Finite Group Databasebeta

← #14656103

Subgroups — #14656103

Order 2816.

644 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622459C211yesmaximal, characteristic
2C2×#10622644C211yesmaximal, characteristic, complemented
3#13073534C211yesmaximal, characteristic
4#13069577C211yesmaximal, characteristic, complemented
5C2×#10622097C211yesmaximal, characteristic
6#13066500C211yesmaximal, characteristic, complemented
7C2×C11×Q8⋊C8C211yesmaximal, characteristic, complemented
8C2×C4×Q8×C11C2211yescharacteristic
9C2×#66999—21no—
10C22×#4326—21no—
11C2×C4×D44C2211yescharacteristic
12C2×#66922C2211yescharacteristic
13C2×C11×C4⋊C8C2211yescharacteristic
14C2×C4×C8×C11C2211yescharacteristic
15C2×#66885—21no—
16C2×#66882—21no—
17#10622644—22no—
18#10622644—22no—
19#10622607—22no—
20#10622600—21no—
21C2×#66874—21no—
22#10622552—21no—
23#10622548C2211yescharacteristic
24#10622541—21no—
25C2×C4⋊(C11⋊C8)C2211yescharacteristic
26#10622459—22no—
27#10622459—22no—
28C11×Q8⋊C8—22no—
29#10622189—22no—
30#10622097—22no—
31C22×Q8×C11D411yescharacteristic
32C22×D44D411yescharacteristic
33C22×C4×D11—21no—
34C22×Dic22—21no—
35C22×C8×C11—21no—
36C22×C8×C11—21no—
37C4×Q8×C11—21no—
38C4×Q8×C11—21no—
39C4×Q8×C11—21no—
40C4×Q8×C11—21no—
41C2×C11×C4⋊C4—21no—
42C2×C11×C4⋊C4D411yescharacteristic
43C2×C42×C11—21no—
44C2×C42×C11C2311yescharacteristic
45#66999—42no—
46#66999—42no—
47C2×#4326—24no—
48C2×#4326—42no—
49C2×#4326—42no—
50C2×(C2×D11)⋊C4—22no—
51C2×(C2×D11)⋊C4—21no—
52C2×(C2×D11)⋊C4—22no—
53C2×C4⋊Dic11—21no—
54C2×C4⋊Dic11—21no—
55C2×C4⋊Dic11—21no—
56C2×C4⋊Dic11—21no—
57C2×C4⋊Dic11D411yescharacteristic
58C2×C4⋊Dic11D412yes—
59C2×Dic11⋊C4—22no—
60C22×C11⋊C8—21no—
61C4×D44—21no—
62C4×D44—21no—
63C4×D44—21no—
64C4×D44—21no—
65#66922—21no—
66#66922—21no—
67#66922—21no—
68#66922D412yes—
69C11×C4⋊C8—21no—
70C11×C4⋊C8D412yes—
71C4×C8×C11—21no—
72C4×C8×C11—21no—
73C11⋊#95—22no—
74#66885—24no—
75#66882—24no—
76#66874—24no—
77C4⋊(C11⋊C8)—21no—
78C4⋊(C11⋊C8)D412yes—
79#10233—111nomaximal, Sylow
80C23×D11—21no—
81C2×Q8×C11—21no—
82C2×Q8×C11—21no—
83C2×Q8×C11—21no—
84C2×Q8×C11—21no—
85C2×Q8×C11—21no—
86C2×Q8×C11D812yes—
87C22×C4×C11—21no—
88C22×C4×C11—21no—
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×D411yescharacteristic
92C22×Dic11—21no—
93C22×Dic11—22no—
94C22×Dic11—41no—
95C2×D44—21no—
96C2×D44—21no—
97C2×D44—21no—
98C2×D44—21no—
99C2×D44—21no—
100C2×D44Q1612yescomplemented
101C2×C4×D11—41no—
102C2×C4×D11—41no—
103C2×C4×D11—41no—
104C2×C4×D11—41no—
105C2×C4×D11—41no—
106C2×C4×D11—41no—
107C2×Dic22—22no—
108C2×Dic22—41no—
109C2×Dic22—41no—
110C2×Dic22—41no—
111C2×Dic22—41no—
112C2×Dic22—41no—
113C2×C8×C11—22no—
114C2×C8×C11—22no—
115C2×C8×C11—41no—
116C2×C8×C11—41no—
117C2×C8×C11—41no—
118C2×C8×C11—41no—
