Finite Group Databasebeta

← #14908916

Subgroups — #14908916

Order 2816.

534 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079276C211yesmaximal, characteristic, complemented
2#13077486C211yesmaximal, characteristic
3#13070820C211yesmaximal, characteristic, complemented
4#13070815C211yesmaximal, characteristic, complemented
5#13070777C211yesmaximal, characteristic, complemented
6#13070667C211yesmaximal, characteristic, complemented
7#13070661C211yesmaximal, characteristic, complemented
8#13070557C211yesmaximal, characteristic
9#13070557C211yesmaximal, characteristic
10#13070486C211yesmaximal, characteristic, complemented
11#13070477C211yesmaximal, characteristic, complemented
12#13070474C211yesmaximal, characteristic, complemented
13#13070471C211yesmaximal, characteristic, complemented
14#13070422C211yesmaximal, characteristic, complemented
15C11×#2228C211yesmaximal, characteristic, complemented
16C2×#66965C2211yescharacteristic
17#10623228—21no—
18#10623077—21no—
19C11×#499C2211yescharacteristic
20C4×C11×D8C2211yescharacteristic
21D8×Dic11C2211yescharacteristic
22C2×#66891C2211yescharacteristic
23C2×#66891C2211yescharacteristic
24#10622682—21no—
25#10622631—21no—
26C2×Dic88C2211yescharacteristic
27C2×Dic88C2211yescharacteristic
28#10622500C2211yescharacteristic
29#10622500C2211yescharacteristic
30D11×#107C2211yescharacteristic
31#10622486C2211yescharacteristic
32#10622486C2211yescharacteristic
33#10622486C2211yescharacteristic
34#10622481—21no—
35#10622466—21no—
36#10622384—21no—
37#10622370—21no—
38#10622312C2211yescharacteristic
39C4×Dic44C2211yescharacteristic
40#10622302C2211yescharacteristic
41C11×#367C2211yescharacteristic
42C11×#366C2211yescharacteristic
43C11×C4⋊C16C2211yescharacteristic
44C11×#357C2211yescharacteristic
45C11×#357C2211yescharacteristic
46(C2×D11)⋊C16C2211yescharacteristic
47(C2×D11)⋊C16C2211yescharacteristic
48#10622141C2211yescharacteristic
49#10622141C2211yescharacteristic
50#10622140C2211yescharacteristic
51C16×Dic11C2211yescharacteristic
52#10622130C2211yescharacteristic
53#10622130C2211yescharacteristic
54#10622130C2211yescharacteristic
55#10622130C2211yescharacteristic
56#10622128C2211yescharacteristic
57#10622127C2211yescharacteristic
58C4⋊(C11⋊C16)C2211yescharacteristic
59C2×#4341—21no—
60C2×C11×D8C2311yescharacteristic
61C11×#125—21no—
62C4×D4×C11—21no—
63D4×Dic11—21no—
64C2×#4324—21no—
65C4×C22⋊D11—41no—
66C2×Dic11⋊C4—41no—
67#66965—22no—
68#66965—22no—
69C2×Dic44—21no—
70C2×Dic44C2311yescharacteristic
71C2×Dic44C2311yescharacteristic
72C2×Dic44C2311yescharacteristic
73C2×#4313D411yescharacteristic
74C2×C8×D11C2311yescharacteristic
75#66951—41no—
76#66951—41no—
77#66950—21no—
78#66950—21no—
79C4⋊C4×D11—21no—
80#66943—41no—
81#66943—41no—
82#66940—21no—
83#66940—21no—
84#66940—21no—
85(C22⋊D11)⋊C4—41no—
86#66930—41no—
