Finite Group Databasebeta

← C2×#21447794 #29833957

Subgroups — C2×#21447794 #29833957

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×#16840576C211yesmaximal, characteristic
2C22×#14519723C211yesmaximal, characteristic, complemented
3C2×#16840034C211yesmaximal, characteristic, complemented
4#21447794C218yesmaximal, direct product factor
5C2×#16839579C211yesmaximal, characteristic, complemented
6C2×#16839569C211yesmaximal, characteristic, complemented
7C2×#16839547C211yesmaximal, characteristic, complemented
8C2×C61×#510C211yesmaximal, characteristic, complemented
9C2×#14519824—21no—
10#16840576—22no—
11#16840576—22no—
12#16840576—22no—
13#16840576C2214yes—
14C2×#14519808—21no—
15C2×#14519807—21no—
16C2×#14519806—22no—
17C2×#14519796—21no—
18C22×Dic244C2211yescharacteristic
19C2×Q16×D61—21no—
20C2×#14519783C2211yescharacteristic
21C2×#14519723—22no—
22C2×#14519723—22no—
23C2×#14519723C2214yescomplemented
24C22×#11758185C2211yescharacteristic
25#16840034—22no—
26#16840034C2214yescomplemented
27C2×#14519713C2211yescharacteristic
28C2×#14519696—21no—
29#16839579C2214yescomplemented
30#16839569C2214yescomplemented
31#16839547C2214yescomplemented
32C2×#135×C61C2211yescharacteristic
33C22×Q16×C61C2211yescharacteristic
34C61×#510—22no—
35C61×#510C2214yescomplemented
36C2×Q32×C61—21no—
37C2×SD32×C61—21no—
38C2×M32×C61C2211yescharacteristic
39#14519824—24no—
40#14519824—24no—
41#14519824—42no—
42#14519824—42no—
43C2×#11758222—41no—
44C2×#11758222D411yescharacteristic
45C2×#11758224—22no—
46C2×#11758224—42no—
47C22×Dic122—21no—
48C22×Dic122—41no—
49C2×Q8×D61—22no—
50#14519808—24no—
51#14519808—42no—
52#14519807—24no—
53#14519807—24no—
54#14519806—28no—
55#14519806—28no—
56#14519796—24no—
57#14519796—24no—
58C2×Dic244—21no—
59C2×Dic244—21no—
60C2×Dic244—21no—
61C2×Dic244D412yes—
62C2×Dic244D412yes—
63C2×Dic244C2312yes—
64C2×#11758202—22no—
65C2×#11758202—41no—
66Q16×D61—24no—
67Q16×D61—24no—
68C2×#11758200—22no—
69C2×#11758201—41no—
70#14519783—21no—
71#14519783—21no—
72#14519783D412yes—
73#14519783C2312yes—
74C2×#11758194—21no—
75C2×#11758194D411yescharacteristic
76C2×#11758189—21no—
77C2×C8×D61—21no—
78#14519723—28no—
79C2×#11758185—21no—
80C2×#11758185—21no—
81C2×#11758185C2312yes—
82#14519713—21no—
83#14519713C2312yes—
84#14519696—24no—
85C2×#41×C61—21no—
86C22×Q8×C61—21no—
87#135×C61—21no—
88#135×C61—21no—
89#135×C61D412yes—
90#135×C61C2312yes—
91C2×Q16×C61—21no—
92C2×Q16×C61—21no—
93C2×Q16×C61—21no—
94C2×Q16×C61—21no—
95C2×Q16×C61—21no—
96C2×Q16×C61D411yescharacteristic
97C2×Q16×C61C2312yes—
98C2×SD16×C61—21no—
99C2×D8×C61D411yescharacteristic
100C22×C8×C61C2311yescharacteristic
101Q32×C61—24no—
102SD32×C61—24no—
103M32×C61—21no—
104M32×C61C2312yes—
105C2×C16×C61—21no—
106#41×C61—22no—
107#41×C61—22no—
108#41×C61—41no—
109#41×C61—41no—
110C2×Q8×C61—21no—
111C2×Q8×C61—22no—
112C2×Q8×C61—41no—
113C2×Q8×C61—41no—
114C2×Q8×C61—41no—
