Finite Group Databasebeta

← #15763205

Subgroups — #15763205

Order 3328.

654 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 654 conjugacy classes of subgroups — too many to draw. Only its 113 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
1C2×#11718704C211yesmaximal, characteristic
2#13120651C211yesmaximal, characteristic
3C2×#11718322C211yesmaximal, characteristic
4#13114923C211yesmaximal, characteristic
5C2×#11718061C211yesmaximal, characteristic
6#13112715C211yesmaximal, characteristic
7C2×C13×#328C211yesmaximal, characteristic
8C2×C13×C22⋊Q8C2211yescharacteristic
9C22×C4⋊Dic13—21no—
10C22×C4⋊Dic13C2211yescharacteristic
11C22×#6101C2211yescharacteristic
12C2×C13×C22⋊C8C2211yescharacteristic
13C2×C13×#95C2211yescharacteristic
14#11718890—21no—
15C2×#88075—21no—
16#11718873C2211yescharacteristic
17C2×#88071—21no—
18C2×C22⋊#1055C2211yescharacteristic
19#11718704—22no—
20#11718704—22no—
21#11718645—22no—
22#11718643—21no—
23C2×#88048—21no—
24#11718607—21no—
25#11718604—21no—
26#11718322—22no—
27#11718322—22no—
28C13×#328—22no—
29#11718143—22no—
30#11718061—22no—
31C22×Q8×C13D411yescharacteristic
32C23×C4×C13—21no—
33C23×C4×C13C2311yescharacteristic
34C23×Dic13—21no—
35C23×Dic13D411yescharacteristic
36C23×Dic13D411yescharacteristic
37C22×C8×C13—21no—
38C13×C22⋊Q8—21no—
39C13×C22⋊Q8—21no—
40C13×C22⋊Q8—21no—
41C13×C22⋊Q8—21no—
42C2×C13×C4⋊C4—21no—
43C2×C13×C4⋊C4D411yescharacteristic
44C2×C13×C22⋊C4—21no—
45C2×C22⋊Dic13—21no—
46C2×C4⋊Dic13—21no—
47C2×C4⋊Dic13—21no—
48C2×C4⋊Dic13—21no—
49C2×C4⋊Dic13—21no—
50C2×C4⋊Dic13—24no—
51C2×C4⋊Dic13—21no—
52C2×C4⋊Dic13—42no—
53C2×C4⋊Dic13—42no—
54C2×C4⋊Dic13D412yes—
55C2×C4⋊Dic13D412yes—
56C2×#6101—21no—
57C2×#6101—21no—
58C2×#6101—21no—
59C2×#6101—21no—
60C2×#6101—21no—
61C2×#6101—21no—
62C2×#6101—22no—
63C22×#1055—21no—
64C13×C22⋊C8—21no—
65C13×C22⋊C8—21no—
66C13×#95—21no—
67C13×#95D412yes—
68#88075—24no—
69#88071—24no—
70#88071—22no—
71#88071—22no—
72#88071—22no—
73#88071—21no—
74C22⋊#1055—21no—
75C22⋊#1055D412yes—
76#88048—24no—
77#9927—131nomaximal, Sylow
78C24×C13C2×D411yescharacteristic
79C2×Q8×C13—21no—
80C2×Q8×C13—21no—
81C2×Q8×C13—42no—
82C22×C4×C13—24no—
83C22×C4×C13—22no—
84C22×C4×C13—21no—
85C22×C4×C13—21no—
86C22×C4×C13—42no—
87C22×C4×C13—42no—
88C22×C4×C13—41no—
89C22×C4×C13—41no—
90C22×C4×C13C2×D411yescharacteristic
91C22×C4×C13C2×D411yescharacteristic
92C22×C4×C13C2×D411yescharacteristic
93C22×C4×C13C2×D411yescharacteristic
94C22×C4×C13C2×D411yescharacteristic
95C22×C4×C13#4111yescharacteristic
