Finite Group Databasebeta

← #25153604

Subgroups — #25153604

Order 11008.

1072 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583605C211yesmaximal, characteristic
2C2×#14583101C211yesmaximal, characteristic
3#19139811C211yesmaximal, characteristic, complemented
4#19135744C212yesmaximal, complemented
5#19135734C212yesmaximal, complemented
6#19135553C211yesmaximal, characteristic, complemented
7#19135535C211yesmaximal, characteristic, complemented
8#19134926C212yesmaximal
9#19134926C212yesmaximal
10#19134421C211yesmaximal, characteristic
11C2×C43×#491C211yesmaximal, characteristic, complemented
12C22×#10621884C2212yes—
13#14583605—24no—
14#14583605—24no—
15C2×#13063324C2211yescharacteristic
16C2×#13063316C2211yescharacteristic
17C2×#13063305—21no—
18C2×#13063303—21no—
19C2×#13063303—21no—
20C2×C4×Dic86C2211yescharacteristic
21C2×C4×D172C2211yescharacteristic
22C2×#13063287C2211yescharacteristic
23C2×#13063287C2211yescharacteristic
24C2×C4⋊C4×D43—21no—
25#14583101—24no—
26C2×C4⋊(C43⋊C8)C2211yescharacteristic
27C2×#13063249C2212yes—
28C2×#13063247C2212yes—
29#14582837—21no—
30#14582837—21no—
31#14582806C2212yes—
32#14582806C2212yes—
33#14582804—21no—
34#14582764—21no—
35C4×C4⋊Dic43C2211yescharacteristic
36#14582662C2212yes—
37#14582661C2212yes—
38#14582661C2212yes—
39#14582653C2212yes—
40#14582653C2212yes—
41C2×C4⋊Q8×C43C2211yescharacteristic
42C2×#125×C43C2211yescharacteristic
43C43×#491—24no—
44C2×#103×C43C2212yes—
45C2×#103×C43C2212yes—
46C2×#97×C43C2211yescharacteristic
47C22×Dic86—21no—
48C22×Dic86D411yescharacteristic
49C22×D172C2311yescharacteristic
50C22×C4×D43—21no—
51C22×C4×D43—21no—
52C22×C4×D43—21no—
53C2×#10621884—24no—
54C2×#10621884—28no—
55C22×C43⋊C8C2312yes—
56#13063324—22no—
57#13063324—22no—
58#13063316—22no—
59#13063316—22no—
60#13063305—28no—
61#13063303—28no—
62#13063303—28no—
63C4×Dic86—22no—
64C4×Dic86—22no—
65C4×D172—22no—
66C4×D172D414yes—
67#13063287—22no—
68#13063287—22no—
69#13063287—22no—
70#13063287—22no—
71C2×C4⋊Dic43—21no—
72C2×C4⋊Dic43D411yescharacteristic
73C2×C4⋊Dic43C2312yes—
74C2×C4⋊Dic43C2311yescharacteristic
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4D411yescharacteristic
78C2×Dic43⋊C4D411yescharacteristic
79C4⋊C4×D43—28no—
80C2×(C2×D43)⋊C4—21no—
81C2×(C2×D43)⋊C4—21no—
82C2×(C2×D43)⋊C4—21no—
83C2×C4×Dic43—21no—
84C2×C4×Dic43C2311yescharacteristic
85C2×C4×Dic43C2311yescharacteristic
86C4⋊(C43⋊C8)—22no—
87#13063249—24no—
88#13063247—24no—
89C43⋊#95—21no—
90C43⋊#95—22no—
91C43⋊#95—22no—
92C43⋊#95—22no—
93C43⋊#95—22no—
94C22×Q8×C43C2312yes—
95C22×C8×C43C2312yes—
96C4⋊Q8×C43—22no—
97C4⋊Q8×C43—22no—
98#125×C43—22no—
99#125×C43D414yes—
100C2×C4⋊C4×C43—21no—
101C2×C4⋊C4×C43—21no—
102C2×C4⋊C4×C43—21no—
103C2×C4⋊C4×C43—21no—
104C2×C4⋊C4×C43C2311yescharacteristic
105C2×C4⋊C4×C43C2311yescharacteristic
