Finite Group Databasebeta

← #14805728

Subgroups — #14805728

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×#10622444C211yesmaximal, characteristic, complemented
2#13073605C211yesmaximal, characteristic, complemented
3#13073538C211yesmaximal, characteristic
4#13070110C212yesmaximal, complemented
5#13069988C212yesmaximal
6#13069578C211yesmaximal, characteristic, complemented
7#13069380C211yesmaximal, characteristic, complemented
8#13069357C212yesmaximal, complemented
9#13069310C212yesmaximal
10C4×#66896C211yesmaximal, characteristic
11C2×C11×#474C211yesmaximal, characteristic
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C4×D4×C11C2211yescharacteristic
14C2×#66997—21no—
15C2×#66977—21no—
16C2×C4×Dic22C2211yescharacteristic
17C11×#474—24no—
18C2×C11×#107C2212yes—
19C2×C11×C4⋊C8C2211yescharacteristic
20C2×C11×#102C2212yes—
21#10622843—21no—
22#10622834C2212yes—
23C2×#66896C2211yescharacteristic
24C2×#66896C2211yescharacteristic
25#10622825—21no—
26C2×#66881C2212yes—
27C2×#66879C2212yes—
28C2×Dic11⋊C8C2212yes—
29#10622593—22no—
30#10622586C2212yes—
31#10622586C2212yes—
32#10622586C2212yes—
33#10622561—22no—
34#10622548C2211yescharacteristic
35C4×C4⋊Dic11C2211yescharacteristic
36C2×C4×C11⋊C8C2211yescharacteristic
37#10622444—24no—
38#10622189C2212yes—
39#10622167C2212yes—
40#10622167C2212yes—
41#10622167C2211yescharacteristic
42#10622167C2211yescharacteristic
43C22×Q8×C11—21no—
44C22×D4×C11C2311yescharacteristic
45C23×C4×C11—21no—
46C22×Dic22D411yescharacteristic
47C22×C8×C11C2312yes—
48C11×C4⋊Q8—22no—
49C11×C4⋊Q8—22no—
50C4×D4×C11—22no—
51C4×D4×C11—22no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4C2311yescharacteristic
54C2×C11×C4⋊C4C2312yes—
55C2×C11×C22⋊C4—21no—
56C2×C42×C11C2311yescharacteristic
57C2×C22⋊Dic11—22no—
58C2×C22⋊Dic11—22no—
59#66997—44no—
60C2×C4⋊Dic11—21no—
61C2×C4⋊Dic11—21no—
62C2×C4⋊Dic11D411yescharacteristic
63C2×C4⋊Dic11C2312yes—
64C2×C4⋊Dic11C2311yescharacteristic
65C2×C4⋊Dic11C2311yescharacteristic
66#66977—44no—
67C2×Dic11⋊C4—22no—
68C2×Dic11⋊C4—22no—
69C2×Dic11⋊C4—22no—
70C2×Dic11⋊C4D412yes—
71C2×C4×Dic11—21no—
72C2×C4×Dic11C2312yes—
73C22×C11⋊C8C2311yescharacteristic
74C22×C11⋊C8C2311yescharacteristic
75C4×Dic22—22no—
76C4×Dic22—22no—
77C11×#107—24no—
78C11×C4⋊C8D414yes—
79C11×#102—24no—
80#66896—22no—
81#66896Q814yescomplemented
82C11⋊#95—21no—
83C11⋊#95—22no—
84C11⋊#95—22no—
85C11⋊#95—22no—
86#66881—24no—
87#66879—24no—
88Dic11⋊C8—24no—
89C4×C11⋊C8—22no—
90#25478—111nomaximal, Sylow
91C24×C11—21no—
92C2×Q8×C11—42no—
93C2×Q8×C11—42no—
94C2×Q8×C11—42no—
95C2×D4×C11—21no—
96C2×D4×C11—21no—
97C2×D4×C11—21no—
98C2×D4×C11—21no—
99C2×D4×C11—21no—
100C2×D4×C11C2×Q812yes—
