Finite Group Databasebeta

← #24988033

Subgroups — #24988033

Order 11008.

684 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
1C2×#14583507C211yesmaximal, characteristic
2#19132991C211yesmaximal, characteristic, complemented
3#19132990C211yesmaximal, characteristic, complemented
4#19132989C211yesmaximal, characteristic, complemented
5#19132907C211yesmaximal, characteristic
6#19132907C211yesmaximal, characteristic
7C43×#1479C211yesmaximal, characteristic, complemented
8#14583507—22no—
9#14583507—22no—
10#14583507—22no—
11#14583507—22no—
12C2×#13063323C411yescharacteristic
13C2×#13063320—21no—
14C2×#13063319—21no—
15C2×#13063317—21no—
16C2×#13063316C411yescharacteristic
17C2×#13063315—21no—
18C2×#13063305C411yescharacteristic
19C2×#13063301C411yescharacteristic
20C2×C4×Dic86C2211yescharacteristic
21C2×#13063282C2211yescharacteristic
22#14582952C2211yescharacteristic
23#14582952C2211yescharacteristic
24#14582631—22no—
25Q8⋊(C43⋊C8)—22no—
26#14582629—22no—
27#14582624—21no—
28#14582624—21no—
29#14582622—21no—
30#14582622—21no—
31C2×C4×Q8×C43C2211yescharacteristic
32C43×#431C2211yescharacteristic
33C43×#431C2211yescharacteristic
34C43×Q8⋊C8—22no—
35C22×Dic86C2×C411yescharacteristic
36C22×C4×D43C2×C411yescharacteristic
37#13063323—22no—
38#13063323—22no—
39#13063320—24no—
40#13063320—24no—
41#13063319—24no—
42#13063319—24no—
43#13063317—24no—
44#13063317—24no—
45#13063316—22no—
46#13063316—22no—
47#13063315—24no—
48#13063315—24no—
49#13063305—22no—
50#13063305—22no—
51#13063301—22no—
52#13063301—22no—
53C4×Dic86—21no—
54C4×Dic86—21no—
55C4×Dic86D412yes—
56C4×Dic86D412yes—
57#13063282—21no—
58#13063282—21no—
59#13063282—21no—
60#13063282—21no—
61C2×C4⋊Dic43—21no—
62C2×C4⋊Dic43—21no—
63C2×C4⋊Dic43C2×C411yescharacteristic
64C2×Dic43⋊C4—21no—
65C2×Dic43⋊C4—21no—
66C2×Dic43⋊C4—21no—
67C2×Dic43⋊C4—21no—
68C2×Dic43⋊C4—21no—
69C2×Dic43⋊C4D411yescharacteristic
70C2×Dic43⋊C4D411yescharacteristic
71C2×(C2×D43)⋊C4—21no—
72C2×(C2×D43)⋊C4—21no—
73C2×(C2×D43)⋊C4D411yescharacteristic
74C2×(C2×D43)⋊C4D411yescharacteristic
75C2×C4×Dic43—21no—
76C2×C4×Dic43C2×C411yescharacteristic
77C4⋊(C43⋊C8)—21no—
78C4⋊(C43⋊C8)—21no—
79C22⋊(C43⋊C8)—21no—
80C22⋊(C43⋊C8)—21no—
81C4×C43⋊C8—21no—
82C4×C43⋊C8—21no—
83C22×Q8×C43C2×C411yescharacteristic
84C4×Q8×C43—21no—
85C4×Q8×C43—21no—
86C4×Q8×C43D412yes—
87C4×Q8×C43D412yes—
88C2×C4⋊C4×C43—21no—
89C2×C4⋊C4×C43C2×C411yescharacteristic
90C2×C42×C43—21no—
91C2×C42×C43C2311yescharacteristic
92C4⋊C8×C43—21no—
93C4⋊C8×C43—21no—
94C22⋊C8×C43—21no—
95C22⋊C8×C43—21no—
96C4×C8×C43—21no—
97C4×C8×C43—21no—