87#66925D411yescharacteristic
88#66922—21no—
89C4×Dic22—21no—
90C2×C11×C16C2311yescharacteristic
91C2×C11×C16C2311yescharacteristic
92C11×#107C2311yescharacteristic
93C11×#107C2311yescharacteristic
94C11×#107C2311yescharacteristic
95C11×#106—21no—
96C11×#102—21no—
97C4×C8×C11C2311yescharacteristic
98#66896—21no—
99#66891—22no—
100#66891—22no—
101#66882C2311yescharacteristic
102#66880—21no—
103#66879D411yescharacteristic
104C8×Dic11C2311yescharacteristic
105C2×C11⋊C16C2311yescharacteristic
106C2×C11⋊C16C2311yescharacteristic
107#66874—21no—
108#66874—21no—
109#66874—21no—
110#66874—21no—
111#66874—21no—
112#66871—21no—
113#66867D411yescharacteristic
114Dic88—22no—
115Dic88—22no—
116#33680—111nomaximal, Sylow
117C2×D4×C11—21no—
118C22×C4×C11—41no—
119C2×C22⋊D11—41no—
120C22×Dic11—41no—
121C22×Dic11—41no—
122#4341—24no—
123#4341—42no—
124C2×C4×D11—41no—
125C2×C4×D11C2×D411yescharacteristic
126C2×Dic22—21no—
127C2×Dic22—21no—
128C2×Dic22—21no—
129C11×D8—21no—
130C11×D8#4112yes—
131C2×C8×C11C2×D411yescharacteristic
132C2×C8×C11C2411yescharacteristic
133C11×C4⋊C4—21no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—41no—
137C11×C4⋊C4—41no—
138C11×C22⋊C4—41no—
139C42×C11C2×D411yescharacteristic
140C22⋊Dic11—41no—
141#4324—24no—
142(C2×D11)⋊C4—41no—
143(C2×D11)⋊C4—41no—
144(C2×D11)⋊C4D811yescharacteristic
145(C2×D11)⋊C4D811yescharacteristic
146C4⋊Dic11—21no—
147C4⋊Dic11—41no—
148C4⋊Dic11—41no—
149C4⋊Dic11—41no—
150C4⋊Dic11—41no—
151Dic11⋊C4—41no—
152Dic11⋊C4—41no—
153Dic11⋊C4—41no—
154Dic11⋊C4—41no—
155Dic11⋊C4—41no—
156Dic11⋊C4D811yescharacteristic
157Dic11⋊C4D811yescharacteristic
158C4×Dic11—41no—
159C4×Dic11—41no—
160C4×Dic11—41no—
161C4×Dic11—41no—
162C4×Dic11C2×D411yescharacteristic
163C2×C11⋊C8C2×D411yescharacteristic
164C2×C11⋊C8C2×D411yescharacteristic
165Dic44—21no—
166Dic44—21no—
167Dic44—21no—
168Dic44—21no—
169Dic44—21no—
170Dic44—42no—
171Dic44#4112yes—
172#4313—41no—
173C8×D11—21no—
174C8×D11—21no—
175C11×C16—21no—
176C11×C16—21no—
177C11⋊C16—21no—
178C11⋊C16—21no—
179#3177—111no—
180#2951—111no—
181#2236—111no—
182#2235—111no—
183#2229—111no—
184#2228D1111yescharacteristic, complemented
185#2209—111no—
186#2208—111no—
187#2189—111no—
188#2189—111no—
189#2176—111no—
190#2175—111no—
191C4×Q32—111no—
192C4×SD32—111no—
193#2164—111no—
194C23×C11—41no—
195C22×D11C2×D811yescharacteristic
196D4×C11—22no—
197D4×C11—41no—
198C2×C4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11—41no—
201C2×C4×C11—161no—
202C2×C4×C11C2×D811yescharacteristic
203C2×C4×C11C2×D811yescharacteristic
204C2×C4×C11C22×D411yescharacteristic
205C22⋊D11—44no—
206C2×Dic11—44no—
207C2×Dic11—41no—
208C2×Dic11—41no—
209C2×Dic11—41no—
210C2×Dic11—41no—
211C2×Dic11—161no—
212C2×Dic11C2×D811yescharacteristic
213C2×Dic11C2×D811yescharacteristic
214C2×Dic11C2×D811yescharacteristic
