Finite Group Databasebeta

← #13075299

Subgroups — #13075299

Order 1408.

554 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66939C211yesmaximal, characteristic, complemented
2C2×#66936C211yesmaximal, characteristic, complemented
3C11×#390C211yesmaximal, characteristic, complemented
4#10622836C211yesmaximal, characteristic
5#10622833C211yesmaximal, characteristic, complemented
6#10622602C211yesmaximal, characteristic, complemented
7#10622597C211yesmaximal, characteristic, complemented
8#10622572C211yesmaximal, characteristic, complemented
9#10622569C211yesmaximal, characteristic, complemented
10#10622566C211yesmaximal, characteristic, complemented
11#10622562C211yesmaximal, characteristic, complemented
12#10622561C211yesmaximal, characteristic, complemented
13#10622555C211yesmaximal, characteristic, complemented
14#10622553C211yesmaximal, characteristic, complemented
15#10622549C211yesmaximal, characteristic, complemented
16C22×D4×C11C2211yescharacteristic
17C22×C22⋊D11C2211yescharacteristic
18C22×C22⋊D11C2211yescharacteristic
19C23×Dic11C2211yescharacteristic
20C22×C4×D11C2211yescharacteristic
21C2×C11×C4⋊C4C2211yescharacteristic
22C2×C11×C22⋊C4C2211yescharacteristic
23C2×C11×C22⋊C4C2211yescharacteristic
24C2×C11×C22⋊C4C2211yescharacteristic
25C2×C11×C22⋊C4C2211yescharacteristic
26C2×C42×C11C2211yescharacteristic
27C2×C22⋊Dic11C2211yescharacteristic
28C2×C22⋊Dic11C2211yescharacteristic
29C2×C22⋊Dic11C2211yescharacteristic
30C2×C22⋊Dic11C2211yescharacteristic
31C2×C22⋊Dic11C2211yescharacteristic
32C2×(C2×D11)⋊C4C2211yescharacteristic
33C2×(C2×D11)⋊C4C2211yescharacteristic
34C2×(C2×D11)⋊C4C2211yescharacteristic
35C2×(C2×D11)⋊C4C2211yescharacteristic
36C2×C4⋊Dic11C2211yescharacteristic
37C2×C4⋊Dic11C2211yescharacteristic
38C2×C4⋊Dic11C2211yescharacteristic
39C2×Dic11⋊C4C2211yescharacteristic
40C2×Dic11⋊C4C2211yescharacteristic
41C2×Dic11⋊C4C2211yescharacteristic
42C2×Dic11⋊C4C2211yescharacteristic
43#66939—24no—
44#66936—24no—
45C11⋊#95C2211yescharacteristic
46C11⋊#95C2211yescharacteristic
47C11⋊#95C2211yescharacteristic
48C11⋊#95C2211yescharacteristic
49C11⋊#95C2211yescharacteristic
50C11⋊#95C2211yescharacteristic
51C11⋊#95C2211yescharacteristic
52C11⋊#95C2211yescharacteristic
53C24×C11C2311yescharacteristic
54C24×C11C2311yescharacteristic
55C23×D11C2311yescharacteristic
56C2×D4×C11—22no—
57C2×D4×C11—22no—
58C2×D4×C11—41no—
59C22×C4×C11C2311yescharacteristic
60C22×C4×C11C2311yescharacteristic
61C22×C4×C11C2311yescharacteristic
62C22×C4×C11C2311yescharacteristic
63C22×C4×C11C2311yescharacteristic
64C2×C22⋊D11—22no—
65C2×C22⋊D11—22no—
66C2×C22⋊D11—22no—
67C2×C22⋊D11—41no—
68C2×C22⋊D11—41no—
69C2×C22⋊D11—41no—
70C22×Dic11—22no—
71C22×Dic11—22no—
72C22×Dic11—41no—
73C22×Dic11C2311yescharacteristic
74C22×Dic11C2311yescharacteristic
75C22×Dic11C2311yescharacteristic
76C22×Dic11C2311yescharacteristic
77C22×Dic11C2311yescharacteristic
78C22×Dic11C2311yescharacteristic
79C22×Dic11C2311yescharacteristic
80C2×C4×D11—22no—
81C2×C4×D11—41no—
82C2×C4×D11—41no—
83C11×C4⋊C4—41no—
84C11×C22⋊C4—22no—
85C11×C22⋊C4—22no—
86C11×C22⋊C4—41no—
87C11×C22⋊C4—41no—
88C42×C11—22no—
89C22⋊Dic11—22no—
90C22⋊Dic11—41no—
91C22⋊Dic11—41no—
92C22⋊Dic11—41no—
93C22⋊Dic11—41no—
94(C2×D11)⋊C4—22no—
95(C2×D11)⋊C4—22no—
96(C2×D11)⋊C4—41no—
97(C2×D11)⋊C4D414yescomplemented
98C4⋊Dic11—22no—
99C4⋊Dic11—22no—
