Finite Group Databasebeta

← #15836841

Subgroups — #15836841

Order 3328.

940 conjugacy classes of subgroups; only the 187 normal subgroups are shown.

normal subgroups only

This group has 940 conjugacy classes of subgroups — too many to draw. Only its 187 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
1C2×#11719205C211yesmaximal, characteristic
2#13125608C212yesmaximal
3#13113877C214yesmaximal, complemented
4#13113809C214yesmaximal, complemented
5#13113407C212yesmaximal
6C2×#11718120C211yesmaximal, characteristic
7C13×#2627C211yesmaximal, characteristic
8C2×C13×C22⋊Q8C2211yescharacteristic
9C22×C13×C4⋊C4C2211yescharacteristic
10C2×#88180—21no—
11C2×#88178—21no—
12C2×#88178C2212yes—
13#11719205—22no—
14#11719205—24no—
15#11719205C2214yes—
16C2×#88144—22no—
17C2×#88142—22no—
18C13×#400C2212yes—
19C13×#398—22no—
20C13×#395C2212yes—
21C13×#385—21no—
22C13×#381—21no—
23C13×#380C2211yescharacteristic
24#11718889C2214yes—
25C2×C22⋊#1055C2212yes—
26#11718712—24no—
27#11718711—22no—
28#11718705—22no—
29#11718631C2214yes—
30#11718120C2214yes—
31#11718044C2218yes—
32C22×Q8×C13C2311yescharacteristic
33C23×C4×C13D411yescharacteristic
34C23×C4×C13D411yescharacteristic
35C23×C4×C13C2311yescharacteristic
36C22×Dic26—21no—
37C22×Dic26D412yes—
38C13×C22⋊Q8—22no—
39C13×C22⋊Q8—22no—
40C2×C13×C4⋊C4—22no—
41C2×C13×C4⋊C4—22no—
42C2×C13×C4⋊C4—21no—
43C2×C13×C4⋊C4—21no—
44C2×C13×C4⋊C4—22no—
45C2×C13×C4⋊C4D412yes—
46C2×C13×C4⋊C4C2311yescharacteristic
47C2×C13×C4⋊C4C2312yes—
48C2×C13×C22⋊C4—21no—
49C2×C13×C22⋊C4—21no—
50C2×C22⋊Dic13—22no—
51C2×#6107—24no—
52#88180—24no—
53#88180—24no—
54C2×C4⋊Dic13—21no—
55C2×C4⋊Dic13—21no—
56C2×C4⋊Dic13—21no—
57C2×C4⋊Dic13D412yes—
58#88178—24no—
59#88178—22no—
60#88178—22no—
61#88178—24no—
62#88178D414yes—
63#88178C2314yes—
64C2×#6101—22no—
65C2×#6101—22no—
66C2×C4×Dic13—22no—
67C22×#1055—22no—
68#88144—28no—
69#88144—28no—
70#88142—28no—
71#88142—28no—
72C13×#95—22no—
73C13×#95—22no—
74C13×#95—22no—
75C13×#95C2312yes—
76#88075—24no—
77C22⋊#1055—22no—
78C22⋊#1055C2314yes—
79#88050—24no—
80#88047—24no—
81#18295—131nomaximal, Sylow
82C24×C13C2×D411yescharacteristic
83C2×Q8×C13—22no—
84C2×Q8×C13—81no—
85C22×C4×C13—21no—
86C22×C4×C13—21no—
87C22×C4×C13—22no—
88C22×C4×C13—21no—
89C22×C4×C13—21no—
90C22×C4×C13—21no—
91C22×C4×C13—22no—
92C22×C4×C13—21no—
93C22×C4×C13—81no—
94C22×C4×C13—81no—
95C22×C4×C13Q1614yescomplemented
96C22×C4×C13C2×D412yes—
97C22×C4×C13C2×D412yes—
98C22×C4×C13C2×D412yes—
99C22×C4×C13C2×D412yes—
100C22×C4×C13C2×D411yescharacteristic
101C22×C4×C13C2411yescharacteristic
102C22×Dic13—22no—
103C22×Dic13—22no—
104C2×Dic26—24no—
105C2×Dic26—22no—
106C2×Dic26—82no—
107C2×Dic26—82no—
108C2×Dic26C2×D414yes—
109C13×C4⋊C4—24no—
110C13×C4⋊C4—24no—
111C13×C4⋊C4—22no—
112C13×C4⋊C4—42no—
113C13×C4⋊C4—81no—
114C13×C4⋊C4—82no—
115C13×C22⋊C4—41no—
116C13×C22⋊C4—41no—
117C13×C22⋊C4—42no—
118C22⋊Dic13—24no—
119C22⋊Dic13—24no—
