Finite Group Databasebeta

← #24998946

Subgroups — #24998946

Order 11008.

628 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583194C211yesmaximal, characteristic, complemented
2C2×#14583190C211yesmaximal, characteristic
3#19139513C211yesmaximal, characteristic
4#19135397C211yesmaximal, characteristic, complemented
5C2×#14582628C211yesmaximal, characteristic
6#19132479C211yesmaximal, characteristic, complemented
7C2×C43×Q8⋊C8C211yesmaximal, characteristic, complemented
8C2×#13063325C2211yescharacteristic
9C2×#13063301—21no—
10C2×C4×D172C2211yescharacteristic
11#14583194—22no—
12#14583194—22no—
13#14583190—22no—
14#14583190—22no—
15C2×#13063258—21no—
16C2×#13063257—21no—
17C2×C4⋊(C43⋊C8)C2211yescharacteristic
18C2×#13063250—22no—
19C2×#13063249—21no—
20C2×#13063247—21no—
21#14582821—22no—
22#14582801—21no—
23#14582797—21no—
24#14582769C2211yescharacteristic
25#14582756—21no—
26#14582628—22no—
27C2×C4×Q8×C43C2211yescharacteristic
28C2×C4⋊C8×C43C2211yescharacteristic
29C2×C4×C8×C43C2211yescharacteristic
30C43×Q8⋊C8—22no—
31C22×Dic86—21no—
32C22×D172D411yescharacteristic
33C22×C4×D43—21no—
34C22×C43⋊C8—21no—
35#13063325—21no—
36#13063325—21no—
37#13063325—21no—
38#13063325D412yes—
39#13063301—42no—
40#13063301—42no—
41C4×D172—21no—
42C4×D172—21no—
43C4×D172—21no—
44C4×D172—21no—
45C2×C4⋊Dic43—21no—
46C2×C4⋊Dic43—21no—
47C2×C4⋊Dic43—21no—
48C2×C4⋊Dic43—21no—
49C2×C4⋊Dic43D411yescharacteristic
50C2×C4⋊Dic43D412yes—
51C2×Dic43⋊C4—22no—
52C2×(C2×D43)⋊C4—22no—
53C2×(C2×D43)⋊C4—21no—
54C2×(C2×D43)⋊C4—22no—
55#13063258—24no—
56#13063257—24no—
57C4⋊(C43⋊C8)—21no—
58C4⋊(C43⋊C8)D412yes—
59#13063250—44no—
60#13063249—24no—
61#13063247—24no—
62C43⋊#95—22no—
63C22×Q8×C43D411yescharacteristic
64C22×C8×C43—21no—
65C22×C8×C43—21no—
66C4×Q8×C43—21no—
67C4×Q8×C43—21no—
68C4×Q8×C43—21no—
69C4×Q8×C43—21no—
70C2×C4⋊C4×C43—21no—
71C2×C4⋊C4×C43D411yescharacteristic
72C2×C42×C43—21no—
73C2×C42×C43C2311yescharacteristic
74C4⋊C8×C43—21no—
75C4⋊C8×C43D412yes—
76C4×C8×C43—21no—
77C4×C8×C43—21no—
78C23×D43—21no—
79C2×Q8×C43—21no—
80C2×Q8×C43—21no—
81C2×Q8×C43—21no—
82C2×Q8×C43—21no—
83C2×Q8×C43—21no—
84C2×Q8×C43SD1612yes—
85C22×C4×C43—21no—
86C22×C4×C43—21no—
87C22×C4×C43C2×D411yescharacteristic
88C22×C4×C43C2×D411yescharacteristic
89C22×C4×C43C2×D411yescharacteristic
90C22×Dic43—21no—
91C22×Dic43—22no—
92C22×Dic43—41no—
93C2×D172—21no—
94C2×D172—21no—
95C2×D172—21no—
96C2×D172—21no—
97C2×D172—21no—
98C2×D172Q1612yes—
99C2×C4×D43—41no—
100C2×C4×D43—41no—
101C2×C4×D43—41no—
102C2×C4×D43—41no—
103C2×C4×D43—41no—
104C2×C4×D43—41no—
105C2×Dic86—22no—
106C2×Dic86—42no—
107C2×Dic86—42no—
108C2×Dic86—41no—
109C2×C8×C43—22no—
110C2×C8×C43—22no—
111C2×C8×C43—41no—
112C2×C8×C43—41no—
113C2×C8×C43—41no—
114C2×C8×C43—41no—
115C4⋊C4×C43—21no—
116C4⋊C4×C43—21no—
