Finite Group Databasebeta

← #15780454

Subgroups — #15780454

Order 3328.

724 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 724 conjugacy classes of subgroups — too many to draw. Only its 111 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×#11718901C211yesmaximal, characteristic
2C2×#11718133C212yesmaximal, complemented
3#13114754C211yesmaximal, characteristic
4#13112961C212yesmaximal, complemented
5C13×#2432C211yesmaximal, characteristic
6C22×C13×#41C2211yescharacteristic
7C2×C13×C4⋊Q8C411yescharacteristic, complemented
8C2×C13×#124C2211yescharacteristic
9C2×C13×C22⋊Q8C411yescharacteristic, complemented
10C2×#88180—21no—
11C13×#394—21no—
12C13×#394—21no—
13C13×#391C411yescharacteristic, complemented
14C13×#390C2211yescharacteristic
15C13×#385—21no—
16C13×#385—21no—
17C4×C13×C22⋊C4C411yescharacteristic, complemented
18#11718901—24no—
19C2×#88074—21no—
20C2×#88074—21no—
21C2×#88074C2212yes—
22C2×#88074C2212yes—
23#11718872—21no—
24#11718133—24no—
25C2×C13×#41—22no—
26C2×C13×#41—22no—
27C2×C13×#41—41no—
28C2×C13×#41—41no—
29C2×C13×#41—42no—
30C22×Q8×C13C2×C411yescharacteristic
31C22×Q8×C13C2×C411yescharacteristic
32C22×D4×C13D411yescharacteristic
33C22×D4×C13D411yescharacteristic
34C22×D4×C13C2311yescharacteristic
35C23×C4×C13C2×C411yescharacteristic
36C23×C4×C13D411yescharacteristic
37C23×C4×C13D411yescharacteristic
38C13×C4⋊Q8—42no—
39C13×#124—22no—
40C13×#124—22no—
41C13×C22⋊Q8—41no—
42C13×C22⋊Q8—41no—
43C2×C13×C4⋊C4—21no—
44C2×C13×C4⋊C4—21no—
45C2×C13×C4⋊C4—21no—
46C2×C13×C4⋊C4C2×C411yescharacteristic
47C2×C13×C22⋊C4—21no—
48C2×C13×C22⋊C4—21no—
49C2×C13×C22⋊C4—21no—
50C2×C13×C22⋊C4—21no—
51C2×C13×C22⋊C4—21no—
52C2×C13×C22⋊C4—21no—
53C2×C42×C13C2×C411yescharacteristic
54C2×C42×C13C2×C411yescharacteristic
55C2×C22⋊Dic13—22no—
56C2×C22⋊Dic13—22no—
57#88180—24no—
58#88180—42no—
59C2×C4⋊Dic13—41no—
60C2×C4×Dic13—41no—
61C13×#95—21no—
62C13×#95—21no—
63C13×#95—21no—
64#88074—24no—
65#88074—22no—
66#88074—22no—
67#88074—22no—
68#88074—42no—
69#88074D414yes—
70#88071—41no—
71#88071—41no—
72#13091—131nomaximal, Sylow
73C24×C13C22⋊C411yescharacteristic
74C24×C13C2×D411yescharacteristic
75C24×C13C2×D411yescharacteristic
76C13×#41—44no—
77C13×#41—44no—
78C13×#41—44no—
79C13×#41—44no—
80C2×Q8×C13—22no—
81C2×Q8×C13—22no—
82C2×Q8×C13—22no—
83C2×Q8×C13—41no—
84C2×Q8×C13—41no—
85C2×Q8×C13—41no—
86C2×D4×C13—21no—
87C2×D4×C13—22no—
88C2×D4×C13—21no—
89C2×D4×C13—22no—
90C2×D4×C13—41no—
91C2×D4×C13—41no—
92C2×D4×C13—41no—
93C2×D4×C13—41no—
94C2×D4×C13—41no—
95C2×D4×C13C2×D412yes—
96C2×D4×C13#4112yes—
97C22×C4×C13—21no—
98C22×C4×C13—21no—
