Finite Group Databasebeta

← C2×#19133908 #25077745

Subgroups — C2×#19133908 #25077745

Order 11008.

958 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583653C211yesmaximal, characteristic
2C2×#14583309C211yesmaximal, characteristic, complemented
3C2×#14583308C211yesmaximal, characteristic, complemented
4C2×#14583293C211yesmaximal, characteristic
5#19133908C218yesmaximal, direct product factor
6C2×#14582640C211yesmaximal, characteristic, complemented
7C2×#14582638C211yesmaximal, characteristic
8C2×C43×#330C211yesmaximal, characteristic, complemented
9C22×Dic172—21no—
10C22×#10621873—21no—
11#14583653—22no—
12#14583653—22no—
13#14583653—22no—
14#14583653C2214yes—
15C2×#13063325C2211yescharacteristic
16C2×#13063324—21no—
17C2×#13063320—21no—
18C2×#13063320—21no—
19C2×#13063317C2211yescharacteristic
20C2×#13063313C2211yescharacteristic
21C2×#13063310—21no—
22C2×#13063305—21no—
23C2×#13063303—21no—
24#14583309—22no—
25#14583309C2214yescomplemented
26#14583308—22no—
27#14583308C2214yescomplemented
28#14583293—22no—
29#14583293C2214yes—
30C2×#13063259—21no—
31C2×#13063258—21no—
32C2×#13063257—21no—
33C2×#13063256—21no—
34C2×#13063236C2211yescharacteristic
35#14582640C2214yescomplemented
36#14582638C2214yes—
37C2×#125×C43C2211yescharacteristic
38C2×#97×C43C2211yescharacteristic
39C2×#97×C43C2211yescharacteristic
40C43×#330C2214yescomplemented
41C22×Dic86—21no—
42C22×Dic86—21no—
43C22×Dic86D411yescharacteristic
44C22×D172D411yescharacteristic
45C22×C4×D43—21no—
46C2×Dic172—24no—
47C2×Dic172—44no—
48C2×#10621873—24no—
49C2×#10621873—44no—
50C22×C43⋊C8—21no—
51#13063325—21no—
52#13063325—21no—
53#13063325—21no—
54#13063325C2312yes—
55#13063324—24no—
56#13063324—24no—
57#13063320—24no—
58#13063320—24no—
59#13063320—24no—
60#13063320—24no—
61#13063317—21no—
62#13063317—21no—
63#13063317D412yes—
64#13063317C2312yes—
65#13063313—21no—
66#13063313—21no—
67#13063313D412yes—
68#13063313C2312yes—
69#13063310—24no—
70#13063310—24no—
71#13063305—24no—
72#13063305—24no—
73#13063303—24no—
74#13063303—24no—
75C2×C4⋊Dic43—21no—
76C2×C4⋊Dic43—21no—
77C2×C4⋊Dic43—21no—
78C2×C4⋊Dic43D411yescharacteristic
79C2×C4⋊Dic43D411yescharacteristic
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×(C2×D43)⋊C4—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×(C2×D43)⋊C4—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×C4×Dic43—21no—
89#13063259—24no—
90#13063258—24no—
91#13063257—24no—
92#13063256—24no—
93#13063236—21no—
94#13063236C2312yes—
95C22×C8×C43—21no—
96C22×C8×C43—21no—
97#125×C43—21no—
98#125×C43—21no—
99#125×C43D412yes—
100#125×C43C2312yes—
101C2×C4⋊C4×C43—21no—
102C2×C4⋊C4×C43—21no—
103C2×C4⋊C4×C43D411yescharacteristic
104C2×C4⋊C4×C43D411yescharacteristic
