Finite Group Databasebeta

← C2×#21444862 #29652249

Subgroups — C2×#21444862 #29652249

Order 15616.

984 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840391C211yesmaximal, characteristic
2C2×#16840098C211yesmaximal, characteristic
3C2×#16840095C211yesmaximal, characteristic
4C2×#16839702C211yesmaximal, characteristic
5#21444862C218yesmaximal, direct product factor
6C2×#16839498C211yesmaximal, characteristic
7C2×#16839487C211yesmaximal, characteristic
8C2×C61×#328C211yesmaximal, characteristic
9#16840391—22no—
10#16840391—22no—
11#16840391—22no—
12#16840391C2214yes—
13C2×#14519776—21no—
14C2×#14519775—21no—
15C2×#14519767—21no—
16C2×#14519767—21no—
17C2×#14519756C2211yescharacteristic
18C2×#14519754—21no—
19C2×#14519733—21no—
20C22×C4⋊Dic61C2211yescharacteristic
21C22×#11758196C2211yescharacteristic
22#16840098—22no—
23#16840098C2214yes—
24#16840095—22no—
25#16840095C2214yes—
26C2×#14519711—21no—
27C2×#14519710—21no—
28C2×#14519702—21no—
29C2×#14519701—21no—
30C2×C22⋊#92418C2211yescharacteristic
31#16839702—22no—
32#16839702C2214yes—
33C2×#14519684—21no—
34C2×#14519684—21no—
35#16839498C2214yes—
36#16839487C2214yes—
37C2×C22⋊Q8×C61C2211yescharacteristic
38C2×C22⋊C8×C61C2211yescharacteristic
39C2×#95×C61C2211yescharacteristic
40C61×#328C2214yes—
41C22×Dic122—21no—
42C22×Dic122D411yescharacteristic
43C23×Dic61—21no—
44C23×Dic61D411yescharacteristic
45C23×Dic61D411yescharacteristic
46C22×#92418—21no—
47#14519776—24no—
48#14519776—24no—
49#14519775—24no—
50#14519775—24no—
51#14519767—24no—
52#14519767—24no—
53#14519767—24no—
54#14519767—24no—
55#14519756—21no—
56#14519756—21no—
57#14519756D412yes—
58#14519756C2312yes—
59#14519754—24no—
60#14519754—24no—
61#14519733—24no—
62#14519733—24no—
63C2×C4⋊Dic61—21no—
64C2×C4⋊Dic61—21no—
65C2×C4⋊Dic61—21no—
66C2×C4⋊Dic61—21no—
67C2×C4⋊Dic61—21no—
68C2×C4⋊Dic61—21no—
69C2×C4⋊Dic61D411yescharacteristic
70C2×C4⋊Dic61C2312yes—
71C2×#11758196—21no—
72C2×#11758196—21no—
73C2×#11758196—21no—
74C2×#11758196—21no—
75C2×#11758196—21no—
76C2×#11758196—21no—
77C2×#11758196—21no—
78C2×#11758196—21no—
79C2×#11758196—21no—
80C2×#11758196D412yes—
81C2×#11758196C2312yes—
82C2×C22⋊Dic61—21no—
83C2×C4×Dic61—21no—
84C2×C4×Dic61—21no—
85#14519711—24no—
86#14519710—24no—
87#14519702—24no—
88#14519701—24no—
89C22⋊#92418—21no—
90C22⋊#92418C2312yes—
91#14519684—24no—
92#14519684—24no—
93C22×Q8×C61D411yescharacteristic
94C23×C4×C61—21no—
95C23×C4×C61C2311yescharacteristic
96C22×C8×C61—21no—
97C22⋊Q8×C61—21no—
98C22⋊Q8×C61—21no—
99C22⋊Q8×C61D412yes—
100C22⋊Q8×C61C2312yes—
101C2×C4⋊C4×C61—21no—
102C2×C4⋊C4×C61D411yescharacteristic
103C2×C22⋊C4×C61—21no—
104C22⋊C8×C61—21no—
105C22⋊C8×C61C2312yes—
106#95×C61—21no—
107#95×C61C2312yes—
108C24×C61C2×D411yescharacteristic
109C2×Q8×C61—21no—
110C2×Q8×C61—42no—
111C2×Q8×C61C2×D412yes—
