Finite Group Databasebeta

← #14853476

Subgroups — #14853476

Order 2816.

842 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077002C211yesmaximal, characteristic, complemented
2#13071178C211yesmaximal, characteristic
3#13070173C211yesmaximal, characteristic, complemented
4#13069851C211yesmaximal, characteristic
5#13069850C211yesmaximal, characteristic
6#13069314C212yesmaximal, complemented
7#13069311C212yesmaximal, complemented
8#13068625C212yesmaximal, complemented
9#13068625C212yesmaximal, complemented
10#13068468C211yesmaximal, characteristic, complemented
11C11×#2099C211yesmaximal, characteristic, complemented
12C2×#66946—21no—
13C2×#66946—21no—
14C2×#66946C2212yes—
15C2×#66927C2211yescharacteristic
16C11×#389C2211yescharacteristic
17C11×#384C2211yescharacteristic
18C2×#66885C2212yes—
19C2×#66885C2212yes—
20C2×#66879C2212yes—
21C2×Dic11⋊C8C2212yes—
22#10622601—21no—
23#10622601—21no—
24#10622601C2212yes—
25#10622598C2211yescharacteristic
26#10622594—21no—
27#10622591—21no—
28#10622590C2211yescharacteristic
29#10622590C2211yescharacteristic
30#10622586C2211yescharacteristic
31C2×#66873C2212yes—
32C2×#66873C2212yes—
33C42×Dic11C2211yescharacteristic
34#10622541C2211yescharacteristic
35#10622266—21no—
36#10622265—21no—
37C11×#340C2212yes—
38C11×#340C2212yes—
39C11×#336C2211yescharacteristic
40#10622167C2212yes—
41#10622167C2212yes—
42#10622162C2211yescharacteristic
43C22×D44—21no—
44C22×D44—21no—
45C22×D44C2312yes—
46C22×C4×D11—22no—
47C22×C8×C11C2312yes—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4C2312yes—
52C2×C11×C4⋊C4C2311yescharacteristic
53C2×C11×C4⋊C4C2311yescharacteristic
54C2×C42×C11C2311yescharacteristic
55C2×(C2×D11)⋊C4—22no—
56C2×(C2×D11)⋊C4—22no—
57C2×(C2×D11)⋊C4—22no—
58C2×C4⋊Dic11—21no—
59C2×C4⋊Dic11C2311yescharacteristic
60C2×C4⋊Dic11C2311yescharacteristic
61C2×Dic11⋊C4—21no—
62C2×Dic11⋊C4—21no—
63C2×C4×Dic11D411yescharacteristic
64C2×C4×Dic11D411yescharacteristic
65C2×C4×Dic11D411yescharacteristic
66C2×C4×Dic11D411yescharacteristic
67C2×C4×Dic11C2311yescharacteristic
68C2×C4×Dic11C2311yescharacteristic
69C22×C11⋊C8C2312yes—
70#66946—24no—
71#66946—24no—
72#66946—44no—
73#66946—44no—
74#66927—24no—
75C11×#95—21no—
76C11⋊#95—21no—
77C11⋊#95—21no—
78C11⋊#95—21no—
79C11⋊#95—21no—
80C11⋊#95—21no—
81C11⋊#95—21no—
82C11⋊#95—21no—
83#66885—24no—
84#66885—42no—
85#66879—42no—
86Dic11⋊C8—24no—
87#66873—24no—
88#66873—42no—
89#29127—111nomaximal, Sylow
90C23×D11—22no—
91C22×C4×C11—21no—
92C22×C4×C11—21no—
93C22×C4×C11—22no—
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2411yescharacteristic
97C22×Dic11—21no—
98C22×Dic11—21no—
99C22×Dic11C2×D411yescharacteristic
100C22×Dic11C2×D411yescharacteristic
101C22×Dic11C2×D411yescharacteristic
102C22×Dic11C2×D411yescharacteristic
103C2×D44—24no—
104C2×D44—24no—
105C2×D44—22no—
106C2×D44—22no—
107C2×D44—22no—
108C2×D44—22no—
109C2×D44—22no—
110C2×D44—42no—
111C2×D44—42no—
112C2×D44—42no—
113C2×D44—42no—
114C2×D44#4114yes—
115C2×C4×D11—44no—
116C2×C4×D11—44no—
117C2×C4×D11—44no—
118C2×C8×C11—22no—
119C2×C8×C11—22no—
120C2×C8×C11—22no—
121C11×C4⋊C4—22no—
122C11×C4⋊C4—22no—
123C11×C4⋊C4—22no—
124C11×C4⋊C4—21no—
125C11×C4⋊C4—21no—
126C11×C4⋊C4—42no—
127C11×C4⋊C4—42no—
128C11×C4⋊C4—42no—
129C42×C11—22no—
130(C2×D11)⋊C4—44no—
131(C2×D11)⋊C4—44no—
132(C2×D11)⋊C4—44no—
133C4⋊Dic11—22no—
134C4⋊Dic11—21no—
135C4⋊Dic11—21no—
136C4⋊Dic11—42no—
137Dic11⋊C4—42no—
138Dic11⋊C4—42no—
139C4×Dic11—22no—
140C4×Dic11—22no—
141C4×Dic11—21no—
142C4×Dic11—21no—
143C4×Dic11—41no—
