Finite Group Databasebeta

← #24992892

Subgroups — #24992892

Order 11008.

588 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19137060C211yesmaximal, characteristic, complemented
2#19135424C211yesmaximal, characteristic, complemented
3#19133090C211yesmaximal, characteristic, complemented
4#19133020C211yesmaximal, characteristic, complemented
5#19132497C211yesmaximal, characteristic, complemented
6#19132427C211yesmaximal, characteristic, complemented
7C43×#3100C211yesmaximal, characteristic
8C2×#13063284—21no—
9#14582952C2211yescharacteristic
10#14582923C2211yescharacteristic
11C2×#13063252—21no—
12C2×#13063252—21no—
13#14582802—21no—
14#14582798—21no—
15#14582792—22no—
16C4×C4⋊Dic43C2211yescharacteristic
17C4×C22⋊Dic43—21no—
18C42×Dic43C2211yescharacteristic
19#14582633—22no—
20D4⋊(C43⋊C8)—22no—
21C43×#532C2211yescharacteristic
22C2×C4×D4×C43C2211yescharacteristic
23C43×#480—21no—
24C43×#474C412yescomplemented
25C43×#459C412yescomplemented
26C43×#447—21no—
27C4×D8×C43—22no—
28C43×#431C2211yescharacteristic
29C2×#10621877—21no—
30#13063284—42no—
31#13063284—42no—
32C2×C4⋊Dic43—22no—
33C2×C4⋊Dic43—21no—
34C2×C22⋊Dic43—22no—
35C2×C22⋊Dic43—22no—
36C2×C4×Dic43—21no—
37C2×C4×Dic43—21no—
38C2×C4×Dic43—21no—
39C2×C4×Dic43D411yescharacteristic
40C2×C4×Dic43D411yescharacteristic
41C4⋊(C43⋊C8)—21no—
42C4⋊(C43⋊C8)—21no—
43C4⋊(C43⋊C8)—21no—
44#13063252—42no—
45#13063252—42no—
46C22⋊(C43⋊C8)—21no—
47C4×C43⋊C8—21no—
48C43⋊#95—22no—
49C43⋊#95D412yes—
50C2×#41×C43—21no—
51C22×D4×C43D411yescharacteristic
52C23×C4×C43—21no—
53C2×D8×C43—22no—
54C4⋊Q8×C43C2×C411yescharacteristic
55#127×C43C2×C411yescharacteristic
56#124×C43—21no—
57#121×C43—21no—
58#121×C43—21no—
59C4×D4×C43—21no—
60C4×D4×C43—21no—
61C4×D4×C43—21no—
62C4×D4×C43—21no—
63C4×D4×C43C2×C412yes—
64C4×D4×C43D412yes—
65C2×C4⋊C4×C43D411yescharacteristic
66C2×C22⋊C4×C43—21no—
67C2×C42×C43C2311yescharacteristic
68#107×C43—22no—
69C4⋊C8×C43C2×C412yes—
70#102×C43—22no—
71#102×C43—22no—
72C22⋊C8×C43—21no—
73C4×C8×C43—21no—
74C24×C43—21no—
75#41×C43—41no—
76#41×C43—41no—
77#41×C43—41no—
78#41×C43—41no—
79C2×Q8×C43—21no—
80C2×D4×C43—21no—
81C2×D4×C43—21no—
82C2×D4×C43—21no—
83C2×D4×C43—21no—
84C2×D4×C43—42no—
85C2×D4×C43—41no—
86C2×D4×C43C22⋊C412yes—
87C22×C4×C43—22no—
88C22×C4×C43—22no—
89C22×C4×C43—21no—
90C22×C4×C43—41no—
91C22×C4×C43—41no—
92C22×C4×C43—41no—
93C22×C4×C43—41no—
94C22×C4×C43—41no—
95C22×C4×C43C2×D411yescharacteristic
96C22×C4×C43C2×D411yescharacteristic
97C22×C4×C43C2×D411yescharacteristic
98C22×Dic43—21no—
99C22×Dic43—21no—
100C22×Dic43—22no—
101D8×C43—44no—
102C2×C8×C43—22no—
103C4⋊C4×C43—21no—
104C4⋊C4×C43—21no—
105C4⋊C4×C43—21no—
106C4⋊C4×C43C22⋊C412yes—
107C22⋊C4×C43—22no—
108C22⋊C4×C43—22no—
109C22⋊C4×C43—41no—
110C22⋊C4×C43—41no—
111C42×C43C22×C411yescharacteristic
112C42×C43C2×D411yescharacteristic
113C42×C43#4111yescharacteristic
114C42×C43#4111yescharacteristic
115C22⋊Dic43—44no—
116C22⋊Dic43—44no—
117C4⋊Dic43—44no—
118C4⋊Dic43—42no—
119C4×Dic43—21no—
120C4×Dic43—21no—
121C4×Dic43—21no—
122C4×Dic43—42no—
123C4×Dic43—42no—
124C4×Dic43—41no—
125C4×Dic43—41no—
126C4×Dic43D812yescomplemented
127#10621877—41no—
128#10621877—41no—
129C2×C43⋊C8—41no—
130C2×C43⋊C8—41no—
131C23×C43—22no—
132C23×C43—42no—
133C23×C43—42no—
134C23×C43—41no—
135C23×C43—41no—
136C23×C43—41no—
137C23×C43#12011yescharacteristic
