Finite Group Databasebeta

← C2×#21456847 #30551288

Subgroups — C2×#21456847 #30551288

Order 15616.

2146 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊Q8×D61C211yesmaximal, characteristic, complemented
2C2×#16840297C211yesmaximal, characteristic
3#21456847C2116yesmaximal, direct product factor
4C2×#16840156C211yesmaximal, characteristic, complemented
5C2×#16840154C211yesmaximal, characteristic, complemented
6C2×#16840132C211yesmaximal, characteristic, complemented
7C2×#16839971C212yesmaximal, complemented
8C2×#16839966C212yesmaximal, complemented
9C2×#16839919C212yesmaximal, complemented
10C2×#16839902C212yesmaximal
11C2×#16839817C211yesmaximal, characteristic, complemented
12C2×C61×#491C211yesmaximal, characteristic, complemented
13C22×Q8×D61C2212yes—
14C22×Dic244C2212yes—
15C22×#11758202C2212yes—
16C22×#11758190C2212yes—
17C22×#11758201C2212yes—
18C2×#14519777C2211yescharacteristic
19C2×#14519776—21no—
20C2×#14519776—21no—
21C2×#14519775C2212yes—
22C4⋊Q8×D61—24no—
23C4⋊Q8×D61C2218yescomplemented
24#16840297—24no—
25#16840297C2218yes—
26C2×#14519772—21no—
27C2×#14519765C2211yescharacteristic
28C2×#14519762—21no—
29C2×#14519757C2211yescharacteristic
30C2×#14519752C2211yescharacteristic
31C2×#14519742C2211yescharacteristic
32C2×#14519739—21no—
33C2×#14519739C2211yescharacteristic
34C2×#14519735—21no—
35C2×C4⋊C4×D61—21no—
36C2×C4⋊C4×D61—21no—
37C2×C42×D61C2211yescharacteristic
38#16840156C2218yescomplemented
39#16840154C2218yescomplemented
40#16840132C2218yescomplemented
41#16839971C22116yescomplemented
42#16839966C22116yescomplemented
43#16839919C22116yescomplemented
44#16839902C22116yes—
45#16839817C2218yescomplemented
46C2×#14519706C2212yes—
47C2×#14519700C2212yes—
48C2×#14519700C2212yes—
49C2×#14519689C2212yes—
50C2×#14519688C2211yescharacteristic
51C2×C4⋊Q8×C61C2211yescharacteristic
52C2×#125×C61C2211yescharacteristic
53C61×#491C2218yescomplemented
54C2×#103×C61C2212yes—
55C2×#103×C61C2212yes—
56C2×#97×C61C2211yescharacteristic
57C22×Dic122—22no—
58C22×Dic122C2311yescharacteristic
59C22×Dic122C2312yes—
60C2×Q8×D61—24no—
61C2×Q8×D61—44no—
62C2×Q8×D61—44no—
63C2×Q8×D61C2318yes—
64C22×D244—21no—
65C22×D244C2311yescharacteristic
66C22×C4×D61—22no—
67C22×C4×D61—21no—
68C22×C4×D61D411yescharacteristic
69C22×C4×D61D411yescharacteristic
70C22×C4×D61C2311yescharacteristic
71C2×Dic244—44no—
72C2×Dic244C2318yes—
73C2×#11758202—44no—
74C2×#11758202C2318yes—
75C2×#11758190—44no—
76C2×#11758190C2318yes—
77C2×#11758201—44no—
78C2×#11758201C2318yes—
79C22×#92418C2312yes—
80#14519777—22no—
81#14519777C2314yes—
82#14519776—28no—
83#14519776—28no—
84#14519775—24no—
85#14519775C2318yes—
86#14519772—28no—
87#14519765—22no—
88#14519765C2314yes—
89#14519762—28no—
90#14519757—22no—
91#14519757C2314yes—
92#14519752—22no—
