Finite Group Databasebeta

← #15773485

Subgroups — #15773485

Order 3328.

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

normal subgroups only

This group has 532 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
1C4×#88074C211yesmaximal, characteristic, complemented
2#13113177C211yesmaximal, characteristic, complemented
3#13112836C212yesmaximal, complemented
4#13112833C212yesmaximal, complemented
5C13×#2543C211yesmaximal, characteristic
6C2×C13×#121—21no—
7C2×C13×#121C411yescharacteristic, complemented
8C2×C4×D4×C13C2211yescharacteristic
9C13×#398C411yescharacteristic, complemented
10C13×#397C2211yescharacteristic
11C13×#394C411yescharacteristic, complemented
12C13×#392C2211yescharacteristic
13C13×#388—21no—
14C13×#386—21no—
15C13×#386—21no—
16C2×C13×#95C411yescharacteristic, complemented
17C2×#88074—21no—
18C4×C22⋊Dic13—21no—
19#11718587—21no—
20#11718118C2212yes—
21#11718117—21no—
22#11718117C2212yes—
23C22×D4×C13—21no—
24C22×D4×C13—21no—
25C22×D4×C13C2×C411yescharacteristic
26C22×D4×C13D411yescharacteristic
27C23×C4×C13—21no—
28C23×C4×C13C2×C411yescharacteristic
29C23×C4×C13D411yescharacteristic
30C13×#121—44no—
31C13×#121—41no—
32C13×#121—41no—
33C4×D4×C13—41no—
34C4×D4×C13—41no—
35C2×C13×C4⋊C4—21no—
36C2×C13×C4⋊C4C2×C411yescharacteristic
37C2×C13×C4⋊C4C2×C411yescharacteristic
38C2×C13×C22⋊C4—21no—
39C2×C13×C22⋊C4—21no—
40C2×C13×C22⋊C4—21no—
41C2×C13×C22⋊C4—21no—
42C2×C13×C22⋊C4—21no—
43C2×C13×C22⋊C4D411yescharacteristic
44C2×C13×C22⋊C4C2311yescharacteristic
45C2×C42×C13D411yescharacteristic
46C2×C22⋊Dic13—22no—
47C2×C4×Dic13—41no—
48C13×#95—21no—
49C13×#95—21no—
50C13×#95—21no—
51C13×#95C2×C411yescharacteristic
52C13×#95C2×C411yescharacteristic
53#88074—24no—
54#88071—41no—
55C22⋊#1055—22no—
56C4⋊#1055—41no—
57#88043—41no—
58#11775—131nomaximal, Sylow
59C24×C13—21no—
60C24×C13C22⋊C411yescharacteristic
61C24×C13C2×D411yescharacteristic
62C2×D4×C13—22no—
63C2×D4×C13—22no—
64C2×D4×C13—41no—
65C2×D4×C13—41no—
66C2×D4×C13—42no—
67C2×D4×C13—42no—
68C2×D4×C13—42no—
69C2×D4×C13—42no—
70C2×D4×C13—42no—
71C2×D4×C13—81no—
72C2×D4×C13—81no—
73C22×C4×C13—21no—
74C22×C4×C13—21no—
75C22×C4×C13—21no—
76C22×C4×C13—21no—
77C22×C4×C13—21no—
78C22×C4×C13—21no—
79C22×C4×C13—21no—
80C22×C4×C13—42no—
81C22×C4×C13—42no—
82C22×C4×C13—81no—
83C22×C4×C13—81no—
84C22×C4×C13—81no—
85C22×C4×C13C22⋊C411yescharacteristic
86C22×C4×C13C22⋊C411yescharacteristic
87C22×C4×C13C22⋊C411yescharacteristic
88C22×C4×C13C22×C411yescharacteristic
89C22×C4×C13C2×D411yescharacteristic
90C22×Dic13—42no—
91C13×C4⋊C4—41no—
92C13×C4⋊C4—41no—
93C13×C4⋊C4—42no—
94C13×C22⋊C4—41no—
95C13×C22⋊C4—41no—
96C13×C22⋊C4—42no—
97C13×C22⋊C4—42no—
98C13×C22⋊C4—42no—
99C13×C22⋊C4—41no—
100C13×C22⋊C4—41no—
101C13×C22⋊C4—81no—
102C42×C13—21no—
103C42×C13—21no—
104C22⋊Dic13—24no—
105C22⋊Dic13—42no—
106C4×Dic13—82no—
107C2×#1055—42no—
108#2543D1311yescharacteristic
109C4×#99—131no—
110#1466—131no—
111#1344—132no—
