Finite Group Databasebeta

← #15773948

Subgroups — #15773948

Order 3328.

522 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 522 conjugacy classes of subgroups — too many to draw. Only its 103 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#13114824C211yesmaximal, characteristic, complemented
2#13113157C211yesmaximal, 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—
18#11718873—21no—
19#11718586—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—42no—
31C13×#121—42no—
32C13×#121—41no—
33C13×#121—41no—
34C4×D4×C13—41no—
35C4×D4×C13—41no—
36C2×C13×C4⋊C4—21no—
37C2×C13×C4⋊C4C2×C411yescharacteristic
38C2×C13×C4⋊C4C2×C411yescharacteristic
39C2×C13×C22⋊C4—21no—
40C2×C13×C22⋊C4—21no—
41C2×C13×C22⋊C4—21no—
42C2×C13×C22⋊C4—21no—
43C2×C13×C22⋊C4—21no—
44C2×C13×C22⋊C4D411yescharacteristic
45C2×C13×C22⋊C4C2311yescharacteristic
46C2×C42×C13D411yescharacteristic
47C2×C22⋊Dic13—22no—
48C2×C4⋊Dic13—41no—
49C13×#95—21no—
50C13×#95—21no—
51C13×#95—21no—
52C13×#95C2×C411yescharacteristic
53C13×#95C2×C411yescharacteristic
54#88074—42no—
55#88071—41no—
56C22⋊#1055—22no—
57C4⋊#1055—41no—
58C4×#1055—41no—
59#11876—131nomaximal, Sylow
60C24×C13—21no—
61C24×C13C22⋊C411yescharacteristic
62C24×C13C2×D411yescharacteristic
63C2×D4×C13—41no—
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—41no—
71C2×D4×C13—41no—
72C2×D4×C13—81no—
73C2×D4×C13—81no—
74C2×D4×C13D812yes—
75C2×D4×C13SD1612yes—
76C22×C4×C13—21no—
77C22×C4×C13—21no—
78C22×C4×C13—21no—
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×C13—81no—
87C22×C4×C13—81no—
88C22×C4×C13C22⋊C411yescharacteristic
89C22×C4×C13C22⋊C411yescharacteristic
90C22×C4×C13C22⋊C411yescharacteristic
91C22×C4×C13C22×C411yescharacteristic
92C22×C4×C13C2×D411yescharacteristic
93C22×Dic13—42no—
94C13×C4⋊C4—41no—
95C13×C4⋊C4—41no—
96C13×C4⋊C4—42no—
97C13×C22⋊C4—41no—
98C13×C22⋊C4—41no—
99C13×C22⋊C4—42no—
100C13×C22⋊C4—41no—
101C13×C22⋊C4—41no—
102C13×C22⋊C4—41no—
103C13×C22⋊C4—41no—
104C13×C22⋊C4—42no—
105C13×C22⋊C4—81no—
106C42×C13—21no—
107C42×C13—21no—
108C22⋊Dic13—42no—
109C22⋊Dic13—42no—
110C4⋊Dic13—82no—
111C2×#1055—42no—
112#2543D1311yescharacteristic
113#1799—131no—
114#1460—131no—
115#1344—132no—
116#1343—132no—
117C23×C13—21no—
118C23×C13—21no—
119C23×C13—21no—
120C23×C13—21no—
121C23×C13—41no—
122C23×C13—41no—
123C23×C13—41no—
124C23×C13—41no—
125C23×C13—41no—
126C23×C13—41no—
127C23×C13—41no—
128C23×C13—41no—
129C23×C13—41no—
130C23×C13—41no—
131C23×C13—41no—
132C23×C13#10212yes—
133C23×C13C2×C22⋊C411yescharacteristic
134C23×C13C2×D811yescharacteristic
135C23×C13C2×SD1611yescharacteristic
136D4×C13—42no—
137D4×C13—42no—
138D4×C13—82no—
139D4×C13—82no—
140D4×C13—82no—
141D4×C13—84no—
142C2×C4×C13—21no—
143C2×C4×C13—21no—
144C2×C4×C13—22no—
145C2×C4×C13—21no—
146C2×C4×C13—21no—
147C2×C4×C13—21no—
