Finite Group Databasebeta

← C2×#21447468 #29832744

Subgroups — C2×#21447468 #29832744

Order 15616.

1406 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840326C211yesmaximal, characteristic
2C2×#16839746C211yesmaximal, characteristic, complemented
3#21447468C218yesmaximal, direct product factor
4C2×#16839548C214yesmaximal, complemented
5C2×C61×#410C211yesmaximal, characteristic, complemented
6C23×D244C411yescharacteristic, complemented
7C22×#11758194—21no—
8#16840326—22no—
9#16840326—22no—
10#16840326C414yescomplemented
11#16840326C2214yes—
12C2×#14519773—21no—
13C2×#14519766—21no—
14C2×#14519751—21no—
15C2×#14519751—21no—
16C2×#14519745C412yescomplemented
17C2×#14519745C2212yes—
18C2×#14519736C411yescharacteristic, complemented
19#16839746—22no—
20#16839746C2214yescomplemented
21C2×#14519696—21no—
22C2×#14519694C2212yes—
23#16839548C22116yescomplemented
24C22×#41×C61C2211yescharacteristic
25C2×#117×C61—21no—
26C61×#410—22no—
27C61×#410C2214yescomplemented
28C2×#99×C61—21no—
29C2×#99×C61C2212yes—
30C24×D61C2×C412yes—
31C22×D244—21no—
32C22×D244—21no—
33C22×D244—22no—
34C22×D244—42no—
35C22×D244—41no—
36C22×D244—41no—
37C22×D244C2×C414yescomplemented
38C22×C22⋊D61—22no—
39C22×C22⋊D61—22no—
40C2×#11758194—22no—
41C2×#11758194—24no—
42C2×#11758194—41no—
43C2×#11758194—42no—
44C22×#92418—41no—
45#14519773—24no—
46#14519773—24no—
47#14519766—24no—
48#14519766—24no—
49#14519751—24no—
50#14519751—24no—
51#14519751—24no—
52#14519751—24no—
53#14519745—24no—
54#14519745—22no—
55#14519745—22no—
56#14519745C2×C414yes—
57#14519745C2×C418yescomplemented
58#14519745C2314yes—
59#14519736—22no—
60#14519736C2×C414yescomplemented
61C2×C4⋊Dic61—21no—
62C2×C22⋊Dic61C2×C412yes—
63C2×#11758198—22no—
64C2×#11758198—22no—
65C2×C4×Dic61—21no—
66#14519696—24no—
67#14519694—22no—
68#14519694C2314yes—
69C2×#41×C61—41no—
70C2×#41×C61—41no—
71C2×#41×C61—42no—
72C2×#41×C61C2×C412yes—
73C2×#41×C61D412yes—
74C2×#41×C61D412yes—
75C2×#41×C61C2312yes—
76C22×Q8×C61D411yescharacteristic
77C22×D4×C61C2×C411yescharacteristic
78C22×D4×C61D411yescharacteristic
79C22×D4×C61C2311yescharacteristic
80C23×C4×C61C2×C411yescharacteristic
81C23×C4×C61D411yescharacteristic
82C23×C4×C61D411yescharacteristic
83#117×C61—24no—
84#117×C61—42no—
85C2×C4⋊C4×C61—41no—
86C2×C22⋊C4×C61—22no—
87C2×C42×C61—41no—
88#99×C61—24no—
89#99×C61—22no—
90#99×C61C2314yes—
91C24×C61C22⋊C411yescharacteristic
92C24×C61C22×C411yescharacteristic
93C24×C61C2×D411yescharacteristic
94C23×D61—22no—
95C23×D61—22no—
96C23×D61—42no—
97C23×D61—42no—
98C23×D61—84no—
99C23×D61C22×C414yes—
100#41×C61—42no—
101#41×C61—42no—
