Finite Group Databasebeta

← C2×#21447795 #29833958

Subgroups — C2×#21447795 #29833958

Order 15616.

1078 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840579C211yesmaximal, characteristic
2C2×#16840203C211yesmaximal, characteristic, complemented
3C22×#14519723C211yesmaximal, characteristic, complemented
4#21447795C218yesmaximal, direct product factor
5C2×#16839577C211yesmaximal, characteristic, complemented
6C2×#16839568C211yesmaximal, characteristic, complemented
7C2×#16839546C211yesmaximal, characteristic, complemented
8C2×C61×#473C211yesmaximal, characteristic, complemented
9C2×#14519824—21no—
10#16840579—22no—
11#16840579—22no—
12#16840579—22no—
13#16840579C2214yes—
14C2×#14519810—22no—
15C2×#14519810—21no—
16C2×#14519799—21no—
17C2×#14519799C2211yescharacteristic
18C22×Dic244—21no—
19C22×Dic244C2211yescharacteristic
20#16840203—22no—
21#16840203C2214yescomplemented
22C2×#14519723—21no—
23C2×#14519723—22no—
24C2×#14519723—22no—
25C2×#14519723C2214yescomplemented
26C2×#14519720—21no—
27C2×#14519717C2211yescharacteristic
28C22×#11758185C2211yescharacteristic
29#16839577C2214yescomplemented
30#16839568C2214yescomplemented
31#16839546C2214yescomplemented
32C2×#137×C61—21no—
33C22×Q16×C61C2211yescharacteristic
34C2×#131×C61C2211yescharacteristic
35C61×#473—22no—
36C61×#473C2214yescomplemented
37C2×#108×C61C2211yescharacteristic
38C2×#101×C61—21no—
39#14519824—24no—
40#14519824—24no—
41#14519824—42no—
42#14519824—42no—
43C2×#11758222—22no—
44C2×#11758222—21no—
45C2×#11758224—42no—
46C2×#11758224—41no—
47C22×Dic122—22no—
48C22×Dic122—21no—
49C2×Q8×D61—41no—
50#14519810—24no—
51#14519810—28no—
52#14519810—24no—
53#14519810—28no—
54#14519799—24no—
55#14519799—21no—
56#14519799—21no—
57#14519799—24no—
58#14519799D412yes—
59#14519799C2312yes—
60C2×Dic244—22no—
61C2×Dic244—24no—
62C2×Dic244—21no—
63C2×Dic244—21no—
64C2×Dic244—21no—
65C2×Dic244—24no—
66C2×Dic244D411yescharacteristic
67C2×Dic244D412yes—
68C2×Dic244D412yes—
69C2×Dic244C2312yes—
70C2×#11758190—22no—
71C2×#11758190—21no—
72C2×D488D411yescharacteristic
73#14519723—24no—
74#14519723—28no—
75#14519720—24no—
76#14519717—21no—
77#14519717C2312yes—
78C2×#11758185—21no—
79C2×#11758185—21no—
80C2×#11758185—21no—
81C2×#11758185C2312yes—
82C2×#41×C61D411yescharacteristic
83C22×Q8×C61—21no—
84#137×C61—24no—
85#137×C61—42no—
86C2×Q16×C61—21no—
87C2×Q16×C61—21no—
88C2×Q16×C61—21no—
89C2×Q16×C61—21no—
90C2×Q16×C61—21no—
91C2×Q16×C61—41no—
92C2×Q16×C61C2312yes—
93C2×SD16×C61—41no—
94#131×C61—21no—
95#131×C61—21no—
96#131×C61D412yes—
97#131×C61C2312yes—
98C2×M16×C61—21no—
99C2×M16×C61—21no—
100C2×M16×C61D411yescharacteristic
101C22×C8×C61—21no—
102C22×C8×C61C2311yescharacteristic
103#108×C61—21no—
104#108×C61C2312yes—
105#101×C61—24no—
106#41×C61—21no—
107#41×C61—21no—
108#41×C61D812yes—
109#41×C61C2×D412yes—
110C2×Q8×C61—22no—
111C2×Q8×C61—41no—
112C2×Q8×C61—41no—
113C2×Q8×C61—41no—
114C2×Q8×C61—41no—
115C2×Q8×C61—41no—
116C2×Q8×C61D811yescharacteristic
117C2×D4×C61—21no—
118C2×D4×C61D811yescharacteristic