105C2×C42×C43C2311yescharacteristic
106#97×C43—21no—
107#97×C43—21no—
108#97×C43C2312yes—
109#97×C43C2312yes—
110C23×D43—21no—
111C22×C4×C43—21no—
112C22×C4×C43—21no—
113C22×C4×C43C2×D411yescharacteristic
114C22×C4×C43C2×D411yescharacteristic
115C22×C4×C43C2×D411yescharacteristic
116C22×Dic43—21no—
117C22×Dic43—21no—
118C22×Dic43—21no—
119C22×Dic43—41no—
120C2×D172—21no—
121C2×D172—42no—
122C2×D172C2×D412yes—
123C2×C4×D43—24no—
124C2×C4×D43—82no—
125C2×Dic86—22no—
126C2×Dic86—24no—
127C2×Dic86—21no—
128C2×Dic86—42no—
129C2×Dic86—42no—
130C2×Dic86—42no—
131C2×Dic86—41no—
132C2×Dic86—82no—
133C2×Dic86C2×D412yes—
134C2×C8×C43—24no—
135C2×C8×C43—24no—
136C2×C8×C43—22no—
137C2×C8×C43—22no—
138C4⋊C4×C43—22no—
139C4⋊C4×C43—22no—
140C4⋊C4×C43—21no—
141C4⋊C4×C43—21no—
142C4⋊C4×C43—22no—
143C4⋊C4×C43—22no—
144C4⋊C4×C43C2×D412yes—
145C4⋊C4×C43C2×D412yes—
146C42×C43C2×D411yescharacteristic
147C42×C43C2×D411yescharacteristic
148C42×C43C2×D411yescharacteristic
149C42×C43C2411yescharacteristic
150(C2×D43)⋊C4—24no—
151(C2×D43)⋊C4—24no—
152(C2×D43)⋊C4—24no—
153(C2×D43)⋊C4—22no—
154(C2×D43)⋊C4—22no—
155(C2×D43)⋊C4—22no—
156(C2×D43)⋊C4—22no—
157C4⋊Dic43—24no—
158C4⋊Dic43—21no—
159C4⋊Dic43—21no—
160C4⋊Dic43—22no—
161C4⋊Dic43—22no—
162C4⋊Dic43—41no—
163C4⋊Dic43—41no—
164C4⋊Dic43C2×D412yes—
165C4⋊Dic43C2×D412yes—
166Dic43⋊C4—24no—
167Dic43⋊C4—22no—
168Dic43⋊C4—22no—
169Dic43⋊C4—22no—
170Dic43⋊C4—22no—
171C4×Dic43—24no—
172C2×C43⋊C8—24no—
173C2×C43⋊C8—22no—
174Dic172—48no—
175#10621873—48no—
176C23×C43#12011yescharacteristic
177C22×D43—22no—
178C22×D43—42no—
179C22×D43—42no—
180C22×D43—42no—
181C2×C4×C43—22no—
182C2×C4×C43—22no—
183C2×C4×C43—22no—
184C2×C4×C43—22no—
185C2×C4×C43—22no—
186C2×C4×C43—42no—
187C2×C4×C43—42no—
188C2×C4×C43#12011yescharacteristic
189C2×C4×C43#12011yescharacteristic
190C2×C4×C43#12011yescharacteristic
191C2×C4×C43C22×D411yescharacteristic
192C2×C4×C43C22×D411yescharacteristic
193C2×C4×C43C22×D411yescharacteristic
194C2×Dic43—22no—
195C2×Dic43—22no—
196C2×Dic43—22no—
197C2×Dic43—42no—
198C2×Dic43—42no—
199C2×Dic43—42no—
200C2×Dic43—42no—
201C2×Dic43—82no—
202D172—42no—
203D172—81no—
204C4×D43—84no—
205Dic86—42no—
206Dic86—42no—
207Dic86—42no—
208Dic86—81no—
209Dic86—84no—
210Dic86—82no—
211C8×C43—24no—
212C8×C43—24no—
213C43⋊C8—24no—
214C2×#1660—431nomaximal, Sylow
215C22×C43#45312yes—
216C22×C43#45612yes—
217C22×C43#45612yes—
218C22×C43C2×#12011yescharacteristic
219C2×D43—42no—
220C2×D43—42no—
221C2×D43—42no—
222C2×D43—84no—
223C4×C43—21no—
224C4×C43—21no—
225C4×C43—21no—
226C4×C43—21no—
227C4×C43—21no—
228C4×C43—21no—
229C4×C43—42no—
230C4×C43—42no—
231Dic43—42no—
232Dic43—42no—
233Dic43—42no—
234Dic43—82no—
235C2×#563—431no—
236C2×#501—431no—
