Finite Group Databasebeta

← C2×#21457205 #30552884

Subgroups — C2×#21457205 #30552884

Order 15616.

2146 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840316C211yesmaximal, characteristic, complemented
2C2×#16840313C211yesmaximal, characteristic
3#21457205C2116yesmaximal, direct product factor
4C2×#16840054C211yesmaximal, characteristic, complemented
5C2×#16840041C212yesmaximal, complemented
6C2×#16840011C212yesmaximal, complemented
7C2×#16840009C212yesmaximal, complemented
8C2×#16839963C211yesmaximal, characteristic, complemented
9C2×#16839962C211yesmaximal, characteristic, complemented
10C2×#16839966C212yesmaximal, complemented
11C2×#16839784C211yesmaximal, characteristic, complemented
12C2×C61×#477C211yesmaximal, characteristic, complemented
13C22×#11758226—21no—
14C22×#11758190C2212yes—
15C22×#11758201C2212yes—
16C22×#11758189C2212yes—
17#16840316—24no—
18#16840316C2218yescomplemented
19#16840313—24no—
20#16840313C2218yes—
21C2×#14519776C2211yescharacteristic
22C2×#14519775C2211yescharacteristic
23C2×#14519774C2211yescharacteristic
24C2×#14519767—21no—
25C2×#14519766—21no—
26C2×#14519757C2211yescharacteristic
27C2×#14519755—21no—
28C2×#14519753C2211yescharacteristic
29C2×#14519752—21no—
30C2×#14519752C2212yes—
31C2×C4×Dic122—21no—
32C2×C4×Dic122C2211yescharacteristic
33C2×#14519739—21no—
34C2×#14519739C2212yes—
35C2×#14519734—21no—
36C2×C42×D61C2211yescharacteristic
37#16840054C2218yescomplemented
38#16840041C22116yescomplemented
39#16840011C22116yescomplemented
40#16840009C22116yescomplemented
41#16839966C22116yescomplemented
42#16839963C2218yescomplemented
43#16839962C2218yescomplemented
44C2×#14519710C2212yes—
45#16839784C2218yescomplemented
46C2×C4⋊#92418C2211yescharacteristic
47C2×#14519706C2212yes—
48C2×#14519700C2212yes—
49C2×#14519699C2212yes—
50C2×#14519697C2212yes—
51C2×C4⋊Q8×C61C2211yescharacteristic
52C2×C4×Q8×C61C2211yescharacteristic
53C61×#477C2218yescomplemented
54C2×#107×C61C2212yes—
55C2×C4⋊C8×C61C2211yescharacteristic
56C2×#103×C61C2212yes—
57C2×#11758226—28no—
58C2×#11758226—48no—
59C22×Dic122—21no—
60C22×Dic122C2311yescharacteristic
61C22×D244—22no—
62C22×D244—21no—
63C22×D244—21no—
64C22×D244C2312yes—
65C22×C4×D61—22no—
66C22×C4×D61D411yescharacteristic
67C22×C4×D61D411yescharacteristic
68C22×C4×D61C2311yescharacteristic
69C2×#11758190—44no—
70C2×#11758190C2318yes—
71C2×#11758201—44no—
72C2×#11758201C2318yes—
73C2×#11758189—44no—
74C2×#11758189C2318yes—
75C22×#92418C2312yes—
76#14519776—22no—
77#14519776C2314yes—
78#14519775—22no—
79#14519775C2314yes—
80#14519774—22no—
81#14519774C2314yes—
82#14519767—28no—
83#14519766—28no—
84#14519757—22no—
85#14519757C2314yes—
86#14519755—28no—
87#14519753—22no—
88#14519753C2314yes—
89#14519752—28no—
90#14519752—24no—
91#14519752C2318yes—
92C4×Dic122—22no—
93C4×Dic122—28no—
