Finite Group Databasebeta

← #15757957

Subgroups — #15757957

Order 3328.

616 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718320C211yesmaximal, characteristic
2#13117453C211yesmaximal, characteristic
3#13114927C211yesmaximal, characteristic
4#13114924C211yesmaximal, characteristic
5C2×#11718061C211yesmaximal, characteristic
6#13112715C211yesmaximal, characteristic
7C13×#1294C211yesmaximal, characteristic
8C22×C4⋊Dic13C2211yescharacteristic
9C22×#6101C2211yescharacteristic
10C2×#88131—21no—
11C2×C13×C22⋊C8C2211yescharacteristic
12C13×#380C2211yescharacteristic
13C2×C13×#95C2211yescharacteristic
14#11718873C2211yescharacteristic
15C2×#88071—21no—
16C2×#88071—21no—
17C2×C22⋊#1055C2211yescharacteristic
18#11718633—22no—
19#11718603—21no—
20#11718320—22no—
21#11718320C414yescomplemented
22#11718308—22no—
23#11718143—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⋊C4D412yes—
33C2×C13×C22⋊C4—21no—
34C2×C22⋊Dic13—21no—
35C2×C4⋊Dic13—21no—
36C2×C4⋊Dic13—21no—
37C2×C4⋊Dic13—21no—
38C2×C4⋊Dic13—21no—
39C2×C4⋊Dic13—21no—
40C2×C4⋊Dic13C2×C412yes—
41C2×C4⋊Dic13D412yes—
42C2×#6101—21no—
43C2×#6101—21no—
44C2×#6101—21no—
45C2×#6101—21no—
46C2×#6101—22no—
47C2×#6101—22no—
48C2×#6101C2×C412yes—
49C2×#6101D412yes—
50C2×C4×Dic13—22no—
51C22×#1055—21no—
52#88131—42no—
53#88131—42no—
54C13×C22⋊C8—21no—
55C13×C22⋊C8—21no—
56C13×#95—21no—
57C13×#95—21no—
58C13×#95C2×C412yes—
59#88071—22no—
60#88071—21no—
61#88071—24no—
62#88071—24no—
63C22⋊#1055—21no—
64C22⋊#1055—21no—
65#9023—131nomaximal, Sylow
66C24×C13C2×D411yescharacteristic
67C22×C4×C13—22no—
68C22×C4×C13—22no—
69C22×C4×C13—42no—
70C22×C4×C13—42no—
71C22×C4×C13—42no—
72C22×C4×C13—41no—
73C22×C4×C13—41no—
74C22×C4×C13C22×C411yescharacteristic
75C22×C4×C13C2×D411yescharacteristic
76C22×C4×C13C2×D411yescharacteristic
77C22×C4×C13C2×D411yescharacteristic
78C22×C4×C13#4111yescharacteristic
79C22×C4×C13#4111yescharacteristic
80C22×Dic13—21no—
81C22×Dic13—21no—
82C22×Dic13—21no—
83C22×Dic13—21no—
84C22×Dic13—21no—
85C22×Dic13—21no—
86C22×Dic13—22no—
87C22×Dic13—22no—
88C22×Dic13—42no—
89C22×Dic13—44no—
90C22×Dic13—41no—
91C22×Dic13—41no—
92C22×Dic13C22⋊C412yes—
93C22×Dic13C22⋊C412yes—
94C22×Dic13SD1612yes—
95C22×Dic13Q1612yes—
96C2×C8×C13—42no—
97C2×C8×C13—41no—
98C13×C4⋊C4—42no—
99C13×C22⋊C4—41no—
100C13×C22⋊C4—41no—
101C22⋊Dic13—41no—
102C22⋊Dic13—41no—
103C4⋊Dic13—22no—
104C4⋊Dic13—22no—
105C4⋊Dic13—41no—
106C4⋊Dic13—41no—
107C4⋊Dic13—42no—
108#6101—22no—
109#6101—22no—
110#6101—22no—
111#6101—22no—
112#6101—44no—
113#6101—82no—
114C4×Dic13—44no—
115C2×#1055—42no—
116C2×#1055—41no—
117C2×#400—131no—
118#2316—131no—
119#1824—131no—
120#1824—131no—
121C2×#324—131no—
122#1294—131no—
123#1294D1311yescharacteristic
124C23×C13—22no—
125C23×C13—22no—
126C23×C13C2×C22⋊C411yescharacteristic
127C23×C13#12011yescharacteristic
128C23×C13#12311yescharacteristic
129C23×C13C2×SD1611yescharacteristic
