Finite Group Databasebeta

← #15773127

Subgroups — #15773127

Order 3328.

514 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 107 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#13120578C211yesmaximal, characteristic
2C2×#11718122C211yesmaximal, characteristic, complemented
3#13112843C212yesmaximal, complemented
4#13112840C212yesmaximal, complemented
5C2×C13×#324C211yesmaximal, characteristic, complemented
6C22×C13×C4⋊C4C2211yescharacteristic
7C2×#88184C411yescharacteristic
8C2×#88183—21no—
9C22×#6099—21no—
10C2×C13×C22⋊C8—21no—
11#11718874—21no—
12#11718873C411yescharacteristic
13#11718655—21no—
14#11718655—21no—
15#11718652C411yescharacteristic
16#11718652C2211yescharacteristic
17#11718644C411yescharacteristic
18#11718644C2211yescharacteristic
19C13×#324—21no—
20C13×#324C2212yes—
21#11718122—21no—
22#11718122C2212yes—
23C23×C4×C13C2×C411yescharacteristic
24C23×C4×C13D411yescharacteristic
25C23×C4×C13D411yescharacteristic
26C22×C22⋊D13—21no—
27C22×D52C2×C411yescharacteristic
28C22×C8×C13—41no—
29C2×C13×C4⋊C4—41no—
30C2×C13×C4⋊C4—41no—
31C2×C13×C4⋊C4C2×C411yescharacteristic
32C2×C13×C4⋊C4D411yescharacteristic
33C2×C13×C4⋊C4D411yescharacteristic
34C2×C13×C4⋊C4C2311yescharacteristic
35C2×C22⋊Dic13—21no—
36#88184—41no—
37#88184—41no—
38#88183—42no—
39#88183—42no—
40C2×#6103—21no—
41C2×#6103—21no—
42C2×#6103—21no—
43C2×#6103—21no—
44C2×#6103—21no—
45C2×C4⋊Dic13—21no—
46C2×C4⋊Dic13C2×C411yescharacteristic
47C2×#6101—21no—
48C2×#6101—21no—
49C2×#6099—24no—
50C2×#6099—22no—
51C2×#6099—41no—
52C2×#6099—42no—
53C22×#1055—41no—
54C13×C22⋊C8—22no—
55C13×C22⋊C8—41no—
56#88071—21no—
57#88071—21no—
58#88071C2×C411yescharacteristic
59#88071C2×C411yescharacteristic
60#11698—131nomaximal, Sylow
61C24×C13C22⋊C411yescharacteristic
62C23×D13—21no—
63C22×C4×C13—21no—
64C22×C4×C13—21no—
65C22×C4×C13—22no—
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13—21no—
69C22×C4×C13—21no—
70C22×C4×C13—81no—
71C22×C4×C13—81no—
72C22×C4×C13C22⋊C411yescharacteristic
73C22×C4×C13C22⋊C411yescharacteristic
74C22×C4×C13C22⋊C411yescharacteristic
75C22×C4×C13D812yes—
76C22×C4×C13SD1612yes—
77C22×C4×C13C22×C411yescharacteristic
78C22×C4×C13C2×D411yescharacteristic
79C22×C4×C13C2×D411yescharacteristic
80C2×C22⋊D13—41no—
81C2×C22⋊D13—41no—
82C2×C22⋊D13—42no—
83C2×C22⋊D13—42no—
84C22×Dic13—21no—
85C22×Dic13—21no—
86C22×Dic13—21no—
87C2×D52—41no—
88C2×D52—81no—
89C2×C8×C13—42no—
90C2×C8×C13—82no—
91C13×C4⋊C4—41no—
92C13×C4⋊C4—41no—
93C13×C4⋊C4—41no—
94C13×C4⋊C4—41no—
95C22⋊Dic13—42no—
96#6103—42no—
97#6103—42no—
98#6103—41no—
99#6103—41no—
100#6103—81no—
101#6103—81no—
102C4⋊Dic13—41no—
103C4⋊Dic13—81no—
104#6101—42no—
105#6101—41no—
106#6101—41no—
107#6099—24no—
108#6099—44no—
109#6099—42no—
110C2×#1055—44no—
111C2×#1055—42no—
112#2618—131no—
113C2×#343—131no—
