Finite Group Databasebeta

← #15837046

Subgroups — #15837046

Order 3328.

1058 conjugacy classes of subgroups; only the 183 normal subgroups are shown.

normal subgroups only

This group has 1058 conjugacy classes of subgroups — too many to draw. Only its 183 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#13125657C212yesmaximal, complemented
2#13119994C211yesmaximal, characteristic
3#13113827C214yesmaximal, complemented
4#13113793C214yesmaximal, complemented
5#13113356C212yesmaximal, complemented
6#13113163C211yesmaximal, characteristic
7C2×C13×#543C211yesmaximal, characteristic
8C13×#543—24no—
9C13×#543—22no—
10C13×#543C2214yes—
11C2×C13×C22⋊Q8—22no—
12C2×C13×C22⋊Q8—21no—
13C2×C13×C22⋊Q8—22no—
14C2×C13×C22⋊Q8C2212yes—
15C22×C13×C22⋊C4—21no—
16C22×C13×C22⋊C4C2211yescharacteristic
17C2×#88178C2211yescharacteristic
18#11718908—21no—
19#11718889—22no—
20#11718872—21no—
21C4×C22⋊Dic13C2211yescharacteristic
22#11718868C2212yes—
23#11718713—24no—
24#11718711C2214yescomplemented
25#11718704C2214yescomplemented
26#11718632—22no—
27#11718614C2212yes—
28#11718608C2212yes—
29#11718606—22no—
30#11718130C2218yescomplemented
31#11718117C2214yes—
32C25×C13D411yescharacteristic
33C22×Q8×C13—21no—
34C22×Q8×C13D412yes—
35C23×C4×C13—21no—
36C23×C4×C13—21no—
37C23×C4×C13D411yescharacteristic
38C23×C4×C13C2311yescharacteristic
39C22×Dic26C2311yescharacteristic
40C13×C22⋊Q8—28no—
41C13×C22⋊Q8—28no—
42C13×C22⋊Q8—24no—
43C13×C22⋊Q8—28no—
44C13×C22⋊Q8—24no—
45C13×C22⋊Q8—22no—
46C13×C22⋊Q8—22no—
47C13×C22⋊Q8—28no—
48C13×C22⋊Q8D414yes—
49C13×C22⋊Q8C2314yes—
50C2×C13×C4⋊C4—21no—
51C2×C13×C4⋊C4—22no—
52C2×C13×C4⋊C4—22no—
53C2×C13×C4⋊C4D412yes—
54C2×C13×C22⋊C4—22no—
55C2×C13×C22⋊C4—24no—
56C2×C13×C22⋊C4—22no—
57C2×C13×C22⋊C4—24no—
58C2×C13×C22⋊C4—22no—
59C2×C13×C22⋊C4—22no—
60C2×C13×C22⋊C4D412yes—
61C2×C13×C22⋊C4C2312yes—
62C2×C22⋊Dic13—21no—
63C2×C22⋊Dic13—22no—
64C2×C22⋊Dic13—21no—
65C2×C22⋊Dic13—22no—
66C2×#6107—24no—
67C2×C4⋊Dic13C2311yescharacteristic
68#88178—22no—
69#88178—22no—
70C2×#6101—21no—
71C2×C4×Dic13—21no—
72C2×#6099—22no—
73#88075—24no—
74#88071—22no—
75#88071—22no—
76#88071C2312yes—
77C22⋊#1055—22no—
78C22⋊#1055C2314yes—
79#88050—24no—
80#88048—24no—
81#18319—131nomaximal, Sylow
82C24×C13—21no—
83C24×C13—21no—
84C24×C13—24no—
85C24×C13—42no—
86C24×C13—81no—
87C24×C13C2×D411yescharacteristic
88C24×C13C2×D412yes—
89C2×Q8×C13—24no—
90C2×Q8×C13—22no—
91C2×Q8×C13—82no—
92C2×Q8×C13—82no—
93C2×Q8×C13C2×D414yes—
94C22×C4×C13—22no—
95C22×C4×C13—21no—
96C22×C4×C13—22no—
97C22×C4×C13—24no—
98C22×C4×C13—24no—
99C22×C4×C13—21no—
100C22×C4×C13—42no—
101C22×C4×C13—81no—
102C22×C4×C13—82no—
103C22×C4×C13—82no—
104C22×C4×C13C2×D412yes—
105C22×C4×C13C2×D411yescharacteristic
106C22×C4×C13C2×D412yes—
107C22×C4×C13C2×D412yes—
108C22×C4×C13C2411yescharacteristic
109C22×Dic13—22no—
110C22×Dic13—21no—
111C22×Dic13—21no—
112C2×Dic26—22no—
113C2×Dic26—81no—
114C13×C4⋊C4—24no—
115C13×C4⋊C4—28no—
116C13×C4⋊C4—24no—
117C13×C4⋊C4—22no—
118C13×C4⋊C4—24no—
119C13×C4⋊C4C2×D414yes—
120C13×C22⋊C4—28no—
121C13×C22⋊C4—24no—
122C13×C22⋊C4—24no—
123C13×C22⋊C4—24no—
124C13×C22⋊C4—24no—