98C23×D43C22⋊C411yescharacteristic
99C2×Q8×C43—21no—
100C2×Q8×C43—22no—
101C2×Q8×C43—22no—
102C2×Q8×C43C22⋊C412yes—
103C22×C4×C43—21no—
104C22×C4×C43—21no—
105C22×C4×C43C22×C411yescharacteristic
106C22×C4×C43C2×D411yescharacteristic
107C22×C4×C43C2×D411yescharacteristic
108C22×Dic43—21no—
109C22×Dic43—21no—
110C22×Dic43C22⋊C411yescharacteristic
111C22×Dic43C22⋊C411yescharacteristic
112C22×Dic43C22⋊C411yescharacteristic
113C2×C4×D43—21no—
114C2×C4×D43—21no—
115C2×C4×D43—22no—
116C2×C4×D43—22no—
117C2×Dic86—22no—
118C2×Dic86—22no—
119C2×Dic86—21no—
120C2×Dic86C22⋊C412yes—
121C2×C8×C43—41no—
122C2×C8×C43—41no—
123C4⋊C4×C43—21no—
124C4⋊C4×C43—22no—
125C4⋊C4×C43—22no—
126C4⋊C4×C43C22⋊C412yes—
127C42×C43—22no—
128C42×C43—22no—
129C42×C43C2×D411yescharacteristic
130C42×C43C2×D411yescharacteristic
131C42×C43C2×D411yescharacteristic
132C42×C43C2×D411yescharacteristic
133(C2×D43)⋊C4—24no—
134(C2×D43)⋊C4—24no—
135(C2×D43)⋊C4—21no—
136(C2×D43)⋊C4—21no—
137(C2×D43)⋊C4—21no—
138(C2×D43)⋊C4—21no—
139C4⋊Dic43—24no—
140C4⋊Dic43—24no—
141C4⋊Dic43—21no—
142C4⋊Dic43C22⋊C412yes—
143Dic43⋊C4—24no—
144Dic43⋊C4—24no—
145Dic43⋊C4—24no—
146Dic43⋊C4—24no—
147Dic43⋊C4—22no—
148Dic43⋊C4—22no—
149Dic43⋊C4—21no—
150Dic43⋊C4—21no—
151Dic43⋊C4—21no—
152Dic43⋊C4—21no—
153C4×Dic43—21no—
154C4×Dic43—21no—
155C4×Dic43—22no—
156C4×Dic43—22no—
157C2×C43⋊C8—41no—
158C2×C43⋊C8—41no—
159C23×C43C2×C22⋊C411yescharacteristic
160C22×D43—21no—
161C22×D43—22no—
162C22×D43—41no—
163C22×D43—41no—
164Q8×C43—22no—
165Q8×C43—22no—
166Q8×C43—42no—
167C2×C4×C43—22no—
168C2×C4×C43—22no—
169C2×C4×C43—41no—
170C2×C4×C43—41no—
171C2×C4×C43—42no—
172C2×C4×C43—42no—
173C2×C4×C43C2×C22⋊C411yescharacteristic
174C2×C4×C43C2×C22⋊C411yescharacteristic
175C2×C4×C43#12011yescharacteristic
176C2×C4×C43#12011yescharacteristic
177C2×C4×C43#12011yescharacteristic
178C2×C4×C43#12011yescharacteristic
179C2×C4×C43#13112yes—
180C2×C4×C43#13112yes—
181C2×Dic43—21no—
182C2×Dic43—21no—
183C2×Dic43—22no—
184C2×Dic43—22no—
185C2×Dic43—21no—
186C2×Dic43—22no—
187C2×Dic43—42no—
188C2×Dic43—42no—
189C2×Dic43—41no—
190C2×Dic43—41no—
191C4×D43—42no—
192C4×D43—41no—
193C4×D43—41no—
194Dic86—24no—
195Dic86—41no—
196Dic86—41no—
197C8×C43—81no—
198C8×C43—81no—
199C43⋊C8—81no—
200C43⋊C8—81no—
201#8327—431nomaximal, Sylow
202C22×C43—21no—
203C22×C43—21no—
204C22×C43#37911yescharacteristic
205C22×C43#40812yes—
206C2×D43—41no—
207C2×D43—41no—
208C2×D43—41no—
209C2×D43—82no—
210C4×C43—21no—
211C4×C43—21no—
212C4×C43—21no—
213C4×C43—21no—
214C4×C43—42no—
215C4×C43—42no—
216C4×C43#40812yes—
217C4×C43#40811yescharacteristic