101C22×C4×C11—21no—
102C22×C4×C11—22no—
103C22×C4×C11—42no—
104C22×C4×C11—42no—
105C22×C4×C11—42no—
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2411yescharacteristic
109C22×Dic11—21no—
110C22×Dic11—21no—
111C22×Dic11—22no—
112C22×Dic11C2×D412yes—
113C22×Dic11C2×D412yes—
114C2×Dic22—22no—
115C2×Dic22—22no—
116C2×Dic22—22no—
117C2×C8×C11—22no—
118C2×C8×C11—22no—
119C2×C8×C11C2×D414yes—
120C11×C4⋊C4—22no—
121C11×C4⋊C4—21no—
122C11×C4⋊C4—21no—
123C11×C4⋊C4—22no—
124C11×C4⋊C4—42no—
125C11×C22⋊C4—42no—
126C42×C11C2×D412yes—
127C42×C11#4112yes—
128C22⋊Dic11—44no—
129C22⋊Dic11—82no—
130C4⋊Dic11—22no—
131C4⋊Dic11—22no—
132C4⋊Dic11—21no—
133C4⋊Dic11—21no—
134C4⋊Dic11—22no—
135C4⋊Dic11—42no—
136C4⋊Dic11—81no—
137C4⋊Dic11C2×Q812yes—
138C4⋊Dic11#4112yes—
139Dic11⋊C4—24no—
140Dic11⋊C4—44no—
141Dic11⋊C4—44no—
142Dic11⋊C4—44no—
143C4×Dic11—22no—
144C4×Dic11—22no—
145C4×Dic11—42no—
146C2×C11⋊C8—21no—
147C2×C11⋊C8—21no—
148C2×C11⋊C8—21no—
149C2×C11⋊C8—21no—
150C2×C11⋊C8—21no—
151C2×C11⋊C8C2×Q812yes—
152C2×#474D1111yescharacteristic
153C2×#446—111no—
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×C11—22no—
164C23×C11—41no—
165C23×C11—41no—
166C23×C11—41no—
167C23×C11—41no—
168C23×C11—41no—
169C23×C11—41no—
170C23×C11C22×D411yescharacteristic
171Q8×C11—84no—
172D4×C11—22no—
173D4×C11—22no—
174D4×C11—41no—
175D4×C11—41no—
176C2×C4×C11—21no—
177C2×C4×C11—21no—
178C2×C4×C11—41no—
179C2×C4×C11—42no—
180C2×C4×C11—41no—
181C2×C4×C11—42no—
182C2×C4×C11—41no—
183C2×C4×C11—42no—
184C2×C4×C11—84no—
185C2×C4×C11#12112yes—
186C2×C4×C11#12112yes—
187C2×C4×C11AGL(1,ℤ/8)12yes—
188C2×C4×C11AGL(1,ℤ/8)12yes—
189C2×C4×C11C22×D411yescharacteristic
190C2×C4×C11C22×Q811yescharacteristic
191C2×C4×C11C2×#4111yescharacteristic
192C2×C4×C11C2×#4111yescharacteristic
193C2×C4×C112−1+411yescharacteristic
194C2×C4×C112−1+411yescharacteristic
195C2×Dic11—22no—
196C2×Dic11—22no—
197C2×Dic11—22no—
198C2×Dic11—22no—
199C2×Dic11—22no—
200C2×Dic11—22no—
201C2×Dic11—22no—
202C2×Dic11—22no—
203C2×Dic11—41no—
204C2×Dic11—41no—
205C2×Dic11—41no—
206C2×Dic11—41no—
207C2×Dic11—42no—
208C2×Dic11—42no—
209C2×Dic11—42no—
210Dic22—44no—
211C8×C11—24no—
212C11⋊C8—22no—
213C11⋊C8—41no—
214C2×C4⋊Q8—221no—
215C2×C4⋊Q8C2×D1111yescharacteristic
216C2×C22⋊Q8—221no—
217C2×C4×Q8—111no—
218C2×C4×D4C2×D1111yescharacteristic
219#474—24no—
220#446—224no—
221C2×#107C2×D1112yes—
222C2×#106—112no—
223C2×C4⋊C8—112no—
224C2×C4⋊C8C2×D1111yescharacteristic
225C2×#102—111no—
226C2×#102—111no—
227C2×#102C2×D1112yes—
228C2×#97—112no—
229C2×C4×C8—111no—
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—112no—
242#340—111no—
243#340—112no—
244#340—111no—
245C22×C11—42no—
246C22×C11—42no—
247C22×C11—42no—