94C4×Dic122C2314yes—
95#14519739—28no—
96#14519739—24no—
97#14519739C2318yes—
98#14519734—28no—
99C2×C4⋊Dic61—21no—
100C2×C4⋊Dic61C2311yescharacteristic
101C2×#11758196—21no—
102C2×#11758196—21no—
103C2×#11758196—21no—
104C2×#11758196—21no—
105C2×#11758196—21no—
106C2×#11758198—21no—
107C2×#11758198—21no—
108C2×#11758198—22no—
109C2×#11758198—22no—
110C2×C4×Dic61—21no—
111C2×C4×Dic61D411yescharacteristic
112C2×C4×Dic61D411yescharacteristic
113C2×C4×Dic61C2311yescharacteristic
114C42×D61D414yes—
115C42×D61C2314yes—
116#14519710C2318yes—
117C4⋊#92418C2314yes—
118#14519706C2318yes—
119#14519700C2318yes—
120#14519699C2318yes—
121#14519697C2318yes—
122C22×Q8×C61—21no—
123C22×Q8×C61C2311yescharacteristic
124C22×C8×C61C2312yes—
125C4⋊Q8×C61—22no—
126C4⋊Q8×C61C2314yes—
127C4×Q8×C61—22no—
128C4×Q8×C61C2314yes—
129C2×C4⋊C4×C61—21no—
130C2×C4⋊C4×C61—21no—
131C2×C4⋊C4×C61C2312yes—
132C2×C4⋊C4×C61C2311yescharacteristic
133C2×C42×C61—21no—
134C2×C42×C61C2311yescharacteristic
135#107×C61C2318yes—
136C4⋊C8×C61C2314yes—
137#103×C61C2318yes—
138C23×D61—22no—
139C23×D61C2×D411yescharacteristic
140C2×Q8×C61—24no—
141C2×Q8×C61—21no—
142C2×Q8×C61—22no—
143C2×Q8×C61—22no—
144C2×Q8×C61—44no—
145C2×Q8×C61C2412yes—
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—21no—
153C22×Dic61—21no—
154C22×Dic61C2×D411yescharacteristic
155C22×Dic61C2×D411yescharacteristic
156C22×Dic61C2×D411yescharacteristic
157#11758226—432no—
158C2×D244—24no—
159C2×D244—24no—
160C2×D244—28no—
161C2×D244—24no—
162C2×D244—24no—
163C2×D244—22no—
164C2×D244—44no—
165C2×D244—48no—
166C2×D244—44no—
167C2×D244C2414yes—
168C2×C4×D61—24no—
169C2×C4×D61—22no—
170C2×C4×D61—22no—
171C2×C4×D61—24no—
172C2×C4×D61—28no—
173C2×C4×D61—48no—
174C2×C4×D61C2×D414yes—
175C2×C4×D61C2×D414yes—
176C2×C4×D61C2×D412yes—
177C2×C4×D61C2412yes—
178C2×Dic122—22no—
179C2×Dic122—22no—
180C2×Dic122—21no—
181C2×Dic122—24no—
182C2×Dic122—44no—
183C2×Dic122C2412yes—
184C2×C8×C61—24no—
185C2×C8×C61C2414yes—
186C4⋊C4×C61—24no—
187C4⋊C4×C61—24no—
188C4⋊C4×C61—21no—
189C4⋊C4×C61—22no—
190C4⋊C4×C61C2414yes—
191C4⋊C4×C61C2412yes—
192C42×C61—24no—
193C42×C61C2×D412yes—
194C42×C61C2412yes—
195#11758201—48no—
196#11758198—24no—
197#11758198—24no—
198#11758198—28no—
199#11758198—28no—
200C4⋊Dic61—21no—
201C4⋊Dic61—24no—
202C4⋊Dic61C2412yes—
203#11758196—24no—
204#11758196—24no—
205#11758196—24no—
206#11758196—24no—
207#11758196—24no—
208C4×Dic61—24no—
209C4×Dic61C2×D412yes—
210C4×Dic61C2×D414yes—
211C4×Dic61C2×D414yes—
212C4×Dic61C2412yes—
213C2×#92418—24no—
214C2×#92418C2414yes—
215#11758190—48no—
216#11758189—48no—
217C23×C61C22×D411yescharacteristic
218C22×D61—22no—
219C22×D61—22no—
220C22×D61—22no—
221C22×D61—24no—
222C22×D61—44no—
223C22×D61—44no—
224C22×D61—44no—
225C22×D61C22×D412yes—
226Q8×C61—22no—
227Q8×C61—22no—
228Q8×C61—48no—
