Finite Group Databasebeta

← #15766076

Subgroups — #15766076

Order 3328.

466 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 95 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#13119847C211yesmaximal, characteristic
2#13115822C211yesmaximal, characteristic
3#13113408C211yesmaximal, characteristic
4#13112715C211yesmaximal, characteristic
5#13112704C211yesmaximal, characteristic
6#13112682C211yesmaximal, characteristic
7C2×C13×#328C211yesmaximal, characteristic
8C2×C13×C22⋊Q8C2211yescharacteristic
9C2×#88178—21no—
10C2×C13×C22⋊C8C2211yescharacteristic
11C2×C13×#95C2211yescharacteristic
12#11718873C2211yescharacteristic
13#11718873C2211yescharacteristic
14#11718871—21no—
15C4×C22⋊Dic13C2211yescharacteristic
16C2×C22⋊#1055C2211yescharacteristic
17#11718318—21no—
18#11718317—21no—
19#11718308—21no—
20#11718307—21no—
21C13×#328—21no—
22C13×#328—21no—
23#11718130—21no—
24#11718130—21no—
25#11718118—21no—
26#11718118—21no—
27C22×Q8×C13Q811yescharacteristic, complemented
28C23×C4×C13—21no—
29C23×C4×C13C2311yescharacteristic
30C22×Dic26—21no—
31C22×C8×C13—21no—
32C13×C22⋊Q8—21no—
33C13×C22⋊Q8—21no—
34C13×C22⋊Q8—21no—
35C13×C22⋊Q8—21no—
36C2×C13×C4⋊C4—21no—
37C2×C13×C4⋊C4Q811yescharacteristic, complemented
38C2×C13×C22⋊C4—21no—
39C2×C22⋊Dic13—21no—
40C2×C22⋊Dic13—21no—
41C2×C22⋊Dic13D411yescharacteristic
42C2×C22⋊Dic13D411yescharacteristic
43C2×C4⋊Dic13—21no—
44C2×C4⋊Dic13—21no—
45C2×C4⋊Dic13—21no—
46#88178—42no—
47#88178—42no—
48C2×#6101—21no—
49C2×#6101—21no—
50C2×#6101—21no—
51C2×#6101—21no—
52C2×C4×Dic13—21no—
53C22×#1055—21no—
54C13×C22⋊C8—21no—
55C13×C22⋊C8—21no—
56C13×#95—21no—
57C13×#95D411yescharacteristic
58C13×#95D411yescharacteristic
59#88071—21no—
60#88071—21no—
61#88071—21no—
62#88071—21no—
63#88071D411yescharacteristic
64#88071D411yescharacteristic
65C22⋊#1055—21no—
66C22⋊#1055—21no—
67#10375—131nomaximal, Sylow
68C24×C13C2×D411yescharacteristic
69C2×Q8×C13—21no—
70C2×Q8×C13—21no—
71C2×Q8×C13—81no—
72C22×C4×C13—21no—
73C22×C4×C13—21no—
74C22×C4×C13—21no—
75C22×C4×C13—21no—
76C22×C4×C13—42no—
77C22×C4×C13—41no—
78C22×C4×C13—41no—
79C22×C4×C13—81no—
80C22×C4×C13—81no—
81C22×C4×C13C2×D411yescharacteristic
82C22×C4×C13C2×D411yescharacteristic
83C22×C4×C13C2×Q811yescharacteristic
84C22×C4×C13#4111yescharacteristic
85C22×C4×C13#4111yescharacteristic
86C22×C4×C13#4111yescharacteristic
87C22×Dic13—21no—
88C22×Dic13—21no—
89C22×Dic13—21no—
90C22×Dic13—21no—
91C22×Dic13—41no—
92C2×Dic26—42no—
93C2×Dic26—42no—
94C2×Dic26—81no—
95C2×C8×C13—41no—
96C2×C8×C13—81no—
97C13×C4⋊C4—21no—
98C13×C4⋊C4—21no—
99C13×C4⋊C4—41no—
100C13×C4⋊C4—41no—
101C13×C22⋊C4—41no—
102C13×C22⋊C4—41no—
103C22⋊Dic13—21no—
104C22⋊Dic13—21no—
105C22⋊Dic13—41no—
106C22⋊Dic13—41no—
107C22⋊Dic13—41no—
108C22⋊Dic13—41no—
109C22⋊Dic13SD1612yes—
110C22⋊Dic13Q1612yes—
111C4⋊Dic13—42no—
112C4⋊Dic13—81no—
113C4⋊Dic13—81no—
114#6101—42no—
115#6101—42no—
116#6101—42no—
117#6101—81no—
118C4×Dic13—81no—
119C2×#1055—41no—
120C2×#1055—81no—
121#2549—131no—
122#1996—131no—
123#1520—131no—
124C2×#328D1311yescharacteristic
125#1294—131no—
126#1289—131no—