237C2×#501—431no—
238C2×#497—431no—
239#1660—438no—
240C2×#330—431no—
241C2×#330D4311yescharacteristic, complemented
242C2×#329—431no—
243C2×C43#166014yescomplemented
244C2×C43C2×#45311yescharacteristic
245C2×C43C2×#45611yescharacteristic
246C2×C43C2×#45611yescharacteristic
247D43—82no—
248C22×Q16—861no—
249C22×SD16—861no—
250#563—434no—
251#563—862no—
252#563—862no—
253#563—862no—
254C2×C4⋊Q8—431no—
255C2×C4⋊Q8—861no—
256C2×#126—861no—
257C2×#126—861no—
258C2×#125—431no—
259C2×#125C2×D4311yescharacteristic
260C2×#124—431no—
261C2×#123—861no—
262C2×C22⋊Q8—861no—
263C2×C22⋊Q8—861no—
264#501—434no—
265#501—434no—
266#501—862no—
267#501—862no—
268#497—434no—
269#497—862no—
270C2×#107—861no—
271C2×#107—861no—
272C2×#106—861no—
273C2×#106—861no—
274C2×#97—431no—
275C2×#97C2×D4311yescharacteristic
276C2×#97C2×D4311yescharacteristic
277#330—434no—
278#330C2×D4314yescomplemented
279#329—434no—
280C43C2×#166011yescharacteristic, complemented, Sylow
281C22×Q8—431no—
282C22×Q8—861no—
283C22×Q8—861no—
284C22×D4—431no—
285C23×C4—861no—
286C2×Q16—864no—
287C2×Q16—1724no—
288C2×SD16—864no—
289C2×SD16—1724no—
290C22×C8—21no—
291C22×C8—21no—
292C22×C8—861no—
293C4⋊Q8—432no—
294C4⋊Q8—864no—
295C4⋊Q8—864no—
296C4⋊Q8—861no—
297C4⋊Q8—861no—
298C4⋊Q8—861no—
299#126—864no—
300#126—864no—
301#126—864no—
302#126—864no—
303#125—21no—
304#125—21no—
305#125—432no—
306#125—432no—
307#125—861no—
308#125—861no—
309#125D17212yes—
310#125C22×D4312yes—
311#124—432no—
312#124—432no—
313#124—861no—
314#124—861no—
315#123—864no—
316#123—864no—
317C22⋊Q8—864no—
318C22⋊Q8—864no—
319C22⋊Q8—864no—
320C22⋊Q8—864no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—431no—
324C2×C4⋊C4—431no—
325C2×C4⋊C4—861no—
326C2×C4⋊C4—861no—
327C2×C4⋊C4—861no—
328C2×C4⋊C4—861no—
329C2×C4⋊C4—861no—
330C2×C4⋊C4—861no—
331C2×C4⋊C4D17211yescharacteristic
332C2×C4⋊C4D17211yescharacteristic
333C2×C22⋊C4—861no—
334C2×C22⋊C4—861no—
335C2×C22⋊C4—861no—
336C2×C22⋊C4—861no—
337C2×C22⋊C4—861no—
338C2×C42—861no—
339C2×C42C22×D4311yescharacteristic
340#107—864no—
341#107—864no—
342#106—864no—
343#106—864no—
344#97—21no—
345#97—21no—
346#97—432no—
347#97—861no—
348#97C22×D4312yes—
349#97C22×D4312yes—
350C24—861no—
351C2×Q8—432no—
352C2×Q8—864no—
353C2×Q8—861no—
354C2×Q8—862no—
355C2×Q8—3442no—
356C2×Q8—1722no—
357C2×Q8—1722no—
358C2×Q8—1722no—
359C2×Q8—1721no—
360C2×D4—432no—
361C2×D4—861no—
362C2×D4—1722no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—864no—
366C22×C4—861no—
367C22×C4—861no—
368C22×C4—861no—
369C22×C4—3442no—
370C22×C4—1721no—
371C22×C4C2×D17211yescharacteristic
372C22×C4D4×D4311yescharacteristic
373C22×C4D4×D4311yescharacteristic
374Q16—1728no—
375SD16—1728no—
376C2×C8—24no—
