Finite Group Databasebeta

← #25013527

Subgroups — #25013527

Order 11008.

518 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144172C211yesmaximal, characteristic
2C2×#108×D43C211yesmaximal, characteristic, complemented
3C2×#14582706C211yesmaximal, characteristic, complemented
4C2×(C2×D43)⋊C16C211yesmaximal, characteristic, complemented
5#19132692C211yesmaximal, characteristic, complemented
6#19132691C211yesmaximal, characteristic, complemented
7C2×C43×#359C211yesmaximal, characteristic, complemented
8C2×M16×D43—21no—
9C22×C8×D43C2211yescharacteristic
10#14583406—21no—
11C22×C43⋊C16C2211yescharacteristic
12#14583137C411yescharacteristic
13#14583137C411yescharacteristic
14#14583132C411yescharacteristic
15#14583132C411yescharacteristic
16#14583125—21no—
17#14583125—21no—
18C2×#13063261C2211yescharacteristic
19C2×#13063260—21no—
20#108×D43—22no—
21#108×D43—22no—
22#14582937C2211yescharacteristic
23#14582895—21no—
24#14582706—22no—
25(C2×D43)⋊C16—21no—
26(C2×D43)⋊C16—21no—
27C2×#135×C43C2211yescharacteristic
28C22×C16×C43C2211yescharacteristic
29C2×#108×C43C2211yescharacteristic
30C43×#359—22no—
31C22×C4×D43D411yescharacteristic
32C2×#10621877—21no—
33C2×#10621872—41no—
34M16×D43—24no—
35M16×D43—42no—
36C22×C43⋊C8D411yescharacteristic
37C2×C8×D43—21no—
38C2×C8×D43—21no—
39C2×C8×D43—21no—
40C2×C8×D43—21no—
41C2×C8×D43—41no—
42C2×C8×D43C2×C411yescharacteristic
43C2×C8×D43C2×C411yescharacteristic
44C2×C8×D43D411yescharacteristic
45C2×C8×D43D411yescharacteristic
46#13063306—41no—
47#13063301—21no—
48#13063301—21no—
49#13063296—21no—
50#13063296—21no—
51#13063293—41no—
52C4×C22⋊D43—41no—
53C4×C22⋊D43—41no—
54#13063284—21no—
55C2×C43⋊C16—21no—
56C2×C43⋊C16—21no—
57C2×C43⋊C16—21no—
58#13063261—21no—
59#13063261D412yescomplemented
60#13063260—24no—
61#13063259C2×C411yescharacteristic
62#13063259C2×C411yescharacteristic
63#13063257—21no—
64#13063249—21no—
65#13063249—21no—
66#13063246—21no—
67#13063246—21no—
68C2×#41×C43—21no—
69#135×C43—21no—
70#135×C43—21no—
71#135×C43—21no—
72#135×C43—21no—
73C2×Q16×C43C2×C411yescharacteristic
74C2×SD16×C43—21no—
75C2×D8×C43C2×C411yescharacteristic
76C2×M16×C43—21no—
77C22×C8×C43C2311yescharacteristic
78C2×C16×C43—21no—
79C2×C16×C43—21no—
80C2×C16×C43—21no—
81#108×C43—21no—
82#108×C43D412yescomplemented
83C23×D43SD1611yescharacteristic
84#41×C43—41no—
85#41×C43—41no—
86#41×C43—41no—
87#41×C43—41no—
88C2×Q8×C43—21no—
89C2×D4×C43—21no—
90C2×D4×C43—41no—
91C22×C4×C43—41no—
92C22×C4×C43C2×D411yescharacteristic
93C2×C22⋊D43—41no—
94C2×C22⋊D43—41no—
95C22×Dic43SD1611yescharacteristic
96C2×C4×D43—21no—
97C2×C4×D43—21no—
98C2×C4×D43—21no—
99C2×C4×D43—21no—
100C2×C4×D43C22⋊C411yescharacteristic
