Finite Group Databasebeta

← C2×#21446480 #29682551

Subgroups — C2×#21446480 #29682551

Order 15616.

1154 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839766C211yesmaximal, characteristic
2C22×#14519697C211yesmaximal, characteristic
3C22×#14519693C211yesmaximal, characteristic
4C2×#16839718C211yesmaximal, characteristic, complemented
5#21446480C218yesmaximal, direct product factor
6C2×#16839531C211yesmaximal, characteristic, complemented
7C2×#16839526C211yesmaximal, characteristic, complemented
8C2×C61×#428C211yesmaximal, characteristic, complemented
9C23×D244C2211yescharacteristic
10C22×#11758194C2211yescharacteristic
11C22×#11758194C2211yescharacteristic
12C23×#92418C2211yescharacteristic
13#16839766—22no—
14#16839766C2214yes—
15C2×#14519697—21no—
16C2×#14519697—21no—
17C2×#14519697—22no—
18C2×#14519697—21no—
19C2×#14519697—21no—
20C2×#14519697C2214yes—
21C2×#14519693C418yescomplemented
22C2×#14519693C2214yes—
23#16839718—22no—
24#16839718C2214yescomplemented
25C2×#14519688—21no—
26C2×C4×#92418—21no—
27#16839531C2214yescomplemented
28#16839526C2214yescomplemented
29C22×M16×C61C2211yescharacteristic
30C2×#117×C61C2211yescharacteristic
31C22×C4⋊C4×C61C2211yescharacteristic
32C61×#428—22no—
33C61×#428C2214yescomplemented
34C2×#107×C61—21no—
35C2×#106×C61—21no—
36C24×D61—21no—
37C22×D244—21no—
38C22×D244—21no—
39C22×D244—21no—
40C22×D244—21no—
41C22×D244—22no—
42C22×D244—22no—
43C22×D244—21no—
44C22×D244—22no—
45C22×D244C2×C414yes—
46C22×D244C2312yes—
47C2×#11758194—21no—
48C2×#11758194—22no—
49C2×#11758194—21no—
50C2×#11758194—22no—
51C2×#11758194—22no—
52C2×#11758194C2×C414yes—
53C2×#11758194C2312yes—
54C2×#11758194C2312yes—
55C22×#92418—21no—
56C22×#92418—22no—
57C22×#92418—22no—
58C22×#92418—21no—
59C22×#92418D411yescharacteristic
60C22×#92418D411yescharacteristic
61C22×#92418D412yes—
62C22×#92418C2312yes—
63#14519697—24no—
64#14519697—24no—
65#14519697—24no—
66#14519697—24no—
67#14519693C2×C4116yescomplemented
68#14519688—24no—
69C4×#92418—24no—
70C23×C4×C61—21no—
71C23×C4×C61C2311yescharacteristic
72C2×M16×C61—21no—
73C2×M16×C61—22no—
74C2×M16×C61C2×C414yes—
75C2×M16×C61C2312yes—
76C22×C8×C61—21no—
77#117×C61—21no—
78#117×C61—21no—
79#117×C61D412yes—
80#117×C61C2312yes—
81C2×C4⋊C4×C61—21no—
82C2×C4⋊C4×C61—21no—
83C2×C4⋊C4×C61—21no—
84C2×C4⋊C4×C61—21no—
85C2×C4⋊C4×C61—21no—
86C2×C4⋊C4×C61D411yescharacteristic
87C2×C4⋊C4×C61D411yescharacteristic
88C2×C4⋊C4×C61C2312yes—
89C2×C22⋊C4×C61—21no—
90C2×C42×C61—21no—
91#107×C61—24no—
92#106×C61—24no—
93C24×C61#4111yescharacteristic
94C23×D61—24no—
95C23×D61—22no—
96C23×D61—41no—
97C23×D61—41no—
98C23×D61—42no—
99C23×D61—82no—
100C23×D61—82no—
101C22×C4×C61—21no—
102C22×C4×C61—21no—
103C22×C4×C61—22no—
104C22×C4×C61—41no—
105C22×C4×C61—41no—
106C22×C4×C61—82no—
107C22×C4×C61C22×C412yes—
108C22×C4×C61C2×D411yescharacteristic
109C22×C4×C61C2×D411yescharacteristic
110C22×C4×C61C2×D411yescharacteristic
111C22×C4×C61C2×D411yescharacteristic
112C22×C4×C61#4111yescharacteristic
113C22×C4×C61#4112yes—
114C22×C4×C61#4112yes—
115C22×C4×C61#4112yes—
116C22×C4×C61C2411yescharacteristic
