Finite Group Databasebeta

← #15773243

Subgroups — #15773243

Order 3328.

648 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 648 conjugacy classes of subgroups — too many to draw. Only its 95 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#13113157C211yesmaximal, characteristic, complemented
3#13112857C212yesmaximal, complemented
4#13112833C212yesmaximal, complemented
5C13×#2388C211yesmaximal, characteristic
6C22×C13×#41C411yescharacteristic, complemented
7C2×C4×D4×C13—21no—
8C2×C4×D4×C13C2211yescharacteristic
9C13×#395C411yescharacteristic, complemented
10C13×#394—21no—
11C13×#394C411yescharacteristic, complemented
12C13×#393C2211yescharacteristic
13C13×#392—21no—
14C13×#392C2211yescharacteristic
15C4×C13×C22⋊C4—21no—
16C4×C13×C22⋊C4C411yescharacteristic, complemented
17C2×#88074—21no—
18C4×C22⋊Dic13—21no—
19#11718586—21no—
20#11718118C2212yes—
21#11718117—21no—
22#11718117C2212yes—
23C2×C13×#41—44no—
24C2×C13×#41—41no—
25C2×C13×#41—41no—
26C22×Q8×C13C2×C411yescharacteristic
27C22×D4×C13—21no—
28C22×D4×C13—21no—
29C22×D4×C13C2×C411yescharacteristic
30C22×D4×C13D411yescharacteristic
31C23×C4×C13—21no—
32C23×C4×C13C2×C411yescharacteristic
33C23×C4×C13D411yescharacteristic
34C4×D4×C13—41no—
35C4×D4×C13—41no—
36C4×D4×C13—44no—
37C2×C13×C4⋊C4—21no—
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×C13—21no—
47C2×C42×C13D411yescharacteristic
48C2×C22⋊Dic13—22no—
49C2×C4×Dic13—41no—
50C13×#95—21no—
51C13×#95—21no—
52C13×#95C2×C411yescharacteristic
53C13×#95C2×C411yescharacteristic
54#88074—24no—
55#88071—41no—
56C22⋊#1055—22no—
57C4⋊#1055—41no—
58C4×#1055—41no—
59#11725—131nomaximal, Sylow
60C24×C13—21no—
61C24×C13C22⋊C411yescharacteristic
62C24×C13C2×D411yescharacteristic
63C13×#41—44no—
64C13×#41—44no—
65C13×#41—44no—
66C13×#41—44no—
67C2×Q8×C13—42no—
68C2×Q8×C13—41no—
69C2×D4×C13—22no—
70C2×D4×C13—22no—
71C2×D4×C13—41no—
72C2×D4×C13—41no—
73C2×D4×C13—42no—
74C2×D4×C13—42no—
75C2×D4×C13—42no—
76C2×D4×C13—42no—
77C2×D4×C13—42no—
78C2×D4×C13—42no—
79C2×D4×C13—42no—
80C22×C4×C13—24no—
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—42no—
90C22×C4×C13—42no—
91C22×C4×C13—41no—
92C22×C4×C13—41no—
93C22×C4×C13C22⋊C411yescharacteristic
94C22×C4×C13C22⋊C411yescharacteristic
95C22×C4×C13C22⋊C411yescharacteristic
96C22×C4×C13C22×C411yescharacteristic
97C22×C4×C13C2×D411yescharacteristic
98C22×Dic13—42no—
99C13×C4⋊C4—41no—
100C13×C4⋊C4—42no—
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—21no—
109C42×C13—21no—
110C42×C13—42no—
111C22⋊Dic13—24no—
112C22⋊Dic13—42no—
113C4×Dic13—82no—
114C2×#1055—42no—
115#2388D1311yescharacteristic
116C4×#99—131no—
117#1460—131no—
118#1351—132no—
119#1343—132no—
120C23×C13—21no—
121C23×C13—21no—
122C23×C13—22no—
123C23×C13—21no—
124C23×C13—21no—
125C23×C13—21no—
126C23×C13—41no—
127C23×C13—41no—
128C23×C13—41no—
129C23×C13—41no—
130C23×C13—41no—
131C23×C13—41no—
132C23×C13—41no—
133C23×C13—41no—
134C23×C13—41no—
135C23×C13—41no—
136C23×C13C2×C22⋊C411yescharacteristic
137C23×C13#13512yes—
138Q8×C13—42no—
139Q8×C13—42no—
