Finite Group Databasebeta

← #24988025

Subgroups — #24988025

Order 11008.

748 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583514C211yesmaximal, characteristic
2#19132991C211yesmaximal, characteristic, complemented
3#19132989C211yesmaximal, characteristic, complemented
4#19132986C211yesmaximal, characteristic, complemented
5#19132907C211yesmaximal, characteristic, complemented
6#19132907C211yesmaximal, characteristic, complemented
7C43×#1478C211yesmaximal, characteristic, complemented
8#14583514—22no—
9#14583514—22no—
10#14583514—22no—
11#14583514—22no—
12C2×#13063324C411yescharacteristic
13C2×#13063318—21no—
14C2×#13063312C411yescharacteristic
15C2×#13063311—21no—
16C2×#13063308—21no—
17C2×#13063305C411yescharacteristic
18C2×#13063304—21no—
19C2×#13063296C411yescharacteristic
20C2×C4×Dic86C2211yescharacteristic
21C2×#13063282C2211yescharacteristic
22#14582952C2211yescharacteristic
23#14582952C2211yescharacteristic
24#14582631—22no—
25#14582629—22no—
26D4⋊(C43⋊C8)—22no—
27#14582624—21no—
28#14582624—21no—
29#14582622—21no—
30#14582622—21no—
31C2×C4×D4×C43C2211yescharacteristic
32C43×#431C2211yescharacteristic
33C43×#431C2211yescharacteristic
34C43×D4⋊C8—22no—
35C22×Dic86—21no—
36C22×Dic86C2×C411yescharacteristic
37C22×C22⋊D43—21no—
38C22×C4×D43C2×C411yescharacteristic
39#13063324—22no—
40#13063324—22no—
41#13063318—24no—
42#13063318—24no—
43#13063312—22no—
44#13063312—22no—
45#13063311—24no—
46#13063311—24no—
47#13063308—24no—
48#13063308—24no—
49#13063305—22no—
50#13063305—22no—
51#13063304—24no—
52#13063304—24no—
53#13063296—22no—
54#13063296—22no—
55C4×Dic86—21no—
56C4×Dic86—21no—
57C4×Dic86D412yes—
58C4×Dic86D412yes—
59#13063282—21no—
60#13063282—21no—
61#13063282—21no—
62#13063282—21no—
63C2×C4⋊Dic43—21no—
64C2×C4⋊Dic43C2×C411yescharacteristic
65C2×Dic43⋊C4—21no—
66C2×Dic43⋊C4—21no—
67C2×Dic43⋊C4D411yescharacteristic
68C2×Dic43⋊C4D411yescharacteristic
69C2×C22⋊Dic43—21no—
70C2×C22⋊Dic43—21no—
71C2×C22⋊Dic43—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×D4×C43C2×C411yescharacteristic
84C23×C4×C43—21no—
85C4×D4×C43—21no—
86C4×D4×C43—21no—
87C4×D4×C43D412yes—
88C4×D4×C43D412yes—
89C2×C4⋊C4×C43C2×C411yescharacteristic
90C2×C22⋊C4×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—
98C24×C43—21no—
99C23×D43C22⋊C411yescharacteristic
100C2×D4×C43—21no—
101C2×D4×C43—22no—
102C2×D4×C43—22no—
103C2×D4×C43C22⋊C412yes—
104C22×C4×C43—22no—
105C22×C4×C43—22no—
106C22×C4×C43—21no—
107C22×C4×C43—82no—
108C22×C4×C43C22×C411yescharacteristic
109C22×C4×C43C2×D411yescharacteristic
110C22×C4×C43C2×D411yescharacteristic
111C2×C22⋊D43—24no—
112C2×C22⋊D43—82no—
