Finite Group Databasebeta

← #15781238

Subgroups — #15781238

Order 3328.

602 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 602 conjugacy classes of subgroups — too many to draw. Only its 107 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
3#13114824C211yesmaximal, characteristic, complemented
4C4×#88074C211yesmaximal, characteristic, complemented
5C13×#2544C211yesmaximal, characteristic
6C2×C13×#127C2211yescharacteristic
7C2×C13×#124C411yescharacteristic, complemented
8C2×C13×#124C2211yescharacteristic
9C2×C4×D4×C13C2211yescharacteristic
10C13×#394—21no—
11C13×#394—21no—
12C13×#391C411yescharacteristic, complemented
13C13×#390C411yescharacteristic, complemented
14C13×#386—21no—
15C13×#386—21no—
16C4×C13×C4⋊C4C411yescharacteristic, complemented
17C2×#88074C2212yes—
18C2×#88074C2212yes—
19#11718873—21no—
20C4×C22⋊Dic13—21no—
21#11718137—24no—
22#11718133—24no—
23#11718118—21no—
24#11718118—21no—
25C22×Q8×C13C2×C411yescharacteristic
26C22×D4×C13—21no—
27C22×D4×C13—21no—
28C22×D4×C13C2×C411yescharacteristic
29C22×D4×C13C2311yescharacteristic
30C23×C4×C13D411yescharacteristic
31C23×C4×C13D411yescharacteristic
32C13×#127—22no—
33C13×#127—22no—
34C13×#124—22no—
35C13×#124—22no—
36C13×#124—41no—
37C13×#124—41no—
38C4×D4×C13—41no—
39C4×D4×C13—41no—
40C2×C13×C4⋊C4—21no—
41C2×C13×C4⋊C4C2×C411yescharacteristic
42C2×C13×C22⋊C4—21no—
43C2×C13×C22⋊C4—21no—
44C2×C13×C22⋊C4—21no—
45C2×C13×C22⋊C4—21no—
46C2×C13×C22⋊C4—21no—
47C2×C13×C22⋊C4—21no—
48C2×C13×C22⋊C4D411yescharacteristic
49C2×C13×C22⋊C4D411yescharacteristic
50C2×C42×C13C2×C411yescharacteristic
51C2×C42×C13C2×C411yescharacteristic
52C2×C42×C13C2×C411yescharacteristic
53C2×C22⋊Dic13—22no—
54C2×C22⋊Dic13—22no—
55C2×C4⋊Dic13—41no—
56C2×C4×Dic13—41no—
57C13×#95—21no—
58C13×#95—21no—
59C13×#95—21no—
60#88074—22no—
61#88074—22no—
62#88074—22no—
63#88074D414yes—
64#88071—41no—
65#88071—41no—
66#13225—131nomaximal, Sylow
67C24×C13—21no—
68C24×C13C2×D411yescharacteristic
69C24×C13C2×D411yescharacteristic
70C2×Q8×C13—22no—
71C2×Q8×C13—41no—
72C2×Q8×C13—41no—
73C2×D4×C13—22no—
74C2×D4×C13—41no—
75C2×D4×C13—41no—
76C2×D4×C13—41no—
77C2×D4×C13—41no—
78C2×D4×C13—42no—
79C2×D4×C13—42no—
80C2×D4×C13—42no—
81C2×D4×C13—41no—
82C2×D4×C13—41no—
83C2×D4×C13—81no—
84C2×D4×C13—81no—
85C2×D4×C13C2×D412yes—
86C2×D4×C13#4112yes—
87C22×C4×C13—21no—
88C22×C4×C13—21no—
89C22×C4×C13—21no—
90C22×C4×C13—21no—
91C22×C4×C13—21no—
92C22×C4×C13—21no—
93C22×C4×C13—21no—
94C22×C4×C13—81no—
95C22×C4×C13—81no—
96C22×C4×C13C22⋊C411yescharacteristic
97C22×C4×C13C22⋊C411yescharacteristic
98C22×C4×C13C22⋊C411yescharacteristic
99C22×C4×C13C22⋊C411yescharacteristic
100C22×C4×C13C22×C411yescharacteristic
101C22×Dic13—42no—
102C22×Dic13—42no—
103C13×C4⋊C4—41no—
104C13×C4⋊C4—42no—
105C13×C22⋊C4—41no—
106C13×C22⋊C4—41no—
107C13×C22⋊C4—42no—
108C13×C22⋊C4—42no—
109C13×C22⋊C4—41no—
110C13×C22⋊C4—41no—
111C13×C22⋊C4—41no—
112C13×C22⋊C4—41no—
113C13×C22⋊C4—81no—
114C13×C22⋊C4—81no—
115C42×C13—21no—
116C42×C13—21no—
117C42×C13—22no—
118C42×C13—22no—
119C22⋊Dic13—24no—
120C22⋊Dic13—42no—
121C22⋊Dic13—42no—
122C22⋊Dic13—42no—
123C4⋊Dic13—82no—
124C4×Dic13—82no—
125#2544D1311yescharacteristic
126C2×#354—132no—
127C2×#353—132no—
128#1799—131no—
129C4×#99—131no—
130C23×C13—21no—
131C23×C13—21no—