218C4×C43#40811yescharacteristic
219Dic43—41no—
220Dic43—41no—
221Dic43—42no—
222Dic43—42no—
223Dic43—41no—
224C2×#541—431no—
225#1479—431no—
226#1479—431no—
227#1479—431no—
228#1479D4311yescharacteristic, complemented
229#1458—431no—
230#1458—431no—
231C2×C43—22no—
232C2×C43#178011yescharacteristic
233C2×C43#179611yescharacteristic
234C2×C43#179611yescharacteristic
235D43—81no—
236#541—862no—
237#541—862no—
238#541—862no—
239#541—862no—
240C2×C4⋊Q8—431no—
241C2×#126—861no—
242C2×#126—861no—
243C2×#125—431no—
244C2×#125—861no—
245C2×#125—861no—
246C2×C22⋊Q8—431no—
247C2×C22⋊Q8—431no—
248C2×C4×Q8—431no—
249C2×C4×Q8C2×D4311yescharacteristic
250C2×#117—431no—
251#431—431no—
252#431—431no—
253#431C2×D4311yescharacteristic
254#431C2×D4311yescharacteristic
255Q8⋊C8—22no—
256Q8⋊C8—862no—
257Q8⋊C8—862no—
258Q8⋊C8—862no—
259#324—861no—
260#324—861no—
261#323—861no—
262#323—861no—
263C43#832711yescharacteristic, complemented, Sylow
264C22×Q8—431no—
265C22×Q8C4×D4311yescharacteristic
266C23×C4—431no—
267C4⋊Q8—862no—
268C4⋊Q8—862no—
269#126—864no—
270#126—864no—
271#126—864no—
272#126—864no—
273#125—864no—
274#125—864no—
275#125—862no—
276#125—864no—
277#125—864no—
278#125—862no—
279C22⋊Q8—862no—
280C22⋊Q8—862no—
281C22⋊Q8—862no—
282C22⋊Q8—862no—
283C4×Q8—21no—
284C4×Q8—21no—
285C4×Q8—432no—
286C4×Q8—432no—
287C4×Q8—861no—
288C4×Q8—861no—
289C4×Q8D17212yes—
290C4×Q8C22⋊D4312yes—
291#117—861no—
292#117—861no—
293#117—861no—
294#117—861no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—431no—
297C2×C4⋊C4—431no—
298C2×C4⋊C4—431no—
299C2×C4⋊C4—861no—
300C2×C4⋊C4—861no—
301C2×C4⋊C4—861no—
302C2×C4⋊C4—861no—
303C2×C4⋊C4—861no—
304C2×C4⋊C4—861no—
305C2×C4⋊C4—861no—
306C2×C4⋊C4C4×D4311yescharacteristic
307C2×C22⋊C4—431no—
308C2×C22⋊C4—431no—
309C2×C22⋊C4—861no—
310C2×C22⋊C4—861no—
311C2×C42—21no—
312C2×C42—431no—
313C2×C42—861no—
314C2×C42C22×D4311yescharacteristic
315C4⋊C8—21no—
316C4⋊C8—21no—
317C4⋊C8—861no—
318C4⋊C8—861no—
319C22⋊C8—21no—
320C22⋊C8—21no—
321C22⋊C8—861no—
322C22⋊C8—861no—
323C4×C8—21no—
324C4×C8—21no—
325C4×C8—861no—
326C4×C8—861no—
327C24—431no—
328C2×Q8—21no—
329C2×Q8—22no—
330C2×Q8—22no—
331C2×Q8—432no—
332C2×Q8—861no—
333C2×Q8—862no—
334C2×Q8—862no—
335C2×Q8(C2×D43)⋊C412yes—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—431no—
339C22×C4—431no—
340C22×C4—431no—
341C22×C4—861no—
342C22×C4—861no—
343C22×C4—861no—
344C22×C4—861no—
345C22×C4—862no—
346C22×C4—862no—
347C22×C4C2×C4×D4311yescharacteristic
348C22×C4D4×D4311yescharacteristic
349C22×C4D4×D4311yescharacteristic
350C2×C8—41no—
351C2×C8—41no—
