Finite Group Databasebeta

← #15766272

Subgroups — #15766272

Order 3328.

576 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 576 conjugacy classes of subgroups — too many to draw. Only its 115 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#13120950C211yesmaximal, characteristic
2#13115143C212yesmaximal
3C2×#11718044C212yesmaximal
4#13112679C211yesmaximal, characteristic
5C13×#1442C211yesmaximal, characteristic
6C22×C13×C4⋊C4C2211yescharacteristic
7C2×#88178C2212yes—
8C2×C13×#95—21no—
9C2×C13×#95—21no—
10C2×C13×#95C2211yescharacteristic
11C2×C13×#95C2211yescharacteristic
12#11718873—21no—
13#11718873—21no—
14C2×C22⋊#1055C2212yes—
15C2×#88050—22no—
16#11718322—22no—
17#11718317—22no—
18#11718121—22no—
19#11718044—24no—
20C23×C4×C13—21no—
21C23×C4×C13—21no—
22C23×C4×C13D411yescharacteristic
23C23×C4×C13D411yescharacteristic
24C23×C4×C13C2311yescharacteristic
25C22×Dic26D412yes—
26C2×C13×C4⋊C4—22no—
27C2×C13×C4⋊C4—42no—
28C2×C22⋊Dic13—22no—
29C2×C4⋊Dic13—21no—
30C2×C4⋊Dic13—21no—
31C2×C4⋊Dic13—21no—
32C2×C4⋊Dic13—21no—
33C2×C4⋊Dic13D412yes—
34#88178—22no—
35#88178—22no—
36#88178—22no—
37#88178—22no—
38C2×#6101—22no—
39C22×#1055—22no—
40C13×#95—22no—
41C13×#95—21no—
42C13×#95—42no—
43C13×#95—42no—
44C13×#95D412yes—
45#88071—22no—
46#88071—22no—
47C22⋊#1055—22no—
48C22⋊#1055—22no—
49#88050—44no—
50#10407—131nomaximal, Sylow
51C24×C13C2×D411yescharacteristic
52C22×C4×C13—21no—
53C22×C4×C13—21no—
54C22×C4×C13—21no—
55C22×C4×C13—21no—
56C22×C4×C13—22no—
57C22×C4×C13—22no—
58C22×C4×C13—41no—
59C22×C4×C13—41no—
60C22×C4×C13—41no—
61C22×C4×C13—41no—
62C22×C4×C13—41no—
63C22×C4×C13—41no—
64C22×C4×C13—41no—
65C22×C4×C13—41no—
66C22×C4×C13—41no—
67C22×C4×C13—41no—
68C22×C4×C13—41no—
69C22×C4×C13—41no—
70C22×C4×C13—41no—
71C22×C4×C13—41no—
72C22×C4×C13—41no—
73C22×C4×C13—41no—
74C22×C4×C13—41no—
75C22×C4×C13—41no—
76C22×C4×C13SD1612yes—
77C22×C4×C13Q1612yes—
78C22×C4×C13C2×D411yescharacteristic
79C22×C4×C13C2×D412yes—
80C22×C4×C13#4111yescharacteristic
81C22×C4×C13#4112yes—
82C22×Dic13—22no—
83C22×Dic13—22no—
84C2×Dic26—22no—
85C2×Dic26—22no—
86C2×Dic26—42no—
87C2×Dic26—42no—
88C13×C4⋊C4—24no—
89C13×C4⋊C4—42no—
90C22⋊Dic13—42no—
91C22⋊Dic13—42no—
92C4⋊Dic13—22no—
93C4⋊Dic13—22no—
94C4⋊Dic13—81no—
95C4⋊Dic13—81no—
96C4⋊Dic13—81no—
97C4⋊Dic13—81no—
98#6101—42no—
99#6101—42no—
100C2×#1055—42no—
101C2×#1055—42no—
102C2×#1055—42no—
103#2659—131no—
104#1872—132no—
105C2×#328—132no—
106#1442D1311yescharacteristic
107#1280—131no—
108C23×C13—21no—
109C23×C13—21no—
110C23×C13—21no—
111C23×C13—21no—
112C23×C13#12011yescharacteristic
113C23×C13#12111yescharacteristic
114C23×C13#12411yescharacteristic
115C23×C13C2×SD1611yescharacteristic
116C23×C13C2×Q1611yescharacteristic
117C23×C13#13711yescharacteristic
118C23×C13#13711yescharacteristic
