Finite Group Databasebeta

← #14657153

Subgroups — #14657153

Order 2816.

572 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073615C211yesmaximal, characteristic
2#13069422C211yesmaximal, characteristic
3#13069375C211yesmaximal, characteristic, complemented
4#13068621C211yesmaximal, characteristic, complemented
5C2×#10622123C211yesmaximal, characteristic
6#13066456C211yesmaximal, characteristic, complemented
7C2×C11×Q8⋊C8C211yesmaximal, characteristic, complemented
8C2×C4×Q8×C11C2211yescharacteristic
9C2×#67000—21no—
10C2×#66927C2211yescharacteristic
11C2×C11×C4⋊C8C2211yescharacteristic
12C2×C4×C8×C11C2211yescharacteristic
13C2×#66899—21no—
14C2×#66885—22no—
15C2×#66882—21no—
16#10622604—22no—
17#10622601—21no—
18#10622552—21no—
19#10622552—21no—
20#10622548C2211yescharacteristic
21C4×C4⋊Dic11C2211yescharacteristic
22C2×C4⋊(C11⋊C8)C2211yescharacteristic
23C11×Q8⋊C8—22no—
24#10622189—21no—
25#10622167—21no—
26#10622123—22no—
27C22×Q8×C11D411yescharacteristic
28C22×D44—21no—
29C22×D44—21no—
30C22×D44D412yes—
31C22×C8×C11—21no—
32C22×C8×C11—21no—
33C4×Q8×C11—21no—
34C4×Q8×C11—21no—
35C4×Q8×C11—21no—
36C4×Q8×C11—21no—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4D411yescharacteristic
39C2×C42×C11—21no—
40C2×C42×C11C2311yescharacteristic
41#67000—42no—
42#67000—42no—
43C2×(C2×D11)⋊C4—22no—
44C2×(C2×D11)⋊C4—22no—
45C2×(C2×D11)⋊C4—22no—
46C2×(C2×D11)⋊C4—22no—
47C2×C4⋊Dic11—21no—
48C2×C4⋊Dic11—21no—
49C2×C4⋊Dic11—21no—
50C2×C4⋊Dic11D411yescharacteristic
51C2×C4⋊Dic11D411yescharacteristic
52C2×C4×Dic11—21no—
53C22×C11⋊C8—21no—
54#66927—21no—
55#66927—21no—
56#66927—21no—
57#66927—21no—
58C11×C4⋊C8—21no—
59C11×C4⋊C8D412yes—
60C4×C8×C11—21no—
61C4×C8×C11—21no—
62#66899—42no—
63C11⋊#95—21no—
64#66885—44no—
65#66882—42no—
66C4⋊(C11⋊C8)—21no—
67C4⋊(C11⋊C8)—21no—
68#10411—111nomaximal, Sylow
69C23×D11—22no—
70C2×Q8×C11—21no—
71C2×Q8×C11—21no—
72C2×Q8×C11—21no—
73C2×Q8×C11—21no—
74C2×Q8×C11—21no—
75C2×Q8×C11D812yes—
76C22×C4×C11—21no—
77C22×C4×C11—21no—
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×Dic11—21no—
82C22×Dic11—21no—
83C22×Dic11—41no—
84C2×D44—22no—
85C2×D44—22no—
86C2×D44—42no—
87C2×D44—42no—
88C2×D44—41no—
89C2×D44—41no—
90C2×D44—41no—
91C2×D44—41no—
92C2×D44—41no—
93C2×D44—41no—
94C2×D44—41no—
95C2×D44—41no—
96C2×D44—41no—
97C2×D44—41no—
98C2×D44—41no—
99C2×D44—41no—
100C2×C8×C11—22no—
101C2×C8×C11—22no—
102C2×C8×C11—41no—
103C2×C8×C11—41no—
104C2×C8×C11—41no—
105C2×C8×C11—41no—
106C11×C4⋊C4—21no—
107C11×C4⋊C4—21no—
108C11×C4⋊C4—41no—
109C11×C4⋊C4—41no—
110C42×C11—41no—
111C42×C11—41no—
112C42×C11C2×D411yescharacteristic
113C42×C11#4111yescharacteristic
114C42×C11#4111yescharacteristic
115C42×C11#4111yescharacteristic
116(C2×D11)⋊C4—44no—
117(C2×D11)⋊C4—44no—
118(C2×D11)⋊C4—82no—
119(C2×D11)⋊C4—82no—
120C4⋊Dic11—21no—
121C4⋊Dic11—21no—
122C4⋊Dic11—21no—
123C4⋊Dic11—21no—
124C4⋊Dic11—42no—
125C4⋊Dic11—41no—
126C4⋊Dic11—41no—
127C4⋊Dic11—41no—
128C4⋊Dic11—41no—
129C4×Dic11—41no—
130C4×Dic11—41no—
131C2×C11⋊C8—41no—
132C2×C11⋊C8—41no—
133C2×C11⋊C8—41no—
134#2548—111no—
135#1957—111no—
136#1947—111no—
137#1803—111no—
138C2×#331—111no—
139C2×Q8⋊C8D1111yescharacteristic, complemented
140#1279—111no—
141C23×C11#12011yescharacteristic
142C22×D11—42no—
143C22×D11—42no—
144C22×D11—42no—
145C22×D11—42no—
146C22×D11—42no—
147C22×D11—42no—
148C22×D11—42no—
149Q8×C11—22no—
150Q8×C11—22no—
151Q8×C11—41no—
152Q8×C11—41no—
153C2×C4×C11—21no—
154C2×C4×C11—21no—
