Finite Group Databasebeta

← #24992080

Subgroups — #24992080

Order 11008.

520 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143562C211yesmaximal, characteristic, complemented
2#19132982C211yesmaximal, characteristic, complemented
3C2×D4⋊(C43⋊C8)C211yesmaximal, characteristic, complemented
4#19132916C211yesmaximal, characteristic, complemented
5#19132446C211yesmaximal, characteristic, complemented
6#19132433C211yesmaximal, characteristic, complemented
7C4×AGL(1,ℤ/8)×C43C211yesmaximal, characteristic
8#14583030—21no—
9#14582977—21no—
10#14582971—22no—
11#14582952—21no—
12#14582952C2211yescharacteristic
13#14582952C2211yescharacteristic
14C2×C4⋊(C43⋊C8)C2211yescharacteristic
15C4×#10621877—21no—
16C2×C4×C43⋊C8C2211yescharacteristic
17Q8⋊(C43⋊C8)—21no—
18D4⋊(C43⋊C8)—21no—
19D4⋊(C43⋊C8)—21no—
20D4⋊(C43⋊C8)—21no—
21#14582623—22no—
22C2×AGL(1,ℤ/8)×C43C411yescharacteristic
23C4×#41×C43C2211yescharacteristic
24C2×C4×D4×C43C2211yescharacteristic
25C43×#442—21no—
26C43×#440—21no—
27C4×SD16×C43—21no—
28C4×D8×C43—21no—
29C43×#428C411yescharacteristic
30C43×#418C411yescharacteristic
31C43×#417C411yescharacteristic
32C4×M16×C43C2211yescharacteristic
33C2×#10621877—22no—
34C22×C43⋊C8—21no—
35C22×C43⋊C8—21no—
36C4⋊(C43⋊C8)—22no—
37C4⋊(C43⋊C8)—21no—
38C4⋊(C43⋊C8)—21no—
39C4⋊(C43⋊C8)—21no—
40C4⋊(C43⋊C8)—21no—
41C22⋊(C43⋊C8)—22no—
42C22⋊(C43⋊C8)—21no—
43C22⋊(C43⋊C8)D412yes—
44#13063236—22no—
45C4×C43⋊C8—21no—
46C4×C43⋊C8—21no—
47C4×C43⋊C8—21no—
48C4×C43⋊C8D411yescharacteristic
49C4×C43⋊C8D411yescharacteristic
50C2×#41×C43C2×C411yescharacteristic
51C22×D4×C43C2×C411yescharacteristic
52C23×C4×C43—21no—
53AGL(1,ℤ/8)×C43—22no—
54AGL(1,ℤ/8)×C43—22no—
55C2×SD16×C43—21no—
56C2×D8×C43—21no—
57C2×M16×C43C2×C411yescharacteristic
58C2×M16×C43C2×C411yescharacteristic
59C4×Q8×C43D411yescharacteristic
60C4×Q8×C43D411yescharacteristic
61C4×D4×C43—21no—
62C4×D4×C43—21no—
63C4×D4×C43—21no—
64C4×D4×C43—21no—
65C4×D4×C43—21no—
66C4×D4×C43—21no—
67C4×D4×C43D411yescharacteristic
68C4×D4×C43D411yescharacteristic
69#117×C43—21no—
70#117×C43C2×C411yescharacteristic
71C2×C4⋊C4×C43C2×C411yescharacteristic
72C2×C22⋊C4×C43—21no—
73C2×C42×C43—21no—
74C2×C42×C43C2311yescharacteristic
75#107×C43—21no—
76#106×C43—21no—
77#103×C43—21no—
78#102×C43—21no—
79#102×C43—21no—
80#102×C43—21no—
81#97×C43—21no—
82C4×C8×C43—21no—
83C24×C43—21no—
84#41×C43—21no—
85#41×C43—21no—
86#41×C43—21no—
87#41×C43—21no—
88C2×Q8×C43C22⋊C411yescharacteristic
89C2×D4×C43—21no—
90C2×D4×C43—21no—
91C2×D4×C43—21no—
92C2×D4×C43—21no—
93C2×D4×C43—21no—
94C2×D4×C43—21no—
95C2×D4×C43C22⋊C411yescharacteristic
96C2×D4×C43M1612yescomplemented
97C22×C4×C43—21no—
98C22×C4×C43—21no—
99C22×C4×C43—21no—