99C22×C4×C13—21no—
100C22×C4×C13—21no—
101C22×C4×C13—22no—
102C22×C4×C13—21no—
103C22×C4×C13—22no—
104C22×C4×C13—21no—
105C22×C4×C13—21no—
106C22×C4×C13—21no—
107C22×C4×C13—21no—
108C22×C4×C13—22no—
109C22×C4×C13—21no—
110C22×C4×C13—21no—
111C22×C4×C13—21no—
112C22×C4×C13—41no—
113C22×C4×C13—41no—
114C22×C4×C13C22⋊C411yescharacteristic
115C22×C4×C13C22⋊C411yescharacteristic
116C22×C4×C13C22⋊C411yescharacteristic
117C22×C4×C13C22×C411yescharacteristic
118C22×Dic13—42no—
119C22×Dic13—42no—
120C13×C4⋊C4—41no—
121C13×C4⋊C4—42no—
122C13×C4⋊C4—41no—
123C13×C4⋊C4—41no—
124C13×C4⋊C4—42no—
125C13×C22⋊C4—42no—
126C13×C22⋊C4—42no—
127C13×C22⋊C4—42no—
128C13×C22⋊C4—42no—
129C13×C22⋊C4—41no—
130C13×C22⋊C4—42no—
131C13×C22⋊C4—41no—
132C42×C13—22no—
133C42×C13—41no—
134C22⋊Dic13—24no—
135C22⋊Dic13—42no—
136C22⋊Dic13—42no—
137C22⋊Dic13—42no—
138C4⋊Dic13—44no—
139C4×Dic13—44no—
140C2×#410—131no—
141#2432D1311yescharacteristic
142C2×#354—132no—
143#1782—131no—
144#1393—132no—
145C23×C13—21no—
146C23×C13—21no—
147C23×C13—21no—
148C23×C13—21no—
149C23×C13—21no—
150C23×C13—21no—
151C23×C13—21no—
152C23×C13—41no—
153C23×C13—41no—
154C23×C13—41no—
155C23×C13—41no—
156C23×C13—41no—
157C23×C13—41no—
158C23×C13C2×C22⋊C411yescharacteristic
159C23×C13#12011yescharacteristic
160C23×C13#12112yes—
161C23×C13#12311yescharacteristic
162Q8×C13—44no—
163Q8×C13—82no—
164D4×C13—42no—
165D4×C13—42no—
166D4×C13—44no—
167D4×C13—42no—
168D4×C13—42no—
169C2×C4×C13—22no—
170C2×C4×C13—22no—
171C2×C4×C13—22no—
172C2×C4×C13—22no—
173C2×C4×C13—21no—
174C2×C4×C13—21no—
175C2×C4×C13—21no—
176C2×C4×C13—21no—
177C2×C4×C13—21no—
178C2×C4×C13—21no—
179C2×C4×C13—22no—
180C2×C4×C13—21no—
181C2×C4×C13—21no—
182C2×C4×C13—21no—
183C2×C4×C13—42no—
184C2×C4×C13—42no—
185C2×C4×C13—42no—
186C2×C4×C13—42no—
187C2×C4×C13—41no—
188C2×C4×C13—41no—
189C2×C4×C13—41no—
190C2×C4×C13—41no—
191C2×C4×C13—41no—
192C2×C4×C13—41no—
193C2×C4×C13—41no—
194C2×C4×C13—41no—
195C2×C4×C13—41no—
196C2×C4×C13—41no—
197C2×C4×C13—41no—
198C2×C4×C13#9911yescharacteristic
199C2×C4×C13#9911yescharacteristic
200C2×C4×C13#9912yes—
201C2×C4×C13C4×D412yes—
202C2×Dic13—44no—
203C2×Dic13—82no—
204C2×Dic13—82no—
205C2×Dic13—82no—
206C2×Dic13—82no—
207C2×Dic13—82no—
208C22×#41C2×D1311yescharacteristic
209C2×C4⋊Q8Dic1311yescharacteristic, complemented
210C2×#124C2×D1311yescharacteristic
211C2×C22⋊Q8Dic1311yescharacteristic, complemented
212C2×#117—261no—
213#410—264no—
214C2×#99—132no—
215C2×#99—132no—
216C2×#99—261no—
217C2×#99—261no—
218#394—21no—
219#394—21no—
220#391Dic1311yescharacteristic, complemented
221#390C2×D1311yescharacteristic