114C2×#324D1311yescharacteristic, complemented
115#1346—132no—
116#1345—132no—
117C23×C13—41no—
118C23×C13—41no—
119C23×C13#9911yescharacteristic
120C23×C13#9911yescharacteristic
121C23×C13#10212yes—
122C23×C13#10412yes—
123C23×C13C2×C22⋊C411yescharacteristic
124C22×D13—41no—
125C22×D13—41no—
126C22×D13—41no—
127C22×D13—41no—
128C22×D13—41no—
129C22×D13—41no—
130C22×D13—41no—
131C2×C4×C13—22no—
132C2×C4×C13—22no—
133C2×C4×C13—22no—
134C2×C4×C13—22no—
135C2×C4×C13—21no—
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—21no—
143C2×C4×C13—42no—
144C2×C4×C13—41no—
145C2×C4×C13—41no—
146C2×C4×C13—41no—
147C2×C4×C13—41no—
148C2×C4×C13—81no—
149C2×C4×C13—81no—
150C2×C4×C13—81no—
151C2×C4×C13#10212yes—
152C2×C4×C13C2×D811yescharacteristic
153C2×C4×C13C2×SD1611yescharacteristic
154C22⋊D13—82no—
155C22⋊D13—82no—
156C2×Dic13—41no—
157C2×Dic13—41no—
158C2×Dic13—41no—
159C2×Dic13—41no—
160C2×Dic13—41no—
161C2×Dic13—41no—
162C2×Dic13—41no—
163C2×Dic13—41no—
164C2×Dic13—41no—
165D52—82no—
166C8×C13—82no—
167#1055—44no—
168C22×M16—261no—
169C2×#123—261no—
170C2×#121—131no—
171C22×C4⋊C4C2×D1311yescharacteristic
172C2×C22⋊C8—21no—
173#398—131no—
174#398—131no—
175#396—261no—
176#396—261no—
177#394—131no—
178#394—131no—
179#386—261no—
180#380—131no—
181#343—132no—
182#343—261no—
183#324—21no—
184#324C2×D1312yes—
185C22×C13—21no—
186C22×C13—21no—
187C22×C13—21no—
188C22×C13—21no—
189C22×C13—21no—
190C22×C13—21no—
191C22×C13—42no—
192C22×C13—42no—
193C22×C13#32712yes—
194C22×C13#32712yes—
195C22×C13C2×#9911yescharacteristic
196C22×C13C2×#10211yescharacteristic
197C22×C13C2×#10411yescharacteristic
198C2×D13—81no—
199C2×D13—81no—
200C2×D13—81no—
201C2×D13—81no—
202C2×D13—81no—
203C2×D13—81no—
204C2×D13—81no—
205C4×C13—21no—
206C4×C13—22no—
207C4×C13—21no—
208C4×C13—41no—
209C4×C13—41no—
210C4×C13—41no—
211C4×C13—41no—
212Dic13—81no—
213Dic13—81no—
214Dic13—81no—
215C22×D4—131no—
216C22×D4—261no—
217C23×C4C4×D1311yescharacteristic
218C23×C4D5211yescharacteristic
219C23×C4C22⋊D1311yescharacteristic
220C2×M16—264no—
221C2×M16—262no—
222C2×M16—521no—
223C2×M16—522no—
224C22×C8—41no—
225C22×C8—521no—
226#123—522no—
227#123—522no—
228#121—521no—
229#121—521no—
230C2×C4⋊C4—41no—
231C2×C4⋊C4—41no—
232C2×C4⋊C4—131no—
233C2×C4⋊C4—261no—
234C2×C4⋊C4—261no—
235C2×C4⋊C4—261no—
236C2×C4⋊C4C4×D1311yescharacteristic
237C2×C4⋊C4D5211yescharacteristic
238C2×C4⋊C4C22⋊D1311yescharacteristic
239C2×C4⋊C4C22×D1311yescharacteristic
240C2×C22⋊C4—261no—
241C2×C22⋊C4—261no—
242C2×C22⋊C4—261no—
243C2×C22⋊C4—261no—
244C2×C22⋊C4—261no—
245C2×C22⋊C4—261no—
246C22⋊C8—22no—
247C22⋊C8—41no—
248#95—131no—
249#95—131no—
250#95—261no—
251#95—261no—
252C2×C13—21no—
253C2×C13—21no—
254C2×C13—22no—
255C2×C13—22no—
256C2×C13C2×#32711yescharacteristic
257C2×C13#212111yescharacteristic
258C2×C13#213311yescharacteristic
259D13—161no—