102#41×C61—42no—
103#41×C61—42no—
104#41×C61—42no—
105#41×C61—42no—
106#41×C61—42no—
107#41×C61—42no—
108C2×Q8×C61—41no—
109C2×Q8×C61—41no—
110C2×Q8×C61C22⋊C412yes—
111C2×Q8×C61C2×D412yes—
112C2×D4×C61—41no—
113C2×D4×C61—41no—
114C2×D4×C61—41no—
115C2×D4×C61—41no—
116C2×D4×C61—41no—
117C2×D4×C61—41no—
118C2×D4×C61C22⋊C412yes—
119C2×D4×C61C22⋊C412yes—
120C2×D4×C61C22×C412yes—
121C2×D4×C61C22×C411yescharacteristic
122C2×D4×C61C2×D412yes—
123C2×D4×C61C2×D411yescharacteristic
124C2×D4×C61C2×D411yescharacteristic
125C2×D4×C61C2411yescharacteristic
126C22×C4×C61—22no—
127C22×C4×C61—21no—
128C22×C4×C61—21no—
129C22×C4×C61—21no—
130C22×C4×C61—21no—
131C22×C4×C61—22no—
132C22×C4×C61—21no—
133C22×C4×C61—21no—
134C22×C4×C61—22no—
135C22×C4×C61—42no—
136C22×C4×C61C22⋊C411yescharacteristic
137C22×C4×C61C22⋊C412yes—
138C22×C4×C61C22⋊C411yescharacteristic
139C22×C4×C61C22⋊C412yes—
140C22×C4×C61C22⋊C412yes—
141C22×C4×C61C22⋊C411yescharacteristic
142C22×C4×C61C22×C412yes—
143C22×C4×C61C2×D412yes—
144C22×C4×C61C2×D411yescharacteristic
145C22×C4×C61C2×D412yes—
146C2×C22⋊D61—24no—
147C2×C22⋊D61—28no—
148C2×C22⋊D61—24no—
149C2×C22⋊D61—84no—
150C2×C22⋊D61—84no—
151C22×Dic61—22no—
152C2×D244—24no—
153C2×D244—24no—
154C2×D244—42no—
155C2×D244—42no—
156C2×D244—44no—
157C2×D244—44no—
158C2×D244—42no—
159C2×D244—41no—
160C2×D244—41no—
161C2×D244—44no—
162C2×D244—44no—
163C4⋊C4×C61—44no—
164C22⋊C4×C61—24no—
165C22⋊C4×C61—42no—
166C42×C61—44no—
167C22⋊Dic61—22no—
168C22⋊Dic61C22×C414yes—
169#11758198—24no—
170#11758198—28no—
171#11758198—24no—
172C4⋊Dic61—24no—
173C4×Dic61—24no—
174#11758194—24no—
175#11758194—42no—
176#11758194—44no—
177C2×#92418—42no—
178C2×#92418—44no—
179C23×C61—21no—
180C23×C61—21no—
181C23×C61—21no—
182C23×C61—21no—
183C23×C61—21no—
184C23×C61—21no—
185C23×C61—42no—
186C23×C61—42no—
187C23×C61—42no—
188C23×C61C2×C22⋊C411yescharacteristic
189C23×C61C2×C22⋊C411yescharacteristic
190C23×C61C2×C22⋊C411yescharacteristic
191C23×C61C2×C22⋊C412yes—
192C23×C61C23×C411yescharacteristic
193C23×C61C22×D411yescharacteristic
194C22×D61—24no—
195C22×D61—44no—
196C22×D61—44no—
197C22×D61—44no—
198C22×D61—42no—
199C22×D61—42no—
200C22×D61—44no—
201C22×D61—84no—
202C22×D61—84no—
203C22×D61—88no—
204C22×D61—88no—
205Q8×C61—42no—
206Q8×C61—42no—
207D4×C61—42no—
208D4×C61—42no—
209D4×C61—42no—
210D4×C61—41no—
211D4×C61—41no—
212D4×C61—42no—
213D4×C61—41no—
214D4×C61—41no—
215C2×C4×C61—21no—
216C2×C4×C61—21no—
217C2×C4×C61—21no—
218C2×C4×C61—21no—
219C2×C4×C61—21no—
220C2×C4×C61—21no—
221C2×C4×C61—22no—
222C2×C4×C61—22no—
223C2×C4×C61—22no—
224C2×C4×C61—22no—
225C2×C4×C61—22no—
