Finite Group Databasebeta

← #15767316

Subgroups — #15767316

Order 3328.

490 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 99 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#13125608C211yesmaximal, characteristic
2#13115821C211yesmaximal, characteristic
3#13115260C211yesmaximal, characteristic
4#13115257C211yesmaximal, characteristic
5#13115016C211yesmaximal, characteristic
6#13112703C211yesmaximal, characteristic
7C13×#1996C211yesmaximal, characteristic
8C2×C13×C22⋊Q8C2211yescharacteristic
9C2×#88178C2211yescharacteristic
10C23×#1055C2211yescharacteristic
11C13×#380C2211yescharacteristic
12C4×C13×C22⋊C4C2211yescharacteristic
13#11718889—21no—
14C2×#88075—21no—
15#11718873C2211yescharacteristic
16C2×C22⋊#1055C2211yescharacteristic
17#11718712—21no—
18#11718712—21no—
19#11718711—21no—
20#11718705—21no—
21#11718631—21no—
22C2×#88050—21no—
23C2×C4⋊#1055—21no—
24C13×#342—21no—
25C13×#342—21no—
26#11718121—21no—
27#11718121—21no—
28#11718119—21no—
29#11718119—21no—
30#11718116—21no—
31C22×Q8×C13D411yescharacteristic
32C23×C4×C13C2311yescharacteristic
33C22×Dic26D411yescharacteristic
34C13×C22⋊Q8—21no—
35C13×C22⋊Q8—21no—
36C13×C22⋊Q8—21no—
37C13×C22⋊Q8—21no—
38C2×C13×C4⋊C4—21no—
39C2×C13×C4⋊C4—21no—
40C2×C13×C4⋊C4D411yescharacteristic
41C2×C13×C22⋊C4—21no—
42C2×C13×C22⋊C4—21no—
43C2×C13×C22⋊C4D411yescharacteristic
44C2×C13×C22⋊C4D411yescharacteristic
45C2×C42×C13—21no—
46C2×C22⋊Dic13—21no—
47C2×C22⋊Dic13—21no—
48C2×#6107—21no—
49C2×#6107—21no—
50C2×C4⋊Dic13—21no—
51C2×C4⋊Dic13D411yescharacteristic
52#88178—21no—
53#88178—21no—
54#88178—21no—
55#88178—21no—
56C2×#6101—21no—
57C22×#1055—21no—
58C22×#1055—21no—
59C22×#1055—21no—
60C22×#1055—42no—
61C22×#1055D411yescharacteristic
62C22×#1055D411yescharacteristic
63C13×#95—21no—
64C13×#95—21no—
65#88075—21no—
66#88075—21no—
67#88075—42no—
68#88071—21no—
69C22⋊#1055—21no—
70C22⋊#1055—21no—
71#88050—21no—
72#88050—21no—
73#88050—42no—
74#88047—21no—
75#88047—21no—
76C4⋊#1055—42no—
77#10566—131nomaximal, Sylow
78C24×C13C2×D411yescharacteristic
79C2×Q8×C13—21no—
80C2×Q8×C13—21no—
81C2×Q8×C13—41no—
82C2×Q8×C13—41no—
83C22×C4×C13—21no—
84C22×C4×C13—21no—
85C22×C4×C13—21no—
86C22×C4×C13—21no—
87C22×C4×C13—41no—
88C22×C4×C13—41no—
89C22×C4×C13—41no—
90C22×C4×C13C2×D411yescharacteristic
91C22×C4×C13C2×D411yescharacteristic
92C22×C4×C13C2×D411yescharacteristic
93C22×C4×C13#4111yescharacteristic
94C22×C4×C13#4111yescharacteristic
95C22×C4×C13#4111yescharacteristic
96C22×Dic13—21no—
97C22×Dic13—21no—
98C22×Dic13—41no—
99C2×Dic26—21no—
100C2×Dic26—21no—
101C2×Dic26—41no—
102C2×Dic26—41no—
103C13×C4⋊C4—21no—
104C13×C4⋊C4—21no—
105C13×C4⋊C4—41no—
106C13×C4⋊C4—41no—
107C13×C4⋊C4—41no—
108C13×C4⋊C4—41no—
109C13×C22⋊C4—21no—
110C13×C22⋊C4—21no—
111C13×C22⋊C4—21no—
112C13×C22⋊C4—41no—
113C13×C22⋊C4—41no—
114C13×C22⋊C4—41no—
115C13×C22⋊C4—41no—
116C13×C22⋊C4Q1612yescomplemented
117C42×C13—41no—
118C42×C13—41no—
119C22⋊Dic13—41no—
120C22⋊Dic13—41no—
121C22⋊Dic13—41no—
122C22⋊Dic13—41no—
123#6107—81no—
124#6107—81no—
125C4⋊Dic13—21no—
126C4⋊Dic13—21no—
127C4⋊Dic13—41no—
128C4⋊Dic13—41no—
129#6101—41no—
130#6101—41no—
131C2×#1055—22no—
132C2×#1055—22no—
133C2×#1055—22no—
134C2×#1055—21no—
135C2×#1055—21no—
136C2×#1055—41no—
137C2×#1055—41no—
138C2×#1055—41no—
139C2×#1055—41no—
140C2×#1055—41no—
141C2×#1055—41no—
142#3189—131no—
143#1996—131no—
