Finite Group Databasebeta

← #24993158

Subgroups — #24993158

Order 11008.

606 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19137647C211yesmaximal, characteristic
2#19135581C211yesmaximal, characteristic, complemented
3#19133163C211yesmaximal, characteristic
4C2×#14582636C211yesmaximal, characteristic, complemented
5#19132475C211yesmaximal, characteristic, complemented
6#19132441C211yesmaximal, characteristic, complemented
7C43×#3187C211yesmaximal, characteristic
8C2×D4×Dic43—21no—
9C2×C22⋊(C43⋊C8)C2211yescharacteristic
10#14582792—21no—
11#14582785—21no—
12#14582779—21no—
13#14582779—21no—
14#14582759C2211yescharacteristic
15C22⋊C4×Dic43—21no—
16C4×C22⋊Dic43C2211yescharacteristic
17C2×C43⋊#95C2211yescharacteristic
18#14582666—21no—
19#14582666—21no—
20#14582636—21no—
21#14582636—21no—
22#14582633—22no—
23C2×C22⋊Q8×C43C2211yescharacteristic
24C2×#121×C43C2211yescharacteristic
25C43×#483—21no—
26C43×#481C412yescomplemented
27C43×#465—22no—
28C43×#450—21no—
29C43×#448C412yescomplemented
30C2×C22⋊C8×C43C2211yescharacteristic
31C23×Dic43—21no—
32C23×Dic43—21no—
33C22×C43⋊C8—21no—
34D4×Dic43—42no—
35D4×Dic43—42no—
36C2×C4⋊Dic43—21no—
37C2×C4⋊Dic43—21no—
38C2×C22⋊Dic43—21no—
39C2×C22⋊Dic43—21no—
40C2×C22⋊Dic43—21no—
41C2×C22⋊Dic43—21no—
42C2×C22⋊Dic43D411yescharacteristic
43C2×C22⋊Dic43D411yescharacteristic
44C2×C4×Dic43—21no—
45C2×C4×Dic43—21no—
46C22⋊(C43⋊C8)—21no—
47C22⋊(C43⋊C8)—21no—
48C43⋊#95—21no—
49C43⋊#95—21no—
50C43⋊#95—21no—
51C43⋊#95—21no—
52C43⋊#95—21no—
53C43⋊#95D411yescharacteristic
54C43⋊#95D411yescharacteristic
55C22×Q8×C43C2×C411yescharacteristic, complemented
56C22×D4×C43—21no—
57C22×D4×C43D411yescharacteristic
58C23×C4×C43C2311yescharacteristic
59C2×SD16×C43—22no—
60C22×C8×C43—21no—
61C22⋊Q8×C43—21no—
62C22⋊Q8×C43—21no—
63C22⋊Q8×C43—21no—
64C22⋊Q8×C43—21no—
65#121×C43—21no—
66#121×C43—21no—
67#121×C43C2×C412yes—
68#121×C43D412yes—
69C2×C4⋊C4×C43—21no—
70C2×C4⋊C4×C43C2×C411yescharacteristic, complemented
71C2×C4⋊C4×C43D411yescharacteristic
72C2×C22⋊C4×C43—21no—
73C2×C22⋊C4×C43—21no—
74#106×C43—22no—
75#103×C43—22no—
76#102×C43—22no—
77C22⋊C8×C43—21no—
78C22⋊C8×C43C2×C412yescomplemented
79C24×C43—21no—
80C24×C43C2×D411yescharacteristic
81C2×Q8×C43—21no—
82C2×Q8×C43—21no—
83C2×Q8×C43—81no—
84C2×D4×C43—21no—
85C2×D4×C43—22no—
86C2×D4×C43—22no—
87C2×D4×C43—41no—
88C2×D4×C43—41no—
89C2×D4×C43—41no—
90C2×D4×C43—41no—
91C2×D4×C43—81no—
92C2×D4×C43C22⋊C412yes—
93C22×C4×C43—21no—
94C22×C4×C43—21no—
95C22×C4×C43—21no—
96C22×C4×C43—81no—
97C22×C4×C43C22×C411yescharacteristic
98C22×C4×C43C2×D411yescharacteristic
99C22×C4×C43C2×D411yescharacteristic
100C22×C4×C43C2×D411yescharacteristic
101C22×C4×C43#4111yescharacteristic
102C22×C4×C43#4111yescharacteristic
103C22×Dic43—21no—
104C22×Dic43—21no—
105C22×Dic43—21no—
106C22×Dic43—21no—
107C22×Dic43—42no—
108C22×Dic43—42no—
