Finite Group Databasebeta

← #25146380

Subgroups — #25146380

Order 11008.

712 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144388C211yesmaximal, characteristic
2C2×#14583101C211yesmaximal, characteristic
3#19143544C211yesmaximal, characteristic, complemented
4#19135962C212yesmaximal, complemented
5#19135855C212yesmaximal
6#19135497C212yesmaximal
7#19135440C211yesmaximal, characteristic, complemented
8#19135370C211yesmaximal, characteristic, complemented
9#19135253C212yesmaximal, complemented
10C4×#13063241C211yesmaximal, characteristic
11C43×#3139C211yesmaximal, characteristic, complemented
12C22×#10621884C2212yes—
13C2×C4×D172C2211yescharacteristic
14#14583196—22no—
15#14583186—21no—
16#14583176—21no—
17#14583101—21no—
18#14583101—21no—
19#14583101—22no—
20#14583030—21no—
21#14583030—22no—
22Q8×C43⋊C8—21no—
23C2×#13063260C2212yes—
24#14582942C2212yes—
25#14582926C2212yes—
26#14582923C2211yescharacteristic
27C2×C4⋊(C43⋊C8)C2211yescharacteristic
28#14582903C2212yes—
29C2×#13063249C2212yes—
30C2×#13063244C2212yes—
31C2×#13063244C2212yes—
32C2×#13063241C2211yescharacteristic
33C2×#13063241C2211yescharacteristic
34#14582855C2212yes—
35C4×#10621877C2211yescharacteristic
36#14582667C2211yescharacteristic
37#14582667C2211yescharacteristic
38#14582663C2212yes—
39C43×#533C2211yescharacteristic
40C2×C4⋊Q8×C43C2211yescharacteristic
41C43×#491—22no—
42C43×#487—21no—
43C43×#487—21no—
44C43×#419C2212yes—
45C43×#419C2212yes—
46C4×M16×C43C2211yescharacteristic
47C22×D172C2311yescharacteristic
48C22×C4×D43—21no—
49C2×#10621884—24no—
50C2×#10621884—22no—
51C2×#10621884—22no—
52C2×#10621884—42no—
53C2×#10621877C2311yescharacteristic
54C2×#10621877C2312yes—
55C2×#10621877C2311yescharacteristic
56C22×C43⋊C8C2312yes—
57C4×D172—21no—
58C4×D172—21no—
59C4×D172—21no—
60C4×D172—21no—
61C2×C4⋊Dic43C2311yescharacteristic
62C2×(C2×D43)⋊C4—21no—
63#13063260—42no—
64#13063258—22no—
65#13063256—22no—
66C4⋊(C43⋊C8)—21no—
67C4⋊(C43⋊C8)—21no—
68C4⋊(C43⋊C8)—22no—
69C4⋊(C43⋊C8)—22no—
70C4⋊(C43⋊C8)D411yescharacteristic
71C4⋊(C43⋊C8)D412yes—
72C4⋊(C43⋊C8)D411yescharacteristic
73#13063249—22no—
74#13063249—22no—
75#13063245—22no—
76#13063245—22no—
77#13063244—24no—
78#13063244—42no—
79#13063241—22no—
80#13063241—22no—
81#13063236—21no—
82#13063236—22no—
83C4×C43⋊C8—21no—
84C4×C43⋊C8—22no—
85C22×Q8×C43C2312yes—
86C2×M16×C43C2311yescharacteristic
87C2×M16×C43C2311yescharacteristic
88C4⋊Q8×C43—21no—
89C4⋊Q8×C43—21no—
90C4⋊Q8×C43—21no—
91C4⋊Q8×C43—21no—
92C4⋊Q8×C43D411yescharacteristic
93C4⋊Q8×C43D411yescharacteristic
94#125×C43D412yes—
95C22⋊Q8×C43—21no—
96C22⋊Q8×C43—21no—
97C4×Q8×C43—21no—
98C4×Q8×C43—21no—
99#117×C43C2312yes—
100C2×C4⋊C4×C43—21no—
101C2×C4⋊C4×C43—21no—
102C2×C42×C43C2311yescharacteristic
103#103×C43—22no—
104#103×C43—22no—
105#103×C43—22no—
