Finite Group Databasebeta

← #14649850

Subgroups — #14649850

Order 2816.

578 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 578 conjugacy classes of subgroups — too many to draw. Only its 105 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#13074361C211yesmaximal, characteristic
2#13071218C211yesmaximal, characteristic, complemented
3#13067185C211yesmaximal, characteristic
4#13067183C211yesmaximal, characteristic
5C2×#10622107C211yesmaximal, characteristic, complemented
6#13066483C211yesmaximal, characteristic, complemented
7C11×#1289C211yesmaximal, characteristic, complemented
8C2×#66983C2211yescharacteristic
9C22×Dic11⋊C4C2211yescharacteristic
10C2×#66939—21no—
11C2×C11×C22⋊C8C2211yescharacteristic
12C11×#380C2211yescharacteristic
13C11×#380C2211yescharacteristic
14#10622825C2211yescharacteristic
15C2×C22⋊(C11⋊C8)C2211yescharacteristic
16#10622607—22no—
17#10622591—22no—
18#10622571—21no—
19#10622556—21no—
20C22⋊C4×Dic11—21no—
21#10622285C412yescomplemented
22#10622274C412yescomplemented
23#10622268—22no—
24#10622108—22no—
25#10622107—22no—
26#10622089—22no—
27C23×C4×C11C2311yescharacteristic
28C22×C22⋊D11—21no—
29C23×Dic11D411yescharacteristic
30C23×Dic11D411yescharacteristic
31C22×D44C2×C411yescharacteristic
32C22×C8×C11—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C22⋊C4—21no—
36C2×C11×C22⋊C4—21no—
37C2×C22⋊Dic11—21no—
38#66983—21no—
39#66983—21no—
40#66983—21no—
41#66983—21no—
42C2×(C2×D11)⋊C4—21no—
43C2×(C2×D11)⋊C4—22no—
44C2×(C2×D11)⋊C4—22no—
45C2×C4⋊Dic11—22no—
46C2×C4⋊Dic11—21no—
47C2×C4⋊Dic11C2×C411yescharacteristic
48C2×Dic11⋊C4—21no—
49C2×Dic11⋊C4—21no—
50C2×Dic11⋊C4—21no—
51C2×Dic11⋊C4—21no—
52C2×Dic11⋊C4C2×C412yes—
53C2×Dic11⋊C4D412yes—
54C2×C4×Dic11—22no—
55C22×C11⋊C8—21no—
56#66939—42no—
57#66939—42no—
58C11×C22⋊C8—21no—
59C11×C22⋊C8—21no—
60C11×#95C2×C412yes—
61C11×#95D412yes—
62C11⋊#95—22no—
63C11⋊#95—24no—
64C11⋊#95—22no—
65C11⋊#95D412yes—
66C22⋊(C11⋊C8)—21no—
67C22⋊(C11⋊C8)—21no—
68#9206—111nomaximal, Sylow
69C24×C11C2×D411yescharacteristic
70C23×D11—21no—
71C22×C4×C11—22no—
72C22×C4×C11—22no—
73C22×C4×C11—81no—
74C22×C4×C11C22×C411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11#4111yescharacteristic
79C22×C4×C11#4111yescharacteristic
80C2×C22⋊D11—41no—
81C2×C22⋊D11—41no—
82C2×C22⋊D11—41no—
83C2×C22⋊D11—41no—
84C2×C22⋊D11—41no—
85C2×C22⋊D11—41no—
86C22×Dic11—21no—
87C22×Dic11—21no—
88C22×Dic11—21no—
89C22×Dic11—22no—
90C22×Dic11—21no—
91C22×Dic11—21no—
92C22×Dic11—21no—
93C22×Dic11—21no—
94C22×Dic11—21no—
95C22×Dic11—21no—
96C22×Dic11—81no—
97C22×Dic11C22⋊C412yes—
98C22×Dic11C22⋊C412yes—
99C2×D44—21no—
100C2×D44—21no—
101C2×D44—81no—
102C2×C8×C11—41no—
103C2×C8×C11—81no—
104C11×C4⋊C4—81no—
105C11×C4⋊C4—81no—
106C11×C22⋊C4—41no—
107C11×C22⋊C4—41no—
108C11×C22⋊C4—41no—
109C11×C22⋊C4—41no—
110C22⋊Dic11—41no—
111C22⋊Dic11—41no—
112(C2×D11)⋊C4—44no—
113(C2×D11)⋊C4—41no—
114(C2×D11)⋊C4—41no—
115(C2×D11)⋊C4—82no—
116C4⋊Dic11—21no—
117C4⋊Dic11—21no—
118C4⋊Dic11—44no—
119C4⋊Dic11—81no—
120Dic11⋊C4—22no—
121Dic11⋊C4—22no—
122Dic11⋊C4—22no—
123Dic11⋊C4—22no—
124C4×Dic11—82no—
125C2×C11⋊C8—41no—
126C2×C11⋊C8—81no—
127#2618—111no—
128#2313—111no—
129#1519—111no—
130#1519—111no—
131C2×#324—111no—
132#1289—111no—
133#1289D1111yescharacteristic, complemented
