Finite Group Databasebeta

← #14853474

Subgroups — #14853474

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#127×Dic11C211yesmaximal, characteristic
3#13070175C211yesmaximal, characteristic, complemented
4#13070174C211yesmaximal, characteristic, complemented
5#13069847C211yesmaximal, characteristic
6#13069315C212yesmaximal, complemented
7#13069310C212yesmaximal, complemented
8#13068624C212yesmaximal, complemented
9#13068624C212yesmaximal, complemented
10#13068468C211yesmaximal, characteristic, complemented
11C11×#2041C211yesmaximal, characteristic
12C2×C11×#127C2211yescharacteristic
13C2×D4×Dic11—21no—
14C2×D4×Dic11—21no—
15C2×D4×Dic11C2212yes—
16C2×C11×#102C2212yes—
17C2×C11×#102C2212yes—
18C11×#389C2211yescharacteristic
19#10622834—21no—
20#10622834—21no—
21#10622834C2212yes—
22C2×#66896C2212yes—
23C2×#66896C2212yes—
24C2×#66879C2212yes—
25C2×Dic11⋊C8C2212yes—
26#10622598C2211yescharacteristic
27#10622594—21no—
28#10622591—21no—
29#10622590C2211yescharacteristic
30#10622590C2211yescharacteristic
31#10622586C2211yescharacteristic
32#10622548C2211yescharacteristic
33C42×Dic11C2211yescharacteristic
34#10622541C2211yescharacteristic
35#10622266—21no—
36#10622265—21no—
37C11×#336C2211yescharacteristic
38#10622189C2212yes—
39#10622189C2212yes—
40#10622167C2212yes—
41#10622167C2212yes—
42#10622162C2211yescharacteristic
43C22×D4×C11—21no—
44C22×D4×C11—21no—
45C22×D4×C11C2312yes—
46C23×Dic11—22no—
47C22×C8×C11C2312yes—
48C11×#127—24no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4C2311yescharacteristic
51C2×C11×C4⋊C4C2311yescharacteristic
52C2×C42×C11C2311yescharacteristic
53C2×C22⋊Dic11—22no—
54C2×C22⋊Dic11—22no—
55C2×C22⋊Dic11—22no—
56D4×Dic11—24no—
57D4×Dic11—24no—
58D4×Dic11—44no—
59D4×Dic11—44no—
60C2×C4⋊Dic11—21no—
61C2×C4⋊Dic11—21no—
62C2×C4⋊Dic11—21no—
63C2×C4⋊Dic11C2311yescharacteristic
64C2×C4⋊Dic11C2311yescharacteristic
65C2×C4⋊Dic11C2312yes—
66C2×Dic11⋊C4—21no—
67C2×Dic11⋊C4—21no—
68C2×C4×Dic11D411yescharacteristic
69C2×C4×Dic11D411yescharacteristic
70C2×C4×Dic11D411yescharacteristic
71C2×C4×Dic11D411yescharacteristic
72C2×C4×Dic11C2311yescharacteristic
73C2×C4×Dic11C2311yescharacteristic
74C22×C11⋊C8C2312yes—
75C11×#102—24no—
76C11×#102—42no—
77C11×#95—21no—
78#66896—24no—
79#66896—42no—
80C11⋊#95—21no—
81C11⋊#95—21no—
82C11⋊#95—21no—
83C11⋊#95—21no—
84C11⋊#95—21no—
85C11⋊#95—21no—
86C11⋊#95—21no—
87#66879—42no—
88Dic11⋊C8—24no—
89#29127—111nomaximal, Sylow
90C24×C11—22no—
91C2×D4×C11—24no—
92C2×D4×C11—24no—
93C2×D4×C11—22no—
94C2×D4×C11—22no—
95C2×D4×C11—22no—
96C2×D4×C11—22no—
97C2×D4×C11—22no—
98C2×D4×C11—42no—
99C2×D4×C11—42no—
100C2×D4×C11—42no—
101C2×D4×C11—42no—
102C2×D4×C11#4114yes—
103C22×C4×C11—21no—
104C22×C4×C11—21no—
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2411yescharacteristic
108C22×Dic11—21no—
109C22×Dic11—21no—
110C22×Dic11—22no—
111C22×Dic11—44no—
112C22×Dic11—44no—
113C22×Dic11—44no—
114C22×Dic11C2×D411yescharacteristic
115C22×Dic11C2×D411yescharacteristic
116C22×Dic11C2×D411yescharacteristic
117C22×Dic11C2×D411yescharacteristic
118C2×C8×C11—22no—
119C2×C8×C11—22no—
120C2×C8×C11—22no—