113C22×Dic43—21no—
114C22×Dic43—21no—
115C22×Dic43C22⋊C411yescharacteristic
116C22×Dic43C22⋊C411yescharacteristic
117C22×Dic43C22⋊C411yescharacteristic
118C2×C4×D43—21no—
119C2×C4×D43—21no—
120C2×C4×D43—22no—
121C2×C4×D43—22no—
122C2×Dic86—22no—
123C2×Dic86—22no—
124C2×Dic86—21no—
125C2×Dic86—24no—
126C2×Dic86—82no—
127C2×Dic86C22⋊C412yes—
128C2×C8×C43—41no—
129C2×C8×C43—41no—
130C4⋊C4×C43—21no—
131C4⋊C4×C43C22⋊C412yes—
132C22⋊C4×C43—22no—
133C22⋊C4×C43—22no—
134C42×C43C2×D411yescharacteristic
135C42×C43C2×D411yescharacteristic
136C42×C43C2×D411yescharacteristic
137C42×C43C2×D411yescharacteristic
138C22⋊Dic43—24no—
139C22⋊Dic43—24no—
140C22⋊Dic43—24no—
141(C2×D43)⋊C4—24no—
142(C2×D43)⋊C4—21no—
143(C2×D43)⋊C4—21no—
144(C2×D43)⋊C4—21no—
145(C2×D43)⋊C4—21no—
146C4⋊Dic43—24no—
147C4⋊Dic43—21no—
148C4⋊Dic43C22⋊C412yes—
149Dic43⋊C4—24no—
150Dic43⋊C4—22no—
151Dic43⋊C4—22no—
152Dic43⋊C4—21no—
153Dic43⋊C4—21no—
154Dic43⋊C4—21no—
155Dic43⋊C4—21no—
156C4×Dic43—21no—
157C4×Dic43—21no—
158C4×Dic43—22no—
159C4×Dic43—22no—
160C2×C43⋊C8—41no—
161C2×C43⋊C8—41no—
162C23×C43—22no—
163C23×C43—42no—
164C23×C43—42no—
165C23×C43—42no—
166C23×C43C2×C22⋊C411yescharacteristic
167C22×D43—21no—
168C22×D43—22no—
169C22×D43—41no—
170C22×D43—41no—
171D4×C43—22no—
172D4×C43—22no—
173D4×C43—42no—
174C2×C4×C43—22no—
175C2×C4×C43—41no—
176C2×C4×C43—41no—
177C2×C4×C43—42no—
178C2×C4×C43—82no—
179C2×C4×C43—82no—
180C2×C4×C43C2×C22⋊C411yescharacteristic
181C2×C4×C43C2×C22⋊C411yescharacteristic
182C2×C4×C43#12011yescharacteristic
183C2×C4×C43#12011yescharacteristic
184C2×C4×C43#12011yescharacteristic
185C2×C4×C43#12011yescharacteristic
186C2×C4×C43#13112yes—
187C2×C4×C43#13112yes—
188C22⋊D43—84no—
189C2×Dic43—21no—
190C2×Dic43—22no—
191C2×Dic43—22no—
192C2×Dic43—21no—
193C2×Dic43—21no—
194C2×Dic43—22no—
195C2×Dic43—42no—
196C2×Dic43—42no—
197C2×Dic43—41no—
198C2×Dic43—41no—
199C4×D43—42no—
200C4×D43—41no—
201C4×D43—41no—
202Dic86—24no—
203Dic86—41no—
204Dic86—41no—
205Dic86—84no—
206C8×C43—81no—
207C8×C43—81no—
208C43⋊C8—81no—
209C43⋊C8—81no—
210#8325—431nomaximal, Sylow
211C22×C43—21no—
212C22×C43—21no—
213C22×C43—42no—
214C22×C43—42no—
215C22×C43—42no—
216C22×C43—84no—
217C22×C43#37911yescharacteristic
218C22×C43#40812yes—
219C2×D43—41no—
220C2×D43—41no—
221C2×D43—41no—
222C2×D43—82no—
223C4×C43—21no—
224C4×C43—21no—
225C4×C43—21no—
226C4×C43—21no—
227C4×C43—42no—
228C4×C43#40812yes—
229C4×C43#40811yescharacteristic
230C4×C43#40811yescharacteristic
231Dic43—41no—
232Dic43—42no—
233Dic43—41no—
234Dic43—42no—
235Dic43—41no—
236C2×#542—431no—
237#1479—431no—
238#1479—431no—
239#1478—431no—
