Finite Group Databasebeta

← #15764973

Subgroups — #15764973

Order 3328.

496 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 105 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#13125987C211yesmaximal, characteristic, complemented
2#13124633C211yesmaximal, characteristic
3#13113517C211yesmaximal, characteristic, complemented
4#13113238C211yesmaximal, characteristic, complemented
5#13113157C211yesmaximal, characteristic
6#13112733C211yesmaximal, characteristic, complemented
7C2×C13×#474C211yesmaximal, characteristic
8C2×C13×C4⋊Q8C2211yescharacteristic
9C2×C4×D4×C13C2211yescharacteristic
10#11719175C2211yescharacteristic
11C13×#474—22no—
12C13×#474—22no—
13C2×C13×#107—21no—
14C2×C13×C4⋊C8C2211yescharacteristic
15C2×C13×#102—21no—
16#11718876—21no—
17#11718754—21no—
18#11718752—22no—
19#11718739—21no—
20#11718670—22no—
21#11718669—21no—
22#11718668—21no—
23#11718631—22no—
24#11718625—21no—
25#11718586C2211yescharacteristic
26#11718586C2211yescharacteristic
27#11718585C2211yescharacteristic
28#11718138—22no—
29#11718117—22no—
30#11718076—22no—
31C22×Q8×C13—21no—
32C22×D4×C13D411yescharacteristic
33C23×C4×C13—21no—
34C22×C8×C13—21no—
35C13×C4⋊Q8—21no—
36C13×C4⋊Q8—21no—
37C13×C4⋊Q8—21no—
38C13×C4⋊Q8D412yes—
39C4×D4×C13—21no—
40C4×D4×C13—21no—
41C4×D4×C13—21no—
42C4×D4×C13—21no—
43C2×C13×C4⋊C4—21no—
44C2×C13×C4⋊C4—21no—
45C2×C13×C4⋊C4D411yescharacteristic
46C2×C13×C22⋊C4—21no—
47C2×C42×C13C2311yescharacteristic
48#88180—21no—
49#88178—21no—
50#88178—21no—
51C2×#6099—21no—
52#88124—21no—
53#88123D411yescharacteristic
54#88123D411yescharacteristic
55C4×Dic26—21no—
56C4×Dic26—21no—
57C13×#107—24no—
58C13×C4⋊C8—21no—
59C13×C4⋊C8D412yes—
60C13×#102—24no—
61#88072—22no—
62#88072—22no—
63C22⋊#1055—21no—
64C22⋊#1055D412yes—
65#88050—24no—
66#88048—22no—
67#88047—22no—
68#88047—24no—
69C4⋊#1055—21no—
70C4⋊#1055—21no—
71C4⋊#1055—21no—
72C4⋊#1055D412yes—
73C4×#1055—21no—
74C4×#1055—21no—
75#10190—131nomaximal, Sylow
76C24×C13—21no—
77C2×Q8×C13—22no—
78C2×Q8×C13—41no—
79C2×Q8×C13—82no—
80C2×D4×C13—21no—
81C2×D4×C13—21no—
82C2×D4×C13—21no—
83C2×D4×C13—21no—
84C2×D4×C13—21no—
85C2×D4×C13Q1612yes—
86C22×C4×C13—21no—
87C22×C4×C13—41no—
88C22×C4×C13—41no—
89C22×C4×C13—41no—
90C22×C4×C13—82no—
91C22×C4×C13C2×D411yescharacteristic
92C22×C4×C13C2×D411yescharacteristic
93C22×C4×C13#4111yescharacteristic
94C2×Dic26—21no—
95C2×Dic26—21no—
96C2×C8×C13—22no—
97C2×C8×C13—41no—
98C2×C8×C13—41no—
99C13×C4⋊C4—22no—
100C13×C4⋊C4—21no—
101C13×C4⋊C4—22no—
102C13×C4⋊C4—21no—
103C13×C4⋊C4—41no—
104C13×C4⋊C4—41no—
105C13×C22⋊C4—41no—
106C13×C22⋊C4—41no—
107C42×C13C2×D411yescharacteristic
108C42×C13C2×D411yescharacteristic
109C42×C13C2×D411yescharacteristic
110C42×C13C2×D411yescharacteristic
111C22⋊Dic13—41no—
112C4⋊Dic13—21no—
113C4⋊Dic13—21no—
114C4⋊Dic13—21no—
115C4⋊Dic13—21no—
116#6101—41no—
117#6101—41no—
118C4×Dic13—41no—
119#6099—41no—
120#6099—41no—