93#14519752C2314yes—
94#14519742—22no—
95#14519742C2314yes—
96#14519739—28no—
97#14519739—22no—
98#14519739C2314yes—
99#14519735—28no—
100C2×C4⋊Dic61—21no—
101C2×C4⋊Dic61—21no—
102C2×C4⋊Dic61—21no—
103C2×#11758196—22no—
104C2×#11758196—22no—
105C2×#11758196—21no—
106C4⋊C4×D61—28no—
107C4⋊C4×D61—28no—
108C2×#11758198—21no—
109C2×#11758198—21no—
110C2×#11758198—21no—
111C2×#11758198—21no—
112C2×#11758198—21no—
113C2×C4×Dic61—21no—
114C2×C4×Dic61D411yescharacteristic
115C2×C4×Dic61D411yescharacteristic
116C2×C4×Dic61C2311yescharacteristic
117C42×D61D414yes—
118C42×D61C2314yes—
119#14519706C2318yes—
120#14519700C2318yes—
121#14519700C2318yes—
122#14519689C2318yes—
123#14519688C2314yes—
124C22×Q8×C61C2312yes—
125C22×C8×C61C2312yes—
126C4⋊Q8×C61—22no—
127C4⋊Q8×C61C2314yes—
128#125×C61—22no—
129#125×C61C2314yes—
130C2×C4⋊C4×C61—21no—
131C2×C4⋊C4×C61—21no—
132C2×C4⋊C4×C61—21no—
133C2×C4⋊C4×C61—21no—
134C2×C4⋊C4×C61C2311yescharacteristic
135C2×C4⋊C4×C61C2311yescharacteristic
136C2×C42×C61C2311yescharacteristic
137#103×C61C2318yes—
138#103×C61C2318yes—
139#97×C61C2314yes—
140C23×D61—21no—
141C23×D61C2×D411yescharacteristic
142C2×Q8×C61—22no—
143C2×Q8×C61—24no—
144C2×Q8×C61—24no—
145C2×Q8×C61C2414yes—
146C22×C4×C61—22no—
147C22×C4×C61—21no—
148C22×C4×C61—21no—
149C22×C4×C61C2×D411yescharacteristic
150C22×C4×C61C2×D411yescharacteristic
151C22×C4×C61C2411yescharacteristic
152C22×Dic61—22no—
153C22×Dic61—21no—
154C22×Dic61C2×D411yescharacteristic
155C22×Dic61C2×D411yescharacteristic
156C22×Dic61C2×D411yescharacteristic
157Q8×D61—48no—
158Q8×D61—48no—
159Q8×D61—416no—
160C2×D244—24no—
161C2×D244—24no—
162C2×D244—21no—
163C2×D244—44no—
164C2×D244C2412yes—
165C2×C4×D61—24no—
166C2×C4×D61—24no—
167C2×C4×D61—24no—
168C2×C4×D61—28no—
169C2×C4×D61—24no—
170C2×C4×D61—48no—
171C2×C4×D61—44no—
172C2×C4×D61C2×D414yes—
173C2×C4×D61C2×D414yes—
174C2×C4×D61C2×D412yes—
175C2×C4×D61C2412yes—
176C2×Dic122—24no—
177C2×Dic122—24no—
178C2×Dic122—24no—
179C2×Dic122—22no—
180C2×Dic122—21no—
181C2×Dic122—28no—
182C2×Dic122—48no—
183C2×Dic122C2414yes—
184C2×Dic122C2412yes—
185C2×C8×C61—24no—
186C2×C8×C61C2414yes—
187C4⋊C4×C61—24no—
188C4⋊C4×C61—24no—
189C4⋊C4×C61—24no—
190C4⋊C4×C61—24no—
191C4⋊C4×C61—21no—
192C4⋊C4×C61—21no—
193C4⋊C4×C61C2412yes—
194C4⋊C4×C61C2412yes—
195C42×C61C2×D412yes—
196C42×C61C2412yes—
197#11758202—48no—
198#11758201—48no—
199#11758198—24no—
200#11758198—24no—
201#11758198—24no—
202#11758198—24no—
203#11758198—24no—
204C4⋊Dic61—24no—
205C4⋊Dic61—24no—
206C4⋊Dic61—24no—
207#11758196—28no—
208#11758196—28no—
209#11758196—24no—
210C4×Dic61—24no—
211C4×Dic61C2×D412yes—
212C4×Dic61C2×D414yes—
213C4×Dic61C2×D414yes—
214C4×Dic61C2412yes—
215C2×#92418—24no—
216C2×#92418C2414yes—
217Dic244—48no—
218#11758190—48no—
219C23×C61C22×D411yescharacteristic
