Finite Group Databasebeta

← C2×#13125783 #16734109

Subgroups — C2×#13125783 #16734109

Order 3328.

2134 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×#11719283C211yesmaximal, characteristic
2C2×D13×C4⋊Q8C211yesmaximal, characteristic
3#13125783C2116yesmaximal, direct product factor
4C2×#11718842C212yesmaximal, complemented
5C2×#11718453C212yesmaximal, complemented
6C2×#11718510C211yesmaximal, characteristic, complemented
7C2×#11718692C211yesmaximal, characteristic, complemented
8C2×#11718751C211yesmaximal, characteristic, complemented
9C2×#11718469C212yesmaximal
10C2×#11718847C212yesmaximal
11C2×#11718494C211yesmaximal, characteristic
12C2×C13×#462C211yesmaximal, characteristic, complemented
13C22×Q8×D13C2212yes—
14C22×C13×Q16C2212yes—
15C2×C13×C4⋊Q8C2211yescharacteristic
16C2×C4×Q8×C13C2211yescharacteristic
17C2×#88200C2211yescharacteristic
18C2×#88198C2212yes—
19C2×#88198C2211yescharacteristic
20C22×#6107C2212yes—
21C22×#6107C2212yes—
22C22×Dic52C2212yes—
23D13×C4⋊Q8—24no—
24D13×C4⋊Q8C2218yes—
25#11719283—24no—
26#11719283C2218yes—
27C2×#88151C2211yescharacteristic
28C2×#88150—21no—
29C2×C4⋊C4×D13—21no—
30C2×C4⋊C4×D13—21no—
31C2×#88143—21no—
32C2×#88142—21no—
33C2×#88142—21no—
34C2×#88142C2211yescharacteristic
35C2×#88126—21no—
36C2×C42×D13C2211yescharacteristic
37C2×#88123C2211yescharacteristic
38C2×C4×Dic26—21no—
39C2×C4×Dic26C2211yescharacteristic
40C13×#462C2218yescomplemented
41C2×C13×C4⋊C8C2211yescharacteristic
42C2×C13×#103C2212yes—
43C2×#88075C2212yes—
44#11718847C22116yes—
45#11718842C22116yescomplemented
46C2×#88060C2212yes—
47C2×#88056C2212yes—
48C2×C8×Dic13C2212yes—
49#11718751C2218yescomplemented
50#11718692C2218yescomplemented
51C2×#88050C2212yes—
52C2×C4⋊#1055C2211yescharacteristic
53#11718510C2218yescomplemented
54#11718494C2218yes—
55#11718469C22116yes—
56#11718453C22116yescomplemented
57C22×Q8×C13C2312yes—
58C22×Q8×C13C2311yescharacteristic
59C2×Q8×D13—24no—
60C2×Q8×D13—44no—
61C2×Q8×D13—44no—
62C2×Q8×D13C2318yes—
63C22×C4×D13—22no—
64C22×C4×D13D411yescharacteristic
65C22×C4×D13D411yescharacteristic
66C22×C4×D13C2311yescharacteristic
67C22×Dic26—21no—
68C22×Dic26—22no—
69C22×Dic26C2311yescharacteristic
70C22×Dic26C2312yes—
71C2×C13×Q16—44no—
72C2×C13×Q16C2318yes—
73C22×C8×C13C2312yes—
74C13×C4⋊Q8—22no—
75C13×C4⋊Q8C2314yes—
76C4×Q8×C13—22no—
77C4×Q8×C13C2314yes—
78C2×C13×C4⋊C4—21no—
79C2×C13×C4⋊C4—21no—
80C2×C13×C4⋊C4—21no—
81C2×C13×C4⋊C4C2311yescharacteristic
82C2×C42×C13—21no—
83C2×C42×C13C2311yescharacteristic
84#88200—22no—
85#88200C2314yes—
86#88198—24no—
87#88198—22no—
88#88198C2318yes—
89#88198C2314yes—
90C2×#6107—44no—
91C2×#6107—44no—
92C2×#6107C2318yes—
93C2×#6107C2318yes—
94C2×#6103—21no—
95C2×#6103—21no—
