Finite Group Databasebeta

← #15773395

Subgroups — #15773395

Order 3328.

700 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 700 conjugacy classes of subgroups — too many to draw. Only its 95 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×#11718118C211yesmaximal, characteristic, complemented
2#13113163C211yesmaximal, characteristic, complemented
3#13112860C212yesmaximal, complemented
4#13112833C212yesmaximal, complemented
5C13×#2539C211yesmaximal, characteristic
6C2×C13×#123—21no—
7C2×C13×#121C411yescharacteristic, complemented
8C2×C13×#120—21no—
9C22×C13×C22⋊C4C2211yescharacteristic
10C22×C22⋊Dic13—21no—
11C13×#399C411yescharacteristic, complemented
12C13×#399C2211yescharacteristic
13C13×#392C411yescharacteristic, complemented
14C13×#392C2211yescharacteristic
15C13×#390—21no—
16C13×#390—21no—
17C4×C13×C22⋊C4C411yescharacteristic, complemented
18#11718868—21no—
19#11718118—21no—
20#11718118C2212yes—
21#11718117—21no—
22#11718117C2212yes—
23C25×C13D411yescharacteristic
24C22×D4×C13—21no—
25C22×D4×C13—21no—
26C22×D4×C13—21no—
27C22×D4×C13C2×C411yescharacteristic, complemented
28C23×C4×C13C2×C411yescharacteristic
29C23×C4×C13D411yescharacteristic
30C23×Dic13—41no—
31C13×#123—44no—
32C13×#121—41no—
33C13×#121—41no—
34C13×#120—44no—
35C2×C13×C4⋊C4—21no—
36C2×C13×C4⋊C4—21no—
37C2×C13×C4⋊C4C2×C411yescharacteristic, complemented
38C2×C13×C22⋊C4—21no—
39C2×C13×C22⋊C4—21no—
40C2×C13×C22⋊C4—21no—
41C2×C13×C22⋊C4—21no—
42C2×C13×C22⋊C4—21no—
43C2×C13×C22⋊C4—21no—
44C2×C13×C22⋊C4—41no—
45C2×C13×C22⋊C4—41no—
46C2×C13×C22⋊C4C2×C411yescharacteristic
47C2×C13×C22⋊C4D411yescharacteristic
48C2×C13×C22⋊C4D411yescharacteristic
49C2×C13×C22⋊C4C2311yescharacteristic
50C2×C42×C13—21no—
51C2×C22⋊Dic13—24no—
52C2×C22⋊Dic13—22no—
53C2×C22⋊Dic13—41no—
54C2×C22⋊Dic13—42no—
55C2×#6099—41no—
56C13×#95C2×C411yescharacteristic, complemented
57C13×#95C2×C411yescharacteristic, complemented
58C22⋊#1055—22no—
59C22⋊#1055—41no—
60#11757—131nomaximal, Sylow
61C24×C13—21no—
62C24×C13—21no—
63C24×C13—22no—
64C24×C13—21no—
65C24×C13—21no—
66C24×C13—21no—
67C24×C13—42no—
68C24×C13—81no—
69C24×C13C22⋊C411yescharacteristic
70C24×C13C22⋊C411yescharacteristic
71C24×C13C2×D411yescharacteristic
72C2×D4×C13—41no—
73C2×D4×C13—42no—
74C2×D4×C13—42no—
75C2×D4×C13—42no—
76C2×D4×C13—42no—
77C2×D4×C13—41no—
78C2×D4×C13—41no—
79C2×D4×C13—42no—
80C2×D4×C13—41no—
81C2×D4×C13—41no—
82C2×D4×C13—81no—
83C2×D4×C13—81no—
84C2×D4×C13—81no—
85C22×C4×C13—21no—
86C22×C4×C13—21no—
87C22×C4×C13—21no—
88C22×C4×C13—21no—
89C22×C4×C13—21no—
90C22×C4×C13—21no—
91C22×C4×C13—21no—
92C22×C4×C13—42no—
93C22×C4×C13—81no—
94C22×C4×C13C22⋊C411yescharacteristic
95C22×C4×C13C22⋊C411yescharacteristic
96C22×C4×C13C22×C411yescharacteristic
