Finite Group Databasebeta

← #14671327

Subgroups — #14671327

Order 2816.

694 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 694 conjugacy classes of subgroups — too many to draw. Only its 107 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
1#13072240C211yesmaximal, characteristic
2C2×#10622116C212yesmaximal, complemented
3#13068544C211yesmaximal, characteristic
4#13066742C212yesmaximal, complemented
5C2×C11×#413C211yesmaximal, characteristic
6C22×C11×#41C2211yescharacteristic
7C22×C11×M16—21no—
8C2×#66997C2211yescharacteristic
9C2×#66989C411yescharacteristic
10C2×#66977C411yescharacteristic
11C11×#413—24no—
12C2×C11×#101C2212yes—
13C2×C11×#100—21no—
14#10622843C2211yescharacteristic
15C2×#66900C2212yes—
16#10622835—21no—
17#10622835—21no—
18#10622834C411yescharacteristic
19C2×#66897—21no—
20#10622823—21no—
21#10622823—21no—
22C4×C22⋊Dic11C411yescharacteristic
23#10622820—21no—
24#10622116—24no—
25C2×C11×#41—22no—
26C2×C11×#41—22no—
27C2×C11×#41—41no—
28C2×C11×#41—41no—
29C2×C11×#41—42no—
30C22×Q8×C11C2311yescharacteristic
31C22×D4×C11C2×C411yescharacteristic
32C22×D4×C11D411yescharacteristic
33C22×D4×C11D411yescharacteristic
34C23×C4×C11C2×C411yescharacteristic
35C23×C4×C11D411yescharacteristic
36C23×C4×C11D411yescharacteristic
37C22×Dic22C2×C411yescharacteristic
38C2×C11×M16—24no—
39C2×C11×M16—22no—
40C2×C11×M16—42no—
41C2×C11×M16—41no—
42C22×C8×C11—41no—
43C2×C22⋊Dic11—21no—
44C2×C22⋊Dic11—21no—
45C2×C22⋊Dic11—21no—
46C2×C22⋊Dic11—21no—
47C2×C22⋊Dic11—21no—
48C2×C22⋊Dic11—21no—
49#66997—22no—
50#66997—22no—
51#66989—42no—
52C2×C4⋊Dic11C2×C411yescharacteristic
53#66977—41no—
54#66977—41no—
55C2×Dic11⋊C4—21no—
56C2×Dic11⋊C4—21no—
57C2×Dic11⋊C4—21no—
58C2×C4×Dic11C2×C411yescharacteristic
59C2×C4×Dic11C2×C411yescharacteristic
60C2×#4318—22no—
61C11×#101—22no—
62C11×#101D414yes—
63C11×#100—24no—
64#66900—22no—
65#66900—22no—
66#66897—42no—
67C11⋊#95—21no—
68C11⋊#95—21no—
69C11⋊#95—21no—
70C22⋊(C11⋊C8)—41no—
71C22⋊(C11⋊C8)—41no—
72#13095—111nomaximal, Sylow
73C24×C11C22⋊C411yescharacteristic
74C24×C11C22⋊C411yescharacteristic
75C24×C11C22⋊C411yescharacteristic
76C11×#41—44no—
77C11×#41—44no—
78C11×#41—44no—
79C11×#41—44no—
80C2×Q8×C11—41no—
81C2×Q8×C11—41no—
82C2×Q8×C11C2×D412yes—
83C2×Q8×C11#4112yes—
84C2×D4×C11—22no—
85C2×D4×C11—22no—
86C2×D4×C11—22no—
87C2×D4×C11—21no—
88C2×D4×C11—22no—
89C2×D4×C11—21no—
90C2×D4×C11—41no—
91C2×D4×C11—41no—
92C2×D4×C11—41no—
93C2×D4×C11—41no—
94C22×C4×C11—22no—
95C22×C4×C11—21no—
96C22×C4×C11—21no—
97C22×C4×C11—21no—
98C22×C4×C11—21no—
99C22×C4×C11—21no—
100C22×C4×C11—21no—
101C22×C4×C11—21no—
102C22×C4×C11—21no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—41no—
106C22×C4×C11—41no—
107C22×C4×C11C22⋊C411yescharacteristic
108C22×C4×C11C22×C411yescharacteristic
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2×D411yescharacteristic
111C22×Dic11—21no—
112C22×Dic11—21no—
113C22×Dic11—21no—
114C22×Dic11—21no—
115C2×Dic22—22no—
116C2×Dic22—41no—
117C2×Dic22—41no—
118C11×M16—24no—
119C11×M16—44no—
120C11×M16—42no—
121C2×C8×C11—44no—
122C2×C8×C11—42no—
123C22⋊Dic11—42no—
124C22⋊Dic11—42no—
125C22⋊Dic11—42no—
126C22⋊Dic11—42no—
127C22⋊Dic11—42no—
128C22⋊Dic11—42no—
129C4⋊Dic11—41no—
130Dic11⋊C4—41no—
131Dic11⋊C4—41no—
