Finite Group Databasebeta

← #24996842

Subgroups — #24996842

Order 11008.

672 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583217C211yesmaximal, characteristic
2#19140337C211yesmaximal, characteristic
3#19134685C211yesmaximal, characteristic, complemented
4C2×#14582632C211yesmaximal, characteristic
5C2×#14582625C211yesmaximal, characteristic, complemented
6#19132474C211yesmaximal, characteristic, complemented
7C2×C43×#400C211yesmaximal, characteristic, complemented
8C2×#13063308—21no—
9C2×#13063299C2211yescharacteristic
10#14583217—22no—
11#14583217—22no—
12C2×#13063256—21no—
13C2×#13063245—21no—
14C2×C22⋊(C43⋊C8)C2211yescharacteristic
15C2×C22⋊(C43⋊C8)C2211yescharacteristic
16#14582829—21no—
17#14582821—22no—
18#14582816—21no—
19#14582778—21no—
20#14582759C2211yescharacteristic
21#14582661—22no—
22#14582632—22no—
23#14582625—22no—
24C22×C4⋊C4×C43C2211yescharacteristic
25C22×C4⋊C4×C43C2211yescharacteristic
26C43×#400—22no—
27C43×#400—22no—
28C2×#95×C43—21no—
29C2×#95×C43—21no—
30C2×#95×C43C2211yescharacteristic
31C22×D172D411yescharacteristic
32C22×C22⋊D43—21no—
33C22×C43⋊C8—21no—
34C22×C43⋊C8—21no—
35#13063308—42no—
36#13063308—42no—
37#13063299—21no—
38#13063299—21no—
39#13063299—21no—
40#13063299—21no—
41C2×C4⋊Dic43D411yescharacteristic
42C2×C4⋊Dic43D412yes—
43C2×Dic43⋊C4—22no—
44C2×C22⋊Dic43—21no—
45C2×(C2×D43)⋊C4—22no—
46C2×(C2×D43)⋊C4—21no—
47C2×(C2×D43)⋊C4—22no—
48#13063256—24no—
49#13063245—24no—
50C22⋊(C43⋊C8)—21no—
51C22⋊(C43⋊C8)—21no—
52C22⋊(C43⋊C8)—21no—
53C22⋊(C43⋊C8)D412yes—
54C43⋊#95—22no—
55C43⋊#95—21no—
56C23×C4×C43—21no—
57C23×C4×C43—21no—
58C23×C4×C43D411yescharacteristic
59C23×C4×C43D411yescharacteristic
60C23×C4×C43C2311yescharacteristic
61C2×C4⋊C4×C43—21no—
62C2×C4⋊C4×C43—21no—
63C2×C4⋊C4×C43—21no—
64C2×C4⋊C4×C43—21no—
65C2×C4⋊C4×C43—21no—
66C2×C4⋊C4×C43—21no—
67C2×C4⋊C4×C43—21no—
68C2×C4⋊C4×C43—21no—
69C2×C4⋊C4×C43—21no—
70C2×C4⋊C4×C43—21no—
71C2×C4⋊C4×C43—21no—
72C2×C4⋊C4×C43D412yes—
73#95×C43—24no—
74#95×C43—24no—
75#95×C43—21no—
76#95×C43D412yes—
77C24×C43C2×D411yescharacteristic
78C23×D43—21no—
79C22×C4×C43—21no—
80C22×C4×C43—21no—
81C22×C4×C43—22no—
82C22×C4×C43—21no—
83C22×C4×C43—22no—
84C22×C4×C43—21no—
85C22×C4×C43—21no—
86C22×C4×C43—21no—
87C22×C4×C43—21no—
88C22×C4×C43—21no—
89C22×C4×C43—21no—
90C22×C4×C43—42no—
91C22×C4×C43—42no—
92C22×C4×C43—42no—
93C22×C4×C43—44no—
94C22×C4×C43—42no—
95C22×C4×C43—41no—
96C22×C4×C43—41no—
97C22×C4×C43—41no—
98C22×C4×C43—41no—
99C22×C4×C43SD1612yes—
100C22×C4×C43C2×D411yescharacteristic
101C22×C4×C43C2×D411yescharacteristic
102C22×C4×C43C2×D411yescharacteristic