96C2×C4⋊Dic13—21no—
97C2×C4⋊Dic13—21no—
98C2×C4⋊Dic13—21no—
99C2×C4⋊Dic13C2311yescharacteristic
100C2×#6101—21no—
101C2×#6101—21no—
102C2×#6101—21no—
103C2×#6101—21no—
104C2×#6101—21no—
105C2×#6101—22no—
106C2×#6101—22no—
107C2×C4×Dic13—21no—
108C2×C4×Dic13D411yescharacteristic
109C2×C4×Dic13D411yescharacteristic
110C2×C4×Dic13C2311yescharacteristic
111C22×#1055C2312yes—
112C2×Dic52—44no—
113C2×Dic52C2318yes—
114#88151—22no—
115#88151C2314yes—
116#88150—28no—
117C4⋊C4×D13—28no—
118C4⋊C4×D13—28no—
119#88143—28no—
120#88142—28no—
121#88142—28no—
122#88142—22no—
123#88142C2314yes—
124#88126—28no—
125C42×D13D414yes—
126C42×D13C2314yes—
127#88123—22no—
128#88123C2314yes—
129C4×Dic26—22no—
130C4×Dic26—28no—
131C4×Dic26C2314yes—
132C13×C4⋊C8C2314yes—
133C13×#103C2318yes—
134#88075C2318yes—
135#88060C2318yes—
136#88056C2318yes—
137C8×Dic13C2318yes—
138#88050C2318yes—
139C4⋊#1055C2314yes—
140C2×#3209—131nomaximal, Sylow
141C23×D13C2×D411yescharacteristic
142C2×Q8×C13—21no—
143C2×Q8×C13—22no—
144C2×Q8×C13—22no—
145C2×Q8×C13—24no—
146C2×Q8×C13—22no—
147C2×Q8×C13—24no—
148C2×Q8×C13C2414yes—
149C2×Q8×C13C2412yes—
150C22×C4×C13—21no—
151C22×C4×C13—22no—
152C22×C4×C13—21no—
153C22×C4×C13C2×D411yescharacteristic
154C22×C4×C13C2×D411yescharacteristic
155C22×C4×C13C2411yescharacteristic
156C22×Dic13—21no—
157C22×Dic13—21no—
158C22×Dic13—22no—
159C22×Dic13C2×D411yescharacteristic
160C22×Dic13C2×D411yescharacteristic
161C22×Dic13C2×D411yescharacteristic
162Q8×D13—48no—
163Q8×D13—48no—
164Q8×D13—416no—
165C2×C4×D13—22no—
166C2×C4×D13—22no—
167C2×C4×D13—24no—
168C2×C4×D13—28no—
169C2×C4×D13—48no—
170C2×C4×D13Q1618yescomplemented
171C2×C4×D13C2×D412yes—
172C2×C4×D13C2×D414yes—
173C2×C4×D13C2×D414yes—
174C2×C4×D13C2412yes—
175C2×Dic26—22no—
176C2×Dic26—24no—
177C2×Dic26—22no—
178C2×Dic26—24no—
179C2×Dic26—21no—
180C2×Dic26—22no—
181C2×Dic26—24no—
182C2×Dic26—28no—
183C2×Dic26—48no—
184C2×Dic26—44no—
185C2×Dic26C2412yes—
186C2×Dic26C2414yes—
187C13×Q16—48no—
188C2×C8×C13—24no—
189C2×C8×C13C2414yes—
190C13×C4⋊C4—24no—
191C13×C4⋊C4—24no—
192C13×C4⋊C4—21no—
193C13×C4⋊C4—24no—
194C13×C4⋊C4C2412yes—
195C42×C13—24no—
196C42×C13C2×D412yes—
197C42×C13C2412yes—
198#6107—48no—
199#6107—48no—
200#6103—24no—
201#6103—24no—
202C4⋊Dic13—21no—
203C4⋊Dic13—24no—
204C4⋊Dic13—24no—
205C4⋊Dic13—24no—
206C4⋊Dic13C2412yes—
207#6101—24no—
208#6101—24no—
209#6101—24no—
210#6101—24no—
211#6101—24no—
212#6101—28no—
213#6101—28no—
214C4×Dic13—24no—
215C4×Dic13C2×D414yes—
216C4×Dic13C2×D412yes—
217C4×Dic13C2×D414yes—
218C4×Dic13C2412yes—
219C2×#1055—24no—
220C2×#1055C2414yes—
221Dic52—48no—
222C2×#533—131no—
223C22×C4⋊Q8—131no—
224#3209—1316no—
225C2×#494—132no—
226C2×#487—132no—
227C2×#462—131no—
