Finite Group Databasebeta

← #15773589

Subgroups — #15773589

Order 3328.

574 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 574 conjugacy classes of subgroups — too many to draw. Only its 87 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
1#13114910C211yesmaximal, characteristic, complemented
2#13113163C211yesmaximal, characteristic, complemented
3#13112836C212yesmaximal, complemented
4#13112833C212yesmaximal, complemented
5C13×#2617C211yesmaximal, characteristic
6C2×C13×#121C411yescharacteristic, complemented
7C2×C13×#120—21no—
8C22×C13×C22⋊C4C2211yescharacteristic
9C13×#397C411yescharacteristic, complemented
10C13×#397C2211yescharacteristic
11C13×#394—21no—
12C13×#394—21no—
13C13×#392C411yescharacteristic, complemented
14C13×#392C2211yescharacteristic
15C13×#386—21no—
16C13×#380C411yescharacteristic, complemented
17#11718908—21no—
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
28C23×C4×C13C2×C411yescharacteristic
29C23×C4×C13D411yescharacteristic
30C13×#121—41no—
31C13×#121—41no—
32C13×#120—44no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4C2×C411yescharacteristic
35C2×C13×C22⋊C4—21no—
36C2×C13×C22⋊C4—21no—
37C2×C13×C22⋊C4—21no—
38C2×C13×C22⋊C4—21no—
39C2×C13×C22⋊C4—21no—
40C2×C13×C22⋊C4—21no—
41C2×C13×C22⋊C4—41no—
42C2×C13×C22⋊C4—41no—
43C2×C13×C22⋊C4C2×C411yescharacteristic
44C2×C13×C22⋊C4D411yescharacteristic
45C2×C13×C22⋊C4D411yescharacteristic
46C2×C13×C22⋊C4C2311yescharacteristic
47C2×C22⋊Dic13—22no—
48C2×C22⋊Dic13—41no—
49C2×C22⋊Dic13—41no—
50C2×#6099—41no—
51C13×#95—21no—
52C13×#95—21no—
53C13×#95C2×C411yescharacteristic
54C13×#95C2×C411yescharacteristic
55C22⋊#1055—22no—
56C22⋊#1055—41no—
57#11799—131nomaximal, Sylow
58C24×C13—21no—
59C24×C13—21no—
60C24×C13—22no—
61C24×C13—21no—
62C24×C13—41no—
63C24×C13—81no—
64C24×C13—81no—
65C24×C13C22⋊C411yescharacteristic
66C24×C13C22⋊C411yescharacteristic
67C24×C13C2×D411yescharacteristic
68C2×D4×C13—41no—
69C2×D4×C13—42no—
70C2×D4×C13—42no—
71C2×D4×C13—42no—
72C2×D4×C13—41no—
73C2×D4×C13—41no—
74C2×D4×C13—42no—
75C2×D4×C13—81no—
76C2×D4×C13—81no—
77C2×D4×C13—81no—
78C2×D4×C13—81no—
79C2×D4×C13—81no—
80C22×C4×C13—21no—
81C22×C4×C13—21no—
82C22×C4×C13—21no—
83C22×C4×C13—21no—
84C22×C4×C13—21no—
85C22×C4×C13—21no—
86C22×C4×C13—21no—
87C22×C4×C13—81no—
88C22×C4×C13—81no—
89C22×C4×C13C22⋊C411yescharacteristic
90C22×C4×C13C22⋊C411yescharacteristic
91C22×C4×C13C22×C411yescharacteristic
92C22×C4×C13C2×D411yescharacteristic
93C22×Dic13—42no—
94C13×C4⋊C4—41no—
95C13×C4⋊C4—81no—
96C13×C22⋊C4—41no—
97C13×C22⋊C4—41no—
98C13×C22⋊C4—41no—
99C13×C22⋊C4—41no—
100C13×C22⋊C4—42no—
101C13×C22⋊C4—42no—
102C13×C22⋊C4—42no—
103C13×C22⋊C4—42no—
104C13×C22⋊C4—81no—
105C13×C22⋊C4—81no—
106C22⋊Dic13—42no—
107C22⋊Dic13—42no—
108C22⋊Dic13—82no—
109C22⋊Dic13—82no—
110#6099—82no—
111C2×#1055—42no—
112#2617D1311yescharacteristic
113#1819—131no—
114#1462—131no—
115#1344—132no—
116#1343—132no—
117C23×C13—21no—
118C23×C13—21no—
119C23×C13—21no—
120C23×C13—21no—
121C23×C13—21no—
122C23×C13—21no—
123C23×C13—21no—
124C23×C13—41no—
125C23×C13—41no—
126C23×C13—42no—
127C23×C13—42no—
128C23×C13—41no—
129C23×C13—41no—
130C23×C13—41no—
131C23×C13—41no—