109C22×Dic43—42no—
110C22×Dic43—41no—
111C22×Dic43—41no—
112C22×Dic43—41no—
113C22×Dic43—81no—
114C22×Dic43—81no—
115SD16×C43—82no—
116C2×C8×C43—22no—
117C2×C8×C43—81no—
118C4⋊C4×C43—21no—
119C4⋊C4×C43—21no—
120C4⋊C4×C43—21no—
121C4⋊C4×C43—41no—
122C4⋊C4×C43—41no—
123C4⋊C4×C43C22⋊C412yes—
124C22⋊C4×C43—22no—
125C22⋊C4×C43—22no—
126C22⋊C4×C43—41no—
127C22⋊C4×C43—41no—
128C22⋊Dic43—21no—
129C22⋊Dic43—21no—
130C22⋊Dic43—21no—
131C22⋊Dic43—42no—
132C22⋊Dic43—42no—
133C22⋊Dic43—41no—
134C22⋊Dic43—41no—
135C22⋊Dic43—81no—
136C22⋊Dic43SD1612yescomplemented
137C4⋊Dic43—42no—
138C4⋊Dic43—81no—
139C4×Dic43—42no—
140C4×Dic43—81no—
141C2×C43⋊C8—41no—
142C2×C43⋊C8—81no—
143C23×C43—22no—
144C23×C43—41no—
145C23×C43—41no—
146C23×C43—41no—
147C23×C43—41no—
148C23×C43—41no—
149C23×C43—41no—
150C23×C43—41no—
151C23×C43—41no—
152C23×C43C4×D411yescharacteristic
153C23×C43#12011yescharacteristic
154C23×C43#12111yescharacteristic
155C23×C43C2×SD1611yescharacteristic
156C23×C43#13511yescharacteristic
157C23×C43AGL(1,ℤ/8)11yescharacteristic
158C23×C43#13711yescharacteristic
159Q8×C43—42no—
160Q8×C43—81no—
161D4×C43—42no—
162D4×C43—42no—
163D4×C43—42no—
164D4×C43—42no—
165D4×C43—42no—
166D4×C43—81no—
167C2×C4×C43—22no—
168C2×C4×C43—41no—
169C2×C4×C43—41no—
170C2×C4×C43—41no—
171C2×C4×C43—41no—
172C2×C4×C43—41no—
173C2×C4×C43—41no—
174C2×C4×C43—41no—
175C2×C4×C43—41no—
176C2×C4×C43—41no—
177C2×C4×C43—41no—
178C2×C4×C43—81no—
179C2×C4×C43—81no—
180C2×C4×C43C2×C22⋊C411yescharacteristic
181C2×C4×C43C4×D411yescharacteristic
182C2×C4×C43#12111yescharacteristic
183C2×C4×C43#12311yescharacteristic
184C2×Dic43—22no—
185C2×Dic43—22no—
186C2×Dic43—41no—
187C2×Dic43—41no—
188C2×Dic43—41no—
189C2×Dic43—41no—
190C2×Dic43—41no—
191C2×Dic43—41no—
192C2×Dic43—41no—
193C2×Dic43—41no—
194C2×Dic43—41no—
195C2×Dic43—41no—
196C2×Dic43—84no—
197C2×Dic43—82no—
198C2×Dic43—82no—
199C2×Dic43—81no—
200C2×Dic43—81no—
201C2×Dic43—81no—
202C8×C43—42no—
203C43⋊C8—81no—
204#9275—431nomaximal, Sylow
205C22×C43—21no—
206C22×C43—21no—
207C22×C43—21no—
208C22×C43—21no—
209C22×C43—21no—
210C22×C43—21no—
211C22×C43—41no—
212C22×C43—41no—
213C22×C43—41no—
214C22×C43—41no—
215C22×C43—42no—
216C22×C43—42no—
217C22×C43—42no—
218C22×C43—81no—
219C22×C43—81no—
220C22×C43—81no—
221C22×C43—81no—
222C22×C43#38611yescharacteristic
223C22×C43C4×SD1611yescharacteristic
224C22×C43#44011yescharacteristic
225C22×C43#45011yescharacteristic
226C22×C43#45211yescharacteristic
227C22×C43#46111yescharacteristic
228C22×C43#46311yescharacteristic
229C4×C43—21no—
230C4×C43—21no—
231C4×C43—21no—
232C4×C43—21no—
233C4×C43—42no—
234C4×C43—81no—
235C4×C43—81no—
236Dic43—42no—
237Dic43—42no—
238Dic43—81no—
239Dic43—81no—
240Dic43—161no—
241#3187D4311yescharacteristic
242#2364—431no—
243#1996—431no—
244#1519—431no—
245C2×#328—431no—
246#1294—431no—
247#1282—431no—
248C2×C43—21no—