125C22⋊Dic13—42no—
126C22⋊Dic13—41no—
127C22⋊Dic13—41no—
128C22⋊Dic13—44no—
129C22⋊Dic13—82no—
130#6107—84no—
131C4⋊Dic13—22no—
132#6101—42no—
133C4×Dic13—81no—
134#6099—82no—
135C2×#1055—24no—
136C2×#543D1311yescharacteristic
137#3195—132no—
138#2561—131no—
139#1608—134no—
140#1602—134no—
141#1508—132no—
142#1462—131no—
143C23×C13—24no—
144C23×C13—24no—
145C23×C13—22no—
146C23×C13—22no—
147C23×C13—22no—
148C23×C13—22no—
149C23×C13—41no—
150C23×C13—42no—
151C23×C13—42no—
152C23×C13—42no—
153C23×C13—42no—
154C23×C13—81no—
155C23×C13—81no—
156C23×C13—88no—
157C23×C13#12011yescharacteristic
158C23×C13#12011yescharacteristic
159C23×C13#13714yes—
160C23×C13C22×D411yescharacteristic
161Q8×C13—44no—
162Q8×C13—82no—
163Q8×C13—84no—
164C2×C4×C13—24no—
165C2×C4×C13—22no—
166C2×C4×C13—24no—
167C2×C4×C13—42no—
168C2×C4×C13—41no—
169C2×C4×C13—41no—
170C2×C4×C13—42no—
171C2×C4×C13—44no—
172C2×C4×C13—42no—
173C2×C4×C13—44no—
174C2×C4×C13—42no—
175C2×C4×C13—81no—
176C2×C4×C13—84no—
177C2×C4×C13—84no—
178C2×C4×C13#12012yes—
179C2×C4×C13C22×D412yes—
180C2×Dic13—42no—
181C2×Dic13—42no—
182C2×Dic13—42no—
183C2×Dic13—41no—
184C2×Dic13—41no—
185C2×Dic13—42no—
186C2×Dic13—42no—
187Dic26—44no—
188#1055—44no—
189#543—24no—
190#543—22no—
191#543C2×D1314yes—
192C2×C22⋊Q8—22no—
193C2×C22⋊Q8—21no—
194C2×C22⋊Q8—22no—
195C2×C22⋊Q8—131no—
196C2×C22⋊Q8C2×D1312yes—
197C22×C22⋊C4—21no—
198C22×C22⋊C4C2×D1311yescharacteristic
199#483—134no—
200#483—262no—
201#470—264no—
202#451—134no—
203#451—262no—
204#407—132no—
205#397—132no—
206#393—132no—
207#388—262no—
208#381—261no—
209#379—261no—
210C4×C22⋊C4—131no—
211#328—138no—
212#323—134no—
213C22×C13—21no—
214C22×C13—21no—
215C22×C13—21no—
216C22×C13—21no—
217C22×C13—21no—
218C22×C13—24no—
219C22×C13—21no—
220C22×C13—21no—
221C22×C13—44no—
222C22×C13—44no—
223C22×C13—48no—
224C22×C13—42no—
225C22×C13—42no—
226C22×C13—82no—
227C22×C13—84no—
228C22×C13#45512yes—
229C22×C13C2×#12011yescharacteristic
230C22×C13C2×#13712yes—
231C4×C13—22no—
232C4×C13—22no—
233C4×C13—42no—
234C4×C13—44no—
235C4×C13—44no—
236Dic13—82no—
237Dic13—81no—
238Dic13—81no—
239C25C22⋊D1311yescharacteristic
240C22×Q8—21no—
241C22×Q8—131no—
242C22×Q8C22⋊D1312yes—
243C23×C4—21no—
244C23×C4—21no—
245C23×C4C22⋊D1311yescharacteristic
246C23×C4C22×D1311yescharacteristic
247C2×Q16—264no—
248C2×M16—262no—
249C22⋊Q8—28no—
250C22⋊Q8—28no—
251C22⋊Q8—24no—
252C22⋊Q8—28no—
253C22⋊Q8—24no—
254C22⋊Q8—22no—
255C22⋊Q8—22no—
256C22⋊Q8—28no—
257C22⋊Q8—262no—
258C22⋊Q8—262no—
259C22⋊Q8C22⋊D1314yes—
260C22⋊Q8C22×D1314yes—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—22no—
263C2×C4⋊C4—22no—
264C2×C4⋊C4—131no—
265C2×C4⋊C4—261no—
266C2×C4⋊C4C22⋊D1312yes—
267C2×C22⋊C4—22no—
268C2×C22⋊C4—24no—
269C2×C22⋊C4—22no—
270C2×C22⋊C4—24no—
271C2×C22⋊C4—22no—
272C2×C22⋊C4—22no—
273C2×C22⋊C4—261no—
274C2×C22⋊C4—261no—
275C2×C22⋊C4—262no—
276C2×C22⋊C4—262no—
277C2×C22⋊C4C22⋊D1312yes—
278C2×C22⋊C4C22×D1312yes—
279C2×C42—261no—
280#106—264no—
281#103—264no—
282#103—264no—
283C22⋊C8—134no—
284C22⋊C8—262no—
285#95—132no—
286#95—262no—
287#95—262no—
288C2×C13—22no—
289C2×C13—22no—
290C2×C13—41no—
291C2×C13—44no—
