Finite Group Databasebeta

← #14737424

Subgroups — #14737424

Order 2816.

606 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
1#13079928C211yesmaximal, characteristic
2#13079012C211yesmaximal, characteristic
3#13077565C211yesmaximal, characteristic, complemented
4#13068186C212yesmaximal, complemented
5#13068172C212yesmaximal, complemented
6#13068062C212yesmaximal, complemented
7#13068048C212yesmaximal, complemented
8#13067369C211yesmaximal, characteristic, complemented
9#13067263C211yesmaximal, characteristic
10C2×#10622185C211yesmaximal, characteristic, complemented
11C11×#3209C211yesmaximal, characteristic, complemented
12C11×#533C2211yescharacteristic
13C2×C11×C4⋊Q8C2211yescharacteristic
14#10623008C2211yescharacteristic
15C11×#494—21no—
16C11×#487—21no—
17C11×#462C2212yes—
18C11×#462C2212yes—
19C11×#451—22no—
20C11×#431C2211yescharacteristic
21#10622706C2212yes—
22#10622702—22no—
23#10622701C2212yes—
24#10622697—21no—
25#10622696—21no—
26#10622661—22no—
27#10622640C2212yes—
28#10622637—22no—
29#10622637C2212yes—
30Q8×C11⋊C8C2212yes—
31#10622633C2212yes—
32#10622612—21no—
33#10622610—21no—
34#10622579—21no—
35#10622579—21no—
36C2×C4⋊(C11⋊C8)C2211yescharacteristic
37C2×C4⋊(C11⋊C8)C2211yescharacteristic
38C4×#4318C2211yescharacteristic
39#10622185C2212yes—
40#10622185C2212yes—
41#10622124C2211yescharacteristic
42#10622124C2211yescharacteristic
43#10622123C2211yescharacteristic
44#10622123C2211yescharacteristic
45#10622118C2212yes—
46#10622117C2212yes—
47C22×Q8×C11—21no—
48C2×#4339—21no—
49C2×C11×Q16—22no—
50C2×C11×Q16—22no—
51C11×C4⋊Q8—21no—
52C11×C4⋊Q8—21no—
53C11×C4⋊Q8—21no—
54C11×C4⋊Q8D411yescharacteristic
55C11×C4⋊Q8D411yescharacteristic
56C11×C4⋊Q8C2312yes—
57C11×#125—21no—
58C11×C22⋊Q8—21no—
59C11×C22⋊Q8D412yes—
60C4×Q8×C11—21no—
61C4×Q8×C11C2312yes—
62C11×#117—21no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—21no—
65C2×C42×C11C2311yescharacteristic
66C2×#4325—22no—
67#66983—21no—
68#66983—21no—
69C2×#4318D411yescharacteristic
70C2×#4318D411yescharacteristic
71C22×C11⋊C8—21no—
72C22×C11⋊C8—21no—
73#66928—21no—
74#66927C2311yescharacteristic
75C4×D44—21no—
76C4×D44—21no—
77#66922C2311yescharacteristic
78C11×C4⋊C8C2311yescharacteristic
79C11×C4⋊C8C2311yescharacteristic
80C11×#103—22no—
81C11×#103—22no—
82C11×C22⋊C8—21no—
83C4×C8×C11—21no—
84#66899—22no—
85#66874—22no—
86#66874—22no—
87#66873—22no—
88#66873—22no—
89#66873—22no—
90#66872—22no—
91C4⋊(C11⋊C8)—21no—
92C4⋊(C11⋊C8)—21no—
93C4⋊(C11⋊C8)—22no—
94C4⋊(C11⋊C8)—22no—
95C4⋊(C11⋊C8)C2312yes—
96C4⋊(C11⋊C8)C2311yescharacteristic
97C4⋊(C11⋊C8)C2311yescharacteristic
98#66867—22no—
99#66867D412yes—
100C4×C11⋊C8—22no—
101C4×C11⋊C8C2312yes—
102#19245—111nomaximal, Sylow
103C2×Q8×C11—21no—
104C2×Q8×C11—22no—
105C2×Q8×C11—41no—
106C2×Q8×C11—81no—
107C2×Q8×C11—81no—
108C2×Q8×C11C2×D412yes—
109C22×C4×C11—41no—
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11#4111yescharacteristic
113C2×C22⋊D11—41no—
114#4339—42no—
115#4339—42no—
116C2×D44—21no—
117C2×D44—21no—
118C2×D44—21no—
119C2×C4×D11—41no—
120C2×Dic22—21no—
121C11×Q16—82no—
122C11×Q16—82no—
123C2×C8×C11—21no—
124C2×C8×C11—21no—
125C11×C4⋊C4—21no—
126C11×C4⋊C4—21no—
127C11×C4⋊C4—21no—
128C11×C4⋊C4—22no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—41no—
133C11×C4⋊C4—41no—