249C2×C43—21no—
250C2×C43—21no—
251C2×C43—21no—
252C2×C43—21no—
253C2×C43—21no—
254C2×C43—82no—
255C2×C43#187711yescharacteristic
256C2×C43#190611yescharacteristic
257C2×C43#191311yescharacteristic
258C2×C22⋊Q8C2×D4311yescharacteristic
259C2×#121C2×D4311yescharacteristic
260C2×C4×D4—861no—
261#483—21no—
262#481Dic4312yescomplemented
263#465—22no—
264#450—21no—
265#448Dic4312yescomplemented
266C2×C22⋊C8—431no—
267C2×C22⋊C8C2×D4311yescharacteristic
268#388—861no—
269#387—861no—
270#386—861no—
271#386—861no—
272#380—431no—
273C4×C22⋊C4—431no—
274C4×C22⋊C4—861no—
275C2×#95—431no—
276#342—861no—
277#342—861no—
278#328—861no—
279#328—861no—
280#327—862no—
281C43#927511yescharacteristic, complemented, Sylow
282C22×Q8C2×Dic4311yescharacteristic, complemented
283C22×D4—21no—
284C22×D4C22⋊D4311yescharacteristic
285C23×C4—861no—
286C23×C4—861no—
287C23×C4C22×D4311yescharacteristic
288C2×SD16—22no—
289C22×C8—21no—
290C22×C8—861no—
291C22⋊Q8—21no—
292C22⋊Q8—21no—
293C22⋊Q8—21no—
294C22⋊Q8—21no—
295#121—21no—
296#121—21no—
297#121C2×Dic4312yes—
298#121C22⋊D4312yes—
299C4×D4—1722no—
300C4×D4—1722no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—861no—
303C2×C4⋊C4—861no—
304C2×C4⋊C4C2×Dic4311yescharacteristic, complemented
305C2×C4⋊C4C22⋊D4311yescharacteristic
306C2×C22⋊C4—21no—
307C2×C22⋊C4—21no—
308C2×C22⋊C4—431no—
309C2×C22⋊C4—431no—
310C2×C22⋊C4—861no—
311C2×C22⋊C4—861no—
312C2×C22⋊C4—861no—
313C2×C22⋊C4—861no—
314C2×C42—861no—
315C2×C42—861no—
316#106—22no—
317#103—22no—
318#102—22no—
319C22⋊C8—21no—
320C22⋊C8—861no—
321C22⋊C8—861no—
322C22⋊C8C2×Dic4312yescomplemented
323#95—431no—
324#95—431no—
325#95—861no—
326#95—861no—
327#95—861no—
328#95—861no—
329#95—861no—
330C24—21no—
331C24D4×D4311yescharacteristic
332C2×Q8—21no—
333C2×Q8—21no—
334C2×Q8—81no—
335C2×D4—22no—
336C2×D4—22no—
337C2×D4—21no—
338C2×D4—41no—
339C2×D4—41no—
340C2×D4—41no—
341C2×D4—41no—
342C2×D4—81no—
343C2×D4C22⋊Dic4312yes—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—81no—
348C22×C4—861no—
349C22×C4—861no—
350C22×C4—861no—
351C22×C4—861no—
352C22×C4—3441no—
353C22×C4—3441no—
354C22×C4—1722no—
355C22×C4—1722no—
356C22×C4—1722no—
357C22×C4—1721no—
358C22×C4—1721no—
359C22×C4—1721no—
360C22×C4D4×D4311yescharacteristic
361C22×C4#1062190011yescharacteristic
362C22×C4#1062190011yescharacteristic
363C22×C4C22×Dic4311yescharacteristic
364C22×C4C2×C22⋊D4311yescharacteristic
365C22×C4C2×C22⋊D4311yescharacteristic
366SD16—82no—
367C2×C8—22no—
368C2×C8—81no—
369C2×C8—3441no—
370C2×C8—1721no—
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—21no—
374C4⋊C4—41no—
375C4⋊C4—41no—
376C4⋊C4—3441no—
377C4⋊C4—1722no—
378C4⋊C4C22⋊Dic4312yes—
379C22⋊C4—22no—
380C22⋊C4—22no—
381C22⋊C4—41no—
382C22⋊C4—41no—
383C22⋊C4—432no—
384C22⋊C4—861no—
385C22⋊C4—861no—
386C22⋊C4—861no—
387C22⋊C4—3441no—
388C22⋊C4—1722no—
389C22⋊C4—1722no—
390C22⋊C4—1721no—