101C2×C4×D43C22⋊C411yescharacteristic
102C2×C4×D43D811yescharacteristic
103C2×C4×D43D811yescharacteristic
104Q16×C43—21no—
105Q16×C43—21no—
106SD16×C43—41no—
107SD16×C43—41no—
108D8×C43—21no—
109D8×C43—21no—
110M16×C43—22no—
111M16×C43—41no—
112C2×C8×C43—41no—
113C2×C8×C43C22×C411yescharacteristic
114C2×C8×C43C2×D411yescharacteristic
115C2×C8×C43C2×D411yescharacteristic
116C2×C8×C43C2×D411yescharacteristic
117C2×C8×C43#4111yescharacteristic
118C2×C8×C43#4111yescharacteristic
119C22⋊Dic43—41no—
120C22⋊Dic43—41no—
121C22⋊Dic43—41no—
122(C2×D43)⋊C4—41no—
123(C2×D43)⋊C4—41no—
124C4⋊Dic43—21no—
125C4⋊Dic43—21no—
126Dic43⋊C4—41no—
127Dic43⋊C4—41no—
128C4×Dic43—41no—
129#10621877—22no—
130#10621877—41no—
131C2×C43⋊C8—21no—
132C2×C43⋊C8—21no—
133C2×C43⋊C8—41no—
134C2×C43⋊C8C22⋊C411yescharacteristic
135C2×C43⋊C8C22⋊C411yescharacteristic
136#10621872—44no—
137C8×D43—21no—
138C8×D43—21no—
139C8×D43—21no—
140C8×D43—21no—
141C8×D43—21no—
142C8×D43—21no—
143C8×D43—21no—
144C8×D43—21no—
145C8×D43—44no—
146C16×C43—41no—
147C43⋊C16—41no—
148C23×C43—41no—
149C23×C43C2×SD1611yescharacteristic
150C22×D43—21no—
151C22×D43—21no—
152C22×D43—22no—
153C22×D43—41no—
154C22×D43#10211yescharacteristic
155C22×D43#10211yescharacteristic
156Q8×C43—41no—
157Q8×C43—41no—
158D4×C43—41no—
159D4×C43—41no—
160D4×C43—81no—
161D4×C43—81no—
162C2×C4×C43—41no—
163C2×C4×C43—81no—
164C2×C4×C43—81no—
165C2×C4×C43C2×C22⋊C411yescharacteristic
166C2×C4×C43#12011yescharacteristic
167C2×C4×C43#12311yescharacteristic
168C2×C4×C43C2×D811yescharacteristic
169C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
170C2×C4×C43#13711yescharacteristic
171C22⋊D43—82no—
172C22⋊D43—82no—
173C2×Dic43—21no—
174C2×Dic43—21no—
175C2×Dic43—41no—
176C2×Dic43—41no—
177C2×Dic43#10211yescharacteristic
178C2×Dic43#10211yescharacteristic
179C4×D43—21no—
180C4×D43—21no—
181C4×D43—21no—
182C4×D43—21no—
183C4×D43—21no—
184C4×D43—21no—
185C4×D43—21no—
186C4×D43—21no—
187C8×C43—42no—
188C8×C43C4×D411yescharacteristic
189C8×C43C4×D411yescharacteristic
190C8×C43#12111yescharacteristic
191C8×C43#12111yescharacteristic
192C43⋊C8—21no—
193C43⋊C8—21no—
194C43⋊C8—42no—
195#12990—431nomaximal, Sylow
196C22×C43—21no—
197C22×C43—21no—
198C22×C43—81no—
199C22×C43—81no—
200C22×C43—81no—
201C22×C43C2×#10211yescharacteristic
202C22×C43#44811yescharacteristic
203C22×C43#48111yescharacteristic
204C2×D43—21no—
205C2×D43—21no—
206C2×D43—21no—
207C2×D43—21no—
208C2×D43—21no—
209C2×D43—42no—
210C2×D43—42no—
211C2×D43#35912yescomplemented
212C4×C43—81no—
213C4×C43#38611yescharacteristic
214C4×C43#41711yescharacteristic
215C4×C43#44711yescharacteristic
216C4×C43#48011yescharacteristic