112#1343—132no—
113C23×C13—21no—
114C23×C13—21no—
115C23×C13—21no—
116C23×C13—21no—
117C23×C13—41no—
118C23×C13—41no—
119C23×C13—41no—
120C23×C13—41no—
121C23×C13—41no—
122C23×C13—41no—
123C23×C13—41no—
124C23×C13—41no—
125C23×C13—41no—
126C23×C13—41no—
127C23×C13—41no—
128C23×C13#10412yes—
129C23×C13C2×C22⋊C411yescharacteristic
130C23×C13AGL(1,ℤ/8)12yes—
131D4×C13—44no—
132D4×C13—84no—
133D4×C13—82no—
134D4×C13—84no—
135C2×C4×C13—22no—
136C2×C4×C13—21no—
137C2×C4×C13—21no—
138C2×C4×C13—21no—
139C2×C4×C13—21no—
140C2×C4×C13—21no—
141C2×C4×C13—21no—
142C2×C4×C13—41no—
143C2×C4×C13—42no—
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—41no—
154C2×C4×C13—41no—
155C2×C4×C13—81no—
156C2×C4×C13—81no—
157C2×C4×C13—81no—
158C2×C4×C13—84no—
159C2×C4×C13#9911yescharacteristic
160C2×C4×C13#9911yescharacteristic
161C2×Dic13—44no—
162C2×Dic13—82no—
163C2×Dic13—82no—
164#1055—82no—
165C2×#121—21no—
166C2×#121Dic1311yescharacteristic, complemented
167C2×C4×D4C2×D1311yescharacteristic
168#432—261no—
169C2×#99—261no—
170#398Dic1311yescharacteristic, complemented
171#397C2×D1311yescharacteristic
172#394Dic1311yescharacteristic, complemented
173#392C2×D1311yescharacteristic
174#388—21no—
175#386—21no—
176#386—21no—
177C4×C22⋊C4—261no—
178C2×#95Dic1311yescharacteristic, complemented
179#342—132no—
180#323—132no—
181#323—261no—
182C22×C13—21no—
183C22×C13—21no—
184C22×C13—22no—
185C22×C13—22no—
186C22×C13—42no—
187C22×C13—42no—
188C22×C13—42no—
189C22×C13—41no—
190C22×C13—41no—
191C22×C13—41no—
192C22×C13—41no—
193C22×C13—81no—
194C22×C13—81no—
195C22×C13—81no—
196C22×C13—81no—
197C22×C13—81no—
198C22×C13—81no—
199C22×C13—81no—
200C22×C13—81no—
201C22×C13C2×#9911yescharacteristic
202C22×C13#41811yescharacteristic
203C22×C13C2×#10411yescharacteristic
204C4×C13—21no—
205C4×C13—21no—
206C4×C13—42no—
207C4×C13—41no—
208C4×C13—41no—
209C4×C13—41no—
210C4×C13—41no—
211C4×C13—81no—
212C4×C13—81no—
213Dic13—84no—
214C22×D4—21no—
215C22×D4—21no—
216C22×D4C2×Dic1311yescharacteristic
217C22×D4C22⋊D1311yescharacteristic
218C23×C4—21no—
219C23×C4C2×Dic1311yescharacteristic
220C23×C4C22⋊D1311yescharacteristic
221#121—44no—
222#121—41no—
223#121—41no—
224C4×D4—41no—
225C4×D4—41no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4C2×Dic1311yescharacteristic
228C2×C4⋊C4C2×Dic1311yescharacteristic
229C2×C22⋊C4—21no—
230C2×C22⋊C4—21no—
231C2×C22⋊C4—21no—
232C2×C22⋊C4—21no—
233C2×C22⋊C4—21no—
234C2×C22⋊C4—262no—
235C2×C22⋊C4C22⋊D1311yescharacteristic
236C2×C22⋊C4C22×D1311yescharacteristic
237C2×C42—521no—
238C2×C42C22⋊D1311yescharacteristic
239C4⋊C8—521no—
240#99—264no—
241C22⋊C8—262no—
242#97—521no—
243#95—21no—
244#95—21no—
245#95—21no—
246#95—521no—
247#95C2×Dic1311yescharacteristic
248#95C2×Dic1311yescharacteristic
249C2×C13—21no—
250C2×C13—21no—
251C2×C13—42no—
252C2×C13—42no—
253C2×C13—161no—
254C2×C13#150711yescharacteristic
255C2×C13#212111yescharacteristic
256C2×C13#212611yescharacteristic
