Finite Group Databasebeta

← #15763642

Subgroups — #15763642

Order 3328.

510 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 89 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#13125657C211yesmaximal, characteristic
2C2×#11718632C211yesmaximal, characteristic
3#13114916C211yesmaximal, characteristic
4#13113200C211yesmaximal, characteristic
5#13113199C211yesmaximal, characteristic
6#13112724C211yesmaximal, characteristic
7C2×C13×#484C211yesmaximal, characteristic
8C2×C13×C22⋊Q8C2211yescharacteristic
9C22×C13×C4⋊C4C2211yescharacteristic
10C2×#88178C2211yescharacteristic
11C13×#484—22no—
12C13×#484—22no—
13C2×C13×#107—21no—
14C2×C13×#103—21no—
15C2×C13×C22⋊C8C2211yescharacteristic
16#11718889—21no—
17#11718868C2211yescharacteristic
18#11718868C2211yescharacteristic
19C2×C22⋊#1055C2211yescharacteristic
20#11718713—22no—
21#11718711—21no—
22#11718704—21no—
23#11718632—21no—
24#11718632—22no—
25#11718632—22no—
26C2×#88050—21no—
27C2×#88048—21no—
28#11718122—22no—
29#11718120—22no—
30#11718061—22no—
31C22×Q8×C13D411yescharacteristic
32C23×C4×C13—21no—
33C23×C4×C13C2311yescharacteristic
34C22×Dic26D411yescharacteristic
35C22×C8×C13—21no—
36C13×C22⋊Q8—21no—
37C13×C22⋊Q8—21no—
38C13×C22⋊Q8—21no—
39C13×C22⋊Q8—21no—
40C2×C13×C4⋊C4—21no—
41C2×C13×C4⋊C4—21no—
42C2×C13×C4⋊C4—21no—
43C2×C13×C4⋊C4—21no—
44C2×C13×C4⋊C4—21no—
45C2×C13×C4⋊C4—21no—
46C2×C13×C4⋊C4D411yescharacteristic
47C2×C13×C4⋊C4D412yes—
48C2×C13×C22⋊C4—21no—
49C2×C22⋊Dic13—21no—
50C2×#6107—22no—
51C2×C4⋊Dic13D411yescharacteristic
52#88178—21no—
53#88178—21no—
54#88178—21no—
55#88178—21no—
56C2×#6101—21no—
57C2×#6099—21no—
58C2×#6099D412yes—
59C22×#1055—21no—
60C13×#107—24no—
61C13×#103—24no—
62C13×C22⋊C8—21no—
63C13×C22⋊C8D412yes—
64#88075—22no—
65C22⋊#1055—21no—
66C22⋊#1055—21no—
67C22⋊#1055—21no—
68C22⋊#1055—21no—
69C22⋊#1055—21no—
70C22⋊#1055D412yes—
71#88050—22no—
72#88050—24no—
73#88048—22no—
74#88048—24no—
75#9995—131nomaximal, Sylow
76C24×C13#4111yescharacteristic
77C2×Q8×C13—21no—
78C2×Q8×C13—21no—
79C2×Q8×C13—42no—
80C22×C4×C13—21no—
81C22×C4×C13—21no—
82C22×C4×C13—22no—
83C22×C4×C13—42no—
84C22×C4×C13—41no—
85C22×C4×C13—41no—
86C22×C4×C13—82no—
87C22×C4×C13C2×D411yescharacteristic
88C22×C4×C13C2×D411yescharacteristic
89C22×C4×C13C2×D411yescharacteristic
90C22×C4×C13C2×D411yescharacteristic
91C22×C4×C13C2×D411yescharacteristic
92C22×C4×C13C2×D411yescharacteristic
93C22×Dic13—21no—
94C22×Dic13—21no—
95C2×Dic26—21no—
96C2×Dic26—21no—
97C2×Dic26—42no—
98C2×C8×C13—22no—
99C2×C8×C13—42no—
100C13×C4⋊C4—22no—
101C13×C4⋊C4—21no—
102C13×C4⋊C4—22no—
103C13×C4⋊C4—21no—
104C13×C4⋊C4—41no—
105C13×C4⋊C4—41no—