292C2×C13#300411yescharacteristic
293C2×C13C2×#45511yescharacteristic
294C2×C13#302611yescharacteristic
295C24—21no—
296C24—24no—
297C24—21no—
298C24—42no—
299C24—81no—
300C24C2×C22⋊D1311yescharacteristic
301C24C2×C22⋊D1312yes—
302C2×Q8—24no—
303C2×Q8—22no—
304C2×Q8—82no—
305C2×Q8—82no—
306C2×Q8—262no—
307C2×Q8—1041no—
308C2×Q8C2×C22⋊D1314yes—
309C22×C4—22no—
310C22×C4—21no—
311C22×C4—22no—
312C22×C4—24no—
313C22×C4—24no—
314C22×C4—21no—
315C22×C4—42no—
316C22×C4—81no—
317C22×C4—82no—
318C22×C4—82no—
319C22×C4—262no—
320C22×C4—261no—
321C22×C4—261no—
322C22×C4C2×C22⋊D1312yes—
323C22×C4C2×C22⋊D1311yescharacteristic
324C22×C4C2×C22⋊D1312yes—
325C22×C4C2×C22⋊D1312yes—
326C22×C4C23×D1311yescharacteristic
327Q16—1044no—
328M16—1042no—
329C2×C8—264no—
330C4⋊C4—24no—
331C4⋊C4—28no—
332C4⋊C4—24no—
333C4⋊C4—22no—
334C4⋊C4—24no—
335C4⋊C4—262no—
336C4⋊C4—522no—
337C4⋊C4C2×C22⋊D1314yes—
338C22⋊C4—28no—
339C22⋊C4—24no—
340C22⋊C4—24no—
341C22⋊C4—24no—
342C22⋊C4—24no—
343C22⋊C4—522no—
344C22⋊C4—524no—
345C22⋊C4—521no—
346C22⋊C4—521no—
347C22⋊C4—1042no—
348C42—1041no—
349C13#1831911yescharacteristic, complemented, Sylow
350C23—24no—
351C23—24no—
352C23—22no—
353C23—22no—
354C23—22no—
355C23—22no—
356C23—41no—
357C23—42no—
358C23—42no—
359C23—42no—
360C23—42no—
361C23—81no—
362C23—81no—
363C23—88no—
364C23#8819614yes—
365C23#8820711yescharacteristic
366C23#8820711yescharacteristic
367C23C22×C22⋊D1311yescharacteristic
368Q8—44no—
369Q8—82no—
370Q8—84no—
371Q8—524no—
372C2×C4—24no—
373C2×C4—22no—
374C2×C4—24no—
375C2×C4—41no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—41no—
379C2×C4—44no—
380C2×C4—42no—
381C2×C4—44no—
382C2×C4—42no—
383C2×C4—81no—
384C2×C4—84no—
385C2×C4—84no—
386C2×C4—522no—
387C2×C4—522no—
388C2×C4—522no—
389C2×C4—522no—
390C2×C4—522no—
391C2×C4—521no—
392C2×C4—521no—
393C2×C4#8820712yes—
394C2×C4C22×C22⋊D1312yes—
395C8—524no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—21no—
401C22—21no—
402C22—24no—
403C22—21no—
404C22—44no—
405C22—44no—
406C22—48no—
407C22—42no—
408C22—42no—
409C22—82no—
410C22—84no—
411C22#1171890312yes—
412C22C2×#8819612yes—
413C22C2×#8820711yescharacteristic
414C4—22no—
415C4—22no—
416C4—42no—
417C4—44no—
418C4—44no—
419C4—1042no—
420C4—1041no—
421C4—1041no—
422C2—22no—
423C2—22no—
424C2—41no—
425C2—44no—
426C2#1312407011yescharacteristic
427C2C2×#1171890311yescharacteristic
428C2#1312423311yescharacteristic
subgroupG/H
centerC22C2×#88207
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC2×C13×#543C2
socleC22×C13C2×#120
prime radicalC25×C13D4
hypercenterC2×#543D13
hypocenterC13#18319
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#543

Complements

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

NH ≅ G/Ntype
1. #13125657C2semidirect
3. #13113827C2semidirect
4. #13113793C2semidirect
5. #13113356C2semidirect
24. #11718711C22semidirect
25. #11718704C22semidirect
30. #11718130C22semidirect
349. C13#18319semidirect

Maximal subgroups

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

subgroupindex
#131256572
#131199942
#131138272
#131137932
#131133562
#131131632
C2×C13×#5432
#1831913