Finite Group Databasebeta

← #15773797

Subgroups — #15773797

Order 3328.

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

normal subgroups only

This group has 620 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
1#13114910C211yesmaximal, characteristic, complemented
2C2×#11718117C211yesmaximal, characteristic, complemented
3#13112860C212yesmaximal, complemented
4#13112833C212yesmaximal, complemented
5C13×#2539C211yesmaximal, characteristic
6C2×C13×#123—21no—
7C2×C13×#121C411yescharacteristic, complemented
8C2×C13×#120—21no—
9C22×C13×C22⋊C4C2211yescharacteristic
10C13×#399C411yescharacteristic, complemented
11C13×#399C2211yescharacteristic
12C13×#392C411yescharacteristic, complemented
13C13×#392C2211yescharacteristic
14C13×#390—21no—
15C13×#390—21no—
16C4×C13×C22⋊C4C411yescharacteristic, complemented
17#11718908—21no—
18C2×C22⋊#1055—21no—
19#11718118—21no—
20#11718118C2212yes—
21#11718117—21no—
22#11718117C2212yes—
23C25×C13D411yescharacteristic
24C22×D4×C13—21no—
25C22×D4×C13—21no—
26C22×D4×C13—21no—
27C22×D4×C13C2×C411yescharacteristic
28C23×C4×C13C2×C411yescharacteristic
29C23×C4×C13D411yescharacteristic
30C13×#123—44no—
31C13×#121—41no—
32C13×#121—41no—
33C13×#120—44no—
34C2×C13×C4⋊C4—21no—
35C2×C13×C4⋊C4—21no—
36C2×C13×C4⋊C4C2×C411yescharacteristic
37C2×C13×C22⋊C4—21no—
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⋊C4—41no—
44C2×C13×C22⋊C4—41no—
45C2×C13×C22⋊C4C2×C411yescharacteristic
46C2×C13×C22⋊C4D411yescharacteristic
47C2×C13×C22⋊C4D411yescharacteristic
48C2×C13×C22⋊C4C2311yescharacteristic
49C2×C42×C13—21no—
50C2×C22⋊Dic13—22no—
51C2×C22⋊Dic13—41no—
52C2×C22⋊Dic13—41no—
53C22×#1055—41no—
54C13×#95C2×C411yescharacteristic
55C13×#95C2×C411yescharacteristic
56C22⋊#1055—22no—
57C22⋊#1055—41no—
58#11843—131nomaximal, Sylow
59C24×C13—21no—
60C24×C13—21no—
61C24×C13—22no—
62C24×C13—21no—
63C24×C13—41no—
64C24×C13—42no—
65C24×C13—81no—
66C24×C13C22⋊C411yescharacteristic
67C24×C13C22⋊C411yescharacteristic
68C24×C13C2×D411yescharacteristic
69C2×D4×C13—41no—
70C2×D4×C13—42no—
71C2×D4×C13—42no—
72C2×D4×C13—42no—
73C2×D4×C13—42no—
74C2×D4×C13—42no—
75C2×D4×C13—41no—
76C2×D4×C13—41no—
77C2×D4×C13—42no—
78C2×D4×C13—81no—
79C2×D4×C13—81no—
80C2×D4×C13—81no—
81C22×C4×C13—21no—
82C22×C4×C13—21no—
83C22×C4×C13—21no—
84C22×C4×C13—21no—
85C22×C4×C13—21no—
86C22×C4×C13—21no—
87C22×C4×C13—21no—
88C22×C4×C13—42no—
89C22×C4×C13—81no—
90C22×C4×C13C22⋊C411yescharacteristic
91C22×C4×C13C22⋊C411yescharacteristic
92C22×C4×C13C22×C411yescharacteristic
93C22×C4×C13C2×D411yescharacteristic
94C22×Dic13—42no—
95C13×C4⋊C4—41no—
96C13×C4⋊C4—42no—
97C13×C4⋊C4—42no—
98C13×C22⋊C4—24no—
99C13×C22⋊C4—41no—
100C13×C22⋊C4—41no—
101C13×C22⋊C4—41no—
102C13×C22⋊C4—41no—
103C13×C22⋊C4—42no—
104C13×C22⋊C4—42no—
105C13×C22⋊C4—42no—
106C13×C22⋊C4—42no—
107C13×C22⋊C4—42no—
108C42×C13—81no—
109C22⋊Dic13—42no—
110C22⋊Dic13—42no—
111C22⋊Dic13—82no—
112C22⋊Dic13—82no—
113C2×#1055—42no—
114C2×#1055—82no—
115#2539D1311yescharacteristic
116#1819—131no—
117C2×#323—131no—
118#1352—132no—
119#1343—132no—
120C23×C13—22no—
121C23×C13—21no—
122C23×C13—21no—
123C23×C13—21no—
124C23×C13—21no—
125C23×C13—21no—
126C23×C13—21no—
127C23×C13—21no—
128C23×C13—41no—
129C23×C13—42no—
130C23×C13—42no—
131C23×C13—41no—
132C23×C13—41no—