148C2×C4×C13—41no—
149C2×C4×C13—42no—
150C2×C4×C13—41no—
151C2×C4×C13—41no—
152C2×C4×C13—41no—
153C2×C4×C13—41no—
154C2×C4×C13—41no—
155C2×C4×C13—41no—
156C2×C4×C13—41no—
157C2×C4×C13—41no—
158C2×C4×C13—41no—
159C2×C4×C13—41no—
160C2×C4×C13—41no—
161C2×C4×C13—81no—
162C2×C4×C13—81no—
163C2×C4×C13—81no—
164C2×C4×C13—84no—
165C2×C4×C13#9911yescharacteristic
166C2×C4×C13#9911yescharacteristic
167C2×C4×C13#10212yes—
168C2×Dic13—82no—
169C2×Dic13—82no—
170C2×Dic13—82no—
171#1055—82no—
172C2×#121—21no—
173C2×#121Dic1311yescharacteristic, complemented
174C2×C4×D4C2×D1311yescharacteristic
175#431—261no—
176C2×#99—261no—
177#398Dic1311yescharacteristic, complemented
178#397C2×D1311yescharacteristic
179#394Dic1311yescharacteristic, complemented
180#392C2×D1311yescharacteristic
181#388—21no—
182#386—21no—
183#386—21no—
184#380—261no—
185C2×#95Dic1311yescharacteristic, complemented
186#342—132no—
187#323—132no—
188#323—261no—
189C22×C13—21no—
190C22×C13—21no—
191C22×C13—21no—
192C22×C13—22no—
193C22×C13—21no—
194C22×C13—42no—
195C22×C13—41no—
196C22×C13—41no—
197C22×C13—42no—
198C22×C13—41no—
199C22×C13—41no—
200C22×C13—41no—
201C22×C13—41no—
202C22×C13—81no—
203C22×C13—81no—
204C22×C13—81no—
205C22×C13—81no—
206C22×C13—81no—
207C22×C13—81no—
208C22×C13—81no—
209C22×C13—81no—
210C22×C13C2×#9911yescharacteristic
211C22×C13C2×#10211yescharacteristic
212C22×C13#42111yescharacteristic
213C4×C13—21no—
214C4×C13—21no—
215C4×C13—22no—
216C4×C13—42no—
217C4×C13—41no—
218C4×C13—41no—
219C4×C13—41no—
220C4×C13—81no—
221C4×C13—81no—
222Dic13—162no—
223C22×D4—21no—
224C22×D4—21no—
225C22×D4C2×Dic1311yescharacteristic
226C22×D4C22⋊D1311yescharacteristic
227C23×C4—21no—
228C23×C4C2×Dic1311yescharacteristic
229C23×C4C22⋊D1311yescharacteristic
230#121—42no—
231#121—42no—
232#121—41no—
233#121—41no—
234C4×D4—41no—
235C4×D4—41no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—521no—
238C2×C4⋊C4C2×Dic1311yescharacteristic
239C2×C4⋊C4C2×Dic1311yescharacteristic
240C2×C22⋊C4—21no—
241C2×C22⋊C4—21no—
242C2×C22⋊C4—21no—
243C2×C22⋊C4—21no—
244C2×C22⋊C4—21no—
245C2×C22⋊C4—262no—
246C2×C22⋊C4C22⋊D1311yescharacteristic
247C2×C22⋊C4C22×D1311yescharacteristic
248C2×C42C22⋊D1311yescharacteristic
249C4⋊C8—521no—
250#99—522no—
251C22⋊C8—262no—
252C4×C8—521no—
253#95—21no—
254#95—21no—
255#95—21no—
256#95—521no—
257#95C2×Dic1311yescharacteristic
258#95C2×Dic1311yescharacteristic
259C2×C13—21no—
260C2×C13—21no—
261C2×C13—41no—
262C2×C13—42no—
263C2×C13—41no—
264C2×C13—161no—
265C2×C13#151911yescharacteristic
266C2×C13#212111yescharacteristic
267C2×C13#212611yescharacteristic
268C24—21no—
269C24C22⋊Dic1311yescharacteristic
270C24C2×C22⋊D1311yescharacteristic
271C2×D4—41no—
272C2×D4—41no—
273C2×D4—41no—
274C2×D4—42no—
275C2×D4—42no—
276C2×D4—42no—
277C2×D4—42no—
278C2×D4—41no—