106C2×C42×C43C2311yescharacteristic
107#103×C43—24no—
108#103×C43—24no—
109#97×C43—22no—
110C23×D43—21no—
111C2×Q8×C43—22no—
112C2×Q8×C43—22no—
113C2×Q8×C43—24no—
114C2×Q8×C43—24no—
115C22×C4×C43—21no—
116C22×C4×C43—21no—
117C22×C4×C43—22no—
118C22×C4×C43C2×D411yescharacteristic
119C22×C4×C43C2×D411yescharacteristic
120C22×C4×C43C2411yescharacteristic
121C22×Dic43—21no—
122C22×Dic43—22no—
123C22×Dic43C2×D411yescharacteristic
124C22×Dic43C2×D411yescharacteristic
125C22×Dic43C2×D411yescharacteristic
126C22×Dic43C2×D411yescharacteristic
127C2×D172—21no—
128C2×D172—22no—
129C2×D172C2×D412yes—
130C2×D172#4114yes—
131C2×C4×D43—24no—
132C2×C4×D43—24no—
133C2×C4×D43—24no—
134C2×C4×D43—42no—
135C2×C4×D43—42no—
136C2×C4×D43—82no—
137C2×C4×D43—82no—
138C2×Dic86—22no—
139C2×Dic86—22no—
140C2×Dic86—24no—
141C2×Dic86—41no—
142C2×Dic86—82no—
143C2×C8×C43—22no—
144C2×C8×C43—22no—
145C2×C8×C43—22no—
146C4⋊C4×C43—24no—
147C4⋊C4×C43—24no—
148C4⋊C4×C43—21no—
149C4⋊C4×C43—21no—
150C4⋊C4×C43—42no—
151C4⋊C4×C43—42no—
152C4⋊C4×C43C2×D412yes—
153C4⋊C4×C43C2×D412yes—
154C42×C43C2×D412yes—
155C42×C43C2×D412yes—
156#10621884—48no—
157(C2×D43)⋊C4—24no—
158(C2×D43)⋊C4—24no—
159(C2×D43)⋊C4—24no—
160C4⋊Dic43—24no—
161C4⋊Dic43—22no—
162C4⋊Dic43—21no—
163C4⋊Dic43—22no—
164C4⋊Dic43—22no—
165C4⋊Dic43C2×D412yes—
166Dic43⋊C4—24no—
167Dic43⋊C4—24no—
168Dic43⋊C4—22no—
169Dic43⋊C4—22no—
170C4×Dic43—21no—
171C4×Dic43—21no—
172C4×Dic43—21no—
173C4×Dic43—21no—
174C4×Dic43—42no—
175C2×C43⋊C8—22no—
176C2×C43⋊C8—24no—
177C23×C43C22×D411yescharacteristic
178C22×D43—22no—
179C22×D43—24no—
180C22×D43—41no—
181C22×D43—41no—
182C22×D43—42no—
183Q8×C43—42no—
184Q8×C43—42no—
185Q8×C43—44no—
186C2×C4×C43—21no—
187C2×C4×C43—21no—
188C2×C4×C43—22no—
189C2×C4×C43—22no—
190C2×C4×C43—22no—
191C2×C4×C43—41no—
192C2×C4×C43—41no—
193C2×C4×C43—42no—
194C2×C4×C43—42no—
195C2×C4×C43—44no—
196C2×C4×C43#12012yes—
197C2×C4×C43#12012yes—
198C2×C4×C43C22×D411yescharacteristic
199C2×C4×C43C22×D411yescharacteristic
200C2×C4×C43C2×#4112yes—
201C2×C4×C432−1+412yes—
202C2×Dic43—21no—
203C2×Dic43—21no—
204C2×Dic43—21no—
205C2×Dic43—21no—
206C2×Dic43—21no—
207C2×Dic43—22no—
208C2×Dic43—21no—
209C2×Dic43—21no—
210C2×Dic43—22no—
211C2×Dic43—22no—
212C2×Dic43—42no—
213C2×Dic43—42no—
214C2×Dic43—42no—
215C2×Dic43—42no—
216C2×Dic43#13712yes—
217D172—22no—
218D172—24no—
219D172#12414yes—
220C4×D43—48no—
221C4×D43—84no—
222C4×D43—84no—
223Dic86—44no—
224Dic86—84no—
225C8×C43—42no—
226C43⋊C8—42no—
227#25945—431nomaximal, Sylow
228C22×C43C2×#12011yescharacteristic
229C22×C43#54812yes—
230C22×C43C2×#13711yescharacteristic
231C22×C43#57511yescharacteristic
232C22×C43#57712yes—
233C2×D43—24no—
234C2×D43—44no—
235C2×D43—44no—
236C2×D43—42no—
237C2×D43—42no—
238C4×C43—22no—
239C4×C43—22no—
240C4×C43—42no—
241C4×C43—42no—
242C4×C43—82no—
243C4×C43C2×#12411yescharacteristic