240#1478D4311yescharacteristic, complemented
241#1458—431no—
242#1458—431no—
243C2×C43—22no—
244C2×C43—82no—
245C2×C43#178011yescharacteristic
246C2×C43#179511yescharacteristic
247C2×C43#179611yescharacteristic
248D43—81no—
249#542—862no—
250#542—862no—
251#542—862no—
252#542—862no—
253C2×C4⋊Q8—431no—
254C2×#126—861no—
255C2×#124—431no—
256C2×#124—861no—
257C2×#123—861no—
258C2×C22⋊Q8—431no—
259C2×C22⋊Q8—861no—
260C2×#121—431no—
261C2×C4×Q8—431no—
262C2×C4×D4C2×D4311yescharacteristic
263C2×#117—431no—
264#431—431no—
265#431—431no—
266#431C2×D4311yescharacteristic
267#431C2×D4311yescharacteristic
268Q8⋊C8—862no—
269Q8⋊C8—862no—
270D4⋊C8—22no—
271D4⋊C8—862no—
272#324—861no—
273#324—861no—
274#323—861no—
275#323—861no—
276C43#832511yescharacteristic, complemented, Sylow
277C22×Q8—431no—
278C22×Q8—861no—
279C22×D4—861no—
280C22×D4C4×D4311yescharacteristic
281C23×C4—21no—
282C23×C4—431no—
283C4⋊Q8—862no—
284C4⋊Q8—862no—
285#126—864no—
286#126—864no—
287#124—864no—
288#124—864no—
289#124—862no—
290#124—862no—
291#123—864no—
292#123—864no—
293C22⋊Q8—862no—
294C22⋊Q8—864no—
295C22⋊Q8—864no—
296C22⋊Q8—862no—
297#121—862no—
298#121—862no—
299C4×Q8—432no—
300C4×Q8—432no—
301C4×Q8—861no—
302C4×Q8—861no—
303C4×D4—21no—
304C4×D4—21no—
305C4×D4D17212yes—
306C4×D4C22⋊D4312yes—
307#117—861no—
308#117—861no—
309#117—861no—
310#117—861no—
311C2×C4⋊C4—431no—
312C2×C4⋊C4—431no—
313C2×C4⋊C4—431no—
314C2×C4⋊C4—861no—
315C2×C4⋊C4—861no—
316C2×C4⋊C4—861no—
317C2×C4⋊C4C4×D4311yescharacteristic
318C2×C22⋊C4—21no—
319C2×C22⋊C4—431no—
320C2×C22⋊C4—431no—
321C2×C22⋊C4—861no—
322C2×C22⋊C4—861no—
323C2×C22⋊C4—861no—
324C2×C22⋊C4—861no—
325C2×C42—431no—
326C2×C42—861no—
327C2×C42C22×D4311yescharacteristic
328C4⋊C8—21no—
329C4⋊C8—21no—
330C4⋊C8—861no—
331C4⋊C8—861no—
332C22⋊C8—21no—
333C22⋊C8—21no—
334C22⋊C8—861no—
335C22⋊C8—861no—
336C4×C8—21no—
337C4×C8—21no—
338C4×C8—861no—
339C4×C8—861no—
340C24—21no—
341C24—431no—
342C2×Q8—432no—
343C2×Q8—864no—
344C2×Q8—861no—
345C2×Q8—862no—
346C2×Q8—862no—
347C2×Q8—3442no—
348C2×D4—21no—
349C2×D4—22no—
350C2×D4—22no—
351C2×D4—864no—
352C2×D4—3442no—
353C2×D4(C2×D43)⋊C412yes—
354C22×C4—21no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—82no—
358C22×C4—431no—
359C22×C4—431no—
360C22×C4—431no—
361C22×C4—861no—
362C22×C4—861no—
363C22×C4—861no—
364C22×C4—861no—
365C22×C4—862no—
366C22×C4—862no—
367C22×C4C2×C4×D4311yescharacteristic
368C22×C4D4×D4311yescharacteristic
369C22×C4D4×D4311yescharacteristic
370C2×C8—41no—
371C2×C8—41no—
372C2×C8—1721no—
373C2×C8—1721no—
374C4⋊C4—21no—
375C4⋊C4—432no—
376C4⋊C4—864no—
377C4⋊C4—864no—
378C4⋊C4—861no—
379C4⋊C4—861no—
