Finite Group Databasebeta

← #15764917

Subgroups — #15764917

Order 3328.

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

normal subgroups only

This group has 508 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#13125784C211yesmaximal, characteristic, complemented
2#13124633C211yesmaximal, characteristic
3#13113521C211yesmaximal, characteristic, complemented
4#13113238C211yesmaximal, characteristic, complemented
5#13113157C211yesmaximal, characteristic
6#13112733C211yesmaximal, characteristic, complemented
7C2×C13×#476C211yesmaximal, characteristic
8C2×C13×C4⋊Q8C2211yescharacteristic
9C2×C4×D4×C13C2211yescharacteristic
10#11719175C2211yescharacteristic
11C13×#476—22no—
12C13×#476—22no—
13C2×C13×#106—21no—
14C2×C13×C4⋊C8C2211yescharacteristic
15C2×C13×#102—21no—
16#11718889—22no—
17#11718876—21no—
18#11718753—21no—
19#11718751—22no—
20#11718742—21no—
21#11718670—22no—
22#11718669—21no—
23#11718668—21no—
24#11718625—21no—
25#11718586C2211yescharacteristic
26#11718586C2211yescharacteristic
27#11718585C2211yescharacteristic
28#11718139—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
48C2×#6107—24no—
49#88180—21no—
50#88178—21no—
51#88178—21no—
52C2×#6099—21no—
53#88124—21no—
54#88123D411yescharacteristic
55#88123D411yescharacteristic
56C4×Dic26—21no—
57C4×Dic26—21no—
58C13×#106—24no—
59C13×C4⋊C8—21no—
60C13×C4⋊C8D412yes—
61C13×#102—24no—
62#88075—24no—
63#88072—22no—
64#88072—22no—
65C22⋊#1055—21no—
66C22⋊#1055D412yes—
67#88048—22no—
68#88047—22no—
69C4⋊#1055—21no—
70C4⋊#1055—21no—
71C4⋊#1055—21no—
72C4⋊#1055D412yes—
73C4×#1055—21no—
74C4×#1055—21no—
75#10182—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×C13Q1612yescomplemented
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—21no—
102C13×C4⋊C4—22no—
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—
112#6107—84no—
113C4⋊Dic13—21no—
114C4⋊Dic13—21no—
115C4⋊Dic13—21no—
116C4⋊Dic13—21no—
117#6101—41no—
118#6101—41no—
119C4×Dic13—41no—
120#6099—41no—
121#6099—41no—
122C2×#1055—22no—
123C2×#1055—22no—
124C2×#1055—41no—
125#3209—131no—
126#3077—131no—
127C2×#476D1311yescharacteristic
128#1549—131no—
129#1481—131no—
130#1460—131no—
131#1301—131no—
132C23×C13—22no—
133C23×C13—41no—
134C23×C13—41no—
135C23×C13—81no—
136C23×C13—81no—
137C23×C13#12111yescharacteristic
138Q8×C13—44no—
139Q8×C13—82no—
140D4×C13—22no—
141D4×C13—22no—
142D4×C13—41no—
143D4×C13—41no—
144C2×C4×C13—22no—
145C2×C4×C13—41no—
146C2×C4×C13—41no—
147C2×C4×C13—42no—
148C2×C4×C13—82no—
149C2×C4×C13—82no—
150C2×C4×C13—82no—
151C2×C4×C13—81no—
152C2×C4×C13#12011yescharacteristic
153C2×C4×C13#12011yescharacteristic
154C2×C4×C13#12011yescharacteristic
155C2×C4×C13#12111yescharacteristic
156C2×C4×C13#12111yescharacteristic
157C2×C4×C13#12711yescharacteristic
158C2×C4×C13C2×Q1611yescharacteristic
159C2×C4×C13#13511yescharacteristic
160C2×C4×C13#13711yescharacteristic
161C2×C4×C13#13711yescharacteristic
162C2×Dic13—41no—
163C2×Dic13—41no—
164Dic26—42no—
165Dic26—42no—
166C8×C13—42no—
167#1055—42no—
168#1055—42no—
169#1055—81no—
170#533—131no—
171C2×C4⋊Q8C2×D1311yescharacteristic
172C2×C4×D4C2×D1311yescharacteristic
173#494—261no—
174#487—261no—
175#478—262no—
176#476—22no—
177#476—22no—
178#476—261no—
179#474—261no—
180#462—262no—
181#451—262no—
182#431—131no—
183#431—131no—
184#428—261no—
185C2×#106—21no—
186#423—131no—
187C2×C4⋊C8C2×D1311yescharacteristic
188#418—261no—
189C2×#102—21no—
190#332—262no—
191Q8⋊C8—262no—
192#323—262no—
193C22×C13—21no—
194C22×C13—21no—
195C22×C13—42no—
196C22×C13—82no—
197C22×C13—82no—
198C22×C13—81no—
199C22×C13—81no—
200C22×C13#39211yescharacteristic
201C22×C13#46711yescharacteristic
202C22×C13#47011yescharacteristic
203C4×C13—21no—
204C4×C13—21no—
205C4×C13—21no—
206C4×C13—82no—
207C4×C13—81no—
208C4×C13#45111yescharacteristic
209C4×C13#45111yescharacteristic
210C4×C13#45211yescharacteristic
211C4×C13#45211yescharacteristic
