Finite Group Databasebeta

← #15757975

Subgroups — #15757975

Order 3328.

660 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718641C211yesmaximal, characteristic
2#13117453C211yesmaximal, characteristic
3#13114922C211yesmaximal, characteristic
4C2×#11718061C211yesmaximal, characteristic
5#13112716C211yesmaximal, characteristic
6#13112714C211yesmaximal, characteristic
7C13×#1823C211yesmaximal, characteristic
8C22×C13×C4⋊C4C2211yescharacteristic
9C22×#6101—21no—
10C22×#6101C2211yescharacteristic
11C2×#88131—21no—
12C2×C13×C22⋊C8C2211yescharacteristic
13C13×#380C2211yescharacteristic
14#11718873C2211yescharacteristic
15C2×#88071—21no—
16C2×#88071C2211yescharacteristic
17C2×C22⋊#1055C2211yescharacteristic
18#11718641—22no—
19#11718641C414yescomplemented
20#11718633—22no—
21#11718603—21no—
22#11718308—22no—
23C13×#340—22no—
24#11718121—22no—
25#11718061—22no—
26C23×C4×C13—21no—
27C23×C4×C13C2311yescharacteristic
28C23×Dic13—21no—
29C23×Dic13D411yescharacteristic
30C23×Dic13D411yescharacteristic
31C22×C8×C13—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4—21no—
35C2×C13×C4⋊C4—21no—
36C2×C13×C4⋊C4—21no—
37C2×C13×C4⋊C4C2×C412yes—
38C2×C13×C4⋊C4D412yes—
39C2×C13×C22⋊C4—21no—
40C2×C22⋊Dic13—21no—
41C2×C4⋊Dic13D412yes—
42C2×#6101—21no—
43C2×#6101—21no—
44C2×#6101—21no—
45C2×#6101—21no—
46C2×#6101—22no—
47C2×#6101—24no—
48C2×#6101—22no—
49C2×#6101—42no—
50C2×#6101—42no—
51C2×#6101C2×C412yes—
52C2×#6101D412yes—
53C2×C4×Dic13—22no—
54C22×#1055—21no—
55#88131—42no—
56#88131—42no—
57C13×C22⋊C8—21no—
58C13×C22⋊C8—21no—
59C13×#95—21no—
60#88071—22no—
61#88071—21no—
62#88071—21no—
63#88071—24no—
64#88071C2×C412yes—
65C22⋊#1055—21no—
66C22⋊#1055—21no—
67#9027—131nomaximal, Sylow
68C24×C13C2×D411yescharacteristic
69C22×C4×C13—22no—
70C22×C4×C13—22no—
71C22×C4×C13—42no—
72C22×C4×C13—41no—
73C22×C4×C13—41no—
74C22×C4×C13—41no—
75C22×C4×C13—41no—
76C22×C4×C13—41no—
77C22×C4×C13—41no—
78C22×C4×C13C22×C411yescharacteristic
79C22×C4×C13C2×D411yescharacteristic
80C22×C4×C13C2×D411yescharacteristic
81C22×C4×C13C2×D411yescharacteristic
82C22×C4×C13#4111yescharacteristic
83C22×C4×C13#4111yescharacteristic
84C22×Dic13—21no—
85C22×Dic13—21no—
86C22×Dic13—21no—
87C22×Dic13—21no—
88C22×Dic13—24no—
89C22×Dic13—22no—
90C22×Dic13—21no—
91C22×Dic13—21no—
92C22×Dic13—22no—
93C22×Dic13—42no—
94C22×Dic13—41no—
95C22×Dic13—41no—
96C22×Dic13—42no—
97C22×Dic13C22⋊C412yes—
98C22×Dic13C22⋊C412yes—
99C22×Dic13D812yes—
100C22×Dic13SD1612yes—
101C2×C8×C13—42no—
102C2×C8×C13—41no—
103C13×C4⋊C4—22no—
104C13×C4⋊C4—22no—
105C13×C4⋊C4—42no—
106C13×C4⋊C4—41no—
107C13×C4⋊C4—41no—
108C13×C22⋊C4—41no—
109C13×C22⋊C4—41no—
110C22⋊Dic13—41no—
111C22⋊Dic13—41no—
112C4⋊Dic13—42no—
113#6101—22no—
114#6101—22no—
115#6101—22no—
116#6101—22no—
117#6101—44no—
118#6101—48no—
119#6101—82no—
120C4×Dic13—44no—
121C2×#1055—42no—
122C2×#1055—41no—
123C2×#398—131no—
124#2316—131no—
125#1823—131no—
126#1823D1311yescharacteristic
127C2×#324—131no—
128#1294—131no—
129#1294—131no—
130C23×C13—22no—
131C23×C13—22no—
132C23×C13C2×C22⋊C411yescharacteristic