155C2×C4×C11—22no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11#12111yescharacteristic
162C2×C4×C11#12111yescharacteristic
163C2×C4×C11#12111yescharacteristic
164C2×C4×C11#12311yescharacteristic
165C2×C4×C11#12311yescharacteristic
166C2×C4×C11#12411yescharacteristic
167C2×C4×C11C2×D811yescharacteristic
168C2×C4×C11#13511yescharacteristic
169C2×C4×C11#13511yescharacteristic
170C2×C4×C11#13511yescharacteristic
171C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
172C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
173C2×C4×C11#13711yescharacteristic
174C2×C4×C11#13711yescharacteristic
175C2×Dic11—41no—
176C2×Dic11—41no—
177C2×Dic11—41no—
178C2×Dic11—41no—
179C2×Dic11—41no—
180C2×Dic11—41no—
181C2×Dic11—81no—
182C2×Dic11—81no—
183C2×Dic11—81no—
184D44—44no—
185D44—82no—
186D44—81no—
187D44—81no—
188D44—81no—
189D44—81no—
190D44—81no—
191D44—81no—
192D44—81no—
193D44—81no—
194C8×C11—42no—
195C8×C11—42no—
196C11⋊C8—81no—
197C2×#127—111no—
198C2×#124—221no—
199C2×C4×Q8C2×D1111yescharacteristic
200C2×#107—221no—
201C2×C4⋊C8—111no—
202C2×C4⋊C8C2×D1111yescharacteristic
203C2×#103—221no—
204C2×#102—222no—
205C2×C4×C8C2×D1111yescharacteristic
206#394—222no—
207#390—221no—
208#390—221no—
209#390—221no—
210#384—111no—
211C4×C4⋊C4—111no—
212#340—221no—
213#340—221no—
214#331—222no—
215Q8⋊C8—22no—
216C22×C11#39411yescharacteristic
217C22×C11#44711yescharacteristic
218C22×C11#44911yescharacteristic
219C22×C11#45211yescharacteristic
220C22×C11#45211yescharacteristic
221C22×C11#45311yescharacteristic
222C22×C11#45511yescharacteristic
223C2×D11—82no—
224C2×D11—82no—
225C2×D11—82no—
226C2×D11—82no—
227C2×D11—82no—
228C2×D11—82no—
229C2×D11—82no—
230C4×C11—21no—
231C4×C11—21no—
232C4×C11—42no—
233C4×C11—81no—
234C4×C11#46311yescharacteristic
235C4×C11#46411yescharacteristic
236C4×C11#46611yescharacteristic
237C4×C11#46811yescharacteristic
238C4×C11#48011yescharacteristic
239C4×C11#48211yescharacteristic
240C4×C11#48811yescharacteristic
241C4×C11#48911yescharacteristic
242Dic11—81no—
243Dic11—81no—
244Dic11—161no—
245C22×Q8D4411yescharacteristic
246C22×D4—112no—
247C22×D4—221no—
248C22×D4—221no—
249C22×C8—21no—
250C22×C8—21no—
251C22×C8—221no—
252#127—221no—
253#127—221no—
254#127—221no—
255#127—221no—
256#124—442no—
257#124—442no—
258C4×Q8—21no—
259C4×Q8—21no—
260C4×Q8—21no—
261C4×Q8—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—111no—
264C2×C4⋊C4—111no—
265C2×C4⋊C4—221no—
266C2×C4⋊C4—221no—
267C2×C4⋊C4—221no—
268C2×C4⋊C4D4411yescharacteristic
269C2×C22⋊C4—222no—
270C2×C22⋊C4—222no—
271C2×C22⋊C4—222no—
272C2×C22⋊C4—222no—
273C2×C42—21no—
274C2×C42—221no—
275C2×C42C22×D1111yescharacteristic
276#107—442no—
277C4⋊C8—21no—
278C4⋊C8—221no—
279C4⋊C8—221no—
280C4⋊C8C22⋊D1112yes—
281#103—442no—
282#102—444no—
283C4×C8—21no—
284C4×C8—21no—
285#95—221no—
286C2×C11#162111yescharacteristic
287C2×C11#163011yescharacteristic
288C2×C11#164011yescharacteristic
289C2×C11#164111yescharacteristic
290C2×C11#203311yescharacteristic
291C2×C11#203711yescharacteristic
292C2×C11#204211yescharacteristic
293D11—162no—
294C24—222no—
295C2×Q8—21no—
296C2×Q8—21no—
297C2×Q8—21no—
298C2×Q8—21no—
299C2×Q8—21no—
300C2×Q8D8812yes—
301C2×D4—222no—
302C2×D4—222no—
303C2×D4—442no—
304C2×D4—442no—
305C2×D4—441no—
306C2×D4—441no—
307C2×D4—441no—
308C2×D4—441no—
309C2×D4—441no—
310C2×D4—441no—
311C2×D4—441no—
312C2×D4—441no—
313C2×D4—441no—
314C2×D4—441no—
315C2×D4—441no—
316C2×D4—441no—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—221no—