97C22×C4×C13C2×D411yescharacteristic
98C22×Dic13—44no—
99C22×Dic13—42no—
100C22×Dic13—82no—
101C22×Dic13—82no—
102C13×C4⋊C4—41no—
103C13×C4⋊C4—42no—
104C13×C4⋊C4—42no—
105C13×C22⋊C4—24no—
106C13×C22⋊C4—41no—
107C13×C22⋊C4—41no—
108C13×C22⋊C4—41no—
109C13×C22⋊C4—41no—
110C13×C22⋊C4—42no—
111C13×C22⋊C4—42no—
112C13×C22⋊C4—42no—
113C13×C22⋊C4—42no—
114C13×C22⋊C4—42no—
115C42×C13—81no—
116C22⋊Dic13—24no—
117C22⋊Dic13—44no—
118C22⋊Dic13—42no—
119#6099—82no—
120C2×#1055—42no—
121#2539D1311yescharacteristic
122C2×#342—131no—
123#1462—131no—
124#1352—132no—
125#1343—132no—
126C23×C13—22no—
127C23×C13—22no—
128C23×C13—22no—
129C23×C13—22no—
130C23×C13—22no—
131C23×C13—21no—
132C23×C13—21no—
133C23×C13—21no—
134C23×C13—21no—
135C23×C13—21no—
136C23×C13—21no—
137C23×C13—41no—
138C23×C13—42no—
139C23×C13—41no—
140C23×C13—41no—
141C23×C13—41no—
142C23×C13—41no—
143C23×C13—41no—
144C23×C13—41no—
145C23×C13—41no—
146C23×C13—41no—
147C23×C13—42no—
148C23×C13—41no—
149C23×C13—41no—
150C23×C13—41no—
151C23×C13—81no—
152C23×C13—81no—
153C23×C13—84no—
154C23×C13—82no—
155C23×C13—82no—
156C23×C13#9911yescharacteristic
157C23×C13#9911yescharacteristic
158C23×C13#10412yes—
159C23×C13C2×C22⋊C411yescharacteristic
160C23×C13AGL(1,ℤ/8)11yescharacteristic
161C23×C13#13711yescharacteristic
162D4×C13—84no—
163D4×C13—82no—
164D4×C13—82no—
165D4×C13—82no—
166D4×C13—82no—
167D4×C13—82no—
168C2×C4×C13—22no—
169C2×C4×C13—22no—
170C2×C4×C13—21no—
171C2×C4×C13—21no—
172C2×C4×C13—21no—
173C2×C4×C13—21no—
174C2×C4×C13—41no—
175C2×C4×C13—41no—
176C2×C4×C13—42no—
177C2×C4×C13—41no—
178C2×C4×C13—41no—
179C2×C4×C13—41no—
180C2×C4×C13—41no—
181C2×C4×C13—41no—
182C2×C4×C13—41no—
183C2×C4×C13—41no—
184C2×C4×C13—41no—
185C2×C4×C13—41no—
186C2×C4×C13—81no—
187C2×C4×C13—81no—
188C2×C4×C13—81no—
189C2×Dic13—44no—
190C2×Dic13—88no—
191C2×Dic13—82no—
192C2×Dic13—82no—
193#1055—82no—
194C2×#123—21no—
195C2×#121Dic1311yescharacteristic, complemented
196C2×#120—21no—
197C22×C22⋊C4—261no—
198C22×C22⋊C4C2×D1311yescharacteristic
199#407—261no—
200#399Dic1311yescharacteristic, complemented
201#399C2×D1311yescharacteristic
202#392Dic1311yescharacteristic, complemented
203#392C2×D1311yescharacteristic
204#390—21no—
205#390—21no—
206C4×C22⋊C4Dic1311yescharacteristic, complemented
207#342—132no—
208#342—261no—
209#323—132no—
210#323—261no—
211C22×C13—21no—
212C22×C13—21no—
213C22×C13—21no—
214C22×C13—21no—
215C22×C13—21no—
216C22×C13—21no—
217C22×C13—21no—
218C22×C13—21no—
219C22×C13—22no—
220C22×C13—21no—
221C22×C13—42no—
222C22×C13—42no—
223C22×C13—42no—
224C22×C13—41no—
225C22×C13—41no—
226C22×C13—44no—
227C22×C13—44no—
228C22×C13—41no—
229C22×C13—41no—
230C22×C13—41no—
231C22×C13—41no—
232C22×C13—81no—
233C22×C13—81no—
234C22×C13—81no—
