Finite Group Databasebeta

← #14654261

Subgroups — #14654261

Order 2816.

770 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 770 conjugacy classes of subgroups — too many to draw. Only its 101 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622663C211yesmaximal, characteristic, complemented
2#13072275C211yesmaximal, characteristic
3#13069602C211yesmaximal, characteristic, complemented
4#13068552C211yesmaximal, characteristic, complemented
5#13067184C211yesmaximal, characteristic
6#13066463C211yesmaximal, characteristic, complemented
7C11×#3187C211yesmaximal, characteristic
8C23×Dic22C2211yescharacteristic
9C2×C11×C22⋊Q8C2211yescharacteristic
10C2×C11×#121C2211yescharacteristic
11C22×#4326—21no—
12C2×#66989—21no—
13C11×#483—21no—
14C11×#481—21no—
15C11×#465—22no—
16C11×#450—21no—
17C11×#448—21no—
18C2×C11×C22⋊C8C2211yescharacteristic
19#10622833—22no—
20#10622825C2211yescharacteristic
21C4×C22⋊Dic11C2211yescharacteristic
22C2×C22⋊(C11⋊C8)C2211yescharacteristic
23C2×#66880—22no—
24#10622663—22no—
25#10622663—22no—
26#10622587—21no—
27C2×#66874—21no—
28#10622560—22no—
29#10622175—22no—
30#10622164—22no—
31C22×Q8×C11D411yescharacteristic
32C22×D4×C11—21no—
33C22×D4×C11D411yescharacteristic
34C23×C4×C11C2311yescharacteristic
35C23×Dic11—21no—
36C22×Dic22—21no—
37C22×Dic22—21no—
38C22×Dic22—21no—
39C22×Dic22—21no—
40C22×Dic22—21no—
41C22×Dic22—44no—
42C22×Dic22D412yes—
43C2×C11×SD16—22no—
44C22×C8×C11D412yes—
45C11×C22⋊Q8—21no—
46C11×C22⋊Q8—21no—
47C11×C22⋊Q8—21no—
48C11×C22⋊Q8—21no—
49C11×#121—21no—
50C11×#121—21no—
51C11×#121—21no—
52C11×#121—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4D411yescharacteristic
55C2×C11×C4⋊C4D411yescharacteristic
56C2×C11×C22⋊C4—21no—
57C2×C11×C22⋊C4—21no—
58C2×C22⋊Dic11—24no—
59C2×C22⋊Dic11—21no—
60C2×C22⋊Dic11D412yes—
61C2×#4326—24no—
62C2×#4326—44no—
63#66989—44no—
64C2×C4⋊Dic11—21no—
65C2×C4×Dic11—21no—
66C22×C11⋊C8—21no—
67C11×#106—22no—
68C11×#103—22no—
69C11×#102—22no—
70C11×C22⋊C8—21no—
71C11×C22⋊C8—21no—
72C11⋊#95—24no—
73C11⋊#95—21no—
74C11⋊#95—21no—
75C22⋊(C11⋊C8)—21no—
76C22⋊(C11⋊C8)D412yes—
77#66880—44no—
78#66874—24no—
79#9956—111nomaximal, Sylow
80C24×C11—21no—
81C24×C11C2×D411yescharacteristic
82C2×Q8×C11—21no—
83C2×Q8×C11—21no—
84C2×Q8×C11—42no—
85C2×D4×C11—21no—
86C2×D4×C11—21no—
87C2×D4×C11—42no—
88C2×D4×C11—41no—
89C2×D4×C11—41no—
90C2×D4×C11—42no—
91C2×D4×C11—42no—
92C22×C4×C11—21no—
93C22×C4×C11—21no—
94C22×C4×C11—21no—
95C22×C4×C11—42no—
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11#4111yescharacteristic
102C22×Dic11—22no—
103C22×Dic11—22no—
104C22×Dic11—44no—
105C22×Dic11—41no—
106C22×Dic11—41no—
107C22×Dic11—41no—
108C2×Dic22—24no—
109C2×Dic22—24no—
110C2×Dic22—24no—
111C2×Dic22—22no—
112C2×Dic22—22no—
113C2×Dic22—42no—
114C2×Dic22—42no—
115C2×Dic22—42no—
116C2×Dic22—44no—
117C2×Dic22—44no—
118C2×Dic22—44no—
119C2×Dic22—41no—
120C2×Dic22—41no—
121C11×SD16—82no—
122C2×C8×C11—22no—
123C2×C8×C11—42no—
124C11×C4⋊C4—21no—
125C11×C4⋊C4—21no—
126C11×C4⋊C4—21no—
127C11×C4⋊C4—21no—
128C11×C4⋊C4—41no—
129C11×C4⋊C4—41no—
130C11×C22⋊C4—41no—
131C11×C22⋊C4—41no—
132C11×C22⋊C4—41no—
133C11×C22⋊C4—41no—
134C22⋊Dic11—22no—
135C22⋊Dic11—22no—
136C22⋊Dic11—48no—
137C22⋊Dic11—42no—
138#4326—48no—
139C4⋊Dic11—42no—