106#103×C43—22no—
107#97×C43—21no—
108C4×C8×C43—21no—
109C23×D43—21no—
110C2×Q8×C43—21no—
111C2×Q8×C43—21no—
112C2×Q8×C43—22no—
113C2×Q8×C43—22no—
114C2×Q8×C43—22no—
115C2×Q8×C43—22no—
116C2×Q8×C43—22no—
117C2×Q8×C43—22no—
118C22×C4×C43—22no—
119C22×C4×C43#4111yescharacteristic
120C22×C4×C43#4111yescharacteristic
121C22×C4×C43C2411yescharacteristic
122C22×Dic43—21no—
123C2×D172—21no—
124C2×D172—21no—
125C2×D172—21no—
126C2×D172—21no—
127C2×D172—21no—
128C2×D172#4112yes—
129C2×C4×D43—41no—
130C2×C4×D43—41no—
131C2×C4×D43—82no—
132M16×C43—21no—
133M16×C43—21no—
134M16×C43—21no—
135M16×C43—21no—
136C2×C8×C43—21no—
137C2×C8×C43—21no—
138C4⋊C4×C43—22no—
139C4⋊C4×C43—22no—
140C4⋊C4×C43—21no—
141C4⋊C4×C43—21no—
142C4⋊C4×C43—41no—
143C4⋊C4×C43—41no—
144C4⋊C4×C43—41no—
145C4⋊C4×C43—41no—
146C4⋊C4×C43C2×D412yes—
147C4⋊C4×C43C2×D412yes—
148C22⋊C4×C43—22no—
149C42×C43—22no—
150C42×C43C2×D411yescharacteristic
151C42×C43C2×D411yescharacteristic
152C42×C43C2×D411yescharacteristic
153C42×C43C2×D411yescharacteristic
154#10621884—44no—
155#10621884—44no—
156(C2×D43)⋊C4—41no—
157(C2×D43)⋊C4—41no—
158C4⋊Dic43—21no—
159C4⋊Dic43—21no—
160#10621877—21no—
161#10621877—21no—
162#10621877—22no—
163#10621877—21no—
164#10621877—22no—
165#10621877#4112yes—
166C2×C43⋊C8—21no—
167C2×C43⋊C8—22no—
168C2×C43⋊C8—22no—
169C2×C43⋊C8—21no—
170C2×C43⋊C8—22no—
171C2×C43⋊C8C2×D412yes—
172C2×C43⋊C8C2×D412yes—
173C23×C43C2×#4111yescharacteristic
174C22×D43—22no—
175C22×D43—41no—
176C22×D43—41no—
177C22×D43—81no—
178C22×D43—81no—
179Q8×C43—42no—
180Q8×C43—42no—
181Q8×C43—42no—
182Q8×C43—42no—
183Q8×C43—42no—
184Q8×C43—81no—
185C2×C4×C43—22no—
186C2×C4×C43—22no—
187C2×C4×C43—22no—
188C2×C4×C43—41no—
189C2×C4×C43—42no—
190C2×C4×C43—42no—
191C2×C4×C43—42no—
192C2×C4×C43#12111yescharacteristic
193C2×C4×C43#12111yescharacteristic
194C2×C4×C43#12111yescharacteristic
195C2×C4×C43#12111yescharacteristic
196C2×C4×C43C22×D411yescharacteristic
197C2×C4×C43C22×D411yescharacteristic
198C2×C4×C43C2×#4111yescharacteristic
199C2×C4×C43C2×#4111yescharacteristic
200C2×C4×C43H(5,𝔽2)11yescharacteristic
201C2×C4×C432−1+411yescharacteristic
202C2×Dic43—41no—
203C2×Dic43—81no—
204D172—22no—
205D172—22no—
206D172—41no—
207D172—41no—
208C4×D43—82no—
209C4×D43—82no—
210C8×C43—41no—
211C8×C43—41no—
212C43⋊C8—22no—
213C43⋊C8—22no—
214C43⋊C8—22no—
215C43⋊C8—41no—
216C43⋊C8—42no—
217#25313—431nomaximal, Sylow
218C22×C43—21no—
219C22×C43—21no—
220C22×C43C2×#12111yescharacteristic
221C22×C43#52911yescharacteristic
222C22×C43#54211yescharacteristic
223C2×D43—42no—
224C2×D43—82no—
225C2×D43—81no—
226C2×D43—81no—
227C2×D43—82no—
228C4×C43—21no—
229C4×C43—21no—
230C4×C43—21no—
231C4×C43—42no—
232C4×C43—42no—
233C4×C43—82no—
234C4×C43#47112yes—
235C4×C43#54611yescharacteristic
236C4×C43#54811yescharacteristic