96C22×Dic13—21no—
97C22×Dic13—21no—
98C22×Dic13—21no—
99C22×Dic13—21no—
100C22×Dic13—21no—
101C22×Dic13—21no—
102C22×Dic13—21no—
103C22×Dic13—22no—
104C22×Dic13—21no—
105C22×Dic13—22no—
106C22×Dic13—21no—
107C22×Dic13—42no—
108C22×Dic13—41no—
109C22×Dic13—41no—
110C22×Dic13—41no—
111C22×Dic13—41no—
112C22×Dic13—41no—
113C22×Dic13—41no—
114C22×Dic13SD1612yes—
115C2×C8×C13—42no—
116C2×C8×C13—41no—
117C13×C4⋊C4—21no—
118C13×C4⋊C4—21no—
119C13×C4⋊C4—41no—
120C13×C4⋊C4—41no—
121C13×C22⋊C4—41no—
122C13×C22⋊C4—41no—
123C22⋊Dic13—41no—
124C22⋊Dic13—41no—
125C4⋊Dic13—22no—
126C4⋊Dic13—22no—
127C4⋊Dic13—48no—
128C4⋊Dic13—41no—
129C4⋊Dic13—41no—
130C4⋊Dic13—42no—
131#6101—41no—
132#6101—41no—
133#6101—41no—
134#6101—41no—
135#6101—82no—
136C2×#1055—22no—
137C2×#1055—42no—
138C2×#483—131no—
139#2627—131no—
140C2×#398—131no—
141#1823—131no—
142C2×#328D1311yescharacteristic
143C2×#324—131no—
144#1294—131no—
145C23×C13—22no—
146C23×C13—22no—
147C23×C13#12011yescharacteristic
148C23×C13#12011yescharacteristic
149C23×C13#12111yescharacteristic
150C23×C13C2×SD1611yescharacteristic
151C23×C13#13511yescharacteristic
152C23×C13AGL(1,ℤ/8)11yescharacteristic
153C23×C13#13711yescharacteristic
154Q8×C13—42no—
155Q8×C13—81no—
156C2×C4×C13—22no—
157C2×C4×C13—22no—
158C2×C4×C13—24no—
159C2×C4×C13—41no—
160C2×C4×C13—41no—
161C2×C4×C13—41no—
162C2×C4×C13—41no—
163C2×C4×C13—44no—
164C2×C4×C13—44no—
165C2×C4×C13—42no—
166C2×C4×C13—42no—
167C2×C4×C13—41no—
168C2×C4×C13—41no—
169C2×C4×C13—42no—
170C2×C4×C13—42no—
171C2×C4×C13#12011yescharacteristic
172C2×C4×C13#12111yescharacteristic
173C2×C4×C13#12111yescharacteristic
174C2×C4×C13#12711yescharacteristic
175C2×Dic13—22no—
176C2×Dic13—22no—
177C2×Dic13—22no—
178C2×Dic13—41no—
179C2×Dic13—41no—
180C2×Dic13—41no—
181C2×Dic13—41no—
182C2×Dic13—42no—
183C2×Dic13—41no—
184C2×Dic13—42no—
185C2×Dic13—42no—
186C2×Dic13—42no—
187C2×Dic13—42no—
188C2×Dic13—42no—
189C2×Dic13—42no—
190C2×Dic13—42no—
191C2×Dic13—81no—
192C2×Dic13—81no—
193C2×Dic13—81no—
194C2×Dic13—81no—
195C2×Dic13—81no—
196C8×C13—81no—
197#1055—42no—
198C2×C22⋊Q8C2×D1311yescharacteristic
199C22×C4⋊C4—131no—
200C22×C4⋊C4—131no—
201C22×C4⋊C4—261no—
202#483—262no—
203#483—262no—
204C2×#106—261no—
205C2×#103—261no—
206C2×C22⋊C8—131no—
207C2×C22⋊C8C2×D1311yescharacteristic
208#400—261no—
209#398—262no—
210#398—262no—
211#398—262no—
212#395—261no—
213#385—261no—
214#381—261no—
215#380—131no—
216C2×#95—261no—
217C2×#95C2×D1311yescharacteristic
218#340—262no—
219#328—22no—
220#324—262no—
221C22×C13—22no—