121C11×C4⋊C4—22no—
122C11×C4⋊C4—21no—
123C11×C4⋊C4—21no—
124C11×C4⋊C4—42no—
125C42×C11—22no—
126C22⋊Dic11—44no—
127C22⋊Dic11—44no—
128C22⋊Dic11—44no—
129C4⋊Dic11—22no—
130C4⋊Dic11—22no—
131C4⋊Dic11—22no—
132C4⋊Dic11—21no—
133C4⋊Dic11—21no—
134C4⋊Dic11—42no—
135C4⋊Dic11—42no—
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#2099—111no—
153#2041—111no—
154#2041D1111yescharacteristic
155#1936—112no—
156#1936—112no—
157#1804—112no—
158#1804—112no—
159#1767—111no—
160C23×C11—24no—
161C23×C11—42no—
162C23×C11—42no—
163C23×C11—42no—
164C23×C11—42no—
165C23×C11—42no—
166C23×C11—42no—
167C23×C11C22×D411yescharacteristic
168D4×C11—24no—
169D4×C11—24no—
170D4×C11—48no—
171D4×C11—48no—
172D4×C11—42no—
173D4×C11—42no—
174C2×C4×C11—21no—
175C2×C4×C11—21no—
176C2×C4×C11—21no—
177C2×C4×C11—21no—
178C2×C4×C11—41no—
179C2×C4×C11—41no—
180C2×C4×C11—41no—
181C2×C4×C11—41no—
182C2×C4×C11—41no—
183C2×C4×C11—41no—
184C2×C4×C11AGL(1,ℤ/8)12yes—
185C2×C4×C11AGL(1,ℤ/8)12yes—
186C2×C4×C11C2×#4112yes—
187C2×C4×C11C2×#4112yes—
188C2×C4×C11H(5,𝔽2)11yescharacteristic
189C2×C4×C112−1+411yescharacteristic
190C2×Dic11—21no—
191C2×Dic11—21no—
192C2×Dic11—21no—
193C2×Dic11—21no—
194C2×Dic11—21no—
195C2×Dic11—21no—
196C2×Dic11—21no—
197C2×Dic11—21no—
198C2×Dic11—21no—
199C2×Dic11—21no—
200C2×Dic11—41no—
201C2×Dic11—42no—
202C2×Dic11—41no—
203C2×Dic11—41no—
204C2×Dic11—41no—
205C2×Dic11—42no—
206C2×Dic11—42no—
207C2×Dic11—41no—
208C2×Dic11—41no—
209C2×Dic11—88no—
210C2×Dic11#12412yes—
211C2×Dic11#12412yes—
212C8×C11—42no—
213C11⋊C8—42no—
214C2×#127C2×D1111yescharacteristic
215C2×C4×D4—112no—
216C2×C4×D4—221no—
217C2×C4×D4—221no—
218C2×C4⋊C8—112no—
219C2×#102—112no—
220C2×#102—112no—
221C2×#102C2×D1112yes—
222C2×#102C2×D1112yes—
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#384—111no—
236#382—111no—
237#382—111no—
238C43—111no—
239#340—112no—
240#340—112no—
241#340—112no—
242#340—112no—
243#336—111no—
244#336C2×D1111yescharacteristic
245C22×C11—44no—
246C22×C11—44no—
247C22×C11—44no—
248C22×C11—82no—
249C22×C11—82no—
250C22×C11—82no—
251C22×C11—82no—
252C22×C11#52511yescharacteristic
253C22×C11C2×#12411yescharacteristic
254C22×C11#53711yescharacteristic
255C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
256C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
257C22×C11#57511yescharacteristic
258C22×C11#57511yescharacteristic
259C4×C11—22no—
260C4×C11—22no—
261C4×C11—81no—
262C4×C11—81no—
263C4×C11#55212yes—
264C4×C11#55312yes—
265Dic11—22no—
266Dic11—22no—
267Dic11—41no—
268Dic11—41no—
269Dic11—81no—
270Dic11—82no—
271Dic11—81no—
272C22×D4—21no—
273C22×D4—21no—
274C22×D4C22×D1112yes—
275C23×C4—222no—
276C22×C8—112no—
277C22×C8C22×D1112yes—
278#127—24no—
279C4×D4—224no—
280C4×D4—224no—
281C4×D4—444no—
282C4×D4—444no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—112no—
285C2×C4⋊C4—111no—
286C2×C4⋊C4—111no—
287C2×C4⋊C4—221no—
288C2×C4⋊C4—221no—
289C2×C4⋊C4—221no—
290C2×C4⋊C4—221no—
291C2×C4⋊C4—221no—
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—24no—
306#102—42no—
307#102—224no—
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—84no—