380C4⋊C4—861no—
381C4⋊C4—862no—
382C4⋊C4—861no—
383C4⋊C4—861no—
384C4⋊C4—862no—
385C4⋊C4(C2×D43)⋊C412yes—
386C22⋊C4—22no—
387C22⋊C4—22no—
388C22⋊C4—864no—
389C22⋊C4—864no—
390C22⋊C4—864no—
391C22⋊C4—864no—
392C22⋊C4—861no—
393C22⋊C4—861no—
394C22⋊C4—861no—
395C22⋊C4—861no—
396C42—861no—
397C42—861no—
398C42—862no—
399C42—862no—
400C42C2×D17211yescharacteristic
401C42D4×D4311yescharacteristic
402C42D4×D4311yescharacteristic
403C42C2×C22⋊D4311yescharacteristic
404C23—22no—
405C23—42no—
406C23—42no—
407C23—42no—
408C23—862no—
409C23—861no—
410C23—1721no—
411C23—1721no—
412C23C22⋊C4×D4311yescharacteristic
413Q8—864no—
414Q8—3444no—
415Q8—1721no—
416Q8—1721no—
417D4—22no—
418D4—22no—
419D4—42no—
420D4—3444no—
421C2×C4—22no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—42no—
425C2×C4—82no—
426C2×C4—82no—
427C2×C4—862no—
428C2×C4—861no—
429C2×C4—862no—
430C2×C4—861no—
431C2×C4—862no—
432C2×C4—861no—
433C2×C4—1722no—
434C2×C4—1722no—
435C2×C4—1722no—
436C2×C4—1721no—
437C2×C4—1721no—
438C2×C4—1721no—
439C2×C4—1721no—
440C2×C4C22⋊C4×D4311yescharacteristic
441C2×C4C2×(C2×D43)⋊C411yescharacteristic
442C2×C4#1306329311yescharacteristic
443C2×C4#1306329311yescharacteristic
444C2×C4#1306329511yescharacteristic
445C2×C4#1306329511yescharacteristic
446C2×C4#1306333112yes—
447C2×C4#1306333312yes—
448C8—81no—
449C8—81no—
450C8—3441no—
451C8—3441no—
452C22—21no—
453C22—21no—
454C22—42no—
455C22—42no—
456C22—42no—
457C22—84no—
458C22—3442no—
459C22—1721no—
460C22—1721no—
461C22—1721no—
462C22#1458275411yescharacteristic
463C22#1458286412yes—
464C4—21no—
465C4—21no—
466C4—21no—
467C4—21no—
468C4—42no—
469C4—1721no—
470C4—1722no—
471C4—1722no—
472C4—1721no—
473C4—1721no—
474C4#1458286412yes—
475C4#1458286511yescharacteristic
476C4#1458286711yescharacteristic
477C2—22no—
478C2—82no—
479C2—3441no—
480C2#1913450611yescharacteristic
481C2#1913456211yescharacteristic
482C2#1913456911yescharacteristic
subgroupG/H
centerC22#14582754
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1478C2
socleC22×C43#379
prime radicalC2×#13063296C4
cosocleC2×C42×C43C23
hypercenter#1478D43
hypocenterC43#8325
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1478

Complements

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

NH ≅ G/Ntype
2. #19132991C2semidirect
3. #19132989C2semidirect
4. #19132986C2semidirect
5. #19132907C2semidirect
6. #19132907C2semidirect
7. C43×#1478C2semidirect
240. #1478D43semidirect
276. C43#8325semidirect

Maximal subgroups

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

subgroupindex
C2×#145835142
#191329912
#191329892
#191329862
#191329072
C43×#14782
#832543