228C2×#462—131no—
229C2×#462—131no—
230C2×#462D1311yescharacteristic, complemented
231C2×#451—132no—
232C2×#451—132no—
233C2×#431—131no—
234C23×C13C22×D411yescharacteristic
235C22×D13—22no—
236C22×D13—22no—
237C22×D13C2×Q1614yes—
238C22×D13C22×D412yes—
239Q8×C13—22no—
240Q8×C13—24no—
241Q8×C13—22no—
242Q8×C13—24no—
243Q8×C13—44no—
244Q8×C13—42no—
245C2×C4×C13—22no—
246C2×C4×C13—22no—
247C2×C4×C13—24no—
248C2×C4×C13—22no—
249C2×C4×C13—44no—
250C2×C4×C13—42no—
251C2×C4×C13—42no—
252C2×C4×C13C2×Q1614yes—
253C2×C4×C13C22×D412yes—
254C2×C4×C13C22×D411yescharacteristic
255C2×C4×C13C22×D412yes—
256C2×C4×C13H(5,𝔽2)12yes—
257C2×C4×C13H(5,𝔽2)12yes—
258C2×C4×C13C2511yescharacteristic
259C2×Dic13—22no—
260C2×Dic13—22no—
261C2×Dic13—22no—
262C2×Dic13—24no—
263C2×Dic13—44no—
264C2×Dic13—42no—
265C2×Dic13—42no—
266C2×Dic13C2×Q1614yes—
267C2×Dic13#13714yes—
268C2×Dic13C22×D412yes—
269C2×Dic13C22×D412yes—
270C2×Dic13C22×D412yes—
271C4×D13—24no—
272C4×D13—22no—
273C4×D13—22no—
274C4×D13—28no—
275C4×D13—416no—
276C4×D13C2×Q16116yescomplemented
277Dic26—22no—
278Dic26—24no—
279Dic26—22no—
280Dic26—24no—
281Dic26—416no—
282Dic26—42no—
283Dic26—44no—
284Dic26—48no—
285C8×C13—24no—
286#1055—24no—
287C23×Q8—132no—
288C22×Q16—132no—
289C22×Q16—132no—
290C22×Q16—132no—
291C22×Q16C2×D1312yes—
292#533—138no—
293#533—264no—
294C2×C4⋊Q8—131no—
295C2×C4⋊Q8—132no—
296C2×C4⋊Q8—131no—
297C2×C4⋊Q8—138no—
298C2×C4⋊Q8—131no—
299C2×C4⋊Q8—261no—
300C2×C4⋊Q8—261no—
301C2×C4⋊Q8—264no—
302C2×C4⋊Q8C2×D1311yescharacteristic
303C2×#125—261no—
304C2×C22⋊Q8—131no—
305C2×C22⋊Q8—131no—
306C2×C22⋊Q8—261no—
307C2×C4×Q8—131no—
308C2×C4×Q8—261no—
309C2×C4×Q8C2×D1311yescharacteristic
310C2×#117—261no—
311C22×C4⋊C4—261no—
312C22×C4⋊C4—261no—
313C22×C42—131no—
314#494—1316no—
315#487—1316no—
316#462—138no—
317#462—138no—
318#462—138no—
319#462C2×D1318yescomplemented
320#451—1316no—
321#451—1316no—
322#431—138no—
323C2×C4⋊C8—131no—
324C2×C4⋊C8C2×D1311yescharacteristic
325C2×#103—132no—
326C2×#103—132no—
327C2×#103—132no—
328C2×#103C2×D1312yes—
329C2×C22⋊C8—132no—
330C2×C4×C8—132no—
331C22×C13#53512yes—
332C22×C13C22×Q1612yes—
333C22×C13C2×#13712yes—
334C22×C13C23×D411yescharacteristic
335C2×D13—22no—
336C2×D13—28no—
337C2×D13—22no—
338C2×D13C22×Q1614yes—
339C4×C13—22no—
340C4×C13—44no—
341C4×C13—42no—
342C4×C13—42no—
343C4×C13#53512yes—
344C4×C13C22×Q1614yes—
345C4×C13C2×H(5,𝔽2)11yescharacteristic
346C4×C13C2×H(5,𝔽2)11yescharacteristic
347Dic13—22no—
348Dic13—44no—
349Dic13—42no—
350Dic13—42no—
351Dic13C22×Q1614yes—
352Dic13C2×#13714yes—
353C22×Q8—138no—
354C22×Q8—131no—
355C22×Q8—132no—
356C22×Q8—261no—
357C22×Q8—262no—
358C22×Q8—264no—
359C22×Q8—524no—
360C22×Q8—524no—
361C22×Q8C22×D1311yescharacteristic
