Finite Group Databasebeta

← #14664101

Subgroups — #14664101

Order 2816.

606 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 606 conjugacy classes of subgroups — too many to draw. Only its 73 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#13071896C211yesmaximal, characteristic
2#13068403C211yesmaximal, characteristic, complemented
3#13066931C211yesmaximal, characteristic, complemented
4#13066640C211yesmaximal, characteristic, complemented
5#13066614C211yesmaximal, characteristic, complemented
6#13066612C211yesmaximal, characteristic, complemented
7C11×#1352C211yesmaximal, characteristic, complemented
8C2×#66946—21no—
9C2×#66946C411yescharacteristic, complemented
10C2×(C22⋊D11)⋊C4—21no—
11C2×(C22⋊D11)⋊C4C2211yescharacteristic
12C11×#399C2211yescharacteristic
13#10622605—21no—
14#10622605C411yescharacteristic, complemented
15#10622573—21no—
16#10622573C2211yescharacteristic
17C2×#66870—21no—
18C22⋊C4×Dic11—21no—
19D11×C22⋊C8—21no—
20#10622284C411yescharacteristic, complemented
21#10622261C411yescharacteristic, complemented
22C11×#342C2211yescharacteristic
23C11×#323C2211yescharacteristic
24#10622164C2211yescharacteristic
25#10622163C2211yescharacteristic
26#10622107—21no—
27C22×C22⋊D11—21no—
28C22×C22⋊D11D411yescharacteristic
29C23×Dic11D411yescharacteristic
30C22×D44—21no—
31C22×D44C2×C411yescharacteristic
32C22×C4×D11—21no—
33C22×C4×D11D411yescharacteristic
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4C2×C411yescharacteristic
36C2×C11×C22⋊C4—21no—
37C2×C11×C22⋊C4—21no—
38C2×C11×C22⋊C4C2311yescharacteristic
39C2×C22⋊Dic11—21no—
40C2×(C2×D11)⋊C4—21no—
41C2×(C2×D11)⋊C4—21no—
42C2×(C2×D11)⋊C4—21no—
43C2×(C2×D11)⋊C4—21no—
44C2×(C2×D11)⋊C4C2×C411yescharacteristic
45C2×Dic11⋊C4—21no—
46C2×Dic11⋊C4D411yescharacteristic
47C2×C4×Dic11—21no—
48C2×C4×Dic11—41no—
49C2×C4×Dic11C2×C411yescharacteristic
50C2×C8×D11—41no—
51#66946—44no—
52#66946—41no—
53#66946—41no—
54(C22⋊D11)⋊C4—41no—
55(C22⋊D11)⋊C4—41no—
56(C22⋊D11)⋊C4—44no—
57C11×C22⋊C8—21no—
58C11×#95C2×C411yescharacteristic
59C11⋊#95—21no—
60C11⋊#95—41no—
61C11⋊#95C2×C411yescharacteristic
62C22⋊(C11⋊C8)—21no—
63(C2×D11)⋊C8—41no—
64#66870—24no—
65#11726—111nomaximal, Sylow
66C24×C11C2×D411yescharacteristic
67C23×D11—21no—
68C23×D11C22⋊C411yescharacteristic
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11—41no—
72C22×C4×C11C22×C411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C2×C22⋊D11—21no—
75C2×C22⋊D11—21no—
76C2×C22⋊D11—22no—
77C2×C22⋊D11—41no—
78C2×C22⋊D11—42no—
79C2×C22⋊D11—42no—
80C2×C22⋊D11—41no—
81C2×C22⋊D11—41no—
82C22×Dic11—21no—
83C22×Dic11—21no—
84C22×Dic11—21no—
85C22×Dic11—41no—
86C22×Dic11—42no—
87C22×Dic11C22⋊C411yescharacteristic
88C22×Dic11C22⋊C411yescharacteristic
89C22×Dic11C22⋊C411yescharacteristic
90C2×D44—42no—
91C2×D44—41no—
92C2×D44—42no—
93C2×D44—42no—
94C2×D44—42no—
95C2×C4×D11—21no—
96C2×C4×D11—21no—
97C2×C4×D11—42no—
98C2×C4×D11—42no—
99C2×C4×D11—42no—
100C2×C4×D11—41no—
101C2×C4×D11—41no—
102C2×C8×C11—41no—
103C11×C4⋊C4—42no—
104C11×C4⋊C4—41no—
105C11×C22⋊C4—22no—
106C11×C22⋊C4—41no—
107C11×C22⋊C4—42no—
108C11×C22⋊C4—41no—
109C22⋊Dic11—22no—
110C22⋊Dic11—41no—
111(C2×D11)⋊C4—41no—
112(C2×D11)⋊C4—42no—
113(C2×D11)⋊C4—42no—
114(C2×D11)⋊C4—42no—
115(C2×D11)⋊C4—42no—
116Dic11⋊C4—41no—
117Dic11⋊C4—42no—
118C4×Dic11—24no—
119C4×Dic11—21no—
120C4×Dic11—21no—