100C22×C4×C43—21no—
101C22×C4×C43—41no—
102C22×C4×C43—41no—
103C22×C4×C43—81no—
104C22×C4×C43—81no—
105C22×C4×C43C22×C411yescharacteristic
106C22×C4×C43C2×D411yescharacteristic
107C22×C4×C43#4111yescharacteristic
108SD16×C43—24no—
109D8×C43—24no—
110M16×C43—21no—
111M16×C43—21no—
112M16×C43—21no—
113M16×C43M1612yescomplemented
114C2×C8×C43—21no—
115C2×C8×C43—21no—
116C4⋊C4×C43—21no—
117C4⋊C4×C43—21no—
118C4⋊C4×C43—21no—
119C4⋊C4×C43—21no—
120C4⋊C4×C43C22⋊C411yescharacteristic
121C4⋊C4×C43C22⋊C411yescharacteristic
122C22⋊C4×C43—21no—
123C22⋊C4×C43—21no—
124C22⋊C4×C43—21no—
125C22⋊C4×C43—41no—
126C22⋊C4×C43—41no—
127C42×C43—21no—
128C42×C43—21no—
129C42×C43—21no—
130C42×C43C2×D411yescharacteristic
131C42×C43C2×D411yescharacteristic
132C42×C43C2×D411yescharacteristic
133C42×C43#4111yescharacteristic
134#10621877—44no—
135C2×C43⋊C8—21no—
136C2×C43⋊C8—21no—
137C2×C43⋊C8—22no—
138C2×C43⋊C8—42no—
139C2×C43⋊C8—41no—
140C2×C43⋊C8—41no—
141C2×C43⋊C8—81no—
142C23×C43—21no—
143C23×C43—22no—
144C23×C43—41no—
145C23×C43—41no—
146C23×C43—81no—
147C23×C43—81no—
148C23×C43C4×D411yescharacteristic
149Q8×C43—21no—
150Q8×C43—21no—
151D4×C43—21no—
152D4×C43—22no—
153D4×C43—21no—
154D4×C43—22no—
155D4×C43—41no—
156D4×C43—41no—
157D4×C43—41no—
158D4×C43—41no—
159C2×C4×C43—21no—
160C2×C4×C43—21no—
161C2×C4×C43—21no—
162C2×C4×C43—21no—
163C2×C4×C43—21no—
164C2×C4×C43—41no—
165C2×C4×C43—42no—
166C2×C4×C43—41no—
167C2×C4×C43—41no—
168C2×C4×C43—41no—
169C2×C4×C43—41no—
170C2×C4×C43—41no—
171C2×C4×C43—82no—
172C2×C4×C43—81no—
173C2×C4×C43—81no—
174C2×C4×C43—81no—
175C2×C4×C43C2×C22⋊C411yescharacteristic
176C2×C4×C43C4×D411yescharacteristic
177C2×C4×C43#12011yescharacteristic
178C2×C4×C43#12111yescharacteristic
179C2×C4×C43#12111yescharacteristic
180C2×C4×C43#12311yescharacteristic
181C2×C4×C43C2×M1611yescharacteristic
182C2×C4×C43C2×M1611yescharacteristic
183C2×C4×C43#13111yescharacteristic
184C2×C4×C43#13111yescharacteristic
185C8×C43—22no—
186C8×C43—41no—
187C43⋊C8—22no—
188C43⋊C8—41no—
189C43⋊C8—42no—
190C43⋊C8—81no—
191C43⋊C8—81no—
192#9097—431nomaximal, Sylow
193C22×C43—21no—
194C22×C43—21no—
195C22×C43—42no—
196C22×C43—41no—
197C22×C43—41no—
198C22×C43—41no—
199C22×C43—82no—
200C22×C43—82no—
201C22×C43—81no—
202C22×C43—81no—
203C22×C43#38611yescharacteristic
204C22×C43#43511yescharacteristic
205C22×C43#43611yescharacteristic
206C4×C43—21no—
207C4×C43—21no—
208C4×C43—21no—
209C4×C43—41no—
210C4×C43—41no—
211C4×C43—41no—
212C4×C43—81no—
213C4×C43#40711yescharacteristic
214C4×C43#40811yescharacteristic
215C4×C43#43511yescharacteristic
216C4×C43#43611yescharacteristic
217C4×C43#47111yescharacteristic
218C4×C43#47211yescharacteristic
