Finite Group Databasebeta

← #15773680

Subgroups — #15773680

Order 3328.

626 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 626 conjugacy classes of subgroups — too many to draw. Only its 91 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#13114824C211yesmaximal, characteristic, complemented
2#13113177C211yesmaximal, characteristic, complemented
3#13112857C212yesmaximal, complemented
4#13112833C212yesmaximal, complemented
5C13×#2388C211yesmaximal, characteristic
6C22×C13×#41C411yescharacteristic, complemented
7C2×C4×D4×C13—21no—
8C2×C4×D4×C13C2211yescharacteristic
9C13×#395C411yescharacteristic, complemented
10C13×#394—21no—
11C13×#394C411yescharacteristic, complemented
12C13×#393C2211yescharacteristic
13C13×#392—21no—
14C13×#392C2211yescharacteristic
15C4×C13×C22⋊C4—21no—
16C4×C13×C22⋊C4C411yescharacteristic, complemented
17C2×#88074—21no—
18#11718873—21no—
19#11718587—21no—
20#11718118C2212yes—
21#11718117—21no—
22#11718117C2212yes—
23C2×C13×#41—44no—
24C2×C13×#41—41no—
25C2×C13×#41—41no—
26C22×Q8×C13C2×C411yescharacteristic
27C22×D4×C13—21no—
28C22×D4×C13—21no—
29C22×D4×C13C2×C411yescharacteristic
30C22×D4×C13D411yescharacteristic
31C23×C4×C13—21no—
32C23×C4×C13C2×C411yescharacteristic
33C23×C4×C13D411yescharacteristic
34C4×D4×C13—41no—
35C4×D4×C13—41no—
36C4×D4×C13—44no—
37C2×C13×C4⋊C4—21no—
38C2×C13×C4⋊C4C2×C411yescharacteristic
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⋊C4D411yescharacteristic
45C2×C13×C22⋊C4C2311yescharacteristic
46C2×C42×C13—21no—
47C2×C42×C13D411yescharacteristic
48C2×C22⋊Dic13—22no—
49C2×C4⋊Dic13—41no—
50C13×#95—21no—
51C13×#95—21no—
52C13×#95C2×C411yescharacteristic
53C13×#95C2×C411yescharacteristic
54#88074—42no—
55#88071—41no—
56C22⋊#1055—22no—
57C4⋊#1055—41no—
58#88043—41no—
59#11820—131nomaximal, Sylow
60C24×C13—21no—
61C24×C13C22⋊C411yescharacteristic
62C24×C13C2×D411yescharacteristic
63C13×#41—44no—
64C13×#41—44no—
65C13×#41—44no—
66C13×#41—44no—
67C2×Q8×C13—42no—
68C2×Q8×C13—41no—
69C2×D4×C13—21no—
70C2×D4×C13—21no—
71C2×D4×C13—41no—
72C2×D4×C13—41no—
73C2×D4×C13—41no—
74C2×D4×C13—42no—
75C2×D4×C13—42no—
76C2×D4×C13—42no—
77C2×D4×C13—42no—
78C2×D4×C13—42no—
79C2×D4×C13—41no—
80C2×D4×C13—41no—
81C2×D4×C13—42no—
82C22×C4×C13—24no—
83C22×C4×C13—21no—
84C22×C4×C13—21no—
85C22×C4×C13—21no—
86C22×C4×C13—21no—
87C22×C4×C13—21no—
88C22×C4×C13—21no—
89C22×C4×C13—21no—
90C22×C4×C13—42no—
91C22×C4×C13—42no—
92C22×C4×C13—42no—
93C22×C4×C13—41no—
94C22×C4×C13—41no—
95C22×C4×C13C22⋊C411yescharacteristic
96C22×C4×C13C22⋊C411yescharacteristic
97C22×C4×C13C22⋊C411yescharacteristic
98C22×C4×C13C22×C411yescharacteristic
99C22×C4×C13C2×D411yescharacteristic
100C22×Dic13—42no—
101C13×C4⋊C4—41no—
102C13×C4⋊C4—42no—
103C13×C22⋊C4—41no—
104C13×C22⋊C4—41no—
105C13×C22⋊C4—42no—
106C13×C22⋊C4—42no—
107C13×C22⋊C4—42no—
108C13×C22⋊C4—42no—
109C13×C22⋊C4—42no—
110C42×C13—21no—
111C42×C13—21no—
112C42×C13—42no—
113C22⋊Dic13—42no—
114C22⋊Dic13—42no—
115C4⋊Dic13—82no—
116C2×#1055—42no—
117#2388D1311yescharacteristic
118#1799—131no—
119#1466—131no—
120#1351—132no—
121#1343—132no—
122C23×C13—21no—
123C23×C13—21no—
124C23×C13—22no—
125C23×C13—21no—
126C23×C13—21no—
127C23×C13—21no—
