Finite Group Databasebeta

← #15751946

Subgroups — #15751946

Order 3328.

430 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 85 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#13121853C211yesmaximal, characteristic
2#13116393C211yesmaximal, characteristic, complemented
3#13116245C211yesmaximal, characteristic, complemented
4#13112661C211yesmaximal, characteristic, complemented
5#13112658C211yesmaximal, characteristic, complemented
6#13112657C211yesmaximal, characteristic
7C13×#2071C211yesmaximal, characteristic
8C2×#88132—21no—
9C2×C13×#102—21no—
10C13×#390C2211yescharacteristic
11C13×#384C2211yescharacteristic
12#11718881—21no—
13#11718645—21no—
14C2×#88050—21no—
15#11718611—21no—
16#11718610—21no—
17#11718609—21no—
18#11718590C2211yescharacteristic
19#11718589C2211yescharacteristic
20C13×#340—21no—
21C13×#336C2211yescharacteristic
22#11718121—21no—
23#11718121—21no—
24#11718121—21no—
25#11718116C2211yescharacteristic
26#11718116C2211yescharacteristic
27C22×D4×C13D411yescharacteristic
28C23×Dic13—21no—
29C22×Dic26D411yescharacteristic
30C22×C8×C13—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4D411yescharacteristic
35C2×C13×C22⋊C4—21no—
36C2×C13×C22⋊C4—21no—
37C2×C42×C13C2311yescharacteristic
38C2×C22⋊Dic13—21no—
39C2×C22⋊Dic13—21no—
40C2×C22⋊Dic13—21no—
41C2×C4⋊Dic13—21no—
42C2×C4⋊Dic13D411yescharacteristic
43C2×C4⋊Dic13D411yescharacteristic
44C2×C4⋊Dic13D411yescharacteristic
45C2×#6101—21no—
46C2×#6101—21no—
47C2×#6101—21no—
48C22×#1055—21no—
49C22×#1055—21no—
50#88132—42no—
51#88132—42no—
52C13×#102—42no—
53#88071—21no—
54#88071—21no—
55#88071—21no—
56#88071—21no—
57#88050—42no—
58#7787—131nomaximal, Sylow
59C24×C13—21no—
60C2×D4×C13—21no—
61C2×D4×C13—41no—
62C2×D4×C13—41no—
63C2×D4×C13SD1612yes—
64C22×C4×C13—21no—
65C22×C4×C13—41no—
66C22×C4×C13C2×D411yescharacteristic
67C22×C4×C13C2×D411yescharacteristic
68C22×C4×C13C2×D411yescharacteristic
69C22×Dic13—21no—
70C22×Dic13—21no—
71C22×Dic13—21no—
72C22×Dic13—21no—
73C22×Dic13—42no—
74C22×Dic13—81no—
75C22×Dic13—81no—
76C2×Dic26—21no—
77C2×Dic26—41no—
78C2×Dic26—41no—
79C2×Dic26D812yes—
80C2×C8×C13—41no—
81C2×C8×C13—41no—
82C2×C8×C13—41no—
83C13×C4⋊C4—41no—
84C13×C4⋊C4—42no—
85C13×C4⋊C4—41no—
86C13×C4⋊C4—41no—
87C13×C4⋊C4—41no—
88C13×C4⋊C4—41no—
89C13×C22⋊C4—41no—
90C13×C22⋊C4—41no—
91C13×C22⋊C4—41no—
92C13×C22⋊C4—41no—
93C42×C13—41no—
94C22⋊Dic13—42no—
95C22⋊Dic13—81no—
96C22⋊Dic13—81no—
97C4⋊Dic13—21no—
98C4⋊Dic13—21no—
99C4⋊Dic13—42no—
100C4⋊Dic13—41no—
101C4⋊Dic13—41no—
102#6101—42no—
103#6101—41no—
104#6101—41no—
105#6101—81no—
106C2×#1055—41no—
107C2×#1055—41no—
108C2×#1055—41no—
109C2×#1055—41no—
110C2×#1055—41no—
111C2×#1055—41no—
112#2732—131no—
113#2099—131no—
114#2072—131no—
115#2071D1311yescharacteristic
116#1272—131no—
117#1271—131no—
118#1270—131no—
119C23×C13—22no—
120C23×C13—41no—
121C23×C13—41no—
