Finite Group Databasebeta

← #15778416

Subgroups — #15778416

Order 3328.

1214 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 1214 conjugacy classes of subgroups — too many to draw. Only its 139 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×#11718133C212yesmaximal, complemented
2C2×#11718137C212yesmaximal, complemented
3#13114751C212yesmaximal, complemented
4C2×C13×#535C211yesmaximal, characteristic
5C22×C13×#41C411yescharacteristic, complemented
6C23×D4×C13C2211yescharacteristic
7C13×#535—24no—
8C13×#535—24no—
9C2×C13×#127C411yescharacteristic, complemented
10C2×C13×#127C2211yescharacteristic
11C2×C13×#124C411yescharacteristic, complemented
12C2×C13×#124C2211yescharacteristic
13C2×C13×#121—22no—
14C2×C13×#120—22no—
15C2×C13×#117C411yescharacteristic, complemented
16#11718908—22no—
17C2×#88074—22no—
18C2×#88074C2214yes—
19#11718137—24no—
20#11718133—24no—
21C25×C13D412yes—
22C2×C13×#41—22no—
23C2×C13×#41—22no—
24C2×C13×#41—42no—
25C2×C13×#41—42no—
26C22×Q8×C13C2×C411yescharacteristic
27C22×D4×C13—21no—
28C22×D4×C13—22no—
29C22×D4×C13—22no—
30C22×D4×C13—22no—
31C22×D4×C13—22no—
32C22×D4×C13—42no—
33C22×D4×C13—42no—
34C22×D4×C13C2×C411yescharacteristic
35C22×D4×C13C2×C411yescharacteristic
36C22×D4×C13D412yes—
37C22×D4×C13C2311yescharacteristic
38C23×C4×C13—21no—
39C23×C4×C13C2×C411yescharacteristic
40C13×#127—22no—
41C13×#127—22no—
42C13×#127—22no—
43C13×#127D414yes—
44C13×#124—22no—
45C13×#124—22no—
46C13×#124—22no—
47C13×#124D414yes—
48C13×#121—216no—
49C13×#120—216no—
50C13×#117—22no—
51C13×#117—22no—
52C2×C13×C4⋊C4—21no—
53C2×C13×C22⋊C4—21no—
54C2×C13×C22⋊C4—22no—
55C2×C13×C22⋊C4—22no—
56C2×C42×C13C2×C411yescharacteristic
57C2×C42×C13C2×C411yescharacteristic
58C2×C22⋊Dic13—24no—
59C2×C22⋊Dic13—44no—
60#88074—24no—
61#88074—24no—
62#88074—44no—
63#12696—131nomaximal, Sylow
64C24×C13—21no—
65C24×C13—24no—
66C24×C13—24no—
67C24×C13—42no—
68C24×C13—84no—
69C24×C13C22⋊C412yes—
70C24×C13C22⋊C411yescharacteristic
71C24×C13C2×D412yes—
72C13×#41—48no—
73C13×#41—48no—
74C2×Q8×C13—21no—
75C2×Q8×C13—41no—
76C2×Q8×C13—41no—
77C2×Q8×C13C22⋊C412yescomplemented
78C2×D4×C13—24no—
79C2×D4×C13—24no—
80C2×D4×C13—28no—
81C2×D4×C13—28no—
82C2×D4×C13—24no—
83C2×D4×C13—21no—
84C2×D4×C13—21no—
85C2×D4×C13—21no—
86C2×D4×C13—41no—
87C2×D4×C13—41no—
88C2×D4×C13—42no—
89C2×D4×C13—41no—
90C2×D4×C13—41no—
91C2×D4×C13—41no—
92C2×D4×C13—41no—
93C2×D4×C13—48no—
94C2×D4×C13—48no—
95C2×D4×C13—42no—
96C2×D4×C13—42no—
97C2×D4×C13—84no—
98C2×D4×C13—84no—
99C2×D4×C13C22⋊C412yescomplemented
100C2×D4×C13C2×D412yes—
101C2×D4×C13C2×D412yes—
102C22×C4×C13—22no—
103C22×C4×C13—22no—
104C22×C4×C13—21no—
105C22×C4×C13—21no—
106C22×C4×C13—24no—
107C22×C4×C13—21no—
108C22×C4×C13—21no—
109C22×C4×C13—21no—
110C22×C4×C13—42no—
111C22×C4×C13—42no—
112C22×C4×C13C22⋊C411yescharacteristic
113C22×C4×C13C22×C411yescharacteristic
114C22×Dic13—44no—
115C13×C4⋊C4—24no—
116C13×C22⋊C4—24no—
117C13×C22⋊C4—28no—
118C13×C22⋊C4—28no—
119C42×C13—21no—
120C42×C13—21no—
121C42×C13C22⋊C412yescomplemented
122C42×C13C22⋊C412yescomplemented
123C22⋊Dic13—44no—
124C22⋊Dic13—44no—
125C22⋊Dic13—88no—
126C2×#535D1311yescharacteristic
127C2×#354—132no—
128C2×#353—132no—
129#1781—132no—
130C23×C13—21no—
131C23×C13—22no—
132C23×C13—21no—