219#2965—431no—
220C4×AGL(1,ℤ/8)D4311yescharacteristic
221#1477—431no—
222C2×D4⋊C8—431no—
223#1460—431no—
224#1283—431no—
225#1278—431no—
226C2×C43—21no—
227C2×C43—21no—
228C2×C43—81no—
229C2×C43—82no—
230C2×C43#187011yescharacteristic
231C2×C43#190611yescharacteristic
232C2×C43#190711yescharacteristic
233C2×AGL(1,ℤ/8)Dic4311yescharacteristic
234C4×#41C2×D4311yescharacteristic
235C2×C4×D4C2×D4311yescharacteristic
236#446—861no—
237#442—21no—
238#440—21no—
239C4×SD16—21no—
240C4×D8—21no—
241#436—861no—
242#435—862no—
243#431—431no—
244#431—431no—
245#431—861no—
246#428Dic4311yescharacteristic
247C2×C4⋊C8—431no—
248#418Dic4311yescharacteristic
249#417Dic4311yescharacteristic
250C4×M16—861no—
251C4×M16C2×D4311yescharacteristic
252C2×C4×C8—431no—
253Q8⋊C8—861no—
254D4⋊C8—861no—
255D4⋊C8—861no—
256D4⋊C8—861no—
257#323—862no—
258C43#909711yescharacteristic, complemented, Sylow
259C2×#41C2×Dic4311yescharacteristic
260C22×D4C2×Dic4311yescharacteristic
261C23×C4—21no—
262AGL(1,ℤ/8)—22no—
263AGL(1,ℤ/8)—22no—
264C2×SD16—21no—
265C2×D8—21no—
266C2×M16—862no—
267C2×M16C2×Dic4311yescharacteristic
268C2×M16C2×Dic4311yescharacteristic
269C22×C8—861no—
270C22×C8—861no—
271C4×Q8C22⋊D4311yescharacteristic
272C4×Q8C22⋊D4311yescharacteristic
273C4×D4—21no—
274C4×D4—21no—
275C4×D4—21no—
276C4×D4—21no—
277C4×D4—21no—
278C4×D4—21no—
279C4×D4C22⋊D4311yescharacteristic
280C4×D4C22⋊D4311yescharacteristic
281#117—21no—
282#117C2×Dic4311yescharacteristic
283C2×C4⋊C4C2×Dic4311yescharacteristic
284C2×C22⋊C4—21no—
285C2×C42—21no—
286C2×C42C22×D4311yescharacteristic
287#107—21no—
288#106—21no—
289C4⋊C8—862no—
290C4⋊C8—861no—
291C4⋊C8—861no—
292C4⋊C8—861no—
293C4⋊C8—861no—
294#103—21no—
295#102—21no—
296#102—21no—
297#102—21no—
298C22⋊C8—432no—
299C22⋊C8—862no—
300C22⋊C8—861no—
301#97—21no—
302#97—862no—
303C4×C8—21no—
304C4×C8—431no—
305C4×C8—431no—
306C4×C8—861no—
307C4×C8—861no—
308C4×C8—861no—
309C24—21no—
310#41—21no—
311#41—21no—
312#41—21no—
313#41—21no—
314C2×Q8C22⋊Dic4311yescharacteristic
315C2×D4—21no—
316C2×D4—21no—
317C2×D4—21no—
318C2×D4—21no—
319C2×D4—21no—
320C2×D4—21no—
321C2×D4#1062187712yescomplemented
322C2×D4C22⋊Dic4311yescharacteristic
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—41no—
328C22×C4—41no—
329C22×C4—81no—
330C22×C4—81no—
331C22×C4D4×D4311yescharacteristic
332C22×C4#1062190011yescharacteristic
333C22×C4C22×Dic4311yescharacteristic
334SD16—24no—
335D8—24no—
336M16—21no—
337M16—21no—
338M16—21no—
339M16—1724no—
340M16#1062187712yescomplemented
341C2×C8—21no—
342C2×C8—21no—
343C2×C8—861no—
344C2×C8—861no—
345C2×C8—862no—
346C2×C8—3441no—
347C2×C8—1722no—
348C2×C8—1721no—
349C2×C8—1721no—
350C4⋊C4—21no—
351C4⋊C4—21no—