222#385—21no—
223#385—21no—
224#381—261no—
225C4×C22⋊C4Dic1311yescharacteristic, complemented
226#354—264no—
227C22×C13—21no—
228C22×C13—21no—
229C22×C13—21no—
230C22×C13—22no—
231C22×C13—21no—
232C22×C13—41no—
233C22×C13—42no—
234C22×C13—41no—
235C22×C13—41no—
236C22×C13—41no—
237C22×C13—41no—
238C22×C13—41no—
239C22×C13—41no—
240C22×C13—41no—
241C22×C13—41no—
242C22×C13—81no—
243C22×C13—81no—
244C22×C13—81no—
245C22×C13—81no—
246C22×C13#38611yescharacteristic
247C22×C13C2×#9911yescharacteristic
248C22×C13C2×#9911yescharacteristic
249C4×C13—21no—
250C4×C13—21no—
251C4×C13—22no—
252C4×C13—22no—
253C4×C13—42no—
254C4×C13—41no—
255C4×C13—81no—
256C4×C13—81no—
257C4×C13—81no—
258Dic13—84no—
259Dic13—162no—
260C2×#41—22no—
261C2×#41—22no—
262C2×#41—41no—
263C2×#41—41no—
264C2×#41—42no—
265C22×Q8C2×Dic1311yescharacteristic
266C22×Q8C2×Dic1311yescharacteristic
267C22×D4C22⋊D1311yescharacteristic
268C22×D4C22⋊D1311yescharacteristic
269C22×D4C22×D1311yescharacteristic
270C23×C4C2×Dic1311yescharacteristic
271C23×C4C22⋊D1311yescharacteristic
272C23×C4C22⋊D1311yescharacteristic
273C4⋊Q8—42no—
274#124—22no—
275#124—22no—
276C22⋊Q8—41no—
277C22⋊Q8—41no—
278#117—264no—
279#117—522no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—521no—
284C2×C4⋊C4C2×Dic1311yescharacteristic
285C2×C22⋊C4—21no—
286C2×C22⋊C4—21no—
287C2×C22⋊C4—21no—
288C2×C22⋊C4—21no—
289C2×C22⋊C4—21no—
290C2×C22⋊C4—21no—
291C2×C22⋊C4—262no—
292C2×C22⋊C4—262no—
293C2×C42—521no—
294C2×C42C2×Dic1311yescharacteristic
295C2×C42C2×Dic1311yescharacteristic
296#99—134no—
297#99—264no—
298#99—262no—
299#99—262no—
300#99—262no—
301#99—522no—
302#95—21no—
303#95—21no—
304#95—21no—
305#95—521no—
306#95—521no—
307C2×C13—21no—
308C2×C13—21no—
309C2×C13—41no—
310C2×C13—42no—
311C2×C13—41no—
312C2×C13—81no—
313C2×C13#189811yescharacteristic
314C2×C13#212611yescharacteristic
315C2×C13#212911yescharacteristic
316C24C22⋊Dic1311yescharacteristic
317C24C2×C22⋊D1311yescharacteristic
318C24C2×C22⋊D1311yescharacteristic
319#41—44no—
320#41—44no—
321#41—44no—
322#41—44no—
323C2×Q8—22no—
324C2×Q8—22no—
325C2×Q8—22no—
326C2×Q8—41no—
327C2×Q8—41no—
328C2×Q8—41no—
329C2×D4—21no—
330C2×D4—21no—
331C2×D4—22no—
332C2×D4—22no—
333C2×D4—41no—
334C2×D4—41no—
335C2×D4—41no—
336C2×D4—41no—
337C2×D4—41no—
338C2×D4D4×D1312yes—
339C2×D4#612912yes—
340C22×C4—21no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—22no—
352C22×C4—21no—
353C22×C4—21no—
354C22×C4—21no—
355C22×C4—41no—
356C22×C4—41no—
357C22×C4—522no—
358C22×C4—522no—
359C22×C4C22⋊Dic1311yescharacteristic
360C22×C4C22⋊Dic1311yescharacteristic