212C4×C13#47112yes—
213Dic13—81no—
214Dic13—81no—
215C22×Q8—21no—
216C22×D4C22⋊D1311yescharacteristic
217C23×C4—21no—
218C2×Q16—264no—
219C2×M16—261no—
220C22×C8—21no—
221C4⋊Q8—21no—
222C4⋊Q8—21no—
223C4⋊Q8—21no—
224C4⋊Q8—131no—
225C4⋊Q8—131no—
226C4⋊Q8C22⋊D1312yes—
227#125—261no—
228C22⋊Q8—261no—
229C22⋊Q8—261no—
230C4×Q8—261no—
231C4×Q8—261no—
232C4×D4—21no—
233C4×D4—21no—
234C4×D4—21no—
235C4×D4—21no—
236#117—261no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4C22⋊D1311yescharacteristic
240C2×C22⋊C4—21no—
241C2×C42C22×D1311yescharacteristic
242#107—262no—
243#106—24no—
244#106—262no—
245C4⋊C8—21no—
246C4⋊C8—132no—
247C4⋊C8—261no—
248C4⋊C8—261no—
249C4⋊C8—261no—
250C4⋊C8C22⋊D1312yes—
251#103—264no—
252#102—24no—
253#102—262no—
254#102—262no—
255C22⋊C8—132no—
256C22⋊C8—261no—
257C4×C8—261no—
258C4×C8—261no—
259C2×C13—21no—
260C2×C13—21no—
261C2×C13—82no—
262C2×C13#200111yescharacteristic
263C2×C13#200811yescharacteristic
264C2×C13#201911yescharacteristic
265C24—21no—
266C2×Q8—22no—
267C2×Q8—41no—
268C2×Q8—82no—
269C2×Q8—261no—
270C2×Q8—261no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—21no—
275C2×D4—21no—
276C2×D4#610712yescomplemented
277C22×C4—21no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4—41no—
281C22×C4—82no—
282C22×C4D4×D1311yescharacteristic
283C22×C4#612911yescharacteristic
284C22×C4C2×C22⋊D1311yescharacteristic
285Q16—1044no—
286M16—521no—
287M16—521no—
288C2×C8—22no—
289C2×C8—41no—
290C2×C8—41no—
291C2×C8—262no—
292C2×C8—262no—
293C2×C8—521no—
294C4⋊C4—21no—
295C4⋊C4—22no—
296C4⋊C4—22no—
297C4⋊C4—21no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4—261no—
301C4⋊C4—261no—
302C4⋊C4—261no—
303C4⋊C4—261no—
304C4⋊C4—521no—
305C4⋊C4—521no—
306C22⋊C4—41no—
307C22⋊C4—41no—
308C22⋊C4—521no—
309C42—521no—
310C42D4×D1311yescharacteristic
311C42D4×D1311yescharacteristic
312C42C2×C22⋊D1311yescharacteristic
313C42C2×C22⋊D1311yescharacteristic
314C13#1018211yescharacteristic, complemented, Sylow
315C23—22no—
316C23—41no—
317C23—41no—
318C23—81no—
319C23—81no—
320C23#8819311yescharacteristic
321Q8—44no—
322Q8—82no—
323Q8—522no—
324Q8—522no—
325D4—22no—
326D4—22no—
327D4—41no—
328D4—41no—
329C2×C4—22no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—42no—
333C2×C4—82no—
334C2×C4—82no—
335C2×C4—82no—
336C2×C4—81no—
337C2×C4—521no—
338C2×C4—521no—
339C2×C4#8819111yescharacteristic
340C2×C4#8819111yescharacteristic
341C2×C4#8819211yescharacteristic
342C2×C4#8819311yescharacteristic
343C2×C4#8819411yescharacteristic
344C2×C4#8819611yescharacteristic
345C2×C4C2×#610711yescharacteristic
346C2×C4#8820411yescharacteristic
347C2×C4#8820511yescharacteristic
348C2×C4#8820711yescharacteristic
349C8—42no—
350C8—522no—
351C8—522no—
352C8—1041no—
353C22—21no—
354C22—21no—
355C22—42no—
356C22—82no—
357C22—82no—
358C22—81no—
359C22—81no—
360C22#1171871211yescharacteristic
361C22#1171871311yescharacteristic
362C22#1171888411yescharacteristic
363C4—21no—
364C4—21no—
365C4—21no—
366C4—81no—
367C4—82no—
368C4—1041no—
369C4—1041no—
370C4#1171870811yescharacteristic
371C4#1171871111yescharacteristic
372C4#1171883812yes—
373C4#1171888911yescharacteristic
374C4#1171890011yescharacteristic
375C2—21no—
376C2—21no—
377C2—82no—
378C2#1311584411yescharacteristic
379C2#1311588711yescharacteristic
380C2#1311594811yescharacteristic
subgroupG/H
centerC22#11718884
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC2×C13×#476C2
socleC22×C13#392
prime radicalC22×D4×C13D4
hypercenterC2×#476D13
hypocenterC13#10182
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
1. #13125784C2semidirect
3. #13113521C2semidirect
4. #13113238C2semidirect
6. #13112733C2semidirect
85. C2×D4×C13Q16semidirect
276. C2×D4#6107semidirect
314. C13#10182semidirect

Maximal subgroups

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

subgroupindex
#131257842
#131246332
#131135212
#131132382
#131131572
#131127332
C2×C13×#4762
#1018213