132C23×C13—21no—
133C23×C13—21no—
134C23×C13—41no—
135C23×C13—41no—
136C23×C13—41no—
137C23×C13—41no—
138C23×C13—41no—
139C23×C13—41no—
140C23×C13—41no—
141C23×C13—41no—
142C23×C13—41no—
143C23×C13—41no—
144C23×C13—41no—
145C23×C13C2×C22⋊C411yescharacteristic
146C23×C13#12112yes—
147C23×C13#12411yescharacteristic
148C23×C13#12711yescharacteristic
149Q8×C13—82no—
150D4×C13—42no—
151D4×C13—42no—
152D4×C13—82no—
153D4×C13—84no—
154D4×C13—82no—
155D4×C13—82no—
156C2×C4×C13—21no—
157C2×C4×C13—21no—
158C2×C4×C13—22no—
159C2×C4×C13—21no—
160C2×C4×C13—21no—
161C2×C4×C13—21no—
162C2×C4×C13—41no—
163C2×C4×C13—42no—
164C2×C4×C13—42no—
165C2×C4×C13—41no—
166C2×C4×C13—41no—
167C2×C4×C13—41no—
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—81no—
177C2×C4×C13—81no—
178C2×C4×C13#9911yescharacteristic
179C2×C4×C13#9911yescharacteristic
180C2×C4×C13C4×D412yes—
181C2×Dic13—44no—
182C2×Dic13—82no—
183C2×Dic13—82no—
184C2×Dic13—82no—
185C2×Dic13—82no—
186C2×Dic13—82no—
187C2×#127C2×D1311yescharacteristic
188C2×#124Dic1311yescharacteristic, complemented
189C2×#124C2×D1311yescharacteristic
190C2×C4×D4C2×D1311yescharacteristic
191C2×#99—132no—
192C2×#99—132no—
193#394—21no—
194#394—21no—
195#391Dic1311yescharacteristic, complemented
196#390Dic1311yescharacteristic, complemented
197#386—21no—
198#386—21no—
199#380—261no—
200C4×C4⋊C4Dic1311yescharacteristic, complemented
201C4×C22⋊C4—261no—
202#354—264no—
203#353—264no—
204#342—261no—
205#342—261no—
206C22×C13—21no—
207C22×C13—21no—
208C22×C13—22no—
209C22×C13—21no—
210C22×C13—21no—
211C22×C13—42no—
212C22×C13—41no—
213C22×C13—41no—
214C22×C13—41no—
215C22×C13—41no—
216C22×C13—41no—
217C22×C13—41no—
218C22×C13—81no—
219C22×C13—81no—
220C22×C13—81no—
221C22×C13—81no—
222C22×C13—81no—
223C22×C13—81no—
224C22×C13—81no—
225C22×C13—81no—
226C22×C13—81no—
227C22×C13#39011yescharacteristic
228C22×C13C2×#9911yescharacteristic
229C22×C13#41011yescharacteristic
230C4×C13—21no—
231C4×C13—21no—
232C4×C13—22no—
233C4×C13—42no—
234C4×C13—41no—
235C4×C13—41no—
236C4×C13—41no—
237C4×C13—81no—
238C4×C13—81no—
239Dic13—84no—
240Dic13—162no—
241C22×Q8C2×Dic1311yescharacteristic
242C22×D4—21no—
243C22×D4—21no—
244C22×D4C2×Dic1311yescharacteristic
245C22×D4C22×D1311yescharacteristic
246C23×C4C22⋊D1311yescharacteristic
247C23×C4C22⋊D1311yescharacteristic
248#127—22no—
249#127—22no—
250#124—22no—
251#124—22no—
252#124—41no—
253#124—41no—
254C4×D4—41no—
255C4×D4—41no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—521no—
258C2×C4⋊C4C2×Dic1311yescharacteristic
259C2×C22⋊C4—21no—
260C2×C22⋊C4—21no—
261C2×C22⋊C4—21no—
262C2×C22⋊C4—21no—
263C2×C22⋊C4—21no—
264C2×C22⋊C4—21no—
265C2×C22⋊C4—262no—
266C2×C22⋊C4—262no—
267C2×C22⋊C4C22⋊D1311yescharacteristic
268C2×C22⋊C4C22⋊D1311yescharacteristic
269C2×C42—521no—
270C2×C42C2×Dic1311yescharacteristic
271C2×C42C2×Dic1311yescharacteristic
272C2×C42C2×Dic1311yescharacteristic
273#99—134no—
274#99—262no—
275#99—262no—
276#99—262no—
277#95—21no—
278#95—21no—
279#95—21no—
280#95—521no—
281#95—521no—
282C2×C13—21no—
283C2×C13—21no—
284C2×C13—42no—
285C2×C13—41no—
286C2×C13—41no—
287C2×C13—161no—
288C2×C13#196411yescharacteristic
289C2×C13#212611yescharacteristic
290C2×C13#212711yescharacteristic
291C24—21no—
292C24C2×C22⋊D1311yescharacteristic