257C24—21no—
258C24C22⋊Dic1311yescharacteristic
259C24C2×C22⋊D1311yescharacteristic
260C2×D4—22no—
261C2×D4—22no—
262C2×D4—41no—
263C2×D4—41no—
264C2×D4—42no—
265C2×D4—42no—
266C2×D4—42no—
267C2×D4—42no—
268C2×D4—42no—
269C2×D4—81no—
270C2×D4—81no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—42no—
279C22×C4—42no—
280C22×C4—81no—
281C22×C4—81no—
282C22×C4—81no—
283C22×C4—522no—
284C22×C4C22⋊Dic1311yescharacteristic
285C22×C4C22⋊Dic1311yescharacteristic
286C22×C4C22⋊Dic1311yescharacteristic
287C22×C4C22×Dic1311yescharacteristic
288C22×C4C2×C22⋊D1311yescharacteristic
289C2×C8—522no—
290C4⋊C4—41no—
291C4⋊C4—41no—
292C4⋊C4—42no—
293C22⋊C4—41no—
294C22⋊C4—41no—
295C22⋊C4—42no—
296C22⋊C4—42no—
297C22⋊C4—42no—
298C22⋊C4—41no—
299C22⋊C4—41no—
300C22⋊C4—81no—
301C22⋊C4—264no—
302C22⋊C4—522no—
303C42—21no—
304C42—21no—
305C42—1042no—
306C13#1177511yescharacteristic, complemented, Sylow
307C23—21no—
308C23—21no—
309C23—21no—
310C23—21no—
311C23—41no—
312C23—41no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23—41no—
322C23#8807712yes—
323C23#8818612yes—
324C23C2×C22⋊Dic1311yescharacteristic
325D4—44no—
326D4—84no—
327D4—82no—
328D4—84no—
329C2×C4—22no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—41no—
337C2×C4—42no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—81no—
350C2×C4—81no—
351C2×C4—81no—
352C2×C4—84no—
353C2×C4—524no—
354C2×C4—1042no—
355C2×C4—1042no—
356C2×C4#8807411yescharacteristic
357C2×C4#8807411yescharacteristic
358C8—1042no—
359C22—21no—
360C22—21no—
361C22—22no—
362C22—22no—
363C22—42no—
364C22—42no—
365C22—42no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—81no—
371C22—81no—
372C22—81no—
373C22—81no—
374C22—81no—
375C22—81no—
376C22—81no—
377C22—81no—
378C22#1171887611yescharacteristic
379C22C2×#8807411yescharacteristic
380C22C2×#8807711yescharacteristic
381C4—21no—
382C4—21no—
383C4—42no—
384C4—41no—
385C4—41no—
386C4—41no—
387C4—41no—
388C4—81no—
389C4—81no—
390C4—1044no—
391C2—21no—
392C2—21no—
393C2—42no—
394C2—42no—
395C2—161no—
396C2#1311335211yescharacteristic
397C2#1311648211yescharacteristic
398C2#1311650111yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C22⋊C4C22×D13
Fitting, prime radicalC13×#2543C2
socleC22×C13C2×#99
cosocleC2×C13×C22⋊C4C23
hypercenter#2543D13
hypocenterC13#11775
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2543

Complements

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

NH ≅ G/Ntype
1. C4×#88074C2semidirect
2. #13113177C2semidirect
3. #13112836C2semidirect
4. #13112833C2semidirect
7. C2×C13×#121C4semidirect
9. C13×#398C4semidirect
11. C13×#394C4semidirect
16. C2×C13×#95C4semidirect
166. C2×#121Dic13semidirect
170. #398Dic13semidirect
172. #394Dic13semidirect
178. C2×#95Dic13semidirect
306. C13#11775semidirect

Maximal subgroups

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

subgroupindex
C4×#880742
#131131772
#131128362
#131128332
C13×#25432
#1177513