119C22×C4×C61—21no—
120C22×C4×C61—41no—
121C22×C4×C61C2×D411yescharacteristic
122C2×C22⋊D61—42no—
123C2×C22⋊D61—41no—
124C22×Dic61—42no—
125C22×Dic61—41no—
126Q8×D61—44no—
127Q8×D61—44no—
128#11758224—48no—
129#11758224—48no—
130#11758224—44no—
131#11758224—44no—
132#11758222—28no—
133#11758222—22no—
134#11758222—22no—
135#11758222—44no—
136#11758222—41no—
137#11758222—41no—
138C2×D244—21no—
139C2×C4×D61—42no—
140C2×C4×D61—41no—
141C2×Dic122—28no—
142C2×Dic122—22no—
143C2×Dic122—21no—
144C2×Dic122—22no—
145C2×Dic122—22no—
146C2×Dic122—42no—
147C2×Dic122—44no—
148C2×Dic122—41no—
149C2×Dic122—41no—
150C2×Dic122—41no—
151Q16×C61—22no—
152Q16×C61—22no—
153Q16×C61—44no—
154Q16×C61—41no—
155Q16×C61—41no—
156SD16×C61—44no—
157M16×C61—21no—
158M16×C61—22no—
159M16×C61—22no—
160M16×C61—22no—
161M16×C61—41no—
162M16×C61C2×D412yes—
163C2×C8×C61—21no—
164C2×C8×C61—22no—
165C2×C8×C61—22no—
166C2×C8×C61—41no—
167C2×C8×C61C2×D411yescharacteristic
168C2×C8×C61C2×D411yescharacteristic
169C2×C8×C61C2×D411yescharacteristic
170C2×C8×C61C2×D411yescharacteristic
171C2×C8×C61C2×D411yescharacteristic
172C2×C8×C61C2411yescharacteristic
173Dic244—28no—
174Dic244—22no—
175Dic244—21no—
176Dic244—22no—
177Dic244—22no—
178Dic244C2×D414yes—
179Dic244C2×D412yes—
180D488—21no—
181D488C2×D412yes—
182#11758190—28no—
183#11758190—22no—
184#11758190—22no—
185#11758185—22no—
186#11758185—22no—
187C23×C61—21no—
188C23×C61AGL(1,ℤ/8)11yescharacteristic
189C22×D61—41no—
190Q8×C61—21no—
191Q8×C61—42no—
192Q8×C61—42no—
193Q8×C61—81no—
194Q8×C61—81no—
195Q8×C61C2×D812yes—
196D4×C61—22no—
197D4×C61—22no—
198D4×C61—21no—
199D4×C61C2×D812yes—
200C2×C4×C61—21no—
201C2×C4×C61—22no—
202C2×C4×C61—22no—
203C2×C4×C61—42no—
204C2×C4×C61—81no—
205C2×C4×C61—81no—
206C2×C4×C61#12011yescharacteristic
207C2×C4×C61#12011yescharacteristic
208C2×C4×C61C2×D811yescharacteristic
209C2×C4×C61C2×D811yescharacteristic
210C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
211C2×C4×C61C22×D411yescharacteristic
212C22⋊D61—48no—
213C22⋊D61—42no—
214C22⋊D61—42no—
215C2×Dic61—48no—
216C2×Dic61—42no—
217C2×Dic61—41no—
218C2×Dic61—42no—
219C2×Dic61—42no—
220D244—22no—
221D244—41no—
222C4×D61—48no—
223C4×D61—42no—
224C4×D61—42no—
225Dic122—24no—
226Dic122—22no—
227Dic122—48no—
228Dic122—42no—
229Dic122—41no—
230Dic122—42no—
231Dic122—42no—
232C8×C61—22no—
233C8×C61—42no—
234C8×C61#12011yescharacteristic
235C8×C61#12011yescharacteristic
236C8×C61C22×D411yescharacteristic
237C8×C61C22×D411yescharacteristic
238C2×#2195—611nomaximal, Sylow
239C22×C61—22no—
240C22×C61—22no—
241C22×C61—42no—
242C22×C61#44711yescharacteristic
243C22×C61#44711yescharacteristic
244C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
245C2×D61—42no—
246C2×D61—82no—
247C4×C61—22no—
248C4×C61—82no—
249C4×C61#44711yescharacteristic
250C4×C61#44711yescharacteristic
251C4×C61C2×#12011yescharacteristic
252C4×C61C22×D811yescharacteristic
253Dic61—42no—
254Dic61—44no—
255C2×#578—611no—
256C2×#510—611no—
257C22×Q32—611no—