117C2×D244—24no—
118C2×D244—24no—
119C2×D244—24no—
120C2×D244—24no—
121C2×D244—22no—
122C2×D244—22no—
123C2×D244—22no—
124C2×D244—22no—
125C2×D244—24no—
126C2×D244—22no—
127C2×D244—41no—
128C2×D244—41no—
129C2×D244—42no—
130C2×D244—42no—
131C2×D244—42no—
132C2×D244—42no—
133C2×D244—42no—
134C2×D244C22×C414yes—
135M16×C61—24no—
136M16×C61—22no—
137M16×C61C22×C414yes—
138C2×C8×C61—24no—
139C2×C8×C61—22no—
140C4⋊C4×C61—21no—
141C4⋊C4×C61—21no—
142C4⋊C4×C61—22no—
143C4⋊C4×C61—22no—
144C4⋊C4×C61—41no—
145C4⋊C4×C61—41no—
146C4⋊C4×C61C2×D412yes—
147C4⋊C4×C61C2×D412yes—
148C22⋊C4×C61—22no—
149C22⋊C4×C61—22no—
150C42×C61—22no—
151C42×C61—22no—
152#11758194—24no—
153#11758194—22no—
154#11758194—22no—
155#11758194—22no—
156#11758194—42no—
157#11758194C22×C414yes—
158C2×#92418—24no—
159C2×#92418—22no—
160C2×#92418—22no—
161C2×#92418—24no—
162C2×#92418—22no—
163C2×#92418—22no—
164C2×#92418—22no—
165C2×#92418—22no—
166C2×#92418—42no—
167C2×#92418C2×D412yes—
168C2×#92418C2×D412yes—
169C23×C61—22no—
170C23×C61—22no—
171C23×C61#11712yes—
172C23×C61#12111yescharacteristic
173C23×C61#12111yescharacteristic
174C23×C61#12612yes—
175C23×C61C2×#4111yescharacteristic
176C22×D61—24no—
177C22×D61—42no—
178C22×D61—42no—
179C22×D61—44no—
180C22×D61—44no—
181C22×D61—88no—
182C22×D61—82no—
183C22×D61—82no—
184C22×D61—82no—
185C22×D61—82no—
186C22×D61—88no—
187C22×D61—82no—
188C22×D61—82no—
189C2×C4×C61—22no—
190C2×C4×C61—22no—
191C2×C4×C61—42no—
192C2×C4×C61—42no—
193C2×C4×C61—42no—
194C2×C4×C61—82no—
195C2×C4×C61—82no—
196C2×C4×C61—82no—
197C2×C4×C61#11712yes—
198C2×C4×C61C4×D412yes—
199C2×C4×C61C4×D412yes—
200C2×C4×C61C4×D412yes—
201C2×C4×C61C4×D412yes—
202C2×C4×C61#12111yescharacteristic
203C2×C4×C61#12111yescharacteristic
204C2×C4×C61#12312yes—
205C2×C4×C61#12312yes—
206C2×C4×C61#12412yes—
207C2×C4×C61#12412yes—
208C2×C4×C61#12612yes—
209C2×C4×C61C23×C411yescharacteristic
210C2×C4×C61C22×D411yescharacteristic
211C2×C4×C61C22×D411yescharacteristic
212C2×C4×C61C2×#4111yescharacteristic
213C2×C4×C61C2×#4111yescharacteristic
214C2×C4×C61C2×#4111yescharacteristic
215D244—24no—
216D244—24no—
217D244—42no—
218D244—42no—
219D244—44no—
220D244—44no—
221C8×C61—24no—
222#92418—24no—
223#92418—22no—
224#92418—22no—
225#92418—42no—
226C2×#1931—611nomaximal, Sylow
227C22×C61—24no—
228C22×C61—24no—
229C22×C61—21no—
230C22×C61—21no—
231C22×C61—21no—
232C22×C61—21no—
233C22×C61#38812yes—
234C22×C61#38812yes—
235C22×C61#47112yes—
236C22×C61#47212yes—
237C22×C61C2×#11711yescharacteristic
238C22×C61C2×#12111yescharacteristic
239C22×C61C2×#12611yescharacteristic
240C2×D61—44no—
241C2×D61—84no—
242C2×D61—88no—
243C2×D61—88no—
244C2×D61—82no—
245C2×D61—82no—
246C2×D61—84no—
247C4×C61—42no—
248C4×C61—42no—
249C4×C61—82no—
250C4×C61#38812yes—
251C4×C61#38812yes—
252C4×C61C2×C4×D411yescharacteristic
253C4×C61C2×C4×D411yescharacteristic
254C4×C61C2×#12311yescharacteristic
255C4×C61C2×#12411yescharacteristic
256C2×#428D6111yescharacteristic, complemented
257C2×#418—611no—
258C22×#102—611no—
259C22×#100—611no—
260C2×#405—611no—
261#1931—618no—
262C2×#343—611no—