103C22×C4×C43C2×D411yescharacteristic
104C22×C4×C43C2×D411yescharacteristic
105C22×C4×C43#4111yescharacteristic
106C2×C22⋊D43—41no—
107C2×C22⋊D43—41no—
108C2×C22⋊D43—41no—
109C2×C22⋊D43—41no—
110C2×C22⋊D43—41no—
111C2×C22⋊D43—41no—
112C22×Dic43—22no—
113C22×Dic43—21no—
114C2×D172—21no—
115C2×D172—21no—
116C2×D172—42no—
117C4⋊C4×C43—22no—
118C4⋊C4×C43—22no—
119C4⋊C4×C43—41no—
120C4⋊C4×C43—41no—
121C4⋊C4×C43—41no—
122C4⋊C4×C43—41no—
123C4⋊C4×C43—41no—
124C4⋊C4×C43—41no—
125C22⋊Dic43—41no—
126C22⋊Dic43—41no—
127(C2×D43)⋊C4—44no—
128(C2×D43)⋊C4—41no—
129(C2×D43)⋊C4—41no—
130(C2×D43)⋊C4—82no—
131C4⋊Dic43—21no—
132C4⋊Dic43—21no—
133C4⋊Dic43—42no—
134Dic43⋊C4—44no—
135C2×C43⋊C8—22no—
136C2×C43⋊C8—42no—
137C2×C43⋊C8—42no—
138C2×C43⋊C8—41no—
139C23×C43—22no—
140C23×C43—22no—
141C23×C43#12011yescharacteristic
142C23×C43#12011yescharacteristic
143C23×C43#12111yescharacteristic
144C23×C43C2×SD1611yescharacteristic
145C23×C43#13511yescharacteristic
146C23×C43AGL(1,ℤ/8)11yescharacteristic
147C23×C43#13711yescharacteristic
148C22×D43—41no—
149C22×D43—41no—
150C22×D43—41no—
151C22×D43—42no—
152C22×D43—42no—
153C2×C4×C43—22no—
154C2×C4×C43—22no—
155C2×C4×C43—22no—
156C2×C4×C43—22no—
157C2×C4×C43—22no—
158C2×C4×C43—41no—
159C2×C4×C43—41no—
160C2×C4×C43—41no—
161C2×C4×C43—41no—
162C2×C4×C43—41no—
163C2×C4×C43—41no—
164C2×C4×C43—41no—
165C2×C4×C43—41no—
166C2×C4×C43—42no—
167C2×C4×C43—42no—
168C2×C4×C43—44no—
169C2×C4×C43—42no—
170C2×C4×C43—42no—
171C2×C4×C43—41no—
172C2×C4×C43—42no—
173C2×C4×C43—42no—
174C2×C4×C43—82no—
175C2×C4×C43—82no—
176C2×C4×C43—82no—
177C2×C4×C43—82no—
178C2×C4×C43—81no—
179C2×C4×C43#12011yescharacteristic
180C2×C4×C43#12111yescharacteristic
181C2×C4×C43#12111yescharacteristic
182C2×C4×C43#12711yescharacteristic
183C22⋊D43—81no—
184C22⋊D43—81no—
185C22⋊D43—81no—
186C22⋊D43—81no—
187C2×Dic43—41no—
188C2×Dic43—41no—
189C2×Dic43—42no—
190C2×Dic43—41no—
191C2×Dic43—42no—
192C2×Dic43—42no—
193D172—42no—
194D172—81no—
195C43⋊C8—42no—
196C43⋊C8—81no—
197#9921—431nomaximal, Sylow
198C22×C43—22no—
199C22×C43—22no—
200C22×C43—22no—
201C22×C43—22no—
202C22×C43—21no—
203C22×C43—21no—
204C22×C43—21no—
205C22×C43—21no—
206C22×C43#39211yescharacteristic
207C22×C43#44811yescharacteristic
208C22×C43#44911yescharacteristic
209C22×C43#45011yescharacteristic
210C22×C43#45211yescharacteristic
211C22×C43#45412yes—
212C22×C43#45812yes—
213C22×C43#46511yescharacteristic
214C22×C43#46811yescharacteristic
215C2×D43—82no—
216C2×D43—82no—
217C2×D43—81no—
218C2×D43—81no—
219C2×D43—81no—
220C4×C43—21no—
221C4×C43—21no—
222C4×C43—21no—
223C4×C43—21no—
224C4×C43—42no—
225C4×C43—82no—