222C22×C13—22no—
223C22×C13—22no—
224C22×C13—22no—
225C22×C13—21no—
226C22×C13—21no—
227C22×C13—21no—
228C22×C13—21no—
229C22×C13#39211yescharacteristic
230C22×C13#44811yescharacteristic
231C22×C13#44911yescharacteristic
232C22×C13#45011yescharacteristic
233C22×C13#45211yescharacteristic
234C22×C13#45612yes—
235C22×C13#45812yes—
236C22×C13#46511yescharacteristic
237C22×C13#46811yescharacteristic
238C4×C13—21no—
239C4×C13—21no—
240C4×C13—21no—
241C4×C13—21no—
242C4×C13—44no—
243C4×C13—81no—
244C4×C13—81no—
245Dic13—42no—
246Dic13—82no—
247Dic13—82no—
248Dic13—81no—
249C22×Q8D5211yescharacteristic
250C23×C4—21no—
251C23×C4—131no—
252C23×C4—131no—
253C23×C4—261no—
254C23×C4C22×D1311yescharacteristic
255C22×C8—21no—
256C22×C8—261no—
257C22⋊Q8—21no—
258C22⋊Q8—21no—
259C22⋊Q8—21no—
260C22⋊Q8—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—132no—
263C2×C4⋊C4—132no—
264C2×C4⋊C4—261no—
265C2×C4⋊C4—261no—
266C2×C4⋊C4—261no—
267C2×C4⋊C4—261no—
268C2×C4⋊C4—264no—
269C2×C4⋊C4—261no—
270C2×C4⋊C4—261no—
271C2×C4⋊C4—261no—
272C2×C4⋊C4—261no—
273C2×C4⋊C4—261no—
274C2×C4⋊C4—261no—
275C2×C4⋊C4—261no—
276C2×C4⋊C4—262no—
277C2×C4⋊C4—522no—
278C2×C4⋊C4—522no—
279C2×C4⋊C4D5211yescharacteristic
280C2×C22⋊C4—21no—
281C2×C22⋊C4—261no—
282#106—264no—
283#103—264no—
284C22⋊C8—21no—
285C22⋊C8—21no—
286C22⋊C8—132no—
287C22⋊C8—261no—
288#95—21no—
289#95—264no—
290#95—262no—
291#95—262no—
292#95—262no—
293#95—261no—
294#95C22⋊D1312yes—
295C2×C13—21no—
296C2×C13—21no—
297C2×C13—21no—
298C2×C13—21no—
299C2×C13#160912yes—
300C2×C13#161112yes—
301C2×C13#200011yescharacteristic
302C2×C13#200511yescharacteristic
303C2×C13#202211yescharacteristic
304C24D4×D1311yescharacteristic
305C2×Q8—21no—
306C2×Q8—21no—
307C2×Q8—42no—
308C22×C4—24no—
309C22×C4—22no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—42no—
313C22×C4—42no—
314C22×C4—41no—
315C22×C4—41no—
316C22×C4—132no—
317C22×C4—261no—
318C22×C4—261no—
319C22×C4—261no—
320C22×C4—261no—
321C22×C4—261no—
322C22×C4—261no—
323C22×C4—262no—
324C22×C4—261no—
325C22×C4—261no—
326C22×C4—262no—
327C22×C4—261no—
328C22×C4—522no—
329C22×C4—521no—
330C22×C4—521no—
331C22×C4—521no—
332C22×C4—521no—
333C22×C4—521no—
334C22×C4—521no—
335C22×C4C2×D5211yescharacteristic
336C22×C4#612711yescharacteristic
337C22×C4D4×D1311yescharacteristic
338C22×C4D4×D1311yescharacteristic
339C22×C4D4×D1311yescharacteristic
340C22×C4C2×C22⋊D1311yescharacteristic
341C2×C8—42no—
342C2×C8—41no—
343C2×C8—262no—
344C2×C8—522no—
345C4⋊C4—21no—
346C4⋊C4—21no—
347C4⋊C4—41no—
348C4⋊C4—41no—