140D4×C13—44no—
141D4×C13—48no—
142D4×C13—48no—
143D4×C13—42no—
144D4×C13—42no—
145C2×C4×C13—21no—
146C2×C4×C13—21no—
147C2×C4×C13—22no—
148C2×C4×C13—22no—
149C2×C4×C13—22no—
150C2×C4×C13—21no—
151C2×C4×C13—21no—
152C2×C4×C13—21no—
153C2×C4×C13—44no—
154C2×C4×C13—42no—
155C2×C4×C13—41no—
156C2×C4×C13—41no—
157C2×C4×C13—41no—
158C2×C4×C13—41no—
159C2×C4×C13—42no—
160C2×C4×C13—44no—
161C2×C4×C13—42no—
162C2×C4×C13—41no—
163C2×C4×C13—41no—
164C2×C4×C13—41no—
165C2×C4×C13—41no—
166C2×C4×C13—41no—
167C2×C4×C13—41no—
168C2×C4×C13—81no—
169C2×C4×C13#9911yescharacteristic
170C2×C4×C13#9911yescharacteristic
171C2×C4×C13#10412yes—
172C2×Dic13—44no—
173C2×Dic13—82no—
174C2×Dic13—82no—
175#1055—82no—
176C22×#41Dic1311yescharacteristic, complemented
177C2×C4×D4—21no—
178C2×C4×D4C2×D1311yescharacteristic
179#431—261no—
180C2×#99—261no—
181#395Dic1311yescharacteristic, complemented
182#394—21no—
183#394Dic1311yescharacteristic, complemented
184#393C2×D1311yescharacteristic
185#392—21no—
186#392C2×D1311yescharacteristic
187C4×C22⋊C4—21no—
188C4×C22⋊C4—261no—
189C4×C22⋊C4Dic1311yescharacteristic, complemented
190#342—132no—
191#323—132no—
192#323—261no—
193C22×C13—21no—
194C22×C13—21no—
195C22×C13—22no—
196C22×C13—42no—
197C22×C13—42no—
198C22×C13—42no—
199C22×C13—41no—
200C22×C13—41no—
201C22×C13—41no—
202C22×C13—42no—
203C22×C13—41no—
204C22×C13—41no—
205C22×C13—81no—
206C22×C13—81no—
207C22×C13—81no—
208C22×C13—81no—
209C22×C13—81no—
210C22×C13—81no—
211C22×C13—81no—
212C22×C13C2×#9911yescharacteristic
213C22×C13#41611yescharacteristic
214C22×C13C2×#10411yescharacteristic
215C4×C13—21no—
216C4×C13—22no—
217C4×C13—42no—
218C4×C13—42no—
219C4×C13—41no—
220C4×C13—41no—
221C4×C13—41no—
222C4×C13—81no—
223C4×C13AΣL(1,𝔽16)12yes—
224Dic13—84no—
225C2×#41—44no—
226C2×#41—41no—
227C2×#41—41no—
228C22×Q8C2×Dic1311yescharacteristic
229C22×D4—21no—
230C22×D4—21no—
231C22×D4C2×Dic1311yescharacteristic
232C22×D4C22⋊D1311yescharacteristic
233C23×C4—21no—
234C23×C4C2×Dic1311yescharacteristic
235C23×C4C22⋊D1311yescharacteristic
236C4×D4—41no—
237C4×D4—41no—
238C4×D4—44no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4C2×Dic1311yescharacteristic
241C2×C22⋊C4—21no—
242C2×C22⋊C4—21no—
243C2×C22⋊C4—21no—
244C2×C22⋊C4—21no—
245C2×C22⋊C4—21no—
246C2×C22⋊C4—262no—
247C2×C22⋊C4C22⋊D1311yescharacteristic
248C2×C22⋊C4C22×D1311yescharacteristic
249C2×C42—21no—
250C2×C42—521no—
251C2×C42C22⋊D1311yescharacteristic
252C4⋊C8—521no—
253#99—264no—
254C22⋊C8—262no—
255C4×C8—521no—
256#95—21no—
257#95—21no—
258#95—521no—
259#95C2×Dic1311yescharacteristic
260#95C2×Dic1311yescharacteristic
261C2×C13—21no—
262C2×C13—21no—
263C2×C13—42no—
264C2×C13—81no—
265C2×C13—82no—
266C2×C13#150111yescharacteristic
267C2×C13C2×AΣL(1,𝔽16)11yescharacteristic
268C2×C13#212611yescharacteristic
269C24—21no—
270C24C22⋊Dic1311yescharacteristic
271C24C2×C22⋊D1311yescharacteristic
272#41—44no—
273#41—44no—
274#41—44no—
275#41—44no—
276C2×Q8—42no—
277C2×Q8—41no—
278C2×D4—22no—
279C2×D4—22no—
280C2×D4—41no—
281C2×D4—41no—
282C2×D4—42no—