119C2×C4×C13—22no—
120C2×C4×C13—22no—
121C2×C4×C13—22no—
122C2×C4×C13—22no—
123C2×C4×C13—41no—
124C2×C4×C13—42no—
125C2×C4×C13—41no—
126C2×C4×C13—41no—
127C2×C4×C13—41no—
128C2×C4×C13—41no—
129C2×C4×C13—41no—
130C2×C4×C13—42no—
131C2×C4×C13—42no—
132C2×C4×C13—42no—
133C2×C4×C13—42no—
134C2×C4×C13—42no—
135C2×C4×C13—42no—
136C2×C4×C13—42no—
137C2×C4×C13—42no—
138C2×C4×C13—81no—
139C2×C4×C13—81no—
140C2×C4×C13—81no—
141C2×C4×C13—81no—
142C2×C4×C13—81no—
143C2×C4×C13—81no—
144C2×C4×C13—81no—
145C2×C4×C13—81no—
146C2×C4×C13—81no—
147C2×C4×C13—81no—
148C2×C4×C13#12112yes—
149C2×C4×C13#12312yes—
150C2×Dic13—42no—
151C2×Dic13—42no—
152C2×Dic13—42no—
153C2×Dic13—42no—
154C2×Dic13—42no—
155C2×Dic13—42no—
156Dic26—44no—
157Dic26—82no—
158#1055—82no—
159C2×C22⋊Q8—132no—
160C22×C4⋊C4C2×D1311yescharacteristic
161C2×#103—262no—
162C2×C22⋊C8—132no—
163#398—262no—
164#395—262no—
165#380—261no—
166#380—261no—
167C2×#95—21no—
168C2×#95—21no—
169C2×#95C2×D1311yescharacteristic
170C2×#95C2×D1311yescharacteristic
171#340—262no—
172#328—264no—
173C22×C13—21no—
174C22×C13—21no—
175C22×C13—21no—
176C22×C13—21no—
177C22×C13—21no—
178C22×C13—21no—
179C22×C13—21no—
180C22×C13—21no—
181C22×C13—21no—
182C22×C13—21no—
183C22×C13—21no—
184C22×C13—21no—
185C22×C13#39411yescharacteristic
186C22×C13#44811yescharacteristic
187C22×C13#45111yescharacteristic
188C22×C13#45411yescharacteristic
189C22×C13#45511yescharacteristic
190C22×C13B(4,𝔽2)11yescharacteristic
191C22×C13#45811yescharacteristic
192C22×C13#46111yescharacteristic
193C22×C13#46211yescharacteristic
194C22×C13#48711yescharacteristic
195C22×C13#49111yescharacteristic
196C4×C13—22no—
197C4×C13—22no—
198C4×C13—42no—
199C4×C13—42no—
200C4×C13—82no—
201C4×C13—82no—
202Dic13—82no—
203Dic13—82no—
204C22×Q8—132no—
205C23×C4—21no—
206C23×C4—21no—
207C23×C4C22⋊D1311yescharacteristic
208C23×C4C22⋊D1311yescharacteristic
209C23×C4C22×D1311yescharacteristic
210C22×C8—262no—
211C22⋊Q8—262no—
212C22⋊Q8—262no—
213C22⋊Q8—262no—
214C22⋊Q8—262no—
215C2×C4⋊C4—22no—
216C2×C4⋊C4—42no—
217C2×C4⋊C4—132no—
218C2×C4⋊C4—262no—
219C2×C4⋊C4—261no—
220C2×C4⋊C4—261no—
221C2×C4⋊C4—261no—
222C2×C4⋊C4—261no—
223C2×C22⋊C4—262no—
224#103—524no—
225C22⋊C8—262no—
226C22⋊C8—262no—
227#95—21no—
228#95—22no—
229#95—42no—
230#95—42no—
231#95—262no—
232#95—262no—
233#95D5212yes—
234C2×C13—21no—
235C2×C13—21no—
236C2×C13—21no—
237C2×C13—21no—
238C2×C13#159911yescharacteristic
239C2×C13#160211yescharacteristic
240C2×C13#160811yescharacteristic
241C2×C13#161711yescharacteristic
242C2×C13#204011yescharacteristic
243C2×C13#204311yescharacteristic
244C2×C13#204411yescharacteristic
245C24C2×C22⋊D1311yescharacteristic
246C2×Q8—262no—
247C2×Q8—262no—
248C2×Q8—522no—
249C2×Q8—522no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—22no—
255C22×C4—22no—