106C13×C4⋊C4—41no—
107C13×C4⋊C4—41no—
108C13×C22⋊C4—41no—
109C13×C22⋊C4—41no—
110C22⋊Dic13—41no—
111C22⋊Dic13—41no—
112#6107—82no—
113C4⋊Dic13—21no—
114C4⋊Dic13—21no—
115#6101—41no—
116#6101—41no—
117#6099—42no—
118#6099—42no—
119C2×#1055—22no—
120C2×#1055—22no—
121C2×#1055—42no—
122C2×#1055—41no—
123#3195—131no—
124C2×#484D1311yescharacteristic
125C2×#483—131no—
126#1821—131no—
127#1472—131no—
128#1472—131no—
129#1298—131no—
130C23×C13—22no—
131C23×C13—22no—
132C23×C13—41no—
133C23×C13#12111yescharacteristic
134C23×C13#12111yescharacteristic
135C23×C13#12111yescharacteristic
136Q8×C13—42no—
137Q8×C13—42no—
138C2×C4×C13—22no—
139C2×C4×C13—22no—
140C2×C4×C13—22no—
141C2×C4×C13—41no—
142C2×C4×C13—41no—
143C2×C4×C13—41no—
144C2×C4×C13—41no—
145C2×C4×C13—41no—
146C2×C4×C13—42no—
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#12711yescharacteristic
156C2×Dic13—41no—
157C2×Dic13—41no—
158C2×Dic13—42no—
159C2×Dic13—81no—
160Dic26—42no—
161Dic26—42no—
162C8×C13—42no—
163#1055—42no—
164#1055—42no—
165#1055—81no—
166C2×C22⋊Q8—131no—
167C2×C22⋊Q8C2×D1311yescharacteristic
168C22×C4⋊C4C2×D1311yescharacteristic
169#484—22no—
170#484—22no—
171#483—262no—
172#483—261no—
173#483—262no—
174#483—261no—
175#470—262no—
176#451—261no—
177#451—261no—
178C2×#107—21no—
179C2×#106—261no—
180C2×#103—21no—
181C2×#103—261no—
182#407—131no—
183#407—131no—
184C2×C22⋊C8—131no—
185C2×C22⋊C8C2×D1311yescharacteristic
186#343—262no—
187#324—262no—
188#324—262no—
189C22×C13—21no—
190C22×C13—21no—
191C22×C13—21no—
192C22×C13—21no—
193C22×C13—21no—
194C22×C13—21no—
195C22×C13—21no—
196C22×C13—44no—
197C22×C13#39211yescharacteristic
198C22×C13#47112yes—
199C22×C13#47312yes—
200C4×C13—21no—
201C4×C13—21no—
202C4×C13—21no—
203C4×C13—81no—
204C4×C13—82no—
205C4×C13—81no—
206C4×C13#45812yes—
207Dic13—81no—
208Dic13—81no—
209C22×Q8—131no—
210C22×Q8C22⋊D1311yescharacteristic
211C23×C4—21no—
212C23×C4C22×D1311yescharacteristic
213C2×Q16—262no—
214C2×M16—132no—
215C2×M16—261no—
216C22×C8—21no—
217C22×C8—261no—
218C22⋊Q8—21no—
219C22⋊Q8—21no—
220C22⋊Q8—21no—
221C22⋊Q8—21no—
222C22⋊Q8—261no—
223C22⋊Q8—261no—
224C22⋊Q8—261no—
225C22⋊Q8—261no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—131no—
233C2×C4⋊C4—261no—
234C2×C4⋊C4C22⋊D1312yes—
235C2×C4⋊C4C22⋊D1311yescharacteristic
236C2×C22⋊C4—21no—
237C2×C22⋊C4—261no—
238#107—24no—
239#106—264no—
240#106—262no—
241#103—24no—
242#103—264no—
243#103—262no—
244#103—262no—
245C22⋊C8—21no—
246C22⋊C8—132no—
247C22⋊C8—261no—
248C22⋊C8—261no—
249C22⋊C8—261no—
250C22⋊C8—261no—
251C22⋊C8—261no—
252C22⋊C8C22⋊D1312yes—
253C2×C13—22no—
254C2×C13—22no—