352C2×C8—1721no—
353C2×C8—1721no—
354C4⋊C4—21no—
355C4⋊C4—22no—
356C4⋊C4—22no—
357C4⋊C4—432no—
358C4⋊C4—864no—
359C4⋊C4—864no—
360C4⋊C4—864no—
361C4⋊C4—864no—
362C4⋊C4—864no—
363C4⋊C4—864no—
364C4⋊C4—861no—
365C4⋊C4—861no—
366C4⋊C4—861no—
367C4⋊C4—862no—
368C4⋊C4—861no—
369C4⋊C4—861no—
370C4⋊C4—862no—
371C4⋊C4(C2×D43)⋊C412yes—
372C22⋊C4—864no—
373C22⋊C4—864no—
374C22⋊C4—861no—
375C22⋊C4—861no—
376C22⋊C4—861no—
377C22⋊C4—861no—
378C42—22no—
379C42—22no—
380C42—861no—
381C42—861no—
382C42—862no—
383C42—862no—
384C42C2×D17211yescharacteristic
385C42D4×D4311yescharacteristic
386C42D4×D4311yescharacteristic
387C42C2×C22⋊D4311yescharacteristic
388C23—862no—
389C23—861no—
390C23—1721no—
391C23—1721no—
392C23C22⋊C4×D4311yescharacteristic
393Q8—22no—
394Q8—22no—
395Q8—42no—
396Q8—864no—
397Q8—1721no—
398Q8—1721no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—862no—
406C2×C4—862no—
407C2×C4—861no—
408C2×C4—861no—
409C2×C4—862no—
410C2×C4—861no—
411C2×C4—1722no—
412C2×C4—1722no—
413C2×C4—1722no—
414C2×C4—1721no—
415C2×C4—1721no—
416C2×C4—1721no—
417C2×C4—1721no—
418C2×C4C22⋊C4×D4311yescharacteristic
419C2×C4C2×(C2×D43)⋊C411yescharacteristic
420C2×C4#1306329311yescharacteristic
421C2×C4#1306329311yescharacteristic
422C2×C4#1306329511yescharacteristic
423C2×C4#1306329511yescharacteristic
424C2×C4#1306333112yes—
425C2×C4#1306333312yes—
426C8—81no—
427C8—81no—
428C8—3441no—
429C8—3441no—
430C22—21no—
431C22—21no—
432C22—3442no—
433C22—1721no—
434C22—1721no—
435C22—1721no—
436C22#1458275411yescharacteristic
437C22#1458286412yes—
438C4—21no—
439C4—21no—
440C4—21no—
441C4—21no—
442C4—42no—
443C4—42no—
444C4—1721no—
445C4—1722no—
446C4—1722no—
447C4—1721no—
448C4—1721no—
449C4#1458286412yes—
450C4#1458286511yescharacteristic
451C4#1458286711yescharacteristic
452C2—22no—
453C2—3441no—
454C2#1913450611yescharacteristic
455C2#1913456711yescharacteristic
456C2#1913456911yescharacteristic
subgroupG/H
centerC22#14582754
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1479C2
socleC22×C43#379
prime radicalC23×D43C22⋊C4
cosocleC2×C42×C43C23
hypercenter#1479D43
hypocenterC43#8327
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1479

Complements

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

NH ≅ G/Ntype
2. #19132991C2semidirect
3. #19132990C2semidirect
4. #19132989C2semidirect
7. C43×#1479C2semidirect
228. #1479D43semidirect
263. C43#8327semidirect

Maximal subgroups

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

subgroupindex
C2×#145835072
#191329912
#191329902
#191329892
#191329072
C43×#14792
#832743