127#1282—131no—
128C23×C13—41no—
129C23×C13—41no—
130C23×C13#12011yescharacteristic
131C23×C13C22⋊Q811yescharacteristic
132C23×C13#12411yescharacteristic
133C23×C13C2×SD1611yescharacteristic
134C23×C13C2×Q1611yescharacteristic
135C23×C13AGL(1,ℤ/8)11yescharacteristic
136C23×C13#13711yescharacteristic
137Q8×C13—81no—
138Q8×C13—81no—
139C2×C4×C13—22no—
140C2×C4×C13—41no—
141C2×C4×C13—41no—
142C2×C4×C13—41no—
143C2×C4×C13—41no—
144C2×C4×C13—41no—
145C2×C4×C13—41no—
146C2×C4×C13—41no—
147C2×C4×C13—41no—
148C2×C4×C13—41no—
149C2×C4×C13—41no—
150C2×C4×C13—41no—
151C2×C4×C13—41no—
152C2×C4×C13—41no—
153C2×C4×C13—82no—
154C2×C4×C13—82no—
155C2×C4×C13—81no—
156C2×C4×C13—81no—
157C2×C4×C13C22⋊Q811yescharacteristic
158C2×C4×C13C22⋊Q811yescharacteristic
159C2×C4×C13#12411yescharacteristic
160C2×C4×C13#12411yescharacteristic
161C2×Dic13—22no—
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—
171C2×Dic13—41no—
172C2×Dic13—41no—
173C2×Dic13—81no—
174C2×Dic13—81no—
175C2×Dic13—81no—
176Dic26—84no—
177C8×C13—81no—
178#1055—81no—
179C2×C22⋊Q8—261no—
180C2×C22⋊Q8C2×D1311yescharacteristic
181C2×C22⋊C8—131no—
182C2×C22⋊C8C2×D1311yescharacteristic
183#398—261no—
184#395—261no—
185#391—261no—
186#389—261no—
187#385—261no—
188#380—131no—
189#380—131no—
190C4×C22⋊C4—131no—
191C2×#95C2×D1311yescharacteristic
192#342—261no—
193#342—261no—
194#328—21no—
195#328—21no—
196#328—261no—
197#328—261no—
198C22×C13—21no—
199C22×C13—21no—
200C22×C13—21no—
201C22×C13—21no—
202C22×C13—21no—
203C22×C13—21no—
204C22×C13—41no—
205C22×C13—41no—
206C22×C13—41no—
207C22×C13—41no—
208C22×C13#39311yescharacteristic
209C22×C13#45011yescharacteristic
210C22×C13#45111yescharacteristic
211C22×C13#47511yescharacteristic
212C22×C13#47711yescharacteristic
213C22×C13#48711yescharacteristic
214C22×C13#48911yescharacteristic
215C4×C13—21no—
216C4×C13—21no—
217C4×C13—21no—
218C4×C13—21no—
219C4×C13—42no—
220C4×C13—81no—
221C4×C13—81no—
222C4×C13—81no—
223Dic13—42no—
224Dic13—42no—
225Dic13—81no—
226Dic13—81no—
227Dic13—161no—
228C22×Q8—261no—
229C22×Q8Dic2611yescharacteristic, complemented
230C23×C4—21no—
231C23×C4C22×D1311yescharacteristic
232C22×C8—21no—
233C22×C8—261no—
234C22⋊Q8—21no—
235C22⋊Q8—21no—
236C22⋊Q8—21no—
237C22⋊Q8—21no—
238C22⋊Q8—522no—
239C22⋊Q8—522no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—261no—
242C2×C4⋊C4—261no—
243C2×C4⋊C4—261no—
244C2×C4⋊C4—261no—
245C2×C4⋊C4—261no—
246C2×C4⋊C4—261no—
247C2×C4⋊C4—261no—
248C2×C4⋊C4Dic2611yescharacteristic, complemented
249C2×C22⋊C4—21no—
250C2×C22⋊C4—131no—
251C2×C22⋊C4—131no—
252C2×C22⋊C4—261no—
253C2×C22⋊C4—261no—
254C2×C42—261no—
255C22⋊C8—21no—
256C22⋊C8—21no—
257C22⋊C8—261no—
258C22⋊C8—261no—
259#95—21no—
260#95—131no—
261#95—131no—
262#95—261no—
263#95—261no—
264#95—261no—
265#95—261no—
266#95C22⋊D1311yescharacteristic
267#95C22⋊D1311yescharacteristic
268C2×C13—21no—
269C2×C13—21no—
270C2×C13—21no—
271C2×C13—21no—
272C2×C13—21no—
273C2×C13—21no—
274C2×C13#202411yescharacteristic
275C2×C13#203111yescharacteristic
276C2×C13#203211yescharacteristic
277C24D4×D1311yescharacteristic
278C2×Q8—21no—