220C22×D61—22no—
221C22×D61—22no—
222C22×D61—22no—
223C22×D61—42no—
224C22×D61—42no—
225C22×D61—42no—
226C22×D61#13714yes—
227C22×D61C22×D412yes—
228Q8×C61—24no—
229Q8×C61—24no—
230Q8×C61—44no—
231C2×C4×C61—22no—
232C2×C4×C61—22no—
233C2×C4×C61—22no—
234C2×C4×C61—24no—
235C2×C4×C61—22no—
236C2×C4×C61—44no—
237C2×C4×C61—42no—
238C2×C4×C61—42no—
239C2×C4×C61C22×D412yes—
240C2×C4×C61C22×D412yes—
241C2×C4×C61C22×D411yescharacteristic
242C2×C4×C61H(5,𝔽2)14yes—
243C2×C4×C61C2511yescharacteristic
244C2×Dic61—22no—
245C2×Dic61—22no—
246C2×Dic61—22no—
247C2×Dic61—24no—
248C2×Dic61—44no—
249C2×Dic61—42no—
250C2×Dic61#13714yes—
251C2×Dic61C22×D412yes—
252C2×Dic61C22×D412yes—
253C2×Dic61C22×D412yes—
254D244—24no—
255D244—48no—
256D244—42no—
257C4×D61—28no—
258C4×D61—24no—
259C4×D61—24no—
260C4×D61—28no—
261C4×D61—416no—
262C4×D61—48no—
263Dic122—24no—
264Dic122—24no—
265Dic122—24no—
266Dic122—416no—
267Dic122—42no—
268Dic122—44no—
269C8×C61—24no—
270#92418—24no—
271C2×#3218—611nomaximal, Sylow
272C22×C61#53512yes—
273C22×C61C2×#13712yes—
274C22×C61C2×#13712yes—
275C22×C61C23×D411yescharacteristic
276C2×D61—22no—
277C2×D61—28no—
278C2×D61—22no—
279C2×D61—42no—
280C2×D61—42no—
281C2×D61—42no—
282C2×D61—84no—
283C2×D61C2×#13714yes—
284C4×C61—22no—
285C4×C61—22no—
286C4×C61—44no—
287C4×C61—42no—
288C4×C61—42no—
289C4×C61#53512yes—
290C4×C61C2×H(5,𝔽2)12yes—
291Dic61—22no—
292Dic61—22no—
293Dic61—44no—
294Dic61—42no—
295Dic61C2×#13714yes—
296C22×C4⋊Q8—611no—
297C2×#529—611no—
298#3218—6116no—
299C2×#497—611no—
300C2×#497—611no—
301C2×#491—611no—
302C2×#491D6111yescharacteristic, complemented
303C2×#462—612no—
304C2×#461—612no—
305C2×#451—612no—
306C2×#448—612no—
307C2×#432—611no—
308C2×C61#321814yescomplemented
309C2×C61C2×#53511yescharacteristic
310C2×C61C22×#13711yescharacteristic
311C2×C61C22×#13711yescharacteristic
312D61—24no—
313D61—82no—
314C23×Q8—612no—
315C22×Q16—612no—
316C22×Q16—612no—
317C22×SD16—612no—
318C22×SD16—612no—
319C2×C4⋊Q8—612no—
320C2×C4⋊Q8—618no—
321C2×C4⋊Q8—611no—
322C2×C4⋊Q8—1221no—
323C2×C4⋊Q8—1221no—
324C2×C4⋊Q8—1224no—
325C2×C4⋊Q8C2×D6111yescharacteristic
326#529—618no—
327#529—1224no—
328C2×#126—1221no—
329C2×#125C2×D6111yescharacteristic
330C2×#124—611no—
331C2×#123—1221no—
332C2×C22⋊Q8—611no—
333C2×#121—611no—
334C2×C4×Q8—611no—
335C2×C4×D4—611no—
336C2×C4×D4—1221no—
337C2×#117—1221no—
338C22×C4⋊C4—1221no—
339C22×C4⋊C4—1221no—
340C22×C42—611no—
341#497—618no—
342#497—618no—
343#491—618no—
344#491C2×D6118yescomplemented
345#462—6116no—
346#461—6116no—
347#451—6116no—
348#448—6116no—
349#432—618no—
350C2×C4⋊C8—612no—
351C2×#103—612no—
352C2×#103—612no—
353C2×#103C2×D6112yes—
354C2×#103C2×D6112yes—
355C2×C22⋊C8—612no—
356C2×#97—611no—
357C2×#97C2×D6111yescharacteristic
358C61C2×#321811yescharacteristic, complemented, Sylow