260C24—261no—
261C24#610311yescharacteristic
262C2×D4—521no—
263C2×D4—522no—
264C2×D4—521no—
265C2×D4—521no—
266C2×D4—522no—
267C2×D4—1041no—
268C22×C4—22no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—81no—
276C22×C4—81no—
277C22×C4—261no—
278C22×C4—261no—
279C22×C4—261no—
280C22×C4#609512yes—
281C22×C4D10412yes—
282C22×C4#610311yescharacteristic
283C22×C4#610311yescharacteristic
284C22×C4#610311yescharacteristic
285C22×C4C2×C4×D1311yescharacteristic
286C22×C4C2×D5211yescharacteristic
287C22×C4C2×C22⋊D1311yescharacteristic
288M16—264no—
289M16—524no—
290M16—522no—
291C2×C8—42no—
292C2×C8—82no—
293C2×C8—524no—
294C2×C8—522no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C4⋊C4—521no—
300C4⋊C4—521no—
301C4⋊C4—521no—
302C4⋊C4—522no—
303C4⋊C4—1041no—
304C22⋊C4—522no—
305C22⋊C4—522no—
306C22⋊C4—521no—
307C22⋊C4—521no—
308C22⋊C4—522no—
309C22⋊C4—1041no—
310C22⋊C4—1041no—
311C13#1169811yescharacteristic, complemented, Sylow
312C23—41no—
313C23—41no—
314C23—521no—
315C23—521no—
316C23—521no—
317C23—521no—
318C23—521no—
319C23—521no—
320C23—521no—
321C23#8804611yescharacteristic
322C23#8804611yescharacteristic
323C23#8806112yes—
324C23#8806512yes—
325C23C2×#610311yescharacteristic
326D4—1042no—
327D4—1042no—
328D4—1042no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—42no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—81no—
347C2×C4—81no—
348C2×C4—81no—
349C2×C4—521no—
350C2×C4—521no—
351C2×C4—521no—
352C2×C4—521no—
353C2×C4—521no—
354C2×C4—521no—
355C2×C4—521no—
356C2×C4—521no—
357C2×C4—521no—
358C2×C4#8806112yes—
359C2×C4C2×#609511yescharacteristic
360C2×C4C2×D10411yescharacteristic
361C8—82no—
362C8—524no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—42no—
370C22—42no—
371C22—1041no—
372C22—1041no—
373C22—1041no—
374C22—1041no—
375C22—1041no—
376C22—1041no—
377C22—1041no—
378C22#1171806212yes—
379C22#1171806212yes—
380C22C2×#8804611yescharacteristic
381C22C2×#8806111yescharacteristic
382C22C2×#8806511yescharacteristic
383C4—21no—
384C4—21no—
385C4—22no—
386C4—41no—
387C4—41no—
388C4—41no—
389C4—41no—
390C4—1041no—
391C4—1041no—
392C4—1041no—
393C2—21no—
394C2—21no—
395C2—22no—
396C2—22no—
397C2—2081no—
398C2C2×#1171806211yescharacteristic
399C2#1311648011yescharacteristic
400C2#1311652311yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC2×C13×#324C2
socleC22×C13C2×#99
prime radicalC2×#88184C4
cosocleC2×C13×C4⋊C4C23
hypercenterC2×#324D13
hypocenterC13#11698
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
2. C2×#11718122C2semidirect
3. #13112843C2semidirect
4. #13112840C2semidirect
5. C2×C13×#324C2semidirect
114. C2×#324D13semidirect
311. C13#11698semidirect

Maximal subgroups

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

subgroupindex
#131205782
C2×#117181222
#131128432
#131128402
C2×C13×#3242
#1169813