140C4×Dic11—42no—
141C2×C11⋊C8—22no—
142C2×C11⋊C8—42no—
143#3187D1111yescharacteristic
144C2×#451—111no—
145#2436—111no—
146#1996—111no—
147#1787—111no—
148#1519—111no—
149#1282—111no—
150C23×C11—41no—
151C23×C11—41no—
152C23×C11—42no—
153C23×C11—42no—
154C23×C11—41no—
155C23×C11—42no—
156C23×C11#12011yescharacteristic
157C23×C11#12111yescharacteristic
158C23×C11#12711yescharacteristic
159C23×C11#13512yes—
160C23×C11#13712yes—
161Q8×C11—42no—
162Q8×C11—42no—
163D4×C11—42no—
164D4×C11—81no—
165D4×C11—82no—
166D4×C11—81no—
167D4×C11—81no—
168C2×C4×C11—22no—
169C2×C4×C11—22no—
170C2×C4×C11—22no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11—42no—
178C2×C4×C11—81no—
179C2×C4×C11—81no—
180C2×C4×C11#12011yescharacteristic
181C2×C4×C11#12011yescharacteristic
182C2×C4×C11#12111yescharacteristic
183C2×C4×C11#12111yescharacteristic
184C2×Dic11—24no—
185C2×Dic11—44no—
186C2×Dic11—44no—
187C2×Dic11—42no—
188C2×Dic11—42no—
189C2×Dic11—42no—
190C2×Dic11—42no—
191C2×Dic11—42no—
192C2×Dic11—81no—
193C2×Dic11—81no—
194C2×Dic11—81no—
195Dic22—24no—
196Dic22—24no—
197Dic22—42no—
198Dic22—44no—
199Dic22—42no—
200Dic22—44no—
201C8×C11—42no—
202C11⋊C8—42no—
203C23×Q8—111no—
204C22×Q16—221no—
205C2×#124—221no—
206C2×C22⋊Q8C2×D1111yescharacteristic
207C2×#121C2×D1111yescharacteristic
208#483—21no—
209#481—21no—
210#465—22no—
211#451—222no—
212#451—222no—
213#450—21no—
214#448—21no—
215C2×#103—221no—
216C2×#103—222no—
217C2×C22⋊C8—111no—
218C2×C22⋊C8C2×D1111yescharacteristic
219#393—222no—
220#391—221no—
221#386—222no—
222#380—111no—
223C4×C22⋊C4—111no—
224#342—222no—
225#327—222no—
226C22×C11—21no—
227C22×C11—21no—
228C22×C11—21no—
229C22×C11—21no—
230C22×C11—21no—
231C22×C11—21no—
232C22×C11—42no—
233C22×C11—42no—
234C22×C11—84no—
235C22×C11—81no—
236C22×C11—81no—
237C22×C11—81no—
238C22×C11#39211yescharacteristic
239C22×C11#45212yes—
240C22×C11#46412yes—
241C22×C11#49511yescharacteristic
242C22×C11#49711yescharacteristic
243C4×C11—21no—
244C4×C11—21no—
245C4×C11—21no—
246C4×C11—81no—
247C4×C11—81no—
248C4×C11—81no—
249C4×C11B(4,𝔽2)12yes—
250Dic11—44no—
251Dic11—82no—
252Dic11—161no—
253C22×Q8—112no—
254C22×Q8—221no—
255C22×Q8—221no—
256C22×Q8—221no—
257C22×Q8—221no—
258C22×Q8—221no—
259C22×Q8—444no—
260C22×Q8C22⋊D1111yescharacteristic
261C22×D4—21no—
262C22×D4C22⋊D1111yescharacteristic
263C23×C4—221no—
264C23×C4C22×D1111yescharacteristic
265C2×Q16—224no—
266C2×Q16—444no—
267C2×SD16—22no—
268C22×C8—221no—
269C22×C8C22⋊D1112yes—
270#124—444no—
271C22⋊Q8—21no—
272C22⋊Q8—21no—
273C22⋊Q8—21no—
274C22⋊Q8—21no—
275#121—21no—
276#121—21no—
277#121—21no—
278#121—21no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—221no—
281C2×C4⋊C4C22⋊D1111yescharacteristic
282C2×C4⋊C4C22⋊D1111yescharacteristic
283C2×C22⋊C4—21no—
284C2×C22⋊C4—21no—
285C2×C22⋊C4—112no—
286C2×C22⋊C4—224no—
287C2×C22⋊C4—221no—
288C2×C42—221no—
289#106—22no—
290#103—22no—
291#103—224no—
292#103—444no—
293#102—22no—
294C22⋊C8—21no—
295C22⋊C8—21no—
296C22⋊C8—112no—
297C22⋊C8—221no—
298#95—224no—
299#95—221no—
300#95—221no—
301C2×C11—22no—
302C2×C11—21no—
303C2×C11—22no—
304C2×C11—21no—
305C2×C11—161no—
306C2×C11#200911yescharacteristic
307C2×C11#201511yescharacteristic
308C2×C11#202111yescharacteristic
309C24—21no—