359C22×Q8—618no—
360C22×Q8—611no—
361C22×Q8—612no—
362C22×Q8—1222no—
363C22×Q8—1224no—
364C22×Q8—2444no—
365C22×Q8—2444no—
366C22×Q8C22×D6112yes—
367C22×D4—611no—
368C22×D4—1221no—
369C23×C4—611no—
370C23×C4—611no—
371C23×C4—611no—
372C23×C4—1221no—
373C23×C4—1222no—
374C2×Q16—618no—
375C2×Q16—618no—
376C2×Q16—2444no—
377C2×Q16—2444no—
378C2×SD16—618no—
379C2×SD16—618no—
380C2×SD16—2444no—
381C2×SD16—2444no—
382C22×C8—612no—
383C22×C8C22×D6112yes—
384C4⋊Q8—22no—
385C4⋊Q8—618no—
386C4⋊Q8—614no—
387C4⋊Q8—1228no—
388C4⋊Q8—1228no—
389C4⋊Q8—1224no—
390C4⋊Q8—1222no—
391C4⋊Q8C22×D6114yes—
392#126—1228no—
393#125—22no—
394#125C22×D6114yes—
395#124—614no—
396#124—1222no—
397#123—1228no—
398C22⋊Q8—614no—
399C22⋊Q8—1222no—
400#121—614no—
401#121—1222no—
402C4×Q8—614no—
403C4×Q8—1222no—
404C4×D4—614no—
405C4×D4—1222no—
406C4×D4—1228no—
407#117—1228no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—1228no—
413C2×C4⋊C4—1228no—
414C2×C4⋊C4—1222no—
415C2×C4⋊C4—1222no—
416C2×C4⋊C4—1221no—
417C2×C4⋊C4—1221no—
418C2×C4⋊C4—1221no—
419C2×C4⋊C4—1221no—
420C2×C4⋊C4C22×D6111yescharacteristic
421C2×C4⋊C4C22×D6111yescharacteristic
422C2×C22⋊C4—1221no—
423C2×C22⋊C4—1221no—
424C2×C22⋊C4—1221no—
425C2×C22⋊C4—1221no—
426C2×C22⋊C4—1221no—
427C2×C42—611no—
428C2×C42—611no—
429C2×C42—611no—
430C2×C42—614no—
431C2×C42—614no—
432C2×C42—1221no—
433C2×C42C22×D6111yescharacteristic
434C4⋊C8—618no—
435#103—618no—
436#103—618no—
437#103C22×D6118yes—
438#103C22×D6118yes—
439C22⋊C8—618no—
440#97—614no—
441#97C22×D6114yes—
442C24—611no—
443C24—1221no—
444C2×Q8—22no—
445C2×Q8—24no—
446C2×Q8—24no—
447C2×Q8—614no—
448C2×Q8—612no—
449C2×Q8—1228no—
450C2×Q8—1221no—
451C2×Q8—1222no—
452C2×Q8—1224no—
453C2×Q8—1224no—
454C2×Q8—1224no—
455C2×Q8—2448no—
456C2×Q8—2448no—
457C2×Q8—2448no—
458C2×Q8—24416no—
459C2×Q8C23×D6114yes—
460C2×D4—612no—
461C2×D4—1224no—
462C2×D4—1221no—
463C2×D4—1224no—
464C2×D4—2444no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—22no—
468C22×C4—611no—
469C22×C4—611no—
470C22×C4—611no—
471C22×C4—614no—
472C22×C4—614no—
473C22×C4—612no—
474C22×C4—612no—
475C22×C4—1224no—
476C22×C4—1224no—
477C22×C4—1224no—
478C22×C4—1228no—
479C22×C4—1224no—
480C22×C4—1221no—
481C22×C4—1222no—
482C22×C4—2444no—
483C22×C4—2448no—
484C22×C4D4×D6111yescharacteristic
485C22×C4D4×D6111yescharacteristic
486C22×C4C23×D6111yescharacteristic
487Q16—2448no—
488Q16—2448no—
489SD16—2448no—
490SD16—2448no—
491C2×C8—24no—
492C2×C8—614no—
493C2×C8—1224no—
494C2×C8C23×D6114yes—
495C4⋊C4—24no—
496C4⋊C4—24no—
497C4⋊C4—24no—
498C4⋊C4—24no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—1228no—
502C4⋊C4—1228no—
503C4⋊C4—1224no—
504C4⋊C4—1224no—
505C4⋊C4—1224no—
506C4⋊C4—1224no—
507C4⋊C4C23×D6112yes—
508C4⋊C4C23×D6112yes—
509C22⋊C4—1224no—
