Finite Group Databasebeta

← #15837100

Subgroups — #15837100

Order 3328.

1230 conjugacy classes of subgroups; only the 183 normal subgroups are shown.

normal subgroups only

This group has 1230 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#13125642C212yesmaximal, complemented
2#13120216C211yesmaximal, characteristic, complemented
3#13113839C214yesmaximal, complemented
4#13113805C214yesmaximal, complemented
5#13113352C212yesmaximal, complemented
6#13113166C211yesmaximal, characteristic, complemented
7C2×C13×#537C211yesmaximal, characteristic
8C22×C13×#41—21no—
9C13×#537—24no—
10C13×#537—22no—
11C13×#537C2214yes—
12C2×C13×C22⋊Q8—22no—
13C2×C13×#121—22no—
14C2×C13×#121—21no—
15C2×C13×#121C2212yes—
16C22×C13×C4⋊C4C2211yescharacteristic
17C2×#88178C2211yescharacteristic
18#11718879—22no—
19#11718871—21no—
20#11718871—21no—
21C4×C22⋊Dic13C2211yescharacteristic
22#11718868C2212yes—
23#11718703—24no—
24#11718701C2214yescomplemented
25#11718694C2214yescomplemented
26#11718644C2212yescomplemented
27#11718640C2212yescomplemented
28#11718633—22no—
29#11718631—22no—
30#11718129C2218yescomplemented
31#11718120C2214yescomplemented
32C2×C13×#41—24no—
33C2×C13×#41—24no—
34C2×C13×#41—48no—
35C22×Q8×C13—21no—
36C22×D4×C13—21no—
37C22×D4×C13—22no—
38C22×D4×C13—21no—
39C22×D4×C13D412yes—
40C23×C4×C13—22no—
41C23×C4×C13D411yescharacteristic
42C23×C4×C13D411yescharacteristic
43C23×C4×C13C2311yescharacteristic
44C22×Dic26C2311yescharacteristic
45C13×C22⋊Q8—28no—
46C13×C22⋊Q8—28no—
47C13×#121—24no—
48C13×#121—28no—
49C13×#121—28no—
50C13×#121—24no—
51C13×#121—22no—
52C13×#121—22no—
53C13×#121D414yes—
54C13×#121C2314yes—
55C2×C13×C4⋊C4—21no—
56C2×C13×C4⋊C4—22no—
57C2×C13×C4⋊C4—22no—
58C2×C13×C4⋊C4D412yes—
59C2×C13×C4⋊C4D412yes—
60C2×C13×C4⋊C4C2312yes—
61C2×C13×C22⋊C4—22no—
62C2×C13×C22⋊C4—22no—
63C2×C22⋊Dic13—21no—
64C2×C22⋊Dic13—21no—
65C2×#6105—24no—
66C2×C4⋊Dic13C2311yescharacteristic
67#88178—22no—
68#88178—22no—
69C2×#6101—21no—
70C2×#6101—22no—
71C2×#6101—22no—
72C2×C4×Dic13—21no—
73C2×#6099—22no—
74#88072—24no—
75#88071—22no—
76#88071—22no—
77#88071C2312yes—
78C22⋊#1055—22no—
79C22⋊#1055C2314yes—
80#88050—24no—
81#88047—24no—
82#18325—131nomaximal, Sylow
83C24×C13—22no—
84C24×C13C2×D411yescharacteristic
85C13×#41—416no—
86C13×#41—48no—
87C13×#41—48no—
88C2×Q8×C13—24no—
89C2×Q8×C13—44no—
90C2×D4×C13—24no—
91C2×D4×C13—24no—
92C2×D4×C13—24no—
93C2×D4×C13—24no—
94C2×D4×C13—22no—
95C2×D4×C13—44no—
96C2×D4×C13—48no—
97C2×D4×C13—82no—
98C2×D4×C13—82no—
99C2×D4×C13C2×D414yes—
100C22×C4×C13—21no—
101C22×C4×C13—21no—
102C22×C4×C13—24no—
103C22×C4×C13—28no—
104C22×C4×C13—21no—
105C22×C4×C13—22no—
106C22×C4×C13—21no—
107C22×C4×C13—48no—
108C22×C4×C13—81no—
109C22×C4×C13—81no—
110C22×C4×C13C2×D412yes—
111C22×C4×C13C2×D412yes—
112C22×C4×C13C2×D411yescharacteristic
113C22×C4×C13C2×D412yes—
114C22×C4×C13C2×D412yes—
115C22×C4×C13C2411yescharacteristic
116C22×Dic13—22no—
117C22×Dic13—21no—
118C22×Dic13—21no—
119C2×Dic26—22no—
120C2×Dic26—81no—
121C13×C4⋊C4—24no—
122C13×C4⋊C4—24no—
123C13×C4⋊C4—22no—
124C13×C4⋊C4—24no—
125C13×C4⋊C4C2×D414yes—
126C13×C22⋊C4—28no—