217Dic43—21no—
218Dic43—21no—
219Dic43—81no—
220Dic43—81no—
221#3050—431no—
222C22×#108—431no—
223C2×#359—431no—
224C2×#359D4311yescharacteristic, complemented
225C2×C22⋊C16—431no—
226#1382—431no—
227#1382—431no—
228C2×C43—21no—
229C2×C43—21no—
230C2×C43—161no—
231C2×C43#187411yescharacteristic
232C2×C43C2×#35911yescharacteristic
233C2×C43#214311yescharacteristic
234D43—22no—
235D43—41no—
236C2×#135C2×D4311yescharacteristic
237C22×M16—861no—
238C23×C8—431no—
239#525—861no—
240C22×C16—431no—
241C22×C16C2×D4311yescharacteristic
242#467—431no—
243#467—431no—
244#466—431no—
245#466—431no—
246#465—861no—
247#465—861no—
248C2×#108—431no—
249C2×#108—862no—
250C2×#108—861no—
251C2×#108—862no—
252C2×#108C2×D4311yescharacteristic
253#427—431no—
254#416—861no—
255#359—22no—
256#359—862no—
257C22⋊C16—861no—
258C22⋊C16—861no—
259C43#1299011yescharacteristic, complemented, Sylow
260C2×#41—21no—
261C23×C4—431no—
262#135—21no—
263#135—21no—
264#135—21no—
265#135—21no—
266C2×Q16C4×D4311yescharacteristic
267C2×SD16—21no—
268C2×D8C4×D4311yescharacteristic
269C2×M16—21no—
270C2×M16—864no—
271C2×M16—861no—
272C2×M16—1721no—
273C2×M16—1722no—
274C22×C8—431no—
275C22×C8—431no—
276C22×C8—431no—
277C22×C8—431no—
278C22×C8—431no—
279C22×C8—861no—
280C22×C8—861no—
281C22×C8—861no—
282C22×C8—861no—
283C22×C8—1721no—
284C22×C8C22×D4311yescharacteristic
285#123—1721no—
286C22⋊Q8—861no—
287C22⋊Q8—861no—
288#121—861no—
289#121—861no—
290#120—1721no—
291C4×D4—1721no—
292C4×D4—1721no—
293#117—861no—
294C2×C16—21no—
295C2×C16—21no—
296C2×C16—21no—
297C2×C16—861no—
298C2×C16—861no—
299C2×C16—861no—
300#108—21no—
301#108—432no—
302#108—864no—
303#108—861no—
304#108C22⋊D4312yescomplemented
305#107—431no—
306#107—431no—
307#106—861no—
308#103—861no—
309#103—861no—
310#102—861no—
311#102—861no—
312C24—431no—
313#41—41no—
314#41—41no—
315#41—41no—
316#41—41no—
317C2×Q8—21no—
318C2×D4—21no—
319C2×D4—41no—
320C2×D4—1721no—
321C2×D4—1721no—
322C22×C4—41no—
323C22×C4—431no—
324C22×C4—431no—
325C22×C4—431no—
326C22×C4—431no—
327C22×C4—431no—
328C22×C4—861no—
329C22×C4—861no—
330C22×C4—861no—
331C22×C4—861no—
332C22×C4D4×D4311yescharacteristic
333Q16—21no—
334Q16—21no—
335SD16—41no—
336SD16—41no—
337D8—21no—
338D8—21no—
339M16—22no—
340M16—41no—
341M16—862no—
342M16—1724no—
343M16—1721no—
344C2×C8—41no—
345C2×C8—431no—
346C2×C8—431no—
347C2×C8—861no—
348C2×C8—861no—
349C2×C8—861no—
350C2×C8—861no—
351C2×C8—861no—
352C2×C8—861no—
353C2×C8—861no—
354C2×C8—861no—
355C2×C8—861no—
356C2×C8—861no—
357C2×C8—1724no—
358C2×C8—1721no—
359C2×C8C2×C4×D4311yescharacteristic
360C2×C8#1062189811yescharacteristic
361C2×C8D4×D4311yescharacteristic
362C2×C8D4×D4311yescharacteristic
