Finite Group Databasebeta

← #14660352

Subgroups — #14660352

Order 2816.

1270 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623356C211yesmaximal, characteristic
2C2×#10622617C212yesmaximal, complemented
3C2×#10622850C211yesmaximal, characteristic
4#13068326C212yesmaximal, complemented
5C2×C11×#410C211yesmaximal, characteristic
6C22×C11×#41C2211yescharacteristic
7C23×Dic22C2211yescharacteristic
8C2×C11×#117C2212yes—
9#10623356—24no—
10#10623356—24no—
11C2×#66997—21no—
12C2×#66989—21no—
13C2×#66988—22no—
14C2×#66979C2211yescharacteristic
15C2×#66977C414yescomplemented
16C22×#4318C2212yes—
17C11×#410—24no—
18C2×C11×#99—22no—
19#10622850—24no—
20C2×#66900—21no—
21C2×#66897—21no—
22#10622617—24no—
23#10622617—24no—
24C2×#66874—24no—
25#10622161—24no—
26C2×C11×#41—22no—
27C2×C11×#41—22no—
28C2×C11×#41—22no—
29C2×C11×#41—22no—
30C2×C11×#41—22no—
31C2×C11×#41—22no—
32C22×Q8×C11D411yescharacteristic
33C22×D4×C11D411yescharacteristic
34C22×D4×C11D412yes—
35C23×C4×C11C2×C412yes—
36C23×C4×C11C2311yescharacteristic
37C23×Dic11—21no—
38C22×Dic22—22no—
39C22×Dic22—22no—
40C22×Dic22—22no—
41C22×Dic22—22no—
42C22×Dic22—21no—
43C22×Dic22—22no—
44C22×Dic22C2×C412yes—
45C22×Dic22D414yes—
46C11×#117—22no—
47C11×#117—22no—
48C11×#117—22no—
49C11×#117D414yes—
50C2×C11×C4⋊C4—22no—
51C2×C11×C22⋊C4—22no—
52C2×C42×C11—22no—
53C2×C22⋊Dic11—24no—
54C2×C22⋊Dic11—21no—
55#66997—28no—
56#66989—28no—
57#66988—216no—
58#66979—22no—
59#66979D414yes—
60C2×C4⋊Dic11C2×C412yes—
61#66977—28no—
62#66977—28no—
63C2×Dic11⋊C4—24no—
64C2×C4×Dic11—21no—
65C2×#4318—22no—
66C2×#4318—22no—
67C2×#4318—22no—
68C2×#4318—22no—
69C2×#4318—22no—
70C2×#4318D414yes—
71C22×C11⋊C8—22no—
72C11×#99—28no—
73#66900—24no—
74#66897—24no—
75#66874—216no—
76#10985—111nomaximal, Sylow
77C24×C11C22⋊C412yes—
78C24×C11C2×D411yescharacteristic
79C11×#41—42no—
80C11×#41—42no—
81C11×#41—42no—
82C11×#41—42no—
83C11×#41—42no—
84C11×#41—42no—
85C11×#41—42no—
86C11×#41—42no—
87C2×Q8×C11—21no—
88C2×Q8×C11—22no—
89C2×Q8×C11—22no—
90C2×Q8×C11—21no—
91C2×D4×C11—22no—
92C2×D4×C11—24no—
93C2×D4×C11—24no—
94C2×D4×C11—22no—
95C2×D4×C11—21no—
96C2×D4×C11—22no—
97C2×D4×C11—22no—
98C2×D4×C11—21no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11—24no—
102C22×C4×C11—24no—
103C22×C4×C11—42no—
104C22×C4×C11C22⋊C412yes—
105C22×C4×C11C22×C411yescharacteristic
106C22×C4×C11C2×D412yes—
107C22×C4×C11C2×D412yes—
108C22×C4×C11C2×D412yes—
109C22×C4×C11C2×D412yes—
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11#4112yes—
112C22×C4×C11#4112yes—
113C22×Dic11—22no—
114C22×Dic11—22no—
115C22×Dic11—24no—
116C22×Dic11—41no—
117C22×Dic11—42no—
118C22×Dic11—41no—
119C2×Dic22—22no—
120C2×Dic22—24no—
121C2×Dic22—24no—
122C2×Dic22—24no—
123C2×Dic22—24no—
124C2×Dic22—24no—
125C2×Dic22—24no—
126C2×Dic22—24no—
127C2×Dic22—41no—
128C2×Dic22—42no—
129C2×Dic22—42no—
130C2×Dic22—42no—
131C2×Dic22—41no—
132C2×Dic22—42no—
133C2×Dic22—42no—
134C2×Dic22C22⋊C414yes—
135C11×C4⋊C4—24no—
136C11×C4⋊C4—42no—
137C11×C22⋊C4—24no—
138C11×C22⋊C4—42no—
139C42×C11—24no—
140C42×C11—42no—
141C22⋊Dic11—216no—
142C22⋊Dic11—24no—
143C4⋊Dic11—22no—
144C4⋊Dic11C22⋊C414yes—
145Dic11⋊C4—216no—
146C4×Dic11—24no—
147#4318—24no—
148#4318—24no—
149#4318—42no—
150#4318—42no—
151C2×C11⋊C8—24no—
152C2×C11⋊C8—42no—
153C2×C11⋊C8—42no—