319C2×C11#256211yescharacteristic
320C2×C11#311411yescharacteristic
321C2×C11#311411yescharacteristic
322C2×C11#313511yescharacteristic
323C2×C11#313811yescharacteristic
324C2×C11#325111yescharacteristic
325C2×C11#325111yescharacteristic
326C24—22no—
327C2×D4—24no—
328C2×D4—24no—
329C2×D4—22no—
330C2×D4—22no—
331C2×D4—22no—
332C2×D4—22no—
333C2×D4—22no—
334C2×D4—42no—
335C2×D4—42no—
336C2×D4—42no—
337C2×D4—42no—
338C2×D4#434114yes—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—111no—
342C22×C4—111no—
343C22×C4—111no—
344C22×C4—111no—
345C22×C4—221no—
346C22×C4—221no—
347C22×C4—222no—
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—22no—
361C4⋊C4—21no—
362C4⋊C4—21no—
363C4⋊C4—42no—
364C4⋊C4—222no—
365C4⋊C4—221no—
366C4⋊C4—222no—
367C4⋊C4—222no—
368C4⋊C4—221no—
369C4⋊C4—442no—
370C4⋊C4—442no—
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—24no—
387C23—42no—
388C23—42no—
389C23—42no—
390C23—42no—
391C23—42no—
392C23—42no—
393C23C2×D4×D1111yescharacteristic
394D4—24no—
395D4—24no—
396D4—48no—
397D4—48no—
398D4—42no—
399D4—42no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—112no—
411C2×C4—112no—
412C2×C4—221no—
413C2×C4—221no—
414C2×C4—221no—
415C2×C4—221no—
416C2×C4—221no—
417C2×C4—221no—
418C2×C4—221no—
419C2×C4—221no—
420C2×C4—221no—
421C2×C4—221no—
422C2×C4—442no—
423C2×C4—442no—
424C2×C4—441no—
425C2×C4—441no—
426C2×C4—441no—
427C2×C4—441no—
428C2×C4—441no—
429C2×C4—441no—
430C2×C4—442no—
431C2×C4—888no—
432C2×C4#6696412yes—
433C2×C4#6696712yes—
434C2×C4C2×#434112yes—
435C2×C4#6703711yescharacteristic
436C2×C4#41×D1112yes—
437C2×C4#6704311yescharacteristic
438C8—42no—
439C8—442no—
440C22—44no—
441C22—44no—
442C22—44no—
443C22—82no—
444C22—82no—
445C22—82no—
446C22—82no—
447C22#1062311711yescharacteristic
448C22#1062313911yescharacteristic
449C22D11×#12411yescharacteristic
450C22C2×#6696411yescharacteristic
451C22C2×#6696711yescharacteristic
452C22#1062330411yescharacteristic
453C22#1062330411yescharacteristic
454C4—22no—
455C4—22no—
456C4—81no—
457C4—81no—
458C4—222no—
459C4—222no—
460C4—441no—
461C4—441no—
462C4—881no—
463C4—882no—
464C4—881no—
465C4#1062313212yes—
466C4#1062318112yes—
467C2—84no—
468C2#1307377611yescharacteristic
469C2#1307874911yescharacteristic
470C2#1307875511yescharacteristic
471C2#1307896011yescharacteristic
472C2#1307898711yescharacteristic
473C2#1307997411yescharacteristic
474C2#1307997611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2041C2
socleC23×C11C22×D4
prime radicalC2×C11×#127C22
hypercenter#2041D11
hypocenterC11#29127
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2041

Complements

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

NH ≅ G/Ntype
1. #13077002C2semidirect
3. #13070175C2semidirect
4. #13070174C2semidirect
6. #13069315C2semidirect
7. #13069310C2semidirect
8. #13068624C2semidirect
9. #13068624C2semidirect
10. #13068468C2semidirect
385. C11#29127semidirect

Maximal subgroups

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

subgroupindex
#130770022
#127×Dic112
#130701752
#130701742
#130698472
#130693152
#130693102
#130686242
#130684682
C11×#20412
#2912711