377C2×C8—24no—
378C2×C8—22no—
379C2×C8—22no—
380C2×C8—864no—
381C2×C8—862no—
382C4⋊C4—22no—
383C4⋊C4—22no—
384C4⋊C4—21no—
385C4⋊C4—21no—
386C4⋊C4—22no—
387C4⋊C4—22no—
388C4⋊C4—432no—
389C4⋊C4—432no—
390C4⋊C4—864no—
391C4⋊C4—864no—
392C4⋊C4—861no—
393C4⋊C4—861no—
394C4⋊C4—862no—
395C4⋊C4—862no—
396C4⋊C4—862no—
397C4⋊C4—862no—
398C4⋊C4—862no—
399C4⋊C4—862no—
400C4⋊C4—1721no—
401C4⋊C4—1721no—
402C4⋊C4C2×D17212yes—
403C4⋊C4C2×D17212yes—
404C22⋊C4—864no—
405C22⋊C4—864no—
406C22⋊C4—864no—
407C22⋊C4—862no—
408C22⋊C4—862no—
409C22⋊C4—862no—
410C22⋊C4—862no—
411C42—864no—
412C42C2×D17211yescharacteristic
413C42D4×D4311yescharacteristic
414C42D4×D4311yescharacteristic
415C42C23×D4311yescharacteristic
416C23—862no—
417C23—1722no—
418C23—1722no—
419C23—1722no—
420C23#1306329511yescharacteristic
421Q8—3442no—
422Q8—3441no—
423Q8—3444no—
424Q8—1722no—
425Q8—1722no—
426Q8—1722no—
427D4—3441no—
428D4—1722no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—862no—
437C2×C4—862no—
438C2×C4—862no—
439C2×C4—3444no—
440C2×C4—3442no—
441C2×C4—1722no—
442C2×C4—1722no—
443C2×C4—1722no—
444C2×C4—1722no—
445C2×C4#1306329511yescharacteristic
446C2×C4#1306329511yescharacteristic
447C2×C4#1306329511yescharacteristic
448C2×C4C2×D4×D4311yescharacteristic
449C2×C4C2×D4×D4311yescharacteristic
450C2×C4C22×D17211yescharacteristic
451C8—24no—
452C8—24no—
453C8—864no—
454C22—3444no—
455C22—1722no—
456C22—1722no—
457C22—1722no—
458C22#1458306812yes—
459C22#1458308312yes—
460C22#1458308412yes—
461C22C2×#1306329511yescharacteristic
462C4—21no—
463C4—21no—
464C4—21no—
465C4—21no—
466C4—21no—
467C4—21no—
468C4—42no—
469C4—42no—
470C4—3442no—
471C4—1722no—
472C4—1722no—
473C4—1722no—
474C2—3442no—
475C2#1913390814yesdirect product factor
476C2C2×#1458306811yescharacteristic
477C2C2×#1458308311yescharacteristic
478C2C2×#1458308411yescharacteristic
subgroupG/H
centerC23#13063295
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC2×C43×#330C2
socleC23×C43#120
prime radicalC22×D172D4
hypercenterC2×#330D43
hypocenterC43C2×#1660
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#330

Complements

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

NH ≅ G/Ntype
2. C2×#14583309C2semidirect
3. C2×#14583308C2semidirect
5. #19133908C2direct (N × H)
6. C2×#14582640C2semidirect
8. C2×C43×#330C2semidirect
25. #14583309C22semidirect
27. #14583308C22semidirect
35. #14582640C22semidirect
40. C43×#330C22semidirect
241. C2×#330D43semidirect
243. C2×C43#1660semidirect
278. #330C2×D43semidirect
280. C43C2×#1660semidirect
475. C2#19133908direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145836532
C2×#145833092
C2×#145833082
C2×#145832932
#191339082
C2×#145826402
C2×#145826382
C2×C43×#3302
C2×#166043