226C2×C4×C61—22no—
227C2×C4×C61—22no—
228C2×C4×C61—22no—
229C2×C4×C61—22no—
230C2×C4×C61—22no—
231C2×C4×C61—22no—
232C2×C4×C61—22no—
233C2×C4×C61—44no—
234C2×C4×C61—84no—
235C2×C4×C61#9912yes—
236C2×C4×C61#9911yescharacteristic
237C2×C4×C61#9911yescharacteristic
238C2×C4×C61C2×C22⋊C412yes—
239C2×C4×C61C2×C22⋊C412yes—
240C2×C4×C61C2×C22⋊C411yescharacteristic
241C2×C4×C61C2×C22⋊C412yes—
242C2×C4×C61C22×D411yescharacteristic
243C22⋊D61—84no—
244C22⋊D61—88no—
245C22⋊D61—84no—
246C2×Dic61—24no—
247C2×Dic61—44no—
248D244—48no—
249D244—44no—
250D244—44no—
251#92418—44no—
252C2×#2122—611nomaximal, Sylow
253C22×C61—22no—
254C22×C61—21no—
255C22×C61—21no—
256C22×C61—21no—
257C22×C61—22no—
258C22×C61—21no—
259C22×C61—42no—
260C22×C61—41no—
261C22×C61—41no—
262C22×C61—41no—
263C22×C61—41no—
264C22×C61—42no—
265C22×C61—42no—
266C22×C61—42no—
267C22×C61—42no—
268C22×C61—81no—
269C22×C61—81no—
270C22×C61C2×#9911yescharacteristic
271C22×C61C2×#9911yescharacteristic
272C22×C61C22×C22⋊C411yescharacteristic
273C2×D61—44no—
274C2×D61—44no—
275C2×D61—44no—
276C2×D61—84no—
277C2×D61—88no—
278C2×D61—84no—
279C2×D61—88no—
280C4×C61—21no—
281C4×C61—22no—
282C4×C61—21no—
283C4×C61—22no—
284C4×C61—84no—
285C4×C61C2×#9912yes—
286C4×C61C2×#9912yes—
287Dic61—44no—
288C2×#535—611no—
289C2×#413—611no—
290C2×#410D6111yescharacteristic, complemented
291#2122—618no—
292C2×AΣL(1,𝔽16)—614no—
293C2×C61—21no—
294C2×C61—21no—
295C2×C61—41no—
296C2×C61—41no—
297C2×C61—41no—
298C2×C61—41no—
299C2×C61—42no—
300C2×C61#212212yescomplemented
301C2×C61C22×#9911yescharacteristic
302D61—84no—
303C22×#41C2×D6111yescharacteristic
304C23×D4—611no—
305C22×M16—1221no—
306#535—614no—
307#535—614no—
308#535—1222no—
309#535—1222no—
310C2×#127—1221no—
311C2×#124—1221no—
312C2×#121—1221no—
313C2×#121—1221no—
314C2×#120—612no—
315C2×#120—612no—
316C2×#117—21no—
317C2×#117—611no—
318#413—614no—
319#413—1222no—
320C2×#101—1221no—
321C2×#100—612no—
322#410—22no—
323#410C2×D6114yescomplemented
324C2×#99—21no—
325C2×#99C2×D6112yes—
326AΣL(1,𝔽16)—6116no—
327C61C2×#212211yescharacteristic, complemented, Sylow
328C25—612no—
329C2×#41—41no—
330C2×#41—41no—
331C2×#41—42no—
332C2×#41C4×D6112yes—
333C2×#41D24412yes—
334C2×#41C22⋊D6112yes—
335C2×#41C22×D6112yes—
336C22×Q8D24411yescharacteristic
337C22×D4—614no—
338C22×D4—1222no—
339C22×D4—1222no—
340C22×D4—1221no—
341C22×D4—1222no—
342C22×D4—1221no—
343C22×D4—2442no—
344C22×D4—2441no—
345C22×D4—2441no—
346C22×D4C4×D6111yescharacteristic
347C22×D4C22⋊D6111yescharacteristic
348C22×D4C22×D6111yescharacteristic
349C23×C4C4×D6111yescharacteristic
350C23×C4D24411yescharacteristic