362C22×Q8C22×D1312yes—
363C23×C4—131no—
364C23×C4—131no—
365C23×C4—131no—
366C23×C4—262no—
367C2×Q16—44no—
368C2×Q16—138no—
369C2×Q16—138no—
370C2×Q16—138no—
371C2×Q16—524no—
372C2×Q16—524no—
373C2×Q16—524no—
374C2×Q16C22×D1318yes—
375C22×C8—132no—
376C22×C8C22×D1312yes—
377C4⋊Q8—22no—
378C4⋊Q8—134no—
379C4⋊Q8—138no—
380C4⋊Q8—134no—
381C4⋊Q8—134no—
382C4⋊Q8—268no—
383C4⋊Q8—268no—
384C4⋊Q8—262no—
385C4⋊Q8—264no—
386C4⋊Q8—262no—
387C4⋊Q8—262no—
388C4⋊Q8C22×D1314yes—
389#125—268no—
390C22⋊Q8—134no—
391C22⋊Q8—134no—
392C22⋊Q8—262no—
393C22⋊Q8—268no—
394C22⋊Q8—262no—
395C4×Q8—22no—
396C4×Q8—134no—
397C4×Q8—268no—
398C4×Q8—262no—
399C4×Q8C22×D1314yes—
400#117—268no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—131no—
405C2×C4⋊C4—268no—
406C2×C4⋊C4—268no—
407C2×C4⋊C4—262no—
408C2×C4⋊C4—262no—
409C2×C4⋊C4—261no—
410C2×C4⋊C4—261no—
411C2×C4⋊C4—261no—
412C2×C4⋊C4—261no—
413C2×C4⋊C4—261no—
414C2×C4⋊C4—261no—
415C2×C4⋊C4—261no—
416C2×C4⋊C4—261no—
417C2×C4⋊C4C22×D1311yescharacteristic
418C2×C22⋊C4—261no—
419C2×C22⋊C4—261no—
420C2×C42—21no—
421C2×C42—131no—
422C2×C42—131no—
423C2×C42—131no—
424C2×C42—134no—
425C2×C42—134no—
426C2×C42—261no—
427C2×C42C22×D1311yescharacteristic
428C4⋊C8—134no—
429C4⋊C8C22×D1314yes—
430#103—138no—
431#103—138no—
432#103—138no—
433#103C22×D1318yes—
434C22⋊C8—138no—
435C4×C8—138no—
436C2×C13#320914yescomplemented
437C2×C13C2×#53511yescharacteristic
438C2×C13C23×Q1611yescharacteristic
439C2×C13C22×#13711yescharacteristic
440D13—24no—
441C24—131no—
442C2×Q8—21no—
443C2×Q8—22no—
444C2×Q8—22no—
445C2×Q8—24no—
446C2×Q8—22no—
447C2×Q8—24no—
448C2×Q8—134no—
449C2×Q8—132no—
450C2×Q8—264no—
451C2×Q8—268no—
452C2×Q8—261no—
453C2×Q8—262no—
454C2×Q8—262no—
455C2×Q8—264no—
456C2×Q8—262no—
457C2×Q8—264no—
458C2×Q8—524no—
459C2×Q8—528no—
460C2×Q8—528no—
461C2×Q8—528no—
462C2×Q8—5216no—
463C2×Q8C23×D1314yes—
464C2×Q8C23×D1312yes—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—22no—
468C22×C4—131no—
469C22×C4—131no—
470C22×C4—138no—
471C22×C4—134no—
472C22×C4—131no—
473C22×C4—134no—
474C22×C4—132no—
475C22×C4—132no—
476C22×C4—264no—
477C22×C4—268no—
478C22×C4—262no—
479C22×C4—262no—
480C22×C4—261no—
481C22×C4—261no—
482C22×C4—262no—
483C22×C4—528no—
484C22×C4D4×D1311yescharacteristic
485C22×C4D4×D1311yescharacteristic
486C22×C4C23×D1311yescharacteristic
487Q16—48no—
488Q16—528no—
489Q16—528no—
490Q16—528no—
491C2×C8—24no—
492C2×C8—134no—
493C2×C8—264no—
494C2×C8C23×D1314yes—
495C4⋊C4—24no—
496C4⋊C4—24no—
497C4⋊C4—24no—
498C4⋊C4—21no—
499C4⋊C4—132no—
500C4⋊C4—268no—
501C4⋊C4—268no—
502C4⋊C4—264no—
503C4⋊C4—264no—
504C4⋊C4—264no—
505C4⋊C4—264no—
506C4⋊C4—264no—
507C4⋊C4—261no—
508C4⋊C4—264no—
509C4⋊C4—264no—
510C4⋊C4—264no—