215C4×D11—21no—
216C4×D11—21no—
217C4×D11—161no—
218Dic22—22no—
219Dic22—41no—
220Dic22—41no—
221Dic22—41no—
222Dic22—41no—
223Dic22—41no—
224C8×C11—21no—
225C8×C11C2×#4111yescharacteristic
226C8×C11C2×#4111yescharacteristic
227C11⋊C8—21no—
228C11⋊C8—21no—
229C2×#135—111no—
230#541—221no—
231#520—221no—
232C2×Q32—111no—
233C2×Q32—111no—
234C2×SD32—111no—
235C2×SD32—111no—
236#499C2×D1111yescharacteristic
237#494—111no—
238#491—221no—
239#470—221no—
240#467—111no—
241#467—111no—
242#441—221no—
243#440—221no—
244#440—221no—
245C4×Q16—111no—
246C4×Q16—111no—
247C4×Q16—111no—
248C4×Q16—111no—
249C4×D8—111no—
250C4×D8C2×D1111yescharacteristic
251C2×#107—111no—
252#417—221no—
253#405—111no—
254#367—111no—
255#367C2×D1111yescharacteristic
256#366—111no—
257#366C2×D1111yescharacteristic
258C4⋊C16—111no—
259C4⋊C16C2×D1111yescharacteristic
260#358—111no—
261#358—111no—
262#358—111no—
263#358—111no—
264#358—111no—
265#358—111no—
266#357C2×D1111yescharacteristic
267#357C2×D1111yescharacteristic
268C22⋊C16—111no—
269C22⋊C16—111no—
270#346—111no—
271C4×C16—111no—
272C22×C11—42no—
273C22×C11—81no—
274C22×C11—81no—
275C22×C11C22×D811yescharacteristic
276C2×D11—21no—
277C2×D11—21no—
278C2×D11—21no—
279C4×C11—21no—
280C4×C11—21no—
281C4×C11—81no—
282C4×C11—81no—
283C4×C11—81no—
284C4×C11#52511yescharacteristic
285C4×C11#57511yescharacteristic
286Dic11—21no—
287Dic11—21no—
288Dic11—21no—
289Dic11—42no—
290Dic11—81no—
291Dic11—81no—
292Dic11—81no—
293C2×#41—221no—
294#135—222no—
295#135—222no—
296C2×Q16—111no—
297C2×Q16—111no—
298C2×Q16—111no—
299C2×Q16—221no—
300C2×SD16—221no—
301C2×D8C22×D1111yescharacteristic
302C2×M16—111no—
303C22×C8—111no—
304C4⋊Q8—221no—
305#126—441no—
306#126—441no—
307#125—21no—
308#125—441no—
309#125—441no—
310C22⋊Q8—221no—
311C22⋊Q8—221no—
312C4×Q8—221no—
313C4×Q8—221no—
314C4×Q8—221no—
315C4×Q8—221no—
316C4×D4—21no—
317C4×D4—221no—
318C4×D4—441no—
319C4×D4—441no—
320#117—111no—
321#117—441no—
322C2×C4⋊C4—221no—
323C2×C4⋊C4—441no—
324Q32—222no—
325Q32—222no—
326SD32—222no—
327SD32—222no—
328C2×C16—111no—
329C2×C16—111no—
330C2×C16C22×D1111yescharacteristic
331C2×C16C22×D1111yescharacteristic
332#107—111no—
333#107—221no—
334#107C22×D1111yescharacteristic
335#107C22×D1111yescharacteristic
336#107C22×D1111yescharacteristic
337#106—21no—
338#103—221no—
339#103—221no—
340#103—221no—
341#103—221no—
342#103—221no—
343#103—221no—
344#102—21no—
345#102—221no—
346#97—111no—
347#97—111no—
348C4×C8—111no—
349C4×C8C22×D1111yescharacteristic
350C2×C11—82no—
351C2×C11#310011yescharacteristic
352C2×C11#341611yescharacteristic
353C2×C11#341711yescharacteristic
354D11—41no—
355#41—224no—
356#41—442no—
357C2×Q8—221no—
358C2×Q8—221no—
359C2×Q8—221no—
360C2×D4—21no—
361C2×D4—441no—
362C22×C4—41no—
363C22×C4—111no—
364C22×C4—441no—
365C22×C4—441no—
366C22×C4—441no—
367Q16—112no—
