Finite Group Databasebeta

← #14782857

Subgroups — #14782857

Order 2816.

874 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622611C211yesmaximal, characteristic
2C2×#10622732C211yesmaximal, characteristic
3#13071234C211yesmaximal, characteristic
4#13071232C211yesmaximal, characteristic
5#13070120C212yesmaximal, complemented
6#13070119C212yesmaximal, complemented
7#13070113C212yesmaximal, complemented
8#13070108C212yesmaximal, complemented
9#13068336C211yesmaximal, characteristic
10C2×#10622167C211yesmaximal, characteristic
11C11×#1736C211yesmaximal, characteristic
12C22×C11×M16C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C2×#66979C2211yescharacteristic
16C2×#66979C2211yescharacteristic
17C22×C4⋊Dic11C2211yescharacteristic
18C23×C11⋊C8C2211yescharacteristic
19#10622825—22no—
20#10622732—24no—
21C2×Dic11⋊C8C2212yes—
22C2×Dic11⋊C8C2212yes—
23#10622611—24no—
24#10622598—21no—
25#10622598—21no—
26#10622598C2212yes—
27#10622598C2212yes—
28#10622586C2212yes—
29#10622586C2212yes—
30C2×#66872C2211yescharacteristic
31C2×#66872C2211yescharacteristic
32C2×#66871C2211yescharacteristic
33C2×#66871C2211yescharacteristic
34#10622555—22no—
35#10622541—21no—
36#10622541—21no—
37C11×#340C2212yes—
38C11×#340C2212yes—
39#10622189C2212yes—
40#10622189C2212yes—
41#10622167C2212yes—
42#10622167C2212yes—
43C23×C4×C11—21no—
44C23×C4×C11C2311yescharacteristic
45C23×Dic11—21no—
46C2×C11×M16—22no—
47C2×C11×M16—22no—
48C2×C11×M16—22no—
49C22×C8×C11C2312yes—
50C11×#117—22no—
51C11×#117—22no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—22no—
54C2×C11×C4⋊C4Q814yes—
55C2×C11×C4⋊C4C2311yescharacteristic
56C2×C11×C4⋊C4C2311yescharacteristic
57C2×C11×C4⋊C4C2312yes—
58C2×C11×C22⋊C4—21no—
59C2×C42×C11—21no—
60C2×C22⋊Dic11—21no—
61C2×C22⋊Dic11D412yes—
62#66979—22no—
63#66979—22no—
64#66979—22no—
65#66979—22no—
66C2×C4⋊Dic11—21no—
67C2×C4⋊Dic11—22no—
68C2×C4⋊Dic11—22no—
69C2×C4⋊Dic11—22no—
70C2×C4⋊Dic11D411yescharacteristic
71C2×C4⋊Dic11D411yescharacteristic
72C2×C4⋊Dic11Q814yes—
73C2×C4⋊Dic11C2311yescharacteristic
74C2×C4⋊Dic11C2311yescharacteristic
75C2×C4⋊Dic11C2312yes—
76C2×Dic11⋊C4—22no—
77C2×Dic11⋊C4—22no—
78C2×C4×Dic11—21no—
79C2×C4×Dic11C2312yes—
80C22×C11⋊C8—22no—
81C22×C11⋊C8—22no—
82C22×C11⋊C8D414yes—
83C22×C11⋊C8C2311yescharacteristic
84C22×C11⋊C8C2311yescharacteristic
85C11⋊#95—22no—
86C11⋊#95—22no—
87C11⋊#95—22no—
88C11⋊#95—22no—
89Dic11⋊C8—24no—
90Dic11⋊C8—24no—
91#66872—22no—
92#66872—22no—
93#66871—22no—
94#66871—22no—
95#23669—111nomaximal, Sylow
96C24×C11C2×D411yescharacteristic
97C22×C4×C11—22no—
98C22×C4×C11—24no—
99C22×C4×C11—21no—
100C22×C4×C11—21no—
101C22×C4×C11—81no—
102C22×C4×C11—81no—
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11C2×D412yes—
105C22×C4×C11C2×Q812yes—
