Finite Group Databasebeta

← #14664649

Subgroups — #14664649

Order 2816.

620 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 83 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#13073547C211yesmaximal, characteristic
2C2×#10622163C211yesmaximal, characteristic, complemented
3#13066639C212yesmaximal, complemented
4#13066612C212yesmaximal, complemented
5C11×#1819C211yesmaximal, characteristic, complemented
6C22×C11×C22⋊C4C2211yescharacteristic
7C2×#67006—21no—
8C2×#66983C411yescharacteristic, complemented
9C2×#66982—21no—
10C11×#379—21no—
11C4×C22⋊Dic11C411yescharacteristic, complemented
12C2×C22⋊(C11⋊C8)—21no—
13#10622573C411yescharacteristic, complemented
14#10622573C2211yescharacteristic
15#10622570—21no—
16#10622570—21no—
17#10622562C411yescharacteristic, complemented
18#10622562C2211yescharacteristic
19C11×#342—21no—
20C11×#342C2212yes—
21#10622163—21no—
22#10622163C2212yes—
23C25×C11D411yescharacteristic
24C23×C4×C11C2×C411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C22×C22⋊D11—21no—
27C22×C22⋊D11—21no—
28C22×C22⋊D11—21no—
29C22×D44C2×C411yescharacteristic
30C2×C11×C22⋊C4—22no—
31C2×C11×C22⋊C4—41no—
32C2×C11×C22⋊C4—41no—
33C2×C11×C22⋊C4—41no—
34C2×C11×C22⋊C4—41no—
35C2×C11×C22⋊C4C2×C411yescharacteristic
36C2×C11×C22⋊C4D411yescharacteristic
37C2×C11×C22⋊C4D411yescharacteristic
38C2×C11×C22⋊C4C2311yescharacteristic
39#67006—44no—
40C2×C22⋊Dic11—21no—
41C2×C22⋊Dic11—21no—
42C2×C22⋊Dic11—21no—
43#66983—41no—
44#66983—41no—
45#66982—44no—
46C2×(C2×D11)⋊C4—21no—
47C2×(C2×D11)⋊C4—21no—
48C2×(C2×D11)⋊C4—21no—
49C2×C4⋊Dic11C2×C411yescharacteristic
50C2×Dic11⋊C4—21no—
51C2×Dic11⋊C4—21no—
52C2×C4×Dic11—21no—
53C22×C11⋊C8—41no—
54C11⋊#95C2×C411yescharacteristic
55C11⋊#95C2×C411yescharacteristic
56C22⋊(C11⋊C8)—22no—
57C22⋊(C11⋊C8)—41no—
58#11843—111nomaximal, Sylow
59C24×C11—21no—
60C24×C11—21no—
61C24×C11—22no—
62C24×C11—41no—
63C24×C11—42no—
64C24×C11—81no—
65C24×C11C22⋊C411yescharacteristic
66C24×C11C22⋊C411yescharacteristic
67C24×C11C2×D411yescharacteristic
68C23×D11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11—21no—
73C22×C4×C11—42no—
74C22×C4×C11—42no—
75C22×C4×C11—81no—
76C22×C4×C11C22⋊C411yescharacteristic
77C22×C4×C11C22⋊C411yescharacteristic
78C22×C4×C11C22×C411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C2×C22⋊D11—42no—
81C2×C22⋊D11—42no—
82C2×C22⋊D11—42no—
83C2×C22⋊D11—42no—
84C2×C22⋊D11—42no—
85C2×C22⋊D11—41no—
86C2×C22⋊D11—41no—
87C2×C22⋊D11—42no—
88C2×C22⋊D11—81no—
89C2×C22⋊D11—81no—
90C22×Dic11—21no—
91C22×Dic11—21no—
92C22×Dic11—21no—
93C2×D44—41no—
94C2×D44—81no—
95C11×C22⋊C4—41no—
96C11×C22⋊C4—41no—
97C11×C22⋊C4—41no—
98C11×C22⋊C4—41no—
99C11×C22⋊C4—42no—
100C11×C22⋊C4—42no—
101C11×C22⋊C4—82no—
102C11×C22⋊C4—82no—
103C22⋊Dic11—24no—
104C22⋊Dic11—42no—
105C22⋊Dic11—42no—
106(C2×D11)⋊C4—42no—
107(C2×D11)⋊C4—42no—
108(C2×D11)⋊C4—42no—
109C4⋊Dic11—41no—
110Dic11⋊C4—42no—
111Dic11⋊C4—42no—
112C4×Dic11—81no—
113C2×C11⋊C8—42no—
114C2×C11⋊C8—82no—
115#2539—111no—
116#1819D1111yescharacteristic, complemented
117C2×#323—111no—
118#1352—112no—
119#1343—112no—
120C23×C11—22no—
121C23×C11—21no—
122C23×C11—21no—
123C23×C11—21no—
124C23×C11—21no—
125C23×C11—21no—
126C23×C11—21no—