117C4⋊C4×C43—41no—
118C4⋊C4×C43—41no—
119C42×C43—41no—
120C42×C43—41no—
121C42×C43C2×D411yescharacteristic
122C42×C43C2×D411yescharacteristic
123C42×C43C2×D411yescharacteristic
124C42×C43#4111yescharacteristic
125(C2×D43)⋊C4—44no—
126(C2×D43)⋊C4—41no—
127(C2×D43)⋊C4—41no—
128(C2×D43)⋊C4—82no—
129C4⋊Dic43—22no—
130C4⋊Dic43—22no—
131C4⋊Dic43—21no—
132C4⋊Dic43—21no—
133C4⋊Dic43—41no—
134C4⋊Dic43—41no—
135C4⋊Dic43—41no—
136C4⋊Dic43—41no—
137C4⋊Dic43—41no—
138C4⋊Dic43—41no—
139C4⋊Dic43—42no—
140Dic43⋊C4—44no—
141C2×C43⋊C8—22no—
142C2×C43⋊C8—41no—
143C2×C43⋊C8—41no—
144C23×C43#12011yescharacteristic
145C22×D43—22no—
146C22×D43—41no—
147C22×D43—41no—
148C22×D43—41no—
149C22×D43—41no—
150C22×D43—41no—
151C22×D43—41no—
152Q8×C43—22no—
153Q8×C43—22no—
154Q8×C43—41no—
155Q8×C43—41no—
156C2×C4×C43—21no—
157C2×C4×C43—21no—
158C2×C4×C43—22no—
159C2×C4×C43—41no—
160C2×C4×C43—41no—
161C2×C4×C43—41no—
162C2×C4×C43—41no—
163C2×C4×C43—41no—
164C2×C4×C43#12011yescharacteristic
165C2×C4×C43#12011yescharacteristic
166C2×C4×C43#12111yescharacteristic
167C2×C4×C43#12111yescharacteristic
168C2×C4×C43#12111yescharacteristic
169C2×C4×C43#12711yescharacteristic
170C2×C4×C43C2×SD1611yescharacteristic
171C2×C4×C43C2×Q1611yescharacteristic
172C2×C4×C43#13511yescharacteristic
173C2×C4×C43#13511yescharacteristic
174C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
175C2×C4×C43#13711yescharacteristic
176C2×C4×C43#13711yescharacteristic
177C2×C4×C43#13711yescharacteristic
178C2×Dic43—42no—
179C2×Dic43—41no—
180C2×Dic43—41no—
181C2×Dic43—42no—
182C2×Dic43—42no—
183C2×Dic43—41no—
184C2×Dic43—42no—
185C2×Dic43—81no—
186C2×Dic43—81no—
187D172—22no—
188D172—22no—
189D172—41no—
190D172—41no—
191C4×D43—81no—
192C4×D43—81no—
193C4×D43—81no—
194C4×D43—81no—
195Dic86—44no—
196Dic86—82no—
197C8×C43—42no—
198C8×C43—42no—
199C43⋊C8—42no—
200#10236—431nomaximal, Sylow
201C22×C43#39211yescharacteristic
202C22×C43#45011yescharacteristic
203C22×C43#45111yescharacteristic
204C22×C43#45211yescharacteristic
205C22×C43#45211yescharacteristic
206C22×C43#45311yescharacteristic
207C22×C43#45411yescharacteristic
208C2×D43—42no—
209C2×D43—42no—
210C2×D43—42no—
211C2×D43—81no—
212C2×D43—81no—
213C2×D43—81no—
214C2×D43—81no—
215C4×C43—21no—
216C4×C43—21no—
217C4×C43—42no—
218C4×C43—81no—
219C4×C43#44811yescharacteristic
220C4×C43#44911yescharacteristic
221C4×C43#45111yescharacteristic
222C4×C43#45211yescharacteristic
223C4×C43#46511yescharacteristic
224C4×C43#46711yescharacteristic
225C4×C43#46811yescharacteristic
226C4×C43#47011yescharacteristic
227Dic43—82no—
228Dic43—81no—
229Dic43—82no—
230C2×#477—431no—
231C2×#476—431no—
232#2538—431no—
233#1956—431no—
234C2×Q8⋊C8D4311yescharacteristic, complemented
235C2×D4⋊C8—431no—
236#1296—431no—
237C2×C43#163111yescharacteristic
238C2×C43#163211yescharacteristic