349C4⋊C4—262no—
350C4⋊C4—262no—
351C4⋊C4—522no—
352C4⋊C4—528no—
353C4⋊C4—521no—
354C4⋊C4—521no—
355C4⋊C4—521no—
356C4⋊C4—521no—
357C4⋊C4—521no—
358C4⋊C4—521no—
359C4⋊C4—1042no—
360C22⋊C4—41no—
361C22⋊C4—41no—
362C22⋊C4—521no—
363C22⋊C4—521no—
364C13#992711yescharacteristic, complemented, Sylow
365C23—22no—
366C23—22no—
367C23#8813611yescharacteristic
368C23#8813811yescharacteristic
369C23SD16×D1311yescharacteristic
370C23#8816811yescharacteristic
371C23#8817211yescharacteristic
372C23#8817311yescharacteristic
373C23#8819111yescharacteristic
374Q8—42no—
375Q8—81no—
376C2×C4—22no—
377C2×C4—22no—
378C2×C4—24no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—42no—
384C2×C4—44no—
385C2×C4—44no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—262no—
392C2×C4—262no—
393C2×C4—262no—
394C2×C4—521no—
395C2×C4—521no—
396C2×C4—521no—
397C2×C4—521no—
398C2×C4—522no—
399C2×C4—522no—
400C2×C4—522no—
401C2×C4—522no—
402C2×C4—522no—
403C2×C4—522no—
404C2×C4—522no—
405C2×C4—522no—
406C2×C4—521no—
407C2×C4—1041no—
408C2×C4—1041no—
409C2×C4—1041no—
410C2×C4—1041no—
411C2×C4—1041no—
412C2×C4#8813611yescharacteristic
413C2×C4#8813811yescharacteristic
414C2×C4#8818411yescharacteristic
415C2×C4#8819411yescharacteristic
416C8—81no—
417C8—522no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—22no—
423C22—22no—
424C22—22no—
425C22—22no—
426C22#1171840312yes—
427C22#1171846711yescharacteristic
428C22#1171846811yescharacteristic
429C22#1171847211yescharacteristic
430C22#1171847311yescharacteristic
431C22#1171848712yes—
432C22#1171862111yescharacteristic
433C22#1171883011yescharacteristic
434C22#1171884811yescharacteristic
435C4—21no—
436C4—21no—
437C4—21no—
438C4—21no—
439C4—44no—
440C4—81no—
441C4—81no—
442C4—522no—
443C4—1041no—
444C4—1042no—
445C4—1042no—
446C2—21no—
447C2—21no—
448C2—21no—
449C2—21no—
450C2#1311383612yes—
451C2#1311384512yes—
452C2#1311583811yescharacteristic
453C2#1311587111yescharacteristic
454C2#1311596611yescharacteristic
subgroupG/H
centerC23#88136
commutator, cosocleC23×C4×C13C23
FrattiniC23×C4C22×D13
FittingC2×C13×#328C2
socleC23×C13#120
prime radicalC24×C13C2×D4
hypercenterC2×#328D13
hypocenterC13#9927
LCSG ▷ C23×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#328

Complements

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

NH ≅ G/Ntype
364. C13#9927semidirect

Maximal subgroups

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

subgroupindex
C2×#117187042
#131206512
C2×#117183222
#131149232
C2×#117180612
#131127152
C2×C13×#3282
#992713