112C22×C4×C61—21no—
113C22×C4×C61—21no—
114C22×C4×C61—22no—
115C22×C4×C61—42no—
116C22×C4×C61—42no—
117C22×C4×C61—42no—
118C22×C4×C61—42no—
119C22×C4×C61C2×D411yescharacteristic
120C22×C4×C61C2×D411yescharacteristic
121C22×C4×C61C2×D411yescharacteristic
122C22×C4×C61C2×D411yescharacteristic
123C22×C4×C61C2×D411yescharacteristic
124C22×C4×C61C2411yescharacteristic
125C22×Dic61—21no—
126C22×Dic61—21no—
127C22×Dic61—22no—
128C22×Dic61—21no—
129C22×Dic61—21no—
130C22×Dic61—21no—
131C22×Dic61—21no—
132C22×Dic61—22no—
133C22×Dic61—42no—
134C22×Dic61—44no—
135C22×Dic61—41no—
136C22×Dic61—41no—
137C22×Dic61Q1614yes—
138C22×Dic61C2×D412yes—
139C22×Dic61C2×D412yes—
140C2×Dic122—24no—
141C2×Dic122—21no—
142C2×Dic122—42no—
143C2×Dic122—82no—
144C2×Dic122C2×D412yes—
145C2×C8×C61—22no—
146C2×C8×C61—42no—
147C4⋊C4×C61—22no—
148C4⋊C4×C61—21no—
149C4⋊C4×C61—22no—
150C4⋊C4×C61C2×D412yes—
151C22⋊C4×C61—22no—
152C22⋊C4×C61—22no—
153C22⋊Dic61—22no—
154C22⋊Dic61—22no—
155C4⋊Dic61—24no—
156C4⋊Dic61—21no—
157C4⋊Dic61—22no—
158C4⋊Dic61—22no—
159C4⋊Dic61—41no—
160C4⋊Dic61—41no—
161C4⋊Dic61C2×D412yes—
162#11758196—24no—
163#11758196—24no—
164#11758196—24no—
165#11758196—24no—
166#11758196—22no—
167#11758196—22no—
168#11758196—22no—
169#11758196—22no—
170#11758196—22no—
171#11758196—22no—
172C4×Dic61—24no—
173C4×Dic61—24no—
174C2×#92418—22no—
175C2×#92418—42no—
176C23×C61—22no—
177C23×C61—22no—
178C23×C61#12011yescharacteristic
179C23×C61#12011yescharacteristic
180C23×C61C2×Q1612yes—
181C23×C61#13712yes—
182C23×C61C22×D411yescharacteristic
183Q8×C61—42no—
184Q8×C61—81no—
185C2×C4×C61—22no—
186C2×C4×C61—22no—
187C2×C4×C61—22no—
188C2×C4×C61—22no—
189C2×C4×C61—41no—
190C2×C4×C61—41no—
191C2×C4×C61—41no—
192C2×C4×C61—41no—
193C2×C4×C61—42no—
194C2×C4×C61—42no—
195C2×C4×C61—42no—
196C2×C4×C61—42no—
197C2×C4×C61—42no—
198C2×C4×C61—84no—
199C2×C4×C61#12011yescharacteristic
200C2×C4×C61#12011yescharacteristic
201C2×C4×C61C22×D411yescharacteristic
202C2×C4×C61C22×D411yescharacteristic
203C2×Dic61—22no—
204C2×Dic61—22no—
205C2×Dic61—24no—
206C2×Dic61—24no—
207C2×Dic61—22no—
208C2×Dic61—22no—
209C2×Dic61—22no—
210C2×Dic61—42no—
211C2×Dic61—42no—
212C2×Dic61—42no—
213C2×Dic61—42no—
214C2×Dic61—44no—
215C2×Dic61—42no—
216C2×Dic61—81no—
217C2×Dic61—82no—
218C2×Dic61—82no—
219C2×Dic61C2×Q1614yes—
220Dic122—42no—
221Dic122—81no—
222Dic122—84no—
223C8×C61—42no—
224#92418—42no—
225C2×#1617—611nomaximal, Sylow
226C22×C61—24no—
227C22×C61—24no—
228C22×C61—21no—
229C22×C61—21no—
230C22×C61—21no—
231C22×C61—21no—
232C22×C61#45112yes—
233C22×C61#45112yes—
234C22×C61#45412yes—
235C22×C61#45812yes—
236C22×C61C2×#12011yescharacteristic
237C22×C61C22×Q1611yescharacteristic
238C22×C61C2×#13711yescharacteristic
239C4×C61—21no—
240C4×C61—21no—
241C4×C61—21no—
242C4×C61—21no—
243C4×C61—42no—
244C4×C61—42no—
