Finite Group Databasebeta

← C2×#21447268 #29708913

Subgroups — C2×#21447268 #29708913

Order 15616.

950 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519708C211yesmaximal, characteristic, complemented
2C2×#16839764C211yesmaximal, characteristic
3C2×#16839761C211yesmaximal, characteristic
4C2×#16839730C211yesmaximal, characteristic
5#21447268C218yesmaximal, direct product factor
6C2×#16839530C211yesmaximal, characteristic, complemented
7C2×#16839526C211yesmaximal, characteristic, complemented
8C2×C61×#343C211yesmaximal, characteristic, complemented
9C22×#11758222C2211yescharacteristic
10C22×#11758194C2211yescharacteristic
11C23×#92418C2211yescharacteristic
12C22×C4⋊Dic61C2211yescharacteristic
13C2×#14519708—22no—
14C2×#14519708—22no—
15C2×#14519708C2214yescomplemented
16#16839764—22no—
17#16839764C2214yes—
18#16839761—22no—
19#16839761C2214yes—
20C2×#14519702—21no—
21C2×#14519700—21no—
22C2×#14519699—21no—
23C2×#14519697—21no—
24#16839730—22no—
25#16839730C2214yes—
26C2×#14519689—22no—
27#16839530C2214yescomplemented
28#16839526C2214yescomplemented
29C22×M16×C61C2211yescharacteristic
30C22×M16×C61C2211yescharacteristic
31C22×C4⋊C4×C61C2211yescharacteristic
32C61×#343C2214yescomplemented
33C2×#11758222—21no—
34C2×#11758222—21no—
35C2×#11758222—22no—
36C2×#11758222—22no—
37C2×#11758222—22no—
38C2×#11758222—22no—
39C2×#11758222D412yes—
40C2×#11758222C2312yes—
41C22×Dic122D411yescharacteristic
42C22×D244D411yescharacteristic
43C22×C22⋊D61—21no—
44C23×Dic61—21no—
45C22×C4×D61—21no—
46C2×#11758194—21no—
47C2×#11758194—22no—
48C2×#11758194—22no—
49C2×#11758194C2312yes—
50C22×#92418—22no—
51C22×#92418—22no—
52C22×#92418—21no—
53C22×#92418D412yes—
54C22×#92418D412yes—
55C22×#92418C2312yes—
56C2×C4⋊Dic61—21no—
57C2×C4⋊Dic61—21no—
58C2×C4⋊Dic61—21no—
59C2×C4⋊Dic61—21no—
60C2×C4⋊Dic61—21no—
61C2×C4⋊Dic61C2312yes—
62#14519708—28no—
63#14519702—24no—
64#14519700—24no—
65#14519699—24no—
66#14519697—24no—
67#14519689—28no—
68C23×C4×C61—21no—
69C23×C4×C61C2311yescharacteristic
70C2×M16×C61—21no—
71C2×M16×C61—21no—
72C2×M16×C61—22no—
73C2×M16×C61—22no—
74C2×M16×C61—22no—
75C2×M16×C61—22no—
76C2×M16×C61C2312yes—
77C2×M16×C61C2312yes—
78C22×C8×C61—21no—
79C22×C8×C61—21no—
80C2×C4⋊C4×C61—21no—
81C2×C4⋊C4×C61—21no—
82C2×C4⋊C4×C61—21no—
83C2×C4⋊C4×C61—21no—
84C2×C4⋊C4×C61—21no—
85C2×C4⋊C4×C61C2312yes—
86C24×C61#4111yescharacteristic
87C23×D61—21no—
88C22×C4×C61—22no—
89C22×C4×C61—41no—
90C22×C4×C61—41no—
91C22×C4×C61—82no—
92C22×C4×C61C2×D411yescharacteristic
93C22×C4×C61C2×D411yescharacteristic
94C22×C4×C61C2×D411yescharacteristic
95C22×C4×C61C2×D411yescharacteristic
96C22×C4×C61#4111yescharacteristic
97C22×C4×C61#4112yes—
98C22×C4×C61#4112yes—
99C22×C4×C61#4112yes—
100C22×C4×C61#4112yes—
101C22×C4×C61C2411yescharacteristic
102C2×C22⋊D61—22no—
103C2×C22⋊D61—22no—
104C2×C22⋊D61—42no—
105C2×C22⋊D61—42no—
106C22×Dic61—21no—
107C22×Dic61—22no—
108C22×Dic61—41no—
109C22×Dic61—41no—
110C22×Dic61—82no—