391C22⋊C4—1721no—
392C42—3441no—
393C42—1722no—
394C23—22no—
395C23—41no—
396C23—41no—
397C23—41no—
398C23—41no—
399C23—41no—
400C23—41no—
401C23—41no—
402C23—41no—
403C23D4×Dic4311yescharacteristic
404C23#1306329311yescharacteristic
405C23#1306329711yescharacteristic
406C23SD16×D4311yescharacteristic
407C23#1306334611yescharacteristic
408C23#1306335211yescharacteristic
409C23#1306335411yescharacteristic
410Q8—42no—
411Q8—81no—
412D4—42no—
413D4—42no—
414D4—42no—
415D4—42no—
416D4—42no—
417D4—81no—
418C2×C4—22no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—81no—
430C2×C4—81no—
431C2×C4—862no—
432C2×C4—862no—
433C2×C4—3442no—
434C2×C4—3442no—
435C2×C4—3444no—
436C2×C4—3441no—
437C2×C4—3441no—
438C2×C4—3441no—
439C2×C4—1721no—
440C2×C4—1721no—
441C2×C4—1721no—
442C2×C4—1721no—
443C2×C4—1721no—
444C2×C4—1721no—
445C2×C4—1721no—
446C2×C4—1721no—
447C2×C4—1721no—
448C2×C4—1721no—
449C2×C4C2×C22⋊Dic4311yescharacteristic
450C2×C4D4×Dic4311yescharacteristic
451C2×C4#1306329711yescharacteristic
452C2×C4#1306330611yescharacteristic
453C8—42no—
454C8—3441no—
455C22—21no—
456C22—21no—
457C22—21no—
458C22—21no—
459C22—21no—
460C22—21no—
461C22—41no—
462C22—41no—
463C22—41no—
464C22—41no—
465C22—42no—
466C22—42no—
467C22—42no—
468C22—81no—
469C22—81no—
470C22—81no—
471C22—81no—
472C22#1458277911yescharacteristic
473C22SD16×Dic4311yescharacteristic
474C22#1458300011yescharacteristic
475C22#1458304811yescharacteristic
476C22#1458305811yescharacteristic
477C22#1458310211yescharacteristic
478C22#1458311611yescharacteristic
479C4—21no—
480C4—21no—
481C4—21no—
482C4—21no—
483C4—42no—
484C4—81no—
485C4—81no—
486C4—3441no—
487C4—3441no—
488C4—1722no—
489C4—1722no—
490C4—6881no—
491C2—21no—
492C2—21no—
493C2—21no—
494C2—21no—
495C2—21no—
496C2—21no—
497C2—82no—
498C2#1913493111yescharacteristic
499C2#1913509811yescharacteristic
500C2#1913513811yescharacteristic
subgroupG/H
centerC22#14582779
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#3187C2
socleC22×C43#386
prime radicalC2×#121×C43C22
cosocleC23×C4×C43C23
hypercenter#3187D43
hypocenterC43#9275
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3187

Complements

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

NH ≅ G/Ntype
2. #19135581C2semidirect
4. C2×#14582636C2semidirect
5. #19132475C2semidirect
6. #19132441C2semidirect
26. C43×#481C4semidirect
29. C43×#448C4semidirect
55. C22×Q8×C43C2×C4semidirect
70. C2×C4⋊C4×C43C2×C4semidirect
78. C22⋊C8×C43C2×C4semidirect
136. C22⋊Dic43SD16semidirect
262. #481Dic43semidirect
265. #448Dic43semidirect
281. C43#9275semidirect
282. C22×Q8C2×Dic43semidirect
304. C2×C4⋊C4C2×Dic43semidirect
322. C22⋊C8C2×Dic43semidirect

Maximal subgroups

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

subgroupindex
#191376472
#191355812
#191331632
C2×#145826362
#191324752
#191324412
C43×#31872
#927543