256C22×C4—41no—
257C22×C4—41no—
258C22×C4—41no—
259C22×C4—41no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4—41no—
266C22×C4—41no—
267C22×C4—41no—
268C22×C4—41no—
269C22×C4—41no—
270C22×C4—41no—
271C22×C4—41no—
272C22×C4—41no—
273C22×C4—41no—
274C22×C4—262no—
275C22×C4—262no—
276C22×C4#610512yes—
277C22×C4#610712yes—
278C22×C4C2×D5211yescharacteristic
279C22×C4#612711yescharacteristic
280C22×C4D4×D1312yes—
281C22×C4#613112yes—
282C2×C8—522no—
283C2×C8—522no—
284C2×C8—522no—
285C4⋊C4—24no—
286C4⋊C4—42no—
287C4⋊C4—262no—
288C4⋊C4—262no—
289C4⋊C4—522no—
290C4⋊C4—522no—
291C4⋊C4—1041no—
292C4⋊C4—1041no—
293C4⋊C4—1041no—
294C4⋊C4—1041no—
295C22⋊C4—522no—
296C22⋊C4—522no—
297C13#1040711yescharacteristic, complemented, Sylow
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23#8818411yescharacteristic
303C23C2×#610511yescharacteristic
304C23#8819111yescharacteristic
305C23C2×#610711yescharacteristic
306C23#8820111yescharacteristic
307C23#8820511yescharacteristic
308C23#8820511yescharacteristic
309Q8—524no—
310Q8—1042no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—42no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—81no—
331C2×C4—81no—
332C2×C4—81no—
333C2×C4—81no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4—81no—
338C2×C4—81no—
339C2×C4—81no—
340C2×C4—522no—
341C2×C4—522no—
342C2×C4—522no—
343C2×C4—522no—
344C2×C4—522no—
345C2×C4—522no—
346C2×C4#8814812yes—
347C2×C4#8814912yes—
348C8—1042no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22#1171865211yescharacteristic
362C22#1171868011yescharacteristic
363C22#1171869211yescharacteristic
364C22#1171869311yescharacteristic
365C22#1171870111yescharacteristic
366C22#1171871111yescharacteristic
367C22#1171871411yescharacteristic
368C22#1171872211yescharacteristic
369C22#1171872311yescharacteristic
370C22#1171873011yescharacteristic
371C22#1171875411yescharacteristic
372C4—22no—
373C4—22no—
374C4—42no—
375C4—42no—
376C4—82no—
377C4—82no—
378C4—1042no—
379C4—1042no—
380C2—21no—
381C2—21no—
382C2—21no—
383C2—21no—
384C2#1311377511yescharacteristic
385C2#1311379211yescharacteristic
386C2#1311382611yescharacteristic
387C2#1311387711yescharacteristic
388C2#1311606511yescharacteristic
389C2#1311608211yescharacteristic
390C2#1311608711yescharacteristic
subgroupG/H
centerC23#88191
commutator, cosocleC23×C4×C13C23
FrattiniC23×C4C22×D13
FittingC13×#1442C2
socleC23×C13#120
prime radicalC24×C13C2×D4
hypercenter#1442D13
hypocenterC13#10407
LCSG ▷ C23×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1442

Complements

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

NH ≅ G/Ntype
297. C13#10407semidirect

Maximal subgroups

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

subgroupindex
#131209502
#131151432
C2×#117180442
#131126792
C13×#14422
#1040713