361C22×C4C22⋊Dic1311yescharacteristic
362C22×C4C22×Dic1311yescharacteristic
363C4⋊C4—41no—
364C4⋊C4—42no—
365C4⋊C4—41no—
366C4⋊C4—41no—
367C4⋊C4—42no—
368C4⋊C4—524no—
369C22⋊C4—42no—
370C22⋊C4—42no—
371C22⋊C4—42no—
372C22⋊C4—42no—
373C22⋊C4—41no—
374C22⋊C4—41no—
375C22⋊C4—42no—
376C22⋊C4—264no—
377C22⋊C4—522no—
378C22⋊C4—522no—
379C22⋊C4—522no—
380C42—22no—
381C42—41no—
382C42—524no—
383C13#1309111yescharacteristic, complemented, Sylow
384C23—21no—
385C23—21no—
386C23—21no—
387C23—21no—
388C23—21no—
389C23—21no—
390C23—21no—
391C23—41no—
392C23—41no—
393C23—41no—
394C23—41no—
395C23—41no—
396C23—41no—
397C23#8818911yescharacteristic
398C23#8819111yescharacteristic
399C23#8819312yes—
400C23C2×C22⋊Dic1311yescharacteristic
401Q8—44no—
402Q8—82no—
403D4—42no—
404D4—42no—
405D4—44no—
406D4—42no—
407D4—42no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—22no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—524no—
438C2×C4—1042no—
439C2×C4—1042no—
440C2×C4—1042no—
441C2×C4—1042no—
442C2×C4—1042no—
443C2×C4#8807412yes—
444C2×C4#8807411yescharacteristic
445C2×C4#8807411yescharacteristic
446C2×C4D4×Dic1312yes—
447C22—21no—
448C22—21no—
449C22—21no—
450C22—21no—
451C22—22no—
452C22—41no—
453C22—41no—
454C22—42no—
455C22—41no—
456C22—41no—
457C22—41no—
458C22—41no—
459C22—41no—
460C22—41no—
461C22—41no—
462C22—81no—
463C22—81no—
464C22—81no—
465C22—81no—
466C22C2×#8807411yescharacteristic
467C22C2×#8807411yescharacteristic
468C22#1171888111yescharacteristic
469C4—21no—
470C4—21no—
471C4—22no—
472C4—22no—
473C4—42no—
474C4—41no—
475C4—81no—
476C4—81no—
477C4—81no—
478C4—1044no—
479C4—2082no—
480C2—21no—
481C2—21no—
482C2—41no—
483C2—42no—
484C2—41no—
485C2—81no—
486C2#1311529011yescharacteristic
487C2#1311650111yescharacteristic
488C2#1311651111yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC22×D4C22×D13
FittingC13×#2432C2
socleC22×C13C2×#99
prime radicalC22×C13×#41C22
cosocleC22×D4×C13C23
hypercenter#2432D13
hypocenterC13#13091
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×#41 ◁ #2432

Complements

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

NH ≅ G/Ntype
2. C2×#11718133C2semidirect
4. #13112961C2semidirect
7. C2×C13×C4⋊Q8C4semidirect
9. C2×C13×C22⋊Q8C4semidirect
13. C13×#391C4semidirect
17. C4×C13×C22⋊C4C4semidirect
209. C2×C4⋊Q8Dic13semidirect
211. C2×C22⋊Q8Dic13semidirect
220. #391Dic13semidirect
225. C4×C22⋊C4Dic13semidirect
383. C13#13091semidirect

Maximal subgroups

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

subgroupindex
C2×#117189012
C2×#117181332
#131147542
#131129612
C13×#24322
#1309113