Finite Group Databasebeta

← #24999970

Subgroups — #24999970

Order 11008.

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#19139594C211yesmaximal, characteristic
2#19135401C211yesmaximal, characteristic
3#19135359C211yesmaximal, characteristic, complemented
4#19134600C211yesmaximal, characteristic, complemented
5C2×#14582642C211yesmaximal, characteristic
6#19132435C211yesmaximal, characteristic, complemented
7C2×C43×Q8⋊C8C211yesmaximal, characteristic, complemented
8C2×#13063322C2211yescharacteristic
9C2×#13063314—21no—
10C2×#13063257—21no—
11C2×C4⋊(C43⋊C8)C2211yescharacteristic
12C2×#13063249—21no—
13C2×#13063247—22no—
14#14582816—22no—
15#14582801—21no—
16#14582801—21no—
17#14582800—21no—
18#14582769C2211yescharacteristic
19C4×C4⋊Dic43C2211yescharacteristic
20#14582662—21no—
21#14582661—21no—
22#14582642—22no—
23C2×C4×Q8×C43C2211yescharacteristic
24C2×C4⋊C8×C43C2211yescharacteristic
25C2×C4×C8×C43C2211yescharacteristic
26C43×Q8⋊C8—22no—
27C22×D172—21no—
28C22×D172—21no—
29C22×D172D412yes—
30C22×C43⋊C8—21no—
31#13063322—21no—
32#13063322—21no—
33#13063322—21no—
34#13063322—21no—
35#13063314—42no—
36#13063314—42no—
37C2×C4⋊Dic43—21no—
38C2×C4⋊Dic43—21no—
39C2×C4⋊Dic43—21no—
40C2×C4⋊Dic43D411yescharacteristic
41C2×C4⋊Dic43D411yescharacteristic
42C2×(C2×D43)⋊C4—22no—
43C2×(C2×D43)⋊C4—22no—
44C2×(C2×D43)⋊C4—22no—
45C2×(C2×D43)⋊C4—22no—
46C2×C4×Dic43—21no—
47#13063257—42no—
48C4⋊(C43⋊C8)—21no—
49C4⋊(C43⋊C8)—21no—
50#13063249—42no—
51#13063247—44no—
52C43⋊#95—21no—
53C22×Q8×C43D411yescharacteristic
54C22×C8×C43—21no—
55C22×C8×C43—21no—
56C4×Q8×C43—21no—
57C4×Q8×C43—21no—
58C4×Q8×C43—21no—
59C4×Q8×C43—21no—
60C2×C4⋊C4×C43—21no—
61C2×C4⋊C4×C43D411yescharacteristic
62C2×C42×C43—21no—
63C2×C42×C43C2311yescharacteristic
64C4⋊C8×C43—21no—
65C4⋊C8×C43D412yes—
66C4×C8×C43—21no—
67C4×C8×C43—21no—
68C23×D43—22no—
69C2×Q8×C43—21no—
70C2×Q8×C43—21no—
71C2×Q8×C43—21no—
72C2×Q8×C43—21no—
73C2×Q8×C43—21no—
74C2×Q8×C43SD1612yes—
75C22×C4×C43—21no—
76C22×C4×C43—21no—
77C22×C4×C43C2×D411yescharacteristic
78C22×C4×C43C2×D411yescharacteristic
79C22×C4×C43C2×D411yescharacteristic
80C22×Dic43—21no—
81C22×Dic43—21no—
82C22×Dic43—41no—
83C2×D172—22no—
84C2×D172—22no—
85C2×D172—41no—
86C2×D172—41no—
87C2×D172—41no—
88C2×D172—41no—
89C2×D172—41no—
90C2×D172—41no—
91C2×D172—41no—
92C2×D172—41no—
93C2×D172—41no—
94C2×D172—41no—
95C2×D172—41no—
96C2×D172—41no—
97C2×D172—42no—
98C2×D172—42no—
99C2×C8×C43—22no—
100C2×C8×C43—22no—
101C2×C8×C43—41no—
102C2×C8×C43—41no—
103C2×C8×C43—41no—
104C2×C8×C43—41no—
105C4⋊C4×C43—21no—
106C4⋊C4×C43—21no—
107C4⋊C4×C43—41no—
108C4⋊C4×C43—41no—
109C42×C43—41no—
110C42×C43—41no—