144C4×Dic11—41no—
145C4×Dic11#4114yes—
146C2×C11⋊C8—22no—
147C2×C11⋊C8—22no—
148C2×C11⋊C8—22no—
149#2864—111no—
150C4×#127—111no—
151#2099—111no—
152#2099D1111yescharacteristic, complemented
153#2041—111no—
154#2041—111no—
155#1936—112no—
156#1936—112no—
157#1804—112no—
158#1804—112no—
159#1767—111no—
160C23×C11C22×D411yescharacteristic
161C22×D11—24no—
162C22×D11—42no—
163C22×D11—42no—
164C22×D11—42no—
165C22×D11—42no—
166C22×D11—42no—
167C22×D11—42no—
168C2×C4×C11—21no—
169C2×C4×C11—21no—
170C2×C4×C11—21no—
171C2×C4×C11—21no—
172C2×C4×C11—41no—
173C2×C4×C11—42no—
174C2×C4×C11—41no—
175C2×C4×C11—42no—
176C2×C4×C11—42no—
177C2×C4×C11—41no—
178C2×C4×C11—41no—
179C2×C4×C11—41no—
180C2×C4×C11—41no—
181C2×C4×C11AGL(1,ℤ/8)12yes—
182C2×C4×C11AGL(1,ℤ/8)12yes—
183C2×C4×C11C2×#4112yes—
184C2×C4×C11C2×#4112yes—
185C2×C4×C11H(5,𝔽2)11yescharacteristic
186C2×C4×C112−1+411yescharacteristic
187C2×Dic11—21no—
188C2×Dic11—21no—
189C2×Dic11—21no—
190C2×Dic11—21no—
191C2×Dic11—21no—
192C2×Dic11—21no—
193C2×Dic11—21no—
194C2×Dic11—21no—
195C2×Dic11—21no—
196C2×Dic11—21no—
197C2×Dic11—41no—
198C2×Dic11—41no—
199C2×Dic11—41no—
200C2×Dic11—41no—
201C2×Dic11—41no—
202C2×Dic11—41no—
203C2×Dic11#12412yes—
204C2×Dic11#12412yes—
205D44—24no—
206D44—24no—
207D44—48no—
208D44—48no—
209D44—42no—
210D44—42no—
211C4×D11—88no—
212C8×C11—42no—
213C11⋊C8—42no—
214C2×#127—111no—
215C2×C4×D4—112no—
216C2×C4×D4—221no—
217C2×C4×D4—221no—
218C2×C4⋊C8—112no—
219C2×#102—112no—
220C2×#102—112no—
221C2×#102—112no—
222C2×#102—112no—
223C2×#97—112no—
224#390—112no—
225#390—221no—
226#390—221no—
227#389—111no—
228#389—111no—
229#389—111no—
230#389C2×D1111yescharacteristic
231#387—221no—
232#387—221no—
233#387—221no—
234#387—221no—
235#384C2×D1111yescharacteristic
236#382—111no—
237#382—111no—
238C43—111no—
239#340—112no—
240#340—112no—
241#340C2×D1112yes—
242#340C2×D1112yes—
243#336—111no—
244#336C2×D1111yescharacteristic
245C22×C11#52511yescharacteristic
246C22×C11C2×#12411yescharacteristic
247C22×C11#53711yescharacteristic
248C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
249C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
250C22×C11#57511yescharacteristic
251C22×C11#57511yescharacteristic
252C2×D11—44no—
253C2×D11—44no—
254C2×D11—44no—
255C2×D11—82no—
256C2×D11—82no—
257C2×D11—82no—
258C2×D11—82no—
259C4×C11—22no—
260C4×C11—22no—
261C4×C11—81no—
262C4×C11—82no—
263C4×C11—81no—
264C4×C11#55212yes—
265C4×C11#55312yes—
266Dic11—22no—
267Dic11—22no—
268Dic11—41no—
269Dic11—41no—
270Dic11—81no—
271Dic11—81no—
272C22×D4—112no—
273C22×D4—221no—
274C22×D4—221no—
275C23×C4—222no—
276C22×C8—112no—
277C22×C8C22×D1112yes—
278#127—224no—
279C4×D4—224no—
280C4×D4—224no—
281C4×D4—444no—
282C4×D4—444no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—111no—
287C2×C4⋊C4—111no—
288C2×C4⋊C4—221no—
289C2×C4⋊C4—221no—
290C2×C4⋊C4—221no—
291C2×C4⋊C4C22×D1112yes—
292C2×C4⋊C4C22×D1111yescharacteristic
293C2×C4⋊C4C22×D1111yescharacteristic
294C2×C22⋊C4—222no—
295C2×C22⋊C4—222no—
296C2×C22⋊C4—222no—
297C2×C42—111no—
298C2×C42—111no—
299C2×C42—111no—
300C2×C42—111no—
301C2×C42—111no—
302C2×C42—111no—
303C2×C42C22×D1111yescharacteristic
304C4⋊C8—224no—
305#102—224no—
306#102—224no—
307#102—442no—
308#102—442no—
309#97—442no—
310#95—21no—
311#95—221no—
312#95—221no—
313#95—221no—
314#95—221no—
315#95—221no—
316#95—221no—
317#95—221no—
318C2×C11#256211yescharacteristic
319C2×C11#311411yescharacteristic
320C2×C11#311411yescharacteristic
321C2×C11#313511yescharacteristic
322C2×C11#313811yescharacteristic