122C23×C13—41no—
123C23×C13—41no—
124C23×C13—41no—
125C23×C13—41no—
126C23×C13#12011yescharacteristic
127D4×C13—42no—
128D4×C13—81no—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—21no—
133C2×C4×C13—21no—
134C2×C4×C13—21no—
135C2×C4×C13—41no—
136C2×C4×C13—41no—
137C2×C4×C13—41no—
138C2×C4×C13—81no—
139C2×C4×C13—81no—
140C2×C4×C13—81no—
141C2×C4×C13C2×D811yescharacteristic
142C2×C4×C13C2×SD1611yescharacteristic
143C2×C4×C13#13511yescharacteristic
144C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
145C2×C4×C13#13711yescharacteristic
146C2×C4×C13#13711yescharacteristic
147C2×Dic13—22no—
148C2×Dic13—41no—
149C2×Dic13—41no—
150C2×Dic13—41no—
151C2×Dic13—41no—
152C2×Dic13—41no—
153C2×Dic13—41no—
154C2×Dic13—41no—
155C2×Dic13—41no—
156C2×Dic13—41no—
157C2×Dic13—41no—
158C2×Dic13—41no—
159C2×Dic13—84no—
160Dic26—42no—
161Dic26—81no—
162C8×C13—81no—
163#1055—81no—
164#1055—81no—
165C2×C22⋊Q8—261no—
166C2×#103—261no—
167C2×#102—21no—
168#399—261no—
169#398—261no—
170#396—261no—
171#391—131no—
172#390C2×D1311yescharacteristic
173#389—131no—
174#386—261no—
175#385—261no—
176#384C2×D1311yescharacteristic
177#340—21no—
178#340—261no—
179#340—261no—
180#340—261no—
181#336—131no—
182#336—131no—
183#336C2×D1311yescharacteristic
184C22×C13—42no—
185C22×C13—42no—
186C22×C13—42no—
187C22×C13—81no—
188C22×C13—81no—
189C22×C13—81no—
190C22×C13—81no—
191C22×C13#44711yescharacteristic
192C22×C13#44811yescharacteristic
193C22×C13#45211yescharacteristic
194C22×C13#45411yescharacteristic
195C22×C13#45511yescharacteristic
196C22×C13#45511yescharacteristic
197C22×C13#45811yescharacteristic
198C4×C13—21no—
199C4×C13—21no—
200C4×C13—21no—
201C4×C13—21no—
202C4×C13—21no—
203C4×C13—21no—
204C4×C13—81no—
205C4×C13—161no—
206Dic13—42no—
207Dic13—81no—
208Dic13—81no—
209Dic13—81no—
210C22×Q8—131no—
211C22×D4C22⋊D1311yescharacteristic
212C23×C4—261no—
213C22×C8—21no—
214C22×C8—261no—
215C22×C8—261no—
216C22⋊Q8—522no—
217C22⋊Q8—522no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—131no—
222C2×C4⋊C4—131no—
223C2×C4⋊C4—131no—
224C2×C4⋊C4—261no—
225C2×C4⋊C4—261no—
226C2×C4⋊C4—261no—
227C2×C4⋊C4—261no—
228C2×C4⋊C4C22⋊D1311yescharacteristic
229C2×C22⋊C4—21no—
230C2×C22⋊C4—21no—
231C2×C22⋊C4—261no—
232C2×C22⋊C4—261no—
233C2×C22⋊C4—261no—
234C2×C42C22×D1311yescharacteristic
235#103—522no—
236#102—42no—
237#95—261no—
238#95—261no—
239#95—261no—
240#95—261no—
241C2×C13—82no—
242C2×C13#160711yescharacteristic
243C2×C13#160811yescharacteristic
244C2×C13#161511yescharacteristic
245C2×C13#162711yescharacteristic
246C2×C13#164111yescharacteristic
247C2×C13#164311yescharacteristic
248C2×C13#166211yescharacteristic
249C24—21no—
250C2×Q8—132no—
251C2×Q8—261no—
252C2×Q8—521no—
253C2×Q8—521no—
254C2×D4—21no—
255C2×D4—41no—
256C2×D4—41no—
257C2×D4#610512yes—
258C22×C4—21no—
259C22×C4—41no—
260C22×C4—261no—