127C23×C11—21no—
128C23×C11—41no—
129C23×C11—42no—
130C23×C11—42no—
131C23×C11—41no—
132C23×C11—41no—
133C23×C11—41no—
134C23×C11—41no—
135C23×C11—42no—
136C23×C11—42no—
137C23×C11—81no—
138C23×C11—81no—
139C23×C11—84no—
140C23×C11—84no—
141C23×C11#9911yescharacteristic
142C23×C11#9911yescharacteristic
143C23×C11C2×C22⋊C411yescharacteristic
144C23×C11#13512yes—
145C22×D11—41no—
146C22×D11—41no—
147C22×D11—41no—
148C22×D11—41no—
149C22×D11—41no—
150C22×D11—41no—
151C22×D11—41no—
152C2×C4×C11—21no—
153C2×C4×C11—21no—
154C2×C4×C11—21no—
155C2×C4×C11—21no—
156C2×C4×C11—42no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—81no—
162C2×C4×C11—81no—
163C2×C4×C11—81no—
164C2×C4×C11—82no—
165C2×C4×C11—82no—
166C2×C4×C11—82no—
167C22⋊D11—84no—
168C22⋊D11—84no—
169C22⋊D11—82no—
170C22⋊D11—82no—
171C2×Dic11—22no—
172C2×Dic11—22no—
173C2×Dic11—41no—
174C2×Dic11—41no—
175C2×Dic11—41no—
176C2×Dic11—41no—
177C2×Dic11—41no—
178C2×Dic11—41no—
179C2×Dic11—41no—
180D44—82no—
181C11⋊C8—82no—
182C2×#123—221no—
183C2×#121—111no—
184C2×#120—221no—
185C22×C22⋊C4C2×D1111yescharacteristic
186C2×C22⋊C8—221no—
187#399—111no—
188#399—111no—
189#392—111no—
190#392—111no—
191#390—221no—
192#390—221no—
193#379—21no—
194C4×C22⋊C4—111no—
195#342—21no—
196#342C2×D1112yes—
197#323—112no—
198#323—221no—
199C22×C11—21no—
200C22×C11—21no—
201C22×C11—21no—
202C22×C11—21no—
203C22×C11—21no—
204C22×C11—21no—
205C22×C11—22no—
206C22×C11—21no—
207C22×C11—42no—
208C22×C11—42no—
209C22×C11—42no—
210C22×C11—42no—
211C22×C11—41no—
212C22×C11—41no—
213C22×C11—41no—
214C22×C11—41no—
215C22×C11—41no—
216C22×C11—81no—
217C22×C11—84no—
218C22×C11—81no—
219C22×C11—84no—
220C22×C11#35312yes—
221C22×C11C2×#9911yescharacteristic
222C22×C11#41611yescharacteristic
223C22×C11#42111yescharacteristic
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—41no—
234C4×C11—41no—
235C4×C11—162no—
236Dic11—42no—
237Dic11—42no—
238Dic11—81no—
239C25C22⋊D1111yescharacteristic
240C22×D4—111no—
241C22×D4—221no—
242C22×D4—221no—
243C22×D4—221no—
244C23×C4C4×D1111yescharacteristic
245C23×C4D4411yescharacteristic
246C22×C8—441no—
247#123—444no—
248#121—441no—
249#121—441no—
250#120—444no—
251C2×C4⋊C4—111no—
252C2×C4⋊C4—221no—
253C2×C4⋊C4—221no—
254C2×C22⋊C4—22no—
255C2×C22⋊C4—41no—
256C2×C22⋊C4—41no—
257C2×C22⋊C4—41no—
258C2×C22⋊C4—41no—
259C2×C22⋊C4—221no—
260C2×C22⋊C4—221no—
261C2×C22⋊C4—221no—
262C2×C22⋊C4—221no—
263C2×C22⋊C4—221no—
264C2×C22⋊C4—221no—
265C2×C22⋊C4C4×D1111yescharacteristic
266C2×C22⋊C4D4411yescharacteristic
267C2×C22⋊C4C22⋊D1111yescharacteristic
268C2×C22⋊C4C22×D1111yescharacteristic
269C2×C42—221no—
270C22⋊C8—222no—
271C22⋊C8—441no—
272#95—111no—
273#95—111no—
274C2×C11—21no—
275C2×C11—21no—
276C2×C11—22no—
277C2×C11—42no—
278C2×C11—41no—
279C2×C11—81no—
280C2×C11#151611yescharacteristic
281C2×C11#212111yescharacteristic
282C2×C11C2×#35311yescharacteristic
283D11—161no—
284C24—21no—
285C24—21no—
286C24—22no—
287C24—41no—
288C24—42no—
289C24—81no—
290C24—221no—
291C24(C2×D11)⋊C411yescharacteristic
292C24(C2×D11)⋊C411yescharacteristic
293C24C2×C22⋊D1111yescharacteristic
294C2×D4—441no—
295C2×D4—442no—
296C2×D4—442no—
297C2×D4—442no—
298C2×D4—442no—
299C2×D4—442no—
300C2×D4—441no—