323C2×C11#325111yescharacteristic
324C2×C11#325111yescharacteristic
325D11—84no—
326C24—222no—
327C2×D4—114no—
328C2×D4—224no—
329C2×D4—224no—
330C2×D4—222no—
331C2×D4—222no—
332C2×D4—222no—
333C2×D4—222no—
334C2×D4—222no—
335C2×D4—442no—
336C2×D4—442no—
337C2×D4—442no—
338C2×D4—442no—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—22no—
342C22×C4—111no—
343C22×C4—111no—
344C22×C4—111no—
345C22×C4—111no—
346C22×C4—221no—
347C22×C4—221no—
348C22×C4—444no—
349C22×C4—444no—
350C22×C4—444no—
351C22×C4D4×D1111yescharacteristic
352C22×C4D4×D1111yescharacteristic
353C22×C4C23×D1111yescharacteristic
354C2×C8—22no—
355C2×C8—22no—
356C2×C8—22no—
357C2×C8—222no—
358C2×C8—222no—
359C2×C8—222no—
360C4⋊C4—21no—
361C4⋊C4—22no—
362C4⋊C4—22no—
363C4⋊C4—22no—
364C4⋊C4—21no—
365C4⋊C4—42no—
366C4⋊C4—42no—
367C4⋊C4—42no—
368C4⋊C4—221no—
369C4⋊C4—222no—
370C4⋊C4—221no—
371C4⋊C4—442no—
372C4⋊C4—442no—
373C4⋊C4—442no—
374C22⋊C4—444no—
375C22⋊C4—444no—
376C22⋊C4—444no—
377C42—22no—
378C42—114no—
379C42—222no—
380C42—222no—
381C42—221no—
382C42—221no—
383C42—441no—
384C42—441no—
385C11#2912711yescharacteristic, complemented, Sylow
386C23—224no—
387C23—442no—
388C23—442no—
389C23—442no—
390C23—442no—
391C23—442no—
392C23—442no—
393C23C2×D4×D1111yescharacteristic
394D4—224no—
395D4—224no—
396D4—448no—
397D4—448no—
398D4—442no—
399D4—442no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—42no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—42no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—42no—
413C2×C4—112no—
414C2×C4—112no—
415C2×C4—221no—
416C2×C4—221no—
417C2×C4—221no—
418C2×C4—221no—
419C2×C4—221no—
420C2×C4—221no—
421C2×C4—221no—
422C2×C4—221no—
423C2×C4—221no—
424C2×C4—221no—
425C2×C4—441no—
426C2×C4—441no—
427C2×C4—441no—
428C2×C4—441no—
429C2×C4—441no—
430C2×C4—441no—
431C2×C4—888no—
432C2×C4#6696412yes—
433C2×C4#6696712yes—
434C2×C4#6704011yescharacteristic
435C2×C4#41×D1112yes—
436C2×C4#41×D1112yes—
437C2×C4#6704211yescharacteristic
438C8—42no—
439C8—442no—
440C22—444no—
441C22—444no—
442C22—444no—
443C22—882no—
444C22—882no—
445C22—882no—
446C22—882no—
447C22#1062316011yescharacteristic
448C22#1062318711yescharacteristic
449C22D11×#12411yescharacteristic
450C22C2×#6696411yescharacteristic
451C22C2×#6696711yescharacteristic
452C22#1062330811yescharacteristic
453C22#1062330811yescharacteristic
454C4—22no—
455C4—22no—
456C4—81no—
457C4—82no—
458C4—81no—
459C4—222no—
460C4—222no—
461C4—441no—
462C4—441no—
463C4—881no—
464C4—881no—
465C4#1062322412yes—
466C4#1062324012yes—
467C2—884no—
468C2#1307377811yescharacteristic
469C2#1307875111yescharacteristic
470C2#1307875711yescharacteristic
471C2#1307896311yescharacteristic
472C2#1307898711yescharacteristic
473C2#1307998011yescharacteristic
474C2#1307998111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2099C2
socleC23×C11C22×D4
prime radicalC2×#66927C22
hypercenter#2099D11
hypocenterC11#29127
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2099

Complements

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

NH ≅ G/Ntype
1. #13077002C2semidirect
3. #13070173C2semidirect
6. #13069314C2semidirect
7. #13069311C2semidirect
8. #13068625C2semidirect
9. #13068625C2semidirect
10. #13068468C2semidirect
11. C11×#2099C2semidirect
152. #2099D11semidirect
385. C11#29127semidirect

Maximal subgroups

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

subgroupindex
#130770022
#130711782
#130701732
#130698512
#130698502
#130693142
#130693112
#130686252
#130684682
C11×#20992
#2912711