144#1996D1311yescharacteristic
145#1892—131no—
146#1892—131no—
147#1850—131no—
148#1289—131no—
149C23×C13—41no—
150C23×C13—41no—
151C23×C13#12111yescharacteristic
152C23×C13#12111yescharacteristic
153C23×C13#12111yescharacteristic
154C23×C13C2×Q1611yescharacteristic
155C23×C13#13511yescharacteristic
156C23×C13#13711yescharacteristic
157C23×C13#13711yescharacteristic
158Q8×C13—42no—
159Q8×C13—41no—
160Q8×C13—41no—
161C2×C4×C13—21no—
162C2×C4×C13—21no—
163C2×C4×C13—21no—
164C2×C4×C13—21no—
165C2×C4×C13—21no—
166C2×C4×C13—21no—
167C2×C4×C13—22no—
168C2×C4×C13—41no—
169C2×C4×C13—41no—
170C2×C4×C13—41no—
171C2×C4×C13—41no—
172C2×C4×C13—41no—
173C2×C4×C13—41no—
174C2×C4×C13—41no—
175C2×C4×C13—41no—
176C2×C4×C13—41no—
177C2×C4×C13—41no—
178C2×C4×C13—81no—
179C2×C4×C13—81no—
180C2×C4×C13—81no—
181C2×C4×C13—81no—
182C2×C4×C13—81no—
183C2×C4×C13#12011yescharacteristic
184C2×C4×C13#12311yescharacteristic
185C2×C4×C13#12311yescharacteristic
186C2×C4×C13#12411yescharacteristic
187C2×Dic13—41no—
188C2×Dic13—41no—
189C2×Dic13—81no—
190C2×Dic13—81no—
191C2×Dic13—81no—
192C2×Dic13—81no—
193C2×Dic13—81no—
194Dic26—42no—
195Dic26—41no—
196Dic26—41no—
197#1055—42no—
198#1055—41no—
199#1055—41no—
200C23×C8—131no—
201C2×C22⋊Q8—131no—
202C2×C22⋊Q8C2×D1311yescharacteristic
203#484—261no—
204#484—261no—
205#467—261no—
206#467—261no—
207#451—261no—
208#451—261no—
209C2×C4⋊C8—261no—
210C2×#103—261no—
211C2×#103—261no—
212C2×C22⋊C8—131no—
213#380—131no—
214#380C2×D1311yescharacteristic
215C4×C22⋊C4C2×D1311yescharacteristic
216#342—21no—
217#342—21no—
218#342—261no—
219#342—261no—
220#340—261no—
221#340—261no—
222#336—261no—
223C22×C13—21no—
224C22×C13—21no—
225C22×C13—21no—
226C22×C13—21no—
227C22×C13—21no—
228C22×C13—21no—
229C22×C13—41no—
230C22×C13—41no—
231C22×C13—41no—
232C22×C13—41no—
233C22×C13#39411yescharacteristic
234C22×C13#46211yescharacteristic
235C22×C13#46211yescharacteristic
236C22×C13#46411yescharacteristic
237C22×C13#46411yescharacteristic
238C22×C13#46711yescharacteristic
239C22×C13#47011yescharacteristic
240C4×C13—21no—
241C4×C13—21no—
242C4×C13—21no—
243C4×C13—42no—
244C4×C13—81no—
245C4×C13—81no—
246C4×C13—81no—
247C4×C13—161no—
248C4×C13B(4,𝔽2)11yescharacteristic
249C4×C13#45811yescharacteristic
250Dic13—81no—
251Dic13—81no—
252Dic13—161no—
253C22×Q8—131no—
254C22×Q8D5211yescharacteristic
255C23×C4C22×D1311yescharacteristic
256C2×Q16—261no—
257C2×Q16—261no—
258C22×C8—131no—
259C22×C8—131no—
260C22×C8—261no—
261C22×C8—261no—
262C22×C8—261no—
263C22×C8—522no—
264C22⋊Q8—21no—
265C22⋊Q8—21no—
266C22⋊Q8—21no—
267C22⋊Q8—21no—
268C22⋊Q8—261no—
269C22⋊Q8—261no—
270C22⋊Q8—261no—
271C22⋊Q8—261no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—131no—
275C2×C4⋊C4—261no—
276C2×C4⋊C4—261no—
277C2×C4⋊C4D5211yescharacteristic
278C2×C22⋊C4—21no—
279C2×C22⋊C4—21no—
280C2×C22⋊C4—261no—
281C2×C22⋊C4—261no—
282C2×C22⋊C4C22⋊D1311yescharacteristic
283C2×C22⋊C4C22⋊D1311yescharacteristic
284C2×C42—21no—
285#107—261no—
286#107—261no—
287C4⋊C8—522no—
288#103—261no—
289#103—261no—
290#103—261no—
291#103—261no—
292#103—522no—
293#103—522no—
294C22⋊C8—261no—
295C22⋊C8—261no—
296#95—21no—
297#95—21no—
298#95—261no—
299C2×C13—21no—
300C2×C13—21no—
301C2×C13—21no—
302C2×C13—21no—
303C2×C13—21no—
304C2×C13—21no—
305C2×C13#204411yescharacteristic
306C2×C13#205311yescharacteristic
307C2×C13#205611yescharacteristic