248C22×C11—81no—
249C22×C11—81no—
250C22×C11—81no—
251C22×C11—81no—
252C22×C11C2×#12111yescharacteristic
253C22×C11#54811yescharacteristic
254C22×C11D4×Q811yescharacteristic
255C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
256C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
257C22×C11#57711yescharacteristic
258C22×C11#57811yescharacteristic
259C4×C11—22no—
260C4×C11—81no—
261C4×C11—82no—
262C4×C11#46914yes—
263C4×C11#53311yescharacteristic
264C4×C11#54111yescharacteristic
265C4×C11#54711yescharacteristic
266C4×C11D4×Q811yescharacteristic
267Dic11—42no—
268Dic11—42no—
269Dic11—42no—
270Dic11—42no—
271Dic11—82no—
272C22×Q8—21no—
273C22×Q8—111no—
274C22×D4C22×D1111yescharacteristic
275C23×C4—21no—
276C22×C8—111no—
277C22×C8—111no—
278C22×C8C22×D1112yes—
279C4⋊Q8—22no—
280C4⋊Q8—22no—
281C4⋊Q8—444no—
282C22⋊Q8—444no—
283C4×Q8—222no—
284C4×Q8—222no—
285C4×D4—22no—
286C4×D4—22no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—111no—
289C2×C4⋊C4—111no—
290C2×C4⋊C4—111no—
291C2×C4⋊C4—112no—
292C2×C4⋊C4—112no—
293C2×C4⋊C4—222no—
294C2×C4⋊C4—222no—
295C2×C4⋊C4—222no—
296C2×C4⋊C4—221no—
297C2×C4⋊C4—221no—
298C2×C4⋊C4C22×D1111yescharacteristic
299C2×C4⋊C4C22×D1112yes—
300C2×C22⋊C4—21no—
301C2×C22⋊C4—222no—
302C2×C22⋊C4—222no—
303C2×C42—112no—
304C2×C42—221no—
305C2×C42C22×D1111yescharacteristic
306#107—24no—
307#106—224no—
308C4⋊C8—224no—
309C4⋊C8C22⋊D1114yes—
310#102—24no—
311#102—114no—
312#102—222no—
313#97—224no—
314C4×C8—222no—
315#95—222no—
316#95—222no—
317#95—222no—
318#95—221no—
319C2×C11—82no—
320C2×C11#242911yescharacteristic
321C2×C11C2×#46911yescharacteristic
322C2×C11#306311yescharacteristic
323C2×C11#336711yescharacteristic
324C2×C11#336811yescharacteristic
325C2×C11#338411yescharacteristic
326C2×C11#338611yescharacteristic
327C24—21no—
328C2×Q8—42no—
329C2×Q8—42no—
330C2×Q8—42no—
331C2×Q8—222no—
332C2×Q8—222no—
333C2×Q8—222no—
334C2×D4—21no—
335C2×D4—21no—
336C2×D4—21no—
337C2×D4—21no—
338C2×D4—21no—
339C2×D4Q8×D1112yes—
340C22×C4—21no—
341C22×C4—22no—
342C22×C4—42no—
343C22×C4—42no—
344C22×C4—42no—
345C22×C4—112no—
346C22×C4—112no—
347C22×C4—221no—
348C22×C4—221no—
349C22×C4—222no—
350C22×C4D4×D1111yescharacteristic
351C22×C4D4×D1111yescharacteristic
352C22×C4C23×D1111yescharacteristic
353C2×C8—22no—
354C2×C8—22no—
355C2×C8—112no—
356C2×C8—221no—
357C2×C8—221no—
358C2×C8—221no—
359C2×C8—221no—
360C2×C8—221no—
361C2×C8C2×C22⋊D1114yes—
362C4⋊C4—21no—
363C4⋊C4—22no—
364C4⋊C4—22no—
365C4⋊C4—21no—
366C4⋊C4—42no—
367C4⋊C4—112no—
368C4⋊C4—112no—
369C4⋊C4—224no—
370C4⋊C4—222no—
371C4⋊C4—221no—
372C4⋊C4—221no—
373C4⋊C4—222no—
374C4⋊C4—222no—
375C4⋊C4—444no—
376C4⋊C4—444no—
377C4⋊C4—444no—
378C4⋊C4—442no—