352C4⋊C4—21no—
353C4⋊C4—21no—
354C4⋊C4C22⋊Dic4311yescharacteristic
355C4⋊C4C22⋊Dic4311yescharacteristic
356C22⋊C4—21no—
357C22⋊C4—21no—
358C22⋊C4—21no—
359C22⋊C4—41no—
360C22⋊C4—41no—
361C42—21no—
362C42—21no—
363C42—21no—
364C42D4×D4311yescharacteristic
365C42#1062190011yescharacteristic
366C42C2×C22⋊D4311yescharacteristic
367C42C2×C22⋊D4311yescharacteristic
368C23—21no—
369C23—22no—
370C23—41no—
371C23—41no—
372C23—81no—
373C23—81no—
374C23D4×Dic4311yescharacteristic
375Q8—21no—
376Q8—21no—
377D4—21no—
378D4—22no—
379D4—21no—
380D4—22no—
381D4—41no—
382D4—41no—
383D4—41no—
384D4—41no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—41no—
391C2×C4—42no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—82no—
398C2×C4—81no—
399C2×C4—81no—
400C2×C4—81no—
401C2×C4C2×C22⋊Dic4311yescharacteristic
402C2×C4D4×Dic4311yescharacteristic
403C2×C4#1306329311yescharacteristic
404C2×C4#1306329711yescharacteristic
405C2×C4#1306329711yescharacteristic
406C2×C4#1306330611yescharacteristic
407C2×C4C2×#1062187711yescharacteristic
408C2×C4C2×#1062187711yescharacteristic
409C2×C4#1306333211yescharacteristic
410C2×C4#1306333211yescharacteristic
411C8—22no—
412C8—41no—
413C8—862no—
414C8—3441no—
415C8—3441no—
416C8—1721no—
417C8—1722no—
418C22—21no—
419C22—21no—
420C22—41no—
421C22—41no—
422C22—41no—
423C22—42no—
424C22—82no—
425C22—82no—
426C22—81no—
427C22—81no—
428C22#1458277911yescharacteristic
429C22#1458297111yescharacteristic
430C22#1458297711yescharacteristic
431C4—21no—
432C4—21no—
433C4—21no—
434C4—41no—
435C4—41no—
436C4—41no—
437C4—81no—
438C4#1458286311yescharacteristic
439C4#1458286611yescharacteristic
440C4#1458297111yescharacteristic
441C4#1458297711yescharacteristic
442C4#1458316011yescharacteristic
443C4#1458316711yescharacteristic
444C2—21no—
445C2—21no—
446C2—81no—
447C2—82no—
448C2#1913489311yescharacteristic
449C2#1913509811yescharacteristic
450C2#1913510511yescharacteristic
subgroupG/H
centerC2×C4#13063297
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC4×AGL(1,ℤ/8)×C43C2
socleC22×C43#386
prime radicalC2×AGL(1,ℤ/8)×C43C4
cosocleC2×C42×C43C23
hypercenterC4×AGL(1,ℤ/8)D43
hypocenterC43#9097
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #19143562C2semidirect
2. #19132982C2semidirect
3. C2×D4⋊(C43⋊C8)C2semidirect
4. #19132916C2semidirect
5. #19132446C2semidirect
6. #19132433C2semidirect
96. C2×D4×C43M16semidirect
113. M16×C43M16semidirect
258. C43#9097semidirect
321. C2×D4#10621877semidirect
340. M16#10621877semidirect

Maximal subgroups

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

subgroupindex
#191435622
#191329822
C2×D4⋊(C43⋊C8)2
#191329162
#191324462
#191324332
C4×AGL(1,ℤ/8)×C432
#909743