132Dic11⋊C4—41no—
133Dic11⋊C4—42no—
134Dic11⋊C4—41no—
135C4×Dic11—22no—
136C4×Dic11—41no—
137#4318—42no—
138#4318—42no—
139C2×C11⋊C8—42no—
140C2×#413D1111yescharacteristic
141#2432—111no—
142C2×#356—112no—
143#1785—111no—
144#1394—112no—
145C23×C11—21no—
146C23×C11—21no—
147C23×C11—21no—
148C23×C11—21no—
149C23×C11—21no—
150C23×C11—21no—
151C23×C11—21no—
152C23×C11—21no—
153C23×C11—41no—
154C23×C11—41no—
155C23×C11—41no—
156C23×C11—41no—
157C23×C11—41no—
158C23×C11—41no—
159C23×C11#9912yes—
160C23×C11C2×C22⋊C411yescharacteristic
161Q8×C11—42no—
162Q8×C11—42no—
163D4×C11—44no—
164D4×C11—44no—
165D4×C11—42no—
166D4×C11—42no—
167C2×C4×C11—22no—
168C2×C4×C11—22no—
169C2×C4×C11—22no—
170C2×C4×C11—22no—
171C2×C4×C11—21no—
172C2×C4×C11—21no—
173C2×C4×C11—21no—
174C2×C4×C11—21no—
175C2×C4×C11—21no—
176C2×C4×C11—21no—
177C2×C4×C11—21no—
178C2×C4×C11—21no—
179C2×C4×C11—42no—
180C2×C4×C11—42no—
181C2×C4×C11—42no—
182C2×C4×C11—42no—
183C2×C4×C11#9911yescharacteristic
184C2×C4×C11#9911yescharacteristic
185C2×C4×C11C4×D412yes—
186C2×C4×C11#12011yescharacteristic
187C2×C4×C11#12112yes—
188C2×C4×C11#12311yescharacteristic
189C2×Dic11—22no—
190C2×Dic11—41no—
191C2×Dic11—41no—
192C2×Dic11—41no—
193C2×Dic11—41no—
194C2×Dic11—41no—
195C2×Dic11—41no—
196C2×Dic11—41no—
197C2×Dic11—41no—
198C2×Dic11—41no—
199C2×Dic11—41no—
200C2×Dic11—41no—
201Dic22—82no—
202C8×C11—44no—
203C11⋊C8—82no—
204C22×#41C2×D1111yescharacteristic
205C22×M16—21no—
206C2×C4⋊Q8—111no—
207C2×#124—111no—
208C2×C22⋊Q8—111no—
209#413—24no—
210C2×#101—112no—
211C2×#101C2×D1112yes—
212C2×#100—21no—
213C2×#100—221no—
214#407—221no—
215#394—221no—
216#394—221no—
217#391—111no—
218#390—111no—
219#385—221no—
220#385—221no—
221C4×C22⋊C4—111no—
222#356—224no—
223C22×C11—21no—
224C22×C11—21no—
225C22×C11—22no—
226C22×C11—42no—
227C22×C11—42no—
228C22×C11—41no—
229C22×C11—41no—
230C22×C11—41no—
231C22×C11—41no—
232C22×C11—41no—
233C22×C11—41no—
234C22×C11—41no—
235C22×C11—41no—
236C22×C11—81no—
237C22×C11—81no—
238C22×C11—81no—
239C22×C11—81no—
240C22×C11#38611yescharacteristic
241C22×C11C2×#9911yescharacteristic
242C22×C11C2×#9911yescharacteristic
243C4×C11—21no—
244C4×C11—21no—
245C4×C11—21no—
246C4×C11—21no—
247C4×C11—22no—
248C4×C11—22no—
249Dic11—42no—
250Dic11—81no—
251Dic11—81no—
252Dic11—81no—
253C2×#41—22no—
254C2×#41—22no—
255C2×#41—41no—
256C2×#41—41no—
257C2×#41—42no—
258C22×Q8—111no—
259C22×Q8C22×D1111yescharacteristic
260C22×D4C4×D1111yescharacteristic
261C22×D4D4411yescharacteristic
262C22×D4C22⋊D1111yescharacteristic
263C23×C4C4×D1111yescharacteristic
264C23×C4D4411yescharacteristic
265C23×C4C22⋊D1111yescharacteristic
266C2×M16—24no—
267C2×M16—22no—
268C2×M16—42no—
269C2×M16—41no—
270C2×M16—222no—
271C22×C8—41no—
272C4⋊Q8—222no—
273C4⋊Q8—222no—
274#124—442no—
275C22⋊Q8—441no—
276C22⋊Q8—441no—
277C2×C4⋊C4—111no—
278C2×C4⋊C4—221no—
279C2×C4⋊C4—221no—
280C2×C4⋊C4—221no—
281C2×C22⋊C4—221no—
282C2×C22⋊C4—221no—
283C2×C22⋊C4—221no—
284C2×C22⋊C4—221no—
285C2×C22⋊C4—221no—
286C2×C22⋊C4—221no—
287C2×C42—111no—
288C2×C42—111no—
289#101—22no—
290#101—222no—
291#101—222no—
292#101C22⋊D1114yes—
293#100—24no—
294#100—442no—
295C22⋊C8—441no—
296C22⋊C8—441no—
297#95—221no—
298#95—221no—
299#95—221no—
300C2×C11—21no—
301C2×C11—21no—