134C11×C4⋊C4C2×D412yes—
135C11×C22⋊C4—22no—
136C42×C11—22no—
137C42×C11C2×D411yescharacteristic
138C42×C11C2×D411yescharacteristic
139C42×C11#4111yescharacteristic
140C42×C11C2411yescharacteristic
141#4325—82no—
142(C2×D11)⋊C4—41no—
143(C2×D11)⋊C4—41no—
144C4⋊Dic11—21no—
145C4⋊Dic11—21no—
146#4318—22no—
147#4318—22no—
148C2×C11⋊C8—21no—
149C2×C11⋊C8—21no—
150C2×C11⋊C8—22no—
151C2×C11⋊C8—42no—
152C2×C11⋊C8—81no—
153C2×C11⋊C8C2×D412yes—
154C2×C11⋊C8C2×D412yes—
155#3246—111no—
156#3209D1111yescharacteristic, complemented
157#3141—111no—
158#2962—111no—
159#1702—112no—
160#1700—112no—
161#1682—112no—
162#1680—112no—
163#1565—111no—
164#1540—111no—
165C2×#332—111no—
166C23×C11#12111yescharacteristic
167C22×D11—41no—
168Q8×C11—22no—
169Q8×C11—22no—
170Q8×C11—42no—
171Q8×C11—42no—
172Q8×C11—81no—
173Q8×C11—82no—
174C2×C4×C11—21no—
175C2×C4×C11—21no—
176C2×C4×C11—22no—
177C2×C4×C11—22no—
178C2×C4×C11—41no—
179C2×C4×C11—42no—
180C2×C4×C11—82no—
181C2×C4×C11#12111yescharacteristic
182C2×C4×C11#12111yescharacteristic
183C2×C4×C11#12111yescharacteristic
184C2×C4×C11#13512yes—
185C2×C4×C11#13712yes—
186C2×C4×C11C22×D411yescharacteristic
187C2×C4×C11C22×D411yescharacteristic
188C2×C4×C11C2×#4111yescharacteristic
189C22⋊D11—82no—
190C2×Dic11—41no—
191D44—41no—
192D44—41no—
193D44—41no—
194D44—41no—
195D44—81no—
196C4×D11—82no—
197Dic22—41no—
198Dic22—41no—
199C8×C11—41no—
200C8×C11—41no—
201C11⋊C8—22no—
202C11⋊C8—22no—
203C11⋊C8—41no—
204C11⋊C8—41no—
205C11⋊C8—42no—
206#533C2×D1111yescharacteristic
207#532—111no—
208C2×C4⋊Q8C2×D1111yescharacteristic
209#494—21no—
210#489—222no—
211#487—21no—
212#487—112no—
213#486—112no—
214#476—221no—
215#475—112no—
216#465—222no—
217#462C2×D1112yes—
218#462C2×D1112yes—
219#461—221no—
220#460—112no—
221#451—22no—
222#446—112no—
223#446—222no—
224C8×Q8—112no—
225#431C2×D1111yescharacteristic
226#424—221no—
227C2×C4⋊C8—111no—
228C2×C4⋊C8—111no—
229#417—221no—
230#417—221no—
231#405—221no—
232C4×M16—111no—
233#335—112no—
234#334—112no—
235#332—112no—
236#332—112no—
237#332—111no—
238#332—111no—
239#331—111no—
240#331—111no—
241C22×C11—21no—
242C22×C11—21no—
243C22×C11#46412yes—
244C22×C11C2×#12111yescharacteristic
245C2×D11—81no—
246C2×D11—81no—
247C2×D11—81no—
248C4×C11—21no—
249C4×C11—21no—
250C4×C11—21no—
251C4×C11—42no—
252C4×C11—42no—
253C4×C11—82no—
254C4×C11#46412yes—
255C4×C11C2×#13511yescharacteristic
256C4×C11C2×#13711yescharacteristic
257C4×C11#57611yescharacteristic
258C4×C11#57711yescharacteristic
259Dic11—81no—
260C2×#41—221no—
261C22×Q8—21no—
262C2×Q16—22no—
263C2×Q16—22no—
264C2×SD16—222no—
265C2×M16—111no—
266C2×M16—111no—
267C22×C8—221no—
268C22×C8—221no—
269C4⋊Q8—21no—
270C4⋊Q8—21no—
271C4⋊Q8—21no—
272C4⋊Q8—111no—
273C4⋊Q8C22⋊D1111yescharacteristic
274C4⋊Q8C22⋊D1111yescharacteristic
275C4⋊Q8C22×D1112yes—
276#127—111no—
277#125—21no—
278#124—221no—
279C22⋊Q8—21no—
280C22⋊Q8C22⋊D1112yes—
281#121—221no—
282#121—221no—
283C4×Q8—21no—
284C4×Q8C22×D1112yes—
285C4×D4—221no—
286C4×D4—221no—
287#117—21no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—21no—
290C2×C42C22×D1111yescharacteristic
291#106—222no—
292C4⋊C8—111no—
293C4⋊C8—111no—
294C4⋊C8—112no—
295C4⋊C8—222no—
296C4⋊C8—222no—
297C4⋊C8—221no—
298C4⋊C8—221no—
299C4⋊C8C22×D1111yescharacteristic
300C4⋊C8C22×D1111yescharacteristic