229Q8×C61—42no—
230C2×C4×C61—22no—
231C2×C4×C61—22no—
232C2×C4×C61—22no—
233C2×C4×C61—24no—
234C2×C4×C61—42no—
235C2×C4×C61—42no—
236C2×C4×C61—44no—
237C2×C4×C61#13714yes—
238C2×C4×C61C22×D412yes—
239C2×C4×C61C22×D411yescharacteristic
240C2×C4×C61C22×D412yes—
241C2×C4×C61H(5,𝔽2)12yes—
242C2×C4×C612−1+412yes—
243C2×C4×C61C2511yescharacteristic
244C2×Dic61—22no—
245C2×Dic61—22no—
246C2×Dic61—22no—
247C2×Dic61—22no—
248C2×Dic61—42no—
249C2×Dic61—42no—
250C2×Dic61AGL(1,ℤ/8)14yes—
251C2×Dic61C22×D412yes—
252C2×Dic61C22×D412yes—
253C2×Dic61C22×D412yes—
254D244—24no—
255D244—24no—
256D244—48no—
257D244—416no—
258D244—44no—
259D244—48no—
260C4×D61—24no—
261C4×D61—28no—
262C4×D61—22no—
263C4×D61—22no—
264C4×D61—28no—
265C4×D61—416no—
266Dic122—22no—
267Dic122—22no—
268Dic122—42no—
269Dic122—48no—
270C8×C61—24no—
271#92418—24no—
272C2×#3254—611nomaximal, Sylow
273C22×C61#53712yes—
274C22×C61C2×AGL(1,ℤ/8)12yes—
275C22×C61C2×#13712yes—
276C22×C61C23×D411yescharacteristic
277C2×D61—22no—
278C2×D61—22no—
279C2×D61—22no—
280C2×D61—44no—
281C2×D61—44no—
282C2×D61—44no—
283C2×D61—44no—
284C2×D61—88no—
285C4×C61—22no—
286C4×C61—42no—
287C4×C61—42no—
288C4×C61—44no—
289C4×C61#53712yes—
290C4×C61C2×#13714yes—
291C4×C61C2×H(5,𝔽2)11yescharacteristic
292C4×C61C2×2−1+411yescharacteristic
293Dic61—22no—
294Dic61—22no—
295Dic61—42no—
296Dic61—42no—
297Dic61C2×AGL(1,ℤ/8)14yes—
298C2×#533—611no—
299C2×#532—611no—
300#3254—6116no—
301C2×#477—611no—
302C2×#477D6111yescharacteristic, complemented
303C2×#474—612no—
304C2×#468—612no—
305C2×#468—612no—
306C2×#460—611no—
307C2×#460—611no—
308C2×#461—612no—
309C2×#423—611no—
310C2×C61#325414yescomplemented
311C2×C61C2×#53711yescharacteristic
312C2×C61C22×AGL(1,ℤ/8)11yescharacteristic
313C2×C61C22×#13711yescharacteristic
314D61—42no—
315D61—84no—
316C22×#41—1221no—
317C22×SD16—612no—
318C22×SD16—612no—
319C22×M16—612no—
320#533—618no—
321#533—1224no—
322#532—618no—
323#532—1224no—
324C2×C4⋊Q8—611no—
325C2×C4⋊Q8—611no—
326C2×C4⋊Q8C2×D6111yescharacteristic
327C2×#127—611no—
328C2×#125—1221no—
329C2×#124—1221no—
330C2×C22⋊Q8—611no—
331C2×C22⋊Q8—611no—
332C2×C22⋊Q8—1221no—
333C2×#121—612no—
334C2×#121—1221no—
335C2×C4×Q8—611no—
336C2×C4×Q8—1221no—
337C2×C4×Q8C2×D6111yescharacteristic
338C2×C4×D4—612no—
339C2×C4×D4—1221no—
340C2×#117—1221no—
341C22×C42—611no—
342#477—618no—
343#477C2×D6118yescomplemented
344#474—6116no—
345#468—6116no—
346#468—6116no—
347#461—6116no—
348#460—618no—
349#460—618no—
350C2×#107—612no—
351C2×#107C2×D6112yes—
352#423—618no—
353C2×C4⋊C8—612no—
354C2×C4⋊C8—611no—
355C2×C4⋊C8C2×D6111yescharacteristic
356C2×#103—612no—
357C2×#103C2×D6112yes—
358C2×#102—612no—
359C2×#102—612no—
360C61C2×#325411yescharacteristic, complemented, Sylow
361C2×#41—1228no—
362C2×#41—2448no—
363C22×Q8—21no—
364C22×Q8—611no—
365C22×Q8—1221no—
