Finite Group Databasebeta

← #14805726

Subgroups — #14805726

Order 2816.

818 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
1C2×#10622459C211yesmaximal, characteristic
2#13073601C211yesmaximal, characteristic, complemented
3#13073534C211yesmaximal, characteristic
4#13070109C212yesmaximal, complemented
5#13069989C212yesmaximal
6#13069577C211yesmaximal, characteristic, complemented
7#13069380C211yesmaximal, characteristic, complemented
8#13069359C212yesmaximal, complemented
9#13069313C212yesmaximal
10C4×#66885C211yesmaximal, characteristic
11C2×C11×#446C211yesmaximal, characteristic, complemented
12C2×C4×Q8×C11C2211yescharacteristic
13C2×#66999—21no—
14C2×#66997—21no—
15C2×C4×D44C2211yescharacteristic
16C2×#66922C2211yescharacteristic
17C11×#446—24no—
18C2×C11×C4⋊C8C2212yes—
19C2×C11×C4⋊C8C2211yescharacteristic
20C2×C11×#97C2212yes—
21C2×C4×C8×C11C2211yescharacteristic
22C2×#66885C2212yes—
23C2×#66885C2211yescharacteristic
24C2×#66885C2211yescharacteristic
25C2×#66882C2212yes—
26C2×#66881C2212yes—
27#10622607—22no—
28#10622600—21no—
29#10622596—22no—
30#10622587—21no—
31#10622552C2212yes—
32#10622548C2211yescharacteristic
33C4×C4⋊Dic11C2211yescharacteristic
34#10622541C2212yes—
35#10622541C2212yes—
36#10622541C2212yes—
37#10622459—24no—
38#10622189C2212yes—
39#10622189C2212yes—
40#10622189C2212yes—
41#10622189C2211yescharacteristic
42#10622189C2211yescharacteristic
43C22×Q8×C11D411yescharacteristic
44C22×D44C2311yescharacteristic
45C22×C4×D11—21no—
46C22×Dic22—21no—
47C22×C8×C11C2311yescharacteristic
48C22×C8×C11C2312yes—
49C22×C8×C11C2311yescharacteristic
50C4×Q8×C11—22no—
51C4×Q8×C11—22no—
52C2×C11×C4⋊C4D411yescharacteristic
53C2×C11×C4⋊C4D412yes—
54C2×C42×C11C2312yes—
55C2×C42×C11C2311yescharacteristic
56#66999—44no—
57#66997—44no—
58C2×(C2×D11)⋊C4—21no—
59C2×(C2×D11)⋊C4—22no—
60C2×(C2×D11)⋊C4—22no—
61C2×C4⋊Dic11—21no—
62C2×C4⋊Dic11—21no—
63C2×C4⋊Dic11—21no—
64C2×C4⋊Dic11C2312yes—
65C2×C4⋊Dic11C2311yescharacteristic
66C2×C4⋊Dic11C2312yes—
67C2×C4⋊Dic11C2311yescharacteristic
68C2×C4⋊Dic11C2311yescharacteristic
69C2×Dic11⋊C4—22no—
70C2×Dic11⋊C4—22no—
71C2×Dic11⋊C4—22no—
72C2×C4×Dic11—21no—
73C4×D44—22no—
74C4×D44—22no—
75#66922—22no—
76#66922—22no—
77C11×C4⋊C8—24no—
78C11×C4⋊C8D414yes—
79C11×#97—24no—
80C4×C8×C11—22no—
81C11⋊#95—22no—
82C11⋊#95—22no—
83C11⋊#95—22no—
84C11⋊#95—21no—
85#66885—24no—
86#66885—22no—
87#66885Q814yescomplemented
88#66882—24no—
89#66881—24no—
90#25478—111nomaximal, Sylow
91C23×D11—21no—
92C2×Q8×C11—22no—
93C2×Q8×C11—22no—
94C2×Q8×C11—22no—
95C22×C4×C11C2×D412yes—
96C22×C4×C11C2×D412yes—
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2411yescharacteristic
100C22×Dic11—21no—
101C22×Dic11—21no—
102C22×Dic11—22no—
103C22×Dic11—21no—