133C23×C13#12011yescharacteristic
134C23×C13#12311yescharacteristic
135C23×C13C2×D811yescharacteristic
136C23×C13C2×SD1611yescharacteristic
137C23×C13AGL(1,ℤ/8)11yescharacteristic
138C23×C13#13711yescharacteristic
139C2×C4×C13—22no—
140C2×C4×C13—22no—
141C2×C4×C13—41no—
142C2×C4×C13—41no—
143C2×C4×C13—41no—
144C2×C4×C13—41no—
145C2×C4×C13—42no—
146C2×C4×C13—42no—
147C2×C4×C13—42no—
148C2×C4×C13—42no—
149C2×C4×C13—42no—
150C2×C4×C13—42no—
151C2×C4×C13—81no—
152C2×C4×C13—81no—
153C2×C4×C13—81no—
154C2×C4×C13—81no—
155C2×C4×C13C4×D411yescharacteristic
156C2×C4×C13C4×D411yescharacteristic
157C2×C4×C13#12111yescharacteristic
158C2×C4×C13#12111yescharacteristic
159C2×Dic13—22no—
160C2×Dic13—22no—
161C2×Dic13—22no—
162C2×Dic13—22no—
163C2×Dic13—22no—
164C2×Dic13—22no—
165C2×Dic13—24no—
166C2×Dic13—22no—
167C2×Dic13—44no—
168C2×Dic13—44no—
169C2×Dic13—42no—
170C2×Dic13—42no—
171C2×Dic13—42no—
172C2×Dic13—42no—
173C2×Dic13—42no—
174C2×Dic13—42no—
175C2×Dic13—42no—
176C2×Dic13—81no—
177C2×Dic13#10214yes—
178C8×C13—81no—
179#1055—81no—
180C2×#117—261no—
181C22×C4⋊C4—131no—
182C22×C4⋊C4—261no—
183C22×C4⋊C4C2×D1311yescharacteristic
184C2×C22⋊C8—131no—
185C2×C22⋊C8C2×D1311yescharacteristic
186#398—134no—
187#398—262no—
188#389—262no—
189#389—262no—
190#380—131no—
191#380—261no—
192#380C2×D1311yescharacteristic
193C2×#95—131no—
194C2×#95—261no—
195#340—22no—
196#340—262no—
197#324—262no—
198C22×C13—22no—
199C22×C13—22no—
200C22×C13—22no—
201C22×C13—22no—
202C22×C13—21no—
203C22×C13—21no—
204C22×C13—21no—
205C22×C13—21no—
206C22×C13#38611yescharacteristic
207C22×C13C2×#10211yescharacteristic
208C22×C13#41711yescharacteristic
209C22×C13#44711yescharacteristic
210C22×C13#44811yescharacteristic
211C22×C13#45612yes—
212C22×C13#45812yes—
213C22×C13#48011yescharacteristic
214C22×C13#48111yescharacteristic
215C4×C13—21no—
216C4×C13—21no—
217C4×C13—21no—
218C4×C13—21no—
219C4×C13—82no—
220C4×C13—82no—
221Dic13—24no—
222Dic13—44no—
223Dic13—42no—
224Dic13—82no—
225C23×C4—21no—
226C23×C4—131no—
227C23×C4—131no—
228C23×C4—261no—
229C23×C4C22×D1311yescharacteristic
230C22×C8—21no—
231C22×C8—261no—
232#117—522no—
233#117—522no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—132no—
240C2×C4⋊C4—132no—
241C2×C4⋊C4—132no—
242C2×C4⋊C4—261no—
243C2×C4⋊C4—261no—
244C2×C4⋊C4—261no—
245C2×C4⋊C4—261no—
246C2×C4⋊C4—264no—
247C2×C4⋊C4—262no—
248C2×C4⋊C4—262no—
249C2×C4⋊C4—522no—
250C2×C4⋊C4—522no—
251C2×C4⋊C4C4×D1312yes—
252C2×C4⋊C4C22⋊D1312yes—
253C2×C22⋊C4—21no—
254C2×C22⋊C4—261no—
255C2×C42—262no—
256C22⋊C8—21no—
257C22⋊C8—21no—
258C22⋊C8—261no—
259C22⋊C8—261no—
260#95—21no—
261#95—132no—
262#95—264no—
263#95—262no—
264#95—261no—
265#95—261no—
266C2×C13—21no—
267C2×C13—21no—
268C2×C13—21no—
269C2×C13—21no—
270C2×C13#161012yes—
271C2×C13#161112yes—
272C2×C13#187411yescharacteristic
273C2×C13#188611yescharacteristic
274C2×C13#189011yescharacteristic
275C24D4×D1311yescharacteristic
276C22×C4—22no—
277C22×C4—22no—
278C22×C4—42no—
279C22×C4—41no—
280C22×C4—41no—
281C22×C4—41no—
282C22×C4—41no—
283C22×C4—41no—