255C2×C13—41no—
256C2×C13#201911yescharacteristic
257C2×C13#202011yescharacteristic
258C2×C13#202211yescharacteristic
259C24#612911yescharacteristic
260C2×Q8—21no—
261C2×Q8—21no—
262C2×Q8—42no—
263C2×Q8—261no—
264C2×Q8—261no—
265C2×Q8—522no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—22no—
269C22×C4—42no—
270C22×C4—41no—
271C22×C4—41no—
272C22×C4—82no—
273C22×C4—261no—
274C22×C4—261no—
275C22×C4D4×D1311yescharacteristic
276C22×C4D4×D1311yescharacteristic
277C22×C4D4×D1311yescharacteristic
278C22×C4C2×C22⋊D1311yescharacteristic
279C22×C4C2×C22⋊D1311yescharacteristic
280C22×C4C2×C22⋊D1311yescharacteristic
281Q16—1042no—
282M16—522no—
283M16—522no—
284C2×C8—22no—
285C2×C8—42no—
286C2×C8—262no—
287C2×C8—262no—
288C2×C8—522no—
289C2×C8—521no—
290C4⋊C4—22no—
291C4⋊C4—21no—
292C4⋊C4—22no—
293C4⋊C4—21no—
294C4⋊C4—41no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—261no—
299C4⋊C4—261no—
300C4⋊C4—521no—
301C4⋊C4—521no—
302C22⋊C4—41no—
303C22⋊C4—41no—
304C22⋊C4—521no—
305C22⋊C4—521no—
306C13#999511yescharacteristic, complemented, Sylow
307C23—22no—
308C23—22no—
309C23—41no—
310C23#8819211yescharacteristic
311C23#8819311yescharacteristic
312C23#8819311yescharacteristic
313Q8—42no—
314Q8—42no—
315Q8—522no—
316Q8—522no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—42no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—42no—
327C2×C4—82no—
328C2×C4—82no—
329C2×C4—82no—
330C2×C4—81no—
331C2×C4—522no—
332C2×C4—521no—
333C2×C4—521no—
334C2×C4—1041no—
335C2×C4#8819111yescharacteristic
336C2×C4#8819111yescharacteristic
337C2×C4#8819411yescharacteristic
338C2×C4#8820711yescharacteristic
339C8—42no—
340C8—522no—
341C8—522no—
342C8—1041no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—44no—
351C22#1171885312yes—
352C22#1171886112yes—
353C22#1171888411yescharacteristic
354C4—21no—
355C4—21no—
356C4—21no—
357C4—81no—
358C4—82no—
359C4—81no—
360C4—1041no—
361C4—1041no—
362C4#1171871412yes—
363C2—22no—
364C2—22no—
365C2—41no—
366C2#1311595011yescharacteristic
367C2#1311595511yescharacteristic
368C2#1311596411yescharacteristic
subgroupG/H
centerC22#11718884
commutator, cosocleC23×C4×C13C23
FrattiniC23×C4C22×D13
FittingC2×C13×#484C2
socleC22×C13#392
prime radicalC24×C13#41
hypercenterC2×#484D13
hypocenterC13#9995
LCSG ▷ C23×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#484

Complements

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

NH ≅ G/Ntype
306. C13#9995semidirect

Maximal subgroups

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

subgroupindex
#131256572
C2×#117186322
#131149162
#131132002
#131131992
#131127242
C2×C13×#4842
#999513