133C23×C13—22no—
134C23×C13—22no—
135C23×C13—22no—
136C23×C13—22no—
137C23×C13—22no—
138C23×C13—42no—
139C23×C13—48no—
140C23×C13—44no—
141C23×C13—44no—
142C23×C13—48no—
143C23×C13—44no—
144C23×C13—41no—
145C23×C13—41no—
146C23×C13—84no—
147C23×C13—88no—
148C23×C13—88no—
149C23×C13#9912yes—
150C23×C13C2×C22⋊C411yescharacteristic
151C23×C13#12014yes—
152Q8×C13—42no—
153Q8×C13—42no—
154D4×C13—42no—
155D4×C13—42no—
156D4×C13—48no—
157D4×C13—42no—
158D4×C13—42no—
159D4×C13—42no—
160D4×C13—42no—
161D4×C13—48no—
162D4×C13—88no—
163D4×C13—88no—
164C2×C4×C13—24no—
165C2×C4×C13—24no—
166C2×C4×C13—21no—
167C2×C4×C13—21no—
168C2×C4×C13—21no—
169C2×C4×C13—21no—
170C2×C4×C13—22no—
171C2×C4×C13—22no—
172C2×C4×C13—22no—
173C2×C4×C13—48no—
174C2×C4×C13—42no—
175C2×C4×C13—42no—
176C2×C4×C13—41no—
177C2×C4×C13—41no—
178C2×C4×C13#9912yes—
179C2×C4×C13C2×C22⋊C411yescharacteristic
180C2×C4×C13C2×C22⋊C411yescharacteristic
181C2×Dic13—84no—
182C2×Dic13—88no—
183C22×#41Dic1311yescharacteristic, complemented
184C23×D4C2×D1311yescharacteristic
185#535—24no—
186#535—24no—
187C2×#127Dic1311yescharacteristic, complemented
188C2×#127C2×D1311yescharacteristic
189C2×#124Dic1311yescharacteristic, complemented
190C2×#124C2×D1311yescharacteristic
191C2×#121—22no—
192C2×#120—22no—
193C2×#117Dic1311yescharacteristic, complemented
194C2×#99—134no—
195C2×#99—262no—
196#379—262no—
197#354—264no—
198#353—264no—
199C22×C13—22no—
200C22×C13—24no—
201C22×C13—24no—
202C22×C13—22no—
203C22×C13—44no—
204C22×C13—42no—
205C22×C13—42no—
206C22×C13—44no—
207C22×C13—44no—
208C22×C13—44no—
209C22×C13—44no—
210C22×C13—42no—
211C22×C13—42no—
212C22×C13—82no—
213C22×C13—82no—
214C22×C13—82no—
215C22×C13—816no—
216C22×C13—82no—
217C22×C13#37911yescharacteristic
218C22×C13C2×#9911yescharacteristic
219C22×C13C2×#9911yescharacteristic
220C4×C13—22no—
221C4×C13—21no—
222C4×C13—21no—
223C4×C13—42no—
224C4×C13—42no—
225C4×C13—42no—
226Dic13—164no—
227C25C22⋊D1312yes—
228C2×#41—22no—
229C2×#41—22no—
230C2×#41—42no—
231C2×#41—42no—
232C22×Q8C2×Dic1311yescharacteristic
233C22×D4—21no—
234C22×D4—22no—
235C22×D4—22no—
236C22×D4—22no—
237C22×D4—22no—
238C22×D4—42no—
239C22×D4—42no—
240C22×D4C2×Dic1311yescharacteristic
241C22×D4C2×Dic1311yescharacteristic
242C22×D4C22⋊D1312yes—
243C22×D4C22×D1311yescharacteristic
244C23×C4—21no—
245C23×C4C2×Dic1311yescharacteristic
246#127—22no—
247#127—22no—
248#127—22no—
249#127C22⋊D1314yes—
250#124—22no—
251#124—22no—
252#124—22no—
253#124C22⋊D1314yes—
254#121—216no—
255#120—216no—
256#117—22no—
257#117—22no—
258C2×C4⋊C4—21no—
259C2×C22⋊C4—22no—
260C2×C22⋊C4—21no—
261C2×C22⋊C4—22no—
262C2×C22⋊C4—264no—
263C2×C22⋊C4—524no—
264C2×C42C2×Dic1311yescharacteristic
265C2×C42C2×Dic1311yescharacteristic
266#99—264no—
267#99—264no—
268#99—524no—
269C2×C13—21no—
270C2×C13—21no—
271C2×C13—44no—
272C2×C13—42no—
273C2×C13—82no—
274C2×C13—82no—
275C2×C13#178111yescharacteristic
276C2×C13#212712yes—
277C24—21no—
278C24—24no—
279C24—24no—
280C24—42no—
281C24—84no—
282C24C22⋊Dic1312yes—
283C24C22⋊Dic1311yescharacteristic
284C24C2×C22⋊D1312yes—
285#41—48no—
286#41—48no—
287C2×Q8—21no—
288C2×Q8—41no—
289C2×Q8—41no—
290C2×Q8C22⋊Dic1312yescomplemented
291C2×D4—24no—
292C2×D4—24no—
293C2×D4—28no—
294C2×D4—28no—
295C2×D4—24no—