284C22×C4—41no—
285C22×C4—132no—
286C22×C4—132no—
287C22×C4—132no—
288C22×C4—132no—
289C22×C4—261no—
290C22×C4—261no—
291C22×C4—261no—
292C22×C4—261no—
293C22×C4—264no—
294C22×C4—262no—
295C22×C4—261no—
296C22×C4—261no—
297C22×C4—262no—
298C22×C4—522no—
299C22×C4—521no—
300C22×C4—521no—
301C22×C4—522no—
302C22×C4C2×C4×D1311yescharacteristic
303C22×C4#612711yescharacteristic
304C22×C4D4×D1311yescharacteristic
305C22×C4D4×D1311yescharacteristic
306C22×C4#612911yescharacteristic
307C22×C4C2×C22⋊D1311yescharacteristic
308C2×C8—42no—
309C2×C8—41no—
310C2×C8—522no—
311C2×C8—521no—
312C4⋊C4—22no—
313C4⋊C4—22no—
314C4⋊C4—42no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4—262no—
318C4⋊C4—262no—
319C4⋊C4—262no—
320C4⋊C4—262no—
321C4⋊C4—522no—
322C4⋊C4—528no—
323C4⋊C4—524no—
324C4⋊C4—1042no—
325C22⋊C4—41no—
326C22⋊C4—41no—
327C22⋊C4—521no—
328C22⋊C4—521no—
329C42—524no—
330C13#902711yescharacteristic, complemented, Sylow
331C23—22no—
332C23—22no—
333C23C22⋊C4×D1311yescharacteristic
334C23#8813711yescharacteristic
335C23D8×D1311yescharacteristic
336C23#8816511yescharacteristic
337C23SD16×D1311yescharacteristic
338C23#8816911yescharacteristic
339C23#8819111yescharacteristic
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—81no—
353C2×C4—81no—
354C2×C4—81no—
355C2×C4—81no—
356C2×C4—134no—
357C2×C4—262no—
358C2×C4—262no—
359C2×C4—262no—
360C2×C4—262no—
361C2×C4—262no—
362C2×C4—262no—
363C2×C4—264no—
364C2×C4—262no—
365C2×C4—522no—
366C2×C4—524no—
367C2×C4—524no—
368C2×C4—522no—
369C2×C4—522no—
370C2×C4—522no—
371C2×C4—522no—
372C2×C4—522no—
373C2×C4—522no—
374C2×C4—1041no—
375C2×C4#8813511yescharacteristic
376C2×C4#8813811yescharacteristic
377C2×C4C4×C22⋊D1311yescharacteristic
378C2×C4#8819211yescharacteristic
379C8—81no—
380C8—1041no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—22no—
386C22—22no—
387C22—22no—
388C22—22no—
389C22D13×#10211yescharacteristic
390C22#1171843211yescharacteristic
391C22#1171843511yescharacteristic
392C22#1171843811yescharacteristic
393C22#1171861711yescharacteristic
394C22#1171871412yes—
395C22#1171881711yescharacteristic
396C22#1171883111yescharacteristic
397C22#1171886612yes—
398C4—21no—
399C4—21no—
400C4—21no—
401C4—21no—
402C4—82no—
403C4—82no—
404C4—264no—
405C4—524no—
406C4—522no—
407C4—1042no—
408C2—21no—
409C2—21no—
410C2—21no—
411C2—21no—
412C2#1311383712yes—
413C2#1311384212yes—
414C2#1311515011yescharacteristic
415C2#1311522611yescharacteristic
416C2#1311524611yescharacteristic
subgroupG/H
centerC23#88191
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#1823C2
socleC23×C13#120
prime radicalC24×C13C2×D4
cosocleC23×C4×C13C23
hypercenter#1823D13
hypocenterC13#9027
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1823

Complements

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

NH ≅ G/Ntype
19. #11718641C4semidirect
330. C13#9027semidirect

Maximal subgroups

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

subgroupindex
C2×#117186412
#131174532
#131149222
C2×#117180612
#131127162
#131127142
C13×#18232
#902713