235C22×C13—81no—
236C22×C13—81no—
237C22×C13—81no—
238C22×C13—82no—
239C22×C13—82no—
240C22×C13—81no—
241C22×C13—81no—
242C22×C13—81no—
243C22×C13#35312yes—
244C22×C13C2×#9911yescharacteristic
245C22×C13#41711yescharacteristic
246C22×C13C2×#10411yescharacteristic
247C4×C13—42no—
248C4×C13—42no—
249C4×C13—41no—
250C4×C13—41no—
251C4×C13—41no—
252C4×C13—41no—
253C4×C13—81no—
254Dic13—84no—
255C25C22⋊D1311yescharacteristic
256C22×D4—21no—
257C22×D4—21no—
258C22×D4—21no—
259C22×D4C2×Dic1311yescharacteristic, complemented
260C23×C4—521no—
261C23×C4C2×Dic1311yescharacteristic
262C23×C4C22⋊D1311yescharacteristic
263C2×M16—521no—
264#123—44no—
265#121—41no—
266#121—41no—
267#120—44no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4C2×Dic1311yescharacteristic, complemented
271C2×C22⋊C4—21no—
272C2×C22⋊C4—21no—
273C2×C22⋊C4—21no—
274C2×C22⋊C4—21no—
275C2×C22⋊C4—21no—
276C2×C22⋊C4—21no—
277C2×C22⋊C4—41no—
278C2×C22⋊C4—41no—
279C2×C22⋊C4—264no—
280C2×C22⋊C4—262no—
281C2×C22⋊C4—521no—
282C2×C22⋊C4—522no—
283C2×C22⋊C4C2×Dic1311yescharacteristic
284C2×C22⋊C4C22⋊D1311yescharacteristic
285C2×C22⋊C4C22⋊D1311yescharacteristic
286C2×C22⋊C4C22×D1311yescharacteristic
287C2×C42—21no—
288C22⋊C8—262no—
289C22⋊C8—521no—
290#95C2×Dic1311yescharacteristic, complemented
291#95C2×Dic1311yescharacteristic, complemented
292C2×C13—21no—
293C2×C13—21no—
294C2×C13—22no—
295C2×C13—41no—
296C2×C13—41no—
297C2×C13—42no—
298C2×C13—41no—
299C2×C13—161no—
300C2×C13#150411yescharacteristic
301C2×C13#212111yescharacteristic
302C2×C13C2×#35311yescharacteristic
303C24—21no—
304C24—21no—
305C24—22no—
306C24—21no—
307C24—21no—
308C24—21no—
309C24—42no—
310C24—81no—
311C24C22⋊Dic1311yescharacteristic
312C24C22⋊Dic1311yescharacteristic
313C24C2×C22⋊D1311yescharacteristic
314C2×D4—41no—
315C2×D4—42no—
316C2×D4—42no—
317C2×D4—42no—
318C2×D4—42no—
319C2×D4—41no—
320C2×D4—41no—
321C2×D4—42no—
322C2×D4—41no—
323C2×D4—41no—
324C2×D4—81no—
325C2×D4—81no—
326C2×D4—81no—
327C22×C4—21no—
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—21no—
331C22×C4—21no—
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—42no—
335C22×C4—81no—
336C22×C4—524no—
337C22×C4—522no—
338C22×C4—1042no—
339C22×C4—1042no—
340C22×C4C22⋊Dic1311yescharacteristic
341C22×C4C22⋊Dic1311yescharacteristic
342C22×C4C22×Dic1311yescharacteristic
343C22×C4C2×C22⋊D1311yescharacteristic
344M16—1042no—
345C2×C8—522no—
346C4⋊C4—41no—
347C4⋊C4—42no—
348C4⋊C4—42no—
349C22⋊C4—24no—
350C22⋊C4—41no—
351C22⋊C4—41no—
352C22⋊C4—41no—
353C22⋊C4—41no—
354C22⋊C4—42no—
355C22⋊C4—42no—
356C22⋊C4—42no—
357C22⋊C4—42no—
358C22⋊C4—42no—
359C22⋊C4—264no—
360C22⋊C4—524no—
361C22⋊C4—522no—
362C42—81no—
363C13#1175711yescharacteristic, complemented, Sylow
364C23—22no—
365C23—22no—
366C23—22no—