104C22×Dic11—22no—
105C2×D44—21no—
106C2×D44—21no—
107C2×D44—21no—
108C2×D44—21no—
109C2×D44—21no—
110C2×D44C2×Q812yes—
111C2×C4×D11—42no—
112C2×C4×D11—42no—
113C2×C4×D11—42no—
114C2×Dic22—42no—
115C2×Dic22—42no—
116C2×Dic22—42no—
117C2×C8×C11—21no—
118C2×C8×C11—21no—
119C2×C8×C11—22no—
120C2×C8×C11—21no—
121C2×C8×C11—21no—
122C2×C8×C11—22no—
123C2×C8×C11—21no—
124C2×C8×C11C2×D414yes—
125C2×C8×C11C2×Q812yes—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—24no—
128C42×C11—22no—
129C42×C11—22no—
130C42×C11C2×D412yes—
131C42×C11#4112yes—
132(C2×D11)⋊C4—44no—
133(C2×D11)⋊C4—42no—
134(C2×D11)⋊C4—82no—
135C4⋊Dic11—21no—
136C4⋊Dic11—22no—
137C4⋊Dic11—22no—
138C4⋊Dic11—22no—
139C4⋊Dic11—21no—
140C4⋊Dic11—21no—
141C4⋊Dic11—21no—
142C4⋊Dic11—22no—
143C4⋊Dic11—42no—
144C4⋊Dic11—42no—
145C4⋊Dic11—81no—
146C4⋊Dic11C2×Q812yes—
147C4⋊Dic11#4112yes—
148Dic11⋊C4—44no—
149Dic11⋊C4—44no—
150Dic11⋊C4—44no—
151C4×Dic11—42no—
152C2×#474—111no—
153C2×#446D1111yescharacteristic, complemented
154#2546—111no—
155#2538—111no—
156#2087—112no—
157#2065—112no—
158#1990—111no—
159#1948—111no—
160#1944—112no—
161#1936—112no—
162C4×#102—111no—
163C23×C11C22×D411yescharacteristic
164C22×D11—22no—
165C22×D11—41no—
166C22×D11—41no—
167C22×D11—41no—
168C22×D11—41no—
169C22×D11—41no—
170C22×D11—41no—
171Q8×C11—44no—
172C2×C4×C11—21no—
173C2×C4×C11—21no—
174C2×C4×C11—22no—
175C2×C4×C11—22no—
176C2×C4×C11—22no—
177C2×C4×C11—22no—
178C2×C4×C11—22no—
179C2×C4×C11—22no—
180C2×C4×C11#12112yes—
181C2×C4×C11#12112yes—
182C2×C4×C11AGL(1,ℤ/8)12yes—
183C2×C4×C11AGL(1,ℤ/8)12yes—
184C2×C4×C11C22×D411yescharacteristic
185C2×C4×C11C22×Q811yescharacteristic
186C2×C4×C11C2×#4111yescharacteristic
187C2×C4×C11C2×#4111yescharacteristic
188C2×C4×C112−1+411yescharacteristic
189C2×C4×C112−1+411yescharacteristic
190C2×Dic11—22no—
191C2×Dic11—22no—
192C2×Dic11—41no—
193C2×Dic11—41no—
194C2×Dic11—41no—
195C2×Dic11—41no—
196C2×Dic11—42no—
197C2×Dic11—41no—
198C2×Dic11—42no—
199C2×Dic11—42no—
200C2×Dic11—41no—
201C2×Dic11—42no—
202C2×Dic11—42no—
203C2×Dic11—41no—
204C2×Dic11—42no—
205D44—22no—
206D44—22no—
207D44—41no—
208D44—41no—
209C4×D11—84no—
210Dic22—84no—
211C8×C11—24no—
212C8×C11—22no—
213C8×C11—41no—
214C2×C4⋊Q8—111no—
215C2×C4⋊Q8—221no—
216C2×C22⋊Q8—221no—
217C2×C4×Q8C2×D1111yescharacteristic
218C2×C4×D4—111no—
219#474—224no—
220#446—24no—
221C2×#107—112no—
222C2×#106—112no—
223C2×C4⋊C8C2×D1112yes—
224C2×C4⋊C8C2×D1111yescharacteristic
225C2×#102—111no—
226C2×#102—111no—
227C2×#102—112no—
228C2×#97C2×D1112yes—
229C2×C4×C8C2×D1111yescharacteristic
230#398—222no—
231#396—222no—
232#391—221no—
233#390—112no—
234#389—112no—
235#389—112no—
236#389—112no—
237#384—111no—
238#380—221no—
239C4×C4⋊C4—111no—
240#340—112no—