115C2×Q8×C61—41no—
116C2×Q8×C61—41no—
117C2×D4×C61—21no—
118C2×D4×C61—41no—
119C22×C4×C61—41no—
120C22×C4×C61—41no—
121C22×C4×C61C2×D411yescharacteristic
122C2×C22⋊D61—21no—
123C2×C22⋊D61—42no—
124C22×Dic61—42no—
125C22×Dic61—41no—
126Q8×D61—28no—
127Q8×D61—44no—
128#11758224—28no—
129#11758224—44no—
130#11758224—48no—
131#11758224—48no—
132#11758222—21no—
133#11758222—21no—
134#11758222—44no—
135#11758222—44no—
136#11758222D812yes—
137#11758222C2×D412yes—
138C2×D244D811yescharacteristic
139C2×C4×D61—21no—
140C2×C4×D61—42no—
141C2×Dic122—22no—
142C2×Dic122—22no—
143C2×Dic122—22no—
144C2×Dic122—44no—
145C2×Dic122—42no—
146C2×Dic122—41no—
147C2×Dic122—41no—
148C2×Dic122—41no—
149C2×Dic122—44no—
150C2×Dic122D811yescharacteristic
151Q16×C61—21no—
152Q16×C61—22no—
153Q16×C61—22no—
154Q16×C61—41no—
155Q16×C61—41no—
156Q16×C61C2×D412yes—
157SD16×C61—22no—
158SD16×C61—22no—
159D8×C61—21no—
160D8×C61C2×D412yes—
161C2×C8×C61C2×D411yescharacteristic
162C2×C8×C61C2×D411yescharacteristic
163C2×C8×C61C2×D411yescharacteristic
164C2×C8×C61C2×D411yescharacteristic
165C2×C8×C61C2×D411yescharacteristic
166C2×C8×C61C2411yescharacteristic
167#11758202—28no—
168#11758202—44no—
169#11758201—44no—
170#11758200—28no—
171#11758194—21no—
172#11758194—22no—
173#11758194—41no—
174#11758194C2×D412yes—
175C2×#92418—21no—
176C2×#92418—41no—
177Dic244—22no—
178Dic244—22no—
179Dic244—22no—
180Dic244C2×D414yes—
181#11758189—22no—
182#11758189—22no—
183C8×D61—22no—
184C8×D61—22no—
185C16×C61—22no—
186#11758185—22no—
187C23×C61—41no—
188C23×C61AGL(1,ℤ/8)11yescharacteristic
189C22×D61—21no—
190Q8×C61—22no—
191Q8×C61—41no—
192Q8×C61—42no—
193Q8×C61—42no—
194Q8×C61—81no—
195Q8×C61—81no—
196D4×C61—22no—
197D4×C61—42no—
198D4×C61—42no—
199D4×C61—41no—
200C2×C4×C61—41no—
201C2×C4×C61—42no—
202C2×C4×C61—42no—
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—22no—
213C22⋊D61—22no—
214C22⋊D61—48no—
215C2×Dic61—21no—
216C2×Dic61—48no—
217C2×Dic61—42no—
218C2×Dic61—42no—
219C2×Dic61—42no—
220D244—21no—
221D244C2×D812yes—
222C4×D61—22no—
223C4×D61—22no—
224C4×D61—48no—
225Dic122—21no—
226Dic122—24no—
227Dic122—48no—
228Dic122—42no—
229Dic122—42no—
230Dic122—42no—
231Dic122C2×D812yes—
232C8×C61#12011yescharacteristic
233C8×C61#12011yescharacteristic
234C8×C61C22×D411yescharacteristic
235C8×C61C22×D411yescharacteristic
236#92418—22no—
237#92418—42no—
238C2×#2195—611nomaximal, Sylow
239C22×C61—22no—
240C22×C61—42no—
241C22×C61—82no—
242C22×C61#44711yescharacteristic
243C22×C61#44711yescharacteristic
244C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
245C2×D61—22no—
246C2×D61—42no—
247C4×C61—42no—
248C4×C61—82no—
249C4×C61#44711yescharacteristic
250C4×C61#44711yescharacteristic
251C4×C61C2×#12011yescharacteristic
252C4×C61C22×D811yescharacteristic
253Dic61—22no—
254Dic61—44no—
255C2×#578—611no—
256C2×#510D6111yescharacteristic, complemented
257C22×Q32—611no—