379C4⋊C4—881no—
380C22⋊C4—42no—
381C22⋊C4—444no—
382C22⋊C4—882no—
383C42—222no—
384C42—222no—
385C42—442no—
386C42#434112yes—
387C42C2×C22⋊D1112yes—
388C11#2547811yescharacteristic, complemented, Sylow
389C23—22no—
390C23—41no—
391C23—41no—
392C23—41no—
393C23—41no—
394C23—41no—
395C23—41no—
396C23C2×D4×D1111yescharacteristic
397Q8—84no—
398Q8—444no—
399D4—22no—
400D4—22no—
401D4—41no—
402D4—41no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—41no—
406C2×C4—42no—
407C2×C4—41no—
408C2×C4—42no—
409C2×C4—41no—
410C2×C4—42no—
411C2×C4—84no—
412C2×C4—222no—
413C2×C4—222no—
414C2×C4—222no—
415C2×C4—222no—
416C2×C4—222no—
417C2×C4—222no—
418C2×C4—222no—
419C2×C4—222no—
420C2×C4—441no—
421C2×C4—441no—
422C2×C4—441no—
423C2×C4—441no—
424C2×C4—442no—
425C2×C4—442no—
426C2×C4—442no—
427C2×C4#6696412yes—
428C2×C4#6696412yes—
429C2×C4#6699112yes—
430C2×C4#6699112yes—
431C2×C4C2×#434111yescharacteristic
432C2×C4C2×Q8×D1111yescharacteristic
433C2×C4#6704011yescharacteristic
434C2×C4#41×D1111yescharacteristic
435C2×C4#6704311yescharacteristic
436C2×C4C22×C22⋊D1111yescharacteristic
437C8—24no—
438C8—222no—
439C8—441no—
440C22—42no—
441C22—42no—
442C22—42no—
443C22—81no—
444C22—81no—
445C22—81no—
446C22—81no—
447C22#1062316311yescharacteristic
448C22#1062316411yescharacteristic
449C22C2×#6696411yescharacteristic
450C22C2×#6696411yescharacteristic
451C22#1062330911yescharacteristic
452C22#1062331011yescharacteristic
453C22C2×#6699111yescharacteristic
454C4—22no—
455C4—81no—
456C4—82no—
457C4—442no—
458C4—442no—
459C4—442no—
460C4—442no—
461C4—882no—
462C4#1062277214yes—
463C4#1062315311yescharacteristic
464C4#1062315611yescharacteristic
465C4Q8×C22⋊D1111yescharacteristic
466C4#1062335511yescharacteristic
467C2—82no—
468C2#1307221111yescharacteristic
469C2C2×#1062277211yescharacteristic
470C2#1307830111yescharacteristic
471C2#1308133311yescharacteristic
472C2#1308134411yescharacteristic
473C2#1308151911yescharacteristic
474C2#1308154111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#474C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenterC2×#474D11
hypocenterC11#25478
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#474

Complements

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

NH ≅ G/Ntype
1. C2×#10622444C2semidirect
2. #13073605C2semidirect
4. #13070110C2semidirect
6. #13069578C2semidirect
7. #13069380C2semidirect
8. #13069357C2semidirect
81. #66896Q8semidirect
388. C11#25478semidirect

Maximal subgroups

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

subgroupindex
C2×#106224442
#130736052
#130735382
#130701102
#130699882
#130695782
#130693802
#130693572
#130693102
C4×#668962
C2×C11×#4742
#2547811