111#11758222—24no—
112#11758222—24no—
113#11758222—22no—
114#11758222—22no—
115#11758222—22no—
116#11758222—22no—
117#11758222—42no—
118#11758222—42no—
119#11758222—42no—
120#11758222—42no—
121C2×D244—22no—
122C2×D244—22no—
123C2×D244—21no—
124C2×D244C2×D412yes—
125C2×C4×D61—22no—
126C2×C4×D61—22no—
127C2×C4×D61—42no—
128C2×C4×D61—42no—
129C2×Dic122—22no—
130C2×Dic122—22no—
131C2×Dic122—21no—
132C2×Dic122C2×D412yes—
133M16×C61—22no—
134M16×C61—22no—
135M16×C61—22no—
136M16×C61—22no—
137M16×C61—42no—
138M16×C61—42no—
139C2×C8×C61—22no—
140C2×C8×C61—22no—
141C2×C8×C61—42no—
142C2×C8×C61—42no—
143C4⋊C4×C61—22no—
144C4⋊C4×C61—22no—
145C4⋊C4×C61—41no—
146C4⋊C4×C61—41no—
147C4⋊Dic61—22no—
148C4⋊Dic61—22no—
149C4⋊Dic61—41no—
150C4⋊Dic61—41no—
151#11758194—22no—
152#11758194—22no—
153#11758194—42no—
154C2×#92418—24no—
155C2×#92418—24no—
156C2×#92418—22no—
157C2×#92418—22no—
158C2×#92418—22no—
159C2×#92418—42no—
160C2×#92418C2×D414yes—
161C23×C61—22no—
162C23×C61—22no—
163C23×C61#12111yescharacteristic
164C23×C61#12111yescharacteristic
165C23×C61#12612yes—
166C23×C61#12612yes—
167C23×C61C2×#4111yescharacteristic
168C22×D61—22no—
169C22×D61—42no—
170C22×D61—42no—
171C22×D61—42no—
172C2×C4×C61—42no—
173C2×C4×C61—82no—
174C2×C4×C61—82no—
175C2×C4×C61—82no—
176C2×C4×C61#12111yescharacteristic
177C2×C4×C61#12111yescharacteristic
178C2×C4×C61#12312yes—
179C2×C4×C61#12312yes—
180C2×C4×C61#12312yes—
181C2×C4×C61#12312yes—
182C2×C4×C61#12312yes—
183C2×C4×C61#12312yes—
184C2×C4×C61#12412yes—
185C2×C4×C61#12412yes—
186C2×C4×C61#12612yes—
187C2×C4×C61#12612yes—
188C2×C4×C61C22×D411yescharacteristic
189C2×C4×C61C22×D411yescharacteristic
190C2×C4×C61C2×#4111yescharacteristic
191C2×C4×C61C2×#4111yescharacteristic
192C2×C4×C61C2×#4111yescharacteristic
193C2×C4×C61C2×#4111yescharacteristic
194C22⋊D61—42no—
195C22⋊D61—42no—
196C22⋊D61—44no—
197C2×Dic61—22no—
198C2×Dic61—42no—
199C2×Dic61—42no—
200C2×Dic61—82no—
201C2×Dic61—82no—
202C2×Dic61—82no—
203D244—22no—
204D244—22no—
205D244—42no—
206C4×D61—42no—
207C4×D61—42no—
208C4×D61—44no—
209Dic122—22no—
210Dic122—22no—
211Dic122—42no—
212C8×C61—42no—
213C8×C61—42no—
214#92418—24no—
215#92418—42no—
216C2×#2079—611nomaximal, Sylow
217C22×C61—24no—
218C22×C61—24no—
219C22×C61—21no—
220C22×C61—21no—
221C22×C61—21no—
222C22×C61—21no—
223C22×C61#39712yes—
224C22×C61#39712yes—
225C22×C61#47112yes—
226C22×C61#47112yes—
227C22×C61C2×#12111yescharacteristic
228C22×C61C2×#12611yescharacteristic
229C22×C61C2×#12611yescharacteristic
230C2×D61—42no—
231C2×D61—42no—
232C2×D61—42no—
233C2×D61—84no—
234C4×C61—82no—
235C4×C61#39712yes—
236C4×C61#39712yes—
237C4×C61C2×#12311yescharacteristic
238C4×C61C2×#12311yescharacteristic
239C4×C61C2×#12311yescharacteristic
240C4×C61C2×#12411yescharacteristic
241Dic61—42no—
242Dic61—82no—
243C22×#106—611no—
244C2×#417—611no—
245C2×#417—611no—
246C2×#408—611no—
247#2079—618no—
248C2×#343—611no—
249C2×#343D6111yescharacteristic, complemented