258C2×#473—611no—
259#2195—618no—
260C2×#362—611no—
261C2×#359—611no—
262C2×#350—611no—
263C2×C61—21no—
264C2×C61—21no—
265C2×C61—82no—
266C2×C61#219512yescomplemented
267C2×C61C2×#44711yescharacteristic
268D61—42no—
269C2×2−1+4—1221no—
270#578—614no—
271#578—1222no—
272#578—1222no—
273#578—1222no—
274C2×#137—1221no—
275C2×#137—1222no—
276C2×#137—1221no—
277C2×#135—1221no—
278C2×#135C2×D6111yescharacteristic
279C22×Q16—611no—
280C22×Q16—1221no—
281C22×Q16C2×D6111yescharacteristic
282C2×#131—611no—
283#510—22no—
284#510C2×D6114yescomplemented
285C2×Q32—21no—
286C2×Q32—614no—
287C2×Q32—1222no—
288C2×Q32—1222no—
289C2×SD32—21no—
290C2×M32C2×D6111yescharacteristic
291C22×C16—611no—
292#473—614no—
293#473—1222no—
294C2×#108—611no—
295C2×#101—1221no—
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—21no—
305C2×#41—611no—
306C2×#41—1222no—
307C2×#41—2441no—
308C2×#41—2442no—
309C22×Q8—21no—
310C22×Q8—1222no—
311C22×Q8—1221no—
312C22×Q8—2441no—
313#137—1224no—
314#137—1228no—
315#137—1228no—
316#137—1224no—
317#137—1224no—
318#137—2442no—
319#135—21no—
320#135—21no—
321#135—1224no—
322#135—1224no—
323#135C22⋊D6112yes—
324#135C22×D6112yes—
325C2×Q16—21no—
326C2×Q16—21no—
327C2×Q16—21no—
328C2×Q16—21no—
329C2×Q16—21no—
330C2×Q16—612no—
331C2×Q16—612no—
332C2×Q16—612no—
333C2×Q16—1224no—
334C2×Q16—1222no—
335C2×Q16—1224no—
336C2×Q16—1221no—
337C2×Q16—1221no—
338C2×Q16—1221no—
339C2×Q16—2441no—
340C2×Q16C22⋊D6111yescharacteristic
341C2×Q16C22×D6112yes—
342C2×SD16—21no—
343C2×SD16—1222no—
344C2×SD16—2441no—
345C2×D8C22⋊D6111yescharacteristic
346#131—612no—
347#131—612no—
348#131—1221no—
349#131—1221no—
350C2×M16—611no—
351C2×M16—1221no—
352C2×M16—1221no—
353C22×C8—1221no—
354C22×C8C22×D6111yescharacteristic
355Q32—24no—
356Q32—1228no—
357SD32—24no—
358M32—21no—
359M32C22×D6112yes—
360C2×C16—21no—
361C2×C16—612no—
362C2×C16—1221no—
363C2×C16—1221no—
364#108—612no—
365#108—1221no—
366#101—1224no—
367#41—22no—
368#41—22no—
369#41—41no—
370#41—41no—
371#41—612no—
372#41—612no—
373#41—1221no—
374#41—1221no—
375#41—1228no—
376#41—2444no—
377#41—2444no—
378#41—2444no—
379#41—2448no—
380#41—2448no—
381C2×Q8—22no—
382C2×Q8—21no—
383C2×Q8—41no—
384C2×Q8—41no—
385C2×Q8—41no—
386C2×Q8—41no—
387C2×Q8—41no—
388C2×Q8—611no—
389C2×Q8—1228no—
390C2×Q8—1222no—
391C2×Q8—1222no—
392C2×Q8—1222no—
393C2×Q8—2442no—
394C2×Q8—2444no—
395C2×Q8—2444no—
396C2×Q8—2444no—
397C2×Q8—2441no—
398C2×Q8—2441no—
399C2×Q8—2441no—
400C2×D4—21no—
401C2×D4—41no—
402C2×D4—611no—
403C2×D4—1221no—
404C2×D4—2442no—
405C22×C4—41no—
406C22×C4—41no—
407C22×C4—1221no—
408C22×C4—2442no—
409C22×C4—2442no—
410C22×C4—2441no—
411C22×C4D4×D6111yescharacteristic
412Q16—22no—
413Q16—22no—
414Q16—21no—
415Q16—41no—
416Q16—41no—
417Q16—614no—
418Q16—1228no—
419Q16—1222no—
420Q16—1222no—
421Q16—1222no—
422Q16—2444no—
423Q16C2×C22⋊D6112yes—
424SD16—22no—
425SD16—22no—
426SD16—1228no—