120#6107—84no—
121C4⋊Dic13—24no—
122C4⋊Dic13—24no—
123C4⋊Dic13—24no—
124C4⋊Dic13—22no—
125C4⋊Dic13C2×D414yes—
126#6101—28no—
127#6101—24no—
128#6101—24no—
129C4×Dic13—28no—
130C2×#1055—24no—
131C2×#1055—82no—
132C2×#544—131no—
133#3189—132no—
134#2627D1311yescharacteristic
135#1617—134no—
136#1605—134no—
137#1520—132no—
138C2×#324—131no—
139C23×C13—41no—
140C23×C13—41no—
141C23×C13#12011yescharacteristic
142C23×C13#12011yescharacteristic
143C23×C13C2×Q1612yes—
144C23×C13#13712yes—
145C23×C13C22×D411yescharacteristic
146Q8×C13—44no—
147C2×C4×C13—22no—
148C2×C4×C13—22no—
149C2×C4×C13—24no—
150C2×C4×C13—24no—
151C2×C4×C13—22no—
152C2×C4×C13—42no—
153C2×C4×C13—41no—
154C2×C4×C13—42no—
155C2×C4×C13—41no—
156C2×C4×C13—42no—
157C2×C4×C13—42no—
158C2×C4×C13—42no—
159C2×C4×C13—42no—
160C2×C4×C13—42no—
161C2×C4×C13—42no—
162C2×C4×C13—41no—
163C2×C4×C13—41no—
164C2×C4×C13—42no—
165C2×C4×C13—81no—
166C2×C4×C13#12012yes—
167C2×C4×C13C2×Q1614yes—
168C2×C4×C13C22×D412yes—
169C2×Dic13—24no—
170C2×Dic13—24no—
171C2×Dic13—44no—
172C2×Dic13—44no—
173Dic26—44no—
174Dic26—82no—
175Dic26—84no—
176#1055—44no—
177#544—134no—
178#544—264no—
179#544—262no—
180C2×C4⋊Q8—262no—
181C2×#125—262no—
182C2×C22⋊Q8—132no—
183C2×C22⋊Q8—261no—
184C2×C22⋊Q8C2×D1311yescharacteristic
185C2×#117—261no—
186C22×C4⋊C4C2×D1311yescharacteristic
187#484—134no—
188#484—262no—
189#467—264no—
190#451—134no—
191#451—262no—
192C2×C22⋊C8—132no—
193#400C2×D1312yes—
194#398—22no—
195#395C2×D1312yes—
196#385—21no—
197#381—21no—
198#380C2×D1311yescharacteristic
199#328—138no—
200#324—134no—
201C22×C13—21no—
202C22×C13—21no—
203C22×C13—21no—
204C22×C13—21no—
205C22×C13—21no—
206C22×C13—21no—
207C22×C13—42no—
208C22×C13—42no—
209C22×C13#45112yes—
210C22×C13#45112yes—
211C22×C13C2×#12011yescharacteristic
212C22×C13C22×Q1611yescharacteristic
213C22×C13C2×#13711yescharacteristic
214C4×C13—24no—
215C4×C13—22no—
216C4×C13—22no—
217C4×C13—42no—
218C4×C13—82no—
219C4×C13—81no—
220C4×C13—81no—
221Dic13—44no—
222Dic13—44no—
223C22×Q8—132no—
224C22×Q8—261no—
225C22×Q8C22×D1311yescharacteristic
226C23×C4C22⋊D1311yescharacteristic
227C23×C4C22⋊D1311yescharacteristic
228C23×C4C22×D1311yescharacteristic
229C2×Q16—264no—
230C22×C8—262no—
231C4⋊Q8—268no—
232C4⋊Q8—268no—
233#125—268no—
234#125—268no—
235C22⋊Q8—22no—
236C22⋊Q8—22no—
237C22⋊Q8—134no—
238C22⋊Q8—134no—
239C22⋊Q8—264no—
240C22⋊Q8—262no—
241C22⋊Q8—262no—
242C22⋊Q8—264no—
243#117—264no—
244#117—264no—
245C2×C4⋊C4—22no—
246C2×C4⋊C4—22no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—22no—
250C2×C4⋊C4—132no—
251C2×C4⋊C4—261no—
252C2×C4⋊C4—261no—
253C2×C4⋊C4—261no—
254C2×C4⋊C4—262no—
255C2×C4⋊C4—262no—
256C2×C4⋊C4C22⋊D1312yes—
257C2×C4⋊C4C22×D1311yescharacteristic
258C2×C4⋊C4C22×D1312yes—
259C2×C22⋊C4—21no—
260C2×C22⋊C4—21no—
261C2×C22⋊C4—262no—
262C2×C42—262no—
263#107—264no—
264#103—264no—
265#103—264no—
266C22⋊C8—134no—
267C22⋊C8—262no—
268#95—22no—