127C13×C22⋊C4—24no—
128C13×C22⋊C4—24no—
129C22⋊Dic13—24no—
130C22⋊Dic13—41no—
131C22⋊Dic13—41no—
132#6105—84no—
133C4⋊Dic13—22no—
134#6101—42no—
135#6101—44no—
136#6101—82no—
137C4×Dic13—81no—
138#6099—82no—
139C2×#1055—24no—
140C2×#537D1311yescharacteristic
141#3193—132no—
142#2583—131no—
143#1610—134no—
144#1604—134no—
145#1507—132no—
146#1463—131no—
147C23×C13—22no—
148C23×C13—22no—
149C23×C13—24no—
150C23×C13—41no—
151C23×C13—44no—
152C23×C13—44no—
153C23×C13—44no—
154C23×C13#12011yescharacteristic
155C23×C13#12011yescharacteristic
156C23×C13C22×D411yescharacteristic
157Q8×C13—48no—
158D4×C13—48no—
159D4×C13—44no—
160D4×C13—48no—
161D4×C13—48no—
162D4×C13—82no—
163D4×C13—84no—
164C2×C4×C13—24no—
165C2×C4×C13—24no—
166C2×C4×C13—22no—
167C2×C4×C13—22no—
168C2×C4×C13—22no—
169C2×C4×C13—24no—
170C2×C4×C13—42no—
171C2×C4×C13—41no—
172C2×C4×C13—41no—
173C2×C4×C13—42no—
174C2×C4×C13—416no—
175C2×C4×C13—44no—
176C2×C4×C13—42no—
177C2×C4×C13—42no—
178C2×C4×C13—81no—
179C2×C4×C13#12012yes—
180C2×C4×C13AGL(1,ℤ/8)14yes—
181C2×C4×C13C22×D412yes—
182C2×Dic13—24no—
183C2×Dic13—42no—
184C2×Dic13—42no—
185C2×Dic13—42no—
186C2×Dic13—41no—
187C2×Dic13—41no—
188C2×Dic13—42no—
189Dic26—44no—
190#1055—44no—
191C22×#41—21no—
192#537—24no—
193#537—22no—
194#537C2×D1314yes—
195C2×C22⋊Q8—22no—
196C2×C22⋊Q8—131no—
197C2×#121—22no—
198C2×#121—21no—
199C2×#121C2×D1312yes—
200C22×C4⋊C4C2×D1311yescharacteristic
201#484—262no—
202#480—134no—
203#468—264no—
204#450—262no—
205#448—134no—
206#407—132no—
207#398—132no—
208#395—132no—
209#389—262no—
210#385—261no—
211#385—261no—
212C4×C22⋊C4—131no—
213#327—138no—
214#324—134no—
215C22×C13—21no—
216C22×C13—21no—
217C22×C13—21no—
218C22×C13—21no—
219C22×C13—21no—
220C22×C13—21no—
221C22×C13—21no—
222C22×C13—44no—
223C22×C13—44no—
224C22×C13—44no—
225C22×C13—44no—
226C22×C13—88no—
227C22×C13#45612yes—
228C22×C13C2×#12011yescharacteristic
229C22×C13C2×AGL(1,ℤ/8)12yes—
230C4×C13—24no—
231C4×C13—22no—
232C4×C13—22no—
233C4×C13—44no—
234C4×C13—42no—
235Dic13—44no—
236Dic13—81no—
237Dic13—81no—
238C2×#41—24no—
239C2×#41—24no—
240C2×#41—48no—
241C22×Q8—21no—
242C22×Q8—131no—
243C22×D4—21no—
244C22×D4—22no—
245C22×D4—21no—
246C22×D4C22⋊D1312yes—
247C23×C4—22no—
248C23×C4C22⋊D1311yescharacteristic
249C23×C4C22⋊D1311yescharacteristic
250C23×C4C22×D1311yescharacteristic
251C2×SD16—264no—
252C2×M16—262no—
253C22⋊Q8—28no—
254C22⋊Q8—28no—
255C22⋊Q8—262no—
256C22⋊Q8—262no—
257#121—24no—
258#121—28no—
259#121—28no—
260#121—24no—
261#121—22no—
262#121—22no—
263#121C22⋊D1314yes—
264#121C22×D1314yes—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—22no—
267C2×C4⋊C4—22no—
268C2×C4⋊C4—131no—
269C2×C4⋊C4—261no—
270C2×C4⋊C4—262no—
271C2×C4⋊C4—262no—
272C2×C4⋊C4C22⋊D1312yes—
273C2×C4⋊C4C22⋊D1312yes—
274C2×C4⋊C4C22×D1312yes—
275C2×C22⋊C4—22no—
276C2×C22⋊C4—22no—
277C2×C22⋊C4—261no—
278C2×C22⋊C4—261no—
279C2×C42—261no—
280#107—264no—
281#103—264no—
282#102—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—84no—
292C2×C13#300311yescharacteristic
293C2×C13C2×#45611yescharacteristic
294C2×C13#302611yescharacteristic
295C24—22no—
296C24C2×C22⋊D1311yescharacteristic