368Q16—221no—
369Q16—221no—
370Q16—221no—
371Q16—221no—
372Q16—221no—
373Q16—442no—
374SD16—224no—
375D8—21no—
376D8#434312yes—
377M16—441no—
378C2×C8—111no—
379C2×C8—111no—
380C2×C8—221no—
381C2×C8—221no—
382C2×C8D4×D1111yescharacteristic
383C2×C8C23×D1111yescharacteristic
384C4⋊C4—21no—
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—41no—
388C4⋊C4—41no—
389C4⋊C4—111no—
390C4⋊C4—111no—
391C4⋊C4—221no—
392C4⋊C4—441no—
393C4⋊C4—441no—
394C4⋊C4—441no—
395C4⋊C4—441no—
396C4⋊C4—441no—
397C4⋊C4—441no—
398C4⋊C4—441no—
399C4⋊C4—441no—
400C4⋊C4—441no—
401C22⋊C4—41no—
402C22⋊C4—111no—
403C22⋊C4—111no—
404C22⋊C4—441no—
405C22⋊C4—441no—
406C22⋊C4—441no—
407C42—111no—
408C42—441no—
409C42—441no—
410C42—441no—
411C42—441no—
412C42D4×D1111yescharacteristic
413C16—21no—
414C16—21no—
415C16—221no—
416C16—221no—
417C11#3368011yescharacteristic, complemented, Sylow
418C23—41no—
419C23—111no—
420Q8—222no—
421Q8—441no—
422Q8—441no—
423Q8—441no—
424Q8—441no—
425Q8—441no—
426D4—22no—
427D4—41no—
428D4—444no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—111no—
433C2×C4—111no—
434C2×C4—111no—
435C2×C4—161no—
436C2×C4—221no—
437C2×C4—221no—
438C2×C4—444no—
439C2×C4—441no—
440C2×C4—441no—
441C2×C4—441no—
442C2×C4—441no—
443C2×C4—1761no—
444C2×C4—1761no—
445C2×C4D8×D1111yescharacteristic
446C2×C4D8×D1111yescharacteristic
447C2×C4C2×D4×D1111yescharacteristic
448C8—21no—
449C8—221no—
450C8—221no—
451C8C2×#434311yescharacteristic
452C8#41×D1111yescharacteristic
453C22—42no—
454C22—81no—
455C22—81no—
456C22—221no—
457C22—221no—
458C22—221no—
459C22C2×D8×D1111yescharacteristic
460C4—21no—
461C4—21no—
462C4—81no—
463C4—81no—
464C4—81no—
465C4—221no—
466C4—221no—
467C4—221no—
468C4—442no—
469C4—881no—
470C4—881no—
471C4—881no—
472C4#1062315811yescharacteristic
473C4#1062330811yescharacteristic
474C2—82no—
475C2—441no—
476C2#1307861811yescharacteristic
477C2#1308176211yescharacteristic
478C2#1308176611yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2228C2
socleC22×C11C22×D8
prime radicalC2×#66965C22
hypercenter#2228D11
hypocenterC11#33680
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2228

Complements

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

NH ≅ G/Ntype
1. #13079276C2semidirect
3. #13070820C2semidirect
4. #13070815C2semidirect
5. #13070777C2semidirect
6. #13070667C2semidirect
7. #13070661C2semidirect
10. #13070486C2semidirect
11. #13070477C2semidirect
12. #13070474C2semidirect
13. #13070471C2semidirect
14. #13070422C2semidirect
15. C11×#2228C2semidirect
184. #2228D11semidirect
417. C11#33680semidirect

Maximal subgroups

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

subgroupindex
#130792762
#130774862
#130708202
#130708152
#130707772
#130706672
#130706612
#130705572
#130704862
#130704772
#130704742
#130704712
#130704222
C11×#22282
#3368011