121C4×Dic11—82no—
122C2×C11⋊C8—41no—
123C8×D11—82no—
124#2397—111no—
125C4×#99—111no—
126#1459—111no—
127#1352—111no—
128#1352D1111yescharacteristic, complemented
129#1343—111no—
130#1343—111no—
131C23×C11—21no—
132C23×C11—21no—
133C23×C11—41no—
134C23×C11—41no—
135C23×C11C2×C22⋊C411yescharacteristic
136C23×C11#13511yescharacteristic
137C23×C11#13511yescharacteristic
138C22×D11—21no—
139C22×D11—21no—
140C22×D11—22no—
141C22×D11—41no—
142C22×D11—41no—
143C22×D11—41no—
144C22×D11—41no—
145C22×D11—41no—
146C22×D11—41no—
147C22×D11—41no—
148C22×D11—41no—
149C22×D11#10412yes—
150C2×C4×C11—22no—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11—41no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—42no—
160C2×C4×C11—41no—
161C2×C4×C11—81no—
162C2×C4×C11—81no—
163C22⋊D11—42no—
164C22⋊D11—42no—
165C22⋊D11—44no—
166C22⋊D11—44no—
167C2×Dic11—22no—
168C2×Dic11—22no—
169C2×Dic11—21no—
170C2×Dic11—21no—
171C2×Dic11—21no—
172C2×Dic11—21no—
173C2×Dic11—41no—
174C2×Dic11—41no—
175C2×Dic11—42no—
176C2×Dic11—41no—
177C2×Dic11—42no—
178C2×Dic11—81no—
179C2×Dic11—81no—
180C2×Dic11—81no—
181C2×Dic11#9911yescharacteristic
182C2×Dic11#9911yescharacteristic
183D44—42no—
184D44—48no—
185D44—42no—
186C4×D11—42no—
187C4×D11—81no—
188C4×D11—82no—
189C4×D11—82no—
190C8×C11—81no—
191C11⋊C8—81no—
192C2×C4×D4—111no—
193C2×C4×D4—111no—
194C2×C4×D4—221no—
195C2×C4×D4—221no—
196C2×#99—221no—
197C2×C22⋊C8—221no—
198#399—111no—
199#399—221no—
200#399C2×D1111yescharacteristic
201#392—111no—
202#392—111no—
203#392—221no—
204C4×C22⋊C4—221no—
205#376—111no—
206#342—111no—
207#342C2×D1111yescharacteristic
208#324—221no—
209#323—111no—
210#323C2×D1111yescharacteristic
211C22×C11—21no—
212C22×C11—21no—
213C22×C11—21no—
214C22×C11—21no—
215C22×C11—41no—
216C22×C11—41no—
217C22×C11—41no—
218C22×C11—41no—
219C22×C11—81no—
220C22×C11C2×#9911yescharacteristic
221C22×C11#41611yescharacteristic
222C22×C11C2×#10411yescharacteristic
223C2×D11—22no—
224C2×D11—41no—
225C2×D11—41no—
226C2×D11—42no—
227C2×D11—42no—
228C2×D11—42no—
229C2×D11—42no—
230C2×D11—81no—
231C2×D11—81no—
232C2×D11—81no—
233C2×D11—81no—
234C2×D11—81no—
235C4×C11—42no—
236C4×C11—41no—
237C4×C11—41no—
238C4×C11—82no—
239C4×C11—81no—
240Dic11—21no—
241Dic11—42no—
242Dic11—41no—
243Dic11—41no—
244Dic11—82no—
245Dic11#35312yes—
246C22×D4—111no—
247C22×D4—111no—
248C22×D4—221no—
249C22×D4—221no—
250C23×C4—111no—
251C23×C4—111no—
252C23×C4—221no—
253C22×C8—441no—
254C4×D4—441no—
255C4×D4—441no—
256C4×D4—444no—
257C4×D4—444no—
258C4×D4—441no—
259C4×D4—441no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—111no—
262C2×C4⋊C4—221no—
263C2×C4⋊C4C4×D1111yescharacteristic
264C2×C22⋊C4—21no—
265C2×C22⋊C4—21no—
266C2×C22⋊C4—111no—
267C2×C22⋊C4—221no—
268C2×C22⋊C4—221no—
269C2×C22⋊C4—221no—
270C2×C22⋊C4—221no—
271C2×C22⋊C4—221no—
272C2×C22⋊C4C22×D1111yescharacteristic
273C2×C42—111no—
274C2×C42—221no—
275C2×C42—441no—
276#99—224no—
277C22⋊C8—21no—
278C22⋊C8—221no—
279C22⋊C8—441no—
280#95—111no—
281#95—221no—
282#95—441no—
283#95C4×D1111yescharacteristic
284C2×C11—21no—
285C2×C11—21no—
286C2×C11—41no—
287C2×C11—41no—
288C2×C11#150111yescharacteristic
289C2×C11#212011yescharacteristic
290C2×C11C2×#35311yescharacteristic
291D11—42no—
292D11—82no—
293C24—111no—
294C24—221no—
295C24D4×D1111yescharacteristic
296C2×D4—222no—
297C2×D4—221no—
298C2×D4—221no—