128C23×C13—41no—
129C23×C13—41no—
130C23×C13—41no—
131C23×C13—41no—
132C23×C13—41no—
133C23×C13—41no—
134C23×C13—41no—
135C23×C13—41no—
136C23×C13—41no—
137C23×C13—41no—
138C23×C13C2×C22⋊C411yescharacteristic
139C23×C13AGL(1,ℤ/8)11yescharacteristic
140C23×C13#13711yescharacteristic
141Q8×C13—42no—
142Q8×C13—42no—
143D4×C13—42no—
144D4×C13—42no—
145D4×C13—44no—
146D4×C13—44no—
147D4×C13—48no—
148D4×C13—42no—
149D4×C13—42no—
150C2×C4×C13—22no—
151C2×C4×C13—22no—
152C2×C4×C13—22no—
153C2×C4×C13—21no—
154C2×C4×C13—21no—
155C2×C4×C13—21no—
156C2×C4×C13—21no—
157C2×C4×C13—21no—
158C2×C4×C13—21no—
159C2×C4×C13—44no—
160C2×C4×C13—42no—
161C2×C4×C13—41no—
162C2×C4×C13—41no—
163C2×C4×C13—41no—
164C2×C4×C13—41no—
165C2×C4×C13—42no—
166C2×C4×C13—44no—
167C2×C4×C13—42no—
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—81no—
175C2×C4×C13#9911yescharacteristic
176C2×C4×C13#9911yescharacteristic
177C2×Dic13—82no—
178C2×Dic13—82no—
179C2×Dic13—82no—
180#1055—82no—
181C22×#41Dic1311yescharacteristic, complemented
182C2×C4×D4—21no—
183C2×C4×D4C2×D1311yescharacteristic
184#432—261no—
185C2×#99—261no—
186#395Dic1311yescharacteristic, complemented
187#394—21no—
188#394Dic1311yescharacteristic, complemented
189#393C2×D1311yescharacteristic
190#392—21no—
191#392C2×D1311yescharacteristic
192#380—261no—
193C4×C22⋊C4—21no—
194C4×C22⋊C4Dic1311yescharacteristic, complemented
195#342—132no—
196#323—132no—
197#323—261no—
198C22×C13—21no—
199C22×C13—21no—
200C22×C13—21no—
201C22×C13—21no—
202C22×C13—41no—
203C22×C13—41no—
204C22×C13—42no—
205C22×C13—42no—
206C22×C13—41no—
207C22×C13—41no—
208C22×C13—41no—
209C22×C13—42no—
210C22×C13—41no—
211C22×C13—41no—
212C22×C13—81no—
213C22×C13—81no—
214C22×C13—81no—
215C22×C13—81no—
216C22×C13—81no—
217C22×C13—81no—
218C22×C13—81no—
219C22×C13C2×#9911yescharacteristic
220C22×C13#41711yescharacteristic
221C22×C13#42111yescharacteristic
222C4×C13—21no—
223C4×C13—42no—
224C4×C13—42no—
225C4×C13—41no—
226C4×C13—41no—
227C4×C13—41no—
228C4×C13—41no—
229C4×C13—81no—
230C4×C13AΣL(1,𝔽16)12yes—
231Dic13—162no—
232C2×#41—44no—
233C2×#41—41no—
234C2×#41—41no—
235C22×Q8C2×Dic1311yescharacteristic
236C22×D4—21no—
237C22×D4—21no—
238C22×D4C2×Dic1311yescharacteristic
239C22×D4C22⋊D1311yescharacteristic
240C23×C4—21no—
241C23×C4C2×Dic1311yescharacteristic
242C23×C4C22⋊D1311yescharacteristic
243C4×D4—41no—
244C4×D4—41no—
245C4×D4—44no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—521no—
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—262no—
255C2×C22⋊C4C22⋊D1311yescharacteristic
256C2×C22⋊C4C22×D1311yescharacteristic
257C2×C42—21no—
258C2×C42C22⋊D1311yescharacteristic
259C4⋊C8—521no—
260#99—522no—
261C22⋊C8—262no—
262#97—521no—
263#95—21no—
264#95—21no—
265#95—521no—
266#95C2×Dic1311yescharacteristic
267#95C2×Dic1311yescharacteristic
268C2×C13—21no—
269C2×C13—21no—
270C2×C13—41no—
271C2×C13—41no—
272C2×C13—81no—
273C2×C13—82no—
274C2×C13#151311yescharacteristic
275C2×C13C2×AΣL(1,𝔽16)11yescharacteristic
276C2×C13#212611yescharacteristic
277C24—21no—
278C24C22⋊Dic1311yescharacteristic
279C24C2×C22⋊D1311yescharacteristic
280#41—44no—
281#41—44no—
282#41—44no—
283#41—44no—
284C2×Q8—42no—