106C22×C4×C11C2×Q812yes—
107C22×C4×C11#4112yes—
108C22×C4×C11#4112yes—
109C22×C4×C11#4112yes—
110C22×C4×C11C2411yescharacteristic
111C22×Dic11—24no—
112C22×Dic11—22no—
113C22×Dic11—21no—
114C22×Dic11—21no—
115C22×Dic11—81no—
116C22×Dic11—81no—
117C22×Dic11C2×D412yes—
118C22×Dic11C2×D412yes—
119C11×M16—44no—
120C2×C8×C11—22no—
121C2×C8×C11—22no—
122C2×C8×C11—22no—
123C11×C4⋊C4—24no—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—21no—
126C11×C4⋊C4—21no—
127C11×C4⋊C4—21no—
128C11×C4⋊C4—21no—
129C11×C4⋊C4C2×Q814yes—
130C11×C22⋊C4—42no—
131C42×C11—42no—
132C22⋊Dic11—24no—
133C22⋊Dic11—42no—
134C4⋊Dic11—22no—
135C4⋊Dic11—22no—
136C4⋊Dic11—24no—
137C4⋊Dic11—21no—
138C4⋊Dic11—21no—
139C4⋊Dic11—22no—
140C4⋊Dic11—21no—
141C4⋊Dic11—21no—
142C4⋊Dic11—82no—
143C4⋊Dic11—82no—
144C4⋊Dic11C2×Q814yes—
145Dic11⋊C4—82no—
146Dic11⋊C4—82no—
147C4×Dic11—22no—
148C4×Dic11—22no—
149C4×Dic11—42no—
150C2×C11⋊C8—28no—
151C2×C11⋊C8—21no—
152C2×C11⋊C8—21no—
153C2×C11⋊C8—21no—
154C2×C11⋊C8—21no—
155C2×C11⋊C8C2×D412yes—
156C2×C11⋊C8C2×D412yes—
157C2×#427—111no—
158C2×#424—111no—
159#2316—111no—
160#2316—111no—
161#2088—112no—
162#2088—112no—
163#2087—112no—
164#2086—112no—
165#1736—111no—
166#1736D1111yescharacteristic
167C2×#340—111no—
168C23×C11—21no—
169C23×C11—21no—
170C23×C11—21no—
171C23×C11—21no—
172C23×C11#12112yes—
173C23×C11C22⋊Q812yes—
174C23×C11C22⋊Q812yes—
175C23×C11C22×D411yescharacteristic
176C2×C4×C11—24no—
177C2×C4×C11—42no—
178C2×C4×C11—42no—
179C2×C4×C11—41no—
180C2×C4×C11—41no—
181C2×C4×C11—41no—
182C2×C4×C11—41no—
183C2×C4×C11—41no—
184C2×C4×C11—41no—
185C2×C4×C11—84no—
186C2×C4×C11#12112yes—
187C2×C4×C11C22⋊Q812yes—
188C2×C4×C11C22⋊Q812yes—
189C2×C4×C11#12314yes—
190C2×C4×C11#12514yes—
191C2×C4×C11#12514yes—
192C2×C4×C11C4⋊Q814yes—
193C2×C4×C11C22×D411yescharacteristic
194C2×C4×C11C22×Q811yescharacteristic
195C2×C4×C11C22×Q811yescharacteristic
196C2×C4×C11C2×#4111yescharacteristic
197C2×C4×C11C2×#4111yescharacteristic
198C2×C4×C11C2×#4111yescharacteristic
199C2×Dic11—22no—
200C2×Dic11—22no—
201C2×Dic11—24no—
202C2×Dic11—22no—
203C2×Dic11—22no—
204C2×Dic11—22no—
205C2×Dic11—22no—
206C2×Dic11—42no—
207C2×Dic11—42no—
208C2×Dic11—41no—
209C2×Dic11—41no—
210C2×Dic11—41no—
211C2×Dic11—41no—
212C2×Dic11—41no—
213C2×Dic11—41no—
214C2×Dic11—84no—
215C8×C11—42no—
216C11⋊C8—22no—
217C11⋊C8—22no—
218C22×M16C2×D1111yescharacteristic
219C23×C8—111no—
220C2×#117—111no—
221C2×#117—111no—
222C2×#117C2×D1111yescharacteristic
223C22×C4⋊C4—111no—
224C22×C4⋊C4C2×D1111yescharacteristic
225#427—224no—
226C2×#107—111no—
227C2×#107—111no—
228C2×#106—111no—
229C2×#106—111no—
230#424—224no—
231C2×C4⋊C8—112no—
232C2×C4⋊C8—112no—
233#389—112no—
234#389—112no—
235#389—112no—
236#389—112no—
237#389—221no—
238#389—221no—
239#389—221no—