299C2×D4—441no—
300C2×D4—442no—
301C2×D4—442no—
302C2×D4—442no—
303C2×D4—442no—
304C2×D4—441no—
305C2×D4—442no—
306C2×D4—442no—
307C2×D4—441no—
308C2×D4—441no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—41no—
312C22×C4—111no—
313C22×C4—111no—
314C22×C4—111no—
315C22×C4—221no—
316C22×C4—221no—
317C22×C4—221no—
318C22×C4—221no—
319C22×C4—221no—
320C22×C4—441no—
321C22×C4—441no—
322C22×C4—442no—
323C22×C4—442no—
324C22×C4—442no—
325C22×C4—442no—
326C22×C4—441no—
327C22×C4C2×C4×D1111yescharacteristic
328C22×C4D4×D1111yescharacteristic
329C2×C8—41no—
330C2×C8—441no—
331C2×C8—882no—
332C4⋊C4—41no—
333C4⋊C4—42no—
334C4⋊C4—441no—
335C4⋊C4—442no—
336C22⋊C4—22no—
337C22⋊C4—41no—
338C22⋊C4—42no—
339C22⋊C4—41no—
340C22⋊C4—222no—
341C22⋊C4—441no—
342C22⋊C4—442no—
343C22⋊C4—442no—
344C22⋊C4—442no—
345C22⋊C4—442no—
346C22⋊C4—441no—
347C42—221no—
348C42—221no—
349C42—224no—
350C42—882no—
351C11#1172611yescharacteristic, complemented, Sylow
352C23—21no—
353C23—21no—
354C23—41no—
355C23—41no—
356C23—112no—
357C23—222no—
358C23—221no—
359C23—221no—
360C23—441no—
361C23—441no—
362C23—441no—
363C23—441no—
364C23—441no—
365C23—441no—
366C23—441no—
367C23—441no—
368C23C22⋊C4×D1111yescharacteristic
369C23#6696911yescharacteristic
370C23#6697211yescharacteristic
371D4—442no—
372D4—448no—
373D4—442no—
374D4—442no—
375D4—442no—
376D4—444no—
377D4—444no—
378C2×C4—22no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—42no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—81no—
390C2×C4—81no—
391C2×C4—111no—
392C2×C4—111no—
393C2×C4—222no—
394C2×C4—222no—
395C2×C4—221no—
396C2×C4—221no—
397C2×C4—221no—
398C2×C4—221no—
399C2×C4—442no—
400C2×C4—442no—
401C2×C4—441no—
402C2×C4—441no—
403C2×C4—441no—
404C2×C4—442no—
405C2×C4—881no—
406C2×C4—882no—
407C2×C4—882no—
408C2×C4—881no—
409C2×C4—881no—
410C2×C4—881no—
411C8—81no—
412C8—881no—
413C22—21no—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—41no—
418C22—41no—
419C22—41no—
420C22—41no—
421C22—81no—
422C22—222no—
423C22—442no—
424C22—442no—
425C22—442no—
426C22—441no—
427C22—441no—
428C22—442no—
429C22—881no—
430C22—881no—
431C22—881no—
432C22—881no—
433C22—881no—
434C22D11×#9911yescharacteristic
435C22#1062241711yescharacteristic
436C22D11×#10411yescharacteristic
437C4—42no—
438C4—41no—
439C4—41no—
440C4—82no—
441C4—81no—
442C4—112no—
443C4—221no—
444C4—442no—
445C4—441no—
446C4—441no—
447C4—882no—
448C2—21no—
449C2—21no—
450C2—41no—
451C2—41no—
452C2—442no—
453C2—882no—
454C2#1306710611yescharacteristic
455C2#1307025611yescharacteristic
456C2D11×#35311yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1352C2
socleC22×C11C2×#99
prime radical#13071896C2
cosocleC2×C11×C22⋊C4C23
hypercenter#1352D11
hypocenterC11#11726
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1352

Complements

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

NH ≅ G/Ntype
2. #13068403C2semidirect
3. #13066931C2semidirect
4. #13066640C2semidirect
5. #13066614C2semidirect
6. #13066612C2semidirect
7. C11×#1352C2semidirect
9. C2×#66946C4semidirect
14. #10622605C4semidirect
20. #10622284C4semidirect
21. #10622261C4semidirect
128. #1352D11semidirect
351. C11#11726semidirect

Maximal subgroups

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

subgroupindex
#130718962
#130684032
#130669312
#130666402
#130666142
#130666122
C11×#13522
#1172611