283C2×D4—42no—
284C2×D4—42no—
285C2×D4—42no—
286C2×D4—42no—
287C2×D4—42no—
288C2×D4—42no—
289C22×C4—24no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—42no—
298C22×C4—42no—
299C22×C4—42no—
300C22×C4—41no—
301C22×C4—41no—
302C22×C4—522no—
303C22×C4C22⋊Dic1311yescharacteristic
304C22×C4C22⋊Dic1311yescharacteristic
305C22×C4C22⋊Dic1311yescharacteristic
306C22×C4C22×Dic1311yescharacteristic
307C22×C4C2×C22⋊D1311yescharacteristic
308C2×C8—522no—
309C4⋊C4—41no—
310C4⋊C4—42no—
311C22⋊C4—41no—
312C22⋊C4—41no—
313C22⋊C4—42no—
314C22⋊C4—42no—
315C22⋊C4—42no—
316C22⋊C4—42no—
317C22⋊C4—42no—
318C22⋊C4—264no—
319C22⋊C4—522no—
320C42—21no—
321C42—21no—
322C42—42no—
323C42—1042no—
324C13#1172511yescharacteristic, complemented, Sylow
325C23—21no—
326C23—21no—
327C23—22no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23—41no—
332C23—41no—
333C23—41no—
334C23—41no—
335C23—41no—
336C23—41no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23—41no—
341C23#8820412yes—
342C23C2×C22⋊Dic1311yescharacteristic
343Q8—42no—
344Q8—42no—
345D4—44no—
346D4—42no—
347D4—48no—
348D4—48no—
349D4—42no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—22no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—44no—
359C2×C4—42no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—42no—
365C2×C4—44no—
366C2×C4—42no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—81no—
374C2×C4—524no—
375C2×C4—1042no—
376C2×C4—1042no—
377C2×C4#8807411yescharacteristic
378C2×C4#8807411yescharacteristic
379C2×C4#8807712yes—
380C8—1042no—
381C22—21no—
382C22—21no—
383C22—22no—
384C22—42no—
385C22—42no—
386C22—42no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—42no—
391C22—41no—
392C22—41no—
393C22—81no—
394C22—81no—
395C22—81no—
396C22—81no—
397C22—81no—
398C22—81no—
399C22—81no—
400C22C2×#8807411yescharacteristic
401C22#1171889411yescharacteristic
402C22C2×#8807711yescharacteristic
403C4—21no—
404C4—22no—
405C4—42no—
406C4—42no—
407C4—41no—
408C4—41no—
409C4—41no—
410C4—81no—
411C4—1044no—
412C4#1171812812yes—
413C2—21no—
414C2—21no—
415C2—42no—
416C2—82no—
417C2—81no—
418C2#1311332711yescharacteristic
419C2C2×#1171812811yescharacteristic
420C2#1311650111yescharacteristic
subgroupG/H
centerC2×C4#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C22⋊C4C22×D13
Fitting, prime radicalC13×#2388C2
socleC22×C13C2×#99
cosocleC2×C13×C22⋊C4C23
hypercenter#2388D13
hypocenterC13#11725
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2388

Complements

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

NH ≅ G/Ntype
1. C4×#88074C2semidirect
2. #13113157C2semidirect
3. #13112857C2semidirect
4. #13112833C2semidirect
6. C22×C13×#41C4semidirect
9. C13×#395C4semidirect
11. C13×#394C4semidirect
16. C4×C13×C22⋊C4C4semidirect
176. C22×#41Dic13semidirect
181. #395Dic13semidirect
183. #394Dic13semidirect
189. C4×C22⋊C4Dic13semidirect
324. C13#11725semidirect

Maximal subgroups

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

subgroupindex
C4×#880742
#131131572
#131128572
#131128332
C13×#23882
#1172513