240#389—221no—
241#380—222no—
242#380—222no—
243#340—112no—
244#340—112no—
245#340—112no—
246#340—112no—
247#340C2×D1112yes—
248#340C2×D1112yes—
249C22×C11—22no—
250C22×C11—22no—
251C22×C11—22no—
252C22×C11—22no—
253C22×C11—22no—
254C22×C11—22no—
255C22×C11#39814yes—
256C22×C11C2×#12111yescharacteristic
257C22×C11C2×C22⋊Q811yescharacteristic
258C22×C11C2×C22⋊Q811yescharacteristic
259C22×C11#57611yescharacteristic
260C22×C11#57711yescharacteristic
261C22×C11#57711yescharacteristic
262C22×C11#57811yescharacteristic
263C4×C11—44no—
264C4×C11—81no—
265C4×C11—81no—
266C4×C11#39814yes—
267C4×C11C2×#12311yescharacteristic
268C4×C11C2×#12511yescharacteristic
269C4×C11C2×#12511yescharacteristic
270C4×C11C2×C4⋊Q811yescharacteristic
271Dic11—44no—
272Dic11—42no—
273Dic11—42no—
274Dic11—81no—
275Dic11—81no—
276C23×C4—21no—
277C23×C4—221no—
278C23×C4C22×D1111yescharacteristic
279C2×M16—22no—
280C2×M16—22no—
281C2×M16—22no—
282C22×C8—114no—
283C22×C8—111no—
284C22×C8—111no—
285C22×C8—222no—
286C22×C8—222no—
287C22×C8C22×D1112yes—
288#117—22no—
289#117—22no—
290#117—222no—
291#117—222no—
292#117—222no—
293#117—222no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—114no—
297C2×C4⋊C4—112no—
298C2×C4⋊C4—111no—
299C2×C4⋊C4—111no—
300C2×C4⋊C4—111no—
301C2×C4⋊C4—111no—
302C2×C4⋊C4—222no—
303C2×C4⋊C4—221no—
304C2×C4⋊C4—222no—
305C2×C4⋊C4—222no—
306C2×C4⋊C4—222no—
307C2×C4⋊C4—222no—
308C2×C4⋊C4Dic2214yes—
309C2×C4⋊C4C22×D1111yescharacteristic
310C2×C4⋊C4C22×D1111yescharacteristic
311C2×C4⋊C4C22×D1112yes—
312C2×C22⋊C4—21no—
313C2×C22⋊C4—112no—
314C2×C22⋊C4—221no—
315C2×C42—21no—
316C2×C42—112no—
317C2×C42—221no—
318#107—222no—
319#107—222no—
320#106—222no—
321#106—222no—
322C4⋊C8—224no—
323C4⋊C8—224no—
324#95—222no—
325#95—222no—
326#95—222no—
327#95—222no—
328C2×C11—24no—
329C2×C11C2×#39811yescharacteristic
330C2×C11#306011yescharacteristic
331C2×C11#306111yescharacteristic
332C2×C11#308111yescharacteristic
333C2×C11#308111yescharacteristic
334C2×C11#308211yescharacteristic
335C2×C11#308211yescharacteristic
336C24D4×D1111yescharacteristic
337C22×C4—22no—
338C22×C4—24no—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—81no—
342C22×C4—81no—
343C22×C4—112no—
344C22×C4—112no—
345C22×C4—222no—
346C22×C4—224no—
347C22×C4—221no—
348C22×C4—221no—
349C22×C4—881no—
350C22×C4—881no—
351C22×C4C2×Dic2212yes—
352C22×C4#433912yes—
353C22×C4#433912yes—
354C22×C4D4×D1111yescharacteristic
355C22×C4D4×D1112yes—
356C22×C4#434112yes—
357C22×C4Q8×D1112yes—
358C22×C4C23×D1111yescharacteristic
359M16—44no—
360C2×C8—22no—
361C2×C8—22no—
362C2×C8—22no—
363C2×C8—112no—
364C2×C8—112no—
365C2×C8—228no—
366C2×C8—221no—
367C2×C8—221no—
368C2×C8—221no—
369C2×C8—221no—
370C4⋊C4—24no—
371C4⋊C4—22no—
372C4⋊C4—21no—
373C4⋊C4—21no—
374C4⋊C4—21no—
375C4⋊C4—21no—