119C11×C4⋊C4—21no—
120C11×C4⋊C4—21no—
121C11×C4⋊C4—41no—
122C11×C4⋊C4—41no—
123C42×C11—41no—
124C42×C11—41no—
125C42×C11C2×D411yescharacteristic
126C42×C11C2×D411yescharacteristic
127C42×C11C2×D411yescharacteristic
128C42×C11#4111yescharacteristic
129#4326—48no—
130(C2×D11)⋊C4—44no—
131(C2×D11)⋊C4—41no—
132(C2×D11)⋊C4—41no—
133(C2×D11)⋊C4—82no—
134C4⋊Dic11—21no—
135C4⋊Dic11—22no—
136C4⋊Dic11—22no—
137C4⋊Dic11—21no—
138C4⋊Dic11—42no—
139C4⋊Dic11—41no—
140C4⋊Dic11—41no—
141C4⋊Dic11—41no—
142C4⋊Dic11—41no—
143C4⋊Dic11—41no—
144C4⋊Dic11—41no—
145Dic11⋊C4—44no—
146C2×C11⋊C8—22no—
147C2×C11⋊C8—41no—
148C2×C11⋊C8—41no—
149C2×#474—111no—
150C2×#462—111no—
151#2538—111no—
152#1990—111no—
153C2×Q8⋊C8D1111yescharacteristic, complemented
154C2×D4⋊C8—111no—
155#1296—111no—
156C23×C11#12011yescharacteristic
157C22×D11—22no—
158C22×D11—41no—
159C22×D11—41no—
160C22×D11—41no—
161C22×D11—41no—
162C22×D11—41no—
163C22×D11—41no—
164Q8×C11—22no—
165Q8×C11—22no—
166Q8×C11—41no—
167Q8×C11—41no—
168C2×C4×C11—21no—
169C2×C4×C11—21no—
170C2×C4×C11—22no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11#12011yescharacteristic
177C2×C4×C11#12011yescharacteristic
178C2×C4×C11#12111yescharacteristic
179C2×C4×C11#12111yescharacteristic
180C2×C4×C11#12111yescharacteristic
181C2×C4×C11#12711yescharacteristic
182C2×C4×C11C2×D811yescharacteristic
183C2×C4×C11C2×Q1611yescharacteristic
184C2×C4×C11#13511yescharacteristic
185C2×C4×C11#13511yescharacteristic
186C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
187C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
188C2×C4×C11#13711yescharacteristic
189C2×C4×C11#13711yescharacteristic
190C2×Dic11—42no—
191C2×Dic11—41no—
192C2×Dic11—41no—
193C2×Dic11—42no—
194C2×Dic11—41no—
195C2×Dic11—42no—
196C2×Dic11—42no—
197C2×Dic11—81no—
198C2×Dic11—81no—
199D44—22no—
200D44—22no—
201D44—41no—
202D44—41no—
203C4×D11—81no—
204C4×D11—81no—
205C4×D11—81no—
206C4×D11—81no—
207Dic22—42no—
208Dic22—42no—
209Dic22—81no—
210Dic22—81no—
211C8×C11—42no—
212C8×C11—42no—
213C11⋊C8—42no—
214C22×Q16—221no—
215C2×C4⋊Q8—111no—
216C2×C22⋊Q8—221no—
217C2×C4×Q8C2×D1111yescharacteristic
218C2×C4×D4—111no—
219#474—222no—
220#474—222no—
221#462—222no—
222#462—222no—
223C2×#107—221no—
224C2×C4⋊C8—111no—
225C2×C4⋊C8C2×D1111yescharacteristic
226C2×#103—221no—
227C2×#102—221no—
228C2×C4×C8C2×D1111yescharacteristic
229#396—222no—
230#390—221no—
231#389—221no—
232#384—111no—
233#380—221no—
234#340—222no—
235Q8⋊C8—22no—
236D4⋊C8—222no—
237C22×C11#39211yescharacteristic
238C22×C11#44711yescharacteristic
239C22×C11#44911yescharacteristic
240C22×C11#45111yescharacteristic
241C22×C11#45211yescharacteristic
242C22×C11#45511yescharacteristic
243C22×C11#45611yescharacteristic
244C2×D11—42no—
245C2×D11—42no—