132C23×C13—42no—
133C23×C13—42no—
134C23×C13—41no—
135C23×C13—41no—
136C23×C13—41no—
137C23×C13—41no—
138C23×C13—41no—
139C23×C13—41no—
140C23×C13—41no—
141C23×C13—81no—
142C23×C13—81no—
143C23×C13—84no—
144C23×C13—84no—
145C23×C13#9911yescharacteristic
146C23×C13#9911yescharacteristic
147C23×C13C2×C22⋊C411yescharacteristic
148C23×C13AGL(1,ℤ/8)12yes—
149D4×C13—82no—
150D4×C13—82no—
151D4×C13—82no—
152D4×C13—84no—
153D4×C13—84no—
154C2×C4×C13—21no—
155C2×C4×C13—21no—
156C2×C4×C13—21no—
157C2×C4×C13—21no—
158C2×C4×C13—42no—
159C2×C4×C13—41no—
160C2×C4×C13—41no—
161C2×C4×C13—41no—
162C2×C4×C13—41no—
163C2×C4×C13—41no—
164C2×C4×C13—41no—
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—81no—
173C2×C4×C13—81no—
174C2×C4×C13—81no—
175C2×Dic13—82no—
176C2×Dic13—82no—
177C2×Dic13—82no—
178#1055—82no—
179C2×#121Dic1311yescharacteristic, complemented
180C2×#120—21no—
181C22×C22⋊C4C2×D1311yescharacteristic
182#407—261no—
183#397Dic1311yescharacteristic, complemented
184#397C2×D1311yescharacteristic
185#394—21no—
186#394—21no—
187#392Dic1311yescharacteristic, complemented
188#392C2×D1311yescharacteristic
189#386—21no—
190#380Dic1311yescharacteristic, complemented
191#379—261no—
192#342—132no—
193#342—261no—
194#323—132no—
195#323—261no—
196C22×C13—21no—
197C22×C13—21no—
198C22×C13—21no—
199C22×C13—21no—
200C22×C13—21no—
201C22×C13—21no—
202C22×C13—22no—
203C22×C13—21no—
204C22×C13—21no—
205C22×C13—42no—
206C22×C13—42no—
207C22×C13—42no—
208C22×C13—42no—
209C22×C13—41no—
210C22×C13—41no—
211C22×C13—41no—
212C22×C13—41no—
213C22×C13—41no—
214C22×C13—81no—
215C22×C13—81no—
216C22×C13—81no—
217C22×C13—81no—
218C22×C13—81no—
219C22×C13—81no—
220C22×C13—84no—
221C22×C13—84no—
222C22×C13—81no—
223C22×C13—81no—
224C22×C13—81no—
225C22×C13C2×#9911yescharacteristic
226C22×C13#41811yescharacteristic
227C22×C13#42111yescharacteristic
228C4×C13—41no—
229C4×C13—41no—
230C4×C13—41no—
231C4×C13—41no—
232C4×C13—81no—
233C4×C13—81no—
234C4×C13—81no—
235Dic13—162no—
236C25C22⋊D1311yescharacteristic
237C22×D4—21no—
238C22×D4—21no—
239C22×D4—21no—
240C22×D4C2×Dic1311yescharacteristic
241C23×C4C2×Dic1311yescharacteristic
242C23×C4C22⋊D1311yescharacteristic
243C2×M16—521no—
244#121—41no—
245#121—41no—
246#120—44no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4C2×Dic1311yescharacteristic
249C2×C22⋊C4—21no—
250C2×C22⋊C4—21no—
251C2×C22⋊C4—21no—
252C2×C22⋊C4—21no—
253C2×C22⋊C4—21no—
254C2×C22⋊C4—21no—
255C2×C22⋊C4—41no—
256C2×C22⋊C4—41no—
257C2×C22⋊C4—262no—
258C2×C22⋊C4—521no—
259C2×C22⋊C4—521no—
260C2×C22⋊C4C2×Dic1311yescharacteristic
261C2×C22⋊C4C22⋊D1311yescharacteristic
262C2×C22⋊C4C22⋊D1311yescharacteristic
263C2×C22⋊C4C22×D1311yescharacteristic
264C22⋊C8—262no—
265C22⋊C8—521no—
266#95—21no—
267#95—21no—
268#95C2×Dic1311yescharacteristic
269#95C2×Dic1311yescharacteristic
270C2×C13—21no—
271C2×C13—21no—
272C2×C13—42no—
273C2×C13—41no—
274C2×C13—41no—
275C2×C13—81no—
276C2×C13—161no—
277C2×C13#151011yescharacteristic
278C2×C13#212111yescharacteristic
279C2×C13#212711yescharacteristic
280C24—21no—
281C24—21no—
282C24—22no—
283C24—21no—
284C24—41no—
285C24—81no—
286C24—81no—
287C24C22⋊Dic1311yescharacteristic