351C23×C4C22⋊D6111yescharacteristic
352C2×M16—1222no—
353C2×M16—1224no—
354C2×M16—2441no—
355C2×M16—2442no—
356C22×C8—2441no—
357#127—1224no—
358#127—1224no—
359#124—1224no—
360#124—1224no—
361#121—1224no—
362#121—1224no—
363#121—1224no—
364#121—1224no—
365#120—614no—
366#120—618no—
367#120—614no—
368#120—1224no—
369#120—1222no—
370#120—1222no—
371#117—24no—
372#117—42no—
373#117—614no—
374#117—1222no—
375C2×C4⋊C4—41no—
376C2×C4⋊C4—1221no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—612no—
379C2×C22⋊C4—1222no—
380C2×C22⋊C4—1222no—
381C2×C42—41no—
382C2×C42—1221no—
383#101—1224no—
384#100—614no—
385#100—1222no—
386#99—24no—
387#99—22no—
388#99C22×D6114yes—
389C24—614no—
390C24—1222no—
391C24—1222no—
392C24—4884no—
393C24—2442no—
394C24—2442no—
395C24#1175819811yescharacteristic
396C24C2×C4×D6111yescharacteristic
397C24C2×C22⋊D6111yescharacteristic
398#41—42no—
399#41—42no—
400#41—42no—
401#41—42no—
402#41—42no—
403#41—42no—
404#41—42no—
405#41—42no—
406C2×Q8—41no—
407C2×Q8—41no—
408C2×Q8#1175819812yes—
409C2×Q8C2×D24412yes—
410C2×D4—41no—
411C2×D4—41no—
412C2×D4—41no—
413C2×D4—41no—
414C2×D4—41no—
415C2×D4—41no—
416C2×D4—1224no—
417C2×D4—1224no—
418C2×D4—1228no—
419C2×D4—1224no—
420C2×D4—1224no—
421C2×D4—4884no—
422C2×D4—4884no—
423C2×D4—2442no—
424C2×D4—2442no—
425C2×D4—2444no—
426C2×D4—2444no—
427C2×D4—2444no—
428C2×D4—2444no—
429C2×D4—2442no—
430C2×D4—2441no—
431C2×D4—2441no—
432C2×D4#1175819812yes—
433C2×D4#1175819812yes—
434C2×D4C2×C4×D6112yes—
435C2×D4C2×C4×D6111yescharacteristic
436C2×D4C2×D24411yescharacteristic
437C2×D4C2×C22⋊D6111yescharacteristic
438C2×D4C2×C22⋊D6112yes—
439C2×D4C23×D6111yescharacteristic
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—22no—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—42no—
450C22×C4—1222no—
451C22×C4#1175819811yescharacteristic
452C22×C4#1175819811yescharacteristic
453C22×C4#1175819812yes—
454C22×C4#1175819812yes—
455C22×C4#1175819812yes—
456C22×C4#1175819811yescharacteristic
457C22×C4C2×C4×D6112yes—
458C22×C4C2×D24411yescharacteristic
459C22×C4C2×D24412yes—
460C22×C4C2×C22⋊D6112yes—
461M16—1224no—
462M16—2442no—
463M16—2444no—
464C2×C8—2442no—
465C2×C8—2444no—
466C4⋊C4—44no—
467C4⋊C4—1224no—
468C22⋊C4—24no—
469C22⋊C4—42no—
470C22⋊C4—614no—
471C22⋊C4—1222no—
472C22⋊C4—1224no—
473C22⋊C4—1224no—
474C22⋊C4—1228no—
475C42—44no—
476C42—1224no—
477C23—21no—
478C23—21no—
479C23—21no—
480C23—21no—
481C23—21no—
482C23—21no—
483C23—42no—
484C23—42no—
485C23—42no—
486C23—1224no—
487C23—4888no—
488C23—4888no—
489C23—4884no—
490C23—4884no—
491C23—2444no—
492C23—2444no—