246C2×D11—42no—
247C2×D11—81no—
248C2×D11—81no—
249C2×D11—81no—
250C2×D11—81no—
251C4×C11—21no—
252C4×C11—21no—
253C4×C11—42no—
254C4×C11—81no—
255C4×C11#44711yescharacteristic
256C4×C11#44911yescharacteristic
257C4×C11#45111yescharacteristic
258C4×C11#45211yescharacteristic
259C4×C11#46611yescharacteristic
260C4×C11#46711yescharacteristic
261C4×C11#46911yescharacteristic
262C4×C11#47011yescharacteristic
263Dic11—82no—
264Dic11—82no—
265Dic11—81no—
266C22×Q8—221no—
267C22×Q8D4411yescharacteristic
268C22×D4—111no—
269C23×C4—221no—
270C2×Q16—224no—
271C2×Q16—442no—
272C2×Q16—442no—
273C22×C8—21no—
274C22×C8—21no—
275C22×C8—221no—
276C4⋊Q8—112no—
277C4⋊Q8—221no—
278C4⋊Q8—221no—
279C4⋊Q8—221no—
280C22⋊Q8—442no—
281C22⋊Q8—442no—
282C4×Q8—21no—
283C4×Q8—21no—
284C4×Q8—21no—
285C4×Q8—21no—
286C4×D4—221no—
287C4×D4—221no—
288C4×D4—221no—
289C4×D4—221no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—111no—
292C2×C4⋊C4—112no—
293C2×C4⋊C4—221no—
294C2×C4⋊C4—221no—
295C2×C4⋊C4—222no—
296C2×C4⋊C4—221no—
297C2×C4⋊C4—221no—
298C2×C4⋊C4D4411yescharacteristic
299C2×C22⋊C4—222no—
300C2×C22⋊C4—221no—
301C2×C22⋊C4—222no—
302C2×C42—21no—
303C2×C42C22×D1111yescharacteristic
304#107—224no—
305C4⋊C8—21no—
306C4⋊C8—112no—
307C4⋊C8—221no—
308C4⋊C8C22⋊D1112yes—
309#103—224no—
310#102—224no—
311C4×C8—21no—
312C4×C8—21no—
313#95—222no—
314C2×C11#164111yescharacteristic
315C2×C11#164411yescharacteristic
316C2×C11#164911yescharacteristic
317C2×C11#165211yescharacteristic
318C2×C11#199911yescharacteristic
319C2×C11#200111yescharacteristic
320C2×C11#200711yescharacteristic
321D11—82no—
322C24—221no—
323C2×Q8—21no—
324C2×Q8—21no—
325C2×Q8—21no—
326C2×Q8—21no—
327C2×Q8—21no—
328C2×Q8—222no—
329C2×Q8—441no—
330C2×Q8—441no—
331C2×Q8—441no—
332C2×Q8—441no—
333C2×Q8—441no—
334C2×Q8D8812yes—
335C2×D4—112no—
336C2×D4—221no—
337C2×D4—221no—
338C2×D4—221no—
339C2×D4—221no—
340C2×D4—221no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—221no—
344C22×C4—222no—
345C22×C4—441no—
346C22×C4—441no—
347C22×C4—441no—
348C22×C4—441no—
349C22×C4—441no—
350C22×C4—441no—
351C22×C4—441no—
352C22×C4C2×D4411yescharacteristic
353C22×C4D4×D1111yescharacteristic
354C22×C4D4×D1111yescharacteristic
355Q16—448no—
356C2×C8—22no—
357C2×C8—22no—
358C2×C8—41no—
359C2×C8—41no—
360C2×C8—41no—
361C2×C8—41no—
362C2×C8—222no—
363C2×C8—441no—
364C2×C8—441no—
365C4⋊C4—21no—
366C4⋊C4—21no—
367C4⋊C4—41no—
368C4⋊C4—41no—
369C4⋊C4—221no—
370C4⋊C4—222no—
371C4⋊C4—222no—
372C4⋊C4—221no—
373C4⋊C4—442no—
374C4⋊C4—444no—
375C4⋊C4—441no—
376C4⋊C4—441no—
377C4⋊C4—441no—
378C4⋊C4—441no—
379C4⋊C4—441no—
380C4⋊C4—441no—
381C22⋊C4—444no—
382C22⋊C4—441no—
383C22⋊C4—441no—
384C22⋊C4—882no—
385C42—41no—
386C42—41no—
387C42#433911yescharacteristic
388C42D4×D1111yescharacteristic