301#103—22no—
302#103—22no—
303#103—222no—
304#103—222no—
305#103—222no—
306#102—222no—
307#102—222no—
308#102—222no—
309C22⋊C8—21no—
310#97—112no—
311#97—222no—
312C4×C8—21no—
313C4×C8—112no—
314C4×C8—222no—
315C2×C11—22no—
316C2×C11C2×#46411yescharacteristic
317C2×C11#306211yescharacteristic
318C2×C11#306911yescharacteristic
319D11—161no—
320#41—442no—
321#41—442no—
322C2×Q8—21no—
323C2×Q8—22no—
324C2×Q8—41no—
325C2×Q8—81no—
326C2×Q8—81no—
327C2×Q8—221no—
328C2×Q8C2×C22⋊D1112yes—
329C2×D4—221no—
330C2×D4—221no—
331C2×D4—221no—
332C2×D4—441no—
333C22×C4—41no—
334C22×C4—441no—
335C22×C4D4×D1111yescharacteristic
336C22×C4#434111yescharacteristic
337C22×C4C2×C22⋊D1111yescharacteristic
338Q16—82no—
339Q16—82no—
340SD16—882no—
341M16—222no—
342M16—222no—
343C2×C8—21no—
344C2×C8—21no—
345C2×C8—112no—
346C2×C8—112no—
347C2×C8—221no—
348C2×C8—221no—
349C2×C8—222no—
350C2×C8—442no—
351C2×C8—881no—
352C4⋊C4—21no—
353C4⋊C4—21no—
354C4⋊C4—21no—
355C4⋊C4—22no—
356C4⋊C4—22no—
357C4⋊C4—22no—
358C4⋊C4—22no—
359C4⋊C4—41no—
360C4⋊C4—41no—
361C4⋊C4—221no—
362C4⋊C4—221no—
363C4⋊C4C2×C22⋊D1112yes—
364C22⋊C4—22no—
365C22⋊C4—441no—
366C22⋊C4—441no—
367C42—22no—
368C42D4×D1111yescharacteristic
369C42#434111yescharacteristic
370C42C2×C22⋊D1111yescharacteristic
371C42C23×D1111yescharacteristic
372C11#1924511yescharacteristic, complemented, Sylow
373C23—441no—
374C23#6699211yescharacteristic
375Q8—22no—
376Q8—22no—
377Q8—42no—
378Q8—42no—
379Q8—81no—
380Q8—82no—
381Q8—441no—
382Q8—441no—
383D4—441no—
384D4—441no—
385D4—441no—
386D4—441no—
387D4—881no—
388D4—882no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—41no—
394C2×C4—42no—
395C2×C4—82no—
396C2×C4—441no—
397C2×C4—882no—
398C2×C4#6697112yes—
399C2×C4#6697212yes—
400C2×C4#6699211yescharacteristic
401C2×C4#6699211yescharacteristic
402C2×C4#6699211yescharacteristic
403C2×C4C2×D4×D1111yescharacteristic
404C2×C4C2×#434111yescharacteristic
405C2×C4C22×C22⋊D1111yescharacteristic
406C8—41no—
407C8—41no—
408C8—222no—
409C8—222no—
410C8—441no—
411C8—441no—
412C8—442no—
413C22—21no—
414C22—21no—
415C22—881no—
416C22—881no—
417C22—881no—
418C22#1062279812yes—
419C22C2×#6699211yescharacteristic
420C4—21no—
421C4—21no—
422C4—21no—
423C4—42no—
424C4—42no—
425C4—82no—
426C4—881no—
427C4#1062279812yes—
428C4C2×#6697111yescharacteristic
429C4C2×#6697211yescharacteristic
430C4#1062336611yescharacteristic
431C4#1062336711yescharacteristic
432C2—22no—
433C2—1761no—
434C2C2×#1062279811yescharacteristic
435C2#1307829211yescharacteristic
436C2#1307835011yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3209C2
socleC22×C11C2×#121
prime radical#10623008C22
hypercenter#3209D11
hypocenterC11#19245
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3209

Complements

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

NH ≅ G/Ntype
3. #13077565C2semidirect
4. #13068186C2semidirect
5. #13068172C2semidirect
6. #13068062C2semidirect
7. #13068048C2semidirect
8. #13067369C2semidirect
10. C2×#10622185C2semidirect
11. C11×#3209C2semidirect
156. #3209D11semidirect
372. C11#19245semidirect

Maximal subgroups

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

subgroupindex
#130799282
#130790122
#130775652
#130681862
#130681722
#130680622
#130680482
#130673692
#130672632
C2×#106221852
C11×#32092
#1924511