130C23×C13C2×Q1611yescharacteristic
131C23×C13AGL(1,ℤ/8)11yescharacteristic
132C23×C13#13711yescharacteristic
133C2×C4×C13—22no—
134C2×C4×C13—22no—
135C2×C4×C13—41no—
136C2×C4×C13—41no—
137C2×C4×C13—41no—
138C2×C4×C13—41no—
139C2×C4×C13—42no—
140C2×C4×C13—42no—
141C2×C4×C13—42no—
142C2×C4×C13—42no—
143C2×C4×C13—42no—
144C2×C4×C13—42no—
145C2×C4×C13—82no—
146C2×C4×C13—82no—
147C2×C4×C13C4×D411yescharacteristic
148C2×C4×C13C4×D411yescharacteristic
149C2×C4×C13#12111yescharacteristic
150C2×C4×C13#12111yescharacteristic
151C2×Dic13—22no—
152C2×Dic13—22no—
153C2×Dic13—22no—
154C2×Dic13—22no—
155C2×Dic13—22no—
156C2×Dic13—22no—
157C2×Dic13—22no—
158C2×Dic13—42no—
159C2×Dic13—42no—
160C2×Dic13—44no—
161C2×Dic13—42no—
162C2×Dic13—42no—
163C2×Dic13—42no—
164C2×Dic13—42no—
165C2×Dic13—81no—
166C2×Dic13—82no—
167C2×Dic13—82no—
168C2×Dic13#10314yes—
169C8×C13—81no—
170#1055—81no—
171C2×#117—261no—
172C22×C4⋊C4—131no—
173C22×C4⋊C4—131no—
174C2×C22⋊C8—131no—
175C2×C22⋊C8C2×D1311yescharacteristic
176#400—134no—
177#400—262no—
178#389—262no—
179#389—262no—
180#380—131no—
181#380—261no—
182#380C2×D1311yescharacteristic
183C2×#95—261no—
184C2×#95—261no—
185C2×#95C2×D1311yescharacteristic
186#340—262no—
187#340—262no—
188#324—262no—
189C22×C13—22no—
190C22×C13—22no—
191C22×C13—22no—
192C22×C13—22no—
193C22×C13—21no—
194C22×C13—21no—
195C22×C13—21no—
196C22×C13—21no—
197C22×C13#38611yescharacteristic
198C22×C13C2×#10311yescharacteristic
199C22×C13#41711yescharacteristic
200C22×C13#45011yescharacteristic
201C22×C13#45111yescharacteristic
202C22×C13#45412yes—
203C22×C13#45812yes—
204C22×C13#48311yescharacteristic
205C22×C13#48411yescharacteristic
206C4×C13—21no—
207C4×C13—21no—
208C4×C13—21no—
209C4×C13—21no—
210C4×C13—82no—
211C4×C13—82no—
212Dic13—24no—
213Dic13—42no—
214Dic13—82no—
215Dic13—82no—
216C23×C4—21no—
217C23×C4—131no—
218C23×C4—131no—
219C23×C4—261no—
220C23×C4C22×D1311yescharacteristic
221C22×C8—21no—
222C22×C8—261no—
223#117—522no—
224#117—522no—
225C2×C4⋊C4—132no—
226C2×C4⋊C4—132no—
227C2×C4⋊C4—132no—
228C2×C4⋊C4—132no—
229C2×C4⋊C4—261no—
230C2×C4⋊C4—261no—
231C2×C4⋊C4—261no—
232C2×C4⋊C4—261no—
233C2×C4⋊C4—261no—
234C2×C4⋊C4—261no—
235C2×C4⋊C4—261no—
236C2×C4⋊C4—261no—
237C2×C4⋊C4—262no—
238C2×C4⋊C4—261no—
239C2×C4⋊C4—262no—
240C2×C4⋊C4D5212yes—
241C2×C22⋊C4—21no—
242C2×C22⋊C4—261no—
243C2×C42—262no—
244C22⋊C8—21no—
245C22⋊C8—21no—
246C22⋊C8—261no—
247C22⋊C8—261no—
248#95—21no—
249#95—21no—
250#95—264no—
251#95—264no—
252#95—262no—
253#95—261no—
254#95C4×D1312yes—
255C2×C13—21no—
256C2×C13—21no—
257C2×C13—21no—
258C2×C13—21no—
259C2×C13#161612yes—
260C2×C13#161712yes—
261C2×C13#187211yescharacteristic
262C2×C13#188811yescharacteristic
263C2×C13#189011yescharacteristic
264C24D4×D1311yescharacteristic
265C22×C4—22no—
266C22×C4—22no—
267C22×C4—42no—
268C22×C4—42no—
269C22×C4—42no—
270C22×C4—41no—
271C22×C4—41no—
272C22×C4—132no—
273C22×C4—132no—
274C22×C4—132no—