134C23×C11—41no—
135C23×C11—41no—
136C23×C11C2×C22⋊C411yescharacteristic
137C23×C11#12011yescharacteristic
138C23×C11#12311yescharacteristic
139C23×C11#13511yescharacteristic
140C23×C11#13511yescharacteristic
141C23×C11AGL(1,ℤ/8)11yescharacteristic
142C23×C11AGL(1,ℤ/8)11yescharacteristic
143C22×D11—42no—
144C22×D11—42no—
145C22×D11—41no—
146C22×D11—41no—
147C22×D11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11—42no—
155C2×C4×C11—42no—
156C2×C4×C11—42no—
157C2×C4×C11—42no—
158C2×C4×C11—42no—
159C2×C4×C11—42no—
160C2×C4×C11C4×D411yescharacteristic
161C2×C4×C11C4×D411yescharacteristic
162C2×C4×C11#12111yescharacteristic
163C2×C4×C11#12111yescharacteristic
164C22⋊D11—81no—
165C22⋊D11—81no—
166C22⋊D11—81no—
167C22⋊D11—81no—
168C2×Dic11—22no—
169C2×Dic11—22no—
170C2×Dic11—22no—
171C2×Dic11—22no—
172C2×Dic11—42no—
173C2×Dic11—41no—
174C2×Dic11—41no—
175C2×Dic11—41no—
176C2×Dic11—41no—
177C2×Dic11—42no—
178C2×Dic11—42no—
179C2×Dic11—42no—
180C2×Dic11—41no—
181C2×Dic11—41no—
182C2×Dic11—41no—
183C2×Dic11—42no—
184C2×Dic11—81no—
185D44—81no—
186D44—81no—
187C8×C11—81no—
188C11⋊C8—81no—
189C2×#123—221no—
190C2×#121—111no—
191C22×C4⋊C4—111no—
192C2×C22⋊C8—111no—
193C2×C22⋊C8C2×D1111yescharacteristic
194#398—112no—
195#396—222no—
196#394—112no—
197#387—222no—
198#387—222no—
199#386—221no—
200#381—221no—
201#380—111no—
202#380C2×D1111yescharacteristic
203#380C2×D1111yescharacteristic
204C4×C22⋊C4—221no—
205#327—222no—
206#327—222no—
207#324—222no—
208C22×C11—21no—
209C22×C11—21no—
210C22×C11—21no—
211C22×C11—21no—
212C22×C11—21no—
213C22×C11—21no—
214C22×C11—41no—
215C22×C11—41no—
216C22×C11—41no—
217C22×C11—41no—
218C22×C11#38611yescharacteristic
219C22×C11#41611yescharacteristic
220C22×C11#41811yescharacteristic
221C22×C11#44911yescharacteristic
222C22×C11#44911yescharacteristic
223C22×C11#48211yescharacteristic
224C22×C11#48211yescharacteristic
225C2×D11—82no—
226C2×D11—82no—
227C2×D11—81no—
228C2×D11—81no—
229C2×D11—81no—
230C4×C11—21no—
231C4×C11—21no—
232C4×C11—21no—
233C4×C11—21no—
234C4×C11—82no—
235C4×C11—82no—
236Dic11—42no—
237Dic11—42no—
238Dic11—82no—
239Dic11—81no—
240C22×D4—111no—
241C22×D4—221no—
242C23×C4—111no—
243C23×C4—111no—
244C23×C4C22×D1111yescharacteristic
245C22×C8—21no—
246C22×C8—221no—
247#123—442no—
248#123—442no—
249#121—221no—
250#121—221no—
251#121—221no—
252#121—221no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—112no—
256C2×C4⋊C4—112no—
257C2×C4⋊C4—111no—
258C2×C4⋊C4—221no—
259C2×C4⋊C4—221no—
260C2×C4⋊C4—221no—
261C2×C4⋊C4—221no—
262C2×C4⋊C4—222no—
263C2×C4⋊C4—221no—
264C2×C22⋊C4—21no—
265C2×C22⋊C4—21no—
266C2×C22⋊C4—222no—
267C2×C22⋊C4—221no—
268C2×C22⋊C4—221no—
269C2×C22⋊C4—222no—
270C2×C42—222no—
271C22⋊C8—21no—
272C22⋊C8—21no—
273C22⋊C8—221no—
274C22⋊C8—221no—
275#95—112no—
276#95—222no—
277#95—222no—
278#95—224no—
279#95C4×D1112yes—
280#95D4412yes—
281C2×C11—21no—
282C2×C11—21no—
283C2×C11—21no—
284C2×C11—21no—
285C2×C11—21no—
286C2×C11—21no—
287C2×C11#187511yescharacteristic
288C2×C11#191211yescharacteristic
289C2×C11#191311yescharacteristic
290D11—161no—
291C24—221no—
292C24D4×D1111yescharacteristic
293C2×D4—221no—
294C2×D4—221no—
295C2×D4—441no—
296C2×D4—441no—
297C2×D4—441no—
298C2×D4—441no—
299C2×D4—441no—
300C2×D4—441no—
301C2×D4—881no—
302C22×C4—22no—
303C22×C4—22no—