269#95—22no—
270#95—22no—
271#95C22×D1312yes—
272C2×C13—21no—
273C2×C13—21no—
274C2×C13—22no—
275C2×C13—22no—
276C2×C13C2×#45111yescharacteristic
277C2×C13#302011yescharacteristic
278C2×C13#302611yescharacteristic
279C24C2×C22⋊D1311yescharacteristic
280C2×Q8—22no—
281C2×Q8—81no—
282C2×Q8—134no—
283C2×Q8—264no—
284C2×Q8—262no—
285C2×Q8—1042no—
286C2×Q8—1042no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—22no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—22no—
294C22×C4—21no—
295C22×C4—81no—
296C22×C4—81no—
297C22×C4—262no—
298C22×C4—262no—
299C22×C4#610714yescomplemented
300C22×C4D4×D1312yes—
301C22×C4D4×D1312yes—
302C22×C4C2×C22⋊D1312yes—
303C22×C4C2×C22⋊D1312yes—
304C22×C4C2×C22⋊D1311yescharacteristic
305C22×C4C23×D1311yescharacteristic
306Q16—1044no—
307C2×C8—264no—
308C2×C8—1042no—
309C4⋊C4—24no—
310C4⋊C4—24no—
311C4⋊C4—22no—
312C4⋊C4—42no—
313C4⋊C4—81no—
314C4⋊C4—82no—
315C4⋊C4—134no—
316C4⋊C4—264no—
317C4⋊C4—264no—
318C4⋊C4—264no—
319C4⋊C4—268no—
320C4⋊C4—262no—
321C4⋊C4—264no—
322C4⋊C4—264no—
323C22⋊C4—41no—
324C22⋊C4—41no—
325C22⋊C4—42no—
326C22⋊C4—264no—
327C22⋊C4—264no—
328C42—268no—
329C13#1829511yescharacteristic, complemented, Sylow
330C23—41no—
331C23—41no—
332C23#8819111yescharacteristic
333C23#8819111yescharacteristic
334C23C2×#610712yes—
335C23#8820512yes—
336C23C22×C22⋊D1311yescharacteristic
337Q8—44no—
338Q8—524no—
339Q8—1042no—
340Q8—1044no—
341C2×C4—24no—
342C2×C4—24no—
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—22no—
346C2×C4—41no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—41no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—42no—
359C2×C4—81no—
360C2×C4—264no—
361C2×C4—264no—
362C2×C4—524no—
363C2×C4—524no—
364C2×C4#8819112yes—
365C2×C4C2×#610714yes—
366C2×C4C2×D4×D1312yes—
367C8—524no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—42no—
375C22—42no—
376C22#1171871112yes—
377C22#1171871112yes—
378C22C2×#8819111yescharacteristic
379C22C22×#610711yescharacteristic
380C22C2×#8820511yescharacteristic
381C4—22no—
382C4—22no—
383C4—24no—
384C4—42no—
385C4—82no—
386C4—81no—
387C4—81no—
388C4—524no—
389C4—524no—
390C2—21no—
391C2—22no—
392C2—22no—
393C2—21no—
394C2C2×#1171871111yescharacteristic
395C2#1312419911yescharacteristic
396C2#1312423211yescharacteristic
subgroupG/H
centerC22C2×#88191
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2627C2
socleC22×C13C2×#120
prime radicalC24×C13C2×D4
hypercenter#2627D13
hypocenterC13#18295
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2627

Complements

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

NH ≅ G/Ntype
3. #13113877C2semidirect
4. #13113809C2semidirect
95. C22×C4×C13Q16semidirect
299. C22×C4#6107semidirect
329. C13#18295semidirect

Maximal subgroups

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

subgroupindex
C2×#117192052
#131256082
#131138772
#131138092
#131134072
C2×#117181202
C13×#26272
#1829513