241#340—111no—
242#340—112no—
243#340—112no—
244#340—111no—
245C22×C11C2×#12111yescharacteristic
246C22×C11#54811yescharacteristic
247C22×C11D4×Q811yescharacteristic
248C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
249C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
250C22×C11#57711yescharacteristic
251C22×C11#57811yescharacteristic
252C2×D11—42no—
253C2×D11—42no—
254C2×D11—42no—
255C2×D11—81no—
256C2×D11—81no—
257C2×D11—81no—
258C2×D11—81no—
259C4×C11—22no—
260C4×C11—42no—
261C4×C11—42no—
262C4×C11#46914yes—
263C4×C11#53311yescharacteristic
264C4×C11#54111yescharacteristic
265C4×C11#54711yescharacteristic
266C4×C11D4×Q811yescharacteristic
267Dic11—42no—
268Dic11—42no—
269Dic11—82no—
270Dic11—82no—
271Dic11—81no—
272C22×Q8—221no—
273C22×Q8D4411yescharacteristic
274C22×D4—111no—
275C23×C4—221no—
276C22×C8C22×D1111yescharacteristic
277C22×C8C22×D1111yescharacteristic
278C22×C8C22×D1112yes—
279C4⋊Q8—222no—
280C4⋊Q8—222no—
281C4⋊Q8—444no—
282C22⋊Q8—444no—
283C4×Q8—22no—
284C4×Q8—22no—
285C4×D4—222no—
286C4×D4—222no—
287C2×C4⋊C4—111no—
288C2×C4⋊C4—111no—
289C2×C4⋊C4—111no—
290C2×C4⋊C4—112no—
291C2×C4⋊C4—112no—
292C2×C4⋊C4—221no—
293C2×C4⋊C4—222no—
294C2×C4⋊C4—221no—
295C2×C4⋊C4—222no—
296C2×C4⋊C4—222no—
297C2×C4⋊C4—221no—
298C2×C4⋊C4D4411yescharacteristic
299C2×C4⋊C4D4412yes—
300C2×C22⋊C4—221no—
301C2×C22⋊C4—222no—
302C2×C22⋊C4—222no—
303C2×C42—221no—
304C2×C42C22×D1112yes—
305C2×C42C22×D1111yescharacteristic
306#107—224no—
307#106—224no—
308C4⋊C8—24no—
309C4⋊C8C22⋊D1114yes—
310#102—114no—
311#102—222no—
312#102—224no—
313#97—24no—
314C4×C8—22no—
315#95—221no—
316#95—222no—
317#95—222no—
318#95—222no—
319C2×C11#242911yescharacteristic
320C2×C11C2×#46911yescharacteristic
321C2×C11#306311yescharacteristic
322C2×C11#336711yescharacteristic
323C2×C11#336811yescharacteristic
324C2×C11#338411yescharacteristic
325C2×C11#338611yescharacteristic
326D11—82no—
327C24—221no—
328C2×Q8—22no—
329C2×Q8—22no—
330C2×Q8—22no—
331C2×Q8—442no—
332C2×Q8—442no—
333C2×Q8—442no—
334C2×D4—112no—
335C2×D4—221no—
336C2×D4—221no—
337C2×D4—221no—
338C2×D4—221no—
339C2×D4—221no—
340C22×C4—221no—
341C22×C4—221no—
342C22×C4—221no—
343C22×C4—222no—
344C22×C4—222no—
345C22×C4—442no—
346C22×C4—442no—
347C22×C4—442no—
348C22×C4C2×D4412yes—
349C22×C4C2×D4412yes—
350C22×C4C2×D4411yescharacteristic
351C22×C4C2×D4411yescharacteristic
352C22×C4C23×D1111yescharacteristic
353C2×C8—21no—
354C2×C8—22no—
355C2×C8—22no—
356C2×C8—21no—
357C2×C8—21no—
358C2×C8—21no—
359C2×C8—21no—
360C2×C8Q8×D1112yes—
361C2×C8C2×C22⋊D1114yes—
362C4⋊C4—22no—
363C4⋊C4—24no—
364C4⋊C4—112no—
365C4⋊C4—112no—
366C4⋊C4—221no—
367C4⋊C4—221no—
368C4⋊C4—221no—
369C4⋊C4—222no—
370C4⋊C4—222no—
371C4⋊C4—222no—
372C4⋊C4—222no—