244C4×C43#53611yescharacteristic
245C4×C43#54812yes—
246Dic43—22no—
247Dic43—41no—
248Dic43—41no—
249Dic43—42no—
250Dic43—41no—
251Dic43—82no—
252C2×#554—431no—
253C2×#491D4311yescharacteristic, complemented
254C2×#461—431no—
255#2568—431no—
256#2026—432no—
257#2024—432no—
258#1989—431no—
259#1985—431no—
260#1877—432no—
261#1877—432no—
262#1762—431no—
263C2×C43#243611yescharacteristic
264C2×C43#300711yescharacteristic
265C2×C43#300911yescharacteristic
266C2×C43#337212yes—
267C2×C43#337612yes—
268D43—44no—
269C22×SD16—432no—
270#554—864no—
271#554—864no—
272C2×C4⋊Q8—431no—
273C2×C4⋊Q8C2×D4311yescharacteristic
274C2×#125—431no—
275C2×#125C2×D4311yescharacteristic
276C2×C22⋊Q8—861no—
277C2×C22⋊Q8—861no—
278C2×C22⋊Q8—861no—
279C2×C4×Q8—431no—
280C2×C4×D4—431no—
281C2×C4×D4—431no—
282C2×C4×D4—431no—
283C22×C4⋊C4—861no—
284#491—24no—
285#461—864no—
286C2×C4⋊C8—431no—
287C2×#103—432no—
288C2×#103C2×D4312yes—
289C2×#103C2×D4312yes—
290C2×#102—432no—
291C2×#97C2×D4311yescharacteristic
292#400—861no—
293#400—861no—
294#391—432no—
295#391—432no—
296#391—861no—
297#382—861no—
298C4×C4⋊C4—431no—
299#340—432no—
300#340—432no—
301#340—432no—
302#336—432no—
303#336—432no—
304C43#2594511yescharacteristic, complemented, Sylow
305C22×Q8—431no—
306C22×Q8—861no—
307C22×Q8C22×D4312yes—
308C22×D4—431no—
309C23×C4—861no—
310C23×C4—861no—
311C23×C4—861no—
312C2×SD16—868no—
313C2×SD16—864no—
314C22×C8—432no—
315C22×C8C22×D4312yes—
316C4⋊Q8—22no—
317C4⋊Q8—22no—
318C4⋊Q8—862no—
319C4⋊Q8—862no—
320#125—22no—
321#125—862no—
322#125—862no—
323#125C22⋊D4314yes—
324C22⋊Q8—868no—
325C22⋊Q8—868no—
326C22⋊Q8—868no—
327C4×Q8—862no—
328C4×Q8—862no—
329C4×D4—434no—
330C4×D4—862no—
331C4×D4—862no—
332C4×D4—862no—
333C4×D4—862no—
334C4×D4—862no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—431no—
340C2×C4⋊C4—431no—
341C2×C4⋊C4—431no—
342C2×C4⋊C4—431no—
343C2×C4⋊C4—432no—
344C2×C4⋊C4—868no—
345C2×C4⋊C4—861no—
346C2×C4⋊C4—861no—
347C2×C4⋊C4—861no—
348C2×C4⋊C4C22×D4311yescharacteristic
349C2×C4⋊C4C22×D4311yescharacteristic
350C2×C22⋊C4—861no—
351C2×C22⋊C4—861no—
352C2×C22⋊C4—861no—
353C2×C42—431no—
354C2×C42—431no—
355C2×C42—861no—
356C2×C42C22×D4311yescharacteristic
357C4⋊C8—862no—
358#103—24no—
359#103—24no—
360#103—864no—
361#102—864no—
362#97—22no—
363#95—862no—
364#95—862no—
365#95—862no—
366#95—862no—
367#95—861no—
368C24—861no—
369C2×Q8—22no—
370C2×Q8—22no—
371C2×Q8—24no—
372C2×Q8—24no—
373C2×Q8—862no—
374C2×Q8—864no—
375C2×Q8—862no—
376C2×Q8—3442no—
377C2×Q8—1721no—
378C2×D4—432no—
379C2×D4—434no—
380C2×D4—861no—
381C2×D4—862no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—22no—
385C22×C4—431no—
386C22×C4—431no—
387C22×C4—431no—
388C22×C4—431no—
389C22×C4—864no—
390C22×C4—864no—
391C22×C4—861no—
392C22×C4—864no—
393C22×C4—862no—
394C22×C4—3442no—
395C22×C4—3442no—