263C2×#341—611no—
264C2×C61—21no—
265C2×C61—21no—
266C2×C61—22no—
267C2×C61#193114yescomplemented
268C2×C61C2×#38811yescharacteristic
269C2×C61C2×#47111yescharacteristic
270C2×C61C2×#47211yescharacteristic
271D61—84no—
272C23×D4—611no—
273C22×M16—611no—
274C22×M16—611no—
275C22×M16C2×D6111yescharacteristic
276C23×C8—611no—
277C2×#117C2×D6111yescharacteristic
278C22×C4⋊C4C2×D6111yescharacteristic
279#428—22no—
280#428C2×D6114yescomplemented
281C2×#107—21no—
282C2×#106—21no—
283#418—614no—
284#418—1222no—
285C2×#102—614no—
286C2×#102—1221no—
287C2×#102—1221no—
288C2×#102—1222no—
289C2×#102—1221no—
290C2×#102—1221no—
291C2×#100—618no—
292C2×#100—614no—
293#405—614no—
294#405—1222no—
295C2×#97—1221no—
296C2×C4×C8—1221no—
297#343—614no—
298#341—614no—
299C61C2×#193111yescharacteristic, complemented, Sylow
300C25—1221no—
301C22×D4—614no—
302C22×D4—612no—
303C22×D4—1222no—
304C22×D4—1221no—
305C22×D4—1221no—
306C22×D4—1221no—
307C22×D4—1222no—
308C22×D4—1222no—
309C22×D4—1221no—
310C22×D4—1221no—
311C23×C4—21no—
312C23×C4C22×D6111yescharacteristic
313C2×M16—22no—
314C2×M16—21no—
315C2×M16—614no—
316C2×M16—612no—
317C2×M16—612no—
318C2×M16—1221no—
319C2×M16—1222no—
320C2×M16—1221no—
321C2×M16—1222no—
322C2×M16—1222no—
323C2×M16C4×D6114yes—
324C2×M16C22×D6112yes—
325C22×C8—21no—
326C22×C8—611no—
327C22×C8—611no—
328C22×C8—612no—
329C22×C8—612no—
330C22×C8—1222no—
331C22×C8—1221no—
332C22×C8—1222no—
333C22×C8—1221no—
334#117—21no—
335#117—21no—
336#117C22⋊D6112yes—
337#117C22×D6112yes—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4C22⋊D6111yescharacteristic
344C2×C4⋊C4C22⋊D6111yescharacteristic
345C2×C4⋊C4C22×D6112yes—
346C2×C22⋊C4—21no—
347C2×C42—21no—
348#107—24no—
349#106—24no—
350#102—1224no—
351#102—1224no—
352#102—1224no—
353#102—1224no—
354#100—6116no—
355#97—1224no—
356C4×C8—1224no—
357C24—1222no—
358C24—1224no—
359C24—4882no—
360C24—4882no—
361C24—2441no—
362C24—2441no—
363C24—2442no—
364C24#1175822411yescharacteristic
365C2×D4—614no—
366C2×D4—1222no—
367C2×D4—1222no—
368C2×D4—1222no—
369C2×D4—1222no—
370C2×D4—1222no—
371C2×D4—1224no—
372C2×D4—1224no—
373C2×D4—1224no—
374C2×D4—1224no—
375C2×D4—1224no—
376C2×D4—2441no—
377C2×D4—2441no—
378C2×D4—2442no—
379C2×D4—2442no—
380C2×D4—2442no—
381C2×D4—2442no—
382C2×D4—2442no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—22no—
386C22×C4—41no—
387C22×C4—41no—
388C22×C4—82no—
389C22×C4C2×C4×D6112yes—
390C22×C4#1175822212yes—
391C22×C4D4×D6111yescharacteristic
392C22×C4D4×D6111yescharacteristic
393C22×C4#1175822411yescharacteristic
394C22×C4#1175822612yes—
395C22×C4#1175822612yes—
396C22×C4C2×C22⋊D6111yescharacteristic
397C22×C4C2×C22⋊D6111yescharacteristic
398C22×C4C23×D6111yescharacteristic
399M16—22no—
400M16—24no—
401M16—614no—
402M16—1222no—
403M16—1224no—
404M16—1222no—
405M16—1222no—
406M16—2442no—
407M16C2×C4×D6114yes—
408C2×C8—22no—
409C2×C8—24no—
410C2×C8—612no—
411C2×C8—612no—
412C2×C8—1222no—
413C2×C8—1222no—
414C2×C8—1222no—
415C2×C8—1224no—
416C2×C8—1222no—
417C2×C8—1222no—
418C2×C8—1224no—
419C2×C8—1222no—
420C2×C8—2442no—
421C4⋊C4—21no—
422C4⋊C4—21no—