133C23×C13—41no—
134C23×C13—41no—
135C23×C13—42no—
136C23×C13—41no—
137C23×C13—41no—
138C23×C13—41no—
139C23×C13—41no—
140C23×C13—42no—
141C23×C13—41no—
142C23×C13—41no—
143C23×C13—41no—
144C23×C13—81no—
145C23×C13—81no—
146C23×C13—84no—
147C23×C13—84no—
148C23×C13#9911yescharacteristic
149C23×C13#9911yescharacteristic
150C23×C13C2×C22⋊C411yescharacteristic
151C23×C13#13512yes—
152D4×C13—84no—
153D4×C13—84no—
154D4×C13—82no—
155D4×C13—82no—
156D4×C13—82no—
157C2×C4×C13—22no—
158C2×C4×C13—22no—
159C2×C4×C13—21no—
160C2×C4×C13—21no—
161C2×C4×C13—21no—
162C2×C4×C13—21no—
163C2×C4×C13—41no—
164C2×C4×C13—41no—
165C2×C4×C13—42no—
166C2×C4×C13—41no—
167C2×C4×C13—41no—
168C2×C4×C13—41no—
169C2×C4×C13—41no—
170C2×C4×C13—41no—
171C2×C4×C13—41no—
172C2×C4×C13—41no—
173C2×C4×C13—41no—
174C2×C4×C13—41no—
175C2×C4×C13—81no—
176C2×C4×C13—81no—
177C2×C4×C13—81no—
178C2×Dic13—82no—
179C2×Dic13—82no—
180C2×Dic13—82no—
181#1055—82no—
182C2×#123—21no—
183C2×#121Dic1311yescharacteristic, complemented
184C2×#120—21no—
185C22×C22⋊C4C2×D1311yescharacteristic
186C2×C22⋊C8—261no—
187#399Dic1311yescharacteristic, complemented
188#399C2×D1311yescharacteristic
189#392Dic1311yescharacteristic, complemented
190#392C2×D1311yescharacteristic
191#390—21no—
192#390—21no—
193#379—261no—
194C4×C22⋊C4Dic1311yescharacteristic, complemented
195#342—132no—
196#342—261no—
197#323—132no—
198#323—261no—
199C22×C13—21no—
200C22×C13—21no—
201C22×C13—21no—
202C22×C13—21no—
203C22×C13—21no—
204C22×C13—21no—
205C22×C13—22no—
206C22×C13—21no—
207C22×C13—42no—
208C22×C13—42no—
209C22×C13—42no—
210C22×C13—42no—
211C22×C13—41no—
212C22×C13—41no—
213C22×C13—41no—
214C22×C13—41no—
215C22×C13—41no—
216C22×C13—81no—
217C22×C13—84no—
218C22×C13—81no—
219C22×C13—81no—
220C22×C13—81no—
221C22×C13—81no—
222C22×C13—81no—
223C22×C13—84no—
224C22×C13—81no—
225C22×C13—81no—
226C22×C13—81no—
227C22×C13#35312yes—
228C22×C13C2×#9911yescharacteristic
229C22×C13#41611yescharacteristic
230C22×C13#42111yescharacteristic
231C4×C13—42no—
232C4×C13—42no—
233C4×C13—41no—
234C4×C13—41no—
235C4×C13—41no—
236C4×C13—41no—
237C4×C13—81no—
238Dic13—162no—
239C25C22⋊D1311yescharacteristic
240C22×D4—21no—
241C22×D4—21no—
242C22×D4—21no—
243C22×D4C2×Dic1311yescharacteristic
244C23×C4C2×Dic1311yescharacteristic
245C23×C4C22⋊D1311yescharacteristic
246C22×C8—521no—
247#123—44no—
248#121—41no—
249#121—41no—
250#120—44no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4C2×Dic1311yescharacteristic
254C2×C22⋊C4—21no—
255C2×C22⋊C4—21no—
256C2×C22⋊C4—21no—
257C2×C22⋊C4—21no—
258C2×C22⋊C4—21no—
259C2×C22⋊C4—21no—
260C2×C22⋊C4—41no—
261C2×C22⋊C4—41no—
262C2×C22⋊C4—262no—
263C2×C22⋊C4—521no—
264C2×C22⋊C4—521no—
265C2×C22⋊C4C2×Dic1311yescharacteristic
266C2×C22⋊C4C22⋊D1311yescharacteristic
267C2×C22⋊C4C22⋊D1311yescharacteristic
268C2×C22⋊C4C22×D1311yescharacteristic
269C2×C42—21no—
270C22⋊C8—262no—
271C22⋊C8—521no—
272#95C2×Dic1311yescharacteristic
273#95C2×Dic1311yescharacteristic
274C2×C13—21no—
275C2×C13—21no—
276C2×C13—22no—
277C2×C13—42no—
278C2×C13—41no—
279C2×C13—81no—
280C2×C13—161no—
281C2×C13#151611yescharacteristic
282C2×C13#212111yescharacteristic
283C2×C13C2×#35311yescharacteristic
284C24—21no—
285C24—21no—
286C24—22no—
287C24—21no—
288C24—41no—
289C24—42no—
290C24—81no—