121C2×#1055—22no—
122C2×#1055—22no—
123C2×#1055—41no—
124#3230—131no—
125#3077—131no—
126C2×#474D1311yescharacteristic
127#1548—131no—
128#1481—131no—
129#1460—131no—
130#1301—131no—
131C23×C13—22no—
132C23×C13—41no—
133C23×C13—41no—
134C23×C13—81no—
135C23×C13—81no—
136C23×C13#12111yescharacteristic
137Q8×C13—82no—
138Q8×C13—82no—
139D4×C13—22no—
140D4×C13—22no—
141D4×C13—41no—
142D4×C13—41no—
143C2×C4×C13—22no—
144C2×C4×C13—41no—
145C2×C4×C13—41no—
146C2×C4×C13—42no—
147C2×C4×C13—82no—
148C2×C4×C13—82no—
149C2×C4×C13—82no—
150C2×C4×C13—81no—
151C2×C4×C13#12011yescharacteristic
152C2×C4×C13#12011yescharacteristic
153C2×C4×C13#12011yescharacteristic
154C2×C4×C13#12111yescharacteristic
155C2×C4×C13#12111yescharacteristic
156C2×C4×C13#12711yescharacteristic
157C2×C4×C13C2×Q1611yescharacteristic
158C2×C4×C13#13511yescharacteristic
159C2×C4×C13#13711yescharacteristic
160C2×C4×C13#13711yescharacteristic
161C2×Dic13—41no—
162C2×Dic13—41no—
163Dic26—42no—
164Dic26—42no—
165C8×C13—42no—
166#1055—42no—
167#1055—42no—
168#1055—81no—
169#533—131no—
170C2×C4⋊Q8C2×D1311yescharacteristic
171C2×C4×D4C2×D1311yescharacteristic
172#500—261no—
173#487—261no—
174#484—262no—
175#478—262no—
176#477—262no—
177#476—261no—
178#474—22no—
179#474—22no—
180#474—261no—
181#431—131no—
182#431—131no—
183#428—261no—
184C2×#107—21no—
185#423—131no—
186C2×C4⋊C8C2×D1311yescharacteristic
187#418—261no—
188C2×#102—21no—
189#333—262no—
190Q8⋊C8—262no—
191#323—262no—
192C22×C13—21no—
193C22×C13—21no—
194C22×C13—42no—
195C22×C13—82no—
196C22×C13—82no—
197C22×C13—81no—
198C22×C13—81no—
199C22×C13#39211yescharacteristic
200C22×C13#46711yescharacteristic
201C22×C13#47011yescharacteristic
202C4×C13—21no—
203C4×C13—21no—
204C4×C13—21no—
205C4×C13—81no—
206C4×C13—82no—
207C4×C13#45111yescharacteristic
208C4×C13#45111yescharacteristic
209C4×C13#45211yescharacteristic
210C4×C13#45211yescharacteristic
211C4×C13#47212yes—
212Dic13—81no—
213Dic13—81no—
214C22×Q8—21no—
215C22×D4C22⋊D1311yescharacteristic
216C23×C4—21no—
217C2×M16—261no—
218C22×C8—21no—
219C4⋊Q8—21no—
220C4⋊Q8—21no—
221C4⋊Q8—21no—
222C4⋊Q8—131no—
223C4⋊Q8—131no—
224C4⋊Q8C22⋊D1312yes—
225#125—261no—
226C22⋊Q8—261no—
227C22⋊Q8—261no—
228C4×Q8—261no—
229C4×Q8—261no—
230C4×D4—21no—
231C4×D4—21no—
232C4×D4—21no—
233C4×D4—21no—
234#117—261no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4C22⋊D1311yescharacteristic
238C2×C22⋊C4—21no—
239C2×C42C22×D1311yescharacteristic
240#107—24no—
241#107—262no—
242#107—264no—
243#106—262no—
244C4⋊C8—21no—
245C4⋊C8—132no—
246C4⋊C8—261no—
247C4⋊C8—261no—
248C4⋊C8—261no—
249C4⋊C8C22⋊D1312yes—
250#103—264no—
251#102—24no—
252#102—262no—
253#102—262no—
254C22⋊C8—132no—
255C22⋊C8—261no—
256C4×C8—261no—
257C4×C8—261no—
258C2×C13—21no—
259C2×C13—21no—
260C2×C13—82no—
261C2×C13#200111yescharacteristic
262C2×C13#200911yescharacteristic
263C2×C13#201811yescharacteristic
264C24—21no—
265C2×Q8—22no—