396C22×C4—1722no—
397C22×C4—1722no—
398C22×C4D4×D4311yescharacteristic
399C22×C4D4×D4311yescharacteristic
400C22×C4C23×D4311yescharacteristic
401SD16—1728no—
402C2×C8—22no—
403C2×C8—22no—
404C2×C8—22no—
405C2×C8—862no—
406C2×C8—864no—
407C4⋊C4—24no—
408C4⋊C4—24no—
409C4⋊C4—21no—
410C4⋊C4—21no—
411C4⋊C4—42no—
412C4⋊C4—42no—
413C4⋊C4—432no—
414C4⋊C4—864no—
415C4⋊C4—864no—
416C4⋊C4—864no—
417C4⋊C4—862no—
418C4⋊C4—862no—
419C4⋊C4—862no—
420C4⋊C4—861no—
421C4⋊C4—862no—
422C4⋊C4—862no—
423C4⋊C4C2×C22⋊D4312yes—
424C4⋊C4C2×C22⋊D4312yes—
425C22⋊C4—864no—
426C22⋊C4—864no—
427C22⋊C4—864no—
428C42—861no—
429C42—861no—
430C42—861no—
431C42—861no—
432C42—1722no—
433C42D4×D4312yes—
434C42C2×C22⋊D4312yes—
435C23—864no—
436C23—862no—
437C23—1721no—
438C23—1721no—
439C23—1722no—
440C23C2×D4×D4311yescharacteristic
441Q8—44no—
442Q8—42no—
443Q8—42no—
444Q8—3444no—
445Q8—1724no—
446D4—434no—
447D4—864no—
448D4—862no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—42no—
457C2×C4—44no—
458C2×C4—42no—
459C2×C4—432no—
460C2×C4—861no—
461C2×C4—861no—
462C2×C4—861no—
463C2×C4—861no—
464C2×C4—861no—
465C2×C4—862no—
466C2×C4—861no—
467C2×C4—861no—
468C2×C4—862no—
469C2×C4—862no—
470C2×C4—3444no—
471C2×C4—3444no—
472C2×C4—1728no—
473C2×C4—1722no—
474C2×C4—1722no—
475C2×C4—1722no—
476C2×C4—1722no—
477C2×C4#1306329312yes—
478C2×C4#1306329312yes—
479C2×C4C2×D4×D4311yescharacteristic
480C2×C4C22×C22⋊D4311yescharacteristic
481C2×C4#41×D4312yes—
482C2×C4#1306337212yes—
483C8—42no—
484C8—1722no—
485C22—864no—
486C22—1724no—
487C22—1724no—
488C22—1722no—
489C22—1722no—
490C22C2×#1306329311yescharacteristic
491C22#1458355712yes—
492C22#137×D4311yescharacteristic
493C22#1458369811yescharacteristic
494C22#1458370812yes—
495C4—22no—
496C4—22no—
497C4—42no—
498C4—42no—
499C4—82no—
500C4—862no—
501C4—3442no—
502C4—1721no—
503C4—1721no—
504C4—1721no—
505C4—1722no—
506C4#124×D4311yescharacteristic
507C4#1458346911yescharacteristic
508C4#1458355612yes—
509C2—1724no—
510C2#1913825011yescharacteristic
511C2#1914385111yescharacteristic
512C2#1914387111yescharacteristic
513C2#1914737312yes—
514C2#1914741712yes—
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#491C2
socleC23×C43C22×D4
prime radicalC22×D172C23
hypercenterC2×#491D43
hypocenterC43#25945
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#491

Complements

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

NH ≅ G/Ntype
3. #19139811C2semidirect
4. #19135744C2semidirect
5. #19135734C2semidirect
6. #19135553C2semidirect
7. #19135535C2semidirect
11. C2×C43×#491C2semidirect
253. C2×#491D43semidirect
304. C43#25945semidirect

Maximal subgroups

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

subgroupindex
C2×#145836052
C2×#145831012
#191398112
#191357442
#191357342
#191355532
#191355352
#191349262
#191344212
C2×C43×#4912
#2594543