226C4×C43—82no—
227C4×C43—81no—
228Dic43—82no—
229Dic43—81no—
230C2×#481—431no—
231#2618—431no—
232C2×#400D4311yescharacteristic, complemented
233#1824—431no—
234C2×#327—431no—
235C2×#324—431no—
236#1294—431no—
237C2×C43—21no—
238C2×C43—21no—
239C2×C43—21no—
240C2×C43—21no—
241C2×C43#161512yes—
242C2×C43#161612yes—
243C2×C43#200011yescharacteristic
244C2×C43#200311yescharacteristic
245C2×C43#202211yescharacteristic
246D43—161no—
247C2×#123—861no—
248C2×#121—431no—
249C22×C4⋊C4C2×D4311yescharacteristic
250C22×C4⋊C4C2×D4311yescharacteristic
251#481—862no—
252#481—862no—
253C2×#106—861no—
254C2×#102—861no—
255C2×C22⋊C8—431no—
256C2×C22⋊C8—431no—
257#400—22no—
258#400—22no—
259#398—861no—
260#396—862no—
261#394—861no—
262#386—861no—
263#380—431no—
264C2×#95—21no—
265C2×#95—21no—
266C2×#95C2×D4311yescharacteristic
267#340—862no—
268#327—862no—
269#324—862no—
270C43#992111yescharacteristic, complemented, Sylow
271C22×D4—431no—
272C22×D4—861no—
273C23×C4—21no—
274C23×C4—21no—
275C23×C4C22⋊D4311yescharacteristic
276C23×C4C22⋊D4311yescharacteristic
277C23×C4C22×D4311yescharacteristic
278C22×C8—861no—
279C22×C8—861no—
280#123—1722no—
281#123—1722no—
282#121—861no—
283#121—861no—
284#121—861no—
285#121—861no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—431no—
298C2×C4⋊C4—432no—
299C2×C4⋊C4—862no—
300C2×C4⋊C4C22⋊D4312yes—
301C2×C22⋊C4—862no—
302C2×C22⋊C4—862no—
303C2×C22⋊C4—861no—
304C2×C22⋊C4—861no—
305#106—864no—
306#102—864no—
307C22⋊C8—432no—
308C22⋊C8—861no—
309C22⋊C8—861no—
310C22⋊C8—861no—
311#95—24no—
312#95—24no—
313#95—21no—
314#95—862no—
315#95—861no—
316#95C22⋊D4312yes—
317C24—861no—
318C24C2×C22⋊D4311yescharacteristic
319C2×D4—861no—
320C2×D4—861no—
321C2×D4—1722no—
322C2×D4—1721no—
323C2×D4—1721no—
324C2×D4—1721no—
325C2×D4—1721no—
326C2×D4—1721no—
327C2×D4—1721no—
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—21no—
331C22×C4—21no—
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—22no—
336C22×C4—21no—
337C22×C4—22no—
338C22×C4—21no—
339C22×C4—42no—
340C22×C4—42no—
341C22×C4—42no—
342C22×C4—42no—
343C22×C4—44no—
344C22×C4—41no—
345C22×C4—41no—
346C22×C4—41no—
347C22×C4—41no—
348C22×C4—862no—
349C22×C4—861no—
350C22×C4#1062188412yes—
351C22×C4D4×D4311yescharacteristic
352C22×C4D4×D4311yescharacteristic
353C22×C4D4×D4311yescharacteristic
354C22×C4#1062190011yescharacteristic
355C22×C4C2×C22⋊D4311yescharacteristic
356C22×C4C2×C22⋊D4311yescharacteristic
357C2×C8—862no—
358C2×C8—1722no—
359C2×C8—1721no—
360C2×C8—1722no—
361C4⋊C4—22no—
362C4⋊C4—22no—
363C4⋊C4—41no—
364C4⋊C4—41no—
365C4⋊C4—41no—
366C4⋊C4—41no—
367C4⋊C4—41no—