376C4⋊C4—114no—
377C4⋊C4—222no—
378C4⋊C4—222no—
379C4⋊C4—224no—
380C4⋊C4—222no—
381C4⋊C4—221no—
382C4⋊C4—221no—
383C4⋊C4—221no—
384C4⋊C4—221no—
385C4⋊C4—882no—
386C4⋊C4—882no—
387C4⋊C4—882no—
388C4⋊C4—882no—
389C4⋊C4C2×Dic2214yes—
390C22⋊C4—42no—
391C22⋊C4—224no—
392C22⋊C4—442no—
393C42—42no—
394C42—222no—
395C42—222no—
396C42—442no—
397C11#2366911yescharacteristic, complemented, Sylow
398C23—21no—
399C23—21no—
400C23—21no—
401C23—21no—
402C23#6693112yes—
403C23#6693712yes—
404C23#6694912yes—
405C23C2×D4×D1111yescharacteristic
406C2×C4—24no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—84no—
416C2×C4—222no—
417C2×C4—222no—
418C2×C4—224no—
419C2×C4—222no—
420C2×C4—222no—
421C2×C4—222no—
422C2×C4—222no—
423C2×C4—442no—
424C2×C4—442no—
425C2×C4—441no—
426C2×C4—441no—
427C2×C4—441no—
428C2×C4—441no—
429C2×C4—441no—
430C2×C4—441no—
431C2×C4—884no—
432C2×C4#6692314yes—
433C2×C4#6693112yes—
434C2×C4#6693614yes—
435C2×C4#6693712yes—
436C2×C4#6694114yes—
437C2×C4#6694214yes—
438C2×C4#6694912yes—
439C2×C4C22×Dic2211yescharacteristic
440C2×C4C2×#433911yescharacteristic
441C2×C4C2×#433911yescharacteristic
442C2×C4C2×D4×D1111yescharacteristic
443C2×C4C2×#434111yescharacteristic
444C2×C4C2×Q8×D1111yescharacteristic
445C8—42no—
446C8—222no—
447C8—222no—
448C22—22no—
449C22—22no—
450C22—22no—
451C22—22no—
452C22—22no—
453C22—22no—
454C22#1062227014yes—
455C22C2×#6693111yescharacteristic
456C22C2×#6693711yescharacteristic
457C22C2×#6694911yescharacteristic
458C22#1062330511yescharacteristic
459C22#1062330611yescharacteristic
460C22#1062330911yescharacteristic
461C22#1062331011yescharacteristic
462C4—44no—
463C4—81no—
464C4—81no—
465C4—442no—
466C4—442no—
467C4—444no—
468C4—881no—
469C4—881no—
470C4#1062227014yes—
471C4C2×#6692311yescharacteristic
472C4C2×#6693611yescharacteristic
473C4C2×#6694111yescharacteristic
474C4C2×#6694211yescharacteristic
475C2—24no—
476C2C2×#1062227011yescharacteristic
477C2#1307827711yescharacteristic
478C2#1307828511yescharacteristic
479C2#1307844511yescharacteristic
480C2#1307844911yescharacteristic
481C2#1307845611yescharacteristic
482C2#1307846011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1736C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenter#1736D11
hypocenterC11#23669
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1736

Complements

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

NH ≅ G/Ntype
5. #13070120C2semidirect
6. #13070119C2semidirect
7. #13070113C2semidirect
8. #13070108C2semidirect
397. C11#23669semidirect

Maximal subgroups

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

subgroupindex
C2×#106226112
C2×#106227322
#130712342
#130712322
#130701202
#130701192
#130701132
#130701082
#130683362
C2×#106221672
C11×#17362
#2366911