285C2×Q8—41no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—41no—
289C2×D4—41no—
290C2×D4—41no—
291C2×D4—42no—
292C2×D4—42no—
293C2×D4—42no—
294C2×D4—42no—
295C2×D4—42no—
296C2×D4—41no—
297C2×D4—41no—
298C2×D4—42no—
299C22×C4—24no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—42no—
308C22×C4—42no—
309C22×C4—42no—
310C22×C4—41no—
311C22×C4—41no—
312C22×C4—522no—
313C22×C4C22⋊Dic1311yescharacteristic
314C22×C4C22⋊Dic1311yescharacteristic
315C22×C4C22⋊Dic1311yescharacteristic
316C22×C4C22×Dic1311yescharacteristic
317C22×C4C2×C22⋊D1311yescharacteristic
318C2×C8—522no—
319C4⋊C4—41no—
320C4⋊C4—42no—
321C4⋊C4—1042no—
322C22⋊C4—41no—
323C22⋊C4—41no—
324C22⋊C4—42no—
325C22⋊C4—42no—
326C22⋊C4—42no—
327C22⋊C4—42no—
328C22⋊C4—42no—
329C22⋊C4—522no—
330C22⋊C4—522no—
331C42—21no—
332C42—21no—
333C42—42no—
334C13#1182011yescharacteristic, complemented, Sylow
335C23—21no—
336C23—21no—
337C23—22no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—41no—
342C23—41no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23—41no—
348C23—41no—
349C23—41no—
350C23—41no—
351C23#8820311yescharacteristic
352C23#8820511yescharacteristic
353C23C2×C22⋊Dic1311yescharacteristic
354Q8—42no—
355Q8—42no—
356D4—42no—
357D4—42no—
358D4—42no—
359D4—44no—
360D4—44no—
361D4—48no—
362D4—42no—
363C2×C4—22no—
364C2×C4—22no—
365C2×C4—22no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—44no—
373C2×C4—42no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—42no—
379C2×C4—44no—
380C2×C4—42no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—81no—
388C2×C4—1042no—
389C2×C4—1042no—
390C2×C4—1042no—
391C2×C4#8807411yescharacteristic
392C2×C4#8807411yescharacteristic
393C8—1042no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—41no—
399C22—41no—
400C22—42no—
401C22—42no—
402C22—41no—
403C22—41no—
404C22—41no—
405C22—41no—
406C22—42no—
407C22—41no—
408C22—81no—
409C22—81no—
410C22—81no—
411C22—81no—
412C22—81no—
413C22—81no—
414C22—81no—
415C22C2×#8807411yescharacteristic
416C22#1171889311yescharacteristic
417C22#1171889711yescharacteristic
418C4—21no—
419C4—42no—
420C4—41no—
421C4—42no—
422C4—41no—
423C4—41no—
424C4—41no—
425C4—81no—
426C4—2082no—
427C4#1171812812yes—
428C2—21no—
429C2—21no—
430C2—41no—
431C2—41no—
432C2—82no—
433C2—81no—
434C2#1311337911yescharacteristic
435C2C2×#1171812811yescharacteristic
436C2#1311650111yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C22⋊C4C22×D13
Fitting, prime radicalC13×#2388C2
socleC22×C13C2×#99
cosocleC2×C13×C22⋊C4C23
hypercenter#2388D13
hypocenterC13#11820
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2388

Complements

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

NH ≅ G/Ntype
1. #13114824C2semidirect
2. #13113177C2semidirect
3. #13112857C2semidirect
4. #13112833C2semidirect
6. C22×C13×#41C4semidirect
9. C13×#395C4semidirect
11. C13×#394C4semidirect
16. C4×C13×C22⋊C4C4semidirect
181. C22×#41Dic13semidirect
186. #395Dic13semidirect
188. #394Dic13semidirect
194. C4×C22⋊C4Dic13semidirect
334. C13#11820semidirect

Maximal subgroups

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

subgroupindex
#131148242
#131131772
#131128572
#131128332
C13×#23882
#1182013