Finite Group Databasebeta

← #14664801

Subgroups — #14664801

Order 2816.

522 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 522 conjugacy classes of subgroups — too many to draw. Only its 77 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#13073573C211yesmaximal, characteristic
2#13068603C211yesmaximal, characteristic, complemented
3#13066935C211yesmaximal, characteristic, complemented
4#13066616C211yesmaximal, characteristic, complemented
5#13066614C211yesmaximal, characteristic, complemented
6#13066612C211yesmaximal, characteristic, complemented
7C11×#1344C211yesmaximal, characteristic, complemented
8C2×#66948C411yescharacteristic, complemented
9C2×#66937—21no—
10C2×(C22⋊D11)⋊C4C2211yescharacteristic
11C11×#397C2211yescharacteristic
12#10622593C411yescharacteristic, complemented
13#10622573C2211yescharacteristic
14#10622571—21no—
15C2×#66870—21no—
16#10622555—21no—
17#10622331—21no—
18#10622285C411yescharacteristic, complemented
19#10622282—21no—
20#10622278—21no—
21D11×#95C411yescharacteristic, complemented
22C11×#342C2211yescharacteristic
23C11×#323C2211yescharacteristic
24#10622164C2211yescharacteristic
25#10622163C2211yescharacteristic
26#10622106—21no—
27C22×C22⋊D11—21no—
28C22×C22⋊D11D411yescharacteristic
29C23×Dic11D411yescharacteristic
30C22×D44—21no—
31C22×D44C2×C411yescharacteristic
32C22×C4×D11—21no—
33C22×C4×D11C2×C411yescharacteristic
34C2×C11×C4⋊C4C2×C411yescharacteristic
35C2×C11×C22⋊C4—21no—
36C2×C11×C22⋊C4—21no—
37C2×C11×C22⋊C4C2311yescharacteristic
38C2×C22⋊Dic11—21no—
39C2×(C2×D11)⋊C4—21no—
40C2×(C2×D11)⋊C4—21no—
41C2×(C2×D11)⋊C4—21no—
42C2×(C2×D11)⋊C4—21no—
43C2×(C2×D11)⋊C4D411yescharacteristic
44C2×Dic11⋊C4—21no—
45C2×Dic11⋊C4—41no—
46C2×Dic11⋊C4C2×C411yescharacteristic
47C2×C4×Dic11D411yescharacteristic
48#66948—41no—
49#66948—41no—
50#66937—42no—
51#66937—42no—
52(C22⋊D11)⋊C4—41no—
53(C22⋊D11)⋊C4—41no—
54C11×C22⋊C8—21no—
55C11×#95—21no—
56C11×#95C2×C411yescharacteristic
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95—41no—
60C11⋊#95C2×C411yescharacteristic
61C22⋊(C11⋊C8)—21no—
62Dic11⋊C8—41no—
63C8×Dic11—41no—
64#66870—42no—
65#11876—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—41no—
75C2×C22⋊D11—41no—
76C2×C22⋊D11—42no—
77C2×C22⋊D11—41no—
78C2×C22⋊D11—41no—
79C2×C22⋊D11—81no—
80C2×C22⋊D11D812yes—
81C2×C22⋊D11SD1612yes—
82C22×Dic11—21no—
83C22×Dic11—21no—
84C22×Dic11—21no—
85C22×Dic11—41no—
86C22×Dic11—81no—
87C22×Dic11C22⋊C411yescharacteristic
88C22×Dic11C22⋊C411yescharacteristic
89C22×Dic11C22⋊C411yescharacteristic
90C2×D44—41no—
91C2×D44—42no—
92C2×D44—42no—
93C2×D44—42no—
94C2×D44—81no—
95C2×C4×D11—21no—
96C2×C4×D11—21no—
97C2×C4×D11—42no—
98C2×C4×D11—42no—
99C2×C4×D11—81no—
100C2×C4×D11—81no—
101C2×C8×C11—41no—
102C11×C4⋊C4—41no—
103C11×C22⋊C4—41no—
104C11×C22⋊C4—41no—
105C11×C22⋊C4—41no—
106C11×C22⋊C4—41no—
107C11×C22⋊C4—41no—
108C22⋊Dic11—41no—
109C22⋊Dic11—41no—
110(C2×D11)⋊C4—41no—
111(C2×D11)⋊C4—42no—
112(C2×D11)⋊C4—41no—
113(C2×D11)⋊C4—41no—
114(C2×D11)⋊C4—42no—
115(C2×D11)⋊C4—81no—
116Dic11⋊C4—41no—
117Dic11⋊C4—42no—
118Dic11⋊C4—82no—
119C4×Dic11—21no—
120C4×Dic11—21no—
121C2×C11⋊C8—41no—
122#2543—111no—
123#1799—111no—