258C2×#473D6111yescharacteristic, complemented
259#2195—618no—
260C2×#362—611no—
261C2×#359—611no—
262C2×#350—611no—
263C2×C61—21no—
264C2×C61—21no—
265C2×C61—42no—
266C2×C61#219512yescomplemented
267C2×C61C2×#44711yescharacteristic
268D61—82no—
269C2×2−1+4—1221no—
270#578—614no—
271#578—1222no—
272#578—1222no—
273#578—1222no—
274C2×#137—21no—
275C2×#137—1222no—
276C2×#137—1221no—
277C2×#135—611no—
278C2×#135—1221no—
279C22×Q16—611no—
280C22×Q16—1221no—
281C22×Q16C2×D6111yescharacteristic
282C2×#131C2×D6111yescharacteristic
283#510—614no—
284#510—1222no—
285C2×Q32—614no—
286C2×Q32—1222no—
287C2×Q32—1222no—
288C2×Q32—1221no—
289C2×SD32—1221no—
290C2×M32—611no—
291C22×C16—611no—
292#473—22no—
293#473C2×D6114yescomplemented
294C2×#108C2×D6111yescharacteristic
295C2×#101—21no—
296#362—614no—
297#359—614no—
298#350—614no—
299C61C2×#219511yescharacteristic, complemented, Sylow
3002−1+4—1224no—
3012−1+4—1224no—
3022−1+4—2442no—
3032−1+4—2442no—
304C2×#41—1222no—
305C2×#41—1221no—
306C2×#41—2442no—
307C2×#41—2441no—
308C2×#41C22⋊D6111yescharacteristic
309C22×Q8—21no—
310C22×Q8—1222no—
311C22×Q8—1221no—
312C22×Q8—2441no—
313#137—24no—
314#137—42no—
315#137—1228no—
316#137—1224no—
317#137—1228no—
318#137—1224no—
319#135—612no—
320#135—612no—
321#135—1224no—
322#135—1224no—
323#135—1221no—
324#135—1221no—
325C2×Q16—21no—
326C2×Q16—21no—
327C2×Q16—21no—
328C2×Q16—21no—
329C2×Q16—21no—
330C2×Q16—41no—
331C2×Q16—612no—
332C2×Q16—612no—
333C2×Q16—611no—
334C2×Q16—612no—
335C2×Q16—1224no—
336C2×Q16—1222no—
337C2×Q16—1224no—
338C2×Q16—1221no—
339C2×Q16—1221no—
340C2×Q16—1221no—
341C2×Q16C22×D6112yes—
342C2×SD16—41no—
343C2×SD16—1222no—
344C2×SD16—1221no—
345C2×D8—611no—
346#131—21no—
347#131—21no—
348#131C22⋊D6112yes—
349#131C22×D6112yes—
350C2×M16—21no—
351C2×M16—21no—
352C2×M16C22⋊D6111yescharacteristic
353C22×C8—21no—
354C22×C8C22×D6111yescharacteristic
355Q32—1228no—
356Q32—1224no—
357SD32—1224no—
358M32—612no—
359M32—1221no—
360C2×C16—612no—
361C2×C16—1221no—
362C2×C16—1221no—
363C2×C16—1221no—
364#108—21no—
365#108C22×D6112yes—
366#101—24no—
367#41—21no—
368#41—21no—
369#41—1228no—
370#41—1222no—
371#41—1222no—
372#41—2444no—
373#41—2448no—
374#41—2448no—
375#41—2444no—
376#41—2444no—
377#41—2441no—
378#41—2441no—
379#41#1175819912yes—
380#41C2×C22⋊D6112yes—
381C2×Q8—22no—
382C2×Q8—41no—
383C2×Q8—41no—
384C2×Q8—41no—
385C2×Q8—41no—
386C2×Q8—41no—
387C2×Q8—1228no—
388C2×Q8—1222no—
389C2×Q8—1222no—
390C2×Q8—1221no—
391C2×Q8—1222no—
392C2×Q8—2442no—
393C2×Q8—2444no—
394C2×Q8—2444no—
395C2×Q8—2444no—
396C2×Q8—2441no—
397C2×Q8—2441no—
398C2×Q8—2441no—
399C2×Q8#1175819911yescharacteristic
400C2×D4—21no—
401C2×D4—1221no—
402C2×D4—2442no—
403C2×D4—2441no—
404C2×D4#1175819911yescharacteristic
405C22×C4—21no—
406C22×C4—41no—
407C22×C4—2442no—
408C22×C4—2442no—
409C22×C4—2441no—
410C22×C4—2441no—
411C22×C4C2×C22⋊D6111yescharacteristic
412Q16—22no—
413Q16—22no—
414Q16—44no—
415Q16—41no—
416Q16—41no—
417Q16—614no—
418Q16—612no—
419Q16—1228no—
420Q16—1222no—
421Q16—1222no—