427SD16—2444no—
428D8—21no—
429D8C2×C22⋊D6112yes—
430M16—612no—
431M16—1221no—
432M16—1222no—
433M16—1222no—
434M16—1222no—
435M16—2441no—
436C2×C8—1221no—
437C2×C8—1222no—
438C2×C8—1222no—
439C2×C8—2441no—
440C2×C8D4×D6111yescharacteristic
441C2×C8D4×D6111yescharacteristic
442C2×C8D4×D6111yescharacteristic
443C2×C8C2×C22⋊D6111yescharacteristic
444C2×C8C2×C22⋊D6111yescharacteristic
445C2×C8C23×D6111yescharacteristic
446C16—22no—
447C16—1222no—
448C23—41no—
449C23—1221no—
450C23#1451980111yescharacteristic
451Q8—22no—
452Q8—41no—
453Q8—42no—
454Q8—42no—
455Q8—81no—
456Q8—81no—
457Q8—612no—
458Q8—1221no—
459Q8—1224no—
460Q8—2448no—
461Q8—2442no—
462Q8—2442no—
463Q8—2442no—
464D4—22no—
465D4—42no—
466D4—42no—
467D4—41no—
468D4—612no—
469D4—1222no—
470D4—1222no—
471D4—1221no—
472D4—2448no—
473C2×C4—41no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—81no—
478C2×C4—81no—
479C2×C4—1221no—
480C2×C4—1222no—
481C2×C4—1222no—
482C2×C4—2448no—
483C2×C4—2448no—
484C2×C4—2442no—
485C2×C4—2442no—
486C2×C4—2442no—
487C2×C4#1451974511yescharacteristic
488C2×C4#1451974511yescharacteristic
489C2×C4D8×D6111yescharacteristic
490C2×C4D8×D6111yescharacteristic
491C2×C4#1451980111yescharacteristic
492C2×C4C2×D4×D6111yescharacteristic
493C8—1222no—
494C8—2442no—
495C8#1451974511yescharacteristic
496C8#1451974511yescharacteristic
497C8C2×D4×D6111yescharacteristic
498C8C22×C22⋊D6111yescharacteristic
499C22—22no—
500C22—42no—
501C22—82no—
502C22—1222no—
503C22—2442no—
504C22#1683989411yescharacteristic
505C22#1683989411yescharacteristic
506C22C2×#1451980111yescharacteristic
507C4—42no—
508C4—82no—
509C4—1222no—
510C4—2444no—
511C4#1683989411yescharacteristic
512C4#1683989411yescharacteristic
513C4C2×#1451974511yescharacteristic
514C4C2×D8×D6111yescharacteristic
515C2—21no—
516C2—21no—
517C2—82no—
518C2—2442no—
519C2#2144779412yesdirect product factor
520C2C2×#1683989411yescharacteristic
subgroupG/H
centerC22#16839894
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC2×C61×#510C2
socleC22×C61#447
prime radicalC2×#16840576C2
hypercenterC2×#510D61
hypocenterC61C2×#2195
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#510

Complements

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

NH ≅ G/Ntype
2. C22×#14519723C2semidirect
3. C2×#16840034C2semidirect
4. #21447794C2direct (N × H)
5. C2×#16839579C2semidirect
6. C2×#16839569C2semidirect
7. C2×#16839547C2semidirect
8. C2×C61×#510C2semidirect
23. C2×#14519723C22semidirect
26. #16840034C22semidirect
29. #16839579C22semidirect
30. #16839569C22semidirect
31. #16839547C22semidirect
35. C61×#510C22semidirect
256. C2×#510D61semidirect
266. C2×C61#2195semidirect
284. #510C2×D61semidirect
299. C61C2×#2195semidirect
519. C2#21447794direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168405762
C22×#145197232
C2×#168400342
#214477942
C2×#168395792
C2×#168395692
C2×#168395472
C2×C61×#5102
C2×#219561