237C4×C43#54811yescharacteristic
238C4×C43#55011yescharacteristic
239Dic43—81no—
240#3139D4311yescharacteristic, complemented
241#3077—431no—
242C2×#461—431no—
243#2962—431no—
244#2064—432no—
245#2046—432no—
246#1977—432no—
247#1966—431no—
248#1950—431no—
249#1930—432no—
250C4×#100—431no—
251C2×C43—21no—
252C2×C43—21no—
253C2×C43#242611yescharacteristic
254C2×C43C2×#47111yescharacteristic
255C2×C43#306911yescharacteristic
256D43—82no—
257C22×SD16—432no—
258#533C2×D4311yescharacteristic
259C2×C4⋊Q8C2×D4311yescharacteristic
260C2×C4×D4—431no—
261#491—22no—
262#487—21no—
263#487—21no—
264#478—862no—
265#476—861no—
266#474—861no—
267#461—861no—
268#461—862no—
269#461—861no—
270#446—862no—
271#446—861no—
272C8×Q8—861no—
273C2×#108—432no—
274#428—432no—
275#424—432no—
276#423—431no—
277C2×C4⋊C8—431no—
278#419C2×D4312yes—
279#419C2×D4312yes—
280#418—432no—
281C2×#103—432no—
282C2×#101—432no—
283C2×#101—432no—
284C2×#100—431no—
285C2×#100—431no—
286#405—432no—
287C4×M16—431no—
288C4×M16C2×D4311yescharacteristic
289#343—431no—
290#343—431no—
291#341—432no—
292C43#2531311yescharacteristic, complemented, Sylow
293C22×Q8C22×D4312yes—
294C22×D4—431no—
295C23×C4—861no—
296C2×SD16—862no—
297C2×SD16—862no—
298C2×SD16—864no—
299C2×SD16—1722no—
300C2×M16—431no—
301C2×M16—432no—
302C2×M16—431no—
303C2×M16C22×D4311yescharacteristic
304C2×M16C22×D4311yescharacteristic
305C22×C8—432no—
306C4⋊Q8—21no—
307C4⋊Q8—21no—
308C4⋊Q8—21no—
309C4⋊Q8—21no—
310C4⋊Q8C22⋊D4311yescharacteristic
311C4⋊Q8C22⋊D4311yescharacteristic
312#125C22⋊D4312yes—
313C22⋊Q8—21no—
314C22⋊Q8—21no—
315C4×Q8—21no—
316C4×Q8—21no—
317C4×D4—861no—
318C4×D4—861no—
319C4×D4—861no—
320C4×D4—861no—
321#117C22×D4312yes—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—431no—
325C2×C22⋊C4—861no—
326C2×C42C22×D4311yescharacteristic
327#108—1722no—
328#107—862no—
329#106—862no—
330C4⋊C8—431no—
331C4⋊C8—431no—
332C4⋊C8—432no—
333C4⋊C8—862no—
334C4⋊C8—862no—
335C4⋊C8—861no—
336C4⋊C8—861no—
337#103—22no—
338#103—22no—
339#103—22no—
340#103—22no—
341#103—862no—
342#103—862no—
343#102—862no—
344#102—862no—
345#101—864no—
346#101—1722no—
347#100—862no—
348#100—862no—
349#97—21no—
350#97—862no—
351#97—861no—
352C4×C8—21no—
353C4×C8—862no—
354C4×C8—861no—
355C24—861no—
356C2×Q8—21no—
357C2×Q8—21no—
358C2×Q8—22no—
359C2×Q8—22no—
360C2×Q8—22no—
361C2×Q8—22no—
362C2×Q8—22no—
363C2×Q8—22no—
364C2×D4—432no—
365C2×D4—861no—
366C2×D4—861no—
367C2×D4—861no—
368C2×D4—861no—
369C2×D4—861no—
370C22×C4—22no—
371C22×C4—861no—
372C22×C4—3442no—
373C22×C4—1721no—
374C22×C4—1721no—
375C22×C4#1062190011yescharacteristic
376C22×C4#1062190011yescharacteristic
377C22×C4C23×D4311yescharacteristic
378SD16—1724no—
379SD16—1724no—
380M16—21no—
381M16—21no—
382M16—21no—
383M16—21no—
384M16—432no—
385M16—861no—
386M16—861no—
387M16—862no—