239C2×C43#163711yescharacteristic
240C2×C43#163811yescharacteristic
241C2×C43#200011yescharacteristic
242C2×C43#200111yescharacteristic
243C2×C43#200611yescharacteristic
244D43—82no—
245C2×C4⋊Q8—431no—
246C2×C22⋊Q8—861no—
247C2×C4×Q8C2×D4311yescharacteristic
248C2×C4×D4—431no—
249#477—862no—
250#477—862no—
251#476—862no—
252#476—862no—
253C2×#107—861no—
254C2×#106—861no—
255C2×C4⋊C8—431no—
256C2×C4⋊C8C2×D4311yescharacteristic
257C2×#103—861no—
258C2×#103—862no—
259C2×#102—861no—
260C2×C4×C8C2×D4311yescharacteristic
261#396—862no—
262#390—861no—
263#389—861no—
264#384—431no—
265#380—861no—
266Q8⋊C8—22no—
267D4⋊C8—862no—
268C43#1023611yescharacteristic, complemented, Sylow
269C22×Q8—861no—
270C22×Q8D17211yescharacteristic
271C22×D4—431no—
272C23×C4—861no—
273C22×C8—21no—
274C22×C8—21no—
275C22×C8—861no—
276C4⋊Q8—432no—
277C4⋊Q8—861no—
278C4⋊Q8—861no—
279C4⋊Q8—861no—
280C22⋊Q8—1722no—
281C22⋊Q8—1722no—
282C4×Q8—21no—
283C4×Q8—21no—
284C4×Q8—21no—
285C4×Q8—21no—
286C4×D4—861no—
287C4×D4—861no—
288C4×D4—861no—
289C4×D4—861no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—431no—
292C2×C4⋊C4—432no—
293C2×C4⋊C4—861no—
294C2×C4⋊C4—861no—
295C2×C4⋊C4—862no—
296C2×C4⋊C4—861no—
297C2×C4⋊C4—861no—
298C2×C4⋊C4D17211yescharacteristic
299C2×C22⋊C4—862no—
300C2×C22⋊C4—862no—
301C2×C22⋊C4—861no—
302C2×C42—21no—
303C2×C42C22×D4311yescharacteristic
304#107—864no—
305#106—864no—
306C4⋊C8—21no—
307C4⋊C8—432no—
308C4⋊C8—861no—
309C4⋊C8C22⋊D4312yes—
310#103—864no—
311#103—1724no—
312#102—864no—
313C4×C8—21no—
314C4×C8—21no—
315#95—862no—
316C24—861no—
317C2×Q8—21no—
318C2×Q8—21no—
319C2×Q8—21no—
320C2×Q8—21no—
321C2×Q8—21no—
322C2×Q8—862no—
323C2×Q8—1722no—
324C2×Q8—1722no—
325C2×Q8—1721no—
326C2×Q8#1062187312yes—
327C2×D4—432no—
328C2×D4—861no—
329C2×D4—861no—
330C2×D4—861no—
331C2×D4—861no—
332C2×D4—861no—
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—861no—
336C22×C4—862no—
337C22×C4—1721no—
338C22×C4—1721no—
339C22×C4—1721no—
340C22×C4—1721no—
341C22×C4—1721no—
342C22×C4—1721no—
343C22×C4—1721no—
344C22×C4C2×D17211yescharacteristic
345C22×C4D4×D4311yescharacteristic
346C22×C4D4×D4311yescharacteristic
347C2×C8—22no—
348C2×C8—22no—
349C2×C8—41no—
350C2×C8—41no—
351C2×C8—41no—
352C2×C8—41no—
353C2×C8—862no—
354C2×C8—1721no—
355C2×C8—1721no—
356C4⋊C4—21no—
357C4⋊C4—21no—
358C4⋊C4—41no—
359C4⋊C4—41no—
360C4⋊C4—862no—
361C4⋊C4—861no—
362C4⋊C4—862no—
363C4⋊C4—861no—
364C4⋊C4—1722no—
365C4⋊C4—1724no—
366C4⋊C4—1721no—
367C4⋊C4—1721no—
368C4⋊C4—1721no—
369C4⋊C4—1721no—
370C4⋊C4—1721no—
371C4⋊C4—1721no—
372C22⋊C4—3442no—
373C22⋊C4—1724no—
374C22⋊C4—1721no—
375C22⋊C4—1721no—
376C42—41no—
377C42—41no—
378C42#1062189811yescharacteristic
379C42D4×D4311yescharacteristic
380C42D4×D4311yescharacteristic
381C42C2×C22⋊D4311yescharacteristic