245C4×C61—82no—
246Dic61—24no—
247Dic61—42no—
248Dic61—42no—
249Dic61—42no—
250Dic61—82no—
251C2×#544—611no—
252C2×#484—611no—
253C2×#484—611no—
254C2×#400—611no—
255#1617—618no—
256C2×#328—611no—
257C2×#328D6111yescharacteristic
258C2×#324—611no—
259C2×C61—21no—
260C2×C61—21no—
261C2×C61—22no—
262C2×C61#161714yescomplemented
263C2×C61C2×#45111yescharacteristic
264C2×C61C2×#45411yescharacteristic
265C2×C61C2×#45811yescharacteristic
266#544—614no—
267#544—1222no—
268#544—1222no—
269#544—1222no—
270C2×C4⋊Q8—1221no—
271C2×C4⋊Q8—1221no—
272C2×#125—1221no—
273C2×#125—1221no—
274C2×C22⋊Q8—611no—
275C2×C22⋊Q8—1221no—
276C2×C22⋊Q8C2×D6111yescharacteristic
277C2×#117—1221no—
278C22×C4⋊C4—611no—
279C22×C4⋊C4—611no—
280#484—614no—
281#484—614no—
282#484—1222no—
283#484—1222no—
284C2×#107—1221no—
285C2×#107—1221no—
286C2×#103—1221no—
287C2×#103—1221no—
288C2×C22⋊C8—611no—
289C2×C22⋊C8C2×D6111yescharacteristic
290#400—614no—
291#400—1222no—
292C2×#95—1221no—
293C2×#95—1221no—
294C2×#95C2×D6111yescharacteristic
295#328—614no—
296#328C2×D6114yes—
297#324—614no—
298C61C2×#161711yescharacteristic, complemented, Sylow
299C22×Q8—611no—
300C22×Q8—1221no—
301C22×Q8D24411yescharacteristic
302C23×C4—21no—
303C23×C4—611no—
304C23×C4—611no—
305C23×C4—1221no—
306C23×C4C22×D6111yescharacteristic
307C22×C8—21no—
308C22×C8—1221no—
309C4⋊Q8—1224no—
310C4⋊Q8—1224no—
311C4⋊Q8—1224no—
312C4⋊Q8—1224no—
313#125—1224no—
314#125—1224no—
315#125—1224no—
316#125—1224no—
317C22⋊Q8—21no—
318C22⋊Q8—21no—
319C22⋊Q8—612no—
320C22⋊Q8—612no—
321C22⋊Q8—1224no—
322C22⋊Q8—1224no—
323C22⋊Q8—1221no—
324C22⋊Q8—1221no—
325C22⋊Q8D24412yes—
326C22⋊Q8C22×D6112yes—
327#117—1224no—
328#117—1224no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—611no—
331C2×C4⋊C4—612no—
332C2×C4⋊C4—612no—
333C2×C4⋊C4—612no—
334C2×C4⋊C4—1221no—
335C2×C4⋊C4—1221no—
336C2×C4⋊C4—1221no—
337C2×C4⋊C4—1221no—
338C2×C4⋊C4—1221no—
339C2×C4⋊C4—1221no—
340C2×C4⋊C4—1221no—
341C2×C4⋊C4—1221no—
342C2×C4⋊C4—1221no—
343C2×C4⋊C4—1221no—
344C2×C4⋊C4—1221no—
345C2×C4⋊C4—1221no—
346C2×C4⋊C4—1221no—
347C2×C4⋊C4—1221no—
348C2×C4⋊C4—1221no—
349C2×C4⋊C4D24411yescharacteristic
350C2×C22⋊C4—21no—
351C2×C22⋊C4—1221no—
352C2×C42—1221no—
353C2×C42—1221no—
354#107—1224no—
355#107—1224no—
356#103—1224no—
357#103—1224no—
358C22⋊C8—21no—
359C22⋊C8—612no—
360C22⋊C8—1221no—
361C22⋊C8C22×D6112yes—
362#95—21no—
363#95—1224no—
364#95—1224no—
365#95C22×D6112yes—
366C24D4×D6111yescharacteristic
367C2×Q8—21no—
368C2×Q8—42no—
369C2×Q8—612no—
370C2×Q8—1224no—
371C2×Q8—1221no—
372C2×Q8—4882no—
373C2×Q8—2442no—
374C2×Q8C2×D24412yes—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—22no—
378C22×C4—42no—
379C22×C4—42no—
380C22×C4—42no—
381C22×C4—42no—
382C22×C4—612no—
383C22×C4—614no—
384C22×C4—612no—
385C22×C4—1221no—
386C22×C4—1221no—
387C22×C4—1222no—