266C2×Q8—41no—
267C2×Q8—82no—
268C2×Q8—261no—
269C2×Q8—261no—
270C2×D4—21no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—21no—
275C2×D4#610712yes—
276C22×C4—21no—
277C22×C4—41no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4—82no—
281C22×C4D4×D1311yescharacteristic
282C22×C4#612911yescharacteristic
283C22×C4C2×C22⋊D1311yescharacteristic
284M16—521no—
285M16—521no—
286C2×C8—22no—
287C2×C8—41no—
288C2×C8—41no—
289C2×C8—262no—
290C2×C8—262no—
291C2×C8—521no—
292C4⋊C4—22no—
293C4⋊C4—21no—
294C4⋊C4—22no—
295C4⋊C4—21no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—261no—
299C4⋊C4—261no—
300C4⋊C4—261no—
301C4⋊C4—261no—
302C4⋊C4—521no—
303C4⋊C4—521no—
304C22⋊C4—41no—
305C22⋊C4—41no—
306C22⋊C4—521no—
307C42—521no—
308C42D4×D1311yescharacteristic
309C42D4×D1311yescharacteristic
310C42C2×C22⋊D1311yescharacteristic
311C42C2×C22⋊D1311yescharacteristic
312C13#1019011yescharacteristic, complemented, Sylow
313C23—22no—
314C23—41no—
315C23—41no—
316C23—81no—
317C23—81no—
318C23#8819311yescharacteristic
319Q8—82no—
320Q8—82no—
321Q8—522no—
322Q8—522no—
323D4—22no—
324D4—22no—
325D4—41no—
326D4—41no—
327C2×C4—22no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—42no—
331C2×C4—82no—
332C2×C4—82no—
333C2×C4—82no—
334C2×C4—81no—
335C2×C4—521no—
336C2×C4—521no—
337C2×C4#8819111yescharacteristic
338C2×C4#8819111yescharacteristic
339C2×C4#8819211yescharacteristic
340C2×C4#8819311yescharacteristic
341C2×C4#8819411yescharacteristic
342C2×C4#8819611yescharacteristic
343C2×C4C2×#610711yescharacteristic
344C2×C4#8820411yescharacteristic
345C2×C4#8820511yescharacteristic
346C2×C4#8820711yescharacteristic
347C8—42no—
348C8—522no—
349C8—522no—
350C8—1041no—
351C22—21no—
352C22—21no—
353C22—42no—
354C22—82no—
355C22—82no—
356C22—81no—
357C22—81no—
358C22#1171871211yescharacteristic
359C22#1171871311yescharacteristic
360C22#1171888411yescharacteristic
361C4—21no—
362C4—21no—
363C4—21no—
364C4—81no—
365C4—82no—
366C4—1041no—
367C4—1041no—
368C4#1171870811yescharacteristic
369C4#1171871111yescharacteristic
370C4#1171882112yes—
371C4#1171888911yescharacteristic
372C4#1171890011yescharacteristic
373C2—21no—
374C2—21no—
375C2—82no—
376C2#1311584411yescharacteristic
377C2#1311589411yescharacteristic
378C2#1311594311yescharacteristic
subgroupG/H
centerC22#11718884
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC2×C13×#474C2
socleC22×C13#392
prime radicalC22×D4×C13D4
hypercenterC2×#474D13
hypocenterC13#10190
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#474

Complements

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

NH ≅ G/Ntype
1. #13125987C2semidirect
3. #13113517C2semidirect
4. #13113238C2semidirect
6. #13112733C2semidirect
312. C13#10190semidirect

Maximal subgroups

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

subgroupindex
#131259872
#131246332
#131135172
#131132382
#131131572
#131127332
C2×C13×#4742
#1019013