279C2×Q8—21no—
280C2×Q8—81no—
281C2×Q8—522no—
282C2×Q8—522no—
283C2×Q8—1041no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—42no—
289C22×C4—41no—
290C22×C4—41no—
291C22×C4—81no—
292C22×C4—81no—
293C22×C4—261no—
294C22×C4—261no—
295C22×C4—261no—
296C22×C4—261no—
297C22×C4—521no—
298C22×C4C2×Dic2611yescharacteristic
299C22×C4#612711yescharacteristic
300C22×C4D4×D1311yescharacteristic
301C22×C4#612911yescharacteristic
302C22×C4#612911yescharacteristic
303C22×C4C2×C22⋊D1311yescharacteristic
304C2×C8—41no—
305C2×C8—81no—
306C2×C8—521no—
307C2×C8—1041no—
308C4⋊C4—21no—
309C4⋊C4—21no—
310C4⋊C4—41no—
311C4⋊C4—41no—
312C4⋊C4—522no—
313C4⋊C4—522no—
314C4⋊C4—522no—
315C4⋊C4—522no—
316C4⋊C4—1041no—
317C4⋊C4—1041no—
318C4⋊C4—1041no—
319C22⋊C4—41no—
320C22⋊C4—41no—
321C22⋊C4—132no—
322C22⋊C4—132no—
323C22⋊C4—261no—
324C22⋊C4—261no—
325C22⋊C4—521no—
326C22⋊C4—521no—
327C22⋊C4—521no—
328C22⋊C4—521no—
329C42—1041no—
330C13#1037511yescharacteristic, complemented, Sylow
331C23—41no—
332C23—41no—
333C23#8813211yescharacteristic
334C23#8813911yescharacteristic
335C23SD16×D1311yescharacteristic
336C23#8816811yescharacteristic
337C23Q16×D1311yescharacteristic
338C23#8817211yescharacteristic
339C23#8819111yescharacteristic
340Q8—81no—
341Q8—81no—
342Q8—1044no—
343C2×C4—22no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—82no—
358C2×C4—82no—
359C2×C4—81no—
360C2×C4—81no—
361C2×C4—262no—
362C2×C4—262no—
363C2×C4—521no—
364C2×C4—521no—
365C2×C4—521no—
366C2×C4—521no—
367C2×C4—521no—
368C2×C4—521no—
369C2×C4—521no—
370C2×C4—521no—
371C2×C4—521no—
372C2×C4—521no—
373C2×C4—1041no—
374C2×C4—1041no—
375C2×C4—1041no—
376C2×C4#8813211yescharacteristic
377C2×C4#8813911yescharacteristic
378C2×C4#8817811yescharacteristic
379C2×C4#8819011yescharacteristic
380C8—81no—
381C8—1041no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22#1171845211yescharacteristic
393C22#1171845311yescharacteristic
394C22#1171845511yescharacteristic
395C22#1171845611yescharacteristic
396C22#1171860811yescharacteristic
397C22#1171883011yescharacteristic
398C22#1171884711yescharacteristic
399C4—21no—
400C4—21no—
401C4—21no—
402C4—21no—
403C4—42no—
404C4—81no—
405C4—81no—
406C4—81no—
407C4—522no—
408C4—522no—
409C4—1041no—
410C4—1041no—
411C4—2081no—
412C2—21no—
413C2—21no—
414C2—21no—
415C2—21no—
416C2—21no—
417C2—21no—
418C2#1311597511yescharacteristic
419C2#1311600811yescharacteristic
420C2#1311601311yescharacteristic
subgroupG/H
centerC22#11718608
commutator, cosocleC23×C4×C13C23
FrattiniC23×C4C22×D13
FittingC2×C13×#328C2
socleC22×C13#393
prime radicalC24×C13C2×D4
hypercenterC2×#328D13
hypocenterC13#10375
LCSG ▷ C23×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#328

Complements

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

NH ≅ G/Ntype
27. C22×Q8×C13Q8semidirect
37. C2×C13×C4⋊C4Q8semidirect
229. C22×Q8Dic26semidirect
248. C2×C4⋊C4Dic26semidirect
330. C13#10375semidirect

Maximal subgroups

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

subgroupindex
#131198472
#131158222
#131134082
#131127152
#131127042
#131126822
C2×C13×#3282
#1037513