Finite Group Databasebeta

← #15752037

Subgroups — #15752037

Order 3328.

516 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 91 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#13116364C211yesmaximal, characteristic, complemented
2#13116312C211yesmaximal, characteristic, complemented
3#13116239C211yesmaximal, characteristic, complemented
4#13112659C211yesmaximal, characteristic, complemented
5#13112657C211yesmaximal, characteristic, complemented
6#13112657C211yesmaximal, characteristic, complemented
7C13×#2682C211yesmaximal, characteristic
8C2×C13×#123—21no—
9C2×C13×#121—21no—
10C13×#396—21no—
11C13×#394—21no—
12C13×#392—21no—
13C13×#390C2211yescharacteristic
14C13×#390C2211yescharacteristic
15C13×#389C2211yescharacteristic
16C13×#385—21no—
17C2×#88072—21no—
18C2×#88072—21no—
19C2×#88048—21no—
20C2×#88047—21no—
21#11718596C2211yescharacteristic
22#11718121—21no—
23#11718121—21no—
24#11718116C2211yescharacteristic
25#11718116C2211yescharacteristic
26#11718116C2211yescharacteristic
27C22×D4×C13—21no—
28C22×D4×C13—21no—
29C22×D4×C13D411yescharacteristic
30C22×D4×C13D411yescharacteristic
31C23×C4×C13—21no—
32C13×#123—42no—
33C13×#123—42no—
34C13×#121—42no—
35C13×#121—42no—
36C2×C13×C4⋊C4—21no—
37C2×C13×C4⋊C4—21no—
38C2×C13×C4⋊C4D411yescharacteristic
39C2×C13×C4⋊C4D411yescharacteristic
40C2×C13×C4⋊C4D411yescharacteristic
41C2×C13×C4⋊C4D411yescharacteristic
42C2×C13×C22⋊C4—21no—
43C2×C13×C22⋊C4—21no—
44C2×C13×C22⋊C4—21no—
45C2×C13×C22⋊C4—21no—
46C2×C13×C22⋊C4—21no—
47C2×C13×C22⋊C4—21no—
48C2×C13×C22⋊C4—21no—
49C2×C42×C13C2311yescharacteristic
50C2×C4⋊Dic13—21no—
51C2×C4⋊Dic13—21no—
52C2×C4⋊Dic13—21no—
53C22×#1055—21no—
54C22×#1055—21no—
55C22×#1055—21no—
56C13×#95—21no—
57C13×#95—21no—
58#88072—42no—
59#88072—42no—
60#88048—42no—
61#88047—42no—
62#7800—131nomaximal, Sylow
63C24×C13—21no—
64C24×C13—21no—
65C2×D4×C13—21no—
66C2×D4×C13—21no—
67C2×D4×C13—21no—
68C2×D4×C13—41no—
69C2×D4×C13—41no—
70C2×D4×C13—41no—
71C2×D4×C13—41no—
72C2×D4×C13—42no—
73C2×D4×C13—42no—
74C2×D4×C13—42no—
75C2×D4×C13—81no—
76C2×D4×C13—81no—
77C2×D4×C13—81no—
78C2×D4×C13SD1612yes—
79C22×C4×C13—21no—
80C22×C4×C13—21no—
81C22×C4×C13—21no—
82C22×C4×C13—21no—
83C22×C4×C13—42no—
84C22×C4×C13—42no—
85C22×C4×C13—81no—
86C22×C4×C13C2×D411yescharacteristic
87C22×C4×C13C2×D411yescharacteristic
88C22×C4×C13C2×D411yescharacteristic
89C22×Dic13—41no—
90C13×C4⋊C4—21no—
91C13×C4⋊C4—41no—
92C13×C4⋊C4—41no—
93C13×C4⋊C4—41no—
94C13×C4⋊C4—42no—
95C13×C4⋊C4—41no—
96C13×C4⋊C4—41no—
97C13×C4⋊C4D812yes—
98C13×C22⋊C4—42no—
99C13×C22⋊C4—42no—
100C13×C22⋊C4—41no—
101C13×C22⋊C4—41no—
102C13×C22⋊C4—41no—
103C13×C22⋊C4—41no—
104C13×C22⋊C4—41no—
105C13×C22⋊C4—41no—
106C13×C22⋊C4—41no—
107C13×C22⋊C4—41no—
108C13×C22⋊C4—81no—
109C42×C13—41no—
110C4⋊Dic13—41no—
111C4⋊Dic13—41no—
112C4⋊Dic13—41no—
113C4⋊Dic13—41no—
114C4⋊Dic13—41no—
115C4⋊Dic13—41no—
116C2×#1055—22no—
117C2×#1055—22no—
118C2×#1055—41no—
119C2×#1055—41no—
120C2×#1055—41no—
121C2×#1055—41no—
122C2×#1055—41no—
123C2×#1055—41no—
124C2×#1055—41no—
125#2682D1311yescharacteristic
126#2093—131no—
127#2084—131no—
128#2071—131no—
129#1271—131no—
130#1270—131no—
131#1270—131no—
132C23×C13—22no—
133C23×C13—41no—