368C4⋊C4—41no—
369C4⋊C4—861no—
370C4⋊C4—861no—
371C4⋊C4—1722no—
372C4⋊C4—1724no—
373C22⋊C4—3442no—
374C22⋊C4—1724no—
375C22⋊C4—1721no—
376C22⋊C4—1721no—
377C22⋊C4—1721no—
378C22⋊C4—1721no—
379C23—22no—
380C23—22no—
381C23—1721no—
382C23—1721no—
383C23—1721no—
384C23—1722no—
385C23—1722no—
386C23#1306329311yescharacteristic
387C23#1306329411yescharacteristic
388C23#1306329711yescharacteristic
389C23C2×#1062188411yescharacteristic
390C23#1306334511yescharacteristic
391C23#1306335011yescharacteristic
392C23#1306335611yescharacteristic
393D4—3441no—
394D4—3441no—
395D4—3441no—
396D4—3441no—
397D4—3441no—
398D4—1722no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—44no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—41no—
419C2×C4—42no—
420C2×C4—82no—
421C2×C4—82no—
422C2×C4—82no—
423C2×C4—82no—
424C2×C4—81no—
425C2×C4—1722no—
426C2×C4—1721no—
427C2×C4—1721no—
428C2×C4—1721no—
429C2×C4—1722no—
430C2×C4—1722no—
431C2×C4#1306329311yescharacteristic
432C2×C4#1306329611yescharacteristic
433C2×C4#1306329711yescharacteristic
434C2×C4#1306332111yescharacteristic
435C8—3441no—
436C8—1722no—
437C22—21no—
438C22—21no—
439C22—22no—
440C22—22no—
441C22—22no—
442C22—22no—
443C22—21no—
444C22—21no—
445C22—3441no—
446C22—3441no—
447C22—3442no—
448C22—3442no—
449C22—3441no—
450C22#1458280711yescharacteristic
451C22#1458303811yescharacteristic
452C22#1458304411yescharacteristic
453C22#1458304911yescharacteristic
454C22#1458305911yescharacteristic
455C22#1458307112yes—
456C22#1458308812yes—
457C22#1458313011yescharacteristic
458C22#1458314711yescharacteristic
459C4—21no—
460C4—21no—
461C4—21no—
462C4—21no—
463C4—42no—
464C4—82no—
465C4—82no—
466C4—81no—
467C4—3441no—
468C4—3442no—
469C2—21no—
470C2—21no—
471C2—21no—
472C2—21no—
473C2—6881no—
474C2#1913362412yes—
475C2#1913363112yes—
476C2#1913559611yescharacteristic
477C2#1913561711yescharacteristic
478C2#1913572311yescharacteristic
subgroupG/H
centerC23#13063293
commutator, cosocleC23×C4×C43C23
FrattiniC23×C4C22×D43
FittingC2×C43×#400C2
socleC23×C43#120
prime radicalC2×#13063299C22
hypercenterC2×#400D43
hypocenterC43#9921
LCSG ▷ C23×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#400

Complements

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

NH ≅ G/Ntype
3. #19134685C2semidirect
5. C2×#14582625C2semidirect
6. #19132474C2semidirect
7. C2×C43×#400C2semidirect
232. C2×#400D43semidirect
270. C43#9921semidirect

Maximal subgroups

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

subgroupindex
C2×#145832172
#191403372
#191346852
C2×#145826322
C2×#145826252
#191324742
C2×C43×#4002
#992143