100C4⋊Dic11—22no—
101Dic11⋊C4—22no—
102Dic11⋊C4—41no—
103Dic11⋊C4—41no—
104Dic11⋊C4—41no—
105#2706—111nomaximal, Sylow
106C23×C11—21no—
107C23×C11—21no—
108C23×C11—21no—
109C23×C11—21no—
110C23×C11—21no—
111C23×C11—21no—
112C23×C11—21no—
113C23×C11—21no—
114C23×C11—21no—
115C23×C11—21no—
116C23×C11—21no—
117C23×C11—21no—
118C23×C11—21no—
119C23×C11#4112yes—
120C23×C11C2411yescharacteristic
121C22×D11—21no—
122C22×D11—21no—
123C22×D11—21no—
124C22×D11—21no—
125C22×D11—21no—
126C22×D11—21no—
127C22×D11C2×D412yes—
128D4×C11—44no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11C2×D412yes—
143C2×C4×C11#4112yes—
144C22⋊D11—44no—
145C22⋊D11—44no—
146C2×Dic11—21no—
147C2×Dic11—21no—
148C2×Dic11—21no—
149C2×Dic11—21no—
150C2×Dic11—21no—
151C2×Dic11—21no—
152C2×Dic11—21no—
153C2×Dic11—21no—
154C2×Dic11—21no—
155C2×Dic11—21no—
156C2×Dic11—21no—
157C2×Dic11—21no—
158C2×Dic11—21no—
159C2×Dic11—21no—
160C2×Dic11—21no—
161C2×Dic11—21no—
162C2×Dic11—21no—
163C2×Dic11—21no—
164C2×Dic11—21no—
165C2×Dic11—21no—
166C2×Dic11—44no—
167C2×Dic11C2×D412yes—
168C4×D11—44no—
169C2×#123—111no—
170C2×#123—111no—
171#399—111no—
172#398—111no—
173#397—111no—
174#396—111no—
175#394—111no—
176#392—111no—
177#390D1111yescharacteristic, complemented
178#388—111no—
179#386—111no—
180#386—111no—
181#385—111no—
182#382—111no—
183#380—111no—
184C22×C11—22no—
185C22×C11—22no—
186C22×C11—22no—
187C22×C11—41no—
188C22×C11—41no—
189C22×C11—41no—
190C22×C11—41no—
191C22×C11—41no—
192C22×C11—41no—
193C22×C11—41no—
194C22×C11—41no—
195C22×C11—41no—
196C22×C11—41no—
197C22×C11—41no—
198C22×C11C22×D411yescharacteristic
199C22×C11C2×#4111yescharacteristic
200C22×C11C2×#4111yescharacteristic
201C22×C11H(5,𝔽2)11yescharacteristic
202C22×C11H(5,𝔽2)11yescharacteristic
203C22×C11H(5,𝔽2)11yescharacteristic
204C22×C112−1+411yescharacteristic
205C2×D11—22no—
206C2×D11—22no—
207C2×D11—22no—
208C2×D11—41no—
209C2×D11—41no—
210C2×D11—41no—
211C2×D11—41no—
212C4×C11—22no—
213C4×C11—22no—
214C4×C11—41no—
215C4×C11—41no—
216C4×C11—41no—
217Dic11—22no—
218Dic11—41no—
219Dic11—41no—
220Dic11—41no—
221Dic11—41no—
222Dic11—41no—
223Dic11—41no—
224C22×D4—111no—
225C22×D4—111no—
226C22×D4C2×D1111yescharacteristic
227C23×C4—111no—
228C23×C4—111no—
229#123—224no—
230#123—224no—
231C2×C4⋊C4—111no—
232C2×C4⋊C4—111no—
233C2×C4⋊C4—111no—
234C2×C4⋊C4—111no—
235C2×C4⋊C4—111no—
236C2×C4⋊C4—111no—
237C2×C4⋊C4—111no—
238C2×C4⋊C4C2×D1111yescharacteristic
239C2×C22⋊C4—111no—
240C2×C22⋊C4—111no—
241C2×C22⋊C4—111no—
242C2×C22⋊C4—111no—
243C2×C22⋊C4—111no—
244C2×C22⋊C4—111no—
245C2×C22⋊C4—111no—
246C2×C22⋊C4—111no—
247C2×C22⋊C4—111no—
248C2×C22⋊C4C2×D1111yescharacteristic
249C2×C22⋊C4C2×D1111yescharacteristic
250C2×C22⋊C4C2×D1111yescharacteristic
251C2×C22⋊C4C2×D1111yescharacteristic
252C2×C42C2×D1111yescharacteristic
253#95—111no—
254#95—111no—
255#95—111no—
256#95—111no—
257#95—111no—
258#95—111no—
259#95—111no—
260#95—111no—
261C2×C11—42no—
262C2×C11—81no—
263C2×C11#53511yescharacteristic
264C2×C11#53911yescharacteristic
265C2×C11#54011yescharacteristic
266C2×C11#54611yescharacteristic
267C2×C11#54711yescharacteristic
268C2×C11#55111yescharacteristic
269C2×C11#56211yescharacteristic
270D11—42no—
271C24—111no—
272C24C22×D1111yescharacteristic
273C24C22×D1111yescharacteristic
274C2×D4—22no—
275C2×D4—22no—
276C2×D4—41no—
277C2×D4—222no—