388C22×C4—1221no—
389C22×C4—1221no—
390C22×C4—1221no—
391C22×C4—1221no—
392C22×C4—1222no—
393C22×C4—2444no—
394C22×C4—2441no—
395C22×C4—2441no—
396C22×C4—2442no—
397C22×C4C2×D24411yescharacteristic
398C22×C4C2×D24411yescharacteristic
399C22×C4D4×D6111yescharacteristic
400C22×C4D4×D6111yescharacteristic
401C22×C4D4×D6111yescharacteristic
402C22×C4C23×D6111yescharacteristic
403C2×C8—22no—
404C2×C8—42no—
405C2×C8—1222no—
406C2×C8—2442no—
407C4⋊C4—22no—
408C4⋊C4—22no—
409C4⋊C4—21no—
410C4⋊C4—612no—
411C4⋊C4—1224no—
412C4⋊C4—1224no—
413C4⋊C4—1224no—
414C4⋊C4—1224no—
415C4⋊C4—1224no—
416C4⋊C4—1222no—
417C4⋊C4—1222no—
418C4⋊C4—1222no—
419C4⋊C4—1222no—
420C4⋊C4—1222no—
421C4⋊C4—1221no—
422C4⋊C4—1222no—
423C4⋊C4—1222no—
424C4⋊C4—1222no—
425C4⋊C4—2441no—
426C4⋊C4—2441no—
427C4⋊C4C2×D24412yes—
428C22⋊C4—22no—
429C22⋊C4—22no—
430C22⋊C4—1222no—
431C22⋊C4—1222no—
432C42—1224no—
433C42—1224no—
434C23—22no—
435C23—22no—
436C23#1451974711yescharacteristic
437C23#1451974711yescharacteristic
438C23Q16×D6112yes—
439C23#1451980612yes—
440C23C2×D4×D6111yescharacteristic
441Q8—42no—
442Q8—81no—
443Q8—4881no—
444Q8—4884no—
445Q8—2442no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—84no—
460C2×C4—614no—
461C2×C4—1222no—
462C2×C4—1222no—
463C2×C4—1224no—
464C2×C4—1224no—
465C2×C4—1222no—
466C2×C4—1222no—
467C2×C4—1222no—
468C2×C4—4882no—
469C2×C4—4882no—
470C2×C4—4881no—
471C2×C4—2444no—
472C2×C4—2442no—
473C2×C4—2442no—
474C2×C4—2442no—
475C2×C4—2442no—
476C2×C4—2442no—
477C2×C4#1451974711yescharacteristic
478C2×C4#1451974711yescharacteristic
479C2×C4C2×D4×D6111yescharacteristic
480C2×C4C22×D24411yescharacteristic
481C8—42no—
482C8—2442no—
483C22—21no—
484C22—21no—
485C22—21no—
486C22—21no—
487C22—24no—
488C22—24no—
489C22#1683991912yes—
490C22#1683991912yes—
491C22#1683993612yes—
492C22#1683995312yes—
493C22C2×#1451974711yescharacteristic
494C22C2×Q16×D6111yescharacteristic
495C22C2×#1451980611yescharacteristic
496C4—21no—
497C4—21no—
498C4—21no—
499C4—21no—
500C4—42no—
501C4—42no—
502C4—82no—
503C4—1224no—
504C4—4882no—
505C4—2442no—
506C4—2442no—
507C4—2442no—
508C2—21no—
509C2—21no—
510C2—22no—
511C2#2144486214yesdirect product factor
512C2C2×#1683991911yescharacteristic
513C2C2×#1683993611yescharacteristic
514C2C2×#1683995311yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#328C2
socleC23×C61#120
prime radicalC24×C61C2×D4
hypercenterC2×#328D61
hypocenterC61C2×#1617
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#328

Complements

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

NH ≅ G/Ntype
5. #21444862C2direct (N × H)
262. C2×C61#1617semidirect
298. C61C2×#1617semidirect
511. C2#21444862direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403912
C2×#168400982
C2×#168400952
C2×#168397022
#214448622
C2×#168394982
C2×#168394872
C2×C61×#3282
C2×#161761