291C24C22⋊Dic1311yescharacteristic
292C24C22⋊Dic1311yescharacteristic
293C24C2×C22⋊D1311yescharacteristic
294C2×D4—41no—
295C2×D4—42no—
296C2×D4—42no—
297C2×D4—42no—
298C2×D4—42no—
299C2×D4—42no—
300C2×D4—41no—
301C2×D4—41no—
302C2×D4—42no—
303C2×D4—81no—
304C2×D4—81no—
305C2×D4—81no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—42no—
314C22×C4—81no—
315C22×C4—522no—
316C22×C4C22⋊Dic1311yescharacteristic
317C22×C4C22⋊Dic1311yescharacteristic
318C22×C4C22×Dic1311yescharacteristic
319C22×C4C2×C22⋊D1311yescharacteristic
320C2×C8—522no—
321C2×C8—1042no—
322C4⋊C4—41no—
323C4⋊C4—42no—
324C4⋊C4—42no—
325C22⋊C4—24no—
326C22⋊C4—41no—
327C22⋊C4—41no—
328C22⋊C4—41no—
329C22⋊C4—41no—
330C22⋊C4—42no—
331C22⋊C4—42no—
332C22⋊C4—42no—
333C22⋊C4—42no—
334C22⋊C4—42no—
335C22⋊C4—522no—
336C22⋊C4—522no—
337C22⋊C4—1042no—
338C22⋊C4—1042no—
339C42—81no—
340C13#1184311yescharacteristic, complemented, Sylow
341C23—21no—
342C23—21no—
343C23—21no—
344C23—22no—
345C23—21no—
346C23—21no—
347C23—21no—
348C23—21no—
349C23—41no—
350C23—42no—
351C23—42no—
352C23—41no—
353C23—41no—
354C23—41no—
355C23—41no—
356C23—42no—
357C23—41no—
358C23—41no—
359C23—41no—
360C23—41no—
361C23—42no—
362C23—41no—
363C23—41no—
364C23—41no—
365C23—81no—
366C23—81no—
367C23—84no—
368C23—84no—
369C23#8807411yescharacteristic
370C23#8807411yescharacteristic
371C23#8820412yes—
372C23C2×C22⋊Dic1311yescharacteristic
373D4—84no—
374D4—84no—
375D4—82no—
376D4—82no—
377D4—82no—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—42no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—81no—
397C2×C4—81no—
398C2×C4—81no—
399C2×C4—1042no—
400C2×C4—1042no—
401C2×C4—1042no—
402C8—1042no—
403C22—21no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—22no—
408C22—21no—
409C22—21no—
410C22—21no—
411C22—42no—
412C22—42no—
413C22—42no—
414C22—42no—
415C22—41no—
416C22—41no—
417C22—41no—
418C22—41no—
419C22—41no—
420C22—81no—
421C22—84no—
422C22—81no—
423C22—81no—
424C22—81no—
425C22—81no—
426C22—81no—
427C22—84no—
428C22—81no—
429C22—81no—
430C22—81no—
431C22#1171813712yes—
432C22C2×#8807411yescharacteristic
433C22#1171889411yescharacteristic
434C22#1171889711yescharacteristic
435C4—42no—
436C4—42no—
437C4—41no—
438C4—41no—
439C4—41no—
440C4—41no—
441C4—81no—
442C4—2082no—
443C2—21no—
444C2—21no—
445C2—22no—
446C2—42no—
447C2—41no—
448C2—81no—
449C2—161no—
450C2#1311339211yescharacteristic
451C2#1311648211yescharacteristic
452C2C2×#1171813711yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C22⋊C4C22×D13
Fitting, prime radicalC13×#2539C2
socleC22×C13C2×#99
cosocleC2×C13×C22⋊C4C23
hypercenter#2539D13
hypocenterC13#11843
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24 ◁ C22×C22⋊C4 ◁ #2539

Complements

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

NH ≅ G/Ntype
1. #13114910C2semidirect
2. C2×#11718117C2semidirect
3. #13112860C2semidirect
4. #13112833C2semidirect
7. C2×C13×#121C4semidirect
10. C13×#399C4semidirect
12. C13×#392C4semidirect
16. C4×C13×C22⋊C4C4semidirect
183. C2×#121Dic13semidirect
187. #399Dic13semidirect
189. #392Dic13semidirect
194. C4×C22⋊C4Dic13semidirect
340. C13#11843semidirect

Maximal subgroups

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

subgroupindex
#131149102
C2×#117181172
#131128602
#131128332
C13×#25392
#1184313