261C22×C4—261no—
262C22×C4—261no—
263C22×C4—261no—
264C22×C4—522no—
265C22×C4—1041no—
266C22×C4—1041no—
267C22×C4D4×D1311yescharacteristic
268C22×C4D4×D1311yescharacteristic
269C22×C4C2×C22⋊D1311yescharacteristic
270C2×C8—41no—
271C2×C8—41no—
272C2×C8—41no—
273C2×C8—521no—
274C2×C8—521no—
275C2×C8—521no—
276C2×C8—521no—
277C2×C8—521no—
278C2×C8—521no—
279C4⋊C4—41no—
280C4⋊C4—42no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—261no—
286C4⋊C4—261no—
287C4⋊C4—521no—
288C4⋊C4—521no—
289C4⋊C4—522no—
290C4⋊C4—522no—
291C4⋊C4—521no—
292C4⋊C4—521no—
293C4⋊C4—1041no—
294C22⋊C4—41no—
295C22⋊C4—41no—
296C22⋊C4—41no—
297C22⋊C4—41no—
298C22⋊C4—522no—
299C22⋊C4—1041no—
300C22⋊C4—1041no—
301C42—41no—
302C13#778711yescharacteristic, complemented, Sylow
303C23—22no—
304C23—41no—
305C23—41no—
306C23—41no—
307C23—41no—
308C23—41no—
309C23—41no—
310C23#8819111yescharacteristic
311Q8—522no—
312Q8—1041no—
313D4—42no—
314D4—81no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—81no—
325C2×C4—81no—
326C2×C4—81no—
327C2×C4—262no—
328C2×C4—521no—
329C2×C4—521no—
330C2×C4—521no—
331C2×C4—521no—
332C2×C4—521no—
333C2×C4—521no—
334C2×C4—521no—
335C2×C4—521no—
336C2×C4—521no—
337C2×C4—521no—
338C2×C4—521no—
339C2×C4—1044no—
340C2×C4D8×D1311yescharacteristic
341C2×C4#8816511yescharacteristic
342C2×C4#8816911yescharacteristic
343C2×C4#8817011yescharacteristic
344C2×C4C2×#610511yescharacteristic
345C2×C4#8820511yescharacteristic
346C8—81no—
347C8—1041no—
348C8—1041no—
349C22—42no—
350C22—42no—
351C22—42no—
352C22—81no—
353C22—81no—
354C22—81no—
355C22—81no—
356C22#1171870111yescharacteristic
357C22#1171871411yescharacteristic
358C22#1171872211yescharacteristic
359C22#1171881711yescharacteristic
360C22#1171883411yescharacteristic
361C22#1171886211yescharacteristic
362C22#1171886311yescharacteristic
363C4—21no—
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—21no—
369C4—81no—
370C4—161no—
371C4—522no—
372C4—1041no—
373C4—1041no—
374C4—1041no—
375C2—82no—
376C2#1311382011yescharacteristic
377C2#1311382611yescharacteristic
378C2#1311386411yescharacteristic
379C2#1311393811yescharacteristic
380C2#1311402611yescharacteristic
381C2#1311404111yescharacteristic
382C2#1311415811yescharacteristic
subgroupG/H
centerC23#88191
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#2071C2
socleC23×C13#120
prime radicalC22×D4×C13D4
hypercenter#2071D13
hypocenterC13#7787
LCSG ▷ C2×C42×C13 ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2071

Complements

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

NH ≅ G/Ntype
2. #13116393C2semidirect
3. #13116245C2semidirect
4. #13112661C2semidirect
5. #13112658C2semidirect
302. C13#7787semidirect

Maximal subgroups

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

subgroupindex
#131218532
#131163932
#131162452
#131126612
#131126582
#131126572
C13×#20712
#778713