382C23—862no—
383C23—1721no—
384C23—1721no—
385C23—1721no—
386C23—1721no—
387C23—1721no—
388C23—1721no—
389C23#1306329511yescharacteristic
390Q8—22no—
391Q8—22no—
392Q8—41no—
393Q8—41no—
394Q8—3442no—
395Q8—1724no—
396D4—862no—
397D4—862no—
398D4—1721no—
399D4—1721no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—22no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—3441no—
409C2×C4—3441no—
410C2×C4—3441no—
411C2×C4—3441no—
412C2×C4—3441no—
413C2×C4—3441no—
414C2×C4—1722no—
415C2×C4—1721no—
416C2×C4—1721no—
417C2×C4—1721no—
418C2×C4—1722no—
419C2×C4—1722no—
420C2×C4—1722no—
421C2×C4#1306329311yescharacteristic
422C2×C4#1306329511yescharacteristic
423C2×C4#1306329811yescharacteristic
424C2×C4#1306329811yescharacteristic
425C2×C4#1306329911yescharacteristic
426C2×C4#1306332111yescharacteristic
427C2×C4C2×#1062187311yescharacteristic
428C2×C4Q16×D4311yescharacteristic
429C2×C4#1306334611yescharacteristic
430C2×C4#1306334711yescharacteristic
431C2×C4#1306335311yescharacteristic
432C2×C4#1306335411yescharacteristic
433C2×C4#1306335711yescharacteristic
434C2×C4#1306335811yescharacteristic
435C8—42no—
436C8—42no—
437C8—1722no—
438C22—3441no—
439C22—3441no—
440C22—3441no—
441C22—3441no—
442C22—1722no—
443C22—1722no—
444C22—1722no—
445C22#1458280811yescharacteristic
446C22#1458305211yescharacteristic
447C22#1458305611yescharacteristic
448C22#1458306311yescharacteristic
449C22#1458306411yescharacteristic
450C22#1458306811yescharacteristic
451C22#1458307311yescharacteristic
452C4—21no—
453C4—21no—
454C4—42no—
455C4—81no—
456C4—3442no—
457C4—3441no—
458C4—3442no—
459C4#1458304011yescharacteristic
460C4#1458304611yescharacteristic
461C4#1458305311yescharacteristic
462C4#1458305811yescharacteristic
463C4#1458312811yescharacteristic
464C4#1458313911yescharacteristic
465C4#1458314511yescharacteristic
466C4#1458315611yescharacteristic
467C2—3442no—
468C2#1913372411yescharacteristic
469C2#1913373211yescharacteristic
470C2#1913376211yescharacteristic
471C2#1913377011yescharacteristic
472C2#1913560011yescharacteristic
473C2#1913560411yescharacteristic
474C2#1913563811yescharacteristic
subgroupG/H
centerC23#13063295
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC2×C43×Q8⋊C8C2
socleC23×C43#120
prime radicalC22×D172D4
hypercenterC2×Q8⋊C8D43
hypocenterC43#10236
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×Q8⋊C8

Complements

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

NH ≅ G/Ntype
1. C2×#14583194C2semidirect
4. #19135397C2semidirect
6. #19132479C2semidirect
7. C2×C43×Q8⋊C8C2semidirect
234. C2×Q8⋊C8D43semidirect
268. C43#10236semidirect

Maximal subgroups

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

subgroupindex
C2×#145831942
C2×#145831902
#191395132
#191353972
C2×#145826282
#191324792
C2×C43×Q8⋊C82
#1023643