111C42×C43C2×D411yescharacteristic
112C42×C43#4111yescharacteristic
113C42×C43#4111yescharacteristic
114C42×C43#4111yescharacteristic
115(C2×D43)⋊C4—44no—
116(C2×D43)⋊C4—44no—
117(C2×D43)⋊C4—82no—
118(C2×D43)⋊C4—82no—
119C4⋊Dic43—21no—
120C4⋊Dic43—21no—
121C4⋊Dic43—21no—
122C4⋊Dic43—21no—
123C4⋊Dic43—42no—
124C4⋊Dic43—41no—
125C4⋊Dic43—41no—
126C4⋊Dic43—41no—
127C4⋊Dic43—41no—
128C4×Dic43—41no—
129C4×Dic43—41no—
130C2×C43⋊C8—41no—
131C2×C43⋊C8—41no—
132C2×C43⋊C8—41no—
133C23×C43#12011yescharacteristic
134C22×D43—42no—
135C22×D43—42no—
136C22×D43—42no—
137C22×D43—42no—
138C22×D43—42no—
139C22×D43—42no—
140C22×D43—42no—
141Q8×C43—22no—
142Q8×C43—22no—
143Q8×C43—41no—
144Q8×C43—41no—
145C2×C4×C43—21no—
146C2×C4×C43—21no—
147C2×C4×C43—22no—
148C2×C4×C43—41no—
149C2×C4×C43—41no—
150C2×C4×C43—41no—
151C2×C4×C43—41no—
152C2×C4×C43—41no—
153C2×C4×C43#12111yescharacteristic
154C2×C4×C43#12111yescharacteristic
155C2×C4×C43#12111yescharacteristic
156C2×C4×C43#12311yescharacteristic
157C2×C4×C43#12311yescharacteristic
158C2×C4×C43#12411yescharacteristic
159C2×C4×C43C2×SD1611yescharacteristic
160C2×C4×C43#13511yescharacteristic
161C2×C4×C43#13511yescharacteristic
162C2×C4×C43#13511yescharacteristic
163C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
164C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
165C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
166C2×C4×C43#13711yescharacteristic
167C2×Dic43—41no—
168C2×Dic43—41no—
169C2×Dic43—41no—
170C2×Dic43—41no—
171C2×Dic43—41no—
172C2×Dic43—41no—
173C2×Dic43—81no—
174C2×Dic43—81no—
175C2×Dic43—81no—
176D172—44no—
177D172—82no—
178D172—81no—
179D172—81no—
180D172—81no—
181D172—81no—
182D172—81no—
183D172—81no—
184D172—81no—
185D172—81no—
186C8×C43—42no—
187C8×C43—42no—
188C43⋊C8—81no—
189#10410—431nomaximal, Sylow
190C22×C43#39411yescharacteristic
191C22×C43#44911yescharacteristic
192C22×C43#44911yescharacteristic
193C22×C43#45011yescharacteristic
194C22×C43#45211yescharacteristic
195C22×C43#45311yescharacteristic
196C22×C43#45511yescharacteristic
197C2×D43—82no—
198C2×D43—82no—
199C2×D43—82no—
200C2×D43—82no—
201C2×D43—82no—
202C2×D43—82no—
203C2×D43—82no—
204C4×C43—21no—
205C4×C43—21no—
206C4×C43—42no—
207C4×C43—81no—
208C4×C43#46311yescharacteristic
209C4×C43#46411yescharacteristic
210C4×C43#46511yescharacteristic
211C4×C43#46911yescharacteristic
212C4×C43#48111yescharacteristic
213C4×C43#48211yescharacteristic
214C4×C43#48811yescharacteristic
215C4×C43#48911yescharacteristic
216Dic43—81no—
217Dic43—81no—
218Dic43—161no—
219#2548—431no—
220#1957—431no—
221#1948—431no—
222#1803—431no—
223C2×#331—431no—
224C2×Q8⋊C8D4311yescharacteristic, complemented