154C2×#536—111no—
155C2×#419—112no—
156C2×#413—111no—
157C2×#410D1111yescharacteristic
158#1733—112no—
159C23×C11—22no—
160C23×C11—22no—
161C23×C11—22no—
162C23×C11—42no—
163C23×C11—44no—
164C23×C11C2×C22⋊C411yescharacteristic
165C23×C11#12012yes—
166C23×C11#12011yescharacteristic
167C23×C11#12112yes—
168C23×C11#12311yescharacteristic
169Q8×C11—42no—
170Q8×C11—42no—
171D4×C11—44no—
172D4×C11—44no—
173D4×C11—42no—
174D4×C11—42no—
175C2×C4×C11—22no—
176C2×C4×C11—22no—
177C2×C4×C11—22no—
178C2×C4×C11—44no—
179C2×C4×C11—44no—
180C2×C4×C11—44no—
181C2×C4×C11—84no—
182C2×C4×C11C2×C22⋊C411yescharacteristic
183C2×C4×C11C2×C22⋊C411yescharacteristic
184C2×C4×C11C4×D412yes—
185C2×C4×C11C4×D412yes—
186C2×C4×C11#12011yescharacteristic
187C2×C4×C11#12012yes—
188C2×C4×C11#12012yes—
189C2×C4×C11#12112yes—
190C2×C4×C11#12112yes—
191C2×C4×C11#12112yes—
192C2×C4×C11#12112yes—
193C2×C4×C11#12112yes—
194C2×C4×C11#12312yes—
195C2×C4×C11#12311yescharacteristic
196C2×C4×C11#12412yes—
197C2×C4×C11#12712yes—
198C2×Dic11—24no—
199C2×Dic11—24no—
200C2×Dic11—44no—
201C2×Dic11—42no—
202C2×Dic11—42no—
203C2×Dic11—44no—
204C2×Dic11—44no—
205Dic22—28no—
206Dic22—44no—
207Dic22—44no—
208Dic22—44no—
209C11⋊C8—44no—
210C22×#41C2×D1111yescharacteristic
211C23×Q8—111no—
212C22×M16—112no—
213#536—224no—
214#536—224no—
215C2×C4⋊Q8—221no—
216C2×#124—221no—
217C2×#123—222no—
218C2×C22⋊Q8—114no—
219C2×#117—111no—
220C2×#117C2×D1112yes—
221#419—224no—
222#419—224no—
223C2×#103—224no—
224#413—224no—
225C2×#101—221no—
226C2×#100—221no—
227#410—24no—
228C2×#99—22no—
229#339—224no—
230C22×C11—24no—
231C22×C11—22no—
232C22×C11—41no—
233C22×C11—42no—
234C22×C11—41no—
235C22×C11—44no—
236C22×C11—42no—
237C22×C11—82no—
238C22×C11—82no—
239C22×C11#37911yescharacteristic
240C22×C11#38611yescharacteristic
241C22×C11#38611yescharacteristic
242C22×C11#39212yes—
243C22×C11#39412yes—
244C4×C11—42no—
245C4×C11—84no—
246C4×C11#38612yes—
247C4×C11#39012yes—
248C4×C11#39212yes—
249C4×C11#39412yes—
250Dic11—44no—
251Dic11—44no—
252C2×#41—22no—
253C2×#41—22no—
254C2×#41—22no—
255C2×#41—22no—
256C2×#41—22no—
257C2×#41—22no—
258C22×Q8—112no—
259C22×Q8—114no—
260C22×Q8—221no—
261C22×Q8—222no—
262C22×Q8—222no—
263C22×Q8—222no—
264C22×Q8—222no—
265C22×Q8—222no—
266C22×Q8D4411yescharacteristic
267C22×D4D4411yescharacteristic
268C22×D4C22⋊D1112yes—
269C23×C4—221no—
270C23×C4C4×D1112yes—
271C23×C4C22×D1111yescharacteristic
272C2×M16—114no—
273C2×M16—222no—
274C2×M16—222no—
275C2×M16—222no—
276C2×M16—222no—
277C2×M16—222no—
278C22×C8—222no—
279C4⋊Q8—228no—
280#124—228no—
281#123—2216no—
282C22⋊Q8—228no—
283C22⋊Q8—228no—
284#117—22no—
285#117—22no—
286#117—22no—
287#117—114no—
288#117—222no—
289#117C22⋊D1114yes—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—112no—
292C2×C4⋊C4—224no—
293C2×C22⋊C4—22no—
294C2×C22⋊C4—224no—
295C2×C22⋊C4—221no—
296C2×C42—22no—
297C2×C42—221no—
298#103—2216no—
299#101—224no—
300#100—224no—
301#99—28no—
302C2×C11—22no—
303C2×C11—21no—
304C2×C11—21no—
305C2×C11—22no—
306C2×C11—82no—
307C2×C11#143811yescharacteristic
308C2×C11#179612yes—
309C24(C2×D11)⋊C412yes—
310C24C2×C22⋊D1111yescharacteristic
311#41—42no—
312#41—42no—
313#41—42no—
314#41—42no—
315#41—42no—
316#41—42no—
317#41—42no—
318#41—42no—
319C2×Q8—21no—
320C2×Q8—22no—
321C2×Q8—21no—