423C4⋊C4—22no—
424C4⋊C4—22no—
425C4⋊C4—41no—
426C4⋊C4—41no—
427C4⋊C4C2×C22⋊D6112yes—
428C4⋊C4C2×C22⋊D6112yes—
429C22⋊C4—22no—
430C22⋊C4—22no—
431C42—22no—
432C42—22no—
433C23—22no—
434C23—22no—
435C23—1224no—
436C23—4888no—
437C23—4882no—
438C23—4882no—
439C23—4888no—
440C23—4882no—
441C23—4882no—
442C23—4882no—
443C23—4882no—
444C23—2442no—
445C23—2442no—
446C23—2444no—
447C23—2444no—
448C23#1451973512yes—
449C23#1451974911yescharacteristic
450C23#1451974911yescharacteristic
451C23#1451977212yes—
452C23C2×#1175822411yescharacteristic
453D4—1224no—
454D4—1224no—
455D4—2442no—
456D4—2442no—
457D4—2444no—
458D4—2444no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—82no—
465C2×C4—82no—
466C2×C4—82no—
467C2×C4#1451973512yes—
468C2×C4C4×C22⋊D6112yes—
469C2×C4C4×C22⋊D6112yes—
470C2×C4#1451973912yes—
471C2×C4#1451973912yes—
472C2×C4#1451974911yescharacteristic
473C2×C4#1451974911yescharacteristic
474C2×C4#1451976212yes—
475C2×C4#1451976212yes—
476C2×C4#1451976612yes—
477C2×C4#1451976612yes—
478C2×C4#1451977212yes—
479C2×C4C22×C4×D6111yescharacteristic
480C2×C4C2×D4×D6111yescharacteristic
481C2×C4C22×C22⋊D6111yescharacteristic
482C2×C4C2×#1175822211yescharacteristic
483C2×C4C2×#1175822611yescharacteristic
484C2×C4C2×#1175822611yescharacteristic
485C8—24no—
486C8—1224no—
487C8—1222no—
488C8—1222no—
489C8—2442no—
490C22—24no—
491C22—24no—
492C22—21no—
493C22—21no—
494C22—21no—
495C22—21no—
496C22—4884no—
497C22—4884no—
498C22—4888no—
499C22—4888no—
500C22—4882no—
501C22—4882no—
502C22—2444no—
503C22#1683965212yes—
504C22#1683965212yes—
505C22#1684002712yes—
506C22#1684003012yes—
507C22C2×#1451973511yescharacteristic
508C22C2×#1451974911yescharacteristic
509C22C2×#1451977211yescharacteristic
510C4—42no—
511C4—42no—
512C4—82no—
513C4#1683965212yes—
514C4#1683965212yes—
515C4C2×C4×C22⋊D6111yescharacteristic
516C4C2×#1451973911yescharacteristic
517C4C2×#1451976211yescharacteristic
518C4C2×#1451976611yescharacteristic
519C2—21no—
520C2—21no—
521C2—22no—
522C2—4884no—
523C2#2144648014yesdirect product factor
524C2C2×#1683965211yescharacteristic
525C2C2×#1684002711yescharacteristic
526C2C2×#1684003011yescharacteristic
subgroupG/H
centerC23#14519749
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#428C2
socleC23×C61#121
prime radicalC23×D244C22
cosocleC22×C4×C61C24
hypercenterC2×#428D61
hypocenterC61C2×#1931
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#428

Complements

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

NH ≅ G/Ntype
4. C2×#16839718C2semidirect
5. #21446480C2direct (N × H)
6. C2×#16839531C2semidirect
7. C2×#16839526C2semidirect
8. C2×C61×#428C2semidirect
21. C2×#14519693C4semidirect
24. #16839718C22semidirect
27. #16839531C22semidirect
28. #16839526C22semidirect
33. C61×#428C22semidirect
67. #14519693C2×C4semidirect
256. C2×#428D61semidirect
267. C2×C61#1931semidirect
280. #428C2×D61semidirect
299. C61C2×#1931semidirect
523. C2#21446480direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168397662
C22×#145196972
C22×#145196932
C2×#168397182
#214464802
C2×#168395312
C2×#168395262
C2×C61×#4282
C2×#193161