275C22×C4—132no—
276C22×C4—261no—
277C22×C4—261no—
278C22×C4—261no—
279C22×C4—261no—
280C22×C4—261no—
281C22×C4—261no—
282C22×C4—262no—
283C22×C4—262no—
284C22×C4—522no—
285C22×C4—524no—
286C22×C4—521no—
287C22×C4—521no—
288C22×C4C2×C4×D1311yescharacteristic
289C22×C4C2×D5211yescharacteristic
290C22×C4#612711yescharacteristic
291C22×C4D4×D1311yescharacteristic
292C22×C4D4×D1311yescharacteristic
293C22×C4#613111yescharacteristic
294C2×C8—42no—
295C2×C8—41no—
296C2×C8—522no—
297C2×C8—521no—
298C4⋊C4—42no—
299C4⋊C4—262no—
300C4⋊C4—262no—
301C4⋊C4—262no—
302C4⋊C4—262no—
303C4⋊C4—262no—
304C4⋊C4—262no—
305C4⋊C4—522no—
306C4⋊C4—524no—
307C4⋊C4—521no—
308C4⋊C4—521no—
309C4⋊C4—1042no—
310C22⋊C4—41no—
311C22⋊C4—41no—
312C22⋊C4—521no—
313C22⋊C4—521no—
314C42—524no—
315C13#902311yescharacteristic, complemented, Sylow
316C23—22no—
317C23—22no—
318C23C22⋊C4×D1311yescharacteristic
319C23#8813611yescharacteristic
320C23#8814811yescharacteristic
321C23#8816511yescharacteristic
322C23SD16×D1311yescharacteristic
323C23#8816911yescharacteristic
324C23Q16×D1311yescharacteristic
325C2×C4—22no—
326C2×C4—22no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—82no—
338C2×C4—82no—
339C2×C4—134no—
340C2×C4—262no—
341C2×C4—262no—
342C2×C4—262no—
343C2×C4—262no—
344C2×C4—262no—
345C2×C4—262no—
346C2×C4—262no—
347C2×C4—522no—
348C2×C4—522no—
349C2×C4—524no—
350C2×C4—522no—
351C2×C4—522no—
352C2×C4—522no—
353C2×C4—522no—
354C2×C4—1041no—
355C2×C4—1042no—
356C2×C4—1042no—
357C2×C4C4×D5211yescharacteristic
358C2×C4#8813811yescharacteristic
359C2×C4#8814711yescharacteristic
360C2×C4#8814911yescharacteristic
361C8—81no—
362C8—1041no—
363C22—22no—
364C22—22no—
365C22—22no—
366C22—22no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22#1171832611yescharacteristic
372C22#1171840312yes—
373C22#1171843211yescharacteristic
374C22#1171843711yescharacteristic
375C22D13×#10311yescharacteristic
376C22#1171846911yescharacteristic
377C22#1171848812yes—
378C22#1171852311yescharacteristic
379C22#1171854511yescharacteristic
380C4—21no—
381C4—21no—
382C4—21no—
383C4—21no—
384C4—82no—
385C4—82no—
386C4—264no—
387C4—522no—
388C4—1042no—
389C4—1042no—
390C2—21no—
391C2—21no—
392C2—21no—
393C2—21no—
394C2#1311387412yes—
395C2#1311387912yes—
396C2#1311514211yescharacteristic
397C2#1311523811yescharacteristic
398C2#1311524811yescharacteristic
subgroupG/H
centerC23#88136
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#1294C2
socleC23×C13#120
prime radicalC24×C13C2×D4
cosocleC23×C4×C13C23
hypercenter#1294D13
hypocenterC13#9023
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1294

Complements

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

NH ≅ G/Ntype
21. #11718320C4semidirect
315. C13#9023semidirect

Maximal subgroups

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

subgroupindex
C2×#117183202
#131174532
#131149272
#131149242
C2×#117180612
#131127152
C13×#12942
#902313