389C42D4×D1111yescharacteristic
390C42C2×C22⋊D1111yescharacteristic
391C11#1023311yescharacteristic, complemented, Sylow
392C23—222no—
393C23—441no—
394C23—441no—
395C23—441no—
396C23—441no—
397C23—441no—
398C23—441no—
399C23#6693511yescharacteristic
400Q8—22no—
401Q8—22no—
402Q8—41no—
403Q8—41no—
404Q8—442no—
405Q8—442no—
406Q8—881no—
407Q8—881no—
408D4—222no—
409D4—222no—
410D4—441no—
411D4—441no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—22no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—441no—
421C2×C4—442no—
422C2×C4—442no—
423C2×C4—441no—
424C2×C4—441no—
425C2×C4—442no—
426C2×C4—442no—
427C2×C4—881no—
428C2×C4—881no—
429C2×C4—881no—
430C2×C4—881no—
431C2×C4—881no—
432C2×C4—881no—
433C2×C4#6693511yescharacteristic
434C2×C4#6693711yescharacteristic
435C2×C4#6693711yescharacteristic
436C2×C4C2×D8811yescharacteristic
437C2×C4#6695711yescharacteristic
438C2×C4#6696111yescharacteristic
439C2×C4#6696111yescharacteristic
440C2×C4#6696811yescharacteristic
441C2×C4#6696911yescharacteristic
442C2×C4Q16×D1111yescharacteristic
443C2×C4#6697111yescharacteristic
444C2×C4#6698311yescharacteristic
445C2×C4#6699011yescharacteristic
446C2×C4#6699311yescharacteristic
447C8—42no—
448C8—42no—
449C8—442no—
450C22—442no—
451C22—442no—
452C22—442no—
453C22—881no—
454C22—881no—
455C22—881no—
456C22—881no—
457C22#1062234511yescharacteristic
458C22#1062234711yescharacteristic
459C22#1062242111yescharacteristic
460C22#1062242311yescharacteristic
461C22#1062243811yescharacteristic
462C22#1062243911yescharacteristic
463C22#1062257311yescharacteristic
464C4—21no—
465C4—21no—
466C4—42no—
467C4—81no—
468C4—882no—
469C4—881no—
470C4—882no—
471C4#1062234511yescharacteristic
472C4#1062234711yescharacteristic
473C4#1062242611yescharacteristic
474C4#1062242911yescharacteristic
475C4#1062272811yescharacteristic
476C4#1062274811yescharacteristic
477C4#1062278611yescharacteristic
478C4#1062279911yescharacteristic
479C2—882no—
480C2#1306781111yescharacteristic
481C2#1306783211yescharacteristic
482C2#1306786711yescharacteristic
483C2#1306788811yescharacteristic
484C2#1306961411yescharacteristic
485C2#1306962511yescharacteristic
486C2#1306966411yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×Q8⋊C8C2
socleC23×C11#120
prime radicalC22×D44D4
hypercenterC2×Q8⋊C8D11
hypocenterC11#10233
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
2. C2×#10622644C2semidirect
4. #13069577C2semidirect
6. #13066500C2semidirect
7. C2×C11×Q8⋊C8C2semidirect
100. C2×D44Q16semidirect
153. C2×Q8⋊C8D11semidirect
391. C11#10233semidirect

Maximal subgroups

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

subgroupindex
C2×#106224592
C2×#106226442
#130735342
#130695772
C2×#106220972
#130665002
C2×C11×Q8⋊C82
#1023311