388M16—861no—
389M16—862no—
390C2×C8—21no—
391C2×C8—21no—
392C2×C8—432no—
393C2×C8—432no—
394C2×C8—861no—
395C2×C8—862no—
396C2×C8—862no—
397C2×C8—861no—
398C2×C8—862no—
399C4⋊C4—22no—
400C4⋊C4—22no—
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—41no—
404C4⋊C4—41no—
405C4⋊C4—41no—
406C4⋊C4—41no—
407C4⋊C4—861no—
408C4⋊C4—861no—
409C4⋊C4C2×C22⋊D4312yes—
410C4⋊C4C2×C22⋊D4312yes—
411C22⋊C4—22no—
412C22⋊C4—1721no—
413C22⋊C4—1721no—
414C42—22no—
415C42D4×D4311yescharacteristic
416C42D4×D4311yescharacteristic
417C42C2×C22⋊D4311yescharacteristic
418C42C2×C22⋊D4311yescharacteristic
419C23—862no—
420C23—3441no—
421C23—3441no—
422C23—1721no—
423C23—1721no—
424C23C2×#1062190011yescharacteristic
425Q8—42no—
426Q8—42no—
427Q8—42no—
428Q8—42no—
429Q8—42no—
430Q8—81no—
431D4—862no—
432D4—862no—
433D4—1721no—
434D4—1721no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—41no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—3442no—
443C2×C4—3442no—
444C2×C4—3441no—
445C2×C4—1721no—
446C2×C4#1306329711yescharacteristic
447C2×C4#1306329711yescharacteristic
448C2×C4#1306329711yescharacteristic
449C2×C4#1306329711yescharacteristic
450C2×C4C2×D4×D4311yescharacteristic
451C2×C4C22×C22⋊D4311yescharacteristic
452C2×C4#41×D4311yescharacteristic
453C2×C4#41×D4311yescharacteristic
454C2×C4#1306337111yescharacteristic
455C2×C4#1306337211yescharacteristic
456C8—41no—
457C8—41no—
458C8—862no—
459C8—862no—
460C8—862no—
461C8—1722no—
462C8—1721no—
463C22—21no—
464C22—21no—
465C22—3442no—
466C22—3442no—
467C22—3441no—
468C22—3441no—
469C22—1722no—
470C22C2×#1306329711yescharacteristic
471C22#1458342811yescharacteristic
472C22#1458351811yescharacteristic
473C4—21no—
474C4—21no—
475C4—21no—
476C4—42no—
477C4—42no—
478C4—82no—
479C4—3441no—
480C4#1458316412yes—
481C4#1458354211yescharacteristic
482C4#1458355611yescharacteristic
483C4#1458355711yescharacteristic
484C4#1458356811yescharacteristic
485C2—21no—
486C2—21no—
487C2—3442no—
488C2#1913816411yescharacteristic
489C2C2×#1458316411yescharacteristic
490C2#1914432911yescharacteristic
subgroupG/H
centerC22C2×#13063297
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#3139C2
socleC22×C43C2×#121
prime radicalC22×D172C23
hypercenter#3139D43
hypocenterC43#25313
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3139

Complements

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

NH ≅ G/Ntype
3. #19143544C2semidirect
4. #19135962C2semidirect
7. #19135440C2semidirect
8. #19135370C2semidirect
9. #19135253C2semidirect
11. C43×#3139C2semidirect
240. #3139D43semidirect
292. C43#25313semidirect

Maximal subgroups

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

subgroupindex
#191443882
C2×#145831012
#191435442
#191359622
#191358552
#191354972
#191354402
#191353702
#191352532
C4×#130632412
C43×#31392
#2531343