no—
94C2×D52C2×C812yescomplemented
95C2×C4×D13—24no—
96C2×C4×D13—42no—
97C2×C4×D13—42no—
98C2×Dic26—21no—
99C2×Dic26—41no—
100C2×Dic26—41no—
101C2×Dic26C2×C812yescomplemented
102C2×C8×C13—42no—
103C2×C8×C13—82no—
104C13×C4⋊C4—41no—
105C13×C4⋊C4—41no—
106C13×C4⋊C4—41no—
107C13×C4⋊C4—41no—
108C22⋊Dic13—42no—
109#6103—81no—
110#6103—81no—
111#6103—81no—
112#6103—81no—
113C4⋊Dic13—42no—
114C4×Dic13—41no—
115C4×Dic13—41no—
116C2×#1055—42no—
117C2×#1055—82no—
118#2311—131no—
119C2×#324—131no—
120C2×#324D1311yescharacteristic, complemented
121#1319—132no—
122#1318—132no—
123C23×C13—41no—
124C23×C13—41no—
125C23×C13C22⋊C812yes—
126C23×C13#9911yescharacteristic
127C23×C13#9911yescharacteristic
128C23×C13#10012yes—
129C23×C13C2×C22⋊C411yescharacteristic
130C22×D13—22no—
131C22×D13—41no—
132C22×D13—41no—
133C22×D13—41no—
134C22×D13—41no—
135C22×D13—41no—
136C22×D13—41no—
137C2×C4×C13—22no—
138C2×C4×C13—22no—
139C2×C4×C13—22no—
140C2×C4×C13—22no—
141C2×C4×C13—21no—
142C2×C4×C13—21no—
143C2×C4×C13—21no—
144C2×C4×C13—21no—
145C2×C4×C13—21no—
146C2×C4×C13—21no—
147C2×C4×C13—21no—
148C2×C4×C13—21no—
149C2×C4×C13—42no—
150C2×C4×C13—42no—
151C2×C4×C13—41no—
152C2×C4×C13—41no—
153C2×C4×C13—41no—
154C2×C4×C13—41no—
155C2×C4×C13—81no—
156C2×C4×C13—81no—
157C2×C4×C13C22⋊C812yes—
158C2×C4×C13C22×C811yescharacteristic
159C2×C4×C13C2×M1611yescharacteristic
160C22⋊D13—44no—
161C22⋊D13—44no—
162C2×Dic13—22no—
163C2×Dic13—41no—
164C2×Dic13—41no—
165C2×Dic13—41no—
166C2×Dic13—41no—
167C2×Dic13—41no—
168C2×Dic13—41no—
169C2×Dic13—41no—
170C2×Dic13—41no—
171D52—42no—
172D52—42no—
173C4×D13—48no—
174Dic26—42no—
175Dic26—42no—
176C8×C13—82no—
177#1055—82no—
178C22×#41—131no—
179C2×#117—131no—
180C22×C4⋊C4C2×D1311yescharacteristic
181C2×C22⋊C8—21no—
182C2×C22⋊C8—261no—
183#391—131no—
184#391—131no—
185#390—131no—
186#390—131no—
187#386—261no—
188#386—261no—
189#380—261no—
190#380—261no—
191#324—21no—
192#324—132no—
193#324—261no—
194#324C2×D1312yes—
195C22×C13—21no—
196C22×C13—21no—
197C22×C13—21no—
198C22×C13—21no—
199C22×C13—21no—
200C22×C13—21no—
201C22×C13—42no—
202C22×C13—42no—
203C22×C13#32312yes—
204C22×C13#32312yes—
205C22×C13C2×C22⋊C811yescharacteristic
206C22×C13C2×#9911yescharacteristic
207C22×C13C2×#10011yescharacteristic
208C2×D13—42no—
209C2×D13—42no—
210C2×D13—42no—
211C2×D13—81no—
212C2×D13—81no—
213C2×D13—81no—
214C2×D13—81no—
215C4×C13—21no—
216C4×C13—21no—
217C4×C13—22no—
218C4×C13—41no—
219C4×C13—41no—
220C4×C13—41no—
221C4×C13—41no—
222Dic13—42no—
223Dic13—81no—
224Dic13—81no—
225C2×#41—134no—
226C2×#41—262no—
227C2×#41—521no—
228C2×#41—521no—
229C2×#41—522no—
230C22×Q8—131no—
231C22×D4—131no—
232C22×D4—261no—
233C23×C4—261no—
234C23×C4C4×D1311yescharacteristic
235C23×C4D5211yescharacteristic
236C23×C4C22⋊D1311yescharacteristic
237C22×C8—41no—
238C22×C8—521no—
239#117—522no—
240C2×C4⋊C4—41no—
241C2×C4⋊C4—41no—
242C2×C4⋊C4—261no—
243C2×C4⋊C4C4×D1311yescharacteristic
244C2×C4⋊C4D5211yescharacteristic
245C2×C4⋊C4C22⋊D1311yescharacteristic
246C2×C4⋊C4C22×D1311yescharacteristic
247C2×C22⋊C4—261no—
248C2×C22⋊C4—261no—
249C2×C22⋊C4—261no—
250C2×C22⋊C4—261no—
251C2×C22⋊C4—261no—
252C2×C42—131no—
253C2×C42—131no—
254C22⋊C8—22no—
255C22⋊C8—41no—
256C22⋊C8—262no—
257C22⋊C8—521no—
258#95—261no—
259#95—261no—
260#95—261no—
261#95—261no—
262C2×C13—21no—
263C2×C13—21no—