296C2×D4—21no—
297C2×D4—21no—
298C2×D4—21no—
299C2×D4—41no—
300C2×D4—41no—
301C2×D4—42no—
302C2×D4—41no—
303C2×D4—41no—
304C2×D4—41no—
305C2×D4—41no—
306C2×D4—48no—
307C2×D4—48no—
308C2×D4—42no—
309C2×D4—42no—
310C2×D4—84no—
311C2×D4—84no—
312C2×D4C22⋊Dic1312yescomplemented
313C2×D4C2×C22⋊D1312yes—
314C2×D4C2×C22⋊D1312yes—
315C22×C4—22no—
316C22×C4—22no—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—24no—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—42no—
324C22×C4—42no—
325C22×C4—524no—
326C22×C4C22⋊Dic1311yescharacteristic
327C22×C4C22×Dic1311yescharacteristic
328C4⋊C4—24no—
329C22⋊C4—24no—
330C22⋊C4—28no—
331C22⋊C4—28no—
332C22⋊C4—524no—
333C22⋊C4—524no—
334C22⋊C4—1048no—
335C42—21no—
336C42—21no—
337C42C22⋊Dic1312yescomplemented
338C42C22⋊Dic1312yescomplemented
339C13#1269611yescharacteristic, complemented, Sylow
340C23—21no—
341C23—22no—
342C23—21no—
343C23—22no—
344C23—22no—
345C23—22no—
346C23—22no—
347C23—22no—
348C23—42no—
349C23—48no—
350C23—44no—
351C23—44no—
352C23—48no—
353C23—44no—
354C23—41no—
355C23—41no—
356C23—84no—
357C23—88no—
358C23—88no—
359C23#8807412yes—
360C23C2×C22⋊Dic1311yescharacteristic
361C23#8820714yes—
362Q8—42no—
363Q8—42no—
364D4—42no—
365D4—42no—
366D4—48no—
367D4—42no—
368D4—42no—
369D4—42no—
370D4—42no—
371D4—48no—
372D4—88no—
373D4—88no—
374C2×C4—24no—
375C2×C4—24no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—22no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—48no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—1044no—
389C2×C4—1048no—
390C2×C4#8807412yes—
391C2×C4C2×C22⋊Dic1311yescharacteristic
392C2×C4C2×C22⋊Dic1311yescharacteristic
393C22—22no—
394C22—24no—
395C22—22no—
396C22—24no—
397C22—44no—
398C22—42no—
399C22—42no—
400C22—44no—
401C22—44no—
402C22—44no—
403C22—44no—
404C22—42no—
405C22—42no—
406C22—82no—
407C22—82no—
408C22—82no—
409C22—816no—
410C22—82no—
411C22C2×#8807411yescharacteristic
412C22C2×#8807411yescharacteristic
413C22#1171890811yescharacteristic
414C4—22no—
415C4—21no—
416C4—21no—
417C4—42no—
418C4—42no—
419C4—42no—
420C4—2084no—
421C2—21no—
422C2—21no—
423C2—44no—
424C2—42no—
425C2—82no—
426C2—82no—
427C2#1311475111yescharacteristic
428C2#1311650512yes—
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC22×D4C22×D13
Fitting, prime radicalC2×C13×#535C2
socleC22×C13C2×#99
cosocleC22×D4×C13C23
hypercenterC2×#535D13
hypocenterC13#12696
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24 ◁ C23×D4 ◁ C2×#535

Complements

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

NH ≅ G/Ntype
1. C2×#11718133C2semidirect
2. C2×#11718137C2semidirect
3. #13114751C2semidirect
5. C22×C13×#41C4semidirect
9. C2×C13×#127C4semidirect
11. C2×C13×#124C4semidirect
15. C2×C13×#117C4semidirect
77. C2×Q8×C13C22⋊C4semidirect
99. C2×D4×C13C22⋊C4semidirect
121. C42×C13C22⋊C4semidirect
122. C42×C13C22⋊C4semidirect
183. C22×#41Dic13semidirect
187. C2×#127Dic13semidirect
189. C2×#124Dic13semidirect
193. C2×#117Dic13semidirect
290. C2×Q8C22⋊Dic13semidirect
312. C2×D4C22⋊Dic13semidirect
337. C42C22⋊Dic13semidirect
338. C42C22⋊Dic13semidirect
339. C13#12696semidirect

Maximal subgroups

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

subgroupindex
C2×#117181332
C2×#117181372
#131147512
C2×C13×#5352
#1269613