225#1279—431no—
226C2×C43#162011yescharacteristic
227C2×C43#163111yescharacteristic
228C2×C43#164011yescharacteristic
229C2×C43#164211yescharacteristic
230C2×C43#203411yescharacteristic
231C2×C43#203711yescharacteristic
232C2×C43#204211yescharacteristic
233D43—162no—
234C2×#127—431no—
235C2×#124—861no—
236C2×C4×Q8C2×D4311yescharacteristic
237C2×#106—861no—
238C2×C4⋊C8—431no—
239C2×C4⋊C8C2×D4311yescharacteristic
240C2×#103—861no—
241C2×#102—862no—
242C2×C4×C8C2×D4311yescharacteristic
243#394—862no—
244#390—861no—
245#390—861no—
246#390—861no—
247#384—431no—
248C4×C4⋊C4—431no—
249#340—861no—
250#340—861no—
251#331—862no—
252Q8⋊C8—22no—
253C43#1041011yescharacteristic, complemented, Sylow
254C22×Q8D17211yescharacteristic
255C22×D4—432no—
256C22×D4—861no—
257C22×D4—861no—
258C22×C8—21no—
259C22×C8—21no—
260C22×C8—861no—
261#127—861no—
262#127—861no—
263#127—861no—
264#127—861no—
265#124—1722no—
266#124—1722no—
267C4×Q8—21no—
268C4×Q8—21no—
269C4×Q8—21no—
270C4×Q8—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—431no—
273C2×C4⋊C4—431no—
274C2×C4⋊C4—861no—
275C2×C4⋊C4—861no—
276C2×C4⋊C4—861no—
277C2×C4⋊C4D17211yescharacteristic
278C2×C22⋊C4—862no—
279C2×C22⋊C4—862no—
280C2×C22⋊C4—862no—
281C2×C22⋊C4—862no—
282C2×C42—21no—
283C2×C42—861no—
284C2×C42C22×D4311yescharacteristic
285#106—1722no—
286C4⋊C8—21no—
287C4⋊C8—861no—
288C4⋊C8—861no—
289C4⋊C8C22⋊D4312yes—
290#103—1722no—
291#102—1724no—
292C4×C8—21no—
293C4×C8—21no—
294#95—861no—
295C24—862no—
296C2×Q8—21no—
297C2×Q8—21no—
298C2×Q8—21no—
299C2×Q8—21no—
300C2×Q8—21no—
301C2×Q8#1062187312yes—
302C2×D4—862no—
303C2×D4—862no—
304C2×D4—1722no—
305C2×D4—1722no—
306C2×D4—1721no—
307C2×D4—1721no—
308C2×D4—1721no—
309C2×D4—1721no—
310C2×D4—1721no—
311C2×D4—1721no—
312C2×D4—1721no—
313C2×D4—1721no—
314C2×D4—1721no—
315C2×D4—1721no—
316C2×D4—1721no—
317C2×D4—1721no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—861no—
321C22×C4—861no—
322C22×C4—1721no—
323C22×C4C2×D17211yescharacteristic
324C22×C4D4×D4311yescharacteristic
325C22×C4D4×D4311yescharacteristic
326C2×C8—22no—
327C2×C8—22no—
328C2×C8—41no—
329C2×C8—41no—
330C2×C8—41no—
331C2×C8—41no—
332C2×C8—1721no—
333C2×C8—1721no—
334C2×C8—1721no—
335C4⋊C4—21no—
336C4⋊C4—21no—
337C4⋊C4—41no—
338C4⋊C4—41no—
339C4⋊C4—861no—
340C4⋊C4—861no—
341C4⋊C4—861no—
342C4⋊C4—861no—
343C4⋊C4—1722no—
344C4⋊C4—1721no—
345C4⋊C4—1721no—
346C4⋊C4—1721no—
347C4⋊C4—1721no—
348C22⋊C4—3442no—
349C22⋊C4—3442no—
350C22⋊C4—1724no—
351C22⋊C4—1724no—
352C42—41no—
353C42—41no—
354C42—1721no—
355C42—1721no—
356C42#1062189811yescharacteristic
357C42#1062190011yescharacteristic
358C42#1062190011yescharacteristic
359C42C2×C22⋊D4311yescharacteristic