138Q8×C43—41no—
139Q8×C43—41no—
140D4×C43—22no—
141D4×C43—22no—
142D4×C43—42no—
143D4×C43—42no—
144D4×C43—41no—
145D4×C43—41no—
146D4×C43—81no—
147D4×C43—81no—
148D4×C43—81no—
149C2×C4×C43—22no—
150C2×C4×C43—22no—
151C2×C4×C43—41no—
152C2×C4×C43—41no—
153C2×C4×C43—41no—
154C2×C4×C43—42no—
155C2×C4×C43—42no—
156C2×C4×C43—42no—
157C2×C4×C43—42no—
158C2×C4×C43—41no—
159C2×C4×C43—81no—
160C2×C4×C43—81no—
161C2×C4×C43C2×C22⋊C411yescharacteristic
162C2×C4×C43C4×D411yescharacteristic
163C2×C4×C43C4×D411yescharacteristic
164C2×C4×C43#12111yescharacteristic
165C2×C4×C43#12111yescharacteristic
166C2×C4×C43#12311yescharacteristic
167C2×C4×C43C2×D811yescharacteristic
168C2×C4×C43#13511yescharacteristic
169C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
170C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
171C2×Dic43—22no—
172C2×Dic43—22no—
173C2×Dic43—41no—
174C2×Dic43—41no—
175C2×Dic43—41no—
176C2×Dic43—41no—
177C2×Dic43—42no—
178C2×Dic43—42no—
179C2×Dic43—42no—
180C8×C43—42no—
181C43⋊C8—81no—
182C43⋊C8—81no—
183#9237—431nomaximal, Sylow
184C22×C43—21no—
185C22×C43—21no—
186C22×C43—42no—
187C22×C43—42no—
188C22×C43—42no—
189C22×C43—82no—
190C22×C43—82no—
191C22×C43—81no—
192C22×C43—81no—
193C22×C43—81no—
194C22×C43#38611yescharacteristic
195C22×C43#44711yescharacteristic
196C22×C43#44911yescharacteristic
197C4×C43—21no—
198C4×C43—21no—
199C4×C43—21no—
200C4×C43—42no—
201C4×C43—81no—
202C4×C43#42112yes—
203C4×C43C4×D811yescharacteristic
204C4×C43#44211yescharacteristic
205C4×C43#45911yescharacteristic
206C4×C43#46311yescharacteristic
207Dic43—42no—
208Dic43—42no—
209Dic43—82no—
210#3100D4311yescharacteristic
211#2293—431no—
212#1962—431no—
213#1502—431no—
214#1486—431no—
215#1303—431no—
216#1276—431no—
217C2×C43—21no—
218C2×C43—21no—
219C2×C43—82no—
220C2×C43—161no—
221C2×C43#187911yescharacteristic
222C2×C43#189711yescharacteristic
223C2×C43#190611yescharacteristic
224#532C2×D4311yescharacteristic
225C2×C4×D4C2×D4311yescharacteristic
226C2×#117—861no—
227#480—21no—
228#474Dic4312yescomplemented
229#459Dic4312yescomplemented
230#447—21no—
231C4×D8—22no—
232#431—431no—
233#431C2×D4311yescharacteristic
234#423—431no—
235C2×#104—861no—
236C2×#104—861no—
237#390—861no—
238#389—861no—
239#388—862no—
240C4×C4⋊C4—431no—
241C4×C22⋊C4—861no—
242C43—431no—
243#327—862no—
244D4⋊C8—862no—
245C43#923711yescharacteristic, complemented, Sylow
246C2×#41—21no—
247C22×D4C22⋊D4311yescharacteristic
248C23×C4—21no—
249C2×D8—22no—
250C2×M16—861no—
251C4⋊Q8C2×Dic4311yescharacteristic
252#127C2×Dic4311yescharacteristic
253#124—21no—
254#121—21no—
255#121—21no—
256C4×D4—21no—
257C4×D4—21no—
258C4×D4—21no—
259C4×D4—21no—
260C4×D4C2×Dic4312yes—
261C4×D4C22⋊D4312yes—
262#117—1722no—
263#117—1722no—
264C2×C4⋊C4—862no—
265C2×C4⋊C4—861no—
266C2×C4⋊C4C22⋊D4311yescharacteristic
267C2×C22⋊C4—21no—
268C2×C22⋊C4—862no—
269C2×C22⋊C4—862no—
270C2×C42—431no—
271C2×C42—431no—
272C2×C42—861no—
273C2×C42—861no—
274C2×C42—861no—
275C2×C42C22×D4311yescharacteristic
276#107—22no—
277C4⋊C8—861no—
278C4⋊C8—861no—
279C4⋊C8—861no—
280C4⋊C8C2×Dic4312yes—
281#104—1722no—
282#104—1722no—
283#102—22no—
284#102—22no—
285C22⋊C8—21no—
286C22⋊C8—861no—
287C4×C8—21no—
288C4×C8—861no—
289#95—432no—
290#95—862no—
291C24—21no—
292#41—41no—
293#41—41no—
294#41—41no—
295#41—41no—
296C2×Q8—21no—