124#1460—111no—
125#1344—111no—
126#1344D1111yescharacteristic, complemented
127#1343—111no—
128#1343—111no—
129C23×C11—21no—
130C23×C11—21no—
131C23×C11—41no—
132C23×C11—41no—
133C23×C11C2×C22⋊C411yescharacteristic
134C23×C11C2×D811yescharacteristic
135C23×C11C2×SD1611yescharacteristic
136C22×D11—21no—
137C22×D11—21no—
138C22×D11—41no—
139C22×D11—41no—
140C22×D11—41no—
141C22×D11—41no—
142C22×D11—41no—
143C22×D11—41no—
144C22×D11—41no—
145C22×D11—41no—
146C22×D11—41no—
147C22×D11#10212yes—
148C2×C4×C11—21no—
149C2×C4×C11—21no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—81no—
159C2×C4×C11—81no—
160C2×C4×C11—81no—
161C22⋊D11—42no—
162C22⋊D11—42no—
163C22⋊D11—82no—
164C22⋊D11—82no—
165C2×Dic11—21no—
166C2×Dic11—21no—
167C2×Dic11—22no—
168C2×Dic11—21no—
169C2×Dic11—41no—
170C2×Dic11—42no—
171C2×Dic11—41no—
172C2×Dic11—41no—
173C2×Dic11—41no—
174C2×Dic11—81no—
175C2×Dic11—81no—
176C2×Dic11—81no—
177C2×Dic11—81no—
178C2×Dic11#9911yescharacteristic
179C2×Dic11#9911yescharacteristic
180C2×Dic11#10212yes—
181D44—82no—
182D44—84no—
183C4×D11—81no—
184C4×D11—81no—
185C4×D11—84no—
186C8×C11—81no—
187C11⋊C8—81no—
188C2×#121—111no—
189C2×#121—221no—
190C2×C4×D4—111no—
191#431—221no—
192C2×#99—221no—
193#398—111no—
194#397C2×D1111yescharacteristic
195#394—111no—
196#392—111no—
197#388—221no—
198#386—221no—
199#386—221no—
200#380—221no—
201C2×#95—111no—
202#342—111no—
203#342C2×D1111yescharacteristic
204#323—111no—
205#323—221no—
206#323C2×D1111yescharacteristic
207C22×C11—21no—
208C22×C11—21no—
209C22×C11—21no—
210C22×C11—21no—
211C22×C11—41no—
212C22×C11—41no—
213C22×C11—41no—
214C22×C11—41no—
215C22×C11—81no—
216C22×C11C2×#9911yescharacteristic
217C22×C11C2×#10211yescharacteristic
218C22×C11#42111yescharacteristic
219C2×D11—22no—
220C2×D11—42no—
221C2×D11—41no—
222C2×D11—41no—
223C2×D11—42no—
224C2×D11—81no—
225C2×D11—81no—
226C2×D11—81no—
227C2×D11—81no—
228C2×D11—81no—
229C2×D11—81no—
230C2×D11—81no—
231C4×C11—41no—
232C4×C11—41no—
233C4×C11—81no—
234C4×C11—81no—
235C4×C11—161no—
236Dic11—21no—
237Dic11—21no—
238Dic11—22no—
239Dic11—42no—
240Dic11—41no—
241Dic11—161no—
242C22×D4—111no—
243C22×D4—111no—
244C22×D4—221no—
245C22×D4—221no—
246C23×C4—111no—
247C23×C4—111no—
248C23×C4—221no—
249#121—442no—
250#121—442no—
251#121—441no—
252#121—441no—
253C4×D4—441no—
254C4×D4—441no—
255C2×C4⋊C4—111no—
256C2×C4⋊C4—221no—
257C2×C4⋊C4—441no—
258C2×C4⋊C4C4×D1111yescharacteristic
259C2×C22⋊C4—21no—
260C2×C22⋊C4—21no—
261C2×C22⋊C4—111no—
262C2×C22⋊C4—221no—
263C2×C22⋊C4—221no—
264C2×C22⋊C4—221no—
265C2×C22⋊C4—221no—
266C2×C22⋊C4—221no—
267C2×C22⋊C4C22×D1111yescharacteristic
268C2×C42—111no—
269C4⋊C8—441no—
270#99—442no—
271C22⋊C8—21no—
272C22⋊C8—221no—
273C4×C8—441no—
274#95—21no—
275#95—111no—
276#95—221no—
277#95—221no—
278#95—441no—
279#95C4×D1111yescharacteristic
280C2×C11—21no—
281C2×C11—21no—
282C2×C11—41no—
283C2×C11—41no—
284C2×C11#151911yescharacteristic
285C2×C11#212111yescharacteristic
286C2×C11#212611yescharacteristic
287D11—42no—
288D11—161no—
289C24—111no—
290C24—221no—
291C24D4×D1111yescharacteristic
292C2×D4—112no—
293C2×D4—112no—
294C2×D4—441no—
295C2×D4—442no—
296C2×D4—442no—
297C2×D4—442no—