322C2×Q8—22no—
323C2×Q8—114no—
324C2×Q8—222no—
325C2×Q8—224no—
326C2×Q8—224no—
327C2×Q8—224no—
328C2×Q8—224no—
329C2×Q8—224no—
330C2×Q8—224no—
331C2×Q8—224no—
332C2×Q8—441no—
333C2×Q8—442no—
334C2×Q8—442no—
335C2×Q8—441no—
336C2×Q8—442no—
337C2×Q8—442no—
338C2×Q8—442no—
339C2×D4—22no—
340C2×D4—24no—
341C2×D4—24no—
342C2×D4—22no—
343C2×D4—21no—
344C2×D4—22no—
345C2×D4—21no—
346C2×D4—22no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—24no—
350C22×C4—24no—
351C22×C4—42no—
352C22×C4—222no—
353C22×C4—222no—
354C22×C4—224no—
355C22×C4—441no—
356C22×C4—442no—
357C22×C4—441no—
358C22×C4(C2×D11)⋊C412yes—
359C22×C4C2×C4×D1111yescharacteristic
360C22×C4C2×D4411yescharacteristic
361C22×C4#433912yes—
362C22×C4D4×D1112yes—
363C22×C4D4×D1112yes—
364C22×C4D4×D1112yes—
365C22×C4#434112yes—
366C22×C4C2×C22⋊D1112yes—
367M16—224no—
368M16—224no—
369M16—442no—
370M16—442no—
371C2×C8—224no—
372C2×C8—442no—
373C2×C8—442no—
374C4⋊C4—24no—
375C4⋊C4—42no—
376C4⋊C4—114no—
377C4⋊C4—2216no—
378C4⋊C4—222no—
379C22⋊C4—24no—
380C22⋊C4—42no—
381C22⋊C4—2216no—
382C22⋊C4—224no—
383C42—24no—
384C42—42no—
385C42—224no—
386C11#1098511yescharacteristic, complemented, Sylow
387C23—22no—
388C23—22no—
389C23—22no—
390C23—42no—
391C23—44no—
392C23C2×(C2×D11)⋊C411yescharacteristic
393C23#6698211yescharacteristic
394C23#6699012yes—
395C23#6699212yes—
396C23#6700611yescharacteristic
397Q8—42no—
398Q8—42no—
399Q8—228no—
400Q8—444no—
401Q8—444no—
402Q8—444no—
403D4—44no—
404D4—44no—
405D4—42no—
406D4—42no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—44no—
411C2×C4—44no—
412C2×C4—44no—
413C2×C4—84no—
414C2×C4—224no—
415C2×C4—224no—
416C2×C4—444no—
417C2×C4—442no—
418C2×C4—442no—
419C2×C4—444no—
420C2×C4—444no—
421C2×C4C22⋊C4×D1111yescharacteristic
422C2×C4C22⋊C4×D1111yescharacteristic
423C2×C4(C22⋊D11)⋊C412yes—
424C2×C4#6693511yescharacteristic
425C2×C4#6693512yes—
426C2×C4#6693612yes—
427C2×C4#6693712yes—
428C2×C4#6693712yes—
429C2×C4#6693812yes—
430C2×C4#6693911yescharacteristic
431C2×C4C4×C22⋊D1112yes—
432C2×C4#6698312yes—
433C2×C4#6699012yes—
434C2×C4#6699112yes—
435C2×C4#6699212yes—
436C2×C4#6699312yes—
437C8—444no—
438C22—24no—
439C22—22no—
440C22—41no—
441C22—42no—
442C22—41no—
443C22—44no—
444C22—42no—
445C22—82no—
446C22—82no—
447C22#1062256811yescharacteristic
448C22#1062257111yescharacteristic
449C22#1062257212yes—
450C22#1062282611yescharacteristic
451C22#1062283612yes—
452C4—42no—
453C4—84no—
454C4—444no—
455C4—444no—
456C4#1062256912yes—
457C4#1062257012yes—
458C4#1062257312yes—
459C4#1062257412yes—
460C2—22no—
461C2—21no—
462C2—21no—
463C2—22no—
464C2—82no—
465C2#1306685511yescharacteristic
466C2#1306858912yes—
subgroupG/H
centerC22#10622568
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC2×C11×#410C2
socleC22×C11#379
prime radicalC22×C11×#41C22
cosocleC23×C4×C11C23
hypercenterC2×#410D11
hypocenterC11#10985
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#410

Complements

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

NH ≅ G/Ntype
2. C2×#10622617C2semidirect
4. #13068326C2semidirect
15. C2×#66977C4semidirect
386. C11#10985semidirect

Maximal subgroups

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

subgroupindex
C2×#106233562
C2×#106226172
C2×#106228502
#130683262
C2×C11×#4102
#1098511