302C2×C11—42no—
303C2×C11—81no—
304C2×C11—81no—
305C2×C11#189811yescharacteristic
306C2×C11#213211yescharacteristic
307C2×C11#213511yescharacteristic
308C24(C2×D11)⋊C411yescharacteristic
309C24(C2×D11)⋊C411yescharacteristic
310C24(C2×D11)⋊C411yescharacteristic
311#41—44no—
312#41—44no—
313#41—44no—
314#41—44no—
315C2×Q8—41no—
316C2×Q8—41no—
317C2×Q8—222no—
318C2×Q8—441no—
319C2×Q8—441no—
320C2×Q8#433912yes—
321C2×Q8C2×C22⋊D1112yes—
322C2×D4—22no—
323C2×D4—22no—
324C2×D4—22no—
325C2×D4—21no—
326C2×D4—22no—
327C2×D4—21no—
328C2×D4—41no—
329C2×D4—41no—
330C2×D4—41no—
331C2×D4—41no—
332C22×C4—22no—
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—41no—
344C22×C4—41no—
345C22×C4—221no—
346C22×C4—221no—
347C22×C4—221no—
348C22×C4—221no—
349C22×C4(C2×D11)⋊C411yescharacteristic
350C22×C4C2×C4×D1111yescharacteristic
351C22×C4C2×D4411yescharacteristic
352C22×C4C2×C22⋊D1111yescharacteristic
353M16—24no—
354M16—44no—
355M16—42no—
356M16—442no—
357M16—442no—
358C2×C8—44no—
359C2×C8—42no—
360C2×C8—442no—
361C4⋊C4—441no—
362C4⋊C4—441no—
363C4⋊C4—441no—
364C4⋊C4—441no—
365C4⋊C4—442no—
366C4⋊C4—441no—
367C22⋊C4—442no—
368C22⋊C4—442no—
369C22⋊C4—442no—
370C22⋊C4—442no—
371C22⋊C4—442no—
372C22⋊C4—442no—
373C42—222no—
374C42—441no—
375C11#1309511yescharacteristic, complemented, Sylow
376C23—21no—
377C23—21no—
378C23—21no—
379C23—21no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—41no—
385C23—41no—
386C23—41no—
387C23—41no—
388C23—41no—
389C23—41no—
390C23#6687012yes—
391C23C2×(C2×D11)⋊C411yescharacteristic
392Q8—42no—
393Q8—42no—
394Q8—882no—
395D4—44no—
396D4—44no—
397D4—42no—
398D4—42no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—222no—
416C2×C4—441no—
417C2×C4—441no—
418C2×C4—441no—
419C2×C4—441no—
420C2×C4—441no—
421C2×C4—441no—
422C2×C4—441no—
423C2×C4—441no—
424C2×C4—441no—
425C2×C4—441no—
426C2×C4—441no—
427C2×C4#6687011yescharacteristic
428C2×C4#6687011yescharacteristic
429C2×C4C4×C22⋊D1112yes—
430C2×C4#6698211yescharacteristic
431C2×C4#6698312yes—
432C2×C4#6700611yescharacteristic
433C8—44no—
434C8—882no—
435C22—21no—
436C22—21no—
437C22—22no—
438C22—42no—
439C22—42no—
440C22—41no—
441C22—41no—
442C22—41no—
443C22—41no—
444C22—41no—
445C22—41no—
446C22—41no—
447C22—41no—
448C22—81no—
449C22—81no—
450C22—81no—
451C22—81no—
452C22C2×#6687011yescharacteristic
453C22C2×#6687011yescharacteristic
454C22#1062282611yescharacteristic
455C4—21no—
456C4—22no—
457C4—21no—
458C4—21no—
459C4—21no—
460C4—22no—
461C4—442no—
462C4—881no—
463C4—881no—
464C4—881no—
465C2—21no—
466C2—21no—
467C2—42no—
468C2—81no—
469C2—81no—
470C2#1306906911yescharacteristic
471C2#1307029911yescharacteristic
472C2#1307031011yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC22×Q8C22×D11
FittingC2×C11×#413C2
socleC22×C11C2×#99
prime radicalC22×C11×#41C22
cosocleC22×Q8×C11C23
hypercenterC2×#413D11
hypocenterC11#13095
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×#41 ◁ C2×#413

Complements

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

NH ≅ G/Ntype
2. C2×#10622116C2semidirect
4. #13066742C2semidirect
375. C11#13095semidirect

Maximal subgroups

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

subgroupindex
#130722402
C2×#106221162
#130685442
#130667422
C2×C11×#4132
#1309511