363C2×C8#1062190011yescharacteristic
364C2×C8C2×C22⋊D4311yescharacteristic
365C4⋊C4—861no—
366C4⋊C4—861no—
367C4⋊C4—1721no—
368C4⋊C4—1721no—
369C22⋊C4—1721no—
370C22⋊C4—1721no—
371C22⋊C4—1721no—
372C22⋊C4—1721no—
373C22⋊C4—1721no—
374C42—1721no—
375C16—41no—
376C16—1721no—
377C23—41no—
378C23—431no—
379C23—431no—
380C23—862no—
381C23—861no—
382C23—861no—
383C23—1721no—
384C23SD16×D4311yescharacteristic
385Q8—41no—
386Q8—41no—
387D4—41no—
388D4—41no—
389D4—81no—
390D4—81no—
391D4—3442no—
392D4—3442no—
393C2×C4—41no—
394C2×C4—81no—
395C2×C4—81no—
396C2×C4—431no—
397C2×C4—431no—
398C2×C4—861no—
399C2×C4—861no—
400C2×C4—861no—
401C2×C4—861no—
402C2×C4—861no—
403C2×C4—861no—
404C2×C4—861no—
405C2×C4—861no—
406C2×C4—861no—
407C2×C4—861no—
408C2×C4—1721no—
409C2×C4—1721no—
410C2×C4C22⋊C4×D4311yescharacteristic
411C2×C4#1306329311yescharacteristic
412C2×C4#1306330711yescharacteristic
413C2×C4D8×D4311yescharacteristic
414C2×C4#1306334911yescharacteristic
415C2×C4#1306335411yescharacteristic
416C8—42no—
417C8—861no—
418C8—861no—
419C8—1722no—
420C8(C22⋊D43)⋊C411yescharacteristic
421C8C4×C22⋊D4311yescharacteristic
422C8#1306329611yescharacteristic
423C8#1306329811yescharacteristic
424C22—21no—
425C22—21no—
426C22—81no—
427C22—81no—
428C22—81no—
429C22—432no—
430C22—861no—
431C22—861no—
432C22—861no—
433C22—861no—
434C22—861no—
435C22—1722no—
436C22—1722no—
437C22#102×D4311yescharacteristic
438C22#1458303611yescharacteristic
439C22#1458321611yescharacteristic
440C4—81no—
441C4—861no—
442C4—861no—
443C4—3441no—
444C4—3441no—
445C4#1458277511yescharacteristic
446C4#1458289711yescharacteristic
447C4#1458303111yescharacteristic
448C4#1458321111yescharacteristic
449C2—21no—
450C2—21no—
451C2—161no—
452C2—862no—
453C2—1721no—
454C2#1913490911yescharacteristic
455C2#359×D4311yescharacteristic
456C2#1913632111yescharacteristic
subgroupG/H
centerC2×C4D8×D43
commutatorC2×C8×C43C22×C4
FrattiniC22×C8C22×D43
FittingC2×C43×#359C2
socleC22×C43C2×#102
prime radical#19144172C2
cosocleC22×C8×C43C23
hypercenterC2×#359D43
hypocenterC43#12990
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ C2×#359

Complements

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

NH ≅ G/Ntype
2. C2×#108×D43C2semidirect
3. C2×#14582706C2semidirect
4. C2×(C2×D43)⋊C16C2semidirect
5. #19132692C2semidirect
6. #19132691C2semidirect
7. C2×C43×#359C2semidirect
59. #13063261D4semidirect
82. #108×C43D4semidirect
211. C2×D43#359semidirect
224. C2×#359D43semidirect
259. C43#12990semidirect
304. #108C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
#191441722
C2×#108×D432
C2×#145827062
C2×(C2×D43)⋊C162
#191326922
#191326912
C2×C43×#3592
#1299043