301C2×D4—441no—
302C2×D4—442no—
303C2×D4—881no—
304C2×D4—881no—
305C2×D4—881no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—42no—
311C22×C4—42no—
312C22×C4—81no—
313C22×C4—221no—
314C22×C4—221no—
315C22×C4—221no—
316C22×C4(C2×D11)⋊C411yescharacteristic
317C22×C4(C2×D11)⋊C411yescharacteristic
318C22×C4C2×C4×D1111yescharacteristic
319C22×C4C2×D4411yescharacteristic
320C2×C8—442no—
321C2×C8—882no—
322C4⋊C4—441no—
323C4⋊C4—442no—
324C4⋊C4—442no—
325C22⋊C4—41no—
326C22⋊C4—41no—
327C22⋊C4—41no—
328C22⋊C4—41no—
329C22⋊C4—42no—
330C22⋊C4—42no—
331C22⋊C4—82no—
332C22⋊C4—82no—
333C22⋊C4—224no—
334C22⋊C4—442no—
335C22⋊C4—442no—
336C22⋊C4—442no—
337C22⋊C4—442no—
338C22⋊C4—442no—
339C42—881no—
340C11#1184311yescharacteristic, complemented, Sylow
341C23—21no—
342C23—21no—
343C23—21no—
344C23—22no—
345C23—21no—
346C23—21no—
347C23—21no—
348C23—21no—
349C23—41no—
350C23—42no—
351C23—42no—
352C23—41no—
353C23—41no—
354C23—41no—
355C23—41no—
356C23—42no—
357C23—42no—
358C23—81no—
359C23—81no—
360C23—84no—
361C23—84no—
362C23—441no—
363C23—441no—
364C23—441no—
365C23—441no—
366C23—441no—
367C23—441no—
368C23—441no—
369C23#6687011yescharacteristic
370C23#6687011yescharacteristic
371C23C2×(C2×D11)⋊C411yescharacteristic
372C23#6700312yes—
373D4—882no—
374D4—884no—
375D4—884no—
376D4—882no—
377D4—882no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—42no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—81no—
388C2×C4—81no—
389C2×C4—81no—
390C2×C4—82no—
391C2×C4—82no—
392C2×C4—82no—
393C2×C4—222no—
394C2×C4—222no—
395C2×C4—441no—
396C2×C4—441no—
397C2×C4—441no—
398C2×C4—441no—
399C2×C4—441no—
400C2×C4—441no—
401C2×C4—441no—
402C8—882no—
403C22—21no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—22no—
408C22—21no—
409C22—21no—
410C22—21no—
411C22—42no—
412C22—42no—
413C22—42no—
414C22—42no—
415C22—41no—
416C22—41no—
417C22—41no—
418C22—41no—
419C22—41no—
420C22—81no—
421C22—84no—
422C22—81no—
423C22—84no—
424C22—881no—
425C22—881no—
426C22—881no—
427C22—881no—
428C22—881no—
429C22—881no—
430C22—881no—
431C22#1062211212yes—
432C22C2×#6687011yescharacteristic
433C22#1062261511yescharacteristic
434C22#1062261811yescharacteristic
435C4—41no—
436C4—41no—
437C4—41no—
438C4—41no—
439C4—162no—
440C4—442no—
441C4—442no—
442C4—881no—
443C2—21no—
444C2—21no—
445C2—22no—
446C2—42no—
447C2—41no—
448C2—81no—
449C2—1761no—
450C2#1306717011yescharacteristic
451C2#1307026011yescharacteristic
452C2C2×#1062211211yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1819C2
socleC22×C11C2×#99
prime radical#13073547C2
cosocleC2×C11×C22⋊C4C23
hypercenter#1819D11
hypocenterC11#11843
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C24 ◁ C22×C22⋊C4 ◁ #1819

Complements

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

NH ≅ G/Ntype
2. C2×#10622163C2semidirect
3. #13066639C2semidirect
4. #13066612C2semidirect
5. C11×#1819C2semidirect
8. C2×#66983C4semidirect
11. C4×C22⋊Dic11C4semidirect
13. #10622573C4semidirect
17. #10622562C4semidirect
116. #1819D11semidirect
340. C11#11843semidirect

Maximal subgroups

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

subgroupindex
#130735472
C2×#106221632
#130666392
#130666122
C11×#18192
#1184311