293C24C2×C22⋊D1311yescharacteristic
294C2×Q8—22no—
295C2×Q8—41no—
296C2×Q8—41no—
297C2×D4—22no—
298C2×D4—41no—
299C2×D4—41no—
300C2×D4—41no—
301C2×D4—41no—
302C2×D4—42no—
303C2×D4—42no—
304C2×D4—41no—
305C2×D4—42no—
306C2×D4—41no—
307C2×D4—81no—
308C2×D4—81no—
309C2×D4D4×D1312yes—
310C2×D4#612912yes—
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—81no—
319C22×C4—81no—
320C22×C4—522no—
321C22×C4—522no—
322C22×C4C22⋊Dic1311yescharacteristic
323C22×C4C22⋊Dic1311yescharacteristic
324C22×C4C22⋊Dic1311yescharacteristic
325C22×C4C22⋊Dic1311yescharacteristic
326C22×C4C22×Dic1311yescharacteristic
327C4⋊C4—41no—
328C4⋊C4—42no—
329C4⋊C4—1042no—
330C22⋊C4—41no—
331C22⋊C4—41no—
332C22⋊C4—42no—
333C22⋊C4—41no—
334C22⋊C4—42no—
335C22⋊C4—41no—
336C22⋊C4—41no—
337C22⋊C4—41no—
338C22⋊C4—81no—
339C22⋊C4—81no—
340C22⋊C4—264no—
341C22⋊C4—522no—
342C22⋊C4—522no—
343C22⋊C4—522no—
344C42—21no—
345C42—21no—
346C42—22no—
347C42—22no—
348C42—1042no—
349C13#1322511yescharacteristic, complemented, Sylow
350C23—21no—
351C23—21no—
352C23—21no—
353C23—21no—
354C23—41no—
355C23—41no—
356C23—41no—
357C23—41no—
358C23—41no—
359C23—41no—
360C23—41no—
361C23—41no—
362C23—41no—
363C23—41no—
364C23—41no—
365C23#8819011yescharacteristic
366C23#8819212yes—
367C23#8819411yescharacteristic
368C23C2×C22⋊Dic1311yescharacteristic
369Q8—82no—
370D4—42no—
371D4—42no—
372D4—82no—
373D4—82no—
374D4—84no—
375D4—82no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—22no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—41no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—81no—
397C2×C4—81no—
398C2×C4—524no—
399C2×C4—1042no—
400C2×C4—1042no—
401C2×C4—1042no—
402C2×C4—1042no—
403C2×C4—1042no—
404C2×C4#8807411yescharacteristic
405C2×C4#8807411yescharacteristic
406C2×C4D4×Dic1312yes—
407C22—21no—
408C22—21no—
409C22—22no—
410C22—21no—
411C22—21no—
412C22—41no—
413C22—42no—
414C22—41no—
415C22—41no—
416C22—41no—
417C22—41no—
418C22—41no—
419C22—81no—
420C22—81no—
421C22—81no—
422C22—81no—
423C22—81no—
424C22—81no—
425C22—81no—
426C22—81no—
427C22—81no—
428C22C2×#8807411yescharacteristic
429C22#1171888211yescharacteristic
430C22#1171890111yescharacteristic
431C4—22no—
432C4—21no—
433C4—21no—
434C4—42no—
435C4—41no—
436C4—41no—
437C4—41no—
438C4—81no—
439C4—81no—
440C4—1044no—
441C4—2082no—
442C2—21no—
443C2—21no—
444C2—42no—
445C2—41no—
446C2—41no—
447C2—161no—
448C2#1311567311yescharacteristic
449C2#1311650111yescharacteristic
450C2#1311650511yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC22×D4C22×D13
FittingC13×#2544C2
socleC22×C13C2×#99
prime radicalC2×C13×#127C22
cosocleC22×D4×C13C23
hypercenter#2544D13
hypocenterC13#13225
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2544

Complements

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

NH ≅ G/Ntype
1. C2×#11718133C2semidirect
3. #13114824C2semidirect
4. C4×#88074C2semidirect
7. C2×C13×#124C4semidirect
12. C13×#391C4semidirect
13. C13×#390C4semidirect
16. C4×C13×C4⋊C4C4semidirect
188. C2×#124Dic13semidirect
195. #391Dic13semidirect
196. #390Dic13semidirect
200. C4×C4⋊C4Dic13semidirect
349. C13#13225semidirect

Maximal subgroups

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

subgroupindex
C2×#117181332
C2×#117181372
#131148242
C4×#880742
C13×#25442
#1322513