422Q16—1221no—
423Q16—1222no—
424SD16—44no—
425SD16—1228no—
426SD16—1222no—
427SD16—1222no—
428D8—612no—
429D8—1221no—
430M16—21no—
431M16—22no—
432M16—22no—
433M16—22no—
434M16—41no—
435M16C2×C22⋊D6112yes—
436C2×C8—21no—
437C2×C8—22no—
438C2×C8—22no—
439C2×C8—41no—
440C2×C8D4×D6111yescharacteristic
441C2×C8D4×D6111yescharacteristic
442C2×C8D4×D6111yescharacteristic
443C2×C8D4×D6111yescharacteristic
444C2×C8C2×C22⋊D6111yescharacteristic
445C2×C8C23×D6111yescharacteristic
446C16—1222no—
447C16—1222no—
448C23—21no—
449C23—2441no—
450C23#1451980211yescharacteristic
451Q8—21no—
452Q8—42no—
453Q8—42no—
454Q8—81no—
455Q8—81no—
456Q8—1224no—
457Q8—1222no—
458Q8—2448no—
459Q8—2442no—
460Q8—2441no—
461Q8—2442no—
462Q8—2442no—
463Q8C2×#1175819912yes—
464D4—22no—
465D4—22no—
466D4—21no—
467D4—1222no—
468D4—2448no—
469D4—2442no—
470D4—2442no—
471D4—2441no—
472D4C2×#1175819912yes—
473C2×C4—21no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—42no—
477C2×C4—81no—
478C2×C4—81no—
479C2×C4—2448no—
480C2×C4—2448no—
481C2×C4—2442no—
482C2×C4—2442no—
483C2×C4—2442no—
484C2×C4—2441no—
485C2×C4—2442no—
486C2×C4—2442no—
487C2×C4#1451974511yescharacteristic
488C2×C4#1451974511yescharacteristic
489C2×C4C2×#1175819911yescharacteristic
490C2×C4C2×#1175819911yescharacteristic
491C2×C4#1451980211yescharacteristic
492C2×C4C22×C22⋊D6111yescharacteristic
493C8—22no—
494C8—42no—
495C8#1451974511yescharacteristic
496C8#1451974511yescharacteristic
497C8C2×D4×D6111yescharacteristic
498C8C2×D4×D6111yescharacteristic
499C22—22no—
500C22—22no—
501C22—42no—
502C22—4882no—
503C22—2442no—
504C22#1683989511yescharacteristic
505C22#1683989511yescharacteristic
506C22C2×#1451980211yescharacteristic
507C4—22no—
508C4—82no—
509C4—2444no—
510C4—2442no—
511C4#1683989511yescharacteristic
512C4#1683989511yescharacteristic
513C4C2×#1451974511yescharacteristic
514C4C22×#1175819911yescharacteristic
515C2—21no—
516C2—21no—
517C2—42no—
518C2—4882no—
519C2#2144779512yesdirect product factor
520C2C2×#1683989511yescharacteristic
subgroupG/H
centerC22#16839895
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC2×C61×#473C2
socleC22×C61#447
prime radicalC2×#16840579C2
hypercenterC2×#473D61
hypocenterC61C2×#2195
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#131 ◁ C2×#473

Complements

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

NH ≅ G/Ntype
2. C2×#16840203C2semidirect
3. C22×#14519723C2semidirect
4. #21447795C2direct (N × H)
5. C2×#16839577C2semidirect
6. C2×#16839568C2semidirect
7. C2×#16839546C2semidirect
8. C2×C61×#473C2semidirect
21. #16840203C22semidirect
25. C2×#14519723C22semidirect
29. #16839577C22semidirect
30. #16839568C22semidirect
31. #16839546C22semidirect
36. C61×#473C22semidirect
258. C2×#473D61semidirect
266. C2×C61#2195semidirect
293. #473C2×D61semidirect
299. C61C2×#2195semidirect
519. C2#21447795direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168405792
C2×#168402032
C22×#145197232
#214477952
C2×#168395772
C2×#168395682
C2×#168395462
C2×C61×#4732
C2×#219561