297#41—416no—
298#41—48no—
299#41—48no—
300C2×Q8—24no—
301C2×Q8—44no—
302C2×Q8—262no—
303C2×Q8—1041no—
304C2×D4—24no—
305C2×D4—24no—
306C2×D4—24no—
307C2×D4—24no—
308C2×D4—22no—
309C2×D4—44no—
310C2×D4—48no—
311C2×D4—82no—
312C2×D4—82no—
313C2×D4C2×C22⋊D1314yes—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—24no—
317C22×C4—28no—
318C22×C4—21no—
319C22×C4—22no—
320C22×C4—21no—
321C22×C4—48no—
322C22×C4—81no—
323C22×C4—81no—
324C22×C4—262no—
325C22×C4—261no—
326C22×C4—261no—
327C22×C4C2×C22⋊D1312yes—
328C22×C4C2×C22⋊D1312yes—
329C22×C4C2×C22⋊D1311yescharacteristic
330C22×C4C2×C22⋊D1312yes—
331C22×C4C2×C22⋊D1312yes—
332C22×C4C23×D1311yescharacteristic
333SD16—1044no—
334M16—1042no—
335C2×C8—264no—
336C4⋊C4—24no—
337C4⋊C4—24no—
338C4⋊C4—22no—
339C4⋊C4—24no—
340C4⋊C4—262no—
341C4⋊C4—524no—
342C4⋊C4—522no—
343C4⋊C4—1042no—
344C4⋊C4C2×C22⋊D1314yes—
345C22⋊C4—28no—
346C22⋊C4—24no—
347C22⋊C4—24no—
348C22⋊C4—264no—
349C22⋊C4—521no—
350C22⋊C4—521no—
351C42—1041no—
352C13#1832511yescharacteristic, complemented, Sylow
353C23—22no—
354C23—22no—
355C23—24no—
356C23—41no—
357C23—44no—
358C23—44no—
359C23—44no—
360C23#8820711yescharacteristic
361C23#8820711yescharacteristic
362C23C22×C22⋊D1311yescharacteristic
363Q8—48no—
364Q8—524no—
365D4—44no—
366D4—48no—
367D4—48no—
368D4—48no—
369D4—82no—
370D4—84no—
371C2×C4—24no—
372C2×C4—24no—
373C2×C4—22no—
374C2×C4—22no—
375C2×C4—22no—
376C2×C4—24no—
377C2×C4—41no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—41no—
381C2×C4—416no—
382C2×C4—44no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—81no—
386C2×C4—264no—
387C2×C4—522no—
388C2×C4—522no—
389C2×C4—522no—
390C2×C4—522no—
391C2×C4—521no—
392C2×C4—521no—
393C2×C4#8818614yes—
394C2×C4#8820712yes—
395C2×C4C22×C22⋊D1312yes—
396C8—524no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—21no—
401C22—21no—
402C22—21no—
403C22—21no—
404C22—44no—
405C22—44no—
406C22—44no—
407C22—44no—
408C22—88no—
409C22#1171890712yes—
410C22C2×#8818612yes—
411C22C2×#8820711yescharacteristic
412C4—22no—
413C4—22no—
414C4—24no—
415C4—42no—
416C4—44no—
417C4—524no—
418C4—1041no—
419C4—1041no—
420C2—22no—
421C2—22no—
422C2—41no—
423C2—84no—
424C2#1312406311yescharacteristic
425C2C2×#1171890711yescharacteristic
426C2#1312423311yescharacteristic
subgroupG/H
centerC22C2×#88207
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
Fitting, prime radicalC2×C13×#537C2
socleC22×C13C2×#120
hypercenterC2×#537D13
hypocenterC13#18325
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#537

Complements

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

NH ≅ G/Ntype
1. #13125642C2semidirect
2. #13120216C2semidirect
3. #13113839C2semidirect
4. #13113805C2semidirect
5. #13113352C2semidirect
6. #13113166C2semidirect
24. #11718701C22semidirect
25. #11718694C22semidirect
26. #11718644C22semidirect
27. #11718640C22semidirect
30. #11718129C22semidirect
31. #11718120C22semidirect
352. C13#18325semidirect

Maximal subgroups

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

subgroupindex
#131256422
#131202162
#131138392
#131138052
#131133522
#131131662
C2×C13×#5372
#1832513