360C23—1722no—
361C23—1722no—
362C23—1722no—
363C23—1722no—
364C23—1722no—
365C23—1722no—
366C23—1722no—
367C23#1306329511yescharacteristic
368Q8—22no—
369Q8—22no—
370Q8—41no—
371Q8—41no—
372D4—3442no—
373D4—3441no—
374D4—3441no—
375D4—3441no—
376D4—3441no—
377D4—3441no—
378D4—3441no—
379D4—3441no—
380D4—3441no—
381D4—1724no—
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—3441no—
391C2×C4—3441no—
392C2×C4—3441no—
393C2×C4—1721no—
394C2×C4—1721no—
395C2×C4—1721no—
396C2×C4—1721no—
397C2×C4—1721no—
398C2×C4—1721no—
399C2×C4#1306329611yescharacteristic
400C2×C4#1306329711yescharacteristic
401C2×C4#1306329911yescharacteristic
402C2×C4#1306330711yescharacteristic
403C2×C4#1306330911yescharacteristic
404C2×C4#1306331111yescharacteristic
405C2×C4C2×#1062187311yescharacteristic
406C2×C4#1306334611yescharacteristic
407C2×C4#1306334711yescharacteristic
408C2×C4#1306334811yescharacteristic
409C2×C4#1306335211yescharacteristic
410C2×C4#1306335311yescharacteristic
411C2×C4#1306335311yescharacteristic
412C2×C4#1306335711yescharacteristic
413C8—42no—
414C8—42no—
415C8—3441no—
416C22—3442no—
417C22—3442no—
418C22—3442no—
419C22—3442no—
420C22—3442no—
421C22—3442no—
422C22—3442no—
423C22#1458281511yescharacteristic
424C22#1458304611yescharacteristic
425C22#1458304711yescharacteristic
426C22#1458305211yescharacteristic
427C22#1458306411yescharacteristic
428C22#1458306811yescharacteristic
429C22#1458307811yescharacteristic
430C4—21no—
431C4—21no—
432C4—42no—
433C4—81no—
434C4—3441no—
435C4—3441no—
436C4—6881no—
437C4#1458311611yescharacteristic
438C4#1458312311yescharacteristic
439C4#1458312811yescharacteristic
440C4#1458315211yescharacteristic
441C4#1458321811yescharacteristic
442C4#1458322411yescharacteristic
443C4#1458325511yescharacteristic
444C4#1458326011yescharacteristic
445C2—6882no—
446C2#1913365611yescharacteristic
447C2#1913372411yescharacteristic
448C2#1913378311yescharacteristic
449C2#1913379811yescharacteristic
450C2#1913578511yescharacteristic
451C2#1913580411yescharacteristic
452C2#1913583311yescharacteristic
subgroupG/H
centerC23#13063295
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC2×C43×Q8⋊C8C2
socleC23×C43#120
prime radicalC2×#13063322C22
hypercenterC2×Q8⋊C8D43
hypocenterC43#10410
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
3. #19135359C2semidirect
4. #19134600C2semidirect
6. #19132435C2semidirect
7. C2×C43×Q8⋊C8C2semidirect
224. C2×Q8⋊C8D43semidirect
253. C43#10410semidirect

Maximal subgroups

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

subgroupindex
#191395942
#191354012
#191353592
#191346002
C2×#145826422
#191324352
C2×C43×Q8⋊C82
#1041043