250C2×#341—611no—
251C2×C61—21no—
252C2×C61—21no—
253C2×C61—22no—
254C2×C61#207914yescomplemented
255C2×C61C2×#39711yescharacteristic
256C2×C61C2×#47111yescharacteristic
257C2×C61C2×#47111yescharacteristic
258D61—82no—
259C22×#41—611no—
260C22×M16—611no—
261C22×M16C2×D6111yescharacteristic
262C22×M16C2×D6111yescharacteristic
263C23×C8—611no—
264C22×C4⋊C4—611no—
265C22×C4⋊C4C2×D6111yescharacteristic
266C2×#106—614no—
267C2×#106—1222no—
268C2×#106—1222no—
269#417—614no—
270#417—614no—
271#417—1222no—
272#417—1222no—
273C2×#103—1221no—
274C2×#103—1221no—
275C2×#102—1221no—
276C2×#102—1221no—
277#408—614no—
278#408—1222no—
279C2×C22⋊C8—1222no—
280#343—614no—
281#343C2×D6114yescomplemented
282#341—614no—
283C61C2×#207911yescharacteristic, complemented, Sylow
284C2×#41—612no—
285C2×#41—612no—
286C2×#41—1221no—
287C2×#41—1221no—
288C2×#41—1222no—
289C2×#41—1222no—
290C2×#41—1222no—
291C2×#41—1222no—
292C22×Q8—611no—
293C22×D4—611no—
294C22×D4—1221no—
295C23×C4—21no—
296C23×C4—1221no—
297C23×C4—1221no—
298C23×C4C22×D6111yescharacteristic
299C2×M16—21no—
300C2×M16—21no—
301C2×M16—22no—
302C2×M16—22no—
303C2×M16—22no—
304C2×M16—22no—
305C2×M16—612no—
306C2×M16—1221no—
307C2×M16—1222no—
308C2×M16—1222no—
309C2×M16C22×D6112yes—
310C2×M16C22×D6112yes—
311C22×C8—21no—
312C22×C8—21no—
313C22×C8—612no—
314C22×C8—612no—
315C22×C8—612no—
316C22×C8—1222no—
317C22×C8—1222no—
318C22×C8—1221no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—612no—
325C2×C4⋊C4—1221no—
326C2×C4⋊C4—1221no—
327C2×C4⋊C4—1221no—
328C2×C4⋊C4—1221no—
329C2×C4⋊C4—1221no—
330C2×C4⋊C4C22×D6112yes—
331#106—1228no—
332#103—1224no—
333#103—1224no—
334#102—1224no—
335#102—1224no—
336C22⋊C8—1228no—
337C24—1221no—
338C24#1175822211yescharacteristic
339#41—1222no—
340#41—1222no—
341#41—1222no—
342#41—1222no—
343#41—1224no—
344#41—1224no—
345#41—2442no—
346#41—2442no—
347#41—2442no—
348#41—2442no—
349C2×Q8—612no—
350C2×Q8—1221no—
351C2×Q8—1222no—
352C2×Q8—1222no—
353C2×D4—612no—
354C2×D4—1222no—
355C2×D4—1222no—
356C2×D4—1221no—
357C2×D4—1222no—
358C2×D4—1222no—
359C2×D4—2442no—
360C2×D4—2442no—
361C22×C4—22no—
362C22×C4—41no—
363C22×C4—41no—
364C22×C4—82no—
365C22×C4—1221no—
366C22×C4—1222no—
367C22×C4—1222no—
368C22×C4—1222no—
369C22×C4—4882no—
370C22×C4—2441no—
371C22×C4—2441no—
372C22×C4—2442no—
373C22×C4—2442no—
374C22×C4#1175822212yes—
375C22×C4#1175822212yes—
376C22×C4#1175822211yescharacteristic
377C22×C4D4×D6111yescharacteristic
378C22×C4D4×D6111yescharacteristic
379C22×C4D4×D6111yescharacteristic
380C22×C4D4×D6111yescharacteristic
381C22×C4#1175822412yes—
382C22×C4#1175822612yes—
383C22×C4C23×D6111yescharacteristic
384M16—22no—
385M16—22no—
386M16—22no—
387M16—22no—
388M16—42no—
389M16—42no—
390M16—1222no—
391M16—1222no—
392M16—2442no—
393C2×C8—22no—
394C2×C8—22no—
395C2×C8—42no—
396C2×C8—42no—
397C2×C8—614no—
398C2×C8—1222no—
399C2×C8—1222no—
400C2×C8—1224no—
401C2×C8—1224no—
402C2×C8—1222no—
403C2×C8—2442no—