511C4⋊C4C23×D1312yes—
512C22⋊C4—264no—
513C22⋊C4—264no—
514C42—24no—
515C42—134no—
516C42—134no—
517C42—132no—
518C42—132no—
519C42—264no—
520C42D4×D1312yes—
521C42C23×D1312yes—
522C13C2×#320911yescharacteristic, complemented, Sylow
523C23—134no—
524C23—132no—
525C23—262no—
526C23—262no—
527C23C2×D4×D1311yescharacteristic
528Q8—22no—
529Q8—24no—
530Q8—22no—
531Q8—24no—
532Q8—44no—
533Q8—42no—
534Q8—262no—
535Q8—264no—
536Q8—262no—
537Q8—264no—
538Q8—528no—
539Q8—5216no—
540Q8—522no—
541Q8—524no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—24no—
546C2×C4—42no—
547C2×C4—44no—
548C2×C4—42no—
549C2×C4—134no—
550C2×C4—134no—
551C2×C4—132no—
552C2×C4—132no—
553C2×C4—1316no—
554C2×C4—132no—
555C2×C4—268no—
556C2×C4—262no—
557C2×C4—264no—
558C2×C4—262no—
559C2×C4—262no—
560C2×C4—262no—
561C2×C4—262no—
562C2×C4—264no—
563C2×C4—5216no—
564C2×C4—522no—
565C2×C4—524no—
566C2×C4—522no—
567C2×C4Q16×D1314yes—
568C2×C4C2×D4×D1312yes—
569C2×C4C2×D4×D1312yes—
570C2×C4C2×D4×D1311yescharacteristic
571C2×C4#8825112yes—
572C2×C4#8825612yes—
573C2×C4C24×D1311yescharacteristic
574C8—24no—
575C8—264no—
576C22—134no—
577C22—262no—
578C22—268no—
579C22—262no—
580C22#1171931212yes—
581C22C2×Q16×D1312yes—
582C22D13×#13712yes—
583C22C22×D4×D1311yescharacteristic
584C4—22no—
585C4—42no—
586C4—44no—
587C4—42no—
588C4—134no—
589C4—134no—
590C4—262no—
591C4—522no—
592C4—524no—
593C4—522no—
594C4#1171931212yes—
595C4C2×Q16×D1314yes—
596C4C2×#8825111yescharacteristic
597C4C2×#8825611yescharacteristic
598C2—264no—
599C2#1312578314yesdirect product factor
600C2C2×#1171931211yescharacteristic
601C2C22×Q16×D1311yescharacteristic
602C2C2×D13×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#462C2
socleC23×C13C22×D4
prime radicalC23×D13C2×D4
hypercenterC2×#462D13
hypocenterC13C2×#3209
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#462

Complements

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

NH ≅ G/Ntype
3. #13125783C2direct (N × H)
4. C2×#11718842C2semidirect
5. C2×#11718453C2semidirect
6. C2×#11718510C2semidirect
7. C2×#11718692C2semidirect
8. C2×#11718751C2semidirect
12. C2×C13×#462C2semidirect
40. C13×#462C22semidirect
45. #11718842C22semidirect
49. #11718751C22semidirect
50. #11718692C22semidirect
53. #11718510C22semidirect
56. #11718453C22semidirect
170. C2×C4×D13Q16semidirect
230. C2×#462D13semidirect
276. C4×D13C2×Q16semidirect
319. #462C2×D13semidirect
436. C2×C13#3209semidirect
522. C13C2×#3209semidirect
599. C2#13125783direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117192832
C2×D13×C4⋊Q82
#131257832
C2×#117188422
C2×#117184532
C2×#117185102
C2×#117186922
C2×#117187512
C2×#117184692
C2×#117188472
C2×#117184942
C2×C13×#4622
C2×#320913