288C24C22⋊Dic1311yescharacteristic
289C24C2×C22⋊D1311yescharacteristic
290C2×D4—41no—
291C2×D4—42no—
292C2×D4—42no—
293C2×D4—42no—
294C2×D4—41no—
295C2×D4—41no—
296C2×D4—42no—
297C2×D4—81no—
298C2×D4—81no—
299C2×D4—81no—
300C2×D4—81no—
301C2×D4—81no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—81no—
310C22×C4—81no—
311C22×C4—522no—
312C22×C4C22⋊Dic1311yescharacteristic
313C22×C4C22⋊Dic1311yescharacteristic
314C22×C4C22×Dic1311yescharacteristic
315C22×C4C2×C22⋊D1311yescharacteristic
316M16—1042no—
317C2×C8—522no—
318C4⋊C4—41no—
319C4⋊C4—81no—
320C22⋊C4—41no—
321C22⋊C4—41no—
322C22⋊C4—41no—
323C22⋊C4—41no—
324C22⋊C4—42no—
325C22⋊C4—42no—
326C22⋊C4—42no—
327C22⋊C4—42no—
328C22⋊C4—81no—
329C22⋊C4—81no—
330C22⋊C4—522no—
331C22⋊C4—522no—
332C22⋊C4—1042no—
333C22⋊C4—1042no—
334C13#1179911yescharacteristic, complemented, Sylow
335C23—21no—
336C23—21no—
337C23—21no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—41no—
343C23—41no—
344C23—42no—
345C23—42no—
346C23—41no—
347C23—41no—
348C23—41no—
349C23—41no—
350C23—42no—
351C23—42no—
352C23—41no—
353C23—41no—
354C23—41no—
355C23—41no—
356C23—41no—
357C23—41no—
358C23—41no—
359C23—81no—
360C23—81no—
361C23—84no—
362C23—84no—
363C23#8807411yescharacteristic
364C23#8807411yescharacteristic
365C23#8818612yes—
366C23C2×C22⋊Dic1311yescharacteristic
367D4—82no—
368D4—82no—
369D4—82no—
370D4—84no—
371D4—84no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—42no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—81no—
391C2×C4—81no—
392C2×C4—81no—
393C2×C4—1042no—
394C2×C4—1042no—
395C2×C4—1042no—
396C8—1042no—
397C22—21no—
398C22—21no—
399C22—22no—
400C22—21no—
401C22—21no—
402C22—21no—
403C22—21no—
404C22—21no—
405C22—21no—
406C22—42no—
407C22—42no—
408C22—42no—
409C22—42no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—41no—
415C22—81no—
416C22—81no—
417C22—81no—
418C22—81no—
419C22—81no—
420C22—81no—
421C22—84no—
422C22—84no—
423C22—81no—
424C22—81no—
425C22—81no—
426C22#1171887611yescharacteristic
427C22C2×#8807411yescharacteristic
428C22#1171889711yescharacteristic
429C4—41no—
430C4—41no—
431C4—41no—
432C4—41no—
433C4—81no—
434C4—81no—
435C4—81no—
436C4—2082no—
437C2—21no—
438C2—21no—
439C2—42no—
440C2—41no—
441C2—41no—
442C2—81no—
443C2—161no—
444C2#1311336511yescharacteristic
445C2#1311648211yescharacteristic
446C2#1311650511yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C22⋊C4C22×D13
Fitting, prime radicalC13×#2617C2
socleC22×C13C2×#99
cosocleC2×C13×C22⋊C4C23
hypercenter#2617D13
hypocenterC13#11799
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24 ◁ C22×C22⋊C4 ◁ #2617

Complements

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

NH ≅ G/Ntype
1. #13114910C2semidirect
2. #13113163C2semidirect
3. #13112836C2semidirect
4. #13112833C2semidirect
6. C2×C13×#121C4semidirect
9. C13×#397C4semidirect
13. C13×#392C4semidirect
16. C13×#380C4semidirect
179. C2×#121Dic13semidirect
183. #397Dic13semidirect
187. #392Dic13semidirect
190. #380Dic13semidirect
334. C13#11799semidirect

Maximal subgroups

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

subgroupindex
#131149102
#131131632
#131128362
#131128332
C13×#26172
#1179913