493C23—2444no—
494C23—2444no—
495C23—2442no—
496C23—2442no—
497C23C2×#1175819811yescharacteristic
498C23C2×#1175819811yescharacteristic
499C23C2×#1175819811yescharacteristic
500C23C2×#1175819812yes—
501C23C22×C4×D6111yescharacteristic
502C23C22×C22⋊D6111yescharacteristic
503Q8—42no—
504Q8—42no—
505D4—42no—
506D4—42no—
507D4—42no—
508D4—41no—
509D4—41no—
510D4—42no—
511D4—41no—
512D4—41no—
513D4—4884no—
514D4—4888no—
515D4—4884no—
516D4—2448no—
517D4—2444no—
518D4—2444no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—44no—
538C2×C4—84no—
539C2×C4—1224no—
540C2×C4—2444no—
541C2×C4#1451969112yes—
542C2×C4#1451969111yescharacteristic
543C2×C4#1451969111yescharacteristic
544C2×C4C2×#1175819812yes—
545C2×C4C2×#1175819811yescharacteristic
546C2×C4C2×#1175819812yes—
547C2×C4C2×#1175819812yes—
548C2×C4C22×D24411yescharacteristic
549C8—2444no—
550C22—22no—
551C22—21no—
552C22—21no—
553C22—21no—
554C22—22no—
555C22—21no—
556C22—41no—
557C22—42no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—42no—
562C22—42no—
563C22—42no—
564C22—42no—
565C22—81no—
566C22—81no—
567C22—4884no—
568C22—4888no—
569C22—4888no—
570C22—4884no—
571C22—2444no—
572C22—2444no—
573C22—2444no—
574C22C2×#1451969111yescharacteristic
575C22C2×#1451969111yescharacteristic
576C22C22×#1175819811yescharacteristic
577C4—21no—
578C4—22no—
579C4—21no—
580C4—22no—
581C4—84no—
582C4—2444no—
583C4C2×#1451969112yes—
584C4C2×#1451969112yes—
585C2—21no—
586C2—21no—
587C2—41no—
588C2—41no—
589C2—41no—
590C2—41no—
591C2—42no—
592C2—4884no—
593C2#2144746812yesdirect product factor
594C2C22×#1451969111yescharacteristic
subgroupG/H
centerC22C2×#14519691
commutatorC23×C61C23×C4
FrattiniC2×D4C23×D61
FittingC2×C61×#410C2
socleC22×C61C2×#99
prime radicalC2×#16840326C2
cosocleC2×D4×C61C24
hypercenterC2×#410D61
hypocenterC61C2×#2122
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×#41 ◁ C2×#410

Complements

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

NH ≅ G/Ntype
2. C2×#16839746C2semidirect
3. #21447468C2direct (N × H)
4. C2×#16839548C2semidirect
5. C2×C61×#410C2semidirect
6. C23×D244C4semidirect
10. #16840326C4semidirect
16. C2×#14519745C4semidirect
18. C2×#14519736C4semidirect
20. #16839746C22semidirect
23. #16839548C22semidirect
27. C61×#410C22semidirect
37. C22×D244C2×C4semidirect
57. #14519745C2×C4semidirect
60. #14519736C2×C4semidirect
290. C2×#410D61semidirect
300. C2×C61#2122semidirect
323. #410C2×D61semidirect
327. C61C2×#2122semidirect
593. C2#21447468direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403262
C2×#168397462
#214474682
C2×#168395482
C2×C61×#4102
C2×#212261