367C23—22no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—22no—
373C23—21no—
374C23—21no—
375C23—41no—
376C23—42no—
377C23—41no—
378C23—41no—
379C23—41no—
380C23—41no—
381C23—41no—
382C23—41no—
383C23—41no—
384C23—41no—
385C23—42no—
386C23—41no—
387C23—41no—
388C23—41no—
389C23—81no—
390C23—81no—
391C23—84no—
392C23—82no—
393C23—82no—
394C23#8807411yescharacteristic
395C23#8807411yescharacteristic
396C23#8807712yes—
397C23#8820311yescharacteristic
398C23#8820511yescharacteristic
399C23C2×C22⋊Dic1311yescharacteristic
400D4—84no—
401D4—82no—
402D4—82no—
403D4—82no—
404D4—82no—
405D4—82no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—42no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—81no—
425C2×C4—81no—
426C2×C4—81no—
427C2×C4—524no—
428C2×C4—1048no—
429C2×C4—1042no—
430C2×C4—1042no—
431C8—1042no—
432C22—21no—
433C22—21no—
434C22—21no—
435C22—21no—
436C22—21no—
437C22—21no—
438C22—21no—
439C22—21no—
440C22—22no—
441C22—21no—
442C22—42no—
443C22—42no—
444C22—42no—
445C22—41no—
446C22—41no—
447C22—44no—
448C22—44no—
449C22—41no—
450C22—41no—
451C22—41no—
452C22—41no—
453C22—81no—
454C22—81no—
455C22—81no—
456C22—81no—
457C22—81no—
458C22—81no—
459C22—82no—
460C22—82no—
461C22—81no—
462C22—81no—
463C22—81no—
464C22#1171813712yes—
465C22C2×#8807411yescharacteristic
466C22#1171889311yescharacteristic
467C22C2×#8807711yescharacteristic
468C4—42no—
469C4—42no—
470C4—41no—
471C4—41no—
472C4—41no—
473C4—41no—
474C4—81no—
475C4—1044no—
476C2—21no—
477C2—21no—
478C2—22no—
479C2—41no—
480C2—41no—
481C2—42no—
482C2—41no—
483C2—161no—
484C2#1311334011yescharacteristic
485C2#1311648211yescharacteristic
486C2C2×#1171813711yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C22⋊C4C22×D13
Fitting, prime radicalC13×#2539C2
socleC22×C13C2×#99
cosocleC2×C13×C22⋊C4C23
hypercenter#2539D13
hypocenterC13#11757
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24 ◁ C22×C22⋊C4 ◁ #2539

Complements

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

NH ≅ G/Ntype
1. C2×#11718118C2semidirect
2. #13113163C2semidirect
3. #13112860C2semidirect
4. #13112833C2semidirect
7. C2×C13×#121C4semidirect
11. C13×#399C4semidirect
13. C13×#392C4semidirect
17. C4×C13×C22⋊C4C4semidirect
27. C22×D4×C13C2×C4semidirect
37. C2×C13×C4⋊C4C2×C4semidirect
56. C13×#95C2×C4semidirect
57. C13×#95C2×C4semidirect
195. C2×#121Dic13semidirect
200. #399Dic13semidirect
202. #392Dic13semidirect
206. C4×C22⋊C4Dic13semidirect
259. C22×D4C2×Dic13semidirect
270. C2×C4⋊C4C2×Dic13semidirect
290. #95C2×Dic13semidirect
291. #95C2×Dic13semidirect
363. C13#11757semidirect

Maximal subgroups

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

subgroupindex
C2×#117181182
#131131632
#131128602
#131128332
C13×#25392
#1175713