264C2×C13—22no—
265C2×C13—22no—
266C2×C13C2×#32311yescharacteristic
267C2×C13#212711yescharacteristic
268C2×C13#213311yescharacteristic
269D13—82no—
270C24—261no—
271C24#610311yescharacteristic
272#41—524no—
273#41—524no—
274#41—524no—
275#41—524no—
276C2×Q8—132no—
277C2×Q8—261no—
278C2×Q8—521no—
279C2×Q8—521no—
280C2×D4—132no—
281C2×D4—264no—
282C2×D4—261no—
283C2×D4—521no—
284C2×D4—521no—
285C2×D4—521no—
286C2×D4—521no—
287C2×D4—522no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—22no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—81no—
296C22×C4—81no—
297C22×C4—261no—
298C22×C4—264no—
299C22×C4—261no—
300C22×C4—261no—
301C22×C4—522no—
302C22×C4—522no—
303C22×C4C8×D1312yes—
304C22×C4#609412yes—
305C22×C4#610311yescharacteristic
306C22×C4#610311yescharacteristic
307C22×C4#610311yescharacteristic
308C22×C4C2×C4×D1311yescharacteristic
309C22×C4C2×D5211yescharacteristic
310C22×C4C2×C22⋊D1311yescharacteristic
311C2×C8—42no—
312C2×C8—82no—
313C2×C8—522no—
314C2×C8—1042no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—522no—
320C22⋊C4—522no—
321C22⋊C4—1041no—
322C22⋊C4—1041no—
323C22⋊C4—1041no—
324C22⋊C4—1041no—
325C42—521no—
326C42—521no—
327C13#1143211yescharacteristic, complemented, Sylow
328C23—41no—
329C23—41no—
330C23—262no—
331C23—521no—
332C23—521no—
333C23—521no—
334C23—521no—
335C23—521no—
336C23—521no—
337C23#8804611yescharacteristic
338C23#8804611yescharacteristic
339C23#8806012yes—
340C23#8806312yes—
341C23C2×#610311yescharacteristic
342Q8—522no—
343Q8—522no—
344D4—522no—
345D4—522no—
346D4—524no—
347D4—524no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—22no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—42no—
361C2×C4—42no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—81no—
367C2×C4—81no—
368C2×C4—262no—
369C2×C4—528no—
370C2×C4—521no—
371C2×C4—521no—
372C2×C4—521no—
373C2×C4—521no—
374C2×C4—521no—
375C2×C4—521no—
376C2×C4—521no—
377C2×C4—521no—
378C2×C4#8806012yes—
379C2×C4C2×C8×D1311yescharacteristic
380C2×C4C2×#609411yescharacteristic
381C8—82no—
382C8—1042no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—42no—
390C22—42no—
391C22—522no—
392C22—522no—
393C22—522no—
394C22—1041no—
395C22—1041no—
396C22—1041no—
397C22—1041no—
398C22#1171806012yes—
399C22#1171806012yes—
400C22C2×#8804611yescharacteristic
401C22C2×#8806011yescharacteristic
402C22C2×#8806311yescharacteristic
403C4—22no—
404C4—21no—
405C4—21no—
406C4—41no—
407C4—41no—
408C4—41no—
409C4—41no—
410C4—522no—
411C4—1041no—
412C4—1041no—
413C2—21no—
414C2—21no—
415C2—22no—
416C2—22no—
417C2—1042no—
418C2C2×#1171806011yescharacteristic
419C2#1311650311yescharacteristic
420C2#1311652311yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC2×C4×C13C22×C8
FrattiniC2×C4⋊C4C22×D13
FittingC2×C13×#324C2
socleC22×C13C2×#99
prime radicalC22×#6127C4
cosocleC2×C13×C4⋊C4C23
hypercenterC2×#324D13
hypocenterC13#11432
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
2. C2×#11718120C2semidirect
3. #13112769C2semidirect
4. #13112767C2semidirect
5. C2×C13×#324C2semidirect
31. C2×#6127C8semidirect
94. C2×D52C2×C8semidirect
101. C2×Dic26C2×C8semidirect
120. C2×#324D13semidirect
327. C13#11432semidirect

Maximal subgroups

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

subgroupindex
#131174292
C2×#117181202
#131127692
#131127672
C2×C13×#3242
#1143213