404C4⋊C4—22no—
405C4⋊C4—22no—
406C4⋊C4—41no—
407C4⋊C4—41no—
408C4⋊C4—1222no—
409C4⋊C4—1222no—
410C4⋊C4—2441no—
411C4⋊C4—2441no—
412C23—22no—
413C23—22no—
414C23—1222no—
415C23—2442no—
416C23—2442no—
417C23—2442no—
418C23#1451975011yescharacteristic
419C23#1451975011yescharacteristic
420C23#1451977112yes—
421C23#1451977212yes—
422C23C2×#1175822211yescharacteristic
423Q8—1222no—
424Q8—1222no—
425Q8—2442no—
426D4—1222no—
427D4—1222no—
428D4—2444no—
429D4—2442no—
430D4—2442no—
431D4—2442no—
432C2×C4—42no—
433C2×C4—82no—
434C2×C4—82no—
435C2×C4—82no—
436C2×C4—1222no—
437C2×C4—4882no—
438C2×C4—4882no—
439C2×C4—4882no—
440C2×C4—2442no—
441C2×C4—2442no—
442C2×C4—2444no—
443C2×C4—2442no—
444C2×C4—2442no—
445C2×C4#1451975011yescharacteristic
446C2×C4#1451975011yescharacteristic
447C2×C4#1451975912yes—
448C2×C4#1451975912yes—
449C2×C4#1451976212yes—
450C2×C4#1451976212yes—
451C2×C4#1451976212yes—
452C2×C4#1451976212yes—
453C2×C4#1451976312yes—
454C2×C4#1451976312yes—
455C2×C4#1451977112yes—
456C2×C4#1451977212yes—
457C2×C4C2×D4×D6111yescharacteristic
458C2×C4C2×D4×D6111yescharacteristic
459C2×C4C2×#1175822411yescharacteristic
460C2×C4C2×#1175822211yescharacteristic
461C2×C4C2×#1175822211yescharacteristic
462C2×C4C2×#1175822611yescharacteristic
463C8—42no—
464C8—42no—
465C8—1224no—
466C8—2442no—
467C22—24no—
468C22—24no—
469C22—21no—
470C22—21no—
471C22—21no—
472C22—21no—
473C22—4884no—
474C22—2442no—
475C22—2442no—
476C22—2442no—
477C22#1683969112yes—
478C22#1683969112yes—
479C22#1684002412yes—
480C22#1684002812yes—
481C22C2×#1451975011yescharacteristic
482C22C2×#1451977111yescharacteristic
483C22C2×#1451977211yescharacteristic
484C4—82no—
485C4—4882no—
486C4—2442no—
487C4#1683969112yes—
488C4#1683969112yes—
489C4C2×#1451975911yescharacteristic
490C4C2×#1451976211yescharacteristic
491C4C2×#1451976211yescharacteristic
492C4C2×#1451976311yescharacteristic
493C2—22no—
494C2—21no—
495C2—21no—
496C2—4882no—
497C2#2144726814yesdirect product factor
498C2C2×#1683969111yescharacteristic
499C2C2×#1684002411yescharacteristic
500C2C2×#1684002811yescharacteristic
subgroupG/H
centerC23#14519750
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#343C2
socleC23×C61#121
prime radicalC22×#11758222C22
hypercenterC2×#343D61
hypocenterC61C2×#2079
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#343

Complements

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

NH ≅ G/Ntype
1. C22×#14519708C2semidirect
5. #21447268C2direct (N × H)
6. C2×#16839530C2semidirect
7. C2×#16839526C2semidirect
8. C2×C61×#343C2semidirect
15. C2×#14519708C22semidirect
27. #16839530C22semidirect
28. #16839526C22semidirect
32. C61×#343C22semidirect
249. C2×#343D61semidirect
254. C2×C61#2079semidirect
281. #343C2×D61semidirect
283. C61C2×#2079semidirect
497. C2#21447268direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197082
C2×#168397642
C2×#168397612
C2×#168397302
#214472682
C2×#168395302
C2×#168395262
C2×C61×#3432
C2×#207961