373C4⋊C4—221no—
374C4⋊C4—444no—
375C4⋊C4—444no—
376C4⋊C4—444no—
377C4⋊C4—442no—
378C4⋊C4—442no—
379C4⋊C4—881no—
380C22⋊C4—444no—
381C22⋊C4—442no—
382C22⋊C4—882no—
383C42—22no—
384C42—22no—
385C42—442no—
386C42#433912yes—
387C42C2×C22⋊D1112yes—
388C11#2547811yescharacteristic, complemented, Sylow
389C23—222no—
390C23—441no—
391C23—441no—
392C23—441no—
393C23—441no—
394C23—441no—
395C23—441no—
396C23C22×D4411yescharacteristic
397Q8—44no—
398Q8—884no—
399D4—222no—
400D4—222no—
401D4—441no—
402D4—441no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—222no—
412C2×C4—222no—
413C2×C4—441no—
414C2×C4—441no—
415C2×C4—441no—
416C2×C4—441no—
417C2×C4—442no—
418C2×C4—441no—
419C2×C4—442no—
420C2×C4—441no—
421C2×C4—442no—
422C2×C4—442no—
423C2×C4—441no—
424C2×C4—442no—
425C2×C4—442no—
426C2×C4—884no—
427C2×C4#6696112yes—
428C2×C4#6696112yes—
429C2×C4#6698312yes—
430C2×C4#6698312yes—
431C2×C4C2×#433911yescharacteristic
432C2×C4C2×Q8×D1111yescharacteristic
433C2×C4#6704011yescharacteristic
434C2×C4#41×D1111yescharacteristic
435C2×C4#6704311yescharacteristic
436C2×C4C22×C22⋊D1111yescharacteristic
437C8—22no—
438C8—24no—
439C8—41no—
440C22—442no—
441C22—442no—
442C22—442no—
443C22—881no—
444C22—881no—
445C22—881no—
446C22—881no—
447C22Q8×D4411yescharacteristic
448C22#1062310711yescharacteristic
449C22C2×#6696111yescharacteristic
450C22C2×#6696111yescharacteristic
451C22#1062328211yescharacteristic
452C22#1062328411yescharacteristic
453C22C2×#6698311yescharacteristic
454C4—22no—
455C4—42no—
456C4—42no—
457C4—442no—
458C4—442no—
459C4—882no—
460C4—881no—
461C4—882no—
462C4#1062274814yes—
463C4#1062310911yescharacteristic
464C4#1062311411yescharacteristic
465C4Q8×C22⋊D1111yescharacteristic
466C4#1062335511yescharacteristic
467C2—882no—
468C2#1307220911yescharacteristic
469C2C2×#1062274811yescharacteristic
470C2#1307830711yescharacteristic
471C2#1308133611yescharacteristic
472C2#1308134711yescharacteristic
473C2#1308151711yescharacteristic
474C2#1308153911yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#446C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenterC2×#446D11
hypocenterC11#25478
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#446

Complements

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

NH ≅ G/Ntype
2. #13073601C2semidirect
4. #13070109C2semidirect
6. #13069577C2semidirect
7. #13069380C2semidirect
8. #13069359C2semidirect
11. C2×C11×#446C2semidirect
87. #66885Q8semidirect
153. C2×#446D11semidirect
388. C11#25478semidirect

Maximal subgroups

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

subgroupindex
C2×#106224592
#130736012
#130735342
#130701092
#130699892
#130695772
#130693802
#130693592
#130693132
C4×#668852
C2×C11×#4462
#2547811