510C22⋊C4—1224no—
511C22⋊C4—1224no—
512C22⋊C4—1224no—
513C22⋊C4—1224no—
514C42—614no—
515C42—612no—
516C42—614no—
517C42—612no—
518C42—1224no—
519C42D4×D6112yes—
520C42C23×D6112yes—
521C23—614no—
522C23—612no—
523C23—1222no—
524C23—1222no—
525C23—1222no—
526C23—2442no—
527C23—2442no—
528C23—2442no—
529C23C2×D4×D6111yescharacteristic
530Q8—24no—
531Q8—24no—
532Q8—44no—
533Q8—1224no—
534Q8—1224no—
535Q8—1224no—
536Q8—24416no—
537Q8—2442no—
538Q8—2444no—
539D4—1224no—
540D4—2448no—
541D4—2442no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—24no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—44no—
550C2×C4—614no—
551C2×C4—612no—
552C2×C4—612no—
553C2×C4—612no—
554C2×C4—1228no—
555C2×C4—1228no—
556C2×C4—1222no—
557C2×C4—1222no—
558C2×C4—1224no—
559C2×C4—1224no—
560C2×C4—1222no—
561C2×C4—1224no—
562C2×C4—2448no—
563C2×C4—24416no—
564C2×C4—2444no—
565C2×C4—2442no—
566C2×C4C2×D4×D6112yes—
567C2×C4C2×D4×D6112yes—
568C2×C4C2×D4×D6111yescharacteristic
569C2×C4#1451982314yes—
570C2×C4C24×D6111yescharacteristic
571C8—24no—
572C8—1224no—
573C22—614no—
574C22—1222no—
575C22—1222no—
576C22—1228no—
577C22—4884no—
578C22—2442no—
579C22—2442no—
580C22—2442no—
581C22#1684033012yes—
582C22#137×D6112yes—
583C22#137×D6112yes—
584C22C22×D4×D6111yescharacteristic
585C4—22no—
586C4—22no—
587C4—42no—
588C4—42no—
589C4—44no—
590C4—614no—
591C4—1222no—
592C4—1222no—
593C4—2444no—
594C4—2442no—
595C4#1684033012yes—
596C4C2×#1451982312yes—
597C2—1224no—
598C2—4882no—
599C2#2145684714yesdirect product factor
600C2C2×#1684033011yescharacteristic
601C2C2×#137×D6111yescharacteristic
602C2C2×#137×D6111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#491C2
socleC23×C61C22×D4
prime radicalC2×#14519752C22
hypercenterC2×#491D61
hypocenterC61C2×#3218
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#491

Complements

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

NH ≅ G/Ntype
1. C2×C4⋊Q8×D61C2semidirect
3. #21456847C2direct (N × H)
4. C2×#16840156C2semidirect
5. C2×#16840154C2semidirect
6. C2×#16840132C2semidirect
7. C2×#16839971C2semidirect
8. C2×#16839966C2semidirect
9. C2×#16839919C2semidirect
11. C2×#16839817C2semidirect
12. C2×C61×#491C2semidirect
23. C4⋊Q8×D61C22semidirect
38. #16840156C22semidirect
39. #16840154C22semidirect
40. #16840132C22semidirect
41. #16839971C22semidirect
42. #16839966C22semidirect
43. #16839919C22semidirect
45. #16839817C22semidirect
53. C61×#491C22semidirect
302. C2×#491D61semidirect
308. C2×C61#3218semidirect
344. #491C2×D61semidirect
358. C61C2×#3218semidirect
599. C2#21456847direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4⋊Q8×D612
C2×#168402972
#214568472
C2×#168401562
C2×#168401542
C2×#168401322
C2×#168399712
C2×#168399662
C2×#168399192
C2×#168399022
C2×#168398172
C2×C61×#4912
C2×#321861