320C22×C4—221no—
321C22×C4—441no—
322C22×C4C2×D4411yescharacteristic
323C22×C4D4×D1111yescharacteristic
324C22×C4D4×D1111yescharacteristic
325C2×C8—22no—
326C2×C8—22no—
327C2×C8—41no—
328C2×C8—41no—
329C2×C8—41no—
330C2×C8—41no—
331C2×C8—441no—
332C2×C8—441no—
333C2×C8—441no—
334C4⋊C4—21no—
335C4⋊C4—21no—
336C4⋊C4—41no—
337C4⋊C4—41no—
338C4⋊C4—221no—
339C4⋊C4—221no—
340C4⋊C4—221no—
341C4⋊C4—221no—
342C4⋊C4—442no—
343C4⋊C4—441no—
344C4⋊C4—441no—
345C4⋊C4—441no—
346C4⋊C4—441no—
347C22⋊C4—444no—
348C22⋊C4—444no—
349C22⋊C4—882no—
350C22⋊C4—882no—
351C42—41no—
352C42—41no—
353C42—441no—
354C42—441no—
355C42#433911yescharacteristic
356C42#434111yescharacteristic
357C42#434111yescharacteristic
358C42C2×C22⋊D1111yescharacteristic
359C11#1041111yescharacteristic, complemented, Sylow
360C23—442no—
361C23—442no—
362C23—442no—
363C23—442no—
364C23—442no—
365C23—442no—
366C23—442no—
367C23#6693511yescharacteristic
368Q8—22no—
369Q8—22no—
370Q8—41no—
371Q8—41no—
372D4—444no—
373D4—882no—
374D4—881no—
375D4—881no—
376D4—881no—
377D4—881no—
378D4—881no—
379D4—881no—
380D4—881no—
381D4—881no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—22no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—441no—
391C2×C4—441no—
392C2×C4—441no—
393C2×C4—441no—
394C2×C4—441no—
395C2×C4—441no—
396C2×C4—881no—
397C2×C4—881no—
398C2×C4—881no—
399C2×C4#6693611yescharacteristic
400C2×C4#6693811yescharacteristic
401C2×C4#6693911yescharacteristic
402C2×C4C2×D8811yescharacteristic
403C2×C4#6695711yescharacteristic
404C2×C4#6696111yescharacteristic
405C2×C4#6696211yescharacteristic
406C2×C4#6696711yescharacteristic
407C2×C4#6696911yescharacteristic
408C2×C4#6697111yescharacteristic
409C2×C4#6697211yescharacteristic
410C2×C4#6698311yescharacteristic
411C2×C4#6699111yescharacteristic
412C2×C4#6699211yescharacteristic
413C8—42no—
414C8—42no—
415C8—881no—
416C22—882no—
417C22—882no—
418C22—882no—
419C22—882no—
420C22—882no—
421C22—882no—
422C22—882no—
423C22#1062234511yescharacteristic
424C22#1062234611yescharacteristic
425C22#1062242311yescharacteristic
426C22#1062242411yescharacteristic
427C22#1062243511yescharacteristic
428C22#1062243811yescharacteristic
429C22#1062257411yescharacteristic
430C4—21no—
431C4—21no—
432C4—42no—
433C4—81no—
434C4—881no—
435C4—881no—
436C4—1761no—
437C4#1062234911yescharacteristic
438C4#1062235011yescharacteristic
439C4#1062240811yescharacteristic
440C4#1062241311yescharacteristic
441C4#1062272811yescharacteristic
442C4#1062274711yescharacteristic
443C4#1062277811yescharacteristic
444C4#1062279811yescharacteristic
445C2—1762no—
446C2#1306768311yescharacteristic
447C2#1306773911yescharacteristic
448C2#1306780511yescharacteristic
449C2#1306781111yescharacteristic
450C2#1306979911yescharacteristic
451C2#1306982511yescharacteristic
452C2#1306985411yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×Q8⋊C8C2
socleC23×C11#120
prime radicalC2×#66927C22
hypercenterC2×Q8⋊C8D11
hypocenterC11#10411
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×Q8⋊C8

Complements

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

NH ≅ G/Ntype
3. #13069375C2semidirect
4. #13068621C2semidirect
6. #13066456C2semidirect
7. C2×C11×Q8⋊C8C2semidirect
139. C2×Q8⋊C8D11semidirect
359. C11#10411semidirect

Maximal subgroups

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

subgroupindex
#130736152
#130694222
#130693752
#130686212
C2×#106221232
#130664562
C2×C11×Q8⋊C82
#1041111