297C2×D4—21no—
298C2×D4—21no—
299C2×D4—21no—
300C2×D4—21no—
301C2×D4—42no—
302C2×D4—41no—
303C2×D4C22⋊Dic4312yes—
304C22×C4—21no—
305C22×C4—22no—
306C22×C4—22no—
307C22×C4—41no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—41no—
312C22×C4—861no—
313C22×C4—861no—
314C22×C4—862no—
315C22×C4D4×D4311yescharacteristic
316C22×C4D4×D4311yescharacteristic
317C22×C4C2×C22⋊D4311yescharacteristic
318D8—44no—
319M16—1721no—
320M16—1721no—
321C2×C8—22no—
322C2×C8—1721no—
323C2×C8—1721no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—1722no—
328C4⋊C4—1724no—
329C4⋊C4C22⋊Dic4312yes—
330C22⋊C4—22no—
331C22⋊C4—22no—
332C22⋊C4—41no—
333C22⋊C4—41no—
334C22⋊C4—1724no—
335C22⋊C4—1724no—
336C42—432no—
337C42—861no—
338C42—861no—
339C42—861no—
340C42—1722no—
341C42—1722no—
342C42—1721no—
343C42—1721no—
344C42#1062190011yescharacteristic
345C42#1062190011yescharacteristic
346C42C22×Dic4311yescharacteristic
347C42C2×C22⋊D4311yescharacteristic
348C23—22no—
349C23—42no—
350C23—42no—
351C23—41no—
352C23—41no—
353C23—41no—
354C23#1306329311yescharacteristic
355Q8—41no—
356Q8—41no—
357D4—22no—
358D4—22no—
359D4—42no—
360D4—42no—
361D4—41no—
362D4—41no—
363D4—81no—
364D4—81no—
365D4—81no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4—42no—
375C2×C4—41no—
376C2×C4—81no—
377C2×C4—81no—
378C2×C4—862no—
379C2×C4—862no—
380C2×C4—1722no—
381C2×C4—1722no—
382C2×C4—1722no—
383C2×C4—1721no—
384C2×C4—1721no—
385C2×C4—1721no—
386C2×C4—1721no—
387C2×C4C2×C22⋊Dic4311yescharacteristic
388C2×C4D4×Dic4311yescharacteristic
389C2×C4D4×Dic4311yescharacteristic
390C2×C4#1306329711yescharacteristic
391C2×C4#1306329711yescharacteristic
392C2×C4#1306330611yescharacteristic
393C2×C4D8×D4311yescharacteristic
394C2×C4#1306334411yescharacteristic
395C2×C4#1306334911yescharacteristic
396C2×C4#1306334911yescharacteristic
397C8—42no—
398C8—3441no—
399C8—3441no—
400C22—21no—
401C22—21no—
402C22—42no—
403C22—42no—
404C22—42no—
405C22—82no—
406C22—82no—
407C22—81no—
408C22—81no—
409C22—81no—
410C22#1458277911yescharacteristic
411C22#1458303111yescharacteristic
412C22#1458304111yescharacteristic
413C4—21no—
414C4—21no—
415C4—21no—
416C4—42no—
417C4—81no—
418C4—3442no—
419C4—1722no—
420C4—1722no—
421C4#1458291612yes—
422C4D8×Dic4311yescharacteristic
423C4#1458301111yescharacteristic
424C4#1458309211yescharacteristic
425C4#1458311211yescharacteristic
426C2—21no—
427C2—21no—
428C2—82no—
429C2—161no—
430C2#1913494511yescharacteristic
431C2#1913504411yescharacteristic
432C2#1913509811yescharacteristic
subgroupG/H
centerC2×C4#13063297
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
Fitting, prime radicalC43×#3100C2
socleC22×C43#386
cosocleC2×C42×C43C23
hypercenter#3100D43
hypocenterC43#9237
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3100

Complements

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

NH ≅ G/Ntype
1. #19137060C2semidirect
2. #19135424C2semidirect
3. #19133090C2semidirect
4. #19133020C2semidirect
5. #19132497C2semidirect
6. #19132427C2semidirect
24. C43×#474C4semidirect
25. C43×#459C4semidirect
126. C4×Dic43D8semidirect
228. #474Dic43semidirect
229. #459Dic43semidirect
245. C43#9237semidirect

Maximal subgroups

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

subgroupindex
#191370602
#191354242
#191330902
#191330202
#191324972
#191324272
C43×#31002
#923743