366C22×Q8C22×D6111yescharacteristic
367C22×D4—612no—
368C22×D4—1222no—
369C22×D4—1221no—
370C22×D4—1221no—
371C23×C4—611no—
372C23×C4—611no—
373C23×C4—611no—
374C23×C4—1222no—
375C2×SD16—618no—
376C2×SD16—618no—
377C2×SD16—2444no—
378C2×SD16—2444no—
379C2×M16—618no—
380C2×M16—2444no—
381C22×C8—612no—
382C22×C8C22×D6112yes—
383C4⋊Q8—22no—
384C4⋊Q8—614no—
385C4⋊Q8—614no—
386C4⋊Q8—1222no—
387C4⋊Q8—1222no—
388C4⋊Q8C22×D6114yes—
389#127—614no—
390#127—1222no—
391#125—1228no—
392#124—1228no—
393C22⋊Q8—614no—
394C22⋊Q8—614no—
395C22⋊Q8—1222no—
396C22⋊Q8—1228no—
397C22⋊Q8—1222no—
398#121—618no—
399#121—1224no—
400#121—1228no—
401C4×Q8—22no—
402C4×Q8—614no—
403C4×Q8—1228no—
404C4×Q8—1222no—
405C4×Q8C22×D6114yes—
406C4×D4—618no—
407C4×D4—1224no—
408C4×D4—1228no—
409#117—1228no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—611no—
413C2×C4⋊C4—1221no—
414C2×C4⋊C4—1221no—
415C2×C4⋊C4—1221no—
416C2×C4⋊C4—1221no—
417C2×C4⋊C4—1221no—
418C2×C4⋊C4—1221no—
419C2×C4⋊C4C22×D6112yes—
420C2×C4⋊C4C22×D6111yescharacteristic
421C2×C22⋊C4—1222no—
422C2×C22⋊C4—1222no—
423C2×C22⋊C4—1221no—
424C2×C22⋊C4—1221no—
425C2×C42—21no—
426C2×C42—611no—
427C2×C42—611no—
428C2×C42—611no—
429C2×C42—614no—
430C2×C42—614no—
431C2×C42—1221no—
432C2×C42C22×D6111yescharacteristic
433#107—618no—
434#107C22×D6118yes—
435C4⋊C8—618no—
436C4⋊C8—614no—
437C4⋊C8C22×D6114yes—
438#103—618no—
439#103C22×D6118yes—
440#102—618no—
441#102—618no—
442C24—611no—
443C24—1222no—
444#41—24432no—
445C2×Q8—21no—
446C2×Q8—24no—
447C2×Q8—22no—
448C2×Q8—22no—
449C2×Q8—44no—
450C2×Q8—612no—
451C2×Q8—1224no—
452C2×Q8—1221no—
453C2×Q8—1222no—
454C2×Q8—1222no—
455C2×Q8—2444no—
456C2×Q8C23×D6112yes—
457C2×D4—614no—
458C2×D4—1228no—
459C2×D4—1224no—
460C2×D4—1222no—
461C2×D4—1224no—
462C2×D4—1224no—
463C2×D4—1224no—
464C2×D4—2444no—
465C2×D4—2448no—
466C2×D4—2444no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—22no—
470C22×C4—611no—
471C22×C4—611no—
472C22×C4—611no—
473C22×C4—614no—
474C22×C4—612no—
475C22×C4—614no—
476C22×C4—612no—
477C22×C4—1224no—
478C22×C4—1228no—
479C22×C4—1224no—
480C22×C4—1222no—
481C22×C4—1222no—
482C22×C4—1221no—
483C22×C4—1221no—
484C22×C4—2448no—
485C22×C4D4×D6111yescharacteristic
486C22×C4D4×D6111yescharacteristic
487C22×C4C23×D6111yescharacteristic
488SD16—2448no—
489SD16—2448no—
490M16—2448no—
491C2×C8—24no—
492C2×C8—614no—
493C2×C8—1224no—
494C2×C8C23×D6114yes—
495C4⋊C4—24no—
496C4⋊C4—24no—
497C4⋊C4—22no—
498C4⋊C4—21no—
499C4⋊C4—612no—
500C4⋊C4—1224no—
501C4⋊C4—1224no—
502C4⋊C4—1224no—
503C4⋊C4—1224no—
504C4⋊C4—1224no—
505C4⋊C4—1221no—
506C4⋊C4—1224no—
507C4⋊C4C23×D6112yes—
508C4⋊C4C23×D6114yes—
509C22⋊C4—1228no—
510C22⋊C4—1228no—
511C22⋊C4—1224no—
512C22⋊C4—1224no—
513C42—24no—
514C42—614no—
515C42—612no—
516C42—614no—
517C42—612no—
518C42—1224no—
519C42D4×D6112yes—
520C42C23×D6112yes—