279C2×D4—41no—
280C2×D4—81no—
281C2×D4—81no—
282C2×D4#610412yes—
283C2×D4#610512yes—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—42no—
292C22×C4—42no—
293C22×C4—81no—
294C22×C4—81no—
295C22×C4—81no—
296C22×C4—522no—
297C22×C4C22⋊Dic1311yescharacteristic
298C22×C4C22⋊Dic1311yescharacteristic
299C22×C4C22⋊Dic1311yescharacteristic
300C22×C4C22×Dic1311yescharacteristic
301C22×C4C2×C22⋊D1311yescharacteristic
302C2×C8—522no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—42no—
306C4⋊C4—1042no—
307C22⋊C4—41no—
308C22⋊C4—41no—
309C22⋊C4—42no—
310C22⋊C4—41no—
311C22⋊C4—41no—
312C22⋊C4—42no—
313C22⋊C4—41no—
314C22⋊C4—41no—
315C22⋊C4—81no—
316C22⋊C4—522no—
317C22⋊C4—522no—
318C42—21no—
319C42—21no—
320C13#1187611yescharacteristic, complemented, Sylow
321C23—21no—
322C23—21no—
323C23—21no—
324C23—21no—
325C23—41no—
326C23—41no—
327C23—41no—
328C23—41no—
329C23—41no—
330C23—41no—
331C23—41no—
332C23—41no—
333C23—41no—
334C23—41no—
335C23—41no—
336C23#8807212yes—
337C23C2×#610411yescharacteristic
338C23C2×#610511yescharacteristic
339C23C2×C22⋊Dic1311yescharacteristic
340D4—42no—
341D4—42no—
342D4—82no—
343D4—82no—
344D4—82no—
345D4—84no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—22no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—41no—
353C2×C4—42no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—81no—
366C2×C4—81no—
367C2×C4—81no—
368C2×C4—84no—
369C2×C4—1042no—
370C2×C4—1042no—
371C2×C4—1042no—
372C2×C4#8807212yes—
373C2×C4#8807411yescharacteristic
374C2×C4#8807411yescharacteristic
375C8—1042no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—22no—
380C22—21no—
381C22—42no—
382C22—41no—
383C22—41no—
384C22—42no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—81no—
390C22—81no—
391C22—81no—
392C22—81no—
393C22—81no—
394C22—81no—
395C22—81no—
396C22—81no—
397C22C2×#8807211yescharacteristic
398C22C2×#8807411yescharacteristic
399C22#1171889711yescharacteristic
400C4—22no—
401C4—21no—
402C4—21no—
403C4—42no—
404C4—41no—
405C4—41no—
406C4—41no—
407C4—81no—
408C4—81no—
409C4—2082no—
410C2—21no—
411C2—21no—
412C2—41no—
413C2—42no—
414C2—41no—
415C2—161no—
416C2#1311340411yescharacteristic
417C2#1311648211yescharacteristic
418C2#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#11876
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. #13114824C2semidirect
2. #13113157C2semidirect
3. #13112836C2semidirect
4. #13112833C2semidirect
7. C2×C13×#121C4semidirect
9. C13×#398C4semidirect
11. C13×#394C4semidirect
16. C2×C13×#95C4semidirect
173. C2×#121Dic13semidirect
177. #398Dic13semidirect
179. #394Dic13semidirect
185. C2×#95Dic13semidirect
320. C13#11876semidirect

Maximal subgroups

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

subgroupindex
#131148242
#131131572
#131128362
#131128332
C13×#25432
#1187613