310C24D4×D1111yescharacteristic
311C2×Q8—21no—
312C2×Q8—21no—
313C2×Q8—42no—
314C2×Q8—224no—
315C2×Q8—224no—
316C2×Q8—224no—
317C2×Q8—222no—
318C2×Q8—222no—
319C2×Q8—442no—
320C2×Q8—442no—
321C2×Q8—442no—
322C2×Q8—444no—
323C2×Q8—444no—
324C2×Q8—444no—
325C2×Q8—441no—
326C2×Q8—441no—
327C2×D4—21no—
328C2×D4—21no—
329C2×D4—42no—
330C2×D4—42no—
331C2×D4—42no—
332C2×D4—41no—
333C2×D4—41no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—42no—
338C22×C4—222no—
339C22×C4—222no—
340C22×C4—444no—
341C22×C4—441no—
342C22×C4—441no—
343C22×C4—441no—
344C22×C4D4×D1111yescharacteristic
345C22×C4D4×D1111yescharacteristic
346C22×C4#434111yescharacteristic
347C22×C4C2×C22⋊D1111yescharacteristic
348C22×C4C2×C22⋊D1111yescharacteristic
349C22×C4C2×C22⋊D1111yescharacteristic
350Q16—448no—
351SD16—82no—
352C2×C8—22no—
353C2×C8—42no—
354C2×C8—222no—
355C2×C8—442no—
356C4⋊C4—21no—
357C4⋊C4—21no—
358C4⋊C4—21no—
359C4⋊C4—21no—
360C4⋊C4—41no—
361C4⋊C4—41no—
362C4⋊C4—442no—
363C22⋊C4—41no—
364C22⋊C4—41no—
365C22⋊C4—41no—
366C22⋊C4—41no—
367C22⋊C4—222no—
368C22⋊C4—222no—
369C22⋊C4—448no—
370C22⋊C4—442no—
371C42—442no—
372C11#995611yescharacteristic, complemented, Sylow
373C23—41no—
374C23—41no—
375C23—42no—
376C23—42no—
377C23—42no—
378C23—41no—
379C23#6696812yes—
380C23#6696912yes—
381C23#6699011yescharacteristic
382C23#6699211yescharacteristic
383C23#6699311yescharacteristic
384Q8—42no—
385Q8—42no—
386Q8—224no—
387Q8—224no—
388Q8—442no—
389Q8—442no—
390Q8—444no—
391Q8—444no—
392D4—42no—
393D4—81no—
394D4—82no—
395D4—81no—
396D4—81no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—22no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—42no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—81no—
408C2×C4—81no—
409C2×C4—224no—
410C2×C4—442no—
411C2×C4—444no—
412C2×C4—444no—
413C2×C4—442no—
414C2×C4—442no—
415C2×C4—442no—
416C2×C4—442no—
417C2×C4—881no—
418C2×C4—881no—
419C2×C4—881no—
420C2×C4#6699011yescharacteristic
421C2×C4#6699111yescharacteristic
422C2×C4#6699211yescharacteristic
423C2×C4#6700611yescharacteristic
424C8—42no—
425C8—442no—
426C22—21no—
427C22—21no—
428C22—21no—
429C22—21no—
430C22—21no—
431C22—21no—
432C22—42no—
433C22—42no—
434C22—84no—
435C22—81no—
436C22—81no—
437C22—81no—
438C22#1062277912yes—
439C22#1062278011yescharacteristic
440C22#1062278111yescharacteristic
441C22#1062278612yes—
442C22#1062283611yescharacteristic
443C4—21no—
444C4—21no—
445C4—21no—
446C4—81no—
447C4—81no—
448C4—81no—
449C4—444no—
450C4—882no—
451C4—1761no—
452C4#1062285712yes—
453C2—22no—
454C2—21no—
455C2—22no—
456C2—21no—
457C2—161no—
458C2#1306967311yescharacteristic
459C2#1306970811yescharacteristic
460C2#1306974011yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#3187C2
socleC22×C11#392
prime radicalC2×C11×#121C22
hypercenter#3187D11
hypocenterC11#9956
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3187

Complements

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

NH ≅ G/Ntype
1. C2×#10622663C2semidirect
3. #13069602C2semidirect
4. #13068552C2semidirect
6. #13066463C2semidirect
372. C11#9956semidirect

Maximal subgroups

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

subgroupindex
C2×#106226632
#130722752
#130696022
#130685522
#130671842
#130664632
C11×#31872
#995611