278C2×D4—222no—
279C2×D4—222no—
280C2×D4—441no—
281C2×D4—441no—
282C2×D4—441no—
283C22×C4—111no—
284C22×C4—111no—
285C22×C4—111no—
286C22×C4—111no—
287C22×C4—111no—
288C22×C4—111no—
289C22×C4—111no—
290C22×C4—222no—
291C22×C4—222no—
292C22×C4—222no—
293C22×C4—441no—
294C22×C4—441no—
295C22×C4—441no—
296C22×C4C22×D1111yescharacteristic
297C22×C4C22×D1111yescharacteristic
298C22×C4C22×D1111yescharacteristic
299C22×C4C22×D1111yescharacteristic
300C22×C4C22×D1111yescharacteristic
301C4⋊C4—41no—
302C4⋊C4—222no—
303C4⋊C4—222no—
304C4⋊C4—222no—
305C4⋊C4—222no—
306C4⋊C4—441no—
307C4⋊C4—441no—
308C4⋊C4—441no—
309C22⋊C4—22no—
310C22⋊C4—22no—
311C22⋊C4—41no—
312C22⋊C4—41no—
313C22⋊C4—114no—
314C22⋊C4—222no—
315C22⋊C4—222no—
316C22⋊C4—222no—
317C22⋊C4—441no—
318C22⋊C4—441no—
319C22⋊C4—441no—
320C22⋊C4—441no—
321C22⋊C4—441no—
322C42—22no—
323C11#270611yescharacteristic, complemented, Sylow
324C23—21no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23—21no—
333C23—21no—
334C23—21no—
335C23—21no—
336C23—21no—
337C23—112no—
338C23—221no—
339C23—221no—
340C23—221no—
341C23—221no—
342C23—221no—
343C23—221no—
344C23#433912yes—
345C23C23×D1111yescharacteristic
346D4—44no—
347D4—444no—
348D4—444no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—112no—
363C2×C4—221no—
364C2×C4—221no—
365C2×C4—221no—
366C2×C4—221no—
367C2×C4—221no—
368C2×C4—221no—
369C2×C4—221no—
370C2×C4—221no—
371C2×C4—221no—
372C2×C4—221no—
373C2×C4—221no—
374C2×C4—221no—
375C2×C4—221no—
376C2×C4—221no—
377C2×C4—221no—
378C2×C4—221no—
379C2×C4—221no—
380C2×C4—221no—
381C2×C4—221no—
382C2×C4—221no—
383C2×C4—444no—
384C2×C4—444no—
385C2×C4D4×D1112yes—
386C2×C4#434112yes—
387C22—22no—
388C22—22no—
389C22—22no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—222no—
402C22—222no—
403C22—222no—
404C22—441no—
405C22—441no—
406C22—441no—
407C22—441no—
408C22C2×#433911yescharacteristic
409C22C2×D4×D1111yescharacteristic
410C22C2×#434111yescharacteristic
411C22#6703711yescharacteristic
412C22#6703711yescharacteristic
413C22#6704211yescharacteristic
414C22#6704311yescharacteristic
415C4—22no—
416C4—22no—
417C4—41no—
418C4—41no—
419C4—41no—
420C4—222no—
421C4—441no—
422C4—441no—
423C4—441no—
424C4—441no—
425C4—441no—
426C4—441no—
427C2—42no—
428C2—81no—
429C2—442no—
430C2#1062302611yescharacteristic
431C2#1062308111yescharacteristic
432C2#1062309511yescharacteristic
433C2#1062314211yescharacteristic
434C2#1062315011yescharacteristic
435C2#1062321511yescharacteristic
436C2#1062324611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#390C2
prime radical#10622836C2
hypercenter#390D11
hypocenterC11#2706
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C2×#66939C2semidirect
2. C2×#66936C2semidirect
3. C11×#390C2semidirect
5. #10622833C2semidirect
6. #10622602C2semidirect
7. #10622597C2semidirect
8. #10622572C2semidirect
9. #10622569C2semidirect
10. #10622566C2semidirect
11. #10622562C2semidirect
12. #10622561C2semidirect
13. #10622555C2semidirect
14. #10622553C2semidirect
15. #10622549C2semidirect
97. (C2×D11)⋊C4D4semidirect
177. #390D11semidirect
323. C11#2706semidirect

Maximal subgroups

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

subgroupindex
C2×#669392
C2×#669362
C11×#3902
#106228362
#106228332
#106226022
#106225972
#106225722
#106225692
#106225662
#106225622
#106225612
#106225552
#106225532
#106225492
#270611