134C23×C13—41no—
135C23×C13—41no—
136C23×C13—41no—
137C23×C13—41no—
138C23×C13—41no—
139C23×C13—41no—
140C23×C13—41no—
141C23×C13—41no—
142C23×C13—41no—
143C23×C13—41no—
144C23×C13—41no—
145C23×C13—41no—
146C23×C13#12011yescharacteristic
147D4×C13—42no—
148D4×C13—42no—
149D4×C13—81no—
150D4×C13—81no—
151D4×C13—84no—
152D4×C13—84no—
153C2×C4×C13—21no—
154C2×C4×C13—21no—
155C2×C4×C13—21no—
156C2×C4×C13—21no—
157C2×C4×C13—21no—
158C2×C4×C13—21no—
159C2×C4×C13—22no—
160C2×C4×C13—41no—
161C2×C4×C13—41no—
162C2×C4×C13—41no—
163C2×C4×C13—41no—
164C2×C4×C13—41no—
165C2×C4×C13—41no—
166C2×C4×C13—41no—
167C2×C4×C13—41no—
168C2×C4×C13—41no—
169C2×C4×C13—41no—
170C2×C4×C13—41no—
171C2×C4×C13—84no—
172C2×C4×C13C2×D811yescharacteristic
173C2×C4×C13C2×SD1611yescharacteristic
174C2×C4×C13#13511yescharacteristic
175C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
176C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
177C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
178C2×Dic13—81no—
179C2×Dic13—81no—
180C2×Dic13—81no—
181#1055—42no—
182#1055—42no—
183#1055—81no—
184C2×#123—21no—
185C2×#121—21no—
186C2×#107—261no—
187C2×#106—261no—
188C2×#102—261no—
189C2×#102—261no—
190#396—21no—
191#394—21no—
192#392—21no—
193#390C2×D1311yescharacteristic
194#390C2×D1311yescharacteristic
195#389C2×D1311yescharacteristic
196#385—21no—
197#384—131no—
198#340—261no—
199#340—261no—
200#336—131no—
201#336—131no—
202#336—131no—
203C22×C13—42no—
204C22×C13—42no—
205C22×C13—42no—
206C22×C13—81no—
207C22×C13—81no—
208C22×C13—81no—
209C22×C13—81no—
210C22×C13—81no—
211C22×C13—81no—
212C22×C13—81no—
213C22×C13—81no—
214C22×C13—81no—
215C22×C13—81no—
216C22×C13—81no—
217C22×C13#44711yescharacteristic
218C22×C13#44911yescharacteristic
219C22×C13#45011yescharacteristic
220C22×C13#45311yescharacteristic
221C22×C13#45511yescharacteristic
222C22×C13#45611yescharacteristic
223C22×C13#45811yescharacteristic
224C4×C13—21no—
225C4×C13—21no—
226C4×C13—21no—
227C4×C13—21no—
228C4×C13—21no—
229C4×C13—21no—
230C4×C13—42no—
231C4×C13—81no—
232C4×C13—81no—
233C4×C13—81no—
234Dic13—161no—
235C22×D4—21no—
236C22×D4—21no—
237C22×D4C22⋊D1311yescharacteristic
238C22×D4C22⋊D1311yescharacteristic
239C23×C4—21no—
240C22×C8—261no—
241C22×C8—261no—
242C22×C8—261no—
243#123—42no—
244#123—42no—
245#121—42no—
246#121—42no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—261no—
250C2×C4⋊C4—261no—
251C2×C4⋊C4—261no—
252C2×C4⋊C4C22⋊D1311yescharacteristic
253C2×C4⋊C4C22⋊D1311yescharacteristic
254C2×C4⋊C4C22⋊D1311yescharacteristic
255C2×C4⋊C4C22⋊D1311yescharacteristic
256C2×C22⋊C4—21no—
257C2×C22⋊C4—21no—
258C2×C22⋊C4—21no—
259C2×C22⋊C4—21no—
260C2×C22⋊C4—21no—
261C2×C22⋊C4—21no—
262C2×C22⋊C4—21no—
263C2×C42C22×D1311yescharacteristic
264#107—522no—
265#106—522no—
266#102—522no—
267#102—522no—
268#95—21no—
269#95—21no—
270C2×C13—82no—
271C2×C13—161no—
272C2×C13#161011yescharacteristic
273C2×C13#161211yescharacteristic
274C2×C13#161311yescharacteristic
275C2×C13#162111yescharacteristic
276C2×C13#163911yescharacteristic
277C2×C13#165411yescharacteristic
278C2×C13#166111yescharacteristic
279C24—21no—
280C24—21no—
281C2×D4—21no—
282C2×D4—21no—
283C2×D4—21no—
284C2×D4—41no—
285C2×D4—41no—