304C22×C4—81no—
305C22×C4—112no—
306C22×C4—112no—
307C22×C4—221no—
308C22×C4—221no—
309C22×C4—221no—
310C22×C4—221no—
311C22×C4—221no—
312C22×C4—221no—
313C22×C4—221no—
314C22×C4—221no—
315C22×C4—221no—
316C22×C4—222no—
317C22×C4—881no—
318C22×C4C2×C4×D1111yescharacteristic
319C22×C4C2×D4411yescharacteristic
320C22×C4#433911yescharacteristic
321C22×C4D4×D1111yescharacteristic
322C22×C4D4×D1111yescharacteristic
323C22×C4#434311yescharacteristic
324C2×C8—41no—
325C2×C8—81no—
326C2×C8—441no—
327C2×C8—881no—
328C4⋊C4—81no—
329C4⋊C4—81no—
330C4⋊C4—222no—
331C4⋊C4—222no—
332C4⋊C4—222no—
333C4⋊C4—222no—
334C4⋊C4—221no—
335C4⋊C4—221no—
336C4⋊C4—444no—
337C4⋊C4—881no—
338C22⋊C4—41no—
339C22⋊C4—41no—
340C22⋊C4—41no—
341C22⋊C4—41no—
342C22⋊C4—444no—
343C22⋊C4—441no—
344C22⋊C4—441no—
345C22⋊C4—441no—
346C22⋊C4—441no—
347C22⋊C4—882no—
348C42—882no—
349C11#920611yescharacteristic, complemented, Sylow
350C23—41no—
351C23—41no—
352C23—442no—
353C23—442no—
354C23—441no—
355C23—441no—
356C23—441no—
357C23C22⋊C4×D1111yescharacteristic
358C23#6693511yescharacteristic
359C23#6694711yescharacteristic
360C23#6696411yescharacteristic
361C23#6696711yescharacteristic
362C23#6696911yescharacteristic
363C23#6697211yescharacteristic
364D4—881no—
365D4—881no—
366D4—881no—
367D4—881no—
368D4—881no—
369D4—881no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—222no—
383C2×C4—222no—
384C2×C4—222no—
385C2×C4—222no—
386C2×C4—442no—
387C2×C4—441no—
388C2×C4—441no—
389C2×C4—441no—
390C2×C4—441no—
391C2×C4—442no—
392C2×C4—442no—
393C2×C4—442no—
394C2×C4—441no—
395C2×C4—441no—
396C2×C4—441no—
397C2×C4—442no—
398C2×C4—881no—
399C2×C4C4×D4411yescharacteristic
400C2×C4#6693711yescharacteristic
401C2×C4#6694611yescharacteristic
402C2×C4#6694811yescharacteristic
403C8—81no—
404C8—881no—
405C22—21no—
406C22—21no—
407C22—21no—
408C22—21no—
409C22—21no—
410C22—21no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—41no—
415C22—882no—
416C22—882no—
417C22—881no—
418C22—881no—
419C22—881no—
420C22#1062227811yescharacteristic
421C22#1062238311yescharacteristic
422C22#1062239411yescharacteristic
423C22#1062241711yescharacteristic
424C22#1062242411yescharacteristic
425C22#1062247911yescharacteristic
426C22#1062249811yescharacteristic
427C4—21no—
428C4—21no—
429C4—21no—
430C4—21no—
431C4—82no—
432C4—82no—
433C4—442no—
434C4—442no—
435C4—882no—
436C4—881no—
437C2—21no—
438C2—21no—
439C2—21no—
440C2—21no—
441C2—21no—
442C2—21no—
443C2—1761no—
444C2#1306893711yescharacteristic
445C2#1306915211yescharacteristic
446C2#1306915711yescharacteristic
subgroupG/H
centerC22#10622278
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1289C2
socleC22×C11#386
prime radicalC2×#66983C22
cosocleC23×C4×C11C23
hypercenter#1289D11
hypocenterC11#9206
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1289

Complements

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

NH ≅ G/Ntype
2. #13071218C2semidirect
5. C2×#10622107C2semidirect
6. #13066483C2semidirect
7. C11×#1289C2semidirect
21. #10622285C4semidirect
22. #10622274C4semidirect
133. #1289D11semidirect
349. C11#9206semidirect

Maximal subgroups

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

subgroupindex
#130743612
#130712182
#130671852
#130671832
C2×#106221072
#130664832
C11×#12892
#920611