521C23—612no—
522C23—1222no—
523C23—1222no—
524C23—1222no—
525C23—1224no—
526C23—2444no—
527C23—2444no—
528C23—2444no—
529C23C2×D4×D6111yescharacteristic
530Q8—22no—
531Q8—22no—
532Q8—48no—
533Q8—42no—
534Q8—1222no—
535Q8—1222no—
536Q8—2448no—
537Q8—2442no—
538D4—1224no—
539D4—1224no—
540D4—2448no—
541D4—24416no—
542D4—2448no—
543D4—2444no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—24no—
548C2×C4—44no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—614no—
552C2×C4—612no—
553C2×C4—612no—
554C2×C4—612no—
555C2×C4—1228no—
556C2×C4—1222no—
557C2×C4—1222no—
558C2×C4—1228no—
559C2×C4—1222no—
560C2×C4—1222no—
561C2×C4—1224no—
562C2×C4—1222no—
563C2×C4—1222no—
564C2×C4—24416no—
565C2×C4—2442no—
566C2×C4—2442no—
567C2×C4#1451980914yes—
568C2×C4C2×D4×D6112yes—
569C2×C4C2×D4×D6112yes—
570C2×C4C2×D4×D6111yescharacteristic
571C2×C4#1451982312yes—
572C2×C4#1451982512yes—
573C2×C4C24×D6111yescharacteristic
574C8—24no—
575C8—1224no—
576C22—1222no—
577C22—1222no—
578C22—1222no—
579C22—4888no—
580C22—2444no—
581C22—2444no—
582C22—2444no—
583C22—2444no—
584C22#1684034212yes—
585C22AGL(1,ℤ/8)×D6112yes—
586C22C2×#1451980912yes—
587C22C22×D4×D6111yescharacteristic
588C4—22no—
589C4—44no—
590C4—42no—
591C4—42no—
592C4—614no—
593C4—1222no—
594C4—1222no—
595C4—2442no—
596C4—2442no—
597C4#1684034212yes—
598C4C2×#1451980914yes—
599C4C2×#1451982311yescharacteristic
600C4C2×#1451982511yescharacteristic
601C2—4884no—
602C2—2442no—
603C2#2145720514yesdirect product factor
604C2C2×#1684034211yescharacteristic
605C2C2×AGL(1,ℤ/8)×D6111yescharacteristic
606C2C22×#1451980911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#477C2
socleC23×C61C22×D4
prime radicalC2×#16840313C2
hypercenterC2×#477D61
hypocenterC61C2×#3254
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#477

Complements

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

NH ≅ G/Ntype
1. C2×#16840316C2semidirect
3. #21457205C2direct (N × H)
4. C2×#16840054C2semidirect
5. C2×#16840041C2semidirect
6. C2×#16840011C2semidirect
7. C2×#16840009C2semidirect
8. C2×#16839963C2semidirect
9. C2×#16839962C2semidirect
10. C2×#16839966C2semidirect
11. C2×#16839784C2semidirect
12. C2×C61×#477C2semidirect
18. #16840316C22semidirect
37. #16840054C22semidirect
38. #16840041C22semidirect
39. #16840011C22semidirect
40. #16840009C22semidirect
41. #16839966C22semidirect
42. #16839963C22semidirect
43. #16839962C22semidirect
45. #16839784C22semidirect
53. C61×#477C22semidirect
302. C2×#477D61semidirect
310. C2×C61#3254semidirect
343. #477C2×D61semidirect
360. C61C2×#3254semidirect
603. C2#21457205direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403162
C2×#168403132
#214572052
C2×#168400542
C2×#168400412
C2×#168400112
C2×#168400092
C2×#168399632
C2×#168399622
C2×#168399662
C2×#168397842
C2×C61×#4772
C2×#325461