286C2×D4—41no—
287C2×D4—41no—
288C2×D4—42no—
289C2×D4—42no—
290C2×D4—42no—
291C2×D4—81no—
292C2×D4—81no—
293C2×D4—81no—
294C2×D4#610512yes—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—42no—
300C22×C4—42no—
301C22×C4—81no—
302C22×C4—521no—
303C22×C4C2×C22⋊D1311yescharacteristic
304C22×C4C2×C22⋊D1311yescharacteristic
305C22×C4C2×C22⋊D1311yescharacteristic
306C2×C8—262no—
307C2×C8—262no—
308C2×C8—521no—
309C2×C8—521no—
310C2×C8—521no—
311C2×C8—521no—
312C2×C8—521no—
313C2×C8—521no—
314C2×C8—521no—
315C4⋊C4—21no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—42no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4—521no—
323C4⋊C4—521no—
324C4⋊C4—521no—
325C4⋊C4—521no—
326C4⋊C4—521no—
327C4⋊C4—521no—
328C4⋊C4#610412yes—
329C22⋊C4—42no—
330C22⋊C4—42no—
331C22⋊C4—41no—
332C22⋊C4—41no—
333C22⋊C4—41no—
334C22⋊C4—41no—
335C22⋊C4—41no—
336C22⋊C4—41no—
337C22⋊C4—41no—
338C22⋊C4—41no—
339C22⋊C4—81no—
340C42—41no—
341C13#780011yescharacteristic, complemented, Sylow
342C23—22no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23—41no—
348C23—41no—
349C23—41no—
350C23—41no—
351C23—41no—
352C23—41no—
353C23—41no—
354C23—41no—
355C23—41no—
356C23#8820711yescharacteristic
357D4—42no—
358D4—42no—
359D4—81no—
360D4—81no—
361D4—84no—
362D4—84no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—22no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—84no—
382C2×C4—1041no—
383C2×C4—1041no—
384C2×C4—1041no—
385C2×C4C2×#610411yescharacteristic
386C2×C4#8818611yescharacteristic
387C2×C4#8818611yescharacteristic
388C2×C4C2×#610511yescharacteristic
389C2×C4#8820311yescharacteristic
390C2×C4#8820411yescharacteristic
391C8—522no—
392C8—522no—
393C8—1041no—
394C22—42no—
395C22—42no—
396C22—42no—
397C22—81no—
398C22—81no—
399C22—81no—
400C22—81no—
401C22—81no—
402C22—81no—
403C22—81no—
404C22—81no—
405C22—81no—
406C22—81no—
407C22—81no—
408C22#1171887811yescharacteristic
409C22#1171887911yescharacteristic
410C22#1171889911yescharacteristic
411C22#1171890211yescharacteristic
412C22#1171890311yescharacteristic
413C22#1171890411yescharacteristic
414C22#1171890711yescharacteristic
415C4—21no—
416C4—21no—
417C4—21no—
418C4—21no—
419C4—21no—
420C4—21no—
421C4—42no—
422C4—81no—
423C4—81no—
424C4—81no—
425C4—2081no—
426C2—82no—
427C2—161no—
428C2#1311383911yescharacteristic
429C2#1311385011yescharacteristic
430C2#1311385611yescharacteristic
431C2#1311390111yescharacteristic
432C2#1311401511yescharacteristic
433C2#1311412011yescharacteristic
434C2#1311415311yescharacteristic
subgroupG/H
centerC23#88207
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
Fitting, prime radicalC13×#2682C2
socleC23×C13#120
hypercenter#2682D13
hypocenterC13#7800
LCSG ▷ C2×C42×C13 ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2682

Complements

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

NH ≅ G/Ntype
1. #13116364C2semidirect
2. #13116312C2semidirect
3. #13116239C2semidirect
4. #13112659C2semidirect
5. #13112657C2semidirect
6. #13112657C2semidirect
341. C13#7800semidirect

Maximal subgroups

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

subgroupindex
#131163642
#131163122
#131162392
#131126592
#131126572
C13×#26822
#780013