298C2×D4—441no—
299C2×D4—441no—
300C2×D4—442no—
301C2×D4—441no—
302C2×D4—441no—
303C2×D4—881no—
304C2×D4—881no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—41no—
308C22×C4—111no—
309C22×C4—111no—
310C22×C4—111no—
311C22×C4—221no—
312C22×C4—221no—
313C22×C4—221no—
314C22×C4—221no—
315C22×C4—221no—
316C22×C4—442no—
317C22×C4—442no—
318C22×C4—441no—
319C22×C4—881no—
320C22×C4—881no—
321C22×C4—881no—
322C22×C4C2×C4×D1111yescharacteristic
323C22×C4D4×D1111yescharacteristic
324C2×C8—41no—
325C2×C8—441no—
326C4⋊C4—41no—
327C4⋊C4—441no—
328C4⋊C4—442no—
329C4⋊C4—882no—
330C22⋊C4—41no—
331C22⋊C4—41no—
332C22⋊C4—41no—
333C22⋊C4—41no—
334C22⋊C4—41no—
335C22⋊C4—441no—
336C22⋊C4—442no—
337C22⋊C4—441no—
338C22⋊C4—441no—
339C22⋊C4—442no—
340C22⋊C4—441no—
341C22⋊C4—441no—
342C22⋊C4—881no—
343C42—221no—
344C42—221no—
345C11#1187611yescharacteristic, complemented, Sylow
346C23—21no—
347C23—21no—
348C23—41no—
349C23—41no—
350C23—112no—
351C23—221no—
352C23—221no—
353C23—441no—
354C23—441no—
355C23—441no—
356C23—441no—
357C23—441no—
358C23—441no—
359C23—441no—
360C23—441no—
361C23—441no—
362C23C22⋊C4×D1111yescharacteristic
363C23D8×D1111yescharacteristic
364C23SD16×D1111yescharacteristic
365D4—442no—
366D4—442no—
367D4—882no—
368D4—884no—
369D4—882no—
370D4—882no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—81no—
382C2×C4—81no—
383C2×C4—81no—
384C2×C4—111no—
385C2×C4—111no—
386C2×C4—112no—
387C2×C4—221no—
388C2×C4—221no—
389C2×C4—222no—
390C2×C4—221no—
391C2×C4—441no—
392C2×C4—442no—
393C2×C4—441no—
394C2×C4—441no—
395C2×C4—441no—
396C2×C4—881no—
397C2×C4—881no—
398C2×C4—884no—
399C2×C4—881no—
400C2×C4—881no—
401C2×C4—881no—
402C2×C4—881no—
403C8—81no—
404C8—881no—
405C22—21no—
406C22—21no—
407C22—21no—
408C22—21no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—81no—
414C22—222no—
415C22—442no—
416C22—442no—
417C22—441no—
418C22—441no—
419C22—881no—
420C22—881no—
421C22—881no—
422C22—881no—
423C22—881no—
424C22—881no—
425C22—881no—
426C22D11×#9911yescharacteristic
427C22D11×#10211yescharacteristic
428C22#1062243411yescharacteristic
429C4—41no—
430C4—41no—
431C4—81no—
432C4—81no—
433C4—161no—
434C4—222no—
435C4—221no—
436C4—221no—
437C4—442no—
438C4—441no—
439C4—1761no—
440C2—21no—
441C2—21no—
442C2—41no—
443C2—41no—
444C2—442no—
445C2—1761no—
446C2#1306718211yescharacteristic
447C2#1307026111yescharacteristic
448C2#1307028011yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1344C2
socleC22×C11C2×#99
prime radical#13073573C2
cosocleC2×C11×C22⋊C4C23
hypercenter#1344D11
hypocenterC11#11876
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1344

Complements

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

NH ≅ G/Ntype
2. #13068603C2semidirect
3. #13066935C2semidirect
4. #13066616C2semidirect
5. #13066614C2semidirect
6. #13066612C2semidirect
7. C11×#1344C2semidirect
8. C2×#66948C4semidirect
12. #10622593C4semidirect
18. #10622285C4semidirect
21. D11×#95C4semidirect
126. #1344D11semidirect
345. C11#11876semidirect

Maximal subgroups

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

subgroupindex
#130735732
#130686032
#130669352
#130666162
#130666142
#130666122
C11×#13442
#1187611