308C24C2×C22⋊D1311yescharacteristic
309C2×Q8—21no—
310C2×Q8—21no—
311C2×Q8—41no—
312C2×Q8—41no—
313C2×Q8—261no—
314C2×Q8—261no—
315C2×Q8—521no—
316C2×Q8—521no—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—41no—
322C22×C4—41no—
323C22×C4—41no—
324C22×C4—261no—
325C22×C4—261no—
326C22×C4—521no—
327C22×C4C2×D5211yescharacteristic
328C22×C4#612711yescharacteristic
329C22×C4D4×D1311yescharacteristic
330C22×C4D4×D1311yescharacteristic
331C22×C4#612911yescharacteristic
332C22×C4#612911yescharacteristic
333Q16—1041no—
334Q16—1041no—
335C2×C8—262no—
336C2×C8—262no—
337C2×C8—262no—
338C2×C8—261no—
339C2×C8—261no—
340C2×C8—521no—
341C2×C8—521no—
342C2×C8—521no—
343C2×C8—521no—
344C2×C8—521no—
345C2×C8—521no—
346C4⋊C4—21no—
347C4⋊C4—21no—
348C4⋊C4—41no—
349C4⋊C4—41no—
350C4⋊C4—41no—
351C4⋊C4—41no—
352C4⋊C4—261no—
353C4⋊C4—261no—
354C4⋊C4—521no—
355C4⋊C4—521no—
356C4⋊C4—521no—
357C4⋊C4—521no—
358C22⋊C4—21no—
359C22⋊C4—21no—
360C22⋊C4—21no—
361C22⋊C4—41no—
362C22⋊C4—41no—
363C22⋊C4—41no—
364C22⋊C4—41no—
365C22⋊C4—521no—
366C22⋊C4—521no—
367C22⋊C4—521no—
368C22⋊C4—521no—
369C22⋊C4#610712yescomplemented
370C42—41no—
371C42—41no—
372C13#1056611yescharacteristic, complemented, Sylow
373C23—41no—
374C23—41no—
375C23#8818411yescharacteristic
376C23#8819211yescharacteristic
377C23#8819311yescharacteristic
378C23#8819611yescharacteristic
379C23C2×#610711yescharacteristic
380C23#8820411yescharacteristic
381C23#8820511yescharacteristic
382Q8—42no—
383Q8—41no—
384Q8—41no—
385Q8—522no—
386Q8—521no—
387Q8—521no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—22no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—81no—
406C2×C4—81no—
407C2×C4—81no—
408C2×C4—81no—
409C2×C4—81no—
410C2×C4—521no—
411C2×C4—521no—
412C2×C4—1041no—
413C2×C4—1041no—
414C2×C4—1041no—
415C2×C4—1041no—
416C2×C4—1041no—
417C2×C4#8813611yescharacteristic
418C2×C4#8813711yescharacteristic
419C2×C4#8813911yescharacteristic
420C2×C4#8814011yescharacteristic
421C8—522no—
422C8—521no—
423C8—521no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—21no—
428C22—21no—
429C22—21no—
430C22—41no—
431C22—41no—
432C22—41no—
433C22—41no—
434C22#1171862211yescharacteristic
435C22#1171868911yescharacteristic
436C22#1171869211yescharacteristic
437C22#1171871211yescharacteristic
438C22#1171871311yescharacteristic
439C22#1171871511yescharacteristic
440C22#1171875111yescharacteristic
441C4—21no—
442C4—21no—
443C4—21no—
444C4—42no—
445C4—81no—
446C4—81no—
447C4—81no—
448C4—161no—
449C4—1041no—
450C4—1041no—
451C4—2081no—
452C4#1171840211yescharacteristic
453C4#1171840311yescharacteristic
454C2—21no—
455C2—21no—
456C2—21no—
457C2—21no—
458C2—21no—
459C2—21no—
460C2#1311608611yescharacteristic
461C2#1311614111yescharacteristic
462C2#1311615811yescharacteristic
subgroupG/H
centerC22#11718622
commutator, cosocleC23×C4×C13C23
FrattiniC23×C4C22×D13
FittingC13×#1996C2
socleC22×C13#394
prime radicalC24×C13C2×D4
hypercenter#1996D13
hypocenterC13#10566
LCSG ▷ C23×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1996

Complements

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

NH ≅ G/Ntype
116. C13×C22⋊C4Q16semidirect
369. C22⋊C4#6107semidirect
372. C13#10566semidirect

Maximal subgroups

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

subgroupindex
#131256082
#131158212
#131152602
#131152572
#131150162
#131127032
C13×#19962
#1056613